Properties

Label 288.2.w.b.251.4
Level $288$
Weight $2$
Character 288.251
Analytic conductor $2.300$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [288,2,Mod(35,288)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(288, base_ring=CyclotomicField(8))
 
chi = DirichletCharacter(H, H._module([4, 3, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("288.35");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 288 = 2^{5} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 288.w (of order \(8\), degree \(4\), 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: \(2.29969157821\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(8\) over \(\Q(\zeta_{8})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 251.4
Character \(\chi\) \(=\) 288.251
Dual form 288.2.w.b.179.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.290763 + 1.38400i) q^{2} +(-1.83091 + 0.804831i) q^{4} +(1.12344 - 2.71222i) q^{5} +(3.03150 - 3.03150i) q^{7} +(-1.64625 - 2.29997i) q^{8} +O(q^{10})\) \(q+(0.290763 + 1.38400i) q^{2} +(-1.83091 + 0.804831i) q^{4} +(1.12344 - 2.71222i) q^{5} +(3.03150 - 3.03150i) q^{7} +(-1.64625 - 2.29997i) q^{8} +(4.08037 + 0.766228i) q^{10} +(-0.616847 + 1.48920i) q^{11} +(3.35133 - 1.38816i) q^{13} +(5.07705 + 3.31415i) q^{14} +(2.70449 - 2.94715i) q^{16} -4.76709 q^{17} +(1.13264 + 2.73444i) q^{19} +(0.125961 + 5.87003i) q^{20} +(-2.24041 - 0.420712i) q^{22} +(-4.11192 + 4.11192i) q^{23} +(-2.55851 - 2.55851i) q^{25} +(2.89566 + 4.23461i) q^{26} +(-3.11057 + 7.99027i) q^{28} +(8.16664 - 3.38273i) q^{29} +6.16305i q^{31} +(4.86523 + 2.88610i) q^{32} +(-1.38609 - 6.59765i) q^{34} +(-4.81640 - 11.6278i) q^{35} +(-9.38963 - 3.88931i) q^{37} +(-3.45513 + 2.36265i) q^{38} +(-8.08750 + 1.88112i) q^{40} +(0.169917 + 0.169917i) q^{41} +(7.57687 + 3.13844i) q^{43} +(-0.0691613 - 3.22306i) q^{44} +(-6.88649 - 4.49531i) q^{46} +2.44049i q^{47} -11.3800i q^{49} +(2.79706 - 4.28490i) q^{50} +(-5.01875 + 5.23886i) q^{52} +(-1.99073 - 0.824586i) q^{53} +(3.34605 + 3.34605i) q^{55} +(-11.9630 - 1.98176i) q^{56} +(7.05626 + 10.3191i) q^{58} +(-1.21488 - 0.503218i) q^{59} +(1.04489 + 2.52258i) q^{61} +(-8.52966 + 1.79198i) q^{62} +(-2.57973 + 7.57265i) q^{64} -10.6491i q^{65} +(3.91551 - 1.62186i) q^{67} +(8.72813 - 3.83670i) q^{68} +(14.6925 - 10.0468i) q^{70} +(5.28919 + 5.28919i) q^{71} +(-1.57482 + 1.57482i) q^{73} +(2.65266 - 14.1261i) q^{74} +(-4.27453 - 4.09494i) q^{76} +(2.64454 + 6.38449i) q^{77} -13.7711 q^{79} +(-4.95501 - 10.6461i) q^{80} +(-0.185759 + 0.284570i) q^{82} +(-3.31934 + 1.37492i) q^{83} +(-5.35554 + 12.9294i) q^{85} +(-2.14053 + 11.3989i) q^{86} +(4.44060 - 1.03286i) q^{88} +(-6.99010 + 6.99010i) q^{89} +(5.95133 - 14.3678i) q^{91} +(4.21917 - 10.8380i) q^{92} +(-3.37763 + 0.709602i) q^{94} +8.68886 q^{95} -13.5584 q^{97} +(15.7499 - 3.30888i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q + 4 q^{2} + 4 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 32 q + 4 q^{2} + 4 q^{8} + 8 q^{10} + 8 q^{11} - 12 q^{14} + 8 q^{16} - 32 q^{20} + 16 q^{22} + 36 q^{26} + 16 q^{29} + 24 q^{32} - 24 q^{35} - 32 q^{38} - 32 q^{40} - 8 q^{44} - 32 q^{46} - 8 q^{50} - 56 q^{52} + 16 q^{53} - 32 q^{55} - 40 q^{56} - 32 q^{58} - 32 q^{59} + 32 q^{61} + 68 q^{62} - 48 q^{64} - 16 q^{67} + 72 q^{68} - 48 q^{70} - 16 q^{71} - 60 q^{74} - 8 q^{76} + 16 q^{77} - 32 q^{79} - 96 q^{80} + 40 q^{82} + 40 q^{83} + 40 q^{86} + 40 q^{88} - 48 q^{91} + 16 q^{92} + 72 q^{94} + 80 q^{95} + 44 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/288\mathbb{Z}\right)^\times\).

\(n\) \(37\) \(65\) \(127\)
\(\chi(n)\) \(e\left(\frac{1}{8}\right)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.290763 + 1.38400i 0.205600 + 0.978636i
\(3\) 0 0
\(4\) −1.83091 + 0.804831i −0.915457 + 0.402416i
\(5\) 1.12344 2.71222i 0.502418 1.21294i −0.445745 0.895160i \(-0.647061\pi\)
0.948163 0.317784i \(-0.102939\pi\)
\(6\) 0 0
\(7\) 3.03150 3.03150i 1.14580 1.14580i 0.158430 0.987370i \(-0.449357\pi\)
0.987370 0.158430i \(-0.0506433\pi\)
\(8\) −1.64625 2.29997i −0.582037 0.813163i
\(9\) 0 0
\(10\) 4.08037 + 0.766228i 1.29033 + 0.242303i
\(11\) −0.616847 + 1.48920i −0.185986 + 0.449011i −0.989180 0.146707i \(-0.953132\pi\)
0.803194 + 0.595718i \(0.203132\pi\)
\(12\) 0 0
\(13\) 3.35133 1.38816i 0.929490 0.385008i 0.134005 0.990981i \(-0.457216\pi\)
0.795485 + 0.605973i \(0.207216\pi\)
\(14\) 5.07705 + 3.31415i 1.35690 + 0.885745i
\(15\) 0 0
\(16\) 2.70449 2.94715i 0.676123 0.736789i
\(17\) −4.76709 −1.15619 −0.578094 0.815970i \(-0.696203\pi\)
−0.578094 + 0.815970i \(0.696203\pi\)
\(18\) 0 0
\(19\) 1.13264 + 2.73444i 0.259846 + 0.627323i 0.998928 0.0462921i \(-0.0147405\pi\)
−0.739082 + 0.673615i \(0.764741\pi\)
\(20\) 0.125961 + 5.87003i 0.0281657 + 1.31258i
\(21\) 0 0
\(22\) −2.24041 0.420712i −0.477657 0.0896962i
\(23\) −4.11192 + 4.11192i −0.857395 + 0.857395i −0.991031 0.133636i \(-0.957335\pi\)
0.133636 + 0.991031i \(0.457335\pi\)
\(24\) 0 0
\(25\) −2.55851 2.55851i −0.511702 0.511702i
\(26\) 2.89566 + 4.23461i 0.567886 + 0.830475i
\(27\) 0 0
\(28\) −3.11057 + 7.99027i −0.587843 + 1.51002i
\(29\) 8.16664 3.38273i 1.51651 0.628158i 0.539620 0.841909i \(-0.318568\pi\)
0.976888 + 0.213751i \(0.0685681\pi\)
\(30\) 0 0
\(31\) 6.16305i 1.10692i 0.832877 + 0.553458i \(0.186692\pi\)
−0.832877 + 0.553458i \(0.813308\pi\)
\(32\) 4.86523 + 2.88610i 0.860059 + 0.510195i
\(33\) 0 0
\(34\) −1.38609 6.59765i −0.237713 1.13149i
\(35\) −4.81640 11.6278i −0.814121 1.96546i
\(36\) 0 0
\(37\) −9.38963 3.88931i −1.54365 0.639399i −0.561493 0.827482i \(-0.689773\pi\)
−0.982153 + 0.188083i \(0.939773\pi\)
\(38\) −3.45513 + 2.36265i −0.560497 + 0.383272i
\(39\) 0 0
\(40\) −8.08750 + 1.88112i −1.27875 + 0.297431i
\(41\) 0.169917 + 0.169917i 0.0265365 + 0.0265365i 0.720251 0.693714i \(-0.244027\pi\)
−0.693714 + 0.720251i \(0.744027\pi\)
\(42\) 0 0
\(43\) 7.57687 + 3.13844i 1.15546 + 0.478608i 0.876361 0.481654i \(-0.159964\pi\)
0.279100 + 0.960262i \(0.409964\pi\)
\(44\) −0.0691613 3.22306i −0.0104265 0.485894i
\(45\) 0 0
\(46\) −6.88649 4.49531i −1.01536 0.662797i
\(47\) 2.44049i 0.355981i 0.984032 + 0.177991i \(0.0569597\pi\)
−0.984032 + 0.177991i \(0.943040\pi\)
\(48\) 0 0
\(49\) 11.3800i 1.62572i
\(50\) 2.79706 4.28490i 0.395564 0.605976i
\(51\) 0 0
