Properties

Label 930.2.s.c.439.10
Level $930$
Weight $2$
Character 930.439
Analytic conductor $7.426$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [930,2,Mod(439,930)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(930, 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("930.439");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 930.s (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: \(7.42608738798\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 439.10
Character \(\chi\) \(=\) 930.439
Dual form 930.2.s.c.769.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000i q^{2} +(0.866025 + 0.500000i) q^{3} -1.00000 q^{4} +(0.981775 + 2.00901i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(0.669647 + 0.386621i) q^{7} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+1.00000i q^{2} +(0.866025 + 0.500000i) q^{3} -1.00000 q^{4} +(0.981775 + 2.00901i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(0.669647 + 0.386621i) q^{7} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(-2.00901 + 0.981775i) q^{10} +(0.0912000 + 0.157963i) q^{11} +(-0.866025 - 0.500000i) q^{12} +(3.35207 - 1.93532i) q^{13} +(-0.386621 + 0.669647i) q^{14} +(-0.154263 + 2.23074i) q^{15} +1.00000 q^{16} +(5.39463 + 3.11459i) q^{17} +(-0.866025 + 0.500000i) q^{18} +(-0.298547 + 0.517099i) q^{19} +(-0.981775 - 2.00901i) q^{20} +(0.386621 + 0.669647i) q^{21} +(-0.157963 + 0.0912000i) q^{22} +3.42650i q^{23} +(0.500000 - 0.866025i) q^{24} +(-3.07224 + 3.94479i) q^{25} +(1.93532 + 3.35207i) q^{26} +1.00000i q^{27} +(-0.669647 - 0.386621i) q^{28} -7.12532 q^{29} +(-2.23074 - 0.154263i) q^{30} +(-4.63168 - 3.08991i) q^{31} +1.00000i q^{32} +0.182400i q^{33} +(-3.11459 + 5.39463i) q^{34} +(-0.119282 + 1.72490i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(5.54979 + 3.20418i) q^{37} +(-0.517099 - 0.298547i) q^{38} +3.87064 q^{39} +(2.00901 - 0.981775i) q^{40} +(0.930631 + 1.61190i) q^{41} +(-0.669647 + 0.386621i) q^{42} +(-5.78617 - 3.34064i) q^{43} +(-0.0912000 - 0.157963i) q^{44} +(-1.24897 + 1.85475i) q^{45} -3.42650 q^{46} -6.17291i q^{47} +(0.866025 + 0.500000i) q^{48} +(-3.20105 - 5.54438i) q^{49} +(-3.94479 - 3.07224i) q^{50} +(3.11459 + 5.39463i) q^{51} +(-3.35207 + 1.93532i) q^{52} +(7.49604 - 4.32784i) q^{53} -1.00000 q^{54} +(-0.227811 + 0.338306i) q^{55} +(0.386621 - 0.669647i) q^{56} +(-0.517099 + 0.298547i) q^{57} -7.12532i q^{58} +(-6.03735 + 10.4570i) q^{59} +(0.154263 - 2.23074i) q^{60} +0.975597 q^{61} +(3.08991 - 4.63168i) q^{62} +0.773241i q^{63} -1.00000 q^{64} +(7.17906 + 4.83430i) q^{65} -0.182400 q^{66} +(0.371098 - 0.214254i) q^{67} +(-5.39463 - 3.11459i) q^{68} +(-1.71325 + 2.96744i) q^{69} +(-1.72490 - 0.119282i) q^{70} +(4.02888 + 6.97823i) q^{71} +(0.866025 - 0.500000i) q^{72} +(-9.05991 + 5.23074i) q^{73} +(-3.20418 + 5.54979i) q^{74} +(-4.63303 + 1.88017i) q^{75} +(0.298547 - 0.517099i) q^{76} +0.141039i q^{77} +3.87064i q^{78} +(3.64065 - 6.30578i) q^{79} +(0.981775 + 2.00901i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-1.61190 + 0.930631i) q^{82} +(6.97624 - 4.02773i) q^{83} +(-0.386621 - 0.669647i) q^{84} +(-0.960930 + 13.8957i) q^{85} +(3.34064 - 5.78617i) q^{86} +(-6.17071 - 3.56266i) q^{87} +(0.157963 - 0.0912000i) q^{88} -0.839983 q^{89} +(-1.85475 - 1.24897i) q^{90} +2.99294 q^{91} -3.42650i q^{92} +(-2.46620 - 4.99178i) q^{93} +6.17291 q^{94} +(-1.33196 - 0.0921094i) q^{95} +(-0.500000 + 0.866025i) q^{96} -9.51682i q^{97} +(5.54438 - 3.20105i) q^{98} +(-0.0912000 + 0.157963i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q - 24 q^{4} + 4 q^{5} - 12 q^{6} + 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 24 q - 24 q^{4} + 4 q^{5} - 12 q^{6} + 12 q^{9} - 4 q^{11} + 12 q^{14} + 24 q^{16} - 4 q^{19} - 4 q^{20} - 12 q^{21} + 12 q^{24} - 4 q^{25} + 16 q^{26} + 32 q^{29} - 8 q^{30} + 24 q^{31} - 20 q^{34} + 48 q^{35} - 12 q^{36} + 32 q^{39} - 12 q^{41} + 4 q^{44} - 4 q^{45} + 56 q^{46} + 24 q^{49} - 16 q^{50} + 20 q^{51} - 24 q^{54} + 36 q^{55} - 12 q^{56} - 4 q^{59} - 40 q^{61} - 24 q^{64} - 4 q^{65} + 8 q^{66} + 28 q^{69} - 32 q^{70} - 56 q^{71} + 12 q^{74} + 16 q^{75} + 4 q^{76} - 72 q^{79} + 4 q^{80} - 12 q^{81} + 12 q^{84} + 40 q^{85} - 24 q^{86} + 128 q^{89} - 160 q^{91} + 56 q^{94} - 56 q^{95} - 12 q^{96} + 4 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/930\mathbb{Z}\right)^\times\).

\(n\) \(187\) \(311\) \(871\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) 0.866025 + 0.500000i 0.500000 + 0.288675i
\(4\) −1.00000 −0.500000
\(5\) 0.981775 + 2.00901i 0.439063 + 0.898456i
\(6\) −0.500000 + 0.866025i −0.204124 + 0.353553i
\(7\) 0.669647 + 0.386621i 0.253103 + 0.146129i 0.621184 0.783665i \(-0.286652\pi\)
−0.368081 + 0.929794i \(0.619985\pi\)
\(8\) 1.00000i 0.353553i
\(9\) 0.500000 + 0.866025i 0.166667 + 0.288675i
\(10\) −2.00901 + 0.981775i −0.635304 + 0.310464i
\(11\) 0.0912000 + 0.157963i 0.0274978 + 0.0476277i 0.879447 0.475997i \(-0.157913\pi\)
−0.851949 + 0.523625i \(0.824579\pi\)
\(12\) −0.866025 0.500000i −0.250000 0.144338i
\(13\) 3.35207 1.93532i 0.929698 0.536761i 0.0429816 0.999076i \(-0.486314\pi\)
0.886716 + 0.462315i \(0.152981\pi\)
\(14\) −0.386621 + 0.669647i −0.103329 + 0.178971i
\(15\) −0.154263 + 2.23074i −0.0398304 + 0.575975i
\(16\) 1.00000 0.250000
\(17\) 5.39463 + 3.11459i 1.30839 + 0.755400i 0.981828 0.189776i \(-0.0607760\pi\)
0.326563 + 0.945175i \(0.394109\pi\)
\(18\) −0.866025 + 0.500000i −0.204124 + 0.117851i
\(19\) −0.298547 + 0.517099i −0.0684915 + 0.118631i −0.898237 0.439511i \(-0.855152\pi\)
0.829746 + 0.558141i \(0.188485\pi\)
\(20\) −0.981775 2.00901i −0.219532 0.449228i
\(21\) 0.386621 + 0.669647i 0.0843676 + 0.146129i
\(22\) −0.157963 + 0.0912000i −0.0336778 + 0.0194439i
\(23\) 3.42650i 0.714475i 0.934014 + 0.357237i \(0.116281\pi\)
−0.934014 + 0.357237i \(0.883719\pi\)
\(24\) 0.500000 0.866025i 0.102062 0.176777i
\(25\) −3.07224 + 3.94479i −0.614447 + 0.788958i
\(26\) 1.93532 + 3.35207i 0.379547 + 0.657395i
\(27\) 1.00000i 0.192450i
\(28\) −0.669647 0.386621i −0.126551 0.0730645i
\(29\) −7.12532 −1.32314 −0.661569 0.749884i \(-0.730109\pi\)
−0.661569 + 0.749884i \(0.730109\pi\)
\(30\) −2.23074 0.154263i −0.407276 0.0281644i
\(31\) −4.63168 3.08991i −0.831874 0.554964i
\(32\) 1.00000i 0.176777i
\(33\) 0.182400i 0.0317518i
\(34\) −3.11459 + 5.39463i −0.534148 + 0.925172i
\(35\) −0.119282 + 1.72490i −0.0201624 + 0.291561i
\(36\) −0.500000 0.866025i −0.0833333 0.144338i
\(37\) 5.54979 + 3.20418i 0.912381 + 0.526763i 0.881196 0.472750i \(-0.156739\pi\)
0.0311843 + 0.999514i \(0.490072\pi\)
\(38\) −0.517099 0.298547i −0.0838846 0.0484308i
\(39\) 3.87064 0.619798
\(40\) 2.00901 0.981775i 0.317652 0.155232i
\(41\) 0.930631 + 1.61190i 0.145340 + 0.251736i 0.929500 0.368823i \(-0.120239\pi\)
−0.784160 + 0.620559i \(0.786906\pi\)
\(42\) −0.669647 + 0.386621i −0.103329 + 0.0596569i
\(43\) −5.78617 3.34064i −0.882382 0.509444i −0.0109390 0.999940i \(-0.503482\pi\)
−0.871443 + 0.490497i \(0.836815\pi\)
\(44\) −0.0912000 0.157963i −0.0137489 0.0238138i
\(45\) −1.24897 + 1.85475i −0.186185 + 0.276489i
\(46\) −3.42650 −0.505210
\(47\) 6.17291i 0.900412i −0.892925 0.450206i \(-0.851351\pi\)
0.892925 0.450206i \(-0.148649\pi\)
\(48\) 0.866025 + 0.500000i 0.125000 + 0.0721688i
\(49\) −3.20105 5.54438i −0.457293 0.792054i
\(50\) −3.94479 3.07224i −0.557878 0.434480i
\(51\) 3.11459 + 5.39463i 0.436130 + 0.755400i
\(52\) −3.35207 + 1.93532i −0.464849 + 0.268381i
\(53\) 7.49604 4.32784i 1.02966 0.594475i 0.112773 0.993621i \(-0.464027\pi\)
