Properties

Label 1386.2.bk.b.703.4
Level $1386$
Weight $2$
Character 1386.703
Analytic conductor $11.067$
Analytic rank $0$
Dimension $16$
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] = [1386,2,Mod(703,1386)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1386, 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("1386.703");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1386.bk (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: \(11.0672657201\)
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: no (minimal twist has level 462)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 703.4
Root \(0.500000 - 3.19339i\) of defining polynomial
Character \(\chi\) \(=\) 1386.703
Dual form 1386.2.bk.b.901.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(2.01555 - 1.16368i) q^{5} +(1.31629 + 2.29508i) q^{7} +1.00000i q^{8} +O(q^{10})\) \(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(2.01555 - 1.16368i) q^{5} +(1.31629 + 2.29508i) q^{7} +1.00000i q^{8} +(-1.16368 + 2.01555i) q^{10} +(-2.46679 - 2.21696i) q^{11} +1.44095 q^{13} +(-2.28748 - 1.32945i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-1.60782 + 2.78483i) q^{17} +(3.07901 + 5.33301i) q^{19} -2.32736i q^{20} +(3.24479 + 0.686549i) q^{22} +(3.14645 + 5.44981i) q^{23} +(0.208304 - 0.360793i) q^{25} +(-1.24790 + 0.720474i) q^{26} +(2.64574 + 0.00760304i) q^{28} +3.26833i q^{29} +(2.67692 + 1.54552i) q^{31} +(0.866025 + 0.500000i) q^{32} -3.21565i q^{34} +(5.32378 + 3.09412i) q^{35} +(-4.57056 - 7.91644i) q^{37} +(-5.33301 - 3.07901i) q^{38} +(1.16368 + 2.01555i) q^{40} +3.41163 q^{41} -1.89247i q^{43} +(-3.15334 + 1.02783i) q^{44} +(-5.44981 - 3.14645i) q^{46} +(9.22249 - 5.32461i) q^{47} +(-3.53478 + 6.04196i) q^{49} +0.416608i q^{50} +(0.720474 - 1.24790i) q^{52} +(-4.60856 + 7.98226i) q^{53} +(-7.55179 - 1.59785i) q^{55} +(-2.29508 + 1.31629i) q^{56} +(-1.63416 - 2.83045i) q^{58} +(0.461345 + 0.266358i) q^{59} +(0.233713 + 0.404803i) q^{61} -3.09104 q^{62} -1.00000 q^{64} +(2.90431 - 1.67680i) q^{65} +(4.61347 - 7.99077i) q^{67} +(1.60782 + 2.78483i) q^{68} +(-6.15759 - 0.0176950i) q^{70} +3.25253 q^{71} +(2.50002 - 4.33016i) q^{73} +(7.91644 + 4.57056i) q^{74} +6.15803 q^{76} +(1.84110 - 8.57965i) q^{77} +(7.21263 - 4.16421i) q^{79} +(-2.01555 - 1.16368i) q^{80} +(-2.95456 + 1.70582i) q^{82} +4.56130 q^{83} +7.48397i q^{85} +(0.946236 + 1.63893i) q^{86} +(2.21696 - 2.46679i) q^{88} +(3.79409 - 2.19052i) q^{89} +(1.89670 + 3.30709i) q^{91} +6.29290 q^{92} +(-5.32461 + 9.22249i) q^{94} +(12.4118 + 7.16598i) q^{95} +17.8026i q^{97} +(0.0402313 - 6.99988i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 8 q^{4} - 12 q^{5} + 6 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 8 q^{4} - 12 q^{5} + 6 q^{7} - 2 q^{10} + 4 q^{11} - 8 q^{14} - 8 q^{16} + 10 q^{19} + 2 q^{22} + 4 q^{23} + 10 q^{25} - 12 q^{26} + 6 q^{31} - 8 q^{35} + 14 q^{37} + 12 q^{38} + 2 q^{40} + 32 q^{41} - 4 q^{44} - 18 q^{46} + 24 q^{47} - 6 q^{49} + 14 q^{55} - 4 q^{56} - 28 q^{61} - 8 q^{62} - 16 q^{64} + 72 q^{65} - 16 q^{67} - 30 q^{70} + 56 q^{71} + 44 q^{73} + 24 q^{74} + 20 q^{76} + 52 q^{77} + 30 q^{79} + 12 q^{80} - 12 q^{82} + 8 q^{83} + 12 q^{86} - 2 q^{88} + 36 q^{89} - 8 q^{91} + 8 q^{92} - 14 q^{94} + 72 q^{95} - 40 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times\).

\(n\) \(155\) \(199\) \(1135\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{6}\right)\) \(-1\)

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 0
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) 2.01555 1.16368i 0.901383 0.520414i 0.0237343 0.999718i \(-0.492444\pi\)
0.877649 + 0.479305i \(0.159111\pi\)
\(6\) 0 0
\(7\) 1.31629 + 2.29508i 0.497509 + 0.867459i
\(8\) 1.00000i 0.353553i
\(9\) 0 0
\(10\) −1.16368 + 2.01555i −0.367988 + 0.637374i
\(11\) −2.46679 2.21696i −0.743767 0.668439i
\(12\) 0 0
\(13\) 1.44095 0.399647 0.199823 0.979832i \(-0.435963\pi\)
0.199823 + 0.979832i \(0.435963\pi\)
\(14\) −2.28748 1.32945i −0.611354 0.355312i
\(15\) 0 0
\(16\) −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 0
\(19\) 3.07901 + 5.33301i 0.706374 + 1.22348i 0.966193 + 0.257819i \(0.0830038\pi\)
−0.259819 + 0.965657i \(0.583663\pi\)
\(20\) 2.32736i 0.520414i
\(21\) 0 0
\(22\) 3.24479 + 0.686549i 0.691791 + 0.146373i
\(23\) 3.14645 + 5.44981i 0.656080 + 1.13636i 0.981622 + 0.190836i \(0.0611199\pi\)
−0.325542 + 0.945528i \(0.605547\pi\)
\(24\) 0 0
\(25\) 0.208304 0.360793i 0.0416608 0.0721586i
\(26\) −1.24790 + 0.720474i −0.244733 + 0.141297i
\(27\) 0 0
\(28\) 2.64574 + 0.00760304i 0.499998 + 0.00143684i
\(29\) 3.26833i 0.606913i 0.952845 + 0.303456i \(0.0981407\pi\)
−0.952845 + 0.303456i \(0.901859\pi\)
\(30\) 0 0
\(31\) 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
\(33\) 0 0
\(34\) 3.21565i 0.551479i
\(35\) 5.32378 + 3.09412i 0.899884 + 0.523002i
\(36\) 0 0
\(37\) −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
\(39\) 0 0
\(40\) 1.16368 + 2.01555i 0.183994 + 0.318687i
\(41\) 3.41163 0.532808 0.266404 0.963861i \(-0.414165\pi\)
0.266404 + 0.963861i \(0.414165\pi\)
\(42\) 0 0
\(43\) 1.89247i 0.288599i −0.989534 0.144300i \(-0.953907\pi\)
0.989534 0.144300i \(-0.0460929\pi\)
\(44\) −3.15334 + 1.02783i −0.475384 + 0.154951i
\(45\) 0 0
\(46\) −5.44981 3.14645i −0.803530 0.463919i
\(47\) 9.22249 5.32461i 1.34524 0.776674i 0.357668 0.933849i \(-0.383572\pi\)
