Properties

Label 476.2.i.a.205.1
Level $476$
Weight $2$
Character 476.205
Analytic conductor $3.801$
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] = [476,2,Mod(137,476)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(476, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 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("476.137");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 476 = 2^{2} \cdot 7 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 476.i (of order \(3\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.80087913621\)
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: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 205.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 476.205
Dual form 476.2.i.a.137.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{3} +(2.00000 - 3.46410i) q^{5} +(-2.00000 - 1.73205i) q^{7} +(1.00000 - 1.73205i) q^{9} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{3} +(2.00000 - 3.46410i) q^{5} +(-2.00000 - 1.73205i) q^{7} +(1.00000 - 1.73205i) q^{9} +(1.50000 + 2.59808i) q^{11} -5.00000 q^{13} -4.00000 q^{15} +(0.500000 + 0.866025i) q^{17} +(-3.00000 + 5.19615i) q^{19} +(-0.500000 + 2.59808i) q^{21} +(2.00000 - 3.46410i) q^{23} +(-5.50000 - 9.52628i) q^{25} -5.00000 q^{27} +8.00000 q^{29} +(1.50000 - 2.59808i) q^{33} +(-10.0000 + 3.46410i) q^{35} +(4.00000 - 6.92820i) q^{37} +(2.50000 + 4.33013i) q^{39} -8.00000 q^{41} +10.0000 q^{43} +(-4.00000 - 6.92820i) q^{45} +(1.00000 - 1.73205i) q^{47} +(1.00000 + 6.92820i) q^{49} +(0.500000 - 0.866025i) q^{51} +(-1.50000 - 2.59808i) q^{53} +12.0000 q^{55} +6.00000 q^{57} +(-1.00000 - 1.73205i) q^{59} +(4.00000 - 6.92820i) q^{61} +(-5.00000 + 1.73205i) q^{63} +(-10.0000 + 17.3205i) q^{65} +(-7.00000 - 12.1244i) q^{67} -4.00000 q^{69} +7.00000 q^{71} +(4.00000 + 6.92820i) q^{73} +(-5.50000 + 9.52628i) q^{75} +(1.50000 - 7.79423i) q^{77} +(-7.50000 + 12.9904i) q^{79} +(-0.500000 - 0.866025i) q^{81} +12.0000 q^{83} +4.00000 q^{85} +(-4.00000 - 6.92820i) q^{87} +(-0.500000 + 0.866025i) q^{89} +(10.0000 + 8.66025i) q^{91} +(12.0000 + 20.7846i) q^{95} +18.0000 q^{97} +6.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - q^{3} + 4 q^{5} - 4 q^{7} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - q^{3} + 4 q^{5} - 4 q^{7} + 2 q^{9} + 3 q^{11} - 10 q^{13} - 8 q^{15} + q^{17} - 6 q^{19} - q^{21} + 4 q^{23} - 11 q^{25} - 10 q^{27} + 16 q^{29} + 3 q^{33} - 20 q^{35} + 8 q^{37} + 5 q^{39} - 16 q^{41} + 20 q^{43} - 8 q^{45} + 2 q^{47} + 2 q^{49} + q^{51} - 3 q^{53} + 24 q^{55} + 12 q^{57} - 2 q^{59} + 8 q^{61} - 10 q^{63} - 20 q^{65} - 14 q^{67} - 8 q^{69} + 14 q^{71} + 8 q^{73} - 11 q^{75} + 3 q^{77} - 15 q^{79} - q^{81} + 24 q^{83} + 8 q^{85} - 8 q^{87} - q^{89} + 20 q^{91} + 24 q^{95} + 36 q^{97} + 12 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/476\mathbb{Z}\right)^\times\).

\(n\) \(239\) \(309\) \(409\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\)

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 0
\(3\) −0.500000 0.866025i −0.288675 0.500000i 0.684819 0.728714i \(-0.259881\pi\)
−0.973494 + 0.228714i \(0.926548\pi\)
\(4\) 0 0
\(5\) 2.00000 3.46410i 0.894427 1.54919i 0.0599153 0.998203i \(-0.480917\pi\)
0.834512 0.550990i \(-0.185750\pi\)
\(6\) 0 0
\(7\) −2.00000 1.73205i −0.755929 0.654654i
\(8\) 0 0
\(9\) 1.00000 1.73205i 0.333333 0.577350i
\(10\) 0 0
\(11\) 1.50000 + 2.59808i 0.452267 + 0.783349i 0.998526 0.0542666i \(-0.0172821\pi\)
−0.546259 + 0.837616i \(0.683949\pi\)
\(12\) 0 0
\(13\) −5.00000 −1.38675 −0.693375 0.720577i \(-0.743877\pi\)
−0.693375 + 0.720577i \(0.743877\pi\)
\(14\) 0 0
\(15\) −4.00000 −1.03280
\(16\) 0 0
\(17\) 0.500000 + 0.866025i 0.121268 + 0.210042i
\(18\) 0 0
\(19\) −3.00000 + 5.19615i −0.688247 + 1.19208i 0.284157 + 0.958778i \(0.408286\pi\)
−0.972404 + 0.233301i \(0.925047\pi\)
\(20\) 0 0
\(21\) −0.500000 + 2.59808i −0.109109 + 0.566947i
\(22\) 0 0
\(23\) 2.00000 3.46410i 0.417029 0.722315i −0.578610 0.815604i \(-0.696405\pi\)
0.995639 + 0.0932891i \(0.0297381\pi\)
\(24\) 0 0
\(25\) −5.50000 9.52628i −1.10000 1.90526i
\(26\) 0 0
\(27\) −5.00000 −0.962250
\(28\) 0 0
\(29\) 8.00000 1.48556 0.742781 0.669534i \(-0.233506\pi\)
