Properties

Label 43.3.d.a.7.4
Level $43$
Weight $3$
Character 43.7
Analytic conductor $1.172$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [43,3,Mod(7,43)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(43, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([5]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("43.7");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 43 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 43.d (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: \(1.17166513675\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} + 37x^{10} + 483x^{8} + 2718x^{6} + 6923x^{4} + 7253x^{2} + 1849 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 7.4
Root \(1.51156i\) of defining polynomial
Character \(\chi\) \(=\) 43.7
Dual form 43.3.d.a.37.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.51156i q^{2} +(-3.66976 + 2.11873i) q^{3} +1.71518 q^{4} +(-4.51092 + 2.60438i) q^{5} +(-3.20260 - 5.54707i) q^{6} +(1.23619 + 0.713712i) q^{7} +8.63885i q^{8} +(4.47807 - 7.75625i) q^{9} +O(q^{10})\) \(q+1.51156i q^{2} +(-3.66976 + 2.11873i) q^{3} +1.71518 q^{4} +(-4.51092 + 2.60438i) q^{5} +(-3.20260 - 5.54707i) q^{6} +(1.23619 + 0.713712i) q^{7} +8.63885i q^{8} +(4.47807 - 7.75625i) q^{9} +(-3.93669 - 6.81854i) q^{10} +19.5852 q^{11} +(-6.29427 + 3.63400i) q^{12} +(4.99698 - 8.65502i) q^{13} +(-1.07882 + 1.86857i) q^{14} +(11.0360 - 19.1149i) q^{15} -6.19747 q^{16} +(-12.5438 + 21.7264i) q^{17} +(11.7241 + 6.76889i) q^{18} +(9.29850 - 5.36849i) q^{19} +(-7.73701 + 4.46697i) q^{20} -6.04866 q^{21} +29.6043i q^{22} +(-16.7391 - 28.9930i) q^{23} +(-18.3034 - 31.7025i) q^{24} +(1.06559 - 1.84565i) q^{25} +(13.0826 + 7.55325i) q^{26} -0.185841i q^{27} +(2.12027 + 1.22414i) q^{28} +(13.9164 + 8.03462i) q^{29} +(28.8934 + 16.6816i) q^{30} +(3.71424 + 6.43325i) q^{31} +25.1875i q^{32} +(-71.8730 + 41.4959i) q^{33} +(-32.8409 - 18.9607i) q^{34} -7.43511 q^{35} +(7.68068 - 13.3033i) q^{36} +(18.9142 - 10.9201i) q^{37} +(8.11482 + 14.0553i) q^{38} +42.3491i q^{39} +(-22.4989 - 38.9692i) q^{40} -22.3015 q^{41} -9.14294i q^{42} +(35.8442 - 23.7528i) q^{43} +33.5921 q^{44} +46.6504i q^{45} +(43.8248 - 25.3022i) q^{46} +78.3686 q^{47} +(22.7432 - 13.1308i) q^{48} +(-23.4812 - 40.6707i) q^{49} +(2.78982 + 1.61070i) q^{50} -106.308i q^{51} +(8.57070 - 14.8449i) q^{52} +(-13.1640 - 22.8006i) q^{53} +0.280911 q^{54} +(-88.3474 + 51.0074i) q^{55} +(-6.16565 + 10.6792i) q^{56} +(-22.7488 + 39.4021i) q^{57} +(-12.1448 + 21.0355i) q^{58} +39.1712 q^{59} +(18.9286 - 32.7854i) q^{60} +(-27.5478 - 15.9047i) q^{61} +(-9.72426 + 5.61430i) q^{62} +(11.0715 - 6.39211i) q^{63} -62.8625 q^{64} +52.0561i q^{65} +(-62.7237 - 108.641i) q^{66} +(61.2076 + 106.015i) q^{67} +(-21.5147 + 37.2646i) q^{68} +(122.857 + 70.9315i) q^{69} -11.2386i q^{70} +(-110.307 - 63.6857i) q^{71} +(67.0051 + 38.6854i) q^{72} +(14.9276 + 8.61845i) q^{73} +(16.5064 + 28.5900i) q^{74} +9.03079i q^{75} +(15.9486 - 9.20790i) q^{76} +(24.2110 + 13.9782i) q^{77} -64.0134 q^{78} +(-18.2494 + 31.6090i) q^{79} +(27.9563 - 16.1406i) q^{80} +(40.6964 + 70.4882i) q^{81} -33.7102i q^{82} +(-42.8675 - 74.2487i) q^{83} -10.3745 q^{84} -130.675i q^{85} +(35.9038 + 54.1808i) q^{86} -68.0929 q^{87} +169.194i q^{88} +(-11.1803 + 6.45493i) q^{89} -70.5150 q^{90} +(12.3544 - 7.13281i) q^{91} +(-28.7105 - 49.7281i) q^{92} +(-27.2607 - 15.7390i) q^{93} +118.459i q^{94} +(-27.9632 + 48.4336i) q^{95} +(-53.3657 - 92.4321i) q^{96} -113.142 q^{97} +(61.4763 - 35.4934i) q^{98} +(87.7041 - 151.908i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 26 q^{4} - 3 q^{5} - 9 q^{6} + 9 q^{7} - 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q - 26 q^{4} - 3 q^{5} - 9 q^{6} + 9 q^{7} - 12 q^{9} - q^{10} + 28 q^{11} - 6 q^{12} + 24 q^{13} - 18 q^{14} - 13 q^{15} + 110 q^{16} - 7 q^{17} + 33 q^{18} + 66 q^{19} - 99 q^{20} - 80 q^{21} - 16 q^{23} - 2 q^{24} - 21 q^{25} + 9 q^{26} - 192 q^{28} - 111 q^{29} + 99 q^{30} - 29 q^{31} - 114 q^{33} + 213 q^{34} + 38 q^{35} + 152 q^{36} + 120 q^{37} + 172 q^{38} - 29 q^{40} + 94 q^{41} + 5 q^{43} - 174 q^{44} + 156 q^{46} - 18 q^{47} - 213 q^{48} - 99 q^{49} - 198 q^{50} - 234 q^{52} - 58 q^{53} + 128 q^{54} - 258 q^{55} + 315 q^{56} + 51 q^{57} - 196 q^{58} + 336 q^{59} - 5 q^{60} + 204 q^{61} + 261 q^{62} - 153 q^{63} - 604 q^{64} - 201 q^{66} + 115 q^{67} - 106 q^{68} + 423 q^{69} - 66 q^{71} + 294 q^{72} + 249 q^{73} - 214 q^{74} - 438 q^{76} + 117 q^{77} + 136 q^{78} + 236 q^{79} + 681 q^{80} + 110 q^{81} - 4 q^{83} + 248 q^{84} + 102 q^{86} - 408 q^{87} - 45 q^{89} - 44 q^{90} - 156 q^{91} - 483 q^{92} - 567 q^{93} - 389 q^{95} - 278 q^{96} - 370 q^{97} - 879 q^{98} + 157 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/43\mathbb{Z}\right)^\times\).

\(n\) \(3\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.51156i 0.755782i 0.925850 + 0.377891i \(0.123351\pi\)
−0.925850 + 0.377891i \(0.876649\pi\)
\(3\) −3.66976 + 2.11873i −1.22325 + 0.706245i −0.965610 0.259996i \(-0.916279\pi\)
−0.257642 + 0.966240i \(0.582946\pi\)
\(4\) 1.71518 0.428794
\(5\) −4.51092 + 2.60438i −0.902184 + 0.520876i −0.877908 0.478829i \(-0.841061\pi\)
−0.0242756 + 0.999705i \(0.507728\pi\)
\(6\) −3.20260 5.54707i −0.533767 0.924512i
\(7\) 1.23619 + 0.713712i 0.176598 + 0.101959i 0.585693 0.810533i \(-0.300822\pi\)
−0.409095 + 0.912492i \(0.634156\pi\)
\(8\) 8.63885i 1.07986i
\(9\) 4.47807 7.75625i 0.497564 0.861805i
\(10\) −3.93669 6.81854i −0.393669 0.681854i
\(11\) 19.5852 1.78048 0.890238 0.455496i \(-0.150538\pi\)
0.890238 + 0.455496i \(0.150538\pi\)
\(12\) −6.29427 + 3.63400i −0.524523 + 0.302833i
\(13\) 4.99698 8.65502i 0.384383 0.665771i −0.607300 0.794472i \(-0.707748\pi\)
0.991683 + 0.128701i \(0.0410808\pi\)
\(14\) −1.07882 + 1.86857i −0.0770587 + 0.133469i
\(15\) 11.0360 19.1149i 0.735732 1.27433i
\(16\) −6.19747 −0.387342
\(17\) −12.5438 + 21.7264i −0.737868 + 1.27802i 0.215586 + 0.976485i \(0.430834\pi\)
−0.953454 + 0.301540i \(0.902499\pi\)
\(18\) 11.7241 + 6.76889i 0.651337 + 0.376049i
\(19\) 9.29850 5.36849i 0.489395 0.282552i −0.234929 0.972013i \(-0.575486\pi\)
0.724323 + 0.689460i \(0.242152\pi\)
\(20\) −7.73701 + 4.46697i −0.386851 + 0.223348i
\(21\) −6.04866 −0.288032
\(22\) 29.6043i 1.34565i
\(23\) −16.7391 28.9930i −0.727788 1.26057i −0.957816 0.287381i \(-0.907215\pi\)
0.230029 0.973184i \(-0.426118\pi\)
\(24\) −18.3034 31.7025i −0.762643 1.32094i
\(25\) 1.06559 1.84565i 0.0426235 0.0738261i
\(26\) 13.0826 + 7.55325i 0.503178 + 0.290510i
\(27\) 0.185841i 0.00688300i
\(28\) 2.12027 + 1.22414i 0.0757241 + 0.0437193i
\(29\) 13.9164 + 8.03462i 0.479875 + 0.277056i 0.720364 0.693596i \(-0.243975\pi\)
−0.240490 + 0.970652i \(0.577308\pi\)
\(30\) 28.8934 + 16.6816i 0.963112 + 0.556053i
\(31\) 3.71424 + 6.43325i 0.119814 + 0.207524i 0.919694 0.392636i \(-0.128437\pi\)
−0.799880 + 0.600160i \(0.795103\pi\)
\(32\) 25.1875i 0.787110i
\(33\) −71.8730 + 41.4959i −2.17797 + 1.25745i
\(34\) −32.8409 18.9607i −0.965908 0.557667i
\(35\) −7.43511 −0.212432
\(36\) 7.68068 13.3033i 0.213352 0.369537i
\(37\) 18.9142 10.9201i 0.511194 0.295138i −0.222130 0.975017i \(-0.571301\pi\)
0.733324 + 0.679879i \(0.237968\pi\)
\(38\) 8.11482 + 14.0553i 0.213548 + 0.369876i
\(39\) 42.3491i 1.08587i
\(40\) −22.4989 38.9692i −0.562471 0.974229i
