Properties

Label 1134.2.g.l.163.2
Level $1134$
Weight $2$
Character 1134.163
Analytic conductor $9.055$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1134,2,Mod(163,1134)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1134, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([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("1134.163");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1134 = 2 \cdot 3^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1134.g (of order \(3\), 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: \(9.05503558921\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.309123.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 126)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 163.2
Root \(0.500000 - 2.05195i\) of defining polynomial
Character \(\chi\) \(=\) 1134.163
Dual form 1134.2.g.l.487.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(0.296790 - 0.514055i) q^{5} +(-2.25729 + 1.38008i) q^{7} +1.00000 q^{8} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(0.296790 - 0.514055i) q^{5} +(-2.25729 + 1.38008i) q^{7} +1.00000 q^{8} +(0.296790 + 0.514055i) q^{10} +(-0.296790 - 0.514055i) q^{11} +2.51459 q^{13} +(-0.0665372 - 2.64491i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-1.46050 - 2.52967i) q^{17} +(2.69076 - 4.66053i) q^{19} -0.593579 q^{20} +0.593579 q^{22} +(2.23025 - 3.86291i) q^{23} +(2.32383 + 4.02499i) q^{25} +(-1.25729 + 2.17770i) q^{26} +(2.32383 + 1.26483i) q^{28} -6.19436 q^{29} +(3.93346 + 6.81296i) q^{31} +(-0.500000 - 0.866025i) q^{32} +2.92101 q^{34} +(0.0394951 + 1.56997i) q^{35} +(0.500000 - 0.866025i) q^{37} +(2.69076 + 4.66053i) q^{38} +(0.296790 - 0.514055i) q^{40} -0.273346 q^{41} +11.1623 q^{43} +(-0.296790 + 0.514055i) q^{44} +(2.23025 + 3.86291i) q^{46} +(6.08113 - 10.5328i) q^{47} +(3.19076 - 6.23049i) q^{49} -4.64766 q^{50} +(-1.25729 - 2.17770i) q^{52} +(-4.02704 - 6.97504i) q^{53} -0.352336 q^{55} +(-2.25729 + 1.38008i) q^{56} +(3.09718 - 5.36447i) q^{58} +(4.32383 + 7.48910i) q^{59} +(3.32383 - 5.75705i) q^{61} -7.86693 q^{62} +1.00000 q^{64} +(0.746304 - 1.29264i) q^{65} +(0.956906 + 1.65741i) q^{67} +(-1.46050 + 2.52967i) q^{68} +(-1.37938 - 0.750780i) q^{70} +14.4107 q^{71} +(3.95691 + 6.85356i) q^{73} +(0.500000 + 0.866025i) q^{74} -5.38151 q^{76} +(1.37938 + 0.750780i) q^{77} +(4.62422 - 8.00938i) q^{79} +(0.296790 + 0.514055i) q^{80} +(0.136673 - 0.236725i) q^{82} +7.70175 q^{83} -1.73385 q^{85} +(-5.58113 + 9.66679i) q^{86} +(-0.296790 - 0.514055i) q^{88} +(6.21780 - 10.7695i) q^{89} +(-5.67617 + 3.47033i) q^{91} -4.46050 q^{92} +(6.08113 + 10.5328i) q^{94} +(-1.59718 - 2.76639i) q^{95} -11.7339 q^{97} +(3.80039 + 5.87852i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - 3 q^{2} - 3 q^{4} - q^{5} + 2 q^{7} + 6 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - 3 q^{2} - 3 q^{4} - q^{5} + 2 q^{7} + 6 q^{8} - q^{10} + q^{11} - 16 q^{13} - 4 q^{14} - 3 q^{16} + 4 q^{17} - 3 q^{19} + 2 q^{20} - 2 q^{22} + 7 q^{23} + 2 q^{25} + 8 q^{26} + 2 q^{28} - 10 q^{29} + 20 q^{31} - 3 q^{32} - 8 q^{34} + 13 q^{35} + 3 q^{37} - 3 q^{38} - q^{40} + 12 q^{43} + q^{44} + 7 q^{46} + 9 q^{47} - 4 q^{50} + 8 q^{52} - 15 q^{53} - 26 q^{55} + 2 q^{56} + 5 q^{58} + 14 q^{59} + 8 q^{61} - 40 q^{62} + 6 q^{64} + 12 q^{65} + q^{67} + 4 q^{68} - 23 q^{70} - 14 q^{71} + 19 q^{73} + 3 q^{74} + 6 q^{76} + 23 q^{77} + 5 q^{79} - q^{80} + 4 q^{83} + 4 q^{85} - 6 q^{86} + q^{88} + 9 q^{89} - 46 q^{91} - 14 q^{92} + 9 q^{94} + 4 q^{95} - 56 q^{97} + 12 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(325\) \(407\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 + 0.866025i −0.353553 + 0.612372i
\(3\) 0 0
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 0.296790 0.514055i 0.132728 0.229892i −0.791999 0.610522i \(-0.790960\pi\)
0.924727 + 0.380630i \(0.124293\pi\)
\(6\) 0 0
\(7\) −2.25729 + 1.38008i −0.853177 + 0.521621i
\(8\) 1.00000 0.353553
\(9\) 0 0
\(10\) 0.296790 + 0.514055i 0.0938531 + 0.162558i
\(11\) −0.296790 0.514055i −0.0894855 0.154993i 0.817808 0.575491i \(-0.195189\pi\)
−0.907294 + 0.420497i \(0.861856\pi\)
\(12\) 0 0
\(13\) 2.51459 0.697422 0.348711 0.937230i \(-0.386620\pi\)
0.348711 + 0.937230i \(0.386620\pi\)
\(14\) −0.0665372 2.64491i −0.0177828 0.706883i
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −1.46050 2.52967i −0.354224 0.613535i 0.632760 0.774348i \(-0.281922\pi\)
−0.986985 + 0.160813i \(0.948588\pi\)
\(18\) 0 0
\(19\) 2.69076 4.66053i 0.617302 1.06920i −0.372674 0.927962i \(-0.621559\pi\)
0.989976 0.141236i \(-0.0451077\pi\)
\(20\) −0.593579 −0.132728
\(21\) 0 0
\(22\) 0.593579 0.126552
\(23\) 2.23025 3.86291i 0.465040 0.805473i −0.534164 0.845381i \(-0.679373\pi\)
0.999203 + 0.0399086i \(0.0127067\pi\)
\(24\) 0 0
\(25\) 2.32383 + 4.02499i 0.464766 + 0.804999i
\(26\) −1.25729 + 2.17770i −0.246576 + 0.427082i
\(27\) 0 0
\(28\) 2.32383 + 1.26483i 0.439163 + 0.239031i
\(29\) −6.19436 −1.15026 −0.575132 0.818061i \(-0.695049\pi\)
−0.575132 + 0.818061i \(0.695049\pi\)
\(30\) 0 0
\(31\) 3.93346 + 6.81296i 0.706471 + 1.22364i 0.966158 + 0.257951i \(0.0830472\pi\)
−0.259687 + 0.965693i \(0.583620\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) 0 0
\(34\) 2.92101 0.500949
\(35\) 0.0394951 + 1.56997i 0.00667590 + 0.265373i
\(36\) 0 0
\(37\) 0.500000 0.866025i 0.0821995 0.142374i −0.821995 0.569495i \(-0.807139\pi\)
0.904194 + 0.427121i \(0.140472\pi\)
\(38\) 2.69076 + 4.66053i 0.436498 + 0.756038i
\(39\) 0 0
\(40\) 0.296790 0.514055i 0.0469266 0.0812792i
\(41\) −0.273346 −0.0426895 −0.0213448 0.999772i \(-0.506795\pi\)
−0.0213448 + 0.999772i \(0.506795\pi\)
\(42\) 0 0
\(43\) 11.1623 1.70223 0.851114 0.524981i \(-0.175928\pi\)
0.851114 + 0.524981i \(0.175928\pi\)
\(44\) −0.296790 + 0.514055i −0.0447427 + 0.0774967i
\(45\) 0 0
\(46\) 2.23025 + 3.86291i 0.328833 + 0.569555i
\(47\) 6.08113 10.5328i 0.887023 1.53637i 0.0436467 0.999047i \(-0.486102\pi\)
0.843377 0.537323i \(-0.180564\pi\)
\(48\) 0 0
\(49\) 3.19076 6.23049i 0.455822 0.890071i
\(50\) −4.64766 −0.657279
\(51\) 0 0
\(52\) −1.25729 2.17770i −0.174355 0.301992i
\(53\) −4.02704 6.97504i −0.553157 0.958096i −0.998044 0.0625092i \(-0.980090\pi\)
0.444888 0.895586i \(-0.353244\pi\)
\(54\) 0 0
\(55\) −0.352336 −0.0475090
\(56\) −2.25729 + 1.38008i −0.301644 + 0.184421i
