Properties

Label 416.2.i.a.289.1
Level $416$
Weight $2$
Character 416.289
Analytic conductor $3.322$
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] = [416,2,Mod(289,416)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(416, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("416.289");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 416 = 2^{5} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 416.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: \(3.32177672409\)
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: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 289.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 416.289
Dual form 416.2.i.a.321.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.00000 - 1.73205i) q^{3} +1.00000 q^{5} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(-1.00000 - 1.73205i) q^{3} +1.00000 q^{5} +(-0.500000 + 0.866025i) q^{9} +(-2.00000 - 3.46410i) q^{11} +(2.50000 - 2.59808i) q^{13} +(-1.00000 - 1.73205i) q^{15} +(-1.50000 + 2.59808i) q^{17} +(1.00000 - 1.73205i) q^{19} +(-1.00000 - 1.73205i) q^{23} -4.00000 q^{25} -4.00000 q^{27} +(-2.50000 - 4.33013i) q^{29} +2.00000 q^{31} +(-4.00000 + 6.92820i) q^{33} +(-2.50000 - 4.33013i) q^{37} +(-7.00000 - 1.73205i) q^{39} +(-1.50000 - 2.59808i) q^{41} +(2.00000 - 3.46410i) q^{43} +(-0.500000 + 0.866025i) q^{45} +6.00000 q^{47} +(3.50000 + 6.06218i) q^{49} +6.00000 q^{51} +13.0000 q^{53} +(-2.00000 - 3.46410i) q^{55} -4.00000 q^{57} +(-6.00000 + 10.3923i) q^{59} +(3.50000 - 6.06218i) q^{61} +(2.50000 - 2.59808i) q^{65} +(7.00000 + 12.1244i) q^{67} +(-2.00000 + 3.46410i) q^{69} +(-3.00000 + 5.19615i) q^{71} +7.00000 q^{73} +(4.00000 + 6.92820i) q^{75} +8.00000 q^{79} +(5.50000 + 9.52628i) q^{81} +4.00000 q^{83} +(-1.50000 + 2.59808i) q^{85} +(-5.00000 + 8.66025i) q^{87} +(-7.00000 - 12.1244i) q^{89} +(-2.00000 - 3.46410i) q^{93} +(1.00000 - 1.73205i) q^{95} +(1.00000 - 1.73205i) q^{97} +4.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 2 q^{3} + 2 q^{5} - q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 2 q^{3} + 2 q^{5} - q^{9} - 4 q^{11} + 5 q^{13} - 2 q^{15} - 3 q^{17} + 2 q^{19} - 2 q^{23} - 8 q^{25} - 8 q^{27} - 5 q^{29} + 4 q^{31} - 8 q^{33} - 5 q^{37} - 14 q^{39} - 3 q^{41} + 4 q^{43} - q^{45} + 12 q^{47} + 7 q^{49} + 12 q^{51} + 26 q^{53} - 4 q^{55} - 8 q^{57} - 12 q^{59} + 7 q^{61} + 5 q^{65} + 14 q^{67} - 4 q^{69} - 6 q^{71} + 14 q^{73} + 8 q^{75} + 16 q^{79} + 11 q^{81} + 8 q^{83} - 3 q^{85} - 10 q^{87} - 14 q^{89} - 4 q^{93} + 2 q^{95} + 2 q^{97} + 8 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/416\mathbb{Z}\right)^\times\).

\(n\) \(261\) \(287\) \(353\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\)

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
\(3\) −1.00000 1.73205i −0.577350 1.00000i −0.995782 0.0917517i \(-0.970753\pi\)
0.418432 0.908248i \(-0.362580\pi\)
\(4\) 0 0
\(5\) 1.00000 0.447214 0.223607 0.974679i \(-0.428217\pi\)
0.223607 + 0.974679i \(0.428217\pi\)
\(6\) 0 0
\(7\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(8\) 0 0
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) 0 0
\(11\) −2.00000 3.46410i −0.603023 1.04447i −0.992361 0.123371i \(-0.960630\pi\)
0.389338 0.921095i \(-0.372704\pi\)
\(12\) 0 0
\(13\) 2.50000 2.59808i 0.693375 0.720577i
\(14\) 0 0
\(15\) −1.00000 1.73205i −0.258199 0.447214i
\(16\) 0 0
\(17\) −1.50000 + 2.59808i −0.363803 + 0.630126i −0.988583 0.150675i \(-0.951855\pi\)
0.624780 + 0.780801i \(0.285189\pi\)
\(18\) 0 0
\(19\) 1.00000 1.73205i 0.229416 0.397360i −0.728219 0.685344i \(-0.759652\pi\)
0.957635 + 0.287984i \(0.0929851\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −1.00000 1.73205i −0.208514 0.361158i 0.742732 0.669588i \(-0.233529\pi\)
−0.951247 + 0.308431i \(0.900196\pi\)
\(24\) 0 0
\(25\) −4.00000 −0.800000
\(26\) 0 0
\(27\) −4.00000 −0.769800
\(28\) 0 0
\(29\) −2.50000 4.33013i −0.464238 0.804084i 0.534928 0.844897i \(-0.320339\pi\)
−0.999167 + 0.0408130i \(0.987005\pi\)
\(30\) 0 0
\(31\) 2.00000 0.359211 0.179605 0.983739i \(-0.442518\pi\)
