Properties

Label 504.2.cj.a.37.4
Level $504$
Weight $2$
Character 504.37
Analytic conductor $4.024$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [504,2,Mod(37,504)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(504, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 3, 0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("504.37");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 504.cj (of order \(6\), degree \(2\), 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: \(4.02446026187\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: 8.0.12960000.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 3x^{6} + 8x^{4} - 3x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 3^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 37.4
Root \(1.40126 - 0.809017i\) of defining polynomial
Character \(\chi\) \(=\) 504.37
Dual form 504.2.cj.a.109.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.40126 - 0.190983i) q^{2} +(1.92705 - 0.535233i) q^{4} +(1.93649 + 1.11803i) q^{5} +(-0.500000 + 2.59808i) q^{7} +(2.59808 - 1.11803i) q^{8} +O(q^{10})\) \(q+(1.40126 - 0.190983i) q^{2} +(1.92705 - 0.535233i) q^{4} +(1.93649 + 1.11803i) q^{5} +(-0.500000 + 2.59808i) q^{7} +(2.59808 - 1.11803i) q^{8} +(2.92705 + 1.19682i) q^{10} +(-1.93649 + 1.11803i) q^{11} +(-0.204441 + 3.73607i) q^{14} +(3.42705 - 2.06284i) q^{16} +(1.73205 + 3.00000i) q^{17} +(-6.70820 - 3.87298i) q^{19} +(4.33013 + 1.11803i) q^{20} +(-2.50000 + 1.93649i) q^{22} +(3.46410 - 6.00000i) q^{23} +(0.427051 + 5.27424i) q^{28} -2.23607i q^{29} +(0.500000 + 0.866025i) q^{31} +(4.40822 - 3.54508i) q^{32} +(3.00000 + 3.87298i) q^{34} +(-3.87298 + 4.47214i) q^{35} +(-6.70820 - 3.87298i) q^{37} +(-10.1396 - 4.14590i) q^{38} +(6.28115 + 0.739674i) q^{40} +10.3923 q^{41} +(-3.13331 + 3.19098i) q^{44} +(3.70820 - 9.06914i) q^{46} +(-1.73205 + 3.00000i) q^{47} +(-6.50000 - 2.59808i) q^{49} +(9.68246 - 5.59017i) q^{53} -5.00000 q^{55} +(1.60570 + 7.30902i) q^{56} +(-0.427051 - 3.13331i) q^{58} +(-1.93649 + 1.11803i) q^{59} +(-6.70820 - 3.87298i) q^{61} +(0.866025 + 1.11803i) q^{62} +(5.50000 - 5.80948i) q^{64} +(-6.70820 + 3.87298i) q^{67} +(4.94345 + 4.85410i) q^{68} +(-4.57295 + 7.00629i) q^{70} -10.3923 q^{71} +(5.00000 + 8.66025i) q^{73} +(-10.1396 - 4.14590i) q^{74} +(-15.0000 - 3.87298i) q^{76} +(-1.93649 - 5.59017i) q^{77} +(6.50000 - 11.2583i) q^{79} +(8.94278 - 0.163119i) q^{80} +(14.5623 - 1.98475i) q^{82} +11.1803i q^{83} +7.74597i q^{85} +(-3.78115 + 5.06980i) q^{88} +(-6.92820 + 12.0000i) q^{89} +(3.46410 - 13.4164i) q^{92} +(-1.85410 + 4.53457i) q^{94} +(-8.66025 - 15.0000i) q^{95} -1.00000 q^{97} +(-9.60437 - 2.39919i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 2 q^{4} - 4 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 2 q^{4} - 4 q^{7} + 10 q^{10} + 14 q^{16} - 20 q^{22} - 10 q^{28} + 4 q^{31} + 24 q^{34} + 10 q^{40} - 24 q^{46} - 52 q^{49} - 40 q^{55} + 10 q^{58} + 44 q^{64} - 50 q^{70} + 40 q^{73} - 120 q^{76} + 52 q^{79} + 36 q^{82} + 10 q^{88} + 12 q^{94} - 8 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/504\mathbb{Z}\right)^\times\).

\(n\) \(73\) \(127\) \(253\) \(281\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(-1\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.40126 0.190983i 0.990839 0.135045i
\(3\) 0 0
\(4\) 1.92705 0.535233i 0.963525 0.267617i
\(5\) 1.93649 + 1.11803i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.5\pi\)
\(6\) 0 0
\(7\) −0.500000 + 2.59808i −0.188982 + 0.981981i
\(8\) 2.59808 1.11803i 0.918559 0.395285i
\(9\) 0 0
\(10\) 2.92705 + 1.19682i 0.925615 + 0.378467i
\(11\) −1.93649 + 1.11803i −0.583874 + 0.337100i −0.762672 0.646786i \(-0.776113\pi\)
0.178797 + 0.983886i \(0.442779\pi\)
\(12\) 0 0
\(13\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(14\) −0.204441 + 3.73607i −0.0546391 + 0.998506i
\(15\) 0 0
\(16\) 3.42705 2.06284i 0.856763 0.515711i
\(17\) 1.73205 + 3.00000i 0.420084 + 0.727607i 0.995947 0.0899392i \(-0.0286673\pi\)
−0.575863 + 0.817546i \(0.695334\pi\)
\(18\) 0 0
\(19\) −6.70820 3.87298i −1.53897 0.888523i −0.998899 0.0469020i \(-0.985065\pi\)
−0.540068 0.841621i \(-0.681602\pi\)
\(20\) 4.33013 + 1.11803i 0.968246 + 0.250000i
\(21\) 0 0
\(22\) −2.50000 + 1.93649i −0.533002 + 0.412861i
\(23\) 3.46410 6.00000i 0.722315 1.25109i −0.237754 0.971325i \(-0.576411\pi\)
0.960070 0.279761i \(-0.0902553\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 0 0
\(28\) 0.427051 + 5.27424i 0.0807050 + 0.996738i
\(29\) 2.23607i 0.415227i −0.978211 0.207614i \(-0.933430\pi\)
0.978211 0.207614i \(-0.0665697\pi\)
\(30\) 0 0
\(31\) 0.500000 + 0.866025i 0.0898027 + 0.155543i 0.907428 0.420208i \(-0.138043\pi\)
−0.817625 + 0.575751i \(0.804710\pi\)
\(32\) 4.40822 3.54508i 0.779270 0.626688i
\(33\) 0 0
\(34\) 3.00000 + 3.87298i 0.514496 + 0.664211i
\(35\) −3.87298 + 4.47214i −0.654654 + 0.755929i
\(36\) 0 0
\(37\) −6.70820 3.87298i −1.10282 0.636715i −0.165861 0.986149i \(-0.553040\pi\)
−0.936961 + 0.349435i \(0.886374\pi\)
\(38\) −10.1396 4.14590i −1.64486 0.672553i
\(39\) 0 0
\(40\) 6.28115 + 0.739674i 0.993137 + 0.116953i
\(41\) 10.3923 1.62301 0.811503 0.584349i \(-0.198650\pi\)
0.811503 + 0.584349i \(0.198650\pi\)
\(42\) 0 0
\(43\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(44\) −3.13331 + 3.19098i −0.472364 + 0.481059i
\(45\) 0 0
\(46\) 3.70820 9.06914i 0.546745 1.33717i
\(47\) −1.73205 + 3.00000i −0.252646 + 0.437595i −0.964253 0.264982i \(-0.914634\pi\)
0.711608 + 0.702577i \(0.247967\pi\)
\(48\) 0 0
\(49\) −6.50000 2.59808i −0.928571 0.371154i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 9.68246 5.59017i 1.32999 0.767869i 0.344690 0.938716i \(-0.387984\pi\)
0.985297 + 0.170848i \(0.0546505\pi\)
\(54\) 0 0
\(55\) −5.00000 −0.674200
\(56\) 1.60570 + 7.30902i 0.214571 + 0.976708i
\(57\) 0 0
\(58\) −0.427051 3.13331i −0.0560745 0.411424i
\(59\) −1.93649 + 1.11803i −0.252110 + 0.145556i −0.620730 0.784024i \(-0.713164\pi\)
