Properties

Label 966.2.i.j.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: \(\Z[a_1, \ldots, a_{5}]\)
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.j.277.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.20711 - 2.09077i) q^{5} -1.00000 q^{6} +(1.62132 + 2.09077i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.20711 - 2.09077i) q^{5} -1.00000 q^{6} +(1.62132 + 2.09077i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-1.20711 - 2.09077i) q^{10} +(-1.00000 - 1.73205i) q^{11} +(-0.500000 + 0.866025i) q^{12} +3.82843 q^{13} +(2.62132 - 0.358719i) q^{14} -2.41421 q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.62132 - 4.54026i) q^{17} +(0.500000 + 0.866025i) q^{18} +(3.82843 - 6.63103i) q^{19} -2.41421 q^{20} +(1.00000 - 2.44949i) q^{21} -2.00000 q^{22} +(-0.500000 + 0.866025i) q^{23} +(0.500000 + 0.866025i) q^{24} +(-0.414214 - 0.717439i) q^{25} +(1.91421 - 3.31552i) q^{26} +1.00000 q^{27} +(1.00000 - 2.44949i) q^{28} -6.82843 q^{29} +(-1.20711 + 2.09077i) q^{30} +(1.00000 + 1.73205i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-1.00000 + 1.73205i) q^{33} -5.24264 q^{34} +(6.32843 - 0.866025i) q^{35} +1.00000 q^{36} +(4.41421 - 7.64564i) q^{37} +(-3.82843 - 6.63103i) q^{38} +(-1.91421 - 3.31552i) q^{39} +(-1.20711 + 2.09077i) q^{40} -5.17157 q^{41} +(-1.62132 - 2.09077i) q^{42} -0.343146 q^{43} +(-1.00000 + 1.73205i) q^{44} +(1.20711 + 2.09077i) q^{45} +(0.500000 + 0.866025i) q^{46} +(-4.50000 + 7.79423i) q^{47} +1.00000 q^{48} +(-1.74264 + 6.77962i) q^{49} -0.828427 q^{50} +(-2.62132 + 4.54026i) q^{51} +(-1.91421 - 3.31552i) q^{52} +(-2.03553 - 3.52565i) q^{53} +(0.500000 - 0.866025i) q^{54} -4.82843 q^{55} +(-1.62132 - 2.09077i) q^{56} -7.65685 q^{57} +(-3.41421 + 5.91359i) q^{58} +(4.82843 + 8.36308i) q^{59} +(1.20711 + 2.09077i) q^{60} +(1.00000 - 1.73205i) q^{61} +2.00000 q^{62} +(-2.62132 + 0.358719i) q^{63} +1.00000 q^{64} +(4.62132 - 8.00436i) q^{65} +(1.00000 + 1.73205i) q^{66} +(2.44975 + 4.24309i) q^{67} +(-2.62132 + 4.54026i) q^{68} +1.00000 q^{69} +(2.41421 - 5.91359i) q^{70} -4.17157 q^{71} +(0.500000 - 0.866025i) q^{72} +(-0.328427 - 0.568852i) q^{73} +(-4.41421 - 7.64564i) q^{74} +(-0.414214 + 0.717439i) q^{75} -7.65685 q^{76} +(2.00000 - 4.89898i) q^{77} -3.82843 q^{78} +(5.00000 - 8.66025i) q^{79} +(1.20711 + 2.09077i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-2.58579 + 4.47871i) q^{82} +7.17157 q^{83} +(-2.62132 + 0.358719i) q^{84} -12.6569 q^{85} +(-0.171573 + 0.297173i) q^{86} +(3.41421 + 5.91359i) q^{87} +(1.00000 + 1.73205i) q^{88} +(-3.41421 + 5.91359i) q^{89} +2.41421 q^{90} +(6.20711 + 8.00436i) q^{91} +1.00000 q^{92} +(1.00000 - 1.73205i) q^{93} +(4.50000 + 7.79423i) q^{94} +(-9.24264 - 16.0087i) q^{95} +(0.500000 - 0.866025i) q^{96} +1.65685 q^{97} +(5.00000 + 4.89898i) q^{98} +2.00000 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 \( 4 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 2 q^{5} - 4 q^{6} - 2 q^{7} - 4 q^{8} - 2 q^{9} - 2 q^{10} - 4 q^{11} - 2 q^{12} + 4 q^{13} + 2 q^{14} - 4 q^{15} - 2 q^{16} - 2 q^{17} + 2 q^{18} + 4 q^{19} - 4 q^{20} + 4 q^{21} - 8 q^{22} - 2 q^{23} + 2 q^{24} + 4 q^{25} + 2 q^{26} + 4 q^{27} + 4 q^{28} - 16 q^{29} - 2 q^{30} + 4 q^{31} + 2 q^{32} - 4 q^{33} - 4 q^{34} + 14 q^{35} + 4 q^{36} + 12 q^{37} - 4 q^{38} - 2 q^{39} - 2 q^{40} - 32 q^{41} + 2 q^{42} - 24 q^{43} - 4 q^{44} + 2 q^{45} + 2 q^{46} - 18 q^{47} + 4 q^{48} + 10 q^{49} + 8 q^{50} - 2 q^{51} - 2 q^{52} + 6 q^{53} + 2 q^{54} - 8 q^{55} + 2 q^{56} - 8 q^{57} - 8 q^{58} + 8 q^{59} + 2 q^{60} + 4 q^{61} + 8 q^{62} - 2 q^{63} + 4 q^{64} + 10 q^{65} + 4 q^{66} - 10 q^{67} - 2 q^{68} + 4 q^{69} + 4 q^{70} - 28 q^{71} + 2 q^{72} + 10 q^{73} - 12 q^{74} + 4 q^{75} - 8 q^{76} + 8 q^{77} - 4 q^{78} + 20 q^{79} + 2 q^{80} - 2 q^{81} - 16 q^{82} + 40 q^{83} - 2 q^{84} - 28 q^{85} - 12 q^{86} + 8 q^{87} + 4 q^{88} - 8 q^{89} + 4 q^{90} + 22 q^{91} + 4 q^{92} + 4 q^{93} + 18 q^{94} - 20 q^{95} + 2 q^{96} - 16 q^{97} + 20 q^{98} + 8 q^{99}+O(q^{100}) \) 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
\(5\) 1.20711 2.09077i 0.539835 0.935021i −0.459078 0.888396i \(-0.651820\pi\)
0.998912 0.0466249i \(-0.0148465\pi\)
\(6\) −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
\(10\) −1.20711 2.09077i −0.381721 0.661160i
\(11\) −1.00000 1.73205i −0.301511 0.522233i 0.674967 0.737848i \(-0.264158\pi\)
−0.976478 + 0.215615i \(0.930824\pi\)
\(12\) −0.500000 + 0.866025i −0.144338 + 0.250000i
\(13\) 3.82843 1.06181 0.530907 0.847430i \(-0.321851\pi\)
0.530907 + 0.847430i \(0.321851\pi\)
\(14\) 2.62132 0.358719i 0.700577 0.0958718i
\(15\) −2.41421 −0.623347
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −2.62132 4.54026i −0.635764 1.10117i −0.986353 0.164645i \(-0.947352\pi\)
0.350589 0.936529i \(-0.385981\pi\)
\(18\) 0.500000 + 0.866025i 0.117851 + 0.204124i
\(19\) 3.82843 6.63103i 0.878301 1.52126i 0.0250976 0.999685i \(-0.492010\pi\)
0.853204 0.521578i \(-0.174656\pi\)
\(20\) −2.41421 −0.539835
\(21\) 1.00000 2.44949i 0.218218 0.534522i
\(22\) −2.00000 −0.426401
\(23\) −0.500000 + 0.866025i −0.104257 + 0.180579i
\(24\) 0.500000 + 0.866025i 0.102062 + 0.176777i
\(25\) −0.414214 0.717439i −0.0828427 0.143488i
\(26\) 1.91421 3.31552i 0.375408 0.650226i
\(27\) 1.00000 0.192450
\(28\) 1.00000 2.44949i 0.188982 0.462910i
\(29\) −6.82843 −1.26801 −0.634004 0.773330i \(-0.718590\pi\)
−0.634004 + 0.773330i \(0.718590\pi\)
\(30\) −1.20711 + 2.09077i −0.220387 + 0.381721i
\(31\) 1.00000 + 1.73205i 0.179605 + 0.311086i 0.941745 0.336327i \(-0.109185\pi\)
−0.762140 + 0.647412i \(0.775851\pi\)
\(32\) 0.500000 + 0.866025i 0.0883883 + 0.153093i
\(33\) −1.00000 + 1.73205i −0.174078 + 0.301511i
\(34\) −5.24264 −0.899105
\(35\) 6.32843 0.866025i 1.06970 0.146385i
\(36\) 1.00000 0.166667
\(37\) 4.41421 7.64564i 0.725692 1.25694i −0.232996 0.972478i \(-0.574853\pi\)
0.958688 0.284458i \(-0.0918137\pi\)
\(38\) −3.82843 6.63103i −0.621053 1.07570i
\(39\) −1.91421 3.31552i −0.306519 0.530907i
\(40\) −1.20711 + 2.09077i −0.190860 + 0.330580i
\(41\) −5.17157 −0.807664 −0.403832 0.914833i \(-0.632322\pi\)
−0.403832 + 0.914833i \(0.632322\pi\)
\(42\) −1.62132 2.09077i −0.250175 0.322613i
\(43\) −0.343146 −0.0523292 −0.0261646 0.999658i \(-0.508329\pi\)
−0.0261646 + 0.999658i \(0.508329\pi\)
\(44\) −1.00000 + 1.73205i −0.150756 + 0.261116i
\(45\) 1.20711 + 2.09077i 0.179945 + 0.311674i
\(46\) 0.500000 + 0.866025i 0.0737210 + 0.127688i
\(47\) −4.50000 + 7.79423i −0.656392 + 1.13691i 0.325150 + 0.945662i \(0.394585\pi\)
−0.981543 + 0.191243i \(0.938748\pi\)
\(48\) 1.00000 0.144338
\(49\) −1.74264 + 6.77962i −0.248949 + 0.968517i
\(50\) −0.828427 −0.117157
\(51\) −2.62132 + 4.54026i −0.367058 + 0.635764i
\(52\) −1.91421 3.31552i −0.265454 0.459779i
\(53\) −2.03553 3.52565i −0.279602 0.484285i 0.691684 0.722200i \(-0.256869\pi\)
−0.971286 + 0.237915i \(0.923536\pi\)
\(54\) 0.500000 0.866025i 0.0680414 0.117851i
\(55\) −4.82843 −0.651065
\(56\) −1.62132 2.09077i −0.216658 0.279391i
\(57\) −7.65685 −1.01418
\(58\) −3.41421 + 5.91359i −0.448308 + 0.776493i
\(59\) 4.82843 + 8.36308i 0.628608 + 1.08878i 0.987831 + 0.155529i \(0.0497082\pi\)
−0.359224 + 0.933251i \(0.616958\pi\)
\(60\) 1.20711 + 2.09077i 0.155837 + 0.269917i
