Properties

Label 527.2.h.c.256.13
Level $527$
Weight $2$
Character 527.256
Analytic conductor $4.208$
Analytic rank $0$
Dimension $96$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [527,2,Mod(35,527)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(527, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 6]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("527.35");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 527 = 17 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 527.h (of order \(5\), degree \(4\), 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: \(4.20811618652\)
Analytic rank: \(0\)
Dimension: \(96\)
Relative dimension: \(24\) over \(\Q(\zeta_{5})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 256.13
Character \(\chi\) \(=\) 527.256
Dual form 527.2.h.c.35.13

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.0573542 - 0.176518i) q^{2} +(-0.417065 - 1.28359i) q^{3} +(1.59016 + 1.15532i) q^{4} +2.24620 q^{5} -0.250498 q^{6} +(2.41959 + 1.75793i) q^{7} +(0.595448 - 0.432618i) q^{8} +(0.953382 - 0.692673i) q^{9} +O(q^{10})\) \(q+(0.0573542 - 0.176518i) q^{2} +(-0.417065 - 1.28359i) q^{3} +(1.59016 + 1.15532i) q^{4} +2.24620 q^{5} -0.250498 q^{6} +(2.41959 + 1.75793i) q^{7} +(0.595448 - 0.432618i) q^{8} +(0.953382 - 0.692673i) q^{9} +(0.128829 - 0.396494i) q^{10} +(-4.52207 - 3.28548i) q^{11} +(0.819762 - 2.52297i) q^{12} +(1.77340 + 5.45795i) q^{13} +(0.449081 - 0.326276i) q^{14} +(-0.936810 - 2.88320i) q^{15} +(1.17256 + 3.60878i) q^{16} +(-0.809017 + 0.587785i) q^{17} +(-0.0675888 - 0.208017i) q^{18} +(-0.737722 + 2.27048i) q^{19} +(3.57183 + 2.59508i) q^{20} +(1.24735 - 3.83894i) q^{21} +(-0.839305 + 0.609791i) q^{22} +(-1.65419 + 1.20184i) q^{23} +(-0.803646 - 0.583883i) q^{24} +0.0454058 q^{25} +1.06514 q^{26} +(-4.56240 - 3.31478i) q^{27} +(1.81657 + 5.59081i) q^{28} +(1.74045 - 5.35656i) q^{29} -0.562667 q^{30} +(-5.56417 + 0.200037i) q^{31} +2.17629 q^{32} +(-2.33122 + 7.17475i) q^{33} +(0.0573542 + 0.176518i) q^{34} +(5.43488 + 3.94867i) q^{35} +2.31630 q^{36} +4.55430 q^{37} +(0.358468 + 0.260443i) q^{38} +(6.26617 - 4.55264i) q^{39} +(1.33749 - 0.971747i) q^{40} +(1.55644 - 4.79022i) q^{41} +(-0.606102 - 0.440359i) q^{42} +(2.97801 - 9.16536i) q^{43} +(-3.39505 - 10.4489i) q^{44} +(2.14149 - 1.55588i) q^{45} +(0.117272 + 0.360925i) q^{46} +(-2.06225 - 6.34694i) q^{47} +(4.14317 - 3.01019i) q^{48} +(0.600961 + 1.84957i) q^{49} +(0.00260421 - 0.00801494i) q^{50} +(1.09189 + 0.793304i) q^{51} +(-3.48570 + 10.7279i) q^{52} +(-2.30288 + 1.67314i) q^{53} +(-0.846791 + 0.615229i) q^{54} +(-10.1575 - 7.37983i) q^{55} +2.20126 q^{56} +3.22205 q^{57} +(-0.845707 - 0.614442i) q^{58} +(0.552196 + 1.69948i) q^{59} +(1.84135 - 5.66709i) q^{60} +3.77827 q^{61} +(-0.283818 + 0.993649i) q^{62} +3.52447 q^{63} +(-2.22031 + 6.83341i) q^{64} +(3.98340 + 12.2596i) q^{65} +(1.13277 + 0.823004i) q^{66} +5.18873 q^{67} -1.96555 q^{68} +(2.23258 + 1.62206i) q^{69} +(1.00872 - 0.732881i) q^{70} +(-12.5288 + 9.10269i) q^{71} +(0.268027 - 0.824902i) q^{72} +(-10.5139 - 7.63877i) q^{73} +(0.261208 - 0.803916i) q^{74} +(-0.0189372 - 0.0582826i) q^{75} +(-3.79623 + 2.75812i) q^{76} +(-5.16590 - 15.8990i) q^{77} +(-0.444232 - 1.36720i) q^{78} +(-0.758945 + 0.551405i) q^{79} +(2.63381 + 8.10604i) q^{80} +(-1.25953 + 3.87644i) q^{81} +(-0.756292 - 0.549478i) q^{82} +(-1.29150 + 3.97482i) q^{83} +(6.41870 - 4.66346i) q^{84} +(-1.81721 + 1.32028i) q^{85} +(-1.44705 - 1.05134i) q^{86} -7.60152 q^{87} -4.11401 q^{88} +(11.6872 + 8.49124i) q^{89} +(-0.151818 - 0.467247i) q^{90} +(-5.30384 + 16.3235i) q^{91} -4.01895 q^{92} +(2.57739 + 7.05870i) q^{93} -1.23863 q^{94} +(-1.65707 + 5.09994i) q^{95} +(-0.907656 - 2.79348i) q^{96} +(-0.642163 - 0.466559i) q^{97} +0.360950 q^{98} -6.58702 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 96 q - 2 q^{2} - 4 q^{3} - 30 q^{4} + 6 q^{5} - 8 q^{6} - 10 q^{7} - 36 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 96 q - 2 q^{2} - 4 q^{3} - 30 q^{4} + 6 q^{5} - 8 q^{6} - 10 q^{7} - 36 q^{9} - 13 q^{10} - 4 q^{11} - 14 q^{12} - 14 q^{13} + 17 q^{14} - 9 q^{15} - 58 q^{16} - 24 q^{17} - 24 q^{18} - 6 q^{19} + 43 q^{20} + 26 q^{21} + 42 q^{22} - 11 q^{23} - 38 q^{24} + 126 q^{25} - 44 q^{26} - q^{27} + 31 q^{28} - 10 q^{29} - 70 q^{30} + 21 q^{31} + 28 q^{32} - 36 q^{33} - 2 q^{34} + 2 q^{35} + 160 q^{36} + 54 q^{37} + 15 q^{38} - 10 q^{39} - 29 q^{40} - 14 q^{41} - 3 q^{42} + 6 q^{43} - 5 q^{44} - q^{45} - 17 q^{46} - 14 q^{47} - 93 q^{48} - 72 q^{49} + 108 q^{50} + q^{51} + 13 q^{52} - 30 q^{53} - 63 q^{54} - 12 q^{55} + 66 q^{56} - 62 q^{57} + 29 q^{58} + 8 q^{59} - 86 q^{60} - 14 q^{61} - 34 q^{62} + 86 q^{63} - 122 q^{64} + 13 q^{65} - 40 q^{66} + 126 q^{67} + 120 q^{68} - 34 q^{69} - 38 q^{70} - 39 q^{71} - 51 q^{72} - 60 q^{73} - 111 q^{74} - 41 q^{75} + 64 q^{76} - 26 q^{77} - 99 q^{78} - 33 q^{79} - 91 q^{80} + 81 q^{81} - 88 q^{82} + 22 q^{83} + 160 q^{84} - 4 q^{85} + 35 q^{86} + 70 q^{87} - 120 q^{88} + 101 q^{89} + 125 q^{90} - 13 q^{91} - 98 q^{92} + 47 q^{93} - 8 q^{94} - 64 q^{95} + 208 q^{96} + 16 q^{97} + 8 q^{98} + 280 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/527\mathbb{Z}\right)^\times\).

\(n\) \(156\) \(375\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{5}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.0573542 0.176518i 0.0405555 0.124817i −0.928729 0.370759i \(-0.879097\pi\)
0.969284 + 0.245942i \(0.0790974\pi\)
\(3\) −0.417065 1.28359i −0.240792 0.741083i −0.996300 0.0859430i \(-0.972610\pi\)
0.755508 0.655140i \(-0.227390\pi\)
\(4\) 1.59016 + 1.15532i 0.795082 + 0.577661i
\(5\) 2.24620 1.00453 0.502265 0.864714i \(-0.332500\pi\)
0.502265 + 0.864714i \(0.332500\pi\)
\(6\) −0.250498 −0.102265
\(7\) 2.41959 + 1.75793i 0.914519 + 0.664437i 0.942154 0.335181i \(-0.108798\pi\)
−0.0276347 + 0.999618i \(0.508798\pi\)
\(8\) 0.595448 0.432618i 0.210523 0.152954i
\(9\) 0.953382 0.692673i 0.317794 0.230891i
\(10\) 0.128829 0.396494i 0.0407393 0.125383i
\(11\) −4.52207 3.28548i −1.36346 0.990608i −0.998217 0.0596941i \(-0.980987\pi\)
−0.365238 0.930914i \(-0.619013\pi\)
\(12\) 0.819762 2.52297i 0.236645 0.728318i
\(13\) 1.77340 + 5.45795i 0.491852 + 1.51376i 0.821806 + 0.569767i \(0.192967\pi\)
−0.329954 + 0.943997i \(0.607033\pi\)
\(14\) 0.449081 0.326276i 0.120022 0.0872010i
\(15\) −0.936810 2.88320i −0.241883 0.744440i
\(16\) 1.17256 + 3.60878i 0.293141 + 0.902196i
\(17\) −0.809017 + 0.587785i −0.196215 + 0.142559i
\(18\) −0.0675888 0.208017i −0.0159308 0.0490300i
\(19\) −0.737722 + 2.27048i −0.169245 + 0.520883i −0.999324 0.0367630i \(-0.988295\pi\)
0.830079 + 0.557646i \(0.188295\pi\)
\(20\) 3.57183 + 2.59508i 0.798684 + 0.580278i
\(21\) 1.24735 3.83894i 0.272194 0.837726i
\(22\) −0.839305 + 0.609791i −0.178940 + 0.130008i
\(23\) −1.65419 + 1.20184i −0.344923 + 0.250601i −0.746736 0.665121i \(-0.768380\pi\)
0.401813 + 0.915722i \(0.368380\pi\)
\(24\) −0.803646 0.583883i −0.164044 0.119185i
\(25\) 0.0454058 0.00908116
\(26\) 1.06514 0.208891
\(27\) −4.56240 3.31478i −0.878035 0.637929i
\(28\) 1.81657 + 5.59081i 0.343299 + 1.05656i
\(29\) 1.74045 5.35656i 0.323194 0.994688i −0.649056 0.760741i \(-0.724836\pi\)
0.972249 0.233947i \(-0.0751642\pi\)
\(30\) −0.562667 −0.102729
\(31\) −5.56417 + 0.200037i −0.999354 + 0.0359277i
\(32\) 2.17629 0.384718
\(33\) −2.33122 + 7.17475i −0.405813 + 1.24896i
\(34\) 0.0573542 + 0.176518i 0.00983616 + 0.0302726i
\(35\) 5.43488 + 3.94867i 0.918662 + 0.667447i
\(36\) 2.31630 0.386049
\(37\) 4.55430 0.748722 0.374361 0.927283i \(-0.377862\pi\)
0.374361 + 0.927283i \(0.377862\pi\)
\(38\) 0.358468 + 0.260443i 0.0581513 + 0.0422494i
\(39\) 6.26617 4.55264i 1.00339 0.729006i
\(40\) 1.33749 0.971747i 0.211476 0.153647i
