Properties

Label 201.3.g.b.29.17
Level $201$
Weight $3$
Character 201.29
Analytic conductor $5.477$
Analytic rank $0$
Dimension $84$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [201,3,Mod(29,201)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(201, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 4]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("201.29");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 201 = 3 \cdot 67 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 201.g (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(5.47685331364\)
Analytic rank: \(0\)
Dimension: \(84\)
Relative dimension: \(42\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 29.17
Character \(\chi\) \(=\) 201.29
Dual form 201.3.g.b.104.17

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.922015 - 0.532326i) q^{2} +(-0.226863 - 2.99141i) q^{3} +(-1.43326 - 2.48248i) q^{4} +3.49902i q^{5} +(-1.38323 + 2.87889i) q^{6} +(-3.66463 - 6.34732i) q^{7} +7.31045i q^{8} +(-8.89707 + 1.35728i) q^{9} +O(q^{10})\) \(q+(-0.922015 - 0.532326i) q^{2} +(-0.226863 - 2.99141i) q^{3} +(-1.43326 - 2.48248i) q^{4} +3.49902i q^{5} +(-1.38323 + 2.87889i) q^{6} +(-3.66463 - 6.34732i) q^{7} +7.31045i q^{8} +(-8.89707 + 1.35728i) q^{9} +(1.86262 - 3.22615i) q^{10} +(-7.57038 + 4.37076i) q^{11} +(-7.10095 + 4.85065i) q^{12} +(7.80551 - 13.5195i) q^{13} +7.80310i q^{14} +(10.4670 - 0.793798i) q^{15} +(-1.84150 + 3.18957i) q^{16} +(5.61889 + 3.24407i) q^{17} +(8.92574 + 3.48470i) q^{18} +(-17.6375 + 30.5490i) q^{19} +(8.68624 - 5.01501i) q^{20} +(-18.1561 + 12.4024i) q^{21} +9.30668 q^{22} +(1.47866 + 0.853704i) q^{23} +(21.8685 - 1.65847i) q^{24} +12.7568 q^{25} +(-14.3936 + 8.31015i) q^{26} +(6.07859 + 26.3069i) q^{27} +(-10.5047 + 18.1947i) q^{28} +(-38.8478 + 22.4288i) q^{29} +(-10.0733 - 4.83996i) q^{30} +(-22.3841 - 38.7704i) q^{31} +(28.7199 - 16.5814i) q^{32} +(14.7922 + 21.6546i) q^{33} +(-3.45380 - 5.98215i) q^{34} +(22.2094 - 12.8226i) q^{35} +(16.1212 + 20.1414i) q^{36} +(2.74210 - 4.74945i) q^{37} +(32.5241 - 18.7778i) q^{38} +(-42.2133 - 20.2824i) q^{39} -25.5794 q^{40} +(7.37884 - 4.26018i) q^{41} +(23.3423 - 1.77023i) q^{42} -61.0618 q^{43} +(21.7006 + 12.5289i) q^{44} +(-4.74915 - 31.1310i) q^{45} +(-0.908897 - 1.57426i) q^{46} +(-61.2387 + 35.3562i) q^{47} +(9.95907 + 4.78508i) q^{48} +(-2.35901 + 4.08593i) q^{49} +(-11.7620 - 6.79079i) q^{50} +(8.42961 - 17.5443i) q^{51} -44.7493 q^{52} -103.769i q^{53} +(8.39926 - 27.4911i) q^{54} +(-15.2934 - 26.4889i) q^{55} +(46.4018 - 26.7901i) q^{56} +(95.3860 + 45.8305i) q^{57} +47.7576 q^{58} -32.6824i q^{59} +(-16.9725 - 24.8464i) q^{60} +(19.3186 - 33.4609i) q^{61} +47.6625i q^{62} +(41.2195 + 51.4986i) q^{63} -20.5749 q^{64} +(47.3052 + 27.3117i) q^{65} +(-2.11134 - 27.8401i) q^{66} +(-30.1071 + 59.8545i) q^{67} -18.5983i q^{68} +(2.21833 - 4.61695i) q^{69} -27.3032 q^{70} +(-25.8373 + 14.9172i) q^{71} +(-9.92232 - 65.0415i) q^{72} +(44.7274 - 77.4701i) q^{73} +(-5.05651 + 2.91938i) q^{74} +(-2.89405 - 38.1609i) q^{75} +101.116 q^{76} +(55.4853 + 32.0345i) q^{77} +(28.1244 + 41.1719i) q^{78} +(5.54828 + 9.60990i) q^{79} +(-11.1604 - 6.44344i) q^{80} +(77.3156 - 24.1516i) q^{81} -9.07120 q^{82} +(-113.146 - 65.3246i) q^{83} +(56.8110 + 27.2962i) q^{84} +(-11.3511 + 19.6606i) q^{85} +(56.2999 + 32.5048i) q^{86} +(75.9067 + 111.121i) q^{87} +(-31.9522 - 55.3429i) q^{88} -105.058i q^{89} +(-12.1931 + 31.2314i) q^{90} -114.417 q^{91} -4.89432i q^{92} +(-110.900 + 75.7556i) q^{93} +75.2840 q^{94} +(-106.892 - 61.7140i) q^{95} +(-56.1174 - 82.1513i) q^{96} +(33.7046 - 58.3781i) q^{97} +(4.35009 - 2.51153i) q^{98} +(61.4219 - 49.1621i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 84 q - 6 q^{3} + 82 q^{4} + 3 q^{6} - 10 q^{7} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 84 q - 6 q^{3} + 82 q^{4} + 3 q^{6} - 10 q^{7} + 2 q^{9} + 6 q^{10} - 58 q^{12} - 6 q^{13} + 78 q^{15} - 130 q^{16} + 11 q^{18} + 72 q^{19} - 36 q^{21} + 140 q^{22} + 72 q^{24} - 428 q^{25} + 138 q^{27} - 8 q^{28} + 29 q^{30} - 28 q^{31} - 30 q^{33} - 54 q^{34} + 105 q^{36} - 24 q^{37} - 103 q^{39} + 128 q^{40} + 252 q^{42} + 148 q^{43} + 276 q^{45} - 146 q^{46} + 137 q^{48} - 176 q^{49} + 15 q^{51} - 792 q^{52} + 72 q^{54} + 28 q^{55} - 205 q^{57} - 120 q^{58} - 64 q^{60} + 162 q^{61} - 106 q^{63} - 604 q^{64} - 462 q^{66} - 460 q^{67} + 101 q^{69} + 636 q^{70} + 212 q^{72} + 238 q^{73} + 628 q^{75} + 40 q^{76} + 96 q^{78} + 462 q^{79} - 726 q^{81} - 344 q^{82} + 385 q^{84} - 94 q^{85} - 91 q^{87} + 234 q^{88} + 482 q^{90} - 536 q^{91} + 281 q^{93} + 580 q^{94} + 40 q^{96} + 68 q^{97} + 379 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/201\mathbb{Z}\right)^\times\).

\(n\) \(68\) \(136\)
\(\chi(n)\) \(-1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.922015 0.532326i −0.461008 0.266163i 0.251460 0.967868i \(-0.419089\pi\)
−0.712468 + 0.701705i \(0.752423\pi\)
\(3\) −0.226863 2.99141i −0.0756209 0.997137i
\(4\) −1.43326 2.48248i −0.358315 0.620619i
\(5\) 3.49902i 0.699805i 0.936786 + 0.349902i \(0.113785\pi\)
−0.936786 + 0.349902i \(0.886215\pi\)
\(6\) −1.38323 + 2.87889i −0.230539 + 0.479815i
\(7\) −3.66463 6.34732i −0.523518 0.906761i −0.999625 0.0273731i \(-0.991286\pi\)
0.476107 0.879387i \(-0.342048\pi\)
\(8\) 7.31045i 0.913806i
\(9\) −8.89707 + 1.35728i −0.988563 + 0.150809i
\(10\) 1.86262 3.22615i 0.186262 0.322615i
\(11\) −7.57038 + 4.37076i −0.688217 + 0.397342i −0.802944 0.596055i \(-0.796734\pi\)
0.114727 + 0.993397i \(0.463401\pi\)
\(12\) −7.10095 + 4.85065i −0.591746 + 0.404221i
\(13\) 7.80551 13.5195i 0.600424 1.03996i −0.392333 0.919823i \(-0.628332\pi\)
0.992757 0.120141i \(-0.0383348\pi\)
\(14\) 7.80310i 0.557365i
\(15\) 10.4670 0.793798i 0.697801 0.0529199i
\(16\) −1.84150 + 3.18957i −0.115094 + 0.199348i
\(17\) 5.61889 + 3.24407i 0.330523 + 0.190827i 0.656073 0.754697i \(-0.272216\pi\)
−0.325550 + 0.945525i \(0.605550\pi\)
\(18\) 8.92574 + 3.48470i 0.495875 + 0.193595i
\(19\) −17.6375 + 30.5490i −0.928289 + 1.60784i −0.142105 + 0.989852i \(0.545387\pi\)
−0.786184 + 0.617992i \(0.787946\pi\)
\(20\) 8.68624 5.01501i 0.434312 0.250750i
\(21\) −18.1561 + 12.4024i −0.864575 + 0.590589i
\(22\) 9.30668 0.423031
\(23\) 1.47866 + 0.853704i 0.0642895 + 0.0371176i 0.531800 0.846870i \(-0.321516\pi\)
−0.467511 + 0.883987i \(0.654849\pi\)
\(24\) 21.8685 1.65847i 0.911189 0.0691029i
\(25\) 12.7568 0.510274
\(26\) −14.3936 + 8.31015i −0.553600 + 0.319621i
\(27\) 6.07859 + 26.3069i 0.225133 + 0.974328i
\(28\) −10.5047 + 18.1947i −0.375169 + 0.649811i
\(29\) −38.8478 + 22.4288i −1.33958 + 0.773406i −0.986745 0.162281i \(-0.948115\pi\)
−0.352833 + 0.935686i \(0.614782\pi\)
\(30\) −10.0733 4.83996i −0.335777 0.161332i
\(31\) −22.3841 38.7704i −0.722068 1.25066i −0.960170 0.279418i \(-0.909859\pi\)
0.238102 0.971240i \(-0.423475\pi\)
\(32\) 28.7199 16.5814i 0.897497 0.518170i
\(33\) 14.7922 + 21.6546i 0.448248 + 0.656199i
\(34\) −3.45380 5.98215i −0.101582 0.175946i
\(35\) 22.2094 12.8226i 0.634555 0.366361i
\(36\) 16.1212 + 20.1414i 0.447811 + 0.559484i
\(37\) 2.74210 4.74945i 0.0741107 0.128363i −0.826589 0.562807i \(-0.809722\pi\)
0.900699 + 0.434443i \(0.143055\pi\)
\(38\) 32.5241 18.7778i 0.855897 0.494152i
\(39\) −42.2133 20.2824i −1.08239 0.520062i
\(40\) −25.5794 −0.639486
\(41\) 7.37884 4.26018i 0.179972 0.103907i −0.407308 0.913291i \(-0.633532\pi\)
0.587279 + 0.809384i \(0.300199\pi\)
\(42\) 23.3423 1.77023i 0.555769 0.0421484i
\(43\) −61.0618 −1.42004 −0.710021 0.704181i \(-0.751314\pi\)
−0.710021 + 0.704181i \(0.751314\pi\)
