Properties

Label 162.2.e.b.127.2
Level $162$
Weight $2$
Character 162.127
Analytic conductor $1.294$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [162,2,Mod(19,162)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(162, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([16]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("162.19");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 162 = 2 \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 162.e (of order \(9\), degree \(6\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(1.29357651274\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(2\) over \(\Q(\zeta_{9})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 6 x^{11} + 33 x^{10} - 110 x^{9} + 318 x^{8} - 678 x^{7} + 1225 x^{6} - 1698 x^{5} + 1905 x^{4} + \cdots + 57 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 3^{3} \)
Twist minimal: no (minimal twist has level 54)
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 127.2
Root \(0.500000 - 1.80139i\) of defining polynomial
Character \(\chi\) \(=\) 162.127
Dual form 162.2.e.b.37.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.766044 - 0.642788i) q^{2} +(0.173648 + 0.984808i) q^{4} +(1.96209 + 0.714144i) q^{5} +(-0.696712 + 3.95125i) q^{7} +(0.500000 - 0.866025i) q^{8} +O(q^{10})\) \(q+(-0.766044 - 0.642788i) q^{2} +(0.173648 + 0.984808i) q^{4} +(1.96209 + 0.714144i) q^{5} +(-0.696712 + 3.95125i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-1.04401 - 1.80828i) q^{10} +(0.199635 - 0.0726611i) q^{11} +(3.98269 - 3.34187i) q^{13} +(3.07353 - 2.57900i) q^{14} +(-0.939693 + 0.342020i) q^{16} +(1.89276 + 3.27836i) q^{17} +(0.636405 - 1.10229i) q^{19} +(-0.362580 + 2.05630i) q^{20} +(-0.199635 - 0.0726611i) q^{22} +(-0.144031 - 0.816841i) q^{23} +(-0.490411 - 0.411503i) q^{25} -5.19903 q^{26} -4.01220 q^{28} +(-7.05621 - 5.92087i) q^{29} +(0.614003 + 3.48219i) q^{31} +(0.939693 + 0.342020i) q^{32} +(0.657349 - 3.72801i) q^{34} +(-4.18878 + 7.25517i) q^{35} +(-1.77730 - 3.07838i) q^{37} +(-1.19605 + 0.435326i) q^{38} +(1.59951 - 1.34215i) q^{40} +(-2.09850 + 1.76085i) q^{41} +(-6.48062 + 2.35875i) q^{43} +(0.106223 + 0.183984i) q^{44} +(-0.414721 + 0.718318i) q^{46} +(0.221796 - 1.25787i) q^{47} +(-8.54912 - 3.11163i) q^{49} +(0.111167 + 0.630460i) q^{50} +(3.98269 + 3.34187i) q^{52} +11.2992 q^{53} +0.443592 q^{55} +(3.07353 + 2.57900i) q^{56} +(1.59951 + 9.07129i) q^{58} +(-8.04363 - 2.92764i) q^{59} +(0.492064 - 2.79063i) q^{61} +(1.76795 - 3.06218i) q^{62} +(-0.500000 - 0.866025i) q^{64} +(10.2010 - 3.71285i) q^{65} +(7.47702 - 6.27396i) q^{67} +(-2.89988 + 2.43329i) q^{68} +(7.87232 - 2.86529i) q^{70} +(-5.86207 - 10.1534i) q^{71} +(-0.375162 + 0.649800i) q^{73} +(-0.617250 + 3.50060i) q^{74} +(1.19605 + 0.435326i) q^{76} +(0.148014 + 0.839430i) q^{77} +(-1.81383 - 1.52198i) q^{79} -2.08802 q^{80} +2.73940 q^{82} +(8.73328 + 7.32809i) q^{83} +(1.37256 + 7.78415i) q^{85} +(6.48062 + 2.35875i) q^{86} +(0.0368910 - 0.209219i) q^{88} +(2.69813 - 4.67329i) q^{89} +(10.4298 + 18.0649i) q^{91} +(0.779421 - 0.283686i) q^{92} +(-0.978448 + 0.821016i) q^{94} +(2.03588 - 1.70830i) q^{95} +(11.8055 - 4.29685i) q^{97} +(4.54889 + 7.87892i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 3 q^{5} - 3 q^{7} + 6 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 3 q^{5} - 3 q^{7} + 6 q^{8} - 3 q^{10} + 12 q^{11} + 12 q^{13} + 3 q^{14} + 6 q^{17} - 9 q^{19} - 6 q^{20} - 12 q^{22} - 30 q^{23} - 9 q^{25} - 18 q^{26} + 12 q^{28} - 15 q^{29} - 15 q^{34} - 3 q^{35} - 15 q^{37} - 3 q^{38} - 3 q^{40} + 12 q^{41} + 9 q^{43} + 3 q^{44} + 3 q^{46} + 9 q^{47} - 39 q^{49} + 27 q^{50} + 12 q^{52} + 12 q^{53} + 18 q^{55} + 3 q^{56} - 3 q^{58} - 12 q^{59} - 36 q^{61} + 12 q^{62} - 6 q^{64} + 15 q^{65} + 36 q^{67} - 3 q^{68} + 39 q^{70} - 12 q^{71} - 21 q^{73} - 33 q^{74} + 3 q^{76} - 3 q^{77} + 39 q^{79} - 6 q^{80} + 6 q^{82} - 18 q^{83} + 45 q^{85} - 9 q^{86} + 6 q^{88} - 12 q^{89} - 6 q^{91} + 6 q^{92} + 36 q^{94} + 15 q^{95} + 39 q^{97} + 12 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/162\mathbb{Z}\right)^\times\).

\(n\) \(83\)
\(\chi(n)\) \(e\left(\frac{2}{9}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.766044 0.642788i −0.541675 0.454519i
\(3\) 0 0
\(4\) 0.173648 + 0.984808i 0.0868241 + 0.492404i
\(5\) 1.96209 + 0.714144i 0.877475 + 0.319375i 0.741190 0.671295i \(-0.234262\pi\)
0.136285 + 0.990670i \(0.456484\pi\)
\(6\) 0 0
\(7\) −0.696712 + 3.95125i −0.263332 + 1.49343i 0.510410 + 0.859931i \(0.329494\pi\)
−0.773742 + 0.633501i \(0.781617\pi\)
\(8\) 0.500000 0.866025i 0.176777 0.306186i
\(9\) 0 0
\(10\) −1.04401 1.80828i −0.330144 0.571827i
\(11\) 0.199635 0.0726611i 0.0601921 0.0219081i −0.311749 0.950165i \(-0.600915\pi\)
0.371941 + 0.928256i \(0.378692\pi\)
\(12\) 0 0
\(13\) 3.98269 3.34187i 1.10460 0.926868i 0.106873 0.994273i \(-0.465916\pi\)
0.997726 + 0.0674046i \(0.0214718\pi\)
\(14\) 3.07353 2.57900i 0.821435 0.689266i
\(15\) 0 0
\(16\) −0.939693 + 0.342020i −0.234923 + 0.0855050i
\(17\) 1.89276 + 3.27836i 0.459062 + 0.795119i 0.998912 0.0466426i \(-0.0148522\pi\)
−0.539850 + 0.841762i \(0.681519\pi\)
\(18\) 0 0
\(19\) 0.636405 1.10229i 0.146001 0.252882i −0.783745 0.621083i \(-0.786693\pi\)
0.929746 + 0.368201i \(0.120026\pi\)
\(20\) −0.362580 + 2.05630i −0.0810754 + 0.459802i
\(21\) 0 0
\(22\) −0.199635 0.0726611i −0.0425622 0.0154914i
\(23\) −0.144031 0.816841i −0.0300326 0.170323i 0.966102 0.258159i \(-0.0831159\pi\)
−0.996135 + 0.0878361i \(0.972005\pi\)
\(24\) 0 0
\(25\) −0.490411 0.411503i −0.0980821 0.0823007i
\(26\) −5.19903 −1.01961
\(27\) 0 0
\(28\) −4.01220 −0.758235
\(29\) −7.05621 5.92087i −1.31031 1.09948i −0.988265 0.152752i \(-0.951187\pi\)
−0.322041 0.946726i \(-0.604369\pi\)
\(30\) 0 0
\(31\) 0.614003 + 3.48219i 0.110278 + 0.625419i 0.988980 + 0.148048i \(0.0472991\pi\)
−0.878702 + 0.477371i \(0.841590\pi\)
\(32\) 0.939693 + 0.342020i 0.166116 + 0.0604612i
\(33\) 0 0
\(34\) 0.657349 3.72801i 0.112734 0.639349i
\(35\) −4.18878 + 7.25517i −0.708032 + 1.22635i
\(36\) 0 0
\(37\) −1.77730 3.07838i −0.292187 0.506082i 0.682140 0.731222i \(-0.261049\pi\)
−0.974326 + 0.225140i \(0.927716\pi\)
\(38\) −1.19605 + 0.435326i −0.194025 + 0.0706193i
\(39\) 0 0
\(40\) 1.59951 1.34215i 0.252905 0.212213i
\(41\) −2.09850 + 1.76085i −0.327730 + 0.274998i −0.791774 0.610814i \(-0.790842\pi\)
0.464044 + 0.885812i \(0.346398\pi\)
\(42\) 0 0
\(43\) −6.48062 + 2.35875i −0.988286 + 0.359707i −0.785056 0.619425i \(-0.787366\pi\)
−0.203229 + 0.979131i \(0.565144\pi\)
