Properties

Label 201.2.f.b.38.3
Level $201$
Weight $2$
Character 201.38
Analytic conductor $1.605$
Analytic rank $0$
Dimension $40$
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] = [201,2,Mod(38,201)]
 
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, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("201.38");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 201 = 3 \cdot 67 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 201.f (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: \(1.60499308063\)
Analytic rank: \(0\)
Dimension: \(40\)
Relative dimension: \(20\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 38.3
Character \(\chi\) \(=\) 201.38
Dual form 201.2.f.b.164.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.22221 + 2.11693i) q^{2} +(1.40479 - 1.01319i) q^{3} +(-1.98761 - 3.44264i) q^{4} +0.554650 q^{5} +(0.427913 + 4.21219i) q^{6} +(0.273771 - 0.158062i) q^{7} +4.82826 q^{8} +(0.946874 - 2.84665i) q^{9} +O(q^{10})\) \(q+(-1.22221 + 2.11693i) q^{2} +(1.40479 - 1.01319i) q^{3} +(-1.98761 - 3.44264i) q^{4} +0.554650 q^{5} +(0.427913 + 4.21219i) q^{6} +(0.273771 - 0.158062i) q^{7} +4.82826 q^{8} +(0.946874 - 2.84665i) q^{9} +(-0.677901 + 1.17416i) q^{10} +(2.42671 + 4.20319i) q^{11} +(-6.28023 - 2.82235i) q^{12} +(4.34339 + 2.50766i) q^{13} +0.772741i q^{14} +(0.779168 - 0.561969i) q^{15} +(-1.92595 + 3.33584i) q^{16} +(1.69341 + 0.977692i) q^{17} +(4.86890 + 5.48368i) q^{18} +(1.70071 - 2.94571i) q^{19} +(-1.10243 - 1.90946i) q^{20} +(0.224444 - 0.499427i) q^{21} -11.8638 q^{22} +(-4.07208 - 2.35102i) q^{23} +(6.78270 - 4.89197i) q^{24} -4.69236 q^{25} +(-10.6171 + 6.12978i) q^{26} +(-1.55405 - 4.95832i) q^{27} +(-1.08830 - 0.628330i) q^{28} +(-4.07773 + 2.35428i) q^{29} +(0.237342 + 2.33629i) q^{30} +(-0.0759515 + 0.0438506i) q^{31} +(0.120428 + 0.208587i) q^{32} +(7.66767 + 3.44587i) q^{33} +(-4.13942 + 2.38989i) q^{34} +(0.151847 - 0.0876691i) q^{35} +(-11.6820 + 2.39828i) q^{36} +(2.84485 - 4.92742i) q^{37} +(4.15725 + 7.20056i) q^{38} +(8.64230 - 0.877965i) q^{39} +2.67800 q^{40} +(-6.23388 - 10.7974i) q^{41} +(0.782937 + 1.08554i) q^{42} +2.81401i q^{43} +(9.64670 - 16.7086i) q^{44} +(0.525184 - 1.57890i) q^{45} +(9.95390 - 5.74688i) q^{46} +(-4.42357 + 2.55395i) q^{47} +(0.674301 + 6.63751i) q^{48} +(-3.45003 + 5.97563i) q^{49} +(5.73506 - 9.93342i) q^{50} +(3.36948 - 0.342303i) q^{51} -19.9369i q^{52} +6.20981 q^{53} +(12.3958 + 2.77029i) q^{54} +(1.34598 + 2.33130i) q^{55} +(1.32184 - 0.763164i) q^{56} +(-0.595440 - 5.86125i) q^{57} -11.5097i q^{58} -5.28317i q^{59} +(-3.48333 - 1.56542i) q^{60} +(6.01339 + 3.47183i) q^{61} -0.214379i q^{62} +(-0.190720 - 0.928996i) q^{63} -8.29254 q^{64} +(2.40906 + 1.39087i) q^{65} +(-16.6662 + 12.0204i) q^{66} +(-1.06651 + 8.11558i) q^{67} -7.77307i q^{68} +(-8.10246 + 0.823124i) q^{69} +0.428601i q^{70} +(-11.2691 + 6.50624i) q^{71} +(4.57175 - 13.7444i) q^{72} +(4.56635 - 7.90915i) q^{73} +(6.95402 + 12.0447i) q^{74} +(-6.59179 + 4.75428i) q^{75} -13.5213 q^{76} +(1.32873 + 0.767141i) q^{77} +(-8.70413 + 19.3682i) q^{78} +(-11.7856 + 6.80443i) q^{79} +(-1.06823 + 1.85022i) q^{80} +(-7.20686 - 5.39084i) q^{81} +30.4765 q^{82} +(-5.31447 - 3.06831i) q^{83} +(-2.16545 + 0.219987i) q^{84} +(0.939251 + 0.542277i) q^{85} +(-5.95706 - 3.43931i) q^{86} +(-3.34302 + 7.43881i) q^{87} +(11.7168 + 20.2941i) q^{88} -10.6357i q^{89} +(2.70053 + 3.04153i) q^{90} +1.58546 q^{91} +18.6916i q^{92} +(-0.0622667 + 0.138555i) q^{93} -12.4859i q^{94} +(0.943297 - 1.63384i) q^{95} +(0.380514 + 0.171004i) q^{96} +(-4.02127 - 2.32168i) q^{97} +(-8.43335 - 14.6070i) q^{98} +(14.2628 - 2.92812i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40 q - 24 q^{4} - 2 q^{6} - 6 q^{7} + 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 40 q - 24 q^{4} - 2 q^{6} - 6 q^{7} + 8 q^{9} - 6 q^{10} + 9 q^{12} - 6 q^{13} - 26 q^{15} - 36 q^{16} + 6 q^{18} - 6 q^{19} + 18 q^{21} + 52 q^{22} - 26 q^{24} + 40 q^{25} - 72 q^{28} + 57 q^{30} - 36 q^{31} + 8 q^{33} - 12 q^{34} + 2 q^{36} + 12 q^{37} + 11 q^{39} - 40 q^{40} + 30 q^{46} - 78 q^{48} - 6 q^{49} - 12 q^{51} + 20 q^{54} - 16 q^{55} + 80 q^{60} + 30 q^{61} + 24 q^{63} + 136 q^{64} + 4 q^{67} - 21 q^{69} - 16 q^{73} + 52 q^{76} - 42 q^{78} - 18 q^{79} - 24 q^{81} + 104 q^{82} + 15 q^{84} - 78 q^{85} - 21 q^{87} - 62 q^{88} - 110 q^{90} - 32 q^{91} - 13 q^{93} - 9 q^{96} - 90 q^{97} + 87 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(68\) \(136\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.22221 + 2.11693i −0.864235 + 1.49690i 0.00357031 + 0.999994i \(0.498864\pi\)
−0.867805 + 0.496905i \(0.834470\pi\)
\(3\) 1.40479 1.01319i 0.811056 0.584968i
\(4\) −1.98761 3.44264i −0.993803 1.72132i
\(5\) 0.554650 0.248047 0.124024 0.992279i \(-0.460420\pi\)
0.124024 + 0.992279i \(0.460420\pi\)
\(6\) 0.427913 + 4.21219i 0.174695 + 1.71962i
\(7\) 0.273771 0.158062i 0.103476 0.0597418i −0.447369 0.894349i \(-0.647639\pi\)
0.550845 + 0.834608i \(0.314306\pi\)
\(8\) 4.82826 1.70705
\(9\) 0.946874 2.84665i 0.315625 0.948884i
\(10\) −0.677901 + 1.17416i −0.214371 + 0.371301i
\(11\) 2.42671 + 4.20319i 0.731681 + 1.26731i 0.956164 + 0.292831i \(0.0945974\pi\)
−0.224483 + 0.974478i \(0.572069\pi\)
\(12\) −6.28023 2.82235i −1.81295 0.814742i
\(13\) 4.34339 + 2.50766i 1.20464 + 0.695499i 0.961583 0.274513i \(-0.0885168\pi\)
0.243056 + 0.970012i \(0.421850\pi\)
\(14\) 0.772741i 0.206524i
\(15\) 0.779168 0.561969i 0.201180 0.145100i
\(16\) −1.92595 + 3.33584i −0.481487 + 0.833960i
\(17\) 1.69341 + 0.977692i 0.410713 + 0.237125i 0.691096 0.722763i \(-0.257128\pi\)
−0.280383 + 0.959888i \(0.590462\pi\)
\(18\) 4.86890 + 5.48368i 1.14761 + 1.29252i
\(19\) 1.70071 2.94571i 0.390169 0.675792i −0.602303 0.798268i \(-0.705750\pi\)
0.992471 + 0.122476i \(0.0390834\pi\)
\(20\) −1.10243 1.90946i −0.246510 0.426968i
\(21\) 0.224444 0.499427i 0.0489776 0.108984i
\(22\) −11.8638 −2.52938
\(23\) −4.07208 2.35102i −0.849088 0.490221i 0.0112553 0.999937i \(-0.496417\pi\)
−0.860343 + 0.509716i \(0.829751\pi\)
\(24\) 6.78270 4.89197i 1.38451 0.998569i
\(25\) −4.69236 −0.938473
\(26\) −10.6171 + 6.12978i −2.08218 + 1.20215i
\(27\) −1.55405 4.95832i −0.299078 0.954229i
\(28\) −1.08830 0.628330i −0.205669 0.118743i
\(29\) −4.07773 + 2.35428i −0.757216 + 0.437179i −0.828295 0.560292i \(-0.810689\pi\)
0.0710791 + 0.997471i \(0.477356\pi\)
\(30\) 0.237342 + 2.33629i 0.0433326 + 0.426547i
\(31\) −0.0759515 + 0.0438506i −0.0136413 + 0.00787580i −0.506805 0.862061i \(-0.669174\pi\)
0.493164 + 0.869936i \(0.335840\pi\)
\(32\) 0.120428 + 0.208587i 0.0212888 + 0.0368732i
\(33\) 7.66767 + 3.44587i 1.33477 + 0.599849i
\(34\) −4.13942 + 2.38989i −0.709904 + 0.409863i
\(35\) 0.151847 0.0876691i 0.0256669 0.0148188i
\(36\) −11.6820 + 2.39828i −1.94700 + 0.399714i
\(37\) 2.84485 4.92742i 0.467690 0.810063i −0.531628 0.846978i \(-0.678420\pi\)
0.999318 + 0.0369148i \(0.0117530\pi\)
\(38\) 4.15725 + 7.20056i 0.674394 + 1.16809i
\(39\) 8.64230 0.877965i 1.38388 0.140587i
\(40\) 2.67800 0.423428
\(41\) −6.23388 10.7974i −0.973569 1.68627i −0.684580 0.728938i \(-0.740014\pi\)
−0.288989 0.957332i \(-0.593319\pi\)
\(42\) 0.782937 + 1.08554i 0.120810 + 0.167502i
\(43\) 2.81401i 0.429132i 0.976710 + 0.214566i \(0.0688337\pi\)
−0.976710 + 0.214566i \(0.931166\pi\)
\(44\) 9.64670 16.7086i 1.45429 2.51891i
\(45\) 0.525184 1.57890i 0.0782898 0.235368i
\(46\) 9.95390 5.74688i 1.46762 0.847332i
\(47\) −4.42357 + 2.55395i −0.645244 + 0.372532i −0.786632 0.617422i \(-0.788177\pi\)
