Properties

Label 567.2.g.k.109.3
Level $567$
Weight $2$
Character 567.109
Analytic conductor $4.528$
Analytic rank $0$
Dimension $8$
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] = [567,2,Mod(109,567)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(567, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("567.109");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 567 = 3^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 567.g (of order \(3\), degree \(2\), not 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: \(4.52751779461\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: 8.0.1767277521.3
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 2x^{7} + x^{6} - 10x^{5} + 38x^{4} - 40x^{3} + 64x^{2} - 38x + 7 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 109.3
Root \(0.0512865 + 1.21608i\) of defining polynomial
Character \(\chi\) \(=\) 567.109
Dual form 567.2.g.k.541.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.768262 - 1.33067i) q^{2} +(-0.180452 - 0.312552i) q^{4} -3.15761 q^{5} +(-0.00900690 + 2.64574i) q^{7} +2.51851 q^{8} +O(q^{10})\) \(q+(0.768262 - 1.33067i) q^{2} +(-0.180452 - 0.312552i) q^{4} -3.15761 q^{5} +(-0.00900690 + 2.64574i) q^{7} +2.51851 q^{8} +(-2.42587 + 4.20173i) q^{10} +5.74916 q^{11} +(0.180452 - 0.312552i) q^{13} +(3.51368 + 2.04460i) q^{14} +(2.29578 - 3.97640i) q^{16} +(1.38842 - 2.40481i) q^{17} +(3.61533 + 6.26193i) q^{19} +(0.569796 + 0.986916i) q^{20} +(4.41686 - 7.65023i) q^{22} +0.824381 q^{23} +4.97047 q^{25} +(-0.277269 - 0.480243i) q^{26} +(0.828555 - 0.474613i) q^{28} +(-2.13910 - 3.70502i) q^{29} +(2.49099 + 4.31453i) q^{31} +(-1.00901 - 1.74765i) q^{32} +(-2.13334 - 3.69505i) q^{34} +(0.0284402 - 8.35419i) q^{35} +(-3.74542 - 6.48725i) q^{37} +11.1101 q^{38} -7.95246 q^{40} +(-1.66569 + 2.88506i) q^{41} +(3.93487 + 6.81540i) q^{43} +(-1.03745 - 1.79691i) q^{44} +(0.633340 - 1.09698i) q^{46} +(-1.74075 + 3.01506i) q^{47} +(-6.99984 - 0.0476598i) q^{49} +(3.81862 - 6.61405i) q^{50} -0.130252 q^{52} +(-1.45772 + 2.52485i) q^{53} -18.1536 q^{55} +(-0.0226840 + 6.66331i) q^{56} -6.57354 q^{58} +(1.19939 + 2.07740i) q^{59} +(-1.60056 + 2.77226i) q^{61} +7.65494 q^{62} +6.08239 q^{64} +(-0.569796 + 0.986916i) q^{65} +(-0.949637 - 1.64482i) q^{67} -1.00217 q^{68} +(-11.0948 - 6.45605i) q^{70} -1.60957 q^{71} +(7.70688 - 13.3487i) q^{73} -11.5098 q^{74} +(1.30478 - 2.25995i) q^{76} +(-0.0517821 + 15.2108i) q^{77} +(-2.73641 + 4.73960i) q^{79} +(-7.24916 + 12.5559i) q^{80} +(2.55937 + 4.43296i) q^{82} +(-6.51742 - 11.2885i) q^{83} +(-4.38408 + 7.59346i) q^{85} +12.0921 q^{86} +14.4793 q^{88} +(-7.13384 - 12.3562i) q^{89} +(0.825304 + 0.480243i) q^{91} +(-0.148761 - 0.257662i) q^{92} +(2.67470 + 4.63271i) q^{94} +(-11.4158 - 19.7727i) q^{95} +(-8.00266 - 13.8610i) q^{97} +(-5.44113 + 9.27785i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + q^{2} - 5 q^{4} - 4 q^{5} - 2 q^{7} + 6 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + q^{2} - 5 q^{4} - 4 q^{5} - 2 q^{7} + 6 q^{8} + 7 q^{10} - 10 q^{11} + 5 q^{13} - 7 q^{14} + q^{16} + 6 q^{17} + 8 q^{19} - 8 q^{20} + 7 q^{22} + 24 q^{23} + 16 q^{25} + q^{26} + 5 q^{28} - 10 q^{29} + 18 q^{31} - 10 q^{32} - 23 q^{35} + 40 q^{38} - 36 q^{40} - 5 q^{41} + 7 q^{43} + 13 q^{44} - 12 q^{46} - 21 q^{47} + 2 q^{49} + 38 q^{50} - 50 q^{52} - 12 q^{53} - 52 q^{55} + 33 q^{56} - 14 q^{58} + 6 q^{59} + 20 q^{61} - 36 q^{62} - 46 q^{64} + 8 q^{65} + 5 q^{67} - 102 q^{68} - 46 q^{70} + 18 q^{71} + 6 q^{73} - 5 q^{76} + 16 q^{77} + 10 q^{79} - 2 q^{80} + 35 q^{82} + 9 q^{83} + 9 q^{85} + 44 q^{86} + 36 q^{88} - 22 q^{89} + 13 q^{91} - 36 q^{92} + 15 q^{94} - 16 q^{95} + 9 q^{97} - 11 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/567\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(407\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.768262 1.33067i 0.543243 0.940925i −0.455472 0.890250i \(-0.650530\pi\)
0.998715 0.0506745i \(-0.0161371\pi\)
\(3\) 0 0
\(4\) −0.180452 0.312552i −0.0902259 0.156276i
\(5\) −3.15761 −1.41212 −0.706062 0.708150i \(-0.749530\pi\)
−0.706062 + 0.708150i \(0.749530\pi\)
\(6\) 0 0
\(7\) −0.00900690 + 2.64574i −0.00340429 + 0.999994i
\(8\) 2.51851 0.890428
\(9\) 0 0
\(10\) −2.42587 + 4.20173i −0.767127 + 1.32870i
\(11\) 5.74916 1.73344 0.866719 0.498797i \(-0.166225\pi\)
0.866719 + 0.498797i \(0.166225\pi\)
\(12\) 0 0
\(13\) 0.180452 0.312552i 0.0500484 0.0866863i −0.839916 0.542717i \(-0.817396\pi\)
0.889964 + 0.456030i \(0.150729\pi\)
\(14\) 3.51368 + 2.04460i 0.939070 + 0.546443i
\(15\) 0 0
\(16\) 2.29578 3.97640i 0.573945 0.994101i
\(17\) 1.38842 2.40481i 0.336741 0.583253i −0.647076 0.762425i \(-0.724009\pi\)
0.983818 + 0.179172i \(0.0573419\pi\)
\(18\) 0 0
\(19\) 3.61533 + 6.26193i 0.829413 + 1.43658i 0.898500 + 0.438974i \(0.144658\pi\)
−0.0690869 + 0.997611i \(0.522009\pi\)
\(20\) 0.569796 + 0.986916i 0.127410 + 0.220681i
\(21\) 0 0
\(22\) 4.41686 7.65023i 0.941678 1.63103i
\(23\) 0.824381 0.171895 0.0859476 0.996300i \(-0.472608\pi\)
0.0859476 + 0.996300i \(0.472608\pi\)
\(24\) 0 0
\(25\) 4.97047 0.994095
\(26\) −0.277269 0.480243i −0.0543768 0.0941834i
\(27\) 0 0
\(28\) 0.828555 0.474613i 0.156582 0.0896934i
\(29\) −2.13910 3.70502i −0.397220 0.688006i 0.596162 0.802864i \(-0.296692\pi\)
−0.993382 + 0.114859i \(0.963358\pi\)
\(30\) 0 0
\(31\) 2.49099 + 4.31453i 0.447396 + 0.774912i 0.998216 0.0597122i \(-0.0190183\pi\)
−0.550820 + 0.834624i \(0.685685\pi\)
\(32\) −1.00901 1.74765i −0.178369 0.308944i
\(33\) 0 0
\(34\) −2.13334 3.69505i −0.365865 0.633696i
\(35\) 0.0284402 8.35419i 0.00480728 1.41212i
\(36\) 0 0
\(37\) −3.74542 6.48725i −0.615743 1.06650i −0.990254 0.139275i \(-0.955523\pi\)
0.374511 0.927222i \(-0.377811\pi\)
\(38\) 11.1101 1.80229
\(39\) 0 0
\(40\) −7.95246 −1.25739
\(41\) −1.66569 + 2.88506i −0.260137 + 0.450570i −0.966278 0.257501i \(-0.917101\pi\)
0.706141 + 0.708071i \(0.250434\pi\)
\(42\) 0 0
\(43\) 3.93487 + 6.81540i 0.600063 + 1.03934i 0.992811 + 0.119693i \(0.0381910\pi\)
−0.392748 + 0.919646i \(0.628476\pi\)
\(44\) −1.03745 1.79691i −0.156401 0.270895i
\(45\) 0 0
