Properties

Label 1134.2.m.c.755.1
Level $1134$
Weight $2$
Character 1134.755
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 755.1
Root \(0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 1134.755
Dual form 1134.2.m.c.377.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-0.866025 - 1.50000i) q^{5} +(0.500000 + 2.59808i) q^{7} -1.00000i q^{8} +O(q^{10})\) \(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-0.866025 - 1.50000i) q^{5} +(0.500000 + 2.59808i) q^{7} -1.00000i q^{8} +1.73205i q^{10} +(-2.59808 - 1.50000i) q^{11} +(-3.00000 + 1.73205i) q^{13} +(0.866025 - 2.50000i) q^{14} +(-0.500000 + 0.866025i) q^{16} +6.92820 q^{17} -1.73205i q^{19} +(0.866025 - 1.50000i) q^{20} +(1.50000 + 2.59808i) q^{22} +(2.59808 - 1.50000i) q^{23} +(1.00000 - 1.73205i) q^{25} +3.46410 q^{26} +(-2.00000 + 1.73205i) q^{28} +(-5.19615 - 3.00000i) q^{29} +(4.50000 - 2.59808i) q^{31} +(0.866025 - 0.500000i) q^{32} +(-6.00000 - 3.46410i) q^{34} +(3.46410 - 3.00000i) q^{35} +7.00000 q^{37} +(-0.866025 + 1.50000i) q^{38} +(-1.50000 + 0.866025i) q^{40} +(6.06218 + 10.5000i) q^{41} +(1.00000 - 1.73205i) q^{43} -3.00000i q^{44} -3.00000 q^{46} +(1.73205 - 3.00000i) q^{47} +(-6.50000 + 2.59808i) q^{49} +(-1.73205 + 1.00000i) q^{50} +(-3.00000 - 1.73205i) q^{52} -12.0000i q^{53} +5.19615i q^{55} +(2.59808 - 0.500000i) q^{56} +(3.00000 + 5.19615i) q^{58} +(-1.73205 - 3.00000i) q^{59} +(6.00000 + 3.46410i) q^{61} -5.19615 q^{62} -1.00000 q^{64} +(5.19615 + 3.00000i) q^{65} +(-1.00000 - 1.73205i) q^{67} +(3.46410 + 6.00000i) q^{68} +(-4.50000 + 0.866025i) q^{70} -3.00000i q^{71} +3.46410i q^{73} +(-6.06218 - 3.50000i) q^{74} +(1.50000 - 0.866025i) q^{76} +(2.59808 - 7.50000i) q^{77} +(5.00000 - 8.66025i) q^{79} +1.73205 q^{80} -12.1244i q^{82} +(8.66025 - 15.0000i) q^{83} +(-6.00000 - 10.3923i) q^{85} +(-1.73205 + 1.00000i) q^{86} +(-1.50000 + 2.59808i) q^{88} -5.19615 q^{89} +(-6.00000 - 6.92820i) q^{91} +(2.59808 + 1.50000i) q^{92} +(-3.00000 + 1.73205i) q^{94} +(-2.59808 + 1.50000i) q^{95} +(12.0000 + 6.92820i) q^{97} +(6.92820 + 1.00000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2 q^{4} + 2 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 2 q^{4} + 2 q^{7} - 12 q^{13} - 2 q^{16} + 6 q^{22} + 4 q^{25} - 8 q^{28} + 18 q^{31} - 24 q^{34} + 28 q^{37} - 6 q^{40} + 4 q^{43} - 12 q^{46} - 26 q^{49} - 12 q^{52} + 12 q^{58} + 24 q^{61} - 4 q^{64} - 4 q^{67} - 18 q^{70} + 6 q^{76} + 20 q^{79} - 24 q^{85} - 6 q^{88} - 24 q^{91} - 12 q^{94} + 48 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

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 \(-0.293258\pi\)
−0.992085 + 0.125567i \(0.959925\pi\)
\(6\) 0 0
\(7\) 0.500000 + 2.59808i 0.188982 + 0.981981i
\(8\) 1.00000i 0.353553i
\(9\) 0 0
\(10\) 1.73205i 0.547723i
\(11\) −2.59808 1.50000i −0.783349 0.452267i 0.0542666 0.998526i \(-0.482718\pi\)
−0.837616 + 0.546259i \(0.816051\pi\)
\(12\) 0 0
\(13\) −3.00000 + 1.73205i −0.832050 + 0.480384i −0.854554 0.519362i \(-0.826170\pi\)
0.0225039 + 0.999747i \(0.492836\pi\)
\(14\) 0.866025 2.50000i 0.231455 0.668153i
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 6.92820 1.68034 0.840168 0.542326i \(-0.182456\pi\)
0.840168 + 0.542326i \(0.182456\pi\)
\(18\) 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 −0.204046 0.978961i \(-0.565409\pi\)
0.745782 + 0.666190i \(0.232076\pi\)
\(24\) 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 −0.0672232 0.997738i \(-0.521414\pi\)
−0.897678 + 0.440652i \(0.854747\pi\)
\(30\) 0 0
