Properties

Label 475.2.e.f.201.4
Level $475$
Weight $2$
Character 475.201
Analytic conductor $3.793$
Analytic rank $0$
Dimension $12$
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [475,2,Mod(26,475)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(475, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("475.26");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 475 = 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 475.e (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: \(3.79289409601\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 3 x^{11} + 17 x^{10} - 18 x^{9} + 109 x^{8} - 93 x^{7} + 484 x^{6} - 147 x^{5} + 1009 x^{4} + \cdots + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 201.4
Root \(1.62208 + 2.80952i\) of defining polynomial
Character \(\chi\) \(=\) 475.201
Dual form 475.2.e.f.26.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.155554 + 0.269427i) q^{2} +(1.12208 - 1.94349i) q^{3} +(0.951606 + 1.64823i) q^{4} +(0.349087 + 0.604636i) q^{6} +3.96928 q^{7} -1.21432 q^{8} +(-1.01811 - 1.76343i) q^{9} +O(q^{10})\) \(q+(-0.155554 + 0.269427i) q^{2} +(1.12208 - 1.94349i) q^{3} +(0.951606 + 1.64823i) q^{4} +(0.349087 + 0.604636i) q^{6} +3.96928 q^{7} -1.21432 q^{8} +(-1.01811 - 1.76343i) q^{9} +0.361495 q^{11} +4.27110 q^{12} +(-1.25807 - 2.17905i) q^{13} +(-0.617436 + 1.06943i) q^{14} +(-1.71432 + 2.96929i) q^{16} +(-0.00464089 + 0.00803826i) q^{17} +0.633487 q^{18} +(-3.45680 + 2.65529i) q^{19} +(4.45383 - 7.71427i) q^{21} +(-0.0562320 + 0.0973967i) q^{22} +(2.70404 + 4.68354i) q^{23} +(-1.36256 + 2.36002i) q^{24} +0.782793 q^{26} +2.16285 q^{27} +(3.77719 + 6.54228i) q^{28} +(-4.72735 - 8.18801i) q^{29} +3.66745 q^{31} +(-1.74766 - 3.02703i) q^{32} +(0.405626 - 0.702564i) q^{33} +(-0.00144382 - 0.00250076i) q^{34} +(1.93769 - 3.35617i) q^{36} +0.0596692 q^{37} +(-0.177689 - 1.34440i) q^{38} -5.64662 q^{39} +(-1.85906 + 3.21998i) q^{41} +(1.38562 + 2.39997i) q^{42} +(2.10671 - 3.64894i) q^{43} +(0.344001 + 0.595827i) q^{44} -1.68250 q^{46} +(-6.45659 - 11.1831i) q^{47} +(3.84720 + 6.66354i) q^{48} +8.75515 q^{49} +(0.0104149 + 0.0180391i) q^{51} +(2.39438 - 4.14719i) q^{52} +(-5.48564 - 9.50140i) q^{53} +(-0.336440 + 0.582731i) q^{54} -4.81997 q^{56} +(1.28175 + 9.69770i) q^{57} +2.94143 q^{58} +(2.65944 - 4.60629i) q^{59} +(4.44875 + 7.70546i) q^{61} +(-0.570486 + 0.988111i) q^{62} +(-4.04118 - 6.99952i) q^{63} -5.76986 q^{64} +(0.126193 + 0.218573i) q^{66} +(2.32498 + 4.02699i) q^{67} -0.0176652 q^{68} +12.1366 q^{69} +(-7.68968 + 13.3189i) q^{71} +(1.23632 + 2.14136i) q^{72} +(-4.83162 + 8.36861i) q^{73} +(-0.00928178 + 0.0160765i) q^{74} +(-7.66603 - 3.17081i) q^{76} +1.43487 q^{77} +(0.878354 - 1.52135i) q^{78} +(-6.70596 + 11.6151i) q^{79} +(5.48123 - 9.49377i) q^{81} +(-0.578367 - 1.00176i) q^{82} -15.5409 q^{83} +16.9532 q^{84} +(0.655415 + 1.13521i) q^{86} -21.2178 q^{87} -0.438971 q^{88} +(2.08578 + 3.61267i) q^{89} +(-4.99364 - 8.64923i) q^{91} +(-5.14637 + 8.91377i) q^{92} +(4.11516 - 7.12767i) q^{93} +4.01739 q^{94} -7.84403 q^{96} +(1.87094 - 3.24056i) q^{97} +(-1.36190 + 2.35888i) q^{98} +(-0.368044 - 0.637470i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 2 q^{2} - 3 q^{3} - 2 q^{4} + q^{6} + 4 q^{7} + 12 q^{8} - 7 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q - 2 q^{2} - 3 q^{3} - 2 q^{4} + q^{6} + 4 q^{7} + 12 q^{8} - 7 q^{9} - 2 q^{11} + 14 q^{12} - 5 q^{13} + 6 q^{14} + 6 q^{16} + 3 q^{17} + 14 q^{18} - 6 q^{19} - 3 q^{21} - 9 q^{22} + 6 q^{23} - 11 q^{24} + 38 q^{26} + 36 q^{27} + 4 q^{28} - 3 q^{29} - 6 q^{31} + 6 q^{32} + 18 q^{33} + q^{34} - 13 q^{36} - 12 q^{37} - 18 q^{38} + 16 q^{39} - 11 q^{41} + 11 q^{42} - 13 q^{43} - 21 q^{44} - 24 q^{46} + 6 q^{47} + 19 q^{48} + 8 q^{49} + 17 q^{51} + q^{52} - 18 q^{53} - 18 q^{54} + 8 q^{56} - 20 q^{57} + 10 q^{58} - 4 q^{59} - 25 q^{61} + 21 q^{62} - 43 q^{63} - 44 q^{64} - 34 q^{66} - 6 q^{67} - 2 q^{68} + 26 q^{69} - 18 q^{71} - 13 q^{72} - q^{73} + 6 q^{74} + 24 q^{76} - 22 q^{77} - 72 q^{78} - 3 q^{79} - 2 q^{81} - 31 q^{82} - 46 q^{83} + 74 q^{84} - 9 q^{86} + 22 q^{87} + 22 q^{88} - 12 q^{89} + 11 q^{91} - 28 q^{92} + 13 q^{93} + 16 q^{94} - 26 q^{96} - 3 q^{97} + 22 q^{98} + 20 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/475\mathbb{Z}\right)^\times\).