\(61\) 1.00000 1.73205i 0.128037 0.221766i −0.794879 0.606768i \(-0.792466\pi\)
0.922916 + 0.385002i \(0.125799\pi\)
\(62\) 2.00000 0.254000
\(63\) −2.62132 + 0.358719i −0.330255 + 0.0451944i
\(64\) 1.00000 0.125000
\(65\) 4.62132 8.00436i 0.573204 0.992819i
\(66\) 1.00000 + 1.73205i 0.123091 + 0.213201i
\(67\) 2.44975 + 4.24309i 0.299284 + 0.518376i 0.975972 0.217894i \(-0.0699188\pi\)
−0.676688 + 0.736270i \(0.736585\pi\)
\(68\) −2.62132 + 4.54026i −0.317882 + 0.550587i
\(69\) 1.00000 0.120386
\(70\) 2.41421 5.91359i 0.288554 0.706809i
\(71\) −4.17157 −0.495075 −0.247537 0.968878i \(-0.579621\pi\)
−0.247537 + 0.968878i \(0.579621\pi\)
\(72\) 0.500000 0.866025i 0.0589256 0.102062i
\(73\) −0.328427 0.568852i −0.0384395 0.0665791i 0.846166 0.532920i \(-0.178905\pi\)
−0.884605 + 0.466341i \(0.845572\pi\)
\(74\) −4.41421 7.64564i −0.513142 0.888788i
\(75\) −0.414214 + 0.717439i −0.0478293 + 0.0828427i
\(76\) −7.65685 −0.878301
\(77\) 2.00000 4.89898i 0.227921 0.558291i
\(78\) −3.82843 −0.433484
\(79\) 5.00000 8.66025i 0.562544 0.974355i −0.434730 0.900561i \(-0.643156\pi\)
0.997274 0.0737937i \(-0.0235106\pi\)
\(80\) 1.20711 + 2.09077i 0.134959 + 0.233755i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) −2.58579 + 4.47871i −0.285552 + 0.494591i
\(83\) 7.17157 0.787182 0.393591 0.919286i \(-0.371233\pi\)
0.393591 + 0.919286i \(0.371233\pi\)
\(84\) −2.62132 + 0.358719i −0.286009 + 0.0391395i
\(85\) −12.6569 −1.37283
\(86\) −0.171573 + 0.297173i −0.0185012 + 0.0320450i
\(87\) 3.41421 + 5.91359i 0.366042 + 0.634004i
\(88\) 1.00000 + 1.73205i 0.106600 + 0.184637i
\(89\) −3.41421 + 5.91359i −0.361906 + 0.626839i −0.988275 0.152688i \(-0.951207\pi\)
0.626369 + 0.779527i \(0.284541\pi\)
\(90\) 2.41421 0.254480
\(91\) 6.20711 + 8.00436i 0.650682 + 0.839085i
\(92\) 1.00000 0.104257
\(93\) 1.00000 1.73205i 0.103695 0.179605i
\(94\) 4.50000 + 7.79423i 0.464140 + 0.803913i
\(95\) −9.24264 16.0087i −0.948275 1.64246i
\(96\) 0.500000 0.866025i 0.0510310 0.0883883i
\(97\) 1.65685 0.168228 0.0841140 0.996456i \(-0.473194\pi\)
0.0841140 + 0.996456i \(0.473194\pi\)
\(98\) 5.00000 + 4.89898i 0.505076 + 0.494872i
\(99\) 2.00000 0.201008
\(100\) −0.414214 + 0.717439i −0.0414214 + 0.0717439i
\(101\) −4.41421 7.64564i −0.439231 0.760770i 0.558400 0.829572i \(-0.311416\pi\)
−0.997630 + 0.0688022i \(0.978082\pi\)
\(102\) 2.62132 + 4.54026i 0.259549 + 0.449553i
\(103\) −5.44975 + 9.43924i −0.536980 + 0.930076i 0.462085 + 0.886836i \(0.347101\pi\)
−0.999065 + 0.0432403i \(0.986232\pi\)
\(104\) −3.82843 −0.375408
\(105\) −3.91421 5.04757i −0.381988 0.492592i
\(106\) −4.07107 −0.395417
\(107\) 2.82843 4.89898i 0.273434 0.473602i −0.696305 0.717746i \(-0.745174\pi\)
0.969739 + 0.244144i \(0.0785070\pi\)
\(108\) −0.500000 0.866025i −0.0481125 0.0833333i
\(109\) −4.58579 7.94282i −0.439239 0.760784i 0.558392 0.829577i \(-0.311418\pi\)
−0.997631 + 0.0687933i \(0.978085\pi\)
\(110\) −2.41421 + 4.18154i −0.230186 + 0.398694i
\(111\) −8.82843 −0.837957
\(112\) −2.62132 + 0.358719i −0.247691 + 0.0338958i
\(113\) 11.7279 1.10327 0.551635 0.834086i \(-0.314004\pi\)
0.551635 + 0.834086i \(0.314004\pi\)
\(114\) −3.82843 + 6.63103i −0.358565 + 0.621053i
\(115\) 1.20711 + 2.09077i 0.112563 + 0.194965i
\(116\) 3.41421 + 5.91359i 0.317002 + 0.549063i
\(117\) −1.91421 + 3.31552i −0.176969 + 0.306519i
\(118\) 9.65685 0.888985
\(119\) 5.24264 12.8418i 0.480592 1.17721i
\(120\) 2.41421 0.220387
\(121\) 3.50000 6.06218i 0.318182 0.551107i
\(122\) −1.00000 1.73205i −0.0905357 0.156813i
\(123\) 2.58579 + 4.47871i 0.233153 + 0.403832i
\(124\) 1.00000 1.73205i 0.0898027 0.155543i
\(125\) 10.0711 0.900784
\(126\) −1.00000 + 2.44949i −0.0890871 + 0.218218i
\(127\) −0.828427 −0.0735110 −0.0367555 0.999324i \(-0.511702\pi\)
−0.0367555 + 0.999324i \(0.511702\pi\)
\(128\) 0.500000 0.866025i 0.0441942 0.0765466i
\(129\) 0.171573 + 0.297173i 0.0151061 + 0.0261646i
\(130\) −4.62132 8.00436i −0.405317 0.702029i
\(131\) 4.57107 7.91732i 0.399376 0.691740i −0.594273 0.804263i \(-0.702560\pi\)
0.993649 + 0.112524i \(0.0358935\pi\)
\(132\) 2.00000 0.174078
\(133\) 20.0711 2.74666i 1.74038 0.238166i
\(134\) 4.89949 0.423252
\(135\) 1.20711 2.09077i 0.103891 0.179945i
\(136\) 2.62132 + 4.54026i 0.224776 + 0.389324i
\(137\) 3.79289 + 6.56948i 0.324049 + 0.561269i 0.981319 0.192386i \(-0.0616225\pi\)
−0.657271 + 0.753655i \(0.728289\pi\)
\(138\) 0.500000 0.866025i 0.0425628 0.0737210i
\(139\) 9.31371 0.789978 0.394989 0.918686i \(-0.370748\pi\)
0.394989 + 0.918686i \(0.370748\pi\)
\(140\) −3.91421 5.04757i −0.330811 0.426597i
\(141\) 9.00000 0.757937
\(142\) −2.08579 + 3.61269i −0.175035 + 0.303170i
\(143\) −3.82843 6.63103i −0.320149 0.554515i
\(144\) −0.500000 0.866025i −0.0416667 0.0721688i
\(145\) −8.24264 + 14.2767i −0.684514 + 1.18561i
\(146\) −0.656854 −0.0543616
\(147\) 6.74264 1.88064i 0.556124 0.155112i
\(148\) −8.82843 −0.725692
\(149\) −4.62132 + 8.00436i −0.378593 + 0.655743i −0.990858 0.134910i \(-0.956925\pi\)
0.612265 + 0.790653i \(0.290259\pi\)
\(150\) 0.414214 + 0.717439i 0.0338204 + 0.0585786i
\(151\) 7.07107 + 12.2474i 0.575435 + 0.996683i 0.995994 + 0.0894180i \(0.0285007\pi\)
−0.420559 + 0.907265i \(0.638166\pi\)
\(152\) −3.82843 + 6.63103i −0.310526 + 0.537848i
\(153\) 5.24264 0.423842
\(154\) −3.24264 4.18154i −0.261299 0.336958i
\(155\) 4.82843 0.387829
\(156\) −1.91421 + 3.31552i −0.153260 + 0.265454i
\(157\) 7.82843 + 13.5592i 0.624777 + 1.08214i 0.988584 + 0.150671i \(0.0481433\pi\)
−0.363808 + 0.931474i \(0.618523\pi\)
\(158\) −5.00000 8.66025i −0.397779 0.688973i
\(159\) −2.03553 + 3.52565i −0.161428 + 0.279602i
\(160\) 2.41421 0.190860
\(161\) −2.62132 + 0.358719i −0.206589 + 0.0282711i
\(162\) −1.00000 −0.0785674
\(163\) −0.828427 + 1.43488i −0.0648874 + 0.112388i −0.896644 0.442752i \(-0.854002\pi\)
0.831757 + 0.555140i \(0.187335\pi\)
\(164\) 2.58579 + 4.47871i 0.201916 + 0.349729i
\(165\) 2.41421 + 4.18154i 0.187946 + 0.325532i
\(166\) 3.58579 6.21076i 0.278311 0.482049i
\(167\) 24.7990 1.91900 0.959502 0.281703i \(-0.0908992\pi\)
0.959502 + 0.281703i \(0.0908992\pi\)
\(168\) −1.00000 + 2.44949i −0.0771517 + 0.188982i
\(169\) 1.65685 0.127450
\(170\) −6.32843 + 10.9612i −0.485368 + 0.840682i
\(171\) 3.82843 + 6.63103i 0.292767 + 0.507088i
\(172\) 0.171573 + 0.297173i 0.0130823 + 0.0226592i
\(173\) 3.65685 6.33386i 0.278025 0.481554i −0.692868 0.721064i \(-0.743653\pi\)
0.970894 + 0.239510i \(0.0769867\pi\)
\(174\) 6.82843 0.517662
\(175\) 0.828427 2.02922i 0.0626232 0.153395i
\(176\) 2.00000 0.150756
\(177\) 4.82843 8.36308i 0.362927 0.628608i
\(178\) 3.41421 + 5.91359i 0.255906 + 0.443242i
\(179\) 10.9853 + 19.0271i 0.821078 + 1.42215i 0.904880 + 0.425667i \(0.139961\pi\)
−0.0838013 + 0.996482i \(0.526706\pi\)
\(180\) 1.20711 2.09077i 0.0899724 0.155837i
\(181\) −9.31371 −0.692283 −0.346141 0.938182i \(-0.612508\pi\)
−0.346141 + 0.938182i \(0.612508\pi\)
\(182\) 10.0355 1.37333i 0.743883 0.101798i
\(183\) −2.00000 −0.147844
\(184\) 0.500000 0.866025i 0.0368605 0.0638442i
\(185\) −10.6569 18.4582i −0.783508 1.35707i
\(186\) −1.00000 1.73205i −0.0733236 0.127000i
\(187\) −5.24264 + 9.08052i −0.383380 + 0.664033i
\(188\) 9.00000 0.656392