\(44\) 0.106223 + 0.183984i 0.0160138 + 0.0277367i
\(45\) 0 0
\(46\) −0.414721 + 0.718318i −0.0611473 + 0.105910i
\(47\) 0.221796 1.25787i 0.0323523 0.183479i −0.964349 0.264633i \(-0.914749\pi\)
0.996702 + 0.0811536i \(0.0258604\pi\)
\(48\) 0 0
\(49\) −8.54912 3.11163i −1.22130 0.444518i
\(50\) 0.111167 + 0.630460i 0.0157214 + 0.0891605i
\(51\) 0 0
\(52\) 3.98269 + 3.34187i 0.552299 + 0.463434i
\(53\) 11.2992 1.55207 0.776036 0.630689i \(-0.217228\pi\)
0.776036 + 0.630689i \(0.217228\pi\)
\(54\) 0 0
\(55\) 0.443592 0.0598140
\(56\) 3.07353 + 2.57900i 0.410717 + 0.344633i
\(57\) 0 0
\(58\) 1.59951 + 9.07129i 0.210026 + 1.19112i
\(59\) −8.04363 2.92764i −1.04719 0.381147i −0.239589 0.970874i \(-0.577013\pi\)
−0.807602 + 0.589728i \(0.799235\pi\)
\(60\) 0 0
\(61\) 0.492064 2.79063i 0.0630023 0.357304i −0.936967 0.349419i \(-0.886379\pi\)
0.999969 0.00788485i \(-0.00250985\pi\)
\(62\) 1.76795 3.06218i 0.224530 0.388898i
\(63\) 0 0
\(64\) −0.500000 0.866025i −0.0625000 0.108253i
\(65\) 10.2010 3.71285i 1.26528 0.460523i
\(66\) 0 0
\(67\) 7.47702 6.27396i 0.913463 0.766487i −0.0593114 0.998240i \(-0.518890\pi\)
0.972775 + 0.231753i \(0.0744460\pi\)
\(68\) −2.89988 + 2.43329i −0.351662 + 0.295079i
\(69\) 0 0
\(70\) 7.87232 2.86529i 0.940923 0.342468i
\(71\) −5.86207 10.1534i −0.695700 1.20499i −0.969944 0.243327i \(-0.921761\pi\)
0.274244 0.961660i \(-0.411572\pi\)
\(72\) 0 0
\(73\) −0.375162 + 0.649800i −0.0439094 + 0.0760534i −0.887145 0.461491i \(-0.847315\pi\)
0.843235 + 0.537544i \(0.180648\pi\)
\(74\) −0.617250 + 3.50060i −0.0717539 + 0.406937i
\(75\) 0 0
\(76\) 1.19605 + 0.435326i 0.137196 + 0.0499354i
\(77\) 0.148014 + 0.839430i 0.0168678 + 0.0956620i
\(78\) 0 0
\(79\) −1.81383 1.52198i −0.204071 0.171236i 0.535024 0.844837i \(-0.320302\pi\)
−0.739096 + 0.673600i \(0.764747\pi\)
\(80\) −2.08802 −0.233447
\(81\) 0 0
\(82\) 2.73940 0.302516
\(83\) 8.73328 + 7.32809i 0.958602 + 0.804363i 0.980725 0.195393i \(-0.0625981\pi\)
−0.0221230 + 0.999755i \(0.507043\pi\)
\(84\) 0 0
\(85\) 1.37256 + 7.78415i 0.148875 + 0.844310i
\(86\) 6.48062 + 2.35875i 0.698823 + 0.254351i
\(87\) 0 0
\(88\) 0.0368910 0.209219i 0.00393259 0.0223028i
\(89\) 2.69813 4.67329i 0.286001 0.495368i −0.686851 0.726799i \(-0.741007\pi\)
0.972851 + 0.231431i \(0.0743407\pi\)
\(90\) 0 0
\(91\) 10.4298 + 18.0649i 1.09334 + 1.89372i
\(92\) 0.779421 0.283686i 0.0812602 0.0295763i
\(93\) 0 0
\(94\) −0.978448 + 0.821016i −0.100919 + 0.0846813i
\(95\) 2.03588 1.70830i 0.208876 0.175268i
\(96\) 0 0
\(97\) 11.8055 4.29685i 1.19867 0.436279i 0.335909 0.941895i \(-0.390957\pi\)
0.862759 + 0.505615i \(0.168734\pi\)
\(98\) 4.54889 + 7.87892i 0.459508 + 0.795891i
\(99\) 0 0
\(100\) 0.320093 0.554417i 0.0320093 0.0554417i
\(101\) 0.502628 2.85055i 0.0500134 0.283640i −0.949536 0.313658i \(-0.898445\pi\)
0.999549 + 0.0300181i \(0.00955651\pi\)
\(102\) 0 0
\(103\) −15.6835 5.70832i −1.54534 0.562458i −0.578022 0.816021i \(-0.696175\pi\)
−0.967319 + 0.253564i \(0.918397\pi\)
\(104\) −0.902802 5.12004i −0.0885270 0.502061i
\(105\) 0 0
\(106\) −8.65573 7.26302i −0.840719 0.705447i
\(107\) −0.321371 −0.0310681 −0.0155341 0.999879i \(-0.504945\pi\)
−0.0155341 + 0.999879i \(0.504945\pi\)
\(108\) 0 0
\(109\) 0.568378 0.0544407 0.0272204 0.999629i \(-0.491334\pi\)
0.0272204 + 0.999629i \(0.491334\pi\)
\(110\) −0.339811 0.285136i −0.0323998 0.0271866i
\(111\) 0 0
\(112\) −0.696712 3.95125i −0.0658331 0.373358i
\(113\) −1.27781 0.465084i −0.120206 0.0437514i 0.281217 0.959644i \(-0.409262\pi\)
−0.401423 + 0.915893i \(0.631484\pi\)
\(114\) 0 0
\(115\) 0.300739 1.70558i 0.0280441 0.159046i
\(116\) 4.60562 7.97716i 0.427621 0.740661i
\(117\) 0 0
\(118\) 4.27993 + 7.41305i 0.393999 + 0.682427i
\(119\) −14.2723 + 5.19470i −1.30834 + 0.476198i
\(120\) 0 0
\(121\) −8.39191 + 7.04165i −0.762901 + 0.640150i
\(122\) −2.17073 + 1.82146i −0.196528 + 0.164907i
\(123\) 0 0
\(124\) −3.32266 + 1.20935i −0.298384 + 0.108603i
\(125\) −5.88840 10.1990i −0.526675 0.912227i
\(126\) 0 0
\(127\) −0.902007 + 1.56232i −0.0800402 + 0.138634i −0.903267 0.429079i \(-0.858838\pi\)
0.823227 + 0.567713i \(0.192172\pi\)
\(128\) −0.173648 + 0.984808i −0.0153485 + 0.0870455i
\(129\) 0 0
\(130\) −10.2010 3.71285i −0.894685 0.325639i
\(131\) 1.68689 + 9.56684i 0.147384 + 0.835859i 0.965422 + 0.260694i \(0.0839512\pi\)
−0.818037 + 0.575165i \(0.804938\pi\)
\(132\) 0 0
\(133\) 3.91201 + 3.28257i 0.339215 + 0.284635i
\(134\) −9.76056 −0.843184
\(135\) 0 0
\(136\) 3.78552 0.324606
\(137\) 6.94643 + 5.82875i 0.593474 + 0.497984i 0.889340 0.457246i \(-0.151164\pi\)
−0.295867 + 0.955229i \(0.595608\pi\)
\(138\) 0 0
\(139\) −1.74358 9.88833i −0.147888 0.838717i −0.965002 0.262241i \(-0.915538\pi\)
0.817114 0.576476i \(-0.195573\pi\)
\(140\) −7.87232 2.86529i −0.665333 0.242161i
\(141\) 0 0
\(142\) −2.03588 + 11.5460i −0.170847 + 0.968921i
\(143\) 0.552258 0.956539i 0.0461822 0.0799898i
\(144\) 0 0
\(145\) −9.61660 16.6564i −0.798615 1.38324i
\(146\) 0.705075 0.256626i 0.0583524 0.0212385i
\(147\) 0 0
\(148\) 2.72298 2.28485i 0.223828 0.187814i
\(149\) −12.1360 + 10.1833i −0.994221 + 0.834250i −0.986173 0.165718i \(-0.947006\pi\)
−0.00804728 + 0.999968i \(0.502562\pi\)
\(150\) 0 0
\(151\) −4.98746 + 1.81529i −0.405874 + 0.147726i −0.536886 0.843655i \(-0.680400\pi\)
0.131012 + 0.991381i \(0.458177\pi\)
\(152\) −0.636405 1.10229i −0.0516192 0.0894071i
\(153\) 0 0
\(154\) 0.426190 0.738183i 0.0343434 0.0594845i
\(155\) −1.28205 + 7.27086i −0.102977 + 0.584010i
\(156\) 0 0
\(157\) 10.8225 + 3.93906i 0.863727 + 0.314371i 0.735624 0.677390i \(-0.236889\pi\)
0.128103 + 0.991761i \(0.459111\pi\)
\(158\) 0.411161 + 2.33181i 0.0327102 + 0.185509i
\(159\) 0 0
\(160\) 1.59951 + 1.34215i 0.126453 + 0.106106i
\(161\) 3.32789 0.262275
\(162\) 0 0
\(163\) 7.66336 0.600241 0.300120 0.953901i \(-0.402973\pi\)
0.300120 + 0.953901i \(0.402973\pi\)
\(164\) −2.09850 1.76085i −0.163865 0.137499i
\(165\) 0 0
\(166\) −1.97967 11.2273i −0.153653 0.871407i
\(167\) 5.74151 + 2.08974i 0.444292 + 0.161709i 0.554472 0.832203i \(-0.312920\pi\)
−0.110180 + 0.993912i \(0.535143\pi\)
\(168\) 0 0
\(169\) 2.43626 13.8167i 0.187405 1.06283i
\(170\) 3.95212 6.84527i 0.303114 0.525008i
\(171\) 0 0
\(172\) −3.44827 5.97257i −0.262928 0.455404i
\(173\) −10.6218 + 3.86602i −0.807561 + 0.293928i −0.712616 0.701554i \(-0.752490\pi\)
−0.0949449 + 0.995483i \(0.530268\pi\)
\(174\) 0 0
\(175\) 1.96763 1.65104i 0.148739 0.124807i
\(176\) −0.162744 + 0.136558i −0.0122673 + 0.0102935i
\(177\) 0 0
\(178\) −5.07082 + 1.84563i −0.380074 + 0.138336i
