Properties

Label 2106.2.e.z.1405.1
Level $2106$
Weight $2$
Character 2106.1405
Analytic conductor $16.816$
Analytic rank $0$
Dimension $2$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [2106,2,Mod(703,2106)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2106, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("2106.703");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2106 = 2 \cdot 3^{4} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2106.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: \(16.8164946657\)
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 234)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 1405.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 2106.1405
Dual form 2106.2.e.z.703.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(1.00000 - 1.73205i) q^{5} +(1.00000 + 1.73205i) q^{7} -1.00000 q^{8} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(1.00000 - 1.73205i) q^{5} +(1.00000 + 1.73205i) q^{7} -1.00000 q^{8} +2.00000 q^{10} +(2.00000 + 3.46410i) q^{11} +(0.500000 - 0.866025i) q^{13} +(-1.00000 + 1.73205i) q^{14} +(-0.500000 - 0.866025i) q^{16} -6.00000 q^{19} +(1.00000 + 1.73205i) q^{20} +(-2.00000 + 3.46410i) q^{22} +(-2.00000 + 3.46410i) q^{23} +(0.500000 + 0.866025i) q^{25} +1.00000 q^{26} -2.00000 q^{28} +(4.00000 + 6.92820i) q^{29} +(1.00000 - 1.73205i) q^{31} +(0.500000 - 0.866025i) q^{32} +4.00000 q^{35} +6.00000 q^{37} +(-3.00000 - 5.19615i) q^{38} +(-1.00000 + 1.73205i) q^{40} +(-3.00000 + 5.19615i) q^{41} +(4.00000 + 6.92820i) q^{43} -4.00000 q^{44} -4.00000 q^{46} +(-4.00000 - 6.92820i) q^{47} +(1.50000 - 2.59808i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(0.500000 + 0.866025i) q^{52} +12.0000 q^{53} +8.00000 q^{55} +(-1.00000 - 1.73205i) q^{56} +(-4.00000 + 6.92820i) q^{58} +(-2.00000 + 3.46410i) q^{59} +(-5.00000 - 8.66025i) q^{61} +2.00000 q^{62} +1.00000 q^{64} +(-1.00000 - 1.73205i) q^{65} +(1.00000 - 1.73205i) q^{67} +(2.00000 + 3.46410i) q^{70} -16.0000 q^{71} +14.0000 q^{73} +(3.00000 + 5.19615i) q^{74} +(3.00000 - 5.19615i) q^{76} +(-4.00000 + 6.92820i) q^{77} +(2.00000 + 3.46410i) q^{79} -2.00000 q^{80} -6.00000 q^{82} +(6.00000 + 10.3923i) q^{83} +(-4.00000 + 6.92820i) q^{86} +(-2.00000 - 3.46410i) q^{88} -6.00000 q^{89} +2.00000 q^{91} +(-2.00000 - 3.46410i) q^{92} +(4.00000 - 6.92820i) q^{94} +(-6.00000 + 10.3923i) q^{95} +(5.00000 + 8.66025i) q^{97} +3.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + q^{2} - q^{4} + 2 q^{5} + 2 q^{7} - 2 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + q^{2} - q^{4} + 2 q^{5} + 2 q^{7} - 2 q^{8} + 4 q^{10} + 4 q^{11} + q^{13} - 2 q^{14} - q^{16} - 12 q^{19} + 2 q^{20} - 4 q^{22} - 4 q^{23} + q^{25} + 2 q^{26} - 4 q^{28} + 8 q^{29} + 2 q^{31} + q^{32} + 8 q^{35} + 12 q^{37} - 6 q^{38} - 2 q^{40} - 6 q^{41} + 8 q^{43} - 8 q^{44} - 8 q^{46} - 8 q^{47} + 3 q^{49} - q^{50} + q^{52} + 24 q^{53} + 16 q^{55} - 2 q^{56} - 8 q^{58} - 4 q^{59} - 10 q^{61} + 4 q^{62} + 2 q^{64} - 2 q^{65} + 2 q^{67} + 4 q^{70} - 32 q^{71} + 28 q^{73} + 6 q^{74} + 6 q^{76} - 8 q^{77} + 4 q^{79} - 4 q^{80} - 12 q^{82} + 12 q^{83} - 8 q^{86} - 4 q^{88} - 12 q^{89} + 4 q^{91} - 4 q^{92} + 8 q^{94} - 12 q^{95} + 10 q^{97} + 6 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2106\mathbb{Z}\right)^\times\).

\(n\) \(1379\) \(1783\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 + 0.866025i 0.353553 + 0.612372i
\(3\) 0 0
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) 1.00000 1.73205i 0.447214 0.774597i −0.550990 0.834512i \(-0.685750\pi\)
0.998203 + 0.0599153i \(0.0190830\pi\)
\(6\) 0 0
\(7\) 1.00000 + 1.73205i 0.377964 + 0.654654i 0.990766 0.135583i \(-0.0432908\pi\)
−0.612801 + 0.790237i \(0.709957\pi\)
\(8\) −1.00000 −0.353553
\(9\) 0 0
\(10\) 2.00000 0.632456
\(11\) 2.00000 + 3.46410i 0.603023 + 1.04447i 0.992361 + 0.123371i \(0.0393705\pi\)
−0.389338 + 0.921095i \(0.627296\pi\)
\(12\) 0 0
\(13\) 0.500000 0.866025i 0.138675 0.240192i
\(14\) −1.00000 + 1.73205i −0.267261 + 0.462910i
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(18\) 0 0
\(19\) −6.00000 −1.37649 −0.688247 0.725476i \(-0.741620\pi\)
−0.688247 + 0.725476i \(0.741620\pi\)
\(20\) 1.00000 + 1.73205i 0.223607 + 0.387298i
\(21\) 0 0
\(22\) −2.00000 + 3.46410i −0.426401 + 0.738549i
\(23\) −2.00000 + 3.46410i −0.417029 + 0.722315i −0.995639 0.0932891i \(-0.970262\pi\)
0.578610 + 0.815604i \(0.303595\pi\)
\(24\) 0 0
\(25\) 0.500000 + 0.866025i 0.100000 + 0.173205i
\(26\) 1.00000 0.196116
\(27\) 0 0