0.368620 + 0.929580i \(0.379830\pi\)
\(60\) 0 0
\(61\) −6.70820 3.87298i −0.858898 0.495885i 0.00474543 0.999989i \(-0.498489\pi\)
−0.863643 + 0.504104i \(0.831823\pi\)
\(62\) 0.866025 + 1.11803i 0.109985 + 0.141990i
\(63\) 0 0
\(64\) 5.50000 5.80948i 0.687500 0.726184i
\(65\) 0 0
\(66\) 0 0
\(67\) −6.70820 + 3.87298i −0.819538 + 0.473160i −0.850257 0.526368i \(-0.823553\pi\)
0.0307194 + 0.999528i \(0.490220\pi\)
\(68\) 4.94345 + 4.85410i 0.599481 + 0.588646i
\(69\) 0 0
\(70\) −4.57295 + 7.00629i −0.546572 + 0.837412i
\(71\) −10.3923 −1.23334 −0.616670 0.787222i \(-0.711519\pi\)
−0.616670 + 0.787222i \(0.711519\pi\)
\(72\) 0 0
\(73\) 5.00000 + 8.66025i 0.585206 + 1.01361i 0.994850 + 0.101361i \(0.0323196\pi\)
−0.409644 + 0.912245i \(0.634347\pi\)
\(74\) −10.1396 4.14590i −1.17870 0.481951i
\(75\) 0 0
\(76\) −15.0000 3.87298i −1.72062 0.444262i
\(77\) −1.93649 5.59017i −0.220684 0.637059i
\(78\) 0 0
\(79\) 6.50000 11.2583i 0.731307 1.26666i −0.225018 0.974355i \(-0.572244\pi\)
0.956325 0.292306i \(-0.0944227\pi\)
\(80\) 8.94278 0.163119i 0.999834 0.0182373i
\(81\) 0 0
\(82\) 14.5623 1.98475i 1.60814 0.219179i
\(83\) 11.1803i 1.22720i 0.789616 + 0.613601i \(0.210280\pi\)
−0.789616 + 0.613601i \(0.789720\pi\)
\(84\) 0 0
\(85\) 7.74597i 0.840168i
\(86\) 0 0
\(87\) 0 0
\(88\) −3.78115 + 5.06980i −0.403072 + 0.540443i
\(89\) −6.92820 + 12.0000i −0.734388 + 1.27200i 0.220603 + 0.975364i \(0.429197\pi\)
−0.954991 + 0.296634i \(0.904136\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 3.46410 13.4164i 0.361158 1.39876i
\(93\) 0 0
\(94\) −1.85410 + 4.53457i −0.191236 + 0.467705i
\(95\) −8.66025 15.0000i −0.888523 1.53897i
\(96\) 0 0
\(97\) −1.00000 −0.101535 −0.0507673 0.998711i \(-0.516167\pi\)
−0.0507673 + 0.998711i \(0.516167\pi\)
\(98\) −9.60437 2.39919i −0.970188 0.242354i
\(99\) 0 0
\(100\) 0 0
\(101\) 3.87298 2.23607i 0.385376 0.222497i −0.294779 0.955566i \(-0.595246\pi\)
0.680155 + 0.733069i \(0.261913\pi\)
\(102\) 0 0
\(103\) −4.00000 + 6.92820i −0.394132 + 0.682656i −0.992990 0.118199i \(-0.962288\pi\)
0.598858 + 0.800855i \(0.295621\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 12.5000 9.68246i 1.21411 0.940443i
\(107\) −9.68246 5.59017i −0.936039 0.540422i −0.0473223 0.998880i \(-0.515069\pi\)
−0.888716 + 0.458458i \(0.848402\pi\)
\(108\) 0 0
\(109\) −6.70820 + 3.87298i −0.642529 + 0.370965i −0.785588 0.618750i \(-0.787640\pi\)
0.143059 + 0.989714i \(0.454306\pi\)
\(110\) −7.00629 + 0.954915i −0.668024 + 0.0910476i
\(111\) 0 0
\(112\) 3.64590 + 9.93516i 0.344505 + 0.938784i
\(113\) −10.3923 −0.977626 −0.488813 0.872389i \(-0.662570\pi\)
−0.488813 + 0.872389i \(0.662570\pi\)
\(114\) 0 0
\(115\) 13.4164 7.74597i 1.25109 0.722315i
\(116\) −1.19682 4.30902i −0.111122 0.400082i
\(117\) 0 0
\(118\) −2.50000 + 1.93649i −0.230144 + 0.178269i
\(119\) −8.66025 + 3.00000i −0.793884 + 0.275010i
\(120\) 0 0
\(121\) −3.00000 + 5.19615i −0.272727 + 0.472377i
\(122\) −10.1396 4.14590i −0.917996 0.375352i
\(123\) 0 0
\(124\) 1.42705 + 1.40126i 0.128153 + 0.125837i
\(125\) 11.1803i 1.00000i
\(126\) 0 0
\(127\) 5.00000 0.443678 0.221839 0.975083i \(-0.428794\pi\)
0.221839 + 0.975083i \(0.428794\pi\)
\(128\) 6.59741 9.19098i 0.583134 0.812376i
\(129\) 0 0
\(130\) 0 0
\(131\) −9.68246 5.59017i −0.845960 0.488415i 0.0133255 0.999911i \(-0.495758\pi\)
−0.859286 + 0.511496i \(0.829092\pi\)
\(132\) 0 0
\(133\) 13.4164 15.4919i 1.16335 1.34332i
\(134\) −8.66025 + 6.70820i −0.748132 + 0.579501i
\(135\) 0 0
\(136\) 7.85410 + 5.85774i 0.673484 + 0.502297i
\(137\) 1.73205 + 3.00000i 0.147979 + 0.256307i 0.930480 0.366342i \(-0.119390\pi\)
−0.782501 + 0.622649i \(0.786057\pi\)
\(138\) 0 0
\(139\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(140\) −5.06980 + 10.6910i −0.428476 + 0.903553i
\(141\) 0 0
\(142\) −14.5623 + 1.98475i −1.22204 + 0.166557i
\(143\) 0 0
\(144\) 0 0
\(145\) 2.50000 4.33013i 0.207614 0.359597i
\(146\) 8.66025 + 11.1803i 0.716728 + 0.925292i
\(147\) 0 0
\(148\) −15.0000 3.87298i −1.23299 0.318357i
\(149\) 19.3649 + 11.1803i 1.58644 + 0.915929i 0.993888 + 0.110394i \(0.0352112\pi\)
0.592548 + 0.805535i \(0.298122\pi\)
\(150\) 0 0
\(151\) 3.50000 + 6.06218i 0.284826 + 0.493333i 0.972567 0.232623i \(-0.0747309\pi\)
−0.687741 + 0.725956i \(0.741398\pi\)
\(152\) −21.7586 2.56231i −1.76485 0.207830i
\(153\) 0 0
\(154\) −3.78115 7.46344i −0.304694 0.601421i
\(155\) 2.23607i 0.179605i
\(156\) 0 0
\(157\) 13.4164 7.74597i 1.07075 0.618195i 0.142361 0.989815i \(-0.454531\pi\)
0.928385 + 0.371619i \(0.121197\pi\)
\(158\) 6.95803 17.0172i 0.553551 1.35382i
\(159\) 0 0
\(160\) 12.5000 1.93649i 0.988212 0.153093i
\(161\) 13.8564 + 12.0000i 1.09204 + 0.945732i
\(162\) 0 0
\(163\) 13.4164 + 7.74597i 1.05085 + 0.606711i 0.922888 0.385068i \(-0.125822\pi\)
0.127966 + 0.991779i \(0.459155\pi\)
\(164\) 20.0265 5.56231i 1.56381 0.434343i
\(165\) 0 0
\(166\) 2.13525 + 15.6665i 0.165728 + 1.21596i
\(167\) 10.3923 0.804181 0.402090 0.915600i \(-0.368284\pi\)
0.402090 + 0.915600i \(0.368284\pi\)
\(168\) 0 0
\(169\) 13.0000 1.00000
\(170\) 1.47935 + 10.8541i 0.113461 + 0.832472i
\(171\) 0 0
\(172\) 0 0
\(173\) −3.87298 2.23607i −0.294457 0.170005i 0.345493 0.938421i \(-0.387712\pi\)
−0.639950 + 0.768416i \(0.721045\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −4.33013 + 7.82624i −0.326396 + 0.589925i
\(177\) 0 0
\(178\) −7.41641 + 18.1383i −0.555883 + 1.35952i
\(179\) −7.74597 + 4.47214i −0.578961 + 0.334263i −0.760720 0.649080i \(-0.775154\pi\)
0.181760 + 0.983343i \(0.441821\pi\)
\(180\) 0 0
\(181\) 23.2379i 1.72726i 0.504127 + 0.863630i \(0.331814\pi\)
−0.504127 + 0.863630i \(0.668186\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 2.29180 19.4614i 0.168953 1.43472i
\(185\) −8.66025 15.0000i −0.636715 1.10282i
\(186\) 0 0
\(187\) −6.70820 3.87298i −0.490552 0.283221i
\(188\) −1.73205 + 6.70820i −0.126323 + 0.489246i
\(189\) 0 0
\(190\) −15.0000 19.3649i −1.08821 1.40488i
