Properties

Label 675.2.r.a.46.3
Level $675$
Weight $2$
Character 675.46
Analytic conductor $5.390$
Analytic rank $0$
Dimension $224$
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] = [675,2,Mod(46,675)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(675, base_ring=CyclotomicField(30))
 
chi = DirichletCharacter(H, H._module([20, 18]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("675.46");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 675 = 3^{3} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 675.r (of order \(15\), degree \(8\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(5.38990213644\)
Analytic rank: \(0\)
Dimension: \(224\)
Relative dimension: \(28\) over \(\Q(\zeta_{15})\)
Twist minimal: no (minimal twist has level 225)
Sato-Tate group: $\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label 46.3
Character \(\chi\) \(=\) 675.46
Dual form 675.2.r.a.631.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.64688 - 1.82905i) q^{2} +(-0.424138 + 4.03540i) q^{4} +(-0.681844 - 2.12957i) q^{5} +(2.55879 - 4.43196i) q^{7} +(4.09710 - 2.97672i) q^{8} +O(q^{10})\) \(q+(-1.64688 - 1.82905i) q^{2} +(-0.424138 + 4.03540i) q^{4} +(-0.681844 - 2.12957i) q^{5} +(2.55879 - 4.43196i) q^{7} +(4.09710 - 2.97672i) q^{8} +(-2.77218 + 4.75428i) q^{10} +(1.05935 + 1.17653i) q^{11} +(0.596899 - 0.662924i) q^{13} +(-12.3203 + 2.61876i) q^{14} +(-4.25406 - 0.904229i) q^{16} +(3.04259 - 2.21057i) q^{17} +(3.69404 - 2.68388i) q^{19} +(8.88289 - 1.84828i) q^{20} +(0.407301 - 3.87521i) q^{22} +(5.36085 - 1.13948i) q^{23} +(-4.07018 + 2.90407i) q^{25} -2.19554 q^{26} +(16.7994 + 12.2055i) q^{28} +(0.0385420 - 0.0171600i) q^{29} +(1.79980 + 0.801323i) q^{31} +(0.287768 + 0.498429i) q^{32} +(-9.05401 - 1.92449i) q^{34} +(-11.1829 - 2.42724i) q^{35} +(-1.43995 - 4.43171i) q^{37} +(-10.9926 - 2.33655i) q^{38} +(-9.13272 - 6.69542i) q^{40} +(-0.511798 + 0.568409i) q^{41} +(-4.11709 + 7.13101i) q^{43} +(-5.19708 + 3.77590i) q^{44} +(-10.9129 - 7.92865i) q^{46} +(-3.72722 + 1.65947i) q^{47} +(-9.59482 - 16.6187i) q^{49} +(12.0148 + 2.66188i) q^{50} +(2.42200 + 2.68990i) q^{52} +(2.00012 + 1.45317i) q^{53} +(1.78319 - 3.05818i) q^{55} +(-2.70906 - 25.7749i) q^{56} +(-0.0948606 - 0.0422347i) q^{58} +(-6.37293 + 7.07785i) q^{59} +(-4.84864 - 5.38496i) q^{61} +(-1.49840 - 4.61160i) q^{62} +(-2.25016 + 6.92529i) q^{64} +(-1.81874 - 0.819131i) q^{65} +(3.28565 + 1.46287i) q^{67} +(7.63006 + 13.2156i) q^{68} +(13.9773 + 24.4514i) q^{70} +(1.57130 + 1.14162i) q^{71} +(-4.42033 + 13.6044i) q^{73} +(-5.73438 + 9.93224i) q^{74} +(9.26375 + 16.0453i) q^{76} +(7.92498 - 1.68451i) q^{77} +(3.10949 - 1.38443i) q^{79} +(0.974982 + 9.67589i) q^{80} +1.88252 q^{82} +(-0.405949 - 3.86235i) q^{83} +(-6.78214 - 4.97215i) q^{85} +(19.8233 - 4.21357i) q^{86} +(7.84246 + 1.66697i) q^{88} +(0.935601 - 2.87948i) q^{89} +(-1.41071 - 4.34171i) q^{91} +(2.32454 + 22.1165i) q^{92} +(9.17353 + 4.08432i) q^{94} +(-8.23428 - 6.03676i) q^{95} +(-4.75481 + 2.11698i) q^{97} +(-14.5949 + 44.9184i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 224 q + 3 q^{2} + 23 q^{4} + 8 q^{5} - 8 q^{7} + 20 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 224 q + 3 q^{2} + 23 q^{4} + 8 q^{5} - 8 q^{7} + 20 q^{8} - 20 q^{10} + 11 q^{11} - 3 q^{13} - q^{14} + 23 q^{16} + 24 q^{17} - 12 q^{19} - q^{20} - 11 q^{22} - q^{23} - 16 q^{25} + 136 q^{26} + 4 q^{28} + 15 q^{29} + 3 q^{31} - 12 q^{32} + q^{34} - 14 q^{35} - 24 q^{37} - 55 q^{38} + q^{40} + 19 q^{41} - 8 q^{43} - 4 q^{44} - 20 q^{46} + 10 q^{47} - 72 q^{49} + 3 q^{50} - 25 q^{52} + 12 q^{53} - 20 q^{55} + 60 q^{56} - 23 q^{58} + 30 q^{59} - 3 q^{61} + 44 q^{62} - 44 q^{64} - 51 q^{65} - 12 q^{67} + 156 q^{68} - 16 q^{70} - 42 q^{71} - 12 q^{73} - 90 q^{74} - 8 q^{76} - 31 q^{77} - 15 q^{79} - 298 q^{80} + 8 q^{82} - 59 q^{83} - 11 q^{85} - 9 q^{86} - 23 q^{88} - 106 q^{89} + 30 q^{91} - 11 q^{92} + 25 q^{94} - 7 q^{95} - 21 q^{97} - 146 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/675\mathbb{Z}\right)^\times\).

\(n\) \(326\) \(352\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{3}{5}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.64688 1.82905i −1.16452 1.29333i −0.948440 0.316956i \(-0.897339\pi\)
−0.216081 0.976376i \(-0.569327\pi\)
\(3\) 0 0
\(4\) −0.424138 + 4.03540i −0.212069 + 2.01770i
\(5\) −0.681844 2.12957i −0.304930 0.952375i
\(6\) 0 0
\(7\) 2.55879 4.43196i 0.967132 1.67512i 0.263357 0.964698i \(-0.415170\pi\)
0.703775 0.710423i \(-0.251496\pi\)
\(8\) 4.09710 2.97672i 1.44854 1.05243i
\(9\) 0 0
\(10\) −2.77218 + 4.75428i −0.876639 + 1.50344i
\(11\) 1.05935 + 1.17653i 0.319406 + 0.354737i 0.881371 0.472424i \(-0.156621\pi\)
−0.561965 + 0.827161i \(0.689954\pi\)
\(12\) 0 0
\(13\) 0.596899 0.662924i 0.165550 0.183862i −0.654662 0.755922i \(-0.727189\pi\)
0.820212 + 0.572060i \(0.193856\pi\)
\(14\) −12.3203 + 2.61876i −3.29273 + 0.699892i
\(15\) 0 0
\(16\) −4.25406 0.904229i −1.06352 0.226057i
\(17\) 3.04259 2.21057i 0.737936 0.536142i −0.154128 0.988051i \(-0.549257\pi\)
0.892064 + 0.451909i \(0.149257\pi\)
\(18\) 0 0
\(19\) 3.69404 2.68388i 0.847472 0.615724i −0.0769761 0.997033i \(-0.524527\pi\)
0.924448 + 0.381309i \(0.124527\pi\)
\(20\) 8.88289 1.84828i 1.98627 0.413288i
\(21\) 0 0
\(22\) 0.407301 3.87521i 0.0868368 0.826197i
\(23\) 5.36085 1.13948i 1.11781 0.237599i 0.388279 0.921542i \(-0.373070\pi\)
0.729536 + 0.683943i \(0.239736\pi\)
\(24\) 0 0
\(25\) −4.07018 + 2.90407i −0.814036 + 0.580815i
\(26\) −2.19554 −0.430581
\(27\) 0 0
\(28\) 16.7994 + 12.2055i 3.17480 + 2.30662i
\(29\) 0.0385420 0.0171600i 0.00715708 0.00318654i −0.403155 0.915132i \(-0.632086\pi\)
0.410312 + 0.911945i \(0.365420\pi\)
\(30\) 0 0
\(31\) 1.79980 + 0.801323i 0.323254 + 0.143922i 0.561947 0.827173i \(-0.310052\pi\)
−0.238693 + 0.971095i \(0.576719\pi\)
\(32\) 0.287768 + 0.498429i 0.0508707 + 0.0881106i
\(33\) 0 0
\(34\) −9.05401 1.92449i −1.55275 0.330047i
\(35\) −11.1829 2.42724i −1.89025 0.410278i
\(36\) 0 0
\(37\) −1.43995 4.43171i −0.236726 0.728569i −0.996888 0.0788345i \(-0.974880\pi\)
0.760161 0.649734i \(-0.225120\pi\)
\(38\) −10.9926 2.33655i −1.78323 0.379038i
\(39\) 0 0
\(40\) −9.13272 6.69542i −1.44401 1.05864i
\(41\) −0.511798 + 0.568409i −0.0799294 + 0.0887706i −0.781783 0.623551i \(-0.785689\pi\)
0.701853 + 0.712321i \(0.252356\pi\)
\(42\) 0 0
\(43\) −4.11709 + 7.13101i −0.627850 + 1.08747i 0.360132 + 0.932901i \(0.382732\pi\)
−0.987982 + 0.154567i \(0.950602\pi\)
