Properties

Label 1110.2.bb.e.1009.6
Level $1110$
Weight $2$
Character 1110.1009
Analytic conductor $8.863$
Analytic rank $0$
Dimension $40$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1110,2,Mod(1009,1110)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1110, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 3, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1110.1009");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1110.bb (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(8.86339462436\)
Analytic rank: \(0\)
Dimension: \(40\)
Relative dimension: \(20\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 1009.6
Character \(\chi\) \(=\) 1110.1009
Dual form 1110.2.bb.e.1099.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.866025 - 0.500000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.329099 - 2.21172i) q^{5} -1.00000 q^{6} +(0.903939 - 0.521889i) q^{7} -1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.866025 - 0.500000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.329099 - 2.21172i) q^{5} -1.00000 q^{6} +(0.903939 - 0.521889i) q^{7} -1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(-0.820851 + 2.07995i) q^{10} +0.877352 q^{11} +(0.866025 + 0.500000i) q^{12} +(-3.82118 + 2.20616i) q^{13} -1.04378 q^{14} +(-1.39087 - 1.75085i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-4.44494 - 2.56629i) q^{17} +(-0.866025 + 0.500000i) q^{18} +(-1.51358 - 2.62160i) q^{19} +(1.75085 - 1.39087i) q^{20} +(0.521889 - 0.903939i) q^{21} +(-0.759809 - 0.438676i) q^{22} -7.11017i q^{23} +(-0.500000 - 0.866025i) q^{24} +(-4.78339 + 1.45575i) q^{25} +4.41232 q^{26} -1.00000i q^{27} +(0.903939 + 0.521889i) q^{28} +5.96130 q^{29} +(0.329099 + 2.21172i) q^{30} -1.73335 q^{31} +(0.866025 - 0.500000i) q^{32} +(0.759809 - 0.438676i) q^{33} +(2.56629 + 4.44494i) q^{34} +(-1.45176 - 1.82750i) q^{35} +1.00000 q^{36} +(-0.0184948 - 6.08273i) q^{37} +3.02716i q^{38} +(-2.20616 + 3.82118i) q^{39} +(-2.21172 + 0.329099i) q^{40} +(3.12701 + 5.41615i) q^{41} +(-0.903939 + 0.521889i) q^{42} +1.46389i q^{43} +(0.438676 + 0.759809i) q^{44} +(-2.07995 - 0.820851i) q^{45} +(-3.55509 + 6.15759i) q^{46} +3.00050i q^{47} +1.00000i q^{48} +(-2.95526 + 5.11867i) q^{49} +(4.87041 + 1.13098i) q^{50} -5.13258 q^{51} +(-3.82118 - 2.20616i) q^{52} +(-11.1687 - 6.44827i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(-0.288735 - 1.94045i) q^{55} +(-0.521889 - 0.903939i) q^{56} +(-2.62160 - 1.51358i) q^{57} +(-5.16264 - 2.98065i) q^{58} +(4.32356 - 7.48863i) q^{59} +(0.820851 - 2.07995i) q^{60} +(1.80822 + 3.13192i) q^{61} +(1.50113 + 0.866676i) q^{62} -1.04378i q^{63} -1.00000 q^{64} +(6.13694 + 7.72532i) q^{65} -0.877352 q^{66} +(-2.30824 + 1.33266i) q^{67} -5.13258i q^{68} +(-3.55509 - 6.15759i) q^{69} +(0.343506 + 2.30854i) q^{70} +(0.582533 + 1.00898i) q^{71} +(-0.866025 - 0.500000i) q^{72} +5.73680i q^{73} +(-3.02535 + 5.27705i) q^{74} +(-3.41466 + 3.65241i) q^{75} +(1.51358 - 2.62160i) q^{76} +(0.793072 - 0.457881i) q^{77} +(3.82118 - 2.20616i) q^{78} +(-5.03878 - 8.72742i) q^{79} +(2.07995 + 0.820851i) q^{80} +(-0.500000 - 0.866025i) q^{81} -6.25403i q^{82} +(-9.72771 - 5.61630i) q^{83} +1.04378 q^{84} +(-4.21308 + 10.6755i) q^{85} +(0.731945 - 1.26777i) q^{86} +(5.16264 - 2.98065i) q^{87} -0.877352i q^{88} +(7.63676 - 13.2273i) q^{89} +(1.39087 + 1.75085i) q^{90} +(-2.30274 + 3.98846i) q^{91} +(6.15759 - 3.55509i) q^{92} +(-1.50113 + 0.866676i) q^{93} +(1.50025 - 2.59851i) q^{94} +(-5.30012 + 4.21038i) q^{95} +(0.500000 - 0.866025i) q^{96} -9.07922i q^{97} +(5.11867 - 2.95526i) q^{98} +(0.438676 - 0.759809i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40 q + 20 q^{4} + 2 q^{5} - 40 q^{6} + 20 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 40 q + 20 q^{4} + 2 q^{5} - 40 q^{6} + 20 q^{9} + 24 q^{14} - 20 q^{16} - 14 q^{19} - 2 q^{20} - 12 q^{21} - 20 q^{24} - 2 q^{25} - 24 q^{26} + 12 q^{29} - 2 q^{30} - 40 q^{31} + 10 q^{34} - 2 q^{35} + 40 q^{36} + 12 q^{39} + 20 q^{41} + 4 q^{45} + 2 q^{46} + 28 q^{49} + 12 q^{50} - 20 q^{51} - 20 q^{54} + 32 q^{55} + 12 q^{56} - 40 q^{59} + 12 q^{61} - 40 q^{64} + 2 q^{65} + 2 q^{69} - 22 q^{70} + 12 q^{71} - 30 q^{74} - 24 q^{75} + 14 q^{76} - 24 q^{79} - 4 q^{80} - 20 q^{81} - 24 q^{84} + 40 q^{85} - 4 q^{86} - 34 q^{89} - 4 q^{91} - 8 q^{94} + 6 q^{95} + 20 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).

\(n\) \(371\) \(631\) \(667\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 0.500000i −0.612372 0.353553i
\(3\) 0.866025 0.500000i 0.500000 0.288675i
\(4\) 0.500000 + 0.866025i 0.250000 + 0.433013i
\(5\) −0.329099 2.21172i −0.147177 0.989110i
\(6\) −1.00000 −0.408248
\(7\) 0.903939 0.521889i 0.341657 0.197256i −0.319348 0.947638i \(-0.603464\pi\)
0.661004 + 0.750382i \(0.270130\pi\)
\(8\) 1.00000i 0.353553i
\(9\) 0.500000 0.866025i 0.166667 0.288675i
\(10\) −0.820851 + 2.07995i −0.259576 + 0.657739i
\(11\) 0.877352 0.264531 0.132266 0.991214i \(-0.457775\pi\)
0.132266 + 0.991214i \(0.457775\pi\)
\(12\) 0.866025 + 0.500000i 0.250000 + 0.144338i
\(13\) −3.82118 + 2.20616i −1.05980 + 0.611878i −0.925378 0.379045i \(-0.876252\pi\)
−0.134426 + 0.990924i \(0.542919\pi\)
\(14\) −1.04378 −0.278962
\(15\) −1.39087 1.75085i −0.359120 0.452069i
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −4.44494 2.56629i −1.07806 0.622417i −0.147686 0.989034i \(-0.547182\pi\)
−0.930372 + 0.366618i \(0.880516\pi\)
\(18\) −0.866025 + 0.500000i −0.204124 + 0.117851i
\(19\) −1.51358 2.62160i −0.347240 0.601437i 0.638518 0.769607i \(-0.279548\pi\)
−0.985758 + 0.168170i \(0.946214\pi\)
\(20\) 1.75085 1.39087i 0.391503 0.311007i
\(21\) 0.521889 0.903939i 0.113886 0.197256i
\(22\) −0.759809 0.438676i −0.161992 0.0935260i
\(23\) 7.11017i 1.48257i −0.671188 0.741287i \(-0.734216\pi\)
0.671188 0.741287i \(-0.265784\pi\)
\(24\) −0.500000 0.866025i −0.102062 0.176777i
\(25\) −4.78339 + 1.45575i −0.956678 + 0.291149i
\(26\) 4.41232 0.865326
\(27\) 1.00000i 0.192450i
\(28\) 0.903939 + 0.521889i 0.170828 + 0.0986278i
\(29\) 5.96130 1.10699 0.553493 0.832854i \(-0.313294\pi\)
0.553493 + 0.832854i \(0.313294\pi\)
\(30\) 0.329099 + 2.21172i 0.0600850 + 0.403803i
\(31\) −1.73335 −0.311319 −0.155660 0.987811i \(-0.549750\pi\)
−0.155660 + 0.987811i \(0.549750\pi\)
\(32\) 0.866025 0.500000i 0.153093 0.0883883i
\(33\) 0.759809 0.438676i 0.132266 0.0763637i
\(34\) 2.56629 + 4.44494i 0.440115 + 0.762302i
\(35\) −1.45176 1.82750i −0.245392 0.308905i
\(36\) 1.00000 0.166667
\(37\) −0.0184948 6.08273i −0.00304052 0.999995i
\(38\) 3.02716i 0.491071i
\(39\) −2.20616 + 3.82118i −0.353268 + 0.611878i
\(40\) −2.21172 + 0.329099i −0.349703 + 0.0520351i
\(41\) 3.12701 + 5.41615i 0.488357 + 0.845860i 0.999910 0.0133920i \(-0.00426293\pi\)
−0.511553 + 0.859252i \(0.670930\pi\)
\(42\) −0.903939 + 0.521889i −0.139481 + 0.0805293i
\(43\) 1.46389i 0.223241i 0.993751 + 0.111621i \(0.0356041\pi\)
−0.993751 + 0.111621i \(0.964396\pi\)
\(44\) 0.438676 + 0.759809i 0.0661329 + 0.114545i
\(45\) −2.07995 0.820851i −0.310061 0.122365i
\(46\) −3.55509 + 6.15759i −0.524169 + 0.907887i
\(47\) 3.00050i 0.437668i 0.975762 + 0.218834i \(0.0702254\pi\)
−0.975762 + 0.218834i \(0.929775\pi\)
\(48\) 1.00000i 0.144338i
\(49\) −2.95526 + 5.11867i −0.422180 + 0.731238i
\(50\) 4.87041 + 1.13098i 0.688780 + 0.159945i
\(51\) −5.13258 −0.718705
\(52\) −3.82118 2.20616i −0.529902 0.305939i
\(53\) −11.1687 6.44827i −1.53414 0.885738i −0.999164 0.0408730i \(-0.986986\pi\)