\(31\) 4.50000 2.59808i 0.808224 0.466628i −0.0381148 0.999273i \(-0.512135\pi\)
0.846339 + 0.532645i \(0.178802\pi\)
\(32\) 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 0.752202 + 0.658932i \(0.228992\pi\)
0.194551 + 0.980892i \(0.437675\pi\)
\(42\) 0 0
\(43\) 1.00000 1.73205i 0.152499 0.264135i −0.779647 0.626219i \(-0.784601\pi\)
0.932145 + 0.362084i \(0.117935\pi\)
\(44\) 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 \(-0.752033\pi\)
0.964253 + 0.264982i \(0.0853660\pi\)
\(48\) 0 0
\(49\) −6.50000 + 2.59808i −0.928571 + 0.371154i
\(50\) −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 \(-0.691646\pi\)
0.566352 0.824163i \(-0.308354\pi\)
\(54\) 0 0
\(55\) 5.19615i 0.700649i
\(56\) 2.59808 0.500000i 0.347183 0.0668153i
\(57\) 0 0
\(58\) 3.00000 + 5.19615i 0.393919 + 0.682288i
\(59\) −1.73205 3.00000i −0.225494 0.390567i 0.730974 0.682406i \(-0.239066\pi\)
−0.956467 + 0.291839i \(0.905733\pi\)
\(60\) 0 0
\(61\) 6.00000 + 3.46410i 0.768221 + 0.443533i 0.832240 0.554416i \(-0.187058\pi\)
−0.0640184 + 0.997949i \(0.520392\pi\)
\(62\) −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 0.798454 0.602056i \(-0.205652\pi\)
−0.920623 + 0.390453i \(0.872318\pi\)
\(68\) 3.46410 + 6.00000i 0.420084 + 0.727607i
\(69\) 0 0
\(70\) −4.50000 + 0.866025i −0.537853 + 0.103510i
\(71\) 3.00000i 0.356034i −0.984027 0.178017i \(-0.943032\pi\)
0.984027 0.178017i \(-0.0569683\pi\)
\(72\) 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
\(77\) 2.59808 7.50000i 0.296078 0.854704i
\(78\) 0 0
\(79\) 5.00000 8.66025i 0.562544 0.974355i −0.434730 0.900561i \(-0.643156\pi\)
0.997274 0.0737937i \(-0.0235106\pi\)
\(80\) 1.73205 0.193649
\(81\) 0 0
\(82\) 12.1244i 1.33891i
\(83\) 8.66025 15.0000i 0.950586 1.64646i 0.206427 0.978462i \(-0.433816\pi\)
0.744160 0.668002i \(-0.232850\pi\)
\(84\) 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 \(-0.588809\pi\)
−0.275396 + 0.961331i \(0.588809\pi\)
\(90\) 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 \(-0.0849741\pi\)
0.253837 + 0.967247i \(0.418307\pi\)
\(98\) 6.92820 + 1.00000i 0.699854 + 0.101015i
\(99\) 0 0
\(100\) 2.00000 0.200000
\(101\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(102\) 0 0
\(103\) 16.5000 9.52628i 1.62579 0.938652i 0.640464 0.767988i \(-0.278742\pi\)
0.985329 0.170664i \(-0.0545913\pi\)
\(104\) 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
\(112\) −2.50000 0.866025i −0.236228 0.0818317i
\(113\) −10.3923 + 6.00000i −0.977626 + 0.564433i −0.901553 0.432670i \(-0.857572\pi\)
−0.0760733 + 0.997102i \(0.524238\pi\)
\(114\) 0 0
\(115\) −4.50000 2.59808i −0.419627 0.242272i
\(116\) 6.00000i 0.557086i
\(117\) 0 0
\(118\) 3.46410i 0.318896i
\(119\) 3.46410 + 18.0000i 0.317554 + 1.65006i
\(120\) 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 \(-0.0166669\pi\)
−0.544640 + 0.838670i \(0.683334\pi\)
\(132\) 0 0
\(133\) 4.50000 0.866025i 0.390199 0.0750939i
\(134\) 2.00000i 0.172774i
\(135\) 0 0
\(136\) 6.92820i 0.594089i
\(137\) −15.5885 9.00000i −1.33181 0.768922i −0.346235 0.938148i \(-0.612540\pi\)
−0.985577 + 0.169226i \(0.945873\pi\)
\(138\) 0 0
\(139\) 3.00000 1.73205i 0.254457 0.146911i −0.367347 0.930084i \(-0.619734\pi\)
0.621803 + 0.783174i \(0.286400\pi\)
\(140\) 4.33013 + 1.50000i 0.365963 + 0.126773i
\(141\) 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 −0.00974235 0.999953i \(-0.503101\pi\)
0.861113 + 0.508413i \(0.169768\pi\)
\(150\) 0 0
\(151\) 4.00000 6.92820i 0.325515 0.563809i −0.656101 0.754673i \(-0.727796\pi\)