\(189\) 1.62132 + 2.09077i 0.117934 + 0.152081i
\(190\) −18.4853 −1.34106
\(191\) 2.58579 4.47871i 0.187101 0.324068i −0.757182 0.653205i \(-0.773424\pi\)
0.944282 + 0.329136i \(0.106758\pi\)
\(192\) −0.500000 0.866025i −0.0360844 0.0625000i
\(193\) 2.74264 + 4.75039i 0.197420 + 0.341941i 0.947691 0.319189i \(-0.103411\pi\)
−0.750271 + 0.661130i \(0.770077\pi\)
\(194\) 0.828427 1.43488i 0.0594776 0.103018i
\(195\) −9.24264 −0.661879
\(196\) 6.74264 1.88064i 0.481617 0.134331i
\(197\) −12.8284 −0.913988 −0.456994 0.889470i \(-0.651074\pi\)
−0.456994 + 0.889470i \(0.651074\pi\)
\(198\) 1.00000 1.73205i 0.0710669 0.123091i
\(199\) 13.8284 + 23.9515i 0.980271 + 1.69788i 0.661312 + 0.750111i \(0.270000\pi\)
0.318959 + 0.947768i \(0.396667\pi\)
\(200\) 0.414214 + 0.717439i 0.0292893 + 0.0507306i
\(201\) 2.44975 4.24309i 0.172792 0.299284i
\(202\) −8.82843 −0.621166
\(203\) −11.0711 14.2767i −0.777037 1.00203i
\(204\) 5.24264 0.367058
\(205\) −6.24264 + 10.8126i −0.436005 + 0.755183i
\(206\) 5.44975 + 9.43924i 0.379702 + 0.657663i
\(207\) −0.500000 0.866025i −0.0347524 0.0601929i
\(208\) −1.91421 + 3.31552i −0.132727 + 0.229890i
\(209\) −15.3137 −1.05927
\(210\) −6.32843 + 0.866025i −0.436703 + 0.0597614i
\(211\) −11.1716 −0.769083 −0.384541 0.923108i \(-0.625640\pi\)
−0.384541 + 0.923108i \(0.625640\pi\)
\(212\) −2.03553 + 3.52565i −0.139801 + 0.242143i
\(213\) 2.08579 + 3.61269i 0.142916 + 0.247537i
\(214\) −2.82843 4.89898i −0.193347 0.334887i
\(215\) −0.414214 + 0.717439i −0.0282491 + 0.0489289i
\(216\) −1.00000 −0.0680414
\(217\) −2.00000 + 4.89898i −0.135769 + 0.332564i
\(218\) −9.17157 −0.621177
\(219\) −0.328427 + 0.568852i −0.0221930 + 0.0384395i
\(220\) 2.41421 + 4.18154i 0.162766 + 0.281919i
\(221\) −10.0355 17.3821i −0.675063 1.16924i
\(222\) −4.41421 + 7.64564i −0.296263 + 0.513142i
\(223\) −12.4853 −0.836076 −0.418038 0.908429i \(-0.637282\pi\)
−0.418038 + 0.908429i \(0.637282\pi\)
\(224\) −1.00000 + 2.44949i −0.0668153 + 0.163663i
\(225\) 0.828427 0.0552285
\(226\) 5.86396 10.1567i 0.390065 0.675612i
\(227\) 5.48528 + 9.50079i 0.364071 + 0.630589i 0.988627 0.150391i \(-0.0480532\pi\)
−0.624556 + 0.780980i \(0.714720\pi\)
\(228\) 3.82843 + 6.63103i 0.253544 + 0.439151i
\(229\) −1.07107 + 1.85514i −0.0707782 + 0.122591i −0.899243 0.437450i \(-0.855882\pi\)
0.828464 + 0.560042i \(0.189215\pi\)
\(230\) 2.41421 0.159189
\(231\) −5.24264 + 0.717439i −0.344940 + 0.0472040i
\(232\) 6.82843 0.448308
\(233\) 4.00000 6.92820i 0.262049 0.453882i −0.704737 0.709468i \(-0.748935\pi\)
0.966786 + 0.255586i \(0.0822686\pi\)
\(234\) 1.91421 + 3.31552i 0.125136 + 0.216742i
\(235\) 10.8640 + 18.8169i 0.708687 + 1.22748i
\(236\) 4.82843 8.36308i 0.314304 0.544390i
\(237\) −10.0000 −0.649570
\(238\) −8.50000 10.9612i −0.550973 0.710506i
\(239\) 10.3431 0.669042 0.334521 0.942388i \(-0.391425\pi\)
0.334521 + 0.942388i \(0.391425\pi\)
\(240\) 1.20711 2.09077i 0.0779184 0.134959i
\(241\) 6.41421 + 11.1097i 0.413176 + 0.715642i 0.995235 0.0975049i \(-0.0310862\pi\)
−0.582059 + 0.813146i \(0.697753\pi\)
\(242\) −3.50000 6.06218i −0.224989 0.389692i
\(243\) −0.500000 + 0.866025i −0.0320750 + 0.0555556i
\(244\) −2.00000 −0.128037
\(245\) 12.0711 + 11.8272i 0.771192 + 0.755611i
\(246\) 5.17157 0.329727
\(247\) 14.6569 25.3864i 0.932593 1.61530i
\(248\) −1.00000 1.73205i −0.0635001 0.109985i
\(249\) −3.58579 6.21076i −0.227240 0.393591i
\(250\) 5.03553 8.72180i 0.318475 0.551615i
\(251\) 17.3137 1.09283 0.546416 0.837514i \(-0.315992\pi\)
0.546416 + 0.837514i \(0.315992\pi\)
\(252\) 1.62132 + 2.09077i 0.102134 + 0.131706i
\(253\) 2.00000 0.125739
\(254\) −0.414214 + 0.717439i −0.0259901 + 0.0450161i
\(255\) 6.32843 + 10.9612i 0.396301 + 0.686414i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −2.75736 + 4.77589i −0.171999 + 0.297912i −0.939119 0.343593i \(-0.888356\pi\)
0.767119 + 0.641504i \(0.221689\pi\)
\(258\) 0.343146 0.0213633
\(259\) 23.1421 3.16693i 1.43798 0.196783i
\(260\) −9.24264 −0.573204
\(261\) 3.41421 5.91359i 0.211335 0.366042i
\(262\) −4.57107 7.91732i −0.282402 0.489134i
\(263\) −9.65685 16.7262i −0.595467 1.03138i −0.993481 0.114000i \(-0.963634\pi\)
0.398014 0.917380i \(-0.369700\pi\)
\(264\) 1.00000 1.73205i 0.0615457 0.106600i
\(265\) −9.82843 −0.603755
\(266\) 7.65685 18.7554i 0.469472 1.14997i
\(267\) 6.82843 0.417893
\(268\) 2.44975 4.24309i 0.149642 0.259188i
\(269\) 6.00000 + 10.3923i 0.365826 + 0.633630i 0.988908 0.148527i \(-0.0474530\pi\)
−0.623082 + 0.782157i \(0.714120\pi\)
\(270\) −1.20711 2.09077i −0.0734622 0.127240i
\(271\) 15.1421 26.2269i 0.919819 1.59317i 0.120131 0.992758i \(-0.461669\pi\)
0.799688 0.600416i \(-0.204998\pi\)
\(272\) 5.24264 0.317882
\(273\) 3.82843 9.37769i 0.231707 0.567564i
\(274\) 7.58579 0.458274
\(275\) −0.828427 + 1.43488i −0.0499560 + 0.0865264i
\(276\) −0.500000 0.866025i −0.0300965 0.0521286i
\(277\) −12.6421 21.8968i −0.759592 1.31565i −0.943059 0.332626i \(-0.892065\pi\)
0.183466 0.983026i \(-0.441268\pi\)
\(278\) 4.65685 8.06591i 0.279300 0.483761i
\(279\) −2.00000 −0.119737
\(280\) −6.32843 + 0.866025i −0.378196 + 0.0517549i
\(281\) −13.5858 −0.810460 −0.405230 0.914215i \(-0.632809\pi\)
−0.405230 + 0.914215i \(0.632809\pi\)
\(282\) 4.50000 7.79423i 0.267971 0.464140i
\(283\) 14.6924 + 25.4480i 0.873372 + 1.51272i 0.858487 + 0.512835i \(0.171405\pi\)
0.0148847 + 0.999889i \(0.495262\pi\)
\(284\) 2.08579 + 3.61269i 0.123769 + 0.214374i
\(285\) −9.24264 + 16.0087i −0.547487 + 0.948275i
\(286\) −7.65685 −0.452759
\(287\) −8.38478 10.8126i −0.494938 0.638246i
\(288\) −1.00000 −0.0589256
\(289\) −5.24264 + 9.08052i −0.308391 + 0.534148i
\(290\) 8.24264 + 14.2767i 0.484025 + 0.838355i
\(291\) −0.828427 1.43488i −0.0485633 0.0841140i
\(292\) −0.328427 + 0.568852i −0.0192197 + 0.0332896i
\(293\) −3.58579 −0.209484 −0.104742 0.994499i \(-0.533402\pi\)
−0.104742 + 0.994499i \(0.533402\pi\)
\(294\) 1.74264 6.77962i 0.101633 0.395395i
\(295\) 23.3137 1.35738
\(296\) −4.41421 + 7.64564i −0.256571 + 0.444394i
\(297\) −1.00000 1.73205i −0.0580259 0.100504i
\(298\) 4.62132 + 8.00436i 0.267706 + 0.463680i
\(299\) −1.91421 + 3.31552i −0.110702 + 0.191741i
\(300\) 0.828427 0.0478293
\(301\) −0.556349 0.717439i −0.0320674 0.0413525i
\(302\) 14.1421 0.813788
\(303\) −4.41421 + 7.64564i −0.253590 + 0.439231i
\(304\) 3.82843 + 6.63103i 0.219575 + 0.380316i
\(305\) −2.41421 4.18154i −0.138237 0.239434i
\(306\) 2.62132 4.54026i 0.149851 0.259549i
\(307\) −14.1421 −0.807134 −0.403567 0.914950i \(-0.632230\pi\)
−0.403567 + 0.914950i \(0.632230\pi\)
\(308\) −5.24264 + 0.717439i −0.298727 + 0.0408799i
\(309\) 10.8995 0.620051
\(310\) 2.41421 4.18154i 0.137118 0.237496i
\(311\) 8.15685 + 14.1281i 0.462533 + 0.801130i 0.999086 0.0427360i \(-0.0136074\pi\)
−0.536554 + 0.843866i \(0.680274\pi\)
\(312\) 1.91421 + 3.31552i 0.108371 + 0.187704i
\(313\) −16.4853 + 28.5533i −0.931803 + 1.61393i −0.151566 + 0.988447i \(0.548431\pi\)
−0.780238 + 0.625483i \(0.784902\pi\)
\(314\) 15.6569 0.883567
\(315\) −2.41421 + 5.91359i −0.136026 + 0.333193i
\(316\) −10.0000 −0.562544
\(317\) 16.3137 28.2562i 0.916269 1.58702i 0.111237 0.993794i \(-0.464519\pi\)
0.805032 0.593231i \(-0.202148\pi\)
\(318\) 2.03553 + 3.52565i 0.114147 + 0.197709i