\(57\) 0 0
\(58\) 3.09718 5.36447i 0.406679 0.704389i
\(59\) 4.32383 + 7.48910i 0.562915 + 0.974997i 0.997240 + 0.0742412i \(0.0236535\pi\)
−0.434325 + 0.900756i \(0.643013\pi\)
\(60\) 0 0
\(61\) 3.32383 5.75705i 0.425573 0.737114i −0.570901 0.821019i \(-0.693406\pi\)
0.996474 + 0.0839050i \(0.0267392\pi\)
\(62\) −7.86693 −0.999101
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 0.746304 1.29264i 0.0925676 0.160332i
\(66\) 0 0
\(67\) 0.956906 + 1.65741i 0.116905 + 0.202485i 0.918540 0.395329i \(-0.129369\pi\)
−0.801635 + 0.597814i \(0.796036\pi\)
\(68\) −1.46050 + 2.52967i −0.177112 + 0.306767i
\(69\) 0 0
\(70\) −1.37938 0.750780i −0.164867 0.0897353i
\(71\) 14.4107 1.71023 0.855117 0.518435i \(-0.173485\pi\)
0.855117 + 0.518435i \(0.173485\pi\)
\(72\) 0 0
\(73\) 3.95691 + 6.85356i 0.463121 + 0.802149i 0.999115 0.0420732i \(-0.0133963\pi\)
−0.535994 + 0.844222i \(0.680063\pi\)
\(74\) 0.500000 + 0.866025i 0.0581238 + 0.100673i
\(75\) 0 0
\(76\) −5.38151 −0.617302
\(77\) 1.37938 + 0.750780i 0.157195 + 0.0855593i
\(78\) 0 0
\(79\) 4.62422 8.00938i 0.520265 0.901126i −0.479457 0.877565i \(-0.659166\pi\)
0.999722 0.0235607i \(-0.00750031\pi\)
\(80\) 0.296790 + 0.514055i 0.0331821 + 0.0574731i
\(81\) 0 0
\(82\) 0.136673 0.236725i 0.0150930 0.0261419i
\(83\) 7.70175 0.845377 0.422688 0.906275i \(-0.361087\pi\)
0.422688 + 0.906275i \(0.361087\pi\)
\(84\) 0 0
\(85\) −1.73385 −0.188063
\(86\) −5.58113 + 9.66679i −0.601828 + 1.04240i
\(87\) 0 0
\(88\) −0.296790 0.514055i −0.0316379 0.0547984i
\(89\) 6.21780 10.7695i 0.659085 1.14157i −0.321767 0.946819i \(-0.604277\pi\)
0.980853 0.194751i \(-0.0623898\pi\)
\(90\) 0 0
\(91\) −5.67617 + 3.47033i −0.595024 + 0.363790i
\(92\) −4.46050 −0.465040
\(93\) 0 0
\(94\) 6.08113 + 10.5328i 0.627220 + 1.08638i
\(95\) −1.59718 2.76639i −0.163867 0.283826i
\(96\) 0 0
\(97\) −11.7339 −1.19139 −0.595696 0.803210i \(-0.703124\pi\)
−0.595696 + 0.803210i \(0.703124\pi\)
\(98\) 3.80039 + 5.87852i 0.383897 + 0.593821i
\(99\) 0 0
\(100\) 2.32383 4.02499i 0.232383 0.402499i
\(101\) −0.811379 1.40535i −0.0807352 0.139837i 0.822831 0.568287i \(-0.192393\pi\)
−0.903566 + 0.428449i \(0.859060\pi\)
\(102\) 0 0
\(103\) −3.19076 + 5.52655i −0.314395 + 0.544548i −0.979309 0.202372i \(-0.935135\pi\)
0.664914 + 0.746920i \(0.268468\pi\)
\(104\) 2.51459 0.246576
\(105\) 0 0
\(106\) 8.05408 0.782282
\(107\) −9.35447 + 16.2024i −0.904331 + 1.56635i −0.0825182 + 0.996590i \(0.526296\pi\)
−0.821813 + 0.569758i \(0.807037\pi\)
\(108\) 0 0
\(109\) −1.43346 2.48283i −0.137301 0.237812i 0.789173 0.614171i \(-0.210509\pi\)
−0.926474 + 0.376359i \(0.877176\pi\)
\(110\) 0.176168 0.305132i 0.0167970 0.0290932i
\(111\) 0 0
\(112\) −0.0665372 2.64491i −0.00628718 0.249921i
\(113\) −12.3202 −1.15899 −0.579495 0.814976i \(-0.696750\pi\)
−0.579495 + 0.814976i \(0.696750\pi\)
\(114\) 0 0
\(115\) −1.32383 2.29294i −0.123448 0.213818i
\(116\) 3.09718 + 5.36447i 0.287566 + 0.498078i
\(117\) 0 0
\(118\) −8.64766 −0.796082
\(119\) 6.78794 + 3.69459i 0.622249 + 0.338683i
\(120\) 0 0
\(121\) 5.32383 9.22115i 0.483985 0.838286i
\(122\) 3.32383 + 5.75705i 0.300926 + 0.521218i
\(123\) 0 0
\(124\) 3.93346 6.81296i 0.353235 0.611822i
\(125\) 5.72665 0.512207
\(126\) 0 0
\(127\) 12.3346 1.09452 0.547261 0.836962i \(-0.315671\pi\)
0.547261 + 0.836962i \(0.315671\pi\)
\(128\) −0.500000 + 0.866025i −0.0441942 + 0.0765466i
\(129\) 0 0
\(130\) 0.746304 + 1.29264i 0.0654552 + 0.113372i
\(131\) −0.593579 + 1.02811i −0.0518613 + 0.0898264i −0.890791 0.454414i \(-0.849849\pi\)
0.838929 + 0.544240i \(0.183182\pi\)
\(132\) 0 0
\(133\) 0.358071 + 14.2336i 0.0310487 + 1.23421i
\(134\) −1.91381 −0.165328
\(135\) 0 0
\(136\) −1.46050 2.52967i −0.125237 0.216917i
\(137\) 1.26089 + 2.18393i 0.107725 + 0.186586i 0.914848 0.403797i \(-0.132310\pi\)
−0.807123 + 0.590383i \(0.798977\pi\)
\(138\) 0 0
\(139\) −4.91381 −0.416784 −0.208392 0.978045i \(-0.566823\pi\)
−0.208392 + 0.978045i \(0.566823\pi\)
\(140\) 1.33988 0.819187i 0.113241 0.0692339i
\(141\) 0 0
\(142\) −7.20535 + 12.4800i −0.604659 + 1.04730i
\(143\) −0.746304 1.29264i −0.0624091 0.108096i
\(144\) 0 0
\(145\) −1.83842 + 3.18424i −0.152673 + 0.264437i
\(146\) −7.91381 −0.654952
\(147\) 0 0
\(148\) −1.00000 −0.0821995
\(149\) 9.02558 15.6328i 0.739404 1.28069i −0.213360 0.976974i \(-0.568441\pi\)
0.952764 0.303712i \(-0.0982261\pi\)
\(150\) 0 0
\(151\) −0.823832 1.42692i −0.0670425 0.116121i 0.830556 0.556936i \(-0.188023\pi\)
−0.897598 + 0.440815i \(0.854690\pi\)
\(152\) 2.69076 4.66053i 0.218249 0.378019i
\(153\) 0 0
\(154\) −1.33988 + 0.819187i −0.107971 + 0.0660120i
\(155\) 4.66964 0.375075
\(156\) 0 0
\(157\) 3.30039 + 5.71644i 0.263400 + 0.456222i 0.967143 0.254233i \(-0.0818229\pi\)
−0.703743 + 0.710454i \(0.748490\pi\)
\(158\) 4.62422 + 8.00938i 0.367883 + 0.637192i
\(159\) 0 0
\(160\) −0.593579 −0.0469266
\(161\) 0.296790 + 11.7977i 0.0233903 + 0.929785i
\(162\) 0 0
\(163\) −2.99115 + 5.18082i −0.234285 + 0.405793i −0.959065 0.283188i \(-0.908608\pi\)
0.724780 + 0.688980i \(0.241941\pi\)
\(164\) 0.136673 + 0.236725i 0.0106724 + 0.0184851i
\(165\) 0 0
\(166\) −3.85087 + 6.66991i −0.298886 + 0.517685i
\(167\) 7.46050 0.577311 0.288656 0.957433i \(-0.406792\pi\)
0.288656 + 0.957433i \(0.406792\pi\)
\(168\) 0 0
\(169\) −6.67684 −0.513603
\(170\) 0.866926 1.50156i 0.0664902 0.115164i
\(171\) 0 0
\(172\) −5.58113 9.66679i −0.425557 0.737086i
\(173\) −12.8296 + 22.2215i −0.975414 + 1.68947i −0.296851 + 0.954924i \(0.595937\pi\)
−0.678562 + 0.734543i \(0.737397\pi\)
\(174\) 0 0
\(175\) −10.8004 5.87852i −0.816433 0.444375i
\(176\) 0.593579 0.0447427
\(177\) 0 0
\(178\) 6.21780 + 10.7695i 0.466044 + 0.807211i
\(179\) −7.51819 13.0219i −0.561936 0.973301i −0.997328 0.0730602i \(-0.976723\pi\)
0.435392 0.900241i \(-0.356610\pi\)
\(180\) 0 0
\(181\) −0.0861875 −0.00640627 −0.00320313 0.999995i \(-0.501020\pi\)
−0.00320313 + 0.999995i \(0.501020\pi\)
\(182\) −0.167314 6.65087i −0.0124021 0.492996i
\(183\) 0 0
\(184\) 2.23025 3.86291i 0.164416 0.284778i
\(185\) −0.296790 0.514055i −0.0218204 0.0377941i
\(186\) 0 0
\(187\) −0.866926 + 1.50156i −0.0633959 + 0.109805i
\(188\) −12.1623 −0.887023
\(189\) 0 0
\(190\) 3.19436 0.231743
\(191\) 1.99115 3.44877i 0.144074 0.249544i −0.784953 0.619555i \(-0.787313\pi\)