\(41\) 1.55644 4.79022i 0.243075 0.748107i −0.752872 0.658166i \(-0.771332\pi\)
0.995947 0.0899405i \(-0.0286677\pi\)
\(42\) −0.606102 0.440359i −0.0935235 0.0679488i
\(43\) 2.97801 9.16536i 0.454142 1.39770i −0.417998 0.908448i \(-0.637268\pi\)
0.872140 0.489256i \(-0.162732\pi\)
\(44\) −3.39505 10.4489i −0.511823 1.57523i
\(45\) 2.14149 1.55588i 0.319234 0.231937i
\(46\) 0.117272 + 0.360925i 0.0172908 + 0.0532155i
\(47\) −2.06225 6.34694i −0.300810 0.925797i −0.981208 0.192954i \(-0.938193\pi\)
0.680398 0.732843i \(-0.261807\pi\)
\(48\) 4.14317 3.01019i 0.598016 0.434484i
\(49\) 0.600961 + 1.84957i 0.0858516 + 0.264224i
\(50\) 0.00260421 0.00801494i 0.000368291 0.00113348i
\(51\) 1.09189 + 0.793304i 0.152895 + 0.111085i
\(52\) −3.48570 + 10.7279i −0.483380 + 1.48769i
\(53\) −2.30288 + 1.67314i −0.316324 + 0.229823i −0.734605 0.678495i \(-0.762633\pi\)
0.418281 + 0.908318i \(0.362633\pi\)
\(54\) −0.846791 + 0.615229i −0.115234 + 0.0837221i
\(55\) −10.1575 7.37983i −1.36963 0.995096i
\(56\) 2.20126 0.294155
\(57\) 3.22205 0.426770
\(58\) −0.845707 0.614442i −0.111047 0.0806802i
\(59\) 0.552196 + 1.69948i 0.0718897 + 0.221254i 0.980545 0.196292i \(-0.0628902\pi\)
−0.908656 + 0.417546i \(0.862890\pi\)
\(60\) 1.84135 5.66709i 0.237717 0.731618i
\(61\) 3.77827 0.483759 0.241879 0.970306i \(-0.422236\pi\)
0.241879 + 0.970306i \(0.422236\pi\)
\(62\) −0.283818 + 0.993649i −0.0360449 + 0.126194i
\(63\) 3.52447 0.444041
\(64\) −2.22031 + 6.83341i −0.277539 + 0.854176i
\(65\) 3.98340 + 12.2596i 0.494080 + 1.52062i
\(66\) 1.13277 + 0.823004i 0.139434 + 0.101305i
\(67\) 5.18873 0.633904 0.316952 0.948442i \(-0.397341\pi\)
0.316952 + 0.948442i \(0.397341\pi\)
\(68\) −1.96555 −0.238358
\(69\) 2.23258 + 1.62206i 0.268771 + 0.195273i
\(70\) 1.00872 0.732881i 0.120566 0.0875960i
\(71\) −12.5288 + 9.10269i −1.48689 + 1.08029i −0.511639 + 0.859201i \(0.670961\pi\)
−0.975253 + 0.221090i \(0.929039\pi\)
\(72\) 0.268027 0.824902i 0.0315873 0.0972156i
\(73\) −10.5139 7.63877i −1.23055 0.894050i −0.233623 0.972327i \(-0.575058\pi\)
−0.996932 + 0.0782771i \(0.975058\pi\)
\(74\) 0.261208 0.803916i 0.0303648 0.0934533i
\(75\) −0.0189372 0.0582826i −0.00218668 0.00672989i
\(76\) −3.79623 + 2.75812i −0.435458 + 0.316379i
\(77\) −5.16590 15.8990i −0.588709 1.81186i
\(78\) −0.444232 1.36720i −0.0502993 0.154805i
\(79\) −0.758945 + 0.551405i −0.0853879 + 0.0620380i −0.629660 0.776871i \(-0.716806\pi\)
0.544272 + 0.838909i \(0.316806\pi\)
\(80\) 2.63381 + 8.10604i 0.294469 + 0.906283i
\(81\) −1.25953 + 3.87644i −0.139948 + 0.430715i
\(82\) −0.756292 0.549478i −0.0835185 0.0606797i
\(83\) −1.29150 + 3.97482i −0.141760 + 0.436294i −0.996580 0.0826314i \(-0.973668\pi\)
0.854820 + 0.518925i \(0.173668\pi\)
\(84\) 6.41870 4.66346i 0.700338 0.508825i
\(85\) −1.81721 + 1.32028i −0.197104 + 0.143205i
\(86\) −1.44705 1.05134i −0.156039 0.113369i
\(87\) −7.60152 −0.814969
\(88\) −4.11401 −0.438555
\(89\) 11.6872 + 8.49124i 1.23884 + 0.900070i 0.997521 0.0703757i \(-0.0224198\pi\)
0.241320 + 0.970446i \(0.422420\pi\)
\(90\) −0.151818 0.467247i −0.0160030 0.0492522i
\(91\) −5.30384 + 16.3235i −0.555993 + 1.71117i
\(92\) −4.01895 −0.419004
\(93\) 2.57739 + 7.05870i 0.267262 + 0.731953i
\(94\) −1.23863 −0.127755
\(95\) −1.65707 + 5.09994i −0.170012 + 0.523243i
\(96\) −0.907656 2.79348i −0.0926372 0.285108i
\(97\) −0.642163 0.466559i −0.0652018 0.0473719i 0.554707 0.832046i \(-0.312830\pi\)
−0.619909 + 0.784674i \(0.712830\pi\)
\(98\) 0.360950 0.0364614
\(99\) −6.58702 −0.662021
\(100\) 0.0722027 + 0.0524584i 0.00722027 + 0.00524584i
\(101\) −12.3764 + 8.99195i −1.23149 + 0.894732i −0.997001 0.0773856i \(-0.975343\pi\)
−0.234492 + 0.972118i \(0.575343\pi\)
\(102\) 0.202657 0.147239i 0.0200660 0.0145788i
\(103\) 5.21834 16.0604i 0.514179 1.58248i −0.270593 0.962694i \(-0.587220\pi\)
0.784771 0.619785i \(-0.212780\pi\)
\(104\) 3.41718 + 2.48272i 0.335082 + 0.243451i
\(105\) 2.80179 8.62302i 0.273427 0.841521i
\(106\) 0.163259 + 0.502460i 0.0158571 + 0.0488033i
\(107\) −1.98946 + 1.44542i −0.192328 + 0.139734i −0.679782 0.733414i \(-0.737926\pi\)
0.487454 + 0.873149i \(0.337926\pi\)
\(108\) −3.42533 10.5421i −0.329603 1.01441i
\(109\) −4.73624 14.5766i −0.453649 1.39619i −0.872714 0.488233i \(-0.837642\pi\)
0.419064 0.907957i \(-0.362358\pi\)
\(110\) −1.88525 + 1.36971i −0.179751 + 0.130597i
\(111\) −1.89944 5.84587i −0.180287 0.554865i
\(112\) −3.50688 + 10.7931i −0.331369 + 1.01985i
\(113\) 1.53953 + 1.11853i 0.144827 + 0.105223i 0.657839 0.753158i \(-0.271471\pi\)
−0.513012 + 0.858381i \(0.671471\pi\)
\(114\) 0.184798 0.568749i 0.0173079 0.0532682i
\(115\) −3.71564 + 2.69957i −0.346485 + 0.251736i
\(116\) 8.95615 6.50703i 0.831558 0.604162i
\(117\) 5.47130 + 3.97513i 0.505822 + 0.367501i
\(118\) 0.331660 0.0305318
\(119\) −2.99078 −0.274164
\(120\) −1.80515 1.31152i −0.164787 0.119725i
\(121\) 6.25557 + 19.2527i 0.568688 + 1.75024i
\(122\) 0.216700 0.666933i 0.0196191 0.0603813i
\(123\) −6.79783 −0.612940
\(124\) −9.07905 6.11032i −0.815323 0.548723i
\(125\) −11.1290 −0.995408
\(126\) 0.202143 0.622132i 0.0180083 0.0554239i
\(127\) 2.43668 + 7.49933i 0.216220 + 0.665458i 0.999065 + 0.0432405i \(0.0137682\pi\)
−0.782844 + 0.622218i \(0.786232\pi\)
\(128\) 4.60019 + 3.34224i 0.406604 + 0.295415i
\(129\) −13.0066 −1.14517
\(130\) 2.39251 0.209837
\(131\) 14.8158 + 10.7643i 1.29446 + 0.940482i 0.999885 0.0151461i \(-0.00482135\pi\)
0.294577 + 0.955628i \(0.404821\pi\)
\(132\) −11.9962 + 8.71573i −1.04413 + 0.758607i
\(133\) −5.77634 + 4.19675i −0.500872 + 0.363905i
\(134\) 0.297595 0.915904i 0.0257083 0.0791221i
\(135\) −10.2481 7.44565i −0.882012 0.640819i
\(136\) −0.227441 + 0.699991i −0.0195029 + 0.0600238i
\(137\) −2.26053 6.95720i −0.193130 0.594394i −0.999993 0.00365530i \(-0.998836\pi\)
0.806863 0.590739i \(-0.201164\pi\)
\(138\) 0.414371 0.301058i 0.0352736 0.0256278i
\(139\) 1.67240 + 5.14712i 0.141851 + 0.436573i 0.996593 0.0824810i \(-0.0262844\pi\)
−0.854741 + 0.519054i \(0.826284\pi\)
\(140\) 4.08037 + 12.5581i 0.344854 + 1.06135i
\(141\) −7.28680 + 5.29417i −0.613659 + 0.445850i
\(142\) 0.888211 + 2.73363i 0.0745370 + 0.229401i
\(143\) 9.91255 30.5077i 0.828929 2.55118i
\(144\) 3.61761 + 2.62835i 0.301467 + 0.219029i
\(145\) 3.90940 12.0319i 0.324658 0.999194i
\(146\) −1.95139 + 1.41777i −0.161498 + 0.117336i
\(147\) 2.12345 1.54278i 0.175139 0.127246i
\(148\) 7.24209 + 5.26169i 0.595296 + 0.432508i
\(149\) −2.06734 −0.169363 −0.0846814 0.996408i \(-0.526987\pi\)
−0.0846814 + 0.996408i \(0.526987\pi\)
\(150\) −0.0113740 −0.000928687
\(151\) −14.4759 10.5173i −1.17803 0.855888i −0.186081 0.982534i \(-0.559579\pi\)
−0.991948 + 0.126646i \(0.959579\pi\)
\(152\) 0.542974 + 1.67110i 0.0440410 + 0.135544i
\(153\) −0.364160 + 1.12077i −0.0294406 + 0.0906087i
\(154\) −3.10275 −0.250026
\(155\) −12.4982 + 0.449323i −1.00388 + 0.0360905i
\(156\) 15.2240 1.21890
\(157\) −5.38891 + 16.5854i −0.430082 + 1.32366i 0.467961 + 0.883749i \(0.344989\pi\)
−0.898043 + 0.439907i \(0.855011\pi\)
\(158\) 0.0538043 + 0.165593i 0.00428044 + 0.0131739i
\(159\) 3.10807 + 2.25815i 0.246486 + 0.179083i
\(160\) 4.88839 0.386461
\(161\) −6.11522 −0.481947
\(162\) 0.612022 + 0.444660i 0.0480850 + 0.0349358i
\(163\) −1.28699 + 0.935056i −0.100805 + 0.0732393i −0.637046 0.770826i \(-0.719844\pi\)
0.536241 + 0.844065i \(0.319844\pi\)
\(164\) 8.00924 5.81906i 0.625417 0.454392i
\(165\) −5.23638 + 16.1159i −0.407652 + 1.25462i
\(166\) 0.627555 + 0.455945i 0.0487077 + 0.0353882i
\(167\) −0.598260 + 1.84126i −0.0462948 + 0.142481i −0.971532 0.236909i \(-0.923866\pi\)
0.925237 + 0.379389i \(0.123866\pi\)
\(168\) −0.918066 2.82552i −0.0708303 0.217993i
\(169\) −16.1271 + 11.7170i −1.24055 + 0.901310i
