Properties

Label 729.2.g.b.703.1
Level $729$
Weight $2$
Character 729.703
Analytic conductor $5.821$
Analytic rank $0$
Dimension $144$
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] = [729,2,Mod(28,729)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(729, base_ring=CyclotomicField(54))
 
chi = DirichletCharacter(H, H._module([44]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("729.28");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 729 = 3^{6} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 729.g (of order \(27\), degree \(18\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(5.82109430735\)
Analytic rank: \(0\)
Dimension: \(144\)
Relative dimension: \(8\) over \(\Q(\zeta_{27})\)
Twist minimal: no (minimal twist has level 81)
Sato-Tate group: $\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label 703.1
Character \(\chi\) \(=\) 729.703
Dual form 729.2.g.b.28.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.23053 - 1.46704i) q^{2} +(2.03089 + 4.70814i) q^{4} +(-1.73981 - 1.84410i) q^{5} +(-0.507474 + 0.0593153i) q^{7} +(1.44988 - 8.22270i) q^{8} +O(q^{10})\) \(q+(-2.23053 - 1.46704i) q^{2} +(2.03089 + 4.70814i) q^{4} +(-1.73981 - 1.84410i) q^{5} +(-0.507474 + 0.0593153i) q^{7} +(1.44988 - 8.22270i) q^{8} +(1.17534 + 6.66569i) q^{10} +(0.440769 + 1.47227i) q^{11} +(-0.328014 - 5.63177i) q^{13} +(1.21896 + 0.612182i) q^{14} +(-8.25967 + 8.75474i) q^{16} +(1.33086 + 0.484393i) q^{17} +(0.986977 - 0.359230i) q^{19} +(5.14888 - 11.9364i) q^{20} +(1.17674 - 3.93058i) q^{22} +(0.258604 + 0.0302265i) q^{23} +(-0.0830100 + 1.42523i) q^{25} +(-7.53041 + 13.0431i) q^{26} +(-1.30989 - 2.26880i) q^{28} +(-1.58935 + 0.798201i) q^{29} +(3.08537 - 4.14437i) q^{31} +(15.0181 - 3.55935i) q^{32} +(-2.25790 - 3.03288i) q^{34} +(0.992294 + 0.832634i) q^{35} +(-5.04999 + 4.23745i) q^{37} +(-2.72849 - 0.646664i) q^{38} +(-17.6860 + 11.6322i) q^{40} +(-5.64575 + 3.71327i) q^{41} +(-5.94513 - 1.40902i) q^{43} +(-6.03650 + 5.06523i) q^{44} +(-0.532481 - 0.446804i) q^{46} +(-4.36612 - 5.86472i) q^{47} +(-6.55730 + 1.55411i) q^{49} +(2.27603 - 3.05723i) q^{50} +(25.8490 - 12.9819i) q^{52} +(-4.74440 - 8.21755i) q^{53} +(1.94815 - 3.37430i) q^{55} +(-0.248047 + 4.25881i) q^{56} +(4.71609 + 0.551232i) q^{58} +(-1.42111 + 4.74684i) q^{59} +(-5.10974 + 11.8457i) q^{61} +(-12.9620 + 4.71777i) q^{62} +(-16.0995 - 5.85975i) q^{64} +(-9.81485 + 10.4031i) q^{65} +(5.73622 + 2.88084i) q^{67} +(0.422242 + 7.24961i) q^{68} +(-0.991833 - 3.31295i) q^{70} +(0.896716 + 5.08553i) q^{71} +(-1.03528 + 5.87137i) q^{73} +(17.4807 - 2.04320i) q^{74} +(3.69575 + 3.91726i) q^{76} +(-0.311007 - 0.720996i) q^{77} +(-8.30647 - 5.46325i) q^{79} +30.5149 q^{80} +18.0405 q^{82} +(10.8213 + 7.11730i) q^{83} +(-1.42218 - 3.29699i) q^{85} +(11.1937 + 11.8646i) q^{86} +(12.7451 - 1.48969i) q^{88} +(1.71260 - 9.71264i) q^{89} +(0.500509 + 2.83853i) q^{91} +(0.382886 + 1.27893i) q^{92} +(1.13497 + 19.4867i) q^{94} +(-2.37961 - 1.19509i) q^{95} +(2.46841 - 2.61636i) q^{97} +(16.9062 + 6.15336i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 144 q - 9 q^{2} + 9 q^{4} - 9 q^{5} + 9 q^{7} + 18 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 144 q - 9 q^{2} + 9 q^{4} - 9 q^{5} + 9 q^{7} + 18 q^{8} - 18 q^{10} - 9 q^{11} + 9 q^{13} - 9 q^{14} + 9 q^{16} + 18 q^{17} - 18 q^{19} + 63 q^{20} + 9 q^{22} - 36 q^{23} + 9 q^{25} - 45 q^{26} - 9 q^{28} + 45 q^{29} + 9 q^{31} - 63 q^{32} + 9 q^{34} - 9 q^{35} - 18 q^{37} + 9 q^{38} + 9 q^{40} + 27 q^{41} + 9 q^{43} - 54 q^{44} - 18 q^{46} - 63 q^{47} + 9 q^{49} + 225 q^{50} + 27 q^{52} - 45 q^{53} - 9 q^{55} - 99 q^{56} + 9 q^{58} + 117 q^{59} + 9 q^{61} - 81 q^{62} - 18 q^{64} - 81 q^{65} + 36 q^{67} + 18 q^{68} + 63 q^{70} + 90 q^{71} - 18 q^{73} - 81 q^{74} + 90 q^{76} - 81 q^{77} + 63 q^{79} + 288 q^{80} - 36 q^{82} - 45 q^{83} + 63 q^{85} - 81 q^{86} + 90 q^{88} + 81 q^{89} - 18 q^{91} + 63 q^{92} + 63 q^{94} - 153 q^{95} + 36 q^{97} - 81 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/729\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{5}{27}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.23053 1.46704i −1.57722 1.03736i −0.970087 0.242758i \(-0.921948\pi\)
−0.607136 0.794598i \(-0.707682\pi\)
\(3\) 0 0
\(4\) 2.03089 + 4.70814i 1.01545 + 2.35407i
\(5\) −1.73981 1.84410i −0.778069 0.824705i 0.210163 0.977666i \(-0.432600\pi\)
−0.988232 + 0.152962i \(0.951119\pi\)
\(6\) 0 0
\(7\) −0.507474 + 0.0593153i −0.191807 + 0.0224191i −0.211454 0.977388i \(-0.567820\pi\)
0.0196468 + 0.999807i \(0.493746\pi\)
\(8\) 1.44988 8.22270i 0.512611 2.90716i
\(9\) 0 0
\(10\) 1.17534 + 6.66569i 0.371676 + 2.10788i
\(11\) 0.440769 + 1.47227i 0.132897 + 0.443907i 0.998372 0.0570461i \(-0.0181682\pi\)
−0.865475 + 0.500953i \(0.832983\pi\)
\(12\) 0 0
\(13\) −0.328014 5.63177i −0.0909746 1.56197i −0.667323 0.744769i \(-0.732560\pi\)
0.576348 0.817204i \(-0.304477\pi\)
\(14\) 1.21896 + 0.612182i 0.325779 + 0.163613i
\(15\) 0 0
\(16\) −8.25967 + 8.75474i −2.06492 + 2.18869i
\(17\) 1.33086 + 0.484393i 0.322781 + 0.117483i 0.498328 0.866988i \(-0.333947\pi\)
−0.175548 + 0.984471i \(0.556170\pi\)
\(18\) 0 0
\(19\) 0.986977 0.359230i 0.226428 0.0824131i −0.226315 0.974054i \(-0.572668\pi\)
0.452743 + 0.891641i \(0.350446\pi\)
\(20\) 5.14888 11.9364i 1.15132 2.66907i
\(21\) 0 0
\(22\) 1.17674 3.93058i 0.250881 0.838001i
\(23\) 0.258604 + 0.0302265i 0.0539227 + 0.00630266i 0.143011 0.989721i \(-0.454321\pi\)
−0.0890888 + 0.996024i \(0.528395\pi\)
\(24\) 0 0
\(25\) −0.0830100 + 1.42523i −0.0166020 + 0.285045i
\(26\) −7.53041 + 13.0431i −1.47684 + 2.55795i
\(27\) 0 0
\(28\) −1.30989 2.26880i −0.247546 0.428762i
\(29\) −1.58935 + 0.798201i −0.295135 + 0.148222i −0.590205 0.807253i \(-0.700953\pi\)
0.295070 + 0.955475i \(0.404657\pi\)
\(30\) 0 0
\(31\) 3.08537 4.14437i 0.554148 0.744350i −0.433480 0.901163i \(-0.642715\pi\)
0.987628 + 0.156813i \(0.0501220\pi\)
\(32\) 15.0181 3.55935i 2.65485 0.629210i
\(33\) 0 0
\(34\) −2.25790 3.03288i −0.387226 0.520135i
\(35\) 0.992294 + 0.832634i 0.167728 + 0.140741i
\(36\) 0 0
\(37\) −5.04999 + 4.23745i −0.830214 + 0.696632i −0.955340 0.295509i \(-0.904511\pi\)
0.125126 + 0.992141i \(0.460066\pi\)
\(38\) −2.72849 0.646664i −0.442619 0.104903i
\(39\) 0 0
\(40\) −17.6860 + 11.6322i −2.79640 + 1.83922i
\(41\) −5.64575 + 3.71327i −0.881718 + 0.579915i −0.907640 0.419749i \(-0.862118\pi\)
0.0259221 + 0.999664i \(0.491748\pi\)
\(42\) 0 0
\(43\) −5.94513 1.40902i −0.906624 0.214874i −0.249251 0.968439i \(-0.580184\pi\)
−0.657373 + 0.753565i \(0.728333\pi\)
