Properties

Label 810.2.e.i.541.1
Level $810$
Weight $2$
Character 810.541
Analytic conductor $6.468$
Analytic rank $0$
Dimension $2$
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] = [810,2,Mod(271,810)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(810, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("810.271");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 810 = 2 \cdot 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 810.e (of order \(3\), degree \(2\), not 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: \(6.46788256372\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 270)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 541.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 810.541
Dual form 810.2.e.i.271.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-1.00000 + 1.73205i) q^{7} -1.00000 q^{8} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-1.00000 + 1.73205i) q^{7} -1.00000 q^{8} -1.00000 q^{10} +(1.50000 - 2.59808i) q^{11} +(-2.50000 - 4.33013i) q^{13} +(1.00000 + 1.73205i) q^{14} +(-0.500000 + 0.866025i) q^{16} +3.00000 q^{17} -4.00000 q^{19} +(-0.500000 + 0.866025i) q^{20} +(-1.50000 - 2.59808i) q^{22} +(-4.50000 - 7.79423i) q^{23} +(-0.500000 + 0.866025i) q^{25} -5.00000 q^{26} +2.00000 q^{28} +(-1.50000 + 2.59808i) q^{29} +(-2.50000 - 4.33013i) q^{31} +(0.500000 + 0.866025i) q^{32} +(1.50000 - 2.59808i) q^{34} +2.00000 q^{35} -10.0000 q^{37} +(-2.00000 + 3.46410i) q^{38} +(0.500000 + 0.866025i) q^{40} +(0.500000 - 0.866025i) q^{43} -3.00000 q^{44} -9.00000 q^{46} +(4.50000 - 7.79423i) q^{47} +(1.50000 + 2.59808i) q^{49} +(0.500000 + 0.866025i) q^{50} +(-2.50000 + 4.33013i) q^{52} +12.0000 q^{53} -3.00000 q^{55} +(1.00000 - 1.73205i) q^{56} +(1.50000 + 2.59808i) q^{58} +(6.00000 + 10.3923i) q^{59} +(-1.00000 + 1.73205i) q^{61} -5.00000 q^{62} +1.00000 q^{64} +(-2.50000 + 4.33013i) q^{65} +(2.00000 + 3.46410i) q^{67} +(-1.50000 - 2.59808i) q^{68} +(1.00000 - 1.73205i) q^{70} -12.0000 q^{71} -10.0000 q^{73} +(-5.00000 + 8.66025i) q^{74} +(2.00000 + 3.46410i) q^{76} +(3.00000 + 5.19615i) q^{77} +(6.50000 - 11.2583i) q^{79} +1.00000 q^{80} +(3.00000 - 5.19615i) q^{83} +(-1.50000 - 2.59808i) q^{85} +(-0.500000 - 0.866025i) q^{86} +(-1.50000 + 2.59808i) q^{88} +12.0000 q^{89} +10.0000 q^{91} +(-4.50000 + 7.79423i) q^{92} +(-4.50000 - 7.79423i) q^{94} +(2.00000 + 3.46410i) q^{95} +(-1.00000 + 1.73205i) q^{97} +3.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + q^{2} - q^{4} - q^{5} - 2 q^{7} - 2 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + q^{2} - q^{4} - q^{5} - 2 q^{7} - 2 q^{8} - 2 q^{10} + 3 q^{11} - 5 q^{13} + 2 q^{14} - q^{16} + 6 q^{17} - 8 q^{19} - q^{20} - 3 q^{22} - 9 q^{23} - q^{25} - 10 q^{26} + 4 q^{28} - 3 q^{29} - 5 q^{31} + q^{32} + 3 q^{34} + 4 q^{35} - 20 q^{37} - 4 q^{38} + q^{40} + q^{43} - 6 q^{44} - 18 q^{46} + 9 q^{47} + 3 q^{49} + q^{50} - 5 q^{52} + 24 q^{53} - 6 q^{55} + 2 q^{56} + 3 q^{58} + 12 q^{59} - 2 q^{61} - 10 q^{62} + 2 q^{64} - 5 q^{65} + 4 q^{67} - 3 q^{68} + 2 q^{70} - 24 q^{71} - 20 q^{73} - 10 q^{74} + 4 q^{76} + 6 q^{77} + 13 q^{79} + 2 q^{80} + 6 q^{83} - 3 q^{85} - q^{86} - 3 q^{88} + 24 q^{89} + 20 q^{91} - 9 q^{92} - 9 q^{94} + 4 q^{95} - 2 q^{97} + 6 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/810\mathbb{Z}\right)^\times\).

\(n\) \(487\) \(731\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 0.866025i 0.353553 0.612372i
\(3\) 0 0
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) −0.500000 0.866025i −0.223607 0.387298i
\(6\) 0 0
\(7\) −1.00000 + 1.73205i −0.377964 + 0.654654i −0.990766 0.135583i \(-0.956709\pi\)
0.612801 + 0.790237i \(0.290043\pi\)
\(8\) −1.00000 −0.353553
\(9\) 0 0
\(10\) −1.00000 −0.316228
\(11\) 1.50000 2.59808i 0.452267 0.783349i −0.546259 0.837616i \(-0.683949\pi\)
0.998526 + 0.0542666i \(0.0172821\pi\)
\(12\) 0 0
\(13\) −2.50000 4.33013i −0.693375 1.20096i −0.970725 0.240192i \(-0.922790\pi\)
0.277350 0.960769i \(-0.410544\pi\)
\(14\) 1.00000 + 1.73205i 0.267261 + 0.462910i
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 3.00000 0.727607 0.363803 0.931476i \(-0.381478\pi\)
0.363803 + 0.931476i \(0.381478\pi\)
\(18\) 0 0
\(19\) −4.00000 −0.917663 −0.458831 0.888523i \(-0.651732\pi\)
−0.458831 + 0.888523i \(0.651732\pi\)
\(20\) −0.500000 + 0.866025i −0.111803 + 0.193649i
\(21\) 0 0
\(22\) −1.50000 2.59808i −0.319801 0.553912i
\(23\) −4.50000 7.79423i −0.938315 1.62521i −0.768613 0.639713i \(-0.779053\pi\)
−0.169701 0.985496i \(-0.554280\pi\)
\(24\) 0 0
\(25\) −0.500000 + 0.866025i −0.100000 + 0.173205i
\(26\) −5.00000 −0.980581
\(27\) 0 0
\(28\) 2.00000 0.377964
\(29\) −1.50000 + 2.59808i −0.278543 + 0.482451i −0.971023 0.238987i \(-0.923185\pi\)
0.692480 + 0.721437i \(0.256518\pi\)
\(30\) 0 0
\(31\) −2.50000 4.33013i −0.449013 0.777714i 0.549309 0.835619i \(-0.314891\pi\)
−0.998322 + 0.0579057i \(0.981558\pi\)
\(32\) 0.500000 + 0.866025i 0.0883883 + 0.153093i
\(33\) 0 0
\(34\) 1.50000 2.59808i 0.257248 0.445566i
\(35\) 2.00000 0.338062
\(36\) 0 0
\(37\) −10.0000 −1.64399 −0.821995 0.569495i \(-0.807139\pi\)
−0.821995 + 0.569495i \(0.807139\pi\)
\(38\) −2.00000 + 3.46410i −0.324443 + 0.561951i
\(39\) 0 0
\(40\) 0.500000 + 0.866025i 0.0790569 + 0.136931i
\(41\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(42\) 0 0
\(43\) 0.500000 0.866025i 0.0762493 0.132068i −0.825380 0.564578i \(-0.809039\pi\)
0.901629 + 0.432511i \(0.142372\pi\)
\(44\) −3.00000 −0.452267
\(45\) 0 0
\(46\) −9.00000 −1.32698
\(47\) 4.50000 7.79423i 0.656392 1.13691i −0.325150 0.945662i \(-0.605415\pi\)
0.981543 0.191243i \(-0.0612518\pi\)
\(48\) 0 0
\(49\) 1.50000 + 2.59808i 0.214286 + 0.371154i
\(50\) 0.500000 + 0.866025i 0.0707107 + 0.122474i
\(51\) 0 0
\(52\) −2.50000 + 4.33013i −0.346688 + 0.600481i
\(53\) 12.0000 1.64833 0.824163 0.566352i \(-0.191646\pi\)
