Properties

Label 288.2.v.c.37.8
Level $288$
Weight $2$
Character 288.37
Analytic conductor $2.300$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [288,2,Mod(37,288)]
 
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([0, 1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("288.37");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 288 = 2^{5} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 288.v (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 37.8
Character \(\chi\) \(=\) 288.37
Dual form 288.2.v.c.109.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.41364 + 0.0402136i) q^{2} +(1.99677 + 0.113695i) q^{4} +(1.51282 + 0.626632i) q^{5} +(-1.32530 - 1.32530i) q^{7} +(2.81814 + 0.241022i) q^{8} +O(q^{10})\) \(q+(1.41364 + 0.0402136i) q^{2} +(1.99677 + 0.113695i) q^{4} +(1.51282 + 0.626632i) q^{5} +(-1.32530 - 1.32530i) q^{7} +(2.81814 + 0.241022i) q^{8} +(2.11339 + 0.946670i) q^{10} +(0.938971 - 2.26688i) q^{11} +(-4.73458 + 1.96113i) q^{13} +(-1.82020 - 1.92679i) q^{14} +(3.97415 + 0.454046i) q^{16} +5.78108i q^{17} +(-1.04283 + 0.431956i) q^{19} +(2.94951 + 1.42324i) q^{20} +(1.41853 - 3.16679i) q^{22} +(4.29232 - 4.29232i) q^{23} +(-1.63956 - 1.63956i) q^{25} +(-6.77187 + 2.58194i) q^{26} +(-2.49563 - 2.79699i) q^{28} +(-0.389398 - 0.940091i) q^{29} -7.43150 q^{31} +(5.59976 + 0.801673i) q^{32} +(-0.232478 + 8.17238i) q^{34} +(-1.17447 - 2.83541i) q^{35} +(-3.67926 - 1.52400i) q^{37} +(-1.49156 + 0.568695i) q^{38} +(4.11232 + 2.13056i) q^{40} +(0.474313 - 0.474313i) q^{41} +(-0.409042 + 0.987514i) q^{43} +(2.13264 - 4.41967i) q^{44} +(6.24042 - 5.89520i) q^{46} +2.73234i q^{47} -3.48718i q^{49} +(-2.25182 - 2.38369i) q^{50} +(-9.67683 + 3.37761i) q^{52} +(-4.55362 + 10.9934i) q^{53} +(2.84100 - 2.84100i) q^{55} +(-3.41544 - 4.05429i) q^{56} +(-0.512665 - 1.34461i) q^{58} +(-8.68022 - 3.59546i) q^{59} +(1.48345 + 3.58137i) q^{61} +(-10.5055 - 0.298848i) q^{62} +(7.88382 + 1.35847i) q^{64} -8.39150 q^{65} +(6.11281 + 14.7576i) q^{67} +(-0.657282 + 11.5435i) q^{68} +(-1.54625 - 4.05549i) q^{70} +(-10.5767 - 10.5767i) q^{71} +(6.86117 - 6.86117i) q^{73} +(-5.13987 - 2.30235i) q^{74} +(-2.13141 + 0.743950i) q^{76} +(-4.24870 + 1.75987i) q^{77} -11.4744i q^{79} +(5.72767 + 3.17722i) q^{80} +(0.689582 - 0.651435i) q^{82} +(15.2335 - 6.30991i) q^{83} +(-3.62261 + 8.74577i) q^{85} +(-0.617950 + 1.37954i) q^{86} +(3.19252 - 6.16206i) q^{88} +(6.07620 + 6.07620i) q^{89} +(8.87380 + 3.67565i) q^{91} +(9.05878 - 8.08275i) q^{92} +(-0.109877 + 3.86255i) q^{94} -1.84830 q^{95} +15.4135 q^{97} +(0.140232 - 4.92962i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q+O(q^{10}) \) Copy content Toggle raw display \( 32 q - 8 q^{10} - 8 q^{16} - 24 q^{22} - 40 q^{28} + 48 q^{31} - 40 q^{34} - 72 q^{40} + 16 q^{43} - 32 q^{46} - 8 q^{52} + 32 q^{55} - 32 q^{58} - 32 q^{61} + 72 q^{64} + 16 q^{67} + 120 q^{70} + 72 q^{76} + 120 q^{82} + 128 q^{88} - 48 q^{91} + 80 q^{94}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.41364 + 0.0402136i 0.999596 + 0.0284353i
\(3\) 0 0
\(4\) 1.99677 + 0.113695i 0.998383 + 0.0568477i
\(5\) 1.51282 + 0.626632i 0.676556 + 0.280239i 0.694386 0.719602i \(-0.255676\pi\)
−0.0178305 + 0.999841i \(0.505676\pi\)
\(6\) 0 0
\(7\) −1.32530 1.32530i −0.500915 0.500915i 0.410807 0.911722i \(-0.365247\pi\)
−0.911722 + 0.410807i \(0.865247\pi\)
\(8\) 2.81814 + 0.241022i 0.996363 + 0.0852141i
\(9\) 0 0
\(10\) 2.11339 + 0.946670i 0.668313 + 0.299363i
\(11\) 0.938971 2.26688i 0.283110 0.683489i −0.716794 0.697285i \(-0.754391\pi\)
0.999905 + 0.0137954i \(0.00439137\pi\)
\(12\) 0 0
\(13\) −4.73458 + 1.96113i −1.31314 + 0.543919i −0.925798 0.378018i \(-0.876606\pi\)
−0.387339 + 0.921937i \(0.626606\pi\)
\(14\) −1.82020 1.92679i −0.486469 0.514956i
\(15\) 0 0
\(16\) 3.97415 + 0.454046i 0.993537 + 0.113512i
\(17\) 5.78108i 1.40212i 0.713103 + 0.701059i \(0.247289\pi\)
−0.713103 + 0.701059i \(0.752711\pi\)
\(18\) 0 0
\(19\) −1.04283 + 0.431956i −0.239243 + 0.0990975i −0.499083 0.866554i \(-0.666330\pi\)
0.259841 + 0.965651i \(0.416330\pi\)
\(20\) 2.94951 + 1.42324i 0.659531 + 0.318246i
\(21\) 0 0
\(22\) 1.41853 3.16679i 0.302431 0.675162i
\(23\) 4.29232 4.29232i 0.895011 0.895011i −0.0999784 0.994990i \(-0.531877\pi\)
0.994990 + 0.0999784i \(0.0318774\pi\)
\(24\) 0 0
\(25\) −1.63956 1.63956i −0.327913 0.327913i
\(26\) −6.77187 + 2.58194i −1.32807 + 0.506360i
\(27\) 0 0
\(28\) −2.49563 2.79699i −0.471629 0.528581i
\(29\) −0.389398 0.940091i −0.0723095 0.174570i 0.883592 0.468257i \(-0.155118\pi\)
−0.955902 + 0.293686i \(0.905118\pi\)
\(30\) 0 0
\(31\) −7.43150 −1.33474 −0.667369 0.744727i \(-0.732580\pi\)
−0.667369 + 0.744727i \(0.732580\pi\)
\(32\) 5.59976 + 0.801673i 0.989907 + 0.141717i
\(33\) 0 0
\(34\) −0.232478 + 8.17238i −0.0398697 + 1.40155i
\(35\) −1.17447 2.83541i −0.198521 0.479272i
\(36\) 0 0
\(37\) −3.67926 1.52400i −0.604867 0.250544i 0.0591650 0.998248i \(-0.481156\pi\)
−0.664032 + 0.747704i \(0.731156\pi\)
\(38\) −1.49156 + 0.568695i −0.241964 + 0.0922545i
\(39\) 0 0
\(40\) 4.11232 + 2.13056i 0.650215 + 0.336871i
\(41\) 0.474313 0.474313i 0.0740752 0.0740752i −0.669098 0.743174i \(-0.733320\pi\)
0.743174 + 0.669098i \(0.233320\pi\)
\(42\) 0 0
\(43\) −0.409042 + 0.987514i −0.0623783 + 0.150594i −0.951995 0.306113i \(-0.900971\pi\)
0.889617 + 0.456708i \(0.150971\pi\)
\(44\) 2.13264 4.41967i 0.321507 0.666290i
\(45\) 0 0
\(46\) 6.24042 5.89520i 0.920099 0.869199i
\(47\) 2.73234i 0.398553i 0.979943 + 0.199277i \(0.0638592\pi\)
−0.979943 + 0.199277i \(0.936141\pi\)
\(48\) 0 0
\(49\) 3.48718i 0.498169i
\(50\) −2.25182 2.38369i −0.318456 0.337104i
\(51\) 0 0
\(52\) −9.67683 + 3.37761i −1.34193 + 0.468391i
\(53\) −4.55362 + 10.9934i −0.625488 + 1.51006i 0.219686 + 0.975571i \(0.429497\pi\)
−0.845174 + 0.534491i \(0.820503\pi\)
\(54\) 0 0
\(55\) 2.84100 2.84100i 0.383080 0.383080i
\(56\) −3.41544 4.05429i −0.456408 0.541778i
\(57\) 0 0
\(58\) −0.512665 1.34461i −0.0673163 0.176556i
\(59\) −8.68022 3.59546i −1.13007 0.468089i −0.262264 0.964996i \(-0.584469\pi\)
−0.867804 + 0.496907i \(0.834469\pi\)
\(60\) 0 0
\(61\) 1.48345 + 3.58137i 0.189937 + 0.458548i 0.989947 0.141438i \(-0.0451727\pi\)
−0.800010 + 0.599986i \(0.795173\pi\)
\(62\) −10.5055 0.298848i −1.33420 0.0379537i
