Properties

Label 966.2.i.h.415.2
Level $966$
Weight $2$
Character 966.415
Analytic conductor $7.714$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [966,2,Mod(277,966)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(966, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 4, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("966.277");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 966.i (of order \(3\), 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: \(7.71354883526\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{2}, \sqrt{-3})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} + 2x^{2} + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 415.2
Root \(-0.707107 - 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 966.415
Dual form 966.2.i.h.277.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +1.00000 q^{6} +(1.62132 - 2.09077i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +1.00000 q^{6} +(1.62132 - 2.09077i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.500000 + 0.866025i) q^{10} +(1.50000 + 2.59808i) q^{11} +(-0.500000 + 0.866025i) q^{12} +1.41421 q^{13} +(1.00000 + 2.44949i) q^{14} -1.00000 q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.707107 + 1.22474i) q^{17} +(-0.500000 - 0.866025i) q^{18} +(1.70711 - 2.95680i) q^{19} -1.00000 q^{20} +(-2.62132 - 0.358719i) q^{21} -3.00000 q^{22} +(0.500000 - 0.866025i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(2.00000 + 3.46410i) q^{25} +(-0.707107 + 1.22474i) q^{26} +1.00000 q^{27} +(-2.62132 - 0.358719i) q^{28} -0.757359 q^{29} +(0.500000 - 0.866025i) q^{30} +(-2.32843 - 4.03295i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(1.50000 - 2.59808i) q^{33} -1.41421 q^{34} +(-1.00000 - 2.44949i) q^{35} +1.00000 q^{36} +(4.53553 - 7.85578i) q^{37} +(1.70711 + 2.95680i) q^{38} +(-0.707107 - 1.22474i) q^{39} +(0.500000 - 0.866025i) q^{40} +1.75736 q^{41} +(1.62132 - 2.09077i) q^{42} -7.65685 q^{43} +(1.50000 - 2.59808i) q^{44} +(0.500000 + 0.866025i) q^{45} +(0.500000 + 0.866025i) q^{46} +(4.65685 - 8.06591i) q^{47} +1.00000 q^{48} +(-1.74264 - 6.77962i) q^{49} -4.00000 q^{50} +(0.707107 - 1.22474i) q^{51} +(-0.707107 - 1.22474i) q^{52} +(1.08579 + 1.88064i) q^{53} +(-0.500000 + 0.866025i) q^{54} +3.00000 q^{55} +(1.62132 - 2.09077i) q^{56} -3.41421 q^{57} +(0.378680 - 0.655892i) q^{58} +(0.378680 + 0.655892i) q^{59} +(0.500000 + 0.866025i) q^{60} +(3.00000 - 5.19615i) q^{61} +4.65685 q^{62} +(1.00000 + 2.44949i) q^{63} +1.00000 q^{64} +(0.707107 - 1.22474i) q^{65} +(1.50000 + 2.59808i) q^{66} +(2.17157 + 3.76127i) q^{67} +(0.707107 - 1.22474i) q^{68} -1.00000 q^{69} +(2.62132 + 0.358719i) q^{70} +5.89949 q^{71} +(-0.500000 + 0.866025i) q^{72} +(-2.82843 - 4.89898i) q^{73} +(4.53553 + 7.85578i) q^{74} +(2.00000 - 3.46410i) q^{75} -3.41421 q^{76} +(7.86396 + 1.07616i) q^{77} +1.41421 q^{78} +(0.207107 - 0.358719i) q^{79} +(0.500000 + 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-0.878680 + 1.52192i) q^{82} +12.3137 q^{83} +(1.00000 + 2.44949i) q^{84} +1.41421 q^{85} +(3.82843 - 6.63103i) q^{86} +(0.378680 + 0.655892i) q^{87} +(1.50000 + 2.59808i) q^{88} +(-7.36396 + 12.7548i) q^{89} -1.00000 q^{90} +(2.29289 - 2.95680i) q^{91} -1.00000 q^{92} +(-2.32843 + 4.03295i) q^{93} +(4.65685 + 8.06591i) q^{94} +(-1.70711 - 2.95680i) q^{95} +(-0.500000 + 0.866025i) q^{96} -3.58579 q^{97} +(6.74264 + 1.88064i) q^{98} -3.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 2 q^{2} - 2 q^{3} - 2 q^{4} + 2 q^{5} + 4 q^{6} - 2 q^{7} + 4 q^{8} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 2 q^{2} - 2 q^{3} - 2 q^{4} + 2 q^{5} + 4 q^{6} - 2 q^{7} + 4 q^{8} - 2 q^{9} + 2 q^{10} + 6 q^{11} - 2 q^{12} + 4 q^{14} - 4 q^{15} - 2 q^{16} - 2 q^{18} + 4 q^{19} - 4 q^{20} - 2 q^{21} - 12 q^{22} + 2 q^{23} - 2 q^{24} + 8 q^{25} + 4 q^{27} - 2 q^{28} - 20 q^{29} + 2 q^{30} + 2 q^{31} - 2 q^{32} + 6 q^{33} - 4 q^{35} + 4 q^{36} + 4 q^{37} + 4 q^{38} + 2 q^{40} + 24 q^{41} - 2 q^{42} - 8 q^{43} + 6 q^{44} + 2 q^{45} + 2 q^{46} - 4 q^{47} + 4 q^{48} + 10 q^{49} - 16 q^{50} + 10 q^{53} - 2 q^{54} + 12 q^{55} - 2 q^{56} - 8 q^{57} + 10 q^{58} + 10 q^{59} + 2 q^{60} + 12 q^{61} - 4 q^{62} + 4 q^{63} + 4 q^{64} + 6 q^{66} + 20 q^{67} - 4 q^{69} + 2 q^{70} - 16 q^{71} - 2 q^{72} + 4 q^{74} + 8 q^{75} - 8 q^{76} + 6 q^{77} - 2 q^{79} + 2 q^{80} - 2 q^{81} - 12 q^{82} + 4 q^{83} + 4 q^{84} + 4 q^{86} + 10 q^{87} + 6 q^{88} - 4 q^{89} - 4 q^{90} + 12 q^{91} - 4 q^{92} + 2 q^{93} - 4 q^{94} - 4 q^{95} - 2 q^{96} - 20 q^{97} + 10 q^{98} - 12 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/966\mathbb{Z}\right)^\times\).

\(n\) \(323\) \(829\) \(925\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 + 0.866025i −0.353553 + 0.612372i
\(3\) −0.500000 0.866025i −0.288675 0.500000i
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 0.500000 0.866025i 0.223607 0.387298i −0.732294 0.680989i \(-0.761550\pi\)
0.955901 + 0.293691i \(0.0948835\pi\)
\(6\) 1.00000 0.408248
\(7\) 1.62132 2.09077i 0.612801 0.790237i
\(8\) 1.00000 0.353553
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) 0.500000 + 0.866025i 0.158114 + 0.273861i
\(11\) 1.50000 + 2.59808i 0.452267 + 0.783349i 0.998526 0.0542666i \(-0.0172821\pi\)
−0.546259 + 0.837616i \(0.683949\pi\)
\(12\) −0.500000 + 0.866025i −0.144338 + 0.250000i
\(13\) 1.41421 0.392232 0.196116 0.980581i \(-0.437167\pi\)
0.196116 + 0.980581i \(0.437167\pi\)
\(14\) 1.00000 + 2.44949i 0.267261 + 0.654654i
\(15\) −1.00000 −0.258199
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 0.707107 + 1.22474i 0.171499 + 0.297044i 0.938944 0.344070i \(-0.111806\pi\)
−0.767445 + 0.641114i \(0.778472\pi\)
\(18\) −0.500000 0.866025i −0.117851 0.204124i
\(19\) 1.70711 2.95680i 0.391637 0.678335i −0.601028 0.799228i \(-0.705242\pi\)
0.992666 + 0.120892i \(0.0385755\pi\)
\(20\) −1.00000 −0.223607
\(21\) −2.62132 0.358719i −0.572019 0.0782790i
\(22\) −3.00000 −0.639602
\(23\) 0.500000 0.866025i 0.104257 0.180579i
\(24\) −0.500000 0.866025i −0.102062 0.176777i
\(25\) 2.00000 + 3.46410i 0.400000 + 0.692820i
\(26\) −0.707107 + 1.22474i −0.138675 + 0.240192i
\(27\) 1.00000 0.192450
\(28\) −2.62132 0.358719i −0.495383 0.0677916i
\(29\) −0.757359 −0.140638 −0.0703190 0.997525i \(-0.522402\pi\)
−0.0703190 + 0.997525i \(0.522402\pi\)
\(30\) 0.500000 0.866025i 0.0912871 0.158114i
\(31\) −2.32843 4.03295i −0.418198 0.724340i 0.577560 0.816348i \(-0.304005\pi\)
−0.995758 + 0.0920080i \(0.970671\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) 1.50000 2.59808i 0.261116 0.452267i
\(34\) −1.41421 −0.242536
\(35\) −1.00000 2.44949i −0.169031 0.414039i
\(36\) 1.00000 0.166667
\(37\) 4.53553 7.85578i 0.745637 1.29148i −0.204259 0.978917i \(-0.565479\pi\)
0.949896 0.312565i \(-0.101188\pi\)
\(38\) 1.70711 + 2.95680i 0.276929 + 0.479656i
\(39\) −0.707107 1.22474i −0.113228 0.196116i
\(40\) 0.500000 0.866025i 0.0790569 0.136931i
\(41\) 1.75736 0.274453 0.137227 0.990540i \(-0.456181\pi\)
0.137227 + 0.990540i \(0.456181\pi\)
\(42\) 1.62132 2.09077i 0.250175 0.322613i
\(43\) −7.65685 −1.16766 −0.583830 0.811876i \(-0.698446\pi\)
−0.583830 + 0.811876i \(0.698446\pi\)
\(44\) 1.50000 2.59808i 0.226134 0.391675i
\(45\) 0.500000 + 0.866025i 0.0745356 + 0.129099i
\(46\) 0.500000 + 0.866025i 0.0737210 + 0.127688i
\(47\) 4.65685 8.06591i 0.679272 1.17653i −0.295928 0.955210i \(-0.595629\pi\)
0.975200 0.221324i \(-0.0710377\pi\)
