Properties

Label 378.2.m.a.251.6
Level $378$
Weight $2$
Character 378.251
Analytic conductor $3.018$
Analytic rank $0$
Dimension $16$
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] = [378,2,Mod(125,378)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(378, 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("378.125");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 378.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: \(3.01834519640\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 6x^{14} + 9x^{12} + 54x^{10} - 288x^{8} + 486x^{6} + 729x^{4} - 4374x^{2} + 6561 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 3^{4} \)
Twist minimal: no (minimal twist has level 126)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 251.6
Root \(1.40917 - 1.00709i\) of defining polynomial
Character \(\chi\) \(=\) 378.251
Dual form 378.2.m.a.125.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-1.17468 - 2.03460i) q^{5} +(1.55364 + 2.14154i) q^{7} +1.00000i q^{8} +O(q^{10})\) \(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-1.17468 - 2.03460i) q^{5} +(1.55364 + 2.14154i) q^{7} +1.00000i q^{8} -2.34936i q^{10} +(4.91614 + 2.83834i) q^{11} +(1.48943 - 0.859925i) q^{13} +(0.274725 + 2.63145i) q^{14} +(-0.500000 + 0.866025i) q^{16} +1.76883 q^{17} -1.13932i q^{19} +(1.17468 - 2.03460i) q^{20} +(2.83834 + 4.91614i) q^{22} +(3.18272 - 1.83755i) q^{23} +(-0.259741 + 0.449885i) q^{25} +1.71985 q^{26} +(-1.07781 + 2.41626i) q^{28} +(-3.59886 - 2.07781i) q^{29} +(-7.24879 + 4.18509i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(1.53185 + 0.884414i) q^{34} +(2.53215 - 5.67667i) q^{35} -9.19773 q^{37} +(0.569660 - 0.986680i) q^{38} +(2.03460 - 1.17468i) q^{40} +(-3.99709 - 6.92317i) q^{41} +(1.76053 - 3.04933i) q^{43} +5.67667i q^{44} +3.67509 q^{46} +(-5.90494 + 10.2277i) q^{47} +(-2.17238 + 6.65438i) q^{49} +(-0.449885 + 0.259741i) q^{50} +(1.48943 + 0.859925i) q^{52} -13.3365i q^{55} +(-2.14154 + 1.55364i) q^{56} +(-2.07781 - 3.59886i) q^{58} +(-1.11483 - 1.93094i) q^{59} +(7.79396 + 4.49985i) q^{61} -8.37019 q^{62} -1.00000 q^{64} +(-3.49921 - 2.02027i) q^{65} +(-5.43562 - 9.41477i) q^{67} +(0.884414 + 1.53185i) q^{68} +(5.03124 - 3.65007i) q^{70} -4.52106i q^{71} +5.34234i q^{73} +(-7.96547 - 4.59886i) q^{74} +(0.986680 - 0.569660i) q^{76} +(1.55953 + 14.9379i) q^{77} +(6.51422 - 11.2830i) q^{79} +2.34936 q^{80} -7.99419i q^{82} +(6.27298 - 10.8651i) q^{83} +(-2.07781 - 3.59886i) q^{85} +(3.04933 - 1.76053i) q^{86} +(-2.83834 + 4.91614i) q^{88} +1.16106 q^{89} +(4.15561 + 1.85366i) q^{91} +(3.18272 + 1.83755i) q^{92} +(-10.2277 + 5.90494i) q^{94} +(-2.31806 + 1.33834i) q^{95} +(-3.97536 - 2.29517i) q^{97} +(-5.20853 + 4.67667i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 8 q^{4} + 2 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 8 q^{4} + 2 q^{7} + 12 q^{11} + 6 q^{14} - 8 q^{16} + 48 q^{23} - 8 q^{25} + 4 q^{28} + 12 q^{29} - 8 q^{37} + 4 q^{43} + 24 q^{46} - 8 q^{49} - 60 q^{50} + 6 q^{56} - 12 q^{58} - 16 q^{64} - 84 q^{65} - 28 q^{67} - 36 q^{74} - 78 q^{77} - 4 q^{79} - 12 q^{85} + 24 q^{86} + 24 q^{91} + 48 q^{92} - 12 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/378\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(325\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.866025 + 0.500000i 0.612372 + 0.353553i
\(3\) 0 0
\(4\) 0.500000 + 0.866025i 0.250000 + 0.433013i
\(5\) −1.17468 2.03460i −0.525332 0.909902i −0.999565 0.0295026i \(-0.990608\pi\)
0.474232 0.880400i \(-0.342726\pi\)
\(6\) 0 0
\(7\) 1.55364 + 2.14154i 0.587222 + 0.809426i
\(8\) 1.00000i 0.353553i
\(9\) 0 0
\(10\) 2.34936i 0.742932i
\(11\) 4.91614 + 2.83834i 1.48227 + 0.855790i 0.999798 0.0201197i \(-0.00640473\pi\)
0.482475 + 0.875910i \(0.339738\pi\)
\(12\) 0 0
\(13\) 1.48943 0.859925i 0.413094 0.238500i −0.279024 0.960284i \(-0.590011\pi\)
0.692118 + 0.721784i \(0.256678\pi\)
\(14\) 0.274725 + 2.63145i 0.0734234 + 0.703284i
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 1.76883 0.429004 0.214502 0.976724i \(-0.431187\pi\)
0.214502 + 0.976724i \(0.431187\pi\)
\(18\) 0 0
\(19\) 1.13932i 0.261378i −0.991423 0.130689i \(-0.958281\pi\)
0.991423 0.130689i \(-0.0417189\pi\)
\(20\) 1.17468 2.03460i 0.262666 0.454951i
\(21\) 0 0
\(22\) 2.83834 + 4.91614i 0.605135 + 1.04812i
\(23\) 3.18272 1.83755i 0.663644 0.383155i −0.130020 0.991511i \(-0.541504\pi\)
0.793664 + 0.608356i \(0.208171\pi\)
\(24\) 0 0
\(25\) −0.259741 + 0.449885i −0.0519482 + 0.0899769i
\(26\) 1.71985 0.337290
\(27\) 0 0
\(28\) −1.07781 + 2.41626i −0.203686 + 0.456631i
\(29\) −3.59886 2.07781i −0.668292 0.385839i 0.127137 0.991885i \(-0.459421\pi\)
−0.795429 + 0.606046i \(0.792755\pi\)
\(30\) 0 0
\(31\) −7.24879 + 4.18509i −1.30192 + 0.751665i −0.980734 0.195350i \(-0.937416\pi\)
−0.321188 + 0.947015i \(0.604082\pi\)
\(32\) −0.866025 + 0.500000i −0.153093 + 0.0883883i
\(33\) 0 0
\(34\) 1.53185 + 0.884414i 0.262710 + 0.151676i
\(35\) 2.53215 5.67667i 0.428012 0.959532i
\(36\) 0 0
\(37\) −9.19773 −1.51210 −0.756049 0.654515i \(-0.772873\pi\)
−0.756049 + 0.654515i \(0.772873\pi\)
\(38\) 0.569660 0.986680i 0.0924111 0.160061i
\(39\) 0 0
\(40\) 2.03460 1.17468i 0.321699 0.185733i
\(41\) −3.99709 6.92317i −0.624241 1.08122i −0.988687 0.149993i \(-0.952075\pi\)
0.364446 0.931225i \(-0.381258\pi\)
\(42\) 0 0
\(43\) 1.76053 3.04933i 0.268478 0.465018i −0.699991 0.714152i \(-0.746813\pi\)
0.968469 + 0.249134i \(0.0801459\pi\)
\(44\) 5.67667i 0.855790i
\(45\) 0 0
\(46\) 3.67509 0.541863
\(47\) −5.90494 + 10.2277i −0.861324 + 1.49186i 0.00932669 + 0.999957i \(0.497031\pi\)
−0.870651 + 0.491901i \(0.836302\pi\)
\(48\) 0 0
\(49\) −2.17238 + 6.65438i −0.310340 + 0.950626i
\(50\) −0.449885 + 0.259741i −0.0636233 + 0.0367329i
\(51\) 0 0
\(52\) 1.48943 + 0.859925i 0.206547 + 0.119250i
\(53\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(54\) 0 0
\(55\) 13.3365i 1.79830i
\(56\) −2.14154 + 1.55364i −0.286175 + 0.207614i
\(57\) 0 0
\(58\) −2.07781 3.59886i −0.272829 0.472554i
\(59\) −1.11483 1.93094i −0.145139 0.251387i 0.784286 0.620399i \(-0.213029\pi\)
−0.929425 + 0.369012i \(0.879696\pi\)
\(60\) 0 0