0.742781 + 0.669534i \(0.233506\pi\)
\(30\) 0 0
\(31\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(32\) 0 0
\(33\) 1.50000 2.59808i 0.261116 0.452267i
\(34\) 0 0
\(35\) −10.0000 + 3.46410i −1.69031 + 0.585540i
\(36\) 0 0
\(37\) 4.00000 6.92820i 0.657596 1.13899i −0.323640 0.946180i \(-0.604907\pi\)
0.981236 0.192809i \(-0.0617599\pi\)
\(38\) 0 0
\(39\) 2.50000 + 4.33013i 0.400320 + 0.693375i
\(40\) 0 0
\(41\) −8.00000 −1.24939 −0.624695 0.780869i \(-0.714777\pi\)
−0.624695 + 0.780869i \(0.714777\pi\)
\(42\) 0 0
\(43\) 10.0000 1.52499 0.762493 0.646997i \(-0.223975\pi\)
0.762493 + 0.646997i \(0.223975\pi\)
\(44\) 0 0
\(45\) −4.00000 6.92820i −0.596285 1.03280i
\(46\) 0 0
\(47\) 1.00000 1.73205i 0.145865 0.252646i −0.783830 0.620975i \(-0.786737\pi\)
0.929695 + 0.368329i \(0.120070\pi\)
\(48\) 0 0
\(49\) 1.00000 + 6.92820i 0.142857 + 0.989743i
\(50\) 0 0
\(51\) 0.500000 0.866025i 0.0700140 0.121268i
\(52\) 0 0
\(53\) −1.50000 2.59808i −0.206041 0.356873i 0.744423 0.667708i \(-0.232725\pi\)
−0.950464 + 0.310835i \(0.899391\pi\)
\(54\) 0 0
\(55\) 12.0000 1.61808
\(56\) 0 0
\(57\) 6.00000 0.794719
\(58\) 0 0
\(59\) −1.00000 1.73205i −0.130189 0.225494i 0.793560 0.608492i \(-0.208225\pi\)
−0.923749 + 0.382998i \(0.874892\pi\)
\(60\) 0 0
\(61\) 4.00000 6.92820i 0.512148 0.887066i −0.487753 0.872982i \(-0.662183\pi\)
0.999901 0.0140840i \(-0.00448323\pi\)
\(62\) 0 0
\(63\) −5.00000 + 1.73205i −0.629941 + 0.218218i
\(64\) 0 0
\(65\) −10.0000 + 17.3205i −1.24035 + 2.14834i
\(66\) 0 0
\(67\) −7.00000 12.1244i −0.855186 1.48123i −0.876472 0.481452i \(-0.840109\pi\)
0.0212861 0.999773i \(-0.493224\pi\)
\(68\) 0 0
\(69\) −4.00000 −0.481543
\(70\) 0 0
\(71\) 7.00000 0.830747 0.415374 0.909651i \(-0.363651\pi\)
0.415374 + 0.909651i \(0.363651\pi\)
\(72\) 0 0
\(73\) 4.00000 + 6.92820i 0.468165 + 0.810885i 0.999338 0.0363782i \(-0.0115821\pi\)
−0.531174 + 0.847263i \(0.678249\pi\)
\(74\) 0 0
\(75\) −5.50000 + 9.52628i −0.635085 + 1.10000i
\(76\) 0 0
\(77\) 1.50000 7.79423i 0.170941 0.888235i
\(78\) 0 0
\(79\) −7.50000 + 12.9904i −0.843816 + 1.46153i 0.0428296 + 0.999082i \(0.486363\pi\)
−0.886646 + 0.462450i \(0.846971\pi\)
\(80\) 0 0
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 0 0
\(83\) 12.0000 1.31717 0.658586 0.752506i \(-0.271155\pi\)
0.658586 + 0.752506i \(0.271155\pi\)
\(84\) 0 0
\(85\) 4.00000 0.433861
\(86\) 0 0
\(87\) −4.00000 6.92820i −0.428845 0.742781i
\(88\) 0 0
\(89\) −0.500000 + 0.866025i −0.0529999 + 0.0917985i −0.891308 0.453398i \(-0.850212\pi\)
0.838308 + 0.545197i \(0.183545\pi\)
\(90\) 0 0
\(91\) 10.0000 + 8.66025i 1.04828 + 0.907841i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 12.0000 + 20.7846i 1.23117 + 2.13246i
\(96\) 0 0
\(97\) 18.0000 1.82762 0.913812 0.406138i \(-0.133125\pi\)
0.913812 + 0.406138i \(0.133125\pi\)
\(98\) 0 0
\(99\) 6.00000 0.603023
\(100\) 0 0
\(101\) 3.00000 + 5.19615i 0.298511 + 0.517036i 0.975796 0.218685i \(-0.0701767\pi\)
−0.677284 + 0.735721i \(0.736843\pi\)
\(102\) 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 0
\(105\) 8.00000 + 6.92820i 0.780720 + 0.676123i
\(106\) 0 0
\(107\) −0.500000 + 0.866025i −0.0483368 + 0.0837218i −0.889182 0.457555i \(-0.848725\pi\)
0.840845 + 0.541276i \(0.182059\pi\)
\(108\) 0 0
\(109\) 4.00000 + 6.92820i 0.383131 + 0.663602i 0.991508 0.130046i \(-0.0415126\pi\)
−0.608377 + 0.793648i \(0.708179\pi\)
\(110\) 0 0
\(111\) −8.00000 −0.759326
\(112\) 0 0
\(113\) −8.00000 −0.752577 −0.376288 0.926503i \(-0.622800\pi\)
−0.376288 + 0.926503i \(0.622800\pi\)
\(114\) 0 0
\(115\) −8.00000 13.8564i −0.746004 1.29212i
\(116\) 0 0
\(117\) −5.00000 + 8.66025i −0.462250 + 0.800641i
\(118\) 0 0
\(119\) 0.500000 2.59808i 0.0458349 0.238165i
\(120\) 0 0
\(121\) 1.00000 1.73205i 0.0909091 0.157459i
\(122\) 0 0
\(123\) 4.00000 + 6.92820i 0.360668 + 0.624695i
\(124\) 0 0
\(125\) −24.0000 −2.14663
\(126\) 0 0
\(127\) 8.00000 0.709885 0.354943 0.934888i \(-0.384500\pi\)
0.354943 + 0.934888i \(0.384500\pi\)
\(128\) 0 0
\(129\) −5.00000 8.66025i −0.440225 0.762493i
\(130\) 0 0
\(131\) 2.00000 3.46410i 0.174741 0.302660i −0.765331 0.643637i \(-0.777425\pi\)
0.940072 + 0.340977i \(0.110758\pi\)
