Properties

Label 552.2.j.d.323.20
Level $552$
Weight $2$
Character 552.323
Analytic conductor $4.408$
Analytic rank $0$
Dimension $42$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [552,2,Mod(323,552)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(552, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1, 1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("552.323");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 552.j (of order \(2\), degree \(1\), 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: \(4.40774219157\)
Analytic rank: \(0\)
Dimension: \(42\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 323.20
Character \(\chi\) \(=\) 552.323
Dual form 552.2.j.d.323.19

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.218758 + 1.39719i) q^{2} +(0.262136 + 1.71210i) q^{3} +(-1.90429 - 0.611292i) q^{4} -0.130526 q^{5} +(-2.44948 - 0.00827965i) q^{6} -3.77863i q^{7} +(1.27067 - 2.52693i) q^{8} +(-2.86257 + 0.897607i) q^{9} +O(q^{10})\) \(q+(-0.218758 + 1.39719i) q^{2} +(0.262136 + 1.71210i) q^{3} +(-1.90429 - 0.611292i) q^{4} -0.130526 q^{5} +(-2.44948 - 0.00827965i) q^{6} -3.77863i q^{7} +(1.27067 - 2.52693i) q^{8} +(-2.86257 + 0.897607i) q^{9} +(0.0285535 - 0.182369i) q^{10} -4.36656i q^{11} +(0.547409 - 3.42058i) q^{12} -5.50350i q^{13} +(5.27947 + 0.826604i) q^{14} +(-0.0342155 - 0.223473i) q^{15} +(3.25264 + 2.32816i) q^{16} +0.402065i q^{17} +(-0.627921 - 4.19592i) q^{18} -2.08168 q^{19} +(0.248559 + 0.0797893i) q^{20} +(6.46939 - 0.990517i) q^{21} +(6.10092 + 0.955218i) q^{22} +1.00000 q^{23} +(4.65945 + 1.51311i) q^{24} -4.98296 q^{25} +(7.68945 + 1.20393i) q^{26} +(-2.28718 - 4.66571i) q^{27} +(-2.30985 + 7.19561i) q^{28} -8.77100 q^{29} +(0.319719 + 0.00108071i) q^{30} +7.75722i q^{31} +(-3.96442 + 4.03526i) q^{32} +(7.47599 - 1.14463i) q^{33} +(-0.561761 - 0.0879546i) q^{34} +0.493208i q^{35} +(5.99986 + 0.0405616i) q^{36} -10.1015i q^{37} +(0.455384 - 2.90851i) q^{38} +(9.42255 - 1.44267i) q^{39} +(-0.165855 + 0.329830i) q^{40} +2.80694i q^{41} +(-0.0312857 + 9.25566i) q^{42} +3.07905 q^{43} +(-2.66925 + 8.31520i) q^{44} +(0.373638 - 0.117161i) q^{45} +(-0.218758 + 1.39719i) q^{46} +3.41142 q^{47} +(-3.13340 + 6.17914i) q^{48} -7.27804 q^{49} +(1.09006 - 6.96216i) q^{50} +(-0.688374 + 0.105396i) q^{51} +(-3.36425 + 10.4803i) q^{52} -0.336698 q^{53} +(7.01923 - 2.17497i) q^{54} +0.569948i q^{55} +(-9.54835 - 4.80139i) q^{56} +(-0.545685 - 3.56405i) q^{57} +(1.91872 - 12.2548i) q^{58} +9.68031i q^{59} +(-0.0714509 + 0.446473i) q^{60} -2.78101i q^{61} +(-10.8383 - 1.69695i) q^{62} +(3.39173 + 10.8166i) q^{63} +(-4.77079 - 6.42180i) q^{64} +0.718348i q^{65} +(-0.0361536 + 10.6958i) q^{66} +12.8230 q^{67} +(0.245779 - 0.765648i) q^{68} +(0.262136 + 1.71210i) q^{69} +(-0.689106 - 0.107893i) q^{70} +8.19053 q^{71} +(-1.36919 + 8.37409i) q^{72} +0.417051 q^{73} +(14.1138 + 2.20979i) q^{74} +(-1.30622 - 8.53133i) q^{75} +(3.96413 + 1.27252i) q^{76} -16.4996 q^{77} +(-0.0455671 + 13.4807i) q^{78} -3.09607i q^{79} +(-0.424553 - 0.303884i) q^{80} +(7.38860 - 5.13893i) q^{81} +(-3.92184 - 0.614040i) q^{82} +3.59045i q^{83} +(-12.9251 - 2.06846i) q^{84} -0.0524797i q^{85} +(-0.673565 + 4.30202i) q^{86} +(-2.29920 - 15.0168i) q^{87} +(-11.0340 - 5.54846i) q^{88} -11.1036i q^{89} +(0.0819598 + 0.547674i) q^{90} -20.7957 q^{91} +(-1.90429 - 0.611292i) q^{92} +(-13.2811 + 2.03345i) q^{93} +(-0.746274 + 4.76641i) q^{94} +0.271713 q^{95} +(-7.94799 - 5.72969i) q^{96} +4.53325 q^{97} +(1.59213 - 10.1688i) q^{98} +(3.91946 + 12.4996i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 42 q + 2 q^{3} + 4 q^{4} + 8 q^{5} + 4 q^{6} - 9 q^{8} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 42 q + 2 q^{3} + 4 q^{4} + 8 q^{5} + 4 q^{6} - 9 q^{8} + 2 q^{9} - 4 q^{10} - 21 q^{12} - 4 q^{14} - 8 q^{15} - 12 q^{16} - 11 q^{18} + 4 q^{19} - 2 q^{20} + 8 q^{21} + 18 q^{22} + 42 q^{23} + 28 q^{24} + 22 q^{25} + 11 q^{26} - 16 q^{27} + 6 q^{28} + 2 q^{30} - 20 q^{32} + 12 q^{33} + 14 q^{34} - 24 q^{36} - 22 q^{38} + 8 q^{39} + 4 q^{40} - 44 q^{42} + 28 q^{43} + 56 q^{44} - 8 q^{45} + 30 q^{48} - 50 q^{49} + 20 q^{50} + 28 q^{51} - q^{52} + 24 q^{53} + 52 q^{54} - 34 q^{56} - 8 q^{57} - 21 q^{58} - 42 q^{60} - 79 q^{62} - 16 q^{63} + 7 q^{64} - 62 q^{66} - 4 q^{67} + 20 q^{68} + 2 q^{69} - 8 q^{70} + 22 q^{72} + 4 q^{73} + 36 q^{74} - 6 q^{75} + 14 q^{76} + 32 q^{77} + 27 q^{78} - 52 q^{80} + 18 q^{81} + 11 q^{82} - 80 q^{84} - 28 q^{86} - 48 q^{87} - 38 q^{88} - 46 q^{90} - 8 q^{91} + 4 q^{92} - 22 q^{93} + q^{94} - 16 q^{95} + 9 q^{96} + 20 q^{97} + 64 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/552\mathbb{Z}\right)^\times\).

\(n\) \(97\) \(185\) \(277\) \(415\)
\(\chi(n)\) \(1\) \(-1\) \(-1\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.218758 + 1.39719i −0.154685 + 0.987964i
\(3\) 0.262136 + 1.71210i 0.151345 + 0.988481i
\(4\) −1.90429 0.611292i −0.952145 0.305646i
\(5\) −0.130526 −0.0583728 −0.0291864 0.999574i \(-0.509292\pi\)
−0.0291864 + 0.999574i \(0.509292\pi\)
\(6\) −2.44948 0.00827965i −0.999994 0.00338015i
\(7\) 3.77863i 1.42819i −0.700050 0.714094i \(-0.746839\pi\)
0.700050 0.714094i \(-0.253161\pi\)
\(8\) 1.27067 2.52693i 0.449250 0.893406i
\(9\) −2.86257 + 0.897607i −0.954190 + 0.299202i
\(10\) 0.0285535 0.182369i 0.00902939 0.0576702i
\(11\) 4.36656i 1.31657i −0.752770 0.658284i \(-0.771283\pi\)
0.752770 0.658284i \(-0.228717\pi\)
\(12\) 0.547409 3.42058i 0.158024 0.987435i
\(13\) 5.50350i 1.52640i −0.646164 0.763199i \(-0.723628\pi\)
0.646164 0.763199i \(-0.276372\pi\)
\(14\) 5.27947 + 0.826604i 1.41100 + 0.220919i
\(15\) −0.0342155 0.223473i −0.00883441 0.0577004i
\(16\) 3.25264 + 2.32816i 0.813161 + 0.582039i
\(17\) 0.402065i 0.0975150i 0.998811 + 0.0487575i \(0.0155261\pi\)
−0.998811 + 0.0487575i \(0.984474\pi\)
\(18\) −0.627921 4.19592i −0.148002 0.988987i
\(19\) −2.08168 −0.477571 −0.238785 0.971072i \(-0.576749\pi\)
−0.238785 + 0.971072i \(0.576749\pi\)
\(20\) 0.248559 + 0.0797893i 0.0555794 + 0.0178414i
\(21\) 6.46939 0.990517i 1.41174 0.216148i
\(22\) 6.10092 + 0.955218i 1.30072 + 0.203653i
\(23\) 1.00000 0.208514
\(24\) 4.65945 + 1.51311i 0.951107 + 0.308863i
\(25\) −4.98296 −0.996593
\(26\) 7.68945 + 1.20393i 1.50803 + 0.236111i
\(27\) −2.28718 4.66571i −0.440167 0.897916i
\(28\) −2.30985 + 7.19561i −0.436520 + 1.35984i
\(29\) −8.77100 −1.62873 −0.814367 0.580350i \(-0.802916\pi\)
−0.814367 + 0.580350i \(0.802916\pi\)
\(30\) 0.319719 + 0.00108071i 0.0583725 + 0.000197309i
\(31\) 7.75722i 1.39324i 0.717442 + 0.696619i \(0.245313\pi\)
−0.717442 + 0.696619i \(0.754687\pi\)
\(32\) −3.96442 + 4.03526i −0.700817 + 0.713341i
\(33\) 7.47599 1.14463i 1.30140 0.199255i
\(34\) −0.561761 0.0879546i −0.0963413 0.0150841i
\(35\) 0.493208i 0.0833673i
\(36\) 5.99986 + 0.0405616i 0.999977 + 0.00676026i
\(37\) 10.1015i 1.66068i −0.557254 0.830342i \(-0.688145\pi\)
0.557254 0.830342i \(-0.311855\pi\)
\(38\) 0.455384 2.90851i 0.0738730 0.471823i
\(39\) 9.42255 1.44267i 1.50882 0.231012i
\(40\) −0.165855 + 0.329830i −0.0262240 + 0.0521506i
\(41\) 2.80694i 0.438371i 0.975683 + 0.219185i \(0.0703399\pi\)
−0.975683 + 0.219185i \(0.929660\pi\)
\(42\) −0.0312857 + 9.25566i −0.00482749 + 1.42818i
\(43\) 3.07905 0.469550 0.234775 0.972050i \(-0.424565\pi\)
0.234775 + 0.972050i \(0.424565\pi\)
\(44\) −2.66925 + 8.31520i −0.402404 + 1.25356i
