Properties

Label 504.2.cz.b.187.7
Level $504$
Weight $2$
Character 504.187
Analytic conductor $4.024$
Analytic rank $0$
Dimension $180$
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] = [504,2,Mod(187,504)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(504, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 3, 4, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("504.187");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 504.cz (of order \(6\), degree \(2\), 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: \(4.02446026187\)
Analytic rank: \(0\)
Dimension: \(180\)
Relative dimension: \(90\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 187.7
Character \(\chi\) \(=\) 504.187
Dual form 504.2.cz.b.283.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.37605 + 0.326323i) q^{2} +(-1.36395 + 1.06753i) q^{3} +(1.78703 - 0.898073i) q^{4} -1.29544 q^{5} +(1.52851 - 1.91407i) q^{6} +(2.57211 + 0.619896i) q^{7} +(-2.16598 + 1.81894i) q^{8} +(0.720742 - 2.91214i) q^{9} +O(q^{10})\) \(q+(-1.37605 + 0.326323i) q^{2} +(-1.36395 + 1.06753i) q^{3} +(1.78703 - 0.898073i) q^{4} -1.29544 q^{5} +(1.52851 - 1.91407i) q^{6} +(2.57211 + 0.619896i) q^{7} +(-2.16598 + 1.81894i) q^{8} +(0.720742 - 2.91214i) q^{9} +(1.78258 - 0.422730i) q^{10} -2.98972 q^{11} +(-1.47870 + 3.13264i) q^{12} +(2.18085 + 3.77734i) q^{13} +(-3.74163 - 0.0136713i) q^{14} +(1.76691 - 1.38292i) q^{15} +(2.38693 - 3.20976i) q^{16} +(5.58434 - 3.22412i) q^{17} +(-0.0414806 + 4.24244i) q^{18} +(0.691565 + 0.399275i) q^{19} +(-2.31498 + 1.16340i) q^{20} +(-4.16999 + 1.90030i) q^{21} +(4.11401 - 0.975615i) q^{22} +2.12001i q^{23} +(1.01251 - 4.79321i) q^{24} -3.32185 q^{25} +(-4.23359 - 4.48614i) q^{26} +(2.12574 + 4.74144i) q^{27} +(5.15313 - 1.20217i) q^{28} +(5.35063 + 3.08919i) q^{29} +(-1.98008 + 2.47955i) q^{30} +(-4.23525 + 7.33567i) q^{31} +(-2.23711 + 5.19570i) q^{32} +(4.07785 - 3.19163i) q^{33} +(-6.63223 + 6.25885i) q^{34} +(-3.33200 - 0.803036i) q^{35} +(-1.32733 - 5.85134i) q^{36} +(-4.14087 - 2.39073i) q^{37} +(-1.08192 - 0.323749i) q^{38} +(-7.00701 - 2.82399i) q^{39} +(2.80588 - 2.35632i) q^{40} +(-8.48089 + 4.89644i) q^{41} +(5.11801 - 3.97567i) q^{42} +(-3.24095 + 5.61349i) q^{43} +(-5.34272 + 2.68499i) q^{44} +(-0.933675 + 3.77248i) q^{45} +(-0.691807 - 2.91724i) q^{46} +(2.10294 + 3.64240i) q^{47} +(0.170868 + 6.92610i) q^{48} +(6.23146 + 3.18888i) q^{49} +(4.57103 - 1.08399i) q^{50} +(-4.17493 + 10.3590i) q^{51} +(7.28956 + 4.79164i) q^{52} +(-5.39904 + 3.11714i) q^{53} +(-4.47237 - 5.83077i) q^{54} +3.87299 q^{55} +(-6.69867 + 3.33583i) q^{56} +(-1.36950 + 0.193676i) q^{57} +(-8.37080 - 2.50484i) q^{58} +(5.71256 + 3.29815i) q^{59} +(1.91556 - 4.05814i) q^{60} +(-4.77473 - 8.27007i) q^{61} +(3.43412 - 11.4763i) q^{62} +(3.65905 - 7.04353i) q^{63} +(1.38291 - 7.87957i) q^{64} +(-2.82515 - 4.89330i) q^{65} +(-4.56982 + 5.72254i) q^{66} +(-2.78647 + 4.82630i) q^{67} +(7.08387 - 10.7767i) q^{68} +(-2.26318 - 2.89159i) q^{69} +(4.84704 + 0.0177102i) q^{70} +15.1319i q^{71} +(3.73589 + 7.61860i) q^{72} +(13.2132 - 7.62862i) q^{73} +(6.47819 + 1.93851i) q^{74} +(4.53085 - 3.54618i) q^{75} +(1.59442 + 0.0924395i) q^{76} +(-7.68989 - 1.85332i) q^{77} +(10.5635 + 1.59940i) q^{78} +(-5.28146 + 3.04925i) q^{79} +(-3.09211 + 4.15804i) q^{80} +(-7.96106 - 4.19780i) q^{81} +(10.0723 - 9.50526i) q^{82} +(6.94136 + 4.00760i) q^{83} +(-5.74528 + 7.14085i) q^{84} +(-7.23416 + 4.17664i) q^{85} +(2.62790 - 8.78204i) q^{86} +(-10.5958 + 1.49847i) q^{87} +(6.47567 - 5.43813i) q^{88} +(-2.85066 - 1.64583i) q^{89} +(0.0537355 - 5.49581i) q^{90} +(3.26781 + 11.0676i) q^{91} +(1.90392 + 3.78851i) q^{92} +(-2.05439 - 14.5268i) q^{93} +(-4.08235 - 4.32589i) q^{94} +(-0.895878 - 0.517235i) q^{95} +(-2.49527 - 9.47490i) q^{96} +(15.4850 + 8.94026i) q^{97} +(-9.61540 - 2.35459i) q^{98} +(-2.15482 + 8.70648i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 180 q + 3 q^{2} + q^{4} + 6 q^{6} - 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 180 q + 3 q^{2} + q^{4} + 6 q^{6} - 8 q^{9} + 16 q^{11} - 3 q^{12} + 7 q^{14} - 7 q^{16} - 18 q^{17} - 13 q^{18} - 6 q^{19} - 36 q^{20} - 16 q^{22} - 24 q^{24} + 156 q^{25} - 6 q^{26} + 16 q^{28} - 8 q^{30} + 13 q^{32} - 36 q^{33} + 12 q^{34} - 12 q^{35} + 2 q^{36} + 42 q^{41} + 31 q^{42} + 14 q^{43} - 21 q^{44} - 12 q^{46} + 9 q^{48} + 20 q^{49} + 15 q^{50} - 42 q^{51} - 12 q^{54} - 40 q^{56} - 26 q^{57} - 38 q^{58} + 18 q^{59} - 38 q^{60} - 8 q^{64} - 12 q^{65} - 21 q^{66} - 14 q^{67} - 42 q^{70} + 5 q^{72} + 18 q^{73} - 98 q^{74} - 48 q^{75} + 12 q^{76} - 33 q^{78} - 63 q^{80} + 8 q^{81} - 54 q^{82} - 6 q^{83} - 77 q^{84} + 26 q^{86} - 58 q^{88} - 66 q^{89} + 51 q^{90} + 2 q^{91} - 60 q^{92} + 9 q^{94} - 30 q^{96} + 6 q^{97} + 31 q^{98} + 4 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/504\mathbb{Z}\right)^\times\).

\(n\) \(73\) \(127\) \(253\) \(281\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(-1\) \(-1\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.37605 + 0.326323i −0.973014 + 0.230745i
\(3\) −1.36395 + 1.06753i −0.787479 + 0.616341i
\(4\) 1.78703 0.898073i 0.893513 0.449037i
\(5\) −1.29544 −0.579336 −0.289668 0.957127i \(-0.593545\pi\)
−0.289668 + 0.957127i \(0.593545\pi\)
\(6\) 1.52851 1.91407i 0.624011 0.781416i
\(7\) 2.57211 + 0.619896i 0.972165 + 0.234299i
\(8\) −2.16598 + 1.81894i −0.765788 + 0.643093i
\(9\) 0.720742 2.91214i 0.240247 0.970712i
\(10\) 1.78258 0.422730i 0.563703 0.133679i
\(11\) −2.98972 −0.901436 −0.450718 0.892666i \(-0.648832\pi\)
−0.450718 + 0.892666i \(0.648832\pi\)
\(12\) −1.47870 + 3.13264i −0.426864 + 0.904316i
\(13\) 2.18085 + 3.77734i 0.604858 + 1.04764i 0.992074 + 0.125656i \(0.0401035\pi\)
−0.387216 + 0.921989i \(0.626563\pi\)
\(14\) −3.74163 0.0136713i −0.999993 0.00365380i
\(15\) 1.76691 1.38292i 0.456215 0.357069i
\(16\) 2.38693 3.20976i 0.596732 0.802440i
\(17\) 5.58434 3.22412i 1.35440 0.781964i 0.365539 0.930796i \(-0.380885\pi\)
0.988863 + 0.148831i \(0.0475512\pi\)
\(18\) −0.0414806 + 4.24244i −0.00977707 + 0.999952i
\(19\) 0.691565 + 0.399275i 0.158656 + 0.0916000i 0.577226 0.816585i \(-0.304135\pi\)
−0.418570 + 0.908185i \(0.637469\pi\)
\(20\) −2.31498 + 1.16340i −0.517645 + 0.260143i
\(21\) −4.16999 + 1.90030i −0.909968 + 0.414680i
\(22\) 4.11401 0.975615i 0.877110 0.208002i
\(23\) 2.12001i 0.442052i 0.975268 + 0.221026i \(0.0709406\pi\)
−0.975268 + 0.221026i \(0.929059\pi\)
\(24\) 1.01251 4.79321i 0.206678 0.978409i
\(25\) −3.32185 −0.664369
\(26\) −4.23359 4.48614i −0.830274 0.879805i
\(27\) 2.12574 + 4.74144i 0.409100 + 0.912490i
\(28\) 5.15313 1.20217i 0.973851 0.227188i
\(29\) 5.35063 + 3.08919i 0.993587 + 0.573648i 0.906344 0.422540i \(-0.138861\pi\)
0.0872423 + 0.996187i \(0.472195\pi\)
\(30\) −1.98008 + 2.47955i −0.361512 + 0.452703i
\(31\) −4.23525 + 7.33567i −0.760673 + 1.31752i 0.181831 + 0.983330i \(0.441798\pi\)
−0.942504 + 0.334195i \(0.891536\pi\)
\(32\) −2.23711 + 5.19570i −0.395470 + 0.918479i
\(33\) 4.07785 3.19163i 0.709862 0.555592i
\(34\) −6.63223 + 6.25885i −1.13742 + 1.07338i
\(35\) −3.33200 0.803036i −0.563210 0.135738i
\(36\) −1.32733 5.85134i −0.221221 0.975224i
\(37\) −4.14087 2.39073i −0.680754 0.393034i 0.119385 0.992848i \(-0.461908\pi\)
−0.800139 + 0.599814i \(0.795241\pi\)
\(38\) −1.08192 0.323749i −0.175511 0.0525190i
\(39\) −7.00701 2.82399i −1.12202 0.452200i
\(40\) 2.80588 2.35632i 0.443649 0.372567i
\(41\) −8.48089 + 4.89644i −1.32449 + 0.764696i −0.984442 0.175711i \(-0.943778\pi\)
−0.340051 + 0.940407i \(0.610444\pi\)
\(42\) 5.11801 3.97567i 0.789726 0.613460i
\(43\) −3.24095 + 5.61349i −0.494240 + 0.856050i −0.999978 0.00663784i \(-0.997887\pi\)
0.505738 + 0.862687i \(0.331220\pi\)
\(44\) −5.34272 + 2.68499i −0.805445 + 0.404778i
\(45\) −0.933675 + 3.77248i −0.139184 + 0.562369i
\(46\) −0.691807 2.91724i −0.102001 0.430123i
\(47\) 2.10294 + 3.64240i 0.306745 + 0.531299i 0.977648 0.210246i \(-0.0674266\pi\)