0.987571 + 0.157175i \(0.0502386\pi\)
\(48\) 0 0
\(49\) −3.53478 + 6.04196i −0.504969 + 0.863137i
\(50\) 0.416608i 0.0589173i
\(51\) 0 0
\(52\) 0.720474 1.24790i 0.0999117 0.173052i
\(53\) −4.60856 + 7.98226i −0.633035 + 1.09645i 0.353893 + 0.935286i \(0.384858\pi\)
−0.986928 + 0.161162i \(0.948476\pi\)
\(54\) 0 0
\(55\) −7.55179 1.59785i −1.01828 0.215454i
\(56\) −2.29508 + 1.31629i −0.306693 + 0.175896i
\(57\) 0 0
\(58\) −1.63416 2.83045i −0.214576 0.371657i
\(59\) 0.461345 + 0.266358i 0.0600620 + 0.0346768i 0.529730 0.848166i \(-0.322293\pi\)
−0.469668 + 0.882843i \(0.655626\pi\)
\(60\) 0 0
\(61\) 0.233713 + 0.404803i 0.0299239 + 0.0518298i 0.880600 0.473861i \(-0.157140\pi\)
−0.850676 + 0.525691i \(0.823807\pi\)
\(62\) −3.09104 −0.392563
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 2.90431 1.67680i 0.360235 0.207982i
\(66\) 0 0
\(67\) 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
\(69\) 0 0
\(70\) −6.15759 0.0176950i −0.735973 0.00211496i
\(71\) 3.25253 0.386004 0.193002 0.981198i \(-0.438178\pi\)
0.193002 + 0.981198i \(0.438178\pi\)
\(72\) 0 0
\(73\) 2.50002 4.33016i 0.292605 0.506807i −0.681820 0.731520i \(-0.738811\pi\)
0.974425 + 0.224713i \(0.0721446\pi\)
\(74\) 7.91644 + 4.57056i 0.920267 + 0.531316i
\(75\) 0 0
\(76\) 6.15803 0.706374
\(77\) 1.84110 8.57965i 0.209813 0.977742i
\(78\) 0 0
\(79\) 7.21263 4.16421i 0.811484 0.468510i −0.0359870 0.999352i \(-0.511457\pi\)
0.847471 + 0.530842i \(0.178124\pi\)
\(80\) −2.01555 1.16368i −0.225346 0.130103i
\(81\) 0 0
\(82\) −2.95456 + 1.70582i −0.326277 + 0.188376i
\(83\) 4.56130 0.500668 0.250334 0.968160i \(-0.419460\pi\)
0.250334 + 0.968160i \(0.419460\pi\)
\(84\) 0 0
\(85\) 7.48397i 0.811750i
\(86\) 0.946236 + 1.63893i 0.102035 + 0.176730i
\(87\) 0 0
\(88\) 2.21696 2.46679i 0.236329 0.262961i
\(89\) 3.79409 2.19052i 0.402173 0.232195i −0.285248 0.958454i \(-0.592076\pi\)
0.687421 + 0.726259i \(0.258743\pi\)
\(90\) 0 0
\(91\) 1.89670 + 3.30709i 0.198828 + 0.346677i
\(92\) 6.29290 0.656080
\(93\) 0 0
\(94\) −5.32461 + 9.22249i −0.549191 + 0.951227i
\(95\) 12.4118 + 7.16598i 1.27343 + 0.735214i
\(96\) 0 0
\(97\) 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 0
\(100\) −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 \(0.988031\pi\)
\(102\) 0 0
\(103\) 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
\(105\) 0 0
\(106\) 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 0
\(109\) −6.18076 3.56846i −0.592009 0.341797i 0.173882 0.984766i \(-0.444369\pi\)
−0.765892 + 0.642970i \(0.777702\pi\)
\(110\) 7.33897 2.39212i 0.699743 0.228080i
\(111\) 0 0
\(112\) 1.32945 2.28748i 0.125622 0.216146i
\(113\) 3.15100 0.296421 0.148210 0.988956i \(-0.452649\pi\)
0.148210 + 0.988956i \(0.452649\pi\)
\(114\) 0 0
\(115\) 12.6837 + 7.32292i 1.18276 + 0.682866i
\(116\) 2.83045 + 1.63416i 0.262801 + 0.151728i
\(117\) 0 0
\(118\) −0.532715 −0.0490404
\(119\) −8.50776 0.0244487i −0.779905 0.00224121i
\(120\) 0 0
\(121\) 1.17015 + 10.9376i 0.106377 + 0.994326i
\(122\) −0.404803 0.233713i −0.0366492 0.0211594i
\(123\) 0 0
\(124\) 2.67692 1.54552i 0.240395 0.138792i
\(125\) 10.6672i 0.954104i
\(126\) 0 0
\(127\) 10.8090i 0.959143i −0.877503 0.479571i \(-0.840792\pi\)
0.877503 0.479571i \(-0.159208\pi\)
\(128\) 0.866025 0.500000i 0.0765466 0.0441942i
\(129\) 0 0
\(130\) −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 \(0.674232\pi\)
\(132\) 0 0
\(133\) −8.18682 + 14.0863i −0.709887 + 1.22144i
\(134\) 9.22694i 0.797086i
\(135\) 0 0
\(136\) −2.78483 1.60782i −0.238797 0.137870i
\(137\) 4.83301 8.37102i 0.412912 0.715185i −0.582295 0.812978i \(-0.697845\pi\)
0.995207 + 0.0977932i \(0.0311784\pi\)
\(138\) 0 0
\(139\) −23.3695 −1.98218 −0.991088 0.133208i \(-0.957472\pi\)
−0.991088 + 0.133208i \(0.957472\pi\)
\(140\) 5.34148 3.06347i 0.451437 0.258911i
\(141\) 0 0
\(142\) −2.81677 + 1.62627i −0.236378 + 0.136473i
\(143\) −3.55452 3.19453i −0.297244 0.267140i
\(144\) 0 0
\(145\) 3.80329 + 6.58749i 0.315846 + 0.547061i
\(146\) 5.00004i 0.413806i
\(147\) 0 0
\(148\) −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 0
\(151\) 11.2506 + 6.49554i 0.915561 + 0.528599i 0.882216 0.470845i \(-0.156051\pi\)
0.0333445 + 0.999444i \(0.489384\pi\)
\(152\) −5.33301 + 3.07901i −0.432564 + 0.249741i
\(153\) 0 0
\(154\) 2.69538 + 8.35074i 0.217200 + 0.672922i
\(155\) 7.19397 0.577833
\(156\) 0 0
\(157\) −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
\(159\) 0 0
\(160\) 2.32736 0.183994
\(161\) −8.36612 + 14.3949i −0.659343 + 1.13447i
\(162\) 0 0
\(163\) 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
\(165\) 0 0
\(166\) −3.95020 + 2.28065i −0.306595 + 0.177013i
\(167\) −15.5338 −1.20204 −0.601022 0.799232i \(-0.705240\pi\)
−0.601022 + 0.799232i \(0.705240\pi\)
\(168\) 0 0
\(169\) −10.9237 −0.840282
\(170\) −3.74198 6.48131i −0.286997 0.497094i
\(171\) 0 0
\(172\) −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 \(-0.334058\pi\)
\(174\) 0 0
\(175\) 1.10224 + 0.00316749i 0.0833213 + 0.000239439i
\(176\) −0.686549 + 3.24479i −0.0517506 + 0.244585i
\(177\) 0 0
\(178\) −2.19052 + 3.79409i −0.164186 + 0.284379i
\(179\) −9.43539 + 16.3426i −0.705234 + 1.22150i 0.261373 + 0.965238i \(0.415825\pi\)
−0.966607 + 0.256263i \(0.917509\pi\)
\(180\) 0 0
\(181\) 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 0
\(184\) −5.44981 + 3.14645i −0.401765 + 0.231959i
\(185\) −18.4244 10.6373i −1.35459 0.782072i