0.824163 + 0.566352i \(0.191646\pi\)
\(54\) 0 0
\(55\) −3.00000 −0.404520
\(56\) 1.00000 1.73205i 0.133631 0.231455i
\(57\) 0 0
\(58\) 1.50000 + 2.59808i 0.196960 + 0.341144i
\(59\) 6.00000 + 10.3923i 0.781133 + 1.35296i 0.931282 + 0.364299i \(0.118692\pi\)
−0.150148 + 0.988663i \(0.547975\pi\)
\(60\) 0 0
\(61\) −1.00000 + 1.73205i −0.128037 + 0.221766i −0.922916 0.385002i \(-0.874201\pi\)
0.794879 + 0.606768i \(0.207534\pi\)
\(62\) −5.00000 −0.635001
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) −2.50000 + 4.33013i −0.310087 + 0.537086i
\(66\) 0 0
\(67\) 2.00000 + 3.46410i 0.244339 + 0.423207i 0.961946 0.273241i \(-0.0880957\pi\)
−0.717607 + 0.696449i \(0.754762\pi\)
\(68\) −1.50000 2.59808i −0.181902 0.315063i
\(69\) 0 0
\(70\) 1.00000 1.73205i 0.119523 0.207020i
\(71\) −12.0000 −1.42414 −0.712069 0.702109i \(-0.752242\pi\)
−0.712069 + 0.702109i \(0.752242\pi\)
\(72\) 0 0
\(73\) −10.0000 −1.17041 −0.585206 0.810885i \(-0.698986\pi\)
−0.585206 + 0.810885i \(0.698986\pi\)
\(74\) −5.00000 + 8.66025i −0.581238 + 1.00673i
\(75\) 0 0
\(76\) 2.00000 + 3.46410i 0.229416 + 0.397360i
\(77\) 3.00000 + 5.19615i 0.341882 + 0.592157i
\(78\) 0 0
\(79\) 6.50000 11.2583i 0.731307 1.26666i −0.225018 0.974355i \(-0.572244\pi\)
0.956325 0.292306i \(-0.0944227\pi\)
\(80\) 1.00000 0.111803
\(81\) 0 0
\(82\) 0 0
\(83\) 3.00000 5.19615i 0.329293 0.570352i −0.653079 0.757290i \(-0.726523\pi\)
0.982372 + 0.186938i \(0.0598564\pi\)
\(84\) 0 0
\(85\) −1.50000 2.59808i −0.162698 0.281801i
\(86\) −0.500000 0.866025i −0.0539164 0.0933859i
\(87\) 0 0
\(88\) −1.50000 + 2.59808i −0.159901 + 0.276956i
\(89\) 12.0000 1.27200 0.635999 0.771690i \(-0.280588\pi\)
0.635999 + 0.771690i \(0.280588\pi\)
\(90\) 0 0
\(91\) 10.0000 1.04828
\(92\) −4.50000 + 7.79423i −0.469157 + 0.812605i
\(93\) 0 0
\(94\) −4.50000 7.79423i −0.464140 0.803913i
\(95\) 2.00000 + 3.46410i 0.205196 + 0.355409i
\(96\) 0 0
\(97\) −1.00000 + 1.73205i −0.101535 + 0.175863i −0.912317 0.409484i \(-0.865709\pi\)
0.810782 + 0.585348i \(0.199042\pi\)
\(98\) 3.00000 0.303046
\(99\) 0 0
\(100\) 1.00000 0.100000
\(101\) 7.50000 12.9904i 0.746278 1.29259i −0.203317 0.979113i \(-0.565172\pi\)
0.949595 0.313478i \(-0.101494\pi\)
\(102\) 0 0
\(103\) −1.00000 1.73205i −0.0985329 0.170664i 0.812545 0.582899i \(-0.198082\pi\)
−0.911078 + 0.412235i \(0.864748\pi\)
\(104\) 2.50000 + 4.33013i 0.245145 + 0.424604i
\(105\) 0 0
\(106\) 6.00000 10.3923i 0.582772 1.00939i
\(107\) −6.00000 −0.580042 −0.290021 0.957020i \(-0.593662\pi\)
−0.290021 + 0.957020i \(0.593662\pi\)
\(108\) 0 0
\(109\) 20.0000 1.91565 0.957826 0.287348i \(-0.0927736\pi\)
0.957826 + 0.287348i \(0.0927736\pi\)
\(110\) −1.50000 + 2.59808i −0.143019 + 0.247717i
\(111\) 0 0
\(112\) −1.00000 1.73205i −0.0944911 0.163663i
\(113\) −7.50000 12.9904i −0.705541 1.22203i −0.966496 0.256681i \(-0.917371\pi\)
0.260955 0.965351i \(-0.415962\pi\)
\(114\) 0 0
\(115\) −4.50000 + 7.79423i −0.419627 + 0.726816i
\(116\) 3.00000 0.278543
\(117\) 0 0
\(118\) 12.0000 1.10469
\(119\) −3.00000 + 5.19615i −0.275010 + 0.476331i
\(120\) 0 0
\(121\) 1.00000 + 1.73205i 0.0909091 + 0.157459i
\(122\) 1.00000 + 1.73205i 0.0905357 + 0.156813i
\(123\) 0 0
\(124\) −2.50000 + 4.33013i −0.224507 + 0.388857i
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) 2.00000 0.177471 0.0887357 0.996055i \(-0.471717\pi\)
0.0887357 + 0.996055i \(0.471717\pi\)
\(128\) 0.500000 0.866025i 0.0441942 0.0765466i
\(129\) 0 0
\(130\) 2.50000 + 4.33013i 0.219265 + 0.379777i
\(131\) −1.50000 2.59808i −0.131056 0.226995i 0.793028 0.609185i \(-0.208503\pi\)
−0.924084 + 0.382190i \(0.875170\pi\)
\(132\) 0 0
\(133\) 4.00000 6.92820i 0.346844 0.600751i
\(134\) 4.00000 0.345547
\(135\) 0 0
\(136\) −3.00000 −0.257248
\(137\) −3.00000 + 5.19615i −0.256307 + 0.443937i −0.965250 0.261329i \(-0.915839\pi\)
0.708942 + 0.705266i \(0.249173\pi\)
\(138\) 0 0
\(139\) −1.00000 1.73205i −0.0848189 0.146911i 0.820495 0.571654i \(-0.193698\pi\)
−0.905314 + 0.424743i \(0.860365\pi\)
\(140\) −1.00000 1.73205i −0.0845154 0.146385i
\(141\) 0 0
\(142\) −6.00000 + 10.3923i −0.503509 + 0.872103i
\(143\) −15.0000 −1.25436
\(144\) 0 0
\(145\) 3.00000 0.249136
\(146\) −5.00000 + 8.66025i −0.413803 + 0.716728i
\(147\) 0 0
\(148\) 5.00000 + 8.66025i 0.410997 + 0.711868i
\(149\) 10.5000 + 18.1865i 0.860194 + 1.48990i 0.871742 + 0.489966i \(0.162991\pi\)
−0.0115483 + 0.999933i \(0.503676\pi\)
\(150\) 0 0
\(151\) −5.50000 + 9.52628i −0.447584 + 0.775238i −0.998228 0.0595022i \(-0.981049\pi\)
0.550645 + 0.834740i \(0.314382\pi\)
\(152\) 4.00000 0.324443
\(153\) 0 0
\(154\) 6.00000 0.483494
\(155\) −2.50000 + 4.33013i −0.200805 + 0.347804i
\(156\) 0 0
\(157\) 6.50000 + 11.2583i 0.518756 + 0.898513i 0.999762 + 0.0217953i \(0.00693820\pi\)
−0.481006 + 0.876717i \(0.659728\pi\)
\(158\) −6.50000 11.2583i −0.517112 0.895665i
\(159\) 0 0
\(160\) 0.500000 0.866025i 0.0395285 0.0684653i
\(161\) 18.0000 1.41860
\(162\) 0 0
\(163\) 11.0000 0.861586 0.430793 0.902451i \(-0.358234\pi\)
0.430793 + 0.902451i \(0.358234\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) −3.00000 5.19615i −0.232845 0.403300i
\(167\) −6.00000 10.3923i −0.464294 0.804181i 0.534875 0.844931i \(-0.320359\pi\)
−0.999169 + 0.0407502i \(0.987025\pi\)
\(168\) 0 0
\(169\) −6.00000 + 10.3923i −0.461538 + 0.799408i
\(170\) −3.00000 −0.230089
\(171\) 0 0
\(172\) −1.00000 −0.0762493
\(173\) 9.00000 15.5885i 0.684257 1.18517i −0.289412 0.957205i \(-0.593460\pi\)
0.973670 0.227964i \(-0.0732068\pi\)
\(174\) 0 0
\(175\) −1.00000 1.73205i −0.0755929 0.130931i
\(176\) 1.50000 + 2.59808i 0.113067 + 0.195837i
\(177\) 0 0
\(178\) 6.00000 10.3923i 0.449719 0.778936i
\(179\) −12.0000 −0.896922 −0.448461 0.893802i \(-0.648028\pi\)
−0.448461 + 0.893802i \(0.648028\pi\)
\(180\) 0 0
\(181\) 20.0000 1.48659 0.743294 0.668965i \(-0.233262\pi\)