\(n\) \(77\) \(401\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.155554 + 0.269427i −0.109993 + 0.190514i −0.915767 0.401709i \(-0.868416\pi\)
0.805774 + 0.592223i \(0.201750\pi\)
\(3\) 1.12208 1.94349i 0.647832 1.12208i −0.335808 0.941930i \(-0.609009\pi\)
0.983640 0.180147i \(-0.0576573\pi\)
\(4\) 0.951606 + 1.64823i 0.475803 + 0.824115i
\(5\) 0 0
\(6\) 0.349087 + 0.604636i 0.142514 + 0.246842i
\(7\) 3.96928 1.50025 0.750123 0.661299i \(-0.229994\pi\)
0.750123 + 0.661299i \(0.229994\pi\)
\(8\) −1.21432 −0.429327
\(9\) −1.01811 1.76343i −0.339371 0.587809i
\(10\) 0 0
\(11\) 0.361495 0.108995 0.0544975 0.998514i \(-0.482644\pi\)
0.0544975 + 0.998514i \(0.482644\pi\)
\(12\) 4.27110 1.23296
\(13\) −1.25807 2.17905i −0.348927 0.604359i 0.637132 0.770754i \(-0.280120\pi\)
−0.986059 + 0.166396i \(0.946787\pi\)
\(14\) −0.617436 + 1.06943i −0.165017 + 0.285817i
\(15\) 0 0
\(16\) −1.71432 + 2.96929i −0.428580 + 0.742322i
\(17\) −0.00464089 + 0.00803826i −0.00112558 + 0.00194956i −0.866588 0.499025i \(-0.833692\pi\)
0.865462 + 0.500974i \(0.167025\pi\)
\(18\) 0.633487 0.149314
\(19\) −3.45680 + 2.65529i −0.793043 + 0.609165i
\(20\) 0 0
\(21\) 4.45383 7.71427i 0.971906 1.68339i
\(22\) −0.0562320 + 0.0973967i −0.0119887 + 0.0207650i
\(23\) 2.70404 + 4.68354i 0.563832 + 0.976586i 0.997157 + 0.0753481i \(0.0240068\pi\)
−0.433325 + 0.901238i \(0.642660\pi\)
\(24\) −1.36256 + 2.36002i −0.278131 + 0.481738i
\(25\) 0 0
\(26\) 0.782793 0.153518
\(27\) 2.16285 0.416241
\(28\) 3.77719 + 6.54228i 0.713821 + 1.23637i
\(29\) −4.72735 8.18801i −0.877847 1.52047i −0.853699 0.520766i \(-0.825646\pi\)
−0.0241473 0.999708i \(-0.507687\pi\)
\(30\) 0 0
\(31\) 3.66745 0.658693 0.329347 0.944209i \(-0.393172\pi\)
0.329347 + 0.944209i \(0.393172\pi\)
\(32\) −1.74766 3.02703i −0.308945 0.535109i
\(33\) 0.405626 0.702564i 0.0706103 0.122301i
\(34\) −0.00144382 0.00250076i −0.000247613 0.000428878i
\(35\) 0 0
\(36\) 1.93769 3.35617i 0.322948 0.559362i
\(37\) 0.0596692 0.00980956 0.00490478 0.999988i \(-0.498439\pi\)
0.00490478 + 0.999988i \(0.498439\pi\)
\(38\) −0.177689 1.34440i −0.0288250 0.218090i
\(39\) −5.64662 −0.904183
\(40\) 0 0
\(41\) −1.85906 + 3.21998i −0.290336 + 0.502877i −0.973889 0.227024i \(-0.927100\pi\)
0.683553 + 0.729901i \(0.260434\pi\)
\(42\) 1.38562 + 2.39997i 0.213806 + 0.370323i
\(43\) 2.10671 3.64894i 0.321271 0.556458i −0.659480 0.751722i \(-0.729223\pi\)
0.980751 + 0.195265i \(0.0625566\pi\)
\(44\) 0.344001 + 0.595827i 0.0518601 + 0.0898243i
\(45\) 0 0
\(46\) −1.68250 −0.248071
\(47\) −6.45659 11.1831i −0.941790 1.63123i −0.762055 0.647513i \(-0.775809\pi\)
−0.179735 0.983715i \(-0.557524\pi\)
\(48\) 3.84720 + 6.66354i 0.555295 + 0.961800i
\(49\) 8.75515 1.25074
\(50\) 0 0
\(51\) 0.0104149 + 0.0180391i 0.00145837 + 0.00252598i
\(52\) 2.39438 4.14719i 0.332041 0.575111i
\(53\) −5.48564 9.50140i −0.753510 1.30512i −0.946112 0.323841i \(-0.895026\pi\)
0.192601 0.981277i \(-0.438308\pi\)
\(54\) −0.336440 + 0.582731i −0.0457837 + 0.0792997i
\(55\) 0 0
\(56\) −4.81997 −0.644095
\(57\) 1.28175 + 9.69770i 0.169772 + 1.28449i
\(58\) 2.94143 0.386229
\(59\) 2.65944 4.60629i 0.346230 0.599688i −0.639346 0.768919i \(-0.720795\pi\)
0.985576 + 0.169231i \(0.0541283\pi\)
\(60\) 0 0
\(61\) 4.44875 + 7.70546i 0.569604 + 0.986583i 0.996605 + 0.0823316i \(0.0262366\pi\)
−0.427001 + 0.904251i \(0.640430\pi\)
\(62\) −0.570486 + 0.988111i −0.0724518 + 0.125490i
\(63\) −4.04118 6.99952i −0.509140 0.881857i
\(64\) −5.76986 −0.721232
\(65\) 0 0
\(66\) 0.126193 + 0.218573i 0.0155333 + 0.0269045i
\(67\) 2.32498 + 4.02699i 0.284042 + 0.491975i 0.972376 0.233418i \(-0.0749912\pi\)
−0.688334 + 0.725393i \(0.741658\pi\)
\(68\) −0.0176652 −0.00214222
\(69\) 12.1366 1.46107
\(70\) 0 0
\(71\) −7.68968 + 13.3189i −0.912597 + 1.58066i −0.102215 + 0.994762i \(0.532593\pi\)
−0.810382 + 0.585902i \(0.800740\pi\)
\(72\) 1.23632 + 2.14136i 0.145701 + 0.252362i
\(73\) −4.83162 + 8.36861i −0.565498 + 0.979471i 0.431505 + 0.902110i \(0.357983\pi\)
−0.997003 + 0.0773609i \(0.975351\pi\)
\(74\) −0.00928178 + 0.0160765i −0.00107898 + 0.00186886i
\(75\) 0 0
\(76\) −7.66603 3.17081i −0.879354 0.363716i
\(77\) 1.43487 0.163519
\(78\) 0.878354 1.52135i 0.0994540 0.172259i
\(79\) −6.70596 + 11.6151i −0.754480 + 1.30680i 0.191153 + 0.981560i \(0.438777\pi\)
−0.945632 + 0.325237i \(0.894556\pi\)
\(80\) 0 0
\(81\) 5.48123 9.49377i 0.609025 1.05486i
\(82\) −0.578367 1.00176i −0.0638700 0.110626i
\(83\) −15.5409 −1.70583 −0.852916 0.522048i \(-0.825168\pi\)
−0.852916 + 0.522048i \(0.825168\pi\)
\(84\) 16.9532 1.84974
\(85\) 0 0
\(86\) 0.655415 + 1.13521i 0.0706753 + 0.122413i
\(87\) −21.2178 −2.27479
\(88\) −0.438971 −0.0467944
\(89\) 2.08578 + 3.61267i 0.221092 + 0.382942i 0.955140 0.296155i \(-0.0957046\pi\)
−0.734048 + 0.679098i \(0.762371\pi\)
\(90\) 0 0
\(91\) −4.99364 8.64923i −0.523475 0.906686i
\(92\) −5.14637 + 8.91377i −0.536546 + 0.929325i
\(93\) 4.11516 7.12767i 0.426722 0.739105i
\(94\) 4.01739 0.414362
\(95\) 0 0
\(96\) −7.84403 −0.800578
\(97\) 1.87094 3.24056i 0.189965 0.329029i −0.755273 0.655410i \(-0.772496\pi\)
0.945238 + 0.326381i \(0.105829\pi\)
\(98\) −1.36190 + 2.35888i −0.137572 + 0.238282i
\(99\) −0.368044 0.637470i −0.0369898 0.0640682i
\(100\) 0 0
\(101\) 8.61953 + 14.9295i 0.857675 + 1.48554i 0.874141 + 0.485672i \(0.161425\pi\)
−0.0164664 + 0.999864i \(0.505242\pi\)
