Properties

Label 475.2.e.f.26.4
Level $475$
Weight $2$
Character 475.26
Analytic conductor $3.793$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [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: \( x^{12} - 3 x^{11} + 17 x^{10} - 18 x^{9} + 109 x^{8} - 93 x^{7} + 484 x^{6} - 147 x^{5} + 1009 x^{4} - 552 x^{3} + 1107 x^{2} + 33 x + 1 \) 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 26.4
Root \(1.62208 - 2.80952i\) of defining polynomial
Character \(\chi\) \(=\) 475.26
Dual form 475.2.e.f.201.4

$q$-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 \(\left(\mathbb{Z}/475\mathbb{Z}\right)^\times\).

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

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 0.805774 0.592223i \(-0.201750\pi\)
−0.915767 + 0.401709i \(0.868416\pi\)
\(3\) 1.12208 + 1.94349i 0.647832 + 1.12208i 0.983640 + 0.180147i \(0.0576573\pi\)
−0.335808 + 0.941930i \(0.609009\pi\)
\(4\) 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 −0.986059 0.166396i \(-0.946787\pi\)
0.637132 + 0.770754i \(0.280120\pi\)
\(14\) −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 0.865462 0.500974i \(-0.167025\pi\)
−0.866588 + 0.499025i \(0.833692\pi\)
\(18\) 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 −0.433325 0.901238i \(-0.642660\pi\)
0.997157 0.0753481i \(-0.0240068\pi\)
\(24\) −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 −0.0241473 + 0.999708i \(0.507687\pi\)
−0.853699 + 0.520766i \(0.825646\pi\)
\(30\) 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 0.683553 0.729901i \(-0.260434\pi\)
−0.973889 + 0.227024i \(0.927100\pi\)
\(42\) 1.38562 2.39997i 0.213806 0.370323i
\(43\) 2.10671 + 3.64894i 0.321271 + 0.556458i 0.980751 0.195265i \(-0.0625566\pi\)
−0.659480 + 0.751722i \(0.729223\pi\)
\(44\) 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 −0.179735 + 0.983715i \(0.557524\pi\)
−0.762055 + 0.647513i \(0.775809\pi\)
\(48\) 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 0.192601 + 0.981277i \(0.438308\pi\)
−0.946112 + 0.323841i \(0.895026\pi\)
\(54\) −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 0.985576 0.169231i \(-0.0541283\pi\)
−0.639346 + 0.768919i \(0.720795\pi\)
\(60\) 0 0
\(61\) 4.44875 7.70546i 0.569604 0.986583i −0.427001 0.904251i \(-0.640430\pi\)
0.996605 0.0823316i \(-0.0262366\pi\)
\(62\) −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 −0.688334 0.725393i \(-0.741658\pi\)
0.972376 + 0.233418i \(0.0749912\pi\)
\(68\) −0.0176652 −0.00214222
\(69\) 12.1366 1.46107
\(70\) 0 0
\(71\) −7.68968 13.3189i −0.912597 1.58066i −0.810382 0.585902i \(-0.800740\pi\)
−0.102215 0.994762i \(-0.532593\pi\)
\(72\) 1.23632 2.14136i 0.145701 0.252362i
\(73\) −4.83162 8.36861i −0.565498 0.979471i −0.997003 0.0773609i \(-0.975351\pi\)
0.431505 0.902110i \(-0.357983\pi\)
\(74\) −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 −0.945632 0.325237i \(-0.894556\pi\)
0.191153 0.981560i \(-0.438777\pi\)
\(80\) 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 −0.734048 0.679098i \(-0.762371\pi\)
