Properties

Label 504.2.cj.a.37.2
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 37.2
Root \(-0.535233 + 0.309017i\) of defining polynomial
Character \(\chi\) \(=\) 504.37
Dual form 504.2.cj.a.109.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.535233 - 1.30902i) q^{2} +(-1.42705 + 1.40126i) q^{4} +(-1.93649 - 1.11803i) q^{5} +(-0.500000 + 2.59808i) q^{7} +(2.59808 + 1.11803i) q^{8} +O(q^{10})\) \(q+(-0.535233 - 1.30902i) q^{2} +(-1.42705 + 1.40126i) q^{4} +(-1.93649 - 1.11803i) q^{5} +(-0.500000 + 2.59808i) q^{7} +(2.59808 + 1.11803i) q^{8} +(-0.427051 + 3.13331i) q^{10} +(1.93649 - 1.11803i) q^{11} +(3.66854 - 0.736068i) q^{14} +(0.0729490 - 3.99933i) q^{16} +(1.73205 + 3.00000i) q^{17} +(6.70820 + 3.87298i) q^{19} +(4.33013 - 1.11803i) q^{20} +(-2.50000 - 1.93649i) q^{22} +(3.46410 - 6.00000i) q^{23} +(-2.92705 - 4.40822i) q^{28} +2.23607i q^{29} +(0.500000 + 0.866025i) q^{31} +(-5.27424 + 2.04508i) q^{32} +(3.00000 - 3.87298i) q^{34} +(3.87298 - 4.47214i) q^{35} +(6.70820 + 3.87298i) q^{37} +(1.47935 - 10.8541i) q^{38} +(-3.78115 - 5.06980i) q^{40} +10.3923 q^{41} +(-1.19682 + 4.30902i) q^{44} +(-9.70820 - 1.32317i) q^{46} +(-1.73205 + 3.00000i) q^{47} +(-6.50000 - 2.59808i) q^{49} +(-9.68246 + 5.59017i) q^{53} -5.00000 q^{55} +(-4.20378 + 6.19098i) q^{56} +(2.92705 - 1.19682i) q^{58} +(1.93649 - 1.11803i) q^{59} +(6.70820 + 3.87298i) q^{61} +(0.866025 - 1.11803i) q^{62} +(5.50000 + 5.80948i) q^{64} +(6.70820 - 3.87298i) q^{67} +(-6.67550 - 1.85410i) q^{68} +(-7.92705 - 2.67617i) q^{70} -10.3923 q^{71} +(5.00000 + 8.66025i) q^{73} +(1.47935 - 10.8541i) q^{74} +(-15.0000 + 3.87298i) q^{76} +(1.93649 + 5.59017i) q^{77} +(6.50000 - 11.2583i) q^{79} +(-4.61266 + 7.66312i) q^{80} +(-5.56231 - 13.6037i) q^{82} -11.1803i q^{83} -7.74597i q^{85} +(6.28115 - 0.739674i) q^{88} +(-6.92820 + 12.0000i) q^{89} +(3.46410 + 13.4164i) q^{92} +(4.85410 + 0.661585i) q^{94} +(-8.66025 - 15.0000i) q^{95} -1.00000 q^{97} +(0.0780895 + 9.89919i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 2 q^{4} - 4 q^{7}+O(q^{10}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.535233 1.30902i −0.378467 0.925615i
\(3\) 0 0
\(4\) −1.42705 + 1.40126i −0.713525 + 0.700629i
\(5\) −1.93649 1.11803i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(6\) 0 0
\(7\) −0.500000 + 2.59808i −0.188982 + 0.981981i
\(8\) 2.59808 + 1.11803i 0.918559 + 0.395285i
\(9\) 0 0
\(10\) −0.427051 + 3.13331i −0.135045 + 0.990839i
\(11\) 1.93649 1.11803i 0.583874 0.337100i −0.178797 0.983886i \(-0.557221\pi\)
0.762672 + 0.646786i \(0.223887\pi\)
\(12\) 0 0
\(13\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(14\) 3.66854 0.736068i 0.980459 0.196722i
\(15\) 0 0
\(16\) 0.0729490 3.99933i 0.0182373 0.999834i
\(17\) 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 \(0.0149348\pi\)
0.540068 + 0.841621i \(0.318398\pi\)
\(20\) 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
\(28\) −2.92705 4.40822i −0.553161 0.833075i
\(29\) 2.23607i 0.415227i 0.978211 + 0.207614i \(0.0665697\pi\)
−0.978211 + 0.207614i \(0.933430\pi\)
\(30\) 0 0
\(31\) 0.500000 + 0.866025i 0.0898027 + 0.155543i 0.907428 0.420208i \(-0.138043\pi\)
−0.817625 + 0.575751i \(0.804710\pi\)
\(32\) −5.27424 + 2.04508i −0.932363 + 0.361523i
\(33\) 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 0.936961 0.349435i \(-0.113626\pi\)
0.165861 + 0.986149i \(0.446960\pi\)
\(38\) 1.47935 10.8541i 0.239982 1.76077i
\(39\) 0 0
\(40\) −3.78115 5.06980i −0.597853 0.801606i
\(41\) 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 \(\pi\)
\(44\) −1.19682 + 4.30902i −0.180427 + 0.649609i
\(45\) 0 0
\(46\) −9.70820 1.32317i −1.43140 0.195091i
\(47\) −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 −0.985297 0.170848i \(-0.945349\pi\)
−0.344690 + 0.938716i \(0.612016\pi\)
\(54\) 0 0
\(55\) −5.00000 −0.674200
\(56\) −4.20378 + 6.19098i −0.561753 + 0.827305i
\(57\) 0 0
\(58\) 2.92705 1.19682i 0.384341 0.157150i
\(59\) 1.93649 1.11803i 0.252110 0.145556i −0.368620 0.929580i \(-0.620170\pi\)
0.620730 + 0.784024i \(0.286836\pi\)