\(44\) −6.03650 + 5.06523i −0.910037 + 0.763612i
\(45\) 0 0
\(46\) −0.532481 0.446804i −0.0785100 0.0658777i
\(47\) −4.36612 5.86472i −0.636864 0.855457i 0.360132 0.932901i \(-0.382732\pi\)
−0.996997 + 0.0774440i \(0.975324\pi\)
\(48\) 0 0
\(49\) −6.55730 + 1.55411i −0.936757 + 0.222016i
\(50\) 2.27603 3.05723i 0.321879 0.432358i
\(51\) 0 0
\(52\) 25.8490 12.9819i 3.58461 1.80026i
\(53\) −4.74440 8.21755i −0.651694 1.12877i −0.982712 0.185142i \(-0.940725\pi\)
0.331018 0.943624i \(-0.392608\pi\)
\(54\) 0 0
\(55\) 1.94815 3.37430i 0.262689 0.454991i
\(56\) −0.248047 + 4.25881i −0.0331467 + 0.569107i
\(57\) 0 0
\(58\) 4.71609 + 0.551232i 0.619253 + 0.0723802i
\(59\) −1.42111 + 4.74684i −0.185013 + 0.617986i 0.814283 + 0.580468i \(0.197130\pi\)
−0.999296 + 0.0375182i \(0.988055\pi\)
\(60\) 0 0
\(61\) −5.10974 + 11.8457i −0.654235 + 1.51669i 0.190604 + 0.981667i \(0.438955\pi\)
−0.844839 + 0.535021i \(0.820304\pi\)
\(62\) −12.9620 + 4.71777i −1.64617 + 0.599157i
\(63\) 0 0
\(64\) −16.0995 5.85975i −2.01244 0.732468i
\(65\) −9.81485 + 10.4031i −1.21738 + 1.29035i
\(66\) 0 0
\(67\) 5.73622 + 2.88084i 0.700791 + 0.351951i 0.763256 0.646097i \(-0.223600\pi\)
−0.0624643 + 0.998047i \(0.519896\pi\)
\(68\) 0.422242 + 7.24961i 0.0512044 + 0.879145i
\(69\) 0 0
\(70\) −0.991833 3.31295i −0.118547 0.395974i
\(71\) 0.896716 + 5.08553i 0.106421 + 0.603541i 0.990643 + 0.136476i \(0.0435776\pi\)
−0.884223 + 0.467065i \(0.845311\pi\)
\(72\) 0 0
\(73\) −1.03528 + 5.87137i −0.121171 + 0.687192i 0.862338 + 0.506332i \(0.168999\pi\)
−0.983509 + 0.180860i \(0.942112\pi\)
\(74\) 17.4807 2.04320i 2.03209 0.237517i
\(75\) 0 0
\(76\) 3.69575 + 3.91726i 0.423931 + 0.449341i
\(77\) −0.311007 0.720996i −0.0354426 0.0821651i
\(78\) 0 0
\(79\) −8.30647 5.46325i −0.934551 0.614664i −0.0117457 0.999931i \(-0.503739\pi\)
−0.922805 + 0.385267i \(0.874109\pi\)
\(80\) 30.5149 3.41167
\(81\) 0 0
\(82\) 18.0405 1.99224
\(83\) 10.8213 + 7.11730i 1.18779 + 0.781225i 0.980397 0.197032i \(-0.0631303\pi\)
0.207397 + 0.978257i \(0.433501\pi\)
\(84\) 0 0
\(85\) −1.42218 3.29699i −0.154257 0.357608i
\(86\) 11.1937 + 11.8646i 1.20705 + 1.27940i
\(87\) 0 0
\(88\) 12.7451 1.48969i 1.35863 0.158801i
\(89\) 1.71260 9.71264i 0.181535 1.02954i −0.748791 0.662806i \(-0.769366\pi\)
0.930327 0.366732i \(-0.119523\pi\)
\(90\) 0 0
\(91\) 0.500509 + 2.83853i 0.0524676 + 0.297558i
\(92\) 0.382886 + 1.27893i 0.0399187 + 0.133338i
\(93\) 0 0
\(94\) 1.13497 + 19.4867i 0.117063 + 2.00990i
\(95\) −2.37961 1.19509i −0.244143 0.122613i
\(96\) 0 0
\(97\) 2.46841 2.61636i 0.250629 0.265651i −0.589829 0.807528i \(-0.700805\pi\)
0.840458 + 0.541877i \(0.182286\pi\)
\(98\) 16.9062 + 6.15336i 1.70778 + 0.621583i
\(99\) 0 0
\(100\) −6.87874 + 2.50366i −0.687874 + 0.250366i
\(101\) −7.05948 + 16.3657i −0.702444 + 1.62845i 0.0732293 + 0.997315i \(0.476669\pi\)
−0.775674 + 0.631134i \(0.782590\pi\)
\(102\) 0 0
\(103\) −1.23827 + 4.13613i −0.122011 + 0.407545i −0.997072 0.0764677i \(-0.975636\pi\)
0.875061 + 0.484012i \(0.160821\pi\)
\(104\) −46.7839 5.46826i −4.58754 0.536207i
\(105\) 0 0
\(106\) −1.47296 + 25.2897i −0.143066 + 2.45636i
\(107\) −3.98940 + 6.90985i −0.385670 + 0.668000i −0.991862 0.127318i \(-0.959363\pi\)
0.606192 + 0.795319i \(0.292696\pi\)
\(108\) 0 0
\(109\) 0.106432 + 0.184345i 0.0101943 + 0.0176571i 0.871078 0.491145i \(-0.163422\pi\)
−0.860883 + 0.508803i \(0.830088\pi\)
\(110\) −9.29566 + 4.66846i −0.886306 + 0.445120i
\(111\) 0 0
\(112\) 3.67228 4.93273i 0.346998 0.466099i
\(113\) −5.39679 + 1.27906i −0.507687 + 0.120324i −0.476474 0.879189i \(-0.658085\pi\)
−0.0312133 + 0.999513i \(0.509937\pi\)
\(114\) 0 0
\(115\) −0.394182 0.529479i −0.0367577 0.0493742i
\(116\) −6.98584 5.86181i −0.648619 0.544256i
\(117\) 0 0
\(118\) 10.1337 8.50315i 0.932878 0.782778i
\(119\) −0.704109 0.166877i −0.0645455 0.0152976i
\(120\) 0 0
\(121\) 7.21706 4.74673i 0.656096 0.431521i
\(122\) 28.7756 18.9260i 2.60522 1.71348i
\(123\) 0 0
\(124\) 25.7783 + 6.10956i 2.31496 + 0.548655i
\(125\) −6.93801 + 5.82168i −0.620554 + 0.520707i
\(126\) 0 0
\(127\) −13.9870 11.7365i −1.24115 1.04145i −0.997434 0.0715979i \(-0.977190\pi\)
−0.243713 0.969847i \(-0.578365\pi\)
\(128\) 8.88076 + 11.9289i 0.784956 + 1.05438i
\(129\) 0 0
\(130\) 37.1542 8.80570i 3.25863 0.772311i
\(131\) −4.80136 + 6.44934i −0.419497 + 0.563482i −0.960763 0.277369i \(-0.910537\pi\)
0.541267 + 0.840851i \(0.317945\pi\)
\(132\) 0 0
\(133\) −0.479558 + 0.240843i −0.0415829 + 0.0208837i
\(134\) −8.56851 14.8411i −0.740206 1.28207i
\(135\) 0 0
\(136\) 5.91261 10.2409i 0.507002 0.878153i
\(137\) 0.496123 8.51811i 0.0423867 0.727751i −0.908438 0.418020i \(-0.862724\pi\)
0.950824 0.309731i \(-0.100239\pi\)
\(138\) 0 0
\(139\) −12.9612 1.51494i −1.09935 0.128496i −0.452981 0.891520i \(-0.649640\pi\)
−0.646370 + 0.763024i \(0.723714\pi\)
\(140\) −1.90491 + 6.36285i −0.160994 + 0.537759i
\(141\) 0 0
\(142\) 5.46054 12.6589i 0.458238 1.06232i
\(143\) 8.14693 2.96524i 0.681280 0.247966i
\(144\) 0 0
\(145\) 4.23713 + 1.54219i 0.351875 + 0.128072i
\(146\) 10.9228 11.5775i 0.903976 0.958159i
\(147\) 0 0
\(148\) −30.2065 15.1703i −2.48296 1.24699i
\(149\) −0.948613 16.2871i −0.0777134 1.33429i −0.781513 0.623889i \(-0.785552\pi\)
0.703799 0.710399i \(-0.251485\pi\)
\(150\) 0 0
\(151\) −6.21112 20.7466i −0.505454 1.68833i −0.705636 0.708575i \(-0.749339\pi\)
0.200182 0.979759i \(-0.435847\pi\)
\(152\) −1.52284 8.63645i −0.123519 0.700509i
\(153\) 0 0
\(154\) −0.364021 + 2.06446i −0.0293336 + 0.166359i
\(155\) −13.0106 + 1.52072i −1.04503 + 0.122147i
\(156\) 0 0
\(157\) 1.73207 + 1.83589i 0.138234 + 0.146520i 0.792792 0.609492i \(-0.208627\pi\)
−0.654558 + 0.756012i \(0.727145\pi\)
\(158\) 10.5130 + 24.3719i 0.836370 + 1.93892i
\(159\) 0 0
\(160\) −32.6924 21.5022i −2.58456 1.69989i
\(161\) −0.133028 −0.0104841
\(162\) 0 0
\(163\) 7.30888 0.572476 0.286238 0.958159i \(-0.407595\pi\)
0.286238 + 0.958159i \(0.407595\pi\)
\(164\) −28.9485 19.0397i −2.26050 1.48675i
\(165\) 0 0
\(166\) −13.6959 31.7507i −1.06301 2.46433i
\(167\) −4.40004 4.66377i −0.340486 0.360894i 0.534393 0.845236i \(-0.320540\pi\)
−0.874878 + 0.484343i \(0.839059\pi\)
\(168\) 0 0
\(169\) −18.6972 + 2.18539i −1.43825 + 0.168107i
\(170\) −1.66460 + 9.44043i −0.127669 + 0.724048i
\(171\) 0 0
\(172\) −5.44005 30.8521i −0.414800 2.35245i
\(173\) −1.40205 4.68318i −0.106596 0.356055i 0.888004 0.459835i \(-0.152091\pi\)
−0.994600 + 0.103780i \(0.966906\pi\)
\(174\) 0 0
\(175\) −0.0424122 0.728190i −0.00320606 0.0550460i
\(176\) −16.5300 8.30166i −1.24599 0.625762i
\(177\) 0 0
