Properties

Label 189.2.s.a.89.1
Level $189$
Weight $2$
Character 189.89
Analytic conductor $1.509$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [189,2,Mod(17,189)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(189, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([5, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("189.17");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 189 = 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 189.s (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: \(1.50917259820\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 63)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 89.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 189.89
Dual form 189.2.s.a.17.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.50000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{4} +3.00000 q^{5} +(-2.50000 - 0.866025i) q^{7} +1.73205i q^{8} +O(q^{10})\) \(q+(1.50000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{4} +3.00000 q^{5} +(-2.50000 - 0.866025i) q^{7} +1.73205i q^{8} +(4.50000 - 2.59808i) q^{10} -1.73205i q^{11} +(-1.50000 + 0.866025i) q^{13} +(-4.50000 + 0.866025i) q^{14} +(2.50000 + 4.33013i) q^{16} +(-1.50000 - 2.59808i) q^{17} +(-4.50000 - 2.59808i) q^{19} +(1.50000 - 2.59808i) q^{20} +(-1.50000 - 2.59808i) q^{22} +5.19615i q^{23} +4.00000 q^{25} +(-1.50000 + 2.59808i) q^{26} +(-2.00000 + 1.73205i) q^{28} +(4.50000 + 2.59808i) q^{29} +(-3.00000 - 1.73205i) q^{31} +(4.50000 + 2.59808i) q^{32} +(-4.50000 - 2.59808i) q^{34} +(-7.50000 - 2.59808i) q^{35} +(-3.50000 + 6.06218i) q^{37} -9.00000 q^{38} +5.19615i q^{40} +(-1.50000 - 2.59808i) q^{41} +(-0.500000 + 0.866025i) q^{43} +(-1.50000 - 0.866025i) q^{44} +(4.50000 + 7.79423i) q^{46} +(5.50000 + 4.33013i) q^{49} +(6.00000 - 3.46410i) q^{50} +1.73205i q^{52} +(7.50000 - 4.33013i) q^{53} -5.19615i q^{55} +(1.50000 - 4.33013i) q^{56} +9.00000 q^{58} +(12.0000 - 6.92820i) q^{61} -6.00000 q^{62} -1.00000 q^{64} +(-4.50000 + 2.59808i) q^{65} +(2.00000 - 3.46410i) q^{67} -3.00000 q^{68} +(-13.5000 + 2.59808i) q^{70} -3.46410i q^{71} +(-4.50000 + 2.59808i) q^{73} +12.1244i q^{74} +(-4.50000 + 2.59808i) q^{76} +(-1.50000 + 4.33013i) q^{77} +(-4.00000 - 6.92820i) q^{79} +(7.50000 + 12.9904i) q^{80} +(-4.50000 - 2.59808i) q^{82} +(7.50000 - 12.9904i) q^{83} +(-4.50000 - 7.79423i) q^{85} +1.73205i q^{86} +3.00000 q^{88} +(-1.50000 + 2.59808i) q^{89} +(4.50000 - 0.866025i) q^{91} +(4.50000 + 2.59808i) q^{92} +(-13.5000 - 7.79423i) q^{95} +(-1.50000 - 0.866025i) q^{97} +(12.0000 + 1.73205i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 3 q^{2} + q^{4} + 6 q^{5} - 5 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 3 q^{2} + q^{4} + 6 q^{5} - 5 q^{7} + 9 q^{10} - 3 q^{13} - 9 q^{14} + 5 q^{16} - 3 q^{17} - 9 q^{19} + 3 q^{20} - 3 q^{22} + 8 q^{25} - 3 q^{26} - 4 q^{28} + 9 q^{29} - 6 q^{31} + 9 q^{32} - 9 q^{34} - 15 q^{35} - 7 q^{37} - 18 q^{38} - 3 q^{41} - q^{43} - 3 q^{44} + 9 q^{46} + 11 q^{49} + 12 q^{50} + 15 q^{53} + 3 q^{56} + 18 q^{58} + 24 q^{61} - 12 q^{62} - 2 q^{64} - 9 q^{65} + 4 q^{67} - 6 q^{68} - 27 q^{70} - 9 q^{73} - 9 q^{76} - 3 q^{77} - 8 q^{79} + 15 q^{80} - 9 q^{82} + 15 q^{83} - 9 q^{85} + 6 q^{88} - 3 q^{89} + 9 q^{91} + 9 q^{92} - 27 q^{95} - 3 q^{97} + 24 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/189\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(136\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.50000 0.866025i 1.06066 0.612372i 0.135045 0.990839i \(-0.456882\pi\)
0.925615 + 0.378467i \(0.123549\pi\)
\(3\) 0 0
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) 3.00000 1.34164 0.670820 0.741620i \(-0.265942\pi\)
0.670820 + 0.741620i \(0.265942\pi\)
\(6\) 0 0
\(7\) −2.50000 0.866025i −0.944911 0.327327i
\(8\) 1.73205i 0.612372i
\(9\) 0 0
\(10\) 4.50000 2.59808i 1.42302 0.821584i
\(11\) 1.73205i 0.522233i −0.965307 0.261116i \(-0.915909\pi\)
0.965307 0.261116i \(-0.0840907\pi\)
\(12\) 0 0
\(13\) −1.50000 + 0.866025i −0.416025 + 0.240192i −0.693375 0.720577i \(-0.743877\pi\)
0.277350 + 0.960769i \(0.410544\pi\)
\(14\) −4.50000 + 0.866025i −1.20268 + 0.231455i
\(15\) 0 0
\(16\) 2.50000 + 4.33013i 0.625000 + 1.08253i
\(17\) −1.50000 2.59808i −0.363803 0.630126i 0.624780 0.780801i \(-0.285189\pi\)
−0.988583 + 0.150675i \(0.951855\pi\)
\(18\) 0 0
\(19\) −4.50000 2.59808i −1.03237 0.596040i −0.114708 0.993399i \(-0.536593\pi\)
−0.917663 + 0.397360i \(0.869927\pi\)
\(20\) 1.50000 2.59808i 0.335410 0.580948i
\(21\) 0 0
\(22\) −1.50000 2.59808i −0.319801 0.553912i
\(23\) 5.19615i 1.08347i 0.840548 + 0.541736i \(0.182233\pi\)
−0.840548 + 0.541736i \(0.817767\pi\)
\(24\) 0 0
\(25\) 4.00000 0.800000
\(26\) −1.50000 + 2.59808i −0.294174 + 0.509525i
\(27\) 0 0
\(28\) −2.00000 + 1.73205i −0.377964 + 0.327327i
\(29\) 4.50000 + 2.59808i 0.835629 + 0.482451i 0.855776 0.517346i \(-0.173080\pi\)
−0.0201471 + 0.999797i \(0.506413\pi\)
\(30\) 0 0
\(31\) −3.00000 1.73205i −0.538816 0.311086i 0.205783 0.978598i \(-0.434026\pi\)
−0.744599 + 0.667512i \(0.767359\pi\)
\(32\) 4.50000 + 2.59808i 0.795495 + 0.459279i
\(33\) 0 0
\(34\) −4.50000 2.59808i −0.771744 0.445566i
\(35\) −7.50000 2.59808i −1.26773 0.439155i
\(36\) 0 0
\(37\) −3.50000 + 6.06218i −0.575396 + 0.996616i 0.420602 + 0.907245i \(0.361819\pi\)
−0.995998 + 0.0893706i \(0.971514\pi\)
\(38\) −9.00000 −1.45999
\(39\) 0 0
\(40\) 5.19615i 0.821584i
\(41\) −1.50000 2.59808i −0.234261 0.405751i 0.724797 0.688963i \(-0.241934\pi\)
−0.959058 + 0.283211i \(0.908600\pi\)
\(42\) 0 0
\(43\) −0.500000 + 0.866025i −0.0762493 + 0.132068i −0.901629 0.432511i \(-0.857628\pi\)
0.825380 + 0.564578i \(0.190961\pi\)
\(44\) −1.50000 0.866025i −0.226134 0.130558i
\(45\) 0 0
\(46\) 4.50000 + 7.79423i 0.663489 + 1.14920i
\(47\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(48\) 0 0
\(49\) 5.50000 + 4.33013i 0.785714 + 0.618590i
\(50\) 6.00000 3.46410i 0.848528 0.489898i
\(51\) 0 0
\(52\) 1.73205i 0.240192i
\(53\) 7.50000 4.33013i 1.03020 0.594789i 0.113161 0.993577i \(-0.463902\pi\)
0.917043 + 0.398788i \(0.130569\pi\)