0.929027 + 0.370011i \(0.120646\pi\)
\(192\) 0 0
\(193\) −3.39037 5.87229i −0.244044 0.422697i 0.717818 0.696230i \(-0.245141\pi\)
−0.961862 + 0.273534i \(0.911808\pi\)
\(194\) 5.86693 10.1618i 0.421221 0.729576i
\(195\) 0 0
\(196\) −6.99115 + 0.351971i −0.499368 + 0.0251408i
\(197\) −11.0584 −0.787875 −0.393938 0.919137i \(-0.628887\pi\)
−0.393938 + 0.919137i \(0.628887\pi\)
\(198\) 0 0
\(199\) 2.80924 + 4.86575i 0.199142 + 0.344924i 0.948250 0.317523i \(-0.102851\pi\)
−0.749109 + 0.662447i \(0.769518\pi\)
\(200\) 2.32383 + 4.02499i 0.164320 + 0.284610i
\(201\) 0 0
\(202\) 1.62276 0.114177
\(203\) 13.9825 8.54871i 0.981378 0.600002i
\(204\) 0 0
\(205\) −0.0811263 + 0.140515i −0.00566611 + 0.00981399i
\(206\) −3.19076 5.52655i −0.222311 0.385053i
\(207\) 0 0
\(208\) −1.25729 + 2.17770i −0.0871777 + 0.150996i
\(209\) −3.19436 −0.220958
\(210\) 0 0
\(211\) −19.3245 −1.33035 −0.665177 0.746686i \(-0.731644\pi\)
−0.665177 + 0.746686i \(0.731644\pi\)
\(212\) −4.02704 + 6.97504i −0.276578 + 0.479048i
\(213\) 0 0
\(214\) −9.35447 16.2024i −0.639459 1.10757i
\(215\) 3.31284 5.73801i 0.225934 0.391329i
\(216\) 0 0
\(217\) −18.2814 9.95036i −1.24102 0.675474i
\(218\) 2.86693 0.194173
\(219\) 0 0
\(220\) 0.176168 + 0.305132i 0.0118773 + 0.0205720i
\(221\) −3.67257 6.36108i −0.247044 0.427892i
\(222\) 0 0
\(223\) −25.3245 −1.69585 −0.847927 0.530113i \(-0.822150\pi\)
−0.847927 + 0.530113i \(0.822150\pi\)
\(224\) 2.32383 + 1.26483i 0.155268 + 0.0845103i
\(225\) 0 0
\(226\) 6.16012 10.6696i 0.409765 0.709734i
\(227\) 2.40856 + 4.17174i 0.159862 + 0.276888i 0.934819 0.355126i \(-0.115562\pi\)
−0.774957 + 0.632014i \(0.782229\pi\)
\(228\) 0 0
\(229\) 4.64766 8.04999i 0.307126 0.531958i −0.670606 0.741814i \(-0.733966\pi\)
0.977732 + 0.209855i \(0.0672993\pi\)
\(230\) 2.64766 0.174582
\(231\) 0 0
\(232\) −6.19436 −0.406679
\(233\) −0.0971780 + 0.168317i −0.00636634 + 0.0110268i −0.869191 0.494476i \(-0.835360\pi\)
0.862825 + 0.505503i \(0.168693\pi\)
\(234\) 0 0
\(235\) −3.60963 6.25206i −0.235466 0.407840i
\(236\) 4.32383 7.48910i 0.281457 0.487499i
\(237\) 0 0
\(238\) −6.59358 + 4.03123i −0.427398 + 0.261306i
\(239\) −13.6549 −0.883260 −0.441630 0.897197i \(-0.645600\pi\)
−0.441630 + 0.897197i \(0.645600\pi\)
\(240\) 0 0
\(241\) 6.50000 + 11.2583i 0.418702 + 0.725213i 0.995809 0.0914555i \(-0.0291519\pi\)
−0.577107 + 0.816668i \(0.695819\pi\)
\(242\) 5.32383 + 9.22115i 0.342229 + 0.592758i
\(243\) 0 0
\(244\) −6.64766 −0.425573
\(245\) −2.25583 3.48937i −0.144120 0.222928i
\(246\) 0 0
\(247\) 6.76615 11.7193i 0.430520 0.745682i
\(248\) 3.93346 + 6.81296i 0.249775 + 0.432623i
\(249\) 0 0
\(250\) −2.86333 + 4.95943i −0.181093 + 0.313662i
\(251\) 19.5438 1.23359 0.616796 0.787123i \(-0.288430\pi\)
0.616796 + 0.787123i \(0.288430\pi\)
\(252\) 0 0
\(253\) −2.64766 −0.166457
\(254\) −6.16731 + 10.6821i −0.386972 + 0.670255i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 4.16372 7.21177i 0.259725 0.449858i −0.706443 0.707770i \(-0.749701\pi\)
0.966168 + 0.257912i \(0.0830346\pi\)
\(258\) 0 0
\(259\) 0.0665372 + 2.64491i 0.00413442 + 0.164347i
\(260\) −1.49261 −0.0925676
\(261\) 0 0
\(262\) −0.593579 1.02811i −0.0366715 0.0635168i
\(263\) −8.54523 14.8008i −0.526921 0.912655i −0.999508 0.0313704i \(-0.990013\pi\)
0.472586 0.881284i \(-0.343320\pi\)
\(264\) 0 0
\(265\) −4.78074 −0.293678
\(266\) −12.5057 6.80672i −0.766776 0.417347i
\(267\) 0 0
\(268\) 0.956906 1.65741i 0.0584524 0.101242i
\(269\) 5.00720 + 8.67272i 0.305294 + 0.528785i 0.977327 0.211737i \(-0.0679119\pi\)
−0.672033 + 0.740522i \(0.734579\pi\)
\(270\) 0 0
\(271\) 5.10457 8.84137i 0.310081 0.537075i −0.668299 0.743893i \(-0.732977\pi\)
0.978380 + 0.206818i \(0.0663106\pi\)
\(272\) 2.92101 0.177112
\(273\) 0 0
\(274\) −2.52179 −0.152347
\(275\) 1.37938 2.38915i 0.0831797 0.144071i
\(276\) 0 0
\(277\) −9.67111 16.7508i −0.581081 1.00646i −0.995352 0.0963074i \(-0.969297\pi\)
0.414271 0.910154i \(-0.364037\pi\)
\(278\) 2.45691 4.25549i 0.147355 0.255227i
\(279\) 0 0
\(280\) 0.0394951 + 1.56997i 0.00236029 + 0.0938235i
\(281\) −12.8027 −0.763746 −0.381873 0.924215i \(-0.624721\pi\)
−0.381873 + 0.924215i \(0.624721\pi\)
\(282\) 0 0
\(283\) 8.17617 + 14.1615i 0.486023 + 0.841816i 0.999871 0.0160650i \(-0.00511388\pi\)
−0.513848 + 0.857881i \(0.671781\pi\)
\(284\) −7.20535 12.4800i −0.427559 0.740553i
\(285\) 0 0
\(286\) 1.49261 0.0882598
\(287\) 0.617023 0.377240i 0.0364217 0.0222678i
\(288\) 0 0
\(289\) 4.23385 7.33325i 0.249050 0.431367i
\(290\) −1.83842 3.18424i −0.107956 0.186985i
\(291\) 0 0
\(292\) 3.95691 6.85356i 0.231560 0.401074i
\(293\) −20.7778 −1.21385 −0.606926 0.794758i \(-0.707598\pi\)
−0.606926 + 0.794758i \(0.707598\pi\)
\(294\) 0 0
\(295\) 5.13307 0.298859
\(296\) 0.500000 0.866025i 0.0290619 0.0503367i
\(297\) 0 0
\(298\) 9.02558 + 15.6328i 0.522838 + 0.905582i
\(299\) 5.60817 9.71363i 0.324329 0.561754i
\(300\) 0 0
\(301\) −25.1965 + 15.4048i −1.45230 + 0.887918i
\(302\) 1.64766 0.0948124
\(303\) 0 0
\(304\) 2.69076 + 4.66053i 0.154326 + 0.267300i
\(305\) −1.97296 3.41726i −0.112971 0.195672i
\(306\) 0 0
\(307\) −22.6768 −1.29424 −0.647118 0.762390i \(-0.724026\pi\)
−0.647118 + 0.762390i \(0.724026\pi\)
\(308\) −0.0394951 1.56997i −0.00225044 0.0894572i
\(309\) 0 0
\(310\) −2.33482 + 4.04403i −0.132609 + 0.229686i
\(311\) −3.25729 5.64180i −0.184704 0.319917i 0.758773 0.651356i \(-0.225799\pi\)
−0.943477 + 0.331439i \(0.892466\pi\)
\(312\) 0 0
\(313\) −0.133074 + 0.230492i −0.00752181 + 0.0130282i −0.869762 0.493472i \(-0.835728\pi\)
0.862240 + 0.506500i \(0.169061\pi\)
\(314\) −6.60078 −0.372503
\(315\) 0 0
\(316\) −9.24844 −0.520265
\(317\) 7.86186 13.6171i 0.441566 0.764815i −0.556240 0.831022i \(-0.687756\pi\)
0.997806 + 0.0662067i \(0.0210897\pi\)
\(318\) 0 0
\(319\) 1.83842 + 3.18424i 0.102932 + 0.178283i
\(320\) 0.296790 0.514055i 0.0165910 0.0287365i
\(321\) 0 0
\(322\) −10.3655 5.64180i −0.577645 0.314405i
\(323\) −15.7195 −0.874654
\(324\) 0 0
\(325\) 5.84348 + 10.1212i 0.324138 + 0.561424i
\(326\) −2.99115 5.18082i −0.165664 0.286939i
\(327\) 0 0
\(328\) −0.273346 −0.0150930
\(329\) 0.809243 + 32.1681i 0.0446150 + 1.77349i
\(330\) 0 0
\(331\) 12.5811 21.7912i 0.691521 1.19775i −0.279818 0.960053i \(-0.590274\pi\)
0.971339 0.237697i \(-0.0763925\pi\)