0.179605 + 0.983739i \(0.442518\pi\)
\(32\) 0 0
\(33\) −4.00000 + 6.92820i −0.696311 + 1.20605i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −2.50000 4.33013i −0.410997 0.711868i 0.584002 0.811752i \(-0.301486\pi\)
−0.994999 + 0.0998840i \(0.968153\pi\)
\(38\) 0 0
\(39\) −7.00000 1.73205i −1.12090 0.277350i
\(40\) 0 0
\(41\) −1.50000 2.59808i −0.234261 0.405751i 0.724797 0.688963i \(-0.241934\pi\)
−0.959058 + 0.283211i \(0.908600\pi\)
\(42\) 0 0
\(43\) 2.00000 3.46410i 0.304997 0.528271i −0.672264 0.740312i \(-0.734678\pi\)
0.977261 + 0.212041i \(0.0680112\pi\)
\(44\) 0 0
\(45\) −0.500000 + 0.866025i −0.0745356 + 0.129099i
\(46\) 0 0
\(47\) 6.00000 0.875190 0.437595 0.899172i \(-0.355830\pi\)
0.437595 + 0.899172i \(0.355830\pi\)
\(48\) 0 0
\(49\) 3.50000 + 6.06218i 0.500000 + 0.866025i
\(50\) 0 0
\(51\) 6.00000 0.840168
\(52\) 0 0
\(53\) 13.0000 1.78569 0.892844 0.450367i \(-0.148707\pi\)
0.892844 + 0.450367i \(0.148707\pi\)
\(54\) 0 0
\(55\) −2.00000 3.46410i −0.269680 0.467099i
\(56\) 0 0
\(57\) −4.00000 −0.529813
\(58\) 0 0
\(59\) −6.00000 + 10.3923i −0.781133 + 1.35296i 0.150148 + 0.988663i \(0.452025\pi\)
−0.931282 + 0.364299i \(0.881308\pi\)
\(60\) 0 0
\(61\) 3.50000 6.06218i 0.448129 0.776182i −0.550135 0.835076i \(-0.685424\pi\)
0.998264 + 0.0588933i \(0.0187572\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 2.50000 2.59808i 0.310087 0.322252i
\(66\) 0 0
\(67\) 7.00000 + 12.1244i 0.855186 + 1.48123i 0.876472 + 0.481452i \(0.159891\pi\)
−0.0212861 + 0.999773i \(0.506776\pi\)
\(68\) 0 0
\(69\) −2.00000 + 3.46410i −0.240772 + 0.417029i
\(70\) 0 0
\(71\) −3.00000 + 5.19615i −0.356034 + 0.616670i −0.987294 0.158901i \(-0.949205\pi\)
0.631260 + 0.775571i \(0.282538\pi\)
\(72\) 0 0
\(73\) 7.00000 0.819288 0.409644 0.912245i \(-0.365653\pi\)
0.409644 + 0.912245i \(0.365653\pi\)
\(74\) 0 0
\(75\) 4.00000 + 6.92820i 0.461880 + 0.800000i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 8.00000 0.900070 0.450035 0.893011i \(-0.351411\pi\)
0.450035 + 0.893011i \(0.351411\pi\)
\(80\) 0 0
\(81\) 5.50000 + 9.52628i 0.611111 + 1.05848i
\(82\) 0 0
\(83\) 4.00000 0.439057 0.219529 0.975606i \(-0.429548\pi\)
0.219529 + 0.975606i \(0.429548\pi\)
\(84\) 0 0
\(85\) −1.50000 + 2.59808i −0.162698 + 0.281801i
\(86\) 0 0
\(87\) −5.00000 + 8.66025i −0.536056 + 0.928477i
\(88\) 0 0
\(89\) −7.00000 12.1244i −0.741999 1.28518i −0.951584 0.307389i \(-0.900545\pi\)
0.209585 0.977790i \(-0.432789\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) −2.00000 3.46410i −0.207390 0.359211i
\(94\) 0 0
\(95\) 1.00000 1.73205i 0.102598 0.177705i
\(96\) 0 0
\(97\) 1.00000 1.73205i 0.101535 0.175863i −0.810782 0.585348i \(-0.800958\pi\)
0.912317 + 0.409484i \(0.134291\pi\)
\(98\) 0 0
\(99\) 4.00000 0.402015
\(100\) 0 0
\(101\) 5.50000 + 9.52628i 0.547270 + 0.947900i 0.998460 + 0.0554722i \(0.0176664\pi\)
−0.451190 + 0.892428i \(0.649000\pi\)
\(102\) 0 0
\(103\) 14.0000 1.37946 0.689730 0.724066i \(-0.257729\pi\)
0.689730 + 0.724066i \(0.257729\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −3.00000 5.19615i −0.290021 0.502331i 0.683793 0.729676i \(-0.260329\pi\)
−0.973814 + 0.227345i \(0.926996\pi\)
\(108\) 0 0
\(109\) −10.0000 −0.957826 −0.478913 0.877862i \(-0.658969\pi\)
−0.478913 + 0.877862i \(0.658969\pi\)
\(110\) 0 0
\(111\) −5.00000 + 8.66025i −0.474579 + 0.821995i
\(112\) 0 0
\(113\) 4.50000 7.79423i 0.423324 0.733219i −0.572938 0.819599i \(-0.694196\pi\)
0.996262 + 0.0863794i \(0.0275297\pi\)
\(114\) 0 0
\(115\) −1.00000 1.73205i −0.0932505 0.161515i
\(116\) 0 0
\(117\) 1.00000 + 3.46410i 0.0924500 + 0.320256i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −2.50000 + 4.33013i −0.227273 + 0.393648i
\(122\) 0 0
\(123\) −3.00000 + 5.19615i −0.270501 + 0.468521i
\(124\) 0 0
\(125\) −9.00000 −0.804984
\(126\) 0 0
\(127\) 11.0000 + 19.0526i 0.976092 + 1.69064i 0.676283 + 0.736642i \(0.263590\pi\)
0.299809 + 0.953999i \(0.403077\pi\)
\(128\) 0 0
\(129\) −8.00000 −0.704361
\(130\) 0 0
\(131\) −18.0000 −1.57267 −0.786334 0.617802i \(-0.788023\pi\)
