Properties

Label 462.2.p.a.241.1
Level $462$
Weight $2$
Character 462.241
Analytic conductor $3.689$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [462,2,Mod(241,462)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(462, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 1, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("462.241");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 462.p (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.68908857338\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 8 x^{15} + 74 x^{14} - 378 x^{13} + 1878 x^{12} - 6718 x^{11} + 22086 x^{10} - 56904 x^{9} + 130215 x^{8} - 239606 x^{7} + 378750 x^{6} - 477124 x^{5} + \cdots + 13417 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 241.1
Root \(0.500000 + 3.19339i\) of defining polynomial
Character \(\chi\) \(=\) 462.241
Dual form 462.2.p.a.439.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.866025 + 0.500000i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-2.01555 + 1.16368i) q^{5} -1.00000 q^{6} +(-1.31629 - 2.29508i) q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.866025 + 0.500000i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-2.01555 + 1.16368i) q^{5} -1.00000 q^{6} +(-1.31629 - 2.29508i) q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(1.16368 - 2.01555i) q^{10} +(-3.15334 - 1.02783i) q^{11} +(0.866025 - 0.500000i) q^{12} -1.44095 q^{13} +(2.28748 + 1.32945i) q^{14} -2.32736 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.60782 + 2.78483i) q^{17} +(-0.866025 - 0.500000i) q^{18} +(-3.07901 - 5.33301i) q^{19} +2.32736i q^{20} +(0.00760304 - 2.64574i) q^{21} +(3.24479 - 0.686549i) q^{22} +(-3.14645 - 5.44981i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(0.208304 - 0.360793i) q^{25} +(1.24790 - 0.720474i) q^{26} +1.00000i q^{27} +(-2.64574 - 0.00760304i) q^{28} +3.26833i q^{29} +(2.01555 - 1.16368i) q^{30} +(2.67692 + 1.54552i) q^{31} +(0.866025 + 0.500000i) q^{32} +(-2.21696 - 2.46679i) q^{33} -3.21565i q^{34} +(5.32378 + 3.09412i) q^{35} +1.00000 q^{36} +(-4.57056 - 7.91644i) q^{37} +(5.33301 + 3.07901i) q^{38} +(-1.24790 - 0.720474i) q^{39} +(-1.16368 - 2.01555i) q^{40} +3.41163 q^{41} +(1.31629 + 2.29508i) q^{42} +1.89247i q^{43} +(-2.46679 + 2.21696i) q^{44} +(-2.01555 - 1.16368i) q^{45} +(5.44981 + 3.14645i) q^{46} +(-9.22249 + 5.32461i) q^{47} -1.00000i q^{48} +(-3.53478 + 6.04196i) q^{49} +0.416608i q^{50} +(-2.78483 + 1.60782i) q^{51} +(-0.720474 + 1.24790i) q^{52} +(4.60856 - 7.98226i) q^{53} +(-0.500000 - 0.866025i) q^{54} +(7.55179 - 1.59785i) q^{55} +(2.29508 - 1.31629i) q^{56} -6.15803i q^{57} +(-1.63416 - 2.83045i) q^{58} +(-0.461345 - 0.266358i) q^{59} +(-1.16368 + 2.01555i) q^{60} +(-0.233713 - 0.404803i) q^{61} -3.09104 q^{62} +(1.32945 - 2.28748i) q^{63} -1.00000 q^{64} +(2.90431 - 1.67680i) q^{65} +(3.15334 + 1.02783i) q^{66} +(4.61347 - 7.99077i) q^{67} +(1.60782 + 2.78483i) q^{68} -6.29290i q^{69} +(-6.15759 - 0.0176950i) q^{70} -3.25253 q^{71} +(-0.866025 + 0.500000i) q^{72} +(-2.50002 + 4.33016i) q^{73} +(7.91644 + 4.57056i) q^{74} +(0.360793 - 0.208304i) q^{75} -6.15803 q^{76} +(1.79176 + 8.59009i) q^{77} +1.44095 q^{78} +(-7.21263 + 4.16421i) q^{79} +(2.01555 + 1.16368i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-2.95456 + 1.70582i) q^{82} +4.56130 q^{83} +(-2.28748 - 1.32945i) q^{84} -7.48397i q^{85} +(-0.946236 - 1.63893i) q^{86} +(-1.63416 + 2.83045i) q^{87} +(1.02783 - 3.15334i) q^{88} +(-3.79409 + 2.19052i) q^{89} +2.32736 q^{90} +(1.89670 + 3.30709i) q^{91} -6.29290 q^{92} +(1.54552 + 2.67692i) q^{93} +(5.32461 - 9.22249i) q^{94} +(12.4118 + 7.16598i) q^{95} +(0.500000 + 0.866025i) q^{96} +17.8026i q^{97} +(0.0402313 - 6.99988i) q^{98} +(-0.686549 - 3.24479i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 8 q^{4} + 12 q^{5} - 16 q^{6} - 6 q^{7} + 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 8 q^{4} + 12 q^{5} - 16 q^{6} - 6 q^{7} + 8 q^{9} + 2 q^{10} - 4 q^{11} + 8 q^{14} - 4 q^{15} - 8 q^{16} - 10 q^{19} - 4 q^{21} + 2 q^{22} - 4 q^{23} - 8 q^{24} + 10 q^{25} + 12 q^{26} - 12 q^{30} + 6 q^{31} + 2 q^{33} - 8 q^{35} + 16 q^{36} + 14 q^{37} - 12 q^{38} - 12 q^{39} - 2 q^{40} + 32 q^{41} + 6 q^{42} + 4 q^{44} + 12 q^{45} + 18 q^{46} - 24 q^{47} - 6 q^{49} + 6 q^{51} - 8 q^{54} - 14 q^{55} + 4 q^{56} - 2 q^{60} + 28 q^{61} - 8 q^{62} - 6 q^{63} - 16 q^{64} + 72 q^{65} + 4 q^{66} - 16 q^{67} - 30 q^{70} - 56 q^{71} - 44 q^{73} + 24 q^{74} - 12 q^{75} - 20 q^{76} + 32 q^{77} - 30 q^{79} - 12 q^{80} - 8 q^{81} - 12 q^{82} + 8 q^{83} - 8 q^{84} - 12 q^{86} + 4 q^{88} - 36 q^{89} + 4 q^{90} - 8 q^{91} - 8 q^{92} + 4 q^{93} + 14 q^{94} + 72 q^{95} + 8 q^{96} - 40 q^{98} - 8 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/462\mathbb{Z}\right)^\times\).

\(n\) \(155\) \(199\) \(211\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{6}\right)\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 + 0.500000i −0.612372 + 0.353553i
\(3\) 0.866025 + 0.500000i 0.500000 + 0.288675i
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) −2.01555 + 1.16368i −0.901383 + 0.520414i −0.877649 0.479305i \(-0.840889\pi\)
−0.0237343 + 0.999718i \(0.507556\pi\)
\(6\) −1.00000 −0.408248
\(7\) −1.31629 2.29508i −0.497509 0.867459i
\(8\) 1.00000i 0.353553i
\(9\) 0.500000 + 0.866025i 0.166667 + 0.288675i
\(10\) 1.16368 2.01555i 0.367988 0.637374i
\(11\) −3.15334 1.02783i −0.950769 0.309901i
\(12\) 0.866025 0.500000i 0.250000 0.144338i
\(13\) −1.44095 −0.399647 −0.199823 0.979832i \(-0.564037\pi\)
−0.199823 + 0.979832i \(0.564037\pi\)
\(14\) 2.28748 + 1.32945i 0.611354 + 0.355312i
\(15\) −2.32736 −0.600922
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −1.60782 + 2.78483i −0.389954 + 0.675421i −0.992443 0.122707i \(-0.960843\pi\)
0.602489 + 0.798127i \(0.294176\pi\)
\(18\) −0.866025 0.500000i −0.204124 0.117851i
\(19\) −3.07901 5.33301i −0.706374 1.22348i −0.966193 0.257819i \(-0.916996\pi\)
0.259819 0.965657i \(-0.416337\pi\)
\(20\) 2.32736i 0.520414i
\(21\) 0.00760304 2.64574i 0.00165912 0.577348i
\(22\) 3.24479 0.686549i 0.691791 0.146373i
\(23\) −3.14645 5.44981i −0.656080 1.13636i −0.981622 0.190836i \(-0.938880\pi\)
0.325542 0.945528i \(-0.394453\pi\)
\(24\) −0.500000 + 0.866025i −0.102062 + 0.176777i
\(25\) 0.208304 0.360793i 0.0416608 0.0721586i
\(26\) 1.24790 0.720474i 0.244733 0.141297i
\(27\) 1.00000i 0.192450i
\(28\) −2.64574 0.00760304i −0.499998 0.00143684i
\(29\) 3.26833i 0.606913i 0.952845 + 0.303456i \(0.0981407\pi\)
−0.952845 + 0.303456i \(0.901859\pi\)
\(30\) 2.01555 1.16368i 0.367988 0.212458i
\(31\) 2.67692 + 1.54552i 0.480789 + 0.277584i 0.720745 0.693200i \(-0.243800\pi\)
−0.239956 + 0.970784i \(0.577133\pi\)
\(32\) 0.866025 + 0.500000i 0.153093 + 0.0883883i
\(33\) −2.21696 2.46679i −0.385924 0.429414i
\(34\) 3.21565i 0.551479i
\(35\) 5.32378 + 3.09412i 0.899884 + 0.523002i
\(36\) 1.00000 0.166667
\(37\) −4.57056 7.91644i −0.751395 1.30145i −0.947147 0.320801i \(-0.896048\pi\)
0.195752 0.980653i \(-0.437285\pi\)
\(38\) 5.33301 + 3.07901i 0.865128 + 0.499482i
\(39\) −1.24790 0.720474i −0.199823 0.115368i
\(40\) −1.16368 2.01555i −0.183994 0.318687i
\(41\) 3.41163 0.532808 0.266404 0.963861i \(-0.414165\pi\)
0.266404 + 0.963861i \(0.414165\pi\)
\(42\) 1.31629 + 2.29508i 0.203107 + 0.354139i
\(43\) 1.89247i 0.288599i 0.989534 + 0.144300i \(0.0460929\pi\)
−0.989534 + 0.144300i \(0.953907\pi\)
\(44\) −2.46679 + 2.21696i −0.371883 + 0.334220i
\(45\) −2.01555 1.16368i −0.300461 0.173471i
\(46\) 5.44981 + 3.14645i 0.803530 + 0.463919i