\(332\) −3.85087 6.66991i −0.211344 0.366059i
\(333\) 0 0
\(334\) −3.73025 + 6.46099i −0.204110 + 0.353529i
\(335\) 1.13600 0.0620663
\(336\) 0 0
\(337\) 18.7339 1.02050 0.510249 0.860027i \(-0.329553\pi\)
0.510249 + 0.860027i \(0.329553\pi\)
\(338\) 3.33842 5.78231i 0.181586 0.314516i
\(339\) 0 0
\(340\) 0.866926 + 1.50156i 0.0470156 + 0.0814335i
\(341\) 2.33482 4.04403i 0.126438 0.218997i
\(342\) 0 0
\(343\) 1.39610 + 18.4676i 0.0753825 + 0.997155i
\(344\) 11.1623 0.601828
\(345\) 0 0
\(346\) −12.8296 22.2215i −0.689722 1.19463i
\(347\) 11.2719 + 19.5235i 0.605106 + 1.04808i 0.992035 + 0.125965i \(0.0402028\pi\)
−0.386928 + 0.922110i \(0.626464\pi\)
\(348\) 0 0
\(349\) −3.79086 −0.202920 −0.101460 0.994840i \(-0.532351\pi\)
−0.101460 + 0.994840i \(0.532351\pi\)
\(350\) 10.4911 6.41415i 0.560775 0.342851i
\(351\) 0 0
\(352\) −0.296790 + 0.514055i −0.0158189 + 0.0273992i
\(353\) 3.41741 + 5.91913i 0.181890 + 0.315043i 0.942524 0.334138i \(-0.108445\pi\)
−0.760634 + 0.649181i \(0.775112\pi\)
\(354\) 0 0
\(355\) 4.27694 7.40789i 0.226997 0.393170i
\(356\) −12.4356 −0.659085
\(357\) 0 0
\(358\) 15.0364 0.794697
\(359\) 6.32237 10.9507i 0.333682 0.577954i −0.649549 0.760320i \(-0.725042\pi\)
0.983231 + 0.182366i \(0.0583755\pi\)
\(360\) 0 0
\(361\) −4.98035 8.62622i −0.262124 0.454012i
\(362\) 0.0430937 0.0746406i 0.00226496 0.00392302i
\(363\) 0 0
\(364\) 5.84348 + 3.18054i 0.306282 + 0.166706i
\(365\) 4.69748 0.245877
\(366\) 0 0
\(367\) −3.27188 5.66707i −0.170791 0.295819i 0.767906 0.640563i \(-0.221299\pi\)
−0.938697 + 0.344744i \(0.887966\pi\)
\(368\) 2.23025 + 3.86291i 0.116260 + 0.201368i
\(369\) 0 0
\(370\) 0.593579 0.0308587
\(371\) 18.7163 + 10.1871i 0.971704 + 0.528887i
\(372\) 0 0
\(373\) −4.71420 + 8.16524i −0.244092 + 0.422780i −0.961876 0.273486i \(-0.911823\pi\)
0.717784 + 0.696266i \(0.245157\pi\)
\(374\) −0.866926 1.50156i −0.0448277 0.0776438i
\(375\) 0 0
\(376\) 6.08113 10.5328i 0.313610 0.543189i
\(377\) −15.5763 −0.802218
\(378\) 0 0
\(379\) −7.27762 −0.373826 −0.186913 0.982376i \(-0.559848\pi\)
−0.186913 + 0.982376i \(0.559848\pi\)
\(380\) −1.59718 + 2.76639i −0.0819335 + 0.141913i
\(381\) 0 0
\(382\) 1.99115 + 3.44877i 0.101876 + 0.176454i
\(383\) −12.0416 + 20.8567i −0.615299 + 1.06573i 0.375033 + 0.927011i \(0.377631\pi\)
−0.990332 + 0.138717i \(0.955702\pi\)
\(384\) 0 0
\(385\) 0.795327 0.486253i 0.0405336 0.0247817i
\(386\) 6.78074 0.345130
\(387\) 0 0
\(388\) 5.86693 + 10.1618i 0.297848 + 0.515888i
\(389\) −8.14913 14.1147i −0.413177 0.715644i 0.582058 0.813147i \(-0.302248\pi\)
−0.995235 + 0.0975035i \(0.968914\pi\)
\(390\) 0 0
\(391\) −13.0292 −0.658914
\(392\) 3.19076 6.23049i 0.161158 0.314688i
\(393\) 0 0
\(394\) 5.52918 9.57682i 0.278556 0.482473i
\(395\) −2.74484 4.75420i −0.138108 0.239210i
\(396\) 0 0
\(397\) −6.08619 + 10.5416i −0.305457 + 0.529067i −0.977363 0.211569i \(-0.932143\pi\)
0.671906 + 0.740636i \(0.265476\pi\)
\(398\) −5.61849 −0.281629
\(399\) 0 0
\(400\) −4.64766 −0.232383
\(401\) −16.6804 + 28.8914i −0.832981 + 1.44277i 0.0626819 + 0.998034i \(0.480035\pi\)
−0.895663 + 0.444733i \(0.853299\pi\)
\(402\) 0 0
\(403\) 9.89104 + 17.1318i 0.492708 + 0.853395i
\(404\) −0.811379 + 1.40535i −0.0403676 + 0.0699187i
\(405\) 0 0
\(406\) 0.412155 + 16.3835i 0.0204549 + 0.813102i
\(407\) −0.593579 −0.0294226
\(408\) 0 0
\(409\) 2.89037 + 5.00627i 0.142920 + 0.247544i 0.928595 0.371095i \(-0.121018\pi\)
−0.785675 + 0.618639i \(0.787684\pi\)
\(410\) −0.0811263 0.140515i −0.00400654 0.00693954i
\(411\) 0 0
\(412\) 6.38151 0.314395
\(413\) −20.0957 10.9379i −0.988846 0.538217i
\(414\) 0 0
\(415\) 2.28580 3.95912i 0.112205 0.194346i
\(416\) −1.25729 2.17770i −0.0616439 0.106770i
\(417\) 0 0
\(418\) 1.59718 2.76639i 0.0781205 0.135309i
\(419\) 30.8712 1.50816 0.754078 0.656784i \(-0.228084\pi\)
0.754078 + 0.656784i \(0.228084\pi\)
\(420\) 0 0
\(421\) 3.73385 0.181977 0.0909884 0.995852i \(-0.470997\pi\)
0.0909884 + 0.995852i \(0.470997\pi\)
\(422\) 9.66225 16.7355i 0.470351 0.814672i
\(423\) 0 0
\(424\) −4.02704 6.97504i −0.195570 0.338738i
\(425\) 6.78794 11.7570i 0.329263 0.570301i
\(426\) 0 0
\(427\) 0.442317 + 17.5825i 0.0214052 + 0.850877i
\(428\) 18.7089 0.904331
\(429\) 0 0
\(430\) 3.31284 + 5.73801i 0.159759 + 0.276711i
\(431\) 14.0979 + 24.4182i 0.679070 + 1.17618i 0.975261 + 0.221055i \(0.0709499\pi\)
−0.296192 + 0.955128i \(0.595717\pi\)
\(432\) 0 0
\(433\) 12.5438 0.602815 0.301407 0.953495i \(-0.402544\pi\)
0.301407 + 0.953495i \(0.402544\pi\)
\(434\) 17.7580 10.8570i 0.852410 0.521152i
\(435\) 0 0
\(436\) −1.43346 + 2.48283i −0.0686504 + 0.118906i
\(437\) −12.0021 20.7883i −0.574140 0.994440i
\(438\) 0 0
\(439\) −13.0203 + 22.5519i −0.621426 + 1.07634i 0.367794 + 0.929907i \(0.380113\pi\)
−0.989220 + 0.146434i \(0.953220\pi\)
\(440\) −0.352336 −0.0167970
\(441\) 0 0
\(442\) 7.34514 0.349373
\(443\) −11.7865 + 20.4148i −0.559992 + 0.969935i 0.437504 + 0.899216i \(0.355863\pi\)
−0.997496 + 0.0707186i \(0.977471\pi\)
\(444\) 0 0
\(445\) −3.69076 6.39258i −0.174959 0.303037i
\(446\) 12.6623 21.9317i 0.599575 1.03849i
\(447\) 0 0
\(448\) −2.25729 + 1.38008i −0.106647 + 0.0652027i
\(449\) −13.6870 −0.645928 −0.322964 0.946411i \(-0.604679\pi\)
−0.322964 + 0.946411i \(0.604679\pi\)
\(450\) 0 0
\(451\) 0.0811263 + 0.140515i 0.00382009 + 0.00661659i
\(452\) 6.16012 + 10.6696i 0.289748 + 0.501857i
\(453\) 0 0
\(454\) −4.81711 −0.226078
\(455\) 0.0993140 + 3.94782i 0.00465591 + 0.185077i
\(456\) 0 0
\(457\) 11.1762 19.3577i 0.522799 0.905515i −0.476849 0.878985i \(-0.658221\pi\)
0.999648 0.0265293i \(-0.00844554\pi\)
\(458\) 4.64766 + 8.04999i 0.217171 + 0.376151i
\(459\) 0 0
\(460\) −1.32383 + 2.29294i −0.0617240 + 0.106909i
\(461\) −7.97509 −0.371437 −0.185719 0.982603i \(-0.559461\pi\)
−0.185719 + 0.982603i \(0.559461\pi\)
\(462\) 0 0
\(463\) 28.7352 1.33544 0.667719 0.744413i \(-0.267271\pi\)
0.667719 + 0.744413i \(0.267271\pi\)
\(464\) 3.09718 5.36447i 0.143783 0.249039i
\(465\) 0 0
\(466\) −0.0971780 0.168317i −0.00450168 0.00779714i
\(467\) −16.7829 + 29.0688i −0.776619 + 1.34514i 0.157261 + 0.987557i \(0.449733\pi\)
−0.933880 + 0.357586i \(0.883600\pi\)
\(468\) 0 0
\(469\) −4.44738 2.42066i −0.205361 0.111775i
\(470\) 7.21926 0.333000
\(471\) 0 0
\(472\) 4.32383 + 7.48910i 0.199020 + 0.344714i