−0.534979 0.844865i \(-0.679681\pi\)
\(54\) −0.500000 + 0.866025i −0.0680414 + 0.117851i
\(55\) −0.288735 1.94045i −0.0389331 0.261651i
\(56\) −0.521889 0.903939i −0.0697404 0.120794i
\(57\) −2.62160 1.51358i −0.347240 0.200479i
\(58\) −5.16264 2.98065i −0.677888 0.391379i
\(59\) 4.32356 7.48863i 0.562880 0.974937i −0.434363 0.900738i \(-0.643027\pi\)
0.997243 0.0741992i \(-0.0236401\pi\)
\(60\) 0.820851 2.07995i 0.105971 0.268521i
\(61\) 1.80822 + 3.13192i 0.231518 + 0.401002i 0.958255 0.285914i \(-0.0922973\pi\)
−0.726737 + 0.686916i \(0.758964\pi\)
\(62\) 1.50113 + 0.866676i 0.190643 + 0.110068i
\(63\) 1.04378i 0.131504i
\(64\) −1.00000 −0.125000
\(65\) 6.13694 + 7.72532i 0.761194 + 0.958208i
\(66\) −0.877352 −0.107995
\(67\) −2.30824 + 1.33266i −0.281997 + 0.162811i −0.634327 0.773065i \(-0.718723\pi\)
0.352330 + 0.935876i \(0.385389\pi\)
\(68\) 5.13258i 0.622417i
\(69\) −3.55509 6.15759i −0.427982 0.741287i
\(70\) 0.343506 + 2.30854i 0.0410569 + 0.275924i
\(71\) 0.582533 + 1.00898i 0.0691340 + 0.119744i 0.898520 0.438932i \(-0.144643\pi\)
−0.829386 + 0.558675i \(0.811310\pi\)
\(72\) −0.866025 0.500000i −0.102062 0.0589256i
\(73\) 5.73680i 0.671441i 0.941962 + 0.335721i \(0.108980\pi\)
−0.941962 + 0.335721i \(0.891020\pi\)
\(74\) −3.02535 + 5.27705i −0.351690 + 0.613445i
\(75\) −3.41466 + 3.65241i −0.394291 + 0.421744i
\(76\) 1.51358 2.62160i 0.173620 0.300718i
\(77\) 0.793072 0.457881i 0.0903790 0.0521803i
\(78\) 3.82118 2.20616i 0.432663 0.249798i
\(79\) −5.03878 8.72742i −0.566907 0.981911i −0.996869 0.0790646i \(-0.974807\pi\)
0.429963 0.902847i \(-0.358527\pi\)
\(80\) 2.07995 + 0.820851i 0.232546 + 0.0917739i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 6.25403i 0.690642i
\(83\) −9.72771 5.61630i −1.06776 0.616469i −0.140188 0.990125i \(-0.544771\pi\)
−0.927567 + 0.373656i \(0.878104\pi\)
\(84\) 1.04378 0.113886
\(85\) −4.21308 + 10.6755i −0.456973 + 1.15792i
\(86\) 0.731945 1.26777i 0.0789277 0.136707i
\(87\) 5.16264 2.98065i 0.553493 0.319559i
\(88\) 0.877352i 0.0935260i
\(89\) 7.63676 13.2273i 0.809495 1.40209i −0.103719 0.994607i \(-0.533074\pi\)
0.913214 0.407480i \(-0.133592\pi\)
\(90\) 1.39087 + 1.75085i 0.146610 + 0.184556i
\(91\) −2.30274 + 3.98846i −0.241393 + 0.418105i
\(92\) 6.15759 3.55509i 0.641973 0.370643i
\(93\) −1.50113 + 0.866676i −0.155660 + 0.0898701i
\(94\) 1.50025 2.59851i 0.154739 0.268016i
\(95\) −5.30012 + 4.21038i −0.543781 + 0.431976i
\(96\) 0.500000 0.866025i 0.0510310 0.0883883i
\(97\) 9.07922i 0.921855i −0.887438 0.460928i \(-0.847517\pi\)
0.887438 0.460928i \(-0.152483\pi\)
\(98\) 5.11867 2.95526i 0.517063 0.298527i
\(99\) 0.438676 0.759809i 0.0440886 0.0763637i
\(100\) −3.65241 3.41466i −0.365241 0.341466i
\(101\) 1.97678 0.196697 0.0983486 0.995152i \(-0.468644\pi\)
0.0983486 + 0.995152i \(0.468644\pi\)
\(102\) 4.44494 + 2.56629i 0.440115 + 0.254101i
\(103\) 5.48507i 0.540460i 0.962796 + 0.270230i \(0.0870998\pi\)
−0.962796 + 0.270230i \(0.912900\pi\)
\(104\) 2.20616 + 3.82118i 0.216332 + 0.374697i
\(105\) −2.17101 0.856787i −0.211869 0.0836138i
\(106\) 6.44827 + 11.1687i 0.626312 + 1.08480i
\(107\) −0.205007 + 0.118361i −0.0198188 + 0.0114424i −0.509877 0.860248i \(-0.670309\pi\)
0.490058 + 0.871690i \(0.336976\pi\)
\(108\) 0.866025 0.500000i 0.0833333 0.0481125i
\(109\) 3.39695 5.88369i 0.325369 0.563555i −0.656218 0.754571i \(-0.727845\pi\)
0.981587 + 0.191016i \(0.0611783\pi\)
\(110\) −0.720175 + 1.82485i −0.0686660 + 0.173993i
\(111\) −3.05738 5.25856i −0.290194 0.499120i
\(112\) 1.04378i 0.0986278i
\(113\) 9.35427 + 5.40069i 0.879976 + 0.508054i 0.870650 0.491902i \(-0.163698\pi\)
0.00932533 + 0.999957i \(0.497032\pi\)
\(114\) 1.51358 + 2.62160i 0.141760 + 0.245535i
\(115\) −15.7257 + 2.33995i −1.46643 + 0.218201i
\(116\) 2.98065 + 5.16264i 0.276747 + 0.479339i
\(117\) 4.41232i 0.407919i
\(118\) −7.48863 + 4.32356i −0.689385 + 0.398016i
\(119\) −5.35728 −0.491101
\(120\) −1.75085 + 1.39087i −0.159830 + 0.126968i
\(121\) −10.2303 −0.930023
\(122\) 3.61643i 0.327416i
\(123\) 5.41615 + 3.12701i 0.488357 + 0.281953i
\(124\) −0.866676 1.50113i −0.0778298 0.134805i
\(125\) 4.79391 + 10.1004i 0.428780 + 0.903409i
\(126\) −0.521889 + 0.903939i −0.0464936 + 0.0805293i
\(127\) 2.96848 + 1.71385i 0.263410 + 0.152080i 0.625889 0.779912i \(-0.284736\pi\)
−0.362479 + 0.931992i \(0.618070\pi\)
\(128\) 0.866025 + 0.500000i 0.0765466 + 0.0441942i
\(129\) 0.731945 + 1.26777i 0.0644442 + 0.111621i
\(130\) −1.45209 9.75880i −0.127357 0.855903i
\(131\) −9.37585 + 16.2395i −0.819172 + 1.41885i 0.0871208 + 0.996198i \(0.472233\pi\)
−0.906293 + 0.422650i \(0.861100\pi\)
\(132\) 0.759809 + 0.438676i 0.0661329 + 0.0381818i
\(133\) −2.73637 1.57985i −0.237274 0.136990i
\(134\) 2.66533 0.230249
\(135\) −2.21172 + 0.329099i −0.190354 + 0.0283243i
\(136\) −2.56629 + 4.44494i −0.220058 + 0.381151i
\(137\) 20.6333i 1.76282i −0.472348 0.881412i \(-0.656593\pi\)
0.472348 0.881412i \(-0.343407\pi\)
\(138\) 7.11017i 0.605258i
\(139\) 3.04472 5.27361i 0.258250 0.447302i −0.707523 0.706690i \(-0.750188\pi\)
0.965773 + 0.259388i \(0.0835209\pi\)
\(140\) 0.856787 2.17101i 0.0724117 0.183484i
\(141\) 1.50025 + 2.59851i 0.126344 + 0.218834i
\(142\) 1.16507i 0.0977702i
\(143\) −3.35252 + 1.93558i −0.280352 + 0.161861i
\(144\) 0.500000 + 0.866025i 0.0416667 + 0.0721688i
\(145\) −1.96186 13.1847i −0.162923 1.09493i
\(146\) 2.86840 4.96821i 0.237390 0.411172i
\(147\) 5.91053i 0.487492i
\(148\) 5.25856 3.05738i 0.432251 0.251315i
\(149\) 10.4868 0.859109 0.429555 0.903041i \(-0.358671\pi\)
0.429555 + 0.903041i \(0.358671\pi\)
\(150\) 4.78339 1.45575i 0.390562 0.118861i
\(151\) −1.64176 2.84361i −0.133604 0.231410i 0.791459 0.611222i \(-0.209322\pi\)
−0.925063 + 0.379813i \(0.875988\pi\)
\(152\) −2.62160 + 1.51358i −0.212640 + 0.122768i
\(153\) −4.44494 + 2.56629i −0.359353 + 0.207472i
\(154\) −0.915761 −0.0737941
\(155\) 0.570444 + 3.83369i 0.0458192 + 0.307929i
\(156\) −4.41232 −0.353268
\(157\) −4.20988 2.43057i −0.335985 0.193981i 0.322510 0.946566i \(-0.395473\pi\)
−0.658495 + 0.752585i \(0.728807\pi\)
\(158\) 10.0776i 0.801727i
\(159\) −12.8965 −1.02276
\(160\) −1.39087 1.75085i −0.109958 0.138417i
\(161\) −3.71072 6.42716i −0.292446 0.506531i
\(162\) 1.00000i 0.0785674i
\(163\) 18.1870 + 10.5002i 1.42451 + 0.822443i 0.996680 0.0814153i \(-0.0259440\pi\)
0.427832 + 0.903858i \(0.359277\pi\)
\(164\) −3.12701 + 5.41615i −0.244179 + 0.422930i
\(165\) −1.22028 1.53611i −0.0949986 0.119586i
\(166\) 5.61630 + 9.72771i 0.435909 + 0.755017i
\(167\) 5.55334 3.20622i 0.429731 0.248105i −0.269501 0.963000i \(-0.586859\pi\)
0.699232 + 0.714895i \(0.253525\pi\)
\(168\) −0.903939 0.521889i −0.0697404 0.0402646i
\(169\) 3.23427 5.60192i 0.248790 0.430917i
\(170\) 8.98640 7.13873i 0.689225 0.547516i
\(171\) −3.02716 −0.231493
\(172\) −1.26777 + 0.731945i −0.0966663 + 0.0558103i
\(173\) −0.334462 0.193102i −0.0254287 0.0146813i 0.487232 0.873273i \(-0.338007\pi\)
−0.512660 + 0.858591i \(0.671340\pi\)
\(174\) −5.96130 −0.451925
\(175\) −3.56415 + 3.81231i −0.269425 + 0.288183i
\(176\) −0.438676 + 0.759809i −0.0330664 + 0.0572727i
\(177\) 8.64713i 0.649958i
\(178\) −13.2273 + 7.63676i −0.991425 + 0.572400i
\(179\) −18.1446 −1.35619 −0.678094 0.734975i \(-0.737194\pi\)
−0.678094 + 0.734975i \(0.737194\pi\)
\(180\) −0.329099 2.21172i −0.0245296 0.164852i
\(181\) 2.94193 + 5.09557i 0.218672 + 0.378750i 0.954402 0.298524i \(-0.0964943\pi\)