\(191\) 3.46410 6.00000i 0.250654 0.434145i −0.713052 0.701111i \(-0.752688\pi\)
0.963706 + 0.266966i \(0.0860212\pi\)
\(192\) 0 0
\(193\) −8.50000 14.7224i −0.611843 1.05974i −0.990930 0.134382i \(-0.957095\pi\)
0.379086 0.925361i \(-0.376238\pi\)
\(194\) −1.40126 + 0.190983i −0.100605 + 0.0137118i
\(195\) 0 0
\(196\) −13.9164 1.52761i −0.994029 0.109115i
\(197\) 4.47214i 0.318626i 0.987228 + 0.159313i \(0.0509280\pi\)
−0.987228 + 0.159313i \(0.949072\pi\)
\(198\) 0 0
\(199\) −4.00000 6.92820i −0.283552 0.491127i 0.688705 0.725042i \(-0.258180\pi\)
−0.972257 + 0.233915i \(0.924846\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 5.00000 3.87298i 0.351799 0.272502i
\(203\) 5.80948 + 1.11803i 0.407745 + 0.0784706i
\(204\) 0 0
\(205\) 20.1246 + 11.6190i 1.40556 + 0.811503i
\(206\) −4.28187 + 10.4721i −0.298332 + 0.729628i
\(207\) 0 0
\(208\) 0 0
\(209\) 17.3205 1.19808
\(210\) 0 0
\(211\) 23.2379i 1.59976i 0.600158 + 0.799882i \(0.295104\pi\)
−0.600158 + 0.799882i \(0.704896\pi\)
\(212\) 15.6665 15.9549i 1.07598 1.09579i
\(213\) 0 0
\(214\) −14.6353 5.98409i −1.00045 0.409064i
\(215\) 0 0
\(216\) 0 0
\(217\) −2.50000 + 0.866025i −0.169711 + 0.0587896i
\(218\) −8.66025 + 6.70820i −0.586546 + 0.454337i
\(219\) 0 0
\(220\) −9.63525 + 2.67617i −0.649609 + 0.180427i
\(221\) 0 0
\(222\) 0 0
\(223\) −7.00000 −0.468755 −0.234377 0.972146i \(-0.575305\pi\)
−0.234377 + 0.972146i \(0.575305\pi\)
\(224\) 7.00629 + 13.2254i 0.468128 + 0.883661i
\(225\) 0 0
\(226\) −14.5623 + 1.98475i −0.968670 + 0.132024i
\(227\) 21.3014 12.2984i 1.41382 0.816272i 0.418078 0.908411i \(-0.362704\pi\)
0.995746 + 0.0921394i \(0.0293705\pi\)
\(228\) 0 0
\(229\) −6.70820 3.87298i −0.443291 0.255934i 0.261702 0.965149i \(-0.415716\pi\)
−0.704992 + 0.709215i \(0.749050\pi\)
\(230\) 17.3205 13.4164i 1.14208 0.884652i
\(231\) 0 0
\(232\) −2.50000 5.80948i −0.164133 0.381411i
\(233\) −1.73205 + 3.00000i −0.113470 + 0.196537i −0.917167 0.398502i \(-0.869530\pi\)
0.803697 + 0.595039i \(0.202863\pi\)
\(234\) 0 0
\(235\) −6.70820 + 3.87298i −0.437595 + 0.252646i
\(236\) −3.13331 + 3.19098i −0.203961 + 0.207715i
\(237\) 0 0
\(238\) −11.5623 + 5.85774i −0.749473 + 0.379701i
\(239\) 20.7846 1.34444 0.672222 0.740349i \(-0.265340\pi\)
0.672222 + 0.740349i \(0.265340\pi\)
\(240\) 0 0
\(241\) −11.5000 19.9186i −0.740780 1.28307i −0.952141 0.305661i \(-0.901123\pi\)
0.211360 0.977408i \(-0.432211\pi\)
\(242\) −3.21140 + 7.85410i −0.206437 + 0.504881i
\(243\) 0 0
\(244\) −15.0000 3.87298i −0.960277 0.247942i
\(245\) −9.68246 12.2984i −0.618590 0.785714i
\(246\) 0 0
\(247\) 0 0
\(248\) 2.26728 + 1.69098i 0.143973 + 0.107378i
\(249\) 0 0
\(250\) −2.13525 15.6665i −0.135045 0.990839i
\(251\) 24.5967i 1.55253i 0.630405 + 0.776266i \(0.282889\pi\)
−0.630405 + 0.776266i \(0.717111\pi\)
\(252\) 0 0
\(253\) 15.4919i 0.973970i
\(254\) 7.00629 0.954915i 0.439614 0.0599167i
\(255\) 0 0
\(256\) 7.48936 14.1389i 0.468085 0.883684i
\(257\) 3.46410 6.00000i 0.216085 0.374270i −0.737523 0.675322i \(-0.764005\pi\)
0.953608 + 0.301052i \(0.0973379\pi\)
\(258\) 0 0
\(259\) 13.4164 15.4919i 0.833655 0.962622i
\(260\) 0 0
\(261\) 0 0
\(262\) −14.6353 5.98409i −0.904169 0.369698i
\(263\) −3.46410 6.00000i −0.213606 0.369976i 0.739235 0.673448i \(-0.235187\pi\)
−0.952840 + 0.303472i \(0.901854\pi\)
\(264\) 0 0
\(265\) 25.0000 1.53574
\(266\) 15.8412 24.2705i 0.971284 1.48812i
\(267\) 0 0
\(268\) −10.8541 + 11.0539i −0.663020 + 0.675224i
\(269\) −25.1744 + 14.5344i −1.53491 + 0.886181i −0.535785 + 0.844355i \(0.679984\pi\)
−0.999125 + 0.0418260i \(0.986682\pi\)
\(270\) 0 0
\(271\) 0.500000 0.866025i 0.0303728 0.0526073i −0.850439 0.526073i \(-0.823664\pi\)
0.880812 + 0.473466i \(0.156997\pi\)
\(272\) 12.1244 + 6.70820i 0.735147 + 0.406745i
\(273\) 0 0
\(274\) 3.00000 + 3.87298i 0.181237 + 0.233975i
\(275\) 0 0
\(276\) 0 0
\(277\) 13.4164 7.74597i 0.806114 0.465410i −0.0394907 0.999220i \(-0.512574\pi\)
0.845605 + 0.533810i \(0.179240\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) −5.06231 + 15.9491i −0.302531 + 0.953140i
\(281\) 10.3923 0.619953 0.309976 0.950744i \(-0.399679\pi\)
0.309976 + 0.950744i \(0.399679\pi\)
\(282\) 0 0
\(283\) 13.4164 7.74597i 0.797523 0.460450i −0.0450815 0.998983i \(-0.514355\pi\)
0.842604 + 0.538533i \(0.181021\pi\)
\(284\) −20.0265 + 5.56231i −1.18835 + 0.330062i
\(285\) 0 0
\(286\) 0 0
\(287\) −5.19615 + 27.0000i −0.306719 + 1.59376i
\(288\) 0 0
\(289\) 2.50000 4.33013i 0.147059 0.254713i
\(290\) 2.67617 6.54508i 0.157150 0.384341i
\(291\) 0 0
\(292\) 14.2705 + 14.0126i 0.835118 + 0.820025i
\(293\) 11.1803i 0.653162i 0.945169 + 0.326581i \(0.105897\pi\)
−0.945169 + 0.326581i \(0.894103\pi\)
\(294\) 0 0
\(295\) −5.00000 −0.291111
\(296\) −21.7586 2.56231i −1.26469 0.148931i
\(297\) 0 0
\(298\) 29.2705 + 11.9682i 1.69560 + 0.693298i
\(299\) 0 0
\(300\) 0 0
\(301\) 0 0
\(302\) 6.06218 + 7.82624i 0.348839 + 0.450349i
\(303\) 0 0
\(304\) −30.9787 + 0.565061i −1.77675 + 0.0324085i
\(305\) −8.66025 15.0000i −0.495885 0.858898i
\(306\) 0 0
\(307\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(308\) −6.72376 9.73607i −0.383122 0.554764i
\(309\) 0 0
\(310\) 0.427051 + 3.13331i 0.0242549 + 0.177960i
\(311\) 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
\(313\) −11.5000 + 19.9186i −0.650018 + 1.12586i 0.333099 + 0.942892i \(0.391906\pi\)
−0.983118 + 0.182973i \(0.941428\pi\)
\(314\) 17.3205 13.4164i 0.977453 0.757132i
\(315\) 0 0
\(316\) 6.50000 25.1744i 0.365654 1.41617i
\(317\) 1.93649 + 1.11803i 0.108764 + 0.0627950i 0.553395 0.832919i \(-0.313332\pi\)
−0.444631 + 0.895714i \(0.646665\pi\)
\(318\) 0 0
\(319\) 2.50000 + 4.33013i 0.139973 + 0.242441i
\(320\) 17.1459 5.10081i 0.958485 0.285144i
\(321\) 0 0
\(322\) 21.7082 + 14.1688i 1.20975 + 0.789594i
\(323\) 26.8328i 1.49302i
\(324\) 0 0
\(325\) 0 0
\(326\) 20.2792 + 8.29180i 1.12316 + 0.459240i
\(327\) 0 0
\(328\) 27.0000 11.6190i 1.49083 0.641549i