0.743294 + 0.668965i \(0.233262\pi\)
\(182\) 5.00000 8.66025i 0.370625 0.641941i
\(183\) 0 0
\(184\) 4.50000 + 7.79423i 0.331744 + 0.574598i
\(185\) 5.00000 + 8.66025i 0.367607 + 0.636715i
\(186\) 0 0
\(187\) 4.50000 7.79423i 0.329073 0.569970i
\(188\) −9.00000 −0.656392
\(189\) 0 0
\(190\) 4.00000 0.290191
\(191\) 3.00000 5.19615i 0.217072 0.375980i −0.736839 0.676068i \(-0.763683\pi\)
0.953912 + 0.300088i \(0.0970159\pi\)
\(192\) 0 0
\(193\) 5.00000 + 8.66025i 0.359908 + 0.623379i 0.987945 0.154805i \(-0.0494748\pi\)
−0.628037 + 0.778183i \(0.716141\pi\)
\(194\) 1.00000 + 1.73205i 0.0717958 + 0.124354i
\(195\) 0 0
\(196\) 1.50000 2.59808i 0.107143 0.185577i
\(197\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(198\) 0 0
\(199\) −7.00000 −0.496217 −0.248108 0.968732i \(-0.579809\pi\)
−0.248108 + 0.968732i \(0.579809\pi\)
\(200\) 0.500000 0.866025i 0.0353553 0.0612372i
\(201\) 0 0
\(202\) −7.50000 12.9904i −0.527698 0.914000i
\(203\) −3.00000 5.19615i −0.210559 0.364698i
\(204\) 0 0
\(205\) 0 0
\(206\) −2.00000 −0.139347
\(207\) 0 0
\(208\) 5.00000 0.346688
\(209\) −6.00000 + 10.3923i −0.415029 + 0.718851i
\(210\) 0 0
\(211\) 11.0000 + 19.0526i 0.757271 + 1.31163i 0.944237 + 0.329266i \(0.106801\pi\)
−0.186966 + 0.982366i \(0.559865\pi\)
\(212\) −6.00000 10.3923i −0.412082 0.713746i
\(213\) 0 0
\(214\) −3.00000 + 5.19615i −0.205076 + 0.355202i
\(215\) −1.00000 −0.0681994
\(216\) 0 0
\(217\) 10.0000 0.678844
\(218\) 10.0000 17.3205i 0.677285 1.17309i
\(219\) 0 0
\(220\) 1.50000 + 2.59808i 0.101130 + 0.175162i
\(221\) −7.50000 12.9904i −0.504505 0.873828i
\(222\) 0 0
\(223\) −4.00000 + 6.92820i −0.267860 + 0.463947i −0.968309 0.249756i \(-0.919650\pi\)
0.700449 + 0.713702i \(0.252983\pi\)
\(224\) −2.00000 −0.133631
\(225\) 0 0
\(226\) −15.0000 −0.997785
\(227\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(228\) 0 0
\(229\) 2.00000 + 3.46410i 0.132164 + 0.228914i 0.924510 0.381157i \(-0.124474\pi\)
−0.792347 + 0.610071i \(0.791141\pi\)
\(230\) 4.50000 + 7.79423i 0.296721 + 0.513936i
\(231\) 0 0
\(232\) 1.50000 2.59808i 0.0984798 0.170572i
\(233\) −6.00000 −0.393073 −0.196537 0.980497i \(-0.562969\pi\)
−0.196537 + 0.980497i \(0.562969\pi\)
\(234\) 0 0
\(235\) −9.00000 −0.587095
\(236\) 6.00000 10.3923i 0.390567 0.676481i
\(237\) 0 0
\(238\) 3.00000 + 5.19615i 0.194461 + 0.336817i
\(239\) −3.00000 5.19615i −0.194054 0.336111i 0.752536 0.658551i \(-0.228830\pi\)
−0.946590 + 0.322440i \(0.895497\pi\)
\(240\) 0 0
\(241\) 9.50000 16.4545i 0.611949 1.05993i −0.378963 0.925412i \(-0.623719\pi\)
0.990912 0.134515i \(-0.0429475\pi\)
\(242\) 2.00000 0.128565
\(243\) 0 0
\(244\) 2.00000 0.128037
\(245\) 1.50000 2.59808i 0.0958315 0.165985i
\(246\) 0 0
\(247\) 10.0000 + 17.3205i 0.636285 + 1.10208i
\(248\) 2.50000 + 4.33013i 0.158750 + 0.274963i
\(249\) 0 0
\(250\) 0.500000 0.866025i 0.0316228 0.0547723i
\(251\) 9.00000 0.568075 0.284037 0.958813i \(-0.408326\pi\)
0.284037 + 0.958813i \(0.408326\pi\)
\(252\) 0 0
\(253\) −27.0000 −1.69748
\(254\) 1.00000 1.73205i 0.0627456 0.108679i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −7.50000 12.9904i −0.467837 0.810318i 0.531487 0.847066i \(-0.321633\pi\)
−0.999325 + 0.0367485i \(0.988300\pi\)
\(258\) 0 0
\(259\) 10.0000 17.3205i 0.621370 1.07624i
\(260\) 5.00000 0.310087
\(261\) 0 0
\(262\) −3.00000 −0.185341
\(263\) 6.00000 10.3923i 0.369976 0.640817i −0.619586 0.784929i \(-0.712699\pi\)
0.989561 + 0.144112i \(0.0460326\pi\)
\(264\) 0 0
\(265\) −6.00000 10.3923i −0.368577 0.638394i
\(266\) −4.00000 6.92820i −0.245256 0.424795i
\(267\) 0 0
\(268\) 2.00000 3.46410i 0.122169 0.211604i
\(269\) 9.00000 0.548740 0.274370 0.961624i \(-0.411531\pi\)
0.274370 + 0.961624i \(0.411531\pi\)
\(270\) 0 0
\(271\) 8.00000 0.485965 0.242983 0.970031i \(-0.421874\pi\)
0.242983 + 0.970031i \(0.421874\pi\)
\(272\) −1.50000 + 2.59808i −0.0909509 + 0.157532i
\(273\) 0 0
\(274\) 3.00000 + 5.19615i 0.181237 + 0.313911i
\(275\) 1.50000 + 2.59808i 0.0904534 + 0.156670i
\(276\) 0 0
\(277\) 5.00000 8.66025i 0.300421 0.520344i −0.675810 0.737075i \(-0.736206\pi\)
0.976231 + 0.216731i \(0.0695395\pi\)
\(278\) −2.00000 −0.119952
\(279\) 0 0
\(280\) −2.00000 −0.119523
\(281\) −15.0000 + 25.9808i −0.894825 + 1.54988i −0.0608039 + 0.998150i \(0.519366\pi\)
−0.834021 + 0.551733i \(0.813967\pi\)
\(282\) 0 0
\(283\) −16.0000 27.7128i −0.951101 1.64736i −0.743048 0.669238i \(-0.766621\pi\)
−0.208053 0.978117i \(-0.566713\pi\)
\(284\) 6.00000 + 10.3923i 0.356034 + 0.616670i
\(285\) 0 0
\(286\) −7.50000 + 12.9904i −0.443484 + 0.768137i
\(287\) 0 0
\(288\) 0 0
\(289\) −8.00000 −0.470588
\(290\) 1.50000 2.59808i 0.0880830 0.152564i
\(291\) 0 0
\(292\) 5.00000 + 8.66025i 0.292603 + 0.506803i
\(293\) 9.00000 + 15.5885i 0.525786 + 0.910687i 0.999549 + 0.0300351i \(0.00956192\pi\)
−0.473763 + 0.880652i \(0.657105\pi\)
\(294\) 0 0
\(295\) 6.00000 10.3923i 0.349334 0.605063i
\(296\) 10.0000 0.581238
\(297\) 0 0
\(298\) 21.0000 1.21650
\(299\) −22.5000 + 38.9711i −1.30121 + 2.25376i
\(300\) 0 0
\(301\) 1.00000 + 1.73205i 0.0576390 + 0.0998337i
\(302\) 5.50000 + 9.52628i 0.316489 + 0.548176i
\(303\) 0 0
\(304\) 2.00000 3.46410i 0.114708 0.198680i
\(305\) 2.00000 0.114520
\(306\) 0 0
\(307\) 11.0000 0.627803 0.313902 0.949456i \(-0.398364\pi\)
0.313902 + 0.949456i \(0.398364\pi\)
\(308\) 3.00000 5.19615i 0.170941 0.296078i
\(309\) 0 0
\(310\) 2.50000 + 4.33013i 0.141990 + 0.245935i
\(311\) −12.0000 20.7846i −0.680458 1.17859i −0.974841 0.222900i \(-0.928448\pi\)
0.294384 0.955687i \(-0.404886\pi\)
\(312\) 0 0
\(313\) −4.00000 + 6.92820i −0.226093 + 0.391605i −0.956647 0.291250i \(-0.905929\pi\)
0.730554 + 0.682855i \(0.239262\pi\)
\(314\) 13.0000 0.733632
\(315\) 0 0
\(316\) −13.0000 −0.731307
\(317\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(318\) 0 0
\(319\) 4.50000 + 7.79423i 0.251952 + 0.436393i