\(186\) 0 0
\(187\) 10.1400 3.30512i 0.741513 0.241695i
\(188\) 10.6492i 0.776674i
\(189\) 0 0
\(190\) −14.3320 −1.03975
\(191\) 11.7619 + 20.3722i 0.851062 + 1.47408i 0.880251 + 0.474508i \(0.157374\pi\)
−0.0291897 + 0.999574i \(0.509293\pi\)
\(192\) 0 0
\(193\) 18.0103 + 10.3983i 1.29641 + 0.748484i 0.979782 0.200066i \(-0.0641156\pi\)
0.316629 + 0.948549i \(0.397449\pi\)
\(194\) −8.90130 15.4175i −0.639076 1.10691i
\(195\) 0 0
\(196\) 3.46510 + 6.08219i 0.247507 + 0.434442i
\(197\) 21.3675i 1.52237i −0.648534 0.761186i \(-0.724618\pi\)
0.648534 0.761186i \(-0.275382\pi\)
\(198\) 0 0
\(199\) 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
\(201\) 0 0
\(202\) 10.6971i 0.752648i
\(203\) −7.50107 + 4.30205i −0.526472 + 0.301945i
\(204\) 0 0
\(205\) 6.87633 3.97005i 0.480264 0.277280i
\(206\) −6.80370 + 11.7844i −0.474036 + 0.821055i
\(207\) 0 0
\(208\) −0.720474 1.24790i −0.0499559 0.0865261i
\(209\) 4.22779 19.9815i 0.292442 1.38215i
\(210\) 0 0
\(211\) 2.04651i 0.140887i 0.997516 + 0.0704437i \(0.0224415\pi\)
−0.997516 + 0.0704437i \(0.977558\pi\)
\(212\) 4.60856 + 7.98226i 0.316517 + 0.548224i
\(213\) 0 0
\(214\) 4.69786 8.13694i 0.321139 0.556229i
\(215\) −2.20223 3.81438i −0.150191 0.260139i
\(216\) 0 0
\(217\) −0.0235013 + 8.17809i −0.00159537 + 0.555165i
\(218\) 7.13693 0.483374
\(219\) 0 0
\(220\) −5.15967 + 5.74112i −0.347865 + 0.387066i
\(221\) −2.31679 + 4.01279i −0.155844 + 0.269930i
\(222\) 0 0
\(223\) 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 0
\(226\) −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 \(0.0134793\pi\)
\(228\) 0 0
\(229\) −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
\(231\) 0 0
\(232\) −3.26833 −0.214576
\(233\) −14.2393 + 8.22109i −0.932850 + 0.538581i −0.887712 0.460399i \(-0.847706\pi\)
−0.0451385 + 0.998981i \(0.514373\pi\)
\(234\) 0 0
\(235\) 12.3923 21.4641i 0.808384 1.40016i
\(236\) 0.461345 0.266358i 0.0300310 0.0173384i
\(237\) 0 0
\(238\) 7.38016 4.23271i 0.478385 0.274366i
\(239\) 24.7950i 1.60386i −0.597419 0.801929i \(-0.703807\pi\)
0.597419 0.801929i \(-0.296193\pi\)
\(240\) 0 0
\(241\) 11.1098 19.2427i 0.715643 1.23953i −0.247068 0.968998i \(-0.579467\pi\)
0.962711 0.270532i \(-0.0871996\pi\)
\(242\) −6.48217 8.88715i −0.416690 0.571288i
\(243\) 0 0
\(244\) 0.467427 0.0299239
\(245\) −0.0936328 + 16.2913i −0.00598198 + 1.04081i
\(246\) 0 0
\(247\) 4.43670 + 7.68458i 0.282300 + 0.488958i
\(248\) −1.54552 + 2.67692i −0.0981407 + 0.169985i
\(249\) 0 0
\(250\) −5.33360 9.23807i −0.337327 0.584267i
\(251\) 4.73415i 0.298817i 0.988776 + 0.149409i \(0.0477370\pi\)
−0.988776 + 0.149409i \(0.952263\pi\)
\(252\) 0 0
\(253\) 4.32038 20.4191i 0.271620 1.28374i
\(254\) 5.40449 + 9.36086i 0.339108 + 0.587353i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 10.5961 6.11764i 0.660965 0.381608i −0.131680 0.991292i \(-0.542037\pi\)
0.792644 + 0.609684i \(0.208704\pi\)
\(258\) 0 0
\(259\) 12.1527 20.9101i 0.755132 1.29929i
\(260\) 3.35360i 0.207982i
\(261\) 0 0
\(262\) −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 \(0.869167\pi\)
\(264\) 0 0
\(265\) 21.4516i 1.31776i
\(266\) 0.0468197 16.2925i 0.00287070 0.998960i
\(267\) 0 0
\(268\) −4.61347 7.99077i −0.281813 0.488114i
\(269\) −19.1299 11.0447i −1.16637 0.673405i −0.213549 0.976932i \(-0.568502\pi\)
−0.952823 + 0.303527i \(0.901836\pi\)
\(270\) 0 0
\(271\) −0.610555 1.05751i −0.0370886 0.0642393i 0.846885 0.531776i \(-0.178475\pi\)
−0.883974 + 0.467536i \(0.845142\pi\)
\(272\) 3.21565 0.194977
\(273\) 0 0
\(274\) 9.66602i 0.583946i
\(275\) −1.31371 + 0.428200i −0.0792196 + 0.0258215i
\(276\) 0 0
\(277\) −10.8330 6.25443i −0.650891 0.375792i 0.137906 0.990445i \(-0.455963\pi\)
−0.788798 + 0.614653i \(0.789296\pi\)
\(278\) 20.2386 11.6848i 1.21383 0.700805i
\(279\) 0 0
\(280\) −3.09412 + 5.32378i −0.184909 + 0.318157i
\(281\) 25.3495i 1.51222i −0.654443 0.756111i \(-0.727097\pi\)
0.654443 0.756111i \(-0.272903\pi\)
\(282\) 0 0
\(283\) 1.38222 2.39408i 0.0821646 0.142313i −0.822015 0.569466i \(-0.807150\pi\)
0.904179 + 0.427153i \(0.140483\pi\)
\(284\) 1.62627 2.81677i 0.0965011 0.167145i
\(285\) 0 0
\(286\) 4.67557 + 0.989280i 0.276472 + 0.0584974i
\(287\) 4.49069 + 7.82997i 0.265077 + 0.462189i
\(288\) 0 0
\(289\) 3.32981 + 5.76740i 0.195871 + 0.339259i
\(290\) −6.58749 3.80329i −0.386831 0.223337i
\(291\) 0 0
\(292\) −2.50002 4.33016i −0.146303 0.253403i
\(293\) −9.03175 −0.527640 −0.263820 0.964572i \(-0.584983\pi\)
−0.263820 + 0.964572i \(0.584983\pi\)
\(294\) 0 0
\(295\) 1.23982 0.0721851
\(296\) 7.91644 4.57056i 0.460134 0.265658i
\(297\) 0 0
\(298\) −7.52705 + 13.0372i −0.436030 + 0.755226i
\(299\) 4.53387 + 7.85289i 0.262200 + 0.454144i
\(300\) 0 0
\(301\) 4.34338 2.49104i 0.250348 0.143581i
\(302\) −12.9911 −0.747552
\(303\) 0 0
\(304\) 3.07901 5.33301i 0.176594 0.305869i
\(305\) 0.942123 + 0.543935i 0.0539458 + 0.0311456i
\(306\) 0 0
\(307\) −3.52291 −0.201063 −0.100531 0.994934i \(-0.532054\pi\)
−0.100531 + 0.994934i \(0.532054\pi\)
\(308\) −6.50964 5.88426i −0.370921 0.335287i
\(309\) 0 0
\(310\) −6.23016 + 3.59698i −0.353849 + 0.204295i
\(311\) −4.83852 2.79352i −0.274367 0.158406i 0.356503 0.934294i \(-0.383969\pi\)
−0.630871 + 0.775888i \(0.717302\pi\)
\(312\) 0 0
\(313\) 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 0
\(316\) 8.32842i 0.468510i
\(317\) 15.8432 + 27.4412i 0.889843 + 1.54125i 0.840060 + 0.542493i \(0.182520\pi\)