\(54\) 0 0
\(55\) 5.19615i 0.700649i
\(56\) 1.50000 4.33013i 0.200446 0.578638i
\(57\) 0 0
\(58\) 9.00000 1.18176
\(59\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(60\) 0 0
\(61\) 12.0000 6.92820i 1.53644 0.887066i 0.537400 0.843328i \(-0.319407\pi\)
0.999043 0.0437377i \(-0.0139266\pi\)
\(62\) −6.00000 −0.762001
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) −4.50000 + 2.59808i −0.558156 + 0.322252i
\(66\) 0 0
\(67\) 2.00000 3.46410i 0.244339 0.423207i −0.717607 0.696449i \(-0.754762\pi\)
0.961946 + 0.273241i \(0.0880957\pi\)
\(68\) −3.00000 −0.363803
\(69\) 0 0
\(70\) −13.5000 + 2.59808i −1.61356 + 0.310530i
\(71\) 3.46410i 0.411113i −0.978645 0.205557i \(-0.934100\pi\)
0.978645 0.205557i \(-0.0659005\pi\)
\(72\) 0 0
\(73\) −4.50000 + 2.59808i −0.526685 + 0.304082i −0.739666 0.672975i \(-0.765016\pi\)
0.212980 + 0.977056i \(0.431683\pi\)
\(74\) 12.1244i 1.40943i
\(75\) 0 0
\(76\) −4.50000 + 2.59808i −0.516185 + 0.298020i
\(77\) −1.50000 + 4.33013i −0.170941 + 0.493464i
\(78\) 0 0
\(79\) −4.00000 6.92820i −0.450035 0.779484i 0.548352 0.836247i \(-0.315255\pi\)
−0.998388 + 0.0567635i \(0.981922\pi\)
\(80\) 7.50000 + 12.9904i 0.838525 + 1.45237i
\(81\) 0 0
\(82\) −4.50000 2.59808i −0.496942 0.286910i
\(83\) 7.50000 12.9904i 0.823232 1.42588i −0.0800311 0.996792i \(-0.525502\pi\)
0.903263 0.429087i \(-0.141165\pi\)
\(84\) 0 0
\(85\) −4.50000 7.79423i −0.488094 0.845403i
\(86\) 1.73205i 0.186772i
\(87\) 0 0
\(88\) 3.00000 0.319801
\(89\) −1.50000 + 2.59808i −0.159000 + 0.275396i −0.934508 0.355942i \(-0.884160\pi\)
0.775509 + 0.631337i \(0.217494\pi\)
\(90\) 0 0
\(91\) 4.50000 0.866025i 0.471728 0.0907841i
\(92\) 4.50000 + 2.59808i 0.469157 + 0.270868i
\(93\) 0 0
\(94\) 0 0
\(95\) −13.5000 7.79423i −1.38507 0.799671i
\(96\) 0 0
\(97\) −1.50000 0.866025i −0.152302 0.0879316i 0.421912 0.906637i \(-0.361359\pi\)
−0.574214 + 0.818705i \(0.694692\pi\)
\(98\) 12.0000 + 1.73205i 1.21218 + 0.174964i
\(99\) 0 0
\(100\) 2.00000 3.46410i 0.200000 0.346410i
\(101\) 3.00000 0.298511 0.149256 0.988799i \(-0.452312\pi\)
0.149256 + 0.988799i \(0.452312\pi\)
\(102\) 0 0
\(103\) 12.1244i 1.19465i 0.802000 + 0.597324i \(0.203769\pi\)
−0.802000 + 0.597324i \(0.796231\pi\)
\(104\) −1.50000 2.59808i −0.147087 0.254762i
\(105\) 0 0
\(106\) 7.50000 12.9904i 0.728464 1.26174i
\(107\) 7.50000 + 4.33013i 0.725052 + 0.418609i 0.816609 0.577191i \(-0.195851\pi\)
−0.0915571 + 0.995800i \(0.529184\pi\)
\(108\) 0 0
\(109\) −9.50000 16.4545i −0.909935 1.57605i −0.814152 0.580651i \(-0.802798\pi\)
−0.0957826 0.995402i \(-0.530535\pi\)
\(110\) −4.50000 7.79423i −0.429058 0.743151i
\(111\) 0 0
\(112\) −2.50000 12.9904i −0.236228 1.22748i
\(113\) −1.50000 + 0.866025i −0.141108 + 0.0814688i −0.568892 0.822412i \(-0.692628\pi\)
0.427784 + 0.903881i \(0.359294\pi\)
\(114\) 0 0
\(115\) 15.5885i 1.45363i
\(116\) 4.50000 2.59808i 0.417815 0.241225i
\(117\) 0 0
\(118\) 0 0
\(119\) 1.50000 + 7.79423i 0.137505 + 0.714496i
\(120\) 0 0
\(121\) 8.00000 0.727273
\(122\) 12.0000 20.7846i 1.08643 1.88175i
\(123\) 0 0
\(124\) −3.00000 + 1.73205i −0.269408 + 0.155543i
\(125\) −3.00000 −0.268328
\(126\) 0 0
\(127\) 20.0000 1.77471 0.887357 0.461084i \(-0.152539\pi\)
0.887357 + 0.461084i \(0.152539\pi\)
\(128\) −10.5000 + 6.06218i −0.928078 + 0.535826i
\(129\) 0 0
\(130\) −4.50000 + 7.79423i −0.394676 + 0.683599i
\(131\) 9.00000 0.786334 0.393167 0.919467i \(-0.371379\pi\)
0.393167 + 0.919467i \(0.371379\pi\)
\(132\) 0 0
\(133\) 9.00000 + 10.3923i 0.780399 + 0.901127i
\(134\) 6.92820i 0.598506i
\(135\) 0 0
\(136\) 4.50000 2.59808i 0.385872 0.222783i
\(137\) 12.1244i 1.03585i 0.855425 + 0.517927i \(0.173296\pi\)
−0.855425 + 0.517927i \(0.826704\pi\)
\(138\) 0 0
\(139\) −7.50000 + 4.33013i −0.636142 + 0.367277i −0.783127 0.621862i \(-0.786376\pi\)
0.146985 + 0.989139i \(0.453043\pi\)
\(140\) −6.00000 + 5.19615i −0.507093 + 0.439155i
\(141\) 0 0
\(142\) −3.00000 5.19615i −0.251754 0.436051i
\(143\) 1.50000 + 2.59808i 0.125436 + 0.217262i
\(144\) 0 0
\(145\) 13.5000 + 7.79423i 1.12111 + 0.647275i
\(146\) −4.50000 + 7.79423i −0.372423 + 0.645055i
\(147\) 0 0
\(148\) 3.50000 + 6.06218i 0.287698 + 0.498308i
\(149\) 1.73205i 0.141895i 0.997480 + 0.0709476i \(0.0226023\pi\)
−0.997480 + 0.0709476i \(0.977398\pi\)
\(150\) 0 0
\(151\) −17.0000 −1.38344 −0.691720 0.722166i \(-0.743147\pi\)
−0.691720 + 0.722166i \(0.743147\pi\)
\(152\) 4.50000 7.79423i 0.364998 0.632195i
\(153\) 0 0
\(154\) 1.50000 + 7.79423i 0.120873 + 0.628077i
\(155\) −9.00000 5.19615i −0.722897 0.417365i
\(156\) 0 0
\(157\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(158\) −12.0000 6.92820i −0.954669 0.551178i
\(159\) 0 0
\(160\) 13.5000 + 7.79423i 1.06727 + 0.616188i
\(161\) 4.50000 12.9904i 0.354650 1.02379i
\(162\) 0 0
\(163\) −5.50000 + 9.52628i −0.430793 + 0.746156i −0.996942 0.0781474i \(-0.975100\pi\)
0.566149 + 0.824303i \(0.308433\pi\)
\(164\) −3.00000 −0.234261
\(165\) 0 0
\(166\) 25.9808i 2.01650i
\(167\) 4.50000 + 7.79423i 0.348220 + 0.603136i 0.985933 0.167139i \(-0.0534527\pi\)
−0.637713 + 0.770274i \(0.720119\pi\)
\(168\) 0 0
\(169\) −5.00000 + 8.66025i −0.384615 + 0.666173i
\(170\) −13.5000 7.79423i −1.03540 0.597790i
\(171\) 0 0
\(172\) 0.500000 + 0.866025i 0.0381246 + 0.0660338i
\(173\) 3.00000 + 5.19615i 0.228086 + 0.395056i 0.957241 0.289292i \(-0.0934200\pi\)
−0.729155 + 0.684349i \(0.760087\pi\)
\(174\) 0 0
\(175\) −10.0000 3.46410i −0.755929 0.261861i
\(176\) 7.50000 4.33013i 0.565334 0.326396i
\(177\) 0 0
\(178\) 5.19615i 0.389468i
\(179\) −13.5000 + 7.79423i −1.00904 + 0.582568i −0.910910 0.412606i \(-0.864619\pi\)
−0.0981277 + 0.995174i \(0.531285\pi\)
\(180\) 0 0
\(181\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(182\) 6.00000 5.19615i 0.444750 0.385164i
\(183\) 0 0
\(184\) −9.00000 −0.663489
\(185\) −10.5000 + 18.1865i −0.771975 + 1.33710i
\(186\) 0 0
\(187\) −4.50000 + 2.59808i −0.329073 + 0.189990i
\(188\) 0 0
\(189\) 0 0
\(190\) −27.0000 −1.95879
\(191\) 15.0000 8.66025i 1.08536 0.626634i 0.153024 0.988222i \(-0.451099\pi\)
0.932338 + 0.361588i \(0.117765\pi\)