0.916888 + 0.399146i \(0.130693\pi\)
\(54\) −1.00000 −0.136083
\(55\) −0.227811 + 0.338306i −0.0307181 + 0.0456172i
\(56\) 0.386621 0.669647i 0.0516644 0.0894853i
\(57\) −0.517099 + 0.298547i −0.0684915 + 0.0395436i
\(58\) 7.12532i 0.935600i
\(59\) −6.03735 + 10.4570i −0.785996 + 1.36139i 0.142406 + 0.989808i \(0.454516\pi\)
−0.928402 + 0.371577i \(0.878817\pi\)
\(60\) 0.154263 2.23074i 0.0199152 0.287987i
\(61\) 0.975597 0.124912 0.0624562 0.998048i \(-0.480107\pi\)
0.0624562 + 0.998048i \(0.480107\pi\)
\(62\) 3.08991 4.63168i 0.392419 0.588224i
\(63\) 0.773241i 0.0974193i
\(64\) −1.00000 −0.125000
\(65\) 7.17906 + 4.83430i 0.890452 + 0.599621i
\(66\) −0.182400 −0.0224519
\(67\) 0.371098 0.214254i 0.0453369 0.0261753i −0.477160 0.878816i \(-0.658334\pi\)
0.522497 + 0.852641i \(0.325001\pi\)
\(68\) −5.39463 3.11459i −0.654195 0.377700i
\(69\) −1.71325 + 2.96744i −0.206251 + 0.357237i
\(70\) −1.72490 0.119282i −0.206165 0.0142570i
\(71\) 4.02888 + 6.97823i 0.478141 + 0.828164i 0.999686 0.0250598i \(-0.00797761\pi\)
−0.521545 + 0.853224i \(0.674644\pi\)
\(72\) 0.866025 0.500000i 0.102062 0.0589256i
\(73\) −9.05991 + 5.23074i −1.06038 + 0.612212i −0.925538 0.378655i \(-0.876387\pi\)
−0.134844 + 0.990867i \(0.543053\pi\)
\(74\) −3.20418 + 5.54979i −0.372478 + 0.645151i
\(75\) −4.63303 + 1.88017i −0.534976 + 0.217103i
\(76\) 0.298547 0.517099i 0.0342457 0.0593153i
\(77\) 0.141039i 0.0160729i
\(78\) 3.87064i 0.438264i
\(79\) 3.64065 6.30578i 0.409605 0.709456i −0.585241 0.810860i \(-0.699000\pi\)
0.994845 + 0.101404i \(0.0323333\pi\)
\(80\) 0.981775 + 2.00901i 0.109766 + 0.224614i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) −1.61190 + 0.930631i −0.178005 + 0.102771i
\(83\) 6.97624 4.02773i 0.765742 0.442101i −0.0656117 0.997845i \(-0.520900\pi\)
0.831353 + 0.555744i \(0.187567\pi\)
\(84\) −0.386621 0.669647i −0.0421838 0.0730645i
\(85\) −0.960930 + 13.8957i −0.104228 + 1.50720i
\(86\) 3.34064 5.78617i 0.360231 0.623938i
\(87\) −6.17071 3.56266i −0.661569 0.381957i
\(88\) 0.157963 0.0912000i 0.0168389 0.00972196i
\(89\) −0.839983 −0.0890380 −0.0445190 0.999009i \(-0.514176\pi\)
−0.0445190 + 0.999009i \(0.514176\pi\)
\(90\) −1.85475 1.24897i −0.195507 0.131653i
\(91\) 2.99294 0.313745
\(92\) 3.42650i 0.357237i
\(93\) −2.46620 4.99178i −0.255733 0.517624i
\(94\) 6.17291 0.636687
\(95\) −1.33196 0.0921094i −0.136657 0.00945022i
\(96\) −0.500000 + 0.866025i −0.0510310 + 0.0883883i
\(97\) 9.51682i 0.966287i −0.875541 0.483143i \(-0.839495\pi\)
0.875541 0.483143i \(-0.160505\pi\)
\(98\) 5.54438 3.20105i 0.560067 0.323355i
\(99\) −0.0912000 + 0.157963i −0.00916595 + 0.0158759i
\(100\) 3.07224 3.94479i 0.307224 0.394479i
\(101\) 11.7568 1.16985 0.584923 0.811089i \(-0.301125\pi\)
0.584923 + 0.811089i \(0.301125\pi\)
\(102\) −5.39463 + 3.11459i −0.534148 + 0.308391i
\(103\) −8.33883 + 4.81443i −0.821650 + 0.474380i −0.850985 0.525190i \(-0.823994\pi\)
0.0293353 + 0.999570i \(0.490661\pi\)
\(104\) −1.93532 3.35207i −0.189774 0.328698i
\(105\) −0.965752 + 1.43417i −0.0942477 + 0.139960i
\(106\) 4.32784 + 7.49604i 0.420357 + 0.728080i
\(107\) −6.18652 3.57179i −0.598073 0.345298i 0.170210 0.985408i \(-0.445555\pi\)
−0.768283 + 0.640110i \(0.778889\pi\)
\(108\) 1.00000i 0.0962250i
\(109\) −15.9921 −1.53177 −0.765883 0.642979i \(-0.777698\pi\)
−0.765883 + 0.642979i \(0.777698\pi\)
\(110\) −0.338306 0.227811i −0.0322562 0.0217210i
\(111\) 3.20418 + 5.54979i 0.304127 + 0.526763i
\(112\) 0.669647 + 0.386621i 0.0632757 + 0.0365322i
\(113\) 12.2956 7.09885i 1.15667 0.667804i 0.206167 0.978517i \(-0.433901\pi\)
0.950504 + 0.310713i \(0.100568\pi\)
\(114\) −0.298547 0.517099i −0.0279615 0.0484308i
\(115\) −6.88387 + 3.36405i −0.641924 + 0.313700i
\(116\) 7.12532 0.661569
\(117\) 3.35207 + 1.93532i 0.309899 + 0.178920i
\(118\) −10.4570 6.03735i −0.962645 0.555783i
\(119\) 2.40833 + 4.17135i 0.220771 + 0.382387i
\(120\) 2.23074 + 0.154263i 0.203638 + 0.0140822i
\(121\) 5.48337 9.49747i 0.498488 0.863406i
\(122\) 0.975597i 0.0883264i
\(123\) 1.86126i 0.167824i
\(124\) 4.63168 + 3.08991i 0.415937 + 0.277482i
\(125\) −10.9414 2.29925i −0.978625 0.205652i
\(126\) −0.773241 −0.0688858
\(127\) 10.3908 + 5.99913i 0.922034 + 0.532337i 0.884283 0.466951i \(-0.154647\pi\)
0.0377506 + 0.999287i \(0.487981\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) −3.34064 5.78617i −0.294127 0.509444i
\(130\) −4.83430 + 7.17906i −0.423996 + 0.629645i
\(131\) 4.14488 7.17915i 0.362140 0.627245i −0.626173 0.779684i \(-0.715379\pi\)
0.988313 + 0.152439i \(0.0487128\pi\)
\(132\) 0.182400i 0.0158759i
\(133\) −0.399843 + 0.230849i −0.0346707 + 0.0200172i
\(134\) 0.214254 + 0.371098i 0.0185087 + 0.0320580i
\(135\) −2.00901 + 0.981775i −0.172908 + 0.0844977i
\(136\) 3.11459 5.39463i 0.267074 0.462586i
\(137\) 11.1202 6.42025i 0.950063 0.548519i 0.0569622 0.998376i \(-0.481859\pi\)
0.893100 + 0.449857i \(0.148525\pi\)
\(138\) −2.96744 1.71325i −0.252605 0.145842i
\(139\) −3.85068 −0.326611 −0.163305 0.986576i \(-0.552216\pi\)
−0.163305 + 0.986576i \(0.552216\pi\)
\(140\) 0.119282 1.72490i 0.0100812 0.145781i
\(141\) 3.08646 5.34590i 0.259926 0.450206i
\(142\) −6.97823 + 4.02888i −0.585600 + 0.338096i
\(143\) 0.611418 + 0.353002i 0.0511294 + 0.0295195i
\(144\) 0.500000 + 0.866025i 0.0416667 + 0.0721688i
\(145\) −6.99546 14.3148i −0.580941 1.18878i
\(146\) −5.23074 9.05991i −0.432899 0.749803i
\(147\) 6.40210i 0.528036i
\(148\) −5.54979 3.20418i −0.456190 0.263382i
\(149\) 6.29694 10.9066i 0.515865 0.893505i −0.483965 0.875087i \(-0.660804\pi\)
0.999830 0.0184175i \(-0.00586282\pi\)
\(150\) −1.88017 4.63303i −0.153515 0.378285i
\(151\) 12.8986 1.04967 0.524835 0.851204i \(-0.324127\pi\)
0.524835 + 0.851204i \(0.324127\pi\)
\(152\) 0.517099 + 0.298547i 0.0419423 + 0.0242154i
\(153\) 6.22919i 0.503600i
\(154\) −0.141039 −0.0113653
\(155\) 1.66039 12.3387i 0.133366 0.991067i
\(156\) −3.87064 −0.309899
\(157\) 14.4319i 1.15179i 0.817522 + 0.575897i \(0.195347\pi\)
−0.817522 + 0.575897i \(0.804653\pi\)
\(158\) 6.30578 + 3.64065i 0.501661 + 0.289634i
\(159\) 8.65569 0.686441
\(160\) −2.00901 + 0.981775i −0.158826 + 0.0776161i
\(161\) −1.32476 + 2.29455i −0.104405 + 0.180835i
\(162\) −0.866025 0.500000i −0.0680414 0.0392837i
\(163\) 1.86439i 0.146030i −0.997331 0.0730150i \(-0.976738\pi\)
0.997331 0.0730150i \(-0.0232621\pi\)
\(164\) −0.930631 1.61190i −0.0726700 0.125868i
\(165\) −0.366443 + 0.179076i −0.0285276 + 0.0139410i
\(166\) 4.02773 + 6.97624i 0.312613 + 0.541461i
\(167\) −0.608695 0.351430i −0.0471022 0.0271945i 0.476264 0.879302i \(-0.341991\pi\)
−0.523366 + 0.852108i \(0.675324\pi\)
\(168\) 0.669647 0.386621i 0.0516644 0.0298284i
\(169\) 0.990925 1.71633i 0.0762250 0.132026i
\(170\) −13.8957 0.960930i −1.06575 0.0737000i
\(171\) −0.597095 −0.0456610
\(172\) 5.78617 + 3.34064i 0.441191 + 0.254722i
\(173\) 6.36230 3.67328i 0.483717 0.279274i −0.238247 0.971205i \(-0.576573\pi\)
0.721964 + 0.691930i \(0.243240\pi\)
\(174\) 3.56266 6.17071i 0.270084 0.467800i
\(175\) −3.58245 + 1.45383i −0.270808 + 0.109899i
\(176\) 0.0912000 + 0.157963i 0.00687446 + 0.0119069i
\(177\) −10.4570 + 6.03735i −0.785996 + 0.453795i
\(178\) 0.839983i 0.0629594i
\(179\) −0.245463 + 0.425154i −0.0183467 + 0.0317775i −0.875053 0.484027i \(-0.839174\pi\)
0.856706 + 0.515805i \(0.172507\pi\)
\(180\) 1.24897 1.85475i 0.0930924 0.138245i
\(181\) 8.47857 + 14.6853i 0.630207 + 1.09155i 0.987509 + 0.157562i \(0.0503633\pi\)
