Properties

Label 855.2.da.b.199.5
Level $855$
Weight $2$
Character 855.199
Analytic conductor $6.827$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [855,2,Mod(199,855)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(855, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([0, 9, 8]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("855.199");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 855 = 3^{2} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 855.da (of order \(18\), degree \(6\), 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: \(6.82720937282\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(8\) over \(\Q(\zeta_{18})\)
Twist minimal: no (minimal twist has level 95)
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 199.5
Character \(\chi\) \(=\) 855.199
Dual form 855.2.da.b.739.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.240763 - 0.0424530i) q^{2} +(-1.82322 + 0.663598i) q^{4} +(1.42562 - 1.72267i) q^{5} +(-1.68032 - 0.970136i) q^{7} +(-0.834240 + 0.481648i) q^{8} +O(q^{10})\) \(q+(0.240763 - 0.0424530i) q^{2} +(-1.82322 + 0.663598i) q^{4} +(1.42562 - 1.72267i) q^{5} +(-1.68032 - 0.970136i) q^{7} +(-0.834240 + 0.481648i) q^{8} +(0.270105 - 0.475278i) q^{10} +(2.11666 + 3.66617i) q^{11} +(0.816227 - 0.972742i) q^{13} +(-0.445745 - 0.162238i) q^{14} +(2.79220 - 2.34293i) q^{16} +(2.42284 - 0.427212i) q^{17} +(-1.64247 - 4.03761i) q^{19} +(-1.45606 + 4.08685i) q^{20} +(0.665255 + 0.792820i) q^{22} +(-1.75701 - 4.82735i) q^{23} +(-0.935198 - 4.91176i) q^{25} +(0.155222 - 0.268852i) q^{26} +(3.70738 + 0.653712i) q^{28} +(1.50053 - 8.50995i) q^{29} +(-2.55042 + 4.41746i) q^{31} +(1.81118 - 2.15849i) q^{32} +(0.565193 - 0.205714i) q^{34} +(-4.06673 + 1.51160i) q^{35} -11.0305i q^{37} +(-0.566855 - 0.902380i) q^{38} +(-0.359589 + 2.12377i) q^{40} +(-1.91387 + 1.60593i) q^{41} +(1.52842 - 4.19929i) q^{43} +(-6.29201 - 5.27962i) q^{44} +(-0.627959 - 1.08766i) q^{46} +(6.66617 + 1.17543i) q^{47} +(-1.61767 - 2.80189i) q^{49} +(-0.433680 - 1.14287i) q^{50} +(-0.842653 + 2.31517i) q^{52} +(0.235926 + 0.648201i) q^{53} +(9.33317 + 1.58026i) q^{55} +1.86906 q^{56} -2.11258i q^{58} +(0.901817 + 5.11446i) q^{59} +(-2.63378 + 0.958619i) q^{61} +(-0.426513 + 1.17183i) q^{62} +(-3.30053 + 5.71668i) q^{64} +(-0.512083 - 2.79285i) q^{65} +(5.13308 + 0.905101i) q^{67} +(-4.13387 + 2.38669i) q^{68} +(-0.914948 + 0.536583i) q^{70} +(0.744158 + 0.270851i) q^{71} +(0.910034 + 1.08454i) q^{73} +(-0.468279 - 2.65574i) q^{74} +(5.67394 + 6.27151i) q^{76} -8.21381i q^{77} +(4.64448 - 3.89718i) q^{79} +(-0.0554826 - 8.15018i) q^{80} +(-0.392614 + 0.467899i) q^{82} +(10.2643 + 5.92611i) q^{83} +(2.71811 - 4.78280i) q^{85} +(0.189714 - 1.07592i) q^{86} +(-3.53161 - 2.03898i) q^{88} +(-1.71051 - 1.43529i) q^{89} +(-2.31522 + 0.842670i) q^{91} +(6.40684 + 7.63537i) q^{92} +1.65487 q^{94} +(-9.29702 - 2.92667i) q^{95} +(-8.47901 + 1.49508i) q^{97} +(-0.508425 - 0.605917i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q - 18 q^{4} + 6 q^{5}+O(q^{10}) \) Copy content Toggle raw display \( 48 q - 18 q^{4} + 6 q^{5} - 15 q^{10} + 12 q^{11} - 6 q^{14} - 42 q^{16} + 12 q^{19} - 42 q^{20} + 12 q^{25} - 12 q^{26} - 42 q^{31} - 36 q^{34} - 6 q^{35} + 66 q^{40} - 6 q^{41} + 6 q^{44} - 6 q^{46} + 12 q^{49} + 18 q^{50} - 36 q^{56} + 36 q^{59} + 48 q^{61} + 18 q^{65} - 123 q^{70} + 24 q^{71} - 84 q^{74} + 66 q^{76} + 48 q^{79} + 39 q^{80} - 84 q^{85} + 42 q^{86} + 12 q^{89} - 30 q^{91} - 72 q^{94} + 63 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/855\mathbb{Z}\right)^\times\).

\(n\) \(172\) \(191\) \(496\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{4}{9}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.240763 0.0424530i 0.170245 0.0300188i −0.0878757 0.996131i \(-0.528008\pi\)
0.258121 + 0.966113i \(0.416897\pi\)
\(3\) 0 0
\(4\) −1.82322 + 0.663598i −0.911610 + 0.331799i
\(5\) 1.42562 1.72267i 0.637558 0.770402i
\(6\) 0 0
\(7\) −1.68032 0.970136i −0.635103 0.366677i 0.147623 0.989044i \(-0.452838\pi\)
−0.782726 + 0.622367i \(0.786171\pi\)
\(8\) −0.834240 + 0.481648i −0.294948 + 0.170288i
\(9\) 0 0
\(10\) 0.270105 0.475278i 0.0854146 0.150296i
\(11\) 2.11666 + 3.66617i 0.638198 + 1.10539i 0.985828 + 0.167760i \(0.0536534\pi\)
−0.347630 + 0.937632i \(0.613013\pi\)
\(12\) 0 0
\(13\) 0.816227 0.972742i 0.226381 0.269790i −0.640884 0.767638i \(-0.721432\pi\)
0.867264 + 0.497848i \(0.165876\pi\)
\(14\) −0.445745 0.162238i −0.119130 0.0433599i
\(15\) 0 0
\(16\) 2.79220 2.34293i 0.698050 0.585733i
\(17\) 2.42284 0.427212i 0.587624 0.103614i 0.128072 0.991765i \(-0.459121\pi\)
0.459552 + 0.888151i \(0.348010\pi\)
\(18\) 0 0
\(19\) −1.64247 4.03761i −0.376809 0.926291i
\(20\) −1.45606 + 4.08685i −0.325586 + 0.913848i
\(21\) 0 0
\(22\) 0.665255 + 0.792820i 0.141833 + 0.169030i
\(23\) −1.75701 4.82735i −0.366362 1.00657i −0.976734 0.214457i \(-0.931202\pi\)
0.610371 0.792115i \(-0.291020\pi\)
\(24\) 0 0
\(25\) −0.935198 4.91176i −0.187040 0.982352i
\(26\) 0.155222 0.268852i 0.0304415 0.0527261i
\(27\) 0 0
\(28\) 3.70738 + 0.653712i 0.700629 + 0.123540i
\(29\) 1.50053 8.50995i 0.278642 1.58026i −0.448508 0.893779i \(-0.648044\pi\)
0.727150 0.686479i \(-0.240845\pi\)
\(30\) 0 0
\(31\) −2.55042 + 4.41746i −0.458069 + 0.793399i −0.998859 0.0477591i \(-0.984792\pi\)
0.540790 + 0.841158i \(0.318125\pi\)
\(32\) 1.81118 2.15849i 0.320175 0.381570i
\(33\) 0 0
\(34\) 0.565193 0.205714i 0.0969299 0.0352796i
\(35\) −4.06673 + 1.51160i −0.687404 + 0.255507i
\(36\) 0 0
\(37\) 11.0305i 1.81341i −0.421770 0.906703i \(-0.638591\pi\)
0.421770 0.906703i \(-0.361409\pi\)
\(38\) −0.566855 0.902380i −0.0919561 0.146385i
\(39\) 0 0
\(40\) −0.359589 + 2.12377i −0.0568560 + 0.335798i
\(41\) −1.91387 + 1.60593i −0.298897 + 0.250804i −0.779885 0.625923i \(-0.784722\pi\)
0.480988 + 0.876727i \(0.340278\pi\)
\(42\) 0 0
\(43\) 1.52842 4.19929i 0.233081 0.640386i −0.766918 0.641745i \(-0.778211\pi\)
0.999999 + 0.00135976i \(0.000432826\pi\)
\(44\) −6.29201 5.27962i −0.948556 0.795933i
\(45\) 0 0
\(46\) −0.627959 1.08766i −0.0925876 0.160366i
\(47\) 6.66617 + 1.17543i 0.972362 + 0.171454i 0.637193 0.770705i \(-0.280096\pi\)
0.335169 + 0.942158i \(0.391207\pi\)
\(48\) 0 0
\(49\) −1.61767 2.80189i −0.231096 0.400270i
\(50\) −0.433680 1.14287i −0.0613317 0.161626i
\(51\) 0 0
\(52\) −0.842653 + 2.31517i −0.116855 + 0.321056i
\(53\) 0.235926 + 0.648201i 0.0324069 + 0.0890373i 0.954841 0.297117i \(-0.0960253\pi\)
−0.922434 + 0.386155i \(0.873803\pi\)
\(54\) 0 0
\(55\) 9.33317 + 1.58026i 1.25849 + 0.213082i