\(319\) 6.82843 + 11.8272i 0.382319 + 0.662195i
\(320\) 1.20711 2.09077i 0.0674793 0.116878i
\(321\) −5.65685 −0.315735
\(322\) −1.00000 + 2.44949i −0.0557278 + 0.136505i
\(323\) −40.1421 −2.23357
\(324\) −0.500000 + 0.866025i −0.0277778 + 0.0481125i
\(325\) −1.58579 2.74666i −0.0879636 0.152357i
\(326\) 0.828427 + 1.43488i 0.0458823 + 0.0794705i
\(327\) −4.58579 + 7.94282i −0.253595 + 0.439239i
\(328\) 5.17157 0.285552
\(329\) −23.5919 + 3.22848i −1.30066 + 0.177992i
\(330\) 4.82843 0.265796
\(331\) 17.2426 29.8651i 0.947741 1.64154i 0.197574 0.980288i \(-0.436694\pi\)
0.750167 0.661248i \(-0.229973\pi\)
\(332\) −3.58579 6.21076i −0.196796 0.340860i
\(333\) 4.41421 + 7.64564i 0.241897 + 0.418979i
\(334\) 12.3995 21.4766i 0.678470 1.17514i
\(335\) 11.8284 0.646256
\(336\) 1.62132 + 2.09077i 0.0884503 + 0.114061i
\(337\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(338\) 0.828427 1.43488i 0.0450605 0.0780471i
\(339\) −5.86396 10.1567i −0.318487 0.551635i
\(340\) 6.32843 + 10.9612i 0.343207 + 0.594452i
\(341\) 2.00000 3.46410i 0.108306 0.187592i
\(342\) 7.65685 0.414035
\(343\) −17.0000 + 7.34847i −0.917914 + 0.396780i
\(344\) 0.343146 0.0185012
\(345\) 1.20711 2.09077i 0.0649884 0.112563i
\(346\) −3.65685 6.33386i −0.196594 0.340510i
\(347\) 16.3284 + 28.2817i 0.876556 + 1.51824i 0.855096 + 0.518470i \(0.173498\pi\)
0.0214599 + 0.999770i \(0.493169\pi\)
\(348\) 3.41421 5.91359i 0.183021 0.317002i
\(349\) −25.1421 −1.34583 −0.672914 0.739721i \(-0.734958\pi\)
−0.672914 + 0.739721i \(0.734958\pi\)
\(350\) −1.34315 1.73205i −0.0717942 0.0925820i
\(351\) 3.82843 0.204346
\(352\) 1.00000 1.73205i 0.0533002 0.0923186i
\(353\) −1.07107 1.85514i −0.0570072 0.0987393i 0.836113 0.548557i \(-0.184822\pi\)
−0.893121 + 0.449817i \(0.851489\pi\)
\(354\) −4.82843 8.36308i −0.256628 0.444493i
\(355\) −5.03553 + 8.72180i −0.267258 + 0.462905i
\(356\) 6.82843 0.361906
\(357\) −13.7426 + 1.88064i −0.727338 + 0.0995339i
\(358\) 21.9706 1.16118
\(359\) −13.4853 + 23.3572i −0.711726 + 1.23275i 0.252483 + 0.967601i \(0.418753\pi\)
−0.964209 + 0.265144i \(0.914580\pi\)
\(360\) −1.20711 2.09077i −0.0636201 0.110193i
\(361\) −19.8137 34.3183i −1.04283 1.80623i
\(362\) −4.65685 + 8.06591i −0.244759 + 0.423935i
\(363\) −7.00000 −0.367405
\(364\) 3.82843 9.37769i 0.200664 0.491525i
\(365\) −1.58579 −0.0830039
\(366\) −1.00000 + 1.73205i −0.0522708 + 0.0905357i
\(367\) −13.3492 23.1216i −0.696825 1.20694i −0.969562 0.244847i \(-0.921262\pi\)
0.272737 0.962089i \(-0.412071\pi\)
\(368\) −0.500000 0.866025i −0.0260643 0.0451447i
\(369\) 2.58579 4.47871i 0.134611 0.233153i
\(370\) −21.3137 −1.10805
\(371\) 4.07107 9.97204i 0.211359 0.517722i
\(372\) −2.00000 −0.103695
\(373\) 0.171573 0.297173i 0.00888371 0.0153870i −0.861549 0.507674i \(-0.830506\pi\)
0.870433 + 0.492287i \(0.163839\pi\)
\(374\) 5.24264 + 9.08052i 0.271090 + 0.469543i
\(375\) −5.03553 8.72180i −0.260034 0.450392i
\(376\) 4.50000 7.79423i 0.232070 0.401957i
\(377\) −26.1421 −1.34639
\(378\) 2.62132 0.358719i 0.134826 0.0184505i
\(379\) −18.8995 −0.970802 −0.485401 0.874292i \(-0.661326\pi\)
−0.485401 + 0.874292i \(0.661326\pi\)
\(380\) −9.24264 + 16.0087i −0.474137 + 0.821230i
\(381\) 0.414214 + 0.717439i 0.0212208 + 0.0367555i
\(382\) −2.58579 4.47871i −0.132300 0.229151i
\(383\) −1.82843 + 3.16693i −0.0934283 + 0.161822i −0.908952 0.416902i \(-0.863116\pi\)
0.815523 + 0.578724i \(0.196449\pi\)
\(384\) −1.00000 −0.0510310
\(385\) −7.82843 10.0951i −0.398974 0.514496i
\(386\) 5.48528 0.279193
\(387\) 0.171573 0.297173i 0.00872154 0.0151061i
\(388\) −0.828427 1.43488i −0.0420570 0.0728449i
\(389\) 18.7279 + 32.4377i 0.949543 + 1.64466i 0.746388 + 0.665511i \(0.231786\pi\)
0.203155 + 0.979147i \(0.434880\pi\)
\(390\) −4.62132 + 8.00436i −0.234010 + 0.405317i
\(391\) 5.24264 0.265132
\(392\) 1.74264 6.77962i 0.0880166 0.342422i
\(393\) −9.14214 −0.461160
\(394\) −6.41421 + 11.1097i −0.323143 + 0.559701i
\(395\) −12.0711 20.9077i −0.607361 1.05198i
\(396\) −1.00000 1.73205i −0.0502519 0.0870388i
\(397\) 4.32843 7.49706i 0.217238 0.376266i −0.736725 0.676193i \(-0.763629\pi\)
0.953962 + 0.299926i \(0.0969620\pi\)
\(398\) 27.6569 1.38631
\(399\) −12.4142 16.0087i −0.621488 0.801439i
\(400\) 0.828427 0.0414214
\(401\) 16.3492 28.3177i 0.816442 1.41412i −0.0918455 0.995773i \(-0.529277\pi\)
0.908288 0.418346i \(-0.137390\pi\)
\(402\) −2.44975 4.24309i −0.122182 0.211626i
\(403\) 3.82843 + 6.63103i 0.190708 + 0.330315i
\(404\) −4.41421 + 7.64564i −0.219615 + 0.380385i
\(405\) −2.41421 −0.119963
\(406\) −17.8995 + 2.44949i −0.888337 + 0.121566i
\(407\) −17.6569 −0.875218
\(408\) 2.62132 4.54026i 0.129775 0.224776i
\(409\) 13.3995 + 23.2086i 0.662562 + 1.14759i 0.979940 + 0.199292i \(0.0638644\pi\)
−0.317378 + 0.948299i \(0.602802\pi\)
\(410\) 6.24264 + 10.8126i 0.308302 + 0.533995i
\(411\) 3.79289 6.56948i 0.187090 0.324049i
\(412\) 10.8995 0.536980
\(413\) −9.65685 + 23.6544i −0.475183 + 1.16396i
\(414\) −1.00000 −0.0491473
\(415\) 8.65685 14.9941i 0.424948 0.736032i
\(416\) 1.91421 + 3.31552i 0.0938520 + 0.162557i
\(417\) −4.65685 8.06591i −0.228047 0.394989i
\(418\) −7.65685 + 13.2621i −0.374509 + 0.648669i
\(419\) 7.51472 0.367118 0.183559 0.983009i \(-0.441238\pi\)
0.183559 + 0.983009i \(0.441238\pi\)
\(420\) −2.41421 + 5.91359i −0.117802 + 0.288554i
\(421\) −7.31371 −0.356448 −0.178224 0.983990i \(-0.557035\pi\)
−0.178224 + 0.983990i \(0.557035\pi\)
\(422\) −5.58579 + 9.67487i −0.271912 + 0.470965i
\(423\) −4.50000 7.79423i −0.218797 0.378968i
\(424\) 2.03553 + 3.52565i 0.0988543 + 0.171221i
\(425\) −2.17157 + 3.76127i −0.105337 + 0.182449i
\(426\) 4.17157 0.202113
\(427\) 5.24264 0.717439i 0.253709 0.0347193i
\(428\) −5.65685 −0.273434
\(429\) −3.82843 + 6.63103i −0.184838 + 0.320149i
\(430\) 0.414214 + 0.717439i 0.0199752 + 0.0345980i
\(431\) 13.6569 + 23.6544i 0.657828 + 1.13939i 0.981177 + 0.193111i \(0.0618578\pi\)
−0.323349 + 0.946280i \(0.604809\pi\)
\(432\) −0.500000 + 0.866025i −0.0240563 + 0.0416667i
\(433\) −14.0000 −0.672797 −0.336399 0.941720i \(-0.609209\pi\)
−0.336399 + 0.941720i \(0.609209\pi\)
\(434\) 3.24264 + 4.18154i 0.155652 + 0.200720i
\(435\) 16.4853 0.790409
\(436\) −4.58579 + 7.94282i −0.219619 + 0.380392i
\(437\) 3.82843 + 6.63103i 0.183139 + 0.317205i
\(438\) 0.328427 + 0.568852i 0.0156929 + 0.0271808i
\(439\) −15.4853 + 26.8213i −0.739072 + 1.28011i 0.213841 + 0.976868i \(0.431402\pi\)
−0.952914 + 0.303242i \(0.901931\pi\)
\(440\) 4.82843 0.230186
\(441\) −5.00000 4.89898i −0.238095 0.233285i
\(442\) −20.0711 −0.954683
\(443\) −5.57107 + 9.64937i −0.264689 + 0.458456i −0.967482 0.252939i \(-0.918603\pi\)
0.702793 + 0.711395i \(0.251936\pi\)
\(444\) 4.41421 + 7.64564i 0.209489 + 0.362846i
\(445\) 8.24264 + 14.2767i 0.390739 + 0.676779i
\(446\) −6.24264 + 10.8126i −0.295598 + 0.511990i
\(447\) 9.24264 0.437162
\(448\) 1.62132 + 2.09077i 0.0766002 + 0.0987796i
\(449\) 9.51472 0.449027 0.224514 0.974471i \(-0.427921\pi\)
0.224514 + 0.974471i \(0.427921\pi\)
\(450\) 0.414214 0.717439i 0.0195262 0.0338204i
\(451\) 5.17157 + 8.95743i 0.243520 + 0.421789i
\(452\) −5.86396 10.1567i −0.275818 0.477730i
\(453\) 7.07107 12.2474i 0.332228 0.575435i
\(454\) 10.9706 0.514874
\(455\) 24.2279 3.31552i 1.13582 0.155434i
