Properties

Label 288.2.i.a.97.1
Level $288$
Weight $2$
Character 288.97
Analytic conductor $2.300$
Analytic rank $1$
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] = [288,2,Mod(97,288)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(288, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("288.97");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 288 = 2^{5} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 288.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: \(2.29969157821\)
Analytic rank: \(1\)
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 97.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 288.97
Dual form 288.2.i.a.193.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.50000 - 0.866025i) q^{3} +(-2.00000 - 3.46410i) q^{5} +(-1.00000 + 1.73205i) q^{7} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\) \(q+(-1.50000 - 0.866025i) q^{3} +(-2.00000 - 3.46410i) q^{5} +(-1.00000 + 1.73205i) q^{7} +(1.50000 + 2.59808i) q^{9} +(-2.50000 + 4.33013i) q^{11} +(1.00000 + 1.73205i) q^{13} +6.92820i q^{15} -3.00000 q^{17} -1.00000 q^{19} +(3.00000 - 1.73205i) q^{21} +(-3.00000 - 5.19615i) q^{23} +(-5.50000 + 9.52628i) q^{25} -5.19615i q^{27} +(1.00000 - 1.73205i) q^{29} +(-2.00000 - 3.46410i) q^{31} +(7.50000 - 4.33013i) q^{33} +8.00000 q^{35} -8.00000 q^{37} -3.46410i q^{39} +(-0.500000 - 0.866025i) q^{41} +(-3.50000 + 6.06218i) q^{43} +(6.00000 - 10.3923i) q^{45} +(1.00000 - 1.73205i) q^{47} +(1.50000 + 2.59808i) q^{49} +(4.50000 + 2.59808i) q^{51} -4.00000 q^{53} +20.0000 q^{55} +(1.50000 + 0.866025i) q^{57} +(2.50000 + 4.33013i) q^{59} -6.00000 q^{63} +(4.00000 - 6.92820i) q^{65} +(-6.50000 - 11.2583i) q^{67} +10.3923i q^{69} -8.00000 q^{71} +3.00000 q^{73} +(16.5000 - 9.52628i) q^{75} +(-5.00000 - 8.66025i) q^{77} +(4.00000 - 6.92820i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(6.00000 - 10.3923i) q^{83} +(6.00000 + 10.3923i) q^{85} +(-3.00000 + 1.73205i) q^{87} -10.0000 q^{89} -4.00000 q^{91} +6.92820i q^{93} +(2.00000 + 3.46410i) q^{95} +(5.50000 - 9.52628i) q^{97} -15.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 3 q^{3} - 4 q^{5} - 2 q^{7} + 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 3 q^{3} - 4 q^{5} - 2 q^{7} + 3 q^{9} - 5 q^{11} + 2 q^{13} - 6 q^{17} - 2 q^{19} + 6 q^{21} - 6 q^{23} - 11 q^{25} + 2 q^{29} - 4 q^{31} + 15 q^{33} + 16 q^{35} - 16 q^{37} - q^{41} - 7 q^{43} + 12 q^{45} + 2 q^{47} + 3 q^{49} + 9 q^{51} - 8 q^{53} + 40 q^{55} + 3 q^{57} + 5 q^{59} - 12 q^{63} + 8 q^{65} - 13 q^{67} - 16 q^{71} + 6 q^{73} + 33 q^{75} - 10 q^{77} + 8 q^{79} - 9 q^{81} + 12 q^{83} + 12 q^{85} - 6 q^{87} - 20 q^{89} - 8 q^{91} + 4 q^{95} + 11 q^{97} - 30 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(37\) \(65\) \(127\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\)

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 0
\(3\) −1.50000 0.866025i −0.866025 0.500000i
\(4\) 0 0
\(5\) −2.00000 3.46410i −0.894427 1.54919i −0.834512 0.550990i \(-0.814250\pi\)
−0.0599153 0.998203i \(-0.519083\pi\)
\(6\) 0 0
\(7\) −1.00000 + 1.73205i −0.377964 + 0.654654i −0.990766 0.135583i \(-0.956709\pi\)
0.612801 + 0.790237i \(0.290043\pi\)
\(8\) 0 0
\(9\) 1.50000 + 2.59808i 0.500000 + 0.866025i
\(10\) 0 0
\(11\) −2.50000 + 4.33013i −0.753778 + 1.30558i 0.192201 + 0.981356i \(0.438437\pi\)
−0.945979 + 0.324227i \(0.894896\pi\)
\(12\) 0 0
\(13\) 1.00000 + 1.73205i 0.277350 + 0.480384i 0.970725 0.240192i \(-0.0772105\pi\)
−0.693375 + 0.720577i \(0.743877\pi\)
\(14\) 0 0
\(15\) 6.92820i 1.78885i
\(16\) 0 0
\(17\) −3.00000 −0.727607 −0.363803 0.931476i \(-0.618522\pi\)
−0.363803 + 0.931476i \(0.618522\pi\)
\(18\) 0 0
\(19\) −1.00000 −0.229416 −0.114708 0.993399i \(-0.536593\pi\)
−0.114708 + 0.993399i \(0.536593\pi\)
\(20\) 0 0
\(21\) 3.00000 1.73205i 0.654654 0.377964i
\(22\) 0 0
\(23\) −3.00000 5.19615i −0.625543 1.08347i −0.988436 0.151642i \(-0.951544\pi\)
0.362892 0.931831i \(-0.381789\pi\)
\(24\) 0 0
\(25\) −5.50000 + 9.52628i −1.10000 + 1.90526i
\(26\) 0 0
\(27\) 5.19615i 1.00000i
\(28\) 0 0
\(29\) 1.00000 1.73205i 0.185695 0.321634i −0.758115 0.652121i \(-0.773880\pi\)
