Properties

Label 429.2.bb.b.25.14
Level $429$
Weight $2$
Character 429.25
Analytic conductor $3.426$
Analytic rank $0$
Dimension $56$
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] = [429,2,Mod(25,429)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(429, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 8, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("429.25");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 429 = 3 \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 429.bb (of order \(10\), degree \(4\), 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: \(3.42558224671\)
Analytic rank: \(0\)
Dimension: \(56\)
Relative dimension: \(14\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 25.14
Character \(\chi\) \(=\) 429.25
Dual form 429.2.bb.b.103.14

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.59022 + 2.18875i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(-1.64379 + 5.05905i) q^{4} +(-0.714239 + 0.983066i) q^{5} +(1.59022 - 2.18875i) q^{6} +(-1.83379 - 0.595836i) q^{7} +(-8.54091 + 2.77511i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\) \(q+(1.59022 + 2.18875i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(-1.64379 + 5.05905i) q^{4} +(-0.714239 + 0.983066i) q^{5} +(1.59022 - 2.18875i) q^{6} +(-1.83379 - 0.595836i) q^{7} +(-8.54091 + 2.77511i) q^{8} +(-0.809017 + 0.587785i) q^{9} -3.28748 q^{10} +(-0.579858 + 3.26554i) q^{11} +5.31940 q^{12} +(2.74377 + 2.33917i) q^{13} +(-1.61200 - 4.96122i) q^{14} +(1.15566 + 0.375498i) q^{15} +(-11.0490 - 8.02753i) q^{16} +(-2.21617 - 1.61014i) q^{17} +(-2.57303 - 0.836027i) q^{18} +(2.24916 - 0.730797i) q^{19} +(-3.79933 - 5.22933i) q^{20} +1.92817i q^{21} +(-8.06954 + 3.92376i) q^{22} +0.986462 q^{23} +(5.27858 + 7.26534i) q^{24} +(1.08880 + 3.35099i) q^{25} +(-0.756659 + 9.72521i) q^{26} +(0.809017 + 0.587785i) q^{27} +(6.02873 - 8.29784i) q^{28} +(1.88082 - 5.78856i) q^{29} +(1.01589 + 3.12658i) q^{30} +(6.17431 + 8.49821i) q^{31} -18.9880i q^{32} +(3.28490 - 0.457630i) q^{33} -7.41111i q^{34} +(1.89551 - 1.37717i) q^{35} +(-1.64379 - 5.05905i) q^{36} +(-2.39088 - 0.776844i) q^{37} +(5.17618 + 3.76072i) q^{38} +(1.37681 - 3.33232i) q^{39} +(3.37214 - 10.3784i) q^{40} +(-1.41427 + 0.459524i) q^{41} +(-4.22027 + 3.06620i) q^{42} +9.90380 q^{43} +(-15.5674 - 8.30139i) q^{44} -1.21514i q^{45} +(1.56869 + 2.15911i) q^{46} +(7.47710 - 2.42946i) q^{47} +(-4.22032 + 12.9888i) q^{48} +(-2.65534 - 1.92922i) q^{49} +(-5.60304 + 7.71193i) q^{50} +(-0.846501 + 2.60526i) q^{51} +(-16.3442 + 10.0358i) q^{52} +(-7.61762 + 5.53453i) q^{53} +2.70544i q^{54} +(-2.79609 - 2.90242i) q^{55} +17.3158 q^{56} +(-1.39006 - 1.91325i) q^{57} +(15.6606 - 5.08844i) q^{58} +(3.65969 + 1.18911i) q^{59} +(-3.79933 + 5.22933i) q^{60} +(1.34340 + 0.976036i) q^{61} +(-8.78193 + 27.0280i) q^{62} +(1.83379 - 0.595836i) q^{63} +(19.4620 - 14.1400i) q^{64} +(-4.25927 + 1.02658i) q^{65} +(6.22534 + 6.46208i) q^{66} -15.2525i q^{67} +(11.7887 - 8.56499i) q^{68} +(-0.304833 - 0.938181i) q^{69} +(6.02856 + 1.95880i) q^{70} +(-3.16800 + 4.36038i) q^{71} +(5.27858 - 7.26534i) q^{72} +(7.00217 + 2.27514i) q^{73} +(-2.10170 - 6.46838i) q^{74} +(2.85053 - 2.07103i) q^{75} +12.5799i q^{76} +(3.00907 - 5.64283i) q^{77} +(9.48305 - 2.28563i) q^{78} +(2.93694 - 2.13381i) q^{79} +(15.7832 - 5.12827i) q^{80} +(0.309017 - 0.951057i) q^{81} +(-3.25478 - 2.36474i) q^{82} +(-7.83621 + 10.7856i) q^{83} +(-9.75469 - 3.16949i) q^{84} +(3.16575 - 1.02861i) q^{85} +(15.7492 + 21.6769i) q^{86} -6.08645 q^{87} +(-4.10972 - 29.4999i) q^{88} +7.77969i q^{89} +(2.65963 - 1.93233i) q^{90} +(-3.63775 - 5.92439i) q^{91} +(-1.62153 + 4.99056i) q^{92} +(6.17431 - 8.49821i) q^{93} +(17.2077 + 12.5021i) q^{94} +(-0.888017 + 2.73304i) q^{95} +(-18.0586 + 5.86761i) q^{96} +(-0.673437 - 0.926906i) q^{97} -8.87974i q^{98} +(-1.45032 - 2.98271i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 56 q + 14 q^{3} + 20 q^{4} - 14 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 56 q + 14 q^{3} + 20 q^{4} - 14 q^{9} + 60 q^{12} - 3 q^{13} - 42 q^{14} - 16 q^{16} - 6 q^{17} - 40 q^{22} + 12 q^{23} + 4 q^{25} - 24 q^{26} + 14 q^{27} - 22 q^{29} - 10 q^{30} - 10 q^{35} + 20 q^{36} - 26 q^{38} + 3 q^{39} - 18 q^{42} + 6 q^{48} - 14 q^{49} - 24 q^{51} + 39 q^{52} + 10 q^{53} - 64 q^{55} - 20 q^{56} + 2 q^{61} - 8 q^{62} + 24 q^{64} - 58 q^{65} + 30 q^{66} + 18 q^{68} - 2 q^{69} - 86 q^{74} - 14 q^{75} + 52 q^{77} + 14 q^{78} - 24 q^{79} - 14 q^{81} + 62 q^{82} - 28 q^{87} - 46 q^{88} - 10 q^{90} - 19 q^{91} + 58 q^{92} + 86 q^{94} + 156 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/429\mathbb{Z}\right)^\times\).

\(n\) \(67\) \(79\) \(287\)
\(\chi(n)\) \(-1\) \(e\left(\frac{4}{5}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.59022 + 2.18875i 1.12445 + 1.54768i 0.798197 + 0.602396i \(0.205787\pi\)
0.326257 + 0.945281i \(0.394213\pi\)
\(3\) −0.309017 0.951057i −0.178411 0.549093i
\(4\) −1.64379 + 5.05905i −0.821893 + 2.52953i
\(5\) −0.714239 + 0.983066i −0.319418 + 0.439640i −0.938289 0.345852i \(-0.887590\pi\)
0.618872 + 0.785492i \(0.287590\pi\)
\(6\) 1.59022 2.18875i 0.649204 0.893552i
\(7\) −1.83379 0.595836i −0.693109 0.225205i −0.0587834 0.998271i \(-0.518722\pi\)
−0.634326 + 0.773066i \(0.718722\pi\)
\(8\) −8.54091 + 2.77511i −3.01967 + 0.981150i
\(9\) −0.809017 + 0.587785i −0.269672 + 0.195928i
\(10\) −3.28748 −1.03959
\(11\) −0.579858 + 3.26554i −0.174834 + 0.984598i
\(12\) 5.31940 1.53558
\(13\) 2.74377 + 2.33917i 0.760985 + 0.648769i
\(14\) −1.61200 4.96122i −0.430825 1.32594i
\(15\) 1.15566 + 0.375498i 0.298391 + 0.0969531i
\(16\) −11.0490 8.02753i −2.76224 2.00688i
\(17\) −2.21617 1.61014i −0.537500 0.390516i 0.285656 0.958332i \(-0.407789\pi\)
−0.823156 + 0.567816i \(0.807789\pi\)
\(18\) −2.57303 0.836027i −0.606468 0.197053i
\(19\) 2.24916 0.730797i 0.515993 0.167656i −0.0394332 0.999222i \(-0.512555\pi\)
0.555426 + 0.831566i \(0.312555\pi\)
\(20\) −3.79933 5.22933i −0.849555 1.16931i
\(21\) 1.92817i 0.420760i
\(22\) −8.06954 + 3.92376i −1.72043 + 0.836548i
\(23\) 0.986462 0.205691 0.102846 0.994697i \(-0.467205\pi\)
0.102846 + 0.994697i \(0.467205\pi\)
\(24\) 5.27858 + 7.26534i 1.07748 + 1.48303i
\(25\) 1.08880 + 3.35099i 0.217761 + 0.670199i
\(26\) −0.756659 + 9.72521i −0.148393 + 1.90727i
\(27\) 0.809017 + 0.587785i 0.155695 + 0.113119i
\(28\) 6.02873 8.29784i 1.13932 1.56814i
\(29\) 1.88082 5.78856i 0.349259 1.07491i −0.610005 0.792398i \(-0.708833\pi\)
0.959264 0.282511i \(-0.0911675\pi\)
\(30\) 1.01589 + 3.12658i 0.185475 + 0.570832i
\(31\) 6.17431 + 8.49821i 1.10894 + 1.52632i 0.822970 + 0.568085i \(0.192316\pi\)
0.285970 + 0.958239i \(0.407684\pi\)
\(32\) 18.9880i 3.35663i
\(33\) 3.28490 0.457630i 0.571828 0.0796632i
\(34\) 7.41111i 1.27099i
\(35\) 1.89551 1.37717i 0.320400 0.232784i
\(36\) −1.64379 5.05905i −0.273964 0.843176i
\(37\) −2.39088 0.776844i −0.393058 0.127712i 0.105818 0.994385i \(-0.466254\pi\)
−0.498876 + 0.866673i \(0.666254\pi\)
\(38\) 5.17618 + 3.76072i 0.839688 + 0.610069i
\(39\) 1.37681 3.33232i 0.220466 0.533599i
\(40\) 3.37214 10.3784i 0.533182 1.64097i
\(41\) −1.41427 + 0.459524i −0.220872 + 0.0717656i −0.417363 0.908740i \(-0.637045\pi\)
0.196491 + 0.980506i \(0.437045\pi\)
\(42\) −4.22027 + 3.06620i −0.651201 + 0.473125i
\(43\) 9.90380 1.51031 0.755157 0.655543i \(-0.227560\pi\)
0.755157 + 0.655543i \(0.227560\pi\)
\(44\) −15.5674 8.30139i −2.34687 1.25148i
\(45\) 1.21514i 0.181142i
\(46\) 1.56869 + 2.15911i 0.231291 + 0.318344i
\(47\) 7.47710 2.42946i 1.09065 0.354373i 0.292151 0.956372i \(-0.405629\pi\)
0.798497 + 0.601999i \(0.205629\pi\)