0.955140 + 0.296155i \(0.0957046\pi\)
\(90\) 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 0.945238 0.326381i \(-0.105829\pi\)
−0.755273 + 0.655410i \(0.772496\pi\)
\(98\) −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 −0.0164664 0.999864i \(-0.505242\pi\)
0.874141 0.485672i \(-0.161425\pi\)
\(102\) −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 0.974279 0.225347i \(-0.0723515\pi\)
−0.682295 + 0.731077i \(0.739018\pi\)
\(110\) 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 0.473624 + 0.880727i \(0.342946\pi\)
−0.999544 + 0.0301937i \(0.990388\pi\)
\(128\) 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 0.913781 0.406207i \(-0.133149\pi\)
−0.808676 + 0.588254i \(0.799816\pi\)
\(132\) 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 −0.953065 0.302765i \(-0.902090\pi\)
0.738735 + 0.673996i \(0.235423\pi\)
\(138\) −1.88789 3.26993i −0.160708 0.278355i
\(139\) −5.84248 + 10.1195i −0.495553 + 0.858323i −0.999987 0.00512757i \(-0.998368\pi\)
0.504434 + 0.863450i \(0.331701\pi\)
\(140\) 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 0.965287 0.261190i \(-0.0841150\pi\)
−0.708841 + 0.705368i \(0.750782\pi\)
\(150\) 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 −0.992963 0.118424i \(-0.962216\pi\)
0.393923 0.919143i \(-0.371118\pi\)
\(158\) −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 −0.691479 0.722397i \(-0.743040\pi\)
0.971353 + 0.237640i \(0.0763737\pi\)
\(168\) −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 0.793097 0.609095i \(-0.208467\pi\)
−0.924040 + 0.382295i \(0.875134\pi\)
\(174\) 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 −0.885823 0.464023i \(-0.846406\pi\)
0.844767 + 0.535134i \(0.179739\pi\)
\(182\) 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 0.985056 0.172232i \(-0.0550979\pi\)
−0.641686 + 0.766968i \(0.721765\pi\)
\(194\) 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 −0.261166 0.965294i \(-0.584107\pi\)
0.966552 0.256471i \(-0.0825598\pi\)
\(200\) 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 0.952197 + 0.305484i \(0.0988182\pi\)
−0.211542 + 0.977369i \(0.567848\pi\)
\(212\) 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 0.943735 0.330704i \(-0.107286\pi\)
−0.758265 + 0.651946i \(0.773953\pi\)
\(224\) −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 −0.999390 0.0349268i \(-0.988880\pi\)
0.469447 0.882960i \(-0.344453\pi\)
\(234\) −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 −0.352130 0.935951i \(-0.614543\pi\)
0.986622 0.163022i \(-0.0521241\pi\)
\(242\) 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 −0.973928 0.226856i \(-0.927155\pi\)
0.683428 + 0.730018i \(0.260489\pi\)
\(252\) 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 −0.873083 0.487571i \(-0.837883\pi\)
0.858790 + 0.512327i \(0.171216\pi\)
\(258\) 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 0.988361 0.152124i \(-0.0486114\pi\)
−0.625924 + 0.779884i \(0.715278\pi\)
\(264\) −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 0.784190 0.620521i \(-0.213079\pi\)