\(178\) −18.0689 + 19.1519i −1.35432 + 1.43549i
\(179\) −0.481678 0.175316i −0.0360023 0.0131038i 0.323956 0.946072i \(-0.394987\pi\)
−0.359959 + 0.932968i \(0.617209\pi\)
\(180\) 0 0
\(181\) 3.55046 1.29226i 0.263904 0.0960531i −0.206680 0.978409i \(-0.566266\pi\)
0.470583 + 0.882356i \(0.344044\pi\)
\(182\) 3.04784 7.06568i 0.225921 0.523743i
\(183\) 0 0
\(184\) 0.623489 2.08260i 0.0459642 0.153531i
\(185\) 16.6003 + 1.94030i 1.22048 + 0.142654i
\(186\) 0 0
\(187\) −0.126557 + 2.17289i −0.00925473 + 0.158898i
\(188\) 18.7448 32.4669i 1.36710 2.36789i
\(189\) 0 0
\(190\) 3.55455 + 6.15667i 0.257874 + 0.446652i
\(191\) 20.2508 10.1703i 1.46530 0.735900i 0.475678 0.879619i \(-0.342203\pi\)
0.989618 + 0.143719i \(0.0459063\pi\)
\(192\) 0 0
\(193\) −3.41785 + 4.59097i −0.246022 + 0.330465i −0.907931 0.419119i \(-0.862339\pi\)
0.661909 + 0.749584i \(0.269746\pi\)
\(194\) −9.34418 + 2.21461i −0.670873 + 0.159000i
\(195\) 0 0
\(196\) −20.6341 27.7164i −1.47387 1.97975i
\(197\) 1.85381 + 1.55553i 0.132078 + 0.110827i 0.706434 0.707779i \(-0.250303\pi\)
−0.574356 + 0.818606i \(0.694747\pi\)
\(198\) 0 0
\(199\) −7.49610 + 6.28997i −0.531384 + 0.445884i −0.868579 0.495550i \(-0.834966\pi\)
0.337195 + 0.941435i \(0.390522\pi\)
\(200\) 11.5988 + 2.74898i 0.820163 + 0.194382i
\(201\) 0 0
\(202\) 39.7556 26.1477i 2.79719 1.83974i
\(203\) 0.759209 0.499339i 0.0532860 0.0350467i
\(204\) 0 0
\(205\) 16.6702 + 3.95091i 1.16430 + 0.275943i
\(206\) 8.82988 7.40915i 0.615207 0.516220i
\(207\) 0 0
\(208\) 52.0140 + 43.6449i 3.60652 + 3.02623i
\(209\) 0.963914 + 1.29476i 0.0666753 + 0.0895605i
\(210\) 0 0
\(211\) −19.0832 + 4.52280i −1.31374 + 0.311362i −0.827009 0.562189i \(-0.809959\pi\)
−0.486732 + 0.873551i \(0.661811\pi\)
\(212\) 29.0540 39.0262i 1.99543 2.68033i
\(213\) 0 0
\(214\) 19.0355 9.56000i 1.30124 0.653508i
\(215\) 7.74505 + 13.4148i 0.528208 + 0.914884i
\(216\) 0 0
\(217\) −1.31992 + 2.28617i −0.0896020 + 0.155195i
\(218\) 0.0330431 0.567328i 0.00223796 0.0384243i
\(219\) 0 0
\(220\) 19.8432 + 2.31933i 1.33783 + 0.156369i
\(221\) 2.29145 7.65399i 0.154140 0.514863i
\(222\) 0 0
\(223\) 1.03775 2.40578i 0.0694930 0.161103i −0.879930 0.475104i \(-0.842410\pi\)
0.949423 + 0.314001i \(0.101670\pi\)
\(224\) −7.41017 + 2.69708i −0.495113 + 0.180206i
\(225\) 0 0
\(226\) 13.9141 + 5.06433i 0.925555 + 0.336874i
\(227\) 0.847597 0.898400i 0.0562570 0.0596289i −0.698634 0.715479i \(-0.746208\pi\)
0.754891 + 0.655850i \(0.227690\pi\)
\(228\) 0 0
\(229\) 4.37803 + 2.19873i 0.289308 + 0.145296i 0.587534 0.809199i \(-0.300099\pi\)
−0.298226 + 0.954495i \(0.596395\pi\)
\(230\) 0.102468 + 1.75930i 0.00675652 + 0.116005i
\(231\) 0 0
\(232\) 4.25899 + 14.2260i 0.279617 + 0.933985i
\(233\) 0.664049 + 3.76601i 0.0435033 + 0.246719i 0.998803 0.0489208i \(-0.0155782\pi\)
−0.955299 + 0.295640i \(0.904467\pi\)
\(234\) 0 0
\(235\) −3.21886 + 18.2551i −0.209975 + 1.19083i
\(236\) −25.2349 + 2.94954i −1.64265 + 0.191999i
\(237\) 0 0
\(238\) 1.32572 + 1.40518i 0.0859337 + 0.0910844i
\(239\) 3.58337 + 8.30719i 0.231789 + 0.537348i 0.993924 0.110071i \(-0.0351078\pi\)
−0.762135 + 0.647419i \(0.775849\pi\)
\(240\) 0 0
\(241\) 19.5722 + 12.8728i 1.26075 + 0.829211i 0.991019 0.133724i \(-0.0426936\pi\)
0.269735 + 0.962935i \(0.413064\pi\)
\(242\) −23.0615 −1.48245
\(243\) 0 0
\(244\) −66.1485 −4.23473
\(245\) 14.2744 + 9.38843i 0.911959 + 0.599805i
\(246\) 0 0
\(247\) −2.34685 5.44060i −0.149326 0.346177i
\(248\) −29.6044 31.3789i −1.87988 1.99256i
\(249\) 0 0
\(250\) 24.0161 2.80708i 1.51891 0.177535i
\(251\) 2.14133 12.1441i 0.135160 0.766530i −0.839588 0.543223i \(-0.817204\pi\)
0.974748 0.223307i \(-0.0716851\pi\)
\(252\) 0 0
\(253\) 0.0694831 + 0.394058i 0.00436837 + 0.0247742i
\(254\) 13.9805 + 46.6981i 0.877215 + 2.93010i
\(255\) 0 0
\(256\) −0.316189 5.42876i −0.0197618 0.339298i
\(257\) −26.3443 13.2306i −1.64331 0.825302i −0.998121 0.0612816i \(-0.980481\pi\)
−0.645192 0.764021i \(-0.723222\pi\)
\(258\) 0 0
\(259\) 2.31140 2.44994i 0.143623 0.152232i
\(260\) −68.9122 25.0820i −4.27376 1.55552i
\(261\) 0 0
\(262\) 20.1710 7.34166i 1.24617 0.453569i
\(263\) 8.15499 18.9054i 0.502858 1.16576i −0.458060 0.888922i \(-0.651455\pi\)
0.960918 0.276834i \(-0.0892854\pi\)
\(264\) 0 0
\(265\) −6.89956 + 23.0461i −0.423837 + 1.41571i
\(266\) 1.42300 + 0.166324i 0.0872494 + 0.0101980i
\(267\) 0 0
\(268\) −1.91374 + 32.8576i −0.116900 + 2.00710i
\(269\) 6.08593 10.5411i 0.371066 0.642705i −0.618664 0.785656i \(-0.712326\pi\)
0.989730 + 0.142951i \(0.0456591\pi\)
\(270\) 0 0
\(271\) −11.5577 20.0185i −0.702078 1.21603i −0.967736 0.251967i \(-0.918922\pi\)
0.265658 0.964067i \(-0.414411\pi\)
\(272\) −15.2332 + 7.65040i −0.923648 + 0.463874i
\(273\) 0 0
\(274\) −13.6030 + 18.2721i −0.821790 + 1.10386i
\(275\) −2.13491 + 0.505983i −0.128740 + 0.0305119i
\(276\) 0 0
\(277\) 0.817359 + 1.09790i 0.0491104 + 0.0659667i 0.826000 0.563670i \(-0.190611\pi\)
−0.776890 + 0.629637i \(0.783204\pi\)
\(278\) 26.6878 + 22.3937i 1.60063 + 1.34308i
\(279\) 0 0
\(280\) 8.28520 6.95211i 0.495136 0.415468i
\(281\) 17.4219 + 4.12908i 1.03931 + 0.246320i 0.714628 0.699505i \(-0.246596\pi\)
0.324678 + 0.945825i \(0.394744\pi\)
\(282\) 0 0
\(283\) −8.15153 + 5.36135i −0.484558 + 0.318699i −0.768176 0.640238i \(-0.778836\pi\)
0.283618 + 0.958937i \(0.408465\pi\)
\(284\) −22.1222 + 14.5500i −1.31271 + 0.863385i
\(285\) 0 0
\(286\) −22.5221 5.33784i −1.33176 0.315633i
\(287\) 2.64482 2.21927i 0.156119 0.130999i
\(288\) 0 0
\(289\) −11.4862 9.63807i −0.675659 0.566945i
\(290\) −7.18859 9.65596i −0.422129 0.567017i
\(291\) 0 0
\(292\) −29.7458 + 7.04988i −1.74074 + 0.412563i
\(293\) −1.83443 + 2.46406i −0.107168 + 0.143952i −0.852472 0.522774i \(-0.824897\pi\)
0.745303 + 0.666726i \(0.232305\pi\)
\(294\) 0 0
\(295\) 11.2261 5.63796i 0.653609 0.328255i
\(296\) 27.5213 + 47.6684i 1.59965 + 2.77067i
\(297\) 0 0
\(298\) −21.7779 + 37.7204i −1.26156 + 2.18509i
\(299\) 0.0854031 1.46631i 0.00493899 0.0847991i
\(300\) 0 0
\(301\) 3.10058 + 0.362406i 0.178714 + 0.0208887i
\(302\) −16.5820 + 55.3879i −0.954189 + 3.18721i
\(303\) 0 0
\(304\) −5.00714 + 11.6079i −0.287179 + 0.665756i
\(305\) 30.7346 11.1865i 1.75986 0.640536i
\(306\) 0 0
\(307\) 5.34825 + 1.94660i 0.305241 + 0.111099i 0.490099 0.871667i \(-0.336960\pi\)
−0.184859 + 0.982765i \(0.559183\pi\)
\(308\) 2.76293 2.92853i 0.157432 0.166868i
\(309\) 0 0
\(310\) 31.2514 + 15.6951i 1.77496 + 0.891419i
\(311\) −0.189058 3.24600i −0.0107205 0.184064i −0.999417 0.0341346i \(-0.989133\pi\)
0.988697 0.149929i \(-0.0479045\pi\)
\(312\) 0 0
