Properties

Label 1950.2.y.l.49.3
Level $1950$
Weight $2$
Character 1950.49
Analytic conductor $15.571$
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] = [1950,2,Mod(49,1950)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1950, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 3, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1950.49");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1950.y (of order \(6\), 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: \(15.5708283941\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{24})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - x^{4} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 49.3
Root \(-0.965926 - 0.258819i\) of defining polynomial
Character \(\chi\) \(=\) 1950.49
Dual form 1950.2.y.l.199.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.866025 + 0.500000i) q^{6} +(0.241181 - 0.417738i) q^{7} -1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.866025 + 0.500000i) q^{6} +(0.241181 - 0.417738i) q^{7} -1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +(-2.00731 + 1.15892i) q^{11} +1.00000i q^{12} +(-1.86250 - 3.08725i) q^{13} +0.482362 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-5.88512 - 3.39778i) q^{17} +1.00000 q^{18} +(-4.39778 - 2.53906i) q^{19} -0.482362i q^{21} +(-2.00731 - 1.15892i) q^{22} +(5.98124 - 3.45327i) q^{23} +(-0.866025 + 0.500000i) q^{24} +(1.74238 - 3.15660i) q^{26} -1.00000i q^{27} +(0.241181 + 0.417738i) q^{28} +(-4.20478 - 7.28290i) q^{29} +0.952516i q^{31} +(0.500000 - 0.866025i) q^{32} +(-1.15892 + 2.00731i) q^{33} -6.79555i q^{34} +(0.500000 + 0.866025i) q^{36} +(3.09429 + 5.35948i) q^{37} -5.07812i q^{38} +(-3.15660 - 1.74238i) q^{39} +(7.55607 - 4.36250i) q^{41} +(0.417738 - 0.241181i) q^{42} +(-9.78170 - 5.64747i) q^{43} -2.31784i q^{44} +(5.98124 + 3.45327i) q^{46} +5.77729 q^{47} +(-0.866025 - 0.500000i) q^{48} +(3.38366 + 5.86068i) q^{49} -6.79555 q^{51} +(3.60488 - 0.0693504i) q^{52} +5.81017i q^{53} +(0.866025 - 0.500000i) q^{54} +(-0.241181 + 0.417738i) q^{56} -5.07812 q^{57} +(4.20478 - 7.28290i) q^{58} +(-10.2397 - 5.91189i) q^{59} +(-4.68764 + 8.11924i) q^{61} +(-0.824903 + 0.476258i) q^{62} +(-0.241181 - 0.417738i) q^{63} +1.00000 q^{64} -2.31784 q^{66} +(-3.69677 - 6.40300i) q^{67} +(5.88512 - 3.39778i) q^{68} +(3.45327 - 5.98124i) q^{69} +(3.01876 + 1.74288i) q^{71} +(-0.500000 + 0.866025i) q^{72} +8.53465 q^{73} +(-3.09429 + 5.35948i) q^{74} +(4.39778 - 2.53906i) q^{76} +1.11804i q^{77} +(-0.0693504 - 3.60488i) q^{78} -9.03820 q^{79} +(-0.500000 - 0.866025i) q^{81} +(7.55607 + 4.36250i) q^{82} +7.94887 q^{83} +(0.417738 + 0.241181i) q^{84} -11.2949i q^{86} +(-7.28290 - 4.20478i) q^{87} +(2.00731 - 1.15892i) q^{88} +(-7.80941 + 4.50877i) q^{89} +(-1.73886 + 0.0334520i) q^{91} +6.90654i q^{92} +(0.476258 + 0.824903i) q^{93} +(2.88865 + 5.00328i) q^{94} -1.00000i q^{96} +(4.59103 - 7.95189i) q^{97} +(-3.38366 + 5.86068i) q^{98} +2.31784i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 4 q^{2} - 4 q^{4} + 4 q^{7} - 8 q^{8} + 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 4 q^{2} - 4 q^{4} + 4 q^{7} - 8 q^{8} + 4 q^{9} - 12 q^{11} + 8 q^{14} - 4 q^{16} + 8 q^{18} - 12 q^{19} - 12 q^{22} + 12 q^{23} + 4 q^{28} - 4 q^{29} + 4 q^{32} - 8 q^{33} + 4 q^{36} + 16 q^{37} - 24 q^{43} + 12 q^{46} - 32 q^{47} + 16 q^{49} - 8 q^{51} - 4 q^{56} + 4 q^{58} + 12 q^{59} - 16 q^{61} + 24 q^{62} - 4 q^{63} + 8 q^{64} - 16 q^{66} - 24 q^{67} - 4 q^{69} + 60 q^{71} - 4 q^{72} + 24 q^{73} - 16 q^{74} + 12 q^{76} + 8 q^{79} - 4 q^{81} + 8 q^{83} + 12 q^{87} + 12 q^{88} - 24 q^{89} + 8 q^{91} - 4 q^{93} - 16 q^{94} - 16 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times\).

\(n\) \(301\) \(1301\) \(1327\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(1\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 + 0.866025i 0.353553 + 0.612372i
\(3\) 0.866025 0.500000i 0.500000 0.288675i
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) 0 0
\(6\) 0.866025 + 0.500000i 0.353553 + 0.204124i
\(7\) 0.241181 0.417738i 0.0911578 0.157890i −0.816841 0.576863i \(-0.804277\pi\)
0.907999 + 0.418973i \(0.137610\pi\)
\(8\) −1.00000 −0.353553
\(9\) 0.500000 0.866025i 0.166667 0.288675i
\(10\) 0 0
\(11\) −2.00731 + 1.15892i −0.605226 + 0.349427i −0.771095 0.636721i \(-0.780290\pi\)
0.165869 + 0.986148i \(0.446957\pi\)
\(12\) 1.00000i 0.288675i
\(13\) −1.86250 3.08725i −0.516565 0.856248i
\(14\) 0.482362 0.128917
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −5.88512 3.39778i −1.42735 0.824082i −0.430441 0.902619i \(-0.641642\pi\)
−0.996911 + 0.0785367i \(0.974975\pi\)
\(18\) 1.00000 0.235702
\(19\) −4.39778 2.53906i −1.00892 0.582500i −0.0980443 0.995182i \(-0.531259\pi\)
−0.910875 + 0.412682i \(0.864592\pi\)
\(20\) 0 0
\(21\) 0.482362i 0.105260i
\(22\) −2.00731 1.15892i −0.427959 0.247082i
\(23\) 5.98124 3.45327i 1.24718 0.720057i 0.276630 0.960976i \(-0.410782\pi\)
0.970545 + 0.240920i \(0.0774490\pi\)
\(24\) −0.866025 + 0.500000i −0.176777 + 0.102062i
\(25\) 0 0
\(26\) 1.74238 3.15660i 0.341709 0.619060i
\(27\) 1.00000i 0.192450i
\(28\) 0.241181 + 0.417738i 0.0455789 + 0.0789450i
\(29\) −4.20478 7.28290i −0.780809 1.35240i −0.931471 0.363815i \(-0.881474\pi\)
0.150662 0.988585i \(-0.451859\pi\)
\(30\) 0 0
\(31\) 0.952516i 0.171077i 0.996335 + 0.0855385i \(0.0272611\pi\)
−0.996335 + 0.0855385i \(0.972739\pi\)
\(32\) 0.500000 0.866025i 0.0883883 0.153093i
\(33\) −1.15892 + 2.00731i −0.201742 + 0.349427i
\(34\) 6.79555i 1.16543i
\(35\) 0 0
\(36\) 0.500000 + 0.866025i 0.0833333 + 0.144338i
\(37\) 3.09429 + 5.35948i 0.508699 + 0.881092i 0.999949 + 0.0100739i \(0.00320667\pi\)
−0.491250 + 0.871018i \(0.663460\pi\)
\(38\) 5.07812i 0.823779i
\(39\) −3.15660 1.74238i −0.505460 0.279005i
\(40\) 0 0
\(41\) 7.55607 4.36250i 1.18006 0.681308i 0.224032 0.974582i \(-0.428078\pi\)
0.956029 + 0.293274i \(0.0947447\pi\)
\(42\) 0.417738 0.241181i 0.0644583 0.0372150i
\(43\) −9.78170 5.64747i −1.49170 0.861231i −0.491740 0.870742i \(-0.663639\pi\)
−0.999955 + 0.00951136i \(0.996972\pi\)
\(44\) 2.31784i 0.349427i
\(45\) 0 0
\(46\) 5.98124 + 3.45327i 0.881886 + 0.509157i
\(47\) 5.77729 0.842705 0.421353 0.906897i \(-0.361556\pi\)
0.421353 + 0.906897i \(0.361556\pi\)
\(48\) −0.866025 0.500000i −0.125000 0.0721688i
\(49\) 3.38366 + 5.86068i 0.483380 + 0.837240i
\(50\) 0 0
\(51\) −6.79555 −0.951568
\(52\) 3.60488 0.0693504i 0.499908 0.00961716i
\(53\) 5.81017i 0.798088i 0.916932 + 0.399044i \(0.130658\pi\)
−0.916932 + 0.399044i \(0.869342\pi\)