\(456\) 7.65685 0.358565
\(457\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(458\) 1.07107 + 1.85514i 0.0500477 + 0.0866852i
\(459\) −2.62132 4.54026i −0.122353 0.211921i
\(460\) 1.20711 2.09077i 0.0562816 0.0974827i
\(461\) 14.0000 0.652045 0.326023 0.945362i \(-0.394291\pi\)
0.326023 + 0.945362i \(0.394291\pi\)
\(462\) −2.00000 + 4.89898i −0.0930484 + 0.227921i
\(463\) −34.6274 −1.60927 −0.804636 0.593768i \(-0.797640\pi\)
−0.804636 + 0.593768i \(0.797640\pi\)
\(464\) 3.41421 5.91359i 0.158501 0.274532i
\(465\) −2.41421 4.18154i −0.111956 0.193914i
\(466\) −4.00000 6.92820i −0.185296 0.320943i
\(467\) −10.8284 + 18.7554i −0.501080 + 0.867896i 0.498919 + 0.866648i \(0.333730\pi\)
−0.999999 + 0.00124735i \(0.999603\pi\)
\(468\) 3.82843 0.176969
\(469\) −4.89949 + 12.0013i −0.226238 + 0.554167i
\(470\) 21.7279 1.00223
\(471\) 7.82843 13.5592i 0.360715 0.624777i
\(472\) −4.82843 8.36308i −0.222246 0.384942i
\(473\) 0.343146 + 0.594346i 0.0157779 + 0.0273281i
\(474\) −5.00000 + 8.66025i −0.229658 + 0.397779i
\(475\) −6.34315 −0.291043
\(476\) −13.7426 + 1.88064i −0.629893 + 0.0861989i
\(477\) 4.07107 0.186401
\(478\) 5.17157 8.95743i 0.236542 0.409703i
\(479\) −2.92893 5.07306i −0.133826 0.231794i 0.791322 0.611399i \(-0.209393\pi\)
−0.925148 + 0.379605i \(0.876060\pi\)
\(480\) −1.20711 2.09077i −0.0550966 0.0954302i
\(481\) 16.8995 29.2708i 0.770551 1.33463i
\(482\) 12.8284 0.584319
\(483\) 1.62132 + 2.09077i 0.0737726 + 0.0951333i
\(484\) −7.00000 −0.318182
\(485\) 2.00000 3.46410i 0.0908153 0.157297i
\(486\) 0.500000 + 0.866025i 0.0226805 + 0.0392837i
\(487\) −20.3848 35.3075i −0.923722 1.59993i −0.793603 0.608436i \(-0.791797\pi\)
−0.130119 0.991498i \(-0.541536\pi\)
\(488\) −1.00000 + 1.73205i −0.0452679 + 0.0784063i
\(489\) 1.65685 0.0749255
\(490\) 16.2782 4.54026i 0.735373 0.205108i
\(491\) −22.6569 −1.02249 −0.511245 0.859435i \(-0.670815\pi\)
−0.511245 + 0.859435i \(0.670815\pi\)
\(492\) 2.58579 4.47871i 0.116576 0.201916i
\(493\) 17.8995 + 31.0028i 0.806153 + 1.39630i
\(494\) −14.6569 25.3864i −0.659443 1.14219i
\(495\) 2.41421 4.18154i 0.108511 0.187946i
\(496\) −2.00000 −0.0898027
\(497\) −6.76346 8.72180i −0.303382 0.391226i
\(498\) −7.17157 −0.321366
\(499\) −3.41421 + 5.91359i −0.152841 + 0.264729i −0.932271 0.361761i \(-0.882176\pi\)
0.779430 + 0.626490i \(0.215509\pi\)
\(500\) −5.03553 8.72180i −0.225196 0.390051i
\(501\) −12.3995 21.4766i −0.553969 0.959502i
\(502\) 8.65685 14.9941i 0.386374 0.669220i
\(503\) 32.3431 1.44211 0.721055 0.692878i \(-0.243658\pi\)
0.721055 + 0.692878i \(0.243658\pi\)
\(504\) 2.62132 0.358719i 0.116763 0.0159786i
\(505\) −21.3137 −0.948448
\(506\) 1.00000 1.73205i 0.0444554 0.0769991i
\(507\) −0.828427 1.43488i −0.0367917 0.0637252i
\(508\) 0.414214 + 0.717439i 0.0183778 + 0.0318312i
\(509\) −22.0711 + 38.2282i −0.978283 + 1.69444i −0.309637 + 0.950855i \(0.600207\pi\)
−0.668646 + 0.743581i \(0.733126\pi\)
\(510\) 12.6569 0.560455
\(511\) 0.656854 1.60896i 0.0290575 0.0711761i
\(512\) −1.00000 −0.0441942
\(513\) 3.82843 6.63103i 0.169029 0.292767i
\(514\) 2.75736 + 4.77589i 0.121622 + 0.210655i
\(515\) 13.1569 + 22.7883i 0.579760 + 1.00417i
\(516\) 0.171573 0.297173i 0.00755307 0.0130823i
\(517\) 18.0000 0.791639
\(518\) 8.82843 21.6251i 0.387899 0.950154i
\(519\) −7.31371 −0.321036
\(520\) −4.62132 + 8.00436i −0.202658 + 0.351014i
\(521\) −14.2071 24.6074i −0.622425 1.07807i −0.989033 0.147696i \(-0.952814\pi\)
0.366608 0.930375i \(-0.380519\pi\)
\(522\) −3.41421 5.91359i −0.149436 0.258831i
\(523\) −0.0355339 + 0.0615465i −0.00155379 + 0.00269124i −0.866801 0.498654i \(-0.833828\pi\)
0.865247 + 0.501345i \(0.167161\pi\)
\(524\) −9.14214 −0.399376
\(525\) −2.17157 + 0.297173i −0.0947752 + 0.0129697i
\(526\) −19.3137 −0.842118
\(527\) 5.24264 9.08052i 0.228373 0.395554i
\(528\) −1.00000 1.73205i −0.0435194 0.0753778i
\(529\) −0.500000 0.866025i −0.0217391 0.0376533i
\(530\) −4.91421 + 8.51167i −0.213460 + 0.369723i
\(531\) −9.65685 −0.419072
\(532\) −12.4142 16.0087i −0.538224 0.694066i
\(533\) −19.7990 −0.857589
\(534\) 3.41421 5.91359i 0.147747 0.255906i
\(535\) −6.82843 11.8272i −0.295219 0.511334i
\(536\) −2.44975 4.24309i −0.105813 0.183273i
\(537\) 10.9853 19.0271i 0.474050 0.821078i
\(538\) 12.0000 0.517357
\(539\) 13.4853 3.76127i 0.580852 0.162010i
\(540\) −2.41421 −0.103891
\(541\) −20.5711 + 35.6301i −0.884419 + 1.53186i −0.0380415 + 0.999276i \(0.512112\pi\)
−0.846378 + 0.532583i \(0.821221\pi\)
\(542\) −15.1421 26.2269i −0.650410 1.12654i
\(543\) 4.65685 + 8.06591i 0.199845 + 0.346141i
\(544\) 2.62132 4.54026i 0.112388 0.194662i
\(545\) −22.1421 −0.948465
\(546\) −6.20711 8.00436i −0.265640 0.342555i
\(547\) 22.2843 0.952807 0.476403 0.879227i \(-0.341940\pi\)
0.476403 + 0.879227i \(0.341940\pi\)
\(548\) 3.79289 6.56948i 0.162024 0.280634i
\(549\) 1.00000 + 1.73205i 0.0426790 + 0.0739221i
\(550\) 0.828427 + 1.43488i 0.0353243 + 0.0611834i
\(551\) −26.1421 + 45.2795i −1.11369 + 1.92897i
\(552\) −1.00000 −0.0425628
\(553\) 26.2132 3.58719i 1.11470 0.152543i
\(554\) −25.2843 −1.07423
\(555\) −10.6569 + 18.4582i −0.452358 + 0.783508i
\(556\) −4.65685 8.06591i −0.197495 0.342071i
\(557\) −7.89949 13.6823i −0.334712 0.579739i 0.648717 0.761030i \(-0.275306\pi\)
−0.983430 + 0.181291i \(0.941972\pi\)
\(558\) −1.00000 + 1.73205i −0.0423334 + 0.0733236i
\(559\) −1.31371 −0.0555639
\(560\) −2.41421 + 5.91359i −0.102019 + 0.249895i
\(561\) 10.4853 0.442689
\(562\) −6.79289 + 11.7656i −0.286541 + 0.496303i
\(563\) −22.7279 39.3659i −0.957868 1.65908i −0.727665 0.685933i \(-0.759394\pi\)
−0.230203 0.973143i \(-0.573939\pi\)
\(564\) −4.50000 7.79423i −0.189484 0.328196i
\(565\) 14.1569 24.5204i 0.595583 1.03158i
\(566\) 29.3848 1.23513
\(567\) 1.00000 2.44949i 0.0419961 0.102869i
\(568\) 4.17157 0.175035
\(569\) −3.79289 + 6.56948i −0.159006 + 0.275407i −0.934511 0.355935i \(-0.884162\pi\)
0.775504 + 0.631342i \(0.217496\pi\)
\(570\) 9.24264 + 16.0087i 0.387132 + 0.670532i
\(571\) 0.550253 + 0.953065i 0.0230274 + 0.0398845i 0.877309 0.479925i \(-0.159336\pi\)
−0.854282 + 0.519810i \(0.826003\pi\)
\(572\) −3.82843 + 6.63103i −0.160075 + 0.277257i
\(573\) −5.17157 −0.216046
\(574\) −13.5563 + 1.85514i −0.565831 + 0.0774322i
\(575\) 0.828427 0.0345478
\(576\) −0.500000 + 0.866025i −0.0208333 + 0.0360844i
\(577\) −17.9706 31.1259i −0.748124 1.29579i −0.948721 0.316115i \(-0.897621\pi\)
0.200596 0.979674i \(-0.435712\pi\)
\(578\) 5.24264 + 9.08052i 0.218065 + 0.377700i
\(579\) 2.74264 4.75039i 0.113980 0.197420i
\(580\) 16.4853 0.684514
\(581\) 11.6274 + 14.9941i 0.482387 + 0.622061i
\(582\) −1.65685 −0.0686788
\(583\) −4.07107 + 7.05130i −0.168606 + 0.292035i
\(584\) 0.328427 + 0.568852i 0.0135904 + 0.0235393i
\(585\) 4.62132 + 8.00436i 0.191068 + 0.330940i
\(586\) −1.79289 + 3.10538i −0.0740637 + 0.128282i
\(587\) −27.1421 −1.12028 −0.560138 0.828399i \(-0.689252\pi\)
−0.560138 + 0.828399i \(0.689252\pi\)
\(588\) −5.00000 4.89898i −0.206197 0.202031i
\(589\) 15.3137 0.630990
\(590\) 11.6569 20.1903i 0.479905 0.831220i
\(591\) 6.41421 + 11.1097i 0.263845 + 0.456994i
\(592\) 4.41421 + 7.64564i 0.181423 + 0.314234i
\(593\) 16.0711 27.8359i 0.659960 1.14308i −0.320666 0.947192i \(-0.603907\pi\)