0.981617 + 0.190864i \(0.0611289\pi\)
\(152\) −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 \(-0.530554\pi\)
0.814119 + 0.580699i \(0.197221\pi\)
\(158\) −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 \(-0.253049\pi\)
−0.968361 + 0.249554i \(0.919716\pi\)
\(168\) 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 \(-0.896625\pi\)
0.750198 + 0.661213i \(0.229958\pi\)
\(174\) 0 0
\(175\) 5.00000 + 1.73205i 0.377964 + 0.130931i
\(176\) 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 \(0.148028\pi\)
−0.893802 + 0.448461i \(0.851972\pi\)
\(180\) 0 0
\(181\) 13.8564i 1.02994i −0.857209 0.514969i \(-0.827803\pi\)
0.857209 0.514969i \(-0.172197\pi\)
\(182\) 1.73205 + 9.00000i 0.128388 + 0.667124i
\(183\) 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 0.983071 0.183223i \(-0.0586530\pi\)
0.332860 + 0.942976i \(0.391986\pi\)
\(192\) 0 0
\(193\) 7.00000 + 12.1244i 0.503871 + 0.872730i 0.999990 + 0.00447566i \(0.00142465\pi\)
−0.496119 + 0.868255i \(0.665242\pi\)
\(194\) −6.92820 12.0000i −0.497416 0.861550i
\(195\) 0 0
\(196\) −5.50000 4.33013i −0.392857 0.309295i
\(197\) 12.0000i 0.854965i 0.904024 + 0.427482i \(0.140599\pi\)
−0.904024 + 0.427482i \(0.859401\pi\)
\(198\) 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
\(203\) 5.19615 15.0000i 0.364698 1.05279i
\(204\) 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 −0.998221 0.0596196i \(-0.981011\pi\)
0.447478 0.894295i \(-0.352322\pi\)
\(212\) 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 \(-0.508125\pi\)
−0.878504 + 0.477734i \(0.841458\pi\)
\(224\) 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 0.282153 + 0.959369i \(0.408951\pi\)
−0.971915 + 0.235333i \(0.924382\pi\)
\(228\) 0 0
\(229\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(230\) 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 \(0.287927\pi\)
−0.618041 + 0.786146i \(0.712073\pi\)
\(234\) 0 0
\(235\) −6.00000 −0.391397
\(236\) 1.73205 3.00000i 0.112747 0.195283i
\(237\) 0 0
\(238\) 6.00000 17.3205i 0.388922 1.12272i
\(239\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(240\) 0 0
\(241\) 15.0000 + 8.66025i 0.966235 + 0.557856i 0.898086 0.439819i \(-0.144957\pi\)
0.0681486 + 0.997675i \(0.478291\pi\)
\(242\) 2.00000i 0.128565i
\(243\) 0 0
\(244\) 6.92820i 0.443533i
\(245\) 9.52628 + 7.50000i 0.608612 + 0.479157i
\(246\) 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 \(-0.644067\pi\)
−0.437304 + 0.899314i \(0.644067\pi\)
\(252\) 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 \(-0.218482\pi\)
−0.935609 + 0.353039i \(0.885148\pi\)
\(258\) 0 0
\(259\) 3.50000 + 18.1865i 0.217479 + 1.13006i
\(260\) 6.00000i 0.372104i
\(261\) 0 0
\(262\) 10.3923i 0.642039i
\(263\) −23.3827 13.5000i −1.44184 0.832446i −0.443866 0.896093i \(-0.646393\pi\)
−0.997972 + 0.0636476i \(0.979727\pi\)
\(264\) 0 0
\(265\) −18.0000 + 10.3923i −1.10573 + 0.638394i
\(266\) −4.33013 1.50000i −0.265497 0.0919709i
\(267\) 0 0
\(268\) 1.00000 1.73205i 0.0610847 0.105802i
\(269\) −1.73205 −0.105605 −0.0528025 0.998605i \(-0.516815\pi\)
−0.0528025 + 0.998605i \(0.516815\pi\)
\(270\) 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 −0.982603 0.185720i \(-0.940538\pi\)
0.652140 + 0.758099i \(0.273872\pi\)
\(278\) −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 0.998150 + 0.0608039i \(0.0193664\pi\)
0.551733 + 0.834021i \(0.313967\pi\)
\(282\) 0 0
\(283\) −27.0000 + 15.5885i −1.60498 + 0.926638i −0.614514 + 0.788906i \(0.710648\pi\)
−0.990470 + 0.137732i \(0.956019\pi\)