\(47\) −9.22249 + 5.32461i −1.34524 + 0.776674i −0.987571 0.157175i \(-0.949761\pi\)
−0.357668 + 0.933849i \(0.616428\pi\)
\(48\) 1.00000i 0.144338i
\(49\) −3.53478 + 6.04196i −0.504969 + 0.863137i
\(50\) 0.416608i 0.0589173i
\(51\) −2.78483 + 1.60782i −0.389954 + 0.225140i
\(52\) −0.720474 + 1.24790i −0.0999117 + 0.173052i
\(53\) 4.60856 7.98226i 0.633035 1.09645i −0.353893 0.935286i \(-0.615142\pi\)
0.986928 0.161162i \(-0.0515242\pi\)
\(54\) −0.500000 0.866025i −0.0680414 0.117851i
\(55\) 7.55179 1.59785i 1.01828 0.215454i
\(56\) 2.29508 1.31629i 0.306693 0.175896i
\(57\) 6.15803i 0.815651i
\(58\) −1.63416 2.83045i −0.214576 0.371657i
\(59\) −0.461345 0.266358i −0.0600620 0.0346768i 0.469668 0.882843i \(-0.344374\pi\)
−0.529730 + 0.848166i \(0.677707\pi\)
\(60\) −1.16368 + 2.01555i −0.150230 + 0.260207i
\(61\) −0.233713 0.404803i −0.0299239 0.0518298i 0.850676 0.525691i \(-0.176193\pi\)
−0.880600 + 0.473861i \(0.842860\pi\)
\(62\) −3.09104 −0.392563
\(63\) 1.32945 2.28748i 0.167496 0.288195i
\(64\) −1.00000 −0.125000
\(65\) 2.90431 1.67680i 0.360235 0.207982i
\(66\) 3.15334 + 1.02783i 0.388150 + 0.126517i
\(67\) 4.61347 7.99077i 0.563625 0.976227i −0.433551 0.901129i \(-0.642740\pi\)
0.997176 0.0750984i \(-0.0239271\pi\)
\(68\) 1.60782 + 2.78483i 0.194977 + 0.337710i
\(69\) 6.29290i 0.757576i
\(70\) −6.15759 0.0176950i −0.735973 0.00211496i
\(71\) −3.25253 −0.386004 −0.193002 0.981198i \(-0.561822\pi\)
−0.193002 + 0.981198i \(0.561822\pi\)
\(72\) −0.866025 + 0.500000i −0.102062 + 0.0589256i
\(73\) −2.50002 + 4.33016i −0.292605 + 0.506807i −0.974425 0.224713i \(-0.927855\pi\)
0.681820 + 0.731520i \(0.261189\pi\)
\(74\) 7.91644 + 4.57056i 0.920267 + 0.531316i
\(75\) 0.360793 0.208304i 0.0416608 0.0240529i
\(76\) −6.15803 −0.706374
\(77\) 1.79176 + 8.59009i 0.204190 + 0.978931i
\(78\) 1.44095 0.163155
\(79\) −7.21263 + 4.16421i −0.811484 + 0.468510i −0.847471 0.530842i \(-0.821876\pi\)
0.0359870 + 0.999352i \(0.488543\pi\)
\(80\) 2.01555 + 1.16368i 0.225346 + 0.130103i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) −2.95456 + 1.70582i −0.326277 + 0.188376i
\(83\) 4.56130 0.500668 0.250334 0.968160i \(-0.419460\pi\)
0.250334 + 0.968160i \(0.419460\pi\)
\(84\) −2.28748 1.32945i −0.249584 0.145055i
\(85\) 7.48397i 0.811750i
\(86\) −0.946236 1.63893i −0.102035 0.176730i
\(87\) −1.63416 + 2.83045i −0.175201 + 0.303456i
\(88\) 1.02783 3.15334i 0.109567 0.336148i
\(89\) −3.79409 + 2.19052i −0.402173 + 0.232195i −0.687421 0.726259i \(-0.741257\pi\)
0.285248 + 0.958454i \(0.407924\pi\)
\(90\) 2.32736 0.245325
\(91\) 1.89670 + 3.30709i 0.198828 + 0.346677i
\(92\) −6.29290 −0.656080
\(93\) 1.54552 + 2.67692i 0.160263 + 0.277584i
\(94\) 5.32461 9.22249i 0.549191 0.951227i
\(95\) 12.4118 + 7.16598i 1.27343 + 0.735214i
\(96\) 0.500000 + 0.866025i 0.0510310 + 0.0883883i
\(97\) 17.8026i 1.80758i 0.427977 + 0.903790i \(0.359226\pi\)
−0.427977 + 0.903790i \(0.640774\pi\)
\(98\) 0.0402313 6.99988i 0.00406398 0.707095i
\(99\) −0.686549 3.24479i −0.0690007 0.326113i
\(100\) −0.208304 0.360793i −0.0208304 0.0360793i
\(101\) −5.34857 + 9.26399i −0.532203 + 0.921802i 0.467091 + 0.884209i \(0.345302\pi\)
−0.999293 + 0.0375924i \(0.988031\pi\)
\(102\) 1.60782 2.78483i 0.159198 0.275739i
\(103\) 11.7844 6.80370i 1.16115 0.670388i 0.209568 0.977794i \(-0.432794\pi\)
0.951579 + 0.307406i \(0.0994609\pi\)
\(104\) 1.44095i 0.141297i
\(105\) 3.06347 + 5.34148i 0.298964 + 0.521275i
\(106\) 9.21712i 0.895246i
\(107\) −8.13694 + 4.69786i −0.786627 + 0.454159i −0.838774 0.544480i \(-0.816727\pi\)
0.0521466 + 0.998639i \(0.483394\pi\)
\(108\) 0.866025 + 0.500000i 0.0833333 + 0.0481125i
\(109\) 6.18076 + 3.56846i 0.592009 + 0.341797i 0.765892 0.642970i \(-0.222298\pi\)
−0.173882 + 0.984766i \(0.555631\pi\)
\(110\) −5.74112 + 5.15967i −0.547394 + 0.491955i
\(111\) 9.14111i 0.867636i
\(112\) −1.32945 + 2.28748i −0.125622 + 0.216146i
\(113\) −3.15100 −0.296421 −0.148210 0.988956i \(-0.547351\pi\)
−0.148210 + 0.988956i \(0.547351\pi\)
\(114\) 3.07901 + 5.33301i 0.288376 + 0.499482i
\(115\) 12.6837 + 7.32292i 1.18276 + 0.682866i
\(116\) 2.83045 + 1.63416i 0.262801 + 0.151728i
\(117\) −0.720474 1.24790i −0.0666078 0.115368i
\(118\) 0.532715 0.0490404
\(119\) 8.50776 + 0.0244487i 0.779905 + 0.00224121i
\(120\) 2.32736i 0.212458i
\(121\) 8.88715 + 6.48217i 0.807923 + 0.589289i
\(122\) 0.404803 + 0.233713i 0.0366492 + 0.0211594i
\(123\) 2.95456 + 1.70582i 0.266404 + 0.153808i
\(124\) 2.67692 1.54552i 0.240395 0.138792i
\(125\) 10.6672i 0.954104i
\(126\) −0.00760304 + 2.64574i −0.000677332 + 0.235701i
\(127\) 10.8090i 0.959143i 0.877503 + 0.479571i \(0.159208\pi\)
−0.877503 + 0.479571i \(0.840792\pi\)
\(128\) 0.866025 0.500000i 0.0765466 0.0441942i
\(129\) −0.946236 + 1.63893i −0.0833115 + 0.144300i
\(130\) −1.67680 + 2.90431i −0.147065 + 0.254725i
\(131\) 5.48559 + 9.50131i 0.479278 + 0.830134i 0.999718 0.0237647i \(-0.00756526\pi\)
−0.520440 + 0.853898i \(0.674232\pi\)
\(132\) −3.24479 + 0.686549i −0.282423 + 0.0597564i
\(133\) −8.18682 + 14.0863i −0.709887 + 1.22144i
\(134\) 9.22694i 0.797086i
\(135\) −1.16368 2.01555i −0.100154 0.173471i
\(136\) −2.78483 1.60782i −0.238797 0.137870i
\(137\) −4.83301 + 8.37102i −0.412912 + 0.715185i −0.995207 0.0977932i \(-0.968822\pi\)
0.582295 + 0.812978i \(0.302155\pi\)
\(138\) 3.14645 + 5.44981i 0.267843 + 0.463919i
\(139\) 23.3695 1.98218 0.991088 0.133208i \(-0.0425277\pi\)
0.991088 + 0.133208i \(0.0425277\pi\)
\(140\) 5.34148 3.06347i 0.451437 0.258911i
\(141\) −10.6492 −0.896826
\(142\) 2.81677 1.62627i 0.236378 0.136473i
\(143\) 4.54380 + 1.48104i 0.379972 + 0.123851i
\(144\) 0.500000 0.866025i 0.0416667 0.0721688i
\(145\) −3.80329 6.58749i −0.315846 0.547061i
\(146\) 5.00004i 0.413806i
\(147\) −6.08219 + 3.46510i −0.501651 + 0.285797i
\(148\) −9.14111 −0.751395
\(149\) 13.0372 7.52705i 1.06805 0.616640i 0.140403 0.990094i \(-0.455160\pi\)
0.927648 + 0.373455i \(0.121827\pi\)
\(150\) −0.208304 + 0.360793i −0.0170080 + 0.0294586i
\(151\) −11.2506 6.49554i −0.915561 0.528599i −0.0333445 0.999444i \(-0.510616\pi\)
−0.882216 + 0.470845i \(0.843949\pi\)
\(152\) 5.33301 3.07901i 0.432564 0.249741i
\(153\) −3.21565 −0.259970
\(154\) −5.84675 6.54335i −0.471145 0.527278i
\(155\) −7.19397 −0.577833
\(156\) −1.24790 + 0.720474i −0.0999117 + 0.0576841i
\(157\) −9.98402 5.76428i −0.796812 0.460039i 0.0455434 0.998962i \(-0.485498\pi\)
−0.842355 + 0.538923i \(0.818831\pi\)
\(158\) 4.16421 7.21263i 0.331287 0.573806i
\(159\) 7.98226 4.60856i 0.633035 0.365483i
\(160\) −2.32736 −0.183994
\(161\) −8.36612 + 14.3949i −0.659343 + 1.13447i
\(162\) 1.00000i 0.0785674i
\(163\) 4.15686 + 7.19989i 0.325590 + 0.563939i 0.981632 0.190786i \(-0.0611037\pi\)
−0.656041 + 0.754725i \(0.727770\pi\)
\(164\) 1.70582 2.95456i 0.133202 0.230713i
\(165\) 7.33897 + 2.39212i 0.571338 + 0.186226i
\(166\) −3.95020 + 2.28065i −0.306595 + 0.177013i
\(167\) −15.5338 −1.20204 −0.601022 0.799232i \(-0.705240\pi\)
−0.601022 + 0.799232i \(0.705240\pi\)
\(168\) 2.64574 + 0.00760304i 0.204123 + 0.000586587i
\(169\) −10.9237 −0.840282
\(170\) 3.74198 + 6.48131i 0.286997 + 0.497094i
\(171\) 3.07901 5.33301i 0.235458 0.407825i
\(172\) 1.63893 + 0.946236i 0.124967 + 0.0721499i
\(173\) −6.60240 11.4357i −0.501971 0.869439i −0.999997 0.00227722i \(-0.999275\pi\)
0.498027 0.867162i \(-0.334058\pi\)
\(174\) 3.26833i 0.247771i
\(175\) −1.10224 0.00316749i −0.0833213 0.000239439i
\(176\) 0.686549 + 3.24479i 0.0517506 + 0.244585i
\(177\) −0.266358 0.461345i −0.0200207 0.0346768i
\(178\) 2.19052 3.79409i 0.164186 0.284379i