0.943811 + 0.330487i \(0.107213\pi\)
\(30\) 0 0
\(31\) −2.00000 3.46410i −0.359211 0.622171i 0.628619 0.777714i \(-0.283621\pi\)
−0.987829 + 0.155543i \(0.950287\pi\)
\(32\) 0 0
\(33\) 7.50000 4.33013i 1.30558 0.753778i
\(34\) 0 0
\(35\) 8.00000 1.35225
\(36\) 0 0
\(37\) −8.00000 −1.31519 −0.657596 0.753371i \(-0.728427\pi\)
−0.657596 + 0.753371i \(0.728427\pi\)
\(38\) 0 0
\(39\) 3.46410i 0.554700i
\(40\) 0 0
\(41\) −0.500000 0.866025i −0.0780869 0.135250i 0.824338 0.566099i \(-0.191548\pi\)
−0.902424 + 0.430848i \(0.858214\pi\)
\(42\) 0 0
\(43\) −3.50000 + 6.06218i −0.533745 + 0.924473i 0.465478 + 0.885059i \(0.345882\pi\)
−0.999223 + 0.0394140i \(0.987451\pi\)
\(44\) 0 0
\(45\) 6.00000 10.3923i 0.894427 1.54919i
\(46\) 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
\(49\) 1.50000 + 2.59808i 0.214286 + 0.371154i
\(50\) 0 0
\(51\) 4.50000 + 2.59808i 0.630126 + 0.363803i
\(52\) 0 0
\(53\) −4.00000 −0.549442 −0.274721 0.961524i \(-0.588586\pi\)
−0.274721 + 0.961524i \(0.588586\pi\)
\(54\) 0 0
\(55\) 20.0000 2.69680
\(56\) 0 0
\(57\) 1.50000 + 0.866025i 0.198680 + 0.114708i
\(58\) 0 0
\(59\) 2.50000 + 4.33013i 0.325472 + 0.563735i 0.981608 0.190909i \(-0.0611434\pi\)
−0.656136 + 0.754643i \(0.727810\pi\)
\(60\) 0 0
\(61\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(62\) 0 0
\(63\) −6.00000 −0.755929
\(64\) 0 0
\(65\) 4.00000 6.92820i 0.496139 0.859338i
\(66\) 0 0
\(67\) −6.50000 11.2583i −0.794101 1.37542i −0.923408 0.383819i \(-0.874609\pi\)
0.129307 0.991605i \(-0.458725\pi\)
\(68\) 0 0
\(69\) 10.3923i 1.25109i
\(70\) 0 0
\(71\) −8.00000 −0.949425 −0.474713 0.880141i \(-0.657448\pi\)
−0.474713 + 0.880141i \(0.657448\pi\)
\(72\) 0 0
\(73\) 3.00000 0.351123 0.175562 0.984468i \(-0.443826\pi\)
0.175562 + 0.984468i \(0.443826\pi\)
\(74\) 0 0
\(75\) 16.5000 9.52628i 1.90526 1.10000i
\(76\) 0 0
\(77\) −5.00000 8.66025i −0.569803 0.986928i
\(78\) 0 0
\(79\) 4.00000 6.92820i 0.450035 0.779484i −0.548352 0.836247i \(-0.684745\pi\)
0.998388 + 0.0567635i \(0.0180781\pi\)
\(80\) 0 0
\(81\) −4.50000 + 7.79423i −0.500000 + 0.866025i
\(82\) 0 0
\(83\) 6.00000 10.3923i 0.658586 1.14070i −0.322396 0.946605i \(-0.604488\pi\)
0.980982 0.194099i \(-0.0621783\pi\)
\(84\) 0 0
\(85\) 6.00000 + 10.3923i 0.650791 + 1.12720i
\(86\) 0 0
\(87\) −3.00000 + 1.73205i −0.321634 + 0.185695i
\(88\) 0 0
\(89\) −10.0000 −1.06000 −0.529999 0.847998i \(-0.677808\pi\)
−0.529999 + 0.847998i \(0.677808\pi\)
\(90\) 0 0
\(91\) −4.00000 −0.419314
\(92\) 0 0
\(93\) 6.92820i 0.718421i
\(94\) 0 0
\(95\) 2.00000 + 3.46410i 0.205196 + 0.355409i
\(96\) 0 0
\(97\) 5.50000 9.52628i 0.558440 0.967247i −0.439187 0.898396i \(-0.644733\pi\)
0.997627 0.0688512i \(-0.0219334\pi\)
\(98\) 0 0
\(99\) −15.0000 −1.50756
\(100\) 0 0
\(101\) −6.00000 + 10.3923i −0.597022 + 1.03407i 0.396236 + 0.918149i \(0.370316\pi\)
−0.993258 + 0.115924i \(0.963017\pi\)
\(102\) 0 0
\(103\) 3.00000 + 5.19615i 0.295599 + 0.511992i 0.975124 0.221660i \(-0.0711475\pi\)
−0.679525 + 0.733652i \(0.737814\pi\)
\(104\) 0 0
\(105\) −12.0000 6.92820i −1.17108 0.676123i
\(106\) 0 0
\(107\) −5.00000 −0.483368 −0.241684 0.970355i \(-0.577700\pi\)
−0.241684 + 0.970355i \(0.577700\pi\)
\(108\) 0 0
\(109\) 8.00000 0.766261 0.383131 0.923694i \(-0.374846\pi\)
0.383131 + 0.923694i \(0.374846\pi\)
\(110\) 0 0
\(111\) 12.0000 + 6.92820i 1.13899 + 0.657596i
\(112\) 0 0
\(113\) 1.00000 + 1.73205i 0.0940721 + 0.162938i 0.909221 0.416314i \(-0.136678\pi\)
−0.815149 + 0.579252i \(0.803345\pi\)
\(114\) 0 0
\(115\) −12.0000 + 20.7846i −1.11901 + 1.93817i
\(116\) 0 0
\(117\) −3.00000 + 5.19615i −0.277350 + 0.480384i
\(118\) 0 0
\(119\) 3.00000 5.19615i 0.275010 0.476331i
\(120\) 0 0
\(121\) −7.00000 12.1244i −0.636364 1.10221i
\(122\) 0 0
\(123\) 1.73205i 0.156174i
\(124\) 0 0
\(125\) 24.0000 2.14663
\(126\) 0 0
\(127\) −2.00000 −0.177471 −0.0887357 0.996055i \(-0.528283\pi\)
−0.0887357 + 0.996055i \(0.528283\pi\)
\(128\) 0 0
\(129\) 10.5000 6.06218i 0.924473 0.533745i
\(130\) 0 0
\(131\) 8.00000 + 13.8564i 0.698963 + 1.21064i 0.968826 + 0.247741i \(0.0796882\pi\)
−0.269863 + 0.962899i \(0.586978\pi\)