0.980626 0.195891i \(-0.0627600\pi\)
\(594\) −2.00000 −0.0820610
\(595\) −20.5208 26.4626i −0.841271 1.08486i
\(596\) 9.24264 0.378593
\(597\) 13.8284 23.9515i 0.565960 0.980271i
\(598\) 1.91421 + 3.31552i 0.0782780 + 0.135581i
\(599\) 5.91421 + 10.2437i 0.241648 + 0.418547i 0.961184 0.275908i \(-0.0889787\pi\)
−0.719536 + 0.694455i \(0.755645\pi\)
\(600\) 0.414214 0.717439i 0.0169102 0.0292893i
\(601\) 42.2843 1.72481 0.862406 0.506218i \(-0.168957\pi\)
0.862406 + 0.506218i \(0.168957\pi\)
\(602\) −0.899495 + 0.123093i −0.0366607 + 0.00501690i
\(603\) −4.89949 −0.199523
\(604\) 7.07107 12.2474i 0.287718 0.498342i
\(605\) −8.44975 14.6354i −0.343531 0.595013i
\(606\) 4.41421 + 7.64564i 0.179315 + 0.310583i
\(607\) −3.92893 + 6.80511i −0.159470 + 0.276211i −0.934678 0.355496i \(-0.884312\pi\)
0.775207 + 0.631707i \(0.217645\pi\)
\(608\) 7.65685 0.310526
\(609\) −6.82843 + 16.7262i −0.276702 + 0.677778i
\(610\) −4.82843 −0.195497
\(611\) −17.2279 + 29.8396i −0.696967 + 1.20718i
\(612\) −2.62132 4.54026i −0.105961 0.183529i
\(613\) −10.8995 18.8785i −0.440226 0.762495i 0.557480 0.830191i \(-0.311769\pi\)
−0.997706 + 0.0676961i \(0.978435\pi\)
\(614\) −7.07107 + 12.2474i −0.285365 + 0.494267i
\(615\) 12.4853 0.503455
\(616\) −2.00000 + 4.89898i −0.0805823 + 0.197386i
\(617\) −21.9289 −0.882826 −0.441413 0.897304i \(-0.645523\pi\)
−0.441413 + 0.897304i \(0.645523\pi\)
\(618\) 5.44975 9.43924i 0.219221 0.379702i
\(619\) −22.0355 38.1667i −0.885683 1.53405i −0.844929 0.534879i \(-0.820357\pi\)
−0.0407539 0.999169i \(-0.512976\pi\)
\(620\) −2.41421 4.18154i −0.0969571 0.167935i
\(621\) −0.500000 + 0.866025i −0.0200643 + 0.0347524i
\(622\) 16.3137 0.654120
\(623\) −17.8995 + 2.44949i −0.717128 + 0.0981367i
\(624\) 3.82843 0.153260
\(625\) 14.2279 24.6435i 0.569117 0.985739i
\(626\) 16.4853 + 28.5533i 0.658884 + 1.14122i
\(627\) 7.65685 + 13.2621i 0.305785 + 0.529636i
\(628\) 7.82843 13.5592i 0.312388 0.541072i
\(629\) −46.2843 −1.84547
\(630\) 3.91421 + 5.04757i 0.155946 + 0.201100i
\(631\) −15.4437 −0.614802 −0.307401 0.951580i \(-0.599459\pi\)
−0.307401 + 0.951580i \(0.599459\pi\)
\(632\) −5.00000 + 8.66025i −0.198889 + 0.344486i
\(633\) 5.58579 + 9.67487i 0.222015 + 0.384541i
\(634\) −16.3137 28.2562i −0.647900 1.12220i
\(635\) −1.00000 + 1.73205i −0.0396838 + 0.0687343i
\(636\) 4.07107 0.161428
\(637\) −6.67157 + 25.9553i −0.264337 + 1.02839i
\(638\) 13.6569 0.540680
\(639\) 2.08579 3.61269i 0.0825124 0.142916i
\(640\) −1.20711 2.09077i −0.0477151 0.0826450i
\(641\) 23.6924 + 41.0364i 0.935793 + 1.62084i 0.773214 + 0.634146i \(0.218648\pi\)
0.162579 + 0.986695i \(0.448019\pi\)
\(642\) −2.82843 + 4.89898i −0.111629 + 0.193347i
\(643\) 29.3137 1.15602 0.578010 0.816030i \(-0.303829\pi\)
0.578010 + 0.816030i \(0.303829\pi\)
\(644\) 1.62132 + 2.09077i 0.0638890 + 0.0823879i
\(645\) 0.828427 0.0326193
\(646\) −20.0711 + 34.7641i −0.789686 + 1.36778i
\(647\) 5.17157 + 8.95743i 0.203316 + 0.352153i 0.949595 0.313480i \(-0.101495\pi\)
−0.746279 + 0.665633i \(0.768162\pi\)
\(648\) 0.500000 + 0.866025i 0.0196419 + 0.0340207i
\(649\) 9.65685 16.7262i 0.379065 0.656559i
\(650\) −3.17157 −0.124399
\(651\) 5.24264 0.717439i 0.205475 0.0281186i
\(652\) 1.65685 0.0648874
\(653\) −17.9706 + 31.1259i −0.703242 + 1.21805i 0.264080 + 0.964501i \(0.414932\pi\)
−0.967322 + 0.253551i \(0.918402\pi\)
\(654\) 4.58579 + 7.94282i 0.179318 + 0.310589i
\(655\) −11.0355 19.1141i −0.431194 0.746850i
\(656\) 2.58579 4.47871i 0.100958 0.174864i
\(657\) 0.656854 0.0256263
\(658\) −9.00000 + 22.0454i −0.350857 + 0.859419i
\(659\) −23.4558 −0.913710 −0.456855 0.889541i \(-0.651024\pi\)
−0.456855 + 0.889541i \(0.651024\pi\)
\(660\) 2.41421 4.18154i 0.0939731 0.162766i
\(661\) 16.7279 + 28.9736i 0.650641 + 1.12694i 0.982968 + 0.183779i \(0.0588329\pi\)
−0.332327 + 0.943164i \(0.607834\pi\)
\(662\) −17.2426 29.8651i −0.670154 1.16074i
\(663\) −10.0355 + 17.3821i −0.389748 + 0.675063i
\(664\) −7.17157 −0.278311
\(665\) 18.4853 45.2795i 0.716828 1.75586i
\(666\) 8.82843 0.342095
\(667\) 3.41421 5.91359i 0.132199 0.228975i
\(668\) −12.3995 21.4766i −0.479751 0.830953i
\(669\) 6.24264 + 10.8126i 0.241354 + 0.418038i
\(670\) 5.91421 10.2437i 0.228486 0.395749i
\(671\) −4.00000 −0.154418
\(672\) 2.62132 0.358719i 0.101120 0.0138379i
\(673\) −6.68629 −0.257738 −0.128869 0.991662i \(-0.541135\pi\)
−0.128869 + 0.991662i \(0.541135\pi\)
\(674\) 0 0
\(675\) −0.414214 0.717439i −0.0159431 0.0276142i
\(676\) −0.828427 1.43488i −0.0318626 0.0551876i
\(677\) 22.8640 39.6015i 0.878733 1.52201i 0.0260016 0.999662i \(-0.491722\pi\)
0.852732 0.522349i \(-0.174944\pi\)
\(678\) −11.7279 −0.450408
\(679\) 2.68629 + 3.46410i 0.103090 + 0.132940i
\(680\) 12.6569 0.485368
\(681\) 5.48528 9.50079i 0.210196 0.364071i
\(682\) −2.00000 3.46410i −0.0765840 0.132647i
\(683\) 8.42893 + 14.5993i 0.322524 + 0.558628i 0.981008 0.193967i \(-0.0621353\pi\)
−0.658484 + 0.752595i \(0.728802\pi\)
\(684\) 3.82843 6.63103i 0.146384 0.253544i
\(685\) 18.3137 0.699731
\(686\) −2.13604 + 18.3967i −0.0815543 + 0.702388i
\(687\) 2.14214 0.0817276
\(688\) 0.171573 0.297173i 0.00654115 0.0113296i
\(689\) −7.79289 13.4977i −0.296886 0.514221i
\(690\) −1.20711 2.09077i −0.0459538 0.0795943i
\(691\) 6.07107 10.5154i 0.230954 0.400025i −0.727135 0.686495i \(-0.759149\pi\)
0.958089 + 0.286470i \(0.0924819\pi\)
\(692\) −7.31371 −0.278025
\(693\) 3.24264 + 4.18154i 0.123178 + 0.158844i
\(694\) 32.6569 1.23964
\(695\) 11.2426 19.4728i 0.426458 0.738646i
\(696\) −3.41421 5.91359i −0.129415 0.224154i
\(697\) 13.5563 + 23.4803i 0.513483 + 0.889379i
\(698\) −12.5711 + 21.7737i −0.475822 + 0.824148i
\(699\) −8.00000 −0.302588
\(700\) −2.17157 + 0.297173i −0.0820777 + 0.0112321i
\(701\) 8.61522 0.325393 0.162696 0.986676i \(-0.447981\pi\)
0.162696 + 0.986676i \(0.447981\pi\)
\(702\) 1.91421 3.31552i 0.0722473 0.125136i
\(703\) −33.7990 58.5416i −1.27475 2.20794i
\(704\) −1.00000 1.73205i −0.0376889 0.0652791i
\(705\) 10.8640 18.8169i 0.409160 0.708687i
\(706\) −2.14214 −0.0806203
\(707\) 8.82843 21.6251i 0.332027 0.813297i
\(708\) −9.65685 −0.362927
\(709\) 4.92893 8.53716i 0.185110 0.320620i −0.758504 0.651669i \(-0.774069\pi\)
0.943614 + 0.331049i \(0.107403\pi\)
\(710\) 5.03553 + 8.72180i 0.188980 + 0.327323i
\(711\) 5.00000 + 8.66025i 0.187515 + 0.324785i
\(712\) 3.41421 5.91359i 0.127953 0.221621i
\(713\) −2.00000 −0.0749006
\(714\) −5.24264 + 12.8418i −0.196201 + 0.480592i
\(715\) −18.4853 −0.691310
\(716\) 10.9853 19.0271i 0.410539 0.711075i
\(717\) −5.17157 8.95743i −0.193136 0.334521i
\(718\) 13.4853 + 23.3572i 0.503266 + 0.871683i
\(719\) −7.32843 + 12.6932i −0.273304 + 0.473377i −0.969706 0.244275i \(-0.921450\pi\)
0.696402 + 0.717652i \(0.254783\pi\)
\(720\) −2.41421 −0.0899724
\(721\) −28.5711 + 3.90986i −1.06404 + 0.145611i
\(722\) −39.6274 −1.47478
\(723\) 6.41421 11.1097i 0.238547 0.413176i
\(724\) 4.65685 + 8.06591i 0.173071 + 0.299767i
\(725\) 2.82843 + 4.89898i 0.105045 + 0.181944i
\(726\) −3.50000 + 6.06218i −0.129897 + 0.224989i
\(727\) −42.0000 −1.55769 −0.778847 0.627214i \(-0.784195\pi\)
−0.778847 + 0.627214i \(0.784195\pi\)
\(728\) −6.20711 8.00436i −0.230051 0.296661i
\(729\) 1.00000 0.0370370
\(730\) −0.792893 + 1.37333i −0.0293463 + 0.0508293i