\(60\) 0 0
\(61\) 6.70820 + 3.87298i 0.858898 + 0.495885i 0.863643 0.504104i \(-0.168177\pi\)
−0.00474543 + 0.999989i \(0.501511\pi\)
\(62\) 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 −0.0307194 0.999528i \(-0.509780\pi\)
0.850257 + 0.526368i \(0.176447\pi\)
\(68\) −6.67550 1.85410i −0.809523 0.224843i
\(69\) 0 0
\(70\) −7.92705 2.67617i −0.947464 0.319863i
\(71\) −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 \(0.634347\pi\)
\(74\) 1.47935 10.8541i 0.171971 1.26176i
\(75\) 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 \(-0.0944227\pi\)
\(80\) −4.61266 + 7.66312i −0.515711 + 0.856763i
\(81\) 0 0
\(82\) −5.56231 13.6037i −0.614254 1.50228i
\(83\) 11.1803i 1.22720i −0.789616 0.613601i \(-0.789720\pi\)
0.789616 0.613601i \(-0.210280\pi\)
\(84\) 0 0
\(85\) 7.74597i 0.840168i
\(86\) 0 0
\(87\) 0 0
\(88\) 6.28115 0.739674i 0.669573 0.0788495i
\(89\) −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
\(94\) 4.85410 + 0.661585i 0.500662 + 0.0682372i
\(95\) −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 \(0.516167\pi\)
\(98\) 0.0780895 + 9.89919i 0.00788823 + 0.999969i
\(99\) 0 0
\(100\) 0 0
\(101\) −3.87298 + 2.23607i −0.385376 + 0.222497i −0.680155 0.733069i \(-0.738087\pi\)
0.294779 + 0.955566i \(0.404754\pi\)
\(102\) 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 0.888716 0.458458i \(-0.151598\pi\)
0.0473223 + 0.998880i \(0.484931\pi\)
\(108\) 0 0
\(109\) 6.70820 3.87298i 0.642529 0.370965i −0.143059 0.989714i \(-0.545694\pi\)
0.785588 + 0.618750i \(0.212360\pi\)
\(110\) 2.67617 + 6.54508i 0.255162 + 0.624049i
\(111\) 0 0
\(112\) 10.3541 + 2.18919i 0.978371 + 0.206859i
\(113\) −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
\(116\) −3.13331 3.19098i −0.290920 0.296275i
\(117\) 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
\(122\) 1.47935 10.8541i 0.133934 0.982684i
\(123\) 0 0
\(124\) −1.92705 0.535233i −0.173054 0.0480654i
\(125\) 11.1803i 1.00000i
\(126\) 0 0
\(127\) 5.00000 0.443678 0.221839 0.975083i \(-0.428794\pi\)
0.221839 + 0.975083i \(0.428794\pi\)
\(128\) 4.66092 10.3090i 0.411971 0.911197i
\(129\) 0 0
\(130\) 0 0
\(131\) 9.68246 + 5.59017i 0.845960 + 0.488415i 0.859286 0.511496i \(-0.170908\pi\)
−0.0133255 + 0.999911i \(0.504242\pi\)
\(132\) 0 0
\(133\) −13.4164 + 15.4919i −1.16335 + 1.34332i
\(134\) −8.66025 6.70820i −0.748132 0.579501i
\(135\) 0 0
\(136\) 1.14590 + 9.73072i 0.0982599 + 0.834402i
\(137\) 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 \(\pi\)
\(140\) 0.739674 + 11.8090i 0.0625139 + 0.998044i
\(141\) 0 0
\(142\) 5.56231 + 13.6037i 0.466778 + 1.14160i
\(143\) 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 \(-0.964789\pi\)
−0.592548 0.805535i \(-0.701878\pi\)
\(150\) 0 0
\(151\) 3.50000 + 6.06218i 0.284826 + 0.493333i 0.972567 0.232623i \(-0.0747309\pi\)
−0.687741 + 0.725956i \(0.741398\pi\)
\(152\) 13.0983 + 17.5623i 1.06241 + 1.42449i
\(153\) 0 0
\(154\) 6.28115 5.52694i 0.506150 0.445374i
\(155\) 2.23607i 0.179605i
\(156\) 0 0
\(157\) −13.4164 + 7.74597i −1.07075 + 0.618195i −0.928385 0.371619i \(-0.878803\pi\)
−0.142361 + 0.989815i \(0.545469\pi\)
\(158\) −18.2164 2.48278i −1.44922 0.197519i
\(159\) 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 −0.127966 0.991779i \(-0.540845\pi\)
−0.922888 + 0.385068i \(0.874178\pi\)
\(164\) −14.8303 + 14.5623i −1.15806 + 1.13713i
\(165\) 0 0
\(166\) −14.6353 + 5.98409i −1.13592 + 0.464455i
\(167\) 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
\(170\) −10.1396 + 4.14590i −0.777672 + 0.317976i
\(171\) 0 0
\(172\) 0 0
\(173\) 3.87298 + 2.23607i 0.294457 + 0.170005i 0.639950 0.768416i \(-0.278955\pi\)
−0.345493 + 0.938421i \(0.612288\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −4.33013 7.82624i −0.326396 0.589925i
\(177\) 0 0
\(178\) 19.4164 + 2.64634i 1.45532 + 0.198351i
\(179\) 7.74597 4.47214i 0.578961 0.334263i −0.181760 0.983343i \(-0.558179\pi\)
0.760720 + 0.649080i \(0.224846\pi\)
\(180\) 0 0
\(181\) 23.2379i 1.72726i −0.504127 0.863630i \(-0.668186\pi\)