\(48\) −4.22032 + 12.9888i −0.609151 + 1.87477i
\(49\) −2.65534 1.92922i −0.379334 0.275602i
\(50\) −5.60304 + 7.71193i −0.792390 + 1.09063i
\(51\) −0.846501 + 2.60526i −0.118534 + 0.364810i
\(52\) −16.3442 + 10.0358i −2.26653 + 1.39171i
\(53\) −7.61762 + 5.53453i −1.04636 + 0.760226i −0.971517 0.236970i \(-0.923846\pi\)
−0.0748438 + 0.997195i \(0.523846\pi\)
\(54\) 2.70544i 0.368164i
\(55\) −2.79609 2.90242i −0.377024 0.391362i
\(56\) 17.3158 2.31392
\(57\) −1.39006 1.91325i −0.184118 0.253416i
\(58\) 15.6606 5.08844i 2.05634 0.668145i
\(59\) 3.65969 + 1.18911i 0.476451 + 0.154808i 0.537391 0.843333i \(-0.319410\pi\)
−0.0609402 + 0.998141i \(0.519410\pi\)
\(60\) −3.79933 + 5.22933i −0.490491 + 0.675103i
\(61\) 1.34340 + 0.976036i 0.172004 + 0.124969i 0.670457 0.741949i \(-0.266098\pi\)
−0.498452 + 0.866917i \(0.666098\pi\)
\(62\) −8.78193 + 27.0280i −1.11531 + 3.43256i
\(63\) 1.83379 0.595836i 0.231036 0.0750683i
\(64\) 19.4620 14.1400i 2.43275 1.76749i
\(65\) −4.25927 + 1.02658i −0.528297 + 0.127332i
\(66\) 6.22534 + 6.46208i 0.766287 + 0.795428i
\(67\) 15.2525i 1.86339i −0.363235 0.931697i \(-0.618328\pi\)
0.363235 0.931697i \(-0.381672\pi\)
\(68\) 11.7887 8.56499i 1.42959 1.03866i
\(69\) −0.304833 0.938181i −0.0366976 0.112944i
\(70\) 6.02856 + 1.95880i 0.720551 + 0.234121i
\(71\) −3.16800 + 4.36038i −0.375973 + 0.517482i −0.954512 0.298172i \(-0.903623\pi\)
0.578539 + 0.815655i \(0.303623\pi\)
\(72\) 5.27858 7.26534i 0.622086 0.856228i
\(73\) 7.00217 + 2.27514i 0.819542 + 0.266285i 0.688634 0.725109i \(-0.258211\pi\)
0.130908 + 0.991395i \(0.458211\pi\)
\(74\) −2.10170 6.46838i −0.244318 0.751934i
\(75\) 2.85053 2.07103i 0.329150 0.239142i
\(76\) 12.5799i 1.44301i
\(77\) 3.00907 5.64283i 0.342915 0.643060i
\(78\) 9.48305 2.28563i 1.07374 0.258797i
\(79\) 2.93694 2.13381i 0.330432 0.240073i −0.410182 0.912004i \(-0.634535\pi\)
0.740614 + 0.671931i \(0.234535\pi\)
\(80\) 15.7832 5.12827i 1.76461 0.573358i
\(81\) 0.309017 0.951057i 0.0343352 0.105673i
\(82\) −3.25478 2.36474i −0.359430 0.261141i
\(83\) −7.83621 + 10.7856i −0.860136 + 1.18388i 0.121401 + 0.992604i \(0.461261\pi\)
−0.981537 + 0.191272i \(0.938739\pi\)
\(84\) −9.75469 3.16949i −1.06432 0.345820i
\(85\) 3.16575 1.02861i 0.343374 0.111569i
\(86\) 15.7492 + 21.6769i 1.69828 + 2.33748i
\(87\) −6.08645 −0.652536
\(88\) −4.10972 29.4999i −0.438098 3.14470i
\(89\) 7.77969i 0.824646i 0.911038 + 0.412323i \(0.135282\pi\)
−0.911038 + 0.412323i \(0.864718\pi\)
\(90\) 2.65963 1.93233i 0.280349 0.203686i
\(91\) −3.63775 5.92439i −0.381340 0.621045i
\(92\) −1.62153 + 4.99056i −0.169056 + 0.520302i
\(93\) 6.17431 8.49821i 0.640246 0.881224i
\(94\) 17.2077 + 12.5021i 1.77484 + 1.28950i
\(95\) −0.888017 + 2.73304i −0.0911087 + 0.280404i
\(96\) −18.0586 + 5.86761i −1.84310 + 0.598860i
\(97\) −0.673437 0.926906i −0.0683772 0.0941131i 0.773459 0.633847i \(-0.218525\pi\)
−0.841836 + 0.539734i \(0.818525\pi\)
\(98\) 8.87974i 0.896989i
\(99\) −1.45032 2.98271i −0.145763 0.299774i
\(100\) −18.7426 −1.87426
\(101\) −8.88423 + 6.45477i −0.884013 + 0.642273i −0.934310 0.356461i \(-0.883983\pi\)
0.0502968 + 0.998734i \(0.483983\pi\)
\(102\) −7.04838 + 2.29016i −0.697894 + 0.226759i
\(103\) 4.57973 14.0950i 0.451255 1.38882i −0.424222 0.905558i \(-0.639452\pi\)
0.875477 0.483261i \(-0.160548\pi\)
\(104\) −29.9258 12.3644i −2.93446 1.21243i
\(105\) −1.89551 1.37717i −0.184983 0.134398i
\(106\) −24.2274 7.87194i −2.35317 0.764591i
\(107\) −0.537531 1.65435i −0.0519650 0.159932i 0.921706 0.387889i \(-0.126796\pi\)
−0.973671 + 0.227957i \(0.926796\pi\)
\(108\) −4.30349 + 3.12667i −0.414103 + 0.300864i
\(109\) 0.825638i 0.0790818i −0.999218 0.0395409i \(-0.987410\pi\)
0.999218 0.0395409i \(-0.0125895\pi\)
\(110\) 1.90627 10.7354i 0.181756 1.02358i
\(111\) 2.51392i 0.238611i
\(112\) 15.4784 + 21.3042i 1.46257 + 2.01306i
\(113\) −4.17463 12.8482i −0.392716 1.20866i −0.930726 0.365717i \(-0.880824\pi\)
0.538010 0.842939i \(-0.319176\pi\)
\(114\) 1.97713 6.08497i 0.185175 0.569909i
\(115\) −0.704570 + 0.969757i −0.0657015 + 0.0904303i
\(116\) 26.1930 + 19.0303i 2.43196 + 1.76692i
\(117\) −3.59469 0.279681i −0.332329 0.0258565i
\(118\) 3.21705 + 9.90107i 0.296154 + 0.911467i
\(119\) 3.10462 + 4.27314i 0.284600 + 0.391718i
\(120\) −10.9125 −0.996168
\(121\) −10.3275 3.78710i −0.938866 0.344282i
\(122\) 4.49247i 0.406729i
\(123\) 0.874067 + 1.20305i 0.0788120 + 0.108475i
\(124\) −53.1422 + 17.2669i −4.77231 + 1.55062i
\(125\) −9.85023 3.20053i −0.881031 0.286264i
\(126\) 4.22027 + 3.06620i 0.375971 + 0.273159i
\(127\) 18.1094 + 13.1573i 1.60695 + 1.16752i 0.872150 + 0.489238i \(0.162725\pi\)
0.734802 + 0.678281i \(0.237275\pi\)
\(128\) 25.7803 + 8.37652i 2.27868 + 0.740387i
\(129\) −3.06044 9.41907i −0.269457 0.829303i
\(130\) −9.02009 7.68997i −0.791114 0.674455i
\(131\) 17.6690 1.54374 0.771872 0.635778i \(-0.219321\pi\)
0.771872 + 0.635778i \(0.219321\pi\)
\(132\) −3.08450 + 17.3707i −0.268471 + 1.51193i
\(133\) −4.55993 −0.395396
\(134\) 33.3840 24.2549i 2.88393 2.09530i
\(135\) −1.15566 + 0.375498i −0.0994637 + 0.0323177i
\(136\) 23.3964 + 7.60196i 2.00623 + 0.651863i
\(137\) −1.74997 + 2.40863i −0.149510 + 0.205783i −0.877202 0.480121i \(-0.840593\pi\)
0.727692 + 0.685904i \(0.240593\pi\)
\(138\) 1.56869 2.15911i 0.133536 0.183796i
\(139\) 0.975748 3.00304i 0.0827619 0.254715i −0.901110 0.433591i \(-0.857246\pi\)
0.983872 + 0.178876i \(0.0572462\pi\)
\(140\) 3.85136 + 11.8533i 0.325500 + 1.00179i
\(141\) −4.62110 6.36040i −0.389167 0.535643i
\(142\) −14.5816 −1.22366
\(143\) −9.22966 + 7.60351i −0.771823 + 0.635838i
\(144\) 13.6573 1.13810
\(145\) 4.34718 + 5.98339i 0.361014 + 0.496893i
\(146\) 6.15526 + 18.9439i 0.509413 + 1.56781i
\(147\) −1.01425 + 3.12154i −0.0836539 + 0.257460i
\(148\) 7.86019 10.8186i 0.646104 0.889285i
\(149\) 2.59451 3.57103i 0.212550 0.292550i −0.689408 0.724373i \(-0.742129\pi\)
0.901959 + 0.431823i \(0.142129\pi\)
\(150\) 9.06591 + 2.94569i 0.740229 + 0.240515i
\(151\) −11.8185 + 3.84007i −0.961777 + 0.312500i −0.747492 0.664271i \(-0.768742\pi\)
−0.214285 + 0.976771i \(0.568742\pi\)
\(152\) −17.1818 + 12.4833i −1.39363 + 1.01253i
\(153\) 2.73933 0.221462
\(154\) 17.1358 2.38724i 1.38084 0.192370i
\(155\) −12.7642 −1.02525
\(156\) 14.5952 + 12.4430i 1.16855 + 0.996237i
\(157\) 3.91971 + 12.0636i 0.312827 + 0.962783i 0.976640 + 0.214884i \(0.0689373\pi\)
−0.663812 + 0.747899i \(0.731063\pi\)
\(158\) 9.34075 + 3.03499i 0.743110 + 0.241451i
\(159\) 7.61762 + 5.53453i 0.604117 + 0.438917i
\(160\) 18.6664 + 13.5620i 1.47571 + 1.07217i
\(161\) −1.80897 0.587769i −0.142567 0.0463227i
\(162\) 2.57303 0.836027i 0.202156 0.0656845i
\(163\) −14.1077 19.4176i −1.10500 1.52090i −0.828584 0.559865i \(-0.810853\pi\)
−0.276417 0.961038i \(-0.589147\pi\)
\(164\) 7.91023i 0.617685i
\(165\) −1.89632 + 3.55613i −0.147629 + 0.276844i
\(166\) −36.0683 −2.79944
\(167\) −7.60357 10.4654i −0.588382 0.809838i 0.406201 0.913784i \(-0.366853\pi\)
−0.994583 + 0.103946i \(0.966853\pi\)
\(168\) −5.35087 16.4683i −0.412829 1.27056i
\(169\) 2.05656 + 12.8363i 0.158197 + 0.987408i
\(170\) 7.28561 + 5.29330i 0.558780 + 0.405978i
\(171\) −1.39006 + 1.91325i −0.106300 + 0.146310i
\(172\) −16.2797 + 50.1038i −1.24132 + 3.82038i
\(173\) −4.61494 14.2033i −0.350867 1.07986i −0.958367 0.285539i \(-0.907828\pi\)
0.607500 0.794320i \(-0.292172\pi\)
\(174\) −9.67879 13.3217i −0.733747 1.00992i
\(175\) 6.79378i 0.513562i
\(176\) 32.6211 31.4260i 2.45891 2.36882i
\(177\) 3.84803i 0.289235i
\(178\) −17.0278 + 12.3714i −1.27629 + 0.927276i
\(179\) 2.02468 + 6.23132i 0.151332 + 0.465751i 0.997771 0.0667347i \(-0.0212581\pi\)
−0.846439 + 0.532485i \(0.821258\pi\)