\(28\) −2.00000 −0.377964
\(29\) 4.00000 + 6.92820i 0.742781 + 1.28654i 0.951224 + 0.308500i \(0.0998271\pi\)
−0.208443 + 0.978035i \(0.566840\pi\)
\(30\) 0 0
\(31\) 1.00000 1.73205i 0.179605 0.311086i −0.762140 0.647412i \(-0.775851\pi\)
0.941745 + 0.336327i \(0.109185\pi\)
\(32\) 0.500000 0.866025i 0.0883883 0.153093i
\(33\) 0 0
\(34\) 0 0
\(35\) 4.00000 0.676123
\(36\) 0 0
\(37\) 6.00000 0.986394 0.493197 0.869918i \(-0.335828\pi\)
0.493197 + 0.869918i \(0.335828\pi\)
\(38\) −3.00000 5.19615i −0.486664 0.842927i
\(39\) 0 0
\(40\) −1.00000 + 1.73205i −0.158114 + 0.273861i
\(41\) −3.00000 + 5.19615i −0.468521 + 0.811503i −0.999353 0.0359748i \(-0.988546\pi\)
0.530831 + 0.847477i \(0.321880\pi\)
\(42\) 0 0
\(43\) 4.00000 + 6.92820i 0.609994 + 1.05654i 0.991241 + 0.132068i \(0.0421616\pi\)
−0.381246 + 0.924473i \(0.624505\pi\)
\(44\) −4.00000 −0.603023
\(45\) 0 0
\(46\) −4.00000 −0.589768
\(47\) −4.00000 6.92820i −0.583460 1.01058i −0.995066 0.0992202i \(-0.968365\pi\)
0.411606 0.911362i \(-0.364968\pi\)
\(48\) 0 0
\(49\) 1.50000 2.59808i 0.214286 0.371154i
\(50\) −0.500000 + 0.866025i −0.0707107 + 0.122474i
\(51\) 0 0
\(52\) 0.500000 + 0.866025i 0.0693375 + 0.120096i
\(53\) 12.0000 1.64833 0.824163 0.566352i \(-0.191646\pi\)
0.824163 + 0.566352i \(0.191646\pi\)
\(54\) 0 0
\(55\) 8.00000 1.07872
\(56\) −1.00000 1.73205i −0.133631 0.231455i
\(57\) 0 0
\(58\) −4.00000 + 6.92820i −0.525226 + 0.909718i
\(59\) −2.00000 + 3.46410i −0.260378 + 0.450988i −0.966342 0.257260i \(-0.917180\pi\)
0.705965 + 0.708247i \(0.250514\pi\)
\(60\) 0 0
\(61\) −5.00000 8.66025i −0.640184 1.10883i −0.985391 0.170305i \(-0.945525\pi\)
0.345207 0.938527i \(-0.387809\pi\)
\(62\) 2.00000 0.254000
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) −1.00000 1.73205i −0.124035 0.214834i
\(66\) 0 0
\(67\) 1.00000 1.73205i 0.122169 0.211604i −0.798454 0.602056i \(-0.794348\pi\)
0.920623 + 0.390453i \(0.127682\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 2.00000 + 3.46410i 0.239046 + 0.414039i
\(71\) −16.0000 −1.89885 −0.949425 0.313993i \(-0.898333\pi\)
−0.949425 + 0.313993i \(0.898333\pi\)
\(72\) 0 0
\(73\) 14.0000 1.63858 0.819288 0.573382i \(-0.194369\pi\)
0.819288 + 0.573382i \(0.194369\pi\)
\(74\) 3.00000 + 5.19615i 0.348743 + 0.604040i
\(75\) 0 0
\(76\) 3.00000 5.19615i 0.344124 0.596040i
\(77\) −4.00000 + 6.92820i −0.455842 + 0.789542i
\(78\) 0 0
\(79\) 2.00000 + 3.46410i 0.225018 + 0.389742i 0.956325 0.292306i \(-0.0944227\pi\)
−0.731307 + 0.682048i \(0.761089\pi\)
\(80\) −2.00000 −0.223607
\(81\) 0 0
\(82\) −6.00000 −0.662589
\(83\) 6.00000 + 10.3923i 0.658586 + 1.14070i 0.980982 + 0.194099i \(0.0621783\pi\)
−0.322396 + 0.946605i \(0.604488\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −4.00000 + 6.92820i −0.431331 + 0.747087i
\(87\) 0 0
\(88\) −2.00000 3.46410i −0.213201 0.369274i
\(89\) −6.00000 −0.635999 −0.317999 0.948091i \(-0.603011\pi\)
−0.317999 + 0.948091i \(0.603011\pi\)
\(90\) 0 0
\(91\) 2.00000 0.209657
\(92\) −2.00000 3.46410i −0.208514 0.361158i
\(93\) 0 0
\(94\) 4.00000 6.92820i 0.412568 0.714590i
\(95\) −6.00000 + 10.3923i −0.615587 + 1.06623i
\(96\) 0 0
\(97\) 5.00000 + 8.66025i 0.507673 + 0.879316i 0.999961 + 0.00888289i \(0.00282755\pi\)
−0.492287 + 0.870433i \(0.663839\pi\)
\(98\) 3.00000 0.303046
\(99\) 0 0
\(100\) −1.00000 −0.100000
\(101\) 8.00000 + 13.8564i 0.796030 + 1.37876i 0.922183 + 0.386753i \(0.126403\pi\)
−0.126153 + 0.992011i \(0.540263\pi\)
\(102\) 0 0
\(103\) −2.00000 + 3.46410i −0.197066 + 0.341328i −0.947576 0.319531i \(-0.896475\pi\)
0.750510 + 0.660859i \(0.229808\pi\)
\(104\) −0.500000 + 0.866025i −0.0490290 + 0.0849208i
\(105\) 0 0
\(106\) 6.00000 + 10.3923i 0.582772 + 1.00939i
\(107\) −20.0000 −1.93347 −0.966736 0.255774i \(-0.917670\pi\)
−0.966736 + 0.255774i \(0.917670\pi\)
\(108\) 0 0
\(109\) 10.0000 0.957826 0.478913 0.877862i \(-0.341031\pi\)
0.478913 + 0.877862i \(0.341031\pi\)
\(110\) 4.00000 + 6.92820i 0.381385 + 0.660578i
\(111\) 0 0
\(112\) 1.00000 1.73205i 0.0944911 0.163663i
\(113\) −2.00000 + 3.46410i −0.188144 + 0.325875i −0.944632 0.328133i \(-0.893581\pi\)
0.756487 + 0.654008i \(0.226914\pi\)
\(114\) 0 0
\(115\) 4.00000 + 6.92820i 0.373002 + 0.646058i
\(116\) −8.00000 −0.742781
\(117\) 0 0
\(118\) −4.00000 −0.368230
\(119\) 0 0
\(120\) 0 0
\(121\) −2.50000 + 4.33013i −0.227273 + 0.393648i
\(122\) 5.00000 8.66025i 0.452679 0.784063i
\(123\) 0 0
\(124\) 1.00000 + 1.73205i 0.0898027 + 0.155543i
\(125\) 12.0000 1.07331
\(126\) 0 0