\(284\) 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 \(-0.101801\pi\)
−0.746918 + 0.664916i \(0.768467\pi\)
\(294\) 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
\(301\) 5.00000 + 1.73205i 0.288195 + 0.0998337i
\(302\) −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 \(-0.146740\pi\)
\(308\) 7.79423 1.50000i 0.444117 0.0854704i
\(309\) 0 0
\(310\) 4.50000 + 7.79423i 0.255583 + 0.442682i
\(311\) 12.1244 + 21.0000i 0.687509 + 1.19080i 0.972641 + 0.232313i \(0.0746292\pi\)
−0.285132 + 0.958488i \(0.592037\pi\)
\(312\) 0 0
\(313\) −15.0000 8.66025i −0.847850 0.489506i 0.0120748 0.999927i \(-0.496156\pi\)
−0.859925 + 0.510421i \(0.829490\pi\)
\(314\) −10.3923 −0.586472
\(315\) 0 0
\(316\) 10.0000 0.562544
\(317\) 15.5885 + 9.00000i 0.875535 + 0.505490i 0.869184 0.494489i \(-0.164645\pi\)
0.00635137 + 0.999980i \(0.497978\pi\)
\(318\) 0 0
\(319\) 9.00000 + 15.5885i 0.503903 + 0.872786i
\(320\) 0.866025 + 1.50000i 0.0484123 + 0.0838525i
\(321\) 0 0
\(322\) −1.50000 7.79423i −0.0835917 0.434355i
\(323\) 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
\(329\) 8.66025 + 3.00000i 0.477455 + 0.165395i
\(330\) 0 0
\(331\) −14.0000 + 24.2487i −0.769510 + 1.33283i 0.168320 + 0.985732i \(0.446166\pi\)
−0.937829 + 0.347097i \(0.887167\pi\)
\(332\) 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 0.926049 0.377403i \(-0.123183\pi\)
−0.789865 + 0.613280i \(0.789850\pi\)
\(338\) 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 −0.972147 0.234372i \(-0.924697\pi\)
−0.283101 + 0.959090i \(0.591363\pi\)
\(348\) 0 0
\(349\) 24.0000 + 13.8564i 1.28469 + 0.741716i 0.977702 0.209997i \(-0.0673454\pi\)
0.306988 + 0.951713i \(0.400679\pi\)
\(350\) −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 −0.492934 0.870067i \(-0.664076\pi\)
0.999967 0.00813978i \(-0.00259100\pi\)
\(354\) 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
\(364\) 3.00000 8.66025i 0.157243 0.453921i
\(365\) 5.19615 3.00000i 0.271979 0.157027i
\(366\) 0 0
\(367\) −1.50000 0.866025i −0.0782994 0.0452062i 0.460339 0.887743i \(-0.347728\pi\)
−0.538639 + 0.842537i \(0.681061\pi\)
\(368\) 3.00000i 0.156386i
\(369\) 0 0
\(370\) 12.1244i 0.630315i
\(371\) 31.1769 6.00000i 1.61862 0.311504i
\(372\) 0 0
\(373\) −2.50000 4.33013i −0.129445 0.224205i 0.794017 0.607896i \(-0.207986\pi\)
−0.923462 + 0.383691i \(0.874653\pi\)
\(374\) 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 \(-0.281850\pi\)
−0.986949 + 0.161034i \(0.948517\pi\)
\(384\) 0 0
\(385\) −13.5000 + 2.59808i −0.688024 + 0.132410i
\(386\) 14.0000i 0.712581i
\(387\) 0 0
\(388\) 13.8564i 0.703452i
\(389\) −20.7846 12.0000i −1.05382 0.608424i −0.130105 0.991500i \(-0.541531\pi\)
−0.923717 + 0.383076i \(0.874865\pi\)
\(390\) 0 0
\(391\) 18.0000 10.3923i 0.910299 0.525561i
\(392\) 2.59808 + 6.50000i 0.131223 + 0.328300i
\(393\) 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 −0.0574304 0.998350i \(-0.518291\pi\)
0.835881 + 0.548911i \(0.184957\pi\)
\(402\) 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 \(-0.639372\pi\)
0.572333 + 0.820021i \(0.306038\pi\)
\(410\) −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 \(-0.220796\pi\)
−0.938150 + 0.346228i \(0.887462\pi\)
\(420\) 0 0
\(421\) 6.50000 11.2583i 0.316791 0.548697i −0.663026 0.748596i \(-0.730728\pi\)
0.979817 + 0.199899i \(0.0640614\pi\)
\(422\) 16.0000i 0.778868i
\(423\) 0 0
\(424\) −12.0000 −0.582772
\(425\) 6.92820 12.0000i 0.336067 0.582086i
\(426\) 0 0
\(427\) −6.00000 + 17.3205i −0.290360 + 0.838198i
\(428\) 0 0
\(429\) 0 0