−0.670903 + 0.741545i \(0.734093\pi\)
\(48\) 0.170868 + 6.92610i 0.0246627 + 0.999696i
\(49\) 6.23146 + 3.18888i 0.890208 + 0.455554i
\(50\) 4.57103 1.08399i 0.646441 0.153300i
\(51\) −4.17493 + 10.3590i −0.584607 + 1.45055i
\(52\) 7.28956 + 4.79164i 1.01088 + 0.664481i
\(53\) −5.39904 + 3.11714i −0.741615 + 0.428172i −0.822656 0.568539i \(-0.807509\pi\)
0.0810409 + 0.996711i \(0.474176\pi\)
\(54\) −4.47237 5.83077i −0.608612 0.793468i
\(55\) 3.87299 0.522234
\(56\) −6.69867 + 3.33583i −0.895148 + 0.445769i
\(57\) −1.36950 + 0.193676i −0.181395 + 0.0256530i
\(58\) −8.37080 2.50484i −1.09914 0.328902i
\(59\) 5.71256 + 3.29815i 0.743713 + 0.429383i 0.823418 0.567436i \(-0.192065\pi\)
−0.0797051 + 0.996818i \(0.525398\pi\)
\(60\) 1.91556 4.05814i 0.247298 0.523903i
\(61\) −4.77473 8.27007i −0.611341 1.05887i −0.991015 0.133754i \(-0.957297\pi\)
0.379673 0.925121i \(-0.376036\pi\)
\(62\) 3.43412 11.4763i 0.436134 1.45749i
\(63\) 3.65905 7.04353i 0.460997 0.887402i
\(64\) 1.38291 7.87957i 0.172863 0.984946i
\(65\) −2.82515 4.89330i −0.350416 0.606939i
\(66\) −4.56982 + 5.72254i −0.562506 + 0.704396i
\(67\) −2.78647 + 4.82630i −0.340421 + 0.589627i −0.984511 0.175323i \(-0.943903\pi\)
0.644090 + 0.764950i \(0.277236\pi\)
\(68\) 7.08387 10.7767i 0.859046 1.30687i
\(69\) −2.26318 2.89159i −0.272455 0.348107i
\(70\) 4.84704 + 0.0177102i 0.579333 + 0.00211678i
\(71\) 15.1319i 1.79583i 0.440167 + 0.897916i \(0.354919\pi\)
−0.440167 + 0.897916i \(0.645081\pi\)
\(72\) 3.73589 + 7.61860i 0.440279 + 0.897861i
\(73\) 13.2132 7.62862i 1.54648 0.892862i 0.548077 0.836428i \(-0.315360\pi\)
0.998406 0.0564342i \(-0.0179731\pi\)
\(74\) 6.47819 + 1.93851i 0.753074 + 0.225347i
\(75\) 4.53085 3.54618i 0.523177 0.409478i
\(76\) 1.59442 + 0.0924395i 0.182893 + 0.0106035i
\(77\) −7.68989 1.85332i −0.876344 0.211205i
\(78\) 10.5635 + 1.59940i 1.19608 + 0.181096i
\(79\) −5.28146 + 3.04925i −0.594210 + 0.343068i −0.766761 0.641933i \(-0.778133\pi\)
0.172550 + 0.985001i \(0.444799\pi\)
\(80\) −3.09211 + 4.15804i −0.345709 + 0.464883i
\(81\) −7.96106 4.19780i −0.884562 0.466422i
\(82\) 10.0723 9.50526i 1.11230 1.04968i
\(83\) 6.94136 + 4.00760i 0.761913 + 0.439891i 0.829982 0.557790i \(-0.188350\pi\)
−0.0680689 + 0.997681i \(0.521684\pi\)
\(84\) −5.74528 + 7.14085i −0.626862 + 0.779130i
\(85\) −7.23416 + 4.17664i −0.784654 + 0.453020i
\(86\) 2.62790 8.78204i 0.283374 0.946992i
\(87\) −10.5958 + 1.49847i −1.13599 + 0.160653i
\(88\) 6.47567 5.43813i 0.690309 0.579707i
\(89\) −2.85066 1.64583i −0.302169 0.174458i 0.341248 0.939973i \(-0.389151\pi\)
−0.643417 + 0.765516i \(0.722484\pi\)
\(90\) 0.0537355 5.49581i 0.00566421 0.579309i
\(91\) 3.26781 + 11.0676i 0.342560 + 1.16020i
\(92\) 1.90392 + 3.78851i 0.198498 + 0.394979i
\(93\) −2.05439 14.5268i −0.213030 1.50636i
\(94\) −4.08235 4.32589i −0.421062 0.446181i
\(95\) −0.895878 0.517235i −0.0919151 0.0530672i
\(96\) −2.49527 9.47490i −0.254672 0.967027i
\(97\) 15.4850 + 8.94026i 1.57226 + 0.907746i 0.995891 + 0.0905572i \(0.0288648\pi\)
0.576370 + 0.817189i \(0.304469\pi\)
\(98\) −9.61540 2.35459i −0.971302 0.237849i
\(99\) −2.15482 + 8.70648i −0.216568 + 0.875034i
\(100\) −5.93623 + 2.98326i −0.593623 + 0.298326i
\(101\) 6.21283 0.618199 0.309100 0.951030i \(-0.399972\pi\)
0.309100 + 0.951030i \(0.399972\pi\)
\(102\) 2.36452 15.6169i 0.234122 1.54631i
\(103\) −1.06791 −0.105224 −0.0526120 0.998615i \(-0.516755\pi\)
−0.0526120 + 0.998615i \(0.516755\pi\)
\(104\) −11.5944 4.21479i −1.13693 0.413294i
\(105\) 5.40196 2.46172i 0.527177 0.240239i
\(106\) 6.41216 6.05117i 0.622804 0.587741i
\(107\) 4.03108 6.98203i 0.389699 0.674978i −0.602710 0.797960i \(-0.705912\pi\)
0.992409 + 0.122982i \(0.0392457\pi\)
\(108\) 8.05692 + 6.56400i 0.775277 + 0.631621i
\(109\) 2.26820 1.30955i 0.217254 0.125432i −0.387424 0.921902i \(-0.626635\pi\)
0.604678 + 0.796470i \(0.293302\pi\)
\(110\) −5.32943 + 1.26385i −0.508142 + 0.120503i
\(111\) 8.20014 1.15967i 0.778323 0.110071i
\(112\) 8.12915 6.77620i 0.768133 0.640291i
\(113\) −2.10974 3.65418i −0.198468 0.343756i 0.749564 0.661932i \(-0.230263\pi\)
−0.948032 + 0.318176i \(0.896930\pi\)
\(114\) 1.82130 0.713408i 0.170581 0.0668168i
\(115\) 2.74633i 0.256097i
\(116\) 12.3360 + 0.715203i 1.14537 + 0.0664050i
\(117\) 12.5719 3.62843i 1.16228 0.335449i
\(118\) −8.93704 2.67428i −0.822721 0.246187i
\(119\) 16.3621 4.83107i 1.49992 0.442863i
\(120\) −1.31164 + 6.20929i −0.119736 + 0.566828i
\(121\) −2.06155 −0.187414
\(122\) 9.26898 + 9.82193i 0.839174 + 0.889236i
\(123\) 6.34042 15.7322i 0.571697 1.41852i
\(124\) −0.980538 + 16.9126i −0.0880549 + 1.51880i
\(125\) 10.7804 0.964230
\(126\) −2.73656 + 10.8863i −0.243793 + 0.969827i
\(127\) 17.7694i 1.57678i −0.615177 0.788389i \(-0.710916\pi\)
0.615177 0.788389i \(-0.289084\pi\)
\(128\) 0.668336 + 11.2940i 0.0590731 + 0.998254i
\(129\) −1.57209 11.1164i −0.138414 0.978742i
\(130\) 5.48434 + 5.81151i 0.481008 + 0.509703i
\(131\) 10.5637i 0.922955i −0.887152 0.461478i \(-0.847320\pi\)
0.887152 0.461478i \(-0.152680\pi\)
\(132\) 4.42090 9.36574i 0.384790 0.815183i
\(133\) 1.53127 + 1.45568i 0.132778 + 0.126223i
\(134\) 2.25939 7.55052i 0.195181 0.652266i
\(135\) −2.75377 6.14222i −0.237006 0.528639i
\(136\) −6.23107 + 17.1410i −0.534309 + 1.46983i
\(137\) 4.10655 0.350846 0.175423 0.984493i \(-0.443871\pi\)
0.175423 + 0.984493i \(0.443871\pi\)
\(138\) 4.05784 + 3.24045i 0.345426 + 0.275845i
\(139\) −5.45433 + 3.14906i −0.462630 + 0.267100i −0.713149 0.701012i \(-0.752732\pi\)
0.250519 + 0.968112i \(0.419399\pi\)
\(140\) −6.67555 + 1.55733i −0.564187 + 0.131619i
\(141\) −6.75670 2.72311i −0.569017 0.229327i
\(142\) −4.93790 20.8223i −0.414379 1.74737i
\(143\) −6.52013 11.2932i −0.545241 0.944384i
\(144\) −7.62690 9.26447i −0.635575 0.772039i
\(145\) −6.93139 4.00184i −0.575621 0.332335i
\(146\) −15.6926 + 14.8091i −1.29873 + 1.22561i
\(147\) −11.9037 + 2.30281i −0.981797 + 0.189933i
\(148\) −9.54689 0.553498i −0.784750 0.0454973i
\(149\) 14.2537i 1.16771i 0.811859 + 0.583853i \(0.198456\pi\)
−0.811859 + 0.583853i \(0.801544\pi\)
\(150\) −5.07747 + 6.35825i −0.414574 + 0.519149i
\(151\) 4.73750i 0.385532i 0.981245 + 0.192766i \(0.0617459\pi\)
−0.981245 + 0.192766i \(0.938254\pi\)
\(152\) −2.22417 + 0.393095i −0.180404 + 0.0318842i
\(153\) −5.36421 18.5861i −0.433671 1.50260i
\(154\) 11.1864 + 0.0408733i 0.901430 + 0.00329367i
\(155\) 5.48649 9.50289i 0.440686 0.763290i
\(156\) −15.0579 + 1.24627i −1.20559 + 0.0997814i
\(157\) 1.44119 2.49622i 0.115020 0.199220i −0.802768 0.596292i \(-0.796640\pi\)
0.917788 + 0.397072i \(0.129974\pi\)
\(158\) 6.27251 5.91938i 0.499014 0.470921i
\(159\) 4.03639 10.0153i 0.320107 0.794265i
\(160\) 2.89804 6.73070i 0.229110 0.532108i
\(161\) −1.31418 + 5.45288i −0.103572 + 0.429747i
\(162\) 12.3247 + 3.17850i 0.968316 + 0.249727i
\(163\) 1.06483 1.84434i 0.0834041 0.144460i −0.821306 0.570488i \(-0.806754\pi\)
0.904710 + 0.426028i \(0.140087\pi\)
\(164\) −10.7582 + 16.3665i −0.840075 + 1.27801i
\(165\) −5.28259 + 4.13455i −0.411249 + 0.321875i
\(166\) −10.8594 3.24953i −0.842855 0.252212i
\(167\) 0.609750 + 1.05612i 0.0471838 + 0.0817248i 0.888653 0.458581i \(-0.151642\pi\)
−0.841469 + 0.540306i \(0.818309\pi\)
\(168\) 5.57557 11.7010i 0.430165 0.902750i
\(169\) −3.01218 + 5.21726i −0.231707 + 0.401327i
\(170\) 8.59163 8.10794i 0.658948 0.621851i
\(171\) 1.66118 1.72616i 0.127034 0.132002i
\(172\) −0.750340 + 12.9421i −0.0572129 + 0.986824i
\(173\) 5.31967 + 9.21393i 0.404447 + 0.700522i 0.994257 0.107020i \(-0.0341308\pi\)
−0.589810 + 0.807542i \(0.700797\pi\)
\(174\) 14.0914 5.51963i 1.06827 0.418442i
\(175\) −8.54414 2.05920i −0.645876 0.155661i
\(176\) −7.13626 + 9.59630i −0.537916 + 0.723348i
\(177\) −11.3126 + 1.59983i −0.850304 + 0.120251i
\(178\) 4.45972 + 1.33451i 0.334270 + 0.100026i
\(179\) −4.41006 7.63846i −0.329624 0.570925i 0.652813 0.757519i \(-0.273589\pi\)
−0.982437 + 0.186594i \(0.940255\pi\)