−0.786334 + 0.617802i \(0.788023\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) −4.00000 −0.344265
\(136\) 0 0
\(137\) 0.500000 0.866025i 0.0427179 0.0739895i −0.843876 0.536538i \(-0.819732\pi\)
0.886594 + 0.462549i \(0.153065\pi\)
\(138\) 0 0
\(139\) 8.00000 13.8564i 0.678551 1.17529i −0.296866 0.954919i \(-0.595942\pi\)
0.975417 0.220366i \(-0.0707252\pi\)
\(140\) 0 0
\(141\) −6.00000 10.3923i −0.505291 0.875190i
\(142\) 0 0
\(143\) −14.0000 3.46410i −1.17074 0.289683i
\(144\) 0 0
\(145\) −2.50000 4.33013i −0.207614 0.359597i
\(146\) 0 0
\(147\) 7.00000 12.1244i 0.577350 1.00000i
\(148\) 0 0
\(149\) −10.5000 + 18.1865i −0.860194 + 1.48990i 0.0115483 + 0.999933i \(0.496324\pi\)
−0.871742 + 0.489966i \(0.837009\pi\)
\(150\) 0 0
\(151\) 22.0000 1.79033 0.895167 0.445730i \(-0.147056\pi\)
0.895167 + 0.445730i \(0.147056\pi\)
\(152\) 0 0
\(153\) −1.50000 2.59808i −0.121268 0.210042i
\(154\) 0 0
\(155\) 2.00000 0.160644
\(156\) 0 0
\(157\) 5.00000 0.399043 0.199522 0.979893i \(-0.436061\pi\)
0.199522 + 0.979893i \(0.436061\pi\)
\(158\) 0 0
\(159\) −13.0000 22.5167i −1.03097 1.78569i
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −8.00000 + 13.8564i −0.626608 + 1.08532i 0.361619 + 0.932326i \(0.382224\pi\)
−0.988227 + 0.152992i \(0.951109\pi\)
\(164\) 0 0
\(165\) −4.00000 + 6.92820i −0.311400 + 0.539360i
\(166\) 0 0
\(167\) 2.00000 + 3.46410i 0.154765 + 0.268060i 0.932973 0.359946i \(-0.117205\pi\)
−0.778209 + 0.628006i \(0.783871\pi\)
\(168\) 0 0
\(169\) −0.500000 12.9904i −0.0384615 0.999260i
\(170\) 0 0
\(171\) 1.00000 + 1.73205i 0.0764719 + 0.132453i
\(172\) 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
\(175\) 0 0
\(176\) 0 0
\(177\) 24.0000 1.80395
\(178\) 0 0
\(179\) −8.00000 13.8564i −0.597948 1.03568i −0.993124 0.117071i \(-0.962650\pi\)
0.395175 0.918606i \(-0.370684\pi\)
\(180\) 0 0
\(181\) 5.00000 0.371647 0.185824 0.982583i \(-0.440505\pi\)
0.185824 + 0.982583i \(0.440505\pi\)
\(182\) 0 0
\(183\) −14.0000 −1.03491
\(184\) 0 0
\(185\) −2.50000 4.33013i −0.183804 0.318357i
\(186\) 0 0
\(187\) 12.0000 0.877527
\(188\) 0 0
\(189\) 0 0
\(190\) 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
\(193\) 10.5000 + 18.1865i 0.755807 + 1.30910i 0.944972 + 0.327150i \(0.106088\pi\)
−0.189166 + 0.981945i \(0.560578\pi\)
\(194\) 0 0
\(195\) −7.00000 1.73205i −0.501280 0.124035i
\(196\) 0 0
\(197\) 9.00000 + 15.5885i 0.641223 + 1.11063i 0.985160 + 0.171639i \(0.0549062\pi\)
−0.343937 + 0.938993i \(0.611761\pi\)
\(198\) 0 0
\(199\) 7.00000 12.1244i 0.496217 0.859473i −0.503774 0.863836i \(-0.668055\pi\)
0.999990 + 0.00436292i \(0.00138876\pi\)
\(200\) 0 0
\(201\) 14.0000 24.2487i 0.987484 1.71037i
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) −1.50000 2.59808i −0.104765 0.181458i
\(206\) 0 0
\(207\) 2.00000 0.139010
\(208\) 0 0
\(209\) −8.00000 −0.553372
\(210\) 0 0
\(211\) −9.00000 15.5885i −0.619586 1.07315i −0.989561 0.144112i \(-0.953967\pi\)
0.369976 0.929041i \(-0.379366\pi\)
\(212\) 0 0
\(213\) 12.0000 0.822226
\(214\) 0 0
\(215\) 2.00000 3.46410i 0.136399 0.236250i
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) −7.00000 12.1244i −0.473016 0.819288i
\(220\) 0 0
\(221\) 3.00000 + 10.3923i 0.201802 + 0.699062i
\(222\) 0 0
\(223\) −9.00000 15.5885i −0.602685 1.04388i −0.992413 0.122950i \(-0.960764\pi\)
0.389728 0.920930i \(-0.372569\pi\)
\(224\) 0 0
\(225\) 2.00000 3.46410i 0.133333 0.230940i
\(226\) 0 0
\(227\) −9.00000 + 15.5885i −0.597351 + 1.03464i 0.395860 + 0.918311i \(0.370447\pi\)
−0.993210 + 0.116331i \(0.962887\pi\)
\(228\) 0 0
\(229\) −18.0000 −1.18947 −0.594737 0.803921i \(-0.702744\pi\)
−0.594737 + 0.803921i \(0.702744\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 6.00000 0.393073 0.196537 0.980497i \(-0.437031\pi\)
0.196537 + 0.980497i \(0.437031\pi\)
\(234\) 0 0
\(235\) 6.00000 0.391397
\(236\) 0 0
\(237\) −8.00000 13.8564i −0.519656 0.900070i
\(238\) 0 0
\(239\) −12.0000 −0.776215 −0.388108 0.921614i \(-0.626871\pi\)
−0.388108 + 0.921614i \(0.626871\pi\)
\(240\) 0 0