\(48\) 1.00000 0.144338
\(49\) −1.74264 6.77962i −0.248949 0.968517i
\(50\) −4.00000 −0.565685
\(51\) 0.707107 1.22474i 0.0990148 0.171499i
\(52\) −0.707107 1.22474i −0.0980581 0.169842i
\(53\) 1.08579 + 1.88064i 0.149144 + 0.258325i 0.930911 0.365245i \(-0.119015\pi\)
−0.781767 + 0.623570i \(0.785681\pi\)
\(54\) −0.500000 + 0.866025i −0.0680414 + 0.117851i
\(55\) 3.00000 0.404520
\(56\) 1.62132 2.09077i 0.216658 0.279391i
\(57\) −3.41421 −0.452224
\(58\) 0.378680 0.655892i 0.0497231 0.0861229i
\(59\) 0.378680 + 0.655892i 0.0492999 + 0.0853899i 0.889622 0.456697i \(-0.150968\pi\)
−0.840322 + 0.542087i \(0.817634\pi\)
\(60\) 0.500000 + 0.866025i 0.0645497 + 0.111803i
\(61\) 3.00000 5.19615i 0.384111 0.665299i −0.607535 0.794293i \(-0.707841\pi\)
0.991645 + 0.128994i \(0.0411748\pi\)
\(62\) 4.65685 0.591421
\(63\) 1.00000 + 2.44949i 0.125988 + 0.308607i
\(64\) 1.00000 0.125000
\(65\) 0.707107 1.22474i 0.0877058 0.151911i
\(66\) 1.50000 + 2.59808i 0.184637 + 0.319801i
\(67\) 2.17157 + 3.76127i 0.265300 + 0.459513i 0.967642 0.252327i \(-0.0811957\pi\)
−0.702342 + 0.711839i \(0.747862\pi\)
\(68\) 0.707107 1.22474i 0.0857493 0.148522i
\(69\) −1.00000 −0.120386
\(70\) 2.62132 + 0.358719i 0.313308 + 0.0428752i
\(71\) 5.89949 0.700141 0.350071 0.936723i \(-0.386158\pi\)
0.350071 + 0.936723i \(0.386158\pi\)
\(72\) −0.500000 + 0.866025i −0.0589256 + 0.102062i
\(73\) −2.82843 4.89898i −0.331042 0.573382i 0.651674 0.758499i \(-0.274067\pi\)
−0.982717 + 0.185117i \(0.940734\pi\)
\(74\) 4.53553 + 7.85578i 0.527245 + 0.913215i
\(75\) 2.00000 3.46410i 0.230940 0.400000i
\(76\) −3.41421 −0.391637
\(77\) 7.86396 + 1.07616i 0.896182 + 0.122640i
\(78\) 1.41421 0.160128
\(79\) 0.207107 0.358719i 0.0233013 0.0403591i −0.854140 0.520044i \(-0.825916\pi\)
0.877441 + 0.479685i \(0.159249\pi\)
\(80\) 0.500000 + 0.866025i 0.0559017 + 0.0968246i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) −0.878680 + 1.52192i −0.0970339 + 0.168068i
\(83\) 12.3137 1.35161 0.675803 0.737083i \(-0.263797\pi\)
0.675803 + 0.737083i \(0.263797\pi\)
\(84\) 1.00000 + 2.44949i 0.109109 + 0.267261i
\(85\) 1.41421 0.153393
\(86\) 3.82843 6.63103i 0.412830 0.715042i
\(87\) 0.378680 + 0.655892i 0.0405987 + 0.0703190i
\(88\) 1.50000 + 2.59808i 0.159901 + 0.276956i
\(89\) −7.36396 + 12.7548i −0.780578 + 1.35200i 0.151027 + 0.988530i \(0.451742\pi\)
−0.931605 + 0.363472i \(0.881591\pi\)
\(90\) −1.00000 −0.105409
\(91\) 2.29289 2.95680i 0.240361 0.309956i
\(92\) −1.00000 −0.104257
\(93\) −2.32843 + 4.03295i −0.241447 + 0.418198i
\(94\) 4.65685 + 8.06591i 0.480318 + 0.831935i
\(95\) −1.70711 2.95680i −0.175145 0.303361i
\(96\) −0.500000 + 0.866025i −0.0510310 + 0.0883883i
\(97\) −3.58579 −0.364081 −0.182041 0.983291i \(-0.558270\pi\)
−0.182041 + 0.983291i \(0.558270\pi\)
\(98\) 6.74264 + 1.88064i 0.681110 + 0.189973i
\(99\) −3.00000 −0.301511
\(100\) 2.00000 3.46410i 0.200000 0.346410i
\(101\) 2.24264 + 3.88437i 0.223151 + 0.386509i 0.955763 0.294137i \(-0.0950323\pi\)
−0.732612 + 0.680646i \(0.761699\pi\)
\(102\) 0.707107 + 1.22474i 0.0700140 + 0.121268i
\(103\) 6.82843 11.8272i 0.672825 1.16537i −0.304275 0.952584i \(-0.598414\pi\)
0.977100 0.212783i \(-0.0682526\pi\)
\(104\) 1.41421 0.138675
\(105\) −1.62132 + 2.09077i −0.158225 + 0.204038i
\(106\) −2.17157 −0.210922
\(107\) 3.74264 6.48244i 0.361815 0.626681i −0.626445 0.779466i \(-0.715491\pi\)
0.988260 + 0.152784i \(0.0488240\pi\)
\(108\) −0.500000 0.866025i −0.0481125 0.0833333i
\(109\) −2.65685 4.60181i −0.254480 0.440773i 0.710274 0.703926i \(-0.248571\pi\)
−0.964754 + 0.263152i \(0.915238\pi\)
\(110\) −1.50000 + 2.59808i −0.143019 + 0.247717i
\(111\) −9.07107 −0.860988
\(112\) 1.00000 + 2.44949i 0.0944911 + 0.231455i
\(113\) −17.4142 −1.63819 −0.819096 0.573657i \(-0.805524\pi\)
−0.819096 + 0.573657i \(0.805524\pi\)
\(114\) 1.70711 2.95680i 0.159885 0.276929i
\(115\) −0.500000 0.866025i −0.0466252 0.0807573i
\(116\) 0.378680 + 0.655892i 0.0351595 + 0.0608981i
\(117\) −0.707107 + 1.22474i −0.0653720 + 0.113228i
\(118\) −0.757359 −0.0697206
\(119\) 3.70711 + 0.507306i 0.339830 + 0.0465047i
\(120\) −1.00000 −0.0912871
\(121\) 1.00000 1.73205i 0.0909091 0.157459i
\(122\) 3.00000 + 5.19615i 0.271607 + 0.470438i
\(123\) −0.878680 1.52192i −0.0792279 0.137227i
\(124\) −2.32843 + 4.03295i −0.209099 + 0.362170i
\(125\) 9.00000 0.804984
\(126\) −2.62132 0.358719i −0.233526 0.0319573i
\(127\) −5.82843 −0.517189 −0.258595 0.965986i \(-0.583259\pi\)
−0.258595 + 0.965986i \(0.583259\pi\)
\(128\) −0.500000 + 0.866025i −0.0441942 + 0.0765466i
\(129\) 3.82843 + 6.63103i 0.337074 + 0.583830i
\(130\) 0.707107 + 1.22474i 0.0620174 + 0.107417i
\(131\) 0.621320 1.07616i 0.0542850 0.0940244i −0.837606 0.546275i \(-0.816045\pi\)
0.891891 + 0.452251i \(0.149379\pi\)
\(132\) −3.00000 −0.261116
\(133\) −3.41421 8.36308i −0.296050 0.725171i
\(134\) −4.34315 −0.375191
\(135\) 0.500000 0.866025i 0.0430331 0.0745356i
\(136\) 0.707107 + 1.22474i 0.0606339 + 0.105021i
\(137\) 9.48528 + 16.4290i 0.810382 + 1.40362i 0.912597 + 0.408861i \(0.134074\pi\)
−0.102214 + 0.994762i \(0.532593\pi\)
\(138\) 0.500000 0.866025i 0.0425628 0.0737210i
\(139\) −5.31371 −0.450703 −0.225351 0.974278i \(-0.572353\pi\)
−0.225351 + 0.974278i \(0.572353\pi\)
\(140\) −1.62132 + 2.09077i −0.137027 + 0.176702i
\(141\) −9.31371 −0.784356
\(142\) −2.94975 + 5.10911i −0.247537 + 0.428747i
\(143\) 2.12132 + 3.67423i 0.177394 + 0.307255i
\(144\) −0.500000 0.866025i −0.0416667 0.0721688i
\(145\) −0.378680 + 0.655892i −0.0314476 + 0.0544689i
\(146\) 5.65685 0.468165
\(147\) −5.00000 + 4.89898i −0.412393 + 0.404061i
\(148\) −9.07107 −0.745637
\(149\) −6.82843 + 11.8272i −0.559407 + 0.968921i 0.438139 + 0.898907i \(0.355638\pi\)
−0.997546 + 0.0700136i \(0.977696\pi\)
\(150\) 2.00000 + 3.46410i 0.163299 + 0.282843i
\(151\) 0.671573 + 1.16320i 0.0546518 + 0.0946597i 0.892057 0.451923i \(-0.149262\pi\)
−0.837405 + 0.546583i \(0.815928\pi\)
\(152\) 1.70711 2.95680i 0.138465 0.239828i
\(153\) −1.41421 −0.114332
\(154\) −4.86396 + 6.27231i −0.391949 + 0.505437i
\(155\) −4.65685 −0.374048
\(156\) −0.707107 + 1.22474i −0.0566139 + 0.0980581i
\(157\) 1.94975 + 3.37706i 0.155607 + 0.269519i 0.933280 0.359150i \(-0.116933\pi\)
−0.777673 + 0.628669i \(0.783600\pi\)
\(158\) 0.207107 + 0.358719i 0.0164765 + 0.0285382i
\(159\) 1.08579 1.88064i 0.0861085 0.149144i
\(160\) −1.00000 −0.0790569
\(161\) −1.00000 2.44949i −0.0788110 0.193047i
\(162\) 1.00000 0.0785674
\(163\) 0.707107 1.22474i 0.0553849 0.0959294i −0.837004 0.547197i \(-0.815695\pi\)
0.892389 + 0.451268i \(0.149028\pi\)
\(164\) −0.878680 1.52192i −0.0686134 0.118842i
\(165\) −1.50000 2.59808i −0.116775 0.202260i
\(166\) −6.15685 + 10.6640i −0.477865 + 0.827686i
\(167\) 18.4853 1.43043 0.715217 0.698902i \(-0.246328\pi\)
0.715217 + 0.698902i \(0.246328\pi\)
\(168\) −2.62132 0.358719i −0.202239 0.0276758i
\(169\) −11.0000 −0.846154
\(170\) −0.707107 + 1.22474i −0.0542326 + 0.0939336i
\(171\) 1.70711 + 2.95680i 0.130546 + 0.226112i
\(172\) 3.82843 + 6.63103i 0.291915 + 0.505611i
\(173\) −2.41421 + 4.18154i −0.183549 + 0.317917i −0.943087 0.332547i \(-0.892092\pi\)
0.759537 + 0.650464i \(0.225425\pi\)
\(174\) −0.757359 −0.0574153
\(175\) 10.4853 + 1.43488i 0.792613 + 0.108467i
\(176\) −3.00000 −0.226134
\(177\) 0.378680 0.655892i 0.0284633 0.0492999i
\(178\) −7.36396 12.7548i −0.551952 0.956009i
\(179\) −8.00000 13.8564i −0.597948 1.03568i −0.993124 0.117071i \(-0.962650\pi\)