\(179\) 9.43539 16.3426i 0.705234 1.22150i −0.261373 0.965238i \(-0.584175\pi\)
0.966607 0.256263i \(-0.0824913\pi\)
\(180\) −2.01555 + 1.16368i −0.150230 + 0.0867356i
\(181\) 3.94448i 0.293191i −0.989197 0.146595i \(-0.953168\pi\)
0.989197 0.146595i \(-0.0468316\pi\)
\(182\) −3.29613 1.91567i −0.244326 0.141999i
\(183\) 0.467427i 0.0345532i
\(184\) 5.44981 3.14645i 0.401765 0.231959i
\(185\) 18.4244 + 10.6373i 1.35459 + 0.782072i
\(186\) −2.67692 1.54552i −0.196281 0.113323i
\(187\) 7.93234 7.12897i 0.580070 0.521322i
\(188\) 10.6492i 0.776674i
\(189\) 2.29508 1.31629i 0.166942 0.0957457i
\(190\) −14.3320 −1.03975
\(191\) −11.7619 20.3722i −0.851062 1.47408i −0.880251 0.474508i \(-0.842626\pi\)
0.0291897 0.999574i \(-0.490707\pi\)
\(192\) −0.866025 0.500000i −0.0625000 0.0360844i
\(193\) −18.0103 10.3983i −1.29641 0.748484i −0.316629 0.948549i \(-0.602551\pi\)
−0.979782 + 0.200066i \(0.935884\pi\)
\(194\) −8.90130 15.4175i −0.639076 1.10691i
\(195\) 3.35360 0.240157
\(196\) 3.46510 + 6.08219i 0.247507 + 0.434442i
\(197\) 21.3675i 1.52237i −0.648534 0.761186i \(-0.724618\pi\)
0.648534 0.761186i \(-0.275382\pi\)
\(198\) 2.21696 + 2.46679i 0.157553 + 0.175307i
\(199\) 17.3579 + 10.0216i 1.23047 + 0.710410i 0.967127 0.254293i \(-0.0818429\pi\)
0.263339 + 0.964703i \(0.415176\pi\)
\(200\) 0.360793 + 0.208304i 0.0255119 + 0.0147293i
\(201\) 7.99077 4.61347i 0.563625 0.325409i
\(202\) 10.6971i 0.752648i
\(203\) 7.50107 4.30205i 0.526472 0.301945i
\(204\) 3.21565i 0.225140i
\(205\) −6.87633 + 3.97005i −0.480264 + 0.277280i
\(206\) −6.80370 + 11.7844i −0.474036 + 0.821055i
\(207\) 3.14645 5.44981i 0.218693 0.378788i
\(208\) 0.720474 + 1.24790i 0.0499559 + 0.0865261i
\(209\) 4.22779 + 19.9815i 0.292442 + 1.38215i
\(210\) −5.32378 3.09412i −0.367376 0.213515i
\(211\) 2.04651i 0.140887i −0.997516 0.0704437i \(-0.977558\pi\)
0.997516 0.0704437i \(-0.0224415\pi\)
\(212\) −4.60856 7.98226i −0.316517 0.548224i
\(213\) −2.81677 1.62627i −0.193002 0.111430i
\(214\) 4.69786 8.13694i 0.321139 0.556229i
\(215\) −2.20223 3.81438i −0.150191 0.260139i
\(216\) −1.00000 −0.0680414
\(217\) 0.0235013 8.17809i 0.00159537 0.555165i
\(218\) −7.13693 −0.483374
\(219\) −4.33016 + 2.50002i −0.292605 + 0.168936i
\(220\) 2.39212 7.33897i 0.161277 0.494793i
\(221\) 2.31679 4.01279i 0.155844 0.269930i
\(222\) 4.57056 + 7.91644i 0.306756 + 0.531316i
\(223\) 23.3804i 1.56567i −0.622230 0.782835i \(-0.713773\pi\)
0.622230 0.782835i \(-0.286227\pi\)
\(224\) 0.00760304 2.64574i 0.000507999 0.176776i
\(225\) 0.416608 0.0277739
\(226\) 2.72884 1.57550i 0.181520 0.104801i
\(227\) 6.97413 12.0796i 0.462890 0.801748i −0.536214 0.844082i \(-0.680146\pi\)
0.999104 + 0.0423338i \(0.0134793\pi\)
\(228\) −5.33301 3.07901i −0.353187 0.203913i
\(229\) −13.0033 + 7.50744i −0.859281 + 0.496106i −0.863771 0.503884i \(-0.831904\pi\)
0.00449072 + 0.999990i \(0.498571\pi\)
\(230\) −14.6458 −0.965718
\(231\) −2.74333 + 8.33511i −0.180498 + 0.548410i
\(232\) −3.26833 −0.214576
\(233\) −14.2393 + 8.22109i −0.932850 + 0.538581i −0.887712 0.460399i \(-0.847706\pi\)
−0.0451385 + 0.998981i \(0.514373\pi\)
\(234\) 1.24790 + 0.720474i 0.0815776 + 0.0470988i
\(235\) 12.3923 21.4641i 0.808384 1.40016i
\(236\) −0.461345 + 0.266358i −0.0300310 + 0.0173384i
\(237\) −8.32842 −0.540989
\(238\) −7.38016 + 4.23271i −0.478385 + 0.274366i
\(239\) 24.7950i 1.60386i −0.597419 0.801929i \(-0.703807\pi\)
0.597419 0.801929i \(-0.296193\pi\)
\(240\) 1.16368 + 2.01555i 0.0751152 + 0.130103i
\(241\) −11.1098 + 19.2427i −0.715643 + 1.23953i 0.247068 + 0.968998i \(0.420533\pi\)
−0.962711 + 0.270532i \(0.912800\pi\)
\(242\) −10.9376 1.17015i −0.703095 0.0752202i
\(243\) −0.866025 + 0.500000i −0.0555556 + 0.0320750i
\(244\) −0.467427 −0.0299239
\(245\) 0.0936328 16.2913i 0.00598198 1.04081i
\(246\) −3.41163 −0.217518
\(247\) 4.43670 + 7.68458i 0.282300 + 0.488958i
\(248\) −1.54552 + 2.67692i −0.0981407 + 0.169985i
\(249\) 3.95020 + 2.28065i 0.250334 + 0.144530i
\(250\) 5.33360 + 9.23807i 0.337327 + 0.584267i
\(251\) 4.73415i 0.298817i −0.988776 0.149409i \(-0.952263\pi\)
0.988776 0.149409i \(-0.0477370\pi\)
\(252\) −1.31629 2.29508i −0.0829182 0.144576i
\(253\) 4.32038 + 20.4191i 0.271620 + 1.28374i
\(254\) −5.40449 9.36086i −0.339108 0.587353i
\(255\) 3.74198 6.48131i 0.234332 0.405875i
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −10.5961 + 6.11764i −0.660965 + 0.381608i −0.792644 0.609684i \(-0.791296\pi\)
0.131680 + 0.991292i \(0.457963\pi\)
\(258\) 1.89247i 0.117820i
\(259\) −12.1527 + 20.9101i −0.755132 + 1.29929i
\(260\) 3.35360i 0.207982i
\(261\) −2.83045 + 1.63416i −0.175201 + 0.101152i
\(262\) −9.50131 5.48559i −0.586993 0.338901i
\(263\) −16.6883 9.63502i −1.02905 0.594121i −0.112336 0.993670i \(-0.535833\pi\)
−0.916712 + 0.399550i \(0.869167\pi\)
\(264\) 2.46679 2.21696i 0.151821 0.136445i
\(265\) 21.4516i 1.31776i
\(266\) 0.0468197 16.2925i 0.00287070 0.998960i
\(267\) −4.38104 −0.268115
\(268\) −4.61347 7.99077i −0.281813 0.488114i
\(269\) 19.1299 + 11.0447i 1.16637 + 0.673405i 0.952823 0.303527i \(-0.0981644\pi\)
0.213549 + 0.976932i \(0.431498\pi\)
\(270\) 2.01555 + 1.16368i 0.122663 + 0.0708193i
\(271\) 0.610555 + 1.05751i 0.0370886 + 0.0642393i 0.883974 0.467536i \(-0.154858\pi\)
−0.846885 + 0.531776i \(0.821525\pi\)
\(272\) 3.21565 0.194977
\(273\) −0.0109556 + 3.81237i −0.000663062 + 0.230735i
\(274\) 9.66602i 0.583946i
\(275\) −1.02769 + 0.923604i −0.0619718 + 0.0556954i
\(276\) −5.44981 3.14645i −0.328040 0.189394i
\(277\) 10.8330 + 6.25443i 0.650891 + 0.375792i 0.788798 0.614653i \(-0.210704\pi\)
−0.137906 + 0.990445i \(0.544037\pi\)
\(278\) −20.2386 + 11.6848i −1.21383 + 0.700805i
\(279\) 3.09104i 0.185056i
\(280\) −3.09412 + 5.32378i −0.184909 + 0.318157i
\(281\) 25.3495i 1.51222i −0.654443 0.756111i \(-0.727097\pi\)
0.654443 0.756111i \(-0.272903\pi\)
\(282\) 9.22249 5.32461i 0.549191 0.317076i
\(283\) −1.38222 + 2.39408i −0.0821646 + 0.142313i −0.904179 0.427153i \(-0.859517\pi\)
0.822015 + 0.569466i \(0.192850\pi\)
\(284\) −1.62627 + 2.81677i −0.0965011 + 0.167145i
\(285\) 7.16598 + 12.4118i 0.424476 + 0.735214i
\(286\) −4.67557 + 0.989280i −0.276472 + 0.0584974i
\(287\) −4.49069 7.82997i −0.265077 0.462189i
\(288\) 1.00000i 0.0589256i
\(289\) 3.32981 + 5.76740i 0.195871 + 0.339259i
\(290\) 6.58749 + 3.80329i 0.386831 + 0.223337i
\(291\) −8.90130 + 15.4175i −0.521803 + 0.903790i
\(292\) 2.50002 + 4.33016i 0.146303 + 0.253403i
\(293\) −9.03175 −0.527640 −0.263820 0.964572i \(-0.584983\pi\)
−0.263820 + 0.964572i \(0.584983\pi\)
\(294\) 3.53478 6.04196i 0.206153 0.352374i
\(295\) 1.23982 0.0721851
\(296\) 7.91644 4.57056i 0.460134 0.265658i
\(297\) 1.02783 3.15334i 0.0596405 0.182976i
\(298\) −7.52705 + 13.0372i −0.436030 + 0.755226i
\(299\) 4.53387 + 7.85289i 0.262200 + 0.454144i
\(300\) 0.416608i 0.0240529i
\(301\) 4.34338 2.49104i 0.250348 0.143581i
\(302\) 12.9911 0.747552
\(303\) −9.26399 + 5.34857i −0.532203 + 0.307267i
\(304\) −3.07901 + 5.33301i −0.176594 + 0.305869i
\(305\) 0.942123 + 0.543935i 0.0539458 + 0.0311456i
\(306\) 2.78483 1.60782i 0.159198 0.0919131i
\(307\) 3.52291 0.201063 0.100531 0.994934i \(-0.467946\pi\)
0.100531 + 0.994934i \(0.467946\pi\)
\(308\) 8.33511 + 2.74333i 0.474937 + 0.156316i
\(309\) 13.6074 0.774098
\(310\) 6.23016 3.59698i 0.353849 0.204295i
\(311\) 4.83852 + 2.79352i 0.274367 + 0.158406i 0.630871 0.775888i \(-0.282698\pi\)
−0.356503 + 0.934294i \(0.616031\pi\)
\(312\) 0.720474 1.24790i 0.0407888 0.0706483i
\(313\) 4.57178 2.63952i 0.258412 0.149194i −0.365198 0.930930i \(-0.618999\pi\)
