Properties

Label 1134.2.m.b.377.1
Level $1134$
Weight $2$
Character 1134.377
Analytic conductor $9.055$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1134,2,Mod(377,1134)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1134, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([5, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1134.377");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1134 = 2 \cdot 3^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1134.m (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: \(9.05503558921\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{12})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 378)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 377.1
Root \(-0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 1134.377
Dual form 1134.2.m.b.755.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(0.866025 - 1.50000i) q^{5} +(-2.50000 - 0.866025i) q^{7} +1.00000i q^{8} +O(q^{10})\) \(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(0.866025 - 1.50000i) q^{5} +(-2.50000 - 0.866025i) q^{7} +1.00000i q^{8} +1.73205i q^{10} +(-2.59808 + 1.50000i) q^{11} +(3.00000 + 1.73205i) q^{13} +(2.59808 - 0.500000i) q^{14} +(-0.500000 - 0.866025i) q^{16} -6.92820 q^{17} -1.73205i q^{19} +(-0.866025 - 1.50000i) q^{20} +(1.50000 - 2.59808i) q^{22} +(2.59808 + 1.50000i) q^{23} +(1.00000 + 1.73205i) q^{25} -3.46410 q^{26} +(-2.00000 + 1.73205i) q^{28} +(-5.19615 + 3.00000i) q^{29} +(-4.50000 - 2.59808i) q^{31} +(0.866025 + 0.500000i) q^{32} +(6.00000 - 3.46410i) q^{34} +(-3.46410 + 3.00000i) q^{35} +7.00000 q^{37} +(0.866025 + 1.50000i) q^{38} +(1.50000 + 0.866025i) q^{40} +(-6.06218 + 10.5000i) q^{41} +(1.00000 + 1.73205i) q^{43} +3.00000i q^{44} -3.00000 q^{46} +(-1.73205 - 3.00000i) q^{47} +(5.50000 + 4.33013i) q^{49} +(-1.73205 - 1.00000i) q^{50} +(3.00000 - 1.73205i) q^{52} +12.0000i q^{53} +5.19615i q^{55} +(0.866025 - 2.50000i) q^{56} +(3.00000 - 5.19615i) q^{58} +(1.73205 - 3.00000i) q^{59} +(-6.00000 + 3.46410i) q^{61} +5.19615 q^{62} -1.00000 q^{64} +(5.19615 - 3.00000i) q^{65} +(-1.00000 + 1.73205i) q^{67} +(-3.46410 + 6.00000i) q^{68} +(1.50000 - 4.33013i) q^{70} +3.00000i q^{71} +3.46410i q^{73} +(-6.06218 + 3.50000i) q^{74} +(-1.50000 - 0.866025i) q^{76} +(7.79423 - 1.50000i) q^{77} +(5.00000 + 8.66025i) q^{79} -1.73205 q^{80} -12.1244i q^{82} +(-8.66025 - 15.0000i) q^{83} +(-6.00000 + 10.3923i) q^{85} +(-1.73205 - 1.00000i) q^{86} +(-1.50000 - 2.59808i) q^{88} +5.19615 q^{89} +(-6.00000 - 6.92820i) q^{91} +(2.59808 - 1.50000i) q^{92} +(3.00000 + 1.73205i) q^{94} +(-2.59808 - 1.50000i) q^{95} +(-12.0000 + 6.92820i) q^{97} +(-6.92820 - 1.00000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2 q^{4} - 10 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 2 q^{4} - 10 q^{7} + 12 q^{13} - 2 q^{16} + 6 q^{22} + 4 q^{25} - 8 q^{28} - 18 q^{31} + 24 q^{34} + 28 q^{37} + 6 q^{40} + 4 q^{43} - 12 q^{46} + 22 q^{49} + 12 q^{52} + 12 q^{58} - 24 q^{61} - 4 q^{64} - 4 q^{67} + 6 q^{70} - 6 q^{76} + 20 q^{79} - 24 q^{85} - 6 q^{88} - 24 q^{91} + 12 q^{94} - 48 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1134\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(407\)
\(\chi(n)\) \(-1\) \(e\left(\frac{5}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 + 0.500000i −0.612372 + 0.353553i
\(3\) 0 0
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) 0.866025 1.50000i 0.387298 0.670820i −0.604787 0.796387i \(-0.706742\pi\)
0.992085 + 0.125567i \(0.0400750\pi\)
\(6\) 0 0
\(7\) −2.50000 0.866025i −0.944911 0.327327i
\(8\) 1.00000i 0.353553i
\(9\) 0 0
\(10\) 1.73205i 0.547723i
\(11\) −2.59808 + 1.50000i −0.783349 + 0.452267i −0.837616 0.546259i \(-0.816051\pi\)
0.0542666 + 0.998526i \(0.482718\pi\)
\(12\) 0 0
\(13\) 3.00000 + 1.73205i 0.832050 + 0.480384i 0.854554 0.519362i \(-0.173830\pi\)
−0.0225039 + 0.999747i \(0.507164\pi\)
\(14\) 2.59808 0.500000i 0.694365 0.133631i
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −6.92820 −1.68034 −0.840168 0.542326i \(-0.817544\pi\)
−0.840168 + 0.542326i \(0.817544\pi\)
\(18\) 0 0
\(19\) 1.73205i 0.397360i −0.980064 0.198680i \(-0.936335\pi\)
0.980064 0.198680i \(-0.0636654\pi\)
\(20\) −0.866025 1.50000i −0.193649 0.335410i
\(21\) 0 0
\(22\) 1.50000 2.59808i 0.319801 0.553912i
\(23\) 2.59808 + 1.50000i 0.541736 + 0.312772i 0.745782 0.666190i \(-0.232076\pi\)
−0.204046 + 0.978961i \(0.565409\pi\)
\(24\) 0 0
\(25\) 1.00000 + 1.73205i 0.200000 + 0.346410i
\(26\) −3.46410 −0.679366
\(27\) 0 0
\(28\) −2.00000 + 1.73205i −0.377964 + 0.327327i
\(29\) −5.19615 + 3.00000i −0.964901 + 0.557086i −0.897678 0.440652i \(-0.854747\pi\)
−0.0672232 + 0.997738i \(0.521414\pi\)
\(30\) 0 0
\(31\) −4.50000 2.59808i −0.808224 0.466628i 0.0381148 0.999273i \(-0.487865\pi\)
−0.846339 + 0.532645i \(0.821198\pi\)
\(32\) 0.866025 + 0.500000i 0.153093 + 0.0883883i
\(33\) 0 0
\(34\) 6.00000 3.46410i 1.02899 0.594089i
\(35\) −3.46410 + 3.00000i −0.585540 + 0.507093i
\(36\) 0 0
\(37\) 7.00000 1.15079 0.575396 0.817875i \(-0.304848\pi\)
0.575396 + 0.817875i \(0.304848\pi\)
\(38\) 0.866025 + 1.50000i 0.140488 + 0.243332i
\(39\) 0 0
\(40\) 1.50000 + 0.866025i 0.237171 + 0.136931i
\(41\) −6.06218 + 10.5000i −0.946753 + 1.63982i −0.194551 + 0.980892i \(0.562325\pi\)
−0.752202 + 0.658932i \(0.771008\pi\)
\(42\) 0 0
\(43\) 1.00000 + 1.73205i 0.152499 + 0.264135i 0.932145 0.362084i \(-0.117935\pi\)
−0.779647 + 0.626219i \(0.784601\pi\)
\(44\) 3.00000i 0.452267i
\(45\) 0 0
\(46\) −3.00000 −0.442326
\(47\) −1.73205 3.00000i −0.252646 0.437595i 0.711608 0.702577i \(-0.247967\pi\)
−0.964253 + 0.264982i \(0.914634\pi\)
\(48\) 0 0
\(49\) 5.50000 + 4.33013i 0.785714 + 0.618590i
\(50\) −1.73205 1.00000i −0.244949 0.141421i
\(51\) 0 0
\(52\) 3.00000 1.73205i 0.416025 0.240192i
\(53\) 12.0000i 1.64833i 0.566352 + 0.824163i \(0.308354\pi\)
−0.566352 + 0.824163i \(0.691646\pi\)
\(54\) 0 0
\(55\) 5.19615i 0.700649i