−0.929482 + 0.368868i \(0.879745\pi\)
\(270\) 0 0
\(271\) 7.75620 + 13.4341i 0.471155 + 0.816065i 0.999456 0.0329925i \(-0.0105038\pi\)
−0.528300 + 0.849058i \(0.677170\pi\)
\(272\) −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 −0.994688 0.102936i \(-0.967176\pi\)
0.586489 + 0.809957i \(0.300510\pi\)
\(282\) 4.50782 + 7.80777i 0.268437 + 0.464946i
\(283\) −8.43386 14.6079i −0.501341 0.868348i −0.999999 0.00154919i \(-0.999507\pi\)
0.498658 0.866799i \(-0.333826\pi\)
\(284\) −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 0.909195 0.416370i \(-0.136698\pi\)
−0.815184 + 0.579202i \(0.803364\pi\)
\(308\) 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 −0.962804 0.270201i \(-0.912910\pi\)
0.715403 + 0.698712i \(0.246243\pi\)
\(314\) −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 −0.724159 0.689633i \(-0.757772\pi\)
0.959319 + 0.282324i \(0.0911054\pi\)
\(318\) 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 0.695180 0.718836i \(-0.255325\pi\)
−0.970120 + 0.242626i \(0.921991\pi\)
\(338\) 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 0.827469 0.561512i \(-0.189780\pi\)
−0.900018 + 0.435853i \(0.856447\pi\)
\(348\) −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 0.996854 + 0.0792550i \(0.0252541\pi\)
−0.429790 + 0.902929i \(0.641413\pi\)
\(360\) 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 0.142475 + 0.989798i \(0.454494\pi\)
−0.928428 + 0.371512i \(0.878839\pi\)
\(368\) −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 −0.951043 0.309059i \(-0.899986\pi\)
0.207868 0.978157i \(-0.433347\pi\)
\(384\) −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 −0.908444 0.418006i \(-0.862729\pi\)
0.816226 + 0.577732i \(0.196062\pi\)
\(390\) 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 0.986190 0.165616i \(-0.0529613\pi\)
−0.636523 + 0.771258i \(0.719628\pi\)
\(398\) −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 −0.979843 0.199767i \(-0.935981\pi\)
0.316918 0.948453i \(-0.397352\pi\)
\(402\) −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 −0.989681 0.143285i \(-0.954234\pi\)
0.618929 + 0.785447i \(0.287567\pi\)
\(410\) 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 0.876663 0.481105i \(-0.159765\pi\)
−0.854981 + 0.518660i \(0.826431\pi\)
\(422\) 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 −0.987097 0.160126i \(-0.948810\pi\)
0.632222 + 0.774787i \(0.282143\pi\)
\(432\) −3.70782 6.42213i −0.178393 0.308985i
\(433\) −0.742440 + 1.28594i −0.0356794 + 0.0617985i −0.883314 0.468782i \(-0.844693\pi\)
0.847634 + 0.530581i \(0.178026\pi\)
\(434\) −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 0.986372 0.164533i \(-0.0526118\pi\)
−0.635676 + 0.771956i \(0.719278\pi\)
\(440\) 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 −0.997915 0.0645421i \(-0.979441\pi\)
0.554853 + 0.831949i \(0.312775\pi\)
\(444\) 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 −0.967289 0.253675i \(-0.918361\pi\)
0.263955 0.964535i \(-0.414973\pi\)