−0.357302 + 0.933989i \(0.616303\pi\)
\(182\) 2.99294i 0.221851i
\(183\) 0.844892 + 0.487799i 0.0624562 + 0.0360591i
\(184\) 3.42650 0.252605
\(185\) −0.988569 + 14.2954i −0.0726810 + 1.05102i
\(186\) 4.99178 2.46620i 0.366015 0.180830i
\(187\) 1.13620i 0.0830875i
\(188\) 6.17291i 0.450206i
\(189\) −0.386621 + 0.669647i −0.0281225 + 0.0487096i
\(190\) 0.0921094 1.33196i 0.00668232 0.0966308i
\(191\) −4.93870 8.55408i −0.357352 0.618952i 0.630166 0.776461i \(-0.282987\pi\)
−0.987518 + 0.157509i \(0.949654\pi\)
\(192\) −0.866025 0.500000i −0.0625000 0.0360844i
\(193\) 7.56580 + 4.36812i 0.544598 + 0.314424i 0.746941 0.664891i \(-0.231522\pi\)
−0.202342 + 0.979315i \(0.564855\pi\)
\(194\) 9.51682 0.683268
\(195\) 3.80010 + 7.77615i 0.272131 + 0.556862i
\(196\) 3.20105 + 5.54438i 0.228646 + 0.396027i
\(197\) 1.14893 0.663337i 0.0818582 0.0472608i −0.458512 0.888688i \(-0.651617\pi\)
0.540370 + 0.841427i \(0.318284\pi\)
\(198\) −0.157963 0.0912000i −0.0112259 0.00648130i
\(199\) −12.3167 21.3331i −0.873107 1.51226i −0.858766 0.512368i \(-0.828768\pi\)
−0.0143404 0.999897i \(-0.504565\pi\)
\(200\) 3.94479 + 3.07224i 0.278939 + 0.217240i
\(201\) 0.428507 0.0302246
\(202\) 11.7568i 0.827206i
\(203\) −4.77145 2.75480i −0.334890 0.193349i
\(204\) −3.11459 5.39463i −0.218065 0.377700i
\(205\) −2.32465 + 3.45217i −0.162361 + 0.241110i
\(206\) −4.81443 8.33883i −0.335437 0.580994i
\(207\) −2.96744 + 1.71325i −0.206251 + 0.119079i
\(208\) 3.35207 1.93532i 0.232424 0.134190i
\(209\) −0.108910 −0.00753347
\(210\) −1.43417 0.965752i −0.0989669 0.0666432i
\(211\) 8.11534 14.0562i 0.558683 0.967667i −0.438924 0.898524i \(-0.644640\pi\)
0.997607 0.0691431i \(-0.0220265\pi\)
\(212\) −7.49604 + 4.32784i −0.514830 + 0.297238i
\(213\) 8.05777i 0.552109i
\(214\) 3.57179 6.18652i 0.244162 0.422902i
\(215\) 1.03067 14.9042i 0.0702913 1.01646i
\(216\) 1.00000 0.0680414
\(217\) −1.90697 3.85985i −0.129453 0.262024i
\(218\) 15.9921i 1.08312i
\(219\) −10.4615 −0.706921
\(220\) 0.227811 0.338306i 0.0153590 0.0228086i
\(221\) 24.1109 1.62188
\(222\) −5.54979 + 3.20418i −0.372478 + 0.215050i
\(223\) −17.2965 9.98614i −1.15826 0.668722i −0.207373 0.978262i \(-0.566492\pi\)
−0.950886 + 0.309540i \(0.899825\pi\)
\(224\) −0.386621 + 0.669647i −0.0258322 + 0.0447427i
\(225\) −4.95241 0.688239i −0.330160 0.0458826i
\(226\) 7.09885 + 12.2956i 0.472209 + 0.817889i
\(227\) 20.2265 11.6778i 1.34248 0.775080i 0.355307 0.934750i \(-0.384376\pi\)
0.987171 + 0.159670i \(0.0510429\pi\)
\(228\) 0.517099 0.298547i 0.0342457 0.0197718i
\(229\) 6.66108 11.5373i 0.440176 0.762408i −0.557526 0.830160i \(-0.688249\pi\)
0.997702 + 0.0677518i \(0.0215826\pi\)
\(230\) −3.36405 6.88387i −0.221819 0.453909i
\(231\) −0.0705196 + 0.122144i −0.00463985 + 0.00803646i
\(232\) 7.12532i 0.467800i
\(233\) 10.6233i 0.695957i 0.937503 + 0.347978i \(0.113132\pi\)
−0.937503 + 0.347978i \(0.886868\pi\)
\(234\) −1.93532 + 3.35207i −0.126516 + 0.219132i
\(235\) 12.4014 6.06041i 0.808980 0.395338i
\(236\) 6.03735 10.4570i 0.392998 0.680693i
\(237\) 6.30578 3.64065i 0.409605 0.236485i
\(238\) −4.17135 + 2.40833i −0.270389 + 0.156109i
\(239\) −4.64700 8.04884i −0.300589 0.520636i 0.675680 0.737195i \(-0.263850\pi\)
−0.976270 + 0.216559i \(0.930517\pi\)
\(240\) −0.154263 + 2.23074i −0.00995761 + 0.143994i
\(241\) −4.18140 + 7.24239i −0.269347 + 0.466523i −0.968693 0.248260i \(-0.920141\pi\)
0.699346 + 0.714783i \(0.253475\pi\)
\(242\) 9.49747 + 5.48337i 0.610520 + 0.352484i
\(243\) −0.866025 + 0.500000i −0.0555556 + 0.0320750i
\(244\) −0.975597 −0.0624562
\(245\) 7.99600 11.8743i 0.510846 0.758619i
\(246\) −1.86126 −0.118670
\(247\) 2.31114i 0.147054i
\(248\) −3.08991 + 4.63168i −0.196209 + 0.294112i
\(249\) 8.05547 0.510495
\(250\) 2.29925 10.9414i 0.145418 0.691993i
\(251\) −9.11474 + 15.7872i −0.575317 + 0.996479i 0.420690 + 0.907205i \(0.361788\pi\)
−0.996007 + 0.0892742i \(0.971545\pi\)
\(252\) 0.773241i 0.0487096i
\(253\) −0.541261 + 0.312497i −0.0340288 + 0.0196465i
\(254\) −5.99913 + 10.3908i −0.376419 + 0.651977i
\(255\) −7.78004 + 11.5536i −0.487205 + 0.723512i
\(256\) 1.00000 0.0625000
\(257\) 1.29328 0.746676i 0.0806727 0.0465764i −0.459121 0.888374i \(-0.651836\pi\)
0.539794 + 0.841797i \(0.318502\pi\)
\(258\) 5.78617 3.34064i 0.360231 0.207979i
\(259\) 2.47760 + 4.29133i 0.153951 + 0.266650i
\(260\) −7.17906 4.83430i −0.445226 0.299810i
\(261\) −3.56266 6.17071i −0.220523 0.381957i
\(262\) 7.17915 + 4.14488i 0.443529 + 0.256072i
\(263\) 21.7443i 1.34081i 0.741996 + 0.670404i \(0.233879\pi\)
−0.741996 + 0.670404i \(0.766121\pi\)
\(264\) 0.182400 0.0112259
\(265\) 16.0541 + 10.8107i 0.986196 + 0.664093i
\(266\) −0.230849 0.399843i −0.0141543 0.0245159i
\(267\) −0.727447 0.419992i −0.0445190 0.0257031i
\(268\) −0.371098 + 0.214254i −0.0226684 + 0.0130876i
\(269\) 6.95564 + 12.0475i 0.424093 + 0.734551i 0.996335 0.0855341i \(-0.0272596\pi\)
−0.572242 + 0.820085i \(0.693926\pi\)
\(270\) −0.981775 2.00901i −0.0597489 0.122264i
\(271\) 16.6543 1.01168 0.505838 0.862629i \(-0.331184\pi\)
0.505838 + 0.862629i \(0.331184\pi\)
\(272\) 5.39463 + 3.11459i 0.327098 + 0.188850i
\(273\) 2.59196 + 1.49647i 0.156873 + 0.0905705i
\(274\) 6.42025 + 11.1202i 0.387861 + 0.671796i
\(275\) −0.903319 0.125535i −0.0544722 0.00757004i
\(276\) 1.71325 2.96744i 0.103126 0.178619i
\(277\) 15.3671i 0.923321i −0.887057 0.461660i \(-0.847254\pi\)
0.887057 0.461660i \(-0.152746\pi\)
\(278\) 3.85068i 0.230949i
\(279\) 0.360101 5.55611i 0.0215587 0.332635i
\(280\) 1.72490 + 0.119282i 0.103083 + 0.00712848i
\(281\) 17.4465 1.04077 0.520384 0.853932i \(-0.325789\pi\)
0.520384 + 0.853932i \(0.325789\pi\)
\(282\) 5.34590 + 3.08646i 0.318344 + 0.183796i
\(283\) 28.9290i 1.71965i −0.510588 0.859826i \(-0.670572\pi\)
0.510588 0.859826i \(-0.329428\pi\)
\(284\) −4.02888 6.97823i −0.239070 0.414082i
\(285\) −1.10746 0.745751i −0.0656002 0.0441745i
\(286\) −0.353002 + 0.611418i −0.0208735 + 0.0361539i
\(287\) 1.43920i 0.0849536i
\(288\) −0.866025 + 0.500000i −0.0510310 + 0.0294628i
\(289\) 10.9014 + 18.8817i 0.641258 + 1.11069i
\(290\) 14.3148 6.99546i 0.840596 0.410787i
\(291\) 4.75841 8.24181i 0.278943 0.483143i
\(292\) 9.05991 5.23074i 0.530191 0.306106i
\(293\) 7.37274 + 4.25665i 0.430720 + 0.248676i 0.699653 0.714482i \(-0.253338\pi\)
−0.268933 + 0.963159i \(0.586671\pi\)
\(294\) 6.40210 0.373378
\(295\) −26.9355 1.86267i −1.56825 0.108449i
\(296\) 3.20418 5.54979i 0.186239 0.322575i
\(297\) −0.157963 + 0.0912000i −0.00916595 + 0.00529196i
\(298\) 10.9066 + 6.29694i 0.631803 + 0.364772i
\(299\) 6.63137 + 11.4859i 0.383502 + 0.664245i
\(300\) 4.63303 1.88017i 0.267488 0.108552i
\(301\) −2.58312 4.47410i −0.148889 0.257883i
\(302\) 12.8986i 0.742229i
\(303\) 10.1817 + 5.87840i 0.584923 + 0.337705i
\(304\) −0.298547 + 0.517099i −0.0171229 + 0.0296577i
\(305\) 0.957817 + 1.95998i 0.0548444 + 0.112228i
\(306\) −6.22919 −0.356099
\(307\) −18.6892 10.7902i −1.06665 0.615830i −0.139385 0.990238i \(-0.544513\pi\)
−0.927264 + 0.374408i \(0.877846\pi\)
\(308\) 0.141039i 0.00803646i
\(309\) −9.62886 −0.547766
\(310\) 12.3387 + 1.66039i 0.700790 + 0.0943039i
\(311\) 7.50012 0.425293 0.212646 0.977129i \(-0.431792\pi\)
0.212646 + 0.977129i \(0.431792\pi\)
\(312\) 3.87064i 0.219132i
\(313\) −10.1694 5.87130i −0.574808 0.331866i 0.184259 0.982878i \(-0.441011\pi\)
−0.759067 + 0.651012i \(0.774345\pi\)
\(314\) −14.4319 −0.814442
\(315\) −1.55345 + 0.759149i −0.0875269 + 0.0427732i
\(316\) −3.64065 + 6.30578i −0.204802 + 0.354728i