\(41\) −22.3015 −0.543940 −0.271970 0.962306i \(-0.587675\pi\)
−0.271970 + 0.962306i \(0.587675\pi\)
\(42\) 9.14294i 0.217689i
\(43\) 35.8442 23.7528i 0.833586 0.552390i
\(44\) 33.5921 0.763457
\(45\) 46.6504i 1.03668i
\(46\) 43.8248 25.3022i 0.952712 0.550049i
\(47\) 78.3686 1.66742 0.833709 0.552204i \(-0.186213\pi\)
0.833709 + 0.552204i \(0.186213\pi\)
\(48\) 22.7432 13.1308i 0.473817 0.273558i
\(49\) −23.4812 40.6707i −0.479209 0.830014i
\(50\) 2.78982 + 1.61070i 0.0557964 + 0.0322141i
\(51\) 106.308i 2.08446i
\(52\) 8.57070 14.8449i 0.164821 0.285478i
\(53\) −13.1640 22.8006i −0.248376 0.430201i 0.714699 0.699432i \(-0.246564\pi\)
−0.963076 + 0.269231i \(0.913230\pi\)
\(54\) 0.280911 0.00520205
\(55\) −88.3474 + 51.0074i −1.60632 + 0.927407i
\(56\) −6.16565 + 10.6792i −0.110101 + 0.190700i
\(57\) −22.7488 + 39.4021i −0.399102 + 0.691265i
\(58\) −12.1448 + 21.0355i −0.209394 + 0.362680i
\(59\) 39.1712 0.663919 0.331959 0.943294i \(-0.392290\pi\)
0.331959 + 0.943294i \(0.392290\pi\)
\(60\) 18.9286 32.7854i 0.315477 0.546423i
\(61\) −27.5478 15.9047i −0.451603 0.260733i 0.256904 0.966437i \(-0.417298\pi\)
−0.708507 + 0.705704i \(0.750631\pi\)
\(62\) −9.72426 + 5.61430i −0.156843 + 0.0905533i
\(63\) 11.0715 6.39211i 0.175737 0.101462i
\(64\) −62.8625 −0.982226
\(65\) 52.0561i 0.800864i
\(66\) −62.7237 108.641i −0.950359 1.64607i
\(67\) 61.2076 + 106.015i 0.913546 + 1.58231i 0.809016 + 0.587787i \(0.200001\pi\)
0.104530 + 0.994522i \(0.466666\pi\)
\(68\) −21.5147 + 37.2646i −0.316393 + 0.548009i
\(69\) 122.857 + 70.9315i 1.78054 + 1.02799i
\(70\) 11.2386i 0.160552i
\(71\) −110.307 63.6857i −1.55362 0.896982i −0.997843 0.0656495i \(-0.979088\pi\)
−0.555776 0.831332i \(-0.687579\pi\)
\(72\) 67.0051 + 38.6854i 0.930626 + 0.537297i
\(73\) 14.9276 + 8.61845i 0.204488 + 0.118061i 0.598747 0.800938i \(-0.295666\pi\)
−0.394259 + 0.918999i \(0.628999\pi\)
\(74\) 16.5064 + 28.5900i 0.223060 + 0.386351i
\(75\) 9.03079i 0.120411i
\(76\) 15.9486 9.20790i 0.209849 0.121157i
\(77\) 24.2110 + 13.9782i 0.314428 + 0.181535i
\(78\) −64.0134 −0.820684
\(79\) −18.2494 + 31.6090i −0.231006 + 0.400113i −0.958104 0.286419i \(-0.907535\pi\)
0.727099 + 0.686533i \(0.240868\pi\)
\(80\) 27.9563 16.1406i 0.349454 0.201757i
\(81\) 40.6964 + 70.4882i 0.502425 + 0.870225i
\(82\) 33.7102i 0.411100i
\(83\) −42.8675 74.2487i −0.516476 0.894562i −0.999817 0.0191303i \(-0.993910\pi\)
0.483341 0.875432i \(-0.339423\pi\)
\(84\) −10.3745 −0.123506
\(85\) 130.675i 1.53735i
\(86\) 35.9038 + 54.1808i 0.417487 + 0.630009i
\(87\) −68.0929 −0.782677
\(88\) 169.194i 1.92266i
\(89\) −11.1803 + 6.45493i −0.125621 + 0.0725273i −0.561494 0.827481i \(-0.689773\pi\)
0.435873 + 0.900008i \(0.356440\pi\)
\(90\) −70.5150 −0.783501
\(91\) 12.3544 7.13281i 0.135763 0.0783825i
\(92\) −28.7105 49.7281i −0.312071 0.540523i
\(93\) −27.2607 15.7390i −0.293126 0.169236i
\(94\) 118.459i 1.26020i
\(95\) −27.9632 + 48.4336i −0.294349 + 0.509828i
\(96\) −53.3657 92.4321i −0.555893 0.962834i
\(97\) −113.142 −1.16642 −0.583208 0.812323i \(-0.698203\pi\)
−0.583208 + 0.812323i \(0.698203\pi\)
\(98\) 61.4763 35.4934i 0.627310 0.362177i
\(99\) 87.7041 151.908i 0.885900 1.53442i
\(100\) 1.82767 3.16562i 0.0182767 0.0316562i
\(101\) 34.0992 59.0615i 0.337616 0.584768i −0.646368 0.763026i \(-0.723713\pi\)
0.983984 + 0.178258i \(0.0570462\pi\)
\(102\) 160.691 1.57540
\(103\) 31.5613 54.6657i 0.306420 0.530735i −0.671156 0.741316i \(-0.734202\pi\)
0.977576 + 0.210581i \(0.0675355\pi\)
\(104\) 74.7695 + 43.1682i 0.718937 + 0.415079i
\(105\) 27.2850 15.7530i 0.259857 0.150029i
\(106\) 34.4646 19.8982i 0.325138 0.187718i
\(107\) −109.460 −1.02299 −0.511497 0.859285i \(-0.670909\pi\)
−0.511497 + 0.859285i \(0.670909\pi\)
\(108\) 0.318750i 0.00295139i
\(109\) 17.3755 + 30.0953i 0.159408 + 0.276103i 0.934655 0.355555i \(-0.115708\pi\)
−0.775247 + 0.631658i \(0.782375\pi\)
\(110\) −77.1009 133.543i −0.700918 1.21402i
\(111\) −46.2736 + 80.1483i −0.416879 + 0.722056i
\(112\) −7.66123 4.42321i −0.0684038 0.0394930i
\(113\) 25.0080i 0.221310i −0.993859 0.110655i \(-0.964705\pi\)
0.993859 0.110655i \(-0.0352949\pi\)
\(114\) −59.5588 34.3863i −0.522445 0.301634i
\(115\) 151.018 + 87.1900i 1.31320 + 0.758174i
\(116\) 23.8690 + 13.7808i 0.205767 + 0.118800i
\(117\) −44.7537 77.5156i −0.382510 0.662527i
\(118\) 59.2098i 0.501778i
\(119\) −31.0128 + 17.9053i −0.260612 + 0.150464i
\(120\) 165.131 + 95.3382i 1.37609 + 0.794485i
\(121\) 262.582 2.17010
\(122\) 24.0410 41.6402i 0.197057 0.341313i
\(123\) 81.8412 47.2510i 0.665375 0.384155i
\(124\) 6.37056 + 11.0341i 0.0513755 + 0.0889850i
\(125\) 119.118i 0.952946i
\(126\) 9.66208 + 16.7352i 0.0766831 + 0.132819i
\(127\) −27.5460 −0.216897 −0.108449 0.994102i \(-0.534588\pi\)
−0.108449 + 0.994102i \(0.534588\pi\)
\(128\) 5.72951i 0.0447618i
\(129\) −81.2135 + 163.111i −0.629562 + 1.26443i
\(130\) −78.6862 −0.605278
\(131\) 30.8157i 0.235234i −0.993059 0.117617i \(-0.962474\pi\)
0.993059 0.117617i \(-0.0375256\pi\)
\(132\) −123.275 + 71.1728i −0.933900 + 0.539188i
\(133\) 15.3262 0.115235
\(134\) −160.248 + 92.5192i −1.19588 + 0.690442i
\(135\) 0.484001 + 0.838314i 0.00358519 + 0.00620973i
\(136\) −187.691 108.364i −1.38008 0.796792i
\(137\) 171.866i 1.25450i −0.778819 0.627249i \(-0.784181\pi\)
0.778819 0.627249i \(-0.215819\pi\)
\(138\) −107.217 + 185.706i −0.776938 + 1.34570i
\(139\) 30.8690 + 53.4666i 0.222079 + 0.384652i 0.955439 0.295188i \(-0.0953824\pi\)
−0.733360 + 0.679840i \(0.762049\pi\)
\(140\) −12.7525 −0.0910894
\(141\) −287.594 + 166.042i −2.03967 + 1.17761i
\(142\) 96.2650 166.736i 0.677923 1.17420i
\(143\) 97.8671 169.511i 0.684385 1.18539i
\(144\) −27.7527 + 48.0691i −0.192727 + 0.333814i
\(145\) −83.7008 −0.577247
\(146\) −13.0273 + 22.5640i −0.0892283 + 0.154548i
\(147\) 172.341 + 99.5010i 1.17239 + 0.676877i
\(148\) 32.4411 18.7299i 0.219197 0.126553i
\(149\) −180.832 + 104.403i −1.21364 + 0.700694i −0.963550 0.267529i \(-0.913793\pi\)
−0.250088 + 0.968223i \(0.580459\pi\)
\(150\) −13.6506 −0.0910041
\(151\) 154.264i 1.02162i −0.859694 0.510810i \(-0.829346\pi\)
0.859694 0.510810i \(-0.170654\pi\)
\(152\) 46.3776 + 80.3283i 0.305116 + 0.528476i
\(153\) 112.344 + 194.585i 0.734272 + 1.27180i
\(154\) −21.1290 + 36.5964i −0.137201 + 0.237639i
\(155\) −33.5092 19.3466i −0.216189 0.124817i
\(156\) 72.6361i 0.465616i
\(157\) 137.667 + 79.4818i 0.876857 + 0.506254i 0.869621 0.493720i \(-0.164363\pi\)
0.00723635 + 0.999974i \(0.497697\pi\)
\(158\) −47.7790 27.5852i −0.302399 0.174590i
\(159\) 96.6170 + 55.7818i 0.607654 + 0.350829i
\(160\) −65.5979 113.619i −0.409987 0.710118i
\(161\) 47.7876i 0.296818i
\(162\) −106.547 + 61.5152i −0.657700 + 0.379723i
\(163\) −34.1370 19.7090i −0.209429 0.120914i 0.391617 0.920128i \(-0.371916\pi\)
−0.601046 + 0.799214i \(0.705249\pi\)
\(164\) −38.2510 −0.233238
\(165\) 216.142 374.369i 1.30995 2.26891i
\(166\) 112.232 64.7969i 0.676094 0.390343i
\(167\) 99.7184 + 172.717i 0.597116 + 1.03424i 0.993244 + 0.116041i \(0.0370203\pi\)
−0.396128 + 0.918195i \(0.629646\pi\)
\(168\) 52.2535i 0.311033i
\(169\) 34.5604 + 59.8603i 0.204499 + 0.354203i
\(170\) 197.523 1.16190
\(171\) 96.1619i 0.562351i
\(172\) 61.4790 40.7402i 0.357436 0.236862i
\(173\) −86.0652 −0.497487 −0.248743 0.968569i \(-0.580018\pi\)