0.141388 + 0.989954i \(0.454844\pi\)
\(48\) 0.674301 + 6.63751i 0.0973269 + 0.958043i
\(49\) −3.45003 + 5.97563i −0.492862 + 0.853662i
\(50\) 5.73506 9.93342i 0.811061 1.40480i
\(51\) 3.36948 0.342303i 0.471822 0.0479321i
\(52\) 19.9369i 2.76476i
\(53\) 6.20981 0.852983 0.426492 0.904491i \(-0.359749\pi\)
0.426492 + 0.904491i \(0.359749\pi\)
\(54\) 12.3958 + 2.77029i 1.68686 + 0.376989i
\(55\) 1.34598 + 2.33130i 0.181491 + 0.314352i
\(56\) 1.32184 0.763164i 0.176638 0.101982i
\(57\) −0.595440 5.86125i −0.0788680 0.776341i
\(58\) 11.5097i 1.51130i
\(59\) 5.28317i 0.687810i −0.939004 0.343905i \(-0.888250\pi\)
0.939004 0.343905i \(-0.111750\pi\)
\(60\) −3.48333 1.56542i −0.449696 0.202095i
\(61\) 6.01339 + 3.47183i 0.769936 + 0.444523i 0.832852 0.553496i \(-0.186707\pi\)
−0.0629156 + 0.998019i \(0.520040\pi\)
\(62\) 0.214379i 0.0272262i
\(63\) −0.190720 0.928996i −0.0240285 0.117042i
\(64\) −8.29254 −1.03657
\(65\) 2.40906 + 1.39087i 0.298807 + 0.172517i
\(66\) −16.6662 + 12.0204i −2.05147 + 1.47961i
\(67\) −1.06651 + 8.11558i −0.130294 + 0.991475i
\(68\) 7.77307i 0.942623i
\(69\) −8.10246 + 0.823124i −0.975421 + 0.0990924i
\(70\) 0.428601i 0.0512276i
\(71\) −11.2691 + 6.50624i −1.33740 + 0.772148i −0.986421 0.164235i \(-0.947484\pi\)
−0.350978 + 0.936384i \(0.614151\pi\)
\(72\) 4.57175 13.7444i 0.538786 1.61979i
\(73\) 4.56635 7.90915i 0.534451 0.925697i −0.464739 0.885448i \(-0.653852\pi\)
0.999190 0.0402486i \(-0.0128150\pi\)
\(74\) 6.95402 + 12.0447i 0.808388 + 1.40017i
\(75\) −6.59179 + 4.75428i −0.761154 + 0.548977i
\(76\) −13.5213 −1.55100
\(77\) 1.32873 + 0.767141i 0.151423 + 0.0874239i
\(78\) −8.70413 + 19.3682i −0.985548 + 2.19302i
\(79\) −11.7856 + 6.80443i −1.32599 + 0.765559i −0.984676 0.174392i \(-0.944204\pi\)
−0.341310 + 0.939951i \(0.610871\pi\)
\(80\) −1.06823 + 1.85022i −0.119431 + 0.206861i
\(81\) −7.20686 5.39084i −0.800762 0.598982i
\(82\) 30.4765 3.36557
\(83\) −5.31447 3.06831i −0.583339 0.336791i 0.179120 0.983827i \(-0.442675\pi\)
−0.762459 + 0.647036i \(0.776008\pi\)
\(84\) −2.16545 + 0.219987i −0.236270 + 0.0240025i
\(85\) 0.939251 + 0.542277i 0.101876 + 0.0588182i
\(86\) −5.95706 3.43931i −0.642367 0.370871i
\(87\) −3.34302 + 7.43881i −0.358409 + 0.797524i
\(88\) 11.7168 + 20.2941i 1.24902 + 2.16336i
\(89\) 10.6357i 1.12738i −0.825986 0.563691i \(-0.809381\pi\)
0.825986 0.563691i \(-0.190619\pi\)
\(90\) 2.70053 + 3.04153i 0.284661 + 0.320605i
\(91\) 1.58546 0.166201
\(92\) 18.6916i 1.94873i
\(93\) −0.0622667 + 0.138555i −0.00645676 + 0.0143674i
\(94\) 12.4859i 1.28782i
\(95\) 0.943297 1.63384i 0.0967802 0.167628i
\(96\) 0.380514 + 0.171004i 0.0388361 + 0.0174530i
\(97\) −4.02127 2.32168i −0.408298 0.235731i 0.281760 0.959485i \(-0.409082\pi\)
−0.690058 + 0.723754i \(0.742415\pi\)
\(98\) −8.43335 14.6070i −0.851897 1.47553i
\(99\) 14.2628 2.92812i 1.43347 0.294287i
\(100\) 9.32657 + 16.1541i 0.932657 + 1.61541i
\(101\) −2.63337 4.56114i −0.262031 0.453850i 0.704751 0.709455i \(-0.251059\pi\)
−0.966781 + 0.255605i \(0.917725\pi\)
\(102\) −3.39359 + 7.55134i −0.336015 + 0.747694i
\(103\) −0.965658 1.67257i −0.0951491 0.164803i 0.814522 0.580133i \(-0.196999\pi\)
−0.909671 + 0.415330i \(0.863666\pi\)
\(104\) 20.9710 + 12.1076i 2.05638 + 1.18725i
\(105\) 0.124488 0.277007i 0.0121488 0.0270332i
\(106\) −7.58971 + 13.1458i −0.737178 + 1.27683i
\(107\) 5.69570i 0.550624i −0.961355 0.275312i \(-0.911219\pi\)
0.961355 0.275312i \(-0.0887811\pi\)
\(108\) −13.9808 + 15.2052i −1.34531 + 1.46312i
\(109\) 18.1860i 1.74191i 0.491366 + 0.870953i \(0.336498\pi\)
−0.491366 + 0.870953i \(0.663502\pi\)
\(110\) −6.58028 −0.627405
\(111\) −0.996020 9.80438i −0.0945381 0.930590i
\(112\) 1.21768i 0.115059i
\(113\) 7.22486 + 12.5138i 0.679658 + 1.17720i 0.975084 + 0.221836i \(0.0712050\pi\)
−0.295426 + 0.955366i \(0.595462\pi\)
\(114\) 13.1356 + 5.90318i 1.23026 + 0.552884i
\(115\) −2.25858 1.30399i −0.210614 0.121598i
\(116\) 16.2099 + 9.35877i 1.50505 + 0.868940i
\(117\) 11.2511 9.98969i 1.04016 0.923547i
\(118\) 11.1841 + 6.45716i 1.02958 + 0.594429i
\(119\) 0.618143 0.0566651
\(120\) 3.76202 2.71333i 0.343424 0.247692i
\(121\) −6.27787 + 10.8736i −0.570715 + 0.988508i
\(122\) −14.6993 + 8.48664i −1.33081 + 0.768344i
\(123\) −19.6972 8.85195i −1.77603 0.798154i
\(124\) 0.301923 + 0.174316i 0.0271135 + 0.0156540i
\(125\) −5.37587 −0.480833
\(126\) 2.19972 + 0.731688i 0.195967 + 0.0651839i
\(127\) −7.75428 13.4308i −0.688081 1.19179i −0.972458 0.233079i \(-0.925120\pi\)
0.284377 0.958713i \(-0.408213\pi\)
\(128\) 9.89439 17.1376i 0.874549 1.51476i
\(129\) 2.85113 + 3.95309i 0.251028 + 0.348050i
\(130\) −5.88877 + 3.39988i −0.516479 + 0.298190i
\(131\) 12.9443i 1.13095i 0.824765 + 0.565475i \(0.191307\pi\)
−0.824765 + 0.565475i \(0.808693\pi\)
\(132\) −3.37744 33.2460i −0.293969 2.89370i
\(133\) 1.07527i 0.0932374i
\(134\) −15.8766 12.1767i −1.37153 1.05191i
\(135\) −0.861956 2.75013i −0.0741854 0.236694i
\(136\) 8.17623 + 4.72055i 0.701106 + 0.404784i
\(137\) 17.2275 1.47184 0.735922 0.677066i \(-0.236749\pi\)
0.735922 + 0.677066i \(0.236749\pi\)
\(138\) 8.16043 18.1584i 0.694662 1.54575i
\(139\) 14.5260i 1.23208i −0.787716 0.616038i \(-0.788737\pi\)
0.787716 0.616038i \(-0.211263\pi\)
\(140\) −0.603625 0.348503i −0.0510156 0.0294539i
\(141\) −3.62654 + 8.06970i −0.305410 + 0.679592i
\(142\) 31.8080i 2.66927i
\(143\) 24.3414i 2.03553i
\(144\) 7.67234 + 8.64112i 0.639362 + 0.720093i
\(145\) −2.26172 + 1.30580i −0.187825 + 0.108441i
\(146\) 11.1621 + 19.3333i 0.923783 + 1.60004i
\(147\) 1.20790 + 11.8901i 0.0996263 + 0.980676i
\(148\) −22.6178 −1.85917
\(149\) 4.68659i 0.383941i 0.981401 + 0.191970i \(0.0614878\pi\)
−0.981401 + 0.191970i \(0.938512\pi\)
\(150\) −2.00793 19.7651i −0.163946 1.61381i
\(151\) −1.94998 + 3.37747i −0.158687 + 0.274855i −0.934396 0.356237i \(-0.884060\pi\)
0.775708 + 0.631092i \(0.217393\pi\)
\(152\) 8.21145 14.2226i 0.666036 1.15361i
\(153\) 4.38660 3.89480i 0.354635 0.314876i
\(154\) −3.24798 + 1.87522i −0.261729 + 0.151109i
\(155\) −0.0421265 + 0.0243218i −0.00338368 + 0.00195357i
\(156\) −20.2000 28.0072i −1.61729 2.24237i
\(157\) 5.17973 8.97156i 0.413388 0.716008i −0.581870 0.813282i \(-0.697679\pi\)
0.995258 + 0.0972734i \(0.0310121\pi\)
\(158\) 33.2659i 2.64649i
\(159\) 8.72349 6.29175i 0.691817 0.498968i
\(160\) 0.0667952 + 0.115693i 0.00528062 + 0.00914630i
\(161\) −1.48642 −0.117147
\(162\) 20.2204 8.66770i 1.58866 0.680999i
\(163\) −7.09012 12.2804i −0.555341 0.961878i −0.997877 0.0651278i \(-0.979254\pi\)
0.442536 0.896751i \(-0.354079\pi\)
\(164\) −24.7810 + 42.9220i −1.93507 + 3.35164i
\(165\) 4.25288 + 1.91125i 0.331086 + 0.148791i
\(166\) 12.9908 7.50026i 1.00828 0.582133i
\(167\) 15.6696 9.04683i 1.21255 0.700065i 0.249234 0.968443i \(-0.419821\pi\)
0.963314 + 0.268379i \(0.0864878\pi\)
\(168\) 1.08367 2.41136i 0.0836072 0.186041i
\(169\) 6.07669 + 10.5251i 0.467437 + 0.809625i
\(170\) −2.29593 + 1.32556i −0.176090 + 0.101665i
\(171\) −6.77505 7.63053i −0.518101 0.583521i
\(172\) 9.68759 5.59314i 0.738672 0.426473i
\(173\) −3.31248 1.91246i −0.251843 0.145402i 0.368765 0.929523i \(-0.379781\pi\)
−0.620608 + 0.784121i \(0.713114\pi\)
\(174\) −11.6616 16.1688i −0.884063 1.22575i
\(175\) −1.28463 + 0.741684i −0.0971092 + 0.0560660i
\(176\) −18.6949 −1.40918
\(177\) −5.35288 7.42175i −0.402347 0.557853i
\(178\) 22.5151 + 12.9991i 1.68758 + 0.974322i
\(179\) −15.2614 −1.14069 −0.570344 0.821406i \(-0.693190\pi\)
−0.570344 + 0.821406i \(0.693190\pi\)
\(180\) −6.47942 + 1.33021i −0.482948 + 0.0991480i
