Properties

Label 1386.2.bu.b.701.2
Level $1386$
Weight $2$
Character 1386.701
Analytic conductor $11.067$
Analytic rank $0$
Dimension $48$
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] = [1386,2,Mod(701,1386)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1386, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([5, 0, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1386.701");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1386.bu (of order \(10\), degree \(4\), 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: \(11.0672657201\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(12\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 701.2
Character \(\chi\) \(=\) 1386.701
Dual form 1386.2.bu.b.953.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.809017 - 0.587785i) q^{2} +(0.309017 - 0.951057i) q^{4} +(-1.25194 + 1.72315i) q^{5} +(-0.951057 - 0.309017i) q^{7} +(-0.309017 - 0.951057i) q^{8} +O(q^{10})\) \(q+(0.809017 - 0.587785i) q^{2} +(0.309017 - 0.951057i) q^{4} +(-1.25194 + 1.72315i) q^{5} +(-0.951057 - 0.309017i) q^{7} +(-0.309017 - 0.951057i) q^{8} +2.12993i q^{10} +(2.72584 - 1.88940i) q^{11} +(0.138223 + 0.190247i) q^{13} +(-0.951057 + 0.309017i) q^{14} +(-0.809017 - 0.587785i) q^{16} +(3.83995 + 2.78988i) q^{17} +(2.37089 - 0.770347i) q^{19} +(1.25194 + 1.72315i) q^{20} +(1.09469 - 3.13076i) q^{22} +7.44695i q^{23} +(0.143197 + 0.440716i) q^{25} +(0.223649 + 0.0726680i) q^{26} +(-0.587785 + 0.809017i) q^{28} +(1.54459 - 4.75376i) q^{29} +(0.902963 - 0.656041i) q^{31} -1.00000 q^{32} +4.74643 q^{34} +(1.72315 - 1.25194i) q^{35} +(3.09832 - 9.53566i) q^{37} +(1.46529 - 2.01680i) q^{38} +(2.02568 + 0.658185i) q^{40} +(0.856678 + 2.63658i) q^{41} -3.37411i q^{43} +(-0.954592 - 3.17628i) q^{44} +(4.37721 + 6.02471i) q^{46} +(11.7182 - 3.80746i) q^{47} +(0.809017 + 0.587785i) q^{49} +(0.374896 + 0.272378i) q^{50} +(0.223649 - 0.0726680i) q^{52} +(4.73611 + 6.51870i) q^{53} +(-0.156877 + 7.06244i) q^{55} +1.00000i q^{56} +(-1.54459 - 4.75376i) q^{58} +(12.9325 + 4.20204i) q^{59} +(-7.05025 + 9.70384i) q^{61} +(0.344901 - 1.06150i) q^{62} +(-0.809017 + 0.587785i) q^{64} -0.500872 q^{65} -1.74844 q^{67} +(3.83995 - 2.78988i) q^{68} +(0.658185 - 2.02568i) q^{70} +(5.46145 - 7.51705i) q^{71} +(4.11077 + 1.33567i) q^{73} +(-3.09832 - 9.53566i) q^{74} -2.49290i q^{76} +(-3.17628 + 0.954592i) q^{77} +(-4.17755 - 5.74990i) q^{79} +(2.02568 - 0.658185i) q^{80} +(2.24281 + 1.62950i) q^{82} +(1.89368 + 1.37584i) q^{83} +(-9.61478 + 3.12403i) q^{85} +(-1.98325 - 2.72971i) q^{86} +(-2.63925 - 2.00857i) q^{88} +9.21315i q^{89} +(-0.0726680 - 0.223649i) q^{91} +(7.08247 + 2.30123i) q^{92} +(7.24222 - 9.96805i) q^{94} +(-1.64079 + 5.04982i) q^{95} +(0.932230 - 0.677305i) q^{97} +1.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q + 12 q^{2} - 12 q^{4} + 12 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 48 q + 12 q^{2} - 12 q^{4} + 12 q^{8} - 4 q^{11} - 12 q^{16} - 24 q^{17} + 4 q^{22} + 24 q^{25} - 40 q^{26} + 16 q^{29} + 40 q^{31} - 48 q^{32} - 16 q^{34} + 12 q^{35} + 16 q^{37} + 40 q^{38} - 24 q^{41} - 4 q^{44} - 40 q^{46} + 40 q^{47} + 12 q^{49} - 4 q^{50} - 40 q^{52} + 40 q^{53} - 32 q^{55} - 16 q^{58} + 40 q^{61} + 40 q^{62} - 12 q^{64} + 48 q^{67} - 24 q^{68} + 8 q^{70} + 40 q^{73} - 16 q^{74} - 32 q^{77} + 40 q^{79} - 16 q^{82} + 16 q^{83} - 20 q^{85} + 4 q^{88} + 20 q^{92} + 52 q^{95} - 8 q^{97} + 48 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times\).

\(n\) \(155\) \(199\) \(1135\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{3}{10}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.809017 0.587785i 0.572061 0.415627i
\(3\) 0 0
\(4\) 0.309017 0.951057i 0.154508 0.475528i
\(5\) −1.25194 + 1.72315i −0.559885 + 0.770616i −0.991312 0.131532i \(-0.958010\pi\)
0.431427 + 0.902148i \(0.358010\pi\)
\(6\) 0 0
\(7\) −0.951057 0.309017i −0.359466 0.116797i
\(8\) −0.309017 0.951057i −0.109254 0.336249i
\(9\) 0 0
\(10\) 2.12993i 0.673543i
\(11\) 2.72584 1.88940i 0.821871 0.569674i
\(12\) 0 0
\(13\) 0.138223 + 0.190247i 0.0383361 + 0.0527651i 0.827755 0.561090i \(-0.189618\pi\)
−0.789419 + 0.613855i \(0.789618\pi\)
\(14\) −0.951057 + 0.309017i −0.254181 + 0.0825883i
\(15\) 0 0
\(16\) −0.809017 0.587785i −0.202254 0.146946i
\(17\) 3.83995 + 2.78988i 0.931324 + 0.676646i 0.946317 0.323241i \(-0.104773\pi\)
−0.0149930 + 0.999888i \(0.504773\pi\)
\(18\) 0 0
\(19\) 2.37089 0.770347i 0.543918 0.176730i −0.0241542 0.999708i \(-0.507689\pi\)
0.568073 + 0.822978i \(0.307689\pi\)
\(20\) 1.25194 + 1.72315i 0.279943 + 0.385308i
\(21\) 0 0
\(22\) 1.09469 3.13076i 0.233389 0.667480i
\(23\) 7.44695i 1.55280i 0.630243 + 0.776398i \(0.282955\pi\)
−0.630243 + 0.776398i \(0.717045\pi\)
\(24\) 0 0
\(25\) 0.143197 + 0.440716i 0.0286395 + 0.0881432i
\(26\) 0.223649 + 0.0726680i 0.0438612 + 0.0142514i
\(27\) 0 0
\(28\) −0.587785 + 0.809017i −0.111081 + 0.152890i
\(29\) 1.54459 4.75376i 0.286823 0.882751i −0.699023 0.715099i \(-0.746382\pi\)
0.985846 0.167652i \(-0.0536184\pi\)
\(30\) 0 0
\(31\) 0.902963 0.656041i 0.162177 0.117828i −0.503737 0.863857i \(-0.668042\pi\)
0.665914 + 0.746029i \(0.268042\pi\)
\(32\) −1.00000 −0.176777
\(33\) 0 0
\(34\) 4.74643 0.814007
\(35\) 1.72315 1.25194i 0.291265 0.211617i
\(36\) 0 0
\(37\) 3.09832 9.53566i 0.509361 1.56765i −0.283952 0.958839i \(-0.591646\pi\)
0.793313 0.608814i \(-0.208354\pi\)
\(38\) 1.46529 2.01680i 0.237701 0.327167i
\(39\) 0 0
\(40\) 2.02568 + 0.658185i 0.320289 + 0.104068i
\(41\) 0.856678 + 2.63658i 0.133791 + 0.411765i 0.995400 0.0958068i \(-0.0305431\pi\)
−0.861609 + 0.507572i \(0.830543\pi\)
\(42\) 0 0
\(43\) 3.37411i 0.514546i −0.966339 0.257273i \(-0.917176\pi\)
0.966339 0.257273i \(-0.0828240\pi\)
\(44\) −0.954592 3.17628i −0.143910 0.478842i
\(45\) 0 0
\(46\) 4.37721 + 6.02471i 0.645384 + 0.888295i
\(47\) 11.7182 3.80746i 1.70927 0.555375i 0.719057 0.694951i \(-0.244574\pi\)
0.990211 + 0.139577i \(0.0445742\pi\)
\(48\) 0 0
\(49\) 0.809017 + 0.587785i 0.115574 + 0.0839693i
\(50\) 0.374896 + 0.272378i 0.0530182 + 0.0385200i
\(51\) 0 0
\(52\) 0.223649 0.0726680i 0.0310146 0.0100772i
\(53\) 4.73611 + 6.51870i 0.650555 + 0.895412i 0.999123 0.0418714i \(-0.0133320\pi\)