\(179\) 3.46495 + 6.00147i 0.258982 + 0.448571i 0.965970 0.258656i \(-0.0832795\pi\)
−0.706987 + 0.707226i \(0.749946\pi\)
\(180\) 0 0
\(181\) −1.51882 + 2.63067i −0.112893 + 0.195536i −0.916935 0.399036i \(-0.869345\pi\)
0.804043 + 0.594572i \(0.202678\pi\)
\(182\) 3.62223 20.5427i 0.268497 1.52272i
\(183\) 0 0
\(184\) −0.779421 0.283686i −0.0574597 0.0209136i
\(185\) −1.28883 7.30931i −0.0947566 0.537391i
\(186\) 0 0
\(187\) 0.616070 + 0.516944i 0.0450515 + 0.0378027i
\(188\) 1.27727 0.0931547
\(189\) 0 0
\(190\) −2.65765 −0.192806
\(191\) 3.90467 + 3.27640i 0.282532 + 0.237072i 0.773029 0.634370i \(-0.218741\pi\)
−0.490498 + 0.871443i \(0.663185\pi\)
\(192\) 0 0
\(193\) 3.27644 + 18.5816i 0.235843 + 1.33753i 0.840830 + 0.541299i \(0.182067\pi\)
−0.604987 + 0.796235i \(0.706822\pi\)
\(194\) −11.8055 4.29685i −0.847586 0.308496i
\(195\) 0 0
\(196\) 1.57981 8.95957i 0.112844 0.639969i
\(197\) −10.0220 + 17.3586i −0.714036 + 1.23675i 0.249294 + 0.968428i \(0.419801\pi\)
−0.963330 + 0.268319i \(0.913532\pi\)
\(198\) 0 0
\(199\) −2.75106 4.76498i −0.195018 0.337780i 0.751889 0.659290i \(-0.229143\pi\)
−0.946906 + 0.321510i \(0.895810\pi\)
\(200\) −0.601578 + 0.218956i −0.0425380 + 0.0154826i
\(201\) 0 0
\(202\) −2.21733 + 1.86056i −0.156011 + 0.130909i
\(203\) 28.3110 23.7557i 1.98704 1.66733i
\(204\) 0 0
\(205\) −5.37495 + 1.95632i −0.375403 + 0.136635i
\(206\) 8.34501 + 14.4540i 0.581425 + 1.00706i
\(207\) 0 0
\(208\) −2.59951 + 4.50249i −0.180244 + 0.312191i
\(209\) 0.0469552 0.266296i 0.00324796 0.0184201i
\(210\) 0 0
\(211\) 23.6287 + 8.60014i 1.62667 + 0.592058i 0.984636 0.174621i \(-0.0558699\pi\)
0.642031 + 0.766679i \(0.278092\pi\)
\(212\) 1.96209 + 11.1276i 0.134757 + 0.764246i
\(213\) 0 0
\(214\) 0.246185 + 0.206573i 0.0168288 + 0.0141211i
\(215\) −14.4001 −0.982077
\(216\) 0 0
\(217\) −14.1868 −0.963061
\(218\) −0.435403 0.365346i −0.0294892 0.0247444i
\(219\) 0 0
\(220\) 0.0770290 + 0.436853i 0.00519329 + 0.0294526i
\(221\) 18.4941 + 6.73131i 1.24405 + 0.452797i
\(222\) 0 0
\(223\) −0.651596 + 3.69539i −0.0436341 + 0.247461i −0.998821 0.0485415i \(-0.984543\pi\)
0.955187 + 0.296003i \(0.0956538\pi\)
\(224\) −2.00610 + 3.47467i −0.134038 + 0.232161i
\(225\) 0 0
\(226\) 0.679907 + 1.17763i 0.0452267 + 0.0783350i
\(227\) 17.5983 6.40524i 1.16804 0.425131i 0.316076 0.948734i \(-0.397635\pi\)
0.851962 + 0.523603i \(0.175412\pi\)
\(228\) 0 0
\(229\) −3.17397 + 2.66328i −0.209742 + 0.175994i −0.741607 0.670835i \(-0.765936\pi\)
0.531865 + 0.846829i \(0.321491\pi\)
\(230\) −1.32670 + 1.11324i −0.0874803 + 0.0734047i
\(231\) 0 0
\(232\) −8.65573 + 3.15043i −0.568276 + 0.206836i
\(233\) −0.958556 1.66027i −0.0627971 0.108768i 0.832918 0.553397i \(-0.186669\pi\)
−0.895715 + 0.444629i \(0.853335\pi\)
\(234\) 0 0
\(235\) 1.33348 2.30966i 0.0869869 0.150666i
\(236\) 1.48640 8.42981i 0.0967566 0.548734i
\(237\) 0 0
\(238\) 14.2723 + 5.19470i 0.925138 + 0.336723i
\(239\) −4.20216 23.8316i −0.271815 1.54154i −0.748900 0.662683i \(-0.769418\pi\)
0.477085 0.878857i \(-0.341693\pi\)
\(240\) 0 0
\(241\) 10.1156 + 8.48797i 0.651601 + 0.546758i 0.907556 0.419931i \(-0.137946\pi\)
−0.255955 + 0.966689i \(0.582390\pi\)
\(242\) 10.9549 0.704205
\(243\) 0 0
\(244\) 2.83368 0.181408
\(245\) −14.5520 12.2106i −0.929695 0.780107i
\(246\) 0 0
\(247\) −1.14909 6.51684i −0.0731151 0.414656i
\(248\) 3.32266 + 1.20935i 0.210989 + 0.0767938i
\(249\) 0 0
\(250\) −2.04502 + 11.5979i −0.129338 + 0.733515i
\(251\) −4.32994 + 7.49967i −0.273303 + 0.473375i −0.969706 0.244276i \(-0.921450\pi\)
0.696402 + 0.717652i \(0.254783\pi\)
\(252\) 0 0
\(253\) −0.0881062 0.152604i −0.00553919 0.00959415i
\(254\) 1.69522 0.617009i 0.106368 0.0387146i
\(255\) 0 0
\(256\) 0.766044 0.642788i 0.0478778 0.0401742i
\(257\) −16.7233 + 14.0326i −1.04317 + 0.875326i −0.992359 0.123382i \(-0.960626\pi\)
−0.0508142 + 0.998708i \(0.516182\pi\)
\(258\) 0 0
\(259\) 13.4017 4.87782i 0.832741 0.303093i
\(260\) 5.42783 + 9.40127i 0.336620 + 0.583042i
\(261\) 0 0
\(262\) 4.85721 8.41294i 0.300080 0.519753i
\(263\) 0.987629 5.60112i 0.0608998 0.345380i −0.939099 0.343648i \(-0.888337\pi\)
0.999998 0.00173240i \(-0.000551441\pi\)
\(264\) 0 0
\(265\) 22.1702 + 8.06929i 1.36190 + 0.495692i
\(266\) −0.886782 5.02919i −0.0543721 0.308359i
\(267\) 0 0
\(268\) 7.47702 + 6.27396i 0.456732 + 0.383243i
\(269\) 22.7662 1.38808 0.694041 0.719936i \(-0.255829\pi\)
0.694041 + 0.719936i \(0.255829\pi\)
\(270\) 0 0
\(271\) −19.8340 −1.20483 −0.602414 0.798184i \(-0.705794\pi\)
−0.602414 + 0.798184i \(0.705794\pi\)
\(272\) −2.89988 2.43329i −0.175831 0.147540i
\(273\) 0 0
\(274\) −1.57463 8.93016i −0.0951268 0.539491i
\(275\) −0.127803 0.0465166i −0.00770683 0.00280506i
\(276\) 0 0
\(277\) −4.19132 + 23.7701i −0.251832 + 1.42821i 0.552244 + 0.833683i \(0.313772\pi\)
−0.804076 + 0.594527i \(0.797339\pi\)
\(278\) −5.02044 + 8.69565i −0.301106 + 0.521530i
\(279\) 0 0
\(280\) 4.18878 + 7.25517i 0.250327 + 0.433579i
\(281\) −22.2287 + 8.09058i −1.32605 + 0.482644i −0.905393 0.424575i \(-0.860424\pi\)
−0.420660 + 0.907219i \(0.638201\pi\)
\(282\) 0 0
\(283\) −8.90462 + 7.47186i −0.529325 + 0.444156i −0.867868 0.496795i \(-0.834510\pi\)
0.338543 + 0.940951i \(0.390066\pi\)
\(284\) 8.98121 7.53613i 0.532937 0.447187i
\(285\) 0 0
\(286\) −1.03791 + 0.377767i −0.0613727 + 0.0223378i
\(287\) −5.49551 9.51850i −0.324390 0.561859i
\(288\) 0 0
\(289\) 1.33491 2.31213i 0.0785239 0.136007i
\(290\) −3.33981 + 18.9410i −0.196120 + 1.11225i
\(291\) 0 0
\(292\) −0.705075 0.256626i −0.0412614 0.0150179i
\(293\) 1.85993 + 10.5482i 0.108658 + 0.616232i 0.989696 + 0.143186i \(0.0457346\pi\)
−0.881037 + 0.473046i \(0.843154\pi\)
\(294\) 0 0
\(295\) −13.6916 11.4886i −0.797156 0.668893i
\(296\) −3.55460 −0.206607
\(297\) 0 0
\(298\) 15.8424 0.917728
\(299\) −3.30341 2.77189i −0.191041 0.160302i
\(300\) 0 0
\(301\) −4.80490 27.2499i −0.276950 1.57066i
\(302\) 4.98746 + 1.81529i 0.286996 + 0.104458i
\(303\) 0 0
\(304\) −0.221021 + 1.25347i −0.0126764 + 0.0718916i
\(305\) 2.95839 5.12408i 0.169397 0.293404i
\(306\) 0 0
\(307\) −12.3938 21.4667i −0.707351 1.22517i −0.965836 0.259153i \(-0.916557\pi\)
0.258485 0.966015i \(-0.416777\pi\)
\(308\) −0.800975 + 0.291531i −0.0456398 + 0.0166115i
\(309\) 0 0
\(310\) 5.65573 4.74572i 0.321224 0.269539i
\(311\) 16.6871 14.0022i 0.946241 0.793990i −0.0324195 0.999474i \(-0.510321\pi\)
0.978660 + 0.205484i \(0.0658768\pi\)
\(312\) 0 0
\(313\) 8.83542 3.21583i 0.499408 0.181770i −0.0800199 0.996793i \(-0.525498\pi\)
0.579428 + 0.815024i \(0.303276\pi\)