\(462\) 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 −0.0246685 0.999696i \(-0.507853\pi\)
0.878096 0.478484i \(-0.158814\pi\)
\(480\) 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 0.999126 0.0418074i \(-0.0133116\pi\)
−0.535769 + 0.844365i \(0.679978\pi\)
\(492\) −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 0.857660 0.514218i \(-0.171918\pi\)
−0.874155 + 0.485646i \(0.838584\pi\)
\(500\) 0 0
\(501\) 16.2332 0.725247
\(502\) 2.86368 0.127812
\(503\) 4.99035 8.64354i 0.222509 0.385397i −0.733060 0.680164i \(-0.761909\pi\)
0.955569 + 0.294767i \(0.0952420\pi\)
\(504\) 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 −0.300217 0.953871i \(-0.597059\pi\)
0.976185 0.216940i \(-0.0696075\pi\)
\(510\) 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 −0.721327 0.692595i \(-0.756468\pi\)
0.960468 + 0.278390i \(0.0898009\pi\)
\(524\) 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 0.354747 + 0.934962i \(0.384567\pi\)
−0.987075 + 0.160261i \(0.948766\pi\)
\(542\) 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 0.268750 + 0.963210i \(0.413390\pi\)
−0.968539 + 0.248861i \(0.919944\pi\)
\(548\) 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 −0.948923 0.315508i \(-0.897825\pi\)
0.747699 + 0.664038i \(0.231159\pi\)
\(558\) 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 0.998198 0.0600130i \(-0.0191142\pi\)
−0.551072 + 0.834458i \(0.685781\pi\)
\(588\) 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 −0.500209 0.865905i \(-0.666743\pi\)
1.00000 0.000240828i \(7.66580e-5\pi\)
\(594\) −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 −0.604861 0.796331i \(-0.706771\pi\)
0.992073 + 0.125659i \(0.0401046\pi\)
\(600\) 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 0.826048 0.563600i \(-0.190584\pi\)
−0.901116 + 0.433578i \(0.857251\pi\)
\(614\) 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 −0.624515 0.781013i \(-0.714703\pi\)
0.988634 + 0.150340i \(0.0480368\pi\)
\(618\) 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 −0.981368 0.192138i \(-0.938458\pi\)
0.657080 + 0.753821i \(0.271791\pi\)
\(632\) 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 0.749284 0.662249i \(-0.230398\pi\)
−0.948166 + 0.317775i \(0.897064\pi\)
\(642\) −0.455842 + 0.789542i −0.0179907 + 0.0311607i
\(643\) 2.14765 + 3.71984i 0.0846950 + 0.146696i 0.905261 0.424855i \(-0.139675\pi\)
−0.820566 + 0.571552i \(0.806342\pi\)
\(644\) −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 0.0142676 + 0.999898i \(0.495458\pi\)
−0.873071 + 0.487593i \(0.837875\pi\)
\(660\) 0 0
\(661\) 22.0688 38.2243i 0.858378 1.48675i −0.0150971 0.999886i \(-0.504806\pi\)
0.873475 0.486869i \(-0.161861\pi\)
\(662\) 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 0.995143 0.0984408i \(-0.0313855\pi\)
−0.582824 + 0.812599i \(0.698052\pi\)
\(702\) 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 −0.859840 0.510563i \(-0.829437\pi\)
0.872081 + 0.489362i \(0.162770\pi\)
\(710\) 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 0.905935 0.423417i \(-0.139169\pi\)
−0.819657 + 0.572854i \(0.805836\pi\)