−0.348568 + 0.937283i \(0.613332\pi\)
\(54\) 0 0
\(55\) −0.156877 + 7.06244i −0.0211533 + 0.952299i
\(56\) 1.00000i 0.133631i
\(57\) 0 0
\(58\) −1.54459 4.75376i −0.202815 0.624199i
\(59\) 12.9325 + 4.20204i 1.68367 + 0.547059i 0.985619 0.168985i \(-0.0540488\pi\)
0.698056 + 0.716044i \(0.254049\pi\)
\(60\) 0 0
\(61\) −7.05025 + 9.70384i −0.902692 + 1.24245i 0.0669094 + 0.997759i \(0.478686\pi\)
−0.969601 + 0.244690i \(0.921314\pi\)
\(62\) 0.344901 1.06150i 0.0438025 0.134810i
\(63\) 0 0
\(64\) −0.809017 + 0.587785i −0.101127 + 0.0734732i
\(65\) −0.500872 −0.0621255
\(66\) 0 0
\(67\) −1.74844 −0.213605 −0.106803 0.994280i \(-0.534061\pi\)
−0.106803 + 0.994280i \(0.534061\pi\)
\(68\) 3.83995 2.78988i 0.465662 0.338323i
\(69\) 0 0
\(70\) 0.658185 2.02568i 0.0786681 0.242116i
\(71\) 5.46145 7.51705i 0.648155 0.892109i −0.350862 0.936427i \(-0.614111\pi\)
0.999017 + 0.0443177i \(0.0141114\pi\)
\(72\) 0 0
\(73\) 4.11077 + 1.33567i 0.481129 + 0.156328i 0.539532 0.841965i \(-0.318601\pi\)
−0.0584037 + 0.998293i \(0.518601\pi\)
\(74\) −3.09832 9.53566i −0.360173 1.10850i
\(75\) 0 0
\(76\) 2.49290i 0.285955i
\(77\) −3.17628 + 0.954592i −0.361971 + 0.108786i
\(78\) 0 0
\(79\) −4.17755 5.74990i −0.470011 0.646914i 0.506536 0.862219i \(-0.330926\pi\)
−0.976547 + 0.215304i \(0.930926\pi\)
\(80\) 2.02568 0.658185i 0.226478 0.0735873i
\(81\) 0 0
\(82\) 2.24281 + 1.62950i 0.247677 + 0.179948i
\(83\) 1.89368 + 1.37584i 0.207859 + 0.151018i 0.686844 0.726804i \(-0.258995\pi\)
−0.478986 + 0.877823i \(0.658995\pi\)
\(84\) 0 0
\(85\) −9.61478 + 3.12403i −1.04287 + 0.338849i
\(86\) −1.98325 2.72971i −0.213859 0.294352i
\(87\) 0 0
\(88\) −2.63925 2.00857i −0.281345 0.214114i
\(89\) 9.21315i 0.976592i 0.872678 + 0.488296i \(0.162381\pi\)
−0.872678 + 0.488296i \(0.837619\pi\)
\(90\) 0 0
\(91\) −0.0726680 0.223649i −0.00761768 0.0234448i
\(92\) 7.08247 + 2.30123i 0.738399 + 0.239920i
\(93\) 0 0
\(94\) 7.24222 9.96805i 0.746977 1.02813i
\(95\) −1.64079 + 5.04982i −0.168341 + 0.518101i
\(96\) 0 0
\(97\) 0.932230 0.677305i 0.0946536 0.0687699i −0.539452 0.842016i \(-0.681369\pi\)
0.634105 + 0.773247i \(0.281369\pi\)
\(98\) 1.00000 0.101015
\(99\) 0 0
\(100\) 0.463396 0.0463396
\(101\) −4.15276 + 3.01716i −0.413215 + 0.300219i −0.774902 0.632081i \(-0.782201\pi\)
0.361687 + 0.932300i \(0.382201\pi\)
\(102\) 0 0
\(103\) −0.125155 + 0.385187i −0.0123319 + 0.0379536i −0.957033 0.289979i \(-0.906352\pi\)
0.944701 + 0.327932i \(0.106352\pi\)
\(104\) 0.138223 0.190247i 0.0135539 0.0186553i
\(105\) 0 0
\(106\) 7.66319 + 2.48992i 0.744315 + 0.241843i
\(107\) −1.33478 4.10805i −0.129039 0.397140i 0.865577 0.500776i \(-0.166952\pi\)
−0.994615 + 0.103637i \(0.966952\pi\)
\(108\) 0 0
\(109\) 13.4299i 1.28635i −0.765719 0.643176i \(-0.777616\pi\)
0.765719 0.643176i \(-0.222384\pi\)
\(110\) 4.02428 + 5.80584i 0.383700 + 0.553565i
\(111\) 0 0
\(112\) 0.587785 + 0.809017i 0.0555405 + 0.0764449i
\(113\) −16.3124 + 5.30023i −1.53455 + 0.498604i −0.949865 0.312660i \(-0.898780\pi\)
−0.584680 + 0.811264i \(0.698780\pi\)
\(114\) 0 0
\(115\) −12.8322 9.32315i −1.19661 0.869388i
\(116\) −4.04379 2.93798i −0.375456 0.272785i
\(117\) 0 0
\(118\) 12.9325 4.20204i 1.19054 0.386829i
\(119\) −2.78988 3.83995i −0.255748 0.352007i
\(120\) 0 0
\(121\) 3.86037 10.3004i 0.350943 0.936397i
\(122\) 11.9946i 1.08594i
\(123\) 0 0
\(124\) −0.344901 1.06150i −0.0309731 0.0953253i
\(125\) −11.0671 3.59592i −0.989873 0.321629i
\(126\) 0 0
\(127\) −10.8429 + 14.9240i −0.962151 + 1.32429i −0.0162370 + 0.999868i \(0.505169\pi\)
−0.945914 + 0.324419i \(0.894831\pi\)
\(128\) −0.309017 + 0.951057i −0.0273135 + 0.0840623i
\(129\) 0 0
\(130\) −0.405214 + 0.294405i −0.0355396 + 0.0258210i
\(131\) 16.8993 1.47650 0.738251 0.674527i \(-0.235652\pi\)
0.738251 + 0.674527i \(0.235652\pi\)
\(132\) 0 0
\(133\) −2.49290 −0.216162
\(134\) −1.41451 + 1.02770i −0.122195 + 0.0887802i
\(135\) 0 0
\(136\) 1.46673 4.51413i 0.125771 0.387083i
\(137\) −6.71611 + 9.24394i −0.573796 + 0.789763i −0.992998 0.118130i \(-0.962310\pi\)
0.419202 + 0.907893i \(0.362310\pi\)
\(138\) 0 0
\(139\) −6.43675 2.09143i −0.545958 0.177393i 0.0230351 0.999735i \(-0.492667\pi\)
−0.568994 + 0.822342i \(0.692667\pi\)
\(140\) −0.658185 2.02568i −0.0556268 0.171202i
\(141\) 0 0
\(142\) 9.29158i 0.779732i
\(143\) 0.736225 + 0.257426i 0.0615663 + 0.0215270i
\(144\) 0 0
\(145\) 6.25770 + 8.61299i 0.519674 + 0.715270i
\(146\) 4.11077 1.33567i 0.340209 0.110541i
\(147\) 0 0
\(148\) −8.11152 5.89336i −0.666762 0.484431i
\(149\) −1.52106 1.10512i −0.124610 0.0905347i 0.523734 0.851882i \(-0.324538\pi\)
−0.648345 + 0.761347i \(0.724538\pi\)
\(150\) 0 0
\(151\) −8.38155 + 2.72333i −0.682081 + 0.221622i −0.629506 0.776995i \(-0.716743\pi\)
−0.0525749 + 0.998617i \(0.516743\pi\)
\(152\) −1.46529 2.01680i −0.118851 0.163584i
\(153\) 0 0
\(154\) −2.00857 + 2.63925i −0.161855 + 0.212677i
\(155\) 2.37727i 0.190947i
\(156\) 0 0
\(157\) 0.149322 + 0.459566i 0.0119172 + 0.0366773i 0.956838 0.290621i \(-0.0938618\pi\)
−0.944921 + 0.327298i \(0.893862\pi\)
\(158\) −6.75941 2.19627i −0.537750 0.174726i
\(159\) 0 0
\(160\) 1.25194 1.72315i 0.0989747 0.136227i
\(161\) 2.30123 7.08247i 0.181363 0.558177i
\(162\) 0 0
\(163\) −0.116427 + 0.0845889i −0.00911924 + 0.00662551i −0.592336 0.805691i \(-0.701794\pi\)
0.583216 + 0.812317i \(0.301794\pi\)
\(164\) 2.77227 0.216478
\(165\) 0 0
\(166\) 2.34072 0.181675
\(167\) −20.7340 + 15.0641i −1.60444 + 1.16570i −0.726201 + 0.687482i \(0.758716\pi\)
−0.878243 + 0.478215i \(0.841284\pi\)
\(168\) 0 0
\(169\) 4.00013 12.3111i 0.307702 0.947011i
\(170\) −5.94226 + 8.17882i −0.455750 + 0.627287i
\(171\) 0 0
\(172\) −3.20896 1.04266i −0.244681 0.0795018i
\(173\) −5.03415 15.4935i −0.382740 1.17795i −0.938107 0.346346i \(-0.887422\pi\)
0.555367 0.831605i \(-0.312578\pi\)
\(174\) 0 0
\(175\) 0.463396i 0.0350295i
\(176\) −3.31581 0.0736535i −0.249938 0.00555184i
\(177\) 0 0
\(178\) 5.41535 + 7.45359i 0.405898 + 0.558670i
\(179\) −11.2316 + 3.64937i −0.839489 + 0.272766i −0.697037 0.717035i \(-0.745499\pi\)
−0.142452 + 0.989802i \(0.545499\pi\)
\(180\) 0 0
\(181\) −19.1140 13.8872i −1.42074 1.03222i −0.991650 0.128961i \(-0.958836\pi\)
−0.429086 0.903264i \(-0.641164\pi\)
