Properties

Label 403.2.f.b.94.12
Level $403$
Weight $2$
Character 403.94
Analytic conductor $3.218$
Analytic rank $0$
Dimension $34$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [403,2,Mod(94,403)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(403, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("403.94");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 403 = 13 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 403.f (of order \(3\), 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: \(3.21797120146\)
Analytic rank: \(0\)
Dimension: \(34\)
Relative dimension: \(17\) over \(\Q(\zeta_{3})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 94.12
Character \(\chi\) \(=\) 403.94
Dual form 403.2.f.b.373.12

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.600575 + 1.04023i) q^{2} +(0.0302705 + 0.0524300i) q^{3} +(0.278620 - 0.482584i) q^{4} +2.34059 q^{5} +(-0.0363594 + 0.0629763i) q^{6} +(-0.828861 + 1.43563i) q^{7} +3.07163 q^{8} +(1.49817 - 2.59490i) q^{9} +O(q^{10})\) \(q+(0.600575 + 1.04023i) q^{2} +(0.0302705 + 0.0524300i) q^{3} +(0.278620 - 0.482584i) q^{4} +2.34059 q^{5} +(-0.0363594 + 0.0629763i) q^{6} +(-0.828861 + 1.43563i) q^{7} +3.07163 q^{8} +(1.49817 - 2.59490i) q^{9} +(1.40570 + 2.43474i) q^{10} +(-0.701103 - 1.21435i) q^{11} +0.0337359 q^{12} +(-2.53337 - 2.56555i) q^{13} -1.99117 q^{14} +(0.0708507 + 0.122717i) q^{15} +(1.28750 + 2.23002i) q^{16} +(-0.0737699 + 0.127773i) q^{17} +3.59905 q^{18} +(-1.76285 + 3.05335i) q^{19} +(0.652134 - 1.12953i) q^{20} -0.100360 q^{21} +(0.842129 - 1.45861i) q^{22} +(1.99132 + 3.44907i) q^{23} +(0.0929797 + 0.161046i) q^{24} +0.478344 q^{25} +(1.14727 - 4.17608i) q^{26} +0.363024 q^{27} +(0.461874 + 0.799990i) q^{28} +(5.06479 + 8.77247i) q^{29} +(-0.0851023 + 0.147401i) q^{30} -1.00000 q^{31} +(1.52515 - 2.64163i) q^{32} +(0.0424454 - 0.0735177i) q^{33} -0.177217 q^{34} +(-1.94002 + 3.36021i) q^{35} +(-0.834839 - 1.44598i) q^{36} +(-2.95348 - 5.11558i) q^{37} -4.23489 q^{38} +(0.0578255 - 0.210485i) q^{39} +7.18941 q^{40} +(-1.20617 - 2.08915i) q^{41} +(-0.0602737 - 0.104397i) q^{42} +(-4.78486 + 8.28762i) q^{43} -0.781365 q^{44} +(3.50659 - 6.07359i) q^{45} +(-2.39187 + 4.14285i) q^{46} -8.13981 q^{47} +(-0.0779466 + 0.135008i) q^{48} +(2.12598 + 3.68230i) q^{49} +(0.287281 + 0.497586i) q^{50} -0.00893220 q^{51} +(-1.94394 + 0.507750i) q^{52} -10.6420 q^{53} +(0.218023 + 0.377627i) q^{54} +(-1.64099 - 2.84228i) q^{55} +(-2.54595 + 4.40972i) q^{56} -0.213449 q^{57} +(-6.08357 + 10.5371i) q^{58} +(6.13986 - 10.6345i) q^{59} +0.0789617 q^{60} +(3.02450 - 5.23859i) q^{61} +(-0.600575 - 1.04023i) q^{62} +(2.48354 + 4.30163i) q^{63} +8.81386 q^{64} +(-5.92957 - 6.00489i) q^{65} +0.101967 q^{66} +(3.60988 + 6.25250i) q^{67} +(0.0411075 + 0.0712003i) q^{68} +(-0.120557 + 0.208810i) q^{69} -4.66051 q^{70} +(-0.242049 + 0.419241i) q^{71} +(4.60181 - 7.97057i) q^{72} -1.86973 q^{73} +(3.54757 - 6.14458i) q^{74} +(0.0144797 + 0.0250796i) q^{75} +(0.982331 + 1.70145i) q^{76} +2.32447 q^{77} +(0.253681 - 0.0662604i) q^{78} -14.5823 q^{79} +(3.01351 + 5.21955i) q^{80} +(-4.48351 - 7.76567i) q^{81} +(1.44879 - 2.50938i) q^{82} -8.47384 q^{83} +(-0.0279623 + 0.0484322i) q^{84} +(-0.172665 + 0.299064i) q^{85} -11.4947 q^{86} +(-0.306627 + 0.531094i) q^{87} +(-2.15353 - 3.73002i) q^{88} +(-7.46453 - 12.9290i) q^{89} +8.42388 q^{90} +(5.78299 - 1.51049i) q^{91} +2.21929 q^{92} +(-0.0302705 - 0.0524300i) q^{93} +(-4.88856 - 8.46724i) q^{94} +(-4.12610 + 7.14662i) q^{95} +0.184668 q^{96} +(4.49646 - 7.78809i) q^{97} +(-2.55362 + 4.42300i) q^{98} -4.20148 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 34 q + 4 q^{2} - 20 q^{4} - 14 q^{5} + 6 q^{6} + 6 q^{7} - 12 q^{8} - 17 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 34 q + 4 q^{2} - 20 q^{4} - 14 q^{5} + 6 q^{6} + 6 q^{7} - 12 q^{8} - 17 q^{9} - 6 q^{10} + 13 q^{11} + 8 q^{12} - 3 q^{13} + 4 q^{15} - 34 q^{16} + 6 q^{17} + 24 q^{18} + 4 q^{19} + 28 q^{20} - 36 q^{21} + 34 q^{22} + 8 q^{23} + 40 q^{24} + 16 q^{25} - 26 q^{26} - 6 q^{27} + 21 q^{28} + 6 q^{29} - 19 q^{30} - 34 q^{31} + 6 q^{32} + 7 q^{33} - 48 q^{34} + 9 q^{35} + 14 q^{37} + 22 q^{38} - 21 q^{39} - 20 q^{40} + 43 q^{41} - 33 q^{42} - 18 q^{43} - 56 q^{44} + 26 q^{45} + 7 q^{46} - 12 q^{47} + 95 q^{48} + q^{49} + 44 q^{50} + 52 q^{51} - 24 q^{52} - 10 q^{53} + 27 q^{54} - 39 q^{55} - 39 q^{56} - 92 q^{57} + 8 q^{58} - q^{59} - 42 q^{60} + 19 q^{61} - 4 q^{62} + 5 q^{63} + 84 q^{64} - 32 q^{65} + 52 q^{66} + 10 q^{67} - 34 q^{68} - 32 q^{69} + 48 q^{70} + 35 q^{71} - 26 q^{72} - 22 q^{73} + 68 q^{74} + 62 q^{75} + 2 q^{76} + 42 q^{77} - 81 q^{78} + 2 q^{79} + 49 q^{80} - 37 q^{81} - 35 q^{82} - 48 q^{83} - 34 q^{84} - 13 q^{85} - 152 q^{86} + 22 q^{87} + 37 q^{88} + 42 q^{89} + 30 q^{90} - 39 q^{91} + 30 q^{92} - 42 q^{94} - 34 q^{95} - 66 q^{96} - 38 q^{97} + 8 q^{98} - 34 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/403\mathbb{Z}\right)^\times\).

\(n\) \(249\) \(313\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.600575 + 1.04023i 0.424670 + 0.735551i 0.996390 0.0848986i \(-0.0270566\pi\)
−0.571719 + 0.820449i \(0.693723\pi\)
\(3\) 0.0302705 + 0.0524300i 0.0174767 + 0.0302705i 0.874631 0.484788i \(-0.161103\pi\)
−0.857155 + 0.515059i \(0.827770\pi\)
\(4\) 0.278620 0.482584i 0.139310 0.241292i
\(5\) 2.34059 1.04674 0.523371 0.852105i \(-0.324674\pi\)
0.523371 + 0.852105i \(0.324674\pi\)
\(6\) −0.0363594 + 0.0629763i −0.0148437 + 0.0257100i
\(7\) −0.828861 + 1.43563i −0.313280 + 0.542617i −0.979070 0.203522i \(-0.934761\pi\)
0.665790 + 0.746139i \(0.268094\pi\)
\(8\) 3.07163 1.08598
\(9\) 1.49817 2.59490i 0.499389 0.864967i
\(10\) 1.40570 + 2.43474i 0.444520 + 0.769932i
\(11\) −0.701103 1.21435i −0.211390 0.366139i 0.740760 0.671770i \(-0.234466\pi\)
−0.952150 + 0.305631i \(0.901132\pi\)
\(12\) 0.0337359 0.00973871
\(13\) −2.53337 2.56555i −0.702630 0.711555i
\(14\) −1.99117 −0.532163
\(15\) 0.0708507 + 0.122717i 0.0182936 + 0.0316854i
\(16\) 1.28750 + 2.23002i 0.321875 + 0.557505i
\(17\) −0.0737699 + 0.127773i −0.0178918 + 0.0309895i −0.874833 0.484425i \(-0.839029\pi\)
0.856941 + 0.515415i \(0.172362\pi\)
\(18\) 3.59905 0.848303
\(19\) −1.76285 + 3.05335i −0.404426 + 0.700486i −0.994254 0.107043i \(-0.965862\pi\)
0.589829 + 0.807528i \(0.299195\pi\)
\(20\) 0.652134 1.12953i 0.145822 0.252571i
\(21\) −0.100360 −0.0219004
\(22\) 0.842129 1.45861i 0.179542 0.310977i
\(23\) 1.99132 + 3.44907i 0.415219 + 0.719180i 0.995451 0.0952705i \(-0.0303716\pi\)
−0.580232 + 0.814451i \(0.697038\pi\)
\(24\) 0.0929797 + 0.161046i 0.0189794 + 0.0328733i
\(25\) 0.478344 0.0956688
\(26\) 1.14727 4.17608i 0.224999 0.818997i
\(27\) 0.363024 0.0698640
\(28\) 0.461874 + 0.799990i 0.0872861 + 0.151184i
\(29\) 5.06479 + 8.77247i 0.940508 + 1.62901i 0.764505 + 0.644618i \(0.222984\pi\)
0.176003 + 0.984390i \(0.443683\pi\)
\(30\) −0.0851023 + 0.147401i −0.0155375 + 0.0269117i
\(31\) −1.00000 −0.179605
\(32\) 1.52515 2.64163i 0.269610 0.466979i
\(33\) 0.0424454 0.0735177i 0.00738880 0.0127978i
\(34\) −0.177217 −0.0303925
\(35\) −1.94002 + 3.36021i −0.327923 + 0.567980i
\(36\) −0.834839 1.44598i −0.139140 0.240997i
\(37\) −2.95348 5.11558i −0.485549 0.840996i 0.514313 0.857603i \(-0.328047\pi\)
−0.999862 + 0.0166065i \(0.994714\pi\)
\(38\) −4.23489 −0.686990
\(39\) 0.0578255 0.210485i 0.00925950 0.0337046i
\(40\) 7.18941 1.13675
\(41\) −1.20617 2.08915i −0.188372 0.326270i 0.756336 0.654184i \(-0.226988\pi\)