0.623610 + 0.781736i \(0.285665\pi\)
\(314\) 11.5286 0.650594
\(315\) −0.0176950 + 6.15759i −0.000997001 + 0.346941i
\(316\) 8.32842i 0.468510i
\(317\) −15.8432 27.4412i −0.889843 1.54125i −0.840060 0.542493i \(-0.817480\pi\)
−0.0497829 0.998760i \(-0.515853\pi\)
\(318\) −4.60856 + 7.98226i −0.258435 + 0.447623i
\(319\) 3.35927 10.3062i 0.188083 0.577034i
\(320\) 2.01555 1.16368i 0.112673 0.0650517i
\(321\) −9.39572 −0.524418
\(322\) 0.0478451 16.6494i 0.00266630 0.927833i
\(323\) 19.8020 1.10181
\(324\) 0.500000 + 0.866025i 0.0277778 + 0.0481125i
\(325\) −0.300155 + 0.519884i −0.0166496 + 0.0288380i
\(326\) −7.19989 4.15686i −0.398765 0.230227i
\(327\) 3.56846 + 6.18076i 0.197336 + 0.341797i
\(328\) 3.41163i 0.188376i
\(329\) 24.3598 + 14.1577i 1.34300 + 0.780537i
\(330\) −7.55179 + 1.59785i −0.415713 + 0.0879586i
\(331\) 1.95793 + 3.39124i 0.107618 + 0.186399i 0.914805 0.403896i \(-0.132344\pi\)
−0.807187 + 0.590296i \(0.799011\pi\)
\(332\) 2.28065 3.95020i 0.125167 0.216796i
\(333\) 4.57056 7.91644i 0.250465 0.433818i
\(334\) 13.4527 7.76692i 0.736099 0.424987i
\(335\) 21.4744i 1.17327i
\(336\) −2.29508 + 1.31629i −0.125207 + 0.0718093i
\(337\) 20.0534i 1.09238i −0.837662 0.546189i \(-0.816078\pi\)
0.837662 0.546189i \(-0.183922\pi\)
\(338\) 9.46018 5.46184i 0.514566 0.297085i
\(339\) −2.72884 1.57550i −0.148210 0.0855694i
\(340\) −6.48131 3.74198i −0.351498 0.202938i
\(341\) −6.85272 7.62496i −0.371096 0.412915i
\(342\) 6.15803i 0.332988i
\(343\) 18.5196 + 0.159662i 0.999963 + 0.00862094i
\(344\) −1.89247 −0.102035
\(345\) 7.32292 + 12.6837i 0.394253 + 0.682866i
\(346\) 11.4357 + 6.60240i 0.614786 + 0.354947i
\(347\) −24.6999 14.2605i −1.32596 0.765545i −0.341290 0.939958i \(-0.610864\pi\)
−0.984673 + 0.174413i \(0.944197\pi\)
\(348\) 1.63416 + 2.83045i 0.0876003 + 0.151728i
\(349\) 15.3941 0.824027 0.412014 0.911178i \(-0.364826\pi\)
0.412014 + 0.911178i \(0.364826\pi\)
\(350\) 0.956149 0.548375i 0.0511083 0.0293119i
\(351\) 1.44095i 0.0769121i
\(352\) −2.21696 2.46679i −0.118165 0.131481i
\(353\) 4.80016 + 2.77137i 0.255487 + 0.147505i 0.622274 0.782800i \(-0.286209\pi\)
−0.366787 + 0.930305i \(0.619542\pi\)
\(354\) 0.461345 + 0.266358i 0.0245202 + 0.0141567i
\(355\) 6.55565 3.78491i 0.347938 0.200882i
\(356\) 4.38104i 0.232195i
\(357\) 7.35572 + 4.27506i 0.389306 + 0.226260i
\(358\) 18.8708i 0.997351i
\(359\) 17.9527 10.3650i 0.947508 0.547044i 0.0552018 0.998475i \(-0.482420\pi\)
0.892306 + 0.451431i \(0.149086\pi\)
\(360\) 1.16368 2.01555i 0.0613313 0.106229i
\(361\) −9.46065 + 16.3863i −0.497929 + 0.862439i
\(362\) 1.97224 + 3.41602i 0.103659 + 0.179542i
\(363\) 4.45541 + 10.0573i 0.233848 + 0.527871i
\(364\) 3.81237 + 0.0109556i 0.199823 + 0.000574228i
\(365\) 11.6369i 0.609103i
\(366\) 0.233713 + 0.404803i 0.0122164 + 0.0211594i
\(367\) −30.3880 17.5445i −1.58624 0.915816i −0.993919 0.110113i \(-0.964879\pi\)
−0.592320 0.805703i \(-0.701788\pi\)
\(368\) −3.14645 + 5.44981i −0.164020 + 0.284091i
\(369\) 1.70582 + 2.95456i 0.0888013 + 0.153808i
\(370\) −21.2747 −1.10602
\(371\) −24.3861 0.0700781i −1.26606 0.00363827i
\(372\) 3.09104 0.160263
\(373\) 21.2225 12.2528i 1.09886 0.634427i 0.162938 0.986636i \(-0.447903\pi\)
0.935921 + 0.352210i \(0.114570\pi\)
\(374\) −3.30512 + 10.1400i −0.170904 + 0.524329i
\(375\) 5.33360 9.23807i 0.275426 0.477052i
\(376\) −5.32461 9.22249i −0.274596 0.475614i
\(377\) 4.70949i 0.242551i
\(378\) −1.32945 + 2.28748i −0.0683798 + 0.117655i
\(379\) −3.42705 −0.176036 −0.0880179 0.996119i \(-0.528053\pi\)
−0.0880179 + 0.996119i \(0.528053\pi\)
\(380\) 12.4118 7.16598i 0.636714 0.367607i
\(381\) −5.40449 + 9.36086i −0.276881 + 0.479571i
\(382\) 20.3722 + 11.7619i 1.04233 + 0.601791i
\(383\) −28.2806 + 16.3278i −1.44507 + 0.834312i −0.998182 0.0602779i \(-0.980801\pi\)
−0.446889 + 0.894590i \(0.647468\pi\)
\(384\) 1.00000 0.0510310
\(385\) −13.6075 15.2287i −0.693503 0.776129i
\(386\) 20.7965 1.05852
\(387\) −1.63893 + 0.946236i −0.0833115 + 0.0480999i
\(388\) 15.4175 + 8.90130i 0.782705 + 0.451895i
\(389\) −9.28386 + 16.0801i −0.470711 + 0.815295i −0.999439 0.0334965i \(-0.989336\pi\)
0.528728 + 0.848791i \(0.322669\pi\)
\(390\) −2.90431 + 1.67680i −0.147065 + 0.0849082i
\(391\) 20.2357 1.02336
\(392\) −6.04196 3.53478i −0.305165 0.178534i
\(393\) 10.9712i 0.553422i
\(394\) 10.6837 + 18.5048i 0.538239 + 0.932258i
\(395\) 9.69162 16.7864i 0.487639 0.844615i
\(396\) −3.15334 1.02783i −0.158461 0.0516502i
\(397\) −4.84409 + 2.79674i −0.243118 + 0.140364i −0.616609 0.787270i \(-0.711494\pi\)
0.373491 + 0.927634i \(0.378161\pi\)
\(398\) −20.0431 −1.00467
\(399\) −14.1332 + 8.10572i −0.707543 + 0.405794i
\(400\) −0.416608 −0.0208304
\(401\) 5.17676 + 8.96641i 0.258515 + 0.447761i 0.965844 0.259123i \(-0.0834335\pi\)
−0.707329 + 0.706884i \(0.750100\pi\)
\(402\) −4.61347 + 7.99077i −0.230099 + 0.398543i
\(403\) −3.85730 2.22701i −0.192146 0.110935i
\(404\) 5.34857 + 9.26399i 0.266101 + 0.460901i
\(405\) 2.32736i 0.115647i
\(406\) −4.34509 + 7.47622i −0.215643 + 0.371039i
\(407\) 6.27582 + 29.6610i 0.311081 + 1.47024i
\(408\) −1.60782 2.78483i −0.0795991 0.137870i
\(409\) 10.4458 18.0927i 0.516512 0.894625i −0.483304 0.875452i \(-0.660564\pi\)
0.999816 0.0191723i \(-0.00610312\pi\)
\(410\) 3.97005 6.87633i 0.196067 0.339598i
\(411\) −8.37102 + 4.83301i −0.412912 + 0.238395i
\(412\) 13.6074i 0.670388i
\(413\) −0.00405025 + 1.40943i −0.000199300 + 0.0693533i
\(414\) 6.29290i 0.309279i
\(415\) −9.19355 + 5.30790i −0.451293 + 0.260554i
\(416\) −1.24790 0.720474i −0.0611832 0.0353241i
\(417\) 20.2386 + 11.6848i 0.991088 + 0.572205i
\(418\) −13.6521 15.1906i −0.667747 0.742996i
\(419\) 7.59471i 0.371026i 0.982642 + 0.185513i \(0.0593946\pi\)
−0.982642 + 0.185513i \(0.940605\pi\)
\(420\) 6.15759 + 0.0176950i 0.300460 + 0.000863428i
\(421\) −29.9360 −1.45899 −0.729496 0.683985i \(-0.760246\pi\)
−0.729496 + 0.683985i \(0.760246\pi\)
\(422\) 1.02325 + 1.77233i 0.0498112 + 0.0862756i
\(423\) −9.22249 5.32461i −0.448413 0.258891i
\(424\) 7.98226 + 4.60856i 0.387653 + 0.223812i
\(425\) 0.669832 + 1.16018i 0.0324916 + 0.0562771i
\(426\) 3.25253 0.157586
\(427\) −0.621422 + 1.06923i −0.0300727 + 0.0517435i
\(428\) 9.39572i 0.454159i
\(429\) 3.19453 + 3.55452i 0.154233 + 0.171614i
\(430\) 3.81438 + 2.20223i 0.183946 + 0.106201i
\(431\) 28.8852 + 16.6769i 1.39135 + 0.803297i 0.993465 0.114138i \(-0.0364105\pi\)
0.397886 + 0.917435i \(0.369744\pi\)
\(432\) 0.866025 0.500000i 0.0416667 0.0240563i
\(433\) 27.7837i 1.33520i −0.744521 0.667599i \(-0.767322\pi\)
0.744521 0.667599i \(-0.232678\pi\)
\(434\) 4.06869 + 7.09419i 0.195304 + 0.340532i
\(435\) 7.60657i 0.364707i
\(436\) 6.18076 3.56846i 0.296005 0.170898i
\(437\) −19.3759 + 33.5601i −0.926876 + 1.60540i
\(438\) 2.50002 4.33016i 0.119456 0.206903i
\(439\) 15.5488 + 26.9314i 0.742105 + 1.28536i 0.951535 + 0.307541i \(0.0995060\pi\)
−0.209429 + 0.977824i \(0.567161\pi\)
\(440\) 1.59785 + 7.55179i 0.0761743 + 0.360018i
\(441\) −6.99988 0.0402313i −0.333328 0.00191578i
\(442\) 4.63358i 0.220397i
\(443\) 2.50430 + 4.33757i 0.118983 + 0.206084i 0.919365 0.393406i \(-0.128703\pi\)
−0.800382 + 0.599490i \(0.795370\pi\)
\(444\) −7.91644 4.57056i −0.375697 0.216909i
\(445\) 5.09813 8.83022i 0.241675 0.418593i
\(446\) 11.6902 + 20.2480i 0.553548 + 0.958773i
\(447\) 15.0541 0.712034
\(448\) 1.31629 + 2.29508i 0.0621887 + 0.108432i
\(449\) 24.8715 1.17376 0.586880 0.809674i \(-0.300356\pi\)
0.586880 + 0.809674i \(0.300356\pi\)
\(450\) −0.360793 + 0.208304i −0.0170080 + 0.00981954i
\(451\) −10.7581 3.50656i −0.506577 0.165118i