\(182\) −0.190247 0.138223i −0.0141021 0.0102458i
\(183\) 0 0
\(184\) 7.08247 2.30123i 0.522127 0.169649i
\(185\) 12.5524 + 17.2770i 0.922874 + 1.27023i
\(186\) 0 0
\(187\) 15.7383 + 0.349591i 1.15090 + 0.0255647i
\(188\) 12.3212i 0.898615i
\(189\) 0 0
\(190\) 1.64079 + 5.04982i 0.119035 + 0.366352i
\(191\) 8.28024 + 2.69041i 0.599137 + 0.194672i 0.592856 0.805309i \(-0.298000\pi\)
0.00628166 + 0.999980i \(0.498000\pi\)
\(192\) 0 0
\(193\) 2.43343 3.34933i 0.175162 0.241090i −0.712405 0.701769i \(-0.752394\pi\)
0.887567 + 0.460679i \(0.152394\pi\)
\(194\) 0.356080 1.09590i 0.0255651 0.0786812i
\(195\) 0 0
\(196\) 0.809017 0.587785i 0.0577869 0.0419847i
\(197\) 1.79437 0.127843 0.0639216 0.997955i \(-0.479639\pi\)
0.0639216 + 0.997955i \(0.479639\pi\)
\(198\) 0 0
\(199\) 0.421161 0.0298553 0.0149276 0.999889i \(-0.495248\pi\)
0.0149276 + 0.999889i \(0.495248\pi\)
\(200\) 0.374896 0.272378i 0.0265091 0.0192600i
\(201\) 0 0
\(202\) −1.58621 + 4.88187i −0.111606 + 0.343487i
\(203\) −2.93798 + 4.04379i −0.206206 + 0.283818i
\(204\) 0 0
\(205\) −5.61574 1.82466i −0.392220 0.127440i
\(206\) 0.125155 + 0.385187i 0.00871996 + 0.0268373i
\(207\) 0 0
\(208\) 0.235159i 0.0163053i
\(209\) 5.00716 6.57938i 0.346352 0.455105i
\(210\) 0 0
\(211\) 10.1482 + 13.9678i 0.698631 + 0.961583i 0.999967 + 0.00806540i \(0.00256733\pi\)
−0.301336 + 0.953518i \(0.597433\pi\)
\(212\) 7.66319 2.48992i 0.526310 0.171008i
\(213\) 0 0
\(214\) −3.49451 2.53891i −0.238880 0.173556i
\(215\) 5.81409 + 4.22418i 0.396518 + 0.288087i
\(216\) 0 0
\(217\) −1.06150 + 0.344901i −0.0720591 + 0.0234134i
\(218\) −7.89390 10.8650i −0.534642 0.735872i
\(219\) 0 0
\(220\) 6.66830 + 2.33161i 0.449577 + 0.157197i
\(221\) 1.11617i 0.0750814i
\(222\) 0 0
\(223\) 2.98554 + 9.18853i 0.199926 + 0.615310i 0.999884 + 0.0152530i \(0.00485537\pi\)
−0.799957 + 0.600057i \(0.795145\pi\)
\(224\) 0.951057 + 0.309017i 0.0635451 + 0.0206471i
\(225\) 0 0
\(226\) −10.0816 + 13.8762i −0.670621 + 0.923031i
\(227\) −0.0993350 + 0.305722i −0.00659310 + 0.0202915i −0.954299 0.298854i \(-0.903396\pi\)
0.947706 + 0.319145i \(0.103396\pi\)
\(228\) 0 0
\(229\) −5.19487 + 3.77429i −0.343287 + 0.249412i −0.746047 0.665893i \(-0.768051\pi\)
0.402761 + 0.915305i \(0.368051\pi\)
\(230\) −15.8615 −1.04588
\(231\) 0 0
\(232\) −4.99840 −0.328161
\(233\) 6.16506 4.47918i 0.403886 0.293441i −0.367236 0.930128i \(-0.619696\pi\)
0.771122 + 0.636687i \(0.219696\pi\)
\(234\) 0 0
\(235\) −8.10962 + 24.9588i −0.529013 + 1.62814i
\(236\) 7.99275 11.0011i 0.520284 0.716109i
\(237\) 0 0
\(238\) −4.51413 1.46673i −0.292607 0.0950739i
\(239\) −9.02839 27.7865i −0.583998 1.79736i −0.603258 0.797546i \(-0.706131\pi\)
0.0192600 0.999815i \(-0.493869\pi\)
\(240\) 0 0
\(241\) 16.4239i 1.05795i −0.848636 0.528977i \(-0.822576\pi\)
0.848636 0.528977i \(-0.177424\pi\)
\(242\) −2.93130 10.6022i −0.188431 0.681538i
\(243\) 0 0
\(244\) 7.05025 + 9.70384i 0.451346 + 0.621224i
\(245\) −2.02568 + 0.658185i −0.129416 + 0.0420499i
\(246\) 0 0
\(247\) 0.474267 + 0.344575i 0.0301769 + 0.0219248i
\(248\) −0.902963 0.656041i −0.0573382 0.0416587i
\(249\) 0 0
\(250\) −11.0671 + 3.59592i −0.699946 + 0.227426i
\(251\) 7.01157 + 9.65060i 0.442566 + 0.609140i 0.970780 0.239971i \(-0.0771380\pi\)
−0.528214 + 0.849112i \(0.677138\pi\)
\(252\) 0 0
\(253\) 14.0702 + 20.2992i 0.884588 + 1.27620i
\(254\) 18.4470i 1.15747i
\(255\) 0 0
\(256\) 0.309017 + 0.951057i 0.0193136 + 0.0594410i
\(257\) −3.23144 1.04996i −0.201572 0.0654946i 0.206491 0.978448i \(-0.433796\pi\)
−0.408063 + 0.912954i \(0.633796\pi\)
\(258\) 0 0
\(259\) −5.89336 + 8.11152i −0.366196 + 0.504025i
\(260\) −0.154778 + 0.476357i −0.00959891 + 0.0295424i
\(261\) 0 0
\(262\) 13.6718 9.93318i 0.844649 0.613674i
\(263\) −20.3065 −1.25215 −0.626077 0.779761i \(-0.715341\pi\)
−0.626077 + 0.779761i \(0.715341\pi\)
\(264\) 0 0
\(265\) −17.1620 −1.05426
\(266\) −2.01680 + 1.46529i −0.123658 + 0.0898426i
\(267\) 0 0
\(268\) −0.540296 + 1.66286i −0.0330039 + 0.101575i
\(269\) −11.0704 + 15.2371i −0.674975 + 0.929024i −0.999860 0.0167299i \(-0.994674\pi\)
0.324885 + 0.945754i \(0.394674\pi\)
\(270\) 0 0
\(271\) −2.33005 0.757078i −0.141540 0.0459892i 0.237390 0.971414i \(-0.423708\pi\)
−0.378930 + 0.925425i \(0.623708\pi\)
\(272\) −1.46673 4.51413i −0.0889335 0.273709i
\(273\) 0 0
\(274\) 11.4261i 0.690278i
\(275\) 1.22302 + 0.930764i 0.0737509 + 0.0561272i
\(276\) 0 0
\(277\) 1.00939 + 1.38930i 0.0606482 + 0.0834750i 0.838264 0.545265i \(-0.183571\pi\)
−0.777616 + 0.628740i \(0.783571\pi\)
\(278\) −6.43675 + 2.09143i −0.386051 + 0.125436i
\(279\) 0 0
\(280\) −1.72315 1.25194i −0.102978 0.0748178i
\(281\) −4.41416 3.20708i −0.263327 0.191318i 0.448286 0.893890i \(-0.352035\pi\)
−0.711612 + 0.702572i \(0.752035\pi\)
\(282\) 0 0
\(283\) 22.4321 7.28863i 1.33345 0.433264i 0.446356 0.894855i \(-0.352721\pi\)
0.887093 + 0.461592i \(0.152721\pi\)
\(284\) −5.46145 7.51705i −0.324078 0.446055i
\(285\) 0 0
\(286\) 0.746930 0.224481i 0.0441669 0.0132738i
\(287\) 2.77227i 0.163642i
\(288\) 0 0
\(289\) 1.70844 + 5.25804i 0.100497 + 0.309297i
\(290\) 10.1252 + 3.28987i 0.594571 + 0.193188i
\(291\) 0 0
\(292\) 2.54059 3.49683i 0.148677 0.204636i
\(293\) 5.97171 18.3790i 0.348871 1.07371i −0.610607 0.791933i \(-0.709075\pi\)
0.959479 0.281782i \(-0.0909253\pi\)
\(294\) 0 0
\(295\) −23.4315 + 17.0240i −1.36424 + 0.991176i
\(296\) −10.0264 −0.582772
\(297\) 0 0
\(298\) −1.88014 −0.108913
\(299\) −1.41676 + 1.02934i −0.0819335 + 0.0595282i
\(300\) 0 0
\(301\) −1.04266 + 3.20896i −0.0600977 + 0.184962i
\(302\) −5.18009 + 7.12978i −0.298080 + 0.410273i
\(303\) 0 0
\(304\) −2.37089 0.770347i −0.135980 0.0441824i
\(305\) −7.89466 24.2973i −0.452047 1.39126i
\(306\) 0 0
\(307\) 22.5480i 1.28688i 0.765495 + 0.643442i \(0.222494\pi\)
−0.765495 + 0.643442i \(0.777506\pi\)
\(308\) −0.0736535 + 3.31581i −0.00419680 + 0.188936i
\(309\) 0 0
\(310\) 1.39732 + 1.92325i 0.0793626 + 0.109233i
\(311\) −13.8491 + 4.49985i −0.785311 + 0.255163i −0.674106 0.738635i \(-0.735471\pi\)
−0.111205 + 0.993798i \(0.535471\pi\)
\(312\) 0 0
\(313\) −3.44931 2.50607i −0.194966 0.141651i 0.486019 0.873948i \(-0.338448\pi\)
−0.680986 + 0.732297i \(0.738448\pi\)
\(314\) 0.390930 + 0.284027i 0.0220615 + 0.0160286i