\(241\) −3.50000 + 6.06218i −0.225455 + 0.390499i −0.956456 0.291877i \(-0.905720\pi\)
0.731001 + 0.682376i \(0.239053\pi\)
\(242\) 0 0
\(243\) 5.00000 8.66025i 0.320750 0.555556i
\(244\) 0 0
\(245\) 3.50000 + 6.06218i 0.223607 + 0.387298i
\(246\) 0 0
\(247\) −2.00000 6.92820i −0.127257 0.440831i
\(248\) 0 0
\(249\) −4.00000 6.92820i −0.253490 0.439057i
\(250\) 0 0
\(251\) 11.0000 19.0526i 0.694314 1.20259i −0.276098 0.961130i \(-0.589041\pi\)
0.970411 0.241457i \(-0.0776254\pi\)
\(252\) 0 0
\(253\) −4.00000 + 6.92820i −0.251478 + 0.435572i
\(254\) 0 0
\(255\) 6.00000 0.375735
\(256\) 0 0
\(257\) −5.50000 9.52628i −0.343081 0.594233i 0.641923 0.766769i \(-0.278137\pi\)
−0.985003 + 0.172536i \(0.944804\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 5.00000 0.309492
\(262\) 0 0
\(263\) −12.0000 20.7846i −0.739952 1.28163i −0.952517 0.304487i \(-0.901515\pi\)
0.212565 0.977147i \(-0.431818\pi\)
\(264\) 0 0
\(265\) 13.0000 0.798584
\(266\) 0 0
\(267\) −14.0000 + 24.2487i −0.856786 + 1.48400i
\(268\) 0 0
\(269\) −7.00000 + 12.1244i −0.426798 + 0.739235i −0.996586 0.0825561i \(-0.973692\pi\)
0.569789 + 0.821791i \(0.307025\pi\)
\(270\) 0 0
\(271\) −6.00000 10.3923i −0.364474 0.631288i 0.624218 0.781251i \(-0.285418\pi\)
−0.988692 + 0.149963i \(0.952085\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 8.00000 + 13.8564i 0.482418 + 0.835573i
\(276\) 0 0
\(277\) −0.500000 + 0.866025i −0.0300421 + 0.0520344i −0.880656 0.473757i \(-0.842897\pi\)
0.850613 + 0.525792i \(0.176231\pi\)
\(278\) 0 0
\(279\) −1.00000 + 1.73205i −0.0598684 + 0.103695i
\(280\) 0 0
\(281\) −21.0000 −1.25275 −0.626377 0.779520i \(-0.715463\pi\)
−0.626377 + 0.779520i \(0.715463\pi\)
\(282\) 0 0
\(283\) 10.0000 + 17.3205i 0.594438 + 1.02960i 0.993626 + 0.112728i \(0.0359589\pi\)
−0.399188 + 0.916869i \(0.630708\pi\)
\(284\) 0 0
\(285\) −4.00000 −0.236940
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 4.00000 + 6.92820i 0.235294 + 0.407541i
\(290\) 0 0
\(291\) −4.00000 −0.234484
\(292\) 0 0
\(293\) 9.50000 16.4545i 0.554996 0.961281i −0.442908 0.896567i \(-0.646053\pi\)
0.997904 0.0647140i \(-0.0206135\pi\)
\(294\) 0 0
\(295\) −6.00000 + 10.3923i −0.349334 + 0.605063i
\(296\) 0 0
\(297\) 8.00000 + 13.8564i 0.464207 + 0.804030i
\(298\) 0 0
\(299\) −7.00000 1.73205i −0.404820 0.100167i
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 11.0000 19.0526i 0.631933 1.09454i
\(304\) 0 0
\(305\) 3.50000 6.06218i 0.200409 0.347119i
\(306\) 0 0
\(307\) 26.0000 1.48390 0.741949 0.670456i \(-0.233902\pi\)
0.741949 + 0.670456i \(0.233902\pi\)
\(308\) 0 0
\(309\) −14.0000 24.2487i −0.796432 1.37946i
\(310\) 0 0
\(311\) 10.0000 0.567048 0.283524 0.958965i \(-0.408496\pi\)
0.283524 + 0.958965i \(0.408496\pi\)
\(312\) 0 0
\(313\) −34.0000 −1.92179 −0.960897 0.276907i \(-0.910691\pi\)
−0.960897 + 0.276907i \(0.910691\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −3.00000 −0.168497 −0.0842484 0.996445i \(-0.526849\pi\)
−0.0842484 + 0.996445i \(0.526849\pi\)
\(318\) 0 0
\(319\) −10.0000 + 17.3205i −0.559893 + 0.969762i
\(320\) 0 0
\(321\) −6.00000 + 10.3923i −0.334887 + 0.580042i
\(322\) 0 0
\(323\) 3.00000 + 5.19615i 0.166924 + 0.289122i
\(324\) 0 0
\(325\) −10.0000 + 10.3923i −0.554700 + 0.576461i
\(326\) 0 0
\(327\) 10.0000 + 17.3205i 0.553001 + 0.957826i
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 4.00000 6.92820i 0.219860 0.380808i −0.734905 0.678170i \(-0.762773\pi\)
0.954765 + 0.297361i \(0.0961066\pi\)
\(332\) 0 0
\(333\) 5.00000 0.273998
\(334\) 0 0
\(335\) 7.00000 + 12.1244i 0.382451 + 0.662424i
\(336\) 0 0
\(337\) −1.00000 −0.0544735 −0.0272367 0.999629i \(-0.508671\pi\)
−0.0272367 + 0.999629i \(0.508671\pi\)
\(338\) 0 0
\(339\) −18.0000 −0.977626
\(340\) 0 0
\(341\) −4.00000 6.92820i −0.216612 0.375183i
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) −2.00000 + 3.46410i −0.107676 + 0.186501i
\(346\) 0 0
\(347\) −5.00000 + 8.66025i −0.268414 + 0.464907i −0.968452 0.249198i \(-0.919833\pi\)
0.700038 + 0.714105i \(0.253166\pi\)
\(348\) 0 0
\(349\) 5.00000 + 8.66025i 0.267644 + 0.463573i 0.968253 0.249973i \(-0.0804216\pi\)