\(56\) 1.86906 0.249763
\(57\) 0 0
\(58\) 2.11258i 0.277396i
\(59\) 0.901817 + 5.11446i 0.117407 + 0.665846i 0.985530 + 0.169498i \(0.0542147\pi\)
−0.868124 + 0.496348i \(0.834674\pi\)
\(60\) 0 0
\(61\) −2.63378 + 0.958619i −0.337221 + 0.122739i −0.505080 0.863073i \(-0.668537\pi\)
0.167859 + 0.985811i \(0.446315\pi\)
\(62\) −0.426513 + 1.17183i −0.0541672 + 0.148823i
\(63\) 0 0
\(64\) −3.30053 + 5.71668i −0.412566 + 0.714585i
\(65\) −0.512083 2.79285i −0.0635160 0.346411i
\(66\) 0 0
\(67\) 5.13308 + 0.905101i 0.627106 + 0.110576i 0.478164 0.878270i \(-0.341302\pi\)
0.148941 + 0.988846i \(0.452413\pi\)
\(68\) −4.13387 + 2.38669i −0.501305 + 0.289429i
\(69\) 0 0
\(70\) −0.914948 + 0.536583i −0.109357 + 0.0641339i
\(71\) 0.744158 + 0.270851i 0.0883153 + 0.0321441i 0.385800 0.922582i \(-0.373925\pi\)
−0.297485 + 0.954727i \(0.596148\pi\)
\(72\) 0 0
\(73\) 0.910034 + 1.08454i 0.106511 + 0.126935i 0.816666 0.577110i \(-0.195820\pi\)
−0.710155 + 0.704045i \(0.751375\pi\)
\(74\) −0.468279 2.65574i −0.0544363 0.308724i
\(75\) 0 0
\(76\) 5.67394 + 6.27151i 0.650845 + 0.719392i
\(77\) 8.21381i 0.936050i
\(78\) 0 0
\(79\) 4.64448 3.89718i 0.522545 0.438467i −0.342973 0.939345i \(-0.611434\pi\)
0.865518 + 0.500878i \(0.166989\pi\)
\(80\) −0.0554826 8.15018i −0.00620315 0.911218i
\(81\) 0 0
\(82\) −0.392614 + 0.467899i −0.0433569 + 0.0516708i
\(83\) 10.2643 + 5.92611i 1.12666 + 0.650476i 0.943092 0.332532i \(-0.107903\pi\)
0.183565 + 0.983008i \(0.441236\pi\)
\(84\) 0 0
\(85\) 2.71811 4.78280i 0.294820 0.518767i
\(86\) 0.189714 1.07592i 0.0204574 0.116019i
\(87\) 0 0
\(88\) −3.53161 2.03898i −0.376471 0.217356i
\(89\) −1.71051 1.43529i −0.181314 0.152140i 0.547614 0.836731i \(-0.315536\pi\)
−0.728927 + 0.684591i \(0.759981\pi\)
\(90\) 0 0
\(91\) −2.31522 + 0.842670i −0.242701 + 0.0883358i
\(92\) 6.40684 + 7.63537i 0.667959 + 0.796043i
\(93\) 0 0
\(94\) 1.65487 0.170687
\(95\) −9.29702 2.92667i −0.953854 0.300270i
\(96\) 0 0
\(97\) −8.47901 + 1.49508i −0.860913 + 0.151802i −0.586638 0.809849i \(-0.699549\pi\)
−0.274275 + 0.961651i \(0.588438\pi\)
\(98\) −0.508425 0.605917i −0.0513587 0.0612069i
\(99\) 0 0
\(100\) 4.96451 + 8.33463i 0.496451 + 0.833463i
\(101\) 10.3041 + 8.64614i 1.02529 + 0.860323i 0.990283 0.139064i \(-0.0444094\pi\)
0.0350095 + 0.999387i \(0.488854\pi\)
\(102\) 0 0
\(103\) 3.49510 2.01789i 0.344382 0.198829i −0.317826 0.948149i \(-0.602953\pi\)
0.662208 + 0.749320i \(0.269619\pi\)
\(104\) −0.212409 + 1.20463i −0.0208285 + 0.118124i
\(105\) 0 0
\(106\) 0.0843204 + 0.146047i 0.00818992 + 0.0141854i
\(107\) −14.6869 8.47947i −1.41983 0.819741i −0.423550 0.905873i \(-0.639216\pi\)
−0.996284 + 0.0861313i \(0.972550\pi\)
\(108\) 0 0
\(109\) 6.42343 + 2.33794i 0.615253 + 0.223934i 0.630800 0.775945i \(-0.282727\pi\)
−0.0155471 + 0.999879i \(0.504949\pi\)
\(110\) 2.31417 0.0157538i 0.220648 0.00150207i
\(111\) 0 0
\(112\) −6.96476 + 1.22808i −0.658108 + 0.116042i
\(113\) 5.92416i 0.557298i −0.960393 0.278649i \(-0.910113\pi\)
0.960393 0.278649i \(-0.0898867\pi\)
\(114\) 0 0
\(115\) −10.8208 3.85523i −1.00904 0.359502i
\(116\) 2.91138 + 16.5113i 0.270315 + 1.53303i
\(117\) 0 0
\(118\) 0.434249 + 1.19309i 0.0399758 + 0.109833i
\(119\) −4.48561 1.63263i −0.411195 0.149663i
\(120\) 0 0
\(121\) −3.46054 + 5.99383i −0.314594 + 0.544893i
\(122\) −0.593422 + 0.342612i −0.0537259 + 0.0310186i
\(123\) 0 0
\(124\) 1.71856 9.74645i 0.154331 0.875257i
\(125\) −9.79460 5.39128i −0.876055 0.482211i
\(126\) 0 0
\(127\) −12.3288 + 14.6929i −1.09400 + 1.30378i −0.144680 + 0.989479i \(0.546215\pi\)
−0.949323 + 0.314303i \(0.898229\pi\)
\(128\) −2.47938 + 6.81203i −0.219148 + 0.602104i
\(129\) 0 0
\(130\) −0.241856 0.650677i −0.0212122 0.0570681i
\(131\) 0.0534819 + 0.303311i 0.00467273 + 0.0265004i 0.987055 0.160382i \(-0.0512727\pi\)
−0.982382 + 0.186883i \(0.940162\pi\)
\(132\) 0 0
\(133\) −1.15714 + 8.37791i −0.100337 + 0.726457i
\(134\) 1.27428 0.110081
\(135\) 0 0
\(136\) −1.81546 + 1.52335i −0.155674 + 0.130626i
\(137\) 4.95907 + 13.6249i 0.423682 + 1.16406i 0.949584 + 0.313512i \(0.101506\pi\)
−0.525902 + 0.850545i \(0.676272\pi\)
\(138\) 0 0
\(139\) −12.1014 10.1543i −1.02643 0.861278i −0.0360091 0.999351i \(-0.511465\pi\)
−0.990422 + 0.138074i \(0.955909\pi\)
\(140\) 6.41146 5.45466i 0.541867 0.461003i
\(141\) 0 0
\(142\) 0.190664 + 0.0336192i 0.0160002 + 0.00282126i
\(143\) 5.29391 + 0.933460i 0.442699 + 0.0780598i
\(144\) 0 0
\(145\) −12.5207 14.7169i −1.03978 1.22217i
\(146\) 0.265144 + 0.222483i 0.0219435 + 0.0184128i
\(147\) 0 0
\(148\) 7.31983 + 20.1111i 0.601686 + 1.65312i
\(149\) −9.54872 + 8.01233i −0.782262 + 0.656396i −0.943817 0.330468i \(-0.892793\pi\)
0.161555 + 0.986864i \(0.448349\pi\)
\(150\) 0 0
\(151\) 13.8400 1.12629 0.563143 0.826360i \(-0.309592\pi\)
0.563143 + 0.826360i \(0.309592\pi\)
\(152\) 3.31492 + 2.57724i 0.268876 + 0.209042i
\(153\) 0 0
\(154\) −0.348701 1.97758i −0.0280991 0.159358i
\(155\) 3.97389 + 10.6912i 0.319191 + 0.858735i
\(156\) 0 0
\(157\) 6.22373 17.0996i 0.496708 1.36469i −0.397731 0.917502i \(-0.630202\pi\)
0.894438 0.447191i \(-0.147576\pi\)
\(158\) 0.952772 1.13547i 0.0757985 0.0903331i
\(159\) 0 0
\(160\) −1.13630 6.19726i −0.0898322 0.489937i
\(161\) −1.73084 + 9.81605i −0.136409 + 0.773613i
\(162\) 0 0
\(163\) −13.2794 + 7.66687i −1.04012 + 0.600516i −0.919868 0.392227i \(-0.871705\pi\)
−0.120256 + 0.992743i \(0.538371\pi\)
\(164\) 2.42372 4.19801i 0.189261 0.327809i
\(165\) 0 0
\(166\) 2.72285 + 0.991038i 0.211334 + 0.0769195i
\(167\) 2.12631 + 5.84198i 0.164539 + 0.452066i 0.994372 0.105945i \(-0.0337868\pi\)
−0.829833 + 0.558011i \(0.811565\pi\)
\(168\) 0 0
\(169\) 1.97743 + 11.2145i 0.152110 + 0.862657i
\(170\) 0.451376 1.26691i 0.0346189 0.0971678i
\(171\) 0 0
\(172\) 8.67048i 0.661118i
\(173\) 2.72401 0.480317i 0.207103 0.0365178i −0.0691341 0.997607i \(-0.522024\pi\)
0.276237 + 0.961090i \(0.410913\pi\)
\(174\) 0 0
\(175\) −3.19364 + 9.16062i −0.241416 + 0.692478i
\(176\) 14.4997 + 5.27747i 1.09296 + 0.397805i
\(177\) 0 0
\(178\) −0.472760 0.272948i −0.0354349 0.0204583i
\(179\) 5.68916 + 9.85392i 0.425228 + 0.736516i 0.996442 0.0842849i \(-0.0268606\pi\)
−0.571214 + 0.820801i \(0.693527\pi\)
\(180\) 0 0
\(181\) 0.619323 3.51236i 0.0460339 0.261071i −0.953101 0.302652i \(-0.902128\pi\)
0.999135 + 0.0415803i \(0.0132392\pi\)
\(182\) −0.521645 + 0.301172i −0.0386669 + 0.0223243i
\(183\) 0 0
\(184\) 3.79085 + 3.18090i 0.279466 + 0.234499i
\(185\) −19.0020 15.7254i −1.39705 1.15615i
\(186\) 0 0
\(187\) 6.69456 + 7.97827i 0.489555 + 0.583429i