\(315\) 0 0
\(316\) −6.75941 + 2.19627i −0.380247 + 0.123550i
\(317\) 10.6524 + 14.6617i 0.598297 + 0.823485i 0.995551 0.0942237i \(-0.0300369\pi\)
−0.397254 + 0.917709i \(0.630037\pi\)
\(318\) 0 0
\(319\) −4.77143 15.8763i −0.267149 0.888903i
\(320\) 2.12993i 0.119067i
\(321\) 0 0
\(322\) −2.30123 7.08247i −0.128243 0.394691i
\(323\) 11.2532 + 3.65640i 0.626148 + 0.203448i
\(324\) 0 0
\(325\) −0.0640519 + 0.0881599i −0.00355296 + 0.00489023i
\(326\) −0.0444710 + 0.136868i −0.00246302 + 0.00758040i
\(327\) 0 0
\(328\) 2.24281 1.62950i 0.123839 0.0899740i
\(329\) −12.3212 −0.679289
\(330\) 0 0
\(331\) 32.1434 1.76676 0.883380 0.468657i \(-0.155262\pi\)
0.883380 + 0.468657i \(0.155262\pi\)
\(332\) 1.89368 1.37584i 0.103929 0.0755091i
\(333\) 0 0
\(334\) −7.91968 + 24.3743i −0.433346 + 1.33370i
\(335\) 2.18894 3.01282i 0.119595 0.164608i
\(336\) 0 0
\(337\) 14.9587 + 4.86037i 0.814851 + 0.264761i 0.686651 0.726987i \(-0.259080\pi\)
0.128200 + 0.991748i \(0.459080\pi\)
\(338\) −4.00013 12.3111i −0.217579 0.669638i
\(339\) 0 0
\(340\) 10.1096i 0.548269i
\(341\) 1.22181 3.49432i 0.0661647 0.189228i
\(342\) 0 0
\(343\) −0.587785 0.809017i −0.0317374 0.0436828i
\(344\) −3.20896 + 1.04266i −0.173016 + 0.0562162i
\(345\) 0 0
\(346\) −13.1796 9.57553i −0.708539 0.514784i
\(347\) 6.59624 + 4.79245i 0.354104 + 0.257272i 0.750589 0.660769i \(-0.229770\pi\)
−0.396484 + 0.918041i \(0.629770\pi\)
\(348\) 0 0
\(349\) −15.8596 + 5.15308i −0.848943 + 0.275838i −0.701003 0.713158i \(-0.747264\pi\)
−0.147940 + 0.988996i \(0.547264\pi\)
\(350\) −0.272378 0.374896i −0.0145592 0.0200390i
\(351\) 0 0
\(352\) −2.72584 + 1.88940i −0.145288 + 0.100705i
\(353\) 25.9808i 1.38282i −0.722462 0.691410i \(-0.756990\pi\)
0.722462 0.691410i \(-0.243010\pi\)
\(354\) 0 0
\(355\) 6.11558 + 18.8218i 0.324581 + 0.998958i
\(356\) 8.76222 + 2.84702i 0.464397 + 0.150892i
\(357\) 0 0
\(358\) −6.94151 + 9.55417i −0.366870 + 0.504953i
\(359\) 3.72488 11.4640i 0.196592 0.605047i −0.803363 0.595490i \(-0.796958\pi\)
0.999954 0.00955663i \(-0.00304202\pi\)
\(360\) 0 0
\(361\) −10.3437 + 7.51511i −0.544403 + 0.395532i
\(362\) −23.6263 −1.24177
\(363\) 0 0
\(364\) −0.235159 −0.0123257
\(365\) −7.44800 + 5.41129i −0.389846 + 0.283240i
\(366\) 0 0
\(367\) 5.50531 16.9436i 0.287375 0.884448i −0.698302 0.715803i \(-0.746061\pi\)
0.985677 0.168645i \(-0.0539392\pi\)
\(368\) 4.37721 6.02471i 0.228178 0.314060i
\(369\) 0 0
\(370\) 20.3103 + 6.59921i 1.05588 + 0.343077i
\(371\) −2.48992 7.66319i −0.129270 0.397853i
\(372\) 0 0
\(373\) 4.29068i 0.222163i −0.993811 0.111082i \(-0.964569\pi\)
0.993811 0.111082i \(-0.0354315\pi\)
\(374\) 12.9380 8.96789i 0.669008 0.463719i
\(375\) 0 0
\(376\) −7.24222 9.96805i −0.373489 0.514063i
\(377\) 1.11789 0.363224i 0.0575741 0.0187070i
\(378\) 0 0
\(379\) 5.68262 + 4.12867i 0.291897 + 0.212075i 0.724090 0.689706i \(-0.242260\pi\)
−0.432193 + 0.901781i \(0.642260\pi\)
\(380\) 4.29563 + 3.12096i 0.220361 + 0.160102i
\(381\) 0 0
\(382\) 8.28024 2.69041i 0.423654 0.137654i
\(383\) 17.3127 + 23.8288i 0.884635 + 1.21760i 0.975115 + 0.221698i \(0.0711598\pi\)
−0.0904803 + 0.995898i \(0.528840\pi\)
\(384\) 0 0
\(385\) 2.33161 6.66830i 0.118830 0.339848i
\(386\) 4.14000i 0.210720i
\(387\) 0 0
\(388\) −0.356080 1.09590i −0.0180772 0.0556360i
\(389\) −30.3015 9.84556i −1.53635 0.499190i −0.585982 0.810324i \(-0.699291\pi\)
−0.950366 + 0.311134i \(0.899291\pi\)
\(390\) 0 0
\(391\) −20.7761 + 28.5959i −1.05069 + 1.44616i
\(392\) 0.309017 0.951057i 0.0156077 0.0480356i
\(393\) 0 0
\(394\) 1.45167 1.05470i 0.0731342 0.0531351i
\(395\) 15.1380 0.761675
\(396\) 0 0
\(397\) 37.8520 1.89973 0.949867 0.312653i \(-0.101218\pi\)
0.949867 + 0.312653i \(0.101218\pi\)
\(398\) 0.340726 0.247552i 0.0170791 0.0124087i
\(399\) 0 0
\(400\) 0.143197 0.440716i 0.00715987 0.0220358i
\(401\) 0.756656 1.04145i 0.0377856 0.0520074i −0.789706 0.613485i \(-0.789767\pi\)
0.827492 + 0.561478i \(0.189767\pi\)
\(402\) 0 0
\(403\) 0.249620 + 0.0811065i 0.0124345 + 0.00404020i
\(404\) 1.58621 + 4.88187i 0.0789171 + 0.242882i
\(405\) 0 0
\(406\) 4.99840i 0.248066i
\(407\) −9.57111 31.8466i −0.474422 1.57858i
\(408\) 0 0
\(409\) −7.10127 9.77406i −0.351135 0.483296i 0.596517 0.802600i \(-0.296551\pi\)
−0.947652 + 0.319304i \(0.896551\pi\)
\(410\) −5.61574 + 1.82466i −0.277342 + 0.0901138i
\(411\) 0 0
\(412\) 0.327660 + 0.238059i 0.0161426 + 0.0117283i
\(413\) −11.0011 7.99275i −0.541328 0.393298i
\(414\) 0 0
\(415\) −4.74156 + 1.54063i −0.232754 + 0.0756264i
\(416\) −0.138223 0.190247i −0.00677693 0.00932764i
\(417\) 0 0
\(418\) 0.183611 8.26596i 0.00898069 0.404301i
\(419\) 13.4057i 0.654911i −0.944867 0.327456i \(-0.893809\pi\)
0.944867 0.327456i \(-0.106191\pi\)
\(420\) 0 0
\(421\) −1.36949 4.21487i −0.0667450 0.205420i 0.912122 0.409920i \(-0.134443\pi\)
−0.978867 + 0.204500i \(0.934443\pi\)
\(422\) 16.4201 + 5.33523i 0.799320 + 0.259715i
\(423\) 0 0
\(424\) 4.73611 6.51870i 0.230006 0.316576i
\(425\) −0.679677 + 2.09183i −0.0329692 + 0.101469i
\(426\) 0 0
\(427\) 9.70384 7.05025i 0.469602 0.341186i
\(428\) −4.31945 −0.208789
\(429\) 0 0
\(430\) 7.18661 0.346569
\(431\) 12.4280 9.02948i 0.598637 0.434935i −0.246758 0.969077i \(-0.579365\pi\)
0.845395 + 0.534142i \(0.179365\pi\)
\(432\) 0 0
\(433\) −6.22804 + 19.1679i −0.299301 + 0.921153i 0.682442 + 0.730940i \(0.260918\pi\)
−0.981743 + 0.190213i \(0.939082\pi\)
\(434\) −0.656041 + 0.902963i −0.0314910 + 0.0433436i
\(435\) 0 0
\(436\) −12.7726 4.15007i −0.611697 0.198752i
\(437\) 5.73674 + 17.6559i 0.274425 + 0.844595i
\(438\) 0 0
\(439\) 28.8015i 1.37462i −0.726365 0.687309i \(-0.758792\pi\)
0.726365 0.687309i \(-0.241208\pi\)
\(440\) 6.76526 2.03321i 0.322521 0.0969297i
\(441\) 0 0
\(442\) 0.656065 + 0.902996i 0.0312058 + 0.0429512i
\(443\) −17.3961 + 5.65233i −0.826513 + 0.268550i −0.691576 0.722304i \(-0.743083\pi\)
−0.134937 + 0.990854i \(0.543083\pi\)
\(444\) 0 0
\(445\) −15.8756 11.5343i −0.752577 0.546779i
\(446\) 7.81623 + 5.67883i 0.370109 + 0.268900i
\(447\) 0 0
\(448\) 0.951057 0.309017i 0.0449332 0.0145997i
\(449\) −14.8883 20.4920i −0.702623 0.967077i −0.999924 0.0122938i \(-0.996087\pi\)
0.297302 0.954784i \(-0.403913\pi\)
\(450\) 0 0