\(52\) −5.01875 + 5.23886i −0.695976 + 0.726499i
\(53\) −1.99073 0.824586i −0.273447 0.113266i 0.241746 0.970340i \(-0.422280\pi\)
−0.515193 + 0.857074i \(0.672280\pi\)
\(54\) 0 0
\(55\) 3.34605 + 3.34605i 0.451182 + 0.451182i
\(56\) −11.9630 1.98176i −1.59862 0.264824i
\(57\) 0 0
\(58\) 7.05626 + 10.3191i 0.926533 + 1.35496i
\(59\) −1.21488 0.503218i −0.158163 0.0655134i 0.302197 0.953245i \(-0.402280\pi\)
−0.460361 + 0.887732i \(0.652280\pi\)
\(60\) 0 0
\(61\) 1.04489 + 2.52258i 0.133784 + 0.322983i 0.976548 0.215300i \(-0.0690731\pi\)
−0.842764 + 0.538283i \(0.819073\pi\)
\(62\) −8.52966 + 1.79198i −1.08327 + 0.227582i
\(63\) 0 0
\(64\) −2.57973 + 7.57265i −0.322467 + 0.946581i
\(65\) 10.6491i 1.32085i
\(66\) 0 0
\(67\) 3.91551 1.62186i 0.478355 0.198141i −0.130459 0.991454i \(-0.541645\pi\)
0.608815 + 0.793312i \(0.291645\pi\)
\(68\) 8.72813 3.83670i 1.05844 0.465268i
\(69\) 0 0
\(70\) 14.6925 10.0468i 1.75609 1.20083i
\(71\) 5.28919 + 5.28919i 0.627711 + 0.627711i 0.947492 0.319781i \(-0.103609\pi\)
−0.319781 + 0.947492i \(0.603609\pi\)
\(72\) 0 0
\(73\) −1.57482 + 1.57482i −0.184319 + 0.184319i −0.793235 0.608916i \(-0.791605\pi\)
0.608916 + 0.793235i \(0.291605\pi\)
\(74\) 2.65266 14.1261i 0.308365 1.64213i
\(75\) 0 0
\(76\) −4.27453 4.09494i −0.490322 0.469721i
\(77\) 2.64454 + 6.38449i 0.301373 + 0.727580i
\(78\) 0 0
\(79\) −13.7711 −1.54937 −0.774684 0.632348i \(-0.782091\pi\)
−0.774684 + 0.632348i \(0.782091\pi\)
\(80\) −4.95501 10.6461i −0.553987 1.19028i
\(81\) 0 0
\(82\) −0.185759 + 0.284570i −0.0205137 + 0.0314255i
\(83\) −3.31934 + 1.37492i −0.364345 + 0.150917i −0.557343 0.830282i \(-0.688179\pi\)
0.192997 + 0.981199i \(0.438179\pi\)
\(84\) 0 0
\(85\) −5.35554 + 12.9294i −0.580890 + 1.40239i
\(86\) −2.14053 + 11.3989i −0.230820 + 1.22918i
\(87\) 0 0
\(88\) 4.44060 1.03286i 0.473370 0.110104i
\(89\) −6.99010 + 6.99010i −0.740949 + 0.740949i −0.972761 0.231811i \(-0.925535\pi\)
0.231811 + 0.972761i \(0.425535\pi\)
\(90\) 0 0
\(91\) 5.95133 14.3678i 0.623869 1.50615i
\(92\) 4.21917 10.8380i 0.439879 1.12994i
\(93\) 0 0
\(94\) −3.37763 + 0.709602i −0.348376 + 0.0731899i
\(95\) 8.68886 0.891459
\(96\) 0 0
\(97\) −13.5584 −1.37665 −0.688323 0.725404i \(-0.741653\pi\)
−0.688323 + 0.725404i \(0.741653\pi\)
\(98\) 15.7499 3.30888i 1.59099 0.334248i
\(99\) 0 0
\(100\) 6.74358 + 2.62524i 0.674358 + 0.262524i
\(101\) 1.10479 2.66720i 0.109931 0.265396i −0.859335 0.511413i \(-0.829122\pi\)
0.969265 + 0.246018i \(0.0791221\pi\)
\(102\) 0 0
\(103\) −12.8009 + 12.8009i −1.26131 + 1.26131i −0.310851 + 0.950459i \(0.600614\pi\)
−0.950459 + 0.310851i \(0.899386\pi\)
\(104\) −8.70985 5.42269i −0.854071 0.531738i
\(105\) 0 0
\(106\) 0.562398 2.99492i 0.0546249 0.290893i
\(107\) 0.720677 1.73987i 0.0696704 0.168199i −0.885209 0.465194i \(-0.845984\pi\)
0.954879 + 0.296995i \(0.0959845\pi\)
\(108\) 0 0
\(109\) 4.45017 1.84332i 0.426249 0.176558i −0.159238 0.987240i \(-0.550904\pi\)
0.585486 + 0.810682i \(0.300904\pi\)
\(110\) −3.65803 + 5.60385i −0.348780 + 0.534306i
\(111\) 0 0
\(112\) −0.735628 17.1330i −0.0695104 1.61891i
\(113\) 13.6612 1.28514 0.642568 0.766229i \(-0.277869\pi\)
0.642568 + 0.766229i \(0.277869\pi\)
\(114\) 0 0
\(115\) 6.53296 + 15.7720i 0.609201 + 1.47074i
\(116\) −12.2299 + 12.7663i −1.13552 + 1.18532i
\(117\) 0 0
\(118\) 0.343213 1.82771i 0.0315954 0.168254i
\(119\) −14.4514 + 14.4514i −1.32476 + 1.32476i
\(120\) 0 0
\(121\) 5.94096 + 5.94096i 0.540087 + 0.540087i
\(122\) −3.18743 + 2.17959i −0.288577 + 0.197331i
\(123\) 0 0
\(124\) −4.96021 11.2840i −0.445440 1.01333i
\(125\) 3.74754 1.55228i 0.335190 0.138840i
\(126\) 0 0
\(127\) 13.2014i 1.17143i −0.810515 0.585717i \(-0.800813\pi\)
0.810515 0.585717i \(-0.199187\pi\)
\(128\) −11.2306 1.36851i −0.992657 0.120960i
\(129\) 0 0
\(130\) 14.7383 3.09635i 1.29264 0.271568i
\(131\) 2.56553 + 6.19375i 0.224152 + 0.541150i 0.995446 0.0953287i \(-0.0303902\pi\)
−0.771294 + 0.636479i \(0.780390\pi\)
\(132\) 0 0
\(133\) 11.7231 + 4.85585i 1.01652 + 0.421056i
\(134\) 3.38313 + 4.94749i 0.292258 + 0.427398i
\(135\) 0 0
\(136\) 7.84781 + 10.9642i 0.672944 + 0.940169i
\(137\) −9.77333 9.77333i −0.834992 0.834992i 0.153203 0.988195i \(-0.451041\pi\)
−0.988195 + 0.153203i \(0.951041\pi\)
\(138\) 0 0
\(139\) −8.26616 3.42396i −0.701127 0.290416i 0.00350050 0.999994i \(-0.498886\pi\)
−0.704627 + 0.709578i \(0.748886\pi\)
\(140\) 18.1769 + 17.4132i 1.53623 + 1.47168i
\(141\) 0 0
\(142\) −5.78234 + 8.85814i −0.485243 + 0.743358i
\(143\) 5.84708i 0.488957i
\(144\) 0 0
\(145\) 25.9501i 2.15504i
\(146\) −2.63745 1.72165i −0.218277 0.142485i
\(147\) 0 0
\(148\) 20.3219 0.436073i 1.67045 0.0358449i
\(149\) 18.9803 + 7.86190i 1.55493 + 0.644072i 0.984199 0.177066i \(-0.0566607\pi\)
0.570729 + 0.821139i \(0.306661\pi\)
\(150\) 0 0
\(151\) 7.83326 + 7.83326i 0.637462 + 0.637462i 0.949929 0.312467i \(-0.101155\pi\)
−0.312467 + 0.949929i \(0.601155\pi\)
\(152\) 4.42452 7.10661i 0.358876 0.576422i
\(153\) 0 0
\(154\) −8.06720 + 5.51642i −0.650073 + 0.444526i
\(155\) 16.7156 + 6.92381i 1.34263 + 0.556134i
\(156\) 0 0
\(157\) 3.58014 + 8.64323i 0.285727 + 0.689805i 0.999949 0.0101140i \(-0.00321944\pi\)
−0.714222 + 0.699919i \(0.753219\pi\)
\(158\) −4.00412 19.0592i −0.318551 1.51627i
\(159\) 0 0
\(160\) 13.2935 9.95323i 1.05095 0.786872i
\(161\) 24.9306i 1.96481i
\(162\) 0 0
\(163\) −4.73693 + 1.96210i −0.371025 + 0.153684i −0.560402 0.828221i \(-0.689353\pi\)
0.189377 + 0.981904i \(0.439353\pi\)
\(164\) −0.447857 0.174349i −0.0349718 0.0136143i
\(165\) 0 0
\(166\) −2.86803 4.19420i −0.222602 0.325533i
\(167\) 4.55199 + 4.55199i 0.352244 + 0.352244i 0.860944 0.508700i \(-0.169874\pi\)
−0.508700 + 0.860944i \(0.669874\pi\)
\(168\) 0 0
\(169\) 0.111994 0.111994i 0.00861490 0.00861490i
\(170\) −19.4515 3.65268i −1.49186 0.280147i
\(171\) 0 0
\(172\) −16.3985 + 0.351884i −1.25037 + 0.0268309i
\(173\) 4.28444 + 10.3436i 0.325740 + 0.786406i 0.998899 + 0.0469083i \(0.0149368\pi\)
−0.673159 + 0.739498i \(0.735063\pi\)
\(174\) 0 0
\(175\) −15.5123 −1.17262
\(176\) 2.72064 + 5.84547i 0.205076 + 0.440619i
\(177\) 0 0
\(178\) −11.7068 7.64184i −0.877459 0.572780i
\(179\) −10.2246 + 4.23519i −0.764226 + 0.316553i −0.730531 0.682880i \(-0.760727\pi\)
−0.0336946 + 0.999432i \(0.510727\pi\)
\(180\) 0 0