\(61\) 7.79396 + 4.49985i 0.997915 + 0.576146i 0.907631 0.419770i \(-0.137889\pi\)
0.0902842 + 0.995916i \(0.471222\pi\)
\(62\) −8.37019 −1.06301
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) −3.49921 2.02027i −0.434024 0.250584i
\(66\) 0 0
\(67\) −5.43562 9.41477i −0.664067 1.15020i −0.979537 0.201262i \(-0.935496\pi\)
0.315470 0.948935i \(-0.397838\pi\)
\(68\) 0.884414 + 1.53185i 0.107251 + 0.185764i
\(69\) 0 0
\(70\) 5.03124 3.65007i 0.601348 0.436266i
\(71\) 4.52106i 0.536551i −0.963342 0.268276i \(-0.913546\pi\)
0.963342 0.268276i \(-0.0864538\pi\)
\(72\) 0 0
\(73\) 5.34234i 0.625274i 0.949873 + 0.312637i \(0.101212\pi\)
−0.949873 + 0.312637i \(0.898788\pi\)
\(74\) −7.96547 4.59886i −0.925967 0.534607i
\(75\) 0 0
\(76\) 0.986680 0.569660i 0.113180 0.0653445i
\(77\) 1.55953 + 14.9379i 0.177724 + 1.70233i
\(78\) 0 0
\(79\) 6.51422 11.2830i 0.732907 1.26943i −0.222729 0.974880i \(-0.571497\pi\)
0.955636 0.294551i \(-0.0951701\pi\)
\(80\) 2.34936 0.262666
\(81\) 0 0
\(82\) 7.99419i 0.882810i
\(83\) 6.27298 10.8651i 0.688549 1.19260i −0.283758 0.958896i \(-0.591581\pi\)
0.972307 0.233707i \(-0.0750855\pi\)
\(84\) 0 0
\(85\) −2.07781 3.59886i −0.225370 0.390352i
\(86\) 3.04933 1.76053i 0.328817 0.189843i
\(87\) 0 0
\(88\) −2.83834 + 4.91614i −0.302568 + 0.524062i
\(89\) 1.16106 0.123072 0.0615360 0.998105i \(-0.480400\pi\)
0.0615360 + 0.998105i \(0.480400\pi\)
\(90\) 0 0
\(91\) 4.15561 + 1.85366i 0.435626 + 0.194317i
\(92\) 3.18272 + 1.83755i 0.331822 + 0.191577i
\(93\) 0 0
\(94\) −10.2277 + 5.90494i −1.05490 + 0.609048i
\(95\) −2.31806 + 1.33834i −0.237828 + 0.137310i
\(96\) 0 0
\(97\) −3.97536 2.29517i −0.403636 0.233039i 0.284416 0.958701i \(-0.408200\pi\)
−0.688052 + 0.725662i \(0.741534\pi\)
\(98\) −5.20853 + 4.67667i −0.526141 + 0.472415i
\(99\) 0 0
\(100\) −0.519482 −0.0519482
\(101\) −3.31155 + 5.73577i −0.329511 + 0.570730i −0.982415 0.186711i \(-0.940217\pi\)
0.652904 + 0.757441i \(0.273551\pi\)
\(102\) 0 0
\(103\) −5.07471 + 2.92989i −0.500026 + 0.288690i −0.728724 0.684807i \(-0.759886\pi\)
0.228698 + 0.973497i \(0.426553\pi\)
\(104\) 0.859925 + 1.48943i 0.0843225 + 0.146051i
\(105\) 0 0
\(106\) 0 0
\(107\) 4.71563i 0.455878i 0.973675 + 0.227939i \(0.0731986\pi\)
−0.973675 + 0.227939i \(0.926801\pi\)
\(108\) 0 0
\(109\) 4.23669 0.405802 0.202901 0.979199i \(-0.434963\pi\)
0.202901 + 0.979199i \(0.434963\pi\)
\(110\) 6.66826 11.5498i 0.635794 1.10123i
\(111\) 0 0
\(112\) −2.63145 + 0.274725i −0.248649 + 0.0259591i
\(113\) −5.91693 + 3.41614i −0.556618 + 0.321363i −0.751787 0.659406i \(-0.770808\pi\)
0.195169 + 0.980770i \(0.437474\pi\)
\(114\) 0 0
\(115\) −7.47736 4.31705i −0.697267 0.402567i
\(116\) 4.15561i 0.385839i
\(117\) 0 0
\(118\) 2.22966i 0.205257i
\(119\) 2.74813 + 3.78802i 0.251921 + 0.347247i
\(120\) 0 0
\(121\) 10.6123 + 18.3810i 0.964754 + 1.67100i
\(122\) 4.49985 + 7.79396i 0.407397 + 0.705632i
\(123\) 0 0
\(124\) −7.24879 4.18509i −0.650961 0.375832i
\(125\) −10.5263 −0.941504
\(126\) 0 0
\(127\) −6.67667 −0.592459 −0.296229 0.955117i \(-0.595729\pi\)
−0.296229 + 0.955117i \(0.595729\pi\)
\(128\) −0.866025 0.500000i −0.0765466 0.0441942i
\(129\) 0 0
\(130\) −2.02027 3.49921i −0.177189 0.306901i
\(131\) −3.73653 6.47185i −0.326462 0.565448i 0.655345 0.755329i \(-0.272523\pi\)
−0.981807 + 0.189881i \(0.939190\pi\)
\(132\) 0 0
\(133\) 2.43990 1.77010i 0.211566 0.153487i
\(134\) 10.8712i 0.939133i
\(135\) 0 0
\(136\) 1.76883i 0.151676i
\(137\) −6.91772 3.99395i −0.591021 0.341226i 0.174480 0.984661i \(-0.444175\pi\)
−0.765501 + 0.643435i \(0.777509\pi\)
\(138\) 0 0
\(139\) 17.9792 10.3803i 1.52498 0.880446i 0.525415 0.850846i \(-0.323910\pi\)
0.999562 0.0295993i \(-0.00942312\pi\)
\(140\) 6.18222 0.645428i 0.522493 0.0545486i
\(141\) 0 0
\(142\) 2.26053 3.91535i 0.189699 0.328569i
\(143\) 9.76302 0.816425
\(144\) 0 0
\(145\) 9.76302i 0.810774i
\(146\) −2.67117 + 4.62660i −0.221068 + 0.382900i
\(147\) 0 0
\(148\) −4.59886 7.96547i −0.378024 0.654757i
\(149\) 1.03726 0.598865i 0.0849760 0.0490609i −0.456910 0.889513i \(-0.651044\pi\)
0.541886 + 0.840452i \(0.317710\pi\)
\(150\) 0 0
\(151\) −7.61229 + 13.1849i −0.619480 + 1.07297i 0.370101 + 0.928991i \(0.379323\pi\)
−0.989581 + 0.143979i \(0.954010\pi\)
\(152\) 1.13932 0.0924111
\(153\) 0 0
\(154\) −6.11835 + 13.7163i −0.493030 + 1.10529i
\(155\) 17.0300 + 9.83228i 1.36788 + 0.789748i
\(156\) 0 0
\(157\) 8.68358 5.01347i 0.693025 0.400118i −0.111719 0.993740i \(-0.535636\pi\)
0.804744 + 0.593621i \(0.202302\pi\)
\(158\) 11.2830 6.51422i 0.897624 0.518243i
\(159\) 0 0
\(160\) 2.03460 + 1.17468i 0.160850 + 0.0928665i
\(161\) 8.88000 + 3.96104i 0.699842 + 0.312173i
\(162\) 0 0
\(163\) 12.0032 0.940160 0.470080 0.882624i \(-0.344225\pi\)
0.470080 + 0.882624i \(0.344225\pi\)
\(164\) 3.99709 6.92317i 0.312121 0.540609i
\(165\) 0 0
\(166\) 10.8651 6.27298i 0.843297 0.486878i
\(167\) −8.57472 14.8518i −0.663532 1.14927i −0.979681 0.200561i \(-0.935723\pi\)
0.316150 0.948709i \(-0.397610\pi\)
\(168\) 0 0
\(169\) −5.02106 + 8.69673i −0.386235 + 0.668979i
\(170\) 4.15561i 0.318721i
\(171\) 0 0
\(172\) 3.52106 0.268478
\(173\) −0.993738 + 1.72121i −0.0755525 + 0.130861i −0.901326 0.433140i \(-0.857405\pi\)
0.825774 + 0.564001i \(0.190739\pi\)
\(174\) 0 0
\(175\) −1.36699 + 0.142715i −0.103335 + 0.0107882i
\(176\) −4.91614 + 2.83834i −0.370568 + 0.213948i
\(177\) 0 0
\(178\) 1.00551 + 0.580529i 0.0753659 + 0.0435125i
\(179\) 8.31122i 0.621210i 0.950539 + 0.310605i \(0.100532\pi\)
−0.950539 + 0.310605i \(0.899468\pi\)
\(180\) 0 0
\(181\) 15.4541i 1.14870i −0.818611 0.574348i \(-0.805256\pi\)
0.818611 0.574348i \(-0.194744\pi\)
\(182\) 2.67203 + 3.68312i 0.198064 + 0.273011i
\(183\) 0 0
\(184\) 1.83755 + 3.18272i 0.135466 + 0.234634i
\(185\) 10.8044 + 18.7137i 0.794354 + 1.37586i
\(186\) 0 0
\(187\) 8.69581 + 5.02053i 0.635901 + 0.367137i
\(188\) −11.8099 −0.861324
\(189\) 0 0
\(190\) −2.67667 −0.194186
\(191\) −10.6851 6.16904i −0.773146 0.446376i 0.0608498 0.998147i \(-0.480619\pi\)
−0.833996 + 0.551771i \(0.813952\pi\)
\(192\) 0 0
\(193\) −2.19694 3.80521i −0.158139 0.273905i 0.776058 0.630661i \(-0.217216\pi\)
−0.934198 + 0.356756i \(0.883883\pi\)
\(194\) −2.29517 3.97536i −0.164784 0.285414i