\(188\) −12.9339 + 2.28060i −0.943303 + 0.166330i
\(189\) 0 0
\(190\) −2.36263 0.309947i −0.171403 0.0224859i
\(191\) 8.67323 0.627573 0.313786 0.949494i \(-0.398402\pi\)
0.313786 + 0.949494i \(0.398402\pi\)
\(192\) 0 0
\(193\) −0.271327 0.323355i −0.0195306 0.0232756i 0.756191 0.654351i \(-0.227058\pi\)
−0.775721 + 0.631076i \(0.782614\pi\)
\(194\) −1.97796 + 0.719919i −0.142009 + 0.0516872i
\(195\) 0 0
\(196\) 4.80871 + 4.03498i 0.343479 + 0.288213i
\(197\) −13.1995 7.62075i −0.940427 0.542956i −0.0503329 0.998732i \(-0.516028\pi\)
−0.890094 + 0.455777i \(0.849362\pi\)
\(198\) 0 0
\(199\) −2.24465 + 12.7301i −0.159119 + 0.902410i 0.795803 + 0.605555i \(0.207049\pi\)
−0.954923 + 0.296855i \(0.904062\pi\)
\(200\) 3.14592 + 3.64715i 0.222450 + 0.257892i
\(201\) 0 0
\(202\) 2.84789 + 1.64423i 0.200377 + 0.115688i
\(203\) −10.7772 + 12.8438i −0.756410 + 0.901455i
\(204\) 0 0
\(205\) 0.0380298 + 5.58643i 0.00265612 + 0.390173i
\(206\) 0.755824 0.634212i 0.0526608 0.0441876i
\(207\) 0 0
\(208\) 4.62845i 0.320926i
\(209\) 11.3260 14.5678i 0.783436 1.00768i
\(210\) 0 0
\(211\) −0.772073 4.37864i −0.0531517 0.301438i 0.946630 0.322322i \(-0.104463\pi\)
−0.999782 + 0.0208833i \(0.993352\pi\)
\(212\) −0.860290 1.02525i −0.0590850 0.0704148i
\(213\) 0 0
\(214\) −3.89604 1.41804i −0.266328 0.0969353i
\(215\) −5.05505 8.61956i −0.344752 0.587849i
\(216\) 0 0
\(217\) 8.57106 4.94851i 0.581842 0.335926i
\(218\) 1.64578 + 0.290195i 0.111466 + 0.0196545i
\(219\) 0 0
\(220\) −18.0651 + 3.31232i −1.21795 + 0.223316i
\(221\) 1.56202 2.70550i 0.105073 0.181991i
\(222\) 0 0
\(223\) 3.14622 8.64417i 0.210687 0.578856i −0.788667 0.614821i \(-0.789228\pi\)
0.999353 + 0.0359647i \(0.0114504\pi\)
\(224\) −5.13740 + 1.86986i −0.343257 + 0.124935i
\(225\) 0 0
\(226\) −0.251499 1.42632i −0.0167294 0.0948774i
\(227\) 0.600308i 0.0398438i 0.999802 + 0.0199219i \(0.00634176\pi\)
−0.999802 + 0.0199219i \(0.993658\pi\)
\(228\) 0 0
\(229\) 7.11499 0.470172 0.235086 0.971975i \(-0.424463\pi\)
0.235086 + 0.971975i \(0.424463\pi\)
\(230\) −2.76891 0.468821i −0.182577 0.0309132i
\(231\) 0 0
\(232\) 2.84700 + 7.82207i 0.186915 + 0.513544i
\(233\) 6.89726 18.9501i 0.451854 1.24146i −0.479563 0.877507i \(-0.659205\pi\)
0.931418 0.363952i \(-0.118573\pi\)
\(234\) 0 0
\(235\) 11.5283 9.80792i 0.752025 0.639798i
\(236\) −5.03816 8.72635i −0.327956 0.568037i
\(237\) 0 0
\(238\) −1.14928 0.202649i −0.0744967 0.0131358i
\(239\) 5.81710 + 10.0755i 0.376277 + 0.651731i 0.990517 0.137388i \(-0.0438707\pi\)
−0.614240 + 0.789119i \(0.710537\pi\)
\(240\) 0 0
\(241\) 19.5572 + 16.4104i 1.25979 + 1.05709i 0.995704 + 0.0925884i \(0.0295141\pi\)
0.264084 + 0.964500i \(0.414930\pi\)
\(242\) −0.578714 + 1.59000i −0.0372011 + 0.102209i
\(243\) 0 0
\(244\) 4.16583 3.49555i 0.266690 0.223779i
\(245\) −7.13293 1.20772i −0.455706 0.0771585i
\(246\) 0 0
\(247\) −5.26818 1.69791i −0.335206 0.108035i
\(248\) 4.91362i 0.312015i
\(249\) 0 0
\(250\) −2.58705 0.882211i −0.163620 0.0557959i
\(251\) 14.4509 5.25969i 0.912131 0.331988i 0.157027 0.987594i \(-0.449809\pi\)
0.755103 + 0.655606i \(0.227587\pi\)
\(252\) 0 0
\(253\) 13.9789 16.6594i 0.878845 1.04737i
\(254\) −2.34456 + 4.06090i −0.147111 + 0.254803i
\(255\) 0 0
\(256\) 1.98477 11.2562i 0.124048 0.703512i
\(257\) −15.8096 2.78765i −0.986173 0.173889i −0.342772 0.939419i \(-0.611366\pi\)
−0.643401 + 0.765530i \(0.722477\pi\)
\(258\) 0 0
\(259\) −10.7011 + 18.5348i −0.664934 + 1.15170i
\(260\) 2.78697 + 4.75217i 0.172841 + 0.294717i
\(261\) 0 0
\(262\) 0.0257529 + 0.0707556i 0.00159102 + 0.00437129i
\(263\) 9.15308 + 10.9082i 0.564403 + 0.672629i 0.970472 0.241213i \(-0.0775453\pi\)
−0.406069 + 0.913842i \(0.633101\pi\)
\(264\) 0 0
\(265\) 1.45298 + 0.517668i 0.0892559 + 0.0318001i
\(266\) 0.0770701 + 2.06622i 0.00472547 + 0.126688i
\(267\) 0 0
\(268\) −9.95937 + 1.75611i −0.608365 + 0.107271i
\(269\) 12.4416 10.4398i 0.758579 0.636523i −0.179178 0.983817i \(-0.557344\pi\)
0.937756 + 0.347294i \(0.112899\pi\)
\(270\) 0 0
\(271\) 5.56796 + 2.02657i 0.338230 + 0.123106i 0.505551 0.862797i \(-0.331289\pi\)
−0.167321 + 0.985902i \(0.553512\pi\)
\(272\) 5.76412 6.86941i 0.349501 0.416519i
\(273\) 0 0
\(274\) 1.77238 + 3.06985i 0.107073 + 0.185457i
\(275\) 16.0279 13.8251i 0.966516 0.833688i
\(276\) 0 0
\(277\) −5.46407 + 3.15468i −0.328304 + 0.189546i −0.655088 0.755553i \(-0.727368\pi\)
0.326784 + 0.945099i \(0.394035\pi\)
\(278\) −3.34466 1.93104i −0.200600 0.115816i
\(279\) 0 0
\(280\) 2.66457 3.21977i 0.159239 0.192418i
\(281\) −2.51801 + 0.916481i −0.150212 + 0.0546727i −0.416032 0.909350i \(-0.636580\pi\)
0.265820 + 0.964023i \(0.414357\pi\)
\(282\) 0 0
\(283\) −30.5923 + 5.39425i −1.81853 + 0.320655i −0.975962 0.217942i \(-0.930066\pi\)
−0.842564 + 0.538597i \(0.818955\pi\)
\(284\) −1.53650 −0.0911745
\(285\) 0 0
\(286\) 1.31421 0.0777107
\(287\) 4.77390 0.841767i 0.281794 0.0496880i
\(288\) 0 0
\(289\) −10.2871 + 3.74421i −0.605126 + 0.220248i
\(290\) −3.63929 3.01175i −0.213706 0.176856i
\(291\) 0 0
\(292\) −2.37889 1.37345i −0.139214 0.0803752i
\(293\) −0.749675 + 0.432825i −0.0437965 + 0.0252859i −0.521738 0.853106i \(-0.674716\pi\)
0.477942 + 0.878391i \(0.341383\pi\)
\(294\) 0 0
\(295\) 10.0962 + 5.73776i 0.587823 + 0.334065i
\(296\) 5.31283 + 9.20209i 0.308802 + 0.534861i
\(297\) 0 0
\(298\) −1.95883 + 2.33445i −0.113472 + 0.135231i
\(299\) −6.12988 2.23110i −0.354500 0.129028i
\(300\) 0 0
\(301\) −6.64212 + 5.57340i −0.382845 + 0.321245i
\(302\) 3.33217 0.587551i 0.191745 0.0338098i
\(303\) 0 0
\(304\) −14.0460 7.42561i −0.805591 0.425888i
\(305\) −2.10340 + 5.90377i −0.120440 + 0.338049i
\(306\) 0 0
\(307\) 5.77995 + 6.88828i 0.329879 + 0.393135i 0.905335 0.424698i \(-0.139620\pi\)
−0.575456 + 0.817833i \(0.695175\pi\)
\(308\) 5.45067 + 14.9756i 0.310581 + 0.853313i
\(309\) 0 0
\(310\) 1.41064 + 2.40533i 0.0801189 + 0.136614i
\(311\) −5.72035 + 9.90793i −0.324371 + 0.561827i −0.981385 0.192051i \(-0.938486\pi\)
0.657014 + 0.753879i \(0.271819\pi\)
\(312\) 0 0
\(313\) 7.74572 + 1.36578i 0.437814 + 0.0771984i 0.388211 0.921571i \(-0.373093\pi\)
0.0496032 + 0.998769i \(0.484204\pi\)
\(314\) 0.772517 4.38116i 0.0435956 0.247243i
\(315\) 0 0
\(316\) −5.88175 + 10.1875i −0.330874 + 0.573091i
\(317\) −10.6230 + 12.6600i −0.596647 + 0.711056i −0.976869 0.213839i \(-0.931403\pi\)
0.380222 + 0.924895i \(0.375848\pi\)
\(318\) 0 0
\(319\) 34.3750 12.5115i 1.92463 0.700509i
\(320\) 5.14266 + 13.8355i 0.287483 + 0.773431i
\(321\) 0 0
\(322\) 2.43682i 0.135799i