\(44\) −5.19708 + 3.77590i −0.783489 + 0.569238i
\(45\) 0 0
\(46\) −10.9129 7.92865i −1.60901 1.16902i
\(47\) −3.72722 + 1.65947i −0.543671 + 0.242058i −0.660148 0.751135i \(-0.729507\pi\)
0.116477 + 0.993193i \(0.462840\pi\)
\(48\) 0 0
\(49\) −9.59482 16.6187i −1.37069 2.37410i
\(50\) 12.0148 + 2.66188i 1.69915 + 0.376447i
\(51\) 0 0
\(52\) 2.42200 + 2.68990i 0.335870 + 0.373022i
\(53\) 2.00012 + 1.45317i 0.274737 + 0.199608i 0.716619 0.697465i \(-0.245689\pi\)
−0.441882 + 0.897073i \(0.645689\pi\)
\(54\) 0 0
\(55\) 1.78319 3.05818i 0.240446 0.412364i
\(56\) −2.70906 25.7749i −0.362013 3.44432i
\(57\) 0 0
\(58\) −0.0948606 0.0422347i −0.0124558 0.00554568i
\(59\) −6.37293 + 7.07785i −0.829684 + 0.921458i −0.997931 0.0642869i \(-0.979523\pi\)
0.168247 + 0.985745i \(0.446189\pi\)
\(60\) 0 0
\(61\) −4.84864 5.38496i −0.620805 0.689474i 0.347944 0.937515i \(-0.386880\pi\)
−0.968749 + 0.248041i \(0.920213\pi\)
\(62\) −1.49840 4.61160i −0.190297 0.585674i
\(63\) 0 0
\(64\) −2.25016 + 6.92529i −0.281270 + 0.865661i
\(65\) −1.81874 0.819131i −0.225587 0.101601i
\(66\) 0 0
\(67\) 3.28565 + 1.46287i 0.401406 + 0.178717i 0.597502 0.801867i \(-0.296160\pi\)
−0.196096 + 0.980585i \(0.562827\pi\)
\(68\) 7.63006 + 13.2156i 0.925280 + 1.60263i
\(69\) 0 0
\(70\) 13.9773 + 24.4514i 1.67061 + 2.92250i
\(71\) 1.57130 + 1.14162i 0.186479 + 0.135485i 0.677108 0.735884i \(-0.263233\pi\)
−0.490629 + 0.871369i \(0.663233\pi\)
\(72\) 0 0
\(73\) −4.42033 + 13.6044i −0.517361 + 1.59227i 0.261584 + 0.965181i \(0.415755\pi\)
−0.778945 + 0.627093i \(0.784245\pi\)
\(74\) −5.73438 + 9.93224i −0.666608 + 1.15460i
\(75\) 0 0
\(76\) 9.26375 + 16.0453i 1.06262 + 1.84052i
\(77\) 7.92498 1.68451i 0.903135 0.191967i
\(78\) 0 0
\(79\) 3.10949 1.38443i 0.349844 0.155761i −0.224289 0.974523i \(-0.572006\pi\)
0.574133 + 0.818762i \(0.305339\pi\)
\(80\) 0.974982 + 9.67589i 0.109006 + 1.08180i
\(81\) 0 0
\(82\) 1.88252 0.207889
\(83\) −0.405949 3.86235i −0.0445587 0.423948i −0.993948 0.109847i \(-0.964964\pi\)
0.949390 0.314100i \(-0.101703\pi\)
\(84\) 0 0
\(85\) −6.78214 4.97215i −0.735626 0.539306i
\(86\) 19.8233 4.21357i 2.13760 0.454361i
\(87\) 0 0
\(88\) 7.84246 + 1.66697i 0.836009 + 0.177699i
\(89\) 0.935601 2.87948i 0.0991735 0.305225i −0.889145 0.457625i \(-0.848700\pi\)
0.988319 + 0.152400i \(0.0487002\pi\)
\(90\) 0 0
\(91\) −1.41071 4.34171i −0.147882 0.455135i
\(92\) 2.32454 + 22.1165i 0.242350 + 2.30580i
\(93\) 0 0
\(94\) 9.17353 + 4.08432i 0.946178 + 0.421265i
\(95\) −8.23428 6.03676i −0.844819 0.619358i
\(96\) 0 0
\(97\) −4.75481 + 2.11698i −0.482777 + 0.214946i −0.633669 0.773604i \(-0.718452\pi\)
0.150892 + 0.988550i \(0.451785\pi\)
\(98\) −14.5949 + 44.9184i −1.47431 + 4.53744i
\(99\) 0 0
\(100\) −9.99279 17.6565i −0.999279 1.76565i
\(101\) −7.78401 + 13.4823i −0.774538 + 1.34154i 0.160516 + 0.987033i \(0.448684\pi\)
−0.935054 + 0.354506i \(0.884649\pi\)
\(102\) 0 0
\(103\) 1.66359 15.8280i 0.163918 1.55958i −0.535295 0.844665i \(-0.679800\pi\)
0.699213 0.714913i \(-0.253534\pi\)
\(104\) 0.472219 4.49286i 0.0463049 0.440561i
\(105\) 0 0
\(106\) −0.636039 6.05150i −0.0617775 0.587774i
\(107\) −2.75485 −0.266322 −0.133161 0.991094i \(-0.542513\pi\)
−0.133161 + 0.991094i \(0.542513\pi\)
\(108\) 0 0
\(109\) 3.89734 + 11.9948i 0.373297 + 1.14889i 0.944620 + 0.328166i \(0.106430\pi\)
−0.571323 + 0.820726i \(0.693570\pi\)
\(110\) −8.53026 + 1.77491i −0.813328 + 0.169231i
\(111\) 0 0
\(112\) −14.8928 + 16.5401i −1.40723 + 1.56289i
\(113\) 8.54130 9.48607i 0.803498 0.892375i −0.192541 0.981289i \(-0.561673\pi\)
0.996039 + 0.0889141i \(0.0283396\pi\)
\(114\) 0 0
\(115\) −6.08188 10.6394i −0.567138 0.992128i
\(116\) 0.0529004 + 0.162811i 0.00491168 + 0.0151166i
\(117\) 0 0
\(118\) 23.4412 2.15794
\(119\) −2.01180 19.1410i −0.184421 1.75465i
\(120\) 0 0
\(121\) 0.887818 8.44703i 0.0807107 0.767911i
\(122\) −1.86421 + 17.7368i −0.168778 + 1.60581i
\(123\) 0 0
\(124\) −3.99702 + 6.92305i −0.358943 + 0.621708i
\(125\) 8.95967 + 6.68763i 0.801377 + 0.598160i
\(126\) 0 0
\(127\) −2.35801 + 7.25722i −0.209240 + 0.643974i 0.790273 + 0.612755i \(0.209939\pi\)
−0.999513 + 0.0312188i \(0.990061\pi\)
\(128\) 17.4240 7.75766i 1.54008 0.685686i
\(129\) 0 0
\(130\) 1.49702 + 4.67557i 0.131297 + 0.410074i
\(131\) −2.37476 1.05731i −0.207484 0.0923778i 0.300364 0.953825i \(-0.402892\pi\)
−0.507847 + 0.861447i \(0.669559\pi\)
\(132\) 0 0
\(133\) −2.44255 23.2393i −0.211796 2.01510i
\(134\) −2.73542 8.41877i −0.236305 0.727271i
\(135\) 0 0
\(136\) 5.88554 18.1138i 0.504681 1.55325i
\(137\) 5.49049 + 1.16704i 0.469085 + 0.0997070i 0.436389 0.899758i \(-0.356257\pi\)
0.0326961 + 0.999465i \(0.489591\pi\)
\(138\) 0 0
\(139\) 1.68680 0.358539i 0.143072 0.0304109i −0.135819 0.990734i \(-0.543367\pi\)
0.278891 + 0.960323i \(0.410033\pi\)
\(140\) 14.5380 44.0979i 1.22868 3.72695i
\(141\) 0 0
\(142\) −0.499675 4.75409i −0.0419318 0.398955i
\(143\) 1.41227 0.118100
\(144\) 0 0
\(145\) −0.0628232 0.0703777i −0.00521718 0.00584455i
\(146\) 32.1628 14.3198i 2.66182 1.18512i
\(147\) 0 0
\(148\) 18.4945 3.93112i 1.52024 0.323136i
\(149\) 6.23532 + 10.7999i 0.510817 + 0.884761i 0.999921 + 0.0125357i \(0.00399034\pi\)
−0.489104 + 0.872225i \(0.662676\pi\)
\(150\) 0 0
\(151\) −3.71371 + 6.43234i −0.302218 + 0.523457i −0.976638 0.214891i \(-0.931060\pi\)
0.674420 + 0.738348i \(0.264394\pi\)
\(152\) 7.14571 21.9922i 0.579594 1.78381i
\(153\) 0 0
\(154\) −16.1325 11.7210i −1.30000 0.944503i
\(155\) 0.479295 4.37919i 0.0384979 0.351745i
\(156\) 0 0
\(157\) 4.70564 + 8.15040i 0.375551 + 0.650473i 0.990409 0.138164i \(-0.0441202\pi\)
−0.614859 + 0.788637i \(0.710787\pi\)
\(158\) −7.65314 3.40740i −0.608852 0.271078i
\(159\) 0 0
\(160\) 0.865229 0.952675i 0.0684024 0.0753155i
\(161\) 8.66715 26.6748i 0.683067 2.10227i
\(162\) 0 0
\(163\) −0.969935 2.98515i −0.0759712 0.233815i 0.905858 0.423581i \(-0.139227\pi\)
−0.981829 + 0.189766i \(0.939227\pi\)
\(164\) −2.07669 2.30639i −0.162162 0.180099i
\(165\) 0 0
\(166\) −6.39587 + 7.10333i −0.496416 + 0.551325i
\(167\) −2.62097 1.16693i −0.202816 0.0902997i 0.302815 0.953049i \(-0.402074\pi\)
−0.505631 + 0.862750i \(0.668740\pi\)
\(168\) 0 0
\(169\) 1.27569 + 12.1374i 0.0981301 + 0.933645i
\(170\) 2.07507 + 20.5934i 0.159151 + 1.57944i
\(171\) 0 0
\(172\) −27.0303 19.6386i −2.06104 1.49743i
\(173\) −10.6348 11.8112i −0.808550 0.897986i 0.187899 0.982188i \(-0.439832\pi\)
−0.996449 + 0.0842025i \(0.973166\pi\)
\(174\) 0 0
\(175\) 2.45599 + 25.4698i 0.185655 + 1.92533i
\(176\) −3.44270 5.96292i −0.259503 0.449472i