\(195\) 0 0
\(196\) −6.84905 + 1.44585i −0.489218 + 0.103275i
\(197\) 10.8865i 0.775632i 0.921737 + 0.387816i \(0.126770\pi\)
−0.921737 + 0.387816i \(0.873230\pi\)
\(198\) 0 0
\(199\) 27.5665i 1.95414i 0.212926 + 0.977068i \(0.431701\pi\)
−0.212926 + 0.977068i \(0.568299\pi\)
\(200\) −0.449885 0.259741i −0.0318116 0.0183665i
\(201\) 0 0
\(202\) −5.73577 + 3.31155i −0.403567 + 0.233000i
\(203\) −1.14165 10.9353i −0.0801282 0.767506i
\(204\) 0 0
\(205\) −9.39060 + 16.2650i −0.655868 + 1.13600i
\(206\) −5.85977 −0.408270
\(207\) 0 0
\(208\) 1.71985i 0.119250i
\(209\) 3.23377 5.60106i 0.223685 0.387433i
\(210\) 0 0
\(211\) 5.15561 + 8.92978i 0.354927 + 0.614751i 0.987105 0.160071i \(-0.0511724\pi\)
−0.632179 + 0.774823i \(0.717839\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) −2.35782 + 4.08386i −0.161177 + 0.279167i
\(215\) −8.27223 −0.564161
\(216\) 0 0
\(217\) −20.2246 9.02143i −1.37293 0.612415i
\(218\) 3.66908 + 2.11835i 0.248502 + 0.143473i
\(219\) 0 0
\(220\) 11.5498 6.66826i 0.778686 0.449574i
\(221\) 2.63455 1.52106i 0.177219 0.102318i
\(222\) 0 0
\(223\) −6.24329 3.60456i −0.418081 0.241379i 0.276175 0.961107i \(-0.410933\pi\)
−0.694256 + 0.719728i \(0.744267\pi\)
\(224\) −2.41626 1.07781i −0.161443 0.0720139i
\(225\) 0 0
\(226\) −6.83228 −0.454477
\(227\) −6.37800 + 11.0470i −0.423323 + 0.733217i −0.996262 0.0863812i \(-0.972470\pi\)
0.572939 + 0.819598i \(0.305803\pi\)
\(228\) 0 0
\(229\) 3.89208 2.24709i 0.257196 0.148492i −0.365859 0.930670i \(-0.619225\pi\)
0.623055 + 0.782178i \(0.285891\pi\)
\(230\) −4.31705 7.47736i −0.284658 0.493042i
\(231\) 0 0
\(232\) 2.07781 3.59886i 0.136415 0.236277i
\(233\) 2.15403i 0.141115i 0.997508 + 0.0705577i \(0.0224779\pi\)
−0.997508 + 0.0705577i \(0.977522\pi\)
\(234\) 0 0
\(235\) 27.7456 1.80993
\(236\) 1.11483 1.93094i 0.0725693 0.125694i
\(237\) 0 0
\(238\) 0.485942 + 4.65458i 0.0314989 + 0.301712i
\(239\) 8.78317 5.07096i 0.568136 0.328013i −0.188269 0.982118i \(-0.560288\pi\)
0.756404 + 0.654104i \(0.226954\pi\)
\(240\) 0 0
\(241\) 9.13490 + 5.27404i 0.588431 + 0.339731i 0.764477 0.644651i \(-0.222997\pi\)
−0.176046 + 0.984382i \(0.556331\pi\)
\(242\) 21.2246i 1.36437i
\(243\) 0 0
\(244\) 8.99970i 0.576146i
\(245\) 16.0909 3.39682i 1.02801 0.217015i
\(246\) 0 0
\(247\) −0.979729 1.69694i −0.0623387 0.107974i
\(248\) −4.18509 7.24879i −0.265754 0.460299i
\(249\) 0 0
\(250\) −9.11608 5.26317i −0.576551 0.332872i
\(251\) 29.3005 1.84943 0.924714 0.380662i \(-0.124304\pi\)
0.924714 + 0.380662i \(0.124304\pi\)
\(252\) 0 0
\(253\) 20.8623 1.31160
\(254\) −5.78217 3.33834i −0.362805 0.209466i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 3.81430 + 6.60656i 0.237930 + 0.412106i 0.960120 0.279588i \(-0.0901979\pi\)
−0.722190 + 0.691694i \(0.756865\pi\)
\(258\) 0 0
\(259\) −14.2900 19.6973i −0.887937 1.22393i
\(260\) 4.04054i 0.250584i
\(261\) 0 0
\(262\) 7.47305i 0.461687i
\(263\) 10.5531 + 6.09281i 0.650729 + 0.375699i 0.788736 0.614733i \(-0.210736\pi\)
−0.138006 + 0.990431i \(0.544069\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 2.99806 0.313000i 0.183823 0.0191913i
\(267\) 0 0
\(268\) 5.43562 9.41477i 0.332034 0.575099i
\(269\) −2.77433 −0.169154 −0.0845771 0.996417i \(-0.526954\pi\)
−0.0845771 + 0.996417i \(0.526954\pi\)
\(270\) 0 0
\(271\) 3.20793i 0.194868i −0.995242 0.0974338i \(-0.968937\pi\)
0.995242 0.0974338i \(-0.0310634\pi\)
\(272\) −0.884414 + 1.53185i −0.0536255 + 0.0928821i
\(273\) 0 0
\(274\) −3.99395 6.91772i −0.241283 0.417915i
\(275\) −2.55385 + 1.47446i −0.154003 + 0.0889135i
\(276\) 0 0
\(277\) −5.04054 + 8.73047i −0.302857 + 0.524563i −0.976782 0.214236i \(-0.931274\pi\)
0.673925 + 0.738800i \(0.264607\pi\)
\(278\) 20.7606 1.24514
\(279\) 0 0
\(280\) 5.67667 + 2.53215i 0.339246 + 0.151325i
\(281\) −4.21999 2.43641i −0.251743 0.145344i 0.368819 0.929501i \(-0.379762\pi\)
−0.620562 + 0.784157i \(0.713096\pi\)
\(282\) 0 0
\(283\) −2.44030 + 1.40891i −0.145061 + 0.0837508i −0.570774 0.821107i \(-0.693357\pi\)
0.425713 + 0.904858i \(0.360023\pi\)
\(284\) 3.91535 2.26053i 0.232333 0.134138i
\(285\) 0 0
\(286\) 8.45502 + 4.88151i 0.499956 + 0.288650i
\(287\) 8.61618 19.3161i 0.508597 1.14019i
\(288\) 0 0
\(289\) −13.8712 −0.815956
\(290\) −4.88151 + 8.45502i −0.286652 + 0.496496i
\(291\) 0 0
\(292\) −4.62660 + 2.67117i −0.270751 + 0.156318i
\(293\) 4.05694 + 7.02683i 0.237009 + 0.410512i 0.959855 0.280498i \(-0.0904995\pi\)
−0.722846 + 0.691010i \(0.757166\pi\)
\(294\) 0 0
\(295\) −2.61914 + 4.53648i −0.152492 + 0.264124i
\(296\) 9.19773i 0.534607i
\(297\) 0 0
\(298\) 1.19773 0.0693826
\(299\) 3.16030 5.47381i 0.182765 0.316558i
\(300\) 0 0
\(301\) 9.26549 0.967324i 0.534054 0.0557556i
\(302\) −13.1849 + 7.61229i −0.758705 + 0.438038i
\(303\) 0 0
\(304\) 0.986680 + 0.569660i 0.0565900 + 0.0326722i
\(305\) 21.1435i 1.21067i
\(306\) 0 0
\(307\) 10.8996i 0.622074i 0.950398 + 0.311037i \(0.100676\pi\)
−0.950398 + 0.311037i \(0.899324\pi\)
\(308\) −12.1568 + 8.81952i −0.692699 + 0.502539i
\(309\) 0 0
\(310\) 9.83228 + 17.0300i 0.558436 + 0.967240i
\(311\) −4.11819 7.13291i −0.233521 0.404470i 0.725321 0.688411i \(-0.241691\pi\)
−0.958842 + 0.283941i \(0.908358\pi\)
\(312\) 0 0
\(313\) −29.2736 16.9011i −1.65464 0.955308i −0.975127 0.221648i \(-0.928857\pi\)
−0.679516 0.733661i \(-0.737810\pi\)
\(314\) 10.0269 0.565853
\(315\) 0 0
\(316\) 13.0284 0.732907
\(317\) −5.82913 3.36545i −0.327396 0.189022i 0.327288 0.944925i \(-0.393865\pi\)
−0.654685 + 0.755902i \(0.727199\pi\)
\(318\) 0 0
\(319\) −11.7950 20.4296i −0.660394 1.14384i
\(320\) 1.17468 + 2.03460i 0.0656665 + 0.113738i
\(321\) 0 0
\(322\) 5.70979 + 7.87036i 0.318194 + 0.438598i
\(323\) 2.01526i 0.112132i
\(324\) 0 0
\(325\) 0.893431i 0.0495586i
\(326\) 10.3950 + 6.00158i 0.575728 + 0.332397i
\(327\) 0 0
\(328\) 6.92317 3.99709i 0.382268 0.220703i
\(329\) −31.0771 + 3.24447i −1.71334 + 0.178874i
\(330\) 0 0
\(331\) 16.0284 27.7621i 0.881002 1.52594i 0.0307744 0.999526i \(-0.490203\pi\)
0.850228 0.526415i \(-0.176464\pi\)
\(332\) 12.5460 0.688549
\(333\) 0 0
\(334\) 17.1494i 0.938375i
\(335\) −12.7702 + 22.1187i −0.697712 + 1.20847i
\(336\) 0 0