\(180\) 6.14744 + 1.99742i 0.458203 + 0.148879i
\(181\) −1.47906 1.07460i −0.109937 0.0798742i 0.531458 0.847084i \(-0.321644\pi\)
−0.641396 + 0.767210i \(0.721644\pi\)
\(182\) 7.18219 17.3832i 0.532379 1.28853i
\(183\) 0.513132 1.57926i 0.0379318 0.116742i
\(184\) −8.42528 + 2.73754i −0.621120 + 0.201814i
\(185\) 2.47135 1.79554i 0.181697 0.132011i
\(186\) 28.4189 2.08378
\(187\) 6.54304 6.30334i 0.478475 0.460946i
\(188\) 41.8206i 3.05008i
\(189\) −1.13335 1.55992i −0.0824389 0.113467i
\(190\) −7.39407 + 2.40248i −0.536422 + 0.174294i
\(191\) 6.67318 20.5379i 0.482855 1.48607i −0.352209 0.935921i \(-0.614570\pi\)
0.835064 0.550153i \(-0.185430\pi\)
\(192\) −19.4620 14.1400i −1.40455 1.02046i
\(193\) −5.86319 + 8.06999i −0.422042 + 0.580891i −0.966104 0.258154i \(-0.916886\pi\)
0.544062 + 0.839045i \(0.316886\pi\)
\(194\) 0.957852 2.94797i 0.0687698 0.211652i
\(195\) 2.29252 + 3.73357i 0.164171 + 0.267367i
\(196\) 14.1248 10.2623i 1.00892 0.733020i
\(197\) 1.00508i 0.0716093i −0.999359 0.0358047i \(-0.988601\pi\)
0.999359 0.0358047i \(-0.0113994\pi\)
\(198\) 4.22207 7.91755i 0.300049 0.562676i
\(199\) 12.8185 0.908676 0.454338 0.890829i \(-0.349876\pi\)
0.454338 + 0.890829i \(0.349876\pi\)
\(200\) −18.5988 25.5990i −1.31513 1.81012i
\(201\) −14.5060 + 4.71330i −1.02318 + 0.332450i
\(202\) −28.2557 9.18083i −1.98806 0.645961i
\(203\) −6.89806 + 9.49437i −0.484149 + 0.666374i
\(204\) −11.7887 8.56499i −0.825374 0.599669i
\(205\) 0.558385 1.71853i 0.0389993 0.120027i
\(206\) 38.1331 12.3902i 2.65686 0.863266i
\(207\) −0.798064 + 0.579828i −0.0554693 + 0.0403008i
\(208\) −11.5380 47.8711i −0.800018 3.31926i
\(209\) 1.08225 + 7.76849i 0.0748610 + 0.537357i
\(210\) 6.33880i 0.437419i
\(211\) 19.0174 13.8169i 1.30921 0.951197i 0.309210 0.950994i \(-0.399935\pi\)
1.00000 0.000203014i \(-6.46214e-5\pi\)
\(212\) −15.4777 47.6355i −1.06301 3.27162i
\(213\) 5.12594 + 1.66552i 0.351223 + 0.114119i
\(214\) 2.76616 3.80729i 0.189091 0.260261i
\(215\) −7.07368 + 9.73609i −0.482421 + 0.663996i
\(216\) −8.54091 2.77511i −0.581136 0.188822i
\(217\) −6.25888 19.2628i −0.424880 1.30765i
\(218\) 1.80711 1.31294i 0.122393 0.0889238i
\(219\) 7.36252i 0.497513i
\(220\) 19.2797 9.37460i 1.29983 0.632035i
\(221\) −2.31427 9.60185i −0.155674 0.645891i
\(222\) −5.50233 + 3.99768i −0.369292 + 0.268307i
\(223\) 5.58334 1.81414i 0.373888 0.121484i −0.116044 0.993244i \(-0.537021\pi\)
0.489932 + 0.871760i \(0.337021\pi\)
\(224\) −11.3137 + 34.8200i −0.755930 + 2.32651i
\(225\) −2.85053 2.07103i −0.190035 0.138069i
\(226\) 21.4829 29.5686i 1.42902 1.96688i
\(227\) −8.61807 2.80018i −0.572001 0.185854i 0.00871295 0.999962i \(-0.497227\pi\)
−0.580714 + 0.814108i \(0.697227\pi\)
\(228\) 11.9642 3.88740i 0.792348 0.257449i
\(229\) −12.5498 17.2733i −0.829312 1.14145i −0.988051 0.154130i \(-0.950743\pi\)
0.158738 0.987321i \(-0.449257\pi\)
\(230\) −3.24297 −0.213835
\(231\) −6.29650 1.11806i −0.414280 0.0735631i
\(232\) 54.6591i 3.58854i
\(233\) 0.737126 0.535553i 0.0482907 0.0350853i −0.563378 0.826199i \(-0.690499\pi\)
0.611669 + 0.791114i \(0.290499\pi\)
\(234\) −5.10419 8.31261i −0.333671 0.543413i
\(235\) −2.95212 + 9.08570i −0.192575 + 0.592686i
\(236\) −12.0315 + 16.5599i −0.783184 + 1.07796i
\(237\) −2.93694 2.13381i −0.190775 0.138606i
\(238\) −4.41580 + 13.5904i −0.286234 + 0.880937i
\(239\) 0.646366 0.210017i 0.0418099 0.0135849i −0.288037 0.957619i \(-0.593003\pi\)
0.329847 + 0.944034i \(0.393003\pi\)
\(240\) −9.75455 13.4260i −0.629653 0.866643i
\(241\) 9.37549i 0.603928i −0.953319 0.301964i \(-0.902358\pi\)
0.953319 0.301964i \(-0.0976423\pi\)
\(242\) −8.13401 28.6267i −0.522874 1.84019i
\(243\) −1.00000 −0.0641500
\(244\) −7.14608 + 5.19193i −0.457481 + 0.332379i
\(245\) 3.79309 1.23245i 0.242332 0.0787384i
\(246\) −1.24322 + 3.82622i −0.0792645 + 0.243951i
\(247\) 7.88064 + 3.25603i 0.501433 + 0.207176i
\(248\) −76.3178 55.4481i −4.84618 3.52096i
\(249\) 12.6793 + 4.11974i 0.803515 + 0.261078i
\(250\) −8.65885 26.6492i −0.547634 1.68544i
\(251\) −23.9026 + 17.3663i −1.50872 + 1.09615i −0.541977 + 0.840393i \(0.682324\pi\)
−0.966742 + 0.255755i \(0.917676\pi\)
\(252\) 10.2567i 0.646111i
\(253\) −0.572008 + 3.22133i −0.0359618 + 0.202523i
\(254\) 60.5599i 3.79987i
\(255\) −1.95654 2.69295i −0.122523 0.168639i
\(256\) 7.79454 + 23.9891i 0.487159 + 1.49932i
\(257\) −1.24014 + 3.81675i −0.0773577 + 0.238082i −0.982256 0.187546i \(-0.939947\pi\)
0.904898 + 0.425628i \(0.139947\pi\)
\(258\) 15.7492 21.6769i 0.980502 1.34955i
\(259\) 3.92151 + 2.84914i 0.243671 + 0.177037i
\(260\) 1.80780 23.2353i 0.112115 1.44100i
\(261\) 1.88082 + 5.78856i 0.116420 + 0.358303i
\(262\) 28.0975 + 38.6729i 1.73587 + 2.38922i
\(263\) 18.7180 1.15420 0.577101 0.816673i \(-0.304184\pi\)
0.577101 + 0.816673i \(0.304184\pi\)
\(264\) −26.7861 + 13.0245i −1.64857 + 0.801605i
\(265\) 11.4416i 0.702852i
\(266\) −7.25128 9.98054i −0.444605 0.611946i
\(267\) 7.39893 2.40406i 0.452807 0.147126i
\(268\) 77.1635 + 25.0719i 4.71351 + 1.53151i
\(269\) 14.1844 + 10.3056i 0.864839 + 0.628342i 0.929197 0.369585i \(-0.120500\pi\)
−0.0643584 + 0.997927i \(0.520500\pi\)
\(270\) −2.65963 1.93233i −0.161860 0.117598i
\(271\) 16.5748 + 5.38548i 1.00685 + 0.327145i 0.765598 0.643319i \(-0.222443\pi\)
0.241249 + 0.970463i \(0.422443\pi\)
\(272\) 11.5609 + 35.5807i 0.700981 + 2.15740i
\(273\) −4.51031 + 5.29044i −0.272976 + 0.320192i
\(274\) −8.05471 −0.486603
\(275\) −11.5742 + 1.61243i −0.697948 + 0.0972334i
\(276\) 5.24739 0.315856
\(277\) 18.2972 13.2937i 1.09937 0.798742i 0.118416 0.992964i \(-0.462218\pi\)
0.980958 + 0.194222i \(0.0622182\pi\)
\(278\) 8.12455 2.63983i 0.487278 0.158326i
\(279\) −9.99025 3.24603i −0.598100 0.194335i
\(280\) −12.3676 + 17.0226i −0.739106 + 1.01729i
\(281\) 4.36954 6.01415i 0.260665 0.358774i −0.658546 0.752541i \(-0.728828\pi\)
0.919211 + 0.393766i \(0.128828\pi\)
\(282\) 6.57275 20.2289i 0.391402 1.20461i
\(283\) 2.73747 + 8.42505i 0.162725 + 0.500817i 0.998861 0.0477047i \(-0.0151907\pi\)
−0.836136 + 0.548522i \(0.815191\pi\)
\(284\) −16.8519 23.1946i −0.999976 1.37635i
\(285\) 2.87368 0.170222
\(286\) −31.3193 8.11014i −1.85195 0.479563i
\(287\) 2.86728 0.169250
\(288\) 11.1609 + 15.3616i 0.657660 + 0.905191i
\(289\) −2.93444 9.03128i −0.172614 0.531252i
\(290\) −6.18315 + 19.0298i −0.363087 + 1.11747i
\(291\) −0.673437 + 0.926906i −0.0394776 + 0.0543362i
\(292\) −23.0201 + 31.6845i −1.34715 + 1.85420i
\(293\) 28.9015 + 9.39066i 1.68844 + 0.548608i 0.986519 0.163645i \(-0.0523251\pi\)
0.701923 + 0.712253i \(0.252325\pi\)
\(294\) −8.44513 + 2.74399i −0.492530 + 0.160033i
\(295\) −3.78286 + 2.74841i −0.220247 + 0.160019i
\(296\) 22.5761 1.31221
\(297\) −2.38855 + 2.30105i −0.138598 + 0.133520i
\(298\) 11.9419 0.691777
\(299\) 2.70662 + 2.30750i 0.156528 + 0.133446i
\(300\) 5.79179 + 17.8253i 0.334389 + 1.02914i
\(301\) −18.1615 5.90104i −1.04681 0.340130i
\(302\) −27.1989 19.7612i −1.56512 1.13713i
\(303\) 8.88423 + 6.45477i 0.510385 + 0.370817i
\(304\) −30.7174 9.98067i −1.76176 0.572431i
\(305\) −1.91901 + 0.623526i −0.109882 + 0.0357030i
\(306\) 4.35614 + 5.99571i 0.249024 + 0.342752i
\(307\) 15.9993i 0.913126i 0.889691 + 0.456563i \(0.150920\pi\)
−0.889691 + 0.456563i \(0.849080\pi\)
\(308\) 23.6011 + 24.4986i 1.34480 + 1.39594i
\(309\) −14.8203 −0.843099
\(310\) −20.2979 27.9377i −1.15284 1.58675i
\(311\) 8.68187 + 26.7200i 0.492304 + 1.51515i 0.821117 + 0.570760i \(0.193351\pi\)
−0.328813 + 0.944395i \(0.606649\pi\)
\(312\) −2.51166 + 32.2819i −0.142195 + 1.82760i
\(313\) 6.08778 + 4.42303i 0.344102 + 0.250004i 0.746390 0.665508i \(-0.231785\pi\)
−0.402289 + 0.915513i \(0.631785\pi\)