\(451\) 7.31671 + 5.56829i 0.344531 + 0.262201i
\(452\) 17.1519i 0.806758i
\(453\) 0 0
\(454\) 0.0993350 + 0.305722i 0.00466202 + 0.0143482i
\(455\) 0.476357 + 0.154778i 0.0223320 + 0.00725610i
\(456\) 0 0
\(457\) 16.9628 23.3474i 0.793488 1.09214i −0.200177 0.979760i \(-0.564152\pi\)
0.993665 0.112383i \(-0.0358484\pi\)
\(458\) −1.98426 + 6.10694i −0.0927186 + 0.285358i
\(459\) 0 0
\(460\) −12.8322 + 9.32315i −0.598305 + 0.434694i
\(461\) −38.2209 −1.78012 −0.890062 0.455840i \(-0.849339\pi\)
−0.890062 + 0.455840i \(0.849339\pi\)
\(462\) 0 0
\(463\) −20.6191 −0.958253 −0.479126 0.877746i \(-0.659046\pi\)
−0.479126 + 0.877746i \(0.659046\pi\)
\(464\) −4.04379 + 2.93798i −0.187728 + 0.136392i
\(465\) 0 0
\(466\) 2.35484 7.24746i 0.109086 0.335732i
\(467\) −7.79147 + 10.7240i −0.360546 + 0.496249i −0.950301 0.311333i \(-0.899224\pi\)
0.589755 + 0.807583i \(0.299224\pi\)
\(468\) 0 0
\(469\) 1.66286 + 0.540296i 0.0767838 + 0.0249486i
\(470\) 8.10962 + 24.9588i 0.374069 + 1.15127i
\(471\) 0 0
\(472\) 13.5981i 0.625903i
\(473\) −6.37502 9.19726i −0.293124 0.422890i
\(474\) 0 0
\(475\) 0.679009 + 0.934576i 0.0311551 + 0.0428813i
\(476\) −4.51413 + 1.46673i −0.206905 + 0.0672274i
\(477\) 0 0
\(478\) −23.6366 17.1730i −1.08111 0.785475i
\(479\) 21.1217 + 15.3458i 0.965076 + 0.701169i 0.954324 0.298773i \(-0.0965775\pi\)
0.0107519 + 0.999942i \(0.496577\pi\)
\(480\) 0 0
\(481\) 2.24239 0.728598i 0.102244 0.0332212i
\(482\) −9.65371 13.2872i −0.439714 0.605215i
\(483\) 0 0
\(484\) −8.60331 6.85442i −0.391060 0.311564i
\(485\) 2.45432i 0.111445i
\(486\) 0 0
\(487\) 7.13651 + 21.9639i 0.323386 + 0.995280i 0.972164 + 0.234302i \(0.0752806\pi\)
−0.648778 + 0.760978i \(0.724719\pi\)
\(488\) 11.4075 + 3.70654i 0.516395 + 0.167787i
\(489\) 0 0
\(490\) −1.25194 + 1.72315i −0.0565570 + 0.0778440i
\(491\) −6.20818 + 19.1068i −0.280171 + 0.862278i 0.707633 + 0.706580i \(0.249763\pi\)
−0.987805 + 0.155699i \(0.950237\pi\)
\(492\) 0 0
\(493\) 19.1936 13.9449i 0.864435 0.628049i
\(494\) 0.586226 0.0263756
\(495\) 0 0
\(496\) −1.11612 −0.0501155
\(497\) −7.51705 + 5.46145i −0.337186 + 0.244980i
\(498\) 0 0
\(499\) −11.6581 + 35.8799i −0.521888 + 1.60621i 0.248502 + 0.968631i \(0.420062\pi\)
−0.770389 + 0.637574i \(0.779938\pi\)
\(500\) −6.83985 + 9.41425i −0.305888 + 0.421018i
\(501\) 0 0
\(502\) 11.3450 + 3.68620i 0.506350 + 0.164523i
\(503\) 0.127130 + 0.391265i 0.00566844 + 0.0174457i 0.953851 0.300281i \(-0.0970805\pi\)
−0.948182 + 0.317727i \(0.897081\pi\)
\(504\) 0 0
\(505\) 10.9331i 0.486518i
\(506\) 23.3146 + 8.15210i 1.03646 + 0.362405i
\(507\) 0 0
\(508\) 10.8429 + 14.9240i 0.481075 + 0.662143i
\(509\) 17.3693 5.64364i 0.769883 0.250150i 0.102368 0.994747i \(-0.467358\pi\)
0.667515 + 0.744597i \(0.267358\pi\)
\(510\) 0 0
\(511\) −3.49683 2.54059i −0.154690 0.112389i
\(512\) 0.809017 + 0.587785i 0.0357538 + 0.0259767i
\(513\) 0 0
\(514\) −3.23144 + 1.04996i −0.142533 + 0.0463117i
\(515\) −0.507049 0.697893i −0.0223432 0.0307528i
\(516\) 0 0
\(517\) 24.7480 32.5187i 1.08841 1.43017i
\(518\) 10.0264i 0.440534i
\(519\) 0 0
\(520\) 0.154778 + 0.476357i 0.00678746 + 0.0208896i
\(521\) 36.2661 + 11.7836i 1.58885 + 0.516248i 0.964317 0.264752i \(-0.0852900\pi\)
0.624531 + 0.781000i \(0.285290\pi\)
\(522\) 0 0
\(523\) −7.32379 + 10.0803i −0.320247 + 0.440782i −0.938543 0.345163i \(-0.887824\pi\)
0.618295 + 0.785946i \(0.287824\pi\)
\(524\) 5.22218 16.0722i 0.228132 0.702118i
\(525\) 0 0
\(526\) −16.4283 + 11.9359i −0.716309 + 0.520429i
\(527\) 5.29761 0.230767
\(528\) 0 0
\(529\) −32.4571 −1.41118
\(530\) −13.8844 + 10.0876i −0.603099 + 0.438177i
\(531\) 0 0
\(532\) −0.770347 + 2.37089i −0.0333988 + 0.102791i
\(533\) −0.383191 + 0.527417i −0.0165978 + 0.0228450i
\(534\) 0 0
\(535\) 8.74985 + 2.84300i 0.378289 + 0.122914i
\(536\) 0.540296 + 1.66286i 0.0233372 + 0.0718247i
\(537\) 0 0
\(538\) 18.8341i 0.811996i
\(539\) 3.31581 + 0.0736535i 0.142822 + 0.00317248i
\(540\) 0 0
\(541\) 19.3145 + 26.5842i 0.830396 + 1.14294i 0.987849 + 0.155415i \(0.0496716\pi\)
−0.157453 + 0.987526i \(0.550328\pi\)
\(542\) −2.33005 + 0.757078i −0.100084 + 0.0325193i
\(543\) 0 0
\(544\) −3.83995 2.78988i −0.164636 0.119615i
\(545\) 23.1417 + 16.8135i 0.991283 + 0.720209i
\(546\) 0 0
\(547\) 32.9159 10.6950i 1.40738 0.457286i 0.495812 0.868430i \(-0.334870\pi\)
0.911571 + 0.411144i \(0.134870\pi\)
\(548\) 6.71611 + 9.24394i 0.286898 + 0.394881i
\(549\) 0 0
\(550\) 1.53653 + 0.0341308i 0.0655180 + 0.00145534i
\(551\) 12.4605i 0.530835i
\(552\) 0 0
\(553\) 2.19627 + 6.75941i 0.0933948 + 0.287440i
\(554\) 1.63322 + 0.530666i 0.0693889 + 0.0225458i
\(555\) 0 0
\(556\) −3.97813 + 5.47543i −0.168710 + 0.232210i
\(557\) −1.85100 + 5.69680i −0.0784295 + 0.241381i −0.982582 0.185828i \(-0.940503\pi\)
0.904153 + 0.427209i \(0.140503\pi\)
\(558\) 0 0
\(559\) 0.641915 0.466378i 0.0271501 0.0197257i
\(560\) −2.12993 −0.0900060
\(561\) 0 0
\(562\) −5.45620 −0.230156
\(563\) 0.543545 0.394908i 0.0229077 0.0166434i −0.576273 0.817258i \(-0.695493\pi\)
0.599180 + 0.800614i \(0.295493\pi\)
\(564\) 0 0
\(565\) 11.2891 34.7444i 0.474937 1.46171i
\(566\) 13.8638 19.0819i 0.582739 0.802071i
\(567\) 0 0
\(568\) −8.83682 2.87126i −0.370785 0.120475i
\(569\) 1.66153 + 5.11366i 0.0696550 + 0.214376i 0.979824 0.199860i \(-0.0640488\pi\)
−0.910169 + 0.414236i \(0.864049\pi\)
\(570\) 0 0
\(571\) 24.7350i 1.03513i −0.855644 0.517565i \(-0.826839\pi\)
0.855644 0.517565i \(-0.173161\pi\)
\(572\) 0.472333 0.620643i 0.0197492 0.0259504i
\(573\) 0 0
\(574\) −1.62950 2.24281i −0.0680139 0.0936132i
\(575\) −3.28199 + 1.06638i −0.136869 + 0.0444713i
\(576\) 0 0
\(577\) −17.9300 13.0269i −0.746436 0.542318i 0.148284 0.988945i \(-0.452625\pi\)
−0.894720 + 0.446627i \(0.852625\pi\)
\(578\) 4.47276 + 3.24965i 0.186042 + 0.135168i
\(579\) 0 0
\(580\) 10.1252 3.28987i 0.420425 0.136604i
\(581\) −1.37584 1.89368i −0.0570796 0.0785633i
\(582\) 0 0
\(583\) 25.2263 + 8.82052i 1.04477 + 0.365309i
\(584\) 4.32231i 0.178859i
\(585\) 0 0
\(586\) −5.97171 18.3790i −0.246689 0.759231i
\(587\) −9.04591 2.93920i −0.373365 0.121314i 0.116323 0.993211i \(-0.462889\pi\)
−0.489688 + 0.871898i \(0.662889\pi\)
\(588\) 0 0
\(589\) 1.63544 2.25099i 0.0673873 0.0927506i
\(590\) −8.95005 + 27.5454i −0.368468 + 1.13403i