\(44\) 21.7006 + 12.5289i 0.493196 + 0.284747i
\(45\) −4.74915 31.1310i −0.105537 0.691801i
\(46\) −0.908897 1.57426i −0.0197586 0.0342230i
\(47\) −61.2387 + 35.3562i −1.30295 + 0.752259i −0.980909 0.194466i \(-0.937703\pi\)
−0.322042 + 0.946725i \(0.604369\pi\)
\(48\) 9.95907 + 4.78508i 0.207481 + 0.0996891i
\(49\) −2.35901 + 4.08593i −0.0481431 + 0.0833863i
\(50\) −11.7620 6.79079i −0.235240 0.135816i
\(51\) 8.42961 17.5443i 0.165287 0.344007i
\(52\) −44.7493 −0.860563
\(53\) 103.769i 1.95790i −0.204096 0.978951i \(-0.565426\pi\)
0.204096 0.978951i \(-0.434574\pi\)
\(54\) 8.39926 27.4911i 0.155542 0.509095i
\(55\) −15.2934 26.4889i −0.278062 0.481617i
\(56\) 46.4018 26.7901i 0.828603 0.478394i
\(57\) 95.3860 + 45.8305i 1.67344 + 0.804044i
\(58\) 47.7576 0.823407
\(59\) 32.6824i 0.553940i −0.960879 0.276970i \(-0.910670\pi\)
0.960879 0.276970i \(-0.0893302\pi\)
\(60\) −16.9725 24.8464i −0.282875 0.414107i
\(61\) 19.3186 33.4609i 0.316699 0.548539i −0.663098 0.748532i \(-0.730759\pi\)
0.979797 + 0.199994i \(0.0640922\pi\)
\(62\) 47.6625i 0.768750i
\(63\) 41.2195 + 51.4986i 0.654278 + 0.817439i
\(64\) −20.5749 −0.321483
\(65\) 47.3052 + 27.3117i 0.727772 + 0.420179i
\(66\) −2.11134 27.8401i −0.0319900 0.421820i
\(67\) −30.1071 + 59.8545i −0.449360 + 0.893351i
\(68\) 18.5983i 0.273505i
\(69\) 2.21833 4.61695i 0.0321497 0.0669123i
\(70\) −27.3032 −0.390046
\(71\) −25.8373 + 14.9172i −0.363906 + 0.210101i −0.670793 0.741645i \(-0.734046\pi\)
0.306887 + 0.951746i \(0.400713\pi\)
\(72\) −9.92232 65.0415i −0.137810 0.903355i
\(73\) 44.7274 77.4701i 0.612704 1.06123i −0.378078 0.925774i \(-0.623415\pi\)
0.990783 0.135461i \(-0.0432516\pi\)
\(74\) −5.05651 + 2.91938i −0.0683312 + 0.0394510i
\(75\) −2.89405 38.1609i −0.0385874 0.508812i
\(76\) 101.116 1.33048
\(77\) 55.4853 + 32.0345i 0.720588 + 0.416032i
\(78\) 28.1244 + 41.1719i 0.360570 + 0.527845i
\(79\) 5.54828 + 9.60990i 0.0702313 + 0.121644i 0.899003 0.437943i \(-0.144293\pi\)
−0.828771 + 0.559587i \(0.810960\pi\)
\(80\) −11.1604 6.44344i −0.139505 0.0805430i
\(81\) 77.3156 24.1516i 0.954513 0.298168i
\(82\) −9.07120 −0.110624
\(83\) −113.146 65.3246i −1.36320 0.787044i −0.373152 0.927770i \(-0.621723\pi\)
−0.990049 + 0.140726i \(0.955056\pi\)
\(84\) 56.8110 + 27.2962i 0.676321 + 0.324955i
\(85\) −11.3511 + 19.6606i −0.133542 + 0.231301i
\(86\) 56.2999 + 32.5048i 0.654650 + 0.377962i
\(87\) 75.9067 + 111.121i 0.872491 + 1.27726i
\(88\) −31.9522 55.3429i −0.363094 0.628896i
\(89\) 105.058i 1.18043i −0.807247 0.590213i \(-0.799044\pi\)
0.807247 0.590213i \(-0.200956\pi\)
\(90\) −12.1931 + 31.2314i −0.135478 + 0.347015i
\(91\) −114.417 −1.25733
\(92\) 4.89432i 0.0531991i
\(93\) −110.900 + 75.7556i −1.19247 + 0.814576i
\(94\) 75.2840 0.800894
\(95\) −106.892 61.7140i −1.12518 0.649621i
\(96\) −56.1174 82.1513i −0.584556 0.855743i
\(97\) 33.7046 58.3781i 0.347470 0.601836i −0.638329 0.769764i \(-0.720374\pi\)
0.985799 + 0.167927i \(0.0537074\pi\)
\(98\) 4.35009 2.51153i 0.0443887 0.0256278i
\(99\) 61.4219 49.1621i 0.620423 0.496587i
\(100\) −18.2839 31.6686i −0.182839 0.316686i
\(101\) −80.3871 + 46.4115i −0.795912 + 0.459520i −0.842040 0.539415i \(-0.818645\pi\)
0.0461275 + 0.998936i \(0.485312\pi\)
\(102\) −17.1115 + 11.6889i −0.167760 + 0.114597i
\(103\) 20.7632 + 35.9630i 0.201585 + 0.349155i 0.949039 0.315158i \(-0.102057\pi\)
−0.747454 + 0.664313i \(0.768724\pi\)
\(104\) 98.8339 + 57.0618i 0.950326 + 0.548671i
\(105\) −43.3962 63.5285i −0.413297 0.605034i
\(106\) −55.2388 + 95.6764i −0.521121 + 0.902607i
\(107\) 37.0884i 0.346621i 0.984867 + 0.173310i \(0.0554464\pi\)
−0.984867 + 0.173310i \(0.944554\pi\)
\(108\) 56.5940 52.7945i 0.524018 0.488838i
\(109\) −76.9467 −0.705933 −0.352966 0.935636i \(-0.614827\pi\)
−0.352966 + 0.935636i \(0.614827\pi\)
\(110\) 32.5643i 0.296039i
\(111\) −14.8296 7.12526i −0.133600 0.0641915i
\(112\) 26.9936 0.241014
\(113\) −53.5363 + 30.9092i −0.473773 + 0.273533i −0.717818 0.696231i \(-0.754859\pi\)
0.244045 + 0.969764i \(0.421526\pi\)
\(114\) −63.5505 93.0328i −0.557461 0.816078i
\(115\) −2.98713 + 5.17386i −0.0259750 + 0.0449901i
\(116\) 111.358 + 64.2924i 0.959981 + 0.554245i
\(117\) −51.0963 + 130.878i −0.436721 + 1.11862i
\(118\) −17.3977 + 30.1337i −0.147438 + 0.255370i
\(119\) 47.5532i 0.399607i
\(120\) 5.80302 + 76.5185i 0.0483585 + 0.637654i
\(121\) −22.2929 + 38.6124i −0.184238 + 0.319110i
\(122\) −35.6241 + 20.5676i −0.292001 + 0.168587i
\(123\) −14.4179 21.1067i −0.117219 0.171599i
\(124\) −64.1644 + 111.136i −0.517455 + 0.896258i
\(125\) 132.112i 1.05690i
\(126\) −10.5910 69.4247i −0.0840555 0.550990i
\(127\) −11.9491 20.6964i −0.0940871 0.162964i 0.815140 0.579264i \(-0.196660\pi\)
−0.909227 + 0.416300i \(0.863327\pi\)
\(128\) −95.9092 55.3732i −0.749291 0.432603i
\(129\) 13.8526 + 182.661i 0.107385 + 1.41598i
\(130\) −29.0774 50.3635i −0.223672 0.387412i
\(131\) 48.1582i 0.367620i −0.982962 0.183810i \(-0.941157\pi\)
0.982962 0.183810i \(-0.0588430\pi\)
\(132\) 32.5559 67.7578i 0.246636 0.513317i
\(133\) 258.539 1.94391
\(134\) 59.6213 39.1600i 0.444935 0.292239i
\(135\) −92.0483 + 21.2691i −0.681839 + 0.157549i
\(136\) −23.7156 + 41.0766i −0.174379 + 0.302034i
\(137\) 256.618i 1.87312i 0.350501 + 0.936562i \(0.386011\pi\)
−0.350501 + 0.936562i \(0.613989\pi\)
\(138\) −4.50305 + 3.07602i −0.0326308 + 0.0222900i
\(139\) 122.839 0.883735 0.441867 0.897080i \(-0.354316\pi\)
0.441867 + 0.897080i \(0.354316\pi\)
\(140\) −63.6637 36.7563i −0.454741 0.262545i
\(141\) 119.658 + 175.169i 0.848636 + 1.24233i
\(142\) 31.7632 0.223684
\(143\) 136.464i 0.954295i
\(144\) 12.0548 30.8772i 0.0837138 0.214425i
\(145\) −78.4787 135.929i −0.541233 0.937443i
\(146\) −82.4787 + 47.6191i −0.564922 + 0.326158i
\(147\) 12.7579 + 6.12983i 0.0867882 + 0.0416995i
\(148\) −15.7205 −0.106220
\(149\) 35.1770i 0.236087i 0.993008 + 0.118044i \(0.0376623\pi\)
−0.993008 + 0.118044i \(0.962338\pi\)
\(150\) −17.6457 + 36.7255i −0.117638 + 0.244837i
\(151\) 53.4378 92.5570i 0.353893 0.612960i −0.633035 0.774123i \(-0.718191\pi\)
0.986928 + 0.161163i \(0.0515244\pi\)
\(152\) −223.327 128.938i −1.46926 0.848276i
\(153\) −54.3947 21.2363i −0.355521 0.138799i
\(154\) −34.1055 59.0725i −0.221464 0.383588i
\(155\) 135.659 78.3225i 0.875216 0.505306i
\(156\) 10.1519 + 133.863i 0.0650766 + 0.858099i
\(157\) 68.8127 119.187i 0.438297 0.759153i −0.559261 0.828992i \(-0.688915\pi\)
0.997558 + 0.0698384i \(0.0222484\pi\)
\(158\) 11.8140i 0.0747719i
\(159\) −310.415 + 23.5413i −1.95230 + 0.148058i
\(160\) 58.0189 + 100.492i 0.362618 + 0.628073i
\(161\) 12.5140i 0.0777269i
\(162\) −84.1427 18.8889i −0.519399 0.116598i
\(163\) 127.665 + 221.122i 0.783221 + 1.35658i 0.930056 + 0.367418i \(0.119758\pi\)
−0.146835 + 0.989161i \(0.546909\pi\)
\(164\) −21.1516 12.2119i −0.128973 0.0744626i
\(165\) −75.7698 + 51.7582i −0.459211 + 0.313686i
\(166\) 69.5480 + 120.461i 0.418964 + 0.725666i
\(167\) 0.664259 0.383510i 0.00397760 0.00229647i −0.498010 0.867171i \(-0.665936\pi\)
0.501987 + 0.864875i \(0.332602\pi\)
\(168\) −90.6669 132.729i −0.539684 0.790054i
\(169\) −37.3520 64.6955i −0.221018 0.382814i
\(170\) 20.9317 12.0849i 0.123128 0.0710878i
\(171\) 115.458 295.736i 0.675195 1.72945i
\(172\) 87.5173 + 151.584i 0.508822 + 0.881305i
\(173\) 17.7375 + 10.2407i 0.102529 + 0.0591949i 0.550388 0.834909i \(-0.314480\pi\)
−0.447859 + 0.894104i \(0.647813\pi\)
\(174\) −10.8344 142.863i −0.0622668 0.821050i
\(175\) −46.7491 80.9718i −0.267138 0.462696i
\(176\) 32.1950i 0.182926i
\(177\) −97.7666 + 7.41443i −0.552353 + 0.0418894i
\(178\) −55.9251 + 96.8650i −0.314186 + 0.544186i