−0.944708 + 0.327914i \(0.893654\pi\)
\(42\) −0.0602737 0.104397i −0.00930044 0.0161088i
\(43\) −4.78486 + 8.28762i −0.729684 + 1.26385i 0.227332 + 0.973817i \(0.427000\pi\)
−0.957017 + 0.290033i \(0.906334\pi\)
\(44\) −0.781365 −0.117795
\(45\) 3.50659 6.07359i 0.522732 0.905398i
\(46\) −2.39187 + 4.14285i −0.352662 + 0.610829i
\(47\) −8.13981 −1.18731 −0.593657 0.804718i \(-0.702316\pi\)
−0.593657 + 0.804718i \(0.702316\pi\)
\(48\) −0.0779466 + 0.135008i −0.0112506 + 0.0194867i
\(49\) 2.12598 + 3.68230i 0.303711 + 0.526044i
\(50\) 0.287281 + 0.497586i 0.0406277 + 0.0703693i
\(51\) −0.00893220 −0.00125076
\(52\) −1.94394 + 0.507750i −0.269576 + 0.0704122i
\(53\) −10.6420 −1.46179 −0.730895 0.682489i \(-0.760897\pi\)
−0.730895 + 0.682489i \(0.760897\pi\)
\(54\) 0.218023 + 0.377627i 0.0296692 + 0.0513885i
\(55\) −1.64099 2.84228i −0.221271 0.383253i
\(56\) −2.54595 + 4.40972i −0.340217 + 0.589273i
\(57\) −0.213449 −0.0282721
\(58\) −6.08357 + 10.5371i −0.798812 + 1.38358i
\(59\) 6.13986 10.6345i 0.799341 1.38450i −0.120704 0.992689i \(-0.538515\pi\)
0.920046 0.391811i \(-0.128151\pi\)
\(60\) 0.0789617 0.0101939
\(61\) 3.02450 5.23859i 0.387247 0.670732i −0.604831 0.796354i \(-0.706759\pi\)
0.992078 + 0.125622i \(0.0400926\pi\)
\(62\) −0.600575 1.04023i −0.0762731 0.132109i
\(63\) 2.48354 + 4.30163i 0.312897 + 0.541954i
\(64\) 8.81386 1.10173
\(65\) −5.92957 6.00489i −0.735472 0.744815i
\(66\) 0.101967 0.0125512
\(67\) 3.60988 + 6.25250i 0.441017 + 0.763865i 0.997765 0.0668170i \(-0.0212844\pi\)
−0.556748 + 0.830682i \(0.687951\pi\)
\(68\) 0.0411075 + 0.0712003i 0.00498502 + 0.00863431i
\(69\) −0.120557 + 0.208810i −0.0145133 + 0.0251378i
\(70\) −4.66051 −0.557037
\(71\) −0.242049 + 0.419241i −0.0287259 + 0.0497547i −0.880031 0.474916i \(-0.842478\pi\)
0.851305 + 0.524671i \(0.175812\pi\)
\(72\) 4.60181 7.97057i 0.542329 0.939341i
\(73\) −1.86973 −0.218835 −0.109417 0.993996i \(-0.534899\pi\)
−0.109417 + 0.993996i \(0.534899\pi\)
\(74\) 3.54757 6.14458i 0.412397 0.714292i
\(75\) 0.0144797 + 0.0250796i 0.00167197 + 0.00289594i
\(76\) 0.982331 + 1.70145i 0.112681 + 0.195169i
\(77\) 2.32447 0.264897
\(78\) 0.253681 0.0662604i 0.0287237 0.00750251i
\(79\) −14.5823 −1.64064 −0.820320 0.571904i \(-0.806205\pi\)
−0.820320 + 0.571904i \(0.806205\pi\)
\(80\) 3.01351 + 5.21955i 0.336921 + 0.583563i
\(81\) −4.48351 7.76567i −0.498168 0.862853i
\(82\) 1.44879 2.50938i 0.159992 0.277114i
\(83\) −8.47384 −0.930125 −0.465062 0.885278i \(-0.653968\pi\)
−0.465062 + 0.885278i \(0.653968\pi\)
\(84\) −0.0279623 + 0.0484322i −0.00305094 + 0.00528439i
\(85\) −0.172665 + 0.299064i −0.0187281 + 0.0324381i
\(86\) −11.4947 −1.23950
\(87\) −0.306627 + 0.531094i −0.0328739 + 0.0569393i
\(88\) −2.15353 3.73002i −0.229567 0.397621i
\(89\) −7.46453 12.9290i −0.791239 1.37047i −0.925200 0.379480i \(-0.876103\pi\)
0.133961 0.990987i \(-0.457230\pi\)
\(90\) 8.42388 0.887955
\(91\) 5.78299 1.51049i 0.606222 0.158343i
\(92\) 2.21929 0.231377
\(93\) −0.0302705 0.0524300i −0.00313890 0.00543674i
\(94\) −4.88856 8.46724i −0.504217 0.873329i
\(95\) −4.12610 + 7.14662i −0.423329 + 0.733228i
\(96\) 0.184668 0.0188476
\(97\) 4.49646 7.78809i 0.456546 0.790761i −0.542230 0.840230i \(-0.682420\pi\)
0.998776 + 0.0494695i \(0.0157530\pi\)
\(98\) −2.55362 + 4.42300i −0.257954 + 0.446790i
\(99\) −4.20148 −0.422264
\(100\) 0.133276 0.230841i 0.0133276 0.0230841i
\(101\) −0.440108 0.762289i −0.0437924 0.0758506i 0.843298 0.537446i \(-0.180611\pi\)
−0.887091 + 0.461595i \(0.847277\pi\)
\(102\) −0.00536446 0.00929151i −0.000531160 0.000919996i
\(103\) 12.7618 1.25746 0.628728 0.777625i \(-0.283576\pi\)
0.628728 + 0.777625i \(0.283576\pi\)
\(104\) −7.78156 7.88041i −0.763045 0.772738i
\(105\) −0.234901 −0.0229240
\(106\) −6.39132 11.0701i −0.620779 1.07522i
\(107\) 1.25780 + 2.17857i 0.121596 + 0.210611i 0.920397 0.390985i \(-0.127865\pi\)
−0.798801 + 0.601595i \(0.794532\pi\)
\(108\) 0.101146 0.175190i 0.00973276 0.0168576i
\(109\) 16.1425 1.54617 0.773087 0.634300i \(-0.218712\pi\)
0.773087 + 0.634300i \(0.218712\pi\)
\(110\) 1.97108 3.41400i 0.187935 0.325512i
\(111\) 0.178807 0.309702i 0.0169716 0.0293956i
\(112\) −4.26864 −0.403348
\(113\) −5.86816 + 10.1640i −0.552030 + 0.956144i 0.446098 + 0.894984i \(0.352813\pi\)
−0.998128 + 0.0611600i \(0.980520\pi\)
\(114\) −0.128192 0.222036i −0.0120063 0.0207955i
\(115\) 4.66086 + 8.07284i 0.434627 + 0.752796i
\(116\) 5.64461 0.524089
\(117\) −10.4528 + 2.73022i −0.966358 + 0.252409i
\(118\) 14.7498 1.35783
\(119\) −0.122290 0.211812i −0.0112103 0.0194168i
\(120\) 0.217627 + 0.376941i 0.0198665 + 0.0344098i
\(121\) 4.51691 7.82352i 0.410628 0.711229i
\(122\) 7.26575 0.657810
\(123\) 0.0730227 0.126479i 0.00658423 0.0114042i
\(124\) −0.278620 + 0.482584i −0.0250208 + 0.0433373i
\(125\) −10.5833 −0.946601
\(126\) −2.98311 + 5.16689i −0.265756 + 0.460304i
\(127\) 8.35200 + 14.4661i 0.741121 + 1.28366i 0.951985 + 0.306143i \(0.0990386\pi\)
−0.210865 + 0.977515i \(0.567628\pi\)
\(128\) 2.24309 + 3.88515i 0.198263 + 0.343402i
\(129\) −0.579360 −0.0510098
\(130\) 2.68529 9.77447i 0.235516 0.857278i
\(131\) 6.70038 0.585415 0.292708 0.956202i \(-0.405444\pi\)
0.292708 + 0.956202i \(0.405444\pi\)
\(132\) −0.0236523 0.0409670i −0.00205867 0.00356572i
\(133\) −2.92231 5.06160i −0.253397 0.438896i
\(134\) −4.33601 + 7.51019i −0.374574 + 0.648781i
\(135\) 0.849689 0.0731296
\(136\) −0.226594 + 0.392472i −0.0194302 + 0.0336542i
\(137\) 2.27314 3.93720i 0.194208 0.336378i −0.752433 0.658669i \(-0.771120\pi\)
0.946641 + 0.322291i \(0.104453\pi\)
\(138\) −0.289613 −0.0246535
\(139\) 4.34021 7.51747i 0.368132 0.637624i −0.621141 0.783699i \(-0.713331\pi\)
0.989274 + 0.146075i \(0.0466641\pi\)
\(140\) 1.08106 + 1.87245i 0.0913660 + 0.158251i
\(141\) −0.246396 0.426771i −0.0207503 0.0359406i
\(142\) −0.581474 −0.0487962
\(143\) −1.33931 + 4.87510i −0.111999 + 0.407676i
\(144\) 7.71557 0.642964
\(145\) 11.8546 + 20.5327i 0.984469 + 1.70515i
\(146\) −1.12291 1.94494i −0.0929327 0.160964i
\(147\) −0.128709 + 0.222930i −0.0106157 + 0.0183870i
\(148\) −3.29160 −0.270568
\(149\) −6.00496 + 10.4009i −0.491945 + 0.852074i −0.999957 0.00927607i \(-0.997047\pi\)
0.508012 + 0.861350i \(0.330381\pi\)
\(150\) −0.0173923 + 0.0301244i −0.00142008 + 0.00245964i
\(151\) −13.6054 −1.10719 −0.553595 0.832786i \(-0.686745\pi\)
−0.553595 + 0.832786i \(0.686745\pi\)
\(152\) −5.41482 + 9.37874i −0.439200 + 0.760716i
\(153\) 0.221039 + 0.382851i 0.0178700 + 0.0309517i
\(154\) 1.39602 + 2.41797i 0.112494 + 0.194846i
\(155\) −2.34059 −0.188000
\(156\) −0.0854654 0.0865510i −0.00684271 0.00692963i
\(157\) −8.51284 −0.679398 −0.339699 0.940534i \(-0.610325\pi\)
−0.339699 + 0.940534i \(0.610325\pi\)
\(158\) −8.75778 15.1689i −0.696732 1.20677i
\(159\) −0.322139 0.557960i −0.0255473 0.0442491i
\(160\) 3.56973 6.18296i 0.282212 0.488806i
\(161\) −6.60211 −0.520319
\(162\) 5.38537 9.32773i 0.423115 0.732856i
\(163\) 2.98251 5.16585i 0.233608 0.404621i −0.725259 0.688476i \(-0.758280\pi\)
0.958867 + 0.283855i \(0.0916135\pi\)
\(164\) −1.34425 −0.104968
\(165\) 0.0993472 0.172074i 0.00773417 0.0133960i
\(166\) −5.08917 8.81471i −0.394997 0.684154i
\(167\) 3.75093 + 6.49681i 0.290256 + 0.502738i 0.973870 0.227105i \(-0.0729262\pi\)
−0.683614 + 0.729844i \(0.739593\pi\)
\(168\) −0.308269 −0.0237835
\(169\) −0.164089 + 12.9990i −0.0126222 + 0.999920i
\(170\) −0.414792 −0.0318131
\(171\) 5.28209 + 9.14885i 0.403931 + 0.699630i
\(172\) 2.66632 + 4.61819i 0.203305 + 0.352134i