\(127\) −8.00000 −0.709885 −0.354943 0.934888i \(-0.615500\pi\)
−0.354943 + 0.934888i \(0.615500\pi\)
\(128\) 0.500000 + 0.866025i 0.0441942 + 0.0765466i
\(129\) 0 0
\(130\) 1.00000 1.73205i 0.0877058 0.151911i
\(131\) −2.00000 + 3.46410i −0.174741 + 0.302660i −0.940072 0.340977i \(-0.889242\pi\)
0.765331 + 0.643637i \(0.222575\pi\)
\(132\) 0 0
\(133\) −6.00000 10.3923i −0.520266 0.901127i
\(134\) 2.00000 0.172774
\(135\) 0 0
\(136\) 0 0
\(137\) 9.00000 + 15.5885i 0.768922 + 1.33181i 0.938148 + 0.346235i \(0.112540\pi\)
−0.169226 + 0.985577i \(0.554127\pi\)
\(138\) 0 0
\(139\) 10.0000 17.3205i 0.848189 1.46911i −0.0346338 0.999400i \(-0.511026\pi\)
0.882823 0.469706i \(-0.155640\pi\)
\(140\) −2.00000 + 3.46410i −0.169031 + 0.292770i
\(141\) 0 0
\(142\) −8.00000 13.8564i −0.671345 1.16280i
\(143\) 4.00000 0.334497
\(144\) 0 0
\(145\) 16.0000 1.32873
\(146\) 7.00000 + 12.1244i 0.579324 + 1.00342i
\(147\) 0 0
\(148\) −3.00000 + 5.19615i −0.246598 + 0.427121i
\(149\) 3.00000 5.19615i 0.245770 0.425685i −0.716578 0.697507i \(-0.754293\pi\)
0.962348 + 0.271821i \(0.0876260\pi\)
\(150\) 0 0
\(151\) −9.00000 15.5885i −0.732410 1.26857i −0.955851 0.293853i \(-0.905062\pi\)
0.223441 0.974717i \(-0.428271\pi\)
\(152\) 6.00000 0.486664
\(153\) 0 0
\(154\) −8.00000 −0.644658
\(155\) −2.00000 3.46410i −0.160644 0.278243i
\(156\) 0 0
\(157\) −1.00000 + 1.73205i −0.0798087 + 0.138233i −0.903167 0.429289i \(-0.858764\pi\)
0.823359 + 0.567521i \(0.192098\pi\)
\(158\) −2.00000 + 3.46410i −0.159111 + 0.275589i
\(159\) 0 0
\(160\) −1.00000 1.73205i −0.0790569 0.136931i
\(161\) −8.00000 −0.630488
\(162\) 0 0
\(163\) −10.0000 −0.783260 −0.391630 0.920123i \(-0.628089\pi\)
−0.391630 + 0.920123i \(0.628089\pi\)
\(164\) −3.00000 5.19615i −0.234261 0.405751i
\(165\) 0 0
\(166\) −6.00000 + 10.3923i −0.465690 + 0.806599i
\(167\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(168\) 0 0
\(169\) −0.500000 0.866025i −0.0384615 0.0666173i
\(170\) 0 0
\(171\) 0 0
\(172\) −8.00000 −0.609994
\(173\) −8.00000 13.8564i −0.608229 1.05348i −0.991532 0.129861i \(-0.958547\pi\)
0.383304 0.923622i \(-0.374786\pi\)
\(174\) 0 0
\(175\) −1.00000 + 1.73205i −0.0755929 + 0.130931i
\(176\) 2.00000 3.46410i 0.150756 0.261116i
\(177\) 0 0
\(178\) −3.00000 5.19615i −0.224860 0.389468i
\(179\) 12.0000 0.896922 0.448461 0.893802i \(-0.351972\pi\)
0.448461 + 0.893802i \(0.351972\pi\)
\(180\) 0 0
\(181\) −18.0000 −1.33793 −0.668965 0.743294i \(-0.733262\pi\)
−0.668965 + 0.743294i \(0.733262\pi\)
\(182\) 1.00000 + 1.73205i 0.0741249 + 0.128388i
\(183\) 0 0
\(184\) 2.00000 3.46410i 0.147442 0.255377i
\(185\) 6.00000 10.3923i 0.441129 0.764057i
\(186\) 0 0
\(187\) 0 0
\(188\) 8.00000 0.583460
\(189\) 0 0
\(190\) −12.0000 −0.870572
\(191\) 2.00000 + 3.46410i 0.144715 + 0.250654i 0.929267 0.369410i \(-0.120440\pi\)
−0.784552 + 0.620063i \(0.787107\pi\)
\(192\) 0 0
\(193\) −1.00000 + 1.73205i −0.0719816 + 0.124676i −0.899770 0.436365i \(-0.856266\pi\)
0.827788 + 0.561041i \(0.189599\pi\)
\(194\) −5.00000 + 8.66025i −0.358979 + 0.621770i
\(195\) 0 0
\(196\) 1.50000 + 2.59808i 0.107143 + 0.185577i
\(197\) −18.0000 −1.28245 −0.641223 0.767354i \(-0.721573\pi\)
−0.641223 + 0.767354i \(0.721573\pi\)
\(198\) 0 0
\(199\) 8.00000 0.567105 0.283552 0.958957i \(-0.408487\pi\)
0.283552 + 0.958957i \(0.408487\pi\)
\(200\) −0.500000 0.866025i −0.0353553 0.0612372i
\(201\) 0 0
\(202\) −8.00000 + 13.8564i −0.562878 + 0.974933i
\(203\) −8.00000 + 13.8564i −0.561490 + 0.972529i
\(204\) 0 0
\(205\) 6.00000 + 10.3923i 0.419058 + 0.725830i
\(206\) −4.00000 −0.278693
\(207\) 0 0
\(208\) −1.00000 −0.0693375
\(209\) −12.0000 20.7846i −0.830057 1.43770i
\(210\) 0 0
\(211\) −4.00000 + 6.92820i −0.275371 + 0.476957i −0.970229 0.242190i \(-0.922134\pi\)
0.694857 + 0.719148i \(0.255467\pi\)
\(212\) −6.00000 + 10.3923i −0.412082 + 0.713746i
\(213\) 0 0
\(214\) −10.0000 17.3205i −0.683586 1.18401i
\(215\) 16.0000 1.09119
\(216\) 0 0
\(217\) 4.00000 0.271538
\(218\) 5.00000 + 8.66025i 0.338643 + 0.586546i
\(219\) 0 0
\(220\) −4.00000 + 6.92820i −0.269680 + 0.467099i
\(221\) 0 0
\(222\) 0 0
\(223\) −3.00000 5.19615i −0.200895 0.347960i 0.747922 0.663786i \(-0.231052\pi\)
−0.948817 + 0.315826i \(0.897718\pi\)
\(224\) 2.00000 0.133631
\(225\) 0 0
\(226\) −4.00000 −0.266076
\(227\) −6.00000 10.3923i −0.398234 0.689761i 0.595274 0.803523i \(-0.297043\pi\)
−0.993508 + 0.113761i \(0.963710\pi\)
\(228\) 0 0
\(229\) 15.0000 25.9808i 0.991228 1.71686i 0.381157 0.924510i \(-0.375526\pi\)
0.610071 0.792347i \(-0.291141\pi\)