\(102\) −0.00648030 −0.000641645
\(103\) 8.81660 0.868725 0.434362 0.900738i \(-0.356974\pi\)
0.434362 + 0.900738i \(0.356974\pi\)
\(104\) 1.52770 + 2.64606i 0.149804 + 0.259467i
\(105\) 0 0
\(106\) 3.41325 0.331524
\(107\) −1.30581 −0.126238 −0.0631188 0.998006i \(-0.520105\pi\)
−0.0631188 + 0.998006i \(0.520105\pi\)
\(108\) 2.05818 + 3.56488i 0.198049 + 0.343030i
\(109\) 3.04839 5.27997i 0.291983 0.505730i −0.682295 0.731077i \(-0.739018\pi\)
0.974279 + 0.225347i \(0.0723515\pi\)
\(110\) 0 0
\(111\) 0.0669535 0.115967i 0.00635494 0.0110071i
\(112\) −6.80461 + 11.7859i −0.642975 + 1.11367i
\(113\) −11.2382 −1.05720 −0.528599 0.848872i \(-0.677282\pi\)
−0.528599 + 0.848872i \(0.677282\pi\)
\(114\) −2.81221 1.16318i −0.263387 0.108942i
\(115\) 0 0
\(116\) 8.99715 15.5835i 0.835364 1.44689i
\(117\) −2.56172 + 4.43704i −0.236831 + 0.410204i
\(118\) 0.827374 + 1.43305i 0.0761659 + 0.131923i
\(119\) −0.0184210 + 0.0319061i −0.00168865 + 0.00292482i
\(120\) 0 0
\(121\) −10.8693 −0.988120
\(122\) −2.76808 −0.250610
\(123\) 4.17201 + 7.22613i 0.376178 + 0.651559i
\(124\) 3.48997 + 6.04480i 0.313408 + 0.542839i
\(125\) 0 0
\(126\) 2.51448 0.224008
\(127\) −5.92682 10.2656i −0.525921 0.910921i −0.999544 0.0301937i \(-0.990388\pi\)
0.473624 0.880727i \(-0.342946\pi\)
\(128\) 4.39284 7.60862i 0.388276 0.672514i
\(129\) −4.72779 8.18878i −0.416259 0.720982i
\(130\) 0 0
\(131\) 1.20298 2.08362i 0.105105 0.182047i −0.808676 0.588254i \(-0.799816\pi\)
0.913781 + 0.406207i \(0.133149\pi\)
\(132\) 1.54398 0.134386
\(133\) −13.7210 + 10.5396i −1.18976 + 0.913897i
\(134\) −1.44664 −0.124971
\(135\) 0 0
\(136\) 0.00563552 0.00976101i 0.000483242 0.000837000i
\(137\) −2.50867 4.34514i −0.214330 0.371230i 0.738735 0.673996i \(-0.235423\pi\)
−0.953065 + 0.302765i \(0.902090\pi\)
\(138\) −1.88789 + 3.26993i −0.160708 + 0.278355i
\(139\) −5.84248 10.1195i −0.495553 0.858323i 0.504434 0.863450i \(-0.331701\pi\)
−0.999987 + 0.00512757i \(0.998368\pi\)
\(140\) 0 0
\(141\) −28.9791 −2.44048
\(142\) −2.39232 4.14362i −0.200759 0.347725i
\(143\) −0.454787 0.787715i −0.0380312 0.0658720i
\(144\) 6.98149 0.581791
\(145\) 0 0
\(146\) −1.50315 2.60354i −0.124402 0.215470i
\(147\) 9.82395 17.0156i 0.810266 1.40342i
\(148\) 0.0567816 + 0.0983486i 0.00466742 + 0.00808420i
\(149\) 3.13033 5.42188i 0.256446 0.444178i −0.708841 0.705368i \(-0.750782\pi\)
0.965287 + 0.261190i \(0.0841150\pi\)
\(150\) 0 0
\(151\) −15.3436 −1.24864 −0.624322 0.781167i \(-0.714625\pi\)
−0.624322 + 0.781167i \(0.714625\pi\)
\(152\) 4.19766 3.22437i 0.340475 0.261531i
\(153\) 0.0188998 0.00152796
\(154\) −0.223200 + 0.386594i −0.0179860 + 0.0311527i
\(155\) 0 0
\(156\) −5.37336 9.30693i −0.430213 0.745151i
\(157\) −7.50595 + 13.0007i −0.599040 + 1.03757i 0.393923 + 0.919143i \(0.371118\pi\)
−0.992963 + 0.118424i \(0.962216\pi\)
\(158\) −2.08628 3.61354i −0.165975 0.287478i
\(159\) −24.6212 −1.95259
\(160\) 0 0
\(161\) 10.7331 + 18.5903i 0.845886 + 1.46512i
\(162\) 1.70525 + 2.95359i 0.133977 + 0.232056i
\(163\) 11.8894 0.931250 0.465625 0.884982i \(-0.345830\pi\)
0.465625 + 0.884982i \(0.345830\pi\)
\(164\) −7.07636 −0.552571
\(165\) 0 0
\(166\) 2.41744 4.18714i 0.187630 0.324985i
\(167\) 3.61678 + 6.26445i 0.279875 + 0.484757i 0.971353 0.237640i \(-0.0763737\pi\)
−0.691479 + 0.722397i \(0.743040\pi\)
\(168\) −5.40838 + 9.36758i −0.417265 + 0.722725i
\(169\) 3.33451 5.77553i 0.256500 0.444272i
\(170\) 0 0
\(171\) 8.20182 + 3.39242i 0.627209 + 0.259425i
\(172\) 8.01905 0.611447
\(173\) −1.72229 + 2.98309i −0.130943 + 0.226800i −0.924040 0.382295i \(-0.875134\pi\)
0.793097 + 0.609095i \(0.208467\pi\)
\(174\) 3.30051 5.71665i 0.250211 0.433378i
\(175\) 0 0
\(176\) −0.619718 + 1.07338i −0.0467130 + 0.0809094i
\(177\) −5.96820 10.3372i −0.448597 0.776994i
\(178\) −1.29780 −0.0972744
\(179\) −5.87847 −0.439378 −0.219689 0.975570i \(-0.570504\pi\)
−0.219689 + 0.975570i \(0.570504\pi\)
\(180\) 0 0
\(181\) −0.552356 0.956709i −0.0410563 0.0711116i 0.844767 0.535134i \(-0.179739\pi\)
−0.885823 + 0.464023i \(0.846406\pi\)
\(182\) 3.10712 0.230315
\(183\) 19.9674 1.47603
\(184\) −3.28357 5.68732i −0.242068 0.419274i
\(185\) 0 0
\(186\) 1.28026 + 2.21747i 0.0938731 + 0.162593i
\(187\) −0.00167766 + 0.00290579i −0.000122683 + 0.000212493i
\(188\) 12.2883 21.2839i 0.896213 1.55229i
\(189\) 8.58495 0.624463
\(190\) 0 0
\(191\) 21.2415 1.53698 0.768491 0.639860i \(-0.221008\pi\)
0.768491 + 0.639860i \(0.221008\pi\)
\(192\) −6.47423 + 11.2137i −0.467237 + 0.809278i
\(193\) 4.77026 8.26233i 0.343371 0.594736i −0.641686 0.766968i \(-0.721765\pi\)
0.985056 + 0.172232i \(0.0550979\pi\)
\(194\) 0.582064 + 1.00816i 0.0417897 + 0.0723820i
\(195\) 0 0
\(196\) 8.33145 + 14.4305i 0.595104 + 1.03075i
\(197\) −2.05919 −0.146711 −0.0733556 0.997306i \(-0.523371\pi\)
−0.0733556 + 0.997306i \(0.523371\pi\)
\(198\) 0.229002 0.0162745
\(199\) 9.95070 + 17.2351i 0.705386 + 1.22176i 0.966552 + 0.256471i \(0.0825598\pi\)
−0.261166 + 0.965294i \(0.584107\pi\)
\(200\) 0 0
\(201\) 10.4352 0.736045
\(202\) −5.36320 −0.377354
\(203\) −18.7641 32.5005i −1.31698 2.28108i
\(204\) −0.0198217 + 0.0343322i −0.00138780 + 0.00240374i
\(205\) 0 0
\(206\) −1.37146 + 2.37543i −0.0955539 + 0.165504i
\(207\) 5.50605 9.53676i 0.382697 0.662851i
\(208\) 8.62696 0.598172
\(209\) −1.24962 + 0.959874i −0.0864377 + 0.0663959i
\(210\) 0 0
\(211\) 10.7586 18.6345i 0.740655 1.28285i −0.211542 0.977369i \(-0.567848\pi\)