−0.735730 + 0.677274i \(0.763161\pi\)
\(182\) 3.98846 2.30274i 0.295645 0.170691i
\(183\) 3.13192 + 1.80822i 0.231518 + 0.133667i
\(184\) −7.11017 −0.524169
\(185\) −13.4472 + 2.04273i −0.988658 + 0.150184i
\(186\) 1.73335 0.127096
\(187\) −3.89978 2.25154i −0.285180 0.164649i
\(188\) −2.59851 + 1.50025i −0.189516 + 0.109417i
\(189\) −0.521889 0.903939i −0.0379619 0.0657519i
\(190\) 6.69523 0.996236i 0.485723 0.0722746i
\(191\) 11.9257 0.862911 0.431455 0.902134i \(-0.358000\pi\)
0.431455 + 0.902134i \(0.358000\pi\)
\(192\) −0.866025 + 0.500000i −0.0625000 + 0.0360844i
\(193\) 2.74542i 0.197620i 0.995106 + 0.0988099i \(0.0315036\pi\)
−0.995106 + 0.0988099i \(0.968496\pi\)
\(194\) −4.53961 + 7.86284i −0.325925 + 0.564519i
\(195\) 9.17741 + 3.62185i 0.657208 + 0.259366i
\(196\) −5.91053 −0.422180
\(197\) 2.67557 + 1.54474i 0.190627 + 0.110058i 0.592276 0.805735i \(-0.298230\pi\)
−0.401649 + 0.915794i \(0.631563\pi\)
\(198\) −0.759809 + 0.438676i −0.0539973 + 0.0311753i
\(199\) 21.7511 1.54189 0.770946 0.636900i \(-0.219784\pi\)
0.770946 + 0.636900i \(0.219784\pi\)
\(200\) 1.45575 + 4.78339i 0.102937 + 0.338237i
\(201\) −1.33266 + 2.30824i −0.0939988 + 0.162811i
\(202\) −1.71194 0.988392i −0.120452 0.0695430i
\(203\) 5.38865 3.11114i 0.378209 0.218359i
\(204\) −2.56629 4.44494i −0.179676 0.311208i
\(205\) 10.9499 8.69852i 0.764773 0.607531i
\(206\) 2.74254 4.75021i 0.191082 0.330963i
\(207\) −6.15759 3.55509i −0.427982 0.247096i
\(208\) 4.41232i 0.305939i
\(209\) −1.32794 2.30007i −0.0918558 0.159099i
\(210\) 1.45176 + 1.82750i 0.100181 + 0.126110i
\(211\) 23.5364 1.62032 0.810158 0.586212i \(-0.199381\pi\)
0.810158 + 0.586212i \(0.199381\pi\)
\(212\) 12.8965i 0.885738i
\(213\) 1.00898 + 0.582533i 0.0691340 + 0.0399145i
\(214\) 0.236722 0.0161820
\(215\) 3.23771 0.481765i 0.220810 0.0328561i
\(216\) −1.00000 −0.0680414
\(217\) −1.56684 + 0.904618i −0.106364 + 0.0614095i
\(218\) −5.88369 + 3.39695i −0.398494 + 0.230070i
\(219\) 2.86840 + 4.96821i 0.193828 + 0.335721i
\(220\) 1.53611 1.22028i 0.103565 0.0822712i
\(221\) 22.6466 1.52337
\(222\) 0.0184948 + 6.08273i 0.00124129 + 0.408246i
\(223\) 21.8135i 1.46074i 0.683051 + 0.730371i \(0.260653\pi\)
−0.683051 + 0.730371i \(0.739347\pi\)
\(224\) 0.521889 0.903939i 0.0348702 0.0603970i
\(225\) −1.13098 + 4.87041i −0.0753987 + 0.324694i
\(226\) −5.40069 9.35427i −0.359249 0.622237i
\(227\) 11.3937 6.57817i 0.756229 0.436609i −0.0717115 0.997425i \(-0.522846\pi\)
0.827940 + 0.560817i \(0.189513\pi\)
\(228\) 3.02716i 0.200479i
\(229\) −7.76074 13.4420i −0.512844 0.888273i −0.999889 0.0148955i \(-0.995258\pi\)
0.487045 0.873377i \(-0.338075\pi\)
\(230\) 14.7888 + 5.83639i 0.975146 + 0.384840i
\(231\) 0.457881 0.793072i 0.0301263 0.0521803i
\(232\) 5.96130i 0.391379i
\(233\) 20.8578i 1.36644i 0.730213 + 0.683220i \(0.239421\pi\)
−0.730213 + 0.683220i \(0.760579\pi\)
\(234\) 2.20616 3.82118i 0.144221 0.249798i
\(235\) 6.63626 0.987462i 0.432902 0.0644149i
\(236\) 8.64713 0.562880
\(237\) −8.72742 5.03878i −0.566907 0.327304i
\(238\) 4.63954 + 2.67864i 0.300737 + 0.173630i
\(239\) 1.58208 2.74024i 0.102336 0.177251i −0.810311 0.586001i \(-0.800702\pi\)
0.912647 + 0.408749i \(0.134035\pi\)
\(240\) 2.21172 0.329099i 0.142766 0.0212432i
\(241\) −3.34456 5.79294i −0.215442 0.373156i 0.737967 0.674836i \(-0.235786\pi\)
−0.953409 + 0.301680i \(0.902453\pi\)
\(242\) 8.85966 + 5.11513i 0.569521 + 0.328813i
\(243\) −0.866025 0.500000i −0.0555556 0.0320750i
\(244\) −1.80822 + 3.13192i −0.115759 + 0.200501i
\(245\) 12.2936 + 4.85166i 0.785410 + 0.309961i
\(246\) −3.12701 5.41615i −0.199371 0.345321i
\(247\) 11.5673 + 6.67840i 0.736012 + 0.424937i
\(248\) 1.73335i 0.110068i
\(249\) −11.2326 −0.711837
\(250\) 0.898562 11.1442i 0.0568300 0.704819i
\(251\) −13.7418 −0.867373 −0.433686 0.901064i \(-0.642787\pi\)
−0.433686 + 0.901064i \(0.642787\pi\)
\(252\) 0.903939 0.521889i 0.0569428 0.0328759i
\(253\) 6.23812i 0.392187i
\(254\) −1.71385 2.96848i −0.107537 0.186259i
\(255\) 1.68913 + 11.3518i 0.105777 + 0.710878i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −0.431560 0.249162i −0.0269200 0.0155423i 0.486480 0.873692i \(-0.338281\pi\)
−0.513400 + 0.858150i \(0.671614\pi\)
\(258\) 1.46389i 0.0911379i
\(259\) −3.19123 5.48877i −0.198294 0.341055i
\(260\) −3.62185 + 9.17741i −0.224618 + 0.569159i
\(261\) 2.98065 5.16264i 0.184498 0.319559i
\(262\) 16.2395 9.37585i 1.00328 0.579242i
\(263\) 20.0619 11.5827i 1.23707 0.714221i 0.268574 0.963259i \(-0.413448\pi\)
0.968494 + 0.249038i \(0.0801143\pi\)
\(264\) −0.438676 0.759809i −0.0269986 0.0467630i
\(265\) −10.5861 + 26.8242i −0.650301 + 1.64780i
\(266\) 1.57985 + 2.73637i 0.0968665 + 0.167778i
\(267\) 15.2735i 0.934725i
\(268\) −2.30824 1.33266i −0.140998 0.0814054i
\(269\) 20.2746 1.23617 0.618083 0.786113i \(-0.287910\pi\)
0.618083 + 0.786113i \(0.287910\pi\)
\(270\) 2.07995 + 0.820851i 0.126582 + 0.0499554i
\(271\) −10.3687 + 17.9591i −0.629852 + 1.09094i 0.357729 + 0.933826i \(0.383551\pi\)
−0.987581 + 0.157111i \(0.949782\pi\)
\(272\) 4.44494 2.56629i 0.269514 0.155604i
\(273\) 4.60548i 0.278736i
\(274\) −10.3167 + 17.8690i −0.623252 + 1.07950i
\(275\) −4.19671 + 1.27720i −0.253071 + 0.0770182i
\(276\) 3.55509 6.15759i 0.213991 0.370643i
\(277\) 9.85578 5.69024i 0.592177 0.341893i −0.173781 0.984784i \(-0.555599\pi\)
0.765958 + 0.642891i \(0.222265\pi\)
\(278\) −5.27361 + 3.04472i −0.316290 + 0.182610i
\(279\) −0.866676 + 1.50113i −0.0518865 + 0.0898701i
\(280\) −1.82750 + 1.45176i −0.109214 + 0.0867591i
\(281\) 6.84750 11.8602i 0.408488 0.707521i −0.586233 0.810143i \(-0.699390\pi\)
0.994721 + 0.102621i \(0.0327229\pi\)
\(282\) 3.00050i 0.178677i
\(283\) 21.3150 12.3062i 1.26704 0.731527i 0.292615 0.956230i \(-0.405474\pi\)
0.974427 + 0.224703i \(0.0721411\pi\)
\(284\) −0.582533 + 1.00898i −0.0345670 + 0.0598718i
\(285\) −2.48485 + 6.29636i −0.147190 + 0.372964i
\(286\) 3.87115 0.228906
\(287\) 5.65326 + 3.26391i 0.333701 + 0.192663i
\(288\) 1.00000i 0.0589256i
\(289\) 4.67169 + 8.09161i 0.274805 + 0.475977i
\(290\) −4.89334 + 12.3992i −0.287347 + 0.728108i
\(291\) −4.53961 7.86284i −0.266117 0.460928i
\(292\) −4.96821 + 2.86840i −0.290743 + 0.167860i
\(293\) 20.6285 11.9099i 1.20513 0.695782i 0.243438 0.969916i \(-0.421725\pi\)
0.961691 + 0.274135i \(0.0883914\pi\)
\(294\) 2.95526 5.11867i 0.172354 0.298527i
\(295\) −17.9856 7.09800i −1.04716 0.413262i
\(296\) −6.08273 + 0.0184948i −0.353552 + 0.00107499i
\(297\) 0.877352i 0.0509091i
\(298\) −9.08180 5.24338i −0.526095 0.303741i
\(299\) 15.6862 + 27.1692i 0.907154 + 1.57124i
\(300\) −4.87041 1.13098i −0.281193 0.0652972i
\(301\) 0.763989 + 1.32327i 0.0440356 + 0.0762719i
\(302\) 3.28352i 0.188945i
\(303\) 1.71194 0.988392i 0.0983486 0.0567816i
\(304\) 3.02716 0.173620
\(305\) 6.33185 5.02998i 0.362560 0.288016i
\(306\) 5.13258 0.293410
\(307\) 11.6875i 0.667039i 0.942743 + 0.333520i \(0.108236\pi\)
−0.942743 + 0.333520i \(0.891764\pi\)
\(308\) 0.793072 + 0.457881i 0.0451895 + 0.0260902i
\(309\) 2.74254 + 4.75021i 0.156017 + 0.270230i
\(310\) 1.42282 3.60529i 0.0808110 0.204767i
\(311\) 9.68464 16.7743i 0.549166 0.951183i −0.449166 0.893448i \(-0.648279\pi\)
0.998332 0.0577348i \(-0.0183878\pi\)
\(312\) 3.82118 + 2.20616i 0.216332 + 0.124899i
\(313\) 12.7904 + 7.38454i 0.722956 + 0.417399i 0.815840 0.578278i \(-0.196275\pi\)
−0.0928839 + 0.995677i \(0.529609\pi\)
\(314\) 2.43057 + 4.20988i 0.137165 + 0.237577i