\(473\) −3.31284 5.73801i −0.152325 0.263834i
\(474\) 0 0
\(475\) 25.0115 1.14760
\(476\) −0.194356 7.72582i −0.00890829 0.354112i
\(477\) 0 0
\(478\) 6.82743 11.8255i 0.312279 0.540884i
\(479\) 0.183560 + 0.317935i 0.00838707 + 0.0145268i 0.870188 0.492719i \(-0.163997\pi\)
−0.861801 + 0.507246i \(0.830664\pi\)
\(480\) 0 0
\(481\) 1.25729 2.17770i 0.0573277 0.0992945i
\(482\) −13.0000 −0.592134
\(483\) 0 0
\(484\) −10.6477 −0.483985
\(485\) −3.48249 + 6.03184i −0.158132 + 0.273892i
\(486\) 0 0
\(487\) −14.9538 25.9007i −0.677621 1.17367i −0.975695 0.219131i \(-0.929678\pi\)
0.298075 0.954543i \(-0.403656\pi\)
\(488\) 3.32383 5.75705i 0.150463 0.260609i
\(489\) 0 0
\(490\) 4.14980 0.208922i 0.187469 0.00943816i
\(491\) −0.510317 −0.0230303 −0.0115151 0.999934i \(-0.503665\pi\)
−0.0115151 + 0.999934i \(0.503665\pi\)
\(492\) 0 0
\(493\) 9.04689 + 15.6697i 0.407451 + 0.705726i
\(494\) 6.76615 + 11.7193i 0.304423 + 0.527277i
\(495\) 0 0
\(496\) −7.86693 −0.353235
\(497\) −32.5292 + 19.8879i −1.45913 + 0.892095i
\(498\) 0 0
\(499\) 9.50953 16.4710i 0.425705 0.737343i −0.570781 0.821102i \(-0.693359\pi\)
0.996486 + 0.0837597i \(0.0266928\pi\)
\(500\) −2.86333 4.95943i −0.128052 0.221792i
\(501\) 0 0
\(502\) −9.77188 + 16.9254i −0.436141 + 0.755418i
\(503\) 37.7807 1.68456 0.842280 0.539040i \(-0.181213\pi\)
0.842280 + 0.539040i \(0.181213\pi\)
\(504\) 0 0
\(505\) −0.963235 −0.0428634
\(506\) 1.32383 2.29294i 0.0588515 0.101934i
\(507\) 0 0
\(508\) −6.16731 10.6821i −0.273630 0.473942i
\(509\) −5.60817 + 9.71363i −0.248578 + 0.430549i −0.963131 0.269031i \(-0.913296\pi\)
0.714554 + 0.699581i \(0.246630\pi\)
\(510\) 0 0
\(511\) −18.3904 10.0097i −0.813542 0.442801i
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) 4.16372 + 7.21177i 0.183654 + 0.318097i
\(515\) 1.89397 + 3.28045i 0.0834582 + 0.144554i
\(516\) 0 0
\(517\) −7.21926 −0.317503
\(518\) −2.32383 1.26483i −0.102103 0.0555736i
\(519\) 0 0
\(520\) 0.746304 1.29264i 0.0327276 0.0566859i
\(521\) 13.7360 + 23.7914i 0.601785 + 1.04232i 0.992551 + 0.121831i \(0.0388767\pi\)
−0.390766 + 0.920490i \(0.627790\pi\)
\(522\) 0 0
\(523\) 11.0919 19.2118i 0.485016 0.840072i −0.514836 0.857289i \(-0.672147\pi\)
0.999852 + 0.0172166i \(0.00548048\pi\)
\(524\) 1.18716 0.0518613
\(525\) 0 0
\(526\) 17.0905 0.745179
\(527\) 11.4897 19.9007i 0.500498 0.866889i
\(528\) 0 0
\(529\) 1.55195 + 2.68805i 0.0674760 + 0.116872i
\(530\) 2.39037 4.14024i 0.103831 0.179841i
\(531\) 0 0
\(532\) 12.1477 7.42692i 0.526668 0.321998i
\(533\) −0.687353 −0.0297726
\(534\) 0 0
\(535\) 5.55262 + 9.61742i 0.240061 + 0.415797i
\(536\) 0.956906 + 1.65741i 0.0413321 + 0.0715892i
\(537\) 0 0
\(538\) −10.0144 −0.431751
\(539\) −4.14980 + 0.208922i −0.178745 + 0.00899893i
\(540\) 0 0
\(541\) 14.9246 25.8502i 0.641659 1.11139i −0.343403 0.939188i \(-0.611580\pi\)
0.985062 0.172198i \(-0.0550869\pi\)
\(542\) 5.10457 + 8.84137i 0.219260 + 0.379770i
\(543\) 0 0
\(544\) −1.46050 + 2.52967i −0.0626186 + 0.108459i
\(545\) −1.70175 −0.0728949
\(546\) 0 0
\(547\) −17.6870 −0.756240 −0.378120 0.925757i \(-0.623429\pi\)
−0.378120 + 0.925757i \(0.623429\pi\)
\(548\) 1.26089 2.18393i 0.0538627 0.0932929i
\(549\) 0 0
\(550\) 1.37938 + 2.38915i 0.0588169 + 0.101874i
\(551\) −16.6675 + 28.8690i −0.710060 + 1.22986i
\(552\) 0 0
\(553\) 0.615366 + 24.4613i 0.0261680 + 1.04020i
\(554\) 19.3422 0.821772
\(555\) 0 0
\(556\) 2.45691 + 4.25549i 0.104196 + 0.180473i
\(557\) −15.0651 26.0935i −0.638328 1.10562i −0.985800 0.167926i \(-0.946293\pi\)
0.347472 0.937690i \(-0.387040\pi\)
\(558\) 0 0
\(559\) 28.0685 1.18717
\(560\) −1.37938 0.750780i −0.0582894 0.0317262i
\(561\) 0 0
\(562\) 6.40136 11.0875i 0.270025 0.467697i
\(563\) 2.04883 + 3.54867i 0.0863478 + 0.149559i 0.905965 0.423353i \(-0.139147\pi\)
−0.819617 + 0.572912i \(0.805814\pi\)
\(564\) 0 0
\(565\) −3.65652 + 6.33327i −0.153831 + 0.266443i
\(566\) −16.3523 −0.687340
\(567\) 0 0
\(568\) 14.4107 0.604659
\(569\) 3.11849 5.40138i 0.130734 0.226437i −0.793226 0.608927i \(-0.791600\pi\)
0.923960 + 0.382490i \(0.124933\pi\)
\(570\) 0 0
\(571\) −17.8011 30.8323i −0.744951 1.29029i −0.950218 0.311587i \(-0.899139\pi\)
0.205266 0.978706i \(-0.434194\pi\)
\(572\) −0.746304 + 1.29264i −0.0312045 + 0.0540479i
\(573\) 0 0
\(574\) 0.0181877 + 0.722977i 0.000759140 + 0.0301765i
\(575\) 20.7309 0.864539
\(576\) 0 0
\(577\) 23.1388 + 40.0776i 0.963281 + 1.66845i 0.714164 + 0.699979i \(0.246807\pi\)
0.249118 + 0.968473i \(0.419859\pi\)
\(578\) 4.23385 + 7.33325i 0.176105 + 0.305023i
\(579\) 0 0
\(580\) 3.67684 0.152673
\(581\) −17.3851 + 10.6290i −0.721256 + 0.440966i
\(582\) 0 0
\(583\) −2.39037 + 4.14024i −0.0989990 + 0.171471i
\(584\) 3.95691 + 6.85356i 0.163738 + 0.283602i
\(585\) 0 0
\(586\) 10.3889 17.9941i 0.429162 0.743330i
\(587\) 2.26322 0.0934132 0.0467066 0.998909i \(-0.485127\pi\)
0.0467066 + 0.998909i \(0.485127\pi\)
\(588\) 0 0
\(589\) 42.3360 1.74442
\(590\) −2.56654 + 4.44537i −0.105663 + 0.183013i
\(591\) 0 0
\(592\) 0.500000 + 0.866025i 0.0205499 + 0.0355934i
\(593\) −23.0979 + 40.0067i −0.948515 + 1.64288i −0.199960 + 0.979804i \(0.564081\pi\)
−0.748555 + 0.663072i \(0.769252\pi\)
\(594\) 0 0
\(595\) 3.91381 2.39285i 0.160451 0.0980974i
\(596\) −18.0512 −0.739404
\(597\) 0 0
\(598\) 5.60817 + 9.71363i 0.229335 + 0.397220i
\(599\) −8.39037 14.5325i −0.342821 0.593784i 0.642134 0.766592i \(-0.278049\pi\)
−0.984955 + 0.172808i \(0.944716\pi\)
\(600\) 0 0
\(601\) 11.3992 0.464984 0.232492 0.972598i \(-0.425312\pi\)
0.232492 + 0.972598i \(0.425312\pi\)
\(602\) −0.742705 29.5232i −0.0302704 1.20328i
\(603\) 0 0
\(604\) −0.823832 + 1.42692i −0.0335212 + 0.0580605i
\(605\) −3.16012 5.47348i −0.128477 0.222529i
\(606\) 0 0
\(607\) 7.21420 12.4954i 0.292815 0.507171i −0.681659 0.731670i \(-0.738741\pi\)
0.974474 + 0.224499i \(0.0720745\pi\)
\(608\) −5.38151 −0.218249
\(609\) 0 0
\(610\) 3.94592 0.159765
\(611\) 15.2915 26.4857i 0.618629 1.07150i
\(612\) 0 0
\(613\) 12.2053 + 21.1403i 0.492969 + 0.853848i 0.999967 0.00809942i \(-0.00257815\pi\)
−0.506998 + 0.861947i \(0.669245\pi\)
\(614\) 11.3384 19.6387i 0.457581 0.792554i
\(615\) 0 0
\(616\) 1.37938 + 0.750780i 0.0555767 + 0.0302498i
\(617\) 48.9397 1.97024 0.985119 0.171876i \(-0.0549828\pi\)
0.985119 + 0.171876i \(0.0549828\pi\)
\(618\) 0 0