0.504127 0.863630i \(-0.331814\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 15.7082 11.7155i 1.15802 0.863676i
\(185\) −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 \(-0.376238\pi\)
\(194\) 0.535233 + 1.30902i 0.0384275 + 0.0939819i
\(195\) 0 0
\(196\) 12.9164 5.40059i 0.922601 0.385757i
\(197\) 4.47214i 0.318626i −0.987228 0.159313i \(-0.949072\pi\)
0.987228 0.159313i \(-0.0509280\pi\)
\(198\) 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
\(206\) 11.2101 + 1.52786i 0.781042 + 0.106451i
\(207\) 0 0
\(208\) 0 0
\(209\) 17.3205 1.19808
\(210\) 0 0
\(211\) 23.2379i 1.59976i −0.600158 0.799882i \(-0.704896\pi\)
0.600158 0.799882i \(-0.295104\pi\)
\(212\) 5.98409 21.5451i 0.410989 1.47972i
\(213\) 0 0
\(214\) 2.13525 15.6665i 0.145963 1.07094i
\(215\) 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
\(220\) 7.13525 7.00629i 0.481059 0.472364i
\(221\) 0 0
\(222\) 0 0
\(223\) −7.00000 −0.468755 −0.234377 0.972146i \(-0.575305\pi\)
−0.234377 + 0.972146i \(0.575305\pi\)
\(224\) −2.67617 14.7254i −0.178809 0.983884i
\(225\) 0 0
\(226\) 5.56231 + 13.6037i 0.369999 + 0.904905i
\(227\) −21.3014 + 12.2984i −1.41382 + 0.816272i −0.995746 0.0921394i \(-0.970629\pi\)
−0.418078 + 0.908411i \(0.637296\pi\)
\(228\) 0 0
\(229\) 6.70820 + 3.87298i 0.443291 + 0.255934i 0.704992 0.709215i \(-0.250950\pi\)
−0.261702 + 0.965149i \(0.584284\pi\)
\(230\) 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
\(236\) −1.19682 + 4.30902i −0.0779062 + 0.280493i
\(237\) 0 0
\(238\) 8.56231 + 9.73072i 0.555012 + 0.630749i
\(239\) 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 \(-0.432211\pi\)
\(242\) 8.40755 + 1.14590i 0.540458 + 0.0736611i
\(243\) 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
\(248\) 0.330792 + 2.80902i 0.0210053 + 0.178373i
\(249\) 0 0
\(250\) 14.6353 5.98409i 0.925615 0.378467i
\(251\) 24.5967i 1.55253i −0.630405 0.776266i \(-0.717111\pi\)
0.630405 0.776266i \(-0.282889\pi\)
\(252\) 0 0
\(253\) 15.4919i 0.973970i
\(254\) −2.67617 6.54508i −0.167918 0.410675i
\(255\) 0 0
\(256\) −15.9894 0.583495i −0.999335 0.0364684i
\(257\) 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
\(262\) 2.13525 15.6665i 0.131916 0.967882i
\(263\) −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
\(266\) 27.4601 + 9.27051i 1.68369 + 0.568411i
\(267\) 0 0
\(268\) −4.14590 + 14.9269i −0.253251 + 0.911804i
\(269\) 25.1744 14.5344i 1.53491 0.886181i 0.535785 0.844355i \(-0.320016\pi\)
0.999125 0.0418260i \(-0.0133175\pi\)
\(270\) 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 −0.845605 0.533810i \(-0.820760\pi\)
0.0394907 + 0.999220i \(0.487426\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 15.0623 7.28882i 0.900145 0.435590i
\(281\) 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 −0.842604 0.538533i \(-0.818979\pi\)
0.0450815 + 0.998983i \(0.485645\pi\)
\(284\) 14.8303 14.5623i 0.880019 0.864114i
\(285\) 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
\(290\) −7.00629 0.954915i −0.411424 0.0560745i
\(291\) 0 0
\(292\) −19.2705 5.35233i −1.12772 0.313222i
\(293\) 11.1803i 0.653162i −0.945169 0.326581i \(-0.894103\pi\)
0.945169 0.326581i \(-0.105897\pi\)
\(294\) 0 0
\(295\) −5.00000 −0.291111
\(296\) 13.0983 + 17.5623i 0.761323 + 1.02079i
\(297\) 0 0
\(298\) −4.27051 + 31.3331i −0.247384 + 1.81508i
\(299\) 0 0
\(300\) 0 0
\(301\) 0 0
\(302\) 6.06218 7.82624i 0.348839 0.450349i
\(303\) 0 0
\(304\) 15.9787 26.5458i 0.916442 1.52251i
\(305\) −8.66025 15.0000i −0.495885 0.858898i
\(306\) 0 0
\(307\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(308\) −10.5967 5.26393i −0.603806 0.299940i
\(309\) 0 0
\(310\) −2.92705 + 1.19682i −0.166245 + 0.0679747i
\(311\) 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 0.444631 0.895714i \(-0.353335\pi\)
−0.553395 + 0.832919i \(0.686668\pi\)
\(318\) 0 0
\(319\) 2.50000 + 4.33013i 0.139973 + 0.242441i
\(320\) −4.15551 17.3992i −0.232300 0.972644i
\(321\) 0 0
\(322\) 8.29180 24.5611i 0.462084 1.36873i
\(323\) 26.8328i 1.49302i
\(324\) 0 0
\(325\) 0 0
\(326\) −2.95870 + 21.7082i −0.163867 + 1.20231i