\(720\) 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 0.681111 0.732180i \(-0.261497\pi\)
−0.974642 + 0.223770i \(0.928164\pi\)
\(728\) 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 −0.999942 0.0108038i \(-0.996561\pi\)
0.490614 0.871377i \(-0.336772\pi\)
\(740\) 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 −0.903731 0.428100i \(-0.859183\pi\)
0.0811199 0.996704i \(-0.474150\pi\)
\(744\) −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 −0.548599 0.836086i \(-0.684838\pi\)
0.998371 + 0.0570573i \(0.0181718\pi\)
\(752\) 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 0.889286 + 0.457352i \(0.151202\pi\)
−0.0485649 + 0.998820i \(0.515465\pi\)
\(758\) −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 −0.750774 0.660559i \(-0.770319\pi\)
0.947448 + 0.319910i \(0.103653\pi\)
\(770\) 0 0
\(771\) −1.02842 −0.0370376
\(772\) 18.1576 0.653508
\(773\) 3.94152 6.82692i 0.141767 0.245547i −0.786395 0.617724i \(-0.788055\pi\)
0.928162 + 0.372176i \(0.121388\pi\)
\(774\) 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
\(778\) 1.13170 0.0405733
\(779\) −2.12360 + 16.0672i −0.0760858 + 0.575665i
\(780\) 0 0
\(781\) −2.77978 4.81472i −0.0994684 0.172284i
\(782\) 0.00780829 + 0.0135244i 0.000279224 + 0.000483630i
\(783\) −10.2246 + 17.7094i −0.365396 + 0.632884i
\(784\) −15.0091 25.9966i −0.536040 0.928449i
\(785\) 0 0
\(786\) 1.67978 0.0599156
\(787\) −35.5229 −1.26625 −0.633127 0.774048i \(-0.718229\pi\)
−0.633127 + 0.774048i \(0.718229\pi\)
\(788\) −1.95954 + 3.39402i −0.0698056 + 0.120907i
\(789\) −13.1906 + 22.8467i −0.469596 + 0.813365i
\(790\) 0 0
\(791\) −44.6074 −1.58605
\(792\) 0.446923 0.774092i 0.0158807 0.0275062i
\(793\) 11.1937 + 19.3881i 0.397500 + 0.688490i
\(794\) 2.16751 3.75424i 0.0769221 0.133233i
\(795\) 0 0
\(796\) −18.9383 32.8021i −0.671250 1.16264i
\(797\) 26.0958 0.924359 0.462180 0.886786i \(-0.347068\pi\)
0.462180 + 0.886786i \(0.347068\pi\)
\(798\) −11.1624 + 4.61697i −0.395145 + 0.163439i
\(799\) 0.119857 0.00424024
\(800\) 0 0
\(801\) 4.24712 + 7.35622i 0.150064 + 0.259919i
\(802\) −4.12998 + 7.15333i −0.145835 + 0.252593i
\(803\) −1.74661 3.02521i −0.0616364 0.106757i
\(804\) 9.93024 17.1997i 0.350213 0.606586i
\(805\) 0 0
\(806\) 2.87085 0.101121
\(807\) 5.34774 9.26256i 0.188249 0.326058i
\(808\) −10.4669 + 18.1291i −0.368223 + 0.637781i
\(809\) 9.65732 0.339533 0.169767 0.985484i \(-0.445699\pi\)
0.169767 + 0.985484i \(0.445699\pi\)
\(810\) 0 0
\(811\) −3.70765 + 6.42183i −0.130193 + 0.225501i −0.923751 0.382994i \(-0.874893\pi\)
0.793558 + 0.608495i \(0.208226\pi\)
\(812\) 35.7121 + 61.8553i 1.25325 + 2.17069i
\(813\) −17.4061 + 30.1483i −0.610459 + 1.05735i
\(814\) −0.00335532 0.00581158i −0.000117604 0.000203696i
\(815\) 0 0
\(816\) −0.0714177 −0.00250012
\(817\) 2.40650 18.2076i 0.0841927 0.637002i
\(818\) 4.66538 0.163121
\(819\) −10.1682 17.6118i −0.355305 0.615407i
\(820\) 0 0
\(821\) −13.4155 + 23.2363i −0.468203 + 0.810951i −0.999340 0.0363349i \(-0.988432\pi\)
0.531137 + 0.847286i \(0.321765\pi\)
