Properties

Label 195.2.v.a.4.10
Level $195$
Weight $2$
Character 195.4
Analytic conductor $1.557$
Analytic rank $0$
Dimension $32$
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] = [195,2,Mod(4,195)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(195, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 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("195.4");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 195 = 3 \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 195.v (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: \(1.55708283941\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(16\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 4.10
Character \(\chi\) \(=\) 195.4
Dual form 195.2.v.a.49.10

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.296043 - 0.512762i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.824717 + 1.42845i) q^{4} +(-0.903471 + 2.04542i) q^{5} +(-0.512762 + 0.296043i) q^{6} +(0.828705 + 1.43536i) q^{7} +2.16078 q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(0.296043 - 0.512762i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.824717 + 1.42845i) q^{4} +(-0.903471 + 2.04542i) q^{5} +(-0.512762 + 0.296043i) q^{6} +(0.828705 + 1.43536i) q^{7} +2.16078 q^{8} +(0.500000 + 0.866025i) q^{9} +(0.781346 + 1.06880i) q^{10} +(-1.22336 - 0.706307i) q^{11} -1.64943i q^{12} +(0.0145731 + 3.60552i) q^{13} +0.981329 q^{14} +(1.80514 - 1.31965i) q^{15} +(-1.00975 + 1.74894i) q^{16} +(2.83926 - 1.63925i) q^{17} +0.592086 q^{18} +(7.29219 - 4.21015i) q^{19} +(-3.66689 + 0.396326i) q^{20} -1.65741i q^{21} +(-0.724334 + 0.418195i) q^{22} +(-5.70016 - 3.29099i) q^{23} +(-1.87129 - 1.08039i) q^{24} +(-3.36748 - 3.69596i) q^{25} +(1.85309 + 1.05992i) q^{26} -1.00000i q^{27} +(-1.36689 + 2.36753i) q^{28} +(0.252903 - 0.438041i) q^{29} +(-0.142267 - 1.31628i) q^{30} +0.791382i q^{31} +(2.75864 + 4.77810i) q^{32} +(0.706307 + 1.22336i) q^{33} -1.94115i q^{34} +(-3.68462 + 0.398243i) q^{35} +(-0.824717 + 1.42845i) q^{36} +(-2.37878 + 4.12017i) q^{37} -4.98554i q^{38} +(1.79014 - 3.12976i) q^{39} +(-1.95220 + 4.41970i) q^{40} +(-7.67224 - 4.42957i) q^{41} +(-0.849856 - 0.490665i) q^{42} +(-1.93289 + 1.11596i) q^{43} -2.33001i q^{44} +(-2.22312 + 0.240280i) q^{45} +(-3.37499 + 1.94855i) q^{46} +3.43727 q^{47} +(1.74894 - 1.00975i) q^{48} +(2.12650 - 3.68320i) q^{49} +(-2.89206 + 0.632552i) q^{50} -3.27850 q^{51} +(-5.13830 + 2.99435i) q^{52} -0.422128i q^{53} +(-0.512762 - 0.296043i) q^{54} +(2.54996 - 1.86416i) q^{55} +(1.79065 + 3.10149i) q^{56} -8.42030 q^{57} +(-0.149740 - 0.259358i) q^{58} +(11.3443 - 6.54963i) q^{59} +(3.37378 + 1.49022i) q^{60} +(-0.463750 - 0.803239i) q^{61} +(0.405790 + 0.234283i) q^{62} +(-0.828705 + 1.43536i) q^{63} -0.772299 q^{64} +(-7.38797 - 3.22768i) q^{65} +0.836389 q^{66} +(6.21154 - 10.7587i) q^{67} +(4.68318 + 2.70384i) q^{68} +(3.29099 + 5.70016i) q^{69} +(-0.886603 + 2.00723i) q^{70} +(0.947838 - 0.547235i) q^{71} +(1.08039 + 1.87129i) q^{72} +11.2130 q^{73} +(1.40844 + 2.43950i) q^{74} +(1.06834 + 4.88453i) q^{75} +(12.0280 + 6.94436i) q^{76} -2.34128i q^{77} +(-1.07486 - 1.84446i) q^{78} -9.25299 q^{79} +(-2.66503 - 3.64548i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-4.54263 + 2.62269i) q^{82} +4.02601 q^{83} +(2.36753 - 1.36689i) q^{84} +(0.787759 + 7.28850i) q^{85} +1.32149i q^{86} +(-0.438041 + 0.252903i) q^{87} +(-2.64341 - 1.52617i) q^{88} +(-0.517890 - 0.299004i) q^{89} +(-0.534933 + 1.21106i) q^{90} +(-5.16314 + 3.00883i) q^{91} -10.8565i q^{92} +(0.395691 - 0.685357i) q^{93} +(1.01758 - 1.76250i) q^{94} +(2.02323 + 18.7193i) q^{95} -5.51728i q^{96} +(-1.57968 - 2.73609i) q^{97} +(-1.25907 - 2.18077i) q^{98} -1.41261i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q - 20 q^{4} + 16 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 32 q - 20 q^{4} + 16 q^{9} + 2 q^{10} - 12 q^{11} + 8 q^{14} - 6 q^{15} - 28 q^{16} - 30 q^{20} - 4 q^{25} + 52 q^{26} - 24 q^{29} + 4 q^{30} - 2 q^{35} + 20 q^{36} + 4 q^{40} - 36 q^{41} + 12 q^{45} - 48 q^{46} - 28 q^{49} + 54 q^{50} - 40 q^{51} + 24 q^{55} - 56 q^{56} + 84 q^{59} - 32 q^{61} + 136 q^{64} + 20 q^{65} + 8 q^{66} - 24 q^{69} + 12 q^{71} + 40 q^{74} - 16 q^{75} + 48 q^{76} - 104 q^{79} + 66 q^{80} - 16 q^{81} - 48 q^{84} - 54 q^{85} - 48 q^{89} + 4 q^{90} + 12 q^{91} - 8 q^{94} + 12 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/195\mathbb{Z}\right)^\times\).

\(n\) \(106\) \(131\) \(157\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(1\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.296043 0.512762i 0.209334 0.362577i −0.742171 0.670211i \(-0.766204\pi\)
0.951505 + 0.307633i \(0.0995371\pi\)
\(3\) −0.866025 0.500000i −0.500000 0.288675i
\(4\) 0.824717 + 1.42845i 0.412359 + 0.714226i
\(5\) −0.903471 + 2.04542i −0.404045 + 0.914739i
\(6\) −0.512762 + 0.296043i −0.209334 + 0.120859i
\(7\) 0.828705 + 1.43536i 0.313221 + 0.542515i 0.979058 0.203583i \(-0.0652586\pi\)
−0.665837 + 0.746097i \(0.731925\pi\)
\(8\) 2.16078 0.763951
\(9\) 0.500000 + 0.866025i 0.166667 + 0.288675i
\(10\) 0.781346 + 1.06880i 0.247083 + 0.337983i
\(11\) −1.22336 0.706307i −0.368857 0.212960i 0.304102 0.952639i \(-0.401644\pi\)
−0.672959 + 0.739680i \(0.734977\pi\)
\(12\) 1.64943i 0.476151i
\(13\) 0.0145731 + 3.60552i 0.00404184 + 0.999992i
\(14\) 0.981329 0.262271
\(15\) 1.80514 1.31965i 0.466085 0.340732i
\(16\) −1.00975 + 1.74894i −0.252438 + 0.437235i
\(17\) 2.83926 1.63925i 0.688623 0.397577i −0.114473 0.993426i \(-0.536518\pi\)
0.803096 + 0.595850i \(0.203185\pi\)
\(18\) 0.592086 0.139556
\(19\) 7.29219 4.21015i 1.67294 0.965875i 0.706967 0.707247i \(-0.250063\pi\)
0.965977 0.258628i \(-0.0832703\pi\)
\(20\) −3.66689 + 0.396326i −0.819942 + 0.0886213i
\(21\) 1.65741i 0.361676i
\(22\) −0.724334 + 0.418195i −0.154429 + 0.0891594i
\(23\) −5.70016 3.29099i −1.18857 0.686219i −0.230585 0.973052i \(-0.574064\pi\)
−0.957980 + 0.286834i \(0.907397\pi\)
\(24\) −1.87129 1.08039i −0.381975 0.220534i
\(25\) −3.36748 3.69596i −0.673496 0.739191i
\(26\) 1.85309 + 1.05992i 0.363420 + 0.207867i
\(27\) 1.00000i 0.192450i
\(28\) −1.36689 + 2.36753i −0.258319 + 0.447421i
\(29\) 0.252903 0.438041i 0.0469629 0.0813422i −0.841588 0.540119i \(-0.818379\pi\)
0.888551 + 0.458777i \(0.151712\pi\)
\(30\) −0.142267 1.31628i −0.0259742 0.240319i
\(31\) 0.791382i 0.142136i 0.997471 + 0.0710682i \(0.0226408\pi\)
−0.997471 + 0.0710682i \(0.977359\pi\)
\(32\) 2.75864 + 4.77810i 0.487663 + 0.844657i
\(33\) 0.706307 + 1.22336i 0.122952 + 0.212960i
\(34\) 1.94115i 0.332905i
\(35\) −3.68462 + 0.398243i −0.622815 + 0.0673153i
\(36\) −0.824717 + 1.42845i −0.137453 + 0.238075i
\(37\) −2.37878 + 4.12017i −0.391069 + 0.677352i −0.992591 0.121504i \(-0.961228\pi\)
0.601521 + 0.798857i \(0.294561\pi\)
\(38\) 4.98554i 0.808762i
\(39\) 1.79014 3.12976i 0.286652 0.501163i
\(40\) −1.95220 + 4.41970i −0.308670 + 0.698816i
\(41\) −7.67224 4.42957i −1.19820 0.691782i −0.238048 0.971253i \(-0.576508\pi\)
−0.960154 + 0.279471i \(0.909841\pi\)
\(42\) −0.849856 0.490665i −0.131136 0.0757112i
\(43\) −1.93289 + 1.11596i −0.294764 + 0.170182i −0.640088 0.768301i \(-0.721102\pi\)
0.345325 + 0.938483i \(0.387769\pi\)
\(44\) 2.33001i 0.351263i
\(45\) −2.22312 + 0.240280i −0.331403 + 0.0358189i
\(46\) −3.37499 + 1.94855i −0.497614 + 0.287298i
\(47\) 3.43727 0.501377 0.250688 0.968068i \(-0.419343\pi\)
0.250688 + 0.968068i \(0.419343\pi\)
\(48\) 1.74894 1.00975i 0.252438 0.145745i
\(49\) 2.12650 3.68320i 0.303785 0.526172i
\(50\) −2.89206 + 0.632552i −0.408999 + 0.0894563i