\(230\) −4.00000 + 6.92820i −0.263752 + 0.456832i
\(231\) 0 0
\(232\) −4.00000 6.92820i −0.262613 0.454859i
\(233\) 20.0000 1.31024 0.655122 0.755523i \(-0.272617\pi\)
0.655122 + 0.755523i \(0.272617\pi\)
\(234\) 0 0
\(235\) −16.0000 −1.04372
\(236\) −2.00000 3.46410i −0.130189 0.225494i
\(237\) 0 0
\(238\) 0 0
\(239\) 12.0000 20.7846i 0.776215 1.34444i −0.157893 0.987456i \(-0.550470\pi\)
0.934109 0.356988i \(-0.116196\pi\)
\(240\) 0 0
\(241\) −3.00000 5.19615i −0.193247 0.334714i 0.753077 0.657932i \(-0.228569\pi\)
−0.946324 + 0.323218i \(0.895235\pi\)
\(242\) −5.00000 −0.321412
\(243\) 0 0
\(244\) 10.0000 0.640184
\(245\) −3.00000 5.19615i −0.191663 0.331970i
\(246\) 0 0
\(247\) −3.00000 + 5.19615i −0.190885 + 0.330623i
\(248\) −1.00000 + 1.73205i −0.0635001 + 0.109985i
\(249\) 0 0
\(250\) 6.00000 + 10.3923i 0.379473 + 0.657267i
\(251\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(252\) 0 0
\(253\) −16.0000 −1.00591
\(254\) −4.00000 6.92820i −0.250982 0.434714i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −6.00000 + 10.3923i −0.374270 + 0.648254i −0.990217 0.139533i \(-0.955440\pi\)
0.615948 + 0.787787i \(0.288773\pi\)
\(258\) 0 0
\(259\) 6.00000 + 10.3923i 0.372822 + 0.645746i
\(260\) 2.00000 0.124035
\(261\) 0 0
\(262\) −4.00000 −0.247121
\(263\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(264\) 0 0
\(265\) 12.0000 20.7846i 0.737154 1.27679i
\(266\) 6.00000 10.3923i 0.367884 0.637193i
\(267\) 0 0
\(268\) 1.00000 + 1.73205i 0.0610847 + 0.105802i
\(269\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(270\) 0 0
\(271\) 22.0000 1.33640 0.668202 0.743980i \(-0.267064\pi\)
0.668202 + 0.743980i \(0.267064\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) −9.00000 + 15.5885i −0.543710 + 0.941733i
\(275\) −2.00000 + 3.46410i −0.120605 + 0.208893i
\(276\) 0 0
\(277\) 3.00000 + 5.19615i 0.180253 + 0.312207i 0.941966 0.335707i \(-0.108975\pi\)
−0.761714 + 0.647913i \(0.775642\pi\)
\(278\) 20.0000 1.19952
\(279\) 0 0
\(280\) −4.00000 −0.239046
\(281\) 5.00000 + 8.66025i 0.298275 + 0.516627i 0.975741 0.218926i \(-0.0702554\pi\)
−0.677466 + 0.735554i \(0.736922\pi\)
\(282\) 0 0
\(283\) 10.0000 17.3205i 0.594438 1.02960i −0.399188 0.916869i \(-0.630708\pi\)
0.993626 0.112728i \(-0.0359589\pi\)
\(284\) 8.00000 13.8564i 0.474713 0.822226i
\(285\) 0 0
\(286\) 2.00000 + 3.46410i 0.118262 + 0.204837i
\(287\) −12.0000 −0.708338
\(288\) 0 0
\(289\) −17.0000 −1.00000
\(290\) 8.00000 + 13.8564i 0.469776 + 0.813676i
\(291\) 0 0
\(292\) −7.00000 + 12.1244i −0.409644 + 0.709524i
\(293\) −1.00000 + 1.73205i −0.0584206 + 0.101187i −0.893757 0.448552i \(-0.851940\pi\)
0.835336 + 0.549740i \(0.185273\pi\)
\(294\) 0 0
\(295\) 4.00000 + 6.92820i 0.232889 + 0.403376i
\(296\) −6.00000 −0.348743
\(297\) 0 0
\(298\) 6.00000 0.347571
\(299\) 2.00000 + 3.46410i 0.115663 + 0.200334i
\(300\) 0 0
\(301\) −8.00000 + 13.8564i −0.461112 + 0.798670i
\(302\) 9.00000 15.5885i 0.517892 0.897015i
\(303\) 0 0
\(304\) 3.00000 + 5.19615i 0.172062 + 0.298020i
\(305\) −20.0000 −1.14520
\(306\) 0 0
\(307\) 2.00000 0.114146 0.0570730 0.998370i \(-0.481823\pi\)
0.0570730 + 0.998370i \(0.481823\pi\)
\(308\) −4.00000 6.92820i −0.227921 0.394771i
\(309\) 0 0
\(310\) 2.00000 3.46410i 0.113592 0.196748i
\(311\) 6.00000 10.3923i 0.340229 0.589294i −0.644246 0.764818i \(-0.722829\pi\)
0.984475 + 0.175525i \(0.0561621\pi\)
\(312\) 0 0
\(313\) −13.0000 22.5167i −0.734803 1.27272i −0.954810 0.297218i \(-0.903941\pi\)
0.220006 0.975499i \(-0.429392\pi\)
\(314\) −2.00000 −0.112867
\(315\) 0 0
\(316\) −4.00000 −0.225018
\(317\) −3.00000 5.19615i −0.168497 0.291845i 0.769395 0.638774i \(-0.220558\pi\)
−0.937892 + 0.346929i \(0.887225\pi\)
\(318\) 0 0
\(319\) −16.0000 + 27.7128i −0.895828 + 1.55162i
\(320\) 1.00000 1.73205i 0.0559017 0.0968246i
\(321\) 0 0
\(322\) −4.00000 6.92820i −0.222911 0.386094i
\(323\) 0 0
\(324\) 0 0
\(325\) 1.00000 0.0554700
\(326\) −5.00000 8.66025i −0.276924 0.479647i
\(327\) 0 0
\(328\) 3.00000 5.19615i 0.165647 0.286910i
\(329\) 8.00000 13.8564i 0.441054 0.763928i
\(330\) 0 0
\(331\) 5.00000 + 8.66025i 0.274825 + 0.476011i 0.970091 0.242742i \(-0.0780468\pi\)
−0.695266 + 0.718752i \(0.744713\pi\)
\(332\) −12.0000 −0.658586
\(333\) 0 0
\(334\) 0 0
\(335\) −2.00000 3.46410i −0.109272 0.189264i
\(336\) 0 0
\(337\) 17.0000 29.4449i 0.926049 1.60396i 0.136184 0.990684i \(-0.456516\pi\)
0.789865 0.613280i \(-0.210150\pi\)
\(338\) 0.500000 0.866025i 0.0271964 0.0471056i
\(339\) 0 0
\(340\) 0 0
\(341\) 8.00000 0.433224