\(181\) −1.33358 + 3.21956i −0.0991246 + 0.239308i −0.965661 0.259806i \(-0.916341\pi\)
0.866536 + 0.499114i \(0.166341\pi\)
\(182\) 21.6154 + 4.05903i 1.60224 + 0.300875i
\(183\) 0 0
\(184\) 16.2265 + 2.68806i 1.19624 + 0.198166i
\(185\) −21.0974 + 21.0974i −1.55111 + 1.55111i
\(186\) 0 0
\(187\) 2.94056 7.09915i 0.215035 0.519141i
\(188\) −1.96418 4.46832i −0.143253 0.325886i
\(189\) 0 0
\(190\) 2.52640 + 12.0254i 0.183284 + 0.872414i
\(191\) −4.82446 −0.349085 −0.174543 0.984650i \(-0.555845\pi\)
−0.174543 + 0.984650i \(0.555845\pi\)
\(192\) 0 0
\(193\) 0.222878 0.0160431 0.00802155 0.999968i \(-0.497447\pi\)
0.00802155 + 0.999968i \(0.497447\pi\)
\(194\) −3.94228 18.7648i −0.283039 1.34724i
\(195\) 0 0
\(196\) 9.15899 + 20.8358i 0.654214 + 1.48827i
\(197\) 9.44160 22.7940i 0.672686 1.62401i −0.104341 0.994542i \(-0.533273\pi\)
0.777028 0.629467i \(-0.216727\pi\)
\(198\) 0 0
\(199\) 14.8710 14.8710i 1.05418 1.05418i 0.0557310 0.998446i \(-0.482251\pi\)
0.998446 0.0557310i \(-0.0177489\pi\)
\(200\) −1.67256 + 10.0964i −0.118268 + 0.713926i
\(201\) 0 0
\(202\) 4.01263 + 0.753507i 0.282328 + 0.0530165i
\(203\) 14.5024 35.0120i 1.01787 2.45736i
\(204\) 0 0
\(205\) 0.651743 0.269961i 0.0455197 0.0188549i
\(206\) −21.4385 13.9944i −1.49369 0.975037i
\(207\) 0 0
\(208\) 4.97250 13.6312i 0.344781 0.945150i
\(209\) −4.77079 −0.330003
\(210\) 0 0
\(211\) −0.644000 1.55475i −0.0443348 0.107034i 0.900161 0.435558i \(-0.143449\pi\)
−0.944496 + 0.328524i \(0.893449\pi\)
\(212\) 4.30850 0.0924532i 0.295909 0.00634971i
\(213\) 0 0
\(214\) 2.61752 + 0.491528i 0.178930 + 0.0336002i
\(215\) 17.0243 17.0243i 1.16105 1.16105i
\(216\) 0 0
\(217\) 18.6833 + 18.6833i 1.26830 + 1.26830i
\(218\) 3.84510 + 5.62306i 0.260423 + 0.380842i
\(219\) 0 0
\(220\) −8.81935 3.43333i −0.594600 0.231475i
\(221\) −15.9761 + 6.61750i −1.07467 + 0.445141i
\(222\) 0 0
\(223\) 23.4280i 1.56885i −0.620221 0.784427i \(-0.712957\pi\)
0.620221 0.784427i \(-0.287043\pi\)
\(224\) 23.4982 5.99974i 1.57004 0.400875i
\(225\) 0 0
\(226\) 3.97216 + 18.9071i 0.264224 + 1.25768i
\(227\) −5.10690 12.3292i −0.338957 0.818315i −0.997816 0.0660486i \(-0.978961\pi\)
0.658859 0.752266i \(-0.271039\pi\)
\(228\) 0 0
\(229\) −7.82666 3.24191i −0.517200 0.214231i 0.108786 0.994065i \(-0.465304\pi\)
−0.625987 + 0.779834i \(0.715304\pi\)
\(230\) −19.9288 + 13.6275i −1.31407 + 0.898571i
\(231\) 0 0
\(232\) −21.2245 13.2142i −1.39346 0.867556i
\(233\) −9.66805 9.66805i −0.633375 0.633375i 0.315538 0.948913i \(-0.397815\pi\)
−0.948913 + 0.315538i \(0.897815\pi\)
\(234\) 0 0
\(235\) 6.61915 + 2.74174i 0.431785 + 0.178851i
\(236\) 2.62934 0.0564212i 0.171155 0.00367270i
\(237\) 0 0
\(238\) −24.2027 15.7989i −1.56883 1.02409i
\(239\) 25.8579i 1.67261i −0.548268 0.836303i \(-0.684713\pi\)
0.548268 0.836303i \(-0.315287\pi\)
\(240\) 0 0
\(241\) 24.9358i 1.60626i 0.595805 + 0.803129i \(0.296833\pi\)
−0.595805 + 0.803129i \(0.703167\pi\)
\(242\) −6.49488 + 9.94970i −0.417507 + 0.639591i
\(243\) 0 0
\(244\) −3.94334 3.77766i −0.252447 0.241840i
\(245\) −30.8652 12.7848i −1.97190 0.816789i
\(246\) 0 0
\(247\) 7.59170 + 7.59170i 0.483048 + 0.483048i
\(248\) 14.1748 10.1459i 0.900102 0.644266i
\(249\) 0 0
\(250\) 3.23800 + 4.73525i 0.204789 + 0.299483i
\(251\) −11.5486 4.78358i −0.728939 0.301937i −0.0128233 0.999918i \(-0.504082\pi\)
−0.716116 + 0.697981i \(0.754082\pi\)
\(252\) 0 0
\(253\) −3.58705 8.65990i −0.225516 0.544443i
\(254\) 18.2707 3.83848i 1.14641 0.240847i
\(255\) 0 0
\(256\) −1.37144 15.9411i −0.0857148 0.996320i
\(257\) 17.0780i 1.06530i −0.846337 0.532648i \(-0.821197\pi\)
0.846337 0.532648i \(-0.178803\pi\)
\(258\) 0 0
\(259\) −40.2552 + 16.6742i −2.50133 + 1.03609i
\(260\) 8.57070 + 19.4975i 0.531532 + 1.20919i
\(261\) 0 0
\(262\) −7.82619 + 5.35161i −0.483503 + 0.330624i
\(263\) 10.4595 + 10.4595i 0.644963 + 0.644963i 0.951771 0.306809i \(-0.0992612\pi\)
−0.306809 + 0.951771i \(0.599261\pi\)
\(264\) 0 0
\(265\) −4.47292 + 4.47292i −0.274770 + 0.274770i
\(266\) −3.31187 + 17.6366i −0.203064 + 1.08137i
\(267\) 0 0
\(268\) −5.86364 + 6.12080i −0.358179 + 0.373888i
\(269\) 3.47587 + 8.39150i 0.211928 + 0.511639i 0.993719 0.111901i \(-0.0356939\pi\)
−0.781792 + 0.623540i \(0.785694\pi\)
\(270\) 0 0
\(271\) −5.66173 −0.343925 −0.171963 0.985103i \(-0.555011\pi\)
−0.171963 + 0.985103i \(0.555011\pi\)
\(272\) −12.8926 + 14.0493i −0.781726 + 0.851866i
\(273\) 0 0
\(274\) 10.6846 16.3680i 0.645479 0.988828i
\(275\) 5.38834 2.23192i 0.324929 0.134590i
\(276\) 0 0
\(277\) −5.27625 + 12.7380i −0.317019 + 0.765352i 0.682390 + 0.730988i \(0.260940\pi\)
−0.999409 + 0.0343637i \(0.989060\pi\)
\(278\) 2.33527 12.4359i 0.140060 0.745858i
\(279\) 0 0
\(280\) −18.8147 + 30.2199i −1.12439 + 1.80598i
\(281\) 5.75892 5.75892i 0.343548 0.343548i −0.514151 0.857700i \(-0.671893\pi\)
0.857700 + 0.514151i \(0.171893\pi\)
\(282\) 0 0
\(283\) 10.4136 25.1407i 0.619025 1.49446i −0.233812 0.972282i \(-0.575120\pi\)
0.852837 0.522177i \(-0.174880\pi\)
\(284\) −13.9410 5.42714i −0.827243 0.322042i
\(285\) 0 0
\(286\) −8.09236 + 1.70011i −0.478511 + 0.100530i
\(287\) 1.03021 0.0608111
\(288\) 0 0
\(289\) 5.72512 0.336772
\(290\) 35.9149 7.54531i 2.10900 0.443076i
\(291\) 0 0
\(292\) 1.61590 4.15083i 0.0945632 0.242909i
\(293\) −5.21345 + 12.5864i −0.304573 + 0.735304i 0.695290 + 0.718729i \(0.255276\pi\)
−0.999863 + 0.0165743i \(0.994724\pi\)
\(294\) 0 0
\(295\) −2.72968 + 2.72968i −0.158928 + 0.158928i
\(296\) 6.51236 + 27.9987i 0.378523 + 1.62739i
\(297\) 0 0
\(298\) −5.36211 + 28.5547i −0.310619 + 1.65413i
\(299\) −8.07236 + 19.4884i −0.466837 + 1.12704i
\(300\) 0 0
\(301\) 32.4835 13.4551i 1.87232 0.775539i
\(302\) −8.56362 + 13.1189i −0.492781 + 0.754905i
\(303\) 0 0
\(304\) 11.1220 + 4.05720i 0.637892 + 0.232696i
\(305\) 8.01566 0.458975
\(306\) 0 0
\(307\) −8.98052 21.6809i −0.512545 1.23739i −0.942398 0.334495i \(-0.891434\pi\)
0.429852 0.902899i \(-0.358566\pi\)
\(308\) −9.98036 9.56104i −0.568684 0.544791i
\(309\) 0 0
\(310\) −4.72230 + 25.1475i −0.268208 + 1.42828i
\(311\) −12.7177 + 12.7177i −0.721157 + 0.721157i −0.968841 0.247684i \(-0.920330\pi\)
0.247684 + 0.968841i \(0.420330\pi\)
\(312\) 0 0
\(313\) 10.1388 + 10.1388i 0.573081 + 0.573081i 0.932988 0.359907i \(-0.117192\pi\)
−0.359907 + 0.932988i \(0.617192\pi\)
\(314\) −10.9213 + 7.46805i −0.616323 + 0.421446i