\(192\) 0 0
\(193\) 1.00000 1.73205i 0.0719816 0.124676i −0.827788 0.561041i \(-0.810401\pi\)
0.899770 + 0.436365i \(0.143734\pi\)
\(194\) −3.00000 −0.215387
\(195\) 0 0
\(196\) 6.50000 2.59808i 0.464286 0.185577i
\(197\) 13.8564i 0.987228i 0.869681 + 0.493614i \(0.164324\pi\)
−0.869681 + 0.493614i \(0.835676\pi\)
\(198\) 0 0
\(199\) −7.50000 + 4.33013i −0.531661 + 0.306955i −0.741693 0.670740i \(-0.765977\pi\)
0.210032 + 0.977695i \(0.432643\pi\)
\(200\) 6.92820i 0.489898i
\(201\) 0 0
\(202\) 4.50000 2.59808i 0.316619 0.182800i
\(203\) −9.00000 10.3923i −0.631676 0.729397i
\(204\) 0 0
\(205\) −4.50000 7.79423i −0.314294 0.544373i
\(206\) 10.5000 + 18.1865i 0.731570 + 1.26712i
\(207\) 0 0
\(208\) −7.50000 4.33013i −0.520031 0.300240i
\(209\) −4.50000 + 7.79423i −0.311272 + 0.539138i
\(210\) 0 0
\(211\) 2.50000 + 4.33013i 0.172107 + 0.298098i 0.939156 0.343490i \(-0.111609\pi\)
−0.767049 + 0.641588i \(0.778276\pi\)
\(212\) 8.66025i 0.594789i
\(213\) 0 0
\(214\) 15.0000 1.02538
\(215\) −1.50000 + 2.59808i −0.102299 + 0.177187i
\(216\) 0 0
\(217\) 6.00000 + 6.92820i 0.407307 + 0.470317i
\(218\) −28.5000 16.4545i −1.93026 1.11444i
\(219\) 0 0
\(220\) −4.50000 2.59808i −0.303390 0.175162i
\(221\) 4.50000 + 2.59808i 0.302703 + 0.174766i
\(222\) 0 0
\(223\) −4.50000 2.59808i −0.301342 0.173980i 0.341703 0.939808i \(-0.388996\pi\)
−0.643046 + 0.765828i \(0.722329\pi\)
\(224\) −9.00000 10.3923i −0.601338 0.694365i
\(225\) 0 0
\(226\) −1.50000 + 2.59808i −0.0997785 + 0.172821i
\(227\) −21.0000 −1.39382 −0.696909 0.717159i \(-0.745442\pi\)
−0.696909 + 0.717159i \(0.745442\pi\)
\(228\) 0 0
\(229\) 8.66025i 0.572286i 0.958187 + 0.286143i \(0.0923732\pi\)
−0.958187 + 0.286143i \(0.907627\pi\)
\(230\) 13.5000 + 23.3827i 0.890164 + 1.54181i
\(231\) 0 0
\(232\) −4.50000 + 7.79423i −0.295439 + 0.511716i
\(233\) −4.50000 2.59808i −0.294805 0.170206i 0.345302 0.938492i \(-0.387777\pi\)
−0.640107 + 0.768286i \(0.721110\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 9.00000 + 10.3923i 0.583383 + 0.673633i
\(239\) −1.50000 + 0.866025i −0.0970269 + 0.0560185i −0.547728 0.836656i \(-0.684507\pi\)
0.450701 + 0.892675i \(0.351174\pi\)
\(240\) 0 0
\(241\) 22.5167i 1.45043i −0.688525 0.725213i \(-0.741741\pi\)
0.688525 0.725213i \(-0.258259\pi\)
\(242\) 12.0000 6.92820i 0.771389 0.445362i
\(243\) 0 0
\(244\) 13.8564i 0.887066i
\(245\) 16.5000 + 12.9904i 1.05415 + 0.829925i
\(246\) 0 0
\(247\) 9.00000 0.572656
\(248\) 3.00000 5.19615i 0.190500 0.329956i
\(249\) 0 0
\(250\) −4.50000 + 2.59808i −0.284605 + 0.164317i
\(251\) −12.0000 −0.757433 −0.378717 0.925513i \(-0.623635\pi\)
−0.378717 + 0.925513i \(0.623635\pi\)
\(252\) 0 0
\(253\) 9.00000 0.565825
\(254\) 30.0000 17.3205i 1.88237 1.08679i
\(255\) 0 0
\(256\) −9.50000 + 16.4545i −0.593750 + 1.02841i
\(257\) 3.00000 0.187135 0.0935674 0.995613i \(-0.470173\pi\)
0.0935674 + 0.995613i \(0.470173\pi\)
\(258\) 0 0
\(259\) 14.0000 12.1244i 0.869918 0.753371i
\(260\) 5.19615i 0.322252i
\(261\) 0 0
\(262\) 13.5000 7.79423i 0.834033 0.481529i
\(263\) 22.5167i 1.38844i −0.719764 0.694218i \(-0.755750\pi\)
0.719764 0.694218i \(-0.244250\pi\)
\(264\) 0 0
\(265\) 22.5000 12.9904i 1.38216 0.797993i
\(266\) 22.5000 + 7.79423i 1.37956 + 0.477895i
\(267\) 0 0
\(268\) −2.00000 3.46410i −0.122169 0.211604i
\(269\) −7.50000 12.9904i −0.457283 0.792038i 0.541533 0.840679i \(-0.317844\pi\)
−0.998816 + 0.0486418i \(0.984511\pi\)
\(270\) 0 0
\(271\) −10.5000 6.06218i −0.637830 0.368251i 0.145948 0.989292i \(-0.453377\pi\)
−0.783778 + 0.621041i \(0.786710\pi\)
\(272\) 7.50000 12.9904i 0.454754 0.787658i
\(273\) 0 0
\(274\) 10.5000 + 18.1865i 0.634328 + 1.09869i
\(275\) 6.92820i 0.417786i
\(276\) 0 0
\(277\) −1.00000 −0.0600842 −0.0300421 0.999549i \(-0.509564\pi\)
−0.0300421 + 0.999549i \(0.509564\pi\)
\(278\) −7.50000 + 12.9904i −0.449820 + 0.779111i
\(279\) 0 0
\(280\) 4.50000 12.9904i 0.268926 0.776324i
\(281\) 16.5000 + 9.52628i 0.984307 + 0.568290i 0.903568 0.428445i \(-0.140938\pi\)
0.0807396 + 0.996735i \(0.474272\pi\)
\(282\) 0 0
\(283\) 3.00000 + 1.73205i 0.178331 + 0.102960i 0.586509 0.809943i \(-0.300502\pi\)
−0.408177 + 0.912903i \(0.633835\pi\)
\(284\) −3.00000 1.73205i −0.178017 0.102778i
\(285\) 0 0
\(286\) 4.50000 + 2.59808i 0.266091 + 0.153627i
\(287\) 1.50000 + 7.79423i 0.0885422 + 0.460079i
\(288\) 0 0
\(289\) 4.00000 6.92820i 0.235294 0.407541i
\(290\) 27.0000 1.58549
\(291\) 0 0
\(292\) 5.19615i 0.304082i
\(293\) 4.50000 + 7.79423i 0.262893 + 0.455344i 0.967009 0.254741i \(-0.0819901\pi\)
−0.704117 + 0.710084i \(0.748657\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) −10.5000 6.06218i −0.610300 0.352357i
\(297\) 0 0
\(298\) 1.50000 + 2.59808i 0.0868927 + 0.150503i
\(299\) −4.50000 7.79423i −0.260242 0.450752i
\(300\) 0 0
\(301\) 2.00000 1.73205i 0.115278 0.0998337i
\(302\) −25.5000 + 14.7224i −1.46736 + 0.847181i
\(303\) 0 0
\(304\) 25.9808i 1.49010i
\(305\) 36.0000 20.7846i 2.06135 1.19012i
\(306\) 0 0
\(307\) 24.2487i 1.38395i 0.721923 + 0.691974i \(0.243259\pi\)
−0.721923 + 0.691974i \(0.756741\pi\)
\(308\) 3.00000 + 3.46410i 0.170941 + 0.197386i
\(309\) 0 0
\(310\) −18.0000 −1.02233
\(311\) 12.0000 20.7846i 0.680458 1.17859i −0.294384 0.955687i \(-0.595114\pi\)
0.974841 0.222900i \(-0.0715523\pi\)
\(312\) 0 0
\(313\) −18.0000 + 10.3923i −1.01742 + 0.587408i −0.913356 0.407163i \(-0.866518\pi\)
−0.104065 + 0.994571i \(0.533185\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) −8.00000 −0.450035
\(317\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(318\) 0 0
\(319\) 4.50000 7.79423i 0.251952 0.436393i
\(320\) −3.00000 −0.167705
\(321\) 0 0
\(322\) −4.50000 23.3827i −0.250775 1.30307i
\(323\) 15.5885i 0.867365i
\(324\) 0 0
\(325\) −6.00000 + 3.46410i −0.332820 + 0.192154i
\(326\) 19.0526i 1.05522i
\(327\) 0 0
\(328\) 4.50000 2.59808i 0.248471 0.143455i
\(329\) 0 0
\(330\) 0 0
\(331\) 4.00000 + 6.92820i 0.219860 + 0.380808i 0.954765 0.297361i \(-0.0961066\pi\)
−0.734905 + 0.678170i \(0.762773\pi\)
\(332\) −7.50000 12.9904i −0.411616 0.712940i
\(333\) 0 0