\(314\) −20.1711 + 27.7631i −1.13832 + 1.56676i
\(315\) −0.724022 + 2.22831i −0.0407940 + 0.125551i
\(316\) 5.96737 + 18.3657i 0.335691 + 1.03315i
\(317\) −5.32941 7.33530i −0.299329 0.411991i 0.632687 0.774408i \(-0.281952\pi\)
−0.932016 + 0.362416i \(0.881952\pi\)
\(318\) 25.4741i 1.42852i
\(319\) 17.8122 + 9.49843i 0.997291 + 0.531810i
\(320\) 29.2317i 1.63410i
\(321\) −1.40727 + 1.02244i −0.0785463 + 0.0570673i
\(322\) −1.59017 4.89405i −0.0886169 0.272735i
\(323\) −6.16120 2.00190i −0.342819 0.111388i
\(324\) 4.30349 + 3.12667i 0.239083 + 0.173704i
\(325\) −4.85112 + 11.7413i −0.269092 + 0.651288i
\(326\) 20.0659 61.7564i 1.11135 3.42037i
\(327\) −0.785228 + 0.255136i −0.0434232 + 0.0141091i
\(328\) 10.8039 7.84952i 0.596547 0.433417i
\(329\) −15.1590 −0.835744
\(330\) −10.7990 + 1.50445i −0.594468 + 0.0828172i
\(331\) 26.9610i 1.48191i 0.671554 + 0.740956i \(0.265627\pi\)
−0.671554 + 0.740956i \(0.734373\pi\)
\(332\) −41.6840 57.3731i −2.28771 3.14876i
\(333\) 2.39088 0.776844i 0.131019 0.0425708i
\(334\) 10.8148 33.2846i 0.591760 1.82125i
\(335\) 14.9943 + 10.8940i 0.819224 + 0.595201i
\(336\) 15.4784 21.3042i 0.844416 1.16224i
\(337\) −4.96834 + 15.2910i −0.270643 + 0.832953i 0.719696 + 0.694289i \(0.244281\pi\)
−0.990339 + 0.138664i \(0.955719\pi\)
\(338\) −24.8250 + 24.9138i −1.35030 + 1.35513i
\(339\) −10.9293 + 7.94062i −0.593599 + 0.431275i
\(340\) 17.7065i 0.960271i
\(341\) −31.3315 + 15.2347i −1.69670 + 0.825006i
\(342\) −6.39811 −0.345970
\(343\) 11.6533 + 16.0394i 0.629218 + 0.866044i
\(344\) −84.5875 + 27.4841i −4.56065 + 1.48185i
\(345\) 1.14002 + 0.370414i 0.0613765 + 0.0199424i
\(346\) 23.7487 32.6873i 1.27674 1.75728i
\(347\) −1.92069 1.39546i −0.103108 0.0749123i 0.535037 0.844829i \(-0.320298\pi\)
−0.638145 + 0.769917i \(0.720298\pi\)
\(348\) 10.0048 30.7917i 0.536315 1.65061i
\(349\) 10.9577 3.56036i 0.586551 0.190582i −0.000682233 1.00000i \(-0.500217\pi\)
0.587233 + 0.809418i \(0.300217\pi\)
\(350\) 14.8699 10.8036i 0.794828 0.577476i
\(351\) 0.844828 + 3.50518i 0.0450936 + 0.187093i
\(352\) 62.0060 + 11.0103i 3.30493 + 0.586853i
\(353\) 20.3791i 1.08467i −0.840162 0.542336i \(-0.817540\pi\)
0.840162 0.542336i \(-0.182460\pi\)
\(354\) 8.42235 6.11920i 0.447643 0.325232i
\(355\) −2.02383 6.22871i −0.107414 0.330586i
\(356\) −39.3579 12.7882i −2.08596 0.677771i
\(357\) 3.10462 4.27314i 0.164314 0.226158i
\(358\) −10.4191 + 14.3407i −0.550667 + 0.757928i
\(359\) −6.08727 1.97787i −0.321274 0.104388i 0.143940 0.989586i \(-0.454023\pi\)
−0.465214 + 0.885198i \(0.654023\pi\)
\(360\) 3.37214 + 10.3784i 0.177727 + 0.546988i
\(361\) −10.8467 + 7.88056i −0.570877 + 0.414766i
\(362\) 4.94612i 0.259962i
\(363\) −0.410365 + 10.9923i −0.0215386 + 0.576948i
\(364\) 35.9515 8.66513i 1.88437 0.454176i
\(365\) −7.23784 + 5.25860i −0.378846 + 0.275248i
\(366\) 4.27259 1.38825i 0.223332 0.0725649i
\(367\) 6.88405 21.1869i 0.359344 1.10595i −0.594103 0.804389i \(-0.702493\pi\)
0.953447 0.301559i \(-0.0975071\pi\)
\(368\) −10.8994 7.91885i −0.568169 0.412799i
\(369\) 0.874067 1.20305i 0.0455021 0.0626283i
\(370\) 7.85996 + 2.55386i 0.408620 + 0.132769i
\(371\) 17.2668 5.61033i 0.896449 0.291274i
\(372\) 32.8437 + 45.2054i 1.70286 + 2.34379i
\(373\) 17.3557 0.898644 0.449322 0.893370i \(-0.351666\pi\)
0.449322 + 0.893370i \(0.351666\pi\)
\(374\) 24.2013 + 4.29739i 1.25142 + 0.222213i
\(375\) 10.3571i 0.534841i
\(376\) −57.1193 + 41.4996i −2.94570 + 2.14018i
\(377\) 18.7010 11.4829i 0.963149 0.591401i
\(378\) 1.61200 4.96122i 0.0829122 0.255178i
\(379\) −15.5738 + 21.4355i −0.799973 + 1.10107i 0.192821 + 0.981234i \(0.438236\pi\)
−0.992794 + 0.119835i \(0.961764\pi\)
\(380\) −12.3669 8.98506i −0.634407 0.460924i
\(381\) 6.91719 21.2889i 0.354378 1.09066i
\(382\) 55.5642 18.0539i 2.84291 0.923718i
\(383\) −13.0407 17.9490i −0.666350 0.917152i 0.333321 0.942813i \(-0.391831\pi\)
−0.999671 + 0.0256618i \(0.991831\pi\)
\(384\) 27.1070i 1.38330i
\(385\) 3.39808 + 6.98844i 0.173182 + 0.356164i
\(386\) −26.9869 −1.37360
\(387\) −8.01234 + 5.82131i −0.407290 + 0.295914i
\(388\) 5.79626 1.88332i 0.294260 0.0956110i
\(389\) 0.854049 2.62849i 0.0433020 0.133270i −0.927068 0.374893i \(-0.877680\pi\)
0.970370 + 0.241623i \(0.0776796\pi\)
\(390\) −4.52624 + 10.9549i −0.229195 + 0.554725i
\(391\) −2.18617 1.58834i −0.110559 0.0803259i
\(392\) 28.0328 + 9.10841i 1.41587 + 0.460044i
\(393\) −5.46001 16.8042i −0.275421 0.847659i
\(394\) 2.19988 1.59830i 0.110828 0.0805214i
\(395\) 4.41126i 0.221954i
\(396\) 17.4737 2.43432i 0.878087 0.122329i
\(397\) 11.0032i 0.552237i 0.961124 + 0.276118i \(0.0890482\pi\)
−0.961124 + 0.276118i \(0.910952\pi\)
\(398\) 20.3841 + 28.0563i 1.02176 + 1.40634i
\(399\) 1.40910 + 4.33675i 0.0705431 + 0.217109i
\(400\) 14.8701 45.7654i 0.743504 2.28827i
\(401\) −0.00210889 + 0.00290264i −0.000105313 + 0.000144951i −0.809070 0.587713i \(-0.800029\pi\)
0.808964 + 0.587858i \(0.200029\pi\)
\(402\) −33.3840 24.2549i −1.66504 1.20972i
\(403\) −2.93787 + 37.7599i −0.146346 + 1.88096i
\(404\) −18.0512 55.5560i −0.898083 2.76402i
\(405\) 0.714239 + 0.983066i 0.0354908 + 0.0488489i
\(406\) −31.7502 −1.57574
\(407\) 3.92319 7.35706i 0.194465 0.364676i
\(408\) 24.6005i 1.21790i
\(409\) −6.35460 8.74636i −0.314215 0.432480i 0.622475 0.782640i \(-0.286127\pi\)
−0.936690 + 0.350160i \(0.886127\pi\)
\(410\) 4.64938 1.51068i 0.229617 0.0746070i
\(411\) 2.83151 + 0.920013i 0.139668 + 0.0453809i
\(412\) 63.7791 + 46.3382i 3.14217 + 2.28292i
\(413\) −6.00261 4.36115i −0.295369 0.214598i
\(414\) −2.53819 0.824708i −0.124745 0.0405322i
\(415\) −5.00605 15.4070i −0.245737 0.756301i
\(416\) 44.4161 52.0987i 2.17768 2.55435i
\(417\) −3.15759 −0.154628
\(418\) −15.2822 + 14.7224i −0.747478 + 0.720094i
\(419\) −15.4908 −0.756773 −0.378387 0.925648i \(-0.623521\pi\)
−0.378387 + 0.925648i \(0.623521\pi\)
\(420\) 10.0830 7.32573i 0.492000 0.357459i
\(421\) −27.5394 + 8.94810i −1.34219 + 0.436104i −0.890058 0.455848i \(-0.849336\pi\)
−0.452131 + 0.891951i \(0.649336\pi\)
\(422\) 60.4835 + 19.6523i 2.94429 + 0.956658i
\(423\) −4.62110 + 6.36040i −0.224686 + 0.309253i
\(424\) 49.7025 68.4097i 2.41377 3.32227i
\(425\) 2.98260 9.17949i 0.144677 0.445271i
\(426\) 4.50596 + 13.8679i 0.218314 + 0.671903i
\(427\) −1.88196 2.59029i −0.0910743 0.125353i
\(428\) 9.25303 0.447262
\(429\) 10.0835 + 6.42831i 0.486836 + 0.310362i
\(430\) −32.5585 −1.57011
\(431\) 10.5105 + 14.4665i 0.506275 + 0.696828i 0.983286 0.182070i \(-0.0582796\pi\)
−0.477010 + 0.878898i \(0.658280\pi\)
\(432\) −4.22032 12.9888i −0.203050 0.624925i
\(433\) −4.41656 + 13.5928i −0.212246 + 0.653227i 0.787091 + 0.616837i \(0.211586\pi\)
−0.999338 + 0.0363908i \(0.988414\pi\)
\(434\) 32.2085 44.3312i 1.54606 2.12797i
\(435\) 4.34718 5.98339i 0.208432 0.286881i
\(436\) 4.17695 + 1.35717i 0.200039 + 0.0649968i
\(437\) 2.21871 0.720903i 0.106135 0.0344855i
\(438\) 16.1147 11.7080i 0.769989 0.559430i
\(439\) −10.3624 −0.494569 −0.247285 0.968943i \(-0.579538\pi\)
−0.247285 + 0.968943i \(0.579538\pi\)
\(440\) 31.9357 + 17.0298i 1.52247 + 0.811866i
\(441\) 3.28218 0.156294
\(442\) 17.3358 20.3344i 0.824582 0.967208i
\(443\) 6.34510 + 19.5282i 0.301465 + 0.927814i 0.980973 + 0.194146i \(0.0621934\pi\)
−0.679508 + 0.733668i \(0.737807\pi\)
\(444\) −12.7181 4.13235i −0.603572 0.196112i
\(445\) −7.64795 5.55656i −0.362548 0.263406i
\(446\) 12.8494 + 9.33564i 0.608437 + 0.442055i
\(447\) −4.19800 1.36401i −0.198559 0.0645156i
\(448\) −44.1144 + 14.3336i −2.08421 + 0.677200i
\(449\) −8.80796 12.1231i −0.415673 0.572125i 0.548917 0.835877i \(-0.315040\pi\)
−0.964591 + 0.263751i \(0.915040\pi\)
\(450\) 9.53246i 0.449365i