\(822\) 1.75149 + 3.03366i 0.0610901 + 0.105811i
\(823\) −18.3038 + 31.7031i −0.638031 + 1.10510i 0.347833 + 0.937556i \(0.386917\pi\)
−0.985864 + 0.167546i \(0.946416\pi\)
\(824\) −10.7062 −0.372967
\(825\) 0 0
\(826\) 3.28407 5.68818i 0.114268 0.197917i
\(827\) −10.2533 + 17.7593i −0.356544 + 0.617552i −0.987381 0.158363i \(-0.949378\pi\)
0.630837 + 0.775915i \(0.282712\pi\)
\(828\) 20.9584 0.728353
\(829\) −19.9749 −0.693758 −0.346879 0.937910i \(-0.612759\pi\)
−0.346879 + 0.937910i \(0.612759\pi\)
\(830\) 0 0
\(831\) 5.50577 + 9.53628i 0.190993 + 0.330810i
\(832\) 7.25890 12.5728i 0.251657 0.435883i
\(833\) −0.0406317 0.0703761i −0.00140780 0.00243839i
\(834\) 4.07907 + 7.06515i 0.141247 + 0.244646i
\(835\) 0 0
\(836\) −2.77124 + 1.14623i −0.0958452 + 0.0396432i
\(837\) 7.93215 0.274175
\(838\) −4.73706 8.20482i −0.163639 0.283431i
\(839\) −9.96670 17.2628i −0.344089 0.595979i 0.641099 0.767458i \(-0.278479\pi\)
−0.985188 + 0.171479i \(0.945145\pi\)
\(840\) 0 0
\(841\) −30.1956 52.3004i −1.04123 1.80346i
\(842\) 0.138404 0.239723i 0.00476973 0.00826141i
\(843\) −30.7120 −1.05778
\(844\) 40.9520 1.40962
\(845\) 0 0
\(846\) −4.09016 + 7.08437i −0.140623 + 0.243566i
\(847\) −43.1433 −1.48242
\(848\) 37.6165 1.29176
\(849\) 18.9269 32.7823i 0.649569 1.12509i
\(850\) 0 0
\(851\) 0.161348 0.279463i 0.00553094 0.00957987i
\(852\) −32.8434 56.8864i −1.12520 1.94890i
\(853\) −0.802795 1.39048i −0.0274872 0.0476092i 0.851955 0.523616i \(-0.175417\pi\)
−0.879442 + 0.476006i \(0.842084\pi\)
\(854\) −10.9873 −0.375977
\(855\) 0 0
\(856\) 1.58567 0.0541972
\(857\) 8.79122 + 15.2268i 0.300302 + 0.520139i 0.976204 0.216853i \(-0.0695791\pi\)
−0.675902 + 0.736991i \(0.736246\pi\)
\(858\) 0.317521 + 0.549962i 0.0108400 + 0.0187754i
\(859\) −6.97697 + 12.0845i −0.238051 + 0.412317i −0.960155 0.279468i \(-0.909842\pi\)
0.722104 + 0.691785i \(0.243175\pi\)
\(860\) 0 0
\(861\) 16.5599 28.6825i 0.564358 0.977498i
\(862\) 4.58411 0.156135
\(863\) 19.9200 0.678085 0.339042 0.940771i \(-0.389897\pi\)
0.339042 + 0.940771i \(0.389897\pi\)
\(864\) −3.77992 + 6.54702i −0.128596 + 0.222734i
\(865\) 0 0
\(866\) 0.461958 0.0156980
\(867\) 38.1504 1.29566
\(868\) 13.8526 23.9935i 0.470189 0.814392i
\(869\) −2.42417 4.19879i −0.0822345 0.142434i
\(870\) 0 0
\(871\) 5.85000 + 10.1325i 0.198220 + 0.343326i
\(872\) −3.70173 6.41158i −0.125356 0.217123i
\(873\) −7.61932 −0.257875
\(874\) 5.81605 + 4.46752i 0.196731 + 0.151116i
\(875\) 0 0
\(876\) −20.6363 35.7432i −0.697237 1.20765i
\(877\) −5.07142 8.78395i −0.171250 0.296613i 0.767607 0.640920i \(-0.221447\pi\)
−0.938857 + 0.344307i \(0.888114\pi\)
\(878\) 2.28599 3.95944i 0.0771483 0.133625i
\(879\) 29.0386 + 50.2964i 0.979449 + 1.69646i
\(880\) 0 0
\(881\) 21.4114 0.721370 0.360685 0.932688i \(-0.382543\pi\)
0.360685 + 0.932688i \(0.382543\pi\)
\(882\) 5.54627 0.186753
\(883\) −11.1287 + 19.2755i −0.374512 + 0.648673i −0.990254 0.139275i \(-0.955523\pi\)
0.615742 + 0.787948i \(0.288856\pi\)
\(884\) 0.0222241 0.0384933i 0.000747477 0.00129467i