\(132\) 0 0
\(133\) 1.00000 1.73205i 0.0867110 0.150188i
\(134\) 0 0
\(135\) −18.0000 + 10.3923i −1.54919 + 0.894427i
\(136\) 0 0
\(137\) 1.50000 2.59808i 0.128154 0.221969i −0.794808 0.606861i \(-0.792428\pi\)
0.922961 + 0.384893i \(0.125762\pi\)
\(138\) 0 0
\(139\) −6.50000 11.2583i −0.551323 0.954919i −0.998179 0.0603135i \(-0.980790\pi\)
0.446857 0.894606i \(-0.352543\pi\)
\(140\) 0 0
\(141\) −3.00000 + 1.73205i −0.252646 + 0.145865i
\(142\) 0 0
\(143\) −10.0000 −0.836242
\(144\) 0 0
\(145\) −8.00000 −0.664364
\(146\) 0 0
\(147\) 5.19615i 0.428571i
\(148\) 0 0
\(149\) 9.00000 + 15.5885i 0.737309 + 1.27706i 0.953703 + 0.300750i \(0.0972370\pi\)
−0.216394 + 0.976306i \(0.569430\pi\)
\(150\) 0 0
\(151\) −9.00000 + 15.5885i −0.732410 + 1.26857i 0.223441 + 0.974717i \(0.428271\pi\)
−0.955851 + 0.293853i \(0.905062\pi\)
\(152\) 0 0
\(153\) −4.50000 7.79423i −0.363803 0.630126i
\(154\) 0 0
\(155\) −8.00000 + 13.8564i −0.642575 + 1.11297i
\(156\) 0 0
\(157\) −10.0000 17.3205i −0.798087 1.38233i −0.920860 0.389892i \(-0.872512\pi\)
0.122774 0.992435i \(-0.460821\pi\)
\(158\) 0 0
\(159\) 6.00000 + 3.46410i 0.475831 + 0.274721i
\(160\) 0 0
\(161\) 12.0000 0.945732
\(162\) 0 0
\(163\) 20.0000 1.56652 0.783260 0.621694i \(-0.213555\pi\)
0.783260 + 0.621694i \(0.213555\pi\)
\(164\) 0 0
\(165\) −30.0000 17.3205i −2.33550 1.34840i
\(166\) 0 0
\(167\) −8.00000 13.8564i −0.619059 1.07224i −0.989658 0.143448i \(-0.954181\pi\)
0.370599 0.928793i \(-0.379152\pi\)
\(168\) 0 0
\(169\) 4.50000 7.79423i 0.346154 0.599556i
\(170\) 0 0
\(171\) −1.50000 2.59808i −0.114708 0.198680i
\(172\) 0 0
\(173\) −9.00000 + 15.5885i −0.684257 + 1.18517i 0.289412 + 0.957205i \(0.406540\pi\)
−0.973670 + 0.227964i \(0.926793\pi\)
\(174\) 0 0
\(175\) −11.0000 19.0526i −0.831522 1.44024i
\(176\) 0 0
\(177\) 8.66025i 0.650945i
\(178\) 0 0
\(179\) −12.0000 −0.896922 −0.448461 0.893802i \(-0.648028\pi\)
−0.448461 + 0.893802i \(0.648028\pi\)
\(180\) 0 0
\(181\) 2.00000 0.148659 0.0743294 0.997234i \(-0.476318\pi\)
0.0743294 + 0.997234i \(0.476318\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 16.0000 + 27.7128i 1.17634 + 2.03749i
\(186\) 0 0
\(187\) 7.50000 12.9904i 0.548454 0.949951i
\(188\) 0 0
\(189\) 9.00000 + 5.19615i 0.654654 + 0.377964i
\(190\) 0 0
\(191\) −3.00000 + 5.19615i −0.217072 + 0.375980i −0.953912 0.300088i \(-0.902984\pi\)
0.736839 + 0.676068i \(0.236317\pi\)
\(192\) 0 0
\(193\) 1.50000 + 2.59808i 0.107972 + 0.187014i 0.914949 0.403570i \(-0.132231\pi\)
−0.806976 + 0.590584i \(0.798898\pi\)
\(194\) 0 0
\(195\) −12.0000 + 6.92820i −0.859338 + 0.496139i
\(196\) 0 0
\(197\) 4.00000 0.284988 0.142494 0.989796i \(-0.454488\pi\)
0.142494 + 0.989796i \(0.454488\pi\)
\(198\) 0 0
\(199\) −2.00000 −0.141776 −0.0708881 0.997484i \(-0.522583\pi\)
−0.0708881 + 0.997484i \(0.522583\pi\)
\(200\) 0 0
\(201\) 22.5167i 1.58820i
\(202\) 0 0
\(203\) 2.00000 + 3.46410i 0.140372 + 0.243132i
\(204\) 0 0
\(205\) −2.00000 + 3.46410i −0.139686 + 0.241943i
\(206\) 0 0
\(207\) 9.00000 15.5885i 0.625543 1.08347i
\(208\) 0 0
\(209\) 2.50000 4.33013i 0.172929 0.299521i
\(210\) 0 0
\(211\) 14.0000 + 24.2487i 0.963800 + 1.66935i 0.712806 + 0.701361i \(0.247424\pi\)
0.250994 + 0.967989i \(0.419243\pi\)
\(212\) 0 0
\(213\) 12.0000 + 6.92820i 0.822226 + 0.474713i
\(214\) 0 0
\(215\) 28.0000 1.90958
\(216\) 0 0
\(217\) 8.00000 0.543075
\(218\) 0 0
\(219\) −4.50000 2.59808i −0.304082 0.175562i
\(220\) 0 0
\(221\) −3.00000 5.19615i −0.201802 0.349531i
\(222\) 0 0
\(223\) −7.00000 + 12.1244i −0.468755 + 0.811907i −0.999362 0.0357107i \(-0.988630\pi\)
0.530607 + 0.847618i \(0.321964\pi\)
\(224\) 0 0
\(225\) −33.0000 −2.20000
\(226\) 0 0
\(227\) 1.50000 2.59808i 0.0995585 0.172440i −0.811943 0.583736i \(-0.801590\pi\)
0.911502 + 0.411296i \(0.134924\pi\)
\(228\) 0 0
\(229\) −7.00000 12.1244i −0.462573 0.801200i 0.536515 0.843891i \(-0.319740\pi\)
−0.999088 + 0.0426906i \(0.986407\pi\)
\(230\) 0 0
\(231\) 17.3205i 1.13961i
\(232\) 0 0
\(233\) −21.0000 −1.37576 −0.687878 0.725826i \(-0.741458\pi\)
−0.687878 + 0.725826i \(0.741458\pi\)
\(234\) 0 0
\(235\) −8.00000 −0.521862
\(236\) 0 0