\(315\) 0 0
\(316\) 25.2137 11.0834i 1.41838 0.623490i
\(317\) −2.52668 + 1.04659i −0.141913 + 0.0587822i −0.452509 0.891760i \(-0.649471\pi\)
0.310597 + 0.950542i \(0.399471\pi\)
\(318\) 0 0
\(319\) 14.2484i 0.797757i
\(320\) 17.6405 + 15.5042i 0.986136 + 0.866713i
\(321\) 0 0
\(322\) −34.5040 + 7.24889i −1.92283 + 0.403965i
\(323\) −5.39940 13.0353i −0.300431 0.725304i
\(324\) 0 0
\(325\) −12.1260 5.02277i −0.672631 0.278613i
\(326\) −4.09287 5.98540i −0.226683 0.331501i
\(327\) 0 0
\(328\) 0.111078 0.670528i 0.00613327 0.0370237i
\(329\) 7.39834 + 7.39834i 0.407884 + 0.407884i
\(330\) 0 0
\(331\) −5.49794 2.27732i −0.302194 0.125173i 0.226434 0.974027i \(-0.427293\pi\)
−0.528628 + 0.848854i \(0.677293\pi\)
\(332\) 4.97086 5.18887i 0.272811 0.284776i
\(333\) 0 0
\(334\) −4.97641 + 7.62351i −0.272297 + 0.417140i
\(335\) 12.4418i 0.679768i
\(336\) 0 0
\(337\) 5.85273i 0.318818i −0.987213 0.159409i \(-0.949041\pi\)
0.987213 0.159409i \(-0.0509589\pi\)
\(338\) 0.187563 + 0.122436i 0.0102021 + 0.00665963i
\(339\) 0 0
\(340\) −0.600467 27.9829i −0.0325649 1.51759i
\(341\) −9.17801 3.80166i −0.497017 0.205871i
\(342\) 0 0
\(343\) −13.2780 13.2780i −0.716946 0.716946i
\(344\) −5.25508 22.5932i −0.283335 1.21815i
\(345\) 0 0
\(346\) −13.0697 + 8.93719i −0.702633 + 0.480466i
\(347\) 7.23994 + 2.99888i 0.388660 + 0.160988i 0.568452 0.822716i \(-0.307542\pi\)
−0.179792 + 0.983705i \(0.557542\pi\)
\(348\) 0 0
\(349\) −4.01973 9.70449i −0.215171 0.519469i 0.779032 0.626984i \(-0.215711\pi\)
−0.994204 + 0.107515i \(0.965711\pi\)
\(350\) −4.51039 21.4690i −0.241090 1.14756i
\(351\) 0 0
\(352\) −7.29908 + 5.46502i −0.389042 + 0.291286i
\(353\) 16.6657i 0.887026i −0.896268 0.443513i \(-0.853732\pi\)
0.896268 0.443513i \(-0.146268\pi\)
\(354\) 0 0
\(355\) 20.2875 8.40338i 1.07675 0.446005i
\(356\) 7.17242 18.4241i 0.380138 0.976477i
\(357\) 0 0
\(358\) −8.83444 12.9195i −0.466915 0.682815i
\(359\) −9.54649 9.54649i −0.503845 0.503845i 0.408786 0.912630i \(-0.365952\pi\)
−0.912630 + 0.408786i \(0.865952\pi\)
\(360\) 0 0
\(361\) 7.24075 7.24075i 0.381092 0.381092i
\(362\) −4.84363 0.909554i −0.254575 0.0478051i
\(363\) 0 0
\(364\) 0.667267 + 31.0960i 0.0349743 + 1.62987i
\(365\) 2.50205 + 6.04049i 0.130963 + 0.316173i
\(366\) 0 0
\(367\) −6.31072 −0.329417 −0.164708 0.986342i \(-0.552668\pi\)
−0.164708 + 0.986342i \(0.552668\pi\)
\(368\) 0.997804 + 23.2391i 0.0520141 + 1.21142i
\(369\) 0 0
\(370\) −35.3331 23.0644i −1.83688 1.19906i
\(371\) −8.53463 + 3.53516i −0.443096 + 0.183536i
\(372\) 0 0
\(373\) −3.06259 + 7.39375i −0.158575 + 0.382834i −0.983120 0.182963i \(-0.941431\pi\)
0.824545 + 0.565797i \(0.191431\pi\)
\(374\) 10.6802 + 2.00557i 0.552261 + 0.103706i
\(375\) 0 0
\(376\) 5.61305 4.01765i 0.289471 0.207194i
\(377\) 22.6733 22.6733i 1.16773 1.16773i
\(378\) 0 0
\(379\) −8.31838 + 20.0823i −0.427286 + 1.03156i 0.552858 + 0.833275i \(0.313537\pi\)
−0.980144 + 0.198285i \(0.936463\pi\)
\(380\) −15.9086 + 6.99307i −0.816092 + 0.358737i
\(381\) 0 0
\(382\) −1.40277 6.67705i −0.0717720 0.341627i
\(383\) 7.95308 0.406383 0.203192 0.979139i \(-0.434869\pi\)
0.203192 + 0.979139i \(0.434869\pi\)
\(384\) 0 0
\(385\) 20.2871 1.03393
\(386\) 0.0648046 + 0.308463i 0.00329847 + 0.0157004i
\(387\) 0 0
\(388\) 24.8243 10.9122i 1.26026 0.553984i
\(389\) 2.38215 5.75102i 0.120780 0.291588i −0.851913 0.523683i \(-0.824558\pi\)
0.972693 + 0.232094i \(0.0745578\pi\)
\(390\) 0 0
\(391\) 19.6019 19.6019i 0.991310 0.991310i
\(392\) −26.1737 + 18.7343i −1.32197 + 0.946227i
\(393\) 0 0
\(394\) 34.2922 + 6.43952i 1.72762 + 0.324418i
\(395\) −15.4710 + 37.3503i −0.778430 + 1.87930i
\(396\) 0 0
\(397\) 25.3118 10.4845i 1.27036 0.526202i 0.357288 0.933994i \(-0.383701\pi\)
0.913075 + 0.407792i \(0.133701\pi\)
\(398\) 24.9054 + 16.2575i 1.24839 + 0.814916i
\(399\) 0 0
\(400\) −14.4598 + 0.620851i −0.722990 + 0.0310426i
\(401\) 1.81017 0.0903954 0.0451977 0.998978i \(-0.485608\pi\)
0.0451977 + 0.998978i \(0.485608\pi\)
\(402\) 0 0
\(403\) 8.55532 + 20.6544i 0.426171 + 1.02887i
\(404\) 0.123870 + 5.77257i 0.00616275 + 0.287196i
\(405\) 0 0
\(406\) 52.6734 + 9.89120i 2.61413 + 0.490892i
\(407\) 11.5839 11.5839i 0.574194 0.574194i
\(408\) 0 0
\(409\) −14.4331 14.4331i −0.713672 0.713672i 0.253630 0.967301i \(-0.418376\pi\)
−0.967301 + 0.253630i \(0.918376\pi\)
\(410\) 0.563129 + 0.823518i 0.0278109 + 0.0406707i
\(411\) 0 0
\(412\) 13.1348 33.7399i 0.647104 1.66225i
\(413\) −5.20841 + 2.15739i −0.256289 + 0.106158i
\(414\) 0 0
\(415\) 10.5474i 0.517754i
\(416\) 20.3113 + 2.91851i 0.995845 + 0.143092i
\(417\) 0 0
\(418\) −1.38717 6.60278i −0.0678486 0.322952i
\(419\) 1.33902 + 3.23269i 0.0654155 + 0.157927i 0.953207 0.302320i \(-0.0977610\pi\)
−0.887791 + 0.460247i \(0.847761\pi\)
\(420\) 0 0
\(421\) −10.5557 4.37232i −0.514454 0.213094i 0.110325 0.993896i \(-0.464811\pi\)
−0.624779 + 0.780802i \(0.714811\pi\)
\(422\) 1.96453 1.34336i 0.0956318 0.0653938i
\(423\) 0 0
\(424\) 1.38071 + 5.93609i 0.0670530 + 0.288282i
\(425\) 12.1966 + 12.1966i 0.591624 + 0.591624i
\(426\) 0 0
\(427\) 10.8148 + 4.47963i 0.523364 + 0.216784i
\(428\) 0.0808028 + 3.76557i 0.00390575 + 0.182016i
\(429\) 0 0
\(430\) 28.5117 + 18.6116i 1.37496 + 0.897532i
\(431\) 3.31967i 0.159903i −0.996799 0.0799513i \(-0.974524\pi\)
0.996799 0.0799513i \(-0.0254765\pi\)
\(432\) 0 0
\(433\) 4.53298i 0.217841i 0.994050 + 0.108921i \(0.0347394\pi\)
−0.994050 + 0.108921i \(0.965261\pi\)
\(434\) −20.4253 + 31.2901i −0.980445 + 1.50197i
\(435\) 0 0
\(436\) −6.66431 + 6.95659i −0.319163 + 0.333160i
\(437\) −15.9011 6.58646i −0.760654 0.315073i
\(438\) 0 0
\(439\) 20.9703 + 20.9703i 1.00086 + 1.00086i 1.00000 0.000858061i \(0.000273129\pi\)
0.000858061 1.00000i \(0.499727\pi\)
\(440\) 2.18739 13.2043i 0.104280 0.629489i
\(441\) 0 0
\(442\) −13.8039 20.1868i −0.656583 0.960186i
\(443\) 31.9708 + 13.2427i 1.51898 + 0.629181i 0.977386 0.211462i \(-0.0678225\pi\)
0.541590 + 0.840643i \(0.317822\pi\)
\(444\) 0 0
\(445\) 11.1058 + 26.8117i 0.526464 + 1.27100i
\(446\) 32.4243 6.81198i 1.53534 0.322557i
\(447\) 0 0
\(448\) 15.1360 + 30.7770i 0.715110 + 1.45407i
\(449\) 21.0485i 0.993340i 0.867940 + 0.496670i \(0.165444\pi\)
−0.867940 + 0.496670i \(0.834556\pi\)
\(450\) 0 0
\(451\) −0.357852 + 0.148227i −0.0168506 + 0.00697975i