0.0497829 + 0.998760i \(0.484147\pi\)
\(318\) 0 0
\(319\) 7.24576 8.06229i 0.405685 0.451402i
\(320\) −2.01555 + 1.16368i −0.112673 + 0.0650517i
\(321\) 0 0
\(322\) 0.0478451 16.6494i 0.00266630 0.927833i
\(323\) −19.8020 −1.10181
\(324\) 0 0
\(325\) 0.300155 0.519884i 0.0166496 0.0288380i
\(326\) −7.19989 4.15686i −0.398765 0.230227i
\(327\) 0 0
\(328\) 3.41163i 0.188376i
\(329\) 24.3598 + 14.1577i 1.34300 + 0.780537i
\(330\) 0 0
\(331\) 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
\(333\) 0 0
\(334\) 13.4527 7.76692i 0.736099 0.424987i
\(335\) 21.4744i 1.17327i
\(336\) 0 0
\(337\) 20.0534i 1.09238i 0.837662 + 0.546189i \(0.183922\pi\)
−0.837662 + 0.546189i \(0.816078\pi\)
\(338\) 9.46018 5.46184i 0.514566 0.297085i
\(339\) 0 0
\(340\) 6.48131 + 3.74198i 0.351498 + 0.202938i
\(341\) −3.17705 9.74711i −0.172047 0.527836i
\(342\) 0 0
\(343\) −18.5196 0.159662i −0.999963 0.00862094i
\(344\) 1.89247 0.102035
\(345\) 0 0
\(346\) 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 \(0.944197\pi\)
\(348\) 0 0
\(349\) −15.3941 −0.824027 −0.412014 0.911178i \(-0.635174\pi\)
−0.412014 + 0.911178i \(0.635174\pi\)
\(350\) −0.956149 + 0.548375i −0.0511083 + 0.0293119i
\(351\) 0 0
\(352\) −1.02783 3.15334i −0.0547833 0.168074i
\(353\) −4.80016 2.77137i −0.255487 0.147505i 0.366787 0.930305i \(-0.380458\pi\)
−0.622274 + 0.782800i \(0.713791\pi\)
\(354\) 0 0
\(355\) 6.55565 3.78491i 0.347938 0.200882i
\(356\) 4.38104i 0.232195i
\(357\) 0 0
\(358\) 18.8708i 0.997351i
\(359\) 17.9527 10.3650i 0.947508 0.547044i 0.0552018 0.998475i \(-0.482420\pi\)
0.892306 + 0.451431i \(0.149086\pi\)
\(360\) 0 0
\(361\) −9.46065 + 16.3863i −0.497929 + 0.862439i
\(362\) 1.97224 + 3.41602i 0.103659 + 0.179542i
\(363\) 0 0
\(364\) 3.81237 + 0.0109556i 0.199823 + 0.000574228i
\(365\) 11.6369i 0.609103i
\(366\) 0 0
\(367\) −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
\(369\) 0 0
\(370\) 21.2747 1.10602
\(371\) −24.3861 0.0700781i −1.26606 0.00363827i
\(372\) 0 0
\(373\) −21.2225 + 12.2528i −1.09886 + 0.634427i −0.935921 0.352210i \(-0.885430\pi\)
−0.162938 + 0.986636i \(0.552097\pi\)
\(374\) −7.12897 + 7.93234i −0.368630 + 0.410171i
\(375\) 0 0
\(376\) 5.32461 + 9.22249i 0.274596 + 0.475614i
\(377\) 4.70949i 0.242551i
\(378\) 0 0
\(379\) −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
\(381\) 0 0
\(382\) −20.3722 11.7619i −1.04233 0.601791i
\(383\) 28.2806 16.3278i 1.44507 0.834312i 0.446889 0.894590i \(-0.352532\pi\)
0.998182 + 0.0602779i \(0.0191987\pi\)
\(384\) 0 0
\(385\) −6.27313 19.4352i −0.319708 0.990509i
\(386\) −20.7965 −1.05852
\(387\) 0 0
\(388\) 15.4175 + 8.90130i 0.782705 + 0.451895i
\(389\) 9.28386 16.0801i 0.470711 0.815295i −0.528728 0.848791i \(-0.677331\pi\)
0.999439 + 0.0334965i \(0.0106643\pi\)
\(390\) 0 0
\(391\) −20.2357 −1.02336
\(392\) −6.04196 3.53478i −0.305165 0.178534i
\(393\) 0 0
\(394\) 10.6837 + 18.5048i 0.538239 + 0.932258i
\(395\) 9.69162 16.7864i 0.487639 0.844615i
\(396\) 0 0
\(397\) −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
\(399\) 0 0
\(400\) −0.416608 −0.0208304
\(401\) −5.17676 8.96641i −0.258515 0.447761i 0.707329 0.706884i \(-0.249900\pi\)
−0.965844 + 0.259123i \(0.916566\pi\)
\(402\) 0 0
\(403\) 3.85730 + 2.22701i 0.192146 + 0.110935i
\(404\) 5.34857 + 9.26399i 0.266101 + 0.460901i
\(405\) 0 0
\(406\) 4.34509 7.47622i 0.215643 0.371039i
\(407\) −6.27582 + 29.6610i −0.311081 + 1.47024i
\(408\) 0 0
\(409\) −10.4458 + 18.0927i −0.516512 + 0.894625i 0.483304 + 0.875452i \(0.339436\pi\)
−0.999816 + 0.0191723i \(0.993897\pi\)
\(410\) −3.97005 + 6.87633i −0.196067 + 0.339598i
\(411\) 0 0
\(412\) 13.6074i 0.670388i
\(413\) −0.00405025 + 1.40943i −0.000199300 + 0.0693533i
\(414\) 0 0
\(415\) 9.19355 5.30790i 0.451293 0.260554i
\(416\) 1.24790 + 0.720474i 0.0611832 + 0.0353241i
\(417\) 0 0
\(418\) 6.32938 + 19.4184i 0.309580 + 0.949784i
\(419\) 7.59471i 0.371026i −0.982642 0.185513i \(-0.940605\pi\)
0.982642 0.185513i \(-0.0593946\pi\)
\(420\) 0 0
\(421\) −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
\(423\) 0 0
\(424\) −7.98226 4.60856i −0.387653 0.223812i
\(425\) 0.669832 + 1.16018i 0.0324916 + 0.0562771i
\(426\) 0 0
\(427\) −0.621422 + 1.06923i −0.0300727 + 0.0517435i
\(428\) 9.39572i 0.454159i
\(429\) 0 0
\(430\) 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 0
\(433\) 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
\(435\) 0 0
\(436\) −6.18076 + 3.56846i −0.296005 + 0.170898i
\(437\) −19.3759 + 33.5601i −0.926876 + 1.60540i
\(438\) 0 0
\(439\) −15.5488 26.9314i −0.742105 1.28536i −0.951535 0.307541i \(-0.900494\pi\)
0.209429 0.977824i \(-0.432839\pi\)
\(440\) 1.59785 7.55179i 0.0761743 0.360018i
\(441\) 0 0
\(442\) 4.63358i 0.220397i
\(443\) −2.50430 4.33757i −0.118983 0.206084i 0.800382 0.599490i \(-0.204630\pi\)
−0.919365 + 0.393406i \(0.871297\pi\)
\(444\) 0 0
\(445\) 5.09813 8.83022i 0.241675 0.418593i
\(446\) 11.6902 + 20.2480i 0.553548 + 0.958773i
\(447\) 0 0
\(448\) −1.31629 2.29508i −0.0621887 0.108432i
\(449\) −24.8715 −1.17376 −0.586880 0.809674i \(-0.699644\pi\)
−0.586880 + 0.809674i \(0.699644\pi\)
\(450\) 0 0
\(451\) −8.41580 7.56347i −0.396285 0.356150i
\(452\) 1.57550 2.72884i 0.0741052 0.128354i
\(453\) 0 0
\(454\) 13.9483i 0.654625i
\(455\) 7.67129 + 4.45846i 0.359636 + 0.209016i
\(456\) 0 0
\(457\) 6.59453 3.80735i 0.308479 0.178100i −0.337767 0.941230i \(-0.609671\pi\)