−0.700609 + 0.713545i \(0.747088\pi\)
\(350\) 0 0
\(351\) −10.0000 + 10.3923i −0.533761 + 0.554700i
\(352\) 0 0
\(353\) −1.50000 2.59808i −0.0798369 0.138282i 0.823343 0.567545i \(-0.192107\pi\)
−0.903179 + 0.429263i \(0.858773\pi\)
\(354\) 0 0
\(355\) −3.00000 + 5.19615i −0.159223 + 0.275783i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 20.0000 1.05556 0.527780 0.849381i \(-0.323025\pi\)
0.527780 + 0.849381i \(0.323025\pi\)
\(360\) 0 0
\(361\) 7.50000 + 12.9904i 0.394737 + 0.683704i
\(362\) 0 0
\(363\) 10.0000 0.524864
\(364\) 0 0
\(365\) 7.00000 0.366397
\(366\) 0 0
\(367\) 11.0000 + 19.0526i 0.574195 + 0.994535i 0.996129 + 0.0879086i \(0.0280183\pi\)
−0.421933 + 0.906627i \(0.638648\pi\)
\(368\) 0 0
\(369\) 3.00000 0.156174
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 1.50000 2.59808i 0.0776671 0.134523i −0.824576 0.565751i \(-0.808586\pi\)
0.902243 + 0.431228i \(0.141920\pi\)
\(374\) 0 0
\(375\) 9.00000 + 15.5885i 0.464758 + 0.804984i
\(376\) 0 0
\(377\) −17.5000 4.33013i −0.901296 0.223013i
\(378\) 0 0
\(379\) −1.00000 1.73205i −0.0513665 0.0889695i 0.839199 0.543825i \(-0.183024\pi\)
−0.890565 + 0.454855i \(0.849691\pi\)
\(380\) 0 0
\(381\) 22.0000 38.1051i 1.12709 1.95218i
\(382\) 0 0
\(383\) −2.00000 + 3.46410i −0.102195 + 0.177007i −0.912589 0.408879i \(-0.865920\pi\)
0.810394 + 0.585886i \(0.199253\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 2.00000 + 3.46410i 0.101666 + 0.176090i
\(388\) 0 0
\(389\) 33.0000 1.67317 0.836583 0.547840i \(-0.184550\pi\)
0.836583 + 0.547840i \(0.184550\pi\)
\(390\) 0 0
\(391\) 6.00000 0.303433
\(392\) 0 0
\(393\) 18.0000 + 31.1769i 0.907980 + 1.57267i
\(394\) 0 0
\(395\) 8.00000 0.402524
\(396\) 0 0
\(397\) 17.0000 29.4449i 0.853206 1.47780i −0.0250943 0.999685i \(-0.507989\pi\)
0.878300 0.478110i \(-0.158678\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 16.5000 + 28.5788i 0.823971 + 1.42716i 0.902703 + 0.430263i \(0.141579\pi\)
−0.0787327 + 0.996896i \(0.525087\pi\)
\(402\) 0 0
\(403\) 5.00000 5.19615i 0.249068 0.258839i
\(404\) 0 0
\(405\) 5.50000 + 9.52628i 0.273297 + 0.473365i
\(406\) 0 0
\(407\) −10.0000 + 17.3205i −0.495682 + 0.858546i
\(408\) 0 0
\(409\) 4.50000 7.79423i 0.222511 0.385400i −0.733059 0.680165i \(-0.761908\pi\)
0.955570 + 0.294765i \(0.0952414\pi\)
\(410\) 0 0
\(411\) −2.00000 −0.0986527
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 4.00000 0.196352
\(416\) 0 0
\(417\) −32.0000 −1.56705
\(418\) 0 0
\(419\) −7.00000 12.1244i −0.341972 0.592314i 0.642827 0.766012i \(-0.277762\pi\)
−0.984799 + 0.173698i \(0.944428\pi\)
\(420\) 0 0
\(421\) 9.00000 0.438633 0.219317 0.975654i \(-0.429617\pi\)
0.219317 + 0.975654i \(0.429617\pi\)
\(422\) 0 0
\(423\) −3.00000 + 5.19615i −0.145865 + 0.252646i
\(424\) 0 0
\(425\) 6.00000 10.3923i 0.291043 0.504101i
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 8.00000 + 27.7128i 0.386244 + 1.33799i
\(430\) 0 0
\(431\) 6.00000 + 10.3923i 0.289010 + 0.500580i 0.973574 0.228373i \(-0.0733406\pi\)
−0.684564 + 0.728953i \(0.740007\pi\)
\(432\) 0 0
\(433\) 0.500000 0.866025i 0.0240285 0.0416185i −0.853761 0.520665i \(-0.825684\pi\)
0.877790 + 0.479046i \(0.159017\pi\)
\(434\) 0 0
\(435\) −5.00000 + 8.66025i −0.239732 + 0.415227i
\(436\) 0 0
\(437\) −4.00000 −0.191346
\(438\) 0 0
\(439\) −4.00000 6.92820i −0.190910 0.330665i 0.754642 0.656136i \(-0.227810\pi\)
−0.945552 + 0.325471i \(0.894477\pi\)
\(440\) 0 0
\(441\) −7.00000 −0.333333
\(442\) 0 0
\(443\) −4.00000 −0.190046 −0.0950229 0.995475i \(-0.530292\pi\)
−0.0950229 + 0.995475i \(0.530292\pi\)
\(444\) 0 0
\(445\) −7.00000 12.1244i −0.331832 0.574750i
\(446\) 0 0
\(447\) 42.0000 1.98653
\(448\) 0 0
\(449\) 5.00000 8.66025i 0.235965 0.408703i −0.723588 0.690232i \(-0.757508\pi\)
0.959553 + 0.281529i \(0.0908417\pi\)
\(450\) 0 0
\(451\) −6.00000 + 10.3923i −0.282529 + 0.489355i
\(452\) 0 0
\(453\) −22.0000 38.1051i −1.03365 1.79033i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 12.5000 + 21.6506i 0.584725 + 1.01277i 0.994910 + 0.100771i \(0.0321310\pi\)