\(132\) 0 0
\(133\) 15.0000 5.19615i 1.30066 0.450564i
\(134\) 0 0
\(135\) −10.0000 + 17.3205i −0.860663 + 1.49071i
\(136\) 0 0
\(137\) 3.50000 + 6.06218i 0.299025 + 0.517927i 0.975913 0.218159i \(-0.0700052\pi\)
−0.676888 + 0.736086i \(0.736672\pi\)
\(138\) 0 0
\(139\) −1.00000 −0.0848189 −0.0424094 0.999100i \(-0.513503\pi\)
−0.0424094 + 0.999100i \(0.513503\pi\)
\(140\) 0 0
\(141\) −2.00000 −0.168430
\(142\) 0 0
\(143\) −7.50000 12.9904i −0.627182 1.08631i
\(144\) 0 0
\(145\) 16.0000 27.7128i 1.32873 2.30142i
\(146\) 0 0
\(147\) 5.50000 4.33013i 0.453632 0.357143i
\(148\) 0 0
\(149\) 5.50000 9.52628i 0.450578 0.780423i −0.547844 0.836580i \(-0.684551\pi\)
0.998422 + 0.0561570i \(0.0178847\pi\)
\(150\) 0 0
\(151\) −5.00000 8.66025i −0.406894 0.704761i 0.587646 0.809118i \(-0.300055\pi\)
−0.994540 + 0.104357i \(0.966722\pi\)
\(152\) 0 0
\(153\) 2.00000 0.161690
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −0.500000 0.866025i −0.0399043 0.0691164i 0.845383 0.534160i \(-0.179372\pi\)
−0.885288 + 0.465044i \(0.846039\pi\)
\(158\) 0 0
\(159\) −1.50000 + 2.59808i −0.118958 + 0.206041i
\(160\) 0 0
\(161\) −10.0000 + 3.46410i −0.788110 + 0.273009i
\(162\) 0 0
\(163\) −2.00000 + 3.46410i −0.156652 + 0.271329i −0.933659 0.358162i \(-0.883403\pi\)
0.777007 + 0.629492i \(0.216737\pi\)
\(164\) 0 0
\(165\) −6.00000 10.3923i −0.467099 0.809040i
\(166\) 0 0
\(167\) −19.0000 −1.47026 −0.735132 0.677924i \(-0.762880\pi\)
−0.735132 + 0.677924i \(0.762880\pi\)
\(168\) 0 0
\(169\) 12.0000 0.923077
\(170\) 0 0
\(171\) 6.00000 + 10.3923i 0.458831 + 0.794719i
\(172\) 0 0
\(173\) 1.00000 1.73205i 0.0760286 0.131685i −0.825505 0.564396i \(-0.809109\pi\)
0.901533 + 0.432710i \(0.142443\pi\)
\(174\) 0 0
\(175\) −5.50000 + 28.5788i −0.415761 + 2.16036i
\(176\) 0 0
\(177\) −1.00000 + 1.73205i −0.0751646 + 0.130189i
\(178\) 0 0
\(179\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(180\) 0 0
\(181\) 18.0000 1.33793 0.668965 0.743294i \(-0.266738\pi\)
0.668965 + 0.743294i \(0.266738\pi\)
\(182\) 0 0
\(183\) −8.00000 −0.591377
\(184\) 0 0
\(185\) −16.0000 27.7128i −1.17634 2.03749i
\(186\) 0 0
\(187\) −1.50000 + 2.59808i −0.109691 + 0.189990i
\(188\) 0 0
\(189\) 10.0000 + 8.66025i 0.727393 + 0.629941i
\(190\) 0 0
\(191\) −6.00000 + 10.3923i −0.434145 + 0.751961i −0.997225 0.0744412i \(-0.976283\pi\)
0.563081 + 0.826402i \(0.309616\pi\)
\(192\) 0 0
\(193\) 5.00000 + 8.66025i 0.359908 + 0.623379i 0.987945 0.154805i \(-0.0494748\pi\)
−0.628037 + 0.778183i \(0.716141\pi\)
\(194\) 0 0
\(195\) 20.0000 1.43223
\(196\) 0 0
\(197\) 18.0000 1.28245 0.641223 0.767354i \(-0.278427\pi\)
0.641223 + 0.767354i \(0.278427\pi\)
\(198\) 0 0
\(199\) 3.50000 + 6.06218i 0.248108 + 0.429736i 0.963001 0.269498i \(-0.0868577\pi\)
−0.714893 + 0.699234i \(0.753524\pi\)
\(200\) 0 0
\(201\) −7.00000 + 12.1244i −0.493742 + 0.855186i
\(202\) 0 0
\(203\) −16.0000 13.8564i −1.12298 0.972529i
\(204\) 0 0
\(205\) −16.0000 + 27.7128i −1.11749 + 1.93555i
\(206\) 0 0
\(207\) −4.00000 6.92820i −0.278019 0.481543i
\(208\) 0 0
\(209\) −18.0000 −1.24509
\(210\) 0 0
\(211\) −4.00000 −0.275371 −0.137686 0.990476i \(-0.543966\pi\)
−0.137686 + 0.990476i \(0.543966\pi\)
\(212\) 0 0
\(213\) −3.50000 6.06218i −0.239816 0.415374i
\(214\) 0 0
\(215\) 20.0000 34.6410i 1.36399 2.36250i
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 4.00000 6.92820i 0.270295 0.468165i
\(220\) 0 0
\(221\) −2.50000 4.33013i −0.168168 0.291276i
\(222\) 0 0
\(223\) −6.00000 −0.401790 −0.200895 0.979613i \(-0.564385\pi\)
−0.200895 + 0.979613i \(0.564385\pi\)
\(224\) 0 0
\(225\) −22.0000 −1.46667
\(226\) 0 0
\(227\) −12.5000 21.6506i −0.829654 1.43700i −0.898310 0.439363i \(-0.855204\pi\)
0.0686556 0.997640i \(-0.478129\pi\)
\(228\) 0 0
\(229\) 5.00000 8.66025i 0.330409 0.572286i −0.652183 0.758062i \(-0.726147\pi\)
0.982592 + 0.185776i \(0.0594799\pi\)
\(230\) 0 0
\(231\) −7.50000 + 2.59808i −0.493464 + 0.170941i
\(232\) 0 0
\(233\) −14.0000 + 24.2487i −0.917170 + 1.58859i −0.113478 + 0.993540i \(0.536199\pi\)
−0.803692 + 0.595045i \(0.797134\pi\)
\(234\) 0 0
\(235\) −4.00000 6.92820i −0.260931 0.451946i
\(236\) 0 0
\(237\) 15.0000 0.974355