\(45\) 0.373638 0.117161i 0.0556987 0.0174653i
\(46\) −0.218758 + 1.39719i −0.0322540 + 0.206005i
\(47\) 3.41142 0.497607 0.248803 0.968554i \(-0.419963\pi\)
0.248803 + 0.968554i \(0.419963\pi\)
\(48\) −3.13340 + 6.17914i −0.452267 + 0.891882i
\(49\) −7.27804 −1.03972
\(50\) 1.09006 6.96216i 0.154158 0.984597i
\(51\) −0.688374 + 0.105396i −0.0963917 + 0.0147584i
\(52\) −3.36425 + 10.4803i −0.466538 + 1.45335i
\(53\) −0.336698 −0.0462490 −0.0231245 0.999733i \(-0.507361\pi\)
−0.0231245 + 0.999733i \(0.507361\pi\)
\(54\) 7.01923 2.17497i 0.955196 0.295975i
\(55\) 0.569948i 0.0768518i
\(56\) −9.54835 4.80139i −1.27595 0.641613i
\(57\) −0.545685 3.56405i −0.0722777 0.472070i
\(58\) 1.91872 12.2548i 0.251941 1.60913i
\(59\) 9.68031i 1.26027i 0.776486 + 0.630134i \(0.217000\pi\)
−0.776486 + 0.630134i \(0.783000\pi\)
\(60\) −0.0714509 + 0.446473i −0.00922428 + 0.0576394i
\(61\) 2.78101i 0.356072i −0.984024 0.178036i \(-0.943026\pi\)
0.984024 0.178036i \(-0.0569744\pi\)
\(62\) −10.8383 1.69695i −1.37647 0.215513i
\(63\) 3.39173 + 10.8166i 0.427317 + 1.36276i
\(64\) −4.77079 6.42180i −0.596349 0.802725i
\(65\) 0.718348i 0.0891001i
\(66\) −0.0361536 + 10.6958i −0.00445020 + 1.31656i
\(67\) 12.8230 1.56658 0.783292 0.621654i \(-0.213539\pi\)
0.783292 + 0.621654i \(0.213539\pi\)
\(68\) 0.245779 0.765648i 0.0298051 0.0928484i
\(69\) 0.262136 + 1.71210i 0.0315575 + 0.206113i
\(70\) −0.689106 0.107893i −0.0823639 0.0128957i
\(71\) 8.19053 0.972037 0.486018 0.873949i \(-0.338449\pi\)
0.486018 + 0.873949i \(0.338449\pi\)
\(72\) −1.36919 + 8.37409i −0.161360 + 0.986896i
\(73\) 0.417051 0.0488121 0.0244061 0.999702i \(-0.492231\pi\)
0.0244061 + 0.999702i \(0.492231\pi\)
\(74\) 14.1138 + 2.20979i 1.64070 + 0.256883i
\(75\) −1.30622 8.53133i −0.150829 0.985113i
\(76\) 3.96413 + 1.27252i 0.454717 + 0.145968i
\(77\) −16.4996 −1.88031
\(78\) −0.0455671 + 13.4807i −0.00515945 + 1.52639i
\(79\) 3.09607i 0.348335i −0.984716 0.174168i \(-0.944277\pi\)
0.984716 0.174168i \(-0.0557235\pi\)
\(80\) −0.424553 0.303884i −0.0474665 0.0339753i
\(81\) 7.38860 5.13893i 0.820956 0.570992i
\(82\) −3.92184 0.614040i −0.433094 0.0678093i
\(83\) 3.59045i 0.394103i 0.980393 + 0.197052i \(0.0631367\pi\)
−0.980393 + 0.197052i \(0.936863\pi\)
\(84\) −12.9251 2.06846i −1.41024 0.225687i
\(85\) 0.0524797i 0.00569222i
\(86\) −0.673565 + 4.30202i −0.0726324 + 0.463899i
\(87\) −2.29920 15.0168i −0.246500 1.60997i
\(88\) −11.0340 5.54846i −1.17623 0.591468i
\(89\) 11.1036i 1.17698i −0.808506 0.588488i \(-0.799724\pi\)
0.808506 0.588488i \(-0.200276\pi\)
\(90\) 0.0819598 + 0.547674i 0.00863932 + 0.0577300i
\(91\) −20.7957 −2.17998
\(92\) −1.90429 0.611292i −0.198536 0.0637316i
\(93\) −13.2811 + 2.03345i −1.37719 + 0.210859i
\(94\) −0.746274 + 4.76641i −0.0769723 + 0.491618i
\(95\) 0.271713 0.0278772
\(96\) −7.94799 5.72969i −0.811189 0.584784i
\(97\) 4.53325 0.460281 0.230141 0.973157i \(-0.426081\pi\)
0.230141 + 0.973157i \(0.426081\pi\)
\(98\) 1.59213 10.1688i 0.160829 1.02721i
\(99\) 3.91946 + 12.4996i 0.393920 + 1.25626i
\(100\) 9.48901 + 3.04605i 0.948901 + 0.304605i
\(101\) 3.79039 0.377158 0.188579 0.982058i \(-0.439612\pi\)
0.188579 + 0.982058i \(0.439612\pi\)
\(102\) 0.00332895 0.984847i 0.000329615 0.0975144i
\(103\) 6.81074i 0.671082i −0.942026 0.335541i \(-0.891081\pi\)
0.942026 0.335541i \(-0.108919\pi\)
\(104\) −13.9070 6.99314i −1.36369 0.685734i
\(105\) −0.844421 + 0.129288i −0.0824070 + 0.0126172i
\(106\) 0.0736551 0.470431i 0.00715402 0.0456923i
\(107\) 6.74888i 0.652439i 0.945294 + 0.326219i \(0.105775\pi\)
−0.945294 + 0.326219i \(0.894225\pi\)
\(108\) 1.50334 + 10.2830i 0.144659 + 0.989482i
\(109\) 18.3211i 1.75485i −0.479716 0.877424i \(-0.659260\pi\)
0.479716 0.877424i \(-0.340740\pi\)
\(110\) −0.796327 0.124680i −0.0759268 0.0118878i
\(111\) 17.2948 2.64798i 1.64155 0.251335i
\(112\) 8.79724 12.2905i 0.831261 1.16135i
\(113\) 14.3459i 1.34955i 0.738023 + 0.674775i \(0.235759\pi\)
−0.738023 + 0.674775i \(0.764241\pi\)
\(114\) 5.09903 + 0.0172356i 0.477568 + 0.00161426i
\(115\) −0.130526 −0.0121716
\(116\) 16.7025 + 5.36165i 1.55079 + 0.497816i
\(117\) 4.93999 + 15.7542i 0.456702 + 1.45647i
\(118\) −13.5252 2.11764i −1.24510 0.194945i
\(119\) 1.51925 0.139270
\(120\) −0.608178 0.197500i −0.0555188 0.0180292i
\(121\) −8.06685 −0.733350
\(122\) 3.88561 + 0.608367i 0.351786 + 0.0550790i
\(123\) −4.80576 + 0.735802i −0.433321 + 0.0663450i
\(124\) 4.74193 14.7720i 0.425838 1.32656i
\(125\) 1.30303 0.116547
\(126\) −15.8548 + 2.37268i −1.41246 + 0.211375i
\(127\) 13.5190i 1.19962i −0.800143 0.599810i \(-0.795243\pi\)
0.800143 0.599810i \(-0.204757\pi\)
\(128\) 10.0161 5.26089i 0.885310 0.465002i
\(129\) 0.807131 + 5.27164i 0.0710639 + 0.464142i
\(130\) −1.00367 0.157144i −0.0880277 0.0137824i
\(131\) 21.6396i 1.89066i −0.326114 0.945331i \(-0.605739\pi\)
0.326114 0.945331i \(-0.394261\pi\)
\(132\) −14.9362 2.39030i −1.30003 0.208049i
\(133\) 7.86591i 0.682061i
\(134\) −2.80514 + 17.9163i −0.242327 + 1.54773i
\(135\) 0.298535 + 0.608994i 0.0256938 + 0.0524139i
\(136\) 1.01599 + 0.510892i 0.0871205 + 0.0438086i
\(137\) 14.9588i 1.27801i 0.769201 + 0.639007i \(0.220655\pi\)
−0.769201 + 0.639007i \(0.779345\pi\)
\(138\) −2.44948 0.00827965i −0.208513 0.000704810i
\(139\) 11.5627 0.980736 0.490368 0.871515i \(-0.336862\pi\)
0.490368 + 0.871515i \(0.336862\pi\)
\(140\) 0.301494 0.939211i 0.0254809 0.0793778i
\(141\) 0.894258 + 5.84069i 0.0753101 + 0.491875i
\(142\) −1.79174 + 11.4437i −0.150359 + 0.960337i
\(143\) −24.0314 −2.00961
\(144\) −11.4007 3.74491i −0.950057 0.312076i
\(145\) 1.14484 0.0950738
\(146\) −0.0912330 + 0.582700i −0.00755050 + 0.0482246i
\(147\) −1.90784 12.4607i −0.157356 1.02774i
\(148\) −6.17500 + 19.2363i −0.507582 + 1.58121i
\(149\) −13.1430 −1.07671 −0.538356 0.842717i \(-0.680955\pi\)
−0.538356 + 0.842717i \(0.680955\pi\)
\(150\) 12.2056 + 0.0412572i 0.996587 + 0.00336863i
\(151\) 1.10155i 0.0896425i 0.998995 + 0.0448213i \(0.0142718\pi\)
−0.998995 + 0.0448213i \(0.985728\pi\)
\(152\) −2.64513 + 5.26028i −0.214549 + 0.426665i
\(153\) −0.360896 1.15094i −0.0291767 0.0930478i
\(154\) 3.60942 23.0531i 0.290855 1.85767i
\(155\) 1.01252i 0.0813272i
\(156\) −18.8252 3.01267i −1.50722 0.241207i
\(157\) 17.3372i 1.38366i 0.722062 + 0.691828i \(0.243195\pi\)
−0.722062 + 0.691828i \(0.756805\pi\)
\(158\) 4.32581 + 0.677289i 0.344143 + 0.0538822i
\(159\) −0.0882607 0.576460i −0.00699953 0.0457162i
\(160\) 0.517458 0.526705i 0.0409087 0.0416397i
\(161\) 3.77863i 0.297798i
\(162\) 5.56375 + 11.4475i 0.437130 + 0.899398i
\(163\) −10.4421 −0.817889 −0.408944 0.912559i \(-0.634103\pi\)
−0.408944 + 0.912559i \(0.634103\pi\)
\(164\) 1.71586 5.34523i 0.133986 0.417393i
\(165\) −0.975807 + 0.149404i −0.0759665 + 0.0116311i
\(166\) −5.01655 0.785438i −0.389360 0.0609618i
\(167\) −1.67012 −0.129238 −0.0646188 0.997910i \(-0.520583\pi\)
−0.0646188 + 0.997910i \(0.520583\pi\)
\(168\) 5.71749 17.6063i 0.441114 1.35836i
\(169\) −17.2886 −1.32989
\(170\) 0.0733242 + 0.0114803i 0.00562371 + 0.000880501i
\(171\) 5.95896 1.86853i 0.455693 0.142890i
\(172\) −5.86340 1.88220i −0.447080 0.143516i
\(173\) −8.55215 −0.650208 −0.325104 0.945678i \(-0.605399\pi\)
−0.325104 + 0.945678i \(0.605399\pi\)
\(174\) 21.4844 + 0.0726208i 1.62872 + 0.00550537i
\(175\) 18.8288i 1.42332i
\(176\) 10.1660 14.2029i 0.766294 1.07058i