\(51\) −3.27850 −0.459082
\(52\) −5.13830 + 2.99435i −0.712553 + 0.415242i
\(53\) 0.422128i 0.0579838i −0.999580 0.0289919i \(-0.990770\pi\)
0.999580 0.0289919i \(-0.00922970\pi\)
\(54\) −0.512762 0.296043i −0.0697780 0.0402864i
\(55\) 2.54996 1.86416i 0.343837 0.251363i
\(56\) 1.79065 + 3.10149i 0.239285 + 0.414454i
\(57\) −8.42030 −1.11530
\(58\) −0.149740 0.259358i −0.0196619 0.0340554i
\(59\) 11.3443 6.54963i 1.47690 0.852689i 0.477241 0.878772i \(-0.341637\pi\)
0.999660 + 0.0260834i \(0.00830355\pi\)
\(60\) 3.37378 + 1.49022i 0.435554 + 0.192386i
\(61\) −0.463750 0.803239i −0.0593771 0.102844i 0.834809 0.550540i \(-0.185578\pi\)
−0.894186 + 0.447696i \(0.852245\pi\)
\(62\) 0.405790 + 0.234283i 0.0515354 + 0.0297540i
\(63\) −0.828705 + 1.43536i −0.104407 + 0.180838i
\(64\) −0.772299 −0.0965374
\(65\) −7.38797 3.22768i −0.916365 0.400344i
\(66\) 0.836389 0.102952
\(67\) 6.21154 10.7587i 0.758861 1.31439i −0.184571 0.982819i \(-0.559090\pi\)
0.943432 0.331567i \(-0.107577\pi\)
\(68\) 4.68318 + 2.70384i 0.567919 + 0.327888i
\(69\) 3.29099 + 5.70016i 0.396188 + 0.686219i
\(70\) −0.886603 + 2.00723i −0.105969 + 0.239910i
\(71\) 0.947838 0.547235i 0.112488 0.0649448i −0.442701 0.896670i \(-0.645980\pi\)
0.555188 + 0.831725i \(0.312646\pi\)
\(72\) 1.08039 + 1.87129i 0.127325 + 0.220534i
\(73\) 11.2130 1.31239 0.656193 0.754593i \(-0.272166\pi\)
0.656193 + 0.754593i \(0.272166\pi\)
\(74\) 1.40844 + 2.43950i 0.163728 + 0.283586i
\(75\) 1.06834 + 4.88453i 0.123362 + 0.564017i
\(76\) 12.0280 + 6.94436i 1.37971 + 0.796573i
\(77\) 2.34128i 0.266814i
\(78\) −1.07486 1.84446i −0.121704 0.208844i
\(79\) −9.25299 −1.04104 −0.520522 0.853849i \(-0.674262\pi\)
−0.520522 + 0.853849i \(0.674262\pi\)
\(80\) −2.66503 3.64548i −0.297960 0.407577i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) −4.54263 + 2.62269i −0.501649 + 0.289627i
\(83\) 4.02601 0.441912 0.220956 0.975284i \(-0.429082\pi\)
0.220956 + 0.975284i \(0.429082\pi\)
\(84\) 2.36753 1.36689i 0.258319 0.149140i
\(85\) 0.787759 + 7.28850i 0.0854445 + 0.790549i
\(86\) 1.32149i 0.142499i
\(87\) −0.438041 + 0.252903i −0.0469629 + 0.0271141i
\(88\) −2.64341 1.52617i −0.281789 0.162691i
\(89\) −0.517890 0.299004i −0.0548962 0.0316943i 0.472301 0.881437i \(-0.343424\pi\)
−0.527197 + 0.849743i \(0.676757\pi\)
\(90\) −0.534933 + 1.21106i −0.0563869 + 0.127657i
\(91\) −5.16314 + 3.00883i −0.541244 + 0.315411i
\(92\) 10.8565i 1.13187i
\(93\) 0.395691 0.685357i 0.0410312 0.0710682i
\(94\) 1.01758 1.76250i 0.104955 0.181788i
\(95\) 2.02323 + 18.7193i 0.207579 + 1.92056i
\(96\) 5.51728i 0.563105i
\(97\) −1.57968 2.73609i −0.160392 0.277808i 0.774617 0.632431i \(-0.217943\pi\)
−0.935009 + 0.354623i \(0.884609\pi\)
\(98\) −1.25907 2.18077i −0.127185 0.220291i
\(99\) 1.41261i 0.141973i
\(100\) 2.50228 7.85840i 0.250228 0.785840i
\(101\) −4.47142 + 7.74473i −0.444923 + 0.770629i −0.998047 0.0624697i \(-0.980102\pi\)
0.553124 + 0.833099i \(0.313436\pi\)
\(102\) −0.970577 + 1.68109i −0.0961015 + 0.166453i
\(103\) 15.0296i 1.48091i −0.672103 0.740457i \(-0.734609\pi\)
0.672103 0.740457i \(-0.265391\pi\)
\(104\) 0.0314892 + 7.79074i 0.00308777 + 0.763945i
\(105\) 3.39010 + 1.49742i 0.330840 + 0.146133i
\(106\) −0.216451 0.124968i −0.0210236 0.0121380i
\(107\) 16.3559 + 9.44308i 1.58118 + 0.912897i 0.994687 + 0.102946i \(0.0328270\pi\)
0.586498 + 0.809951i \(0.300506\pi\)
\(108\) 1.42845 0.824717i 0.137453 0.0793584i
\(109\) 6.71317i 0.643005i 0.946909 + 0.321502i \(0.104188\pi\)
−0.946909 + 0.321502i \(0.895812\pi\)
\(110\) −0.200968 1.85939i −0.0191615 0.177286i
\(111\) 4.12017 2.37878i 0.391069 0.225784i
\(112\) −3.34714 −0.316275
\(113\) −16.9895 + 9.80892i −1.59824 + 0.922745i −0.606416 + 0.795148i \(0.707393\pi\)
−0.991826 + 0.127598i \(0.959273\pi\)
\(114\) −2.49277 + 4.31761i −0.233469 + 0.404381i
\(115\) 11.8814 8.68590i 1.10794 0.809964i
\(116\) 0.834294 0.0774623
\(117\) −3.11519 + 1.81538i −0.287999 + 0.167832i
\(118\) 7.75589i 0.713987i
\(119\) 4.70582 + 2.71691i 0.431382 + 0.249059i
\(120\) 3.90051 2.85147i 0.356066 0.260302i
\(121\) −4.50226 7.79814i −0.409296 0.708922i
\(122\) −0.549160 −0.0497186
\(123\) 4.42957 + 7.67224i 0.399401 + 0.691782i
\(124\) −1.13045 + 0.652666i −0.101518 + 0.0586112i
\(125\) 10.6022 3.54871i 0.948290 0.317407i
\(126\) 0.490665 + 0.849856i 0.0437119 + 0.0757112i
\(127\) −14.2398 8.22136i −1.26358 0.729527i −0.289813 0.957083i \(-0.593593\pi\)
−0.973765 + 0.227556i \(0.926927\pi\)
\(128\) −5.74591 + 9.95221i −0.507872 + 0.879659i
\(129\) 2.23191 0.196509
\(130\) −3.84219 + 2.83274i −0.336982 + 0.248447i
\(131\) 6.11561 0.534323 0.267162 0.963652i \(-0.413914\pi\)
0.267162 + 0.963652i \(0.413914\pi\)
\(132\) −1.16501 + 2.01785i −0.101401 + 0.175631i
\(133\) 12.0861 + 6.97794i 1.04800 + 0.605064i
\(134\) −3.67777 6.37008i −0.317711 0.550291i
\(135\) 2.04542 + 0.903471i 0.176042 + 0.0777584i
\(136\) 6.13502 3.54206i 0.526074 0.303729i
\(137\) 6.47453 + 11.2142i 0.553156 + 0.958095i 0.998044 + 0.0625088i \(0.0199101\pi\)
−0.444888 + 0.895586i \(0.646757\pi\)
\(138\) 3.89710 0.331743
\(139\) 5.62458 + 9.74205i 0.477070 + 0.826310i 0.999655 0.0262776i \(-0.00836540\pi\)
−0.522584 + 0.852588i \(0.675032\pi\)
\(140\) −3.60764 4.93487i −0.304901 0.417072i
\(141\) −2.97676 1.71863i −0.250688 0.144735i
\(142\) 0.648020i 0.0543806i
\(143\) 2.52878 4.42114i 0.211467 0.369715i
\(144\) −2.01950 −0.168292
\(145\) 0.667487 + 0.913050i 0.0554318 + 0.0758247i
\(146\) 3.31954 5.74961i 0.274727 0.475841i
\(147\) −3.68320 + 2.12650i −0.303785 + 0.175391i
\(148\) −7.84729 −0.645043
\(149\) −17.0840 + 9.86345i −1.39958 + 0.808045i −0.994348 0.106171i \(-0.966141\pi\)
−0.405228 + 0.914216i \(0.632808\pi\)
\(150\) 2.82088 + 0.898226i 0.230324 + 0.0733398i
\(151\) 3.42805i 0.278971i −0.990224 0.139485i \(-0.955455\pi\)
0.990224 0.139485i \(-0.0445448\pi\)
\(152\) 15.7568 9.09720i 1.27805 0.737881i
\(153\) 2.83926 + 1.63925i 0.229541 + 0.132526i
\(154\) −1.20052 0.693120i −0.0967405 0.0558532i
\(155\) −1.61871 0.714991i −0.130018 0.0574295i
\(156\) 5.94707 0.0240373i 0.476147 0.00192453i
\(157\) 3.96627i 0.316543i −0.987396 0.158271i \(-0.949408\pi\)
0.987396 0.158271i \(-0.0505921\pi\)
\(158\) −2.73928 + 4.74458i −0.217926 + 0.377459i
\(159\) −0.211064 + 0.365574i −0.0167385 + 0.0289919i
\(160\) −12.2656 + 1.32569i −0.969679 + 0.104805i
\(161\) 10.9090i 0.859752i
\(162\) 0.296043 + 0.512762i 0.0232593 + 0.0402864i
\(163\) 0.997316 + 1.72740i 0.0781158 + 0.135301i 0.902437 0.430822i \(-0.141776\pi\)
−0.824321 + 0.566122i \(0.808443\pi\)
\(164\) 14.6126i 1.14105i
\(165\) −3.14041 + 0.339423i −0.244481 + 0.0264241i
\(166\) 1.19187 2.06439i 0.0925073 0.160227i
\(167\) −5.74274 + 9.94672i −0.444387 + 0.769701i −0.998009 0.0630672i \(-0.979912\pi\)
0.553622 + 0.832768i \(0.313245\pi\)
\(168\) 3.58130i 0.276303i
\(169\) −12.9996 + 0.105087i −0.999967 + 0.00808362i
\(170\) 3.97047 + 1.75378i 0.304522 + 0.134509i
\(171\) 7.29219 + 4.21015i 0.557648 + 0.321958i
\(172\) −3.18818 1.84070i −0.243097 0.140352i
\(173\) −10.9729 + 6.33521i −0.834254 + 0.481657i −0.855307 0.518122i \(-0.826631\pi\)
0.0210530 + 0.999778i \(0.493298\pi\)
\(174\) 0.299481i 0.0227036i
\(175\) 2.51438 7.89640i 0.190069 0.596911i
\(176\) 2.47058 1.42639i 0.186227 0.107518i
\(177\) −13.0993 −0.984601
\(178\) −0.306635 + 0.177036i −0.0229833 + 0.0132694i
\(179\) −4.28745 + 7.42609i −0.320459 + 0.555052i −0.980583 0.196105i \(-0.937171\pi\)
0.660124 + 0.751157i \(0.270504\pi\)
\(180\) −2.17667 2.97746i −0.162240 0.221927i
\(181\) −22.9517 −1.70599 −0.852994 0.521921i \(-0.825215\pi\)