\(173\) −8.91193 + 15.4359i −0.677561 + 1.17357i 0.298152 + 0.954518i \(0.403630\pi\)
−0.975713 + 0.219052i \(0.929704\pi\)
\(174\) −0.736611 −0.0558423
\(175\) −0.396481 + 0.686725i −0.0299711 + 0.0519115i
\(176\) 1.80534 3.12694i 0.136083 0.235702i
\(177\) 0.743426 0.0558793
\(178\) 8.96602 15.5296i 0.672032 1.16399i
\(179\) −3.05431 5.29021i −0.228290 0.395409i 0.729012 0.684501i \(-0.239980\pi\)
−0.957301 + 0.289092i \(0.906647\pi\)
\(180\) −1.95401 3.38445i −0.145644 0.252262i
\(181\) 12.8598 0.955862 0.477931 0.878397i \(-0.341387\pi\)
0.477931 + 0.878397i \(0.341387\pi\)
\(182\) 5.04437 + 5.10845i 0.373914 + 0.378663i
\(183\) 0.366212 0.0270712
\(184\) 6.11659 + 10.5943i 0.450921 + 0.781019i
\(185\) −6.91288 11.9735i −0.508245 0.880306i
\(186\) 0.0363594 0.0629763i 0.00266600 0.00461765i
\(187\) 0.206881 0.0151286
\(188\) −2.26791 + 3.92814i −0.165405 + 0.286489i
\(189\) −0.300896 + 0.521168i −0.0218870 + 0.0379094i
\(190\) −9.91213 −0.719102
\(191\) 9.10001 15.7617i 0.658453 1.14047i −0.322563 0.946548i \(-0.604544\pi\)
0.981016 0.193927i \(-0.0621223\pi\)
\(192\) 0.266800 + 0.462111i 0.0192546 + 0.0333500i
\(193\) −4.46227 7.72887i −0.321201 0.556336i 0.659535 0.751674i \(-0.270753\pi\)
−0.980736 + 0.195337i \(0.937420\pi\)
\(194\) 10.8018 0.775526
\(195\) 0.135346 0.492658i 0.00969230 0.0352800i
\(196\) 2.36936 0.169240
\(197\) −0.430483 0.745618i −0.0306706 0.0531231i 0.850283 0.526326i \(-0.176431\pi\)
−0.880953 + 0.473203i \(0.843098\pi\)
\(198\) −2.52330 4.37048i −0.179323 0.310597i
\(199\) −9.48486 + 16.4283i −0.672364 + 1.16457i 0.304868 + 0.952395i \(0.401388\pi\)
−0.977232 + 0.212174i \(0.931946\pi\)
\(200\) 1.46930 0.103895
\(201\) −0.218546 + 0.378533i −0.0154150 + 0.0266996i
\(202\) 0.528635 0.915623i 0.0371946 0.0644230i
\(203\) −16.7920 −1.17857
\(204\) −0.00248869 + 0.00431054i −0.000174243 + 0.000301798i
\(205\) −2.82314 4.88983i −0.197177 0.341520i
\(206\) 7.66441 + 13.2751i 0.534004 + 0.924923i
\(207\) 11.9333 0.829423
\(208\) 2.45951 8.95261i 0.170536 0.620752i
\(209\) 4.94375 0.341967
\(210\) −0.141076 0.244351i −0.00973516 0.0168618i
\(211\) 2.05003 + 3.55076i 0.141130 + 0.244444i 0.927922 0.372773i \(-0.121593\pi\)
−0.786792 + 0.617218i \(0.788260\pi\)
\(212\) −2.96507 + 5.13566i −0.203642 + 0.352719i
\(213\) −0.0293078 −0.00200813
\(214\) −1.51081 + 2.61679i −0.103277 + 0.178880i
\(215\) −11.1994 + 19.3979i −0.763791 + 1.32293i
\(216\) 1.11507 0.0758712
\(217\) 0.828861 1.43563i 0.0562667 0.0974568i
\(218\) 9.69480 + 16.7919i 0.656614 + 1.13729i
\(219\) −0.0565976 0.0980298i −0.00382451 0.00662424i
\(220\) −1.82885 −0.123301
\(221\) 0.514695 0.134436i 0.0346221 0.00904316i
\(222\) 0.429547 0.0288293
\(223\) 4.39466 + 7.61178i 0.294288 + 0.509722i 0.974819 0.222997i \(-0.0715841\pi\)
−0.680531 + 0.732720i \(0.738251\pi\)
\(224\) 2.52827 + 4.37909i 0.168927 + 0.292590i
\(225\) 0.716640 1.24126i 0.0477760 0.0827504i
\(226\) −14.0971 −0.937723
\(227\) 2.85795 4.95011i 0.189689 0.328550i −0.755458 0.655197i \(-0.772585\pi\)
0.945146 + 0.326647i \(0.105919\pi\)
\(228\) −0.0594713 + 0.103007i −0.00393858 + 0.00682182i
\(229\) 18.6835 1.23464 0.617320 0.786712i \(-0.288219\pi\)
0.617320 + 0.786712i \(0.288219\pi\)
\(230\) −5.59839 + 9.69669i −0.369147 + 0.639381i
\(231\) 0.0703627 + 0.121872i 0.00462953 + 0.00801858i
\(232\) 15.5572 + 26.9458i 1.02138 + 1.76908i
\(233\) 22.6389 1.48312 0.741561 0.670885i \(-0.234086\pi\)
0.741561 + 0.670885i \(0.234086\pi\)
\(234\) −9.11771 9.23353i −0.596043 0.603615i
\(235\) −19.0519 −1.24281
\(236\) −3.42138 5.92600i −0.222713 0.385749i
\(237\) −0.441414 0.764552i −0.0286729 0.0496630i
\(238\) 0.146888 0.254418i 0.00952137 0.0164915i
\(239\) 16.7666 1.08454 0.542272 0.840203i \(-0.317564\pi\)
0.542272 + 0.840203i \(0.317564\pi\)
\(240\) −0.182441 + 0.315997i −0.0117765 + 0.0203975i
\(241\) 0.362988 0.628713i 0.0233821 0.0404990i −0.854098 0.520113i \(-0.825890\pi\)
0.877480 + 0.479614i \(0.159223\pi\)
\(242\) 10.8510 0.697527
\(243\) 0.815972 1.41331i 0.0523447 0.0906636i
\(244\) −1.68537 2.91915i −0.107895 0.186879i
\(245\) 4.97604 + 8.61875i 0.317907 + 0.550632i
\(246\) 0.175422 0.0111845
\(247\) 12.2995 3.21257i 0.782596 0.204411i
\(248\) −3.07163 −0.195049
\(249\) −0.256507 0.444284i −0.0162555 0.0281553i
\(250\) −6.35608 11.0090i −0.401994 0.696273i
\(251\) −0.223767 + 0.387576i −0.0141241 + 0.0244636i −0.873001 0.487718i \(-0.837829\pi\)
0.858877 + 0.512182i \(0.171163\pi\)
\(252\) 2.76786 0.174359
\(253\) 2.79224 4.83630i 0.175547 0.304056i
\(254\) −10.0320 + 17.3759i −0.629464 + 1.09026i
\(255\) −0.0209066 −0.00130922
\(256\) 6.11957 10.5994i 0.382473 0.662463i
\(257\) 6.34001 + 10.9812i 0.395479 + 0.684990i 0.993162 0.116743i \(-0.0372452\pi\)
−0.597683 + 0.801732i \(0.703912\pi\)
\(258\) −0.347949 0.602666i −0.0216624 0.0375203i
\(259\) 9.79210 0.608451
\(260\) −4.54996 + 1.18843i −0.282177 + 0.0737034i
\(261\) 30.3516 1.87872
\(262\) 4.02408 + 6.96991i 0.248608 + 0.430602i
\(263\) 4.34953 + 7.53360i 0.268203 + 0.464542i 0.968398 0.249410i \(-0.0802368\pi\)
−0.700195 + 0.713952i \(0.746903\pi\)
\(264\) 0.130377 0.225819i 0.00802412 0.0138982i
\(265\) −24.9085 −1.53012
\(266\) 3.51014 6.07973i 0.215220 0.372772i
\(267\) 0.451910 0.782732i 0.0276565 0.0479024i
\(268\) 4.02314 0.245753
\(269\) 12.1367 21.0215i 0.739991 1.28170i −0.212508 0.977159i \(-0.568163\pi\)
0.952499 0.304542i \(-0.0985035\pi\)
\(270\) 0.510302 + 0.883869i 0.0310560 + 0.0537905i
\(271\) −8.75692 15.1674i −0.531945 0.921355i −0.999305 0.0372881i \(-0.988128\pi\)
0.467360 0.884067i \(-0.345205\pi\)
\(272\) −0.379915 −0.0230358
\(273\) 0.254249 + 0.257479i 0.0153879 + 0.0155833i
\(274\) 5.46077 0.329897
\(275\) −0.335368 0.580875i −0.0202235 0.0350281i
\(276\) 0.0671789 + 0.116357i 0.00404370 + 0.00700389i
\(277\) 8.10187 14.0329i 0.486794 0.843152i −0.513091 0.858335i \(-0.671499\pi\)
0.999885 + 0.0151822i \(0.00483282\pi\)
\(278\) 10.4265 0.625339
\(279\) −1.49817 + 2.59490i −0.0896929 + 0.155353i
\(280\) −5.95902 + 10.3213i −0.356120 + 0.616817i
\(281\) −30.4658 −1.81743 −0.908717 0.417412i \(-0.862937\pi\)
−0.908717 + 0.417412i \(0.862937\pi\)
\(282\) 0.295959 0.512615i 0.0176241 0.0305258i
\(283\) −7.40655 12.8285i −0.440274 0.762576i 0.557436 0.830220i \(-0.311785\pi\)
−0.997710 + 0.0676437i \(0.978452\pi\)
\(284\) 0.134879 + 0.233618i 0.00800361 + 0.0138627i
\(285\) −0.499597 −0.0295936
\(286\) −5.87556 + 1.53467i −0.347429 + 0.0907471i
\(287\) 3.99899 0.236053
\(288\) −4.56985 7.91521i −0.269281 0.466408i
\(289\) 8.48912 + 14.7036i 0.499360 + 0.864916i
\(290\) −14.2391 + 24.6629i −0.836150 + 1.44825i
\(291\) 0.544440 0.0319156
\(292\) −0.520943 + 0.902300i −0.0304859 + 0.0528031i
\(293\) −0.348053 + 0.602846i −0.0203335 + 0.0352186i −0.876013 0.482287i \(-0.839806\pi\)
0.855680 + 0.517506i \(0.173139\pi\)
\(294\) −0.309197 −0.0180328
\(295\) 14.3709 24.8911i 0.836704 1.44921i
\(296\) −9.07199 15.7132i −0.527299 0.913309i
\(297\) −0.254517 0.440837i −0.0147686 0.0255799i
\(298\) −14.4257 −0.835658
\(299\) 3.80401 13.8466i 0.219991 0.800769i
\(300\) 0.0161374 0.000931691
\(301\) −7.93197 13.7386i −0.457191 0.791878i
\(302\) −8.17105 14.1527i −0.470191 0.814395i
\(303\) 0.0266446 0.0461497i 0.00153069 0.00265123i
\(304\) −9.07869 −0.520699
\(305\) 7.07910 12.2614i 0.405348 0.702084i
\(306\) −0.265501 + 0.459862i −0.0151777 + 0.0262885i
\(307\) 26.6000 1.51814 0.759071 0.651008i \(-0.225654\pi\)
0.759071 + 0.651008i \(0.225654\pi\)