\(317\) −21.7925 12.5819i −1.22399 0.706672i −0.258225 0.966085i \(-0.583138\pi\)
−0.965766 + 0.259413i \(0.916471\pi\)
\(318\) 8.65569i 0.485387i
\(319\) −0.649829 1.12554i −0.0363834 0.0630180i
\(320\) −0.981775 2.00901i −0.0548829 0.112307i
\(321\) −3.57179 6.18652i −0.199358 0.345298i
\(322\) −2.29455 1.32476i −0.127870 0.0738258i
\(323\) −3.22111 + 1.85971i −0.179227 + 0.103477i
\(324\) 0.500000 0.866025i 0.0277778 0.0481125i
\(325\) −2.66393 + 19.1690i −0.147768 + 1.06330i
\(326\) 1.86439 0.103259
\(327\) −13.8496 7.99606i −0.765883 0.442183i
\(328\) 1.61190 0.930631i 0.0890023 0.0513855i
\(329\) 2.38658 4.13367i 0.131576 0.227897i
\(330\) −0.179076 0.366443i −0.00985780 0.0201720i
\(331\) −16.4267 28.4518i −0.902891 1.56385i −0.823724 0.566991i \(-0.808107\pi\)
−0.0791671 0.996861i \(-0.525226\pi\)
\(332\) −6.97624 + 4.02773i −0.382871 + 0.221051i
\(333\) 6.40835i 0.351175i
\(334\) 0.351430 0.608695i 0.0192294 0.0333063i
\(335\) 0.794773 + 0.535191i 0.0434231 + 0.0292406i
\(336\) 0.386621 + 0.669647i 0.0210919 + 0.0365322i
\(337\) 12.7086i 0.692281i −0.938183 0.346140i \(-0.887492\pi\)
0.938183 0.346140i \(-0.112508\pi\)
\(338\) 1.71633 + 0.990925i 0.0933562 + 0.0538992i
\(339\) 14.1977 0.771114
\(340\) 0.960930 13.8957i 0.0521138 0.753600i
\(341\) 0.0656824 1.01343i 0.00355690 0.0548805i
\(342\) 0.597095i 0.0322872i
\(343\) 10.3631i 0.559553i
\(344\) −3.34064 + 5.78617i −0.180115 + 0.311969i
\(345\) −7.64363 0.528581i −0.411519 0.0284578i
\(346\) 3.67328 + 6.36230i 0.197477 + 0.342040i
\(347\) −26.0657 15.0491i −1.39928 0.807876i −0.404964 0.914332i \(-0.632716\pi\)
−0.994317 + 0.106457i \(0.966049\pi\)
\(348\) 6.17071 + 3.56266i 0.330785 + 0.190979i
\(349\) 8.86982 0.474790 0.237395 0.971413i \(-0.423706\pi\)
0.237395 + 0.971413i \(0.423706\pi\)
\(350\) −1.45383 3.58245i −0.0777102 0.191490i
\(351\) 1.93532 + 3.35207i 0.103300 + 0.178920i
\(352\) −0.157963 + 0.0912000i −0.00841946 + 0.00486098i
\(353\) 10.3613 + 5.98210i 0.551476 + 0.318395i 0.749717 0.661758i \(-0.230190\pi\)
−0.198241 + 0.980153i \(0.563523\pi\)
\(354\) −6.03735 10.4570i −0.320882 0.555783i
\(355\) −10.0639 + 14.9451i −0.534135 + 0.793205i
\(356\) 0.839983 0.0445190
\(357\) 4.81667i 0.254925i
\(358\) −0.425154 0.245463i −0.0224701 0.0129731i
\(359\) −2.64689 4.58455i −0.139697 0.241963i 0.787685 0.616079i \(-0.211280\pi\)
−0.927382 + 0.374116i \(0.877946\pi\)
\(360\) 1.85475 + 1.24897i 0.0977537 + 0.0658263i
\(361\) 9.32174 + 16.1457i 0.490618 + 0.849775i
\(362\) −14.6853 + 8.47857i −0.771843 + 0.445624i
\(363\) 9.49747 5.48337i 0.498488 0.287802i
\(364\) −2.99294 −0.156873
\(365\) −19.4034 13.0660i −1.01562 0.683907i
\(366\) −0.487799 + 0.844892i −0.0254976 + 0.0441632i
\(367\) −19.4298 + 11.2178i −1.01423 + 0.585564i −0.912427 0.409240i \(-0.865794\pi\)
−0.101801 + 0.994805i \(0.532460\pi\)
\(368\) 3.42650i 0.178619i
\(369\) −0.930631 + 1.61190i −0.0484467 + 0.0839121i
\(370\) −14.2954 0.988569i −0.743181 0.0513932i
\(371\) 6.69294 0.347480
\(372\) 2.46620 + 4.99178i 0.127866 + 0.258812i
\(373\) 3.89756i 0.201808i −0.994896 0.100904i \(-0.967826\pi\)
0.994896 0.100904i \(-0.0321735\pi\)
\(374\) −1.13620 −0.0587517
\(375\) −8.32587 7.46189i −0.429946 0.385331i
\(376\) −6.17291 −0.318344
\(377\) −23.8846 + 13.7898i −1.23012 + 0.710209i
\(378\) −0.669647 0.386621i −0.0344429 0.0198856i
\(379\) 11.7489 20.3497i 0.603499 1.04529i −0.388787 0.921327i \(-0.627106\pi\)
0.992287 0.123964i \(-0.0395607\pi\)
\(380\) 1.33196 + 0.0921094i 0.0683283 + 0.00472511i
\(381\) 5.99913 + 10.3908i 0.307345 + 0.532337i
\(382\) 8.55408 4.93870i 0.437665 0.252686i
\(383\) −5.23407 + 3.02189i −0.267449 + 0.154412i −0.627728 0.778433i \(-0.716015\pi\)
0.360279 + 0.932845i \(0.382682\pi\)
\(384\) 0.500000 0.866025i 0.0255155 0.0441942i
\(385\) −0.283349 + 0.138469i −0.0144408 + 0.00705703i
\(386\) −4.36812 + 7.56580i −0.222331 + 0.385089i
\(387\) 6.68129i 0.339629i
\(388\) 9.51682i 0.483143i
\(389\) 3.21583 5.56997i 0.163049 0.282409i −0.772912 0.634513i \(-0.781201\pi\)
0.935961 + 0.352105i \(0.114534\pi\)
\(390\) −7.77615 + 3.80010i −0.393761 + 0.192425i
\(391\) −10.6722 + 18.4847i −0.539714 + 0.934812i
\(392\) −5.54438 + 3.20105i −0.280033 + 0.161677i
\(393\) 7.17915 4.14488i 0.362140 0.209082i
\(394\) 0.663337 + 1.14893i 0.0334185 + 0.0578825i
\(395\) 16.2427 + 1.12323i 0.817257 + 0.0565159i
\(396\) 0.0912000 0.157963i 0.00458297 0.00793794i
\(397\) 29.5449 + 17.0578i 1.48282 + 0.856105i 0.999810 0.0195106i \(-0.00621081\pi\)
0.483008 + 0.875616i \(0.339544\pi\)
\(398\) 21.3331 12.3167i 1.06933 0.617380i
\(399\) −0.461698 −0.0231138
\(400\) −3.07224 + 3.94479i −0.153612 + 0.197239i
\(401\) −36.6374 −1.82959 −0.914793 0.403924i \(-0.867646\pi\)
−0.914793 + 0.403924i \(0.867646\pi\)
\(402\) 0.428507i 0.0213720i
\(403\) −21.5057 1.39382i −1.07127 0.0694312i
\(404\) −11.7568 −0.584923
\(405\) −2.23074 0.154263i −0.110846 0.00766537i
\(406\) 2.75480 4.77145i 0.136718 0.236803i
\(407\) 1.16888i 0.0579394i
\(408\) 5.39463 3.11459i 0.267074 0.154195i
\(409\) −10.5653 + 18.2997i −0.522422 + 0.904861i 0.477238 + 0.878774i \(0.341638\pi\)
−0.999660 + 0.0260870i \(0.991695\pi\)
\(410\) −3.45217 2.32465i −0.170490 0.114806i
\(411\) 12.8405 0.633375
\(412\) 8.33883 4.81443i 0.410825 0.237190i
\(413\) −8.08579 + 4.66833i −0.397876 + 0.229714i
\(414\) −1.71325 2.96744i −0.0842017 0.145842i
\(415\) 14.9409 + 10.0610i 0.733418 + 0.493875i
\(416\) 1.93532 + 3.35207i 0.0948869 + 0.164349i
\(417\) −3.33479 1.92534i −0.163305 0.0942844i
\(418\) 0.108910i 0.00532697i
\(419\) −22.8606 −1.11681 −0.558406 0.829568i \(-0.688587\pi\)
−0.558406 + 0.829568i \(0.688587\pi\)
\(420\) 0.965752 1.43417i 0.0471239 0.0699802i
\(421\) −6.83483 11.8383i −0.333109 0.576962i 0.650010 0.759925i \(-0.274765\pi\)
−0.983120 + 0.182963i \(0.941431\pi\)
\(422\) 14.0562 + 8.11534i 0.684244 + 0.395049i
\(423\) 5.34590 3.08646i 0.259926 0.150069i
\(424\) −4.32784 7.49604i −0.210179 0.364040i
\(425\) −28.8600 + 11.7119i −1.39992 + 0.568112i
\(426\) −8.05777 −0.390400
\(427\) 0.653305 + 0.377186i 0.0316157 + 0.0182533i
\(428\) 6.18652 + 3.57179i 0.299037 + 0.172649i
\(429\) 0.353002 + 0.611418i 0.0170431 + 0.0295195i
\(430\) 14.9042 + 1.03067i 0.718745 + 0.0497035i
\(431\) −9.10321 + 15.7672i −0.438486 + 0.759480i −0.997573 0.0696289i \(-0.977818\pi\)
0.559087 + 0.829109i \(0.311152\pi\)
\(432\) 1.00000i 0.0481125i
\(433\) 2.97874i 0.143149i −0.997435 0.0715746i \(-0.977198\pi\)
0.997435 0.0715746i \(-0.0228024\pi\)
\(434\) 3.85985 1.90697i 0.185279 0.0915373i
\(435\) 1.09917 15.8947i 0.0527012 0.762094i
\(436\) 15.9921 0.765883
\(437\) −1.77184 1.02297i −0.0847586 0.0489354i
\(438\) 10.4615i 0.499869i
\(439\) 1.88163 + 3.25908i 0.0898052 + 0.155547i 0.907429 0.420206i \(-0.138042\pi\)
−0.817623 + 0.575753i \(0.804709\pi\)
\(440\) 0.338306 + 0.227811i 0.0161281 + 0.0108605i
\(441\) 3.20105 5.54438i 0.152431 0.264018i
\(442\) 24.1109i 1.14684i
\(443\) −23.4960 + 13.5654i −1.11633 + 0.644512i −0.940461 0.339903i \(-0.889606\pi\)
−0.175866 + 0.984414i \(0.556273\pi\)
\(444\) −3.20418 5.54979i −0.152063 0.263382i
\(445\) −0.824674 1.68753i −0.0390933 0.0799968i
\(446\) 9.98614 17.2965i 0.472858 0.819013i
\(447\) 10.9066 6.29694i 0.515865 0.297835i
\(448\) −0.669647 0.386621i −0.0316378 0.0182661i
\(449\) −41.4038 −1.95397 −0.976983 0.213316i \(-0.931574\pi\)
−0.976983 + 0.213316i \(0.931574\pi\)
\(450\) 0.688239 4.95241i 0.0324439 0.233459i
\(451\) −0.169747 + 0.294011i −0.00799308 + 0.0138444i