\(452\) −25.0125 + 10.9950i −1.17649 + 0.517159i
\(453\) 0 0
\(454\) 15.5787 10.6528i 0.731143 0.499961i
\(455\) −32.2827 32.2827i −1.51344 1.51344i
\(456\) 0 0
\(457\) −4.62656 + 4.62656i −0.216421 + 0.216421i −0.806988 0.590567i \(-0.798904\pi\)
0.590567 + 0.806988i \(0.298904\pi\)
\(458\) 2.21110 11.7747i 0.103318 0.550197i
\(459\) 0 0
\(460\) −24.6550 23.6192i −1.14955 1.10125i
\(461\) −4.84388 11.6942i −0.225602 0.544652i 0.770031 0.638007i \(-0.220241\pi\)
−0.995633 + 0.0933550i \(0.970241\pi\)
\(462\) 0 0
\(463\) 14.2219 0.660950 0.330475 0.943815i \(-0.392791\pi\)
0.330475 + 0.943815i \(0.392791\pi\)
\(464\) 12.1172 33.2169i 0.562526 1.54206i
\(465\) 0 0
\(466\) 10.5695 16.1917i 0.489622 0.750066i
\(467\) 34.5241 14.3003i 1.59758 0.661741i 0.606512 0.795074i \(-0.292568\pi\)
0.991071 + 0.133333i \(0.0425681\pi\)
\(468\) 0 0
\(469\) 6.95321 16.7865i 0.321069 0.775130i
\(470\) −1.86997 + 9.95809i −0.0862552 + 0.459333i
\(471\) 0 0
\(472\) 0.842601 + 3.62260i 0.0387838 + 0.166744i
\(473\) −9.34754 + 9.34754i −0.429800 + 0.429800i
\(474\) 0 0
\(475\) 4.09821 9.89396i 0.188039 0.453966i
\(476\) 14.8284 38.0903i 0.679657 1.74587i
\(477\) 0 0
\(478\) 35.7873 7.51850i 1.63687 0.343888i
\(479\) −13.4016 −0.612333 −0.306167 0.951978i \(-0.599046\pi\)
−0.306167 + 0.951978i \(0.599046\pi\)
\(480\) 0 0
\(481\) −36.8667 −1.68098
\(482\) −34.5112 + 7.25041i −1.57194 + 0.330247i
\(483\) 0 0
\(484\) −15.6589 6.09591i −0.711766 0.277087i
\(485\) −15.2320 + 36.7734i −0.691652 + 1.66979i
\(486\) 0 0
\(487\) 1.26750 1.26750i 0.0574358 0.0574358i −0.677805 0.735241i \(-0.737069\pi\)
0.735241 + 0.677805i \(0.237069\pi\)
\(488\) 4.08171 6.55599i 0.184770 0.296776i
\(489\) 0 0
\(490\) 8.71969 46.4347i 0.393915 2.09771i
\(491\) −8.81902 + 21.2910i −0.397997 + 0.960849i 0.590144 + 0.807298i \(0.299071\pi\)
−0.988141 + 0.153551i \(0.950929\pi\)
\(492\) 0 0
\(493\) −38.9311 + 16.1258i −1.75337 + 0.726269i
\(494\) −8.29953 + 12.7143i −0.373414 + 0.572043i
\(495\) 0 0
\(496\) 18.1634 + 16.6679i 0.815563 + 0.748411i
\(497\) 32.0684 1.43846
\(498\) 0 0
\(499\) −2.76574 6.67709i −0.123812 0.298908i 0.849805 0.527097i \(-0.176719\pi\)
−0.973617 + 0.228189i \(0.926719\pi\)
\(500\) −5.61209 + 5.85823i −0.250980 + 0.261988i
\(501\) 0 0
\(502\) 3.26258 17.3741i 0.145616 0.775445i
\(503\) −17.1789 + 17.1789i −0.765968 + 0.765968i −0.977394 0.211426i \(-0.932189\pi\)
0.211426 + 0.977394i \(0.432189\pi\)
\(504\) 0 0
\(505\) −5.99287 5.99287i −0.266679 0.266679i
\(506\) 10.9423 7.48245i 0.486446 0.332636i
\(507\) 0 0
\(508\) 10.6249 + 24.1706i 0.471404 + 1.07240i
\(509\) −0.432418 + 0.179113i −0.0191666 + 0.00793905i −0.392246 0.919860i \(-0.628302\pi\)
0.373080 + 0.927799i \(0.378302\pi\)
\(510\) 0 0
\(511\) 9.54815i 0.422385i
\(512\) 21.6637 6.53315i 0.957411 0.288727i
\(513\) 0 0
\(514\) 23.6359 4.96564i 1.04254 0.219025i
\(515\) 20.3379 + 49.0999i 0.896193 + 2.16360i
\(516\) 0 0
\(517\) −3.63437 1.50541i −0.159839 0.0662077i
\(518\) −34.7818 50.8649i −1.52823 2.23488i
\(519\) 0 0
\(520\) −24.4925 + 17.5310i −1.07407 + 0.768786i
\(521\) 20.6495 + 20.6495i 0.904670 + 0.904670i 0.995836 0.0911655i \(-0.0290592\pi\)
−0.0911655 + 0.995836i \(0.529059\pi\)
\(522\) 0 0
\(523\) −40.6453 16.8358i −1.77729 0.736180i −0.993321 0.115386i \(-0.963190\pi\)
−0.783974 0.620794i \(-0.786810\pi\)
\(524\) −9.68219 9.27540i −0.422969 0.405198i
\(525\) 0 0
\(526\) −11.4348 + 17.5172i −0.498579 + 0.763788i
\(527\) 29.3798i 1.27980i
\(528\) 0 0
\(529\) 10.8158i 0.470252i
\(530\) −7.49109 4.88997i −0.325392 0.212407i
\(531\) 0 0
\(532\) −25.3721 + 0.544441i −1.10002 + 0.0236045i
\(533\) 0.805318 + 0.333574i 0.0348822 + 0.0144487i
\(534\) 0 0
\(535\) −3.90927 3.90927i −0.169013 0.169013i
\(536\) −10.1761 6.33557i −0.439541 0.273655i
\(537\) 0 0
\(538\) −10.6032 + 7.25055i −0.457136 + 0.312593i
\(539\) 16.9471 + 7.01973i 0.729964 + 0.302361i
\(540\) 0 0
\(541\) −7.26862 17.5480i −0.312502 0.754447i −0.999611 0.0278925i \(-0.991120\pi\)
0.687109 0.726555i \(-0.258880\pi\)
\(542\) −1.64622 7.83583i −0.0707111 0.336578i
\(543\) 0 0
\(544\) −23.1930 13.7583i −0.994390 0.589881i
\(545\) 14.1407i 0.605721i
\(546\) 0 0
\(547\) −5.22407 + 2.16388i −0.223365 + 0.0925208i −0.491560 0.870844i \(-0.663573\pi\)
0.268195 + 0.963365i \(0.413573\pi\)
\(548\) 25.7600 + 10.0282i 1.10041 + 0.428386i
\(549\) 0 0
\(550\) 4.65571 + 6.80851i 0.198520 + 0.290316i
\(551\) 18.4998 + 18.4998i 0.788116 + 0.788116i
\(552\) 0 0
\(553\) −41.7471 + 41.7471i −1.77527 + 1.77527i
\(554\) −19.1635 3.59860i −0.814180 0.152890i
\(555\) 0 0
\(556\) 17.8903 0.383896i 0.758719 0.0162808i
\(557\) −7.20051 17.3836i −0.305095 0.736565i −0.999850 0.0173184i \(-0.994487\pi\)
0.694755 0.719247i \(-0.255513\pi\)
\(558\) 0 0
\(559\) 29.7492 1.25826
\(560\) −47.2949 17.2527i −1.99858 0.729059i
\(561\) 0 0
\(562\) 9.64483 + 6.29587i 0.406843 + 0.265575i
\(563\) −43.4445 + 17.9953i −1.83097 + 0.758411i −0.864007 + 0.503479i \(0.832053\pi\)
−0.966959 + 0.254932i \(0.917947\pi\)
\(564\) 0 0
\(565\) 15.3475 37.0522i 0.645675 1.55880i
\(566\) 37.8226 + 7.10247i 1.58980 + 0.298539i
\(567\) 0 0
\(568\) 3.45766 20.8723i 0.145080 0.875782i
\(569\) 5.66061 5.66061i 0.237305 0.237305i −0.578428 0.815733i \(-0.696334\pi\)
0.815733 + 0.578428i \(0.196334\pi\)
\(570\) 0 0
\(571\) −13.7365 + 33.1629i −0.574856 + 1.38783i 0.322522 + 0.946562i \(0.395469\pi\)
−0.897378 + 0.441263i \(0.854531\pi\)
\(572\) −4.70591 10.7055i −0.196764 0.447619i
\(573\) 0 0
\(574\) 0.299545 + 1.42581i 0.0125028 + 0.0595120i
\(575\) 21.0408 0.877461
\(576\) 0 0
\(577\) 4.38583 0.182584 0.0912922 0.995824i \(-0.470900\pi\)
0.0912922 + 0.995824i \(0.470900\pi\)
\(578\) 1.66465 + 7.92357i 0.0692404 + 0.329577i
\(579\) 0 0
\(580\) 20.8854 + 47.5124i 0.867220 + 1.97284i
\(581\) −5.89454 + 14.2307i −0.244547 + 0.590388i
\(582\) 0 0
\(583\) 2.45595 2.45595i 0.101715 0.101715i
\(584\) 6.21459 + 1.02950i 0.257162 + 0.0426008i
\(585\) 0 0
\(586\) −18.9354 3.55576i −0.782215 0.146887i
\(587\) 4.24918 10.2584i 0.175382 0.423411i −0.811605 0.584206i \(-0.801406\pi\)
0.986988 + 0.160795i \(0.0514060\pi\)
\(588\) 0 0
\(589\) −16.8525 + 6.98052i −0.694394 + 0.287627i
\(590\) −4.57157 2.98419i −0.188208 0.122857i
\(591\) 0 0
\(592\) −36.8566 + 17.1541i −1.51480 + 0.705028i
\(593\) −5.76763 −0.236848 −0.118424 0.992963i \(-0.537784\pi\)