\(56\) 0.866025 2.50000i 0.115728 0.334077i
\(57\) 0 0
\(58\) 3.00000 5.19615i 0.393919 0.682288i
\(59\) 1.73205 3.00000i 0.225494 0.390567i −0.730974 0.682406i \(-0.760934\pi\)
0.956467 + 0.291839i \(0.0942671\pi\)
\(60\) 0 0
\(61\) −6.00000 + 3.46410i −0.768221 + 0.443533i −0.832240 0.554416i \(-0.812942\pi\)
0.0640184 + 0.997949i \(0.479608\pi\)
\(62\) 5.19615 0.659912
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 5.19615 3.00000i 0.644503 0.372104i
\(66\) 0 0
\(67\) −1.00000 + 1.73205i −0.122169 + 0.211604i −0.920623 0.390453i \(-0.872318\pi\)
0.798454 + 0.602056i \(0.205652\pi\)
\(68\) −3.46410 + 6.00000i −0.420084 + 0.727607i
\(69\) 0 0
\(70\) 1.50000 4.33013i 0.179284 0.517549i
\(71\) 3.00000i 0.356034i 0.984027 + 0.178017i \(0.0569683\pi\)
−0.984027 + 0.178017i \(0.943032\pi\)
\(72\) 0 0
\(73\) 3.46410i 0.405442i 0.979236 + 0.202721i \(0.0649785\pi\)
−0.979236 + 0.202721i \(0.935021\pi\)
\(74\) −6.06218 + 3.50000i −0.704714 + 0.406867i
\(75\) 0 0
\(76\) −1.50000 0.866025i −0.172062 0.0993399i
\(77\) 7.79423 1.50000i 0.888235 0.170941i
\(78\) 0 0
\(79\) 5.00000 + 8.66025i 0.562544 + 0.974355i 0.997274 + 0.0737937i \(0.0235106\pi\)
−0.434730 + 0.900561i \(0.643156\pi\)
\(80\) −1.73205 −0.193649
\(81\) 0 0
\(82\) 12.1244i 1.33891i
\(83\) −8.66025 15.0000i −0.950586 1.64646i −0.744160 0.668002i \(-0.767150\pi\)
−0.206427 0.978462i \(-0.566184\pi\)
\(84\) 0 0
\(85\) −6.00000 + 10.3923i −0.650791 + 1.12720i
\(86\) −1.73205 1.00000i −0.186772 0.107833i
\(87\) 0 0
\(88\) −1.50000 2.59808i −0.159901 0.276956i
\(89\) 5.19615 0.550791 0.275396 0.961331i \(-0.411191\pi\)
0.275396 + 0.961331i \(0.411191\pi\)
\(90\) 0 0
\(91\) −6.00000 6.92820i −0.628971 0.726273i
\(92\) 2.59808 1.50000i 0.270868 0.156386i
\(93\) 0 0
\(94\) 3.00000 + 1.73205i 0.309426 + 0.178647i
\(95\) −2.59808 1.50000i −0.266557 0.153897i
\(96\) 0 0
\(97\) −12.0000 + 6.92820i −1.21842 + 0.703452i −0.964579 0.263795i \(-0.915026\pi\)
−0.253837 + 0.967247i \(0.581693\pi\)
\(98\) −6.92820 1.00000i −0.699854 0.101015i
\(99\) 0 0
\(100\) 2.00000 0.200000
\(101\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(102\) 0 0
\(103\) −16.5000 9.52628i −1.62579 0.938652i −0.985329 0.170664i \(-0.945409\pi\)
−0.640464 0.767988i \(-0.721258\pi\)
\(104\) −1.73205 + 3.00000i −0.169842 + 0.294174i
\(105\) 0 0
\(106\) −6.00000 10.3923i −0.582772 1.00939i
\(107\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(108\) 0 0
\(109\) 13.0000 1.24517 0.622587 0.782551i \(-0.286082\pi\)
0.622587 + 0.782551i \(0.286082\pi\)
\(110\) −2.59808 4.50000i −0.247717 0.429058i
\(111\) 0 0
\(112\) 0.500000 + 2.59808i 0.0472456 + 0.245495i
\(113\) −10.3923 6.00000i −0.977626 0.564433i −0.0760733 0.997102i \(-0.524238\pi\)
−0.901553 + 0.432670i \(0.857572\pi\)
\(114\) 0 0
\(115\) 4.50000 2.59808i 0.419627 0.242272i
\(116\) 6.00000i 0.557086i
\(117\) 0 0
\(118\) 3.46410i 0.318896i
\(119\) 17.3205 + 6.00000i 1.58777 + 0.550019i
\(120\) 0 0
\(121\) −1.00000 + 1.73205i −0.0909091 + 0.157459i
\(122\) 3.46410 6.00000i 0.313625 0.543214i
\(123\) 0 0
\(124\) −4.50000 + 2.59808i −0.404112 + 0.233314i
\(125\) 12.1244 1.08444
\(126\) 0 0
\(127\) −22.0000 −1.95218 −0.976092 0.217357i \(-0.930256\pi\)
−0.976092 + 0.217357i \(0.930256\pi\)
\(128\) 0.866025 0.500000i 0.0765466 0.0441942i
\(129\) 0 0
\(130\) −3.00000 + 5.19615i −0.263117 + 0.455733i
\(131\) −5.19615 + 9.00000i −0.453990 + 0.786334i −0.998630 0.0523366i \(-0.983333\pi\)
0.544640 + 0.838670i \(0.316666\pi\)
\(132\) 0 0
\(133\) −1.50000 + 4.33013i −0.130066 + 0.375470i
\(134\) 2.00000i 0.172774i
\(135\) 0 0
\(136\) 6.92820i 0.594089i
\(137\) −15.5885 + 9.00000i −1.33181 + 0.768922i −0.985577 0.169226i \(-0.945873\pi\)
−0.346235 + 0.938148i \(0.612540\pi\)
\(138\) 0 0
\(139\) −3.00000 1.73205i −0.254457 0.146911i 0.367347 0.930084i \(-0.380266\pi\)
−0.621803 + 0.783174i \(0.713600\pi\)
\(140\) 0.866025 + 4.50000i 0.0731925 + 0.380319i
\(141\) 0 0
\(142\) −1.50000 2.59808i −0.125877 0.218026i
\(143\) −10.3923 −0.869048
\(144\) 0 0
\(145\) 10.3923i 0.863034i
\(146\) −1.73205 3.00000i −0.143346 0.248282i
\(147\) 0 0
\(148\) 3.50000 6.06218i 0.287698 0.498308i
\(149\) 10.3923 + 6.00000i 0.851371 + 0.491539i 0.861113 0.508413i \(-0.169768\pi\)
−0.00974235 + 0.999953i \(0.503101\pi\)
\(150\) 0 0
\(151\) 4.00000 + 6.92820i 0.325515 + 0.563809i 0.981617 0.190864i \(-0.0611289\pi\)
−0.656101 + 0.754673i \(0.727796\pi\)
\(152\) 1.73205 0.140488
\(153\) 0 0
\(154\) −6.00000 + 5.19615i −0.483494 + 0.418718i
\(155\) −7.79423 + 4.50000i −0.626048 + 0.361449i
\(156\) 0 0
\(157\) −9.00000 5.19615i −0.718278 0.414698i 0.0958404 0.995397i \(-0.469446\pi\)
−0.814119 + 0.580699i \(0.802779\pi\)
\(158\) −8.66025 5.00000i −0.688973 0.397779i
\(159\) 0 0
\(160\) 1.50000 0.866025i 0.118585 0.0684653i
\(161\) −5.19615 6.00000i −0.409514 0.472866i
\(162\) 0 0
\(163\) 2.00000 0.156652 0.0783260 0.996928i \(-0.475042\pi\)
0.0783260 + 0.996928i \(0.475042\pi\)
\(164\) 6.06218 + 10.5000i 0.473377 + 0.819912i
\(165\) 0 0
\(166\) 15.0000 + 8.66025i 1.16423 + 0.672166i
\(167\) 3.46410 6.00000i 0.268060 0.464294i −0.700301 0.713848i \(-0.746951\pi\)
0.968361 + 0.249554i \(0.0802840\pi\)
\(168\) 0 0
\(169\) −0.500000 0.866025i −0.0384615 0.0666173i
\(170\) 12.0000i 0.920358i
\(171\) 0 0
\(172\) 2.00000 0.152499
\(173\) 2.59808 + 4.50000i 0.197528 + 0.342129i 0.947726 0.319084i \(-0.103375\pi\)
−0.750198 + 0.661213i \(0.770042\pi\)
\(174\) 0 0
\(175\) −1.00000 5.19615i −0.0755929 0.392792i
\(176\) 2.59808 + 1.50000i 0.195837 + 0.113067i
\(177\) 0 0
\(178\) −4.50000 + 2.59808i −0.337289 + 0.194734i
\(179\) 12.0000i 0.896922i −0.893802 0.448461i \(-0.851972\pi\)
0.893802 0.448461i \(-0.148028\pi\)
\(180\) 0 0
\(181\) 13.8564i 1.02994i −0.857209 0.514969i \(-0.827803\pi\)
0.857209 0.514969i \(-0.172197\pi\)
\(182\) 8.66025 + 3.00000i 0.641941 + 0.222375i
\(183\) 0 0
\(184\) −1.50000 + 2.59808i −0.110581 + 0.191533i