\(323\) −5.70435 9.08079i −0.317399 0.505269i
\(324\) 0 0
\(325\) −5.54121 3.09941i −0.307371 0.171924i
\(326\) −2.87171 + 2.40965i −0.159049 + 0.133458i
\(327\) 0 0
\(328\) 0.823135 2.26155i 0.0454500 0.124873i
\(329\) −10.0610 8.44219i −0.554682 0.465433i
\(330\) 0 0
\(331\) −3.95723 6.85412i −0.217509 0.376736i 0.736537 0.676397i \(-0.236460\pi\)
−0.954046 + 0.299661i \(0.903126\pi\)
\(332\) −22.6467 3.99322i −1.24290 0.219157i
\(333\) 0 0
\(334\) 0.759946 + 1.31627i 0.0415824 + 0.0720228i
\(335\) 8.87703 7.55229i 0.485004 0.412626i
\(336\) 0 0
\(337\) 6.51071 17.8880i 0.354661 0.974423i −0.626191 0.779670i \(-0.715387\pi\)
0.980852 0.194754i \(-0.0623908\pi\)
\(338\) 0.952183 + 2.61610i 0.0517919 + 0.142297i
\(339\) 0 0
\(340\) −1.78185 + 10.5238i −0.0966346 + 0.570734i
\(341\) −21.5935 −1.16936
\(342\) 0 0
\(343\) 19.8594i 1.07230i
\(344\) 0.747516 + 4.23937i 0.0403034 + 0.228572i
\(345\) 0 0
\(346\) 0.635451 0.231285i 0.0341621 0.0124340i
\(347\) −1.86887 + 5.13467i −0.100326 + 0.275644i −0.979694 0.200500i \(-0.935743\pi\)
0.879368 + 0.476143i \(0.157966\pi\)
\(348\) 0 0
\(349\) −3.13218 + 5.42509i −0.167662 + 0.290398i −0.937597 0.347723i \(-0.886955\pi\)
0.769936 + 0.638121i \(0.220288\pi\)
\(350\) −0.380014 + 2.34112i −0.0203126 + 0.125138i
\(351\) 0 0
\(352\) 11.7470 + 2.07132i 0.626120 + 0.110402i
\(353\) 7.18280 4.14699i 0.382302 0.220722i −0.296517 0.955027i \(-0.595825\pi\)
0.678819 + 0.734305i \(0.262492\pi\)
\(354\) 0 0
\(355\) 1.52748 0.895808i 0.0810700 0.0475446i
\(356\) 4.07109 + 1.48176i 0.215767 + 0.0785329i
\(357\) 0 0
\(358\) 1.78807 + 2.13094i 0.0945024 + 0.112624i
\(359\) 2.27231 + 12.8869i 0.119928 + 0.680145i 0.984192 + 0.177106i \(0.0566735\pi\)
−0.864264 + 0.503039i \(0.832215\pi\)
\(360\) 0 0
\(361\) −13.6046 + 13.2633i −0.716030 + 0.698069i
\(362\) 0.871938i 0.0458281i
\(363\) 0 0
\(364\) 3.66196 3.07275i 0.191939 0.161056i
\(365\) 3.16567 0.0215504i 0.165699 0.00112800i
\(366\) 0 0
\(367\) 16.7730 19.9893i 0.875545 1.04343i −0.123151 0.992388i \(-0.539300\pi\)
0.998696 0.0510458i \(-0.0162555\pi\)
\(368\) −16.2161 9.36236i −0.845322 0.488047i
\(369\) 0 0
\(370\) −5.24256 2.97940i −0.272548 0.154891i
\(371\) 0.232411 1.31807i 0.0120662 0.0684307i
\(372\) 0 0
\(373\) −23.5532 13.5984i −1.21954 0.704100i −0.254718 0.967015i \(-0.581983\pi\)
−0.964819 + 0.262915i \(0.915316\pi\)
\(374\) 1.95051 + 1.63667i 0.100858 + 0.0846301i
\(375\) 0 0
\(376\) −6.12733 + 2.23017i −0.315993 + 0.115012i
\(377\) −7.05320 8.40568i −0.363258 0.432915i
\(378\) 0 0
\(379\) −13.6999 −0.703714 −0.351857 0.936054i \(-0.614450\pi\)
−0.351857 + 0.936054i \(0.614450\pi\)
\(380\) 18.8927 0.833522i 0.969173 0.0427588i
\(381\) 0 0
\(382\) 2.08819 0.368205i 0.106841 0.0188390i
\(383\) −6.58953 7.85310i −0.336709 0.401275i 0.570948 0.820986i \(-0.306576\pi\)
−0.907658 + 0.419711i \(0.862131\pi\)
\(384\) 0 0
\(385\) −14.1497 11.7098i −0.721135 0.596786i
\(386\) −0.0790530 0.0663333i −0.00402369 0.00337628i
\(387\) 0 0
\(388\) 14.4670 8.35251i 0.734449 0.424035i
\(389\) −0.878089 + 4.97989i −0.0445209 + 0.252490i −0.998943 0.0459703i \(-0.985362\pi\)
0.954422 + 0.298461i \(0.0964732\pi\)
\(390\) 0 0
\(391\) −6.31925 10.9453i −0.319578 0.553526i
\(392\) 2.69905 + 1.55830i 0.136323 + 0.0787060i
\(393\) 0 0
\(394\) −3.50148 1.27444i −0.176402 0.0642051i
\(395\) −0.0922885 13.5568i −0.00464354 0.682118i
\(396\) 0 0
\(397\) 23.5131 4.14599i 1.18009 0.208081i 0.451014 0.892517i \(-0.351062\pi\)
0.729073 + 0.684435i \(0.239951\pi\)
\(398\) 3.16022i 0.158408i
\(399\) 0 0
\(400\) −14.1192 11.5235i −0.705960 0.576176i
\(401\) 4.30049 + 24.3893i 0.214756 + 1.21794i 0.881329 + 0.472503i \(0.156649\pi\)
−0.666573 + 0.745440i \(0.732240\pi\)
\(402\) 0 0
\(403\) 2.21532 + 6.08655i 0.110353 + 0.303192i
\(404\) −24.5241 8.92606i −1.22012 0.444088i
\(405\) 0 0
\(406\) −2.04949 + 3.54983i −0.101715 + 0.176175i
\(407\) 40.4398 23.3479i 2.00452 1.15731i
\(408\) 0 0
\(409\) 1.71911 9.74958i 0.0850047 0.482086i −0.912351 0.409409i \(-0.865735\pi\)
0.997356 0.0726764i \(-0.0231540\pi\)
\(410\) 0.246317 + 1.34339i 0.0121647 + 0.0663454i
\(411\) 0 0
\(412\) −5.03326 + 5.99841i −0.247971 + 0.295520i
\(413\) 3.44637 9.46884i 0.169585 0.465931i
\(414\) 0 0
\(415\) 24.8418 9.23367i 1.21944 0.453263i
\(416\) −0.621311 3.52363i −0.0304623 0.172760i
\(417\) 0 0
\(418\) 2.10843 3.98822i 0.103127 0.195070i
\(419\) 4.00810 0.195808 0.0979042 0.995196i \(-0.468786\pi\)
0.0979042 + 0.995196i \(0.468786\pi\)
\(420\) 0 0
\(421\) 15.5339 13.0345i 0.757077 0.635263i −0.180287 0.983614i \(-0.557703\pi\)
0.937364 + 0.348351i \(0.113258\pi\)
\(422\) −0.371774 1.02144i −0.0180977 0.0497229i
\(423\) 0 0
\(424\) −0.509024 0.427122i −0.0247204 0.0207429i
\(425\) −4.36419 11.5009i −0.211695 0.557874i
\(426\) 0 0
\(427\) 5.35560 + 0.944337i 0.259176 + 0.0456997i
\(428\) 32.4044 + 5.71377i 1.56632 + 0.276185i
\(429\) 0 0
\(430\) −1.58300 1.86067i −0.0763389 0.0897295i
\(431\) −10.3250 8.66371i −0.497338 0.417316i 0.359309 0.933219i \(-0.383012\pi\)
−0.856648 + 0.515902i \(0.827457\pi\)
\(432\) 0 0
\(433\) −11.7578 32.3043i −0.565045 1.55245i −0.812144 0.583458i \(-0.801699\pi\)
0.247099 0.968990i \(-0.420523\pi\)
\(434\) 1.85352 1.55529i 0.0889717 0.0746561i
\(435\) 0 0
\(436\) −13.2628 −0.635172
\(437\) −16.6051 + 15.0229i −0.794330 + 0.718643i
\(438\) 0 0
\(439\) −4.06648 23.0621i −0.194082 1.10070i −0.913720 0.406345i \(-0.866803\pi\)
0.719637 0.694350i \(-0.244308\pi\)
\(440\) −8.54723 + 3.17700i −0.407473 + 0.151457i
\(441\) 0 0
\(442\) 0.261220 0.717696i 0.0124250 0.0341373i
\(443\) −1.54197 + 1.83765i −0.0732612 + 0.0873093i −0.801430 0.598088i \(-0.795927\pi\)
0.728169 + 0.685398i \(0.240372\pi\)
\(444\) 0 0
\(445\) −4.91107 + 0.900468i −0.232807 + 0.0426863i
\(446\) 0.390523 2.21476i 0.0184918 0.104872i
\(447\) 0 0
\(448\) 11.0919 6.40391i 0.524043 0.302557i
\(449\) −19.1010 + 33.0838i −0.901430 + 1.56132i −0.0757922 + 0.997124i \(0.524149\pi\)
−0.825638 + 0.564200i \(0.809185\pi\)
\(450\) 0 0
\(451\) −9.93864 3.61737i −0.467992 0.170335i
\(452\) 3.93126 + 10.8011i 0.184911 + 0.508039i
\(453\) 0 0
\(454\) 0.0254849 + 0.144532i 0.00119606 + 0.00678322i
\(455\) −1.84898 + 5.18969i −0.0866816 + 0.243296i
\(456\) 0 0
\(457\) 1.87605i 0.0877581i −0.999037 0.0438790i \(-0.986028\pi\)
0.999037 0.0438790i \(-0.0139716\pi\)
\(458\) 1.71303 0.302053i 0.0800445 0.0141140i
\(459\) 0 0
\(460\) 22.2870 0.151719i 1.03914 0.00707395i
\(461\) 15.8060 + 5.75290i 0.736157 + 0.267939i 0.682769 0.730634i \(-0.260776\pi\)
0.0533885 + 0.998574i \(0.482998\pi\)
\(462\) 0 0