\(181\) 11.7000 + 20.2649i 0.869652 + 1.50628i 0.862353 + 0.506308i \(0.168990\pi\)
0.00729935 + 0.999973i \(0.497677\pi\)
\(182\) −1.93777 + 3.35631i −0.143637 + 0.248786i
\(183\) 11.9652 1.21554i 0.884493 0.0898551i
\(184\) −19.6611 11.3513i −1.44943 0.836831i
\(185\) 1.57790 2.73300i 0.116009 0.200934i
\(186\) −0.217208 0.301158i −0.0159264 0.0220820i
\(187\) 9.49031i 0.694000i
\(188\) 17.5846 + 10.1525i 1.28249 + 0.740447i
\(189\) −1.20918 1.11181i −0.0879546 0.0808721i
\(190\) 2.30582 + 3.99379i 0.167282 + 0.289740i
\(191\) −0.0929143 + 0.160932i −0.00672304 + 0.0116447i −0.869367 0.494166i \(-0.835473\pi\)
0.862644 + 0.505811i \(0.168807\pi\)
\(192\) −11.6493 + 8.40196i −0.840715 + 0.606359i
\(193\) 9.21072 0.663002 0.331501 0.943455i \(-0.392445\pi\)
0.331501 + 0.943455i \(0.392445\pi\)
\(194\) 9.82969 5.67517i 0.705730 0.407454i
\(195\) 4.79345 0.486964i 0.343266 0.0348722i
\(196\) 27.4292 1.95923
\(197\) 2.07645 + 3.59652i 0.147941 + 0.256241i 0.930466 0.366377i \(-0.119402\pi\)
−0.782525 + 0.622619i \(0.786069\pi\)
\(198\) −11.2335 + 33.7722i −0.798334 + 2.40009i
\(199\) −9.03504 + 15.6491i −0.640477 + 1.10934i 0.344849 + 0.938658i \(0.387930\pi\)
−0.985326 + 0.170681i \(0.945403\pi\)
\(200\) −22.6560 −1.60202
\(201\) 6.72444 + 12.4813i 0.474305 + 0.880360i
\(202\) 12.8742 0.905823
\(203\) −0.744244 + 1.28907i −0.0522357 + 0.0904749i
\(204\) −7.87563 10.9195i −0.551404 0.764520i
\(205\) −3.45762 5.98878i −0.241491 0.418275i
\(206\) 4.72096 0.328925
\(207\) −10.5483 + 9.36568i −0.733156 + 0.650960i
\(208\) −16.7303 + 9.65923i −1.16004 + 0.669747i
\(209\) 16.5085 1.14192
\(210\) 0.434256 + 0.602094i 0.0299665 + 0.0415485i
\(211\) 8.36031 14.4805i 0.575547 0.996877i −0.420435 0.907323i \(-0.638122\pi\)
0.995982 0.0895544i \(-0.0285443\pi\)
\(212\) −12.3427 21.3781i −0.847698 1.46826i
\(213\) −9.23869 + 20.5577i −0.633024 + 1.40859i
\(214\) 12.0574 + 6.96135i 0.824228 + 0.475868i
\(215\) 1.56079i 0.106445i
\(216\) −7.50338 23.9401i −0.510540 1.62891i
\(217\) −0.0138622 + 0.0240101i −0.000941029 + 0.00162991i
\(218\) −38.4986 22.2272i −2.60746 1.50542i
\(219\) −1.59874 15.7373i −0.108033 1.06343i
\(220\) 5.35055 9.26742i 0.360734 0.624809i
\(221\) 4.90343 + 8.49299i 0.329840 + 0.571300i
\(222\) 21.9726 + 9.87452i 1.47470 + 0.662735i
\(223\) 0.125563 0.00840834 0.00420417 0.999991i \(-0.498662\pi\)
0.00420417 + 0.999991i \(0.498662\pi\)
\(224\) 0.0659392 + 0.0380700i 0.00440574 + 0.00254366i
\(225\) −4.44307 + 13.3575i −0.296205 + 0.890502i
\(226\) −35.3213 −2.34954
\(227\) 4.67009 2.69628i 0.309965 0.178958i −0.336946 0.941524i \(-0.609394\pi\)
0.646911 + 0.762566i \(0.276061\pi\)
\(228\) −18.9946 + 13.6997i −1.25795 + 0.907287i
\(229\) −18.4704 10.6639i −1.22056 0.704689i −0.255521 0.966804i \(-0.582247\pi\)
−0.965037 + 0.262114i \(0.915580\pi\)
\(230\) 5.52093 3.18751i 0.364039 0.210178i
\(231\) 2.64385 0.268587i 0.173952 0.0176717i
\(232\) −19.6884 + 11.3671i −1.29260 + 0.746286i
\(233\) −4.37106 7.57090i −0.286358 0.495986i 0.686580 0.727054i \(-0.259111\pi\)
−0.972938 + 0.231068i \(0.925778\pi\)
\(234\) 7.39631 + 36.0273i 0.483512 + 2.35518i
\(235\) −2.45354 + 1.41655i −0.160051 + 0.0924055i
\(236\) −18.1880 + 10.5009i −1.18394 + 0.683548i
\(237\) −9.66212 + 21.4999i −0.627622 + 1.39657i
\(238\) −0.755502 + 1.30857i −0.0489719 + 0.0848219i
\(239\) −1.63739 2.83604i −0.105914 0.183448i 0.808197 0.588912i \(-0.200443\pi\)
−0.914111 + 0.405463i \(0.867110\pi\)
\(240\) 0.374001 + 3.68150i 0.0241417 + 0.237640i
\(241\) 22.2128 1.43085 0.715426 0.698689i \(-0.246233\pi\)
0.715426 + 0.698689i \(0.246233\pi\)
\(242\) −15.3458 26.5797i −0.986464 1.70861i
\(243\) −15.5861 0.271049i −0.999849 0.0173878i
\(244\) 27.6026i 1.76707i
\(245\) −1.91356 + 3.31439i −0.122253 + 0.211748i
\(246\) 42.8131 30.8786i 2.72966 1.96875i
\(247\) 14.7736 8.52957i 0.940025 0.542724i
\(248\) −0.366714 + 0.211722i −0.0232863 + 0.0134444i
\(249\) −10.5745 + 1.07426i −0.670133 + 0.0680784i
\(250\) 6.57046 11.3804i 0.415552 0.719758i
\(251\) −5.06113 + 8.76613i −0.319456 + 0.553313i −0.980375 0.197144i \(-0.936833\pi\)
0.660919 + 0.750457i \(0.270167\pi\)
\(252\) −2.81912 + 2.50306i −0.177588 + 0.157678i
\(253\) 22.8210i 1.43474i
\(254\) 37.9095 2.37865
\(255\) 1.86888 0.189859i 0.117034 0.0118894i
\(256\) 15.8936 + 27.5284i 0.993347 + 1.72053i
\(257\) 2.18750 1.26296i 0.136453 0.0787810i −0.430220 0.902724i \(-0.641564\pi\)
0.566672 + 0.823943i \(0.308231\pi\)
\(258\) −11.8531 + 1.20415i −0.737943 + 0.0749672i
\(259\) 1.79865i 0.111763i
\(260\) 11.0580i 0.685790i
\(261\) 2.84072 + 13.8371i 0.175836 + 0.856495i
\(262\) −27.4023 15.8207i −1.69292 0.977406i
\(263\) 19.7948i 1.22060i 0.792170 + 0.610301i \(0.208951\pi\)
−0.792170 + 0.610301i \(0.791049\pi\)
\(264\) 37.0215 + 16.6376i 2.27852 + 1.02397i
\(265\) 3.44427 0.211580
\(266\) 2.27627 + 1.31420i 0.139567 + 0.0805790i
\(267\) −10.7760 14.9409i −0.659482 0.914370i
\(268\) 30.0588 12.4590i 1.83613 0.761053i
\(269\) 4.19080i 0.255517i −0.991805 0.127759i \(-0.959222\pi\)
0.991805 0.127759i \(-0.0407783\pi\)
\(270\) 6.87534 + 1.53654i 0.418420 + 0.0935109i
\(271\) 27.5947i 1.67626i 0.545474 + 0.838128i \(0.316350\pi\)
−0.545474 + 0.838128i \(0.683650\pi\)
\(272\) −6.52284 + 3.76597i −0.395505 + 0.228345i
\(273\) 2.22724 1.60638i 0.134799 0.0972225i
\(274\) −21.0557 + 36.4695i −1.27202 + 2.20320i
\(275\) −11.3870 19.7229i −0.686663 1.18934i
\(276\) 18.9382 + 26.2578i 1.13995 + 1.58053i
\(277\) 18.3013 1.09962 0.549809 0.835290i \(-0.314700\pi\)
0.549809 + 0.835290i \(0.314700\pi\)
\(278\) 30.7505 + 17.7538i 1.84429 + 1.06480i
\(279\) 0.0529110 + 0.257728i 0.00316770 + 0.0154298i
\(280\) 0.733158 0.423289i 0.0438146 0.0252964i
\(281\) 11.5843 20.0646i 0.691063 1.19696i −0.280427 0.959875i \(-0.590476\pi\)
0.971490 0.237081i \(-0.0761906\pi\)
\(282\) −12.6506 17.5400i −0.753334 1.04449i
\(283\) 1.87184 0.111269 0.0556346 0.998451i \(-0.482282\pi\)
0.0556346 + 0.998451i \(0.482282\pi\)
\(284\) 44.7972 + 25.8637i 2.65822 + 1.53473i
\(285\) −0.330261 3.25094i −0.0195630 0.192569i
\(286\) −51.5292 29.7504i −3.04699 1.75918i
\(287\) −3.41331 1.97068i −0.201482 0.116325i
\(288\) 0.707803 0.145310i 0.0417077 0.00856248i
\(289\) −6.58824 11.4112i −0.387543 0.671245i
\(290\) 6.38387i 0.374874i
\(291\) −8.00135 + 0.812852i −0.469048 + 0.0476502i
\(292\) −36.3045 −2.12456
\(293\) 9.42262i 0.550475i 0.961376 + 0.275238i \(0.0887565\pi\)
−0.961376 + 0.275238i \(0.911244\pi\)
\(294\) −26.6468 11.9751i −1.55407 0.698404i
\(295\) 2.93031i 0.170609i
\(296\) 13.7357 23.7909i 0.798369 1.38282i
\(297\) 17.0695 18.5644i 0.990473 1.07722i
\(298\) −9.92121 5.72801i −0.574720 0.331815i
\(299\) −11.7911 20.4228i −0.681896 1.18108i
\(300\) 29.4691 + 13.2435i 1.70140 + 0.764613i
\(301\) 0.444787 + 0.770393i 0.0256371 + 0.0444047i
\(302\) −4.76659 8.25597i −0.274286 0.475078i
\(303\) −8.32066 3.73932i −0.478009 0.214819i
\(304\) 6.55094 + 11.3466i 0.375722 + 0.650770i
\(305\) 3.33533 + 1.92565i 0.190980 + 0.110263i
\(306\) 2.88369 + 14.0464i 0.164850 + 0.802980i
\(307\) −15.5499 + 26.9332i −0.887480 + 1.53716i −0.0446359 + 0.999003i \(0.514213\pi\)
−0.842844 + 0.538158i \(0.819121\pi\)
\(308\) 6.09910i 0.347529i
\(309\) −3.05118 1.37121i −0.173576 0.0780054i
\(310\) 0.118905i 0.00675337i
\(311\) 18.6474 1.05740 0.528698 0.848810i \(-0.322680\pi\)
0.528698 + 0.848810i \(0.322680\pi\)
\(312\) 41.7273 4.23905i 2.36234 0.239989i
\(313\) 10.5279i 0.595073i −0.954710 0.297537i \(-0.903835\pi\)
0.954710 0.297537i \(-0.0961650\pi\)