\(185\) 6.06218 10.5000i 0.445700 0.771975i
\(186\) 0 0
\(187\) 18.0000 10.3923i 1.31629 0.759961i
\(188\) −3.46410 −0.252646
\(189\) 0 0
\(190\) 3.00000 0.217643
\(191\) 18.1865 10.5000i 1.31593 0.759753i 0.332860 0.942976i \(-0.391986\pi\)
0.983071 + 0.183223i \(0.0586530\pi\)
\(192\) 0 0
\(193\) 7.00000 12.1244i 0.503871 0.872730i −0.496119 0.868255i \(-0.665242\pi\)
0.999990 0.00447566i \(-0.00142465\pi\)
\(194\) 6.92820 12.0000i 0.497416 0.861550i
\(195\) 0 0
\(196\) 6.50000 2.59808i 0.464286 0.185577i
\(197\) 12.0000i 0.854965i −0.904024 0.427482i \(-0.859401\pi\)
0.904024 0.427482i \(-0.140599\pi\)
\(198\) 0 0
\(199\) 1.73205i 0.122782i 0.998114 + 0.0613909i \(0.0195536\pi\)
−0.998114 + 0.0613909i \(0.980446\pi\)
\(200\) −1.73205 + 1.00000i −0.122474 + 0.0707107i
\(201\) 0 0
\(202\) 0 0
\(203\) 15.5885 3.00000i 1.09410 0.210559i
\(204\) 0 0
\(205\) 10.5000 + 18.1865i 0.733352 + 1.27020i
\(206\) 19.0526 1.32745
\(207\) 0 0
\(208\) 3.46410i 0.240192i
\(209\) 2.59808 + 4.50000i 0.179713 + 0.311272i
\(210\) 0 0
\(211\) −8.00000 + 13.8564i −0.550743 + 0.953914i 0.447478 + 0.894295i \(0.352322\pi\)
−0.998221 + 0.0596196i \(0.981011\pi\)
\(212\) 10.3923 + 6.00000i 0.713746 + 0.412082i
\(213\) 0 0
\(214\) 0 0
\(215\) 3.46410 0.236250
\(216\) 0 0
\(217\) 9.00000 + 10.3923i 0.610960 + 0.705476i
\(218\) −11.2583 + 6.50000i −0.762510 + 0.440236i
\(219\) 0 0
\(220\) 4.50000 + 2.59808i 0.303390 + 0.175162i
\(221\) −20.7846 12.0000i −1.39812 0.807207i
\(222\) 0 0
\(223\) 13.5000 7.79423i 0.904027 0.521940i 0.0255224 0.999674i \(-0.491875\pi\)
0.878504 + 0.477734i \(0.158542\pi\)
\(224\) −1.73205 2.00000i −0.115728 0.133631i
\(225\) 0 0
\(226\) 12.0000 0.798228
\(227\) 10.3923 + 18.0000i 0.689761 + 1.19470i 0.971915 + 0.235333i \(0.0756180\pi\)
−0.282153 + 0.959369i \(0.591049\pi\)
\(228\) 0 0
\(229\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(230\) −2.59808 + 4.50000i −0.171312 + 0.296721i
\(231\) 0 0
\(232\) −3.00000 5.19615i −0.196960 0.341144i
\(233\) 24.0000i 1.57229i −0.618041 0.786146i \(-0.712073\pi\)
0.618041 0.786146i \(-0.287927\pi\)
\(234\) 0 0
\(235\) −6.00000 −0.391397
\(236\) −1.73205 3.00000i −0.112747 0.195283i
\(237\) 0 0
\(238\) −18.0000 + 3.46410i −1.16677 + 0.224544i
\(239\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(240\) 0 0
\(241\) −15.0000 + 8.66025i −0.966235 + 0.557856i −0.898086 0.439819i \(-0.855043\pi\)
−0.0681486 + 0.997675i \(0.521709\pi\)
\(242\) 2.00000i 0.128565i
\(243\) 0 0
\(244\) 6.92820i 0.443533i
\(245\) 11.2583 4.50000i 0.719268 0.287494i
\(246\) 0 0
\(247\) 3.00000 5.19615i 0.190885 0.330623i
\(248\) 2.59808 4.50000i 0.164978 0.285750i
\(249\) 0 0
\(250\) −10.5000 + 6.06218i −0.664078 + 0.383406i
\(251\) 13.8564 0.874609 0.437304 0.899314i \(-0.355933\pi\)
0.437304 + 0.899314i \(0.355933\pi\)
\(252\) 0 0
\(253\) −9.00000 −0.565825
\(254\) 19.0526 11.0000i 1.19546 0.690201i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 2.59808 4.50000i 0.162064 0.280702i −0.773545 0.633741i \(-0.781518\pi\)
0.935609 + 0.353039i \(0.114852\pi\)
\(258\) 0 0
\(259\) −17.5000 6.06218i −1.08740 0.376685i
\(260\) 6.00000i 0.372104i
\(261\) 0 0
\(262\) 10.3923i 0.642039i
\(263\) −23.3827 + 13.5000i −1.44184 + 0.832446i −0.997972 0.0636476i \(-0.979727\pi\)
−0.443866 + 0.896093i \(0.646393\pi\)
\(264\) 0 0
\(265\) 18.0000 + 10.3923i 1.10573 + 0.638394i
\(266\) −0.866025 4.50000i −0.0530994 0.275913i
\(267\) 0 0
\(268\) 1.00000 + 1.73205i 0.0610847 + 0.105802i
\(269\) 1.73205 0.105605 0.0528025 0.998605i \(-0.483185\pi\)
0.0528025 + 0.998605i \(0.483185\pi\)
\(270\) 0 0
\(271\) 17.3205i 1.05215i 0.850439 + 0.526073i \(0.176336\pi\)
−0.850439 + 0.526073i \(0.823664\pi\)
\(272\) 3.46410 + 6.00000i 0.210042 + 0.363803i
\(273\) 0 0
\(274\) 9.00000 15.5885i 0.543710 0.941733i
\(275\) −5.19615 3.00000i −0.313340 0.180907i
\(276\) 0 0
\(277\) −5.50000 9.52628i −0.330463 0.572379i 0.652140 0.758099i \(-0.273872\pi\)
−0.982603 + 0.185720i \(0.940538\pi\)
\(278\) 3.46410 0.207763
\(279\) 0 0
\(280\) −3.00000 3.46410i −0.179284 0.207020i
\(281\) 25.9808 15.0000i 1.54988 0.894825i 0.551733 0.834021i \(-0.313967\pi\)
0.998150 0.0608039i \(-0.0193664\pi\)
\(282\) 0 0
\(283\) 27.0000 + 15.5885i 1.60498 + 0.926638i 0.990470 + 0.137732i \(0.0439811\pi\)
0.614514 + 0.788906i \(0.289352\pi\)
\(284\) 2.59808 + 1.50000i 0.154167 + 0.0890086i
\(285\) 0 0
\(286\) 9.00000 5.19615i 0.532181 0.307255i
\(287\) 24.2487 21.0000i 1.43136 1.23959i
\(288\) 0 0
\(289\) 31.0000 1.82353
\(290\) −5.19615 9.00000i −0.305129 0.528498i
\(291\) 0 0
\(292\) 3.00000 + 1.73205i 0.175562 + 0.101361i
\(293\) −3.46410 + 6.00000i −0.202375 + 0.350524i −0.949293 0.314392i \(-0.898199\pi\)
0.746918 + 0.664916i \(0.231533\pi\)
\(294\) 0 0
\(295\) −3.00000 5.19615i −0.174667 0.302532i
\(296\) 7.00000i 0.406867i
\(297\) 0 0
\(298\) −12.0000 −0.695141
\(299\) 5.19615 + 9.00000i 0.300501 + 0.520483i
\(300\) 0 0
\(301\) −1.00000 5.19615i −0.0576390 0.299501i
\(302\) −6.92820 4.00000i −0.398673 0.230174i
\(303\) 0 0
\(304\) −1.50000 + 0.866025i −0.0860309 + 0.0496700i
\(305\) 12.0000i 0.687118i
\(306\) 0 0
\(307\) 15.5885i 0.889680i −0.895610 0.444840i \(-0.853260\pi\)
0.895610 0.444840i \(-0.146740\pi\)
\(308\) 2.59808 7.50000i 0.148039 0.427352i
\(309\) 0 0
\(310\) 4.50000 7.79423i 0.255583 0.442682i
\(311\) −12.1244 + 21.0000i −0.687509 + 1.19080i 0.285132 + 0.958488i \(0.407963\pi\)
−0.972641 + 0.232313i \(0.925371\pi\)
\(312\) 0 0
\(313\) 15.0000 8.66025i 0.847850 0.489506i −0.0120748 0.999927i \(-0.503844\pi\)
0.859925 + 0.510421i \(0.170510\pi\)
\(314\) 10.3923 0.586472
\(315\) 0 0
\(316\) 10.0000 0.562544
\(317\) 15.5885 9.00000i 0.875535 0.505490i 0.00635137 0.999980i \(-0.497978\pi\)
0.869184 + 0.494489i \(0.164645\pi\)
\(318\) 0 0
\(319\) 9.00000 15.5885i 0.503903 0.872786i
\(320\) −0.866025 + 1.50000i −0.0484123 + 0.0838525i
\(321\) 0 0
\(322\) 7.50000 + 2.59808i 0.417959 + 0.144785i