\(452\) −12.2956 + 7.09885i −0.578335 + 0.333902i
\(453\) 11.1705 + 6.44928i 0.524835 + 0.303014i
\(454\) 11.6778 + 20.2265i 0.548064 + 0.949275i
\(455\) 2.93839 + 6.01284i 0.137754 + 0.281886i
\(456\) 0.298547 + 0.517099i 0.0139808 + 0.0242154i
\(457\) 24.6010i 1.15079i −0.817877 0.575393i \(-0.804849\pi\)
0.817877 0.575393i \(-0.195151\pi\)
\(458\) 11.5373 + 6.66108i 0.539104 + 0.311252i
\(459\) −3.11459 + 5.39463i −0.145377 + 0.251800i
\(460\) 6.88387 3.36405i 0.320962 0.156850i
\(461\) −5.75649 −0.268106 −0.134053 0.990974i \(-0.542799\pi\)
−0.134053 + 0.990974i \(0.542799\pi\)
\(462\) −0.122144 0.0705196i −0.00568263 0.00328087i
\(463\) 30.2945i 1.40791i 0.710246 + 0.703953i \(0.248583\pi\)
−0.710246 + 0.703953i \(0.751417\pi\)
\(464\) −7.12532 −0.330785
\(465\) 7.60728 9.85542i 0.352779 0.457034i
\(466\) −10.6233 −0.492116
\(467\) 24.8358i 1.14927i −0.818412 0.574633i \(-0.805145\pi\)
0.818412 0.574633i \(-0.194855\pi\)
\(468\) −3.35207 1.93532i −0.154950 0.0894602i
\(469\) 0.331340 0.0152998
\(470\) 6.06041 + 12.4014i 0.279546 + 0.572036i
\(471\) −7.21597 + 12.4984i −0.332494 + 0.575897i
\(472\) 10.4570 + 6.03735i 0.481323 + 0.277892i
\(473\) 1.21867i 0.0560344i
\(474\) 3.64065 + 6.30578i 0.167220 + 0.289634i
\(475\) −1.12264 2.76636i −0.0515102 0.126929i
\(476\) −2.40833 4.17135i −0.110386 0.191194i
\(477\) 7.49604 + 4.32784i 0.343220 + 0.198158i
\(478\) 8.04884 4.64700i 0.368145 0.212549i
\(479\) −19.4463 + 33.6819i −0.888523 + 1.53897i −0.0469010 + 0.998900i \(0.514935\pi\)
−0.841622 + 0.540067i \(0.818399\pi\)
\(480\) −2.23074 0.154263i −0.101819 0.00704109i
\(481\) 24.8044 1.13098
\(482\) −7.24239 4.18140i −0.329882 0.190457i
\(483\) −2.29455 + 1.32476i −0.104405 + 0.0602785i
\(484\) −5.48337 + 9.49747i −0.249244 + 0.431703i
\(485\) 19.1194 9.34338i 0.868166 0.424261i
\(486\) −0.500000 0.866025i −0.0226805 0.0392837i
\(487\) 1.68240 0.971337i 0.0762370 0.0440155i −0.461397 0.887194i \(-0.652652\pi\)
0.537634 + 0.843178i \(0.319318\pi\)
\(488\) 0.975597i 0.0441632i
\(489\) 0.932193 1.61461i 0.0421552 0.0730150i
\(490\) 11.8743 + 7.99600i 0.536425 + 0.361222i
\(491\) 14.8550 + 25.7295i 0.670395 + 1.16116i 0.977792 + 0.209576i \(0.0672085\pi\)
−0.307398 + 0.951581i \(0.599458\pi\)
\(492\) 1.86126i 0.0839121i
\(493\) −38.4385 22.1925i −1.73118 0.999498i
\(494\) −2.31114 −0.103983
\(495\) −0.406887 0.0281375i −0.0182882 0.00126469i
\(496\) −4.63168 3.08991i −0.207969 0.138741i
\(497\) 6.23060i 0.279481i
\(498\) 8.05547i 0.360974i
\(499\) −1.99859 + 3.46166i −0.0894693 + 0.154965i −0.907287 0.420512i \(-0.861850\pi\)
0.817818 + 0.575477i \(0.195184\pi\)
\(500\) 10.9414 + 2.29925i 0.489313 + 0.102826i
\(501\) −0.351430 0.608695i −0.0157007 0.0271945i
\(502\) −15.7872 9.11474i −0.704617 0.406811i
\(503\) 20.2717 + 11.7039i 0.903871 + 0.521850i 0.878454 0.477827i \(-0.158575\pi\)
0.0254170 + 0.999677i \(0.491909\pi\)
\(504\) 0.773241 0.0344429
\(505\) 11.5425 + 23.6195i 0.513636 + 1.05106i
\(506\) −0.312497 0.541261i −0.0138922 0.0240620i
\(507\) 1.71633 0.990925i 0.0762250 0.0440085i
\(508\) −10.3908 5.99913i −0.461017 0.266168i
\(509\) 16.9298 + 29.3232i 0.750399 + 1.29973i 0.947629 + 0.319372i \(0.103472\pi\)
−0.197230 + 0.980357i \(0.563195\pi\)
\(510\) −11.5536 7.78004i −0.511600 0.344506i
\(511\) −8.08925 −0.357847
\(512\) 1.00000i 0.0441942i
\(513\) −0.517099 0.298547i −0.0228305 0.0131812i
\(514\) 0.746676 + 1.29328i 0.0329345 + 0.0570442i
\(515\) −17.8591 12.0261i −0.786965 0.529934i
\(516\) 3.34064 + 5.78617i 0.147064 + 0.254722i
\(517\) 0.975092 0.562970i 0.0428845 0.0247594i
\(518\) −4.29133 + 2.47760i −0.188550 + 0.108860i
\(519\) 7.34656 0.322478
\(520\) 4.83430 7.17906i 0.211998 0.314822i
\(521\) −9.26685 + 16.0507i −0.405988 + 0.703192i −0.994436 0.105343i \(-0.966406\pi\)
0.588448 + 0.808535i \(0.299739\pi\)
\(522\) 6.17071 3.56266i 0.270084 0.155933i
\(523\) 19.2334i 0.841019i 0.907288 + 0.420509i \(0.138149\pi\)
−0.907288 + 0.420509i \(0.861851\pi\)
\(524\) −4.14488 + 7.17915i −0.181070 + 0.313623i
\(525\) −3.82941 0.532175i −0.167129 0.0232260i
\(526\) −21.7443 −0.948095
\(527\) −15.3624 31.0947i −0.669197 1.35451i
\(528\) 0.182400i 0.00793794i
\(529\) 11.2591 0.489526
\(530\) −10.8107 + 16.0541i −0.469585 + 0.697346i
\(531\) −12.0747 −0.523998
\(532\) 0.399843 0.230849i 0.0173354 0.0100086i
\(533\) 6.23908 + 3.60214i 0.270245 + 0.156026i
\(534\) 0.419992 0.727447i 0.0181748 0.0314797i
\(535\) 1.10199 15.9355i 0.0476430 0.688950i
\(536\) −0.214254 0.371098i −0.00925435 0.0160290i
\(537\) −0.425154 + 0.245463i −0.0183467 + 0.0105925i
\(538\) −12.0475 + 6.95564i −0.519406 + 0.299879i
\(539\) 0.583871 1.01130i 0.0251491 0.0435596i
\(540\) 2.00901 0.981775i 0.0864540 0.0422489i
\(541\) −4.65254 + 8.05844i −0.200028 + 0.346459i −0.948537 0.316665i \(-0.897437\pi\)
0.748509 + 0.663125i \(0.230770\pi\)
\(542\) 16.6543i 0.715362i
\(543\) 16.9571i 0.727700i
\(544\) −3.11459 + 5.39463i −0.133537 + 0.231293i
\(545\) −15.7007 32.1283i −0.672542 1.37623i
\(546\) −1.49647 + 2.59196i −0.0640430 + 0.110926i
\(547\) 0.685180 0.395589i 0.0292962 0.0169141i −0.485280 0.874359i \(-0.661282\pi\)
0.514577 + 0.857444i \(0.327949\pi\)
\(548\) −11.1202 + 6.42025i −0.475031 + 0.274259i
\(549\) 0.487799 + 0.844892i 0.0208187 + 0.0360591i
\(550\) 0.125535 0.903319i 0.00535283 0.0385177i
\(551\) 2.12724 3.68450i 0.0906237 0.156965i
\(552\) 2.96744 + 1.71325i 0.126302 + 0.0729208i
\(553\) 4.87589 2.81510i 0.207344 0.119710i
\(554\) 15.3671 0.652886
\(555\) −8.00381 + 11.8859i −0.339743 + 0.504527i
\(556\) 3.85068 0.163305
\(557\) 25.2701i 1.07073i 0.844621 + 0.535365i \(0.179826\pi\)
−0.844621 + 0.535365i \(0.820174\pi\)
\(558\) 5.55611 + 0.360101i 0.235209 + 0.0152443i
\(559\) −25.8609 −1.09380
\(560\) −0.119282 + 1.72490i −0.00504059 + 0.0728904i
\(561\) −0.568102 + 0.983981i −0.0239853 + 0.0415437i
\(562\) 17.4465i 0.735934i
\(563\) −38.7751 + 22.3868i −1.63418 + 0.943492i −0.651389 + 0.758744i \(0.725814\pi\)
−0.982786 + 0.184748i \(0.940853\pi\)
\(564\) −3.08646 + 5.34590i −0.129963 + 0.225103i
\(565\) 26.3331 + 17.7324i 1.10784 + 0.746010i
\(566\) 28.9290 1.21598
\(567\) −0.669647 + 0.386621i −0.0281225 + 0.0162365i
\(568\) 6.97823 4.02888i 0.292800 0.169048i
\(569\) −14.8782 25.7699i −0.623728 1.08033i −0.988785 0.149344i \(-0.952284\pi\)
0.365057 0.930985i \(-0.381049\pi\)
\(570\) 0.745751 1.10746i 0.0312361 0.0463864i
\(571\) −5.85732 10.1452i −0.245121 0.424562i 0.717045 0.697027i \(-0.245494\pi\)
−0.962166 + 0.272465i \(0.912161\pi\)
\(572\) −0.611418 0.353002i −0.0255647 0.0147598i
\(573\) 9.87740i 0.412634i
\(574\) −1.43920 −0.0600712
\(575\) −13.5168 10.5270i −0.563691 0.439007i
\(576\) −0.500000 0.866025i −0.0208333 0.0360844i
\(577\) 26.0152 + 15.0199i 1.08303 + 0.625286i 0.931712 0.363199i \(-0.118315\pi\)
0.151316 + 0.988485i \(0.451649\pi\)
\(578\) −18.8817 + 10.9014i −0.785377 + 0.453438i
\(579\) 4.36812 + 7.56580i 0.181533 + 0.314424i
\(580\) 6.99546 + 14.3148i 0.290471 + 0.594391i
\(581\) 6.22882 0.258415
\(582\) 8.24181 + 4.75841i 0.341634 + 0.197242i
\(583\) 1.36728 + 0.789399i 0.0566269 + 0.0326936i
\(584\) 5.23074 + 9.05991i 0.216450 + 0.374902i
\(585\) −0.597095 + 8.63439i −0.0246868 + 0.356988i
\(586\) −4.25665 + 7.37274i −0.175841 + 0.304565i
\(587\) 37.1122i 1.53178i −0.642969 0.765892i \(-0.722298\pi\)
0.642969 0.765892i \(-0.277702\pi\)
\(588\) 6.40210i 0.264018i
\(589\) 2.98057 1.47255i 0.122812 0.0606755i
\(590\) 1.86267 26.9355i 0.0766851 1.10892i
\(591\) 1.32667 0.0545721