\(334\) 13.5000 + 7.79423i 0.738687 + 0.426481i
\(335\) 6.00000 10.3923i 0.327815 0.567792i
\(336\) 0 0
\(337\) −9.50000 16.4545i −0.517498 0.896333i −0.999793 0.0203242i \(-0.993530\pi\)
0.482295 0.876009i \(-0.339803\pi\)
\(338\) 17.3205i 0.942111i
\(339\) 0 0
\(340\) −9.00000 −0.488094
\(341\) −3.00000 + 5.19615i −0.162459 + 0.281387i
\(342\) 0 0
\(343\) −10.0000 15.5885i −0.539949 0.841698i
\(344\) −1.50000 0.866025i −0.0808746 0.0466930i
\(345\) 0 0
\(346\) 9.00000 + 5.19615i 0.483843 + 0.279347i
\(347\) 3.00000 + 1.73205i 0.161048 + 0.0929814i 0.578358 0.815783i \(-0.303694\pi\)
−0.417310 + 0.908764i \(0.637027\pi\)
\(348\) 0 0
\(349\) 10.5000 + 6.06218i 0.562052 + 0.324501i 0.753969 0.656910i \(-0.228137\pi\)
−0.191917 + 0.981411i \(0.561470\pi\)
\(350\) −18.0000 + 3.46410i −0.962140 + 0.185164i
\(351\) 0 0
\(352\) 4.50000 7.79423i 0.239851 0.415434i
\(353\) −21.0000 −1.11772 −0.558859 0.829263i \(-0.688761\pi\)
−0.558859 + 0.829263i \(0.688761\pi\)
\(354\) 0 0
\(355\) 10.3923i 0.551566i
\(356\) 1.50000 + 2.59808i 0.0794998 + 0.137698i
\(357\) 0 0
\(358\) −13.5000 + 23.3827i −0.713497 + 1.23581i
\(359\) 19.5000 + 11.2583i 1.02917 + 0.594192i 0.916747 0.399468i \(-0.130805\pi\)
0.112424 + 0.993660i \(0.464139\pi\)
\(360\) 0 0
\(361\) 4.00000 + 6.92820i 0.210526 + 0.364642i
\(362\) 0 0
\(363\) 0 0
\(364\) 1.50000 4.33013i 0.0786214 0.226960i
\(365\) −13.5000 + 7.79423i −0.706622 + 0.407969i
\(366\) 0 0
\(367\) 5.19615i 0.271237i 0.990761 + 0.135618i \(0.0433021\pi\)
−0.990761 + 0.135618i \(0.956698\pi\)
\(368\) −22.5000 + 12.9904i −1.17289 + 0.677170i
\(369\) 0 0
\(370\) 36.3731i 1.89095i
\(371\) −22.5000 + 4.33013i −1.16814 + 0.224809i
\(372\) 0 0
\(373\) −37.0000 −1.91579 −0.957894 0.287123i \(-0.907301\pi\)
−0.957894 + 0.287123i \(0.907301\pi\)
\(374\) −4.50000 + 7.79423i −0.232689 + 0.403030i
\(375\) 0 0
\(376\) 0 0
\(377\) −9.00000 −0.463524
\(378\) 0 0
\(379\) −20.0000 −1.02733 −0.513665 0.857991i \(-0.671713\pi\)
−0.513665 + 0.857991i \(0.671713\pi\)
\(380\) −13.5000 + 7.79423i −0.692535 + 0.399835i
\(381\) 0 0
\(382\) 15.0000 25.9808i 0.767467 1.32929i
\(383\) 9.00000 0.459879 0.229939 0.973205i \(-0.426147\pi\)
0.229939 + 0.973205i \(0.426147\pi\)
\(384\) 0 0
\(385\) −4.50000 + 12.9904i −0.229341 + 0.662051i
\(386\) 3.46410i 0.176318i
\(387\) 0 0
\(388\) −1.50000 + 0.866025i −0.0761510 + 0.0439658i
\(389\) 36.3731i 1.84419i −0.386966 0.922094i \(-0.626477\pi\)
0.386966 0.922094i \(-0.373523\pi\)
\(390\) 0 0
\(391\) 13.5000 7.79423i 0.682724 0.394171i
\(392\) −7.50000 + 9.52628i −0.378807 + 0.481150i
\(393\) 0 0
\(394\) 12.0000 + 20.7846i 0.604551 + 1.04711i
\(395\) −12.0000 20.7846i −0.603786 1.04579i
\(396\) 0 0
\(397\) 7.50000 + 4.33013i 0.376414 + 0.217323i 0.676257 0.736666i \(-0.263601\pi\)
−0.299843 + 0.953989i \(0.596934\pi\)
\(398\) −7.50000 + 12.9904i −0.375941 + 0.651149i
\(399\) 0 0
\(400\) 10.0000 + 17.3205i 0.500000 + 0.866025i
\(401\) 32.9090i 1.64340i −0.569924 0.821698i \(-0.693027\pi\)
0.569924 0.821698i \(-0.306973\pi\)
\(402\) 0 0
\(403\) 6.00000 0.298881
\(404\) 1.50000 2.59808i 0.0746278 0.129259i
\(405\) 0 0
\(406\) −22.5000 7.79423i −1.11666 0.386821i
\(407\) 10.5000 + 6.06218i 0.520466 + 0.300491i
\(408\) 0 0
\(409\) −6.00000 3.46410i −0.296681 0.171289i 0.344270 0.938871i \(-0.388126\pi\)
−0.640951 + 0.767582i \(0.721460\pi\)
\(410\) −13.5000 7.79423i −0.666717 0.384930i
\(411\) 0 0
\(412\) 10.5000 + 6.06218i 0.517298 + 0.298662i
\(413\) 0 0
\(414\) 0 0
\(415\) 22.5000 38.9711i 1.10448 1.91302i
\(416\) −9.00000 −0.441261
\(417\) 0 0
\(418\) 15.5885i 0.762456i
\(419\) 16.5000 + 28.5788i 0.806078 + 1.39617i 0.915561 + 0.402179i \(0.131747\pi\)
−0.109483 + 0.993989i \(0.534920\pi\)
\(420\) 0 0
\(421\) −5.50000 + 9.52628i −0.268054 + 0.464282i −0.968359 0.249561i \(-0.919714\pi\)
0.700306 + 0.713843i \(0.253047\pi\)
\(422\) 7.50000 + 4.33013i 0.365094 + 0.210787i
\(423\) 0 0
\(424\) 7.50000 + 12.9904i 0.364232 + 0.630869i
\(425\) −6.00000 10.3923i −0.291043 0.504101i
\(426\) 0 0
\(427\) −36.0000 + 6.92820i −1.74216 + 0.335279i
\(428\) 7.50000 4.33013i 0.362526 0.209305i
\(429\) 0 0
\(430\) 5.19615i 0.250581i
\(431\) −13.5000 + 7.79423i −0.650272 + 0.375435i −0.788560 0.614957i \(-0.789173\pi\)
0.138288 + 0.990392i \(0.455840\pi\)
\(432\) 0 0
\(433\) 13.8564i 0.665896i −0.942945 0.332948i \(-0.891957\pi\)
0.942945 0.332948i \(-0.108043\pi\)
\(434\) 15.0000 + 5.19615i 0.720023 + 0.249423i
\(435\) 0 0
\(436\) −19.0000 −0.909935
\(437\) 13.5000 23.3827i 0.645793 1.11855i
\(438\) 0 0
\(439\) 27.0000 15.5885i 1.28864 0.743996i 0.310228 0.950662i \(-0.399595\pi\)
0.978412 + 0.206666i \(0.0662612\pi\)
\(440\) 9.00000 0.429058
\(441\) 0 0
\(442\) 9.00000 0.428086
\(443\) −27.0000 + 15.5885i −1.28281 + 0.740630i −0.977361 0.211579i \(-0.932139\pi\)
−0.305448 + 0.952209i \(0.598806\pi\)
\(444\) 0 0
\(445\) −4.50000 + 7.79423i −0.213320 + 0.369482i
\(446\) −9.00000 −0.426162
\(447\) 0 0
\(448\) 2.50000 + 0.866025i 0.118114 + 0.0409159i
\(449\) 34.6410i 1.63481i −0.576063 0.817405i \(-0.695412\pi\)
0.576063 0.817405i \(-0.304588\pi\)
\(450\) 0 0
\(451\) −4.50000 + 2.59808i −0.211897 + 0.122339i
\(452\) 1.73205i 0.0814688i
\(453\) 0 0
\(454\) −31.5000 + 18.1865i −1.47837 + 0.853536i
\(455\) 13.5000 2.59808i 0.632890 0.121800i
\(456\) 0 0
\(457\) 13.0000 + 22.5167i 0.608114 + 1.05328i 0.991551 + 0.129718i \(0.0414071\pi\)
−0.383437 + 0.923567i \(0.625260\pi\)
\(458\) 7.50000 + 12.9904i 0.350452 + 0.607001i
\(459\) 0 0
\(460\) 13.5000 + 7.79423i 0.629441 + 0.363408i
\(461\) −7.50000 + 12.9904i −0.349310 + 0.605022i −0.986127 0.165992i \(-0.946917\pi\)
0.636817 + 0.771015i \(0.280251\pi\)
\(462\) 0 0
\(463\) 0.500000 + 0.866025i 0.0232370 + 0.0402476i 0.877410 0.479741i \(-0.159269\pi\)
−0.854173 + 0.519989i \(0.825936\pi\)
\(464\) 25.9808i 1.20613i
\(465\) 0 0
\(466\) −9.00000 −0.416917
\(467\) −1.50000 + 2.59808i −0.0694117 + 0.120225i −0.898642 0.438682i \(-0.855446\pi\)
0.829231 + 0.558906i \(0.188779\pi\)
\(468\) 0 0
\(469\) −8.00000 + 6.92820i −0.369406 + 0.319915i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 1.50000 + 0.866025i 0.0689701 + 0.0398199i