\(238\) 0 0
\(239\) 2.00000 0.129369 0.0646846 0.997906i \(-0.479396\pi\)
0.0646846 + 0.997906i \(0.479396\pi\)
\(240\) 0 0
\(241\) 4.00000 + 6.92820i 0.257663 + 0.446285i 0.965615 0.259975i \(-0.0837143\pi\)
−0.707953 + 0.706260i \(0.750381\pi\)
\(242\) 0 0
\(243\) −8.00000 + 13.8564i −0.513200 + 0.888889i
\(244\) 0 0
\(245\) 26.0000 + 10.3923i 1.66108 + 0.663940i
\(246\) 0 0
\(247\) 15.0000 25.9808i 0.954427 1.65312i
\(248\) 0 0
\(249\) −6.00000 10.3923i −0.380235 0.658586i
\(250\) 0 0
\(251\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(252\) 0 0
\(253\) 12.0000 0.754434
\(254\) 0 0
\(255\) −2.00000 3.46410i −0.125245 0.216930i
\(256\) 0 0
\(257\) −1.50000 + 2.59808i −0.0935674 + 0.162064i −0.909010 0.416775i \(-0.863160\pi\)
0.815442 + 0.578838i \(0.196494\pi\)
\(258\) 0 0
\(259\) −20.0000 + 6.92820i −1.24274 + 0.430498i
\(260\) 0 0
\(261\) 8.00000 13.8564i 0.495188 0.857690i
\(262\) 0 0
\(263\) −2.00000 3.46410i −0.123325 0.213606i 0.797752 0.602986i \(-0.206023\pi\)
−0.921077 + 0.389380i \(0.872689\pi\)
\(264\) 0 0
\(265\) −12.0000 −0.737154
\(266\) 0 0
\(267\) 1.00000 0.0611990
\(268\) 0 0
\(269\) 9.00000 + 15.5885i 0.548740 + 0.950445i 0.998361 + 0.0572259i \(0.0182255\pi\)
−0.449622 + 0.893219i \(0.648441\pi\)
\(270\) 0 0
\(271\) 12.0000 20.7846i 0.728948 1.26258i −0.228380 0.973572i \(-0.573343\pi\)
0.957328 0.289003i \(-0.0933238\pi\)
\(272\) 0 0
\(273\) 2.50000 12.9904i 0.151307 0.786214i
\(274\) 0 0
\(275\) 16.5000 28.5788i 0.994987 1.72337i
\(276\) 0 0
\(277\) −4.00000 6.92820i −0.240337 0.416275i 0.720473 0.693482i \(-0.243925\pi\)
−0.960810 + 0.277207i \(0.910591\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −19.0000 −1.13344 −0.566722 0.823909i \(-0.691789\pi\)
−0.566722 + 0.823909i \(0.691789\pi\)
\(282\) 0 0
\(283\) −7.50000 12.9904i −0.445829 0.772198i 0.552281 0.833658i \(-0.313758\pi\)
−0.998110 + 0.0614601i \(0.980424\pi\)
\(284\) 0 0
\(285\) 12.0000 20.7846i 0.710819 1.23117i
\(286\) 0 0
\(287\) 16.0000 + 13.8564i 0.944450 + 0.817918i
\(288\) 0 0
\(289\) −0.500000 + 0.866025i −0.0294118 + 0.0509427i
\(290\) 0 0
\(291\) −9.00000 15.5885i −0.527589 0.913812i
\(292\) 0 0
\(293\) −15.0000 −0.876309 −0.438155 0.898900i \(-0.644368\pi\)
−0.438155 + 0.898900i \(0.644368\pi\)
\(294\) 0 0
\(295\) −8.00000 −0.465778
\(296\) 0 0
\(297\) −7.50000 12.9904i −0.435194 0.753778i
\(298\) 0 0
\(299\) −10.0000 + 17.3205i −0.578315 + 1.00167i
\(300\) 0 0
\(301\) −20.0000 17.3205i −1.15278 0.998337i
\(302\) 0 0
\(303\) 3.00000 5.19615i 0.172345 0.298511i
\(304\) 0 0
\(305\) −16.0000 27.7128i −0.916157 1.58683i
\(306\) 0 0
\(307\) 28.0000 1.59804 0.799022 0.601302i \(-0.205351\pi\)
0.799022 + 0.601302i \(0.205351\pi\)
\(308\) 0 0
\(309\) 4.00000 0.227552
\(310\) 0 0
\(311\) 6.50000 + 11.2583i 0.368581 + 0.638401i 0.989344 0.145597i \(-0.0465103\pi\)
−0.620763 + 0.783998i \(0.713177\pi\)
\(312\) 0 0
\(313\) −15.0000 + 25.9808i −0.847850 + 1.46852i 0.0352727 + 0.999378i \(0.488770\pi\)
−0.883123 + 0.469142i \(0.844563\pi\)
\(314\) 0 0
\(315\) −4.00000 + 20.7846i −0.225374 + 1.17108i
\(316\) 0 0
\(317\) 1.00000 1.73205i 0.0561656 0.0972817i −0.836576 0.547852i \(-0.815446\pi\)
0.892741 + 0.450570i \(0.148779\pi\)
\(318\) 0 0
\(319\) 12.0000 + 20.7846i 0.671871 + 1.16371i
\(320\) 0 0
\(321\) 1.00000 0.0558146
\(322\) 0 0
\(323\) −6.00000 −0.333849
\(324\) 0 0
\(325\) 27.5000 + 47.6314i 1.52543 + 2.64211i
\(326\) 0 0
\(327\) 4.00000 6.92820i 0.221201 0.383131i
\(328\) 0 0
\(329\) −5.00000 + 1.73205i −0.275659 + 0.0954911i
\(330\) 0 0
\(331\) 3.00000 5.19615i 0.164895 0.285606i −0.771723 0.635959i \(-0.780605\pi\)
0.936618 + 0.350352i \(0.113938\pi\)
\(332\) 0 0
\(333\) −8.00000 13.8564i −0.438397 0.759326i
\(334\) 0 0
\(335\) −56.0000 −3.05961
\(336\) 0 0
\(337\) 8.00000 0.435788 0.217894 0.975972i \(-0.430081\pi\)
0.217894 + 0.975972i \(0.430081\pi\)
\(338\) 0 0
\(339\) 4.00000 + 6.92820i 0.217250 + 0.376288i
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 10.0000 15.5885i 0.539949 0.841698i
\(344\) 0 0
\(345\) −8.00000 + 13.8564i −0.430706 + 0.746004i
\(346\) 0 0
\(347\) 6.00000 + 10.3923i 0.322097 + 0.557888i 0.980921 0.194409i \(-0.0622790\pi\)