−0.410184 + 0.912003i \(0.634536\pi\)
\(458\) 0 0
\(459\) 6.00000 10.3923i 0.280056 0.485071i
\(460\) 0 0
\(461\) −10.5000 + 18.1865i −0.489034 + 0.847031i −0.999920 0.0126168i \(-0.995984\pi\)
0.510887 + 0.859648i \(0.329317\pi\)
\(462\) 0 0
\(463\) −20.0000 −0.929479 −0.464739 0.885448i \(-0.653852\pi\)
−0.464739 + 0.885448i \(0.653852\pi\)
\(464\) 0 0
\(465\) −2.00000 3.46410i −0.0927478 0.160644i
\(466\) 0 0
\(467\) 24.0000 1.11059 0.555294 0.831654i \(-0.312606\pi\)
0.555294 + 0.831654i \(0.312606\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) −5.00000 8.66025i −0.230388 0.399043i
\(472\) 0 0
\(473\) −16.0000 −0.735681
\(474\) 0 0
\(475\) −4.00000 + 6.92820i −0.183533 + 0.317888i
\(476\) 0 0
\(477\) −6.50000 + 11.2583i −0.297615 + 0.515484i
\(478\) 0 0
\(479\) −3.00000 5.19615i −0.137073 0.237418i 0.789314 0.613990i \(-0.210436\pi\)
−0.926388 + 0.376571i \(0.877103\pi\)
\(480\) 0 0
\(481\) −17.5000 4.33013i −0.797931 0.197437i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 1.00000 1.73205i 0.0454077 0.0786484i
\(486\) 0 0
\(487\) −16.0000 + 27.7128i −0.725029 + 1.25579i 0.233933 + 0.972253i \(0.424840\pi\)
−0.958962 + 0.283535i \(0.908493\pi\)
\(488\) 0 0
\(489\) 32.0000 1.44709
\(490\) 0 0
\(491\) 8.00000 + 13.8564i 0.361035 + 0.625331i 0.988131 0.153611i \(-0.0490902\pi\)
−0.627096 + 0.778942i \(0.715757\pi\)
\(492\) 0 0
\(493\) 15.0000 0.675566
\(494\) 0 0
\(495\) 4.00000 0.179787
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) −14.0000 −0.626726 −0.313363 0.949633i \(-0.601456\pi\)
−0.313363 + 0.949633i \(0.601456\pi\)
\(500\) 0 0
\(501\) 4.00000 6.92820i 0.178707 0.309529i
\(502\) 0 0
\(503\) 14.0000 24.2487i 0.624229 1.08120i −0.364460 0.931219i \(-0.618746\pi\)
0.988689 0.149978i \(-0.0479202\pi\)
\(504\) 0 0
\(505\) 5.50000 + 9.52628i 0.244747 + 0.423914i
\(506\) 0 0
\(507\) −22.0000 + 13.8564i −0.977054 + 0.615385i
\(508\) 0 0
\(509\) 1.50000 + 2.59808i 0.0664863 + 0.115158i 0.897352 0.441315i \(-0.145488\pi\)
−0.830866 + 0.556473i \(0.812154\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) −4.00000 + 6.92820i −0.176604 + 0.305888i
\(514\) 0 0
\(515\) 14.0000 0.616914
\(516\) 0 0
\(517\) −12.0000 20.7846i −0.527759 0.914106i
\(518\) 0 0
\(519\) −4.00000 −0.175581
\(520\) 0 0
\(521\) −25.0000 −1.09527 −0.547635 0.836717i \(-0.684472\pi\)
−0.547635 + 0.836717i \(0.684472\pi\)
\(522\) 0 0
\(523\) −8.00000 13.8564i −0.349816 0.605898i 0.636401 0.771358i \(-0.280422\pi\)
−0.986216 + 0.165460i \(0.947089\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −3.00000 + 5.19615i −0.130682 + 0.226348i
\(528\) 0 0
\(529\) 9.50000 16.4545i 0.413043 0.715412i
\(530\) 0 0
\(531\) −6.00000 10.3923i −0.260378 0.450988i
\(532\) 0 0
\(533\) −10.5000 2.59808i −0.454805 0.112535i
\(534\) 0 0
\(535\) −3.00000 5.19615i −0.129701 0.224649i
\(536\) 0 0
\(537\) −16.0000 + 27.7128i −0.690451 + 1.19590i
\(538\) 0 0
\(539\) 14.0000 24.2487i 0.603023 1.04447i
\(540\) 0 0
\(541\) −23.0000 −0.988847 −0.494424 0.869221i \(-0.664621\pi\)
−0.494424 + 0.869221i \(0.664621\pi\)
\(542\) 0 0
\(543\) −5.00000 8.66025i −0.214571 0.371647i
\(544\) 0 0
\(545\) −10.0000 −0.428353
\(546\) 0 0
\(547\) 22.0000 0.940652 0.470326 0.882493i \(-0.344136\pi\)
0.470326 + 0.882493i \(0.344136\pi\)
\(548\) 0 0
\(549\) 3.50000 + 6.06218i 0.149376 + 0.258727i
\(550\) 0 0
\(551\) −10.0000 −0.426014
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) −5.00000 + 8.66025i −0.212238 + 0.367607i
\(556\) 0 0
\(557\) 11.5000 + 19.9186i 0.487271 + 0.843978i 0.999893 0.0146368i \(-0.00465919\pi\)
−0.512622 + 0.858614i \(0.671326\pi\)
\(558\) 0 0
\(559\) −4.00000 13.8564i −0.169182 0.586064i
\(560\) 0 0
\(561\) −12.0000 20.7846i −0.506640 0.877527i
\(562\) 0 0
\(563\) −12.0000 + 20.7846i −0.505740 + 0.875967i 0.494238 + 0.869326i \(0.335447\pi\)
−0.999978 + 0.00664037i \(0.997886\pi\)
\(564\) 0 0
\(565\) 4.50000 7.79423i 0.189316 0.327906i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −3.00000 5.19615i −0.125767 0.217834i 0.796266 0.604947i \(-0.206806\pi\)