\(329\) −6.92820 6.00000i −0.381964 0.330791i
\(330\) 0 0
\(331\) 13.4164 + 7.74597i 0.737432 + 0.425757i 0.821135 0.570734i \(-0.193341\pi\)
−0.0837026 + 0.996491i \(0.526675\pi\)
\(332\) 5.98409 + 21.5451i 0.328420 + 1.18244i
\(333\) 0 0
\(334\) 14.5623 1.98475i 0.796814 0.108601i
\(335\) −17.3205 −0.946320
\(336\) 0 0
\(337\) −19.0000 −1.03500 −0.517498 0.855684i \(-0.673136\pi\)
−0.517498 + 0.855684i \(0.673136\pi\)
\(338\) 18.2164 2.48278i 0.990839 0.135045i
\(339\) 0 0
\(340\) 4.14590 + 14.9269i 0.224843 + 0.809523i
\(341\) −1.93649 1.11803i −0.104867 0.0605449i
\(342\) 0 0
\(343\) 10.0000 15.5885i 0.539949 0.841698i
\(344\) 0 0
\(345\) 0 0
\(346\) −5.85410 2.39364i −0.314718 0.128683i
\(347\) 15.4919 8.94427i 0.831651 0.480154i −0.0227669 0.999741i \(-0.507248\pi\)
0.854417 + 0.519587i \(0.173914\pi\)
\(348\) 0 0
\(349\) 23.2379i 1.24390i −0.783058 0.621948i \(-0.786341\pi\)
0.783058 0.621948i \(-0.213659\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −4.57295 + 11.7936i −0.243739 + 0.628599i
\(353\) −13.8564 24.0000i −0.737502 1.27739i −0.953617 0.301023i \(-0.902672\pi\)
0.216115 0.976368i \(-0.430661\pi\)
\(354\) 0 0
\(355\) −20.1246 11.6190i −1.06810 0.616670i
\(356\) −6.92820 + 26.8328i −0.367194 + 1.42214i
\(357\) 0 0
\(358\) −10.0000 + 7.74597i −0.528516 + 0.409387i
\(359\) 8.66025 15.0000i 0.457071 0.791670i −0.541734 0.840550i \(-0.682232\pi\)
0.998805 + 0.0488803i \(0.0155653\pi\)
\(360\) 0 0
\(361\) 20.5000 + 35.5070i 1.07895 + 1.86879i
\(362\) 4.43804 + 32.5623i 0.233258 + 1.71144i
\(363\) 0 0
\(364\) 0 0
\(365\) 22.3607i 1.17041i
\(366\) 0 0
\(367\) −2.50000 4.33013i −0.130499 0.226031i 0.793370 0.608740i \(-0.208325\pi\)
−0.923869 + 0.382709i \(0.874991\pi\)
\(368\) −0.505406 27.7082i −0.0263461 1.44439i
\(369\) 0 0
\(370\) −15.0000 19.3649i −0.779813 1.00673i
\(371\) 9.68246 + 27.9508i 0.502688 + 1.45114i
\(372\) 0 0
\(373\) −6.70820 3.87298i −0.347338 0.200535i 0.316174 0.948701i \(-0.397602\pi\)
−0.663512 + 0.748166i \(0.730935\pi\)
\(374\) −10.1396 4.14590i −0.524306 0.214379i
\(375\) 0 0
\(376\) −1.14590 + 9.73072i −0.0590952 + 0.501824i
\(377\) 0 0
\(378\) 0 0
\(379\) 23.2379i 1.19365i 0.802371 + 0.596825i \(0.203571\pi\)
−0.802371 + 0.596825i \(0.796429\pi\)
\(380\) −24.7172 24.2705i −1.26797 1.24505i
\(381\) 0 0
\(382\) 3.70820 9.06914i 0.189728 0.464017i
\(383\) 3.46410 6.00000i 0.177007 0.306586i −0.763847 0.645398i \(-0.776692\pi\)
0.940854 + 0.338812i \(0.110025\pi\)
\(384\) 0 0
\(385\) 2.50000 12.9904i 0.127412 0.662051i
\(386\) −14.7224 19.0066i −0.749352 0.967409i
\(387\) 0 0
\(388\) −1.92705 + 0.535233i −0.0978312 + 0.0271723i
\(389\) 3.87298 2.23607i 0.196368 0.113373i −0.398592 0.917128i \(-0.630501\pi\)
0.594960 + 0.803755i \(0.297168\pi\)
\(390\) 0 0
\(391\) 24.0000 1.21373
\(392\) −19.7922 + 0.517221i −0.999659 + 0.0261236i
\(393\) 0 0
\(394\) 0.854102 + 6.26662i 0.0430290 + 0.315708i
\(395\) 25.1744 14.5344i 1.26666 0.731307i
\(396\) 0 0
\(397\) −26.8328 15.4919i −1.34670 0.777518i −0.358920 0.933368i \(-0.616855\pi\)
−0.987781 + 0.155851i \(0.950188\pi\)
\(398\) −6.92820 8.94427i −0.347279 0.448336i
\(399\) 0 0
\(400\) 0 0
\(401\) −17.3205 + 30.0000i −0.864945 + 1.49813i 0.00215698 + 0.999998i \(0.499313\pi\)
−0.867102 + 0.498131i \(0.834020\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 6.26662 6.38197i 0.311776 0.317515i
\(405\) 0 0
\(406\) 8.35410 + 0.457144i 0.414607 + 0.0226877i
\(407\) 17.3205 0.858546
\(408\) 0 0
\(409\) 3.50000 + 6.06218i 0.173064 + 0.299755i 0.939490 0.342578i \(-0.111300\pi\)
−0.766426 + 0.642333i \(0.777967\pi\)
\(410\) 30.4188 + 12.4377i 1.50228 + 0.614254i
\(411\) 0 0
\(412\) −4.00000 + 15.4919i −0.197066 + 0.763233i
\(413\) −1.93649 5.59017i −0.0952885 0.275074i
\(414\) 0 0
\(415\) −12.5000 + 21.6506i −0.613601 + 1.06279i
\(416\) 0 0
\(417\) 0 0
\(418\) 24.2705 3.30792i 1.18711 0.161796i
\(419\) 35.7771i 1.74783i −0.486083 0.873913i \(-0.661575\pi\)
0.486083 0.873913i \(-0.338425\pi\)
\(420\) 0 0
\(421\) 23.2379i 1.13255i 0.824218 + 0.566273i \(0.191615\pi\)
−0.824218 + 0.566273i \(0.808385\pi\)
\(422\) 4.43804 + 32.5623i 0.216041 + 1.58511i
\(423\) 0 0
\(424\) 18.9058 25.3490i 0.918145 1.23106i
\(425\) 0 0
\(426\) 0 0
\(427\) 13.4164 15.4919i 0.649265 0.749707i
\(428\) −21.6506 5.59017i −1.04652 0.270211i
\(429\) 0 0
\(430\) 0 0
\(431\) 12.1244 + 21.0000i 0.584010 + 1.01153i 0.994998 + 0.0998939i \(0.0318503\pi\)
−0.410988 + 0.911641i \(0.634816\pi\)
\(432\) 0 0
\(433\) −22.0000 −1.05725 −0.528626 0.848855i \(-0.677293\pi\)
−0.528626 + 0.848855i \(0.677293\pi\)
\(434\) −3.33775 + 1.69098i −0.160217 + 0.0811698i
\(435\) 0 0
\(436\) −10.8541 + 11.0539i −0.519817 + 0.529385i
\(437\) −46.4758 + 26.8328i −2.22324 + 1.28359i
\(438\) 0 0
\(439\) 3.50000 6.06218i 0.167046 0.289332i −0.770334 0.637641i \(-0.779911\pi\)
0.937380 + 0.348309i \(0.113244\pi\)
\(440\) −12.9904 + 5.59017i −0.619292 + 0.266501i
\(441\) 0 0
\(442\) 0 0
\(443\) −21.3014 12.2984i −1.01206 0.584313i −0.100266 0.994961i \(-0.531969\pi\)
−0.911794 + 0.410647i \(0.865303\pi\)
\(444\) 0 0
\(445\) −26.8328 + 15.4919i −1.27200 + 0.734388i
\(446\) −9.80881 + 1.33688i −0.464461 + 0.0633032i
\(447\) 0 0
\(448\) 12.3435 + 17.1942i 0.583174 + 0.812348i
\(449\) −20.7846 −0.980886 −0.490443 0.871473i \(-0.663165\pi\)
−0.490443 + 0.871473i \(0.663165\pi\)
\(450\) 0 0
\(451\) −20.1246 + 11.6190i −0.947631 + 0.547115i
\(452\) −20.0265 + 5.56231i −0.941967 + 0.261629i
\(453\) 0 0
\(454\) 27.5000 21.3014i 1.29064 0.999725i
\(455\) 0 0
\(456\) 0 0
\(457\) −2.50000 + 4.33013i −0.116945 + 0.202555i −0.918556 0.395292i \(-0.870643\pi\)
0.801611 + 0.597847i \(0.203977\pi\)
\(458\) −10.1396 4.14590i −0.473792 0.193725i
\(459\) 0 0
\(460\) 21.7082 22.1078i 1.01215 1.03078i
\(461\) 22.3607i 1.04144i −0.853727 0.520720i \(-0.825663\pi\)
0.853727 0.520720i \(-0.174337\pi\)
\(462\) 0 0
\(463\) 8.00000 0.371792 0.185896 0.982569i \(-0.440481\pi\)
0.185896 + 0.982569i \(0.440481\pi\)