\(619\) 22.3296 + 38.6759i 0.897501 + 1.55452i 0.830678 + 0.556753i \(0.187953\pi\)
0.0668227 + 0.997765i \(0.478714\pi\)
\(620\) −2.33482 4.04403i −0.0937687 0.162412i
\(621\) 0 0
\(622\) 6.51459 0.261211
\(623\) 0.827430 + 32.8911i 0.0331503 + 1.31775i
\(624\) 0 0
\(625\) −9.91955 + 17.1812i −0.396782 + 0.687246i
\(626\) −0.133074 0.230492i −0.00531873 0.00921230i
\(627\) 0 0
\(628\) 3.30039 5.71644i 0.131700 0.228111i
\(629\) −2.92101 −0.116468
\(630\) 0 0
\(631\) 33.2852 1.32506 0.662532 0.749034i \(-0.269482\pi\)
0.662532 + 0.749034i \(0.269482\pi\)
\(632\) 4.62422 8.00938i 0.183942 0.318596i
\(633\) 0 0
\(634\) 7.86186 + 13.6171i 0.312235 + 0.540806i
\(635\) 3.66079 6.34067i 0.145274 0.251622i
\(636\) 0 0
\(637\) 8.02344 15.6671i 0.317900 0.620754i
\(638\) −3.67684 −0.145568
\(639\) 0 0
\(640\) 0.296790 + 0.514055i 0.0117316 + 0.0203198i
\(641\) 15.3940 + 26.6631i 0.608025 + 1.05313i 0.991566 + 0.129606i \(0.0413714\pi\)
−0.383540 + 0.923524i \(0.625295\pi\)
\(642\) 0 0
\(643\) 27.4690 1.08327 0.541637 0.840613i \(-0.317805\pi\)
0.541637 + 0.840613i \(0.317805\pi\)
\(644\) 10.0687 6.15585i 0.396761 0.242575i
\(645\) 0 0
\(646\) 7.85973 13.6134i 0.309237 0.535614i
\(647\) 6.63521 + 11.4925i 0.260857 + 0.451818i 0.966470 0.256780i \(-0.0826615\pi\)
−0.705613 + 0.708598i \(0.749328\pi\)
\(648\) 0 0
\(649\) 2.56654 4.44537i 0.100745 0.174496i
\(650\) −11.6870 −0.458400
\(651\) 0 0
\(652\) 5.98229 0.234285
\(653\) −8.57081 + 14.8451i −0.335402 + 0.580933i −0.983562 0.180571i \(-0.942205\pi\)
0.648160 + 0.761504i \(0.275539\pi\)
\(654\) 0 0
\(655\) 0.352336 + 0.610265i 0.0137669 + 0.0238450i
\(656\) 0.136673 0.236725i 0.00533619 0.00924255i
\(657\) 0 0
\(658\) −28.2630 15.3832i −1.10181 0.599701i
\(659\) 8.52179 0.331962 0.165981 0.986129i \(-0.446921\pi\)
0.165981 + 0.986129i \(0.446921\pi\)
\(660\) 0 0
\(661\) −17.1680 29.7358i −0.667757 1.15659i −0.978530 0.206105i \(-0.933921\pi\)
0.310773 0.950484i \(-0.399412\pi\)
\(662\) 12.5811 + 21.7912i 0.488979 + 0.846937i
\(663\) 0 0
\(664\) 7.70175 0.298886
\(665\) 7.42315 + 4.04033i 0.287857 + 0.156677i
\(666\) 0 0
\(667\) −13.8150 + 23.9282i −0.534918 + 0.926505i
\(668\) −3.73025 6.46099i −0.144328 0.249983i
\(669\) 0 0
\(670\) −0.568000 + 0.983804i −0.0219437 + 0.0380077i
\(671\) −3.94592 −0.152330
\(672\) 0 0
\(673\) 15.4031 0.593746 0.296873 0.954917i \(-0.404056\pi\)
0.296873 + 0.954917i \(0.404056\pi\)
\(674\) −9.36693 + 16.2240i −0.360800 + 0.624925i
\(675\) 0 0
\(676\) 3.33842 + 5.78231i 0.128401 + 0.222397i
\(677\) −3.69076 + 6.39258i −0.141847 + 0.245687i −0.928192 0.372101i \(-0.878638\pi\)
0.786345 + 0.617788i \(0.211971\pi\)
\(678\) 0 0
\(679\) 26.4868 16.1937i 1.01647 0.621455i
\(680\) −1.73385 −0.0664902
\(681\) 0 0
\(682\) 2.33482 + 4.04403i 0.0894050 + 0.154854i
\(683\) −4.79893 8.31198i −0.183626 0.318049i 0.759487 0.650523i \(-0.225450\pi\)
−0.943113 + 0.332474i \(0.892117\pi\)
\(684\) 0 0
\(685\) 1.49688 0.0571929
\(686\) −16.6914 8.02472i −0.637282 0.306385i
\(687\) 0 0
\(688\) −5.58113 + 9.66679i −0.212778 + 0.368543i
\(689\) −10.1264 17.5394i −0.385783 0.668197i
\(690\) 0 0
\(691\) 7.07227 12.2495i 0.269042 0.465994i −0.699573 0.714561i \(-0.746626\pi\)
0.968615 + 0.248567i \(0.0799597\pi\)
\(692\) 25.6591 0.975414
\(693\) 0 0
\(694\) −22.5438 −0.855750
\(695\) −1.45837 + 2.52597i −0.0553191 + 0.0958155i
\(696\) 0 0
\(697\) 0.399223 + 0.691475i 0.0151217 + 0.0261915i
\(698\) 1.89543 3.28298i 0.0717431 0.124263i
\(699\) 0 0
\(700\) 0.309243 + 12.2927i 0.0116883 + 0.464619i
\(701\) −37.3753 −1.41164 −0.705822 0.708389i \(-0.749422\pi\)
−0.705822 + 0.708389i \(0.749422\pi\)
\(702\) 0 0
\(703\) −2.69076 4.66053i −0.101484 0.175775i
\(704\) −0.296790 0.514055i −0.0111857 0.0193742i
\(705\) 0 0
\(706\) −6.83482 −0.257232
\(707\) 3.77102 + 2.05252i 0.141824 + 0.0771929i
\(708\) 0 0
\(709\) 5.24338 9.08180i 0.196919 0.341074i −0.750609 0.660747i \(-0.770240\pi\)
0.947528 + 0.319673i \(0.103573\pi\)
\(710\) 4.27694 + 7.40789i 0.160511 + 0.278013i
\(711\) 0 0
\(712\) 6.21780 10.7695i 0.233022 0.403606i
\(713\) 35.0905 1.31415
\(714\) 0 0
\(715\) −0.885981 −0.0331338
\(716\) −7.51819 + 13.0219i −0.280968 + 0.486651i
\(717\) 0 0
\(718\) 6.32237 + 10.9507i 0.235949 + 0.408675i
\(719\) −1.11995 + 1.93981i −0.0417670 + 0.0723426i −0.886153 0.463392i \(-0.846632\pi\)
0.844386 + 0.535735i \(0.179965\pi\)
\(720\) 0 0
\(721\) −0.424608 16.8786i −0.0158132 0.628590i
\(722\) 9.96070 0.370699
\(723\) 0 0
\(724\) 0.0430937 + 0.0746406i 0.00160157 + 0.00277399i
\(725\) −14.3946 24.9322i −0.534604 0.925961i
\(726\) 0 0
\(727\) −0.370045 −0.0137242 −0.00686211 0.999976i \(-0.502184\pi\)
−0.00686211 + 0.999976i \(0.502184\pi\)
\(728\) −5.67617 + 3.47033i −0.210373 + 0.128619i
\(729\) 0 0
\(730\) −2.34874 + 4.06813i −0.0869307 + 0.150568i
\(731\) −16.3025 28.2368i −0.602971 1.04438i
\(732\) 0 0
\(733\) −7.00953 + 12.1409i −0.258903 + 0.448433i −0.965948 0.258735i \(-0.916694\pi\)
0.707045 + 0.707168i \(0.250028\pi\)
\(734\) 6.54377 0.241535
\(735\) 0 0
\(736\) −4.46050 −0.164416
\(737\) 0.568000 0.983804i 0.0209225 0.0362389i
\(738\) 0 0
\(739\) 13.3872 + 23.1874i 0.492458 + 0.852962i 0.999962 0.00868705i \(-0.00276521\pi\)
−0.507504 + 0.861649i \(0.669432\pi\)
\(740\) −0.296790 + 0.514055i −0.0109102 + 0.0188970i
\(741\) 0 0
\(742\) −18.1804 + 11.1153i −0.667425 + 0.408055i
\(743\) −10.0934 −0.370290 −0.185145 0.982711i \(-0.559276\pi\)
−0.185145 + 0.982711i \(0.559276\pi\)
\(744\) 0 0
\(745\) −5.35740 9.27928i −0.196280 0.339967i
\(746\) −4.71420 8.16524i −0.172599 0.298951i
\(747\) 0 0
\(748\) 1.73385 0.0633959
\(749\) −1.24484 49.4836i −0.0454855 1.80809i
\(750\) 0 0
\(751\) −5.75729 + 9.97193i −0.210087 + 0.363881i −0.951741 0.306901i \(-0.900708\pi\)
0.741655 + 0.670782i \(0.234041\pi\)
\(752\) 6.08113 + 10.5328i 0.221756 + 0.384092i
\(753\) 0 0
\(754\) 7.78813 13.4894i 0.283627 0.491256i
\(755\) −0.978019 −0.0355938
\(756\) 0 0
\(757\) −15.2484 −0.554214 −0.277107 0.960839i \(-0.589376\pi\)
−0.277107 + 0.960839i \(0.589376\pi\)
\(758\) 3.63881 6.30260i 0.132168 0.228921i
\(759\) 0 0
\(760\) −1.59718 2.76639i −0.0579357 0.100348i
\(761\) −0.850874 + 1.47376i −0.0308442 + 0.0534236i −0.881035 0.473050i \(-0.843153\pi\)
0.850191 + 0.526474i \(0.176486\pi\)
\(762\) 0 0
\(763\) 6.66225 + 3.62619i 0.241190 + 0.131277i