−0.248743 + 0.968569i \(0.580018\pi\)
\(174\) 102.927i 0.591533i
\(175\) 2.63453 1.52105i 0.0150545 0.00869169i
\(176\) −121.379 −0.689653
\(177\) −143.749 + 82.9934i −0.812140 + 0.468889i
\(178\) −9.75704 16.8997i −0.0548148 0.0949421i
\(179\) −70.6225 40.7739i −0.394539 0.227787i 0.289586 0.957152i \(-0.406482\pi\)
−0.684125 + 0.729365i \(0.739816\pi\)
\(180\) 80.0136i 0.444520i
\(181\) −84.7687 + 146.824i −0.468335 + 0.811181i −0.999345 0.0361849i \(-0.988479\pi\)
0.531010 + 0.847366i \(0.321813\pi\)
\(182\) 10.7817 + 18.6744i 0.0592401 + 0.102607i
\(183\) 134.791 0.736566
\(184\) 250.466 144.607i 1.36123 0.785906i
\(185\) −56.8802 + 98.5194i −0.307461 + 0.532537i
\(186\) 23.7904 41.2063i 0.127906 0.221539i
\(187\) −245.672 + 425.517i −1.31376 + 2.27549i
\(188\) 134.416 0.714978
\(189\) 0.132637 0.229734i 0.000701783 0.00121552i
\(190\) −73.2105 42.2681i −0.385319 0.222464i
\(191\) 85.6498 49.4499i 0.448428 0.258900i −0.258738 0.965948i \(-0.583307\pi\)
0.707166 + 0.707047i \(0.249973\pi\)
\(192\) 230.690 133.189i 1.20151 0.693692i
\(193\) −243.765 −1.26303 −0.631515 0.775363i \(-0.717567\pi\)
−0.631515 + 0.775363i \(0.717567\pi\)
\(194\) 171.022i 0.881556i
\(195\) −110.293 191.033i −0.565606 0.979658i
\(196\) −40.2744 69.7573i −0.205482 0.355905i
\(197\) 160.733 278.398i 0.815903 1.41319i −0.0927748 0.995687i \(-0.529574\pi\)
0.908678 0.417498i \(-0.137093\pi\)
\(198\) 229.619 + 132.570i 1.15969 + 0.669547i
\(199\) 39.2071i 0.197021i 0.995136 + 0.0985103i \(0.0314077\pi\)
−0.995136 + 0.0985103i \(0.968592\pi\)
\(200\) 15.9443 + 9.20546i 0.0797216 + 0.0460273i
\(201\) −449.234 259.365i −2.23499 1.29037i
\(202\) 89.2753 + 51.5431i 0.441957 + 0.255164i
\(203\) 11.4688 + 19.8645i 0.0564966 + 0.0978549i
\(204\) 182.336i 0.893804i
\(205\) 100.600 58.0817i 0.490734 0.283325i
\(206\) 82.6307 + 47.7069i 0.401120 + 0.231587i
\(207\) −299.836 −1.44848
\(208\) −30.9687 + 53.6393i −0.148888 + 0.257881i
\(209\) 182.113 105.143i 0.871355 0.503077i
\(210\) 23.8117 + 41.2431i 0.113389 + 0.196396i
\(211\) 378.026i 1.79159i 0.444466 + 0.895796i \(0.353394\pi\)
−0.444466 + 0.895796i \(0.646606\pi\)
\(212\) −22.5785 39.1071i −0.106502 0.184467i
\(213\) 539.732 2.53396
\(214\) 165.456i 0.773161i
\(215\) −99.8289 + 200.499i −0.464320 + 0.932552i
\(216\) 1.60545 0.00743266
\(217\) 10.6036i 0.0488644i
\(218\) −45.4909 + 26.2642i −0.208674 + 0.120478i
\(219\) −73.0408 −0.333520
\(220\) −151.531 + 87.4866i −0.688778 + 0.397666i
\(221\) 125.362 + 217.133i 0.567248 + 0.982502i
\(222\) −121.149 69.9455i −0.545717 0.315070i
\(223\) 222.482i 0.997678i −0.866695 0.498839i \(-0.833760\pi\)
0.866695 0.498839i \(-0.166240\pi\)
\(224\) −17.9766 + 31.1365i −0.0802529 + 0.139002i
\(225\) −9.54356 16.5299i −0.0424158 0.0734664i
\(226\) 37.8012 0.167262
\(227\) −175.306 + 101.213i −0.772271 + 0.445871i −0.833684 0.552241i \(-0.813773\pi\)
0.0614129 + 0.998112i \(0.480439\pi\)
\(228\) −39.0182 + 67.5815i −0.171132 + 0.296410i
\(229\) 70.4417 122.009i 0.307606 0.532789i −0.670232 0.742151i \(-0.733806\pi\)
0.977838 + 0.209363i \(0.0671389\pi\)
\(230\) −131.793 + 228.273i −0.573014 + 0.992490i
\(231\) −118.465 −0.512833
\(232\) −69.4098 + 120.221i −0.299180 + 0.518196i
\(233\) 43.7817 + 25.2774i 0.187904 + 0.108487i 0.591001 0.806671i \(-0.298733\pi\)
−0.403097 + 0.915157i \(0.632066\pi\)
\(234\) 117.170 67.6480i 0.500726 0.289094i
\(235\) −353.515 + 204.102i −1.50432 + 0.868518i
\(236\) 67.1855 0.284684
\(237\) 154.663i 0.652586i
\(238\) −27.0649 46.8778i −0.113718 0.196966i
\(239\) −5.88438 10.1920i −0.0246208 0.0426445i 0.853452 0.521171i \(-0.174505\pi\)
−0.878073 + 0.478526i \(0.841171\pi\)
\(240\) −68.3952 + 118.464i −0.284980 + 0.493600i
\(241\) 131.634 + 75.9987i 0.546198 + 0.315348i 0.747587 0.664164i \(-0.231212\pi\)
−0.201389 + 0.979511i \(0.564546\pi\)
\(242\) 396.909i 1.64012i
\(243\) −297.243 171.613i −1.22322 0.706228i
\(244\) −47.2493 27.2794i −0.193645 0.111801i
\(245\) 211.844 + 122.308i 0.864669 + 0.499217i
\(246\) 71.4229 + 123.708i 0.290337 + 0.502879i
\(247\) 107.305i 0.434433i
\(248\) −55.5759 + 32.0867i −0.224096 + 0.129382i
\(249\) 314.626 + 181.650i 1.26356 + 0.729517i
\(250\) 180.055 0.720219
\(251\) −21.4395 + 37.1344i −0.0854165 + 0.147946i −0.905569 0.424200i \(-0.860555\pi\)
0.820152 + 0.572146i \(0.193889\pi\)
\(252\) 18.9895 10.9636i 0.0753551 0.0435063i
\(253\) −327.840 567.835i −1.29581 2.24441i
\(254\) 41.6375i 0.163927i
\(255\) 276.865 + 479.545i 1.08575 + 1.88057i
\(256\) −260.110 −1.01606
\(257\) 169.737i 0.660455i 0.943901 + 0.330227i \(0.107125\pi\)
−0.943901 + 0.330227i \(0.892875\pi\)
\(258\) −246.553 122.759i −0.955632 0.475812i
\(259\) 31.1752 0.120368
\(260\) 89.2854i 0.343405i
\(261\) 124.637 71.9592i 0.477536 0.275706i
\(262\) 46.5799 0.177786
\(263\) 241.781 139.592i 0.919319 0.530769i 0.0359012 0.999355i \(-0.488570\pi\)
0.883418 + 0.468586i \(0.155237\pi\)
\(264\) −358.477 620.901i −1.35787 2.35190i
\(265\) 118.763 + 68.5679i 0.448162 + 0.258747i
\(266\) 23.1666i 0.0870923i
\(267\) 27.3526 47.3760i 0.102444 0.177438i
\(268\) 104.982 + 181.834i 0.391723 + 0.678484i
\(269\) −112.264 −0.417337 −0.208668 0.977986i \(-0.566913\pi\)
−0.208668 + 0.977986i \(0.566913\pi\)
\(270\) −1.26717 + 0.731598i −0.00469320 + 0.00270962i
\(271\) −16.6159 + 28.7796i −0.0613133 + 0.106198i −0.895053 0.445960i \(-0.852862\pi\)
0.833739 + 0.552158i \(0.186196\pi\)
\(272\) 77.7396 134.649i 0.285807 0.495033i
\(273\) −30.2251 + 52.3513i −0.110715 + 0.191763i
\(274\) 259.787 0.948127
\(275\) 20.8698 36.1476i 0.0758902 0.131446i
\(276\) 210.721 + 121.660i 0.763482 + 0.440797i
\(277\) 81.5518 47.0839i 0.294411 0.169978i −0.345519 0.938412i \(-0.612297\pi\)
0.639929 + 0.768434i \(0.278964\pi\)
\(278\) −80.8182 + 46.6604i −0.290713 + 0.167843i
\(279\) 66.5305 0.238460
\(280\) 64.2308i 0.229396i
\(281\) −38.5912 66.8420i −0.137335 0.237872i 0.789152 0.614198i \(-0.210520\pi\)
−0.926487 + 0.376326i \(0.877187\pi\)
\(282\) −250.984 434.716i −0.890013 1.54155i
\(283\) 82.1091 142.217i 0.290138 0.502534i −0.683704 0.729759i \(-0.739632\pi\)
0.973842 + 0.227225i \(0.0729654\pi\)
\(284\) −189.196 109.232i −0.666182 0.384620i
\(285\) 236.986i 0.831530i
\(286\) 256.226 + 147.932i 0.895896 + 0.517246i
\(287\) −27.5688 15.9169i −0.0960586 0.0554595i
\(288\) 195.361 + 112.792i 0.678336 + 0.391637i
\(289\) −170.192 294.781i −0.588898 1.02000i
\(290\) 126.519i 0.436273i
\(291\) 415.205 239.719i 1.42682 0.823775i
\(292\) 25.6034 + 14.7822i 0.0876830 + 0.0506238i
\(293\) 177.674 0.606394 0.303197 0.952928i \(-0.401946\pi\)
0.303197 + 0.952928i \(0.401946\pi\)
\(294\) −150.402 + 260.504i −0.511572 + 0.886068i
\(295\) −176.698 + 102.017i −0.598977 + 0.345819i
\(296\) 94.3372 + 163.397i 0.318707 + 0.552016i
\(297\) 3.63974i 0.0122550i
\(298\) −157.812 273.339i −0.529572 0.917245i
\(299\) −334.580 −1.11900
\(300\) 15.4894i 0.0516313i
\(301\) 61.2627 3.78043i 0.203531 0.0125596i
\(302\) 233.181 0.772121
\(303\) 288.989i 0.953757i
\(304\) −57.6272 + 33.2711i −0.189563 + 0.109444i
\(305\) 165.688 0.543238
\(306\) −294.128 + 169.815i −0.961201 + 0.554950i
\(307\) −120.549 208.796i −0.392666 0.680118i 0.600134 0.799900i \(-0.295114\pi\)
−0.992800 + 0.119781i \(0.961781\pi\)
\(308\) 41.5261 + 23.9751i 0.134825 + 0.0778412i
\(309\) 267.480i 0.865630i