\(177\) 0 0
\(178\) −6.80754 + 3.03091i −0.510246 + 0.227176i
\(179\) −14.4077 10.4678i −1.07688 0.782399i −0.0997433 0.995013i \(-0.531802\pi\)
−0.977136 + 0.212614i \(0.931802\pi\)
\(180\) 0 0
\(181\) 14.8249 10.7709i 1.10192 0.800594i 0.120550 0.992707i \(-0.461534\pi\)
0.981373 + 0.192114i \(0.0615342\pi\)
\(182\) −5.61793 + 9.73054i −0.416429 + 0.721275i
\(183\) 0 0
\(184\) 18.5720 20.6263i 1.36915 1.52059i
\(185\) −8.45584 + 6.08822i −0.621686 + 0.447615i
\(186\) 0 0
\(187\) 5.82397 + 1.23792i 0.425891 + 0.0905258i
\(188\) −5.11576 15.7447i −0.373105 1.14830i
\(189\) 0 0
\(190\) 2.51937 + 25.0027i 0.182775 + 1.81389i
\(191\) 10.7709 + 2.28943i 0.779356 + 0.165657i 0.580379 0.814347i \(-0.302905\pi\)
0.198978 + 0.980004i \(0.436238\pi\)
\(192\) 0 0
\(193\) −3.22947 5.59361i −0.232463 0.402637i 0.726070 0.687621i \(-0.241345\pi\)
−0.958532 + 0.284984i \(0.908012\pi\)
\(194\) 11.7026 + 5.21035i 0.840201 + 0.374082i
\(195\) 0 0
\(196\) 71.1327 31.6703i 5.08091 2.26217i
\(197\) 20.4081 + 14.8274i 1.45402 + 1.05641i 0.984872 + 0.173284i \(0.0554379\pi\)
0.469145 + 0.883121i \(0.344562\pi\)
\(198\) 0 0
\(199\) 2.48202 0.175946 0.0879729 0.996123i \(-0.471961\pi\)
0.0879729 + 0.996123i \(0.471961\pi\)
\(200\) −8.03132 + 24.0140i −0.567900 + 1.69805i
\(201\) 0 0
\(202\) 37.4791 7.96643i 2.63702 0.560516i
\(203\) 0.0225686 0.214725i 0.00158400 0.0150708i
\(204\) 0 0
\(205\) 1.55944 + 0.702346i 0.108916 + 0.0490540i
\(206\) −31.6899 + 23.0240i −2.20794 + 1.60416i
\(207\) 0 0
\(208\) −3.13868 + 2.28039i −0.217628 + 0.158116i
\(209\) 7.07095 + 1.50298i 0.489108 + 0.103963i
\(210\) 0 0
\(211\) 6.74542 1.43378i 0.464374 0.0987057i 0.0302177 0.999543i \(-0.490380\pi\)
0.434156 + 0.900838i \(0.357047\pi\)
\(212\) −6.71245 + 7.45493i −0.461013 + 0.512007i
\(213\) 0 0
\(214\) 4.53692 + 5.03876i 0.310137 + 0.344442i
\(215\) 17.9932 + 3.90542i 1.22713 + 0.266347i
\(216\) 0 0
\(217\) 8.15674 5.92622i 0.553716 0.402298i
\(218\) 15.5206 26.8824i 1.05118 1.82071i
\(219\) 0 0
\(220\) 11.5847 + 8.49299i 0.781037 + 0.572598i
\(221\) 0.350679 3.33649i 0.0235892 0.224437i
\(222\) 0 0
\(223\) −8.82544 9.80164i −0.590995 0.656366i 0.371256 0.928531i \(-0.378927\pi\)
−0.962251 + 0.272164i \(0.912261\pi\)
\(224\) 2.94535 0.196795
\(225\) 0 0
\(226\) −31.4170 −2.08983
\(227\) 11.7306 + 13.0281i 0.778586 + 0.864707i 0.993722 0.111877i \(-0.0356863\pi\)
−0.215136 + 0.976584i \(0.569020\pi\)
\(228\) 0 0
\(229\) −1.69849 + 16.1600i −0.112239 + 1.06788i 0.782915 + 0.622128i \(0.213732\pi\)
−0.895154 + 0.445756i \(0.852935\pi\)
\(230\) −9.44380 + 28.6458i −0.622706 + 1.88885i
\(231\) 0 0
\(232\) 0.106830 0.185035i 0.00701373 0.0121481i
\(233\) 15.4281 11.2092i 1.01073 0.734339i 0.0463684 0.998924i \(-0.485235\pi\)
0.964362 + 0.264586i \(0.0852352\pi\)
\(234\) 0 0
\(235\) 6.07534 + 6.80590i 0.396311 + 0.443968i
\(236\) −25.8590 28.7193i −1.68328 1.86947i
\(237\) 0 0
\(238\) −31.6966 + 35.2026i −2.05458 + 2.28185i
\(239\) −6.81591 + 1.44877i −0.440884 + 0.0937129i −0.423005 0.906127i \(-0.639025\pi\)
−0.0178793 + 0.999840i \(0.505691\pi\)
\(240\) 0 0
\(241\) 2.96735 + 0.630730i 0.191144 + 0.0406289i 0.302489 0.953153i \(-0.402183\pi\)
−0.111345 + 0.993782i \(0.535516\pi\)
\(242\) −16.9121 + 12.2874i −1.08715 + 0.789863i
\(243\) 0 0
\(244\) 23.7870 17.2823i 1.52281 1.10638i
\(245\) −28.8486 + 31.7642i −1.84307 + 2.02934i
\(246\) 0 0
\(247\) 0.425764 4.05087i 0.0270907 0.257751i
\(248\) 9.75927 2.07440i 0.619714 0.131724i
\(249\) 0 0
\(250\) −2.52353 27.4014i −0.159602 1.73302i
\(251\) −14.6208 −0.922854 −0.461427 0.887178i \(-0.652662\pi\)
−0.461427 + 0.887178i \(0.652662\pi\)
\(252\) 0 0
\(253\) 7.01966 + 5.10008i 0.441322 + 0.320639i
\(254\) 17.1572 7.63886i 1.07654 0.479305i
\(255\) 0 0
\(256\) −29.5801 13.1699i −1.84875 0.823118i
\(257\) −8.94002 15.4846i −0.557663 0.965900i −0.997691 0.0679164i \(-0.978365\pi\)
0.440028 0.897984i \(-0.354968\pi\)
\(258\) 0 0
\(259\) −23.3257 4.95803i −1.44939 0.308077i
\(260\) 4.07692 6.99191i 0.252840 0.433620i
\(261\) 0 0
\(262\) 1.97708 + 6.08482i 0.122144 + 0.375921i
\(263\) 12.0007 + 2.55082i 0.739993 + 0.157290i 0.562460 0.826824i \(-0.309855\pi\)
0.177533 + 0.984115i \(0.443188\pi\)
\(264\) 0 0
\(265\) 1.73087 5.25023i 0.106326 0.322519i
\(266\) −38.4832 + 42.7399i −2.35956 + 2.62055i
\(267\) 0 0
\(268\) −7.29682 + 12.6385i −0.445724 + 0.772017i
\(269\) 18.8007 13.6595i 1.14630 0.832835i 0.158314 0.987389i \(-0.449394\pi\)
0.987984 + 0.154554i \(0.0493941\pi\)
\(270\) 0 0
\(271\) 22.0116 + 15.9923i 1.33711 + 0.971466i 0.999545 + 0.0301632i \(0.00960270\pi\)
0.337563 + 0.941303i \(0.390397\pi\)
\(272\) −14.9422 + 6.65270i −0.906005 + 0.403379i
\(273\) 0 0
\(274\) −6.90762 11.9643i −0.417305 0.722793i
\(275\) −7.72848 1.71225i −0.466045 0.103252i
\(276\) 0 0
\(277\) 11.7830 + 13.0863i 0.707972 + 0.786282i 0.984624 0.174688i \(-0.0558917\pi\)
−0.276652 + 0.960970i \(0.589225\pi\)
\(278\) −3.43374 2.49476i −0.205942 0.149626i
\(279\) 0 0
\(280\) −53.0425 + 23.3436i −3.16990 + 1.39505i
\(281\) 1.50810 + 14.3486i 0.0899657 + 0.855967i 0.942704 + 0.333629i \(0.108273\pi\)
−0.852739 + 0.522338i \(0.825060\pi\)
\(282\) 0 0
\(283\) −11.3496 5.05317i −0.674663 0.300379i 0.0406600 0.999173i \(-0.487054\pi\)
−0.715323 + 0.698794i \(0.753721\pi\)
\(284\) −5.27333 + 5.85663i −0.312915 + 0.347527i
\(285\) 0 0
\(286\) −2.32585 2.58312i −0.137530 0.152743i
\(287\) 1.20958 + 3.72271i 0.0713993 + 0.219744i
\(288\) 0 0
\(289\) −0.882569 + 2.71627i −0.0519158 + 0.159781i
\(290\) −0.0252618 + 0.230810i −0.00148342 + 0.0135536i
\(291\) 0 0
\(292\) −53.0244 23.6080i −3.10302 1.38155i
\(293\) −11.2824 19.5417i −0.659125 1.14164i −0.980843 0.194802i \(-0.937594\pi\)
0.321718 0.946836i \(-0.395740\pi\)
\(294\) 0 0
\(295\) 19.4182 + 8.74564i 1.13057 + 0.509191i
\(296\) −19.0916 13.8708i −1.10967 0.806226i
\(297\) 0 0
\(298\) 9.48467 29.1908i 0.549432 1.69098i
\(299\) 2.44450 4.23399i 0.141369 0.244858i
\(300\) 0 0
\(301\) 21.0695 + 36.4935i 1.21443 + 2.10345i
\(302\) 17.8811 3.80074i 1.02894 0.218708i
\(303\) 0 0
\(304\) −18.1415 + 8.07713i −1.04049 + 0.463255i
\(305\) −8.16167 + 13.9973i −0.467336 + 0.801480i
\(306\) 0 0
\(307\) −27.5455 −1.57211 −0.786054 0.618158i \(-0.787879\pi\)
−0.786054 + 0.618158i \(0.787879\pi\)
\(308\) 3.43638 + 32.6949i 0.195806 + 1.86297i
\(309\) 0 0
\(310\) −8.79908 + 6.33535i −0.499754 + 0.359824i
\(311\) 0.496015 0.105431i 0.0281264 0.00597846i −0.193827 0.981036i \(-0.562090\pi\)
0.221953 + 0.975057i \(0.428757\pi\)