\(591\) 0 0
\(592\) −8.11152 + 5.89336i −0.333381 + 0.242216i
\(593\) −26.3797 −1.08328 −0.541642 0.840609i \(-0.682197\pi\)
−0.541642 + 0.840609i \(0.682197\pi\)
\(594\) 0 0
\(595\) 10.1096 0.414452
\(596\) −1.52106 + 1.10512i −0.0623052 + 0.0452674i
\(597\) 0 0
\(598\) −0.541155 + 1.66550i −0.0221295 + 0.0681075i
\(599\) 13.5717 18.6798i 0.554524 0.763237i −0.436093 0.899902i \(-0.643638\pi\)
0.990617 + 0.136664i \(0.0436381\pi\)
\(600\) 0 0
\(601\) 5.79519 + 1.88297i 0.236391 + 0.0768081i 0.424817 0.905279i \(-0.360339\pi\)
−0.188426 + 0.982087i \(0.560339\pi\)
\(602\) 1.04266 + 3.20896i 0.0424955 + 0.130788i
\(603\) 0 0
\(604\) 8.81289i 0.358591i
\(605\) 12.9161 + 19.5475i 0.525115 + 0.794717i
\(606\) 0 0
\(607\) −2.40603 3.31162i −0.0976578 0.134414i 0.757392 0.652961i \(-0.226473\pi\)
−0.855050 + 0.518546i \(0.826473\pi\)
\(608\) −2.37089 + 0.770347i −0.0961521 + 0.0312417i
\(609\) 0 0
\(610\) −20.6685 15.0165i −0.836843 0.608002i
\(611\) 2.34407 + 1.70307i 0.0948311 + 0.0688988i
\(612\) 0 0
\(613\) 8.68005 2.82032i 0.350584 0.113912i −0.128431 0.991718i \(-0.540994\pi\)
0.479015 + 0.877807i \(0.340994\pi\)
\(614\) 13.2534 + 18.2417i 0.534863 + 0.736176i
\(615\) 0 0
\(616\) 1.88940 + 2.72584i 0.0761259 + 0.109827i
\(617\) 27.2597i 1.09743i −0.836009 0.548716i \(-0.815117\pi\)
0.836009 0.548716i \(-0.184883\pi\)
\(618\) 0 0
\(619\) −3.92885 12.0918i −0.157914 0.486009i 0.840530 0.541764i \(-0.182243\pi\)
−0.998444 + 0.0557549i \(0.982243\pi\)
\(620\) 2.26091 + 0.734616i 0.0908005 + 0.0295029i
\(621\) 0 0
\(622\) −8.55922 + 11.7808i −0.343193 + 0.472365i
\(623\) 2.84702 8.76222i 0.114063 0.351051i
\(624\) 0 0
\(625\) 18.1772 13.2065i 0.727089 0.528261i
\(626\) −4.26358 −0.170407
\(627\) 0 0
\(628\) 0.483216 0.0192824
\(629\) 38.5008 27.9724i 1.53513 1.11533i
\(630\) 0 0
\(631\) −6.55862 + 20.1854i −0.261095 + 0.803567i 0.731473 + 0.681871i \(0.238833\pi\)
−0.992567 + 0.121696i \(0.961167\pi\)
\(632\) −4.17755 + 5.74990i −0.166174 + 0.228719i
\(633\) 0 0
\(634\) 17.2359 + 5.60028i 0.684525 + 0.222416i
\(635\) −12.1415 37.3678i −0.481823 1.48290i
\(636\) 0 0
\(637\) 0.235159i 0.00931733i
\(638\) −13.1920 10.0396i −0.522277 0.397473i
\(639\) 0 0
\(640\) −1.25194 1.72315i −0.0494873 0.0681135i
\(641\) −36.3616 + 11.8146i −1.43620 + 0.466649i −0.920709 0.390249i \(-0.872389\pi\)
−0.515487 + 0.856897i \(0.672389\pi\)
\(642\) 0 0
\(643\) −2.77532 2.01639i −0.109448 0.0795186i 0.531715 0.846923i \(-0.321548\pi\)
−0.641163 + 0.767405i \(0.721548\pi\)
\(644\) −6.02471 4.37721i −0.237407 0.172486i
\(645\) 0 0
\(646\) 11.2532 3.65640i 0.442753 0.143859i
\(647\) 15.3920 + 21.1853i 0.605122 + 0.832879i 0.996165 0.0874933i \(-0.0278856\pi\)
−0.391043 + 0.920372i \(0.627886\pi\)
\(648\) 0 0
\(649\) 43.1913 12.9806i 1.69541 0.509534i
\(650\) 0.108972i 0.00427422i
\(651\) 0 0
\(652\) 0.0444710 + 0.136868i 0.00174162 + 0.00536015i
\(653\) 23.3122 + 7.57460i 0.912278 + 0.296417i 0.727295 0.686325i \(-0.240777\pi\)
0.184982 + 0.982742i \(0.440777\pi\)
\(654\) 0 0
\(655\) −21.1570 + 29.1201i −0.826671 + 1.13782i
\(656\) 0.856678 2.63658i 0.0334477 0.102941i
\(657\) 0 0
\(658\) −9.96805 + 7.24222i −0.388595 + 0.282331i
\(659\) 3.58143 0.139513 0.0697564 0.997564i \(-0.477778\pi\)
0.0697564 + 0.997564i \(0.477778\pi\)
\(660\) 0 0
\(661\) 5.17432 0.201258 0.100629 0.994924i \(-0.467915\pi\)
0.100629 + 0.994924i \(0.467915\pi\)
\(662\) 26.0045 18.8934i 1.01070 0.734313i
\(663\) 0 0
\(664\) 0.723323 2.22616i 0.0280704 0.0863917i
\(665\) 3.12096 4.29563i 0.121026 0.166578i
\(666\) 0 0
\(667\) 35.4010 + 11.5025i 1.37073 + 0.445378i
\(668\) 7.91968 + 24.3743i 0.306422 + 0.943069i
\(669\) 0 0
\(670\) 3.72405i 0.143872i
\(671\) −0.883444 + 39.7718i −0.0341050 + 1.53537i
\(672\) 0 0
\(673\) −17.6103 24.2386i −0.678829 0.934328i 0.321090 0.947049i \(-0.395951\pi\)
−0.999919 + 0.0127207i \(0.995951\pi\)
\(674\) 14.9587 4.86037i 0.576186 0.187214i
\(675\) 0 0
\(676\) −10.4725 7.60870i −0.402788 0.292642i
\(677\) 19.2821 + 14.0092i 0.741070 + 0.538419i 0.893046 0.449965i \(-0.148564\pi\)
−0.151976 + 0.988384i \(0.548564\pi\)
\(678\) 0 0
\(679\) −1.09590 + 0.356080i −0.0420569 + 0.0136651i
\(680\) 5.94226 + 8.17882i 0.227875 + 0.313643i
\(681\) 0 0
\(682\) −1.06544 3.54512i −0.0407979 0.135750i
\(683\) 21.9330i 0.839244i −0.907699 0.419622i \(-0.862163\pi\)
0.907699 0.419622i \(-0.137837\pi\)
\(684\) 0 0
\(685\) −7.52051 23.1457i −0.287344 0.884353i
\(686\) −0.951057 0.309017i −0.0363115 0.0117983i
\(687\) 0 0
\(688\) −1.98325 + 2.72971i −0.0756107 + 0.104069i
\(689\) −0.585527 + 1.80207i −0.0223068 + 0.0686532i
\(690\) 0 0
\(691\) 5.28133 3.83711i 0.200911 0.145970i −0.482781 0.875741i \(-0.660373\pi\)
0.683692 + 0.729771i \(0.260373\pi\)
\(692\) −16.2909 −0.619286
\(693\) 0 0
\(694\) 8.15340 0.309499
\(695\) 11.6623 8.47315i 0.442376 0.321405i
\(696\) 0 0
\(697\) −4.06617 + 12.5144i −0.154017 + 0.474016i
\(698\) −9.80175 + 13.4909i −0.371002 + 0.510640i
\(699\) 0 0
\(700\) −0.440716 0.143197i −0.0166575 0.00541235i
\(701\) −4.79560 14.7593i −0.181127 0.557452i 0.818733 0.574175i \(-0.194677\pi\)
−0.999860 + 0.0167222i \(0.994677\pi\)
\(702\) 0 0
\(703\) 24.9947i 0.942694i
\(704\) −1.09469 + 3.13076i −0.0412577 + 0.117995i
\(705\) 0 0
\(706\) −15.2712 21.0189i −0.574737 0.791058i
\(707\) 4.88187 1.58621i 0.183601 0.0596557i
\(708\) 0 0
\(709\) −33.8403 24.5864i −1.27090 0.923363i −0.271662 0.962393i \(-0.587573\pi\)
−0.999238 + 0.0390293i \(0.987573\pi\)
\(710\) 16.0108 + 11.6325i 0.600874 + 0.436561i
\(711\) 0 0
\(712\) 8.76222 2.84702i 0.328378 0.106697i
\(713\) 4.88551 + 6.72432i 0.182964 + 0.251828i
\(714\) 0 0
\(715\) −1.36529 + 0.946345i −0.0510591 + 0.0353913i
\(716\) 11.8096i 0.441345i
\(717\) 0 0
\(718\) −3.72488 11.4640i −0.139011 0.427832i
\(719\) −16.8573 5.47728i −0.628673 0.204268i −0.0226857 0.999743i \(-0.507222\pi\)
−0.605987 + 0.795474i \(0.707222\pi\)
\(720\) 0 0
\(721\) 0.238059 0.327660i 0.00886578 0.0122027i
\(722\) −3.95093 + 12.1597i −0.147038 + 0.452537i
\(723\) 0 0
\(724\) −19.1140 + 13.8872i −0.710368 + 0.516112i
\(725\) 2.31624 0.0860230
\(726\) 0 0
\(727\) −45.4758 −1.68661 −0.843303 0.537439i \(-0.819392\pi\)
−0.843303 + 0.537439i \(0.819392\pi\)