\(54\) 0.866025 0.500000i 0.117851 0.0680414i
\(55\) 0 0
\(56\) −0.241181 + 0.417738i −0.0322292 + 0.0558225i
\(57\) −5.07812 −0.672613
\(58\) 4.20478 7.28290i 0.552115 0.956292i
\(59\) −10.2397 5.91189i −1.33309 0.769663i −0.347322 0.937746i \(-0.612909\pi\)
−0.985773 + 0.168083i \(0.946242\pi\)
\(60\) 0 0
\(61\) −4.68764 + 8.11924i −0.600191 + 1.03956i 0.392600 + 0.919709i \(0.371576\pi\)
−0.992792 + 0.119853i \(0.961758\pi\)
\(62\) −0.824903 + 0.476258i −0.104763 + 0.0604848i
\(63\) −0.241181 0.417738i −0.0303859 0.0526300i
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) −2.31784 −0.285306
\(67\) −3.69677 6.40300i −0.451633 0.782251i 0.546855 0.837227i \(-0.315825\pi\)
−0.998488 + 0.0549764i \(0.982492\pi\)
\(68\) 5.88512 3.39778i 0.713676 0.412041i
\(69\) 3.45327 5.98124i 0.415725 0.720057i
\(70\) 0 0
\(71\) 3.01876 + 1.74288i 0.358261 + 0.206842i 0.668318 0.743876i \(-0.267015\pi\)
−0.310057 + 0.950718i \(0.600348\pi\)
\(72\) −0.500000 + 0.866025i −0.0589256 + 0.102062i
\(73\) 8.53465 0.998906 0.499453 0.866341i \(-0.333534\pi\)
0.499453 + 0.866341i \(0.333534\pi\)
\(74\) −3.09429 + 5.35948i −0.359704 + 0.623026i
\(75\) 0 0
\(76\) 4.39778 2.53906i 0.504460 0.291250i
\(77\) 1.11804i 0.127412i
\(78\) −0.0693504 3.60488i −0.00785238 0.408173i
\(79\) −9.03820 −1.01688 −0.508438 0.861098i \(-0.669777\pi\)
−0.508438 + 0.861098i \(0.669777\pi\)
\(80\) 0 0
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 7.55607 + 4.36250i 0.834429 + 0.481758i
\(83\) 7.94887 0.872502 0.436251 0.899825i \(-0.356306\pi\)
0.436251 + 0.899825i \(0.356306\pi\)
\(84\) 0.417738 + 0.241181i 0.0455789 + 0.0263150i
\(85\) 0 0
\(86\) 11.2949i 1.21796i
\(87\) −7.28290 4.20478i −0.780809 0.450800i
\(88\) 2.00731 1.15892i 0.213980 0.123541i
\(89\) −7.80941 + 4.50877i −0.827796 + 0.477928i −0.853097 0.521752i \(-0.825279\pi\)
0.0253015 + 0.999680i \(0.491945\pi\)
\(90\) 0 0
\(91\) −1.73886 + 0.0334520i −0.182282 + 0.00350672i
\(92\) 6.90654i 0.720057i
\(93\) 0.476258 + 0.824903i 0.0493857 + 0.0855385i
\(94\) 2.88865 + 5.00328i 0.297941 + 0.516049i
\(95\) 0 0
\(96\) 1.00000i 0.102062i
\(97\) 4.59103 7.95189i 0.466148 0.807392i −0.533104 0.846050i \(-0.678975\pi\)
0.999253 + 0.0386571i \(0.0123080\pi\)
\(98\) −3.38366 + 5.86068i −0.341802 + 0.592018i
\(99\) 2.31784i 0.232951i
\(100\) 0 0
\(101\) −5.34108 9.25102i −0.531457 0.920511i −0.999326 0.0367132i \(-0.988311\pi\)
0.467868 0.883798i \(-0.345022\pi\)
\(102\) −3.39778 5.88512i −0.336430 0.582714i
\(103\) 9.17449i 0.903990i 0.892021 + 0.451995i \(0.149287\pi\)
−0.892021 + 0.451995i \(0.850713\pi\)
\(104\) 1.86250 + 3.08725i 0.182633 + 0.302729i
\(105\) 0 0
\(106\) −5.03175 + 2.90508i −0.488727 + 0.282167i
\(107\) 2.78629 1.60867i 0.269361 0.155516i −0.359236 0.933247i \(-0.616963\pi\)
0.628597 + 0.777731i \(0.283629\pi\)
\(108\) 0.866025 + 0.500000i 0.0833333 + 0.0481125i
\(109\) 17.0669i 1.63471i −0.576132 0.817356i \(-0.695439\pi\)
0.576132 0.817356i \(-0.304561\pi\)
\(110\) 0 0
\(111\) 5.35948 + 3.09429i 0.508699 + 0.293697i
\(112\) −0.482362 −0.0455789
\(113\) 1.43488 + 0.828427i 0.134982 + 0.0779319i 0.565970 0.824426i \(-0.308502\pi\)
−0.430988 + 0.902357i \(0.641835\pi\)
\(114\) −2.53906 4.39778i −0.237805 0.411890i
\(115\) 0 0
\(116\) 8.40957 0.780809
\(117\) −3.60488 + 0.0693504i −0.333272 + 0.00641144i
\(118\) 11.8238i 1.08847i
\(119\) −2.83876 + 1.63896i −0.260229 + 0.150243i
\(120\) 0 0
\(121\) −2.81382 + 4.87367i −0.255801 + 0.443061i
\(122\) −9.37529 −0.848799
\(123\) 4.36250 7.55607i 0.393353 0.681308i
\(124\) −0.824903 0.476258i −0.0740785 0.0427692i
\(125\) 0 0
\(126\) 0.241181 0.417738i 0.0214861 0.0372150i
\(127\) 16.3843 9.45946i 1.45387 0.839391i 0.455170 0.890405i \(-0.349578\pi\)
0.998698 + 0.0510134i \(0.0162451\pi\)
\(128\) 0.500000 + 0.866025i 0.0441942 + 0.0765466i
\(129\) −11.2949 −0.994463
\(130\) 0 0
\(131\) −6.96812 −0.608808 −0.304404 0.952543i \(-0.598457\pi\)
−0.304404 + 0.952543i \(0.598457\pi\)
\(132\) −1.15892 2.00731i −0.100871 0.174714i
\(133\) −2.12132 + 1.22474i −0.183942 + 0.106199i
\(134\) 3.69677 6.40300i 0.319353 0.553135i
\(135\) 0 0
\(136\) 5.88512 + 3.39778i 0.504645 + 0.291357i
\(137\) 10.2547 17.7616i 0.876116 1.51748i 0.0205465 0.999789i \(-0.493459\pi\)
0.855569 0.517688i \(-0.173207\pi\)
\(138\) 6.90654 0.587924
\(139\) −4.25467 + 7.36931i −0.360877 + 0.625057i −0.988105 0.153778i \(-0.950856\pi\)
0.627229 + 0.778835i \(0.284189\pi\)
\(140\) 0 0
\(141\) 5.00328 2.88865i 0.421353 0.243268i
\(142\) 3.48576i 0.292519i
\(143\) 7.31648 + 4.03856i 0.611835 + 0.337721i
\(144\) −1.00000 −0.0833333
\(145\) 0 0
\(146\) 4.26733 + 7.39123i 0.353166 + 0.611702i
\(147\) 5.86068 + 3.38366i 0.483380 + 0.279080i
\(148\) −6.18859 −0.508699
\(149\) −6.27439 3.62252i −0.514018 0.296769i 0.220466 0.975395i \(-0.429242\pi\)
−0.734484 + 0.678626i \(0.762576\pi\)
\(150\) 0 0
\(151\) 7.82743i 0.636987i 0.947925 + 0.318494i \(0.103177\pi\)
−0.947925 + 0.318494i \(0.896823\pi\)
\(152\) 4.39778 + 2.53906i 0.356707 + 0.205945i
\(153\) −5.88512 + 3.39778i −0.475784 + 0.274694i
\(154\) −0.968248 + 0.559018i −0.0780236 + 0.0450470i
\(155\) 0 0
\(156\) 3.08725 1.86250i 0.247178 0.149119i
\(157\) 4.42267i 0.352967i −0.984304 0.176484i \(-0.943528\pi\)
0.984304 0.176484i \(-0.0564723\pi\)
\(158\) −4.51910 7.82731i −0.359520 0.622707i
\(159\) 2.90508 + 5.03175i 0.230388 + 0.399044i
\(160\) 0 0
\(161\) 3.33145i 0.262555i
\(162\) 0.500000 0.866025i 0.0392837 0.0680414i
\(163\) −5.61219 + 9.72060i −0.439581 + 0.761376i −0.997657 0.0684135i \(-0.978206\pi\)
0.558076 + 0.829790i \(0.311540\pi\)
\(164\) 8.72500i 0.681308i
\(165\) 0 0
\(166\) 3.97443 + 6.88392i 0.308476 + 0.534296i
\(167\) 7.52898 + 13.0406i 0.582610 + 1.00911i 0.995169 + 0.0981794i \(0.0313019\pi\)
−0.412558 + 0.910931i \(0.635365\pi\)
\(168\) 0.482362i 0.0372150i
\(169\) −6.06218 + 11.5000i −0.466321 + 0.884615i
\(170\) 0 0
\(171\) −4.39778 + 2.53906i −0.336306 + 0.194167i
\(172\) 9.78170 5.64747i 0.745848 0.430615i
\(173\) 12.7727 + 7.37429i 0.971087 + 0.560657i 0.899567 0.436782i \(-0.143882\pi\)
0.0715193 + 0.997439i \(0.477215\pi\)
\(174\) 8.40957i 0.637528i
\(175\) 0 0
\(176\) 2.00731 + 1.15892i 0.151306 + 0.0873568i
\(177\) −11.8238 −0.888730
\(178\) −7.80941 4.50877i −0.585340 0.337946i
\(179\) −4.30589 7.45802i −0.321837 0.557438i 0.659030 0.752117i \(-0.270967\pi\)
−0.980867 + 0.194678i \(0.937634\pi\)
\(180\) 0 0
\(181\) 2.84493 0.211462 0.105731 0.994395i \(-0.466282\pi\)
0.105731 + 0.994395i \(0.466282\pi\)