\(430\) 3.00000 + 1.73205i 0.144673 + 0.0835269i
\(431\) 21.0000i 1.01153i −0.862670 0.505767i \(-0.831209\pi\)
0.862670 0.505767i \(-0.168791\pi\)
\(432\) 0 0
\(433\) 10.3923i 0.499422i −0.968320 0.249711i \(-0.919664\pi\)
0.968320 0.249711i \(-0.0803357\pi\)
\(434\) −2.59808 13.5000i −0.124712 0.648021i
\(435\) 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 \(-0.413106\pi\)
−0.699153 + 0.714972i \(0.746440\pi\)
\(440\) 5.19615 0.247717
\(441\) 0 0
\(442\) 24.0000 1.14156
\(443\) 7.79423 + 4.50000i 0.370315 + 0.213801i 0.673596 0.739100i \(-0.264749\pi\)
−0.303281 + 0.952901i \(0.598082\pi\)
\(444\) 0 0
\(445\) 4.50000 + 7.79423i 0.213320 + 0.369482i
\(446\) 7.79423 + 13.5000i 0.369067 + 0.639244i
\(447\) 0 0
\(448\) −0.500000 2.59808i −0.0236228 0.122748i
\(449\) 12.0000i 0.566315i −0.959073 0.283158i \(-0.908618\pi\)
0.959073 0.283158i \(-0.0913819\pi\)
\(450\) 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
\(455\) −5.19615 + 15.0000i −0.243599 + 0.703211i
\(456\) 0 0
\(457\) 8.50000 14.7224i 0.397613 0.688686i −0.595818 0.803120i \(-0.703172\pi\)
0.993431 + 0.114433i \(0.0365053\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 5.19615i 0.242272i
\(461\) −9.52628 + 16.5000i −0.443683 + 0.768482i −0.997959 0.0638511i \(-0.979662\pi\)
0.554276 + 0.832333i \(0.312995\pi\)
\(462\) 0 0
\(463\) −16.0000 27.7128i −0.743583 1.28792i −0.950854 0.309640i \(-0.899791\pi\)
0.207271 0.978284i \(-0.433542\pi\)
\(464\) 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 \(-0.243523\pi\)
0.721348 + 0.692573i \(0.243523\pi\)
\(468\) 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 −0.353796 0.935323i \(-0.615109\pi\)
0.986911 0.161265i \(-0.0515575\pi\)
\(480\) 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
\(490\) −4.50000 11.2583i −0.203289 0.508600i
\(491\) 7.79423 4.50000i 0.351749 0.203082i −0.313707 0.949520i \(-0.601571\pi\)
0.665455 + 0.746438i \(0.268237\pi\)
\(492\) 0 0
\(493\) −36.0000 20.7846i −1.62136 0.936092i
\(494\) 6.00000i 0.269953i
\(495\) 0 0
\(496\) 5.19615i 0.233314i
\(497\) 7.79423 1.50000i 0.349619 0.0672842i
\(498\) 0 0
\(499\) −5.00000 8.66025i −0.223831 0.387686i 0.732137 0.681157i \(-0.238523\pi\)
−0.955968 + 0.293471i \(0.905190\pi\)
\(500\) −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 \(-0.318198\pi\)
0.540598 + 0.841281i \(0.318198\pi\)
\(504\) 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 \(-0.266021\pi\)
−0.977724 + 0.209895i \(0.932688\pi\)
\(510\) 0 0
\(511\) −9.00000 + 1.73205i −0.398137 + 0.0766214i
\(512\) 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
\(518\) 6.06218 17.5000i 0.266357 0.768906i
\(519\) 0 0
\(520\) 3.00000 5.19615i 0.131559 0.227866i
\(521\) −22.5167 −0.986473 −0.493236 0.869895i \(-0.664186\pi\)
−0.493236 + 0.869895i \(0.664186\pi\)
\(522\) 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 −0.938779 0.344519i \(-0.888042\pi\)
0.767752 + 0.640747i \(0.221375\pi\)
\(548\) 18.0000i 0.768922i
\(549\) 0 0
\(550\) 6.00000 0.255841
\(551\) −5.19615 + 9.00000i −0.221364 + 0.383413i
\(552\) 0 0
\(553\) 25.0000 + 8.66025i 1.06311 + 0.368271i
\(554\) 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 \(0.0818214\pi\)
−0.967144 + 0.254228i \(0.918179\pi\)
\(558\) 0 0
\(559\) 6.92820i 0.293032i
\(560\) 0.866025 + 4.50000i 0.0365963 + 0.190160i
\(561\) 0 0
\(562\) −15.0000 25.9808i −0.632737 1.09593i
\(563\) −5.19615 9.00000i −0.218992 0.379305i 0.735508 0.677516i \(-0.236943\pi\)
−0.954500 + 0.298211i \(0.903610\pi\)