\(592\) 5.54979 + 3.20418i 0.228095 + 0.131691i
\(593\) 11.8545i 0.486806i −0.969925 0.243403i \(-0.921736\pi\)
0.969925 0.243403i \(-0.0782638\pi\)
\(594\) −0.0912000 0.157963i −0.00374198 0.00648130i
\(595\) −6.01585 + 8.93369i −0.246626 + 0.366246i
\(596\) −6.29694 + 10.9066i −0.257933 + 0.446752i
\(597\) 24.6334i 1.00818i
\(598\) −11.4859 + 6.63137i −0.469692 + 0.271177i
\(599\) 8.73826 + 15.1351i 0.357036 + 0.618404i 0.987464 0.157843i \(-0.0504541\pi\)
−0.630428 + 0.776247i \(0.717121\pi\)
\(600\) 1.88017 + 4.63303i 0.0767576 + 0.189143i
\(601\) −12.7413 + 22.0685i −0.519728 + 0.900195i 0.480009 + 0.877263i \(0.340633\pi\)
−0.999737 + 0.0229313i \(0.992700\pi\)
\(602\) 4.47410 2.58312i 0.182351 0.105280i
\(603\) 0.371098 + 0.214254i 0.0151123 + 0.00872509i
\(604\) −12.8986 −0.524835
\(605\) 24.4639 + 1.69176i 0.994600 + 0.0687797i
\(606\) −5.87840 + 10.1817i −0.238794 + 0.413603i
\(607\) 30.6602 17.7016i 1.24446 0.718488i 0.274459 0.961599i \(-0.411501\pi\)
0.969998 + 0.243111i \(0.0781680\pi\)
\(608\) −0.517099 0.298547i −0.0209711 0.0121077i
\(609\) −2.75480 4.77145i −0.111630 0.193349i
\(610\) −1.95998 + 0.957817i −0.0793574 + 0.0387809i
\(611\) −11.9466 20.6920i −0.483306 0.837111i
\(612\) 6.22919i 0.251800i
\(613\) 4.02516 + 2.32392i 0.162574 + 0.0938624i 0.579080 0.815271i \(-0.303412\pi\)
−0.416505 + 0.909133i \(0.636745\pi\)
\(614\) 10.7902 18.6892i 0.435458 0.754235i
\(615\) −3.73929 + 1.82734i −0.150783 + 0.0736855i
\(616\) 0.141039 0.00568263
\(617\) 33.5728 + 19.3833i 1.35159 + 0.780341i 0.988472 0.151401i \(-0.0483786\pi\)
0.363119 + 0.931743i \(0.381712\pi\)
\(618\) 9.62886i 0.387329i
\(619\) −26.0289 −1.04619 −0.523096 0.852274i \(-0.675223\pi\)
−0.523096 + 0.852274i \(0.675223\pi\)
\(620\) −1.66039 + 12.3387i −0.0666829 + 0.495533i
\(621\) −3.42650 −0.137501
\(622\) 7.50012i 0.300727i
\(623\) −0.562492 0.324755i −0.0225358 0.0130110i
\(624\) 3.87064 0.154950
\(625\) −6.12273 24.2386i −0.244909 0.969546i
\(626\) 5.87130 10.1694i 0.234664 0.406451i
\(627\) −0.0943189 0.0544551i −0.00376674 0.00217473i
\(628\) 14.4319i 0.575897i
\(629\) 19.9594 + 34.5707i 0.795834 + 1.37842i
\(630\) −0.759149 1.55345i −0.0302452 0.0618909i
\(631\) −3.96941 6.87523i −0.158020 0.273698i 0.776135 0.630567i \(-0.217178\pi\)
−0.934155 + 0.356869i \(0.883844\pi\)
\(632\) −6.30578 3.64065i −0.250831 0.144817i
\(633\) 14.0562 8.11534i 0.558683 0.322556i
\(634\) 12.5819 21.7925i 0.499692 0.865493i
\(635\) −1.85088 + 26.7650i −0.0734500 + 1.06214i
\(636\) −8.65569 −0.343220
\(637\) −21.4603 12.3901i −0.850288 0.490914i
\(638\) 1.12554 0.649829i 0.0445604 0.0257270i
\(639\) −4.02888 + 6.97823i −0.159380 + 0.276055i
\(640\) 2.00901 0.981775i 0.0794131 0.0388081i
\(641\) 4.48266 + 7.76419i 0.177054 + 0.306667i 0.940870 0.338767i \(-0.110010\pi\)
−0.763816 + 0.645434i \(0.776676\pi\)
\(642\) 6.18652 3.57179i 0.244162 0.140967i
\(643\) 3.96229i 0.156257i −0.996943 0.0781287i \(-0.975106\pi\)
0.996943 0.0781287i \(-0.0248945\pi\)
\(644\) 1.32476 2.29455i 0.0522027 0.0904177i
\(645\) 8.34470 12.3921i 0.328572 0.487938i
\(646\) −1.85971 3.22111i −0.0731692 0.126733i
\(647\) 4.25345i 0.167220i 0.996499 + 0.0836102i \(0.0266451\pi\)
−0.996499 + 0.0836102i \(0.973355\pi\)
\(648\) 0.866025 + 0.500000i 0.0340207 + 0.0196419i
\(649\) −2.20243 −0.0864528
\(650\) −19.1690 2.66393i −0.751869 0.104488i
\(651\) 0.278445 4.29621i 0.0109131 0.168382i
\(652\) 1.86439i 0.0730150i
\(653\) 22.0646i 0.863455i 0.902004 + 0.431727i \(0.142096\pi\)
−0.902004 + 0.431727i \(0.857904\pi\)
\(654\) 7.99606 13.8496i 0.312671 0.541561i
\(655\) 18.4923 + 1.27880i 0.722555 + 0.0499669i
\(656\) 0.930631 + 1.61190i 0.0363350 + 0.0629341i
\(657\) −9.05991 5.23074i −0.353461 0.204071i
\(658\) 4.13367 + 2.38658i 0.161147 + 0.0930384i
\(659\) −6.39574 −0.249143 −0.124571 0.992211i \(-0.539756\pi\)
−0.124571 + 0.992211i \(0.539756\pi\)
\(660\) 0.366443 0.179076i 0.0142638 0.00697052i
\(661\) −13.5355 23.4443i −0.526472 0.911876i −0.999524 0.0308417i \(-0.990181\pi\)
0.473052 0.881034i \(-0.343152\pi\)
\(662\) 28.4518 16.4267i 1.10581 0.638440i
\(663\) 20.8807 + 12.0555i 0.810938 + 0.468196i
\(664\) −4.02773 6.97624i −0.156306 0.270731i
\(665\) −0.856334 0.576645i −0.0332072 0.0223614i
\(666\) −6.40835 −0.248319
\(667\) 24.4149i 0.945349i
\(668\) 0.608695 + 0.351430i 0.0235511 + 0.0135972i
\(669\) −9.98614 17.2965i −0.386087 0.668722i
\(670\) −0.535191 + 0.794773i −0.0206762 + 0.0307048i
\(671\) 0.0889745 + 0.154108i 0.00343482 + 0.00594929i
\(672\) −0.669647 + 0.386621i −0.0258322 + 0.0149142i
\(673\) −6.01517 + 3.47286i −0.231868 + 0.133869i −0.611433 0.791296i \(-0.709407\pi\)
0.379566 + 0.925165i \(0.376073\pi\)
\(674\) 12.7086 0.489516
\(675\) −3.94479 3.07224i −0.151835 0.118250i
\(676\) −0.990925 + 1.71633i −0.0381125 + 0.0660128i
\(677\) 5.78792 3.34166i 0.222448 0.128430i −0.384635 0.923069i \(-0.625673\pi\)
0.607083 + 0.794638i \(0.292339\pi\)
\(678\) 14.1977i 0.545260i
\(679\) 3.67940 6.37291i 0.141202 0.244570i
\(680\) 13.8957 + 0.960930i 0.532876 + 0.0368500i
\(681\) 23.3555 0.894985
\(682\) 1.01343 + 0.0656824i 0.0388064 + 0.00251511i
\(683\) 5.17502i 0.198017i −0.995087 0.0990083i \(-0.968433\pi\)
0.995087 0.0990083i \(-0.0315671\pi\)
\(684\) 0.597095 0.0228305
\(685\) 23.8159 + 16.0373i 0.909958 + 0.612755i
\(686\) 10.3631 0.395663
\(687\) 11.5373 6.66108i 0.440176 0.254136i
\(688\) −5.78617 3.34064i −0.220596 0.127361i
\(689\) 16.7515 29.0145i 0.638182 1.10536i
\(690\) 0.528581 7.64363i 0.0201227 0.290988i
\(691\) −21.5450 37.3170i −0.819610 1.41961i −0.905970 0.423341i \(-0.860857\pi\)
0.0863607 0.996264i \(-0.472476\pi\)
\(692\) −6.36230 + 3.67328i −0.241858 + 0.139637i
\(693\) −0.122144 + 0.0705196i −0.00463985 + 0.00267882i
\(694\) 15.0491 26.0657i 0.571254 0.989442i
\(695\) −3.78051 7.73606i −0.143403 0.293445i
\(696\) −3.56266 + 6.17071i −0.135042 + 0.233900i
\(697\) 11.5941i 0.439160i
\(698\) 8.86982i 0.335727i
\(699\) −5.31166 + 9.20007i −0.200905 + 0.347978i
\(700\) 3.58245 1.45383i 0.135404 0.0549494i
\(701\) −7.89296 + 13.6710i −0.298113 + 0.516347i −0.975704 0.219092i \(-0.929691\pi\)
0.677591 + 0.735439i \(0.263024\pi\)
\(702\) −3.35207 + 1.93532i −0.126516 + 0.0730439i
\(703\) −3.31375 + 1.91320i −0.124981 + 0.0721576i
\(704\) −0.0912000 0.157963i −0.00343723 0.00595346i
\(705\) 13.7702 + 0.952249i 0.518614 + 0.0358638i
\(706\) −5.98210 + 10.3613i −0.225139 + 0.389953i
\(707\) 7.87290 + 4.54542i 0.296091 + 0.170948i
\(708\) 10.4570 6.03735i 0.392998 0.226898i
\(709\) 12.5564 0.471567 0.235783 0.971806i \(-0.424234\pi\)
0.235783 + 0.971806i \(0.424234\pi\)
\(710\) −14.9451 10.0639i −0.560880 0.377690i
\(711\) 7.28129 0.273070
\(712\) 0.839983i 0.0314797i
\(713\) 10.5876 15.8705i 0.396508 0.594353i
\(714\) −4.81667 −0.180259
\(715\) −0.108910 + 1.57491i −0.00407301 + 0.0588984i
\(716\) 0.245463 0.425154i 0.00917337 0.0158887i
\(717\) 9.29400i 0.347091i
\(718\) 4.58455 2.64689i 0.171094 0.0987810i
\(719\) 7.65650 13.2615i 0.285539 0.494569i −0.687200 0.726468i \(-0.741161\pi\)
0.972740 + 0.231899i \(0.0744939\pi\)
\(720\) −1.24897 + 1.85475i −0.0465462 + 0.0691223i
\(721\) −7.44543 −0.277282
\(722\) −16.1457 + 9.32174i −0.600882 + 0.346919i
\(723\) −7.24239 + 4.18140i −0.269347 + 0.155508i
\(724\) −8.47857 14.6853i −0.315103 0.545775i
\(725\) 21.8907 28.1079i 0.812999 1.04390i
\(726\) 5.48337 + 9.49747i 0.203507 + 0.352484i
\(727\) 1.68725 + 0.974136i 0.0625768 + 0.0361287i 0.530962 0.847396i \(-0.321831\pi\)