\(315\) −2.30854 + 0.343506i −0.130072 + 0.0193544i
\(316\) 5.03878 8.72742i 0.283453 0.490956i
\(317\) −5.38368 3.10827i −0.302378 0.174578i 0.341133 0.940015i \(-0.389189\pi\)
−0.643511 + 0.765437i \(0.722523\pi\)
\(318\) 11.1687 + 6.44827i 0.626312 + 0.361601i
\(319\) 5.23016 0.292833
\(320\) 0.329099 + 2.21172i 0.0183972 + 0.123639i
\(321\) −0.118361 + 0.205007i −0.00660627 + 0.0114424i
\(322\) 7.42145i 0.413581i
\(323\) 15.5372i 0.864511i
\(324\) 0.500000 0.866025i 0.0277778 0.0481125i
\(325\) 15.0666 16.1156i 0.835743 0.893932i
\(326\) −10.5002 18.1870i −0.581555 1.00728i
\(327\) 6.79390i 0.375703i
\(328\) 5.41615 3.12701i 0.299057 0.172660i
\(329\) 1.56593 + 2.71227i 0.0863325 + 0.149532i
\(330\) 0.288735 + 1.94045i 0.0158944 + 0.106818i
\(331\) −11.5832 + 20.0626i −0.636668 + 1.10274i 0.349491 + 0.936940i \(0.386354\pi\)
−0.986159 + 0.165801i \(0.946979\pi\)
\(332\) 11.2326i 0.616469i
\(333\) −5.27705 3.02535i −0.289181 0.165788i
\(334\) −6.41245 −0.350874
\(335\) 3.70711 + 4.66660i 0.202541 + 0.254964i
\(336\) 0.521889 + 0.903939i 0.0284714 + 0.0493139i
\(337\) 10.2042 5.89139i 0.555857 0.320924i −0.195624 0.980679i \(-0.562673\pi\)
0.751481 + 0.659755i \(0.229340\pi\)
\(338\) −5.60192 + 3.23427i −0.304704 + 0.175921i
\(339\) 10.8014 0.586650
\(340\) −11.3518 + 1.68913i −0.615639 + 0.0916057i
\(341\) −1.52076 −0.0823538
\(342\) 2.62160 + 1.51358i 0.141760 + 0.0818452i
\(343\) 13.4757i 0.727621i
\(344\) 1.46389 0.0789277
\(345\) −12.4489 + 9.88930i −0.670225 + 0.532422i
\(346\) 0.193102 + 0.334462i 0.0103812 + 0.0179808i
\(347\) 20.6749i 1.10988i −0.831889 0.554942i \(-0.812740\pi\)
0.831889 0.554942i \(-0.187260\pi\)
\(348\) 5.16264 + 2.98065i 0.276747 + 0.159780i
\(349\) 9.11242 15.7832i 0.487777 0.844854i −0.512124 0.858911i \(-0.671141\pi\)
0.999901 + 0.0140571i \(0.00447465\pi\)
\(350\) 4.99280 1.51948i 0.266876 0.0812195i
\(351\) 2.20616 + 3.82118i 0.117756 + 0.203959i
\(352\) 0.759809 0.438676i 0.0404979 0.0233815i
\(353\) −24.8210 14.3304i −1.32109 0.762731i −0.337186 0.941438i \(-0.609475\pi\)
−0.983902 + 0.178707i \(0.942808\pi\)
\(354\) −4.32356 + 7.48863i −0.229795 + 0.398016i
\(355\) 2.03986 1.62045i 0.108265 0.0860046i
\(356\) 15.2735 0.809495
\(357\) −4.63954 + 2.67864i −0.245550 + 0.141769i
\(358\) 15.7137 + 9.07228i 0.830493 + 0.479485i
\(359\) 23.0581 1.21696 0.608480 0.793569i \(-0.291780\pi\)
0.608480 + 0.793569i \(0.291780\pi\)
\(360\) −0.820851 + 2.07995i −0.0432626 + 0.109623i
\(361\) 4.91814 8.51846i 0.258849 0.448340i
\(362\) 5.88385i 0.309248i
\(363\) −8.85966 + 5.11513i −0.465012 + 0.268475i
\(364\) −4.60548 −0.241393
\(365\) 12.6882 1.88797i 0.664130 0.0988211i
\(366\) −1.80822 3.13192i −0.0945170 0.163708i
\(367\) 22.8357 13.1842i 1.19201 0.688210i 0.233251 0.972416i \(-0.425063\pi\)
0.958763 + 0.284207i \(0.0917302\pi\)
\(368\) 6.15759 + 3.55509i 0.320987 + 0.185322i
\(369\) 6.25403 0.325572
\(370\) 12.6670 + 4.95455i 0.658525 + 0.257575i
\(371\) −13.4611 −0.698867
\(372\) −1.50113 0.866676i −0.0778298 0.0449351i
\(373\) 23.6605 13.6604i 1.22509 0.707308i 0.259094 0.965852i \(-0.416576\pi\)
0.965999 + 0.258544i \(0.0832427\pi\)
\(374\) 2.25154 + 3.89978i 0.116424 + 0.201653i
\(375\) 9.20186 + 6.35026i 0.475182 + 0.327926i
\(376\) 3.00050 0.154739
\(377\) −22.7792 + 13.1516i −1.17319 + 0.677341i
\(378\) 1.04378i 0.0536862i
\(379\) 2.47817 4.29231i 0.127295 0.220481i −0.795333 0.606173i \(-0.792704\pi\)
0.922628 + 0.385692i \(0.126037\pi\)
\(380\) −6.29636 2.48485i −0.322996 0.127470i
\(381\) 3.42770 0.175607
\(382\) −10.3279 5.96283i −0.528423 0.305085i
\(383\) −30.3000 + 17.4937i −1.54826 + 0.893886i −0.549980 + 0.835178i \(0.685365\pi\)
−0.998275 + 0.0587078i \(0.981302\pi\)
\(384\) 1.00000 0.0510310
\(385\) −1.27370 1.60336i −0.0649138 0.0817150i
\(386\) 1.37271 2.37760i 0.0698691 0.121017i
\(387\) 1.26777 + 0.731945i 0.0644442 + 0.0372069i
\(388\) 7.86284 4.53961i 0.399175 0.230464i
\(389\) −16.5222 28.6172i −0.837707 1.45095i −0.891807 0.452415i \(-0.850563\pi\)
0.0541006 0.998535i \(-0.482771\pi\)
\(390\) −6.13694 7.72532i −0.310756 0.391187i
\(391\) −18.2468 + 31.6043i −0.922779 + 1.59830i
\(392\) 5.11867 + 2.95526i 0.258532 + 0.149263i
\(393\) 18.7517i 0.945899i
\(394\) −1.54474 2.67557i −0.0778230 0.134793i
\(395\) −17.6443 + 14.0165i −0.887782 + 0.705248i
\(396\) 0.877352 0.0440886
\(397\) 17.4364i 0.875109i −0.899192 0.437554i \(-0.855845\pi\)
0.899192 0.437554i \(-0.144155\pi\)
\(398\) −18.8370 10.8755i −0.944212 0.545141i
\(399\) −3.15969 −0.158182
\(400\) 1.13098 4.87041i 0.0565490 0.243520i
\(401\) −25.6014 −1.27847 −0.639237 0.769010i \(-0.720750\pi\)
−0.639237 + 0.769010i \(0.720750\pi\)
\(402\) 2.30824 1.33266i 0.115125 0.0664672i
\(403\) 6.62345 3.82405i 0.329937 0.190489i
\(404\) 0.988392 + 1.71194i 0.0491743 + 0.0851724i
\(405\) −1.75085 + 1.39087i −0.0870006 + 0.0691127i
\(406\) −6.22228 −0.308807
\(407\) −0.0162264 5.33670i −0.000804313 0.264530i
\(408\) 5.13258i 0.254101i
\(409\) −3.56975 + 6.18298i −0.176513 + 0.305729i −0.940684 0.339285i \(-0.889815\pi\)
0.764171 + 0.645014i \(0.223148\pi\)
\(410\) −13.8321 + 2.05819i −0.683121 + 0.101647i
\(411\) −10.3167 17.8690i −0.508884 0.881412i
\(412\) −4.75021 + 2.74254i −0.234026 + 0.135115i
\(413\) 9.02569i 0.444125i
\(414\) 3.55509 + 6.15759i 0.174723 + 0.302629i
\(415\) −9.22028 + 23.3633i −0.452606 + 1.14686i
\(416\) −2.20616 + 3.82118i −0.108166 + 0.187349i
\(417\) 6.08944i 0.298201i
\(418\) 2.65589i 0.129904i
\(419\) −10.8835 + 18.8507i −0.531693 + 0.920919i 0.467623 + 0.883928i \(0.345111\pi\)
−0.999316 + 0.0369911i \(0.988223\pi\)
\(420\) −0.343506 2.30854i −0.0167614 0.112645i
\(421\) 31.9568 1.55748 0.778738 0.627349i \(-0.215860\pi\)
0.778738 + 0.627349i \(0.215860\pi\)
\(422\) −20.3832 11.7682i −0.992237 0.572868i
\(423\) 2.59851 + 1.50025i 0.126344 + 0.0729447i
\(424\) −6.44827 + 11.1687i −0.313156 + 0.542402i
\(425\) 24.9978 + 5.80485i 1.21257 + 0.281576i
\(426\) −0.582533 1.00898i −0.0282238 0.0488851i
\(427\) 3.26903 + 1.88738i 0.158200 + 0.0913366i
\(428\) −0.205007 0.118361i −0.00990941 0.00572120i
\(429\) −1.93558 + 3.35252i −0.0934505 + 0.161861i
\(430\) −3.04482 1.20164i −0.146834 0.0579480i
\(431\) 9.19553 + 15.9271i 0.442933 + 0.767182i 0.997906 0.0646862i \(-0.0206046\pi\)
−0.554973 + 0.831869i \(0.687271\pi\)
\(432\) 0.866025 + 0.500000i 0.0416667 + 0.0240563i
\(433\) 15.3476i 0.737559i 0.929517 + 0.368780i \(0.120224\pi\)
−0.929517 + 0.368780i \(0.879776\pi\)
\(434\) 1.80924 0.0868461
\(435\) −8.29138 10.4374i −0.397541 0.500434i
\(436\) 6.79390 0.325369
\(437\) −18.6400 + 10.7618i −0.891674 + 0.514808i
\(438\) 5.73680i 0.274115i
\(439\) −4.20538 7.28393i −0.200712 0.347643i 0.748046 0.663647i \(-0.230992\pi\)
−0.948758 + 0.316004i \(0.897659\pi\)
\(440\) −1.94045 + 0.288735i −0.0925075 + 0.0137649i
\(441\) 2.95526 + 5.11867i 0.140727 + 0.243746i
\(442\) −19.6125 11.3233i −0.932872 0.538594i
\(443\) 25.4261i 1.20803i −0.796973 0.604014i \(-0.793567\pi\)
0.796973 0.604014i \(-0.206433\pi\)
\(444\) 3.02535 5.27705i 0.143577 0.250438i
\(445\) −31.7682 12.5373i −1.50596 0.594324i
\(446\) 10.9068 18.8911i 0.516450 0.894518i
\(447\) 9.08180 5.24338i 0.429555 0.248003i
\(448\) −0.903939 + 0.521889i −0.0427071 + 0.0246570i
\(449\) −1.18209 2.04745i −0.0557864 0.0966250i 0.836784 0.547534i \(-0.184433\pi\)
−0.892570 + 0.450909i \(0.851100\pi\)
\(450\) 3.41466 3.65241i 0.160969 0.172176i