\(312\) 0 0
\(313\) 12.9331 + 2.74901i 0.731021 + 0.155383i 0.558361 0.829598i \(-0.311430\pi\)
0.172660 + 0.984981i \(0.444764\pi\)
\(314\) 7.15784 22.0296i 0.403941 1.24320i
\(315\) 0 0
\(316\) 4.26789 + 13.1352i 0.240088 + 0.738914i
\(317\) −1.09655 10.4330i −0.0615883 0.585973i −0.981180 0.193097i \(-0.938147\pi\)
0.919591 0.392876i \(-0.128520\pi\)
\(318\) 0 0
\(319\) 0.0610188 + 0.0271673i 0.00341640 + 0.00152108i
\(320\) 16.2822 + 0.0699267i 0.910201 + 0.00390902i
\(321\) 0 0
\(322\) −63.0631 + 28.0775i −3.51437 + 1.56470i
\(323\) 5.30655 16.3319i 0.295264 0.908730i
\(324\) 0 0
\(325\) −0.504307 + 4.43166i −0.0279739 + 0.245824i
\(326\) −3.86262 + 6.69025i −0.213931 + 0.370539i
\(327\) 0 0
\(328\) −0.404894 + 3.85231i −0.0223565 + 0.212708i
\(329\) −2.18250 + 20.7651i −0.120325 + 1.14482i
\(330\) 0 0
\(331\) 0.255661 + 2.43245i 0.0140524 + 0.133700i 0.999299 0.0374422i \(-0.0119210\pi\)
−0.985246 + 0.171142i \(0.945254\pi\)
\(332\) 15.7583 0.864850
\(333\) 0 0
\(334\) 2.18205 + 6.71566i 0.119397 + 0.367465i
\(335\) 0.874982 7.99448i 0.0478054 0.436785i
\(336\) 0 0
\(337\) 1.22740 1.36317i 0.0668607 0.0742564i −0.708786 0.705423i \(-0.750757\pi\)
0.775647 + 0.631167i \(0.217424\pi\)
\(338\) 20.0989 22.3221i 1.09324 1.21416i
\(339\) 0 0
\(340\) 22.9412 25.2598i 1.24416 1.36990i
\(341\) 0.963842 + 2.96640i 0.0521950 + 0.160640i
\(342\) 0 0
\(343\) −62.3814 −3.36828
\(344\) 4.35887 + 41.4718i 0.235014 + 2.23601i
\(345\) 0 0
\(346\) −4.08889 + 38.9032i −0.219820 + 2.09145i
\(347\) −0.0311880 + 0.296734i −0.00167426 + 0.0159295i −0.995327 0.0965604i \(-0.969216\pi\)
0.993653 + 0.112490i \(0.0358826\pi\)
\(348\) 0 0
\(349\) −8.44783 + 14.6321i −0.452202 + 0.783237i −0.998523 0.0543395i \(-0.982695\pi\)
0.546321 + 0.837576i \(0.316028\pi\)
\(350\) 42.5407 46.4378i 2.27389 2.48220i
\(351\) 0 0
\(352\) −0.281569 + 0.866579i −0.0150077 + 0.0461888i
\(353\) −6.64968 + 2.96063i −0.353927 + 0.157578i −0.575996 0.817453i \(-0.695386\pi\)
0.222069 + 0.975031i \(0.428719\pi\)
\(354\) 0 0
\(355\) 1.35978 4.12461i 0.0721695 0.218912i
\(356\) 11.2231 + 4.99683i 0.594821 + 0.264831i
\(357\) 0 0
\(358\) 4.58165 + 43.5915i 0.242148 + 2.30388i
\(359\) 8.36007 + 25.7297i 0.441228 + 1.35796i 0.886568 + 0.462598i \(0.153083\pi\)
−0.445340 + 0.895361i \(0.646917\pi\)
\(360\) 0 0
\(361\) 0.571423 1.75866i 0.0300749 0.0925610i
\(362\) −44.1152 9.37698i −2.31864 0.492843i
\(363\) 0 0
\(364\) 18.1189 3.85129i 0.949688 0.201862i
\(365\) 31.9855 + 0.137368i 1.67420 + 0.00719014i
\(366\) 0 0
\(367\) −0.804907 7.65818i −0.0420158 0.399754i −0.995237 0.0974811i \(-0.968921\pi\)
0.953222 0.302272i \(-0.0977452\pi\)
\(368\) −23.8358 −1.24252
\(369\) 0 0
\(370\) 25.0614 + 5.43956i 1.30288 + 0.282789i
\(371\) 11.5583 5.14607i 0.600075 0.267171i
\(372\) 0 0
\(373\) 22.9033 4.86824i 1.18589 0.252068i 0.427587 0.903974i \(-0.359364\pi\)
0.758300 + 0.651906i \(0.226030\pi\)
\(374\) −7.32716 12.6910i −0.378879 0.656237i
\(375\) 0 0
\(376\) −10.3310 + 17.8939i −0.532782 + 0.922806i
\(377\) 0.0116299 0.0357932i 0.000598972 0.00184345i
\(378\) 0 0
\(379\) −5.93052 4.30878i −0.304630 0.221327i 0.424959 0.905213i \(-0.360289\pi\)
−0.729589 + 0.683886i \(0.760289\pi\)
\(380\) 27.8532 30.6682i 1.42884 1.57325i
\(381\) 0 0
\(382\) −13.5509 23.4709i −0.693327 1.20088i
\(383\) −16.0311 7.13749i −0.819149 0.364709i −0.0460067 0.998941i \(-0.514650\pi\)
−0.773142 + 0.634232i \(0.781316\pi\)
\(384\) 0 0
\(385\) −8.99088 15.7283i −0.458218 0.801587i
\(386\) −4.91242 + 15.1189i −0.250035 + 0.769530i
\(387\) 0 0
\(388\) −6.52616 20.0854i −0.331315 1.01968i
\(389\) −0.222858 0.247509i −0.0112993 0.0125492i 0.737469 0.675381i \(-0.236021\pi\)
−0.748768 + 0.662832i \(0.769354\pi\)
\(390\) 0 0
\(391\) 13.7919 15.3175i 0.697489 0.774640i
\(392\) −88.7801 39.5274i −4.48407 1.99644i
\(393\) 0 0
\(394\) −6.48979 61.7463i −0.326951 3.11073i
\(395\) −5.06843 5.67792i −0.255021 0.285687i
\(396\) 0 0
\(397\) 19.6674 + 14.2892i 0.987079 + 0.717155i 0.959279 0.282459i \(-0.0911501\pi\)
0.0277993 + 0.999614i \(0.491150\pi\)
\(398\) −4.08759 4.53973i −0.204892 0.227556i
\(399\) 0 0
\(400\) 19.9407 8.67374i 0.997037 0.433687i
\(401\) 10.6053 + 18.3689i 0.529604 + 0.917301i 0.999404 + 0.0345279i \(0.0109927\pi\)
−0.469800 + 0.882773i \(0.655674\pi\)
\(402\) 0 0
\(403\) 1.60552 0.714822i 0.0799764 0.0356078i
\(404\) −51.1050 37.1300i −2.54257 1.84729i
\(405\) 0 0
\(406\) −0.429911 + 0.312348i −0.0213361 + 0.0155016i
\(407\) 3.68862 6.38888i 0.182838 0.316685i
\(408\) 0 0
\(409\) −10.8116 + 12.0075i −0.534601 + 0.593734i −0.948574 0.316555i \(-0.897474\pi\)
0.413974 + 0.910289i \(0.364141\pi\)
\(410\) −1.28358 4.00896i −0.0633916 0.197989i
\(411\) 0 0
\(412\) 63.1667 + 13.4265i 3.11200 + 0.661476i
\(413\) 15.0617 + 46.3553i 0.741140 + 2.28099i
\(414\) 0 0
\(415\) −7.94837 + 3.49802i −0.390170 + 0.171711i
\(416\) 0.502189 + 0.106744i 0.0246218 + 0.00523353i
\(417\) 0 0
\(418\) −8.89600 15.4083i −0.435118 0.753646i
\(419\) −12.9294 5.75655i −0.631644 0.281226i 0.0658358 0.997830i \(-0.479029\pi\)
−0.697480 + 0.716604i \(0.745695\pi\)
\(420\) 0 0
\(421\) −22.8321 + 10.1655i −1.11277 + 0.495436i −0.878983 0.476852i \(-0.841778\pi\)
−0.233784 + 0.972288i \(0.575111\pi\)
\(422\) −13.7314 9.97642i −0.668432 0.485644i
\(423\) 0 0
\(424\) 12.5203 0.608042
\(425\) −5.96422 + 17.8333i −0.289307 + 0.865042i
\(426\) 0 0
\(427\) −36.2726 + 7.70998i −1.75535 + 0.373112i
\(428\) 1.16844 11.1169i 0.0564786 0.537358i
\(429\) 0 0
\(430\) −22.4895 39.3422i −1.08454 1.89725i
\(431\) −4.09020 + 2.97170i −0.197018 + 0.143142i −0.681921 0.731426i \(-0.738855\pi\)
0.484903 + 0.874568i \(0.338855\pi\)
\(432\) 0 0
\(433\) 16.2872 11.8334i 0.782715 0.568676i −0.123078 0.992397i \(-0.539276\pi\)
0.905793 + 0.423721i \(0.139276\pi\)
\(434\) −24.2725 5.15928i −1.16512 0.247654i
\(435\) 0 0
\(436\) −50.0568 + 10.6399i −2.39728 + 0.509558i
\(437\) 16.7450 18.5972i 0.801021 0.889624i
\(438\) 0 0
\(439\) −26.5647 29.5031i −1.26787 1.40811i −0.871783 0.489892i \(-0.837036\pi\)
−0.396083 0.918215i \(-0.629631\pi\)
\(440\) −1.79740 17.8377i −0.0856877 0.850380i
\(441\) 0 0
\(442\) −6.68012 + 4.85339i −0.317741 + 0.230852i
\(443\) −14.2137 + 24.6188i −0.675313 + 1.16968i 0.301065 + 0.953604i \(0.402658\pi\)
−0.976377 + 0.216072i \(0.930675\pi\)
\(444\) 0 0
\(445\) −6.77001 0.0290750i −0.320929 0.00137829i
\(446\) −3.39321 + 32.2843i −0.160673 + 1.52870i
\(447\) 0 0
\(448\) 24.9349 + 27.6930i 1.17806 + 1.30837i