\(314\) −5.75852 9.97404i −0.324972 0.562868i
\(315\) 0 0
\(316\) 1.18389 2.05056i 0.0665990 0.115353i
\(317\) 2.51892 14.2855i 0.141477 0.802353i −0.828652 0.559763i \(-0.810892\pi\)
0.970129 0.242590i \(-0.0779969\pi\)
\(318\) 0 0
\(319\) −1.83888 0.669298i −0.102958 0.0374735i
\(320\) −0.362580 2.05630i −0.0202689 0.114950i
\(321\) 0 0
\(322\) −2.54931 2.13913i −0.142068 0.119209i
\(323\) 4.81825 0.268095
\(324\) 0 0
\(325\) −3.32834 −0.184623
\(326\) −5.87047 4.92591i −0.325135 0.272821i
\(327\) 0 0
\(328\) 0.475691 + 2.69778i 0.0262656 + 0.148960i
\(329\) 4.81563 + 1.75274i 0.265494 + 0.0966319i
\(330\) 0 0
\(331\) 0.140089 0.794483i 0.00769998 0.0436688i −0.980716 0.195440i \(-0.937387\pi\)
0.988416 + 0.151771i \(0.0484977\pi\)
\(332\) −5.70024 + 9.87311i −0.312842 + 0.541857i
\(333\) 0 0
\(334\) −3.05500 5.29141i −0.167162 0.289533i
\(335\) 19.1511 6.97044i 1.04634 0.380836i
\(336\) 0 0
\(337\) −20.4272 + 17.1404i −1.11274 + 0.933700i −0.998215 0.0597207i \(-0.980979\pi\)
−0.114525 + 0.993420i \(0.536535\pi\)
\(338\) −10.7475 + 9.01824i −0.584588 + 0.490527i
\(339\) 0 0
\(340\) −7.42755 + 2.70341i −0.402816 + 0.146613i
\(341\) 0.375596 + 0.650551i 0.0203396 + 0.0352293i
\(342\) 0 0
\(343\) 4.20838 7.28912i 0.227231 0.393576i
\(344\) −1.19757 + 6.79176i −0.0645687 + 0.366187i
\(345\) 0 0
\(346\) 10.6218 + 3.86602i 0.571032 + 0.207839i
\(347\) 5.05391 + 28.6621i 0.271308 + 1.53866i 0.750450 + 0.660927i \(0.229837\pi\)
−0.479142 + 0.877737i \(0.659052\pi\)
\(348\) 0 0
\(349\) −22.6355 18.9934i −1.21165 1.01669i −0.999219 0.0395179i \(-0.987418\pi\)
−0.212430 0.977176i \(-0.568138\pi\)
\(350\) −2.56856 −0.137295
\(351\) 0 0
\(352\) 0.212447 0.0113235
\(353\) −4.78974 4.01907i −0.254932 0.213913i 0.506361 0.862322i \(-0.330990\pi\)
−0.761293 + 0.648408i \(0.775435\pi\)
\(354\) 0 0
\(355\) −4.25094 24.1083i −0.225617 1.27954i
\(356\) 5.07082 + 1.84563i 0.268753 + 0.0978180i
\(357\) 0 0
\(358\) 1.20336 6.82462i 0.0635998 0.360692i
\(359\) −1.29314 + 2.23979i −0.0682495 + 0.118212i −0.898131 0.439728i \(-0.855075\pi\)
0.829881 + 0.557940i \(0.188408\pi\)
\(360\) 0 0
\(361\) 8.68998 + 15.0515i 0.457367 + 0.792183i
\(362\) 2.85444 1.03893i 0.150026 0.0546050i
\(363\) 0 0
\(364\) −15.9794 + 13.4083i −0.837546 + 0.702784i
\(365\) −1.20015 + 1.00705i −0.0628190 + 0.0527114i
\(366\) 0 0
\(367\) −17.5546 + 6.38935i −0.916342 + 0.333521i −0.756782 0.653667i \(-0.773230\pi\)
−0.159560 + 0.987188i \(0.551007\pi\)
\(368\) 0.414721 + 0.718318i 0.0216188 + 0.0374449i
\(369\) 0 0
\(370\) −3.71104 + 6.42770i −0.192928 + 0.334160i
\(371\) −7.87232 + 44.6462i −0.408711 + 2.31791i
\(372\) 0 0
\(373\) −12.7104 4.62621i −0.658120 0.239536i −0.00869564 0.999962i \(-0.502768\pi\)
−0.649425 + 0.760426i \(0.724990\pi\)
\(374\) −0.139652 0.792004i −0.00722122 0.0409536i
\(375\) 0 0
\(376\) −0.978448 0.821016i −0.0504596 0.0423406i
\(377\) −47.8894 −2.46643
\(378\) 0 0
\(379\) 30.2178 1.55218 0.776092 0.630620i \(-0.217199\pi\)
0.776092 + 0.630620i \(0.217199\pi\)
\(380\) 2.03588 + 1.70830i 0.104438 + 0.0876341i
\(381\) 0 0
\(382\) −0.885116 5.01974i −0.0452865 0.256832i
\(383\) −36.2619 13.1982i −1.85289 0.674398i −0.983670 0.179980i \(-0.942397\pi\)
−0.869224 0.494419i \(-0.835381\pi\)
\(384\) 0 0
\(385\) −0.309056 + 1.75274i −0.0157510 + 0.0893281i
\(386\) 9.43413 16.3404i 0.480185 0.831704i
\(387\) 0 0
\(388\) 6.28158 + 10.8800i 0.318899 + 0.552349i
\(389\) −5.28688 + 1.92427i −0.268056 + 0.0975642i −0.472551 0.881303i \(-0.656667\pi\)
0.204496 + 0.978867i \(0.434445\pi\)
\(390\) 0 0
\(391\) 2.40528 2.01827i 0.121640 0.102068i
\(392\) −6.96931 + 5.84795i −0.352003 + 0.295366i
\(393\) 0 0
\(394\) 18.8352 6.85544i 0.948901 0.345372i
\(395\) −2.47198 4.28160i −0.124379 0.215431i
\(396\) 0 0
\(397\) −3.85809 + 6.68240i −0.193632 + 0.335380i −0.946451 0.322847i \(-0.895360\pi\)
0.752819 + 0.658227i \(0.228693\pi\)
\(398\) −0.955433 + 5.41853i −0.0478915 + 0.271606i
\(399\) 0 0
\(400\) 0.601578 + 0.218956i 0.0300789 + 0.0109478i
\(401\) −6.31721 35.8267i −0.315466 1.78910i −0.569593 0.821927i \(-0.692899\pi\)
0.254126 0.967171i \(-0.418212\pi\)
\(402\) 0 0
\(403\) 14.0824 + 11.8165i 0.701494 + 0.588623i
\(404\) 2.89452 0.144008
\(405\) 0 0
\(406\) −36.9574 −1.83416
\(407\) −0.578489 0.485410i −0.0286746 0.0240609i
\(408\) 0 0
\(409\) 1.01891 + 5.77853i 0.0503819 + 0.285730i 0.999581 0.0289462i \(-0.00921516\pi\)
−0.949199 + 0.314676i \(0.898104\pi\)
\(410\) 5.37495 + 1.95632i 0.265450 + 0.0966159i
\(411\) 0 0
\(412\) 2.89819 16.4365i 0.142784 0.809766i
\(413\) 17.1719 29.7427i 0.844976 1.46354i
\(414\) 0 0
\(415\) 11.9022 + 20.6152i 0.584256 + 1.01196i
\(416\) 4.88549 1.77817i 0.239531 0.0871821i
\(417\) 0 0
\(418\) −0.207142 + 0.173812i −0.0101316 + 0.00850145i
\(419\) −16.1908 + 13.5857i −0.790972 + 0.663704i −0.945986 0.324208i \(-0.894902\pi\)
0.155014 + 0.987912i \(0.450458\pi\)
\(420\) 0 0
\(421\) −6.99405 + 2.54563i −0.340869 + 0.124066i −0.506782 0.862074i \(-0.669165\pi\)
0.165913 + 0.986140i \(0.446943\pi\)
\(422\) −12.5726 21.7763i −0.612023 1.06005i
\(423\) 0 0
\(424\) 5.64962 9.78544i 0.274370 0.475223i
\(425\) 0.420826 2.38662i 0.0204130 0.115768i
\(426\) 0 0
\(427\) 10.6837 + 3.88853i 0.517018 + 0.188179i
\(428\) −0.0558055 0.316489i −0.00269746 0.0152981i
\(429\) 0 0
\(430\) 11.0311 + 9.25619i 0.531967 + 0.446373i
\(431\) 13.0502 0.628607 0.314303 0.949323i \(-0.398229\pi\)
0.314303 + 0.949323i \(0.398229\pi\)
\(432\) 0 0
\(433\) 0.143533 0.00689775 0.00344887 0.999994i \(-0.498902\pi\)
0.00344887 + 0.999994i \(0.498902\pi\)
\(434\) 10.8677 + 9.11908i 0.521666 + 0.437730i
\(435\) 0 0
\(436\) 0.0986977 + 0.559743i 0.00472676 + 0.0268068i
\(437\) −0.992054 0.361078i −0.0474564 0.0172727i
\(438\) 0 0
\(439\) 2.35406 13.3506i 0.112353 0.637187i −0.875673 0.482904i \(-0.839582\pi\)
0.988027 0.154283i \(-0.0493069\pi\)
\(440\) 0.221796 0.384162i 0.0105737 0.0183142i
\(441\) 0 0
\(442\) −9.84052 17.0443i −0.468066 0.810714i
\(443\) 11.5406 4.20044i 0.548311 0.199569i −0.0529847 0.998595i \(-0.516873\pi\)
0.601296 + 0.799026i \(0.294651\pi\)
\(444\) 0 0
\(445\) 8.63138 7.24258i 0.409166 0.343331i
\(446\) 2.87450 2.41199i 0.136112 0.114211i
\(447\) 0 0
\(448\) 3.77024 1.37225i 0.178127 0.0648329i
\(449\) 20.3323 + 35.2165i 0.959540 + 1.66197i 0.723620 + 0.690199i \(0.242477\pi\)
0.235920 + 0.971772i \(0.424190\pi\)
\(450\) 0 0
\(451\) −0.290988 + 0.504006i −0.0137021 + 0.0237327i
\(452\) 0.236129 1.33916i 0.0111066 0.0629886i
\(453\) 0 0
\(454\) −17.5983 6.40524i −0.825928 0.300613i
\(455\) 7.56327 + 42.8934i 0.354571 + 2.01087i