\(180\) 1.71946 + 7.58004i 0.128161 + 0.564983i
\(181\) −0.570360 −0.0423945 −0.0211973 0.999775i \(-0.506748\pi\)
−0.0211973 + 0.999775i \(0.506748\pi\)
\(182\) −8.10829 14.1632i −0.601026 1.04985i
\(183\) 15.3411 + 6.18281i 1.13405 + 0.457047i
\(184\) −3.85617 4.59188i −0.284280 0.338518i
\(185\) 5.36423 + 3.09704i 0.394386 + 0.227699i
\(186\) 7.56736 + 19.3192i 0.554866 + 1.41655i
\(187\) −16.6956 + 9.63923i −1.22091 + 0.704891i
\(188\) 7.02915 + 4.62047i 0.512654 + 0.336983i
\(189\) 2.52844 + 13.5132i 0.183917 + 0.982942i
\(190\) 1.40156 + 0.419396i 0.101680 + 0.0304262i
\(191\) −0.995333 + 0.574656i −0.0720198 + 0.0415806i −0.535577 0.844486i \(-0.679906\pi\)
0.463558 + 0.886067i \(0.346573\pi\)
\(192\) 6.52549 + 12.2237i 0.470936 + 0.882167i
\(193\) 5.24266 9.08055i 0.377375 0.653632i −0.613305 0.789846i \(-0.710160\pi\)
0.990679 + 0.136214i \(0.0434936\pi\)
\(194\) −24.2255 7.24914i −1.73929 0.520458i
\(195\) 9.07713 + 3.65829i 0.650027 + 0.261976i
\(196\) 13.9996 + 0.102306i 0.999973 + 0.00730755i
\(197\) 3.02860i 0.215779i −0.994163 0.107889i \(-0.965591\pi\)
0.994163 0.107889i \(-0.0344092\pi\)
\(198\) 0.124016 12.6837i 0.00881340 0.901393i
\(199\) 5.80546 + 10.0554i 0.411538 + 0.712806i 0.995058 0.0992934i \(-0.0316582\pi\)
−0.583520 + 0.812099i \(0.698325\pi\)
\(200\) 7.19504 6.04224i 0.508766 0.427251i
\(201\) −1.35163 9.55751i −0.0953366 0.674134i
\(202\) −8.54916 + 2.02739i −0.601517 + 0.142646i
\(203\) 11.8474 + 11.2626i 0.831525 + 0.790476i
\(204\) 1.84246 + 22.2613i 0.128998 + 1.55860i
\(205\) 10.9864 6.34303i 0.767327 0.443016i
\(206\) 1.46949 0.348482i 0.102384 0.0242799i
\(207\) 6.17375 + 1.52798i 0.429105 + 0.106202i
\(208\) 17.3299 + 2.01624i 1.20161 + 0.139801i
\(209\) −2.06759 1.19372i −0.143018 0.0825715i
\(210\) −6.63005 + 5.15023i −0.457517 + 0.355400i
\(211\) −5.40209 9.35669i −0.371895 0.644141i 0.617962 0.786208i \(-0.287959\pi\)
−0.989857 + 0.142067i \(0.954625\pi\)
\(212\) −6.84881 + 10.4191i −0.470378 + 0.715590i
\(213\) −16.1539 20.6393i −1.10684 1.41418i
\(214\) −3.26857 + 10.9231i −0.223435 + 0.746685i
\(215\) 4.19844 7.27192i 0.286331 0.495941i
\(216\) −13.2287 6.40323i −0.900099 0.435685i
\(217\) −15.4409 + 16.2427i −1.04819 + 1.10263i
\(218\) −2.69382 + 2.54217i −0.182449 + 0.172177i
\(219\) −9.87833 + 24.5106i −0.667516 + 1.65627i
\(220\) 6.92114 3.47823i 0.466623 0.234502i
\(221\) 24.3572 + 14.0626i 1.63844 + 0.945955i
\(222\) −10.9054 + 4.27166i −0.731921 + 0.286695i
\(223\) −8.99116 + 15.5731i −0.602092 + 1.04285i 0.390411 + 0.920641i \(0.372333\pi\)
−0.992504 + 0.122214i \(0.961001\pi\)
\(224\) −8.97489 + 11.9771i −0.599660 + 0.800255i
\(225\) −2.39419 + 9.67367i −0.159613 + 0.644911i
\(226\) 4.09555 + 4.33987i 0.272432 + 0.288684i
\(227\) 13.2026i 0.876288i −0.898905 0.438144i \(-0.855636\pi\)
0.898905 0.438144i \(-0.144364\pi\)
\(228\) −2.27340 + 1.57602i −0.150560 + 0.104374i
\(229\) −2.61733 −0.172958 −0.0864792 0.996254i \(-0.527562\pi\)
−0.0864792 + 0.996254i \(0.527562\pi\)
\(230\) 0.896191 + 3.77909i 0.0590931 + 0.249186i
\(231\) 12.4671 5.68137i 0.820277 0.373807i
\(232\) −17.2084 + 3.04137i −1.12979 + 0.199676i
\(233\) −12.5660 + 21.7650i −0.823229 + 1.42587i 0.0800362 + 0.996792i \(0.474496\pi\)
−0.903265 + 0.429083i \(0.858837\pi\)
\(234\) −16.1156 + 9.09542i −1.05351 + 0.594586i
\(235\) −2.72422 4.71850i −0.177709 0.307801i
\(236\) 13.1705 + 0.763582i 0.857326 + 0.0497050i
\(237\) 3.94849 9.79717i 0.256482 0.636395i
\(238\) −20.9386 + 11.9871i −1.35725 + 0.777010i
\(239\) 8.31881 4.80287i 0.538099 0.310672i −0.206209 0.978508i \(-0.566113\pi\)
0.744308 + 0.667836i \(0.232779\pi\)
\(240\) −0.221348 8.97231i −0.0142880 0.579160i
\(241\) 18.3114i 1.17954i 0.807572 + 0.589769i \(0.200781\pi\)
−0.807572 + 0.589769i \(0.799219\pi\)
\(242\) 2.83680 0.672732i 0.182356 0.0432448i
\(243\) 15.3398 2.77310i 0.984050 0.177895i
\(244\) −15.9597 10.4908i −1.02171 0.671604i
\(245\) −8.07245 4.13099i −0.515730 0.263919i
\(246\) −3.59098 + 23.7173i −0.228952 + 1.51216i
\(247\) 3.48303i 0.221620i
\(248\) −4.16970 23.5926i −0.264776 1.49813i
\(249\) −13.7459 + 1.94396i −0.871114 + 0.123194i
\(250\) −14.8344 + 3.51790i −0.938209 + 0.222491i
\(251\) 5.91016i 0.373046i −0.982451 0.186523i \(-0.940278\pi\)
0.982451 0.186523i \(-0.0597219\pi\)
\(252\) 0.213205 15.8731i 0.0134306 0.999910i
\(253\) 6.33824i 0.398481i
\(254\) 5.79855 + 24.4516i 0.363834 + 1.53423i
\(255\) 5.40835 13.4195i 0.338684 0.840359i
\(256\) −4.60514 15.3229i −0.287821 0.957684i
\(257\) 7.73903i 0.482748i 0.970432 + 0.241374i \(0.0775980\pi\)
−0.970432 + 0.241374i \(0.922402\pi\)
\(258\) 5.79079 + 14.7837i 0.360519 + 0.920391i
\(259\) −9.16874 8.71612i −0.569718 0.541593i
\(260\) −9.44315 6.20726i −0.585639 0.384958i
\(261\) 12.8526 13.3552i 0.795553 0.826669i
\(262\) 3.44718 + 14.5362i 0.212967 + 0.898048i
\(263\) 13.5681i 0.836643i −0.908299 0.418321i \(-0.862619\pi\)
0.908299 0.418321i \(-0.137381\pi\)
\(264\) −3.02713 + 14.3304i −0.186307 + 0.881973i
\(265\) 6.99411 4.03805i 0.429645 0.248056i
\(266\) −2.58212 1.50340i −0.158320 0.0921791i
\(267\) 5.64515 0.798341i 0.345478 0.0488577i
\(268\) −0.645118 + 11.1272i −0.0394069 + 0.679701i
\(269\) −1.71964 2.97850i −0.104848 0.181603i 0.808828 0.588045i \(-0.200102\pi\)
−0.913676 + 0.406443i \(0.866769\pi\)
\(270\) 5.79367 + 7.55339i 0.352591 + 0.459685i
\(271\) 1.23681 2.14222i 0.0751308 0.130130i −0.826012 0.563652i \(-0.809396\pi\)
0.901143 + 0.433522i \(0.142729\pi\)
\(272\) 2.98077 25.6202i 0.180736 1.55345i
\(273\) −16.2722 11.6072i −0.984838 0.702501i
\(274\) −5.65081 + 1.34006i −0.341378 + 0.0809560i
\(275\) 9.93140 0.598886
\(276\) −6.64122 3.13485i −0.399755 0.188696i
\(277\) 28.9981i 1.74233i 0.490993 + 0.871164i \(0.336634\pi\)
−0.490993 + 0.871164i \(0.663366\pi\)
\(278\) 6.47782 6.11313i 0.388514 0.366641i
\(279\) 18.3099 + 17.6207i 1.09619 + 1.05493i
\(280\) 8.67770 4.32135i 0.518592 0.258250i
\(281\) 12.6078 21.8373i 0.752118 1.30271i −0.194677 0.980867i \(-0.562366\pi\)
0.946795 0.321839i \(-0.104301\pi\)
\(282\) 10.1862 + 1.54226i 0.606578 + 0.0918405i
\(283\) −2.32788 1.34400i −0.138378 0.0798926i 0.429213 0.903203i \(-0.358791\pi\)
−0.567591 + 0.823311i \(0.692124\pi\)
\(284\) 13.5896 + 27.0412i 0.806394 + 1.60460i
\(285\) 1.77410 0.250895i 0.105089 0.0148617i
\(286\) 12.6573 + 13.4123i 0.748439 + 0.793088i
\(287\) −24.8490 + 7.33690i −1.46679 + 0.433084i
\(288\) 13.5182 + 10.2595i 0.796568 + 0.604549i
\(289\) 12.2899 21.2868i 0.722937 1.25216i
\(290\) 10.8438 + 3.24486i 0.636772 + 0.190545i
\(291\) −30.6648 + 4.33664i −1.79760 + 0.254219i
\(292\) 16.7612 25.4989i 0.980875 1.49221i
\(293\) −9.75157 16.8902i −0.569693 0.986737i −0.996596 0.0824399i \(-0.973729\pi\)
0.426903 0.904297i \(-0.359605\pi\)
\(294\) 15.6286 7.05322i 0.911477 0.411352i
\(295\) −7.40026 4.27254i −0.430860 0.248757i
\(296\) 13.3176 2.35373i 0.774071 0.136808i
\(297\) −6.35539 14.1756i −0.368777 0.822551i
\(298\) −4.65130 19.6138i −0.269442 1.13619i
\(299\) −8.00798 + 4.62341i −0.463114 + 0.267379i
\(300\) 4.91201 10.4062i 0.283595 0.600800i
\(301\) −11.8159 + 12.4294i −0.681054 + 0.716421i
\(302\) −1.54595 6.51904i −0.0889597 0.375128i
\(303\) −8.47401 + 6.63240i −0.486819 + 0.381022i
\(304\) 2.93229 1.26672i 0.168179 0.0726512i
\(305\) 6.18535 + 10.7133i 0.354172 + 0.613444i
\(306\) 13.4465 + 23.8250i 0.768685 + 1.36198i
\(307\) 17.3252i 0.988803i 0.869234 + 0.494402i \(0.164613\pi\)
−0.869234 + 0.494402i \(0.835387\pi\)
\(308\) −15.4064 + 3.59415i −0.877864 + 0.204796i
\(309\) 1.45658 1.14003i 0.0828617 0.0648538i
\(310\) −4.44868 + 14.8668i −0.252668 + 0.844378i
\(311\) −4.92098 + 8.52339i −0.279043 + 0.483317i −0.971147 0.238481i \(-0.923351\pi\)
0.692104 + 0.721798i \(0.256684\pi\)
\(312\) 20.3137 6.62865i 1.15004 0.375274i
\(313\) 21.7251 12.5430i 1.22797 0.708971i 0.261369 0.965239i \(-0.415826\pi\)
0.966606 + 0.256268i \(0.0824929\pi\)
\(314\) −1.16858 + 3.90522i −0.0659468 + 0.220384i