−0.118424 + 0.992963i \(0.537784\pi\)
\(594\) 0 0
\(595\) 22.9602 + 55.4309i 0.941277 + 2.27244i
\(596\) −41.0788 + 0.881482i −1.68265 + 0.0361069i
\(597\) 0 0
\(598\) −29.3191 5.50565i −1.19895 0.225143i
\(599\) 13.4401 13.4401i 0.549149 0.549149i −0.377045 0.926195i \(-0.623060\pi\)
0.926195 + 0.377045i \(0.123060\pi\)
\(600\) 0 0
\(601\) 8.58677 + 8.58677i 0.350262 + 0.350262i 0.860207 0.509945i \(-0.170334\pi\)
−0.509945 + 0.860207i \(0.670334\pi\)
\(602\) 28.0669 + 41.0449i 1.14392 + 1.67287i
\(603\) 0 0
\(604\) −20.6465 8.03757i −0.840093 0.327044i
\(605\) 22.7875 9.43890i 0.926444 0.383746i
\(606\) 0 0
\(607\) 13.3743i 0.542847i 0.962460 + 0.271424i \(0.0874944\pi\)
−0.962460 + 0.271424i \(0.912506\pi\)
\(608\) −2.38129 + 16.5726i −0.0965742 + 0.672107i
\(609\) 0 0
\(610\) 2.33066 + 11.0937i 0.0943655 + 0.449170i
\(611\) 3.38780 + 8.17886i 0.137056 + 0.330881i
\(612\) 0 0
\(613\) −10.6749 4.42168i −0.431154 0.178590i 0.156542 0.987671i \(-0.449965\pi\)
−0.587697 + 0.809081i \(0.699965\pi\)
\(614\) 27.3952 18.7330i 1.10558 0.756004i
\(615\) 0 0
\(616\) 10.3306 16.5928i 0.416230 0.668544i
\(617\) 14.8713 + 14.8713i 0.598695 + 0.598695i 0.939965 0.341270i \(-0.110857\pi\)
−0.341270 + 0.939965i \(0.610857\pi\)
\(618\) 0 0
\(619\) −6.25062 2.58909i −0.251234 0.104064i 0.253513 0.967332i \(-0.418414\pi\)
−0.504746 + 0.863268i \(0.668414\pi\)
\(620\) −36.1773 + 0.776303i −1.45291 + 0.0311771i
\(621\) 0 0
\(622\) −21.2992 13.9035i −0.854020 0.557480i
\(623\) 42.3810i 1.69796i
\(624\) 0 0
\(625\) 29.9995i 1.19998i
\(626\) −11.0842 + 16.9801i −0.443012 + 0.678663i
\(627\) 0 0
\(628\) −13.5113 12.9436i −0.539159 0.516506i
\(629\) 44.7612 + 18.5407i 1.78475 + 0.739266i
\(630\) 0 0
\(631\) −5.78346 5.78346i −0.230236 0.230236i 0.582555 0.812791i \(-0.302053\pi\)
−0.812791 + 0.582555i \(0.802053\pi\)
\(632\) 22.6706 + 31.6731i 0.901789 + 1.25989i
\(633\) 0 0
\(634\) −2.18314 3.19262i −0.0867037 0.126795i
\(635\) −35.8052 14.8310i −1.42088 0.588550i
\(636\) 0 0
\(637\) −15.7973 38.1381i −0.625913 1.51109i
\(638\) −19.7198 + 4.14290i −0.780714 + 0.164019i
\(639\) 0 0
\(640\) −16.3286 + 28.9226i −0.645446 + 1.14327i
\(641\) 29.5203i 1.16598i −0.812479 0.582990i \(-0.801883\pi\)
0.812479 0.582990i \(-0.198117\pi\)
\(642\) 0 0
\(643\) 10.0660 4.16947i 0.396964 0.164428i −0.175266 0.984521i \(-0.556079\pi\)
0.572230 + 0.820093i \(0.306079\pi\)
\(644\) −20.0649 45.6458i −0.790669 1.79870i
\(645\) 0 0
\(646\) 16.4709 11.2630i 0.648040 0.443135i
\(647\) −31.9256 31.9256i −1.25512 1.25512i −0.953393 0.301730i \(-0.902436\pi\)
−0.301730 0.953393i \(-0.597564\pi\)
\(648\) 0 0
\(649\) 1.49878 1.49878i 0.0588324 0.0588324i
\(650\) 3.42571 18.2429i 0.134368 0.715544i
\(651\) 0 0
\(652\) 7.09375 7.40486i 0.277813 0.289997i
\(653\) −6.05626 14.6211i −0.237000 0.572168i 0.759970 0.649958i \(-0.225214\pi\)
−0.996970 + 0.0777900i \(0.975214\pi\)
\(654\) 0 0
\(655\) 19.6811 0.769002
\(656\) 0.960309 0.0412322i 0.0374938 0.00160985i
\(657\) 0 0
\(658\) −8.08814 + 12.3905i −0.315309 + 0.483031i
\(659\) −28.2612 + 11.7062i −1.10090 + 0.456008i −0.857795 0.513992i \(-0.828166\pi\)
−0.243106 + 0.970000i \(0.578166\pi\)
\(660\) 0 0
\(661\) 6.64573 16.0442i 0.258489 0.624047i −0.740350 0.672221i \(-0.765340\pi\)
0.998839 + 0.0481743i \(0.0153403\pi\)
\(662\) 1.55322 8.27131i 0.0603675 0.321474i
\(663\) 0 0
\(664\) 8.62674 + 5.37094i 0.334782 + 0.208433i
\(665\) 26.3403 26.3403i 1.02143 1.02143i
\(666\) 0 0
\(667\) −19.6711 + 47.4901i −0.761666 + 1.83883i
\(668\) −11.9979 4.67072i −0.464212 0.180716i
\(669\) 0 0
\(670\) 17.2194 3.61761i 0.665245 0.139760i
\(671\) −4.40116 −0.169905
\(672\) 0 0
\(673\) 34.2884 1.32172 0.660860 0.750509i \(-0.270192\pi\)
0.660860 + 0.750509i \(0.270192\pi\)
\(674\) 8.10018 1.70176i 0.312007 0.0655492i
\(675\) 0 0
\(676\) −0.114915 + 0.295187i −0.00441980 + 0.0113533i
\(677\) 16.6560 40.2112i 0.640142 1.54544i −0.186345 0.982484i \(-0.559664\pi\)
0.826487 0.562956i \(-0.190336\pi\)
\(678\) 0 0
\(679\) −41.1023 + 41.1023i −1.57736 + 1.57736i
\(680\) 38.5538 8.96744i 1.47847 0.343886i
\(681\) 0 0
\(682\) 2.59287 13.8077i 0.0992861 0.528726i
\(683\) 5.35596 12.9304i 0.204940 0.494769i −0.787673 0.616094i \(-0.788714\pi\)
0.992613 + 0.121325i \(0.0387142\pi\)
\(684\) 0 0
\(685\) −37.4872 + 15.5277i −1.43231 + 0.593284i
\(686\) 14.5160 22.2376i 0.554225 0.849034i
\(687\) 0 0
\(688\) 29.7411 13.8423i 1.13387 0.527733i
\(689\) −7.81623 −0.297775
\(690\) 0 0
\(691\) −19.9998 48.2837i −0.760826 1.83680i −0.480898 0.876777i \(-0.659689\pi\)
−0.279929 0.960021i \(-0.590311\pi\)
\(692\) −16.1693 15.4899i −0.614663 0.588838i
\(693\) 0 0
\(694\) −2.04535 + 10.8920i −0.0776404 + 0.413456i
\(695\) −18.5731 + 18.5731i −0.704517 + 0.704517i
\(696\) 0 0
\(697\) −0.810008 0.810008i −0.0306812 0.0306812i
\(698\) 12.2622 8.38501i 0.464132 0.317377i
\(699\) 0 0
\(700\) 28.4016 12.4848i 1.07348 0.471879i
\(701\) −22.6661 + 9.38859i −0.856085 + 0.354602i −0.767175 0.641438i \(-0.778338\pi\)
−0.0889098 + 0.996040i \(0.528338\pi\)
\(702\) 0 0
\(703\) 30.0806i 1.13451i
\(704\) −9.68589 8.51290i −0.365051 0.320842i
\(705\) 0 0
\(706\) 23.0653 4.84577i 0.868076 0.182373i
\(707\) −4.73644 11.4348i −0.178132 0.430049i
\(708\) 0 0
\(709\) −6.91323 2.86355i −0.259632 0.107543i 0.249071 0.968485i \(-0.419875\pi\)
−0.508703 + 0.860942i \(0.669875\pi\)
\(710\) 17.5291 + 25.6346i 0.657857 + 0.962049i
\(711\) 0 0
\(712\) 27.5845 + 4.56959i 1.03377 + 0.171253i
\(713\) −25.3420 25.3420i −0.949064 0.949064i
\(714\) 0 0
\(715\) 15.8586 + 6.56884i 0.593078 + 0.245661i
\(716\) 15.3118 15.9834i 0.572230 0.597327i
\(717\) 0 0
\(718\) 10.4366 15.9881i 0.389490 0.596671i
\(719\) 32.1395i 1.19860i 0.800525 + 0.599300i \(0.204554\pi\)
−0.800525 + 0.599300i \(0.795446\pi\)
\(720\) 0 0
\(721\) 77.6119i 2.89042i
\(722\) 12.1265 + 7.91587i 0.451303 + 0.294598i
\(723\) 0 0
\(724\) −0.149522 6.96805i −0.00555696 0.258965i
\(725\) −29.5492 12.2397i −1.09743 0.454570i
\(726\) 0 0
\(727\) 24.0313 + 24.0313i 0.891271 + 0.891271i 0.994643 0.103372i \(-0.0329632\pi\)
−0.103372 + 0.994643i \(0.532963\pi\)
\(728\) −42.8428 + 9.96505i −1.58786 + 0.369329i
\(729\) 0 0
\(730\) −7.63253 + 5.21919i −0.282493 + 0.193171i
\(731\) −36.1196 14.9612i −1.33593 0.553361i
\(732\) 0 0