\(46\) 0.633340 1.09698i 0.0933809 0.161740i
\(47\) −1.74075 + 3.01506i −0.253914 + 0.439792i −0.964600 0.263718i \(-0.915051\pi\)
0.710686 + 0.703509i \(0.248385\pi\)
\(48\) 0 0
\(49\) −6.99984 0.0476598i −0.999977 0.00680854i
\(50\) 3.81862 6.61405i 0.540035 0.935368i
\(51\) 0 0
\(52\) −0.130252 −0.0180626
\(53\) −1.45772 + 2.52485i −0.200233 + 0.346814i −0.948604 0.316467i \(-0.897503\pi\)
0.748370 + 0.663281i \(0.230837\pi\)
\(54\) 0 0
\(55\) −18.1536 −2.44783
\(56\) −0.0226840 + 6.66331i −0.00303127 + 0.890422i
\(57\) 0 0
\(58\) −6.57354 −0.863148
\(59\) 1.19939 + 2.07740i 0.156147 + 0.270455i 0.933476 0.358639i \(-0.116759\pi\)
−0.777329 + 0.629094i \(0.783426\pi\)
\(60\) 0 0
\(61\) −1.60056 + 2.77226i −0.204931 + 0.354951i −0.950111 0.311913i \(-0.899030\pi\)
0.745180 + 0.666864i \(0.232364\pi\)
\(62\) 7.65494 0.972178
\(63\) 0 0
\(64\) 6.08239 0.760298
\(65\) −0.569796 + 0.986916i −0.0706745 + 0.122412i
\(66\) 0 0
\(67\) −0.949637 1.64482i −0.116017 0.200947i 0.802169 0.597097i \(-0.203679\pi\)
−0.918186 + 0.396150i \(0.870346\pi\)
\(68\) −1.00217 −0.121531
\(69\) 0 0
\(70\) −11.0948 6.45605i −1.32608 0.771645i
\(71\) −1.60957 −0.191021 −0.0955104 0.995428i \(-0.530448\pi\)
−0.0955104 + 0.995428i \(0.530448\pi\)
\(72\) 0 0
\(73\) 7.70688 13.3487i 0.902022 1.56235i 0.0771572 0.997019i \(-0.475416\pi\)
0.824865 0.565330i \(-0.191251\pi\)
\(74\) −11.5098 −1.33799
\(75\) 0 0
\(76\) 1.30478 2.25995i 0.149669 0.259234i
\(77\) −0.0517821 + 15.2108i −0.00590112 + 1.73343i
\(78\) 0 0
\(79\) −2.73641 + 4.73960i −0.307870 + 0.533247i −0.977896 0.209091i \(-0.932950\pi\)
0.670026 + 0.742337i \(0.266283\pi\)
\(80\) −7.24916 + 12.5559i −0.810481 + 1.40379i
\(81\) 0 0
\(82\) 2.55937 + 4.43296i 0.282635 + 0.489538i
\(83\) −6.51742 11.2885i −0.715380 1.23907i −0.962813 0.270170i \(-0.912920\pi\)
0.247433 0.968905i \(-0.420413\pi\)
\(84\) 0 0
\(85\) −4.38408 + 7.59346i −0.475521 + 0.823626i
\(86\) 12.0921 1.30392
\(87\) 0 0
\(88\) 14.4793 1.54350
\(89\) −7.13384 12.3562i −0.756185 1.30975i −0.944783 0.327697i \(-0.893728\pi\)
0.188598 0.982054i \(-0.439606\pi\)
\(90\) 0 0
\(91\) 0.825304 + 0.480243i 0.0865154 + 0.0503432i
\(92\) −0.148761 0.257662i −0.0155094 0.0268631i
\(93\) 0 0
\(94\) 2.67470 + 4.63271i 0.275874 + 0.477827i
\(95\) −11.4158 19.7727i −1.17123 2.02864i
\(96\) 0 0
\(97\) −8.00266 13.8610i −0.812547 1.40737i −0.911076 0.412239i \(-0.864747\pi\)
0.0985289 0.995134i \(-0.468586\pi\)
\(98\) −5.44113 + 9.27785i −0.549637 + 0.937204i
\(99\) 0 0
\(100\) −0.896931 1.55353i −0.0896931 0.155353i
\(101\) −3.00749 −0.299257 −0.149628 0.988742i \(-0.547808\pi\)
−0.149628 + 0.988742i \(0.547808\pi\)
\(102\) 0 0
\(103\) 9.72063 0.957802 0.478901 0.877869i \(-0.341035\pi\)
0.478901 + 0.877869i \(0.341035\pi\)
\(104\) 0.454470 0.787165i 0.0445644 0.0771879i
\(105\) 0 0
\(106\) 2.23982 + 3.87948i 0.217551 + 0.376809i
\(107\) 5.21214 + 9.02770i 0.503877 + 0.872740i 0.999990 + 0.00448241i \(0.00142680\pi\)
−0.496113 + 0.868258i \(0.665240\pi\)
\(108\) 0 0
\(109\) 2.33713 4.04803i 0.223857 0.387731i −0.732119 0.681177i \(-0.761469\pi\)
0.955976 + 0.293445i \(0.0948019\pi\)
\(110\) −13.9467 + 24.1564i −1.32977 + 2.30322i
\(111\) 0 0
\(112\) 10.4998 + 6.10984i 0.992141 + 0.577325i
\(113\) 2.34332 4.05875i 0.220441 0.381815i −0.734501 0.678608i \(-0.762584\pi\)
0.954942 + 0.296793i \(0.0959171\pi\)
\(114\) 0 0
\(115\) −2.60307 −0.242737
\(116\) −0.772008 + 1.33716i −0.0716791 + 0.124152i
\(117\) 0 0
\(118\) 3.68578 0.339304
\(119\) 6.35000 + 3.69505i 0.582103 + 0.338725i
\(120\) 0 0
\(121\) 22.0529 2.00481
\(122\) 2.45930 + 4.25964i 0.222655 + 0.385649i
\(123\) 0 0
\(124\) 0.899009 1.55713i 0.0807334 0.139834i
\(125\) 0.0932326 0.00833898
\(126\) 0 0
\(127\) −9.15945 −0.812770 −0.406385 0.913702i \(-0.633211\pi\)
−0.406385 + 0.913702i \(0.633211\pi\)
\(128\) 6.69088 11.5889i 0.591396 1.02433i
\(129\) 0 0
\(130\) 0.875505 + 1.51642i 0.0767868 + 0.132999i
\(131\) −9.21165 −0.804825 −0.402413 0.915458i \(-0.631828\pi\)
−0.402413 + 0.915458i \(0.631828\pi\)
\(132\) 0 0
\(133\) −16.6000 + 9.50880i −1.43940 + 0.824517i
\(134\) −2.91828 −0.252101
\(135\) 0 0
\(136\) 3.49675 6.05655i 0.299844 0.519345i
\(137\) −6.82438 −0.583046 −0.291523 0.956564i \(-0.594162\pi\)
−0.291523 + 0.956564i \(0.594162\pi\)
\(138\) 0 0
\(139\) 2.84332 4.92477i 0.241167 0.417714i −0.719880 0.694099i \(-0.755803\pi\)
0.961047 + 0.276385i \(0.0891365\pi\)
\(140\) −2.61625 + 1.49864i −0.221113 + 0.126658i
\(141\) 0 0
\(142\) −1.23657 + 2.14180i −0.103771 + 0.179736i
\(143\) 1.03745 1.79691i 0.0867557 0.150265i
\(144\) 0 0
\(145\) 6.75442 + 11.6990i 0.560924 + 0.971549i
\(146\) −11.8418 20.5106i −0.980035 1.69747i
\(147\) 0 0
\(148\) −1.35173 + 2.34127i −0.111112 + 0.192451i
\(149\) −21.5885 −1.76860 −0.884301 0.466918i \(-0.845364\pi\)
−0.884301 + 0.466918i \(0.845364\pi\)
\(150\) 0 0
\(151\) −5.55553 −0.452102 −0.226051 0.974115i \(-0.572582\pi\)
−0.226051 + 0.974115i \(0.572582\pi\)
\(152\) 9.10523 + 15.7707i 0.738532 + 1.27917i
\(153\) 0 0
\(154\) 20.2007 + 11.7548i 1.62782 + 0.947225i
\(155\) −7.86557 13.6236i −0.631778 1.09427i
\(156\) 0 0
\(157\) −3.03560 5.25781i −0.242267 0.419619i 0.719093 0.694914i \(-0.244558\pi\)
−0.961360 + 0.275295i \(0.911224\pi\)
\(158\) 4.20456 + 7.28250i 0.334496 + 0.579365i
\(159\) 0 0
\(160\) 3.18605 + 5.51839i 0.251879 + 0.436267i
\(161\) −0.00742511 + 2.18109i −0.000585181 + 0.171894i
\(162\) 0 0
\(163\) 1.92630 + 3.33644i 0.150879 + 0.261330i 0.931551 0.363611i \(-0.118456\pi\)
−0.780672 + 0.624941i \(0.785123\pi\)
\(164\) 1.20231 0.0938844
\(165\) 0 0
\(166\) −20.0283 −1.55450
\(167\) −1.76919 + 3.06432i −0.136904 + 0.237124i −0.926323 0.376730i \(-0.877048\pi\)
0.789419 + 0.613854i \(0.210382\pi\)
\(168\) 0 0
\(169\) 6.43487 + 11.1455i 0.494990 + 0.857348i
\(170\) 6.73625 + 11.6675i 0.516647 + 0.894858i
\(171\) 0 0
\(172\) 1.42011 2.45970i 0.108282 0.187551i
\(173\) −4.92679 + 8.53345i −0.374577 + 0.648786i −0.990264 0.139205i \(-0.955545\pi\)
0.615687 + 0.787991i \(0.288879\pi\)
\(174\) 0 0
\(175\) −0.0447686 + 13.1506i −0.00338419 + 0.994089i
\(176\) 13.1988 22.8610i 0.994897 1.72321i