\(310\) 29.2436 50.6513i 0.0943341 0.163391i
\(311\) 23.5430 + 40.7777i 0.0757009 + 0.131118i 0.901391 0.433006i \(-0.142547\pi\)
−0.825690 + 0.564124i \(0.809214\pi\)
\(312\) −365.848 −1.17259
\(313\) 3.18599 1.83943i 0.0101789 0.00587678i −0.494902 0.868949i \(-0.664796\pi\)
0.505081 + 0.863072i \(0.331463\pi\)
\(314\) −120.142 + 208.092i −0.382617 + 0.662713i
\(315\) −33.2949 + 57.6685i −0.105698 + 0.183075i
\(316\) −31.3010 + 54.2149i −0.0990538 + 0.171566i
\(317\) −78.3317 −0.247103 −0.123552 0.992338i \(-0.539428\pi\)
−0.123552 + 0.992338i \(0.539428\pi\)
\(318\) −84.3178 + 146.043i −0.265150 + 0.459254i
\(319\) 272.555 + 157.360i 0.854405 + 0.493291i
\(320\) 283.567 163.718i 0.886148 0.511618i
\(321\) 401.693 231.918i 1.25138 0.722484i
\(322\) 72.2341 0.224329
\(323\) 269.364i 0.833945i
\(324\) 69.8014 + 120.900i 0.215437 + 0.373147i
\(325\) −10.6494 18.4454i −0.0327675 0.0567550i
\(326\) 29.7914 51.6002i 0.0913847 0.158283i
\(327\) −127.528 73.6282i −0.389993 0.225163i
\(328\) 192.660i 0.587377i
\(329\) 96.8782 + 55.9326i 0.294463 + 0.170008i
\(330\) 565.883 + 326.713i 1.71480 + 0.990039i
\(331\) −65.0459 37.5543i −0.196513 0.113457i 0.398515 0.917162i \(-0.369526\pi\)
−0.595028 + 0.803705i \(0.702859\pi\)
\(332\) −73.5253 127.349i −0.221462 0.383583i
\(333\) 195.604i 0.587400i
\(334\) −261.073 + 150.731i −0.781657 + 0.451290i
\(335\) −552.205 318.816i −1.64837 0.951688i
\(336\) 37.4864 0.111567
\(337\) −131.845 + 228.363i −0.391232 + 0.677634i −0.992612 0.121329i \(-0.961284\pi\)
0.601380 + 0.798963i \(0.294618\pi\)
\(338\) −90.4827 + 52.2402i −0.267700 + 0.154557i
\(339\) 52.9854 + 91.7734i 0.156299 + 0.270718i
\(340\) 224.130i 0.659206i
\(341\) 72.7442 + 125.997i 0.213326 + 0.369492i
\(342\) 145.355 0.425014
\(343\) 136.979i 0.399356i
\(344\) 205.197 + 309.653i 0.596502 + 0.900153i
\(345\) −738.930 −2.14183
\(346\) 130.093i 0.375991i
\(347\) 508.938 293.836i 1.46668 0.846789i 0.467376 0.884059i \(-0.345199\pi\)
0.999305 + 0.0372699i \(0.0118661\pi\)
\(348\) −116.791 −0.335607
\(349\) 384.482 221.981i 1.10167 0.636048i 0.165009 0.986292i \(-0.447235\pi\)
0.936659 + 0.350244i \(0.113901\pi\)
\(350\) 2.29916 + 3.98226i 0.00656902 + 0.0113779i
\(351\) −1.60846 0.928644i −0.00458250 0.00264571i
\(352\) 493.304i 1.40143i
\(353\) −298.730 + 517.416i −0.846262 + 1.46577i 0.0382591 + 0.999268i \(0.487819\pi\)
−0.884521 + 0.466501i \(0.845515\pi\)
\(354\) −125.450 217.285i −0.354378 0.613801i
\(355\) 663.447 1.86887
\(356\) −19.1761 + 11.0713i −0.0538655 + 0.0310993i
\(357\) 75.8730 131.416i 0.212529 0.368112i
\(358\) 61.6324 106.750i 0.172158 0.298186i
\(359\) 127.194 220.307i 0.354302 0.613668i −0.632697 0.774400i \(-0.718052\pi\)
0.986998 + 0.160731i \(0.0513853\pi\)
\(360\) −403.006 −1.11946
\(361\) −122.859 + 212.797i −0.340329 + 0.589466i
\(362\) −221.933 128.133i −0.613076 0.353959i
\(363\) −963.610 + 556.341i −2.65457 + 1.53262i
\(364\) 21.1899 12.2340i 0.0582141 0.0336099i
\(365\) −89.7829 −0.245980
\(366\) 203.746i 0.556683i
\(367\) −142.193 246.286i −0.387447 0.671078i 0.604658 0.796485i \(-0.293310\pi\)
−0.992105 + 0.125407i \(0.959976\pi\)
\(368\) 103.740 + 179.683i 0.281903 + 0.488270i
\(369\) −99.8679 + 172.976i −0.270645 + 0.468770i
\(370\) −148.918 85.9781i −0.402482 0.232373i
\(371\) 37.5811i 0.101297i
\(372\) −46.7568 26.9951i −0.125690 0.0725674i
\(373\) −229.260 132.363i −0.614637 0.354861i 0.160141 0.987094i \(-0.448805\pi\)
−0.774778 + 0.632233i \(0.782138\pi\)
\(374\) −643.196 371.350i −1.71978 0.992913i
\(375\) 252.380 + 437.135i 0.673013 + 1.16569i
\(376\) 677.015i 1.80057i
\(377\) 139.080 80.2976i 0.368911 0.212991i
\(378\) 0.347258 + 0.200489i 0.000918671 + 0.000530395i
\(379\) −98.0731 −0.258768 −0.129384 0.991595i \(-0.541300\pi\)
−0.129384 + 0.991595i \(0.541300\pi\)
\(380\) −47.9617 + 83.0722i −0.126215 + 0.218611i
\(381\) 101.087 58.3626i 0.265320 0.153183i
\(382\) 74.7467 + 129.465i 0.195672 + 0.338914i
\(383\) 439.727i 1.14811i −0.818816 0.574056i \(-0.805369\pi\)
0.818816 0.574056i \(-0.194631\pi\)
\(384\) −12.1393 21.0259i −0.0316128 0.0547550i
\(385\) −145.618 −0.378230
\(386\) 368.466i 0.954576i
\(387\) −23.7197 384.383i −0.0612911 0.993238i
\(388\) −194.059 −0.500152
\(389\) 279.833i 0.719366i 0.933075 + 0.359683i \(0.117115\pi\)
−0.933075 + 0.359683i \(0.882885\pi\)
\(390\) 288.759 166.715i 0.740408 0.427475i
\(391\) 839.886 2.14804
\(392\) 351.348 202.851i 0.896296 0.517477i
\(393\) 65.2903 + 113.086i 0.166133 + 0.287751i
\(394\) 420.816 + 242.958i 1.06806 + 0.616645i
\(395\) 190.114i 0.481301i
\(396\) 150.428 260.549i 0.379868 0.657951i
\(397\) −108.633 188.157i −0.273634 0.473948i 0.696156 0.717891i \(-0.254892\pi\)
−0.969790 + 0.243943i \(0.921559\pi\)
\(398\) −59.2640 −0.148905
\(399\) −56.2435 + 32.4722i −0.140961 + 0.0813840i
\(400\) −6.60396 + 11.4384i −0.0165099 + 0.0285960i
\(401\) −203.564 + 352.583i −0.507641 + 0.879260i 0.492320 + 0.870414i \(0.336149\pi\)
−0.999961 + 0.00884561i \(0.997184\pi\)
\(402\) 392.047 679.046i 0.975242 1.68917i
\(403\) 74.2399 0.184218
\(404\) 58.4861 101.301i 0.144768 0.250745i
\(405\) −367.156 211.978i −0.906559 0.523402i
\(406\) −30.0265 + 17.3358i −0.0739570 + 0.0426991i
\(407\) 370.439 213.873i 0.910169 0.525486i
\(408\) 918.375 2.25092
\(409\) 63.1215i 0.154331i −0.997018 0.0771656i \(-0.975413\pi\)
0.997018 0.0771656i \(-0.0245870\pi\)
\(410\) 87.7941 + 152.064i 0.214132 + 0.370888i
\(411\) 364.139 + 630.707i 0.885983 + 1.53457i
\(412\) 54.1331 93.7613i 0.131391 0.227576i
\(413\) 48.4229 + 27.9570i 0.117247 + 0.0676924i
\(414\) 453.221i 1.09474i
\(415\) 386.743 + 223.286i 0.931912 + 0.538040i
\(416\) 217.999 + 125.862i 0.524035 + 0.302552i
\(417\) −226.563 130.806i −0.543317 0.313684i
\(418\) 158.931 + 275.276i 0.380217 + 0.658555i
\(419\) 182.446i 0.435432i −0.976012 0.217716i \(-0.930139\pi\)
0.976012 0.217716i \(-0.0698606\pi\)
\(420\) 46.7986 27.0192i 0.111425 0.0643314i
\(421\) −310.193 179.090i −0.736800 0.425392i 0.0841044 0.996457i \(-0.473197\pi\)
−0.820905 + 0.571065i \(0.806530\pi\)
\(422\) −571.410 −1.35405
\(423\) 350.940 607.847i 0.829646 1.43699i
\(424\) 196.971 113.721i 0.464555 0.268211i
\(425\) 26.7330 + 46.3028i 0.0629011 + 0.108948i
\(426\) 815.840i 1.91512i
\(427\) −22.7028 39.3224i −0.0531681 0.0920898i
\(428\) −187.744 −0.438654
\(429\) 829.417i 1.93337i
\(430\) −303.067 150.898i −0.704806 0.350925i
\(431\) −201.977 −0.468624 −0.234312 0.972161i \(-0.575284\pi\)
−0.234312 + 0.972161i \(0.575284\pi\)
\(432\) 1.15175i 0.00266608i
\(433\) −404.038 + 233.272i −0.933114 + 0.538734i −0.887795 0.460239i \(-0.847764\pi\)
−0.0453190 + 0.998973i \(0.514430\pi\)
\(434\) −16.0280 −0.0369308
\(435\) 307.161 177.340i 0.706118 0.407677i
\(436\) 29.8020 + 51.6187i 0.0683533 + 0.118391i
\(437\) −311.297 179.728i −0.712351 0.411276i
\(438\) 110.406i 0.252068i
\(439\) 319.089 552.679i 0.726855 1.25895i −0.231351 0.972870i \(-0.574315\pi\)
0.958206 0.286079i \(-0.0923520\pi\)
\(440\) −440.645 763.220i −1.00147 1.73459i
\(441\) −420.603 −0.953747
\(442\) −328.210 + 189.492i −0.742557 + 0.428716i
\(443\) −181.021 + 313.538i −0.408626 + 0.707761i −0.994736 0.102470i \(-0.967325\pi\)
0.586110 + 0.810231i \(0.300659\pi\)
\(444\) −79.3674 + 137.468i −0.178755 + 0.309613i
\(445\) 33.6222 58.2353i 0.0755555 0.130866i
\(446\) 336.296 0.754027