\(564\) 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 \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(570\) 0 0
\(571\) −16.0000 27.7128i −0.669579 1.15975i −0.978022 0.208502i \(-0.933141\pi\)
0.308443 0.951243i \(-0.400192\pi\)
\(572\) 5.19615 + 9.00000i 0.217262 + 0.376309i
\(573\) 0 0
\(574\) 31.5000 6.06218i 1.31478 0.253030i
\(575\) 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
\(581\) 43.3013 + 15.0000i 1.79644 + 0.622305i
\(582\) 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 0.0160815 + 0.999871i \(0.494881\pi\)
−0.873954 + 0.486008i \(0.838452\pi\)
\(588\) 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 \(-0.372061\pi\)
0.391197 + 0.920307i \(0.372061\pi\)
\(594\) 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 −0.650708 0.759328i \(-0.725528\pi\)
0.332244 + 0.943193i \(0.392194\pi\)
\(600\) 0 0
\(601\) −9.00000 5.19615i −0.367118 0.211955i 0.305081 0.952326i \(-0.401317\pi\)
−0.672198 + 0.740371i \(0.734650\pi\)
\(602\) −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 \(-0.552335\pi\)
0.772508 + 0.635005i \(0.219002\pi\)
\(608\) −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
\(616\) −7.50000 2.59808i −0.302184 0.104679i
\(617\) 15.5885 9.00000i 0.627568 0.362326i −0.152242 0.988343i \(-0.548649\pi\)
0.779809 + 0.626017i \(0.215316\pi\)
\(618\) 0 0
\(619\) 16.5000 + 9.52628i 0.663191 + 0.382893i 0.793492 0.608581i \(-0.208261\pi\)
−0.130301 + 0.991475i \(0.541594\pi\)
\(620\) 9.00000i 0.361449i
\(621\) 0 0
\(622\) 24.2487i 0.972285i
\(623\) −2.59808 13.5000i −0.104090 0.540866i
\(624\) 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
\(637\) 15.0000 19.0526i 0.594322 0.754890i
\(638\) 18.0000i 0.712627i
\(639\) 0 0
\(640\) 1.73205i 0.0684653i
\(641\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(642\) 0 0
\(643\) 4.50000 2.59808i 0.177463 0.102458i −0.408637 0.912697i \(-0.633996\pi\)
0.586100 + 0.810239i \(0.300663\pi\)
\(644\) −2.59808 + 7.50000i −0.102379 + 0.295541i
\(645\) 0 0
\(646\) −6.00000 + 10.3923i −0.236067 + 0.408880i
\(647\) 10.3923 0.408564 0.204282 0.978912i \(-0.434514\pi\)
0.204282 + 0.978912i \(0.434514\pi\)
\(648\) 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 −0.772975 0.634437i \(-0.781232\pi\)
0.162951 + 0.986634i \(0.447899\pi\)
\(654\) 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 0.810486 0.585758i \(-0.199203\pi\)
−0.102039 + 0.994780i \(0.532537\pi\)
\(660\) 0 0
\(661\) 33.0000 19.0526i 1.28355 0.741059i 0.306055 0.952014i \(-0.400991\pi\)
0.977496 + 0.210955i \(0.0676574\pi\)
\(662\) 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 −0.698988 0.715134i \(-0.746366\pi\)
0.968818 + 0.247774i \(0.0796991\pi\)
\(674\) 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 \(-0.666938\pi\)
1.00000 0.000853228i \(0.000271591\pi\)
\(678\) 0 0
\(679\) −12.0000 + 34.6410i −0.460518 + 1.32940i
\(680\) −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 \(-0.782499\pi\)
0.775494 0.631355i \(-0.217501\pi\)
\(684\) 0 0
\(685\) 31.1769i 1.19121i
\(686\) 0.866025 + 18.5000i 0.0330650 + 0.706333i
\(687\) 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 \(-0.269996\pi\)
−0.318946 + 0.947773i \(0.603329\pi\)
\(692\) −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
\(700\) 1.00000 + 5.19615i 0.0377964 + 0.196396i
\(701\) 6.00000i 0.226617i −0.993560 0.113308i \(-0.963855\pi\)
0.993560 0.113308i \(-0.0361448\pi\)
\(702\) 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 −0.875262 0.483650i \(-0.839311\pi\)
0.856484 + 0.516174i \(0.172644\pi\)