−0.658824 + 0.752297i \(0.728946\pi\)
\(348\) 0 0
\(349\) −2.00000 −0.107058 −0.0535288 0.998566i \(-0.517047\pi\)
−0.0535288 + 0.998566i \(0.517047\pi\)
\(350\) 0 0
\(351\) 25.0000 1.33440
\(352\) 0 0
\(353\) 10.5000 + 18.1865i 0.558859 + 0.967972i 0.997592 + 0.0693543i \(0.0220939\pi\)
−0.438733 + 0.898617i \(0.644573\pi\)
\(354\) 0 0
\(355\) 14.0000 24.2487i 0.743043 1.28699i
\(356\) 0 0
\(357\) −2.50000 + 0.866025i −0.132314 + 0.0458349i
\(358\) 0 0
\(359\) −11.0000 + 19.0526i −0.580558 + 1.00556i 0.414855 + 0.909887i \(0.363832\pi\)
−0.995413 + 0.0956683i \(0.969501\pi\)
\(360\) 0 0
\(361\) −8.50000 14.7224i −0.447368 0.774865i
\(362\) 0 0
\(363\) −2.00000 −0.104973
\(364\) 0 0
\(365\) 32.0000 1.67496
\(366\) 0 0
\(367\) 4.50000 + 7.79423i 0.234898 + 0.406855i 0.959243 0.282582i \(-0.0911910\pi\)
−0.724345 + 0.689438i \(0.757858\pi\)
\(368\) 0 0
\(369\) −8.00000 + 13.8564i −0.416463 + 0.721336i
\(370\) 0 0
\(371\) −1.50000 + 7.79423i −0.0778761 + 0.404656i
\(372\) 0 0
\(373\) −15.5000 + 26.8468i −0.802560 + 1.39007i 0.115367 + 0.993323i \(0.463196\pi\)
−0.917926 + 0.396751i \(0.870138\pi\)
\(374\) 0 0
\(375\) 12.0000 + 20.7846i 0.619677 + 1.07331i
\(376\) 0 0
\(377\) −40.0000 −2.06010
\(378\) 0 0
\(379\) 1.00000 0.0513665 0.0256833 0.999670i \(-0.491824\pi\)
0.0256833 + 0.999670i \(0.491824\pi\)
\(380\) 0 0
\(381\) −4.00000 6.92820i −0.204926 0.354943i
\(382\) 0 0
\(383\) −1.00000 + 1.73205i −0.0510976 + 0.0885037i −0.890443 0.455095i \(-0.849605\pi\)
0.839345 + 0.543599i \(0.182939\pi\)
\(384\) 0 0
\(385\) −24.0000 20.7846i −1.22315 1.05928i
\(386\) 0 0
\(387\) 10.0000 17.3205i 0.508329 0.880451i
\(388\) 0 0
\(389\) 13.5000 + 23.3827i 0.684477 + 1.18555i 0.973601 + 0.228257i \(0.0733028\pi\)
−0.289124 + 0.957292i \(0.593364\pi\)
\(390\) 0 0
\(391\) 4.00000 0.202289
\(392\) 0 0
\(393\) −4.00000 −0.201773
\(394\) 0 0
\(395\) 30.0000 + 51.9615i 1.50946 + 2.61447i
\(396\) 0 0
\(397\) −13.0000 + 22.5167i −0.652451 + 1.13008i 0.330075 + 0.943955i \(0.392926\pi\)
−0.982526 + 0.186124i \(0.940407\pi\)
\(398\) 0 0
\(399\) −12.0000 10.3923i −0.600751 0.520266i
\(400\) 0 0
\(401\) 9.00000 15.5885i 0.449439 0.778450i −0.548911 0.835881i \(-0.684957\pi\)
0.998350 + 0.0574304i \(0.0182907\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) −4.00000 −0.198762
\(406\) 0 0
\(407\) 24.0000 1.18964
\(408\) 0 0
\(409\) −5.50000 9.52628i −0.271957 0.471044i 0.697406 0.716677i \(-0.254338\pi\)
−0.969363 + 0.245633i \(0.921004\pi\)
\(410\) 0 0
\(411\) 3.50000 6.06218i 0.172642 0.299025i
\(412\) 0 0
\(413\) −1.00000 + 5.19615i −0.0492068 + 0.255686i
\(414\) 0 0
\(415\) 24.0000 41.5692i 1.17811 2.04055i
\(416\) 0 0
\(417\) 0.500000 + 0.866025i 0.0244851 + 0.0424094i
\(418\) 0 0
\(419\) 37.0000 1.80757 0.903784 0.427989i \(-0.140778\pi\)
0.903784 + 0.427989i \(0.140778\pi\)
\(420\) 0 0
\(421\) 6.00000 0.292422 0.146211 0.989253i \(-0.453292\pi\)
0.146211 + 0.989253i \(0.453292\pi\)
\(422\) 0 0
\(423\) −2.00000 3.46410i −0.0972433 0.168430i
\(424\) 0 0
\(425\) 5.50000 9.52628i 0.266789 0.462092i
\(426\) 0 0
\(427\) −20.0000 + 6.92820i −0.967868 + 0.335279i
\(428\) 0 0
\(429\) −7.50000 + 12.9904i −0.362103 + 0.627182i
\(430\) 0 0
\(431\) 7.50000 + 12.9904i 0.361262 + 0.625725i 0.988169 0.153370i \(-0.0490126\pi\)
−0.626907 + 0.779094i \(0.715679\pi\)
\(432\) 0 0
\(433\) −10.0000 −0.480569 −0.240285 0.970702i \(-0.577241\pi\)
−0.240285 + 0.970702i \(0.577241\pi\)
\(434\) 0 0
\(435\) −32.0000 −1.53428
\(436\) 0 0
\(437\) 12.0000 + 20.7846i 0.574038 + 0.994263i
\(438\) 0 0
\(439\) 0.500000 0.866025i 0.0238637 0.0413331i −0.853847 0.520524i \(-0.825737\pi\)
0.877711 + 0.479191i \(0.159070\pi\)
\(440\) 0 0
\(441\) 13.0000 + 5.19615i 0.619048 + 0.247436i
\(442\) 0 0
\(443\) −13.0000 + 22.5167i −0.617649 + 1.06980i 0.372265 + 0.928126i \(0.378581\pi\)
−0.989914 + 0.141672i \(0.954752\pi\)
\(444\) 0 0
\(445\) 2.00000 + 3.46410i 0.0948091 + 0.164214i
\(446\) 0 0
\(447\) −11.0000 −0.520282
\(448\) 0 0
\(449\) −18.0000 −0.849473 −0.424736 0.905317i \(-0.639633\pi\)
−0.424736 + 0.905317i \(0.639633\pi\)
\(450\) 0 0
\(451\) −12.0000 20.7846i −0.565058 0.978709i
\(452\) 0 0
\(453\) −5.00000 + 8.66025i −0.234920 + 0.406894i