\(764\) −3.98229 −0.144074
\(765\) 0 0
\(766\) −12.0416 20.8567i −0.435082 0.753584i
\(767\) 10.8727 + 18.8320i 0.392589 + 0.679984i
\(768\) 0 0
\(769\) −48.2422 −1.73966 −0.869829 0.493353i \(-0.835771\pi\)
−0.869829 + 0.493353i \(0.835771\pi\)
\(770\) 0.0234435 + 0.931900i 0.000844845 + 0.0335833i
\(771\) 0 0
\(772\) −3.39037 + 5.87229i −0.122022 + 0.211348i
\(773\) −3.10243 5.37357i −0.111587 0.193274i 0.804823 0.593514i \(-0.202260\pi\)
−0.916410 + 0.400240i \(0.868927\pi\)
\(774\) 0 0
\(775\) −18.2814 + 31.6643i −0.656688 + 1.13742i
\(776\) −11.7339 −0.421221
\(777\) 0 0
\(778\) 16.2983 0.584321
\(779\) −0.735508 + 1.27394i −0.0263523 + 0.0456436i
\(780\) 0 0
\(781\) −4.27694 7.40789i −0.153041 0.265075i
\(782\) 6.51459 11.2836i 0.232961 0.403501i
\(783\) 0 0
\(784\) 3.80039 + 5.87852i 0.135728 + 0.209947i
\(785\) 3.91808 0.139842
\(786\) 0 0
\(787\) −3.04883 5.28073i −0.108679 0.188238i 0.806556 0.591157i \(-0.201329\pi\)
−0.915235 + 0.402920i \(0.867995\pi\)
\(788\) 5.52918 + 9.57682i 0.196969 + 0.341160i
\(789\) 0 0
\(790\) 5.48968 0.195314
\(791\) 27.8104 17.0029i 0.988824 0.604554i
\(792\) 0 0
\(793\) 8.35807 14.4766i 0.296804 0.514079i
\(794\) −6.08619 10.5416i −0.215991 0.374107i
\(795\) 0 0
\(796\) 2.80924 4.86575i 0.0995710 0.172462i
\(797\) −12.4572 −0.441256 −0.220628 0.975358i \(-0.570811\pi\)
−0.220628 + 0.975358i \(0.570811\pi\)
\(798\) 0 0
\(799\) −35.5261 −1.25682
\(800\) 2.32383 4.02499i 0.0821599 0.142305i
\(801\) 0 0
\(802\) −16.6804 28.8914i −0.589007 1.02019i
\(803\) 2.34874 4.06813i 0.0828852 0.143561i
\(804\) 0 0
\(805\) 6.15272 + 3.34886i 0.216855 + 0.118032i
\(806\) −19.7821 −0.696794
\(807\) 0 0
\(808\) −0.811379 1.40535i −0.0285442 0.0494400i
\(809\) 2.81644 + 4.87822i 0.0990208 + 0.171509i 0.911280 0.411788i \(-0.135096\pi\)
−0.812259 + 0.583297i \(0.801762\pi\)
\(810\) 0 0
\(811\) −45.6414 −1.60269 −0.801344 0.598204i \(-0.795881\pi\)
−0.801344 + 0.598204i \(0.795881\pi\)
\(812\) −14.3946 7.83483i −0.505153 0.274949i
\(813\) 0 0
\(814\) 0.296790 0.514055i 0.0104025 0.0180176i
\(815\) 1.77548 + 3.07523i 0.0621924 + 0.107720i
\(816\) 0 0
\(817\) 30.0349 52.0220i 1.05079 1.82002i
\(818\) −5.78074 −0.202119
\(819\) 0 0
\(820\) 0.162253 0.00566611
\(821\) 16.3473 28.3143i 0.570524 0.988176i −0.425988 0.904729i \(-0.640074\pi\)
0.996512 0.0834476i \(-0.0265931\pi\)
\(822\) 0 0
\(823\) 5.21994 + 9.04119i 0.181956 + 0.315156i 0.942546 0.334075i \(-0.108424\pi\)
−0.760591 + 0.649231i \(0.775091\pi\)
\(824\) −3.19076 + 5.52655i −0.111155 + 0.192527i
\(825\) 0 0
\(826\) 19.5203 11.9345i 0.679199 0.415253i
\(827\) −16.7060 −0.580925 −0.290463 0.956886i \(-0.593809\pi\)
−0.290463 + 0.956886i \(0.593809\pi\)
\(828\) 0 0
\(829\) −13.1046 22.6978i −0.455141 0.788327i 0.543556 0.839373i \(-0.317078\pi\)
−0.998696 + 0.0510466i \(0.983744\pi\)
\(830\) 2.28580 + 3.95912i 0.0793412 + 0.137423i
\(831\) 0 0
\(832\) 2.51459 0.0871777
\(833\) −20.4212 + 1.02811i −0.707553 + 0.0356219i
\(834\) 0 0
\(835\) 2.21420 3.83511i 0.0766256 0.132719i
\(836\) 1.59718 + 2.76639i 0.0552396 + 0.0956777i
\(837\) 0 0
\(838\) −15.4356 + 26.7352i −0.533214 + 0.923554i
\(839\) 22.3772 0.772548 0.386274 0.922384i \(-0.373762\pi\)
0.386274 + 0.922384i \(0.373762\pi\)
\(840\) 0 0
\(841\) 9.37005 0.323105
\(842\) −1.86693 + 3.23361i −0.0643385 + 0.111438i
\(843\) 0 0
\(844\) 9.66225 + 16.7355i 0.332588 + 0.576060i
\(845\) −1.98162 + 3.43226i −0.0681697 + 0.118073i
\(846\) 0 0
\(847\) 0.708466 + 28.1622i 0.0243432 + 0.967663i
\(848\) 8.05408 0.276578
\(849\) 0 0
\(850\) 6.78794 + 11.7570i 0.232824 + 0.403263i
\(851\) −2.23025 3.86291i −0.0764521 0.132419i
\(852\) 0 0
\(853\) −9.92528 −0.339835 −0.169918 0.985458i \(-0.554350\pi\)
−0.169918 + 0.985458i \(0.554350\pi\)
\(854\) −15.4481 8.40819i −0.528621 0.287722i
\(855\) 0 0
\(856\) −9.35447 + 16.2024i −0.319729 + 0.553787i
\(857\) 3.89776 + 6.75112i 0.133145 + 0.230614i 0.924887 0.380241i \(-0.124159\pi\)
−0.791742 + 0.610855i \(0.790826\pi\)
\(858\) 0 0
\(859\) −8.17111 + 14.1528i −0.278795 + 0.482886i −0.971085 0.238732i \(-0.923268\pi\)
0.692291 + 0.721619i \(0.256602\pi\)
\(860\) −6.62568 −0.225934
\(861\) 0 0
\(862\) −28.1957 −0.960349
\(863\) −0.730252 + 1.26483i −0.0248581 + 0.0430555i −0.878187 0.478318i \(-0.841247\pi\)
0.853329 + 0.521373i \(0.174580\pi\)
\(864\) 0 0
\(865\) 7.61537 + 13.1902i 0.258930 + 0.448480i
\(866\) −6.27188 + 10.8632i −0.213127 + 0.369147i
\(867\) 0 0
\(868\) 0.523443 + 20.8073i 0.0177668 + 0.706247i
\(869\) −5.48968 −0.186225
\(870\) 0 0
\(871\) 2.40623 + 4.16771i 0.0815319 + 0.141217i
\(872\) −1.43346 2.48283i −0.0485432 0.0840792i
\(873\) 0 0
\(874\) 24.0043 0.811957
\(875\) −12.9267 + 7.90324i −0.437004 + 0.267178i
\(876\) 0 0
\(877\) 1.20467 2.08655i 0.0406789 0.0704579i −0.844969 0.534815i \(-0.820381\pi\)
0.885648 + 0.464357i \(0.153715\pi\)
\(878\) −13.0203 22.5519i −0.439415 0.761088i
\(879\) 0 0
\(880\) 0.176168 0.305132i 0.00593863 0.0102860i
\(881\) 18.9607 0.638802 0.319401 0.947620i \(-0.396518\pi\)
0.319401 + 0.947620i \(0.396518\pi\)
\(882\) 0 0
\(883\) 3.64008 0.122498 0.0612492 0.998123i \(-0.480492\pi\)
0.0612492 + 0.998123i \(0.480492\pi\)
\(884\) −3.67257 + 6.36108i −0.123522 + 0.213946i
\(885\) 0 0
\(886\) −11.7865 20.4148i −0.395974 0.685848i
\(887\) −12.2286 + 21.1805i −0.410596 + 0.711173i −0.994955 0.100322i \(-0.968013\pi\)
0.584359 + 0.811495i \(0.301346\pi\)
\(888\) 0 0
\(889\) −27.8429 + 17.0228i −0.933820 + 0.570926i
\(890\) 7.38151 0.247429
\(891\) 0 0
\(892\) 12.6623 + 21.9317i 0.423964 + 0.734326i
\(893\) −32.7257 56.6825i −1.09512 1.89681i
\(894\) 0 0
\(895\) −8.92528 −0.298339
\(896\) −0.0665372 2.64491i −0.00222285 0.0883604i
\(897\) 0 0
\(898\) 6.84348 11.8533i 0.228370 0.395548i
\(899\) −24.3653 42.2019i −0.812627 1.40751i
\(900\) 0 0
\(901\) −11.7630 + 20.3742i −0.391883 + 0.678762i
\(902\) −0.162253 −0.00540242
\(903\) 0 0
\(904\) −12.3202 −0.409765
\(905\) −0.0255796 + 0.0443051i −0.000850293 + 0.00147275i
\(906\) 0 0
\(907\) −5.01838 8.69209i −0.166633 0.288616i 0.770601 0.637318i \(-0.219956\pi\)
−0.937234 + 0.348701i \(0.886623\pi\)
\(908\) 2.40856 4.17174i 0.0799308 0.138444i
\(909\) 0 0
\(910\) −3.46857 1.88790i −0.114982 0.0625833i
\(911\) 22.8918 0.758440 0.379220 0.925306i \(-0.376192\pi\)
0.379220 + 0.925306i \(0.376192\pi\)