\(342\) 0 0
\(343\) 20.0000 1.07990
\(344\) −4.00000 6.92820i −0.215666 0.373544i
\(345\) 0 0
\(346\) 8.00000 13.8564i 0.430083 0.744925i
\(347\) 12.0000 20.7846i 0.644194 1.11578i −0.340293 0.940319i \(-0.610526\pi\)
0.984487 0.175457i \(-0.0561403\pi\)
\(348\) 0 0
\(349\) −11.0000 19.0526i −0.588817 1.01986i −0.994388 0.105797i \(-0.966261\pi\)
0.405571 0.914063i \(-0.367073\pi\)
\(350\) −2.00000 −0.106904
\(351\) 0 0
\(352\) 4.00000 0.213201
\(353\) −7.00000 12.1244i −0.372572 0.645314i 0.617388 0.786659i \(-0.288191\pi\)
−0.989960 + 0.141344i \(0.954858\pi\)
\(354\) 0 0
\(355\) −16.0000 + 27.7128i −0.849192 + 1.47084i
\(356\) 3.00000 5.19615i 0.159000 0.275396i
\(357\) 0 0
\(358\) 6.00000 + 10.3923i 0.317110 + 0.549250i
\(359\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(360\) 0 0
\(361\) 17.0000 0.894737
\(362\) −9.00000 15.5885i −0.473029 0.819311i
\(363\) 0 0
\(364\) −1.00000 + 1.73205i −0.0524142 + 0.0907841i
\(365\) 14.0000 24.2487i 0.732793 1.26924i
\(366\) 0 0
\(367\) −4.00000 6.92820i −0.208798 0.361649i 0.742538 0.669804i \(-0.233622\pi\)
−0.951336 + 0.308155i \(0.900289\pi\)
\(368\) 4.00000 0.208514
\(369\) 0 0
\(370\) 12.0000 0.623850
\(371\) 12.0000 + 20.7846i 0.623009 + 1.07908i
\(372\) 0 0
\(373\) 5.00000 8.66025i 0.258890 0.448411i −0.707055 0.707159i \(-0.749977\pi\)
0.965945 + 0.258748i \(0.0833099\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 4.00000 + 6.92820i 0.206284 + 0.357295i
\(377\) 8.00000 0.412021
\(378\) 0 0
\(379\) 10.0000 0.513665 0.256833 0.966456i \(-0.417321\pi\)
0.256833 + 0.966456i \(0.417321\pi\)
\(380\) −6.00000 10.3923i −0.307794 0.533114i
\(381\) 0 0
\(382\) −2.00000 + 3.46410i −0.102329 + 0.177239i
\(383\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(384\) 0 0
\(385\) 8.00000 + 13.8564i 0.407718 + 0.706188i
\(386\) −2.00000 −0.101797
\(387\) 0 0
\(388\) −10.0000 −0.507673
\(389\) 6.00000 + 10.3923i 0.304212 + 0.526911i 0.977086 0.212847i \(-0.0682735\pi\)
−0.672874 + 0.739758i \(0.734940\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −1.50000 + 2.59808i −0.0757614 + 0.131223i
\(393\) 0 0
\(394\) −9.00000 15.5885i −0.453413 0.785335i
\(395\) 8.00000 0.402524
\(396\) 0 0
\(397\) −10.0000 −0.501886 −0.250943 0.968002i \(-0.580741\pi\)
−0.250943 + 0.968002i \(0.580741\pi\)
\(398\) 4.00000 + 6.92820i 0.200502 + 0.347279i
\(399\) 0 0
\(400\) 0.500000 0.866025i 0.0250000 0.0433013i
\(401\) 3.00000 5.19615i 0.149813 0.259483i −0.781345 0.624099i \(-0.785466\pi\)
0.931158 + 0.364615i \(0.118800\pi\)
\(402\) 0 0
\(403\) −1.00000 1.73205i −0.0498135 0.0862796i
\(404\) −16.0000 −0.796030
\(405\) 0 0
\(406\) −16.0000 −0.794067
\(407\) 12.0000 + 20.7846i 0.594818 + 1.03025i
\(408\) 0 0
\(409\) 13.0000 22.5167i 0.642809 1.11338i −0.341994 0.939702i \(-0.611102\pi\)
0.984803 0.173675i \(-0.0555643\pi\)
\(410\) −6.00000 + 10.3923i −0.296319 + 0.513239i
\(411\) 0 0
\(412\) −2.00000 3.46410i −0.0985329 0.170664i
\(413\) −8.00000 −0.393654
\(414\) 0 0
\(415\) 24.0000 1.17811
\(416\) −0.500000 0.866025i −0.0245145 0.0424604i
\(417\) 0 0
\(418\) 12.0000 20.7846i 0.586939 1.01661i
\(419\) −18.0000 + 31.1769i −0.879358 + 1.52309i −0.0273103 + 0.999627i \(0.508694\pi\)
−0.852047 + 0.523465i \(0.824639\pi\)
\(420\) 0 0
\(421\) −5.00000 8.66025i −0.243685 0.422075i 0.718076 0.695965i \(-0.245023\pi\)
−0.961761 + 0.273890i \(0.911690\pi\)
\(422\) −8.00000 −0.389434
\(423\) 0 0
\(424\) −12.0000 −0.582772
\(425\) 0 0
\(426\) 0 0
\(427\) 10.0000 17.3205i 0.483934 0.838198i
\(428\) 10.0000 17.3205i 0.483368 0.837218i
\(429\) 0 0
\(430\) 8.00000 + 13.8564i 0.385794 + 0.668215i
\(431\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(432\) 0 0
\(433\) −2.00000 −0.0961139 −0.0480569 0.998845i \(-0.515303\pi\)
−0.0480569 + 0.998845i \(0.515303\pi\)
\(434\) 2.00000 + 3.46410i 0.0960031 + 0.166282i
\(435\) 0 0
\(436\) −5.00000 + 8.66025i −0.239457 + 0.414751i
\(437\) 12.0000 20.7846i 0.574038 0.994263i
\(438\) 0 0
\(439\) 2.00000 + 3.46410i 0.0954548 + 0.165333i 0.909798 0.415051i \(-0.136236\pi\)
−0.814344 + 0.580383i \(0.802903\pi\)
\(440\) −8.00000 −0.381385
\(441\) 0 0
\(442\) 0 0
\(443\) −18.0000 31.1769i −0.855206 1.48126i −0.876454 0.481486i \(-0.840097\pi\)
0.0212481 0.999774i \(-0.493236\pi\)
\(444\) 0 0
\(445\) −6.00000 + 10.3923i −0.284427 + 0.492642i
\(446\) 3.00000 5.19615i 0.142054 0.246045i
\(447\) 0 0
\(448\) 1.00000 + 1.73205i 0.0472456 + 0.0818317i
\(449\) 26.0000 1.22702 0.613508 0.789689i \(-0.289758\pi\)
0.613508 + 0.789689i \(0.289758\pi\)