\(323\) 12.0000i 0.667698i
\(324\) 0 0
\(325\) 6.92820i 0.384308i
\(326\) −1.73205 + 1.00000i −0.0959294 + 0.0553849i
\(327\) 0 0
\(328\) −10.5000 6.06218i −0.579766 0.334728i
\(329\) 1.73205 + 9.00000i 0.0954911 + 0.496186i
\(330\) 0 0
\(331\) −14.0000 24.2487i −0.769510 1.33283i −0.937829 0.347097i \(-0.887167\pi\)
0.168320 0.985732i \(-0.446166\pi\)
\(332\) −17.3205 −0.950586
\(333\) 0 0
\(334\) 6.92820i 0.379094i
\(335\) 1.73205 + 3.00000i 0.0946320 + 0.163908i
\(336\) 0 0
\(337\) 2.50000 4.33013i 0.136184 0.235877i −0.789865 0.613280i \(-0.789850\pi\)
0.926049 + 0.377403i \(0.123183\pi\)
\(338\) 0.866025 + 0.500000i 0.0471056 + 0.0271964i
\(339\) 0 0
\(340\) 6.00000 + 10.3923i 0.325396 + 0.563602i
\(341\) 15.5885 0.844162
\(342\) 0 0
\(343\) −10.0000 15.5885i −0.539949 0.841698i
\(344\) −1.73205 + 1.00000i −0.0933859 + 0.0539164i
\(345\) 0 0
\(346\) −4.50000 2.59808i −0.241921 0.139673i
\(347\) −23.3827 13.5000i −1.25525 0.724718i −0.283101 0.959090i \(-0.591363\pi\)
−0.972147 + 0.234372i \(0.924697\pi\)
\(348\) 0 0
\(349\) −24.0000 + 13.8564i −1.28469 + 0.741716i −0.977702 0.209997i \(-0.932655\pi\)
−0.306988 + 0.951713i \(0.599321\pi\)
\(350\) 3.46410 + 4.00000i 0.185164 + 0.213809i
\(351\) 0 0
\(352\) −3.00000 −0.159901
\(353\) −9.52628 16.5000i −0.507033 0.878206i −0.999967 0.00813978i \(-0.997409\pi\)
0.492934 0.870067i \(-0.335924\pi\)
\(354\) 0 0
\(355\) 4.50000 + 2.59808i 0.238835 + 0.137892i
\(356\) 2.59808 4.50000i 0.137698 0.238500i
\(357\) 0 0
\(358\) 6.00000 + 10.3923i 0.317110 + 0.549250i
\(359\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(360\) 0 0
\(361\) 16.0000 0.842105
\(362\) 6.92820 + 12.0000i 0.364138 + 0.630706i
\(363\) 0 0
\(364\) −9.00000 + 1.73205i −0.471728 + 0.0907841i
\(365\) 5.19615 + 3.00000i 0.271979 + 0.157027i
\(366\) 0 0
\(367\) 1.50000 0.866025i 0.0782994 0.0452062i −0.460339 0.887743i \(-0.652272\pi\)
0.538639 + 0.842537i \(0.318939\pi\)
\(368\) 3.00000i 0.156386i
\(369\) 0 0
\(370\) 12.1244i 0.630315i
\(371\) 10.3923 30.0000i 0.539542 1.55752i
\(372\) 0 0
\(373\) −2.50000 + 4.33013i −0.129445 + 0.224205i −0.923462 0.383691i \(-0.874653\pi\)
0.794017 + 0.607896i \(0.207986\pi\)
\(374\) −10.3923 + 18.0000i −0.537373 + 0.930758i
\(375\) 0 0
\(376\) 3.00000 1.73205i 0.154713 0.0893237i
\(377\) −20.7846 −1.07046
\(378\) 0 0
\(379\) −2.00000 −0.102733 −0.0513665 0.998680i \(-0.516358\pi\)
−0.0513665 + 0.998680i \(0.516358\pi\)
\(380\) −2.59808 + 1.50000i −0.133278 + 0.0769484i
\(381\) 0 0
\(382\) −10.5000 + 18.1865i −0.537227 + 0.930504i
\(383\) 6.92820 12.0000i 0.354015 0.613171i −0.632934 0.774206i \(-0.718150\pi\)
0.986949 + 0.161034i \(0.0514830\pi\)
\(384\) 0 0
\(385\) 4.50000 12.9904i 0.229341 0.662051i
\(386\) 14.0000i 0.712581i
\(387\) 0 0
\(388\) 13.8564i 0.703452i
\(389\) −20.7846 + 12.0000i −1.05382 + 0.608424i −0.923717 0.383076i \(-0.874865\pi\)
−0.130105 + 0.991500i \(0.541531\pi\)
\(390\) 0 0
\(391\) −18.0000 10.3923i −0.910299 0.525561i
\(392\) −4.33013 + 5.50000i −0.218704 + 0.277792i
\(393\) 0 0
\(394\) 6.00000 + 10.3923i 0.302276 + 0.523557i
\(395\) 17.3205 0.871489
\(396\) 0 0
\(397\) 20.7846i 1.04315i 0.853206 + 0.521575i \(0.174655\pi\)
−0.853206 + 0.521575i \(0.825345\pi\)
\(398\) −0.866025 1.50000i −0.0434099 0.0751882i
\(399\) 0 0
\(400\) 1.00000 1.73205i 0.0500000 0.0866025i
\(401\) 15.5885 + 9.00000i 0.778450 + 0.449439i 0.835881 0.548911i \(-0.184957\pi\)
−0.0574304 + 0.998350i \(0.518291\pi\)
\(402\) 0 0
\(403\) −9.00000 15.5885i −0.448322 0.776516i
\(404\) 0 0
\(405\) 0 0
\(406\) −12.0000 + 10.3923i −0.595550 + 0.515761i
\(407\) −18.1865 + 10.5000i −0.901473 + 0.520466i
\(408\) 0 0
\(409\) −3.00000 1.73205i −0.148340 0.0856444i 0.423993 0.905666i \(-0.360628\pi\)
−0.572333 + 0.820021i \(0.693962\pi\)
\(410\) −18.1865 10.5000i −0.898169 0.518558i
\(411\) 0 0
\(412\) −16.5000 + 9.52628i −0.812897 + 0.469326i
\(413\) −6.92820 + 6.00000i −0.340915 + 0.295241i
\(414\) 0 0
\(415\) −30.0000 −1.47264
\(416\) 1.73205 + 3.00000i 0.0849208 + 0.147087i
\(417\) 0 0
\(418\) −4.50000 2.59808i −0.220102 0.127076i
\(419\) 3.46410 6.00000i 0.169232 0.293119i −0.768918 0.639348i \(-0.779204\pi\)
0.938150 + 0.346228i \(0.112538\pi\)
\(420\) 0 0
\(421\) 6.50000 + 11.2583i 0.316791 + 0.548697i 0.979817 0.199899i \(-0.0640614\pi\)
−0.663026 + 0.748596i \(0.730728\pi\)
\(422\) 16.0000i 0.778868i
\(423\) 0 0
\(424\) −12.0000 −0.582772
\(425\) −6.92820 12.0000i −0.336067 0.582086i
\(426\) 0 0
\(427\) 18.0000 3.46410i 0.871081 0.167640i
\(428\) 0 0
\(429\) 0 0
\(430\) −3.00000 + 1.73205i −0.144673 + 0.0835269i
\(431\) 21.0000i 1.01153i 0.862670 + 0.505767i \(0.168791\pi\)
−0.862670 + 0.505767i \(0.831209\pi\)
\(432\) 0 0
\(433\) 10.3923i 0.499422i −0.968320 0.249711i \(-0.919664\pi\)
0.968320 0.249711i \(-0.0803357\pi\)
\(434\) −12.9904 4.50000i −0.623558 0.216007i
\(435\) 0 0
\(436\) 6.50000 11.2583i 0.311294 0.539176i
\(437\) 2.59808 4.50000i 0.124283 0.215264i
\(438\) 0 0
\(439\) 9.00000 5.19615i 0.429547 0.247999i −0.269607 0.962970i \(-0.586894\pi\)
0.699153 + 0.714972i \(0.253560\pi\)
\(440\) −5.19615 −0.247717
\(441\) 0 0
\(442\) 24.0000 1.14156
\(443\) 7.79423 4.50000i 0.370315 0.213801i −0.303281 0.952901i \(-0.598082\pi\)
0.673596 + 0.739100i \(0.264749\pi\)
\(444\) 0 0
\(445\) 4.50000 7.79423i 0.213320 0.369482i
\(446\) −7.79423 + 13.5000i −0.369067 + 0.639244i
\(447\) 0 0
\(448\) 2.50000 + 0.866025i 0.118114 + 0.0409159i
\(449\) 12.0000i 0.566315i 0.959073 + 0.283158i \(0.0913819\pi\)
−0.959073 + 0.283158i \(0.908618\pi\)
\(450\) 0 0
\(451\) 36.3731i 1.71274i
\(452\) −10.3923 + 6.00000i −0.488813 + 0.282216i
\(453\) 0 0
\(454\) −18.0000 10.3923i −0.844782 0.487735i
\(455\) −15.5885 + 3.00000i −0.730798 + 0.140642i
\(456\) 0 0
\(457\) 8.50000 + 14.7224i 0.397613 + 0.688686i 0.993431 0.114433i \(-0.0365053\pi\)
−0.595818 + 0.803120i \(0.703172\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 5.19615i 0.242272i