\(733\) −3.28110 7.92127i −0.121190 0.292579i 0.851629 0.524145i \(-0.175615\pi\)
−0.972819 + 0.231566i \(0.925615\pi\)
\(734\) −1.83492 8.73404i −0.0677282 0.322379i
\(735\) 0 0
\(736\) −31.8728 + 8.13803i −1.17485 + 0.299972i
\(737\) 6.83141i 0.251638i
\(738\) 0 0
\(739\) 4.01435 1.66280i 0.147670 0.0611671i −0.307624 0.951508i \(-0.599534\pi\)
0.455295 + 0.890341i \(0.349534\pi\)
\(740\) 21.6477 55.6073i 0.795784 2.04417i
\(741\) 0 0
\(742\) −7.37421 10.7840i −0.270716 0.395894i
\(743\) 20.6253 + 20.6253i 0.756669 + 0.756669i 0.975715 0.219046i \(-0.0702944\pi\)
−0.219046 + 0.975715i \(0.570294\pi\)
\(744\) 0 0
\(745\) 42.6465 42.6465i 1.56245 1.56245i
\(746\) −11.1234 2.08880i −0.407258 0.0764765i
\(747\) 0 0
\(748\) 0.329698 + 15.3646i 0.0120550 + 0.561785i
\(749\) −3.08968 7.45915i −0.112894 0.272551i
\(750\) 0 0
\(751\) 13.6475 0.498004 0.249002 0.968503i \(-0.419897\pi\)
0.249002 + 0.968503i \(0.419897\pi\)
\(752\) 7.19249 + 6.60028i 0.262283 + 0.240687i
\(753\) 0 0
\(754\) 37.9724 + 24.7873i 1.38287 + 0.902700i
\(755\) 30.0458 12.4454i 1.09348 0.452933i
\(756\) 0 0
\(757\) 1.50145 3.62481i 0.0545710 0.131746i −0.894243 0.447582i \(-0.852285\pi\)
0.948814 + 0.315836i \(0.102285\pi\)
\(758\) −30.2126 5.67344i −1.09737 0.206069i
\(759\) 0 0
\(760\) −14.3040 19.9841i −0.518862 0.724901i
\(761\) 10.5824 10.5824i 0.383612 0.383612i −0.488790 0.872402i \(-0.662562\pi\)
0.872402 + 0.488790i \(0.162562\pi\)
\(762\) 0 0
\(763\) 7.90266 19.0787i 0.286096 0.690696i
\(764\) 8.83316 3.88287i 0.319573 0.140477i
\(765\) 0 0
\(766\) 2.31246 + 11.0071i 0.0835525 + 0.397701i
\(767\) −4.76999 −0.172234
\(768\) 0 0
\(769\) −42.6343 −1.53743 −0.768715 0.639591i \(-0.779104\pi\)
−0.768715 + 0.639591i \(0.779104\pi\)
\(770\) 5.89875 + 28.0774i 0.212576 + 1.01184i
\(771\) 0 0
\(772\) −0.408070 + 0.179379i −0.0146868 + 0.00645600i
\(773\) −13.5374 + 32.6822i −0.486906 + 1.17550i 0.469362 + 0.883006i \(0.344484\pi\)
−0.956268 + 0.292490i \(0.905516\pi\)
\(774\) 0 0
\(775\) 15.7682 15.7682i 0.566411 0.566411i
\(776\) 22.3205 + 31.1839i 0.801259 + 1.11944i
\(777\) 0 0
\(778\) 8.65206 + 1.62472i 0.310191 + 0.0582489i
\(779\) −0.272172 + 0.657081i −0.00975157 + 0.0235424i
\(780\) 0 0
\(781\) −11.1393 + 4.61404i −0.398595 + 0.165103i
\(782\) 32.8285 + 21.4295i 1.17395 + 0.766318i
\(783\) 0 0
\(784\) −33.5387 30.7772i −1.19781 1.09918i
\(785\) 27.4645 0.980249
\(786\) 0 0
\(787\) −11.1547 26.9298i −0.397622 0.959945i −0.988228 0.152985i \(-0.951111\pi\)
0.590606 0.806960i \(-0.298889\pi\)
\(788\) 1.05860 + 49.3328i 0.0377110 + 1.75741i
\(789\) 0 0
\(790\) −56.1912 10.5518i −1.99919 0.375416i
\(791\) 41.4139 41.4139i 1.47251 1.47251i
\(792\) 0 0
\(793\) 7.00350 + 7.00350i 0.248702 + 0.248702i
\(794\) 21.8703 + 31.9830i 0.776147 + 1.13504i
\(795\) 0 0
\(796\) −15.2589 + 39.1962i −0.540836 + 1.38927i
\(797\) −3.44606 + 1.42740i −0.122066 + 0.0505612i −0.442880 0.896581i \(-0.646043\pi\)
0.320815 + 0.947142i \(0.396043\pi\)
\(798\) 0 0
\(799\) 11.6340i 0.411582i
\(800\) −5.06363 19.8318i −0.179026 0.701162i
\(801\) 0 0
\(802\) 0.526329 + 2.50527i 0.0185853 + 0.0884642i
\(803\) −1.37380 3.31665i −0.0484804 0.117042i
\(804\) 0 0
\(805\) 67.6174 + 28.0080i 2.38320 + 0.987154i
\(806\) −26.0981 + 17.8461i −0.919266 + 0.628602i
\(807\) 0 0
\(808\) −7.95323 + 1.84988i −0.279794 + 0.0650787i
\(809\) −27.7746 27.7746i −0.976503 0.976503i 0.0232274 0.999730i \(-0.492606\pi\)
−0.999730 + 0.0232274i \(0.992606\pi\)
\(810\) 0 0
\(811\) 13.7402 + 5.69137i 0.482483 + 0.199851i 0.610649 0.791902i \(-0.290909\pi\)
−0.128165 + 0.991753i \(0.540909\pi\)
\(812\) 1.62602 + 75.7759i 0.0570622 + 2.65921i
\(813\) 0 0
\(814\) 19.4003 + 12.6640i 0.679982 + 0.443873i
\(815\) 15.0519i 0.527246i
\(816\) 0 0
\(817\) 24.2732i 0.849212i
\(818\) 15.7788 24.1721i 0.551694 0.845156i
\(819\) 0 0
\(820\) −0.976013 + 1.01882i −0.0340839 + 0.0355787i
\(821\) 9.08495 + 3.76311i 0.317067 + 0.131333i 0.535541 0.844509i \(-0.320108\pi\)
−0.218474 + 0.975843i \(0.570108\pi\)
\(822\) 0 0
\(823\) −37.7132 37.7132i −1.31460 1.31460i −0.917985 0.396615i \(-0.870185\pi\)
−0.396615 0.917985i \(-0.629815\pi\)
\(824\) 50.5151 + 8.36823i 1.75978 + 0.291521i
\(825\) 0 0
\(826\) −4.50024 6.58115i −0.156583 0.228987i
\(827\) −23.6871 9.81150i −0.823680 0.341179i −0.0692824 0.997597i \(-0.522071\pi\)
−0.754398 + 0.656418i \(0.772071\pi\)
\(828\) 0 0
\(829\) −6.99320 16.8831i −0.242884 0.586374i 0.754683 0.656090i \(-0.227791\pi\)
−0.997567 + 0.0697159i \(0.977791\pi\)
\(830\) −14.5977 + 3.06680i −0.506692 + 0.106450i
\(831\) 0 0
\(832\) 1.86656 + 28.9595i 0.0647112 + 1.00399i
\(833\) 54.2495i 1.87964i
\(834\) 0 0
\(835\) 17.4599 7.23214i 0.604225 0.250278i
\(836\) 8.73491 3.83968i 0.302103 0.132798i
\(837\) 0 0
\(838\) −4.08470 + 2.79315i −0.141104 + 0.0964879i
\(839\) 9.56749 + 9.56749i 0.330306 + 0.330306i 0.852703 0.522396i \(-0.174962\pi\)
−0.522396 + 0.852703i \(0.674962\pi\)
\(840\) 0 0
\(841\) 34.7451 34.7451i 1.19811 1.19811i
\(842\) 2.98209 15.8804i 0.102769 0.547276i
\(843\) 0 0
\(844\) 2.43042 + 2.32831i 0.0836586 + 0.0801437i
\(845\) −0.177934 0.429570i −0.00612111 0.0147777i
\(846\) 0 0
\(847\) 36.0201 1.23766
\(848\) −7.81409 + 3.63689i −0.268337 + 0.124891i
\(849\) 0 0
\(850\) −13.3338 + 20.4265i −0.457347 + 0.700623i
\(851\) 54.6020 22.6169i 1.87173 0.775297i
\(852\) 0 0
\(853\) −3.73365 + 9.01383i −0.127838 + 0.308628i −0.974820 0.222994i \(-0.928417\pi\)
0.846982 + 0.531621i \(0.178417\pi\)
\(854\) −3.05527 + 16.2702i −0.104549 + 0.556753i
\(855\) 0 0
\(856\) −5.18806 + 1.20672i −0.177324 + 0.0412448i
\(857\) −19.7027 + 19.7027i −0.673032 + 0.673032i −0.958414 0.285382i \(-0.907880\pi\)
0.285382 + 0.958414i \(0.407880\pi\)
\(858\) 0 0
\(859\) 8.30760 20.0563i 0.283452 0.684313i −0.716460 0.697629i \(-0.754239\pi\)
0.999911 + 0.0133155i \(0.00423857\pi\)
\(860\) −17.4684 + 44.8718i −0.595666 + 1.53011i
\(861\) 0 0
\(862\) 4.59442 0.965235i 0.156487 0.0328760i
\(863\) −29.3303 −0.998415 −0.499207 0.866483i \(-0.666375\pi\)
−0.499207 + 0.866483i \(0.666375\pi\)
\(864\) 0 0
\(865\) 32.8674 1.11752
\(866\) −6.27364 + 1.31802i −0.213187 + 0.0447882i
\(867\) 0 0
\(868\) −49.2444 19.1706i −1.67146 0.650693i
\(869\) 8.49465 20.5079i 0.288161 0.695683i
\(870\) 0 0
\(871\) 10.8707 10.8707i 0.368341 0.368341i