\(327\) 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 0.0837026 0.996491i \(-0.473325\pi\)
−0.821135 + 0.570734i \(0.806659\pi\)
\(332\) 15.6665 + 15.9549i 0.859813 + 0.875640i
\(333\) 0 0
\(334\) −5.56231 13.6037i −0.304356 0.744362i
\(335\) −17.3205 −0.946320
\(336\) 0 0
\(337\) −19.0000 −1.03500 −0.517498 0.855684i \(-0.673136\pi\)
−0.517498 + 0.855684i \(0.673136\pi\)
\(338\) −6.95803 17.0172i −0.378467 0.925615i
\(339\) 0 0
\(340\) 10.8541 + 11.0539i 0.588646 + 0.599481i
\(341\) 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
\(346\) 0.854102 6.26662i 0.0459168 0.336896i
\(347\) −15.4919 + 8.94427i −0.831651 + 0.480154i −0.854417 0.519587i \(-0.826086\pi\)
0.0227669 + 0.999741i \(0.492752\pi\)
\(348\) 0 0
\(349\) 23.2379i 1.24390i 0.783058 + 0.621948i \(0.213659\pi\)
−0.783058 + 0.621948i \(0.786341\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −7.92705 + 9.85707i −0.422513 + 0.525384i
\(353\) −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
\(362\) −30.4188 + 12.4377i −1.59878 + 0.653711i
\(363\) 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 \(0.874991\pi\)
\(368\) −23.7433 14.2918i −1.23771 0.745011i
\(369\) 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 0.663512 0.748166i \(-0.269065\pi\)
−0.316174 + 0.948701i \(0.602398\pi\)
\(374\) 1.47935 10.8541i 0.0764953 0.561252i
\(375\) 0 0
\(376\) −7.85410 + 5.85774i −0.405044 + 0.302090i
\(377\) 0 0
\(378\) 0 0
\(379\) 23.2379i 1.19365i −0.802371 0.596825i \(-0.796429\pi\)
0.802371 0.596825i \(-0.203571\pi\)
\(380\) 33.3775 + 9.27051i 1.71223 + 0.475567i
\(381\) 0 0
\(382\) −9.70820 1.32317i −0.496715 0.0676992i
\(383\) 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
\(388\) 1.42705 1.40126i 0.0724475 0.0711381i
\(389\) −3.87298 + 2.23607i −0.196368 + 0.113373i −0.594960 0.803755i \(-0.702832\pi\)
0.398592 + 0.917128i \(0.369499\pi\)
\(390\) 0 0
\(391\) 24.0000 1.21373
\(392\) −13.9828 14.0172i −0.706236 0.707977i
\(393\) 0 0
\(394\) −5.85410 + 2.39364i −0.294925 + 0.120590i
\(395\) −25.1744 + 14.5344i −1.26666 + 0.731307i
\(396\) 0 0
\(397\) 26.8328 + 15.4919i 1.34670 + 0.777518i 0.987781 0.155851i \(-0.0498118\pi\)
0.358920 + 0.933368i \(0.383145\pi\)
\(398\) −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
\(404\) 2.39364 8.61803i 0.119088 0.428763i
\(405\) 0 0
\(406\) 1.64590 + 8.20311i 0.0816845 + 0.407114i
\(407\) 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 \(0.777967\pi\)
\(410\) −4.43804 + 32.5623i −0.219179 + 1.60814i
\(411\) 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
\(418\) −9.27051 22.6728i −0.453435 1.10896i
\(419\) 35.7771i 1.74783i 0.486083 + 0.873913i \(0.338425\pi\)
−0.486083 + 0.873913i \(0.661575\pi\)
\(420\) 0 0
\(421\) 23.2379i 1.13255i −0.824218 0.566273i \(-0.808385\pi\)
0.824218 0.566273i \(-0.191615\pi\)
\(422\) −30.4188 + 12.4377i −1.48076 + 0.605457i
\(423\) 0 0
\(424\) −31.4058 + 3.69837i −1.52520 + 0.179609i
\(425\) 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 \(0.677293\pi\)
\(434\) 2.47172 + 2.80902i 0.118647 + 0.134837i
\(435\) 0 0
\(436\) −4.14590 + 14.9269i −0.198553 + 0.714868i
\(437\) 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 0.911794 0.410647i \(-0.134697\pi\)
0.100266 + 0.994961i \(0.468031\pi\)
\(444\) 0 0
\(445\) 26.8328 15.4919i 1.27200 0.734388i
\(446\) 3.74663 + 9.16312i 0.177408 + 0.433886i
\(447\) 0 0
\(448\) −17.8435 + 11.3847i −0.843024 + 0.537876i
\(449\) −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
\(452\) 14.8303 14.5623i 0.697561 0.684953i
\(453\) 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 \(0.203977\pi\)
\(458\) 1.47935 10.8541i 0.0691254 0.507179i
\(459\) 0 0
\(460\) 8.29180 29.8537i 0.386607 1.39194i
\(461\) 22.3607i 1.04144i 0.853727 + 0.520720i \(0.174337\pi\)
−0.853727 + 0.520720i \(0.825663\pi\)
\(462\) 0 0
\(463\) 8.00000 0.371792 0.185896 0.982569i \(-0.440481\pi\)
0.185896 + 0.982569i \(0.440481\pi\)
\(464\) 8.94278 + 0.163119i 0.415158 + 0.00757261i
\(465\) 0 0
\(466\) 4.85410 + 0.661585i 0.224862 + 0.0306473i