\(464\) −4.61266 7.66312i −0.214137 0.355751i
\(465\) 0 0
\(466\) −1.85410 + 4.53457i −0.0858896 + 0.210060i
\(467\) 7.74597 + 4.47214i 0.358441 + 0.206946i 0.668397 0.743805i \(-0.266981\pi\)
−0.309956 + 0.950751i \(0.600314\pi\)
\(468\) 0 0
\(469\) −6.70820 19.3649i −0.309756 0.894189i
\(470\) −8.66025 + 6.70820i −0.399468 + 0.309426i
\(471\) 0 0
\(472\) −3.78115 + 5.06980i −0.174042 + 0.233357i
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) −15.0831 + 10.4164i −0.691331 + 0.477435i
\(477\) 0 0
\(478\) 29.1246 3.96951i 1.33213 0.181561i
\(479\) 6.92820 + 12.0000i 0.316558 + 0.548294i 0.979767 0.200140i \(-0.0641396\pi\)
−0.663210 + 0.748434i \(0.730806\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) −19.9186 25.7148i −0.907267 1.17128i
\(483\) 0 0
\(484\) −3.00000 + 11.6190i −0.136364 + 0.528134i
\(485\) −1.93649 1.11803i −0.0879316 0.0507673i
\(486\) 0 0
\(487\) 0.500000 + 0.866025i 0.0226572 + 0.0392434i 0.877132 0.480250i \(-0.159454\pi\)
−0.854475 + 0.519493i \(0.826121\pi\)
\(488\) −21.7586 2.56231i −0.984963 0.115990i
\(489\) 0 0
\(490\) −15.9164 15.3840i −0.719030 0.694979i
\(491\) 29.0689i 1.31186i −0.754822 0.655930i \(-0.772277\pi\)
0.754822 0.655930i \(-0.227723\pi\)
\(492\) 0 0
\(493\) 6.70820 3.87298i 0.302122 0.174430i
\(494\) 0 0
\(495\) 0 0
\(496\) 3.50000 + 1.93649i 0.157155 + 0.0869510i
\(497\) 5.19615 27.0000i 0.233079 1.21112i
\(498\) 0 0
\(499\) −26.8328 15.4919i −1.20120 0.693514i −0.240379 0.970679i \(-0.577272\pi\)
−0.960822 + 0.277165i \(0.910605\pi\)
\(500\) −5.98409 21.5451i −0.267617 0.963525i
\(501\) 0 0
\(502\) 4.69756 + 34.4664i 0.209662 + 1.53831i
\(503\) −31.1769 −1.39011 −0.695055 0.718957i \(-0.744620\pi\)
−0.695055 + 0.718957i \(0.744620\pi\)
\(504\) 0 0
\(505\) 10.0000 0.444994
\(506\) 2.95870 + 21.7082i 0.131530 + 0.965047i
\(507\) 0 0
\(508\) 9.63525 2.67617i 0.427495 0.118736i
\(509\) 25.1744 + 14.5344i 1.11584 + 0.644228i 0.940334 0.340251i \(-0.110512\pi\)
0.175501 + 0.984479i \(0.443846\pi\)
\(510\) 0 0
\(511\) −25.0000 + 8.66025i −1.10593 + 0.383107i
\(512\) 7.79423 21.2426i 0.344459 0.938801i
\(513\) 0 0
\(514\) 3.70820 9.06914i 0.163562 0.400022i
\(515\) −15.4919 + 8.94427i −0.682656 + 0.394132i
\(516\) 0 0
\(517\) 7.74597i 0.340667i
\(518\) 15.8412 24.2705i 0.696021 1.06638i
\(519\) 0 0
\(520\) 0 0
\(521\) −13.8564 24.0000i −0.607060 1.05146i −0.991722 0.128402i \(-0.959015\pi\)
0.384662 0.923057i \(-0.374318\pi\)
\(522\) 0 0
\(523\) −26.8328 15.4919i −1.17332 0.677415i −0.218858 0.975757i \(-0.570233\pi\)
−0.954459 + 0.298342i \(0.903566\pi\)
\(524\) −21.6506 5.59017i −0.945812 0.244208i
\(525\) 0 0
\(526\) −6.00000 7.74597i −0.261612 0.337740i
\(527\) −1.73205 + 3.00000i −0.0754493 + 0.130682i
\(528\) 0 0
\(529\) −12.5000 21.6506i −0.543478 0.941332i
\(530\) 35.0315 4.77458i 1.52167 0.207394i
\(531\) 0 0
\(532\) 17.5623 37.0347i 0.761423 1.60566i
\(533\) 0 0
\(534\) 0 0
\(535\) −12.5000 21.6506i −0.540422 0.936039i
\(536\) −13.0983 + 17.5623i −0.565760 + 0.758576i
\(537\) 0 0
\(538\) −32.5000 + 25.1744i −1.40117 + 1.08535i
\(539\) 15.4919 2.23607i 0.667285 0.0963143i
\(540\) 0 0
\(541\) 13.4164 + 7.74597i 0.576816 + 0.333025i 0.759867 0.650078i \(-0.225264\pi\)
−0.183051 + 0.983103i \(0.558597\pi\)
\(542\) 0.535233 1.30902i 0.0229902 0.0562271i
\(543\) 0 0
\(544\) 18.2705 + 7.08438i 0.783342 + 0.303740i
\(545\) −17.3205 −0.741929
\(546\) 0 0
\(547\) 23.2379i 0.993581i −0.867871 0.496790i \(-0.834512\pi\)
0.867871 0.496790i \(-0.165488\pi\)
\(548\) 4.94345 + 4.85410i 0.211174 + 0.207357i
\(549\) 0 0
\(550\) 0 0
\(551\) −8.66025 + 15.0000i −0.368939 + 0.639021i
\(552\) 0 0
\(553\) 26.0000 + 22.5167i 1.10563 + 0.957506i
\(554\) 17.3205 13.4164i 0.735878 0.570009i
\(555\) 0 0
\(556\) 0 0
\(557\) −13.5554 + 7.82624i −0.574362 + 0.331608i −0.758890 0.651219i \(-0.774258\pi\)
0.184527 + 0.982827i \(0.440925\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) −4.04760 + 23.3156i −0.171042 + 0.985264i
\(561\) 0 0
\(562\) 14.5623 1.98475i 0.614274 0.0837218i
\(563\) 32.9204 19.0066i 1.38743 0.801032i 0.394403 0.918938i \(-0.370951\pi\)
0.993025 + 0.117906i \(0.0376181\pi\)
\(564\) 0 0
\(565\) −20.1246 11.6190i −0.846649 0.488813i
\(566\) 17.3205 13.4164i 0.728035 0.563934i
\(567\) 0 0
\(568\) −27.0000 + 11.6190i −1.13289 + 0.487520i
\(569\) −1.73205 + 3.00000i −0.0726113 + 0.125767i −0.900045 0.435797i \(-0.856467\pi\)
0.827434 + 0.561563i \(0.189800\pi\)
\(570\) 0 0
\(571\) −6.70820 + 3.87298i −0.280730 + 0.162079i −0.633754 0.773535i \(-0.718487\pi\)
0.353024 + 0.935614i \(0.385153\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) −2.12461 + 38.8264i −0.0886796 + 1.62058i
\(575\) 0 0
\(576\) 0 0
\(577\) −17.5000 30.3109i −0.728535 1.26186i −0.957503 0.288425i \(-0.906868\pi\)
0.228968 0.973434i \(-0.426465\pi\)
\(578\) 2.67617 6.54508i 0.111314 0.272240i
\(579\) 0 0
\(580\) 2.50000 9.68246i 0.103807 0.402042i
\(581\) −29.0474 5.59017i −1.20509 0.231919i
\(582\) 0 0
\(583\) −12.5000 + 21.6506i −0.517697 + 0.896678i
\(584\) 22.6728 + 16.9098i 0.938209 + 0.699734i
\(585\) 0 0
\(586\) 2.13525 + 15.6665i 0.0882066 + 0.647179i
\(587\) 38.0132i 1.56897i 0.620147 + 0.784485i \(0.287073\pi\)
−0.620147 + 0.784485i \(0.712927\pi\)
\(588\) 0 0
\(589\) 7.74597i 0.319167i
\(590\) −7.00629 + 0.954915i −0.288445 + 0.0393132i
\(591\) 0 0
\(592\) −30.9787 + 0.565061i −1.27322 + 0.0232238i
\(593\) 3.46410 6.00000i 0.142254 0.246390i −0.786091 0.618110i \(-0.787898\pi\)
0.928345 + 0.371720i \(0.121232\pi\)
\(594\) 0 0
\(595\) −20.1246 3.87298i −0.825029 0.158777i
\(596\) 43.3013 + 11.1803i 1.77369 + 0.457965i
\(597\) 0 0
\(598\) 0 0
\(599\) 1.73205 + 3.00000i 0.0707697 + 0.122577i 0.899239 0.437458i \(-0.144121\pi\)
−0.828469 + 0.560035i \(0.810788\pi\)
\(600\) 0 0
\(601\) −7.00000 −0.285536 −0.142768 0.989756i \(-0.545600\pi\)
−0.142768 + 0.989756i \(0.545600\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 9.98936 + 9.80881i 0.406461 + 0.399115i