\(308\) 0.647643 1.12175i 0.0369029 0.0639176i
\(309\) 0.386306 + 0.669101i 0.0219762 + 0.0380638i
\(310\) −1.40570 2.43474i −0.0798382 0.138284i
\(311\) −3.79985 −0.215470 −0.107735 0.994180i \(-0.534360\pi\)
−0.107735 + 0.994180i \(0.534360\pi\)
\(312\) 0.177619 0.646532i 0.0100557 0.0366026i
\(313\) −6.95115 −0.392902 −0.196451 0.980514i \(-0.562942\pi\)
−0.196451 + 0.980514i \(0.562942\pi\)
\(314\) −5.11260 8.85528i −0.288520 0.499732i
\(315\) 5.81295 + 10.0683i 0.327523 + 0.567286i
\(316\) −4.06293 + 7.03720i −0.228558 + 0.395874i
\(317\) −10.0888 −0.566643 −0.283321 0.959025i \(-0.591436\pi\)
−0.283321 + 0.959025i \(0.591436\pi\)
\(318\) 0.386937 0.670194i 0.0216983 0.0375826i
\(319\) 7.10188 12.3008i 0.397629 0.688713i
\(320\) 20.6296 1.15323
\(321\) −0.0761484 + 0.131893i −0.00425019 + 0.00736155i
\(322\) −3.96506 6.86769i −0.220964 0.382721i
\(323\) −0.260090 0.450490i −0.0144718 0.0250659i
\(324\) −4.99679 −0.277599
\(325\) −1.21182 1.22722i −0.0672198 0.0680737i
\(326\) 7.16487 0.396825
\(327\) 0.488642 + 0.846353i 0.0270220 + 0.0468035i
\(328\) −3.70490 6.41708i −0.204569 0.354324i
\(329\) 6.74677 11.6857i 0.371961 0.644256i
\(330\) 0.238662 0.0131379
\(331\) −16.0533 + 27.8051i −0.882367 + 1.52830i −0.0336642 + 0.999433i \(0.510718\pi\)
−0.848702 + 0.528871i \(0.822616\pi\)
\(332\) −2.36098 + 4.08934i −0.129576 + 0.224432i
\(333\) −17.6992 −0.969912
\(334\) −4.50543 + 7.80364i −0.246526 + 0.426996i
\(335\) 8.44924 + 14.6345i 0.461631 + 0.799569i
\(336\) −0.129214 0.223805i −0.00704919 0.0122096i
\(337\) 7.52316 0.409813 0.204906 0.978782i \(-0.434311\pi\)
0.204906 + 0.978782i \(0.434311\pi\)
\(338\) −13.6204 + 7.63616i −0.740852 + 0.415352i
\(339\) −0.710529 −0.0385906
\(340\) 0.0962157 + 0.166651i 0.00521803 + 0.00903789i
\(341\) 0.701103 + 1.21435i 0.0379668 + 0.0657605i
\(342\) −6.34458 + 10.9891i −0.343075 + 0.594224i
\(343\) −18.6526 −1.00715
\(344\) −14.6973 + 25.4565i −0.792426 + 1.37252i
\(345\) −0.282173 + 0.488738i −0.0151917 + 0.0263128i
\(346\) −21.4091 −1.15096
\(347\) 8.54638 14.8028i 0.458794 0.794654i −0.540104 0.841598i \(-0.681615\pi\)
0.998897 + 0.0469445i \(0.0149484\pi\)
\(348\) 0.170865 + 0.295947i 0.00915933 + 0.0158644i
\(349\) 7.81794 + 13.5411i 0.418485 + 0.724837i 0.995787 0.0916935i \(-0.0292280\pi\)
−0.577303 + 0.816530i \(0.695895\pi\)
\(350\) −0.952465 −0.0509114
\(351\) −0.919674 0.931356i −0.0490885 0.0497121i
\(352\) −4.27713 −0.227972
\(353\) −8.10588 14.0398i −0.431433 0.747263i 0.565564 0.824704i \(-0.308658\pi\)
−0.996997 + 0.0774410i \(0.975325\pi\)
\(354\) 0.446483 + 0.773331i 0.0237303 + 0.0411021i
\(355\) −0.566536 + 0.981269i −0.0300686 + 0.0520804i
\(356\) −8.31908 −0.440910
\(357\) 0.00740355 0.0128233i 0.000391838 0.000678683i
\(358\) 3.66868 6.35434i 0.193896 0.335837i
\(359\) 4.49983 0.237492 0.118746 0.992925i \(-0.462113\pi\)
0.118746 + 0.992925i \(0.462113\pi\)
\(360\) 10.7709 18.6558i 0.567678 0.983248i
\(361\) 3.28472 + 5.68930i 0.172880 + 0.299437i
\(362\) 7.72327 + 13.3771i 0.405926 + 0.703085i
\(363\) 0.546916 0.0287057
\(364\) 0.882316 3.21163i 0.0462459 0.168335i
\(365\) −4.37626 −0.229064
\(366\) 0.219938 + 0.380944i 0.0114963 + 0.0199122i
\(367\) 0.113121 + 0.195931i 0.00590486 + 0.0102275i 0.868963 0.494878i \(-0.164787\pi\)
−0.863058 + 0.505105i \(0.831454\pi\)
\(368\) −5.12766 + 8.88136i −0.267298 + 0.462973i
\(369\) −7.22817 −0.376284
\(370\) 8.30340 14.3819i 0.431673 0.747680i
\(371\) 8.82074 15.2780i 0.457950 0.793192i
\(372\) −0.0337359 −0.00174912
\(373\) 2.03649 3.52731i 0.105446 0.182637i −0.808475 0.588531i \(-0.799706\pi\)
0.913920 + 0.405894i \(0.133040\pi\)
\(374\) 0.124247 + 0.215203i 0.00642469 + 0.0111279i
\(375\) −0.320363 0.554884i −0.0165434 0.0286541i
\(376\) −25.0025 −1.28940
\(377\) 9.67524 35.2179i 0.498300 1.81381i
\(378\) −0.722843 −0.0371790
\(379\) 6.93346 + 12.0091i 0.356148 + 0.616867i 0.987314 0.158781i \(-0.0507565\pi\)
−0.631166 + 0.775648i \(0.717423\pi\)
\(380\) 2.29923 + 3.98238i 0.117948 + 0.204292i
\(381\) −0.505639 + 0.875792i −0.0259047 + 0.0448682i
\(382\) 21.8609 1.11850
\(383\) 10.6710 18.4827i 0.545264 0.944424i −0.453327 0.891344i \(-0.649763\pi\)
0.998590 0.0530798i \(-0.0169038\pi\)
\(384\) −0.135799 + 0.235211i −0.00692996 + 0.0120030i
\(385\) 5.44061 0.277279
\(386\) 5.35985 9.28353i 0.272809 0.472519i
\(387\) 14.3370 + 24.8325i 0.728793 + 1.26231i
\(388\) −2.50561 4.33984i −0.127203 0.220322i
\(389\) −10.6405 −0.539493 −0.269747 0.962931i \(-0.586940\pi\)
−0.269747 + 0.962931i \(0.586940\pi\)
\(390\) 0.593761 0.155088i 0.0300663 0.00785319i
\(391\) −0.587598 −0.0297161
\(392\) 6.53022 + 11.3107i 0.329826 + 0.571275i
\(393\) 0.202824 + 0.351301i 0.0102311 + 0.0177208i
\(394\) 0.517074 0.895599i 0.0260498 0.0451196i
\(395\) −34.1312 −1.71733
\(396\) −1.17062 + 2.02757i −0.0588256 + 0.101889i
\(397\) 5.51157 9.54632i 0.276618 0.479116i −0.693924 0.720048i \(-0.744120\pi\)
0.970542 + 0.240932i \(0.0774531\pi\)
\(398\) −22.7855 −1.14213
\(399\) 0.176920 0.306434i 0.00885707 0.0153409i
\(400\) 0.615869 + 1.06672i 0.0307934 + 0.0533358i
\(401\) 1.05787 + 1.83229i 0.0528277 + 0.0915003i 0.891230 0.453552i \(-0.149843\pi\)
−0.838402 + 0.545052i \(0.816510\pi\)
\(402\) −0.525013 −0.0261852
\(403\) 2.53337 + 2.56555i 0.126196 + 0.127799i
\(404\) −0.490491 −0.0244029
\(405\) −10.4940 18.1762i −0.521454 0.903184i
\(406\) −10.0849 17.4675i −0.500503 0.866897i
\(407\) −4.14139 + 7.17309i −0.205281 + 0.355557i
\(408\) −0.0274364 −0.00135830
\(409\) 3.28266 5.68573i 0.162317 0.281141i −0.773382 0.633940i \(-0.781437\pi\)
0.935699 + 0.352799i \(0.114770\pi\)
\(410\) 3.39102 5.87341i 0.167470 0.290067i
\(411\) 0.275237 0.0135764
\(412\) 3.55569 6.15863i 0.175176 0.303414i
\(413\) 10.1782 + 17.6291i 0.500835 + 0.867472i
\(414\) 7.16685 + 12.4134i 0.352232 + 0.610083i
\(415\) −19.8338 −0.973601
\(416\) −10.6410 + 2.77938i −0.521717 + 0.136271i
\(417\) 0.525522 0.0257349
\(418\) 2.96909 + 5.14262i 0.145223 + 0.251534i
\(419\) 8.23564 + 14.2645i 0.402337 + 0.696868i 0.994008 0.109312i \(-0.0348646\pi\)
−0.591670 + 0.806180i \(0.701531\pi\)
\(420\) −0.0654483 + 0.113360i −0.00319355 + 0.00553139i
\(421\) 1.14696 0.0558992 0.0279496 0.999609i \(-0.491102\pi\)
0.0279496 + 0.999609i \(0.491102\pi\)
\(422\) −2.46239 + 4.26499i −0.119867 + 0.207617i
\(423\) −12.1948 + 21.1220i −0.592931 + 1.02699i
\(424\) −32.6883 −1.58748
\(425\) −0.0352874 + 0.0611196i −0.00171169 + 0.00296473i
\(426\) −0.0176015 0.0304867i −0.000852795 0.00147708i
\(427\) 5.01378 + 8.68412i 0.242634 + 0.420254i
\(428\) 1.40179 0.0677582
\(429\) −0.296143 + 0.0773514i −0.0142979 + 0.00373456i
\(430\) −26.9043 −1.29744
\(431\) −6.45553 11.1813i −0.310952 0.538584i 0.667617 0.744505i \(-0.267314\pi\)
−0.978569 + 0.205921i \(0.933981\pi\)
\(432\) 0.467394 + 0.809550i 0.0224875 + 0.0389495i
\(433\) 18.5338 32.1016i 0.890680 1.54270i 0.0516178 0.998667i \(-0.483562\pi\)
0.839062 0.544036i \(-0.183104\pi\)
\(434\) 1.99117 0.0955793
\(435\) −0.717688 + 1.24307i −0.0344105 + 0.0596007i
\(436\) 4.49763 7.79013i 0.215398 0.373079i
\(437\) −14.0416 −0.671701
\(438\) 0.0679821 0.117748i 0.00324831 0.00562624i
\(439\) −1.16890 2.02459i −0.0557884 0.0966283i 0.836782 0.547535i \(-0.184434\pi\)
−0.892571 + 0.450907i \(0.851101\pi\)
\(440\) −5.04051 8.73042i −0.240297 0.416207i
\(441\) 12.7403 0.606681
\(442\) 0.448957 + 0.454660i 0.0213547 + 0.0216260i
\(443\) −33.6602 −1.59924 −0.799621 0.600505i \(-0.794966\pi\)
−0.799621 + 0.600505i \(0.794966\pi\)