\(731\) 0.899495 + 1.55797i 0.0332690 + 0.0576236i
\(732\) 1.00000 + 1.73205i 0.0369611 + 0.0640184i
\(733\) 4.24264 7.34847i 0.156706 0.271422i −0.776973 0.629534i \(-0.783246\pi\)
0.933679 + 0.358112i \(0.116579\pi\)
\(734\) −26.6985 −0.985459
\(735\) 4.20711 16.3674i 0.155181 0.603722i
\(736\) −1.00000 −0.0368605
\(737\) 4.89949 8.48617i 0.180475 0.312592i
\(738\) −2.58579 4.47871i −0.0951841 0.164864i
\(739\) 22.6274 + 39.1918i 0.832363 + 1.44169i 0.896160 + 0.443732i \(0.146346\pi\)
−0.0637965 + 0.997963i \(0.520321\pi\)
\(740\) −10.6569 + 18.4582i −0.391754 + 0.678537i
\(741\) −29.3137 −1.07687
\(742\) −6.60051 8.51167i −0.242312 0.312473i
\(743\) 15.4558 0.567020 0.283510 0.958969i \(-0.408501\pi\)
0.283510 + 0.958969i \(0.408501\pi\)
\(744\) −1.00000 + 1.73205i −0.0366618 + 0.0635001i
\(745\) 11.1569 + 19.3242i 0.408756 + 0.707985i
\(746\) −0.171573 0.297173i −0.00628173 0.0108803i
\(747\) −3.58579 + 6.21076i −0.131197 + 0.227240i
\(748\) 10.4853 0.383380
\(749\) 14.8284 2.02922i 0.541819 0.0741462i
\(750\) −10.0711 −0.367743
\(751\) −18.7990 + 32.5608i −0.685985 + 1.18816i 0.287141 + 0.957888i \(0.407295\pi\)
−0.973126 + 0.230272i \(0.926038\pi\)
\(752\) −4.50000 7.79423i −0.164098 0.284226i
\(753\) −8.65685 14.9941i −0.315473 0.546416i
\(754\) −13.0711 + 22.6398i −0.476020 + 0.824491i
\(755\) 34.1421 1.24256
\(756\) 1.00000 2.44949i 0.0363696 0.0890871i
\(757\) 28.9706 1.05295 0.526477 0.850190i \(-0.323513\pi\)
0.526477 + 0.850190i \(0.323513\pi\)
\(758\) −9.44975 + 16.3674i −0.343230 + 0.594492i
\(759\) −1.00000 1.73205i −0.0362977 0.0628695i
\(760\) 9.24264 + 16.0087i 0.335266 + 0.580697i
\(761\) 10.8284 18.7554i 0.392530 0.679882i −0.600252 0.799811i \(-0.704933\pi\)
0.992783 + 0.119928i \(0.0382665\pi\)
\(762\) 0.828427 0.0300107
\(763\) 9.17157 22.4657i 0.332033 0.813312i
\(764\) −5.17157 −0.187101
\(765\) 6.32843 10.9612i 0.228805 0.396301i
\(766\) 1.82843 + 3.16693i 0.0660638 + 0.114426i
\(767\) 18.4853 + 32.0174i 0.667465 + 1.15608i
\(768\) −0.500000 + 0.866025i −0.0180422 + 0.0312500i
\(769\) 33.3137 1.20132 0.600662 0.799503i \(-0.294904\pi\)
0.600662 + 0.799503i \(0.294904\pi\)
\(770\) −12.6569 + 1.73205i −0.456121 + 0.0624188i
\(771\) 5.51472 0.198608
\(772\) 2.74264 4.75039i 0.0987098 0.170970i
\(773\) 0.378680 + 0.655892i 0.0136202 + 0.0235908i 0.872755 0.488158i \(-0.162331\pi\)
−0.859135 + 0.511749i \(0.828998\pi\)
\(774\) −0.171573 0.297173i −0.00616706 0.0106817i
\(775\) 0.828427 1.43488i 0.0297580 0.0515423i
\(776\) −1.65685 −0.0594776
\(777\) −14.3137 18.4582i −0.513501 0.662185i
\(778\) 37.4558 1.34286
\(779\) −19.7990 + 34.2929i −0.709372 + 1.22867i
\(780\) 4.62132 + 8.00436i 0.165470 + 0.286602i
\(781\) 4.17157 + 7.22538i 0.149271 + 0.258544i
\(782\) 2.62132 4.54026i 0.0937382 0.162359i
\(783\) −6.82843 −0.244028
\(784\) −5.00000 4.89898i −0.178571 0.174964i
\(785\) 37.7990 1.34910
\(786\) −4.57107 + 7.91732i −0.163045 + 0.282402i
\(787\) 18.5208 + 32.0790i 0.660196 + 1.14349i 0.980564 + 0.196200i \(0.0628600\pi\)
−0.320368 + 0.947293i \(0.603807\pi\)
\(788\) 6.41421 + 11.1097i 0.228497 + 0.395768i
\(789\) −9.65685 + 16.7262i −0.343793 + 0.595467i
\(790\) −24.1421 −0.858939
\(791\) 19.0147 + 24.5204i 0.676086 + 0.871845i
\(792\) −2.00000 −0.0710669
\(793\) 3.82843 6.63103i 0.135951 0.235475i
\(794\) −4.32843 7.49706i −0.153610 0.266061i
\(795\) 4.91421 + 8.51167i 0.174289 + 0.301878i
\(796\) 13.8284 23.9515i 0.490136 0.848940i
\(797\) −39.8701 −1.41227 −0.706135 0.708077i \(-0.749563\pi\)
−0.706135 + 0.708077i \(0.749563\pi\)
\(798\) −20.0711 + 2.74666i −0.710508 + 0.0972308i
\(799\) 47.1838 1.66924
\(800\) 0.414214 0.717439i 0.0146447 0.0253653i
\(801\) −3.41421 5.91359i −0.120635 0.208946i
\(802\) −16.3492 28.3177i −0.577312 0.999933i
\(803\) −0.656854 + 1.13770i −0.0231799 + 0.0401487i
\(804\) −4.89949 −0.172792
\(805\) −2.41421 + 5.91359i −0.0850898 + 0.208427i
\(806\) 7.65685 0.269701
\(807\) 6.00000 10.3923i 0.211210 0.365826i
\(808\) 4.41421 + 7.64564i 0.155291 + 0.268973i
\(809\) 12.0711 + 20.9077i 0.424396 + 0.735076i 0.996364 0.0852005i \(-0.0271531\pi\)
−0.571968 + 0.820276i \(0.693820\pi\)
\(810\) −1.20711 + 2.09077i −0.0424134 + 0.0734622i
\(811\) 21.1127 0.741367 0.370684 0.928759i \(-0.379123\pi\)
0.370684 + 0.928759i \(0.379123\pi\)
\(812\) −6.82843 + 16.7262i −0.239631 + 0.586973i
\(813\) −30.2843 −1.06212
\(814\) −8.82843 + 15.2913i −0.309436 + 0.535959i
\(815\) 2.00000 + 3.46410i 0.0700569 + 0.121342i
\(816\) −2.62132 4.54026i −0.0917646 0.158941i
\(817\) −1.31371 + 2.27541i −0.0459608 + 0.0796065i
\(818\) 26.7990 0.937005
\(819\) −10.0355 + 1.37333i −0.350670 + 0.0479881i
\(820\) 12.4853 0.436005
\(821\) 1.14214 1.97824i 0.0398608 0.0690409i −0.845407 0.534123i \(-0.820642\pi\)
0.885268 + 0.465082i \(0.153975\pi\)
\(822\) −3.79289 6.56948i −0.132292 0.229137i
\(823\) 6.89949 + 11.9503i 0.240501 + 0.416560i 0.960857 0.277044i \(-0.0893548\pi\)
−0.720356 + 0.693605i \(0.756022\pi\)
\(824\) 5.44975 9.43924i 0.189851 0.328831i
\(825\) 1.65685 0.0576843
\(826\) 15.6569 + 20.1903i 0.544772 + 0.702509i
\(827\) −42.6274 −1.48230 −0.741150 0.671339i \(-0.765719\pi\)
−0.741150 + 0.671339i \(0.765719\pi\)
\(828\) −0.500000 + 0.866025i −0.0173762 + 0.0300965i
\(829\) −8.08579 14.0050i −0.280831 0.486414i 0.690759 0.723085i \(-0.257277\pi\)
−0.971590 + 0.236672i \(0.923943\pi\)
\(830\) −8.65685 14.9941i −0.300484 0.520453i
\(831\) −12.6421 + 21.8968i −0.438551 + 0.759592i
\(832\) 3.82843 0.132727
\(833\) 35.3492 9.85951i 1.22478 0.341612i
\(834\) −9.31371 −0.322507
\(835\) 29.9350 51.8490i 1.03594 1.79431i
\(836\) 7.65685 + 13.2621i 0.264818 + 0.458678i
\(837\) 1.00000 + 1.73205i 0.0345651 + 0.0598684i
\(838\) 3.75736 6.50794i 0.129796 0.224813i
\(839\) 24.9706 0.862080 0.431040 0.902333i \(-0.358147\pi\)
0.431040 + 0.902333i \(0.358147\pi\)
\(840\) 3.91421 + 5.04757i 0.135053 + 0.174158i
\(841\) 17.6274 0.607842
\(842\) −3.65685 + 6.33386i −0.126024 + 0.218279i
\(843\) 6.79289 + 11.7656i 0.233960 + 0.405230i
\(844\) 5.58579 + 9.67487i 0.192271 + 0.333023i
\(845\) 2.00000 3.46410i 0.0688021 0.119169i
\(846\) −9.00000 −0.309426
\(847\) 18.3492 2.51104i 0.630487 0.0862802i
\(848\) 4.07107 0.139801
\(849\) 14.6924 25.4480i 0.504241 0.873372i
\(850\) 2.17157 + 3.76127i 0.0744843 + 0.129011i
\(851\) 4.41421 + 7.64564i 0.151317 + 0.262089i
\(852\) 2.08579 3.61269i 0.0714579 0.123769i
\(853\) −52.9117 −1.81166 −0.905831 0.423640i \(-0.860752\pi\)
−0.905831 + 0.423640i \(0.860752\pi\)
\(854\) 2.00000 4.89898i 0.0684386 0.167640i
\(855\) 18.4853 0.632183
\(856\) −2.82843 + 4.89898i −0.0966736 + 0.167444i
\(857\) 0.313708 + 0.543359i 0.0107161 + 0.0185608i 0.871334 0.490691i \(-0.163256\pi\)
−0.860618 + 0.509252i \(0.829922\pi\)
\(858\) 3.82843 + 6.63103i 0.130700 + 0.226380i
\(859\) 17.6569 30.5826i 0.602444 1.04346i −0.390006 0.920812i \(-0.627527\pi\)
0.992450 0.122651i \(-0.0391397\pi\)
\(860\) 0.828427 0.0282491
\(861\) −5.17157 + 12.6677i −0.176247 + 0.431715i
\(862\) 27.3137 0.930309
\(863\) −21.3284 + 36.9419i −0.726028 + 1.25752i 0.232521 + 0.972591i \(0.425302\pi\)
−0.958549 + 0.284926i \(0.908031\pi\)
\(864\) 0.500000 + 0.866025i 0.0170103 + 0.0294628i
\(865\) −8.82843 15.2913i −0.300176 0.519919i