\(177\) −16.5736 + 2.53756i −1.24575 + 0.190735i
\(178\) 15.5138 + 2.42899i 1.16281 + 0.182060i
\(179\) 14.7284i 1.10085i −0.834885 0.550425i \(-0.814466\pi\)
0.834885 0.550425i \(-0.185534\pi\)
\(180\) −0.783136 0.00529432i −0.0583715 0.000394616i
\(181\) 21.7258i 1.61487i −0.589959 0.807433i \(-0.700856\pi\)
0.589959 0.807433i \(-0.299144\pi\)
\(182\) 4.54922 29.0556i 0.337210 2.15374i
\(183\) 4.76137 0.729005i 0.351971 0.0538896i
\(184\) 1.27067 2.52693i 0.0936751 0.186288i
\(185\) 1.31851i 0.0969388i
\(186\) 0.0642270 19.0011i 0.00470935 1.39323i
\(187\) 1.75564 0.128385
\(188\) −6.49634 2.08538i −0.473794 0.152092i
\(189\) −17.6300 + 8.64240i −1.28239 + 0.628642i
\(190\) −0.0594392 + 0.379635i −0.00431218 + 0.0275416i
\(191\) 10.7127 0.775145 0.387572 0.921839i \(-0.373314\pi\)
0.387572 + 0.921839i \(0.373314\pi\)
\(192\) 9.74416 9.85146i 0.703225 0.710968i
\(193\) 14.8172 1.06657 0.533283 0.845937i \(-0.320958\pi\)
0.533283 + 0.845937i \(0.320958\pi\)
\(194\) −0.991682 + 6.33381i −0.0711986 + 0.454741i
\(195\) −1.22988 + 0.188305i −0.0880738 + 0.0134848i
\(196\) 13.8595 + 4.44901i 0.989965 + 0.317787i
\(197\) −17.5258 −1.24866 −0.624331 0.781160i \(-0.714628\pi\)
−0.624331 + 0.781160i \(0.714628\pi\)
\(198\) −18.3217 + 2.74186i −1.30207 + 0.194855i
\(199\) 23.3044i 1.65201i 0.563666 + 0.826003i \(0.309391\pi\)
−0.563666 + 0.826003i \(0.690609\pi\)
\(200\) −6.33170 + 12.5916i −0.447719 + 0.890362i
\(201\) 3.36139 + 21.9543i 0.237094 + 1.54854i
\(202\) −0.829176 + 5.29590i −0.0583406 + 0.372618i
\(203\) 33.1424i 2.32614i
\(204\) 1.37529 + 0.220094i 0.0962897 + 0.0154097i
\(205\) 0.366378i 0.0255889i
\(206\) 9.51591 + 1.48990i 0.663005 + 0.103806i
\(207\) −2.86257 + 0.897607i −0.198962 + 0.0623880i
\(208\) 12.8130 17.9009i 0.888423 1.24121i
\(209\) 9.08979i 0.628754i
\(210\) 0.00408359 1.20810i 0.000281794 0.0833669i
\(211\) 16.0748 1.10664 0.553319 0.832970i \(-0.313361\pi\)
0.553319 + 0.832970i \(0.313361\pi\)
\(212\) 0.641170 + 0.205821i 0.0440357 + 0.0141358i
\(213\) 2.14704 + 14.0230i 0.147112 + 0.960840i
\(214\) −9.42948 1.47637i −0.644586 0.100922i
\(215\) −0.401894 −0.0274090
\(216\) −14.6962 0.149031i −0.999949 0.0101403i
\(217\) 29.3117 1.98980
\(218\) 25.5982 + 4.00789i 1.73373 + 0.271448i
\(219\) 0.109324 + 0.714033i 0.00738745 + 0.0482499i
\(220\) 0.348405 1.08535i 0.0234894 0.0731740i
\(221\) 2.21276 0.148847
\(222\) −0.0836372 + 24.7435i −0.00561336 + 1.66067i
\(223\) 16.7322i 1.12047i 0.828333 + 0.560237i \(0.189290\pi\)
−0.828333 + 0.560237i \(0.810710\pi\)
\(224\) 15.2478 + 14.9801i 1.01878 + 1.00090i
\(225\) 14.2641 4.47274i 0.950938 0.298183i
\(226\) −20.0440 3.13828i −1.33331 0.208755i
\(227\) 5.60178i 0.371803i −0.982568 0.185902i \(-0.940479\pi\)
0.982568 0.185902i \(-0.0595206\pi\)
\(228\) −1.13953 + 7.12056i −0.0754674 + 0.471570i
\(229\) 17.9554i 1.18653i 0.805008 + 0.593264i \(0.202161\pi\)
−0.805008 + 0.593264i \(0.797839\pi\)
\(230\) 0.0285535 0.182369i 0.00188276 0.0120251i
\(231\) −4.32515 28.2490i −0.284574 1.85865i
\(232\) −11.1451 + 22.1637i −0.731709 + 1.45512i
\(233\) 24.5310i 1.60708i −0.595252 0.803539i \(-0.702948\pi\)
0.595252 0.803539i \(-0.297052\pi\)
\(234\) −23.0922 + 3.45577i −1.50959 + 0.225911i
\(235\) −0.445278 −0.0290467
\(236\) 5.91750 18.4341i 0.385196 1.19996i
\(237\) 5.30078 0.811594i 0.344323 0.0527187i
\(238\) −0.332348 + 2.12269i −0.0215429 + 0.137593i
\(239\) −3.73158 −0.241376 −0.120688 0.992691i \(-0.538510\pi\)
−0.120688 + 0.992691i \(0.538510\pi\)
\(240\) 0.408989 0.806536i 0.0264001 0.0520617i
\(241\) 8.92696 0.575036 0.287518 0.957775i \(-0.407170\pi\)
0.287518 + 0.957775i \(0.407170\pi\)
\(242\) 1.76468 11.2709i 0.113438 0.724524i
\(243\) 10.7352 + 11.3029i 0.688662 + 0.725083i
\(244\) −1.70001 + 5.29585i −0.108832 + 0.339032i
\(245\) 0.949971 0.0606914
\(246\) 0.0232405 6.87554i 0.00148176 0.438368i
\(247\) 11.4566i 0.728963i
\(248\) 19.6020 + 9.85687i 1.24473 + 0.625912i
\(249\) −6.14721 + 0.941188i −0.389564 + 0.0596454i
\(250\) −0.285048 + 1.82059i −0.0180280 + 0.115144i
\(251\) 15.0476i 0.949798i −0.880040 0.474899i \(-0.842485\pi\)
0.880040 0.474899i \(-0.157515\pi\)
\(252\) 0.153267 22.6713i 0.00965493 1.42816i
\(253\) 4.36656i 0.274523i
\(254\) 18.8887 + 2.95739i 1.18518 + 0.185563i
\(255\) 0.0898505 0.0137568i 0.00562666 0.000861487i
\(256\) 5.15937 + 15.1453i 0.322461 + 0.946583i
\(257\) 7.84239i 0.489195i 0.969625 + 0.244597i \(0.0786558\pi\)
−0.969625 + 0.244597i \(0.921344\pi\)
\(258\) −7.54205 0.0254934i −0.469548 0.00158715i
\(259\) −38.1700 −2.37177
\(260\) 0.439121 1.36794i 0.0272331 0.0848362i
\(261\) 25.1076 7.87292i 1.55412 0.487321i
\(262\) 30.2347 + 4.73383i 1.86790 + 0.292457i
\(263\) 18.6358 1.14913 0.574566 0.818458i \(-0.305171\pi\)
0.574566 + 0.818458i \(0.305171\pi\)
\(264\) 6.60710 20.3458i 0.406639 1.25220i
\(265\) 0.0439477 0.00269968
\(266\) −10.9902 1.72073i −0.673851 0.105505i
\(267\) 19.0104 2.91065i 1.16342 0.178129i
\(268\) −24.4188 7.83863i −1.49162 0.478821i
\(269\) 5.72570 0.349102 0.174551 0.984648i \(-0.444153\pi\)
0.174551 + 0.984648i \(0.444153\pi\)
\(270\) −0.916188 + 0.283889i −0.0557575 + 0.0172769i
\(271\) 10.0447i 0.610173i 0.952325 + 0.305086i \(0.0986853\pi\)
−0.952325 + 0.305086i \(0.901315\pi\)
\(272\) −0.936069 + 1.30777i −0.0567575 + 0.0792954i
\(273\) −5.45131 35.6043i −0.329928 2.15487i
\(274\) −20.9003 3.27235i −1.26263 0.197690i
\(275\) 21.7584i 1.31208i
\(276\) 0.547409 3.42058i 0.0329502 0.205895i
\(277\) 12.6894i 0.762431i 0.924486 + 0.381215i \(0.124494\pi\)
−0.924486 + 0.381215i \(0.875506\pi\)
\(278\) −2.52943 + 16.1553i −0.151705 + 0.968932i
\(279\) −6.96294 22.2056i −0.416860 1.32941i
\(280\) 1.24630 + 0.626705i 0.0744809 + 0.0374528i
\(281\) 25.8591i 1.54262i −0.636458 0.771311i \(-0.719601\pi\)
0.636458 0.771311i \(-0.280399\pi\)
\(282\) −8.35619 0.0282454i −0.497604 0.00168199i
\(283\) 21.0898 1.25366 0.626828 0.779158i \(-0.284353\pi\)
0.626828 + 0.779158i \(0.284353\pi\)
\(284\) −15.5971 5.00681i −0.925520 0.297099i
\(285\) 0.0712259 + 0.465199i 0.00421906 + 0.0275560i
\(286\) 5.25705 33.5765i 0.310856 1.98542i
\(287\) 10.6064 0.626076
\(288\) 7.72635 15.1097i 0.455279 0.890349i
\(289\) 16.8383 0.990491
\(290\) −0.250442 + 1.59956i −0.0147065 + 0.0939295i
\(291\) 1.18833 + 7.76137i 0.0696611 + 0.454979i
\(292\) −0.794186 0.254940i −0.0464762 0.0149192i
\(293\) 17.5822 1.02717 0.513583 0.858040i \(-0.328318\pi\)
0.513583 + 0.858040i \(0.328318\pi\)
\(294\) 17.8274 + 0.0602596i 1.03971 + 0.00351441i
\(295\) 1.26353i 0.0735654i
\(296\) −25.5259 12.8357i −1.48367 0.746062i
\(297\) −20.3731 + 9.98710i −1.18217 + 0.579510i
\(298\) 2.87512 18.3632i 0.166551 1.06375i
\(299\) 5.50350i 0.318276i
\(300\) −2.72772 + 17.0446i −0.157485 + 0.984071i
\(301\) 11.6346i 0.670606i
\(302\) −1.53907 0.240971i −0.0885636 0.0138663i
\(303\) 0.993599 + 6.48952i 0.0570808 + 0.372813i
\(304\) −6.77097 4.84648i −0.388342 0.277965i
\(305\) 0.362993i 0.0207849i
\(306\) 1.68703 0.252465i 0.0964410 0.0144325i
\(307\) −12.0490 −0.687674 −0.343837 0.939029i \(-0.611727\pi\)
−0.343837 + 0.939029i \(0.611727\pi\)
\(308\) 31.4201 + 10.0861i 1.79032 + 0.574708i
\(309\) 11.6607 1.78534i 0.663352 0.101565i
\(310\) 1.41468 + 0.221495i 0.0803483 + 0.0125801i
\(311\) −8.92121 −0.505876 −0.252938 0.967483i \(-0.581397\pi\)
−0.252938 + 0.967483i \(0.581397\pi\)
\(312\) 8.32742 25.6433i 0.471448 1.45177i