\(451\) −0.680520 4.88482i −0.0320444 0.230017i
\(452\) 71.8619 3.38010
\(453\) 7.30424 + 10.0534i 0.343183 + 0.472351i
\(454\) −7.57572 23.3157i −0.355546 1.09426i
\(455\) 8.42229 + 0.655287i 0.394843 + 0.0307203i
\(456\) 17.1818 + 12.4833i 0.804614 + 0.584586i
\(457\) 8.19652 11.2815i 0.383417 0.527728i −0.573069 0.819507i \(-0.694247\pi\)
0.956486 + 0.291779i \(0.0942472\pi\)
\(458\) 17.8500 54.9365i 0.834074 2.56702i
\(459\) −0.846501 2.60526i −0.0395113 0.121603i
\(460\) −3.74789 5.15853i −0.174746 0.240518i
\(461\) 23.0055i 1.07147i 0.844386 + 0.535736i \(0.179966\pi\)
−0.844386 + 0.535736i \(0.820034\pi\)
\(462\) −7.56566 15.5594i −0.351986 0.723890i
\(463\) 13.5304i 0.628811i −0.949289 0.314405i \(-0.898195\pi\)
0.949289 0.314405i \(-0.101805\pi\)
\(464\) −67.2489 + 48.8592i −3.12195 + 2.26823i
\(465\) 3.94437 + 12.1395i 0.182916 + 0.562956i
\(466\) 2.34438 + 0.761736i 0.108601 + 0.0352867i
\(467\) 24.3851 + 17.7168i 1.12841 + 0.819835i 0.985462 0.169895i \(-0.0543429\pi\)
0.142945 + 0.989731i \(0.454343\pi\)
\(468\) 7.32382 17.7260i 0.338544 0.819384i
\(469\) −9.08801 + 27.9700i −0.419645 + 1.29154i
\(470\) −24.5808 + 7.98679i −1.13383 + 0.368403i
\(471\) 10.2619 7.45574i 0.472845 0.343542i
\(472\) −34.5570 −1.59061
\(473\) −5.74280 + 32.3413i −0.264054 + 1.48705i
\(474\) 9.82144i 0.451114i
\(475\) 4.89779 + 6.74123i 0.224726 + 0.309309i
\(476\) −26.7214 + 8.68230i −1.22477 + 0.397952i
\(477\) 2.90967 8.95505i 0.133225 0.410024i
\(478\) 1.48754 + 1.08076i 0.0680383 + 0.0494328i
\(479\) 7.77481 10.7011i 0.355240 0.488946i −0.593575 0.804779i \(-0.702284\pi\)
0.948815 + 0.315833i \(0.102284\pi\)
\(480\) 7.12994 21.9437i 0.325436 1.00159i
\(481\) −4.74286 7.72416i −0.216256 0.352191i
\(482\) 20.5206 14.9091i 0.934686 0.679089i
\(483\) 1.90206i 0.0865468i
\(484\) 36.1354 46.0223i 1.64252 2.09192i
\(485\) 1.39221 0.0632168
\(486\) −1.59022 2.18875i −0.0721337 0.0992836i
\(487\) 18.3774 5.97117i 0.832759 0.270580i 0.138552 0.990355i \(-0.455755\pi\)
0.694207 + 0.719775i \(0.255755\pi\)
\(488\) −14.1825 4.60816i −0.642009 0.208601i
\(489\) −14.1077 + 19.4176i −0.637972 + 0.878094i
\(490\) 8.72937 + 6.34226i 0.394353 + 0.286514i
\(491\) −7.17345 + 22.0776i −0.323733 + 0.996348i 0.648276 + 0.761405i \(0.275490\pi\)
−0.972009 + 0.234943i \(0.924510\pi\)
\(492\) −7.52308 + 2.44440i −0.339166 + 0.110202i
\(493\) −13.4886 + 9.80005i −0.607496 + 0.441372i
\(494\) 5.40530 + 22.4265i 0.243196 + 1.00902i
\(495\) 3.96808 + 0.704607i 0.178352 + 0.0316697i
\(496\) 143.461i 6.44158i
\(497\) 8.40754 6.10844i 0.377130 0.274001i
\(498\) 11.1457 + 34.3030i 0.499451 + 1.53715i
\(499\) −28.1973 9.16187i −1.26229 0.410142i −0.399978 0.916525i \(-0.630982\pi\)
−0.862309 + 0.506383i \(0.830982\pi\)
\(500\) 32.3834 44.5719i 1.44823 1.99331i
\(501\) −7.60357 + 10.4654i −0.339702 + 0.467560i
\(502\) −76.0207 24.7006i −3.39297 1.10244i
\(503\) −8.98394 27.6497i −0.400574 1.23284i −0.924535 0.381098i \(-0.875546\pi\)
0.523961 0.851742i \(-0.324454\pi\)
\(504\) −14.0088 + 10.1780i −0.624000 + 0.453363i
\(505\) 13.3440i 0.593801i
\(506\) −7.96030 + 3.87064i −0.353878 + 0.172071i
\(507\) 11.5725 5.92254i 0.513954 0.263029i
\(508\) −96.3314 + 69.9889i −4.27402 + 3.10525i
\(509\) 15.1280 4.91539i 0.670537 0.217871i 0.0460894 0.998937i \(-0.485324\pi\)
0.624448 + 0.781067i \(0.285324\pi\)
\(510\) 2.78285 8.56474i 0.123227 0.379253i
\(511\) −11.4849 8.34429i −0.508063 0.369130i
\(512\) −8.24494 + 11.3482i −0.364378 + 0.501524i
\(513\) 2.24916 + 0.730797i 0.0993029 + 0.0322655i
\(514\) −10.3260 + 3.35512i −0.455460 + 0.147988i
\(515\) 10.5853 + 14.5694i 0.466442 + 0.642003i
\(516\) 52.6823 2.31921
\(517\) 3.59784 + 25.8255i 0.158233 + 1.13581i
\(518\) 13.1139i 0.576194i
\(519\) −12.0821 + 8.77813i −0.530344 + 0.385317i
\(520\) 33.5292 20.5879i 1.47035 0.902838i
\(521\) 9.01842 27.7558i 0.395104 1.21601i −0.533776 0.845626i \(-0.679228\pi\)
0.928880 0.370380i \(-0.120772\pi\)
\(522\) −9.67879 + 13.3217i −0.423629 + 0.583075i
\(523\) 20.2593 + 14.7193i 0.885879 + 0.643629i 0.934800 0.355174i \(-0.115578\pi\)
−0.0489215 + 0.998803i \(0.515578\pi\)
\(524\) −29.0440 + 89.3882i −1.26879 + 3.90494i
\(525\) −6.46127 + 2.09939i −0.281993 + 0.0916251i
\(526\) 29.7657 + 40.9690i 1.29785 + 1.78633i
\(527\) 28.7750i 1.25346i
\(528\) −39.9683 21.3133i −1.73940 0.927543i
\(529\) −22.0269 −0.957691
\(530\) 25.0428 18.1946i 1.08779 0.790324i
\(531\) −3.65969 + 1.18911i −0.158817 + 0.0516028i
\(532\) 7.49555 23.0689i 0.324973 1.00017i
\(533\) −4.95534 2.04739i −0.214640 0.0886823i
\(534\) 17.0278 + 12.3714i 0.736864 + 0.535363i
\(535\) 2.01026 + 0.653173i 0.0869111 + 0.0282391i
\(536\) 42.3275 + 130.271i 1.82827 + 5.62684i
\(537\) 5.30068 3.85117i 0.228741 0.166190i
\(538\) 47.4342i 2.04503i
\(539\) 7.83966 7.55245i 0.337678 0.325307i
\(540\) 6.46380i 0.278158i
\(541\) 15.2004 + 20.9216i 0.653516 + 0.899488i 0.999245 0.0388464i \(-0.0123683\pi\)
−0.345729 + 0.938334i \(0.612368\pi\)
\(542\) 14.5701 + 44.8421i 0.625839 + 1.92613i
\(543\) −0.564949 + 1.73873i −0.0242443 + 0.0746162i
\(544\) −30.5733 + 42.0806i −1.31082 + 1.80419i
\(545\) 0.811657 + 0.589703i 0.0347676 + 0.0252601i
\(546\) −18.7518 1.45896i −0.802504 0.0624379i
\(547\) −7.36010 22.6521i −0.314695 0.968532i −0.975880 0.218309i \(-0.929946\pi\)
0.661185 0.750223i \(-0.270054\pi\)
\(548\) −9.30880 12.8125i −0.397652 0.547321i
\(549\) −1.66053 −0.0708697
\(550\) −21.9346 22.7688i −0.935297 0.970864i
\(551\) 14.3939i 0.613201i
\(552\) 5.20711 + 7.16697i 0.221629 + 0.305047i
\(553\) −6.65714 + 2.16304i −0.283091 + 0.0919817i
\(554\) 58.1932 + 18.9081i 2.47239 + 0.803328i
\(555\) −2.47135 1.79554i −0.104903 0.0762164i
\(556\) 13.5886 + 9.87272i 0.576287 + 0.418697i
\(557\) 20.9212 + 6.79771i 0.886459 + 0.288028i 0.716637 0.697447i \(-0.245681\pi\)
0.169822 + 0.985475i \(0.445681\pi\)
\(558\) −8.78193 27.0280i −0.371769 1.14419i
\(559\) 27.1738 + 23.1667i 1.14933 + 0.979846i
\(560\) −31.9987 −1.35219
\(561\) −8.01674 4.27497i −0.338467 0.180489i
\(562\) 20.1120 0.848372
\(563\) −18.5761 + 13.4963i −0.782889 + 0.568802i −0.905845 0.423610i \(-0.860763\pi\)
0.122956 + 0.992412i \(0.460763\pi\)
\(564\) 39.7737 12.9233i 1.67478 0.544168i
\(565\) 15.6123 + 5.07274i 0.656814 + 0.213412i
\(566\) −14.0871 + 19.3893i −0.592127 + 0.814992i
\(567\) −1.13335 + 1.55992i −0.0475961 + 0.0655104i
\(568\) 14.9571 46.0332i 0.627586 1.93151i
\(569\) 0.302125 + 0.929846i 0.0126658 + 0.0389812i 0.957190 0.289462i \(-0.0934762\pi\)
−0.944524 + 0.328443i \(0.893476\pi\)
\(570\) 4.56978 + 6.28977i 0.191407 + 0.263449i
\(571\) −22.7151 −0.950596 −0.475298 0.879825i \(-0.657660\pi\)
−0.475298 + 0.879825i \(0.657660\pi\)
\(572\) −23.2950 59.1919i −0.974013 2.47494i
\(573\) −21.5949 −0.902139
\(574\) 4.55960 + 6.27575i 0.190314 + 0.261945i
\(575\) 1.07406 + 3.30563i 0.0447915 + 0.137854i
\(576\) −7.43381 + 22.8789i −0.309742 + 0.953289i
\(577\) −9.68501 + 13.3303i −0.403192 + 0.554946i −0.961542 0.274659i \(-0.911435\pi\)
0.558349 + 0.829606i \(0.311435\pi\)
\(578\) 15.1008 20.7844i 0.628110 0.864519i
\(579\) 9.48685 + 3.08246i 0.394260 + 0.128103i
\(580\) −37.4161 + 12.1572i −1.55362 + 0.504802i
\(581\) 20.7965 15.1095i 0.862782 0.626848i
\(582\) −3.09967 −0.128486
\(583\) −13.6561 28.0849i −0.565577 1.16316i
\(584\) −66.1187 −2.73601
\(585\) 2.84241 3.33406i 0.117519 0.137846i
\(586\) 25.4059 + 78.1912i 1.04951 + 3.23005i
\(587\) −13.8937 4.51434i −0.573455 0.186327i 0.00791126 0.999969i \(-0.497482\pi\)
−0.581367 + 0.813642i \(0.697482\pi\)
\(588\) −14.1248 10.2623i −0.582498 0.423209i
\(589\) 20.0975 + 14.6017i 0.828102 + 0.601652i
\(590\) −12.0311 3.90916i −0.495315 0.160937i