0.395175 0.918606i \(-0.370684\pi\)
\(180\) 0.500000 0.866025i 0.0372678 0.0645497i
\(181\) −12.4853 −0.928024 −0.464012 0.885829i \(-0.653590\pi\)
−0.464012 + 0.885829i \(0.653590\pi\)
\(182\) 1.41421 + 3.46410i 0.104828 + 0.256776i
\(183\) −6.00000 −0.443533
\(184\) 0.500000 0.866025i 0.0368605 0.0638442i
\(185\) −4.53553 7.85578i −0.333459 0.577568i
\(186\) −2.32843 4.03295i −0.170729 0.295711i
\(187\) −2.12132 + 3.67423i −0.155126 + 0.268687i
\(188\) −9.31371 −0.679272
\(189\) 1.62132 2.09077i 0.117934 0.152081i
\(190\) 3.41421 0.247693
\(191\) −0.707107 + 1.22474i −0.0511645 + 0.0886194i −0.890473 0.455035i \(-0.849627\pi\)
0.839309 + 0.543655i \(0.182960\pi\)
\(192\) −0.500000 0.866025i −0.0360844 0.0625000i
\(193\) 9.81371 + 16.9978i 0.706406 + 1.22353i 0.966182 + 0.257862i \(0.0830181\pi\)
−0.259775 + 0.965669i \(0.583649\pi\)
\(194\) 1.79289 3.10538i 0.128722 0.222953i
\(195\) −1.41421 −0.101274
\(196\) −5.00000 + 4.89898i −0.357143 + 0.349927i
\(197\) −3.17157 −0.225965 −0.112983 0.993597i \(-0.536040\pi\)
−0.112983 + 0.993597i \(0.536040\pi\)
\(198\) 1.50000 2.59808i 0.106600 0.184637i
\(199\) −2.65685 4.60181i −0.188339 0.326213i 0.756357 0.654159i \(-0.226977\pi\)
−0.944697 + 0.327945i \(0.893644\pi\)
\(200\) 2.00000 + 3.46410i 0.141421 + 0.244949i
\(201\) 2.17157 3.76127i 0.153171 0.265300i
\(202\) −4.48528 −0.315583
\(203\) −1.22792 + 1.58346i −0.0861832 + 0.111137i
\(204\) −1.41421 −0.0990148
\(205\) 0.878680 1.52192i 0.0613696 0.106295i
\(206\) 6.82843 + 11.8272i 0.475759 + 0.824039i
\(207\) 0.500000 + 0.866025i 0.0347524 + 0.0601929i
\(208\) −0.707107 + 1.22474i −0.0490290 + 0.0849208i
\(209\) 10.2426 0.708498
\(210\) −1.00000 2.44949i −0.0690066 0.169031i
\(211\) 4.82843 0.332403 0.166201 0.986092i \(-0.446850\pi\)
0.166201 + 0.986092i \(0.446850\pi\)
\(212\) 1.08579 1.88064i 0.0745721 0.129163i
\(213\) −2.94975 5.10911i −0.202113 0.350071i
\(214\) 3.74264 + 6.48244i 0.255842 + 0.443131i
\(215\) −3.82843 + 6.63103i −0.261097 + 0.452233i
\(216\) 1.00000 0.0680414
\(217\) −12.2071 1.67050i −0.828672 0.113401i
\(218\) 5.31371 0.359890
\(219\) −2.82843 + 4.89898i −0.191127 + 0.331042i
\(220\) −1.50000 2.59808i −0.101130 0.175162i
\(221\) 1.00000 + 1.73205i 0.0672673 + 0.116510i
\(222\) 4.53553 7.85578i 0.304405 0.527245i
\(223\) −10.1716 −0.681139 −0.340569 0.940219i \(-0.610620\pi\)
−0.340569 + 0.940219i \(0.610620\pi\)
\(224\) −2.62132 0.358719i −0.175144 0.0239680i
\(225\) −4.00000 −0.266667
\(226\) 8.70711 15.0812i 0.579188 1.00318i
\(227\) 3.91421 + 6.77962i 0.259795 + 0.449979i 0.966187 0.257842i \(-0.0830115\pi\)
−0.706392 + 0.707821i \(0.749678\pi\)
\(228\) 1.70711 + 2.95680i 0.113056 + 0.195819i
\(229\) −11.3640 + 19.6830i −0.750952 + 1.30069i 0.196410 + 0.980522i \(0.437072\pi\)
−0.947362 + 0.320165i \(0.896262\pi\)
\(230\) 1.00000 0.0659380
\(231\) −3.00000 7.34847i −0.197386 0.483494i
\(232\) −0.757359 −0.0497231
\(233\) −7.60660 + 13.1750i −0.498325 + 0.863124i −0.999998 0.00193299i \(-0.999385\pi\)
0.501673 + 0.865057i \(0.332718\pi\)
\(234\) −0.707107 1.22474i −0.0462250 0.0800641i
\(235\) −4.65685 8.06591i −0.303780 0.526162i
\(236\) 0.378680 0.655892i 0.0246499 0.0426950i
\(237\) −0.414214 −0.0269061
\(238\) −2.29289 + 2.95680i −0.148626 + 0.191661i
\(239\) −23.3137 −1.50804 −0.754019 0.656852i \(-0.771887\pi\)
−0.754019 + 0.656852i \(0.771887\pi\)
\(240\) 0.500000 0.866025i 0.0322749 0.0559017i
\(241\) 4.96447 + 8.59871i 0.319789 + 0.553891i 0.980444 0.196799i \(-0.0630545\pi\)
−0.660655 + 0.750690i \(0.729721\pi\)
\(242\) 1.00000 + 1.73205i 0.0642824 + 0.111340i
\(243\) −0.500000 + 0.866025i −0.0320750 + 0.0555556i
\(244\) −6.00000 −0.384111
\(245\) −6.74264 1.88064i −0.430772 0.120150i
\(246\) 1.75736 0.112045
\(247\) 2.41421 4.18154i 0.153613 0.266065i
\(248\) −2.32843 4.03295i −0.147855 0.256093i
\(249\) −6.15685 10.6640i −0.390175 0.675803i
\(250\) −4.50000 + 7.79423i −0.284605 + 0.492950i
\(251\) 25.8284 1.63028 0.815138 0.579267i \(-0.196661\pi\)
0.815138 + 0.579267i \(0.196661\pi\)
\(252\) 1.62132 2.09077i 0.102134 0.131706i
\(253\) 3.00000 0.188608
\(254\) 2.91421 5.04757i 0.182854 0.316712i
\(255\) −0.707107 1.22474i −0.0442807 0.0766965i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 0.707107 1.22474i 0.0441081 0.0763975i −0.843129 0.537712i \(-0.819289\pi\)
0.887237 + 0.461315i \(0.152622\pi\)
\(258\) −7.65685 −0.476695
\(259\) −9.07107 22.2195i −0.563649 1.38065i
\(260\) −1.41421 −0.0877058
\(261\) 0.378680 0.655892i 0.0234397 0.0405987i
\(262\) 0.621320 + 1.07616i 0.0383853 + 0.0664853i
\(263\) −5.48528 9.50079i −0.338237 0.585844i 0.645864 0.763452i \(-0.276497\pi\)
−0.984101 + 0.177609i \(0.943164\pi\)
\(264\) 1.50000 2.59808i 0.0923186 0.159901i
\(265\) 2.17157 0.133399
\(266\) 8.94975 + 1.22474i 0.548744 + 0.0750939i
\(267\) 14.7279 0.901334
\(268\) 2.17157 3.76127i 0.132650 0.229756i
\(269\) −0.792893 1.37333i −0.0483436 0.0837335i 0.840841 0.541282i \(-0.182061\pi\)
−0.889185 + 0.457549i \(0.848728\pi\)
\(270\) 0.500000 + 0.866025i 0.0304290 + 0.0527046i
\(271\) 3.50000 6.06218i 0.212610 0.368251i −0.739921 0.672694i \(-0.765137\pi\)
0.952531 + 0.304443i \(0.0984703\pi\)
\(272\) −1.41421 −0.0857493
\(273\) −3.70711 0.507306i −0.224364 0.0307036i
\(274\) −18.9706 −1.14605
\(275\) −6.00000 + 10.3923i −0.361814 + 0.626680i
\(276\) 0.500000 + 0.866025i 0.0300965 + 0.0521286i
\(277\) 1.41421 + 2.44949i 0.0849719 + 0.147176i 0.905379 0.424604i \(-0.139587\pi\)
−0.820407 + 0.571779i \(0.806253\pi\)
\(278\) 2.65685 4.60181i 0.159348 0.275998i
\(279\) 4.65685 0.278799
\(280\) −1.00000 2.44949i −0.0597614 0.146385i
\(281\) −26.7279 −1.59445 −0.797227 0.603680i \(-0.793701\pi\)
−0.797227 + 0.603680i \(0.793701\pi\)
\(282\) 4.65685 8.06591i 0.277312 0.480318i
\(283\) 12.0711 + 20.9077i 0.717551 + 1.24283i 0.961968 + 0.273164i \(0.0880701\pi\)
−0.244417 + 0.969670i \(0.578597\pi\)
\(284\) −2.94975 5.10911i −0.175035 0.303170i
\(285\) −1.70711 + 2.95680i −0.101120 + 0.175145i
\(286\) −4.24264 −0.250873
\(287\) 2.84924 3.67423i 0.168185 0.216883i
\(288\) 1.00000 0.0589256
\(289\) 7.50000 12.9904i 0.441176 0.764140i
\(290\) −0.378680 0.655892i −0.0222368 0.0385153i
\(291\) 1.79289 + 3.10538i 0.105101 + 0.182041i
\(292\) −2.82843 + 4.89898i −0.165521 + 0.286691i
\(293\) −21.6274 −1.26349 −0.631744 0.775177i \(-0.717660\pi\)
−0.631744 + 0.775177i \(0.717660\pi\)
\(294\) −1.74264 6.77962i −0.101633 0.395395i
\(295\) 0.757359 0.0440952
\(296\) 4.53553 7.85578i 0.263623 0.456608i
\(297\) 1.50000 + 2.59808i 0.0870388 + 0.150756i
\(298\) −6.82843 11.8272i −0.395560 0.685130i
\(299\) 0.707107 1.22474i 0.0408930 0.0708288i
\(300\) −4.00000 −0.230940
\(301\) −12.4142 + 16.0087i −0.715543 + 0.922727i
\(302\) −1.34315 −0.0772894
\(303\) 2.24264 3.88437i 0.128836 0.223151i
\(304\) 1.70711 + 2.95680i 0.0979093 + 0.169584i
\(305\) −3.00000 5.19615i −0.171780 0.297531i
\(306\) 0.707107 1.22474i 0.0404226 0.0700140i
\(307\) 25.8995 1.47816 0.739081 0.673616i \(-0.235260\pi\)
0.739081 + 0.673616i \(0.235260\pi\)
\(308\) −3.00000 7.34847i −0.170941 0.418718i
\(309\) −13.6569 −0.776911
\(310\) 2.32843 4.03295i 0.132246 0.229056i
\(311\) −1.70711 2.95680i −0.0968011 0.167665i 0.813558 0.581484i \(-0.197528\pi\)
−0.910359 + 0.413820i \(0.864194\pi\)
\(312\) −0.707107 1.22474i −0.0400320 0.0693375i
\(313\) −8.37868 + 14.5123i −0.473591 + 0.820284i −0.999543 0.0302306i \(-0.990376\pi\)