\(320\) −0.500000 0.866025i −0.0279508 0.0484123i
\(321\) 0 0
\(322\) 9.00000 15.5885i 0.501550 0.868711i
\(323\) −12.0000 −0.667698
\(324\) 0 0
\(325\) 5.00000 0.277350
\(326\) 5.50000 9.52628i 0.304617 0.527612i
\(327\) 0 0
\(328\) 0 0
\(329\) 9.00000 + 15.5885i 0.496186 + 0.859419i
\(330\) 0 0
\(331\) −7.00000 + 12.1244i −0.384755 + 0.666415i −0.991735 0.128302i \(-0.959047\pi\)
0.606980 + 0.794717i \(0.292381\pi\)
\(332\) −6.00000 −0.329293
\(333\) 0 0
\(334\) −12.0000 −0.656611
\(335\) 2.00000 3.46410i 0.109272 0.189264i
\(336\) 0 0
\(337\) −16.0000 27.7128i −0.871576 1.50961i −0.860366 0.509676i \(-0.829765\pi\)
−0.0112091 0.999937i \(-0.503568\pi\)
\(338\) 6.00000 + 10.3923i 0.326357 + 0.565267i
\(339\) 0 0
\(340\) −1.50000 + 2.59808i −0.0813489 + 0.140900i
\(341\) −15.0000 −0.812296
\(342\) 0 0
\(343\) −20.0000 −1.07990
\(344\) −0.500000 + 0.866025i −0.0269582 + 0.0466930i
\(345\) 0 0
\(346\) −9.00000 15.5885i −0.483843 0.838041i
\(347\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(348\) 0 0
\(349\) −7.00000 + 12.1244i −0.374701 + 0.649002i −0.990282 0.139072i \(-0.955588\pi\)
0.615581 + 0.788074i \(0.288921\pi\)
\(350\) −2.00000 −0.106904
\(351\) 0 0
\(352\) 3.00000 0.159901
\(353\) 1.50000 2.59808i 0.0798369 0.138282i −0.823343 0.567545i \(-0.807893\pi\)
0.903179 + 0.429263i \(0.141227\pi\)
\(354\) 0 0
\(355\) 6.00000 + 10.3923i 0.318447 + 0.551566i
\(356\) −6.00000 10.3923i −0.317999 0.550791i
\(357\) 0 0
\(358\) −6.00000 + 10.3923i −0.317110 + 0.549250i
\(359\) −12.0000 −0.633336 −0.316668 0.948536i \(-0.602564\pi\)
−0.316668 + 0.948536i \(0.602564\pi\)
\(360\) 0 0
\(361\) −3.00000 −0.157895
\(362\) 10.0000 17.3205i 0.525588 0.910346i
\(363\) 0 0
\(364\) −5.00000 8.66025i −0.262071 0.453921i
\(365\) 5.00000 + 8.66025i 0.261712 + 0.453298i
\(366\) 0 0
\(367\) −13.0000 + 22.5167i −0.678594 + 1.17536i 0.296810 + 0.954937i \(0.404077\pi\)
−0.975404 + 0.220423i \(0.929256\pi\)
\(368\) 9.00000 0.469157
\(369\) 0 0
\(370\) 10.0000 0.519875
\(371\) −12.0000 + 20.7846i −0.623009 + 1.07908i
\(372\) 0 0
\(373\) 0.500000 + 0.866025i 0.0258890 + 0.0448411i 0.878680 0.477412i \(-0.158425\pi\)
−0.852791 + 0.522253i \(0.825092\pi\)
\(374\) −4.50000 7.79423i −0.232689 0.403030i
\(375\) 0 0
\(376\) −4.50000 + 7.79423i −0.232070 + 0.401957i
\(377\) 15.0000 0.772539
\(378\) 0 0
\(379\) −16.0000 −0.821865 −0.410932 0.911666i \(-0.634797\pi\)
−0.410932 + 0.911666i \(0.634797\pi\)
\(380\) 2.00000 3.46410i 0.102598 0.177705i
\(381\) 0 0
\(382\) −3.00000 5.19615i −0.153493 0.265858i
\(383\) −4.50000 7.79423i −0.229939 0.398266i 0.727851 0.685736i \(-0.240519\pi\)
−0.957790 + 0.287469i \(0.907186\pi\)
\(384\) 0 0
\(385\) 3.00000 5.19615i 0.152894 0.264820i
\(386\) 10.0000 0.508987
\(387\) 0 0
\(388\) 2.00000 0.101535
\(389\) 4.50000 7.79423i 0.228159 0.395183i −0.729103 0.684403i \(-0.760063\pi\)
0.957263 + 0.289220i \(0.0933960\pi\)
\(390\) 0 0
\(391\) −13.5000 23.3827i −0.682724 1.18251i
\(392\) −1.50000 2.59808i −0.0757614 0.131223i
\(393\) 0 0
\(394\) 0 0
\(395\) −13.0000 −0.654101
\(396\) 0 0
\(397\) −7.00000 −0.351320 −0.175660 0.984451i \(-0.556206\pi\)
−0.175660 + 0.984451i \(0.556206\pi\)
\(398\) −3.50000 + 6.06218i −0.175439 + 0.303870i
\(399\) 0 0
\(400\) −0.500000 0.866025i −0.0250000 0.0433013i
\(401\) 18.0000 + 31.1769i 0.898877 + 1.55690i 0.828932 + 0.559350i \(0.188949\pi\)
0.0699455 + 0.997551i \(0.477717\pi\)
\(402\) 0 0
\(403\) −12.5000 + 21.6506i −0.622669 + 1.07849i
\(404\) −15.0000 −0.746278
\(405\) 0 0
\(406\) −6.00000 −0.297775
\(407\) −15.0000 + 25.9808i −0.743522 + 1.28782i
\(408\) 0 0
\(409\) −11.5000 19.9186i −0.568638 0.984911i −0.996701 0.0811615i \(-0.974137\pi\)
0.428063 0.903749i \(-0.359196\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) −1.00000 + 1.73205i −0.0492665 + 0.0853320i
\(413\) −24.0000 −1.18096
\(414\) 0 0
\(415\) −6.00000 −0.294528
\(416\) 2.50000 4.33013i 0.122573 0.212302i
\(417\) 0 0
\(418\) 6.00000 + 10.3923i 0.293470 + 0.508304i
\(419\) −1.50000 2.59808i −0.0732798 0.126924i 0.827057 0.562118i \(-0.190013\pi\)
−0.900337 + 0.435194i \(0.856680\pi\)
\(420\) 0 0
\(421\) 2.00000 3.46410i 0.0974740 0.168830i −0.813164 0.582034i \(-0.802257\pi\)
0.910638 + 0.413204i \(0.135590\pi\)
\(422\) 22.0000 1.07094
\(423\) 0 0
\(424\) −12.0000 −0.582772
\(425\) −1.50000 + 2.59808i −0.0727607 + 0.126025i
\(426\) 0 0
\(427\) −2.00000 3.46410i −0.0967868 0.167640i
\(428\) 3.00000 + 5.19615i 0.145010 + 0.251166i
\(429\) 0 0
\(430\) −0.500000 + 0.866025i −0.0241121 + 0.0417635i
\(431\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(432\) 0 0
\(433\) 2.00000 0.0961139 0.0480569 0.998845i \(-0.484697\pi\)
0.0480569 + 0.998845i \(0.484697\pi\)
\(434\) 5.00000 8.66025i 0.240008 0.415705i
\(435\) 0 0
\(436\) −10.0000 17.3205i −0.478913 0.829502i
\(437\) 18.0000 + 31.1769i 0.861057 + 1.49139i
\(438\) 0 0
\(439\) −4.00000 + 6.92820i −0.190910 + 0.330665i −0.945552 0.325471i \(-0.894477\pi\)
0.754642 + 0.656136i \(0.227810\pi\)
\(440\) 3.00000 0.143019
\(441\) 0 0
\(442\) −15.0000 −0.713477
\(443\) −6.00000 + 10.3923i −0.285069 + 0.493753i −0.972626 0.232377i \(-0.925350\pi\)
0.687557 + 0.726130i \(0.258683\pi\)
\(444\) 0 0
\(445\) −6.00000 10.3923i −0.284427 0.492642i
\(446\) 4.00000 + 6.92820i 0.189405 + 0.328060i
\(447\) 0 0
\(448\) −1.00000 + 1.73205i −0.0472456 + 0.0818317i
\(449\) 6.00000 0.283158 0.141579 0.989927i \(-0.454782\pi\)
0.141579 + 0.989927i \(0.454782\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) −7.50000 + 12.9904i −0.352770 + 0.611016i
\(453\) 0 0
\(454\) 0 0
\(455\) −5.00000 8.66025i −0.234404 0.405999i
\(456\) 0 0
\(457\) 14.0000 24.2487i 0.654892 1.13431i −0.327028 0.945015i \(-0.606047\pi\)
0.981921 0.189292i \(-0.0606194\pi\)
\(458\) 4.00000 0.186908
\(459\) 0 0
\(460\) 9.00000 0.419627