0.952197 0.305484i \(-0.0988182\pi\)
\(212\) 10.4403 18.0832i 0.717045 1.24196i
\(213\) 17.2568 + 29.8897i 1.18242 + 2.04801i
\(214\) 0.203124 0.351822i 0.0138853 0.0240500i
\(215\) 0 0
\(216\) −2.62639 −0.178703
\(217\) 14.5571 0.988201
\(218\) 0.948379 + 1.64264i 0.0642323 + 0.111254i
\(219\) 10.8429 + 18.7804i 0.732695 + 1.26906i
\(220\) 0 0
\(221\) 0.0233543 0.00157098
\(222\) 0.0208297 + 0.0360782i 0.00139800 + 0.00242141i
\(223\) 2.76965 4.79718i 0.185470 0.321243i −0.758265 0.651946i \(-0.773953\pi\)
0.943735 + 0.330704i \(0.107286\pi\)
\(224\) −6.93694 12.0151i −0.463494 0.802794i
\(225\) 0 0
\(226\) 1.74814 3.02787i 0.116285 0.201411i
\(227\) 16.2401 1.07789 0.538947 0.842340i \(-0.318822\pi\)
0.538947 + 0.842340i \(0.318822\pi\)
\(228\) −14.7643 + 11.3410i −0.977791 + 0.751077i
\(229\) 10.5436 0.696739 0.348369 0.937357i \(-0.386736\pi\)
0.348369 + 0.937357i \(0.386736\pi\)
\(230\) 0 0
\(231\) 1.61004 2.78867i 0.105933 0.183481i
\(232\) 5.74051 + 9.94286i 0.376883 + 0.652781i
\(233\) −8.08922 + 14.0109i −0.529942 + 0.917887i 0.469447 + 0.882960i \(0.344453\pi\)
−0.999390 + 0.0349268i \(0.988880\pi\)
\(234\) −0.796972 1.38040i −0.0520997 0.0902394i
\(235\) 0 0
\(236\) 10.1230 0.658949
\(237\) 15.0492 + 26.0660i 0.977552 + 1.69317i
\(238\) −0.00573091 0.00992622i −0.000371480 0.000643421i
\(239\) −9.62683 −0.622708 −0.311354 0.950294i \(-0.600782\pi\)
−0.311354 + 0.950294i \(0.600782\pi\)
\(240\) 0 0
\(241\) 9.84997 + 17.0606i 0.634492 + 1.09897i 0.986622 + 0.163022i \(0.0521241\pi\)
−0.352130 + 0.935951i \(0.614543\pi\)
\(242\) 1.69077 2.92849i 0.108687 0.188251i
\(243\) −9.05645 15.6862i −0.580971 1.00627i
\(244\) −8.46691 + 14.6651i −0.542038 + 0.938838i
\(245\) 0 0
\(246\) −2.59589 −0.165508
\(247\) 10.1349 + 4.19197i 0.644868 + 0.266729i
\(248\) −4.45346 −0.282795
\(249\) −17.4381 + 30.2036i −1.10509 + 1.91408i
\(250\) 0 0
\(251\) −4.60240 7.97158i −0.290501 0.503162i 0.683428 0.730018i \(-0.260489\pi\)
−0.973928 + 0.226856i \(0.927155\pi\)
\(252\) 7.69121 13.3216i 0.484501 0.839180i
\(253\) 0.977499 + 1.69308i 0.0614548 + 0.106443i
\(254\) 3.68776 0.231391
\(255\) 0 0
\(256\) −4.40321 7.62659i −0.275201 0.476662i
\(257\) −0.229133 0.396869i −0.0142929 0.0247560i 0.858790 0.512327i \(-0.171216\pi\)
−0.873083 + 0.487571i \(0.837883\pi\)
\(258\) 2.94171 0.183143
\(259\) 0.236844 0.0147167
\(260\) 0 0
\(261\) −9.62596 + 16.6727i −0.595832 + 1.03201i
\(262\) 0.374256 + 0.648230i 0.0231216 + 0.0400478i
\(263\) 5.87774 10.1806i 0.362437 0.627760i −0.625924 0.779884i \(-0.715278\pi\)
0.988361 + 0.152124i \(0.0486114\pi\)
\(264\) −0.492559 + 0.853137i −0.0303149 + 0.0525070i
\(265\) 0 0
\(266\) −0.705297 5.33628i −0.0432445 0.327188i
\(267\) 9.36161 0.572921
\(268\) −4.42494 + 7.66421i −0.270296 + 0.468166i
\(269\) −2.38296 + 4.12742i −0.145292 + 0.251653i −0.929482 0.368868i \(-0.879745\pi\)
0.784190 + 0.620521i \(0.213079\pi\)
\(270\) 0 0
\(271\) 7.75620 13.4341i 0.471155 0.816065i −0.528300 0.849058i \(-0.677170\pi\)
0.999456 + 0.0329925i \(0.0105038\pi\)
\(272\) −0.0159119 0.0275603i −0.000964803 0.00167109i
\(273\) −22.4130 −1.35650
\(274\) 1.56093 0.0942994
\(275\) 0 0
\(276\) 11.5492 + 20.0039i 0.695183 + 1.20409i
\(277\) 4.90677 0.294819 0.147410 0.989076i \(-0.452906\pi\)
0.147410 + 0.989076i \(0.452906\pi\)
\(278\) 3.63528 0.218030
\(279\) −3.73388 6.46727i −0.223542 0.387186i
\(280\) 0 0
\(281\) −6.84266 11.8518i −0.408199 0.707021i 0.586489 0.809957i \(-0.300510\pi\)
−0.994688 + 0.102936i \(0.967176\pi\)
\(282\) 4.50782 7.80777i 0.268437 0.464946i
\(283\) −8.43386 + 14.6079i −0.501341 + 0.868348i 0.498658 + 0.866799i \(0.333826\pi\)
−0.999999 + 0.00154919i \(0.999507\pi\)
\(284\) −29.2702 −1.73687
\(285\) 0 0
\(286\) 0.282976 0.0167327
\(287\) −7.37911 + 12.7810i −0.435575 + 0.754438i
\(288\) −3.55863 + 6.16373i −0.209694 + 0.363201i
\(289\) 8.49996 + 14.7224i 0.499997 + 0.866021i
\(290\) 0 0
\(291\) −4.19868 7.27232i −0.246131 0.426311i
\(292\) −18.3912 −1.07626
\(293\) 25.8794 1.51189 0.755944 0.654636i \(-0.227178\pi\)
0.755944 + 0.654636i \(0.227178\pi\)
\(294\) 3.05631 + 5.29368i 0.178247 + 0.308734i
\(295\) 0 0
\(296\) −0.0724575 −0.00421151
\(297\) 0.781861 0.0453681
\(298\) 0.973869 + 1.68679i 0.0564147 + 0.0977132i
\(299\) 6.80377 11.7845i 0.393472 0.681514i
\(300\) 0 0
\(301\) 8.36213 14.4836i 0.481985 0.834823i
\(302\) 2.38676 4.13398i 0.137342 0.237884i
\(303\) 38.6871 2.22252
\(304\) −1.95827 14.8162i −0.112314 0.849770i
\(305\) 0 0
\(306\) −0.00293994 + 0.00509213i −0.000168065 + 0.000291098i
\(307\) 1.64721 2.85305i 0.0940111 0.162832i −0.815184 0.579202i \(-0.803364\pi\)
0.909195 + 0.416370i \(0.136698\pi\)
\(308\) 1.36543 + 2.36500i 0.0778029 + 0.134759i
\(309\) 9.89290 17.1350i 0.562787 0.974776i
\(310\) 0 0
\(311\) 30.4253 1.72526 0.862629 0.505837i \(-0.168816\pi\)
0.862629 + 0.505837i \(0.168816\pi\)
\(312\) 6.85680 0.388190
\(313\) −4.37696 7.58112i −0.247401 0.428510i 0.715403 0.698712i \(-0.246243\pi\)
−0.962804 + 0.270201i \(0.912910\pi\)
\(314\) −2.33516 4.04461i −0.131781 0.228251i
\(315\) 0 0
\(316\) −25.5257 −1.43594
\(317\) 4.18690 + 7.25192i 0.235160 + 0.407308i 0.959319 0.282324i \(-0.0911054\pi\)
−0.724159 + 0.689633i \(0.757772\pi\)
\(318\) 3.82993 6.63363i 0.214772 0.371996i
\(319\) −1.70891 2.95993i −0.0956808 0.165724i
\(320\) 0 0
\(321\) −1.46522 + 2.53784i −0.0817808 + 0.141648i