\(449\) 32.9656 1.55574 0.777871 0.628424i \(-0.216300\pi\)
0.777871 + 0.628424i \(0.216300\pi\)
\(450\) 0 0
\(451\) −1.21092 −0.0570202
\(452\) 34.6574 + 38.4910i 1.63015 + 1.81046i
\(453\) 0 0
\(454\) 4.51018 42.9115i 0.211673 2.01394i
\(455\) −8.28412 + 5.96458i −0.388366 + 0.279624i
\(456\) 0 0
\(457\) 14.1520 24.5120i 0.662004 1.14663i −0.318084 0.948063i \(-0.603039\pi\)
0.980088 0.198563i \(-0.0636273\pi\)
\(458\) 32.3547 23.5070i 1.51183 1.09841i
\(459\) 0 0
\(460\) 45.5137 20.0303i 2.12209 0.933916i
\(461\) −11.1242 12.3547i −0.518107 0.575416i 0.426139 0.904658i \(-0.359874\pi\)
−0.944246 + 0.329242i \(0.893207\pi\)
\(462\) 0 0
\(463\) 7.28894 8.09519i 0.338746 0.376216i −0.549570 0.835447i \(-0.685209\pi\)
0.888316 + 0.459232i \(0.151875\pi\)
\(464\) −0.179477 + 0.0381490i −0.00833200 + 0.00177102i
\(465\) 0 0
\(466\) −45.9104 9.75857i −2.12676 0.452057i
\(467\) −19.9438 + 14.4900i −0.922888 + 0.670517i −0.944241 0.329255i \(-0.893203\pi\)
0.0213532 + 0.999772i \(0.493203\pi\)
\(468\) 0 0
\(469\) 14.8906 10.8187i 0.687586 0.499560i
\(470\) 2.44295 22.3206i 0.112685 1.02957i
\(471\) 0 0
\(472\) −5.04175 + 47.9690i −0.232065 + 2.20795i
\(473\) −12.7513 + 2.71037i −0.586304 + 0.124623i
\(474\) 0 0
\(475\) −7.24123 + 21.6516i −0.332250 + 0.993446i
\(476\) 78.0949 3.57947
\(477\) 0 0
\(478\) 13.8749 + 10.0807i 0.634621 + 0.461079i
\(479\) 35.3981 15.7603i 1.61738 0.720105i 0.619490 0.785004i \(-0.287339\pi\)
0.997892 + 0.0648994i \(0.0206727\pi\)
\(480\) 0 0
\(481\) −3.79739 1.69071i −0.173146 0.0770896i
\(482\) −3.73324 6.46616i −0.170044 0.294526i
\(483\) 0 0
\(484\) 33.7106 + 7.16541i 1.53230 + 0.325700i
\(485\) 7.75029 + 8.68227i 0.351923 + 0.394242i
\(486\) 0 0
\(487\) −0.280386 0.862940i −0.0127055 0.0391036i 0.944503 0.328503i \(-0.106544\pi\)
−0.957208 + 0.289400i \(0.906544\pi\)
\(488\) −35.8949 7.62969i −1.62488 0.345380i
\(489\) 0 0
\(490\) 105.609 + 0.453554i 4.77091 + 0.0204895i
\(491\) −3.13305 + 3.47961i −0.141393 + 0.157032i −0.809682 0.586869i \(-0.800360\pi\)
0.668289 + 0.743902i \(0.267027\pi\)
\(492\) 0 0
\(493\) 0.0793341 0.137411i 0.00357303 0.00618866i
\(494\) −8.11042 + 5.89257i −0.364905 + 0.265119i
\(495\) 0 0
\(496\) −6.93189 5.03631i −0.311251 0.226137i
\(497\) 9.08023 4.04278i 0.407304 0.181343i
\(498\) 0 0
\(499\) 7.00291 + 12.1294i 0.313493 + 0.542986i 0.979116 0.203302i \(-0.0651673\pi\)
−0.665623 + 0.746288i \(0.731834\pi\)
\(500\) −30.7874 + 33.3194i −1.37685 + 1.49009i
\(501\) 0 0
\(502\) 24.0787 + 26.7421i 1.07468 + 1.19356i
\(503\) −23.8114 17.3000i −1.06170 0.771370i −0.0872979 0.996182i \(-0.527823\pi\)
−0.974402 + 0.224812i \(0.927823\pi\)
\(504\) 0 0
\(505\) 34.0191 + 7.38381i 1.51383 + 0.328575i
\(506\) −2.23226 21.2385i −0.0992360 0.944167i
\(507\) 0 0
\(508\) −28.2857 12.5936i −1.25497 0.558750i
\(509\) −3.82486 + 4.24793i −0.169534 + 0.188286i −0.821924 0.569596i \(-0.807099\pi\)
0.652391 + 0.757883i \(0.273766\pi\)
\(510\) 0 0
\(511\) 48.9833 + 54.4015i 2.16690 + 2.40658i
\(512\) 12.8388 + 39.5137i 0.567399 + 1.74628i
\(513\) 0 0
\(514\) −13.5988 + 41.8529i −0.599819 + 1.84605i
\(515\) −34.8412 + 7.24948i −1.53529 + 0.319450i
\(516\) 0 0
\(517\) −5.90085 2.62723i −0.259519 0.115545i
\(518\) 29.3462 + 50.8290i 1.28940 + 2.23330i
\(519\) 0 0
\(520\) −9.88987 + 2.05780i −0.433699 + 0.0902407i
\(521\) 6.83148 + 4.96336i 0.299293 + 0.217449i 0.727288 0.686332i \(-0.240780\pi\)
−0.427996 + 0.903781i \(0.640780\pi\)
\(522\) 0 0
\(523\) −0.335514 + 1.03260i −0.0146710 + 0.0451527i −0.958124 0.286354i \(-0.907557\pi\)
0.943453 + 0.331506i \(0.107557\pi\)
\(524\) 5.27390 9.13467i 0.230392 0.399050i
\(525\) 0 0
\(526\) −15.0981 26.1507i −0.658309 1.14022i
\(527\) 7.24743 1.54049i 0.315703 0.0671047i
\(528\) 0 0
\(529\) 6.42876 2.86227i 0.279511 0.124446i
\(530\) −12.4535 + 5.48067i −0.540943 + 0.238065i
\(531\) 0 0
\(532\) 94.8160 4.11079
\(533\) 0.0713202 + 0.678566i 0.00308922 + 0.0293920i
\(534\) 0 0
\(535\) 1.87838 + 5.86667i 0.0812094 + 0.253638i
\(536\) 17.8162 3.78694i 0.769541 0.163571i
\(537\) 0 0
\(538\) −55.9464 11.8918i −2.41202 0.512691i
\(539\) 9.38811 28.8936i 0.404375 1.24454i
\(540\) 0 0
\(541\) 3.62252 + 11.1490i 0.155744 + 0.479331i 0.998236 0.0593787i \(-0.0189120\pi\)
−0.842491 + 0.538710i \(0.818912\pi\)
\(542\) −6.99970 66.5977i −0.300663 2.86062i
\(543\) 0 0
\(544\) 1.97737 + 0.880382i 0.0847791 + 0.0377461i
\(545\) 22.8864 16.4782i 0.980346 0.705850i
\(546\) 0 0
\(547\) −17.4993 + 7.79121i −0.748217 + 0.333128i −0.745176 0.666867i \(-0.767635\pi\)
−0.00304116 + 0.999995i \(0.500968\pi\)
\(548\) −7.03820 + 21.6614i −0.300657 + 0.925328i
\(549\) 0 0
\(550\) 9.59610 + 16.9556i 0.409179 + 0.722990i
\(551\) 0.0963205 0.166832i 0.00410339 0.00710728i
\(552\) 0 0
\(553\) 1.82078 17.3236i 0.0774275 0.736673i
\(554\) 4.53034 43.1033i 0.192476 1.83128i
\(555\) 0 0
\(556\) 0.731417 + 6.95897i 0.0310190 + 0.295126i
\(557\) −18.2151 −0.771799 −0.385899 0.922541i \(-0.626109\pi\)
−0.385899 + 0.922541i \(0.626109\pi\)
\(558\) 0 0
\(559\) 2.26983 + 6.98581i 0.0960034 + 0.295468i
\(560\) 45.3779 + 20.4375i 1.91757 + 0.863642i
\(561\) 0 0
\(562\) 23.7606 26.3889i 1.00228 1.11315i
\(563\) 9.06124 10.0635i 0.381886 0.424127i −0.521302 0.853372i \(-0.674554\pi\)
0.903188 + 0.429245i \(0.141220\pi\)
\(564\) 0 0
\(565\) −26.0251 11.7213i −1.09489 0.493120i
\(566\) 9.44896 + 29.0809i 0.397169 + 1.22236i
\(567\) 0 0
\(568\) 9.83605 0.412711
\(569\) 2.47240 + 23.5233i 0.103648 + 0.986150i 0.915509 + 0.402298i \(0.131788\pi\)
−0.811860 + 0.583852i \(0.801545\pi\)
\(570\) 0 0
\(571\) 3.79953 36.1501i 0.159006 1.51284i −0.566179 0.824282i \(-0.691579\pi\)
0.725185 0.688554i \(-0.241754\pi\)
\(572\) −0.598999 + 5.69910i −0.0250454 + 0.238291i
\(573\) 0 0
\(574\) 4.81697 8.34323i 0.201056 0.348240i
\(575\) −18.5105 + 20.2062i −0.771940 + 0.842657i
\(576\) 0 0
\(577\) 10.9221 33.6148i 0.454694 1.39940i −0.416801 0.908998i \(-0.636849\pi\)
0.871494 0.490406i \(-0.163151\pi\)
\(578\) 6.42167 2.85911i 0.267106 0.118923i
\(579\) 0 0
\(580\) 0.310648 0.223667i 0.0128990 0.00928726i
\(581\) −18.1565 8.08379i −0.753258 0.335372i
\(582\) 0 0
\(583\) 0.409130 + 3.89261i 0.0169444 + 0.161215i
\(584\) 22.3859 + 68.8966i 0.926334 + 2.85096i
\(585\) 0 0
\(586\) −17.1619 + 52.8189i −0.708951 + 2.18193i
\(587\) 37.0299 + 7.87095i 1.52839 + 0.324869i 0.893972 0.448123i \(-0.147907\pi\)
0.634416 + 0.772992i \(0.281240\pi\)
\(588\) 0 0
\(589\) 8.79920 1.87033i 0.362565 0.0770655i
\(590\) −15.9832 49.9197i −0.658019 2.05516i
\(591\) 0 0