\(463\) 21.0999 + 12.1821i 0.980598 + 0.566148i 0.902450 0.430794i \(-0.141766\pi\)
0.0781471 + 0.996942i \(0.475100\pi\)
\(464\) −15.7485 27.2771i −0.731104 1.26631i
\(465\) 0 0
\(466\) 0.856118 4.85529i 0.0396589 0.224917i
\(467\) 11.8222 6.82553i 0.547065 0.315848i −0.200873 0.979617i \(-0.564378\pi\)
0.747937 + 0.663770i \(0.231044\pi\)
\(468\) 0 0
\(469\) −7.74717 6.50065i −0.357731 0.300172i
\(470\) 2.35922 2.85080i 0.108823 0.131497i
\(471\) 0 0
\(472\) −3.21570 3.83233i −0.148015 0.176397i
\(473\) 18.6305 3.28505i 0.856629 0.151047i
\(474\) 0 0
\(475\) −18.2957 + 11.8434i −0.839466 + 0.543412i
\(476\) 9.26166 0.424507
\(477\) 0 0
\(478\) 1.82828 + 2.17886i 0.0836236 + 0.0996587i
\(479\) 20.4294 7.43570i 0.933444 0.339746i 0.169870 0.985466i \(-0.445665\pi\)
0.763574 + 0.645720i \(0.223443\pi\)
\(480\) 0 0
\(481\) −10.7298 9.00341i −0.489239 0.410520i
\(482\) 5.40532 + 3.12076i 0.246206 + 0.142147i
\(483\) 0 0
\(484\) 2.33183 13.2245i 0.105992 0.601112i
\(485\) −9.51234 + 16.7380i −0.431933 + 0.760032i
\(486\) 0 0
\(487\) −25.3273 14.6227i −1.14769 0.662618i −0.199366 0.979925i \(-0.563888\pi\)
−0.948323 + 0.317307i \(0.897222\pi\)
\(488\) 1.73549 2.06828i 0.0785619 0.0936264i
\(489\) 0 0
\(490\) −1.76862 + 0.0120399i −0.0798981 + 0.000543909i
\(491\) 14.0612 11.7987i 0.634572 0.532469i −0.267774 0.963482i \(-0.586288\pi\)
0.902346 + 0.431012i \(0.141843\pi\)
\(492\) 0 0
\(493\) 21.2593i 0.957469i
\(494\) −1.34046 0.185143i −0.0603104 0.00832997i
\(495\) 0 0
\(496\) 3.22853 + 18.3099i 0.144965 + 0.822138i
\(497\) −0.987664 1.17705i −0.0443028 0.0527980i
\(498\) 0 0
\(499\) 9.78774 + 3.56245i 0.438159 + 0.159477i 0.551675 0.834059i \(-0.313989\pi\)
−0.113516 + 0.993536i \(0.536211\pi\)
\(500\) 21.4354 + 3.32982i 0.958618 + 0.148914i
\(501\) 0 0
\(502\) 3.25595 1.87982i 0.145320 0.0839006i
\(503\) −4.29111 0.756638i −0.191331 0.0337368i 0.0771614 0.997019i \(-0.475414\pi\)
−0.268492 + 0.963282i \(0.586525\pi\)
\(504\) 0 0
\(505\) 29.5842 5.42439i 1.31648 0.241382i
\(506\) 2.65836 4.60441i 0.118178 0.204691i
\(507\) 0 0
\(508\) 12.7279 34.9697i 0.564711 1.55153i
\(509\) 35.9534 13.0860i 1.59361 0.580026i 0.615502 0.788135i \(-0.288953\pi\)
0.978106 + 0.208109i \(0.0667310\pi\)
\(510\) 0 0
\(511\) −0.477005 2.70523i −0.0211015 0.119672i
\(512\) 17.2928i 0.764239i
\(513\) 0 0
\(514\) −3.92470 −0.173111
\(515\) 1.50652 8.89766i 0.0663851 0.392078i
\(516\) 0 0
\(517\) 9.80074 + 26.9273i 0.431036 + 1.18426i
\(518\) −1.78957 + 4.91680i −0.0786292 + 0.216032i
\(519\) 0 0
\(520\) 1.77237 + 2.08327i 0.0777237 + 0.0913573i
\(521\) −1.24406 2.15478i −0.0545033 0.0944025i 0.837486 0.546458i \(-0.184024\pi\)
−0.891990 + 0.452056i \(0.850691\pi\)
\(522\) 0 0
\(523\) 19.1578 + 3.37803i 0.837712 + 0.147711i 0.576015 0.817439i \(-0.304607\pi\)
0.261696 + 0.965150i \(0.415718\pi\)
\(524\) −0.298786 0.517512i −0.0130525 0.0226076i
\(525\) 0 0
\(526\) 2.66681 + 2.23772i 0.116278 + 0.0975692i
\(527\) −4.29206 + 11.7923i −0.186965 + 0.513683i
\(528\) 0 0
\(529\) −2.59720 + 2.17931i −0.112922 + 0.0947525i
\(530\) 0.371801 + 0.0629519i 0.0161500 + 0.00273445i
\(531\) 0 0
\(532\) −3.44984 16.0427i −0.149569 0.695538i
\(533\) 3.17251i 0.137417i
\(534\) 0 0
\(535\) −35.5453 + 13.2121i −1.53676 + 0.571211i
\(536\) −4.71816 + 1.71727i −0.203794 + 0.0741748i
\(537\) 0 0
\(538\) 2.55228 3.04169i 0.110037 0.131137i
\(539\) 6.84814 11.8613i 0.294970 0.510904i
\(540\) 0 0
\(541\) 2.51035 14.2369i 0.107928 0.612093i −0.882082 0.471097i \(-0.843858\pi\)
0.990010 0.140996i \(-0.0450305\pi\)
\(542\) 1.42659 + 0.251547i 0.0612775 + 0.0108049i
\(543\) 0 0
\(544\) 3.46608 6.00342i 0.148607 0.257394i
\(545\) 13.1849 7.73245i 0.564779 0.331222i
\(546\) 0 0
\(547\) 10.7381 + 29.5027i 0.459128 + 1.26144i 0.926136 + 0.377191i \(0.123110\pi\)
−0.467007 + 0.884253i \(0.654668\pi\)
\(548\) −18.0830 21.5504i −0.772466 0.920589i
\(549\) 0 0
\(550\) 3.27200 4.00902i 0.139518 0.170945i
\(551\) −36.8244 + 7.91878i −1.56877 + 0.337351i
\(552\) 0 0
\(553\) −11.5850 + 2.04275i −0.492646 + 0.0868667i
\(554\) −1.18162 + 0.991497i −0.0502022 + 0.0421247i
\(555\) 0 0
\(556\) 28.8020 + 10.4831i 1.22148 + 0.444581i
\(557\) 19.5718 23.3248i 0.829286 0.988304i −0.170710 0.985321i \(-0.554606\pi\)
0.999996 0.00298303i \(-0.000949529\pi\)
\(558\) 0 0
\(559\) −2.83729 4.91433i −0.120005 0.207854i
\(560\) −7.81356 + 13.7488i −0.330183 + 0.580992i
\(561\) 0 0
\(562\) −0.567337 + 0.327552i −0.0239317 + 0.0138169i
\(563\) −23.1239 13.3506i −0.974558 0.562661i −0.0739355 0.997263i \(-0.523556\pi\)
−0.900623 + 0.434602i \(0.856889\pi\)
\(564\) 0 0
\(565\) −10.2054 8.44562i −0.429344 0.355310i
\(566\) −7.13650 + 2.59747i −0.299970 + 0.109180i
\(567\) 0 0
\(568\) −0.751261 + 0.132468i −0.0315222 + 0.00555822i
\(569\) −25.6513 −1.07536 −0.537679 0.843150i \(-0.680699\pi\)
−0.537679 + 0.843150i \(0.680699\pi\)
\(570\) 0 0
\(571\) 2.93559 0.122851 0.0614253 0.998112i \(-0.480435\pi\)
0.0614253 + 0.998112i \(0.480435\pi\)
\(572\) −10.2714 + 1.81113i −0.429470 + 0.0757271i
\(573\) 0 0
\(574\) 1.11364 0.405333i 0.0464826 0.0169183i
\(575\) −22.0676 + 13.1446i −0.920284 + 0.548166i
\(576\) 0 0
\(577\) −15.3921 8.88661i −0.640780 0.369954i 0.144135 0.989558i \(-0.453960\pi\)
−0.784915 + 0.619604i \(0.787293\pi\)
\(578\) −2.31781 + 1.33819i −0.0964083 + 0.0556613i
\(579\) 0 0
\(580\) 32.5940 + 18.5235i 1.35339 + 0.769146i
\(581\) −11.4983 19.9156i −0.477029 0.826238i
\(582\) 0 0
\(583\) −1.87704 + 2.23697i −0.0777391 + 0.0926458i
\(584\) −1.28155 0.466447i −0.0530310 0.0193017i
\(585\) 0 0
\(586\) −0.162119 + 0.136034i −0.00669709 + 0.00561952i
\(587\) −22.7723 + 4.01538i −0.939915 + 0.165732i −0.622558 0.782574i \(-0.713906\pi\)
−0.317357 + 0.948306i \(0.602795\pi\)
\(588\) 0 0
\(589\) 22.0250 + 3.04205i 0.907522 + 0.125346i
\(590\) 2.67438 + 0.952826i 0.110102 + 0.0392272i
\(591\) 0 0
\(592\) −25.8438 30.7994i −1.06217 1.26585i
\(593\) 5.86817 + 16.1227i 0.240977 + 0.662078i 0.999940 + 0.0109447i \(0.00348389\pi\)
−0.758963 + 0.651133i \(0.774294\pi\)
\(594\) 0 0
\(595\) −9.20726 + 5.39972i −0.377461 + 0.221367i
\(596\) 12.0925 20.9448i 0.495327 0.857931i
\(597\) 0 0
\(598\) −1.57057 0.276933i −0.0642253 0.0113246i
\(599\) −2.32632 + 13.1932i −0.0950508 + 0.539060i 0.899681 + 0.436548i \(0.143799\pi\)
−0.994732 + 0.102512i \(0.967312\pi\)
\(600\) 0 0
\(601\) −4.13126 + 7.15554i −0.168517 + 0.291881i −0.937899 0.346909i \(-0.887231\pi\)
0.769381 + 0.638790i \(0.220565\pi\)
\(602\) −1.36257 + 1.62385i −0.0555342 + 0.0661830i
\(603\) 0 0