\(63\) 0 0
\(64\) 7.88382 + 1.35847i 0.985477 + 0.169808i
\(65\) −8.39150 −1.04084
\(66\) 0 0
\(67\) 6.11281 + 14.7576i 0.746799 + 1.80293i 0.575668 + 0.817683i \(0.304742\pi\)
0.171131 + 0.985248i \(0.445258\pi\)
\(68\) −0.657282 + 11.5435i −0.0797072 + 1.39985i
\(69\) 0 0
\(70\) −1.54625 4.05549i −0.184813 0.484724i
\(71\) −10.5767 10.5767i −1.25522 1.25522i −0.953349 0.301869i \(-0.902389\pi\)
−0.301869 0.953349i \(-0.597611\pi\)
\(72\) 0 0
\(73\) 6.86117 6.86117i 0.803040 0.803040i −0.180530 0.983570i \(-0.557781\pi\)
0.983570 + 0.180530i \(0.0577812\pi\)
\(74\) −5.13987 2.30235i −0.597498 0.267642i
\(75\) 0 0
\(76\) −2.13141 + 0.743950i −0.244489 + 0.0853369i
\(77\) −4.24870 + 1.75987i −0.484184 + 0.200556i
\(78\) 0 0
\(79\) 11.4744i 1.29097i −0.763771 0.645487i \(-0.776655\pi\)
0.763771 0.645487i \(-0.223345\pi\)
\(80\) 5.72767 + 3.17722i 0.640373 + 0.355224i
\(81\) 0 0
\(82\) 0.689582 0.651435i 0.0761516 0.0719389i
\(83\) 15.2335 6.30991i 1.67209 0.692603i 0.673191 0.739469i \(-0.264923\pi\)
0.998901 + 0.0468660i \(0.0149234\pi\)
\(84\) 0 0
\(85\) −3.62261 + 8.74577i −0.392928 + 0.948611i
\(86\) −0.617950 + 1.37954i −0.0666353 + 0.148760i
\(87\) 0 0
\(88\) 3.19252 6.16206i 0.340324 0.656878i
\(89\) 6.07620 + 6.07620i 0.644076 + 0.644076i 0.951555 0.307479i \(-0.0994854\pi\)
−0.307479 + 0.951555i \(0.599485\pi\)
\(90\) 0 0
\(91\) 8.87380 + 3.67565i 0.930227 + 0.385313i
\(92\) 9.05878 8.08275i 0.944443 0.842685i
\(93\) 0 0
\(94\) −0.109877 + 3.86255i −0.0113330 + 0.398392i
\(95\) −1.84830 −0.189632
\(96\) 0 0
\(97\) 15.4135 1.56500 0.782501 0.622649i \(-0.213944\pi\)
0.782501 + 0.622649i \(0.213944\pi\)
\(98\) 0.140232 4.92962i 0.0141656 0.497967i
\(99\) 0 0
\(100\) −3.08741 3.46024i −0.308741 0.346024i
\(101\) 10.3874 + 4.30260i 1.03358 + 0.428124i 0.834005 0.551757i \(-0.186043\pi\)
0.199579 + 0.979882i \(0.436043\pi\)
\(102\) 0 0
\(103\) −8.05089 8.05089i −0.793278 0.793278i 0.188748 0.982026i \(-0.439557\pi\)
−0.982026 + 0.188748i \(0.939557\pi\)
\(104\) −13.8154 + 4.38560i −1.35471 + 0.430043i
\(105\) 0 0
\(106\) −6.87927 + 15.3576i −0.668174 + 1.49167i
\(107\) −1.76437 + 4.25957i −0.170568 + 0.411788i −0.985929 0.167165i \(-0.946539\pi\)
0.815361 + 0.578953i \(0.196539\pi\)
\(108\) 0 0
\(109\) −5.20159 + 2.15457i −0.498222 + 0.206370i −0.617621 0.786476i \(-0.711903\pi\)
0.119399 + 0.992846i \(0.461903\pi\)
\(110\) 4.13040 3.90191i 0.393818 0.372032i
\(111\) 0 0
\(112\) −4.66518 5.86867i −0.440818 0.554537i
\(113\) 4.12616i 0.388156i 0.980986 + 0.194078i \(0.0621715\pi\)
−0.980986 + 0.194078i \(0.937829\pi\)
\(114\) 0 0
\(115\) 9.18324 3.80382i 0.856342 0.354708i
\(116\) −0.670653 1.92141i −0.0622686 0.178399i
\(117\) 0 0
\(118\) −12.1261 5.43176i −1.11630 0.500034i
\(119\) 7.66165 7.66165i 0.702342 0.702342i
\(120\) 0 0
\(121\) 3.52111 + 3.52111i 0.320101 + 0.320101i
\(122\) 1.95305 + 5.12243i 0.176821 + 0.463763i
\(123\) 0 0
\(124\) −14.8390 0.844928i −1.33258 0.0758767i
\(125\) −4.58613 11.0719i −0.410196 0.990301i
\(126\) 0 0
\(127\) 7.68466 0.681904 0.340952 0.940081i \(-0.389251\pi\)
0.340952 + 0.940081i \(0.389251\pi\)
\(128\) 11.0903 + 2.23742i 0.980250 + 0.197762i
\(129\) 0 0
\(130\) −11.8626 0.337453i −1.04042 0.0295966i
\(131\) 6.42051 + 15.5005i 0.560963 + 1.35428i 0.908997 + 0.416802i \(0.136849\pi\)
−0.348034 + 0.937482i \(0.613151\pi\)
\(132\) 0 0
\(133\) 1.95453 + 0.809594i 0.169480 + 0.0702007i
\(134\) 8.04787 + 21.1078i 0.695230 + 1.82344i
\(135\) 0 0
\(136\) −1.39337 + 16.2919i −0.119480 + 1.39702i
\(137\) 16.1360 16.1360i 1.37859 1.37859i 0.531598 0.846997i \(-0.321592\pi\)
0.846997 0.531598i \(-0.178408\pi\)
\(138\) 0 0
\(139\) −2.88036 + 6.95381i −0.244309 + 0.589814i −0.997702 0.0677564i \(-0.978416\pi\)
0.753393 + 0.657571i \(0.228416\pi\)
\(140\) −2.02276 5.79519i −0.170955 0.489783i
\(141\) 0 0
\(142\) −14.5263 15.3769i −1.21902 1.29040i
\(143\) 12.5742i 1.05150i
\(144\) 0 0
\(145\) 1.66620i 0.138371i
\(146\) 9.97516 9.42333i 0.825550 0.779880i
\(147\) 0 0
\(148\) −7.17336 3.46139i −0.589646 0.284524i
\(149\) 1.57271 3.79687i 0.128842 0.311051i −0.846274 0.532748i \(-0.821159\pi\)
0.975116 + 0.221696i \(0.0711594\pi\)
\(150\) 0 0
\(151\) −4.12337 + 4.12337i −0.335555 + 0.335555i −0.854692 0.519136i \(-0.826254\pi\)
0.519136 + 0.854692i \(0.326254\pi\)
\(152\) −3.04296 + 0.965966i −0.246817 + 0.0783502i
\(153\) 0 0
\(154\) −6.07691 + 2.31697i −0.489691 + 0.186707i
\(155\) −11.2426 4.65682i −0.903024 0.374045i
\(156\) 0 0
\(157\) 0.772760 + 1.86561i 0.0616730 + 0.148892i 0.951712 0.306993i \(-0.0993229\pi\)
−0.890039 + 0.455885i \(0.849323\pi\)
\(158\) 0.461428 16.2207i 0.0367093 1.29045i
\(159\) 0 0
\(160\) 7.96910 + 4.72178i 0.630013 + 0.373290i
\(161\) −11.3772 −0.896649
\(162\) 0 0
\(163\) −4.46436 10.7779i −0.349676 0.844192i −0.996658 0.0816870i \(-0.973969\pi\)
0.646982 0.762505i \(-0.276031\pi\)
\(164\) 1.00102 0.893165i 0.0781665 0.0697444i
\(165\) 0 0
\(166\) 21.7884 8.30736i 1.69111 0.644777i
\(167\) 9.15618 + 9.15618i 0.708527 + 0.708527i 0.966225 0.257699i \(-0.0829642\pi\)
−0.257699 + 0.966225i \(0.582964\pi\)
\(168\) 0 0
\(169\) 9.37787 9.37787i 0.721374 0.721374i
\(170\) −5.47278 + 12.2177i −0.419743 + 0.937055i
\(171\) 0 0
\(172\) −0.929036 + 1.92533i −0.0708383 + 0.146805i
\(173\) −7.27037 + 3.01148i −0.552756 + 0.228959i −0.641537 0.767092i \(-0.721703\pi\)
0.0887811 + 0.996051i \(0.471703\pi\)
\(174\) 0 0
\(175\) 4.34581i 0.328513i
\(176\) 4.76088 8.58257i 0.358865 0.646935i
\(177\) 0 0
\(178\) 8.34522 + 8.83391i 0.625501 + 0.662130i
\(179\) 5.62849 2.33140i 0.420693 0.174257i −0.162286 0.986744i \(-0.551887\pi\)
0.582979 + 0.812487i \(0.301887\pi\)
\(180\) 0 0
\(181\) −1.09419 + 2.64161i −0.0813306 + 0.196349i −0.959314 0.282342i \(-0.908889\pi\)
0.877983 + 0.478691i \(0.158889\pi\)
\(182\) 12.3966 + 5.55290i 0.918894 + 0.411608i
\(183\) 0 0
\(184\) 13.1309 11.0618i 0.968023 0.815488i
\(185\) −4.61109 4.61109i −0.339014 0.339014i
\(186\) 0 0
\(187\) 13.1050 + 5.42827i 0.958333 + 0.396955i
\(188\) −0.310655 + 5.45585i −0.0226568 + 0.397909i
\(189\) 0 0
\(190\) −2.61284 0.0743270i −0.189555 0.00539225i
\(191\) −4.24424 −0.307102 −0.153551 0.988141i \(-0.549071\pi\)
−0.153551 + 0.988141i \(0.549071\pi\)
\(192\) 0 0