−0.852994 + 0.521921i \(0.825215\pi\)
\(182\) 0.0143010 + 3.53820i 0.00106006 + 0.262269i
\(183\) 0.927500i 0.0685628i
\(184\) −12.3168 7.11110i −0.908005 0.524237i
\(185\) −6.27832 8.58807i −0.461591 0.631407i
\(186\) −0.234283 0.405790i −0.0171785 0.0297540i
\(187\) −4.63126 −0.338671
\(188\) 2.83477 + 4.90997i 0.206747 + 0.358096i
\(189\) 1.43536 0.828705i 0.104407 0.0602794i
\(190\) 10.1975 + 4.50430i 0.739806 + 0.326776i
\(191\) −2.14865 3.72158i −0.155471 0.269284i 0.777759 0.628562i \(-0.216356\pi\)
−0.933230 + 0.359278i \(0.883023\pi\)
\(192\) 0.668830 + 0.386149i 0.0482687 + 0.0278679i
\(193\) 3.16587 5.48344i 0.227884 0.394707i −0.729297 0.684198i \(-0.760153\pi\)
0.957181 + 0.289491i \(0.0934859\pi\)
\(194\) −1.87062 −0.134302
\(195\) 4.78433 + 6.48924i 0.342613 + 0.464704i
\(196\) 7.01503 0.501074
\(197\) 11.1207 19.2617i 0.792320 1.37234i −0.132207 0.991222i \(-0.542207\pi\)
0.924527 0.381116i \(-0.124460\pi\)
\(198\) −0.724334 0.418195i −0.0514762 0.0297198i
\(199\) −2.19713 3.80554i −0.155750 0.269768i 0.777582 0.628782i \(-0.216446\pi\)
−0.933332 + 0.359014i \(0.883113\pi\)
\(200\) −7.27638 7.98614i −0.514518 0.564706i
\(201\) −10.7587 + 6.21154i −0.758861 + 0.438129i
\(202\) 2.64747 + 4.58555i 0.186275 + 0.322638i
\(203\) 0.838328 0.0588391
\(204\) −2.70384 4.68318i −0.189306 0.327888i
\(205\) 15.9920 11.6910i 1.11693 0.816532i
\(206\) −7.70662 4.44942i −0.536946 0.310006i
\(207\) 6.58198i 0.457479i
\(208\) −6.32055 3.61519i −0.438251 0.250668i
\(209\) −11.8946 −0.822769
\(210\) 1.77144 1.29501i 0.122241 0.0893642i
\(211\) 3.35237 5.80648i 0.230787 0.399734i −0.727253 0.686369i \(-0.759203\pi\)
0.958040 + 0.286635i \(0.0925367\pi\)
\(212\) 0.602990 0.348136i 0.0414135 0.0239101i
\(213\) −1.09447 −0.0749918
\(214\) 9.68410 5.59112i 0.661991 0.382201i
\(215\) −0.536285 4.96181i −0.0365743 0.338393i
\(216\) 2.16078i 0.147022i
\(217\) −1.13592 + 0.655822i −0.0771111 + 0.0445201i
\(218\) 3.44225 + 1.98739i 0.233139 + 0.134603i
\(219\) −9.71077 5.60652i −0.656193 0.378853i
\(220\) 4.76586 + 2.10510i 0.321314 + 0.141926i
\(221\) 5.95173 + 10.2131i 0.400357 + 0.687010i
\(222\) 2.81689i 0.189057i
\(223\) −6.78573 + 11.7532i −0.454406 + 0.787055i −0.998654 0.0518698i \(-0.983482\pi\)
0.544248 + 0.838925i \(0.316815\pi\)
\(224\) −4.57219 + 7.91927i −0.305493 + 0.529129i
\(225\) 1.51705 4.76430i 0.101137 0.317620i
\(226\) 11.6154i 0.772648i
\(227\) 0.148503 + 0.257216i 0.00985652 + 0.0170720i 0.870912 0.491440i \(-0.163529\pi\)
−0.861055 + 0.508512i \(0.830196\pi\)
\(228\) −6.94436 12.0280i −0.459902 0.796573i
\(229\) 14.3158i 0.946014i 0.881059 + 0.473007i \(0.156832\pi\)
−0.881059 + 0.473007i \(0.843168\pi\)
\(230\) −0.936396 8.66372i −0.0617441 0.571269i
\(231\) −1.17064 + 2.02761i −0.0770225 + 0.133407i
\(232\) 0.546468 0.946510i 0.0358774 0.0621414i
\(233\) 12.9800i 0.850345i −0.905112 0.425173i \(-0.860213\pi\)
0.905112 0.425173i \(-0.139787\pi\)
\(234\) 0.00862852 + 2.13478i 0.000564064 + 0.139555i
\(235\) −3.10547 + 7.03065i −0.202579 + 0.458629i
\(236\) 18.7117 + 10.8032i 1.21803 + 0.703227i
\(237\) 8.01333 + 4.62650i 0.520522 + 0.300523i
\(238\) 2.78625 1.60864i 0.180606 0.104273i
\(239\) 13.6665i 0.884015i 0.897011 + 0.442007i \(0.145734\pi\)
−0.897011 + 0.442007i \(0.854266\pi\)
\(240\) 0.485246 + 4.48959i 0.0313225 + 0.289802i
\(241\) 10.5045 6.06478i 0.676655 0.390667i −0.121939 0.992538i \(-0.538911\pi\)
0.798594 + 0.601871i \(0.205578\pi\)
\(242\) −5.33145 −0.342719
\(243\) 0.866025 0.500000i 0.0555556 0.0320750i
\(244\) 0.764925 1.32489i 0.0489693 0.0848173i
\(245\) 5.61246 + 7.67724i 0.358567 + 0.490481i
\(246\) 5.24537 0.334433
\(247\) 15.2861 + 26.2308i 0.972628 + 1.66903i
\(248\) 1.71000i 0.108585i
\(249\) −3.48663 2.01301i −0.220956 0.127569i
\(250\) 1.31906 6.48697i 0.0834249 0.410272i
\(251\) −6.88951 11.9330i −0.434862 0.753203i 0.562422 0.826850i \(-0.309870\pi\)
−0.997284 + 0.0736468i \(0.976536\pi\)
\(252\) −2.73379 −0.172212
\(253\) 4.64890 + 8.05213i 0.292274 + 0.506233i
\(254\) −8.43119 + 4.86775i −0.529020 + 0.305430i
\(255\) 2.96203 6.70591i 0.185490 0.419940i
\(256\) 2.62977 + 4.55490i 0.164361 + 0.284681i
\(257\) 4.84978 + 2.80002i 0.302521 + 0.174661i 0.643575 0.765383i \(-0.277450\pi\)
−0.341054 + 0.940044i \(0.610784\pi\)
\(258\) 0.660743 1.14444i 0.0411360 0.0712497i
\(259\) −7.88523 −0.489965
\(260\) −1.48240 13.2153i −0.0919346 0.819577i
\(261\) 0.505806 0.0313086
\(262\) 1.81048 3.13585i 0.111852 0.193733i
\(263\) −7.77693 4.49001i −0.479546 0.276866i 0.240681 0.970604i \(-0.422629\pi\)
−0.720227 + 0.693738i \(0.755962\pi\)
\(264\) 1.52617 + 2.64341i 0.0939295 + 0.162691i
\(265\) 0.863429 + 0.381381i 0.0530401 + 0.0234280i
\(266\) 7.15604 4.13154i 0.438765 0.253321i
\(267\) 0.299004 + 0.517890i 0.0182987 + 0.0316943i
\(268\) 20.4911 1.25169
\(269\) 2.03862 + 3.53099i 0.124297 + 0.215288i 0.921458 0.388478i \(-0.126999\pi\)
−0.797161 + 0.603767i \(0.793666\pi\)
\(270\) 1.06880 0.781346i 0.0650449 0.0475512i
\(271\) 17.1435 + 9.89780i 1.04139 + 0.601249i 0.920228 0.391384i \(-0.128003\pi\)
0.121166 + 0.992632i \(0.461337\pi\)
\(272\) 6.62093i 0.401453i
\(273\) 5.97583 0.0241536i 0.361673 0.00146184i
\(274\) 7.66696 0.463178
\(275\) 1.50916 + 6.89996i 0.0910057 + 0.416083i
\(276\) −5.42827 + 9.40204i −0.326743 + 0.565936i
\(277\) 12.5813 7.26380i 0.755935 0.436439i −0.0718991 0.997412i \(-0.522906\pi\)
0.827834 + 0.560972i \(0.189573\pi\)
\(278\) 6.66047 0.399468
\(279\) −0.685357 + 0.395691i −0.0410312 + 0.0236894i
\(280\) −7.96165 + 0.860515i −0.475800 + 0.0514256i
\(281\) 11.7874i 0.703176i 0.936155 + 0.351588i \(0.114358\pi\)
−0.936155 + 0.351588i \(0.885642\pi\)
\(282\) −1.76250 + 1.01758i −0.104955 + 0.0605959i
\(283\) −20.0067 11.5509i −1.18928 0.686630i −0.231135 0.972922i \(-0.574244\pi\)
−0.958142 + 0.286292i \(0.907577\pi\)
\(284\) 1.56340 + 0.902628i 0.0927705 + 0.0535611i
\(285\) 7.60750 17.2230i 0.450629 1.02020i
\(286\) −1.51837 2.60551i −0.0897828 0.154067i
\(287\) 14.6832i 0.866723i
\(288\) −2.75864 + 4.77810i −0.162554 + 0.281552i
\(289\) −3.12572 + 5.41390i −0.183866 + 0.318465i
\(290\) 0.665782 0.0719593i 0.0390961 0.00422560i
\(291\) 3.15936i 0.185205i
\(292\) 9.24758 + 16.0173i 0.541174 + 0.937340i
\(293\) −4.79244 8.30075i −0.279977 0.484935i 0.691401 0.722471i \(-0.256994\pi\)
−0.971379 + 0.237536i \(0.923660\pi\)
\(294\) 2.51814i 0.146861i
\(295\) 3.14749 + 29.1212i 0.183254 + 1.69550i
\(296\) −5.14002 + 8.90278i −0.298758 + 0.517464i
\(297\) −0.706307 + 1.22336i −0.0409841 + 0.0709865i
\(298\) 11.6800i 0.676606i
\(299\) 11.7827 20.6000i 0.681409 1.19133i
\(300\) −6.09624 + 5.55443i −0.351966 + 0.320685i
\(301\) −3.20360 1.84960i −0.184652 0.106609i
\(302\) −1.75777 1.01485i −0.101148 0.0583980i
\(303\) 7.74473 4.47142i 0.444923 0.256876i
\(304\) 17.0048i 0.975292i
\(305\) 2.06194 0.222860i 0.118067 0.0127609i
\(306\) 1.68109 0.970577i 0.0961015 0.0554842i
\(307\) −25.2144 −1.43906 −0.719530 0.694461i \(-0.755643\pi\)
−0.719530 + 0.694461i \(0.755643\pi\)
\(308\) 3.34441 1.93089i 0.190565 0.110023i
\(309\) −7.51482 + 13.0161i −0.427503 + 0.740457i
\(310\) −0.845827 + 0.618343i −0.0480398 + 0.0351195i
\(311\) 1.70269 0.0965509 0.0482755 0.998834i \(-0.484627\pi\)
0.0482755 + 0.998834i \(0.484627\pi\)
\(312\) 3.86810 6.76272i 0.218988 0.382864i
\(313\) 25.1073i 1.41915i 0.704632 + 0.709573i \(0.251112\pi\)
−0.704632 + 0.709573i \(0.748888\pi\)
\(314\) −2.03375 1.17419i −0.114771 0.0662632i
\(315\) −2.18720 2.99185i −0.123235 0.168572i
\(316\) −7.63110 13.2175i −0.429283 0.743540i
\(317\) 1.89871 0.106642 0.0533210 0.998577i \(-0.483019\pi\)