\(237\) −12.0000 + 6.92820i −0.779484 + 0.450035i
\(238\) 0 0
\(239\) 3.00000 + 5.19615i 0.194054 + 0.336111i 0.946590 0.322440i \(-0.104503\pi\)
−0.752536 + 0.658551i \(0.771170\pi\)
\(240\) 0 0
\(241\) 11.5000 19.9186i 0.740780 1.28307i −0.211360 0.977408i \(-0.567789\pi\)
0.952141 0.305661i \(-0.0988773\pi\)
\(242\) 0 0
\(243\) 13.5000 7.79423i 0.866025 0.500000i
\(244\) 0 0
\(245\) 6.00000 10.3923i 0.383326 0.663940i
\(246\) 0 0
\(247\) −1.00000 1.73205i −0.0636285 0.110208i
\(248\) 0 0
\(249\) −18.0000 + 10.3923i −1.14070 + 0.658586i
\(250\) 0 0
\(251\) 21.0000 1.32551 0.662754 0.748837i \(-0.269387\pi\)
0.662754 + 0.748837i \(0.269387\pi\)
\(252\) 0 0
\(253\) 30.0000 1.88608
\(254\) 0 0
\(255\) 20.7846i 1.30158i
\(256\) 0 0
\(257\) 2.50000 + 4.33013i 0.155946 + 0.270106i 0.933403 0.358830i \(-0.116824\pi\)
−0.777457 + 0.628936i \(0.783491\pi\)
\(258\) 0 0
\(259\) 8.00000 13.8564i 0.497096 0.860995i
\(260\) 0 0
\(261\) 6.00000 0.371391
\(262\) 0 0
\(263\) 3.00000 5.19615i 0.184988 0.320408i −0.758585 0.651575i \(-0.774109\pi\)
0.943572 + 0.331166i \(0.107442\pi\)
\(264\) 0 0
\(265\) 8.00000 + 13.8564i 0.491436 + 0.851192i
\(266\) 0 0
\(267\) 15.0000 + 8.66025i 0.917985 + 0.529999i
\(268\) 0 0
\(269\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(270\) 0 0
\(271\) 12.0000 0.728948 0.364474 0.931214i \(-0.381249\pi\)
0.364474 + 0.931214i \(0.381249\pi\)
\(272\) 0 0
\(273\) 6.00000 + 3.46410i 0.363137 + 0.209657i
\(274\) 0 0
\(275\) −27.5000 47.6314i −1.65831 2.87228i
\(276\) 0 0
\(277\) 7.00000 12.1244i 0.420589 0.728482i −0.575408 0.817867i \(-0.695157\pi\)
0.995997 + 0.0893846i \(0.0284900\pi\)
\(278\) 0 0
\(279\) 6.00000 10.3923i 0.359211 0.622171i
\(280\) 0 0
\(281\) 9.00000 15.5885i 0.536895 0.929929i −0.462174 0.886789i \(-0.652930\pi\)
0.999069 0.0431402i \(-0.0137362\pi\)
\(282\) 0 0
\(283\) −14.0000 24.2487i −0.832214 1.44144i −0.896279 0.443491i \(-0.853740\pi\)
0.0640654 0.997946i \(-0.479593\pi\)
\(284\) 0 0
\(285\) 6.92820i 0.410391i
\(286\) 0 0
\(287\) 2.00000 0.118056
\(288\) 0 0
\(289\) −8.00000 −0.470588
\(290\) 0 0
\(291\) −16.5000 + 9.52628i −0.967247 + 0.558440i
\(292\) 0 0
\(293\) −15.0000 25.9808i −0.876309 1.51781i −0.855361 0.518032i \(-0.826665\pi\)
−0.0209480 0.999781i \(-0.506668\pi\)
\(294\) 0 0
\(295\) 10.0000 17.3205i 0.582223 1.00844i
\(296\) 0 0
\(297\) 22.5000 + 12.9904i 1.30558 + 0.753778i
\(298\) 0 0
\(299\) 6.00000 10.3923i 0.346989 0.601003i
\(300\) 0 0
\(301\) −7.00000 12.1244i −0.403473 0.698836i
\(302\) 0 0
\(303\) 18.0000 10.3923i 1.03407 0.597022i
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 9.00000 0.513657 0.256829 0.966457i \(-0.417322\pi\)
0.256829 + 0.966457i \(0.417322\pi\)
\(308\) 0 0
\(309\) 10.3923i 0.591198i
\(310\) 0 0
\(311\) 9.00000 + 15.5885i 0.510343 + 0.883940i 0.999928 + 0.0119847i \(0.00381495\pi\)
−0.489585 + 0.871956i \(0.662852\pi\)
\(312\) 0 0
\(313\) −6.50000 + 11.2583i −0.367402 + 0.636358i −0.989158 0.146852i \(-0.953086\pi\)
0.621757 + 0.783210i \(0.286419\pi\)
\(314\) 0 0
\(315\) 12.0000 + 20.7846i 0.676123 + 1.17108i
\(316\) 0 0
\(317\) −9.00000 + 15.5885i −0.505490 + 0.875535i 0.494489 + 0.869184i \(0.335355\pi\)
−0.999980 + 0.00635137i \(0.997978\pi\)
\(318\) 0 0
\(319\) 5.00000 + 8.66025i 0.279946 + 0.484881i
\(320\) 0 0
\(321\) 7.50000 + 4.33013i 0.418609 + 0.241684i
\(322\) 0 0
\(323\) 3.00000 0.166924
\(324\) 0 0
\(325\) −22.0000 −1.22034
\(326\) 0 0
\(327\) −12.0000 6.92820i −0.663602 0.383131i
\(328\) 0 0
\(329\) 2.00000 + 3.46410i 0.110264 + 0.190982i
\(330\) 0 0
\(331\) −2.00000 + 3.46410i −0.109930 + 0.190404i −0.915742 0.401768i \(-0.868396\pi\)
0.805812 + 0.592172i \(0.201729\pi\)
\(332\) 0 0
\(333\) −12.0000 20.7846i −0.657596 1.13899i
\(334\) 0 0
\(335\) −26.0000 + 45.0333i −1.42053 + 2.46043i
\(336\) 0 0
\(337\) 12.5000 + 21.6506i 0.680918 + 1.17939i 0.974701 + 0.223513i \(0.0717525\pi\)
−0.293783 + 0.955872i \(0.594914\pi\)
\(338\) 0 0
\(339\) 3.46410i 0.188144i
\(340\) 0 0
\(341\) 20.0000 1.08306
\(342\) 0 0
\(343\) −20.0000 −1.07990
\(344\) 0 0
\(345\) 36.0000 20.7846i 1.93817 1.11901i
\(346\) 0 0