\(728\) −0.190247 + 0.138223i −0.00705104 + 0.00512288i
\(729\) 0 0
\(730\) −2.84488 + 8.75564i −0.105294 + 0.324061i
\(731\) 9.41336 12.9564i 0.348166 0.479209i
\(732\) 0 0
\(733\) −44.7912 14.5535i −1.65440 0.537547i −0.674714 0.738079i \(-0.735733\pi\)
−0.979687 + 0.200532i \(0.935733\pi\)
\(734\) −5.50531 16.9436i −0.203205 0.625399i
\(735\) 0 0
\(736\) 7.44695i 0.274498i
\(737\) −4.76595 + 3.30349i −0.175556 + 0.121685i
\(738\) 0 0
\(739\) 0.819908 + 1.12851i 0.0301608 + 0.0415128i 0.823831 0.566835i \(-0.191832\pi\)
−0.793670 + 0.608348i \(0.791832\pi\)
\(740\) 20.3103 6.59921i 0.746621 0.242592i
\(741\) 0 0
\(742\) −6.51870 4.73611i −0.239309 0.173868i
\(743\) 26.1461 + 18.9962i 0.959206 + 0.696904i 0.952966 0.303077i \(-0.0980139\pi\)
0.00623956 + 0.999981i \(0.498014\pi\)
\(744\) 0 0
\(745\) 3.80856 1.23748i 0.139535 0.0453377i
\(746\) −2.52200 3.47124i −0.0923370 0.127091i
\(747\) 0 0
\(748\) 5.19587 14.8599i 0.189980 0.543333i
\(749\) 4.31945i 0.157829i
\(750\) 0 0
\(751\) −7.57535 23.3145i −0.276428 0.850759i −0.988838 0.148995i \(-0.952396\pi\)
0.712410 0.701764i \(-0.247604\pi\)
\(752\) −11.7182 3.80746i −0.427317 0.138844i
\(753\) 0 0
\(754\) 0.690892 0.950932i 0.0251608 0.0346309i
\(755\) 5.80051 17.8521i 0.211102 0.649705i
\(756\) 0 0
\(757\) 30.7454 22.3379i 1.11746 0.811884i 0.133640 0.991030i \(-0.457334\pi\)
0.983822 + 0.179146i \(0.0573335\pi\)
\(758\) 7.02411 0.255127
\(759\) 0 0
\(760\) 5.30970 0.192603
\(761\) −16.7796 + 12.1911i −0.608258 + 0.441926i −0.848801 0.528713i \(-0.822675\pi\)
0.240542 + 0.970639i \(0.422675\pi\)
\(762\) 0 0
\(763\) −4.15007 + 12.7726i −0.150243 + 0.462399i
\(764\) 5.11747 7.04359i 0.185144 0.254828i
\(765\) 0 0
\(766\) 28.0125 + 9.10180i 1.01213 + 0.328861i
\(767\) 0.988146 + 3.04120i 0.0356799 + 0.109811i
\(768\) 0 0
\(769\) 46.8600i 1.68982i −0.534912 0.844908i \(-0.679655\pi\)
0.534912 0.844908i \(-0.320345\pi\)
\(770\) −2.03321 6.76526i −0.0732720 0.243803i
\(771\) 0 0
\(772\) −2.43343 3.34933i −0.0875810 0.120545i
\(773\) −1.29905 + 0.422086i −0.0467234 + 0.0151814i −0.332285 0.943179i \(-0.607820\pi\)
0.285562 + 0.958360i \(0.407820\pi\)
\(774\) 0 0
\(775\) 0.418430 + 0.304007i 0.0150304 + 0.0109203i
\(776\) −0.932230 0.677305i −0.0334651 0.0243138i
\(777\) 0 0
\(778\) −30.3015 + 9.84556i −1.08636 + 0.352980i
\(779\) 4.06217 + 5.59110i 0.145542 + 0.200322i
\(780\) 0 0
\(781\) 0.684358 30.8091i 0.0244882 1.10244i
\(782\) 35.3465i 1.26399i
\(783\) 0 0
\(784\) −0.309017 0.951057i −0.0110363 0.0339663i
\(785\) −0.978843 0.318045i −0.0349364 0.0113515i
\(786\) 0 0
\(787\) 23.7405 32.6760i 0.846258 1.16477i −0.138417 0.990374i \(-0.544201\pi\)
0.984675 0.174400i \(-0.0557986\pi\)
\(788\) 0.554490 1.70654i 0.0197529 0.0607931i
\(789\) 0 0
\(790\) 12.2469 8.89789i 0.435725 0.316573i
\(791\) 17.1519 0.609852
\(792\) 0 0
\(793\) −2.82063 −0.100164
\(794\) 30.6229 22.2488i 1.08677 0.789581i
\(795\) 0 0
\(796\) 0.130146 0.400547i 0.00461289 0.0141970i
\(797\) −30.4201 + 41.8697i −1.07754 + 1.48310i −0.215332 + 0.976541i \(0.569083\pi\)
−0.862204 + 0.506560i \(0.830917\pi\)
\(798\) 0 0
\(799\) 55.6194 + 18.0718i 1.96767 + 0.639336i
\(800\) −0.143197 0.440716i −0.00506279 0.0155817i
\(801\) 0 0
\(802\) 1.28730i 0.0454562i
\(803\) 13.7289 4.12605i 0.484482 0.145605i
\(804\) 0 0
\(805\) 9.32315 + 12.8322i 0.328598 + 0.452276i
\(806\) 0.249620 0.0811065i 0.00879250 0.00285686i
\(807\) 0 0
\(808\) 4.15276 + 3.01716i 0.146094 + 0.106143i
\(809\) −11.3568 8.25119i −0.399284 0.290096i 0.369966 0.929045i \(-0.379369\pi\)
−0.769249 + 0.638949i \(0.779369\pi\)
\(810\) 0 0
\(811\) −18.5112 + 6.01464i −0.650014 + 0.211203i −0.615421 0.788199i \(-0.711014\pi\)
−0.0345939 + 0.999401i \(0.511014\pi\)
\(812\) 2.93798 + 4.04379i 0.103103 + 0.141909i
\(813\) 0 0
\(814\) −26.4622 20.1387i −0.927498 0.705861i
\(815\) 0.306521i 0.0107370i
\(816\) 0 0
\(817\) −2.59923 7.99962i −0.0909357 0.279871i
\(818\) −11.4901 3.73336i −0.401742 0.130534i
\(819\) 0 0
\(820\) −3.47072 + 4.77703i −0.121203 + 0.166821i
\(821\) 16.2615 50.0477i 0.567529 1.74668i −0.0927848 0.995686i \(-0.529577\pi\)
0.660314 0.750990i \(-0.270423\pi\)
\(822\) 0 0
\(823\) −3.92822 + 2.85402i −0.136929 + 0.0994850i −0.654141 0.756372i \(-0.726970\pi\)
0.517212 + 0.855857i \(0.326970\pi\)
\(824\) 0.405010 0.0141092
\(825\) 0 0
\(826\) −13.5981 −0.473138
\(827\) −20.5296 + 14.9156i −0.713884 + 0.518667i −0.884424 0.466683i \(-0.845449\pi\)
0.170540 + 0.985351i \(0.445449\pi\)
\(828\) 0 0
\(829\) −13.1108 + 40.3510i −0.455358 + 1.40145i 0.415357 + 0.909658i \(0.363657\pi\)
−0.870715 + 0.491788i \(0.836343\pi\)
\(830\) −2.93045 + 4.03342i −0.101717 + 0.140002i
\(831\) 0 0
\(832\) −0.223649 0.0726680i −0.00775364 0.00251931i
\(833\) 1.46673 + 4.51413i 0.0508191 + 0.156405i
\(834\) 0 0
\(835\) 54.5872i 1.88907i
\(836\) −4.71007 6.79523i −0.162901 0.235018i
\(837\) 0 0
\(838\) −7.87967 10.8454i −0.272199 0.374649i
\(839\) −46.7259 + 15.1822i −1.61316 + 0.524147i −0.970314 0.241850i \(-0.922246\pi\)
−0.642845 + 0.765997i \(0.722246\pi\)
\(840\) 0 0
\(841\) 3.24904 + 2.36056i 0.112036 + 0.0813987i
\(842\) −3.58538 2.60493i −0.123560 0.0897718i
\(843\) 0 0
\(844\) 16.4201 5.33523i 0.565205 0.183646i
\(845\) 16.2060 + 22.3057i 0.557504 + 0.767338i
\(846\) 0 0
\(847\) −6.85442 + 8.60331i −0.235521 + 0.295613i
\(848\) 8.05755i 0.276698i
\(849\) 0 0
\(850\) 0.679677 + 2.09183i 0.0233127 + 0.0717492i
\(851\) 71.0116 + 23.0731i 2.43425 + 0.790934i
\(852\) 0 0
\(853\) −6.98237 + 9.61041i −0.239072 + 0.329054i −0.911647 0.410975i \(-0.865188\pi\)
0.672575 + 0.740029i \(0.265188\pi\)
\(854\) 3.70654 11.4075i 0.126835 0.390358i
\(855\) 0 0
\(856\) −3.49451 + 2.53891i −0.119440 + 0.0867782i
\(857\) −0.316482 −0.0108108 −0.00540541 0.999985i \(-0.501721\pi\)
−0.00540541 + 0.999985i \(0.501721\pi\)
\(858\) 0 0
\(859\) −0.944089 −0.0322119 −0.0161060 0.999870i \(-0.505127\pi\)
−0.0161060 + 0.999870i \(0.505127\pi\)
\(860\) 5.81409 4.22418i 0.198259 0.144043i
\(861\) 0 0
\(862\) 4.74708 14.6100i 0.161686 0.497619i
\(863\) −28.9133 + 39.7958i −0.984221 + 1.35466i −0.0496972 + 0.998764i \(0.515826\pi\)
−0.934524 + 0.355900i \(0.884174\pi\)
\(864\) 0 0
\(865\) 33.0001 + 10.7224i 1.12204 + 0.364572i