\(452\) −1.57550 + 2.72884i −0.0741052 + 0.128354i
\(453\) −6.49554 11.2506i −0.305187 0.528599i
\(454\) 13.9483i 0.654625i
\(455\) −7.67129 4.45846i −0.359636 0.209016i
\(456\) 6.15803 0.288376
\(457\) −6.59453 + 3.80735i −0.308479 + 0.178100i −0.646246 0.763129i \(-0.723662\pi\)
0.337767 + 0.941230i \(0.390329\pi\)
\(458\) 7.50744 13.0033i 0.350800 0.607603i
\(459\) −2.78483 1.60782i −0.129985 0.0750467i
\(460\) 12.6837 7.32292i 0.591379 0.341433i
\(461\) 8.56061 0.398707 0.199354 0.979928i \(-0.436116\pi\)
0.199354 + 0.979928i \(0.436116\pi\)
\(462\) −1.79176 8.59009i −0.0833602 0.399647i
\(463\) −2.87221 −0.133483 −0.0667415 0.997770i \(-0.521260\pi\)
−0.0667415 + 0.997770i \(0.521260\pi\)
\(464\) 2.83045 1.63416i 0.131401 0.0758641i
\(465\) −6.23016 3.59698i −0.288917 0.166806i
\(466\) 8.22109 14.2393i 0.380835 0.659625i
\(467\) −7.84052 + 4.52673i −0.362816 + 0.209472i −0.670315 0.742076i \(-0.733841\pi\)
0.307499 + 0.951548i \(0.400508\pi\)
\(468\) −1.44095 −0.0666078
\(469\) −24.4121 0.0701528i −1.12725 0.00323935i
\(470\) 24.7846i 1.14323i
\(471\) −5.76428 9.98402i −0.265604 0.460039i
\(472\) 0.266358 0.461345i 0.0122601 0.0212351i
\(473\) 1.94513 5.96762i 0.0894373 0.274391i
\(474\) 7.21263 4.16421i 0.331287 0.191269i
\(475\) −2.56548 −0.117712
\(476\) 4.27506 7.35572i 0.195947 0.337149i
\(477\) 9.21712 0.422023
\(478\) 12.3975 + 21.4731i 0.567050 + 0.982159i
\(479\) 15.5977 27.0160i 0.712677 1.23439i −0.251172 0.967943i \(-0.580816\pi\)
0.963849 0.266450i \(-0.0858507\pi\)
\(480\) −2.01555 1.16368i −0.0919970 0.0531145i
\(481\) 6.58593 + 11.4072i 0.300293 + 0.520122i
\(482\) 22.2195i 1.01207i
\(483\) −14.4427 + 8.28325i −0.657166 + 0.376901i
\(484\) 10.0573 4.45541i 0.457150 0.202519i
\(485\) −20.7165 35.8821i −0.940689 1.62932i
\(486\) 0.500000 0.866025i 0.0226805 0.0392837i
\(487\) −18.0368 + 31.2407i −0.817327 + 1.41565i 0.0903185 + 0.995913i \(0.471211\pi\)
−0.907645 + 0.419738i \(0.862122\pi\)
\(488\) 0.404803 0.233713i 0.0183246 0.0105797i
\(489\) 8.31371i 0.375959i
\(490\) 8.06454 + 14.1555i 0.364319 + 0.639478i
\(491\) 26.7561i 1.20749i 0.797179 + 0.603744i \(0.206325\pi\)
−0.797179 + 0.603744i \(0.793675\pi\)
\(492\) 2.95456 1.70582i 0.133202 0.0769042i
\(493\) −9.10174 5.25489i −0.409922 0.236668i
\(494\) −7.68458 4.43670i −0.345746 0.199616i
\(495\) 5.15967 + 5.74112i 0.231910 + 0.258044i
\(496\) 3.09104i 0.138792i
\(497\) 4.28126 + 7.46482i 0.192041 + 0.334843i
\(498\) −4.56130 −0.204397
\(499\) −14.0487 24.3330i −0.628906 1.08930i −0.987772 0.155907i \(-0.950170\pi\)
0.358866 0.933389i \(-0.383164\pi\)
\(500\) −9.23807 5.33360i −0.413139 0.238526i
\(501\) −13.4527 7.76692i −0.601022 0.347000i
\(502\) 2.36708 + 4.09990i 0.105648 + 0.182987i
\(503\) −16.3197 −0.727660 −0.363830 0.931465i \(-0.618531\pi\)
−0.363830 + 0.931465i \(0.618531\pi\)
\(504\) 2.28748 + 1.32945i 0.101892 + 0.0592186i
\(505\) 24.8961i 1.10786i
\(506\) −13.9511 15.5233i −0.620203 0.690094i
\(507\) −9.46018 5.46184i −0.420141 0.242569i
\(508\) 9.36086 + 5.40449i 0.415321 + 0.239786i
\(509\) 3.92989 2.26892i 0.174189 0.100568i −0.410370 0.911919i \(-0.634601\pi\)
0.584560 + 0.811351i \(0.301267\pi\)
\(510\) 7.48397i 0.331396i
\(511\) 13.2288 + 0.0380155i 0.585208 + 0.00168171i
\(512\) 1.00000i 0.0441942i
\(513\) 5.33301 3.07901i 0.235458 0.135942i
\(514\) 6.11764 10.5961i 0.269838 0.467373i
\(515\) −15.8347 + 27.4264i −0.697758 + 1.20855i
\(516\) 0.946236 + 1.63893i 0.0416557 + 0.0721499i
\(517\) 34.5545 7.31121i 1.51970 0.321546i
\(518\) 0.0695002 24.1850i 0.00305366 1.06263i
\(519\) 13.2048i 0.579626i
\(520\) 1.67680 + 2.90431i 0.0735326 + 0.127362i
\(521\) −0.675518 0.390011i −0.0295950 0.0170867i 0.485130 0.874442i \(-0.338772\pi\)
−0.514725 + 0.857356i \(0.672106\pi\)
\(522\) 1.63416 2.83045i 0.0715254 0.123886i
\(523\) 5.88383 + 10.1911i 0.257282 + 0.445626i 0.965513 0.260355i \(-0.0838397\pi\)
−0.708231 + 0.705981i \(0.750506\pi\)
\(524\) 10.9712 0.479278
\(525\) −0.952981 0.553861i −0.0415915 0.0241725i
\(526\) 19.2700 0.840214
\(527\) −8.60803 + 4.96985i −0.374972 + 0.216490i
\(528\) −1.02783 + 3.15334i −0.0447304 + 0.137232i
\(529\) −8.30028 + 14.3765i −0.360882 + 0.625065i
\(530\) −10.7258 18.5776i −0.465898 0.806959i
\(531\) 0.532715i 0.0231179i
\(532\) 8.10572 + 14.1332i 0.351428 + 0.612750i
\(533\) −4.91598 −0.212935
\(534\) 3.79409 2.19052i 0.164186 0.0947931i
\(535\) 10.9336 18.9376i 0.472702 0.818743i
\(536\) 7.99077 + 4.61347i 0.345149 + 0.199272i
\(537\) 16.3426 9.43539i 0.705234 0.407167i
\(538\) −22.0893 −0.952338
\(539\) 17.3565 15.4192i 0.747596 0.664154i
\(540\) −2.32736 −0.100154
\(541\) −9.27327 + 5.35393i −0.398689 + 0.230183i −0.685918 0.727679i \(-0.740599\pi\)
0.287229 + 0.957862i \(0.407266\pi\)
\(542\) −1.05751 0.610555i −0.0454240 0.0262256i
\(543\) 1.97224 3.41602i 0.0846369 0.146595i
\(544\) −2.78483 + 1.60782i −0.119399 + 0.0689348i
\(545\) −16.6102 −0.711503
\(546\) −1.89670 3.30709i −0.0811712 0.141530i
\(547\) 19.5154i 0.834419i 0.908810 + 0.417210i \(0.136992\pi\)
−0.908810 + 0.417210i \(0.863008\pi\)
\(548\) 4.83301 + 8.37102i 0.206456 + 0.357592i
\(549\) 0.233713 0.404803i 0.00997464 0.0172766i
\(550\) 0.428200 1.31371i 0.0182585 0.0560167i
\(551\) 17.4300 10.0632i 0.742544 0.428708i
\(552\) 6.29290 0.267843
\(553\) 19.0511 + 11.0723i 0.810134 + 0.470841i
\(554\) −12.5089 −0.531450
\(555\) 10.6373 + 18.4244i 0.451530 + 0.782072i
\(556\) 11.6848 20.2386i 0.495544 0.858308i
\(557\) −5.25260 3.03259i −0.222560 0.128495i 0.384575 0.923094i \(-0.374348\pi\)
−0.607135 + 0.794599i \(0.707681\pi\)
\(558\) −1.54552 2.67692i −0.0654271 0.113323i
\(559\) 2.72695i 0.115338i
\(560\) 0.0176950 6.15759i 0.000747751 0.260206i
\(561\) 10.4341 2.20770i 0.440528 0.0932091i
\(562\) 12.6747 + 21.9533i 0.534651 + 0.926043i
\(563\) −0.122186 + 0.211633i −0.00514953 + 0.00891925i −0.868589 0.495534i \(-0.834972\pi\)
0.863439 + 0.504453i \(0.168306\pi\)
\(564\) −5.32461 + 9.22249i −0.224206 + 0.388337i
\(565\) 6.35100 3.66675i 0.267189 0.154262i
\(566\) 2.76444i 0.116198i
\(567\) 2.64574 + 0.00760304i 0.111111 + 0.000319298i
\(568\) 3.25253i 0.136473i
\(569\) 7.44979 4.30114i 0.312311 0.180313i −0.335649 0.941987i \(-0.608956\pi\)
0.647960 + 0.761674i \(0.275622\pi\)
\(570\) −12.4118 7.16598i −0.519875 0.300150i
\(571\) −26.9418 15.5548i −1.12748 0.650950i −0.184178 0.982893i \(-0.558962\pi\)
−0.943299 + 0.331943i \(0.892296\pi\)
\(572\) 3.55452 3.19453i 0.148622 0.133570i
\(573\) 23.5238i 0.982721i
\(574\) 7.80403 + 4.53561i 0.325734 + 0.189313i
\(575\) −2.62167 −0.109331
\(576\) −0.500000 0.866025i −0.0208333 0.0360844i
\(577\) −35.4669 20.4768i −1.47651 0.852462i −0.476859 0.878980i \(-0.658225\pi\)
−0.999648 + 0.0265176i \(0.991558\pi\)
\(578\) −5.76740 3.32981i −0.239892 0.138502i
\(579\) −10.3983 18.0103i −0.432137 0.748484i
\(580\) −7.60657 −0.315846
\(581\) −6.00398 10.4686i −0.249087 0.434309i
\(582\) 17.8026i 0.737941i
\(583\) −22.7367 + 20.4340i −0.941660 + 0.846290i
\(584\) −4.33016 2.50002i −0.179183 0.103451i
\(585\) 2.90431 + 1.67680i 0.120078 + 0.0693272i
\(586\) 7.82172 4.51587i 0.323112 0.186549i
\(587\) 33.6048i 1.38702i 0.720449 + 0.693508i \(0.243936\pi\)
−0.720449 + 0.693508i \(0.756064\pi\)
\(588\) −0.0402313 + 6.99988i −0.00165911 + 0.288670i
\(589\) 19.0347i 0.784312i
\(590\) −1.07372 + 0.619910i −0.0442042 + 0.0255213i
\(591\) 10.6837 18.5048i 0.439471 0.761186i
\(592\) −4.57056 + 7.91644i −0.187849 + 0.325364i
\(593\) 13.3626 + 23.1448i 0.548738 + 0.950442i 0.998361 + 0.0572237i \(0.0182248\pi\)
−0.449624 + 0.893218i \(0.648442\pi\)