\(313\) 2.71298 + 9.06199i 0.153347 + 0.512214i 0.999795 0.0202573i \(-0.00644855\pi\)
−0.846448 + 0.532471i \(0.821263\pi\)
\(314\) −1.17011 6.63603i −0.0660332 0.374493i
\(315\) 0 0
\(316\) 8.85219 50.2032i 0.497974 2.82415i
\(317\) 20.3710 2.38103i 1.14415 0.133732i 0.477172 0.878810i \(-0.341662\pi\)
0.666977 + 0.745078i \(0.267588\pi\)
\(318\) 0 0
\(319\) −1.87571 1.98813i −0.105019 0.111314i
\(320\) 17.2042 + 39.8839i 0.961747 + 2.22958i
\(321\) 0 0
\(322\) 0.296723 + 0.195158i 0.0165357 + 0.0108757i
\(323\) 1.48754 0.0827687
\(324\) 0 0
\(325\) 8.05378 0.446744
\(326\) −16.3027 10.7224i −0.902922 0.593861i
\(327\) 0 0
\(328\) 22.3474 + 51.8071i 1.23393 + 2.86057i
\(329\) 2.56356 + 2.71722i 0.141334 + 0.149805i
\(330\) 0 0
\(331\) 6.85491 0.801224i 0.376780 0.0440393i 0.0744045 0.997228i \(-0.476294\pi\)
0.302376 + 0.953189i \(0.402220\pi\)
\(332\) −11.5323 + 65.4027i −0.632915 + 3.58944i
\(333\) 0 0
\(334\) 2.97247 + 16.8577i 0.162647 + 0.922415i
\(335\) −4.66742 15.5903i −0.255008 0.851788i
\(336\) 0 0
\(337\) −1.57688 27.0740i −0.0858981 1.47481i −0.715891 0.698212i \(-0.753979\pi\)
0.629993 0.776601i \(-0.283058\pi\)
\(338\) 44.9107 + 22.5550i 2.44282 + 1.22683i
\(339\) 0 0
\(340\) 12.6344 13.3916i 0.685194 0.726264i
\(341\) 7.46157 + 2.71579i 0.404067 + 0.147068i
\(342\) 0 0
\(343\) 6.59630 2.40086i 0.356166 0.129634i
\(344\) −20.2057 + 46.8421i −1.08942 + 2.52556i
\(345\) 0 0
\(346\) −3.74310 + 12.5028i −0.201231 + 0.672157i
\(347\) 23.0562 + 2.69489i 1.23772 + 0.144669i 0.709665 0.704539i \(-0.248846\pi\)
0.528058 + 0.849209i \(0.322920\pi\)
\(348\) 0 0
\(349\) −0.178494 + 3.06463i −0.00955458 + 0.164046i 0.990156 + 0.139971i \(0.0447010\pi\)
−0.999710 + 0.0240746i \(0.992336\pi\)
\(350\) −0.973684 + 1.68647i −0.0520456 + 0.0901456i
\(351\) 0 0
\(352\) 11.8598 + 20.5418i 0.632131 + 1.09488i
\(353\) −9.38433 + 4.71299i −0.499477 + 0.250847i −0.680656 0.732603i \(-0.738305\pi\)
0.181179 + 0.983450i \(0.442009\pi\)
\(354\) 0 0
\(355\) 7.81808 10.5015i 0.414941 0.557362i
\(356\) 49.2065 11.6622i 2.60794 0.618093i
\(357\) 0 0
\(358\) 0.817201 + 1.09769i 0.0431904 + 0.0580148i
\(359\) −23.6540 19.8481i −1.24841 1.04754i −0.996818 0.0797090i \(-0.974601\pi\)
−0.251594 0.967833i \(-0.580955\pi\)
\(360\) 0 0
\(361\) −13.7098 + 11.5039i −0.721567 + 0.605466i
\(362\) −9.81522 2.32625i −0.515876 0.122265i
\(363\) 0 0
\(364\) −12.3477 + 8.12120i −0.647194 + 0.425667i
\(365\) 12.6286 8.30594i 0.661010 0.434753i
\(366\) 0 0
\(367\) 14.8135 + 3.51087i 0.773260 + 0.183266i 0.598259 0.801302i \(-0.295859\pi\)
0.175000 + 0.984568i \(0.444007\pi\)
\(368\) −2.40061 + 2.01435i −0.125140 + 0.105005i
\(369\) 0 0
\(370\) −34.1810 28.6813i −1.77699 1.49107i
\(371\) 2.89509 + 3.88878i 0.150306 + 0.201895i
\(372\) 0 0
\(373\) −0.908175 + 0.215242i −0.0470235 + 0.0111448i −0.254060 0.967188i \(-0.581766\pi\)
0.207037 + 0.978333i \(0.433618\pi\)
\(374\) 3.47001 4.66104i 0.179430 0.241017i
\(375\) 0 0
\(376\) −54.5542 + 27.3981i −2.81342 + 1.41295i
\(377\) 5.01662 + 8.68904i 0.258369 + 0.447508i
\(378\) 0 0
\(379\) 19.2328 33.3122i 0.987924 1.71113i 0.359781 0.933037i \(-0.382851\pi\)
0.628143 0.778098i \(-0.283815\pi\)
\(380\) 0.793893 13.6306i 0.0407259 0.699236i
\(381\) 0 0
\(382\) −60.0904 7.02356i −3.07449 0.359356i
\(383\) 4.23110 14.1329i 0.216199 0.722156i −0.779237 0.626729i \(-0.784393\pi\)
0.995436 0.0954267i \(-0.0304216\pi\)
\(384\) 0 0
\(385\) −0.788491 + 1.82793i −0.0401852 + 0.0931598i
\(386\) 14.3588 5.22616i 0.730841 0.266005i
\(387\) 0 0
\(388\) 17.3313 + 6.30806i 0.879862 + 0.320243i
\(389\) −11.7270 + 12.4299i −0.594583 + 0.630221i −0.952866 0.303392i \(-0.901881\pi\)
0.358283 + 0.933613i \(0.383362\pi\)
\(390\) 0 0
\(391\) 0.329524 + 0.165493i 0.0166647 + 0.00836935i
\(392\) 3.27164 + 56.1720i 0.165243 + 2.83711i
\(393\) 0 0
\(394\) −1.85294 6.18926i −0.0933500 0.311811i
\(395\) 4.37696 + 24.8230i 0.220229 + 1.24898i
\(396\) 0 0
\(397\) −4.37414 + 24.8070i −0.219532 + 1.24503i 0.653335 + 0.757069i \(0.273369\pi\)
−0.872867 + 0.487958i \(0.837742\pi\)
\(398\) 25.9479 3.03288i 1.30065 0.152024i
\(399\) 0 0
\(400\) −11.7919 12.4986i −0.589593 0.624932i
\(401\) 8.17128 + 18.9432i 0.408054 + 0.945976i 0.991049 + 0.133500i \(0.0426216\pi\)
−0.582995 + 0.812476i \(0.698119\pi\)
\(402\) 0 0
\(403\) −24.3522 16.0167i −1.21307 0.797847i
\(404\) −91.3890 −4.54677
\(405\) 0 0
\(406\) −2.42599 −0.120400
\(407\) −8.46456 5.56723i −0.419573 0.275957i
\(408\) 0 0
\(409\) 13.9343 + 32.3033i 0.689006 + 1.59729i 0.797585 + 0.603207i \(0.206111\pi\)
−0.108579 + 0.994088i \(0.534630\pi\)
\(410\) −31.3872 33.2685i −1.55010 1.64301i
\(411\) 0 0
\(412\) −21.9882 + 2.57006i −1.08328 + 0.126618i
\(413\) 0.439618 2.49319i 0.0216322 0.122682i
\(414\) 0 0
\(415\) −5.70212 32.3383i −0.279906 1.58743i
\(416\) −24.9716 83.4109i −1.22433 4.08956i
\(417\) 0 0
\(418\) −0.250569 4.30211i −0.0122557 0.210423i
\(419\) 24.2225 + 12.1650i 1.18335 + 0.594299i 0.928011 0.372553i \(-0.121518\pi\)
0.255336 + 0.966852i \(0.417814\pi\)
\(420\) 0 0
\(421\) 20.8880 22.1400i 1.01802 1.07904i 0.0211670 0.999776i \(-0.493262\pi\)
0.996854 0.0792630i \(-0.0252567\pi\)
\(422\) 49.2008 + 17.9076i 2.39506 + 0.871729i
\(423\) 0 0
\(424\) −74.4492 + 27.0973i −3.61557 + 1.31596i
\(425\) −0.800844 + 1.85657i −0.0388467 + 0.0900567i
\(426\) 0 0
\(427\) 1.89043 6.31448i 0.0914844 0.305579i
\(428\) −40.6346 4.74950i −1.96415 0.229576i
\(429\) 0 0
\(430\) 2.40455 41.2845i 0.115958 1.99092i
\(431\) 4.50933 7.81039i 0.217207 0.376213i −0.736746 0.676170i \(-0.763639\pi\)
0.953953 + 0.299956i \(0.0969720\pi\)
\(432\) 0 0
\(433\) −11.8523 20.5287i −0.569584 0.986548i −0.996607 0.0823075i \(-0.973771\pi\)
0.427023 0.904241i \(-0.359562\pi\)
\(434\) 6.29803 3.16299i 0.302315 0.151828i
\(435\) 0 0
\(436\) −0.651772 + 0.875481i −0.0312142 + 0.0419279i
\(437\) 0.266094 0.0630655i 0.0127290 0.00301683i
\(438\) 0 0
\(439\) 2.40340 + 3.22832i 0.114708 + 0.154080i 0.855769 0.517358i \(-0.173084\pi\)
−0.741061 + 0.671438i \(0.765677\pi\)
\(440\) −24.9213 20.9114i −1.18807 0.996913i
\(441\) 0 0
\(442\) −16.3399 + 13.7108i −0.777209 + 0.652156i
\(443\) −7.74314 1.83516i −0.367888 0.0871909i 0.0425140 0.999096i \(-0.486463\pi\)
−0.410402 + 0.911905i \(0.634611\pi\)
\(444\) 0 0
\(445\) −20.8906 + 13.7400i −0.990311 + 0.651338i
\(446\) −5.84412 + 3.84374i −0.276727 + 0.182006i
\(447\) 0 0
\(448\) 8.51767 + 2.01872i 0.402422 + 0.0953758i
\(449\) 11.2889 9.47253i 0.532757 0.447037i −0.336295 0.941757i \(-0.609174\pi\)
0.869052 + 0.494720i \(0.164729\pi\)
\(450\) 0 0
\(451\) −7.95542 6.67539i −0.374606 0.314332i