\(315\) −4.74006 + 9.12445i −0.267072 + 0.514104i
\(316\) −6.69966 + 10.1922i −0.376885 + 0.573358i
\(317\) 15.6620 9.04247i 0.879667 0.507876i 0.00911817 0.999958i \(-0.497098\pi\)
0.870548 + 0.492083i \(0.163764\pi\)
\(318\) −2.28606 + 15.0987i −0.128196 + 0.846694i
\(319\) −15.9969 9.23582i −0.895655 0.517106i
\(320\) −1.79146 + 10.2075i −0.100146 + 0.570615i
\(321\) 1.95535 + 13.8265i 0.109137 + 0.771719i
\(322\) 0.0289832 7.93229i 0.00161517 0.442049i
\(323\) 5.14925 0.286512
\(324\) −17.9966 0.351958i −0.999809 0.0195532i
\(325\) −7.24444 12.5477i −0.401849 0.696023i
\(326\) −0.863411 + 2.88539i −0.0478199 + 0.159807i
\(327\) −1.69574 + 4.20754i −0.0937744 + 0.232678i
\(328\) 9.46306 26.0318i 0.522510 1.43737i
\(329\) 3.15108 + 10.6722i 0.173724 + 0.588380i
\(330\) 5.91990 7.41318i 0.325880 0.408082i
\(331\) −13.6829 23.6995i −0.752080 1.30264i −0.946813 0.321785i \(-0.895717\pi\)
0.194733 0.980856i \(-0.437616\pi\)
\(332\) 16.0035 + 0.927832i 0.878307 + 0.0509214i
\(333\) −9.94663 + 10.3357i −0.545072 + 0.566391i
\(334\) −1.18368 1.25429i −0.0647682 0.0686320i
\(335\) 3.60969 6.25217i 0.197218 0.341592i
\(336\) −3.85397 + 17.9206i −0.210251 + 0.977647i
\(337\) 9.41616 + 16.3093i 0.512931 + 0.888423i 0.999888 + 0.0149964i \(0.00477369\pi\)
−0.486956 + 0.873426i \(0.661893\pi\)
\(338\) 2.44241 8.16215i 0.132849 0.443962i
\(339\) 6.77855 + 2.73191i 0.368160 + 0.148377i
\(340\) −9.17670 + 13.9606i −0.497676 + 0.757118i
\(341\) 12.6622 21.9316i 0.685698 1.18766i
\(342\) −1.72259 + 2.91736i −0.0931468 + 0.157753i
\(343\) 14.0512 + 12.0650i 0.758693 + 0.651448i
\(344\) −3.19079 18.0538i −0.172036 0.973395i
\(345\) 2.93180 + 3.74587i 0.157843 + 0.201671i
\(346\) −10.3268 10.9429i −0.555174 0.588294i
\(347\) 10.9055 18.8888i 0.585435 1.01400i −0.409386 0.912361i \(-0.634257\pi\)
0.994821 0.101642i \(-0.0324097\pi\)
\(348\) −17.5893 + 12.1936i −0.942885 + 0.653647i
\(349\) 10.1457 17.5730i 0.543089 0.940658i −0.455635 0.890167i \(-0.650588\pi\)
0.998724 0.0504918i \(-0.0160789\pi\)
\(350\) 12.4291 + 0.0454139i 0.664365 + 0.00242747i
\(351\) −13.2741 + 18.3700i −0.708518 + 0.980518i
\(352\) 6.68836 15.5337i 0.356491 0.827950i
\(353\) 20.8193i 1.10810i −0.832483 0.554051i \(-0.813081\pi\)
0.832483 0.554051i \(-0.186919\pi\)
\(354\) 15.0446 5.89300i 0.799611 0.313209i
\(355\) 19.6025i 1.04039i
\(356\) −6.57228 0.381040i −0.348330 0.0201951i
\(357\) −17.1599 + 24.0565i −0.908197 + 1.27321i
\(358\) 8.56107 + 9.07179i 0.452467 + 0.479459i
\(359\) −11.9694 6.91053i −0.631720 0.364724i 0.149698 0.988732i \(-0.452170\pi\)
−0.781418 + 0.624008i \(0.785503\pi\)
\(360\) −4.83961 9.86941i −0.255070 0.520164i
\(361\) −9.18116 15.9022i −0.483219 0.836960i
\(362\) 0.784843 0.186121i 0.0412505 0.00978232i
\(363\) 2.81186 2.20078i 0.147585 0.115511i
\(364\) 15.7792 + 16.8434i 0.827054 + 0.882833i
\(365\) −17.1168 + 9.88239i −0.895934 + 0.517268i
\(366\) −23.1277 3.50171i −1.20890 0.183037i
\(367\) −5.93144 −0.309618 −0.154809 0.987944i \(-0.549476\pi\)
−0.154809 + 0.987944i \(0.549476\pi\)
\(368\) 6.80472 + 5.06031i 0.354720 + 0.263787i
\(369\) 8.14657 + 28.2266i 0.424094 + 1.46942i
\(370\) −8.39208 2.51121i −0.436283 0.130552i
\(371\) −15.8192 + 4.67076i −0.821292 + 0.242494i
\(372\) −16.7174 24.1148i −0.866755 1.25029i
\(373\) 14.1749i 0.733948i −0.930231 0.366974i \(-0.880394\pi\)
0.930231 0.366974i \(-0.119606\pi\)
\(374\) 19.8285 18.7122i 1.02531 0.967587i
\(375\) −14.7040 + 11.5085i −0.759311 + 0.594294i
\(376\) −11.1802 4.06423i −0.576576 0.209596i
\(377\) 26.9482i 1.38790i
\(378\) −7.88893 17.7698i −0.405763 0.913978i
\(379\) 5.49974 0.282502 0.141251 0.989974i \(-0.454887\pi\)
0.141251 + 0.989974i \(0.454887\pi\)
\(380\) −2.06547 0.119749i −0.105956 0.00614302i
\(381\) 18.9694 + 24.2366i 0.971833 + 1.24168i
\(382\) 1.18210 1.11556i 0.0604817 0.0570768i
\(383\) −4.65367 −0.237792 −0.118896 0.992907i \(-0.537935\pi\)
−0.118896 + 0.992907i \(0.537935\pi\)
\(384\) −12.9683 14.6910i −0.661784 0.749695i
\(385\) 9.96175 + 2.40086i 0.507698 + 0.122359i
\(386\) −4.25097 + 14.2061i −0.216368 + 0.723071i
\(387\) 14.0114 + 13.4840i 0.712237 + 0.685429i
\(388\) 35.7011 + 2.06983i 1.81245 + 0.105080i
\(389\) 4.46691i 0.226481i 0.993568 + 0.113241i \(0.0361231\pi\)
−0.993568 + 0.113241i \(0.963877\pi\)
\(390\) −13.6844 2.07192i −0.692935 0.104916i
\(391\) 6.83516 + 11.8388i 0.345669 + 0.598716i
\(392\) −19.2976 + 4.42762i −0.974674 + 0.223629i
\(393\) 11.2771 + 14.4084i 0.568855 + 0.726808i
\(394\) 0.988302 + 4.16751i 0.0497899 + 0.209956i
\(395\) 6.84179 3.95011i 0.344248 0.198752i
\(396\) 3.96834 + 17.4939i 0.199416 + 0.879101i
\(397\) −11.8784 + 20.5740i −0.596159 + 1.03258i 0.397224 + 0.917722i \(0.369974\pi\)
−0.993382 + 0.114855i \(0.963360\pi\)
\(398\) −11.2699 11.9422i −0.564909 0.598609i
\(399\) −3.64256 0.350794i −0.182356 0.0175617i
\(400\) −7.92901 + 10.6623i −0.396451 + 0.533117i
\(401\) −19.7578 −0.986659 −0.493329 0.869843i \(-0.664220\pi\)
−0.493329 + 0.869843i \(0.664220\pi\)
\(402\) 4.97874 + 12.7105i 0.248317 + 0.633944i
\(403\) −36.9457 −1.84040
\(404\) 11.1025 5.57957i 0.552369 0.277594i
\(405\) 10.3130 + 5.43797i 0.512459 + 0.270215i
\(406\) −19.9779 11.6318i −0.991484 0.577274i
\(407\) 12.3800 + 7.14762i 0.613656 + 0.354295i
\(408\) −9.79967 30.0314i −0.485156 1.48677i
\(409\) −2.73101 1.57675i −0.135040 0.0779653i 0.430958 0.902372i \(-0.358176\pi\)
−0.565998 + 0.824407i \(0.691509\pi\)
\(410\) −13.0480 + 12.3135i −0.644396 + 0.608118i
\(411\) −5.60114 + 4.38388i −0.276284 + 0.216241i
\(412\) −1.90838 + 0.959058i −0.0940190 + 0.0472494i
\(413\) 12.6488 + 12.0244i 0.622407 + 0.591682i
\(414\) −8.99400 0.0879392i −0.442031 0.00432197i
\(415\) −8.99209 5.19158i −0.441404 0.254845i
\(416\) −24.5047 + 2.88069i −1.20144 + 0.141238i
\(417\) 4.07773 10.1179i 0.199687 0.495473i
\(418\) 3.23464 + 0.967920i 0.158212 + 0.0473425i
\(419\) 11.4750 6.62512i 0.560593 0.323658i −0.192791 0.981240i \(-0.561754\pi\)
0.753383 + 0.657582i \(0.228420\pi\)
\(420\) 7.44265 9.25051i 0.363164 0.451379i
\(421\) −32.3202 18.6601i −1.57519 0.909436i −0.995517 0.0945869i \(-0.969847\pi\)
−0.579673 0.814849i \(-0.696820\pi\)
\(422\) 10.4868 + 11.1125i 0.510492 + 0.540946i
\(423\) 12.1228 3.49882i 0.589433 0.170118i
\(424\) 6.02430 16.5722i 0.292566 0.804817i
\(425\) −18.5503 + 10.7100i −0.899823 + 0.519513i
\(426\) 28.9636 + 23.1293i 1.40329 + 1.12062i
\(427\) −7.15452 24.2313i −0.346231 1.17264i
\(428\) 0.933268 16.0973i 0.0451112 0.778091i
\(429\) 20.9490 + 8.44294i 1.01143 + 0.407629i
\(430\) −3.40427 + 11.3766i −0.164169 + 0.548627i
\(431\) 23.6556 13.6575i 1.13945 0.657861i 0.193154 0.981168i \(-0.438128\pi\)
0.946294 + 0.323308i \(0.104795\pi\)
\(432\) 20.2929 + 4.49434i 0.976342 + 0.216234i
\(433\) 13.4073i 0.644313i 0.946686 + 0.322157i \(0.104408\pi\)
−0.946686 + 0.322157i \(0.895592\pi\)
\(434\) 15.9470 27.3895i 0.765482 1.31474i
\(435\) 13.7262 1.94117i 0.658121 0.0930720i
\(436\) 2.87727 4.37720i 0.137796 0.209630i
\(437\) −0.846466 + 1.46612i −0.0404920 + 0.0701341i
\(438\) 5.59471 36.9513i 0.267326 1.76560i
\(439\) −0.443628 0.768386i −0.0211732 0.0366731i 0.855245 0.518224i \(-0.173407\pi\)
−0.876418 + 0.481551i \(0.840073\pi\)
\(440\) −8.38881 + 7.04475i −0.399921 + 0.335845i
\(441\) 13.7777 15.8485i 0.656082 0.754690i
\(442\) −38.1057 11.4026i −1.81250 0.542365i
\(443\) −8.92719 15.4623i −0.424143 0.734638i 0.572197 0.820117i \(-0.306091\pi\)
−0.996340 + 0.0854785i \(0.972758\pi\)
\(444\) 13.6124 9.43669i 0.646016 0.447845i
\(445\) 3.69285 + 2.13207i 0.175058 + 0.101070i
\(446\) 7.29041 24.3634i 0.345211 1.15364i
\(447\) −15.2163 19.4414i −0.719705 0.919544i
\(448\) 8.44149 19.4098i 0.398823 0.917028i
\(449\) −22.2234 −1.04879 −0.524393 0.851476i \(-0.675708\pi\)
−0.524393 + 0.851476i \(0.675708\pi\)
\(450\) 0.137792 14.0927i 0.00649559 0.664338i
\(451\) 25.3555 14.6390i 1.19394 0.689324i
\(452\) −7.05188 4.63541i −0.331693 0.218031i