\(474\) 0 0
\(475\) −18.0000 10.3923i −0.825897 0.476832i
\(476\) 7.50000 + 2.59808i 0.343762 + 0.119083i
\(477\) 0 0
\(478\) −1.50000 + 2.59808i −0.0686084 + 0.118833i
\(479\) 27.0000 1.23366 0.616831 0.787096i \(-0.288416\pi\)
0.616831 + 0.787096i \(0.288416\pi\)
\(480\) 0 0
\(481\) 12.1244i 0.552823i
\(482\) −19.5000 33.7750i −0.888201 1.53841i
\(483\) 0 0
\(484\) 4.00000 6.92820i 0.181818 0.314918i
\(485\) −4.50000 2.59808i −0.204334 0.117973i
\(486\) 0 0
\(487\) 11.5000 + 19.9186i 0.521115 + 0.902597i 0.999698 + 0.0245553i \(0.00781698\pi\)
−0.478584 + 0.878042i \(0.658850\pi\)
\(488\) 12.0000 + 20.7846i 0.543214 + 0.940875i
\(489\) 0 0
\(490\) 36.0000 + 5.19615i 1.62631 + 0.234738i
\(491\) 22.5000 12.9904i 1.01541 0.586248i 0.102639 0.994719i \(-0.467271\pi\)
0.912771 + 0.408471i \(0.133938\pi\)
\(492\) 0 0
\(493\) 15.5885i 0.702069i
\(494\) 13.5000 7.79423i 0.607394 0.350679i
\(495\) 0 0
\(496\) 17.3205i 0.777714i
\(497\) −3.00000 + 8.66025i −0.134568 + 0.388465i
\(498\) 0 0
\(499\) 25.0000 1.11915 0.559577 0.828778i \(-0.310964\pi\)
0.559577 + 0.828778i \(0.310964\pi\)
\(500\) −1.50000 + 2.59808i −0.0670820 + 0.116190i
\(501\) 0 0
\(502\) −18.0000 + 10.3923i −0.803379 + 0.463831i
\(503\) 24.0000 1.07011 0.535054 0.844818i \(-0.320291\pi\)
0.535054 + 0.844818i \(0.320291\pi\)
\(504\) 0 0
\(505\) 9.00000 0.400495
\(506\) 13.5000 7.79423i 0.600148 0.346496i
\(507\) 0 0
\(508\) 10.0000 17.3205i 0.443678 0.768473i
\(509\) −33.0000 −1.46270 −0.731350 0.682003i \(-0.761109\pi\)
−0.731350 + 0.682003i \(0.761109\pi\)
\(510\) 0 0
\(511\) 13.5000 2.59808i 0.597205 0.114932i
\(512\) 8.66025i 0.382733i
\(513\) 0 0
\(514\) 4.50000 2.59808i 0.198486 0.114596i
\(515\) 36.3731i 1.60279i
\(516\) 0 0
\(517\) 0 0
\(518\) 10.5000 30.3109i 0.461344 1.33178i
\(519\) 0 0
\(520\) −4.50000 7.79423i −0.197338 0.341800i
\(521\) 22.5000 + 38.9711i 0.985743 + 1.70736i 0.638588 + 0.769549i \(0.279519\pi\)
0.347155 + 0.937808i \(0.387148\pi\)
\(522\) 0 0
\(523\) −16.5000 9.52628i −0.721495 0.416555i 0.0938079 0.995590i \(-0.470096\pi\)
−0.815303 + 0.579035i \(0.803429\pi\)
\(524\) 4.50000 7.79423i 0.196583 0.340492i
\(525\) 0 0
\(526\) −19.5000 33.7750i −0.850240 1.47266i
\(527\) 10.3923i 0.452696i
\(528\) 0 0
\(529\) −4.00000 −0.173913
\(530\) 22.5000 38.9711i 0.977338 1.69280i
\(531\) 0 0
\(532\) 13.5000 2.59808i 0.585299 0.112641i
\(533\) 4.50000 + 2.59808i 0.194917 + 0.112535i
\(534\) 0 0
\(535\) 22.5000 + 12.9904i 0.972760 + 0.561623i
\(536\) 6.00000 + 3.46410i 0.259161 + 0.149626i
\(537\) 0 0
\(538\) −22.5000 12.9904i −0.970044 0.560055i
\(539\) 7.50000 9.52628i 0.323048 0.410326i
\(540\) 0 0
\(541\) 6.50000 11.2583i 0.279457 0.484033i −0.691793 0.722096i \(-0.743179\pi\)
0.971250 + 0.238062i \(0.0765123\pi\)
\(542\) −21.0000 −0.902027
\(543\) 0 0
\(544\) 15.5885i 0.668350i
\(545\) −28.5000 49.3634i −1.22081 2.11450i
\(546\) 0 0
\(547\) 9.50000 16.4545i 0.406191 0.703543i −0.588269 0.808666i \(-0.700190\pi\)
0.994459 + 0.105123i \(0.0335235\pi\)
\(548\) 10.5000 + 6.06218i 0.448538 + 0.258963i
\(549\) 0 0
\(550\) −6.00000 10.3923i −0.255841 0.443129i
\(551\) −13.5000 23.3827i −0.575119 0.996136i
\(552\) 0 0
\(553\) 4.00000 + 20.7846i 0.170097 + 0.883852i
\(554\) −1.50000 + 0.866025i −0.0637289 + 0.0367939i
\(555\) 0 0
\(556\) 8.66025i 0.367277i
\(557\) −10.5000 + 6.06218i −0.444899 + 0.256863i −0.705674 0.708537i \(-0.749355\pi\)
0.260774 + 0.965400i \(0.416022\pi\)
\(558\) 0 0
\(559\) 1.73205i 0.0732579i
\(560\) −7.50000 38.9711i −0.316933 1.64683i
\(561\) 0 0
\(562\) 33.0000 1.39202
\(563\) −18.0000 + 31.1769i −0.758610 + 1.31395i 0.184950 + 0.982748i \(0.440788\pi\)
−0.943560 + 0.331202i \(0.892546\pi\)
\(564\) 0 0
\(565\) −4.50000 + 2.59808i −0.189316 + 0.109302i
\(566\) 6.00000 0.252199
\(567\) 0 0
\(568\) 6.00000 0.251754
\(569\) −6.00000 + 3.46410i −0.251533 + 0.145223i −0.620466 0.784233i \(-0.713057\pi\)
0.368933 + 0.929456i \(0.379723\pi\)
\(570\) 0 0
\(571\) −16.0000 + 27.7128i −0.669579 + 1.15975i 0.308443 + 0.951243i \(0.400192\pi\)
−0.978022 + 0.208502i \(0.933141\pi\)
\(572\) 3.00000 0.125436
\(573\) 0 0
\(574\) 9.00000 + 10.3923i 0.375653 + 0.433766i
\(575\) 20.7846i 0.866778i
\(576\) 0 0
\(577\) −34.5000 + 19.9186i −1.43625 + 0.829222i −0.997587 0.0694283i \(-0.977883\pi\)
−0.438667 + 0.898650i \(0.644549\pi\)
\(578\) 13.8564i 0.576351i
\(579\) 0 0
\(580\) 13.5000 7.79423i 0.560557 0.323638i
\(581\) −30.0000 + 25.9808i −1.24461 + 1.07786i
\(582\) 0 0
\(583\) −7.50000 12.9904i −0.310618 0.538007i
\(584\) −4.50000 7.79423i −0.186211 0.322527i
\(585\) 0 0
\(586\) 13.5000 + 7.79423i 0.557680 + 0.321977i
\(587\) −10.5000 + 18.1865i −0.433381 + 0.750639i −0.997162 0.0752860i \(-0.976013\pi\)
0.563781 + 0.825925i \(0.309346\pi\)
\(588\) 0 0
\(589\) 9.00000 + 15.5885i 0.370839 + 0.642311i
\(590\) 0 0
\(591\) 0 0
\(592\) −35.0000 −1.43849
\(593\) −19.5000 + 33.7750i −0.800769 + 1.38697i 0.118342 + 0.992973i \(0.462242\pi\)
−0.919111 + 0.394000i \(0.871091\pi\)
\(594\) 0 0
\(595\) 4.50000 + 23.3827i 0.184482 + 0.958597i
\(596\) 1.50000 + 0.866025i 0.0614424 + 0.0354738i
\(597\) 0 0
\(598\) −13.5000 7.79423i −0.552056 0.318730i
\(599\) 21.0000 + 12.1244i 0.858037 + 0.495388i 0.863354 0.504598i \(-0.168359\pi\)
−0.00531761 + 0.999986i \(0.501693\pi\)
\(600\) 0 0
\(601\) −25.5000 14.7224i −1.04017 0.600541i −0.120286 0.992739i \(-0.538381\pi\)
−0.919881 + 0.392199i \(0.871715\pi\)
\(602\) 1.50000 4.33013i 0.0611354 0.176483i
\(603\) 0 0
\(604\) −8.50000 + 14.7224i −0.345860 + 0.599047i
\(605\) 24.0000 0.975739
\(606\) 0 0
\(607\) 15.5885i 0.632716i −0.948640 0.316358i \(-0.897540\pi\)
0.948640 0.316358i \(-0.102460\pi\)
\(608\) −13.5000 23.3827i −0.547497 0.948293i
\(609\) 0 0
\(610\) 36.0000 62.3538i 1.45760 2.52463i
\(611\) 0 0
\(612\) 0 0
\(613\) −23.5000 40.7032i −0.949156 1.64399i −0.747208 0.664590i \(-0.768606\pi\)
−0.201948 0.979396i \(-0.564727\pi\)
\(614\) 21.0000 + 36.3731i 0.847491 + 1.46790i
\(615\) 0 0
\(616\) −7.50000 2.59808i −0.302184 0.104679i