\(450\) 0 0
\(451\) −24.0000 −1.13012
\(452\) −2.00000 3.46410i −0.0940721 0.162938i
\(453\) 0 0
\(454\) 6.00000 10.3923i 0.281594 0.487735i
\(455\) 2.00000 3.46410i 0.0937614 0.162400i
\(456\) 0 0
\(457\) 1.00000 + 1.73205i 0.0467780 + 0.0810219i 0.888466 0.458942i \(-0.151771\pi\)
−0.841688 + 0.539964i \(0.818438\pi\)
\(458\) 30.0000 1.40181
\(459\) 0 0
\(460\) −8.00000 −0.373002
\(461\) −15.0000 25.9808i −0.698620 1.21004i −0.968945 0.247276i \(-0.920465\pi\)
0.270326 0.962769i \(-0.412869\pi\)
\(462\) 0 0
\(463\) −11.0000 + 19.0526i −0.511213 + 0.885448i 0.488702 + 0.872451i \(0.337470\pi\)
−0.999916 + 0.0129968i \(0.995863\pi\)
\(464\) 4.00000 6.92820i 0.185695 0.321634i
\(465\) 0 0
\(466\) 10.0000 + 17.3205i 0.463241 + 0.802357i
\(467\) −8.00000 −0.370196 −0.185098 0.982720i \(-0.559260\pi\)
−0.185098 + 0.982720i \(0.559260\pi\)
\(468\) 0 0
\(469\) 4.00000 0.184703
\(470\) −8.00000 13.8564i −0.369012 0.639148i
\(471\) 0 0
\(472\) 2.00000 3.46410i 0.0920575 0.159448i
\(473\) −16.0000 + 27.7128i −0.735681 + 1.27424i
\(474\) 0 0
\(475\) −3.00000 5.19615i −0.137649 0.238416i
\(476\) 0 0
\(477\) 0 0
\(478\) 24.0000 1.09773
\(479\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(480\) 0 0
\(481\) 3.00000 5.19615i 0.136788 0.236924i
\(482\) 3.00000 5.19615i 0.136646 0.236678i
\(483\) 0 0
\(484\) −2.50000 4.33013i −0.113636 0.196824i
\(485\) 20.0000 0.908153
\(486\) 0 0
\(487\) 38.0000 1.72194 0.860972 0.508652i \(-0.169856\pi\)
0.860972 + 0.508652i \(0.169856\pi\)
\(488\) 5.00000 + 8.66025i 0.226339 + 0.392031i
\(489\) 0 0
\(490\) 3.00000 5.19615i 0.135526 0.234738i
\(491\) 8.00000 13.8564i 0.361035 0.625331i −0.627096 0.778942i \(-0.715757\pi\)
0.988131 + 0.153611i \(0.0490902\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) −6.00000 −0.269953
\(495\) 0 0
\(496\) −2.00000 −0.0898027
\(497\) −16.0000 27.7128i −0.717698 1.24309i
\(498\) 0 0
\(499\) −11.0000 + 19.0526i −0.492428 + 0.852910i −0.999962 0.00872186i \(-0.997224\pi\)
0.507534 + 0.861632i \(0.330557\pi\)
\(500\) −6.00000 + 10.3923i −0.268328 + 0.464758i
\(501\) 0 0
\(502\) 0 0
\(503\) 32.0000 1.42681 0.713405 0.700752i \(-0.247152\pi\)
0.713405 + 0.700752i \(0.247152\pi\)
\(504\) 0 0
\(505\) 32.0000 1.42398
\(506\) −8.00000 13.8564i −0.355643 0.615992i
\(507\) 0 0
\(508\) 4.00000 6.92820i 0.177471 0.307389i
\(509\) 5.00000 8.66025i 0.221621 0.383859i −0.733679 0.679496i \(-0.762199\pi\)
0.955300 + 0.295637i \(0.0955319\pi\)
\(510\) 0 0
\(511\) 14.0000 + 24.2487i 0.619324 + 1.07270i
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) −12.0000 −0.529297
\(515\) 4.00000 + 6.92820i 0.176261 + 0.305293i
\(516\) 0 0
\(517\) 16.0000 27.7128i 0.703679 1.21881i
\(518\) −6.00000 + 10.3923i −0.263625 + 0.456612i
\(519\) 0 0
\(520\) 1.00000 + 1.73205i 0.0438529 + 0.0759555i
\(521\) −36.0000 −1.57719 −0.788594 0.614914i \(-0.789191\pi\)
−0.788594 + 0.614914i \(0.789191\pi\)
\(522\) 0 0
\(523\) −12.0000 −0.524723 −0.262362 0.964970i \(-0.584501\pi\)
−0.262362 + 0.964970i \(0.584501\pi\)
\(524\) −2.00000 3.46410i −0.0873704 0.151330i
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) 3.50000 + 6.06218i 0.152174 + 0.263573i
\(530\) 24.0000 1.04249
\(531\) 0 0
\(532\) 12.0000 0.520266
\(533\) 3.00000 + 5.19615i 0.129944 + 0.225070i
\(534\) 0 0
\(535\) −20.0000 + 34.6410i −0.864675 + 1.49766i
\(536\) −1.00000 + 1.73205i −0.0431934 + 0.0748132i
\(537\) 0 0
\(538\) 0 0
\(539\) 12.0000 0.516877
\(540\) 0 0
\(541\) 2.00000 0.0859867 0.0429934 0.999075i \(-0.486311\pi\)
0.0429934 + 0.999075i \(0.486311\pi\)
\(542\) 11.0000 + 19.0526i 0.472490 + 0.818377i
\(543\) 0 0
\(544\) 0 0
\(545\) 10.0000 17.3205i 0.428353 0.741929i
\(546\) 0 0
\(547\) 10.0000 + 17.3205i 0.427569 + 0.740571i 0.996657 0.0817056i \(-0.0260367\pi\)
−0.569087 + 0.822277i \(0.692703\pi\)
\(548\) −18.0000 −0.768922
\(549\) 0 0
\(550\) −4.00000 −0.170561
\(551\) −24.0000 41.5692i −1.02243 1.77091i
\(552\) 0 0
\(553\) −4.00000 + 6.92820i −0.170097 + 0.294617i
\(554\) −3.00000 + 5.19615i −0.127458 + 0.220763i
\(555\) 0 0
\(556\) 10.0000 + 17.3205i 0.424094 + 0.734553i
\(557\) 18.0000 0.762684 0.381342 0.924434i \(-0.375462\pi\)
0.381342 + 0.924434i \(0.375462\pi\)
\(558\) 0 0
\(559\) 8.00000 0.338364
\(560\) −2.00000 3.46410i −0.0845154 0.146385i
\(561\) 0 0
\(562\) −5.00000 + 8.66025i −0.210912 + 0.365311i
\(563\) 10.0000 17.3205i 0.421450 0.729972i −0.574632 0.818412i \(-0.694855\pi\)
0.996082 + 0.0884397i \(0.0281881\pi\)
\(564\) 0 0
\(565\) 4.00000 + 6.92820i 0.168281 + 0.291472i