\(170\) 0.128829 + 0.396494i 0.00988072 + 0.0304097i
\(171\) 0.869366 + 2.67563i 0.0664821 + 0.204611i
\(172\) 15.3245 11.1339i 1.16848 0.848950i
\(173\) −4.95819 15.2597i −0.376964 1.16018i −0.942144 0.335209i \(-0.891193\pi\)
0.565180 0.824968i \(-0.308807\pi\)
\(174\) −0.435979 + 1.34181i −0.0330515 + 0.101722i
\(175\) 0.109863 + 0.0798205i 0.00830490 + 0.00603386i
\(176\) 6.55415 20.1716i 0.494037 1.52049i
\(177\) 1.95114 1.41759i 0.146657 0.106553i
\(178\) 2.16917 1.57599i 0.162586 0.118126i
\(179\) −0.119949 0.0871481i −0.00896542 0.00651376i 0.583294 0.812261i \(-0.301764\pi\)
−0.592259 + 0.805748i \(0.701764\pi\)
\(180\) 5.20286 0.387798
\(181\) 1.59739 0.118733 0.0593666 0.998236i \(-0.481092\pi\)
0.0593666 + 0.998236i \(0.481092\pi\)
\(182\) 2.57720 + 1.87244i 0.191035 + 0.138795i
\(183\) −1.57579 4.84977i −0.116485 0.358505i
\(184\) −0.465047 + 1.43127i −0.0342837 + 0.105514i
\(185\) 10.2299 0.752114
\(186\) 1.39381 0.0501088i 0.102199 0.00367416i
\(187\) 5.58958 0.408751
\(188\) 4.05345 12.4752i 0.295628 0.909851i
\(189\) −5.21197 16.0408i −0.379115 1.16680i
\(190\) 0.805191 + 0.585006i 0.0584147 + 0.0424408i
\(191\) −2.51252 −0.181799 −0.0908997 0.995860i \(-0.528974\pi\)
−0.0908997 + 0.995860i \(0.528974\pi\)
\(192\) 9.69733 0.699845
\(193\) 15.6726 + 11.3868i 1.12814 + 0.819641i 0.985423 0.170123i \(-0.0544165\pi\)
0.142716 + 0.989764i \(0.454416\pi\)
\(194\) −0.119187 + 0.0865943i −0.00855711 + 0.00621711i
\(195\) 14.0751 10.2261i 1.00794 0.732309i
\(196\) −1.18122 + 3.63542i −0.0843728 + 0.259673i
\(197\) 10.2526 + 7.44891i 0.730464 + 0.530713i 0.889710 0.456526i \(-0.150906\pi\)
−0.159246 + 0.987239i \(0.550906\pi\)
\(198\) −0.377793 + 1.16273i −0.0268486 + 0.0826315i
\(199\) −3.36414 10.3537i −0.238477 0.733958i −0.996641 0.0818934i \(-0.973903\pi\)
0.758164 0.652064i \(-0.226097\pi\)
\(200\) 0.0270368 0.0196434i 0.00191179 0.00138900i
\(201\) −2.16404 6.66022i −0.152639 0.469776i
\(202\) 0.877405 + 2.70038i 0.0617340 + 0.189998i
\(203\) 13.6277 9.90107i 0.956474 0.694919i
\(204\) 0.819762 + 2.52297i 0.0573948 + 0.176643i
\(205\) 3.49607 10.7598i 0.244176 0.751496i
\(206\) −2.53566 1.84226i −0.176668 0.128357i
\(207\) −0.744595 + 2.29163i −0.0517529 + 0.159279i
\(208\) −17.6171 + 12.7996i −1.22153 + 0.887493i
\(209\) 10.7956 7.84348i 0.746749 0.542545i
\(210\) −1.36142 0.989133i −0.0939472 0.0682566i
\(211\) −4.65283 −0.320314 −0.160157 0.987092i \(-0.551200\pi\)
−0.160157 + 0.987092i \(0.551200\pi\)
\(212\) −5.59496 −0.384264
\(213\) 16.9095 + 12.2854i 1.15862 + 0.841785i
\(214\) 0.141040 + 0.434076i 0.00964128 + 0.0296728i
\(215\) 6.68919 20.5872i 0.456199 1.40404i
\(216\) −4.15071 −0.282420
\(217\) −13.8147 9.29744i −0.937800 0.631151i
\(218\) −2.84468 −0.192666
\(219\) −5.42011 + 16.6814i −0.366257 + 1.12722i
\(220\) −7.62596 23.4703i −0.514142 1.58237i
\(221\) −4.64281 3.37320i −0.312309 0.226906i
\(222\) −1.14084 −0.0765683
\(223\) 5.98045 0.400480 0.200240 0.979747i \(-0.435828\pi\)
0.200240 + 0.979747i \(0.435828\pi\)
\(224\) 5.26574 + 3.82578i 0.351832 + 0.255621i
\(225\) 0.0432891 0.0314514i 0.00288594 0.00209676i
\(226\) 0.285740 0.207602i 0.0190071 0.0138095i
\(227\) 0.784955 2.41584i 0.0520993 0.160345i −0.921622 0.388090i \(-0.873135\pi\)
0.973721 + 0.227745i \(0.0731351\pi\)
\(228\) 5.12358 + 3.72250i 0.339318 + 0.246529i
\(229\) −7.21892 + 22.2175i −0.477040 + 1.46818i 0.366148 + 0.930557i \(0.380676\pi\)
−0.843187 + 0.537620i \(0.819324\pi\)
\(230\) 0.263415 + 0.810709i 0.0173691 + 0.0534566i
\(231\) −18.2533 + 13.2618i −1.20098 + 0.872564i
\(232\) −1.28100 3.94250i −0.0841016 0.258838i
\(233\) −0.519099 1.59762i −0.0340073 0.104664i 0.932612 0.360881i \(-0.117524\pi\)
−0.966619 + 0.256217i \(0.917524\pi\)
\(234\) 1.01548 0.737793i 0.0663843 0.0482310i
\(235\) −4.63221 14.2565i −0.302172 0.929991i
\(236\) −1.08537 + 3.34042i −0.0706515 + 0.217443i
\(237\) 1.02431 + 0.744204i 0.0665360 + 0.0483413i
\(238\) −0.171534 + 0.527926i −0.0111189 + 0.0342204i
\(239\) −16.4703 + 11.9664i −1.06537 + 0.774040i −0.975075 0.221875i \(-0.928782\pi\)
−0.0902993 + 0.995915i \(0.528782\pi\)
\(240\) 9.30639 6.76149i 0.600725 0.436452i
\(241\) 20.4991 + 14.8935i 1.32047 + 0.959374i 0.999926 + 0.0121393i \(0.00386414\pi\)
0.320539 + 0.947235i \(0.396136\pi\)
\(242\) 3.75723 0.241524
\(243\) −11.4172 −0.732416
\(244\) 6.00808 + 4.36513i 0.384628 + 0.279449i
\(245\) 1.34988 + 4.15449i 0.0862405 + 0.265421i
\(246\) −0.389884 + 1.19994i −0.0248581 + 0.0765053i
\(247\) −13.7004 −0.871738
\(248\) −3.22663 + 2.52627i −0.204891 + 0.160419i
\(249\) 5.64069 0.357464
\(250\) −0.638295 + 1.96447i −0.0403693 + 0.124244i
\(251\) 7.43040 + 22.8684i 0.469003 + 1.44344i 0.853878 + 0.520474i \(0.174245\pi\)
−0.384875 + 0.922969i \(0.625755\pi\)
\(252\) 5.60449 + 4.07190i 0.353049 + 0.256505i
\(253\) 11.4290 0.718534
\(254\) 1.46352 0.0918295
\(255\) 2.45260 + 1.78192i 0.153588 + 0.111588i
\(256\) −10.7719 + 7.82623i −0.673243 + 0.489140i
\(257\) 15.4720 11.2411i 0.965116 0.701198i 0.0107828 0.999942i \(-0.496568\pi\)
0.954333 + 0.298744i \(0.0965677\pi\)
\(258\) −0.745983 + 2.29590i −0.0464429 + 0.142937i
\(259\) 11.0195 + 8.00616i 0.684721 + 0.497479i
\(260\) −7.82958 + 24.0970i −0.485570 + 1.49443i
\(261\) −2.05103 6.31241i −0.126955 0.390728i
\(262\) 2.74984 1.99788i 0.169886 0.123429i
\(263\) −9.68621 29.8111i −0.597277 1.83823i −0.543048 0.839702i \(-0.682730\pi\)
−0.0542290 0.998529i \(-0.517270\pi\)
\(264\) 1.71581 + 5.28072i 0.105601 + 0.325006i
\(265\) −5.17271 + 3.75820i −0.317757 + 0.230864i
\(266\) 0.409505 + 1.26033i 0.0251084 + 0.0772757i
\(267\) 6.02499 18.5430i 0.368723 1.13481i
\(268\) 8.25094 + 5.99466i 0.504006 + 0.366182i
\(269\) −1.44675 + 4.45262i −0.0882096 + 0.271481i −0.985425 0.170113i \(-0.945587\pi\)
0.897215 + 0.441594i \(0.145587\pi\)
\(270\) −1.90206 + 1.38193i −0.115756 + 0.0841014i
\(271\) −15.3081 + 11.1220i −0.929899 + 0.675611i −0.945968 0.324260i \(-0.894885\pi\)
0.0160693 + 0.999871i \(0.494885\pi\)
\(272\) −3.06981 2.23035i −0.186135 0.135235i
\(273\) 23.1648 1.40200
\(274\) −1.35772 −0.0820230
\(275\) −0.205328 0.149180i −0.0123818 0.00899587i
\(276\) 1.67616 + 5.15870i 0.100893 + 0.310517i
\(277\) 3.13013 9.63355i 0.188071 0.578824i −0.811916 0.583774i \(-0.801576\pi\)
0.999988 + 0.00494965i \(0.00157553\pi\)
\(278\) 1.00448 0.0602446
\(279\) −5.16622 + 4.04486i −0.309294 + 0.242160i
\(280\) 4.94445 0.295488
\(281\) 3.05874 9.41384i 0.182469 0.561582i −0.817426 0.576033i \(-0.804600\pi\)
0.999896 + 0.0144507i \(0.00459995\pi\)
\(282\) 0.516588 + 1.58989i 0.0307624 + 0.0946768i
\(283\) 17.8997 + 13.0049i 1.06403 + 0.773062i 0.974830 0.222951i \(-0.0715691\pi\)
0.0891995 + 0.996014i \(0.471569\pi\)
\(284\) −30.4394 −1.80624
\(285\) 7.23735 0.428704
\(286\) −4.81663 3.49949i −0.284813 0.206929i
\(287\) 12.1868 8.85426i 0.719366 0.522650i
\(288\) 2.07484 1.50746i 0.122261 0.0888280i
\(289\) 0.309017 0.951057i 0.0181775 0.0559445i
\(290\) −1.89962 1.38016i −0.111550 0.0810457i
\(291\) −0.331048 + 1.01886i −0.0194064 + 0.0597267i
\(292\) −7.89353 24.2938i −0.461934 1.42169i
\(293\) 4.46676 3.24529i 0.260951 0.189592i −0.449615 0.893222i \(-0.648439\pi\)
0.710566 + 0.703630i \(0.248439\pi\)
\(294\) −0.150539 0.463312i −0.00877963 0.0270209i
\(295\) 1.24034 + 3.81738i 0.0722154 + 0.222256i
\(296\) 2.71185 1.97027i 0.157623 0.114520i
\(297\) 9.74087 + 29.9793i 0.565223 + 1.73958i
\(298\) −0.118570 + 0.364922i −0.00686859 + 0.0211394i
\(299\) −9.49313 6.89716i −0.549002 0.398873i
\(300\) 0.0372220 0.114557i 0.00214901 0.00661398i
\(301\) 23.3177 16.9413i 1.34401 0.976478i
\(302\) −2.68675 + 1.95204i −0.154605 + 0.112327i
\(303\) 16.7037 + 12.1360i 0.959605 + 0.697194i
\(304\) −9.05868 −0.519551
\(305\) 8.48675 0.485950
\(306\) 0.176950 + 0.128561i 0.0101155 + 0.00734937i