\(872\) −11.5657 7.20069i −0.391663 0.243846i
\(873\) 0 0
\(874\) 4.49221 23.9223i 0.151951 0.809183i
\(875\) 6.65492 16.0664i 0.224977 0.543144i
\(876\) 0 0
\(877\) 43.0165 17.8180i 1.45256 0.601672i 0.489756 0.871859i \(-0.337086\pi\)
0.962808 + 0.270188i \(0.0870858\pi\)
\(878\) −22.9255 + 35.1203i −0.773699 + 1.18525i
\(879\) 0 0
\(880\) 18.9107 0.811958i 0.637480 0.0273711i
\(881\) −54.5605 −1.83819 −0.919095 0.394035i \(-0.871079\pi\)
−0.919095 + 0.394035i \(0.871079\pi\)
\(882\) 0 0
\(883\) −4.61420 11.1397i −0.155280 0.374879i 0.827026 0.562164i \(-0.190031\pi\)
−0.982306 + 0.187285i \(0.940031\pi\)
\(884\) 23.9248 24.9741i 0.804679 0.839970i
\(885\) 0 0
\(886\) −9.03203 + 48.0980i −0.303437 + 1.61588i
\(887\) 20.2635 20.2635i 0.680383 0.680383i −0.279704 0.960086i \(-0.590236\pi\)
0.960086 + 0.279704i \(0.0902363\pi\)
\(888\) 0 0
\(889\) −40.0201 40.0201i −1.34223 1.34223i
\(890\) −33.8782 + 23.1662i −1.13560 + 0.776534i
\(891\) 0 0
\(892\) 18.8556 + 42.8946i 0.631331 + 1.43622i
\(893\) −6.67336 + 2.76419i −0.223315 + 0.0925003i
\(894\) 0 0
\(895\) 32.4895i 1.08600i
\(896\) −38.1943 + 29.8971i −1.27598 + 0.998791i
\(897\) 0 0
\(898\) −29.1311 + 6.12012i −0.972118 + 0.204231i
\(899\) 20.8479 + 50.3314i 0.695318 + 1.67865i
\(900\) 0 0
\(901\) 9.48997 + 3.93087i 0.316157 + 0.130956i
\(902\) −0.309197 0.452169i −0.0102951 0.0150556i
\(903\) 0 0
\(904\) −22.4897 31.4203i −0.747997 1.04502i
\(905\) 7.23396 + 7.23396i 0.240465 + 0.240465i
\(906\) 0 0
\(907\) 31.3520 + 12.9864i 1.04103 + 0.431208i 0.836681 0.547691i \(-0.184493\pi\)
0.204347 + 0.978899i \(0.434493\pi\)
\(908\) 19.2732 + 18.4634i 0.639603 + 0.612730i
\(909\) 0 0
\(910\) 35.2926 54.0658i 1.16994 1.79226i
\(911\) 44.6280i 1.47859i −0.673380 0.739296i \(-0.735158\pi\)
0.673380 0.739296i \(-0.264842\pi\)
\(912\) 0 0
\(913\) 5.79128i 0.191663i
\(914\) −7.74839 5.05793i −0.256294 0.167301i
\(915\) 0 0
\(916\) 16.9391 0.363485i 0.559685 0.0120099i
\(917\) 26.5538 + 10.9989i 0.876883 + 0.363217i
\(918\) 0 0
\(919\) 7.85821 + 7.85821i 0.259219 + 0.259219i 0.824736 0.565518i \(-0.191324\pi\)
−0.565518 + 0.824736i \(0.691324\pi\)
\(920\) 25.5202 40.9902i 0.841375 1.35141i
\(921\) 0 0
\(922\) 14.7763 10.1042i 0.486632 0.332763i
\(923\) 25.0680 + 10.3835i 0.825125 + 0.341778i
\(924\) 0 0
\(925\) 14.0726 + 33.9743i 0.462705 + 1.11707i
\(926\) 4.13521 + 19.6832i 0.135892 + 0.646830i
\(927\) 0 0
\(928\) 49.4955 + 7.11195i 1.62477 + 0.233461i
\(929\) 14.8136i 0.486018i 0.970024 + 0.243009i \(0.0781344\pi\)
−0.970024 + 0.243009i \(0.921866\pi\)
\(930\) 0 0
\(931\) 31.1180 12.8895i 1.01985 0.422436i
\(932\) 25.4825 + 9.92022i 0.834708 + 0.324948i
\(933\) 0 0
\(934\) 29.8300 + 43.6233i 0.976067 + 1.42740i
\(935\) −15.9509 15.9509i −0.521651 0.521651i
\(936\) 0 0
\(937\) −10.7125 + 10.7125i −0.349961 + 0.349961i −0.860095 0.510134i \(-0.829596\pi\)
0.510134 + 0.860095i \(0.329596\pi\)
\(938\) 25.2543 + 4.74235i 0.824582 + 0.154843i
\(939\) 0 0
\(940\) −14.3257 + 0.307406i −0.467254 + 0.0100265i
\(941\) 1.84380 + 4.45134i 0.0601063 + 0.145109i 0.951079 0.308947i \(-0.0999765\pi\)
−0.890973 + 0.454056i \(0.849977\pi\)
\(942\) 0 0
\(943\) −1.39737 −0.0455046
\(944\) −4.76868 + 2.21948i −0.155207 + 0.0722378i
\(945\) 0 0
\(946\) −15.6549 10.2191i −0.508985 0.332251i
\(947\) −46.3221 + 19.1872i −1.50527 + 0.623501i −0.974574 0.224064i \(-0.928068\pi\)
−0.530691 + 0.847565i \(0.678068\pi\)
\(948\) 0 0
\(949\) −3.09163 + 7.46385i −0.100358 + 0.242287i
\(950\) 14.8849 + 2.79513i 0.482928 + 0.0906861i
\(951\) 0 0
\(952\) 57.0285 + 9.44723i 1.84831 + 0.306186i
\(953\) 2.40430 2.40430i 0.0778828 0.0778828i −0.667092 0.744975i \(-0.732461\pi\)
0.744975 + 0.667092i \(0.232461\pi\)
\(954\) 0 0
\(955\) −5.41999 + 13.0850i −0.175387 + 0.423421i
\(956\) 20.8112 + 47.3435i 0.673083 + 1.53120i
\(957\) 0 0
\(958\) −3.89668 18.5478i −0.125896 0.599251i
\(959\) −59.2558 −1.91347
\(960\) 0 0
\(961\) −6.98312 −0.225262
\(962\) −10.7195 51.0236i −0.345609 1.64507i
\(963\) 0 0
\(964\) −20.0691 45.6554i −0.646383 1.47046i
\(965\) 0.250390 0.604495i 0.00806034 0.0194594i
\(966\) 0 0
\(967\) −12.6984 + 12.6984i −0.408354 + 0.408354i −0.881164 0.472811i \(-0.843239\pi\)
0.472811 + 0.881164i \(0.343239\pi\)
\(968\) 3.88374 23.4443i 0.124828 0.753529i
\(969\) 0 0
\(970\) −55.3233 10.3888i −1.77633 0.333565i
\(971\) 5.19719 12.5471i 0.166786 0.402657i −0.818283 0.574815i \(-0.805074\pi\)
0.985069 + 0.172158i \(0.0550740\pi\)
\(972\) 0 0
\(973\) −35.4386 + 14.6792i −1.13611 + 0.470592i
\(974\) 2.12276 + 1.38568i 0.0680175 + 0.0443999i
\(975\) 0 0
\(976\) 10.2603 + 3.74285i 0.328424 + 0.119806i
\(977\) −20.3021 −0.649521 −0.324761 0.945796i \(-0.605284\pi\)
−0.324761 + 0.945796i \(0.605284\pi\)
\(978\) 0 0
\(979\) −6.09784 14.7215i −0.194888 0.470501i
\(980\) 66.8010 1.43344i 2.13388 0.0457895i
\(981\) 0 0
\(982\) −32.0310 6.01490i −1.02215 0.191943i
\(983\) 11.4130 11.4130i 0.364017 0.364017i −0.501272 0.865290i \(-0.667134\pi\)
0.865290 + 0.501272i \(0.167134\pi\)
\(984\) 0 0
\(985\) −51.2155 51.2155i −1.63186 1.63186i
\(986\) −33.6378 49.1919i −1.07125 1.56659i
\(987\) 0 0
\(988\) −20.0098 7.78971i −0.636596 0.247824i
\(989\) −44.0605 + 18.2505i −1.40104 + 0.580331i
\(990\) 0 0
\(991\) 12.0390i 0.382431i 0.981548 + 0.191216i \(0.0612430\pi\)
−0.981548 + 0.191216i \(0.938757\pi\)
\(992\) −17.7871 + 29.9846i −0.564742 + 0.952013i
\(993\) 0 0
\(994\) 9.32429 + 44.3826i 0.295748 + 1.40773i
\(995\) −23.6268 57.0401i −0.749020 1.80829i
\(996\) 0 0
\(997\) 17.2248 + 7.13474i 0.545514 + 0.225959i 0.638383 0.769719i \(-0.279604\pi\)
−0.0928685 + 0.995678i \(0.529604\pi\)
\(998\) 8.43692 5.76923i 0.267066 0.182622i
\(999\) 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 288.2.w.b.251.4 yes 32
3.2 odd 2 288.2.w.a.251.5 yes 32
4.3 odd 2 1152.2.w.a.143.7 32
12.11 even 2 1152.2.w.b.143.2 32
32.13 even 8 1152.2.w.b.1007.2 32
32.19 odd 8 288.2.w.a.179.5 32
96.77 odd 8 1152.2.w.a.1007.7 32
96.83 even 8 inner 288.2.w.b.179.4 yes 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
288.2.w.a.179.5 32 32.19 odd 8
288.2.w.a.251.5 yes 32 3.2 odd 2
288.2.w.b.179.4 yes 32 96.83 even 8 inner
288.2.w.b.251.4 yes 32 1.1 even 1 trivial
1152.2.w.a.143.7 32 4.3 odd 2
1152.2.w.a.1007.7 32 96.77 odd 8
1152.2.w.b.143.2 32 12.11 even 2
1152.2.w.b.1007.2 32 32.13 even 8