\(605\) −11.6190 + 6.70820i −0.472377 + 0.272727i
\(606\) 0 0
\(607\) −14.5000 + 25.1147i −0.588537 + 1.01938i 0.405887 + 0.913923i \(0.366962\pi\)
−0.994424 + 0.105453i \(0.966371\pi\)
\(608\) −43.3013 + 6.70820i −1.75610 + 0.272054i
\(609\) 0 0
\(610\) −15.0000 19.3649i −0.607332 0.784063i
\(611\) 0 0
\(612\) 0 0
\(613\) −26.8328 + 15.4919i −1.08377 + 0.625713i −0.931910 0.362689i \(-0.881859\pi\)
−0.151857 + 0.988402i \(0.548525\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) −11.2812 12.3586i −0.454531 0.497943i
\(617\) −31.1769 −1.25514 −0.627568 0.778562i \(-0.715949\pi\)
−0.627568 + 0.778562i \(0.715949\pi\)
\(618\) 0 0
\(619\) −6.70820 + 3.87298i −0.269625 + 0.155668i −0.628717 0.777634i \(-0.716420\pi\)
0.359092 + 0.933302i \(0.383086\pi\)
\(620\) 1.19682 + 4.30902i 0.0480654 + 0.173054i
\(621\) 0 0
\(622\) 21.0000 + 27.1109i 0.842023 + 1.08705i
\(623\) −27.7128 24.0000i −1.11029 0.961540i
\(624\) 0 0
\(625\) 12.5000 21.6506i 0.500000 0.866025i
\(626\) −12.3104 + 30.1074i −0.492021 + 1.20333i
\(627\) 0 0
\(628\) 21.7082 22.1078i 0.866252 0.882196i
\(629\) 26.8328i 1.06989i
\(630\) 0 0
\(631\) 11.0000 0.437903 0.218952 0.975736i \(-0.429736\pi\)
0.218952 + 0.975736i \(0.429736\pi\)
\(632\) 4.30030 36.5172i 0.171057 1.45258i
\(633\) 0 0
\(634\) 2.92705 + 1.19682i 0.116248 + 0.0475317i
\(635\) 9.68246 + 5.59017i 0.384237 + 0.221839i
\(636\) 0 0
\(637\) 0 0
\(638\) 4.33013 + 5.59017i 0.171431 + 0.221317i
\(639\) 0 0
\(640\) 23.0517 10.4221i 0.911197 0.411971i
\(641\) 22.5167 + 39.0000i 0.889355 + 1.54041i 0.840640 + 0.541595i \(0.182179\pi\)
0.0487148 + 0.998813i \(0.484487\pi\)
\(642\) 0 0
\(643\) 23.2379i 0.916413i 0.888846 + 0.458207i \(0.151508\pi\)
−0.888846 + 0.458207i \(0.848492\pi\)
\(644\) 33.1248 + 15.7082i 1.30530 + 0.618990i
\(645\) 0 0
\(646\) −5.12461 37.5997i −0.201625 1.47934i
\(647\) 22.5167 + 39.0000i 0.885221 + 1.53325i 0.845460 + 0.534039i \(0.179326\pi\)
0.0397614 + 0.999209i \(0.487340\pi\)
\(648\) 0 0
\(649\) 2.50000 4.33013i 0.0981336 0.169972i
\(650\) 0 0
\(651\) 0 0
\(652\) 30.0000 + 7.74597i 1.17489 + 0.303355i
\(653\) 36.7933 + 21.2426i 1.43983 + 0.831289i 0.997838 0.0657275i \(-0.0209368\pi\)
0.441997 + 0.897016i \(0.354270\pi\)
\(654\) 0 0
\(655\) −12.5000 21.6506i −0.488415 0.845960i
\(656\) 35.6150 21.4377i 1.39053 0.837001i
\(657\) 0 0
\(658\) −10.8541 7.08438i −0.423137 0.276178i
\(659\) 17.8885i 0.696839i 0.937339 + 0.348419i \(0.113281\pi\)
−0.937339 + 0.348419i \(0.886719\pi\)
\(660\) 0 0
\(661\) 13.4164 7.74597i 0.521838 0.301283i −0.215848 0.976427i \(-0.569252\pi\)
0.737686 + 0.675144i \(0.235918\pi\)
\(662\) 20.2792 + 8.29180i 0.788174 + 0.322270i
\(663\) 0 0
\(664\) 12.5000 + 29.0474i 0.485094 + 1.12726i
\(665\) 43.3013 15.0000i 1.67915 0.581675i
\(666\) 0 0
\(667\) −13.4164 7.74597i −0.519485 0.299925i
\(668\) 20.0265 5.56231i 0.774849 0.215212i
\(669\) 0 0
\(670\) −24.2705 + 3.30792i −0.937652 + 0.127796i
\(671\) 17.3205 0.668651
\(672\) 0 0
\(673\) −7.00000 −0.269830 −0.134915 0.990857i \(-0.543076\pi\)
−0.134915 + 0.990857i \(0.543076\pi\)
\(674\) −26.6239 + 3.62868i −1.02551 + 0.139771i
\(675\) 0 0
\(676\) 25.0517 6.95803i 0.963525 0.267617i
\(677\) −21.3014 12.2984i −0.818680 0.472665i 0.0312813 0.999511i \(-0.490041\pi\)
−0.849961 + 0.526846i \(0.823375\pi\)
\(678\) 0 0
\(679\) 0.500000 2.59808i 0.0191882 0.0997050i
\(680\) 8.66025 + 20.1246i 0.332106 + 0.771744i
\(681\) 0 0
\(682\) −2.92705 1.19682i −0.112083 0.0458285i
\(683\) 9.68246 5.59017i 0.370489 0.213902i −0.303183 0.952932i \(-0.598049\pi\)
0.673672 + 0.739030i \(0.264716\pi\)
\(684\) 0 0
\(685\) 7.74597i 0.295958i
\(686\) 11.0355 23.7533i 0.421336 0.906905i
\(687\) 0 0
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 33.5410 + 19.3649i 1.27596 + 0.736676i 0.976103 0.217308i \(-0.0697276\pi\)
0.299857 + 0.953984i \(0.403061\pi\)
\(692\) −8.66025 2.23607i −0.329213 0.0850026i
\(693\) 0 0
\(694\) 20.0000 15.4919i 0.759190 0.588066i
\(695\) 0 0
\(696\) 0 0
\(697\) 18.0000 + 31.1769i 0.681799 + 1.18091i
\(698\) −4.43804 32.5623i −0.167982 1.23250i
\(699\) 0 0
\(700\) 0 0
\(701\) 24.5967i 0.929006i 0.885571 + 0.464503i \(0.153767\pi\)
−0.885571 + 0.464503i \(0.846233\pi\)
\(702\) 0 0
\(703\) 30.0000 + 51.9615i 1.13147 + 1.95977i
\(704\) −4.15551 + 17.3992i −0.156617 + 0.655757i
\(705\) 0 0
\(706\) −24.0000 30.9839i −0.903252 1.16609i
\(707\) 3.87298 + 11.1803i 0.145659 + 0.420480i
\(708\) 0 0
\(709\) 13.4164 + 7.74597i 0.503864 + 0.290906i 0.730308 0.683118i \(-0.239377\pi\)
−0.226444 + 0.974024i \(0.572710\pi\)
\(710\) −30.4188 12.4377i −1.14160 0.466778i
\(711\) 0 0
\(712\) −4.58359 + 38.9229i −0.171777 + 1.45870i
\(713\) 6.92820 0.259463
\(714\) 0 0
\(715\) 0 0
\(716\) −12.5332 + 12.7639i −0.468389 + 0.477011i
\(717\) 0 0
\(718\) 9.27051 22.6728i 0.345972 0.846143i
\(719\) 24.2487 42.0000i 0.904324 1.56634i 0.0825027 0.996591i \(-0.473709\pi\)
0.821822 0.569745i \(-0.192958\pi\)
\(720\) 0 0
\(721\) −16.0000 13.8564i −0.595871 0.516040i
\(722\) 35.5070 + 45.8394i 1.32144 + 1.70597i
\(723\) 0 0
\(724\) 12.4377 + 44.7806i 0.462243 + 1.66426i
\(725\) 0 0
\(726\) 0 0
\(727\) 29.0000 1.07555 0.537775 0.843088i \(-0.319265\pi\)
0.537775 + 0.843088i \(0.319265\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 4.27051 + 31.3331i 0.158059 + 1.15969i
\(731\) 0 0
\(732\) 0 0
\(733\) 13.4164 + 7.74597i 0.495546 + 0.286104i 0.726872 0.686772i \(-0.240973\pi\)
−0.231326 + 0.972876i \(0.574306\pi\)
\(734\) −4.33013 5.59017i −0.159828 0.206337i
\(735\) 0 0
\(736\) −6.00000 38.7298i −0.221163 1.42760i
\(737\) 8.66025 15.0000i 0.319005 0.552532i
\(738\) 0 0
\(739\) 13.4164 7.74597i 0.493531 0.284940i −0.232507 0.972595i \(-0.574693\pi\)
0.726038 + 0.687655i \(0.241360\pi\)
\(740\) −24.7172 24.2705i −0.908624 0.892202i
\(741\) 0 0
\(742\) 18.9058 + 37.3172i 0.694052 + 1.36996i
\(743\) 10.3923 0.381257 0.190628 0.981662i \(-0.438947\pi\)
0.190628 + 0.981662i \(0.438947\pi\)