\(452\) −16.9823 22.8112i −0.798780 1.07295i
\(453\) 0 0
\(454\) −3.20858 + 0.760448i −0.150586 + 0.0356896i
\(455\) 4.36372 5.86149i 0.204574 0.274791i
\(456\) 0 0
\(457\) −7.02454 + 3.52786i −0.328594 + 0.165026i −0.605446 0.795886i \(-0.707005\pi\)
0.276852 + 0.960913i \(0.410709\pi\)
\(458\) −6.53970 11.3271i −0.305580 0.529280i
\(459\) 0 0
\(460\) 1.69232 2.93118i 0.0789047 0.136667i
\(461\) 0.192100 3.29823i 0.00894699 0.153614i −0.990876 0.134779i \(-0.956967\pi\)
0.999823 0.0188344i \(-0.00599554\pi\)
\(462\) 0 0
\(463\) 17.5818 + 2.05502i 0.817095 + 0.0955047i 0.514365 0.857572i \(-0.328028\pi\)
0.302730 + 0.953076i \(0.402102\pi\)
\(464\) 6.13946 20.5072i 0.285017 0.952024i
\(465\) 0 0
\(466\) 4.04371 9.37438i 0.187321 0.434260i
\(467\) −37.4545 + 13.6323i −1.73319 + 0.630829i −0.998849 0.0479555i \(-0.984729\pi\)
−0.734338 + 0.678784i \(0.762507\pi\)
\(468\) 0 0
\(469\) −3.08187 1.12171i −0.142307 0.0517956i
\(470\) 33.9607 35.9963i 1.56649 1.66038i
\(471\) 0 0
\(472\) 36.9714 + 18.5677i 1.70175 + 0.854649i
\(473\) −0.545968 9.37391i −0.0251036 0.431013i
\(474\) 0 0
\(475\) 0.430056 + 1.43649i 0.0197323 + 0.0659105i
\(476\) −0.644290 3.65395i −0.0295310 0.167478i
\(477\) 0 0
\(478\) 4.19419 23.7864i 0.191838 1.08797i
\(479\) −38.9258 + 4.54978i −1.77857 + 0.207885i −0.940990 0.338435i \(-0.890102\pi\)
−0.837577 + 0.546320i \(0.816028\pi\)
\(480\) 0 0
\(481\) 25.5208 + 27.0505i 1.16365 + 1.23340i
\(482\) −24.7713 57.4264i −1.12830 2.61570i
\(483\) 0 0
\(484\) 37.0053 + 24.3388i 1.68206 + 1.10631i
\(485\) −9.11940 −0.414091
\(486\) 0 0
\(487\) 35.0579 1.58863 0.794313 0.607509i \(-0.207831\pi\)
0.794313 + 0.607509i \(0.207831\pi\)
\(488\) 89.9951 + 59.1907i 4.07389 + 2.67944i
\(489\) 0 0
\(490\) −18.0663 41.8824i −0.816152 1.89205i
\(491\) 14.1243 + 14.9709i 0.637421 + 0.675627i 0.962880 0.269929i \(-0.0870003\pi\)
−0.325459 + 0.945556i \(0.605519\pi\)
\(492\) 0 0
\(493\) −2.50184 + 0.292423i −0.112677 + 0.0131701i
\(494\) −2.74688 + 15.5783i −0.123588 + 0.700903i
\(495\) 0 0
\(496\) 10.7987 + 61.2427i 0.484878 + 2.74988i
\(497\) −0.756710 2.52759i −0.0339431 0.113378i
\(498\) 0 0
\(499\) −0.479420 8.23132i −0.0214618 0.368484i −0.991890 0.127096i \(-0.959434\pi\)
0.970429 0.241388i \(-0.0776027\pi\)
\(500\) −41.4996 20.8419i −1.85592 0.932077i
\(501\) 0 0
\(502\) −22.5922 + 23.9464i −1.00834 + 1.06878i
\(503\) −15.9904 5.82003i −0.712977 0.259503i −0.0400358 0.999198i \(-0.512747\pi\)
−0.672941 + 0.739696i \(0.734969\pi\)
\(504\) 0 0
\(505\) 42.4621 15.4549i 1.88954 0.687736i
\(506\) 0.423116 0.980894i 0.0188098 0.0436061i
\(507\) 0 0
\(508\) 26.8509 89.6883i 1.19132 3.97927i
\(509\) −16.2943 1.90453i −0.722232 0.0844168i −0.252968 0.967475i \(-0.581407\pi\)
−0.469264 + 0.883058i \(0.655481\pi\)
\(510\) 0 0
\(511\) 0.177117 3.04098i 0.00783519 0.134525i
\(512\) 7.61274 13.1856i 0.336439 0.582729i
\(513\) 0 0
\(514\) 39.3519 + 68.1595i 1.73574 + 3.00639i
\(515\) 9.78178 4.91259i 0.431037 0.216475i
\(516\) 0 0
\(517\) 6.71001 9.01311i 0.295106 0.396396i
\(518\) −8.74981 + 2.07374i −0.384444 + 0.0911150i
\(519\) 0 0
\(520\) 71.3114 + 95.7878i 3.12721 + 4.20057i
\(521\) 9.25237 + 7.76366i 0.405354 + 0.340132i 0.822559 0.568680i \(-0.192546\pi\)
−0.417205 + 0.908812i \(0.636990\pi\)
\(522\) 0 0
\(523\) −5.53110 + 4.64114i −0.241858 + 0.202943i −0.755657 0.654968i \(-0.772682\pi\)
0.513799 + 0.857911i \(0.328238\pi\)
\(524\) −40.1154 9.50753i −1.75245 0.415338i
\(525\) 0 0
\(526\) −45.9250 + 30.2053i −2.00242 + 1.31701i
\(527\) 6.11369 4.02104i 0.266316 0.175159i
\(528\) 0 0
\(529\) −22.3141 5.28853i −0.970177 0.229936i
\(530\) 49.1993 41.2832i 2.13708 1.79323i
\(531\) 0 0
\(532\) −2.10785 1.76870i −0.0913869 0.0766827i
\(533\) 22.7642 + 30.5776i 0.986026 + 1.32446i
\(534\) 0 0
\(535\) 19.6832 4.66501i 0.850981 0.201686i
\(536\) 32.0051 42.9903i 1.38241 1.85690i
\(537\) 0 0
\(538\) −29.0392 + 14.5840i −1.25197 + 0.628762i
\(539\) −5.17833 8.96913i −0.223046 0.386328i
\(540\) 0 0
\(541\) −19.0806 + 33.0486i −0.820339 + 1.42087i 0.0850910 + 0.996373i \(0.472882\pi\)
−0.905430 + 0.424496i \(0.860451\pi\)
\(542\) −3.58822 + 61.6074i −0.154127 + 2.64626i
\(543\) 0 0
\(544\) 21.7111 + 2.53766i 0.930854 + 0.108801i
\(545\) 0.154779 0.516997i 0.00663000 0.0221457i
\(546\) 0 0
\(547\) −14.7275 + 34.1421i −0.629702 + 1.45981i 0.242247 + 0.970215i \(0.422116\pi\)
−0.871949 + 0.489598i \(0.837144\pi\)
\(548\) 41.1120 14.9635i 1.75622 0.639211i
\(549\) 0 0
\(550\) 5.50428 + 2.00339i 0.234703 + 0.0854250i
\(551\) −1.28191 + 1.35875i −0.0546113 + 0.0578846i
\(552\) 0 0
\(553\) 4.53937 + 2.27976i 0.193034 + 0.0969452i
\(554\) −0.212472 3.64801i −0.00902709 0.154989i
\(555\) 0 0
\(556\) −19.1901 64.0996i −0.813844 2.71843i
\(557\) −4.26215 24.1719i −0.180593 1.02420i −0.931488 0.363773i \(-0.881488\pi\)
0.750894 0.660422i \(-0.229623\pi\)
\(558\) 0 0
\(559\) −5.98521 + 33.9438i −0.253147 + 1.43567i
\(560\) −15.4855 + 1.81000i −0.654383 + 0.0764864i
\(561\) 0 0
\(562\) −32.8026 34.7688i −1.38370 1.46663i
\(563\) −2.79634 6.48265i −0.117852 0.273211i 0.849072 0.528278i \(-0.177162\pi\)
−0.966924 + 0.255066i \(0.917903\pi\)
\(564\) 0 0
\(565\) 11.7481 + 7.72686i 0.494247 + 0.325071i
\(566\) 26.0476 1.09486
\(567\) 0 0
\(568\) 43.1169 1.80914
\(569\) −7.06923 4.64950i −0.296357 0.194917i 0.392619 0.919701i \(-0.371569\pi\)
−0.688976 + 0.724784i \(0.741940\pi\)
\(570\) 0 0
\(571\) −0.175018 0.405738i −0.00732428 0.0169796i 0.914515 0.404553i \(-0.132573\pi\)
−0.921839 + 0.387573i \(0.873313\pi\)
\(572\) 30.5063 + 32.3348i 1.27553 + 1.35198i
\(573\) 0 0
\(574\) −9.15512 + 1.07008i −0.382127 + 0.0446643i
\(575\) −0.0645463 + 0.366060i −0.00269177 + 0.0152658i
\(576\) 0 0
\(577\) 1.80812 + 10.2544i 0.0752730 + 0.426894i 0.999035 + 0.0439266i \(0.0139868\pi\)
−0.923762 + 0.382968i \(0.874902\pi\)
\(578\) 11.4809 + 38.3488i 0.477541 + 1.59510i
\(579\) 0 0
\(580\) 1.34432 + 23.0810i 0.0558197 + 0.958387i
\(581\) −5.91371 2.96998i −0.245342 0.123215i
\(582\) 0 0
\(583\) 10.0073 10.6071i 0.414459 0.439301i
\(584\) 46.7775 + 17.0256i 1.93567 + 0.704525i
\(585\) 0 0
\(586\) 7.70663 2.80498i 0.318358 0.115873i
\(587\) 14.6266 33.9083i 0.603705 1.39955i −0.292655 0.956218i \(-0.594539\pi\)
0.896360 0.443327i \(-0.146202\pi\)
\(588\) 0 0
\(589\) 1.55640 5.19875i 0.0641305 0.214211i
\(590\) −33.3113 3.89353i −1.37140 0.160294i
\(591\) 0 0
\(592\) 4.61353 79.2113i 0.189615 3.25557i
\(593\) −1.15692 + 2.00385i −0.0475091 + 0.0822881i −0.888802 0.458291i \(-0.848462\pi\)
0.841293 + 0.540579i \(0.181795\pi\)
\(594\) 0 0
\(595\) 0.917282 + 1.58878i 0.0376049 + 0.0651336i