\(617\) 4.50000 2.59808i 0.181163 0.104595i −0.406676 0.913573i \(-0.633312\pi\)
0.587839 + 0.808978i \(0.299979\pi\)
\(618\) 0 0
\(619\) 19.0526i 0.765787i 0.923792 + 0.382893i \(0.125072\pi\)
−0.923792 + 0.382893i \(0.874928\pi\)
\(620\) −9.00000 + 5.19615i −0.361449 + 0.208683i
\(621\) 0 0
\(622\) 41.5692i 1.66677i
\(623\) 6.00000 5.19615i 0.240385 0.208179i
\(624\) 0 0
\(625\) −29.0000 −1.16000
\(626\) −18.0000 + 31.1769i −0.719425 + 1.24608i
\(627\) 0 0
\(628\) 0 0
\(629\) 21.0000 0.837325
\(630\) 0 0
\(631\) 8.00000 0.318475 0.159237 0.987240i \(-0.449096\pi\)
0.159237 + 0.987240i \(0.449096\pi\)
\(632\) 12.0000 6.92820i 0.477334 0.275589i
\(633\) 0 0
\(634\) 0 0
\(635\) 60.0000 2.38103
\(636\) 0 0
\(637\) −12.0000 1.73205i −0.475457 0.0686264i
\(638\) 15.5885i 0.617153i
\(639\) 0 0
\(640\) −31.5000 + 18.1865i −1.24515 + 0.718886i
\(641\) 12.1244i 0.478883i 0.970911 + 0.239442i \(0.0769644\pi\)
−0.970911 + 0.239442i \(0.923036\pi\)
\(642\) 0 0
\(643\) 10.5000 6.06218i 0.414080 0.239069i −0.278462 0.960447i \(-0.589824\pi\)
0.692541 + 0.721378i \(0.256491\pi\)
\(644\) −9.00000 10.3923i −0.354650 0.409514i
\(645\) 0 0
\(646\) 13.5000 + 23.3827i 0.531150 + 0.919979i
\(647\) 1.50000 + 2.59808i 0.0589711 + 0.102141i 0.894004 0.448059i \(-0.147885\pi\)
−0.835033 + 0.550200i \(0.814551\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) −6.00000 + 10.3923i −0.235339 + 0.407620i
\(651\) 0 0
\(652\) 5.50000 + 9.52628i 0.215397 + 0.373078i
\(653\) 39.8372i 1.55895i −0.626434 0.779474i \(-0.715486\pi\)
0.626434 0.779474i \(-0.284514\pi\)
\(654\) 0 0
\(655\) 27.0000 1.05498
\(656\) 7.50000 12.9904i 0.292826 0.507189i
\(657\) 0 0
\(658\) 0 0
\(659\) −10.5000 6.06218i −0.409022 0.236149i 0.281347 0.959606i \(-0.409219\pi\)
−0.690369 + 0.723457i \(0.742552\pi\)
\(660\) 0 0
\(661\) 36.0000 + 20.7846i 1.40024 + 0.808428i 0.994417 0.105525i \(-0.0336523\pi\)
0.405821 + 0.913953i \(0.366986\pi\)
\(662\) 12.0000 + 6.92820i 0.466393 + 0.269272i
\(663\) 0 0
\(664\) 22.5000 + 12.9904i 0.873169 + 0.504125i
\(665\) 27.0000 + 31.1769i 1.04702 + 1.20899i
\(666\) 0 0
\(667\) −13.5000 + 23.3827i −0.522722 + 0.905381i
\(668\) 9.00000 0.348220
\(669\) 0 0
\(670\) 20.7846i 0.802980i
\(671\) −12.0000 20.7846i −0.463255 0.802381i
\(672\) 0 0
\(673\) 14.5000 25.1147i 0.558934 0.968102i −0.438652 0.898657i \(-0.644544\pi\)
0.997586 0.0694449i \(-0.0221228\pi\)
\(674\) −28.5000 16.4545i −1.09778 0.633803i
\(675\) 0 0
\(676\) 5.00000 + 8.66025i 0.192308 + 0.333087i
\(677\) −9.00000 15.5885i −0.345898 0.599113i 0.639618 0.768693i \(-0.279092\pi\)
−0.985517 + 0.169580i \(0.945759\pi\)
\(678\) 0 0
\(679\) 3.00000 + 3.46410i 0.115129 + 0.132940i
\(680\) 13.5000 7.79423i 0.517701 0.298895i
\(681\) 0 0
\(682\) 10.3923i 0.397942i
\(683\) −7.50000 + 4.33013i −0.286980 + 0.165688i −0.636579 0.771212i \(-0.719651\pi\)
0.349599 + 0.936899i \(0.386318\pi\)
\(684\) 0 0
\(685\) 36.3731i 1.38974i
\(686\) −28.5000 14.7224i −1.08814 0.562105i
\(687\) 0 0
\(688\) −5.00000 −0.190623
\(689\) −7.50000 + 12.9904i −0.285727 + 0.494894i
\(690\) 0 0
\(691\) −3.00000 + 1.73205i −0.114125 + 0.0658903i −0.555976 0.831198i \(-0.687655\pi\)
0.441851 + 0.897089i \(0.354322\pi\)
\(692\) 6.00000 0.228086
\(693\) 0 0
\(694\) 6.00000 0.227757
\(695\) −22.5000 + 12.9904i −0.853474 + 0.492753i
\(696\) 0 0
\(697\) −4.50000 + 7.79423i −0.170450 + 0.295227i
\(698\) 21.0000 0.794862
\(699\) 0 0
\(700\) −8.00000 + 6.92820i −0.302372 + 0.261861i
\(701\) 34.6410i 1.30837i −0.756333 0.654187i \(-0.773011\pi\)
0.756333 0.654187i \(-0.226989\pi\)
\(702\) 0 0
\(703\) 31.5000 18.1865i 1.18805 0.685918i
\(704\) 1.73205i 0.0652791i
\(705\) 0 0
\(706\) −31.5000 + 18.1865i −1.18552 + 0.684459i
\(707\) −7.50000 2.59808i −0.282067 0.0977107i
\(708\) 0 0
\(709\) −5.00000 8.66025i −0.187779 0.325243i 0.756730 0.653727i \(-0.226796\pi\)
−0.944509 + 0.328484i \(0.893462\pi\)
\(710\) −9.00000 15.5885i −0.337764 0.585024i
\(711\) 0 0
\(712\) −4.50000 2.59808i −0.168645 0.0973670i
\(713\) 9.00000 15.5885i 0.337053 0.583792i
\(714\) 0 0
\(715\) 4.50000 + 7.79423i 0.168290 + 0.291488i
\(716\) 15.5885i 0.582568i
\(717\) 0 0
\(718\) 39.0000 1.45547
\(719\) 4.50000 7.79423i 0.167822 0.290676i −0.769832 0.638247i \(-0.779660\pi\)
0.937654 + 0.347571i \(0.112993\pi\)
\(720\) 0 0
\(721\) 10.5000 30.3109i 0.391040 1.12884i
\(722\) 12.0000 + 6.92820i 0.446594 + 0.257841i
\(723\) 0 0
\(724\) 0 0
\(725\) 18.0000 + 10.3923i 0.668503 + 0.385961i
\(726\) 0 0
\(727\) −10.5000 6.06218i −0.389423 0.224834i 0.292487 0.956270i \(-0.405517\pi\)
−0.681910 + 0.731436i \(0.738851\pi\)
\(728\) 1.50000 + 7.79423i 0.0555937 + 0.288873i
\(729\) 0 0
\(730\) −13.5000 + 23.3827i −0.499657 + 0.865432i
\(731\) 3.00000 0.110959
\(732\) 0 0
\(733\) 43.3013i 1.59937i 0.600420 + 0.799684i \(0.295000\pi\)
−0.600420 + 0.799684i \(0.705000\pi\)
\(734\) 4.50000 + 7.79423i 0.166098 + 0.287690i
\(735\) 0 0
\(736\) −13.5000 + 23.3827i −0.497617 + 0.861897i
\(737\) −6.00000 3.46410i −0.221013 0.127602i
\(738\) 0 0
\(739\) 3.50000 + 6.06218i 0.128750 + 0.223001i 0.923192 0.384338i \(-0.125570\pi\)
−0.794443 + 0.607339i \(0.792237\pi\)
\(740\) 10.5000 + 18.1865i 0.385988 + 0.668550i
\(741\) 0 0
\(742\) −30.0000 + 25.9808i −1.10133 + 0.953784i
\(743\) 10.5000 6.06218i 0.385208 0.222400i −0.294874 0.955536i \(-0.595278\pi\)
0.680082 + 0.733136i \(0.261944\pi\)
\(744\) 0 0
\(745\) 5.19615i 0.190372i
\(746\) −55.5000 + 32.0429i −2.03200 + 1.17318i
\(747\) 0 0
\(748\) 5.19615i 0.189990i
\(749\) −15.0000 17.3205i −0.548088 0.632878i
\(750\) 0 0
\(751\) 37.0000 1.35015 0.675075 0.737749i \(-0.264111\pi\)
0.675075 + 0.737749i \(0.264111\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) −13.5000 + 7.79423i −0.491641 + 0.283849i
\(755\) −51.0000 −1.85608
\(756\) 0 0
\(757\) 10.0000 0.363456 0.181728 0.983349i \(-0.441831\pi\)
0.181728 + 0.983349i \(0.441831\pi\)
\(758\) −30.0000 + 17.3205i −1.08965 + 0.629109i
\(759\) 0 0
\(760\) 13.5000 23.3827i 0.489696 0.848179i
\(761\) −45.0000 −1.63125 −0.815624 0.578582i \(-0.803606\pi\)
−0.815624 + 0.578582i \(0.803606\pi\)