\(453\) −5.05744 6.46173i −0.237619 0.303599i
\(454\) 4.30831 + 18.1674i 0.202199 + 0.852641i
\(455\) −4.23324 14.3374i −0.198457 0.672147i
\(456\) 2.61402 2.91054i 0.122413 0.136299i
\(457\) 11.6642 + 20.2030i 0.545628 + 0.945056i 0.998567 + 0.0535141i \(0.0170422\pi\)
−0.452939 + 0.891542i \(0.649624\pi\)
\(458\) 3.60158 0.854096i 0.168291 0.0399093i
\(459\) 27.1579 + 19.6241i 1.26762 + 0.915977i
\(460\) −2.46641 4.90777i −0.114997 0.228826i
\(461\) 18.4051 31.8785i 0.857209 1.48473i −0.0173713 0.999849i \(-0.505530\pi\)
0.874580 0.484881i \(-0.161137\pi\)
\(462\) −15.3014 + 11.8862i −0.711887 + 0.552994i
\(463\) 29.5910 17.0844i 1.37521 0.793977i 0.383631 0.923486i \(-0.374673\pi\)
0.991578 + 0.129509i \(0.0413401\pi\)
\(464\) 22.6871 9.80057i 1.05322 0.454980i
\(465\) 2.66133 + 18.8185i 0.123416 + 0.872688i
\(466\) 10.1891 34.0504i 0.472000 1.57735i
\(467\) 29.6445 + 17.1153i 1.37178 + 0.791999i 0.991153 0.132728i \(-0.0423736\pi\)
0.380631 + 0.924727i \(0.375707\pi\)
\(468\) 19.2078 17.7746i 0.887881 0.821633i
\(469\) −10.1589 + 10.6864i −0.469094 + 0.493454i
\(470\) 5.28842 + 5.60391i 0.243937 + 0.258489i
\(471\) 0.699078 + 4.94325i 0.0322118 + 0.227773i
\(472\) −18.3724 + 3.24710i −0.845659 + 0.149460i
\(473\) 9.68955 16.7828i 0.445526 0.771674i
\(474\) −2.23627 + 14.7699i −0.102715 + 0.678403i
\(475\) −2.29727 1.32633i −0.105406 0.0608562i
\(476\) 24.9009 23.3277i 1.14133 1.06922i
\(477\) 5.18621 + 17.9694i 0.237460 + 0.822762i
\(478\) −9.87981 + 9.32360i −0.451892 + 0.426452i
\(479\) −32.5963 −1.48936 −0.744682 0.667419i \(-0.767399\pi\)
−0.744682 + 0.667419i \(0.767399\pi\)
\(480\) 3.23246 + 12.2741i 0.147541 + 0.560234i
\(481\) 20.8553i 0.950918i
\(482\) −5.97542 25.1974i −0.272173 1.14771i
\(483\) −4.02865 8.84042i −0.183310 0.402253i
\(484\) −3.68405 + 1.85142i −0.167457 + 0.0841557i
\(485\) −20.0598 11.5815i −0.910868 0.525890i
\(486\) −20.2034 + 8.82166i −0.916446 + 0.400159i
\(487\) −3.06210 + 1.76790i −0.138757 + 0.0801114i −0.567771 0.823186i \(-0.692194\pi\)
0.429014 + 0.903298i \(0.358861\pi\)
\(488\) 25.3847 + 9.22783i 1.14911 + 0.417724i
\(489\) 0.516517 + 3.65235i 0.0233577 + 0.165165i
\(490\) 12.4561 + 3.05022i 0.562711 + 0.137795i
\(491\) −10.5476 18.2690i −0.476006 0.824466i 0.523616 0.851954i \(-0.324583\pi\)
−0.999622 + 0.0274879i \(0.991249\pi\)
\(492\) −2.79813 33.8080i −0.126149 1.52418i
\(493\) 39.8397 1.79429
\(494\) −1.13659 4.79282i −0.0511377 0.215639i
\(495\) 2.79143 11.2787i 0.125465 0.506939i
\(496\) 13.4365 + 31.1039i 0.603317 + 1.39660i
\(497\) −9.38024 + 38.9210i −0.420761 + 1.74584i
\(498\) 18.2807 7.16061i 0.819180 0.320874i
\(499\) 38.0133 1.70171 0.850854 0.525402i \(-0.176085\pi\)
0.850854 + 0.525402i \(0.176085\pi\)
\(500\) 19.2649 9.68160i 0.861552 0.432974i
\(501\) −1.95911 0.789567i −0.0875267 0.0352753i
\(502\) 1.92862 + 8.13268i 0.0860786 + 0.362979i
\(503\) −11.2166 −0.500124 −0.250062 0.968230i \(-0.580451\pi\)
−0.250062 + 0.968230i \(0.580451\pi\)
\(504\) 4.88637 + 21.9117i 0.217656 + 0.976026i
\(505\) −8.04832 −0.358145
\(506\) 2.06831 + 8.72173i 0.0919477 + 0.387728i
\(507\) −1.46112 10.3317i −0.0648905 0.458847i
\(508\) −15.9582 31.7544i −0.708031 1.40887i
\(509\) 6.21583 0.275512 0.137756 0.990466i \(-0.456011\pi\)
0.137756 + 0.990466i \(0.456011\pi\)
\(510\) −3.06308 + 20.2307i −0.135636 + 0.895831i
\(511\) 38.7146 11.4308i 1.71263 0.505670i
\(512\) 11.3371 + 19.5824i 0.501035 + 0.865427i
\(513\) −0.423047 + 4.12777i −0.0186780 + 0.182245i
\(514\) −2.52542 10.6493i −0.111392 0.469720i
\(515\) 1.38340 0.0609601
\(516\) −12.7927 18.4534i −0.563166 0.812366i
\(517\) −6.28721 10.8898i −0.276511 0.478932i
\(518\) 15.4609 + 9.00185i 0.679314 + 0.395518i
\(519\) −17.0920 6.88846i −0.750254 0.302370i
\(520\) 15.0198 + 5.45999i 0.658663 + 0.239436i
\(521\) −12.4039 + 7.16139i −0.543424 + 0.313746i −0.746466 0.665424i \(-0.768251\pi\)
0.203041 + 0.979170i \(0.434917\pi\)
\(522\) −13.3276 + 22.5716i −0.583335 + 0.987931i
\(523\) 17.4171 + 10.0558i 0.761597 + 0.439708i 0.829869 0.557959i \(-0.188415\pi\)
−0.0682722 + 0.997667i \(0.521749\pi\)
\(524\) −9.48698 18.8776i −0.414441 0.824673i
\(525\) 13.8521 6.31251i 0.604554 0.275500i
\(526\) 4.42757 + 18.6703i 0.193051 + 0.814065i
\(527\) 54.6198i 2.37928i
\(528\) −0.510848 20.7071i −0.0222318 0.901161i
\(529\) 18.5056 0.804590
\(530\) −8.30654 + 7.83890i −0.360813 + 0.340500i
\(531\) 13.7219 14.2586i 0.595482 0.618772i
\(532\) 4.04372 + 1.22614i 0.175318 + 0.0531600i
\(533\) −36.9910 21.3568i −1.60226 0.925065i
\(534\) −7.50749 + 2.94070i −0.324881 + 0.127256i
\(535\) −5.22200 + 9.04477i −0.225767 + 0.391040i
\(536\) −2.74334 15.5221i −0.118494 0.670452i
\(537\) 14.1694 + 5.71061i 0.611456 + 0.246431i
\(538\) 3.33826 + 3.53741i 0.143923 + 0.152509i
\(539\) −18.6303 9.53386i −0.802465 0.410653i
\(540\) −10.4372 8.50324i −0.449146 0.365921i
\(541\) 23.7198 + 13.6947i 1.01980 + 0.588779i 0.914045 0.405614i \(-0.132942\pi\)
0.105751 + 0.994393i \(0.466275\pi\)
\(542\) −1.00286 + 3.35139i −0.0430764 + 0.143955i
\(543\) 0.777944 0.608878i 0.0333848 0.0261295i
\(544\) 4.25876 + 36.2273i 0.182593 + 1.55323i
\(545\) −2.93831 + 1.69643i −0.125863 + 0.0726672i
\(546\) 26.1791 + 10.6621i 1.12036 + 0.456296i
\(547\) 11.4035 19.7514i 0.487578 0.844510i −0.512320 0.858795i \(-0.671214\pi\)
0.999898 + 0.0142849i \(0.00454719\pi\)
\(548\) 7.33851 3.68798i 0.313486 0.157543i
\(549\) −27.5249 + 7.94407i −1.17473 + 0.339044i
\(550\) −13.6661 + 3.24084i −0.582725 + 0.138190i
\(551\) 2.46687 + 4.27274i 0.105092 + 0.182025i
\(552\) 10.1616 + 2.14653i 0.432508 + 0.0913624i
\(553\) −15.4747 + 4.56904i −0.658051 + 0.194295i
\(554\) −9.46275 39.9028i −0.402034 1.69531i
\(555\) −10.6228 + 1.50228i −0.450911 + 0.0637681i
\(556\) −6.91895 + 10.5258i −0.293429 + 0.446395i
\(557\) −33.6484 + 19.4269i −1.42573 + 0.823145i −0.996780 0.0801838i \(-0.974449\pi\)
−0.428949 + 0.903329i \(0.641116\pi\)
\(558\) −30.9454 18.2721i −1.31002 0.773518i
\(559\) −28.2721 −1.19578
\(560\) −10.5308 + 8.77813i −0.445007 + 0.370944i
\(561\) 12.4819 30.9706i 0.526985 1.30758i
\(562\) −10.2229 + 34.1635i −0.431228 + 1.44110i
\(563\) 20.9471 + 12.0938i 0.882817 + 0.509694i 0.871586 0.490243i \(-0.163092\pi\)
0.0112305 + 0.999937i \(0.496425\pi\)
\(564\) −14.5200 + 1.20175i −0.611400 + 0.0506028i
\(565\) 2.73303 + 4.73375i 0.114980 + 0.199150i
\(566\) 3.64186 + 1.08977i 0.153079 + 0.0458066i
\(567\) −17.8745 15.7322i −0.750658 0.660691i
\(568\) −27.5241 32.7754i −1.15489 1.37523i
\(569\) 15.1973 + 26.3225i 0.637105 + 1.10350i 0.986065 + 0.166360i \(0.0532014\pi\)
−0.348961 + 0.937137i \(0.613465\pi\)
\(570\) −2.35938 + 0.924174i −0.0988236 + 0.0387094i
\(571\) −17.0302 + 29.4971i −0.712690 + 1.23442i 0.251154 + 0.967947i \(0.419190\pi\)
−0.963844 + 0.266468i \(0.914143\pi\)
\(572\) −21.7938 14.3257i −0.911243 0.598987i
\(573\) 0.744124 1.84636i 0.0310862 0.0771326i
\(574\) 31.7993 18.2047i 1.32728 0.759852i
\(575\) 7.04234i 0.293686i
\(576\) −21.9496 9.70634i −0.914569 0.404431i
\(577\) −6.11735 + 3.53185i −0.254668 + 0.147033i −0.621900 0.783097i \(-0.713639\pi\)
0.367232 + 0.930130i \(0.380306\pi\)
\(578\) −9.96519 + 33.3021i −0.414497 + 1.38519i
\(579\) 2.54305 + 17.9822i 0.105686 + 0.747313i
\(580\) −15.9805 0.926500i −0.663556 0.0384708i
\(581\) 15.3696 + 14.6109i 0.637639 + 0.606162i
\(582\) 40.7812 15.9741i 1.69044 0.662147i
\(583\) 16.1416 9.31938i 0.668519 0.385969i
\(584\) −14.7434 + 40.5574i −0.610085 + 1.67828i
\(585\) −16.2861 + 4.70040i −0.673349 + 0.194338i
\(586\) 18.9303 + 20.0596i 0.782004 + 0.828656i
\(587\) −6.20896 3.58474i −0.256271 0.147958i 0.366361 0.930473i \(-0.380603\pi\)
−0.622632 + 0.782514i \(0.713937\pi\)
\(588\) −19.2041 + 14.8055i −0.791962 + 0.610570i
\(589\) −5.85790 + 3.38206i −0.241370 + 0.139355i
\(590\) 11.5774 + 3.46436i 0.476632 + 0.142625i
\(591\) 3.23313 + 4.13087i 0.132993 + 0.169921i
\(592\) −17.5576 + 7.58469i −0.721614 + 0.311729i