\(591\) −0.955893 + 0.310588i −0.0393202 + 0.0127759i
\(592\) 20.1806 + 27.7762i 0.829416 + 1.14159i
\(593\) 37.8274i 1.55339i −0.629879 0.776694i \(-0.716895\pi\)
0.629879 0.776694i \(-0.283105\pi\)
\(594\) −8.83473 1.56877i −0.362493 0.0643674i
\(595\) −6.41822 −0.263121
\(596\) 13.8012 + 18.9958i 0.565321 + 0.778097i
\(597\) −3.96112 12.1911i −0.162118 0.498947i
\(598\) −0.746415 + 9.59355i −0.0305232 + 0.392309i
\(599\) 21.7624 + 15.8113i 0.889187 + 0.646032i 0.935666 0.352887i \(-0.114800\pi\)
−0.0464790 + 0.998919i \(0.514800\pi\)
\(600\) −18.5988 + 25.5990i −0.759291 + 1.04507i
\(601\) 5.84273 17.9821i 0.238330 0.733505i −0.758332 0.651868i \(-0.773985\pi\)
0.996662 0.0816361i \(-0.0260145\pi\)
\(602\) −15.9649 49.1349i −0.650681 2.00259i
\(603\) 8.96522 + 12.3396i 0.365092 + 0.502506i
\(604\) 66.1028i 2.68968i
\(605\) 11.0993 7.44775i 0.451251 0.302794i
\(606\) 29.7098i 1.20688i
\(607\) 26.5175 19.2661i 1.07631 0.781986i 0.0992754 0.995060i \(-0.468348\pi\)
0.977036 + 0.213074i \(0.0683475\pi\)
\(608\) −13.8763 42.7070i −0.562760 1.73200i
\(609\) 11.1613 + 3.62653i 0.452279 + 0.146954i
\(610\) −4.41639 3.20870i −0.178814 0.129916i
\(611\) 26.1984 + 10.8243i 1.05987 + 0.437906i
\(612\) −4.50288 + 13.8584i −0.182018 + 0.560194i
\(613\) −1.93861 + 0.629893i −0.0782998 + 0.0254412i −0.347905 0.937530i \(-0.613107\pi\)
0.269605 + 0.962971i \(0.413107\pi\)
\(614\) −35.0183 + 25.4423i −1.41322 + 1.02677i
\(615\) −1.80697 −0.0728641
\(616\) −10.0407 + 56.5454i −0.404551 + 2.27828i
\(617\) 23.8751i 0.961176i −0.876947 0.480588i \(-0.840423\pi\)
0.876947 0.480588i \(-0.159577\pi\)
\(618\) −23.5675 32.4379i −0.948026 1.30485i
\(619\) −13.6125 + 4.42298i −0.547134 + 0.177775i −0.569524 0.821975i \(-0.692872\pi\)
0.0223901 + 0.999749i \(0.492872\pi\)
\(620\) 20.9817 64.5750i 0.842645 2.59339i
\(621\) 0.798064 + 0.579828i 0.0320252 + 0.0232677i
\(622\) −44.6774 + 61.4931i −1.79140 + 2.46565i
\(623\) 4.63542 14.2664i 0.185714 0.571569i
\(624\) −41.9627 + 25.7663i −1.67985 + 1.03148i
\(625\) −4.07087 + 2.95766i −0.162835 + 0.118306i
\(626\) 20.3582i 0.813677i
\(627\) 7.05383 3.42988i 0.281703 0.136976i
\(628\) −67.4738 −2.69250
\(629\) 4.04776 + 5.57127i 0.161395 + 0.222141i
\(630\) −6.02856 + 1.95880i −0.240184 + 0.0780404i
\(631\) 16.7634 + 5.44675i 0.667339 + 0.216832i 0.623044 0.782187i \(-0.285896\pi\)
0.0442953 + 0.999018i \(0.485896\pi\)
\(632\) −19.1626 + 26.3750i −0.762247 + 1.04914i
\(633\) −19.0174 13.8169i −0.755873 0.549174i
\(634\) 7.58020 23.3294i 0.301048 0.926531i
\(635\) −25.8689 + 8.40533i −1.02658 + 0.333555i
\(636\) −40.5212 + 29.4404i −1.60677 + 1.16739i
\(637\) −2.77288 11.5046i −0.109865 0.455830i
\(638\) 7.53558 + 54.0909i 0.298337 + 2.14148i
\(639\) 5.38973i 0.213214i
\(640\) −26.6480 + 19.3609i −1.05335 + 0.765306i
\(641\) −11.8328 36.4177i −0.467369 1.43841i −0.855978 0.517012i \(-0.827044\pi\)
0.388609 0.921403i \(-0.372956\pi\)
\(642\) −4.47574 1.45426i −0.176643 0.0573949i
\(643\) 1.78417 2.45570i 0.0703608 0.0968433i −0.772386 0.635153i \(-0.780937\pi\)
0.842747 + 0.538310i \(0.180937\pi\)
\(644\) 5.94711 8.18550i 0.234349 0.322554i
\(645\) 11.4455 + 3.71885i 0.450664 + 0.146430i
\(646\) −5.41601 16.6688i −0.213090 0.655824i
\(647\) −16.1606 + 11.7414i −0.635338 + 0.461600i −0.858246 0.513239i \(-0.828445\pi\)
0.222907 + 0.974840i \(0.428445\pi\)
\(648\) 8.98045i 0.352785i
\(649\) −6.00517 + 11.2614i −0.235724 + 0.442047i
\(650\) −33.4130 + 8.05329i −1.31056 + 0.315876i
\(651\) −16.3860 + 11.9051i −0.642216 + 0.466597i
\(652\) 121.425 39.4533i 4.75536 1.54511i
\(653\) −6.53137 + 20.1015i −0.255592 + 0.786632i 0.738120 + 0.674669i \(0.235714\pi\)
−0.993712 + 0.111963i \(0.964286\pi\)
\(654\) −1.80711 1.31294i −0.0706637 0.0513402i
\(655\) −12.6199 + 17.3698i −0.493099 + 0.678692i
\(656\) 19.3151 + 6.27584i 0.754126 + 0.245030i
\(657\) −7.00217 + 2.27514i −0.273181 + 0.0887618i
\(658\) −24.1062 33.1793i −0.939756 1.29346i
\(659\) −17.7965 −0.693253 −0.346626 0.938003i \(-0.612673\pi\)
−0.346626 + 0.938003i \(0.612673\pi\)
\(660\) −14.8735 15.4391i −0.578951 0.600967i
\(661\) 15.2744i 0.594105i 0.954861 + 0.297052i \(0.0960036\pi\)
−0.954861 + 0.297052i \(0.903996\pi\)
\(662\) −59.0109 + 42.8739i −2.29352 + 1.66634i
\(663\) −8.41676 + 5.16813i −0.326880 + 0.200714i
\(664\) 36.9971 113.865i 1.43577 4.41883i
\(665\) 3.25688 4.48271i 0.126296 0.173832i
\(666\) 5.50233 + 3.99768i 0.213211 + 0.154907i
\(667\) 1.85535 5.71019i 0.0718396 0.221100i
\(668\) 65.4437 21.2640i 2.53209 0.822727i
\(669\) −3.45069 4.74947i −0.133411 0.183625i
\(670\) 50.1424i 1.93717i
\(671\) −3.96626 + 3.82096i −0.153116 + 0.147507i
\(672\) 36.6120 1.41234
\(673\) 26.0932 18.9578i 1.00582 0.730770i 0.0424907 0.999097i \(-0.486471\pi\)
0.963328 + 0.268327i \(0.0864707\pi\)
\(674\) −41.3689 + 13.4416i −1.59347 + 0.517749i
\(675\) −1.08880 + 3.35099i −0.0419081 + 0.128980i
\(676\) −68.3201 10.6959i −2.62770 0.411380i
\(677\) 5.39787 + 3.92178i 0.207457 + 0.150726i 0.686662 0.726976i \(-0.259075\pi\)
−0.479205 + 0.877703i \(0.659075\pi\)
\(678\) −34.7600 11.2942i −1.33495 0.433751i
\(679\) 0.682661 + 2.10101i 0.0261981 + 0.0806295i
\(680\) −24.1839 + 17.5706i −0.927409 + 0.673802i
\(681\) 9.06157i 0.347240i
\(682\) −83.1688 44.3502i −3.18470 1.69826i
\(683\) 40.8610i 1.56350i −0.623591 0.781751i \(-0.714327\pi\)
0.623591 0.781751i \(-0.285673\pi\)
\(684\) −7.39428 10.1774i −0.282727 0.389141i
\(685\) −1.11794 3.44067i −0.0427144 0.131461i
\(686\) −16.5749 + 51.0121i −0.632831 + 1.94765i
\(687\) −12.5498 + 17.2733i −0.478804 + 0.659017i
\(688\) −109.427 79.5031i −4.17185 3.03103i
\(689\) −33.8472 2.63344i −1.28948 0.100326i
\(690\) 1.00213 + 3.08425i 0.0381506 + 0.117415i
\(691\) −0.617164 0.849453i −0.0234780 0.0323147i 0.797117 0.603825i \(-0.206358\pi\)
−0.820595 + 0.571511i \(0.806358\pi\)
\(692\) 79.4413 3.01991
\(693\) 0.882387 + 6.33383i 0.0335191 + 0.240602i
\(694\) 6.42299i 0.243813i
\(695\) 2.25527 + 3.10412i 0.0855474 + 0.117746i
\(696\) 51.9839 16.8906i 1.97044 0.640236i
\(697\) 3.87416 + 1.25879i 0.146744 + 0.0476801i
\(698\) 25.2178 + 18.3218i 0.954509 + 0.693491i
\(699\) −0.737126 0.535553i −0.0278807 0.0202565i
\(700\) 34.3701 + 11.1675i 1.29907 + 0.422093i
\(701\) −10.8894 33.5141i −0.411287 1.26581i −0.915530 0.402250i \(-0.868228\pi\)
0.504243 0.863562i \(-0.331772\pi\)
\(702\) −6.32849 + 7.42311i −0.238853 + 0.280167i
\(703\) −5.94519 −0.224227
\(704\) 34.8894 + 71.7531i 1.31494 + 2.70430i
\(705\) 9.55327 0.359797
\(706\) 44.6048 32.4073i 1.67872 1.21966i
\(707\) 20.1378 6.54317i 0.757361 0.246081i
\(708\) 19.4674 + 6.32533i 0.731628 + 0.237720i
\(709\) 18.8227 25.9073i 0.706903 0.972969i −0.292955 0.956126i \(-0.594639\pi\)
0.999858 0.0168424i \(-0.00536135\pi\)
\(710\) 10.4147 14.3347i 0.390858 0.537970i
\(711\) −1.12181 + 3.45258i −0.0420712 + 0.129482i
\(712\) −21.5895 66.4457i −0.809101 2.49016i
\(713\) 6.09072 + 8.38316i 0.228099 + 0.313952i
\(714\) 14.2898 0.534784
\(715\) −0.882572 14.5041i −0.0330063 0.542422i
\(716\) −34.8527 −1.30251
\(717\) −0.399476 0.549832i −0.0149187 0.0205338i
\(718\) −5.35102 16.4687i −0.199698 0.614608i
\(719\) 5.25397 16.1701i 0.195940 0.603042i −0.804024 0.594597i \(-0.797312\pi\)
0.999964 0.00844517i \(-0.00268821\pi\)
\(720\) −9.75455 + 13.4260i −0.363530 + 0.500357i
\(721\) −16.7966 + 23.1185i −0.625537 + 0.860978i
\(722\) −34.4971 11.2088i −1.28385 0.417148i
\(723\) −8.91662 + 2.89718i −0.331613 + 0.107747i
\(724\) 7.86770 5.71622i 0.292401 0.212441i
\(725\) 21.4453 0.796458
\(726\) −24.7120 + 16.5820i −0.917149 + 0.615417i
\(727\) 36.1247 1.33979 0.669896 0.742455i \(-0.266339\pi\)