\(322\) −6.67830 −0.372167
\(323\) −0.00530128 0.0401095i −0.000294971 0.00223175i
\(324\) 20.8639 1.15910
\(325\) 0 0
\(326\) −1.84944 + 3.20333i −0.102431 + 0.177416i
\(327\) −6.84107 11.8491i −0.378312 0.655255i
\(328\) 2.25749 3.91009i 0.124649 0.215898i
\(329\) −25.6280 44.3889i −1.41292 2.44724i
\(330\) 0 0
\(331\) −17.8536 −0.981321 −0.490661 0.871351i \(-0.663245\pi\)
−0.490661 + 0.871351i \(0.663245\pi\)
\(332\) −14.7888 25.6149i −0.811640 1.40580i
\(333\) −0.0607501 0.105222i −0.00332908 0.00576614i
\(334\) −2.25042 −0.123137
\(335\) 0 0
\(336\) 15.2706 + 26.4494i 0.833079 + 1.44293i
\(337\) −5.04723 + 8.74205i −0.274940 + 0.476210i −0.970120 0.242626i \(-0.921991\pi\)
0.695180 + 0.718836i \(0.255325\pi\)
\(338\) 1.03739 + 1.79681i 0.0564266 + 0.0977338i
\(339\) −12.6101 + 21.8413i −0.684886 + 1.18626i
\(340\) 0 0
\(341\) 1.32577 0.0717942
\(342\) −2.18983 + 1.68209i −0.118413 + 0.0909570i
\(343\) 6.96666 0.376164
\(344\) −2.55823 + 4.43098i −0.137930 + 0.238902i
\(345\) 0 0
\(346\) −0.535818 0.928063i −0.0288057 0.0498930i
\(347\) −1.35145 + 2.34077i −0.0725494 + 0.125659i −0.900018 0.435853i \(-0.856447\pi\)
0.827469 + 0.561512i \(0.189780\pi\)
\(348\) −20.1910 34.9718i −1.08235 1.87469i
\(349\) −11.2187 −0.600524 −0.300262 0.953857i \(-0.597074\pi\)
−0.300262 + 0.953857i \(0.597074\pi\)
\(350\) 0 0
\(351\) −2.72102 4.71295i −0.145238 0.251559i
\(352\) −0.631770 1.09426i −0.0336735 0.0583241i
\(353\) 9.37058 0.498746 0.249373 0.968408i \(-0.419776\pi\)
0.249373 + 0.968408i \(0.419776\pi\)
\(354\) 3.71351 0.197371
\(355\) 0 0
\(356\) −3.96967 + 6.87568i −0.210392 + 0.364410i
\(357\) 0.0413395 + 0.0716021i 0.00218792 + 0.00378959i
\(358\) 0.914419 1.58382i 0.0483286 0.0837075i
\(359\) 10.7443 18.6097i 0.567064 0.982184i −0.429790 0.902929i \(-0.641413\pi\)
0.996854 0.0792550i \(-0.0252541\pi\)
\(360\) 0 0
\(361\) 4.89888 18.3576i 0.257836 0.966189i
\(362\) 0.343685 0.0180637
\(363\) −12.1962 + 21.1245i −0.640135 + 1.10875i
\(364\) 9.50395 16.4613i 0.498142 0.862808i
\(365\) 0 0
\(366\) −3.10600 + 5.37975i −0.162353 + 0.281204i
\(367\) −15.0567 26.0790i −0.785953 1.36131i −0.928428 0.371512i \(-0.878839\pi\)
0.142475 0.989798i \(-0.454494\pi\)
\(368\) −18.5424 −0.966588
\(369\) 7.57093 0.394127
\(370\) 0 0
\(371\) −21.7740 37.7137i −1.13045 1.95800i
\(372\) 15.6640 0.812143
\(373\) 26.7206 1.38354 0.691769 0.722119i \(-0.256831\pi\)
0.691769 + 0.722119i \(0.256831\pi\)
\(374\) −0.000521933 0 0.000904015i −2.69885e−5 0 4.67455e-5i
\(375\) 0 0
\(376\) 7.84036 + 13.5799i 0.404336 + 0.700330i
\(377\) −11.8947 + 20.6022i −0.612608 + 1.06107i
\(378\) −1.33542 + 2.31302i −0.0686867 + 0.118969i
\(379\) 22.9732 1.18005 0.590026 0.807384i \(-0.299117\pi\)
0.590026 + 0.807384i \(0.299117\pi\)
\(380\) 0 0
\(381\) −26.6014 −1.36283
\(382\) −3.30420 + 5.72305i −0.169058 + 0.292816i
\(383\) −14.5442 + 25.1913i −0.743174 + 1.28722i 0.207868 + 0.978157i \(0.433347\pi\)
−0.951043 + 0.309059i \(0.899986\pi\)
\(384\) −9.85821 17.0749i −0.503075 0.871351i
\(385\) 0 0
\(386\) 1.48407 + 2.57048i 0.0755369 + 0.130834i
\(387\) −8.57951 −0.436121
\(388\) 7.12159 0.361544
\(389\) −1.81882 3.15029i −0.0922178 0.159726i 0.816226 0.577732i \(-0.196062\pi\)
−0.908444 + 0.418006i \(0.862729\pi\)
\(390\) 0 0
\(391\) −0.0501967 −0.00253855
\(392\) −10.6315 −0.536974
\(393\) −2.69967 4.67596i −0.136180 0.235871i
\(394\) 0.320315 0.554802i 0.0161372 0.0279505i
\(395\) 0 0
\(396\) 0.700465 1.21324i 0.0351997 0.0609676i
\(397\) 6.96707 12.0673i 0.349667 0.605641i −0.636523 0.771258i \(-0.719628\pi\)
0.986190 + 0.165616i \(0.0529613\pi\)
\(398\) −6.19148 −0.310351
\(399\) 5.08761 + 38.4929i 0.254699 + 1.92705i
\(400\) 0 0
\(401\) −13.2751 + 22.9931i −0.662925 + 1.14822i 0.316918 + 0.948453i \(0.397352\pi\)
−0.979843 + 0.199767i \(0.935981\pi\)
\(402\) −1.62324 + 2.81154i −0.0809600 + 0.140227i
\(403\) −4.61392 7.99154i −0.229836 0.398087i
\(404\) −16.4048 + 28.4139i −0.816168 + 1.41365i
\(405\) 0 0
\(406\) 11.6753 0.579438
\(407\) 0.0215701 0.00106919
\(408\) −0.0126470 0.0219052i −0.000626119 0.00108447i
\(409\) −7.49800 12.9869i −0.370752 0.642162i 0.618929 0.785447i \(-0.287567\pi\)
−0.989681 + 0.143285i \(0.954234\pi\)
\(410\) 0 0
\(411\) −11.2597 −0.555399
\(412\) 8.38993 + 14.5318i 0.413342 + 0.715929i
\(413\) 10.5561 18.2836i 0.519430 0.899679i
\(414\) 1.71298 + 2.96696i 0.0841881 + 0.145818i
\(415\) 0 0
\(416\) −4.39736 + 7.61646i −0.215598 + 0.373427i
\(417\) −26.2229 −1.28414
\(418\) −0.0642337 0.485993i −0.00314177 0.0237707i
\(419\) 30.4528 1.48772 0.743859 0.668337i \(-0.232993\pi\)
0.743859 + 0.668337i \(0.232993\pi\)
\(420\) 0 0
\(421\) 0.444876 0.770547i 0.0216819 0.0375542i −0.854981 0.518660i \(-0.826431\pi\)
0.876663 + 0.481105i \(0.159765\pi\)
\(422\) 3.34710 + 5.79734i 0.162934 + 0.282210i
\(423\) −13.1471 + 22.7714i −0.639233 + 1.10718i
\(424\) 6.66132 + 11.5377i 0.323502 + 0.560322i
\(425\) 0 0
\(426\) −10.7375 −0.520232
\(427\) 17.6583 + 30.5851i 0.854545 + 1.48012i
\(428\) −1.24262 2.15228i −0.0600643 0.104034i
\(429\) −2.04123 −0.0985513
\(430\) 0 0
\(431\) −7.36739 12.7607i −0.354875 0.614661i 0.632222 0.774787i \(-0.282143\pi\)
−0.987097 + 0.160126i \(0.948810\pi\)
\(432\) −3.70782 + 6.42213i −0.178393 + 0.308985i
\(433\) −0.742440 1.28594i −0.0356794 0.0617985i 0.847634 0.530581i \(-0.178026\pi\)
−0.883314 + 0.468782i \(0.844693\pi\)