\(179\) 189.671i 1.05961i −0.848118 0.529807i \(-0.822264\pi\)
0.848118 0.529807i \(-0.177736\pi\)
\(180\) −70.4753 + 56.4085i −0.391530 + 0.313381i
\(181\) −101.194 175.273i −0.559082 0.968359i −0.997573 0.0696232i \(-0.977820\pi\)
0.438491 0.898735i \(-0.355513\pi\)
\(182\) 105.494 + 60.9072i 0.579639 + 0.334655i
\(183\) −104.478 50.1989i −0.570917 0.274311i
\(184\) −6.24096 + 10.8097i −0.0339182 + 0.0587481i
\(185\) 16.6184 + 9.59465i 0.0898293 + 0.0518630i
\(186\) 142.578 10.8129i 0.766549 0.0581336i
\(187\) −56.7162 −0.303295
\(188\) 175.542 + 101.349i 0.933733 + 0.539091i
\(189\) 144.702 134.988i 0.765621 0.714220i
\(190\) 65.7039 + 113.802i 0.345810 + 0.598960i
\(191\) 27.4349 + 15.8396i 0.143638 + 0.0829296i 0.570097 0.821577i \(-0.306906\pi\)
−0.426459 + 0.904507i \(0.640239\pi\)
\(192\) 4.66769 + 61.5481i 0.0243109 + 0.320563i
\(193\) 52.2310 0.270627 0.135314 0.990803i \(-0.456796\pi\)
0.135314 + 0.990803i \(0.456796\pi\)
\(194\) −62.1523 + 35.8837i −0.320373 + 0.184967i
\(195\) 70.9686 147.705i 0.363941 0.757462i
\(196\) 13.5243 0.0690016
\(197\) 178.120 102.837i 0.904160 0.522017i 0.0256125 0.999672i \(-0.491846\pi\)
0.878548 + 0.477655i \(0.158513\pi\)
\(198\) −82.8021 + 12.6318i −0.418193 + 0.0637968i
\(199\) 28.3985 49.1876i 0.142706 0.247174i −0.785809 0.618470i \(-0.787753\pi\)
0.928515 + 0.371296i \(0.121086\pi\)
\(200\) 93.2582i 0.466291i
\(201\) 185.880 + 76.4839i 0.924774 + 0.380517i
\(202\) 98.8242 0.489229
\(203\) 284.725 + 164.386i 1.40259 + 0.809784i
\(204\) −55.6353 + 4.21927i −0.272722 + 0.0206827i
\(205\) 14.9065 + 25.8187i 0.0727144 + 0.125945i
\(206\) 44.2112i 0.214618i
\(207\) −14.3144 5.58851i −0.0691519 0.0269976i
\(208\) 28.7476 + 49.7924i 0.138210 + 0.239386i
\(209\) 308.357i 1.47539i
\(210\) 6.19409 + 81.6752i 0.0294957 + 0.388929i
\(211\) 37.0172 64.1157i 0.175437 0.303866i −0.764875 0.644178i \(-0.777200\pi\)
0.940312 + 0.340312i \(0.110533\pi\)
\(212\) −257.604 + 148.728i −1.21511 + 0.701545i
\(213\) 50.4849 + 73.9058i 0.237018 + 0.346976i
\(214\) 19.7431 34.1961i 0.0922576 0.159795i
\(215\) 213.657i 0.993752i
\(216\) −192.315 + 44.4372i −0.890347 + 0.205728i
\(217\) −164.059 + 284.158i −0.756032 + 1.30949i
\(218\) 70.9460 + 40.9607i 0.325440 + 0.187893i
\(219\) −241.892 116.223i −1.10453 0.530698i
\(220\) −43.8388 + 75.9310i −0.199267 + 0.345141i
\(221\) 87.7165 50.6432i 0.396907 0.229155i
\(222\) 9.88018 + 14.4638i 0.0445053 + 0.0651522i
\(223\) 310.836 1.39388 0.696941 0.717128i \(-0.254544\pi\)
0.696941 + 0.717128i \(0.254544\pi\)
\(224\) −210.496 121.530i −0.939713 0.542543i
\(225\) −113.498 + 17.3146i −0.504438 + 0.0769537i
\(226\) 65.8150 0.291217
\(227\) −257.878 + 148.886i −1.13603 + 0.655885i −0.945443 0.325787i \(-0.894371\pi\)
−0.190582 + 0.981671i \(0.561038\pi\)
\(228\) −22.9395 302.481i −0.100612 1.32667i
\(229\) −12.8588 + 22.2721i −0.0561519 + 0.0972579i −0.892735 0.450582i \(-0.851216\pi\)
0.836583 + 0.547840i \(0.184550\pi\)
\(230\) 5.50836 3.18025i 0.0239494 0.0138272i
\(231\) 83.2406 173.247i 0.360349 0.749986i
\(232\) −163.964 283.994i −0.706743 1.22411i
\(233\) −0.274420 + 0.158436i −0.00117777 + 0.000679985i −0.500589 0.865685i \(-0.666883\pi\)
0.499411 + 0.866365i \(0.333550\pi\)
\(234\) 116.782 93.4721i 0.499067 0.399453i
\(235\) −123.712 214.276i −0.526434 0.911811i
\(236\) −81.1334 + 46.8424i −0.343786 + 0.198485i
\(237\) 27.4884 18.7773i 0.115985 0.0792291i
\(238\) −25.3138 + 43.8448i −0.106360 + 0.184222i
\(239\) 341.120 196.946i 1.42728 0.824040i 0.430374 0.902651i \(-0.358382\pi\)
0.996905 + 0.0786104i \(0.0250483\pi\)
\(240\) −16.7431 + 34.8470i −0.0697629 + 0.145196i
\(241\) −351.412 −1.45814 −0.729071 0.684438i \(-0.760048\pi\)
−0.729071 + 0.684438i \(0.760048\pi\)
\(242\) 41.1087 23.7341i 0.169871 0.0980749i
\(243\) −89.7874 225.804i −0.369495 0.929233i
\(244\) −110.754 −0.453911
\(245\) −14.2968 8.25424i −0.0583541 0.0336908i
\(246\) 2.05792 + 27.1357i 0.00836552 + 0.110308i
\(247\) 275.339 + 476.902i 1.11473 + 1.93078i
\(248\) 283.429 163.638i 1.14286 0.659830i
\(249\) −169.744 + 353.285i −0.681704 + 1.41881i
\(250\) 70.3266 121.809i 0.281307 0.487237i
\(251\) 227.364 + 131.268i 0.905831 + 0.522982i 0.879087 0.476661i \(-0.158153\pi\)
0.0267434 + 0.999642i \(0.491486\pi\)
\(252\) 68.7659 176.137i 0.272881 0.698958i
\(253\) −14.9254 −0.0589935
\(254\) 25.4432i 0.100170i
\(255\) 61.3881 + 29.4954i 0.240738 + 0.115668i
\(256\) 100.103 + 173.384i 0.391028 + 0.677280i
\(257\) −92.6308 + 53.4804i −0.360431 + 0.208095i −0.669270 0.743019i \(-0.733393\pi\)
0.308839 + 0.951114i \(0.400060\pi\)
\(258\) 84.4627 175.790i 0.327375 0.681357i
\(259\) −40.1950 −0.155193
\(260\) 156.579i 0.602226i
\(261\) 315.189 252.277i 1.20762 0.966580i
\(262\) −25.6358 + 44.4026i −0.0978467 + 0.169475i
\(263\) 391.796i 1.48972i −0.667222 0.744859i \(-0.732517\pi\)
0.667222 0.744859i \(-0.267483\pi\)
\(264\) −158.305 + 108.137i −0.599638 + 0.409612i
\(265\) 363.089 1.37015
\(266\) −238.377 137.627i −0.896155 0.517395i
\(267\) −314.271 + 23.8337i −1.17705 + 0.0892650i
\(268\) 191.739 11.0468i 0.715443 0.0412194i
\(269\) 228.018i 0.847649i 0.905744 + 0.423824i \(0.139313\pi\)
−0.905744 + 0.423824i \(0.860687\pi\)
\(270\) 96.1920 + 29.3892i 0.356267 + 0.108849i
\(271\) −119.513 −0.441009 −0.220504 0.975386i \(-0.570770\pi\)
−0.220504 + 0.975386i \(0.570770\pi\)
\(272\) −20.6943 + 11.9479i −0.0760821 + 0.0439260i
\(273\) 25.9570 + 342.269i 0.0950806 + 1.25373i
\(274\) 136.604 236.606i 0.498556 0.863525i
\(275\) −96.5742 + 55.7571i −0.351179 + 0.202753i
\(276\) −14.6409 + 1.11034i −0.0530467 + 0.00402296i
\(277\) 333.903 1.20543 0.602713 0.797958i \(-0.294086\pi\)
0.602713 + 0.797958i \(0.294086\pi\)
\(278\) −113.260 65.3904i −0.407408 0.235217i
\(279\) 251.775 + 314.561i 0.902420 + 1.12746i
\(280\) 93.7391 + 162.361i 0.334782 + 0.579860i
\(281\) 183.796 + 106.115i 0.654078 + 0.377632i 0.790017 0.613085i \(-0.210072\pi\)
−0.135939 + 0.990717i \(0.543405\pi\)
\(282\) −17.0791 225.205i −0.0605643 0.798601i
\(283\) −116.411 −0.411347 −0.205674 0.978621i \(-0.565938\pi\)
−0.205674 + 0.978621i \(0.565938\pi\)
\(284\) 74.0631 + 42.7603i 0.260786 + 0.150565i
\(285\) −160.362 + 333.758i −0.562674 + 1.17108i
\(286\) 72.6434 125.822i 0.253998 0.439937i
\(287\) −54.0814 31.2239i −0.188437 0.108794i
\(288\) −233.017 + 186.507i −0.809088 + 0.647594i
\(289\) −123.452 213.825i −0.427170 0.739880i
\(290\) 167.105i 0.576224i
\(291\) −182.279 87.5805i −0.626389 0.300964i
\(292\) −256.424 −0.878164
\(293\) 25.2338i 0.0861221i 0.999072 + 0.0430610i \(0.0137110\pi\)
−0.999072 + 0.0430610i \(0.986289\pi\)
\(294\) −8.49988 12.4431i −0.0289112 0.0423236i
\(295\) 114.357 0.387649
\(296\) 34.7206 + 20.0459i 0.117299 + 0.0677228i
\(297\) −160.998 172.585i −0.542082 0.581094i
\(298\) 18.7256 32.4337i 0.0628376 0.108838i
\(299\) 23.0834 13.3272i 0.0772019 0.0445725i
\(300\) −90.5857 + 61.8789i −0.301952 + 0.206263i
\(301\) 223.769 + 387.579i 0.743418 + 1.28764i
\(302\) −98.5410 + 56.8927i −0.326295 + 0.188386i
\(303\) 157.073 + 229.942i 0.518392 + 0.758884i
\(304\) −64.9588 112.512i −0.213680 0.370105i
\(305\) 117.080 + 67.5963i 0.383870 + 0.221627i
\(306\) 38.8481 + 48.5359i 0.126955 + 0.158614i
\(307\) −15.2405 + 26.3972i −0.0496432 + 0.0859845i −0.889779 0.456391i \(-0.849142\pi\)
0.840136 + 0.542376i \(0.182475\pi\)
\(308\) 183.655i 0.596281i
\(309\) 102.870 70.2700i 0.332911 0.227411i
\(310\) −166.772 −0.537975
\(311\) 98.5812i 0.316981i 0.987360 + 0.158491i \(0.0506628\pi\)
−0.987360 + 0.158491i \(0.949337\pi\)
\(312\) 148.273 308.598i 0.475235 0.989096i