\(461\) 9.00000 15.5885i 0.419172 0.726027i −0.576685 0.816967i \(-0.695654\pi\)
0.995856 + 0.0909401i \(0.0289872\pi\)
\(462\) 0 0
\(463\) −19.0000 32.9090i −0.883005 1.52941i −0.847983 0.530023i \(-0.822183\pi\)
−0.0350215 0.999387i \(-0.511150\pi\)
\(464\) −1.50000 2.59808i −0.0696358 0.120613i
\(465\) 0 0
\(466\) −3.00000 + 5.19615i −0.138972 + 0.240707i
\(467\) −12.0000 −0.555294 −0.277647 0.960683i \(-0.589555\pi\)
−0.277647 + 0.960683i \(0.589555\pi\)
\(468\) 0 0
\(469\) −8.00000 −0.369406
\(470\) −4.50000 + 7.79423i −0.207570 + 0.359521i
\(471\) 0 0
\(472\) −6.00000 10.3923i −0.276172 0.478345i
\(473\) −1.50000 2.59808i −0.0689701 0.119460i
\(474\) 0 0
\(475\) 2.00000 3.46410i 0.0917663 0.158944i
\(476\) 6.00000 0.275010
\(477\) 0 0
\(478\) −6.00000 −0.274434
\(479\) 18.0000 31.1769i 0.822441 1.42451i −0.0814184 0.996680i \(-0.525945\pi\)
0.903859 0.427830i \(-0.140722\pi\)
\(480\) 0 0
\(481\) 25.0000 + 43.3013i 1.13990 + 1.97437i
\(482\) −9.50000 16.4545i −0.432713 0.749481i
\(483\) 0 0
\(484\) 1.00000 1.73205i 0.0454545 0.0787296i
\(485\) 2.00000 0.0908153
\(486\) 0 0
\(487\) 20.0000 0.906287 0.453143 0.891438i \(-0.350303\pi\)
0.453143 + 0.891438i \(0.350303\pi\)
\(488\) 1.00000 1.73205i 0.0452679 0.0784063i
\(489\) 0 0
\(490\) −1.50000 2.59808i −0.0677631 0.117369i
\(491\) −6.00000 10.3923i −0.270776 0.468998i 0.698285 0.715820i \(-0.253947\pi\)
−0.969061 + 0.246822i \(0.920614\pi\)
\(492\) 0 0
\(493\) −4.50000 + 7.79423i −0.202670 + 0.351034i
\(494\) 20.0000 0.899843
\(495\) 0 0
\(496\) 5.00000 0.224507
\(497\) 12.0000 20.7846i 0.538274 0.932317i
\(498\) 0 0
\(499\) 2.00000 + 3.46410i 0.0895323 + 0.155074i 0.907314 0.420455i \(-0.138129\pi\)
−0.817781 + 0.575529i \(0.804796\pi\)
\(500\) −0.500000 0.866025i −0.0223607 0.0387298i
\(501\) 0 0
\(502\) 4.50000 7.79423i 0.200845 0.347873i
\(503\) 9.00000 0.401290 0.200645 0.979664i \(-0.435696\pi\)
0.200645 + 0.979664i \(0.435696\pi\)
\(504\) 0 0
\(505\) −15.0000 −0.667491
\(506\) −13.5000 + 23.3827i −0.600148 + 1.03949i
\(507\) 0 0
\(508\) −1.00000 1.73205i −0.0443678 0.0768473i
\(509\) 4.50000 + 7.79423i 0.199459 + 0.345473i 0.948353 0.317217i \(-0.102748\pi\)
−0.748894 + 0.662690i \(0.769415\pi\)
\(510\) 0 0
\(511\) 10.0000 17.3205i 0.442374 0.766214i
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) −15.0000 −0.661622
\(515\) −1.00000 + 1.73205i −0.0440653 + 0.0763233i
\(516\) 0 0
\(517\) −13.5000 23.3827i −0.593729 1.02837i
\(518\) −10.0000 17.3205i −0.439375 0.761019i
\(519\) 0 0
\(520\) 2.50000 4.33013i 0.109632 0.189889i
\(521\) 12.0000 0.525730 0.262865 0.964833i \(-0.415333\pi\)
0.262865 + 0.964833i \(0.415333\pi\)
\(522\) 0 0
\(523\) −31.0000 −1.35554 −0.677768 0.735276i \(-0.737052\pi\)
−0.677768 + 0.735276i \(0.737052\pi\)
\(524\) −1.50000 + 2.59808i −0.0655278 + 0.113497i
\(525\) 0 0
\(526\) −6.00000 10.3923i −0.261612 0.453126i
\(527\) −7.50000 12.9904i −0.326705 0.565870i
\(528\) 0 0
\(529\) −29.0000 + 50.2295i −1.26087 + 2.18389i
\(530\) −12.0000 −0.521247
\(531\) 0 0
\(532\) −8.00000 −0.346844
\(533\) 0 0
\(534\) 0 0
\(535\) 3.00000 + 5.19615i 0.129701 + 0.224649i
\(536\) −2.00000 3.46410i −0.0863868 0.149626i
\(537\) 0 0
\(538\) 4.50000 7.79423i 0.194009 0.336033i
\(539\) 9.00000 0.387657
\(540\) 0 0
\(541\) −22.0000 −0.945854 −0.472927 0.881102i \(-0.656803\pi\)
−0.472927 + 0.881102i \(0.656803\pi\)
\(542\) 4.00000 6.92820i 0.171815 0.297592i
\(543\) 0 0
\(544\) 1.50000 + 2.59808i 0.0643120 + 0.111392i
\(545\) −10.0000 17.3205i −0.428353 0.741929i
\(546\) 0 0
\(547\) 6.50000 11.2583i 0.277920 0.481371i −0.692948 0.720988i \(-0.743688\pi\)
0.970868 + 0.239616i \(0.0770217\pi\)
\(548\) 6.00000 0.256307
\(549\) 0 0
\(550\) 3.00000 0.127920
\(551\) 6.00000 10.3923i 0.255609 0.442727i
\(552\) 0 0
\(553\) 13.0000 + 22.5167i 0.552816 + 0.957506i
\(554\) −5.00000 8.66025i −0.212430 0.367939i
\(555\) 0 0
\(556\) −1.00000 + 1.73205i −0.0424094 + 0.0734553i
\(557\) −12.0000 −0.508456 −0.254228 0.967144i \(-0.581821\pi\)
−0.254228 + 0.967144i \(0.581821\pi\)
\(558\) 0 0
\(559\) −5.00000 −0.211477
\(560\) −1.00000 + 1.73205i −0.0422577 + 0.0731925i
\(561\) 0 0
\(562\) 15.0000 + 25.9808i 0.632737 + 1.09593i
\(563\) 3.00000 + 5.19615i 0.126435 + 0.218992i 0.922293 0.386492i \(-0.126313\pi\)
−0.795858 + 0.605483i \(0.792980\pi\)
\(564\) 0 0
\(565\) −7.50000 + 12.9904i −0.315527 + 0.546509i
\(566\) −32.0000 −1.34506
\(567\) 0 0
\(568\) 12.0000 0.503509
\(569\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(570\) 0 0
\(571\) 5.00000 + 8.66025i 0.209243 + 0.362420i 0.951476 0.307722i \(-0.0995665\pi\)
−0.742233 + 0.670142i \(0.766233\pi\)
\(572\) 7.50000 + 12.9904i 0.313591 + 0.543155i
\(573\) 0 0
\(574\) 0 0
\(575\) 9.00000 0.375326
\(576\) 0 0
\(577\) 32.0000 1.33218 0.666089 0.745873i \(-0.267967\pi\)
0.666089 + 0.745873i \(0.267967\pi\)
\(578\) −4.00000 + 6.92820i −0.166378 + 0.288175i
\(579\) 0 0
\(580\) −1.50000 2.59808i −0.0622841 0.107879i
\(581\) 6.00000 + 10.3923i 0.248922 + 0.431145i
\(582\) 0 0
\(583\) 18.0000 31.1769i 0.745484 1.29122i
\(584\) 10.0000 0.413803
\(585\) 0 0
\(586\) 18.0000 0.743573
\(587\) −9.00000 + 15.5885i −0.371470 + 0.643404i −0.989792 0.142520i \(-0.954479\pi\)
0.618322 + 0.785925i \(0.287813\pi\)
\(588\) 0 0
\(589\) 10.0000 + 17.3205i 0.412043 + 0.713679i
\(590\) −6.00000 10.3923i −0.247016 0.427844i
\(591\) 0 0
\(592\) 5.00000 8.66025i 0.205499 0.355934i
\(593\) 27.0000 1.10876 0.554379 0.832265i \(-0.312956\pi\)
0.554379 + 0.832265i \(0.312956\pi\)
\(594\) 0 0
\(595\) 6.00000 0.245976
\(596\) 10.5000 18.1865i 0.430097 0.744949i
\(597\) 0 0
\(598\) 22.5000 + 38.9711i 0.920093 + 1.59365i
\(599\) −15.0000 25.9808i −0.612883 1.06155i −0.990752 0.135686i \(-0.956676\pi\)
0.377869 0.925859i \(-0.376657\pi\)
\(600\) 0 0
\(601\) 9.50000 16.4545i 0.387513 0.671192i −0.604601 0.796528i \(-0.706668\pi\)
0.992114 + 0.125336i \(0.0400009\pi\)