\(594\) 0.686549 + 3.24479i 0.0281694 + 0.133135i
\(595\) −17.1763 + 9.85104i −0.704160 + 0.403853i
\(596\) 15.0541i 0.616640i
\(597\) 10.0216 + 17.3579i 0.410155 + 0.710410i
\(598\) −7.85289 4.53387i −0.321128 0.185404i
\(599\) −12.4072 + 21.4899i −0.506945 + 0.878055i 0.493022 + 0.870017i \(0.335892\pi\)
−0.999968 + 0.00803859i \(0.997441\pi\)
\(600\) 0.208304 + 0.360793i 0.00850398 + 0.0147293i
\(601\) −17.8950 −0.729952 −0.364976 0.931017i \(-0.618923\pi\)
−0.364976 + 0.931017i \(0.618923\pi\)
\(602\) −2.51596 + 4.32899i −0.102543 + 0.176436i
\(603\) 9.22694 0.375750
\(604\) −11.2506 + 6.49554i −0.457780 + 0.264300i
\(605\) −25.4557 2.72337i −1.03492 0.110721i
\(606\) 5.34857 9.26399i 0.217271 0.376324i
\(607\) −16.4712 28.5290i −0.668546 1.15796i −0.978311 0.207142i \(-0.933584\pi\)
0.309765 0.950813i \(-0.399750\pi\)
\(608\) 6.15803i 0.249741i
\(609\) 8.64714 + 0.0248492i 0.350400 + 0.00100694i
\(610\) −1.08787 −0.0440466
\(611\) 13.2891 7.67248i 0.537620 0.310395i
\(612\) −1.60782 + 2.78483i −0.0649924 + 0.112570i
\(613\) −7.51244 4.33731i −0.303425 0.175182i 0.340556 0.940224i \(-0.389385\pi\)
−0.643980 + 0.765042i \(0.722718\pi\)
\(614\) −3.05093 + 1.76145i −0.123125 + 0.0710865i
\(615\) −7.94010 −0.320176
\(616\) −8.59009 + 1.79176i −0.346104 + 0.0721920i
\(617\) 32.6421 1.31412 0.657061 0.753837i \(-0.271799\pi\)
0.657061 + 0.753837i \(0.271799\pi\)
\(618\) −11.7844 + 6.80370i −0.474036 + 0.273685i
\(619\) −13.6975 7.90825i −0.550549 0.317859i 0.198795 0.980041i \(-0.436297\pi\)
−0.749343 + 0.662182i \(0.769631\pi\)
\(620\) −3.59698 + 6.23016i −0.144458 + 0.250209i
\(621\) 5.44981 3.14645i 0.218693 0.126263i
\(622\) −5.58704 −0.224020
\(623\) 10.0215 + 5.82439i 0.401504 + 0.233349i
\(624\) 1.44095i 0.0576841i
\(625\) 13.4547 + 23.3043i 0.538190 + 0.932172i
\(626\) −2.63952 + 4.57178i −0.105496 + 0.182725i
\(627\) −6.32938 + 19.4184i −0.252771 + 0.775495i
\(628\) −9.98402 + 5.76428i −0.398406 + 0.230020i
\(629\) 29.3946 1.17204
\(630\) −3.06347 5.34148i −0.122052 0.212810i
\(631\) 40.7984 1.62416 0.812080 0.583546i \(-0.198335\pi\)
0.812080 + 0.583546i \(0.198335\pi\)
\(632\) −4.16421 7.21263i −0.165643 0.286903i
\(633\) 1.02325 1.77233i 0.0406707 0.0704437i
\(634\) 27.4412 + 15.8432i 1.08983 + 0.629214i
\(635\) −12.5782 21.7861i −0.499151 0.864555i
\(636\) 9.21712i 0.365483i
\(637\) 5.09344 8.70615i 0.201809 0.344950i
\(638\) 2.24387 + 10.6050i 0.0888355 + 0.419857i
\(639\) −1.62627 2.81677i −0.0643341 0.111430i
\(640\) −1.16368 + 2.01555i −0.0459985 + 0.0796717i
\(641\) −11.9591 + 20.7137i −0.472354 + 0.818142i −0.999500 0.0316335i \(-0.989929\pi\)
0.527145 + 0.849775i \(0.323262\pi\)
\(642\) 8.13694 4.69786i 0.321139 0.185410i
\(643\) 19.6140i 0.773502i −0.922184 0.386751i \(-0.873597\pi\)
0.922184 0.386751i \(-0.126403\pi\)
\(644\) 8.28325 + 14.4427i 0.326406 + 0.569122i
\(645\) 4.40447i 0.173426i
\(646\) −17.1491 + 9.90102i −0.674721 + 0.389550i
\(647\) 22.5941 + 13.0447i 0.888267 + 0.512841i 0.873375 0.487048i \(-0.161926\pi\)
0.0148918 + 0.999889i \(0.495260\pi\)
\(648\) −0.866025 0.500000i −0.0340207 0.0196419i
\(649\) 1.18101 + 1.31410i 0.0463587 + 0.0515829i
\(650\) 0.600310i 0.0235461i
\(651\) 4.10940 7.07068i 0.161060 0.277122i
\(652\) 8.31371 0.325590
\(653\) 10.8589 + 18.8082i 0.424942 + 0.736020i 0.996415 0.0846002i \(-0.0269613\pi\)
−0.571473 + 0.820621i \(0.693628\pi\)
\(654\) −6.18076 3.56846i −0.241687 0.139538i
\(655\) −22.1130 12.7669i −0.864026 0.498846i
\(656\) −1.70582 2.95456i −0.0666010 0.115356i
\(657\) −5.00004 −0.195070
\(658\) −28.1751 0.0809664i −1.09838 0.00315640i
\(659\) 12.7596i 0.497044i 0.968626 + 0.248522i \(0.0799448\pi\)
−0.968626 + 0.248522i \(0.920055\pi\)
\(660\) 5.74112 5.15967i 0.223473 0.200840i
\(661\) −19.9646 11.5266i −0.776533 0.448332i 0.0586670 0.998278i \(-0.481315\pi\)
−0.835200 + 0.549946i \(0.814648\pi\)
\(662\) −3.39124 1.95793i −0.131804 0.0760972i
\(663\) 4.01279 2.31679i 0.155844 0.0899766i
\(664\) 4.56130i 0.177013i
\(665\) 0.108966 37.9186i 0.00422553 1.47042i
\(666\) 9.14111i 0.354211i
\(667\) 17.8118 10.2836i 0.689674 0.398183i
\(668\) −7.76692 + 13.4527i −0.300511 + 0.520500i
\(669\) 11.6902 20.2480i 0.451970 0.782835i
\(670\) −10.7372 18.5974i −0.414815 0.718480i
\(671\) 0.320911 + 1.51670i 0.0123886 + 0.0585516i
\(672\) 1.32945 2.28748i 0.0512848 0.0882413i
\(673\) 10.4212i 0.401709i 0.979621 + 0.200854i \(0.0643718\pi\)
−0.979621 + 0.200854i \(0.935628\pi\)
\(674\) 10.0267 + 17.3668i 0.386214 + 0.668942i
\(675\) 0.360793 + 0.208304i 0.0138869 + 0.00801762i
\(676\) −5.46184 + 9.46018i −0.210071 + 0.363853i
\(677\) 7.14285 + 12.3718i 0.274522 + 0.475486i 0.970014 0.243047i \(-0.0781470\pi\)
−0.695492 + 0.718534i \(0.744814\pi\)
\(678\) 3.15100 0.121013
\(679\) 40.8584 23.4333i 1.56800 0.899287i
\(680\) 7.48397 0.286997
\(681\) 12.0796 6.97413i 0.462890 0.267249i
\(682\) 9.74711 + 3.17705i 0.373236 + 0.121656i
\(683\) 17.3671 30.0806i 0.664532 1.15100i −0.314880 0.949132i \(-0.601964\pi\)
0.979412 0.201872i \(-0.0647025\pi\)
\(684\) −3.07901 5.33301i −0.117729 0.203913i
\(685\) 22.4963i 0.859540i
\(686\) −16.1182 + 9.12151i −0.615398 + 0.348261i
\(687\) −15.0149 −0.572854
\(688\) 1.63893 0.946236i 0.0624836 0.0360749i
\(689\) −6.64069 + 11.5020i −0.252990 + 0.438192i
\(690\) −12.6837 7.32292i −0.482859 0.278779i
\(691\) 7.08434 4.09015i 0.269501 0.155596i −0.359160 0.933276i \(-0.616937\pi\)
0.628661 + 0.777680i \(0.283603\pi\)
\(692\) −13.2048 −0.501971
\(693\) −6.54335 + 5.84675i −0.248561 + 0.222100i
\(694\) 28.5210 1.08264
\(695\) −47.1025 + 27.1946i −1.78670 + 1.03155i
\(696\) −2.83045 1.63416i −0.107288 0.0619428i
\(697\) −5.48530 + 9.50082i −0.207771 + 0.359869i
\(698\) −13.3317 + 7.69705i −0.504612 + 0.291338i
\(699\) −16.4422 −0.621900
\(700\) −0.553861 + 0.952981i −0.0209340 + 0.0360193i
\(701\) 15.9970i 0.604198i −0.953277 0.302099i \(-0.902313\pi\)
0.953277 0.302099i \(-0.0976874\pi\)
\(702\) 0.720474 + 1.24790i 0.0271925 + 0.0470988i
\(703\) −28.1456 + 48.7496i −1.06153 + 1.83863i
\(704\) 3.15334 + 1.02783i 0.118846 + 0.0387376i
\(705\) 21.4641 12.3923i 0.808384 0.466720i
\(706\) −5.54275 −0.208604
\(707\) 28.3019 + 0.0813307i 1.06440 + 0.00305876i
\(708\) −0.532715 −0.0200207
\(709\) 4.39355 + 7.60985i 0.165003 + 0.285794i 0.936656 0.350250i \(-0.113903\pi\)
−0.771653 + 0.636043i \(0.780570\pi\)
\(710\) −3.78491 + 6.55565i −0.142045 + 0.246029i
\(711\) −7.21263 4.16421i −0.270495 0.156170i
\(712\) −2.19052 3.79409i −0.0820932 0.142190i
\(713\) 19.4516i 0.728468i
\(714\) −8.50776 0.0244487i −0.318395 0.000914969i
\(715\) −10.8817 + 2.30241i −0.406954 + 0.0861053i
\(716\) −9.43539 16.3426i −0.352617 0.610750i
\(717\) 12.3975 21.4731i 0.462994 0.801929i
\(718\) −10.3650 + 17.9527i −0.386818 + 0.669989i
\(719\) −27.2393 + 15.7266i −1.01585 + 0.586503i −0.912900 0.408183i \(-0.866163\pi\)
−0.102953 + 0.994686i \(0.532829\pi\)
\(720\) 2.32736i 0.0867356i
\(721\) −31.1266 18.0904i −1.15922 0.673722i
\(722\) 18.9213i 0.704178i
\(723\) −19.2427 + 11.1098i −0.715643 + 0.413177i
\(724\) −3.41602 1.97224i −0.126955 0.0732977i
\(725\) 1.17919 + 0.680805i 0.0437940 + 0.0252845i
\(726\) −8.88715 6.48217i −0.329833 0.240576i
\(727\) 50.7040i 1.88051i 0.340475 + 0.940254i \(0.389412\pi\)
−0.340475 + 0.940254i \(0.610588\pi\)
\(728\) −3.30709 + 1.89670i −0.122569 + 0.0702963i
\(729\) −1.00000 −0.0370370
\(730\) 5.81844 + 10.0778i 0.215350 + 0.372998i
\(731\) −5.27022 3.04276i −0.194926 0.112541i
\(732\) −0.404803 0.233713i −0.0149620 0.00863829i
\(733\) 3.99023 + 6.91128i 0.147382 + 0.255274i 0.930259 0.366903i \(-0.119582\pi\)