\(744\) 0 0
\(745\) 25.0000 + 43.3013i 0.915929 + 1.58644i
\(746\) −10.1396 4.14590i −0.371237 0.151792i
\(747\) 0 0
\(748\) −15.0000 3.87298i −0.548454 0.141610i
\(749\) 19.3649 22.3607i 0.707579 0.817041i
\(750\) 0 0
\(751\) 21.5000 37.2391i 0.784546 1.35887i −0.144724 0.989472i \(-0.546229\pi\)
0.929270 0.369402i \(-0.120437\pi\)
\(752\) 0.252703 + 13.8541i 0.00921512 + 0.505207i
\(753\) 0 0
\(754\) 0 0
\(755\) 15.6525i 0.569652i
\(756\) 0 0
\(757\) 23.2379i 0.844596i −0.906457 0.422298i \(-0.861224\pi\)
0.906457 0.422298i \(-0.138776\pi\)
\(758\) 4.43804 + 32.5623i 0.161197 + 1.18272i
\(759\) 0 0
\(760\) −39.2705 29.2887i −1.42449 1.06241i
\(761\) 3.46410 6.00000i 0.125574 0.217500i −0.796383 0.604792i \(-0.793256\pi\)
0.921957 + 0.387292i \(0.126590\pi\)
\(762\) 0 0
\(763\) −6.70820 19.3649i −0.242853 0.701057i
\(764\) 3.46410 13.4164i 0.125327 0.485389i
\(765\) 0 0
\(766\) 3.70820 9.06914i 0.133983 0.327681i
\(767\) 0 0
\(768\) 0 0
\(769\) −31.0000 −1.11789 −0.558944 0.829205i \(-0.688793\pi\)
−0.558944 + 0.829205i \(0.688793\pi\)
\(770\) 1.02220 18.6803i 0.0368377 0.673193i
\(771\) 0 0
\(772\) −24.2599 23.8214i −0.873132 0.857351i
\(773\) 3.87298 2.23607i 0.139302 0.0804258i −0.428730 0.903433i \(-0.641039\pi\)
0.568031 + 0.823007i \(0.307705\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) −2.59808 + 1.11803i −0.0932655 + 0.0401351i
\(777\) 0 0
\(778\) 5.00000 3.87298i 0.179259 0.138853i
\(779\) −69.7137 40.2492i −2.49775 1.44208i
\(780\) 0 0
\(781\) 20.1246 11.6190i 0.720115 0.415759i
\(782\) 33.6302 4.58359i 1.20261 0.163909i
\(783\) 0 0
\(784\) −27.6353 + 4.50474i −0.986973 + 0.160884i
\(785\) 34.6410 1.23639
\(786\) 0 0
\(787\) 33.5410 19.3649i 1.19561 0.690285i 0.236035 0.971745i \(-0.424152\pi\)
0.959573 + 0.281460i \(0.0908186\pi\)
\(788\) 2.39364 + 8.61803i 0.0852697 + 0.307005i
\(789\) 0 0
\(790\) 32.5000 25.1744i 1.15630 0.895665i
\(791\) 5.19615 27.0000i 0.184754 0.960009i
\(792\) 0 0
\(793\) 0 0
\(794\) −40.5584 16.5836i −1.43936 0.588530i
\(795\) 0 0
\(796\) −11.4164 11.2101i −0.404644 0.397330i
\(797\) 15.6525i 0.554439i −0.960807 0.277220i \(-0.910587\pi\)
0.960807 0.277220i \(-0.0894129\pi\)
\(798\) 0 0
\(799\) −12.0000 −0.424529
\(800\) 0 0
\(801\) 0 0
\(802\) −18.5410 + 45.3457i −0.654706 + 1.60121i
\(803\) −19.3649 11.1803i −0.683373 0.394546i
\(804\) 0 0
\(805\) 13.4164 + 38.7298i 0.472866 + 1.36505i
\(806\) 0 0
\(807\) 0 0
\(808\) 7.56231 10.1396i 0.266041 0.356710i
\(809\) 17.3205 + 30.0000i 0.608957 + 1.05474i 0.991413 + 0.130770i \(0.0417450\pi\)
−0.382456 + 0.923974i \(0.624922\pi\)
\(810\) 0 0
\(811\) 23.2379i 0.815993i 0.912983 + 0.407997i \(0.133772\pi\)
−0.912983 + 0.407997i \(0.866228\pi\)
\(812\) 11.7936 0.954915i 0.413873 0.0335109i
\(813\) 0 0
\(814\) 24.2705 3.30792i 0.850681 0.115943i
\(815\) 17.3205 + 30.0000i 0.606711 + 1.05085i
\(816\) 0 0
\(817\) 0 0
\(818\) 6.06218 + 7.82624i 0.211959 + 0.273638i
\(819\) 0 0
\(820\) 45.0000 + 11.6190i 1.57147 + 0.405751i
\(821\) 13.5554 + 7.82624i 0.473088 + 0.273138i 0.717532 0.696526i \(-0.245272\pi\)
−0.244443 + 0.969664i \(0.578605\pi\)
\(822\) 0 0
\(823\) −10.0000 17.3205i −0.348578 0.603755i 0.637419 0.770517i \(-0.280002\pi\)
−0.985997 + 0.166762i \(0.946669\pi\)
\(824\) −2.64634 + 22.4721i −0.0921896 + 0.782854i
\(825\) 0 0
\(826\) −3.78115 7.46344i −0.131563 0.259686i
\(827\) 24.5967i 0.855313i 0.903941 + 0.427656i \(0.140661\pi\)
−0.903941 + 0.427656i \(0.859339\pi\)
\(828\) 0 0
\(829\) −6.70820 + 3.87298i −0.232986 + 0.134514i −0.611949 0.790898i \(-0.709614\pi\)
0.378963 + 0.925412i \(0.376281\pi\)
\(830\) −13.3808 + 32.7254i −0.464455 + 1.13592i
\(831\) 0 0
\(832\) 0 0
\(833\) −3.46410 24.0000i −0.120024 0.831551i
\(834\) 0 0
\(835\) 20.1246 + 11.6190i 0.696441 + 0.402090i
\(836\) 33.3775 9.27051i 1.15439 0.320627i
\(837\) 0 0
\(838\) −6.83282 50.1329i −0.236036 1.73181i
\(839\) −31.1769 −1.07635 −0.538173 0.842834i \(-0.680885\pi\)
−0.538173 + 0.842834i \(0.680885\pi\)
\(840\) 0 0
\(841\) 24.0000 0.827586
\(842\) 4.43804 + 32.5623i 0.152945 + 1.12217i
\(843\) 0 0
\(844\) 12.4377 + 44.7806i 0.428123 + 1.54141i
\(845\) 25.1744 + 14.5344i 0.866025 + 0.500000i
\(846\) 0 0
\(847\) −12.0000 10.3923i −0.412325 0.357084i
\(848\) 21.6506 39.1312i 0.743486 1.34377i
\(849\) 0 0
\(850\) 0 0
\(851\) −46.4758 + 26.8328i −1.59317 + 0.919817i
\(852\) 0 0
\(853\) 23.2379i 0.795651i −0.917461 0.397825i \(-0.869765\pi\)
0.917461 0.397825i \(-0.130235\pi\)
\(854\) 15.8412 24.2705i 0.542073 0.830520i
\(855\) 0 0
\(856\) −31.4058 3.69837i −1.07343 0.126408i
\(857\) 12.1244 + 21.0000i 0.414160 + 0.717346i 0.995340 0.0964289i \(-0.0307420\pi\)
−0.581180 + 0.813775i \(0.697409\pi\)
\(858\) 0 0
\(859\) 13.4164 + 7.74597i 0.457762 + 0.264289i 0.711103 0.703088i \(-0.248196\pi\)
−0.253341 + 0.967377i \(0.581529\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 21.0000 + 27.1109i 0.715263 + 0.923400i
\(863\) 13.8564 24.0000i 0.471678 0.816970i −0.527797 0.849370i \(-0.676982\pi\)
0.999475 + 0.0324008i \(0.0103153\pi\)
\(864\) 0 0
\(865\) −5.00000 8.66025i −0.170005 0.294457i
\(866\) −30.8277 + 4.20163i −1.04757 + 0.142777i
\(867\) 0 0
\(868\) −4.35410 + 3.00696i −0.147788 + 0.102063i
\(869\) 29.0689i 0.986094i
\(870\) 0 0
\(871\) 0 0
\(872\) −13.0983 + 17.5623i −0.443564 + 0.594735i
\(873\) 0 0
\(874\) −60.0000 + 46.4758i −2.02953 + 1.57207i
\(875\) 29.0474 + 5.59017i 0.981981 + 0.188982i
\(876\) 0 0
\(877\) −26.8328 15.4919i −0.906080 0.523125i −0.0269120 0.999638i \(-0.508567\pi\)
−0.879168 + 0.476512i \(0.841901\pi\)
\(878\) 3.74663 9.16312i 0.126443 0.309240i
\(879\) 0 0
\(880\) −17.1353 + 10.3142i −0.577629 + 0.347692i
\(881\) 10.3923 0.350126 0.175063 0.984557i \(-0.443987\pi\)
0.175063 + 0.984557i \(0.443987\pi\)
\(882\) 0 0
\(883\) 23.2379i 0.782018i 0.920387 + 0.391009i \(0.127874\pi\)
−0.920387 + 0.391009i \(0.872126\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) −32.1976 13.1650i −1.08170 0.442287i