0.0533210 + 0.998577i \(0.483019\pi\)
\(318\) 0.124968 + 0.216451i 0.00700787 + 0.0121380i
\(319\) −0.618783 + 0.357255i −0.0346452 + 0.0200024i
\(320\) 0.697750 1.57967i 0.0390054 0.0883065i
\(321\) −9.44308 16.3559i −0.527061 0.912897i
\(322\) −5.59373 3.22954i −0.311727 0.179975i
\(323\) 13.8030 23.9075i 0.768018 1.33025i
\(324\) −1.64943 −0.0916352
\(325\) 13.2768 12.1954i 0.736463 0.676478i
\(326\) 1.18099 0.0654092
\(327\) 3.35658 5.81377i 0.185620 0.321502i
\(328\) −16.5780 9.57132i −0.915368 0.528488i
\(329\) 2.84848 + 4.93371i 0.157042 + 0.272004i
\(330\) −0.755654 + 1.71077i −0.0415974 + 0.0941746i
\(331\) −17.5641 + 10.1406i −0.965410 + 0.557380i −0.897834 0.440334i \(-0.854860\pi\)
−0.0675763 + 0.997714i \(0.521527\pi\)
\(332\) 3.32032 + 5.75097i 0.182226 + 0.315625i
\(333\) −4.75757 −0.260713
\(334\) 3.40020 + 5.88932i 0.186051 + 0.322249i
\(335\) 16.3941 + 22.4254i 0.895706 + 1.22523i
\(336\) 2.89871 + 1.67357i 0.158137 + 0.0913007i
\(337\) 16.8233i 0.916421i 0.888844 + 0.458211i \(0.151509\pi\)
−0.888844 + 0.458211i \(0.848491\pi\)
\(338\) −3.79455 + 6.69679i −0.206396 + 0.364258i
\(339\) 19.6178 1.06549
\(340\) −9.76160 + 7.13623i −0.529397 + 0.387016i
\(341\) 0.558959 0.968145i 0.0302693 0.0524280i
\(342\) 4.31761 2.49277i 0.233469 0.134794i
\(343\) 18.6508 1.00705
\(344\) −4.17656 + 2.41134i −0.225185 + 0.130011i
\(345\) −14.6325 + 1.58152i −0.787789 + 0.0851461i
\(346\) 7.50197i 0.403309i
\(347\) −7.06423 + 4.07853i −0.379228 + 0.218947i −0.677482 0.735539i \(-0.736929\pi\)
0.298255 + 0.954486i \(0.403596\pi\)
\(348\) −0.722520 0.417147i −0.0387311 0.0223614i
\(349\) 12.7740 + 7.37508i 0.683777 + 0.394779i 0.801277 0.598294i \(-0.204155\pi\)
−0.117500 + 0.993073i \(0.537488\pi\)
\(350\) −3.30460 3.62695i −0.176639 0.193869i
\(351\) 3.60552 0.0145731i 0.192449 0.000777853i
\(352\) 7.79378i 0.415410i
\(353\) 7.81315 13.5328i 0.415852 0.720277i −0.579666 0.814854i \(-0.696817\pi\)
0.995517 + 0.0945779i \(0.0301502\pi\)
\(354\) −3.87794 + 6.71680i −0.206110 + 0.356994i
\(355\) 0.262979 + 2.43314i 0.0139575 + 0.129138i
\(356\) 0.986374i 0.0522777i
\(357\) −2.71691 4.70582i −0.143794 0.249059i
\(358\) 2.53854 + 4.39688i 0.134166 + 0.232382i
\(359\) 23.5802i 1.24452i −0.782812 0.622258i \(-0.786215\pi\)
0.782812 0.622258i \(-0.213785\pi\)
\(360\) −4.80367 + 0.519193i −0.253176 + 0.0273639i
\(361\) 25.9507 44.9480i 1.36583 2.36568i
\(362\) −6.79469 + 11.7688i −0.357121 + 0.618552i
\(363\) 9.00452i 0.472615i
\(364\) −8.55610 4.89386i −0.448461 0.256508i
\(365\) −10.1307 + 22.9354i −0.530263 + 1.20049i
\(366\) 0.475586 + 0.274580i 0.0248593 + 0.0143525i
\(367\) −12.4839 7.20758i −0.651654 0.376233i 0.137435 0.990511i \(-0.456114\pi\)
−0.789090 + 0.614278i \(0.789447\pi\)
\(368\) 11.5115 6.64615i 0.600077 0.346455i
\(369\) 8.85914i 0.461188i
\(370\) −6.26228 + 0.676843i −0.325561 + 0.0351874i
\(371\) 0.605906 0.349820i 0.0314571 0.0181617i
\(372\) 1.30533 0.0676783
\(373\) 9.00480 5.19893i 0.466251 0.269190i −0.248418 0.968653i \(-0.579911\pi\)
0.714669 + 0.699463i \(0.246577\pi\)
\(374\) −1.37105 + 2.37473i −0.0708954 + 0.122794i
\(375\) −10.9561 2.22782i −0.565772 0.115044i
\(376\) 7.42717 0.383027
\(377\) 1.58305 + 0.905464i 0.0815313 + 0.0466338i
\(378\) 0.981329i 0.0504741i
\(379\) −3.38172 1.95244i −0.173708 0.100290i 0.410625 0.911804i \(-0.365310\pi\)
−0.584333 + 0.811514i \(0.698644\pi\)
\(380\) −25.0711 + 18.3282i −1.28612 + 0.940219i
\(381\) 8.22136 + 14.2398i 0.421193 + 0.729527i
\(382\) −2.54437 −0.130182
\(383\) −16.2604 28.1639i −0.830869 1.43911i −0.897350 0.441320i \(-0.854510\pi\)
0.0664805 0.997788i \(-0.478823\pi\)
\(384\) 9.95221 5.74591i 0.507872 0.293220i
\(385\) 4.78890 + 2.11528i 0.244065 + 0.107805i
\(386\) −1.87447 3.24667i −0.0954078 0.165251i
\(387\) −1.93289 1.11596i −0.0982545 0.0567273i
\(388\) 2.60558 4.51300i 0.132278 0.229113i
\(389\) 36.5188 1.85158 0.925789 0.378042i \(-0.123402\pi\)
0.925789 + 0.378042i \(0.123402\pi\)
\(390\) 4.74380 0.532128i 0.240212 0.0269453i
\(391\) −21.5790 −1.09130
\(392\) 4.59489 7.95858i 0.232077 0.401969i
\(393\) −5.29627 3.05780i −0.267162 0.154246i
\(394\) −6.58443 11.4046i −0.331719 0.574554i
\(395\) 8.35982 18.9263i 0.420628 0.952283i
\(396\) 2.01785 1.16501i 0.101401 0.0585438i
\(397\) 5.15633 + 8.93103i 0.258789 + 0.448235i 0.965918 0.258849i \(-0.0833433\pi\)
−0.707129 + 0.707085i \(0.750010\pi\)
\(398\) −2.60178 −0.130415
\(399\) −6.97794 12.0861i −0.349334 0.605064i
\(400\) 9.86431 2.15752i 0.493216 0.107876i
\(401\) −18.0710 10.4333i −0.902421 0.521013i −0.0244360 0.999701i \(-0.507779\pi\)
−0.877985 + 0.478689i \(0.841112\pi\)
\(402\) 7.35554i 0.366861i
\(403\) −2.85335 + 0.0115329i −0.142135 + 0.000574493i
\(404\) −14.7506 −0.733871
\(405\) −1.31965 1.80514i −0.0655739 0.0896981i
\(406\) 0.248181 0.429862i 0.0123170 0.0213337i
\(407\) 5.82021 3.36030i 0.288497 0.166564i
\(408\) −7.08412 −0.350716
\(409\) 3.35024 1.93426i 0.165659 0.0956432i −0.414878 0.909877i \(-0.636176\pi\)
0.580537 + 0.814234i \(0.302843\pi\)
\(410\) −1.26036 11.6611i −0.0622447 0.575900i
\(411\) 12.9491i 0.638730i
\(412\) 21.4691 12.3952i 1.05771 0.610668i
\(413\) 18.8021 + 10.8554i 0.925192 + 0.534160i
\(414\) −3.37499 1.94855i −0.165871 0.0957659i
\(415\) −3.63739 + 8.23489i −0.178552 + 0.404235i
\(416\) −17.1873 + 10.0160i −0.842679 + 0.491073i
\(417\) 11.2492i 0.550873i
\(418\) −3.52132 + 6.09911i −0.172234 + 0.298317i
\(419\) 10.8008 18.7076i 0.527656 0.913926i −0.471825 0.881692i \(-0.656405\pi\)
0.999480 0.0322339i \(-0.0102621\pi\)
\(420\) 0.656875 + 6.07754i 0.0320522 + 0.296554i
\(421\) 11.8818i 0.579085i −0.957165 0.289542i \(-0.906497\pi\)
0.957165 0.289542i \(-0.0935031\pi\)
\(422\) −1.98489 3.43793i −0.0966230 0.167356i
\(423\) 1.71863 + 2.97676i 0.0835628 + 0.144735i
\(424\) 0.912126i 0.0442968i
\(425\) −15.6198 4.97366i −0.757670 0.241258i
\(426\) −0.324010 + 0.561202i −0.0156983 + 0.0271903i
\(427\) 0.768624 1.33130i 0.0371963 0.0644259i
\(428\) 31.1515i 1.50576i
\(429\) −4.40056 + 2.56443i −0.212461 + 0.123812i
\(430\) −2.70299 1.19392i −0.130350 0.0575761i
\(431\) −9.43023 5.44454i −0.454238 0.262254i 0.255380 0.966841i \(-0.417799\pi\)
−0.709618 + 0.704586i \(0.751133\pi\)
\(432\) 1.74894 + 1.00975i 0.0841459 + 0.0485816i
\(433\) −27.7614 + 16.0280i −1.33413 + 0.770258i −0.985929 0.167163i \(-0.946539\pi\)
−0.348197 + 0.937421i \(0.613206\pi\)
\(434\) 0.776606i 0.0372783i
\(435\) −0.121535 1.12447i −0.00582717 0.0539141i
\(436\) −9.58944 + 5.53646i −0.459251 + 0.265149i
\(437\) −55.4222 −2.65120
\(438\) −5.74961 + 3.31954i −0.274727 + 0.158614i
\(439\) 12.5421 21.7235i 0.598600 1.03681i −0.394427 0.918927i \(-0.629057\pi\)
0.993028 0.117879i \(-0.0376096\pi\)
\(440\) 5.50991 4.02803i 0.262675 0.192029i
\(441\) 4.25299 0.202524
\(442\) 6.99888 0.0282886i 0.332903 0.00134555i
\(443\) 32.0707i 1.52373i 0.647738 + 0.761863i \(0.275715\pi\)
−0.647738 + 0.761863i \(0.724285\pi\)
\(444\) 6.79595 + 3.92365i 0.322522 + 0.186208i
\(445\) 1.07949 0.789160i 0.0511726 0.0374098i
\(446\) 4.01774 + 6.95893i 0.190245 + 0.329515i
\(447\) 19.7269 0.933050
\(448\) −0.640008 1.10853i −0.0302375 0.0523729i
\(449\) −20.8143 + 12.0171i −0.982286 + 0.567123i −0.902960 0.429725i \(-0.858610\pi\)
−0.0793266 + 0.996849i \(0.525277\pi\)
\(450\) −1.99384 2.18832i −0.0939904 0.103159i
\(451\) 6.25727 + 10.8379i 0.294643 + 0.510337i
\(452\) −28.0231 16.1792i −1.31810 0.761004i
\(453\) −1.71402 + 2.96878i −0.0805319 + 0.139485i
\(454\) 0.175854 0.00825322
\(455\) −1.48957 13.2792i −0.0698321 0.622537i
\(456\) −18.1944 −0.852031