\(313\) 0.481564 0.0272196 0.0136098 0.999907i \(-0.495668\pi\)
0.0136098 + 0.999907i \(0.495668\pi\)
\(314\) −24.2234 3.79264i −1.36700 0.214031i
\(315\) −0.442707 1.41184i −0.0249437 0.0795483i
\(316\) −1.89261 + 5.89582i −0.106467 + 0.331666i
\(317\) −6.46721 −0.363235 −0.181617 0.983369i \(-0.558133\pi\)
−0.181617 + 0.983369i \(0.558133\pi\)
\(318\) 0.824733 + 0.00278774i 0.0462487 + 0.000156329i
\(319\) 38.2991i 2.14434i
\(320\) 0.622710 + 0.838209i 0.0348106 + 0.0468573i
\(321\) −11.5548 + 1.76913i −0.644923 + 0.0987431i
\(322\) 5.27947 + 0.826604i 0.294213 + 0.0460648i
\(323\) 0.836971i 0.0465703i
\(324\) −17.2114 + 5.26941i −0.956191 + 0.292745i
\(325\) 27.4238i 1.52120i
\(326\) 2.28429 14.5896i 0.126515 0.808045i
\(327\) 31.3676 4.80264i 1.73463 0.265587i
\(328\) 7.09296 + 3.56670i 0.391643 + 0.196938i
\(329\) 12.8905i 0.710676i
\(330\) 0.00471897 1.39607i 0.000259771 0.0768513i
\(331\) 25.1117 1.38026 0.690132 0.723683i \(-0.257552\pi\)
0.690132 + 0.723683i \(0.257552\pi\)
\(332\) 2.19482 6.83726i 0.120456 0.375243i
\(333\) 9.06722 + 28.9164i 0.496881 + 1.58461i
\(334\) 0.365351 2.33347i 0.0199911 0.127682i
\(335\) −1.67374 −0.0914459
\(336\) 23.3487 + 11.8400i 1.27378 + 0.645923i
\(337\) −10.0318 −0.546465 −0.273232 0.961948i \(-0.588093\pi\)
−0.273232 + 0.961948i \(0.588093\pi\)
\(338\) 3.78200 24.1554i 0.205714 1.31388i
\(339\) −24.5616 + 3.76059i −1.33401 + 0.204247i
\(340\) −0.0320804 + 0.0999366i −0.00173981 + 0.00541982i
\(341\) 33.8724 1.83429
\(342\) 1.30713 + 8.73457i 0.0706817 + 0.472311i
\(343\) 1.05062i 0.0567283i
\(344\) 3.91246 7.78055i 0.210945 0.419499i
\(345\) −0.0342155 0.223473i −0.00184210 0.0120314i
\(346\) 1.87085 11.9490i 0.100577 0.642382i
\(347\) 12.4062i 0.665998i −0.942927 0.332999i \(-0.891939\pi\)
0.942927 0.332999i \(-0.108061\pi\)
\(348\) −4.80133 + 30.0019i −0.257378 + 1.60827i
\(349\) 17.9711i 0.961969i −0.876729 0.480985i \(-0.840279\pi\)
0.876729 0.480985i \(-0.159721\pi\)
\(350\) −26.3074 4.11894i −1.40619 0.220166i
\(351\) −25.6777 + 12.5875i −1.37058 + 0.671870i
\(352\) 17.6202 + 17.3109i 0.939161 + 0.922673i
\(353\) 25.5729i 1.36111i −0.732698 0.680554i \(-0.761739\pi\)
0.732698 0.680554i \(-0.238261\pi\)
\(354\) 0.0801495 23.7117i 0.00425990 1.26026i
\(355\) −1.06907 −0.0567405
\(356\) −6.78752 + 21.1444i −0.359738 + 1.12065i
\(357\) 0.398252 + 2.60111i 0.0210777 + 0.137665i
\(358\) 20.5784 + 3.22194i 1.08760 + 0.170285i
\(359\) −20.5959 −1.08701 −0.543506 0.839405i \(-0.682904\pi\)
−0.543506 + 0.839405i \(0.682904\pi\)
\(360\) 0.178714 1.09303i 0.00941905 0.0576079i
\(361\) −14.6666 −0.771926
\(362\) 30.3551 + 4.75268i 1.59543 + 0.249796i
\(363\) −2.11462 13.8113i −0.110989 0.724903i
\(364\) 39.6011 + 12.7123i 2.07566 + 0.666303i
\(365\) −0.0544358 −0.00284930
\(366\) −0.0230258 + 6.81202i −0.00120358 + 0.356070i
\(367\) 0.995463i 0.0519628i 0.999662 + 0.0259814i \(0.00827106\pi\)
−0.999662 + 0.0259814i \(0.991729\pi\)
\(368\) 3.25264 + 2.32816i 0.169556 + 0.121364i
\(369\) −2.51953 8.03507i −0.131162 0.418289i
\(370\) −1.84221 0.288434i −0.0957720 0.0149950i
\(371\) 1.27226i 0.0660522i
\(372\) 26.5342 + 4.24637i 1.37573 + 0.220164i
\(373\) 19.8991i 1.03034i −0.857089 0.515168i \(-0.827729\pi\)
0.857089 0.515168i \(-0.172271\pi\)
\(374\) −0.384059 + 2.45296i −0.0198592 + 0.126840i
\(375\) 0.341572 + 2.23092i 0.0176387 + 0.115204i
\(376\) 4.33479 8.62044i 0.223550 0.444565i
\(377\) 48.2713i 2.48610i
\(378\) −8.21839 26.5231i −0.422709 1.36420i
\(379\) −13.7477 −0.706172 −0.353086 0.935591i \(-0.614868\pi\)
−0.353086 + 0.935591i \(0.614868\pi\)
\(380\) −0.517420 0.166096i −0.0265431 0.00852055i
\(381\) 23.1459 3.54383i 1.18580 0.181556i
\(382\) −2.34349 + 14.9677i −0.119903 + 0.765815i
\(383\) 5.57295 0.284764 0.142382 0.989812i \(-0.454524\pi\)
0.142382 + 0.989812i \(0.454524\pi\)
\(384\) 11.6328 + 15.7695i 0.593632 + 0.804736i
\(385\) 2.15362 0.109759
\(386\) −3.24138 + 20.7025i −0.164982 + 1.05373i
\(387\) −8.81399 + 2.76378i −0.448040 + 0.140491i
\(388\) −8.63262 2.77114i −0.438255 0.140683i
\(389\) −14.5658 −0.738516 −0.369258 0.929327i \(-0.620388\pi\)
−0.369258 + 0.929327i \(0.620388\pi\)
\(390\) 0.00594767 1.75958i 0.000301172 0.0890996i
\(391\) 0.402065i 0.0203333i
\(392\) −9.24800 + 18.3911i −0.467094 + 0.928893i
\(393\) 37.0492 5.67253i 1.86888 0.286141i
\(394\) 3.83390 24.4869i 0.193149 1.23363i
\(395\) 0.404117i 0.0203333i
\(396\) 0.177115 26.1988i 0.00890035 1.31654i
\(397\) 1.50196i 0.0753812i 0.999289 + 0.0376906i \(0.0120001\pi\)
−0.999289 + 0.0376906i \(0.988000\pi\)
\(398\) −32.5607 5.09802i −1.63212 0.255540i
\(399\) −13.4672 + 2.06194i −0.674204 + 0.103226i
\(400\) −16.2078 11.6011i −0.810390 0.580056i
\(401\) 21.6674i 1.08202i 0.841016 + 0.541010i \(0.181958\pi\)
−0.841016 + 0.541010i \(0.818042\pi\)
\(402\) −31.4097 0.106170i −1.56658 0.00529529i
\(403\) 42.6919 2.12663
\(404\) −7.21800 2.31703i −0.359109 0.115277i
\(405\) −0.964402 + 0.670761i −0.0479215 + 0.0333304i
\(406\) −46.3063 7.25014i −2.29814 0.359819i
\(407\) −44.1090 −2.18640
\(408\) −0.608369 + 1.87340i −0.0301188 + 0.0927471i
\(409\) 7.53712 0.372687 0.186343 0.982485i \(-0.440336\pi\)
0.186343 + 0.982485i \(0.440336\pi\)
\(410\) 0.511900 + 0.0801479i 0.0252809 + 0.00395822i
\(411\) −25.6109 + 3.92124i −1.26329 + 0.193421i
\(412\) −4.16335 + 12.9696i −0.205114 + 0.638968i
\(413\) 36.5783 1.79990
\(414\) −0.627921 4.19592i −0.0308607 0.206218i
\(415\) 0.468646i 0.0230049i
\(416\) 22.2081 + 21.8182i 1.08884 + 1.06973i
\(417\) 3.03101 + 19.7965i 0.148429 + 0.969439i
\(418\) −12.7002 1.98846i −0.621186 0.0972588i
\(419\) 4.47808i 0.218768i −0.994000 0.109384i \(-0.965112\pi\)
0.994000 0.109384i \(-0.0348879\pi\)
\(420\) 1.68706 + 0.269987i 0.0823199 + 0.0131740i
\(421\) 8.65241i 0.421693i −0.977519 0.210846i \(-0.932378\pi\)
0.977519 0.210846i \(-0.0676220\pi\)
\(422\) −3.51649 + 22.4596i −0.171180 + 1.09332i
\(423\) −9.76543 + 3.06212i −0.474811 + 0.148885i
\(424\) −0.427832 + 0.850813i −0.0207774 + 0.0413191i
\(425\) 2.00347i 0.0971827i
\(426\) −20.0625 0.0678147i −0.972031 0.00328563i
\(427\) −10.5084 −0.508538
\(428\) 4.12554 12.8518i 0.199415 0.621216i
\(429\) −6.29950 41.1441i −0.304143 1.98646i
\(430\) 0.0879174 0.561524i 0.00423976 0.0270791i
\(431\) −12.6268 −0.608214 −0.304107 0.952638i \(-0.598358\pi\)
−0.304107 + 0.952638i \(0.598358\pi\)
\(432\) 3.42313 20.5008i 0.164695 0.986345i
\(433\) −30.6380 −1.47237 −0.736185 0.676781i \(-0.763375\pi\)
−0.736185 + 0.676781i \(0.763375\pi\)
\(434\) −6.41214 + 40.9540i −0.307793 + 1.96586i
\(435\) 0.300104 + 1.96008i 0.0143889 + 0.0939787i
\(436\) −11.1996 + 34.8888i −0.536362 + 1.67087i
\(437\) −2.08168 −0.0995804
\(438\) −1.02156 0.00345303i −0.0488118 0.000164992i
\(439\) 30.6982i 1.46514i −0.680689 0.732572i \(-0.738319\pi\)
0.680689 0.732572i \(-0.261681\pi\)
\(440\) 1.44022 + 0.724216i 0.0686598 + 0.0345256i
\(441\) 20.8339 6.53283i 0.992091 0.311087i
\(442\) −0.484059 + 3.09166i −0.0230243 + 0.147055i
\(443\) 1.20435i 0.0572206i −0.999591 0.0286103i \(-0.990892\pi\)
0.999591 0.0286103i \(-0.00910818\pi\)
\(444\) −34.5531 5.52968i −1.63982 0.262427i
\(445\) 1.44930i 0.0687034i
\(446\) −23.3781 3.66030i −1.10699 0.173320i
\(447\) −3.44525 22.5020i −0.162955 1.06431i
\(448\) −24.2656 + 18.0271i −1.14644 + 0.851698i
\(449\) 30.8882i 1.45771i 0.684670 + 0.728853i \(0.259946\pi\)