\(762\) 0 0
\(763\) 9.50000 + 49.3634i 0.343923 + 1.78708i
\(764\) 17.3205i 0.626634i
\(765\) 0 0
\(766\) 13.5000 7.79423i 0.487775 0.281617i
\(767\) 0 0
\(768\) 0 0
\(769\) −13.5000 + 7.79423i −0.486822 + 0.281067i −0.723255 0.690581i \(-0.757355\pi\)
0.236433 + 0.971648i \(0.424022\pi\)
\(770\) 4.50000 + 23.3827i 0.162169 + 0.842654i
\(771\) 0 0
\(772\) −1.00000 1.73205i −0.0359908 0.0623379i
\(773\) −25.5000 44.1673i −0.917171 1.58859i −0.803691 0.595047i \(-0.797133\pi\)
−0.113480 0.993540i \(-0.536200\pi\)
\(774\) 0 0
\(775\) −12.0000 6.92820i −0.431053 0.248868i
\(776\) 1.50000 2.59808i 0.0538469 0.0932655i
\(777\) 0 0
\(778\) −31.5000 54.5596i −1.12933 1.95606i
\(779\) 15.5885i 0.558514i
\(780\) 0 0
\(781\) −6.00000 −0.214697
\(782\) 13.5000 23.3827i 0.482759 0.836163i
\(783\) 0 0
\(784\) −5.00000 + 34.6410i −0.178571 + 1.23718i
\(785\) 0 0
\(786\) 0 0
\(787\) −33.0000 19.0526i −1.17632 0.679150i −0.221162 0.975237i \(-0.570985\pi\)
−0.955161 + 0.296087i \(0.904318\pi\)
\(788\) 12.0000 + 6.92820i 0.427482 + 0.246807i
\(789\) 0 0
\(790\) −36.0000 20.7846i −1.28082 0.739483i
\(791\) 4.50000 0.866025i 0.160002 0.0307923i
\(792\) 0 0
\(793\) −12.0000 + 20.7846i −0.426132 + 0.738083i
\(794\) 15.0000 0.532330
\(795\) 0 0
\(796\) 8.66025i 0.306955i
\(797\) 22.5000 + 38.9711i 0.796991 + 1.38043i 0.921567 + 0.388219i \(0.126909\pi\)
−0.124576 + 0.992210i \(0.539757\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 18.0000 + 10.3923i 0.636396 + 0.367423i
\(801\) 0 0
\(802\) −28.5000 49.3634i −1.00637 1.74308i
\(803\) 4.50000 + 7.79423i 0.158802 + 0.275052i
\(804\) 0 0
\(805\) 13.5000 38.9711i 0.475812 1.37355i
\(806\) 9.00000 5.19615i 0.317011 0.183027i
\(807\) 0 0
\(808\) 5.19615i 0.182800i
\(809\) 1.50000 0.866025i 0.0527372 0.0304478i −0.473400 0.880848i \(-0.656973\pi\)
0.526137 + 0.850400i \(0.323640\pi\)
\(810\) 0 0
\(811\) 10.3923i 0.364923i 0.983213 + 0.182462i \(0.0584065\pi\)
−0.983213 + 0.182462i \(0.941593\pi\)
\(812\) −13.5000 + 2.59808i −0.473757 + 0.0911746i
\(813\) 0 0
\(814\) 21.0000 0.736050
\(815\) −16.5000 + 28.5788i −0.577970 + 1.00107i
\(816\) 0 0
\(817\) 4.50000 2.59808i 0.157435 0.0908952i
\(818\) −12.0000 −0.419570
\(819\) 0 0
\(820\) −9.00000 −0.314294
\(821\) −6.00000 + 3.46410i −0.209401 + 0.120898i −0.601033 0.799224i \(-0.705244\pi\)
0.391632 + 0.920122i \(0.371911\pi\)
\(822\) 0 0
\(823\) 8.00000 13.8564i 0.278862 0.483004i −0.692240 0.721668i \(-0.743376\pi\)
0.971102 + 0.238664i \(0.0767093\pi\)
\(824\) −21.0000 −0.731570
\(825\) 0 0
\(826\) 0 0
\(827\) 24.2487i 0.843210i 0.906780 + 0.421605i \(0.138533\pi\)
−0.906780 + 0.421605i \(0.861467\pi\)
\(828\) 0 0
\(829\) 31.5000 18.1865i 1.09404 0.631644i 0.159391 0.987216i \(-0.449047\pi\)
0.934649 + 0.355571i \(0.115714\pi\)
\(830\) 77.9423i 2.70542i
\(831\) 0 0
\(832\) 1.50000 0.866025i 0.0520031 0.0300240i
\(833\) 3.00000 20.7846i 0.103944 0.720144i
\(834\) 0 0
\(835\) 13.5000 + 23.3827i 0.467187 + 0.809191i
\(836\) 4.50000 + 7.79423i 0.155636 + 0.269569i
\(837\) 0 0
\(838\) 49.5000 + 28.5788i 1.70995 + 0.987240i
\(839\) 19.5000 33.7750i 0.673215 1.16604i −0.303773 0.952745i \(-0.598246\pi\)
0.976987 0.213298i \(-0.0684204\pi\)
\(840\) 0 0
\(841\) −1.00000 1.73205i −0.0344828 0.0597259i
\(842\) 19.0526i 0.656595i
\(843\) 0 0
\(844\) 5.00000 0.172107
\(845\) −15.0000 + 25.9808i −0.516016 + 0.893765i
\(846\) 0 0
\(847\) −20.0000 6.92820i −0.687208 0.238056i
\(848\) 37.5000 + 21.6506i 1.28776 + 0.743486i
\(849\) 0 0
\(850\) −18.0000 10.3923i −0.617395 0.356453i
\(851\) −31.5000 18.1865i −1.07981 0.623426i
\(852\) 0 0
\(853\) 22.5000 + 12.9904i 0.770385 + 0.444782i 0.833012 0.553255i \(-0.186614\pi\)
−0.0626267 + 0.998037i \(0.519948\pi\)
\(854\) −48.0000 + 41.5692i −1.64253 + 1.42247i
\(855\) 0 0
\(856\) −7.50000 + 12.9904i −0.256345 + 0.444002i
\(857\) 27.0000 0.922302 0.461151 0.887322i \(-0.347437\pi\)
0.461151 + 0.887322i \(0.347437\pi\)
\(858\) 0 0
\(859\) 50.2295i 1.71381i −0.515476 0.856904i \(-0.672385\pi\)
0.515476 0.856904i \(-0.327615\pi\)
\(860\) 1.50000 + 2.59808i 0.0511496 + 0.0885937i
\(861\) 0 0
\(862\) −13.5000 + 23.3827i −0.459812 + 0.796417i
\(863\) 37.5000 + 21.6506i 1.27651 + 0.736996i 0.976206 0.216846i \(-0.0695769\pi\)
0.300309 + 0.953842i \(0.402910\pi\)
\(864\) 0 0
\(865\) 9.00000 + 15.5885i 0.306009 + 0.530023i
\(866\) −12.0000 20.7846i −0.407777 0.706290i
\(867\) 0 0
\(868\) 9.00000 1.73205i 0.305480 0.0587896i
\(869\) −12.0000 + 6.92820i −0.407072 + 0.235023i
\(870\) 0 0
\(871\) 6.92820i 0.234753i
\(872\) 28.5000 16.4545i 0.965132 0.557219i
\(873\) 0 0
\(874\) 46.7654i 1.58186i
\(875\) 7.50000 + 2.59808i 0.253546 + 0.0878310i
\(876\) 0 0
\(877\) 23.0000 0.776655 0.388327 0.921521i \(-0.373053\pi\)
0.388327 + 0.921521i \(0.373053\pi\)
\(878\) 27.0000 46.7654i 0.911206 1.57825i
\(879\) 0 0
\(880\) 22.5000 12.9904i 0.758475 0.437906i
\(881\) 54.0000 1.81931 0.909653 0.415369i \(-0.136347\pi\)
0.909653 + 0.415369i \(0.136347\pi\)
\(882\) 0 0
\(883\) 4.00000 0.134611 0.0673054 0.997732i \(-0.478560\pi\)
0.0673054 + 0.997732i \(0.478560\pi\)
\(884\) 4.50000 2.59808i 0.151351 0.0873828i
\(885\) 0 0
\(886\) −27.0000 + 46.7654i −0.907083 + 1.57111i
\(887\) −15.0000 −0.503651 −0.251825 0.967773i \(-0.581031\pi\)
−0.251825 + 0.967773i \(0.581031\pi\)
\(888\) 0 0
\(889\) −50.0000 17.3205i −1.67695 0.580911i
\(890\) 15.5885i 0.522526i
\(891\) 0 0
\(892\) −4.50000 + 2.59808i −0.150671 + 0.0869900i
\(893\) 0 0
\(894\) 0 0
\(895\) −40.5000 + 23.3827i −1.35377 + 0.781597i
\(896\) 31.5000 6.06218i 1.05234 0.202523i
\(897\) 0 0
\(898\) −30.0000 51.9615i −1.00111 1.73398i
\(899\) −9.00000 15.5885i −0.300167 0.519904i
\(900\) 0 0
\(901\) −22.5000 12.9904i −0.749584 0.432772i
\(902\) −4.50000 + 7.79423i −0.149834 + 0.259519i
\(903\) 0 0
\(904\) −1.50000 2.59808i −0.0498893 0.0864107i
\(905\) 0 0
\(906\) 0 0
\(907\) 19.0000 0.630885 0.315442 0.948945i \(-0.397847\pi\)
0.315442 + 0.948945i \(0.397847\pi\)
\(908\) −10.5000 + 18.1865i −0.348455 + 0.603541i
\(909\) 0 0
\(910\) 18.0000 15.5885i 0.596694 0.516752i