−0.782877 + 0.622177i \(0.786249\pi\)
\(734\) 35.0890 1.29516
\(735\) 8.22672 14.0618i 0.303447 0.518678i
\(736\) 6.29290i 0.231959i
\(737\) −22.7610 + 20.4558i −0.838411 + 0.753499i
\(738\) −2.95456 1.70582i −0.108759 0.0627920i
\(739\) −38.2867 22.1048i −1.40840 0.813140i −0.413166 0.910656i \(-0.635577\pi\)
−0.995234 + 0.0975161i \(0.968910\pi\)
\(740\) 18.4244 10.6373i 0.677295 0.391036i
\(741\) 8.87339i 0.325972i
\(742\) 21.1540 12.1324i 0.776589 0.445393i
\(743\) 17.1346i 0.628607i 0.949323 + 0.314304i \(0.101771\pi\)
−0.949323 + 0.314304i \(0.898229\pi\)
\(744\) −2.67692 + 1.54552i −0.0981407 + 0.0566615i
\(745\) −17.5182 + 30.3423i −0.641815 + 1.11166i
\(746\) −12.2528 + 21.2225i −0.448607 + 0.777011i
\(747\) 2.28065 + 3.95020i 0.0834446 + 0.144530i
\(748\) −2.20770 10.4341i −0.0807214 0.381508i
\(749\) 21.4925 + 12.4912i 0.785319 + 0.456418i
\(750\) 10.6672i 0.389511i
\(751\) 20.4417 + 35.4061i 0.745928 + 1.29199i 0.949760 + 0.312979i \(0.101327\pi\)
−0.203832 + 0.979006i \(0.565340\pi\)
\(752\) 9.22249 + 5.32461i 0.336310 + 0.194168i
\(753\) 2.36708 4.09990i 0.0862611 0.149409i
\(754\) 2.35474 + 4.07853i 0.0857547 + 0.148531i
\(755\) 30.2349 1.10036
\(756\) 0.00760304 2.64574i 0.000276520 0.0962246i
\(757\) −20.2420 −0.735709 −0.367855 0.929883i \(-0.619908\pi\)
−0.367855 + 0.929883i \(0.619908\pi\)
\(758\) 2.96791 1.71353i 0.107799 0.0622380i
\(759\) −6.46800 + 19.8437i −0.234774 + 0.720279i
\(760\) −7.16598 + 12.4118i −0.259937 + 0.450225i
\(761\) −22.7554 39.4136i −0.824884 1.42874i −0.902008 0.431719i \(-0.857907\pi\)
0.0771248 0.997021i \(-0.475426\pi\)
\(762\) 10.8090i 0.391568i
\(763\) 0.0542623 18.8825i 0.00196443 0.683591i
\(764\) −23.5238 −0.851062
\(765\) 6.48131 3.74198i 0.234332 0.135292i
\(766\) 16.3278 28.2806i 0.589947 1.02182i
\(767\) 0.664773 + 0.383807i 0.0240036 + 0.0138585i
\(768\) −0.866025 + 0.500000i −0.0312500 + 0.0180422i
\(769\) 2.76998 0.0998881 0.0499440 0.998752i \(-0.484096\pi\)
0.0499440 + 0.998752i \(0.484096\pi\)
\(770\) 19.3988 + 6.38473i 0.699085 + 0.230090i
\(771\) −12.2353 −0.440643
\(772\) −18.0103 + 10.3983i −0.648206 + 0.374242i
\(773\) −9.93494 5.73594i −0.357335 0.206307i 0.310576 0.950548i \(-0.399478\pi\)
−0.667911 + 0.744241i \(0.732811\pi\)
\(774\) 0.946236 1.63893i 0.0340118 0.0589101i
\(775\) 1.11523 0.643876i 0.0400601 0.0231287i
\(776\) −17.8026 −0.639076
\(777\) −20.9796 + 12.0323i −0.752639 + 0.431657i
\(778\) 18.5677i 0.665685i
\(779\) −10.5045 18.1943i −0.376362 0.651877i
\(780\) 1.67680 2.90431i 0.0600391 0.103991i
\(781\) 10.2563 + 3.34303i 0.367001 + 0.119623i
\(782\) −17.5247 + 10.1179i −0.626680 + 0.361814i
\(783\) −3.26833 −0.116800
\(784\) 6.99988 + 0.0402313i 0.249996 + 0.00143683i
\(785\) 26.8311 0.957643
\(786\) −5.48559 9.50131i −0.195664 0.338901i
\(787\) 14.7757 25.5923i 0.526698 0.912268i −0.472818 0.881160i \(-0.656763\pi\)
0.999516 0.0311080i \(-0.00990358\pi\)
\(788\) −18.5048 10.6837i −0.659206 0.380593i
\(789\) −9.63502 16.6883i −0.343016 0.594121i
\(790\) 19.3832i 0.689625i
\(791\) 4.14761 + 7.23179i 0.147472 + 0.257133i
\(792\) 3.24479 0.686549i 0.115299 0.0243954i
\(793\) 0.336769 + 0.583300i 0.0119590 + 0.0207136i
\(794\) 2.79674 4.84409i 0.0992525 0.171910i
\(795\) −10.7258 + 18.5776i −0.380404 + 0.658880i
\(796\) 17.3579 10.0216i 0.615233 0.355205i
\(797\) 3.17035i 0.112300i −0.998422 0.0561498i \(-0.982118\pi\)
0.998422 0.0561498i \(-0.0178824\pi\)
\(798\) 8.18682 14.0863i 0.289810 0.498651i
\(799\) 34.2441i 1.21147i
\(800\) 0.360793 0.208304i 0.0127560 0.00736466i
\(801\) −3.79409 2.19052i −0.134058 0.0773982i
\(802\) −8.96641 5.17676i −0.316615 0.182798i
\(803\) 12.3341 11.0849i 0.435260 0.391177i
\(804\) 9.22694i 0.325409i
\(805\) 0.111353 38.7491i 0.00392467 1.36573i
\(806\) 4.45403 0.156886
\(807\) 11.0447 + 19.1299i 0.388791 + 0.673405i
\(808\) −9.26399 5.34857i −0.325906 0.188162i
\(809\) 34.3262 + 19.8183i 1.20685 + 0.696773i 0.962069 0.272806i \(-0.0879518\pi\)
0.244777 + 0.969579i \(0.421285\pi\)
\(810\) 1.16368 + 2.01555i 0.0408876 + 0.0708193i
\(811\) −24.9006 −0.874377 −0.437188 0.899370i \(-0.644026\pi\)
−0.437188 + 0.899370i \(0.644026\pi\)
\(812\) 0.0248492 8.64714i 0.000872036 0.303455i
\(813\) 1.22111i 0.0428262i
\(814\) −20.2655 22.5493i −0.710306 0.790351i
\(815\) −16.7567 9.67451i −0.586963 0.338883i
\(816\) 2.78483 + 1.60782i 0.0974886 + 0.0562851i
\(817\) 10.0926 5.82695i 0.353094 0.203859i
\(818\) 20.8916i 0.730458i
\(819\) −1.91567 + 3.29613i −0.0669391 + 0.115176i
\(820\) 7.94010i 0.277280i
\(821\) −11.6214 + 6.70962i −0.405590 + 0.234167i −0.688893 0.724863i \(-0.741903\pi\)
0.283303 + 0.959030i \(0.408570\pi\)
\(822\) 4.83301 8.37102i 0.168571 0.291973i
\(823\) 13.2288 22.9130i 0.461127 0.798696i −0.537890 0.843015i \(-0.680778\pi\)
0.999017 + 0.0443189i \(0.0141118\pi\)
\(824\) 6.80370 + 11.7844i 0.237018 + 0.410527i
\(825\) −1.35180 + 0.286022i −0.0470638 + 0.00995800i
\(826\) −0.701205 1.22262i −0.0243981 0.0425405i
\(827\) 43.1986i 1.50216i 0.660209 + 0.751081i \(0.270467\pi\)
−0.660209 + 0.751081i \(0.729533\pi\)
\(828\) −3.14645 5.44981i −0.109347 0.189394i
\(829\) −4.77405 2.75630i −0.165810 0.0957303i 0.414799 0.909913i \(-0.363852\pi\)
−0.580609 + 0.814183i \(0.697185\pi\)
\(830\) 5.30790 9.19355i 0.184240 0.319113i
\(831\) 6.25443 + 10.8330i 0.216964 + 0.375792i
\(832\) 1.44095 0.0499559
\(833\) −11.1425 19.5582i −0.386066 0.677651i
\(834\) −23.3695 −0.809220
\(835\) 31.3093 18.0764i 1.08350 0.625560i
\(836\) 19.4184 + 6.32938i 0.671599 + 0.218906i
\(837\) −1.54552 + 2.67692i −0.0534210 + 0.0925279i
\(838\) −3.79735 6.57721i −0.131177 0.227206i
\(839\) 25.5783i 0.883062i −0.897246 0.441531i \(-0.854436\pi\)
0.897246 0.441531i \(-0.145564\pi\)
\(840\) −5.34148 + 3.06347i −0.184299 + 0.105700i
\(841\) 18.3180 0.631657
\(842\) 25.9254 14.9680i 0.893447 0.515832i
\(843\) 12.6747 21.9533i 0.436541 0.756111i
\(844\) −1.77233 1.02325i −0.0610060 0.0352219i
\(845\) 22.0172 12.7117i 0.757416 0.437294i
\(846\) 10.6492 0.366128
\(847\) 3.17908 28.9291i 0.109234 0.994016i
\(848\) −9.21712 −0.316517
\(849\) −2.39408 + 1.38222i −0.0821646 + 0.0474378i
\(850\) −1.16018 0.669832i −0.0397939 0.0229750i
\(851\) −28.7620 + 49.8173i −0.985950 + 1.70772i
\(852\) −2.81677 + 1.62627i −0.0965011 + 0.0557149i
\(853\) −26.6616 −0.912877 −0.456439 0.889755i \(-0.650875\pi\)
−0.456439 + 0.889755i \(0.650875\pi\)
\(854\) 0.00355386 1.23669i 0.000121611 0.0423186i
\(855\) 14.3320i 0.490142i
\(856\) −4.69786 8.13694i −0.160570 0.278115i
\(857\) 16.9270 29.3183i 0.578214 1.00150i −0.417470 0.908690i \(-0.637083\pi\)
0.995684 0.0928052i \(-0.0295834\pi\)
\(858\) −4.54380 1.48104i −0.155123 0.0505620i
\(859\) −9.66594 + 5.58063i −0.329798 + 0.190409i −0.655751 0.754977i \(-0.727648\pi\)
0.325954 + 0.945386i \(0.394315\pi\)
\(860\) −4.40447 −0.150191
\(861\) 0.0259388 9.02630i 0.000883991 0.307615i
\(862\) −33.3538 −1.13603
\(863\) −7.56384 13.1010i −0.257476 0.445962i 0.708089 0.706123i \(-0.249558\pi\)
−0.965565 + 0.260161i \(0.916224\pi\)
\(864\) −0.500000 + 0.866025i −0.0170103 + 0.0294628i
\(865\) 26.6150 + 15.3662i 0.904936 + 0.522465i
\(866\) 13.8918 + 24.0614i 0.472064 + 0.817639i
\(867\) 6.65962i 0.226173i
\(868\) −7.07068 4.10940i −0.239995 0.139482i
\(869\) 27.0240 5.71787i 0.916726 0.193965i
\(870\) 3.80329 + 6.58749i 0.128944 + 0.223337i
\(871\) −6.64777 + 11.5143i −0.225251 + 0.390146i
\(872\) −3.56846 + 6.18076i −0.120843 + 0.209307i
\(873\) −15.4175 + 8.90130i −0.521803 + 0.301263i
\(874\) 38.7518i 1.31080i