\(461\) 9.52628 + 16.5000i 0.443683 + 0.768482i 0.997959 0.0638511i \(-0.0203383\pi\)
−0.554276 + 0.832333i \(0.687005\pi\)
\(462\) 0 0
\(463\) −16.0000 + 27.7128i −0.743583 + 1.28792i 0.207271 + 0.978284i \(0.433542\pi\)
−0.950854 + 0.309640i \(0.899791\pi\)
\(464\) 5.19615 + 3.00000i 0.241225 + 0.139272i
\(465\) 0 0
\(466\) 12.0000 + 20.7846i 0.555889 + 0.962828i
\(467\) −31.1769 −1.44270 −0.721348 0.692573i \(-0.756477\pi\)
−0.721348 + 0.692573i \(0.756477\pi\)
\(468\) 0 0
\(469\) 4.00000 3.46410i 0.184703 0.159957i
\(470\) 5.19615 3.00000i 0.239681 0.138380i
\(471\) 0 0
\(472\) 3.00000 + 1.73205i 0.138086 + 0.0797241i
\(473\) −5.19615 3.00000i −0.238919 0.137940i
\(474\) 0 0
\(475\) 3.00000 1.73205i 0.137649 0.0794719i
\(476\) 13.8564 12.0000i 0.635107 0.550019i
\(477\) 0 0
\(478\) 0 0
\(479\) −13.8564 24.0000i −0.633115 1.09659i −0.986911 0.161265i \(-0.948443\pi\)
0.353796 0.935323i \(-0.384891\pi\)
\(480\) 0 0
\(481\) 21.0000 + 12.1244i 0.957518 + 0.552823i
\(482\) 8.66025 15.0000i 0.394464 0.683231i
\(483\) 0 0
\(484\) 1.00000 + 1.73205i 0.0454545 + 0.0787296i
\(485\) 24.0000i 1.08978i
\(486\) 0 0
\(487\) 10.0000 0.453143 0.226572 0.973995i \(-0.427248\pi\)
0.226572 + 0.973995i \(0.427248\pi\)
\(488\) −3.46410 6.00000i −0.156813 0.271607i
\(489\) 0 0
\(490\) −7.50000 + 9.52628i −0.338815 + 0.430353i
\(491\) 7.79423 + 4.50000i 0.351749 + 0.203082i 0.665455 0.746438i \(-0.268237\pi\)
−0.313707 + 0.949520i \(0.601571\pi\)
\(492\) 0 0
\(493\) 36.0000 20.7846i 1.62136 0.936092i
\(494\) 6.00000i 0.269953i
\(495\) 0 0
\(496\) 5.19615i 0.233314i
\(497\) 2.59808 7.50000i 0.116540 0.336421i
\(498\) 0 0
\(499\) −5.00000 + 8.66025i −0.223831 + 0.387686i −0.955968 0.293471i \(-0.905190\pi\)
0.732137 + 0.681157i \(0.238523\pi\)
\(500\) 6.06218 10.5000i 0.271109 0.469574i
\(501\) 0 0
\(502\) −12.0000 + 6.92820i −0.535586 + 0.309221i
\(503\) −24.2487 −1.08120 −0.540598 0.841281i \(-0.681802\pi\)
−0.540598 + 0.841281i \(0.681802\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 7.79423 4.50000i 0.346496 0.200049i
\(507\) 0 0
\(508\) −11.0000 + 19.0526i −0.488046 + 0.845321i
\(509\) 6.92820 12.0000i 0.307087 0.531891i −0.670637 0.741786i \(-0.733979\pi\)
0.977724 + 0.209895i \(0.0673123\pi\)
\(510\) 0 0
\(511\) 3.00000 8.66025i 0.132712 0.383107i
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) 5.19615i 0.229192i
\(515\) −28.5788 + 16.5000i −1.25933 + 0.727077i
\(516\) 0 0
\(517\) 9.00000 + 5.19615i 0.395820 + 0.228527i
\(518\) 18.1865 3.50000i 0.799070 0.153781i
\(519\) 0 0
\(520\) 3.00000 + 5.19615i 0.131559 + 0.227866i
\(521\) 22.5167 0.986473 0.493236 0.869895i \(-0.335814\pi\)
0.493236 + 0.869895i \(0.335814\pi\)
\(522\) 0 0
\(523\) 39.8372i 1.74196i −0.491320 0.870979i \(-0.663486\pi\)
0.491320 0.870979i \(-0.336514\pi\)
\(524\) 5.19615 + 9.00000i 0.226995 + 0.393167i
\(525\) 0 0
\(526\) 13.5000 23.3827i 0.588628 1.01953i
\(527\) 31.1769 + 18.0000i 1.35809 + 0.784092i
\(528\) 0 0
\(529\) −7.00000 12.1244i −0.304348 0.527146i
\(530\) −20.7846 −0.902826
\(531\) 0 0
\(532\) 3.00000 + 3.46410i 0.130066 + 0.150188i
\(533\) −36.3731 + 21.0000i −1.57549 + 0.909611i
\(534\) 0 0
\(535\) 0 0
\(536\) −1.73205 1.00000i −0.0748132 0.0431934i
\(537\) 0 0
\(538\) −1.50000 + 0.866025i −0.0646696 + 0.0373370i
\(539\) −20.7846 3.00000i −0.895257 0.129219i
\(540\) 0 0
\(541\) −25.0000 −1.07483 −0.537417 0.843317i \(-0.680600\pi\)
−0.537417 + 0.843317i \(0.680600\pi\)
\(542\) −8.66025 15.0000i −0.371990 0.644305i
\(543\) 0 0
\(544\) −6.00000 3.46410i −0.257248 0.148522i
\(545\) 11.2583 19.5000i 0.482254 0.835288i
\(546\) 0 0
\(547\) −4.00000 6.92820i −0.171028 0.296229i 0.767752 0.640747i \(-0.221375\pi\)
−0.938779 + 0.344519i \(0.888042\pi\)
\(548\) 18.0000i 0.768922i
\(549\) 0 0
\(550\) 6.00000 0.255841
\(551\) 5.19615 + 9.00000i 0.221364 + 0.383413i
\(552\) 0 0
\(553\) −5.00000 25.9808i −0.212622 1.10481i
\(554\) 9.52628 + 5.50000i 0.404733 + 0.233673i
\(555\) 0 0
\(556\) −3.00000 + 1.73205i −0.127228 + 0.0734553i
\(557\) 12.0000i 0.508456i −0.967144 0.254228i \(-0.918179\pi\)
0.967144 0.254228i \(-0.0818214\pi\)
\(558\) 0 0
\(559\) 6.92820i 0.293032i
\(560\) 4.33013 + 1.50000i 0.182981 + 0.0633866i
\(561\) 0 0
\(562\) −15.0000 + 25.9808i −0.632737 + 1.09593i
\(563\) 5.19615 9.00000i 0.218992 0.379305i −0.735508 0.677516i \(-0.763057\pi\)
0.954500 + 0.298211i \(0.0963899\pi\)
\(564\) 0 0
\(565\) −18.0000 + 10.3923i −0.757266 + 0.437208i
\(566\) −31.1769 −1.31046
\(567\) 0 0
\(568\) −3.00000 −0.125877
\(569\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(570\) 0 0
\(571\) −16.0000 + 27.7128i −0.669579 + 1.15975i 0.308443 + 0.951243i \(0.400192\pi\)
−0.978022 + 0.208502i \(0.933141\pi\)
\(572\) −5.19615 + 9.00000i −0.217262 + 0.376309i
\(573\) 0 0
\(574\) −10.5000 + 30.3109i −0.438262 + 1.26515i
\(575\) 6.00000i 0.250217i
\(576\) 0 0
\(577\) 34.6410i 1.44212i 0.692870 + 0.721062i \(0.256346\pi\)
−0.692870 + 0.721062i \(0.743654\pi\)
\(578\) −26.8468 + 15.5000i −1.11668 + 0.644715i
\(579\) 0 0
\(580\) 9.00000 + 5.19615i 0.373705 + 0.215758i
\(581\) 8.66025 + 45.0000i 0.359288 + 1.86691i
\(582\) 0 0
\(583\) −18.0000 31.1769i −0.745484 1.29122i
\(584\) −3.46410 −0.143346
\(585\) 0 0
\(586\) 6.92820i 0.286201i
\(587\) 20.7846 + 36.0000i 0.857873 + 1.48588i 0.873954 + 0.486008i \(0.161548\pi\)
−0.0160815 + 0.999871i \(0.505119\pi\)
\(588\) 0 0
\(589\) −4.50000 + 7.79423i −0.185419 + 0.321156i
\(590\) 5.19615 + 3.00000i 0.213922 + 0.123508i
\(591\) 0 0
\(592\) −3.50000 6.06218i −0.143849 0.249154i
\(593\) −19.0526 −0.782395 −0.391197 0.920307i \(-0.627939\pi\)
−0.391197 + 0.920307i \(0.627939\pi\)
\(594\) 0 0
\(595\) 24.0000 20.7846i 0.983904 0.852086i
\(596\) 10.3923 6.00000i 0.425685 0.245770i
\(597\) 0 0
\(598\) −9.00000 5.19615i −0.368037 0.212486i
\(599\) −7.79423 4.50000i −0.318464 0.183865i 0.332244 0.943193i \(-0.392194\pi\)
−0.650708 + 0.759328i \(0.725528\pi\)
\(600\) 0 0