\(596\) 74.7552 37.5435i 3.06209 1.53784i
\(597\) 0 0
\(598\) −2.34164 + 3.14537i −0.0957568 + 0.128624i
\(599\) −7.85260 + 1.86110i −0.320848 + 0.0760425i −0.387884 0.921708i \(-0.626794\pi\)
0.0670358 + 0.997751i \(0.478646\pi\)
\(600\) 0 0
\(601\) 9.09918 + 12.2223i 0.371163 + 0.498559i 0.947987 0.318310i \(-0.103115\pi\)
−0.576823 + 0.816869i \(0.695708\pi\)
\(602\) −6.38427 5.35704i −0.260203 0.218337i
\(603\) 0 0
\(604\) 85.0636 71.3769i 3.46119 2.90428i
\(605\) −21.3098 5.05051i −0.866365 0.205332i
\(606\) 0 0
\(607\) 24.4698 16.0940i 0.993198 0.653237i 0.0546933 0.998503i \(-0.482582\pi\)
0.938505 + 0.345267i \(0.112212\pi\)
\(608\) 13.5439 8.90794i 0.549276 0.361265i
\(609\) 0 0
\(610\) −84.9656 20.1372i −3.44015 0.815332i
\(611\) −31.5966 + 26.5127i −1.27826 + 1.07259i
\(612\) 0 0
\(613\) 5.16392 + 4.33305i 0.208569 + 0.175010i 0.741088 0.671408i \(-0.234310\pi\)
−0.532519 + 0.846418i \(0.678755\pi\)
\(614\) −9.07368 12.1881i −0.366184 0.491871i
\(615\) 0 0
\(616\) −6.37946 + 1.51196i −0.257036 + 0.0609186i
\(617\) −7.19212 + 9.66070i −0.289544 + 0.388925i −0.922966 0.384881i \(-0.874242\pi\)
0.633422 + 0.773807i \(0.281650\pi\)
\(618\) 0 0
\(619\) −12.0062 + 6.02974i −0.482570 + 0.242356i −0.673415 0.739264i \(-0.735173\pi\)
0.190845 + 0.981620i \(0.438877\pi\)
\(620\) −33.5828 58.1671i −1.34872 2.33605i
\(621\) 0 0
\(622\) −4.34032 + 7.51765i −0.174031 + 0.301430i
\(623\) −0.292993 + 5.03050i −0.0117385 + 0.201543i
\(624\) 0 0
\(625\) 29.8965 + 3.49440i 1.19586 + 0.139776i
\(626\) 7.24294 24.1931i 0.289486 0.966951i
\(627\) 0 0
\(628\) −5.12597 + 11.8833i −0.204548 + 0.474196i
\(629\) −8.77342 + 3.19326i −0.349819 + 0.127324i
\(630\) 0 0
\(631\) −0.571023 0.207835i −0.0227321 0.00827379i 0.330629 0.943761i \(-0.392739\pi\)
−0.353361 + 0.935487i \(0.614961\pi\)
\(632\) −56.9660 + 60.3805i −2.26599 + 2.40181i
\(633\) 0 0
\(634\) −48.9312 24.5742i −1.94331 0.975965i
\(635\) 2.69158 + 46.2127i 0.106812 + 1.83390i
\(636\) 0 0
\(637\) 10.9033 + 36.4195i 0.432004 + 1.44299i
\(638\) 1.26714 + 7.18633i 0.0501667 + 0.284510i
\(639\) 0 0
\(640\) 6.54721 37.1311i 0.258801 1.46774i
\(641\) −22.5001 + 2.62988i −0.888700 + 0.103874i −0.548177 0.836362i \(-0.684678\pi\)
−0.340523 + 0.940236i \(0.610604\pi\)
\(642\) 0 0
\(643\) −33.4459 35.4506i −1.31898 1.39803i −0.860604 0.509275i \(-0.829913\pi\)
−0.458374 0.888759i \(-0.651568\pi\)
\(644\) −0.270165 0.626313i −0.0106460 0.0246802i
\(645\) 0 0
\(646\) −3.31799 2.18228i −0.130545 0.0858606i
\(647\) 20.1953 0.793960 0.396980 0.917827i \(-0.370058\pi\)
0.396980 + 0.917827i \(0.370058\pi\)
\(648\) 0 0
\(649\) −7.61503 −0.298916
\(650\) −17.9642 11.8152i −0.704614 0.463432i
\(651\) 0 0
\(652\) 14.8435 + 34.4112i 0.581318 + 1.34765i
\(653\) 13.1374 + 13.9248i 0.514107 + 0.544921i 0.931470 0.363819i \(-0.118527\pi\)
−0.417363 + 0.908740i \(0.637046\pi\)
\(654\) 0 0
\(655\) 20.2467 2.36650i 0.791103 0.0924667i
\(656\) 14.1233 80.0975i 0.551424 3.12728i
\(657\) 0 0
\(658\) −1.73183 9.82169i −0.0675137 0.382889i
\(659\) −11.8035 39.4263i −0.459798 1.53583i −0.802655 0.596444i \(-0.796580\pi\)
0.342857 0.939388i \(-0.388605\pi\)
\(660\) 0 0
\(661\) 1.65588 + 28.4304i 0.0644065 + 1.10582i 0.863414 + 0.504496i \(0.168322\pi\)
−0.799008 + 0.601321i \(0.794641\pi\)
\(662\) −16.4655 8.26930i −0.639951 0.321395i
\(663\) 0 0
\(664\) 74.2130 78.6612i 2.88002 3.05265i
\(665\) 1.27848 + 0.465328i 0.0495773 + 0.0180447i
\(666\) 0 0
\(667\) −0.435139 + 0.158378i −0.0168486 + 0.00613241i
\(668\) 13.0217 30.1876i 0.503824 1.16799i
\(669\) 0 0
\(670\) −12.4608 + 41.6219i −0.481402 + 1.60799i
\(671\) −19.6923 2.30170i −0.760214 0.0888562i
\(672\) 0 0
\(673\) 2.12301 36.4506i 0.0818359 1.40507i −0.668353 0.743844i \(-0.733001\pi\)
0.750189 0.661223i \(-0.229962\pi\)
\(674\) −36.2014 + 62.7027i −1.39443 + 2.41522i
\(675\) 0 0
\(676\) −48.2611 83.5906i −1.85620 3.21502i
\(677\) −1.58178 + 0.794398i −0.0607926 + 0.0305312i −0.478936 0.877850i \(-0.658977\pi\)
0.418143 + 0.908381i \(0.362681\pi\)
\(678\) 0 0
\(679\) −1.09747 + 1.47415i −0.0421168 + 0.0565727i
\(680\) −29.1721 + 6.91391i −1.11870 + 0.265137i
\(681\) 0 0
\(682\) −12.6591 17.0041i −0.484741 0.651120i
\(683\) −17.5030 14.6868i −0.669734 0.561973i 0.243253 0.969963i \(-0.421786\pi\)
−0.912987 + 0.407989i \(0.866230\pi\)
\(684\) 0 0
\(685\) −16.5714 + 13.9050i −0.633159 + 0.531284i
\(686\) −18.2354 4.32187i −0.696231 0.165010i
\(687\) 0 0
\(688\) 61.4405 40.4100i 2.34240 1.54062i
\(689\) −44.7231 + 29.4149i −1.70382 + 1.12062i
\(690\) 0 0
\(691\) 5.50438 + 1.30456i 0.209396 + 0.0496279i 0.333975 0.942582i \(-0.391610\pi\)
−0.124579 + 0.992210i \(0.539758\pi\)
\(692\) 19.2016 16.1121i 0.729936 0.612489i
\(693\) 0 0
\(694\) −47.4741 39.8355i −1.80209 1.51213i
\(695\) 19.7563 + 26.5373i 0.749399 + 1.00662i
\(696\) 0 0
\(697\) −9.31238 + 2.20707i −0.352732 + 0.0835989i
\(698\) 4.89408 6.57389i 0.185244 0.248825i
\(699\) 0 0
\(700\) 3.34228 1.67856i 0.126326 0.0634435i
\(701\) 12.8656 + 22.2838i 0.485926 + 0.841648i 0.999869 0.0161763i \(-0.00514928\pi\)
−0.513944 + 0.857824i \(0.671816\pi\)
\(702\) 0 0
\(703\) −3.46201 + 5.99637i −0.130572 + 0.226157i
\(704\) 1.53097 26.2857i 0.0577005 0.990679i
\(705\) 0 0
\(706\) 27.8462 + 3.25475i 1.04800 + 0.122494i
\(707\) 2.61177 8.72392i 0.0982257 0.328097i
\(708\) 0 0
\(709\) 13.2718 30.7675i 0.498433 1.15550i −0.464455 0.885597i \(-0.653750\pi\)
0.962888 0.269901i \(-0.0869908\pi\)
\(710\) −32.8446 + 11.9545i −1.23264 + 0.448643i
\(711\) 0 0
\(712\) −77.3810 28.1644i −2.89997 1.05550i
\(713\) 0.923158 0.978490i 0.0345725 0.0366447i
\(714\) 0 0
\(715\) −19.6423 9.86474i −0.734581 0.368921i
\(716\) −0.152822 2.62385i −0.00571123 0.0980580i
\(717\) 0 0
\(718\) 23.6430 + 78.9732i 0.882350 + 2.94726i
\(719\) 0.373099 + 2.11595i 0.0139143 + 0.0789116i 0.990974 0.134053i \(-0.0427992\pi\)
−0.977060 + 0.212965i \(0.931688\pi\)
\(720\) 0 0
\(721\) 0.383057 2.17243i 0.0142658 0.0809054i
\(722\) 47.4567 5.54689i 1.76616 0.206434i
\(723\) 0 0
\(724\) 13.2948 + 14.0916i 0.494096 + 0.523711i
\(725\) −1.00569 2.33144i −0.0373502 0.0865876i
\(726\) 0 0
\(727\) −9.24322 6.07936i −0.342812 0.225471i 0.366415 0.930452i \(-0.380585\pi\)
−0.709226 + 0.704981i \(0.750956\pi\)
\(728\) 24.0660 0.891946
\(729\) 0 0
\(730\) −40.3536 −1.49355
\(731\) −7.22961 4.75499i −0.267397 0.175870i
\(732\) 0 0
\(733\) −6.73459 15.6125i −0.248748 0.576662i 0.747398 0.664377i \(-0.231303\pi\)
−0.996146 + 0.0877145i \(0.972044\pi\)
\(734\) −27.8914 29.5632i −1.02949 1.09120i
\(735\) 0 0
\(736\) 3.99132 0.466519i 0.147122 0.0171961i