\(347\) −0.500000 0.866025i −0.0268414 0.0464907i 0.852293 0.523065i \(-0.175212\pi\)
−0.879134 + 0.476575i \(0.841878\pi\)
\(348\) 0 0
\(349\) −8.00000 + 13.8564i −0.428230 + 0.741716i −0.996716 0.0809766i \(-0.974196\pi\)
0.568486 + 0.822693i \(0.307529\pi\)
\(350\) 0 0
\(351\) 9.00000 5.19615i 0.480384 0.277350i
\(352\) 0 0
\(353\) −17.5000 + 30.3109i −0.931431 + 1.61329i −0.150553 + 0.988602i \(0.548106\pi\)
−0.780878 + 0.624684i \(0.785228\pi\)
\(354\) 0 0
\(355\) 16.0000 + 27.7128i 0.849192 + 1.47084i
\(356\) 0 0
\(357\) −9.00000 + 5.19615i −0.476331 + 0.275010i
\(358\) 0 0
\(359\) 14.0000 0.738892 0.369446 0.929252i \(-0.379548\pi\)
0.369446 + 0.929252i \(0.379548\pi\)
\(360\) 0 0
\(361\) −18.0000 −0.947368
\(362\) 0 0
\(363\) 24.2487i 1.27273i
\(364\) 0 0
\(365\) −6.00000 10.3923i −0.314054 0.543958i
\(366\) 0 0
\(367\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(368\) 0 0
\(369\) 1.50000 2.59808i 0.0780869 0.135250i
\(370\) 0 0
\(371\) 4.00000 6.92820i 0.207670 0.359694i
\(372\) 0 0
\(373\) 11.0000 + 19.0526i 0.569558 + 0.986504i 0.996610 + 0.0822766i \(0.0262191\pi\)
−0.427051 + 0.904227i \(0.640448\pi\)
\(374\) 0 0
\(375\) −36.0000 20.7846i −1.85903 1.07331i
\(376\) 0 0
\(377\) 4.00000 0.206010
\(378\) 0 0
\(379\) −1.00000 −0.0513665 −0.0256833 0.999670i \(-0.508176\pi\)
−0.0256833 + 0.999670i \(0.508176\pi\)
\(380\) 0 0
\(381\) 3.00000 + 1.73205i 0.153695 + 0.0887357i
\(382\) 0 0
\(383\) 10.0000 + 17.3205i 0.510976 + 0.885037i 0.999919 + 0.0127209i \(0.00404928\pi\)
−0.488943 + 0.872316i \(0.662617\pi\)
\(384\) 0 0
\(385\) −20.0000 + 34.6410i −1.01929 + 1.76547i
\(386\) 0 0
\(387\) −21.0000 −1.06749
\(388\) 0 0
\(389\) 3.00000 5.19615i 0.152106 0.263455i −0.779895 0.625910i \(-0.784728\pi\)
0.932002 + 0.362454i \(0.118061\pi\)
\(390\) 0 0
\(391\) 9.00000 + 15.5885i 0.455150 + 0.788342i
\(392\) 0 0
\(393\) 27.7128i 1.39793i
\(394\) 0 0
\(395\) −32.0000 −1.61009
\(396\) 0 0
\(397\) −32.0000 −1.60603 −0.803017 0.595956i \(-0.796773\pi\)
−0.803017 + 0.595956i \(0.796773\pi\)
\(398\) 0 0
\(399\) −3.00000 + 1.73205i −0.150188 + 0.0867110i
\(400\) 0 0
\(401\) −2.50000 4.33013i −0.124844 0.216236i 0.796828 0.604206i \(-0.206510\pi\)
−0.921672 + 0.387970i \(0.873176\pi\)
\(402\) 0 0
\(403\) 4.00000 6.92820i 0.199254 0.345118i
\(404\) 0 0
\(405\) 36.0000 1.78885
\(406\) 0 0
\(407\) 20.0000 34.6410i 0.991363 1.71709i
\(408\) 0 0
\(409\) −12.5000 21.6506i −0.618085 1.07056i −0.989835 0.142222i \(-0.954575\pi\)
0.371750 0.928333i \(-0.378758\pi\)
\(410\) 0 0
\(411\) −4.50000 + 2.59808i −0.221969 + 0.128154i
\(412\) 0 0
\(413\) −10.0000 −0.492068
\(414\) 0 0
\(415\) −48.0000 −2.35623
\(416\) 0 0
\(417\) 22.5167i 1.10265i
\(418\) 0 0
\(419\) 2.00000 + 3.46410i 0.0977064 + 0.169232i 0.910735 0.412991i \(-0.135516\pi\)
−0.813029 + 0.582224i \(0.802183\pi\)
\(420\) 0 0
\(421\) −4.00000 + 6.92820i −0.194948 + 0.337660i −0.946883 0.321577i \(-0.895787\pi\)
0.751935 + 0.659237i \(0.229121\pi\)
\(422\) 0 0
\(423\) 6.00000 0.291730
\(424\) 0 0
\(425\) 16.5000 28.5788i 0.800368 1.38628i
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 15.0000 + 8.66025i 0.724207 + 0.418121i
\(430\) 0 0
\(431\) −30.0000 −1.44505 −0.722525 0.691345i \(-0.757018\pi\)
−0.722525 + 0.691345i \(0.757018\pi\)
\(432\) 0 0
\(433\) 1.00000 0.0480569 0.0240285 0.999711i \(-0.492351\pi\)
0.0240285 + 0.999711i \(0.492351\pi\)
\(434\) 0 0
\(435\) 12.0000 + 6.92820i 0.575356 + 0.332182i
\(436\) 0 0
\(437\) 3.00000 + 5.19615i 0.143509 + 0.248566i
\(438\) 0 0
\(439\) −4.00000 + 6.92820i −0.190910 + 0.330665i −0.945552 0.325471i \(-0.894477\pi\)
0.754642 + 0.656136i \(0.227810\pi\)
\(440\) 0 0
\(441\) −4.50000 + 7.79423i −0.214286 + 0.371154i
\(442\) 0 0
\(443\) −13.5000 + 23.3827i −0.641404 + 1.11094i 0.343715 + 0.939074i \(0.388315\pi\)
−0.985119 + 0.171871i \(0.945019\pi\)
\(444\) 0 0
\(445\) 20.0000 + 34.6410i 0.948091 + 1.64214i
\(446\) 0 0
\(447\) 31.1769i 1.47462i
\(448\) 0 0
\(449\) −31.0000 −1.46298 −0.731490 0.681852i \(-0.761175\pi\)
−0.731490 + 0.681852i \(0.761175\pi\)
\(450\) 0 0
\(451\) 5.00000 0.235441
\(452\) 0 0
\(453\) 27.0000 15.5885i 1.26857 0.732410i
\(454\) 0 0