\(457\) −2.15807 + 3.73789i −0.100950 + 0.174851i −0.912077 0.410020i \(-0.865522\pi\)
0.811126 + 0.584871i \(0.198855\pi\)
\(458\) 7.34059 + 4.23809i 0.343003 + 0.198033i
\(459\) −1.63925 2.83926i −0.0765137 0.132526i
\(460\) 22.2062 + 9.80857i 1.03537 + 0.457327i
\(461\) −0.533988 + 0.308298i −0.0248703 + 0.0143589i −0.512384 0.858757i \(-0.671237\pi\)
0.487513 + 0.873116i \(0.337904\pi\)
\(462\) 0.693120 + 1.20052i 0.0322468 + 0.0558532i
\(463\) −13.3637 −0.621062 −0.310531 0.950563i \(-0.600507\pi\)
−0.310531 + 0.950563i \(0.600507\pi\)
\(464\) 0.510738 + 0.884624i 0.0237104 + 0.0410676i
\(465\) 1.04435 + 1.42855i 0.0484304 + 0.0662476i
\(466\) −6.65562 3.84263i −0.308316 0.178006i
\(467\) 26.1210i 1.20873i 0.796706 + 0.604367i \(0.206574\pi\)
−0.796706 + 0.604367i \(0.793426\pi\)
\(468\) −5.16233 2.95272i −0.238629 0.136489i
\(469\) 20.5901 0.950765
\(470\) 2.68569 + 3.67374i 0.123882 + 0.169457i
\(471\) −1.98314 + 3.43489i −0.0913781 + 0.158271i
\(472\) 24.5125 14.1523i 1.12828 0.651412i
\(473\) 3.15283 0.144967
\(474\) 4.74458 2.73928i 0.217926 0.125820i
\(475\) −40.1168 12.7740i −1.84069 0.586113i
\(476\) 8.96272i 0.410806i
\(477\) 0.365574 0.211064i 0.0167385 0.00966397i
\(478\) 7.00768 + 4.04588i 0.320524 + 0.185054i
\(479\) −7.51515 4.33887i −0.343376 0.198248i 0.318388 0.947960i \(-0.396859\pi\)
−0.661764 + 0.749712i \(0.730192\pi\)
\(480\) 11.2851 + 4.98470i 0.515094 + 0.227519i
\(481\) −14.8900 8.51671i −0.678927 0.388329i
\(482\) 7.18175i 0.327120i
\(483\) −5.45452 + 9.44750i −0.248189 + 0.429876i
\(484\) 7.42618 12.8625i 0.337554 0.584660i
\(485\) 7.02365 0.759133i 0.318927 0.0344704i
\(486\) 0.592086i 0.0268576i
\(487\) −14.2580 24.6955i −0.646090 1.11906i −0.984049 0.177899i \(-0.943070\pi\)
0.337959 0.941161i \(-0.390263\pi\)
\(488\) −1.00206 1.73562i −0.0453612 0.0785679i
\(489\) 1.99463i 0.0902004i
\(490\) 5.59813 0.605059i 0.252898 0.0273338i
\(491\) −16.2907 + 28.2163i −0.735189 + 1.27338i 0.219452 + 0.975623i \(0.429573\pi\)
−0.954641 + 0.297761i \(0.903760\pi\)
\(492\) −7.30628 + 12.6548i −0.329393 + 0.570525i
\(493\) 1.65829i 0.0746854i
\(494\) 17.9755 0.0726547i 0.808755 0.00326889i
\(495\) 2.88939 + 1.27626i 0.129868 + 0.0573635i
\(496\) −1.38408 0.799098i −0.0621470 0.0358806i
\(497\) 1.57096 + 0.906992i 0.0704670 + 0.0406842i
\(498\) −2.06439 + 1.19187i −0.0925073 + 0.0534091i
\(499\) 28.2348i 1.26396i −0.774983 0.631982i \(-0.782242\pi\)
0.774983 0.631982i \(-0.217758\pi\)
\(500\) 13.8130 + 12.2180i 0.617735 + 0.546408i
\(501\) 9.94672 5.74274i 0.444387 0.256567i
\(502\) −8.15837 −0.364126
\(503\) −4.34699 + 2.50973i −0.193823 + 0.111903i −0.593771 0.804634i \(-0.702361\pi\)
0.399948 + 0.916538i \(0.369028\pi\)
\(504\) −1.79065 + 3.10149i −0.0797618 + 0.138151i
\(505\) −11.8014 16.1431i −0.525156 0.718357i
\(506\) 5.50510 0.244731
\(507\) 11.3105 + 6.40878i 0.502317 + 0.284624i
\(508\) 27.1212i 1.20331i
\(509\) 19.8608 + 11.4666i 0.880313 + 0.508249i 0.870762 0.491705i \(-0.163626\pi\)
0.00955142 + 0.999954i \(0.496960\pi\)
\(510\) −2.56164 3.50405i −0.113431 0.155162i
\(511\) 9.29229 + 16.0947i 0.411067 + 0.711989i
\(512\) −19.8695 −0.878118
\(513\) −4.21015 7.29219i −0.185883 0.321958i
\(514\) 2.87149 1.65786i 0.126656 0.0731249i
\(515\) 30.7419 + 13.5789i 1.35465 + 0.598356i
\(516\) 1.84070 + 3.18818i 0.0810322 + 0.140352i
\(517\) −4.20501 2.42777i −0.184936 0.106773i
\(518\) −2.33437 + 4.04325i −0.102566 + 0.177650i
\(519\) 12.6704 0.556169
\(520\) −15.9638 6.97430i −0.700058 0.305843i
\(521\) 42.3619 1.85591 0.927955 0.372692i \(-0.121565\pi\)
0.927955 + 0.372692i \(0.121565\pi\)
\(522\) 0.149740 0.259358i 0.00655396 0.0113518i
\(523\) 1.31741 + 0.760610i 0.0576065 + 0.0332591i 0.528527 0.848917i \(-0.322745\pi\)
−0.470920 + 0.882176i \(0.656078\pi\)
\(524\) 5.04365 + 8.73585i 0.220333 + 0.381627i
\(525\) −6.12571 + 5.58129i −0.267348 + 0.243587i
\(526\) −4.60461 + 2.65847i −0.200771 + 0.115915i
\(527\) 1.29727 + 2.24694i 0.0565101 + 0.0978784i
\(528\) −2.85278 −0.124151
\(529\) 10.1612 + 17.5997i 0.441792 + 0.765206i
\(530\) 0.451170 0.329828i 0.0195976 0.0143268i
\(531\) 11.3443 + 6.54963i 0.492300 + 0.284230i
\(532\) 23.0193i 0.998014i
\(533\) 15.8591 27.7270i 0.686934 1.20099i
\(534\) 0.354072 0.0153222
\(535\) −34.0922 + 24.9231i −1.47393 + 1.07752i
\(536\) 13.4218 23.2472i 0.579732 1.00413i
\(537\) 7.42609 4.28745i 0.320459 0.185017i
\(538\) 2.41408 0.104078
\(539\) −5.20294 + 3.00392i −0.224107 + 0.129388i
\(540\) 0.396326 + 3.66689i 0.0170552 + 0.157798i
\(541\) 38.8503i 1.67030i 0.550019 + 0.835152i \(0.314620\pi\)
−0.550019 + 0.835152i \(0.685380\pi\)
\(542\) 10.1504 5.86035i 0.435998 0.251724i
\(543\) 19.8768 + 11.4759i 0.852994 + 0.492476i
\(544\) 15.6650 + 9.04420i 0.671632 + 0.387767i
\(545\) −13.7312 6.06516i −0.588182 0.259803i
\(546\) 1.75672 3.07132i 0.0751805 0.131441i
\(547\) 25.8936i 1.10713i −0.832806 0.553565i \(-0.813267\pi\)
0.832806 0.553565i \(-0.186733\pi\)
\(548\) −10.6793 + 18.4971i −0.456198 + 0.790157i
\(549\) 0.463750 0.803239i 0.0197924 0.0342814i
\(550\) 3.98481 + 1.26885i 0.169913 + 0.0541038i
\(551\) 4.25904i 0.181441i
\(552\) 7.11110 + 12.3168i 0.302668 + 0.524237i
\(553\) −7.66800 13.2814i −0.326077 0.564781i
\(554\) 8.60159i 0.365447i
\(555\) 1.14315 + 10.5766i 0.0485240 + 0.448953i
\(556\) −9.27737 + 16.0689i −0.393448 + 0.681472i
\(557\) 0.649455 1.12489i 0.0275183 0.0476631i −0.851938 0.523642i \(-0.824573\pi\)
0.879457 + 0.475979i \(0.157906\pi\)
\(558\) 0.468566i 0.0198360i
\(559\) −4.05178 6.95283i −0.171372 0.294073i
\(560\) 3.02405 6.84630i 0.127789 0.289309i
\(561\) 4.01079 + 2.31563i 0.169336 + 0.0977659i
\(562\) 6.04411 + 3.48957i 0.254955 + 0.147199i
\(563\) 19.1708 11.0683i 0.807955 0.466473i −0.0382903 0.999267i \(-0.512191\pi\)
0.846245 + 0.532794i \(0.178858\pi\)
\(564\) 5.66955i 0.238731i
\(565\) −4.71378 43.6128i −0.198310 1.83481i
\(566\) −11.8457 + 6.83913i −0.497913 + 0.287470i
\(567\) −1.65741 −0.0696047
\(568\) 2.04807 1.18245i 0.0859351 0.0496146i
\(569\) 18.6123 32.2374i 0.780267 1.35146i −0.151519 0.988454i \(-0.548416\pi\)
0.931786 0.363008i \(-0.118250\pi\)
\(570\) −6.57917 8.99960i −0.275571 0.376952i
\(571\) −2.36985 −0.0991752 −0.0495876 0.998770i \(-0.515791\pi\)
−0.0495876 + 0.998770i \(0.515791\pi\)
\(572\) 8.40092 0.0339555i 0.351260 0.00141975i
\(573\) 4.29731i 0.179523i
\(574\) −7.52899 4.34686i −0.314254 0.181435i
\(575\) 7.03182 + 32.1499i 0.293247 + 1.34074i
\(576\) −0.386149 0.668830i −0.0160896 0.0278679i
\(577\) 18.2135 0.758238 0.379119 0.925348i \(-0.376227\pi\)
0.379119 + 0.925348i \(0.376227\pi\)
\(578\) 1.85069 + 3.20550i 0.0769787 + 0.133331i
\(579\) −5.48344 + 3.16587i −0.227884 + 0.131569i
\(580\) −0.753761 + 1.70648i −0.0312982 + 0.0708578i
\(581\) 3.33638 + 5.77877i 0.138416 + 0.239744i
\(582\) 1.62000 + 0.935308i 0.0671512 + 0.0387698i
\(583\) −0.298152 + 0.516415i −0.0123482 + 0.0213877i
\(584\) 24.2289 1.00260
\(585\) −0.898733 8.01201i −0.0371581 0.331256i
\(586\) −5.67508 −0.234435
\(587\) −13.0547 + 22.6115i −0.538827 + 0.933275i 0.460141 + 0.887846i \(0.347799\pi\)
−0.998968 + 0.0454293i \(0.985534\pi\)
\(588\) −6.07520 3.50752i −0.250537 0.144648i
\(589\) 3.33184 + 5.77091i 0.137286 + 0.237786i
\(590\) 15.8640 + 7.00722i 0.653112 + 0.288483i
\(591\) −19.2617 + 11.1207i −0.792320 + 0.457446i
\(592\) −4.80395 8.32069i −0.197441 0.341978i
\(593\) −24.8984 −1.02245 −0.511226 0.859446i \(-0.670809\pi\)
−0.511226 + 0.859446i \(0.670809\pi\)
\(594\) 0.418195 + 0.724334i 0.0171587 + 0.0297198i
\(595\) −9.80880 + 7.17073i −0.402121 + 0.293971i