\(737\) −1.71303 + 9.71507i −0.0631002 + 0.357859i
\(738\) 0 0
\(739\) −4.23694 24.0289i −0.155858 0.883917i −0.957997 0.286779i \(-0.907416\pi\)
0.802138 0.597138i \(-0.203696\pi\)
\(740\) 24.5782 + 82.0970i 0.903514 + 3.01795i
\(741\) 0 0
\(742\) −0.752578 12.9213i −0.0276280 0.474354i
\(743\) 5.27562 + 2.64951i 0.193544 + 0.0972012i 0.542932 0.839777i \(-0.317314\pi\)
−0.349388 + 0.936978i \(0.613611\pi\)
\(744\) 0 0
\(745\) −28.3845 + 30.0858i −1.03993 + 1.10226i
\(746\) 2.34148 + 0.852230i 0.0857277 + 0.0312023i
\(747\) 0 0
\(748\) −10.4873 + 3.81706i −0.383453 + 0.139566i
\(749\) 1.61466 3.74320i 0.0589984 0.136774i
\(750\) 0 0
\(751\) 9.90970 33.1007i 0.361610 1.20786i −0.562842 0.826564i \(-0.690292\pi\)
0.924452 0.381298i \(-0.124523\pi\)
\(752\) 87.4068 + 10.2164i 3.18740 + 0.372554i
\(753\) 0 0
\(754\) 1.55747 26.7408i 0.0567198 0.973841i
\(755\) −27.4525 + 47.5491i −0.999099 + 1.73049i
\(756\) 0 0
\(757\) 19.4091 + 33.6176i 0.705437 + 1.22185i 0.966534 + 0.256540i \(0.0825824\pi\)
−0.261097 + 0.965313i \(0.584084\pi\)
\(758\) −91.7699 + 46.0886i −3.33323 + 1.67401i
\(759\) 0 0
\(760\) −13.2770 + 17.8341i −0.481607 + 0.646910i
\(761\) 39.7704 9.42575i 1.44167 0.341683i 0.565928 0.824455i \(-0.308518\pi\)
0.875746 + 0.482771i \(0.160370\pi\)
\(762\) 0 0
\(763\) −0.0649459 0.0872375i −0.00235120 0.00315821i
\(764\) 89.0105 + 74.6887i 3.22029 + 2.70214i
\(765\) 0 0
\(766\) −30.1711 + 25.3166i −1.09013 + 0.914725i
\(767\) 27.1993 + 6.44635i 0.982109 + 0.232764i
\(768\) 0 0
\(769\) 25.8208 16.9826i 0.931122 0.612409i 0.00927263 0.999957i \(-0.497048\pi\)
0.921849 + 0.387548i \(0.126678\pi\)
\(770\) 4.44040 2.92050i 0.160021 0.105247i
\(771\) 0 0
\(772\) −28.5562 6.76794i −1.02776 0.243583i
\(773\) −22.5762 + 18.9437i −0.812009 + 0.681356i −0.951086 0.308925i \(-0.900031\pi\)
0.139077 + 0.990282i \(0.455586\pi\)
\(774\) 0 0
\(775\) 5.65054 + 4.74137i 0.202974 + 0.170315i
\(776\) −17.9346 24.0904i −0.643816 0.864795i
\(777\) 0 0
\(778\) 44.3927 10.5213i 1.59155 0.377205i
\(779\) −4.23831 + 5.69304i −0.151853 + 0.203974i
\(780\) 0 0
\(781\) −7.09204 + 3.56175i −0.253773 + 0.127450i
\(782\) −0.492228 0.852563i −0.0176020 0.0304876i
\(783\) 0 0
\(784\) 40.5553 70.2439i 1.44841 2.50871i
\(785\) 0.372071 6.38821i 0.0132798 0.228005i
\(786\) 0 0
\(787\) −16.3206 1.90760i −0.581765 0.0679986i −0.179880 0.983689i \(-0.557571\pi\)
−0.401885 + 0.915690i \(0.631645\pi\)
\(788\) −3.55876 + 11.8871i −0.126775 + 0.423460i
\(789\) 0 0
\(790\) 26.6534 61.7896i 0.948286 2.19837i
\(791\) 2.66286 0.969203i 0.0946805 0.0344609i
\(792\) 0 0
\(793\) 68.3884 + 24.8914i 2.42854 + 0.883918i
\(794\) 46.1496 48.9157i 1.63779 1.73595i
\(795\) 0 0
\(796\) −44.8378 22.5184i −1.58923 0.798143i
\(797\) −0.488972 8.39532i −0.0173203 0.297378i −0.995833 0.0911925i \(-0.970932\pi\)
0.978513 0.206185i \(-0.0661049\pi\)
\(798\) 0 0
\(799\) −2.96986 9.92003i −0.105066 0.350946i
\(800\) 3.82623 + 21.6996i 0.135278 + 0.767198i
\(801\) 0 0
\(802\) 9.56414 54.2409i 0.337721 1.91531i
\(803\) −9.10058 + 1.06371i −0.321152 + 0.0375373i
\(804\) 0 0
\(805\) 0.231444 + 0.245316i 0.00815732 + 0.00864625i
\(806\) 30.8211 + 71.4514i 1.08563 + 2.51677i
\(807\) 0 0
\(808\) 124.335 + 81.7763i 4.37408 + 2.87688i
\(809\) 1.83823 0.0646289 0.0323144 0.999478i \(-0.489712\pi\)
0.0323144 + 0.999478i \(0.489712\pi\)
\(810\) 0 0
\(811\) −8.25761 −0.289964 −0.144982 0.989434i \(-0.546312\pi\)
−0.144982 + 0.989434i \(0.546312\pi\)
\(812\) 3.89283 + 2.56035i 0.136611 + 0.0898508i
\(813\) 0 0
\(814\) 10.7131 + 24.8357i 0.375494 + 0.870492i
\(815\) −12.7161 13.4783i −0.445425 0.472123i
\(816\) 0 0
\(817\) −6.37387 + 0.744999i −0.222994 + 0.0260642i
\(818\) 16.3095 92.4956i 0.570248 3.23403i
\(819\) 0 0
\(820\) 15.2539 + 86.5093i 0.532690 + 3.02104i
\(821\) −7.32243 24.4586i −0.255554 0.853611i −0.985437 0.170039i \(-0.945611\pi\)
0.729883 0.683572i \(-0.239575\pi\)
\(822\) 0 0
\(823\) 0.204192 + 3.50585i 0.00711770 + 0.122206i 0.999995 + 0.00306726i \(0.000976340\pi\)
−0.992878 + 0.119139i \(0.961987\pi\)
\(824\) 32.2147 + 16.1789i 1.12225 + 0.563617i
\(825\) 0 0
\(826\) −4.63820 + 4.91621i −0.161384 + 0.171057i
\(827\) −29.3726 10.6908i −1.02139 0.371754i −0.223591 0.974683i \(-0.571778\pi\)
−0.797795 + 0.602929i \(0.794000\pi\)
\(828\) 0 0
\(829\) 44.5589 16.2181i 1.54759 0.563278i 0.579743 0.814800i \(-0.303153\pi\)
0.967852 + 0.251521i \(0.0809308\pi\)
\(830\) −34.7230 + 80.4969i −1.20525 + 2.79409i
\(831\) 0 0
\(832\) −27.7199 + 92.5910i −0.961015 + 3.21001i
\(833\) −9.47964 1.10801i −0.328450 0.0383903i
\(834\) 0 0
\(835\) −0.945185 + 16.2282i −0.0327095 + 0.561600i
\(836\) −4.13831 + 7.16776i −0.143126 + 0.247902i
\(837\) 0 0
\(838\) −36.1825 62.6699i −1.24990 2.16489i
\(839\) −26.5599 + 13.3389i −0.916950 + 0.460509i −0.843707 0.536805i \(-0.819631\pi\)
−0.0732431 + 0.997314i \(0.523335\pi\)
\(840\) 0 0
\(841\) −15.4287 + 20.7243i −0.532024 + 0.714632i
\(842\) −79.0718 + 18.7404i −2.72499 + 0.645835i
\(843\) 0 0
\(844\) −60.0498 80.6609i −2.06700 2.77646i
\(845\) 36.5597 + 30.6772i 1.25769 + 1.05533i
\(846\) 0 0
\(847\) −3.38092 + 2.83693i −0.116170 + 0.0974780i
\(848\) 111.130 + 26.3382i 3.81621 + 0.904458i
\(849\) 0 0
\(850\) 4.50997 2.96625i 0.154691 0.101742i
\(851\) −1.43403 + 0.943177i −0.0491580 + 0.0323317i
\(852\) 0 0
\(853\) 10.2598 + 2.43161i 0.351287 + 0.0832566i 0.402471 0.915433i \(-0.368151\pi\)
−0.0511840 + 0.998689i \(0.516300\pi\)
\(854\) −13.4803 + 11.3113i −0.461286 + 0.387065i
\(855\) 0 0
\(856\) 51.0334 + 42.8221i 1.74429 + 1.46363i
\(857\) −8.85593 11.8956i −0.302513 0.406345i 0.624709 0.780858i \(-0.285218\pi\)
−0.927222 + 0.374512i \(0.877810\pi\)
\(858\) 0 0
\(859\) 30.7582 7.28983i 1.04946 0.248726i 0.330518 0.943800i \(-0.392777\pi\)
0.718938 + 0.695074i \(0.244628\pi\)
\(860\) −47.4295 + 63.7088i −1.61733 + 2.17245i
\(861\) 0 0
\(862\) −21.5164 + 10.8059i −0.732851 + 0.368052i
\(863\) −1.64562 2.85030i −0.0560177 0.0970255i 0.836657 0.547728i \(-0.184507\pi\)
−0.892674 + 0.450702i \(0.851174\pi\)
\(864\) 0 0
\(865\) −6.19692 + 10.7334i −0.210701 + 0.364946i
\(866\) −3.67969 + 63.1778i −0.125041 + 2.14687i
\(867\) 0 0
\(868\) −13.4442 1.57140i −0.456326 0.0533369i
\(869\) 4.38215 14.6374i 0.148654 0.496540i
\(870\) 0 0
\(871\) 14.3427 33.2501i 0.485983 1.12664i
\(872\) 1.67013 0.607878i 0.0565577 0.0205853i
\(873\) 0 0
\(874\) −0.686052 0.249702i −0.0232060 0.00844631i
\(875\) 3.17555 3.36588i 0.107353 0.113788i
\(876\) 0 0
\(877\) −33.0068 16.5766i −1.11456 0.559753i −0.206439 0.978459i \(-0.566187\pi\)
−0.908122 + 0.418706i \(0.862484\pi\)