\(193\) −8.04323 −0.578964 −0.289482 0.957183i \(-0.593483\pi\)
−0.289482 + 0.957183i \(0.593483\pi\)
\(194\) 21.7891 + 0.619832i 1.56437 + 0.0445014i
\(195\) 0 0
\(196\) 0.396476 6.96308i 0.0283197 0.497363i
\(197\) 20.4709 + 8.47934i 1.45849 + 0.604128i 0.964202 0.265169i \(-0.0854277\pi\)
0.494291 + 0.869296i \(0.335428\pi\)
\(198\) 0 0
\(199\) 2.58390 + 2.58390i 0.183168 + 0.183168i 0.792735 0.609567i \(-0.208657\pi\)
−0.609567 + 0.792735i \(0.708657\pi\)
\(200\) −4.22535 5.01569i −0.298777 0.354663i
\(201\) 0 0
\(202\) 14.5110 + 6.50004i 1.02099 + 0.457342i
\(203\) −0.729831 + 1.76197i −0.0512241 + 0.123666i
\(204\) 0 0
\(205\) 1.01477 0.420332i 0.0708748 0.0293573i
\(206\) −11.0573 11.7048i −0.770400 0.815514i
\(207\) 0 0
\(208\) −19.7064 + 5.64409i −1.36639 + 0.391348i
\(209\) 2.76957i 0.191575i
\(210\) 0 0
\(211\) −1.04546 + 0.433043i −0.0719723 + 0.0298119i −0.418379 0.908272i \(-0.637402\pi\)
0.346407 + 0.938084i \(0.387402\pi\)
\(212\) −10.3424 + 21.4335i −0.710320 + 1.47206i
\(213\) 0 0
\(214\) −2.66548 + 5.95055i −0.182209 + 0.406771i
\(215\) −1.23762 + 1.23762i −0.0844048 + 0.0844048i
\(216\) 0 0
\(217\) 9.84894 + 9.84894i 0.668590 + 0.668590i
\(218\) −7.43982 + 2.83661i −0.503889 + 0.192120i
\(219\) 0 0
\(220\) 5.99582 5.34980i 0.404238 0.360683i
\(221\) −11.3374 27.3710i −0.762639 1.84117i
\(222\) 0 0
\(223\) −7.40345 −0.495772 −0.247886 0.968789i \(-0.579736\pi\)
−0.247886 + 0.968789i \(0.579736\pi\)
\(224\) −6.35889 8.48379i −0.424871 0.566847i
\(225\) 0 0
\(226\) −0.165928 + 5.83290i −0.0110373 + 0.387999i
\(227\) 5.13477 + 12.3964i 0.340806 + 0.822780i 0.997635 + 0.0687393i \(0.0218977\pi\)
−0.656828 + 0.754040i \(0.728102\pi\)
\(228\) 0 0
\(229\) −10.6519 4.41217i −0.703899 0.291564i 0.00187845 0.999998i \(-0.499402\pi\)
−0.705777 + 0.708434i \(0.749402\pi\)
\(230\) 13.1348 5.00795i 0.866082 0.330215i
\(231\) 0 0
\(232\) −0.870797 2.74316i −0.0571706 0.180097i
\(233\) 10.6029 10.6029i 0.694620 0.694620i −0.268625 0.963245i \(-0.586569\pi\)
0.963245 + 0.268625i \(0.0865691\pi\)
\(234\) 0 0
\(235\) −1.71217 + 4.13355i −0.111690 + 0.269643i
\(236\) −16.9236 8.16620i −1.10163 0.531574i
\(237\) 0 0
\(238\) 11.1389 10.5227i 0.722029 0.682087i
\(239\) 27.7222i 1.79320i 0.442844 + 0.896598i \(0.353969\pi\)
−0.442844 + 0.896598i \(0.646031\pi\)
\(240\) 0 0
\(241\) 19.1370i 1.23273i −0.787462 0.616363i \(-0.788606\pi\)
0.787462 0.616363i \(-0.211394\pi\)
\(242\) 4.83599 + 5.11918i 0.310869 + 0.329074i
\(243\) 0 0
\(244\) 2.55492 + 7.31982i 0.163562 + 0.468604i
\(245\) 2.18518 5.27549i 0.139606 0.337039i
\(246\) 0 0
\(247\) 4.09026 4.09026i 0.260257 0.260257i
\(248\) −20.9430 1.79115i −1.32988 0.113738i
\(249\) 0 0
\(250\) −6.03790 15.8361i −0.381871 1.00156i
\(251\) −22.9873 9.52164i −1.45094 0.601001i −0.488520 0.872553i \(-0.662463\pi\)
−0.962424 + 0.271552i \(0.912463\pi\)
\(252\) 0 0
\(253\) −5.69980 13.7605i −0.358343 0.865118i
\(254\) 10.8634 + 0.309028i 0.681628 + 0.0193902i
\(255\) 0 0
\(256\) 15.5877 + 3.60889i 0.974230 + 0.225556i
\(257\) −11.2303 −0.700525 −0.350263 0.936651i \(-0.613908\pi\)
−0.350263 + 0.936651i \(0.613908\pi\)
\(258\) 0 0
\(259\) 2.85636 + 6.89587i 0.177486 + 0.428488i
\(260\) −16.7559 0.954075i −1.03915 0.0591692i
\(261\) 0 0
\(262\) 8.45297 + 22.1703i 0.522227 + 1.36969i
\(263\) −8.63436 8.63436i −0.532417 0.532417i 0.388874 0.921291i \(-0.372864\pi\)
−0.921291 + 0.388874i \(0.872864\pi\)
\(264\) 0 0
\(265\) −13.7777 + 13.7777i −0.846355 + 0.846355i
\(266\) 2.73045 + 1.22308i 0.167415 + 0.0749915i
\(267\) 0 0
\(268\) 10.5280 + 30.1625i 0.643099 + 1.84247i
\(269\) 11.4515 4.74335i 0.698208 0.289207i −0.00520737 0.999986i \(-0.501658\pi\)
0.703415 + 0.710779i \(0.251658\pi\)
\(270\) 0 0
\(271\) 4.02905i 0.244747i −0.992484 0.122374i \(-0.960949\pi\)
0.992484 0.122374i \(-0.0390506\pi\)
\(272\) −2.62488 + 22.9749i −0.159157 + 1.39306i
\(273\) 0 0
\(274\) 23.4595 22.1617i 1.41724 1.33884i
\(275\) −5.25619 + 2.17719i −0.316960 + 0.131289i
\(276\) 0 0
\(277\) −4.46812 + 10.7870i −0.268464 + 0.648128i −0.999411 0.0343049i \(-0.989078\pi\)
0.730948 + 0.682433i \(0.239078\pi\)
\(278\) −4.35144 + 9.71436i −0.260982 + 0.582629i
\(279\) 0 0
\(280\) −2.62641 8.27366i −0.156958 0.494446i
\(281\) −4.45827 4.45827i −0.265958 0.265958i 0.561511 0.827469i \(-0.310220\pi\)
−0.827469 + 0.561511i \(0.810220\pi\)
\(282\) 0 0
\(283\) −16.9317 7.01336i −1.00649 0.416901i −0.182315 0.983240i \(-0.558359\pi\)
−0.824172 + 0.566339i \(0.808359\pi\)
\(284\) −19.9166 22.3216i −1.18183 1.32454i
\(285\) 0 0
\(286\) −0.505653 + 17.7754i −0.0298999 + 1.05108i
\(287\) −1.25721 −0.0742108
\(288\) 0 0
\(289\) −16.4209 −0.965937
\(290\) 0.0670041 2.35541i 0.00393461 0.138315i
\(291\) 0 0
\(292\) 14.4802 12.9201i 0.847392 0.756090i
\(293\) −16.9534 7.02234i −0.990429 0.410249i −0.172150 0.985071i \(-0.555072\pi\)
−0.818279 + 0.574821i \(0.805072\pi\)
\(294\) 0 0
\(295\) −10.8786 10.8786i −0.633377 0.633377i
\(296\) −10.0014 5.18163i −0.581317 0.301176i
\(297\) 0 0
\(298\) 2.37594 5.30416i 0.137634 0.307262i
\(299\) −11.9046 + 28.7402i −0.688459 + 1.66209i
\(300\) 0 0
\(301\) 1.85085 0.766647i 0.106681 0.0441888i
\(302\) −5.99479 + 5.66316i −0.344961 + 0.325878i
\(303\) 0 0
\(304\) −4.34050 + 1.24316i −0.248945 + 0.0713002i
\(305\) 6.34757i 0.363461i
\(306\) 0 0
\(307\) −26.8443 + 11.1193i −1.53209 + 0.634611i −0.979968 0.199155i \(-0.936180\pi\)
−0.552118 + 0.833766i \(0.686180\pi\)
\(308\) −8.68374 + 3.03099i −0.494802 + 0.172707i
\(309\) 0 0
\(310\) −15.7057 7.03518i −0.892023 0.399572i
\(311\) 11.6197 11.6197i 0.658895 0.658895i −0.296224 0.955119i \(-0.595727\pi\)
0.955119 + 0.296224i \(0.0957274\pi\)
\(312\) 0 0
\(313\) −12.9034 12.9034i −0.729344 0.729344i 0.241145 0.970489i \(-0.422477\pi\)
−0.970489 + 0.241145i \(0.922477\pi\)
\(314\) 1.01738 + 2.66838i 0.0574143 + 0.150585i
\(315\) 0 0
\(316\) 1.30459 22.9117i 0.0733889 1.28889i
\(317\) −6.08877 14.6996i −0.341979 0.825612i −0.997515 0.0704476i \(-0.977557\pi\)
0.655536 0.755164i \(-0.272443\pi\)
\(318\) 0 0
\(319\) −2.49670 −0.139789
\(320\) 11.0756 + 6.99538i 0.619143 + 0.391053i
\(321\) 0 0
\(322\) −16.0833 0.457519i −0.896286 0.0254965i
\(323\) −2.49717 6.02871i −0.138946 0.335446i
\(324\) 0 0
\(325\) 10.9780 + 4.54726i 0.608953 + 0.252236i