\(456\) 0 0
\(457\) 24.9661 + 20.9491i 1.16787 + 0.979956i 0.999983 0.00585037i \(-0.00186224\pi\)
0.167884 + 0.985807i \(0.446307\pi\)
\(458\) 4.14333 0.193605
\(459\) 0 0
\(460\) 1.73189 0.0807498
\(461\) 20.9287 + 17.5612i 0.974745 + 0.817909i 0.983288 0.182055i \(-0.0582749\pi\)
−0.00854291 + 0.999964i \(0.502719\pi\)
\(462\) 0 0
\(463\) −0.590262 3.34754i −0.0274318 0.155574i 0.968015 0.250892i \(-0.0807240\pi\)
−0.995447 + 0.0953189i \(0.969613\pi\)
\(464\) 8.65573 + 3.15043i 0.401832 + 0.146255i
\(465\) 0 0
\(466\) −0.332903 + 1.88799i −0.0154214 + 0.0874593i
\(467\) 16.4988 28.5767i 0.763473 1.32237i −0.177577 0.984107i \(-0.556826\pi\)
0.941050 0.338267i \(-0.109841\pi\)
\(468\) 0 0
\(469\) 19.5807 + 33.9147i 0.904152 + 1.56604i
\(470\) −2.50613 + 0.912157i −0.115599 + 0.0420747i
\(471\) 0 0
\(472\) −6.55723 + 5.50217i −0.301821 + 0.253258i
\(473\) −1.12237 + 0.941778i −0.0516065 + 0.0433030i
\(474\) 0 0
\(475\) −0.765694 + 0.278690i −0.0351324 + 0.0127872i
\(476\) −7.59415 13.1534i −0.348077 0.602887i
\(477\) 0 0
\(478\) −12.0996 + 20.9572i −0.553424 + 0.958559i
\(479\) 4.00142 22.6932i 0.182830 1.03688i −0.745883 0.666077i \(-0.767972\pi\)
0.928712 0.370801i \(-0.120917\pi\)
\(480\) 0 0
\(481\) −17.3660 6.32070i −0.791820 0.288199i
\(482\) −2.29301 13.0043i −0.104444 0.592331i
\(483\) 0 0
\(484\) −8.39191 7.04165i −0.381451 0.320075i
\(485\) 26.2321 1.19114
\(486\) 0 0
\(487\) 26.9315 1.22038 0.610192 0.792254i \(-0.291092\pi\)
0.610192 + 0.792254i \(0.291092\pi\)
\(488\) −2.17073 1.82146i −0.0982641 0.0824534i
\(489\) 0 0
\(490\) 3.29868 + 18.7077i 0.149019 + 0.845129i
\(491\) −0.233037 0.0848187i −0.0105168 0.00382781i 0.336756 0.941592i \(-0.390670\pi\)
−0.347273 + 0.937764i \(0.612892\pi\)
\(492\) 0 0
\(493\) 6.05500 34.3396i 0.272703 1.54658i
\(494\) −3.30869 + 5.73081i −0.148865 + 0.257841i
\(495\) 0 0
\(496\) −1.76795 3.06218i −0.0793834 0.137496i
\(497\) 44.2028 16.0885i 1.98277 0.721668i
\(498\) 0 0
\(499\) −20.4674 + 17.1742i −0.916247 + 0.768822i −0.973297 0.229549i \(-0.926275\pi\)
0.0570505 + 0.998371i \(0.481830\pi\)
\(500\) 9.02155 7.56998i 0.403456 0.338540i
\(501\) 0 0
\(502\) 8.13762 2.96185i 0.363200 0.132194i
\(503\) 13.0871 + 22.6676i 0.583527 + 1.01070i 0.995057 + 0.0993022i \(0.0316611\pi\)
−0.411530 + 0.911396i \(0.635006\pi\)
\(504\) 0 0
\(505\) 3.02190 5.23409i 0.134473 0.232914i
\(506\) −0.0305989 + 0.173535i −0.00136029 + 0.00771458i
\(507\) 0 0
\(508\) −1.69522 0.617009i −0.0752132 0.0273754i
\(509\) −0.947739 5.37490i −0.0420078 0.238238i 0.956573 0.291492i \(-0.0941518\pi\)
−0.998581 + 0.0532542i \(0.983041\pi\)
\(510\) 0 0
\(511\) −2.30614 1.93508i −0.102018 0.0856031i
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) 21.8308 0.962914
\(515\) −26.6959 22.4005i −1.17636 0.987086i
\(516\) 0 0
\(517\) −0.0471199 0.267230i −0.00207233 0.0117528i
\(518\) −13.4017 4.87782i −0.588837 0.214319i
\(519\) 0 0
\(520\) 1.88506 10.6907i 0.0826656 0.468820i
\(521\) −13.0596 + 22.6199i −0.572151 + 0.990995i 0.424194 + 0.905572i \(0.360558\pi\)
−0.996345 + 0.0854234i \(0.972776\pi\)
\(522\) 0 0
\(523\) −3.70382 6.41521i −0.161957 0.280518i 0.773614 0.633658i \(-0.218447\pi\)
−0.935570 + 0.353140i \(0.885114\pi\)
\(524\) −9.12858 + 3.32253i −0.398784 + 0.145145i
\(525\) 0 0
\(526\) −4.35690 + 3.65587i −0.189970 + 0.159404i
\(527\) −10.2537 + 8.60387i −0.446658 + 0.374791i
\(528\) 0 0
\(529\) 20.9664 7.63116i 0.911585 0.331790i
\(530\) −11.7965 20.4322i −0.512408 0.887516i
\(531\) 0 0
\(532\) −2.55339 + 4.42259i −0.110703 + 0.191744i
\(533\) −2.47313 + 14.0258i −0.107123 + 0.607526i
\(534\) 0 0
\(535\) −0.630560 0.229505i −0.0272615 0.00992238i
\(536\) −1.69490 9.61227i −0.0732086 0.415187i
\(537\) 0 0
\(538\) −17.4399 14.6339i −0.751889 0.630910i
\(539\) −1.93280 −0.0832514
\(540\) 0 0
\(541\) 11.3209 0.486725 0.243362 0.969935i \(-0.421750\pi\)
0.243362 + 0.969935i \(0.421750\pi\)
\(542\) 15.1937 + 12.7490i 0.652625 + 0.547617i
\(543\) 0 0
\(544\) 0.657349 + 3.72801i 0.0281836 + 0.159837i
\(545\) 1.11521 + 0.405903i 0.0477704 + 0.0173870i
\(546\) 0 0
\(547\) −1.84721 + 10.4761i −0.0789811 + 0.447924i 0.919513 + 0.393060i \(0.128584\pi\)
−0.998494 + 0.0548639i \(0.982528\pi\)
\(548\) −4.53396 + 7.85305i −0.193681 + 0.335466i
\(549\) 0 0
\(550\) 0.0680027 + 0.117784i 0.00289964 + 0.00502233i
\(551\) −11.0171 + 4.00989i −0.469344 + 0.170827i
\(552\) 0 0
\(553\) 7.27744 6.10650i 0.309468 0.259675i
\(554\) 18.4899 15.5149i 0.785560 0.659163i
\(555\) 0 0
\(556\) 9.43533 3.43418i 0.400147 0.145642i
\(557\) −5.92385 10.2604i −0.251001 0.434747i 0.712800 0.701367i \(-0.247427\pi\)
−0.963802 + 0.266620i \(0.914093\pi\)
\(558\) 0 0
\(559\) −17.9276 + 31.0516i −0.758258 + 1.31334i
\(560\) 1.45475 8.25028i 0.0614743 0.348638i
\(561\) 0 0
\(562\) 22.2287 + 8.09058i 0.937661 + 0.341281i
\(563\) −1.04327 5.91667i −0.0439686 0.249358i 0.954899 0.296930i \(-0.0959628\pi\)
−0.998868 + 0.0475719i \(0.984852\pi\)
\(564\) 0 0
\(565\) −2.17504 1.82508i −0.0915047 0.0767815i
\(566\) 11.6242 0.488600
\(567\) 0 0
\(568\) −11.7241 −0.491934
\(569\) 22.3596 + 18.7619i 0.937363 + 0.786541i 0.977124 0.212669i \(-0.0682155\pi\)
−0.0397618 + 0.999209i \(0.512660\pi\)
\(570\) 0 0
\(571\) 3.78797 + 21.4826i 0.158522 + 0.899021i 0.955495 + 0.295007i \(0.0953219\pi\)
−0.796974 + 0.604014i \(0.793567\pi\)
\(572\) 1.03791 + 0.377767i 0.0433970 + 0.0157952i
\(573\) 0 0
\(574\) −1.90857 + 10.8240i −0.0796622 + 0.451787i
\(575\) −0.265499 + 0.459857i −0.0110721 + 0.0191774i
\(576\) 0 0
\(577\) −20.0399 34.7102i −0.834273 1.44500i −0.894621 0.446826i \(-0.852554\pi\)
0.0603476 0.998177i \(-0.480779\pi\)
\(578\) −2.50880 + 0.913130i −0.104353 + 0.0379812i
\(579\) 0 0
\(580\) 14.7335 12.3629i 0.611775 0.513340i
\(581\) −35.0397 + 29.4018i −1.45369 + 1.21979i
\(582\) 0 0
\(583\) 2.25572 0.821016i 0.0934224 0.0340030i
\(584\) 0.375162 + 0.649800i 0.0155243 + 0.0268889i
\(585\) 0 0
\(586\) 5.35546 9.27593i 0.221232 0.383185i
\(587\) 4.66518 26.4576i 0.192553 1.09202i −0.723309 0.690525i \(-0.757380\pi\)
0.915861 0.401495i \(-0.131509\pi\)
\(588\) 0 0
\(589\) 4.22912 + 1.53927i 0.174258 + 0.0634246i
\(590\) 3.10363 + 17.6016i 0.127775 + 0.724646i
\(591\) 0 0
\(592\) 2.72298 + 2.28485i 0.111914 + 0.0939070i
\(593\) −30.4609 −1.25088 −0.625440 0.780272i \(-0.715081\pi\)
−0.625440 + 0.780272i \(0.715081\pi\)
\(594\) 0 0
\(595\) −31.7134 −1.30012
\(596\) −12.1360 10.1833i −0.497110 0.417125i
\(597\) 0 0
\(598\) 0.748822 + 4.24678i 0.0306216 + 0.173664i
\(599\) −27.4285 9.98317i −1.12070 0.407901i −0.285792 0.958292i \(-0.592257\pi\)