\(875\) −24.4821 + 14.0411i −0.827646 + 0.474676i
\(876\) 5.00004i 0.168936i
\(877\) −8.64012 + 4.98837i −0.291756 + 0.168445i −0.638733 0.769428i \(-0.720541\pi\)
0.346977 + 0.937873i \(0.387208\pi\)
\(878\) −26.9314 15.5488i −0.908890 0.524748i
\(879\) −7.82172 4.51587i −0.263820 0.152317i
\(880\) −5.15967 5.74112i −0.173933 0.193533i
\(881\) 3.10955i 0.104763i 0.998627 + 0.0523816i \(0.0166812\pi\)
−0.998627 + 0.0523816i \(0.983319\pi\)
\(882\) 6.08219 3.46510i 0.204798 0.116676i
\(883\) 28.8971 0.972465 0.486233 0.873829i \(-0.338371\pi\)
0.486233 + 0.873829i \(0.338371\pi\)
\(884\) −2.31679 4.01279i −0.0779220 0.134965i
\(885\) 1.07372 + 0.619910i 0.0360926 + 0.0208380i
\(886\) −4.33757 2.50430i −0.145723 0.0841335i
\(887\) −6.85833 11.8790i −0.230280 0.398857i 0.727610 0.685991i \(-0.240631\pi\)
−0.957890 + 0.287134i \(0.907298\pi\)
\(888\) 9.14111 0.306756
\(889\) 24.8075 14.2277i 0.832017 0.477182i
\(890\) 10.1963i 0.341779i
\(891\) 2.46679 2.21696i 0.0826407 0.0742710i
\(892\) −20.2480 11.6902i −0.677955 0.391417i
\(893\) 56.7924 + 32.7891i 1.90048 + 1.09724i
\(894\) −13.0372 + 7.52705i −0.436030 + 0.251742i
\(895\) 43.9191i 1.46805i
\(896\) −2.28748 1.32945i −0.0764192 0.0444140i
\(897\) 9.06773i 0.302763i
\(898\) −21.5394 + 12.4358i −0.718778 + 0.414987i
\(899\) −5.05127 + 8.74905i −0.168469 + 0.291797i
\(900\) 0.208304 0.360793i 0.00694347 0.0120264i
\(901\) 14.8195 + 25.6681i 0.493709 + 0.855129i
\(902\) 11.0700 2.34225i 0.368592 0.0779885i
\(903\) 5.00699 + 0.0143885i 0.166622 + 0.000478821i
\(904\) 3.15100i 0.104801i
\(905\) 4.59012 + 7.95031i 0.152581 + 0.264277i
\(906\) 11.2506 + 6.49554i 0.373776 + 0.215800i
\(907\) 24.4939 42.4247i 0.813307 1.40869i −0.0972300 0.995262i \(-0.530998\pi\)
0.910537 0.413427i \(-0.135668\pi\)
\(908\) −6.97413 12.0796i −0.231445 0.400874i
\(909\) −10.6971 −0.354802
\(910\) 8.87277 + 0.0254976i 0.294129 + 0.000845236i
\(911\) −26.6937 −0.884401 −0.442200 0.896916i \(-0.645802\pi\)
−0.442200 + 0.896916i \(0.645802\pi\)
\(912\) −5.33301 + 3.07901i −0.176594 + 0.101956i
\(913\) −14.3834 4.68822i −0.476019 0.155158i
\(914\) 3.80735 6.59453i 0.125936 0.218128i
\(915\) 0.543935 + 0.942123i 0.0179819 + 0.0311456i
\(916\) 15.0149i 0.496106i
\(917\) 14.5857 25.0963i 0.481661 0.828753i
\(918\) 3.21565 0.106132
\(919\) 39.8952 23.0335i 1.31602 0.759806i 0.332936 0.942949i \(-0.391961\pi\)
0.983086 + 0.183144i \(0.0586274\pi\)
\(920\) −7.32292 + 12.6837i −0.241430 + 0.418168i
\(921\) 3.05093 + 1.76145i 0.100531 + 0.0580419i
\(922\) −7.41371 + 4.28031i −0.244157 + 0.140964i
\(923\) 4.68672 0.154265
\(924\) 5.84675 + 6.54335i 0.192344 + 0.215261i
\(925\) −3.80826 −0.125215
\(926\) 2.48741 1.43611i 0.0817413 0.0471933i
\(927\) 11.7844 + 6.80370i 0.387049 + 0.223463i
\(928\) −1.63416 + 2.83045i −0.0536440 + 0.0929142i
\(929\) 10.5117 6.06892i 0.344877 0.199115i −0.317550 0.948242i \(-0.602860\pi\)
0.662427 + 0.749127i \(0.269527\pi\)
\(930\) 7.19397 0.235899
\(931\) 43.1055 + 0.247746i 1.41273 + 0.00811953i
\(932\) 16.4422i 0.538581i
\(933\) 2.79352 + 4.83852i 0.0914557 + 0.158406i
\(934\) 4.52673 7.84052i 0.148119 0.256550i
\(935\) −7.69221 + 23.5995i −0.251562 + 0.771787i
\(936\) 1.24790 0.720474i 0.0407888 0.0235494i
\(937\) 43.9719 1.43650 0.718250 0.695786i \(-0.244944\pi\)
0.718250 + 0.695786i \(0.244944\pi\)
\(938\) 21.1766 12.1453i 0.691439 0.396558i
\(939\) 5.27903 0.172275
\(940\) −12.3923 21.4641i −0.404192 0.700081i
\(941\) −20.8247 + 36.0694i −0.678866 + 1.17583i 0.296457 + 0.955046i \(0.404195\pi\)
−0.975323 + 0.220784i \(0.929138\pi\)
\(942\) 9.98402 + 5.76428i 0.325297 + 0.187810i
\(943\) −10.7345 18.5928i −0.349564 0.605463i
\(944\) 0.532715i 0.0173384i
\(945\) −3.09412 + 5.32378i −0.100652 + 0.173183i
\(946\) 1.29927 + 6.14067i 0.0422431 + 0.199651i
\(947\) 9.94370 + 17.2230i 0.323127 + 0.559672i 0.981131 0.193342i \(-0.0619326\pi\)
−0.658005 + 0.753014i \(0.728599\pi\)
\(948\) −4.16421 + 7.21263i −0.135247 + 0.234255i
\(949\) 3.60239 6.23953i 0.116939 0.202544i
\(950\) 2.22177 1.28274i 0.0720839 0.0416176i
\(951\) 31.6864i 1.02750i
\(952\) −0.0244487 + 8.50776i −0.000792386 + 0.275738i
\(953\) 42.1430i 1.36514i 0.730818 + 0.682572i \(0.239139\pi\)
−0.730818 + 0.682572i \(0.760861\pi\)
\(954\) −7.98226 + 4.60856i −0.258435 + 0.149208i
\(955\) 47.4135 + 27.3742i 1.53426 + 0.885808i
\(956\) −21.4731 12.3975i −0.694491 0.400965i
\(957\) 8.06229 7.24576i 0.260617 0.234222i
\(958\) 31.1954i 1.00788i
\(959\) 25.5738 + 0.0734911i 0.825821 + 0.00237315i
\(960\) 2.32736 0.0751152
\(961\) −10.7227 18.5723i −0.345895 0.599107i
\(962\) −11.4072 6.58593i −0.367782 0.212339i
\(963\) −8.13694 4.69786i −0.262209 0.151386i
\(964\) 11.1098 + 19.2427i 0.357822 + 0.619765i
\(965\) 48.4010 1.55808
\(966\) 8.36612 14.3949i 0.269176 0.463147i
\(967\) 32.5204i 1.04578i 0.852399 + 0.522892i \(0.175147\pi\)
−0.852399 + 0.522892i \(0.824853\pi\)
\(968\) −6.48217 + 8.88715i −0.208345 + 0.285644i
\(969\) 17.1491 + 9.90102i 0.550907 + 0.318067i
\(970\) 35.8821 + 20.7165i 1.15210 + 0.665168i
\(971\) −35.8435 + 20.6943i −1.15027 + 0.664111i −0.948954 0.315415i \(-0.897856\pi\)
−0.201319 + 0.979526i \(0.564523\pi\)
\(972\) 1.00000i 0.0320750i
\(973\) −30.7610 53.6349i −0.986151 1.71946i
\(974\) 36.0737i 1.15587i
\(975\) −0.519884 + 0.300155i −0.0166496 + 0.00961266i
\(976\) −0.233713 + 0.404803i −0.00748098 + 0.0129574i
\(977\) −7.05105 + 12.2128i −0.225583 + 0.390721i −0.956494 0.291751i \(-0.905762\pi\)
0.730911 + 0.682473i \(0.239095\pi\)
\(978\) −4.15686 7.19989i −0.132922 0.230227i
\(979\) 14.2155 3.00780i 0.454331 0.0961296i
\(980\) −14.0618 8.22672i −0.449189 0.262793i
\(981\) 7.13693i 0.227865i
\(982\) −13.3781 23.1715i −0.426911 0.739432i
\(983\) 38.2844 + 22.1035i 1.22108 + 0.704992i 0.965149 0.261703i \(-0.0842840\pi\)
0.255933 + 0.966695i \(0.417617\pi\)
\(984\) −1.70582 + 2.95456i −0.0543795 + 0.0941880i
\(985\) 24.8649 + 43.0673i 0.792263 + 1.37224i
\(986\) 10.5098 0.334700
\(987\) 14.0174 + 24.4408i 0.446179 + 0.777959i
\(988\) 8.87339 0.282300
\(989\) 10.3136 5.95457i 0.327954 0.189344i
\(990\) −7.33897 2.39212i −0.233248 0.0760266i
\(991\) −22.7546 + 39.4121i −0.722824 + 1.25197i 0.237039 + 0.971500i \(0.423823\pi\)
−0.959863 + 0.280468i \(0.909510\pi\)
\(992\) 1.54552 + 2.67692i 0.0490703 + 0.0849923i
\(993\) 3.91587i 0.124266i
\(994\) −7.44009 4.32409i −0.235985 0.137152i
\(995\) −46.6476 −1.47883
\(996\) 3.95020 2.28065i 0.125167 0.0722652i
\(997\) −24.1616 + 41.8491i −0.765205 + 1.32537i 0.174934 + 0.984580i \(0.444029\pi\)
−0.940138 + 0.340793i \(0.889304\pi\)
\(998\) 24.3330 + 14.0487i 0.770249 + 0.444703i
\(999\) 7.91644 4.57056i 0.250465 0.144606i
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 462.2.p.a.241.1 16
3.2 odd 2 1386.2.bk.a.703.8 16
7.3 odd 6 3234.2.e.b.2155.7 16
7.4 even 3 3234.2.e.a.2155.2 16
7.5 odd 6 462.2.p.b.439.5 yes 16
11.10 odd 2 462.2.p.b.241.5 yes 16
21.5 even 6 1386.2.bk.b.901.4 16
33.32 even 2 1386.2.bk.b.703.4 16
77.10 even 6 3234.2.e.a.2155.15 16
77.32 odd 6 3234.2.e.b.2155.10 16
77.54 even 6 inner 462.2.p.a.439.1 yes 16
231.131 odd 6 1386.2.bk.a.901.8 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
462.2.p.a.241.1 16 1.1 even 1 trivial
462.2.p.a.439.1 yes 16 77.54 even 6 inner
462.2.p.b.241.5 yes 16 11.10 odd 2
462.2.p.b.439.5 yes 16 7.5 odd 6
1386.2.bk.a.703.8 16 3.2 odd 2
1386.2.bk.a.901.8 16 231.131 odd 6
1386.2.bk.b.703.4 16 33.32 even 2
1386.2.bk.b.901.4 16 21.5 even 6
3234.2.e.a.2155.2 16 7.4 even 3
3234.2.e.a.2155.15 16 77.10 even 6
3234.2.e.b.2155.7 16 7.3 odd 6
3234.2.e.b.2155.10 16 77.32 odd 6