\(434\) −2.26442 + 3.92208i −0.108695 + 0.188266i
\(435\) 0 0
\(436\) 11.6035 0.555706
\(437\) −21.7835 9.01003i −1.04205 0.431008i
\(438\) −6.74662 −0.322366
\(439\) 7.34789 12.7269i 0.350696 0.607423i −0.635676 0.771956i \(-0.719278\pi\)
0.986372 + 0.164533i \(0.0526118\pi\)
\(440\) 0 0
\(441\) −8.91374 15.4391i −0.424464 0.735193i
\(442\) −0.00363285 + 0.00629229i −0.000172797 + 0.000299294i
\(443\) −9.32539 16.1520i −0.443062 0.767407i 0.554853 0.831949i \(-0.312775\pi\)
−0.997915 + 0.0645421i \(0.979441\pi\)
\(444\) 0.254853 0.0120948
\(445\) 0 0
\(446\) 0.861660 + 1.49244i 0.0408008 + 0.0706690i
\(447\) −7.02494 12.1675i −0.332268 0.575505i
\(448\) −22.9022 −1.08203
\(449\) 5.17365 0.244160 0.122080 0.992520i \(-0.461044\pi\)
0.122080 + 0.992520i \(0.461044\pi\)
\(450\) 0 0
\(451\) −0.672040 + 1.16401i −0.0316451 + 0.0548110i
\(452\) −10.6943 18.5231i −0.503018 0.871252i
\(453\) −17.2167 + 29.8202i −0.808911 + 1.40107i
\(454\) −2.52621 + 4.37553i −0.118561 + 0.205354i
\(455\) 0 0
\(456\) −1.55645 11.7761i −0.0728875 0.551467i
\(457\) −20.2319 −0.946409 −0.473204 0.880953i \(-0.656903\pi\)
−0.473204 + 0.880953i \(0.656903\pi\)
\(458\) −1.64009 + 2.84072i −0.0766365 + 0.132738i
\(459\) −0.0100376 + 0.0173856i −0.000468513 + 0.000811488i
\(460\) 0 0
\(461\) −15.1012 + 26.1561i −0.703334 + 1.21821i 0.263955 + 0.964535i \(0.414973\pi\)
−0.967289 + 0.253675i \(0.918361\pi\)
\(462\) 0.500896 + 0.867577i 0.0233038 + 0.0403633i
\(463\) −20.4060 −0.948345 −0.474173 0.880432i \(-0.657253\pi\)
−0.474173 + 0.880432i \(0.657253\pi\)
\(464\) 32.4167 1.50491
\(465\) 0 0
\(466\) −2.51662 4.35891i −0.116580 0.201923i
\(467\) 15.9143 0.736425 0.368212 0.929742i \(-0.379970\pi\)
0.368212 + 0.929742i \(0.379970\pi\)
\(468\) −9.75101 −0.450741
\(469\) 9.22850 + 15.9842i 0.426132 + 0.738083i
\(470\) 0 0
\(471\) 16.8445 + 29.1755i 0.776154 + 1.34434i
\(472\) −3.22941 + 5.59351i −0.148646 + 0.257462i
\(473\) 0.761567 1.31907i 0.0350169 0.0606511i
\(474\) −9.36386 −0.430096
\(475\) 0 0
\(476\) −0.0701180 −0.00321385
\(477\) −11.1700 + 19.3470i −0.511440 + 0.885839i
\(478\) 1.49749 2.59373i 0.0684936 0.118634i
\(479\) 18.6782 + 32.3515i 0.853428 + 1.47818i 0.878096 + 0.478484i \(0.158814\pi\)
−0.0246685 + 0.999696i \(0.507853\pi\)
\(480\) 0 0
\(481\) −0.0750682 0.130022i −0.00342282 0.00592849i
\(482\) −6.12881 −0.279159
\(483\) 48.1734 2.19197
\(484\) −10.3433 17.9151i −0.470150 0.814325i
\(485\) 0 0
\(486\) 5.63506 0.255612
\(487\) 39.0070 1.76757 0.883787 0.467889i \(-0.154985\pi\)
0.883787 + 0.467889i \(0.154985\pi\)
\(488\) −5.40220 9.35689i −0.244546 0.423566i
\(489\) 13.3408 23.1070i 0.603293 1.04493i
\(490\) 0 0
\(491\) 10.2673 17.7835i 0.463357 0.802557i −0.535769 0.844365i \(-0.679978\pi\)
0.999126 + 0.0418074i \(0.0133116\pi\)
\(492\) −7.94022 + 13.7529i −0.357973 + 0.620027i
\(493\) 0.0877564 0.00395235
\(494\) −2.70595 + 2.07854i −0.121747 + 0.0935180i
\(495\) 0 0
\(496\) −6.28718 + 10.8897i −0.282303 + 0.488963i
\(497\) −30.5225 + 52.8664i −1.36912 + 2.37138i
\(498\) −5.42512 9.39658i −0.243105 0.421071i
\(499\) −0.368486 + 0.638237i −0.0164957 + 0.0285714i −0.874155 0.485646i \(-0.838584\pi\)
0.857660 + 0.514218i \(0.171918\pi\)
\(500\) 0 0
\(501\) 16.2332 0.725247
\(502\) 2.86368 0.127812
\(503\) 4.99035 + 8.64354i 0.222509 + 0.385397i 0.955569 0.294767i \(-0.0952420\pi\)
−0.733060 + 0.680164i \(0.761909\pi\)
\(504\) 4.90728 + 8.49966i 0.218588 + 0.378605i
\(505\) 0 0
\(506\) −0.608215 −0.0270385
\(507\) −7.48314 12.9612i −0.332338 0.575626i
\(508\) 11.2800 19.5375i 0.500469 0.866838i
\(509\) 15.2505 + 26.4147i 0.675968 + 1.17081i 0.976185 + 0.216940i \(0.0696075\pi\)
−0.300217 + 0.953871i \(0.597059\pi\)
\(510\) 0 0
\(511\) −19.1780 + 33.2173i −0.848386 + 1.46945i
\(512\) 20.3111 0.897633
\(513\) −7.47654 + 5.74300i −0.330097 + 0.253559i
\(514\) 0.142570 0.00628849
\(515\) 0 0
\(516\) 8.99799 15.5850i 0.396115 0.686090i
\(517\) −2.33402 4.04265i −0.102650 0.177796i
\(518\) −0.0368419 + 0.0638121i −0.00161874 + 0.00280374i
\(519\) 3.86508 + 6.69452i 0.169658 + 0.293857i
\(520\) 0 0
\(521\) 23.5752 1.03285 0.516424 0.856333i \(-0.327263\pi\)
0.516424 + 0.856333i \(0.327263\pi\)
\(522\) −2.99471 5.18699i −0.131075 0.227029i
\(523\) 5.46896 + 9.47252i 0.239141 + 0.414204i 0.960468 0.278390i \(-0.0898009\pi\)
−0.721327 + 0.692595i \(0.756468\pi\)
\(524\) 4.57904 0.200036
\(525\) 0 0
\(526\) 1.82861 + 3.16725i 0.0797313 + 0.138099i
\(527\) −0.0170202 + 0.0294799i −0.000741413 + 0.00128416i
\(528\) 1.39074 + 2.40884i 0.0605244 + 0.104831i
\(529\) −3.12370 + 5.41041i −0.135813 + 0.235235i
\(530\) 0 0
\(531\) −10.8305 −0.470002
\(532\) −30.4286 12.5858i −1.31925 0.545664i
\(533\) 9.35532 0.405224
\(534\) −1.45623 + 2.52227i −0.0630174 + 0.109149i
\(535\) 0 0
\(536\) −2.82327 4.89005i −0.121947 0.211218i
\(537\) −6.59610 + 11.4248i −0.284643 + 0.493016i
\(538\) −0.741359 1.28407i −0.0319623 0.0553603i
\(539\) 3.16494 0.136324
\(540\) 0 0
\(541\) −14.7076 25.4743i −0.632328 1.09522i −0.987075 0.160261i \(-0.948766\pi\)
0.354747 0.934962i \(-0.384567\pi\)
\(542\) 2.41301 + 4.17946i 0.103648 + 0.179523i
\(543\) −2.47914 −0.106390
\(544\) 0.0324428 0.00139097
\(545\) 0 0
\(546\) 3.48643 6.03867i 0.149205 0.258431i
\(547\) −16.3667 28.3480i −0.699790 1.21207i −0.968539 0.248861i \(-0.919944\pi\)
0.268750 0.963210i \(-0.413390\pi\)
\(548\) 4.77453 8.26973i 0.203958 0.353265i