−0.834908 + 0.550390i \(0.814479\pi\)
\(600\) 0 0
\(601\) −4.03243 + 22.8690i −0.164486 + 0.932847i 0.785106 + 0.619361i \(0.212608\pi\)
−0.949593 + 0.313487i \(0.898503\pi\)
\(602\) −13.8352 + 23.9632i −0.563879 + 0.976667i
\(603\) 0 0
\(604\) −2.65377 4.59647i −0.107981 0.187028i
\(605\) −21.4945 + 7.82335i −0.873875 + 0.318064i
\(606\) 0 0
\(607\) 32.6881 27.4286i 1.32677 1.11329i 0.341950 0.939718i \(-0.388913\pi\)
0.984821 0.173574i \(-0.0555317\pi\)
\(608\) 0.975029 0.818146i 0.0395426 0.0331802i
\(609\) 0 0
\(610\) −5.55995 + 2.02366i −0.225116 + 0.0819354i
\(611\) −3.32029 5.75091i −0.134325 0.232657i
\(612\) 0 0
\(613\) 6.80411 11.7851i 0.274815 0.475994i −0.695273 0.718746i \(-0.744717\pi\)
0.970089 + 0.242752i \(0.0780500\pi\)
\(614\) −4.30432 + 24.4110i −0.173708 + 0.985148i
\(615\) 0 0
\(616\) 0.800975 + 0.291531i 0.0322722 + 0.0117461i
\(617\) −4.88447 27.7012i −0.196641 1.11521i −0.910062 0.414472i \(-0.863966\pi\)
0.713421 0.700736i \(-0.247145\pi\)
\(618\) 0 0
\(619\) −14.9355 12.5323i −0.600307 0.503717i 0.291237 0.956651i \(-0.405933\pi\)
−0.891544 + 0.452934i \(0.850377\pi\)
\(620\) −7.38303 −0.296510
\(621\) 0 0
\(622\) −21.7835 −0.873439
\(623\) 16.5855 + 13.9169i 0.664485 + 0.557569i
\(624\) 0 0
\(625\) −3.71420 21.0643i −0.148568 0.842571i
\(626\) −8.83542 3.21583i −0.353135 0.128530i
\(627\) 0 0
\(628\) −1.99991 + 11.3421i −0.0798052 + 0.452598i
\(629\) 6.72802 11.6533i 0.268264 0.464646i
\(630\) 0 0
\(631\) −6.27471 10.8681i −0.249792 0.432653i 0.713676 0.700476i \(-0.247029\pi\)
−0.963468 + 0.267823i \(0.913696\pi\)
\(632\) −2.22499 + 0.809829i −0.0885052 + 0.0322133i
\(633\) 0 0
\(634\) −11.1121 + 9.32419i −0.441319 + 0.370311i
\(635\) −2.88555 + 2.42126i −0.114509 + 0.0960848i
\(636\) 0 0
\(637\) −44.4471 + 16.1774i −1.76106 + 0.640973i
\(638\) 0.978448 + 1.69472i 0.0387371 + 0.0670947i
\(639\) 0 0
\(640\) −1.04401 + 1.80828i −0.0412681 + 0.0714784i
\(641\) 2.42288 13.7409i 0.0956981 0.542731i −0.898833 0.438291i \(-0.855584\pi\)
0.994531 0.104440i \(-0.0333050\pi\)
\(642\) 0 0
\(643\) −38.5754 14.0403i −1.52127 0.553695i −0.559802 0.828627i \(-0.689123\pi\)
−0.961464 + 0.274931i \(0.911345\pi\)
\(644\) 0.577882 + 3.27733i 0.0227718 + 0.129145i
\(645\) 0 0
\(646\) −3.69099 3.09711i −0.145220 0.121854i
\(647\) −0.303995 −0.0119513 −0.00597563 0.999982i \(-0.501902\pi\)
−0.00597563 + 0.999982i \(0.501902\pi\)
\(648\) 0 0
\(649\) −1.81851 −0.0713829
\(650\) 2.54966 + 2.13942i 0.100006 + 0.0839149i
\(651\) 0 0
\(652\) 1.33073 + 7.54693i 0.0521153 + 0.295561i
\(653\) 44.2755 + 16.1150i 1.73263 + 0.630627i 0.998813 0.0487170i \(-0.0155132\pi\)
0.733820 + 0.679344i \(0.237735\pi\)
\(654\) 0 0
\(655\) −3.52226 + 19.9757i −0.137626 + 0.780516i
\(656\) 1.36970 2.37239i 0.0534777 0.0926261i
\(657\) 0 0
\(658\) −2.56234 4.43811i −0.0998905 0.173015i
\(659\) −40.3746 + 14.6952i −1.57277 + 0.572442i −0.973617 0.228190i \(-0.926719\pi\)
−0.599156 + 0.800633i \(0.704497\pi\)
\(660\) 0 0
\(661\) 21.0863 17.6935i 0.820161 0.688197i −0.132849 0.991136i \(-0.542412\pi\)
0.953010 + 0.302939i \(0.0979680\pi\)
\(662\) −0.617998 + 0.518562i −0.0240192 + 0.0201545i
\(663\) 0 0
\(664\) 10.7130 3.89920i 0.415743 0.151318i
\(665\) 5.33151 + 9.23445i 0.206747 + 0.358097i
\(666\) 0 0
\(667\) −3.82009 + 6.61659i −0.147915 + 0.256196i
\(668\) −1.06099 + 6.01717i −0.0410509 + 0.232811i
\(669\) 0 0
\(670\) −19.1511 6.97044i −0.739873 0.269292i
\(671\) −0.104537 0.592861i −0.00403562 0.0228871i
\(672\) 0 0
\(673\) −25.7719 21.6252i −0.993433 0.833589i −0.00737169 0.999973i \(-0.502347\pi\)
−0.986061 + 0.166384i \(0.946791\pi\)
\(674\) 26.6658 1.02713
\(675\) 0 0
\(676\) 14.0299 0.539611
\(677\) −26.1138 21.9120i −1.00363 0.842148i −0.0161497 0.999870i \(-0.505141\pi\)
−0.987484 + 0.157721i \(0.949585\pi\)
\(678\) 0 0
\(679\) 8.75290 + 49.6402i 0.335906 + 1.90502i
\(680\) 7.42755 + 2.70341i 0.284834 + 0.103671i
\(681\) 0 0
\(682\) 0.130443 0.739779i 0.00499492 0.0283276i
\(683\) −8.22650 + 14.2487i −0.314778 + 0.545212i −0.979390 0.201976i \(-0.935264\pi\)
0.664612 + 0.747189i \(0.268597\pi\)
\(684\) 0 0
\(685\) 9.46699 + 16.3973i 0.361715 + 0.626509i
\(686\) −7.90916 + 2.87870i −0.301973 + 0.109909i
\(687\) 0 0
\(688\) 5.28305 4.43301i 0.201414 0.169007i
\(689\) 45.0014 37.7606i 1.71442 1.43857i
\(690\) 0 0
\(691\) 13.4086 4.88033i 0.510087 0.185657i −0.0741383 0.997248i \(-0.523621\pi\)
0.584225 + 0.811591i \(0.301398\pi\)
\(692\) −5.65174 9.78911i −0.214847 0.372126i
\(693\) 0 0
\(694\) 14.5521 25.2051i 0.552392 0.956771i
\(695\) 3.64062 20.6470i 0.138097 0.783185i
\(696\) 0 0
\(697\) −9.74465 3.54676i −0.369105 0.134343i
\(698\) 5.13104 + 29.0996i 0.194213 + 1.10144i
\(699\) 0 0
\(700\) 1.96763 + 1.65104i 0.0743694 + 0.0624033i
\(701\) −15.8891 −0.600123 −0.300062 0.953920i \(-0.597007\pi\)
−0.300062 + 0.953920i \(0.597007\pi\)
\(702\) 0 0
\(703\) −4.52433 −0.170638
\(704\) −0.162744 0.136558i −0.00613363 0.00514673i
\(705\) 0 0
\(706\) 1.08575 + 6.15757i 0.0408626 + 0.231743i
\(707\) 10.9130 + 3.97202i 0.410427 + 0.149383i
\(708\) 0 0
\(709\) −1.43117 + 8.11659i −0.0537488 + 0.304825i −0.999817 0.0191436i \(-0.993906\pi\)
0.946068 + 0.323968i \(0.105017\pi\)
\(710\) −12.2401 + 21.2005i −0.459363 + 0.795640i
\(711\) 0 0
\(712\) −2.69813 4.67329i −0.101117 0.175139i
\(713\) 2.75596 1.00309i 0.103211 0.0375659i
\(714\) 0 0
\(715\) 1.76669 1.48243i 0.0660704 0.0554397i
\(716\) −5.30861 + 4.45445i −0.198392 + 0.166471i
\(717\) 0 0
\(718\) 2.43032 0.884563i 0.0906986 0.0330116i
\(719\) 10.9348 + 18.9397i 0.407801 + 0.706331i 0.994643 0.103370i \(-0.0329625\pi\)
−0.586842 + 0.809701i \(0.699629\pi\)
\(720\) 0 0
\(721\) 33.4819 57.9923i 1.24693 2.15975i
\(722\) 3.01800 17.1159i 0.112318 0.636988i
\(723\) 0 0
\(724\) −2.85444 1.03893i −0.106084 0.0386116i
\(725\) 1.02399 + 5.80731i 0.0380299 + 0.215678i
\(726\) 0 0
\(727\) 37.2742 + 31.2768i 1.38242 + 1.15999i 0.968305 + 0.249769i \(0.0803548\pi\)
0.414119 + 0.910223i \(0.364090\pi\)
\(728\) 20.8596 0.773107
\(729\) 0 0
\(730\) 1.56669 0.0579858
\(731\) −19.9991 16.7812i −0.739694 0.620677i
\(732\) 0 0
\(733\) −4.54580 25.7805i −0.167903 0.952226i −0.946020 0.324107i \(-0.894936\pi\)
0.778117 0.628119i \(-0.216175\pi\)
\(734\) 17.5546 + 6.38935i 0.647951 + 0.235835i
\(735\) 0 0
\(736\) 0.144031 0.816841i 0.00530906 0.0301092i
\(737\) 1.03680 1.79579i 0.0381910 0.0661487i
\(738\) 0 0
\(739\) −1.28655 2.22838i −0.0473267 0.0819722i 0.841392 0.540426i \(-0.181737\pi\)
−0.888718 + 0.458454i \(0.848404\pi\)