\(596\) −28.1789 16.2691i −1.15425 0.666409i
\(597\) 4.39426i 0.179845i
\(598\) −7.07472 12.1402i −0.289307 0.496449i
\(599\) −6.57002 −0.268444 −0.134222 0.990951i \(-0.542853\pi\)
−0.134222 + 0.990951i \(0.542853\pi\)
\(600\) 2.30846 + 10.5544i 0.0942423 + 0.430881i
\(601\) −12.8209 + 22.2064i −0.522975 + 0.905819i 0.476668 + 0.879084i \(0.341845\pi\)
−0.999643 + 0.0267356i \(0.991489\pi\)
\(602\) −1.89681 + 1.09512i −0.0773080 + 0.0446338i
\(603\) 12.4231 0.505907
\(604\) 4.89680 2.82717i 0.199248 0.115036i
\(605\) 20.0181 2.16361i 0.813853 0.0879632i
\(606\) 5.29493i 0.215092i
\(607\) 34.4882 19.9118i 1.39983 0.808195i 0.405460 0.914113i \(-0.367111\pi\)
0.994375 + 0.105918i \(0.0337781\pi\)
\(608\) 40.2330 + 23.2286i 1.63167 + 0.942043i
\(609\) −0.726013 0.419164i −0.0294195 0.0169854i
\(610\) 0.496150 1.12326i 0.0200885 0.0454796i
\(611\) 0.0500916 + 12.3931i 0.00202649 + 0.501373i
\(612\) 5.40767i 0.218592i
\(613\) 17.7378 30.7228i 0.716423 1.24088i −0.245985 0.969274i \(-0.579111\pi\)
0.962408 0.271608i \(-0.0875553\pi\)
\(614\) −7.46454 + 12.9290i −0.301244 + 0.521771i
\(615\) −19.6949 + 2.12868i −0.794176 + 0.0858365i
\(616\) 5.05899i 0.203833i
\(617\) 5.58683 + 9.67668i 0.224917 + 0.389568i 0.956295 0.292405i \(-0.0944554\pi\)
−0.731377 + 0.681973i \(0.761122\pi\)
\(618\) 4.44942 + 7.70662i 0.178982 + 0.310006i
\(619\) 35.2047i 1.41500i 0.706715 + 0.707498i \(0.250176\pi\)
−0.706715 + 0.707498i \(0.749824\pi\)
\(620\) −0.313646 2.90191i −0.0125963 0.116544i
\(621\) −3.29099 + 5.70016i −0.132063 + 0.228740i
\(622\) 0.504071 0.873076i 0.0202114 0.0350072i
\(623\) 0.991143i 0.0397093i
\(624\) 3.66616 + 6.29112i 0.146764 + 0.251846i
\(625\) −2.32018 + 24.8921i −0.0928071 + 0.995684i
\(626\) 12.8740 + 7.43283i 0.514550 + 0.297076i
\(627\) 10.3011 + 5.94732i 0.411385 + 0.237513i
\(628\) 5.66563 3.27105i 0.226083 0.130529i
\(629\) 15.5977i 0.621920i
\(630\) −2.18161 + 0.235794i −0.0869175 + 0.00939426i
\(631\) 4.83806 2.79326i 0.192600 0.111198i −0.400599 0.916253i \(-0.631198\pi\)
0.593199 + 0.805056i \(0.297865\pi\)
\(632\) −19.9937 −0.795306
\(633\) −5.80648 + 3.35237i −0.230787 + 0.133245i
\(634\) 0.562099 0.973584i 0.0223238 0.0386659i
\(635\) 29.6814 21.6986i 1.17787 0.861083i
\(636\) −0.696273 −0.0276090
\(637\) 13.3109 + 7.61346i 0.527395 + 0.301656i
\(638\) 0.423051i 0.0167487i
\(639\) 0.947838 + 0.547235i 0.0374959 + 0.0216483i
\(640\) −15.1652 20.7443i −0.599456 0.819992i
\(641\) −10.8579 18.8064i −0.428861 0.742809i 0.567911 0.823090i \(-0.307752\pi\)
−0.996772 + 0.0802807i \(0.974418\pi\)
\(642\) −11.1822 −0.441328
\(643\) −8.01232 13.8777i −0.315975 0.547285i 0.663669 0.748026i \(-0.268998\pi\)
−0.979644 + 0.200741i \(0.935665\pi\)
\(644\) 15.5830 8.99686i 0.614057 0.354526i
\(645\) −2.01647 + 4.56520i −0.0793985 + 0.179755i
\(646\) −8.17255 14.1553i −0.321545 0.556932i
\(647\) −9.58441 5.53356i −0.376802 0.217547i 0.299624 0.954057i \(-0.403139\pi\)
−0.676426 + 0.736511i \(0.736472\pi\)
\(648\) −1.08039 + 1.87129i −0.0424417 + 0.0735112i
\(649\) −18.5042 −0.726353
\(650\) −2.32283 10.4182i −0.0911087 0.408635i
\(651\) 1.31164 0.0514074
\(652\) −1.64501 + 2.84924i −0.0644234 + 0.111585i
\(653\) −24.6070 14.2069i −0.962946 0.555957i −0.0658676 0.997828i \(-0.520981\pi\)
−0.897079 + 0.441871i \(0.854315\pi\)
\(654\) −1.98739 3.44225i −0.0777130 0.134603i
\(655\) −5.52528 + 12.5090i −0.215890 + 0.488766i
\(656\) 15.4941 8.94552i 0.604943 0.349264i
\(657\) 5.60652 + 9.71077i 0.218731 + 0.378853i
\(658\) 3.37309 0.131497
\(659\) −13.1876 22.8416i −0.513717 0.889783i −0.999873 0.0159116i \(-0.994935\pi\)
0.486157 0.873872i \(-0.338398\pi\)
\(660\) −3.07480 4.20600i −0.119686 0.163718i
\(661\) 25.3928 + 14.6606i 0.987667 + 0.570230i 0.904576 0.426312i \(-0.140188\pi\)
0.0830907 + 0.996542i \(0.473521\pi\)
\(662\) 12.0083i 0.466714i
\(663\) −0.0477778 11.8207i −0.00185554 0.459078i
\(664\) 8.69933 0.337599
\(665\) −25.1923 + 18.4169i −0.976916 + 0.714176i
\(666\) −1.40844 + 2.43950i −0.0545761 + 0.0945286i
\(667\) −2.88318 + 1.66460i −0.111637 + 0.0644537i
\(668\) −18.9446 −0.732987
\(669\) 11.7532 6.78573i 0.454406 0.262352i
\(670\) 16.3522 1.76739i 0.631742 0.0682803i
\(671\) 1.31020i 0.0505797i
\(672\) 7.91927 4.57219i 0.305493 0.176376i
\(673\) 35.3958 + 20.4358i 1.36441 + 0.787741i 0.990207 0.139607i \(-0.0445839\pi\)
0.374200 + 0.927348i \(0.377917\pi\)
\(674\) 8.62632 + 4.98041i 0.332274 + 0.191838i
\(675\) −3.69596 + 3.36748i −0.142257 + 0.129614i
\(676\) −10.8711 18.4826i −0.418119 0.710869i
\(677\) 33.8996i 1.30287i −0.758705 0.651435i \(-0.774167\pi\)
0.758705 0.651435i \(-0.225833\pi\)
\(678\) 5.80772 10.0593i 0.223044 0.386324i
\(679\) 2.61818 4.53482i 0.100477 0.174030i
\(680\) 1.70217 + 15.7488i 0.0652754 + 0.603941i
\(681\) 0.297007i 0.0113813i
\(682\) −0.330952 0.573225i −0.0126728 0.0219499i
\(683\) 5.28626 + 9.15608i 0.202273 + 0.350347i 0.949261 0.314491i \(-0.101834\pi\)
−0.746987 + 0.664838i \(0.768500\pi\)
\(684\) 13.8887i 0.531049i
\(685\) −28.7873 + 3.11140i −1.09991 + 0.118881i
\(686\) 5.52145 9.56342i 0.210810 0.365133i
\(687\) 7.15790 12.3978i 0.273091 0.473007i
\(688\) 4.50735i 0.171841i
\(689\) 1.52199 0.00615171i 0.0579833 0.000234361i
\(690\) −3.52092 + 7.97120i −0.134039 + 0.303458i
\(691\) 8.65326 + 4.99596i 0.329186 + 0.190055i 0.655479 0.755213i \(-0.272467\pi\)
−0.326294 + 0.945268i \(0.605800\pi\)
\(692\) −18.0991 10.4495i −0.688024 0.397231i
\(693\) 2.02761 1.17064i 0.0770225 0.0444689i
\(694\) 4.82968i 0.183332i
\(695\) −25.0082 + 2.70295i −0.948616 + 0.102529i
\(696\) −0.946510 + 0.546468i −0.0358774 + 0.0207138i
\(697\) −29.0447 −1.10015
\(698\) 7.56331 4.36668i 0.286276 0.165281i
\(699\) −6.48998 + 11.2410i −0.245473 + 0.425173i
\(700\) 13.3533 2.92063i 0.504706 0.110389i
\(701\) 30.4957 1.15181 0.575903 0.817518i \(-0.304651\pi\)
0.575903 + 0.817518i \(0.304651\pi\)
\(702\) 1.05992 1.85309i 0.0400040 0.0699403i
\(703\) 40.0601i 1.51090i
\(704\) 0.944799 + 0.545480i 0.0356085 + 0.0205586i
\(705\) 6.20474 4.53599i 0.233684 0.170835i
\(706\) −4.62606 8.01256i −0.174104 0.301557i
\(707\) −14.8220 −0.557437
\(708\) −10.8032 18.7117i −0.406008 0.703227i
\(709\) −9.17071 + 5.29471i −0.344413 + 0.198847i −0.662222 0.749308i \(-0.730386\pi\)
0.317809 + 0.948155i \(0.397053\pi\)
\(710\) 1.32547 + 0.585468i 0.0497441 + 0.0219722i
\(711\) −4.62650 8.01333i −0.173507 0.300523i
\(712\) −1.11905 0.646081i −0.0419380 0.0242129i
\(713\) 2.60443 4.51100i 0.0975366 0.168938i
\(714\) −3.21729 −0.120404
\(715\) 6.75841 + 9.16679i 0.252750 + 0.342818i
\(716\) −14.1437 −0.528576
\(717\) 6.83327 11.8356i 0.255193 0.442007i
\(718\) −12.0910 6.98076i −0.451233 0.260520i
\(719\) −3.68101 6.37570i −0.137279 0.237774i 0.789187 0.614153i \(-0.210502\pi\)
−0.926466 + 0.376379i \(0.877169\pi\)
\(720\) 1.82456 4.13073i 0.0679974 0.153943i
\(721\) 21.5729 12.4551i 0.803418 0.463854i
\(722\) −15.3651 26.6131i −0.571828 0.990436i
\(723\) −12.1296 −0.451103
\(724\) −18.9287 32.7854i −0.703478 1.21846i
\(725\) −2.47063 + 0.540375i −0.0917567 + 0.0200690i
\(726\) 4.61717 + 2.66573i 0.171359 + 0.0989344i
\(727\) 30.8420i 1.14387i 0.820300 + 0.571934i \(0.193807\pi\)
−0.820300 + 0.571934i \(0.806193\pi\)
\(728\) −11.1564 + 6.50142i −0.413484 + 0.240959i
\(729\) −1.00000 −0.0370370
\(730\) 8.76126 + 11.9845i 0.324269 + 0.443565i
\(731\) −3.65867 + 6.33700i −0.135321 + 0.234382i
\(732\) −1.32489 + 0.764925i −0.0489693 + 0.0282724i
\(733\) −30.7552 −1.13597 −0.567985 0.823039i \(-0.692277\pi\)
−0.567985 + 0.823039i \(0.692277\pi\)
\(734\) −7.39154 + 4.26751i −0.272827 + 0.157517i