\(549\) 9.05867 15.6901i 0.386614 0.669636i
\(550\) 0 0
\(551\) 38.0830 + 15.7518i 1.62239 + 0.671049i
\(552\) −14.7377 −0.627278
\(553\) −26.6178 + 46.1034i −1.13190 + 1.96052i
\(554\) −0.763267 + 1.32202i −0.0324281 + 0.0561671i
\(555\) 0 0
\(556\) 11.1195 19.2595i 0.471571 0.816785i
\(557\) −4.74905 8.22560i −0.201224 0.348530i 0.747699 0.664038i \(-0.231159\pi\)
−0.948923 + 0.315508i \(0.897825\pi\)
\(558\) 2.32328 0.0983523
\(559\) −10.6016 −0.448400
\(560\) 0 0
\(561\) 0.00376493 + 0.00652105i 0.000158955 + 0.000275319i
\(562\) 4.25761 0.179596
\(563\) −33.1253 −1.39607 −0.698033 0.716065i \(-0.745941\pi\)
−0.698033 + 0.716065i \(0.745941\pi\)
\(564\) −27.5767 47.7643i −1.16119 2.01124i
\(565\) 0 0
\(566\) −2.62384 4.54462i −0.110288 0.191025i
\(567\) 21.7565 37.6834i 0.913687 1.58255i
\(568\) 9.33773 16.1734i 0.391802 0.678622i
\(569\) 26.5756 1.11411 0.557054 0.830476i \(-0.311932\pi\)
0.557054 + 0.830476i \(0.311932\pi\)
\(570\) 0 0
\(571\) −6.14212 −0.257040 −0.128520 0.991707i \(-0.541023\pi\)
−0.128520 + 0.991707i \(0.541023\pi\)
\(572\) 0.865557 1.49919i 0.0361907 0.0626842i
\(573\) 23.8346 41.2828i 0.995706 1.72461i
\(574\) −2.29570 3.97627i −0.0958206 0.165966i
\(575\) 0 0
\(576\) 5.87438 + 10.1747i 0.244766 + 0.423947i
\(577\) 11.1455 0.463992 0.231996 0.972717i \(-0.425474\pi\)
0.231996 + 0.972717i \(0.425474\pi\)
\(578\) −5.28881 −0.219985
\(579\) −10.7052 18.5420i −0.444893 0.770577i
\(580\) 0 0
\(581\) −61.6860 −2.55917
\(582\) 2.61248 0.108291
\(583\) −1.98303 3.43471i −0.0821288 0.142251i
\(584\) 5.86713 10.1622i 0.242784 0.420513i
\(585\) 0 0
\(586\) −4.02564 + 6.97261i −0.166297 + 0.288036i
\(587\) 10.8330 18.7633i 0.447126 0.774445i −0.551072 0.834458i \(-0.685781\pi\)
0.998198 + 0.0600130i \(0.0191142\pi\)
\(588\) 37.3941 1.54211
\(589\) −12.6776 + 9.73814i −0.522372 + 0.401253i
\(590\) 0 0
\(591\) −2.31057 + 4.00202i −0.0950441 + 0.164621i
\(592\) −0.102292 + 0.177175i −0.00420418 + 0.00728185i
\(593\) 12.1707 + 21.0803i 0.499791 + 0.865664i 1.00000 0.000240828i \(-7.66580e-5\pi\)
−0.500209 + 0.865905i \(0.666743\pi\)
\(594\) −0.121621 + 0.210655i −0.00499019 + 0.00864326i
\(595\) 0 0
\(596\) 11.9153 0.488072
\(597\) 44.6618 1.82789
\(598\) 2.11671 + 3.66624i 0.0865585 + 0.149924i
\(599\) 9.47682 + 16.4143i 0.387212 + 0.670672i 0.992073 0.125659i \(-0.0401046\pi\)
−0.604861 + 0.796331i \(0.706771\pi\)
\(600\) 0 0
\(601\) 4.40461 0.179668 0.0898339 0.995957i \(-0.471366\pi\)
0.0898339 + 0.995957i \(0.471366\pi\)
\(602\) 2.60152 + 4.50597i 0.106030 + 0.183650i
\(603\) 4.73420 8.19987i 0.192791 0.333925i
\(604\) −14.6011 25.2898i −0.594108 1.02903i
\(605\) 0 0
\(606\) −6.01793 + 10.4234i −0.244462 + 0.423420i
\(607\) 17.3015 0.702246 0.351123 0.936329i \(-0.385800\pi\)
0.351123 + 0.936329i \(0.385800\pi\)
\(608\) 14.0789 + 5.82330i 0.570977 + 0.236166i
\(609\) −84.2193 −3.41274
\(610\) 0 0
\(611\) −16.2457 + 28.1384i −0.657231 + 1.13836i
\(612\) 0.0179852 + 0.0311513i 0.000727008 + 0.00125922i
\(613\) −1.85860 + 3.21918i −0.0750680 + 0.130022i −0.901116 0.433578i \(-0.857251\pi\)
0.826048 + 0.563600i \(0.190584\pi\)
\(614\) 0.512459 + 0.887606i 0.0206812 + 0.0358208i
\(615\) 0 0
\(616\) −1.74240 −0.0702031
\(617\) 9.04453 + 15.6656i 0.364119 + 0.630673i 0.988634 0.150340i \(-0.0480368\pi\)
−0.624515 + 0.781013i \(0.714703\pi\)
\(618\) 3.07776 + 5.33083i 0.123806 + 0.214438i
\(619\) −40.6682 −1.63459 −0.817297 0.576216i \(-0.804529\pi\)
−0.817297 + 0.576216i \(0.804529\pi\)
\(620\) 0 0
\(621\) 5.84844 + 10.1298i 0.234690 + 0.406495i
\(622\) −4.73277 + 8.19739i −0.189767 + 0.328686i
\(623\) 8.27902 + 14.3397i 0.331692 + 0.574507i
\(624\) 9.68011 16.7664i 0.387515 0.671195i
\(625\) 0 0
\(626\) 2.72342 0.108850
\(627\) 0.463346 + 3.50567i 0.0185042 + 0.140003i
\(628\) −28.5708 −1.14010
\(629\) −0.000276918 0 0.000479637i −1.10415e−5 0 1.91244e-5i
\(630\) 0 0
\(631\) −8.14602 14.1093i −0.324288 0.561683i 0.657080 0.753821i \(-0.271791\pi\)
−0.981368 + 0.192138i \(0.938458\pi\)
\(632\) 8.14318 14.1044i 0.323918 0.561043i
\(633\) −24.1441 41.8187i −0.959640 1.66215i
\(634\) −2.60515 −0.103464
\(635\) 0 0
\(636\) −23.4297 40.5814i −0.929048 1.60916i
\(637\) −11.0146 19.0779i −0.436415 0.755893i
\(638\) 1.06331 0.0420970
\(639\) 31.3159 1.23884
\(640\) 0 0
\(641\) −5.03530 + 8.72139i −0.198882 + 0.344474i −0.948166 0.317775i \(-0.897064\pi\)
0.749284 + 0.662249i \(0.230398\pi\)
\(642\) −0.455842 0.789542i −0.0179907 0.0311607i
\(643\) 2.14765 3.71984i 0.0846950 0.146696i −0.820566 0.571552i \(-0.806342\pi\)
0.905261 + 0.424855i \(0.139675\pi\)
\(644\) −20.4273 + 35.3812i −0.804950 + 1.39421i
\(645\) 0 0
\(646\) 0.0116312 + 0.00481088i 0.000457625 + 0.000189282i
\(647\) −11.5451 −0.453884 −0.226942 0.973908i \(-0.572873\pi\)
−0.226942 + 0.973908i \(0.572873\pi\)
\(648\) −6.65597 + 11.5285i −0.261471 + 0.452881i
\(649\) 0.961376 1.66515i 0.0377373 0.0653629i
\(650\) 0 0
\(651\) 16.3342 28.2917i 0.640188 1.10884i
\(652\) 11.3140 + 19.5965i 0.443092 + 0.767457i
\(653\) 46.8302 1.83261 0.916304 0.400483i \(-0.131158\pi\)
0.916304 + 0.400483i \(0.131158\pi\)
\(654\) 4.25662 0.166447
\(655\) 0 0
\(656\) −6.37404 11.0402i −0.248864 0.431046i
\(657\) 19.6766 0.767656
\(658\) 15.9461 0.621644
\(659\) −22.0463 38.1854i −0.858803 1.48749i −0.873071 0.487593i \(-0.837875\pi\)
0.0142676 0.999898i \(-0.495458\pi\)
\(660\) 0 0
\(661\) 22.0688 + 38.2243i 0.858378 + 1.48675i 0.873475 + 0.486869i \(0.161861\pi\)