0.669896 + 0.742455i \(0.266339\pi\)
\(728\) 47.5106 + 40.5046i 1.76086 + 1.50120i
\(729\) 0.309017 + 0.951057i 0.0114451 + 0.0352243i
\(730\) −23.0195 7.47948i −0.851989 0.276828i
\(731\) −21.9485 15.9465i −0.811794 0.589803i
\(732\) 7.14608 + 5.19193i 0.264127 + 0.191899i
\(733\) −7.13510 2.31833i −0.263541 0.0856297i 0.174266 0.984699i \(-0.444245\pi\)
−0.437807 + 0.899069i \(0.644245\pi\)
\(734\) 57.3199 18.6244i 2.11572 0.687438i
\(735\) −2.34426 3.22660i −0.0864694 0.119015i
\(736\) 18.7309i 0.690431i
\(737\) 49.8078 + 8.84431i 1.83469 + 0.325784i
\(738\) 4.02313 0.148093
\(739\) −11.6254 16.0010i −0.427647 0.588606i 0.539764 0.841816i \(-0.318513\pi\)
−0.967411 + 0.253211i \(0.918513\pi\)
\(740\) 5.02136 + 15.4542i 0.184589 + 0.568107i
\(741\) 0.661419 8.50110i 0.0242978 0.312296i
\(742\) 39.7376 + 28.8711i 1.45881 + 1.05989i
\(743\) 28.5645 39.3157i 1.04793 1.44235i 0.157341 0.987544i \(-0.449708\pi\)
0.890590 0.454808i \(-0.150292\pi\)
\(744\) −29.1508 + 89.7169i −1.06872 + 3.28918i
\(745\) 1.65746 + 5.10114i 0.0607247 + 0.186891i
\(746\) 27.5993 + 37.9872i 1.01048 + 1.39081i
\(747\) 13.3318i 0.487783i
\(748\) 21.1336 + 43.4630i 0.772720 + 1.58916i
\(749\) 3.35402i 0.122553i
\(750\) −22.6692 + 16.4701i −0.827761 + 0.601404i
\(751\) 6.12412 + 18.8481i 0.223472 + 0.687778i 0.998443 + 0.0557802i \(0.0177646\pi\)
−0.774971 + 0.631997i \(0.782235\pi\)
\(752\) −102.117 33.1797i −3.72381 1.20994i
\(753\) 23.9026 + 17.3663i 0.871059 + 0.632861i
\(754\) 54.8718 + 22.6713i 1.99831 + 0.825641i
\(755\) 4.66621 14.3611i 0.169821 0.522654i
\(756\) 9.75469 3.16949i 0.354775 0.115273i
\(757\) −13.3834 + 9.72364i −0.486429 + 0.353412i −0.803809 0.594887i \(-0.797197\pi\)
0.317380 + 0.948298i \(0.397197\pi\)
\(758\) −71.6827 −2.60363
\(759\) 3.24043 0.451435i 0.117620 0.0163860i
\(760\) 25.8070i 0.936117i
\(761\) 19.8624 + 27.3383i 0.720012 + 0.991012i 0.999523 + 0.0308697i \(0.00982768\pi\)
−0.279511 + 0.960143i \(0.590172\pi\)
\(762\) 57.5959 18.7140i 2.08648 0.677938i
\(763\) −0.491945 + 1.51405i −0.0178096 + 0.0548123i
\(764\) 92.9333 + 67.5200i 3.36221 + 2.44279i
\(765\) −1.95654 + 2.69295i −0.0707389 + 0.0973637i
\(766\) 18.5483 57.0857i 0.670176 2.06259i
\(767\) 7.25983 + 11.8233i 0.262137 + 0.426914i
\(768\) 20.4064 14.8261i 0.736352 0.534991i
\(769\) 7.92037i 0.285616i −0.989750 0.142808i \(-0.954387\pi\)
0.989750 0.142808i \(-0.0456131\pi\)
\(770\) −9.89224 + 18.5507i −0.356492 + 0.668520i
\(771\) 4.01317 0.144531
\(772\) −31.1887 42.9276i −1.12251 1.54500i
\(773\) −37.2174 + 12.0927i −1.33862 + 0.434944i −0.888849 0.458201i \(-0.848494\pi\)
−0.449770 + 0.893144i \(0.648494\pi\)
\(774\) −25.4827 8.27984i −0.915958 0.297613i
\(775\) −21.7548 + 29.9430i −0.781457 + 1.07558i
\(776\) 8.32404 + 6.04777i 0.298815 + 0.217102i
\(777\) 1.49788 4.61001i 0.0537363 0.165383i
\(778\) 7.11123 2.31058i 0.254950 0.0828383i
\(779\) −2.84510 + 2.06709i −0.101936 + 0.0740611i
\(780\) −22.6568 + 5.46080i −0.811242 + 0.195528i
\(781\) −12.4020 12.8737i −0.443779 0.460656i
\(782\) 7.31077i 0.261433i
\(783\) 4.92404 3.57753i 0.175971 0.127850i
\(784\) 13.8519 + 42.6316i 0.494709 + 1.52256i
\(785\) −14.6590 4.76299i −0.523201 0.169998i
\(786\) 28.0975 38.6729i 1.00220 1.37942i
\(787\) 26.5689 36.5690i 0.947080 1.30354i −0.00573165 0.999984i \(-0.501824\pi\)
0.952812 0.303561i \(-0.0981755\pi\)
\(788\) 5.08478 + 1.65214i 0.181138 + 0.0588552i
\(789\) −5.78418 17.8019i −0.205922 0.633764i
\(790\) −9.65513 + 7.01486i −0.343514 + 0.249577i
\(791\) 26.0483i 0.926172i
\(792\) 20.6644 + 21.4503i 0.734279 + 0.762202i
\(793\) 1.40286 + 5.82045i 0.0498171 + 0.206690i
\(794\) −24.0833 + 17.4975i −0.854684 + 0.620964i
\(795\) −10.8816 + 3.53565i −0.385931 + 0.125397i
\(796\) −21.0708 + 64.8493i −0.746835 + 2.29852i
\(797\) −14.3464 10.4233i −0.508176 0.369212i 0.303955 0.952686i \(-0.401693\pi\)
−0.812131 + 0.583475i \(0.801693\pi\)
\(798\) −7.25128 + 9.98054i −0.256693 + 0.353307i
\(799\) −20.4823 6.65510i −0.724611 0.235441i
\(800\) 63.6286 20.6742i 2.24961 0.730943i
\(801\) −4.57279 6.29390i −0.161572 0.222384i
\(802\) −0.00970673 −0.000342757
\(803\) −11.4898 + 21.5466i −0.405468 + 0.760364i
\(804\) 81.1345i 2.86139i
\(805\) 1.86985 1.35853i 0.0659036 0.0478818i
\(806\) −87.3188 + 53.6162i −3.07567 + 1.88855i
\(807\) 5.41796 16.6748i 0.190721 0.586980i
\(808\) 57.9667 79.7843i 2.03926 2.80680i
\(809\) −24.9891 18.1557i −0.878570 0.638319i 0.0543025 0.998525i \(-0.482706\pi\)
−0.932873 + 0.360206i \(0.882706\pi\)
\(810\) −1.01589 + 3.12658i −0.0356946 + 0.109857i
\(811\) −27.4163 + 8.90809i −0.962716 + 0.312806i −0.747872 0.663843i \(-0.768924\pi\)
−0.214844 + 0.976648i \(0.568924\pi\)
\(812\) −36.6936 50.5044i −1.28769 1.77236i
\(813\) 17.4278i 0.611219i
\(814\) 22.3415 3.11246i 0.783068 0.109092i
\(815\) 29.1650 1.02161
\(816\) 30.2668 21.9901i 1.05955 0.769807i
\(817\) 22.2752 7.23766i 0.779312 0.253214i
\(818\) 9.03837 27.8172i 0.316019 0.972607i
\(819\) 6.42527 + 2.65472i 0.224517 + 0.0927634i
\(820\) 7.77628 + 5.64980i 0.271559 + 0.197299i
\(821\) −23.8589 7.75224i −0.832682 0.270555i −0.138508 0.990361i \(-0.544231\pi\)
−0.694175 + 0.719807i \(0.744231\pi\)
\(822\) 2.48904 + 7.66048i 0.0868153 + 0.267190i
\(823\) 26.1405 18.9922i 0.911201 0.662027i −0.0301170 0.999546i \(-0.509588\pi\)
0.941318 + 0.337520i \(0.109588\pi\)
\(824\) 133.093i 4.63652i
\(825\) 5.11013 + 10.5094i 0.177912 + 0.365891i
\(826\) 20.0734i 0.698441i
\(827\) −2.92957 4.03221i −0.101871 0.140214i 0.755038 0.655681i \(-0.227618\pi\)
−0.856909 + 0.515467i \(0.827618\pi\)
\(828\) −1.62153 4.99056i −0.0563521 0.173434i
\(829\) −6.03225 + 18.5653i −0.209509 + 0.644801i 0.789989 + 0.613120i \(0.210086\pi\)
−0.999498 + 0.0316807i \(0.989914\pi\)
\(830\) 25.7614 35.4575i 0.894190 1.23075i
\(831\) −18.2972 13.2937i −0.634724 0.461154i
\(832\) 86.4750 + 6.72809i 2.99798 + 0.233254i
\(833\) 2.77837 + 8.55094i 0.0962647 + 0.296272i
\(834\) −5.02125 6.91116i −0.173872 0.239314i
\(835\) 15.7190 0.543977
\(836\) −41.0802 7.29455i −1.42079 0.252287i
\(837\) 10.5044i 0.363084i
\(838\) −24.6337 33.9053i −0.850956 1.17124i
\(839\) −19.4056 + 6.30525i −0.669955 + 0.217681i −0.624192 0.781271i \(-0.714572\pi\)
−0.0457626 + 0.998952i \(0.514572\pi\)
\(840\) 20.0112 + 6.50204i 0.690453 + 0.224342i
\(841\) −6.50848 4.72868i −0.224430 0.163058i
\(842\) −63.3788 46.0474i −2.18418 1.58690i
\(843\) −7.07006 2.29720i −0.243506 0.0791198i
\(844\) 38.6401 + 118.922i 1.33005 + 4.09346i
\(845\) −14.0878 7.14645i −0.484635 0.245845i
\(846\) −21.2699 −0.731273
\(847\) 16.6821 + 13.0983i 0.573203 + 0.450062i
\(848\) 128.595 4.41598
\(849\) 7.16678 5.20697i 0.245963 0.178703i
\(850\) 24.8346 8.06924i 0.851819 0.276773i
\(851\) −2.35851 0.766327i −0.0808487 0.0262693i
\(852\) −16.8519 + 23.1946i −0.577336 + 0.794635i
\(853\) 11.0558 15.2170i 0.378543 0.521019i −0.576655 0.816988i \(-0.695642\pi\)
0.955198 + 0.295969i \(0.0956424\pi\)
\(854\) 2.67677 8.23826i 0.0915973 0.281907i
\(855\) −0.888017 2.73304i −0.0303696 0.0934679i
\(856\) 9.18200 + 12.6379i 0.313834 + 0.431956i
\(857\) 9.11688 0.311427 0.155713 0.987802i \(-0.450232\pi\)
0.155713 + 0.987802i \(0.450232\pi\)
\(858\) 1.96500 + 32.2926i 0.0670840 + 1.10245i
\(859\) −34.8274 −1.18829 −0.594147 0.804356i \(-0.702510\pi\)
−0.594147 + 0.804356i \(0.702510\pi\)
\(860\) −37.6278 51.7902i −1.28310 1.76603i
\(861\) −0.886039 2.72695i −0.0301961 0.0929341i
\(862\) −14.9495 + 46.0098i −0.509182 + 1.56710i
\(863\) −13.7470 + 18.9211i −0.467953 + 0.644082i −0.976134 0.217168i \(-0.930318\pi\)
0.508181 + 0.861250i \(0.330318\pi\)
\(864\) 11.1609 15.3616i 0.379700 0.522612i
\(865\) 17.2590 + 5.60778i 0.586823 + 0.190670i