\(177\) 0 0
\(178\) −21.9226 −1.64317
\(179\) −9.94855 + 17.2314i −0.743590 + 1.28794i 0.207261 + 0.978286i \(0.433545\pi\)
−0.950851 + 0.309649i \(0.899788\pi\)
\(180\) 0 0
\(181\) 12.0930 0.898869 0.449434 0.893313i \(-0.351626\pi\)
0.449434 + 0.893313i \(0.351626\pi\)
\(182\) 1.27309 0.729254i 0.0943680 0.0540559i
\(183\) 0 0
\(184\) 2.07621 0.153060
\(185\) 11.8265 + 20.4842i 0.869505 + 1.50603i
\(186\) 0 0
\(187\) 7.98225 13.8257i 0.583720 1.01103i
\(188\) 1.25648 0.0916385
\(189\) 0 0
\(190\) −35.0812 −2.54506
\(191\) 4.85982 8.41745i 0.351644 0.609065i −0.634894 0.772600i \(-0.718956\pi\)
0.986538 + 0.163534i \(0.0522894\pi\)
\(192\) 0 0
\(193\) 1.15093 + 1.99346i 0.0828454 + 0.143492i 0.904471 0.426535i \(-0.140266\pi\)
−0.821626 + 0.570027i \(0.806933\pi\)
\(194\) −24.5925 −1.76564
\(195\) 0 0
\(196\) 1.24824 + 2.19641i 0.0891598 + 0.156887i
\(197\) −5.06470 −0.360845 −0.180422 0.983589i \(-0.557746\pi\)
−0.180422 + 0.983589i \(0.557746\pi\)
\(198\) 0 0
\(199\) 4.97666 8.61982i 0.352786 0.611043i −0.633951 0.773374i \(-0.718568\pi\)
0.986736 + 0.162330i \(0.0519011\pi\)
\(200\) 12.5182 0.885169
\(201\) 0 0
\(202\) −2.31054 + 4.00197i −0.162569 + 0.281578i
\(203\) 9.82178 5.62611i 0.689354 0.394876i
\(204\) 0 0
\(205\) 5.25959 9.10987i 0.367346 0.636261i
\(206\) 7.46798 12.9349i 0.520319 0.901219i
\(207\) 0 0
\(208\) −0.828555 1.43510i −0.0574500 0.0995062i
\(209\) 20.7851 + 36.0008i 1.43774 + 2.49023i
\(210\) 0 0
\(211\) 11.6503 20.1790i 0.802042 1.38918i −0.116228 0.993223i \(-0.537080\pi\)
0.918270 0.395955i \(-0.129586\pi\)
\(212\) 1.05219 0.0722650
\(213\) 0 0
\(214\) 16.0172 1.09491
\(215\) −12.4248 21.5204i −0.847363 1.46768i
\(216\) 0 0
\(217\) −11.4375 + 6.55165i −0.776430 + 0.444755i
\(218\) −3.59106 6.21990i −0.243217 0.421265i
\(219\) 0 0
\(220\) 3.27585 + 5.67394i 0.220858 + 0.382537i
\(221\) −0.501086 0.867907i −0.0337067 0.0583817i
\(222\) 0 0
\(223\) 5.93770 + 10.2844i 0.397618 + 0.688694i 0.993431 0.114429i \(-0.0365037\pi\)
−0.595814 + 0.803123i \(0.703170\pi\)
\(224\) 4.63291 2.65382i 0.309549 0.177316i
\(225\) 0 0
\(226\) −3.60056 6.23636i −0.239506 0.414836i
\(227\) −5.96081 −0.395633 −0.197816 0.980239i \(-0.563385\pi\)
−0.197816 + 0.980239i \(0.563385\pi\)
\(228\) 0 0
\(229\) −23.7206 −1.56750 −0.783752 0.621074i \(-0.786696\pi\)
−0.783752 + 0.621074i \(0.786696\pi\)
\(230\) −1.99984 + 3.46382i −0.131865 + 0.228398i
\(231\) 0 0
\(232\) −5.38733 9.33114i −0.353696 0.612619i
\(233\) −6.92961 12.0024i −0.453974 0.786306i 0.544654 0.838661i \(-0.316661\pi\)
−0.998629 + 0.0523544i \(0.983327\pi\)
\(234\) 0 0
\(235\) 5.49659 9.52037i 0.358558 0.621040i
\(236\) 0.432864 0.749743i 0.0281771 0.0488041i
\(237\) 0 0
\(238\) 9.79535 5.61097i 0.634938 0.363705i
\(239\) 11.1713 19.3492i 0.722610 1.25160i −0.237340 0.971427i \(-0.576276\pi\)
0.959950 0.280171i \(-0.0903911\pi\)
\(240\) 0 0
\(241\) 9.72063 0.626161 0.313080 0.949727i \(-0.398639\pi\)
0.313080 + 0.949727i \(0.398639\pi\)
\(242\) 16.9424 29.3450i 1.08910 1.88637i
\(243\) 0 0
\(244\) 1.15530 0.0739604
\(245\) 22.1027 + 0.150491i 1.41209 + 0.00961450i
\(246\) 0 0
\(247\) 2.60957 0.166043
\(248\) 6.27359 + 10.8662i 0.398373 + 0.690003i
\(249\) 0 0
\(250\) 0.0716270 0.124062i 0.00453009 0.00784635i
\(251\) 6.51950 0.411507 0.205754 0.978604i \(-0.434035\pi\)
0.205754 + 0.978604i \(0.434035\pi\)
\(252\) 0 0
\(253\) 4.73950 0.297970
\(254\) −7.03686 + 12.1882i −0.441532 + 0.764755i
\(255\) 0 0
\(256\) −4.19830 7.27167i −0.262394 0.454480i
\(257\) −5.53002 −0.344953 −0.172477 0.985014i \(-0.555177\pi\)
−0.172477 + 0.985014i \(0.555177\pi\)
\(258\) 0 0
\(259\) 17.1973 9.85095i 1.06859 0.612108i
\(260\) 0.411283 0.0255067
\(261\) 0 0
\(262\) −7.07696 + 12.2576i −0.437216 + 0.757280i
\(263\) −8.69499 −0.536156 −0.268078 0.963397i \(-0.586388\pi\)
−0.268078 + 0.963397i \(0.586388\pi\)
\(264\) 0 0
\(265\) 4.60291 7.97247i 0.282754 0.489745i
\(266\) −0.100067 + 29.3943i −0.00613552 + 1.80228i
\(267\) 0 0
\(268\) −0.342728 + 0.593622i −0.0209354 + 0.0362612i
\(269\) −1.88951 + 3.27272i −0.115205 + 0.199541i −0.917862 0.396900i \(-0.870086\pi\)
0.802657 + 0.596442i \(0.203419\pi\)
\(270\) 0 0
\(271\) −3.30995 5.73300i −0.201065 0.348255i 0.747807 0.663916i \(-0.231107\pi\)
−0.948872 + 0.315661i \(0.897774\pi\)
\(272\) −6.37501 11.0418i −0.386542 0.669510i
\(273\) 0 0
\(274\) −5.24291 + 9.08099i −0.316736 + 0.548602i
\(275\) 28.5761 1.72320
\(276\) 0 0
\(277\) −25.2658 −1.51808 −0.759038 0.651046i \(-0.774330\pi\)
−0.759038 + 0.651046i \(0.774330\pi\)
\(278\) −4.36882 7.56703i −0.262025 0.453840i
\(279\) 0 0
\(280\) 0.0716270 21.0401i 0.00428053 1.25739i
\(281\) 3.71221 + 6.42974i 0.221452 + 0.383566i 0.955249 0.295803i \(-0.0955871\pi\)
−0.733797 + 0.679369i \(0.762254\pi\)
\(282\) 0 0
\(283\) −7.71013 13.3543i −0.458320 0.793833i 0.540553 0.841310i \(-0.318215\pi\)
−0.998872 + 0.0474771i \(0.984882\pi\)
\(284\) 0.290450 + 0.503074i 0.0172350 + 0.0298520i
\(285\) 0 0
\(286\) −1.59406 2.76100i −0.0942588 0.163261i
\(287\) −7.61810 4.43296i −0.449682 0.261669i
\(288\) 0 0
\(289\) 4.64458 + 8.04465i 0.273211 + 0.473215i
\(290\) 20.7567 1.21887
\(291\) 0 0
\(292\) −5.56289 −0.325543
\(293\) 15.2899 26.4828i 0.893243 1.54714i 0.0572791 0.998358i \(-0.481758\pi\)
0.835964 0.548784i \(-0.184909\pi\)
\(294\) 0 0
\(295\) −3.78720 6.55962i −0.220499 0.381916i
\(296\) −9.43286 16.3382i −0.548274 0.949639i
\(297\) 0 0
\(298\) −16.5856 + 28.7272i −0.960780 + 1.66412i
\(299\) 0.148761 0.257662i 0.00860307 0.0149010i
\(300\) 0 0
\(301\) −18.0672 + 10.3493i −1.04138 + 0.596521i
\(302\) −4.26810 + 7.39256i −0.245602 + 0.425394i
\(303\) 0 0
\(304\) 33.1999 1.90415
\(305\) 5.05395 8.75369i 0.289388 0.501235i
\(306\) 0 0
\(307\) −28.7794 −1.64252 −0.821262 0.570551i \(-0.806730\pi\)
−0.821262 + 0.570551i \(0.806730\pi\)
\(308\) 4.76350 2.72863i 0.271425 0.155478i
\(309\) 0 0
\(310\) −24.1713 −1.37284
\(311\) −1.28628 2.22789i −0.0729380 0.126332i 0.827250 0.561834i \(-0.189904\pi\)
−0.900188 + 0.435502i \(0.856571\pi\)
\(312\) 0 0
\(313\) 9.25724 16.0340i 0.523250 0.906296i −0.476383 0.879238i \(-0.658053\pi\)