\(601\) 9.00000 5.19615i 0.367118 0.211955i −0.305081 0.952326i \(-0.598683\pi\)
0.672198 + 0.740371i \(0.265350\pi\)
\(602\) 3.46410 + 4.00000i 0.141186 + 0.163028i
\(603\) 0 0
\(604\) 8.00000 0.325515
\(605\) 1.73205 + 3.00000i 0.0704179 + 0.121967i
\(606\) 0 0
\(607\) −15.0000 8.66025i −0.608831 0.351509i 0.163677 0.986514i \(-0.447665\pi\)
−0.772508 + 0.635005i \(0.780998\pi\)
\(608\) 0.866025 1.50000i 0.0351220 0.0608330i
\(609\) 0 0
\(610\) −6.00000 10.3923i −0.242933 0.420772i
\(611\) 12.0000i 0.485468i
\(612\) 0 0
\(613\) −19.0000 −0.767403 −0.383701 0.923457i \(-0.625351\pi\)
−0.383701 + 0.923457i \(0.625351\pi\)
\(614\) 7.79423 + 13.5000i 0.314549 + 0.544816i
\(615\) 0 0
\(616\) 1.50000 + 7.79423i 0.0604367 + 0.314038i
\(617\) 15.5885 + 9.00000i 0.627568 + 0.362326i 0.779809 0.626017i \(-0.215316\pi\)
−0.152242 + 0.988343i \(0.548649\pi\)
\(618\) 0 0
\(619\) −16.5000 + 9.52628i −0.663191 + 0.382893i −0.793492 0.608581i \(-0.791739\pi\)
0.130301 + 0.991475i \(0.458406\pi\)
\(620\) 9.00000i 0.361449i
\(621\) 0 0
\(622\) 24.2487i 0.972285i
\(623\) −12.9904 4.50000i −0.520449 0.180289i
\(624\) 0 0
\(625\) 5.50000 9.52628i 0.220000 0.381051i
\(626\) −8.66025 + 15.0000i −0.346133 + 0.599521i
\(627\) 0 0
\(628\) −9.00000 + 5.19615i −0.359139 + 0.207349i
\(629\) −48.4974 −1.93372
\(630\) 0 0
\(631\) −34.0000 −1.35352 −0.676759 0.736204i \(-0.736616\pi\)
−0.676759 + 0.736204i \(0.736616\pi\)
\(632\) −8.66025 + 5.00000i −0.344486 + 0.198889i
\(633\) 0 0
\(634\) −9.00000 + 15.5885i −0.357436 + 0.619097i
\(635\) −19.0526 + 33.0000i −0.756078 + 1.30957i
\(636\) 0 0
\(637\) 9.00000 + 22.5167i 0.356593 + 0.892143i
\(638\) 18.0000i 0.712627i
\(639\) 0 0
\(640\) 1.73205i 0.0684653i
\(641\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(642\) 0 0
\(643\) −4.50000 2.59808i −0.177463 0.102458i 0.408637 0.912697i \(-0.366004\pi\)
−0.586100 + 0.810239i \(0.699337\pi\)
\(644\) −7.79423 + 1.50000i −0.307136 + 0.0591083i
\(645\) 0 0
\(646\) −6.00000 10.3923i −0.236067 0.408880i
\(647\) −10.3923 −0.408564 −0.204282 0.978912i \(-0.565486\pi\)
−0.204282 + 0.978912i \(0.565486\pi\)
\(648\) 0 0
\(649\) 10.3923i 0.407934i
\(650\) −3.46410 6.00000i −0.135873 0.235339i
\(651\) 0 0
\(652\) 1.00000 1.73205i 0.0391630 0.0678323i
\(653\) −15.5885 9.00000i −0.610023 0.352197i 0.162951 0.986634i \(-0.447899\pi\)
−0.772975 + 0.634437i \(0.781232\pi\)
\(654\) 0 0
\(655\) 9.00000 + 15.5885i 0.351659 + 0.609091i
\(656\) 12.1244 0.473377
\(657\) 0 0
\(658\) −6.00000 6.92820i −0.233904 0.270089i
\(659\) 18.1865 10.5000i 0.708447 0.409022i −0.102039 0.994780i \(-0.532537\pi\)
0.810486 + 0.585758i \(0.199203\pi\)
\(660\) 0 0
\(661\) −33.0000 19.0526i −1.28355 0.741059i −0.306055 0.952014i \(-0.599009\pi\)
−0.977496 + 0.210955i \(0.932343\pi\)
\(662\) 24.2487 + 14.0000i 0.942453 + 0.544125i
\(663\) 0 0
\(664\) 15.0000 8.66025i 0.582113 0.336083i
\(665\) 5.19615 + 6.00000i 0.201498 + 0.232670i
\(666\) 0 0
\(667\) −18.0000 −0.696963
\(668\) −3.46410 6.00000i −0.134030 0.232147i
\(669\) 0 0
\(670\) −3.00000 1.73205i −0.115900 0.0669150i
\(671\) 10.3923 18.0000i 0.401190 0.694882i
\(672\) 0 0
\(673\) 7.00000 + 12.1244i 0.269830 + 0.467360i 0.968818 0.247774i \(-0.0796991\pi\)
−0.698988 + 0.715134i \(0.746366\pi\)
\(674\) 5.00000i 0.192593i
\(675\) 0 0
\(676\) −1.00000 −0.0384615
\(677\) −12.9904 22.5000i −0.499261 0.864745i 0.500739 0.865598i \(-0.333062\pi\)
−1.00000 0.000853228i \(0.999728\pi\)
\(678\) 0 0
\(679\) 36.0000 6.92820i 1.38155 0.265880i
\(680\) −10.3923 6.00000i −0.398527 0.230089i
\(681\) 0 0
\(682\) −13.5000 + 7.79423i −0.516942 + 0.298456i
\(683\) 33.0000i 1.26271i 0.775494 + 0.631355i \(0.217501\pi\)
−0.775494 + 0.631355i \(0.782499\pi\)
\(684\) 0 0
\(685\) 31.1769i 1.19121i
\(686\) 16.4545 + 8.50000i 0.628235 + 0.324532i
\(687\) 0 0
\(688\) 1.00000 1.73205i 0.0381246 0.0660338i
\(689\) −20.7846 + 36.0000i −0.791831 + 1.37149i
\(690\) 0 0
\(691\) −9.00000 + 5.19615i −0.342376 + 0.197671i −0.661322 0.750102i \(-0.730004\pi\)
0.318946 + 0.947773i \(0.396671\pi\)
\(692\) 5.19615 0.197528
\(693\) 0 0
\(694\) 27.0000 1.02491
\(695\) −5.19615 + 3.00000i −0.197101 + 0.113796i
\(696\) 0 0
\(697\) 42.0000 72.7461i 1.59086 2.75546i
\(698\) 13.8564 24.0000i 0.524473 0.908413i
\(699\) 0 0
\(700\) −5.00000 1.73205i −0.188982 0.0654654i
\(701\) 6.00000i 0.226617i 0.993560 + 0.113308i \(0.0361448\pi\)
−0.993560 + 0.113308i \(0.963855\pi\)
\(702\) 0 0
\(703\) 12.1244i 0.457279i
\(704\) 2.59808 1.50000i 0.0979187 0.0565334i
\(705\) 0 0
\(706\) 16.5000 + 9.52628i 0.620986 + 0.358526i
\(707\) 0 0
\(708\) 0 0
\(709\) −0.500000 0.866025i −0.0187779 0.0325243i 0.856484 0.516174i \(-0.172644\pi\)
−0.875262 + 0.483650i \(0.839311\pi\)
\(710\) −5.19615 −0.195008
\(711\) 0 0
\(712\) 5.19615i 0.194734i
\(713\) −7.79423 13.5000i −0.291896 0.505579i
\(714\) 0 0
\(715\) −9.00000 + 15.5885i −0.336581 + 0.582975i
\(716\) −10.3923 6.00000i −0.388379 0.224231i
\(717\) 0 0
\(718\) 0 0
\(719\) −3.46410 −0.129189 −0.0645946 0.997912i \(-0.520575\pi\)
−0.0645946 + 0.997912i \(0.520575\pi\)
\(720\) 0 0
\(721\) 33.0000 + 38.1051i 1.22898 + 1.41911i
\(722\) −13.8564 + 8.00000i −0.515682 + 0.297729i
\(723\) 0 0
\(724\) −12.0000 6.92820i −0.445976 0.257485i
\(725\) −10.3923 6.00000i −0.385961 0.222834i
\(726\) 0 0
\(727\) 45.0000 25.9808i 1.66896 0.963573i 0.700756 0.713401i \(-0.252846\pi\)
0.968201 0.250172i \(-0.0804873\pi\)
\(728\) 6.92820 6.00000i 0.256776 0.222375i
\(729\) 0 0
\(730\) −6.00000 −0.222070
\(731\) −6.92820 12.0000i −0.256249 0.443836i
\(732\) 0 0
\(733\) −9.00000 5.19615i −0.332423 0.191924i 0.324494 0.945888i \(-0.394806\pi\)
−0.656916 + 0.753964i \(0.728139\pi\)
\(734\) −0.866025 + 1.50000i −0.0319656 + 0.0553660i
\(735\) 0 0
\(736\) 1.50000 + 2.59808i 0.0552907 + 0.0957664i
\(737\) 6.00000i 0.221013i
\(738\) 0 0
\(739\) 20.0000 0.735712 0.367856 0.929883i \(-0.380092\pi\)
0.367856 + 0.929883i \(0.380092\pi\)
\(740\) −6.06218 10.5000i −0.222850 0.385988i