\(326\) −5.87759 15.4156i −0.325530 0.853794i
\(327\) 0 0
\(328\) 1.45100 1.22236i 0.0801181 0.0674936i
\(329\) 3.62116 3.62116i 0.199641 0.199641i
\(330\) 0 0
\(331\) 3.88508 9.37942i 0.213543 0.515539i −0.780419 0.625256i \(-0.784994\pi\)
0.993963 + 0.109717i \(0.0349944\pi\)
\(332\) 31.1351 10.8674i 1.70876 0.596429i
\(333\) 0 0
\(334\) 12.5754 + 13.3118i 0.688093 + 0.728387i
\(335\) 26.1562i 1.42907i
\(336\) 0 0
\(337\) 26.4416i 1.44037i 0.693784 + 0.720183i \(0.255942\pi\)
−0.693784 + 0.720183i \(0.744058\pi\)
\(338\) 13.6341 12.8798i 0.741595 0.700570i
\(339\) 0 0
\(340\) −8.22787 + 17.0514i −0.446219 + 0.924740i
\(341\) −6.97797 + 16.8463i −0.377878 + 0.912279i
\(342\) 0 0
\(343\) −13.8986 + 13.8986i −0.750455 + 0.750455i
\(344\) −1.39075 + 2.68436i −0.0749842 + 0.144731i
\(345\) 0 0
\(346\) −10.3988 + 3.96479i −0.559043 + 0.213149i
\(347\) 21.7583 + 9.01258i 1.16805 + 0.483820i 0.880546 0.473960i \(-0.157176\pi\)
0.287500 + 0.957781i \(0.407176\pi\)
\(348\) 0 0
\(349\) 2.65403 + 6.40740i 0.142067 + 0.342980i 0.978858 0.204543i \(-0.0655708\pi\)
−0.836791 + 0.547523i \(0.815571\pi\)
\(350\) −0.174761 + 6.14343i −0.00934137 + 0.328380i
\(351\) 0 0
\(352\) 7.07531 11.9412i 0.377115 0.636469i
\(353\) −9.15953 −0.487512 −0.243756 0.969837i \(-0.578380\pi\)
−0.243756 + 0.969837i \(0.578380\pi\)
\(354\) 0 0
\(355\) −9.37295 22.6283i −0.497465 1.20099i
\(356\) 11.4419 + 12.8236i 0.606420 + 0.679648i
\(357\) 0 0
\(358\) 8.05042 3.06942i 0.425478 0.162224i
\(359\) −14.5008 14.5008i −0.765322 0.765322i 0.211957 0.977279i \(-0.432016\pi\)
−0.977279 + 0.211957i \(0.932016\pi\)
\(360\) 0 0
\(361\) −12.5341 + 12.5341i −0.659690 + 0.659690i
\(362\) −1.65302 + 3.69029i −0.0868810 + 0.193957i
\(363\) 0 0
\(364\) 17.3010 + 8.34832i 0.906819 + 0.437571i
\(365\) 14.6792 6.08032i 0.768344 0.318258i
\(366\) 0 0
\(367\) 5.62846i 0.293803i 0.989151 + 0.146901i \(0.0469300\pi\)
−0.989151 + 0.146901i \(0.953070\pi\)
\(368\) 19.0072 15.1094i 0.990821 0.787632i
\(369\) 0 0
\(370\) −6.33300 6.70386i −0.329237 0.348517i
\(371\) 20.6044 8.53463i 1.06973 0.443096i
\(372\) 0 0
\(373\) 11.8400 28.5842i 0.613050 1.48003i −0.246584 0.969122i \(-0.579308\pi\)
0.859633 0.510911i \(-0.170692\pi\)
\(374\) 18.3075 + 8.20063i 0.946658 + 0.424045i
\(375\) 0 0
\(376\) −0.658554 + 7.70012i −0.0339623 + 0.397103i
\(377\) 3.68728 + 3.68728i 0.189904 + 0.189904i
\(378\) 0 0
\(379\) −24.8544 10.2950i −1.27668 0.528820i −0.361694 0.932297i \(-0.617802\pi\)
−0.914990 + 0.403477i \(0.867802\pi\)
\(380\) −3.69063 0.210143i −0.189325 0.0107801i
\(381\) 0 0
\(382\) −5.99983 0.170676i −0.306978 0.00873256i
\(383\) 3.10697 0.158759 0.0793795 0.996844i \(-0.474706\pi\)
0.0793795 + 0.996844i \(0.474706\pi\)
\(384\) 0 0
\(385\) −7.53033 −0.383781
\(386\) −11.3702 0.323447i −0.578730 0.0164630i
\(387\) 0 0
\(388\) 30.7771 + 1.75244i 1.56247 + 0.0889667i
\(389\) 8.30581 + 3.44038i 0.421121 + 0.174434i 0.583173 0.812348i \(-0.301811\pi\)
−0.162051 + 0.986782i \(0.551811\pi\)
\(390\) 0 0
\(391\) 24.8143 + 24.8143i 1.25491 + 1.25491i
\(392\) 0.840486 9.82736i 0.0424510 0.496357i
\(393\) 0 0
\(394\) 28.5976 + 12.8100i 1.44072 + 0.645356i
\(395\) 7.19025 17.3588i 0.361781 0.873416i
\(396\) 0 0
\(397\) 15.9030 6.58725i 0.798150 0.330605i 0.0539347 0.998544i \(-0.482824\pi\)
0.744215 + 0.667940i \(0.232824\pi\)
\(398\) 3.54880 + 3.75662i 0.177885 + 0.188302i
\(399\) 0 0
\(400\) −5.77143 7.26030i −0.288571 0.363015i
\(401\) 17.8067i 0.889227i −0.895723 0.444613i \(-0.853341\pi\)
0.895723 0.444613i \(-0.146659\pi\)
\(402\) 0 0
\(403\) 35.1851 14.5741i 1.75269 0.725990i
\(404\) 20.2520 + 9.77228i 1.00757 + 0.486189i
\(405\) 0 0
\(406\) −1.10257 + 2.46144i −0.0547198 + 0.122159i
\(407\) −6.90945 + 6.90945i −0.342489 + 0.342489i
\(408\) 0 0
\(409\) −15.4187 15.4187i −0.762408 0.762408i 0.214349 0.976757i \(-0.431237\pi\)
−0.976757 + 0.214349i \(0.931237\pi\)
\(410\) 1.45143 0.553392i 0.0716809 0.0273301i
\(411\) 0 0
\(412\) −15.1604 16.9911i −0.746899 0.837091i
\(413\) 6.73880 + 16.2689i 0.331595 + 0.800541i
\(414\) 0 0
\(415\) 26.9996 1.32536
\(416\) −28.0847 + 7.18626i −1.37697 + 0.352335i
\(417\) 0 0
\(418\) −0.111375 + 3.91518i −0.00544751 + 0.191498i
\(419\) 5.74289 + 13.8646i 0.280559 + 0.677328i 0.999849 0.0173813i \(-0.00553291\pi\)
−0.719290 + 0.694710i \(0.755533\pi\)
\(420\) 0 0
\(421\) 3.87628 + 1.60561i 0.188918 + 0.0782525i 0.475137 0.879912i \(-0.342398\pi\)
−0.286219 + 0.958164i \(0.592398\pi\)
\(422\) −1.49532 + 0.570126i −0.0727909 + 0.0277533i
\(423\) 0 0
\(424\) −15.4824 + 29.8835i −0.751891 + 1.45127i
\(425\) 9.47846 9.47846i 0.459773 0.459773i
\(426\) 0 0
\(427\) 2.78036 6.71239i 0.134551 0.324835i
\(428\) −4.00733 + 8.30476i −0.193702 + 0.401426i
\(429\) 0 0
\(430\) −1.79932 + 1.69978i −0.0867707 + 0.0819706i
\(431\) 16.2867i 0.784503i −0.919858 0.392252i \(-0.871696\pi\)
0.919858 0.392252i \(-0.128304\pi\)
\(432\) 0 0
\(433\) 28.2864i 1.35936i 0.733510 + 0.679678i \(0.237881\pi\)
−0.733510 + 0.679678i \(0.762119\pi\)
\(434\) 13.5268 + 14.3189i 0.649308 + 0.687331i
\(435\) 0 0
\(436\) −10.6313 + 3.71077i −0.509148 + 0.177714i
\(437\) −2.62209 + 6.33028i −0.125431 + 0.302818i
\(438\) 0 0
\(439\) 13.8438 13.8438i 0.660730 0.660730i −0.294822 0.955552i \(-0.595260\pi\)
0.955552 + 0.294822i \(0.0952604\pi\)
\(440\) 8.69107 7.32158i 0.414330 0.349043i
\(441\) 0 0
\(442\) −14.9264 39.1487i −0.709977 1.86212i
\(443\) −5.95791 2.46785i −0.283069 0.117251i 0.236632 0.971599i \(-0.423957\pi\)
−0.519701 + 0.854348i \(0.673957\pi\)
\(444\) 0 0
\(445\) 5.38468 + 12.9998i 0.255258 + 0.616248i
\(446\) −10.4658 0.297720i −0.495571 0.0140974i
\(447\) 0 0
\(448\) −8.64802 12.2488i −0.408581 0.578700i
\(449\) 27.7832 1.31117 0.655585 0.755121i \(-0.272422\pi\)
0.655585 + 0.755121i \(0.272422\pi\)
\(450\) 0 0
\(451\) −0.629843 1.52058i −0.0296581 0.0716011i
\(452\) −0.469125 + 8.23897i −0.0220658 + 0.387528i
\(453\) 0 0
\(454\) 6.76022 + 17.7306i 0.317273 + 0.832138i
\(455\) 11.1212 + 11.1212i 0.521371 + 0.521371i
\(456\) 0 0
\(457\) 6.61796 6.61796i 0.309575 0.309575i −0.535170 0.844745i \(-0.679752\pi\)
0.844745 + 0.535170i \(0.179752\pi\)
\(458\) −14.8806 6.66558i −0.695323 0.311462i
\(459\) 0 0
\(460\) 18.7693 6.55125i 0.875121 0.305454i