\(593\) 15.4594 + 8.92547i 0.634840 + 0.366525i 0.782624 0.622494i \(-0.213881\pi\)
−0.147784 + 0.989020i \(0.547214\pi\)
\(594\) 13.3711 + 17.4324i 0.548625 + 0.715260i
\(595\) −21.1961 + 6.25834i −0.868955 + 0.256567i
\(596\) 12.8008 + 25.4717i 0.524343 + 1.04336i
\(597\) −18.6528 7.51752i −0.763409 0.307672i
\(598\) 9.51066 8.97523i 0.388920 0.367024i
\(599\) −35.7198 20.6229i −1.45947 0.842627i −0.460488 0.887666i \(-0.652326\pi\)
−0.998985 + 0.0450388i \(0.985659\pi\)
\(600\) −3.36340 + 15.9223i −0.137310 + 0.650025i
\(601\) 9.40261 + 5.42860i 0.383541 + 0.221437i 0.679358 0.733807i \(-0.262259\pi\)
−0.295817 + 0.955245i \(0.595592\pi\)
\(602\) 12.2032 20.9593i 0.497365 0.854238i
\(603\) 12.0465 + 11.5931i 0.490572 + 0.472107i
\(604\) 4.25462 + 8.46604i 0.173118 + 0.344478i
\(605\) 2.67061 0.108576
\(606\) 9.49636 11.8918i 0.385763 0.483071i
\(607\) −30.1147 −1.22232 −0.611158 0.791509i \(-0.709296\pi\)
−0.611158 + 0.791509i \(0.709296\pi\)
\(608\) −3.62162 + 2.69994i −0.146876 + 0.109497i
\(609\) −28.1825 2.71409i −1.14201 0.109981i
\(610\) −12.0074 12.7237i −0.486164 0.515167i
\(611\) −9.17238 + 15.8870i −0.371075 + 0.642721i
\(612\) −26.2777 28.3964i −1.06221 1.14786i
\(613\) 33.5461 19.3678i 1.35491 0.782260i 0.365981 0.930622i \(-0.380734\pi\)
0.988933 + 0.148362i \(0.0474002\pi\)
\(614\) −5.65362 23.8404i −0.228162 0.962120i
\(615\) −8.21361 + 20.3800i −0.331205 + 0.821801i
\(616\) 20.0272 9.97321i 0.806918 0.401832i
\(617\) 9.27415 + 16.0633i 0.373363 + 0.646684i 0.990081 0.140501i \(-0.0448712\pi\)
−0.616717 + 0.787185i \(0.711538\pi\)
\(618\) −1.63230 + 2.04405i −0.0656609 + 0.0822236i
\(619\) 22.3298i 0.897512i −0.893654 0.448756i \(-0.851867\pi\)
0.893654 0.448756i \(-0.148133\pi\)
\(620\) 1.27022 21.9092i 0.0510134 0.879894i
\(621\) −10.0519 + 4.50659i −0.403368 + 0.180843i
\(622\) 3.99014 13.3344i 0.159990 0.534662i
\(623\) −6.31196 6.00036i −0.252883 0.240399i
\(624\) −25.7896 + 15.7502i −1.03241 + 0.630512i
\(625\) 2.64390 0.105756
\(626\) −25.8017 + 24.3492i −1.03124 + 0.973188i
\(627\) 4.09443 0.579038i 0.163516 0.0231245i
\(628\) 0.333663 5.75511i 0.0133146 0.229654i
\(629\) −30.8320 −1.22935
\(630\) 3.54504 14.1025i 0.141238 0.561856i
\(631\) 2.58700i 0.102987i 0.998673 + 0.0514935i \(0.0163981\pi\)
−0.998673 + 0.0514935i \(0.983602\pi\)
\(632\) 5.89310 16.2113i 0.234415 0.644850i
\(633\) 17.3568 + 6.99519i 0.689870 + 0.278034i
\(634\) −18.6010 + 17.5538i −0.738738 + 0.697149i
\(635\) 23.0191i 0.913485i
\(636\) −1.78132 21.5226i −0.0706341 0.853426i
\(637\) 1.54438 + 30.4928i 0.0611908 + 1.20817i
\(638\) 25.0264 + 7.48879i 0.990804 + 0.296484i
\(639\) 44.0663 + 10.9062i 1.74323 + 0.431444i
\(640\) −0.865787 14.6306i −0.0342232 0.578325i
\(641\) 4.82382 0.190529 0.0952647 0.995452i \(-0.469630\pi\)
0.0952647 + 0.995452i \(0.469630\pi\)
\(642\) −7.20256 18.3879i −0.284262 0.725711i
\(643\) 3.81298 2.20143i 0.150369 0.0868157i −0.422928 0.906163i \(-0.638998\pi\)
0.573297 + 0.819348i \(0.305664\pi\)
\(644\) 2.54860 + 10.9247i 0.100429 + 0.430493i
\(645\) 2.03654 + 14.4005i 0.0801885 + 0.567021i
\(646\) −7.08562 + 1.68032i −0.278780 + 0.0661112i
\(647\) −15.1554 26.2500i −0.595821 1.03199i −0.993430 0.114438i \(-0.963493\pi\)
0.397609 0.917555i \(-0.369840\pi\)
\(648\) 24.8790 5.38838i 0.977340 0.211675i
\(649\) −17.0790 9.86056i −0.670409 0.387061i
\(650\) 14.0633 + 14.9023i 0.551609 + 0.584516i
\(651\) 3.72100 38.6379i 0.145837 1.51434i
\(652\) 0.246528 4.25219i 0.00965479 0.166529i
\(653\) 36.4315i 1.42568i 0.701329 + 0.712838i \(0.252590\pi\)
−0.701329 + 0.712838i \(0.747410\pi\)
\(654\) 0.960400 6.34314i 0.0375546 0.248037i
\(655\) 13.6846i 0.534701i
\(656\) −4.52687 + 38.9091i −0.176744 + 1.51915i
\(657\) −12.6923 43.9768i −0.495174 1.71570i
\(658\) −7.81864 13.6573i −0.304802 0.532416i
\(659\) 16.3106 28.2508i 0.635371 1.10049i −0.351066 0.936351i \(-0.614181\pi\)
0.986436 0.164144i \(-0.0524860\pi\)
\(660\) −5.72699 + 12.1327i −0.222923 + 0.472265i
\(661\) 19.0448 32.9865i 0.740755 1.28303i −0.211397 0.977400i \(-0.567801\pi\)
0.952152 0.305625i \(-0.0988654\pi\)
\(662\) 26.5620 + 28.1466i 1.03236 + 1.09395i
\(663\) −48.2344 + 6.82135i −1.87327 + 0.264919i
\(664\) −22.3244 + 3.94557i −0.866355 + 0.153118i
\(665\) −1.98366 1.88573i −0.0769230 0.0731257i
\(666\) 10.3143 17.4682i 0.399671 0.676879i
\(667\) −6.54910 + 11.3434i −0.253582 + 0.439217i
\(668\) 2.03811 + 1.33971i 0.0788568 + 0.0518349i
\(669\) −4.36133 30.8394i −0.168619 1.19232i
\(670\) −2.92689 + 9.78122i −0.113076 + 0.377881i
\(671\) 14.2751 + 24.7252i 0.551085 + 0.954507i
\(672\) −0.544636 25.9172i −0.0210098 0.999779i
\(673\) −1.64553 + 2.85014i −0.0634305 + 0.109865i −0.895997 0.444061i \(-0.853537\pi\)
0.832566 + 0.553926i \(0.186871\pi\)
\(674\) −18.2792 19.3697i −0.704088 0.746092i
\(675\) −7.06140 15.7503i −0.271793 0.606230i
\(676\) −0.697376 + 12.0285i −0.0268222 + 0.462636i
\(677\) 23.9808 + 41.5360i 0.921658 + 1.59636i 0.796849 + 0.604178i \(0.206499\pi\)
0.124809 + 0.992181i \(0.460168\pi\)
\(678\) −10.2191 1.54725i −0.392462 0.0594218i
\(679\) 34.2870 + 32.5944i 1.31581 + 1.25086i
\(680\) 8.07194 22.2050i 0.309545 0.851523i
\(681\) 14.0942 + 18.0078i 0.540092 + 0.690059i
\(682\) −10.2671 + 34.3110i −0.393146 + 1.31384i
\(683\) −6.42001 11.1198i −0.245655 0.425487i 0.716661 0.697422i \(-0.245670\pi\)
−0.962316 + 0.271935i \(0.912336\pi\)
\(684\) 1.41836 4.57655i 0.0542325 0.174989i
\(685\) −5.31977 −0.203258
\(686\) −23.2722 12.0168i −0.888538 0.458804i
\(687\) 3.56992 2.79409i 0.136201 0.106601i
\(688\) 10.2821 + 23.8017i 0.392000 + 0.907431i
\(689\) −23.5490 13.5960i −0.897144 0.517966i
\(690\) −5.25667 4.19779i −0.200118 0.159807i
\(691\) −17.5881 + 10.1545i −0.669081 + 0.386294i −0.795728 0.605654i \(-0.792912\pi\)
0.126647 + 0.991948i \(0.459578\pi\)
\(692\) 17.7812 + 11.6881i 0.675939 + 0.444315i
\(693\) −10.9395 + 21.0582i −0.415559 + 0.799936i
\(694\) −8.84260 + 29.5506i −0.335660 + 1.12173i
\(695\) 7.06573 4.07940i 0.268018 0.154741i
\(696\) 20.2247 22.5188i 0.766614 0.853574i
\(697\) −31.5735 + 54.6868i −1.19593 + 2.07141i
\(698\) −8.22660 + 27.4920i −0.311381 + 1.04059i
\(699\) −6.09540 43.1012i −0.230549 1.63024i
\(700\) −17.1179 + 3.99342i −0.646997 + 0.150937i
\(701\) 17.9424i 0.677676i −0.940845 0.338838i \(-0.889966\pi\)
0.940845 0.338838i \(-0.110034\pi\)
\(702\) 12.2712 29.6097i 0.463148 1.11754i
\(703\) −1.90912 3.30669i −0.0720038 0.124714i
\(704\) −4.13451 + 23.5577i −0.155825 + 0.887865i
\(705\) 8.75287 + 3.52761i 0.329652 + 0.132857i
\(706\) 6.79383 + 28.6485i 0.255689 + 1.07820i
\(707\) 15.9800 + 3.85131i 0.600992 + 0.144843i
\(708\) −18.7791 + 13.0185i −0.705761 + 0.489263i
\(709\) −9.74153 + 5.62428i −0.365851 + 0.211224i −0.671644 0.740874i \(-0.734412\pi\)
0.305793 + 0.952098i \(0.401078\pi\)
\(710\) 6.39673 + 26.9740i 0.240065 + 1.01231i
\(711\) 5.07326 + 17.5780i 0.190262 + 0.659228i
\(712\) 9.16813 1.62036i 0.343590 0.0607254i
\(713\) −15.5517 8.97876i −0.582414 0.336257i
\(714\) 15.7627 38.7026i 0.589903 1.44841i
\(715\) 8.44641 + 14.6296i 0.315878 + 0.547116i
\(716\) −14.7408 9.68956i −0.550889 0.362116i
\(717\) −6.21925 + 15.4315i −0.232262 + 0.576300i
\(718\) 18.7255 + 5.60335i 0.698831 + 0.209115i
\(719\) −6.01899 + 10.4252i −0.224471 + 0.388795i −0.956160 0.292843i \(-0.905399\pi\)
0.731690 + 0.681638i \(0.238732\pi\)
\(720\) 9.88016 + 12.0015i 0.368212 + 0.447270i
\(721\) −2.74677 0.661991i −0.102295 0.0246538i
\(722\) 17.8230 + 18.8862i 0.663303 + 0.702873i
\(723\) −19.5480 24.9759i −0.726998 0.928862i
\(724\) −1.01925 + 0.512225i −0.0378801 + 0.0190367i
\(725\) −17.7740 10.2618i −0.660109 0.381114i
\(726\) −3.15110 + 3.94595i −0.116948 + 0.146448i
\(727\) −10.5009 + 18.1880i −0.389456 + 0.674557i −0.992376 0.123244i \(-0.960670\pi\)
0.602921 + 0.797801i \(0.294004\pi\)
\(728\) −27.2093 18.0282i −1.00844 0.668170i
\(729\) −17.9624 + 20.1582i −0.665275 + 0.746599i