\(182\) −0.898400 1.48917i −0.0665938 0.110385i
\(183\) 9.37529i 0.693041i
\(184\) −5.98124 + 3.45327i −0.440943 + 0.254579i
\(185\) 0 0
\(186\) −0.476258 + 0.824903i −0.0349209 + 0.0604848i
\(187\) 15.7510 1.15183
\(188\) −2.88865 + 5.00328i −0.210676 + 0.364902i
\(189\) −0.417738 0.241181i −0.0303859 0.0175433i
\(190\) 0 0
\(191\) 1.71794 2.97555i 0.124306 0.215304i −0.797156 0.603774i \(-0.793663\pi\)
0.921461 + 0.388470i \(0.126996\pi\)
\(192\) 0.866025 0.500000i 0.0625000 0.0360844i
\(193\) −1.32843 2.30090i −0.0956223 0.165623i 0.814246 0.580520i \(-0.197151\pi\)
−0.909868 + 0.414898i \(0.863817\pi\)
\(194\) 9.18206 0.659233
\(195\) 0 0
\(196\) −6.76733 −0.483380
\(197\) −10.5579 18.2868i −0.752219 1.30288i −0.946745 0.321984i \(-0.895650\pi\)
0.194526 0.980897i \(-0.437683\pi\)
\(198\) −2.00731 + 1.15892i −0.142653 + 0.0823608i
\(199\) −5.26941 + 9.12688i −0.373538 + 0.646988i −0.990107 0.140314i \(-0.955189\pi\)
0.616569 + 0.787301i \(0.288522\pi\)
\(200\) 0 0
\(201\) −6.40300 3.69677i −0.451633 0.260750i
\(202\) 5.34108 9.25102i 0.375797 0.650900i
\(203\) −4.05646 −0.284707
\(204\) 3.39778 5.88512i 0.237892 0.412041i
\(205\) 0 0
\(206\) −7.94534 + 4.58725i −0.553578 + 0.319609i
\(207\) 6.90654i 0.480038i
\(208\) −1.74238 + 3.15660i −0.120813 + 0.218871i
\(209\) 11.7702 0.814165
\(210\) 0 0
\(211\) 5.74384 + 9.94863i 0.395422 + 0.684892i 0.993155 0.116804i \(-0.0372649\pi\)
−0.597733 + 0.801696i \(0.703932\pi\)
\(212\) −5.03175 2.90508i −0.345582 0.199522i
\(213\) 3.48576 0.238840
\(214\) 2.78629 + 1.60867i 0.190467 + 0.109966i
\(215\) 0 0
\(216\) 1.00000i 0.0680414i
\(217\) 0.397902 + 0.229729i 0.0270113 + 0.0155950i
\(218\) 14.7804 8.53345i 1.00105 0.577958i
\(219\) 7.39123 4.26733i 0.499453 0.288359i
\(220\) 0 0
\(221\) 0.471274 + 24.4972i 0.0317013 + 1.64786i
\(222\) 6.18859i 0.415351i
\(223\) −2.61389 4.52739i −0.175039 0.303176i 0.765136 0.643869i \(-0.222672\pi\)
−0.940175 + 0.340693i \(0.889338\pi\)
\(224\) −0.241181 0.417738i −0.0161146 0.0279113i
\(225\) 0 0
\(226\) 1.65685i 0.110212i
\(227\) −5.43443 + 9.41271i −0.360696 + 0.624744i −0.988076 0.153970i \(-0.950794\pi\)
0.627380 + 0.778714i \(0.284127\pi\)
\(228\) 2.53906 4.39778i 0.168153 0.291250i
\(229\) 21.1932i 1.40048i 0.713905 + 0.700242i \(0.246925\pi\)
−0.713905 + 0.700242i \(0.753075\pi\)
\(230\) 0 0
\(231\) 0.559018 + 0.968248i 0.0367807 + 0.0637060i
\(232\) 4.20478 + 7.28290i 0.276058 + 0.478146i
\(233\) 21.8423i 1.43094i −0.698645 0.715469i \(-0.746213\pi\)
0.698645 0.715469i \(-0.253787\pi\)
\(234\) −1.86250 3.08725i −0.121756 0.201820i
\(235\) 0 0
\(236\) 10.2397 5.91189i 0.666547 0.384831i
\(237\) −7.82731 + 4.51910i −0.508438 + 0.293547i
\(238\) −2.83876 1.63896i −0.184009 0.106238i
\(239\) 8.23027i 0.532372i −0.963922 0.266186i \(-0.914236\pi\)
0.963922 0.266186i \(-0.0857635\pi\)
\(240\) 0 0
\(241\) −2.68678 1.55121i −0.173071 0.0999225i 0.410962 0.911652i \(-0.365193\pi\)
−0.584033 + 0.811730i \(0.698526\pi\)
\(242\) −5.62763 −0.361758
\(243\) −0.866025 0.500000i −0.0555556 0.0320750i
\(244\) −4.68764 8.11924i −0.300096 0.519781i
\(245\) 0 0
\(246\) 8.72500 0.556286
\(247\) 0.352169 + 18.3060i 0.0224080 + 1.16478i
\(248\) 0.952516i 0.0604848i
\(249\) 6.88392 3.97443i 0.436251 0.251870i
\(250\) 0 0
\(251\) 7.81042 13.5281i 0.492990 0.853883i −0.506978 0.861959i \(-0.669237\pi\)
0.999967 + 0.00807605i \(0.00257072\pi\)
\(252\) 0.482362 0.0303859
\(253\) −8.00412 + 13.8635i −0.503215 + 0.871594i
\(254\) 16.3843 + 9.45946i 1.02804 + 0.593539i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −3.05205 + 1.76210i −0.190382 + 0.109917i −0.592161 0.805819i \(-0.701725\pi\)
0.401780 + 0.915736i \(0.368392\pi\)
\(258\) −5.64747 9.78170i −0.351596 0.608982i
\(259\) 2.98514 0.185488
\(260\) 0 0
\(261\) −8.40957 −0.520539
\(262\) −3.48406 6.03457i −0.215246 0.372817i
\(263\) −20.1637 + 11.6415i −1.24334 + 0.717845i −0.969774 0.244006i \(-0.921538\pi\)
−0.273571 + 0.961852i \(0.588205\pi\)
\(264\) 1.15892 2.00731i 0.0713265 0.123541i
\(265\) 0 0
\(266\) −2.12132 1.22474i −0.130066 0.0750939i
\(267\) −4.50877 + 7.80941i −0.275932 + 0.477928i
\(268\) 7.39355 0.451633
\(269\) 4.90873 8.50217i 0.299291 0.518387i −0.676683 0.736274i \(-0.736583\pi\)
0.975974 + 0.217888i \(0.0699166\pi\)
\(270\) 0 0
\(271\) −18.8862 + 10.9040i −1.14726 + 0.662369i −0.948217 0.317623i \(-0.897115\pi\)
−0.199039 + 0.979992i \(0.563782\pi\)
\(272\) 6.79555i 0.412041i
\(273\) −1.48917 + 0.898400i −0.0901287 + 0.0543736i
\(274\) 20.5093 1.23901
\(275\) 0 0
\(276\) 3.45327 + 5.98124i 0.207863 + 0.360028i
\(277\) −11.6697 6.73753i −0.701167 0.404819i 0.106615 0.994300i \(-0.465999\pi\)
−0.807782 + 0.589481i \(0.799332\pi\)
\(278\) −8.50935 −0.510357
\(279\) 0.824903 + 0.476258i 0.0493857 + 0.0285128i
\(280\) 0 0
\(281\) 29.6167i 1.76678i −0.468635 0.883392i \(-0.655254\pi\)
0.468635 0.883392i \(-0.344746\pi\)
\(282\) 5.00328 + 2.88865i 0.297941 + 0.172016i
\(283\) −10.5516 + 6.09197i −0.627228 + 0.362130i −0.779678 0.626181i \(-0.784617\pi\)
0.152450 + 0.988311i \(0.451284\pi\)
\(284\) −3.01876 + 1.74288i −0.179130 + 0.103421i
\(285\) 0 0
\(286\) 0.160743 + 8.35554i 0.00950492 + 0.494073i
\(287\) 4.20861i 0.248426i
\(288\) −0.500000 0.866025i −0.0294628 0.0510310i
\(289\) 14.5898 + 25.2702i 0.858223 + 1.48649i
\(290\) 0 0
\(291\) 9.18206i 0.538262i
\(292\) −4.26733 + 7.39123i −0.249726 + 0.432539i
\(293\) −7.51047 + 13.0085i −0.438766 + 0.759965i −0.997595 0.0693181i \(-0.977918\pi\)
0.558829 + 0.829283i \(0.311251\pi\)
\(294\) 6.76733i 0.394679i
\(295\) 0 0
\(296\) −3.09429 5.35948i −0.179852 0.311513i
\(297\) 1.15892 + 2.00731i 0.0672473 + 0.116476i
\(298\) 7.24504i 0.419694i
\(299\) −21.8012 12.0338i −1.26079 0.695935i
\(300\) 0 0
\(301\) −4.71832 + 2.72412i −0.271959 + 0.157016i
\(302\) −6.77875 + 3.91372i −0.390073 + 0.225209i
\(303\) −9.25102 5.34108i −0.531457 0.306837i
\(304\) 5.07812i 0.291250i
\(305\) 0 0
\(306\) −5.88512 3.39778i −0.336430 0.194238i
\(307\) 27.9569 1.59558 0.797791 0.602934i \(-0.206002\pi\)
0.797791 + 0.602934i \(0.206002\pi\)
\(308\) −0.968248 0.559018i −0.0551710 0.0318530i
\(309\) 4.58725 + 7.94534i 0.260959 + 0.451995i
\(310\) 0 0
\(311\) 14.3067 0.811256 0.405628 0.914038i \(-0.367053\pi\)
0.405628 + 0.914038i \(0.367053\pi\)
\(312\) 3.15660 + 1.74238i 0.178707 + 0.0986430i
\(313\) 13.9895i 0.790731i 0.918524 + 0.395366i \(0.129382\pi\)
−0.918524 + 0.395366i \(0.870618\pi\)
\(314\) 3.83014 2.21134i 0.216148 0.124793i
\(315\) 0 0
\(316\) 4.51910 7.82731i 0.254219 0.440320i