\(566\) 20.0000 0.840663
\(567\) 0 0
\(568\) 16.0000 0.671345
\(569\) 2.00000 + 3.46410i 0.0838444 + 0.145223i 0.904898 0.425628i \(-0.139947\pi\)
−0.821054 + 0.570851i \(0.806613\pi\)
\(570\) 0 0
\(571\) −18.0000 + 31.1769i −0.753277 + 1.30471i 0.192950 + 0.981209i \(0.438194\pi\)
−0.946227 + 0.323505i \(0.895139\pi\)
\(572\) −2.00000 + 3.46410i −0.0836242 + 0.144841i
\(573\) 0 0
\(574\) −6.00000 10.3923i −0.250435 0.433766i
\(575\) −4.00000 −0.166812
\(576\) 0 0
\(577\) −30.0000 −1.24892 −0.624458 0.781058i \(-0.714680\pi\)
−0.624458 + 0.781058i \(0.714680\pi\)
\(578\) −8.50000 14.7224i −0.353553 0.612372i
\(579\) 0 0
\(580\) −8.00000 + 13.8564i −0.332182 + 0.575356i
\(581\) −12.0000 + 20.7846i −0.497844 + 0.862291i
\(582\) 0 0
\(583\) 24.0000 + 41.5692i 0.993978 + 1.72162i
\(584\) −14.0000 −0.579324
\(585\) 0 0
\(586\) −2.00000 −0.0826192
\(587\) −14.0000 24.2487i −0.577842 1.00085i −0.995726 0.0923513i \(-0.970562\pi\)
0.417885 0.908500i \(-0.362772\pi\)
\(588\) 0 0
\(589\) −6.00000 + 10.3923i −0.247226 + 0.428207i
\(590\) −4.00000 + 6.92820i −0.164677 + 0.285230i
\(591\) 0 0
\(592\) −3.00000 5.19615i −0.123299 0.213561i
\(593\) −38.0000 −1.56047 −0.780236 0.625485i \(-0.784901\pi\)
−0.780236 + 0.625485i \(0.784901\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 3.00000 + 5.19615i 0.122885 + 0.212843i
\(597\) 0 0
\(598\) −2.00000 + 3.46410i −0.0817861 + 0.141658i
\(599\) 20.0000 34.6410i 0.817178 1.41539i −0.0905757 0.995890i \(-0.528871\pi\)
0.907754 0.419504i \(-0.137796\pi\)
\(600\) 0 0
\(601\) −5.00000 8.66025i −0.203954 0.353259i 0.745845 0.666120i \(-0.232046\pi\)
−0.949799 + 0.312861i \(0.898713\pi\)
\(602\) −16.0000 −0.652111
\(603\) 0 0
\(604\) 18.0000 0.732410
\(605\) 5.00000 + 8.66025i 0.203279 + 0.352089i
\(606\) 0 0
\(607\) −12.0000 + 20.7846i −0.487065 + 0.843621i −0.999889 0.0148722i \(-0.995266\pi\)
0.512824 + 0.858494i \(0.328599\pi\)
\(608\) −3.00000 + 5.19615i −0.121666 + 0.210732i
\(609\) 0 0
\(610\) −10.0000 17.3205i −0.404888 0.701287i
\(611\) −8.00000 −0.323645
\(612\) 0 0
\(613\) −34.0000 −1.37325 −0.686624 0.727013i \(-0.740908\pi\)
−0.686624 + 0.727013i \(0.740908\pi\)
\(614\) 1.00000 + 1.73205i 0.0403567 + 0.0698999i
\(615\) 0 0
\(616\) 4.00000 6.92820i 0.161165 0.279145i
\(617\) −7.00000 + 12.1244i −0.281809 + 0.488108i −0.971830 0.235681i \(-0.924268\pi\)
0.690021 + 0.723789i \(0.257601\pi\)
\(618\) 0 0
\(619\) −17.0000 29.4449i −0.683288 1.18349i −0.973972 0.226670i \(-0.927216\pi\)
0.290684 0.956819i \(-0.406117\pi\)
\(620\) 4.00000 0.160644
\(621\) 0 0
\(622\) 12.0000 0.481156
\(623\) −6.00000 10.3923i −0.240385 0.416359i
\(624\) 0 0
\(625\) 9.50000 16.4545i 0.380000 0.658179i
\(626\) 13.0000 22.5167i 0.519584 0.899947i
\(627\) 0 0
\(628\) −1.00000 1.73205i −0.0399043 0.0691164i
\(629\) 0 0
\(630\) 0 0
\(631\) −14.0000 −0.557331 −0.278666 0.960388i \(-0.589892\pi\)
−0.278666 + 0.960388i \(0.589892\pi\)
\(632\) −2.00000 3.46410i −0.0795557 0.137795i
\(633\) 0 0
\(634\) 3.00000 5.19615i 0.119145 0.206366i
\(635\) −8.00000 + 13.8564i −0.317470 + 0.549875i
\(636\) 0 0
\(637\) −1.50000 2.59808i −0.0594322 0.102940i
\(638\) −32.0000 −1.26689
\(639\) 0 0
\(640\) 2.00000 0.0790569
\(641\) 20.0000 + 34.6410i 0.789953 + 1.36824i 0.925995 + 0.377535i \(0.123228\pi\)
−0.136043 + 0.990703i \(0.543438\pi\)
\(642\) 0 0
\(643\) 5.00000 8.66025i 0.197181 0.341527i −0.750432 0.660947i \(-0.770155\pi\)
0.947613 + 0.319420i \(0.103488\pi\)
\(644\) 4.00000 6.92820i 0.157622 0.273009i
\(645\) 0 0
\(646\) 0 0
\(647\) 8.00000 0.314512 0.157256 0.987558i \(-0.449735\pi\)
0.157256 + 0.987558i \(0.449735\pi\)
\(648\) 0 0
\(649\) −16.0000 −0.628055
\(650\) 0.500000 + 0.866025i 0.0196116 + 0.0339683i
\(651\) 0 0
\(652\) 5.00000 8.66025i 0.195815 0.339162i
\(653\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(654\) 0 0
\(655\) 4.00000 + 6.92820i 0.156293 + 0.270707i
\(656\) 6.00000 0.234261
\(657\) 0 0
\(658\) 16.0000 0.623745
\(659\) 24.0000 + 41.5692i 0.934907 + 1.61931i 0.774799 + 0.632207i \(0.217851\pi\)
0.160108 + 0.987099i \(0.448816\pi\)
\(660\) 0 0
\(661\) −7.00000 + 12.1244i −0.272268 + 0.471583i −0.969442 0.245319i \(-0.921107\pi\)
0.697174 + 0.716902i \(0.254441\pi\)
\(662\) −5.00000 + 8.66025i −0.194331 + 0.336590i
\(663\) 0 0
\(664\) −6.00000 10.3923i −0.232845 0.403300i
\(665\) −24.0000 −0.930680
\(666\) 0 0
\(667\) −32.0000 −1.23904
\(668\) 0 0
\(669\) 0 0
\(670\) 2.00000 3.46410i 0.0772667 0.133830i
\(671\) 20.0000 34.6410i 0.772091 1.33730i
\(672\) 0 0