\(592\) 2.11836 + 20.1548i 0.0870640 + 0.828358i
\(593\) −33.1095 −1.35964 −0.679822 0.733377i \(-0.737943\pi\)
−0.679822 + 0.733377i \(0.737943\pi\)
\(594\) 0 0
\(595\) −39.3904 + 17.3354i −1.61485 + 0.710684i
\(596\) −46.2265 + 20.5814i −1.89351 + 0.843046i
\(597\) 0 0
\(598\) −11.7700 + 2.50178i −0.481310 + 0.102306i
\(599\) −16.9563 29.3692i −0.692816 1.19999i −0.970912 0.239439i \(-0.923037\pi\)
0.278096 0.960553i \(-0.410297\pi\)
\(600\) 0 0
\(601\) 7.45268 12.9084i 0.304001 0.526545i −0.673037 0.739608i \(-0.735011\pi\)
0.977038 + 0.213063i \(0.0683441\pi\)
\(602\) 32.0493 98.6376i 1.30623 4.02017i
\(603\) 0 0
\(604\) −24.3820 17.7145i −0.992088 0.720794i
\(605\) −18.5939 + 3.86887i −0.755951 + 0.157292i
\(606\) 0 0
\(607\) −1.90528 3.30004i −0.0773328 0.133944i 0.824766 0.565475i \(-0.191307\pi\)
−0.902098 + 0.431530i \(0.857974\pi\)
\(608\) 2.40075 + 1.06888i 0.0973633 + 0.0433490i
\(609\) 0 0
\(610\) 39.0429 8.12374i 1.58080 0.328921i
\(611\) −1.12468 + 3.46140i −0.0454995 + 0.140033i
\(612\) 0 0
\(613\) 0.301134 + 0.926794i 0.0121627 + 0.0374329i 0.956954 0.290241i \(-0.0937354\pi\)
−0.944791 + 0.327674i \(0.893735\pi\)
\(614\) 45.3642 + 50.3821i 1.83075 + 2.03326i
\(615\) 0 0
\(616\) 27.4551 30.4920i 1.10620 1.22856i
\(617\) −26.9664 12.0062i −1.08563 0.483352i −0.215663 0.976468i \(-0.569191\pi\)
−0.869964 + 0.493115i \(0.835858\pi\)
\(618\) 0 0
\(619\) 0.456050 + 4.33902i 0.0183302 + 0.174400i 0.999857 0.0169259i \(-0.00538792\pi\)
−0.981527 + 0.191326i \(0.938721\pi\)
\(620\) 17.4685 + 3.79153i 0.701552 + 0.152271i
\(621\) 0 0
\(622\) −1.00972 0.733602i −0.0404859 0.0294148i
\(623\) −10.3677 11.5145i −0.415375 0.461320i
\(624\) 0 0
\(625\) 8.13271 23.6402i 0.325308 0.945608i
\(626\) −16.2712 28.1825i −0.650327 1.12640i
\(627\) 0 0
\(628\) −34.8860 + 15.5322i −1.39210 + 0.619804i
\(629\) −14.1778 10.3008i −0.565305 0.410718i
\(630\) 0 0
\(631\) 39.3657 28.6008i 1.56712 1.13858i 0.637274 0.770637i \(-0.280062\pi\)
0.929848 0.367944i \(-0.119938\pi\)
\(632\) 8.61881 14.9282i 0.342838 0.593812i
\(633\) 0 0
\(634\) −17.2765 + 19.1875i −0.686137 + 0.762032i
\(635\) 17.0626 + 0.0732783i 0.677108 + 0.00290796i
\(636\) 0 0
\(637\) −16.7441 3.55906i −0.663424 0.141015i
\(638\) −0.0508004 0.156348i −0.00201121 0.00618986i
\(639\) 0 0
\(640\) −28.4009 31.8162i −1.12265 1.25764i
\(641\) 4.86398 + 1.03387i 0.192116 + 0.0408354i 0.302965 0.953002i \(-0.402024\pi\)
−0.110849 + 0.993837i \(0.535357\pi\)
\(642\) 0 0
\(643\) 1.30748 + 2.26463i 0.0515621 + 0.0893081i 0.890654 0.454681i \(-0.150247\pi\)
−0.839092 + 0.543989i \(0.816913\pi\)
\(644\) 103.967 + 46.2892i 4.09688 + 1.82405i
\(645\) 0 0
\(646\) −38.6110 + 17.1907i −1.51913 + 0.676360i
\(647\) −13.0683 9.49465i −0.513767 0.373273i 0.300484 0.953787i \(-0.402852\pi\)
−0.814251 + 0.580514i \(0.802852\pi\)
\(648\) 0 0
\(649\) −15.0785 −0.591882
\(650\) 8.93624 6.37601i 0.350508 0.250088i
\(651\) 0 0
\(652\) 12.4577 2.64796i 0.487880 0.103702i
\(653\) −1.81745 + 17.2919i −0.0711222 + 0.676683i 0.899639 + 0.436635i \(0.143830\pi\)
−0.970761 + 0.240048i \(0.922837\pi\)
\(654\) 0 0
\(655\) −0.632409 + 5.77815i −0.0247103 + 0.225771i
\(656\) 2.69119 1.95527i 0.105073 0.0763403i
\(657\) 0 0
\(658\) 41.5747 30.2058i 1.62075 1.17754i
\(659\) −44.0854 9.37064i −1.71732 0.365028i −0.759083 0.650993i \(-0.774353\pi\)
−0.958240 + 0.285965i \(0.907686\pi\)
\(660\) 0 0
\(661\) 29.8878 6.35285i 1.16250 0.247097i 0.414029 0.910263i \(-0.364121\pi\)
0.748472 + 0.663166i \(0.230788\pi\)
\(662\) 4.02803 4.47358i 0.156554 0.173871i
\(663\) 0 0
\(664\) −13.1603 14.6160i −0.510720 0.567212i
\(665\) −47.8244 + 21.0472i −1.85455 + 0.816174i
\(666\) 0 0
\(667\) 0.187065 0.135910i 0.00724317 0.00526247i
\(668\) 5.82068 10.0817i 0.225209 0.390073i
\(669\) 0 0
\(670\) −16.0633 + 11.5656i −0.620578 + 0.446817i
\(671\) 1.19915 11.4091i 0.0462926 0.440445i
\(672\) 0 0
\(673\) −9.69457 10.7669i −0.373698 0.415034i 0.526734 0.850030i \(-0.323416\pi\)
−0.900432 + 0.434996i \(0.856750\pi\)
\(674\) −4.51468 −0.173899
\(675\) 0 0
\(676\) −49.5203 −1.90463
\(677\) 7.87728 + 8.74860i 0.302748 + 0.336236i 0.875253 0.483665i \(-0.160695\pi\)
−0.572505 + 0.819901i \(0.694028\pi\)
\(678\) 0 0
\(679\) −2.78421 + 26.4900i −0.106848 + 1.01659i
\(680\) −42.5878 0.182901i −1.63317 0.00701392i
\(681\) 0 0
\(682\) 3.83835 6.64822i 0.146978 0.254574i
\(683\) 7.80859 5.67327i 0.298787 0.217082i −0.428283 0.903645i \(-0.640881\pi\)
0.727070 + 0.686563i \(0.240881\pi\)
\(684\) 0 0
\(685\) −1.25836 12.4882i −0.0480794 0.477148i
\(686\) 102.735 + 114.099i 3.92243 + 4.35630i
\(687\) 0 0
\(688\) 23.9624 26.6130i 0.913559 1.01461i
\(689\) 2.15721 0.458529i 0.0821831 0.0174686i
\(690\) 0 0
\(691\) −0.843717 0.179338i −0.0320965 0.00682233i 0.191835 0.981427i \(-0.438556\pi\)
−0.223932 + 0.974605i \(0.571889\pi\)
\(692\) 52.1734 37.9062i 1.98334 1.44098i
\(693\) 0 0
\(694\) 0.594103 0.431641i 0.0225518 0.0163849i
\(695\) −1.91367 3.34769i −0.0725895 0.126985i
\(696\) 0 0
\(697\) −0.300682 + 2.86080i −0.0113891 + 0.108360i
\(698\) 40.6753 8.64580i 1.53958 0.327248i
\(699\) 0 0
\(700\) −103.822 0.891783i −3.92412 0.0337062i
\(701\) 9.06128 0.342240 0.171120 0.985250i \(-0.445261\pi\)
0.171120 + 0.985250i \(0.445261\pi\)
\(702\) 0 0
\(703\) −17.2134 12.5063i −0.649216 0.471683i
\(704\) −10.5315 + 4.68893i −0.396921 + 0.176721i
\(705\) 0 0
\(706\) 16.3664 + 7.28677i 0.615956 + 0.274241i
\(707\) 39.8353 + 68.9968i 1.49816 + 2.59489i
\(708\) 0 0
\(709\) 42.1213 + 8.95316i 1.58190 + 0.336243i 0.913270 0.407354i \(-0.133548\pi\)
0.668628 + 0.743597i \(0.266882\pi\)
\(710\) −9.78350 + 4.30564i −0.367168 + 0.161588i
\(711\) 0 0
\(712\) −4.73816 14.5825i −0.177570 0.546504i
\(713\) 10.5616 + 2.24493i 0.395534 + 0.0840733i
\(714\) 0 0
\(715\) −0.962950 3.00754i −0.0360123 0.112476i
\(716\) 48.3525 53.7009i 1.80702 2.00690i
\(717\) 0 0
\(718\) 33.2927 57.6647i 1.24247 2.15203i
\(719\) −22.4736 + 16.3280i −0.838124 + 0.608933i −0.921846 0.387556i \(-0.873319\pi\)
0.0837219 + 0.996489i \(0.473319\pi\)
\(720\) 0 0
\(721\) −65.8922 47.8735i −2.45395 1.78290i
\(722\) −4.15773 + 1.85114i −0.154735 + 0.0688924i
\(723\) 0 0
\(724\) 37.1771 + 64.3926i 1.38167 + 2.39313i
\(725\) −0.107039 + 0.181773i −0.00397533 + 0.00675089i
\(726\) 0 0
\(727\) 19.2729 + 21.4047i 0.714792 + 0.793857i 0.985657 0.168761i \(-0.0539765\pi\)
−0.270865 + 0.962617i \(0.587310\pi\)
\(728\) −18.7039 13.5891i −0.693211 0.503647i
\(729\) 0 0
\(730\) −52.4251 58.7293i −1.94034 2.17367i