−0.684670 + 0.728853i \(0.740054\pi\)
\(450\) 3.12891 + 20.9081i 0.147498 + 0.985617i
\(451\) 12.2567 0.577145
\(452\) 8.76955 27.3188i 0.412485 1.28497i
\(453\) −1.88596 + 0.288755i −0.0886099 + 0.0135669i
\(454\) 7.82676 + 1.22543i 0.367328 + 0.0575124i
\(455\) 2.71437 0.127252
\(456\) −9.69950 3.14982i −0.454221 0.147504i
\(457\) −2.41262 −0.112858 −0.0564289 0.998407i \(-0.517971\pi\)
−0.0564289 + 0.998407i \(0.517971\pi\)
\(458\) −25.0872 3.92789i −1.17225 0.183538i
\(459\) 1.87592 0.919593i 0.0875602 0.0429229i
\(460\) 0.248559 + 0.0797893i 0.0115891 + 0.00372020i
\(461\) 26.7626 1.24646 0.623230 0.782039i \(-0.285820\pi\)
0.623230 + 0.782039i \(0.285820\pi\)
\(462\) 40.4154 + 0.136611i 1.88030 + 0.00635572i
\(463\) 4.03126i 0.187349i 0.995603 + 0.0936743i \(0.0298613\pi\)
−0.995603 + 0.0936743i \(0.970139\pi\)
\(464\) −28.5289 20.4203i −1.32442 0.947987i
\(465\) 1.73353 0.265417i 0.0803904 0.0123084i
\(466\) 34.2745 + 5.36633i 1.58773 + 0.248591i
\(467\) 19.4906i 0.901918i 0.892545 + 0.450959i \(0.148918\pi\)
−0.892545 + 0.450959i \(0.851082\pi\)
\(468\) 0.223231 33.0203i 0.0103189 1.52636i
\(469\) 48.4535i 2.23738i
\(470\) 0.0974078 0.622138i 0.00449309 0.0286971i
\(471\) −29.6830 + 4.54470i −1.36772 + 0.209409i
\(472\) 24.4615 + 12.3005i 1.12593 + 0.566176i
\(473\) 13.4448i 0.618195i
\(474\) −0.0256344 + 7.58375i −0.00117743 + 0.348333i
\(475\) 10.3729 0.475944
\(476\) −2.89310 0.928708i −0.132605 0.0425673i
\(477\) 0.963820 0.302222i 0.0441303 0.0138378i
\(478\) 0.816310 5.21373i 0.0373372 0.238470i
\(479\) −11.7760 −0.538061 −0.269030 0.963132i \(-0.586703\pi\)
−0.269030 + 0.963132i \(0.586703\pi\)
\(480\) 1.03742 + 0.747872i 0.0473514 + 0.0341355i
\(481\) −55.5939 −2.53486
\(482\) −1.95284 + 12.4727i −0.0889494 + 0.568115i
\(483\) 6.46939 0.990517i 0.294367 0.0450701i
\(484\) 15.3616 + 4.93121i 0.698256 + 0.224146i
\(485\) −0.591705 −0.0268679
\(486\) −18.1407 + 12.5265i −0.822881 + 0.568214i
\(487\) 7.24525i 0.328314i 0.986434 + 0.164157i \(0.0524903\pi\)
−0.986434 + 0.164157i \(0.947510\pi\)
\(488\) −7.02743 3.53375i −0.318117 0.159965i
\(489\) −2.73726 17.8779i −0.123783 0.808468i
\(490\) −0.207813 + 1.32729i −0.00938805 + 0.0599609i
\(491\) 16.2051i 0.731328i 0.930747 + 0.365664i \(0.119158\pi\)
−0.930747 + 0.365664i \(0.880842\pi\)
\(492\) 9.60136 + 1.53655i 0.432863 + 0.0692729i
\(493\) 3.52651i 0.158826i
\(494\) −16.0070 2.50621i −0.720189 0.112760i
\(495\) −0.511589 1.63152i −0.0229942 0.0733312i
\(496\) −18.0600 + 25.2315i −0.810919 + 1.13293i
\(497\) 30.9490i 1.38825i
\(498\) 0.0297277 8.79472i 0.00133213 0.394101i
\(499\) 5.30706 0.237576 0.118788 0.992920i \(-0.462099\pi\)
0.118788 + 0.992920i \(0.462099\pi\)
\(500\) −2.48135 0.796534i −0.110969 0.0356221i
\(501\) −0.437799 2.85941i −0.0195594 0.127749i
\(502\) 21.0244 + 3.29178i 0.938366 + 0.146919i
\(503\) 0.131455 0.00586131 0.00293065 0.999996i \(-0.499067\pi\)
0.00293065 + 0.999996i \(0.499067\pi\)
\(504\) 31.6426 + 5.17365i 1.40947 + 0.230453i
\(505\) −0.494742 −0.0220157
\(506\) 6.10092 + 0.955218i 0.271219 + 0.0424646i
\(507\) −4.53196 29.5997i −0.201272 1.31457i
\(508\) −8.26408 + 25.7442i −0.366659 + 1.14221i
\(509\) −35.3633 −1.56745 −0.783725 0.621108i \(-0.786683\pi\)
−0.783725 + 0.621108i \(0.786683\pi\)
\(510\) −0.000434513 0.128548i −1.92406e−5 0.00569219i
\(511\) 1.57588i 0.0697129i
\(512\) −22.2896 + 3.89548i −0.985069 + 0.172158i
\(513\) 4.76118 + 9.71252i 0.210211 + 0.428818i
\(514\) −10.9573 1.71558i −0.483307 0.0756711i
\(515\) 0.888976i 0.0391730i
\(516\) 1.68550 10.5321i 0.0742000 0.463651i
\(517\) 14.8962i 0.655133i
\(518\) 8.34997 53.3308i 0.366877 2.34322i
\(519\) −2.24183 14.6421i −0.0984055 0.642719i
\(520\) 1.81522 + 0.912784i 0.0796026 + 0.0400282i
\(521\) 0.362476i 0.0158804i −0.999968 0.00794019i \(-0.997473\pi\)
0.999968 0.00794019i \(-0.00252747\pi\)
\(522\) 5.50750 + 36.8024i 0.241057 + 1.61080i
\(523\) −0.701562 −0.0306772 −0.0153386 0.999882i \(-0.504883\pi\)
−0.0153386 + 0.999882i \(0.504883\pi\)
\(524\) −13.2281 + 41.2081i −0.577873 + 1.80018i
\(525\) −32.2367 + 4.93571i −1.40693 + 0.215412i
\(526\) −4.07672 + 26.0378i −0.177754 + 1.13530i
\(527\) −3.11890 −0.135862
\(528\) 26.9816 + 13.6822i 1.17422 + 0.595440i
\(529\) 1.00000 0.0434783
\(530\) −0.00961388 + 0.0614033i −0.000417600 + 0.00266719i
\(531\) −8.68912 27.7105i −0.377076 1.20254i
\(532\) 4.80837 14.9790i 0.208469 0.649421i
\(533\) 15.4480 0.669128
\(534\) −0.0919336 + 27.1979i −0.00397836 + 1.17697i
\(535\) 0.880901i 0.0380847i
\(536\) 16.2939 32.4030i 0.703788 1.39960i
\(537\) 25.2164 3.86084i 1.08817 0.166608i
\(538\) −1.25254 + 7.99990i −0.0540008 + 0.344900i
\(539\) 31.7800i 1.36886i
\(540\) −0.196224 1.34219i −0.00844414 0.0577588i
\(541\) 8.62101i 0.370646i 0.982678 + 0.185323i \(0.0593332\pi\)
−0.982678 + 0.185323i \(0.940667\pi\)
\(542\) −14.0344 2.19736i −0.602828 0.0943845i
\(543\) 37.1967 5.69513i 1.59627 0.244401i
\(544\) −1.62244 1.59395i −0.0695614 0.0683402i
\(545\) 2.39138i 0.102435i
\(546\) 50.9386 + 0.172181i 2.17997 + 0.00736867i
\(547\) −7.45918 −0.318931 −0.159466 0.987203i \(-0.550977\pi\)
−0.159466 + 0.987203i \(0.550977\pi\)
\(548\) 9.14419 28.4859i 0.390620 1.21686i
\(549\) 2.49626 + 7.96084i 0.106538 + 0.339760i
\(550\) −30.4007 4.75982i −1.29629 0.202959i
\(551\) 18.2584 0.777836
\(552\) 4.65945 + 1.51311i 0.198319 + 0.0644024i
\(553\) −11.6989 −0.497488
\(554\) −17.7295 2.77590i −0.753254 0.117937i
\(555\) −2.25742 + 0.345630i −0.0958222 + 0.0146712i
\(556\) −22.0187 7.06819i −0.933803 0.299758i
\(557\) 24.0703 1.01989 0.509945 0.860207i \(-0.329666\pi\)
0.509945 + 0.860207i \(0.329666\pi\)
\(558\) 32.5486 4.87092i 1.37789 0.206203i
\(559\) 16.9456i 0.716720i
\(560\) −1.14827 + 1.60423i −0.0485231 + 0.0677911i
\(561\) 0.460217 + 3.00583i 0.0194304 + 0.126906i
\(562\) 36.1301 + 5.65687i 1.52406 + 0.238620i
\(563\) 3.51983i 0.148343i −0.997246 0.0741715i \(-0.976369\pi\)
0.997246 0.0741715i \(-0.0236312\pi\)
\(564\) 1.86744 11.6690i 0.0786336 0.491355i
\(565\) 1.87251i 0.0787771i
\(566\) −4.61354 + 29.4664i −0.193922 + 1.23857i
\(567\) −19.4181 27.9188i −0.815484 1.17248i
\(568\) 10.4075 20.6969i 0.436687 0.868424i
\(569\) 34.0590i 1.42783i 0.700233 + 0.713914i \(0.253079\pi\)
−0.700233 + 0.713914i \(0.746921\pi\)
\(570\) −0.665554 0.00224969i −0.0278770 9.42290e-5i
\(571\) −9.16056 −0.383357 −0.191679 0.981458i \(-0.561393\pi\)
−0.191679 + 0.981458i \(0.561393\pi\)
\(572\) 45.7627 + 14.6902i 1.91344 + 0.614228i
\(573\) 2.80819 + 18.3412i 0.117314 + 0.766216i
\(574\) −2.32023 + 14.8192i −0.0968445 + 0.618540i
\(575\) −4.98296 −0.207804
\(576\) 19.4210 + 14.1006i 0.809207 + 0.587523i
\(577\) 14.7661 0.614720 0.307360 0.951593i \(-0.400554\pi\)
0.307360 + 0.951593i \(0.400554\pi\)
\(578\) −3.68351 + 23.5264i −0.153214 + 0.978569i
\(579\) 3.88413 + 25.3686i 0.161419 + 1.05428i
\(580\) −2.18011 0.699832i −0.0905241 0.0290589i
\(581\) 13.5670 0.562853
\(582\) −11.1041 0.0375337i −0.460279 0.00155582i
\(583\) 1.47021i 0.0608899i
\(584\) 0.529934 1.05386i 0.0219288 0.0436090i
\(585\) −0.644795 2.05632i −0.0266590 0.0850184i
\(586\) −3.84625 + 24.5658i −0.158887 + 1.01480i
\(587\) 0.974726i 0.0402313i −0.999798 0.0201156i \(-0.993597\pi\)
0.999798 0.0201156i \(-0.00640344\pi\)
\(588\) −3.98407 + 24.8951i −0.164300 + 1.02666i
\(589\) 16.1481i 0.665370i
\(590\) 1.76539 + 0.276406i 0.0726800 + 0.0113795i