\(451\) 2.74349 + 4.75186i 0.129186 + 0.223757i
\(452\) 10.8014i 0.508054i
\(453\) −2.84361 1.64176i −0.133604 0.0771365i
\(454\) −13.1563 −0.617458
\(455\) 9.57919 + 3.78041i 0.449079 + 0.177229i
\(456\) −1.51358 + 2.62160i −0.0708800 + 0.122768i
\(457\) −4.33201 + 2.50109i −0.202643 + 0.116996i −0.597888 0.801580i \(-0.703993\pi\)
0.395245 + 0.918576i \(0.370660\pi\)
\(458\) 15.5215i 0.725272i
\(459\) −2.56629 + 4.44494i −0.119784 + 0.207472i
\(460\) −9.88930 12.4489i −0.461091 0.580432i
\(461\) 3.31413 5.74025i 0.154355 0.267350i −0.778469 0.627683i \(-0.784004\pi\)
0.932824 + 0.360333i \(0.117337\pi\)
\(462\) −0.793072 + 0.457881i −0.0368971 + 0.0213025i
\(463\) −2.10365 + 1.21454i −0.0977651 + 0.0564447i −0.548085 0.836422i \(-0.684643\pi\)
0.450320 + 0.892867i \(0.351310\pi\)
\(464\) −2.98065 + 5.16264i −0.138373 + 0.239670i
\(465\) 2.41086 + 3.03485i 0.111801 + 0.140738i
\(466\) 10.4289 18.0634i 0.483109 0.836770i
\(467\) 10.9068i 0.504706i 0.967635 + 0.252353i \(0.0812045\pi\)
−0.967635 + 0.252353i \(0.918796\pi\)
\(468\) −3.82118 + 2.20616i −0.176634 + 0.101980i
\(469\) −1.39101 + 2.40929i −0.0642307 + 0.111251i
\(470\) −6.24090 2.46296i −0.287871 0.113608i
\(471\) −4.86115 −0.223990
\(472\) −7.48863 4.32356i −0.344692 0.199008i
\(473\) 1.28435i 0.0590543i
\(474\) 5.03878 + 8.72742i 0.231439 + 0.400864i
\(475\) 11.0564 + 10.3367i 0.507304 + 0.474282i
\(476\) −2.67864 4.63954i −0.122775 0.212653i
\(477\) −11.1687 + 6.44827i −0.511381 + 0.295246i
\(478\) −2.74024 + 1.58208i −0.125335 + 0.0723625i
\(479\) −9.06499 + 15.7010i −0.414190 + 0.717398i −0.995343 0.0963964i \(-0.969268\pi\)
0.581153 + 0.813794i \(0.302602\pi\)
\(480\) −2.07995 0.820851i −0.0949364 0.0374665i
\(481\) 13.4901 + 23.2024i 0.615098 + 1.05794i
\(482\) 6.68912i 0.304681i
\(483\) −6.42716 3.71072i −0.292446 0.168844i
\(484\) −5.11513 8.85966i −0.232506 0.402712i
\(485\) −20.0807 + 2.98796i −0.911816 + 0.135676i
\(486\) 0.500000 + 0.866025i 0.0226805 + 0.0392837i
\(487\) 26.7285i 1.21118i 0.795776 + 0.605591i \(0.207063\pi\)
−0.795776 + 0.605591i \(0.792937\pi\)
\(488\) 3.13192 1.80822i 0.141775 0.0818541i
\(489\) 21.0005 0.949675
\(490\) −8.22075 10.3485i −0.371376 0.467496i
\(491\) −35.4896 −1.60162 −0.800811 0.598917i \(-0.795598\pi\)
−0.800811 + 0.598917i \(0.795598\pi\)
\(492\) 6.25403i 0.281953i
\(493\) −26.4977 15.2984i −1.19339 0.689007i
\(494\) −6.67840 11.5673i −0.300476 0.520439i
\(495\) −1.82485 0.720175i −0.0820209 0.0323694i
\(496\) 0.866676 1.50113i 0.0389149 0.0674026i
\(497\) 1.05315 + 0.608036i 0.0472402 + 0.0272741i
\(498\) 9.72771 + 5.61630i 0.435909 + 0.251672i
\(499\) 4.80871 + 8.32892i 0.215267 + 0.372854i 0.953355 0.301851i \(-0.0976044\pi\)
−0.738088 + 0.674704i \(0.764271\pi\)
\(500\) −6.35026 + 9.20186i −0.283992 + 0.411519i
\(501\) 3.20622 5.55334i 0.143244 0.248105i
\(502\) 11.9007 + 6.87089i 0.531155 + 0.306663i
\(503\) −34.5034 19.9206i −1.53843 0.888214i −0.998931 0.0462284i \(-0.985280\pi\)
−0.539500 0.841985i \(-0.681387\pi\)
\(504\) −1.04378 −0.0464936
\(505\) −0.650557 4.37209i −0.0289494 0.194555i
\(506\) −3.11906 + 5.40237i −0.138659 + 0.240165i
\(507\) 6.46854i 0.287278i
\(508\) 3.42770i 0.152080i
\(509\) 0.416041 0.720604i 0.0184407 0.0319402i −0.856658 0.515885i \(-0.827463\pi\)
0.875098 + 0.483945i \(0.160796\pi\)
\(510\) 4.21308 10.6755i 0.186558 0.472720i
\(511\) 2.99397 + 5.18572i 0.132446 + 0.229403i
\(512\) 1.00000i 0.0441942i
\(513\) −2.62160 + 1.51358i −0.115747 + 0.0668263i
\(514\) 0.249162 + 0.431560i 0.0109900 + 0.0190353i
\(515\) 12.1314 1.80513i 0.534575 0.0795436i
\(516\) −0.731945 + 1.26777i −0.0322221 + 0.0558103i
\(517\) 2.63250i 0.115777i
\(518\) 0.0193044 + 6.34903i 0.000848189 + 0.278960i
\(519\) −0.386203 −0.0169525
\(520\) 7.72532 6.13694i 0.338778 0.269123i
\(521\) −14.0682 24.3668i −0.616337 1.06753i −0.990148 0.140022i \(-0.955283\pi\)
0.373811 0.927505i \(-0.378051\pi\)
\(522\) −5.16264 + 2.98065i −0.225963 + 0.130460i
\(523\) 3.62695 2.09402i 0.158595 0.0915651i −0.418602 0.908170i \(-0.637480\pi\)
0.577197 + 0.816605i \(0.304146\pi\)
\(524\) −18.7517 −0.819172
\(525\) −1.18049 + 5.08363i −0.0515209 + 0.221868i
\(526\) −23.1654 −1.01006
\(527\) 7.70466 + 4.44829i 0.335620 + 0.193770i
\(528\) 0.877352i 0.0381818i
\(529\) −27.5546 −1.19802
\(530\) 22.5800 17.9374i 0.980811 0.779150i
\(531\) −4.32356 7.48863i −0.187627 0.324979i
\(532\) 3.15969i 0.136990i
\(533\) −23.8977 13.7974i −1.03513 0.597630i
\(534\) −7.63676 + 13.2273i −0.330475 + 0.572400i
\(535\) 0.329249 + 0.414466i 0.0142347 + 0.0179189i
\(536\) 1.33266 + 2.30824i 0.0575623 + 0.0997008i
\(537\) −15.7137 + 9.07228i −0.678094 + 0.391498i
\(538\) −17.5583 10.1373i −0.756993 0.437050i
\(539\) −2.59280 + 4.49087i −0.111680 + 0.193435i
\(540\) −1.39087 1.75085i −0.0598534 0.0753448i
\(541\) 39.4818 1.69746 0.848728 0.528830i \(-0.177369\pi\)
0.848728 + 0.528830i \(0.177369\pi\)
\(542\) 17.9591 10.3687i 0.771408 0.445373i
\(543\) 5.09557 + 2.94193i 0.218672 + 0.126250i
\(544\) −5.13258 −0.220058
\(545\) −14.1310 5.57678i −0.605305 0.238883i
\(546\) 2.30274 3.98846i 0.0985482 0.170691i
\(547\) 22.8132i 0.975420i −0.873006 0.487710i \(-0.837832\pi\)
0.873006 0.487710i \(-0.162168\pi\)
\(548\) 17.8690 10.3167i 0.763325 0.440706i
\(549\) 3.61643 0.154346
\(550\) 4.27306 + 0.992267i 0.182204 + 0.0423104i
\(551\) −9.02292 15.6282i −0.384389 0.665782i
\(552\) −6.15759 + 3.55509i −0.262084 + 0.151315i
\(553\) −9.10949 5.25937i −0.387375 0.223651i
\(554\) −11.3805 −0.483510
\(555\) −10.6243 + 8.49265i −0.450975 + 0.360493i
\(556\) 6.08944 0.258250
\(557\) 4.86784 + 2.81045i 0.206257 + 0.119082i 0.599571 0.800322i \(-0.295338\pi\)
−0.393314 + 0.919404i \(0.628671\pi\)
\(558\) 1.50113 0.866676i 0.0635478 0.0366893i
\(559\) −3.22957 5.59379i −0.136596 0.236592i
\(560\) 2.30854 0.343506i 0.0975538 0.0145158i
\(561\) −4.50308 −0.190120
\(562\) −11.8602 + 6.84750i −0.500293 + 0.288844i
\(563\) 34.4290i 1.45101i 0.688218 + 0.725504i \(0.258393\pi\)
−0.688218 + 0.725504i \(0.741607\pi\)
\(564\) −1.50025 + 2.59851i −0.0631720 + 0.109417i
\(565\) 8.86632 22.4664i 0.373009 0.945167i
\(566\) −24.6124 −1.03454
\(567\) −0.903939 0.521889i −0.0379619 0.0219173i
\(568\) 1.00898 0.582533i 0.0423357 0.0244425i
\(569\) −45.5928 −1.91135 −0.955675 0.294423i \(-0.904872\pi\)
−0.955675 + 0.294423i \(0.904872\pi\)
\(570\) 5.30012 4.21038i 0.221998 0.176354i
\(571\) −8.56659 + 14.8378i −0.358501 + 0.620941i −0.987711 0.156294i \(-0.950045\pi\)
0.629210 + 0.777235i \(0.283379\pi\)
\(572\) −3.35252 1.93558i −0.140176 0.0809305i
\(573\) 10.3279 5.96283i 0.431455 0.249101i
\(574\) −3.26391 5.65326i −0.136233 0.235962i
\(575\) 10.3506 + 34.0107i 0.431650 + 1.41834i
\(576\) −0.500000 + 0.866025i −0.0208333 + 0.0360844i
\(577\) −18.3761 10.6094i −0.765006 0.441677i 0.0660839 0.997814i \(-0.478949\pi\)
−0.831090 + 0.556137i \(0.812283\pi\)
\(578\) 9.34338i 0.388633i
\(579\) 1.37271 + 2.37760i 0.0570479 + 0.0988099i
\(580\) 10.4374 8.29138i 0.433388 0.344281i
\(581\) −11.7243 −0.486408
\(582\) 9.07922i 0.376346i
\(583\) −9.79891 5.65740i −0.405829 0.234306i
\(584\) 5.73680 0.237390
\(585\) 9.75880 1.45209i 0.403477 0.0600365i
\(586\) −23.8197 −0.983984
\(587\) 1.16286 0.671378i 0.0479964 0.0277107i −0.475810 0.879548i \(-0.657845\pi\)
0.523806 + 0.851837i \(0.324512\pi\)
\(588\) −5.11867 + 2.95526i −0.211090 + 0.121873i
\(589\) 2.62357 + 4.54416i 0.108102 + 0.187239i
\(590\) 12.0270 + 15.1399i 0.495144 + 0.623298i