0.646246 + 0.763129i \(0.276338\pi\)
\(458\) 7.50744 13.0033i 0.350800 0.607603i
\(459\) 0 0
\(460\) 12.6837 7.32292i 0.591379 0.341433i
\(461\) 8.56061 0.398707 0.199354 0.979928i \(-0.436116\pi\)
0.199354 + 0.979928i \(0.436116\pi\)
\(462\) 0 0
\(463\) −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
\(465\) 0 0
\(466\) 8.22109 14.2393i 0.380835 0.659625i
\(467\) 7.84052 4.52673i 0.362816 0.209472i −0.307499 0.951548i \(-0.599492\pi\)
0.670315 + 0.742076i \(0.266159\pi\)
\(468\) 0 0
\(469\) 24.4121 + 0.0701528i 1.12725 + 0.00323935i
\(470\) 24.7846i 1.14323i
\(471\) 0 0
\(472\) −0.266358 + 0.461345i −0.0122601 + 0.0212351i
\(473\) −4.19554 + 4.66834i −0.192911 + 0.214651i
\(474\) 0 0
\(475\) 2.56548 0.117712
\(476\) −4.27506 + 7.35572i −0.195947 + 0.337149i
\(477\) 0 0
\(478\) 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 \(-0.0858507\pi\)
\(480\) 0 0
\(481\) −6.58593 11.4072i −0.300293 0.520122i
\(482\) 22.2195i 1.01207i
\(483\) 0 0
\(484\) 10.0573 + 4.45541i 0.457150 + 0.202519i
\(485\) 20.7165 + 35.8821i 0.940689 + 1.62932i
\(486\) 0 0
\(487\) −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
\(489\) 0 0
\(490\) −8.06454 14.1555i −0.364319 0.639478i
\(491\) 26.7561i 1.20749i 0.797179 + 0.603744i \(0.206325\pi\)
−0.797179 + 0.603744i \(0.793675\pi\)
\(492\) 0 0
\(493\) −9.10174 5.25489i −0.409922 0.236668i
\(494\) −7.68458 4.43670i −0.345746 0.199616i
\(495\) 0 0
\(496\) 3.09104i 0.138792i
\(497\) 4.28126 + 7.46482i 0.192041 + 0.334843i
\(498\) 0 0
\(499\) −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
\(501\) 0 0
\(502\) −2.36708 4.09990i −0.105648 0.182987i
\(503\) −16.3197 −0.727660 −0.363830 0.931465i \(-0.618531\pi\)
−0.363830 + 0.931465i \(0.618531\pi\)
\(504\) 0 0
\(505\) 24.8961i 1.10786i
\(506\) 6.46800 + 19.8437i 0.287538 + 0.882159i
\(507\) 0 0
\(508\) −9.36086 5.40449i −0.415321 0.239786i
\(509\) −3.92989 + 2.26892i −0.174189 + 0.100568i −0.584560 0.811351i \(-0.698733\pi\)
0.410370 + 0.911919i \(0.365399\pi\)
\(510\) 0 0
\(511\) 13.2288 + 0.0380155i 0.585208 + 0.00168171i
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) −6.11764 + 10.5961i −0.269838 + 0.467373i
\(515\) 15.8347 27.4264i 0.697758 1.20855i
\(516\) 0 0
\(517\) −34.5545 7.31121i −1.51970 0.321546i
\(518\) −0.0695002 + 24.1850i −0.00305366 + 1.06263i
\(519\) 0 0
\(520\) 1.67680 + 2.90431i 0.0735326 + 0.127362i
\(521\) 0.675518 + 0.390011i 0.0295950 + 0.0170867i 0.514725 0.857356i \(-0.327894\pi\)
−0.485130 + 0.874442i \(0.661228\pi\)
\(522\) 0 0
\(523\) −5.88383 10.1911i −0.257282 0.445626i 0.708231 0.705981i \(-0.249494\pi\)
−0.965513 + 0.260355i \(0.916160\pi\)
\(524\) 10.9712 0.479278
\(525\) 0 0
\(526\) 19.2700 0.840214
\(527\) −8.60803 + 4.96985i −0.374972 + 0.216490i
\(528\) 0 0
\(529\) −8.30028 + 14.3765i −0.360882 + 0.625065i
\(530\) −10.7258 18.5776i −0.465898 0.806959i
\(531\) 0 0
\(532\) 8.10572 + 14.1332i 0.351428 + 0.612750i
\(533\) 4.91598 0.212935
\(534\) 0 0
\(535\) −10.9336 + 18.9376i −0.472702 + 0.818743i
\(536\) 7.99077 + 4.61347i 0.345149 + 0.199272i
\(537\) 0 0
\(538\) 22.0893 0.952338
\(539\) 22.1144 7.06780i 0.952534 0.304432i
\(540\) 0 0
\(541\) 9.27327 5.35393i 0.398689 0.230183i −0.287229 0.957862i \(-0.592734\pi\)
0.685918 + 0.727679i \(0.259401\pi\)
\(542\) 1.05751 + 0.610555i 0.0454240 + 0.0262256i
\(543\) 0 0
\(544\) −2.78483 + 1.60782i −0.119399 + 0.0689348i
\(545\) −16.6102 −0.711503
\(546\) 0 0
\(547\) 19.5154i 0.834419i −0.908810 0.417210i \(-0.863008\pi\)
0.908810 0.417210i \(-0.136992\pi\)
\(548\) −4.83301 8.37102i −0.206456 0.357592i
\(549\) 0 0
\(550\) 0.923604 1.02769i 0.0393826 0.0438207i
\(551\) −17.4300 + 10.0632i −0.742544 + 0.428708i
\(552\) 0 0
\(553\) 19.0511 + 11.0723i 0.810134 + 0.470841i
\(554\) 12.5089 0.531450
\(555\) 0 0
\(556\) −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 \(0.707681\pi\)
\(558\) 0 0
\(559\) 2.72695i 0.115338i
\(560\) 0.0176950 6.15759i 0.000747751 0.260206i
\(561\) 0 0
\(562\) 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 \(0.168306\pi\)
\(564\) 0 0
\(565\) 6.35100 3.66675i 0.267189 0.154262i
\(566\) 2.76444i 0.116198i
\(567\) 0 0
\(568\) 3.25253i 0.136473i
\(569\) 7.44979 4.30114i 0.312311 0.180313i −0.335649 0.941987i \(-0.608956\pi\)
0.647960 + 0.761674i \(0.275622\pi\)
\(570\) 0 0
\(571\) 26.9418 + 15.5548i 1.12748 + 0.650950i 0.943299 0.331943i \(-0.107704\pi\)
0.184178 + 0.982893i \(0.441038\pi\)
\(572\) −4.54380 + 1.48104i −0.189986 + 0.0619255i
\(573\) 0 0
\(574\) −7.80403 4.53561i −0.325734 0.189313i
\(575\) 2.62167 0.109331
\(576\) 0 0
\(577\) −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
\(579\) 0 0
\(580\) 7.60657 0.315846
\(581\) 6.00398 + 10.4686i 0.249087 + 0.434309i
\(582\) 0 0
\(583\) 29.0648 9.47359i 1.20374 0.392356i
\(584\) 4.33016 + 2.50002i 0.179183 + 0.103451i
\(585\) 0 0
\(586\) 7.82172 4.51587i 0.323112 0.186549i
\(587\) 33.6048i 1.38702i −0.720449 0.693508i \(-0.756064\pi\)
0.720449 0.693508i \(-0.243936\pi\)
\(588\) 0 0
\(589\) 19.0347i 0.784312i
\(590\) −1.07372 + 0.619910i −0.0442042 + 0.0255213i
\(591\) 0 0
\(592\) −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 0
\(595\) −17.1763 + 9.85104i −0.704160 + 0.403853i
\(596\) 15.0541i 0.616640i
\(597\) 0 0
\(598\) −7.85289 4.53387i −0.321128 0.185404i
\(599\) 12.4072 21.4899i 0.506945 0.878055i −0.493022 0.870017i \(-0.664108\pi\)