\(314\) 12.6615 + 21.9303i 0.714528 + 1.23760i
\(315\) −0.105783 0.515268i −0.00596021 0.0290321i
\(316\) 46.8504 + 27.0491i 2.63554 + 1.52163i
\(317\) 20.9867 + 12.1167i 1.17873 + 0.680541i 0.955721 0.294275i \(-0.0950782\pi\)
0.223011 + 0.974816i \(0.428412\pi\)
\(318\) 2.65726 + 26.1569i 0.149012 + 1.46681i
\(319\) −19.7910 11.4263i −1.10808 0.639752i
\(320\) −4.59946 −0.257118
\(321\) −5.77085 8.00126i −0.322097 0.446587i
\(322\) 1.81673 3.14666i 0.101242 0.175357i
\(323\) 5.75999 3.32553i 0.320494 0.185037i
\(324\) −4.23429 + 35.5255i −0.235238 + 1.97364i
\(325\) −20.3808 11.7668i −1.13052 0.652707i
\(326\) 34.6625 1.91978
\(327\) 18.4260 + 25.5476i 1.01896 + 1.41278i
\(328\) −30.0988 52.1327i −1.66193 2.87854i
\(329\) −0.807364 + 1.39840i −0.0445114 + 0.0770961i
\(330\) −9.24391 + 6.66710i −0.508861 + 0.367012i
\(331\) −11.6099 + 6.70295i −0.638135 + 0.368428i −0.783896 0.620892i \(-0.786770\pi\)
0.145760 + 0.989320i \(0.453437\pi\)
\(332\) 24.3944i 1.33882i
\(333\) −11.3329 12.7639i −0.621041 0.699459i
\(334\) 44.2286i 2.42008i
\(335\) −0.591538 + 4.50131i −0.0323192 + 0.245933i
\(336\) 1.23374 + 1.71058i 0.0673061 + 0.0933197i
\(337\) 7.18974 + 4.15100i 0.391650 + 0.226119i 0.682875 0.730535i \(-0.260729\pi\)
−0.291225 + 0.956655i \(0.594063\pi\)
\(338\) −29.7080 −1.61590
\(339\) 22.8284 + 10.2591i 1.23987 + 0.557199i
\(340\) 4.31133i 0.233815i
\(341\) −0.368625 0.212826i −0.0199622 0.0115252i
\(342\) 24.4339 5.01621i 1.32123 0.271246i
\(343\) 4.39414i 0.237261i
\(344\) 13.5868i 0.732549i
\(345\) −4.49403 + 0.456546i −0.241951 + 0.0245796i
\(346\) 8.09712 4.67487i 0.435304 0.251323i
\(347\) −10.2571 17.7658i −0.550629 0.953717i −0.998229 0.0594833i \(-0.981055\pi\)
0.447601 0.894234i \(-0.352279\pi\)
\(348\) 32.2537 3.27663i 1.72898 0.175646i
\(349\) 16.8339 0.901099 0.450549 0.892752i \(-0.351228\pi\)
0.450549 + 0.892752i \(0.351228\pi\)
\(350\) 3.62598i 0.193817i
\(351\) 5.68390 25.4329i 0.303384 1.35751i
\(352\) −0.584486 + 1.01236i −0.0311532 + 0.0539589i
\(353\) 8.11194 14.0503i 0.431755 0.747822i −0.565269 0.824906i \(-0.691228\pi\)
0.997025 + 0.0770845i \(0.0245611\pi\)
\(354\) 22.2537 2.26074i 1.18277 0.120157i
\(355\) −6.25043 + 3.60869i −0.331738 + 0.191529i
\(356\) −36.6148 + 21.1396i −1.94058 + 1.12040i
\(357\) 0.868362 0.626299i 0.0459586 0.0331473i
\(358\) 18.6526 32.3073i 0.985822 1.70749i
\(359\) 19.1819i 1.01238i −0.862421 0.506192i \(-0.831053\pi\)
0.862421 0.506192i \(-0.168947\pi\)
\(360\) 2.53572 7.62333i 0.133644 0.401785i
\(361\) 3.71520 + 6.43492i 0.195537 + 0.338680i
\(362\) −57.1994 −3.00633
\(363\) 2.19797 + 21.6358i 0.115363 + 1.13559i
\(364\) −3.15127 5.45816i −0.165171 0.286085i
\(365\) 2.53273 4.38682i 0.132569 0.229616i
\(366\) −12.0508 + 26.8152i −0.629906 + 1.40165i
\(367\) −10.0787 + 5.81895i −0.526105 + 0.303747i −0.739429 0.673235i \(-0.764904\pi\)
0.213324 + 0.976982i \(0.431571\pi\)
\(368\) 15.6852 9.05587i 0.817649 0.472070i
\(369\) −36.6391 + 7.52192i −1.90736 + 0.391576i
\(370\) 3.85705 + 6.68060i 0.200518 + 0.347308i
\(371\) 1.70007 0.981534i 0.0882631 0.0509587i
\(372\) 0.600755 0.0610303i 0.0311477 0.00316427i
\(373\) −24.5353 + 14.1655i −1.27039 + 0.733460i −0.975061 0.221935i \(-0.928763\pi\)
−0.295329 + 0.955396i \(0.595429\pi\)
\(374\) −20.0904 11.5992i −1.03885 0.599779i
\(375\) −7.55198 + 5.44680i −0.389982 + 0.281272i
\(376\) −21.3582 + 12.3311i −1.10146 + 0.635930i
\(377\) −23.6149 −1.21623
\(378\) 3.83149 1.20088i 0.197071 0.0617666i
\(379\) −5.46399 3.15464i −0.280667 0.162043i 0.353059 0.935601i \(-0.385142\pi\)
−0.633725 + 0.773558i \(0.718475\pi\)
\(380\) −7.49961 −0.384722
\(381\) −24.5012 11.0109i −1.25523 0.564104i
\(382\) −0.227122 0.393387i −0.0116206 0.0201274i
\(383\) 8.10051 14.0305i 0.413917 0.716925i −0.581397 0.813620i \(-0.697494\pi\)
0.995314 + 0.0966951i \(0.0308272\pi\)
\(384\) −3.46416 34.0997i −0.176780 1.74014i
\(385\) 0.736979 + 0.425495i 0.0375599 + 0.0216852i
\(386\) −11.2575 + 19.4985i −0.572990 + 0.992447i
\(387\) 8.01050 + 2.66451i 0.407196 + 0.135445i
\(388\) 18.4583i 0.937080i
\(389\) −2.73555 1.57937i −0.138698 0.0800773i 0.429045 0.903283i \(-0.358850\pi\)
−0.567743 + 0.823206i \(0.692183\pi\)
\(390\) −4.82775 + 10.7426i −0.244462 + 0.543973i
\(391\) −4.59714 7.96248i −0.232487 0.402680i
\(392\) −16.6577 + 28.8519i −0.841339 + 1.45724i
\(393\) 13.1151 + 18.1841i 0.661570 + 0.917264i
\(394\) −10.1515 −0.511423
\(395\) −6.53690 + 3.77408i −0.328907 + 0.189895i
\(396\) −38.4293 43.2817i −1.93115 2.17499i
\(397\) 24.6917 1.23924 0.619621 0.784901i \(-0.287286\pi\)
0.619621 + 0.784901i \(0.287286\pi\)
\(398\) −22.0855 38.2532i −1.10704 1.91746i
\(399\) −1.08945 1.51052i −0.0545409 0.0756208i
\(400\) 9.03724 15.6530i 0.451862 0.782648i
\(401\) 6.63572 0.331372 0.165686 0.986179i \(-0.447016\pi\)
0.165686 + 0.986179i \(0.447016\pi\)
\(402\) −34.6407 1.01956i −1.72772 0.0508511i
\(403\) −0.439849 −0.0219104
\(404\) −10.4682 + 18.1315i −0.520814 + 0.902076i
\(405\) −3.99729 2.99003i −0.198627 0.148576i
\(406\) −1.81925 3.15103i −0.0902878 0.156383i
\(407\) 27.6145 1.36880
\(408\) 16.2687 1.65273i 0.805422 0.0818223i
\(409\) 22.1899 12.8113i 1.09722 0.633480i 0.161730 0.986835i \(-0.448293\pi\)
0.935489 + 0.353355i \(0.114959\pi\)
\(410\) 16.9038 0.834819
\(411\) 24.2010 17.4548i 1.19375 0.860982i
\(412\) −3.83870 + 6.64882i −0.189119 + 0.327564i
\(413\) −0.835068 1.44638i −0.0410910 0.0711717i
\(414\) −6.93430 33.7769i −0.340802 1.66004i
\(415\) −2.94767 1.70184i −0.144696 0.0835401i
\(416\) 1.20796i 0.0592253i
\(417\) −14.7176 20.4059i −0.720726 0.999283i
\(418\) −20.1769 + 34.9474i −0.986884 + 1.70933i
\(419\) 8.79700 + 5.07895i 0.429761 + 0.248123i 0.699245 0.714882i \(-0.253520\pi\)
−0.269484 + 0.963005i \(0.586853\pi\)
\(420\) −1.20107 + 0.122016i −0.0586061 + 0.00595376i
\(421\) −0.461960 + 0.800138i −0.0225146 + 0.0389963i −0.877063 0.480375i \(-0.840501\pi\)
0.854549 + 0.519371i \(0.173834\pi\)
\(422\) 20.4361 + 35.3964i 0.994816 + 1.72307i
\(423\) 3.08165 + 15.0106i 0.149835 + 0.729842i
\(424\) 29.9826 1.45608
\(425\) −7.94610 4.58768i −0.385443 0.222535i
\(426\) −32.2277 44.6836i −1.56144 2.16493i
\(427\) 2.19506 0.106226
\(428\) −19.6082 + 11.3208i −0.947799 + 0.547212i
\(429\) 24.6626 + 34.1946i 1.19072 + 1.65093i
\(430\) −3.30409 1.90762i −0.159337 0.0919934i
\(431\) 2.96212 1.71018i 0.142680 0.0823766i −0.426960 0.904270i \(-0.640416\pi\)
0.569641 + 0.821894i \(0.307082\pi\)
\(432\) 19.5332 + 4.36539i 0.939790 + 0.210030i
\(433\) 13.9947 8.07984i 0.672542 0.388293i −0.124497 0.992220i \(-0.539732\pi\)
0.797039 + 0.603927i \(0.206398\pi\)
\(434\) −0.0338852 0.0586908i −0.00162654 0.00281725i
\(435\) −1.85421 + 4.12594i −0.0889024 + 0.197824i
\(436\) 62.6079 36.1467i 2.99838 1.73111i
\(437\) −13.8508 + 7.99677i −0.662574 + 0.382538i
\(438\) 35.2689 + 15.8499i 1.68521 + 0.757338i
\(439\) −9.74150 + 16.8728i −0.464937 + 0.805294i −0.999199 0.0400251i \(-0.987256\pi\)
0.534262 + 0.845319i \(0.320590\pi\)
\(440\) 6.49873 + 11.2561i 0.309815 + 0.536615i
\(441\) 13.7438 + 15.4792i 0.654467 + 0.737105i
\(442\) −23.9721 −1.14024
\(443\) 5.35484 + 9.27486i 0.254416 + 0.440662i 0.964737 0.263217i \(-0.0847834\pi\)
−0.710321 + 0.703878i \(0.751450\pi\)
\(444\) −31.7732 + 22.9162i −1.50789 + 1.08755i
\(445\) 5.89909i 0.279644i
\(446\) −0.153465 + 0.265809i −0.00726678 + 0.0125864i
\(447\) 4.74843 + 6.58368i 0.224593 + 0.311398i
\(448\) −2.27026 + 1.31073i −0.107260 + 0.0619264i
\(449\) −25.7361 + 14.8588i −1.21456 + 0.701228i −0.963750 0.266807i \(-0.914031\pi\)