\(591\) 3.08949 0.127084
\(592\) 5.27705 + 3.02535i 0.216885 + 0.124341i
\(593\) 8.07531i 0.331613i 0.986158 + 0.165807i \(0.0530227\pi\)
−0.986158 + 0.165807i \(0.946977\pi\)
\(594\) −0.438676 + 0.759809i −0.0179991 + 0.0311753i
\(595\) 1.76307 + 11.8488i 0.0722790 + 0.485753i
\(596\) 5.24338 + 9.08180i 0.214777 + 0.372005i
\(597\) 18.8370 10.8755i 0.770946 0.445106i
\(598\) 31.3723i 1.28291i
\(599\) 2.05315 + 3.55616i 0.0838894 + 0.145301i 0.904917 0.425587i \(-0.139932\pi\)
−0.821028 + 0.570888i \(0.806599\pi\)
\(600\) 3.65241 + 3.41466i 0.149109 + 0.139403i
\(601\) 10.6565 18.4576i 0.434688 0.752902i −0.562582 0.826741i \(-0.690192\pi\)
0.997270 + 0.0738397i \(0.0235253\pi\)
\(602\) 1.52798i 0.0622757i
\(603\) 2.66533i 0.108541i
\(604\) 1.64176 2.84361i 0.0668022 0.115705i
\(605\) 3.36676 + 22.6264i 0.136878 + 0.919895i
\(606\) −1.97678 −0.0803013
\(607\) −17.5424 10.1281i −0.712025 0.411088i 0.0997855 0.995009i \(-0.468184\pi\)
−0.811810 + 0.583921i \(0.801518\pi\)
\(608\) −2.62160 1.51358i −0.106320 0.0613839i
\(609\) 3.11114 5.38865i 0.126070 0.218359i
\(610\) −7.99853 + 1.19016i −0.323851 + 0.0481883i
\(611\) −6.61958 11.4655i −0.267800 0.463843i
\(612\) −4.44494 2.56629i −0.179676 0.103736i
\(613\) −1.40671 0.812164i −0.0568165 0.0328030i 0.471323 0.881961i \(-0.343777\pi\)
−0.528139 + 0.849158i \(0.677110\pi\)
\(614\) 5.84373 10.1216i 0.235834 0.408476i
\(615\) 5.13362 13.0081i 0.207008 0.524536i
\(616\) −0.457881 0.793072i −0.0184485 0.0319538i
\(617\) 42.3655 + 24.4597i 1.70557 + 0.984712i 0.939882 + 0.341500i \(0.110935\pi\)
0.765689 + 0.643211i \(0.222398\pi\)
\(618\) 5.48507i 0.220642i
\(619\) 21.4035 0.860280 0.430140 0.902762i \(-0.358464\pi\)
0.430140 + 0.902762i \(0.358464\pi\)
\(620\) −3.03485 + 2.41086i −0.121882 + 0.0968226i
\(621\) −7.11017 −0.285321
\(622\) −16.7743 + 9.68464i −0.672588 + 0.388319i
\(623\) 15.9422i 0.638710i
\(624\) −2.20616 3.82118i −0.0883170 0.152970i
\(625\) 20.7616 13.9268i 0.830464 0.557072i
\(626\) −7.38454 12.7904i −0.295145 0.511207i
\(627\) −2.30007 1.32794i −0.0918558 0.0530330i
\(628\) 4.86115i 0.193981i
\(629\) −15.5279 + 27.0849i −0.619136 + 1.07994i
\(630\) 2.17101 + 0.856787i 0.0864951 + 0.0341352i
\(631\) −6.88944 + 11.9329i −0.274264 + 0.475040i −0.969949 0.243307i \(-0.921768\pi\)
0.695685 + 0.718347i \(0.255101\pi\)
\(632\) −8.72742 + 5.03878i −0.347158 + 0.200432i
\(633\) 20.3832 11.7682i 0.810158 0.467745i
\(634\) 3.10827 + 5.38368i 0.123445 + 0.213813i
\(635\) 2.81363 7.12946i 0.111656 0.282924i
\(636\) −6.44827 11.1687i −0.255691 0.442869i
\(637\) 26.0791i 1.03329i
\(638\) −4.52945 2.61508i −0.179323 0.103532i
\(639\) 1.16507 0.0460893
\(640\) 0.820851 2.07995i 0.0324470 0.0822174i
\(641\) 4.64508 8.04552i 0.183470 0.317779i −0.759590 0.650402i \(-0.774600\pi\)
0.943060 + 0.332623i \(0.107934\pi\)
\(642\) 0.205007 0.118361i 0.00809100 0.00467134i
\(643\) 50.2018i 1.97977i 0.141885 + 0.989883i \(0.454684\pi\)
−0.141885 + 0.989883i \(0.545316\pi\)
\(644\) 3.71072 6.42716i 0.146223 0.253266i
\(645\) 2.56306 2.03608i 0.100920 0.0801704i
\(646\) 7.76858 13.4556i 0.305651 0.529403i
\(647\) −12.4180 + 7.16955i −0.488203 + 0.281864i −0.723829 0.689980i \(-0.757619\pi\)
0.235626 + 0.971844i \(0.424286\pi\)
\(648\) −0.866025 + 0.500000i −0.0340207 + 0.0196419i
\(649\) 3.79329 6.57016i 0.148900 0.257902i
\(650\) −21.1058 + 6.42322i −0.827838 + 0.251939i
\(651\) −0.904618 + 1.56684i −0.0354548 + 0.0614095i
\(652\) 21.0005i 0.822443i
\(653\) 16.4993 9.52590i 0.645669 0.372777i −0.141126 0.989992i \(-0.545072\pi\)
0.786795 + 0.617214i \(0.211739\pi\)
\(654\) −3.39695 + 5.88369i −0.132831 + 0.230070i
\(655\) 39.0027 + 15.3924i 1.52396 + 0.601429i
\(656\) −6.25403 −0.244179
\(657\) 4.96821 + 2.86840i 0.193828 + 0.111907i
\(658\) 3.13186i 0.122093i
\(659\) −13.2234 22.9036i −0.515111 0.892199i −0.999846 0.0175378i \(-0.994417\pi\)
0.484735 0.874661i \(-0.338916\pi\)
\(660\) 0.720175 1.82485i 0.0280328 0.0710322i
\(661\) −7.69031 13.3200i −0.299119 0.518089i 0.676816 0.736152i \(-0.263359\pi\)
−0.975935 + 0.218064i \(0.930026\pi\)
\(662\) 20.0626 11.5832i 0.779756 0.450192i
\(663\) 19.6125 11.3233i 0.761687 0.439760i
\(664\) −5.61630 + 9.72771i −0.217955 + 0.377508i
\(665\) −2.59363 + 6.57201i −0.100577 + 0.254851i
\(666\) 3.05738 + 5.25856i 0.118471 + 0.203765i
\(667\) 42.3859i 1.64119i
\(668\) 5.55334 + 3.20622i 0.214865 + 0.124053i
\(669\) 10.9068 + 18.8911i 0.421680 + 0.730371i
\(670\) −0.877156 5.89495i −0.0338875 0.227742i
\(671\) 1.58644 + 2.74780i 0.0612439 + 0.106078i
\(672\) 1.04378i 0.0402646i
\(673\) 6.96587 4.02175i 0.268515 0.155027i −0.359698 0.933069i \(-0.617120\pi\)
0.628212 + 0.778042i \(0.283787\pi\)
\(674\) −11.7828 −0.453855
\(675\) 1.45575 + 4.78339i 0.0560317 + 0.184113i
\(676\) 6.46854 0.248790
\(677\) 8.07075i 0.310184i −0.987900 0.155092i \(-0.950433\pi\)
0.987900 0.155092i \(-0.0495674\pi\)
\(678\) −9.35427 5.40069i −0.359249 0.207412i
\(679\) −4.73835 8.20706i −0.181841 0.314958i
\(680\) 10.6755 + 4.21308i 0.409388 + 0.161564i
\(681\) 6.57817 11.3937i 0.252076 0.436609i
\(682\) 1.31702 + 0.760380i 0.0504312 + 0.0291164i
\(683\) −39.8914 23.0313i −1.52640 0.881269i −0.999509 0.0313372i \(-0.990023\pi\)
−0.526893 0.849931i \(-0.676643\pi\)
\(684\) −1.51358 2.62160i −0.0578733 0.100239i
\(685\) −45.6351 + 6.79040i −1.74363 + 0.259448i
\(686\) 6.73787 11.6703i 0.257253 0.445575i
\(687\) −13.4420 7.76074i −0.512844 0.296091i
\(688\) −1.26777 0.731945i −0.0483331 0.0279052i
\(689\) 56.9036 2.16786
\(690\) 15.7257 2.33995i 0.598667 0.0890804i
\(691\) 0.294937 0.510846i 0.0112199 0.0194335i −0.860361 0.509685i \(-0.829762\pi\)
0.871581 + 0.490252i \(0.163095\pi\)
\(692\) 0.386203i 0.0146813i
\(693\) 0.915761i 0.0347869i
\(694\) −10.3374 + 17.9049i −0.392403 + 0.679662i
\(695\) −12.6657 4.99852i −0.480439 0.189605i
\(696\) −2.98065 5.16264i −0.112981 0.195689i
\(697\) 32.0993i 1.21585i
\(698\) −15.7832 + 9.11242i −0.597402 + 0.344910i
\(699\) 10.4289 + 18.0634i 0.394457 + 0.683220i
\(700\) −5.08363 1.18049i −0.192143 0.0446184i
\(701\) 13.3161 23.0642i 0.502942 0.871121i −0.497052 0.867721i \(-0.665584\pi\)
0.999994 0.00340039i \(-0.00108238\pi\)
\(702\) 4.41232i 0.166532i
\(703\) −15.9185 + 9.25520i −0.600378 + 0.349067i
\(704\) −0.877352 −0.0330664
\(705\) 5.25344 4.17330i 0.197856 0.157176i
\(706\) 14.3304 + 24.8210i 0.539332 + 0.934151i
\(707\) 1.78689 1.03166i 0.0672030 0.0387997i
\(708\) 7.48863 4.32356i 0.281440 0.162489i
\(709\) 32.8494 1.23369 0.616843 0.787086i \(-0.288411\pi\)
0.616843 + 0.787086i \(0.288411\pi\)
\(710\) −2.57680 + 0.383422i −0.0967055 + 0.0143896i
\(711\) −10.0776 −0.377938
\(712\) −13.2273 7.63676i −0.495713 0.286200i
\(713\) 12.3244i 0.461554i
\(714\) 5.35728 0.200491
\(715\) 5.38426 + 6.77782i 0.201360 + 0.253476i
\(716\) −9.07228 15.7137i −0.339047 0.587247i
\(717\) 3.16415i 0.118167i
\(718\) −19.9689 11.5291i −0.745233 0.430260i
\(719\) 0.522177 0.904437i 0.0194739 0.0337298i −0.856124 0.516770i \(-0.827134\pi\)
0.875598 + 0.483040i \(0.160468\pi\)
\(720\) 1.75085 1.39087i 0.0652505 0.0518345i
\(721\) 2.86260 + 4.95817i 0.106609 + 0.184652i
\(722\) −8.51846 + 4.91814i −0.317024 + 0.183034i
\(723\) −5.79294 3.34456i −0.215442 0.124385i
\(724\) −2.94193 + 5.09557i −0.109336 + 0.189375i
\(725\) −28.5152 + 8.67815i −1.05903 + 0.322298i
\(726\) 10.2303 0.379680
\(727\) −4.42461 + 2.55455i −0.164100 + 0.0947430i −0.579801 0.814758i \(-0.696870\pi\)