\(307\) 2.18357 + 6.72035i 0.124623 + 0.383551i 0.993832 0.110894i \(-0.0353715\pi\)
−0.869209 + 0.494445i \(0.835371\pi\)
\(308\) 10.1538 31.2503i 0.578569 1.78065i
\(309\) −22.7914 −1.29656
\(310\) −0.637512 + 2.23193i −0.0362082 + 0.126765i
\(311\) 27.2628 1.54593 0.772966 0.634447i \(-0.218772\pi\)
0.772966 + 0.634447i \(0.218772\pi\)
\(312\) 1.76162 5.42172i 0.0997323 0.306945i
\(313\) −1.03708 3.19180i −0.0586192 0.180411i 0.917459 0.397830i \(-0.130236\pi\)
−0.976079 + 0.217418i \(0.930236\pi\)
\(314\) 2.61854 + 1.90248i 0.147773 + 0.107363i
\(315\) 7.91665 0.446053
\(316\) −1.84390 −0.103727
\(317\) 7.49484 + 5.44532i 0.420952 + 0.305840i 0.778021 0.628239i \(-0.216224\pi\)
−0.357069 + 0.934078i \(0.616224\pi\)
\(318\) 0.576865 0.419117i 0.0323490 0.0235029i
\(319\) −25.4693 + 18.5045i −1.42601 + 1.03605i
\(320\) −4.98725 + 15.3492i −0.278796 + 0.858046i
\(321\) 2.68507 + 1.95082i 0.149866 + 0.108884i
\(322\) −0.350733 + 1.07945i −0.0195456 + 0.0601552i
\(323\) −0.737722 2.27048i −0.0410480 0.126333i
\(324\) −6.48140 + 4.70901i −0.360078 + 0.261612i
\(325\) 0.0805225 + 0.247823i 0.00446659 + 0.0137467i
\(326\) 0.0912397 + 0.280807i 0.00505330 + 0.0155525i
\(327\) −16.7352 + 12.1588i −0.925457 + 0.672384i
\(328\) −1.14556 3.52567i −0.0632530 0.194673i
\(329\) 6.16772 18.9823i 0.340037 1.04653i
\(330\) 2.54442 + 1.84863i 0.140066 + 0.101764i
\(331\) 3.46959 10.6783i 0.190706 0.586933i −0.809294 0.587404i \(-0.800150\pi\)
1.00000 0.000471352i \(0.000150036\pi\)
\(332\) −6.64590 + 4.82853i −0.364741 + 0.265000i
\(333\) 4.34199 3.15464i 0.237940 0.172873i
\(334\) 0.290702 + 0.211207i 0.0159065 + 0.0115568i
\(335\) 11.6549 0.636776
\(336\) 15.3165 0.835584
\(337\) −15.9590 11.5949i −0.869340 0.631613i 0.0610696 0.998134i \(-0.480549\pi\)
−0.930410 + 0.366521i \(0.880549\pi\)
\(338\) 1.14331 + 3.51875i 0.0621879 + 0.191395i
\(339\) 0.793660 2.44263i 0.0431057 0.132666i
\(340\) −4.41502 −0.239438
\(341\) 25.8188 + 17.3764i 1.39817 + 0.940983i
\(342\) 0.522159 0.0282351
\(343\) 4.67207 14.3791i 0.252268 0.776401i
\(344\) −2.19185 6.74583i −0.118177 0.363711i
\(345\) 5.01481 + 3.64348i 0.269989 + 0.196158i
\(346\) −2.97799 −0.160098
\(347\) 27.3170 1.46646 0.733228 0.679983i \(-0.238013\pi\)
0.733228 + 0.679983i \(0.238013\pi\)
\(348\) −12.0877 8.78221i −0.647967 0.470776i
\(349\) 18.1163 13.1623i 0.969744 0.704560i 0.0143508 0.999897i \(-0.495432\pi\)
0.955393 + 0.295337i \(0.0954318\pi\)
\(350\) 0.0203909 0.0148148i 0.00108994 0.000791886i
\(351\) 10.0010 30.7798i 0.533812 1.64290i
\(352\) −9.84136 7.15016i −0.524546 0.381105i
\(353\) −6.97222 + 21.4583i −0.371094 + 1.14211i 0.574982 + 0.818166i \(0.305009\pi\)
−0.946076 + 0.323944i \(0.894991\pi\)
\(354\) −0.138324 0.425717i −0.00735182 0.0226266i
\(355\) −28.1421 + 20.4464i −1.49363 + 1.08518i
\(356\) 8.77444 + 27.0050i 0.465044 + 1.43126i
\(357\) 1.24735 + 3.83894i 0.0660166 + 0.203178i
\(358\) −0.0222628 + 0.0161749i −0.00117663 + 0.000854868i
\(359\) −2.31765 7.13300i −0.122321 0.376465i 0.871083 0.491137i \(-0.163418\pi\)
−0.993403 + 0.114672i \(0.963418\pi\)
\(360\) 0.602041 1.85289i 0.0317304 0.0976560i
\(361\) 10.7605 + 7.81796i 0.566342 + 0.411471i
\(362\) 0.0916172 0.281969i 0.00481529 0.0148199i
\(363\) 22.1036 16.0592i 1.16014 0.842890i
\(364\) −27.2929 + 19.8295i −1.43054 + 1.03935i
\(365\) −23.6162 17.1582i −1.23613 0.898101i
\(366\) −0.946449 −0.0494717
\(367\) −11.3120 −0.590484 −0.295242 0.955423i \(-0.595400\pi\)
−0.295242 + 0.955423i \(0.595400\pi\)
\(368\) −6.27683 4.56038i −0.327202 0.237726i
\(369\) −1.83418 5.64502i −0.0954834 0.293868i
\(370\) 0.586725 1.80575i 0.0305024 0.0938767i
\(371\) −8.51328 −0.441987
\(372\) −4.05661 + 14.2022i −0.210325 + 0.736350i
\(373\) 18.9749 0.982482 0.491241 0.871024i \(-0.336544\pi\)
0.491241 + 0.871024i \(0.336544\pi\)
\(374\) 0.320586 0.986662i 0.0165771 0.0510191i
\(375\) 4.64151 + 14.2851i 0.239687 + 0.737680i
\(376\) −3.97376 2.88711i −0.204931 0.148891i
\(377\) 32.3224 1.66469
\(378\) −3.13042 −0.161011
\(379\) −10.1649 7.38524i −0.522136 0.379354i 0.295272 0.955413i \(-0.404590\pi\)
−0.817408 + 0.576059i \(0.804590\pi\)
\(380\) −8.52709 + 6.19529i −0.437430 + 0.317812i
\(381\) 8.60984 6.25541i 0.441095 0.320475i
\(382\) −0.144103 + 0.443504i −0.00737297 + 0.0226917i
\(383\) 8.99671 + 6.53649i 0.459710 + 0.333999i 0.793418 0.608678i \(-0.208300\pi\)
−0.333707 + 0.942677i \(0.608300\pi\)
\(384\) 2.37149 7.29871i 0.121020 0.372461i
\(385\) −11.6036 35.7123i −0.591376 1.82007i
\(386\) 2.90887 2.11342i 0.148057 0.107570i
\(387\) −3.50942 10.8009i −0.178394 0.549039i
\(388\) −0.482120 1.48381i −0.0244759 0.0753291i
\(389\) −25.6734 + 18.6528i −1.30169 + 0.945735i −0.999971 0.00766074i \(-0.997561\pi\)
−0.301722 + 0.953396i \(0.597561\pi\)
\(390\) −0.997833 3.07101i −0.0505272 0.155507i
\(391\) 0.631845 1.94462i 0.0319538 0.0983436i
\(392\) 1.15800 + 0.841335i 0.0584877 + 0.0424938i
\(393\) 7.63784 23.5069i 0.385278 1.18576i
\(394\) 1.90289 1.38253i 0.0958664 0.0696510i
\(395\) −1.70474 + 1.23857i −0.0857748 + 0.0623190i
\(396\) −10.4744 7.61013i −0.526361 0.382424i
\(397\) 11.0618 0.555175 0.277588 0.960700i \(-0.410465\pi\)
0.277588 + 0.960700i \(0.410465\pi\)
\(398\) −2.02057 −0.101282
\(399\) 7.79603 + 5.66415i 0.390290 + 0.283562i
\(400\) 0.0532412 + 0.163860i 0.00266206 + 0.00819298i
\(401\) −3.60036 + 11.0808i −0.179793 + 0.553347i −0.999820 0.0189782i \(-0.993959\pi\)
0.820026 + 0.572326i \(0.193959\pi\)
\(402\) −1.29976 −0.0648264
\(403\) −10.9593 30.0142i −0.545920 1.49512i
\(404\) −30.0690 −1.49599
\(405\) −2.82916 + 8.70725i −0.140582 + 0.432667i
\(406\) −0.966114 2.97339i −0.0479474 0.147567i
\(407\) −20.5949 14.9630i −1.02085 0.741691i
\(408\) 0.993362 0.0491787
\(409\) 32.9083 1.62721 0.813604 0.581419i \(-0.197502\pi\)
0.813604 + 0.581419i \(0.197502\pi\)
\(410\) −1.69878 1.23424i −0.0838969 0.0609546i
\(411\) −7.98743 + 5.80321i −0.393991 + 0.286251i
\(412\) 26.8530 19.5098i 1.32295 0.961180i
\(413\) −1.65149 + 5.08278i −0.0812647 + 0.250107i
\(414\) 0.361808 + 0.262869i 0.0177819 + 0.0129193i
\(415\) −2.90096 + 8.92824i −0.142403 + 0.438270i
\(416\) 3.85943 + 11.8781i 0.189224 + 0.582373i
\(417\) 5.90931 4.29336i 0.289380 0.210247i
\(418\) −0.765341 2.35548i −0.0374341 0.115210i
\(419\) 2.45188 + 7.54611i 0.119782 + 0.368652i 0.992914 0.118832i \(-0.0379150\pi\)
−0.873132 + 0.487483i \(0.837915\pi\)
\(420\) 14.4177 10.4751i 0.703511 0.511131i
\(421\) 6.17746 + 19.0123i 0.301071 + 0.926601i 0.981114 + 0.193429i \(0.0619610\pi\)
−0.680043 + 0.733172i \(0.738039\pi\)
\(422\) −0.266859 + 0.821308i −0.0129905 + 0.0399806i
\(423\) −6.36246 4.62260i −0.309354 0.224759i
\(424\) −0.647413 + 1.99253i −0.0314412 + 0.0967659i
\(425\) −0.0367341 + 0.0266889i −0.00178186 + 0.00129460i
\(426\) 3.13843 2.28020i 0.152057 0.110476i
\(427\) 9.14188 + 6.64196i 0.442406 + 0.321427i
\(428\) −4.83350 −0.233636
\(429\) −43.2937 −2.09024
\(430\) −3.25036 2.36152i −0.156746 0.113883i
\(431\) −8.76077 26.9629i −0.421991 1.29876i −0.905846 0.423608i \(-0.860764\pi\)
0.483854 0.875149i \(-0.339236\pi\)
\(432\) 6.61260 20.3515i 0.318149 0.979162i
\(433\) 0.860962 0.0413752 0.0206876 0.999786i \(-0.493414\pi\)
0.0206876 + 0.999786i \(0.493414\pi\)
\(434\) −2.43349 + 1.90529i −0.116811 + 0.0914568i
\(435\) −17.0745 −0.818661
\(436\) 9.30932 28.6511i 0.445836 1.37214i
\(437\) −1.50842 4.64243i −0.0721573 0.222077i
\(438\) 2.63370 + 1.91349i 0.125843 + 0.0914303i
\(439\) −25.2605 −1.20562 −0.602808 0.797886i \(-0.705952\pi\)
−0.602808 + 0.797886i \(0.705952\pi\)
\(440\) −9.24089 −0.440542
\(441\) 1.85409 + 1.34708i 0.0882900 + 0.0641465i
\(442\) −0.861715 + 0.626073i −0.0409876 + 0.0297793i