0.525952 + 0.850514i \(0.323709\pi\)
\(314\) −3.89949 −0.220061
\(315\) 2.62132 + 0.358719i 0.147695 + 0.0202116i
\(316\) −0.414214 −0.0233013
\(317\) −4.96447 + 8.59871i −0.278832 + 0.482952i −0.971095 0.238694i \(-0.923281\pi\)
0.692263 + 0.721646i \(0.256614\pi\)
\(318\) 1.08579 + 1.88064i 0.0608879 + 0.105461i
\(319\) −1.13604 1.96768i −0.0636060 0.110169i
\(320\) 0.500000 0.866025i 0.0279508 0.0484123i
\(321\) −7.48528 −0.417788
\(322\) 2.62132 + 0.358719i 0.146080 + 0.0199907i
\(323\) 4.82843 0.268661
\(324\) −0.500000 + 0.866025i −0.0277778 + 0.0481125i
\(325\) 2.82843 + 4.89898i 0.156893 + 0.271746i
\(326\) 0.707107 + 1.22474i 0.0391630 + 0.0678323i
\(327\) −2.65685 + 4.60181i −0.146924 + 0.254480i
\(328\) 1.75736 0.0970339
\(329\) −9.31371 22.8138i −0.513481 1.25777i
\(330\) 3.00000 0.165145
\(331\) −12.9497 + 22.4296i −0.711782 + 1.23284i 0.252405 + 0.967622i \(0.418778\pi\)
−0.964187 + 0.265222i \(0.914555\pi\)
\(332\) −6.15685 10.6640i −0.337901 0.585262i
\(333\) 4.53553 + 7.85578i 0.248546 + 0.430494i
\(334\) −9.24264 + 16.0087i −0.505735 + 0.875958i
\(335\) 4.34315 0.237291
\(336\) 1.62132 2.09077i 0.0884503 0.114061i
\(337\) −13.9289 −0.758757 −0.379379 0.925242i \(-0.623862\pi\)
−0.379379 + 0.925242i \(0.623862\pi\)
\(338\) 5.50000 9.52628i 0.299161 0.518161i
\(339\) 8.70711 + 15.0812i 0.472905 + 0.819096i
\(340\) −0.707107 1.22474i −0.0383482 0.0664211i
\(341\) 6.98528 12.0989i 0.378274 0.655190i
\(342\) −3.41421 −0.184620
\(343\) −17.0000 7.34847i −0.917914 0.396780i
\(344\) −7.65685 −0.412830
\(345\) −0.500000 + 0.866025i −0.0269191 + 0.0466252i
\(346\) −2.41421 4.18154i −0.129789 0.224801i
\(347\) 7.31371 + 12.6677i 0.392620 + 0.680039i 0.992794 0.119831i \(-0.0382353\pi\)
−0.600174 + 0.799870i \(0.704902\pi\)
\(348\) 0.378680 0.655892i 0.0202994 0.0351595i
\(349\) 26.0416 1.39398 0.696988 0.717083i \(-0.254523\pi\)
0.696988 + 0.717083i \(0.254523\pi\)
\(350\) −6.48528 + 8.36308i −0.346653 + 0.447025i
\(351\) 1.41421 0.0754851
\(352\) 1.50000 2.59808i 0.0799503 0.138478i
\(353\) 11.3640 + 19.6830i 0.604843 + 1.04762i 0.992076 + 0.125637i \(0.0400973\pi\)
−0.387234 + 0.921982i \(0.626569\pi\)
\(354\) 0.378680 + 0.655892i 0.0201266 + 0.0348603i
\(355\) 2.94975 5.10911i 0.156556 0.271164i
\(356\) 14.7279 0.780578
\(357\) −1.41421 3.46410i −0.0748481 0.183340i
\(358\) 16.0000 0.845626
\(359\) −1.00000 + 1.73205i −0.0527780 + 0.0914141i −0.891207 0.453596i \(-0.850141\pi\)
0.838429 + 0.545010i \(0.183474\pi\)
\(360\) 0.500000 + 0.866025i 0.0263523 + 0.0456435i
\(361\) 3.67157 + 6.35935i 0.193241 + 0.334703i
\(362\) 6.24264 10.8126i 0.328106 0.568296i
\(363\) −2.00000 −0.104973
\(364\) −3.70711 0.507306i −0.194305 0.0265901i
\(365\) −5.65685 −0.296093
\(366\) 3.00000 5.19615i 0.156813 0.271607i
\(367\) 17.3492 + 30.0498i 0.905623 + 1.56859i 0.820079 + 0.572251i \(0.193930\pi\)
0.0855444 + 0.996334i \(0.472737\pi\)
\(368\) 0.500000 + 0.866025i 0.0260643 + 0.0451447i
\(369\) −0.878680 + 1.52192i −0.0457422 + 0.0792279i
\(370\) 9.07107 0.471582
\(371\) 5.69239 + 0.778985i 0.295534 + 0.0404429i
\(372\) 4.65685 0.241447
\(373\) 7.17157 12.4215i 0.371330 0.643162i −0.618440 0.785832i \(-0.712235\pi\)
0.989770 + 0.142669i \(0.0455685\pi\)
\(374\) −2.12132 3.67423i −0.109691 0.189990i
\(375\) −4.50000 7.79423i −0.232379 0.402492i
\(376\) 4.65685 8.06591i 0.240159 0.415967i
\(377\) −1.07107 −0.0551628
\(378\) 1.00000 + 2.44949i 0.0514344 + 0.125988i
\(379\) 28.9706 1.48812 0.744059 0.668114i \(-0.232898\pi\)
0.744059 + 0.668114i \(0.232898\pi\)
\(380\) −1.70711 + 2.95680i −0.0875727 + 0.151680i
\(381\) 2.91421 + 5.04757i 0.149300 + 0.258595i
\(382\) −0.707107 1.22474i −0.0361787 0.0626634i
\(383\) 0.636039 1.10165i 0.0325001 0.0562918i −0.849318 0.527882i \(-0.822986\pi\)
0.881818 + 0.471590i \(0.156320\pi\)
\(384\) 1.00000 0.0510310
\(385\) 4.86396 6.27231i 0.247890 0.319667i
\(386\) −19.6274 −0.999009
\(387\) 3.82843 6.63103i 0.194610 0.337074i
\(388\) 1.79289 + 3.10538i 0.0910204 + 0.157652i
\(389\) 0.585786 + 1.01461i 0.0297006 + 0.0514429i 0.880494 0.474058i \(-0.157211\pi\)
−0.850793 + 0.525501i \(0.823878\pi\)
\(390\) 0.707107 1.22474i 0.0358057 0.0620174i
\(391\) 1.41421 0.0715199
\(392\) −1.74264 6.77962i −0.0880166 0.342422i
\(393\) −1.24264 −0.0626829
\(394\) 1.58579 2.74666i 0.0798908 0.138375i
\(395\) −0.207107 0.358719i −0.0104207 0.0180491i
\(396\) 1.50000 + 2.59808i 0.0753778 + 0.130558i
\(397\) −0.221825 + 0.384213i −0.0111331 + 0.0192831i −0.871538 0.490327i \(-0.836877\pi\)
0.860405 + 0.509611i \(0.170211\pi\)
\(398\) 5.31371 0.266352
\(399\) −5.53553 + 7.13834i −0.277123 + 0.357364i
\(400\) −4.00000 −0.200000
\(401\) 0.242641 0.420266i 0.0121169 0.0209871i −0.859903 0.510457i \(-0.829476\pi\)
0.872020 + 0.489470i \(0.162810\pi\)
\(402\) 2.17157 + 3.76127i 0.108308 + 0.187595i
\(403\) −3.29289 5.70346i −0.164031 0.284109i
\(404\) 2.24264 3.88437i 0.111576 0.193255i
\(405\) −1.00000 −0.0496904
\(406\) −0.757359 1.85514i −0.0375871 0.0920692i
\(407\) 27.2132 1.34891
\(408\) 0.707107 1.22474i 0.0350070 0.0606339i
\(409\) 6.67157 + 11.5555i 0.329888 + 0.571383i 0.982489 0.186319i \(-0.0596557\pi\)
−0.652601 + 0.757701i \(0.726322\pi\)
\(410\) 0.878680 + 1.52192i 0.0433949 + 0.0751622i
\(411\) 9.48528 16.4290i 0.467874 0.810382i
\(412\) −13.6569 −0.672825
\(413\) 1.98528 + 0.271680i 0.0976893 + 0.0133685i
\(414\) −1.00000 −0.0491473
\(415\) 6.15685 10.6640i 0.302228 0.523474i
\(416\) −0.707107 1.22474i −0.0346688 0.0600481i
\(417\) 2.65685 + 4.60181i 0.130107 + 0.225351i
\(418\) −5.12132 + 8.87039i −0.250492 + 0.433865i
\(419\) −6.00000 −0.293119 −0.146560 0.989202i \(-0.546820\pi\)
−0.146560 + 0.989202i \(0.546820\pi\)
\(420\) 2.62132 + 0.358719i 0.127907 + 0.0175037i
\(421\) 31.4558 1.53306 0.766532 0.642206i \(-0.221981\pi\)
0.766532 + 0.642206i \(0.221981\pi\)
\(422\) −2.41421 + 4.18154i −0.117522 + 0.203554i
\(423\) 4.65685 + 8.06591i 0.226424 + 0.392178i
\(424\) 1.08579 + 1.88064i 0.0527305 + 0.0913318i
\(425\) −2.82843 + 4.89898i −0.137199 + 0.237635i
\(426\) 5.89949 0.285831
\(427\) −6.00000 14.6969i −0.290360 0.711235i
\(428\) −7.48528 −0.361815
\(429\) 2.12132 3.67423i 0.102418 0.177394i
\(430\) −3.82843 6.63103i −0.184623 0.319777i
\(431\) −3.17157 5.49333i −0.152769 0.264604i 0.779475 0.626433i \(-0.215486\pi\)
−0.932245 + 0.361829i \(0.882152\pi\)
\(432\) −0.500000 + 0.866025i −0.0240563 + 0.0416667i
\(433\) 30.0000 1.44171 0.720854 0.693087i \(-0.243750\pi\)
0.720854 + 0.693087i \(0.243750\pi\)
\(434\) 7.55025 9.73641i 0.362424 0.467363i
\(435\) 0.757359 0.0363126
\(436\) −2.65685 + 4.60181i −0.127240 + 0.220387i
\(437\) −1.70711 2.95680i −0.0816620 0.141443i
\(438\) −2.82843 4.89898i −0.135147 0.234082i
\(439\) −5.57107 + 9.64937i −0.265893 + 0.460539i −0.967797 0.251732i \(-0.919000\pi\)
0.701905 + 0.712271i \(0.252333\pi\)
\(440\) 3.00000 0.143019
\(441\) 6.74264 + 1.88064i 0.321078 + 0.0895542i
\(442\) −2.00000 −0.0951303
\(443\) −5.13604 + 8.89588i −0.244021 + 0.422656i −0.961856 0.273557i \(-0.911800\pi\)
0.717835 + 0.696213i \(0.245133\pi\)
\(444\) 4.53553 + 7.85578i 0.215247 + 0.372819i
\(445\) 7.36396 + 12.7548i 0.349085 + 0.604633i
\(446\) 5.08579 8.80884i 0.240819 0.417111i
\(447\) 13.6569 0.645947
\(448\) 1.62132 2.09077i 0.0766002 0.0987796i
\(449\) −1.75736 −0.0829349 −0.0414675 0.999140i \(-0.513203\pi\)
−0.0414675 + 0.999140i \(0.513203\pi\)