\(444\) −0.0996383 0.172579i −0.00472862 0.00819021i
\(445\) −17.4714 30.2613i −0.828223 1.43452i
\(446\) −5.27865 + 9.14288i −0.249951 + 0.432928i
\(447\) −0.727092 −0.0343903
\(448\) −7.30546 + 12.6534i −0.345151 + 0.597819i
\(449\) 12.8288 22.2202i 0.605431 1.04864i −0.386552 0.922267i \(-0.626334\pi\)
0.991983 0.126369i \(-0.0403325\pi\)
\(450\) 1.72158 0.0811562
\(451\) −1.69130 + 2.92941i −0.0796401 + 0.137941i
\(452\) 3.26997 + 5.66376i 0.153807 + 0.266401i
\(453\) −0.411842 0.713331i −0.0193500 0.0335152i
\(454\) 6.86565 0.322221
\(455\) 13.5356 3.53544i 0.634558 0.165744i
\(456\) −0.655637 −0.0307030
\(457\) 6.82392 + 11.8194i 0.319210 + 0.552887i 0.980323 0.197398i \(-0.0632493\pi\)
−0.661114 + 0.750286i \(0.729916\pi\)
\(458\) 11.2208 + 19.4350i 0.524315 + 0.908140i
\(459\) −0.0267802 + 0.0463847i −0.00124999 + 0.00216505i
\(460\) 5.19443 0.242192
\(461\) 6.16708 10.6817i 0.287229 0.497496i −0.685918 0.727679i \(-0.740599\pi\)
0.973147 + 0.230183i \(0.0739324\pi\)
\(462\) −0.0845162 + 0.146386i −0.00393205 + 0.00681051i
\(463\) 17.2096 0.799796 0.399898 0.916560i \(-0.369046\pi\)
0.399898 + 0.916560i \(0.369046\pi\)
\(464\) −13.0419 + 22.5892i −0.605453 + 1.04868i
\(465\) −0.0708507 0.122717i −0.00328562 0.00569087i
\(466\) 13.5963 + 23.5495i 0.629838 + 1.09091i
\(467\) −35.7440 −1.65404 −0.827018 0.562175i \(-0.809965\pi\)
−0.827018 + 0.562175i \(0.809965\pi\)
\(468\) −1.59479 + 5.80503i −0.0737191 + 0.268338i
\(469\) −11.9684 −0.552648
\(470\) −11.4421 19.8183i −0.527785 0.914150i
\(471\) −0.257688 0.446328i −0.0118736 0.0205657i
\(472\) 18.8594 32.6654i 0.868072 1.50355i
\(473\) 13.4187 0.616993
\(474\) 0.530205 0.918341i 0.0243531 0.0421808i
\(475\) −0.843249 + 1.46055i −0.0386909 + 0.0670146i
\(476\) −0.136290 −0.00624683
\(477\) −15.9435 + 27.6149i −0.730003 + 1.26440i
\(478\) 10.0696 + 17.4411i 0.460574 + 0.797737i
\(479\) −16.1387 27.9531i −0.737396 1.27721i −0.953664 0.300874i \(-0.902722\pi\)
0.216268 0.976334i \(-0.430612\pi\)
\(480\) 0.432231 0.0197285
\(481\) −5.64202 + 20.5370i −0.257254 + 0.936404i
\(482\) 0.872005 0.0397187
\(483\) −0.199849 0.346149i −0.00909345 0.0157503i
\(484\) −2.51700 4.35958i −0.114409 0.198163i
\(485\) 10.5243 18.2287i 0.477886 0.827723i
\(486\) 1.96021 0.0889169
\(487\) −11.2876 + 19.5507i −0.511490 + 0.885927i 0.488421 + 0.872608i \(0.337573\pi\)
−0.999911 + 0.0133191i \(0.995760\pi\)
\(488\) 9.29013 16.0910i 0.420545 0.728405i
\(489\) 0.361128 0.0163308
\(490\) −5.97697 + 10.3524i −0.270012 + 0.467674i
\(491\) −2.40307 4.16223i −0.108449 0.187839i 0.806693 0.590971i \(-0.201255\pi\)
−0.915142 + 0.403132i \(0.867922\pi\)
\(492\) −0.0406912 0.0704792i −0.00183450 0.00317745i
\(493\) −1.49452 −0.0673096
\(494\) 10.7285 + 10.8648i 0.482700 + 0.488832i
\(495\) −9.83392 −0.442002
\(496\) −1.28750 2.23002i −0.0578105 0.100131i
\(497\) −0.401250 0.694985i −0.0179985 0.0311743i
\(498\) 0.308104 0.533651i 0.0138065 0.0239135i
\(499\) −27.3606 −1.22483 −0.612413 0.790538i \(-0.709801\pi\)
−0.612413 + 0.790538i \(0.709801\pi\)
\(500\) −2.94873 + 5.10734i −0.131871 + 0.228407i
\(501\) −0.227085 + 0.393323i −0.0101454 + 0.0175724i
\(502\) −0.537556 −0.0239923
\(503\) −19.8910 + 34.4523i −0.886897 + 1.53615i −0.0433731 + 0.999059i \(0.513810\pi\)
−0.843524 + 0.537092i \(0.819523\pi\)
\(504\) 7.62852 + 13.2130i 0.339801 + 0.588553i
\(505\) −1.03011 1.78420i −0.0458393 0.0793960i
\(506\) 6.70779 0.298198
\(507\) −0.686503 + 0.384882i −0.0304887 + 0.0170932i
\(508\) 9.30814 0.412982
\(509\) 4.16230 + 7.20932i 0.184491 + 0.319548i 0.943405 0.331643i \(-0.107603\pi\)
−0.758914 + 0.651191i \(0.774270\pi\)
\(510\) −0.0125560 0.0217476i −0.000555988 0.000962999i
\(511\) 1.54974 2.68423i 0.0685566 0.118744i
\(512\) 23.6734 1.04623
\(513\) −0.639957 + 1.10844i −0.0282548 + 0.0489387i
\(514\) −7.61530 + 13.1901i −0.335897 + 0.581790i
\(515\) 29.8701 1.31623
\(516\) −0.161421 + 0.279590i −0.00710618 + 0.0123083i
\(517\) 5.70684 + 9.88454i 0.250987 + 0.434722i
\(518\) 5.88089 + 10.1860i 0.258391 + 0.447547i
\(519\) −1.07907 −0.0473661
\(520\) −18.2134 18.4448i −0.798711 0.808857i
\(521\) −17.5630 −0.769451 −0.384725 0.923031i \(-0.625704\pi\)
−0.384725 + 0.923031i \(0.625704\pi\)
\(522\) 18.2284 + 31.5725i 0.797836 + 1.38189i
\(523\) −3.69591 6.40151i −0.161611 0.279918i 0.773836 0.633386i \(-0.218336\pi\)
−0.935447 + 0.353468i \(0.885002\pi\)
\(524\) 1.86686 3.23350i 0.0815542 0.141256i
\(525\) −0.0480067 −0.00209518
\(526\) −5.22443 + 9.04898i −0.227796 + 0.394554i
\(527\) 0.0737699 0.127773i 0.00321347 0.00556589i
\(528\) 0.218594 0.00951310
\(529\) 3.56929 6.18218i 0.155186 0.268791i
\(530\) −14.9594 25.9105i −0.649796 1.12548i
\(531\) −18.3971 31.8647i −0.798365 1.38281i
\(532\) −3.25686 −0.141203
\(533\) −2.30414 + 8.38707i −0.0998033 + 0.363284i
\(534\) 1.08562 0.0469795
\(535\) 2.94399 + 5.09914i 0.127280 + 0.220455i
\(536\) 11.0882 + 19.2054i 0.478938 + 0.829545i
\(537\) 0.184911 0.320275i 0.00797949 0.0138209i
\(538\) 29.1561 1.25701
\(539\) 2.98106 5.16335i 0.128403 0.222401i
\(540\) 0.236740 0.410046i 0.0101877 0.0176456i
\(541\) 44.9745 1.93360 0.966802 0.255525i \(-0.0822483\pi\)
0.966802 + 0.255525i \(0.0822483\pi\)
\(542\) 10.5184 18.2183i 0.451802 0.782545i
\(543\) 0.389273 + 0.674240i 0.0167053 + 0.0289344i
\(544\) 0.225020 + 0.389745i 0.00964764 + 0.0167102i
\(545\) 37.7830 1.61845
\(546\) −0.115141 + 0.419112i −0.00492756 + 0.0179363i
\(547\) 37.0545 1.58434 0.792169 0.610302i \(-0.208952\pi\)
0.792169 + 0.610302i \(0.208952\pi\)
\(548\) −1.26669 2.19397i −0.0541102 0.0937216i
\(549\) −9.06241 15.6966i −0.386774 0.669913i
\(550\) 0.402827 0.697718i 0.0171766 0.0297508i
\(551\) −35.7139 −1.52146
\(552\) −0.370305 + 0.641387i −0.0157612 + 0.0272992i
\(553\) 12.0867 20.9348i 0.513980 0.890239i
\(554\) 19.4631 0.826908
\(555\) 0.418512 0.724885i 0.0177649 0.0307697i
\(556\) −2.41854 4.18904i −0.102569 0.177655i
\(557\) 18.0039 + 31.1836i 0.762848 + 1.32129i 0.941377 + 0.337357i \(0.109533\pi\)
−0.178529 + 0.983935i \(0.557134\pi\)
\(558\) −3.59905 −0.152360
\(559\) 33.3841 8.71980i 1.41200 0.368808i
\(560\) −9.99112 −0.422202
\(561\) 0.00626239 + 0.0108468i 0.000264398 + 0.000457951i
\(562\) −18.2970 31.6913i −0.771811 1.33682i
\(563\) 1.67200 2.89599i 0.0704664 0.122051i −0.828639 0.559783i \(-0.810885\pi\)
0.899106 + 0.437731i \(0.144218\pi\)
\(564\) −0.274604 −0.0115629
\(565\) −13.7349 + 23.7896i −0.577833 + 1.00084i
\(566\) 8.89637 15.4090i 0.373942 0.647687i
\(567\) 14.8648 0.624264
\(568\) −0.743484 + 1.28775i −0.0311959 + 0.0540329i
\(569\) 3.02286 + 5.23575i 0.126725 + 0.219494i 0.922406 0.386222i \(-0.126220\pi\)
−0.795681 + 0.605716i \(0.792887\pi\)
\(570\) −0.300045 0.519693i −0.0125675 0.0217676i
\(571\) 5.81265 0.243252 0.121626 0.992576i \(-0.461189\pi\)
0.121626 + 0.992576i \(0.461189\pi\)
\(572\) 1.97949 + 2.00463i 0.0827664 + 0.0838178i
\(573\) 1.10185 0.0460303
\(574\) 2.40169 + 4.15985i 0.100245 + 0.173629i
\(575\) 0.952537 + 1.64984i 0.0397235 + 0.0688032i
\(576\) 13.2046 22.8711i 0.550193 0.952963i
\(577\) −40.5214 −1.68693 −0.843464 0.537185i \(-0.819488\pi\)
−0.843464 + 0.537185i \(0.819488\pi\)
\(578\) −10.1967 + 17.6612i −0.424127 + 0.734609i
\(579\) 0.270150 0.467913i 0.0112270 0.0194458i
\(580\) 13.2117 0.548586
\(581\) 7.02363 12.1653i 0.291389 0.504701i
\(582\) 0.326977 + 0.566340i 0.0135536 + 0.0234756i
\(583\) 7.46113 + 12.9231i 0.309009 + 0.535219i
\(584\) −5.74310 −0.237651
\(585\) −24.4656 + 6.39032i −1.01153 + 0.264207i