\(443\) −6.62170 + 4.81095i −0.314607 + 0.228575i −0.733871 0.679289i \(-0.762288\pi\)
0.419264 + 0.907864i \(0.362288\pi\)
\(444\) 3.73344 11.4904i 0.177181 0.545308i
\(445\) 26.2518 + 19.0730i 1.24445 + 0.904148i
\(446\) 0.343004 1.05566i 0.0162417 0.0499868i
\(447\) 0.862213 + 2.65362i 0.0407813 + 0.125512i
\(448\) −17.3849 + 12.6309i −0.821361 + 0.596753i
\(449\) −0.732660 2.25490i −0.0345764 0.106415i 0.932279 0.361741i \(-0.117817\pi\)
−0.966855 + 0.255325i \(0.917817\pi\)
\(450\) −0.00306892 0.00944517i −0.000144670 0.000445250i
\(451\) −22.7765 + 16.5481i −1.07250 + 0.779219i
\(452\) 1.15584 + 3.55731i 0.0543661 + 0.167322i
\(453\) −7.46260 + 22.9675i −0.350624 + 1.07911i
\(454\) −0.381419 0.277117i −0.0179009 0.0130058i
\(455\) −11.9135 + 36.6659i −0.558512 + 1.71892i
\(456\) 1.91856 1.39392i 0.0898448 0.0652761i
\(457\) −17.7127 + 12.8690i −0.828565 + 0.601988i −0.919153 0.393900i \(-0.871125\pi\)
0.0905877 + 0.995888i \(0.471125\pi\)
\(458\) 3.50776 + 2.54854i 0.163907 + 0.119085i
\(459\) 5.63944 0.263226
\(460\) −9.02736 −0.420903
\(461\) −0.254950 0.185232i −0.0118742 0.00862710i 0.581832 0.813309i \(-0.302336\pi\)
−0.593707 + 0.804682i \(0.702336\pi\)
\(462\) 1.29405 + 3.98266i 0.0602045 + 0.185290i
\(463\) 6.25538 19.2521i 0.290712 0.894720i −0.693916 0.720056i \(-0.744116\pi\)
0.984628 0.174664i \(-0.0558839\pi\)
\(464\) 21.3714 0.992144
\(465\) 5.78932 + 15.8552i 0.268473 + 0.735269i
\(466\) −0.311782 −0.0144430
\(467\) 6.49105 19.9774i 0.300370 0.924443i −0.680995 0.732288i \(-0.738452\pi\)
0.981365 0.192155i \(-0.0615477\pi\)
\(468\) 4.10771 + 12.6422i 0.189879 + 0.584388i
\(469\) 12.5546 + 9.12145i 0.579717 + 0.421189i
\(470\) −2.78220 −0.128333
\(471\) 23.5364 1.08450
\(472\) 1.06403 + 0.773064i 0.0489760 + 0.0355832i
\(473\) −43.5793 + 31.6622i −2.00378 + 1.45583i
\(474\) 0.190114 0.138126i 0.00873222 0.00634433i
\(475\) −0.0334969 + 0.103093i −0.00153694 + 0.00473022i
\(476\) −4.75583 3.45531i −0.217983 0.158374i
\(477\) −1.03658 + 3.19028i −0.0474619 + 0.146073i
\(478\) 1.16764 + 3.59362i 0.0534066 + 0.164368i
\(479\) −8.56614 + 6.22367i −0.391397 + 0.284367i −0.766028 0.642808i \(-0.777770\pi\)
0.374631 + 0.927174i \(0.377770\pi\)
\(480\) −2.03877 6.27470i −0.0930569 0.286400i
\(481\) 8.07658 + 24.8572i 0.368260 + 1.13339i
\(482\) 3.80468 2.76426i 0.173298 0.125909i
\(483\) 2.55044 + 7.84946i 0.116049 + 0.357163i
\(484\) −12.2957 + 37.8421i −0.558893 + 1.72010i
\(485\) −1.44243 1.04798i −0.0654972 0.0475865i
\(486\) −0.654826 + 2.01535i −0.0297035 + 0.0914180i
\(487\) 7.12183 5.17432i 0.322721 0.234471i −0.414615 0.909997i \(-0.636084\pi\)
0.737336 + 0.675526i \(0.236084\pi\)
\(488\) 2.24977 1.63455i 0.101842 0.0739927i
\(489\) 1.73699 + 1.26200i 0.0785495 + 0.0570695i
\(490\) 0.810764 0.0366266
\(491\) −13.3373 −0.601902 −0.300951 0.953640i \(-0.597304\pi\)
−0.300951 + 0.953640i \(0.597304\pi\)
\(492\) −10.8097 7.85369i −0.487338 0.354072i
\(493\) 1.74045 + 5.35656i 0.0783860 + 0.241247i
\(494\) −0.785777 + 2.41837i −0.0353538 + 0.108808i
\(495\) −14.7958 −0.665020
\(496\) −7.24624 19.8453i −0.325366 0.891081i
\(497\) −46.3164 −2.07758
\(498\) 0.323517 0.995684i 0.0144972 0.0446177i
\(499\) 11.4675 + 35.2932i 0.513354 + 1.57994i 0.786257 + 0.617900i \(0.212016\pi\)
−0.272903 + 0.962042i \(0.587984\pi\)
\(500\) −17.6969 12.8576i −0.791431 0.575009i
\(501\) 2.61294 0.116737
\(502\) 4.46285 0.199187
\(503\) 11.1082 + 8.07056i 0.495289 + 0.359849i 0.807215 0.590258i \(-0.200974\pi\)
−0.311926 + 0.950107i \(0.600974\pi\)
\(504\) 2.09864 1.52475i 0.0934808 0.0679178i
\(505\) −27.7997 + 20.1977i −1.23707 + 0.898786i
\(506\) 0.655500 2.01742i 0.0291405 0.0896853i
\(507\) 21.7660 + 15.8139i 0.966660 + 0.702319i
\(508\) −4.78942 + 14.7403i −0.212496 + 0.653996i
\(509\) −2.03593 6.26594i −0.0902408 0.277733i 0.895743 0.444572i \(-0.146644\pi\)
−0.985984 + 0.166839i \(0.946644\pi\)
\(510\) 0.455207 0.330728i 0.0201569 0.0146449i
\(511\) −12.0108 36.9654i −0.531326 1.63525i
\(512\) 4.27789 + 13.1660i 0.189058 + 0.581861i
\(513\) 10.8919 7.91344i 0.480890 0.349387i
\(514\) −1.09687 3.37581i −0.0483807 0.148900i
\(515\) 11.7214 36.0749i 0.516508 1.58965i
\(516\) −20.6827 15.0268i −0.910503 0.661519i
\(517\) −11.5271 + 35.4768i −0.506961 + 1.56027i
\(518\) 2.04525 1.48596i 0.0898631 0.0652893i
\(519\) −17.5194 + 12.7286i −0.769017 + 0.558723i
\(520\) 7.67566 + 5.57669i 0.336600 + 0.244554i
\(521\) −22.9346 −1.00478 −0.502391 0.864641i \(-0.667546\pi\)
−0.502391 + 0.864641i \(0.667546\pi\)
\(522\) −1.23189 −0.0539183
\(523\) 30.2470 + 21.9757i 1.32261 + 0.960931i 0.999896 + 0.0144336i \(0.00459451\pi\)
0.322712 + 0.946497i \(0.395405\pi\)
\(524\) 11.1233 + 34.2340i 0.485924 + 1.49552i
\(525\) 0.0566368 0.174310i 0.00247183 0.00760752i
\(526\) −5.81774 −0.253665
\(527\) 4.38393 3.43237i 0.190967 0.149516i
\(528\) −28.6256 −1.24577
\(529\) −5.81546 + 17.8982i −0.252846 + 0.778181i
\(530\) 0.366713 + 1.12863i 0.0159290 + 0.0490243i
\(531\) 1.70364 + 1.23777i 0.0739317 + 0.0537145i
\(532\) −14.0339 −0.608448
\(533\) 28.9050 1.25201
\(534\) −2.92762 2.12704i −0.126690 0.0920459i
\(535\) −4.46871 + 3.24671i −0.193199 + 0.140368i
\(536\) 3.08962 2.24474i 0.133451 0.0969580i
\(537\) −0.0618362 + 0.190312i −0.00266843 + 0.00821258i
\(538\) 0.702991 + 0.510753i 0.0303081 + 0.0220201i
\(539\) 3.35912 10.3383i 0.144688 0.445303i
\(540\) −7.69397 23.6796i −0.331096 1.01901i
\(541\) 28.0355 20.3690i 1.20534 0.875732i 0.210543 0.977585i \(-0.432477\pi\)
0.994800 + 0.101852i \(0.0324769\pi\)
\(542\) 1.08524 + 3.34004i 0.0466152 + 0.143467i
\(543\) −0.666216 2.05040i −0.0285901 0.0879912i
\(544\) −1.76066 + 1.27919i −0.0754877 + 0.0548450i
\(545\) −10.6385 32.7420i −0.455705 1.40251i
\(546\) 1.32860 4.08901i 0.0568588 0.174993i
\(547\) −37.6640 27.3645i −1.61039 1.17002i −0.862248 0.506486i \(-0.830944\pi\)
−0.748146 0.663534i \(-0.769056\pi\)
\(548\) 4.44319 13.6747i 0.189804 0.584156i
\(549\) 3.60214 2.61711i 0.153736 0.111695i
\(550\) −0.0381093 + 0.0276880i −0.00162499 + 0.00118062i
\(551\) 10.8780 + 7.90331i 0.463417 + 0.336692i
\(552\) 2.03112 0.0864502
\(553\) −2.80567 −0.119309
\(554\) −1.52097 1.10505i −0.0646198 0.0469490i
\(555\) −4.26651 13.1310i −0.181103 0.557379i
\(556\) −3.28719 + 10.1169i −0.139408 + 0.429053i
\(557\) −36.9039 −1.56367 −0.781835 0.623485i \(-0.785716\pi\)
−0.781835 + 0.623485i \(0.785716\pi\)
\(558\) 0.417686 + 1.14392i 0.0176821 + 0.0484260i
\(559\) 55.3053 2.33916
\(560\) −7.87715 + 24.2434i −0.332870 + 1.02447i
\(561\) −2.33122 7.17475i −0.0984241 0.302918i
\(562\) −1.48628 1.07985i −0.0626949 0.0455505i
\(563\) 43.6679 1.84038 0.920191 0.391470i \(-0.128033\pi\)
0.920191 + 0.391470i \(0.128033\pi\)
\(564\) −17.7037 −0.745460
\(565\) 3.45809 + 2.51245i 0.145483 + 0.105700i
\(566\) 3.32223 2.41374i 0.139644 0.101457i
\(567\) −9.86208 + 7.16522i −0.414168 + 0.300911i
\(568\) −3.52225 + 10.8404i −0.147790 + 0.454851i
\(569\) −18.1847 13.2120i −0.762343 0.553875i 0.137285 0.990532i \(-0.456162\pi\)
−0.899628 + 0.436657i \(0.856162\pi\)
\(570\) 0.415092 1.27752i 0.0173863 0.0535095i
\(571\) 7.94905 + 24.4647i 0.332657 + 1.02381i 0.967864 + 0.251472i \(0.0809148\pi\)
−0.635207 + 0.772342i \(0.719085\pi\)
\(572\) 51.0088 37.0601i 2.13279 1.54956i
\(573\) 1.04788 + 3.22505i 0.0437759 + 0.134728i
\(574\) −0.863969 2.65902i −0.0360614 0.110986i
\(575\) −0.0751099 + 0.0545705i −0.00313230 + 0.00227575i
\(576\) 2.61651 + 8.05280i 0.109021 + 0.335533i
\(577\) −2.22442 + 6.84605i −0.0926037 + 0.285005i −0.986622 0.163026i \(-0.947875\pi\)
0.894018 + 0.448031i \(0.147875\pi\)
\(578\) −0.150155 0.109094i −0.00624563 0.00453772i
\(579\) 8.07955 24.8663i 0.335774 1.03341i
\(580\) 20.1173 14.6161i 0.835325 0.606899i
\(581\) −10.1124 + 7.34707i −0.419532 + 0.304808i