\(447\) 442.406 766.270i 0.989723 1.71425i
\(448\) −77.7096 44.8657i −0.173459 0.100147i
\(449\) −613.878 + 354.423i −1.36721 + 0.789360i −0.990571 0.137000i \(-0.956254\pi\)
−0.376640 + 0.926360i \(0.622921\pi\)
\(450\) 24.9860 14.4257i 0.0555245 0.0320571i
\(451\) −436.781 −0.968472
\(452\) 42.8932i 0.0948964i
\(453\) 326.845 + 566.113i 0.721513 + 1.24970i
\(454\) −152.990 264.986i −0.336981 0.583669i
\(455\) −37.1531 + 64.3510i −0.0816551 + 0.141431i
\(456\) −340.389 196.524i −0.746467 0.430973i
\(457\) 444.549i 0.972755i 0.873749 + 0.486378i \(0.161682\pi\)
−0.873749 + 0.486378i \(0.838318\pi\)
\(458\) 184.424 + 106.477i 0.402672 + 0.232483i
\(459\) 4.03766 + 2.33115i 0.00879665 + 0.00507875i
\(460\) 259.022 + 149.546i 0.563090 + 0.325100i
\(461\) 250.340 + 433.602i 0.543038 + 0.940569i 0.998728 + 0.0504301i \(0.0160592\pi\)
−0.455690 + 0.890139i \(0.650607\pi\)
\(462\) 179.067i 0.387590i
\(463\) −756.342 + 436.674i −1.63357 + 0.943141i −0.650588 + 0.759431i \(0.725478\pi\)
−0.982980 + 0.183710i \(0.941189\pi\)
\(464\) −86.2463 49.7943i −0.185876 0.107315i
\(465\) 163.961 0.352604
\(466\) −38.2084 + 66.1788i −0.0819922 + 0.142015i
\(467\) −19.1619 + 11.0631i −0.0410320 + 0.0236898i −0.520376 0.853937i \(-0.674208\pi\)
0.479344 + 0.877627i \(0.340875\pi\)
\(468\) −76.7604 132.953i −0.164018 0.284087i
\(469\) 174.738i 0.372576i
\(470\) −308.513 534.360i −0.656410 1.13694i
\(471\) −673.604 −1.43016
\(472\) 338.394i 0.716937i
\(473\) 702.017 465.204i 1.48418 0.983518i
\(474\) 233.783 0.493213
\(475\) 22.8824i 0.0481735i
\(476\) −53.1924 + 30.7107i −0.111749 + 0.0645182i
\(477\) −235.797 −0.494332
\(478\) 15.4059 8.89461i 0.0322300 0.0186080i
\(479\) 366.668 + 635.088i 0.765487 + 1.32586i 0.939989 + 0.341205i \(0.110835\pi\)
−0.174502 + 0.984657i \(0.555832\pi\)
\(480\) 481.456 + 277.969i 1.00303 + 0.579102i
\(481\) 218.270i 0.453784i
\(482\) −114.877 + 198.973i −0.238334 + 0.412806i
\(483\) 101.249 + 175.369i 0.209626 + 0.363083i
\(484\) 450.373 0.930523
\(485\) 510.376 294.666i 1.05232 0.607558i
\(486\) 259.405 449.302i 0.533754 0.924490i
\(487\) −237.862 + 411.988i −0.488422 + 0.845972i −0.999911 0.0133179i \(-0.995761\pi\)
0.511489 + 0.859290i \(0.329094\pi\)
\(488\) 137.398 237.981i 0.281554 0.487666i
\(489\) 167.033 0.341580
\(490\) −184.876 + 320.215i −0.377299 + 0.653501i
\(491\) 40.6876 + 23.4910i 0.0828669 + 0.0478432i 0.540861 0.841112i \(-0.318099\pi\)
−0.457994 + 0.888955i \(0.651432\pi\)
\(492\) 140.372 81.0438i 0.285309 0.164723i
\(493\) −349.127 + 201.569i −0.708168 + 0.408861i
\(494\) 162.198 0.328337
\(495\) 913.659i 1.84578i
\(496\) −23.0189 39.8699i −0.0464090 0.0803828i
\(497\) −90.9065 157.455i −0.182910 0.316810i
\(498\) −274.575 + 475.578i −0.551356 + 0.954976i
\(499\) −476.488 275.101i −0.954886 0.551304i −0.0602909 0.998181i \(-0.519203\pi\)
−0.894595 + 0.446877i \(0.852536\pi\)
\(500\) 204.309i 0.408617i
\(501\) −731.885 422.554i −1.46085 0.843421i
\(502\) −56.1310 32.4072i −0.111815 0.0645563i
\(503\) −515.731 297.757i −1.02531 0.591963i −0.109672 0.993968i \(-0.534980\pi\)
−0.915638 + 0.402005i \(0.868313\pi\)
\(504\) 55.2205 + 95.6446i 0.109564 + 0.189771i
\(505\) 355.229i 0.703424i
\(506\) 858.319 495.550i 1.69628 0.979349i
\(507\) −253.656 146.449i −0.500308 0.288853i
\(508\) −47.2462 −0.0930043
\(509\) −2.32623 + 4.02916i −0.00457021 + 0.00791583i −0.868301 0.496037i \(-0.834788\pi\)
0.863731 + 0.503953i \(0.168121\pi\)
\(510\) −724.862 + 418.499i −1.42130 + 0.820587i
\(511\) 12.3022 + 21.3080i 0.0240747 + 0.0416986i
\(512\) 370.255i 0.723155i
\(513\) −0.997686 1.72804i −0.00194481 0.00336851i
\(514\) −256.568 −0.499160
\(515\) 328.790i 0.638427i
\(516\) −139.295 + 279.764i −0.269952 + 0.542179i
\(517\) 1534.87 2.96880
\(518\) 47.1234i 0.0909718i
\(519\) 315.838 182.349i 0.608552 0.351347i
\(520\) −449.705 −0.864818
\(521\) 428.671 247.493i 0.822785 0.475035i −0.0285906 0.999591i \(-0.509102\pi\)
0.851376 + 0.524556i \(0.175769\pi\)
\(522\) 108.771 + 188.397i 0.208373 + 0.360913i
\(523\) 531.027 + 306.589i 1.01535 + 0.586212i 0.912753 0.408511i \(-0.133952\pi\)
0.102596 + 0.994723i \(0.467285\pi\)
\(524\) 52.8543i 0.100867i
\(525\) −6.44539 + 11.1637i −0.0122769 + 0.0212643i
\(526\) 211.003 + 365.467i 0.401146 + 0.694805i
\(527\) −186.362 −0.353628
\(528\) 445.431 257.170i 0.843620 0.487064i
\(529\) −295.896 + 512.507i −0.559350 + 0.968822i
\(530\) −103.645 + 179.518i −0.195556 + 0.338713i
\(531\) 175.412 303.822i 0.330342 0.572169i
\(532\) 26.2872 0.0494119
\(533\) −111.440 + 193.020i −0.209081 + 0.362139i
\(534\) 71.6119 + 41.3452i 0.134105 + 0.0774254i
\(535\) 493.767 285.076i 0.922929 0.532853i
\(536\) −915.845 + 528.763i −1.70867 + 0.986499i
\(537\) 345.557 0.643495
\(538\) 169.693i 0.315415i
\(539\) −459.885 796.545i −0.853220 1.47782i
\(540\) 0.830146 + 1.43786i 0.00153731 + 0.00266269i
\(541\) 392.586 679.979i 0.725668 1.25689i −0.233031 0.972469i \(-0.574864\pi\)
0.958699 0.284424i \(-0.0918024\pi\)
\(542\) −43.5022 25.1160i −0.0802623 0.0463394i
\(543\) 718.410i 1.32304i
\(544\) −547.235 315.946i −1.00595 0.580783i
\(545\) −156.759 90.5049i −0.287631 0.166064i
\(546\) −79.1324 45.6871i −0.144931 0.0836760i
\(547\) 81.3090 + 140.831i 0.148645 + 0.257461i 0.930727 0.365715i \(-0.119175\pi\)
−0.782082 + 0.623176i \(0.785842\pi\)
\(548\) 294.781i 0.537921i
\(549\) −246.722 + 142.445i −0.449402 + 0.259463i
\(550\) 54.6393 + 31.5460i 0.0993442 + 0.0573564i
\(551\) 172.535 0.313131
\(552\) −612.767 + 1061.34i −1.11008 + 1.92272i
\(553\) −45.1194 + 26.0497i −0.0815902 + 0.0471061i
\(554\) 71.1704 + 123.271i 0.128466 + 0.222510i
\(555\) 482.056i 0.868570i
\(556\) 52.9457 + 91.7046i 0.0952260 + 0.164936i
\(557\) 46.2986 0.0831213 0.0415607 0.999136i \(-0.486767\pi\)
0.0415607 + 0.999136i \(0.486767\pi\)
\(558\) 100.565i 0.180224i
\(559\) −26.4683 428.924i −0.0473493 0.767307i
\(560\) 46.0789 0.0822837
\(561\) 2082.06i 3.71133i
\(562\) 101.036 58.3331i 0.179779 0.103796i
\(563\) −246.469 −0.437778 −0.218889 0.975750i \(-0.570243\pi\)
−0.218889 + 0.975750i \(0.570243\pi\)
\(564\) −493.274 + 284.792i −0.874599 + 0.504950i
\(565\) 65.1304 + 112.809i 0.115275 + 0.199662i
\(566\) 214.970 + 124.113i 0.379806 + 0.219281i
\(567\) 116.182i 0.204907i
\(568\) 550.171 952.925i 0.968612 1.67768i
\(569\) 424.894 + 735.938i 0.746738 + 1.29339i 0.949378 + 0.314135i \(0.101715\pi\)
−0.202640 + 0.979253i \(0.564952\pi\)
\(570\) 358.220 0.628456
\(571\) 175.177 101.138i 0.306790 0.177125i −0.338699 0.940895i \(-0.609987\pi\)
0.645489 + 0.763770i \(0.276654\pi\)
\(572\) 167.859 290.741i 0.293460 0.508288i
\(573\) −209.542 + 362.938i −0.365694 + 0.633400i
\(574\) 24.0594 41.6720i 0.0419153 0.0725994i
\(575\) −71.3480 −0.124084
\(576\) −281.503 + 487.577i −0.488720 + 0.846487i
\(577\) −634.982 366.607i −1.10049 0.635368i −0.164140 0.986437i \(-0.552485\pi\)
−0.936349 + 0.351069i \(0.885818\pi\)
\(578\) 445.580 257.256i 0.770899 0.445079i
\(579\) 894.558 516.473i 1.54500 0.892009i
\(580\) −143.561 −0.247520
\(581\) 122.380i 0.210637i
\(582\) 362.350 + 627.608i 0.622594 + 1.07836i
\(583\) −257.819 446.556i −0.442228 0.765962i
\(584\) −74.4535 + 128.957i −0.127489 + 0.220817i
\(585\) 403.760 + 233.111i 0.690189 + 0.398481i
\(586\) 268.565i 0.458302i
\(587\) 549.572 + 317.295i 0.936238 + 0.540537i 0.888779 0.458336i \(-0.151554\pi\)