\(586\) −0.836128 −0.0345401
\(587\) 19.3034 + 33.4344i 0.796735 + 1.37999i 0.921732 + 0.387828i \(0.126775\pi\)
−0.124997 + 0.992157i \(0.539892\pi\)
\(588\) 0.0717218 + 0.124226i 0.00295776 + 0.00512298i
\(589\) 1.76285 3.05335i 0.0726370 0.125811i
\(590\) 34.5231 1.42129
\(591\) 0.0260619 0.0451405i 0.00107204 0.00185683i
\(592\) 7.60522 13.1726i 0.312573 0.541392i
\(593\) −30.5973 −1.25648 −0.628241 0.778019i \(-0.716225\pi\)
−0.628241 + 0.778019i \(0.716225\pi\)
\(594\) 0.305713 0.529511i 0.0125436 0.0217261i
\(595\) −0.286230 0.495765i −0.0117343 0.0203244i
\(596\) 3.34620 + 5.79579i 0.137066 + 0.237405i
\(597\) −1.14845 −0.0470028
\(598\) 16.6882 4.35889i 0.682430 0.178248i
\(599\) 48.8894 1.99757 0.998783 0.0493114i \(-0.0157027\pi\)
0.998783 + 0.0493114i \(0.0157027\pi\)
\(600\) 0.0444763 + 0.0770352i 0.00181574 + 0.00314495i
\(601\) −8.53983 14.7914i −0.348347 0.603355i 0.637609 0.770360i \(-0.279924\pi\)
−0.985956 + 0.167005i \(0.946590\pi\)
\(602\) 9.52748 16.5021i 0.388311 0.672574i
\(603\) 21.6328 0.880957
\(604\) −3.79073 + 6.56574i −0.154243 + 0.267156i
\(605\) 10.5722 18.3116i 0.429822 0.744473i
\(606\) 0.0640082 0.00260016
\(607\) −6.85414 + 11.8717i −0.278201 + 0.481858i −0.970938 0.239332i \(-0.923071\pi\)
0.692737 + 0.721191i \(0.256405\pi\)
\(608\) 5.37721 + 9.31359i 0.218074 + 0.377716i
\(609\) −0.508303 0.880407i −0.0205975 0.0356759i
\(610\) 17.0061 0.688557
\(611\) 20.6211 + 20.8831i 0.834242 + 0.844839i
\(612\) 0.246344 0.00995786
\(613\) 0.315136 + 0.545831i 0.0127282 + 0.0220459i 0.872319 0.488937i \(-0.162615\pi\)
−0.859591 + 0.510982i \(0.829282\pi\)
\(614\) 15.9753 + 27.6700i 0.644710 + 1.11667i
\(615\) 0.170916 0.296035i 0.00689199 0.0119373i
\(616\) 7.13989 0.287674
\(617\) 7.47004 12.9385i 0.300732 0.520884i −0.675570 0.737296i \(-0.736102\pi\)
0.976302 + 0.216412i \(0.0694355\pi\)
\(618\) −0.464011 + 0.803690i −0.0186652 + 0.0323292i
\(619\) −3.49612 −0.140521 −0.0702604 0.997529i \(-0.522383\pi\)
−0.0702604 + 0.997529i \(0.522383\pi\)
\(620\) −0.652134 + 1.12953i −0.0261903 + 0.0453630i
\(621\) 0.722897 + 1.25209i 0.0290089 + 0.0502448i
\(622\) −2.28209 3.95270i −0.0915036 0.158489i
\(623\) 24.7482 0.991517
\(624\) 0.543836 0.142048i 0.0217709 0.00568646i
\(625\) −27.1629 −1.08652
\(626\) −4.17469 7.23077i −0.166854 0.289000i
\(627\) 0.149650 + 0.259201i 0.00597644 + 0.0103515i
\(628\) −2.37185 + 4.10816i −0.0946470 + 0.163933i
\(629\) 0.871512 0.0347495
\(630\) −6.98222 + 12.0936i −0.278178 + 0.481819i
\(631\) −14.8653 + 25.7474i −0.591778 + 1.02499i 0.402215 + 0.915545i \(0.368240\pi\)
−0.993993 + 0.109444i \(0.965093\pi\)
\(632\) −44.7915 −1.78171
\(633\) −0.124111 + 0.214966i −0.00493297 + 0.00854415i
\(634\) −6.05907 10.4946i −0.240636 0.416794i
\(635\) 19.5486 + 33.8591i 0.775762 + 1.34366i
\(636\) −0.359017 −0.0142360
\(637\) 4.06125 14.7829i 0.160912 0.585721i
\(638\) 17.0608 0.675445
\(639\) 0.725259 + 1.25619i 0.0286908 + 0.0496939i
\(640\) 5.25015 + 9.09352i 0.207530 + 0.359453i
\(641\) 8.02885 13.9064i 0.317121 0.549269i −0.662765 0.748827i \(-0.730617\pi\)
0.979886 + 0.199558i \(0.0639507\pi\)
\(642\) −0.182931 −0.00721972
\(643\) 4.66074 8.07264i 0.183802 0.318354i −0.759370 0.650659i \(-0.774493\pi\)
0.943172 + 0.332305i \(0.107826\pi\)
\(644\) −1.83948 + 3.18607i −0.0724857 + 0.125549i
\(645\) −1.35604 −0.0533941
\(646\) 0.312408 0.541106i 0.0122915 0.0212895i
\(647\) −6.81851 11.8100i −0.268063 0.464299i 0.700298 0.713850i \(-0.253050\pi\)
−0.968362 + 0.249551i \(0.919717\pi\)
\(648\) −13.7717 23.8533i −0.541003 0.937044i
\(649\) −17.2187 −0.675892
\(650\) 0.548792 1.99760i 0.0215254 0.0783525i
\(651\) 0.100360 0.00393342
\(652\) −1.66197 2.87862i −0.0650878 0.112735i
\(653\) 4.56646 + 7.90935i 0.178700 + 0.309517i 0.941435 0.337193i \(-0.109478\pi\)
−0.762736 + 0.646710i \(0.776144\pi\)
\(654\) −0.586933 + 1.01660i −0.0229509 + 0.0397521i
\(655\) 15.6828 0.612779
\(656\) 3.10589 5.37956i 0.121265 0.210037i
\(657\) −2.80116 + 4.85176i −0.109284 + 0.189285i
\(658\) 16.2078 0.631844
\(659\) 10.5798 18.3248i 0.412132 0.713833i −0.582991 0.812479i \(-0.698118\pi\)
0.995123 + 0.0986455i \(0.0314510\pi\)
\(660\) −0.0553603 0.0958868i −0.00215490 0.00373239i
\(661\) 3.75419 + 6.50245i 0.146021 + 0.252916i 0.929753 0.368183i \(-0.120020\pi\)
−0.783732 + 0.621099i \(0.786687\pi\)
\(662\) −38.5647 −1.49886
\(663\) 0.0226286 + 0.0229160i 0.000878821 + 0.000889984i
\(664\) −26.0285 −1.01010
\(665\) −6.83993 11.8471i −0.265241 0.459411i
\(666\) −10.6297 18.4112i −0.411893 0.713420i
\(667\) −20.1712 + 34.9376i −0.781034 + 1.35279i
\(668\) 4.18034 0.161742
\(669\) −0.266057 + 0.460825i −0.0102864 + 0.0178165i
\(670\) −10.1488 + 17.5782i −0.392082 + 0.679107i
\(671\) −8.48194 −0.327441
\(672\) −0.153064 + 0.265114i −0.00590456 + 0.0102270i
\(673\) 22.6402 + 39.2140i 0.872716 + 1.51159i 0.859176 + 0.511680i \(0.170977\pi\)
0.0135397 + 0.999908i \(0.495690\pi\)
\(674\) 4.51822 + 7.82579i 0.174035 + 0.301438i
\(675\) 0.173650 0.00668381
\(676\) 6.22737 + 3.70096i 0.239514 + 0.142345i
\(677\) 41.1887 1.58301 0.791505 0.611163i \(-0.209298\pi\)
0.791505 + 0.611163i \(0.209298\pi\)
\(678\) −0.426725 0.739110i −0.0163883 0.0283854i
\(679\) 7.45387 + 12.9105i 0.286053 + 0.495459i
\(680\) −0.530362 + 0.918614i −0.0203384 + 0.0352272i
\(681\) 0.346046 0.0132605
\(682\) −0.842129 + 1.45861i −0.0322468 + 0.0558531i
\(683\) 11.0992 19.2244i 0.424699 0.735600i −0.571693 0.820467i \(-0.693713\pi\)
0.996392 + 0.0848671i \(0.0270466\pi\)
\(684\) 5.88678 0.225087
\(685\) 5.32049 9.21536i 0.203285 0.352101i
\(686\) −11.2023 19.4029i −0.427705 0.740807i
\(687\) 0.565558 + 0.979576i 0.0215774 + 0.0373731i
\(688\) −24.6421 −0.939470
\(689\) 26.9601 + 27.3026i 1.02710 + 1.04015i
\(690\) −0.677864 −0.0258058
\(691\) −12.2302 21.1833i −0.465259 0.805852i 0.533954 0.845513i \(-0.320705\pi\)
−0.999213 + 0.0396613i \(0.987372\pi\)
\(692\) 4.96608 + 8.60151i 0.188782 + 0.326980i
\(693\) 3.48244 6.03176i 0.132287 0.229128i
\(694\) 20.5310 0.779344
\(695\) 10.1586 17.5953i 0.385339 0.667427i
\(696\) −0.941845 + 1.63132i −0.0357006 + 0.0618352i
\(697\) 0.355916 0.0134813
\(698\) −9.39051 + 16.2648i −0.355436 + 0.615634i
\(699\) 0.685290 + 1.18696i 0.0259200 + 0.0448948i
\(700\) 0.220935 + 0.382671i 0.00835056 + 0.0144636i
\(701\) −35.3072 −1.33354 −0.666768 0.745265i \(-0.732323\pi\)
−0.666768 + 0.745265i \(0.732323\pi\)
\(702\) 0.416488 1.51602i 0.0157193 0.0572184i
\(703\) 20.8262 0.785474
\(704\) −6.17942 10.7031i −0.232896 0.403387i
\(705\) −0.576711 0.998893i −0.0217202 0.0376205i
\(706\) 9.73638 16.8639i 0.366433 0.634681i
\(707\) 1.45915 0.0548771
\(708\) 0.207133 0.358766i 0.00778455 0.0134832i
\(709\) 2.75771 4.77649i 0.103568 0.179385i −0.809584 0.587004i \(-0.800307\pi\)
0.913152 + 0.407619i \(0.133641\pi\)
\(710\) −1.36099 −0.0510770
\(711\) −21.8468 + 37.8397i −0.819318 + 1.41910i
\(712\) −22.9283 39.7129i −0.859273 1.48830i
\(713\) −1.99132 3.44907i −0.0745755 0.129169i
\(714\) 0.0177855 0.000665607
\(715\) −3.13478 + 11.4106i −0.117234 + 0.426732i
\(716\) −3.40396 −0.127212
\(717\) 0.507534 + 0.879075i 0.0189542 + 0.0328297i
\(718\) 2.70249 + 4.68084i 0.100856 + 0.174688i
\(719\) 21.4617 37.1728i 0.800386 1.38631i −0.118976 0.992897i \(-0.537961\pi\)
0.919362 0.393413i \(-0.128706\pi\)
\(720\) 18.0590 0.673018
\(721\) −10.5777 + 18.3212i −0.393936 + 0.682317i
\(722\) −3.94544 + 6.83370i −0.146834 + 0.254324i
\(723\) 0.0439513 0.00163456