\(741\) 0 0
\(742\) 6.00000 + 31.1769i 0.220267 + 1.14454i
\(743\) −23.3827 13.5000i −0.857828 0.495267i 0.00545664 0.999985i \(-0.498263\pi\)
−0.863284 + 0.504718i \(0.831596\pi\)
\(744\) 0 0
\(745\) 18.0000 10.3923i 0.659469 0.380745i
\(746\) 5.00000i 0.183063i
\(747\) 0 0
\(748\) 20.7846i 0.759961i
\(749\) 0 0
\(750\) 0 0
\(751\) 1.00000 1.73205i 0.0364905 0.0632034i −0.847203 0.531269i \(-0.821715\pi\)
0.883694 + 0.468065i \(0.155049\pi\)
\(752\) −1.73205 + 3.00000i −0.0631614 + 0.109399i
\(753\) 0 0
\(754\) 18.0000 10.3923i 0.655521 0.378465i
\(755\) 13.8564 0.504286
\(756\) 0 0
\(757\) −2.00000 −0.0726912 −0.0363456 0.999339i \(-0.511572\pi\)
−0.0363456 + 0.999339i \(0.511572\pi\)
\(758\) 1.73205 1.00000i 0.0629109 0.0363216i
\(759\) 0 0
\(760\) 1.50000 2.59808i 0.0544107 0.0942421i
\(761\) 6.92820 12.0000i 0.251147 0.435000i −0.712695 0.701474i \(-0.752526\pi\)
0.963842 + 0.266475i \(0.0858589\pi\)
\(762\) 0 0
\(763\) −32.5000 11.2583i −1.17658 0.407579i
\(764\) 21.0000i 0.759753i
\(765\) 0 0
\(766\) 13.8564i 0.500652i
\(767\) 10.3923 6.00000i 0.375244 0.216647i
\(768\) 0 0
\(769\) 33.0000 + 19.0526i 1.19001 + 0.687053i 0.958309 0.285734i \(-0.0922374\pi\)
0.231701 + 0.972787i \(0.425571\pi\)
\(770\) 2.59808 + 13.5000i 0.0936282 + 0.486506i
\(771\) 0 0
\(772\) −7.00000 12.1244i −0.251936 0.436365i
\(773\) 19.0526 0.685273 0.342636 0.939468i \(-0.388680\pi\)
0.342636 + 0.939468i \(0.388680\pi\)
\(774\) 0 0
\(775\) 10.3923i 0.373303i
\(776\) −6.92820 12.0000i −0.248708 0.430775i
\(777\) 0 0
\(778\) 12.0000 20.7846i 0.430221 0.745164i
\(779\) 18.1865 + 10.5000i 0.651600 + 0.376202i
\(780\) 0 0
\(781\) −4.50000 7.79423i −0.161023 0.278899i
\(782\) 20.7846 0.743256
\(783\) 0 0
\(784\) 1.00000 6.92820i 0.0357143 0.247436i
\(785\) −15.5885 + 9.00000i −0.556376 + 0.321224i
\(786\) 0 0
\(787\) −15.0000 8.66025i −0.534692 0.308705i 0.208233 0.978079i \(-0.433229\pi\)
−0.742925 + 0.669375i \(0.766562\pi\)
\(788\) −10.3923 6.00000i −0.370211 0.213741i
\(789\) 0 0
\(790\) −15.0000 + 8.66025i −0.533676 + 0.308118i
\(791\) 20.7846 + 24.0000i 0.739016 + 0.853342i
\(792\) 0 0
\(793\) −24.0000 −0.852265
\(794\) −10.3923 18.0000i −0.368809 0.638796i
\(795\) 0 0
\(796\) 1.50000 + 0.866025i 0.0531661 + 0.0306955i
\(797\) 7.79423 13.5000i 0.276086 0.478195i −0.694323 0.719664i \(-0.744296\pi\)
0.970408 + 0.241469i \(0.0776293\pi\)
\(798\) 0 0
\(799\) 12.0000 + 20.7846i 0.424529 + 0.735307i
\(800\) 2.00000i 0.0707107i
\(801\) 0 0
\(802\) −18.0000 −0.635602
\(803\) −5.19615 9.00000i −0.183368 0.317603i
\(804\) 0 0
\(805\) −13.5000 + 2.59808i −0.475812 + 0.0915702i
\(806\) 15.5885 + 9.00000i 0.549080 + 0.317011i
\(807\) 0 0
\(808\) 0 0
\(809\) 6.00000i 0.210949i 0.994422 + 0.105474i \(0.0336361\pi\)
−0.994422 + 0.105474i \(0.966364\pi\)
\(810\) 0 0
\(811\) 36.3731i 1.27723i 0.769526 + 0.638616i \(0.220493\pi\)
−0.769526 + 0.638616i \(0.779507\pi\)
\(812\) 5.19615 15.0000i 0.182349 0.526397i
\(813\) 0 0
\(814\) 10.5000 18.1865i 0.368025 0.637438i
\(815\) 1.73205 3.00000i 0.0606711 0.105085i
\(816\) 0 0
\(817\) 3.00000 1.73205i 0.104957 0.0605968i
\(818\) 3.46410 0.121119
\(819\) 0 0
\(820\) 21.0000 0.733352
\(821\) 25.9808 15.0000i 0.906735 0.523504i 0.0273557 0.999626i \(-0.491291\pi\)
0.879379 + 0.476122i \(0.157958\pi\)
\(822\) 0 0
\(823\) 2.00000 3.46410i 0.0697156 0.120751i −0.829060 0.559159i \(-0.811124\pi\)
0.898776 + 0.438408i \(0.144457\pi\)
\(824\) 9.52628 16.5000i 0.331864 0.574805i
\(825\) 0 0
\(826\) 3.00000 8.66025i 0.104383 0.301329i
\(827\) 3.00000i 0.104320i 0.998639 + 0.0521601i \(0.0166106\pi\)
−0.998639 + 0.0521601i \(0.983389\pi\)
\(828\) 0 0
\(829\) 38.1051i 1.32345i 0.749749 + 0.661723i \(0.230174\pi\)
−0.749749 + 0.661723i \(0.769826\pi\)
\(830\) 25.9808 15.0000i 0.901805 0.520658i
\(831\) 0 0
\(832\) −3.00000 1.73205i −0.104006 0.0600481i
\(833\) −38.1051 30.0000i −1.32026 1.03944i
\(834\) 0 0
\(835\) −6.00000 10.3923i −0.207639 0.359641i
\(836\) 5.19615 0.179713
\(837\) 0 0
\(838\) 6.92820i 0.239331i
\(839\) −12.1244 21.0000i −0.418579 0.725001i 0.577218 0.816590i \(-0.304138\pi\)
−0.995797 + 0.0915899i \(0.970805\pi\)
\(840\) 0 0
\(841\) 3.50000 6.06218i 0.120690 0.209041i
\(842\) −11.2583 6.50000i −0.387988 0.224005i
\(843\) 0 0
\(844\) 8.00000 + 13.8564i 0.275371 + 0.476957i
\(845\) −1.73205 −0.0595844
\(846\) 0 0
\(847\) 4.00000 3.46410i 0.137442 0.119028i
\(848\) 10.3923 6.00000i 0.356873 0.206041i
\(849\) 0 0
\(850\) 12.0000 + 6.92820i 0.411597 + 0.237635i
\(851\) 18.1865 + 10.5000i 0.623426 + 0.359935i
\(852\) 0 0
\(853\) −12.0000 + 6.92820i −0.410872 + 0.237217i −0.691164 0.722698i \(-0.742902\pi\)
0.280292 + 0.959915i \(0.409569\pi\)
\(854\) −13.8564 + 12.0000i −0.474156 + 0.410632i
\(855\) 0 0
\(856\) 0 0
\(857\) 21.6506 + 37.5000i 0.739572 + 1.28098i 0.952688 + 0.303949i \(0.0983052\pi\)
−0.213117 + 0.977027i \(0.568361\pi\)
\(858\) 0 0
\(859\) 25.5000 + 14.7224i 0.870049 + 0.502323i 0.867364 0.497674i \(-0.165812\pi\)
0.00268433 + 0.999996i \(0.499146\pi\)
\(860\) 1.73205 3.00000i 0.0590624 0.102299i
\(861\) 0 0
\(862\) −10.5000 18.1865i −0.357631 0.619436i
\(863\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(864\) 0 0
\(865\) 9.00000 0.306009
\(866\) 5.19615 + 9.00000i 0.176572 + 0.305832i
\(867\) 0 0
\(868\) 13.5000 2.59808i 0.458220 0.0881845i
\(869\) −25.9808 15.0000i −0.881337 0.508840i
\(870\) 0 0
\(871\) −6.00000 + 3.46410i −0.203302 + 0.117377i
\(872\) 13.0000i 0.440236i
\(873\) 0 0
\(874\) 5.19615i 0.175762i
\(875\) −30.3109 10.5000i −1.02470 0.354965i
\(876\) 0 0
\(877\) −25.0000 + 43.3013i −0.844190 + 1.46218i 0.0421327 + 0.999112i \(0.486585\pi\)
−0.886323 + 0.463068i \(0.846749\pi\)
\(878\) −5.19615 + 9.00000i −0.175362 + 0.303735i
\(879\) 0 0
\(880\) 4.50000 2.59808i 0.151695 0.0875811i
\(881\) 25.9808 0.875314 0.437657 0.899142i \(-0.355808\pi\)
0.437657 + 0.899142i \(0.355808\pi\)
\(882\) 0 0