\(317\) 7.29868 0.409935 0.204967 0.978769i \(-0.434291\pi\)
0.204967 + 0.978769i \(0.434291\pi\)
\(318\) −2.90508 + 5.03175i −0.162909 + 0.282167i
\(319\) 16.8806 + 9.74601i 0.945131 + 0.545672i
\(320\) 0 0
\(321\) 1.60867 2.78629i 0.0897870 0.155516i
\(322\) 2.88512 1.66573i 0.160782 0.0928273i
\(323\) 17.2543 + 29.8853i 0.960055 + 1.66286i
\(324\) 1.00000 0.0555556
\(325\) 0 0
\(326\) −11.2244 −0.621661
\(327\) −8.53345 14.7804i −0.471901 0.817356i
\(328\) −7.55607 + 4.36250i −0.417214 + 0.240879i
\(329\) 1.39337 2.41339i 0.0768192 0.133055i
\(330\) 0 0
\(331\) 22.8279 + 13.1797i 1.25474 + 0.724423i 0.972046 0.234788i \(-0.0754397\pi\)
0.282690 + 0.959211i \(0.408773\pi\)
\(332\) −3.97443 + 6.88392i −0.218125 + 0.377804i
\(333\) 6.18859 0.339133
\(334\) −7.52898 + 13.0406i −0.411968 + 0.713549i
\(335\) 0 0
\(336\) −0.417738 + 0.241181i −0.0227895 + 0.0131575i
\(337\) 24.4240i 1.33046i 0.746639 + 0.665229i \(0.231666\pi\)
−0.746639 + 0.665229i \(0.768334\pi\)
\(338\) −12.9904 + 0.500000i −0.706584 + 0.0271964i
\(339\) 1.65685 0.0899880
\(340\) 0 0
\(341\) −1.10389 1.91199i −0.0597789 0.103540i
\(342\) −4.39778 2.53906i −0.237805 0.137297i
\(343\) 6.64083 0.358571
\(344\) 9.78170 + 5.64747i 0.527394 + 0.304491i
\(345\) 0 0
\(346\) 14.7486i 0.792889i
\(347\) 11.6189 + 6.70818i 0.623736 + 0.360114i 0.778322 0.627865i \(-0.216071\pi\)
−0.154586 + 0.987979i \(0.549404\pi\)
\(348\) 7.28290 4.20478i 0.390404 0.225400i
\(349\) −0.824457 + 0.476000i −0.0441322 + 0.0254797i −0.521904 0.853004i \(-0.674778\pi\)
0.477772 + 0.878484i \(0.341445\pi\)
\(350\) 0 0
\(351\) −3.08725 + 1.86250i −0.164785 + 0.0994130i
\(352\) 2.31784i 0.123541i
\(353\) 7.22380 + 12.5120i 0.384484 + 0.665946i 0.991697 0.128593i \(-0.0410460\pi\)
−0.607213 + 0.794539i \(0.707713\pi\)
\(354\) −5.91189 10.2397i −0.314213 0.544234i
\(355\) 0 0
\(356\) 9.01753i 0.477928i
\(357\) −1.63896 + 2.83876i −0.0867429 + 0.150243i
\(358\) 4.30589 7.45802i 0.227573 0.394168i
\(359\) 8.11291i 0.428183i −0.976814 0.214092i \(-0.931321\pi\)
0.976814 0.214092i \(-0.0686791\pi\)
\(360\) 0 0
\(361\) 3.39363 + 5.87794i 0.178612 + 0.309365i
\(362\) 1.42246 + 2.46378i 0.0747630 + 0.129493i
\(363\) 5.62763i 0.295374i
\(364\) 0.840459 1.52262i 0.0440520 0.0798071i
\(365\) 0 0
\(366\) −8.11924 + 4.68764i −0.424399 + 0.245027i
\(367\) 20.7806 11.9977i 1.08474 0.626274i 0.152568 0.988293i \(-0.451246\pi\)
0.932171 + 0.362019i \(0.117912\pi\)
\(368\) −5.98124 3.45327i −0.311794 0.180014i
\(369\) 8.72500i 0.454205i
\(370\) 0 0
\(371\) 2.42713 + 1.40130i 0.126010 + 0.0727520i
\(372\) −0.952516 −0.0493857
\(373\) −23.2593 13.4288i −1.20432 0.695316i −0.242809 0.970074i \(-0.578069\pi\)
−0.961513 + 0.274758i \(0.911402\pi\)
\(374\) 7.87550 + 13.6408i 0.407232 + 0.705347i
\(375\) 0 0
\(376\) −5.77729 −0.297941
\(377\) −14.6527 + 26.5456i −0.754652 + 1.36717i
\(378\) 0.482362i 0.0248100i
\(379\) 13.2638 7.65785i 0.681315 0.393357i −0.119035 0.992890i \(-0.537980\pi\)
0.800350 + 0.599533i \(0.204647\pi\)
\(380\) 0 0
\(381\) 9.45946 16.3843i 0.484623 0.839391i
\(382\) 3.43587 0.175795
\(383\) 17.6198 30.5185i 0.900332 1.55942i 0.0732675 0.997312i \(-0.476657\pi\)
0.827064 0.562108i \(-0.190009\pi\)
\(384\) 0.866025 + 0.500000i 0.0441942 + 0.0255155i
\(385\) 0 0
\(386\) 1.32843 2.30090i 0.0676152 0.117113i
\(387\) −9.78170 + 5.64747i −0.497232 + 0.287077i
\(388\) 4.59103 + 7.95189i 0.233074 + 0.403696i
\(389\) 18.0946 0.917433 0.458717 0.888583i \(-0.348309\pi\)
0.458717 + 0.888583i \(0.348309\pi\)
\(390\) 0 0
\(391\) −46.9338 −2.37354
\(392\) −3.38366 5.86068i −0.170901 0.296009i
\(393\) −6.03457 + 3.48406i −0.304404 + 0.175748i
\(394\) 10.5579 18.2868i 0.531899 0.921276i
\(395\) 0 0
\(396\) −2.00731 1.15892i −0.100871 0.0582379i
\(397\) 5.22562 9.05105i 0.262267 0.454259i −0.704577 0.709627i \(-0.748863\pi\)
0.966844 + 0.255368i \(0.0821967\pi\)
\(398\) −10.5388 −0.528263
\(399\) −1.22474 + 2.12132i −0.0613139 + 0.106199i
\(400\) 0 0
\(401\) −1.21317 + 0.700423i −0.0605827 + 0.0349775i −0.529985 0.848007i \(-0.677803\pi\)
0.469403 + 0.882984i \(0.344469\pi\)
\(402\) 7.39355i 0.368757i
\(403\) 2.94065 1.77406i 0.146484 0.0883723i
\(404\) 10.6822 0.531457
\(405\) 0 0
\(406\) −2.02823 3.51299i −0.100659 0.174347i
\(407\) −12.4224 7.17207i −0.615755 0.355506i
\(408\) 6.79555 0.336430
\(409\) −5.83817 3.37067i −0.288679 0.166669i 0.348667 0.937247i \(-0.386634\pi\)
−0.637346 + 0.770578i \(0.719968\pi\)
\(410\) 0 0
\(411\) 20.5093i 1.01165i
\(412\) −7.94534 4.58725i −0.391439 0.225997i
\(413\) −4.93924 + 2.85167i −0.243044 + 0.140322i
\(414\) 5.98124 3.45327i 0.293962 0.169719i
\(415\) 0 0
\(416\) −3.60488 + 0.0693504i −0.176744 + 0.00340018i
\(417\) 8.50935i 0.416704i
\(418\) 5.88512 + 10.1933i 0.287851 + 0.498572i
\(419\) 18.2539 + 31.6166i 0.891760 + 1.54457i 0.837765 + 0.546032i \(0.183862\pi\)
0.0539949 + 0.998541i \(0.482805\pi\)
\(420\) 0 0
\(421\) 40.8490i 1.99086i −0.0955005 0.995429i \(-0.530445\pi\)
0.0955005 0.995429i \(-0.469555\pi\)
\(422\) −5.74384 + 9.94863i −0.279606 + 0.484292i
\(423\) 2.88865 5.00328i 0.140451 0.243268i
\(424\) 5.81017i 0.282167i
\(425\) 0 0
\(426\) 1.74288 + 3.01876i 0.0844429 + 0.146259i
\(427\) 2.26114 + 3.91641i 0.109424 + 0.189528i
\(428\) 3.21733i 0.155516i
\(429\) 8.35554 0.160743i 0.403409 0.00776074i
\(430\) 0 0
\(431\) −15.9145 + 9.18824i −0.766575 + 0.442582i −0.831651 0.555298i \(-0.812604\pi\)
0.0650767 + 0.997880i \(0.479271\pi\)
\(432\) −0.866025 + 0.500000i −0.0416667 + 0.0240563i
\(433\) −1.21087 0.699097i −0.0581907 0.0335964i 0.470622 0.882335i \(-0.344029\pi\)
−0.528813 + 0.848738i \(0.677363\pi\)
\(434\) 0.459457i 0.0220547i
\(435\) 0 0
\(436\) 14.7804 + 8.53345i 0.707851 + 0.408678i
\(437\) −35.0722 −1.67773
\(438\) 7.39123 + 4.26733i 0.353166 + 0.203901i
\(439\) 7.65685 + 13.2621i 0.365442 + 0.632964i 0.988847 0.148935i \(-0.0475846\pi\)
−0.623405 + 0.781899i \(0.714251\pi\)
\(440\) 0 0
\(441\) 6.76733 0.322254
\(442\) −20.9796 + 12.6567i −0.997895 + 0.602019i
\(443\) 33.1769i 1.57628i −0.615495 0.788141i \(-0.711044\pi\)
0.615495 0.788141i \(-0.288956\pi\)
\(444\) −5.35948 + 3.09429i −0.254349 + 0.146849i
\(445\) 0 0
\(446\) 2.61389 4.52739i 0.123771 0.214378i
\(447\) −7.24504 −0.342679
\(448\) 0.241181 0.417738i 0.0113947 0.0197362i
\(449\) −13.3408 7.70234i −0.629593 0.363496i 0.151001 0.988534i \(-0.451750\pi\)
−0.780595 + 0.625038i \(0.785084\pi\)
\(450\) 0 0
\(451\) −10.1116 + 17.5137i −0.476135 + 0.824690i
\(452\) −1.43488 + 0.828427i −0.0674910 + 0.0389659i