−0.468385 + 0.883524i \(0.655164\pi\)
\(728\) 2.99294i 0.110926i
\(729\) −1.00000 −0.0370370
\(730\) 13.0660 19.4034i 0.483595 0.718152i
\(731\) −20.8095 36.0431i −0.769667 1.33310i
\(732\) −0.844892 0.487799i −0.0312281 0.0180296i
\(733\) 7.42242 4.28533i 0.274153 0.158282i −0.356620 0.934249i \(-0.616071\pi\)
0.630774 + 0.775967i \(0.282738\pi\)
\(734\) −11.2178 19.4298i −0.414057 0.717167i
\(735\) 12.8619 6.28542i 0.474417 0.231841i
\(736\) −3.42650 −0.126302
\(737\) 0.0676884 + 0.0390799i 0.00249333 + 0.00143953i
\(738\) −1.61190 0.930631i −0.0593348 0.0342570i
\(739\) 16.2472 + 28.1409i 0.597662 + 1.03518i 0.993165 + 0.116716i \(0.0372367\pi\)
−0.395504 + 0.918464i \(0.629430\pi\)
\(740\) 0.988569 14.2954i 0.0363405 0.525508i
\(741\) −1.15557 + 2.00150i −0.0424509 + 0.0735271i
\(742\) 6.69294i 0.245705i
\(743\) 39.0832i 1.43383i 0.697163 + 0.716913i \(0.254445\pi\)
−0.697163 + 0.716913i \(0.745555\pi\)
\(744\) −4.99178 + 2.46620i −0.183008 + 0.0904152i
\(745\) 28.0937 + 1.94276i 1.02927 + 0.0711773i
\(746\) 3.89756 0.142700
\(747\) 6.97624 + 4.02773i 0.255247 + 0.147367i
\(748\) 1.13620i 0.0415437i
\(749\) −2.76186 4.78367i −0.100916 0.174792i
\(750\) 7.46189 8.32587i 0.272470 0.304018i
\(751\) 11.3158 19.5996i 0.412920 0.715199i −0.582287 0.812983i \(-0.697842\pi\)
0.995208 + 0.0977840i \(0.0311754\pi\)
\(752\) 6.17291i 0.225103i
\(753\) −15.7872 + 9.11474i −0.575317 + 0.332160i
\(754\) −13.7898 23.8846i −0.502194 0.869825i
\(755\) 12.6635 + 25.9133i 0.460871 + 0.943082i
\(756\) 0.386621 0.669647i 0.0140613 0.0243548i
\(757\) 13.7398 7.93270i 0.499383 0.288319i −0.229076 0.973409i \(-0.573570\pi\)
0.728459 + 0.685090i \(0.240237\pi\)
\(758\) 20.3497 + 11.7489i 0.739133 + 0.426738i
\(759\) −0.624994 −0.0226858
\(760\) −0.0921094 + 1.33196i −0.00334116 + 0.0483154i
\(761\) −21.8886 + 37.9122i −0.793462 + 1.37432i 0.130349 + 0.991468i \(0.458390\pi\)
−0.923811 + 0.382849i \(0.874943\pi\)
\(762\) −10.3908 + 5.99913i −0.376419 + 0.217326i
\(763\) −10.7091 6.18288i −0.387694 0.223835i
\(764\) 4.93870 + 8.55408i 0.178676 + 0.309476i
\(765\) −12.5145 + 6.11566i −0.452462 + 0.221112i
\(766\) −3.02189 5.23407i −0.109185 0.189115i
\(767\) 46.7368i 1.68757i
\(768\) 0.866025 + 0.500000i 0.0312500 + 0.0180422i
\(769\) −10.3459 + 17.9196i −0.373081 + 0.646196i −0.990038 0.140801i \(-0.955032\pi\)
0.616956 + 0.786997i \(0.288365\pi\)
\(770\) −0.138469 0.283349i −0.00499007 0.0102112i
\(771\) 1.49335 0.0537818
\(772\) −7.56580 4.36812i −0.272299 0.157212i
\(773\) 4.79978i 0.172636i −0.996268 0.0863180i \(-0.972490\pi\)
0.996268 0.0863180i \(-0.0275101\pi\)
\(774\) 6.68129 0.240154
\(775\) 26.4187 8.77807i 0.948986 0.315318i
\(776\) −9.51682 −0.341634
\(777\) 4.95520i 0.177767i
\(778\) 5.56997 + 3.21583i 0.199693 + 0.115293i
\(779\) −1.11135 −0.0398182
\(780\) −3.80010 7.77615i −0.136065 0.278431i
\(781\) −0.734869 + 1.27283i −0.0262957 + 0.0455454i
\(782\) −18.4847 10.6722i −0.661012 0.381635i
\(783\) 7.12532i 0.254638i
\(784\) −3.20105 5.54438i −0.114323 0.198014i
\(785\) −28.9939 + 14.1689i −1.03484 + 0.505711i
\(786\) 4.14488 + 7.17915i 0.147843 + 0.256072i
\(787\) −32.8966 18.9928i −1.17264 0.677022i −0.218336 0.975874i \(-0.570063\pi\)
−0.954299 + 0.298852i \(0.903396\pi\)
\(788\) −1.14893 + 0.663337i −0.0409291 + 0.0236304i
\(789\) −10.8721 + 18.8311i −0.387058 + 0.670404i
\(790\) −1.12323 + 16.2427i −0.0399628 + 0.577888i
\(791\) 10.9783 0.390342
\(792\) 0.157963 + 0.0912000i 0.00561297 + 0.00324065i
\(793\) 3.27027 1.88809i 0.116131 0.0670481i
\(794\) −17.0578 + 29.5449i −0.605358 + 1.04851i
\(795\) 8.49794 + 17.3894i 0.301391 + 0.616737i
\(796\) 12.3167 + 21.3331i 0.436553 + 0.756132i
\(797\) −1.01175 + 0.584137i −0.0358382 + 0.0206912i −0.517812 0.855494i \(-0.673253\pi\)
0.481974 + 0.876186i \(0.339920\pi\)
\(798\) 0.461698i 0.0163439i
\(799\) 19.2261 33.3006i 0.680171 1.17809i
\(800\) −3.94479 3.07224i −0.139469 0.108620i
\(801\) −0.419992 0.727447i −0.0148397 0.0257031i
\(802\) 36.6374i 1.29371i
\(803\) −1.65253 0.954087i −0.0583164 0.0336690i
\(804\) −0.428507 −0.0151123
\(805\) −5.91037 0.408721i −0.208313 0.0144055i
\(806\) 1.39382 21.5057i 0.0490952 0.757506i
\(807\) 13.9113i 0.489700i
\(808\) 11.7568i 0.413603i
\(809\) 26.1993 45.3786i 0.921119 1.59543i 0.123433 0.992353i \(-0.460610\pi\)
0.797687 0.603072i \(-0.206057\pi\)
\(810\) 0.154263 2.23074i 0.00542023 0.0783802i
\(811\) −12.9976 22.5125i −0.456408 0.790522i 0.542360 0.840146i \(-0.317531\pi\)
−0.998768 + 0.0496241i \(0.984198\pi\)
\(812\) 4.77145 + 2.75480i 0.167445 + 0.0966744i
\(813\) 14.4230 + 8.32714i 0.505838 + 0.292045i
\(814\) −1.16888 −0.0409693
\(815\) 3.74557 1.83041i 0.131202 0.0641164i
\(816\) 3.11459 + 5.39463i 0.109033 + 0.188850i
\(817\) 3.45489 1.99468i 0.120871 0.0697851i
\(818\) −18.2997 10.5653i −0.639833 0.369408i
\(819\) 1.49647 + 2.59196i 0.0522909 + 0.0905705i
\(820\) 2.32465 3.45217i 0.0811803 0.120555i
\(821\) −34.7207 −1.21176 −0.605880 0.795556i \(-0.707179\pi\)
−0.605880 + 0.795556i \(0.707179\pi\)
\(822\) 12.8405i 0.447864i
\(823\) 23.9449 + 13.8246i 0.834667 + 0.481895i 0.855448 0.517889i \(-0.173282\pi\)
−0.0207808 + 0.999784i \(0.506615\pi\)
\(824\) 4.81443 + 8.33883i 0.167719 + 0.290497i
\(825\) −0.719530 0.560376i −0.0250508 0.0195098i
\(826\) −4.66833 8.08579i −0.162432 0.281341i
\(827\) −13.7054 + 7.91284i −0.476585 + 0.275156i −0.718992 0.695018i \(-0.755396\pi\)
0.242407 + 0.970175i \(0.422063\pi\)
\(828\) 2.96744 1.71325i 0.103126 0.0595396i
\(829\) 40.3193 1.40035 0.700173 0.713973i \(-0.253106\pi\)
0.700173 + 0.713973i \(0.253106\pi\)
\(830\) −10.0610 + 14.9409i −0.349222 + 0.518605i
\(831\) 7.68356 13.3083i 0.266540 0.461660i
\(832\) −3.35207 + 1.93532i −0.116212 + 0.0670951i
\(833\) 39.8799i 1.38176i
\(834\) 1.92534 3.33479i 0.0666691 0.115474i
\(835\) 0.108425 1.56790i 0.00375220 0.0542593i
\(836\) 0.108910 0.00376674
\(837\) 3.08991 4.63168i 0.106803 0.160094i
\(838\) 22.8606i 0.789706i
\(839\) 34.2514 1.18249 0.591245 0.806492i \(-0.298637\pi\)
0.591245 + 0.806492i \(0.298637\pi\)
\(840\) 1.43417 + 0.965752i 0.0494835 + 0.0333216i
\(841\) 21.7701 0.750695
\(842\) 11.8383 6.83483i 0.407974 0.235544i
\(843\) 15.1091 + 8.72323i 0.520384 + 0.300444i
\(844\) −8.11534 + 14.0562i −0.279342 + 0.483834i
\(845\) 4.42099 + 0.305725i 0.152087 + 0.0105173i
\(846\) 3.08646 + 5.34590i 0.106115 + 0.183796i
\(847\) 7.34384 4.23997i 0.252337 0.145687i
\(848\) 7.49604 4.32784i 0.257415 0.148619i
\(849\) 14.4645 25.0533i 0.496421 0.859826i
\(850\) −11.7119 28.8600i −0.401716 0.989890i
\(851\) −10.9791 + 19.0164i −0.376359 + 0.651873i
\(852\) 8.05777i 0.276055i
\(853\) 32.9827i 1.12931i −0.825328 0.564654i \(-0.809010\pi\)
0.825328 0.564654i \(-0.190990\pi\)
\(854\) −0.377186 + 0.653305i −0.0129070 + 0.0223557i
\(855\) −0.586213 1.19957i −0.0200481 0.0410244i
\(856\) −3.57179 + 6.18652i −0.122081 + 0.211451i
\(857\) −16.7037 + 9.64390i −0.570588 + 0.329429i −0.757384 0.652969i \(-0.773523\pi\)
0.186796 + 0.982399i \(0.440190\pi\)
\(858\) −0.611418 + 0.353002i −0.0208735 + 0.0120513i
\(859\) −18.9369 32.7997i −0.646120 1.11911i −0.984042 0.177938i \(-0.943057\pi\)
0.337922 0.941174i \(-0.390276\pi\)
\(860\) −1.03067 + 14.9042i −0.0351456 + 0.508230i
\(861\) −0.719602 + 1.24639i −0.0245240 + 0.0424768i
\(862\) −15.7672 9.10321i −0.537034 0.310057i
\(863\) 0.655557 0.378486i 0.0223154 0.0128838i −0.488801 0.872395i \(-0.662566\pi\)
0.511116 + 0.859512i \(0.329232\pi\)
\(864\) −1.00000 −0.0340207
\(865\) 13.6260 + 9.17559i 0.463298 + 0.311980i