\(591\) −4.59415 30.0059i −0.188978 1.23428i
\(592\) 23.5180 32.8567i 0.966583 1.35040i
\(593\) 20.2807i 0.832828i −0.909175 0.416414i \(-0.863287\pi\)
0.909175 0.416414i \(-0.136713\pi\)
\(594\) −9.49712 30.6499i −0.389672 1.25758i
\(595\) −0.198301 −0.00812956
\(596\) 25.0280 + 8.03419i 1.02519 + 0.329093i
\(597\) −39.8995 + 6.10894i −1.63298 + 0.250022i
\(598\) 7.68945 + 1.20393i 0.314445 + 0.0492325i
\(599\) −31.5805 −1.29034 −0.645172 0.764037i \(-0.723214\pi\)
−0.645172 + 0.764037i \(0.723214\pi\)
\(600\) −23.2179 7.53979i −0.947866 0.307810i
\(601\) 7.95503 0.324492 0.162246 0.986750i \(-0.448126\pi\)
0.162246 + 0.986750i \(0.448126\pi\)
\(602\) 16.2557 + 2.54515i 0.662535 + 0.103733i
\(603\) −36.7069 + 11.5101i −1.49482 + 0.468726i
\(604\) 0.673367 2.09766i 0.0273989 0.0853527i
\(605\) 1.05293 0.0428077
\(606\) −9.28446 0.0313831i −0.377155 0.00127485i
\(607\) 5.15628i 0.209287i 0.994510 + 0.104643i \(0.0333701\pi\)
−0.994510 + 0.104643i \(0.966630\pi\)
\(608\) 8.25267 8.40014i 0.334690 0.340671i
\(609\) −56.7430 + 8.68782i −2.29934 + 0.352048i
\(610\) −0.507171 0.0794075i −0.0205348 0.00321512i
\(611\) 18.7748i 0.759546i
\(612\) −0.0163084 + 2.41233i −0.000659227 + 0.0975127i
\(613\) 34.3625i 1.38789i 0.720029 + 0.693944i \(0.244129\pi\)
−0.720029 + 0.693944i \(0.755871\pi\)
\(614\) 2.63582 16.8348i 0.106373 0.679398i
\(615\) 0.627275 0.0960410i 0.0252942 0.00387275i
\(616\) −20.9656 + 41.6934i −0.844727 + 1.67988i
\(617\) 0.319112i 0.0128470i −0.999979 0.00642349i \(-0.997955\pi\)
0.999979 0.00642349i \(-0.00204467\pi\)
\(618\) −0.0563905 + 16.6827i −0.00226836 + 0.671078i
\(619\) 1.90822 0.0766978 0.0383489 0.999264i \(-0.487790\pi\)
0.0383489 + 0.999264i \(0.487790\pi\)
\(620\) −0.618943 + 1.92812i −0.0248573 + 0.0774353i
\(621\) −2.28718 4.66571i −0.0917812 0.187228i
\(622\) 1.95158 12.4646i 0.0782513 0.499787i
\(623\) −41.9563 −1.68094
\(624\) 34.0069 + 17.2447i 1.36137 + 0.690340i
\(625\) 24.7447 0.989789
\(626\) −0.105346 + 0.672837i −0.00421046 + 0.0268920i
\(627\) −15.5626 + 2.38277i −0.621512 + 0.0951585i
\(628\) 10.5981 33.0150i 0.422909 1.31744i
\(629\) 4.06147 0.161942
\(630\) 2.06946 0.309696i 0.0824492 0.0123386i
\(631\) 37.3783i 1.48801i −0.668175 0.744004i \(-0.732924\pi\)
0.668175 0.744004i \(-0.267076\pi\)
\(632\) −7.82357 3.93409i −0.311205 0.156490i
\(633\) 4.21380 + 27.5217i 0.167484 + 1.09389i
\(634\) 1.41475 9.03593i 0.0561869 0.358863i
\(635\) 1.76458i 0.0700252i
\(636\) −0.184312 + 1.15170i −0.00730843 + 0.0456679i
\(637\) 40.0547i 1.58703i
\(638\) −53.5112 8.37822i −2.11853 0.331697i
\(639\) −23.4459 + 7.35188i −0.927507 + 0.290836i
\(640\) −1.30736 + 0.686681i −0.0516780 + 0.0271435i
\(641\) 20.2501i 0.799831i −0.916552 0.399915i \(-0.869039\pi\)
0.916552 0.399915i \(-0.130961\pi\)
\(642\) 0.0558783 16.5312i 0.00220534 0.652435i
\(643\) −28.2916 −1.11571 −0.557856 0.829938i \(-0.688376\pi\)
−0.557856 + 0.829938i \(0.688376\pi\)
\(644\) −2.30985 + 7.19561i −0.0910208 + 0.283547i
\(645\) −0.105351 0.688083i −0.00414820 0.0270933i
\(646\) 1.16941 + 0.183094i 0.0460098 + 0.00720372i
\(647\) 47.8762 1.88221 0.941104 0.338118i \(-0.109790\pi\)
0.941104 + 0.338118i \(0.109790\pi\)
\(648\) −3.59725 25.2004i −0.141313 0.989965i
\(649\) 42.2696 1.65923
\(650\) −38.3163 5.99915i −1.50289 0.235306i
\(651\) 7.68365 + 50.1845i 0.301146 + 1.96688i
\(652\) 19.8848 + 6.38318i 0.778749 + 0.249985i
\(653\) −9.67576 −0.378642 −0.189321 0.981915i \(-0.560629\pi\)
−0.189321 + 0.981915i \(0.560629\pi\)
\(654\) −0.151693 + 44.8772i −0.00593165 + 1.75484i
\(655\) 2.82452i 0.110363i
\(656\) −6.53500 + 9.12998i −0.255149 + 0.356466i
\(657\) −1.19384 + 0.374348i −0.0465760 + 0.0146047i
\(658\) 18.0105 + 2.81989i 0.702122 + 0.109931i
\(659\) 18.2791i 0.712052i −0.934476 0.356026i \(-0.884131\pi\)
0.934476 0.356026i \(-0.115869\pi\)
\(660\) 1.94955 + 0.311995i 0.0758861 + 0.0121444i
\(661\) 1.38156i 0.0537364i 0.999639 + 0.0268682i \(0.00855344\pi\)
−0.999639 + 0.0268682i \(0.991447\pi\)
\(662\) −5.49337 + 35.0859i −0.213506 + 1.36365i
\(663\) 0.580046 + 3.78847i 0.0225271 + 0.147132i
\(664\) 9.07283 + 4.56228i 0.352094 + 0.177051i
\(665\) 1.02670i 0.0398138i
\(666\) −42.3852 + 6.34298i −1.64239 + 0.245785i
\(667\) −8.77100 −0.339615
\(668\) 3.18039 + 1.02093i 0.123053 + 0.0395010i
\(669\) −28.6472 + 4.38613i −1.10757 + 0.169578i
\(670\) 0.366142 2.33853i 0.0141453 0.0903453i
\(671\) −12.1435 −0.468793
\(672\) −21.6504 + 30.0325i −0.835182 + 1.15853i
\(673\) −21.5643 −0.831243 −0.415621 0.909538i \(-0.636436\pi\)
−0.415621 + 0.909538i \(0.636436\pi\)
\(674\) 2.19452 14.0163i 0.0845299 0.539887i
\(675\) 11.3969 + 23.2490i 0.438668 + 0.894856i
\(676\) 32.9224 + 10.5684i 1.26625 + 0.406476i
\(677\) −24.7287 −0.950401 −0.475201 0.879878i \(-0.657624\pi\)
−0.475201 + 0.879878i \(0.657624\pi\)
\(678\) 0.118779 35.1400i 0.00456169 1.34954i
\(679\) 17.1295i 0.657368i
\(680\) −0.132613 0.0666844i −0.00508547 0.00255723i
\(681\) 9.59081 1.46843i 0.367520 0.0562704i
\(682\) −7.40983 + 47.3262i −0.283737 + 1.81221i
\(683\) 35.4360i 1.35592i −0.735098 0.677961i \(-0.762864\pi\)
0.735098 0.677961i \(-0.237136\pi\)
\(684\) −12.4898 0.0844364i −0.477560 0.00322851i
\(685\) 1.95250i 0.0746013i
\(686\) −1.46792 0.229832i −0.0560455 0.00877502i
\(687\) −30.7415 + 4.70677i −1.17286 + 0.179575i
\(688\) 10.0150 + 7.16850i 0.381820 + 0.273297i
\(689\) 1.85302i 0.0705943i
\(690\) 0.319719 + 0.00108071i 0.0121715 + 4.11418e-5i
\(691\) 47.3180 1.80006 0.900032 0.435824i \(-0.143543\pi\)
0.900032 + 0.435824i \(0.143543\pi\)
\(692\) 16.2858 + 5.22787i 0.619093 + 0.198734i
\(693\) 47.2313 14.8102i 1.79417 0.562592i
\(694\) 17.3338 + 2.71394i 0.657982 + 0.103020i
\(695\) −1.50923 −0.0572483
\(696\) −40.8681 13.2715i −1.54910 0.503056i
\(697\) −1.12857 −0.0427477
\(698\) 25.1090 + 3.93131i 0.950391 + 0.148802i
\(699\) 41.9995 6.43046i 1.58857 0.243222i
\(700\) 11.5099 35.8554i 0.435033 1.35521i
\(701\) 30.6619 1.15808 0.579042 0.815298i \(-0.303427\pi\)
0.579042 + 0.815298i \(0.303427\pi\)
\(702\) −11.9699 38.6303i −0.451776 1.45801i
\(703\) 21.0282i 0.793094i
\(704\) −28.0412 + 20.8320i −1.05684 + 0.785134i
\(705\) −0.116724 0.762360i −0.00439606 0.0287121i
\(706\) 35.7302 + 5.59426i 1.34473 + 0.210543i
\(707\) 14.3225i 0.538652i
\(708\) 33.1122 + 5.29909i 1.24443 + 0.199152i
\(709\) 19.6131i 0.736586i −0.929710 0.368293i \(-0.879942\pi\)
0.929710 0.368293i \(-0.120058\pi\)
\(710\) 0.233868 1.49370i 0.00877690 0.0560576i
\(711\) 2.77906 + 8.86272i 0.104223 + 0.332378i
\(712\) −28.0580 14.1090i −1.05152 0.528756i
\(713\) 7.75722i 0.290510i
\(714\) −3.72137 0.0125789i −0.139269 0.000470753i
\(715\) 3.13671 0.117306
\(716\) −9.00334 + 28.0471i −0.336471 + 1.04817i
\(717\) −0.978182 6.38883i −0.0365309 0.238595i
\(718\) 4.50552 28.7765i 0.168144 1.07393i
\(719\) 42.9444 1.60156 0.800778 0.598961i \(-0.204420\pi\)
0.800778 + 0.598961i \(0.204420\pi\)
\(720\) 1.48808 + 0.488807i 0.0554575 + 0.0182168i
\(721\) −25.7353 −0.958432
\(722\) 3.20843 20.4920i 0.119405 0.762635i
\(723\) 2.34008 + 15.2838i 0.0870285 + 0.568412i
\(724\) −13.2808 + 41.3722i −0.493578 + 1.53759i
\(725\) 43.7056 1.62318
\(726\) 19.7596 + 0.0667907i 0.733346 + 0.00247884i
\(727\) 51.8477i 1.92292i −0.274937 0.961462i \(-0.588657\pi\)
0.274937 0.961462i \(-0.411343\pi\)
\(728\) −26.4245 + 52.5494i −0.979357 + 1.94761i