\(454\) 0 0
\(455\) 50.0000 17.3205i 2.34404 0.811998i
\(456\) 0 0
\(457\) 13.0000 22.5167i 0.608114 1.05328i −0.383437 0.923567i \(-0.625260\pi\)
0.991551 0.129718i \(-0.0414071\pi\)
\(458\) 0 0
\(459\) −2.50000 4.33013i −0.116690 0.202113i
\(460\) 0 0
\(461\) 15.0000 0.698620 0.349310 0.937007i \(-0.386416\pi\)
0.349310 + 0.937007i \(0.386416\pi\)
\(462\) 0 0
\(463\) −16.0000 −0.743583 −0.371792 0.928316i \(-0.621256\pi\)
−0.371792 + 0.928316i \(0.621256\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 14.0000 24.2487i 0.647843 1.12210i −0.335794 0.941935i \(-0.609005\pi\)
0.983637 0.180161i \(-0.0576619\pi\)
\(468\) 0 0
\(469\) −7.00000 + 36.3731i −0.323230 + 1.67955i
\(470\) 0 0
\(471\) −0.500000 + 0.866025i −0.0230388 + 0.0399043i
\(472\) 0 0
\(473\) 15.0000 + 25.9808i 0.689701 + 1.19460i
\(474\) 0 0
\(475\) 66.0000 3.02829
\(476\) 0 0
\(477\) −6.00000 −0.274721
\(478\) 0 0
\(479\) −16.0000 27.7128i −0.731059 1.26623i −0.956431 0.291958i \(-0.905693\pi\)
0.225372 0.974273i \(-0.427640\pi\)
\(480\) 0 0
\(481\) −20.0000 + 34.6410i −0.911922 + 1.57949i
\(482\) 0 0
\(483\) 8.00000 + 6.92820i 0.364013 + 0.315244i
\(484\) 0 0
\(485\) 36.0000 62.3538i 1.63468 2.83134i
\(486\) 0 0
\(487\) 2.50000 + 4.33013i 0.113286 + 0.196217i 0.917093 0.398673i \(-0.130529\pi\)
−0.803807 + 0.594890i \(0.797196\pi\)
\(488\) 0 0
\(489\) 4.00000 0.180886
\(490\) 0 0
\(491\) −18.0000 −0.812329 −0.406164 0.913800i \(-0.633134\pi\)
−0.406164 + 0.913800i \(0.633134\pi\)
\(492\) 0 0
\(493\) 4.00000 + 6.92820i 0.180151 + 0.312031i
\(494\) 0 0
\(495\) 12.0000 20.7846i 0.539360 0.934199i
\(496\) 0 0
\(497\) −14.0000 12.1244i −0.627986 0.543852i
\(498\) 0 0
\(499\) −19.5000 + 33.7750i −0.872940 + 1.51198i −0.0139987 + 0.999902i \(0.504456\pi\)
−0.858941 + 0.512074i \(0.828877\pi\)
\(500\) 0 0
\(501\) 9.50000 + 16.4545i 0.424429 + 0.735132i
\(502\) 0 0
\(503\) 21.0000 0.936344 0.468172 0.883637i \(-0.344913\pi\)
0.468172 + 0.883637i \(0.344913\pi\)
\(504\) 0 0
\(505\) 24.0000 1.06799
\(506\) 0 0
\(507\) −6.00000 10.3923i −0.266469 0.461538i
\(508\) 0 0
\(509\) −19.0000 + 32.9090i −0.842160 + 1.45866i 0.0459045 + 0.998946i \(0.485383\pi\)
−0.888065 + 0.459718i \(0.847950\pi\)
\(510\) 0 0
\(511\) 4.00000 20.7846i 0.176950 0.919457i
\(512\) 0 0
\(513\) 15.0000 25.9808i 0.662266 1.14708i
\(514\) 0 0
\(515\) 8.00000 + 13.8564i 0.352522 + 0.610586i
\(516\) 0 0
\(517\) 6.00000 0.263880
\(518\) 0 0
\(519\) −2.00000 −0.0877903
\(520\) 0 0
\(521\) 12.0000 + 20.7846i 0.525730 + 0.910590i 0.999551 + 0.0299693i \(0.00954094\pi\)
−0.473821 + 0.880621i \(0.657126\pi\)
\(522\) 0 0
\(523\) −3.00000 + 5.19615i −0.131181 + 0.227212i −0.924132 0.382073i \(-0.875210\pi\)
0.792951 + 0.609285i \(0.208544\pi\)
\(524\) 0 0
\(525\) 27.5000 9.52628i 1.20020 0.415761i
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) 3.50000 + 6.06218i 0.152174 + 0.263573i
\(530\) 0 0
\(531\) −4.00000 −0.173585
\(532\) 0 0
\(533\) 40.0000 1.73259
\(534\) 0 0
\(535\) 2.00000 + 3.46410i 0.0864675 + 0.149766i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −16.5000 + 12.9904i −0.710705 + 0.559535i
\(540\) 0 0
\(541\) −7.00000 + 12.1244i −0.300954 + 0.521267i −0.976352 0.216186i \(-0.930638\pi\)
0.675399 + 0.737453i \(0.263972\pi\)
\(542\) 0 0
\(543\) −9.00000 15.5885i −0.386227 0.668965i
\(544\) 0 0
\(545\) 32.0000 1.37073
\(546\) 0 0
\(547\) −13.0000 −0.555840 −0.277920 0.960604i \(-0.589645\pi\)
−0.277920 + 0.960604i \(0.589645\pi\)
\(548\) 0 0
\(549\) −8.00000 13.8564i −0.341432 0.591377i
\(550\) 0 0
\(551\) −24.0000 + 41.5692i −1.02243 + 1.77091i
\(552\) 0 0
\(553\) 37.5000 12.9904i 1.59466 0.552407i
\(554\) 0 0
\(555\) −16.0000 + 27.7128i −0.679162 + 1.17634i
\(556\) 0 0
\(557\) −11.5000 19.9186i −0.487271 0.843978i 0.512622 0.858614i \(-0.328674\pi\)
−0.999893 + 0.0146368i \(0.995341\pi\)
\(558\) 0 0
\(559\) −50.0000 −2.11477
\(560\) 0 0
\(561\) 3.00000 0.126660
\(562\) 0 0
\(563\) −15.0000 25.9808i −0.632175 1.09496i −0.987106 0.160066i \(-0.948829\pi\)
0.354932 0.934892i \(-0.384504\pi\)
\(564\) 0 0
\(565\) −16.0000 + 27.7128i −0.673125 + 1.16589i
\(566\) 0 0
\(567\) −0.500000 + 2.59808i −0.0209980 + 0.109109i
\(568\) 0 0