\(453\) 3.91372 + 6.77875i 0.183882 + 0.318494i
\(454\) −10.8689 −0.510101
\(455\) 0 0
\(456\) 5.07812 0.237805
\(457\) −3.73097 6.46224i −0.174528 0.302291i 0.765470 0.643471i \(-0.222506\pi\)
−0.939998 + 0.341181i \(0.889173\pi\)
\(458\) −18.3538 + 10.5966i −0.857618 + 0.495146i
\(459\) −3.39778 + 5.88512i −0.158595 + 0.274694i
\(460\) 0 0
\(461\) −3.97457 2.29472i −0.185114 0.106876i 0.404579 0.914503i \(-0.367418\pi\)
−0.589693 + 0.807627i \(0.700751\pi\)
\(462\) −0.559018 + 0.968248i −0.0260079 + 0.0450470i
\(463\) 9.20888 0.427973 0.213986 0.976837i \(-0.431355\pi\)
0.213986 + 0.976837i \(0.431355\pi\)
\(464\) −4.20478 + 7.28290i −0.195202 + 0.338100i
\(465\) 0 0
\(466\) 18.9160 10.9212i 0.876267 0.505913i
\(467\) 0.219469i 0.0101558i 0.999987 + 0.00507792i \(0.00161636\pi\)
−0.999987 + 0.00507792i \(0.998384\pi\)
\(468\) 1.74238 3.15660i 0.0805417 0.145914i
\(469\) −3.56637 −0.164680
\(470\) 0 0
\(471\) −2.21134 3.83014i −0.101893 0.176484i
\(472\) 10.2397 + 5.91189i 0.471320 + 0.272117i
\(473\) 26.1798 1.20375
\(474\) −7.82731 4.51910i −0.359520 0.207569i
\(475\) 0 0
\(476\) 3.27792i 0.150243i
\(477\) 5.03175 + 2.90508i 0.230388 + 0.133015i
\(478\) 7.12762 4.11513i 0.326010 0.188222i
\(479\) 5.49422 3.17209i 0.251037 0.144936i −0.369202 0.929349i \(-0.620369\pi\)
0.620239 + 0.784413i \(0.287036\pi\)
\(480\) 0 0
\(481\) 10.7829 19.5349i 0.491658 0.890714i
\(482\) 3.10243i 0.141312i
\(483\) −1.66573 2.88512i −0.0757932 0.131278i
\(484\) −2.81382 4.87367i −0.127901 0.221530i
\(485\) 0 0
\(486\) 1.00000i 0.0453609i
\(487\) −18.5972 + 32.2113i −0.842720 + 1.45963i 0.0448662 + 0.998993i \(0.485714\pi\)
−0.887586 + 0.460641i \(0.847619\pi\)
\(488\) 4.68764 8.11924i 0.212200 0.367541i
\(489\) 11.2244i 0.507584i
\(490\) 0 0
\(491\) 2.99901 + 5.19444i 0.135344 + 0.234422i 0.925729 0.378188i \(-0.123453\pi\)
−0.790385 + 0.612610i \(0.790120\pi\)
\(492\) 4.36250 + 7.55607i 0.196677 + 0.340654i
\(493\) 57.1477i 2.57380i
\(494\) −15.6774 + 9.45800i −0.705359 + 0.425535i
\(495\) 0 0
\(496\) 0.824903 0.476258i 0.0370392 0.0213846i
\(497\) 1.45613 0.840699i 0.0653165 0.0377105i
\(498\) 6.88392 + 3.97443i 0.308476 + 0.178099i
\(499\) 21.2908i 0.953107i 0.879145 + 0.476554i \(0.158114\pi\)
−0.879145 + 0.476554i \(0.841886\pi\)
\(500\) 0 0
\(501\) 13.0406 + 7.52898i 0.582610 + 0.336370i
\(502\) 15.6208 0.697193
\(503\) −16.4925 9.52194i −0.735363 0.424562i 0.0850178 0.996379i \(-0.472905\pi\)
−0.820381 + 0.571817i \(0.806239\pi\)
\(504\) 0.241181 + 0.417738i 0.0107431 + 0.0186075i
\(505\) 0 0
\(506\) −16.0082 −0.711653
\(507\) 0.500000 + 12.9904i 0.0222058 + 0.576923i
\(508\) 18.9189i 0.839391i
\(509\) 24.6679 14.2420i 1.09339 0.631267i 0.158911 0.987293i \(-0.449202\pi\)
0.934476 + 0.356026i \(0.115868\pi\)
\(510\) 0 0
\(511\) 2.05840 3.56525i 0.0910581 0.157717i
\(512\) −1.00000 −0.0441942
\(513\) −2.53906 + 4.39778i −0.112102 + 0.194167i
\(514\) −3.05205 1.76210i −0.134620 0.0777230i
\(515\) 0 0
\(516\) 5.64747 9.78170i 0.248616 0.430615i
\(517\) −11.5968 + 6.69541i −0.510027 + 0.294464i
\(518\) 1.49257 + 2.58521i 0.0655797 + 0.113587i
\(519\) 14.7486 0.647391
\(520\) 0 0
\(521\) −27.6617 −1.21188 −0.605940 0.795511i \(-0.707203\pi\)
−0.605940 + 0.795511i \(0.707203\pi\)
\(522\) −4.20478 7.28290i −0.184038 0.318764i
\(523\) −14.6308 + 8.44709i −0.639759 + 0.369365i −0.784522 0.620101i \(-0.787092\pi\)
0.144762 + 0.989466i \(0.453758\pi\)
\(524\) 3.48406 6.03457i 0.152202 0.263622i
\(525\) 0 0
\(526\) −20.1637 11.6415i −0.879177 0.507593i
\(527\) 3.23644 5.60567i 0.140981 0.244187i
\(528\) 2.31784 0.100871
\(529\) 12.3502 21.3911i 0.536964 0.930049i
\(530\) 0 0
\(531\) −10.2397 + 5.91189i −0.444365 + 0.256554i
\(532\) 2.44949i 0.106199i
\(533\) −27.5413 15.2023i −1.19295 0.658485i
\(534\) −9.01753 −0.390227
\(535\) 0 0
\(536\) 3.69677 + 6.40300i 0.159676 + 0.276568i
\(537\) −7.45802 4.30589i −0.321837 0.185813i
\(538\) 9.81746 0.423261
\(539\) −13.5841 7.84278i −0.585108 0.337813i
\(540\) 0 0
\(541\) 30.6639i 1.31834i −0.751993 0.659171i \(-0.770907\pi\)
0.751993 0.659171i \(-0.229093\pi\)
\(542\) −18.8862 10.9040i −0.811233 0.468365i
\(543\) 2.46378 1.42246i 0.105731 0.0610438i
\(544\) −5.88512 + 3.39778i −0.252323 + 0.145679i
\(545\) 0 0
\(546\) −1.52262 0.840459i −0.0651622 0.0359683i
\(547\) 40.6726i 1.73903i 0.493903 + 0.869517i \(0.335570\pi\)
−0.493903 + 0.869517i \(0.664430\pi\)
\(548\) 10.2547 + 17.7616i 0.438058 + 0.758739i
\(549\) 4.68764 + 8.11924i 0.200064 + 0.346521i
\(550\) 0 0
\(551\) 42.7048i 1.81928i
\(552\) −3.45327 + 5.98124i −0.146981 + 0.254579i
\(553\) −2.17984 + 3.77559i −0.0926963 + 0.160555i
\(554\) 13.4751i 0.572501i
\(555\) 0 0
\(556\) −4.25467 7.36931i −0.180438 0.312528i
\(557\) −9.22730 15.9822i −0.390973 0.677186i 0.601605 0.798794i \(-0.294528\pi\)
−0.992578 + 0.121608i \(0.961195\pi\)
\(558\) 0.952516i 0.0403232i
\(559\) 0.783308 + 40.7169i 0.0331304 + 1.72214i
\(560\) 0 0
\(561\) 13.6408 7.87550i 0.575913 0.332504i
\(562\) 25.6488 14.8083i 1.08193 0.624652i
\(563\) −8.17129 4.71770i −0.344379 0.198827i 0.317828 0.948148i \(-0.397047\pi\)
−0.662207 + 0.749321i \(0.730380\pi\)
\(564\) 5.77729i 0.243268i
\(565\) 0 0
\(566\) −10.5516 6.09197i −0.443517 0.256065i
\(567\) −0.482362 −0.0202573
\(568\) −3.01876 1.74288i −0.126664 0.0731297i
\(569\) −5.33503 9.24054i −0.223656 0.387384i 0.732259 0.681026i \(-0.238466\pi\)
−0.955915 + 0.293642i \(0.905133\pi\)
\(570\) 0 0
\(571\) 0.532730 0.0222941 0.0111470 0.999938i \(-0.496452\pi\)
0.0111470 + 0.999938i \(0.496452\pi\)
\(572\) −7.15573 + 4.31697i −0.299196 + 0.180502i
\(573\) 3.43587i 0.143536i
\(574\) 3.64476 2.10430i 0.152129 0.0878320i
\(575\) 0 0
\(576\) 0.500000 0.866025i 0.0208333 0.0360844i
\(577\) −26.0683 −1.08524 −0.542620 0.839978i \(-0.682568\pi\)
−0.542620 + 0.839978i \(0.682568\pi\)
\(578\) −14.5898 + 25.2702i −0.606855 + 1.05110i
\(579\) −2.30090 1.32843i −0.0956223 0.0552075i
\(580\) 0 0
\(581\) 1.91712 3.32054i 0.0795354 0.137759i
\(582\) 7.95189 4.59103i 0.329617 0.190304i
\(583\) −6.73351 11.6628i −0.278874 0.483023i
\(584\) −8.53465 −0.353166
\(585\) 0 0
\(586\) −15.0209 −0.620509
\(587\) 7.37501 + 12.7739i 0.304399 + 0.527235i 0.977127 0.212655i \(-0.0682110\pi\)
−0.672728 + 0.739890i \(0.734878\pi\)
\(588\) −5.86068 + 3.38366i −0.241690 + 0.139540i
\(589\) 2.41849 4.18895i 0.0996523 0.172603i
\(590\) 0 0
\(591\) −18.2868 10.5579i −0.752219 0.434294i
\(592\) 3.09429 5.35948i 0.127175 0.220273i
\(593\) 23.4887 0.964566 0.482283 0.876015i \(-0.339808\pi\)