\(337\) −12.1123 20.9791i −0.659799 1.14280i −0.980668 0.195681i \(-0.937308\pi\)
0.320869 0.947124i \(-0.396025\pi\)
\(338\) −8.69673 + 5.02106i −0.473040 + 0.273110i
\(339\) 0 0
\(340\) 2.07781 3.59886i 0.112685 0.195176i
\(341\) −47.5148 −2.57307
\(342\) 0 0
\(343\) −17.6257 + 5.68629i −0.951700 + 0.307031i
\(344\) 3.04933 + 1.76053i 0.164409 + 0.0949214i
\(345\) 0 0
\(346\) −1.72121 + 0.993738i −0.0925326 + 0.0534237i
\(347\) −19.7453 + 11.3999i −1.05998 + 0.611981i −0.925427 0.378926i \(-0.876294\pi\)
−0.134554 + 0.990906i \(0.542960\pi\)
\(348\) 0 0
\(349\) −2.46389 1.42253i −0.131889 0.0761461i 0.432604 0.901584i \(-0.357595\pi\)
−0.564493 + 0.825438i \(0.690928\pi\)
\(350\) −1.25521 0.559901i −0.0670936 0.0299279i
\(351\) 0 0
\(352\) −5.67667 −0.302568
\(353\) 3.57212 6.18709i 0.190125 0.329306i −0.755167 0.655533i \(-0.772444\pi\)
0.945291 + 0.326227i \(0.105777\pi\)
\(354\) 0 0
\(355\) −9.19856 + 5.31079i −0.488209 + 0.281868i
\(356\) 0.580529 + 1.00551i 0.0307680 + 0.0532917i
\(357\) 0 0
\(358\) −4.15561 + 7.19773i −0.219631 + 0.380412i
\(359\) 11.6037i 0.612421i 0.951964 + 0.306210i \(0.0990611\pi\)
−0.951964 + 0.306210i \(0.900939\pi\)
\(360\) 0 0
\(361\) 17.7019 0.931682
\(362\) 7.72706 13.3837i 0.406125 0.703429i
\(363\) 0 0
\(364\) 0.472486 + 4.52570i 0.0247650 + 0.237211i
\(365\) 10.8695 6.27554i 0.568938 0.328477i
\(366\) 0 0
\(367\) 6.78525 + 3.91747i 0.354187 + 0.204490i 0.666528 0.745480i \(-0.267780\pi\)
−0.312341 + 0.949970i \(0.601113\pi\)
\(368\) 3.67509i 0.191577i
\(369\) 0 0
\(370\) 21.6088i 1.12339i
\(371\) 0 0
\(372\) 0 0
\(373\) −12.8339 22.2289i −0.664512 1.15097i −0.979417 0.201845i \(-0.935306\pi\)
0.314905 0.949123i \(-0.398027\pi\)
\(374\) 5.02053 + 8.69581i 0.259605 + 0.449650i
\(375\) 0 0
\(376\) −10.2277 5.90494i −0.527451 0.304524i
\(377\) −7.14702 −0.368091
\(378\) 0 0
\(379\) −15.1045 −0.775868 −0.387934 0.921687i \(-0.626811\pi\)
−0.387934 + 0.921687i \(0.626811\pi\)
\(380\) −2.31806 1.33834i −0.118914 0.0686551i
\(381\) 0 0
\(382\) −6.16904 10.6851i −0.315636 0.546697i
\(383\) −0.763322 1.32211i −0.0390040 0.0675568i 0.845864 0.533398i \(-0.179085\pi\)
−0.884868 + 0.465841i \(0.845752\pi\)
\(384\) 0 0
\(385\) 28.5607 20.7202i 1.45559 1.05600i
\(386\) 4.39388i 0.223643i
\(387\) 0 0
\(388\) 4.59035i 0.233039i
\(389\) −12.8948 7.44483i −0.653794 0.377468i 0.136115 0.990693i \(-0.456538\pi\)
−0.789908 + 0.613225i \(0.789872\pi\)
\(390\) 0 0
\(391\) 5.62969 3.25030i 0.284706 0.164375i
\(392\) −6.65438 2.17238i −0.336097 0.109722i
\(393\) 0 0
\(394\) −5.44325 + 9.42799i −0.274227 + 0.474975i
\(395\) −30.6085 −1.54008
\(396\) 0 0
\(397\) 28.7869i 1.44478i 0.691488 + 0.722388i \(0.256955\pi\)
−0.691488 + 0.722388i \(0.743045\pi\)
\(398\) −13.7832 + 23.8733i −0.690892 + 1.19666i
\(399\) 0 0
\(400\) −0.259741 0.449885i −0.0129871 0.0224942i
\(401\) 33.0592 19.0868i 1.65090 0.953147i 0.674196 0.738552i \(-0.264490\pi\)
0.976703 0.214595i \(-0.0688431\pi\)
\(402\) 0 0
\(403\) −7.19773 + 12.4668i −0.358544 + 0.621017i
\(404\) −6.62310 −0.329511
\(405\) 0 0
\(406\) 4.47894 10.0411i 0.222286 0.498329i
\(407\) −45.2173 26.1062i −2.24134 1.29404i
\(408\) 0 0
\(409\) 6.03355 3.48347i 0.298340 0.172247i −0.343357 0.939205i \(-0.611564\pi\)
0.641697 + 0.766958i \(0.278231\pi\)
\(410\) −16.2650 + 9.39060i −0.803271 + 0.463769i
\(411\) 0 0
\(412\) −5.07471 2.92989i −0.250013 0.144345i
\(413\) 2.40314 5.38745i 0.118251 0.265099i
\(414\) 0 0
\(415\) −29.4750 −1.44687
\(416\) −0.859925 + 1.48943i −0.0421613 + 0.0730255i
\(417\) 0 0
\(418\) 5.60106 3.23377i 0.273957 0.158169i
\(419\) 17.4232 + 30.1778i 0.851177 + 1.47428i 0.880146 + 0.474702i \(0.157444\pi\)
−0.0289690 + 0.999580i \(0.509222\pi\)
\(420\) 0 0
\(421\) 2.84597 4.92936i 0.138704 0.240242i −0.788302 0.615288i \(-0.789040\pi\)
0.927006 + 0.375046i \(0.122373\pi\)
\(422\) 10.3112i 0.501942i
\(423\) 0 0
\(424\) 0 0
\(425\) −0.459437 + 0.795769i −0.0222860 + 0.0386005i
\(426\) 0 0
\(427\) 2.47244 + 23.6822i 0.119650 + 1.14606i
\(428\) −4.08386 + 2.35782i −0.197401 + 0.113969i
\(429\) 0 0
\(430\) −7.16396 4.13611i −0.345477 0.199461i
\(431\) 30.2936i 1.45919i −0.683880 0.729595i \(-0.739709\pi\)
0.683880 0.729595i \(-0.260291\pi\)
\(432\) 0 0
\(433\) 23.6094i 1.13459i 0.823513 + 0.567297i \(0.192011\pi\)
−0.823513 + 0.567297i \(0.807989\pi\)
\(434\) −13.0043 17.9251i −0.624226 0.860432i
\(435\) 0 0
\(436\) 2.11835 + 3.66908i 0.101450 + 0.175717i
\(437\) −2.09355 3.62614i −0.100148 0.173462i
\(438\) 0 0
\(439\) 21.6681 + 12.5101i 1.03416 + 0.597075i 0.918175 0.396175i \(-0.129663\pi\)
0.115989 + 0.993250i \(0.462996\pi\)
\(440\) 13.3365 0.635794
\(441\) 0 0
\(442\) 3.04212 0.144699
\(443\) 19.9446 + 11.5150i 0.947595 + 0.547094i 0.892333 0.451377i \(-0.149067\pi\)
0.0552622 + 0.998472i \(0.482401\pi\)
\(444\) 0 0
\(445\) −1.36387 2.36229i −0.0646537 0.111983i
\(446\) −3.60456 6.24329i −0.170681 0.295628i
\(447\) 0 0
\(448\) −1.55364 2.14154i −0.0734028 0.101178i
\(449\) 15.9028i 0.750501i 0.926923 + 0.375251i \(0.122443\pi\)
−0.926923 + 0.375251i \(0.877557\pi\)
\(450\) 0 0
\(451\) 45.3804i 2.13688i
\(452\) −5.91693 3.41614i −0.278309 0.160682i
\(453\) 0 0
\(454\) −11.0470 + 6.37800i −0.518462 + 0.299334i
\(455\) −1.11004 10.6325i −0.0520394 0.498458i
\(456\) 0 0
\(457\) 2.83307 4.90702i 0.132525 0.229541i −0.792124 0.610360i \(-0.791025\pi\)
0.924649 + 0.380819i \(0.124358\pi\)
\(458\) 4.49418 0.209999
\(459\) 0 0
\(460\) 8.63411i 0.402567i
\(461\) 15.7292 27.2438i 0.732582 1.26887i −0.223194 0.974774i \(-0.571648\pi\)
0.955776 0.294095i \(-0.0950183\pi\)
\(462\) 0 0
\(463\) 4.55148 + 7.88340i 0.211525 + 0.366373i 0.952192 0.305500i \(-0.0988236\pi\)
−0.740667 + 0.671873i \(0.765490\pi\)
\(464\) 3.59886 2.07781i 0.167073 0.0964597i
\(465\) 0 0
\(466\) −1.07702 + 1.86545i −0.0498918 + 0.0864152i
\(467\) 30.3032 1.40226 0.701132 0.713032i \(-0.252678\pi\)
0.701132 + 0.713032i \(0.252678\pi\)
\(468\) 0 0
\(469\) 11.7171 26.2678i 0.541045 1.21293i
\(470\) 24.0284 + 13.8728i 1.10835 + 0.639906i
\(471\) 0 0
\(472\) 1.93094 1.11483i 0.0888788 0.0513142i
\(473\) 17.3100 9.99395i 0.795916 0.459522i
\(474\) 0 0
\(475\) 0.512563 + 0.295928i 0.0235180 + 0.0135781i