\(569\) −16.5000 + 28.5788i −0.691716 + 1.19809i 0.279559 + 0.960128i \(0.409812\pi\)
−0.971275 + 0.237959i \(0.923522\pi\)
\(570\) 0 0
\(571\) −18.0000 31.1769i −0.753277 1.30471i −0.946227 0.323505i \(-0.895139\pi\)
0.192950 0.981209i \(-0.438194\pi\)
\(572\) 0 0
\(573\) 12.0000 0.501307
\(574\) 0 0
\(575\) −44.0000 −1.83493
\(576\) 0 0
\(577\) −6.50000 11.2583i −0.270599 0.468690i 0.698417 0.715691i \(-0.253888\pi\)
−0.969015 + 0.247001i \(0.920555\pi\)
\(578\) 0 0
\(579\) 5.00000 8.66025i 0.207793 0.359908i
\(580\) 0 0
\(581\) −24.0000 20.7846i −0.995688 0.862291i
\(582\) 0 0
\(583\) 4.50000 7.79423i 0.186371 0.322804i
\(584\) 0 0
\(585\) 20.0000 + 34.6410i 0.826898 + 1.43223i
\(586\) 0 0
\(587\) −2.00000 −0.0825488 −0.0412744 0.999148i \(-0.513142\pi\)
−0.0412744 + 0.999148i \(0.513142\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) −9.00000 15.5885i −0.370211 0.641223i
\(592\) 0 0
\(593\) −10.5000 + 18.1865i −0.431183 + 0.746831i −0.996976 0.0777165i \(-0.975237\pi\)
0.565792 + 0.824548i \(0.308570\pi\)
\(594\) 0 0
\(595\) −8.00000 6.92820i −0.327968 0.284029i
\(596\) 0 0
\(597\) 3.50000 6.06218i 0.143245 0.248108i
\(598\) 0 0
\(599\) 17.0000 + 29.4449i 0.694601 + 1.20308i 0.970315 + 0.241845i \(0.0777525\pi\)
−0.275714 + 0.961240i \(0.588914\pi\)
\(600\) 0 0
\(601\) −14.0000 −0.571072 −0.285536 0.958368i \(-0.592172\pi\)
−0.285536 + 0.958368i \(0.592172\pi\)
\(602\) 0 0
\(603\) −28.0000 −1.14025
\(604\) 0 0
\(605\) −4.00000 6.92820i −0.162623 0.281672i
\(606\) 0 0
\(607\) 11.5000 19.9186i 0.466771 0.808470i −0.532509 0.846424i \(-0.678751\pi\)
0.999279 + 0.0379540i \(0.0120840\pi\)
\(608\) 0 0
\(609\) −4.00000 + 20.7846i −0.162088 + 0.842235i
\(610\) 0 0
\(611\) −5.00000 + 8.66025i −0.202278 + 0.350356i
\(612\) 0 0
\(613\) −8.50000 14.7224i −0.343312 0.594633i 0.641734 0.766927i \(-0.278215\pi\)
−0.985046 + 0.172294i \(0.944882\pi\)
\(614\) 0 0
\(615\) 32.0000 1.29036
\(616\) 0 0
\(617\) −36.0000 −1.44931 −0.724653 0.689114i \(-0.758000\pi\)
−0.724653 + 0.689114i \(0.758000\pi\)
\(618\) 0 0
\(619\) 8.50000 + 14.7224i 0.341644 + 0.591744i 0.984738 0.174042i \(-0.0556830\pi\)
−0.643094 + 0.765787i \(0.722350\pi\)
\(620\) 0 0
\(621\) −10.0000 + 17.3205i −0.401286 + 0.695048i
\(622\) 0 0
\(623\) 2.50000 0.866025i 0.100160 0.0346966i
\(624\) 0 0
\(625\) −20.5000 + 35.5070i −0.820000 + 1.42028i
\(626\) 0 0
\(627\) 9.00000 + 15.5885i 0.359425 + 0.622543i
\(628\) 0 0
\(629\) 8.00000 0.318981
\(630\) 0 0
\(631\) −30.0000 −1.19428 −0.597141 0.802137i \(-0.703697\pi\)
−0.597141 + 0.802137i \(0.703697\pi\)
\(632\) 0 0
\(633\) 2.00000 + 3.46410i 0.0794929 + 0.137686i
\(634\) 0 0
\(635\) 16.0000 27.7128i 0.634941 1.09975i
\(636\) 0 0
\(637\) −5.00000 34.6410i −0.198107 1.37253i
\(638\) 0 0
\(639\) 7.00000 12.1244i 0.276916 0.479632i
\(640\) 0 0
\(641\) −11.0000 19.0526i −0.434474 0.752531i 0.562779 0.826608i \(-0.309732\pi\)
−0.997253 + 0.0740768i \(0.976399\pi\)
\(642\) 0 0
\(643\) −1.00000 −0.0394362 −0.0197181 0.999806i \(-0.506277\pi\)
−0.0197181 + 0.999806i \(0.506277\pi\)
\(644\) 0 0
\(645\) −40.0000 −1.57500
\(646\) 0 0
\(647\) −14.0000 24.2487i −0.550397 0.953315i −0.998246 0.0592060i \(-0.981143\pi\)
0.447849 0.894109i \(-0.352190\pi\)
\(648\) 0 0
\(649\) 3.00000 5.19615i 0.117760 0.203967i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 5.00000 8.66025i 0.195665 0.338902i −0.751453 0.659786i \(-0.770647\pi\)
0.947118 + 0.320884i \(0.103980\pi\)
\(654\) 0 0
\(655\) −8.00000 13.8564i −0.312586 0.541415i
\(656\) 0 0
\(657\) 16.0000 0.624219
\(658\) 0 0
\(659\) −30.0000 −1.16863 −0.584317 0.811525i \(-0.698638\pi\)
−0.584317 + 0.811525i \(0.698638\pi\)
\(660\) 0 0
\(661\) −9.00000 15.5885i −0.350059 0.606321i 0.636200 0.771524i \(-0.280505\pi\)
−0.986260 + 0.165203i \(0.947172\pi\)
\(662\) 0 0
\(663\) −2.50000 + 4.33013i −0.0970920 + 0.168168i
\(664\) 0 0
\(665\) 12.0000 62.3538i 0.465340 2.41798i
\(666\) 0 0
\(667\) 16.0000 27.7128i 0.619522 1.07304i
\(668\) 0 0
\(669\) 3.00000 + 5.19615i 0.115987 + 0.200895i
\(670\) 0 0
\(671\) 24.0000 0.926510
\(672\) 0 0
\(673\) 28.0000 1.07932 0.539660 0.841883i \(-0.318553\pi\)
0.539660 + 0.841883i \(0.318553\pi\)
\(674\) 0 0