\(724\) 3.58300 6.20594i 0.133161 0.230642i
\(725\) 2.42271 + 4.19626i 0.0899773 + 0.155845i
\(726\) 0.328464 + 0.568917i 0.0121904 + 0.0211145i
\(727\) −33.4500 −1.24059 −0.620296 0.784368i \(-0.712987\pi\)
−0.620296 + 0.784368i \(0.712987\pi\)
\(728\) 17.7632 4.63967i 0.658347 0.171958i
\(729\) −26.8023 −0.992677
\(730\) −2.62827 4.55230i −0.0972766 0.168488i
\(731\) −0.705957 1.22275i −0.0261108 0.0452252i
\(732\) 0.102034 0.176728i 0.00377129 0.00653206i
\(733\) 7.98154 0.294805 0.147402 0.989077i \(-0.452909\pi\)
0.147402 + 0.989077i \(0.452909\pi\)
\(734\) −0.135875 + 0.235343i −0.00501524 + 0.00868665i
\(735\) −0.301254 + 0.521788i −0.0111119 + 0.0192464i
\(736\) 12.1482 0.447789
\(737\) 5.06180 8.76729i 0.186454 0.322947i
\(738\) −4.34106 7.51893i −0.159797 0.276776i
\(739\) 7.90558 + 13.6929i 0.290812 + 0.503700i 0.974002 0.226540i \(-0.0727414\pi\)
−0.683190 + 0.730240i \(0.739408\pi\)
\(740\) −7.70427 −0.283214
\(741\) 0.540746 + 0.547615i 0.0198648 + 0.0201171i
\(742\) 21.1900 0.777911
\(743\) −15.5203 26.8819i −0.569383 0.986200i −0.996627 0.0820637i \(-0.973849\pi\)
0.427244 0.904136i \(-0.359484\pi\)
\(744\) −0.0929797 0.161046i −0.00340880 0.00590422i
\(745\) −14.0551 + 24.3442i −0.514940 + 0.891902i
\(746\) 4.89227 0.179119
\(747\) −12.6952 + 21.9888i −0.464494 + 0.804528i
\(748\) 0.0576412 0.0998375i 0.00210757 0.00365042i
\(749\) −4.17016 −0.152374
\(750\) 0.384803 0.666499i 0.0140510 0.0243371i
\(751\) −11.7388 20.3322i −0.428355 0.741933i 0.568372 0.822772i \(-0.307573\pi\)
−0.996727 + 0.0808388i \(0.974240\pi\)
\(752\) −10.4800 18.1519i −0.382167 0.661933i
\(753\) −0.0270942 −0.000987367
\(754\) 42.4453 11.0865i 1.54577 0.403748i
\(755\) −31.8446 −1.15894
\(756\) 0.167672 + 0.290416i 0.00609816 + 0.0105623i
\(757\) 15.9702 + 27.6611i 0.580446 + 1.00536i 0.995426 + 0.0955312i \(0.0304550\pi\)
−0.414981 + 0.909830i \(0.636212\pi\)
\(758\) −8.32813 + 14.4247i −0.302491 + 0.523930i
\(759\) 0.338090 0.0122719
\(760\) −12.6738 + 21.9518i −0.459729 + 0.796274i
\(761\) −13.3828 + 23.1797i −0.485126 + 0.840263i −0.999854 0.0170906i \(-0.994560\pi\)
0.514728 + 0.857354i \(0.327893\pi\)
\(762\) −1.21470 −0.0440038
\(763\) −13.3799 + 23.1747i −0.484385 + 0.838980i
\(764\) −5.07089 8.78304i −0.183458 0.317759i
\(765\) 0.517361 + 0.896096i 0.0187052 + 0.0323984i
\(766\) 25.6350 0.926229
\(767\) −42.8380 + 11.1891i −1.54679 + 0.404015i
\(768\) 0.740970 0.0267375
\(769\) −3.65769 6.33530i −0.131900 0.228457i 0.792509 0.609860i \(-0.208774\pi\)
−0.924409 + 0.381403i \(0.875441\pi\)
\(770\) 3.26749 + 5.65947i 0.117752 + 0.203953i
\(771\) −0.383831 + 0.664814i −0.0138233 + 0.0239427i
\(772\) −4.97311 −0.178986
\(773\) 8.76052 15.1737i 0.315094 0.545759i −0.664364 0.747410i \(-0.731297\pi\)
0.979457 + 0.201651i \(0.0646307\pi\)
\(774\) −17.2209 + 29.8275i −0.618994 + 1.07213i
\(775\) −0.478344 −0.0171826
\(776\) 13.8114 23.9221i 0.495802 0.858754i
\(777\) 0.296412 + 0.513400i 0.0106337 + 0.0184181i
\(778\) −6.39040 11.0685i −0.229107 0.396825i
\(779\) 8.50518 0.304730
\(780\) −0.200039 0.202580i −0.00716255 0.00725353i
\(781\) 0.678804 0.0242895
\(782\) −0.352896 0.611235i −0.0126195 0.0218577i
\(783\) 1.83864 + 3.18462i 0.0657077 + 0.113809i
\(784\) −5.47440 + 9.48195i −0.195514 + 0.338641i
\(785\) −19.9250 −0.711155
\(786\) −0.243622 + 0.421965i −0.00868970 + 0.0150510i
\(787\) 3.60005 6.23547i 0.128328 0.222270i −0.794701 0.607001i \(-0.792372\pi\)
0.923029 + 0.384731i \(0.125706\pi\)
\(788\) −0.479765 −0.0170909
\(789\) −0.263325 + 0.456092i −0.00937461 + 0.0162373i
\(790\) −20.4983 35.5042i −0.729298 1.26318i
\(791\) −9.72778 16.8490i −0.345880 0.599082i
\(792\) −12.9054 −0.458572
\(793\) −21.1020 + 5.51177i −0.749355 + 0.195729i
\(794\) 13.2404 0.469885
\(795\) −0.753993 1.30595i −0.0267414 0.0463174i
\(796\) 5.28535 + 9.15449i 0.187334 + 0.324472i
\(797\) −3.01534 + 5.22272i −0.106809 + 0.184998i −0.914476 0.404641i \(-0.867397\pi\)
0.807667 + 0.589639i \(0.200730\pi\)
\(798\) 0.425014 0.0150453
\(799\) 0.600473 1.04005i 0.0212432 0.0367943i
\(800\) 0.729545 1.26361i 0.0257933 0.0446753i
\(801\) −44.7325 −1.58054
\(802\) −1.27066 + 2.20086i −0.0448687 + 0.0777149i
\(803\) 1.31087 + 2.27049i 0.0462596 + 0.0801240i
\(804\) 0.121783 + 0.210934i 0.00429494 + 0.00743905i
\(805\) −15.4528 −0.544640
\(806\) −1.14727 + 4.17608i −0.0404110 + 0.147096i
\(807\) 1.46954 0.0517303
\(808\) −1.35185 2.34147i −0.0475578 0.0823726i
\(809\) −23.8352 41.2837i −0.838000 1.45146i −0.891564 0.452895i \(-0.850391\pi\)
0.0535636 0.998564i \(-0.482942\pi\)
\(810\) 12.6049 21.8324i 0.442892 0.767111i
\(811\) −53.9710 −1.89518 −0.947589 0.319493i \(-0.896487\pi\)
−0.947589 + 0.319493i \(0.896487\pi\)
\(812\) −4.67860 + 8.10356i −0.164187 + 0.284379i
\(813\) 0.530152 0.918251i 0.0185933 0.0322045i
\(814\) −9.94885 −0.348707
\(815\) 6.98081 12.0911i 0.244527 0.423534i
\(816\) −0.0115002 0.0199190i −0.000402588 0.000697304i
\(817\) −16.8700 29.2197i −0.590206 1.02227i
\(818\) 7.88593 0.275725
\(819\) 4.74430 17.2693i 0.165779 0.603437i
\(820\) −3.14634 −0.109875
\(821\) 13.8494 + 23.9879i 0.483348 + 0.837184i 0.999817 0.0191223i \(-0.00608720\pi\)
−0.516469 + 0.856306i \(0.672754\pi\)
\(822\) 0.165300 + 0.286308i 0.00576551 + 0.00998615i
\(823\) −9.94603 + 17.2270i −0.346697 + 0.600496i −0.985661 0.168740i \(-0.946030\pi\)
0.638964 + 0.769237i \(0.279363\pi\)
\(824\) 39.1994 1.36558
\(825\) 0.0203035 0.0351667i 0.000706878 0.00122435i
\(826\) −12.2255 + 21.1752i −0.425380 + 0.736780i
\(827\) 18.0723 0.628436 0.314218 0.949351i \(-0.398258\pi\)
0.314218 + 0.949351i \(0.398258\pi\)
\(828\) 3.32486 5.75883i 0.115547 0.200133i
\(829\) 19.4456 + 33.6807i 0.675372 + 1.16978i 0.976360 + 0.216151i \(0.0693502\pi\)
−0.300988 + 0.953628i \(0.597316\pi\)
\(830\) −11.9117 20.6316i −0.413459 0.716133i
\(831\) 0.980991 0.0340302
\(832\) −22.3288 22.6124i −0.774110 0.783944i
\(833\) −0.627333 −0.0217358
\(834\) 0.315615 + 0.546661i 0.0109289 + 0.0189293i
\(835\) 8.77938 + 15.2063i 0.303823 + 0.526237i
\(836\) 1.37743 2.38578i 0.0476394 0.0825138i
\(837\) −0.363024 −0.0125479
\(838\) −9.89223 + 17.1338i −0.341721 + 0.591879i
\(839\) 13.4474 23.2916i 0.464256 0.804115i −0.534912 0.844908i \(-0.679655\pi\)
0.999168 + 0.0407930i \(0.0129884\pi\)
\(840\) −0.721530 −0.0248951
\(841\) −36.8042 + 63.7468i −1.26911 + 2.19816i
\(842\) 0.688832 + 1.19309i 0.0237387 + 0.0411167i
\(843\) −0.922214 1.59732i −0.0317627 0.0550146i
\(844\) 2.28472 0.0786433
\(845\) −0.384065 + 30.4252i −0.0132122 + 1.04666i
\(846\) −29.2955 −1.00720
\(847\) 7.48778 + 12.9692i 0.257283 + 0.445628i
\(848\) −13.7016 23.7319i −0.470515 0.814955i
\(849\) 0.448400 0.776651i 0.0153890 0.0266546i
\(850\) −0.0847709 −0.00290762
\(851\) 11.7627 20.3735i 0.403219 0.698395i
\(852\) −0.00816573 + 0.0141435i −0.000279753 + 0.000484547i
\(853\) 49.8820 1.70793 0.853964 0.520332i \(-0.174192\pi\)
0.853964 + 0.520332i \(0.174192\pi\)
\(854\) −6.02230 + 10.4309i −0.206079 + 0.356939i
\(855\) 12.3632 + 21.4137i 0.422812 + 0.732332i
\(856\) 3.86349 + 6.69176i 0.132051 + 0.228720i
\(857\) 7.54639 0.257780 0.128890 0.991659i \(-0.458859\pi\)
0.128890 + 0.991659i \(0.458859\pi\)
\(858\) −0.258319 0.261600i −0.00881887 0.00893089i
\(859\) −18.4433 −0.629276 −0.314638 0.949212i \(-0.601883\pi\)
−0.314638 + 0.949212i \(0.601883\pi\)
\(860\) 6.24074 + 10.8093i 0.212808 + 0.368593i
\(861\) 0.121051 + 0.209667i 0.00412542 + 0.00714543i
\(862\) 7.75405 13.4304i 0.264104 0.457442i