\(885\) 0 0
\(886\) 5.80240 0.194935
\(887\) −15.1467 + 26.2349i −0.508577 + 0.880881i 0.491374 + 0.870949i \(0.336495\pi\)
−0.999951 + 0.00993225i \(0.996838\pi\)
\(888\) −0.0813029 0.140821i −0.00272835 0.00472564i
\(889\) −23.5252 + 40.7468i −0.789010 + 1.36660i
\(890\) 0 0
\(891\) 1.98144 + 3.43195i 0.0663807 + 0.114975i
\(892\) 10.5425 0.352988
\(893\) 52.0135 21.5137i 1.74057 0.719929i
\(894\) 4.37102 0.146189
\(895\) 0 0
\(896\) 17.4364 + 30.2007i 0.582509 + 1.00894i
\(897\) −15.2687 + 26.4462i −0.509807 + 0.883012i
\(898\) −0.804782 1.39392i −0.0268559 0.0465158i
\(899\) −17.3373 + 30.0291i −0.578232 + 1.00153i
\(900\) 0 0
\(901\) 0.101833 0.00339255
\(902\) −0.209077 + 0.362132i −0.00696150 + 0.0120577i
\(903\) −18.7659 + 32.5035i −0.624490 + 1.08165i
\(904\) 13.6467 0.453883
\(905\) 0 0
\(906\) −5.35625 + 9.27729i −0.177949 + 0.308217i
\(907\) −19.8755 34.4254i −0.659956 1.14308i −0.980626 0.195887i \(-0.937241\pi\)
0.320670 0.947191i \(-0.396092\pi\)
\(908\) 15.4542 26.7674i 0.512865 0.888308i
\(909\) 17.5513 + 30.3998i 0.582141 + 1.00830i
\(910\) 0 0
\(911\) 25.5927 0.847924 0.423962 0.905680i \(-0.360639\pi\)
0.423962 + 0.905680i \(0.360639\pi\)
\(912\) −30.9926 + 12.8191i −1.02627 + 0.424482i
\(913\) −5.61795 −0.185927
\(914\) 3.14715 + 5.45103i 0.104099 + 0.180304i
\(915\) 0 0
\(916\) 10.0333 17.3782i 0.331510 0.574193i
\(917\) 4.77495 + 8.27046i 0.157683 + 0.273115i
\(918\) −0.00312276 + 0.00540878i −0.000103067 + 0.000178516i
\(919\) 37.3594 1.23237 0.616186 0.787601i \(-0.288677\pi\)
0.616186 + 0.787601i \(0.288677\pi\)
\(920\) 0 0
\(921\) −3.69659 + 6.40268i −0.121807 + 0.210975i
\(922\) −4.69811 + 8.13736i −0.154724 + 0.267990i
\(923\) 38.6967 1.27372
\(924\) 6.12849 0.201613
\(925\) 0 0
\(926\) 3.17423 + 5.49792i 0.104312 + 0.180673i
\(927\) −8.97630 + 15.5474i −0.294820 + 0.510644i
\(928\) −16.5236 28.6197i −0.542413 0.939487i
\(929\) −1.05742 1.83151i −0.0346929 0.0600898i 0.848158 0.529744i \(-0.177712\pi\)
−0.882851 + 0.469654i \(0.844379\pi\)
\(930\) 0 0
\(931\) −30.2648 23.2474i −0.991887 0.761904i
\(932\) −30.7910 −1.00859
\(933\) 34.1395 + 59.1313i 1.11768 + 1.93587i
\(934\) −2.47553 4.28774i −0.0810017 0.140299i
\(935\) 0 0
\(936\) 3.11075 + 5.38798i 0.101678 + 0.176112i
\(937\) −22.3198 + 38.6590i −0.729156 + 1.26294i 0.228084 + 0.973642i \(0.426754\pi\)
−0.957240 + 0.289294i \(0.906579\pi\)
\(938\) −5.74212 −0.187487
\(939\) −19.6452 −0.641096
\(940\) 0 0
\(941\) −8.90021 + 15.4156i −0.290139 + 0.502535i −0.973842 0.227225i \(-0.927035\pi\)
0.683704 + 0.729760i \(0.260368\pi\)
\(942\) −10.4809 −0.341487
\(943\) −20.1079 −0.654803
\(944\) 9.11827 15.7933i 0.296774 0.514028i
\(945\) 0 0
\(946\) 0.236930 0.410374i 0.00770324 0.0133424i
\(947\) −29.4788 51.0587i −0.957932 1.65919i −0.727512 0.686095i \(-0.759324\pi\)
−0.230419 0.973091i \(-0.574010\pi\)
\(948\) −28.6419 49.6091i −0.930244 1.61123i
\(949\) 24.3141 0.789269
\(950\) 0 0
\(951\) 18.7921 0.609375
\(952\) 0.0223689 + 0.0387442i 0.000724982 + 0.00125571i