\(476\) −1.90645 + 4.27396i −0.0873821 + 0.195897i
\(477\) 0 0
\(478\) 10.1419 0.463881
\(479\) 2.33143 4.03816i 0.106526 0.184508i −0.807835 0.589409i \(-0.799361\pi\)
0.914361 + 0.404901i \(0.132694\pi\)
\(480\) 0 0
\(481\) −13.6994 + 7.90935i −0.624639 + 0.360636i
\(482\) 5.27404 + 9.13490i 0.240226 + 0.416083i
\(483\) 0 0
\(484\) −10.6123 + 18.3810i −0.482377 + 0.835501i
\(485\) 10.7844i 0.489693i
\(486\) 0 0
\(487\) −19.4821 −0.882818 −0.441409 0.897306i \(-0.645521\pi\)
−0.441409 + 0.897306i \(0.645521\pi\)
\(488\) −4.49985 + 7.79396i −0.203699 + 0.352816i
\(489\) 0 0
\(490\) 15.6335 + 5.10370i 0.706250 + 0.230562i
\(491\) 17.7437 10.2443i 0.800762 0.462320i −0.0429758 0.999076i \(-0.513684\pi\)
0.843737 + 0.536756i \(0.180351\pi\)
\(492\) 0 0
\(493\) −6.36577 3.67528i −0.286700 0.165526i
\(494\) 1.95946i 0.0881602i
\(495\) 0 0
\(496\) 8.37019i 0.375832i
\(497\) 9.68203 7.02412i 0.434298 0.315075i
\(498\) 0 0
\(499\) 5.12598 + 8.87845i 0.229470 + 0.397454i 0.957651 0.287931i \(-0.0929673\pi\)
−0.728181 + 0.685385i \(0.759634\pi\)
\(500\) −5.26317 9.11608i −0.235376 0.407683i
\(501\) 0 0
\(502\) 25.3749 + 14.6502i 1.13254 + 0.653872i
\(503\) 14.5521 0.648845 0.324422 0.945912i \(-0.394830\pi\)
0.324422 + 0.945912i \(0.394830\pi\)
\(504\) 0 0
\(505\) 15.5600 0.692412
\(506\) 18.0673 + 10.4311i 0.803188 + 0.463721i
\(507\) 0 0
\(508\) −3.33834 5.78217i −0.148115 0.256542i
\(509\) 16.6617 + 28.8589i 0.738517 + 1.27915i 0.953163 + 0.302457i \(0.0978068\pi\)
−0.214646 + 0.976692i \(0.568860\pi\)
\(510\) 0 0
\(511\) −11.4408 + 8.30010i −0.506113 + 0.367175i
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) 7.62860i 0.336483i
\(515\) 11.9223 + 6.88335i 0.525360 + 0.303317i
\(516\) 0 0
\(517\) −58.0591 + 33.5204i −2.55343 + 1.47423i
\(518\) −2.52685 24.2034i −0.111023 1.06343i
\(519\) 0 0
\(520\) 2.02027 3.49921i 0.0885947 0.153451i
\(521\) 6.53925 0.286490 0.143245 0.989687i \(-0.454246\pi\)
0.143245 + 0.989687i \(0.454246\pi\)
\(522\) 0 0
\(523\) 0.786858i 0.0344069i −0.999852 0.0172034i \(-0.994524\pi\)
0.999852 0.0172034i \(-0.00547630\pi\)
\(524\) 3.73653 6.47185i 0.163231 0.282724i
\(525\) 0 0
\(526\) 6.09281 + 10.5531i 0.265659 + 0.460135i
\(527\) −12.8219 + 7.40271i −0.558530 + 0.322467i
\(528\) 0 0
\(529\) −4.74685 + 8.22178i −0.206385 + 0.357469i
\(530\) 0 0
\(531\) 0 0
\(532\) 2.75290 + 1.22797i 0.119353 + 0.0532391i
\(533\) −11.9068 6.87440i −0.515741 0.297763i
\(534\) 0 0
\(535\) 9.59445 5.53936i 0.414804 0.239487i
\(536\) 9.41477 5.43562i 0.406656 0.234783i
\(537\) 0 0
\(538\) −2.40264 1.38717i −0.103585 0.0598050i
\(539\) −29.5671 + 26.5479i −1.27354 + 1.14350i
\(540\) 0 0
\(541\) 5.60454 0.240958 0.120479 0.992716i \(-0.461557\pi\)
0.120479 + 0.992716i \(0.461557\pi\)
\(542\) 1.60396 2.77815i 0.0688961 0.119332i
\(543\) 0 0
\(544\) −1.53185 + 0.884414i −0.0656775 + 0.0379189i
\(545\) −4.97675 8.61999i −0.213181 0.369240i
\(546\) 0 0
\(547\) −6.91456 + 11.9764i −0.295645 + 0.512073i −0.975135 0.221612i \(-0.928868\pi\)
0.679489 + 0.733685i \(0.262201\pi\)
\(548\) 7.98789i 0.341226i
\(549\) 0 0
\(550\) −2.94893 −0.125743
\(551\) −2.36729 + 4.10026i −0.100850 + 0.174677i
\(552\) 0 0
\(553\) 34.2837 3.57924i 1.45789 0.152205i
\(554\) −8.73047 + 5.04054i −0.370922 + 0.214152i
\(555\) 0 0
\(556\) 17.9792 + 10.3803i 0.762488 + 0.440223i
\(557\) 27.8233i 1.17891i 0.807800 + 0.589456i \(0.200658\pi\)
−0.807800 + 0.589456i \(0.799342\pi\)
\(558\) 0 0
\(559\) 6.05569i 0.256128i
\(560\) 3.65007 + 5.03124i 0.154243 + 0.212609i
\(561\) 0 0
\(562\) −2.43641 4.21999i −0.102774 0.178009i
\(563\) −12.2650 21.2436i −0.516909 0.895312i −0.999807 0.0196359i \(-0.993749\pi\)
0.482898 0.875676i \(-0.339584\pi\)
\(564\) 0 0
\(565\) 13.9010 + 8.02574i 0.584819 + 0.337645i
\(566\) −2.81781 −0.118441
\(567\) 0 0
\(568\) 4.52106 0.189699
\(569\) 23.4762 + 13.5540i 0.984172 + 0.568212i 0.903527 0.428531i \(-0.140969\pi\)
0.0806449 + 0.996743i \(0.474302\pi\)
\(570\) 0 0
\(571\) 14.9177 + 25.8382i 0.624287 + 1.08130i 0.988678 + 0.150051i \(0.0479438\pi\)
−0.364391 + 0.931246i \(0.618723\pi\)
\(572\) 4.88151 + 8.45502i 0.204106 + 0.353522i
\(573\) 0 0
\(574\) 17.1199 12.4201i 0.714570 0.518406i
\(575\) 1.90915i 0.0796169i
\(576\) 0 0
\(577\) 28.1666i 1.17259i −0.810097 0.586296i \(-0.800585\pi\)
0.810097 0.586296i \(-0.199415\pi\)
\(578\) −12.0129 6.93562i −0.499669 0.288484i
\(579\) 0 0
\(580\) −8.45502 + 4.88151i −0.351076 + 0.202694i
\(581\) 33.0141 3.44670i 1.36965 0.142993i
\(582\) 0 0
\(583\) 0 0
\(584\) −5.34234 −0.221068
\(585\) 0 0
\(586\) 8.11389i 0.335182i
\(587\) −4.95928 + 8.58973i −0.204692 + 0.354536i −0.950034 0.312145i \(-0.898952\pi\)
0.745343 + 0.666681i \(0.232286\pi\)
\(588\) 0 0
\(589\) 4.76816 + 8.25870i 0.196469 + 0.340294i
\(590\) −4.53648 + 2.61914i −0.186764 + 0.107828i
\(591\) 0 0
\(592\) 4.59886 7.96547i 0.189012 0.327379i
\(593\) 4.69872 0.192953 0.0964766 0.995335i \(-0.469243\pi\)
0.0964766 + 0.995335i \(0.469243\pi\)
\(594\) 0 0
\(595\) 4.47894 10.0411i 0.183619 0.411643i
\(596\) 1.03726 + 0.598865i 0.0424880 + 0.0245305i
\(597\) 0 0
\(598\) 5.47381 3.16030i 0.223841 0.129234i
\(599\) −12.7309 + 7.35019i −0.520170 + 0.300320i −0.737004 0.675888i \(-0.763760\pi\)
0.216834 + 0.976208i \(0.430427\pi\)
\(600\) 0 0
\(601\) 16.2923 + 9.40634i 0.664575 + 0.383693i 0.794018 0.607894i \(-0.207986\pi\)
−0.129443 + 0.991587i \(0.541319\pi\)
\(602\) 8.50781 + 3.79502i 0.346752 + 0.154673i
\(603\) 0 0
\(604\) −15.2246 −0.619480
\(605\) 24.9321 43.1836i 1.01363 1.75566i
\(606\) 0 0
\(607\) 10.9051 6.29608i 0.442625 0.255550i −0.262085 0.965045i \(-0.584410\pi\)
0.704711 + 0.709495i \(0.251077\pi\)
\(608\) 0.569660 + 0.986680i 0.0231028 + 0.0400152i
\(609\) 0 0
\(610\) 10.5718 18.3108i 0.428038 0.741383i
\(611\) 20.3112i 0.821704i
\(612\) 0 0
\(613\) −9.82017 −0.396633 −0.198317 0.980138i \(-0.563547\pi\)
−0.198317 + 0.980138i \(0.563547\pi\)
\(614\) −5.44981 + 9.43935i −0.219937 + 0.380941i
\(615\) 0 0
\(616\) −14.9379 + 1.55953i −0.601864 + 0.0628351i
\(617\) 3.25158 1.87730i 0.130904 0.0755772i −0.433118 0.901337i \(-0.642587\pi\)
0.564022 + 0.825760i \(0.309253\pi\)
\(618\) 0 0
\(619\) 9.56902 + 5.52468i 0.384611 + 0.222055i 0.679823 0.733376i \(-0.262057\pi\)