\(450\) 2.00000 3.46410i 0.0942809 0.163299i
\(451\) 2.63604 + 4.56575i 0.124126 + 0.214993i
\(452\) 8.70711 + 15.0812i 0.409548 + 0.709358i
\(453\) 0.671573 1.16320i 0.0315532 0.0546518i
\(454\) −7.82843 −0.367406
\(455\) −1.41421 3.46410i −0.0662994 0.162400i
\(456\) −3.41421 −0.159885
\(457\) −10.1066 + 17.5051i −0.472767 + 0.818856i −0.999514 0.0311656i \(-0.990078\pi\)
0.526747 + 0.850022i \(0.323411\pi\)
\(458\) −11.3640 19.6830i −0.531003 0.919724i
\(459\) 0.707107 + 1.22474i 0.0330049 + 0.0571662i
\(460\) −0.500000 + 0.866025i −0.0233126 + 0.0403786i
\(461\) 30.9706 1.44244 0.721221 0.692705i \(-0.243581\pi\)
0.721221 + 0.692705i \(0.243581\pi\)
\(462\) 7.86396 + 1.07616i 0.365865 + 0.0500674i
\(463\) −13.7990 −0.641293 −0.320647 0.947199i \(-0.603900\pi\)
−0.320647 + 0.947199i \(0.603900\pi\)
\(464\) 0.378680 0.655892i 0.0175798 0.0304490i
\(465\) 2.32843 + 4.03295i 0.107978 + 0.187024i
\(466\) −7.60660 13.1750i −0.352369 0.610321i
\(467\) −14.4142 + 24.9662i −0.667010 + 1.15530i 0.311726 + 0.950172i \(0.399093\pi\)
−0.978736 + 0.205124i \(0.934240\pi\)
\(468\) 1.41421 0.0653720
\(469\) 11.3848 + 1.55797i 0.525700 + 0.0719404i
\(470\) 9.31371 0.429609
\(471\) 1.94975 3.37706i 0.0898396 0.155607i
\(472\) 0.378680 + 0.655892i 0.0174301 + 0.0301899i
\(473\) −11.4853 19.8931i −0.528094 0.914685i
\(474\) 0.207107 0.358719i 0.00951273 0.0164765i
\(475\) 13.6569 0.626619
\(476\) −1.41421 3.46410i −0.0648204 0.158777i
\(477\) −2.17157 −0.0994295
\(478\) 11.6569 20.1903i 0.533172 0.923481i
\(479\) −15.2635 26.4371i −0.697405 1.20794i −0.969363 0.245632i \(-0.921005\pi\)
0.271958 0.962309i \(-0.412329\pi\)
\(480\) 0.500000 + 0.866025i 0.0228218 + 0.0395285i
\(481\) 6.41421 11.1097i 0.292463 0.506561i
\(482\) −9.92893 −0.452250
\(483\) −1.62132 + 2.09077i −0.0737726 + 0.0951333i
\(484\) −2.00000 −0.0909091
\(485\) −1.79289 + 3.10538i −0.0814111 + 0.141008i
\(486\) −0.500000 0.866025i −0.0226805 0.0392837i
\(487\) 14.7426 + 25.5350i 0.668053 + 1.15710i 0.978448 + 0.206494i \(0.0662053\pi\)
−0.310395 + 0.950608i \(0.600461\pi\)
\(488\) 3.00000 5.19615i 0.135804 0.235219i
\(489\) −1.41421 −0.0639529
\(490\) 5.00000 4.89898i 0.225877 0.221313i
\(491\) −9.10051 −0.410700 −0.205350 0.978689i \(-0.565833\pi\)
−0.205350 + 0.978689i \(0.565833\pi\)
\(492\) −0.878680 + 1.52192i −0.0396139 + 0.0686134i
\(493\) −0.535534 0.927572i −0.0241192 0.0417757i
\(494\) 2.41421 + 4.18154i 0.108621 + 0.188136i
\(495\) −1.50000 + 2.59808i −0.0674200 + 0.116775i
\(496\) 4.65685 0.209099
\(497\) 9.56497 12.3345i 0.429048 0.553277i
\(498\) 12.3137 0.551790
\(499\) 6.89949 11.9503i 0.308864 0.534968i −0.669250 0.743037i \(-0.733385\pi\)
0.978114 + 0.208069i \(0.0667179\pi\)
\(500\) −4.50000 7.79423i −0.201246 0.348569i
\(501\) −9.24264 16.0087i −0.412931 0.715217i
\(502\) −12.9142 + 22.3681i −0.576390 + 0.998336i
\(503\) −6.82843 −0.304465 −0.152232 0.988345i \(-0.548646\pi\)
−0.152232 + 0.988345i \(0.548646\pi\)
\(504\) 1.00000 + 2.44949i 0.0445435 + 0.109109i
\(505\) 4.48528 0.199592
\(506\) −1.50000 + 2.59808i −0.0666831 + 0.115499i
\(507\) 5.50000 + 9.52628i 0.244264 + 0.423077i
\(508\) 2.91421 + 5.04757i 0.129297 + 0.223950i
\(509\) −20.8640 + 36.1374i −0.924779 + 1.60176i −0.132862 + 0.991135i \(0.542417\pi\)
−0.791917 + 0.610629i \(0.790917\pi\)
\(510\) 1.41421 0.0626224
\(511\) −14.8284 2.02922i −0.655971 0.0897676i
\(512\) 1.00000 0.0441942
\(513\) 1.70711 2.95680i 0.0753706 0.130546i
\(514\) 0.707107 + 1.22474i 0.0311891 + 0.0540212i
\(515\) −6.82843 11.8272i −0.300896 0.521168i
\(516\) 3.82843 6.63103i 0.168537 0.291915i
\(517\) 27.9411 1.22885
\(518\) 23.7782 + 3.25397i 1.04475 + 0.142971i
\(519\) 4.82843 0.211944
\(520\) 0.707107 1.22474i 0.0310087 0.0537086i
\(521\) −13.0000 22.5167i −0.569540 0.986473i −0.996611 0.0822547i \(-0.973788\pi\)
0.427071 0.904218i \(-0.359545\pi\)
\(522\) 0.378680 + 0.655892i 0.0165744 + 0.0287076i
\(523\) 8.14214 14.1026i 0.356031 0.616663i −0.631263 0.775569i \(-0.717463\pi\)
0.987294 + 0.158905i \(0.0507965\pi\)
\(524\) −1.24264 −0.0542850
\(525\) −4.00000 9.79796i −0.174574 0.427618i
\(526\) 10.9706 0.478339
\(527\) 3.29289 5.70346i 0.143441 0.248447i
\(528\) 1.50000 + 2.59808i 0.0652791 + 0.113067i
\(529\) −0.500000 0.866025i −0.0217391 0.0376533i
\(530\) −1.08579 + 1.88064i −0.0471635 + 0.0816897i
\(531\) −0.757359 −0.0328666
\(532\) −5.53553 + 7.13834i −0.239996 + 0.309486i
\(533\) 2.48528 0.107649
\(534\) −7.36396 + 12.7548i −0.318670 + 0.551952i
\(535\) −3.74264 6.48244i −0.161808 0.280260i
\(536\) 2.17157 + 3.76127i 0.0937977 + 0.162462i
\(537\) −8.00000 + 13.8564i −0.345225 + 0.597948i
\(538\) 1.58579 0.0683681
\(539\) 15.0000 14.6969i 0.646096 0.633042i
\(540\) −1.00000 −0.0430331
\(541\) 19.8492 34.3799i 0.853386 1.47811i −0.0247491 0.999694i \(-0.507879\pi\)
0.878135 0.478413i \(-0.158788\pi\)
\(542\) 3.50000 + 6.06218i 0.150338 + 0.260393i
\(543\) 6.24264 + 10.8126i 0.267897 + 0.464012i
\(544\) 0.707107 1.22474i 0.0303170 0.0525105i
\(545\) −5.31371 −0.227614
\(546\) 2.29289 2.95680i 0.0981268 0.126539i
\(547\) 24.2426 1.03654 0.518270 0.855217i \(-0.326576\pi\)
0.518270 + 0.855217i \(0.326576\pi\)
\(548\) 9.48528 16.4290i 0.405191 0.701812i
\(549\) 3.00000 + 5.19615i 0.128037 + 0.221766i
\(550\) −6.00000 10.3923i −0.255841 0.443129i
\(551\) −1.29289 + 2.23936i −0.0550791 + 0.0953998i
\(552\) −1.00000 −0.0425628
\(553\) −0.414214 1.01461i −0.0176142 0.0431457i
\(554\) −2.82843 −0.120168
\(555\) −4.53553 + 7.85578i −0.192523 + 0.333459i
\(556\) 2.65685 + 4.60181i 0.112676 + 0.195160i
\(557\) 20.1569 + 34.9127i 0.854073 + 1.47930i 0.877502 + 0.479573i \(0.159208\pi\)
−0.0234287 + 0.999726i \(0.507458\pi\)
\(558\) −2.32843 + 4.03295i −0.0985702 + 0.170729i
\(559\) −10.8284 −0.457994
\(560\) 2.62132 + 0.358719i 0.110771 + 0.0151587i
\(561\) 4.24264 0.179124
\(562\) 13.3640 23.1471i 0.563725 0.976400i
\(563\) 6.57107 + 11.3814i 0.276937 + 0.479670i 0.970622 0.240609i \(-0.0773472\pi\)
−0.693685 + 0.720279i \(0.744014\pi\)
\(564\) 4.65685 + 8.06591i 0.196089 + 0.339636i
\(565\) −8.70711 + 15.0812i −0.366311 + 0.634469i
\(566\) −24.1421 −1.01477
\(567\) −2.62132 0.358719i −0.110085 0.0150648i
\(568\) 5.89949 0.247537
\(569\) 2.92893 5.07306i 0.122787 0.212674i −0.798079 0.602553i \(-0.794150\pi\)
0.920866 + 0.389880i \(0.127483\pi\)
\(570\) −1.70711 2.95680i −0.0715028 0.123847i
\(571\) −20.2635 35.0973i −0.847999 1.46878i −0.882991 0.469390i \(-0.844474\pi\)
0.0349916 0.999388i \(-0.488860\pi\)
\(572\) 2.12132 3.67423i 0.0886969 0.153627i
\(573\) 1.41421 0.0590796
\(574\) 1.75736 + 4.30463i 0.0733508 + 0.179672i
\(575\) 4.00000 0.166812
\(576\) −0.500000 + 0.866025i −0.0208333 + 0.0360844i
\(577\) 3.81371 + 6.60554i 0.158767 + 0.274992i 0.934424 0.356162i \(-0.115915\pi\)
−0.775657 + 0.631154i \(0.782582\pi\)
\(578\) 7.50000 + 12.9904i 0.311959 + 0.540329i
\(579\) 9.81371 16.9978i 0.407844 0.706406i
\(580\) 0.757359 0.0314476
\(581\) 19.9645 25.7451i 0.828266 1.06809i
\(582\) −3.58579 −0.148636
\(583\) −3.25736 + 5.64191i −0.134906 + 0.233664i
\(584\) −2.82843 4.89898i −0.117041 0.202721i
\(585\) 0.707107 + 1.22474i 0.0292353 + 0.0506370i
\(586\) 10.8137 18.7299i 0.446710 0.773725i
\(587\) −2.41421 −0.0996453 −0.0498226 0.998758i \(-0.515866\pi\)
−0.0498226 + 0.998758i \(0.515866\pi\)
\(588\) 6.74264 + 1.88064i 0.278062 + 0.0775562i
\(589\) −15.8995 −0.655127
\(590\) −0.378680 + 0.655892i −0.0155900 + 0.0270027i