\(313\) −70.6652 −0.225767 −0.112884 0.993608i \(-0.536009\pi\)
−0.112884 + 0.993608i \(0.536009\pi\)
\(314\) −126.893 + 73.2615i −0.404117 + 0.233317i
\(315\) −180.195 + 144.228i −0.572047 + 0.457867i
\(316\) 15.9042 27.5469i 0.0503298 0.0871738i
\(317\) −351.005 202.653i −1.10727 0.639283i −0.169149 0.985591i \(-0.554102\pi\)
−0.938121 + 0.346308i \(0.887435\pi\)
\(318\) 298.739 + 143.536i 0.939431 + 0.451372i
\(319\) 196.062 339.589i 0.614613 1.06454i
\(320\) 71.9922i 0.224976i
\(321\) 110.947 8.41398i 0.345628 0.0262118i
\(322\) −6.66154 + 11.5381i −0.0206880 + 0.0358327i
\(323\) −198.206 + 114.434i −0.613641 + 0.354286i
\(324\) −170.769 157.319i −0.527065 0.485551i
\(325\) 99.5736 172.467i 0.306380 0.530666i
\(326\) 271.838i 0.833857i
\(327\) 17.4563 + 230.179i 0.0533833 + 0.703911i
\(328\) 31.1438 + 53.9426i 0.0949506 + 0.164459i
\(329\) 448.834 + 259.135i 1.36424 + 0.787643i
\(330\) 97.4131 7.38762i 0.295191 0.0223867i
\(331\) −83.8706 145.268i −0.253386 0.438877i 0.711070 0.703121i \(-0.248211\pi\)
−0.964456 + 0.264244i \(0.914877\pi\)
\(332\) 374.509i 1.12804i
\(333\) −17.9503 + 45.9779i −0.0539047 + 0.138072i
\(334\) −0.816609 −0.00244494
\(335\) −209.432 105.345i −0.625171 0.314464i
\(336\) −6.12385 80.7490i −0.0182257 0.240324i
\(337\) −158.869 + 275.170i −0.471422 + 0.816527i −0.999466 0.0326900i \(-0.989593\pi\)
0.528043 + 0.849218i \(0.322926\pi\)
\(338\) 79.5336i 0.235307i
\(339\) 104.607 + 153.137i 0.308577 + 0.451731i
\(340\) 65.0760 0.191400
\(341\) 338.912 + 195.671i 0.993878 + 0.573816i
\(342\) −263.882 + 211.211i −0.771585 + 0.617577i
\(343\) −324.554 −0.946222
\(344\) 446.389i 1.29764i
\(345\) 16.1548 + 7.76197i 0.0468255 + 0.0224985i
\(346\) −10.9028 18.8842i −0.0315110 0.0545786i
\(347\) −301.912 + 174.309i −0.870063 + 0.502331i −0.867369 0.497665i \(-0.834191\pi\)
−0.00269406 + 0.999996i \(0.500858\pi\)
\(348\) 167.062 347.702i 0.480064 0.999145i
\(349\) −263.699 −0.755584 −0.377792 0.925890i \(-0.623317\pi\)
−0.377792 + 0.925890i \(0.623317\pi\)
\(350\) 99.5429i 0.284408i
\(351\) 403.103 + 123.159i 1.14844 + 0.350879i
\(352\) −144.947 + 251.056i −0.411782 + 0.713227i
\(353\) 24.1915 + 13.9670i 0.0685311 + 0.0395664i 0.533874 0.845564i \(-0.320736\pi\)
−0.465343 + 0.885130i \(0.654069\pi\)
\(354\) 94.0891 + 45.2074i 0.265788 + 0.127705i
\(355\) −52.1955 90.4053i −0.147030 0.254663i
\(356\) −260.804 + 150.575i −0.732596 + 0.422964i
\(357\) −142.251 + 10.7880i −0.398462 + 0.0302186i
\(358\) −100.967 + 174.879i −0.282030 + 0.488490i
\(359\) 512.479i 1.42752i −0.700391 0.713760i \(-0.746991\pi\)
0.700391 0.713760i \(-0.253009\pi\)
\(360\) 227.582 34.7184i 0.632172 0.0964400i
\(361\) −441.662 764.982i −1.22344 2.11906i
\(362\) 215.472i 0.595228i
\(363\) 120.563 + 57.9274i 0.332129 + 0.159580i
\(364\) 163.989 + 284.038i 0.450520 + 0.780324i
\(365\) 271.070 + 156.502i 0.742657 + 0.428773i
\(366\) 69.6079 + 101.900i 0.190186 + 0.278416i
\(367\) −182.779 316.583i −0.498037 0.862625i 0.501961 0.864890i \(-0.332612\pi\)
−0.999997 + 0.00226548i \(0.999279\pi\)
\(368\) −5.44589 + 3.14419i −0.0147986 + 0.00854398i
\(369\) −59.8678 + 47.9182i −0.162243 + 0.129860i
\(370\) −10.2150 17.6928i −0.0276080 0.0478185i
\(371\) −658.654 + 380.274i −1.77535 + 1.02500i
\(372\) 347.010 + 166.729i 0.932822 + 0.448197i
\(373\) −69.8619 121.004i −0.187297 0.324409i 0.757051 0.653356i \(-0.226639\pi\)
−0.944348 + 0.328947i \(0.893306\pi\)
\(374\) 52.2932 + 30.1915i 0.139821 + 0.0807259i
\(375\) 395.201 29.9713i 1.05387 0.0799235i
\(376\) −258.470 447.682i −0.687419 1.19064i
\(377\) 700.272i 1.85748i
\(378\) −205.275 + 47.4319i −0.543056 + 0.125481i
\(379\) −133.778 + 231.710i −0.352976 + 0.611373i −0.986769 0.162130i \(-0.948164\pi\)
0.633793 + 0.773503i \(0.281497\pi\)
\(380\) 353.808i 0.931075i
\(381\) −59.2006 + 40.4398i −0.155382 + 0.106141i
\(382\) −16.8636 29.2086i −0.0441456 0.0764624i
\(383\) −46.1988 26.6729i −0.120624 0.0696420i 0.438474 0.898744i \(-0.355519\pi\)
−0.559098 + 0.829102i \(0.688852\pi\)
\(384\) −143.886 + 299.466i −0.374702 + 0.779859i
\(385\) −112.089 + 194.144i −0.291141 + 0.504271i
\(386\) −48.1578 27.8039i −0.124761 0.0720309i
\(387\) 543.271 82.8779i 1.40380 0.214155i
\(388\) −193.230 −0.498015
\(389\) −228.037 131.657i −0.586213 0.338450i 0.177386 0.984141i \(-0.443236\pi\)
−0.763599 + 0.645691i \(0.776569\pi\)
\(390\) −144.061 + 98.4080i −0.369388 + 0.252328i
\(391\) 5.53894 + 9.59373i 0.0141661 + 0.0245364i
\(392\) −29.8700 17.2454i −0.0761989 0.0439935i
\(393\) −144.061 + 10.9253i −0.366567 + 0.0277997i
\(394\) −218.972 −0.555766
\(395\) −33.6252 + 19.4135i −0.0851272 + 0.0491482i
\(396\) −210.077 82.0164i −0.530498 0.207112i
\(397\) 189.072 0.476252 0.238126 0.971234i \(-0.423467\pi\)
0.238126 + 0.971234i \(0.423467\pi\)
\(398\) −52.3676 + 30.2345i −0.131577 + 0.0759660i
\(399\) −58.6530 773.398i −0.147000 1.93834i
\(400\) −23.4917 + 40.6888i −0.0587292 + 0.101722i
\(401\) 544.149i 1.35698i −0.734610 0.678490i \(-0.762635\pi\)
0.734610 0.678490i \(-0.237365\pi\)
\(402\) −130.669 169.468i −0.325048 0.421562i
\(403\) −698.877 −1.73419
\(404\) 230.431 + 133.039i 0.570374 + 0.329306i
\(405\) 84.5070 + 270.529i 0.208659 + 0.667973i
\(406\) −175.014 303.133i −0.431069 0.746633i
\(407\) 47.9402i 0.117789i
\(408\) 128.257 + 61.6242i 0.314355 + 0.151040i
\(409\) 397.545 + 688.568i 0.971993 + 1.68354i 0.689522 + 0.724265i \(0.257821\pi\)
0.282471 + 0.959276i \(0.408846\pi\)
\(410\) 31.7403i 0.0774155i
\(411\) 767.650 58.2171i 1.86776 0.141647i
\(412\) 59.5182 103.089i 0.144462 0.250215i
\(413\) −207.446 + 119.769i −0.502291 + 0.289998i
\(414\) 10.2232 + 12.7726i 0.0246938 + 0.0308518i
\(415\) 228.572 395.899i 0.550777 0.953974i
\(416\) 517.707i 1.24449i
\(417\) −27.8676 367.462i −0.0668288 0.881204i
\(418\) −164.146 + 284.310i −0.392695 + 0.680168i
\(419\) 84.4576 + 48.7616i 0.201569 + 0.116376i 0.597387 0.801953i \(-0.296206\pi\)
−0.395818 + 0.918329i \(0.629539\pi\)
\(420\) −95.5101 + 198.783i −0.227405 + 0.473293i
\(421\) −149.078 + 258.211i −0.354104 + 0.613327i −0.986964 0.160940i \(-0.948548\pi\)
0.632860 + 0.774266i \(0.281881\pi\)
\(422\) −68.2608 + 39.4104i −0.161756 + 0.0933896i
\(423\) 496.857 397.684i 1.17460 0.940152i
\(424\) 758.596 1.78914
\(425\) 71.6792 + 41.3840i 0.168657 + 0.0973742i
\(426\) −7.20588 95.0167i −0.0169152 0.223044i
\(427\) −283.182 −0.663191
\(428\) 92.0711 53.1573i 0.215120 0.124199i
\(429\) 408.220 30.9586i 0.951562 0.0721647i
\(430\) −113.735 + 196.995i −0.264500 + 0.458127i
\(431\) −500.706 + 289.083i −1.16173 + 0.670726i −0.951718 0.306973i \(-0.900684\pi\)
−0.210013 + 0.977699i \(0.567351\pi\)
\(432\) −95.1012 29.0559i −0.220142 0.0672591i
\(433\) −389.708 674.995i −0.900019 1.55888i −0.827467 0.561514i \(-0.810219\pi\)
−0.0725523 0.997365i \(-0.523114\pi\)
\(434\) 302.529 174.665i 0.697073 0.402455i
\(435\) −388.816 + 265.599i −0.893830 + 0.610573i
\(436\) 110.284 + 191.018i 0.252946 + 0.438115i
\(437\) −52.1597 + 30.1144i −0.119359 + 0.0689117i
\(438\) 161.160 + 235.925i 0.367944 + 0.538641i
\(439\) −55.3872 + 95.9335i −0.126167 + 0.218527i −0.922188 0.386741i \(-0.873601\pi\)
0.796022 + 0.605268i \(0.206934\pi\)
\(440\) 193.646 111.802i 0.440105 0.254095i
\(441\) 15.4425 39.5546i 0.0350171 0.0896930i
\(442\) −107.835 −0.243970
\(443\) 287.978 166.264i 0.650064 0.375315i −0.138417 0.990374i \(-0.544201\pi\)
0.788481 + 0.615060i \(0.210868\pi\)
\(444\) 3.56640 + 47.0265i 0.00803244 + 0.105916i
\(445\) 367.600 0.826068
\(446\) −286.595 165.466i −0.642590 0.371000i
\(447\) 105.229 7.98035i 0.235411 0.0178531i