\(866\) −7.00000 + 12.1244i −0.237870 + 0.412002i
\(867\) 10.4853 0.356099
\(868\) 5.24264 0.717439i 0.177947 0.0243515i
\(869\) −20.0000 −0.678454
\(870\) 8.24264 14.2767i 0.279452 0.484025i
\(871\) 9.37868 + 16.2443i 0.317784 + 0.550419i
\(872\) 4.58579 + 7.94282i 0.155294 + 0.268978i
\(873\) −0.828427 + 1.43488i −0.0280380 + 0.0485633i
\(874\) 7.65685 0.258997
\(875\) 16.3284 + 21.0563i 0.552002 + 0.711832i
\(876\) 0.656854 0.0221930
\(877\) 8.84315 15.3168i 0.298612 0.517211i −0.677207 0.735793i \(-0.736810\pi\)
0.975819 + 0.218582i \(0.0701431\pi\)
\(878\) 15.4853 + 26.8213i 0.522603 + 0.905175i
\(879\) 1.79289 + 3.10538i 0.0604728 + 0.104742i
\(880\) 2.41421 4.18154i 0.0813831 0.140960i
\(881\) −6.27208 −0.211312 −0.105656 0.994403i \(-0.533694\pi\)
−0.105656 + 0.994403i \(0.533694\pi\)
\(882\) −6.74264 + 1.88064i −0.227037 + 0.0633244i
\(883\) −44.2843 −1.49028 −0.745142 0.666906i \(-0.767618\pi\)
−0.745142 + 0.666906i \(0.767618\pi\)
\(884\) −10.0355 + 17.3821i −0.337532 + 0.584622i
\(885\) −11.6569 20.1903i −0.391841 0.678688i
\(886\) 5.57107 + 9.64937i 0.187164 + 0.324177i
\(887\) −20.4853 + 35.4815i −0.687828 + 1.19135i 0.284711 + 0.958614i \(0.408103\pi\)
−0.972539 + 0.232740i \(0.925231\pi\)
\(888\) 8.82843 0.296263
\(889\) −1.34315 1.73205i −0.0450477 0.0580911i
\(890\) 16.4853 0.552588
\(891\) −1.00000 + 1.73205i −0.0335013 + 0.0580259i
\(892\) 6.24264 + 10.8126i 0.209019 + 0.362032i
\(893\) 34.4558 + 59.6793i 1.15302 + 1.99709i
\(894\) 4.62132 8.00436i 0.154560 0.267706i
\(895\) 53.0416 1.77299
\(896\) 2.62132 0.358719i 0.0875722 0.0119840i
\(897\) 3.82843 0.127827
\(898\) 4.75736 8.23999i 0.158755 0.274972i
\(899\) −6.82843 11.8272i −0.227741 0.394459i
\(900\) −0.414214 0.717439i −0.0138071 0.0239146i
\(901\) −10.6716 + 18.4837i −0.355522 + 0.615782i
\(902\) 10.3431 0.344389
\(903\) −0.343146 + 0.840532i −0.0114192 + 0.0279712i
\(904\) −11.7279 −0.390065
\(905\) −11.2426 + 19.4728i −0.373718 + 0.647299i
\(906\) −7.07107 12.2474i −0.234920 0.406894i
\(907\) −21.4497 37.1521i −0.712227 1.23361i −0.964019 0.265832i \(-0.914353\pi\)
0.251792 0.967781i \(-0.418980\pi\)
\(908\) 5.48528 9.50079i 0.182035 0.315295i
\(909\) 8.82843 0.292820
\(910\) 9.24264 22.6398i 0.306391 0.750501i
\(911\) 8.48528 0.281130 0.140565 0.990071i \(-0.455108\pi\)
0.140565 + 0.990071i \(0.455108\pi\)
\(912\) 3.82843 6.63103i 0.126772 0.219575i
\(913\) −7.17157 12.4215i −0.237344 0.411093i
\(914\) 0 0
\(915\) −2.41421 + 4.18154i −0.0798114 + 0.138237i
\(916\) 2.14214 0.0707782
\(917\) 23.9645 3.27946i 0.791376 0.108297i
\(918\) −5.24264 −0.173033
\(919\) 11.8640 20.5490i 0.391356 0.677848i −0.601273 0.799044i \(-0.705339\pi\)
0.992629 + 0.121195i \(0.0386728\pi\)
\(920\) −1.20711 2.09077i −0.0397971 0.0689307i
\(921\) 7.07107 + 12.2474i 0.233000 + 0.403567i
\(922\) 7.00000 12.1244i 0.230533 0.399294i
\(923\) −15.9706 −0.525677
\(924\) 3.24264 + 4.18154i 0.106675 + 0.137563i
\(925\) −7.31371 −0.240473
\(926\) −17.3137 + 29.9882i −0.568964 + 0.985474i
\(927\) −5.44975 9.43924i −0.178993 0.310025i
\(928\) −3.41421 5.91359i −0.112077 0.194123i
\(929\) 2.68629 4.65279i 0.0881344 0.152653i −0.818588 0.574381i \(-0.805243\pi\)
0.906723 + 0.421728i \(0.138576\pi\)
\(930\) −4.82843 −0.158330
\(931\) 38.2843 + 37.5108i 1.25472 + 1.22937i
\(932\) −8.00000 −0.262049
\(933\) 8.15685 14.1281i 0.267043 0.462533i
\(934\) 10.8284 + 18.7554i 0.354317 + 0.613695i
\(935\) 12.6569 + 21.9223i 0.413923 + 0.716936i
\(936\) 1.91421 3.31552i 0.0625680 0.108371i
\(937\) 4.48528 0.146528 0.0732639 0.997313i \(-0.476658\pi\)
0.0732639 + 0.997313i \(0.476658\pi\)
\(938\) 7.94365 + 10.2437i 0.259369 + 0.334469i
\(939\) 32.9706 1.07595
\(940\) 10.8640 18.8169i 0.354343 0.613741i
\(941\) −15.7574 27.2925i −0.513675 0.889712i −0.999874 0.0158634i \(-0.994950\pi\)
0.486199 0.873848i \(-0.338383\pi\)
\(942\) −7.82843 13.5592i −0.255064 0.441784i
\(943\) 2.58579 4.47871i 0.0842048 0.145847i
\(944\) −9.65685 −0.314304
\(945\) 6.32843 0.866025i 0.205864 0.0281718i
\(946\) 0.686292 0.0223133
\(947\) 5.84315 10.1206i 0.189877 0.328876i −0.755332 0.655342i \(-0.772524\pi\)
0.945209 + 0.326466i \(0.105858\pi\)
\(948\) 5.00000 + 8.66025i 0.162392 + 0.281272i
\(949\) −1.25736 2.17781i −0.0408156 0.0706947i
\(950\) −3.17157 + 5.49333i −0.102899 + 0.178227i
\(951\) −32.6274 −1.05802
\(952\) −5.24264 + 12.8418i −0.169915 + 0.416205i
\(953\) 11.7990 0.382207 0.191103 0.981570i \(-0.438793\pi\)
0.191103 + 0.981570i \(0.438793\pi\)
\(954\) 2.03553 3.52565i 0.0659028 0.114147i
\(955\) −6.24264 10.8126i −0.202007 0.349887i
\(956\) −5.17157 8.95743i −0.167261 0.289704i
\(957\) 6.82843 11.8272i 0.220732 0.382319i
\(958\) −5.85786 −0.189259
\(959\) −7.58579 + 18.5813i −0.244958 + 0.600022i
\(960\) −2.41421 −0.0779184
\(961\) 13.5000 23.3827i 0.435484 0.754280i
\(962\) −16.8995 29.2708i −0.544862 0.943728i
\(963\) 2.82843 + 4.89898i 0.0911448 + 0.157867i
\(964\) 6.41421 11.1097i 0.206588 0.357821i
\(965\) 13.2426 0.426296
\(966\) 2.62132 0.358719i 0.0843396 0.0115416i
\(967\) −10.8284 −0.348219 −0.174109 0.984726i \(-0.555705\pi\)
−0.174109 + 0.984726i \(0.555705\pi\)
\(968\) −3.50000 + 6.06218i −0.112494 + 0.194846i
\(969\) 20.0711 + 34.7641i 0.644776 + 1.11678i
\(970\) −2.00000 3.46410i −0.0642161 0.111226i
\(971\) −6.82843 + 11.8272i −0.219135 + 0.379552i −0.954544 0.298071i \(-0.903657\pi\)
0.735409 + 0.677623i \(0.236990\pi\)
\(972\) 1.00000 0.0320750
\(973\) 15.1005 + 19.4728i 0.484100 + 0.624270i
\(974\) −40.7696 −1.30634
\(975\) −1.58579 + 2.74666i −0.0507858 + 0.0879636i
\(976\) 1.00000 + 1.73205i 0.0320092 + 0.0554416i
\(977\) −12.1777 21.0923i −0.389598 0.674804i 0.602797 0.797894i \(-0.294053\pi\)
−0.992395 + 0.123091i \(0.960719\pi\)
\(978\) 0.828427 1.43488i 0.0264902 0.0458823i
\(979\) 13.6569 0.436475
\(980\) 4.20711 16.3674i 0.134391 0.522839i
\(981\) 9.17157 0.292826
\(982\) −11.3284 + 19.6214i −0.361505 + 0.626144i
\(983\) −0.272078 0.471253i −0.00867794 0.0150306i 0.861654 0.507496i \(-0.169429\pi\)
−0.870332 + 0.492466i \(0.836096\pi\)
\(984\) −2.58579 4.47871i −0.0824319 0.142776i
\(985\) −15.4853 + 26.8213i −0.493402 + 0.854597i
\(986\) 35.7990 1.14007
\(987\) 14.5919 + 18.8169i 0.464465 + 0.598950i
\(988\) −29.3137 −0.932593
\(989\) 0.171573 0.297173i 0.00545570 0.00944955i
\(990\) −2.41421 4.18154i −0.0767287 0.132898i
\(991\) −9.97056 17.2695i −0.316725 0.548584i 0.663077 0.748551i \(-0.269250\pi\)
−0.979803 + 0.199966i \(0.935917\pi\)
\(992\) −1.00000 + 1.73205i −0.0317500 + 0.0549927i
\(993\) −34.4853 −1.09436
\(994\) −10.9350 + 1.49642i −0.346838 + 0.0474637i
\(995\) 66.7696 2.11674
\(996\) −3.58579 + 6.21076i −0.113620 + 0.196796i
\(997\) 12.3137 + 21.3280i 0.389979 + 0.675464i 0.992446 0.122680i \(-0.0391489\pi\)
−0.602467 + 0.798144i \(0.705816\pi\)
\(998\) 3.41421 + 5.91359i 0.108075 + 0.187191i
\(999\) 4.41421 7.64564i 0.139660 0.241897i
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.j.415.2 yes 4
7.2 even 3 6762.2.a.bv.1.1 2
7.4 even 3 inner 966.2.i.j.277.2 4
7.5 odd 6 6762.2.a.bt.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
966.2.i.j.277.2 4 7.4 even 3 inner
966.2.i.j.415.2 yes 4 1.1 even 1 trivial
6762.2.a.bt.1.2 2 7.5 odd 6
6762.2.a.bv.1.1 2 7.2 even 3