0.999634 0.0270587i \(-0.00861409\pi\)
\(314\) −9.32854 −0.526440
\(315\) 0 0
\(316\) 1.97516 0.111111
\(317\) 7.75909 13.4391i 0.435794 0.754817i −0.561566 0.827432i \(-0.689801\pi\)
0.997360 + 0.0726145i \(0.0231343\pi\)
\(318\) 0 0
\(319\) −12.2980 21.3008i −0.688556 1.19261i
\(320\) −19.2058 −1.07364
\(321\) 0 0
\(322\) 2.89661 + 1.68553i 0.161422 + 0.0939309i
\(323\) 20.0784 1.11719
\(324\) 0 0
\(325\) 0.896931 1.55353i 0.0497528 0.0861744i
\(326\) 5.91960 0.327856
\(327\) 0 0
\(328\) −4.19505 + 7.26604i −0.231633 + 0.401200i
\(329\) −7.96137 4.63271i −0.438925 0.255409i
\(330\) 0 0
\(331\) −15.7952 + 27.3581i −0.868182 + 1.50374i −0.00432948 + 0.999991i \(0.501378\pi\)
−0.863853 + 0.503745i \(0.831955\pi\)
\(332\) −2.35216 + 4.07407i −0.129092 + 0.223593i
\(333\) 0 0
\(334\) 2.71839 + 4.70840i 0.148744 + 0.257632i
\(335\) 2.99858 + 5.19369i 0.163830 + 0.283762i
\(336\) 0 0
\(337\) 5.70406 9.87972i 0.310720 0.538183i −0.667798 0.744342i \(-0.732763\pi\)
0.978518 + 0.206159i \(0.0660965\pi\)
\(338\) 19.7747 1.07560
\(339\) 0 0
\(340\) 3.16446 0.171617
\(341\) 14.3211 + 24.8049i 0.775532 + 1.34326i
\(342\) 0 0
\(343\) 0.189142 18.5193i 0.0102127 0.999948i
\(344\) 9.91002 + 17.1647i 0.534312 + 0.925456i
\(345\) 0 0
\(346\) 7.57013 + 13.1118i 0.406973 + 0.704897i
\(347\) −2.04070 3.53459i −0.109550 0.189747i 0.806038 0.591864i \(-0.201608\pi\)
−0.915588 + 0.402117i \(0.868274\pi\)
\(348\) 0 0
\(349\) 12.1389 + 21.0253i 0.649782 + 1.12546i 0.983175 + 0.182668i \(0.0584733\pi\)
−0.333392 + 0.942788i \(0.608193\pi\)
\(350\) 17.4646 + 10.1626i 0.933524 + 0.543216i
\(351\) 0 0
\(352\) −5.80094 10.0475i −0.309191 0.535535i
\(353\) 34.0790 1.81384 0.906922 0.421299i \(-0.138426\pi\)
0.906922 + 0.421299i \(0.138426\pi\)
\(354\) 0 0
\(355\) 5.08239 0.269745
\(356\) −2.57463 + 4.45939i −0.136455 + 0.236347i
\(357\) 0 0
\(358\) 15.2862 + 26.4764i 0.807900 + 1.39932i
\(359\) 2.74465 + 4.75388i 0.144857 + 0.250900i 0.929320 0.369276i \(-0.120394\pi\)
−0.784462 + 0.620176i \(0.787061\pi\)
\(360\) 0 0
\(361\) −16.6412 + 28.8233i −0.875851 + 1.51702i
\(362\) 9.29062 16.0918i 0.488304 0.845768i
\(363\) 0 0
\(364\) 0.00117316 0.344611i 6.14904e−5 0.0180625i
\(365\) −24.3353 + 42.1500i −1.27377 + 2.20623i
\(366\) 0 0
\(367\) −13.6391 −0.711955 −0.355978 0.934495i \(-0.615852\pi\)
−0.355978 + 0.934495i \(0.615852\pi\)
\(368\) 1.89259 3.27807i 0.0986583 0.170881i
\(369\) 0 0
\(370\) 36.3435 1.88941
\(371\) −6.66695 3.87948i −0.346131 0.201413i
\(372\) 0 0
\(373\) 8.92379 0.462056 0.231028 0.972947i \(-0.425791\pi\)
0.231028 + 0.972947i \(0.425791\pi\)
\(374\) −12.2649 21.2435i −0.634204 1.09847i
\(375\) 0 0
\(376\) −4.38408 + 7.59346i −0.226092 + 0.391603i
\(377\) −1.54402 −0.0795209
\(378\) 0 0
\(379\) 29.7035 1.52576 0.762882 0.646537i \(-0.223784\pi\)
0.762882 + 0.646537i \(0.223784\pi\)
\(380\) −4.12000 + 7.13604i −0.211351 + 0.366071i
\(381\) 0 0
\(382\) −7.46722 12.9336i −0.382056 0.661741i
\(383\) 17.7101 0.904944 0.452472 0.891779i \(-0.350542\pi\)
0.452472 + 0.891779i \(0.350542\pi\)
\(384\) 0 0
\(385\) 0.163508 48.0296i 0.00833312 2.44781i
\(386\) 3.53685 0.180021
\(387\) 0 0
\(388\) −2.88819 + 5.00249i −0.146626 + 0.253963i
\(389\) −21.3255 −1.08125 −0.540624 0.841264i \(-0.681812\pi\)
−0.540624 + 0.841264i \(0.681812\pi\)
\(390\) 0 0
\(391\) 1.14459 1.98248i 0.0578842 0.100258i
\(392\) −17.6292 0.120032i −0.890407 0.00606251i
\(393\) 0 0
\(394\) −3.89101 + 6.73943i −0.196026 + 0.339528i
\(395\) 8.64050 14.9658i 0.434751 0.753010i
\(396\) 0 0
\(397\) 1.11783 + 1.93614i 0.0561024 + 0.0971722i 0.892713 0.450626i \(-0.148799\pi\)
−0.836610 + 0.547799i \(0.815466\pi\)
\(398\) −7.64675 13.2446i −0.383297 0.663890i
\(399\) 0 0
\(400\) 11.4111 19.7646i 0.570555 0.988231i
\(401\) −8.73702 −0.436306 −0.218153 0.975915i \(-0.570003\pi\)
−0.218153 + 0.975915i \(0.570003\pi\)
\(402\) 0 0
\(403\) 1.79802 0.0895656
\(404\) 0.542708 + 0.939997i 0.0270007 + 0.0467666i
\(405\) 0 0
\(406\) 0.0592072 17.3919i 0.00293841 0.863143i
\(407\) −21.5330 37.2962i −1.06735 1.84871i
\(408\) 0 0
\(409\) 14.3460 + 24.8480i 0.709363 + 1.22865i 0.965094 + 0.261905i \(0.0843506\pi\)
−0.255731 + 0.966748i \(0.582316\pi\)
\(410\) −8.08148 13.9975i −0.399116 0.691289i
\(411\) 0 0
\(412\) −1.75411 3.03820i −0.0864186 0.149681i
\(413\) −5.50706 + 3.15456i −0.270985 + 0.155226i
\(414\) 0 0
\(415\) 20.5795 + 35.6447i 1.01021 + 1.74973i
\(416\) −0.728309 −0.0357083
\(417\) 0 0
\(418\) 63.8736 3.12416
\(419\) 4.32221 7.48628i 0.211154 0.365729i −0.740922 0.671591i \(-0.765611\pi\)
0.952076 + 0.305862i \(0.0989446\pi\)
\(420\) 0 0
\(421\) −9.23347 15.9928i −0.450012 0.779444i 0.548374 0.836233i \(-0.315247\pi\)
−0.998386 + 0.0567894i \(0.981914\pi\)
\(422\) −17.9010 31.0055i −0.871408 1.50932i
\(423\) 0 0
\(424\) −3.67128 + 6.35885i −0.178293 + 0.308813i
\(425\) 6.90111 11.9531i 0.334753 0.579809i
\(426\) 0 0
\(427\) −7.32024 4.25964i −0.354251 0.206138i
\(428\) 1.88108 3.25813i 0.0909255 0.157488i
\(429\) 0 0
\(430\) −38.1819 −1.84130
\(431\) −2.90368 + 5.02932i −0.139865 + 0.242254i −0.927445 0.373958i \(-0.878000\pi\)
0.787580 + 0.616212i \(0.211334\pi\)
\(432\) 0 0
\(433\) 3.63877 0.174868 0.0874341 0.996170i \(-0.472133\pi\)
0.0874341 + 0.996170i \(0.472133\pi\)
\(434\) −0.0689473 + 20.2529i −0.00330958 + 0.972172i
\(435\) 0 0
\(436\) −1.68696 −0.0807908
\(437\) 2.98040 + 5.16221i 0.142572 + 0.246942i
\(438\) 0 0
\(439\) 9.33095 16.1617i 0.445342 0.771355i −0.552734 0.833358i \(-0.686415\pi\)
0.998076 + 0.0620029i \(0.0197488\pi\)
\(440\) −45.7200 −2.17961
\(441\) 0 0
\(442\) −1.53986 −0.0732437
\(443\) −13.0455 + 22.5955i −0.619812 + 1.07355i 0.369708 + 0.929148i \(0.379458\pi\)
−0.989520 + 0.144398i \(0.953876\pi\)
\(444\) 0 0
\(445\) 22.5258 + 39.0159i 1.06783 + 1.84953i
\(446\) 18.2468 0.864012
\(447\) 0 0
\(448\) −0.0547835 + 16.0924i −0.00258828 + 0.760294i
\(449\) 5.63824 0.266085 0.133042 0.991110i \(-0.457525\pi\)
0.133042 + 0.991110i \(0.457525\pi\)
\(450\) 0 0
\(451\) −9.57631 + 16.5867i −0.450931 + 0.781035i
\(452\) −1.69142 −0.0795579
\(453\) 0 0
\(454\) −4.57946 + 7.93186i −0.214925 + 0.372261i