\(448\) 75.3995 + 130.596i 0.168303 + 0.291509i
\(449\) −572.363 + 330.454i −1.27475 + 0.735977i −0.975878 0.218316i \(-0.929944\pi\)
−0.298872 + 0.954293i \(0.596610\pi\)
\(450\) 113.864 + 44.4538i 0.253032 + 0.0987863i
\(451\) −37.2404 + 64.5023i −0.0825730 + 0.143021i
\(452\) 153.463 + 88.6018i 0.339519 + 0.196022i
\(453\) −288.999 138.857i −0.637967 0.306527i
\(454\) 317.023 0.698289
\(455\) 400.348i 0.879887i
\(456\) −335.042 + 697.314i −0.734741 + 1.52920i
\(457\) 390.886 + 677.035i 0.855331 + 1.48148i 0.876337 + 0.481698i \(0.159980\pi\)
−0.0210063 + 0.999779i \(0.506687\pi\)
\(458\) 23.7120 13.6901i 0.0517729 0.0298911i
\(459\) −51.1862 + 167.535i −0.111517 + 0.364999i
\(460\) 17.1253 0.0372290
\(461\) 490.543i 1.06409i 0.846718 + 0.532043i \(0.178575\pi\)
−0.846718 + 0.532043i \(0.821425\pi\)
\(462\) −168.973 + 115.425i −0.365742 + 0.249838i
\(463\) 263.098 455.699i 0.568246 0.984231i −0.428494 0.903545i \(-0.640956\pi\)
0.996740 0.0806859i \(-0.0257111\pi\)
\(464\) 165.210i 0.356056i
\(465\) −265.071 388.042i −0.570044 0.834498i
\(466\) 0.337359 0.000723947
\(467\) −167.537 96.7278i −0.358752 0.207126i 0.309781 0.950808i \(-0.399744\pi\)
−0.668533 + 0.743682i \(0.733078\pi\)
\(468\) 398.137 60.7372i 0.850720 0.129780i
\(469\) 490.247 28.2450i 1.04530 0.0602240i
\(470\) 263.420i 0.560469i
\(471\) −372.148 178.808i −0.790124 0.379634i
\(472\) 238.923 0.506193
\(473\) 462.261 266.887i 0.977296 0.564242i
\(474\) −35.3404 + 2.68015i −0.0745578 + 0.00565432i
\(475\) −224.999 + 389.709i −0.473681 + 0.820440i
\(476\) −118.050 + 68.1560i −0.248004 + 0.143185i
\(477\) 140.843 + 923.238i 0.295269 + 1.93551i
\(478\) −419.357 −0.877315
\(479\) 751.774 + 434.037i 1.56947 + 0.906132i 0.996231 + 0.0867414i \(0.0276454\pi\)
0.573236 + 0.819391i \(0.305688\pi\)
\(480\) 287.449 196.356i 0.598853 0.409075i
\(481\) −42.8069 74.1437i −0.0889956 0.154145i
\(482\) 324.007 + 187.066i 0.672214 + 0.388103i
\(483\) −37.4346 + 2.83897i −0.0775044 + 0.00587778i
\(484\) 127.806 0.264061
\(485\) 204.266 + 117.933i 0.421168 + 0.243161i
\(486\) −37.4157 + 255.990i −0.0769870 + 0.526729i
\(487\) −66.2305 + 114.715i −0.135997 + 0.235554i −0.925978 0.377578i \(-0.876757\pi\)
0.789981 + 0.613131i \(0.210090\pi\)
\(488\) 244.614 + 141.228i 0.501258 + 0.289401i
\(489\) 632.505 432.063i 1.29347 0.883564i
\(490\) 8.78789 + 15.2211i 0.0179345 + 0.0310634i
\(491\) 600.161i 1.22232i −0.791506 0.611162i \(-0.790702\pi\)
0.791506 0.611162i \(-0.209298\pi\)
\(492\) −31.7322 + 66.0434i −0.0644963 + 0.134235i
\(493\) −291.041 −0.590348
\(494\) 586.281i 1.18680i
\(495\) 172.019 + 214.917i 0.347514 + 0.434175i
\(496\) 164.881 0.332421
\(497\) 189.368 + 109.332i 0.381023 + 0.219984i
\(498\) 344.569 235.375i 0.691906 0.472640i
\(499\) 313.823 543.558i 0.628905 1.08929i −0.358867 0.933389i \(-0.616837\pi\)
0.987772 0.155906i \(-0.0498298\pi\)
\(500\) 327.965 189.351i 0.655930 0.378701i
\(501\) −1.29793 1.90007i −0.00259068 0.00379255i
\(502\) −139.755 242.063i −0.278397 0.482197i
\(503\) 606.698 350.277i 1.20616 0.696377i 0.244242 0.969714i \(-0.421461\pi\)
0.961918 + 0.273338i \(0.0881276\pi\)
\(504\) −376.478 + 301.333i −0.746980 + 0.597883i
\(505\) −162.395 281.276i −0.321574 0.556983i
\(506\) 13.7614 + 7.94515i 0.0271964 + 0.0157019i
\(507\) −185.057 + 126.412i −0.365004 + 0.249333i
\(508\) −34.2522 + 59.3266i −0.0674256 + 0.116785i
\(509\) 234.115i 0.459950i −0.973197 0.229975i \(-0.926136\pi\)
0.973197 0.229975i \(-0.0738645\pi\)
\(510\) −40.8996 59.8737i −0.0801952 0.117399i
\(511\) −655.637 −1.28305
\(512\) 229.836i 0.448899i
\(513\) −910.860 278.292i −1.77556 0.542479i
\(514\) 113.876 0.221549
\(515\) −125.835 + 72.6511i −0.244340 + 0.141070i
\(516\) 433.597 296.189i 0.840304 0.574010i
\(517\) 309.067 535.320i 0.597809 1.03543i
\(518\) 37.0604 + 21.3969i 0.0715452 + 0.0413067i
\(519\) 26.6102 55.3832i 0.0512721 0.106711i
\(520\) −199.660 + 345.822i −0.383962 + 0.665042i
\(521\) 963.753i 1.84981i −0.380194 0.924907i \(-0.624143\pi\)
0.380194 0.924907i \(-0.375857\pi\)
\(522\) −424.903 + 64.8204i −0.813990 + 0.124177i
\(523\) 413.249 715.768i 0.790151 1.36858i −0.135722 0.990747i \(-0.543335\pi\)
0.925873 0.377835i \(-0.123331\pi\)
\(524\) −119.552 + 69.0231i −0.228152 + 0.131723i
\(525\) −231.614 + 158.215i −0.441170 + 0.301362i
\(526\) −208.563 + 361.242i −0.396508 + 0.686771i
\(527\) 290.462i 0.551161i
\(528\) −96.3084 + 7.30385i −0.182402 + 0.0138330i
\(529\) −263.042 455.603i −0.497245 0.861253i
\(530\) −334.774 193.282i −0.631649 0.364683i
\(531\) 44.3592 + 290.778i 0.0835390 + 0.547604i
\(532\) −370.554 641.818i −0.696530 1.20643i
\(533\) 133.011i 0.249552i
\(534\) 302.450 + 145.320i 0.566386 + 0.272134i
\(535\) −129.773 −0.242567
\(536\) −437.563 220.096i −0.816349 0.410628i
\(537\) −567.383 + 43.0293i −1.05658 + 0.0801290i
\(538\) 121.380 210.236i 0.225613 0.390772i
\(539\) 41.2428i 0.0765172i
\(540\) 184.729 + 198.024i 0.342091 + 0.366710i
\(541\) −321.404 −0.594093 −0.297046 0.954863i \(-0.596002\pi\)
−0.297046 + 0.954863i \(0.596002\pi\)
\(542\) 110.193 + 63.6200i 0.203308 + 0.117380i
\(543\) −501.356 + 342.475i −0.923308 + 0.630709i
\(544\) 215.165 0.395524
\(545\) 269.238i 0.494015i
\(546\) 158.266 329.395i 0.289864 0.603287i
\(547\) 11.8406 + 20.5086i 0.0216465 + 0.0374928i 0.876646 0.481136i \(-0.159776\pi\)
−0.854999 + 0.518629i \(0.826443\pi\)
\(548\) 637.048 367.800i 1.16250 0.671168i
\(549\) −126.463 + 323.924i −0.230352 + 0.590026i
\(550\) 118.724 0.215861
\(551\) 1582.35i 2.87178i
\(552\) 33.7520 + 16.2170i 0.0611448 + 0.0293785i
\(553\) 40.6647 70.4334i 0.0735348 0.127366i
\(554\) −307.864 177.745i −0.555711 0.320840i
\(555\) 24.9314 51.8892i 0.0449215 0.0934940i
\(556\) −176.060 304.945i −0.316655 0.548463i
\(557\) −425.153 + 245.462i −0.763291 + 0.440686i −0.830476 0.557054i \(-0.811932\pi\)
0.0671849 + 0.997741i \(0.478598\pi\)
\(558\) −64.6914 424.057i −0.115934 0.759958i
\(559\) −476.618 + 825.527i −0.852627 + 1.47679i
\(560\) 94.4513i 0.168663i
\(561\) 12.8668 + 169.661i 0.0229355 + 0.302427i
\(562\) −112.975 195.678i −0.201023 0.348182i
\(563\) 601.353i 1.06812i 0.845446 + 0.534061i \(0.179335\pi\)
−0.845446 + 0.534061i \(0.820665\pi\)
\(564\) 263.353 548.110i 0.466938 0.971826i
\(565\) −108.152 187.325i −0.191419 0.331548i
\(566\) 107.333 + 61.9687i 0.189634 + 0.109485i
\(567\) −436.631 402.240i −0.770072 0.709419i
\(568\) −109.051 188.882i −0.191992 0.332539i
\(569\) −325.936 + 188.179i −0.572823 + 0.330719i −0.758276 0.651934i \(-0.773958\pi\)
0.185453 + 0.982653i \(0.440625\pi\)
\(570\) 325.524 222.365i 0.571095 0.390114i
\(571\) −31.4877 54.5383i −0.0551448 0.0955136i 0.837135 0.546996i \(-0.184229\pi\)
−0.892280 + 0.451482i \(0.850895\pi\)
\(572\) 338.769 195.588i 0.592254 0.341938i
\(573\) 41.1586 85.6625i 0.0718301 0.149498i
\(574\) 33.2426 + 57.5779i 0.0579139 + 0.100310i
\(575\) 18.8630 + 10.8906i 0.0328052 + 0.0189401i
\(576\) 183.057 27.9259i 0.317807 0.0484825i
\(577\) 389.743 + 675.054i 0.675464 + 1.16994i 0.976333 + 0.216273i \(0.0693900\pi\)
−0.300869 + 0.953666i \(0.597277\pi\)
\(578\) 262.867i 0.454787i
\(579\) −11.8493 156.244i −0.0204651 0.269852i
\(580\) −224.961 + 389.643i −0.387863 + 0.671799i
\(581\) 957.562i 1.64813i
\(582\) 121.443 + 177.782i 0.208665 + 0.305468i
\(583\) 453.549 + 785.570i 0.777957 + 1.34746i
\(584\) 566.341 + 326.977i 0.969763 + 0.559893i
\(585\) −457.947 178.787i −0.782815 0.305619i
\(586\) 13.4326 23.2659i 0.0229225 0.0397029i
\(587\) 218.603 + 126.210i 0.372407 + 0.215009i 0.674509 0.738266i \(-0.264355\pi\)
−0.302103 + 0.953275i \(0.597688\pi\)