−0.295211 + 0.955432i \(0.595390\pi\)
\(620\) 19.6646i 0.789748i
\(621\) 0 0
\(622\) 8.23637i 0.330248i
\(623\) 1.80387 + 2.48645i 0.0722706 + 0.0996176i
\(624\) 0 0
\(625\) 13.6638 + 23.6664i 0.546551 + 0.946654i
\(626\) −16.9011 29.2736i −0.675505 1.17001i
\(627\) 0 0
\(628\) 8.68358 + 5.01347i 0.346513 + 0.200059i
\(629\) −16.2692 −0.648696
\(630\) 0 0
\(631\) 19.4921 0.775969 0.387984 0.921666i \(-0.373171\pi\)
0.387984 + 0.921666i \(0.373171\pi\)
\(632\) 11.2830 + 6.51422i 0.448812 + 0.259122i
\(633\) 0 0
\(634\) −3.36545 5.82913i −0.133659 0.231504i
\(635\) 7.84294 + 13.5844i 0.311238 + 0.539080i
\(636\) 0 0
\(637\) 2.48665 + 11.7793i 0.0985245 + 0.466714i
\(638\) 23.5900i 0.933938i
\(639\) 0 0
\(640\) 2.34936i 0.0928665i
\(641\) 22.6669 + 13.0868i 0.895290 + 0.516896i 0.875669 0.482912i \(-0.160421\pi\)
0.0196208 + 0.999807i \(0.493754\pi\)
\(642\) 0 0
\(643\) 9.50955 5.49034i 0.375020 0.216518i −0.300629 0.953741i \(-0.597197\pi\)
0.675649 + 0.737223i \(0.263863\pi\)
\(644\) 1.00964 + 9.67082i 0.0397854 + 0.381084i
\(645\) 0 0
\(646\) 1.00763 1.74527i 0.0396447 0.0686666i
\(647\) −32.0126 −1.25855 −0.629273 0.777185i \(-0.716647\pi\)
−0.629273 + 0.777185i \(0.716647\pi\)
\(648\) 0 0
\(649\) 12.6570i 0.496833i
\(650\) −0.446715 + 0.773734i −0.0175216 + 0.0303483i
\(651\) 0 0
\(652\) 6.00158 + 10.3950i 0.235040 + 0.407101i
\(653\) −19.3686 + 11.1825i −0.757952 + 0.437604i −0.828560 0.559900i \(-0.810839\pi\)
0.0706080 + 0.997504i \(0.477506\pi\)
\(654\) 0 0
\(655\) −8.77843 + 15.2047i −0.343002 + 0.594097i
\(656\) 7.99419 0.312121
\(657\) 0 0
\(658\) −28.5358 12.7288i −1.11244 0.496219i
\(659\) 19.2546 + 11.1166i 0.750053 + 0.433043i 0.825713 0.564091i \(-0.190773\pi\)
−0.0756603 + 0.997134i \(0.524106\pi\)
\(660\) 0 0
\(661\) −9.13646 + 5.27494i −0.355367 + 0.205171i −0.667047 0.745016i \(-0.732442\pi\)
0.311679 + 0.950187i \(0.399108\pi\)
\(662\) 27.7621 16.0284i 1.07900 0.622963i
\(663\) 0 0
\(664\) 10.8651 + 6.27298i 0.421649 + 0.243439i
\(665\) −6.46754 2.88493i −0.250801 0.111873i
\(666\) 0 0
\(667\) −15.2723 −0.591344
\(668\) 8.57472 14.8518i 0.331766 0.574635i
\(669\) 0 0
\(670\) −22.1187 + 12.7702i −0.854519 + 0.493357i
\(671\) 25.5442 + 44.2438i 0.986121 + 1.70801i
\(672\) 0 0
\(673\) 9.93562 17.2090i 0.382990 0.663358i −0.608498 0.793555i \(-0.708228\pi\)
0.991488 + 0.130197i \(0.0415610\pi\)
\(674\) 24.2246i 0.933096i
\(675\) 0 0
\(676\) −10.0421 −0.386235
\(677\) 7.96449 13.7949i 0.306100 0.530181i −0.671405 0.741090i \(-0.734309\pi\)
0.977506 + 0.210909i \(0.0676424\pi\)
\(678\) 0 0
\(679\) −1.26108 12.0793i −0.0483960 0.463560i
\(680\) 3.59886 2.07781i 0.138010 0.0796802i
\(681\) 0 0
\(682\) −41.1490 23.7574i −1.57568 0.909718i
\(683\) 19.0269i 0.728042i −0.931391 0.364021i \(-0.881404\pi\)
0.931391 0.364021i \(-0.118596\pi\)
\(684\) 0 0
\(685\) 18.7664i 0.717028i
\(686\) −18.1075 3.88839i −0.691346 0.148459i
\(687\) 0 0
\(688\) 1.76053 + 3.04933i 0.0671196 + 0.116254i
\(689\) 0 0
\(690\) 0 0
\(691\) 0.139477 + 0.0805273i 0.00530597 + 0.00306340i 0.502651 0.864490i \(-0.332358\pi\)
−0.497345 + 0.867553i \(0.665692\pi\)
\(692\) −1.98748 −0.0755525
\(693\) 0 0
\(694\) −22.7999 −0.865471
\(695\) −42.2396 24.3870i −1.60224 0.925053i
\(696\) 0 0
\(697\) −7.07017 12.2459i −0.267802 0.463847i
\(698\) −1.42253 2.46389i −0.0538434 0.0932595i
\(699\) 0 0
\(700\) −0.807090 1.11249i −0.0305051 0.0420482i
\(701\) 9.98234i 0.377028i 0.982071 + 0.188514i \(0.0603670\pi\)
−0.982071 + 0.188514i \(0.939633\pi\)
\(702\) 0 0
\(703\) 10.4792i 0.395229i
\(704\) −4.91614 2.83834i −0.185284 0.106974i
\(705\) 0 0
\(706\) 6.18709 3.57212i 0.232854 0.134438i
\(707\) −17.4283 + 1.81953i −0.655460 + 0.0684306i
\(708\) 0 0
\(709\) 12.1962 21.1244i 0.458036 0.793342i −0.540821 0.841138i \(-0.681886\pi\)
0.998857 + 0.0477959i \(0.0152197\pi\)
\(710\) −10.6216 −0.398621
\(711\) 0 0
\(712\) 1.16106i 0.0435125i
\(713\) −15.3806 + 26.6400i −0.576008 + 0.997676i
\(714\) 0 0
\(715\) −11.4684 19.8639i −0.428894 0.742867i
\(716\) −7.19773 + 4.15561i −0.268992 + 0.155302i
\(717\) 0 0
\(718\) −5.80186 + 10.0491i −0.216523 + 0.375030i
\(719\) 16.2692 0.606739 0.303370 0.952873i \(-0.401888\pi\)
0.303370 + 0.952873i \(0.401888\pi\)
\(720\) 0 0
\(721\) −14.1588 6.31570i −0.527300 0.235209i
\(722\) 15.3303 + 8.85097i 0.570536 + 0.329399i
\(723\) 0 0
\(724\) 13.3837 7.72706i 0.497400 0.287174i
\(725\) 1.86955 1.07938i 0.0694332 0.0400873i
\(726\) 0 0
\(727\) 20.6626 + 11.9296i 0.766335 + 0.442444i 0.831566 0.555427i \(-0.187445\pi\)
−0.0652306 + 0.997870i \(0.520778\pi\)
\(728\) −1.85366 + 4.15561i −0.0687013 + 0.154017i
\(729\) 0 0
\(730\) 12.5511 0.464536
\(731\) 3.11408 5.39374i 0.115178 0.199495i
\(732\) 0 0
\(733\) 10.6259 6.13486i 0.392476 0.226596i −0.290756 0.956797i \(-0.593907\pi\)
0.683233 + 0.730201i \(0.260574\pi\)
\(734\) 3.91747 + 6.78525i 0.144596 + 0.250448i
\(735\) 0 0
\(736\) −1.83755 + 3.18272i −0.0677329 + 0.117317i
\(737\) 61.7125i 2.27321i
\(738\) 0 0
\(739\) 41.8891 1.54092 0.770459 0.637490i \(-0.220027\pi\)
0.770459 + 0.637490i \(0.220027\pi\)
\(740\) −10.8044 + 18.7137i −0.397177 + 0.687931i
\(741\) 0 0
\(742\) 0 0
\(743\) −43.9160 + 25.3549i −1.61112 + 0.930182i −0.622011 + 0.783008i \(0.713684\pi\)
−0.989111 + 0.147173i \(0.952982\pi\)
\(744\) 0 0
\(745\) −2.43690 1.40695i −0.0892813 0.0515466i
\(746\) 25.6677i 0.939762i
\(747\) 0 0
\(748\) 10.0411i 0.367137i
\(749\) −10.0987 + 7.32642i −0.368999 + 0.267701i
\(750\) 0 0
\(751\) 16.3683 + 28.3508i 0.597289 + 1.03454i 0.993219 + 0.116255i \(0.0370890\pi\)
−0.395930 + 0.918281i \(0.629578\pi\)
\(752\) −5.90494 10.2277i −0.215331 0.372964i
\(753\) 0 0
\(754\) −6.18951 3.57351i −0.225408 0.130140i
\(755\) 35.7680 1.30173
\(756\) 0 0
\(757\) −17.9255 −0.651512 −0.325756 0.945454i \(-0.605619\pi\)
−0.325756 + 0.945454i \(0.605619\pi\)
\(758\) −13.0809 7.55227i −0.475120 0.274311i
\(759\) 0 0
\(760\) −1.33834 2.31806i −0.0485465 0.0840850i
\(761\) −21.8509 37.8469i −0.792096 1.37195i −0.924667 0.380777i \(-0.875657\pi\)
0.132571 0.991174i \(-0.457677\pi\)
\(762\) 0 0
\(763\) 6.58231 + 9.07305i 0.238296 + 0.328466i
\(764\) 12.3381i 0.446376i