0.415701 + 0.909501i \(0.363536\pi\)
\(728\) 3.98846 + 2.30274i 0.147822 + 0.0853453i
\(729\) −1.00000 −0.0370370
\(730\) −11.9323 4.70906i −0.441633 0.174290i
\(731\) 3.75677 6.50691i 0.138949 0.240667i
\(732\) 3.61643i 0.133667i
\(733\) 16.8016 9.70040i 0.620581 0.358293i −0.156514 0.987676i \(-0.550026\pi\)
0.777095 + 0.629383i \(0.216692\pi\)
\(734\) −26.3684 −0.973276
\(735\) 13.0724 1.94515i 0.482183 0.0717478i
\(736\) −3.55509 6.15759i −0.131042 0.226972i
\(737\) −2.02514 + 1.16921i −0.0745970 + 0.0430686i
\(738\) −5.41615 3.12701i −0.199371 0.115107i
\(739\) −10.0534 −0.369820 −0.184910 0.982755i \(-0.559199\pi\)
−0.184910 + 0.982755i \(0.559199\pi\)
\(740\) −8.49265 10.6243i −0.312196 0.390555i
\(741\) 13.3568 0.490675
\(742\) 11.6577 + 6.73057i 0.427967 + 0.247087i
\(743\) 9.28566 5.36108i 0.340658 0.196679i −0.319905 0.947450i \(-0.603651\pi\)
0.660563 + 0.750771i \(0.270318\pi\)
\(744\) 0.866676 + 1.50113i 0.0317739 + 0.0550340i
\(745\) −3.45118 23.1938i −0.126442 0.849754i
\(746\) −27.3208 −1.00028
\(747\) −9.72771 + 5.61630i −0.355918 + 0.205490i
\(748\) 4.50308i 0.164649i
\(749\) −0.123543 + 0.213982i −0.00451416 + 0.00781875i
\(750\) −4.79391 10.1004i −0.175049 0.368815i
\(751\) −32.1895 −1.17461 −0.587306 0.809365i \(-0.699812\pi\)
−0.587306 + 0.809365i \(0.699812\pi\)
\(752\) −2.59851 1.50025i −0.0947579 0.0547085i
\(753\) −11.9007 + 6.87089i −0.433686 + 0.250389i
\(754\) 26.3032 0.957905
\(755\) −5.74896 + 4.56693i −0.209226 + 0.166208i
\(756\) 0.521889 0.903939i 0.0189809 0.0328759i
\(757\) 7.21272 + 4.16427i 0.262151 + 0.151353i 0.625315 0.780372i \(-0.284970\pi\)
−0.363165 + 0.931725i \(0.618304\pi\)
\(758\) −4.29231 + 2.47817i −0.155904 + 0.0900110i
\(759\) −3.11906 5.40237i −0.113215 0.196094i
\(760\) 4.21038 + 5.30012i 0.152727 + 0.192256i
\(761\) −23.8904 + 41.3795i −0.866028 + 1.50000i −5.16912e−6 1.00000i \(0.500002\pi\)
−0.866023 + 0.500004i \(0.833332\pi\)
\(762\) −2.96848 1.71385i −0.107537 0.0620863i
\(763\) 7.09133i 0.256723i
\(764\) 5.96283 + 10.3279i 0.215728 + 0.373651i
\(765\) 7.13873 + 8.98640i 0.258102 + 0.324904i
\(766\) 34.9874 1.26415
\(767\) 38.1539i 1.37766i
\(768\) −0.866025 0.500000i −0.0312500 0.0180422i
\(769\) −13.1836 −0.475414 −0.237707 0.971337i \(-0.576396\pi\)
−0.237707 + 0.971337i \(0.576396\pi\)
\(770\) 0.301376 + 2.02540i 0.0108608 + 0.0729905i
\(771\) −0.498323 −0.0179467
\(772\) −2.37760 + 1.37271i −0.0855719 + 0.0494049i
\(773\) −25.6873 + 14.8306i −0.923908 + 0.533419i −0.884880 0.465819i \(-0.845760\pi\)
−0.0390284 + 0.999238i \(0.512426\pi\)
\(774\) −0.731945 1.26777i −0.0263092 0.0455689i
\(775\) 8.29130 2.52332i 0.297832 0.0906404i
\(776\) −9.07922 −0.325925
\(777\) −5.50807 3.15780i −0.197601 0.113285i
\(778\) 33.0443i 1.18470i
\(779\) 9.46598 16.3956i 0.339154 0.587432i
\(780\) 1.45209 + 9.75880i 0.0519931 + 0.349421i
\(781\) 0.511086 + 0.885228i 0.0182881 + 0.0316759i
\(782\) 31.6043 18.2468i 1.13017 0.652503i
\(783\) 5.96130i 0.213040i
\(784\) −2.95526 5.11867i −0.105545 0.182809i
\(785\) −3.99027 + 10.1110i −0.142419 + 0.360875i
\(786\) 9.37585 16.2395i 0.334426 0.579242i
\(787\) 46.8019i 1.66831i 0.551533 + 0.834153i \(0.314043\pi\)
−0.551533 + 0.834153i \(0.685957\pi\)
\(788\) 3.08949i 0.110058i
\(789\) 11.5827 20.0619i 0.412356 0.714221i
\(790\) 22.2887 3.31651i 0.792996 0.117996i
\(791\) 11.2743 0.400866
\(792\) −0.759809 0.438676i −0.0269986 0.0155877i
\(793\) −13.8190 7.97842i −0.490728 0.283322i
\(794\) −8.71821 + 15.1004i −0.309398 + 0.535892i
\(795\) 4.24424 + 28.5235i 0.150528 + 1.01162i
\(796\) 10.8755 + 18.8370i 0.385473 + 0.667659i
\(797\) 20.7986 + 12.0081i 0.736726 + 0.425349i 0.820878 0.571104i \(-0.193485\pi\)
−0.0841519 + 0.996453i \(0.526818\pi\)
\(798\) 2.73637 + 1.57985i 0.0968665 + 0.0559259i
\(799\) 7.70016 13.3371i 0.272412 0.471831i
\(800\) −3.41466 + 3.65241i −0.120727 + 0.129132i
\(801\) −7.63676 13.2273i −0.269832 0.467362i
\(802\) 22.1715 + 12.8007i 0.782902 + 0.452009i
\(803\) 5.03319i 0.177617i
\(804\) −2.66533 −0.0939988
\(805\) −12.9939 + 10.3222i −0.457974 + 0.363811i
\(806\) −7.64810 −0.269393
\(807\) 17.5583 10.1373i 0.618083 0.356850i
\(808\) 1.97678i 0.0695430i
\(809\) 21.6639 + 37.5229i 0.761661 + 1.31923i 0.941994 + 0.335629i \(0.108949\pi\)
−0.180334 + 0.983606i \(0.557718\pi\)
\(810\) 2.21172 0.329099i 0.0777118 0.0115634i
\(811\) 21.8114 + 37.7784i 0.765902 + 1.32658i 0.939769 + 0.341811i \(0.111040\pi\)
−0.173867 + 0.984769i \(0.555626\pi\)
\(812\) 5.38865 + 3.11114i 0.189105 + 0.109180i
\(813\) 20.7374i 0.727291i
\(814\) −2.65430 + 4.62983i −0.0930330 + 0.162275i
\(815\) 17.2383 43.6800i 0.603830 1.53004i
\(816\) 2.56629 4.44494i 0.0898381 0.155604i
\(817\) 3.83774 2.21572i 0.134265 0.0775182i
\(818\) 6.18298 3.56975i 0.216183 0.124813i
\(819\) 2.30274 + 3.98846i 0.0804643 + 0.139368i
\(820\) 13.0081 + 5.13362i 0.454262 + 0.179274i
\(821\) 3.25519 + 5.63816i 0.113607 + 0.196773i 0.917222 0.398376i \(-0.130426\pi\)
−0.803615 + 0.595149i \(0.797093\pi\)
\(822\) 20.6333i 0.719670i
\(823\) −30.7094 17.7301i −1.07046 0.618031i −0.142154 0.989845i \(-0.545403\pi\)
−0.928307 + 0.371814i \(0.878736\pi\)
\(824\) 5.48507 0.191082
\(825\) −2.99586 + 3.20445i −0.104302 + 0.111564i
\(826\) −4.51284 + 7.81648i −0.157022 + 0.271970i
\(827\) −12.9493 + 7.47628i −0.450291 + 0.259976i −0.707953 0.706259i \(-0.750381\pi\)
0.257662 + 0.966235i \(0.417048\pi\)
\(828\) 7.11017i 0.247096i
\(829\) 24.1406 41.8128i 0.838439 1.45222i −0.0527599 0.998607i \(-0.516802\pi\)
0.891199 0.453612i \(-0.149865\pi\)
\(830\) 19.6666 15.6230i 0.682639 0.542284i
\(831\) 5.69024 9.85578i 0.197392 0.341893i
\(832\) 3.82118 2.20616i 0.132476 0.0764848i
\(833\) 26.2720 15.1681i 0.910270 0.525544i
\(834\) −3.04472 + 5.27361i −0.105430 + 0.182610i
\(835\) −8.91886 11.2273i −0.308650 0.388535i
\(836\) 1.32794 2.30007i 0.0459279 0.0795495i
\(837\) 1.73335i 0.0599134i
\(838\) 18.8507 10.8835i 0.651188 0.375964i
\(839\) −14.8588 + 25.7363i −0.512984 + 0.888514i 0.486903 + 0.873456i \(0.338127\pi\)
−0.999887 + 0.0150581i \(0.995207\pi\)
\(840\) −0.856787 + 2.17101i −0.0295619 + 0.0749070i
\(841\) 6.53714 0.225419
\(842\) −27.6754 15.9784i −0.953756 0.550651i
\(843\) 13.6950i 0.471681i
\(844\) 11.7682 + 20.3832i 0.405079 + 0.701617i
\(845\) −13.4543 5.30970i −0.462840 0.182659i
\(846\) −1.50025 2.59851i −0.0515797 0.0893386i
\(847\) −9.24753 + 5.33906i −0.317749 + 0.183452i
\(848\) 11.1687 6.44827i 0.383536 0.221435i
\(849\) 12.3062 21.3150i 0.422348 0.731527i
\(850\) −18.7463 17.5260i −0.642992 0.601138i
\(851\) −43.2493 + 0.131501i −1.48257 + 0.00450780i
\(852\) 1.16507i 0.0399145i
\(853\) −0.910252 0.525534i −0.0311664 0.0179940i 0.484336 0.874882i \(-0.339061\pi\)
−0.515502 + 0.856888i \(0.672395\pi\)
\(854\) −1.88738 3.26903i −0.0645847 0.111864i
\(855\) 0.996236 + 6.69523i 0.0340706 + 0.228972i
\(856\) 0.118361 + 0.205007i 0.00404550 + 0.00700701i
\(857\) 30.7011i 1.04873i 0.851493 + 0.524365i \(0.175697\pi\)
−0.851493 + 0.524365i \(0.824303\pi\)
\(858\) 3.35252 1.93558i 0.114453 0.0660795i
\(859\) 31.0164 1.05827 0.529133 0.848539i \(-0.322517\pi\)
0.529133 + 0.848539i \(0.322517\pi\)
\(860\) 2.03608 + 2.56306i 0.0694296 + 0.0873996i
\(861\) 6.52782 0.222467
\(862\) 18.3911i 0.626402i
\(863\) 24.2054 + 13.9750i 0.823962 + 0.475715i 0.851781 0.523898i \(-0.175523\pi\)
−0.0278186 + 0.999613i \(0.508856\pi\)
\(864\) −0.500000 0.866025i −0.0170103 0.0294628i