\(710\) 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 \(-0.479425\pi\)
0.0645946 + 0.997912i \(0.479425\pi\)
\(720\) 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 −0.968201 0.250172i \(-0.919513\pi\)
−0.700756 0.713401i \(-0.747154\pi\)
\(728\) −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 \(-0.605194\pi\)
0.656916 + 0.753964i \(0.271861\pi\)
\(734\) 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
\(742\) −30.0000 10.3923i −1.10133 0.381514i
\(743\) −23.3827 + 13.5000i −0.857828 + 0.495267i −0.863284 0.504718i \(-0.831596\pi\)
0.00545664 + 0.999985i \(0.498263\pi\)
\(744\) 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 0.883694 0.468065i \(-0.155049\pi\)
−0.847203 + 0.531269i \(0.821715\pi\)
\(752\) 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 \(-0.247474\pi\)
−0.963842 + 0.266475i \(0.914141\pi\)
\(762\) 0 0
\(763\) 6.50000 + 33.7750i 0.235316 + 1.22274i
\(764\) 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 \(-0.907763\pi\)
−0.231701 + 0.972787i \(0.574429\pi\)
\(770\) 12.9904 + 4.50000i 0.468141 + 0.162169i
\(771\) 0 0
\(772\) −7.00000 + 12.1244i −0.251936 + 0.436365i
\(773\) −19.0526 −0.685273 −0.342636 0.939468i \(-0.611320\pi\)
−0.342636 + 0.939468i \(0.611320\pi\)
\(774\) 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 \(-0.566771\pi\)
0.742925 + 0.669375i \(0.233438\pi\)
\(788\) −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 \(-0.255704\pi\)
−0.970408 + 0.241469i \(0.922371\pi\)
\(798\) 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
\(805\) 4.50000 12.9904i 0.158604 0.457851i
\(806\) 15.5885 9.00000i 0.549080 0.317011i
\(807\) 0 0
\(808\) 0 0
\(809\) 6.00000i 0.210949i −0.994422 0.105474i \(-0.966364\pi\)
0.994422 0.105474i \(-0.0336361\pi\)
\(810\) 0 0
\(811\) 36.3731i 1.27723i 0.769526 + 0.638616i \(0.220493\pi\)
−0.769526 + 0.638616i \(0.779507\pi\)
\(812\) 15.5885 3.00000i 0.547048 0.105279i
\(813\) 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 0.879379 0.476122i \(-0.157958\pi\)
0.0273557 + 0.999626i \(0.491291\pi\)
\(822\) 0 0
\(823\) 2.00000 + 3.46410i 0.0697156 + 0.120751i 0.898776 0.438408i \(-0.144457\pi\)
−0.829060 + 0.559159i \(0.811124\pi\)
\(824\) −9.52628 16.5000i −0.331864 0.574805i
\(825\) 0 0
\(826\) −9.00000 + 1.73205i −0.313150 + 0.0602658i
\(827\) 3.00000i 0.104320i −0.998639 0.0521601i \(-0.983389\pi\)
0.998639 0.0521601i \(-0.0166106\pi\)
\(828\) 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
\(833\) −45.0333 + 18.0000i −1.56031 + 0.623663i
\(834\) 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 \(-0.695862\pi\)
0.995797 + 0.0915899i \(0.0291949\pi\)
\(840\) 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 \(-0.257098\pi\)
−0.280292 + 0.959915i \(0.590431\pi\)
\(854\) 13.8564 12.0000i 0.474156 0.410632i
\(855\) 0 0
\(856\) 0 0
\(857\) −21.6506 + 37.5000i −0.739572 + 1.28098i 0.213117 + 0.977027i \(0.431639\pi\)
−0.952688 + 0.303949i \(0.901695\pi\)
\(858\) 0 0
\(859\) −25.5000 + 14.7224i −0.870049 + 0.502323i −0.867364 0.497674i \(-0.834188\pi\)
−0.00268433 + 0.999996i \(0.500854\pi\)
\(860\) −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
\(868\) −4.50000 + 12.9904i −0.152740 + 0.440922i
\(869\) −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
\(875\) −6.06218 31.5000i −0.204939 1.06489i
\(876\) 0 0
\(877\) −25.0000 43.3013i −0.844190 1.46218i −0.886323 0.463068i \(-0.846749\pi\)
0.0421327 0.999112i \(-0.486585\pi\)
\(878\) 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 \(-0.644192\pi\)