\(731\) 3.23698 + 30.7978i 0.119724 + 1.13910i
\(732\) 0 0
\(733\) 11.4914 + 5.11632i 0.424446 + 0.188976i 0.607832 0.794065i \(-0.292039\pi\)
−0.183386 + 0.983041i \(0.558706\pi\)
\(734\) −12.6816 + 14.0843i −0.468086 + 0.519862i
\(735\) 0 0
\(736\) 2.11063 + 2.34410i 0.0777990 + 0.0864046i
\(737\) 1.75955 + 5.41535i 0.0648140 + 0.199477i
\(738\) 0 0
\(739\) −14.5062 + 44.6456i −0.533620 + 1.64231i 0.212992 + 0.977054i \(0.431679\pi\)
−0.746612 + 0.665259i \(0.768321\pi\)
\(740\) −20.9820 36.7050i −0.771312 1.34930i
\(741\) 0 0
\(742\) −28.4475 12.6656i −1.04434 0.464970i
\(743\) −3.97180 6.87937i −0.145711 0.252379i 0.783927 0.620853i \(-0.213214\pi\)
−0.929638 + 0.368474i \(0.879880\pi\)
\(744\) 0 0
\(745\) 18.7477 20.6424i 0.686861 0.756279i
\(746\) −46.6232 33.8738i −1.70700 1.24021i
\(747\) 0 0
\(748\) −7.46568 + 22.9770i −0.272972 + 0.840122i
\(749\) −7.04910 + 12.2094i −0.257568 + 0.446121i
\(750\) 0 0
\(751\) 6.40667 + 11.0967i 0.233783 + 0.404923i 0.958918 0.283683i \(-0.0915563\pi\)
−0.725136 + 0.688606i \(0.758223\pi\)
\(752\) 17.3564 3.68921i 0.632922 0.134532i
\(753\) 0 0
\(754\) −0.0846206 + 0.0376755i −0.00308170 + 0.00137206i
\(755\) 16.2303 + 3.52278i 0.590682 + 0.128207i
\(756\) 0 0
\(757\) 4.66915 0.169703 0.0848516 0.996394i \(-0.472958\pi\)
0.0848516 + 0.996394i \(0.472958\pi\)
\(758\) 1.88591 + 17.9432i 0.0684994 + 0.651728i
\(759\) 0 0
\(760\) −51.7064 0.222062i −1.87559 0.00805504i
\(761\) −0.470836 + 0.100079i −0.0170678 + 0.00362787i −0.216438 0.976296i \(-0.569444\pi\)
0.199370 + 0.979924i \(0.436110\pi\)
\(762\) 0 0
\(763\) 63.1328 + 13.4193i 2.28556 + 0.485811i
\(764\) −13.8071 + 42.4939i −0.499524 + 1.53738i
\(765\) 0 0
\(766\) 13.3465 + 41.0762i 0.482227 + 1.48414i
\(767\) 0.888081 + 8.44953i 0.0320668 + 0.305095i
\(768\) 0 0
\(769\) 10.7723 + 4.79612i 0.388458 + 0.172952i 0.591666 0.806183i \(-0.298470\pi\)
−0.203209 + 0.979135i \(0.565137\pi\)
\(770\) −13.9608 + 42.3473i −0.503113 + 1.52609i
\(771\) 0 0
\(772\) 23.9422 10.6598i 0.861699 0.383653i
\(773\) 9.94328 30.6023i 0.357635 1.10069i −0.596831 0.802367i \(-0.703574\pi\)
0.954466 0.298320i \(-0.0964262\pi\)
\(774\) 0 0
\(775\) −9.65261 + 1.96523i −0.346732 + 0.0705930i
\(776\) −13.1793 + 22.8272i −0.473108 + 0.819447i
\(777\) 0 0
\(778\) −0.0856846 + 0.815235i −0.00307194 + 0.0292276i
\(779\) −0.365062 + 3.47333i −0.0130797 + 0.124445i
\(780\) 0 0
\(781\) 0.321415 + 3.05806i 0.0115011 + 0.109426i
\(782\) −50.7301 −1.81411
\(783\) 0 0
\(784\) 25.7898 + 79.3730i 0.921066 + 2.83475i
\(785\) 14.1484 15.5783i 0.504978 0.556014i
\(786\) 0 0
\(787\) −15.5391 + 17.2580i −0.553911 + 0.615180i −0.953456 0.301533i \(-0.902502\pi\)
0.399545 + 0.916714i \(0.369168\pi\)
\(788\) −68.4902 + 76.0661i −2.43986 + 2.70974i
\(789\) 0 0
\(790\) −2.03807 + 18.6213i −0.0725111 + 0.662515i
\(791\) −20.1865 62.1275i −0.717748 2.20900i
\(792\) 0 0
\(793\) −6.46397 −0.229542
\(794\) −6.25425 59.5052i −0.221955 2.11176i
\(795\) 0 0
\(796\) −1.05272 + 10.0159i −0.0373126 + 0.355006i
\(797\) −4.96592 + 47.2475i −0.175902 + 1.67359i 0.449492 + 0.893285i \(0.351605\pi\)
−0.625394 + 0.780310i \(0.715062\pi\)
\(798\) 0 0
\(799\) −7.67203 + 13.2883i −0.271417 + 0.470108i
\(800\) −2.61874 1.19300i −0.0925865 0.0421788i
\(801\) 0 0
\(802\) 16.1320 49.6491i 0.569639 1.75317i
\(803\) −20.6886 + 9.21118i −0.730087 + 0.325055i
\(804\) 0 0
\(805\) −62.7155 0.269343i −2.21043 0.00949309i
\(806\) −3.95154 1.75934i −0.139187 0.0619700i
\(807\) 0 0
\(808\) 8.24113 + 78.4091i 0.289922 + 2.75842i
\(809\) −8.12369 25.0022i −0.285614 0.879029i −0.986214 0.165475i \(-0.947084\pi\)
0.700600 0.713554i \(-0.252916\pi\)
\(810\) 0 0
\(811\) −4.66526 + 14.3582i −0.163819 + 0.504184i −0.998947 0.0458715i \(-0.985394\pi\)
0.835128 + 0.550056i \(0.185394\pi\)
\(812\) 0.856931 + 0.182146i 0.0300724 + 0.00639208i
\(813\) 0 0
\(814\) −17.7603 + 3.77507i −0.622498 + 0.132316i
\(815\) −5.69576 + 4.10096i −0.199514 + 0.143650i
\(816\) 0 0
\(817\) 3.93006 + 37.3920i 0.137495 + 1.30818i
\(818\) 39.7678 1.39045
\(819\) 0 0
\(820\) −3.49566 + 5.99506i −0.122074 + 0.209357i
\(821\) −3.68804 + 1.64202i −0.128714 + 0.0573070i −0.470083 0.882622i \(-0.655776\pi\)
0.341369 + 0.939929i \(0.389109\pi\)
\(822\) 0 0
\(823\) −38.8703 + 8.26213i −1.35493 + 0.288000i −0.827437 0.561558i \(-0.810202\pi\)
−0.527495 + 0.849558i \(0.676869\pi\)
\(824\) −40.2995 69.8009i −1.40390 2.43163i
\(825\) 0 0
\(826\) 59.9811 103.890i 2.08701 3.61480i
\(827\) −11.8321 + 36.4154i −0.411441 + 1.26629i 0.503954 + 0.863730i \(0.331878\pi\)
−0.915396 + 0.402556i \(0.868122\pi\)
\(828\) 0 0
\(829\) 31.2683 + 22.7178i 1.08599 + 0.789020i 0.978718 0.205209i \(-0.0657874\pi\)
0.107275 + 0.994229i \(0.465787\pi\)
\(830\) 19.4881 + 8.77712i 0.676440 + 0.304658i
\(831\) 0 0
\(832\) 3.24782 + 5.62538i 0.112598 + 0.195025i
\(833\) −65.9299 29.3539i −2.28433 1.01705i
\(834\) 0 0
\(835\) −0.697975 + 6.37721i −0.0241544 + 0.220692i
\(836\) −9.06417 + 27.8967i −0.313491 + 0.964826i
\(837\) 0 0
\(838\) 10.7642 + 33.1289i 0.371844 + 1.14442i
\(839\) 22.1018 + 24.5466i 0.763039 + 0.847441i 0.992032 0.125987i \(-0.0402098\pi\)
−0.228993 + 0.973428i \(0.573543\pi\)
\(840\) 0 0
\(841\) −19.4036 + 21.5499i −0.669090 + 0.743099i
\(842\) 56.1949 + 25.0196i 1.93660 + 0.862232i
\(843\) 0 0
\(844\) 2.92490 + 27.8286i 0.100679 + 0.957900i
\(845\) 24.9777 10.9925i 0.859257 0.378153i
\(846\) 0 0
\(847\) −35.1651 25.5489i −1.20829 0.877872i
\(848\) −7.19462 7.99044i −0.247064 0.274393i
\(849\) 0 0
\(850\) 42.4403 18.4605i 1.45569 0.633190i
\(851\) −12.7692 22.1169i −0.437723 0.758159i
\(852\) 0 0
\(853\) 14.4168 6.41879i 0.493623 0.219775i −0.144800 0.989461i \(-0.546254\pi\)
0.638423 + 0.769686i \(0.279587\pi\)
\(854\) 73.8385 + 53.6468i 2.52670 + 1.83576i
\(855\) 0 0
\(856\) −11.2869 + 8.20042i −0.385779 + 0.280285i
\(857\) 19.9971 34.6359i 0.683086 1.18314i −0.290948 0.956739i \(-0.593971\pi\)
0.974034 0.226401i \(-0.0726961\pi\)
\(858\) 0 0
\(859\) 37.3537 41.4854i 1.27449 1.41547i 0.410576 0.911826i \(-0.365328\pi\)
0.863914 0.503639i \(-0.168006\pi\)
\(860\) −23.3915 + 70.9535i −0.797645 + 2.41949i
\(861\) 0 0
\(862\) 12.1715 + 2.58712i 0.414562 + 0.0881178i
\(863\) −2.37722 7.31633i −0.0809215 0.249051i 0.902408 0.430882i \(-0.141797\pi\)
−0.983330 + 0.181831i \(0.941797\pi\)
\(864\) 0 0
\(865\) −17.9015 + 30.7010i −0.608668 + 1.04387i
\(866\) −48.4670 10.3020i −1.64697 0.350075i
\(867\) 0 0
\(868\) 20.4551 + 35.4293i 0.694291 + 1.20255i
\(869\) 4.92286 + 2.19180i 0.166997 + 0.0743517i
\(870\) 0 0