\(467\) −7.74597 4.47214i −0.358441 0.206946i 0.309956 0.950751i \(-0.399686\pi\)
−0.668397 + 0.743805i \(0.733019\pi\)
\(468\) 0 0
\(469\) 6.70820 + 19.3649i 0.309756 + 0.894189i
\(470\) −8.66025 6.70820i −0.399468 0.309426i
\(471\) 0 0
\(472\) 6.28115 0.739674i 0.289113 0.0340463i
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 8.15485 16.4164i 0.373777 0.752445i
\(477\) 0 0
\(478\) −11.1246 27.2074i −0.508828 1.24444i
\(479\) 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 \(0.826121\pi\)
\(488\) 13.0983 + 17.5623i 0.592932 + 0.795008i
\(489\) 0 0
\(490\) 10.9164 19.2570i 0.493153 0.869943i
\(491\) 29.0689i 1.31186i 0.754822 + 0.655930i \(0.227723\pi\)
−0.754822 + 0.655930i \(0.772277\pi\)
\(492\) 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 0.960822 0.277165i \(-0.0893948\pi\)
0.240379 + 0.970679i \(0.422728\pi\)
\(500\) −15.6665 15.9549i −0.700629 0.713525i
\(501\) 0 0
\(502\) −32.1976 + 13.1650i −1.43705 + 0.587582i
\(503\) −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
\(506\) −20.2792 + 8.29180i −0.901521 + 0.368615i
\(507\) 0 0
\(508\) −7.13525 + 7.00629i −0.316576 + 0.310854i
\(509\) −25.1744 14.5344i −1.11584 0.644228i −0.175501 0.984479i \(-0.556154\pi\)
−0.940334 + 0.340251i \(0.889488\pi\)
\(510\) 0 0
\(511\) −25.0000 + 8.66025i −1.10593 + 0.383107i
\(512\) 7.79423 + 21.2426i 0.344459 + 0.938801i
\(513\) 0 0
\(514\) −9.70820 1.32317i −0.428211 0.0583625i
\(515\) 15.4919 8.94427i 0.682656 0.394132i
\(516\) 0 0
\(517\) 7.74597i 0.340667i
\(518\) 27.4601 + 9.27051i 1.20653 + 0.407323i
\(519\) 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 0.954459 0.298342i \(-0.0964335\pi\)
0.218858 + 0.975757i \(0.429767\pi\)
\(524\) −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
\(530\) −13.3808 32.7254i −0.581226 1.42150i
\(531\) 0 0
\(532\) −2.56231 40.9076i −0.111090 1.77357i
\(533\) 0 0
\(534\) 0 0
\(535\) −12.5000 21.6506i −0.540422 0.936039i
\(536\) 21.7586 2.56231i 0.939826 0.110675i
\(537\) 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 0.183051 0.983103i \(-0.441403\pi\)
−0.759867 + 0.650078i \(0.774736\pi\)
\(542\) −1.40126 0.190983i −0.0601892 0.00820342i
\(543\) 0 0
\(544\) −15.2705 12.2805i −0.654718 0.526524i
\(545\) −17.3205 −0.741929
\(546\) 0 0
\(547\) 23.2379i 0.993581i 0.867871 + 0.496790i \(0.165488\pi\)
−0.867871 + 0.496790i \(0.834512\pi\)
\(548\) −6.67550 1.85410i −0.285163 0.0792033i
\(549\) 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 −0.184527 0.982827i \(-0.559075\pi\)
0.758890 + 0.651219i \(0.225742\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) −17.6030 15.8156i −0.743864 0.668331i
\(561\) 0 0
\(562\) −5.56231 13.6037i −0.234632 0.573838i
\(563\) −32.9204 + 19.0066i −1.38743 + 0.801032i −0.993025 0.117906i \(-0.962382\pi\)
−0.394403 + 0.918938i \(0.629049\pi\)
\(564\) 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 −0.353024 0.935614i \(-0.614847\pi\)
0.633754 + 0.773535i \(0.281513\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 38.1246 7.64944i 1.59129 0.319282i
\(575\) 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 \(-0.426465\pi\)
\(578\) −7.00629 0.954915i −0.291423 0.0397192i
\(579\) 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
\(584\) 3.30792 + 28.0902i 0.136883 + 1.16238i
\(585\) 0 0
\(586\) −14.6353 + 5.98409i −0.604577 + 0.247200i
\(587\) 38.0132i 1.56897i −0.620147 0.784485i \(-0.712927\pi\)
0.620147 0.784485i \(-0.287073\pi\)
\(588\) 0 0
\(589\) 7.74597i 0.319167i
\(590\) 2.67617 + 6.54508i 0.110176 + 0.269457i
\(591\) 0 0
\(592\) 15.9787 26.5458i 0.656721 1.09103i
\(593\) 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
\(604\) −13.4894 3.74663i −0.548874 0.152448i
\(605\) 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 0.151857 0.988402i \(-0.451475\pi\)
0.931910 + 0.362689i \(0.118141\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) −1.21885 + 16.6888i −0.0491087 + 0.672409i
\(617\) −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 −0.359092 0.933302i \(-0.616914\pi\)
0.628717 + 0.777634i \(0.283580\pi\)