\(591\) 1.58579 + 2.74666i 0.0652305 + 0.112983i
\(592\) 4.53553 + 7.85578i 0.186409 + 0.322870i
\(593\) −4.48528 + 7.76874i −0.184188 + 0.319024i −0.943303 0.331934i \(-0.892299\pi\)
0.759114 + 0.650957i \(0.225632\pi\)
\(594\) −3.00000 −0.123091
\(595\) 2.29289 2.95680i 0.0939995 0.121217i
\(596\) 13.6569 0.559407
\(597\) −2.65685 + 4.60181i −0.108738 + 0.188339i
\(598\) 0.707107 + 1.22474i 0.0289157 + 0.0500835i
\(599\) 0.464466 + 0.804479i 0.0189776 + 0.0328701i 0.875358 0.483475i \(-0.160626\pi\)
−0.856381 + 0.516345i \(0.827292\pi\)
\(600\) 2.00000 3.46410i 0.0816497 0.141421i
\(601\) −40.9411 −1.67002 −0.835012 0.550232i \(-0.814539\pi\)
−0.835012 + 0.550232i \(0.814539\pi\)
\(602\) −7.65685 18.7554i −0.312070 0.764412i
\(603\) −4.34315 −0.176867
\(604\) 0.671573 1.16320i 0.0273259 0.0473299i
\(605\) −1.00000 1.73205i −0.0406558 0.0704179i
\(606\) 2.24264 + 3.88437i 0.0911011 + 0.157792i
\(607\) −9.64214 + 16.7007i −0.391362 + 0.677859i −0.992629 0.121189i \(-0.961329\pi\)
0.601267 + 0.799048i \(0.294663\pi\)
\(608\) −3.41421 −0.138465
\(609\) 1.98528 + 0.271680i 0.0804477 + 0.0110090i
\(610\) 6.00000 0.242933
\(611\) 6.58579 11.4069i 0.266432 0.461474i
\(612\) 0.707107 + 1.22474i 0.0285831 + 0.0495074i
\(613\) 8.00000 + 13.8564i 0.323117 + 0.559655i 0.981129 0.193352i \(-0.0619359\pi\)
−0.658012 + 0.753007i \(0.728603\pi\)
\(614\) −12.9497 + 22.4296i −0.522609 + 0.905186i
\(615\) −1.75736 −0.0708636
\(616\) 7.86396 + 1.07616i 0.316848 + 0.0433597i
\(617\) −31.9411 −1.28590 −0.642951 0.765908i \(-0.722290\pi\)
−0.642951 + 0.765908i \(0.722290\pi\)
\(618\) 6.82843 11.8272i 0.274680 0.475759i
\(619\) −4.94975 8.57321i −0.198947 0.344587i 0.749240 0.662298i \(-0.230419\pi\)
−0.948187 + 0.317712i \(0.897086\pi\)
\(620\) 2.32843 + 4.03295i 0.0935119 + 0.161967i
\(621\) 0.500000 0.866025i 0.0200643 0.0347524i
\(622\) 3.41421 0.136897
\(623\) 14.7279 + 36.0759i 0.590062 + 1.44535i
\(624\) 1.41421 0.0566139
\(625\) −5.50000 + 9.52628i −0.220000 + 0.381051i
\(626\) −8.37868 14.5123i −0.334879 0.580028i
\(627\) −5.12132 8.87039i −0.204526 0.354249i
\(628\) 1.94975 3.37706i 0.0778034 0.134759i
\(629\) 12.8284 0.511503
\(630\) −1.62132 + 2.09077i −0.0645949 + 0.0832983i
\(631\) 2.41421 0.0961083 0.0480542 0.998845i \(-0.484698\pi\)
0.0480542 + 0.998845i \(0.484698\pi\)
\(632\) 0.207107 0.358719i 0.00823827 0.0142691i
\(633\) −2.41421 4.18154i −0.0959564 0.166201i
\(634\) −4.96447 8.59871i −0.197164 0.341498i
\(635\) −2.91421 + 5.04757i −0.115647 + 0.200307i
\(636\) −2.17157 −0.0861085
\(637\) −2.46447 9.58783i −0.0976457 0.379883i
\(638\) 2.27208 0.0899524
\(639\) −2.94975 + 5.10911i −0.116690 + 0.202113i
\(640\) 0.500000 + 0.866025i 0.0197642 + 0.0342327i
\(641\) −19.8492 34.3799i −0.783998 1.35792i −0.929596 0.368580i \(-0.879844\pi\)
0.145598 0.989344i \(-0.453489\pi\)
\(642\) 3.74264 6.48244i 0.147710 0.255842i
\(643\) −10.5858 −0.417463 −0.208731 0.977973i \(-0.566933\pi\)
−0.208731 + 0.977973i \(0.566933\pi\)
\(644\) −1.62132 + 2.09077i −0.0638890 + 0.0823879i
\(645\) 7.65685 0.301488
\(646\) −2.41421 + 4.18154i −0.0949860 + 0.164521i
\(647\) 0.414214 + 0.717439i 0.0162844 + 0.0282054i 0.874053 0.485831i \(-0.161483\pi\)
−0.857768 + 0.514036i \(0.828150\pi\)
\(648\) −0.500000 0.866025i −0.0196419 0.0340207i
\(649\) −1.13604 + 1.96768i −0.0445934 + 0.0772381i
\(650\) −5.65685 −0.221880
\(651\) 4.65685 + 11.4069i 0.182517 + 0.447072i
\(652\) −1.41421 −0.0553849
\(653\) −22.8640 + 39.6015i −0.894736 + 1.54973i −0.0606049 + 0.998162i \(0.519303\pi\)
−0.834131 + 0.551566i \(0.814030\pi\)
\(654\) −2.65685 4.60181i −0.103891 0.179945i
\(655\) −0.621320 1.07616i −0.0242770 0.0420490i
\(656\) −0.878680 + 1.52192i −0.0343067 + 0.0594209i
\(657\) 5.65685 0.220695
\(658\) 24.4142 + 3.34101i 0.951765 + 0.130246i
\(659\) −43.9411 −1.71170 −0.855852 0.517221i \(-0.826966\pi\)
−0.855852 + 0.517221i \(0.826966\pi\)
\(660\) −1.50000 + 2.59808i −0.0583874 + 0.101130i
\(661\) −5.48528 9.50079i −0.213353 0.369538i 0.739409 0.673256i \(-0.235105\pi\)
−0.952762 + 0.303719i \(0.901772\pi\)
\(662\) −12.9497 22.4296i −0.503306 0.871752i
\(663\) 1.00000 1.73205i 0.0388368 0.0672673i
\(664\) 12.3137 0.477865
\(665\) −8.94975 1.22474i −0.347056 0.0474936i
\(666\) −9.07107 −0.351497
\(667\) −0.378680 + 0.655892i −0.0146625 + 0.0253963i
\(668\) −9.24264 16.0087i −0.357609 0.619396i
\(669\) 5.08579 + 8.80884i 0.196628 + 0.340569i
\(670\) −2.17157 + 3.76127i −0.0838952 + 0.145311i
\(671\) 18.0000 0.694882
\(672\) 1.00000 + 2.44949i 0.0385758 + 0.0944911i
\(673\) 10.0294 0.386606 0.193303 0.981139i \(-0.438080\pi\)
0.193303 + 0.981139i \(0.438080\pi\)
\(674\) 6.96447 12.0628i 0.268261 0.464642i
\(675\) 2.00000 + 3.46410i 0.0769800 + 0.133333i
\(676\) 5.50000 + 9.52628i 0.211538 + 0.366395i
\(677\) 21.3284 36.9419i 0.819718 1.41979i −0.0861720 0.996280i \(-0.527463\pi\)
0.905890 0.423513i \(-0.139203\pi\)
\(678\) −17.4142 −0.668789
\(679\) −5.81371 + 7.49706i −0.223110 + 0.287711i
\(680\) 1.41421 0.0542326
\(681\) 3.91421 6.77962i 0.149993 0.259795i
\(682\) 6.98528 + 12.0989i 0.267480 + 0.463289i
\(683\) 3.52082 + 6.09823i 0.134720 + 0.233342i 0.925491 0.378771i \(-0.123653\pi\)
−0.790770 + 0.612113i \(0.790320\pi\)
\(684\) 1.70711 2.95680i 0.0652729 0.113056i
\(685\) 18.9706 0.724828
\(686\) 14.8640 11.0482i 0.567509 0.421822i
\(687\) 22.7279 0.867124
\(688\) 3.82843 6.63103i 0.145957 0.252806i
\(689\) 1.53553 + 2.65962i 0.0584992 + 0.101324i
\(690\) −0.500000 0.866025i −0.0190347 0.0329690i
\(691\) 23.2929 40.3445i 0.886103 1.53478i 0.0416597 0.999132i \(-0.486735\pi\)
0.844444 0.535644i \(-0.179931\pi\)
\(692\) 4.82843 0.183549
\(693\) −4.86396 + 6.27231i −0.184767 + 0.238265i
\(694\) −14.6274 −0.555249
\(695\) −2.65685 + 4.60181i −0.100780 + 0.174556i
\(696\) 0.378680 + 0.655892i 0.0143538 + 0.0248615i
\(697\) 1.24264 + 2.15232i 0.0470684 + 0.0815248i
\(698\) −13.0208 + 22.5527i −0.492845 + 0.853633i
\(699\) 15.2132 0.575416
\(700\) −4.00000 9.79796i −0.151186 0.370328i
\(701\) 0.514719 0.0194407 0.00972033 0.999953i \(-0.496906\pi\)
0.00972033 + 0.999953i \(0.496906\pi\)
\(702\) −0.707107 + 1.22474i −0.0266880 + 0.0462250i
\(703\) −15.4853 26.8213i −0.584038 1.01158i
\(704\) 1.50000 + 2.59808i 0.0565334 + 0.0979187i
\(705\) −4.65685 + 8.06591i −0.175387 + 0.303780i
\(706\) −22.7279 −0.855377
\(707\) 11.7574 + 1.60896i 0.442181 + 0.0605111i
\(708\) −0.757359 −0.0284633
\(709\) 3.29289 5.70346i 0.123667 0.214198i −0.797544 0.603261i \(-0.793868\pi\)
0.921211 + 0.389063i \(0.127201\pi\)
\(710\) 2.94975 + 5.10911i 0.110702 + 0.191742i
\(711\) 0.207107 + 0.358719i 0.00776711 + 0.0134530i
\(712\) −7.36396 + 12.7548i −0.275976 + 0.478005i
\(713\) −4.65685 −0.174401
\(714\) 3.70711 + 0.507306i 0.138735 + 0.0189854i
\(715\) 4.24264 0.158666
\(716\) −8.00000 + 13.8564i −0.298974 + 0.517838i
\(717\) 11.6569 + 20.1903i 0.435333 + 0.754019i
\(718\) −1.00000 1.73205i −0.0373197 0.0646396i
\(719\) 0.0710678 0.123093i 0.00265038 0.00459060i −0.864697 0.502294i \(-0.832490\pi\)
0.867348 + 0.497703i \(0.165823\pi\)
\(720\) −1.00000 −0.0372678
\(721\) −13.6569 33.4523i −0.508608 1.24583i
\(722\) −7.34315 −0.273284
\(723\) 4.96447 8.59871i 0.184630 0.319789i
\(724\) 6.24264 + 10.8126i 0.232006 + 0.401846i
\(725\) −1.51472 2.62357i −0.0562552 0.0974369i
\(726\) 1.00000 1.73205i 0.0371135 0.0642824i
\(727\) −5.44365 −0.201894 −0.100947 0.994892i \(-0.532187\pi\)