0.0474590 + 0.998873i \(0.484888\pi\)
\(588\) 295.595 + 170.662i 0.502712 + 0.290241i
\(589\) 69.0736 + 39.8797i 0.117273 + 0.0677074i
\(590\) −154.205 267.091i −0.261364 0.452696i
\(591\) 1362.20i 2.30491i
\(592\) −117.220 + 67.6771i −0.198007 + 0.114319i
\(593\) 577.047 + 333.158i 0.973098 + 0.561818i 0.900179 0.435520i \(-0.143435\pi\)
0.0729186 + 0.997338i \(0.476769\pi\)
\(594\) 5.50170 0.00926213
\(595\) 93.2642 161.538i 0.156747 0.271493i
\(596\) −310.158 + 179.070i −0.520400 + 0.300453i
\(597\) −83.0694 143.881i −0.139145 0.241006i
\(598\) 505.739i 0.845718i
\(599\) −354.761 614.463i −0.592255 1.02582i −0.993928 0.110032i \(-0.964905\pi\)
0.401673 0.915783i \(-0.368429\pi\)
\(600\) −78.0157 −0.130026
\(601\) 389.979i 0.648884i −0.945906 0.324442i \(-0.894824\pi\)
0.945906 0.324442i \(-0.105176\pi\)
\(602\) 5.71435 + 92.6025i 0.00949228 + 0.153825i
\(603\) 1096.37 1.81819
\(604\) 264.591i 0.438064i
\(605\) −1184.48 + 683.862i −1.95782 + 1.13035i
\(606\) −436.825 −0.720833
\(607\) −818.471 + 472.545i −1.34839 + 0.778492i −0.988021 0.154319i \(-0.950682\pi\)
−0.360366 + 0.932811i \(0.617348\pi\)
\(608\) 135.219 + 234.206i 0.222400 + 0.385208i
\(609\) −84.1754 48.5987i −0.138219 0.0798008i
\(610\) 250.448i 0.410570i
\(611\) 391.607 678.283i 0.640927 1.11012i
\(612\) 192.689 + 333.747i 0.314851 + 0.545339i
\(613\) −89.2278 −0.145559 −0.0727796 0.997348i \(-0.523187\pi\)
−0.0727796 + 0.997348i \(0.523187\pi\)
\(614\) 315.609 182.217i 0.514021 0.296770i
\(615\) −246.119 + 426.291i −0.400194 + 0.693156i
\(616\) −120.756 + 209.155i −0.196032 + 0.339537i
\(617\) −46.9205 + 81.2687i −0.0760462 + 0.131716i −0.901541 0.432694i \(-0.857563\pi\)
0.825495 + 0.564410i \(0.190896\pi\)
\(618\) −404.313 −0.654228
\(619\) 113.587 196.739i 0.183501 0.317834i −0.759569 0.650427i \(-0.774590\pi\)
0.943071 + 0.332593i \(0.107923\pi\)
\(620\) −57.4742 33.1827i −0.0927003 0.0535206i
\(621\) −5.38809 + 3.11082i −0.00867648 + 0.00500937i
\(622\) −61.6380 + 35.5867i −0.0990965 + 0.0572134i
\(623\) −18.4278 −0.0295792
\(624\) 262.457i 0.420605i
\(625\) 336.869 + 583.474i 0.538990 + 0.933558i
\(626\) 2.78042 + 4.81582i 0.00444156 + 0.00769301i
\(627\) −445.541 + 771.699i −0.710591 + 1.23078i
\(628\) 236.122 + 136.325i 0.375991 + 0.217078i
\(629\) 547.917i 0.871092i
\(630\) −87.1697 50.3274i −0.138365 0.0798848i
\(631\) −405.265 233.980i −0.642259 0.370808i 0.143225 0.989690i \(-0.454253\pi\)
−0.785484 + 0.618882i \(0.787586\pi\)
\(632\) −273.065 157.654i −0.432065 0.249453i
\(633\) −800.936 1387.26i −1.26530 2.19157i
\(634\) 118.403i 0.186756i
\(635\) 124.258 71.7402i 0.195681 0.112977i
\(636\) 165.715 + 95.6756i 0.260558 + 0.150433i
\(637\) −469.341 −0.736799
\(638\) −237.859 + 411.985i −0.372820 + 0.645744i
\(639\) −987.924 + 570.378i −1.54605 + 0.892611i
\(640\) −14.9218 25.8454i −0.0233153 0.0403834i
\(641\) 1181.26i 1.84283i 0.388577 + 0.921416i \(0.372967\pi\)
−0.388577 + 0.921416i \(0.627033\pi\)
\(642\) 350.558 + 607.184i 0.546041 + 0.945770i
\(643\) 1130.33 1.75790 0.878948 0.476917i \(-0.158246\pi\)
0.878948 + 0.476917i \(0.158246\pi\)
\(644\) 81.9642i 0.127274i
\(645\) −58.4559 947.292i −0.0906293 1.46867i
\(646\) −407.161 −0.630280
\(647\) 1275.13i 1.97084i 0.170149 + 0.985418i \(0.445575\pi\)
−0.170149 + 0.985418i \(0.554425\pi\)
\(648\) −608.937 + 351.570i −0.939718 + 0.542546i
\(649\) 767.178 1.18209
\(650\) 27.8814 16.0973i 0.0428944 0.0247651i
\(651\) −22.4662 38.9125i −0.0345102 0.0597735i
\(652\) −58.5509 33.8044i −0.0898020 0.0518472i
\(653\) 185.383i 0.283894i 0.989874 + 0.141947i \(0.0453363\pi\)
−0.989874 + 0.141947i \(0.954664\pi\)
\(654\) 111.294 192.766i 0.170174 0.294750i
\(655\) 80.2558 + 139.007i 0.122528 + 0.212225i
\(656\) 138.213 0.210691
\(657\) 133.694 77.1881i 0.203491 0.117486i
\(658\) −84.5458 + 146.438i −0.128489 + 0.222549i
\(659\) 119.493 206.969i 0.181325 0.314065i −0.761007 0.648744i \(-0.775295\pi\)
0.942332 + 0.334679i \(0.108628\pi\)
\(660\) 370.722 642.109i 0.561700 0.972892i
\(661\) −1149.01 −1.73829 −0.869144 0.494559i \(-0.835330\pi\)
−0.869144 + 0.494559i \(0.835330\pi\)
\(662\) 56.7657 98.3211i 0.0857488 0.148521i
\(663\) −920.094 531.217i −1.38777 0.801232i
\(664\) 641.423 370.326i 0.965999 0.557720i
\(665\) −69.1353 + 39.9153i −0.103963 + 0.0600230i
\(666\) 295.668 0.443946
\(667\) 537.969i 0.806551i
\(668\) 171.035 + 296.241i 0.256040 + 0.443474i
\(669\) 471.381 + 816.455i 0.704605 + 1.22041i
\(670\) 481.910 834.693i 0.719269 1.24581i
\(671\) −539.530 311.498i −0.804068 0.464229i
\(672\) 152.351i 0.226713i
\(673\) 106.943 + 61.7437i 0.158905 + 0.0917440i 0.577344 0.816501i \(-0.304089\pi\)
−0.418439 + 0.908245i \(0.637423\pi\)
\(674\) −345.185 199.292i −0.512143 0.295686i
\(675\) −0.342998 0.198030i −0.000508145 0.000293378i
\(676\) 59.2771 + 102.671i 0.0876880 + 0.151880i
\(677\) 444.331i 0.656323i −0.944622 0.328162i \(-0.893571\pi\)
0.944622 0.328162i \(-0.106429\pi\)
\(678\) −138.721 + 80.0908i −0.204604 + 0.118128i
\(679\) −139.865 80.7510i −0.205987 0.118926i
\(680\) 1128.88 1.66012
\(681\) 428.886 742.852i 0.629788 1.09083i
\(682\) −190.452 + 109.957i −0.279255 + 0.161228i
\(683\) 162.804 + 281.985i 0.238366 + 0.412863i 0.960246 0.279156i \(-0.0900547\pi\)
−0.721879 + 0.692019i \(0.756721\pi\)
\(684\) 164.935i 0.241132i
\(685\) 447.605 + 775.274i 0.653438 + 1.13179i
\(686\) 207.053 0.301826
\(687\) 596.989i 0.868980i
\(688\) −222.143 + 147.207i −0.322883 + 0.213964i
\(689\) −263.120 −0.381887
\(690\) 1116.94i 1.61875i
\(691\) 6.60671 3.81439i 0.00956109 0.00552010i −0.495212 0.868772i \(-0.664910\pi\)
0.504773 + 0.863252i \(0.331576\pi\)
\(692\) −147.617 −0.213319
\(693\) 216.837 125.191i 0.312896 0.180651i
\(694\) 444.151 + 769.293i 0.639988 + 1.10849i
\(695\) −278.495 160.789i −0.400712 0.231351i
\(696\) 588.244i 0.845178i
\(697\) 279.745 484.533i 0.401356 0.695169i
\(698\) 335.538 + 581.169i 0.480714 + 0.832620i
\(699\) −214.224 −0.306472
\(700\) 4.51868 2.60886i 0.00645526 0.00372694i
\(701\) 154.353 267.347i 0.220189 0.381379i −0.734676 0.678418i \(-0.762666\pi\)
0.954865 + 0.297039i \(0.0959991\pi\)
\(702\) 1.40371 2.43129i 0.00199958 0.00346337i
\(703\) 117.249 203.081i 0.166784 0.288878i
\(704\) −1231.18 −1.74883
\(705\) 864.875 1498.01i 1.22677 2.12483i
\(706\) −782.108 451.550i −1.10780 0.639589i
\(707\) 84.3058 48.6740i 0.119244 0.0688458i
\(708\) −246.554 + 142.348i −0.348241 + 0.201057i
\(709\) −85.3563 −0.120390 −0.0601949 0.998187i \(-0.519172\pi\)
−0.0601949 + 0.998187i \(0.519172\pi\)
\(710\) 1002.84i 1.41245i
\(711\) 163.445 + 283.094i 0.229880 + 0.398164i
\(712\) −55.7632 96.5847i −0.0783191 0.135653i
\(713\) 124.346 215.374i 0.174398 0.302067i
\(714\) 198.643 + 114.687i 0.278212 + 0.160626i
\(715\) 1019.53i 1.42592i
\(716\) −121.130 69.9345i −0.169176 0.0976738i
\(717\) 43.1885 + 24.9349i 0.0602349 + 0.0347767i
\(718\) 333.008 + 192.262i 0.463800 + 0.267775i
\(719\) −253.076 438.341i −0.351984 0.609654i 0.634613 0.772830i \(-0.281159\pi\)
−0.986597 + 0.163176i \(0.947826\pi\)
\(720\) 289.115i 0.401548i
\(721\) 78.0311 45.0513i 0.108226 0.0624845i
\(722\) −321.657 185.709i −0.445508 0.257214i
\(723\) −644.085 −0.890850
\(724\) −145.393 + 251.828i −0.200819 + 0.347829i
\(725\) 29.6582 17.1232i 0.0409079 0.0236182i