\(461\) −25.1777 + 10.4289i −1.17264 + 0.485724i −0.882065 0.471128i \(-0.843847\pi\)
−0.290576 + 0.956852i \(0.593847\pi\)
\(462\) 0 0
\(463\) 33.3492i 1.54987i 0.632040 + 0.774935i \(0.282218\pi\)
−0.632040 + 0.774935i \(0.717782\pi\)
\(464\) −1.12068 3.91286i −0.0520263 0.181650i
\(465\) 0 0
\(466\) 15.4151 14.5623i 0.714091 0.674588i
\(467\) −7.09498 + 2.93884i −0.328317 + 0.135993i −0.540752 0.841182i \(-0.681860\pi\)
0.212436 + 0.977175i \(0.431860\pi\)
\(468\) 0 0
\(469\) 11.4569 27.6595i 0.529033 1.27720i
\(470\) −2.58663 + 5.77451i −0.119312 + 0.266358i
\(471\) 0 0
\(472\) −23.5955 12.2246i −1.08607 0.562685i
\(473\) 1.85449 + 1.85449i 0.0852698 + 0.0852698i
\(474\) 0 0
\(475\) 2.41801 + 1.00157i 0.110946 + 0.0459553i
\(476\) 16.1696 14.4274i 0.741133 0.661280i
\(477\) 0 0
\(478\) −1.11481 + 39.1892i −0.0509902 + 1.79247i
\(479\) −1.66547 −0.0760971 −0.0380485 0.999276i \(-0.512114\pi\)
−0.0380485 + 0.999276i \(0.512114\pi\)
\(480\) 0 0
\(481\) 20.4085 0.930549
\(482\) 0.769570 27.0529i 0.0350530 1.23223i
\(483\) 0 0
\(484\) 6.63050 + 7.43116i 0.301386 + 0.337780i
\(485\) 23.3179 + 9.65859i 1.05881 + 0.438574i
\(486\) 0 0
\(487\) 15.4292 + 15.4292i 0.699165 + 0.699165i 0.964230 0.265066i \(-0.0853936\pi\)
−0.265066 + 0.964230i \(0.585394\pi\)
\(488\) 3.31739 + 10.4504i 0.150171 + 0.473065i
\(489\) 0 0
\(490\) 3.30121 7.36978i 0.149133 0.332933i
\(491\) 7.65362 18.4775i 0.345403 0.833877i −0.651747 0.758436i \(-0.725964\pi\)
0.997150 0.0754405i \(-0.0240363\pi\)
\(492\) 0 0
\(493\) 5.43474 2.25114i 0.244769 0.101386i
\(494\) 5.94665 5.61768i 0.267553 0.252751i
\(495\) 0 0
\(496\) −29.5339 3.37425i −1.32611 0.151508i
\(497\) 28.0344i 1.25751i
\(498\) 0 0
\(499\) −27.2740 + 11.2973i −1.22095 + 0.505735i −0.897712 0.440582i \(-0.854772\pi\)
−0.323240 + 0.946317i \(0.604772\pi\)
\(500\) −7.89861 22.6294i −0.353236 1.01202i
\(501\) 0 0
\(502\) −32.1129 14.3846i −1.43327 0.642016i
\(503\) 22.9821 22.9821i 1.02472 1.02472i 0.0250340 0.999687i \(-0.492031\pi\)
0.999687 0.0250340i \(-0.00796941\pi\)
\(504\) 0 0
\(505\) 13.0181 + 13.0181i 0.579300 + 0.579300i
\(506\) −7.50412 19.6817i −0.333599 0.874957i
\(507\) 0 0
\(508\) 15.3445 + 0.873711i 0.680801 + 0.0387646i
\(509\) 6.17413 + 14.9057i 0.273663 + 0.660682i 0.999634 0.0270437i \(-0.00860933\pi\)
−0.725971 + 0.687725i \(0.758609\pi\)
\(510\) 0 0
\(511\) −18.1862 −0.804509
\(512\) 21.8903 + 5.72852i 0.967423 + 0.253167i
\(513\) 0 0
\(514\) −15.8756 0.451610i −0.700242 0.0199197i
\(515\) −7.13463 17.2245i −0.314390 0.759004i
\(516\) 0 0
\(517\) 6.19388 + 2.56559i 0.272407 + 0.112835i
\(518\) 3.76056 + 9.86315i 0.165230 + 0.433362i
\(519\) 0 0
\(520\) −23.6484 2.02253i −1.03705 0.0886940i
\(521\) −10.2507 + 10.2507i −0.449093 + 0.449093i −0.895053 0.445960i \(-0.852862\pi\)
0.445960 + 0.895053i \(0.352862\pi\)
\(522\) 0 0
\(523\) 7.70945 18.6123i 0.337111 0.813857i −0.660880 0.750492i \(-0.729817\pi\)
0.997990 0.0633655i \(-0.0201834\pi\)
\(524\) 11.0579 + 31.6808i 0.483068 + 1.38398i
\(525\) 0 0
\(526\) −11.8587 12.5531i −0.517063 0.547342i
\(527\) 42.9622i 1.87146i
\(528\) 0 0
\(529\) 13.8481i 0.602090i
\(530\) −20.0307 + 18.9226i −0.870079 + 0.821946i
\(531\) 0 0
\(532\) 3.81070 + 1.83879i 0.165215 + 0.0797217i
\(533\) −1.31549 + 3.17586i −0.0569800 + 0.137562i
\(534\) 0 0
\(535\) −5.33837 + 5.33837i −0.230798 + 0.230798i
\(536\) 13.6698 + 43.0624i 0.590447 + 1.86001i
\(537\) 0 0
\(538\) 16.3790 6.24489i 0.706149 0.269236i
\(539\) −7.90501 3.27436i −0.340493 0.141037i
\(540\) 0 0
\(541\) −10.8201 26.1221i −0.465194 1.12308i −0.966237 0.257655i \(-0.917050\pi\)
0.501043 0.865422i \(-0.332950\pi\)
\(542\) 0.162023 5.69563i 0.00695947 0.244648i
\(543\) 0 0
\(544\) −4.63454 + 32.3727i −0.198704 + 1.38797i
\(545\) −9.21921 −0.394908
\(546\) 0 0
\(547\) 3.17792 + 7.67217i 0.135878 + 0.328038i 0.977143 0.212585i \(-0.0681883\pi\)
−0.841265 + 0.540624i \(0.818188\pi\)
\(548\) 34.0545 30.3853i 1.45474 1.29800i
\(549\) 0 0
\(550\) −7.51793 + 2.86639i −0.320565 + 0.122223i
\(551\) 0.812156 + 0.812156i 0.0345990 + 0.0345990i
\(552\) 0 0
\(553\) −15.2070 + 15.2070i −0.646668 + 0.646668i
\(554\) −6.75011 + 15.0693i −0.286785 + 0.640233i
\(555\) 0 0
\(556\) −6.54202 + 13.5576i −0.277444 + 0.574972i
\(557\) −21.1381 + 8.75569i −0.895650 + 0.370991i −0.782546 0.622593i \(-0.786079\pi\)
−0.113104 + 0.993583i \(0.536079\pi\)
\(558\) 0 0
\(559\) 5.47765i 0.231680i
\(560\) −3.38010 11.8016i −0.142835 0.498709i
\(561\) 0 0
\(562\) −6.12311 6.48168i −0.258288 0.273413i
\(563\) −4.49306 + 1.86108i −0.189360 + 0.0784354i −0.475348 0.879798i \(-0.657678\pi\)
0.285989 + 0.958233i \(0.407678\pi\)
\(564\) 0 0
\(565\) −2.58558 + 6.24215i −0.108776 + 0.262609i
\(566\) −23.6534 10.5953i −0.994226 0.445352i
\(567\) 0 0
\(568\) −27.2573 32.3557i −1.14369 1.35762i
\(569\) 1.97117 + 1.97117i 0.0826359 + 0.0826359i 0.747217 0.664581i \(-0.231390\pi\)
−0.664581 + 0.747217i \(0.731390\pi\)
\(570\) 0 0
\(571\) −4.41522 1.82884i −0.184771 0.0765347i 0.288380 0.957516i \(-0.406883\pi\)
−0.473151 + 0.880981i \(0.656883\pi\)
\(572\) −1.42962 + 25.1077i −0.0597756 + 1.04980i
\(573\) 0 0
\(574\) −1.77724 0.0505570i −0.0741808 0.00211021i
\(575\) −14.0751 −0.586971
\(576\) 0 0
\(577\) −5.08446 −0.211669 −0.105834 0.994384i \(-0.533751\pi\)
−0.105834 + 0.994384i \(0.533751\pi\)
\(578\) −23.2133 0.660345i −0.965546 0.0274667i
\(579\) 0 0
\(580\) 0.189439 3.32702i 0.00786605 0.138147i
\(581\) −28.5514 11.8264i −1.18451 0.490640i
\(582\) 0 0
\(583\) 20.6450 + 20.6450i 0.855029 + 0.855029i
\(584\) 20.9894 17.6821i 0.868549 0.731689i
\(585\) 0 0
\(586\) −23.6837 10.6088i −0.978363 0.438247i
\(587\) 1.78191 4.30191i 0.0735473 0.177559i −0.882830 0.469692i \(-0.844365\pi\)
0.956378 + 0.292133i \(0.0943650\pi\)
\(588\) 0 0
\(589\) 7.74983 3.21008i 0.319326 0.132269i
\(590\) −14.9410 15.8159i −0.615111 0.651131i
\(591\) 0 0
\(592\) −13.9300 7.72716i −0.572518 0.317584i
\(593\) 29.2644i 1.20174i 0.799345 + 0.600872i \(0.205180\pi\)
−0.799345 + 0.600872i \(0.794820\pi\)
\(594\) 0 0
\(595\) 16.3918 6.78969i 0.671997 0.278350i
\(596\) 3.57203 7.40264i 0.146316 0.303224i
\(597\) 0 0
\(598\) −17.9845 + 40.1496i −0.735442 + 1.64184i
\(599\) −26.1363 + 26.1363i −1.06790 + 1.06790i −0.0703791 + 0.997520i \(0.522421\pi\)