−0.100947 + 0.994892i \(0.532187\pi\)
\(728\) 2.29289 2.95680i 0.0849803 0.109586i
\(729\) 1.00000 0.0370370
\(730\) 2.82843 4.89898i 0.104685 0.181319i
\(731\) −5.41421 9.37769i −0.200252 0.346847i
\(732\) 3.00000 + 5.19615i 0.110883 + 0.192055i
\(733\) −7.77817 + 13.4722i −0.287293 + 0.497607i −0.973163 0.230118i \(-0.926089\pi\)
0.685869 + 0.727725i \(0.259422\pi\)
\(734\) −34.6985 −1.28074
\(735\) 1.74264 + 6.77962i 0.0642783 + 0.250070i
\(736\) −1.00000 −0.0368605
\(737\) −6.51472 + 11.2838i −0.239973 + 0.415645i
\(738\) −0.878680 1.52192i −0.0323446 0.0560226i
\(739\) −10.4142 18.0379i −0.383093 0.663537i 0.608410 0.793623i \(-0.291808\pi\)
−0.991503 + 0.130087i \(0.958474\pi\)
\(740\) −4.53553 + 7.85578i −0.166730 + 0.288784i
\(741\) −4.82843 −0.177377
\(742\) −3.52082 + 4.54026i −0.129253 + 0.166678i
\(743\) −6.24264 −0.229020 −0.114510 0.993422i \(-0.536530\pi\)
−0.114510 + 0.993422i \(0.536530\pi\)
\(744\) −2.32843 + 4.03295i −0.0853643 + 0.147855i
\(745\) 6.82843 + 11.8272i 0.250174 + 0.433314i
\(746\) 7.17157 + 12.4215i 0.262570 + 0.454784i
\(747\) −6.15685 + 10.6640i −0.225268 + 0.390175i
\(748\) 4.24264 0.155126
\(749\) −7.48528 18.3351i −0.273506 0.669951i
\(750\) 9.00000 0.328634
\(751\) −17.7635 + 30.7672i −0.648198 + 1.12271i 0.335355 + 0.942092i \(0.391144\pi\)
−0.983553 + 0.180620i \(0.942190\pi\)
\(752\) 4.65685 + 8.06591i 0.169818 + 0.294133i
\(753\) −12.9142 22.3681i −0.470620 0.815138i
\(754\) 0.535534 0.927572i 0.0195030 0.0337802i
\(755\) 1.34315 0.0488821
\(756\) −2.62132 0.358719i −0.0953365 0.0130465i
\(757\) 39.0711 1.42006 0.710031 0.704170i \(-0.248681\pi\)
0.710031 + 0.704170i \(0.248681\pi\)
\(758\) −14.4853 + 25.0892i −0.526129 + 0.911282i
\(759\) −1.50000 2.59808i −0.0544466 0.0943042i
\(760\) −1.70711 2.95680i −0.0619233 0.107254i
\(761\) −2.29289 + 3.97141i −0.0831173 + 0.143963i −0.904587 0.426288i \(-0.859821\pi\)
0.821470 + 0.570252i \(0.193154\pi\)
\(762\) −5.82843 −0.211142
\(763\) −13.9289 1.90613i −0.504261 0.0690066i
\(764\) 1.41421 0.0511645
\(765\) −0.707107 + 1.22474i −0.0255655 + 0.0442807i
\(766\) 0.636039 + 1.10165i 0.0229810 + 0.0398043i
\(767\) 0.535534 + 0.927572i 0.0193370 + 0.0334927i
\(768\) −0.500000 + 0.866025i −0.0180422 + 0.0312500i
\(769\) −42.0122 −1.51500 −0.757499 0.652836i \(-0.773579\pi\)
−0.757499 + 0.652836i \(0.773579\pi\)
\(770\) 3.00000 + 7.34847i 0.108112 + 0.264820i
\(771\) −1.41421 −0.0509317
\(772\) 9.81371 16.9978i 0.353203 0.611766i
\(773\) −11.4142 19.7700i −0.410541 0.711077i 0.584408 0.811460i \(-0.301327\pi\)
−0.994949 + 0.100382i \(0.967993\pi\)
\(774\) 3.82843 + 6.63103i 0.137610 + 0.238347i
\(775\) 9.31371 16.1318i 0.334558 0.579472i
\(776\) −3.58579 −0.128722
\(777\) −14.7071 + 18.9655i −0.527615 + 0.680384i
\(778\) −1.17157 −0.0420029
\(779\) 3.00000 5.19615i 0.107486 0.186171i
\(780\) 0.707107 + 1.22474i 0.0253185 + 0.0438529i
\(781\) 8.84924 + 15.3273i 0.316651 + 0.548455i
\(782\) −0.707107 + 1.22474i −0.0252861 + 0.0437968i
\(783\) −0.757359 −0.0270658
\(784\) 6.74264 + 1.88064i 0.240809 + 0.0671656i
\(785\) 3.89949 0.139179
\(786\) 0.621320 1.07616i 0.0221618 0.0383853i
\(787\) −11.7279 20.3134i −0.418055 0.724093i 0.577689 0.816257i \(-0.303955\pi\)
−0.995744 + 0.0921643i \(0.970621\pi\)
\(788\) 1.58579 + 2.74666i 0.0564913 + 0.0978458i
\(789\) −5.48528 + 9.50079i −0.195281 + 0.338237i
\(790\) 0.414214 0.0147371
\(791\) −28.2340 + 36.4091i −1.00389 + 1.29456i
\(792\) −3.00000 −0.106600
\(793\) 4.24264 7.34847i 0.150661 0.260952i
\(794\) −0.221825 0.384213i −0.00787229 0.0136352i
\(795\) −1.08579 1.88064i −0.0385089 0.0666993i
\(796\) −2.65685 + 4.60181i −0.0941697 + 0.163107i
\(797\) −3.97056 −0.140645 −0.0703223 0.997524i \(-0.522403\pi\)
−0.0703223 + 0.997524i \(0.522403\pi\)
\(798\) −3.41421 8.36308i −0.120862 0.296050i
\(799\) 13.1716 0.465977
\(800\) 2.00000 3.46410i 0.0707107 0.122474i
\(801\) −7.36396 12.7548i −0.260193 0.450667i
\(802\) 0.242641 + 0.420266i 0.00856794 + 0.0148401i
\(803\) 8.48528 14.6969i 0.299439 0.518644i
\(804\) −4.34315 −0.153171
\(805\) −2.62132 0.358719i −0.0923894 0.0126432i
\(806\) 6.58579 0.231974
\(807\) −0.792893 + 1.37333i −0.0279112 + 0.0483436i
\(808\) 2.24264 + 3.88437i 0.0788958 + 0.136652i
\(809\) −25.2635 43.7576i −0.888216 1.53843i −0.841983 0.539504i \(-0.818612\pi\)
−0.0462329 0.998931i \(-0.514722\pi\)
\(810\) 0.500000 0.866025i 0.0175682 0.0304290i
\(811\) −42.2843 −1.48480 −0.742401 0.669956i \(-0.766313\pi\)
−0.742401 + 0.669956i \(0.766313\pi\)
\(812\) 1.98528 + 0.271680i 0.0696697 + 0.00953408i
\(813\) −7.00000 −0.245501
\(814\) −13.6066 + 23.5673i −0.476911 + 0.826034i
\(815\) −0.707107 1.22474i −0.0247689 0.0429009i
\(816\) 0.707107 + 1.22474i 0.0247537 + 0.0428746i
\(817\) −13.0711 + 22.6398i −0.457299 + 0.792065i
\(818\) −13.3431 −0.466532
\(819\) 1.41421 + 3.46410i 0.0494166 + 0.121046i
\(820\) −1.75736 −0.0613696
\(821\) −7.37868 + 12.7802i −0.257518 + 0.446034i −0.965576 0.260120i \(-0.916238\pi\)
0.708059 + 0.706154i \(0.249571\pi\)
\(822\) 9.48528 + 16.4290i 0.330837 + 0.573027i
\(823\) −23.3137 40.3805i −0.812665 1.40758i −0.910993 0.412423i \(-0.864683\pi\)
0.0983278 0.995154i \(-0.468651\pi\)
\(824\) 6.82843 11.8272i 0.237880 0.412019i
\(825\) 12.0000 0.417786
\(826\) −1.22792 + 1.58346i −0.0427249 + 0.0550958i
\(827\) 20.7990 0.723252 0.361626 0.932323i \(-0.382222\pi\)
0.361626 + 0.932323i \(0.382222\pi\)
\(828\) 0.500000 0.866025i 0.0173762 0.0300965i
\(829\) 13.7574 + 23.8284i 0.477813 + 0.827596i 0.999677 0.0254328i \(-0.00809638\pi\)
−0.521864 + 0.853029i \(0.674763\pi\)
\(830\) 6.15685 + 10.6640i 0.213708 + 0.370152i
\(831\) 1.41421 2.44949i 0.0490585 0.0849719i
\(832\) 1.41421 0.0490290
\(833\) 7.07107 6.92820i 0.244998 0.240048i
\(834\) −5.31371 −0.183999
\(835\) 9.24264 16.0087i 0.319855 0.554005i
\(836\) −5.12132 8.87039i −0.177125 0.306789i
\(837\) −2.32843 4.03295i −0.0804822 0.139399i
\(838\) 3.00000 5.19615i 0.103633 0.179498i
\(839\) −17.6985 −0.611020 −0.305510 0.952189i \(-0.598827\pi\)
−0.305510 + 0.952189i \(0.598827\pi\)
\(840\) −1.62132 + 2.09077i −0.0559409 + 0.0721384i
\(841\) −28.4264 −0.980221
\(842\) −15.7279 + 27.2416i −0.542020 + 0.938806i
\(843\) 13.3640 + 23.1471i 0.460279 + 0.797227i
\(844\) −2.41421 4.18154i −0.0831007 0.143935i
\(845\) −5.50000 + 9.52628i −0.189206 + 0.327714i
\(846\) −9.31371 −0.320212
\(847\) −2.00000 4.89898i −0.0687208 0.168331i
\(848\) −2.17157 −0.0745721
\(849\) 12.0711 20.9077i 0.414278 0.717551i
\(850\) −2.82843 4.89898i −0.0970143 0.168034i
\(851\) −4.53553 7.85578i −0.155476 0.269293i
\(852\) −2.94975 + 5.10911i −0.101057 + 0.175035i
\(853\) −28.1421 −0.963568 −0.481784 0.876290i \(-0.660011\pi\)
−0.481784 + 0.876290i \(0.660011\pi\)
\(854\) 15.7279 + 2.15232i 0.538198 + 0.0736508i
\(855\) 3.41421 0.116764
\(856\) 3.74264 6.48244i 0.127921 0.221565i
\(857\) −13.4350 23.2702i −0.458932 0.794893i 0.539973 0.841682i \(-0.318434\pi\)
−0.998905 + 0.0467891i \(0.985101\pi\)
\(858\) 2.12132 + 3.67423i 0.0724207 + 0.125436i
\(859\) −9.70711 + 16.8132i −0.331202 + 0.573659i −0.982748 0.184950i \(-0.940788\pi\)
0.651546 + 0.758609i \(0.274121\pi\)
\(860\) 7.65685 0.261097
\(861\) −4.60660 0.630399i −0.156993 0.0214839i
\(862\) 6.34315 0.216048
\(863\) −19.4350 + 33.6625i −0.661576 + 1.14588i 0.318625 + 0.947881i \(0.396779\pi\)
−0.980201 + 0.198003i \(0.936555\pi\)
\(864\) −0.500000 0.866025i −0.0170103 0.0294628i