\(730\) 20.3287 19.1843i 0.752399 0.710041i
\(731\) 41.7969i 1.54591i
\(732\) 32.9676 2.72857i 1.21852 0.100851i
\(733\) 40.1301 1.48224 0.741120 0.671372i \(-0.234295\pi\)
0.741120 + 0.671372i \(0.234295\pi\)
\(734\) 8.16195 1.93556i 0.301263 0.0714429i
\(735\) 15.4204 2.98314i 0.568791 0.110035i
\(736\) −11.0149 4.74270i −0.406015 0.174818i
\(737\) 8.33077 14.4293i 0.306868 0.531511i
\(738\) −20.4211 36.1828i −0.751710 1.33191i
\(739\) 12.4121 + 21.4984i 0.456587 + 0.790832i 0.998778 0.0494232i \(-0.0157383\pi\)
−0.542191 + 0.840255i \(0.682405\pi\)
\(740\) 12.3674 + 0.717021i 0.454634 + 0.0263582i
\(741\) −3.71825 4.75069i −0.136593 0.174521i
\(742\) 20.2438 11.5894i 0.743175 0.425459i
\(743\) 43.1285 24.9002i 1.58223 0.913501i 0.587697 0.809081i \(-0.300035\pi\)
0.994533 0.104419i \(-0.0332984\pi\)
\(744\) 30.8731 + 27.7279i 1.13186 + 1.01655i
\(745\) 18.4647i 0.676495i
\(746\) 4.62559 + 19.5054i 0.169355 + 0.714142i
\(747\) 16.6736 17.3257i 0.610055 0.633916i
\(748\) −21.1788 + 32.2195i −0.774374 + 1.17806i
\(749\) 14.6965 15.4597i 0.536998 0.564884i
\(750\) 16.4780 20.6345i 0.601690 0.753464i
\(751\) 39.4233i 1.43858i −0.694712 0.719288i \(-0.744468\pi\)
0.694712 0.719288i \(-0.255532\pi\)
\(752\) 16.7108 + 1.94421i 0.609380 + 0.0708981i
\(753\) 6.30930 + 8.06119i 0.229924 + 0.293766i
\(754\) −8.79381 37.0820i −0.320251 1.35045i
\(755\) 6.13713i 0.223353i
\(756\) 16.6542 + 21.8778i 0.605709 + 0.795686i
\(757\) 6.93533i 0.252069i −0.992026 0.126034i \(-0.959775\pi\)
0.992026 0.126034i \(-0.0402250\pi\)
\(758\) −7.56791 + 1.79469i −0.274879 + 0.0651861i
\(759\) 6.76628 + 8.64506i 0.245600 + 0.313796i
\(760\) 2.88127 0.509230i 0.104515 0.0184717i
\(761\) 3.63210i 0.131663i −0.997831 0.0658317i \(-0.979030\pi\)
0.997831 0.0658317i \(-0.0209700\pi\)
\(762\) −34.0118 27.1606i −1.23212 0.983926i
\(763\) 6.64583 1.96224i 0.240595 0.0710379i
\(764\) −1.26260 + 1.92081i −0.0456794 + 0.0694924i
\(765\) 6.94899 + 24.0771i 0.251241 + 0.870510i
\(766\) 6.40369 1.51860i 0.231375 0.0548693i
\(767\) 28.7710i 1.03886i
\(768\) 22.6390 + 15.9837i 0.816913 + 0.576760i
\(769\) −41.0812 + 23.7182i −1.48143 + 0.855301i −0.999778 0.0210640i \(-0.993295\pi\)
−0.481647 + 0.876365i \(0.659961\pi\)
\(770\) −14.4913 0.0529487i −0.522231 0.00190814i
\(771\) −8.26168 10.5557i −0.297537 0.380154i
\(772\) 1.21377 20.9355i 0.0436846 0.753484i
\(773\) 7.94203 + 13.7560i 0.285655 + 0.494769i 0.972768 0.231782i \(-0.0744555\pi\)
−0.687113 + 0.726551i \(0.741122\pi\)
\(774\) −23.6805 13.9824i −0.851176 0.502586i
\(775\) 14.0688 24.3680i 0.505368 0.875323i
\(776\) −49.8019 + 8.80189i −1.78778 + 0.315969i
\(777\) 21.8105 + 2.10044i 0.782447 + 0.0753530i
\(778\) −1.45766 6.14669i −0.0522595 0.220370i
\(779\) −7.82011 −0.280185
\(780\) 19.5065 1.61446i 0.698444 0.0578070i
\(781\) 45.2403i 1.61883i
\(782\) −13.2688 14.0604i −0.474492 0.502798i
\(783\) −3.27311 + 31.9365i −0.116971 + 1.14132i
\(784\) 25.1096 12.3899i 0.896771 0.442495i
\(785\) −1.86697 + 3.23369i −0.0666351 + 0.115415i
\(786\) −20.2197 16.1467i −0.721211 0.575934i
\(787\) −11.7154 6.76386i −0.417607 0.241106i 0.276446 0.961030i \(-0.410843\pi\)
−0.694053 + 0.719924i \(0.744177\pi\)
\(788\) −2.71990 5.41219i −0.0968926 0.192801i
\(789\) 14.4844 + 18.5062i 0.515657 + 0.658839i
\(790\) −8.12563 + 7.66818i −0.289097 + 0.272822i
\(791\) −3.16126 10.7067i −0.112402 0.380688i
\(792\) −11.1693 22.7775i −0.396883 0.809364i
\(793\) 20.8259 36.0715i 0.739549 1.28094i
\(794\) 9.63149 32.1870i 0.341809 1.14227i
\(795\) −5.22889 + 12.9742i −0.185450 + 0.460146i
\(796\) 19.4050 + 12.7555i 0.687791 + 0.452105i
\(797\) −2.17106 3.76039i −0.0769030 0.133200i 0.825009 0.565119i \(-0.191170\pi\)
−0.901912 + 0.431919i \(0.857836\pi\)
\(798\) 5.12682 0.705941i 0.181488 0.0249901i
\(799\) 23.4871 + 13.5603i 0.830913 + 0.479728i
\(800\) 7.43135 17.2593i 0.262738 0.610209i
\(801\) −6.84747 + 7.11529i −0.241943 + 0.251406i
\(802\) 27.1878 6.44743i 0.960033 0.227667i
\(803\) −39.5037 + 22.8075i −1.39405 + 0.804858i
\(804\) −10.9987 15.8657i −0.387896 0.559539i
\(805\) 1.70244 7.06386i 0.0600032 0.248968i
\(806\) 50.8392 12.0562i 1.79073 0.424663i
\(807\) 5.52516 + 2.22677i 0.194495 + 0.0783860i
\(808\) −13.4568 + 11.3008i −0.473410 + 0.397560i
\(809\) −7.90455 13.6911i −0.277909 0.481353i 0.692956 0.720980i \(-0.256308\pi\)
−0.970865 + 0.239627i \(0.922975\pi\)
\(810\) −15.9658 4.11754i −0.560981 0.144676i
\(811\) 41.5589i 1.45933i 0.683804 + 0.729666i \(0.260324\pi\)
−0.683804 + 0.729666i \(0.739676\pi\)
\(812\) 31.2862 + 9.48664i 1.09793 + 0.332916i
\(813\) 0.599938 + 4.24222i 0.0210407 + 0.148781i
\(814\) −19.3680 5.79560i −0.678848 0.203136i
\(815\) −1.37942 + 2.38923i −0.0483190 + 0.0836910i
\(816\) 23.2848 + 38.1268i 0.815130 + 1.33470i
\(817\) −4.48265 + 2.58806i −0.156828 + 0.0905448i
\(818\) 4.27254 + 1.27850i 0.149386 + 0.0447016i
\(819\) 34.5856 1.53942i 1.20852 0.0537915i
\(820\) 13.9366 21.2018i 0.486686 0.740399i
\(821\) −44.9450 + 25.9490i −1.56859 + 0.905627i −0.572259 + 0.820073i \(0.693933\pi\)
−0.996333 + 0.0855546i \(0.972734\pi\)
\(822\) 6.27689 7.86022i 0.218932 0.274157i
\(823\) −12.0141 6.93632i −0.418784 0.241785i 0.275773 0.961223i \(-0.411066\pi\)
−0.694557 + 0.719438i \(0.744400\pi\)
\(824\) 2.31306 1.94246i 0.0805792 0.0676688i
\(825\) −13.5460 + 10.6021i −0.471610 + 0.369118i
\(826\) −21.3292 12.4186i −0.742139 0.432097i
\(827\) −31.3188 −1.08906 −0.544531 0.838741i \(-0.683292\pi\)
−0.544531 + 0.838741i \(0.683292\pi\)
\(828\) 12.4049 2.81394i 0.431100 0.0977911i
\(829\) −7.69392 13.3263i −0.267221 0.462840i 0.700922 0.713238i \(-0.252772\pi\)
−0.968143 + 0.250397i \(0.919439\pi\)
\(830\) 14.0677 + 4.20955i 0.488297 + 0.146116i
\(831\) −30.9565 39.5521i −1.07387 1.37205i
\(832\) 32.7797 11.9604i 1.13643 0.414653i
\(833\) 45.0799 2.28319i 1.56193 0.0791078i
\(834\) −2.30947 + 15.2533i −0.0799704 + 0.528179i
\(835\) −0.789891 1.36813i −0.0273353 0.0473462i
\(836\) −4.76688 0.276369i −0.164866 0.00955841i
\(837\) −43.7847 4.48741i −1.51342 0.155108i
\(838\) −13.6283 + 12.8611i −0.470782 + 0.444278i
\(839\) 16.1555 27.9822i 0.557750 0.966051i −0.439934 0.898030i \(-0.644998\pi\)
0.997684 0.0680211i \(-0.0216685\pi\)
\(840\) −7.22280 + 15.1579i −0.249210 + 0.522996i
\(841\) 4.58615 + 7.94345i 0.158143 + 0.273912i
\(842\) 50.5634 + 15.1304i 1.74253 + 0.521427i
\(843\) 6.11565 + 43.2444i 0.210634 + 1.48941i
\(844\) −18.0567 11.8692i −0.621536 0.408554i
\(845\) 3.90209 6.75862i 0.134236 0.232504i
\(846\) −15.5399 + 8.77051i −0.534272 + 0.301536i
\(847\) −5.30253 1.27795i −0.182197 0.0439108i
\(848\) −2.88186 + 24.7700i −0.0989635 + 0.850606i
\(849\) 4.60989 0.651934i 0.158211 0.0223743i
\(850\) 22.0312 20.7909i 0.755666 0.713123i
\(851\) 5.06837 8.77867i 0.173741 0.300929i
\(852\) −47.4030 22.3756i −1.62400 0.766575i
\(853\) 10.3947 18.0042i 0.355908 0.616451i −0.631365 0.775486i \(-0.717505\pi\)
0.987273 + 0.159035i \(0.0508382\pi\)
\(854\) 17.7522 + 31.0088i 0.607468 + 1.06110i
\(855\) −2.15196 + 2.23612i −0.0735953 + 0.0764738i
\(856\) 3.96869 + 22.4552i 0.135647 + 0.767503i
\(857\) 8.53673i 0.291609i −0.989313 0.145805i \(-0.953423\pi\)
0.989313 0.145805i \(-0.0465771\pi\)
\(858\) −31.5820 4.78176i −1.07819 0.163247i
\(859\) 49.4619i 1.68762i −0.536643 0.843809i \(-0.680308\pi\)
0.536643 0.843809i \(-0.319692\pi\)
\(860\) 0.972017 16.7656i 0.0331455 0.571703i
\(861\) 26.0606 36.5344i 0.888141 1.24509i
\(862\) −28.0945 + 26.5128i −0.956901 + 0.903030i
\(863\) 0.0464640 + 0.0268260i 0.00158165 + 0.000913168i 0.500791 0.865568i \(-0.333043\pi\)
−0.499209 + 0.866482i \(0.666376\pi\)
\(864\) −29.3906 + 0.437598i −0.999889 + 0.0148874i
\(865\) −6.89128 11.9361i −0.234311 0.405838i
\(866\) −4.37511 18.4491i −0.148672 0.626926i
\(867\) 5.96146 + 42.1541i 0.202462 + 1.43163i
\(868\) −13.0061 + 42.8932i −0.441456 + 1.45589i
\(869\) 15.7901 9.11642i 0.535642 0.309253i
\(870\) −18.2545 + 7.15032i −0.618885 + 0.242419i