\(740\) 6.97447 2.53850i 0.256386 0.0933170i
\(741\) 0 0
\(742\) 34.7285 29.1407i 1.27493 1.06979i
\(743\) 37.5339 31.4947i 1.37699 1.15543i 0.406673 0.913574i \(-0.366689\pi\)
0.970313 0.241854i \(-0.0777555\pi\)
\(744\) 0 0
\(745\) −31.0843 + 11.3138i −1.13884 + 0.414505i
\(746\) 6.76307 + 11.7140i 0.247614 + 0.428879i
\(747\) 0 0
\(748\) −0.402111 + 0.696477i −0.0147026 + 0.0254657i
\(749\) 0.223903 1.26982i 0.00818124 0.0463981i
\(750\) 0 0
\(751\) −7.99761 2.91089i −0.291837 0.106220i 0.191953 0.981404i \(-0.438518\pi\)
−0.483790 + 0.875184i \(0.660740\pi\)
\(752\) 0.221796 + 1.25787i 0.00808808 + 0.0458698i
\(753\) 0 0
\(754\) 36.6854 + 30.7827i 1.33601 + 1.12104i
\(755\) −11.0822 −0.403324
\(756\) 0 0
\(757\) 17.3242 0.629658 0.314829 0.949148i \(-0.398053\pi\)
0.314829 + 0.949148i \(0.398053\pi\)
\(758\) −23.1482 19.4236i −0.840779 0.705497i
\(759\) 0 0
\(760\) −0.461496 2.61727i −0.0167402 0.0949384i
\(761\) 9.81674 + 3.57300i 0.355856 + 0.129521i 0.513761 0.857933i \(-0.328252\pi\)
−0.157905 + 0.987454i \(0.550474\pi\)
\(762\) 0 0
\(763\) −0.395996 + 2.24580i −0.0143360 + 0.0813035i
\(764\) −2.54859 + 4.41429i −0.0922047 + 0.159703i
\(765\) 0 0
\(766\) 19.2945 + 33.4191i 0.697140 + 1.20748i
\(767\) −41.8191 + 15.2209i −1.51000 + 0.549595i
\(768\) 0 0
\(769\) 30.2202 25.3577i 1.08977 0.914423i 0.0930721 0.995659i \(-0.470331\pi\)
0.996695 + 0.0812363i \(0.0258868\pi\)
\(770\) 1.36339 1.14402i 0.0491333 0.0412277i
\(771\) 0 0
\(772\) −17.7304 + 6.45333i −0.638130 + 0.232260i
\(773\) −11.6713 20.2152i −0.419786 0.727091i 0.576131 0.817357i \(-0.304562\pi\)
−0.995918 + 0.0902659i \(0.971228\pi\)
\(774\) 0 0
\(775\) 1.13182 1.96037i 0.0406561 0.0704184i
\(776\) 2.18157 12.3723i 0.0783138 0.444140i
\(777\) 0 0
\(778\) 5.28688 + 1.92427i 0.189544 + 0.0689883i
\(779\) 0.605464 + 3.43376i 0.0216930 + 0.123027i
\(780\) 0 0
\(781\) −1.90803 1.60103i −0.0682747 0.0572893i
\(782\) −3.13987 −0.112282
\(783\) 0 0
\(784\) 9.09779 0.324921
\(785\) 18.4216 + 15.4576i 0.657497 + 0.551705i
\(786\) 0 0
\(787\) 6.57945 + 37.3139i 0.234532 + 1.33010i 0.843597 + 0.536977i \(0.180434\pi\)
−0.609065 + 0.793120i \(0.708455\pi\)
\(788\) −18.8352 6.85544i −0.670975 0.244215i
\(789\) 0 0
\(790\) −0.858511 + 4.86886i −0.0305444 + 0.173226i
\(791\) 2.72793 4.72491i 0.0969939 0.167998i
\(792\) 0 0
\(793\) −7.36619 12.7586i −0.261581 0.453072i
\(794\) 7.25083 2.63909i 0.257322 0.0936577i
\(795\) 0 0
\(796\) 4.21487 3.53670i 0.149392 0.125355i
\(797\) 2.07175 1.73841i 0.0733853 0.0615776i −0.605357 0.795954i \(-0.706970\pi\)
0.678742 + 0.734376i \(0.262525\pi\)
\(798\) 0 0
\(799\) 4.54355 1.65372i 0.160739 0.0585043i
\(800\) −0.320093 0.554417i −0.0113170 0.0196016i
\(801\) 0 0
\(802\) −18.1897 + 31.5054i −0.642300 + 1.11250i
\(803\) −0.0276802 + 0.156982i −0.000976814 + 0.00553979i
\(804\) 0 0
\(805\) 6.52964 + 2.37659i 0.230139 + 0.0837639i
\(806\) −3.19222 18.1040i −0.112441 0.637685i
\(807\) 0 0
\(808\) −2.21733 1.86056i −0.0780055 0.0654544i
\(809\) 22.3977 0.787460 0.393730 0.919226i \(-0.371185\pi\)
0.393730 + 0.919226i \(0.371185\pi\)
\(810\) 0 0
\(811\) −35.0916 −1.23223 −0.616117 0.787655i \(-0.711295\pi\)
−0.616117 + 0.787655i \(0.711295\pi\)
\(812\) 28.3110 + 23.7557i 0.993520 + 0.833663i
\(813\) 0 0
\(814\) 0.131133 + 0.743691i 0.00459620 + 0.0260664i
\(815\) 15.0362 + 5.47274i 0.526696 + 0.191702i
\(816\) 0 0
\(817\) −1.52428 + 8.64462i −0.0533278 + 0.302437i
\(818\) 2.93384 5.08156i 0.102579 0.177672i
\(819\) 0 0
\(820\) −2.85995 4.95358i −0.0998739 0.172987i
\(821\) 13.3135 4.84571i 0.464644 0.169117i −0.0990807 0.995079i \(-0.531590\pi\)
0.563724 + 0.825963i \(0.309368\pi\)
\(822\) 0 0
\(823\) −26.5050 + 22.2404i −0.923907 + 0.775250i −0.974713 0.223458i \(-0.928265\pi\)
0.0508063 + 0.998709i \(0.483821\pi\)
\(824\) −12.7853 + 10.7281i −0.445397 + 0.373732i
\(825\) 0 0
\(826\) −32.2727 + 11.7463i −1.12291 + 0.408706i
\(827\) 25.3847 + 43.9676i 0.882713 + 1.52890i 0.848312 + 0.529496i \(0.177619\pi\)
0.0344011 + 0.999408i \(0.489048\pi\)
\(828\) 0 0
\(829\) −27.2911 + 47.2695i −0.947859 + 1.64174i −0.197935 + 0.980215i \(0.563423\pi\)
−0.749924 + 0.661524i \(0.769910\pi\)
\(830\) 4.13359 23.4428i 0.143479 0.813710i
\(831\) 0 0
\(832\) −4.88549 1.77817i −0.169374 0.0616470i
\(833\) −5.98042 33.9167i −0.207209 1.17514i
\(834\) 0 0
\(835\) 9.77302 + 8.20053i 0.338209 + 0.283791i
\(836\) 0.270404 0.00935213
\(837\) 0 0
\(838\) 21.1356 0.730117
\(839\) 8.48661 + 7.12111i 0.292990 + 0.245848i 0.777420 0.628982i \(-0.216528\pi\)
−0.484429 + 0.874830i \(0.660973\pi\)
\(840\) 0 0
\(841\) 9.69769 + 54.9984i 0.334403 + 1.89650i
\(842\) 6.99405 + 2.54563i 0.241031 + 0.0877281i
\(843\) 0 0
\(844\) −4.36641 + 24.7631i −0.150298 + 0.852382i
\(845\) 14.6473 25.3699i 0.503883 0.872751i
\(846\) 0 0
\(847\) −21.9766 38.0646i −0.755124 1.30791i
\(848\) −10.6178 + 3.86457i −0.364617 + 0.132710i
\(849\) 0 0
\(850\) −1.85646 + 1.55776i −0.0636761 + 0.0534306i
\(851\) −2.25856 + 1.89516i −0.0774224 + 0.0649651i
\(852\) 0 0
\(853\) 23.9039 8.70031i 0.818454 0.297893i 0.101343 0.994852i \(-0.467686\pi\)
0.717111 + 0.696959i \(0.245464\pi\)
\(854\) −5.68465 9.84611i −0.194525 0.336927i
\(855\) 0 0
\(856\) −0.160686 + 0.278316i −0.00549212 + 0.00951263i
\(857\) −8.19583 + 46.4809i −0.279964 + 1.58776i 0.442773 + 0.896634i \(0.353995\pi\)
−0.722738 + 0.691123i \(0.757116\pi\)
\(858\) 0 0
\(859\) 23.0571 + 8.39211i 0.786699 + 0.286335i 0.703963 0.710236i \(-0.251412\pi\)
0.0827360 + 0.996571i \(0.473634\pi\)
\(860\) −2.50055 14.1813i −0.0852680 0.483579i
\(861\) 0 0
\(862\) −9.99704 8.38851i −0.340501 0.285714i
\(863\) −28.4215 −0.967479 −0.483740 0.875212i \(-0.660722\pi\)
−0.483740 + 0.875212i \(0.660722\pi\)
\(864\) 0 0
\(865\) −23.6019 −0.802488
\(866\) −0.109953 0.0922611i −0.00373634 0.00313516i
\(867\) 0 0
\(868\) −2.46351 13.9712i −0.0836169 0.474215i
\(869\) −0.472691 0.172045i −0.0160349 0.00583624i
\(870\) 0 0
\(871\) 8.81185 49.9745i 0.298578 1.69332i
\(872\) 0.284189 0.492229i 0.00962385 0.0166690i
\(873\) 0 0
\(874\) 0.527861 + 0.914282i 0.0178552 + 0.0309261i
\(875\) 44.4014 16.1608i 1.50104 0.546334i
\(876\) 0 0
\(877\) 33.1323 27.8013i 1.11880 0.938784i 0.120256 0.992743i \(-0.461628\pi\)
0.998543 + 0.0539587i \(0.0171839\pi\)
\(878\) −10.3849 + 8.71396i −0.350473 + 0.294082i
\(879\) 0 0
\(880\) −0.416841 + 0.151718i −0.0140517 + 0.00511440i
\(881\) −10.2218 17.7047i −0.344381 0.596485i 0.640860 0.767658i \(-0.278578\pi\)
−0.985241 + 0.171173i \(0.945244\pi\)
\(882\) 0 0