−0.437657 + 0.899142i \(0.644192\pi\)
\(882\) 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 \(-0.0332081\pi\)
−0.587467 + 0.809248i \(0.699875\pi\)
\(888\) 0 0
\(889\) −11.0000 57.1577i −0.368928 1.91701i
\(890\) 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
\(896\) −0.866025 + 2.50000i −0.0289319 + 0.0835191i
\(897\) 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 −0.791944 0.610594i \(-0.790931\pi\)
0.924762 + 0.380547i \(0.124264\pi\)
\(908\) −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 0.662177 0.749347i \(-0.269633\pi\)
−0.317865 + 0.948136i \(0.602966\pi\)
\(912\) 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 \(-0.983556\pi\)
0.544052 + 0.839052i \(0.316889\pi\)
\(930\) 0 0
\(931\) 4.50000 + 11.2583i 0.147482 + 0.368977i
\(932\) −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 \(-0.0360996\pi\)
\(938\) −5.19615 + 1.00000i −0.169660 + 0.0326512i
\(939\) 0 0
\(940\) −3.00000 5.19615i −0.0978492 0.169480i
\(941\) 6.06218 + 10.5000i 0.197621 + 0.342290i 0.947757 0.318994i \(-0.103345\pi\)
−0.750135 + 0.661284i \(0.770012\pi\)
\(942\) 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 0.695988 0.718053i \(-0.254966\pi\)
−0.273858 + 0.961770i \(0.588300\pi\)
\(948\) 0 0
\(949\) −6.00000 10.3923i −0.194768 0.337348i
\(950\) 1.73205 + 3.00000i 0.0561951 + 0.0973329i
\(951\) 0 0
\(952\) 18.0000 3.46410i 0.583383 0.112272i
\(953\) 18.0000i 0.583077i 0.956559 + 0.291539i \(0.0941672\pi\)
−0.956559 + 0.291539i \(0.905833\pi\)
\(954\) 0 0
\(955\) 36.3731i 1.17700i
\(956\) 0 0
\(957\) 0 0
\(958\) −24.0000 + 13.8564i −0.775405 + 0.447680i
\(959\) 15.5885 45.0000i 0.503378 1.45313i
\(960\) 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 0.965508 0.260375i \(-0.0838461\pi\)
−0.708245 + 0.705967i \(0.750513\pi\)
\(968\) −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 \(-0.482298\pi\)
0.0555842 + 0.998454i \(0.482298\pi\)
\(972\) 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 0.344631 0.938738i \(-0.388004\pi\)
0.985287 + 0.170910i \(0.0546709\pi\)
\(978\) 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 \(-0.850927\pi\)
0.837081 + 0.547079i \(0.184260\pi\)
\(984\) 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
\(994\) −7.50000 2.59808i −0.237886 0.0824060i
\(995\) 2.59808 1.50000i 0.0823646 0.0475532i
\(996\) 0 0
\(997\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(998\) 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.c.755.1 4
3.2 odd 2 inner 1134.2.m.c.755.2 4
7.6 odd 2 1134.2.m.b.755.1 4
9.2 odd 6 378.2.d.b.377.1 4
9.4 even 3 1134.2.m.b.377.2 4
9.5 odd 6 1134.2.m.b.377.1 4
9.7 even 3 378.2.d.b.377.4 yes 4
21.20 even 2 1134.2.m.b.755.2 4
36.7 odd 6 3024.2.k.e.1889.4 4
36.11 even 6 3024.2.k.e.1889.2 4
63.13 odd 6 inner 1134.2.m.c.377.2 4
63.20 even 6 378.2.d.b.377.2 yes 4
63.34 odd 6 378.2.d.b.377.3 yes 4
63.41 even 6 inner 1134.2.m.c.377.1 4
252.83 odd 6 3024.2.k.e.1889.3 4
252.223 even 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 9.2 odd 6
378.2.d.b.377.2 yes 4 63.20 even 6
378.2.d.b.377.3 yes 4 63.34 odd 6
378.2.d.b.377.4 yes 4 9.7 even 3
1134.2.m.b.377.1 4 9.5 odd 6
1134.2.m.b.377.2 4 9.4 even 3
1134.2.m.b.755.1 4 7.6 odd 2
1134.2.m.b.755.2 4 21.20 even 2
1134.2.m.c.377.1 4 63.41 even 6 inner
1134.2.m.c.377.2 4 63.13 odd 6 inner
1134.2.m.c.755.1 4 1.1 even 1 trivial
1134.2.m.c.755.2 4 3.2 odd 2 inner
3024.2.k.e.1889.1 4 252.223 even 6
3024.2.k.e.1889.2 4 36.11 even 6
3024.2.k.e.1889.3 4 252.83 odd 6
3024.2.k.e.1889.4 4 36.7 odd 6