\(865\) −0.317015 + 0.803285i −0.0107788 + 0.0273125i
\(866\) 7.67381 13.2914i 0.260767 0.451661i
\(867\) 8.09161 + 4.67169i 0.274805 + 0.158659i
\(868\) −1.56684 0.904618i −0.0531822 0.0307047i
\(869\) −4.42078 7.65701i −0.149965 0.259746i
\(870\) 1.96186 + 13.1847i 0.0665132 + 0.447004i
\(871\) 5.88013 10.1847i 0.199241 0.345095i
\(872\) −5.88369 3.39695i −0.199247 0.115035i
\(873\) −7.86284 4.53961i −0.266117 0.153643i
\(874\) 21.5237 0.728049
\(875\) 9.60470 + 6.62827i 0.324698 + 0.224076i
\(876\) −2.86840 + 4.96821i −0.0969142 + 0.167860i
\(877\) 20.1349i 0.679908i 0.940442 + 0.339954i \(0.110412\pi\)
−0.940442 + 0.339954i \(0.889588\pi\)
\(878\) 8.41076i 0.283849i
\(879\) 11.9099 20.6285i 0.401710 0.695782i
\(880\) 1.82485 + 0.720175i 0.0615157 + 0.0242771i
\(881\) 22.8164 + 39.5191i 0.768703 + 1.33143i 0.938266 + 0.345914i \(0.112431\pi\)
−0.169563 + 0.985519i \(0.554236\pi\)
\(882\) 5.91053i 0.199018i
\(883\) 13.5576 7.82751i 0.456251 0.263417i −0.254215 0.967148i \(-0.581817\pi\)
0.710467 + 0.703731i \(0.248484\pi\)
\(884\) 11.3233 + 19.6125i 0.380843 + 0.659640i
\(885\) −19.1250 + 2.84576i −0.642880 + 0.0956592i
\(886\) −12.7130 + 22.0196i −0.427103 + 0.739763i
\(887\) 33.8991i 1.13822i 0.822261 + 0.569111i \(0.192712\pi\)
−0.822261 + 0.569111i \(0.807288\pi\)
\(888\) −5.25856 + 3.05738i −0.176466 + 0.102599i
\(889\) 3.57776 0.119994
\(890\) 21.2434 + 26.7417i 0.712082 + 0.896384i
\(891\) −0.438676 0.759809i −0.0146962 0.0254546i
\(892\) −18.8911 + 10.9068i −0.632520 + 0.365185i
\(893\) 7.86612 4.54151i 0.263230 0.151976i
\(894\) −10.4868 −0.350730
\(895\) 5.97136 + 40.1307i 0.199600 + 1.34142i
\(896\) 1.04378 0.0348702
\(897\) 27.1692 + 15.6862i 0.907154 + 0.523746i
\(898\) 2.36419i 0.0788939i
\(899\) −10.3330 −0.344626
\(900\) −4.78339 + 1.45575i −0.159446 + 0.0485249i
\(901\) 33.0963 + 57.3244i 1.10260 + 1.90975i
\(902\) 5.48698i 0.182696i
\(903\) 1.32327 + 0.763989i 0.0440356 + 0.0254240i
\(904\) 5.40069 9.35427i 0.179624 0.311118i
\(905\) 10.3018 8.18365i 0.342442 0.272034i
\(906\) 1.64176 + 2.84361i 0.0545438 + 0.0944725i
\(907\) −35.3558 + 20.4127i −1.17397 + 0.677791i −0.954612 0.297853i \(-0.903729\pi\)
−0.219357 + 0.975645i \(0.570396\pi\)
\(908\) 11.3937 + 6.57817i 0.378114 + 0.218304i
\(909\) 0.988392 1.71194i 0.0327829 0.0567816i
\(910\) −6.40561 8.06353i −0.212344 0.267303i
\(911\) −37.9616 −1.25772 −0.628862 0.777517i \(-0.716479\pi\)
−0.628862 + 0.777517i \(0.716479\pi\)
\(912\) 2.62160 1.51358i 0.0868099 0.0501197i
\(913\) −8.53462 4.92747i −0.282455 0.163075i
\(914\) 5.00217 0.165457
\(915\) 2.96855 7.52201i 0.0981373 0.248670i
\(916\) 7.76074 13.4420i 0.256422 0.444136i
\(917\) 19.5726i 0.646345i
\(918\) 4.44494 2.56629i 0.146705 0.0847002i
\(919\) −18.1870 −0.599932 −0.299966 0.953950i \(-0.596975\pi\)
−0.299966 + 0.953950i \(0.596975\pi\)
\(920\) 2.33995 + 15.7257i 0.0771459 + 0.518461i
\(921\) 5.84373 + 10.1216i 0.192558 + 0.333520i
\(922\) −5.74025 + 3.31413i −0.189045 + 0.109145i
\(923\) −4.45193 2.57032i −0.146537 0.0846031i
\(924\) 0.915761 0.0301263
\(925\) 8.94339 + 29.0692i 0.294057 + 0.955788i
\(926\) 2.42909 0.0798248
\(927\) 4.75021 + 2.74254i 0.156017 + 0.0900767i
\(928\) 5.16264 2.98065i 0.169472 0.0978447i
\(929\) −14.4907 25.0986i −0.475424 0.823459i 0.524180 0.851608i \(-0.324372\pi\)
−0.999604 + 0.0281490i \(0.991039\pi\)
\(930\) −0.570444 3.83369i −0.0187056 0.125712i
\(931\) 17.8921 0.586391
\(932\) −18.0634 + 10.4289i −0.591686 + 0.341610i
\(933\) 19.3693i 0.634122i
\(934\) 5.45340 9.44556i 0.178441 0.309068i
\(935\) −3.69635 + 9.36619i −0.120884 + 0.306307i
\(936\) 4.41232 0.144221
\(937\) 4.53863 + 2.62038i 0.148271 + 0.0856041i 0.572300 0.820044i \(-0.306051\pi\)
−0.424029 + 0.905648i \(0.639385\pi\)
\(938\) 2.40929 1.39101i 0.0786662 0.0454180i
\(939\) 14.7691 0.481970
\(940\) 4.17330 + 5.25344i 0.136118 + 0.171348i
\(941\) 14.7595 25.5641i 0.481145 0.833367i −0.518621 0.855004i \(-0.673554\pi\)
0.999766 + 0.0216370i \(0.00688782\pi\)
\(942\) 4.20988 + 2.43057i 0.137165 + 0.0791923i
\(943\) 38.5097 22.2336i 1.25405 0.724026i
\(944\) 4.32356 + 7.48863i 0.140720 + 0.243734i
\(945\) −1.82750 + 1.45176i −0.0594487 + 0.0472257i
\(946\) 0.642173 1.11228i 0.0208789 0.0361632i
\(947\) −12.2476 7.07114i −0.397992 0.229781i 0.287625 0.957743i \(-0.407134\pi\)
−0.685617 + 0.727962i \(0.740468\pi\)
\(948\) 10.0776i 0.327304i
\(949\) −12.6563 21.9213i −0.410840 0.711596i
\(950\) −4.40679 14.4801i −0.142975 0.469797i
\(951\) −6.21654 −0.201585
\(952\) 5.35728i 0.173630i
\(953\) 49.4257 + 28.5359i 1.60105 + 0.924369i 0.991277 + 0.131796i \(0.0420744\pi\)
0.609777 + 0.792573i \(0.291259\pi\)
\(954\) 12.8965 0.417541
\(955\) −3.92472 26.3762i −0.127001 0.853514i
\(956\) 3.16415 0.102336
\(957\) 4.52945 2.61508i 0.146416 0.0845335i
\(958\) 15.7010 9.06499i 0.507277 0.292876i
\(959\) −10.7683 18.6513i −0.347727 0.602281i
\(960\) 1.39087 + 1.75085i 0.0448900 + 0.0565086i
\(961\) −27.9955 −0.903080
\(962\) −0.0816048 26.8389i −0.00263104 0.865322i
\(963\) 0.236722i 0.00762827i
\(964\) 3.34456 5.79294i 0.107721 0.186578i
\(965\) 6.07210 0.903515i 0.195468 0.0290852i
\(966\) 3.71072 + 6.42716i 0.119391 + 0.206791i
\(967\) 9.29892 5.36874i 0.299033 0.172647i −0.342975 0.939344i \(-0.611435\pi\)
0.642008 + 0.766698i \(0.278101\pi\)
\(968\) 10.2303i 0.328813i
\(969\) 7.76858 + 13.4556i 0.249563 + 0.432255i
\(970\) 18.8844 + 7.45269i 0.606340 + 0.239291i
\(971\) 15.9497 27.6258i 0.511852 0.886553i −0.488054 0.872813i \(-0.662293\pi\)
0.999906 0.0137397i \(-0.00437361\pi\)
\(972\) 1.00000i 0.0320750i
\(973\) 6.35603i 0.203765i
\(974\) 13.3642 23.1475i 0.428218 0.741695i
\(975\) 4.99024 21.4898i 0.159816 0.688224i
\(976\) −3.61643 −0.115759
\(977\) −31.3706 18.1118i −1.00363 0.579449i −0.0943128 0.995543i \(-0.530065\pi\)
−0.909322 + 0.416094i \(0.863399\pi\)
\(978\) −18.1870 10.5002i −0.581555 0.335761i
\(979\) 6.70013 11.6050i 0.214137 0.370896i
\(980\) 1.94515 + 13.0724i 0.0621354 + 0.417583i
\(981\) −3.39695 5.88369i −0.108456 0.187852i
\(982\) 30.7349 + 17.7448i 0.980789 + 0.566259i
\(983\) 23.8412 + 13.7647i 0.760415 + 0.439026i 0.829445 0.558589i \(-0.188657\pi\)
−0.0690299 + 0.997615i \(0.521990\pi\)
\(984\) 3.12701 5.41615i 0.0996855 0.172660i
\(985\) 2.53601 6.42599i 0.0808039 0.204749i
\(986\) 15.2984 + 26.4977i 0.487201 + 0.843858i
\(987\) 2.71227 + 1.56593i 0.0863325 + 0.0498441i
\(988\) 13.3568i 0.424937i
\(989\) 10.4085 0.330972
\(990\) 1.22028 + 1.53611i 0.0387830 + 0.0488209i
\(991\) −14.9113 −0.473673 −0.236836 0.971550i \(-0.576111\pi\)
−0.236836 + 0.971550i \(0.576111\pi\)
\(992\) −1.50113 + 0.866676i −0.0476608 + 0.0275170i
\(993\) 23.1663i 0.735161i
\(994\) −0.608036 1.05315i −0.0192857 0.0334038i
\(995\) −7.15825 48.1072i −0.226932 1.52510i
\(996\) −5.61630 9.72771i −0.177959 0.308234i
\(997\) 4.22014 + 2.43650i 0.133653 + 0.0771647i 0.565336 0.824861i \(-0.308747\pi\)
−0.431683 + 0.902026i \(0.642080\pi\)
\(998\) 9.61741i 0.304434i
\(999\) −6.08273 + 0.0184948i −0.192449 + 0.000585148i
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 1110.2.bb.e.1009.6 40
5.4 even 2 inner 1110.2.bb.e.1009.15 yes 40
37.26 even 3 inner 1110.2.bb.e.1099.15 yes 40
185.174 even 6 inner 1110.2.bb.e.1099.6 yes 40
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1110.2.bb.e.1009.6 40 1.1 even 1 trivial
1110.2.bb.e.1009.15 yes 40 5.4 even 2 inner
1110.2.bb.e.1099.6 yes 40 185.174 even 6 inner
1110.2.bb.e.1099.15 yes 40 37.26 even 3 inner