\(588\) −3.06816 40.4567i −0.00521796 0.0688040i
\(589\) 1579.20 2.68115
\(590\) −105.438 60.8749i −0.178709 0.103178i
\(591\) −348.037 509.499i −0.588896 0.862096i
\(592\) 10.0991 + 17.4922i 0.0170593 + 0.0295476i
\(593\) 45.1074 + 26.0427i 0.0760664 + 0.0439169i 0.537551 0.843231i \(-0.319350\pi\)
−0.461484 + 0.887148i \(0.652683\pi\)
\(594\) 56.5715 + 244.829i 0.0952382 + 0.412171i
\(595\) 166.390 0.279647
\(596\) 87.3261 50.4177i 0.146520 0.0845935i
\(597\) −153.583 73.7927i −0.257258 0.123606i
\(598\) −28.3776 −0.0474542
\(599\) 19.2844 11.1339i 0.0321943 0.0185874i −0.483816 0.875169i \(-0.660750\pi\)
0.516011 + 0.856582i \(0.327416\pi\)
\(600\) 278.973 21.1568i 0.464956 0.0352614i
\(601\) 221.789 384.151i 0.369034 0.639186i −0.620381 0.784301i \(-0.713022\pi\)
0.989415 + 0.145115i \(0.0463552\pi\)
\(602\) 476.471i 0.791481i
\(603\) 186.626 573.393i 0.309495 0.950901i
\(604\) −306.361 −0.507220
\(605\) −135.106 78.0032i −0.223315 0.128931i
\(606\) −22.4195 295.624i −0.0369959 0.487828i
\(607\) 370.650 + 641.985i 0.610626 + 1.05764i 0.991135 + 0.132859i \(0.0424156\pi\)
−0.380509 + 0.924777i \(0.624251\pi\)
\(608\) 1169.82i 1.92405i
\(609\) 427.153 889.023i 0.701400 1.45981i
\(610\) −71.9665 124.650i −0.117978 0.204344i
\(611\) 1103.89i 1.80670i
\(612\) 25.2431 + 165.471i 0.0412470 + 0.270377i
\(613\) −319.697 + 553.732i −0.521529 + 0.903314i 0.478158 + 0.878274i \(0.341305\pi\)
−0.999686 + 0.0250403i \(0.992029\pi\)
\(614\) 28.1039 16.2258i 0.0457718 0.0264263i
\(615\) 73.8527 50.4486i 0.120086 0.0820303i
\(616\) −234.186 + 405.622i −0.380172 + 0.658478i
\(617\) 153.362i 0.248561i 0.992247 + 0.124281i \(0.0396623\pi\)
−0.992247 + 0.124281i \(0.960338\pi\)
\(618\) −132.254 + 10.0299i −0.214003 + 0.0162296i
\(619\) −484.552 + 839.269i −0.782798 + 1.35585i 0.147507 + 0.989061i \(0.452875\pi\)
−0.930305 + 0.366786i \(0.880458\pi\)
\(620\) −388.868 224.513i −0.627206 0.362117i
\(621\) −13.4701 + 44.0882i −0.0216910 + 0.0709955i
\(622\) 52.4773 90.8934i 0.0843687 0.146131i
\(623\) −666.837 + 384.999i −1.07036 + 0.617975i
\(624\) 142.428 97.2920i 0.228249 0.155917i
\(625\) −143.342 −0.229347
\(626\) 65.1543 + 37.6169i 0.104080 + 0.0600909i
\(627\) −922.423 + 69.9548i −1.47117 + 0.111571i
\(628\) −394.506 −0.628194
\(629\) 30.8150 17.7911i 0.0489905 0.0282847i
\(630\) 242.919 37.0581i 0.385585 0.0588224i
\(631\) −66.0443 + 114.392i −0.104666 + 0.181287i −0.913602 0.406610i \(-0.866711\pi\)
0.808936 + 0.587897i \(0.200044\pi\)
\(632\) −70.2526 + 40.5604i −0.111159 + 0.0641778i
\(633\) −200.194 96.1882i −0.316262 0.151956i
\(634\) 215.754 + 373.697i 0.340306 + 0.589428i
\(635\) 72.4171 41.8101i 0.114043 0.0658426i
\(636\) 503.346 + 736.857i 0.791424 + 1.15858i
\(637\) 36.8266 + 63.7855i 0.0578126 + 0.100134i
\(638\) −361.544 + 208.737i −0.566683 + 0.327174i
\(639\) 209.629 167.788i 0.328059 0.262578i
\(640\) 193.752 335.589i 0.302738 0.524357i
\(641\) 760.362 438.995i 1.18621 0.684859i 0.228768 0.973481i \(-0.426530\pi\)
0.957443 + 0.288621i \(0.0931969\pi\)
\(642\) −106.773 51.3019i −0.166314 0.0799096i
\(643\) 390.141 0.606751 0.303375 0.952871i \(-0.401886\pi\)
0.303375 + 0.952871i \(0.401886\pi\)
\(644\) −31.0658 + 17.9358i −0.0482388 + 0.0278507i
\(645\) −639.134 + 48.4707i −0.990906 + 0.0751484i
\(646\) 243.665 0.377191
\(647\) 319.328 + 184.364i 0.493552 + 0.284952i 0.726047 0.687645i \(-0.241356\pi\)
−0.232495 + 0.972598i \(0.574689\pi\)
\(648\) 176.559 + 565.211i 0.272468 + 0.872240i
\(649\) 142.847 + 247.419i 0.220104 + 0.381230i
\(650\) −183.617 + 106.011i −0.282487 + 0.163094i
\(651\) 887.253 + 426.302i 1.36291 + 0.654842i
\(652\) 365.954 633.851i 0.561279 0.972164i
\(653\) 51.4118 + 29.6826i 0.0787317 + 0.0454558i 0.538849 0.842402i \(-0.318859\pi\)
−0.460117 + 0.887858i \(0.652193\pi\)
\(654\) 106.435 221.521i 0.162745 0.338717i
\(655\) 168.507 0.257262
\(656\) 31.3804i 0.0478360i
\(657\) −292.794 + 749.965i −0.445653 + 1.14150i
\(658\) −275.888 477.852i −0.419283 0.726219i
\(659\) −523.913 + 302.481i −0.795012 + 0.459000i −0.841724 0.539908i \(-0.818459\pi\)
0.0467122 + 0.998908i \(0.485126\pi\)
\(660\) 237.086 + 113.914i 0.359222 + 0.172597i
\(661\) 831.325 1.25768 0.628839 0.777536i \(-0.283531\pi\)
0.628839 + 0.777536i \(0.283531\pi\)
\(662\) 178.586i 0.269767i
\(663\) −171.394 250.907i −0.258513 0.378442i
\(664\) 477.552 827.145i 0.719205 1.24570i
\(665\) 904.636i 1.36035i
\(666\) 41.0257 32.8370i 0.0616001 0.0493048i
\(667\) −76.5901 −0.114828
\(668\) −1.90411 1.09934i −0.00285046 0.00164572i
\(669\) −70.5171 929.837i −0.105407 1.38989i
\(670\) 137.022 + 208.616i 0.204510 + 0.311368i
\(671\) 337.749i 0.503351i
\(672\) −315.792 + 657.249i −0.469928 + 0.978049i
\(673\) −36.6995 −0.0545312 −0.0272656 0.999628i \(-0.508680\pi\)
−0.0272656 + 0.999628i \(0.508680\pi\)
\(674\) 292.960 169.140i 0.434659 0.250950i
\(675\) 77.5436 + 335.592i 0.114879 + 0.497174i
\(676\) −107.070 + 185.451i −0.158388 + 0.274335i
\(677\) −341.830 + 197.356i −0.504919 + 0.291515i −0.730743 0.682653i \(-0.760826\pi\)
0.225823 + 0.974168i \(0.427493\pi\)
\(678\) −14.9310 196.880i −0.0220221 0.290383i
\(679\) −494.060 −0.727628
\(680\) −143.728 82.9813i −0.211364 0.122031i
\(681\) 503.881 + 737.642i 0.739914 + 1.08317i
\(682\) −208.322 360.824i −0.305457 0.529067i
\(683\) −932.720 538.506i −1.36562 0.788442i −0.375256 0.926921i \(-0.622445\pi\)
−0.990365 + 0.138479i \(0.955779\pi\)
\(684\) −899.639 + 137.243i −1.31526 + 0.200648i
\(685\) −897.913 −1.31082
\(686\) 299.244 + 172.768i 0.436215 + 0.251849i
\(687\) 69.5421 + 33.4132i 0.101226 + 0.0486364i
\(688\) 112.445 194.761i 0.163438 0.283082i
\(689\) −1402.91 809.968i −2.03615 1.17557i
\(690\) −10.7631 15.7563i −0.0155987 0.0228352i
\(691\) 364.082 + 630.609i 0.526891 + 0.912603i 0.999509 + 0.0313351i \(0.00997592\pi\)
−0.472617 + 0.881268i \(0.656691\pi\)
\(692\) 58.7104i 0.0848417i
\(693\) −537.136 209.704i −0.775088 0.302603i
\(694\) 371.157 0.534808
\(695\) 429.817i 0.618441i
\(696\) −812.346 + 554.912i −1.16716 + 0.797288i
\(697\) 55.2811 0.0793130
\(698\) 243.134 + 140.374i 0.348330 + 0.201108i
\(699\) 0.536204 + 0.784959i 0.000767102 + 0.00112297i
\(700\) −134.007 + 232.107i −0.191439 + 0.331582i
\(701\) 87.2945 50.3995i 0.124528 0.0718965i −0.436442 0.899732i \(-0.643762\pi\)
0.560970 + 0.827836i \(0.310428\pi\)
\(702\) −306.107 328.136i −0.436049 0.467431i
\(703\) 96.7274 + 167.537i 0.137592 + 0.238317i
\(704\) 155.760 89.9282i 0.221250 0.127739i
\(705\) −612.921 + 418.685i −0.869391 + 0.593879i
\(706\) −14.8699 25.7555i −0.0210622 0.0364809i
\(707\) 589.178 + 340.162i 0.833350 + 0.481135i
\(708\) 158.531 + 232.076i 0.223914 + 0.327792i
\(709\) 125.673 217.671i 0.177253 0.307012i −0.763685 0.645589i \(-0.776612\pi\)
0.940939 + 0.338577i \(0.109945\pi\)
\(710\) 111.140i 0.156535i
\(711\) −62.4067 77.9693i −0.0877731 0.109661i
\(712\) 768.021 1.07868
\(713\) 76.4376i 0.107206i
\(714\) 136.900 + 65.7771i 0.191737 + 0.0921249i
\(715\) −477.491 −0.667820
\(716\) −470.854 + 271.848i −0.657617 + 0.379675i
\(717\) −666.532 975.750i −0.929613 1.36088i
\(718\) −272.806 + 472.514i −0.379953 + 0.658097i
\(719\) −333.541 192.570i −0.463895 0.267830i 0.249785 0.968301i \(-0.419640\pi\)
−0.713681 + 0.700471i \(0.752973\pi\)
\(720\) 108.040 + 42.1800i 0.150056 + 0.0585833i
\(721\) 152.179 263.582i 0.211067 0.365578i
\(722\) 940.433i 1.30254i
\(723\) 79.7223 + 1051.22i 0.110266 + 1.45397i
\(724\) −290.074 + 502.423i −0.400655 + 0.693954i
\(725\) −495.575 + 286.120i −0.683551 + 0.394648i
\(726\) −80.3245 117.589i −0.110640 0.161968i