0.999968 0.00803859i \(-0.00255879\pi\)
\(600\) 0 0
\(601\) 17.8950 0.729952 0.364976 0.931017i \(-0.381077\pi\)
0.364976 + 0.931017i \(0.381077\pi\)
\(602\) −2.51596 + 4.32899i −0.102543 + 0.176436i
\(603\) 0 0
\(604\) 11.2506 6.49554i 0.457780 0.264300i
\(605\) 15.0864 + 20.6836i 0.613348 + 0.840908i
\(606\) 0 0
\(607\) 16.4712 + 28.5290i 0.668546 + 1.15796i 0.978311 + 0.207142i \(0.0664162\pi\)
−0.309765 + 0.950813i \(0.600250\pi\)
\(608\) 6.15803i 0.249741i
\(609\) 0 0
\(610\) −1.08787 −0.0440466
\(611\) 13.2891 7.67248i 0.537620 0.310395i
\(612\) 0 0
\(613\) 7.51244 + 4.33731i 0.303425 + 0.175182i 0.643980 0.765042i \(-0.277282\pi\)
−0.340556 + 0.940224i \(0.610615\pi\)
\(614\) 3.05093 1.76145i 0.123125 0.0710865i
\(615\) 0 0
\(616\) 8.57965 + 1.84110i 0.345684 + 0.0741800i
\(617\) −32.6421 −1.31412 −0.657061 0.753837i \(-0.728201\pi\)
−0.657061 + 0.753837i \(0.728201\pi\)
\(618\) 0 0
\(619\) −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
\(621\) 0 0
\(622\) 5.58704 0.224020
\(623\) 10.0215 + 5.82439i 0.401504 + 0.233349i
\(624\) 0 0
\(625\) 13.4547 + 23.3043i 0.538190 + 0.932172i
\(626\) −2.63952 + 4.57178i −0.105496 + 0.182725i
\(627\) 0 0
\(628\) −9.98402 + 5.76428i −0.398406 + 0.230020i
\(629\) 29.3946 1.17204
\(630\) 0 0
\(631\) 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
\(633\) 0 0
\(634\) −27.4412 15.8432i −1.08983 0.629214i
\(635\) −12.5782 21.7861i −0.499151 0.864555i
\(636\) 0 0
\(637\) −5.09344 + 8.70615i −0.201809 + 0.344950i
\(638\) −2.24387 + 10.6050i −0.0888355 + 0.419857i
\(639\) 0 0
\(640\) 1.16368 2.01555i 0.0459985 0.0796717i
\(641\) 11.9591 20.7137i 0.472354 0.818142i −0.527145 0.849775i \(-0.676738\pi\)
0.999500 + 0.0316335i \(0.0100709\pi\)
\(642\) 0 0
\(643\) 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
\(645\) 0 0
\(646\) 17.1491 9.90102i 0.674721 0.389550i
\(647\) −22.5941 13.0447i −0.888267 0.512841i −0.0148918 0.999889i \(-0.504740\pi\)
−0.873375 + 0.487048i \(0.838074\pi\)
\(648\) 0 0
\(649\) −0.547538 1.67983i −0.0214928 0.0659392i
\(650\) 0.600310i 0.0235461i
\(651\) 0 0
\(652\) 8.31371 0.325590
\(653\) −10.8589 18.8082i −0.424942 0.736020i 0.571473 0.820621i \(-0.306372\pi\)
−0.996415 + 0.0846002i \(0.973039\pi\)
\(654\) 0 0
\(655\) 22.1130 + 12.7669i 0.864026 + 0.498846i
\(656\) −1.70582 2.95456i −0.0666010 0.115356i
\(657\) 0 0
\(658\) −28.1751 0.0809664i −1.09838 0.00315640i
\(659\) 12.7596i 0.497044i 0.968626 + 0.248522i \(0.0799448\pi\)
−0.968626 + 0.248522i \(0.920055\pi\)
\(660\) 0 0
\(661\) −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
\(663\) 0 0
\(664\) 4.56130i 0.177013i
\(665\) −0.108966 + 37.9186i −0.00422553 + 1.47042i
\(666\) 0 0
\(667\) −17.8118 + 10.2836i −0.689674 + 0.398183i
\(668\) −7.76692 + 13.4527i −0.300511 + 0.520500i
\(669\) 0 0
\(670\) 10.7372 + 18.5974i 0.414815 + 0.718480i
\(671\) 0.320911 1.51670i 0.0123886 0.0585516i
\(672\) 0 0
\(673\) 10.4212i 0.401709i −0.979621 0.200854i \(-0.935628\pi\)
0.979621 0.200854i \(-0.0643718\pi\)
\(674\) −10.0267 17.3668i −0.386214 0.668942i
\(675\) 0 0
\(676\) −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 \(0.744814\pi\)
\(678\) 0 0
\(679\) −40.8584 + 23.4333i −1.56800 + 0.899287i
\(680\) −7.48397 −0.286997
\(681\) 0 0
\(682\) 7.62496 + 6.85272i 0.291975 + 0.262404i
\(683\) −17.3671 + 30.0806i −0.664532 + 1.15100i 0.314880 + 0.949132i \(0.398036\pi\)
−0.979412 + 0.201872i \(0.935297\pi\)
\(684\) 0 0
\(685\) 22.4963i 0.859540i
\(686\) 16.1182 9.12151i 0.615398 0.348261i
\(687\) 0 0
\(688\) −1.63893 + 0.946236i −0.0624836 + 0.0360749i
\(689\) −6.64069 + 11.5020i −0.252990 + 0.438192i
\(690\) 0 0
\(691\) 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
\(693\) 0 0
\(694\) 28.5210 1.08264
\(695\) −47.1025 + 27.1946i −1.78670 + 1.03155i
\(696\) 0 0
\(697\) −5.48530 + 9.50082i −0.207771 + 0.359869i
\(698\) 13.3317 7.69705i 0.504612 0.291338i
\(699\) 0 0
\(700\) 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 0
\(703\) 28.1456 48.7496i 1.06153 1.83863i
\(704\) 2.46679 + 2.21696i 0.0929708 + 0.0835549i
\(705\) 0 0
\(706\) 5.54275 0.208604
\(707\) −28.3019 0.0813307i −1.06440 0.00305876i
\(708\) 0 0
\(709\) 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
\(711\) 0 0
\(712\) 2.19052 + 3.79409i 0.0820932 + 0.142190i
\(713\) 19.4516i 0.728468i
\(714\) 0 0
\(715\) −10.8817 2.30241i −0.406954 0.0861053i
\(716\) 9.43539 + 16.3426i 0.352617 + 0.610750i
\(717\) 0 0
\(718\) −10.3650 + 17.9527i −0.386818 + 0.669989i
\(719\) 27.2393 15.7266i 1.01585 0.586503i 0.102953 0.994686i \(-0.467171\pi\)
0.912900 + 0.408183i \(0.133837\pi\)
\(720\) 0 0
\(721\) 31.1266 + 18.0904i 1.15922 + 0.673722i
\(722\) 18.9213i 0.704178i
\(723\) 0 0
\(724\) −3.41602 1.97224i −0.126955 0.0732977i
\(725\) 1.17919 + 0.680805i 0.0437940 + 0.0252845i
\(726\) 0 0
\(727\) 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
\(729\) 0 0
\(730\) 5.81844 + 10.0778i 0.215350 + 0.372998i
\(731\) 5.27022 + 3.04276i 0.194926 + 0.112541i
\(732\) 0 0
\(733\) −3.99023 6.91128i −0.147382 0.255274i 0.782877 0.622177i \(-0.213751\pi\)
−0.930259 + 0.366903i \(0.880418\pi\)
\(734\) 35.0890 1.29516
\(735\) 0 0
\(736\) 6.29290i 0.231959i
\(737\) −29.0957 + 9.48369i −1.07175 + 0.349336i
\(738\) 0 0
\(739\) 38.2867 + 22.1048i 1.40840 + 0.813140i 0.995234 0.0975161i \(-0.0310898\pi\)
0.413166 + 0.910656i \(0.364423\pi\)
\(740\) −18.4244 + 10.6373i −0.677295 + 0.391036i