\(866\) 6.22804 + 19.1679i 0.211638 + 0.651353i
\(867\) 0 0
\(868\) 1.11612i 0.0378837i
\(869\) −22.2511 7.78025i −0.754819 0.263927i
\(870\) 0 0
\(871\) −0.241674 0.332635i −0.00818880 0.0112709i
\(872\) −12.7726 + 4.15007i −0.432535 + 0.140539i
\(873\) 0 0
\(874\) 15.0190 + 10.9119i 0.508024 + 0.369101i
\(875\) 9.41425 + 6.83985i 0.318260 + 0.231229i
\(876\) 0 0
\(877\) 30.3115 9.84880i 1.02355 0.332570i 0.251311 0.967906i \(-0.419138\pi\)
0.772236 + 0.635336i \(0.219138\pi\)
\(878\) −16.9291 23.3009i −0.571329 0.786366i
\(879\) 0 0
\(880\) 4.27811 5.62142i 0.144215 0.189498i
\(881\) 19.4291i 0.654585i 0.944923 + 0.327292i \(0.106136\pi\)
−0.944923 + 0.327292i \(0.893864\pi\)
\(882\) 0 0
\(883\) 12.7853 + 39.3490i 0.430259 + 1.32420i 0.897868 + 0.440265i \(0.145116\pi\)
−0.467609 + 0.883935i \(0.654884\pi\)
\(884\) 1.06154 + 0.344914i 0.0357033 + 0.0116007i
\(885\) 0 0
\(886\) −10.7514 + 14.7980i −0.361199 + 0.497148i
\(887\) 12.5007 38.4732i 0.419732 1.29180i −0.488217 0.872722i \(-0.662353\pi\)
0.907949 0.419080i \(-0.137647\pi\)
\(888\) 0 0
\(889\) 14.9240 10.8429i 0.500533 0.363659i
\(890\) −19.6234 −0.657777
\(891\) 0 0
\(892\) 9.66140 0.323488
\(893\) 24.8493 18.0541i 0.831551 0.604157i
\(894\) 0 0
\(895\) 7.77290 23.9225i 0.259819 0.799642i
\(896\) 0.587785 0.809017i 0.0196365 0.0270274i
\(897\) 0 0
\(898\) −24.0898 7.82725i −0.803887 0.261199i
\(899\) −1.72395 5.30578i −0.0574971 0.176958i
\(900\) 0 0
\(901\) 38.2446i 1.27411i
\(902\) 9.19231 + 0.204187i 0.306070 + 0.00679869i
\(903\) 0 0
\(904\) 10.0816 + 13.8762i 0.335310 + 0.461515i
\(905\) 47.8593 15.5504i 1.59090 0.516914i
\(906\) 0 0
\(907\) 31.0279 + 22.5431i 1.03026 + 0.748530i 0.968361 0.249552i \(-0.0802834\pi\)
0.0619020 + 0.998082i \(0.480283\pi\)
\(908\) 0.260062 + 0.188946i 0.00863048 + 0.00627041i
\(909\) 0 0
\(910\) 0.476357 0.154778i 0.0157911 0.00513084i
\(911\) 13.1916 + 18.1567i 0.437058 + 0.601559i 0.969555 0.244873i \(-0.0787463\pi\)
−0.532497 + 0.846432i \(0.678746\pi\)
\(912\) 0 0
\(913\) 7.76138 + 0.172402i 0.256864 + 0.00570569i
\(914\) 28.8589i 0.954568i
\(915\) 0 0
\(916\) 1.98426 + 6.10694i 0.0655619 + 0.201779i
\(917\) −16.0722 5.22218i −0.530751 0.172452i
\(918\) 0 0
\(919\) 4.98239 6.85767i 0.164354 0.226214i −0.718894 0.695119i \(-0.755352\pi\)
0.883248 + 0.468906i \(0.155352\pi\)
\(920\) −4.90147 + 15.0852i −0.161597 + 0.497343i
\(921\) 0 0
\(922\) −30.9213 + 22.4657i −1.01834 + 0.739867i
\(923\) 2.18500 0.0719200
\(924\) 0 0
\(925\) 4.64619 0.152766
\(926\) −16.6812 + 12.1196i −0.548179 + 0.398276i
\(927\) 0 0
\(928\) −1.54459 + 4.75376i −0.0507036 + 0.156050i
\(929\) −10.9089 + 15.0148i −0.357910 + 0.492621i −0.949565 0.313570i \(-0.898475\pi\)
0.591655 + 0.806191i \(0.298475\pi\)
\(930\) 0 0
\(931\) 2.37089 + 0.770347i 0.0777026 + 0.0252471i
\(932\) −2.35484 7.24746i −0.0771354 0.237398i
\(933\) 0 0
\(934\) 13.2556i 0.433738i
\(935\) −20.3058 + 26.6817i −0.664070 + 0.872585i
\(936\) 0 0
\(937\) −25.2597 34.7670i −0.825200 1.13579i −0.988798 0.149263i \(-0.952310\pi\)
0.163598 0.986527i \(-0.447690\pi\)
\(938\) 1.66286 0.540296i 0.0542943 0.0176413i
\(939\) 0 0
\(940\) 21.2313 + 15.4254i 0.692487 + 0.503122i
\(941\) 9.88935 + 7.18504i 0.322384 + 0.234225i 0.737192 0.675683i \(-0.236151\pi\)
−0.414808 + 0.909909i \(0.636151\pi\)
\(942\) 0 0
\(943\) −19.6345 + 6.37964i −0.639388 + 0.207750i
\(944\) −7.99275 11.0011i −0.260142 0.358055i
\(945\) 0 0
\(946\) −10.5635 3.69360i −0.343449 0.120089i
\(947\) 14.7538i 0.479435i −0.970843 0.239718i \(-0.922945\pi\)
0.970843 0.239718i \(-0.0770549\pi\)
\(948\) 0 0
\(949\) 0.314094 + 0.966682i 0.0101959 + 0.0313798i
\(950\) 1.09866 + 0.356976i 0.0356452 + 0.0115818i
\(951\) 0 0
\(952\) −2.78988 + 3.83995i −0.0904206 + 0.124453i
\(953\) 9.55006 29.3921i 0.309357 0.952102i −0.668659 0.743570i \(-0.733131\pi\)
0.978015 0.208533i \(-0.0668688\pi\)
\(954\) 0 0
\(955\) −15.0024 + 10.8999i −0.485465 + 0.352711i
\(956\) −29.2165 −0.944928
\(957\) 0 0
\(958\) 26.1079 0.843507
\(959\) 9.24394 6.71611i 0.298502 0.216875i
\(960\) 0 0
\(961\) −9.19457 + 28.2980i −0.296599 + 0.912838i
\(962\) 1.38587 1.90749i 0.0446824 0.0615001i
\(963\) 0 0
\(964\) −15.6200 5.07525i −0.503087 0.163463i
\(965\) 2.72488 + 8.38632i 0.0877171 + 0.269965i
\(966\) 0 0
\(967\) 43.2159i 1.38973i −0.719141 0.694865i \(-0.755464\pi\)
0.719141 0.694865i \(-0.244536\pi\)
\(968\) −10.9892 0.488442i −0.353205 0.0156991i
\(969\) 0 0
\(970\) 1.44261 + 1.98559i 0.0463195 + 0.0637533i
\(971\) 24.8261 8.06650i 0.796708 0.258866i 0.117750 0.993043i \(-0.462432\pi\)
0.678958 + 0.734177i \(0.262432\pi\)
\(972\) 0 0
\(973\) 5.47543 + 3.97813i 0.175534 + 0.127533i
\(974\) 18.6836 + 13.5745i 0.598662 + 0.434954i
\(975\) 0 0
\(976\) 11.4075 3.70654i 0.365147 0.118643i
\(977\) −8.24873 11.3534i −0.263900 0.363228i 0.656418 0.754397i \(-0.272071\pi\)
−0.920319 + 0.391169i \(0.872071\pi\)
\(978\) 0 0
\(979\) 17.4073 + 25.1135i 0.556339 + 0.802632i
\(980\) 2.12993i 0.0680381i
\(981\) 0 0
\(982\) 6.20818 + 19.1068i 0.198111 + 0.609723i
\(983\) 53.5117 + 17.3870i 1.70676 + 0.554559i 0.989788 0.142546i \(-0.0455288\pi\)
0.716969 + 0.697105i \(0.245529\pi\)
\(984\) 0 0
\(985\) −2.24644 + 3.09196i −0.0715776 + 0.0985181i
\(986\) 7.33129 22.5634i 0.233476 0.718565i
\(987\) 0 0
\(988\) 0.474267 0.344575i 0.0150884 0.0109624i
\(989\) 25.1268 0.798986
\(990\) 0 0
\(991\) −43.4611 −1.38059 −0.690293 0.723530i \(-0.742518\pi\)
−0.690293 + 0.723530i \(0.742518\pi\)
\(992\) −0.902963 + 0.656041i −0.0286691 + 0.0208293i
\(993\) 0 0
\(994\) −2.87126 + 8.83682i −0.0910707 + 0.280287i
\(995\) −0.527268 + 0.725723i −0.0167155 + 0.0230070i
\(996\) 0 0
\(997\) 8.79489 + 2.85763i 0.278537 + 0.0905021i 0.444954 0.895553i \(-0.353220\pi\)
−0.166417 + 0.986055i \(0.553220\pi\)
\(998\) 11.6581 + 35.8799i 0.369030 + 1.13576i
\(999\) 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 1386.2.bu.b.701.2 yes 48
3.2 odd 2 1386.2.bu.a.701.11 48
11.7 odd 10 1386.2.bu.a.953.11 yes 48
33.29 even 10 inner 1386.2.bu.b.953.2 yes 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1386.2.bu.a.701.11 48 3.2 odd 2
1386.2.bu.a.953.11 yes 48 11.7 odd 10
1386.2.bu.b.701.2 yes 48 1.1 even 1 trivial
1386.2.bu.b.953.2 yes 48 33.29 even 10 inner