\(887\) 13.8564 24.0000i 0.465253 0.805841i −0.533960 0.845510i \(-0.679297\pi\)
0.999213 + 0.0396684i \(0.0126302\pi\)
\(888\) 0 0
\(889\) −2.50000 + 12.9904i −0.0838473 + 0.435683i
\(890\) −34.6410 + 26.8328i −1.16117 + 0.899438i
\(891\) 0 0
\(892\) −13.4894 + 3.74663i −0.451657 + 0.125447i
\(893\) 23.2379 13.4164i 0.777627 0.448963i
\(894\) 0 0
\(895\) −20.0000 −0.668526
\(896\) 20.5802 + 21.7361i 0.687535 + 0.726151i
\(897\) 0 0
\(898\) −29.1246 + 3.96951i −0.971901 + 0.132464i
\(899\) 1.93649 1.11803i 0.0645856 0.0372885i
\(900\) 0 0
\(901\) 33.5410 + 19.3649i 1.11741 + 0.645139i
\(902\) −25.9808 + 20.1246i −0.865065 + 0.670076i
\(903\) 0 0
\(904\) −27.0000 + 11.6190i −0.898007 + 0.386441i
\(905\) −25.9808 + 45.0000i −0.863630 + 1.49585i
\(906\) 0 0
\(907\) 13.4164 7.74597i 0.445485 0.257201i −0.260437 0.965491i \(-0.583867\pi\)
0.705921 + 0.708290i \(0.250533\pi\)
\(908\) 34.4664 35.1008i 1.14381 1.16486i
\(909\) 0 0
\(910\) 0 0
\(911\) −10.3923 −0.344312 −0.172156 0.985070i \(-0.555073\pi\)
−0.172156 + 0.985070i \(0.555073\pi\)
\(912\) 0 0
\(913\) −12.5000 21.6506i −0.413690 0.716531i
\(914\) −2.67617 + 6.54508i −0.0885197 + 0.216492i
\(915\) 0 0
\(916\) −15.0000 3.87298i −0.495614 0.127967i
\(917\) 19.3649 22.3607i 0.639486 0.738415i
\(918\) 0 0
\(919\) −4.00000 + 6.92820i −0.131948 + 0.228540i −0.924427 0.381358i \(-0.875456\pi\)
0.792480 + 0.609898i \(0.208790\pi\)
\(920\) 26.1966 35.1246i 0.863676 1.15802i
\(921\) 0 0
\(922\) −4.27051 31.3331i −0.140642 1.03190i
\(923\) 0 0
\(924\) 0 0
\(925\) 0 0
\(926\) 11.2101 1.52786i 0.368386 0.0502087i
\(927\) 0 0
\(928\) −7.92705 9.85707i −0.260218 0.323574i
\(929\) −17.3205 + 30.0000i −0.568267 + 0.984268i 0.428470 + 0.903556i \(0.359053\pi\)
−0.996737 + 0.0807121i \(0.974281\pi\)
\(930\) 0 0
\(931\) 33.5410 + 42.6028i 1.09926 + 1.39625i
\(932\) −1.73205 + 6.70820i −0.0567352 + 0.219735i
\(933\) 0 0
\(934\) 11.7082 + 4.78727i 0.383104 + 0.156644i
\(935\) −8.66025 15.0000i −0.283221 0.490552i
\(936\) 0 0
\(937\) 5.00000 0.163343 0.0816714 0.996659i \(-0.473974\pi\)
0.0816714 + 0.996659i \(0.473974\pi\)
\(938\) −13.0983 25.8541i −0.427675 0.844166i
\(939\) 0 0
\(940\) −10.8541 + 11.0539i −0.354022 + 0.360538i
\(941\) 9.68246 5.59017i 0.315639 0.182234i −0.333808 0.942641i \(-0.608334\pi\)
0.649447 + 0.760407i \(0.275000\pi\)
\(942\) 0 0
\(943\) 36.0000 62.3538i 1.17232 2.03052i
\(944\) −4.33013 + 7.82624i −0.140934 + 0.254722i
\(945\) 0 0
\(946\) 0 0
\(947\) 30.9839 + 17.8885i 1.00684 + 0.581300i 0.910265 0.414026i \(-0.135878\pi\)
0.0965754 + 0.995326i \(0.469211\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 0 0
\(951\) 0 0
\(952\) −19.1459 + 17.4767i −0.620522 + 0.566423i
\(953\) −20.7846 −0.673280 −0.336640 0.941634i \(-0.609290\pi\)
−0.336640 + 0.941634i \(0.609290\pi\)
\(954\) 0 0
\(955\) 13.4164 7.74597i 0.434145 0.250654i
\(956\) 40.0530 11.1246i 1.29541 0.359796i
\(957\) 0 0
\(958\) 12.0000 + 15.4919i 0.387702 + 0.500522i
\(959\) −8.66025 + 3.00000i −0.279654 + 0.0968751i
\(960\) 0 0
\(961\) 15.0000 25.9808i 0.483871 0.838089i
\(962\) 0 0
\(963\) 0 0
\(964\) −32.8222 32.2289i −1.05713 1.03802i
\(965\) 38.0132i 1.22369i
\(966\) 0 0
\(967\) −19.0000 −0.610999 −0.305499 0.952192i \(-0.598823\pi\)
−0.305499 + 0.952192i \(0.598823\pi\)
\(968\) −1.98475 + 16.8541i −0.0637924 + 0.541711i
\(969\) 0 0
\(970\) −2.92705 1.19682i −0.0939819 0.0384275i
\(971\) −9.68246 5.59017i −0.310725 0.179397i 0.336526 0.941674i \(-0.390748\pi\)
−0.647251 + 0.762277i \(0.724081\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0.866025 + 1.11803i 0.0277492 + 0.0358241i
\(975\) 0 0
\(976\) −30.9787 + 0.565061i −0.991604 + 0.0180872i
\(977\) 6.92820 + 12.0000i 0.221653 + 0.383914i 0.955310 0.295606i \(-0.0955215\pi\)
−0.733657 + 0.679520i \(0.762188\pi\)
\(978\) 0 0
\(979\) 30.9839i 0.990249i
\(980\) −25.2411 18.5172i −0.806297 0.591511i
\(981\) 0 0
\(982\) −5.55166 40.7330i −0.177161 1.29984i
\(983\) −19.0526 33.0000i −0.607682 1.05254i −0.991621 0.129178i \(-0.958766\pi\)
0.383939 0.923358i \(-0.374567\pi\)
\(984\) 0 0
\(985\) −5.00000 + 8.66025i −0.159313 + 0.275939i
\(986\) 8.66025 6.70820i 0.275799 0.213633i
\(987\) 0 0
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) 0.500000 + 0.866025i 0.0158830 + 0.0275102i 0.873858 0.486182i \(-0.161611\pi\)
−0.857975 + 0.513692i \(0.828277\pi\)
\(992\) 5.27424 + 2.04508i 0.167457 + 0.0649315i
\(993\) 0 0
\(994\) 2.12461 38.8264i 0.0673886 1.23150i
\(995\) 17.8885i 0.567105i
\(996\) 0 0
\(997\) −6.70820 + 3.87298i −0.212451 + 0.122659i −0.602450 0.798157i \(-0.705809\pi\)
0.389999 + 0.920815i \(0.372475\pi\)
\(998\) −40.5584 16.5836i −1.28385 0.524944i
\(999\) 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 504.2.cj.a.37.4 yes 8
3.2 odd 2 inner 504.2.cj.a.37.1 8
4.3 odd 2 2016.2.cr.a.1297.4 8
7.4 even 3 inner 504.2.cj.a.109.2 yes 8
8.3 odd 2 2016.2.cr.a.1297.2 8
8.5 even 2 inner 504.2.cj.a.37.2 yes 8
12.11 even 2 2016.2.cr.a.1297.1 8
21.11 odd 6 inner 504.2.cj.a.109.3 yes 8
24.5 odd 2 inner 504.2.cj.a.37.3 yes 8
24.11 even 2 2016.2.cr.a.1297.3 8
28.11 odd 6 2016.2.cr.a.1873.2 8
56.11 odd 6 2016.2.cr.a.1873.4 8
56.53 even 6 inner 504.2.cj.a.109.4 yes 8
84.11 even 6 2016.2.cr.a.1873.3 8
168.11 even 6 2016.2.cr.a.1873.1 8
168.53 odd 6 inner 504.2.cj.a.109.1 yes 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
504.2.cj.a.37.1 8 3.2 odd 2 inner
504.2.cj.a.37.2 yes 8 8.5 even 2 inner
504.2.cj.a.37.3 yes 8 24.5 odd 2 inner
504.2.cj.a.37.4 yes 8 1.1 even 1 trivial
504.2.cj.a.109.1 yes 8 168.53 odd 6 inner
504.2.cj.a.109.2 yes 8 7.4 even 3 inner
504.2.cj.a.109.3 yes 8 21.11 odd 6 inner
504.2.cj.a.109.4 yes 8 56.53 even 6 inner
2016.2.cr.a.1297.1 8 12.11 even 2
2016.2.cr.a.1297.2 8 8.3 odd 2
2016.2.cr.a.1297.3 8 24.11 even 2
2016.2.cr.a.1297.4 8 4.3 odd 2
2016.2.cr.a.1873.1 8 168.11 even 6
2016.2.cr.a.1873.2 8 28.11 odd 6
2016.2.cr.a.1873.3 8 84.11 even 6
2016.2.cr.a.1873.4 8 56.11 odd 6