−0.922032 + 0.387113i \(0.873472\pi\)
\(570\) 0 0
\(571\) −20.0000 −0.836974 −0.418487 0.908223i \(-0.637439\pi\)
−0.418487 + 0.908223i \(0.637439\pi\)
\(572\) 0 0
\(573\) 12.0000 0.501307
\(574\) 0 0
\(575\) 4.00000 + 6.92820i 0.166812 + 0.288926i
\(576\) 0 0
\(577\) −29.0000 −1.20729 −0.603643 0.797255i \(-0.706285\pi\)
−0.603643 + 0.797255i \(0.706285\pi\)
\(578\) 0 0
\(579\) 21.0000 36.3731i 0.872730 1.51161i
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −26.0000 45.0333i −1.07681 1.86509i
\(584\) 0 0
\(585\) 1.00000 + 3.46410i 0.0413449 + 0.143223i
\(586\) 0 0
\(587\) −8.00000 13.8564i −0.330195 0.571915i 0.652355 0.757914i \(-0.273781\pi\)
−0.982550 + 0.185999i \(0.940448\pi\)
\(588\) 0 0
\(589\) 2.00000 3.46410i 0.0824086 0.142736i
\(590\) 0 0
\(591\) 18.0000 31.1769i 0.740421 1.28245i
\(592\) 0 0
\(593\) −1.00000 −0.0410651 −0.0205325 0.999789i \(-0.506536\pi\)
−0.0205325 + 0.999789i \(0.506536\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −28.0000 −1.14596
\(598\) 0 0
\(599\) −30.0000 −1.22577 −0.612883 0.790173i \(-0.709990\pi\)
−0.612883 + 0.790173i \(0.709990\pi\)
\(600\) 0 0
\(601\) 4.50000 + 7.79423i 0.183559 + 0.317933i 0.943090 0.332538i \(-0.107905\pi\)
−0.759531 + 0.650471i \(0.774572\pi\)
\(602\) 0 0
\(603\) −14.0000 −0.570124
\(604\) 0 0
\(605\) −2.50000 + 4.33013i −0.101639 + 0.176045i
\(606\) 0 0
\(607\) 17.0000 29.4449i 0.690009 1.19513i −0.281826 0.959466i \(-0.590940\pi\)
0.971834 0.235665i \(-0.0757267\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 15.0000 15.5885i 0.606835 0.630641i
\(612\) 0 0
\(613\) −0.500000 0.866025i −0.0201948 0.0349784i 0.855751 0.517387i \(-0.173095\pi\)
−0.875946 + 0.482409i \(0.839762\pi\)
\(614\) 0 0
\(615\) −3.00000 + 5.19615i −0.120972 + 0.209529i
\(616\) 0 0
\(617\) 18.5000 32.0429i 0.744782 1.29000i −0.205515 0.978654i \(-0.565887\pi\)
0.950297 0.311346i \(-0.100780\pi\)
\(618\) 0 0
\(619\) −36.0000 −1.44696 −0.723481 0.690344i \(-0.757459\pi\)
−0.723481 + 0.690344i \(0.757459\pi\)
\(620\) 0 0
\(621\) 4.00000 + 6.92820i 0.160514 + 0.278019i
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 11.0000 0.440000
\(626\) 0 0
\(627\) 8.00000 + 13.8564i 0.319489 + 0.553372i
\(628\) 0 0
\(629\) 15.0000 0.598089
\(630\) 0 0
\(631\) −10.0000 + 17.3205i −0.398094 + 0.689519i −0.993491 0.113913i \(-0.963661\pi\)
0.595397 + 0.803432i \(0.296995\pi\)
\(632\) 0 0
\(633\) −18.0000 + 31.1769i −0.715436 + 1.23917i
\(634\) 0 0
\(635\) 11.0000 + 19.0526i 0.436522 + 0.756078i
\(636\) 0 0
\(637\) 24.5000 + 6.06218i 0.970725 + 0.240192i
\(638\) 0 0
\(639\) −3.00000 5.19615i −0.118678 0.205557i
\(640\) 0 0
\(641\) 8.50000 14.7224i 0.335730 0.581501i −0.647895 0.761730i \(-0.724350\pi\)
0.983625 + 0.180229i \(0.0576838\pi\)
\(642\) 0 0
\(643\) 2.00000 3.46410i 0.0788723 0.136611i −0.823891 0.566748i \(-0.808201\pi\)
0.902764 + 0.430137i \(0.141535\pi\)
\(644\) 0 0
\(645\) −8.00000 −0.315000
\(646\) 0 0
\(647\) −19.0000 32.9090i −0.746967 1.29378i −0.949270 0.314462i \(-0.898176\pi\)
0.202303 0.979323i \(-0.435157\pi\)
\(648\) 0 0
\(649\) 48.0000 1.88416
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −7.00000 12.1244i −0.273931 0.474463i 0.695934 0.718106i \(-0.254991\pi\)
−0.969865 + 0.243643i \(0.921657\pi\)
\(654\) 0 0
\(655\) −18.0000 −0.703318
\(656\) 0 0
\(657\) −3.50000 + 6.06218i −0.136548 + 0.236508i
\(658\) 0 0
\(659\) −14.0000 + 24.2487i −0.545363 + 0.944596i 0.453221 + 0.891398i \(0.350275\pi\)
−0.998584 + 0.0531977i \(0.983059\pi\)
\(660\) 0 0
\(661\) −6.50000 11.2583i −0.252821 0.437898i 0.711481 0.702706i \(-0.248025\pi\)
−0.964301 + 0.264807i \(0.914692\pi\)
\(662\) 0 0
\(663\) 15.0000 15.5885i 0.582552 0.605406i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −5.00000 + 8.66025i −0.193601 + 0.335326i
\(668\) 0 0
\(669\) −18.0000 + 31.1769i −0.695920 + 1.20537i
\(670\) 0 0
\(671\) −28.0000 −1.08093
\(672\) 0 0
\(673\) 2.50000 + 4.33013i 0.0963679 + 0.166914i 0.910179 0.414216i \(-0.135944\pi\)
−0.813811 + 0.581130i \(0.802611\pi\)
\(674\) 0 0
\(675\) 16.0000 0.615840
\(676\) 0 0