0.482283 + 0.876015i \(0.339808\pi\)
\(594\) −1.15892 + 2.00731i −0.0475510 + 0.0823608i
\(595\) 0 0
\(596\) 6.27439 3.62252i 0.257009 0.148384i
\(597\) 10.5388i 0.431325i
\(598\) −0.478971 24.8973i −0.0195866 1.01813i
\(599\) −3.72087 −0.152031 −0.0760154 0.997107i \(-0.524220\pi\)
−0.0760154 + 0.997107i \(0.524220\pi\)
\(600\) 0 0
\(601\) 21.1757 + 36.6773i 0.863773 + 1.49610i 0.868261 + 0.496109i \(0.165238\pi\)
−0.00448765 + 0.999990i \(0.501428\pi\)
\(602\) −4.71832 2.72412i −0.192304 0.111027i
\(603\) −7.39355 −0.301089
\(604\) −6.77875 3.91372i −0.275824 0.159247i
\(605\) 0 0
\(606\) 10.6822i 0.433933i
\(607\) 16.4692 + 9.50853i 0.668466 + 0.385939i 0.795495 0.605960i \(-0.207211\pi\)
−0.127029 + 0.991899i \(0.540544\pi\)
\(608\) −4.39778 + 2.53906i −0.178353 + 0.102972i
\(609\) −3.51299 + 2.02823i −0.142354 + 0.0821879i
\(610\) 0 0
\(611\) −10.7602 17.8359i −0.435312 0.721565i
\(612\) 6.79555i 0.274694i
\(613\) −11.4126 19.7672i −0.460951 0.798390i 0.538058 0.842908i \(-0.319158\pi\)
−0.999009 + 0.0445178i \(0.985825\pi\)
\(614\) 13.9784 + 24.2114i 0.564124 + 0.977091i
\(615\) 0 0
\(616\) 1.11804i 0.0450470i
\(617\) 8.66682 15.0114i 0.348913 0.604335i −0.637144 0.770745i \(-0.719884\pi\)
0.986057 + 0.166410i \(0.0532175\pi\)
\(618\) −4.58725 + 7.94534i −0.184526 + 0.319609i
\(619\) 0.972021i 0.0390688i −0.999809 0.0195344i \(-0.993782\pi\)
0.999809 0.0195344i \(-0.00621839\pi\)
\(620\) 0 0
\(621\) −3.45327 5.98124i −0.138575 0.240019i
\(622\) 7.15333 + 12.3899i 0.286822 + 0.496791i
\(623\) 4.34971i 0.174268i
\(624\) 0.0693504 + 3.60488i 0.00277624 + 0.144311i
\(625\) 0 0
\(626\) −12.1152 + 6.99473i −0.484222 + 0.279566i
\(627\) 10.1933 5.88512i 0.407082 0.235029i
\(628\) 3.83014 + 2.21134i 0.152839 + 0.0882419i
\(629\) 42.0549i 1.67684i
\(630\) 0 0
\(631\) 4.53981 + 2.62106i 0.180727 + 0.104343i 0.587634 0.809127i \(-0.300059\pi\)
−0.406907 + 0.913470i \(0.633393\pi\)
\(632\) 9.03820 0.359520
\(633\) 9.94863 + 5.74384i 0.395422 + 0.228297i
\(634\) 3.64934 + 6.32085i 0.144934 + 0.251033i
\(635\) 0 0
\(636\) −5.81017 −0.230388
\(637\) 11.7913 21.3617i 0.467187 0.846382i
\(638\) 19.4920i 0.771696i
\(639\) 3.01876 1.74288i 0.119420 0.0689473i
\(640\) 0 0
\(641\) −16.4075 + 28.4186i −0.648057 + 1.12247i 0.335529 + 0.942030i \(0.391085\pi\)
−0.983586 + 0.180439i \(0.942248\pi\)
\(642\) 3.21733 0.126978
\(643\) 5.82478 10.0888i 0.229707 0.397864i −0.728014 0.685562i \(-0.759557\pi\)
0.957721 + 0.287698i \(0.0928899\pi\)
\(644\) 2.88512 + 1.66573i 0.113690 + 0.0656388i
\(645\) 0 0
\(646\) −17.2543 + 29.8853i −0.678862 + 1.17582i
\(647\) 19.2123 11.0922i 0.755314 0.436081i −0.0722970 0.997383i \(-0.523033\pi\)
0.827611 + 0.561303i \(0.189700\pi\)
\(648\) 0.500000 + 0.866025i 0.0196419 + 0.0340207i
\(649\) 27.4056 1.07576
\(650\) 0 0
\(651\) 0.459457 0.0180076
\(652\) −5.61219 9.72060i −0.219790 0.380688i
\(653\) 28.8844 16.6764i 1.13033 0.652598i 0.186314 0.982490i \(-0.440346\pi\)
0.944019 + 0.329892i \(0.107012\pi\)
\(654\) 8.53345 14.7804i 0.333684 0.577958i
\(655\) 0 0
\(656\) −7.55607 4.36250i −0.295015 0.170327i
\(657\) 4.26733 7.39123i 0.166484 0.288359i
\(658\) 2.78675 0.108639
\(659\) −12.2280 + 21.1796i −0.476337 + 0.825039i −0.999632 0.0271118i \(-0.991369\pi\)
0.523296 + 0.852151i \(0.324702\pi\)
\(660\) 0 0
\(661\) 28.8737 16.6702i 1.12306 0.648396i 0.180876 0.983506i \(-0.442107\pi\)
0.942179 + 0.335109i \(0.108773\pi\)
\(662\) 26.3594i 1.02449i
\(663\) 12.6567 + 20.9796i 0.491547 + 0.814778i
\(664\) −7.94887 −0.308476
\(665\) 0 0
\(666\) 3.09429 + 5.35948i 0.119901 + 0.207675i
\(667\) −50.2997 29.0405i −1.94761 1.12445i
\(668\) −15.0580 −0.582610
\(669\) −4.52739 2.61389i −0.175039 0.101059i
\(670\) 0 0
\(671\) 21.7304i 0.838893i
\(672\) −0.417738 0.241181i −0.0161146 0.00930376i
\(673\) 29.4265 16.9894i 1.13431 0.654893i 0.189293 0.981921i \(-0.439380\pi\)
0.945015 + 0.327028i \(0.106047\pi\)
\(674\) −21.1518 + 12.2120i −0.814736 + 0.470388i
\(675\) 0 0
\(676\) −6.92820 11.0000i −0.266469 0.423077i
\(677\) 10.3145i 0.396417i 0.980160 + 0.198208i \(0.0635123\pi\)
−0.980160 + 0.198208i \(0.936488\pi\)
\(678\) 0.828427 + 1.43488i 0.0318156 + 0.0551062i
\(679\) −2.21454 3.83569i −0.0849861 0.147200i
\(680\) 0 0
\(681\) 10.8689i 0.416496i
\(682\) 1.10389 1.91199i 0.0422701 0.0732139i
\(683\) −24.5191 + 42.4682i −0.938196 + 1.62500i −0.169362 + 0.985554i \(0.554171\pi\)
−0.768834 + 0.639448i \(0.779163\pi\)
\(684\) 5.07812i 0.194167i
\(685\) 0 0
\(686\) 3.32042 + 5.75113i 0.126774 + 0.219579i
\(687\) 10.5966 + 18.3538i 0.404285 + 0.700242i
\(688\) 11.2949i 0.430615i
\(689\) 17.9374 10.8214i 0.683361 0.412264i
\(690\) 0 0
\(691\) 29.7340 17.1669i 1.13113 0.653061i 0.186914 0.982376i \(-0.440151\pi\)
0.944220 + 0.329315i \(0.106818\pi\)
\(692\) −12.7727 + 7.37429i −0.485543 + 0.280329i
\(693\) 0.968248 + 0.559018i 0.0367807 + 0.0212353i
\(694\) 13.4164i 0.509278i
\(695\) 0 0
\(696\) 7.28290 + 4.20478i 0.276058 + 0.159382i
\(697\) −59.2912 −2.24582
\(698\) −0.824457 0.476000i −0.0312061 0.0180169i
\(699\) −10.9212 18.9160i −0.413076 0.715469i
\(700\) 0 0
\(701\) −32.0303 −1.20977 −0.604885 0.796313i \(-0.706781\pi\)
−0.604885 + 0.796313i \(0.706781\pi\)
\(702\) −3.15660 1.74238i −0.119138 0.0657620i
\(703\) 31.4264i 1.18527i
\(704\) −2.00731 + 1.15892i −0.0756532 + 0.0436784i
\(705\) 0 0
\(706\) −7.22380 + 12.5120i −0.271871 + 0.470895i
\(707\) −5.15267 −0.193786
\(708\) 5.91189 10.2397i 0.222182 0.384831i
\(709\) −27.0809 15.6352i −1.01704 0.587190i −0.103797 0.994598i \(-0.533099\pi\)
−0.913246 + 0.407408i \(0.866433\pi\)
\(710\) 0 0
\(711\) −4.51910 + 7.82731i −0.169479 + 0.293547i
\(712\) 7.80941 4.50877i 0.292670 0.168973i
\(713\) 3.28930 + 5.69723i 0.123185 + 0.213363i
\(714\) −3.27792 −0.122673
\(715\) 0 0
\(716\) 8.61177 0.321837
\(717\) −4.11513 7.12762i −0.153683 0.266186i
\(718\) 7.02599 4.05646i 0.262208 0.151386i
\(719\) 10.6716 18.4838i 0.397984 0.689328i −0.595494 0.803360i \(-0.703043\pi\)
0.993477 + 0.114032i \(0.0363768\pi\)
\(720\) 0 0
\(721\) 3.83253 + 2.21271i 0.142731 + 0.0824057i
\(722\) −3.39363 + 5.87794i −0.126298 + 0.218754i
\(723\) −3.10243 −0.115381
\(724\) −1.42246 + 2.46378i −0.0528655 + 0.0915656i
\(725\) 0 0
\(726\) −4.87367 + 2.81382i −0.180879 + 0.104430i
\(727\) 8.80283i 0.326479i 0.986586 + 0.163240i \(0.0521943\pi\)
−0.986586 + 0.163240i \(0.947806\pi\)
\(728\) 1.73886 0.0334520i 0.0644464 0.00123981i
\(729\) −1.00000 −0.0370370
\(730\) 0 0
\(731\) 38.3777 + 66.4721i 1.41945 + 2.45856i
\(732\) −8.11924 4.68764i −0.300096 0.173260i