\(620\) 3.13331 + 3.19098i 0.125837 + 0.128153i
\(621\) 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
\(626\) 32.2289 + 4.39261i 1.28813 + 0.175564i
\(627\) 0 0
\(628\) 8.29180 29.8537i 0.330879 1.19129i
\(629\) 26.8328i 1.06989i
\(630\) 0 0
\(631\) 11.0000 0.437903 0.218952 0.975736i \(-0.429736\pi\)
0.218952 + 0.975736i \(0.429736\pi\)
\(632\) 29.4747 21.9828i 1.17244 0.874428i
\(633\) 0 0
\(634\) −0.427051 + 3.13331i −0.0169604 + 0.124440i
\(635\) −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
\(640\) −20.5517 + 14.7523i −0.812376 + 0.583134i
\(641\) 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 \(-0.848492\pi\)
0.888846 0.458207i \(-0.151508\pi\)
\(644\) −36.5889 + 2.29180i −1.44180 + 0.0903094i
\(645\) 0 0
\(646\) 35.1246 14.3618i 1.38196 0.565058i
\(647\) 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 −0.441997 0.897016i \(-0.645730\pi\)
−0.997838 + 0.0657275i \(0.979063\pi\)
\(654\) 0 0
\(655\) −12.5000 21.6506i −0.488415 0.845960i
\(656\) 0.758108 41.5623i 0.0295992 1.62274i
\(657\) 0 0
\(658\) −4.14590 + 12.2805i −0.161624 + 0.478745i
\(659\) 17.8885i 0.696839i −0.937339 0.348419i \(-0.886719\pi\)
0.937339 0.348419i \(-0.113281\pi\)
\(660\) 0 0
\(661\) −13.4164 + 7.74597i −0.521838 + 0.301283i −0.737686 0.675144i \(-0.764082\pi\)
0.215848 + 0.976427i \(0.430748\pi\)
\(662\) −2.95870 + 21.7082i −0.114993 + 0.843713i
\(663\) 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
\(668\) −14.8303 + 14.5623i −0.573803 + 0.563433i
\(669\) 0 0
\(670\) 9.27051 + 22.6728i 0.358151 + 0.875928i
\(671\) 17.3205 0.668651
\(672\) 0 0
\(673\) −7.00000 −0.269830 −0.134915 0.990857i \(-0.543076\pi\)
−0.134915 + 0.990857i \(0.543076\pi\)
\(674\) 10.1694 + 24.8713i 0.391712 + 0.958008i
\(675\) 0 0
\(676\) −18.5517 + 18.2164i −0.713525 + 0.700629i
\(677\) 21.3014 + 12.2984i 0.818680 + 0.472665i 0.849961 0.526846i \(-0.176625\pi\)
−0.0312813 + 0.999511i \(0.509959\pi\)
\(678\) 0 0
\(679\) 0.500000 2.59808i 0.0191882 0.0997050i
\(680\) 8.66025 20.1246i 0.332106 0.771744i
\(681\) 0 0
\(682\) 0.427051 3.13331i 0.0163526 0.119981i
\(683\) −9.68246 + 5.59017i −0.370489 + 0.213902i −0.673672 0.739030i \(-0.735284\pi\)
0.303183 + 0.952932i \(0.401951\pi\)
\(684\) 0 0
\(685\) 7.74597i 0.295958i
\(686\) −25.7579 4.74671i −0.983441 0.181230i
\(687\) 0 0
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) −33.5410 19.3649i −1.27596 0.736676i −0.299857 0.953984i \(-0.596939\pi\)
−0.976103 + 0.217308i \(0.930272\pi\)
\(692\) −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
\(698\) 30.4188 12.4377i 1.15137 0.470774i
\(699\) 0 0
\(700\) 0 0
\(701\) 24.5967i 0.929006i −0.885571 0.464503i \(-0.846233\pi\)
0.885571 0.464503i \(-0.153767\pi\)
\(702\) 0 0
\(703\) 30.0000 + 51.9615i 1.13147 + 1.95977i
\(704\) 17.1459 + 5.10081i 0.646210 + 0.192244i
\(705\) 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 0.226444 0.974024i \(-0.427290\pi\)
−0.730308 + 0.683118i \(0.760623\pi\)
\(710\) 4.43804 32.5623i 0.166557 1.22204i
\(711\) 0 0
\(712\) −31.4164 + 23.4309i −1.17738 + 0.878112i
\(713\) 6.92820 0.259463
\(714\) 0 0
\(715\) 0 0
\(716\) −4.78727 + 17.2361i −0.178909 + 0.644142i
\(717\) 0 0
\(718\) −24.2705 3.30792i −0.905767 0.123451i
\(719\) 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
\(724\) 32.5623 + 33.1617i 1.21017 + 1.23244i
\(725\) 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
\(730\) −29.2705 + 11.9682i −1.08335 + 0.442962i
\(731\) 0 0
\(732\) 0 0
\(733\) −13.4164 7.74597i −0.495546 0.286104i 0.231326 0.972876i \(-0.425694\pi\)
−0.726872 + 0.686772i \(0.759027\pi\)
\(734\) −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 −0.726038 0.687655i \(-0.758640\pi\)
0.232507 + 0.972595i \(0.425307\pi\)
\(740\) 33.3775 + 9.27051i 1.22698 + 0.340791i
\(741\) 0 0
\(742\) −31.4058 + 27.6347i −1.15294 + 1.01450i
\(743\) 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
\(746\) 1.47935 10.8541i 0.0541628 0.397397i
\(747\) 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 \(-0.120437\pi\)