\(602\) 2.00000 0.0815139
\(603\) 0 0
\(604\) 11.0000 0.447584
\(605\) 1.00000 1.73205i 0.0406558 0.0704179i
\(606\) 0 0
\(607\) 17.0000 + 29.4449i 0.690009 + 1.19513i 0.971834 + 0.235665i \(0.0757267\pi\)
−0.281826 + 0.959466i \(0.590940\pi\)
\(608\) −2.00000 3.46410i −0.0811107 0.140488i
\(609\) 0 0
\(610\) 1.00000 1.73205i 0.0404888 0.0701287i
\(611\) −45.0000 −1.82051
\(612\) 0 0
\(613\) −19.0000 −0.767403 −0.383701 0.923457i \(-0.625351\pi\)
−0.383701 + 0.923457i \(0.625351\pi\)
\(614\) 5.50000 9.52628i 0.221962 0.384449i
\(615\) 0 0
\(616\) −3.00000 5.19615i −0.120873 0.209359i
\(617\) 1.50000 + 2.59808i 0.0603877 + 0.104595i 0.894639 0.446790i \(-0.147433\pi\)
−0.834251 + 0.551385i \(0.814100\pi\)
\(618\) 0 0
\(619\) 17.0000 29.4449i 0.683288 1.18349i −0.290684 0.956819i \(-0.593883\pi\)
0.973972 0.226670i \(-0.0727838\pi\)
\(620\) 5.00000 0.200805
\(621\) 0 0
\(622\) −24.0000 −0.962312
\(623\) −12.0000 + 20.7846i −0.480770 + 0.832718i
\(624\) 0 0
\(625\) −0.500000 0.866025i −0.0200000 0.0346410i
\(626\) 4.00000 + 6.92820i 0.159872 + 0.276907i
\(627\) 0 0
\(628\) 6.50000 11.2583i 0.259378 0.449256i
\(629\) −30.0000 −1.19618
\(630\) 0 0
\(631\) −16.0000 −0.636950 −0.318475 0.947931i \(-0.603171\pi\)
−0.318475 + 0.947931i \(0.603171\pi\)
\(632\) −6.50000 + 11.2583i −0.258556 + 0.447832i
\(633\) 0 0
\(634\) 0 0
\(635\) −1.00000 1.73205i −0.0396838 0.0687343i
\(636\) 0 0
\(637\) 7.50000 12.9904i 0.297161 0.514698i
\(638\) 9.00000 0.356313
\(639\) 0 0
\(640\) −1.00000 −0.0395285
\(641\) 15.0000 25.9808i 0.592464 1.02618i −0.401435 0.915888i \(-0.631488\pi\)
0.993899 0.110291i \(-0.0351782\pi\)
\(642\) 0 0
\(643\) −11.5000 19.9186i −0.453516 0.785512i 0.545086 0.838380i \(-0.316497\pi\)
−0.998602 + 0.0528680i \(0.983164\pi\)
\(644\) −9.00000 15.5885i −0.354650 0.614271i
\(645\) 0 0
\(646\) −6.00000 + 10.3923i −0.236067 + 0.408880i
\(647\) −12.0000 −0.471769 −0.235884 0.971781i \(-0.575799\pi\)
−0.235884 + 0.971781i \(0.575799\pi\)
\(648\) 0 0
\(649\) 36.0000 1.41312
\(650\) 2.50000 4.33013i 0.0980581 0.169842i
\(651\) 0 0
\(652\) −5.50000 9.52628i −0.215397 0.373078i
\(653\) 18.0000 + 31.1769i 0.704394 + 1.22005i 0.966910 + 0.255119i \(0.0821147\pi\)
−0.262515 + 0.964928i \(0.584552\pi\)
\(654\) 0 0
\(655\) −1.50000 + 2.59808i −0.0586098 + 0.101515i
\(656\) 0 0
\(657\) 0 0
\(658\) 18.0000 0.701713
\(659\) 24.0000 41.5692i 0.934907 1.61931i 0.160108 0.987099i \(-0.448816\pi\)
0.774799 0.632207i \(-0.217851\pi\)
\(660\) 0 0
\(661\) −1.00000 1.73205i −0.0388955 0.0673690i 0.845922 0.533306i \(-0.179051\pi\)
−0.884818 + 0.465937i \(0.845717\pi\)
\(662\) 7.00000 + 12.1244i 0.272063 + 0.471226i
\(663\) 0 0
\(664\) −3.00000 + 5.19615i −0.116423 + 0.201650i
\(665\) −8.00000 −0.310227
\(666\) 0 0
\(667\) 27.0000 1.04544
\(668\) −6.00000 + 10.3923i −0.232147 + 0.402090i
\(669\) 0 0
\(670\) −2.00000 3.46410i −0.0772667 0.133830i
\(671\) 3.00000 + 5.19615i 0.115814 + 0.200595i
\(672\) 0 0
\(673\) 11.0000 19.0526i 0.424019 0.734422i −0.572309 0.820038i \(-0.693952\pi\)
0.996328 + 0.0856156i \(0.0272857\pi\)
\(674\) −32.0000 −1.23259
\(675\) 0 0
\(676\) 12.0000 0.461538
\(677\) 6.00000 10.3923i 0.230599 0.399409i −0.727386 0.686229i \(-0.759265\pi\)
0.957984 + 0.286820i \(0.0925982\pi\)
\(678\) 0 0
\(679\) −2.00000 3.46410i −0.0767530 0.132940i
\(680\) 1.50000 + 2.59808i 0.0575224 + 0.0996317i
\(681\) 0 0
\(682\) −7.50000 + 12.9904i −0.287190 + 0.497427i
\(683\) 48.0000 1.83667 0.918334 0.395805i \(-0.129534\pi\)
0.918334 + 0.395805i \(0.129534\pi\)
\(684\) 0 0
\(685\) 6.00000 0.229248
\(686\) −10.0000 + 17.3205i −0.381802 + 0.661300i
\(687\) 0 0
\(688\) 0.500000 + 0.866025i 0.0190623 + 0.0330169i
\(689\) −30.0000 51.9615i −1.14291 1.97958i
\(690\) 0 0
\(691\) 5.00000 8.66025i 0.190209 0.329452i −0.755110 0.655598i \(-0.772417\pi\)
0.945319 + 0.326146i \(0.105750\pi\)
\(692\) −18.0000 −0.684257
\(693\) 0 0
\(694\) 0 0
\(695\) −1.00000 + 1.73205i −0.0379322 + 0.0657004i
\(696\) 0 0
\(697\) 0 0
\(698\) 7.00000 + 12.1244i 0.264954 + 0.458914i
\(699\) 0 0
\(700\) −1.00000 + 1.73205i −0.0377964 + 0.0654654i
\(701\) −21.0000 −0.793159 −0.396580 0.918000i \(-0.629803\pi\)
−0.396580 + 0.918000i \(0.629803\pi\)
\(702\) 0 0
\(703\) 40.0000 1.50863
\(704\) 1.50000 2.59808i 0.0565334 0.0979187i
\(705\) 0 0
\(706\) −1.50000 2.59808i −0.0564532 0.0977799i
\(707\) 15.0000 + 25.9808i 0.564133 + 0.977107i
\(708\) 0 0
\(709\) −10.0000 + 17.3205i −0.375558 + 0.650485i −0.990410 0.138157i \(-0.955882\pi\)
0.614852 + 0.788642i \(0.289216\pi\)
\(710\) 12.0000 0.450352
\(711\) 0 0
\(712\) −12.0000 −0.449719
\(713\) −22.5000 + 38.9711i −0.842632 + 1.45948i
\(714\) 0 0
\(715\) 7.50000 + 12.9904i 0.280484 + 0.485813i
\(716\) 6.00000 + 10.3923i 0.224231 + 0.388379i
\(717\) 0 0
\(718\) −6.00000 + 10.3923i −0.223918 + 0.387837i
\(719\) 30.0000 1.11881 0.559406 0.828894i \(-0.311029\pi\)
0.559406 + 0.828894i \(0.311029\pi\)
\(720\) 0 0
\(721\) 4.00000 0.148968
\(722\) −1.50000 + 2.59808i −0.0558242 + 0.0966904i
\(723\) 0 0
\(724\) −10.0000 17.3205i −0.371647 0.643712i
\(725\) −1.50000 2.59808i −0.0557086 0.0964901i
\(726\) 0 0
\(727\) −22.0000 + 38.1051i −0.815935 + 1.41324i 0.0927199 + 0.995692i \(0.470444\pi\)
−0.908655 + 0.417548i \(0.862889\pi\)
\(728\) −10.0000 −0.370625
\(729\) 0 0
\(730\) 10.0000 0.370117
\(731\) 1.50000 2.59808i 0.0554795 0.0960933i
\(732\) 0 0
\(733\) 11.0000 + 19.0526i 0.406294 + 0.703722i 0.994471 0.105010i \(-0.0334875\pi\)
−0.588177 + 0.808732i \(0.700154\pi\)
\(734\) 13.0000 + 22.5167i 0.479839 + 0.831105i
\(735\) 0 0
\(736\) 4.50000 7.79423i 0.165872 0.287299i
\(737\) 12.0000 0.442026
\(738\) 0 0
\(739\) 20.0000 0.735712 0.367856 0.929883i \(-0.380092\pi\)
0.367856 + 0.929883i \(0.380092\pi\)
\(740\) 5.00000 8.66025i 0.183804 0.318357i
\(741\) 0 0
\(742\) 12.0000 + 20.7846i 0.440534 + 0.763027i