\(733\) 7.86883 0.290642 0.145321 0.989385i \(-0.453579\pi\)
0.145321 + 0.989385i \(0.453579\pi\)
\(734\) 20.7806 + 11.9977i 0.767026 + 0.442843i
\(735\) 0 0
\(736\) 6.90654i 0.254579i
\(737\) 14.8411 + 8.56852i 0.546680 + 0.315626i
\(738\) 7.55607 4.36250i 0.278143 0.160586i
\(739\) −15.6988 + 9.06368i −0.577488 + 0.333413i −0.760134 0.649766i \(-0.774867\pi\)
0.182646 + 0.983179i \(0.441534\pi\)
\(740\) 0 0
\(741\) 9.45800 + 15.6774i 0.347448 + 0.575923i
\(742\) 2.80260i 0.102887i
\(743\) −0.687322 1.19048i −0.0252154 0.0436744i 0.853142 0.521678i \(-0.174694\pi\)
−0.878358 + 0.478004i \(0.841360\pi\)
\(744\) −0.476258 0.824903i −0.0174605 0.0302424i
\(745\) 0 0
\(746\) 26.8576i 0.983325i
\(747\) 3.97443 6.88392i 0.145417 0.251870i
\(748\) −7.87550 + 13.6408i −0.287957 + 0.498756i
\(749\) 1.55192i 0.0567059i
\(750\) 0 0
\(751\) −19.0127 32.9310i −0.693784 1.20167i −0.970589 0.240743i \(-0.922609\pi\)
0.276805 0.960926i \(-0.410724\pi\)
\(752\) −2.88865 5.00328i −0.105338 0.182451i
\(753\) 15.6208i 0.569255i
\(754\) −30.3155 + 0.583207i −1.10403 + 0.0212391i
\(755\) 0 0
\(756\) 0.417738 0.241181i 0.0151930 0.00877167i
\(757\) 32.0033 18.4771i 1.16318 0.671562i 0.211115 0.977461i \(-0.432290\pi\)
0.952064 + 0.305899i \(0.0989571\pi\)
\(758\) 13.2638 + 7.65785i 0.481762 + 0.278146i
\(759\) 16.0082i 0.581062i
\(760\) 0 0
\(761\) 25.9967 + 15.0092i 0.942380 + 0.544084i 0.890706 0.454580i \(-0.150211\pi\)
0.0516746 + 0.998664i \(0.483544\pi\)
\(762\) 18.9189 0.685360
\(763\) −7.12949 4.11621i −0.258105 0.149017i
\(764\) 1.71794 + 2.97555i 0.0621528 + 0.107652i
\(765\) 0 0
\(766\) 35.2397 1.27326
\(767\) 0.819984 + 42.6234i 0.0296079 + 1.53904i
\(768\) 1.00000i 0.0360844i
\(769\) 39.3038 22.6921i 1.41733 0.818297i 0.421268 0.906936i \(-0.361585\pi\)
0.996064 + 0.0886391i \(0.0282518\pi\)
\(770\) 0 0
\(771\) −1.76210 + 3.05205i −0.0634606 + 0.109917i
\(772\) 2.65685 0.0956223
\(773\) 12.7671 22.1132i 0.459200 0.795358i −0.539719 0.841845i \(-0.681469\pi\)
0.998919 + 0.0464877i \(0.0148028\pi\)
\(774\) −9.78170 5.64747i −0.351596 0.202994i
\(775\) 0 0
\(776\) −4.59103 + 7.95189i −0.164808 + 0.285456i
\(777\) 2.58521 1.49257i 0.0927438 0.0535456i
\(778\) 9.04731 + 15.6704i 0.324362 + 0.561811i
\(779\) −44.3066 −1.58745
\(780\) 0 0
\(781\) −8.07943 −0.289105
\(782\) −23.4669 40.6459i −0.839175 1.45349i
\(783\) −7.28290 + 4.20478i −0.260270 + 0.150267i
\(784\) 3.38366 5.86068i 0.120845 0.209310i
\(785\) 0 0
\(786\) −6.03457 3.48406i −0.215246 0.124272i
\(787\) 15.7499 27.2796i 0.561423 0.972413i −0.435949 0.899971i \(-0.643587\pi\)
0.997373 0.0724422i \(-0.0230793\pi\)
\(788\) 21.1158 0.752219
\(789\) −11.6415 + 20.1637i −0.414448 + 0.717845i
\(790\) 0 0
\(791\) 0.692130 0.399602i 0.0246093 0.0142082i
\(792\) 2.31784i 0.0823608i
\(793\) 33.7968 0.650180i 1.20016 0.0230886i
\(794\) 10.4512 0.370901
\(795\) 0 0
\(796\) −5.26941 9.12688i −0.186769 0.323494i
\(797\) −37.5831 21.6986i −1.33126 0.768605i −0.345769 0.938320i \(-0.612382\pi\)
−0.985493 + 0.169715i \(0.945715\pi\)
\(798\) −2.44949 −0.0867110
\(799\) −34.0001 19.6300i −1.20284 0.694458i
\(800\) 0 0
\(801\) 9.01753i 0.318619i
\(802\) −1.21317 0.700423i −0.0428385 0.0247328i
\(803\) −17.1317 + 9.89097i −0.604563 + 0.349045i
\(804\) 6.40300 3.69677i 0.225816 0.130375i
\(805\) 0 0
\(806\) 3.00671 + 1.65965i 0.105907 + 0.0584586i
\(807\) 9.81746i 0.345591i
\(808\) 5.34108 + 9.25102i 0.187899 + 0.325450i
\(809\) 16.3279 + 28.2807i 0.574057 + 0.994296i 0.996143 + 0.0877407i \(0.0279647\pi\)
−0.422086 + 0.906556i \(0.638702\pi\)
\(810\) 0 0
\(811\) 30.1669i 1.05930i 0.848216 + 0.529651i \(0.177677\pi\)
−0.848216 + 0.529651i \(0.822323\pi\)
\(812\) 2.02823 3.51299i 0.0711768 0.123282i
\(813\) −10.9040 + 18.8862i −0.382419 + 0.662369i
\(814\) 14.3441i 0.502762i
\(815\) 0 0
\(816\) 3.39778 + 5.88512i 0.118946 + 0.206021i
\(817\) 28.6785 + 49.6726i 1.00333 + 1.73782i
\(818\) 6.74134i 0.235705i
\(819\) −0.840459 + 1.52262i −0.0293680 + 0.0532047i
\(820\) 0 0
\(821\) 6.92648 3.99900i 0.241736 0.139566i −0.374238 0.927332i \(-0.622096\pi\)
0.615974 + 0.787766i \(0.288763\pi\)
\(822\) 17.7616 10.2547i 0.619507 0.357673i
\(823\) −35.5109 20.5022i −1.23783 0.714663i −0.269182 0.963089i \(-0.586753\pi\)
−0.968651 + 0.248426i \(0.920087\pi\)
\(824\) 9.17449i 0.319609i
\(825\) 0 0
\(826\) −4.93924 2.85167i −0.171858 0.0992223i
\(827\) 32.0321 1.11386 0.556932 0.830558i \(-0.311978\pi\)
0.556932 + 0.830558i \(0.311978\pi\)
\(828\) 5.98124 + 3.45327i 0.207863 + 0.120009i
\(829\) 9.75006 + 16.8876i 0.338634 + 0.586531i 0.984176 0.177194i \(-0.0567019\pi\)
−0.645542 + 0.763725i \(0.723369\pi\)
\(830\) 0 0
\(831\) −13.4751 −0.467445
\(832\) −1.86250 3.08725i −0.0645706 0.107031i
\(833\) 45.9877i 1.59338i
\(834\) −7.36931 + 4.25467i −0.255178 + 0.147327i
\(835\) 0 0
\(836\) −5.88512 + 10.1933i −0.203541 + 0.352544i
\(837\) 0.952516 0.0329238
\(838\) −18.2539 + 31.6166i −0.630569 + 1.09218i
\(839\) 7.55900 + 4.36419i 0.260966 + 0.150669i 0.624775 0.780805i \(-0.285191\pi\)
−0.363809 + 0.931473i \(0.618524\pi\)
\(840\) 0 0
\(841\) −20.8604 + 36.1313i −0.719325 + 1.24591i
\(842\) 35.3763 20.4245i 1.21915 0.703875i
\(843\) −14.8083 25.6488i −0.510026 0.883392i
\(844\) −11.4877 −0.395422
\(845\) 0 0
\(846\) 5.77729 0.198627
\(847\) 1.35728 + 2.35087i 0.0466366 + 0.0807770i
\(848\) 5.03175 2.90508i 0.172791 0.0997610i
\(849\) −6.09197 + 10.5516i −0.209076 + 0.362130i
\(850\) 0 0
\(851\) 37.0154 + 21.3709i 1.26887 + 0.732584i
\(852\) −1.74288 + 3.01876i −0.0597101 + 0.103421i
\(853\) −25.1210 −0.860125 −0.430063 0.902799i \(-0.641509\pi\)
−0.430063 + 0.902799i \(0.641509\pi\)
\(854\) −2.26114 + 3.91641i −0.0773747 + 0.134017i
\(855\) 0 0
\(856\) −2.78629 + 1.60867i −0.0952335 + 0.0549831i
\(857\) 48.1300i 1.64409i −0.569423 0.822045i \(-0.692833\pi\)
0.569423 0.822045i \(-0.307167\pi\)
\(858\) 4.31697 + 7.15573i 0.147379 + 0.244293i
\(859\) 47.1707 1.60944 0.804721 0.593653i \(-0.202315\pi\)
0.804721 + 0.593653i \(0.202315\pi\)
\(860\) 0 0
\(861\) −2.10430 3.64476i −0.0717145 0.124213i
\(862\) −15.9145 9.18824i −0.542050 0.312953i
\(863\) −26.6095 −0.905799 −0.452900 0.891562i \(-0.649610\pi\)
−0.452900 + 0.891562i \(0.649610\pi\)
\(864\) −0.866025 0.500000i −0.0294628 0.0170103i
\(865\) 0 0
\(866\) 1.39819i 0.0475125i
\(867\) 25.2702 + 14.5898i 0.858223 + 0.495495i
\(868\) −0.397902 + 0.229729i −0.0135057 + 0.00779750i
\(869\) 18.1424 10.4745i 0.615440 0.355324i
\(870\) 0 0
\(871\) −12.8824 + 23.3385i −0.436503 + 0.790793i