\(865\) 2.41421 + 4.18154i 0.0820857 + 0.142177i
\(866\) −15.0000 + 25.9808i −0.509721 + 0.882862i
\(867\) −15.0000 −0.509427
\(868\) 4.65685 + 11.4069i 0.158064 + 0.387176i
\(869\) 1.24264 0.0421537
\(870\) −0.378680 + 0.655892i −0.0128384 + 0.0222368i
\(871\) 3.07107 + 5.31925i 0.104059 + 0.180236i
\(872\) −2.65685 4.60181i −0.0899724 0.155837i
\(873\) 1.79289 3.10538i 0.0606802 0.105101i
\(874\) 3.41421 0.115487
\(875\) 14.5919 18.8169i 0.493296 0.636128i
\(876\) 5.65685 0.191127
\(877\) −18.9497 + 32.8219i −0.639888 + 1.10832i 0.345570 + 0.938393i \(0.387686\pi\)
−0.985457 + 0.169925i \(0.945648\pi\)
\(878\) −5.57107 9.64937i −0.188014 0.325651i
\(879\) 10.8137 + 18.7299i 0.364737 + 0.631744i
\(880\) −1.50000 + 2.59808i −0.0505650 + 0.0875811i
\(881\) 8.14214 0.274316 0.137158 0.990549i \(-0.456203\pi\)
0.137158 + 0.990549i \(0.456203\pi\)
\(882\) −5.00000 + 4.89898i −0.168359 + 0.164957i
\(883\) 53.6985 1.80710 0.903549 0.428485i \(-0.140952\pi\)
0.903549 + 0.428485i \(0.140952\pi\)
\(884\) 1.00000 1.73205i 0.0336336 0.0582552i
\(885\) −0.378680 0.655892i −0.0127292 0.0220476i
\(886\) −5.13604 8.89588i −0.172549 0.298863i
\(887\) 22.8284 39.5400i 0.766504 1.32762i −0.172944 0.984932i \(-0.555328\pi\)
0.939448 0.342692i \(-0.111339\pi\)
\(888\) −9.07107 −0.304405
\(889\) −9.44975 + 12.1859i −0.316934 + 0.408702i
\(890\) −14.7279 −0.493681
\(891\) 1.50000 2.59808i 0.0502519 0.0870388i
\(892\) 5.08579 + 8.80884i 0.170285 + 0.294942i
\(893\) −15.8995 27.5387i −0.532056 0.921549i
\(894\) −6.82843 + 11.8272i −0.228377 + 0.395560i
\(895\) −16.0000 −0.534821
\(896\) 1.00000 + 2.44949i 0.0334077 + 0.0818317i
\(897\) −1.41421 −0.0472192
\(898\) 0.878680 1.52192i 0.0293219 0.0507871i
\(899\) 1.76346 + 3.05440i 0.0588145 + 0.101870i
\(900\) 2.00000 + 3.46410i 0.0666667 + 0.115470i
\(901\) −1.53553 + 2.65962i −0.0511561 + 0.0886049i
\(902\) −5.27208 −0.175541
\(903\) 20.0711 + 2.74666i 0.667923 + 0.0914032i
\(904\) −17.4142 −0.579188
\(905\) −6.24264 + 10.8126i −0.207512 + 0.359422i
\(906\) 0.671573 + 1.16320i 0.0223115 + 0.0386447i
\(907\) 12.5355 + 21.7122i 0.416236 + 0.720941i 0.995557 0.0941578i \(-0.0300158\pi\)
−0.579322 + 0.815099i \(0.696682\pi\)
\(908\) 3.91421 6.77962i 0.129898 0.224989i
\(909\) −4.48528 −0.148767
\(910\) 3.70711 + 0.507306i 0.122889 + 0.0168170i
\(911\) −4.34315 −0.143895 −0.0719474 0.997408i \(-0.522921\pi\)
−0.0719474 + 0.997408i \(0.522921\pi\)
\(912\) 1.70711 2.95680i 0.0565280 0.0979093i
\(913\) 18.4706 + 31.9920i 0.611286 + 1.05878i
\(914\) −10.1066 17.5051i −0.334297 0.579019i
\(915\) −3.00000 + 5.19615i −0.0991769 + 0.171780i
\(916\) 22.7279 0.750952
\(917\) −1.24264 3.04384i −0.0410356 0.100516i
\(918\) −1.41421 −0.0466760
\(919\) −18.1421 + 31.4231i −0.598454 + 1.03655i 0.394596 + 0.918855i \(0.370885\pi\)
−0.993049 + 0.117698i \(0.962449\pi\)
\(920\) −0.500000 0.866025i −0.0164845 0.0285520i
\(921\) −12.9497 22.4296i −0.426709 0.739081i
\(922\) −15.4853 + 26.8213i −0.509981 + 0.883312i
\(923\) 8.34315 0.274618
\(924\) −4.86396 + 6.27231i −0.160013 + 0.206344i
\(925\) 36.2843 1.19302
\(926\) 6.89949 11.9503i 0.226731 0.392710i
\(927\) 6.82843 + 11.8272i 0.224275 + 0.388456i
\(928\) 0.378680 + 0.655892i 0.0124308 + 0.0215307i
\(929\) −0.363961 + 0.630399i −0.0119412 + 0.0206827i −0.871934 0.489623i \(-0.837134\pi\)
0.859993 + 0.510306i \(0.170468\pi\)
\(930\) −4.65685 −0.152704
\(931\) −23.0208 6.42090i −0.754477 0.210436i
\(932\) 15.2132 0.498325
\(933\) −1.70711 + 2.95680i −0.0558882 + 0.0968011i
\(934\) −14.4142 24.9662i −0.471647 0.816917i
\(935\) 2.12132 + 3.67423i 0.0693746 + 0.120160i
\(936\) −0.707107 + 1.22474i −0.0231125 + 0.0400320i
\(937\) 47.1838 1.54143 0.770713 0.637182i \(-0.219900\pi\)
0.770713 + 0.637182i \(0.219900\pi\)
\(938\) −7.04163 + 9.08052i −0.229917 + 0.296489i
\(939\) 16.7574 0.546856
\(940\) −4.65685 + 8.06591i −0.151890 + 0.263081i
\(941\) −17.7426 30.7312i −0.578394 1.00181i −0.995664 0.0930246i \(-0.970346\pi\)
0.417270 0.908782i \(-0.362987\pi\)
\(942\) 1.94975 + 3.37706i 0.0635262 + 0.110031i
\(943\) 0.878680 1.52192i 0.0286137 0.0495605i
\(944\) −0.757359 −0.0246499
\(945\) −1.00000 2.44949i −0.0325300 0.0796819i
\(946\) 22.9706 0.746837
\(947\) 3.14214 5.44234i 0.102106 0.176852i −0.810446 0.585813i \(-0.800775\pi\)
0.912552 + 0.408961i \(0.134109\pi\)
\(948\) 0.207107 + 0.358719i 0.00672652 + 0.0116507i
\(949\) −4.00000 6.92820i −0.129845 0.224899i
\(950\) −6.82843 + 11.8272i −0.221543 + 0.383724i
\(951\) 9.92893 0.321968
\(952\) 3.70711 + 0.507306i 0.120148 + 0.0164419i
\(953\) −37.7990 −1.22443 −0.612215 0.790692i \(-0.709721\pi\)
−0.612215 + 0.790692i \(0.709721\pi\)
\(954\) 1.08579 1.88064i 0.0351536 0.0608879i
\(955\) 0.707107 + 1.22474i 0.0228814 + 0.0396318i
\(956\) 11.6569 + 20.1903i 0.377010 + 0.653000i
\(957\) −1.13604 + 1.96768i −0.0367229 + 0.0636060i
\(958\) 30.5269 0.986280
\(959\) 49.7279 + 6.80511i 1.60580 + 0.219748i
\(960\) −1.00000 −0.0322749
\(961\) 4.65685 8.06591i 0.150221 0.260191i
\(962\) 6.41421 + 11.1097i 0.206803 + 0.358193i
\(963\) 3.74264 + 6.48244i 0.120605 + 0.208894i
\(964\) 4.96447 8.59871i 0.159895 0.276946i
\(965\) 19.6274 0.631829
\(966\) −1.00000 2.44949i −0.0321745 0.0788110i
\(967\) −35.9706 −1.15674 −0.578368 0.815776i \(-0.696310\pi\)
−0.578368 + 0.815776i \(0.696310\pi\)
\(968\) 1.00000 1.73205i 0.0321412 0.0556702i
\(969\) −2.41421 4.18154i −0.0775557 0.134330i
\(970\) −1.79289 3.10538i −0.0575663 0.0997078i
\(971\) −1.98528 + 3.43861i −0.0637107 + 0.110350i −0.896121 0.443809i \(-0.853627\pi\)
0.832411 + 0.554159i \(0.186960\pi\)
\(972\) 1.00000 0.0320750
\(973\) −8.61522 + 11.1097i −0.276191 + 0.356162i
\(974\) −29.4853 −0.944769
\(975\) 2.82843 4.89898i 0.0905822 0.156893i
\(976\) 3.00000 + 5.19615i 0.0960277 + 0.166325i
\(977\) −17.4853 30.2854i −0.559404 0.968916i −0.997546 0.0700102i \(-0.977697\pi\)
0.438143 0.898905i \(-0.355637\pi\)
\(978\) 0.707107 1.22474i 0.0226108 0.0391630i
\(979\) −44.1838 −1.41212
\(980\) 1.74264 + 6.77962i 0.0556666 + 0.216567i
\(981\) 5.31371 0.169654
\(982\) 4.55025 7.88127i 0.145204 0.251501i
\(983\) −3.29289 5.70346i −0.105027 0.181912i 0.808722 0.588191i \(-0.200160\pi\)
−0.913749 + 0.406279i \(0.866826\pi\)
\(984\) −0.878680 1.52192i −0.0280113 0.0485170i
\(985\) −1.58579 + 2.74666i −0.0505274 + 0.0875159i
\(986\) 1.07107 0.0341097
\(987\) −15.1005 + 19.4728i −0.480654 + 0.619827i
\(988\) −4.82843 −0.153613
\(989\) −3.82843 + 6.63103i −0.121737 + 0.210854i
\(990\) −1.50000 2.59808i −0.0476731 0.0825723i
\(991\) 17.8848 + 30.9773i 0.568129 + 0.984028i 0.996751 + 0.0805440i \(0.0256657\pi\)
−0.428622 + 0.903484i \(0.641001\pi\)
\(992\) −2.32843 + 4.03295i −0.0739276 + 0.128046i
\(993\) 25.8995 0.821896
\(994\) 5.89949 + 14.4508i 0.187121 + 0.458350i
\(995\) −5.31371 −0.168456
\(996\) −6.15685 + 10.6640i −0.195087 + 0.337901i
\(997\) 22.4350 + 38.8586i 0.710524 + 1.23066i 0.964660 + 0.263496i \(0.0848756\pi\)
−0.254136 + 0.967168i \(0.581791\pi\)
\(998\) 6.89949 + 11.9503i 0.218400 + 0.378279i
\(999\) 4.53553 7.85578i 0.143498 0.248546i
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 966.2.i.h.415.2 yes 4
7.2 even 3 6762.2.a.cc.1.2 2
7.4 even 3 inner 966.2.i.h.277.2 4
7.5 odd 6 6762.2.a.ca.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
966.2.i.h.277.2 4 7.4 even 3 inner
966.2.i.h.415.2 yes 4 1.1 even 1 trivial
6762.2.a.ca.1.1 2 7.5 odd 6
6762.2.a.cc.1.2 2 7.2 even 3