\(871\) 2.93097 1.30495i 0.0993121 0.0442166i
\(872\) 51.6728 + 37.5425i 1.74986 + 1.27135i
\(873\) 0 0
\(874\) −61.5921 −2.08338
\(875\) 52.5652 22.5966i 1.77703 0.763905i
\(876\) 0 0
\(877\) 5.86040 1.24567i 0.197892 0.0420632i −0.107899 0.994162i \(-0.534412\pi\)
0.305791 + 0.952099i \(0.401079\pi\)
\(878\) −10.2136 + 97.1763i −0.344694 + 3.27954i
\(879\) 0 0
\(880\) −10.3511 + 11.3973i −0.348936 + 0.384202i
\(881\) 35.8213 26.0257i 1.20685 0.876829i 0.211910 0.977289i \(-0.432032\pi\)
0.994941 + 0.100461i \(0.0320317\pi\)
\(882\) 0 0
\(883\) 37.8054 27.4673i 1.27225 0.924347i 0.272964 0.962024i \(-0.411996\pi\)
0.999290 + 0.0376774i \(0.0119959\pi\)
\(884\) 13.3153 + 2.83026i 0.447843 + 0.0951920i
\(885\) 0 0
\(886\) 68.4372 14.5468i 2.29919 0.488709i
\(887\) −24.3581 + 27.0524i −0.817865 + 0.908331i −0.997148 0.0754668i \(-0.975955\pi\)
0.179284 + 0.983797i \(0.442622\pi\)
\(888\) 0 0
\(889\) 26.1300 + 29.0203i 0.876372 + 0.973310i
\(890\) 11.0962 + 12.4306i 0.371946 + 0.416673i
\(891\) 0 0
\(892\) 43.2968 31.4569i 1.44968 1.05326i
\(893\) −9.31471 + 16.1336i −0.311705 + 0.539889i
\(894\) 0 0
\(895\) −12.4682 + 37.8196i −0.416764 + 1.26417i
\(896\) 10.2027 97.0725i 0.340849 3.24297i
\(897\) 0 0
\(898\) −54.2904 60.2956i −1.81169 2.01209i
\(899\) 0.0831187 0.00277216
\(900\) 0 0
\(901\) 9.29786 0.309757
\(902\) 1.99425 + 2.21484i 0.0664012 + 0.0737460i
\(903\) 0 0
\(904\) 6.75719 64.2904i 0.224741 2.13827i
\(905\) −33.0456 24.2266i −1.09847 0.805319i
\(906\) 0 0
\(907\) 7.52629 13.0359i 0.249906 0.432850i −0.713593 0.700560i \(-0.752934\pi\)
0.963500 + 0.267710i \(0.0862669\pi\)
\(908\) −57.5491 + 41.8119i −1.90983 + 1.38758i
\(909\) 0 0
\(910\) 24.5525 + 5.32909i 0.813906 + 0.176658i
\(911\) −39.2302 43.5696i −1.29976 1.44352i −0.826862 0.562405i \(-0.809876\pi\)
−0.472894 0.881120i \(-0.656791\pi\)
\(912\) 0 0
\(913\) 4.11412 4.56920i 0.136158 0.151218i
\(914\) −68.1404 + 14.4837i −2.25388 + 0.479078i
\(915\) 0 0
\(916\) −64.4918 13.7082i −2.13087 0.452930i
\(917\) −10.7625 + 7.81939i −0.355408 + 0.258219i
\(918\) 0 0
\(919\) −5.91856 + 4.30008i −0.195235 + 0.141847i −0.681108 0.732183i \(-0.738502\pi\)
0.485873 + 0.874029i \(0.338502\pi\)
\(920\) −56.5885 25.4866i −1.86567 0.840267i
\(921\) 0 0
\(922\) −4.27706 + 40.6935i −0.140857 + 1.34017i
\(923\) 1.69471 0.360223i 0.0557822 0.0118569i
\(924\) 0 0
\(925\) 18.7309 + 13.8561i 0.615867 + 0.455587i
\(926\) −26.8105 −0.881048
\(927\) 0 0
\(928\) 0.0196442 + 0.0142724i 0.000644853 + 0.000468513i
\(929\) 18.1828 8.09550i 0.596558 0.265605i −0.0861664 0.996281i \(-0.527462\pi\)
0.682724 + 0.730676i \(0.260795\pi\)
\(930\) 0 0
\(931\) −80.0463 35.6389i −2.62341 1.16802i
\(932\) 38.6899 + 67.0130i 1.26733 + 2.19508i
\(933\) 0 0
\(934\) 59.3479 + 12.6148i 1.94192 + 0.412769i
\(935\) −1.33479 13.2466i −0.0436522 0.433211i
\(936\) 0 0
\(937\) 5.65299 + 17.3981i 0.184675 + 0.568371i 0.999943 0.0107132i \(-0.00341019\pi\)
−0.815268 + 0.579084i \(0.803410\pi\)
\(938\) −44.3110 9.41859i −1.44681 0.307528i
\(939\) 0 0
\(940\) −30.0413 + 21.6298i −0.979840 + 0.705486i
\(941\) 12.6090 14.0037i 0.411041 0.456507i −0.501703 0.865040i \(-0.667293\pi\)
0.912743 + 0.408533i \(0.133960\pi\)
\(942\) 0 0
\(943\) −2.09598 + 3.63034i −0.0682545 + 0.118220i
\(944\) 33.5108 24.3470i 1.09068 0.792429i
\(945\) 0 0
\(946\) 25.9572 + 18.8590i 0.843942 + 0.613160i
\(947\) −27.7953 + 12.3753i −0.903226 + 0.402142i −0.805174 0.593039i \(-0.797928\pi\)
−0.0980527 + 0.995181i \(0.531261\pi\)
\(948\) 0 0
\(949\) 6.38018 + 11.0508i 0.207109 + 0.358724i
\(950\) 51.5273 22.4131i 1.67177 0.727178i
\(951\) 0 0
\(952\) −65.2198 72.4339i −2.11379 2.34760i
\(953\) 6.16233 + 4.47720i 0.199617 + 0.145031i 0.683104 0.730321i \(-0.260630\pi\)
−0.483486 + 0.875352i \(0.660630\pi\)
\(954\) 0 0
\(955\) −2.46857 24.4985i −0.0798810 0.792753i
\(956\) −2.95547 28.1194i −0.0955867 0.909446i
\(957\) 0 0
\(958\) −87.1228 38.7896i −2.81481 1.25323i
\(959\) 19.2213 21.3474i 0.620688 0.689344i
\(960\) 0 0
\(961\) −18.1459 20.1530i −0.585351 0.650098i
\(962\) 3.16147 + 9.73000i 0.101930 + 0.313708i
\(963\) 0 0
\(964\) −3.80381 + 11.7069i −0.122513 + 0.377055i
\(965\) −9.71002 + 10.6914i −0.312577 + 0.344167i
\(966\) 0 0
\(967\) 45.3597 + 20.1955i 1.45867 + 0.649442i 0.974266 0.225402i \(-0.0723695\pi\)
0.484405 + 0.874844i \(0.339036\pi\)
\(968\) −21.5069 37.2511i −0.691258 1.19729i
\(969\) 0 0
\(970\) 3.11647 28.4743i 0.100064 0.914255i
\(971\) 0.472976 + 0.343637i 0.0151785 + 0.0110278i 0.595349 0.803467i \(-0.297014\pi\)
−0.580170 + 0.814495i \(0.697014\pi\)
\(972\) 0 0
\(973\) 2.72713 8.39323i 0.0874276 0.269075i
\(974\) −1.11660 + 1.93400i −0.0357780 + 0.0619693i
\(975\) 0 0
\(976\) 15.7572 + 27.2923i 0.504376 + 0.873604i
\(977\) 53.8166 11.4391i 1.72174 0.365968i 0.762160 0.647389i \(-0.224139\pi\)
0.959585 + 0.281420i \(0.0908055\pi\)
\(978\) 0 0
\(979\) 4.37893 1.94962i 0.139951 0.0623103i
\(980\) −115.946 129.888i −3.70375 4.14913i
\(981\) 0 0
\(982\) 11.5241 0.367750
\(983\) 6.11179 + 58.1498i 0.194936 + 1.85469i 0.456778 + 0.889581i \(0.349003\pi\)
−0.261842 + 0.965111i \(0.584330\pi\)
\(984\) 0 0
\(985\) 17.6608 53.5705i 0.562721 1.70690i
\(986\) −0.381984 + 0.0811933i −0.0121649 + 0.00258572i
\(987\) 0 0
\(988\) 16.1663 + 3.43626i 0.514319 + 0.109322i
\(989\) −13.9454 + 42.9196i −0.443439 + 1.36476i
\(990\) 0 0
\(991\) −14.9966 46.1549i −0.476384 1.46616i −0.844082 0.536213i \(-0.819854\pi\)
0.367699 0.929945i \(-0.380146\pi\)
\(992\) 0.118523 + 1.12767i 0.00376310 + 0.0358035i
\(993\) 0 0
\(994\) −22.3485 9.95019i −0.708851 0.315601i
\(995\) −1.69235 5.28565i −0.0536511 0.167566i
\(996\) 0 0
\(997\) 42.4960 18.9204i 1.34586 0.599216i 0.397849 0.917451i \(-0.369757\pi\)
0.948012 + 0.318235i \(0.103090\pi\)
\(998\) 10.6523 32.7843i 0.337192 1.03777i
\(999\) 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 675.2.r.a.46.3 224
3.2 odd 2 225.2.q.a.196.26 yes 224
9.4 even 3 inner 675.2.r.a.496.26 224
9.5 odd 6 225.2.q.a.121.3 yes 224
25.6 even 5 inner 675.2.r.a.181.26 224
75.56 odd 10 225.2.q.a.106.3 yes 224
225.31 even 15 inner 675.2.r.a.631.3 224
225.131 odd 30 225.2.q.a.31.26 224
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
225.2.q.a.31.26 224 225.131 odd 30
225.2.q.a.106.3 yes 224 75.56 odd 10
225.2.q.a.121.3 yes 224 9.5 odd 6
225.2.q.a.196.26 yes 224 3.2 odd 2
675.2.r.a.46.3 224 1.1 even 1 trivial
675.2.r.a.181.26 224 25.6 even 5 inner
675.2.r.a.496.26 224 9.4 even 3 inner
675.2.r.a.631.3 224 225.31 even 15 inner