−0.997520 + 0.0703791i \(0.977579\pi\)
\(600\) 0 0
\(601\) 6.06830 + 6.06830i 0.247531 + 0.247531i 0.819957 0.572426i \(-0.193997\pi\)
−0.572426 + 0.819957i \(0.693997\pi\)
\(602\) 2.64727 1.00933i 0.107895 0.0411374i
\(603\) 0 0
\(604\) −8.70222 + 7.76461i −0.354088 + 0.315937i
\(605\) 3.12038 + 7.53326i 0.126861 + 0.306271i
\(606\) 0 0
\(607\) 22.7677 0.924111 0.462055 0.886851i \(-0.347112\pi\)
0.462055 + 0.886851i \(0.347112\pi\)
\(608\) −6.18591 + 1.58284i −0.250872 + 0.0641926i
\(609\) 0 0
\(610\) −0.255259 + 8.97319i −0.0103351 + 0.363314i
\(611\) −5.35847 12.9365i −0.216781 0.523355i
\(612\) 0 0
\(613\) 24.3883 + 10.1020i 0.985034 + 0.408015i 0.816288 0.577645i \(-0.196028\pi\)
0.168746 + 0.985660i \(0.446028\pi\)
\(614\) −38.3954 + 14.6392i −1.54951 + 0.590789i
\(615\) 0 0
\(616\) −12.3976 + 3.93553i −0.499513 + 0.158567i
\(617\) −28.1146 + 28.1146i −1.13185 + 1.13185i −0.141980 + 0.989870i \(0.545347\pi\)
−0.989870 + 0.141980i \(0.954653\pi\)
\(618\) 0 0
\(619\) 9.80079 23.6612i 0.393927 0.951024i −0.595149 0.803616i \(-0.702907\pi\)
0.989076 0.147408i \(-0.0470931\pi\)
\(620\) −21.9193 10.5768i −0.880301 0.424775i
\(621\) 0 0
\(622\) 16.8934 15.9589i 0.677364 0.639892i
\(623\) 16.1055i 0.645254i
\(624\) 0 0
\(625\) 8.03019i 0.321208i
\(626\) −17.7219 18.7597i −0.708310 0.749788i
\(627\) 0 0
\(628\) 1.33091 + 3.81304i 0.0531091 + 0.152157i
\(629\) 8.81038 21.2701i 0.351293 0.848096i
\(630\) 0 0
\(631\) 29.2246 29.2246i 1.16341 1.16341i 0.179689 0.983723i \(-0.442491\pi\)
0.983723 0.179689i \(-0.0575091\pi\)
\(632\) 2.76559 32.3365i 0.110009 1.28628i
\(633\) 0 0
\(634\) −8.01622 21.0248i −0.318365 0.835002i
\(635\) 11.6255 + 4.81546i 0.461346 + 0.191096i
\(636\) 0 0
\(637\) 6.83881 + 16.5104i 0.270964 + 0.654164i
\(638\) −3.52945 0.100402i −0.139732 0.00397494i
\(639\) 0 0
\(640\) 15.3756 + 10.3343i 0.607773 + 0.408501i
\(641\) −23.2229 −0.917249 −0.458624 0.888630i \(-0.651658\pi\)
−0.458624 + 0.888630i \(0.651658\pi\)
\(642\) 0 0
\(643\) −2.52528 6.09658i −0.0995875 0.240425i 0.866232 0.499643i \(-0.166535\pi\)
−0.965819 + 0.259217i \(0.916535\pi\)
\(644\) −22.7176 1.29353i −0.895199 0.0509724i
\(645\) 0 0
\(646\) −3.28767 8.62286i −0.129352 0.339262i
\(647\) −2.80148 2.80148i −0.110138 0.110138i 0.649890 0.760028i \(-0.274815\pi\)
−0.760028 + 0.649890i \(0.774815\pi\)
\(648\) 0 0
\(649\) −16.3009 + 16.3009i −0.639868 + 0.639868i
\(650\) 15.3362 + 6.86966i 0.601534 + 0.269450i
\(651\) 0 0
\(652\) −7.68888 22.0286i −0.301120 0.862705i
\(653\) 13.9194 5.76560i 0.544708 0.225625i −0.0933235 0.995636i \(-0.529749\pi\)
0.638031 + 0.770011i \(0.279749\pi\)
\(654\) 0 0
\(655\) 27.4728i 1.07345i
\(656\) 2.10035 1.66963i 0.0820049 0.0651881i
\(657\) 0 0
\(658\) 5.26465 4.97341i 0.205237 0.193884i
\(659\) −3.09009 + 1.27996i −0.120373 + 0.0498600i −0.442057 0.896987i \(-0.645751\pi\)
0.321684 + 0.946847i \(0.395751\pi\)
\(660\) 0 0
\(661\) 4.40456 10.6336i 0.171318 0.413598i −0.814779 0.579772i \(-0.803142\pi\)
0.986096 + 0.166175i \(0.0531415\pi\)
\(662\) 5.86929 13.1029i 0.228117 0.509259i
\(663\) 0 0
\(664\) 44.4509 14.1106i 1.72503 0.547598i
\(665\) 2.44955 + 2.44955i 0.0949894 + 0.0949894i
\(666\) 0 0
\(667\) −5.70660 2.36375i −0.220960 0.0915248i
\(668\) 17.2417 + 19.3238i 0.667103 + 0.747659i
\(669\) 0 0
\(670\) −1.05184 + 36.9755i −0.0406360 + 1.42849i
\(671\) 9.51145 0.367186
\(672\) 0 0
\(673\) −32.6492 −1.25853 −0.629267 0.777190i \(-0.716645\pi\)
−0.629267 + 0.777190i \(0.716645\pi\)
\(674\) −1.06331 + 37.3790i −0.0409573 + 1.43978i
\(675\) 0 0
\(676\) 19.7916 17.6592i 0.761216 0.679199i
\(677\) 5.71034 + 2.36530i 0.219466 + 0.0909059i 0.489708 0.871887i \(-0.337104\pi\)
−0.270241 + 0.962793i \(0.587104\pi\)
\(678\) 0 0
\(679\) −20.4274 20.4274i −0.783933 0.783933i
\(680\) −12.3170 + 23.7737i −0.472334 + 0.911678i
\(681\) 0 0
\(682\) −10.5418 + 23.5340i −0.403666 + 0.901165i
\(683\) 5.03873 12.1646i 0.192802 0.465465i −0.797685 0.603075i \(-0.793942\pi\)
0.990486 + 0.137610i \(0.0439421\pi\)
\(684\) 0 0
\(685\) 34.5224 14.2996i 1.31903 0.546361i
\(686\) −20.2066 + 19.0888i −0.771491 + 0.728812i
\(687\) 0 0
\(688\) −2.07397 + 3.73880i −0.0790693 + 0.142540i
\(689\) 60.9795i 2.32313i
\(690\) 0 0
\(691\) −33.3930 + 13.8318i −1.27033 + 0.526187i −0.913064 0.407816i \(-0.866291\pi\)
−0.357265 + 0.934003i \(0.616291\pi\)
\(692\) −14.8596 + 5.18662i −0.564878 + 0.197166i
\(693\) 0 0
\(694\) 30.3960 + 13.6155i 1.15382 + 0.516839i
\(695\) −8.71497 + 8.71497i −0.330577 + 0.330577i
\(696\) 0 0
\(697\) 2.74204 + 2.74204i 0.103862 + 0.103862i
\(698\) 3.49419 + 9.16450i 0.132257 + 0.346881i
\(699\) 0 0
\(700\) −0.494099 + 8.67757i −0.0186752 + 0.327981i
\(701\) 10.9582 + 26.4553i 0.413884 + 0.999204i 0.984085 + 0.177699i \(0.0568652\pi\)
−0.570201 + 0.821505i \(0.693135\pi\)
\(702\) 0 0
\(703\) 4.49516 0.169538
\(704\) 10.4822 16.5961i 0.395061 0.625488i
\(705\) 0 0
\(706\) −12.9483 0.368338i −0.487315 0.0138626i
\(707\) −8.06415 19.4686i −0.303284 0.732191i
\(708\) 0 0
\(709\) 7.29870 + 3.02322i 0.274109 + 0.113539i 0.515503 0.856887i \(-0.327605\pi\)
−0.241395 + 0.970427i \(0.577605\pi\)
\(710\) −12.3400 32.3652i −0.463113 1.21465i
\(711\) 0 0
\(712\) 15.6591 + 18.5881i 0.586849 + 0.696617i
\(713\) −31.8984 + 31.8984i −1.19461 + 1.19461i
\(714\) 0 0
\(715\) −7.87938 + 19.0225i −0.294672 + 0.711401i
\(716\) 11.5038 4.01532i 0.429919 0.150059i
\(717\) 0 0
\(718\) −19.9158 21.0820i −0.743251 0.786775i
\(719\) 18.4601i 0.688447i −0.938888 0.344223i \(-0.888142\pi\)
0.938888 0.344223i \(-0.111858\pi\)
\(720\) 0 0
\(721\) 21.3396i 0.794729i
\(722\) −18.2228 + 17.2147i −0.678182 + 0.640665i
\(723\) 0 0
\(724\) −2.48518 + 5.15027i −0.0923611 + 0.191408i
\(725\) −0.902895 + 2.17978i −0.0335327 + 0.0809551i
\(726\) 0 0
\(727\) −30.9545 + 30.9545i −1.14804 + 1.14804i −0.161099 + 0.986938i \(0.551504\pi\)
−0.986938 + 0.161099i \(0.948496\pi\)
\(728\) 24.1217 + 12.4973i 0.894009 + 0.463180i
\(729\) 0 0
\(730\) 20.9956 8.00509i 0.777083 0.296282i
\(731\) −5.70890 2.36470i −0.211151 0.0874618i
\(732\) 0 0
\(733\) 2.44239 + 5.89645i 0.0902118 + 0.217791i 0.962545 0.271121i \(-0.0873942\pi\)
−0.872334 + 0.488911i \(0.837394\pi\)
\(734\) −0.226341 + 7.95662i −0.00835439 + 0.293684i