\(729\) −16.5376 + 21.3426i −0.612505 + 0.790466i
\(730\) 0.0119082 0.0760573i 0.000440744 0.00281501i
\(731\) 1.23798i 0.0457882i
\(732\) −9.51266 1.52235i −0.351598 0.0562678i
\(733\) 25.2940i 0.934254i 0.884190 + 0.467127i \(0.154711\pi\)
−0.884190 + 0.467127i \(0.845289\pi\)
\(734\) −1.39085 0.217765i −0.0513373 0.00803786i
\(735\) 0.249022 + 1.62644i 0.00918532 + 0.0599923i
\(736\) −3.96442 + 4.03526i −0.146131 + 0.148742i
\(737\) 55.9926i 2.06251i
\(738\) 11.7777 1.76254i 0.433543 0.0648800i
\(739\) 2.11141 0.0776696 0.0388348 0.999246i \(-0.487635\pi\)
0.0388348 + 0.999246i \(0.487635\pi\)
\(740\) 0.805995 2.51083i 0.0296290 0.0922998i
\(741\) −19.6148 + 3.00318i −0.720566 + 0.110325i
\(742\) −1.77759 0.278316i −0.0652572 0.0102173i
\(743\) −6.40799 −0.235087 −0.117543 0.993068i \(-0.537502\pi\)
−0.117543 + 0.993068i \(0.537502\pi\)
\(744\) −11.7375 + 36.1444i −0.430319 + 1.32512i
\(745\) 1.71549 0.0628508
\(746\) 27.8029 + 4.35308i 1.01793 + 0.159377i
\(747\) −3.22282 10.2779i −0.117917 0.376049i
\(748\) −3.34325 1.07321i −0.122241 0.0392404i
\(749\) 25.5015 0.931805
\(750\) −3.19175 0.0107886i −0.116546 0.000393946i
\(751\) 24.3046i 0.886888i 0.896302 + 0.443444i \(0.146244\pi\)
−0.896302 + 0.443444i \(0.853756\pi\)
\(752\) 11.0961 + 7.94232i 0.404634 + 0.289627i
\(753\) 25.7630 3.94453i 0.938857 0.143747i
\(754\) −67.4442 10.5597i −2.45617 0.384562i
\(755\) 0.143780i 0.00523269i
\(756\) 38.8556 5.68056i 1.41317 0.206600i
\(757\) 18.6833i 0.679054i 0.940596 + 0.339527i \(0.110267\pi\)
−0.940596 + 0.339527i \(0.889733\pi\)
\(758\) 3.00741 19.2082i 0.109234 0.697673i
\(759\) 7.47599 1.14463i 0.271361 0.0415476i
\(760\) 0.345258 0.686601i 0.0125238 0.0249056i
\(761\) 30.2497i 1.09655i −0.836297 0.548276i \(-0.815284\pi\)
0.836297 0.548276i \(-0.184716\pi\)
\(762\) −0.111933 + 33.1145i −0.00405490 + 1.19961i
\(763\) −69.2288 −2.50625
\(764\) −20.4001 6.54860i −0.738050 0.236920i
\(765\) 0.0471062 + 0.150227i 0.00170313 + 0.00543146i
\(766\) −1.21912 + 7.78648i −0.0440488 + 0.281337i
\(767\) 53.2756 1.92367
\(768\) −24.5778 + 12.8035i −0.886876 + 0.462007i
\(769\) 47.4784 1.71211 0.856057 0.516882i \(-0.172907\pi\)
0.856057 + 0.516882i \(0.172907\pi\)
\(770\) −0.471121 + 3.00902i −0.0169780 + 0.108438i
\(771\) −13.4270 + 2.05578i −0.483560 + 0.0740370i
\(772\) −28.2163 9.05765i −1.01553 0.325992i
\(773\) 30.2729 1.08884 0.544421 0.838812i \(-0.316750\pi\)
0.544421 + 0.838812i \(0.316750\pi\)
\(774\) −1.93340 12.9194i −0.0694946 0.464379i
\(775\) 38.6539i 1.38849i
\(776\) 5.76026 11.4552i 0.206781 0.411218i
\(777\) −10.0057 65.3508i −0.358954 2.34445i
\(778\) 3.18638 20.3512i 0.114237 0.729627i
\(779\) 5.84316i 0.209353i
\(780\) 2.45716 + 0.393231i 0.0879806 + 0.0140799i
\(781\) 35.7644i 1.27975i
\(782\) −0.561761 0.0879546i −0.0200885 0.00314525i
\(783\) 20.0608 + 40.9229i 0.716916 + 1.46247i
\(784\) −23.6729 16.9444i −0.845460 0.605158i
\(785\) 2.26294i 0.0807679i
\(786\) −0.179168 + 53.0057i −0.00639072 + 1.89065i
\(787\) −11.7940 −0.420411 −0.210205 0.977657i \(-0.567413\pi\)
−0.210205 + 0.977657i \(0.567413\pi\)
\(788\) 33.3742 + 10.7134i 1.18891 + 0.381649i
\(789\) 4.88512 + 31.9064i 0.173915 + 1.13590i
\(790\) −0.564629 0.0884036i −0.0200886 0.00314526i
\(791\) 54.2079 1.92741
\(792\) 36.5660 + 5.97864i 1.29931 + 0.212442i
\(793\) −15.3053 −0.543508
\(794\) −2.09853 0.328565i −0.0744739 0.0116603i
\(795\) 0.0115203 + 0.0752428i 0.000408582 + 0.00266859i
\(796\) 14.2458 44.3784i 0.504929 1.57295i
\(797\) 13.6252 0.482629 0.241314 0.970447i \(-0.422421\pi\)
0.241314 + 0.970447i \(0.422421\pi\)
\(798\) 0.0651269 19.2674i 0.00230547 0.682057i
\(799\) 1.37161i 0.0485241i
\(800\) 19.7546 20.1076i 0.698429 0.710910i
\(801\) 9.96664 + 31.7847i 0.352154 + 1.12306i
\(802\) −30.2735 4.73991i −1.06900 0.167372i
\(803\) 1.82108i 0.0642645i
\(804\) 7.01946 43.8622i 0.247557 1.54690i
\(805\) 0.493208i 0.0173833i
\(806\) −9.33917 + 59.6488i −0.328958 + 2.10104i
\(807\) 1.50091 + 9.80297i 0.0528347 + 0.345081i
\(808\) 4.81633 9.57806i 0.169438 0.336955i
\(809\) 5.37668i 0.189034i −0.995523 0.0945170i \(-0.969869\pi\)
0.995523 0.0945170i \(-0.0301307\pi\)
\(810\) −0.726212 1.49419i −0.0255165 0.0525004i
\(811\) −20.2058 −0.709521 −0.354761 0.934957i \(-0.615438\pi\)
−0.354761 + 0.934957i \(0.615438\pi\)
\(812\) 20.2597 63.1127i 0.710975 2.21482i
\(813\) −17.1975 + 2.63308i −0.603144 + 0.0923463i
\(814\) 9.64918 61.6288i 0.338203 2.16009i
\(815\) 1.36296 0.0477425
\(816\) −2.48441 1.25983i −0.0869719 0.0441028i
\(817\) −6.40960 −0.224244
\(818\) −1.64880 + 10.5308i −0.0576490 + 0.368201i
\(819\) 59.5291 18.6664i 2.08012 0.652256i
\(820\) −0.223964 + 0.697690i −0.00782116 + 0.0243644i
\(821\) −26.7962 −0.935193 −0.467596 0.883942i \(-0.654880\pi\)
−0.467596 + 0.883942i \(0.654880\pi\)
\(822\) 0.123853 36.6412i 0.00431988 1.27801i
\(823\) 1.87513i 0.0653629i 0.999466 + 0.0326815i \(0.0104047\pi\)
−0.999466 + 0.0326815i \(0.989595\pi\)
\(824\) −17.2103 8.65421i −0.599549 0.301484i
\(825\) −37.2526 + 5.70367i −1.29697 + 0.198576i
\(826\) −8.00178 + 51.1069i −0.278417 + 1.77824i
\(827\) 53.8718i 1.87331i 0.350260 + 0.936653i \(0.386093\pi\)
−0.350260 + 0.936653i \(0.613907\pi\)
\(828\) 5.99986 + 0.0405616i 0.208510 + 0.00140961i
\(829\) 36.9767i 1.28425i −0.766599 0.642127i \(-0.778052\pi\)
0.766599 0.642127i \(-0.221948\pi\)
\(830\) 0.654788 + 0.102520i 0.0227280 + 0.00355851i
\(831\) −21.7255 + 3.32635i −0.753648 + 0.115390i
\(832\) −35.3424 + 26.2561i −1.22528 + 0.910266i
\(833\) 2.92624i 0.101388i
\(834\) −28.3226 0.0957351i −0.980730 0.00331504i
\(835\) 0.217993 0.00754396
\(836\) 5.55652 17.3096i 0.192176 0.598665i
\(837\) 36.1929 17.7421i 1.25101 0.613258i
\(838\) 6.25673 + 0.979613i 0.216135 + 0.0338402i
\(839\) 12.1566 0.419693 0.209847 0.977734i \(-0.432704\pi\)
0.209847 + 0.977734i \(0.432704\pi\)
\(840\) −0.746279 + 2.29808i −0.0257491 + 0.0792912i
\(841\) 47.9305 1.65278
\(842\) 12.0891 + 1.89278i 0.416617 + 0.0652295i
\(843\) 44.2733 6.77860i 1.52485 0.233468i
\(844\) −30.6111 9.82642i −1.05368 0.338239i
\(845\) 2.25660 0.0776294
\(846\) −2.14210 14.3140i −0.0736471 0.492127i
\(847\) 30.4817i 1.04736i
\(848\) −1.09516 0.783885i −0.0376079 0.0269187i
\(849\) 5.52840 + 36.1078i 0.189734 + 1.23922i
\(850\) 2.79924 + 0.438275i 0.0960130 + 0.0150327i
\(851\) 10.1015i 0.346277i
\(852\) 4.48357 28.0163i 0.153605 0.959823i
\(853\) 19.4838i 0.667114i 0.942730 + 0.333557i \(0.108249\pi\)
−0.942730 + 0.333557i \(0.891751\pi\)
\(854\) 2.29879 14.6823i 0.0786631 0.502417i
\(855\) −0.777797 + 0.243891i −0.0266001 + 0.00834091i
\(856\) 17.0540 + 8.57560i 0.582893 + 0.293108i
\(857\) 23.9656i 0.818649i 0.912389 + 0.409324i \(0.134236\pi\)
−0.912389 + 0.409324i \(0.865764\pi\)
\(858\) 58.8643 + 0.198971i 2.00959 + 0.00679277i
\(859\) −3.22143 −0.109914 −0.0549568 0.998489i \(-0.517502\pi\)
−0.0549568 + 0.998489i \(0.517502\pi\)
\(860\) 0.765324 + 0.245675i 0.0260973 + 0.00837745i
\(861\) 2.78032 + 18.1592i 0.0947532 + 0.618864i
\(862\) 2.76222 17.6421i 0.0940815 0.600893i
\(863\) 28.5105 0.970509 0.485255 0.874373i \(-0.338727\pi\)
0.485255 + 0.874373i \(0.338727\pi\)
\(864\) 27.8947 + 9.26746i 0.948997 + 0.315286i
\(865\) 1.11627 0.0379545
\(866\) 6.70230 42.8072i 0.227753 1.45465i
\(867\) 4.41394 + 28.8289i 0.149905 + 0.979081i
\(868\) −55.8179 17.9180i −1.89458 0.608176i