\(455\) −2.60599 1.51642i −0.122170 0.0710908i
\(456\) 0 0
\(457\) 9.99616 17.3139i 0.467601 0.809908i −0.531714 0.846924i \(-0.678452\pi\)
0.999315 + 0.0370159i \(0.0117852\pi\)
\(458\) −18.2236 + 31.5643i −0.851535 + 1.47490i
\(459\) 0 0
\(460\) 0.469729 + 0.813594i 0.0219012 + 0.0379340i
\(461\) 18.7247 + 32.4322i 0.872098 + 1.51052i 0.859823 + 0.510593i \(0.170574\pi\)
0.0122753 + 0.999925i \(0.496093\pi\)
\(462\) 0 0
\(463\) −1.22756 + 2.12620i −0.0570497 + 0.0988130i −0.893140 0.449779i \(-0.851503\pi\)
0.836090 + 0.548592i \(0.184836\pi\)
\(464\) −19.6436 −0.911929
\(465\) 0 0
\(466\) −21.2950 −0.986473
\(467\) 16.7054 + 28.9345i 0.773032 + 1.33893i 0.935894 + 0.352282i \(0.114594\pi\)
−0.162862 + 0.986649i \(0.552072\pi\)
\(468\) 0 0
\(469\) 4.36031 2.49768i 0.201341 0.115332i
\(470\) −8.44563 14.6283i −0.389568 0.674752i
\(471\) 0 0
\(472\) 3.02067 + 5.23196i 0.139038 + 0.240821i
\(473\) 22.6222 + 39.1828i 1.04017 + 1.80163i
\(474\) 0 0
\(475\) 17.9699 + 31.1248i 0.824515 + 1.42810i
\(476\) 0.00902647 2.65148i 0.000413727 0.121531i
\(477\) 0 0
\(478\) −17.1649 29.7305i −0.785106 1.35984i
\(479\) −34.6936 −1.58519 −0.792595 0.609748i \(-0.791271\pi\)
−0.792595 + 0.609748i \(0.791271\pi\)
\(480\) 0 0
\(481\) −2.70347 −0.123268
\(482\) 7.46798 12.9349i 0.340157 0.589170i
\(483\) 0 0
\(484\) −3.97948 6.89266i −0.180885 0.313303i
\(485\) 25.2692 + 43.7676i 1.14742 + 1.98739i
\(486\) 0 0
\(487\) −0.479909 + 0.831226i −0.0217467 + 0.0376665i −0.876694 0.481049i \(-0.840256\pi\)
0.854947 + 0.518715i \(0.173589\pi\)
\(488\) −4.03103 + 6.98195i −0.182476 + 0.316058i
\(489\) 0 0
\(490\) 17.1809 29.2958i 0.776155 1.32345i
\(491\) 7.88691 13.6605i 0.355931 0.616491i −0.631346 0.775501i \(-0.717497\pi\)
0.987277 + 0.159011i \(0.0508305\pi\)
\(492\) 0 0
\(493\) −11.8799 −0.535042
\(494\) 2.00483 3.47247i 0.0902017 0.156234i
\(495\) 0 0
\(496\) 22.8751 1.02712
\(497\) 0.0144972 4.25850i 0.000650290 0.191020i
\(498\) 0 0
\(499\) −19.1287 −0.856320 −0.428160 0.903703i \(-0.640838\pi\)
−0.428160 + 0.903703i \(0.640838\pi\)
\(500\) −0.0168240 0.0291400i −0.000752392 0.00130318i
\(501\) 0 0
\(502\) 5.00868 8.67529i 0.223548 0.387197i
\(503\) 33.3898 1.48878 0.744388 0.667747i \(-0.232741\pi\)
0.744388 + 0.667747i \(0.232741\pi\)
\(504\) 0 0
\(505\) 9.49648 0.422588
\(506\) 3.64117 6.30670i 0.161870 0.280367i
\(507\) 0 0
\(508\) 1.65284 + 2.86280i 0.0733330 + 0.127016i
\(509\) −33.5176 −1.48564 −0.742822 0.669489i \(-0.766513\pi\)
−0.742822 + 0.669489i \(0.766513\pi\)
\(510\) 0 0
\(511\) 35.2478 + 20.5106i 1.55927 + 0.907336i
\(512\) 13.8619 0.612617
\(513\) 0 0
\(514\) −4.24850 + 7.35862i −0.187393 + 0.324575i
\(515\) −30.6939 −1.35254
\(516\) 0 0
\(517\) −10.0078 + 17.3341i −0.440144 + 0.762351i
\(518\) 0.103668 30.4520i 0.00455491 1.33798i
\(519\) 0 0
\(520\) −1.43504 + 2.48556i −0.0629305 + 0.108999i
\(521\) −13.3622 + 23.1439i −0.585407 + 1.01395i 0.409418 + 0.912347i \(0.365732\pi\)
−0.994825 + 0.101607i \(0.967601\pi\)
\(522\) 0 0
\(523\) −8.53219 14.7782i −0.373086 0.646205i 0.616952 0.787001i \(-0.288367\pi\)
−0.990039 + 0.140796i \(0.955034\pi\)
\(524\) 1.66226 + 2.87912i 0.0726161 + 0.125775i
\(525\) 0 0
\(526\) −6.68002 + 11.5701i −0.291263 + 0.504482i
\(527\) 13.8342 0.602626
\(528\) 0 0
\(529\) −22.3204 −0.970452
\(530\) −7.07247 12.2499i −0.307209 0.532101i
\(531\) 0 0
\(532\) 5.96749 + 3.47247i 0.258723 + 0.150551i
\(533\) 0.601153 + 1.04123i 0.0260388 + 0.0451006i
\(534\) 0 0
\(535\) −16.4579 28.5059i −0.711537 1.23242i
\(536\) −2.39167 4.14250i −0.103304 0.178929i
\(537\) 0 0
\(538\) 2.90327 + 5.02861i 0.125169 + 0.216799i
\(539\) −40.2432 0.274004i −1.73340 0.0118022i
\(540\) 0 0
\(541\) −6.17128 10.6890i −0.265324 0.459555i 0.702324 0.711857i \(-0.252146\pi\)
−0.967648 + 0.252302i \(0.918812\pi\)
\(542\) −10.1716 −0.436909
\(543\) 0 0
\(544\) −5.60370 −0.240257
\(545\) −7.37975 + 12.7821i −0.316114 + 0.547525i
\(546\) 0 0
\(547\) −11.7212 20.3017i −0.501163 0.868040i −0.999999 0.00134350i \(-0.999572\pi\)
0.498836 0.866696i \(-0.333761\pi\)
\(548\) 1.23147 + 2.13297i 0.0526059 + 0.0911161i
\(549\) 0 0
\(550\) 21.9539 38.0252i 0.936117 1.62140i
\(551\) 15.4671 26.7897i 0.658919 1.14128i
\(552\) 0 0
\(553\) −12.5151 7.28250i −0.532195 0.309684i
\(554\) −19.4108 + 33.6204i −0.824684 + 1.42840i
\(555\) 0 0
\(556\) −2.05233 −0.0870381
\(557\) −12.2557 + 21.2275i −0.519292 + 0.899440i 0.480457 + 0.877018i \(0.340471\pi\)
−0.999749 + 0.0224216i \(0.992862\pi\)
\(558\) 0 0
\(559\) 2.84022 0.120129
\(560\) −33.1543 19.2925i −1.40103 0.815255i
\(561\) 0 0
\(562\) 11.4078 0.481209
\(563\) −6.68571 11.5800i −0.281769 0.488039i 0.690051 0.723760i \(-0.257588\pi\)
−0.971821 + 0.235722i \(0.924255\pi\)
\(564\) 0 0
\(565\) −7.39927 + 12.8159i −0.311290 + 0.539170i
\(566\) −23.6936 −0.995916
\(567\) 0 0
\(568\) −4.05372 −0.170090
\(569\) −7.12440 + 12.3398i −0.298670 + 0.517312i −0.975832 0.218522i \(-0.929876\pi\)
0.677162 + 0.735834i \(0.263210\pi\)
\(570\) 0 0
\(571\) 14.6618 + 25.3951i 0.613579 + 1.06275i 0.990632 + 0.136559i \(0.0436042\pi\)
−0.377053 + 0.926192i \(0.623062\pi\)
\(572\) −0.748837 −0.0313105
\(573\) 0 0
\(574\) −11.7515 + 6.73149i −0.490498 + 0.280967i
\(575\) 4.09756 0.170880
\(576\) 0 0
\(577\) 9.05004 15.6751i 0.376758 0.652564i −0.613830 0.789438i \(-0.710372\pi\)
0.990588 + 0.136874i \(0.0437055\pi\)
\(578\) 14.2730 0.593679
\(579\) 0 0
\(580\) 2.43770 4.22221i 0.101220 0.175318i
\(581\) 29.9251 17.1417i 1.24150 0.711158i
\(582\) 0 0
\(583\) −8.38067 + 14.5157i −0.347092 + 0.601181i
\(584\) 19.4099 33.6189i 0.803186 1.39116i
\(585\) 0 0
\(586\) −23.4932 40.6915i −0.970496 1.68095i
\(587\) 3.26402 + 5.65345i 0.134721 + 0.233343i 0.925491 0.378770i \(-0.123653\pi\)
−0.790770 + 0.612113i \(0.790320\pi\)
\(588\) 0 0
\(589\) −18.0115 + 31.1968i −0.742151 + 1.28544i
\(590\) −11.6382 −0.479139
\(591\) 0 0
\(592\) −34.3946 −1.41361
\(593\) −12.7202 22.0321i −0.522357 0.904749i −0.999662 0.0260111i \(-0.991719\pi\)
0.477305 0.878738i \(-0.341614\pi\)
\(594\) 0 0
\(595\) −20.0508 11.6675i −0.822002 0.478322i
\(596\) 3.89569 + 6.74753i 0.159574 + 0.276390i
\(597\) 0 0