\(735\) 0 0
\(736\) 27.4770 20.5949i 1.01282 0.759140i
\(737\) 39.1935 1.44371
\(738\) 0 0
\(739\) −17.8479 43.0886i −0.656545 1.58504i −0.803104 0.595839i \(-0.796820\pi\)
0.146559 0.989202i \(-0.453180\pi\)
\(740\) −8.68301 9.73153i −0.319194 0.357738i
\(741\) 0 0
\(742\) 29.4705 11.2363i 1.08190 0.412499i
\(743\) 18.7851 + 18.7851i 0.689157 + 0.689157i 0.962046 0.272889i \(-0.0879790\pi\)
−0.272889 + 0.962046i \(0.587979\pi\)
\(744\) 0 0
\(745\) 4.75848 4.75848i 0.174337 0.174337i
\(746\) 17.8869 39.9317i 0.654887 1.46200i
\(747\) 0 0
\(748\) 25.5505 + 12.3290i 0.934217 + 0.450792i
\(749\) 7.98350 3.30688i 0.291711 0.120831i
\(750\) 0 0
\(751\) 31.0990i 1.13482i −0.823436 0.567409i \(-0.807946\pi\)
0.823436 0.567409i \(-0.192054\pi\)
\(752\) −1.24061 + 10.8587i −0.0452404 + 0.395977i
\(753\) 0 0
\(754\) 5.06421 + 5.36077i 0.184428 + 0.195228i
\(755\) −8.82178 + 3.65410i −0.321058 + 0.132986i
\(756\) 0 0
\(757\) 0.986433 2.38146i 0.0358525 0.0865556i −0.904939 0.425541i \(-0.860084\pi\)
0.940792 + 0.338986i \(0.110084\pi\)
\(758\) −34.7212 15.5530i −1.26113 0.564909i
\(759\) 0 0
\(760\) −5.20877 0.445481i −0.188942 0.0161593i
\(761\) 28.0768 + 28.0768i 1.01778 + 1.01778i 0.999839 + 0.0179435i \(0.00571189\pi\)
0.0179435 + 0.999839i \(0.494288\pi\)
\(762\) 0 0
\(763\) 9.74908 + 4.03820i 0.352941 + 0.146193i
\(764\) −8.47475 0.482550i −0.306606 0.0174581i
\(765\) 0 0
\(766\) 4.39215 + 0.124943i 0.158695 + 0.00451437i
\(767\) 48.1484 1.73854
\(768\) 0 0
\(769\) 1.73480 0.0625585 0.0312793 0.999511i \(-0.490042\pi\)
0.0312793 + 0.999511i \(0.490042\pi\)
\(770\) −10.6452 0.302822i −0.383626 0.0109129i
\(771\) 0 0
\(772\) −16.0604 0.914478i −0.578028 0.0329128i
\(773\) −31.1210 12.8907i −1.11934 0.463647i −0.255197 0.966889i \(-0.582140\pi\)
−0.864146 + 0.503242i \(0.832140\pi\)
\(774\) 0 0
\(775\) 12.1844 + 12.1844i 0.437678 + 0.437678i
\(776\) 43.4373 + 3.71498i 1.55931 + 0.133360i
\(777\) 0 0
\(778\) 11.6031 + 5.19747i 0.415991 + 0.186338i
\(779\) −0.289747 + 0.699512i −0.0103813 + 0.0250626i
\(780\) 0 0
\(781\) −33.9072 + 14.0448i −1.21329 + 0.502563i
\(782\) 34.0806 + 36.0764i 1.21872 + 1.29009i
\(783\) 0 0
\(784\) 1.58334 13.8586i 0.0565479 0.494949i
\(785\) 3.30658i 0.118017i
\(786\) 0 0
\(787\) 45.0368 18.6548i 1.60539 0.664974i 0.613223 0.789910i \(-0.289873\pi\)
0.992165 + 0.124936i \(0.0398726\pi\)
\(788\) 39.9116 + 19.2587i 1.42179 + 0.686063i
\(789\) 0 0
\(790\) 10.8625 24.2500i 0.386470 0.862775i
\(791\) 5.46838 5.46838i 0.194433 0.194433i
\(792\) 0 0
\(793\) −14.0471 14.0471i −0.498826 0.498826i
\(794\) 22.7461 8.67249i 0.807228 0.307775i
\(795\) 0 0
\(796\) 4.86566 + 5.45322i 0.172459 + 0.193284i
\(797\) 12.8982 + 31.1390i 0.456877 + 1.10300i 0.969655 + 0.244478i \(0.0786164\pi\)
−0.512778 + 0.858521i \(0.671384\pi\)
\(798\) 0 0
\(799\) −15.7959 −0.558819
\(800\) −7.86677 10.4956i −0.278132 0.371074i
\(801\) 0 0
\(802\) 0.716074 25.1724i 0.0252855 0.888867i
\(803\) −9.11099 21.9959i −0.321520 0.776218i
\(804\) 0 0
\(805\) −17.2117 7.12932i −0.606633 0.251276i
\(806\) 50.3252 19.1877i 1.77263 0.675857i
\(807\) 0 0
\(808\) 28.2361 + 14.6289i 0.993342 + 0.514643i
\(809\) 1.33912 1.33912i 0.0470811 0.0470811i −0.683174 0.730255i \(-0.739401\pi\)
0.730255 + 0.683174i \(0.239401\pi\)
\(810\) 0 0
\(811\) −19.8815 + 47.9981i −0.698132 + 1.68544i 0.0295838 + 0.999562i \(0.490582\pi\)
−0.727716 + 0.685878i \(0.759418\pi\)
\(812\) −1.65763 + 3.43526i −0.0581713 + 0.120554i
\(813\) 0 0
\(814\) −10.0453 + 9.48963i −0.352089 + 0.332611i
\(815\) 19.1026i 0.669136i
\(816\) 0 0
\(817\) 1.20650i 0.0422101i
\(818\) −21.1765 22.4166i −0.740420 0.783779i
\(819\) 0 0
\(820\) 2.07405 0.723930i 0.0724290 0.0252807i
\(821\) −0.106271 + 0.256562i −0.00370889 + 0.00895406i −0.925723 0.378202i \(-0.876543\pi\)
0.922014 + 0.387156i \(0.126543\pi\)
\(822\) 0 0
\(823\) 1.33537 1.33537i 0.0465479 0.0465479i −0.683450 0.729998i \(-0.739521\pi\)
0.729998 + 0.683450i \(0.239521\pi\)
\(824\) −20.7481 24.6290i −0.722794 0.857991i
\(825\) 0 0
\(826\) 8.87202 + 23.2694i 0.308697 + 0.809646i
\(827\) 23.3468 + 9.67056i 0.811848 + 0.336278i 0.749691 0.661788i \(-0.230202\pi\)
0.0621568 + 0.998066i \(0.480202\pi\)
\(828\) 0 0
\(829\) −10.2848 24.8297i −0.357205 0.862370i −0.995691 0.0927359i \(-0.970439\pi\)
0.638486 0.769634i \(-0.279561\pi\)
\(830\) 38.1677 + 1.08575i 1.32482 + 0.0376870i
\(831\) 0 0
\(832\) −39.9907 + 9.02941i −1.38643 + 0.313039i
\(833\) 20.1597 0.698492
\(834\) 0 0
\(835\) 8.11414 + 19.5893i 0.280801 + 0.677914i
\(836\) −0.314887 + 5.53018i −0.0108906 + 0.191265i
\(837\) 0 0
\(838\) 7.56084 + 19.8305i 0.261185 + 0.685032i
\(839\) −7.12216 7.12216i −0.245884 0.245884i 0.573395 0.819279i \(-0.305626\pi\)
−0.819279 + 0.573395i \(0.805626\pi\)
\(840\) 0 0
\(841\) 19.7740 19.7740i 0.681861 0.681861i
\(842\) 5.41510 + 2.42563i 0.186617 + 0.0835928i
\(843\) 0 0
\(844\) −2.13677 + 0.745821i −0.0735506 + 0.0256722i
\(845\) 20.0635 8.31059i 0.690207 0.285893i
\(846\) 0 0
\(847\) 9.33302i 0.320687i
\(848\) −23.0883 + 41.6219i −0.792855 + 1.42930i
\(849\) 0 0
\(850\) 13.7803 13.0180i 0.472661 0.446513i
\(851\) −22.3341 + 9.25108i −0.765603 + 0.317123i
\(852\) 0 0
\(853\) −10.6705 + 25.7608i −0.365349 + 0.882032i 0.629149 + 0.777284i \(0.283403\pi\)
−0.994499 + 0.104747i \(0.966597\pi\)
\(854\) 4.20037 9.37711i 0.143734 0.320878i
\(855\) 0 0
\(856\) −5.99889 + 11.5788i −0.205038 + 0.395755i
\(857\) −20.0048 20.0048i −0.683349 0.683349i 0.277404 0.960753i \(-0.410526\pi\)
−0.960753 + 0.277404i \(0.910526\pi\)
\(858\) 0 0
\(859\) −1.53664 0.636496i −0.0524294 0.0217170i 0.356315 0.934366i \(-0.384033\pi\)
−0.408744 + 0.912649i \(0.634033\pi\)
\(860\) −2.61194 + 2.33052i −0.0890665 + 0.0794701i
\(861\) 0 0
\(862\) 0.654948 23.0236i 0.0223076 0.784186i
\(863\) −3.22858 −0.109902 −0.0549510 0.998489i \(-0.517500\pi\)
−0.0549510 + 0.998489i \(0.517500\pi\)
\(864\) 0 0
\(865\) −12.8859 −0.438133
\(866\) −1.13750 + 39.9868i −0.0386538 + 1.35881i
\(867\) 0 0
\(868\) 18.5463 + 20.7858i 0.629501 + 0.705516i
\(869\) −26.0111 10.7742i −0.882366 0.365488i
\(870\) 0 0
\(871\) −57.8832 57.8832i −1.96130 1.96130i
\(872\) −15.1781 + 4.81818i −0.513995 + 0.163164i
\(873\) 0 0
\(874\) −3.96125 + 8.84330i −0.133991 + 0.299129i