\(675\) 27.5000 + 47.6314i 1.05848 + 1.83333i
\(676\) 0 0
\(677\) 4.00000 6.92820i 0.153732 0.266272i −0.778864 0.627192i \(-0.784204\pi\)
0.932597 + 0.360920i \(0.117537\pi\)
\(678\) 0 0
\(679\) −36.0000 31.1769i −1.38155 1.19646i
\(680\) 0 0
\(681\) −12.5000 + 21.6506i −0.479001 + 0.829654i
\(682\) 0 0
\(683\) 10.5000 + 18.1865i 0.401771 + 0.695888i 0.993940 0.109926i \(-0.0350613\pi\)
−0.592168 + 0.805814i \(0.701728\pi\)
\(684\) 0 0
\(685\) 28.0000 1.06983
\(686\) 0 0
\(687\) −10.0000 −0.381524
\(688\) 0 0
\(689\) 7.50000 + 12.9904i 0.285727 + 0.494894i
\(690\) 0 0
\(691\) −4.00000 + 6.92820i −0.152167 + 0.263561i −0.932024 0.362397i \(-0.881959\pi\)
0.779857 + 0.625958i \(0.215292\pi\)
\(692\) 0 0
\(693\) −12.0000 10.3923i −0.455842 0.394771i
\(694\) 0 0
\(695\) −2.00000 + 3.46410i −0.0758643 + 0.131401i
\(696\) 0 0
\(697\) −4.00000 6.92820i −0.151511 0.262424i
\(698\) 0 0
\(699\) 28.0000 1.05906
\(700\) 0 0
\(701\) 31.0000 1.17085 0.585427 0.810725i \(-0.300927\pi\)
0.585427 + 0.810725i \(0.300927\pi\)
\(702\) 0 0
\(703\) 24.0000 + 41.5692i 0.905177 + 1.56781i
\(704\) 0 0
\(705\) −4.00000 + 6.92820i −0.150649 + 0.260931i
\(706\) 0 0
\(707\) 3.00000 15.5885i 0.112827 0.586264i
\(708\) 0 0
\(709\) 25.0000 43.3013i 0.938895 1.62621i 0.171358 0.985209i \(-0.445185\pi\)
0.767537 0.641004i \(-0.221482\pi\)
\(710\) 0 0
\(711\) 15.0000 + 25.9808i 0.562544 + 0.974355i
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) −60.0000 −2.24387
\(716\) 0 0
\(717\) −1.00000 1.73205i −0.0373457 0.0646846i
\(718\) 0 0
\(719\) 17.5000 30.3109i 0.652640 1.13041i −0.329840 0.944037i \(-0.606995\pi\)
0.982480 0.186369i \(-0.0596719\pi\)
\(720\) 0 0
\(721\) 10.0000 3.46410i 0.372419 0.129010i
\(722\) 0 0
\(723\) 4.00000 6.92820i 0.148762 0.257663i
\(724\) 0 0
\(725\) −44.0000 76.2102i −1.63412 2.83038i
\(726\) 0 0
\(727\) 18.0000 0.667583 0.333792 0.942647i \(-0.391672\pi\)
0.333792 + 0.942647i \(0.391672\pi\)
\(728\) 0 0
\(729\) 13.0000 0.481481
\(730\) 0 0
\(731\) 5.00000 + 8.66025i 0.184932 + 0.320311i
\(732\) 0 0
\(733\) −1.50000 + 2.59808i −0.0554038 + 0.0959621i −0.892397 0.451251i \(-0.850978\pi\)
0.836993 + 0.547213i \(0.184311\pi\)
\(734\) 0 0
\(735\) −4.00000 27.7128i −0.147542 1.02220i
\(736\) 0 0
\(737\) 21.0000 36.3731i 0.773545 1.33982i
\(738\) 0 0
\(739\) −15.0000 25.9808i −0.551784 0.955718i −0.998146 0.0608653i \(-0.980614\pi\)
0.446362 0.894852i \(-0.352719\pi\)
\(740\) 0 0
\(741\) −30.0000 −1.10208
\(742\) 0 0
\(743\) 1.00000 0.0366864 0.0183432 0.999832i \(-0.494161\pi\)
0.0183432 + 0.999832i \(0.494161\pi\)
\(744\) 0 0
\(745\) −22.0000 38.1051i −0.806018 1.39606i
\(746\) 0 0
\(747\) 12.0000 20.7846i 0.439057 0.760469i
\(748\) 0 0
\(749\) 2.50000 0.866025i 0.0913480 0.0316439i
\(750\) 0 0
\(751\) −1.50000 + 2.59808i −0.0547358 + 0.0948051i −0.892095 0.451848i \(-0.850765\pi\)
0.837359 + 0.546653i \(0.184098\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −40.0000 −1.45575
\(756\) 0 0
\(757\) 9.00000 0.327111 0.163555 0.986534i \(-0.447704\pi\)
0.163555 + 0.986534i \(0.447704\pi\)
\(758\) 0 0
\(759\) −6.00000 10.3923i −0.217786 0.377217i
\(760\) 0 0
\(761\) −22.5000 + 38.9711i −0.815624 + 1.41270i 0.0932544 + 0.995642i \(0.470273\pi\)
−0.908879 + 0.417061i \(0.863060\pi\)
\(762\) 0 0
\(763\) 4.00000 20.7846i 0.144810 0.752453i
\(764\) 0 0
\(765\) 4.00000 6.92820i 0.144620 0.250490i
\(766\) 0 0
\(767\) 5.00000 + 8.66025i 0.180540 + 0.312704i
\(768\) 0 0
\(769\) 1.00000 0.0360609 0.0180305 0.999837i \(-0.494260\pi\)
0.0180305 + 0.999837i \(0.494260\pi\)
\(770\) 0 0
\(771\) 3.00000 0.108042
\(772\) 0 0
\(773\) −4.50000 7.79423i −0.161854 0.280339i 0.773680 0.633577i \(-0.218414\pi\)
−0.935534 + 0.353238i \(0.885081\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 16.0000 + 13.8564i 0.573997 + 0.497096i
\(778\) 0 0
\(779\) 24.0000 41.5692i 0.859889 1.48937i
\(780\) 0 0
\(781\) 10.5000 + 18.1865i 0.375720 + 0.650765i
\(782\) 0 0
\(783\) −40.0000 −1.42948
\(784\) 0 0
\(785\) −4.00000 −0.142766
\(786\) 0 0
\(787\) −2.00000 3.46410i −0.0712923 0.123482i 0.828176 0.560469i \(-0.189379\pi\)
−0.899468 + 0.436987i \(0.856046\pi\)
\(788\) 0 0
\(789\) −2.00000 + 3.46410i −0.0712019 +