\(582\) 0.160860 + 0.116872i 0.00666788 + 0.00484450i
\(583\) 15.9108 0.658958
\(584\) −9.56513 −0.395808
\(585\) 12.2896 + 8.92894i 0.508114 + 0.369166i
\(586\) −0.316665 0.974595i −0.0130813 0.0402601i
\(587\) −2.47917 + 7.63010i −0.102326 + 0.314928i −0.989094 0.147288i \(-0.952946\pi\)
0.886767 + 0.462216i \(0.152946\pi\)
\(588\) 5.15905 0.212755
\(589\) 3.65063 12.7809i 0.150422 0.526627i
\(590\) 0.744974 0.0306701
\(591\) 5.28540 16.2668i 0.217412 0.669126i
\(592\) 5.34021 + 16.4355i 0.219481 + 0.675494i
\(593\) −19.3058 14.0265i −0.792794 0.575999i 0.115997 0.993250i \(-0.462994\pi\)
−0.908791 + 0.417251i \(0.862994\pi\)
\(594\) 5.85057 0.240052
\(595\) −6.71788 −0.275406
\(596\) −3.28740 2.38844i −0.134657 0.0978343i
\(597\) −11.8869 + 8.63636i −0.486500 + 0.353463i
\(598\) −1.76194 + 1.28013i −0.0720512 + 0.0523483i
\(599\) 2.36927 7.29185i 0.0968056 0.297937i −0.890914 0.454171i \(-0.849935\pi\)
0.987720 + 0.156234i \(0.0499355\pi\)
\(600\) −0.0364902 0.0265117i −0.00148971 0.00108234i
\(601\) 9.93615 30.5803i 0.405304 1.24740i −0.515337 0.856988i \(-0.672333\pi\)
0.920641 0.390410i \(-0.127667\pi\)
\(602\) −1.65307 5.08764i −0.0673743 0.207357i
\(603\) 4.94684 3.59409i 0.201451 0.146363i
\(604\) −10.8681 33.4486i −0.442217 1.36100i
\(605\) 14.0513 + 43.2453i 0.571265 + 1.75817i
\(606\) 3.10025 2.25246i 0.125939 0.0915000i
\(607\) −6.55842 20.1847i −0.266198 0.819274i −0.991415 0.130753i \(-0.958260\pi\)
0.725217 0.688521i \(-0.241740\pi\)
\(608\) −1.60550 + 4.94123i −0.0651117 + 0.200393i
\(609\) −18.3926 13.3630i −0.745304 0.541495i
\(610\) 0.486751 1.49806i 0.0197080 0.0606549i
\(611\) 30.9841 22.5113i 1.25348 0.910709i
\(612\) −1.87392 + 1.36148i −0.0757488 + 0.0550348i
\(613\) −12.7956 9.29658i −0.516811 0.375485i 0.298590 0.954381i \(-0.403484\pi\)
−0.815401 + 0.578896i \(0.803484\pi\)
\(614\) 1.31150 0.0529278
\(615\) −15.2693 −0.615717
\(616\) −9.95423 7.23217i −0.401067 0.291392i
\(617\) −0.443810 1.36591i −0.0178671 0.0549894i 0.941725 0.336383i \(-0.109204\pi\)
−0.959593 + 0.281393i \(0.909204\pi\)
\(618\) −1.30718 + 4.02310i −0.0525826 + 0.161833i
\(619\) 29.6858 1.19317 0.596586 0.802549i \(-0.296524\pi\)
0.596586 + 0.802549i \(0.296524\pi\)
\(620\) −20.3934 13.7250i −0.819017 0.551209i
\(621\) 11.5309 0.462720
\(622\) 1.56364 4.81238i 0.0626961 0.192959i
\(623\) 13.3512 + 41.0907i 0.534903 + 1.64626i
\(624\) 23.7770 + 17.2750i 0.951841 + 0.691553i
\(625\) −25.2250 −1.00900
\(626\) −0.622892 −0.0248958
\(627\) −14.5703 10.5860i −0.581882 0.422762i
\(628\) −27.7307 + 20.1475i −1.10658 + 0.803974i
\(629\) −3.68451 + 2.67695i −0.146911 + 0.106737i
\(630\) 0.454053 1.39743i 0.0180899 0.0556750i
\(631\) −22.1890 16.1213i −0.883331 0.641778i 0.0507997 0.998709i \(-0.483823\pi\)
−0.934131 + 0.356931i \(0.883823\pi\)
\(632\) −0.213364 + 0.656667i −0.00848716 + 0.0261208i
\(633\) 1.94053 + 5.97234i 0.0771292 + 0.237379i
\(634\) 1.39106 1.01066i 0.0552459 0.0401385i
\(635\) 5.47327 + 16.8450i 0.217200 + 0.668473i
\(636\) 2.33346 + 7.18166i 0.0925278 + 0.284771i
\(637\) −9.02911 + 6.56003i −0.357746 + 0.259918i
\(638\) 1.80561 + 5.55710i 0.0714848 + 0.220008i
\(639\) −5.63953 + 17.3567i −0.223096 + 0.686620i
\(640\) 10.3329 + 7.50733i 0.408446 + 0.296753i
\(641\) −2.90757 + 8.94858i −0.114842 + 0.353447i −0.991914 0.126911i \(-0.959494\pi\)
0.877072 + 0.480359i \(0.159494\pi\)
\(642\) 0.498354 0.362076i 0.0196685 0.0142900i
\(643\) −18.5880 + 13.5050i −0.733040 + 0.532585i −0.890524 0.454937i \(-0.849662\pi\)
0.157483 + 0.987522i \(0.449662\pi\)
\(644\) −9.72421 7.06505i −0.383188 0.278402i
\(645\) −29.2154 −1.15036
\(646\) −0.443091 −0.0174332
\(647\) 16.0027 + 11.6266i 0.629131 + 0.457090i 0.856099 0.516812i \(-0.172881\pi\)
−0.226968 + 0.973902i \(0.572881\pi\)
\(648\) 0.927033 + 2.85311i 0.0364173 + 0.112081i
\(649\) 3.08654 9.49941i 0.121157 0.372884i
\(650\) 0.0483635 0.00189697
\(651\) −6.17252 + 21.6100i −0.241920 + 0.846964i
\(652\) −3.12683 −0.122456
\(653\) −12.6408 + 38.9045i −0.494675 + 1.52245i 0.322789 + 0.946471i \(0.395380\pi\)
−0.817463 + 0.575981i \(0.804620\pi\)
\(654\) 1.18642 + 3.65142i 0.0463926 + 0.142782i
\(655\) 33.2792 + 24.1788i 1.30033 + 0.944742i
\(656\) 19.1119 0.746194
\(657\) −15.3149 −0.597491
\(658\) −2.99697 2.17743i −0.116834 0.0848849i
\(659\) 30.0815 21.8555i 1.17181 0.851369i 0.180585 0.983559i \(-0.442201\pi\)
0.991224 + 0.132190i \(0.0422009\pi\)
\(660\) −26.9458 + 19.5773i −1.04886 + 0.762044i
\(661\) 12.1017 37.2452i 0.470701 1.44867i −0.380968 0.924588i \(-0.624409\pi\)
0.851669 0.524080i \(-0.175591\pi\)
\(662\) −1.68592 1.22489i −0.0655250 0.0476067i
\(663\) −2.39346 + 7.36633i −0.0929545 + 0.286084i
\(664\) 0.950561 + 2.92553i 0.0368889 + 0.113532i
\(665\) −12.9748 + 9.42674i −0.503141 + 0.365553i
\(666\) −0.307820 0.947371i −0.0119278 0.0367099i
\(667\) 3.55869 + 10.9525i 0.137793 + 0.424083i
\(668\) −3.07858 + 2.23672i −0.119114 + 0.0865412i
\(669\) −2.49423 7.67646i −0.0964327 0.296789i
\(670\) 0.668458 2.05730i 0.0258248 0.0794805i
\(671\) −17.0856 12.4134i −0.659583 0.479215i
\(672\) 2.71460 8.35467i 0.104718 0.322288i
\(673\) −7.27359 + 5.28457i −0.280376 + 0.203705i −0.719081 0.694926i \(-0.755437\pi\)
0.438705 + 0.898631i \(0.355437\pi\)
\(674\) −2.96202 + 2.15203i −0.114093 + 0.0828931i
\(675\) −0.207160 0.150510i −0.00797357 0.00579314i
\(676\) −39.1817 −1.50699
\(677\) 47.4214 1.82255 0.911277 0.411795i \(-0.135098\pi\)
0.911277 + 0.411795i \(0.135098\pi\)
\(678\) −0.385649 0.280190i −0.0148108 0.0107606i
\(679\) −0.733592 2.25776i −0.0281527 0.0866450i
\(680\) −0.510877 + 1.57232i −0.0195913 + 0.0602957i
\(681\) −3.42834 −0.131374
\(682\) 4.54805 3.56087i 0.174154 0.136353i
\(683\) 0.811231 0.0310409 0.0155205 0.999880i \(-0.495059\pi\)
0.0155205 + 0.999880i \(0.495059\pi\)
\(684\) −1.70878 + 5.25909i −0.0653370 + 0.201087i
\(685\) −5.07760 15.6273i −0.194005 0.597087i
\(686\) −2.27022 1.64941i −0.0866772 0.0629747i
\(687\) 31.5290 1.20291
\(688\) 36.5677 1.39413
\(689\) −13.2158 9.60185i −0.503482 0.365801i
\(690\) 0.930759 0.676236i 0.0354334 0.0257439i
\(691\) 30.9831 22.5105i 1.17865 0.856342i 0.186634 0.982430i \(-0.440242\pi\)
0.992019 + 0.126088i \(0.0402421\pi\)
\(692\) 9.74558 29.9938i 0.370471 1.14019i
\(693\) −15.9379 11.5796i −0.605430 0.439871i
\(694\) 1.56675 4.82195i 0.0594729 0.183039i
\(695\) 3.75654 + 11.5614i 0.142494 + 0.438551i
\(696\) −4.52631 + 3.28856i −0.171569 + 0.124652i
\(697\) 1.55644 + 4.79022i 0.0589543 + 0.181443i
\(698\) −1.28433 3.95277i −0.0486127 0.149614i
\(699\) −1.83420 + 1.33262i −0.0693759 + 0.0504045i
\(700\) 0.0824826 + 0.253855i 0.00311755 + 0.00959483i
\(701\) 8.56663 26.3654i 0.323557 0.995807i −0.648530 0.761189i \(-0.724616\pi\)
0.972088 0.234618i \(-0.0753839\pi\)
\(702\) −4.85959 3.53070i −0.183413 0.133258i
\(703\) −3.35981 + 10.3404i −0.126718 + 0.389997i
\(704\) 32.4914 23.6064i 1.22457 0.889699i
\(705\) −16.3676 + 11.8918i −0.616439 + 0.447869i
\(706\) 3.38789 + 2.46145i 0.127505 + 0.0926377i
\(707\) −45.7530 −1.72072
\(708\) 4.74041 0.178156
\(709\) −10.2342 7.43558i −0.384353 0.279249i 0.378784 0.925485i \(-0.376342\pi\)
−0.763138 + 0.646236i \(0.776342\pi\)
\(710\) 1.99510 + 6.14028i 0.0748747 + 0.230441i
\(711\) −0.341621 + 1.05140i −0.0128118 + 0.0394306i
\(712\) 10.6326 0.398473
\(713\) 8.96379 7.01814i 0.335697 0.262832i
\(714\) 0.749183 0.0280375
\(715\) 22.2656 68.5263i 0.832685 2.56274i
\(716\) −0.0900547 0.277160i −0.00336550 0.0103579i
\(717\) 22.2291 + 16.1504i 0.830162 + 0.603148i
\(718\) −1.39203 −0.0519501
\(719\) −17.6425 −0.657954 −0.328977 0.944338i \(-0.606704\pi\)
−0.328977 + 0.944338i \(0.606704\pi\)
\(720\) 8.12586 + 5.90379i 0.302833 + 0.220021i
\(721\) 40.8594 29.6861i 1.52168 1.10557i
\(722\) 1.99717 1.45103i 0.0743269 0.0540017i