\(598\) −0.228575 0.395903i −0.00934712 0.0161897i
\(599\) 3.08966 + 5.35144i 0.126240 + 0.218654i 0.922217 0.386673i \(-0.126376\pi\)
−0.795977 + 0.605327i \(0.793042\pi\)
\(600\) 0 0
\(601\) 6.46722 + 11.2016i 0.263804 + 0.456921i 0.967249 0.253828i \(-0.0816896\pi\)
−0.703446 + 0.710749i \(0.748356\pi\)
\(602\) −0.108912 + 31.9924i −0.00443892 + 1.30391i
\(603\) 0 0
\(604\) 1.00251 + 1.73639i 0.0407914 + 0.0706527i
\(605\) −69.6342 −2.83103
\(606\) 0 0
\(607\) −23.0756 −0.936608 −0.468304 0.883567i \(-0.655135\pi\)
−0.468304 + 0.883567i \(0.655135\pi\)
\(608\) 7.29578 12.6367i 0.295883 0.512484i
\(609\) 0 0
\(610\) −7.76551 13.4503i −0.314416 0.544585i
\(611\) 0.628242 + 1.08815i 0.0254159 + 0.0440217i
\(612\) 0 0
\(613\) 8.81363 15.2657i 0.355979 0.616574i −0.631306 0.775534i \(-0.717481\pi\)
0.987285 + 0.158960i \(0.0508141\pi\)
\(614\) −22.1101 + 38.2958i −0.892290 + 1.54549i
\(615\) 0 0
\(616\) −0.130414 + 38.3085i −0.00525452 + 1.54349i
\(617\) 10.8220 18.7443i 0.435679 0.754618i −0.561672 0.827360i \(-0.689842\pi\)
0.997351 + 0.0727418i \(0.0231749\pi\)
\(618\) 0 0
\(619\) −9.57941 −0.385029 −0.192514 0.981294i \(-0.561664\pi\)
−0.192514 + 0.981294i \(0.561664\pi\)
\(620\) −2.83872 + 4.91680i −0.114006 + 0.197463i
\(621\) 0 0
\(622\) −3.95278 −0.158492
\(623\) 32.7554 18.7630i 1.31232 0.751722i
\(624\) 0 0
\(625\) −25.1468 −1.00587
\(626\) −14.2240 24.6366i −0.568504 0.984678i
\(627\) 0 0
\(628\) −1.09556 + 1.89756i −0.0437176 + 0.0757211i
\(629\) −20.8008 −0.829384
\(630\) 0 0
\(631\) −31.1742 −1.24103 −0.620514 0.784196i \(-0.713076\pi\)
−0.620514 + 0.784196i \(0.713076\pi\)
\(632\) −6.89167 + 11.9367i −0.274136 + 0.474817i
\(633\) 0 0
\(634\) −11.9220 20.6496i −0.473484 0.820099i
\(635\) 28.9219 1.14773
\(636\) 0 0
\(637\) −1.27803 + 2.17921i −0.0506374 + 0.0863435i
\(638\) −37.7924 −1.49621
\(639\) 0 0
\(640\) −21.1272 + 36.5933i −0.835124 + 1.44648i
\(641\) 8.25214 0.325940 0.162970 0.986631i \(-0.447893\pi\)
0.162970 + 0.986631i \(0.447893\pi\)
\(642\) 0 0
\(643\) −12.2159 + 21.1585i −0.481748 + 0.834411i −0.999781 0.0209493i \(-0.993331\pi\)
0.518033 + 0.855361i \(0.326664\pi\)
\(644\) 0.683045 0.391262i 0.0269157 0.0154179i
\(645\) 0 0
\(646\) 15.4254 26.7176i 0.606906 1.05119i
\(647\) 19.3432 33.5034i 0.760461 1.31716i −0.182153 0.983270i \(-0.558307\pi\)
0.942613 0.333886i \(-0.108360\pi\)
\(648\) 0 0
\(649\) 6.89548 + 11.9433i 0.270671 + 0.468817i
\(650\) −1.37816 2.38704i −0.0540557 0.0936273i
\(651\) 0 0
\(652\) 0.695207 1.20413i 0.0272264 0.0471575i
\(653\) −7.65430 −0.299536 −0.149768 0.988721i \(-0.547853\pi\)
−0.149768 + 0.988721i \(0.547853\pi\)
\(654\) 0 0
\(655\) 29.0867 1.13651
\(656\) 7.64810 + 13.2469i 0.298608 + 0.517205i
\(657\) 0 0
\(658\) −12.2810 + 7.03481i −0.478764 + 0.274246i
\(659\) 19.2572 + 33.3545i 0.750156 + 1.29931i 0.947747 + 0.319023i \(0.103355\pi\)
−0.197591 + 0.980285i \(0.563312\pi\)
\(660\) 0 0
\(661\) −16.1066 27.8974i −0.626474 1.08508i −0.988254 0.152821i \(-0.951164\pi\)
0.361780 0.932263i \(-0.382169\pi\)
\(662\) 24.2697 + 42.0363i 0.943268 + 1.63379i
\(663\) 0 0
\(664\) −16.4142 28.4302i −0.636994 1.10331i
\(665\) 52.4162 30.0250i 2.03261 1.16432i
\(666\) 0 0
\(667\) −1.76343 3.05435i −0.0682803 0.118265i
\(668\) 1.27701 0.0494091
\(669\) 0 0
\(670\) 9.21478 0.355998
\(671\) −9.20190 + 15.9382i −0.355235 + 0.615285i
\(672\) 0 0
\(673\) −0.630680 1.09237i −0.0243109 0.0421077i 0.853614 0.520906i \(-0.174406\pi\)
−0.877925 + 0.478798i \(0.841073\pi\)
\(674\) −8.76442 15.1804i −0.337593 0.584728i
\(675\) 0 0
\(676\) 2.32237 4.02246i 0.0893219 0.154710i
\(677\) 7.41589 12.8447i 0.285016 0.493662i −0.687597 0.726092i \(-0.741335\pi\)
0.972613 + 0.232431i \(0.0746679\pi\)
\(678\) 0 0
\(679\) 36.7447 21.0481i 1.41013 0.807751i
\(680\) −11.0414 + 19.1242i −0.423417 + 0.733379i
\(681\) 0 0
\(682\) 44.0095 1.68521
\(683\) −2.76560 + 4.79016i −0.105823 + 0.183290i −0.914074 0.405547i \(-0.867081\pi\)
0.808251 + 0.588838i \(0.200414\pi\)
\(684\) 0 0
\(685\) 21.5487 0.823334
\(686\) −24.4977 14.4793i −0.935327 0.552824i
\(687\) 0 0
\(688\) 36.1344 1.37761
\(689\) 0.526097 + 0.911226i 0.0200427 + 0.0347150i
\(690\) 0 0
\(691\) −4.31896 + 7.48065i −0.164301 + 0.284577i −0.936407 0.350916i \(-0.885870\pi\)
0.772106 + 0.635494i \(0.219203\pi\)
\(692\) 3.55620 0.135186
\(693\) 0 0
\(694\) −6.27116 −0.238050
\(695\) −8.97808 + 15.5505i −0.340558 + 0.589864i
\(696\) 0 0
\(697\) 4.62535 + 8.01134i 0.175198 + 0.303451i
\(698\) 37.3035 1.41196
\(699\) 0 0
\(700\) 4.11831 2.35905i 0.155658 0.0891638i
\(701\) −26.5897 −1.00428 −0.502140 0.864786i \(-0.667454\pi\)
−0.502140 + 0.864786i \(0.667454\pi\)
\(702\) 0 0
\(703\) 27.0818 46.9070i 1.02141 1.76913i
\(704\) 34.9686 1.31793
\(705\) 0 0
\(706\) 26.1816 45.3479i 0.985358 1.70669i
\(707\) 0.0270882 7.95703i 0.00101876 0.299255i
\(708\) 0 0
\(709\) −5.06305 + 8.76946i −0.190147 + 0.329344i −0.945299 0.326206i \(-0.894230\pi\)
0.755152 + 0.655550i \(0.227563\pi\)
\(710\) 3.90460 6.76297i 0.146537 0.253810i
\(711\) 0 0
\(712\) −17.9666 31.1191i −0.673328 1.16624i
\(713\) 2.05353 + 3.55681i 0.0769052 + 0.133204i
\(714\) 0 0
\(715\) −3.27585 + 5.67394i −0.122510 + 0.212193i
\(716\) 7.18094 0.268364
\(717\) 0 0
\(718\) 8.43445 0.314771
\(719\) 16.1938 + 28.0485i 0.603927 + 1.04603i 0.992220 + 0.124496i \(0.0397315\pi\)
−0.388293 + 0.921536i \(0.626935\pi\)
\(720\) 0 0
\(721\) −0.0875527 + 25.7182i −0.00326063 + 0.957796i
\(722\) 25.5695 + 44.2877i 0.951600 + 1.64822i
\(723\) 0 0
\(724\) −2.18221 3.77970i −0.0811013 0.140472i
\(725\) −10.6323 18.4157i −0.394874 0.683943i
\(726\) 0 0
\(727\) −12.6174 21.8540i −0.467953 0.810519i 0.531376 0.847136i \(-0.321675\pi\)
−0.999329 + 0.0366171i \(0.988342\pi\)
\(728\) 2.07854 + 1.20950i 0.0770357 + 0.0448269i
\(729\) 0 0
\(730\) 37.3917 + 64.7644i 1.38393 + 2.39704i
\(731\) 21.8530 0.808264
\(732\) 0 0
\(733\) 2.84672 0.105146 0.0525731 0.998617i \(-0.483258\pi\)
0.0525731 + 0.998617i \(0.483258\pi\)
\(734\) −10.4784 + 18.1491i −0.386765 + 0.669896i
\(735\) 0 0
\(736\) −0.831806 1.44073i −0.0306608 0.0531060i
\(737\) −5.45962 9.45634i −0.201108 0.348329i