\(752\) 11.8717 + 7.14590i 0.432915 + 0.260584i
\(753\) 0 0
\(754\) 0 0
\(755\) 15.6525i 0.569652i
\(756\) 0 0
\(757\) 23.2379i 0.844596i 0.906457 + 0.422298i \(0.138776\pi\)
−0.906457 + 0.422298i \(0.861224\pi\)
\(758\) −30.4188 + 12.4377i −1.10486 + 0.451757i
\(759\) 0 0
\(760\) −5.72949 48.6536i −0.207830 1.76485i
\(761\) 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
\(766\) −9.70820 1.32317i −0.350772 0.0478080i
\(767\) 0 0
\(768\) 0 0
\(769\) −31.0000 −1.11789 −0.558944 0.829205i \(-0.688793\pi\)
−0.558944 + 0.829205i \(0.688793\pi\)
\(770\) −18.3427 + 3.68034i −0.661025 + 0.132630i
\(771\) 0 0
\(772\) 32.7599 + 9.09896i 1.17905 + 0.327479i
\(773\) −3.87298 + 2.23607i −0.139302 + 0.0804258i −0.568031 0.823007i \(-0.692295\pi\)
0.428730 + 0.903433i \(0.358961\pi\)
\(774\) 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
\(782\) −12.8456 31.4164i −0.459358 1.12345i
\(783\) 0 0
\(784\) −10.8647 + 25.8061i −0.388027 + 0.921648i
\(785\) 34.6410 1.23639
\(786\) 0 0
\(787\) −33.5410 + 19.3649i −1.19561 + 0.690285i −0.959573 0.281460i \(-0.909181\pi\)
−0.236035 + 0.971745i \(0.575848\pi\)
\(788\) 6.26662 + 6.38197i 0.223239 + 0.227348i
\(789\) 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
\(794\) 5.91739 43.4164i 0.210000 1.54079i
\(795\) 0 0
\(796\) 15.4164 + 4.28187i 0.546420 + 0.151767i
\(797\) 15.6525i 0.554439i 0.960807 + 0.277220i \(0.0894129\pi\)
−0.960807 + 0.277220i \(0.910587\pi\)
\(798\) 0 0
\(799\) −12.0000 −0.424529
\(800\) 0 0
\(801\) 0 0
\(802\) 48.5410 + 6.61585i 1.71404 + 0.233614i
\(803\) 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
\(808\) −12.5623 + 1.47935i −0.441940 + 0.0520433i
\(809\) 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 \(-0.866228\pi\)
0.912983 0.407997i \(-0.133772\pi\)
\(812\) 9.85707 6.54508i 0.345915 0.229687i
\(813\) 0 0
\(814\) −9.27051 22.6728i −0.324931 0.794683i
\(815\) 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 0.244443 0.969664i \(-0.421395\pi\)
−0.717532 + 0.696526i \(0.754728\pi\)
\(822\) 0 0
\(823\) −10.0000 17.3205i −0.348578 0.603755i 0.637419 0.770517i \(-0.280002\pi\)
−0.985997 + 0.166762i \(0.946669\pi\)
\(824\) −18.1383 + 13.5279i −0.631877 + 0.471265i
\(825\) 0 0
\(826\) 6.28115 5.52694i 0.218549 0.192307i
\(827\) 24.5967i 0.855313i −0.903941 0.427656i \(-0.859339\pi\)
0.903941 0.427656i \(-0.140661\pi\)
\(828\) 0 0
\(829\) 6.70820 3.87298i 0.232986 0.134514i −0.378963 0.925412i \(-0.623719\pi\)
0.611949 + 0.790898i \(0.290386\pi\)
\(830\) 35.0315 + 4.77458i 1.21596 + 0.165728i
\(831\) 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
\(836\) −24.7172 + 24.2705i −0.854864 + 0.839413i
\(837\) 0 0
\(838\) 46.8328 19.1491i 1.61781 0.661494i
\(839\) −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
\(842\) −30.4188 + 12.4377i −1.04830 + 0.428631i
\(843\) 0 0
\(844\) 32.5623 + 33.1617i 1.12084 + 1.14147i
\(845\) −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 \(0.130235\pi\)
−0.917461 + 0.397825i \(0.869765\pi\)
\(854\) 27.4601 + 9.27051i 0.939666 + 0.317230i
\(855\) 0 0
\(856\) 18.9058 + 25.3490i 0.646186 + 0.866411i
\(857\) 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 0.253341 0.967377i \(-0.418471\pi\)
−0.711103 + 0.703088i \(0.751804\pi\)
\(860\) 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
\(866\) 11.7751 + 28.7984i 0.400135 + 0.978609i
\(867\) 0 0
\(868\) 2.35410 4.73901i 0.0799034 0.160852i
\(869\) 29.0689i 0.986094i
\(870\) 0 0
\(871\) 0 0
\(872\) 21.7586 2.56231i 0.736838 0.0867706i
\(873\) 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 0.879168 0.476512i \(-0.158099\pi\)
0.0269120 + 0.999638i \(0.491433\pi\)
\(878\) −9.80881 1.33688i −0.331031 0.0451175i
\(879\) 0 0
\(880\) −0.364745 + 19.9967i −0.0122956 + 0.674088i
\(881\) 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 \(-0.872126\pi\)
0.920387 0.391009i \(-0.127874\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 4.69756 34.4664i 0.157818 1.15792i
\(887\) 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
\(892\) 9.98936 9.80881i 0.334468 0.328423i