\(455\) 8.00000 + 13.8564i 0.375046 + 0.649598i
\(456\) 0 0
\(457\) 3.50000 6.06218i 0.163723 0.283577i −0.772478 0.635042i \(-0.780983\pi\)
0.936201 + 0.351465i \(0.114316\pi\)
\(458\) 0 0
\(459\) 15.5885i 0.727607i
\(460\) 0 0
\(461\) 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
\(463\) −8.00000 13.8564i −0.371792 0.643962i 0.618050 0.786139i \(-0.287923\pi\)
−0.989841 + 0.142177i \(0.954590\pi\)
\(464\) 0 0
\(465\) 24.0000 13.8564i 1.11297 0.642575i
\(466\) 0 0
\(467\) −7.00000 −0.323921 −0.161961 0.986797i \(-0.551782\pi\)
−0.161961 + 0.986797i \(0.551782\pi\)
\(468\) 0 0
\(469\) 26.0000 1.20057
\(470\) 0 0
\(471\) 34.6410i 1.59617i
\(472\) 0 0
\(473\) −17.5000 30.3109i −0.804651 1.39370i
\(474\) 0 0
\(475\) 5.50000 9.52628i 0.252357 0.437096i
\(476\) 0 0
\(477\) −6.00000 10.3923i −0.274721 0.475831i
\(478\) 0 0
\(479\) 9.00000 15.5885i 0.411220 0.712255i −0.583803 0.811895i \(-0.698436\pi\)
0.995023 + 0.0996406i \(0.0317693\pi\)
\(480\) 0 0
\(481\) −8.00000 13.8564i −0.364769 0.631798i
\(482\) 0 0
\(483\) −18.0000 10.3923i −0.819028 0.472866i
\(484\) 0 0
\(485\) −44.0000 −1.99794
\(486\) 0 0
\(487\) −22.0000 −0.996915 −0.498458 0.866914i \(-0.666100\pi\)
−0.498458 + 0.866914i \(0.666100\pi\)
\(488\) 0 0
\(489\) −30.0000 17.3205i −1.35665 0.783260i
\(490\) 0 0
\(491\) 3.50000 + 6.06218i 0.157953 + 0.273582i 0.934130 0.356932i \(-0.116177\pi\)
−0.776178 + 0.630514i \(0.782844\pi\)
\(492\) 0 0
\(493\) −3.00000 + 5.19615i −0.135113 + 0.234023i
\(494\) 0 0
\(495\) 30.0000 + 51.9615i 1.34840 + 2.33550i
\(496\) 0 0
\(497\) 8.00000 13.8564i 0.358849 0.621545i
\(498\) 0 0
\(499\) 10.5000 + 18.1865i 0.470045 + 0.814141i 0.999413 0.0342508i \(-0.0109045\pi\)
−0.529369 + 0.848392i \(0.677571\pi\)
\(500\) 0 0
\(501\) 27.7128i 1.23812i
\(502\) 0 0
\(503\) −24.0000 −1.07011 −0.535054 0.844818i \(-0.679709\pi\)
−0.535054 + 0.844818i \(0.679709\pi\)
\(504\) 0 0
\(505\) 48.0000 2.13597
\(506\) 0 0
\(507\) −13.5000 + 7.79423i −0.599556 + 0.346154i
\(508\) 0 0
\(509\) −12.0000 20.7846i −0.531891 0.921262i −0.999307 0.0372243i \(-0.988148\pi\)
0.467416 0.884037i \(-0.345185\pi\)
\(510\) 0 0
\(511\) −3.00000 + 5.19615i −0.132712 + 0.229864i
\(512\) 0 0
\(513\) 5.19615i 0.229416i
\(514\) 0 0
\(515\) 12.0000 20.7846i 0.528783 0.915879i
\(516\) 0 0
\(517\) 5.00000 + 8.66025i 0.219900 + 0.380878i
\(518\) 0 0
\(519\) 27.0000 15.5885i 1.18517 0.684257i
\(520\) 0 0
\(521\) −3.00000 −0.131432 −0.0657162 0.997838i \(-0.520933\pi\)
−0.0657162 + 0.997838i \(0.520933\pi\)
\(522\) 0 0
\(523\) 12.0000 0.524723 0.262362 0.964970i \(-0.415499\pi\)
0.262362 + 0.964970i \(0.415499\pi\)
\(524\) 0 0
\(525\) 38.1051i 1.66304i
\(526\) 0 0
\(527\) 6.00000 + 10.3923i 0.261364 + 0.452696i
\(528\) 0 0
\(529\) −6.50000 + 11.2583i −0.282609 + 0.489493i
\(530\) 0 0
\(531\) −7.50000 + 12.9904i −0.325472 + 0.563735i
\(532\) 0 0
\(533\) 1.00000 1.73205i 0.0433148 0.0750234i
\(534\) 0 0
\(535\) 10.0000 + 17.3205i 0.432338 + 0.748831i
\(536\) 0 0
\(537\) 18.0000 + 10.3923i 0.776757 + 0.448461i
\(538\) 0 0
\(539\) −15.0000 −0.646096
\(540\) 0 0
\(541\) −32.0000 −1.37579 −0.687894 0.725811i \(-0.741464\pi\)
−0.687894 + 0.725811i \(0.741464\pi\)
\(542\) 0 0
\(543\) −3.00000 1.73205i −0.128742 0.0743294i
\(544\) 0 0
\(545\) −16.0000 27.7128i −0.685365 1.18709i
\(546\) 0 0
\(547\) 16.5000 28.5788i 0.705489 1.22194i −0.261026 0.965332i \(-0.584061\pi\)
0.966515 0.256611i \(-0.0826059\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −1.00000 + 1.73205i −0.0426014 + 0.0737878i
\(552\) 0 0
\(553\) 8.00000 + 13.8564i 0.340195 + 0.589234i
\(554\) 0 0
\(555\) 55.4256i 2.35269i
\(556\) 0 0
\(557\) 10.0000 0.423714 0.211857 0.977301i \(-0.432049\pi\)
0.211857 + 0.977301i \(0.432049\pi\)
\(558\) 0 0
\(559\) −14.0000 −0.592137
\(560\) 0 0
\(561\) −22.5000 + 12.9904i −0.949951 + 0.548454i
\(562\) 0 0
\(563\) 7.50000 + 12.9904i 0.316087 + 0.547479i 0.979668 0.200625i \(-0.0642974\pi\)
−0.663581 + 0.748105i \(0.730964\pi\)
\(564\) 0 0
\(565\) 4.00000 6.92820i 0.168281 0.291472i
\(566\) 0 0
\(567\) −9.00000 15.5885i −0.377964 0.654654i
\(568\) 0 0