\(912\) 0 0
\(913\) −2.28580 3.95912i −0.0756489 0.131028i
\(914\) 11.1762 + 19.3577i 0.369675 + 0.640296i
\(915\) 0 0
\(916\) −9.29533 −0.307126
\(917\) −0.0789903 3.13993i −0.00260849 0.103690i
\(918\) 0 0
\(919\) 10.8910 18.8638i 0.359262 0.622261i −0.628575 0.777749i \(-0.716362\pi\)
0.987838 + 0.155488i \(0.0496950\pi\)
\(920\) −1.32383 2.29294i −0.0436454 0.0755961i
\(921\) 0 0
\(922\) 3.98755 6.90663i 0.131323 0.227458i
\(923\) 36.2370 1.19275
\(924\) 0 0
\(925\) 4.64766 0.152814
\(926\) −14.3676 + 24.8854i −0.472149 + 0.817785i
\(927\) 0 0
\(928\) 3.09718 + 5.36447i 0.101670 + 0.176097i
\(929\) −16.4189 + 28.4383i −0.538686 + 0.933031i 0.460289 + 0.887769i \(0.347746\pi\)
−0.998975 + 0.0452622i \(0.985588\pi\)
\(930\) 0 0
\(931\) −20.4518 31.6354i −0.670282 1.03681i
\(932\) 0.194356 0.00636634
\(933\) 0 0
\(934\) −16.7829 29.0688i −0.549152 0.951160i
\(935\) 0.514589 + 0.891294i 0.0168289 + 0.0291484i
\(936\) 0 0
\(937\) −8.78074 −0.286854 −0.143427 0.989661i \(-0.545812\pi\)
−0.143427 + 0.989661i \(0.545812\pi\)
\(938\) 4.32004 2.64121i 0.141054 0.0862387i
\(939\) 0 0
\(940\) −3.60963 + 6.25206i −0.117733 + 0.203920i
\(941\) 2.13307 + 3.69459i 0.0695362 + 0.120440i 0.898697 0.438570i \(-0.144515\pi\)
−0.829161 + 0.559010i \(0.811181\pi\)
\(942\) 0 0
\(943\) −0.609631 + 1.05591i −0.0198523 + 0.0343852i
\(944\) −8.64766 −0.281457
\(945\) 0 0
\(946\) 6.62568 0.215420
\(947\) −11.5292 + 19.9691i −0.374648 + 0.648909i −0.990274 0.139129i \(-0.955570\pi\)
0.615626 + 0.788038i \(0.288903\pi\)
\(948\) 0 0
\(949\) 9.94999 + 17.2339i 0.322990 + 0.559436i
\(950\) −12.5057 + 21.6606i −0.405740 + 0.702762i
\(951\) 0 0
\(952\) 6.78794 + 3.69459i 0.219998 + 0.119742i
\(953\) 36.5552 1.18414 0.592070 0.805886i \(-0.298311\pi\)
0.592070 + 0.805886i \(0.298311\pi\)
\(954\) 0 0
\(955\) −1.18190 2.04712i −0.0382455 0.0662431i
\(956\) 6.82743 + 11.8255i 0.220815 + 0.382463i
\(957\) 0 0
\(958\) −0.367120 −0.0118611
\(959\) −5.86021 3.18964i −0.189236 0.102999i
\(960\) 0 0
\(961\) −15.4443 + 26.7502i −0.498202 + 0.862911i
\(962\) 1.25729 + 2.17770i 0.0405368 + 0.0702118i
\(963\) 0 0
\(964\) 6.50000 11.2583i 0.209351 0.362606i
\(965\) −4.02491 −0.129566
\(966\) 0 0
\(967\) −53.5438 −1.72185 −0.860926 0.508731i \(-0.830115\pi\)
−0.860926 + 0.508731i \(0.830115\pi\)
\(968\) 5.32383 9.22115i 0.171114 0.296379i
\(969\) 0 0
\(970\) −3.48249 6.03184i −0.111816 0.193671i
\(971\) 15.9897 27.6949i 0.513133 0.888773i −0.486751 0.873541i \(-0.661818\pi\)
0.999884 0.0152321i \(-0.00484870\pi\)
\(972\) 0 0
\(973\) 11.0919 6.78146i 0.355591 0.217403i
\(974\) 29.9076 0.958300
\(975\) 0 0
\(976\) 3.32383 + 5.75705i 0.106393 + 0.184279i
\(977\) −13.7104 23.7471i −0.438635 0.759738i 0.558950 0.829202i \(-0.311204\pi\)
−0.997584 + 0.0694638i \(0.977871\pi\)
\(978\) 0 0
\(979\) −7.38151 −0.235914
\(980\) −1.89397 + 3.69829i −0.0605006 + 0.118138i
\(981\) 0 0
\(982\) 0.255158 0.441947i 0.00814243 0.0141031i
\(983\) −29.5782 51.2309i −0.943398 1.63401i −0.758927 0.651175i \(-0.774276\pi\)
−0.184471 0.982838i \(-0.559057\pi\)
\(984\) 0 0
\(985\) −3.28201 + 5.68460i −0.104573 + 0.181126i
\(986\) −18.0938 −0.576223
\(987\) 0 0
\(988\) −13.5323 −0.430520
\(989\) 24.8946 43.1188i 0.791604 1.37110i
\(990\) 0 0
\(991\) 6.41887 + 11.1178i 0.203902 + 0.353169i 0.949782 0.312911i \(-0.101304\pi\)
−0.745880 + 0.666080i \(0.767971\pi\)
\(992\) 3.93346 6.81296i 0.124888 0.216312i
\(993\) 0 0
\(994\) −0.958848 38.1151i −0.0304128 1.20894i
\(995\) 3.33502 0.105727
\(996\) 0 0
\(997\) 2.89037 + 5.00627i 0.0915389 + 0.158550i 0.908159 0.418626i \(-0.137488\pi\)
−0.816620 + 0.577176i \(0.804155\pi\)
\(998\) 9.50953 + 16.4710i 0.301019 + 0.521380i
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 1134.2.g.l.163.2 6
3.2 odd 2 1134.2.g.m.163.2 6
7.2 even 3 7938.2.a.ca.1.2 3
7.4 even 3 inner 1134.2.g.l.487.2 6
7.5 odd 6 7938.2.a.bz.1.2 3
9.2 odd 6 126.2.e.c.121.2 yes 6
9.4 even 3 378.2.h.c.289.2 6
9.5 odd 6 126.2.h.d.79.2 yes 6
9.7 even 3 378.2.e.d.37.2 6
21.2 odd 6 7938.2.a.bv.1.2 3
21.5 even 6 7938.2.a.bw.1.2 3
21.11 odd 6 1134.2.g.m.487.2 6
36.7 odd 6 3024.2.q.g.2305.2 6
36.11 even 6 1008.2.q.g.625.2 6
36.23 even 6 1008.2.t.h.961.2 6
36.31 odd 6 3024.2.t.h.289.2 6
63.2 odd 6 882.2.f.n.589.1 6
63.4 even 3 378.2.e.d.235.2 6
63.5 even 6 882.2.f.o.295.3 6
63.11 odd 6 126.2.h.d.67.2 yes 6
63.13 odd 6 2646.2.h.o.667.2 6
63.16 even 3 2646.2.f.l.1765.2 6
63.20 even 6 882.2.e.o.373.2 6
63.23 odd 6 882.2.f.n.295.1 6
63.25 even 3 378.2.h.c.361.2 6
63.31 odd 6 2646.2.e.p.2125.2 6
63.32 odd 6 126.2.e.c.25.2 6
63.34 odd 6 2646.2.e.p.1549.2 6
63.38 even 6 882.2.h.p.67.2 6
63.40 odd 6 2646.2.f.m.883.2 6
63.41 even 6 882.2.h.p.79.2 6
63.47 even 6 882.2.f.o.589.3 6
63.52 odd 6 2646.2.h.o.361.2 6
63.58 even 3 2646.2.f.l.883.2 6
63.59 even 6 882.2.e.o.655.2 6
63.61 odd 6 2646.2.f.m.1765.2 6
252.11 even 6 1008.2.t.h.193.2 6
252.67 odd 6 3024.2.q.g.2881.2 6
252.95 even 6 1008.2.q.g.529.2 6
252.151 odd 6 3024.2.t.h.1873.2 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
126.2.e.c.25.2 6 63.32 odd 6
126.2.e.c.121.2 yes 6 9.2 odd 6
126.2.h.d.67.2 yes 6 63.11 odd 6
126.2.h.d.79.2 yes 6 9.5 odd 6
378.2.e.d.37.2 6 9.7 even 3
378.2.e.d.235.2 6 63.4 even 3
378.2.h.c.289.2 6 9.4 even 3
378.2.h.c.361.2 6 63.25 even 3
882.2.e.o.373.2 6 63.20 even 6
882.2.e.o.655.2 6 63.59 even 6
882.2.f.n.295.1 6 63.23 odd 6
882.2.f.n.589.1 6 63.2 odd 6
882.2.f.o.295.3 6 63.5 even 6
882.2.f.o.589.3 6 63.47 even 6
882.2.h.p.67.2 6 63.38 even 6
882.2.h.p.79.2 6 63.41 even 6
1008.2.q.g.529.2 6 252.95 even 6
1008.2.q.g.625.2 6 36.11 even 6
1008.2.t.h.193.2 6 252.11 even 6
1008.2.t.h.961.2 6 36.23 even 6
1134.2.g.l.163.2 6 1.1 even 1 trivial
1134.2.g.l.487.2 6 7.4 even 3 inner
1134.2.g.m.163.2 6 3.2 odd 2
1134.2.g.m.487.2 6 21.11 odd 6
2646.2.e.p.1549.2 6 63.34 odd 6
2646.2.e.p.2125.2 6 63.31 odd 6
2646.2.f.l.883.2 6 63.58 even 3
2646.2.f.l.1765.2 6 63.16 even 3
2646.2.f.m.883.2 6 63.40 odd 6
2646.2.f.m.1765.2 6 63.61 odd 6
2646.2.h.o.361.2 6 63.52 odd 6
2646.2.h.o.667.2 6 63.13 odd 6
3024.2.q.g.2305.2 6 36.7 odd 6
3024.2.q.g.2881.2 6 252.67 odd 6
3024.2.t.h.289.2 6 36.31 odd 6
3024.2.t.h.1873.2 6 252.151 odd 6
7938.2.a.bv.1.2 3 21.2 odd 6
7938.2.a.bw.1.2 3 21.5 even 6
7938.2.a.bz.1.2 3 7.5 odd 6
7938.2.a.ca.1.2 3 7.2 even 3