\(604\) −25.2334 + 9.18421i −1.02673 + 0.373700i
\(605\) 5.39198 + 14.5063i 0.219215 + 0.589765i
\(606\) 0 0
\(607\) 23.5191i 0.954612i 0.878737 + 0.477306i \(0.158387\pi\)
−0.878737 + 0.477306i \(0.841613\pi\)
\(608\) −11.6899 3.76761i −0.474090 0.152797i
\(609\) 0 0
\(610\) −0.255787 + 1.51071i −0.0103565 + 0.0611667i
\(611\) 6.58450 5.52505i 0.266380 0.223520i
\(612\) 0 0
\(613\) −10.2029 + 28.0323i −0.412092 + 1.13221i 0.543984 + 0.839095i \(0.316915\pi\)
−0.956076 + 0.293118i \(0.905307\pi\)
\(614\) 1.68403 + 1.41307i 0.0679619 + 0.0570268i
\(615\) 0 0
\(616\) 3.95617 + 6.85228i 0.159399 + 0.276086i
\(617\) 11.4142 + 2.01262i 0.459516 + 0.0810251i 0.398614 0.917119i \(-0.369491\pi\)
0.0609020 + 0.998144i \(0.480602\pi\)
\(618\) 0 0
\(619\) 14.8349 + 25.6947i 0.596264 + 1.03276i 0.993367 + 0.114985i \(0.0366820\pi\)
−0.397104 + 0.917774i \(0.629985\pi\)
\(620\) −14.3399 16.8553i −0.575905 0.676924i
\(621\) 0 0
\(622\) −0.956627 + 2.62831i −0.0383573 + 0.105386i
\(623\) 1.48179 + 4.07118i 0.0593666 + 0.163108i
\(624\) 0 0
\(625\) −23.2508 + 9.18694i −0.930032 + 0.367478i
\(626\) 1.92287 0.0768532
\(627\) 0 0
\(628\) 35.3063i 1.40888i
\(629\) −4.71236 26.7251i −0.187894 1.06560i
\(630\) 0 0
\(631\) 23.0191 8.37827i 0.916376 0.333534i 0.159580 0.987185i \(-0.448986\pi\)
0.756796 + 0.653651i \(0.226764\pi\)
\(632\) −1.99754 + 5.48819i −0.0794578 + 0.218308i
\(633\) 0 0
\(634\) −2.02017 + 3.49904i −0.0802313 + 0.138965i
\(635\) 7.73480 + 42.1849i 0.306946 + 1.67406i
\(636\) 0 0
\(637\) −4.04591 0.713402i −0.160305 0.0282660i
\(638\) 7.74509 4.47163i 0.306631 0.177034i
\(639\) 0 0
\(640\) 8.20024 + 13.9825i 0.324143 + 0.552709i
\(641\) 11.6336 + 4.23428i 0.459499 + 0.167244i 0.561390 0.827552i \(-0.310267\pi\)
−0.101890 + 0.994796i \(0.532489\pi\)
\(642\) 0 0
\(643\) 29.5099 + 35.1685i 1.16376 + 1.38691i 0.907369 + 0.420336i \(0.138088\pi\)
0.256387 + 0.966574i \(0.417468\pi\)
\(644\) −3.35822 19.0454i −0.132332 0.750494i
\(645\) 0 0
\(646\) −1.75891 1.94415i −0.0692032 0.0764916i
\(647\) 33.6773i 1.32399i 0.749508 + 0.661996i \(0.230290\pi\)
−0.749508 + 0.661996i \(0.769710\pi\)
\(648\) 0 0
\(649\) −16.8416 + 14.1318i −0.661092 + 0.554722i
\(650\) −1.46570 0.510982i −0.0574894 0.0200424i
\(651\) 0 0
\(652\) 19.1236 22.7906i 0.748937 0.892549i
\(653\) 17.0057 + 9.81827i 0.665486 + 0.384219i 0.794364 0.607442i \(-0.207804\pi\)
−0.128878 + 0.991660i \(0.541138\pi\)
\(654\) 0 0
\(655\) 0.598750 + 0.340275i 0.0233951 + 0.0132956i
\(656\) −1.58133 + 8.96816i −0.0617405 + 0.350148i
\(657\) 0 0
\(658\) −2.78072 1.60545i −0.108404 0.0625869i
\(659\) 15.9102 + 13.3503i 0.619775 + 0.520053i 0.897733 0.440540i \(-0.145213\pi\)
−0.277958 + 0.960593i \(0.589658\pi\)
\(660\) 0 0
\(661\) −12.4567 + 4.53386i −0.484508 + 0.176347i −0.572713 0.819756i \(-0.694109\pi\)
0.0882049 + 0.996102i \(0.471887\pi\)
\(662\) −1.24373 1.48222i −0.0483390 0.0576082i
\(663\) 0 0
\(664\) −11.4172 −0.443074
\(665\) 12.7827 + 13.9371i 0.495694 + 0.540459i
\(666\) 0 0
\(667\) −43.7170 + 7.70848i −1.69273 + 0.298473i
\(668\) −7.75345 9.24020i −0.299990 0.357514i
\(669\) 0 0
\(670\) 1.81665 2.19517i 0.0701831 0.0848068i
\(671\) −9.08930 7.62682i −0.350888 0.294430i
\(672\) 0 0
\(673\) 11.1350 6.42879i 0.429223 0.247812i −0.269793 0.962918i \(-0.586955\pi\)
0.699015 + 0.715107i \(0.253622\pi\)
\(674\) 0.808138 4.58318i 0.0311283 0.176537i
\(675\) 0 0
\(676\) −11.0472 19.1344i −0.424894 0.735937i
\(677\) 22.1332 + 12.7786i 0.850649 + 0.491122i 0.860870 0.508825i \(-0.169920\pi\)
−0.0102207 + 0.999948i \(0.503253\pi\)
\(678\) 0 0
\(679\) 15.6979 + 5.71357i 0.602431 + 0.219267i
\(680\) 0.0360743 + 5.29917i 0.00138338 + 0.203214i
\(681\) 0 0
\(682\) −5.19893 + 0.916711i −0.199077 + 0.0351027i
\(683\) 22.8692i 0.875064i 0.899203 + 0.437532i \(0.144147\pi\)
−0.899203 + 0.437532i \(0.855853\pi\)
\(684\) 0 0
\(685\) 30.5411 + 10.8812i 1.16691 + 0.415748i
\(686\) 0.843090 + 4.78140i 0.0321893 + 0.182555i
\(687\) 0 0
\(688\) −5.57101 15.3062i −0.212393 0.583545i
\(689\) 0.823102 + 0.299585i 0.0313577 + 0.0114133i
\(690\) 0 0
\(691\) 16.1574 27.9854i 0.614657 1.06462i −0.375788 0.926706i \(-0.622628\pi\)
0.990445 0.137911i \(-0.0440388\pi\)
\(692\) −4.64774 + 2.68337i −0.176681 + 0.102007i
\(693\) 0 0
\(694\) −0.231972 + 1.31558i −0.00880554 + 0.0499387i
\(695\) −34.7447 + 6.37059i −1.31794 + 0.241650i
\(696\) 0 0
\(697\) −3.95093 + 4.70854i −0.149652 + 0.178349i
\(698\) −0.523801 + 1.43913i −0.0198262 + 0.0544719i
\(699\) 0 0
\(700\) −0.256263 18.8211i −0.00968582 0.711372i
\(701\) −6.03353 34.2179i −0.227883 1.29239i −0.857096 0.515157i \(-0.827734\pi\)
0.629212 0.777233i \(-0.283378\pi\)
\(702\) 0 0
\(703\) −44.5369 + 18.1173i −1.67974 + 0.683307i
\(704\) −27.9444 −1.05319
\(705\) 0 0
\(706\) 1.55330 1.30337i 0.0584593 0.0490531i
\(707\) −8.92625 24.5247i −0.335706 0.922345i
\(708\) 0 0
\(709\) −6.13431 5.14730i −0.230379 0.193311i 0.520290 0.853990i \(-0.325824\pi\)
−0.750669 + 0.660679i \(0.770268\pi\)
\(710\) 0.329730 0.280524i 0.0123746 0.0105279i
\(711\) 0 0
\(712\) 2.11828 + 0.373510i 0.0793859 + 0.0139979i
\(713\) 25.8057 + 4.55025i 0.966432 + 0.170408i
\(714\) 0 0
\(715\) 9.15517 7.78892i 0.342384 0.291289i
\(716\) −16.9116 14.1905i −0.632018 0.530326i
\(717\) 0 0
\(718\) 1.09418 + 3.00622i 0.0408343 + 0.112191i
\(719\) 10.9307 9.17191i 0.407645 0.342055i −0.415795 0.909458i \(-0.636497\pi\)
0.823440 + 0.567404i \(0.192052\pi\)
\(720\) 0 0
\(721\) −7.83053 −0.291624
\(722\) −2.71241 + 3.77087i −0.100946 + 0.140337i
\(723\) 0 0
\(724\) 1.20163 + 6.81478i 0.0446582 + 0.253269i
\(725\) −43.2021 + 0.588227i −1.60449 + 0.0218462i
\(726\) 0 0
\(727\) −1.07271 + 2.94724i −0.0397846 + 0.109307i −0.957994 0.286788i \(-0.907413\pi\)
0.918210 + 0.396095i \(0.129635\pi\)
\(728\) 1.52558 1.81811i 0.0565416 0.0673836i
\(729\) 0 0
\(730\) 0.761261 0.139581i 0.0281755 0.00516611i
\(731\) 1.90912 10.8272i 0.0706113 0.400457i
\(732\) 0 0
\(733\) 10.7391 6.20021i 0.396657 0.229010i −0.288384 0.957515i \(-0.593118\pi\)
0.685041 + 0.728505i \(0.259784\pi\)
\(734\) 3.18972 5.52476i 0.117735 0.203922i
\(735\) 0 0
\(736\) −13.6020 4.95074i −0.501378 0.182487i
\(737\) 7.54676 + 20.7346i 0.277988 + 0.763767i
\(738\) 0 0
\(739\) 1.62242 + 9.20119i 0.0596816 + 0.338471i 0.999998 0.00182926i \(-0.000582271\pi\)
−0.940317 + 0.340301i \(0.889471\pi\)
\(740\) 45.0801 + 16.0611i 1.65718 + 0.590419i
\(741\) 0 0
\(742\) 0.327209i 0.0120122i
\(743\) −37.7365 + 6.65396i −1.38442 + 0.244110i −0.815725 0.578441i \(-0.803661\pi\)
−0.568692 + 0.822551i \(0.692550\pi\)
\(744\) 0 0