\(765\) 0 0
\(766\) 1.52664i 0.0551599i
\(767\) −3.32093 1.91734i −0.119912 0.0692311i
\(768\) 0 0
\(769\) −37.0864 + 21.4118i −1.33737 + 0.772131i −0.986417 0.164262i \(-0.947476\pi\)
−0.350953 + 0.936393i \(0.614142\pi\)
\(770\) 35.0944 3.66388i 1.26471 0.132037i
\(771\) 0 0
\(772\) 2.19694 3.80521i 0.0790696 0.136953i
\(773\) 21.6051 0.777080 0.388540 0.921432i \(-0.372980\pi\)
0.388540 + 0.921432i \(0.372980\pi\)
\(774\) 0 0
\(775\) 4.34816i 0.156191i
\(776\) 2.29517 3.97536i 0.0823919 0.142707i
\(777\) 0 0
\(778\) −7.44483 12.8948i −0.266910 0.462302i
\(779\) −7.88771 + 4.55397i −0.282606 + 0.163163i
\(780\) 0 0
\(781\) 12.8323 22.2262i 0.459175 0.795315i
\(782\) 6.50061 0.232461
\(783\) 0 0
\(784\) −4.67667 5.20853i −0.167024 0.186019i
\(785\) −20.4008 11.7784i −0.728137 0.420390i
\(786\) 0 0
\(787\) −44.4307 + 25.6521i −1.58378 + 0.914398i −0.589484 + 0.807780i \(0.700669\pi\)
−0.994300 + 0.106618i \(0.965998\pi\)
\(788\) −9.42799 + 5.44325i −0.335858 + 0.193908i
\(789\) 0 0
\(790\) −26.5077 15.3042i −0.943102 0.544500i
\(791\) −16.5086 7.36387i −0.586978 0.261829i
\(792\) 0 0
\(793\) 15.4781 0.549644
\(794\) −14.3935 + 24.9302i −0.510805 + 0.884740i
\(795\) 0 0
\(796\) −23.8733 + 13.7832i −0.846166 + 0.488534i
\(797\) 0.899094 + 1.55728i 0.0318476 + 0.0551616i 0.881510 0.472166i \(-0.156528\pi\)
−0.849662 + 0.527327i \(0.823194\pi\)
\(798\) 0 0
\(799\) −10.4448 + 18.0910i −0.369512 + 0.640013i
\(800\) 0.519482i 0.0183665i
\(801\) 0 0
\(802\) 38.1735 1.34795
\(803\) −15.1634 + 26.2637i −0.535103 + 0.926826i
\(804\) 0 0
\(805\) −2.37201 22.7202i −0.0836023 0.800783i
\(806\) −12.4668 + 7.19773i −0.439125 + 0.253529i
\(807\) 0 0
\(808\) −5.73577 3.31155i −0.201784 0.116500i
\(809\) 40.6883i 1.43052i 0.698857 + 0.715262i \(0.253692\pi\)
−0.698857 + 0.715262i \(0.746308\pi\)
\(810\) 0 0
\(811\) 0.378710i 0.0132983i −0.999978 0.00664916i \(-0.997883\pi\)
0.999978 0.00664916i \(-0.00211651\pi\)
\(812\) 8.89940 6.45634i 0.312308 0.226573i
\(813\) 0 0
\(814\) −26.1062 45.2173i −0.915023 1.58487i
\(815\) −14.0999 24.4217i −0.493896 0.855453i
\(816\) 0 0
\(817\) −3.47416 2.00581i −0.121545 0.0701743i
\(818\) 6.96694 0.243593
\(819\) 0 0
\(820\) −18.7812 −0.655868
\(821\) −11.4968 6.63771i −0.401243 0.231658i 0.285777 0.958296i \(-0.407748\pi\)
−0.687020 + 0.726638i \(0.741082\pi\)
\(822\) 0 0
\(823\) −13.8711 24.0255i −0.483517 0.837476i 0.516304 0.856405i \(-0.327308\pi\)
−0.999821 + 0.0189295i \(0.993974\pi\)
\(824\) −2.92989 5.07471i −0.102067 0.176786i
\(825\) 0 0
\(826\) 4.77491 3.46410i 0.166140 0.120531i
\(827\) 27.7183i 0.963859i 0.876210 + 0.481929i \(0.160064\pi\)
−0.876210 + 0.481929i \(0.839936\pi\)
\(828\) 0 0
\(829\) 42.7361i 1.48429i −0.670242 0.742143i \(-0.733810\pi\)
0.670242 0.742143i \(-0.266190\pi\)
\(830\) −25.5261 14.7375i −0.886023 0.511545i
\(831\) 0 0
\(832\) −1.48943 + 0.859925i −0.0516368 + 0.0298125i
\(833\) −3.84257 + 11.7705i −0.133137 + 0.407822i
\(834\) 0 0
\(835\) −20.1451 + 34.8923i −0.697149 + 1.20750i
\(836\) 6.46754 0.223685
\(837\) 0 0
\(838\) 34.8463i 1.20375i
\(839\) 1.92438 3.33313i 0.0664370 0.115072i −0.830894 0.556431i \(-0.812170\pi\)
0.897331 + 0.441359i \(0.145504\pi\)
\(840\) 0 0
\(841\) −5.86545 10.1593i −0.202257 0.350319i
\(842\) 4.92936 2.84597i 0.169877 0.0980785i
\(843\) 0 0
\(844\) −5.15561 + 8.92978i −0.177463 + 0.307376i
\(845\) 23.5925 0.811608
\(846\) 0 0
\(847\) −22.8760 + 51.2842i −0.786028 + 1.76215i
\(848\) 0 0
\(849\) 0 0
\(850\) −0.795769 + 0.459437i −0.0272946 + 0.0157586i
\(851\) −29.2738 + 16.9013i −1.00349 + 0.579368i
\(852\) 0 0
\(853\) −26.3470 15.2114i −0.902103 0.520830i −0.0242213 0.999707i \(-0.507711\pi\)
−0.877882 + 0.478877i \(0.841044\pi\)
\(854\) −9.69992 + 21.7456i −0.331924 + 0.744121i
\(855\) 0 0
\(856\) −4.71563 −0.161177
\(857\) −19.4657 + 33.7156i −0.664937 + 1.15170i 0.314366 + 0.949302i \(0.398208\pi\)
−0.979303 + 0.202402i \(0.935125\pi\)
\(858\) 0 0
\(859\) 11.5922 6.69275i 0.395520 0.228354i −0.289029 0.957320i \(-0.593332\pi\)
0.684549 + 0.728967i \(0.259999\pi\)
\(860\) −4.13611 7.16396i −0.141040 0.244289i
\(861\) 0 0
\(862\) 15.1468 26.2350i 0.515901 0.893567i
\(863\) 21.7219i 0.739424i −0.929146 0.369712i \(-0.879456\pi\)
0.929146 0.369712i \(-0.120544\pi\)
\(864\) 0 0
\(865\) 4.66929 0.158761
\(866\) −11.8047 + 20.4463i −0.401139 + 0.694794i
\(867\) 0 0
\(868\) −2.29950 22.0257i −0.0780502 0.747602i
\(869\) 64.0496 36.9791i 2.17273 1.25443i
\(870\) 0 0
\(871\) −16.1920 9.34845i −0.548645 0.316760i
\(872\) 4.23669i 0.143473i
\(873\) 0 0
\(874\) 4.18711i 0.141631i
\(875\) −16.3542 22.5426i −0.552872 0.762078i
\(876\) 0 0
\(877\) −0.196152 0.339746i −0.00662360 0.0114724i 0.862695 0.505725i \(-0.168775\pi\)
−0.869318 + 0.494253i \(0.835442\pi\)
\(878\) 12.5101 + 21.6681i 0.422196 + 0.731265i
\(879\) 0 0
\(880\) 11.5498 + 6.66826i 0.389343 + 0.224787i
\(881\) −43.3363 −1.46004 −0.730018 0.683427i \(-0.760489\pi\)
−0.730018 + 0.683427i \(0.760489\pi\)
\(882\) 0 0
\(883\) 2.17403 0.0731618 0.0365809 0.999331i \(-0.488353\pi\)
0.0365809 + 0.999331i \(0.488353\pi\)
\(884\) 2.63455 + 1.52106i 0.0886096 + 0.0511588i
\(885\) 0 0
\(886\) 11.5150 + 19.9446i 0.386854 + 0.670051i
\(887\) 5.72215 + 9.91105i 0.192131 + 0.332781i 0.945956 0.324294i \(-0.105127\pi\)
−0.753825 + 0.657075i \(0.771793\pi\)
\(888\) 0 0
\(889\) −10.3732 14.2984i −0.347905 0.479551i
\(890\) 2.72774i 0.0914341i
\(891\) 0 0
\(892\) 7.20913i 0.241379i
\(893\) 11.6526 + 6.72762i 0.389939 + 0.225131i
\(894\) 0 0
\(895\) 16.9100 9.76302i 0.565240 0.326342i
\(896\) −0.274725 2.63145i −0.00917793 0.0879106i
\(897\) 0 0
\(898\) −7.95142 + 13.7723i −0.265342 + 0.459586i
\(899\) 34.7832 1.16009
\(900\) 0 0
\(901\) 0 0
\(902\) 22.6902 39.3006i 0.755501 1.30857i
\(903\) 0 0
\(904\) −3.41614 5.91693i −0.113619 0.196794i
\(905\) −31.4430 + 18.1536i −1.04520 + 0.603447i
\(906\) 0 0
\(907\) 26.9446 46.6694i 0.894680 1.54963i 0.0604797 0.998169i \(-0.480737\pi\)
0.834200 0.551462i \(-0.185930\pi\)
\(908\) −12.7560 −0.423323
\(909\) 0 0
\(910\) 4.35492 9.76302i 0.144364 0.323641i
\(911\) 7.00460 + 4.04411i 0.232073 + 0.133987i 0.611528 0.791223i \(-0.290555\pi\)