\(871\) −24.3074 −0.823626
\(872\) −2.53088 + 6.96217i −0.0857064 + 0.235769i
\(873\) 37.1959 38.6507i 1.25889 1.30813i
\(874\) 0.686350 2.29368i 0.0232161 0.0775848i
\(875\) 27.7284 + 6.68274i 0.937390 + 0.225918i
\(876\) 4.35946 + 52.6725i 0.147292 + 1.77964i
\(877\) 0.869488i 0.0293605i −0.999892 0.0146803i \(-0.995327\pi\)
0.999892 0.0146803i \(-0.00467304\pi\)
\(878\) 0.861196 + 0.912571i 0.0290640 + 0.0307978i
\(879\) 31.3316 + 12.6274i 1.05679 + 0.425910i
\(880\) 9.24456 12.4314i 0.311634 0.419062i
\(881\) 32.9667i 1.11067i −0.831625 0.555337i \(-0.812589\pi\)
0.831625 0.555337i \(-0.187411\pi\)
\(882\) −13.7871 + 26.3043i −0.464236 + 0.885712i
\(883\) −25.2601 −0.850070 −0.425035 0.905177i \(-0.639738\pi\)
−0.425035 + 0.905177i \(0.639738\pi\)
\(884\) 56.1562 + 3.25576i 1.88874 + 0.109503i
\(885\) 14.6547 2.07248i 0.492612 0.0696656i
\(886\) 17.3300 + 18.3638i 0.582212 + 0.616944i
\(887\) −30.0845 −1.01014 −0.505070 0.863079i \(-0.668533\pi\)
−0.505070 + 0.863079i \(0.668533\pi\)
\(888\) −15.6519 + 17.4274i −0.525245 + 0.584825i
\(889\) 11.0152 45.7047i 0.369437 1.53289i
\(890\) −5.77728 1.72877i −0.193655 0.0579485i
\(891\) 23.8014 + 12.5503i 0.797376 + 0.420449i
\(892\) −2.08162 + 35.9043i −0.0696977 + 1.20217i
\(893\) 3.35861i 0.112392i
\(894\) 27.2825 + 21.7868i 0.912464 + 0.728661i
\(895\) 5.71295 + 9.89513i 0.190963 + 0.330758i
\(896\) −5.28205 + 29.4635i −0.176461 + 0.984308i
\(897\) 5.98687 14.8549i 0.199896 0.495991i
\(898\) 30.5805 7.25200i 1.02048 0.242002i
\(899\) −45.3225 + 26.1670i −1.51159 + 0.872717i
\(900\) 4.40917 + 19.4373i 0.146972 + 0.647909i
\(901\) −20.1001 + 34.8143i −0.669630 + 1.15983i
\(902\) −30.1134 + 28.4181i −1.00267 + 0.946219i
\(903\) 2.84743 29.5670i 0.0947565 0.983929i
\(904\) 11.2164 + 4.07737i 0.373051 + 0.135611i
\(905\) 0.738864 0.0245607
\(906\) 9.06790 + 7.24131i 0.301261 + 0.240576i
\(907\) 41.6763 1.38384 0.691919 0.721975i \(-0.256765\pi\)
0.691919 + 0.721975i \(0.256765\pi\)
\(908\) −11.8569 23.5934i −0.393485 0.782975i
\(909\) 4.47784 18.0926i 0.148521 0.600093i
\(910\) 10.5038 + 18.3475i 0.348196 + 0.608215i
\(911\) 36.5098 + 21.0789i 1.20962 + 0.698377i 0.962677 0.270653i \(-0.0872395\pi\)
0.246947 + 0.969029i \(0.420573\pi\)
\(912\) −2.64725 + 4.85807i −0.0876592 + 0.160867i
\(913\) −20.7528 11.9816i −0.686816 0.396533i
\(914\) −22.6432 23.9940i −0.748971 0.793652i
\(915\) −19.8734 8.00944i −0.656994 0.264784i
\(916\) −4.67725 + 2.35056i −0.154541 + 0.0776646i
\(917\) 6.54840 27.1710i 0.216247 0.897264i
\(918\) −43.7744 18.1416i −1.44477 0.598761i
\(919\) −11.4205 6.59361i −0.376727 0.217503i 0.299666 0.954044i \(-0.403125\pi\)
−0.676393 + 0.736541i \(0.736458\pi\)
\(920\) 4.99542 + 5.94849i 0.164694 + 0.196116i
\(921\) −18.4953 23.6308i −0.609440 0.778662i
\(922\) −14.9236 + 49.8724i −0.491482 + 1.64246i
\(923\) −57.1585 + 33.0005i −1.88139 + 1.08622i
\(924\) 17.1768 21.3492i 0.565076 0.702336i
\(925\) 13.7553 + 7.94164i 0.452272 + 0.261120i
\(926\) −35.1436 + 33.1651i −1.15489 + 1.08987i
\(927\) −0.769685 + 3.10989i −0.0252798 + 0.102142i
\(928\) −28.0205 + 20.8894i −0.919817 + 0.685728i
\(929\) −12.6072 + 7.27877i −0.413629 + 0.238809i −0.692348 0.721564i \(-0.743424\pi\)
0.278719 + 0.960373i \(0.410090\pi\)
\(930\) −9.80303 25.0268i −0.321454 0.820660i
\(931\) 3.03622 + 4.69338i 0.0995080 + 0.153819i
\(932\) −2.90927 + 50.1799i −0.0952963 + 1.64370i
\(933\) −2.38702 16.8788i −0.0781474 0.552588i
\(934\) −46.3774 13.8778i −1.51751 0.454094i
\(935\) 21.6281 12.4870i 0.707315 0.408369i
\(936\) −20.6306 + 30.7267i −0.674333 + 1.00433i
\(937\) 22.0761i 0.721195i −0.932721 0.360598i \(-0.882573\pi\)
0.932721 0.360598i \(-0.117427\pi\)
\(938\) 10.4919 18.0202i 0.342573 0.588379i
\(939\) −16.2420 + 40.3003i −0.530036 + 1.31515i
\(940\) −9.10582 5.98552i −0.296999 0.195226i
\(941\) 7.81760 13.5405i 0.254847 0.441407i −0.710007 0.704194i \(-0.751308\pi\)
0.964854 + 0.262787i \(0.0846417\pi\)
\(942\) −2.57506 6.57404i −0.0839001 0.214194i
\(943\) −10.3805 17.9795i −0.338035 0.585495i
\(944\) 24.2218 10.4635i 0.788351 0.340558i
\(945\) −3.27543 17.5055i −0.106550 0.569454i
\(946\) −7.85669 + 26.2559i −0.255443 + 0.853652i
\(947\) −7.80879 13.5252i −0.253751 0.439510i 0.710804 0.703390i \(-0.248331\pi\)
−0.964556 + 0.263880i \(0.914998\pi\)
\(948\) −1.74253 21.0538i −0.0565947 0.683797i
\(949\) 57.6317 + 33.2737i 1.87081 + 1.08011i
\(950\) 3.59397 + 1.07544i 0.116604 + 0.0348920i
\(951\) −11.7091 + 29.0533i −0.379695 + 0.942116i
\(952\) −26.6526 + 40.2258i −0.863815 + 1.30372i
\(953\) −22.9094 −0.742107 −0.371054 0.928611i \(-0.621003\pi\)
−0.371054 + 0.928611i \(0.621003\pi\)
\(954\) −13.0003 23.0344i −0.420901 0.745766i
\(955\) 1.28939 0.744430i 0.0417237 0.0240892i
\(956\) 10.5526 16.0538i 0.341296 0.519215i
\(957\) 31.6786 4.48001i 1.02402 0.144818i
\(958\) 44.8542 10.6369i 1.44917 0.343664i
\(959\) 10.5625 + 2.54563i 0.341080 + 0.0822028i
\(960\) −8.45335 15.8350i −0.272831 0.511072i
\(961\) −20.3747 35.2900i −0.657248 1.13839i
\(962\) 6.80555 + 28.6979i 0.219420 + 0.925257i
\(963\) −17.4272 16.7713i −0.561585 0.540447i
\(964\) 16.4449 + 32.7229i 0.529656 + 1.05393i
\(965\) −6.79152 + 11.7633i −0.218627 + 0.378673i
\(966\) 8.42845 + 10.8502i 0.271181 + 0.349100i
\(967\) 51.2047 29.5630i 1.64663 0.950684i 0.668235 0.743950i \(-0.267050\pi\)
0.978397 0.206733i \(-0.0662832\pi\)
\(968\) 4.46527 3.74984i 0.143519 0.120524i
\(969\) −7.02333 + 5.49700i −0.225622 + 0.176589i
\(970\) 31.3826 + 9.39079i 1.00763 + 0.301520i
\(971\) −10.7872 6.22798i −0.346177 0.199865i 0.316823 0.948485i \(-0.397384\pi\)
−0.663000 + 0.748619i \(0.730717\pi\)
\(972\) 24.9222 18.7319i 0.799380 0.600826i
\(973\) −15.9812 + 4.71859i −0.512334 + 0.151271i
\(974\) 3.63670 3.43196i 0.116527 0.109967i
\(975\) 23.2762 + 9.38085i 0.745435 + 0.300428i
\(976\) −37.9419 4.41434i −1.21449 0.141299i
\(977\) 13.3423 23.1095i 0.426858 0.739339i −0.569734 0.821829i \(-0.692954\pi\)
0.996592 + 0.0824897i \(0.0262872\pi\)
\(978\) −1.90260 4.85726i −0.0608384 0.155318i
\(979\) 8.52269 + 4.92058i 0.272386 + 0.157262i
\(980\) −18.1356 0.132530i −0.579321 0.00423353i
\(981\) −2.17879 7.54915i −0.0695633 0.241026i
\(982\) 20.4756 + 21.6971i 0.653402 + 0.692381i
\(983\) −30.7980 −0.982303 −0.491152 0.871074i \(-0.663424\pi\)
−0.491152 + 0.871074i \(0.663424\pi\)
\(984\) 14.8827 + 45.6084i 0.474442 + 1.45394i
\(985\) 3.92336i 0.125009i
\(986\) −54.8214 + 13.0006i −1.74587 + 0.414023i
\(987\) −15.6909 11.1926i −0.499447 0.356263i
\(988\) 3.12802 + 6.22427i 0.0995155 + 0.198020i
\(989\) −11.9006 6.87084i −0.378418 0.218480i
\(990\) −0.160654 + 16.4309i −0.00510592 + 0.522210i
\(991\) 21.7549 12.5602i 0.691066 0.398987i −0.112945 0.993601i \(-0.536028\pi\)
0.804011 + 0.594614i \(0.202695\pi\)
\(992\) −28.6392 38.4158i −0.909296 1.21970i
\(993\) 43.9628 + 17.7180i 1.39512 + 0.562265i
\(994\) 0.206873 56.6182i 0.00656161 1.79582i
\(995\) −7.52061 13.0261i −0.238419 0.412954i
\(996\) −22.8186 + 15.8188i −0.723034 + 0.501237i
\(997\) −54.4985 −1.72598 −0.862992 0.505217i \(-0.831412\pi\)
−0.862992 + 0.505217i \(0.831412\pi\)
\(998\) −52.3082 + 12.4046i −1.65579 + 0.392661i
\(999\) 2.53307 24.7157i 0.0801428 0.781971i
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 504.2.cz.b.187.7 yes 180
7.3 odd 6 504.2.bf.b.115.55 180
8.3 odd 2 inner 504.2.cz.b.187.67 yes 180
9.4 even 3 504.2.bf.b.355.55 yes 180
56.3 even 6 504.2.bf.b.115.56 yes 180
63.31 odd 6 inner 504.2.cz.b.283.67 yes 180
72.67 odd 6 504.2.bf.b.355.56 yes 180
504.283 even 6 inner 504.2.cz.b.283.7 yes 180
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
504.2.bf.b.115.55 180 7.3 odd 6
504.2.bf.b.115.56 yes 180 56.3 even 6
504.2.bf.b.355.55 yes 180 9.4 even 3
504.2.bf.b.355.56 yes 180 72.67 odd 6
504.2.cz.b.187.7 yes 180 1.1 even 1 trivial
504.2.cz.b.187.67 yes 180 8.3 odd 2 inner
504.2.cz.b.283.7 yes 180 504.283 even 6 inner
504.2.cz.b.283.67 yes 180 63.31 odd 6 inner