\(745\) 0.189739 + 27.8719i 0.00695149 + 1.02115i
\(746\) −6.24803 2.27410i −0.228757 0.0832606i
\(747\) 0 0
\(748\) −17.5000 10.1036i −0.639864 0.369426i
\(749\) 16.4525 + 28.4965i 0.601160 + 1.04124i
\(750\) 0 0
\(751\) −8.51519 + 48.2921i −0.310724 + 1.76220i 0.284533 + 0.958666i \(0.408162\pi\)
−0.595257 + 0.803536i \(0.702950\pi\)
\(752\) 21.3672 12.3364i 0.779183 0.449861i
\(753\) 0 0
\(754\) −2.05500 1.72435i −0.0748386 0.0627971i
\(755\) 19.7307 23.8418i 0.718072 0.867693i
\(756\) 0 0
\(757\) 23.6504 + 28.1855i 0.859590 + 1.02442i 0.999414 + 0.0342429i \(0.0109020\pi\)
−0.139824 + 0.990176i \(0.544654\pi\)
\(758\) −3.29842 + 0.581600i −0.119804 + 0.0211247i
\(759\) 0 0
\(760\) 9.16557 2.03635i 0.332470 0.0738663i
\(761\) 0.255560 0.00926406 0.00463203 0.999989i \(-0.498526\pi\)
0.00463203 + 0.999989i \(0.498526\pi\)
\(762\) 0 0
\(763\) −8.52533 10.1601i −0.308638 0.367820i
\(764\) −15.8132 + 5.75554i −0.572102 + 0.208228i
\(765\) 0 0
\(766\) −1.91990 1.61099i −0.0693690 0.0582075i
\(767\) 5.71114 + 3.29733i 0.206217 + 0.119060i
\(768\) 0 0
\(769\) 1.64209 9.31277i 0.0592154 0.335827i −0.940780 0.339019i \(-0.889905\pi\)
0.999995 + 0.00319194i \(0.00101603\pi\)
\(770\) −3.90384 2.21859i −0.140685 0.0799524i
\(771\) 0 0
\(772\) 0.709267 + 0.409495i 0.0255271 + 0.0147381i
\(773\) −19.4288 + 23.1544i −0.698807 + 0.832806i −0.992391 0.123128i \(-0.960708\pi\)
0.293584 + 0.955933i \(0.405152\pi\)
\(774\) 0 0
\(775\) 24.0826 + 8.39586i 0.865074 + 0.301588i
\(776\) 6.35342 5.33116i 0.228075 0.191377i
\(777\) 0 0
\(778\) 1.23625i 0.0443217i
\(779\) 9.62760 + 5.08978i 0.344945 + 0.182360i
\(780\) 0 0
\(781\) 0.582145 + 3.30151i 0.0208308 + 0.118137i
\(782\) −1.98610 2.36695i −0.0710229 0.0846418i
\(783\) 0 0
\(784\) −11.0815 4.03334i −0.395768 0.144048i
\(785\) −20.5842 35.0990i −0.734683 1.25274i
\(786\) 0 0
\(787\) −31.5212 + 18.1988i −1.12361 + 0.648717i −0.942320 0.334712i \(-0.891361\pi\)
−0.181291 + 0.983430i \(0.558027\pi\)
\(788\) 29.1228 + 5.13513i 1.03746 + 0.182931i
\(789\) 0 0
\(790\) −0.597748 3.26007i −0.0212669 0.115988i
\(791\) −5.74724 + 9.95452i −0.204348 + 0.353942i
\(792\) 0 0
\(793\) −1.21728 + 3.34444i −0.0432268 + 0.118765i
\(794\) 5.48507 1.99640i 0.194658 0.0708497i
\(795\) 0 0
\(796\) −4.35514 24.6993i −0.154364 0.875442i
\(797\) 19.2118i 0.680517i −0.940332 0.340258i \(-0.889485\pi\)
0.940332 0.340258i \(-0.110515\pi\)
\(798\) 0 0
\(799\) 16.6532 0.589148
\(800\) −12.2958 6.87750i −0.434722 0.243156i
\(801\) 0 0
\(802\) 2.07080 + 5.68947i 0.0731224 + 0.200902i
\(803\) −2.04986 + 5.63194i −0.0723379 + 0.198747i
\(804\) 0 0
\(805\) 14.4423 + 16.9757i 0.509025 + 0.598313i
\(806\) 0.791760 + 1.37137i 0.0278886 + 0.0483044i
\(807\) 0 0
\(808\) −12.7605 2.25001i −0.448911 0.0791552i
\(809\) 21.5251 + 37.2825i 0.756781 + 1.31078i 0.944484 + 0.328557i \(0.106562\pi\)
−0.187703 + 0.982226i \(0.560104\pi\)
\(810\) 0 0
\(811\) −23.9988 20.1373i −0.842710 0.707118i 0.115461 0.993312i \(-0.463165\pi\)
−0.958172 + 0.286194i \(0.907610\pi\)
\(812\) 11.1261 30.5687i 0.390450 1.07275i
\(813\) 0 0
\(814\) 8.74521 7.33810i 0.306520 0.257200i
\(815\) −5.72393 + 33.8062i −0.200501 + 1.18418i
\(816\) 0 0
\(817\) −19.4655 + 0.726064i −0.681011 + 0.0254018i
\(818\) 2.42032i 0.0846245i
\(819\) 0 0
\(820\) −3.77648 10.1601i −0.131880 0.354805i
\(821\) 16.0413 5.83857i 0.559847 0.203768i −0.0465693 0.998915i \(-0.514829\pi\)
0.606416 + 0.795148i \(0.292607\pi\)
\(822\) 0 0
\(823\) 23.3420 27.8179i 0.813650 0.969670i −0.186268 0.982499i \(-0.559639\pi\)
0.999918 + 0.0128292i \(0.00408378\pi\)
\(824\) −1.94383 + 3.36682i −0.0677166 + 0.117289i
\(825\) 0 0
\(826\) 0.427779 2.42606i 0.0148843 0.0844133i
\(827\) 19.0492 + 3.35888i 0.662404 + 0.116800i 0.494735 0.869044i \(-0.335265\pi\)
0.167669 + 0.985843i \(0.446376\pi\)
\(828\) 0 0
\(829\) −10.0921 + 17.4801i −0.350514 + 0.607109i −0.986340 0.164724i \(-0.947327\pi\)
0.635825 + 0.771833i \(0.280660\pi\)
\(830\) 5.58900 3.27774i 0.193997 0.113772i
\(831\) 0 0
\(832\) 2.86687 + 7.87666i 0.0993909 + 0.273074i
\(833\) −5.11636 6.09744i −0.177271 0.211264i
\(834\) 0 0
\(835\) 13.0951 + 4.66553i 0.453176 + 0.161457i
\(836\) −10.9826 + 34.0763i −0.379841 + 1.17855i
\(837\) 0 0
\(838\) 0.965002 0.170156i 0.0333355 0.00587794i
\(839\) 19.7800 16.5974i 0.682880 0.573005i −0.233966 0.972245i \(-0.575170\pi\)
0.916846 + 0.399240i \(0.130726\pi\)
\(840\) 0 0
\(841\) −42.9165 15.6203i −1.47988 0.538632i
\(842\) 3.18664 3.79769i 0.109819 0.130877i
\(843\) 0 0
\(844\) 4.31332 + 7.47089i 0.148471 + 0.257159i
\(845\) 22.1380 + 12.5813i 0.761572 + 0.432808i
\(846\) 0 0
\(847\) 11.6296 6.71438i 0.399599 0.230709i
\(848\) 2.17745 + 1.25715i 0.0747738 + 0.0431707i
\(849\) 0 0
\(850\) −1.53898 2.58371i −0.0527867 0.0886206i
\(851\) −53.2482 + 19.3807i −1.82532 + 0.664363i
\(852\) 0 0
\(853\) −14.1058 + 2.48724i −0.482974 + 0.0851613i −0.409834 0.912160i \(-0.634413\pi\)
−0.0731404 + 0.997322i \(0.523302\pi\)
\(854\) 1.32952 0.0454953
\(855\) 0 0
\(856\) 16.3365 0.558370
\(857\) −23.8963 + 4.21356i −0.816281 + 0.143932i −0.566174 0.824286i \(-0.691577\pi\)
−0.250107 + 0.968218i \(0.580466\pi\)
\(858\) 0 0
\(859\) 38.0794 13.8598i 1.29925 0.472889i 0.402499 0.915421i \(-0.368142\pi\)
0.896753 + 0.442532i \(0.145920\pi\)
\(860\) 14.9364 + 12.3608i 0.509327 + 0.421501i
\(861\) 0 0
\(862\) −2.85368 1.64757i −0.0971968 0.0561166i
\(863\) −19.8458 + 11.4580i −0.675560 + 0.390035i −0.798180 0.602419i \(-0.794204\pi\)
0.122620 + 0.992454i \(0.460870\pi\)
\(864\) 0 0
\(865\) 3.05599 5.37733i 0.103907 0.182835i
\(866\) −4.20227 7.27854i −0.142799 0.247335i
\(867\) 0 0
\(868\) −12.3431 + 14.7100i −0.418953 + 0.499289i
\(869\) 24.1185 + 8.77843i 0.818165 + 0.297788i
\(870\) 0 0
\(871\) 5.07019 4.25440i 0.171797 0.144155i
\(872\) −6.48474 + 1.14344i −0.219601 + 0.0387216i
\(873\) 0 0
\(874\) −3.36013 + 4.32190i −0.113658 + 0.146190i
\(875\) 11.2278 + 18.5612i 0.379570 + 0.627483i
\(876\) 0 0
\(877\) −31.9434 38.0686i −1.07865 1.28549i −0.956105 0.293024i \(-0.905338\pi\)
−0.122546 0.992463i \(-0.539106\pi\)
\(878\) −1.95812 5.37988i −0.0660832 0.181562i
\(879\) 0 0
\(880\) 29.7625 17.4546i 1.00329 0.588395i
\(881\) −5.51788 + 9.55725i −0.185902 + 0.321992i −0.943880 0.330288i \(-0.892854\pi\)
0.757978 + 0.652280i \(0.226187\pi\)
\(882\) 0 0
\(883\) 21.7883 + 3.84187i 0.733235 + 0.129289i 0.527785 0.849378i \(-0.323023\pi\)
0.205451 + 0.978667i \(0.434134\pi\)
\(884\) −1.05254 + 5.96927i −0.0354009 + 0.200768i
\(885\) 0 0
\(886\) −0.293236 + 0.507899i −0.00985145 + 0.0170632i