−0.0150971 + 0.999886i \(0.504806\pi\)
\(662\) 2.77719 4.81024i 0.107939 0.186955i
\(663\) 0.0262053 0.0453890i 0.00101773 0.00176276i
\(664\) 18.8716 0.732360
\(665\) 0 0
\(666\) 0.0377997 0.00146471
\(667\) 25.5659 44.2815i 0.989916 1.71458i
\(668\) −6.88350 + 11.9226i −0.266331 + 0.461298i
\(669\) −6.21552 10.7656i −0.240306 0.416222i
\(670\) 0 0
\(671\) 1.60820 + 2.78549i 0.0620839 + 0.107532i
\(672\) −31.1351 −1.20106
\(673\) 26.1730 1.00889 0.504447 0.863443i \(-0.331696\pi\)
0.504447 + 0.863443i \(0.331696\pi\)
\(674\) −1.57023 2.71972i −0.0604831 0.104760i
\(675\) 0 0
\(676\) 12.6925 0.488175
\(677\) −19.7693 −0.759796 −0.379898 0.925028i \(-0.624041\pi\)
−0.379898 + 0.925028i \(0.624041\pi\)
\(678\) −3.92310 6.79500i −0.150666 0.260960i
\(679\) 7.42627 12.8627i 0.284994 0.493624i
\(680\) 0 0
\(681\) 18.2227 31.5626i 0.698294 1.20948i
\(682\) −0.206228 + 0.357197i −0.00789688 + 0.0136778i
\(683\) −38.8945 −1.48826 −0.744128 0.668037i \(-0.767135\pi\)
−0.744128 + 0.668037i \(0.767135\pi\)
\(684\) 2.21342 + 16.7467i 0.0846321 + 0.640327i
\(685\) 0 0
\(686\) −1.08369 + 1.87701i −0.0413755 + 0.0716645i
\(687\) 11.8307 20.4914i 0.451369 0.781795i
\(688\) 7.22317 + 12.5109i 0.275381 + 0.476973i
\(689\) −13.8027 + 23.9069i −0.525840 + 0.910781i
\(690\) 0 0
\(691\) 22.6319 0.860959 0.430479 0.902600i \(-0.358345\pi\)
0.430479 + 0.902600i \(0.358345\pi\)
\(692\) −6.55576 −0.249213
\(693\) −1.46087 2.53029i −0.0554937 0.0961179i
\(694\) −0.420445 0.728233i −0.0159599 0.0276433i
\(695\) 0 0
\(696\) 25.7652 0.976627
\(697\) −0.0172554 0.0298872i −0.000653593 0.00113206i
\(698\) 1.74511 3.02263i 0.0660535 0.114408i
\(699\) 18.1535 + 31.4427i 0.686627 + 1.18927i
\(700\) 0 0
\(701\) 10.9167 18.9083i 0.412319 0.714158i −0.582824 0.812599i \(-0.698052\pi\)
0.995143 + 0.0984408i \(0.0313855\pi\)
\(702\) 1.69306 0.0639006
\(703\) −0.206264 + 0.158439i −0.00777941 + 0.00597564i
\(704\) −2.08578 −0.0786107
\(705\) 0 0
\(706\) −1.45763 + 2.52469i −0.0548586 + 0.0950179i
\(707\) 34.2133 + 59.2591i 1.28672 + 2.22867i
\(708\) 11.3588 19.6739i 0.426888 0.739392i
\(709\) 0.325939 + 0.564543i 0.0122409 + 0.0212019i 0.872081 0.489362i \(-0.162770\pi\)
−0.859840 + 0.510563i \(0.829437\pi\)
\(710\) 0 0
\(711\) 27.3098 1.02420
\(712\) −2.53280 4.38694i −0.0949206 0.164407i
\(713\) 9.91694 + 17.1766i 0.371392 + 0.643270i
\(714\) −0.0257221 −0.000962625
\(715\) 0 0
\(716\) −5.59399 9.68907i −0.209057 0.362098i
\(717\) −10.8020 + 18.7097i −0.403410 + 0.698726i
\(718\) 3.34264 + 5.78963i 0.124746 + 0.216067i
\(719\) 2.31346 4.00704i 0.0862777 0.149437i −0.819657 0.572854i \(-0.805836\pi\)
0.905935 + 0.423417i \(0.139169\pi\)
\(720\) 0 0
\(721\) 34.9955 1.30330
\(722\) 4.18399 + 4.17549i 0.155712 + 0.155396i
\(723\) 44.2097 1.64418
\(724\) 1.05125 1.82082i 0.0390694 0.0676702i
\(725\) 0 0
\(726\) −3.79434 6.57199i −0.140821 0.243909i
\(727\) −7.91445 + 13.7082i −0.293531 + 0.508410i −0.974642 0.223770i \(-0.928164\pi\)
0.681111 + 0.732180i \(0.261497\pi\)
\(728\) 6.06387 + 10.5029i 0.224742 + 0.389265i
\(729\) −7.76076 −0.287435
\(730\) 0 0
\(731\) 0.0195541 + 0.0338686i 0.000723233 + 0.00125268i
\(732\) 19.0011 + 32.9108i 0.702299 + 1.21642i
\(733\) −28.8257 −1.06470 −0.532350 0.846524i \(-0.678691\pi\)
−0.532350 + 0.846524i \(0.678691\pi\)
\(734\) 9.36851 0.345798
\(735\) 0 0
\(736\) 9.45149 16.3705i 0.348386 0.603423i
\(737\) 0.840470 + 1.45574i 0.0309591 + 0.0536228i
\(738\) −1.17769 + 2.03981i −0.0433513 + 0.0750866i
\(739\) −13.8458 + 23.9817i −0.509327 + 0.882180i 0.490614 + 0.871377i \(0.336772\pi\)
−0.999942 + 0.0108038i \(0.996561\pi\)
\(740\) 0 0
\(741\) 19.5192 14.9934i 0.717056 0.550797i
\(742\) 13.5481 0.497367
\(743\) −22.4228 + 38.8374i −0.822611 + 1.42480i 0.0811199 + 0.996704i \(0.474150\pi\)
−0.903731 + 0.428100i \(0.859183\pi\)
\(744\) −4.99712 + 8.65527i −0.183203 + 0.317318i
\(745\) 0 0
\(746\) −4.15649 + 7.19925i −0.152180 + 0.263583i
\(747\) 15.8224 + 27.4052i 0.578911 + 1.00270i
\(748\) −0.00638588 −0.000233491
\(749\) −5.18313 −0.189387
\(750\) 0 0
\(751\) 12.3257 + 21.3488i 0.449772 + 0.779029i 0.998371 0.0570573i \(-0.0181718\pi\)
−0.548599 + 0.836086i \(0.684838\pi\)
\(752\) 44.2746 1.61453
\(753\) −20.6570 −0.752782
\(754\) −3.70053 6.40951i −0.134765 0.233421i
\(755\) 0 0
\(756\) 8.16949 + 14.1500i 0.297122 + 0.514630i
\(757\) 23.1313 40.0646i 0.840721 1.45617i −0.0485649 0.998820i \(-0.515465\pi\)
0.889286 0.457352i \(-0.151202\pi\)
\(758\) −3.57356 + 6.18960i −0.129798 + 0.224816i
\(759\) 4.38732 0.159250
\(760\) 0 0
\(761\) −18.7036 −0.678004 −0.339002 0.940786i \(-0.610089\pi\)
−0.339002 + 0.940786i \(0.610089\pi\)
\(762\) 4.13795 7.16715i 0.149902 0.259638i
\(763\) 12.0999 20.9577i 0.438046 0.758719i
\(764\) 20.2136 + 35.0109i 0.731301 + 1.26665i
\(765\) 0 0
\(766\) −4.52482 7.83721i −0.163488 0.283170i
\(767\) −13.3831 −0.483235
\(768\) −19.7630 −0.713135
\(769\) 5.45393 + 9.44648i 0.196674 + 0.340649i 0.947448 0.319910i \(-0.103653\pi\)
−0.750774 + 0.660559i \(0.770319\pi\)
\(770\) 0 0
\(771\) −1.02842 −0.0370376
\(772\) 18.1576 0.653508
\(773\) 3.94152 + 6.82692i 0.141767 + 0.245547i 0.928162 0.372176i \(-0.121388\pi\)
−0.786395 + 0.617724i \(0.788055\pi\)
\(774\) 1.33458 2.31155i 0.0479703 0.0830871i
\(775\) 0 0
\(776\) −2.27192 + 3.93508i −0.0815571 + 0.141261i
\(777\) 0.265757 0.460304i 0.00953397 0.0165133i