\(727\) 325.341 563.507i 0.447511 0.775113i −0.550712 0.834695i \(-0.685644\pi\)
0.998223 + 0.0595829i \(0.0189771\pi\)
\(728\) 836.441i 1.14896i
\(729\) −655.101 + 319.817i −0.898630 + 0.438707i
\(730\) −166.620 288.595i −0.228247 0.395335i
\(731\) −343.099 198.088i −0.469356 0.270983i
\(732\) 25.1261 + 331.312i 0.0343252 + 0.452612i
\(733\) 489.009 + 846.989i 0.667134 + 1.15551i 0.978702 + 0.205287i \(0.0658126\pi\)
−0.311568 + 0.950224i \(0.600854\pi\)
\(734\) 389.193i 0.530235i
\(735\) −21.4484 + 44.6401i −0.0291815 + 0.0607348i
\(736\) 56.6226 0.0769329
\(737\) −33.6876 584.713i −0.0457090 0.793369i
\(738\) 80.7071 12.3122i 0.109359 0.0166831i
\(739\) −425.788 + 737.486i −0.576168 + 0.997952i 0.419746 + 0.907642i \(0.362119\pi\)
−0.995914 + 0.0903101i \(0.971214\pi\)
\(740\) 55.0065i 0.0743331i
\(741\) 1364.14 931.844i 1.84095 1.25755i
\(742\) 809.719 1.09127
\(743\) −207.273 119.669i −0.278968 0.161062i 0.353988 0.935250i \(-0.384825\pi\)
−0.632956 + 0.774188i \(0.718159\pi\)
\(744\) −553.807 810.729i −0.744364 1.08969i
\(745\) −123.085 −0.165215
\(746\) 148.757i 0.199406i
\(747\) 1095.33 + 427.628i 1.46630 + 0.572460i
\(748\) 81.2889 + 140.797i 0.108675 + 0.188231i
\(749\) 235.412 135.915i 0.314302 0.181462i
\(750\) −380.336 182.742i −0.507115 0.243656i
\(751\) −662.294 −0.881883 −0.440941 0.897536i \(-0.645355\pi\)
−0.440941 + 0.897536i \(0.645355\pi\)
\(752\) 260.433i 0.346321i
\(753\) 341.097 709.917i 0.452984 0.942785i
\(754\) 372.773 645.661i 0.494393 0.856314i
\(755\) 323.859 + 186.980i 0.428953 + 0.247656i
\(756\) −542.500 165.748i −0.717592 0.219243i
\(757\) 352.447 + 610.455i 0.465583 + 0.806414i 0.999228 0.0392950i \(-0.0125112\pi\)
−0.533644 + 0.845709i \(0.679178\pi\)
\(758\) 246.691 142.427i 0.325450 0.187898i
\(759\) 3.38601 + 44.6478i 0.00446114 + 0.0588246i
\(760\) 451.157 781.427i 0.593627 1.02819i
\(761\) 1060.15i 1.39310i −0.717506 0.696552i \(-0.754716\pi\)
0.717506 0.696552i \(-0.245284\pi\)
\(762\) 76.1110 5.77211i 0.0998832 0.00757495i
\(763\) 281.981 + 488.405i 0.369569 + 0.640112i
\(764\) 90.8087i 0.118860i
\(765\) 74.3062 190.328i 0.0971323 0.248795i
\(766\) 28.3973 + 49.1856i 0.0370722 + 0.0642110i
\(767\) −441.851 255.103i −0.576077 0.332598i
\(768\) 495.952 338.784i 0.645770 0.441124i
\(769\) 189.494 + 328.213i 0.246416 + 0.426805i 0.962529 0.271180i \(-0.0874138\pi\)
−0.716113 + 0.697984i \(0.754080\pi\)
\(770\) 206.696 119.336i 0.268436 0.154982i
\(771\) 180.996 + 264.964i 0.234755 + 0.343663i
\(772\) −74.8606 129.662i −0.0969697 0.167956i
\(773\) 1234.85 712.939i 1.59747 0.922301i 0.605501 0.795845i \(-0.292973\pi\)
0.991972 0.126456i \(-0.0403604\pi\)
\(774\) −545.022 212.782i −0.704163 0.274913i
\(775\) −285.550 494.588i −0.368452 0.638178i
\(776\) 426.770 + 246.396i 0.549961 + 0.317520i
\(777\) 9.11876 + 120.240i 0.0117359 + 0.154749i
\(778\) 140.169 + 242.780i 0.180166 + 0.312056i
\(779\) 300.555i 0.385822i
\(780\) −468.391 + 35.5219i −0.600501 + 0.0455409i
\(781\) 130.399 225.857i 0.166964 0.289190i
\(782\) 11.7941i 0.0150820i
\(783\) −826.170 885.627i −1.05513 1.13107i
\(784\) −8.68823 15.0485i −0.0110819 0.0191945i
\(785\) 417.038 + 240.777i 0.531259 + 0.306722i
\(786\) 138.642 + 66.6140i 0.176389 + 0.0847506i
\(787\) −342.283 + 592.852i −0.434922 + 0.753307i −0.997289 0.0735808i \(-0.976557\pi\)
0.562367 + 0.826887i \(0.309891\pi\)
\(788\) −510.583 294.785i −0.647948 0.374093i
\(789\) −1172.02 + 88.8839i −1.48545 + 0.112654i
\(790\) 41.3373 0.0523257
\(791\) 392.381 + 226.542i 0.496057 + 0.286399i
\(792\) 359.397 + 449.021i 0.453784 + 0.566946i
\(793\) −301.584 522.358i −0.380307 0.658711i
\(794\) −174.327 100.648i −0.219556 0.126761i
\(795\) −82.3715 1086.15i −0.103612 1.36623i
\(796\) −162.809 −0.204535
\(797\) −1038.03 + 599.306i −1.30242 + 0.751953i −0.980819 0.194923i \(-0.937554\pi\)
−0.321601 + 0.946875i \(0.604221\pi\)
\(798\) −357.620 + 744.307i −0.448146 + 0.932715i
\(799\) −458.791 −0.574207
\(800\) 366.375 211.527i 0.457969 0.264409i
\(801\) 142.593 + 934.708i 0.178019 + 1.16693i
\(802\) −289.664 + 501.713i −0.361177 + 0.625578i
\(803\) 781.972i 0.973813i
\(804\) −76.5439 571.063i −0.0952039 0.710277i
\(805\) 43.7869 0.0543937
\(806\) 644.375 + 372.030i 0.799473 + 0.461576i
\(807\) 682.094 51.7287i 0.845222 0.0641000i
\(808\) −339.289 587.666i −0.419912 0.727309i
\(809\) 39.0854i 0.0483132i −0.999708 0.0241566i \(-0.992310\pi\)
0.999708 0.0241566i \(-0.00769003\pi\)
\(810\) 66.0928 294.417i 0.0815960 0.363478i
\(811\) −30.7515 53.2631i −0.0379180 0.0656759i 0.846444 0.532478i \(-0.178739\pi\)
−0.884362 + 0.466802i \(0.845406\pi\)
\(812\) 942.432i 1.16063i
\(813\) 27.1131 + 357.513i 0.0333495 + 0.439746i
\(814\) 25.5198 44.2016i 0.0313511 0.0543017i
\(815\) −773.712 + 446.703i −0.949340 + 0.548102i
\(816\) 40.4358 + 59.1947i 0.0495536 + 0.0725425i
\(817\) 1076.98 1865.38i 1.31821 2.28321i
\(818\) 846.494i 1.03483i
\(819\) 1017.98 155.296i 1.24295 0.189617i
\(820\) 42.7296 74.0098i 0.0521093 0.0902559i
\(821\) 1303.07 + 752.328i 1.58717 + 0.916356i 0.993770 + 0.111452i \(0.0355501\pi\)
0.593405 + 0.804904i \(0.297783\pi\)
\(822\) −738.775 354.963i −0.898753 0.431828i
\(823\) −543.813 + 941.911i −0.660769 + 1.14449i 0.319645 + 0.947537i \(0.396436\pi\)
−0.980414 + 0.196948i \(0.936897\pi\)
\(824\) −262.906 + 151.789i −0.319060 + 0.184209i
\(825\) 188.702 + 276.244i 0.228729 + 0.334841i
\(826\) 255.024 0.308746
\(827\) −1141.79 659.212i −1.38064 0.797113i −0.388405 0.921489i \(-0.626974\pi\)
−0.992235 + 0.124376i \(0.960307\pi\)
\(828\) 6.64295 + 43.5450i 0.00802289 + 0.0525906i
\(829\) 241.393 0.291186 0.145593 0.989345i \(-0.453491\pi\)
0.145593 + 0.989345i \(0.453491\pi\)
\(830\) −421.494 + 243.350i −0.507825 + 0.293193i
\(831\) −75.7502 998.841i −0.0911555 1.20197i
\(832\) −160.598 + 278.164i −0.193026 + 0.334331i
\(833\) −26.5100 + 15.3056i −0.0318248 + 0.0183741i
\(834\) −169.915 + 353.640i −0.203735 + 0.424029i
\(835\) 1.34191 + 2.32426i 0.00160708 + 0.00278354i
\(836\) −765.490 + 441.956i −0.915658 + 0.528655i
\(837\) 883.864 824.525i 1.05599 0.985095i
\(838\) −51.9141 89.9178i −0.0619500 0.107301i
\(839\) 701.075 404.766i 0.835607 0.482438i −0.0201613 0.999797i \(-0.506418\pi\)
0.855769 + 0.517359i \(0.173085\pi\)
\(840\) 464.422 317.246i 0.552883 0.377673i
\(841\) 585.599 1014.29i 0.696312 1.20605i
\(842\) 274.904 158.716i 0.326490 0.188499i
\(843\) 275.736 573.882i 0.327089 0.680762i
\(844\) −212.221 −0.251447
\(845\) 226.371 130.695i 0.267895 0.154669i
\(846\) −669.807 + 102.181i −0.791734 + 0.120782i
\(847\) 326.780 0.385809
\(848\) 330.977 + 191.090i 0.390304 + 0.225342i
\(849\) 26.4094 + 348.234i 0.0311064 + 0.410169i
\(850\) −44.0595 76.3134i −0.0518348 0.0897804i
\(851\) 8.10925 4.68187i 0.00952908 0.00550162i
\(852\) 111.112 231.254i 0.130413 0.271425i
\(853\) −275.856 + 477.797i −0.323395 + 0.560137i −0.981186 0.193063i \(-0.938158\pi\)
0.657791 + 0.753201i \(0.271491\pi\)
\(854\) 261.099 + 150.745i 0.305736 + 0.176517i
\(855\) 1034.79 + 403.992i 1.21028 + 0.472505i
\(856\) −271.133 −0.316744
\(857\) 313.636i 0.365969i 0.983116 + 0.182985i \(0.0585758\pi\)
−0.983116 + 0.182985i \(0.941424\pi\)
\(858\) −392.865 188.762i −0.457885 0.220002i
\(859\) −332.548 575.990i −0.387134 0.670535i 0.604929 0.796279i \(-0.293201\pi\)
−0.992063 + 0.125744i \(0.959868\pi\)
\(860\) −530.398 + 306.225i −0.616741 + 0.356076i
\(861\) −81.1345 + 168.863i −0.0942329 + 0.196125i
\(862\) 615.545 0.714089
\(863\) 1175.87i 1.36254i −0.732033 0.681269i \(-0.761428\pi\)
0.732033 0.681269i \(-0.238572\pi\)
\(864\) 610.782 + 654.739i 0.706924 + 0.757799i