\(741\) 0 0
\(742\) 21.1540 12.1324i 0.776589 0.445393i
\(743\) 17.1346i 0.628607i 0.949323 + 0.314304i \(0.101771\pi\)
−0.949323 + 0.314304i \(0.898229\pi\)
\(744\) 0 0
\(745\) 17.5182 30.3423i 0.641815 1.11166i
\(746\) 12.2528 21.2225i 0.448607 0.777011i
\(747\) 0 0
\(748\) 2.20770 10.4341i 0.0807214 0.381508i
\(749\) −21.4925 12.4912i −0.785319 0.456418i
\(750\) 0 0
\(751\) 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
\(753\) 0 0
\(754\) −2.35474 4.07853i −0.0857547 0.148531i
\(755\) 30.2349 1.10036
\(756\) 0 0
\(757\) −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
\(759\) 0 0
\(760\) −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 \(-0.475426\pi\)
\(762\) 0 0
\(763\) 0.0542623 18.8825i 0.00196443 0.683591i
\(764\) 23.5238 0.851062
\(765\) 0 0
\(766\) −16.3278 + 28.2806i −0.589947 + 1.02182i
\(767\) 0.664773 + 0.383807i 0.0240036 + 0.0138585i
\(768\) 0 0
\(769\) −2.76998 −0.0998881 −0.0499440 0.998752i \(-0.515904\pi\)
−0.0499440 + 0.998752i \(0.515904\pi\)
\(770\) 15.1503 + 13.6948i 0.545978 + 0.493526i
\(771\) 0 0
\(772\) 18.0103 10.3983i 0.648206 0.374242i
\(773\) 9.93494 + 5.73594i 0.357335 + 0.206307i 0.667911 0.744241i \(-0.267189\pi\)
−0.310576 + 0.950548i \(0.600522\pi\)
\(774\) 0 0
\(775\) 1.11523 0.643876i 0.0400601 0.0231287i
\(776\) −17.8026 −0.639076
\(777\) 0 0
\(778\) 18.5677i 0.665685i
\(779\) 10.5045 + 18.1943i 0.376362 + 0.651877i
\(780\) 0 0
\(781\) −8.02332 7.21074i −0.287097 0.258021i
\(782\) 17.5247 10.1179i 0.626680 0.361814i
\(783\) 0 0
\(784\) 6.99988 + 0.0402313i 0.249996 + 0.00143683i
\(785\) −26.8311 −0.957643
\(786\) 0 0
\(787\) −14.7757 + 25.5923i −0.526698 + 0.912268i 0.472818 + 0.881160i \(0.343237\pi\)
−0.999516 + 0.0311080i \(0.990096\pi\)
\(788\) −18.5048 10.6837i −0.659206 0.380593i
\(789\) 0 0
\(790\) 19.3832i 0.689625i
\(791\) 4.14761 + 7.23179i 0.147472 + 0.257133i
\(792\) 0 0
\(793\) 0.336769 + 0.583300i 0.0119590 + 0.0207136i
\(794\) 2.79674 4.84409i 0.0992525 0.171910i
\(795\) 0 0
\(796\) 17.3579 10.0216i 0.615233 0.355205i
\(797\) 3.17035i 0.112300i 0.998422 + 0.0561498i \(0.0178824\pi\)
−0.998422 + 0.0561498i \(0.982118\pi\)
\(798\) 0 0
\(799\) 34.2441i 1.21147i
\(800\) 0.360793 0.208304i 0.0127560 0.00736466i
\(801\) 0 0
\(802\) 8.96641 + 5.17676i 0.316615 + 0.182798i
\(803\) −15.7668 + 5.13917i −0.556399 + 0.181357i
\(804\) 0 0
\(805\) −0.111353 + 38.7491i −0.00392467 + 1.36573i
\(806\) −4.45403 −0.156886
\(807\) 0 0
\(808\) −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 \(0.421285\pi\)
\(810\) 0 0
\(811\) 24.9006 0.874377 0.437188 0.899370i \(-0.355974\pi\)
0.437188 + 0.899370i \(0.355974\pi\)
\(812\) −0.0248492 + 8.64714i −0.000872036 + 0.303455i
\(813\) 0 0
\(814\) −9.39547 28.8251i −0.329311 1.01032i
\(815\) 16.7567 + 9.67451i 0.586963 + 0.338883i
\(816\) 0 0
\(817\) 10.0926 5.82695i 0.353094 0.203859i
\(818\) 20.8916i 0.730458i
\(819\) 0 0
\(820\) 7.94010i 0.277280i
\(821\) −11.6214 + 6.70962i −0.405590 + 0.234167i −0.688893 0.724863i \(-0.741903\pi\)
0.283303 + 0.959030i \(0.408570\pi\)
\(822\) 0 0
\(823\) 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
\(825\) 0 0
\(826\) −0.701205 1.22262i −0.0243981 0.0425405i
\(827\) 43.1986i 1.50216i 0.660209 + 0.751081i \(0.270467\pi\)
−0.660209 + 0.751081i \(0.729533\pi\)
\(828\) 0 0
\(829\) −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
\(831\) 0 0
\(832\) −1.44095 −0.0499559
\(833\) −11.1425 19.5582i −0.386066 0.677651i
\(834\) 0 0
\(835\) −31.3093 + 18.0764i −1.08350 + 0.625560i
\(836\) −15.1906 13.6521i −0.525378 0.472168i
\(837\) 0 0
\(838\) 3.79735 + 6.57721i 0.131177 + 0.227206i
\(839\) 25.5783i 0.883062i 0.897246 + 0.441531i \(0.145564\pi\)
−0.897246 + 0.441531i \(0.854436\pi\)
\(840\) 0 0
\(841\) 18.3180 0.631657
\(842\) 25.9254 14.9680i 0.893447 0.515832i
\(843\) 0 0
\(844\) 1.77233 + 1.02325i 0.0610060 + 0.0352219i
\(845\) −22.0172 + 12.7117i −0.757416 + 0.437294i
\(846\) 0 0
\(847\) −23.5624 + 17.0826i −0.809613 + 0.586964i
\(848\) 9.21712 0.316517
\(849\) 0 0
\(850\) −1.16018 0.669832i −0.0397939 0.0229750i
\(851\) 28.7620 49.8173i 0.985950 1.70772i
\(852\) 0 0
\(853\) 26.6616 0.912877 0.456439 0.889755i \(-0.349125\pi\)
0.456439 + 0.889755i \(0.349125\pi\)
\(854\) 0.00355386 1.23669i 0.000121611 0.0423186i
\(855\) 0 0
\(856\) −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 \(-0.0295834\pi\)
\(858\) 0 0
\(859\) −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 0
\(862\) −33.3538 −1.13603
\(863\) 7.56384 + 13.1010i 0.257476 + 0.445962i 0.965565 0.260161i \(-0.0837758\pi\)
−0.708089 + 0.706123i \(0.750442\pi\)
\(864\) 0 0
\(865\) −26.6150 15.3662i −0.904936 0.522465i
\(866\) 13.8918 + 24.0614i 0.472064 + 0.817639i
\(867\) 0 0
\(868\) 7.07068 + 4.10940i 0.239995 + 0.139482i
\(869\) −27.0240 5.71787i −0.916726 0.193965i
\(870\) 0 0
\(871\) 6.64777 11.5143i 0.225251 0.390146i
\(872\) 3.56846 6.18076i 0.120843 0.209307i
\(873\) 0 0
\(874\) 38.7518i 1.31080i
\(875\) −24.4821 + 14.0411i −0.827646 + 0.474676i
\(876\) 0 0
\(877\) 8.64012 4.98837i 0.291756 0.168445i −0.346977 0.937873i \(-0.612792\pi\)
0.638733 + 0.769428i \(0.279459\pi\)
\(878\) 26.9314 + 15.5488i 0.908890 + 0.524748i
\(879\) 0 0
\(880\) 2.39212 + 7.33897i 0.0806384 + 0.247397i
\(881\) 3.10955i 0.104763i −0.998627 0.0523816i \(-0.983319\pi\)
0.998627 0.0523816i \(-0.0166812\pi\)
\(882\) 0 0
\(883\) 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