\(883\) 16.0000 0.538443 0.269221 0.963078i \(-0.413234\pi\)
0.269221 + 0.963078i \(0.413234\pi\)
\(884\) −20.7846 + 12.0000i −0.699062 + 0.403604i
\(885\) 0 0
\(886\) −4.50000 + 7.79423i −0.151180 + 0.261852i
\(887\) −12.1244 + 21.0000i −0.407096 + 0.705111i −0.994563 0.104137i \(-0.966792\pi\)
0.587467 + 0.809248i \(0.300125\pi\)
\(888\) 0 0
\(889\) 55.0000 + 19.0526i 1.84464 + 0.639002i
\(890\) 9.00000i 0.301681i
\(891\) 0 0
\(892\) 15.5885i 0.521940i
\(893\) −5.19615 + 3.00000i −0.173883 + 0.100391i
\(894\) 0 0
\(895\) −18.0000 10.3923i −0.601674 0.347376i
\(896\) −2.59808 + 0.500000i −0.0867956 + 0.0167038i
\(897\) 0 0
\(898\) −6.00000 10.3923i −0.200223 0.346796i
\(899\) 31.1769 1.03981
\(900\) 0 0
\(901\) 83.1384i 2.76974i
\(902\) 18.1865 + 31.5000i 0.605545 + 1.04884i
\(903\) 0 0
\(904\) 6.00000 10.3923i 0.199557 0.345643i
\(905\) −20.7846 12.0000i −0.690904 0.398893i
\(906\) 0 0
\(907\) 4.00000 + 6.92820i 0.132818 + 0.230047i 0.924762 0.380547i \(-0.124264\pi\)
−0.791944 + 0.610594i \(0.790931\pi\)
\(908\) 20.7846 0.689761
\(909\) 0 0
\(910\) 12.0000 10.3923i 0.397796 0.344502i
\(911\) 10.3923 6.00000i 0.344312 0.198789i −0.317865 0.948136i \(-0.602966\pi\)
0.662177 + 0.749347i \(0.269633\pi\)
\(912\) 0 0
\(913\) 45.0000 + 25.9808i 1.48928 + 0.859838i
\(914\) −14.7224 8.50000i −0.486975 0.281155i
\(915\) 0 0
\(916\) 0 0
\(917\) 20.7846 18.0000i 0.686368 0.594412i
\(918\) 0 0
\(919\) 4.00000 0.131948 0.0659739 0.997821i \(-0.478985\pi\)
0.0659739 + 0.997821i \(0.478985\pi\)
\(920\) 2.59808 + 4.50000i 0.0856560 + 0.148361i
\(921\) 0 0
\(922\) −16.5000 9.52628i −0.543399 0.313731i
\(923\) −5.19615 + 9.00000i −0.171033 + 0.296239i
\(924\) 0 0
\(925\) 7.00000 + 12.1244i 0.230159 + 0.398646i
\(926\) 32.0000i 1.05159i
\(927\) 0 0
\(928\) −6.00000 −0.196960
\(929\) 13.8564 + 24.0000i 0.454614 + 0.787414i 0.998666 0.0516371i \(-0.0164439\pi\)
−0.544052 + 0.839052i \(0.683111\pi\)
\(930\) 0 0
\(931\) 7.50000 9.52628i 0.245803 0.312211i
\(932\) −20.7846 12.0000i −0.680823 0.393073i
\(933\) 0 0
\(934\) 27.0000 15.5885i 0.883467 0.510070i
\(935\) 36.0000i 1.17733i
\(936\) 0 0
\(937\) 6.92820i 0.226335i −0.993576 0.113167i \(-0.963900\pi\)
0.993576 0.113167i \(-0.0360996\pi\)
\(938\) −1.73205 + 5.00000i −0.0565535 + 0.163256i
\(939\) 0 0
\(940\) −3.00000 + 5.19615i −0.0978492 + 0.169480i
\(941\) −6.06218 + 10.5000i −0.197621 + 0.342290i −0.947757 0.318994i \(-0.896655\pi\)
0.750135 + 0.661284i \(0.229988\pi\)
\(942\) 0 0
\(943\) −31.5000 + 18.1865i −1.02578 + 0.592235i
\(944\) −3.46410 −0.112747
\(945\) 0 0
\(946\) 6.00000 0.195077
\(947\) 12.9904 7.50000i 0.422131 0.243717i −0.273858 0.961770i \(-0.588300\pi\)
0.695988 + 0.718053i \(0.254966\pi\)
\(948\) 0 0
\(949\) −6.00000 + 10.3923i −0.194768 + 0.337348i
\(950\) −1.73205 + 3.00000i −0.0561951 + 0.0973329i
\(951\) 0 0
\(952\) −6.00000 + 17.3205i −0.194461 + 0.561361i
\(953\) 18.0000i 0.583077i −0.956559 0.291539i \(-0.905833\pi\)
0.956559 0.291539i \(-0.0941672\pi\)
\(954\) 0 0
\(955\) 36.3731i 1.17700i
\(956\) 0 0
\(957\) 0 0
\(958\) 24.0000 + 13.8564i 0.775405 + 0.447680i
\(959\) 46.7654 9.00000i 1.51013 0.290625i
\(960\) 0 0
\(961\) −2.00000 3.46410i −0.0645161 0.111745i
\(962\) −24.2487 −0.781810
\(963\) 0 0
\(964\) 17.3205i 0.557856i
\(965\) −12.1244 21.0000i −0.390297 0.676014i
\(966\) 0 0
\(967\) 8.00000 13.8564i 0.257263 0.445592i −0.708245 0.705967i \(-0.750513\pi\)
0.965508 + 0.260375i \(0.0838461\pi\)
\(968\) −1.73205 1.00000i −0.0556702 0.0321412i
\(969\) 0 0
\(970\) −12.0000 20.7846i −0.385297 0.667354i
\(971\) −3.46410 −0.111168 −0.0555842 0.998454i \(-0.517702\pi\)
−0.0555842 + 0.998454i \(0.517702\pi\)
\(972\) 0 0
\(973\) 6.00000 + 6.92820i 0.192351 + 0.222108i
\(974\) −8.66025 + 5.00000i −0.277492 + 0.160210i
\(975\) 0 0
\(976\) 6.00000 + 3.46410i 0.192055 + 0.110883i
\(977\) 41.5692 + 24.0000i 1.32992 + 0.767828i 0.985287 0.170910i \(-0.0546709\pi\)
0.344631 + 0.938738i \(0.388004\pi\)
\(978\) 0 0
\(979\) −13.5000 + 7.79423i −0.431462 + 0.249105i
\(980\) 1.73205 12.0000i 0.0553283 0.383326i
\(981\) 0 0
\(982\) −9.00000 −0.287202
\(983\) 1.73205 + 3.00000i 0.0552438 + 0.0956851i 0.892325 0.451394i \(-0.149073\pi\)
−0.837081 + 0.547079i \(0.815740\pi\)
\(984\) 0 0
\(985\) −18.0000 10.3923i −0.573528 0.331126i
\(986\) −20.7846 + 36.0000i −0.661917 + 1.14647i
\(987\) 0 0
\(988\) −3.00000 5.19615i −0.0954427 0.165312i
\(989\) 6.00000i 0.190789i
\(990\) 0 0
\(991\) −2.00000 −0.0635321 −0.0317660 0.999495i \(-0.510113\pi\)
−0.0317660 + 0.999495i \(0.510113\pi\)
\(992\) −2.59808 4.50000i −0.0824890 0.142875i
\(993\) 0 0
\(994\) 1.50000 + 7.79423i 0.0475771 + 0.247218i
\(995\) 2.59808 + 1.50000i 0.0823646 + 0.0475532i
\(996\) 0 0
\(997\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(998\) 10.0000i 0.316544i
\(999\) 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 1134.2.m.b.377.1 4
3.2 odd 2 inner 1134.2.m.b.377.2 4
7.6 odd 2 1134.2.m.c.377.1 4
9.2 odd 6 1134.2.m.c.755.1 4
9.4 even 3 378.2.d.b.377.1 4
9.5 odd 6 378.2.d.b.377.4 yes 4
9.7 even 3 1134.2.m.c.755.2 4
21.20 even 2 1134.2.m.c.377.2 4
36.23 even 6 3024.2.k.e.1889.4 4
36.31 odd 6 3024.2.k.e.1889.2 4
63.13 odd 6 378.2.d.b.377.2 yes 4
63.20 even 6 inner 1134.2.m.b.755.1 4
63.34 odd 6 inner 1134.2.m.b.755.2 4
63.41 even 6 378.2.d.b.377.3 yes 4
252.139 even 6 3024.2.k.e.1889.3 4
252.167 odd 6 3024.2.k.e.1889.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
378.2.d.b.377.1 4 9.4 even 3
378.2.d.b.377.2 yes 4 63.13 odd 6
378.2.d.b.377.3 yes 4 63.41 even 6
378.2.d.b.377.4 yes 4 9.5 odd 6
1134.2.m.b.377.1 4 1.1 even 1 trivial
1134.2.m.b.377.2 4 3.2 odd 2 inner
1134.2.m.b.755.1 4 63.20 even 6 inner
1134.2.m.b.755.2 4 63.34 odd 6 inner
1134.2.m.c.377.1 4 7.6 odd 2
1134.2.m.c.377.2 4 21.20 even 2
1134.2.m.c.755.1 4 9.2 odd 6
1134.2.m.c.755.2 4 9.7 even 3
3024.2.k.e.1889.1 4 252.167 odd 6
3024.2.k.e.1889.2 4 36.31 odd 6
3024.2.k.e.1889.3 4 252.139 even 6
3024.2.k.e.1889.4 4 36.23 even 6