−0.250813 + 0.968035i \(0.580698\pi\)
\(450\) −22.8466 25.7314i −1.07700 1.21299i
\(451\) 30.2557 52.4044i 1.42468 2.46763i
\(452\) 28.7204 49.7451i 1.35089 2.33981i
\(453\) 0.682716 + 6.72035i 0.0320768 + 0.315750i
\(454\) 13.1817i 0.618648i
\(455\) 0.879376 0.0412258
\(456\) −2.87494 28.2996i −0.134631 1.32525i
\(457\) 2.03063 + 3.51716i 0.0949889 + 0.164526i 0.909604 0.415476i \(-0.136385\pi\)
−0.814615 + 0.580002i \(0.803052\pi\)
\(458\) 45.1495 26.0671i 2.10970 1.21803i
\(459\) 2.21605 9.91586i 0.103437 0.462833i
\(460\) 10.3673i 0.483378i
\(461\) 6.54079i 0.304635i −0.988332 0.152318i \(-0.951326\pi\)
0.988332 0.152318i \(-0.0486736\pi\)
\(462\) −2.66276 + 5.92512i −0.123883 + 0.275662i
\(463\) 16.6896 + 9.63572i 0.775629 + 0.447810i 0.834879 0.550433i \(-0.185538\pi\)
−0.0592498 + 0.998243i \(0.518871\pi\)
\(464\) 18.1369i 0.841984i
\(465\) −0.0345363 + 0.0768493i −0.00160158 + 0.00356380i
\(466\) 21.3695 0.989921
\(467\) 4.90194 + 2.83014i 0.226835 + 0.130963i 0.609111 0.793085i \(-0.291526\pi\)
−0.382276 + 0.924048i \(0.624860\pi\)
\(468\) −56.7535 18.8778i −2.62343 0.872625i
\(469\) 0.990784 + 2.39038i 0.0457502 + 0.110378i
\(470\) 6.92530i 0.319440i
\(471\) −1.81350 17.8512i −0.0835615 0.822542i
\(472\) 25.5085i 1.17412i
\(473\) −11.8278 + 6.82878i −0.543843 + 0.313988i
\(474\) −33.7048 46.7316i −1.54811 2.14645i
\(475\) −7.98033 + 13.8223i −0.366162 + 0.634212i
\(476\) −1.22863 2.12804i −0.0563139 0.0975386i
\(477\) 5.87991 17.6772i 0.269222 0.809382i
\(478\) 8.00496 0.366138
\(479\) 3.26198 + 1.88330i 0.149043 + 0.0860503i 0.572667 0.819788i \(-0.305909\pi\)
−0.423624 + 0.905838i \(0.639242\pi\)
\(480\) 0.211052 + 0.0948474i 0.00963318 + 0.00432917i
\(481\) 24.7126 14.2678i 1.12680 0.650556i
\(482\) −27.1487 + 47.0230i −1.23659 + 2.14184i
\(483\) −2.08812 + 1.50604i −0.0950125 + 0.0685271i
\(484\) 49.9117 2.26871
\(485\) −2.23040 1.28772i −0.101277 0.0584724i
\(486\) 19.6233 32.6635i 0.890132 1.48165i
\(487\) −7.53258 4.34894i −0.341334 0.197069i 0.319528 0.947577i \(-0.396476\pi\)
−0.660862 + 0.750508i \(0.729809\pi\)
\(488\) 29.0342 + 16.7629i 1.31432 + 0.758822i
\(489\) −22.4026 10.0678i −1.01308 0.455281i
\(490\) −4.67756 8.10177i −0.211311 0.366001i
\(491\) 20.5724i 0.928421i −0.885725 0.464211i \(-0.846338\pi\)
0.885725 0.464211i \(-0.153662\pi\)
\(492\) 8.67617 + 85.4044i 0.391152 + 3.85033i
\(493\) −9.20705 −0.414664
\(494\) 41.6998i 1.87616i
\(495\) 7.91087 1.62408i 0.355567 0.0729971i
\(496\) 0.337816i 0.0151684i
\(497\) −2.05678 + 3.56244i −0.0922590 + 0.159797i
\(498\) 10.6502 23.6985i 0.477246 1.06196i
\(499\) −19.4497 11.2293i −0.870688 0.502692i −0.00311098 0.999995i \(-0.500990\pi\)
−0.867577 + 0.497303i \(0.834324\pi\)
\(500\) 10.6851 + 18.5072i 0.477853 + 0.827666i
\(501\) 12.8463 28.5852i 0.573929 1.27709i
\(502\) −12.3715 21.4282i −0.552169 0.956385i
\(503\) 6.78638 + 11.7543i 0.302590 + 0.524100i 0.976722 0.214510i \(-0.0688155\pi\)
−0.674132 + 0.738611i \(0.735482\pi\)
\(504\) −0.920848 4.48543i −0.0410178 0.199797i
\(505\) −1.46060 2.52984i −0.0649959 0.112576i
\(506\) 48.3105 + 27.8921i 2.14766 + 1.23995i
\(507\) 19.2005 + 8.62874i 0.852723 + 0.383216i
\(508\) −30.8249 + 53.3903i −1.36763 + 2.36881i
\(509\) 23.8855i 1.05871i 0.848401 + 0.529354i \(0.177566\pi\)
−0.848401 + 0.529354i \(0.822434\pi\)
\(510\) −1.88225 + 4.18835i −0.0833476 + 0.185463i
\(511\) 2.88706i 0.127716i
\(512\) −38.1236 −1.68484
\(513\) −17.2487 3.85485i −0.761551 0.170196i
\(514\) 6.17440i 0.272341i
\(515\) −0.535602 0.927691i −0.0236015 0.0408789i
\(516\) 7.94211 17.6726i 0.349632 0.777993i
\(517\) −21.4695 12.3954i −0.944226 0.545149i
\(518\) 3.80762 + 2.19833i 0.167297 + 0.0965890i
\(519\) −6.59104 + 0.669580i −0.289315 + 0.0293913i
\(520\) 11.6316 + 6.71550i 0.510079 + 0.294494i
\(521\) −19.0625 −0.835142 −0.417571 0.908644i \(-0.637118\pi\)
−0.417571 + 0.908644i \(0.637118\pi\)
\(522\) −32.7642 10.8983i −1.43405 0.477004i
\(523\) 1.61705 2.80081i 0.0707086 0.122471i −0.828503 0.559984i \(-0.810807\pi\)
0.899212 + 0.437513i \(0.144141\pi\)
\(524\) 44.5626 25.7282i 1.94672 1.12394i
\(525\) −1.05317 + 2.34349i −0.0459642 + 0.102278i
\(526\) −41.9044 24.1935i −1.82712 1.05489i
\(527\) −0.171490 −0.00747020
\(528\) −26.2624 + 18.9416i −1.14292 + 0.824325i
\(529\) −0.445437 0.771520i −0.0193668 0.0335443i
\(530\) −4.20964 + 7.29130i −0.182855 + 0.316714i
\(531\) −15.0393 5.00249i −0.652652 0.217090i
\(532\) −3.70175 + 2.13721i −0.160491 + 0.0926597i
\(533\) 62.5297i 2.70846i
\(534\) 44.7996 4.55116i 1.93867 0.196948i
\(535\) 3.15912i 0.136581i
\(536\) −5.14937 + 39.1841i −0.222419 + 1.69250i
\(537\) −21.4390 + 15.4627i −0.925162 + 0.667266i
\(538\) 8.87164 + 5.12204i 0.382484 + 0.220827i
\(539\) −33.4890 −1.44247
\(540\) −7.75447 + 8.43358i −0.333699 + 0.362924i
\(541\) 34.8913i 1.50009i −0.661384 0.750047i \(-0.730031\pi\)
0.661384 0.750047i \(-0.269969\pi\)
\(542\) −58.4161 33.7265i −2.50918 1.44868i
\(543\) 36.9683 + 16.6137i 1.58646 + 0.712960i
\(544\) 0.470964i 0.0201924i
\(545\) 10.0869i 0.432075i
\(546\) 0.678439 + 6.67825i 0.0290345 + 0.285803i
\(547\) 34.5288 19.9352i 1.47635 0.852368i 0.476702 0.879065i \(-0.341832\pi\)
0.999644 + 0.0266968i \(0.00849886\pi\)
\(548\) −34.2415 59.3080i −1.46272 2.53351i
\(549\) 15.5770 13.8307i 0.664811 0.590278i
\(550\) 55.6694 2.37375
\(551\) 16.0158i 0.682294i
\(552\) −39.1208 + 3.97426i −1.66509 + 0.169156i
\(553\) −2.15104 + 3.72572i −0.0914716 + 0.158434i
\(554\) −22.3681 + 38.7427i −0.950329 + 1.64602i
\(555\) −0.552443 5.43800i −0.0234499 0.230830i
\(556\) −50.0076 + 28.8719i −2.12080 + 1.22444i
\(557\) −11.2429 + 6.49112i −0.476379 + 0.275038i −0.718906 0.695107i \(-0.755357\pi\)
0.242527 + 0.970145i \(0.422024\pi\)
\(558\) −0.610263 0.202990i −0.0258345 0.00859325i
\(559\) −7.05656 + 12.2223i −0.298461 + 0.516949i
\(560\) 0.675384i 0.0285402i
\(561\) 9.61553 + 13.3319i 0.405968 + 0.562873i
\(562\) 28.3170 + 49.0465i 1.19448 + 2.06890i
\(563\) 31.3358 1.32065 0.660324 0.750981i \(-0.270419\pi\)
0.660324 + 0.750981i \(0.270419\pi\)
\(564\) 34.9892 3.55453i 1.47331 0.149673i
\(565\) 4.00727 + 6.94080i 0.168587 + 0.292002i
\(566\) −2.28778 + 3.96256i −0.0961627 + 0.166559i
\(567\) −2.82512 0.336727i −0.118644 0.0141412i
\(568\) −54.4103 + 31.4138i −2.28301 + 1.31809i
\(569\) −34.4866 + 19.9109i −1.44576 + 0.834707i −0.998225 0.0595616i \(-0.981030\pi\)
−0.447531 + 0.894269i \(0.647696\pi\)
\(570\) 7.28568 + 3.27420i 0.305164 + 0.137141i
\(571\) 7.90831 + 13.6976i 0.330952 + 0.573226i 0.982699 0.185211i \(-0.0592967\pi\)
−0.651747 + 0.758437i \(0.725963\pi\)
\(572\) 83.7987 48.3812i 3.50380 2.02292i
\(573\) 0.0325306 + 0.320217i 0.00135898 + 0.0133772i
\(574\) 8.34359 4.81717i 0.348255 0.201065i
\(575\) 19.1077 + 11.0318i 0.796845 + 0.460059i
\(576\) −7.85199 + 23.6060i −0.327166 + 0.983583i
\(577\) −31.6191 + 18.2553i −1.31632 + 0.759978i −0.983135 0.182883i \(-0.941457\pi\)
−0.333186 + 0.942861i \(0.608124\pi\)
\(578\) 32.2089 1.33971
\(579\) 12.9391 9.33225i 0.537732 0.387835i
\(580\) 8.99081 + 5.19085i 0.373323 + 0.215538i
\(581\) −1.93993 −0.0804820
\(582\) 8.05860 17.9318i 0.334040 0.743298i
\(583\) 15.0694 + 26.1010i 0.624112 + 1.08099i
\(584\) 22.0475 38.1875i 0.912334 1.58021i
\(585\) 6.24041 5.54078i 0.258009 0.229083i
\(586\) −19.9471 11.5164i −0.824005 0.475740i
\(587\) 5.53643 9.58937i 0.228513 0.395796i −0.728855 0.684668i \(-0.759947\pi\)
0.957368 + 0.288873i \(0.0932804\pi\)
\(588\) 38.5323 27.7912i 1.58905 1.14609i
\(589\) 0.298308i 0.0122916i
\(590\) 6.20328 + 3.58146i 0.255385 + 0.147447i