\(869\) −13.5192 −0.458607
\(870\) −2.80426 0.00947887i −0.0950733 0.000321364i
\(871\) 70.5717i 2.39123i
\(872\) −46.2963 23.2801i −1.56779 0.788365i
\(873\) −12.9767 + 4.06908i −0.439196 + 0.137717i
\(874\) 0.455384 2.90851i 0.0154036 0.0983818i
\(875\) 4.92368i 0.166451i
\(876\) 0.228298 1.42655i 0.00771346 0.0481988i
\(877\) 26.6860i 0.901123i −0.892746 0.450561i \(-0.851224\pi\)
0.892746 0.450561i \(-0.148776\pi\)
\(878\) 42.8913 + 6.71546i 1.44751 + 0.226636i
\(879\) 4.60894 + 30.1025i 0.155456 + 1.01533i
\(880\) −1.32693 + 1.85384i −0.0447307 + 0.0624928i
\(881\) 7.40195i 0.249378i −0.992196 0.124689i \(-0.960207\pi\)
0.992196 0.124689i \(-0.0397933\pi\)
\(882\) 4.57004 + 30.5381i 0.153881 + 1.02827i
\(883\) −7.09453 −0.238750 −0.119375 0.992849i \(-0.538089\pi\)
−0.119375 + 0.992849i \(0.538089\pi\)
\(884\) −4.21375 1.35265i −0.141724 0.0454944i
\(885\) 2.16329 0.331217i 0.0727180 0.0111337i
\(886\) 1.68271 + 0.263461i 0.0565319 + 0.00885116i
\(887\) 27.4157 0.920529 0.460264 0.887782i \(-0.347755\pi\)
0.460264 + 0.887782i \(0.347755\pi\)
\(888\) 15.2848 47.0677i 0.512924 1.57949i
\(889\) −51.0834 −1.71328
\(890\) −2.02495 0.317045i −0.0678764 0.0106274i
\(891\) −22.4394 32.2628i −0.751749 1.08084i
\(892\) 10.2283 31.8630i 0.342468 1.06685i
\(893\) −7.10150 −0.237643
\(894\) 32.1933 + 0.108819i 1.07671 + 0.00363945i
\(895\) 1.92243i 0.0642597i
\(896\) −19.8790 37.8473i −0.664110 1.26439i
\(897\) 9.42255 1.44267i 0.314610 0.0481693i
\(898\) −43.1568 6.75703i −1.44016 0.225485i
\(899\) 68.0386i 2.26921i
\(900\) −29.8971 0.202117i −0.996570 0.00673723i
\(901\) 0.135374i 0.00450997i
\(902\) −2.68124 + 17.1249i −0.0892756 + 0.570198i
\(903\) 19.9196 3.04985i 0.662881 0.101493i
\(904\) 36.2512 + 18.2289i 1.20570 + 0.606285i
\(905\) 2.83577i 0.0942643i
\(906\) 0.00912041 2.69821i 0.000303005 0.0896420i
\(907\) 17.7447 0.589203 0.294601 0.955620i \(-0.404813\pi\)
0.294601 + 0.955620i \(0.404813\pi\)
\(908\) −3.42433 + 10.6674i −0.113640 + 0.354011i
\(909\) −10.8502 + 3.40228i −0.359880 + 0.112846i
\(910\) −0.593789 + 3.79250i −0.0196839 + 0.125720i
\(911\) −40.5517 −1.34354 −0.671769 0.740761i \(-0.734465\pi\)
−0.671769 + 0.740761i \(0.734465\pi\)
\(912\) 6.52274 12.8630i 0.215990 0.425937i
\(913\) 15.6779 0.518864
\(914\) 0.527779 3.37090i 0.0174574 0.111499i
\(915\) −0.621481 + 0.0951538i −0.0205455 + 0.00314569i
\(916\) 10.9760 34.1924i 0.362658 1.12975i
\(917\) −81.7681 −2.70022
\(918\) 0.874477 + 2.82218i 0.0288620 + 0.0931459i
\(919\) 42.2700i 1.39436i 0.716896 + 0.697180i \(0.245562\pi\)
−0.716896 + 0.697180i \(0.754438\pi\)
\(920\) −0.165855 + 0.329830i −0.00546808 + 0.0108742i
\(921\) −3.15849 20.6291i −0.104076 0.679753i
\(922\) −5.85452 + 37.3925i −0.192808 + 1.23146i
\(923\) 45.0766i 1.48371i
\(924\) −9.03205 + 56.4382i −0.297133 + 1.85668i
\(925\) 50.3356i 1.65503i
\(926\) −5.63245 0.881869i −0.185094 0.0289800i
\(927\) 6.11337 + 19.4962i 0.200789 + 0.640340i
\(928\) 34.7720 35.3933i 1.14145 1.16184i
\(929\) 28.1066i 0.922147i −0.887362 0.461073i \(-0.847464\pi\)
0.887362 0.461073i \(-0.152536\pi\)
\(930\) −0.00838327 + 2.48013i −0.000274898 + 0.0813267i
\(931\) 15.1506 0.496540
\(932\) −14.9956 + 46.7141i −0.491197 + 1.53017i
\(933\) −2.33858 15.2740i −0.0765615 0.500049i
\(934\) −27.2321 4.26372i −0.891062 0.139513i
\(935\) −0.229156 −0.00749420
\(936\) 46.0868 + 7.53533i 1.50639 + 0.246300i
\(937\) 19.6450 0.641773 0.320887 0.947118i \(-0.396019\pi\)
0.320887 + 0.947118i \(0.396019\pi\)
\(938\) 67.6989 + 10.5996i 2.21045 + 0.346088i
\(939\) 0.126235 + 0.824485i 0.00411954 + 0.0269061i
\(940\) 0.847938 + 0.272195i 0.0276567 + 0.00887802i
\(941\) 39.9096 1.30101 0.650507 0.759500i \(-0.274556\pi\)
0.650507 + 0.759500i \(0.274556\pi\)
\(942\) 0.143546 42.4670i 0.00467697 1.38365i
\(943\) 2.80694i 0.0914066i
\(944\) −22.5373 + 31.4866i −0.733526 + 1.02480i
\(945\) 2.30116 1.12805i 0.0748568 0.0366956i
\(946\) 18.7850 + 2.94116i 0.610754 + 0.0956254i
\(947\) 40.6728i 1.32169i 0.750523 + 0.660845i \(0.229802\pi\)
−0.750523 + 0.660845i \(0.770198\pi\)
\(948\) −10.5904 1.69482i −0.343959 0.0550452i
\(949\) 2.29524i 0.0745067i
\(950\) −2.26916 + 14.4930i −0.0736213 + 0.470215i
\(951\) −1.69529 11.0725i −0.0549736 0.359051i
\(952\) 1.93047 3.83905i 0.0625669 0.124424i
\(953\) 10.4493i 0.338484i 0.985574 + 0.169242i \(0.0541320\pi\)
−0.985574 + 0.169242i \(0.945868\pi\)
\(954\) 0.211420 + 1.41276i 0.00684496 + 0.0457396i
\(955\) −1.39828 −0.0452474
\(956\) 7.10600 + 2.28108i 0.229825 + 0.0737755i
\(957\) −65.5719 + 10.0396i −2.11964 + 0.324534i
\(958\) 2.57610 16.4534i 0.0832299 0.531585i
\(959\) 56.5237 1.82525
\(960\) −1.27186 + 1.28587i −0.0410492 + 0.0415012i
\(961\) −29.1744 −0.941111
\(962\) 12.1616 77.6753i 0.392105 2.50435i
\(963\) −6.05784 19.3191i −0.195211 0.622550i
\(964\) −16.9995 5.45698i −0.547517 0.175758i
\(965\) −1.93403 −0.0622585
\(966\) −0.0312857 + 9.25566i −0.00100660 + 0.297796i
\(967\) 10.6501i 0.342484i −0.985229 0.171242i \(-0.945222\pi\)
0.985229 0.171242i \(-0.0547779\pi\)
\(968\) −10.2503 + 20.3844i −0.329458 + 0.655180i
\(969\) 1.43298 0.219401i 0.0460339 0.00704816i
\(970\) 0.129440 0.826725i 0.00415606 0.0265445i
\(971\) 27.4861i 0.882070i −0.897490 0.441035i \(-0.854611\pi\)
0.897490 0.441035i \(-0.145389\pi\)
\(972\) −13.5335 28.0864i −0.434087 0.900871i
\(973\) 43.6912i 1.40068i
\(974\) −10.1230 1.58495i −0.324362 0.0507852i
\(975\) −46.9522 + 7.18877i −1.50367 + 0.230225i
\(976\) 6.47463 9.04564i 0.207248 0.289544i
\(977\) 49.0762i 1.57009i 0.619441 + 0.785043i \(0.287359\pi\)
−0.619441 + 0.785043i \(0.712641\pi\)
\(978\) 25.5777 + 0.0864569i 0.817884 + 0.00276459i
\(979\) −48.4844 −1.54957
\(980\) −1.80902 0.580710i −0.0577870 0.0185501i
\(981\) 16.4452 + 52.4455i 0.525055 + 1.67446i
\(982\) −22.6417 3.54500i −0.722525 0.113125i
\(983\) 26.9525 0.859651 0.429825 0.902912i \(-0.358575\pi\)
0.429825 + 0.902912i \(0.358575\pi\)
\(984\) −4.24722 + 13.0788i −0.135396 + 0.416937i
\(985\) 2.28756 0.0728879
\(986\) 4.92721 + 0.771450i 0.156914 + 0.0245680i
\(987\) 22.0698 3.37907i 0.702490 0.107557i
\(988\) 7.00330 21.8166i 0.222805 0.694078i
\(989\) 3.07905 0.0979080
\(990\) 2.39145 0.357882i 0.0760054 0.0113743i
\(991\) 44.4537i 1.41212i 0.708153 + 0.706059i \(0.249529\pi\)
−0.708153 + 0.706059i \(0.750471\pi\)
\(992\) −31.3024 30.7529i −0.993853 0.976405i
\(993\) 6.58269 + 42.9937i 0.208895 + 1.36437i
\(994\) 43.2416 + 6.77032i 1.37154 + 0.214741i
\(995\) 3.04182i 0.0964323i
\(996\) 12.2814 + 1.96545i 0.389151 + 0.0622776i
\(997\) 10.5458i 0.333989i 0.985958 + 0.166994i \(0.0534062\pi\)
−0.985958 + 0.166994i \(0.946594\pi\)
\(998\) −1.16096 + 7.41498i −0.0367495 + 0.234717i
\(999\) −47.1308 + 23.1040i −1.49115 + 0.730979i
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 552.2.j.d.323.20 yes 42
3.2 odd 2 552.2.j.c.323.23 42
4.3 odd 2 2208.2.j.d.47.19 42
8.3 odd 2 552.2.j.c.323.24 yes 42
8.5 even 2 2208.2.j.c.47.19 42
12.11 even 2 2208.2.j.c.47.20 42
24.5 odd 2 2208.2.j.d.47.20 42
24.11 even 2 inner 552.2.j.d.323.19 yes 42
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
552.2.j.c.323.23 42 3.2 odd 2
552.2.j.c.323.24 yes 42 8.3 odd 2
552.2.j.d.323.19 yes 42 24.11 even 2 inner
552.2.j.d.323.20 yes 42 1.1 even 1 trivial
2208.2.j.c.47.19 42 8.5 even 2
2208.2.j.c.47.20 42 12.11 even 2
2208.2.j.d.47.19 42 4.3 odd 2
2208.2.j.d.47.20 42 24.5 odd 2