\(875\) −8.59556 + 20.7515i −0.290583 + 0.701530i
\(876\) 0 0
\(877\) −23.7751 + 9.84797i −0.802828 + 0.332542i −0.746089 0.665847i \(-0.768070\pi\)
−0.0567395 + 0.998389i \(0.518070\pi\)
\(878\) 20.1269 19.0135i 0.679251 0.641675i
\(879\) 0 0
\(880\) 12.5805 10.0006i 0.424088 0.337120i
\(881\) 2.67200i 0.0900220i −0.998986 0.0450110i \(-0.985668\pi\)
0.998986 0.0450110i \(-0.0143323\pi\)
\(882\) 0 0
\(883\) −39.5907 + 16.3990i −1.33233 + 0.551870i −0.931320 0.364202i \(-0.881342\pi\)
−0.401013 + 0.916072i \(0.631342\pi\)
\(884\) −19.5263 55.9425i −0.656740 1.88155i
\(885\) 0 0
\(886\) −8.32311 3.72824i −0.279620 0.125253i
\(887\) −33.5579 + 33.5579i −1.12676 + 1.12676i −0.136063 + 0.990700i \(0.543445\pi\)
−0.990700 + 0.136063i \(0.956555\pi\)
\(888\) 0 0
\(889\) −10.1845 10.1845i −0.341576 0.341576i
\(890\) 7.08924 + 18.5935i 0.237632 + 0.623257i
\(891\) 0 0
\(892\) −14.7830 0.841738i −0.494970 0.0281835i
\(893\) −1.18025 2.84938i −0.0394956 0.0953508i
\(894\) 0 0
\(895\) 9.97584 0.333456
\(896\) −11.7326 17.6631i −0.391960 0.590084i
\(897\) 0 0
\(898\) 39.2755 + 1.11726i 1.31064 + 0.0372836i
\(899\) 2.89382 + 6.98629i 0.0965142 + 0.233006i
\(900\) 0 0
\(901\) −63.5538 26.3249i −2.11729 0.877008i
\(902\) −0.829224 2.17488i −0.0276102 0.0724155i
\(903\) 0 0
\(904\) −0.994493 + 11.6281i −0.0330763 + 0.386744i
\(905\) −3.31064 + 3.31064i −0.110049 + 0.110049i
\(906\) 0 0
\(907\) −6.58909 + 15.9075i −0.218787 + 0.528199i −0.994721 0.102615i \(-0.967279\pi\)
0.775934 + 0.630814i \(0.217279\pi\)
\(908\) 8.84351 + 25.3366i 0.293482 + 0.840823i
\(909\) 0 0
\(910\) 15.2742 + 16.1686i 0.506335 + 0.535986i
\(911\) 16.6033i 0.550091i 0.961431 + 0.275045i \(0.0886929\pi\)
−0.961431 + 0.275045i \(0.911307\pi\)
\(912\) 0 0
\(913\) 40.4573i 1.33894i
\(914\) 9.62155 9.08929i 0.318253 0.300647i
\(915\) 0 0
\(916\) −20.7677 10.0211i −0.686186 0.331108i
\(917\) 12.0337 29.0518i 0.397386 0.959376i
\(918\) 0 0
\(919\) −29.2819 + 29.2819i −0.965922 + 0.965922i −0.999438 0.0335164i \(-0.989329\pi\)
0.0335164 + 0.999438i \(0.489329\pi\)
\(920\) 26.7965 8.50634i 0.883453 0.280446i
\(921\) 0 0
\(922\) −36.0116 + 13.7303i −1.18598 + 0.452183i
\(923\) 70.8183 + 29.3339i 2.33101 + 0.965537i
\(924\) 0 0
\(925\) 3.53369 + 8.53108i 0.116187 + 0.280500i
\(926\) −1.34109 + 47.1439i −0.0440711 + 1.54924i
\(927\) 0 0
\(928\) −1.42689 5.57645i −0.0468400 0.183056i
\(929\) 48.4425 1.58935 0.794674 0.607036i \(-0.207642\pi\)
0.794674 + 0.607036i \(0.207642\pi\)
\(930\) 0 0
\(931\) 1.50631 + 3.63655i 0.0493673 + 0.119183i
\(932\) 22.3770 19.9660i 0.732984 0.654009i
\(933\) 0 0
\(934\) −10.1479 + 3.86915i −0.332051 + 0.126602i
\(935\) 16.4240 + 16.4240i 0.537124 + 0.537124i
\(936\) 0 0
\(937\) 6.17378 6.17378i 0.201689 0.201689i −0.599035 0.800723i \(-0.704449\pi\)
0.800723 + 0.599035i \(0.204449\pi\)
\(938\) 17.3083 38.6399i 0.565136 1.26164i
\(939\) 0 0
\(940\) −3.88878 + 8.05907i −0.126838 + 0.262858i
\(941\) 28.8812 11.9630i 0.941500 0.389982i 0.141470 0.989942i \(-0.454817\pi\)
0.800030 + 0.599960i \(0.204817\pi\)
\(942\) 0 0
\(943\) 4.07181i 0.132596i
\(944\) −32.8639 18.2301i −1.06963 0.593340i
\(945\) 0 0
\(946\) 2.54702 + 2.69617i 0.0828106 + 0.0876599i
\(947\) −31.3266 + 12.9759i −1.01798 + 0.421660i −0.828359 0.560198i \(-0.810725\pi\)
−0.189618 + 0.981858i \(0.560725\pi\)
\(948\) 0 0
\(949\) −19.0292 + 45.9405i −0.617713 + 1.49129i
\(950\) 3.37793 + 1.51310i 0.109594 + 0.0490916i
\(951\) 0 0
\(952\) 23.4382 19.7450i 0.759637 0.639938i
\(953\) −28.8836 28.8836i −0.935631 0.935631i 0.0624188 0.998050i \(-0.480119\pi\)
−0.998050 + 0.0624188i \(0.980119\pi\)
\(954\) 0 0
\(955\) −6.42079 2.65958i −0.207772 0.0860619i
\(956\) −3.15188 + 55.3546i −0.101939 + 1.79030i
\(957\) 0 0
\(958\) −2.35437 0.0669745i −0.0760663 0.00216385i
\(959\) −42.7701 −1.38112
\(960\) 0 0
\(961\) 24.2273 0.781525
\(962\) 28.8504 + 0.820702i 0.930173 + 0.0264605i
\(963\) 0 0
\(964\) 2.17579 38.2122i 0.0700776 1.23073i
\(965\) −12.1680 5.04015i −0.391702 0.162248i
\(966\) 0 0
\(967\) 17.5627 + 17.5627i 0.564777 + 0.564777i 0.930661 0.365884i \(-0.119233\pi\)
−0.365884 + 0.930661i \(0.619233\pi\)
\(968\) 9.07431 + 10.7716i 0.291659 + 0.346214i
\(969\) 0 0
\(970\) 32.5747 + 14.5915i 1.04591 + 0.468504i
\(971\) 0.119416 0.288295i 0.00383224 0.00925184i −0.921952 0.387305i \(-0.873406\pi\)
0.925784 + 0.378053i \(0.123406\pi\)
\(972\) 0 0
\(973\) 13.0332 5.39852i 0.417825 0.173069i
\(974\) 21.1909 + 22.4319i 0.679001 + 0.718763i
\(975\) 0 0
\(976\) 4.26935 + 14.9065i 0.136659 + 0.477144i
\(977\) 46.5011i 1.48770i −0.668345 0.743851i \(-0.732997\pi\)
0.668345 0.743851i \(-0.267003\pi\)
\(978\) 0 0
\(979\) 19.4794 8.06862i 0.622563 0.257874i
\(980\) 4.96309 10.2855i 0.158540 0.328558i
\(981\) 0 0
\(982\) 11.5625 25.8127i 0.368975 0.823718i
\(983\) 12.1301 12.1301i 0.386891 0.386891i −0.486686 0.873577i \(-0.661795\pi\)
0.873577 + 0.486686i \(0.161795\pi\)
\(984\) 0 0
\(985\) 25.6555 + 25.6555i 0.817452 + 0.817452i
\(986\) 7.77331 2.96376i 0.247553 0.0943854i
\(987\) 0 0
\(988\) 8.63234 7.70225i 0.274631 0.245041i
\(989\) 2.48299 + 5.99447i 0.0789545 + 0.190613i
\(990\) 0 0
\(991\) −0.0269571 −0.000856319 −0.000428160 1.00000i \(-0.500136\pi\)
−0.000428160 1.00000i \(0.500136\pi\)
\(992\) −41.6146 5.95764i −1.32127 0.189155i
\(993\) 0 0
\(994\) −1.12737 + 39.6306i −0.0357579 + 1.25701i
\(995\) 2.28983 + 5.52814i 0.0725925 + 0.175254i
\(996\) 0 0
\(997\) 8.81063 + 3.64948i 0.279036 + 0.115580i 0.517813 0.855494i \(-0.326746\pi\)
−0.238777 + 0.971074i \(0.576746\pi\)
\(998\) −39.0100 + 14.8735i −1.23484 + 0.470812i
\(999\) 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.v.c.37.8 yes 32
3.2 odd 2 inner 288.2.v.c.37.1 32
4.3 odd 2 1152.2.v.d.1009.6 32
12.11 even 2 1152.2.v.d.1009.3 32
32.13 even 8 inner 288.2.v.c.109.8 yes 32
32.19 odd 8 1152.2.v.d.145.6 32
96.77 odd 8 inner 288.2.v.c.109.1 yes 32
96.83 even 8 1152.2.v.d.145.3 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
288.2.v.c.37.1 32 3.2 odd 2 inner
288.2.v.c.37.8 yes 32 1.1 even 1 trivial
288.2.v.c.109.1 yes 32 96.77 odd 8 inner
288.2.v.c.109.8 yes 32 32.13 even 8 inner
1152.2.v.d.145.3 32 96.83 even 8
1152.2.v.d.145.6 32 32.19 odd 8
1152.2.v.d.1009.3 32 12.11 even 2
1152.2.v.d.1009.6 32 4.3 odd 2