\(735\) −1.02191 9.45492i −0.0376937 0.348750i
\(736\) 36.3146i 1.33857i
\(737\) −15.1979 + 8.77452i −0.559822 + 0.323213i
\(738\) −4.54263 2.62269i −0.167216 0.0965424i
\(739\) −31.3327 18.0899i −1.15259 0.665449i −0.203074 0.979163i \(-0.565093\pi\)
−0.949517 + 0.313715i \(0.898426\pi\)
\(740\) 7.08980 16.0510i 0.260626 0.590046i
\(741\) −0.122710 30.3596i −0.00450785 1.11529i
\(742\) 0.414247i 0.0152075i
\(743\) −7.22170 + 12.5084i −0.264938 + 0.458887i −0.967547 0.252689i \(-0.918685\pi\)
0.702609 + 0.711576i \(0.252018\pi\)
\(744\) 0.855001 1.48091i 0.0313459 0.0542926i
\(745\) −4.73998 43.8553i −0.173660 1.60673i
\(746\) 6.15642i 0.225403i
\(747\) 2.01301 + 3.48663i 0.0736521 + 0.127569i
\(748\) −3.81948 6.61553i −0.139654 0.241888i
\(749\) 31.3021i 1.14375i
\(750\) −4.38583 + 4.95835i −0.160148 + 0.181053i
\(751\) −0.691642 + 1.19796i −0.0252384 + 0.0437142i −0.878369 0.477984i \(-0.841368\pi\)
0.853130 + 0.521698i \(0.174701\pi\)
\(752\) −3.47078 + 6.01157i −0.126566 + 0.219219i
\(753\) 13.7790i 0.502136i
\(754\) 0.932939 0.543672i 0.0339756 0.0197994i
\(755\) 7.01179 + 3.09714i 0.255185 + 0.112717i
\(756\) 2.36753 + 1.36689i 0.0861062 + 0.0497134i
\(757\) 44.1964 + 25.5168i 1.60635 + 0.927424i 0.990179 + 0.139808i \(0.0446485\pi\)
0.616167 + 0.787616i \(0.288685\pi\)
\(758\) −2.00227 + 1.15601i −0.0727258 + 0.0419883i
\(759\) 9.29780i 0.337489i
\(760\) 4.37176 + 40.4484i 0.158580 + 1.46722i
\(761\) −2.32993 + 1.34518i −0.0844598 + 0.0487629i −0.541635 0.840614i \(-0.682195\pi\)
0.457175 + 0.889377i \(0.348861\pi\)
\(762\) 9.73550 0.352680
\(763\) −9.63580 + 5.56323i −0.348840 + 0.201403i
\(764\) 3.54406 6.13849i 0.128220 0.222083i
\(765\) −5.91815 + 4.32647i −0.213971 + 0.156424i
\(766\) −19.2552 −0.695717
\(767\) 23.7802 + 40.8066i 0.858651 + 1.47344i
\(768\) 5.25955i 0.189788i
\(769\) 8.85248 + 5.11098i 0.319228 + 0.184307i 0.651049 0.759036i \(-0.274329\pi\)
−0.331820 + 0.943343i \(0.607663\pi\)
\(770\) 2.50235 1.82935i 0.0901786 0.0659252i
\(771\) −2.80002 4.84978i −0.100840 0.174661i
\(772\) 10.4438 0.375880
\(773\) 9.46421 + 16.3925i 0.340404 + 0.589597i 0.984508 0.175341i \(-0.0561028\pi\)
−0.644104 + 0.764938i \(0.722770\pi\)
\(774\) −1.14444 + 0.660743i −0.0411360 + 0.0237499i
\(775\) 2.92491 2.66496i 0.105066 0.0957283i
\(776\) −3.41334 5.91208i −0.122532 0.212231i
\(777\) 6.82881 + 3.94262i 0.244982 + 0.141441i
\(778\) 10.8111 18.7254i 0.387598 0.671340i
\(779\) −74.5966 −2.67270
\(780\) −5.32384 + 12.1860i −0.190624 + 0.436328i
\(781\) −1.54606 −0.0553225
\(782\) −6.38832 + 11.0649i −0.228446 + 0.395680i
\(783\) −0.438041 0.252903i −0.0156543 0.00903802i
\(784\) 4.29446 + 7.43823i 0.153374 + 0.265651i
\(785\) 8.11269 + 3.58341i 0.289554 + 0.127898i
\(786\) −3.13585 + 1.81048i −0.111852 + 0.0645778i
\(787\) 10.9136 + 18.9030i 0.389029 + 0.673818i 0.992319 0.123703i \(-0.0394772\pi\)
−0.603290 + 0.797522i \(0.706144\pi\)
\(788\) 36.6858 1.30688
\(789\) 4.49001 + 7.77693i 0.159849 + 0.276866i
\(790\) −7.22979 9.88958i −0.257224 0.351855i
\(791\) −28.1586 16.2574i −1.00121 0.578046i
\(792\) 3.05235i 0.108460i
\(793\) 2.88934 1.68377i 0.102603 0.0597923i
\(794\) 6.10598 0.216693
\(795\) −0.557061 0.762000i −0.0197569 0.0270254i
\(796\) 3.62402 6.27699i 0.128450 0.222482i
\(797\) 33.5184 19.3519i 1.18728 0.685478i 0.229594 0.973286i \(-0.426260\pi\)
0.957688 + 0.287809i \(0.0929267\pi\)
\(798\) −8.26308 −0.292510
\(799\) 9.75931 5.63454i 0.345260 0.199336i
\(800\) 8.37000 26.2860i 0.295924 0.929349i
\(801\) 0.598008i 0.0211296i
\(802\) −10.6996 + 6.17740i −0.377815 + 0.218131i
\(803\) −13.7176 7.91985i −0.484083 0.279485i
\(804\) −17.7458 10.2455i −0.625846 0.361332i
\(805\) 22.3135 + 9.85600i 0.786449 + 0.347378i
\(806\) −0.838799 + 1.46650i −0.0295454 + 0.0516553i
\(807\) 4.07724i 0.143526i
\(808\) −9.66175 + 16.7347i −0.339899 + 0.588723i
\(809\) −21.3022 + 36.8965i −0.748946 + 1.29721i 0.199383 + 0.979922i \(0.436106\pi\)
−0.948328 + 0.317291i \(0.897227\pi\)
\(810\) −1.31628 + 0.142267i −0.0462493 + 0.00499874i
\(811\) 9.60428i 0.337252i 0.985680 + 0.168626i \(0.0539330\pi\)
−0.985680 + 0.168626i \(0.946067\pi\)
\(812\) 0.691383 + 1.19751i 0.0242628 + 0.0420244i
\(813\) −9.89780 17.1435i −0.347131 0.601249i
\(814\) 3.97918i 0.139470i
\(815\) −4.43431 + 0.479271i −0.155327 + 0.0167881i
\(816\) 3.31047 5.73390i 0.115890 0.200727i
\(817\) −9.39669 + 16.2755i −0.328749 + 0.569409i
\(818\) 2.29050i 0.0800855i
\(819\) −5.18729 2.96700i −0.181259 0.103675i
\(820\) 29.8888 + 13.2020i 1.04376 + 0.461035i
\(821\) −29.9683 17.3022i −1.04590 0.603851i −0.124402 0.992232i \(-0.539701\pi\)
−0.921499 + 0.388381i \(0.873035\pi\)
\(822\) −6.63978 3.83348i −0.231589 0.133708i
\(823\) −24.0422 + 13.8808i −0.838057 + 0.483853i −0.856603 0.515975i \(-0.827430\pi\)
0.0185460 + 0.999828i \(0.494096\pi\)
\(824\) 32.4757i 1.13135i
\(825\) 2.14301 6.73012i 0.0746100 0.234313i
\(826\) 11.1325 6.42734i 0.387349 0.223636i
\(827\) −27.8932 −0.969943 −0.484971 0.874530i \(-0.661170\pi\)
−0.484971 + 0.874530i \(0.661170\pi\)
\(828\) 9.40204 5.42827i 0.326743 0.188645i
\(829\) −7.47706 + 12.9507i −0.259689 + 0.449795i −0.966159 0.257949i \(-0.916953\pi\)
0.706469 + 0.707744i \(0.250287\pi\)
\(830\) 3.14571 + 4.30299i 0.109189 + 0.149359i
\(831\) −14.5276 −0.503957
\(832\) −0.0112548 2.78454i −0.000390189 0.0965366i
\(833\) 13.9434i 0.483112i
\(834\) −5.76813 3.33023i −0.199734 0.115317i
\(835\) −15.1568 20.7329i −0.524523 0.717492i
\(836\) −9.80971 16.9909i −0.339276 0.587643i
\(837\) 0.791382 0.0273542
\(838\) −6.39503 11.0765i −0.220913 0.382632i
\(839\) 20.9723 12.1084i 0.724044 0.418027i −0.0921951 0.995741i \(-0.529388\pi\)
0.816239 + 0.577714i \(0.196055\pi\)
\(840\) 7.32525 + 3.23560i 0.252745 + 0.111639i
\(841\) 14.3721 + 24.8932i 0.495589 + 0.858385i
\(842\) −6.09254 3.51753i −0.209963 0.121222i
\(843\) 5.89369 10.2082i 0.202989 0.351588i
\(844\) 11.0590 0.380667
\(845\) 11.5298 26.6845i 0.396637 0.917975i
\(846\) 2.03516 0.0699702
\(847\) 7.46209 12.9247i 0.256400 0.444099i
\(848\) 0.738277 + 0.426244i 0.0253525 + 0.0146373i
\(849\) 11.5509 + 20.0067i 0.396426 + 0.686630i
\(850\) −7.17442 + 6.53680i −0.246081 + 0.224210i
\(851\) 27.1189 15.6571i 0.929623 0.536718i
\(852\) −0.902628 1.56340i −0.0309235 0.0535611i
\(853\) 25.6140 0.877008 0.438504 0.898729i \(-0.355508\pi\)
0.438504 + 0.898729i \(0.355508\pi\)
\(854\) −0.455091 0.788242i −0.0155729 0.0269731i
\(855\) −15.1998 + 11.1118i −0.519822 + 0.380017i
\(856\) 35.3415 + 20.4044i 1.20795 + 0.697409i
\(857\) 38.9380i 1.33010i −0.746800 0.665049i \(-0.768411\pi\)
0.746800 0.665049i \(-0.231589\pi\)
\(858\) 0.0121888 + 3.01562i 0.000416118 + 0.102952i
\(859\) −32.9648 −1.12474 −0.562372 0.826885i \(-0.690111\pi\)
−0.562372 + 0.826885i \(0.690111\pi\)
\(860\) 6.64543 4.85815i 0.226607 0.165662i
\(861\) −7.34161 + 12.7160i −0.250201 + 0.433361i
\(862\) −5.58351 + 3.22364i −0.190175 + 0.109798i
\(863\) 12.9022 0.439197 0.219598 0.975590i \(-0.429525\pi\)
0.219598 + 0.975590i \(0.429525\pi\)
\(864\) 4.77810 2.75864i 0.162554 0.0938508i
\(865\) −3.04445 28.1679i −0.103514 0.957736i
\(866\) 18.9799i 0.644965i
\(867\) 5.41390 3.12572i 0.183866 0.106155i
\(868\) −1.87362 1.08174i −0.0635948 0.0367165i
\(869\) 11.3197 + 6.53546i 0.383996 + 0.221700i
\(870\) −0.612564 0.270572i −0.0207679 0.00917326i
\(871\) 38.8813 + 22.2391i 1.31744 + 0.753542i
\(872\) 14.5057i 0.491224i
\(873\) 1.57968 2.73609i 0.0534641 0.0926026i
\(874\) −16.4074 + 28.4184i −0.554987 + 0.961266i
\(875\) 13.8798 + 12.2771i 0.469222 + 0.415042i
\(876\) 18.4952i 0.624894i