\(743\) −13.5000 23.3827i −0.495267 0.857828i 0.504718 0.863284i \(-0.331596\pi\)
−0.999985 + 0.00545664i \(0.998263\pi\)
\(744\) 0 0
\(745\) 10.5000 18.1865i 0.384690 0.666303i
\(746\) 1.00000 0.0366126
\(747\) 0 0
\(748\) −9.00000 −0.329073
\(749\) 6.00000 10.3923i 0.219235 0.379727i
\(750\) 0 0
\(751\) 12.5000 + 21.6506i 0.456131 + 0.790043i 0.998752 0.0499348i \(-0.0159013\pi\)
−0.542621 + 0.839978i \(0.682568\pi\)
\(752\) 4.50000 + 7.79423i 0.164098 + 0.284226i
\(753\) 0 0
\(754\) 7.50000 12.9904i 0.273134 0.473082i
\(755\) 11.0000 0.400331
\(756\) 0 0
\(757\) −13.0000 −0.472493 −0.236247 0.971693i \(-0.575917\pi\)
−0.236247 + 0.971693i \(0.575917\pi\)
\(758\) −8.00000 + 13.8564i −0.290573 + 0.503287i
\(759\) 0 0
\(760\) −2.00000 3.46410i −0.0725476 0.125656i
\(761\) −9.00000 15.5885i −0.326250 0.565081i 0.655515 0.755182i \(-0.272452\pi\)
−0.981764 + 0.190101i \(0.939118\pi\)
\(762\) 0 0
\(763\) −20.0000 + 34.6410i −0.724049 + 1.25409i
\(764\) −6.00000 −0.217072
\(765\) 0 0
\(766\) −9.00000 −0.325183
\(767\) 30.0000 51.9615i 1.08324 1.87622i
\(768\) 0 0
\(769\) −11.5000 19.9186i −0.414701 0.718283i 0.580696 0.814120i \(-0.302780\pi\)
−0.995397 + 0.0958377i \(0.969447\pi\)
\(770\) −3.00000 5.19615i −0.108112 0.187256i
\(771\) 0 0
\(772\) 5.00000 8.66025i 0.179954 0.311689i
\(773\) 42.0000 1.51064 0.755318 0.655359i \(-0.227483\pi\)
0.755318 + 0.655359i \(0.227483\pi\)
\(774\) 0 0
\(775\) 5.00000 0.179605
\(776\) 1.00000 1.73205i 0.0358979 0.0621770i
\(777\) 0 0
\(778\) −4.50000 7.79423i −0.161333 0.279437i
\(779\) 0 0
\(780\) 0 0
\(781\) −18.0000 + 31.1769i −0.644091 + 1.11560i
\(782\) −27.0000 −0.965518
\(783\) 0 0
\(784\) −3.00000 −0.107143
\(785\) 6.50000 11.2583i 0.231995 0.401827i
\(786\) 0 0
\(787\) 0.500000 + 0.866025i 0.0178231 + 0.0308705i 0.874799 0.484485i \(-0.160993\pi\)
−0.856976 + 0.515356i \(0.827660\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) −6.50000 + 11.2583i −0.231260 + 0.400553i
\(791\) 30.0000 1.06668
\(792\) 0 0
\(793\) 10.0000 0.355110
\(794\) −3.50000 + 6.06218i −0.124210 + 0.215139i
\(795\) 0 0
\(796\) 3.50000 + 6.06218i 0.124054 + 0.214868i
\(797\) −18.0000 31.1769i −0.637593 1.10434i −0.985959 0.166985i \(-0.946597\pi\)
0.348367 0.937358i \(-0.386736\pi\)
\(798\) 0 0
\(799\) 13.5000 23.3827i 0.477596 0.827220i
\(800\) −1.00000 −0.0353553
\(801\) 0 0
\(802\) 36.0000 1.27120
\(803\) −15.0000 + 25.9808i −0.529339 + 0.916841i
\(804\) 0 0
\(805\) −9.00000 15.5885i −0.317208 0.549421i
\(806\) 12.5000 + 21.6506i 0.440294 + 0.762611i
\(807\) 0 0
\(808\) −7.50000 + 12.9904i −0.263849 + 0.457000i
\(809\) −24.0000 −0.843795 −0.421898 0.906644i \(-0.638636\pi\)
−0.421898 + 0.906644i \(0.638636\pi\)
\(810\) 0 0
\(811\) 38.0000 1.33436 0.667180 0.744896i \(-0.267501\pi\)
0.667180 + 0.744896i \(0.267501\pi\)
\(812\) −3.00000 + 5.19615i −0.105279 + 0.182349i
\(813\) 0 0
\(814\) 15.0000 + 25.9808i 0.525750 + 0.910625i
\(815\) −5.50000 9.52628i −0.192657 0.333691i
\(816\) 0 0
\(817\) −2.00000 + 3.46410i −0.0699711 + 0.121194i
\(818\) −23.0000 −0.804176
\(819\) 0 0
\(820\) 0 0
\(821\) −21.0000 + 36.3731i −0.732905 + 1.26943i 0.222731 + 0.974880i \(0.428503\pi\)
−0.955636 + 0.294549i \(0.904831\pi\)
\(822\) 0 0
\(823\) 2.00000 + 3.46410i 0.0697156 + 0.120751i 0.898776 0.438408i \(-0.144457\pi\)
−0.829060 + 0.559159i \(0.811124\pi\)
\(824\) 1.00000 + 1.73205i 0.0348367 + 0.0603388i
\(825\) 0 0
\(826\) −12.0000 + 20.7846i −0.417533 + 0.723189i
\(827\) 42.0000 1.46048 0.730242 0.683189i \(-0.239408\pi\)
0.730242 + 0.683189i \(0.239408\pi\)
\(828\) 0 0
\(829\) 44.0000 1.52818 0.764092 0.645108i \(-0.223188\pi\)
0.764092 + 0.645108i \(0.223188\pi\)
\(830\) −3.00000 + 5.19615i −0.104132 + 0.180361i
\(831\) 0 0
\(832\) −2.50000 4.33013i −0.0866719 0.150120i
\(833\) 4.50000 + 7.79423i 0.155916 + 0.270054i
\(834\) 0 0
\(835\) −6.00000 + 10.3923i −0.207639 + 0.359641i
\(836\) 12.0000 0.415029
\(837\) 0 0
\(838\) −3.00000 −0.103633
\(839\) 3.00000 5.19615i 0.103572 0.179391i −0.809582 0.587007i \(-0.800306\pi\)
0.913154 + 0.407615i \(0.133640\pi\)
\(840\) 0 0
\(841\) 10.0000 + 17.3205i 0.344828 + 0.597259i
\(842\) −2.00000 3.46410i −0.0689246 0.119381i
\(843\) 0 0
\(844\) 11.0000 19.0526i 0.378636 0.655816i
\(845\) 12.0000 0.412813
\(846\) 0 0
\(847\) −4.00000 −0.137442
\(848\) −6.00000 + 10.3923i −0.206041 + 0.356873i
\(849\) 0 0
\(850\) 1.50000 + 2.59808i 0.0514496 + 0.0891133i
\(851\) 45.0000 + 77.9423i 1.54258 + 2.67183i
\(852\) 0 0
\(853\) 9.50000 16.4545i 0.325274 0.563391i −0.656294 0.754505i \(-0.727877\pi\)
0.981568 + 0.191115i \(0.0612102\pi\)
\(854\) −4.00000 −0.136877
\(855\) 0 0
\(856\) 6.00000 0.205076
\(857\) −3.00000 + 5.19615i −0.102478 + 0.177497i −0.912705 0.408619i \(-0.866010\pi\)
0.810227 + 0.586116i \(0.199344\pi\)
\(858\) 0 0
\(859\) −1.00000 1.73205i −0.0341196 0.0590968i 0.848461 0.529257i \(-0.177529\pi\)
−0.882581 + 0.470160i \(0.844196\pi\)
\(860\) 0.500000 + 0.866025i 0.0170499 + 0.0295312i
\(861\) 0 0
\(862\) 0 0
\(863\) −21.0000 −0.714848 −0.357424 0.933942i \(-0.616345\pi\)
−0.357424 + 0.933942i \(0.616345\pi\)
\(864\) 0 0
\(865\) −18.0000 −0.612018
\(866\) 1.00000 1.73205i 0.0339814 0.0588575i
\(867\) 0 0
\(868\) −5.00000 8.66025i −0.169711 0.293948i
\(869\) −19.5000 33.7750i −0.661492 1.14574i
\(870\) 0 0
\(871\) 10.0000 17.3205i 0.338837 0.586883i
\(872\) −20.0000 −0.677285
\(873\) 0 0
\(874\) 36.0000 1.21772
\(875\) −1.00000 + 1.73205i −0.0338062 + 0.0585540i
\(876\) 0 0
\(877\) 0.500000 + 0.866025i 0.0168838 + 0.0292436i 0.874344 0.485307i \(-0.161292\pi\)
−0.857460 + 0.514551i \(0.827959\pi\)
\(878\) 4.00000 + 6.92820i 0.134993 + 0.233816i
\(879\) 0 0
\(880\) 1.50000 2.59808i 0.0505650 0.0875811i
\(881\) 18.0000 0.606435 0.303218 0.952921i \(-0.401939\pi\)
0.303218 + 0.952921i \(0.401939\pi\)
\(882\) 0 0