\(866\) 2.97874 0.101222
\(867\) 21.8028i 0.740461i
\(868\) 1.90697 + 3.85985i 0.0647266 + 0.131012i
\(869\) 1.32811 0.0450530
\(870\) 15.8947 + 1.09917i 0.538882 + 0.0372653i
\(871\) 0.829299 1.43639i 0.0280997 0.0486702i
\(872\) 15.9921i 0.541561i
\(873\) 8.24181 4.75841i 0.278943 0.161048i
\(874\) 1.02297 1.77184i 0.0346026 0.0599334i
\(875\) −6.43791 5.76985i −0.217641 0.195056i
\(876\) 10.4615 0.353461
\(877\) 1.71623 0.990863i 0.0579528 0.0334591i −0.470744 0.882270i \(-0.656014\pi\)
0.528696 + 0.848811i \(0.322681\pi\)
\(878\) −3.25908 + 1.88163i −0.109989 + 0.0635019i
\(879\) 4.25665 + 7.37274i 0.143573 + 0.248676i
\(880\) −0.227811 + 0.338306i −0.00767952 + 0.0114043i
\(881\) −25.1594 43.5774i −0.847643 1.46816i −0.883306 0.468796i \(-0.844688\pi\)
0.0356635 0.999364i \(-0.488646\pi\)
\(882\) 5.54438 + 3.20105i 0.186689 + 0.107785i
\(883\) 11.1079i 0.373809i 0.982378 + 0.186905i \(0.0598456\pi\)
−0.982378 + 0.186905i \(0.940154\pi\)
\(884\) −24.1109 −0.810938
\(885\) −22.3955 15.0809i −0.752817 0.506939i
\(886\) −13.5654 23.4960i −0.455739 0.789362i
\(887\) −15.3394 8.85623i −0.515048 0.297363i 0.219858 0.975532i \(-0.429441\pi\)
−0.734906 + 0.678169i \(0.762774\pi\)
\(888\) 5.54979 3.20418i 0.186239 0.107525i
\(889\) 4.63878 + 8.03459i 0.155580 + 0.269472i
\(890\) 1.68753 0.824674i 0.0565663 0.0276432i
\(891\) −0.182400 −0.00611063
\(892\) 17.2965 + 9.98614i 0.579130 + 0.334361i
\(893\) 3.19201 + 1.84291i 0.106816 + 0.0616705i
\(894\) 6.29694 + 10.9066i 0.210601 + 0.364772i
\(895\) −1.09513 0.0757314i −0.0366060 0.00253142i
\(896\) 0.386621 0.669647i 0.0129161 0.0223713i
\(897\) 13.2627i 0.442830i
\(898\) 41.4038i 1.38166i
\(899\) 33.0022 + 22.0166i 1.10068 + 0.734294i
\(900\) 4.95241 + 0.688239i 0.165080 + 0.0229413i
\(901\) 53.9179 1.79627
\(902\) −0.294011 0.169747i −0.00978948 0.00565196i
\(903\) 5.16625i 0.171922i
\(904\) −7.09885 12.2956i −0.236104 0.408945i
\(905\) −21.1789 + 31.4512i −0.704010 + 1.04547i
\(906\) −6.44928 + 11.1705i −0.214263 + 0.371114i
\(907\) 0.154060i 0.00511547i 0.999997 + 0.00255774i \(0.000814153\pi\)
−0.999997 + 0.00255774i \(0.999186\pi\)
\(908\) −20.2265 + 11.6778i −0.671239 + 0.387540i
\(909\) 5.87840 + 10.1817i 0.194974 + 0.337705i
\(910\) −6.01284 + 2.93839i −0.199324 + 0.0974068i
\(911\) −5.64684 + 9.78062i −0.187088 + 0.324046i −0.944278 0.329148i \(-0.893238\pi\)
0.757190 + 0.653195i \(0.226572\pi\)
\(912\) −0.517099 + 0.298547i −0.0171229 + 0.00988589i
\(913\) 1.27247 + 0.734659i 0.0421125 + 0.0243137i
\(914\) 24.6010 0.813729
\(915\) −0.150498 + 2.17630i −0.00497531 + 0.0719464i
\(916\) −6.66108 + 11.5373i −0.220088 + 0.381204i
\(917\) 5.55122 3.20500i 0.183317 0.105838i
\(918\) −5.39463 3.11459i −0.178049 0.102797i
\(919\) −1.62927 2.82198i −0.0537446 0.0930884i 0.837901 0.545822i \(-0.183782\pi\)
−0.891646 + 0.452733i \(0.850449\pi\)
\(920\) 3.36405 + 6.88387i 0.110910 + 0.226955i
\(921\) −10.7902 18.6892i −0.355550 0.615830i
\(922\) 5.75649i 0.189580i
\(923\) 27.0102 + 15.5944i 0.889052 + 0.513295i
\(924\) 0.0705196 0.122144i 0.00231993 0.00401823i
\(925\) −29.6901 + 12.0488i −0.976204 + 0.396162i
\(926\) −30.2945 −0.995540
\(927\) −8.33883 4.81443i −0.273883 0.158127i
\(928\) 7.12532i 0.233900i
\(929\) 5.49130 0.180164 0.0900819 0.995934i \(-0.471287\pi\)
0.0900819 + 0.995934i \(0.471287\pi\)
\(930\) 9.85542 + 7.60728i 0.323172 + 0.249453i
\(931\) 3.82266 0.125283
\(932\) 10.6233i 0.347978i
\(933\) 6.49529 + 3.75006i 0.212646 + 0.122771i
\(934\) 24.8358 0.812653
\(935\) −2.28264 + 1.11550i −0.0746504 + 0.0364806i
\(936\) 1.93532 3.35207i 0.0632579 0.109566i
\(937\) 39.2023 + 22.6335i 1.28068 + 0.739403i 0.976973 0.213362i \(-0.0684412\pi\)
0.303710 + 0.952764i \(0.401775\pi\)
\(938\) 0.331340i 0.0108186i
\(939\) −5.87130 10.1694i −0.191603 0.331866i
\(940\) −12.4014 + 6.06041i −0.404490 + 0.197669i
\(941\) −0.692766 1.19991i −0.0225835 0.0391158i 0.854513 0.519430i \(-0.173856\pi\)
−0.877096 + 0.480315i \(0.840523\pi\)
\(942\) −12.4984 7.21597i −0.407221 0.235109i
\(943\) −5.52318 + 3.18881i −0.179859 + 0.103842i
\(944\) −6.03735 + 10.4570i −0.196499 + 0.340346i
\(945\) −1.72490 0.119282i −0.0561110 0.00388025i
\(946\) 1.21867 0.0396223
\(947\) 11.0470 + 6.37797i 0.358978 + 0.207256i 0.668633 0.743593i \(-0.266880\pi\)
−0.309654 + 0.950849i \(0.600213\pi\)
\(948\) −6.30578 + 3.64065i −0.204802 + 0.118243i
\(949\) −20.2463 + 35.0676i −0.657223 + 1.13834i
\(950\) 2.76636 1.12264i 0.0897525 0.0364232i
\(951\) −12.5819 21.7925i −0.407997 0.706672i
\(952\) 4.17135 2.40833i 0.135194 0.0780545i
\(953\) 34.8545i 1.12905i 0.825417 + 0.564524i \(0.190940\pi\)
−0.825417 + 0.564524i \(0.809060\pi\)
\(954\) −4.32784 + 7.49604i −0.140119 + 0.242693i
\(955\) 12.3365 18.3201i 0.399201 0.592824i
\(956\) 4.64700 + 8.04884i 0.150295 + 0.260318i
\(957\) 1.29966i 0.0420120i
\(958\) −33.6819 19.4463i −1.08821 0.628281i
\(959\) 9.92881 0.320618
\(960\) 0.154263 2.23074i 0.00497880 0.0719968i
\(961\) 11.9049 + 28.6229i 0.384029 + 0.923321i
\(962\) 24.8044i 0.799726i
\(963\) 7.14358i 0.230199i
\(964\) 4.18140 7.24239i 0.134674 0.233262i
\(965\) −1.34767 + 19.4883i −0.0433832 + 0.627350i
\(966\) −1.32476 2.29455i −0.0426233 0.0738258i
\(967\) 38.4657 + 22.2082i 1.23697 + 0.714168i 0.968475 0.249112i \(-0.0801387\pi\)
0.268500 + 0.963280i \(0.413472\pi\)
\(968\) −9.49747 5.48337i −0.305260 0.176242i
\(969\) −3.71941 −0.119485
\(970\) 9.34338 + 19.1194i 0.299998 + 0.613886i
\(971\) 3.59816 + 6.23220i 0.115470 + 0.200001i 0.917968 0.396655i \(-0.129829\pi\)
−0.802497 + 0.596656i \(0.796496\pi\)
\(972\) 0.866025 0.500000i 0.0277778 0.0160375i
\(973\) −2.57860 1.48875i −0.0826661 0.0477273i
\(974\) 0.971337 + 1.68240i 0.0311236 + 0.0539077i
\(975\) −11.8915 + 15.2689i −0.380833 + 0.488995i
\(976\) 0.975597 0.0312281
\(977\) 42.7392i 1.36735i −0.729788 0.683673i \(-0.760381\pi\)
0.729788 0.683673i \(-0.239619\pi\)
\(978\) 1.61461 + 0.932193i 0.0516294 + 0.0298082i
\(979\) −0.0766065 0.132686i −0.00244835 0.00424067i
\(980\) −7.99600 + 11.8743i −0.255423 + 0.379310i
\(981\) −7.99606 13.8496i −0.255294 0.442183i
\(982\) −25.7295 + 14.8550i −0.821062 + 0.474041i
\(983\) −0.451740 + 0.260812i −0.0144083 + 0.00831862i −0.507187 0.861836i \(-0.669315\pi\)
0.492779 + 0.870155i \(0.335981\pi\)
\(984\) 1.86126 0.0593348
\(985\) 2.46065 + 1.65697i 0.0784027 + 0.0527955i
\(986\) 22.1925 38.4385i 0.706752 1.22413i
\(987\) 4.13367 2.38658i 0.131576 0.0759655i
\(988\) 2.31114i 0.0735271i
\(989\) 11.4467 19.8263i 0.363985 0.630440i
\(990\) 0.0281375 0.406887i 0.000894268 0.0129317i
\(991\) −61.1300 −1.94186 −0.970930 0.239365i \(-0.923061\pi\)
−0.970930 + 0.239365i \(0.923061\pi\)
\(992\) 3.08991 4.63168i 0.0981047 0.147056i
\(993\) 32.8533i 1.04257i
\(994\) −6.23060 −0.197623
\(995\) 30.7662 45.6887i 0.975355 1.44843i
\(996\) −8.05547 −0.255247
\(997\) −16.8876 + 9.75004i −0.534834 + 0.308787i −0.742983 0.669310i \(-0.766590\pi\)
0.208148 + 0.978097i \(0.433256\pi\)
\(998\) −3.46166 1.99859i −0.109577 0.0632643i
\(999\) −3.20418 + 5.54979i −0.101376 + 0.175588i
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 930.2.s.c.439.10 yes 24
5.4 even 2 inner 930.2.s.c.439.5 24
31.25 even 3 inner 930.2.s.c.769.11 yes 24
155.149 even 6 inner 930.2.s.c.769.4 yes 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
930.2.s.c.439.5 24 5.4 even 2 inner
930.2.s.c.439.10 yes 24 1.1 even 1 trivial
930.2.s.c.769.4 yes 24 155.149 even 6 inner
930.2.s.c.769.11 yes 24 31.25 even 3 inner