\(953\) −19.3641 33.5396i −0.627265 1.08645i −0.988098 0.153824i \(-0.950841\pi\)
0.360833 0.932630i \(-0.382492\pi\)
\(954\) −3.47508 + 6.01901i −0.112510 + 0.194873i
\(955\) 0 0
\(956\) −9.16095 + 15.8672i −0.296286 + 0.513183i
\(957\) −7.67013 −0.247940
\(958\) −11.6219 −0.375485
\(959\) −9.95760 + 17.2471i −0.321548 + 0.556937i
\(960\) 0 0
\(961\) −17.5498 −0.566123
\(962\) 0.0467086 0.00150595
\(963\) 1.32947 2.30270i 0.0428415 0.0742036i
\(964\) −18.7466 32.4700i −0.603787 1.04579i
\(965\) 0 0
\(966\) −7.49357 12.9792i −0.241102 0.417600i
\(967\) 3.39611 + 5.88224i 0.109212 + 0.189160i 0.915451 0.402429i \(-0.131834\pi\)
−0.806239 + 0.591589i \(0.798501\pi\)
\(968\) 13.1988 0.424227
\(969\) −0.0839011 + 0.0347030i −0.00269529 + 0.00111482i
\(970\) 0 0
\(971\) 20.1819 + 34.9560i 0.647667 + 1.12179i 0.983679 + 0.179935i \(0.0575887\pi\)
−0.336011 + 0.941858i \(0.609078\pi\)
\(972\) 17.2363 + 29.8542i 0.552856 + 0.957574i
\(973\) −23.1904 + 40.1670i −0.743451 + 1.28769i
\(974\) −6.06769 10.5095i −0.194421 0.336747i
\(975\) 0 0
\(976\) −30.5063 −0.976483
\(977\) −29.7383 −0.951412 −0.475706 0.879604i \(-0.657807\pi\)
−0.475706 + 0.879604i \(0.657807\pi\)
\(978\) 4.15044 7.18877i 0.132716 0.229871i
\(979\) 0.753998 1.30596i 0.0240979 0.0417388i
\(980\) 0 0
\(981\) −12.4145 −0.396363
\(982\) 3.19424 5.53258i 0.101932 0.176552i
\(983\) −1.76233 3.05245i −0.0562097 0.0973580i 0.836551 0.547888i \(-0.184568\pi\)
−0.892761 + 0.450530i \(0.851235\pi\)
\(984\) −5.06615 + 8.77484i −0.161503 + 0.279732i
\(985\) 0 0
\(986\) −0.0136509 0.0236440i −0.000434732 0.000752977i
\(987\) −115.026 −3.66132
\(988\) 2.73510 20.6937i 0.0870150 0.658356i
\(989\) 22.7866 0.724571
\(990\) 0 0
\(991\) 8.39292 + 14.5370i 0.266610 + 0.461782i 0.967984 0.251011i \(-0.0807631\pi\)
−0.701374 + 0.712793i \(0.747430\pi\)
\(992\) −6.40945 + 11.1015i −0.203500 + 0.352473i
\(993\) −20.0331 34.6983i −0.635731 1.10112i
\(994\) −9.49577 + 16.4472i −0.301188 + 0.521672i
\(995\) 0 0
\(996\) −66.3767 −2.10322
\(997\) 8.62648 14.9415i 0.273203 0.473202i −0.696477 0.717579i \(-0.745250\pi\)
0.969680 + 0.244377i \(0.0785835\pi\)
\(998\) −0.114639 + 0.198560i −0.00362883 + 0.00628532i
\(999\) 0.129056 0.00408314
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 475.2.e.f.26.4 12
5.2 odd 4 475.2.j.d.349.8 24
5.3 odd 4 475.2.j.d.349.5 24
5.4 even 2 475.2.e.h.26.3 yes 12
19.7 even 3 9025.2.a.bz.1.3 6
19.11 even 3 inner 475.2.e.f.201.4 yes 12
19.12 odd 6 9025.2.a.bs.1.4 6
95.49 even 6 475.2.e.h.201.3 yes 12
95.64 even 6 9025.2.a.br.1.4 6
95.68 odd 12 475.2.j.d.49.8 24
95.69 odd 6 9025.2.a.by.1.3 6
95.87 odd 12 475.2.j.d.49.5 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
475.2.e.f.26.4 12 1.1 even 1 trivial
475.2.e.f.201.4 yes 12 19.11 even 3 inner
475.2.e.h.26.3 yes 12 5.4 even 2
475.2.e.h.201.3 yes 12 95.49 even 6
475.2.j.d.49.5 24 95.87 odd 12
475.2.j.d.49.8 24 95.68 odd 12
475.2.j.d.349.5 24 5.3 odd 4
475.2.j.d.349.8 24 5.2 odd 4
9025.2.a.br.1.4 6 95.64 even 6
9025.2.a.bs.1.4 6 19.12 odd 6
9025.2.a.by.1.3 6 95.69 odd 6
9025.2.a.bz.1.3 6 19.7 even 3