\(726\) −840.944 1456.56i −1.15833 2.00628i
\(727\) 230.282i 0.316757i 0.987379 + 0.158378i \(0.0506265\pi\)
−0.987379 + 0.158378i \(0.949373\pi\)
\(728\) 61.6193 + 106.728i 0.0846419 + 0.146604i
\(729\) 721.878 0.990230
\(730\) 135.713i 0.185908i
\(731\) 66.4424 + 1076.71i 0.0908925 + 1.47293i
\(732\) 231.191 0.315835
\(733\) 500.013i 0.682147i 0.940037 + 0.341073i \(0.110790\pi\)
−0.940037 + 0.341073i \(0.889210\pi\)
\(734\) 372.277 214.934i 0.507189 0.292826i
\(735\) −1036.55 −1.41028
\(736\) 730.262 421.617i 0.992204 0.572849i
\(737\) 1198.77 + 2076.32i 1.62655 + 2.81726i
\(738\) −261.465 150.957i −0.354288 0.204548i
\(739\) 865.575i 1.17128i −0.810572 0.585639i \(-0.800843\pi\)
0.810572 0.585639i \(-0.199157\pi\)
\(740\) −97.5595 + 168.978i −0.131837 + 0.228349i
\(741\) 227.351 + 393.783i 0.306816 + 0.531421i
\(742\) 56.8062 0.0765582
\(743\) 1045.99 603.905i 1.40780 0.812793i 0.412622 0.910902i \(-0.364613\pi\)
0.995176 + 0.0981096i \(0.0312796\pi\)
\(744\) 135.967 235.501i 0.182751 0.316534i
\(745\) 543.812 941.910i 0.729949 1.26431i
\(746\) 200.075 346.540i 0.268197 0.464531i
\(747\) −767.855 −1.02792
\(748\) −421.371 + 729.836i −0.563331 + 0.975717i
\(749\) −135.313 78.1232i −0.180659 0.104303i
\(750\) −660.757 + 381.488i −0.881009 + 0.508651i
\(751\) 405.939 234.369i 0.540532 0.312076i −0.204763 0.978812i \(-0.565642\pi\)
0.745294 + 0.666735i \(0.232309\pi\)
\(752\) −485.688 −0.645861
\(753\) 181.699i 0.241300i
\(754\) 121.375 + 210.228i 0.160975 + 0.278817i
\(755\) 401.763 + 695.874i 0.532137 + 0.921688i
\(756\) 0.227496 0.394034i 0.000300920 0.000521209i
\(757\) 591.471 + 341.486i 0.781336 + 0.451104i 0.836903 0.547351i \(-0.184364\pi\)
−0.0555678 + 0.998455i \(0.517697\pi\)
\(758\) 148.244i 0.195572i
\(759\) 2406.18 + 1389.21i 3.17020 + 1.83032i
\(760\) −418.411 241.570i −0.550541 0.317855i
\(761\) −284.325 164.155i −0.373620 0.215710i 0.301419 0.953492i \(-0.402540\pi\)
−0.675039 + 0.737782i \(0.735873\pi\)
\(762\) 88.2188 + 152.799i 0.115773 + 0.200524i
\(763\) 49.6044i 0.0650124i
\(764\) 146.904 84.8153i 0.192283 0.111015i
\(765\) −1013.55 585.171i −1.32490 0.764930i
\(766\) 664.675 0.867723
\(767\) 195.738 339.028i 0.255199 0.442018i
\(768\) 954.541 551.105i 1.24289 0.717584i
\(769\) −278.216 481.884i −0.361789 0.626637i 0.626466 0.779449i \(-0.284501\pi\)
−0.988255 + 0.152811i \(0.951167\pi\)
\(770\) 220.111i 0.285859i
\(771\) −359.627 622.893i −0.466443 0.807903i
\(772\) −418.100 −0.541580
\(773\) 440.683i 0.570095i −0.958513 0.285047i \(-0.907991\pi\)
0.958513 0.285047i \(-0.0920093\pi\)
\(774\) 581.019 35.8538i 0.750671 0.0463227i
\(775\) 15.8314 0.0204276
\(776\) 977.420i 1.25956i
\(777\) −114.406 + 66.0521i −0.147240 + 0.0850091i
\(778\) −422.986 −0.543683
\(779\) −207.371 + 119.726i −0.266201 + 0.153691i
\(780\) −189.172 327.656i −0.242528 0.420071i
\(781\) −2160.39 1247.30i −2.76618 1.59705i
\(782\) 1269.54i 1.62345i
\(783\) 1.49316 2.58623i 0.00190698 0.00330298i
\(784\) 145.524 + 252.056i 0.185618 + 0.321499i
\(785\) −828.004 −1.05478
\(786\) −170.937 + 98.6904i −0.217477 + 0.125560i
\(787\) 81.7718 141.633i 0.103903 0.179966i −0.809386 0.587277i \(-0.800200\pi\)
0.913290 + 0.407311i \(0.133533\pi\)
\(788\) 275.685 477.500i 0.349854 0.605965i
\(789\) −591.518 + 1024.54i −0.749706 + 1.29853i
\(790\) 287.369 0.363759
\(791\) 17.8485 30.9146i 0.0225645 0.0390829i
\(792\) 1312.31 + 757.663i 1.65696 + 0.956645i
\(793\) −275.311 + 158.951i −0.347177 + 0.200443i
\(794\) 284.412 164.205i 0.358201 0.206807i
\(795\) −581.108 −0.730954
\(796\) 67.2471i 0.0844812i
\(797\) 527.628 + 913.878i 0.662017 + 1.14665i 0.980085 + 0.198579i \(0.0636327\pi\)
−0.318068 + 0.948068i \(0.603034\pi\)
\(798\) −49.0838 85.0156i −0.0615085 0.106536i
\(799\) −983.037 + 1702.67i −1.23033 + 2.13100i
\(800\) 46.4874 + 26.8395i 0.0581093 + 0.0335494i
\(801\) 115.623i 0.144348i
\(802\) −532.952 307.700i −0.664529 0.383666i
\(803\) 292.360 + 168.794i 0.364085 + 0.210205i
\(804\) −770.515 444.857i −0.958352 0.553305i
\(805\) 124.457 + 215.566i 0.154605 + 0.267784i
\(806\) 112.218i 0.139229i
\(807\) 411.980 237.857i 0.510508 0.294742i
\(808\) 510.224 + 294.578i 0.631465 + 0.364577i
\(809\) −1278.56 −1.58042 −0.790209 0.612837i \(-0.790028\pi\)
−0.790209 + 0.612837i \(0.790028\pi\)
\(810\) 320.418 554.980i 0.395578 0.685160i
\(811\) −1346.24 + 777.252i −1.65998 + 0.958387i −0.687252 + 0.726419i \(0.741183\pi\)
−0.972723 + 0.231968i \(0.925484\pi\)
\(812\) 19.6710 + 34.0712i 0.0242254 + 0.0419596i
\(813\) 140.819i 0.173209i
\(814\) 323.283 + 559.942i 0.397153 + 0.687889i
\(815\) 205.319 0.251925
\(816\) 658.838i 0.807400i
\(817\) 205.780 413.294i 0.251873 0.505868i
\(818\) 95.4121 0.116641
\(819\) 127.765i 0.156001i
\(820\) 172.547 99.6202i 0.210423 0.121488i
\(821\) −271.907 −0.331189 −0.165595 0.986194i \(-0.552954\pi\)
−0.165595 + 0.986194i \(0.552954\pi\)
\(822\) −953.354 + 550.419i −1.15980 + 0.669610i
\(823\) −311.057 538.766i −0.377955 0.654637i 0.612810 0.790230i \(-0.290039\pi\)
−0.990765 + 0.135594i \(0.956706\pi\)
\(824\) 472.249 + 272.653i 0.573118 + 0.330890i
\(825\) 176.870i 0.214388i
\(826\) −42.2587 + 73.1943i −0.0511607 + 0.0886129i
\(827\) −529.310 916.791i −0.640036 1.10857i −0.985424 0.170115i \(-0.945586\pi\)
0.345388 0.938460i \(-0.387747\pi\)
\(828\) −514.271 −0.621100
\(829\) 269.501 155.597i 0.325092 0.187692i −0.328568 0.944480i \(-0.606566\pi\)
0.653660 + 0.756788i \(0.273233\pi\)
\(830\) −337.512 + 584.587i −0.406641 + 0.704322i
\(831\) −199.517 + 345.573i −0.240092 + 0.415852i
\(832\) −314.122 + 544.076i −0.377551 + 0.653938i
\(833\) 1178.17 1.41437
\(834\) 197.722 342.465i 0.237077 0.410629i
\(835\) −899.643 519.409i −1.07742 0.622047i
\(836\) 312.356 180.339i 0.373632 0.215716i
\(837\) 1.19556 0.690258i 0.00142839 0.000824681i
\(838\) 275.779 0.329091
\(839\) 827.992i 0.986879i −0.869780 0.493440i \(-0.835739\pi\)
0.869780 0.493440i \(-0.164261\pi\)
\(840\) 136.088 + 235.711i 0.162010 + 0.280609i
\(841\) −291.390 504.702i −0.346480 0.600121i
\(842\) 270.706 468.876i 0.321504 0.556860i
\(843\) 283.241 + 163.529i 0.335991 + 0.193985i
\(844\) 648.380i 0.768223i
\(845\) −311.798 180.017i −0.368992 0.213037i
\(846\) 918.799 + 530.469i 1.08605 + 0.627032i
\(847\) 324.599 + 187.408i 0.383234 + 0.221260i
\(848\) 81.5833 + 141.306i 0.0962067 + 0.166635i
\(849\) 695.869i 0.819634i
\(850\) −69.9897 + 40.4086i −0.0823408 + 0.0475395i
\(851\) −633.213 365.586i −0.744082 0.429596i
\(852\) 925.736 1.08654
\(853\) −764.869 + 1324.79i −0.896682 + 1.55310i −0.0649722 + 0.997887i \(0.520696\pi\)
−0.831709 + 0.555211i \(0.812637\pi\)
\(854\) 59.4382 34.3167i 0.0695998 0.0401835i
\(855\) 250.442 + 433.779i 0.292915 + 0.507343i
\(856\) 945.612i 1.10469i
\(857\) −622.430 1078.08i −0.726289 1.25797i −0.958441 0.285290i \(-0.907910\pi\)
0.232152 0.972679i \(-0.425423\pi\)
\(858\) −1253.72 −1.46121
\(859\) 158.942i 0.185032i −0.995711 0.0925159i \(-0.970509\pi\)
0.995711 0.0925159i \(-0.0294909\pi\)
\(860\) −171.224 + 343.890i −0.199098 + 0.399873i
\(861\) 134.894 0.156672
\(862\) 305.301i 0.354177i
\(863\) −320.063 + 184.788i −0.370872 + 0.214123i −0.673839 0.738878i \(-0.735356\pi\)
0.302967 + 0.953001i \(0.402023\pi\)
\(864\) 4.68088 0.00541768
\(865\) 388.233 224.146i 0.448824 0.259129i
\(866\) −352.605 610.730i −0.407165 0.705231i