\(893\) −23.2379 + 13.4164i −0.777627 + 0.448963i
\(894\) 0 0
\(895\) −20.0000 −0.668526
\(896\) 24.4532 + 17.2639i 0.816922 + 0.576747i
\(897\) 0 0
\(898\) 11.1246 + 27.2074i 0.371233 + 0.907923i
\(899\) −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 −0.705921 0.708290i \(-0.749467\pi\)
0.260437 + 0.965491i \(0.416133\pi\)
\(908\) 13.1650 47.3992i 0.436896 1.57300i
\(909\) 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
\(914\) 7.00629 + 0.954915i 0.231748 + 0.0315858i
\(915\) 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 \(0.208790\pi\)
\(920\) −43.5171 + 5.12461i −1.43472 + 0.168953i
\(921\) 0 0
\(922\) 29.2705 11.9682i 0.963973 0.394151i
\(923\) 0 0
\(924\) 0 0
\(925\) 0 0
\(926\) −4.28187 10.4721i −0.140711 0.344136i
\(927\) 0 0
\(928\) −4.57295 11.7936i −0.150114 0.387143i
\(929\) −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
\(934\) −1.70820 + 12.5332i −0.0558941 + 0.410100i
\(935\) −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 \(0.473974\pi\)
\(938\) 21.7586 19.1459i 0.710442 0.625136i
\(939\) 0 0
\(940\) −4.14590 + 14.9269i −0.135224 + 0.486861i
\(941\) −9.68246 + 5.59017i −0.315639 + 0.182234i −0.649447 0.760407i \(-0.725000\pi\)
0.333808 + 0.942641i \(0.391666\pi\)
\(942\) 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 −0.0965754 0.995326i \(-0.530789\pi\)
−0.910265 + 0.414026i \(0.864122\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 0 0
\(951\) 0 0
\(952\) −25.8541 1.88823i −0.837936 0.0611979i
\(953\) −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
\(956\) −29.6607 + 29.1246i −0.959296 + 0.941957i
\(957\) 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
\(964\) 44.3222 + 12.3104i 1.42752 + 0.396490i
\(965\) 38.0132i 1.22369i
\(966\) 0 0
\(967\) −19.0000 −0.610999 −0.305499 0.952192i \(-0.598823\pi\)
−0.305499 + 0.952192i \(0.598823\pi\)
\(968\) −13.6037 + 10.1459i −0.437240 + 0.326102i
\(969\) 0 0
\(970\) 0.427051 3.13331i 0.0137118 0.100605i
\(971\) 9.68246 + 5.59017i 0.310725 + 0.179397i 0.647251 0.762277i \(-0.275919\pi\)
−0.336526 + 0.941674i \(0.609252\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0.866025 1.11803i 0.0277492 0.0358241i
\(975\) 0 0
\(976\) 15.9787 26.5458i 0.511466 0.849711i
\(977\) 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
\(980\) −31.0506 3.98278i −0.991874 0.127225i
\(981\) 0 0
\(982\) 38.0517 15.5586i 1.21428 0.496496i
\(983\) −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 \(0.828277\pi\)
\(992\) −4.40822 3.54508i −0.139961 0.112557i
\(993\) 0 0
\(994\) −38.1246 + 7.64944i −1.20924 + 0.242626i
\(995\) 17.8885i 0.567105i
\(996\) 0 0
\(997\) 6.70820 3.87298i 0.212451 0.122659i −0.389999 0.920815i \(-0.627525\pi\)
0.602450 + 0.798157i \(0.294191\pi\)
\(998\) 5.91739 43.4164i 0.187312 1.37432i
\(999\) 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.37.2 yes 8
3.2 odd 2 inner 504.2.cj.a.37.3 yes 8
4.3 odd 2 2016.2.cr.a.1297.2 8
7.4 even 3 inner 504.2.cj.a.109.4 yes 8
8.3 odd 2 2016.2.cr.a.1297.4 8
8.5 even 2 inner 504.2.cj.a.37.4 yes 8
12.11 even 2 2016.2.cr.a.1297.3 8
21.11 odd 6 inner 504.2.cj.a.109.1 yes 8
24.5 odd 2 inner 504.2.cj.a.37.1 8
24.11 even 2 2016.2.cr.a.1297.1 8
28.11 odd 6 2016.2.cr.a.1873.4 8
56.11 odd 6 2016.2.cr.a.1873.2 8
56.53 even 6 inner 504.2.cj.a.109.2 yes 8
84.11 even 6 2016.2.cr.a.1873.1 8
168.11 even 6 2016.2.cr.a.1873.3 8
168.53 odd 6 inner 504.2.cj.a.109.3 yes 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
504.2.cj.a.37.1 8 24.5 odd 2 inner
504.2.cj.a.37.2 yes 8 1.1 even 1 trivial
504.2.cj.a.37.3 yes 8 3.2 odd 2 inner
504.2.cj.a.37.4 yes 8 8.5 even 2 inner
504.2.cj.a.109.1 yes 8 21.11 odd 6 inner
504.2.cj.a.109.2 yes 8 56.53 even 6 inner
504.2.cj.a.109.3 yes 8 168.53 odd 6 inner
504.2.cj.a.109.4 yes 8 7.4 even 3 inner
2016.2.cr.a.1297.1 8 24.11 even 2
2016.2.cr.a.1297.2 8 4.3 odd 2
2016.2.cr.a.1297.3 8 12.11 even 2
2016.2.cr.a.1297.4 8 8.3 odd 2
2016.2.cr.a.1873.1 8 84.11 even 6
2016.2.cr.a.1873.2 8 56.11 odd 6
2016.2.cr.a.1873.3 8 168.11 even 6
2016.2.cr.a.1873.4 8 28.11 odd 6