\(863\) −30.5612 −1.04032 −0.520158 0.854070i \(-0.674127\pi\)
−0.520158 + 0.854070i \(0.674127\pi\)
\(864\) 0.553665 0.958975i 0.0188361 0.0326250i
\(865\) −20.8591 + 36.1291i −0.709232 + 1.22843i
\(866\) 44.5238 1.51298
\(867\) −0.513939 + 0.890169i −0.0174543 + 0.0302317i
\(868\) −0.461874 0.799990i −0.0156770 0.0271534i
\(869\) 10.2237 + 17.7080i 0.346816 + 0.600702i
\(870\) −1.72410 −0.0584525
\(871\) 6.89594 25.1012i 0.233660 0.850522i
\(872\) 49.5838 1.67912
\(873\) −13.4729 23.3357i −0.455988 0.789795i
\(874\) −8.43303 14.6064i −0.285251 0.494070i
\(875\) 8.77210 15.1937i 0.296551 0.513642i
\(876\) −0.0630769 −0.00213117
\(877\) 1.95916 3.39336i 0.0661560 0.114586i −0.831050 0.556197i \(-0.812260\pi\)
0.897206 + 0.441612i \(0.145593\pi\)
\(878\) 1.40402 2.43183i 0.0473834 0.0820704i
\(879\) −0.0421430 −0.00142145
\(880\) 4.22556 7.31888i 0.142444 0.246719i
\(881\) −27.7225 48.0169i −0.933996 1.61773i −0.776414 0.630223i \(-0.782963\pi\)
−0.157582 0.987506i \(-0.550370\pi\)
\(882\) 7.65150 + 13.2528i 0.257639 + 0.446244i
\(883\) −31.2191 −1.05061 −0.525303 0.850915i \(-0.676048\pi\)
−0.525303 + 0.850915i \(0.676048\pi\)
\(884\) 0.0785275 0.285840i 0.00264116 0.00961384i
\(885\) 1.74005 0.0584912
\(886\) −20.2154 35.0142i −0.679151 1.17632i
\(887\) −5.58183 9.66802i −0.187420 0.324620i 0.756970 0.653450i \(-0.226679\pi\)
−0.944389 + 0.328830i \(0.893346\pi\)
\(888\) 0.549228 0.951290i 0.0184309 0.0319232i
\(889\) −27.6906 −0.928713
\(890\) 20.9857 36.3484i 0.703444 1.21840i
\(891\) −6.28681 + 10.8891i −0.210616 + 0.364797i
\(892\) 4.89776 0.163989
\(893\) 14.3493 24.8537i 0.480180 0.831696i
\(894\) −0.436673 0.756340i −0.0146045 0.0252958i
\(895\) −7.14887 12.3822i −0.238960 0.413891i
\(896\) −7.43684 −0.248447
\(897\) 0.841126 0.219699i 0.0280844 0.00733553i
\(898\) 30.8187 1.02843
\(899\) −5.06479 8.77247i −0.168920 0.292578i
\(900\) −0.399340 0.691678i −0.0133113 0.0230559i
\(901\) 0.785059 1.35976i 0.0261541 0.0453002i
\(902\) −4.06300 −0.135283
\(903\) 0.480209 0.831746i 0.0159804 0.0276788i
\(904\) −18.0248 + 31.2199i −0.599496 + 1.03836i
\(905\) 30.0995 1.00054
\(906\) 0.494684 0.856817i 0.0164348 0.0284658i
\(907\) −3.98360 6.89980i −0.132273 0.229104i 0.792279 0.610159i \(-0.208894\pi\)
−0.924553 + 0.381055i \(0.875561\pi\)
\(908\) −1.59256 2.75840i −0.0528511 0.0915407i
\(909\) −2.63742 −0.0874777
\(910\) 11.8068 + 11.9568i 0.391391 + 0.396363i
\(911\) −10.2908 −0.340949 −0.170475 0.985362i \(-0.554530\pi\)
−0.170475 + 0.985362i \(0.554530\pi\)
\(912\) −0.274816 0.475996i −0.00910008 0.0157618i
\(913\) 5.94103 + 10.2902i 0.196619 + 0.340555i
\(914\) −8.19655 + 14.1968i −0.271118 + 0.469590i
\(915\) 0.857152 0.0283366
\(916\) 5.20559 9.01635i 0.171998 0.297909i
\(917\) −5.55368 + 9.61926i −0.183399 + 0.317656i
\(918\) −0.0643341 −0.00212334
\(919\) −4.85265 + 8.40503i −0.160074 + 0.277257i −0.934895 0.354924i \(-0.884507\pi\)
0.774821 + 0.632181i \(0.217840\pi\)
\(920\) 14.3164 + 24.7968i 0.471998 + 0.817525i
\(921\) 0.805195 + 1.39464i 0.0265321 + 0.0459549i
\(922\) 14.8152 0.487911
\(923\) 1.68878 0.441103i 0.0555869 0.0145191i
\(924\) 0.0784179 0.00257976
\(925\) −1.41278 2.44701i −0.0464519 0.0804571i
\(926\) 10.3356 + 17.9018i 0.339650 + 0.588290i
\(927\) 19.1193 33.1156i 0.627960 1.08766i
\(928\) 30.8982 1.01428
\(929\) −15.0835 + 26.1254i −0.494874 + 0.857147i −0.999983 0.00590908i \(-0.998119\pi\)
0.505109 + 0.863056i \(0.331452\pi\)
\(930\) 0.0851023 0.147401i 0.00279061 0.00483348i
\(931\) −14.9911 −0.491315
\(932\) 6.30765 10.9252i 0.206614 0.357866i
\(933\) −0.115023 0.199226i −0.00376569 0.00652237i
\(934\) −21.4670 37.1819i −0.702421 1.21663i
\(935\) 0.484223 0.0158358
\(936\) −32.1070 + 8.38622i −1.04945 + 0.274112i
\(937\) −22.7638 −0.743662 −0.371831 0.928300i \(-0.621270\pi\)
−0.371831 + 0.928300i \(0.621270\pi\)
\(938\) −7.18790 12.4498i −0.234693 0.406500i
\(939\) −0.210415 0.364449i −0.00686663 0.0118934i
\(940\) −5.30825 + 9.19416i −0.173136 + 0.299880i
\(941\) 23.2269 0.757175 0.378587 0.925566i \(-0.376410\pi\)
0.378587 + 0.925566i \(0.376410\pi\)
\(942\) 0.309522 0.536107i 0.0100848 0.0174673i
\(943\) 4.80374 8.32032i 0.156431 0.270947i
\(944\) 31.6203 1.02915
\(945\) −0.704274 + 1.21984i −0.0229100 + 0.0396813i
\(946\) 8.05894 + 13.9585i 0.262019 + 0.453830i
\(947\) −14.9986 25.9784i −0.487389 0.844183i 0.512506 0.858684i \(-0.328717\pi\)
−0.999895 + 0.0145009i \(0.995384\pi\)
\(948\) −0.491948 −0.0159777
\(949\) 4.73671 + 4.79688i 0.153760 + 0.155713i
\(950\) −2.02574 −0.0657236
\(951\) −0.305393 0.528955i −0.00990303 0.0171526i
\(952\) −0.375629 0.650609i −0.0121742 0.0210863i
\(953\) −5.64400 + 9.77569i −0.182827 + 0.316666i −0.942842 0.333240i \(-0.891858\pi\)
0.760015 + 0.649905i \(0.225191\pi\)
\(954\) −38.3010 −1.24004
\(955\) 21.2993 36.8916i 0.689231 1.19378i
\(956\) 4.67152 8.09131i 0.151088 0.261692i
\(957\) 0.859909 0.0277969
\(958\) 19.3850 33.5758i 0.626301 1.08478i
\(959\) 3.76824 + 6.52678i 0.121683 + 0.210761i
\(960\) 0.624468 + 1.08161i 0.0201546 + 0.0349088i
\(961\) 1.00000 0.0322581
\(962\) −24.7515 + 6.46500i −0.798021 + 0.208440i
\(963\) 7.53758 0.242895
\(964\) −0.202271 0.350344i −0.00651472 0.0112838i
\(965\) −10.4443 18.0901i −0.336214 0.582341i
\(966\) 0.240049 0.415776i 0.00772344 0.0133774i
\(967\) 16.5261 0.531445 0.265722 0.964050i \(-0.414390\pi\)
0.265722 + 0.964050i \(0.414390\pi\)
\(968\) 13.8743 24.0309i 0.445936 0.772383i
\(969\) 0.0157461 0.0272731i 0.000505839 0.000876138i
\(970\) 25.2826 0.811776
\(971\) −23.3610 + 40.4624i −0.749690 + 1.29850i 0.198282 + 0.980145i \(0.436464\pi\)
−0.947971 + 0.318356i \(0.896869\pi\)
\(972\) −0.454693 0.787551i −0.0145843 0.0252607i
\(973\) 7.19487 + 12.4619i 0.230657 + 0.399509i
\(974\) −27.1162 −0.868859
\(975\) 0.0276605 0.100684i 0.000885845 0.00322448i
\(976\) 15.5762 0.498582
\(977\) −17.7141 30.6816i −0.566723 0.981593i −0.996887 0.0788422i \(-0.974878\pi\)
0.430164 0.902751i \(-0.358456\pi\)
\(978\) 0.216884 + 0.375654i 0.00693519 + 0.0120121i
\(979\) −10.4668 + 18.1290i −0.334521 + 0.579407i
\(980\) 5.54570 0.177151
\(981\) 24.1842 41.8883i 0.772142 1.33739i
\(982\) 2.88644 4.99947i 0.0921101 0.159539i
\(983\) −21.6882 −0.691746 −0.345873 0.938281i \(-0.612417\pi\)
−0.345873 + 0.938281i \(0.612417\pi\)
\(984\) 0.224299 0.388496i 0.00715038 0.0123848i
\(985\) −1.00758 1.74518i −0.0321043 0.0556062i
\(986\) −0.897569 1.55463i −0.0285844 0.0495096i
\(987\) 0.816912 0.0260026
\(988\) 1.87654 6.83061i 0.0597007 0.217311i
\(989\) −38.1128 −1.21192
\(990\) −5.90600 10.2295i −0.187705 0.325115i
\(991\) −12.0283 20.8336i −0.382091 0.661800i 0.609270 0.792963i \(-0.291462\pi\)
−0.991361 + 0.131162i \(0.958129\pi\)
\(992\) −1.52515 + 2.64163i −0.0484234 + 0.0838718i
\(993\) −1.94376 −0.0616834
\(994\) 0.481961 0.834780i 0.0152869 0.0264776i
\(995\) −22.2001 + 38.4518i −0.703792 + 1.21900i
\(996\) −0.285872 −0.00905821
\(997\) −14.1996 + 24.5945i −0.449707 + 0.778915i −0.998367 0.0571304i \(-0.981805\pi\)
0.548660 + 0.836046i \(0.315138\pi\)
\(998\) −16.4321 28.4612i −0.520148 0.900922i
\(999\) −1.07218 1.85708i −0.0339224 0.0587554i
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 403.2.f.b.94.12 34
13.3 even 3 5239.2.a.m.1.6 17
13.9 even 3 inner 403.2.f.b.373.12 yes 34
13.10 even 6 5239.2.a.n.1.12 17
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
403.2.f.b.94.12 34 1.1 even 1 trivial
403.2.f.b.373.12 yes 34 13.9 even 3 inner
5239.2.a.m.1.6 17 13.3 even 3
5239.2.a.n.1.12 17 13.10 even 6