\(723\) 10.5677 32.5241i 0.393018 1.20958i
\(724\) 2.54012 + 1.84550i 0.0944028 + 0.0685876i
\(725\) 0.0790266 0.243219i 0.00293497 0.00903292i
\(726\) −1.56701 4.82275i −0.0581571 0.178989i
\(727\) 14.6480 10.6424i 0.543264 0.394704i −0.282032 0.959405i \(-0.591008\pi\)
0.825296 + 0.564701i \(0.191008\pi\)
\(728\) 3.90370 + 12.0144i 0.144681 + 0.445281i
\(729\) 8.54032 + 26.2844i 0.316308 + 0.973496i
\(730\) −4.38322 + 3.18459i −0.162230 + 0.117867i
\(731\) 2.97801 + 9.16536i 0.110146 + 0.338993i
\(732\) 3.09729 9.53247i 0.114479 0.352330i
\(733\) −9.84881 7.15558i −0.363774 0.264297i 0.390850 0.920454i \(-0.372181\pi\)
−0.754625 + 0.656157i \(0.772181\pi\)
\(734\) −0.648793 + 1.99678i −0.0239474 + 0.0737024i
\(735\) 4.76969 3.46539i 0.175933 0.127823i
\(736\) −3.60001 + 2.61556i −0.132698 + 0.0964108i
\(737\) −23.4638 17.0474i −0.864300 0.627951i
\(738\) −1.10164 −0.0405521
\(739\) 5.03196 0.185104 0.0925518 0.995708i \(-0.470498\pi\)
0.0925518 + 0.995708i \(0.470498\pi\)
\(740\) 16.2672 + 11.8188i 0.597993 + 0.434467i
\(741\) 5.71397 + 17.5858i 0.209908 + 0.646030i
\(742\) −0.488272 + 1.50275i −0.0179250 + 0.0551676i
\(743\) 28.8768 1.05939 0.529693 0.848190i \(-0.322307\pi\)
0.529693 + 0.848190i \(0.322307\pi\)
\(744\) 4.58842 + 3.08807i 0.168220 + 0.113214i
\(745\) −4.64364 −0.170130
\(746\) 1.08829 3.34941i 0.0398451 0.122630i
\(747\) 1.52196 + 4.68411i 0.0556856 + 0.171383i
\(748\) 8.88836 + 6.45777i 0.324991 + 0.236120i
\(749\) −7.35463 −0.268732
\(750\) 2.78779 0.101796
\(751\) 1.56164 + 1.13460i 0.0569852 + 0.0414022i 0.615913 0.787814i \(-0.288787\pi\)
−0.558928 + 0.829216i \(0.688787\pi\)
\(752\) 20.4866 14.8844i 0.747070 0.542778i
\(753\) 26.2548 19.0752i 0.956778 0.695140i
\(754\) 1.85382 5.70548i 0.0675122 0.207781i
\(755\) −32.5157 23.6240i −1.18337 0.859766i
\(756\) 10.2444 31.5290i 0.372585 1.14670i
\(757\) −0.321758 0.990270i −0.0116945 0.0359920i 0.945039 0.326958i \(-0.106023\pi\)
−0.956733 + 0.290966i \(0.906023\pi\)
\(758\) −1.88663 + 1.37072i −0.0685254 + 0.0497866i
\(759\) −4.76663 14.6702i −0.173018 0.532493i
\(760\) 1.21963 + 3.75363i 0.0442405 + 0.136158i
\(761\) −1.12002 + 0.813743i −0.0406007 + 0.0294982i −0.607901 0.794013i \(-0.707988\pi\)
0.567300 + 0.823511i \(0.307988\pi\)
\(762\) −0.610383 1.87857i −0.0221118 0.0680533i
\(763\) 14.1650 43.5955i 0.512809 1.57826i
\(764\) −3.99532 2.90277i −0.144545 0.105018i
\(765\) −0.817975 + 2.51747i −0.0295739 + 0.0910192i
\(766\) 1.66981 1.21319i 0.0603326 0.0438342i
\(767\) −8.29644 + 6.02772i −0.299567 + 0.217648i
\(768\) 14.5383 + 10.5627i 0.524605 + 0.381148i
\(769\) −34.3668 −1.23930 −0.619649 0.784879i \(-0.712725\pi\)
−0.619649 + 0.784879i \(0.712725\pi\)
\(770\) −6.96938 −0.251159
\(771\) −20.8818 15.1715i −0.752038 0.546388i
\(772\) 11.7666 + 36.2138i 0.423489 + 1.30336i
\(773\) 10.3628 31.8933i 0.372722 1.14712i −0.572280 0.820058i \(-0.693941\pi\)
0.945002 0.327063i \(-0.106059\pi\)
\(774\) −2.10783 −0.0757643
\(775\) −0.252646 + 0.00908285i −0.00907530 + 0.000326266i
\(776\) −0.584217 −0.0209722
\(777\) 5.68080 17.4837i 0.203797 0.627224i
\(778\) 1.82008 + 5.60163i 0.0652531 + 0.200828i
\(779\) 9.72787 + 7.06771i 0.348537 + 0.253227i
\(780\) 34.1962 1.22442
\(781\) 86.5627 3.09746
\(782\) −0.307021 0.223064i −0.0109791 0.00797675i
\(783\) −25.6964 + 18.6696i −0.918316 + 0.667195i
\(784\) −5.97002 + 4.33747i −0.213215 + 0.154910i
\(785\) −12.1046 + 37.2540i −0.432030 + 1.32965i
\(786\) −3.71132 2.69643i −0.132378 0.0961786i
\(787\) −13.3365 + 41.0455i −0.475395 + 1.46311i 0.370030 + 0.929020i \(0.379347\pi\)
−0.845425 + 0.534095i \(0.820653\pi\)
\(788\) 7.69735 + 23.6900i 0.274207 + 0.843922i
\(789\) −34.2255 + 24.8663i −1.21846 + 0.885264i
\(790\) 0.120855 + 0.371954i 0.00429984 + 0.0132335i
\(791\) 1.75872 + 5.41279i 0.0625330 + 0.192457i
\(792\) −3.92223 + 2.84967i −0.139370 + 0.101258i
\(793\) 6.70038 + 20.6217i 0.237938 + 0.732296i
\(794\) 0.634439 1.95260i 0.0225154 0.0692953i
\(795\) 6.98135 + 5.07225i 0.247603 + 0.179894i
\(796\) 6.61238 20.3508i 0.234370 0.721316i
\(797\) 15.2395 11.0722i 0.539812 0.392196i −0.284203 0.958764i \(-0.591729\pi\)
0.824015 + 0.566568i \(0.191729\pi\)
\(798\) 1.44696 1.05128i 0.0512218 0.0372148i
\(799\) 5.39903 + 3.92263i 0.191004 + 0.138773i
\(800\) 0.0988164 0.00349369
\(801\) 17.0240 0.601514
\(802\) 1.74946 + 1.27106i 0.0617756 + 0.0448826i
\(803\) 22.4474 + 69.0861i 0.792152 + 2.43799i
\(804\) 4.25353 13.0910i 0.150010 0.461684i
\(805\) −13.7360 −0.484130
\(806\) −5.92661 + 0.213067i −0.208756 + 0.00750498i
\(807\) 6.31874 0.222430
\(808\) −3.47940 + 10.7085i −0.122405 + 0.376723i
\(809\) 3.15310 + 9.70426i 0.110857 + 0.341184i 0.991060 0.133413i \(-0.0425938\pi\)
−0.880203 + 0.474597i \(0.842594\pi\)
\(810\) 1.37472 + 0.998794i 0.0483028 + 0.0350941i
\(811\) −4.91233 −0.172495 −0.0862476 0.996274i \(-0.527488\pi\)
−0.0862476 + 0.996274i \(0.527488\pi\)
\(812\) 33.1092 1.16190
\(813\) 20.6605 + 15.0108i 0.724596 + 0.526450i
\(814\) −3.82245 + 2.77717i −0.133977 + 0.0973398i
\(815\) −2.89084 + 2.10032i −0.101262 + 0.0735711i
\(816\) −1.58255 + 4.87059i −0.0554004 + 0.170505i
\(817\) 18.6128 + 13.5230i 0.651179 + 0.473109i
\(818\) 1.88743 5.80890i 0.0659923 0.203103i
\(819\) 6.25028 + 19.2364i 0.218403 + 0.672174i
\(820\) 17.9903 13.0708i 0.628250 0.456450i
\(821\) 16.4456 + 50.6144i 0.573956 + 1.76646i 0.639707 + 0.768619i \(0.279056\pi\)
−0.0657505 + 0.997836i \(0.520944\pi\)
\(822\) 0.566258 + 1.74276i 0.0197505 + 0.0607858i
\(823\) 29.8227 21.6674i 1.03955 0.755280i 0.0693548 0.997592i \(-0.477906\pi\)
0.970198 + 0.242313i \(0.0779059\pi\)
\(824\) −3.84078 11.8207i −0.133800 0.411793i
\(825\) −0.105851 + 0.325775i −0.00368525 + 0.0113420i
\(826\) 0.802481 + 0.583037i 0.0279219 + 0.0202864i
\(827\) 6.89861 21.2318i 0.239888 0.738300i −0.756547 0.653939i \(-0.773115\pi\)
0.996435 0.0843610i \(-0.0268849\pi\)
\(828\) −3.83160 + 2.78382i −0.133157 + 0.0967444i
\(829\) −40.0956 + 29.1312i −1.39258 + 1.01177i −0.397001 + 0.917818i \(0.629949\pi\)
−0.995577 + 0.0939489i \(0.970051\pi\)
\(830\) 1.40961 + 1.02414i 0.0489284 + 0.0355485i
\(831\) −13.6710 −0.474243
\(832\) −41.2339 −1.42953
\(833\) −1.57334 1.14310i −0.0545129 0.0396059i
\(834\) −0.418932 1.28934i −0.0145064 0.0446462i
\(835\) −1.34381 + 4.13582i −0.0465045 + 0.143126i
\(836\) 26.2286 0.907134
\(837\) 26.0491 + 17.5313i 0.900387 + 0.605972i
\(838\) 1.47265 0.0508718
\(839\) −1.45200 + 4.46881i −0.0501288 + 0.154281i −0.972987 0.230859i \(-0.925847\pi\)
0.922859 + 0.385139i \(0.125847\pi\)
\(840\) −2.06216 6.34667i −0.0711512 0.218981i
\(841\) −2.20204 1.59988i −0.0759326 0.0551682i
\(842\) 3.71031 0.127866
\(843\) −13.3592 −0.460116
\(844\) −7.39876 5.37552i −0.254676 0.185033i
\(845\) −36.2247 + 26.3188i −1.24617 + 0.905393i
\(846\) −1.18089 + 0.857964i −0.0405997 + 0.0294974i
\(847\) −18.7090 + 57.5805i −0.642850 + 1.97849i
\(848\) −8.73826 6.34871i −0.300073 0.218016i
\(849\) 9.22768 28.3999i 0.316693 0.974681i
\(850\) 0.00260421 + 0.00801494i 8.93237e−5 + 0.000274910i
\(851\) −7.53368 + 5.47354i −0.258251 + 0.187631i
\(852\) 12.6952 + 39.0718i 0.434930 + 1.33858i
\(853\) −3.38089 10.4053i −0.115760 0.356271i 0.876345 0.481684i \(-0.159975\pi\)
−0.992105 + 0.125413i \(0.959975\pi\)
\(854\) 1.69675 1.23276i 0.0580616 0.0421842i
\(855\) 1.95277 + 6.01000i 0.0667832 + 0.205538i
\(856\) −0.559301 + 1.72135i −0.0191165 + 0.0588346i
\(857\) −38.1993 27.7534i −1.30486 0.948038i −0.304872 0.952393i \(-0.598614\pi\)
−0.999991 + 0.00435571i \(0.998614\pi\)
\(858\) −2.48307 + 7.64211i −0.0847707 + 0.260897i
\(859\) 41.9697 30.4927i 1.43199 1.04040i 0.442343 0.896846i \(-0.354147\pi\)
0.989643 0.143553i \(-0.0458527\pi\)
\(860\) 34.4218 25.0089i 1.17377 0.852796i