\(887\) 12.8769 15.3461i 0.432365 0.515272i −0.505238 0.862980i \(-0.668595\pi\)
0.937603 + 0.347708i \(0.113040\pi\)
\(888\) 0 0
\(889\) 34.9704 12.7282i 1.17287 0.426890i
\(890\) −1.14418 + 0.425289i −0.0383529 + 0.0142557i
\(891\) 0 0
\(892\) 17.8481i 0.597597i
\(893\) −6.20309 28.8460i −0.207578 0.965295i
\(894\) 0 0
\(895\) 25.0857 + 4.24741i 0.838521 + 0.141975i
\(896\) 10.7748 9.04109i 0.359959 0.302042i
\(897\) 0 0
\(898\) −3.19430 + 8.77627i −0.106595 + 0.292868i
\(899\) 33.7653 + 28.3325i 1.12614 + 0.944941i
\(900\) 0 0
\(901\) 0.848530 + 1.46970i 0.0282686 + 0.0489627i
\(902\) −2.54643 0.449004i −0.0847868 0.0149502i
\(903\) 0 0
\(904\) 2.85336 + 4.94217i 0.0949015 + 0.164374i
\(905\) −5.16772 6.07419i −0.171781 0.201913i
\(906\) 0 0
\(907\) −0.233041 + 0.640274i −0.00773799 + 0.0212600i −0.943501 0.331368i \(-0.892490\pi\)
0.935763 + 0.352628i \(0.114712\pi\)
\(908\) −0.398363 1.09449i −0.0132201 0.0363220i
\(909\) 0 0
\(910\) −0.224849 + 1.32798i −0.00745366 + 0.0440221i
\(911\) −28.7169 −0.951433 −0.475716 0.879599i \(-0.657811\pi\)
−0.475716 + 0.879599i \(0.657811\pi\)
\(912\) 0 0
\(913\) 50.1744i 1.66053i
\(914\) −0.0796442 0.451684i −0.00263439 0.0149404i
\(915\) 0 0
\(916\) −12.9722 + 4.72149i −0.428613 + 0.156002i
\(917\) 0.204386 0.561545i 0.00674941 0.0185439i
\(918\) 0 0
\(919\) 3.45629 5.98648i 0.114013 0.197476i −0.803372 0.595477i \(-0.796963\pi\)
0.917385 + 0.398002i \(0.130296\pi\)
\(920\) 10.8840 1.99563i 0.358834 0.0657939i
\(921\) 0 0
\(922\) 4.04972 + 0.714075i 0.133371 + 0.0235168i
\(923\) 0.870870 0.502797i 0.0286650 0.0165498i
\(924\) 0 0
\(925\) −54.1793 + 10.3157i −1.78140 + 0.339179i
\(926\) 5.59725 + 2.03723i 0.183937 + 0.0669477i
\(927\) 0 0
\(928\) −15.6509 18.6520i −0.513765 0.612281i
\(929\) 7.09009 + 40.2099i 0.232618 + 1.31924i 0.847572 + 0.530681i \(0.178064\pi\)
−0.614953 + 0.788563i \(0.710825\pi\)
\(930\) 0 0
\(931\) −8.65596 + 11.1336i −0.283688 + 0.364888i
\(932\) 39.1272i 1.28165i
\(933\) 0 0
\(934\) 2.55658 2.14522i 0.0836538 0.0701938i
\(935\) 23.2879 0.158533i 0.761595 0.00518458i
\(936\) 0 0
\(937\) 9.47723 11.2945i 0.309608 0.368976i −0.588694 0.808356i \(-0.700358\pi\)
0.898301 + 0.439380i \(0.144802\pi\)
\(938\) −2.14121 1.23623i −0.0699129 0.0403642i
\(939\) 0 0
\(940\) −14.5102 + 25.5322i −0.473269 + 0.832768i
\(941\) 9.06681 51.4204i 0.295570 1.67626i −0.369309 0.929307i \(-0.620406\pi\)
0.664878 0.746952i \(-0.268483\pi\)
\(942\) 0 0
\(943\) 11.1151 + 6.41730i 0.361957 + 0.208976i
\(944\) 14.5009 + 12.1677i 0.471964 + 0.396025i
\(945\) 0 0
\(946\) 4.34607 1.58184i 0.141303 0.0514300i
\(947\) 36.8577 + 43.9252i 1.19771 + 1.42738i 0.877194 + 0.480137i \(0.159413\pi\)
0.320519 + 0.947242i \(0.396143\pi\)
\(948\) 0 0
\(949\) 1.79777 0.0583580
\(950\) −3.90215 + 3.62816i −0.126603 + 0.117713i
\(951\) 0 0
\(952\) 4.52842 0.798483i 0.146767 0.0258790i
\(953\) −5.98927 7.13773i −0.194011 0.231214i 0.660265 0.751033i \(-0.270444\pi\)
−0.854277 + 0.519819i \(0.825999\pi\)
\(954\) 0 0
\(955\) 12.3648 14.9411i 0.400114 0.483484i
\(956\) −17.2920 14.5097i −0.559262 0.469277i
\(957\) 0 0
\(958\) 4.60298 2.65753i 0.148716 0.0858610i
\(959\) 4.88519 27.7053i 0.157751 0.894650i
\(960\) 0 0
\(961\) 2.49072 + 4.31405i 0.0803458 + 0.139163i
\(962\) −2.96557 1.71217i −0.0956139 0.0552027i
\(963\) 0 0
\(964\) −46.5470 16.9417i −1.49918 0.545656i
\(965\) −0.943845 + 0.00642525i −0.0303834 + 0.000206836i
\(966\) 0 0
\(967\) −8.69287 + 1.53279i −0.279544 + 0.0492911i −0.311662 0.950193i \(-0.600886\pi\)
0.0321185 + 0.999484i \(0.489775\pi\)
\(968\) 6.66705i 0.214287i
\(969\) 0 0
\(970\) −1.57964 + 4.43371i −0.0507193 + 0.142358i
\(971\) −9.72287 55.1412i −0.312022 1.76956i −0.588454 0.808531i \(-0.700263\pi\)
0.276432 0.961033i \(-0.410848\pi\)
\(972\) 0 0
\(973\) 10.4833 + 28.8026i 0.336079 + 0.923369i
\(974\) −6.71866 2.44539i −0.215280 0.0783554i
\(975\) 0 0
\(976\) −5.10807 + 8.84743i −0.163505 + 0.283199i
\(977\) −35.5965 + 20.5517i −1.13883 + 0.657506i −0.946142 0.323753i \(-0.895055\pi\)
−0.192693 + 0.981259i \(0.561722\pi\)
\(978\) 0 0
\(979\) 1.64144 9.30905i 0.0524605 0.297518i
\(980\) 13.8064 2.53146i 0.441028 0.0808645i
\(981\) 0 0
\(982\) 2.88452 3.43764i 0.0920488 0.109700i
\(983\) −0.854584 + 2.34795i −0.0272570 + 0.0748880i −0.952575 0.304305i \(-0.901576\pi\)
0.925318 + 0.379193i \(0.123798\pi\)
\(984\) 0 0
\(985\) −31.9456 + 11.8741i −1.01787 + 0.378341i
\(986\) −0.902520 5.11845i −0.0287421 0.163005i
\(987\) 0 0
\(988\) 10.7318 0.400297i 0.341423 0.0127351i
\(989\) −22.9569 −0.729986
\(990\) 0 0
\(991\) 13.3471 11.1995i 0.423983 0.355764i −0.405693 0.914010i \(-0.632970\pi\)
0.829676 + 0.558245i \(0.188525\pi\)
\(992\) 4.91574 + 13.5059i 0.156075 + 0.428812i
\(993\) 0 0
\(994\) −0.287762 0.241461i −0.00912727 0.00765869i
\(995\) 18.7297 + 22.0151i 0.593771 + 0.697924i
\(996\) 0 0
\(997\) −12.6065 2.22287i −0.399253 0.0703990i −0.0295832 0.999562i \(-0.509418\pi\)
−0.369670 + 0.929163i \(0.620529\pi\)
\(998\) 2.50776 + 0.442186i 0.0793819 + 0.0139972i
\(999\) 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 855.2.da.b.199.5 48
3.2 odd 2 95.2.p.a.9.4 48
5.4 even 2 inner 855.2.da.b.199.4 48
15.2 even 4 475.2.l.f.351.4 48
15.8 even 4 475.2.l.f.351.5 48
15.14 odd 2 95.2.p.a.9.5 yes 48
19.17 even 9 inner 855.2.da.b.739.4 48
57.17 odd 18 95.2.p.a.74.5 yes 48
57.32 even 18 1805.2.b.l.1084.12 24
57.44 odd 18 1805.2.b.k.1084.13 24
95.74 even 18 inner 855.2.da.b.739.5 48
285.17 even 36 475.2.l.f.226.4 48
285.32 odd 36 9025.2.a.ct.1.13 24
285.44 odd 18 1805.2.b.k.1084.12 24
285.74 odd 18 95.2.p.a.74.4 yes 48
285.89 even 18 1805.2.b.l.1084.13 24
285.158 even 36 9025.2.a.cu.1.13 24
285.188 even 36 475.2.l.f.226.5 48
285.203 odd 36 9025.2.a.ct.1.12 24
285.272 even 36 9025.2.a.cu.1.12 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
95.2.p.a.9.4 48 3.2 odd 2
95.2.p.a.9.5 yes 48 15.14 odd 2
95.2.p.a.74.4 yes 48 285.74 odd 18
95.2.p.a.74.5 yes 48 57.17 odd 18
475.2.l.f.226.4 48 285.17 even 36
475.2.l.f.226.5 48 285.188 even 36
475.2.l.f.351.4 48 15.2 even 4
475.2.l.f.351.5 48 15.8 even 4
855.2.da.b.199.4 48 5.4 even 2 inner
855.2.da.b.199.5 48 1.1 even 1 trivial
855.2.da.b.739.4 48 19.17 even 9 inner
855.2.da.b.739.5 48 95.74 even 18 inner
1805.2.b.k.1084.12 24 285.44 odd 18
1805.2.b.k.1084.13 24 57.44 odd 18
1805.2.b.l.1084.12 24 57.32 even 18
1805.2.b.l.1084.13 24 285.89 even 18
9025.2.a.ct.1.12 24 285.203 odd 36
9025.2.a.ct.1.13 24 285.32 odd 36
9025.2.a.cu.1.12 24 285.272 even 36
9025.2.a.cu.1.13 24 285.158 even 36