\(872\) 17.0669i 0.577958i
\(873\) −4.59103 7.95189i −0.155383 0.269131i
\(874\) −17.5361 30.3734i −0.593168 1.02740i
\(875\) 0 0
\(876\) 8.53465i 0.288359i
\(877\) −3.35180 + 5.80548i −0.113182 + 0.196037i −0.917052 0.398769i \(-0.869438\pi\)
0.803870 + 0.594806i \(0.202771\pi\)
\(878\) −7.65685 + 13.2621i −0.258406 + 0.447573i
\(879\) 15.0209i 0.506643i
\(880\) 0 0
\(881\) −5.09215 8.81986i −0.171559 0.297149i 0.767406 0.641161i \(-0.221547\pi\)
−0.938965 + 0.344013i \(0.888214\pi\)
\(882\) 3.38366 + 5.86068i 0.113934 + 0.197339i
\(883\) 45.3554i 1.52633i −0.646204 0.763165i \(-0.723644\pi\)
0.646204 0.763165i \(-0.276356\pi\)
\(884\) −21.4508 11.8405i −0.721469 0.398238i
\(885\) 0 0
\(886\) 28.7320 16.5884i 0.965272 0.557300i
\(887\) 29.7753 17.1908i 0.999757 0.577210i 0.0915805 0.995798i \(-0.470808\pi\)
0.908176 + 0.418588i \(0.137475\pi\)
\(888\) −5.35948 3.09429i −0.179852 0.103838i
\(889\) 9.12576i 0.306068i
\(890\) 0 0
\(891\) 2.00731 + 1.15892i 0.0672473 + 0.0388252i
\(892\) 5.22778 0.175039
\(893\) −25.4073 14.6689i −0.850221 0.490876i
\(894\) −3.62252 6.27439i −0.121155 0.209847i
\(895\) 0 0
\(896\) 0.482362 0.0161146
\(897\) −24.8973 + 0.478971i −0.831296 + 0.0159924i
\(898\) 15.4047i 0.514061i
\(899\) 6.93708 4.00512i 0.231365 0.133578i
\(900\) 0 0
\(901\) 19.7417 34.1935i 0.657690 1.13915i
\(902\) −20.2231 −0.673357
\(903\) −2.72412 + 4.71832i −0.0906531 + 0.157016i
\(904\) −1.43488 0.828427i −0.0477233 0.0275531i
\(905\) 0 0
\(906\) −3.91372 + 6.77875i −0.130024 + 0.225209i
\(907\) 29.4110 16.9804i 0.976575 0.563826i 0.0753408 0.997158i \(-0.475996\pi\)
0.901234 + 0.433332i \(0.142662\pi\)
\(908\) −5.43443 9.41271i −0.180348 0.312372i
\(909\) −10.6822 −0.354305
\(910\) 0 0
\(911\) 35.0487 1.16121 0.580607 0.814184i \(-0.302815\pi\)
0.580607 + 0.814184i \(0.302815\pi\)
\(912\) 2.53906 + 4.39778i 0.0840766 + 0.145625i
\(913\) −15.9558 + 9.21209i −0.528060 + 0.304876i
\(914\) 3.73097 6.46224i 0.123410 0.213752i
\(915\) 0 0
\(916\) −18.3538 10.5966i −0.606428 0.350121i
\(917\) −1.68058 + 2.91085i −0.0554976 + 0.0961247i
\(918\) −6.79555 −0.224287
\(919\) −8.74038 + 15.1388i −0.288319 + 0.499383i −0.973409 0.229076i \(-0.926430\pi\)
0.685090 + 0.728459i \(0.259763\pi\)
\(920\) 0 0
\(921\) 24.2114 13.9784i 0.797791 0.460605i
\(922\) 4.58943i 0.151145i
\(923\) −0.241739 12.5658i −0.00795693 0.413607i
\(924\) −1.11804 −0.0367807
\(925\) 0 0
\(926\) 4.60444 + 7.97512i 0.151311 + 0.262079i
\(927\) 7.94534 + 4.58725i 0.260959 + 0.150665i
\(928\) −8.40957 −0.276058
\(929\) −6.74907 3.89658i −0.221430 0.127842i 0.385182 0.922840i \(-0.374139\pi\)
−0.606612 + 0.794998i \(0.707472\pi\)
\(930\) 0 0
\(931\) 34.3653i 1.12628i
\(932\) 18.9160 + 10.9212i 0.619614 + 0.357734i
\(933\) 12.3899 7.15333i 0.405628 0.234190i
\(934\) −0.190066 + 0.109735i −0.00621915 + 0.00359063i
\(935\) 0 0
\(936\) 3.60488 0.0693504i 0.117829 0.00226679i
\(937\) 39.5690i 1.29266i −0.763057 0.646331i \(-0.776303\pi\)
0.763057 0.646331i \(-0.223697\pi\)
\(938\) −1.78318 3.08856i −0.0582230 0.100845i
\(939\) 6.99473 + 12.1152i 0.228265 + 0.395366i
\(940\) 0 0
\(941\) 23.6107i 0.769687i −0.922982 0.384844i \(-0.874255\pi\)
0.922982 0.384844i \(-0.125745\pi\)
\(942\) 2.21134 3.83014i 0.0720492 0.124793i
\(943\) 30.1298 52.1864i 0.981161 1.69942i
\(944\) 11.8238i 0.384831i
\(945\) 0 0
\(946\) 13.0899 + 22.6724i 0.425590 + 0.737143i
\(947\) 9.60036 + 16.6283i 0.311970 + 0.540348i 0.978789 0.204872i \(-0.0656778\pi\)
−0.666819 + 0.745220i \(0.732345\pi\)
\(948\) 9.03820i 0.293547i
\(949\) −15.8958 26.3486i −0.516000 0.855311i
\(950\) 0 0
\(951\) 6.32085 3.64934i 0.204967 0.118338i
\(952\) 2.83876 1.63896i 0.0920047 0.0531189i
\(953\) −0.525090 0.303161i −0.0170093 0.00982035i 0.491471 0.870894i \(-0.336459\pi\)
−0.508481 + 0.861073i \(0.669793\pi\)
\(954\) 5.81017i 0.188111i
\(955\) 0 0
\(956\) 7.12762 + 4.11513i 0.230524 + 0.133093i
\(957\) 19.4920 0.630087
\(958\) 5.49422 + 3.17209i 0.177510 + 0.102486i
\(959\) −4.94646 8.56753i −0.159730 0.276660i
\(960\) 0 0
\(961\) 30.0927 0.970733
\(962\) 22.3091 0.429181i 0.719276 0.0138373i
\(963\) 3.21733i 0.103677i
\(964\) 2.68678 1.55121i 0.0865354 0.0499613i
\(965\) 0 0
\(966\) 1.66573 2.88512i 0.0535939 0.0928273i
\(967\) −1.49478 −0.0480690 −0.0240345 0.999711i \(-0.507651\pi\)
−0.0240345 + 0.999711i \(0.507651\pi\)
\(968\) 2.81382 4.87367i 0.0904394 0.156646i
\(969\) 29.8853 + 17.2543i 0.960055 + 0.554288i
\(970\) 0 0
\(971\) −1.72859 + 2.99401i −0.0554731 + 0.0960823i −0.892428 0.451189i \(-0.851000\pi\)
0.836955 + 0.547271i \(0.184333\pi\)
\(972\) 0.866025 0.500000i 0.0277778 0.0160375i
\(973\) 2.05229 + 3.55467i 0.0657935 + 0.113958i
\(974\) −37.1944 −1.19179
\(975\) 0 0
\(976\) 9.37529 0.300096
\(977\) −23.7932 41.2109i −0.761210 1.31845i −0.942227 0.334975i \(-0.891272\pi\)
0.181017 0.983480i \(-0.442061\pi\)
\(978\) −9.72060 + 5.61219i −0.310830 + 0.179458i
\(979\) 10.4506 18.1009i 0.334002 0.578509i
\(980\) 0 0
\(981\) −14.7804 8.53345i −0.471901 0.272452i
\(982\) −2.99901 + 5.19444i −0.0957024 + 0.165761i
\(983\) 27.8101 0.887003 0.443502 0.896274i \(-0.353736\pi\)
0.443502 + 0.896274i \(0.353736\pi\)
\(984\) −4.36250 + 7.55607i −0.139071 + 0.240879i
\(985\) 0 0
\(986\) −49.4914 + 28.5738i −1.57613 + 0.909977i
\(987\) 2.78675i 0.0887031i
\(988\) −16.0296 8.84802i −0.509968 0.281493i
\(989\) −78.0089 −2.48054
\(990\) 0 0
\(991\) −24.0369 41.6331i −0.763557 1.32252i −0.941006 0.338390i \(-0.890118\pi\)
0.177449 0.984130i \(-0.443216\pi\)
\(992\) 0.824903 + 0.476258i 0.0261907 + 0.0151212i
\(993\) 26.3594 0.836491
\(994\) 1.45613 + 0.840699i 0.0461858 + 0.0266654i
\(995\) 0 0
\(996\) 7.94887i 0.251870i
\(997\) −14.5645 8.40884i −0.461264 0.266311i 0.251312 0.967906i \(-0.419138\pi\)
−0.712575 + 0.701596i \(0.752471\pi\)
\(998\) −18.4384 + 10.6454i −0.583657 + 0.336974i
\(999\) 5.35948 3.09429i 0.169566 0.0978991i
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 1950.2.y.l.49.3 8
5.2 odd 4 1950.2.bc.e.751.1 8
5.3 odd 4 1950.2.bc.f.751.4 yes 8
5.4 even 2 1950.2.y.i.49.2 8
13.4 even 6 1950.2.y.i.199.2 8
65.4 even 6 inner 1950.2.y.l.199.3 8
65.17 odd 12 1950.2.bc.e.901.1 yes 8
65.43 odd 12 1950.2.bc.f.901.4 yes 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1950.2.y.i.49.2 8 5.4 even 2
1950.2.y.i.199.2 8 13.4 even 6
1950.2.y.l.49.3 8 1.1 even 1 trivial
1950.2.y.l.199.3 8 65.4 even 6 inner
1950.2.bc.e.751.1 8 5.2 odd 4
1950.2.bc.e.901.1 yes 8 65.17 odd 12
1950.2.bc.f.751.4 yes 8 5.3 odd 4
1950.2.bc.f.901.4 yes 8 65.43 odd 12