\(866\) −36.7745 + 11.9487i −1.24965 + 0.406035i
\(867\) −7.68246 + 5.58164i −0.260910 + 0.189562i
\(868\) 107.740 3.65694
\(869\) 5.26504 + 10.8280i 0.178604 + 0.367315i
\(870\) 20.0091 0.678371
\(871\) 35.6783 41.8495i 1.20891 1.41802i
\(872\) 2.29124 + 7.05170i 0.0775911 + 0.238801i
\(873\) 1.08964 + 0.354047i 0.0368789 + 0.0119827i
\(874\) 5.10611 + 3.70980i 0.172717 + 0.125486i
\(875\) 16.1563 + 11.7382i 0.546183 + 0.396825i
\(876\) 37.2474 + 12.1024i 1.25847 + 0.408902i
\(877\) −35.4075 + 11.5046i −1.19563 + 0.388483i −0.838151 0.545439i \(-0.816363\pi\)
−0.357477 + 0.933922i \(0.616363\pi\)
\(878\) −16.4784 22.6806i −0.556120 0.765434i
\(879\) 30.3888i 1.02499i
\(880\) 7.59457 + 54.5143i 0.256013 + 1.83768i
\(881\) −12.2069 −0.411259 −0.205630 0.978630i \(-0.565924\pi\)
−0.205630 + 0.978630i \(0.565924\pi\)
\(882\) 5.21938 + 7.18386i 0.175746 + 0.241893i
\(883\) −10.5672 32.5225i −0.355615 1.09447i −0.955652 0.294498i \(-0.904848\pi\)
0.600037 0.799972i \(-0.295152\pi\)
\(884\) 52.3805 + 4.07540i 1.76175 + 0.137071i
\(885\) 3.78286 + 2.74841i 0.127160 + 0.0923868i
\(886\) −32.6522 + 44.9420i −1.09697 + 1.50985i
\(887\) 10.8775 33.4776i 0.365232 1.12407i −0.584604 0.811319i \(-0.698750\pi\)
0.949836 0.312749i \(-0.101250\pi\)
\(888\) −6.97641 21.4712i −0.234113 0.720525i
\(889\) −25.3694 34.9180i −0.850862 1.17111i
\(890\) 25.5756i 0.857295i
\(891\) 2.92653 + 1.56059i 0.0980424 + 0.0522816i
\(892\) 31.2285i 1.04561i
\(893\) 15.0418 10.9285i 0.503354 0.365708i
\(894\) −3.69026 11.3574i −0.123421 0.379850i
\(895\) −7.57190 2.46026i −0.253101 0.0822375i
\(896\) −42.2847 30.7216i −1.41263 1.02634i
\(897\) 1.35817 3.28721i 0.0453480 0.109757i
\(898\) 12.5279 38.5568i 0.418060 1.28666i
\(899\) 60.8052 19.7568i 2.02797 0.658926i
\(900\) 15.1631 11.0166i 0.505437 0.367221i
\(901\) 25.7933 0.859299
\(902\) 9.60946 9.25741i 0.319960 0.308238i
\(903\) 19.0962i 0.635480i
\(904\) 71.3103 + 98.1502i 2.37175 + 3.26443i
\(905\) 2.11280 0.686490i 0.0702318 0.0228197i
\(906\) −10.3891 + 31.9743i −0.345154 + 1.06227i
\(907\) −42.2606 30.7041i −1.40324 1.01951i −0.994263 0.106967i \(-0.965886\pi\)
−0.408976 0.912545i \(-0.634114\pi\)
\(908\) 28.3325 38.9964i 0.940248 1.29414i
\(909\) 3.39347 10.4440i 0.112554 0.346407i
\(910\) 11.9590 + 19.4763i 0.396438 + 0.645634i
\(911\) 19.2858 14.0119i 0.638966 0.464236i −0.220529 0.975380i \(-0.570778\pi\)
0.859495 + 0.511145i \(0.170778\pi\)
\(912\) 32.2981i 1.06950i
\(913\) −30.6770 31.8436i −1.01526 1.05387i
\(914\) 37.7267 1.24789
\(915\) 1.18602 + 1.63241i 0.0392085 + 0.0539659i
\(916\) 108.016 35.0964i 3.56894 1.15962i
\(917\) −32.4012 10.5278i −1.06998 0.347659i
\(918\) 4.35614 5.99571i 0.143774 0.197888i
\(919\) −43.4742 31.5859i −1.43408 1.04192i −0.989238 0.146314i \(-0.953259\pi\)
−0.444845 0.895608i \(-0.646741\pi\)
\(920\) 3.32649 10.2379i 0.109671 0.337533i
\(921\) 15.2162 4.94404i 0.501391 0.162912i
\(922\) −50.3531 + 36.5837i −1.65829 + 1.20482i
\(923\) −18.8920 + 4.55339i −0.621836 + 0.149877i
\(924\) 16.0064 30.0165i 0.526573 0.987470i
\(925\) 8.85765i 0.291238i
\(926\) 29.6146 21.5163i 0.973196 0.707069i
\(927\) 4.57973 + 14.0950i 0.150418 + 0.462940i
\(928\) −109.913 35.7129i −3.60807 1.17233i
\(929\) 7.71954 10.6250i 0.253270 0.348596i −0.663383 0.748280i \(-0.730880\pi\)
0.916653 + 0.399684i \(0.130880\pi\)
\(930\) −20.2979 + 27.9377i −0.665595 + 0.916113i
\(931\) −7.38215 2.39860i −0.241940 0.0786111i
\(932\) 1.49772 + 4.60949i 0.0490593 + 0.150989i
\(933\) 22.7294 16.5139i 0.744128 0.540641i
\(934\) 81.5463i 2.66828i
\(935\) 1.52330 + 10.9343i 0.0498172 + 0.357591i
\(936\) 31.4781 7.58693i 1.02889 0.247987i
\(937\) −24.2528 + 17.6207i −0.792305 + 0.575643i −0.908647 0.417566i \(-0.862883\pi\)
0.116342 + 0.993209i \(0.462883\pi\)
\(938\) −75.6712 + 24.5871i −2.47075 + 0.802796i
\(939\) 2.32532 7.15661i 0.0758841 0.233547i
\(940\) −41.1124 29.8699i −1.34094 0.974249i
\(941\) −10.3739 + 14.2784i −0.338178 + 0.465462i −0.943908 0.330208i \(-0.892881\pi\)
0.605730 + 0.795670i \(0.292881\pi\)
\(942\) 32.6374 + 10.6045i 1.06339 + 0.345515i
\(943\) −1.39512 + 0.453303i −0.0454315 + 0.0147616i
\(944\) −30.8901 42.5166i −1.00539 1.38380i
\(945\) 2.34298 0.0762173
\(946\) −79.9191 + 38.8601i −2.59840 + 1.26345i
\(947\) 31.6547i 1.02864i −0.857598 0.514320i \(-0.828044\pi\)
0.857598 0.514320i \(-0.171956\pi\)
\(948\) 15.6228 11.3506i 0.507404 0.368651i
\(949\) 13.8904 + 22.6217i 0.450902 + 0.734333i
\(950\) −6.96629 + 21.4400i −0.226016 + 0.695607i
\(951\) −5.32941 + 7.33530i −0.172818 + 0.237863i
\(952\) −38.3747 27.8809i −1.24373 0.903624i
\(953\) −9.06048 + 27.8853i −0.293498 + 0.903293i 0.690224 + 0.723596i \(0.257512\pi\)
−0.983722 + 0.179698i \(0.942488\pi\)
\(954\) 24.2274 7.87194i 0.784390 0.254864i
\(955\) 15.4239 + 21.2292i 0.499106 + 0.686960i
\(956\) 3.61522i 0.116925i
\(957\) 3.52928 19.8756i 0.114085 0.642486i
\(958\) 35.7857 1.15618
\(959\) 4.64423 3.37423i 0.149970 0.108960i
\(960\) 27.8010 9.03310i 0.897274 0.291542i
\(961\) −24.5179 + 75.4585i −0.790902 + 2.43414i
\(962\) 9.36405 22.6640i 0.301909 0.730717i
\(963\) 1.40727 + 1.02244i 0.0453487 + 0.0329478i
\(964\) 47.4311 + 15.4113i 1.52765 + 0.496364i
\(965\) −3.74561 11.5278i −0.120576 0.371093i
\(966\) −4.16313 + 3.02469i −0.133947 + 0.0973178i
\(967\) 35.5965i 1.14471i −0.820007 0.572353i \(-0.806031\pi\)
0.820007 0.572353i \(-0.193969\pi\)
\(968\) 98.7162 + 3.68526i 3.17286 + 0.118449i
\(969\) 6.47827i 0.208112i
\(970\) 2.21391 + 3.04718i 0.0710843 + 0.0978392i
\(971\) −4.13149 12.7154i −0.132586 0.408057i 0.862621 0.505851i \(-0.168821\pi\)
−0.995207 + 0.0977936i \(0.968821\pi\)
\(972\) 1.64379 5.05905i 0.0527245 0.162269i
\(973\) −3.57864 + 4.92558i −0.114726 + 0.157907i
\(974\) 42.2934 + 30.7280i 1.35517 + 0.984588i
\(975\) 12.6657 + 0.985439i 0.405626 + 0.0315593i
\(976\) −7.00798 21.5683i −0.224320 0.690386i
\(977\) 4.57595 + 6.29825i 0.146398 + 0.201499i 0.875918 0.482460i \(-0.160257\pi\)
−0.729520 + 0.683959i \(0.760257\pi\)
\(978\) −64.9345 −2.07638
\(979\) −25.4049 4.51112i −0.811944 0.144176i
\(980\) 21.2154i 0.677700i
\(981\) 0.485298 + 0.667955i 0.0154944 + 0.0213262i
\(982\) −59.7296 + 19.4073i −1.90605 + 0.619313i
\(983\) −26.3550 8.56326i −0.840594 0.273126i −0.143093 0.989709i \(-0.545705\pi\)
−0.697501 + 0.716584i \(0.745705\pi\)
\(984\) −10.8039 7.84952i −0.344417 0.250233i
\(985\) 0.988065 + 0.717871i 0.0314824 + 0.0228733i
\(986\) −42.8996 13.9389i −1.36620 0.443906i
\(987\) 4.68440 + 14.4171i 0.149106 + 0.458901i
\(988\) −29.4265 + 34.5164i −0.936183 + 1.09811i
\(989\) 9.76972 0.310659
\(990\) 4.76790 + 9.80560i 0.151534 + 0.311642i
\(991\) −26.5955 −0.844834 −0.422417 0.906402i \(-0.638818\pi\)
−0.422417 + 0.906402i \(0.638818\pi\)
\(992\) 161.364 117.238i 5.12331 3.72230i
\(993\) 25.6415 8.33141i 0.813707 0.264389i
\(994\) 26.7396 + 8.68823i 0.848130 + 0.275574i
\(995\) −9.15544 + 12.6014i −0.290247 + 0.399491i
\(996\) −41.6840 + 57.3731i −1.32081 + 1.81794i
\(997\) −5.63430 + 17.3406i −0.178440 + 0.549182i −0.999774 0.0212660i \(-0.993230\pi\)
0.821334 + 0.570448i \(0.193230\pi\)
\(998\) −24.7869 76.2862i −0.784616 2.41480i
\(999\) −1.47764 2.03380i −0.0467506 0.0643467i
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 429.2.bb.b.25.14 yes 56
11.4 even 5 inner 429.2.bb.b.103.1 yes 56
13.12 even 2 inner 429.2.bb.b.25.1 56
143.103 even 10 inner 429.2.bb.b.103.14 yes 56
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
429.2.bb.b.25.1 56 13.12 even 2 inner
429.2.bb.b.25.14 yes 56 1.1 even 1 trivial
429.2.bb.b.103.1 yes 56 11.4 even 5 inner
429.2.bb.b.103.14 yes 56 143.103 even 10 inner