\(677\) 26.0000 0.999261 0.499631 0.866239i \(-0.333469\pi\)
0.499631 + 0.866239i \(0.333469\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 36.0000 1.37952
\(682\) 0 0
\(683\) 19.0000 32.9090i 0.727015 1.25923i −0.231125 0.972924i \(-0.574240\pi\)
0.958139 0.286302i \(-0.0924262\pi\)
\(684\) 0 0
\(685\) 0.500000 0.866025i 0.0191040 0.0330891i
\(686\) 0 0
\(687\) 18.0000 + 31.1769i 0.686743 + 1.18947i
\(688\) 0 0
\(689\) 32.5000 33.7750i 1.23815 1.28672i
\(690\) 0 0
\(691\) −10.0000 17.3205i −0.380418 0.658903i 0.610704 0.791859i \(-0.290887\pi\)
−0.991122 + 0.132956i \(0.957553\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 8.00000 13.8564i 0.303457 0.525603i
\(696\) 0 0
\(697\) 9.00000 0.340899
\(698\) 0 0
\(699\) −6.00000 10.3923i −0.226941 0.393073i
\(700\) 0 0
\(701\) −10.0000 −0.377695 −0.188847 0.982006i \(-0.560475\pi\)
−0.188847 + 0.982006i \(0.560475\pi\)
\(702\) 0 0
\(703\) −10.0000 −0.377157
\(704\) 0 0
\(705\) −6.00000 10.3923i −0.225973 0.391397i
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −10.5000 + 18.1865i −0.394336 + 0.683010i −0.993016 0.117978i \(-0.962359\pi\)
0.598680 + 0.800988i \(0.295692\pi\)
\(710\) 0 0
\(711\) −4.00000 + 6.92820i −0.150012 + 0.259828i
\(712\) 0 0
\(713\) −2.00000 3.46410i −0.0749006 0.129732i
\(714\) 0 0
\(715\) −14.0000 3.46410i −0.523570 0.129550i
\(716\) 0 0
\(717\) 12.0000 + 20.7846i 0.448148 + 0.776215i
\(718\) 0 0
\(719\) 24.0000 41.5692i 0.895049 1.55027i 0.0613050 0.998119i \(-0.480474\pi\)
0.833744 0.552151i \(-0.186193\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 14.0000 0.520666
\(724\) 0 0
\(725\) 10.0000 + 17.3205i 0.371391 + 0.643268i
\(726\) 0 0
\(727\) −28.0000 −1.03846 −0.519231 0.854634i \(-0.673782\pi\)
−0.519231 + 0.854634i \(0.673782\pi\)
\(728\) 0 0
\(729\) 13.0000 0.481481
\(730\) 0 0
\(731\) 6.00000 + 10.3923i 0.221918 + 0.384373i
\(732\) 0 0
\(733\) 1.00000 0.0369358 0.0184679 0.999829i \(-0.494121\pi\)
0.0184679 + 0.999829i \(0.494121\pi\)
\(734\) 0 0
\(735\) 7.00000 12.1244i 0.258199 0.447214i
\(736\) 0 0
\(737\) 28.0000 48.4974i 1.03139 1.78643i
\(738\) 0 0
\(739\) −10.0000 17.3205i −0.367856 0.637145i 0.621374 0.783514i \(-0.286575\pi\)
−0.989230 + 0.146369i \(0.953241\pi\)
\(740\) 0 0
\(741\) −10.0000 + 10.3923i −0.367359 + 0.381771i
\(742\) 0 0
\(743\) 24.0000 + 41.5692i 0.880475 + 1.52503i 0.850814 + 0.525467i \(0.176109\pi\)
0.0296605 + 0.999560i \(0.490557\pi\)
\(744\) 0 0
\(745\) −10.5000 + 18.1865i −0.384690 + 0.666303i
\(746\) 0 0
\(747\) −2.00000 + 3.46410i −0.0731762 + 0.126745i
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 10.0000 + 17.3205i 0.364905 + 0.632034i 0.988761 0.149505i \(-0.0477681\pi\)
−0.623856 + 0.781540i \(0.714435\pi\)
\(752\) 0 0
\(753\) −44.0000 −1.60345
\(754\) 0 0
\(755\) 22.0000 0.800662
\(756\) 0 0
\(757\) −19.0000 32.9090i −0.690567 1.19610i −0.971652 0.236414i \(-0.924028\pi\)
0.281086 0.959683i \(-0.409305\pi\)
\(758\) 0 0
\(759\) 16.0000 0.580763
\(760\) 0 0
\(761\) −19.0000 + 32.9090i −0.688749 + 1.19295i 0.283493 + 0.958974i \(0.408507\pi\)
−0.972243 + 0.233975i \(0.924827\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) −1.50000 2.59808i −0.0542326 0.0939336i
\(766\) 0 0
\(767\) 12.0000 + 41.5692i 0.433295 + 1.50098i
\(768\) 0 0
\(769\) −19.0000 32.9090i −0.685158 1.18673i −0.973387 0.229166i \(-0.926400\pi\)
0.288230 0.957561i \(-0.406933\pi\)
\(770\) 0 0
\(771\) −11.0000 + 19.0526i −0.396155 + 0.686161i
\(772\) 0 0
\(773\) 3.00000 5.19615i 0.107903 0.186893i −0.807018 0.590527i \(-0.798920\pi\)
0.914920 + 0.403634i \(0.132253\pi\)
\(774\) 0 0
\(775\) −8.00000 −0.287368
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −6.00000 −0.214972
\(780\) 0 0
\(781\) 24.0000 0.858788
\(782\) 0 0
\(783\) 10.0000 + 17.3205i 0.357371 + 0.618984i
\(784\) 0 0
\(785\) 5.00000 0.178458
\(786\) 0 0
\(787\) −11.0000 + 19.0526i −0.392108 + 0.679150i −0.992727 0.120384i \(-0.961587\pi\)
0.600620 + 0.799535i \(0.294921\pi\)
\(788\) 0 0
\(789\) −24.0000 + 41.5692i −0.854423 + 1.47990i
\(790\) 0 0
\(791\) 0 0
\(792\) 0