−0.379455 + 0.925210i \(0.623889\pi\)
\(912\) 0 0
\(913\) 61.6777 35.6097i 2.04124 1.17851i
\(914\) 4.90702 2.83307i 0.162310 0.0937096i
\(915\) 0 0
\(916\) 3.89208 + 2.24709i 0.128598 + 0.0742460i
\(917\) 8.05450 18.0569i 0.265983 0.596290i
\(918\) 0 0
\(919\) 25.6751 0.846943 0.423472 0.905909i \(-0.360811\pi\)
0.423472 + 0.905909i \(0.360811\pi\)
\(920\) 4.31705 7.47736i 0.142329 0.246521i
\(921\) 0 0
\(922\) 27.2438 15.7292i 0.897226 0.518014i
\(923\) −3.88777 6.73382i −0.127968 0.221646i
\(924\) 0 0
\(925\) 2.38903 4.13792i 0.0785507 0.136054i
\(926\) 9.10296i 0.299142i
\(927\) 0 0
\(928\) 4.15561 0.136415
\(929\) −5.42618 + 9.39842i −0.178027 + 0.308352i −0.941205 0.337837i \(-0.890305\pi\)
0.763177 + 0.646189i \(0.223638\pi\)
\(930\) 0 0
\(931\) 7.58147 + 2.47504i 0.248473 + 0.0811161i
\(932\) −1.86545 + 1.07702i −0.0611048 + 0.0352789i
\(933\) 0 0
\(934\) 26.2433 + 15.1516i 0.858708 + 0.495775i
\(935\) 23.5900i 0.771477i
\(936\) 0 0
\(937\) 0.458120i 0.0149661i −0.999972 0.00748306i \(-0.997618\pi\)
0.999972 0.00748306i \(-0.00238195\pi\)
\(938\) 23.2812 16.8900i 0.760158 0.551479i
\(939\) 0 0
\(940\) 13.8728 + 24.0284i 0.452482 + 0.783721i
\(941\) 3.68890 + 6.38937i 0.120255 + 0.208287i 0.919868 0.392228i \(-0.128296\pi\)
−0.799613 + 0.600515i \(0.794962\pi\)
\(942\) 0 0
\(943\) −25.4433 14.6897i −0.828548 0.478362i
\(944\) 2.22966 0.0725693
\(945\) 0 0
\(946\) 19.9879 0.649862
\(947\) 10.3846 + 5.99552i 0.337453 + 0.194828i 0.659145 0.752016i \(-0.270918\pi\)
−0.321692 + 0.946844i \(0.604252\pi\)
\(948\) 0 0
\(949\) 4.59401 + 7.95706i 0.149128 + 0.258297i
\(950\) 0.295928 + 0.512563i 0.00960118 + 0.0166297i
\(951\) 0 0
\(952\) −3.78802 + 2.74813i −0.122770 + 0.0890674i
\(953\) 58.6883i 1.90110i 0.310572 + 0.950550i \(0.399479\pi\)
−0.310572 + 0.950550i \(0.600521\pi\)
\(954\) 0 0
\(955\) 28.9866i 0.937983i
\(956\) 8.78317 + 5.07096i 0.284068 + 0.164007i
\(957\) 0 0
\(958\) 4.03816 2.33143i 0.130467 0.0753251i
\(959\) −2.19448 21.0197i −0.0708633 0.678763i
\(960\) 0 0
\(961\) 19.5300 33.8270i 0.630000 1.09119i
\(962\) −15.8187 −0.510016
\(963\) 0 0
\(964\) 10.5481i 0.339731i
\(965\) −5.16140 + 8.93981i −0.166151 + 0.287783i
\(966\) 0 0
\(967\) −3.37560 5.84671i −0.108552 0.188018i 0.806632 0.591054i \(-0.201288\pi\)
−0.915184 + 0.403037i \(0.867955\pi\)
\(968\) −18.3810 + 10.6123i −0.590789 + 0.341092i
\(969\) 0 0
\(970\) −5.39218 + 9.33953i −0.173133 + 0.299874i
\(971\) 6.40724 0.205618 0.102809 0.994701i \(-0.467217\pi\)
0.102809 + 0.994701i \(0.467217\pi\)
\(972\) 0 0
\(973\) 50.1631 + 22.3759i 1.60816 + 0.717338i
\(974\) −16.8720 9.74105i −0.540613 0.312123i
\(975\) 0 0
\(976\) −7.79396 + 4.49985i −0.249479 + 0.144037i
\(977\) −11.7769 + 6.79937i −0.376775 + 0.217531i −0.676414 0.736521i \(-0.736467\pi\)
0.299639 + 0.954053i \(0.403134\pi\)
\(978\) 0 0
\(979\) 5.70793 + 3.29547i 0.182426 + 0.105324i
\(980\) 10.9872 + 12.2367i 0.350972 + 0.390887i
\(981\) 0 0
\(982\) 20.4886 0.653819
\(983\) −11.3849 + 19.7192i −0.363122 + 0.628946i −0.988473 0.151398i \(-0.951623\pi\)
0.625351 + 0.780344i \(0.284956\pi\)
\(984\) 0 0
\(985\) 22.1497 12.7882i 0.705749 0.407464i
\(986\) −3.67528 6.36577i −0.117045 0.202728i
\(987\) 0 0
\(988\) 0.979729 1.69694i 0.0311693 0.0539869i
\(989\) 12.9402i 0.411475i
\(990\) 0 0
\(991\) −26.9905 −0.857383 −0.428691 0.903451i \(-0.641025\pi\)
−0.428691 + 0.903451i \(0.641025\pi\)
\(992\) 4.18509 7.24879i 0.132877 0.230149i
\(993\) 0 0
\(994\) 11.8969 1.24205i 0.377348 0.0393954i
\(995\) 56.0869 32.3818i 1.77807 1.02657i
\(996\) 0 0
\(997\) −16.7263 9.65694i −0.529728 0.305838i 0.211178 0.977448i \(-0.432270\pi\)
−0.740906 + 0.671609i \(0.765603\pi\)
\(998\) 10.2520i 0.324520i
\(999\) 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 378.2.m.a.251.6 16
3.2 odd 2 126.2.m.a.83.3 yes 16
4.3 odd 2 3024.2.cc.b.2897.2 16
7.2 even 3 2646.2.l.b.521.2 16
7.3 odd 6 2646.2.t.a.1979.2 16
7.4 even 3 2646.2.t.a.1979.3 16
7.5 odd 6 2646.2.l.b.521.3 16
7.6 odd 2 inner 378.2.m.a.251.7 16
9.2 odd 6 1134.2.d.a.1133.10 16
9.4 even 3 126.2.m.a.41.2 16
9.5 odd 6 inner 378.2.m.a.125.7 16
9.7 even 3 1134.2.d.a.1133.7 16
12.11 even 2 1008.2.cc.b.209.3 16
21.2 odd 6 882.2.l.a.227.7 16
21.5 even 6 882.2.l.a.227.6 16
21.11 odd 6 882.2.t.b.803.5 16
21.17 even 6 882.2.t.b.803.8 16
21.20 even 2 126.2.m.a.83.2 yes 16
28.27 even 2 3024.2.cc.b.2897.7 16
36.23 even 6 3024.2.cc.b.881.7 16
36.31 odd 6 1008.2.cc.b.545.6 16
63.4 even 3 882.2.l.a.509.2 16
63.5 even 6 2646.2.t.a.2285.3 16
63.13 odd 6 126.2.m.a.41.3 yes 16
63.20 even 6 1134.2.d.a.1133.15 16
63.23 odd 6 2646.2.t.a.2285.2 16
63.31 odd 6 882.2.l.a.509.3 16
63.32 odd 6 2646.2.l.b.1097.7 16
63.34 odd 6 1134.2.d.a.1133.2 16
63.40 odd 6 882.2.t.b.815.5 16
63.41 even 6 inner 378.2.m.a.125.6 16
63.58 even 3 882.2.t.b.815.8 16
63.59 even 6 2646.2.l.b.1097.6 16
84.83 odd 2 1008.2.cc.b.209.6 16
252.139 even 6 1008.2.cc.b.545.3 16
252.167 odd 6 3024.2.cc.b.881.2 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
126.2.m.a.41.2 16 9.4 even 3
126.2.m.a.41.3 yes 16 63.13 odd 6
126.2.m.a.83.2 yes 16 21.20 even 2
126.2.m.a.83.3 yes 16 3.2 odd 2
378.2.m.a.125.6 16 63.41 even 6 inner
378.2.m.a.125.7 16 9.5 odd 6 inner
378.2.m.a.251.6 16 1.1 even 1 trivial
378.2.m.a.251.7 16 7.6 odd 2 inner
882.2.l.a.227.6 16 21.5 even 6
882.2.l.a.227.7 16 21.2 odd 6
882.2.l.a.509.2 16 63.4 even 3
882.2.l.a.509.3 16 63.31 odd 6
882.2.t.b.803.5 16 21.11 odd 6
882.2.t.b.803.8 16 21.17 even 6
882.2.t.b.815.5 16 63.40 odd 6
882.2.t.b.815.8 16 63.58 even 3
1008.2.cc.b.209.3 16 12.11 even 2
1008.2.cc.b.209.6 16 84.83 odd 2
1008.2.cc.b.545.3 16 252.139 even 6
1008.2.cc.b.545.6 16 36.31 odd 6
1134.2.d.a.1133.2 16 63.34 odd 6
1134.2.d.a.1133.7 16 9.7 even 3
1134.2.d.a.1133.10 16 9.2 odd 6
1134.2.d.a.1133.15 16 63.20 even 6
2646.2.l.b.521.2 16 7.2 even 3
2646.2.l.b.521.3 16 7.5 odd 6
2646.2.l.b.1097.6 16 63.59 even 6
2646.2.l.b.1097.7 16 63.32 odd 6
2646.2.t.a.1979.2 16 7.3 odd 6
2646.2.t.a.1979.3 16 7.4 even 3
2646.2.t.a.2285.2 16 63.23 odd 6
2646.2.t.a.2285.3 16 63.5 even 6
3024.2.cc.b.881.2 16 252.167 odd 6
3024.2.cc.b.881.7 16 36.23 even 6
3024.2.cc.b.2897.2 16 4.3 odd 2
3024.2.cc.b.2897.7 16 28.27 even 2