\(885\) 0 0
\(886\) 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 \(0.907298\pi\)
\(888\) 0 0
\(889\) 24.8075 14.2277i 0.832017 0.477182i
\(890\) 10.1963i 0.341779i
\(891\) 0 0
\(892\) −20.2480 11.6902i −0.677955 0.391417i
\(893\) 56.7924 + 32.7891i 1.90048 + 1.09724i
\(894\) 0 0
\(895\) 43.9191i 1.46805i
\(896\) 2.28748 + 1.32945i 0.0764192 + 0.0444140i
\(897\) 0 0
\(898\) 21.5394 12.4358i 0.718778 0.414987i
\(899\) −5.05127 + 8.74905i −0.168469 + 0.291797i
\(900\) 0 0
\(901\) −14.8195 25.6681i −0.493709 0.855129i
\(902\) 11.0700 + 2.34225i 0.368592 + 0.0779885i
\(903\) 0 0
\(904\) 3.15100i 0.104801i
\(905\) −4.59012 7.95031i −0.152581 0.264277i
\(906\) 0 0
\(907\) 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
\(909\) 0 0
\(910\) −8.87277 0.0254976i −0.294129 0.000845236i
\(911\) 26.6937 0.884401 0.442200 0.896916i \(-0.354198\pi\)
0.442200 + 0.896916i \(0.354198\pi\)
\(912\) 0 0
\(913\) −11.2518 10.1122i −0.372380 0.334666i
\(914\) −3.80735 + 6.59453i −0.125936 + 0.218128i
\(915\) 0 0
\(916\) 15.0149i 0.496106i
\(917\) −14.5857 + 25.0963i −0.481661 + 0.828753i
\(918\) 0 0
\(919\) −39.8952 + 23.0335i −1.31602 + 0.759806i −0.983086 0.183144i \(-0.941373\pi\)
−0.332936 + 0.942949i \(0.608039\pi\)
\(920\) −7.32292 + 12.6837i −0.241430 + 0.418168i
\(921\) 0 0
\(922\) −7.41371 + 4.28031i −0.244157 + 0.140964i
\(923\) 4.68672 0.154265
\(924\) 0 0
\(925\) −3.80826 −0.125215
\(926\) 2.48741 1.43611i 0.0817413 0.0471933i
\(927\) 0 0
\(928\) −1.63416 + 2.83045i −0.0536440 + 0.0929142i
\(929\) −10.5117 + 6.06892i −0.344877 + 0.199115i −0.662427 0.749127i \(-0.730473\pi\)
0.317550 + 0.948242i \(0.397140\pi\)
\(930\) 0 0
\(931\) −43.1055 0.247746i −1.41273 0.00811953i
\(932\) 16.4422i 0.538581i
\(933\) 0 0
\(934\) −4.52673 + 7.84052i −0.148119 + 0.256550i
\(935\) 16.5917 18.4614i 0.542606 0.603753i
\(936\) 0 0
\(937\) −43.9719 −1.43650 −0.718250 0.695786i \(-0.755056\pi\)
−0.718250 + 0.695786i \(0.755056\pi\)
\(938\) −21.1766 + 12.1453i −0.691439 + 0.396558i
\(939\) 0 0
\(940\) −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 \(0.929138\pi\)
\(942\) 0 0
\(943\) 10.7345 + 18.5928i 0.349564 + 0.605463i
\(944\) 0.532715i 0.0173384i
\(945\) 0 0
\(946\) 1.29927 6.14067i 0.0422431 0.199651i
\(947\) −9.94370 17.2230i −0.323127 0.559672i 0.658005 0.753014i \(-0.271401\pi\)
−0.981131 + 0.193342i \(0.938067\pi\)
\(948\) 0 0
\(949\) 3.60239 6.23953i 0.116939 0.202544i
\(950\) −2.22177 + 1.28274i −0.0720839 + 0.0416176i
\(951\) 0 0
\(952\) 0.0244487 8.50776i 0.000792386 0.275738i
\(953\) 42.1430i 1.36514i 0.730818 + 0.682572i \(0.239139\pi\)
−0.730818 + 0.682572i \(0.760861\pi\)
\(954\) 0 0
\(955\) 47.4135 + 27.3742i 1.53426 + 0.885808i
\(956\) −21.4731 12.3975i −0.694491 0.400965i
\(957\) 0 0
\(958\) 31.1954i 1.00788i
\(959\) 25.5738 + 0.0734911i 0.825821 + 0.00237315i
\(960\) 0 0
\(961\) −10.7227 18.5723i −0.345895 0.599107i
\(962\) 11.4072 + 6.58593i 0.367782 + 0.212339i
\(963\) 0 0
\(964\) −11.1098 19.2427i −0.357822 0.619765i
\(965\) 48.4010 1.55808
\(966\) 0 0
\(967\) 32.5204i 1.04578i −0.852399 0.522892i \(-0.824853\pi\)
0.852399 0.522892i \(-0.175147\pi\)
\(968\) −10.9376 + 1.17015i −0.351547 + 0.0376101i
\(969\) 0 0
\(970\) −35.8821 20.7165i −1.15210 0.665168i
\(971\) 35.8435 20.6943i 1.15027 0.664111i 0.201319 0.979526i \(-0.435477\pi\)
0.948954 + 0.315415i \(0.102144\pi\)
\(972\) 0 0
\(973\) −30.7610 53.6349i −0.986151 1.71946i
\(974\) 36.0737i 1.15587i
\(975\) 0 0
\(976\) 0.233713 0.404803i 0.00748098 0.0129574i
\(977\) 7.05105 12.2128i 0.225583 0.390721i −0.730911 0.682473i \(-0.760905\pi\)
0.956494 + 0.291751i \(0.0942380\pi\)
\(978\) 0 0
\(979\) −14.2155 3.00780i −0.454331 0.0961296i
\(980\) 14.0618 + 8.22672i 0.449189 + 0.262793i
\(981\) 0 0
\(982\) −13.3781 23.1715i −0.426911 0.739432i
\(983\) −38.2844 22.1035i −1.22108 0.704992i −0.255933 0.966695i \(-0.582383\pi\)
−0.965149 + 0.261703i \(0.915716\pi\)
\(984\) 0 0
\(985\) −24.8649 43.0673i −0.792263 1.37224i
\(986\) 10.5098 0.334700
\(987\) 0 0
\(988\) 8.87339 0.282300
\(989\) 10.3136 5.95457i 0.327954 0.189344i
\(990\) 0 0
\(991\) −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
\(993\) 0 0
\(994\) −7.44009 4.32409i −0.235985 0.137152i
\(995\) 46.6476 1.47883
\(996\) 0 0
\(997\) 24.1616 41.8491i 0.765205 1.32537i −0.174934 0.984580i \(-0.555971\pi\)
0.940138 0.340793i \(-0.110696\pi\)
\(998\) 24.3330 + 14.0487i 0.770249 + 0.444703i
\(999\) 0 0
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 1386.2.bk.b.703.4 16
3.2 odd 2 462.2.p.b.241.5 yes 16
7.5 odd 6 1386.2.bk.a.901.8 16
11.10 odd 2 1386.2.bk.a.703.8 16
21.5 even 6 462.2.p.a.439.1 yes 16
21.11 odd 6 3234.2.e.b.2155.10 16
21.17 even 6 3234.2.e.a.2155.15 16
33.32 even 2 462.2.p.a.241.1 16
77.54 even 6 inner 1386.2.bk.b.901.4 16
231.32 even 6 3234.2.e.a.2155.2 16
231.131 odd 6 462.2.p.b.439.5 yes 16
231.164 odd 6 3234.2.e.b.2155.7 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
462.2.p.a.241.1 16 33.32 even 2
462.2.p.a.439.1 yes 16 21.5 even 6
462.2.p.b.241.5 yes 16 3.2 odd 2
462.2.p.b.439.5 yes 16 231.131 odd 6
1386.2.bk.a.703.8 16 11.10 odd 2
1386.2.bk.a.901.8 16 7.5 odd 6
1386.2.bk.b.703.4 16 1.1 even 1 trivial
1386.2.bk.b.901.4 16 77.54 even 6 inner
3234.2.e.a.2155.2 16 231.32 even 6
3234.2.e.a.2155.15 16 21.17 even 6
3234.2.e.b.2155.7 16 231.164 odd 6
3234.2.e.b.2155.10 16 21.11 odd 6