\(877\) 5.73911 + 9.94043i 0.193796 + 0.335664i 0.946505 0.322689i \(-0.104587\pi\)
−0.752709 + 0.658353i \(0.771253\pi\)
\(878\) −7.42599 12.8622i −0.250615 0.434078i
\(879\) 9.58488i 0.323290i
\(880\) 0.685466 + 6.34206i 0.0231070 + 0.213791i
\(881\) 0.584497 1.01238i 0.0196922 0.0341079i −0.856011 0.516957i \(-0.827065\pi\)
0.875704 + 0.482849i \(0.160398\pi\)
\(882\) 1.25907 2.18077i 0.0423951 0.0734304i
\(883\) 1.40478i 0.0472746i −0.999721 0.0236373i \(-0.992475\pi\)
0.999721 0.0236373i \(-0.00752468\pi\)
\(884\) −9.68049 + 16.9247i −0.325590 + 0.569240i
\(885\) 11.8348 26.7935i 0.397823 0.900653i
\(886\) 16.4446 + 9.49431i 0.552468 + 0.318968i
\(887\) −15.0410 8.68394i −0.505028 0.291578i 0.225759 0.974183i \(-0.427514\pi\)
−0.730788 + 0.682605i \(0.760847\pi\)
\(888\) 8.90278 5.14002i 0.298758 0.172488i
\(889\) 27.2523i 0.914013i
\(890\) −0.0850765 0.787145i −0.00285177 0.0263851i
\(891\) 1.22336 0.706307i 0.0409841 0.0236622i
\(892\) −22.3852 −0.749513
\(893\) 25.0652 14.4714i 0.838775 0.484267i
\(894\) 5.84001 10.1152i 0.195319 0.338303i
\(895\) −11.3159 15.4789i −0.378248 0.517402i
\(896\) −19.0467 −0.636304
\(897\) −20.5041 + 11.9488i −0.684612 + 0.398959i
\(898\) 14.2303i 0.474873i
\(899\) 0.346658 + 0.200143i 0.0115617 + 0.00667514i
\(900\) 8.05671 1.76216i 0.268557 0.0587388i
\(901\) −0.691974 1.19853i −0.0230530 0.0399290i
\(902\) 7.40969 0.246716
\(903\) 1.84960 + 3.20360i 0.0615508 + 0.106609i
\(904\) −36.7107 + 21.1949i −1.22098 + 0.704932i
\(905\) 20.7362 46.9459i 0.689295 1.56053i
\(906\) 1.01485 + 1.75777i 0.0337161 + 0.0583980i
\(907\) −7.93327 4.58028i −0.263420 0.152086i 0.362474 0.931994i \(-0.381932\pi\)
−0.625894 + 0.779908i \(0.715266\pi\)
\(908\) −0.244947 + 0.424260i −0.00812884 + 0.0140796i
\(909\) −8.94284 −0.296615
\(910\) −7.25003 3.16741i −0.240336 0.104999i
\(911\) 46.2229 1.53143 0.765717 0.643177i \(-0.222384\pi\)
0.765717 + 0.643177i \(0.222384\pi\)
\(912\) 8.50240 14.7266i 0.281543 0.487646i
\(913\) −4.92526 2.84360i −0.163002 0.0941095i
\(914\) 1.27777 + 2.21316i 0.0422647 + 0.0732047i
\(915\) −1.89713 0.837970i −0.0627171 0.0277024i
\(916\) −20.4494 + 11.8065i −0.675668 + 0.390097i
\(917\) 5.06803 + 8.77809i 0.167361 + 0.289878i
\(918\) −1.94115 −0.0640676
\(919\) −6.81590 11.8055i −0.224836 0.389427i 0.731434 0.681912i \(-0.238851\pi\)
−0.956270 + 0.292485i \(0.905518\pi\)
\(920\) 25.6730 18.7683i 0.846415 0.618773i
\(921\) 21.8363 + 12.6072i 0.719530 + 0.415421i
\(922\) 0.365078i 0.0120232i
\(923\) 1.98688 + 3.40948i 0.0653989 + 0.112224i
\(924\) −3.86179 −0.127043
\(925\) 23.2385 5.08272i 0.764076 0.167119i
\(926\) −3.95622 + 6.85238i −0.130010 + 0.225183i
\(927\) 13.0161 7.51482i 0.427503 0.246819i
\(928\) 2.79067 0.0916083
\(929\) −37.6193 + 21.7195i −1.23425 + 0.712594i −0.967913 0.251286i \(-0.919147\pi\)
−0.266336 + 0.963880i \(0.585813\pi\)
\(930\) 1.04168 0.112587i 0.0341580 0.00369188i
\(931\) 35.8115i 1.17367i
\(932\) 18.5412 10.7048i 0.607338 0.350647i
\(933\) −1.47458 0.851347i −0.0482755 0.0278719i
\(934\) 13.3938 + 7.73293i 0.438260 + 0.253029i
\(935\) 4.18421 9.47286i 0.136838 0.309796i
\(936\) −6.73123 + 3.92264i −0.220017 + 0.128215i
\(937\) 30.4186i 0.993731i −0.867828 0.496865i \(-0.834484\pi\)
0.867828 0.496865i \(-0.165516\pi\)
\(938\) 6.09557 10.5578i 0.199027 0.344726i
\(939\) 12.5536 21.7435i 0.409672 0.709573i
\(940\) −12.6041 + 1.36228i −0.411100 + 0.0444327i
\(941\) 55.9477i 1.82384i 0.410363 + 0.911922i \(0.365402\pi\)
−0.410363 + 0.911922i \(0.634598\pi\)
\(942\) 1.17419 + 2.03375i 0.0382571 + 0.0662632i
\(943\) 29.1553 + 50.4985i 0.949428 + 1.64446i
\(944\) 26.4540i 0.861003i
\(945\) 0.398243 + 3.68462i 0.0129548 + 0.119861i
\(946\) 0.933375 1.61665i 0.0303466 0.0525619i
\(947\) −12.1131 + 20.9804i −0.393622 + 0.681773i −0.992924 0.118750i \(-0.962111\pi\)
0.599303 + 0.800523i \(0.295445\pi\)
\(948\) 15.2622i 0.495693i
\(949\) 0.163408 + 40.4288i 0.00530446 + 1.31238i
\(950\) −18.4263 + 16.7887i −0.597829 + 0.544698i
\(951\) −1.64433 0.949353i −0.0533210 0.0307849i
\(952\) 10.1682 + 5.87064i 0.329555 + 0.190269i
\(953\) −33.2441 + 19.1935i −1.07688 + 0.621739i −0.930054 0.367423i \(-0.880240\pi\)
−0.146830 + 0.989162i \(0.546907\pi\)
\(954\) 0.249936i 0.00809199i
\(955\) 9.55343 1.03256i 0.309142 0.0334128i
\(956\) −19.5220 + 11.2710i −0.631386 + 0.364531i
\(957\) 0.714509 0.0230968
\(958\) −4.44961 + 2.56899i −0.143760 + 0.0830002i
\(959\) −10.7309 + 18.5865i −0.346520 + 0.600191i
\(960\) −1.39411 + 1.01916i −0.0449946 + 0.0328934i
\(961\) 30.3737 0.979797
\(962\) −8.77513 + 5.11373i −0.282922 + 0.164873i
\(963\) 18.8862i 0.608598i
\(964\) 17.3265 + 10.0035i 0.558049 + 0.322190i
\(965\) 8.35567 + 11.4297i 0.268978 + 0.367934i
\(966\) 3.22954 + 5.59373i 0.103909 + 0.179975i
\(967\) −2.66874 −0.0858209 −0.0429104 0.999079i \(-0.513663\pi\)
−0.0429104 + 0.999079i \(0.513663\pi\)
\(968\) −9.72839 16.8501i −0.312682 0.541582i
\(969\) −23.9075 + 13.8030i −0.768018 + 0.443416i
\(970\) 1.69005 3.82619i 0.0542642 0.122852i
\(971\) 20.4823 + 35.4763i 0.657307 + 1.13849i 0.981310 + 0.192433i \(0.0616380\pi\)
−0.324003 + 0.946056i \(0.605029\pi\)
\(972\) 1.42845 + 0.824717i 0.0458176 + 0.0264528i
\(973\) −9.32222 + 16.1466i −0.298857 + 0.517635i
\(974\) −16.8839 −0.540994
\(975\) −17.5957 + 3.92312i −0.563514 + 0.125640i
\(976\) 1.87309 0.0599561
\(977\) 21.7302 37.6377i 0.695209 1.20414i −0.274901 0.961473i \(-0.588645\pi\)
0.970110 0.242665i \(-0.0780217\pi\)
\(978\) −1.02277 0.590497i −0.0327046 0.0188820i
\(979\) 0.422377 + 0.731578i 0.0134992 + 0.0233813i
\(980\) −6.33788 + 14.3487i −0.202456 + 0.458352i
\(981\) −5.81377 + 3.35658i −0.185620 + 0.107167i
\(982\) 9.64549 + 16.7065i 0.307800 + 0.533125i
\(983\) 22.1143 0.705337 0.352669 0.935748i \(-0.385274\pi\)
0.352669 + 0.935748i \(0.385274\pi\)
\(984\) 9.57132 + 16.5780i 0.305123 + 0.528488i
\(985\) 29.3509 + 40.1490i 0.935199 + 1.27925i
\(986\) −0.850305 0.490924i −0.0270792 0.0156342i
\(987\) 5.69696i 0.181336i
\(988\) −24.8628 + 43.4684i −0.790990 + 1.38291i
\(989\) 14.6904 0.467128
\(990\) 1.50980 1.10374i 0.0479846 0.0350792i
\(991\) −21.4294 + 37.1168i −0.680727 + 1.17905i 0.294033 + 0.955795i \(0.405003\pi\)
−0.974759 + 0.223258i \(0.928331\pi\)
\(992\) −3.78130 + 2.18314i −0.120057 + 0.0693147i
\(993\) 20.2813 0.643607
\(994\) 0.930141 0.537017i 0.0295023 0.0170332i
\(995\) 9.76897 1.05585i 0.309697 0.0334728i
\(996\) 6.64065i 0.210417i
\(997\) −22.6378 + 13.0699i −0.716946 + 0.413929i −0.813627 0.581387i \(-0.802510\pi\)
0.0966819 + 0.995315i \(0.469177\pi\)
\(998\) −14.4777 8.35872i −0.458285 0.264591i
\(999\) 4.12017 + 2.37878i 0.130356 + 0.0752614i
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 195.2.v.a.4.10 yes 32
3.2 odd 2 585.2.bf.c.199.7 32
5.2 odd 4 975.2.bc.m.901.5 16
5.3 odd 4 975.2.bc.n.901.4 16
5.4 even 2 inner 195.2.v.a.4.7 32
13.10 even 6 inner 195.2.v.a.49.7 yes 32
15.14 odd 2 585.2.bf.c.199.10 32
39.23 odd 6 585.2.bf.c.244.10 32
65.23 odd 12 975.2.bc.n.751.4 16
65.49 even 6 inner 195.2.v.a.49.10 yes 32
65.62 odd 12 975.2.bc.m.751.5 16
195.179 odd 6 585.2.bf.c.244.7 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
195.2.v.a.4.7 32 5.4 even 2 inner
195.2.v.a.4.10 yes 32 1.1 even 1 trivial
195.2.v.a.49.7 yes 32 13.10 even 6 inner
195.2.v.a.49.10 yes 32 65.49 even 6 inner
585.2.bf.c.199.7 32 3.2 odd 2
585.2.bf.c.199.10 32 15.14 odd 2
585.2.bf.c.244.7 32 195.179 odd 6
585.2.bf.c.244.10 32 39.23 odd 6
975.2.bc.m.751.5 16 65.62 odd 12
975.2.bc.m.901.5 16 5.2 odd 4
975.2.bc.n.751.4 16 65.23 odd 12
975.2.bc.n.901.4 16 5.3 odd 4