\(569\) 5.50000 9.52628i 0.230572 0.399362i −0.727405 0.686209i \(-0.759274\pi\)
0.957977 + 0.286846i \(0.0926069\pi\)
\(570\) 0 0
\(571\) 6.50000 + 11.2583i 0.272017 + 0.471146i 0.969378 0.245573i \(-0.0789761\pi\)
−0.697362 + 0.716720i \(0.745643\pi\)
\(572\) 0 0
\(573\) 9.00000 5.19615i 0.375980 0.217072i
\(574\) 0 0
\(575\) 66.0000 2.75239
\(576\) 0 0
\(577\) 3.00000 0.124892 0.0624458 0.998048i \(-0.480110\pi\)
0.0624458 + 0.998048i \(0.480110\pi\)
\(578\) 0 0
\(579\) 5.19615i 0.215945i
\(580\) 0 0
\(581\) 12.0000 + 20.7846i 0.497844 + 0.862291i
\(582\) 0 0
\(583\) 10.0000 17.3205i 0.414158 0.717342i
\(584\) 0 0
\(585\) 24.0000 0.992278
\(586\) 0 0
\(587\) 4.50000 7.79423i 0.185735 0.321702i −0.758089 0.652151i \(-0.773867\pi\)
0.943824 + 0.330449i \(0.107200\pi\)
\(588\) 0 0
\(589\) 2.00000 + 3.46410i 0.0824086 + 0.142736i
\(590\) 0 0
\(591\) −6.00000 3.46410i −0.246807 0.142494i
\(592\) 0 0
\(593\) 6.00000 0.246390 0.123195 0.992382i \(-0.460686\pi\)
0.123195 + 0.992382i \(0.460686\pi\)
\(594\) 0 0
\(595\) −24.0000 −0.983904
\(596\) 0 0
\(597\) 3.00000 + 1.73205i 0.122782 + 0.0708881i
\(598\) 0 0
\(599\) −20.0000 34.6410i −0.817178 1.41539i −0.907754 0.419504i \(-0.862204\pi\)
0.0905757 0.995890i \(-0.471129\pi\)
\(600\) 0 0
\(601\) −9.50000 + 16.4545i −0.387513 + 0.671192i −0.992114 0.125336i \(-0.959999\pi\)
0.604601 + 0.796528i \(0.293332\pi\)
\(602\) 0 0
\(603\) 19.5000 33.7750i 0.794101 1.37542i
\(604\) 0 0
\(605\) −28.0000 + 48.4974i −1.13836 + 1.97170i
\(606\) 0 0
\(607\) 10.0000 + 17.3205i 0.405887 + 0.703018i 0.994424 0.105453i \(-0.0336291\pi\)
−0.588537 + 0.808470i \(0.700296\pi\)
\(608\) 0 0
\(609\) 6.92820i 0.280745i
\(610\) 0 0
\(611\) 4.00000 0.161823
\(612\) 0 0
\(613\) 12.0000 0.484675 0.242338 0.970192i \(-0.422086\pi\)
0.242338 + 0.970192i \(0.422086\pi\)
\(614\) 0 0
\(615\) 6.00000 3.46410i 0.241943 0.139686i
\(616\) 0 0
\(617\) 22.5000 + 38.9711i 0.905816 + 1.56892i 0.819818 + 0.572624i \(0.194074\pi\)
0.0859976 + 0.996295i \(0.472592\pi\)
\(618\) 0 0
\(619\) 10.5000 18.1865i 0.422031 0.730978i −0.574107 0.818780i \(-0.694651\pi\)
0.996138 + 0.0878015i \(0.0279841\pi\)
\(620\) 0 0
\(621\) −27.0000 + 15.5885i −1.08347 + 0.625543i
\(622\) 0 0
\(623\) 10.0000 17.3205i 0.400642 0.693932i
\(624\) 0 0
\(625\) −20.5000 35.5070i −0.820000 1.42028i
\(626\) 0 0
\(627\) −7.50000 + 4.33013i −0.299521 + 0.172929i
\(628\) 0 0
\(629\) 24.0000 0.956943
\(630\) 0 0
\(631\) 28.0000 1.11466 0.557331 0.830290i \(-0.311825\pi\)
0.557331 + 0.830290i \(0.311825\pi\)
\(632\) 0 0
\(633\) 48.4974i 1.92760i
\(634\) 0 0
\(635\) 4.00000 + 6.92820i 0.158735 + 0.274937i
\(636\) 0 0
\(637\) −3.00000 + 5.19615i −0.118864 + 0.205879i
\(638\) 0 0
\(639\) −12.0000 20.7846i −0.474713 0.822226i
\(640\) 0 0
\(641\) −2.50000 + 4.33013i −0.0987441 + 0.171030i −0.911165 0.412042i \(-0.864816\pi\)
0.812421 + 0.583071i \(0.198149\pi\)
\(642\) 0 0
\(643\) −7.50000 12.9904i −0.295771 0.512291i 0.679393 0.733775i \(-0.262243\pi\)
−0.975164 + 0.221484i \(0.928910\pi\)
\(644\) 0 0
\(645\) −42.0000 24.2487i −1.65375 0.954792i
\(646\) 0 0
\(647\) −6.00000 −0.235884 −0.117942 0.993020i \(-0.537630\pi\)
−0.117942 + 0.993020i \(0.537630\pi\)
\(648\) 0 0
\(649\) −25.0000 −0.981336
\(650\) 0 0
\(651\) −12.0000 6.92820i −0.470317 0.271538i
\(652\) 0 0
\(653\) 11.0000 + 19.0526i 0.430463 + 0.745584i 0.996913 0.0785119i \(-0.0250169\pi\)
−0.566450 + 0.824096i \(0.691684\pi\)
\(654\) 0 0
\(655\) 32.0000 55.4256i 1.25034 2.16566i
\(656\) 0 0
\(657\) 4.50000 + 7.79423i 0.175562 + 0.304082i
\(658\) 0 0
\(659\) −6.00000 + 10.3923i −0.233727 + 0.404827i −0.958902 0.283738i \(-0.908425\pi\)
0.725175 + 0.688565i \(0.241759\pi\)
\(660\) 0 0
\(661\) −16.0000 27.7128i −0.622328 1.07790i −0.989051 0.147573i \(-0.952854\pi\)
0.366723 0.930330i \(-0.380480\pi\)
\(662\) 0 0
\(663\) 10.3923i 0.403604i
\(664\) 0 0
\(665\) −8.00000 −0.310227
\(666\) 0 0
\(667\) −12.0000 −0.464642
\(668\) 0 0
\(669\) 21.0000 12.1244i 0.811907 0.468755i
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) −1.00000 + 1.73205i −0.0385472 + 0.0667657i −0.884655 0.466246i \(-0.845606\pi\)
0.846108 + 0.533011i \(0.178940\pi\)