\(591\) 6.56096 + 2.94851i 0.269882 + 0.121285i
\(592\) 10.9581 + 18.9799i 0.450373 + 0.780069i
\(593\) −5.92238 + 10.2579i −0.243203 + 0.421240i −0.961625 0.274368i \(-0.911531\pi\)
0.718422 + 0.695608i \(0.244865\pi\)
\(594\) 18.4370 + 58.8247i 0.756481 + 2.41360i
\(595\) 0.342853 0.0140556
\(596\) 16.1342 9.31511i 0.660884 0.381562i
\(597\) 3.16329 + 31.1380i 0.129465 + 1.27439i
\(598\) 57.6449 2.35727
\(599\) 6.70993 + 11.6219i 0.274160 + 0.474860i 0.969923 0.243412i \(-0.0782668\pi\)
−0.695763 + 0.718272i \(0.744933\pi\)
\(600\) −31.8269 + 22.9549i −1.29933 + 0.937129i
\(601\) −12.1980 + 21.1275i −0.497566 + 0.861809i −0.999996 0.00280871i \(-0.999106\pi\)
0.502430 + 0.864618i \(0.332439\pi\)
\(602\) −2.17450 −0.0886258
\(603\) 22.0924 + 10.7204i 0.899671 + 0.436568i
\(604\) 15.5032 0.630816
\(605\) −3.48202 + 6.03104i −0.141564 + 0.245197i
\(606\) 18.0855 13.0440i 0.734674 0.529878i
\(607\) 7.77840 + 13.4726i 0.315715 + 0.546835i 0.979589 0.201009i \(-0.0644222\pi\)
−0.663874 + 0.747845i \(0.731089\pi\)
\(608\) 0.819247 0.0332248
\(609\) 0.260570 + 2.56494i 0.0105588 + 0.103936i
\(610\) −8.15297 + 4.70712i −0.330104 + 0.190586i
\(611\) −25.6177 −1.03638
\(612\) −22.1272 7.36011i −0.894440 0.297515i
\(613\) 13.2263 22.9087i 0.534206 0.925272i −0.464995 0.885313i \(-0.653944\pi\)
0.999201 0.0399589i \(-0.0127227\pi\)
\(614\) −38.0106 65.8363i −1.53398 2.65694i
\(615\) −10.9250 4.90974i −0.440540 0.197980i
\(616\) 6.41544 + 3.70396i 0.258486 + 0.149237i
\(617\) 23.6066i 0.950364i −0.879888 0.475182i \(-0.842382\pi\)
0.879888 0.475182i \(-0.157618\pi\)
\(618\) 6.63195 4.78325i 0.266776 0.192410i
\(619\) −5.92015 + 10.2540i −0.237951 + 0.412143i −0.960126 0.279567i \(-0.909809\pi\)
0.722175 + 0.691710i \(0.243142\pi\)
\(620\) 0.167462 + 0.0966842i 0.00672543 + 0.00388293i
\(621\) −5.32886 + 23.8443i −0.213840 + 0.956838i
\(622\) −22.7911 + 39.4753i −0.913838 + 1.58281i
\(623\) −1.68110 2.91175i −0.0673518 0.116657i
\(624\) −13.7159 + 30.5202i −0.549074 + 1.22179i
\(625\) 20.4801 0.819203
\(626\) 22.2869 + 12.8674i 0.890764 + 0.514283i
\(627\) 23.1910 16.7263i 0.926158 0.667985i
\(628\) −41.1811 −1.64330
\(629\) 9.63500 5.56277i 0.384172 0.221802i
\(630\) 1.22008 + 0.405831i 0.0486091 + 0.0161687i
\(631\) 3.33223 + 1.92386i 0.132654 + 0.0765878i 0.564858 0.825188i \(-0.308931\pi\)
−0.432204 + 0.901776i \(0.642264\pi\)
\(632\) −56.9041 + 32.8536i −2.26352 + 1.30685i
\(633\) −2.92706 28.8127i −0.116340 1.14520i
\(634\) −51.3005 + 29.6183i −2.03740 + 1.17629i
\(635\) −4.30091 7.44940i −0.170677 0.295620i
\(636\) −38.9991 17.5263i −1.54641 0.694962i
\(637\) −29.9697 + 17.3030i −1.18744 + 0.685570i
\(638\) 48.3776 27.9308i 1.91529 1.10579i
\(639\) 7.85055 + 38.2399i 0.310563 + 1.51275i
\(640\) 5.48793 9.50537i 0.216929 0.375733i
\(641\) 4.19692 + 7.26927i 0.165768 + 0.287119i 0.936928 0.349523i \(-0.113656\pi\)
−0.771160 + 0.636642i \(0.780323\pi\)
\(642\) 23.9913 2.43727i 0.946863 0.0961912i
\(643\) 1.84759 0.0728618 0.0364309 0.999336i \(-0.488401\pi\)
0.0364309 + 0.999336i \(0.488401\pi\)
\(644\) 2.95443 + 5.11722i 0.116421 + 0.201647i
\(645\) 1.58138 + 2.19258i 0.0622669 + 0.0863328i
\(646\) 16.2580i 0.639663i
\(647\) −1.06831 + 1.85036i −0.0419995 + 0.0727453i −0.886261 0.463186i \(-0.846706\pi\)
0.844261 + 0.535931i \(0.180039\pi\)
\(648\) −34.7966 26.0284i −1.36694 1.02249i
\(649\) 22.2062 12.8207i 0.871668 0.503258i
\(650\) 49.8192 28.7631i 1.95407 1.12818i
\(651\) 0.00485335 + 0.0477742i 0.000190218 + 0.00187242i
\(652\) −28.1847 + 48.8174i −1.10380 + 1.91184i
\(653\) −13.9839 + 24.2208i −0.547232 + 0.947834i 0.451230 + 0.892408i \(0.350985\pi\)
−0.998463 + 0.0554268i \(0.982348\pi\)
\(654\) −76.6030 + 7.78205i −2.99542 + 0.304302i
\(655\) 7.17957i 0.280529i
\(656\) 48.0245 1.87504
\(657\) −18.1909 20.4878i −0.709693 0.799305i
\(658\) −1.97354 3.41827i −0.0769366 0.133258i
\(659\) 14.6289 8.44598i 0.569860 0.329009i −0.187234 0.982315i \(-0.559952\pi\)
0.757093 + 0.653307i \(0.226619\pi\)
\(660\) −1.87330 18.4399i −0.0729181 0.717773i
\(661\) 24.6063i 0.957073i −0.878068 0.478537i \(-0.841167\pi\)
0.878068 0.478537i \(-0.158833\pi\)
\(662\) 32.7697i 1.27363i
\(663\) 15.4933 + 6.96275i 0.601712 + 0.270411i
\(664\) −25.6597 14.8146i −0.995788 0.574919i
\(665\) 0.596397i 0.0231273i
\(666\) 40.8717 8.39085i 1.58375 0.325139i
\(667\) 22.1398 0.857257
\(668\) −62.2899 35.9631i −2.41007 1.39145i
\(669\) 0.176390 0.127220i 0.00681963 0.00491861i
\(670\) −8.80598 6.75380i −0.340205 0.260922i
\(671\) 33.7006i 1.30100i
\(672\) 0.131203 0.0133288i 0.00506127 0.000514171i
\(673\) 2.61136i 0.100661i −0.998733 0.0503303i \(-0.983973\pi\)
0.998733 0.0503303i \(-0.0160274\pi\)
\(674\) −17.5748 + 10.1468i −0.676955 + 0.390840i
\(675\) 7.29218 + 23.2662i 0.280676 + 0.895518i
\(676\) 24.1561 41.8396i 0.929082 1.60922i
\(677\) 9.10514 + 15.7706i 0.349939 + 0.606112i 0.986238 0.165330i \(-0.0528690\pi\)
−0.636299 + 0.771442i \(0.719536\pi\)
\(678\) −49.6190 + 35.7873i −1.90561 + 1.37440i
\(679\) −1.46788 −0.0563319
\(680\) 4.53495 + 2.61825i 0.173907 + 0.100405i
\(681\) 3.82865 8.51942i 0.146714 0.326465i
\(682\) 0.901076 0.520236i 0.0345040 0.0199209i
\(683\) −21.2686 + 36.8382i −0.813819 + 1.40958i 0.0963545 + 0.995347i \(0.469282\pi\)
−0.910173 + 0.414228i \(0.864052\pi\)
\(684\) −12.8030 + 38.4905i −0.489535 + 1.47172i
\(685\) 9.55524 0.365087
\(686\) −9.30210 5.37057i −0.355156 0.205049i
\(687\) −36.7516 + 3.73357i −1.40216 + 0.142445i
\(688\) −9.38707 5.41963i −0.357879 0.206621i
\(689\) 26.9716 + 15.5721i 1.02754 + 0.593249i
\(690\) 4.52618 10.0716i 0.172309 0.383418i
\(691\) −19.7288 34.1712i −0.750517 1.29993i −0.947572 0.319542i \(-0.896471\pi\)
0.197055 0.980392i \(-0.436862\pi\)
\(692\) 15.2049i 0.578003i
\(693\) 3.44192 3.05604i 0.130748 0.116089i
\(694\) 50.1453 1.90349
\(695\) 8.05683i 0.305613i
\(696\) −16.1410 + 35.9165i −0.611822 + 1.36141i
\(697\) 24.3793i 0.923430i
\(698\) −20.5746 + 35.6363i −0.778761 + 1.34885i
\(699\) −13.8112 6.20679i −0.522388 0.234763i
\(700\) 5.10669 + 2.94835i 0.193015 + 0.111437i
\(701\) 1.93484 + 3.35124i 0.0730778 + 0.126574i 0.900249 0.435376i \(-0.143385\pi\)
−0.827171 + 0.561950i \(0.810051\pi\)
\(702\) 46.8929 + 43.1169i 1.76986 + 1.62734i
\(703\) −9.67649 16.7602i −0.364956 0.632122i
\(704\) −20.1236 34.8551i −0.758437 1.31365i
\(705\) −2.01146 + 4.47586i −0.0757561 + 0.168571i
\(706\) 19.8290 + 34.3449i 0.746276 + 1.29259i
\(707\) −1.44188 0.832472i −0.0542276 0.0313083i
\(708\) −14.9110 + 33.1795i −0.560388 + 1.24696i
\(709\) 17.9371 31.0679i 0.673641 1.16678i −0.303223 0.952920i \(-0.598063\pi\)
0.976864 0.213861i \(-0.0686041\pi\)
\(710\) 17.6423i 0.662105i
\(711\) 8.21036 + 39.9925i 0.307913 + 1.49984i
\(712\) 51.3519i 1.92449i
\(713\) 0.412374 0.0154435
\(714\) 0.264512 + 2.60373i 0.00989910 + 0.0974423i
\(715\) 13.5010i 0.504909i
\(716\) 30.3336 + 52.5393i 1.13362 + 1.96349i
\(717\) −5.17365 2.32505i −0.193214 0.0868307i
\(718\) 40.6069 + 23.4444i 1.51544 + 0.874938i
\(719\) −18.0990 10.4495i −0.674980 0.389700i 0.122981 0.992409i \(-0.460755\pi\)
−0.797961 + 0.602709i \(0.794088\pi\)
\(720\) 4.25547 + 4.79280i 0.158592 + 0.178617i
\(721\) −0.528738 0.305267i −0.0196912 0.0113687i
\(722\) −18.1631 −0.675960
\(723\) 31.2043 22.5059i 1.16050 0.837002i
\(724\) 46.5099 80.5575i 1.72853 2.99390i
\(725\) 19.1342 11.0471i 0.710627 0.410281i
\(726\) −48.4880 21.7906i −1.79956 0.808725i
\(727\) 0.668064 + 0.385707i 0.0247771 + 0.0143051i 0.512337 0.858784i \(-0.328780\pi\)