\(861\) −16.4480 11.9501i −0.560545 0.407260i
\(862\) −5.26190 −0.179221
\(863\) −17.2524 −0.587278 −0.293639 0.955916i \(-0.594866\pi\)
−0.293639 + 0.955916i \(0.594866\pi\)
\(864\) −9.92913 7.21394i −0.337796 0.245423i
\(865\) −11.1371 34.2764i −0.378672 1.16543i
\(866\) 0.0493798 0.151975i 0.00167799 0.00516433i
\(867\) −1.34965 −0.0458365
\(868\) −11.2260 30.7449i −0.381037 1.04355i
\(869\) 5.24363 0.177878
\(870\) −0.979295 + 3.01396i −0.0332012 + 0.102183i
\(871\) 9.20168 + 28.3199i 0.311787 + 0.959582i
\(872\) −9.12631 6.63065i −0.309056 0.224542i
\(873\) −0.935400 −0.0316585
\(874\) −0.905986 −0.0306454
\(875\) −26.9276 19.5641i −0.910320 0.661386i
\(876\) −27.8912 + 20.2642i −0.942358 + 0.684663i
\(877\) 4.29516 3.12062i 0.145037 0.105376i −0.512900 0.858448i \(-0.671429\pi\)
0.657938 + 0.753072i \(0.271429\pi\)
\(878\) −1.44879 + 4.45893i −0.0488944 + 0.150482i
\(879\) −6.02856 4.38001i −0.203338 0.147734i
\(880\) 14.7219 45.3094i 0.496276 1.52738i
\(881\) −14.6119 44.9707i −0.492286 1.51510i −0.821144 0.570721i \(-0.806664\pi\)
0.328858 0.944379i \(-0.393336\pi\)
\(882\) 0.344123 0.250020i 0.0115872 0.00841861i
\(883\) 7.46758 + 22.9829i 0.251304 + 0.773435i 0.994535 + 0.104400i \(0.0332922\pi\)
−0.743231 + 0.669035i \(0.766708\pi\)
\(884\) −3.48570 10.7279i −0.117237 0.360818i
\(885\) 4.38266 3.18419i 0.147321 0.107035i
\(886\) 0.469437 + 1.44478i 0.0157710 + 0.0485382i
\(887\) 3.30107 10.1597i 0.110839 0.341128i −0.880217 0.474571i \(-0.842603\pi\)
0.991056 + 0.133443i \(0.0426033\pi\)
\(888\) −3.66005 2.65918i −0.122823 0.0892362i
\(889\) −7.28757 + 22.4288i −0.244417 + 0.752239i
\(890\) 4.87238 3.53999i 0.163322 0.118661i
\(891\) 18.4316 13.3914i 0.617483 0.448628i
\(892\) 9.50990 + 6.90935i 0.318415 + 0.231342i
\(893\) 15.9319 0.533142
\(894\) 0.517863 0.0173199
\(895\) −0.269429 0.195752i −0.00900603 0.00654327i
\(896\) 5.25515 + 16.1737i 0.175562 + 0.540325i
\(897\) −4.89390 + 15.0619i −0.163403 + 0.502901i
\(898\) −0.440051 −0.0146847
\(899\) −8.61265 + 30.1529i −0.287248 + 1.00566i
\(900\) 0.105173 0.00350578
\(901\) 0.879620 2.70719i 0.0293044 0.0901896i
\(902\) 1.61471 + 4.96956i 0.0537639 + 0.165468i
\(903\) −31.4707 22.8648i −1.04728 0.760892i
\(904\) 1.40061 0.0465836
\(905\) 3.58806 0.119271
\(906\) 3.62617 + 2.63457i 0.120471 + 0.0875276i
\(907\) −13.7618 + 9.99855i −0.456954 + 0.331996i −0.792335 0.610086i \(-0.791135\pi\)
0.335381 + 0.942082i \(0.391135\pi\)
\(908\) 4.03928 2.93471i 0.134048 0.0973918i
\(909\) −5.57092 + 17.1455i −0.184776 + 0.568681i
\(910\) 5.78890 + 4.20588i 0.191900 + 0.139424i
\(911\) −9.18592 + 28.2713i −0.304343 + 0.936672i 0.675579 + 0.737288i \(0.263894\pi\)
−0.979922 + 0.199383i \(0.936106\pi\)
\(912\) 3.77806 + 11.6277i 0.125104 + 0.385030i
\(913\) 18.8994 13.7312i 0.625480 0.454438i
\(914\) 1.25572 + 3.86470i 0.0415355 + 0.127833i
\(915\) −3.53953 10.8935i −0.117013 0.360129i
\(916\) −37.1477 + 26.9894i −1.22739 + 0.891754i
\(917\) 16.9252 + 52.0904i 0.558919 + 1.72018i
\(918\) 0.323445 0.995462i 0.0106753 0.0328551i
\(919\) 23.5129 + 17.0831i 0.775618 + 0.563519i 0.903661 0.428249i \(-0.140869\pi\)
−0.128043 + 0.991769i \(0.540869\pi\)
\(920\) −1.04459 + 3.21491i −0.0344390 + 0.105992i
\(921\) 7.71550 5.60564i 0.254234 0.184712i
\(922\) −0.0473192 + 0.0343794i −0.00155837 + 0.00113222i
\(923\) −71.9006 52.2388i −2.36664 1.71946i
\(924\) −44.3475 −1.45893
\(925\) 0.206792 0.00679927
\(926\) −3.03957 2.20837i −0.0998863 0.0725717i
\(927\) −6.14953 18.9263i −0.201977 0.621622i
\(928\) 3.78773 11.6574i 0.124338 0.382675i
\(929\) −0.898497 −0.0294787 −0.0147394 0.999891i \(-0.504692\pi\)
−0.0147394 + 0.999891i \(0.504692\pi\)
\(930\) 3.13078 0.112554i 0.102662 0.00369080i
\(931\) −4.64274 −0.152160
\(932\) 1.02032 3.14021i 0.0334216 0.102861i
\(933\) −11.3704 34.9944i −0.372249 1.14566i
\(934\) −3.15408 2.29157i −0.103205 0.0749826i
\(935\) 12.5553 0.410603
\(936\) 4.97759 0.162698
\(937\) 20.3164 + 14.7607i 0.663708 + 0.482212i 0.867913 0.496716i \(-0.165461\pi\)
−0.204205 + 0.978928i \(0.565461\pi\)
\(938\) 2.33016 1.69296i 0.0760824 0.0552771i
\(939\) −3.66445 + 2.66238i −0.119585 + 0.0868834i
\(940\) 9.10486 28.0219i 0.296968 0.913973i
\(941\) 44.4225 + 32.2749i 1.44813 + 1.05213i 0.986263 + 0.165183i \(0.0528214\pi\)
0.461870 + 0.886948i \(0.347179\pi\)
\(942\) 1.34991 4.15460i 0.0439824 0.135364i
\(943\) 3.18244 + 9.79453i 0.103634 + 0.318954i
\(944\) −5.48558 + 3.98551i −0.178540 + 0.129717i
\(945\) −11.7071 36.0308i −0.380833 1.17208i
\(946\) 3.08950 + 9.50849i 0.100448 + 0.309148i
\(947\) −39.9197 + 29.0033i −1.29721 + 0.942481i −0.999924 0.0123057i \(-0.996083\pi\)
−0.297290 + 0.954787i \(0.596083\pi\)
\(948\) 0.769025 + 2.36682i 0.0249768 + 0.0768706i
\(949\) 23.0468 70.9308i 0.748131 2.30251i
\(950\) 0.0162765 + 0.0118256i 0.000528081 + 0.000383673i
\(951\) 3.86374 11.8914i 0.125290 0.385604i
\(952\) −1.78085 + 1.29387i −0.0577178 + 0.0419344i
\(953\) 36.6696 26.6420i 1.18785 0.863021i 0.194811 0.980841i \(-0.437591\pi\)
0.993035 + 0.117820i \(0.0375907\pi\)
\(954\) 0.503689 + 0.365952i 0.0163075 + 0.0118481i
\(955\) −5.64361 −0.182623
\(956\) −40.0155 −1.29419
\(957\) 34.3746 + 24.9746i 1.11117 + 0.807315i
\(958\) 0.607285 + 1.86903i 0.0196205 + 0.0603857i
\(959\) 6.76075 20.8074i 0.218316 0.671907i
\(960\) 21.7821 0.703015
\(961\) 30.9200 2.22608i 0.997418 0.0718091i
\(962\) 4.85096 0.156401
\(963\) −0.895506 + 2.75609i −0.0288573 + 0.0888136i
\(964\) 15.3902 + 47.3662i 0.495686 + 1.52556i
\(965\) 35.2038 + 25.5770i 1.13325 + 0.823354i
\(966\) 1.53185 0.0492864
\(967\) −57.8870 −1.86152 −0.930759 0.365632i \(-0.880853\pi\)
−0.930759 + 0.365632i \(0.880853\pi\)
\(968\) 12.0539 + 8.75769i 0.387428 + 0.281483i
\(969\) −2.60669 + 1.89387i −0.0837389 + 0.0608399i
\(970\) −0.267717 + 0.194508i −0.00859588 + 0.00624527i
\(971\) −7.53706 + 23.1967i −0.241876 + 0.744417i 0.754259 + 0.656577i \(0.227996\pi\)
−0.996135 + 0.0878398i \(0.972004\pi\)
\(972\) −18.1553 13.1906i −0.582331 0.423088i
\(973\) −5.00178 + 15.3939i −0.160350 + 0.493505i
\(974\) −0.504893 1.55390i −0.0161778 0.0497902i
\(975\) 0.284521 0.206716i 0.00911195 0.00662022i
\(976\) 4.43027 + 13.6350i 0.141810 + 0.436445i
\(977\) 12.3971 + 38.1542i 0.396617 + 1.22066i 0.927695 + 0.373339i \(0.121787\pi\)
−0.531078 + 0.847323i \(0.678213\pi\)
\(978\) 0.322389 0.234229i 0.0103089 0.00748983i
\(979\) −24.9525 76.7960i −0.797486 2.45441i
\(980\) −2.65325 + 8.16587i −0.0847551 + 0.260849i
\(981\) −14.6123 10.6165i −0.466535 0.338957i
\(982\) −0.764947 + 2.35427i −0.0244104 + 0.0751276i
\(983\) 9.94738 7.22719i 0.317272 0.230512i −0.417738 0.908567i \(-0.637177\pi\)
0.735011 + 0.678056i \(0.237177\pi\)
\(984\) −4.04776 + 2.94087i −0.129038 + 0.0937514i
\(985\) 23.0293 + 16.7317i 0.733773 + 0.533118i
\(986\) 1.04535 0.0332908
\(987\) −26.9379 −0.857442
\(988\) −21.7859 15.8284i −0.693103 0.503569i
\(989\) 6.08911 + 18.7403i 0.193622 + 0.595908i
\(990\) −0.848598 + 2.61172i −0.0269702 + 0.0830058i
\(991\) 59.0907 1.87708 0.938538 0.345175i \(-0.112180\pi\)
0.938538 + 0.345175i \(0.112180\pi\)
\(992\) −12.1093 + 0.435340i −0.384470 + 0.0138221i
\(993\) −15.1536 −0.480886
\(994\) −2.65644 + 8.17568i −0.0842572 + 0.259317i
\(995\) −7.55652 23.2566i −0.239558 0.737283i
\(996\) 8.96963 + 6.51682i 0.284214 + 0.206493i
\(997\) −36.3574 −1.15145 −0.575726 0.817643i \(-0.695280\pi\)
−0.575726 + 0.817643i \(0.695280\pi\)
\(998\) 6.88759 0.218023
\(999\) −20.7785 15.0965i −0.657404 0.477632i
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 527.2.h.c.256.13 yes 96
31.4 even 5 inner 527.2.h.c.35.13 96
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
527.2.h.c.35.13 96 31.4 even 5 inner
527.2.h.c.256.13 yes 96 1.1 even 1 trivial