\(865\) −35.8325 + 62.0637i −0.0414249 + 0.0717500i
\(866\) 829.807i 0.958207i
\(867\) −611.632 + 417.805i −0.705458 + 0.481897i
\(868\) 940.555 1.08359
\(869\) −84.0052 48.5004i −0.0966688 0.0558117i
\(870\) 499.880 37.9099i 0.574574 0.0435746i
\(871\) 574.204 + 874.229i 0.659247 + 1.00371i
\(872\) 562.515i 0.645086i
\(873\) −220.637 + 565.140i −0.252734 + 0.647354i
\(874\) 64.1227 0.0733669
\(875\) 838.558 484.142i 0.958352 0.553305i
\(876\) 58.1730 + 767.069i 0.0664076 + 0.875649i
\(877\) −711.872 + 1233.00i −0.811713 + 1.40593i 0.0999510 + 0.994992i \(0.468131\pi\)
−0.911664 + 0.410936i \(0.865202\pi\)
\(878\) 102.136 58.9681i 0.116328 0.0671618i
\(879\) 75.4846 5.72460i 0.0858755 0.00651263i
\(880\) 112.651 0.128012
\(881\) −535.757 309.320i −0.608124 0.351101i 0.164107 0.986443i \(-0.447526\pi\)
−0.772231 + 0.635342i \(0.780859\pi\)
\(882\) −35.2942 + 28.2495i −0.0400161 + 0.0320289i
\(883\) 342.094 + 592.525i 0.387423 + 0.671036i 0.992102 0.125433i \(-0.0400320\pi\)
−0.604679 + 0.796469i \(0.706699\pi\)
\(884\) −251.441 145.170i −0.284436 0.164219i
\(885\) −25.9433 342.087i −0.0293144 0.386539i
\(886\) −354.027 −0.399579
\(887\) 203.804 + 117.666i 0.229767 + 0.132656i 0.610465 0.792043i \(-0.290983\pi\)
−0.380697 + 0.924700i \(0.624316\pi\)
\(888\) 52.0888 108.411i 0.0586586 0.122085i
\(889\) −87.5778 + 151.689i −0.0985127 + 0.170629i
\(890\) −338.933 195.683i −0.380824 0.219869i
\(891\) −479.748 + 520.765i −0.538437 + 0.584473i
\(892\) −445.508 771.643i −0.499448 0.865070i
\(893\) 2494.38i 2.79326i
\(894\) −101.271 48.6580i −0.113278 0.0544273i
\(895\) 663.663 0.741523
\(896\) 811.689i 0.905903i
\(897\) −45.1038 66.0284i −0.0502830 0.0736102i
\(898\) 703.636 0.783559
\(899\) 1739.14 + 1004.10i 1.93453 + 1.11690i
\(900\) 205.656 + 256.941i 0.228506 + 0.285490i
\(901\) 336.633 583.065i 0.373621 0.647131i
\(902\) 68.6725 39.6481i 0.0761336 0.0439557i
\(903\) 1108.64 757.311i 1.22773 0.838662i
\(904\) −225.960 391.374i −0.249956 0.432936i
\(905\) 613.284 354.080i 0.677662 0.391248i
\(906\) 192.545 + 281.870i 0.212522 + 0.311114i
\(907\) −485.244 840.467i −0.534999 0.926645i −0.999163 0.0408958i \(-0.986979\pi\)
0.464165 0.885749i \(-0.346355\pi\)
\(908\) 739.211 + 426.784i 0.814109 + 0.470026i
\(909\) 652.216 522.034i 0.717510 0.574295i
\(910\) −213.116 + 369.127i −0.234193 + 0.405634i
\(911\) 1570.90i 1.72436i −0.506598 0.862182i \(-0.669097\pi\)
0.506598 0.862182i \(-0.330903\pi\)
\(912\) −321.832 + 219.843i −0.352886 + 0.241056i
\(913\) 1142.07 1.25090
\(914\) 832.315i 0.910629i
\(915\) 175.647 365.570i 0.191964 0.399530i
\(916\) 73.7199 0.0804802
\(917\) −305.675 + 176.482i −0.333343 + 0.192456i
\(918\) 136.377 127.222i 0.148559 0.138586i
\(919\) −231.732 + 401.372i −0.252157 + 0.436748i −0.964119 0.265469i \(-0.914473\pi\)
0.711963 + 0.702217i \(0.247807\pi\)
\(920\) −37.8232 21.8373i −0.0411122 0.0237361i
\(921\) 82.4225 + 39.6019i 0.0894924 + 0.0429988i
\(922\) 261.129 452.288i 0.283220 0.490551i
\(923\) 465.745i 0.504599i
\(924\) −549.386 + 41.6644i −0.594574 + 0.0450914i
\(925\) 34.9805 60.5879i 0.0378167 0.0655005i
\(926\) −485.160 + 280.107i −0.523931 + 0.302492i
\(927\) −233.544 291.784i −0.251935 0.314761i
\(928\) −743.803 + 1288.30i −0.801511 + 1.38826i
\(929\) 802.955i 0.864322i 0.901796 + 0.432161i \(0.142249\pi\)
−0.901796 + 0.432161i \(0.857751\pi\)
\(930\) 37.8344 + 498.884i 0.0406822 + 0.536435i
\(931\) −83.2142 144.131i −0.0893815 0.154813i
\(932\) 0.786630 + 0.454161i 0.000844023 + 0.000487297i
\(933\) 294.897 22.3644i 0.316074 0.0239704i
\(934\) 102.981 + 178.369i 0.110258 + 0.190973i
\(935\) 198.451i 0.212247i
\(936\) −956.780 373.537i −1.02220 0.399078i
\(937\) −731.336 −0.780508 −0.390254 0.920707i \(-0.627613\pi\)
−0.390254 + 0.920707i \(0.627613\pi\)
\(938\) −467.051 234.929i −0.497922 0.250457i
\(939\) 16.0313 + 211.388i 0.0170727 + 0.225121i
\(940\) −354.623 + 614.225i −0.377258 + 0.653431i
\(941\) 1606.75i 1.70749i 0.520688 + 0.853747i \(0.325676\pi\)
−0.520688 + 0.853747i \(0.674324\pi\)
\(942\) 247.942 + 362.968i 0.263209 + 0.385316i
\(943\) 14.5477 0.0154271
\(944\) 104.243 + 60.1846i 0.110427 + 0.0637549i
\(945\) 472.325 + 506.317i 0.499815 + 0.535785i
\(946\) −568.282 −0.600721
\(947\) 1389.67i 1.46745i −0.679449 0.733723i \(-0.737781\pi\)
0.679449 0.733723i \(-0.262219\pi\)
\(948\) −86.0123 41.3267i −0.0907302 0.0435936i
\(949\) −698.240 1209.39i −0.735764 1.27438i
\(950\) 414.904 239.545i 0.436741 0.252153i
\(951\) −526.587 + 1095.97i −0.553719 + 1.15244i
\(952\) 347.635 0.365163
\(953\) 210.833i 0.221231i −0.993863 0.110616i \(-0.964718\pi\)
0.993863 0.110616i \(-0.0352822\pi\)
\(954\) 361.604 926.214i 0.379039 0.970874i
\(955\) −55.4230 + 95.9954i −0.0580345 + 0.100519i
\(956\) −977.826 564.548i −1.02283 0.590531i
\(957\) −1060.33 509.461i −1.10797 0.532352i
\(958\) −462.098 800.378i −0.482357 0.835467i
\(959\) 1628.84 940.410i 1.69848 0.980615i
\(960\) −215.358 + 16.3323i −0.224331 + 0.0170129i
\(961\) −521.596 + 903.431i −0.542764 + 0.940094i
\(962\) 91.1488i 0.0947493i
\(963\) −50.3393 329.978i −0.0522735 0.342656i
\(964\) 503.665 + 872.373i 0.522474 + 0.904951i
\(965\) 182.758i 0.189386i
\(966\) 36.0265 + 17.3098i 0.0372945 + 0.0179191i
\(967\) −411.360 712.496i −0.425398 0.736811i 0.571060 0.820909i \(-0.306532\pi\)
−0.996457 + 0.0840980i \(0.973199\pi\)
\(968\) −282.274 162.971i −0.291605 0.168358i
\(969\) 387.286 + 566.955i 0.399676 + 0.585093i
\(970\) −125.558 217.472i −0.129441 0.224198i
\(971\) −1473.64 + 850.805i −1.51765 + 0.876215i −0.517864 + 0.855463i \(0.673273\pi\)
−0.999785 + 0.0207517i \(0.993394\pi\)
\(972\) −431.863 + 546.530i −0.444304 + 0.562274i
\(973\) −450.160 779.700i −0.462651 0.801336i
\(974\) 122.131 70.5124i 0.125391 0.0723947i
\(975\) −538.508 258.739i −0.552316 0.265374i
\(976\) 71.1504 + 123.236i 0.0729000 + 0.126267i
\(977\) −786.461 454.064i −0.804976 0.464753i 0.0402322 0.999190i \(-0.487190\pi\)
−0.845208 + 0.534437i \(0.820524\pi\)
\(978\) −813.177 + 61.6698i −0.831470 + 0.0630571i
\(979\) 459.184 + 795.329i 0.469033 + 0.812389i
\(980\) 47.3219i 0.0482876i
\(981\) 684.600 104.438i 0.697859 0.106461i
\(982\) −319.481 + 553.358i −0.325337 + 0.563501i
\(983\) 1440.01i 1.46491i 0.680814 + 0.732456i \(0.261626\pi\)
−0.680814 + 0.732456i \(0.738374\pi\)
\(984\) 154.299 105.401i 0.156808 0.107115i
\(985\) 359.830 + 623.244i 0.365310 + 0.632735i
\(986\) 268.345 + 154.929i 0.272155 + 0.157129i
\(987\) 673.354 1401.44i 0.682223 1.41989i
\(988\) 789.265 1367.05i 0.798851 1.38365i
\(989\) −90.2895 52.1287i −0.0912938 0.0527085i
\(990\) −44.1988 289.727i −0.0446453 0.292653i
\(991\) −709.114 −0.715554 −0.357777 0.933807i \(-0.616465\pi\)
−0.357777 + 0.933807i \(0.616465\pi\)
\(992\) −1285.74 742.322i −1.29611 0.748308i
\(993\) −415.530 + 283.847i −0.418459 + 0.285848i
\(994\) −116.400 201.611i −0.117103 0.202828i
\(995\) 172.109 + 99.3669i 0.172973 + 0.0998663i
\(996\) 1120.31 84.9621i 1.12481 0.0853033i
\(997\) 759.121 0.761405 0.380702 0.924698i \(-0.375682\pi\)
0.380702 + 0.924698i \(0.375682\pi\)
\(998\) −578.700 + 334.113i −0.579860 + 0.334782i
\(999\) 141.611 + 43.2659i 0.141753 + 0.0433093i
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 201.3.g.b.29.17 84
3.2 odd 2 inner 201.3.g.b.29.26 yes 84
67.37 even 3 inner 201.3.g.b.104.26 yes 84
201.104 odd 6 inner 201.3.g.b.104.17 yes 84
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
201.3.g.b.29.17 84 1.1 even 1 trivial
201.3.g.b.29.26 yes 84 3.2 odd 2 inner
201.3.g.b.104.17 yes 84 201.104 odd 6 inner
201.3.g.b.104.26 yes 84 67.37 even 3 inner