−0.487560 + 0.873089i \(0.662113\pi\)
\(728\) 7.65501 0.283714
\(729\) −22.1698 + 15.4110i −0.821105 + 0.570777i
\(730\) 6.19107 + 10.7232i 0.229142 + 0.396885i
\(731\) −2.75123 + 4.76527i −0.101758 + 0.176250i
\(732\) −27.9668 38.7758i −1.03368 1.43320i
\(733\) −43.8173 + 25.2979i −1.61843 + 0.934400i −0.631101 + 0.775701i \(0.717397\pi\)
−0.987327 + 0.158699i \(0.949270\pi\)
\(734\) 28.4480i 1.05003i
\(735\) 0.669964 + 6.59483i 0.0247120 + 0.243254i
\(736\) 1.13251i 0.0417448i
\(737\) −36.6994 + 15.2114i −1.35184 + 0.560321i
\(738\) 28.8574 86.7560i 1.06226 3.19353i
\(739\) −3.77677 2.18052i −0.138931 0.0802117i 0.428924 0.903341i \(-0.358893\pi\)
−0.567854 + 0.823129i \(0.692226\pi\)
\(740\) −12.5449 −0.461161
\(741\) 12.1118 26.9508i 0.444937 0.990064i
\(742\) 4.79857i 0.176161i
\(743\) 21.1968 + 12.2380i 0.777637 + 0.448969i 0.835592 0.549350i \(-0.185125\pi\)
−0.0579552 + 0.998319i \(0.518458\pi\)
\(744\) −0.300640 + 0.668978i −0.0110220 + 0.0245259i
\(745\) 2.59942i 0.0952354i
\(746\) 69.2528i 2.53553i
\(747\) −13.7666 + 12.2232i −0.503692 + 0.447222i
\(748\) 32.6717 18.8630i 1.19459 0.689699i
\(749\) −0.900272 1.55932i −0.0328952 0.0569762i
\(750\) −2.30041 22.6442i −0.0839990 0.826849i
\(751\) −22.8657 −0.834382 −0.417191 0.908819i \(-0.636985\pi\)
−0.417191 + 0.908819i \(0.636985\pi\)
\(752\) 19.6751i 0.717477i
\(753\) 1.77197 + 17.4425i 0.0645742 + 0.635640i
\(754\) 28.8624 49.9912i 1.05111 1.82057i
\(755\) −1.08156 + 1.87331i −0.0393620 + 0.0681769i
\(756\) −1.42418 + 6.37259i −0.0517970 + 0.231769i
\(757\) 34.3592 19.8373i 1.24881 0.720999i 0.277936 0.960600i \(-0.410350\pi\)
0.970872 + 0.239600i \(0.0770165\pi\)
\(758\) 13.3563 7.71128i 0.485124 0.280086i
\(759\) −23.1221 32.0587i −0.839278 1.16366i
\(760\) 4.55448 7.88859i 0.165208 0.286149i
\(761\) 12.2506i 0.444084i −0.975037 0.222042i \(-0.928728\pi\)
0.975037 0.222042i \(-0.0712723\pi\)
\(762\) 53.2549 38.4097i 1.92922 1.39144i
\(763\) 2.87452 + 4.97881i 0.104065 + 0.180245i
\(764\) 0.738709 0.0267255
\(765\) 2.43303 2.16025i 0.0879663 0.0781042i
\(766\) 19.8011 + 34.2965i 0.715442 + 1.23918i
\(767\) 13.2484 22.9469i 0.478371 0.828563i
\(768\) 50.2188 + 22.5684i 1.81211 + 0.814368i
\(769\) −0.214768 + 0.123996i −0.00774472 + 0.00447142i −0.503867 0.863781i \(-0.668090\pi\)
0.496123 + 0.868252i \(0.334757\pi\)
\(770\) −1.80149 + 1.04009i −0.0649212 + 0.0374823i
\(771\) 1.79336 3.99056i 0.0645864 0.143716i
\(772\) −18.3073 31.7092i −0.658894 1.14124i
\(773\) 5.31156 3.06663i 0.191044 0.110299i −0.401427 0.915891i \(-0.631486\pi\)
0.592471 + 0.805592i \(0.298152\pi\)
\(774\) −15.4311 + 13.7011i −0.554660 + 0.492476i
\(775\) 0.356392 0.205763i 0.0128020 0.00739123i
\(776\) −19.4157 11.2097i −0.696984 0.402404i
\(777\) −1.82238 2.52672i −0.0653775 0.0906457i
\(778\) 6.68685 3.86065i 0.239735 0.138411i
\(779\) −42.4080 −1.51942
\(780\) −11.2039 15.5342i −0.401165 0.556214i
\(781\) −54.6939 31.5775i −1.95710 1.12993i
\(782\) 22.4747 0.803695
\(783\) 18.0103 + 16.5600i 0.643635 + 0.591807i
\(784\) −13.2892 23.0175i −0.474613 0.822054i
\(785\) 2.87294 4.97608i 0.102540 0.177604i
\(786\) −54.5239 + 5.53905i −1.94480 + 0.197571i
\(787\) −3.20544 1.85066i −0.114262 0.0659689i 0.441780 0.897123i \(-0.354347\pi\)
−0.556042 + 0.831154i \(0.687680\pi\)
\(788\) 8.25434 14.2969i 0.294049 0.509307i
\(789\) 20.0560 + 27.8076i 0.714013 + 0.989977i
\(790\) 18.4509i 0.656454i
\(791\) 3.95592 + 2.28395i 0.140656 + 0.0812079i
\(792\) 68.8646 14.1377i 2.44700 0.502362i
\(793\) 17.4123 + 30.1591i 0.618330 + 1.07098i
\(794\) −30.1785 + 52.2707i −1.07100 + 1.85502i
\(795\) 4.83848 3.48972i 0.171603 0.123768i
\(796\) 71.8324 2.54603
\(797\) 0.352241 0.203367i 0.0124770 0.00720362i −0.493749 0.869605i \(-0.664374\pi\)
0.506226 + 0.862401i \(0.331040\pi\)
\(798\) 4.52922 0.460121i 0.160333 0.0162881i
\(799\) −9.98790 −0.353347
\(800\) −0.565090 0.978764i −0.0199789 0.0346045i
\(801\) −30.2761 10.0707i −1.06975 0.355829i
\(802\) −8.11026 + 14.0474i −0.286383 + 0.496030i
\(803\) 44.3249 1.56419
\(804\) 29.6029 47.9576i 1.04401 1.69134i
\(805\) −0.824446 −0.0290579
\(806\) 0.537589 0.931132i 0.0189358 0.0327977i
\(807\) −4.24609 5.88719i −0.149470 0.207239i
\(808\) −12.7146 22.0224i −0.447299 0.774744i
\(809\) 22.3994 0.787519 0.393760 0.919213i \(-0.371174\pi\)
0.393760 + 0.919213i \(0.371174\pi\)
\(810\) 11.2152 4.80754i 0.394063 0.168920i
\(811\) 11.0833 6.39897i 0.389189 0.224698i −0.292620 0.956229i \(-0.594527\pi\)
0.681809 + 0.731531i \(0.261194\pi\)
\(812\) 5.91706 0.207648
\(813\) 27.9588 + 38.7647i 0.980556 + 1.35954i
\(814\) −33.7508 + 58.4581i −1.18296 + 2.04896i
\(815\) −3.93254 6.81135i −0.137751 0.238591i
\(816\) −5.34757 + 11.8993i −0.187203 + 0.416559i
\(817\) 8.28924 + 4.78579i 0.290004 + 0.167434i
\(818\) 62.6327i 2.18990i
\(819\) 1.50123 4.51325i 0.0524572 0.157706i
\(820\) −13.7448 + 23.8067i −0.479989 + 0.831365i
\(821\) −39.3647 22.7272i −1.37384 0.793186i −0.382429 0.923985i \(-0.624912\pi\)
−0.991409 + 0.130799i \(0.958246\pi\)
\(822\) 7.37188 + 72.5655i 0.257124 + 2.53101i
\(823\) 2.01983 3.49846i 0.0704070 0.121949i −0.828673 0.559733i \(-0.810904\pi\)
0.899080 + 0.437785i \(0.144237\pi\)
\(824\) −4.66245 8.07560i −0.162424 0.281327i
\(825\) −35.9795 16.1693i −1.25265 0.562942i
\(826\) 4.08252 0.142049
\(827\) 29.4880 + 17.0249i 1.02540 + 0.592015i 0.915663 0.401946i \(-0.131666\pi\)
0.109736 + 0.993961i \(0.464999\pi\)
\(828\) 53.2085 + 17.6986i 1.84912 + 0.615068i
\(829\) −28.6915 −0.996498 −0.498249 0.867034i \(-0.666023\pi\)
−0.498249 + 0.867034i \(0.666023\pi\)
\(830\) 7.20537 4.16002i 0.250102 0.144396i
\(831\) 25.7095 18.5428i 0.891853 0.643242i
\(832\) −36.0177 20.7948i −1.24869 0.720932i
\(833\) −11.6847 + 6.74614i −0.404849 + 0.233740i
\(834\) 61.1861 6.21586i 2.11870 0.215238i
\(835\) 8.69113 5.01783i 0.300769 0.173649i
\(836\) −32.8124 56.8327i −1.13484 1.96560i
\(837\) 0.335458 + 0.308445i 0.0115951 + 0.0106614i
\(838\) −21.5036 + 12.4151i −0.742829 + 0.428873i
\(839\) 23.4244 13.5241i 0.808699 0.466903i −0.0378049 0.999285i \(-0.512037\pi\)
0.846504 + 0.532383i \(0.178703\pi\)
\(840\) 0.601060 1.33746i 0.0207385 0.0461469i
\(841\) −3.41472 + 5.91447i −0.117749 + 0.203947i
\(842\) −1.12923 1.95588i −0.0389157 0.0674040i
\(843\) −4.05583 39.9238i −0.139690 1.37505i
\(844\) −66.4680 −2.28792
\(845\) 3.37044 + 5.83777i 0.115947 + 0.200825i
\(846\) −35.5430 11.8225i −1.22199 0.406468i
\(847\) 3.96917i 0.136382i
\(848\) −11.9598 + 20.7149i −0.410700 + 0.711354i
\(849\) 2.62954 1.89654i 0.0902456 0.0650890i
\(850\) 19.4237 11.2143i 0.666226 0.384646i
\(851\) −23.1689 + 13.3766i −0.794220 + 0.458543i
\(852\) 89.1356 9.05523i 3.05374 0.310227i
\(853\) −19.8568 + 34.3930i −0.679883 + 1.17759i 0.295133 + 0.955456i \(0.404636\pi\)
−0.975016 + 0.222136i \(0.928697\pi\)
\(854\) −2.68283 + 4.64679i −0.0918045 + 0.159010i
\(855\) −3.75779 4.23228i −0.128514 0.144741i
\(856\) 27.5003i 0.939941i
\(857\) −0.248334 −0.00848293 −0.00424147 0.999991i \(-0.501350\pi\)
−0.00424147 + 0.999991i \(0.501350\pi\)
\(858\) −102.531 + 10.4160i −3.50034 + 0.355598i
\(859\) 6.65866 + 11.5331i 0.227191 + 0.393506i 0.956974 0.290172i \(-0.0937126\pi\)
−0.729784 + 0.683678i \(0.760379\pi\)
\(860\) 5.37323 3.10223i 0.183226 0.105785i
\(861\) −6.79167 + 0.689961i −0.231460 + 0.0235138i
\(862\) 8.36083i 0.284771i
\(863\) 2.72688i 0.0928239i −0.998922 0.0464120i \(-0.985221\pi\)
0.998922 0.0464120i \(-0.0147787\pi\)
\(864\) 0.847088 0.921273i 0.0288185 0.0313423i
\(865\) −1.83727 1.06075i −0.0624690 0.0360665i