\(674\) 0 0
\(675\) 49.5000 + 28.5788i 1.90526 + 1.10000i
\(676\) 0 0
\(677\) 14.0000 24.2487i 0.538064 0.931954i −0.460945 0.887429i \(-0.652489\pi\)
0.999008 0.0445248i \(-0.0141774\pi\)
\(678\) 0 0
\(679\) 11.0000 + 19.0526i 0.422141 + 0.731170i
\(680\) 0 0
\(681\) −4.50000 + 2.59808i −0.172440 + 0.0995585i
\(682\) 0 0
\(683\) 15.0000 0.573959 0.286980 0.957937i \(-0.407349\pi\)
0.286980 + 0.957937i \(0.407349\pi\)
\(684\) 0 0
\(685\) −12.0000 −0.458496
\(686\) 0 0
\(687\) 24.2487i 0.925146i
\(688\) 0 0
\(689\) −4.00000 6.92820i −0.152388 0.263944i
\(690\) 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
\(693\) 15.0000 25.9808i 0.569803 0.986928i
\(694\) 0 0
\(695\) −26.0000 + 45.0333i −0.986236 + 1.70821i
\(696\) 0 0
\(697\) 1.50000 + 2.59808i 0.0568166 + 0.0984092i
\(698\) 0 0
\(699\) 31.5000 + 18.1865i 1.19144 + 0.687878i
\(700\) 0 0
\(701\) 42.0000 1.58632 0.793159 0.609015i \(-0.208435\pi\)
0.793159 + 0.609015i \(0.208435\pi\)
\(702\) 0 0
\(703\) 8.00000 0.301726
\(704\) 0 0
\(705\) 12.0000 + 6.92820i 0.451946 + 0.260931i
\(706\) 0 0
\(707\) −12.0000 20.7846i −0.451306 0.781686i
\(708\) 0 0
\(709\) 10.0000 17.3205i 0.375558 0.650485i −0.614852 0.788642i \(-0.710784\pi\)
0.990410 + 0.138157i \(0.0441178\pi\)
\(710\) 0 0
\(711\) 24.0000 0.900070
\(712\) 0 0
\(713\) −12.0000 + 20.7846i −0.449404 + 0.778390i
\(714\) 0 0
\(715\) 20.0000 + 34.6410i 0.747958 + 1.29550i
\(716\) 0 0
\(717\) 10.3923i 0.388108i
\(718\) 0 0
\(719\) −32.0000 −1.19340 −0.596699 0.802465i \(-0.703521\pi\)
−0.596699 + 0.802465i \(0.703521\pi\)
\(720\) 0 0
\(721\) −12.0000 −0.446903
\(722\) 0 0
\(723\) −34.5000 + 19.9186i −1.28307 + 0.740780i
\(724\) 0 0
\(725\) 11.0000 + 19.0526i 0.408530 + 0.707594i
\(726\) 0 0
\(727\) −15.0000 + 25.9808i −0.556319 + 0.963573i 0.441480 + 0.897271i \(0.354453\pi\)
−0.997800 + 0.0663022i \(0.978880\pi\)
\(728\) 0 0
\(729\) −27.0000 −1.00000
\(730\) 0 0
\(731\) 10.5000 18.1865i 0.388357 0.672653i
\(732\) 0 0
\(733\) 17.0000 + 29.4449i 0.627909 + 1.08757i 0.987971 + 0.154642i \(0.0494225\pi\)
−0.360061 + 0.932929i \(0.617244\pi\)
\(734\) 0 0
\(735\) −18.0000 + 10.3923i −0.663940 + 0.383326i
\(736\) 0 0
\(737\) 65.0000 2.39431
\(738\) 0 0
\(739\) −49.0000 −1.80249 −0.901247 0.433306i \(-0.857347\pi\)
−0.901247 + 0.433306i \(0.857347\pi\)
\(740\) 0 0
\(741\) 3.46410i 0.127257i
\(742\) 0 0
\(743\) −3.00000 5.19615i −0.110059 0.190628i 0.805735 0.592277i \(-0.201771\pi\)
−0.915794 + 0.401648i \(0.868437\pi\)
\(744\) 0 0
\(745\) 36.0000 62.3538i 1.31894 2.28447i
\(746\) 0 0
\(747\) 36.0000 1.31717
\(748\) 0 0
\(749\) 5.00000 8.66025i 0.182696 0.316439i
\(750\) 0 0
\(751\) −26.0000 45.0333i −0.948753 1.64329i −0.748056 0.663636i \(-0.769012\pi\)
−0.200698 0.979653i \(-0.564321\pi\)
\(752\) 0 0
\(753\) −31.5000 18.1865i −1.14792 0.662754i
\(754\) 0 0
\(755\) 72.0000 2.62035
\(756\) 0 0
\(757\) 18.0000 0.654221 0.327111 0.944986i \(-0.393925\pi\)
0.327111 + 0.944986i \(0.393925\pi\)
\(758\) 0 0
\(759\) −45.0000 25.9808i −1.63340 0.943042i
\(760\) 0 0
\(761\) 15.0000 + 25.9808i 0.543750 + 0.941802i 0.998684 + 0.0512772i \(0.0163292\pi\)
−0.454935 + 0.890525i \(0.650337\pi\)
\(762\) 0 0
\(763\) −8.00000 + 13.8564i −0.289619 + 0.501636i
\(764\) 0 0
\(765\) −18.0000 + 31.1769i −0.650791 + 1.12720i
\(766\) 0 0
\(767\) −5.00000 + 8.66025i −0.180540 + 0.312704i
\(768\) 0 0
\(769\) −5.00000 8.66025i −0.180305 0.312297i 0.761680 0.647954i \(-0.224375\pi\)
−0.941984 + 0.335657i \(0.891042\pi\)
\(770\) 0 0
\(771\) 8.66025i 0.311891i
\(772\) 0 0
\(773\) −42.0000 −1.51064 −0.755318 0.655359i \(-0.772517\pi\)
−0.755318 + 0.655359i \(0.772517\pi\)
\(774\) 0 0
\(775\) 44.0000 1.58053
\(776\) 0 0
\(777\) −24.0000 + 13.8564i −0.860995 + 0.497096i
\(778\) 0 0
\(779\) 0.500000 + 0.866025i 0.0179144 + 0.0310286i
\(780\) 0 0
\(781\) 20.0000 34.6410i 0.715656 1.23955i
\(782\) 0 0
\(783\) −9.00000 5.19615i −0.321634 0.185695i
\(784\) 0 0
\(785\) −40.0000 + 69.2820i −1.42766 + 2.47278i
\(786\) 0 0
\(787\) −18.0000 31.1769i −0.641631 1.11134i −0.985069 0.172162i \(-0.944925\pi\)
0.343438 0.939175i \(-0.388408\pi\)
\(788\) 0 0
\(789\) −9.00000 +