\(911\) −4.50000 2.59808i −0.149092 0.0860781i 0.423598 0.905850i \(-0.360767\pi\)
−0.572690 + 0.819772i \(0.694100\pi\)
\(912\) 0 0
\(913\) −22.5000 12.9904i −0.744641 0.429919i
\(914\) 39.0000 + 22.5167i 1.29001 + 0.744785i
\(915\) 0 0
\(916\) 7.50000 + 4.33013i 0.247807 + 0.143071i
\(917\) −22.5000 7.79423i −0.743015 0.257388i
\(918\) 0 0
\(919\) 14.5000 25.1147i 0.478311 0.828459i −0.521380 0.853325i \(-0.674583\pi\)
0.999691 + 0.0248659i \(0.00791589\pi\)
\(920\) −27.0000 −0.890164
\(921\) 0 0
\(922\) 25.9808i 0.855631i
\(923\) 3.00000 + 5.19615i 0.0987462 + 0.171033i
\(924\) 0 0
\(925\) −14.0000 + 24.2487i −0.460317 + 0.797293i
\(926\) 1.50000 + 0.866025i 0.0492931 + 0.0284594i
\(927\) 0 0
\(928\) 13.5000 + 23.3827i 0.443159 + 0.767574i
\(929\) 15.0000 + 25.9808i 0.492134 + 0.852401i 0.999959 0.00905914i \(-0.00288365\pi\)
−0.507825 + 0.861460i \(0.669550\pi\)
\(930\) 0 0
\(931\) −13.5000 33.7750i −0.442445 1.10693i
\(932\) −4.50000 + 2.59808i −0.147402 + 0.0851028i
\(933\) 0 0
\(934\) 5.19615i 0.170023i
\(935\) −13.5000 + 7.79423i −0.441497 + 0.254899i
\(936\) 0 0
\(937\) 13.8564i 0.452669i −0.974050 0.226335i \(-0.927326\pi\)
0.974050 0.226335i \(-0.0726743\pi\)
\(938\) −6.00000 + 17.3205i −0.195907 + 0.565535i
\(939\) 0 0
\(940\) 0 0
\(941\) −9.00000 + 15.5885i −0.293392 + 0.508169i −0.974609 0.223912i \(-0.928117\pi\)
0.681218 + 0.732081i \(0.261451\pi\)
\(942\) 0 0
\(943\) 13.5000 7.79423i 0.439620 0.253815i
\(944\) 0 0
\(945\) 0 0
\(946\) 3.00000 0.0975384
\(947\) 45.0000 25.9808i 1.46230 0.844261i 0.463186 0.886261i \(-0.346706\pi\)
0.999118 + 0.0419998i \(0.0133729\pi\)
\(948\) 0 0
\(949\) 4.50000 7.79423i 0.146076 0.253011i
\(950\) −36.0000 −1.16799
\(951\) 0 0
\(952\) −13.5000 + 2.59808i −0.437538 + 0.0842041i
\(953\) 20.7846i 0.673280i −0.941634 0.336640i \(-0.890710\pi\)
0.941634 0.336640i \(-0.109290\pi\)
\(954\) 0 0
\(955\) 45.0000 25.9808i 1.45617 0.840718i
\(956\) 1.73205i 0.0560185i
\(957\) 0 0
\(958\) 40.5000 23.3827i 1.30850 0.755460i
\(959\) 10.5000 30.3109i 0.339063 0.978790i
\(960\) 0 0
\(961\) −9.50000 16.4545i −0.306452 0.530790i
\(962\) −10.5000 18.1865i −0.338534 0.586357i
\(963\) 0 0
\(964\) −19.5000 11.2583i −0.628053 0.362606i
\(965\) 3.00000 5.19615i 0.0965734 0.167270i
\(966\) 0 0
\(967\) 12.5000 + 21.6506i 0.401973 + 0.696237i 0.993964 0.109707i \(-0.0349913\pi\)
−0.591991 + 0.805945i \(0.701658\pi\)
\(968\) 13.8564i 0.445362i
\(969\) 0 0
\(970\) −9.00000 −0.288973
\(971\) 28.5000 49.3634i 0.914609 1.58415i 0.107135 0.994244i \(-0.465832\pi\)
0.807473 0.589904i \(-0.200834\pi\)
\(972\) 0 0
\(973\) 22.5000 4.33013i 0.721317 0.138817i
\(974\) 34.5000 + 19.9186i 1.10545 + 0.638233i
\(975\) 0 0
\(976\) 60.0000 + 34.6410i 1.92055 + 1.10883i
\(977\) 36.0000 + 20.7846i 1.15174 + 0.664959i 0.949311 0.314338i \(-0.101783\pi\)
0.202431 + 0.979297i \(0.435116\pi\)
\(978\) 0 0
\(979\) 4.50000 + 2.59808i 0.143821 + 0.0830349i
\(980\) 19.5000 7.79423i 0.622905 0.248978i
\(981\) 0 0
\(982\) 22.5000 38.9711i 0.718004 1.24362i
\(983\) 39.0000 1.24391 0.621953 0.783054i \(-0.286339\pi\)
0.621953 + 0.783054i \(0.286339\pi\)
\(984\) 0 0
\(985\) 41.5692i 1.32451i
\(986\) −13.5000 23.3827i −0.429928 0.744656i
\(987\) 0 0
\(988\) 4.50000 7.79423i 0.143164 0.247967i
\(989\) −4.50000 2.59808i −0.143092 0.0826140i
\(990\) 0 0
\(991\) 23.5000 + 40.7032i 0.746502 + 1.29298i 0.949490 + 0.313798i \(0.101602\pi\)
−0.202988 + 0.979181i \(0.565065\pi\)
\(992\) −9.00000 15.5885i −0.285750 0.494934i
\(993\) 0 0
\(994\) 3.00000 + 15.5885i 0.0951542 + 0.494436i
\(995\) −22.5000 + 12.9904i −0.713298 + 0.411823i
\(996\) 0 0
\(997\) 8.66025i 0.274273i −0.990552 0.137136i \(-0.956210\pi\)
0.990552 0.137136i \(-0.0437899\pi\)
\(998\) 37.5000 21.6506i 1.18704 0.685339i
\(999\) 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 189.2.s.a.89.1 2
3.2 odd 2 63.2.s.a.47.1 yes 2
4.3 odd 2 3024.2.df.a.1601.1 2
7.2 even 3 1323.2.o.a.440.1 2
7.3 odd 6 189.2.i.a.143.1 2
7.4 even 3 1323.2.i.a.521.1 2
7.5 odd 6 1323.2.o.b.440.1 2
7.6 odd 2 1323.2.s.a.656.1 2
9.2 odd 6 567.2.p.b.404.1 2
9.4 even 3 63.2.i.a.5.1 2
9.5 odd 6 189.2.i.a.152.1 2
9.7 even 3 567.2.p.a.404.1 2
12.11 even 2 1008.2.df.a.929.1 2
21.2 odd 6 441.2.o.b.146.1 2
21.5 even 6 441.2.o.a.146.1 2
21.11 odd 6 441.2.i.a.227.1 2
21.17 even 6 63.2.i.a.38.1 yes 2
21.20 even 2 441.2.s.a.362.1 2
28.3 even 6 3024.2.ca.a.2033.1 2
36.23 even 6 3024.2.ca.a.2609.1 2
36.31 odd 6 1008.2.ca.a.257.1 2
63.4 even 3 441.2.s.a.374.1 2
63.5 even 6 1323.2.o.a.881.1 2
63.13 odd 6 441.2.i.a.68.1 2
63.23 odd 6 1323.2.o.b.881.1 2
63.31 odd 6 63.2.s.a.59.1 yes 2
63.32 odd 6 1323.2.s.a.962.1 2
63.38 even 6 567.2.p.a.80.1 2
63.40 odd 6 441.2.o.b.293.1 2
63.41 even 6 1323.2.i.a.1097.1 2
63.52 odd 6 567.2.p.b.80.1 2
63.58 even 3 441.2.o.a.293.1 2
63.59 even 6 inner 189.2.s.a.17.1 2
84.59 odd 6 1008.2.ca.a.353.1 2
252.31 even 6 1008.2.df.a.689.1 2
252.59 odd 6 3024.2.df.a.17.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
63.2.i.a.5.1 2 9.4 even 3
63.2.i.a.38.1 yes 2 21.17 even 6
63.2.s.a.47.1 yes 2 3.2 odd 2
63.2.s.a.59.1 yes 2 63.31 odd 6
189.2.i.a.143.1 2 7.3 odd 6
189.2.i.a.152.1 2 9.5 odd 6
189.2.s.a.17.1 2 63.59 even 6 inner
189.2.s.a.89.1 2 1.1 even 1 trivial
441.2.i.a.68.1 2 63.13 odd 6
441.2.i.a.227.1 2 21.11 odd 6
441.2.o.a.146.1 2 21.5 even 6
441.2.o.a.293.1 2 63.58 even 3
441.2.o.b.146.1 2 21.2 odd 6
441.2.o.b.293.1 2 63.40 odd 6
441.2.s.a.362.1 2 21.20 even 2
441.2.s.a.374.1 2 63.4 even 3
567.2.p.a.80.1 2 63.38 even 6
567.2.p.a.404.1 2 9.7 even 3
567.2.p.b.80.1 2 63.52 odd 6
567.2.p.b.404.1 2 9.2 odd 6
1008.2.ca.a.257.1 2 36.31 odd 6
1008.2.ca.a.353.1 2 84.59 odd 6
1008.2.df.a.689.1 2 252.31 even 6
1008.2.df.a.929.1 2 12.11 even 2
1323.2.i.a.521.1 2 7.4 even 3
1323.2.i.a.1097.1 2 63.41 even 6
1323.2.o.a.440.1 2 7.2 even 3
1323.2.o.a.881.1 2 63.5 even 6
1323.2.o.b.440.1 2 7.5 odd 6
1323.2.o.b.881.1 2 63.23 odd 6
1323.2.s.a.656.1 2 7.6 odd 2
1323.2.s.a.962.1 2 63.32 odd 6
3024.2.ca.a.2033.1 2 28.3 even 6
3024.2.ca.a.2609.1 2 36.23 even 6
3024.2.df.a.17.1 2 252.59 odd 6
3024.2.df.a.1601.1 2 4.3 odd 2