\(866\) 39.5011i 1.34230i
\(867\) −20.8168 9.35513i −0.706976 0.317717i
\(868\) 0.110211 0.00374079
\(869\) −57.2007 33.0248i −1.94040 1.12029i
\(870\) −6.46811 8.96801i −0.219289 0.304044i
\(871\) −24.9833 + 32.5747i −0.846528 + 1.10375i
\(872\) 87.8069i 2.97352i
\(873\) −10.4166 + 9.24881i −0.352550 + 0.313025i
\(874\) 39.0950i 1.32241i
\(875\) −1.47176 + 0.849720i −0.0497545 + 0.0287258i
\(876\) −51.0002 + 36.7835i −1.72314 + 1.24280i
\(877\) 5.13963 8.90211i 0.173553 0.300603i −0.766106 0.642714i \(-0.777809\pi\)
0.939660 + 0.342111i \(0.111142\pi\)
\(878\) −23.8124 41.2442i −0.803629 1.39193i
\(879\) 9.54694 + 13.2368i 0.322010 + 0.446466i
\(880\) −10.3691 −0.349543
\(881\) −40.7153 23.5070i −1.37173 0.791970i −0.380586 0.924745i \(-0.624278\pi\)
−0.991146 + 0.132775i \(0.957611\pi\)
\(882\) −49.5663 + 10.1758i −1.66898 + 0.342638i
\(883\) −22.5648 + 13.0278i −0.759368 + 0.438421i −0.829069 0.559147i \(-0.811129\pi\)
0.0697010 + 0.997568i \(0.477795\pi\)
\(884\) 19.4922 33.7615i 0.655593 1.13552i
\(885\) −2.96898 4.11647i −0.0998010 0.138374i
\(886\) −26.1790 −0.879501
\(887\) 29.3529 + 16.9469i 0.985575 + 0.569022i 0.903949 0.427641i \(-0.140655\pi\)
0.0816261 + 0.996663i \(0.473989\pi\)
\(888\) −4.80905 47.3381i −0.161381 1.58856i
\(889\) −4.24580 2.45131i −0.142399 0.0822143i
\(890\) 12.4880 + 7.20994i 0.418598 + 0.241678i
\(891\) 5.16974 43.3738i 0.173193 1.45308i
\(892\) −0.249570 0.432268i −0.00835623 0.0144734i
\(893\) 17.3741i 0.581401i
\(894\) −19.7408 + 2.00546i −0.660232 + 0.0670725i
\(895\) −8.46472 −0.282945
\(896\) 6.25570i 0.208988i
\(897\) −37.2562 16.7430i −1.24395 0.559034i
\(898\) 72.6423i 2.42410i
\(899\) 0.206473 0.357622i 0.00688627 0.0119274i
\(900\) 54.8162 11.2536i 1.82721 0.375121i
\(901\) 10.5158 + 6.07128i 0.350331 + 0.202264i
\(902\) 73.9577 + 128.099i 2.46252 + 4.26522i
\(903\) 1.40539 + 0.631586i 0.0467685 + 0.0210179i
\(904\) 34.8835 + 60.4200i 1.16021 + 2.00954i
\(905\) 6.48939 + 11.2400i 0.215715 + 0.373629i
\(906\) −15.0610 6.76843i −0.500367 0.224866i
\(907\) 6.04032 + 10.4621i 0.200565 + 0.347390i 0.948711 0.316145i \(-0.102389\pi\)
−0.748145 + 0.663535i \(0.769055\pi\)
\(908\) −18.5646 10.7183i −0.616088 0.355699i
\(909\) −15.4774 + 3.17748i −0.513354 + 0.105390i
\(910\) −1.07478 + 1.86158i −0.0356287 + 0.0617108i
\(911\) 4.77638i 0.158249i 0.996865 + 0.0791243i \(0.0252124\pi\)
−0.996865 + 0.0791243i \(0.974788\pi\)
\(912\) 20.6990 + 9.30216i 0.685411 + 0.308025i
\(913\) 29.7837i 0.985695i
\(914\) −9.92745 −0.328371
\(915\) 6.63650 0.674198i 0.219396 0.0222883i
\(916\) 84.7824i 2.80129i
\(917\) 2.04600 + 3.54378i 0.0675649 + 0.117026i
\(918\) 18.2827 + 16.8105i 0.603420 + 0.554830i
\(919\) −29.6436 17.1148i −0.977854 0.564564i −0.0762322 0.997090i \(-0.524289\pi\)
−0.901621 + 0.432526i \(0.857622\pi\)
\(920\) −10.9050 6.29602i −0.359528 0.207573i
\(921\) 5.44424 + 53.5906i 0.179394 + 1.76587i
\(922\) 13.8464 + 7.99424i 0.456008 + 0.263276i
\(923\) −65.2616 −2.14811
\(924\) −6.17958 8.56796i −0.203293 0.281865i
\(925\) −13.3491 + 23.1212i −0.438914 + 0.760222i
\(926\) −40.7964 + 23.5538i −1.34065 + 0.774026i
\(927\) −5.67558 + 1.16518i −0.186410 + 0.0382696i
\(928\) −0.982143 0.567040i −0.0322404 0.0186140i
\(929\) 23.0215 0.755311 0.377656 0.925946i \(-0.376730\pi\)
0.377656 + 0.925946i \(0.376730\pi\)
\(930\) −0.120474 0.167037i −0.00395051 0.00547737i
\(931\) 11.7350 + 20.3256i 0.384598 + 0.666144i
\(932\) −17.3759 + 30.0959i −0.569167 + 0.985825i
\(933\) 26.1957 18.8934i 0.857607 0.618543i
\(934\) −11.9824 + 6.91806i −0.392077 + 0.226366i
\(935\) 5.26380i 0.172145i
\(936\) 54.3231 48.2328i 1.77561 1.57654i
\(937\) 0.449957i 0.0146994i 0.999973 + 0.00734972i \(0.00233951\pi\)
−0.999973 + 0.00734972i \(0.997660\pi\)
\(938\) −6.27123 0.824133i −0.204763 0.0269089i
\(939\) −10.6668 14.7895i −0.348099 0.482638i
\(940\) 9.75333 + 5.63109i 0.318118 + 0.183666i
\(941\) 59.5842 1.94239 0.971194 0.238289i \(-0.0765865\pi\)
0.971194 + 0.238289i \(0.0765865\pi\)
\(942\) 40.0064 + 17.9790i 1.30348 + 0.585786i
\(943\) 58.6238i 1.90906i
\(944\) 17.6238 + 10.1751i 0.573606 + 0.331171i
\(945\) −0.670670 0.616665i −0.0218169 0.0200601i
\(946\) 33.3849i 1.08544i
\(947\) 29.1289i 0.946562i −0.880912 0.473281i \(-0.843070\pi\)
0.880912 0.473281i \(-0.156930\pi\)
\(948\) 93.2210 9.47026i 3.02768 0.307580i
\(949\) 39.6669 22.9017i 1.28764 0.743420i
\(950\) −19.5073 33.7876i −0.632901 1.09622i
\(951\) 41.7585 4.24222i 1.35411 0.137563i
\(952\) 2.98456 0.0967300
\(953\) 52.6439i 1.70530i 0.522481 + 0.852651i \(0.325007\pi\)
−0.522481 + 0.852651i \(0.674993\pi\)
\(954\) 30.2349 + 34.0526i 0.978892 + 1.10250i
\(955\) −0.0515350 + 0.0892612i −0.00166763 + 0.00288842i
\(956\) −6.50898 + 11.2739i −0.210515 + 0.364623i
\(957\) −39.3793 + 4.00052i −1.27295 + 0.129318i
\(958\) −7.97366 + 4.60359i −0.257617 + 0.148735i
\(959\) 4.71639 2.72301i 0.152300 0.0879306i
\(960\) −6.46128 + 4.66015i −0.208537 + 0.150406i
\(961\) −15.4962 + 26.8401i −0.499876 + 0.865811i
\(962\) 69.7531i 2.24893i
\(963\) −16.2137 5.39310i −0.522478 0.173790i
\(964\) −44.1503 76.4705i −1.42198 2.46295i
\(965\) 5.10873 0.164456
\(966\) −0.636061 6.26110i −0.0204649 0.201448i
\(967\) −13.1261 22.7351i −0.422108 0.731112i 0.574038 0.818829i \(-0.305376\pi\)
−0.996145 + 0.0877169i \(0.972043\pi\)
\(968\) −30.3112 + 52.5005i −0.974238 + 1.68743i
\(969\) 4.72217 10.5077i 0.151698 0.337555i
\(970\) 5.45204 3.14774i 0.175054 0.101068i
\(971\) 33.6646 19.4363i 1.08035 0.623739i 0.149357 0.988783i \(-0.452279\pi\)
0.930990 + 0.365044i \(0.118946\pi\)
\(972\) 30.0459 + 54.1960i 0.963723 + 1.73834i
\(973\) −2.29600 3.97679i −0.0736064 0.127490i
\(974\) 18.4128 10.6306i 0.589985 0.340628i
\(975\) −40.5528 + 4.11973i −1.29873 + 0.131937i
\(976\) −23.1630 + 13.3731i −0.741428 + 0.428064i
\(977\) 11.7002 + 6.75513i 0.374323 + 0.216116i 0.675346 0.737501i \(-0.263994\pi\)
−0.301022 + 0.953617i \(0.597328\pi\)
\(978\) 48.6936 35.1199i 1.55705 1.12301i
\(979\) 44.7038 25.8098i 1.42874 0.824884i
\(980\) 15.2136 0.485982
\(981\) 51.7693 + 17.2199i 1.65287 + 0.549788i
\(982\) 43.5505 + 25.1439i 1.38975 + 0.802374i
\(983\) −37.5622 −1.19805 −0.599024 0.800731i \(-0.704445\pi\)
−0.599024 + 0.800731i \(0.704445\pi\)
\(984\) −95.1030 42.7395i −3.03177 1.36249i
\(985\) 1.15170 + 1.99481i 0.0366964 + 0.0635600i
\(986\) 11.2530 19.4907i 0.358367 0.620711i
\(987\) 0.282669 + 2.78247i 0.00899747 + 0.0885670i
\(988\) −58.7284 33.9069i −1.86840 1.07872i
\(989\) 6.61577 11.4589i 0.210369 0.364370i
\(990\) −6.23069 + 18.7318i −0.198024 + 0.595335i
\(991\) 49.1587i 1.56158i 0.624795 + 0.780789i \(0.285182\pi\)
−0.624795 + 0.780789i \(0.714818\pi\)
\(992\) −0.0182933 0.0105616i −0.000580813 0.000335332i
\(993\) −9.51802 + 21.1793i −0.302045 + 0.672105i
\(994\) −5.02763 8.70811i −0.159467 0.276205i
\(995\) −5.01129 + 8.67980i −0.158868 + 0.275168i
\(996\) 24.7163 + 34.2690i 0.783165 + 1.08586i
\(997\) 3.15161 0.0998125 0.0499063 0.998754i \(-0.484108\pi\)
0.0499063 + 0.998754i \(0.484108\pi\)
\(998\) 47.5433 27.4491i 1.50496 0.868887i
\(999\) −28.8528 6.44818i −0.912861 0.204011i
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 201.2.f.b.38.3 40
3.2 odd 2 inner 201.2.f.b.38.18 yes 40
67.30 odd 6 inner 201.2.f.b.164.18 yes 40
201.164 even 6 inner 201.2.f.b.164.3 yes 40
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
201.2.f.b.38.3 40 1.1 even 1 trivial
201.2.f.b.38.18 yes 40 3.2 odd 2 inner
201.2.f.b.164.3 yes 40 201.164 even 6 inner
201.2.f.b.164.18 yes 40 67.30 odd 6 inner