\(878\) −0.624763 10.7268i −0.0210847 0.362011i
\(879\) 0 0
\(880\) 13.4500 + 44.9262i 0.453400 + 1.51446i
\(881\) −5.05857 28.6886i −0.170427 0.966542i −0.943290 0.331969i \(-0.892287\pi\)
0.772863 0.634573i \(-0.218824\pi\)
\(882\) 0 0
\(883\) −3.27904 + 18.5963i −0.110348 + 0.625817i 0.878600 + 0.477558i \(0.158478\pi\)
−0.988949 + 0.148259i \(0.952633\pi\)
\(884\) 40.6897 4.75594i 1.36854 0.159960i
\(885\) 0 0
\(886\) 14.5790 + 15.4529i 0.489793 + 0.519150i
\(887\) −9.62067 22.3032i −0.323031 0.748869i −0.999918 0.0127828i \(-0.995931\pi\)
0.676888 0.736086i \(-0.263328\pi\)
\(888\) 0 0
\(889\) 7.79420 + 5.12633i 0.261409 + 0.171932i
\(890\) 66.7543 2.23761
\(891\) 0 0
\(892\) 13.4343 0.449814
\(893\) −6.41605 4.21990i −0.214705 0.141214i
\(894\) 0 0
\(895\) 0.514730 + 1.19328i 0.0172055 + 0.0398869i
\(896\) −5.21433 5.52686i −0.174198 0.184640i
\(897\) 0 0
\(898\) −39.0769 + 4.56744i −1.30401 + 0.152417i
\(899\) −1.59569 + 9.04959i −0.0532191 + 0.301821i
\(900\) 0 0
\(901\) −2.33361 13.2346i −0.0777438 0.440907i
\(902\) 7.95172 + 26.5606i 0.264763 + 0.884371i
\(903\) 0 0
\(904\) 2.69263 + 46.2306i 0.0895555 + 1.53761i
\(905\) −8.56020 4.29909i −0.284551 0.142907i
\(906\) 0 0
\(907\) −27.0555 + 28.6772i −0.898364 + 0.952211i −0.999088 0.0427038i \(-0.986403\pi\)
0.100723 + 0.994914i \(0.467884\pi\)
\(908\) 5.95117 + 2.16605i 0.197496 + 0.0718828i
\(909\) 0 0
\(910\) −18.3325 + 6.67247i −0.607715 + 0.221190i
\(911\) −16.3902 + 37.9968i −0.543032 + 1.25889i 0.397004 + 0.917817i \(0.370050\pi\)
−0.940037 + 0.341073i \(0.889210\pi\)
\(912\) 0 0
\(913\) −5.70889 + 19.0690i −0.188937 + 0.631092i
\(914\) 20.8440 + 2.43631i 0.689457 + 0.0805860i
\(915\) 0 0
\(916\) −1.46061 + 25.0777i −0.0482600 + 0.828592i
\(917\) 2.05402 3.55767i 0.0678298 0.117485i
\(918\) 0 0
\(919\) 0.677038 + 1.17266i 0.0223334 + 0.0386826i 0.876976 0.480534i \(-0.159557\pi\)
−0.854643 + 0.519217i \(0.826224\pi\)
\(920\) −4.92526 + 2.47356i −0.162381 + 0.0815509i
\(921\) 0 0
\(922\) −5.26713 + 7.07498i −0.173464 + 0.233002i
\(923\) 28.3464 6.71822i 0.933034 0.221133i
\(924\) 0 0
\(925\) −5.62012 7.54913i −0.184788 0.248214i
\(926\) −36.2019 30.3770i −1.18967 0.998250i
\(927\) 0 0
\(928\) −21.0279 + 17.6445i −0.690274 + 0.579209i
\(929\) 25.9999 + 6.16209i 0.853029 + 0.202172i 0.633796 0.773501i \(-0.281496\pi\)
0.219234 + 0.975672i \(0.429644\pi\)
\(930\) 0 0
\(931\) −5.91362 + 3.88945i −0.193811 + 0.127472i
\(932\) −16.3823 + 10.7748i −0.536619 + 0.352940i
\(933\) 0 0
\(934\) 103.543 + 24.5400i 3.38802 + 0.802975i
\(935\) 4.22721 3.54705i 0.138244 0.116001i
\(936\) 0 0
\(937\) −2.08507 1.74958i −0.0681162 0.0571563i 0.608094 0.793865i \(-0.291934\pi\)
−0.676210 + 0.736709i \(0.736379\pi\)
\(938\) 5.22860 + 7.02323i 0.170720 + 0.229317i
\(939\) 0 0
\(940\) −92.4845 + 21.9192i −3.01651 + 0.714926i
\(941\) −13.6172 + 18.2911i −0.443908 + 0.596272i −0.966613 0.256242i \(-0.917516\pi\)
0.522705 + 0.852514i \(0.324923\pi\)
\(942\) 0 0
\(943\) −1.57225 + 0.789615i −0.0511996 + 0.0257134i
\(944\) −29.8195 51.6488i −0.970541 1.68103i
\(945\) 0 0
\(946\) −12.5341 + 21.7097i −0.407520 + 0.705845i
\(947\) 0.952785 16.3587i 0.0309613 0.531586i −0.946794 0.321839i \(-0.895699\pi\)
0.977756 0.209747i \(-0.0672639\pi\)
\(948\) 0 0
\(949\) 33.4058 + 3.90458i 1.08440 + 0.126748i
\(950\) 1.14813 3.83503i 0.0372504 0.124425i
\(951\) 0 0
\(952\) −2.39305 + 5.54772i −0.0775593 + 0.179803i
\(953\) −33.5144 + 12.1982i −1.08564 + 0.395140i −0.822003 0.569483i \(-0.807143\pi\)
−0.263634 + 0.964623i \(0.584921\pi\)
\(954\) 0 0
\(955\) −53.9877 19.6499i −1.74700 0.635857i
\(956\) −31.8340 + 33.7420i −1.02958 + 1.09129i
\(957\) 0 0
\(958\) 93.5000 + 46.9574i 3.02085 + 1.51713i
\(959\) 0.253484 + 4.35215i 0.00818542 + 0.140538i
\(960\) 0 0
\(961\) 1.23462 + 4.12391i 0.0398263 + 0.133029i
\(962\) −17.2407 97.7770i −0.555863 3.15246i
\(963\) 0 0
\(964\) −20.8580 + 118.292i −0.671791 + 3.80992i
\(965\) 14.4126 1.68459i 0.463958 0.0542289i
\(966\) 0 0
\(967\) 5.52220 + 5.85319i 0.177582 + 0.188226i 0.810050 0.586360i \(-0.199440\pi\)
−0.632469 + 0.774586i \(0.717958\pi\)
\(968\) −28.5671 66.2259i −0.918180 2.12858i
\(969\) 0 0
\(970\) 20.3411 + 13.3785i 0.653113 + 0.429559i
\(971\) 44.9410 1.44223 0.721113 0.692818i \(-0.243631\pi\)
0.721113 + 0.692818i \(0.243631\pi\)
\(972\) 0 0
\(973\) 6.66731 0.213744
\(974\) −78.1977 51.4314i −2.50562 1.64797i
\(975\) 0 0
\(976\) −61.5013 142.576i −1.96861 4.56375i
\(977\) −19.0563 20.1985i −0.609664 0.646206i 0.346840 0.937924i \(-0.387255\pi\)
−0.956504 + 0.291718i \(0.905773\pi\)
\(978\) 0 0
\(979\) 15.0545 1.75962i 0.481144 0.0562377i
\(980\) −15.2122 + 86.2728i −0.485936 + 2.75588i
\(981\) 0 0
\(982\) −9.54176 54.1140i −0.304490 1.72685i
\(983\) −2.00822 6.70794i −0.0640524 0.213950i 0.919972 0.391984i \(-0.128211\pi\)
−0.984024 + 0.178035i \(0.943026\pi\)
\(984\) 0 0
\(985\) −0.356736 6.12492i −0.0113666 0.195156i
\(986\) 6.00943 + 3.01805i 0.191379 + 0.0961143i
\(987\) 0 0
\(988\) 20.8489 22.0985i 0.663292 0.703048i
\(989\) −1.49485 0.544079i −0.0475333 0.0173007i
\(990\) 0 0
\(991\) 55.0238 20.0270i 1.74789 0.636179i 0.748259 0.663407i \(-0.230890\pi\)
0.999629 + 0.0272280i \(0.00866800\pi\)
\(992\) 31.5850 73.2223i 1.00283 2.32481i
\(993\) 0 0
\(994\) −2.02021 + 6.74799i −0.0640773 + 0.214033i
\(995\) 24.6411 + 2.88014i 0.781176 + 0.0913064i
\(996\) 0 0
\(997\) 2.23842 38.4322i 0.0708916 1.21716i −0.755913 0.654672i \(-0.772807\pi\)
0.826805 0.562489i \(-0.190156\pi\)
\(998\) −11.0063 + 19.0635i −0.348400 + 0.603446i
\(999\) 0 0
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 729.2.g.b.703.1 144
3.2 odd 2 729.2.g.c.703.8 144
9.2 odd 6 729.2.g.d.217.8 144
9.4 even 3 243.2.g.a.73.8 144
9.5 odd 6 81.2.g.a.25.1 yes 144
9.7 even 3 729.2.g.a.217.1 144
81.13 even 27 729.2.g.a.514.1 144
81.14 odd 54 729.2.g.c.28.8 144
81.38 odd 54 6561.2.a.c.1.2 72
81.40 even 27 243.2.g.a.10.8 144
81.41 odd 54 81.2.g.a.13.1 144
81.43 even 27 6561.2.a.d.1.71 72
81.67 even 27 inner 729.2.g.b.28.1 144
81.68 odd 54 729.2.g.d.514.8 144
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
81.2.g.a.13.1 144 81.41 odd 54
81.2.g.a.25.1 yes 144 9.5 odd 6
243.2.g.a.10.8 144 81.40 even 27
243.2.g.a.73.8 144 9.4 even 3
729.2.g.a.217.1 144 9.7 even 3
729.2.g.a.514.1 144 81.13 even 27
729.2.g.b.28.1 144 81.67 even 27 inner
729.2.g.b.703.1 144 1.1 even 1 trivial
729.2.g.c.28.8 144 81.14 odd 54
729.2.g.c.703.8 144 3.2 odd 2
729.2.g.d.217.8 144 9.2 odd 6
729.2.g.d.514.8 144 81.68 odd 54
6561.2.a.c.1.2 72 81.38 odd 54
6561.2.a.d.1.71 72 81.43 even 27