\(867\) 1249.12 + 721.182i 1.44074 + 0.831813i
\(868\) 18.1870i 0.0209528i
\(869\) −357.420 + 619.069i −0.411300 + 0.712393i
\(870\) 268.060 + 464.294i 0.308115 + 0.533671i
\(871\) 1223.41 1.40461
\(872\) −259.989 + 150.104i −0.298152 + 0.172138i
\(873\) −506.659 + 877.560i −0.580366 + 1.00522i
\(874\) 271.670 470.546i 0.310835 0.538382i
\(875\) 85.0161 147.252i 0.0971612 0.168288i
\(876\) −125.278 −0.143011
\(877\) 411.371 712.516i 0.469067 0.812447i −0.530308 0.847805i \(-0.677924\pi\)
0.999375 + 0.0353577i \(0.0112571\pi\)
\(878\) 835.409 + 482.324i 0.951491 + 0.549344i
\(879\) −652.018 + 376.443i −0.741773 + 0.428263i
\(880\) 547.531 316.117i 0.622194 0.359224i
\(881\) 1688.29 1.91634 0.958169 0.286205i \(-0.0923937\pi\)
0.958169 + 0.286205i \(0.0923937\pi\)
\(882\) 635.768i 0.720825i
\(883\) 299.386 + 518.552i 0.339055 + 0.587261i 0.984255 0.176753i \(-0.0565592\pi\)
−0.645200 + 0.764014i \(0.723226\pi\)
\(884\) 215.017 + 372.421i 0.243232 + 0.421291i
\(885\) 432.293 748.753i 0.488466 0.846048i
\(886\) −473.933 273.625i −0.534913 0.308832i
\(887\) 1583.51i 1.78524i −0.450810 0.892620i \(-0.648865\pi\)
0.450810 0.892620i \(-0.351135\pi\)
\(888\) −692.389 399.751i −0.779717 0.450170i
\(889\) −34.0519 19.6599i −0.0383036 0.0221146i
\(890\) 88.0264 + 50.8221i 0.0989061 + 0.0571035i
\(891\) 797.049 + 1380.53i 0.894555 + 1.54941i
\(892\) 381.596i 0.427798i
\(893\) 728.711 420.721i 0.816025 0.471133i
\(894\) 1158.27 + 668.725i 1.29560 + 0.748015i
\(895\) 424.763 0.474596
\(896\) −4.08922 + 7.08274i −0.00456386 + 0.00790484i
\(897\) 1227.83 708.887i 1.36882 0.790286i
\(898\) −535.732 927.915i −0.596584 1.03331i
\(899\) 119.370i 0.132781i
\(900\) −16.3689 28.3517i −0.0181876 0.0315019i
\(901\) 660.502 0.733076
\(902\) 660.222i 0.731953i
\(903\) −216.809 + 143.673i −0.240099 + 0.159106i
\(904\) 216.041 0.238983
\(905\) 883.080i 0.975779i
\(906\) −855.716 + 494.048i −0.944499 + 0.545307i
\(907\) 1250.79 1.37904 0.689518 0.724269i \(-0.257822\pi\)
0.689518 + 0.724269i \(0.257822\pi\)
\(908\) −300.680 + 173.598i −0.331145 + 0.191187i
\(909\) −305.397 528.964i −0.335971 0.581918i
\(910\) −97.2707 56.1593i −0.106891 0.0617135i
\(911\) 170.898i 0.187594i −0.995591 0.0937970i \(-0.970100\pi\)
0.995591 0.0937970i \(-0.0299005\pi\)
\(912\) 140.985 244.193i 0.154589 0.267756i
\(913\) −839.570 1454.18i −0.919573 1.59275i
\(914\) −671.964 −0.735191
\(915\) −608.033 + 351.048i −0.664517 + 0.383659i
\(916\) 120.820 209.266i 0.131899 0.228457i
\(917\) 21.9935 38.0939i 0.0239842 0.0415419i
\(918\) −3.52367 + 6.10318i −0.00383843 + 0.00664835i
\(919\) −169.349 −0.184275 −0.0921377 0.995746i \(-0.529370\pi\)
−0.0921377 + 0.995746i \(0.529370\pi\)
\(920\) −753.222 + 1304.62i −0.818719 + 1.41806i
\(921\) 884.768 + 510.821i 0.960660 + 0.554637i
\(922\) −655.417 + 378.405i −0.710865 + 0.410418i
\(923\) −1102.40 + 636.473i −1.19437 + 0.689569i
\(924\) −203.187 −0.219900
\(925\) 46.5454i 0.0503193i
\(926\) −660.061 1143.26i −0.712809 1.23462i
\(927\) −282.667 489.594i −0.304927 0.528149i
\(928\) −202.372 + 350.519i −0.218073 + 0.377714i
\(929\) −850.652 491.124i −0.915665 0.528659i −0.0334152 0.999442i \(-0.510638\pi\)
−0.882249 + 0.470782i \(0.843972\pi\)
\(930\) 247.837i 0.266492i
\(931\) −436.680 252.118i −0.469044 0.270803i
\(932\) 75.0933 + 43.3551i 0.0805722 + 0.0465184i
\(933\) −172.794 99.7627i −0.185203 0.106927i
\(934\) −16.7227 28.9645i −0.0179043 0.0310112i
\(935\) 2559.30i 2.73722i
\(936\) 669.646 386.620i 0.715434 0.413056i
\(937\) 999.637 + 577.141i 1.06685 + 0.615945i 0.927319 0.374273i \(-0.122108\pi\)
0.139530 + 0.990218i \(0.455441\pi\)
\(938\) −264.128 −0.281587
\(939\) −7.79453 + 13.5005i −0.00830089 + 0.0143776i
\(940\) −606.339 + 350.070i −0.645042 + 0.372415i
\(941\) 832.384 + 1441.73i 0.884574 + 1.53213i 0.846201 + 0.532864i \(0.178884\pi\)
0.0383733 + 0.999263i \(0.487782\pi\)
\(942\) 1018.19i 1.08089i
\(943\) 373.308 + 646.588i 0.395873 + 0.685672i
\(944\) −242.763 −0.257164
\(945\) 1.38175i 0.00146217i
\(946\) 703.185 + 1061.14i 0.743325 + 1.12172i
\(947\) −451.815 −0.477101 −0.238551 0.971130i \(-0.576672\pi\)
−0.238551 + 0.971130i \(0.576672\pi\)
\(948\) 265.274i 0.279825i
\(949\) 149.186 86.1325i 0.157203 0.0907613i
\(950\) 34.5882 0.0364086
\(951\) 287.458 165.964i 0.302270 0.174515i
\(952\) −154.681 267.915i −0.162480 0.281423i
\(953\) 538.083 + 310.662i 0.564620 + 0.325984i 0.754998 0.655727i \(-0.227638\pi\)
−0.190378 + 0.981711i \(0.560971\pi\)
\(954\) 356.421i 0.373607i
\(955\) −257.573 + 446.129i −0.269710 + 0.467151i
\(956\) −10.0927 17.4811i −0.0105573 0.0182857i
\(957\) −1333.61 −1.39354
\(958\) −959.976 + 554.242i −1.00206 + 0.578541i
\(959\) 122.663 212.459i 0.127907 0.221542i
\(960\) −693.749 + 1201.61i −0.722655 + 1.25167i
\(961\) 452.909 784.461i 0.471289 0.816297i
\(962\) 329.929 0.342962
\(963\) −490.171 + 849.002i −0.509005 + 0.881622i
\(964\) 225.775 + 130.351i 0.234206 + 0.135219i
\(965\) 1099.60 634.856i 1.13949 0.657882i
\(966\) −265.081 + 153.045i −0.274411 + 0.158431i
\(967\) 19.2812 0.0199392 0.00996961 0.999950i \(-0.496827\pi\)
0.00996961 + 0.999950i \(0.496827\pi\)
\(968\) 2268.40i 2.34339i
\(969\) −570.711 988.501i −0.588969 1.02012i
\(970\) 445.406 + 771.465i 0.459181 + 0.795325i
\(971\) 454.351 786.958i 0.467920 0.810462i −0.531408 0.847116i \(-0.678337\pi\)
0.999328 + 0.0366546i \(0.0116701\pi\)
\(972\) −509.824 294.347i −0.524510 0.302826i
\(973\) 88.1262i 0.0905716i
\(974\) −622.746 359.543i −0.639370 0.369140i
\(975\) 78.1617 + 45.1267i 0.0801659 + 0.0462838i
\(976\) 170.727 + 98.5691i 0.174925 + 0.100993i
\(977\) −464.004 803.679i −0.474928 0.822599i 0.524660 0.851312i \(-0.324192\pi\)
−0.999588 + 0.0287130i \(0.990859\pi\)
\(978\) 252.480i 0.258160i
\(979\) −218.968 + 126.421i −0.223665 + 0.129133i
\(980\) 363.349 + 209.780i 0.370765 + 0.214061i
\(981\) 311.235 0.317263
\(982\) −35.5082 + 61.5019i −0.0361590 + 0.0626293i
\(983\) 895.385 516.951i 0.910869 0.525891i 0.0301586 0.999545i \(-0.490399\pi\)
0.880711 + 0.473654i \(0.157065\pi\)
\(984\) 408.195 + 707.014i 0.414832 + 0.718510i
\(985\) 1674.44i 1.69994i
\(986\) −304.684 527.728i −0.309010 0.535221i
\(987\) −474.026 −0.480269
\(988\) 184.047i 0.186282i
\(989\) −1288.66 641.630i −1.30300 0.648766i
\(990\) −1381.05 −1.39500
\(991\) 1837.99i 1.85469i 0.374212 + 0.927343i \(0.377913\pi\)
−0.374212 + 0.927343i \(0.622087\pi\)
\(992\) −162.038 + 93.5524i −0.163344 + 0.0943069i
\(993\) 318.270 0.320514
\(994\) 238.003 137.411i 0.239439 0.138240i
\(995\) −102.110 176.860i −0.102623 0.177749i
\(996\) 539.639 + 311.561i 0.541807 + 0.312812i
\(997\) 1108.28i 1.11161i 0.831312 + 0.555806i \(0.187590\pi\)
−0.831312 + 0.555806i \(0.812410\pi\)
\(998\) 415.832 720.242i 0.416666 0.721686i
\(999\) −2.02940 3.51503i −0.00203144 0.00351855i
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 43.3.d.a.7.4 12
3.2 odd 2 387.3.j.c.136.3 12
4.3 odd 2 688.3.t.c.609.6 12
43.37 odd 6 inner 43.3.d.a.37.3 yes 12
129.80 even 6 387.3.j.c.37.4 12
172.123 even 6 688.3.t.c.209.6 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
43.3.d.a.7.4 12 1.1 even 1 trivial
43.3.d.a.37.3 yes 12 43.37 odd 6 inner
387.3.j.c.37.4 12 129.80 even 6
387.3.j.c.136.3 12 3.2 odd 2
688.3.t.c.209.6 12 172.123 even 6
688.3.t.c.609.6 12 4.3 odd 2