\(883\) −4.00000 −0.134611 −0.0673054 0.997732i \(-0.521440\pi\)
−0.0673054 + 0.997732i \(0.521440\pi\)
\(884\) −7.50000 + 12.9904i −0.252252 + 0.436914i
\(885\) 0 0
\(886\) 6.00000 + 10.3923i 0.201574 + 0.349136i
\(887\) −1.50000 2.59808i −0.0503651 0.0872349i 0.839744 0.542983i \(-0.182705\pi\)
−0.890109 + 0.455748i \(0.849372\pi\)
\(888\) 0 0
\(889\) −2.00000 + 3.46410i −0.0670778 + 0.116182i
\(890\) −12.0000 −0.402241
\(891\) 0 0
\(892\) 8.00000 0.267860
\(893\) −18.0000 + 31.1769i −0.602347 + 1.04330i
\(894\) 0 0
\(895\) 6.00000 + 10.3923i 0.200558 + 0.347376i
\(896\) 1.00000 + 1.73205i 0.0334077 + 0.0578638i
\(897\) 0 0
\(898\) 3.00000 5.19615i 0.100111 0.173398i
\(899\) 15.0000 0.500278
\(900\) 0 0
\(901\) 36.0000 1.19933
\(902\) 0 0
\(903\) 0 0
\(904\) 7.50000 + 12.9904i 0.249446 + 0.432054i
\(905\) −10.0000 17.3205i −0.332411 0.575753i
\(906\) 0 0
\(907\) −29.5000 + 51.0955i −0.979531 + 1.69660i −0.315442 + 0.948945i \(0.602153\pi\)
−0.664089 + 0.747653i \(0.731180\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) −10.0000 −0.331497
\(911\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(912\) 0 0
\(913\) −9.00000 15.5885i −0.297857 0.515903i
\(914\) −14.0000 24.2487i −0.463079 0.802076i
\(915\) 0 0
\(916\) 2.00000 3.46410i 0.0660819 0.114457i
\(917\) 6.00000 0.198137
\(918\) 0 0
\(919\) −25.0000 −0.824674 −0.412337 0.911031i \(-0.635287\pi\)
−0.412337 + 0.911031i \(0.635287\pi\)
\(920\) 4.50000 7.79423i 0.148361 0.256968i
\(921\) 0 0
\(922\) −9.00000 15.5885i −0.296399 0.513378i
\(923\) 30.0000 + 51.9615i 0.987462 + 1.71033i
\(924\) 0 0
\(925\) 5.00000 8.66025i 0.164399 0.284747i
\(926\) −38.0000 −1.24876
\(927\) 0 0
\(928\) −3.00000 −0.0984798
\(929\) 18.0000 31.1769i 0.590561 1.02288i −0.403596 0.914937i \(-0.632240\pi\)
0.994157 0.107944i \(-0.0344268\pi\)
\(930\) 0 0
\(931\) −6.00000 10.3923i −0.196642 0.340594i
\(932\) 3.00000 + 5.19615i 0.0982683 + 0.170206i
\(933\) 0 0
\(934\) −6.00000 + 10.3923i −0.196326 + 0.340047i
\(935\) −9.00000 −0.294331
\(936\) 0 0
\(937\) −22.0000 −0.718709 −0.359354 0.933201i \(-0.617003\pi\)
−0.359354 + 0.933201i \(0.617003\pi\)
\(938\) −4.00000 + 6.92820i −0.130605 + 0.226214i
\(939\) 0 0
\(940\) 4.50000 + 7.79423i 0.146774 + 0.254220i
\(941\) 16.5000 + 28.5788i 0.537885 + 0.931644i 0.999018 + 0.0443125i \(0.0141097\pi\)
−0.461133 + 0.887331i \(0.652557\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) −12.0000 −0.390567
\(945\) 0 0
\(946\) −3.00000 −0.0975384
\(947\) −21.0000 + 36.3731i −0.682408 + 1.18197i 0.291835 + 0.956469i \(0.405734\pi\)
−0.974244 + 0.225497i \(0.927599\pi\)
\(948\) 0 0
\(949\) 25.0000 + 43.3013i 0.811534 + 1.40562i
\(950\) −2.00000 3.46410i −0.0648886 0.112390i
\(951\) 0 0
\(952\) 3.00000 5.19615i 0.0972306 0.168408i
\(953\) −15.0000 −0.485898 −0.242949 0.970039i \(-0.578115\pi\)
−0.242949 + 0.970039i \(0.578115\pi\)
\(954\) 0 0
\(955\) −6.00000 −0.194155
\(956\) −3.00000 + 5.19615i −0.0970269 + 0.168056i
\(957\) 0 0
\(958\) −18.0000 31.1769i −0.581554 1.00728i
\(959\) −6.00000 10.3923i −0.193750 0.335585i
\(960\) 0 0
\(961\) 3.00000 5.19615i 0.0967742 0.167618i
\(962\) 50.0000 1.61206
\(963\) 0 0
\(964\) −19.0000 −0.611949
\(965\) 5.00000 8.66025i 0.160956 0.278783i
\(966\) 0 0
\(967\) −1.00000 1.73205i −0.0321578 0.0556990i 0.849499 0.527591i \(-0.176905\pi\)
−0.881656 + 0.471892i \(0.843571\pi\)
\(968\) −1.00000 1.73205i −0.0321412 0.0556702i
\(969\) 0 0
\(970\) 1.00000 1.73205i 0.0321081 0.0556128i
\(971\) 57.0000 1.82922 0.914609 0.404341i \(-0.132499\pi\)
0.914609 + 0.404341i \(0.132499\pi\)
\(972\) 0 0
\(973\) 4.00000 0.128234
\(974\) 10.0000 17.3205i 0.320421 0.554985i
\(975\) 0 0
\(976\) −1.00000 1.73205i −0.0320092 0.0554416i
\(977\) 16.5000 + 28.5788i 0.527882 + 0.914318i 0.999472 + 0.0325001i \(0.0103469\pi\)
−0.471590 + 0.881818i \(0.656320\pi\)
\(978\) 0 0
\(979\) 18.0000 31.1769i 0.575282 0.996419i
\(980\) −3.00000 −0.0958315
\(981\) 0 0
\(982\) −12.0000 −0.382935
\(983\) 19.5000 33.7750i 0.621953 1.07725i −0.367168 0.930155i \(-0.619673\pi\)
0.989122 0.147100i \(-0.0469940\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 4.50000 + 7.79423i 0.143309 + 0.248219i
\(987\) 0 0
\(988\) 10.0000 17.3205i 0.318142 0.551039i
\(989\) −9.00000 −0.286183
\(990\) 0 0
\(991\) 5.00000 0.158830 0.0794151 0.996842i \(-0.474695\pi\)
0.0794151 + 0.996842i \(0.474695\pi\)
\(992\) 2.50000 4.33013i 0.0793751 0.137482i
\(993\) 0 0
\(994\) −12.0000 20.7846i −0.380617 0.659248i
\(995\) 3.50000 + 6.06218i 0.110957 + 0.192184i
\(996\) 0 0
\(997\) 18.5000 32.0429i 0.585901 1.01481i −0.408862 0.912596i \(-0.634074\pi\)
0.994762 0.102214i \(-0.0325925\pi\)
\(998\) 4.00000 0.126618
\(999\) 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 810.2.e.i.541.1 2
3.2 odd 2 810.2.e.d.541.1 2
9.2 odd 6 270.2.a.c.1.1 yes 1
9.4 even 3 inner 810.2.e.i.271.1 2
9.5 odd 6 810.2.e.d.271.1 2
9.7 even 3 270.2.a.b.1.1 1
36.7 odd 6 2160.2.a.q.1.1 1
36.11 even 6 2160.2.a.b.1.1 1
45.2 even 12 1350.2.c.j.649.2 2
45.7 odd 12 1350.2.c.c.649.1 2
45.29 odd 6 1350.2.a.d.1.1 1
45.34 even 6 1350.2.a.o.1.1 1
45.38 even 12 1350.2.c.j.649.1 2
45.43 odd 12 1350.2.c.c.649.2 2
72.11 even 6 8640.2.a.bn.1.1 1
72.29 odd 6 8640.2.a.bx.1.1 1
72.43 odd 6 8640.2.a.e.1.1 1
72.61 even 6 8640.2.a.y.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
270.2.a.b.1.1 1 9.7 even 3
270.2.a.c.1.1 yes 1 9.2 odd 6
810.2.e.d.271.1 2 9.5 odd 6
810.2.e.d.541.1 2 3.2 odd 2
810.2.e.i.271.1 2 9.4 even 3 inner
810.2.e.i.541.1 2 1.1 even 1 trivial
1350.2.a.d.1.1 1 45.29 odd 6
1350.2.a.o.1.1 1 45.34 even 6
1350.2.c.c.649.1 2 45.7 odd 12
1350.2.c.c.649.2 2 45.43 odd 12
1350.2.c.j.649.1 2 45.38 even 12
1350.2.c.j.649.2 2 45.2 even 12
2160.2.a.b.1.1 1 36.11 even 6
2160.2.a.q.1.1 1 36.7 odd 6
8640.2.a.e.1.1 1 72.43 odd 6
8640.2.a.y.1.1 1 72.61 even 6
8640.2.a.bn.1.1 1 72.11 even 6
8640.2.a.bx.1.1 1 72.29 odd 6