\(738\) 0 0
\(739\) −12.2708 + 21.2537i −0.451390 + 0.781830i −0.998473 0.0552485i \(-0.982405\pi\)
0.547083 + 0.837078i \(0.315738\pi\)
\(740\) 4.26824 7.39282i 0.156904 0.271765i
\(741\) 0 0
\(742\) −10.2843 + 5.89103i −0.377547 + 0.216267i
\(743\) 2.29535 3.97566i 0.0842082 0.145853i −0.820845 0.571151i \(-0.806497\pi\)
0.905054 + 0.425298i \(0.139831\pi\)
\(744\) 0 0
\(745\) 68.1681 2.49748
\(746\) 6.85581 11.8746i 0.251009 0.434760i
\(747\) 0 0
\(748\) −5.76165 −0.210667
\(749\) −23.9318 + 13.7086i −0.874451 + 0.500903i
\(750\) 0 0
\(751\) 31.4356 1.14710 0.573551 0.819170i \(-0.305566\pi\)
0.573551 + 0.819170i \(0.305566\pi\)
\(752\) 7.99273 + 13.8438i 0.291465 + 0.504832i
\(753\) 0 0
\(754\) −1.18621 + 2.05457i −0.0431992 + 0.0748231i
\(755\) 17.5422 0.638425
\(756\) 0 0
\(757\) 29.5432 1.07376 0.536882 0.843657i \(-0.319602\pi\)
0.536882 + 0.843657i \(0.319602\pi\)
\(758\) 22.8200 39.5255i 0.828861 1.43563i
\(759\) 0 0
\(760\) −28.7507 49.7977i −1.04290 1.80635i
\(761\) 46.4873 1.68516 0.842582 0.538567i \(-0.181034\pi\)
0.842582 + 0.538567i \(0.181034\pi\)
\(762\) 0 0
\(763\) 10.6890 + 6.21990i 0.386967 + 0.225175i
\(764\) −3.50785 −0.126910
\(765\) 0 0
\(766\) 13.6060 23.5663i 0.491605 0.851484i
\(767\) 0.865728 0.0312596
\(768\) 0 0
\(769\) −7.08532 + 12.2721i −0.255503 + 0.442545i −0.965032 0.262132i \(-0.915574\pi\)
0.709529 + 0.704676i \(0.248908\pi\)
\(770\) −63.7858 37.1169i −2.29868 1.33760i
\(771\) 0 0
\(772\) 0.415373 0.719448i 0.0149496 0.0258935i
\(773\) −17.0042 + 29.4522i −0.611600 + 1.05932i 0.379371 + 0.925245i \(0.376140\pi\)
−0.990971 + 0.134078i \(0.957193\pi\)
\(774\) 0 0
\(775\) 12.3814 + 21.4452i 0.444754 + 0.770336i
\(776\) −20.1548 34.9091i −0.723514 1.25316i
\(777\) 0 0
\(778\) −16.3836 + 28.3772i −0.587380 + 1.01737i
\(779\) −24.0880 −0.863043
\(780\) 0 0
\(781\) −9.25368 −0.331123
\(782\) −1.75868 3.04613i −0.0628904 0.108929i
\(783\) 0 0
\(784\) −16.2596 + 27.7248i −0.580700 + 0.990170i
\(785\) 9.58523 + 16.6021i 0.342111 + 0.592554i
\(786\) 0 0
\(787\) 14.5530 + 25.2065i 0.518757 + 0.898514i 0.999762 + 0.0217964i \(0.00693855\pi\)
−0.481005 + 0.876718i \(0.659728\pi\)
\(788\) 0.913934 + 1.58298i 0.0325576 + 0.0563914i
\(789\) 0 0
\(790\) −13.2763 22.9953i −0.472351 0.818135i
\(791\) 10.7173 + 6.23636i 0.381062 + 0.221739i
\(792\) 0 0
\(793\) 0.577649 + 1.00052i 0.0205129 + 0.0355294i
\(794\) 3.43515 0.121909
\(795\) 0 0
\(796\) −3.59219 −0.127322
\(797\) −9.25192 + 16.0248i −0.327720 + 0.567627i −0.982059 0.188574i \(-0.939613\pi\)
0.654339 + 0.756201i \(0.272947\pi\)
\(798\) 0 0
\(799\) 4.83377 + 8.37234i 0.171007 + 0.296192i
\(800\) −5.01524 8.68665i −0.177316 0.307120i
\(801\) 0 0
\(802\) −6.71231 + 11.6261i −0.237020 + 0.410531i
\(803\) 44.3081 76.7439i 1.56360 2.70823i
\(804\) 0 0
\(805\) 0.0234456 6.88703i 0.000826348 0.242736i
\(806\) 1.38135 2.39257i 0.0486559 0.0842745i
\(807\) 0 0
\(808\) −7.57440 −0.266466
\(809\) 20.5407 35.5775i 0.722172 1.25084i −0.237956 0.971276i \(-0.576477\pi\)
0.960128 0.279562i \(-0.0901892\pi\)
\(810\) 0 0
\(811\) −43.1361 −1.51471 −0.757357 0.653001i \(-0.773510\pi\)
−0.757357 + 0.653001i \(0.773510\pi\)
\(812\) −3.53081 2.05457i −0.123907 0.0721014i
\(813\) 0 0
\(814\) −66.1719 −2.31932
\(815\) −6.08248 10.5352i −0.213060 0.369031i
\(816\) 0 0
\(817\) −28.4517 + 49.2798i −0.995399 + 1.72408i
\(818\) 44.0859 1.54143
\(819\) 0 0
\(820\) −3.79641 −0.132576
\(821\) 6.58738 11.4097i 0.229901 0.398201i −0.727877 0.685707i \(-0.759493\pi\)
0.957779 + 0.287507i \(0.0928264\pi\)
\(822\) 0 0
\(823\) 5.99083 + 10.3764i 0.208827 + 0.361699i 0.951345 0.308127i \(-0.0997020\pi\)
−0.742518 + 0.669826i \(0.766369\pi\)
\(824\) 24.4815 0.852853
\(825\) 0 0
\(826\) −0.0331975 + 9.75160i −0.00115509 + 0.339302i
\(827\) −29.9879 −1.04278 −0.521391 0.853318i \(-0.674587\pi\)
−0.521391 + 0.853318i \(0.674587\pi\)
\(828\) 0 0
\(829\) −13.4619 + 23.3167i −0.467551 + 0.809822i −0.999313 0.0370721i \(-0.988197\pi\)
0.531762 + 0.846894i \(0.321530\pi\)
\(830\) 63.2416 2.19515
\(831\) 0 0
\(832\) 1.09758 1.90106i 0.0380517 0.0659074i
\(833\) −9.83333 + 16.7671i −0.340705 + 0.580947i
\(834\) 0 0
\(835\) 5.58639 9.67591i 0.193325 0.334849i
\(836\) 7.50142 12.9928i 0.259442 0.449367i
\(837\) 0 0
\(838\) −6.64117 11.5029i −0.229416 0.397359i
\(839\) −5.61191 9.72012i −0.193745 0.335576i 0.752744 0.658314i \(-0.228730\pi\)
−0.946488 + 0.322738i \(0.895397\pi\)
\(840\) 0 0
\(841\) 5.34853 9.26393i 0.184432 0.319446i
\(842\) −28.3749 −0.977864
\(843\) 0 0
\(844\) −8.40930 −0.289460
\(845\) −20.3188 35.1932i −0.698988 1.21068i
\(846\) 0 0
\(847\) −0.198628 + 58.3460i −0.00682494 + 2.00479i
\(848\) 6.69321 + 11.5930i 0.229846 + 0.398104i
\(849\) 0 0
\(850\) −10.6037 18.3662i −0.363704 0.629954i
\(851\) −3.08765 5.34796i −0.105843 0.183326i
\(852\) 0 0
\(853\) 6.09672 + 10.5598i 0.208748 + 0.361562i 0.951320 0.308204i \(-0.0997279\pi\)
−0.742573 + 0.669766i \(0.766395\pi\)
\(854\) −11.2920 + 6.46830i −0.386405 + 0.221341i
\(855\) 0 0
\(856\) 13.1268 + 22.7363i 0.448666 + 0.777112i
\(857\) 37.4382 1.27887 0.639433 0.768847i \(-0.279169\pi\)
0.639433 + 0.768847i \(0.279169\pi\)
\(858\) 0 0
\(859\) 0.757734 0.0258535 0.0129268 0.999916i \(-0.495885\pi\)
0.0129268 + 0.999916i \(0.495885\pi\)
\(860\) −4.48415 + 7.76678i −0.152908 + 0.264845i
\(861\) 0 0
\(862\) 4.46157 + 7.72767i 0.151962 + 0.263205i
\(863\) 11.7796 + 20.4029i 0.400983 + 0.694522i 0.993845 0.110782i \(-0.0353354\pi\)
−0.592862 + 0.805304i \(0.702002\pi\)
\(864\) 0 0
\(865\) 15.5569 26.9453i 0.528949 0.916167i
\(866\) 2.79553 4.84200i 0.0949959 0.164538i
\(867\) 0 0
\(868\) 4.11166 + 2.39257i 0.139559 + 0.0812089i
\(869\) −15.7321 + 27.2487i −0.533673 + 0.924349i
\(870\) 0 0
\(871\) −0.685455 −0.0232258
\(872\) 5.88609 10.1950i 0.199328 0.345247i
\(873\) 0 0
\(874\) 9.15892 0.309805
\(875\) −0.000839737 0.246669i −2.83883e−5 0.00833893i
\(876\) 0 0
\(877\) 36.6739 1.23839 0.619196 0.785237i \(-0.287459\pi\)
0.619196 + 0.785237i \(0.287459\pi\)
\(878\) −14.3372 24.8328i −0.483858 0.838066i
\(879\) 0 0
\(880\) −41.6766 + 72.1860i −1.40492 + 2.43339i