\(673\) −11.0000 19.0526i −0.424019 0.734422i 0.572309 0.820038i \(-0.306048\pi\)
−0.996328 + 0.0856156i \(0.972714\pi\)
\(674\) 34.0000 1.30963
\(675\) 0 0
\(676\) 1.00000 0.0384615
\(677\) 6.00000 + 10.3923i 0.230599 + 0.399409i 0.957984 0.286820i \(-0.0925982\pi\)
−0.727386 + 0.686229i \(0.759265\pi\)
\(678\) 0 0
\(679\) −10.0000 + 17.3205i −0.383765 + 0.664700i
\(680\) 0 0
\(681\) 0 0
\(682\) 4.00000 + 6.92820i 0.153168 + 0.265295i
\(683\) −4.00000 −0.153056 −0.0765279 0.997067i \(-0.524383\pi\)
−0.0765279 + 0.997067i \(0.524383\pi\)
\(684\) 0 0
\(685\) 36.0000 1.37549
\(686\) 10.0000 + 17.3205i 0.381802 + 0.661300i
\(687\) 0 0
\(688\) 4.00000 6.92820i 0.152499 0.264135i
\(689\) 6.00000 10.3923i 0.228582 0.395915i
\(690\) 0 0
\(691\) 13.0000 + 22.5167i 0.494543 + 0.856574i 0.999980 0.00628943i \(-0.00200200\pi\)
−0.505437 + 0.862864i \(0.668669\pi\)
\(692\) 16.0000 0.608229
\(693\) 0 0
\(694\) 24.0000 0.911028
\(695\) −20.0000 34.6410i −0.758643 1.31401i
\(696\) 0 0
\(697\) 0 0
\(698\) 11.0000 19.0526i 0.416356 0.721150i
\(699\) 0 0
\(700\) −1.00000 1.73205i −0.0377964 0.0654654i
\(701\) −12.0000 −0.453234 −0.226617 0.973984i \(-0.572767\pi\)
−0.226617 + 0.973984i \(0.572767\pi\)
\(702\) 0 0
\(703\) −36.0000 −1.35777
\(704\) 2.00000 + 3.46410i 0.0753778 + 0.130558i
\(705\) 0 0
\(706\) 7.00000 12.1244i 0.263448 0.456306i
\(707\) −16.0000 + 27.7128i −0.601742 + 1.04225i
\(708\) 0 0
\(709\) 11.0000 + 19.0526i 0.413114 + 0.715534i 0.995228 0.0975728i \(-0.0311079\pi\)
−0.582115 + 0.813107i \(0.697775\pi\)
\(710\) −32.0000 −1.20094
\(711\) 0 0
\(712\) 6.00000 0.224860
\(713\) 4.00000 + 6.92820i 0.149801 + 0.259463i
\(714\) 0 0
\(715\) 4.00000 6.92820i 0.149592 0.259100i
\(716\) −6.00000 + 10.3923i −0.224231 + 0.388379i
\(717\) 0 0
\(718\) 0 0
\(719\) 28.0000 1.04422 0.522112 0.852877i \(-0.325144\pi\)
0.522112 + 0.852877i \(0.325144\pi\)
\(720\) 0 0
\(721\) −8.00000 −0.297936
\(722\) 8.50000 + 14.7224i 0.316337 + 0.547912i
\(723\) 0 0
\(724\) 9.00000 15.5885i 0.334482 0.579340i
\(725\) −4.00000 + 6.92820i −0.148556 + 0.257307i
\(726\) 0 0
\(727\) 4.00000 + 6.92820i 0.148352 + 0.256953i 0.930618 0.365991i \(-0.119270\pi\)
−0.782267 + 0.622944i \(0.785937\pi\)
\(728\) −2.00000 −0.0741249
\(729\) 0 0
\(730\) 28.0000 1.03633
\(731\) 0 0
\(732\) 0 0
\(733\) 11.0000 19.0526i 0.406294 0.703722i −0.588177 0.808732i \(-0.700154\pi\)
0.994471 + 0.105010i \(0.0334875\pi\)
\(734\) 4.00000 6.92820i 0.147643 0.255725i
\(735\) 0 0
\(736\) 2.00000 + 3.46410i 0.0737210 + 0.127688i
\(737\) 8.00000 0.294684
\(738\) 0 0
\(739\) −54.0000 −1.98642 −0.993211 0.116326i \(-0.962888\pi\)
−0.993211 + 0.116326i \(0.962888\pi\)
\(740\) 6.00000 + 10.3923i 0.220564 + 0.382029i
\(741\) 0 0
\(742\) −12.0000 + 20.7846i −0.440534 + 0.763027i
\(743\) 20.0000 34.6410i 0.733729 1.27086i −0.221550 0.975149i \(-0.571112\pi\)
0.955279 0.295707i \(-0.0955551\pi\)
\(744\) 0 0
\(745\) −6.00000 10.3923i −0.219823 0.380745i
\(746\) 10.0000 0.366126
\(747\) 0 0
\(748\) 0 0
\(749\) −20.0000 34.6410i −0.730784 1.26576i
\(750\) 0 0
\(751\) 6.00000 10.3923i 0.218943 0.379221i −0.735542 0.677479i \(-0.763072\pi\)
0.954485 + 0.298259i \(0.0964058\pi\)
\(752\) −4.00000 + 6.92820i −0.145865 + 0.252646i
\(753\) 0 0
\(754\) 4.00000 + 6.92820i 0.145671 + 0.252310i
\(755\) −36.0000 −1.31017
\(756\) 0 0
\(757\) −18.0000 −0.654221 −0.327111 0.944986i \(-0.606075\pi\)
−0.327111 + 0.944986i \(0.606075\pi\)
\(758\) 5.00000 + 8.66025i 0.181608 + 0.314555i
\(759\) 0 0
\(760\) 6.00000 10.3923i 0.217643 0.376969i
\(761\) −15.0000 + 25.9808i −0.543750 + 0.941802i 0.454935 + 0.890525i \(0.349663\pi\)
−0.998684 + 0.0512772i \(0.983671\pi\)
\(762\) 0 0
\(763\) 10.0000 + 17.3205i 0.362024 + 0.627044i
\(764\) −4.00000 −0.144715
\(765\) 0 0
\(766\) 0 0
\(767\) 2.00000 + 3.46410i 0.0722158 + 0.125081i
\(768\) 0 0
\(769\) 15.0000 25.9808i 0.540914 0.936890i −0.457938 0.888984i \(-0.651412\pi\)
0.998852 0.0479061i \(-0.0152548\pi\)
\(770\) −8.00000 + 13.8564i −0.288300 + 0.499350i
\(771\) 0 0
\(772\) −1.00000 1.73205i −0.0359908 0.0623379i
\(773\) −14.0000 −0.503545 −0.251773 0.967786i \(-0.581013\pi\)
−0.251773 + 0.967786i \(0.581013\pi\)
\(774\) 0 0
\(775\) 2.00000 0.0718421
\(776\) −5.00000 8.66025i −0.179490 0.310885i
\(777\) 0 0
\(778\) −6.00000 + 10.3923i −0.215110 + 0.372582i
\(779\) 18.0000 31.1769i 0.644917 1.11703i
\(780\) 0 0
\(781\) −32.0000 55.4256i −1.14505 1.98328i
\(782\) 0 0
\(783\) 0 0
\(784\) −3.00000 −0.107143
\(785\) 2.00000 + 3.46410i 0.0713831 + 0.123639i
\(786\) 0 0