\(883\) 14.1469 24.5031i 0.476080 0.824595i −0.523544 0.851999i \(-0.675391\pi\)
0.999624 + 0.0274033i \(0.00872385\pi\)
\(884\) −3.41758 + 19.3820i −0.114946 + 0.651889i
\(885\) 0 0
\(886\) −11.5406 4.20044i −0.387715 0.141117i
\(887\) 9.97456 + 56.5686i 0.334913 + 1.89939i 0.428088 + 0.903737i \(0.359187\pi\)
−0.0931752 + 0.995650i \(0.529702\pi\)
\(888\) 0 0
\(889\) −5.54469 4.65255i −0.185963 0.156041i
\(890\) −11.2675 −0.377686
\(891\) 0 0
\(892\) −3.75239 −0.125639
\(893\) −1.24538 1.04500i −0.0416750 0.0349695i
\(894\) 0 0
\(895\) 2.51264 + 14.2499i 0.0839885 + 0.476322i
\(896\) −3.77024 1.37225i −0.125955 0.0458438i
\(897\) 0 0
\(898\) 7.06133 40.0468i 0.235640 1.33638i
\(899\) 16.2850 28.2065i 0.543136 0.940739i
\(900\) 0 0
\(901\) 21.3868 + 37.0430i 0.712497 + 1.23408i
\(902\) 0.546878 0.199047i 0.0182091 0.00662755i
\(903\) 0 0
\(904\) −1.04168 + 0.874072i −0.0346457 + 0.0290712i
\(905\) −4.85873 + 4.07696i −0.161510 + 0.135523i
\(906\) 0 0
\(907\) 26.7707 9.74375i 0.888908 0.323536i 0.143109 0.989707i \(-0.454290\pi\)
0.745799 + 0.666171i \(0.232068\pi\)
\(908\) 9.36384 + 16.2186i 0.310750 + 0.538235i
\(909\) 0 0
\(910\) 21.7776 37.7198i 0.721919 1.25040i
\(911\) 3.29560 18.6903i 0.109188 0.619236i −0.880277 0.474461i \(-0.842643\pi\)
0.989465 0.144775i \(-0.0462459\pi\)
\(912\) 0 0
\(913\) 2.27593 + 0.828372i 0.0753224 + 0.0274151i
\(914\) −5.65936 32.0958i −0.187195 1.06164i
\(915\) 0 0
\(916\) −3.17397 2.66328i −0.104871 0.0879972i
\(917\) −38.9763 −1.28711
\(918\) 0 0
\(919\) −13.1481 −0.433715 −0.216857 0.976203i \(-0.569581\pi\)
−0.216857 + 0.976203i \(0.569581\pi\)
\(920\) −1.32670 1.11324i −0.0437401 0.0367023i
\(921\) 0 0
\(922\) −4.74414 26.9054i −0.156240 0.886082i
\(923\) −57.2782 20.8475i −1.88533 0.686205i
\(924\) 0 0
\(925\) −0.395155 + 2.24103i −0.0129926 + 0.0736848i
\(926\) −1.69959 + 2.94378i −0.0558521 + 0.0967386i
\(927\) 0 0
\(928\) −4.60562 7.97716i −0.151187 0.261863i
\(929\) 25.7306 9.36519i 0.844195 0.307262i 0.116524 0.993188i \(-0.462825\pi\)
0.727671 + 0.685926i \(0.240603\pi\)
\(930\) 0 0
\(931\) −8.87060 + 7.44332i −0.290722 + 0.243945i
\(932\) 1.46859 1.23230i 0.0481053 0.0403652i
\(933\) 0 0
\(934\) −31.0076 + 11.2858i −1.01460 + 0.369284i
\(935\) 0.839615 + 1.45426i 0.0274583 + 0.0475592i
\(936\) 0 0
\(937\) −20.0466 + 34.7218i −0.654895 + 1.13431i 0.327025 + 0.945016i \(0.393954\pi\)
−0.981920 + 0.189296i \(0.939380\pi\)
\(938\) 6.80030 38.5664i 0.222038 1.25924i
\(939\) 0 0
\(940\) 2.50613 + 0.912157i 0.0817410 + 0.0297513i
\(941\) 0.591978 + 3.35727i 0.0192979 + 0.109444i 0.992935 0.118658i \(-0.0378592\pi\)
−0.973637 + 0.228102i \(0.926748\pi\)
\(942\) 0 0
\(943\) 1.74058 + 1.46052i 0.0566812 + 0.0475612i
\(944\) 8.55985 0.278600
\(945\) 0 0
\(946\) 1.46515 0.0476360
\(947\) −2.93783 2.46513i −0.0954666 0.0801060i 0.593805 0.804609i \(-0.297625\pi\)
−0.689272 + 0.724503i \(0.742069\pi\)
\(948\) 0 0
\(949\) 0.677394 + 3.84169i 0.0219892 + 0.124707i
\(950\) 0.765694 + 0.278690i 0.0248424 + 0.00904189i
\(951\) 0 0
\(952\) −2.63742 + 14.9576i −0.0854793 + 0.484777i
\(953\) −26.3964 + 45.7200i −0.855065 + 1.48102i 0.0215205 + 0.999768i \(0.493149\pi\)
−0.876585 + 0.481247i \(0.840184\pi\)
\(954\) 0 0
\(955\) 5.32150 + 9.21711i 0.172200 + 0.298259i
\(956\) 22.7399 8.27664i 0.735460 0.267686i
\(957\) 0 0
\(958\) −17.6522 + 14.8119i −0.570316 + 0.478552i
\(959\) −27.8705 + 23.3861i −0.899986 + 0.755178i
\(960\) 0 0
\(961\) 17.3819 6.32648i 0.560705 0.204080i
\(962\) 9.24024 + 16.0046i 0.297917 + 0.516008i
\(963\) 0 0
\(964\) −6.60247 + 11.4358i −0.212651 + 0.368323i
\(965\) −6.84126 + 38.7987i −0.220228 + 1.24898i
\(966\) 0 0
\(967\) −9.43802 3.43516i −0.303506 0.110467i 0.185778 0.982592i \(-0.440520\pi\)
−0.489284 + 0.872125i \(0.662742\pi\)
\(968\) 1.90229 + 10.7884i 0.0611420 + 0.346754i
\(969\) 0 0
\(970\) −20.0949 16.8617i −0.645210 0.541395i
\(971\) −4.06174 −0.130348 −0.0651738 0.997874i \(-0.520760\pi\)
−0.0651738 + 0.997874i \(0.520760\pi\)
\(972\) 0 0
\(973\) 40.2860 1.29151
\(974\) −20.6307 17.3113i −0.661052 0.554688i
\(975\) 0 0
\(976\) 0.492064 + 2.79063i 0.0157506 + 0.0893259i
\(977\) 17.1297 + 6.23470i 0.548027 + 0.199466i 0.601170 0.799121i \(-0.294702\pi\)
−0.0531425 + 0.998587i \(0.516924\pi\)
\(978\) 0 0
\(979\) 0.199073 1.12900i 0.00636240 0.0360830i
\(980\) 9.49817 16.4513i 0.303408 0.525518i
\(981\) 0 0
\(982\) 0.123997 + 0.214768i 0.00395689 + 0.00685354i
\(983\) −39.5076 + 14.3796i −1.26010 + 0.458638i −0.883802 0.467862i \(-0.845025\pi\)
−0.376296 + 0.926500i \(0.622802\pi\)
\(984\) 0 0
\(985\) −32.0606 + 26.9020i −1.02153 + 0.857170i
\(986\) −26.7115 + 22.4136i −0.850666 + 0.713794i
\(987\) 0 0
\(988\) 6.21829 2.26327i 0.197830 0.0720043i
\(989\) 2.86014 + 4.95391i 0.0909471 + 0.157525i
\(990\) 0 0
\(991\) 15.9365 27.6029i 0.506241 0.876834i −0.493733 0.869613i \(-0.664368\pi\)
0.999974 0.00722097i \(-0.00229853\pi\)
\(992\) −0.614003 + 3.48219i −0.0194946 + 0.110560i
\(993\) 0 0
\(994\) −44.2028 16.0885i −1.40203 0.510297i
\(995\) −1.99496 11.3140i −0.0632445 0.358677i
\(996\) 0 0
\(997\) −24.5132 20.5690i −0.776342 0.651428i 0.165983 0.986129i \(-0.446920\pi\)
−0.942324 + 0.334701i \(0.891365\pi\)
\(998\) 26.7183 0.845753
\(999\) 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 162.2.e.b.127.2 12
3.2 odd 2 54.2.e.b.43.2 12
9.2 odd 6 486.2.e.f.217.2 12
9.4 even 3 486.2.e.e.55.1 12
9.5 odd 6 486.2.e.h.55.2 12
9.7 even 3 486.2.e.g.217.1 12
12.11 even 2 432.2.u.b.97.1 12
27.2 odd 18 1458.2.c.f.973.3 12
27.4 even 9 486.2.e.g.271.1 12
27.5 odd 18 54.2.e.b.49.2 yes 12
27.7 even 9 1458.2.a.f.1.3 6
27.11 odd 18 1458.2.c.f.487.3 12
27.13 even 9 486.2.e.e.433.1 12
27.14 odd 18 486.2.e.h.433.2 12
27.16 even 9 1458.2.c.g.487.4 12
27.20 odd 18 1458.2.a.g.1.4 6
27.22 even 9 inner 162.2.e.b.37.2 12
27.23 odd 18 486.2.e.f.271.2 12
27.25 even 9 1458.2.c.g.973.4 12
108.59 even 18 432.2.u.b.49.1 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
54.2.e.b.43.2 12 3.2 odd 2
54.2.e.b.49.2 yes 12 27.5 odd 18
162.2.e.b.37.2 12 27.22 even 9 inner
162.2.e.b.127.2 12 1.1 even 1 trivial
432.2.u.b.49.1 12 108.59 even 18
432.2.u.b.97.1 12 12.11 even 2
486.2.e.e.55.1 12 9.4 even 3
486.2.e.e.433.1 12 27.13 even 9
486.2.e.f.217.2 12 9.2 odd 6
486.2.e.f.271.2 12 27.23 odd 18
486.2.e.g.217.1 12 9.7 even 3
486.2.e.g.271.1 12 27.4 even 9
486.2.e.h.55.2 12 9.5 odd 6
486.2.e.h.433.2 12 27.14 odd 18
1458.2.a.f.1.3 6 27.7 even 9
1458.2.a.g.1.4 6 27.20 odd 18
1458.2.c.f.487.3 12 27.11 odd 18
1458.2.c.f.973.3 12 27.2 odd 18
1458.2.c.g.487.4 12 27.16 even 9
1458.2.c.g.973.4 12 27.25 even 9