\(881\) 39.4357 1.32862 0.664311 0.747456i \(-0.268725\pi\)
0.664311 + 0.747456i \(0.268725\pi\)
\(882\) 0 0
\(883\) −8.76912 −0.295105 −0.147552 0.989054i \(-0.547139\pi\)
−0.147552 + 0.989054i \(0.547139\pi\)
\(884\) −0.180844 + 0.313231i −0.00608244 + 0.0105351i
\(885\) 0 0
\(886\) 20.0448 + 34.7185i 0.673417 + 1.16639i
\(887\) −7.82601 −0.262772 −0.131386 0.991331i \(-0.541943\pi\)
−0.131386 + 0.991331i \(0.541943\pi\)
\(888\) 0 0
\(889\) 0.0824983 24.2335i 0.00276690 0.812765i
\(890\) 69.2230 2.32036
\(891\) 0 0
\(892\) 2.14294 3.71168i 0.0717508 0.124276i
\(893\) −25.1734 −0.842397
\(894\) 0 0
\(895\) 31.4136 54.4100i 1.05004 1.81872i
\(896\) 30.6010 + 17.8067i 1.02231 + 0.594879i
\(897\) 0 0
\(898\) 4.33164 7.50263i 0.144549 0.250366i
\(899\) 10.6569 18.4584i 0.355429 0.615621i
\(900\) 0 0
\(901\) 4.04786 + 7.01109i 0.134854 + 0.233573i
\(902\) 14.7142 + 25.4858i 0.489930 + 0.848584i
\(903\) 0 0
\(904\) 5.90167 10.2220i 0.196287 0.339978i
\(905\) −38.1851 −1.26931
\(906\) 0 0
\(907\) 51.9332 1.72442 0.862208 0.506555i \(-0.169081\pi\)
0.862208 + 0.506555i \(0.169081\pi\)
\(908\) 1.07564 + 1.86306i 0.0356963 + 0.0618279i
\(909\) 0 0
\(910\) −4.01993 + 2.30270i −0.133259 + 0.0763336i
\(911\) 18.0762 + 31.3089i 0.598891 + 1.03731i 0.992985 + 0.118240i \(0.0377252\pi\)
−0.394094 + 0.919070i \(0.628941\pi\)
\(912\) 0 0
\(913\) −37.4697 64.8995i −1.24007 2.14786i
\(914\) −15.3593 26.6031i −0.508042 0.879954i
\(915\) 0 0
\(916\) 4.28043 + 7.41393i 0.141429 + 0.244963i
\(917\) 0.0829684 24.3716i 0.00273986 0.804821i
\(918\) 0 0
\(919\) 5.58842 + 9.67942i 0.184345 + 0.319295i 0.943356 0.331783i \(-0.107650\pi\)
−0.759011 + 0.651078i \(0.774317\pi\)
\(920\) −6.55585 −0.216140
\(921\) 0 0
\(922\) 57.5420 1.89504
\(923\) −0.290450 + 0.503074i −0.00956028 + 0.0165589i
\(924\) 0 0
\(925\) −18.6165 32.2447i −0.612106 1.06020i
\(926\) 1.88618 + 3.26696i 0.0619837 + 0.107359i
\(927\) 0 0
\(928\) −4.31673 + 7.47679i −0.141703 + 0.245438i
\(929\) 16.4192 28.4389i 0.538696 0.933049i −0.460279 0.887775i \(-0.652250\pi\)
0.998975 0.0452744i \(-0.0144162\pi\)
\(930\) 0 0
\(931\) −25.0083 44.0048i −0.819612 1.44220i
\(932\) −2.50092 + 4.33173i −0.0819205 + 0.141890i
\(933\) 0 0
\(934\) 51.3364 1.67978
\(935\) −25.2048 + 43.6560i −0.824285 + 1.42770i
\(936\) 0 0
\(937\) −25.9566 −0.847965 −0.423983 0.905670i \(-0.639368\pi\)
−0.423983 + 0.905670i \(0.639368\pi\)
\(938\) 0.0262847 7.72100i 0.000858225 0.252100i
\(939\) 0 0
\(940\) −3.96748 −0.129405
\(941\) 14.7340 + 25.5200i 0.480314 + 0.831928i 0.999745 0.0225845i \(-0.00718949\pi\)
−0.519431 + 0.854512i \(0.673856\pi\)
\(942\) 0 0
\(943\) −1.37316 + 2.37839i −0.0447163 + 0.0774509i
\(944\) 11.0141 0.358479
\(945\) 0 0
\(946\) 69.5192 2.26026
\(947\) −5.76137 + 9.97898i −0.187219 + 0.324273i −0.944322 0.329022i \(-0.893281\pi\)
0.757103 + 0.653296i \(0.226614\pi\)
\(948\) 0 0
\(949\) −2.78144 4.81760i −0.0902895 0.156386i
\(950\) 55.2223 1.79165
\(951\) 0 0
\(952\) 15.9925 + 9.30603i 0.518321 + 0.301610i
\(953\) −29.2912 −0.948835 −0.474417 0.880300i \(-0.657341\pi\)
−0.474417 + 0.880300i \(0.657341\pi\)
\(954\) 0 0
\(955\) −15.3454 + 26.5790i −0.496565 + 0.860076i
\(956\) −8.06352 −0.260793
\(957\) 0 0
\(958\) −26.6537 + 46.1656i −0.861144 + 1.49154i
\(959\) 0.0614665 18.0555i 0.00198486 0.583043i
\(960\) 0 0
\(961\) 3.08991 5.35188i 0.0996744 0.172641i
\(962\) −2.07697 + 3.59742i −0.0669643 + 0.115985i
\(963\) 0 0
\(964\) −1.75411 3.03820i −0.0564959 0.0978538i
\(965\) −3.63417 6.29457i −0.116988 0.202629i
\(966\) 0 0
\(967\) −21.0402 + 36.4427i −0.676606 + 1.17192i 0.299390 + 0.954131i \(0.403217\pi\)
−0.975997 + 0.217786i \(0.930117\pi\)
\(968\) 55.5403 1.78513
\(969\) 0 0
\(970\) 77.6536 2.49331
\(971\) −17.5774 30.4450i −0.564087 0.977027i −0.997134 0.0756560i \(-0.975895\pi\)
0.433047 0.901371i \(-0.357438\pi\)
\(972\) 0 0
\(973\) 13.0040 + 7.56703i 0.416890 + 0.242588i
\(974\) 0.737391 + 1.27720i 0.0236275 + 0.0409241i
\(975\) 0 0
\(976\) 7.34907 + 12.7290i 0.235238 + 0.407444i
\(977\) −2.21513 3.83671i −0.0708682 0.122747i 0.828414 0.560117i \(-0.189244\pi\)
−0.899282 + 0.437369i \(0.855910\pi\)
\(978\) 0 0
\(979\) −41.0136 71.0376i −1.31080 2.27037i
\(980\) −3.94144 6.93540i −0.125905 0.221543i
\(981\) 0 0
\(982\) −12.1184 20.9897i −0.386714 0.669809i
\(983\) −22.1601 −0.706798 −0.353399 0.935473i \(-0.614974\pi\)
−0.353399 + 0.935473i \(0.614974\pi\)
\(984\) 0 0
\(985\) 15.9923 0.509558
\(986\) −9.12684 + 15.8081i −0.290658 + 0.503434i
\(987\) 0 0
\(988\) −0.470902 0.815626i −0.0149814 0.0259485i
\(989\) 3.24383 + 5.61848i 0.103148 + 0.178657i
\(990\) 0 0
\(991\) 18.3602 31.8007i 0.583229 1.01018i −0.411864 0.911245i \(-0.635122\pi\)
0.995094 0.0989378i \(-0.0315445\pi\)
\(992\) 5.02686 8.70677i 0.159603 0.276440i
\(993\) 0 0
\(994\) −5.65551 3.29093i −0.179382 0.104382i
\(995\) −15.7143 + 27.2180i −0.498178 + 0.862869i
\(996\) 0 0
\(997\) −39.9031 −1.26374 −0.631872 0.775073i \(-0.717713\pi\)
−0.631872 + 0.775073i \(0.717713\pi\)
\(998\) −14.6959 + 25.4540i −0.465190 + 0.805733i
\(999\) 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 567.2.g.k.109.3 8
3.2 odd 2 567.2.g.j.109.2 8
7.2 even 3 567.2.h.j.352.2 8
9.2 odd 6 567.2.h.k.298.3 8
9.4 even 3 567.2.e.d.487.3 yes 8
9.5 odd 6 567.2.e.c.487.2 yes 8
9.7 even 3 567.2.h.j.298.2 8
21.2 odd 6 567.2.h.k.352.3 8
63.2 odd 6 567.2.g.j.541.2 8
63.4 even 3 3969.2.a.s.1.2 4
63.16 even 3 inner 567.2.g.k.541.3 8
63.23 odd 6 567.2.e.c.163.2 8
63.31 odd 6 3969.2.a.t.1.2 4
63.32 odd 6 3969.2.a.x.1.3 4
63.58 even 3 567.2.e.d.163.3 yes 8
63.59 even 6 3969.2.a.w.1.3 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
567.2.e.c.163.2 8 63.23 odd 6
567.2.e.c.487.2 yes 8 9.5 odd 6
567.2.e.d.163.3 yes 8 63.58 even 3
567.2.e.d.487.3 yes 8 9.4 even 3
567.2.g.j.109.2 8 3.2 odd 2
567.2.g.j.541.2 8 63.2 odd 6
567.2.g.k.109.3 8 1.1 even 1 trivial
567.2.g.k.541.3 8 63.16 even 3 inner
567.2.h.j.298.2 8 9.7 even 3
567.2.h.j.352.2 8 7.2 even 3
567.2.h.k.298.3 8 9.2 odd 6
567.2.h.k.352.3 8 21.2 odd 6
3969.2.a.s.1.2 4 63.4 even 3
3969.2.a.t.1.2 4 63.31 odd 6
3969.2.a.w.1.3 4 63.59 even 6
3969.2.a.x.1.3 4 63.32 odd 6