Properties

Label 2640.2.d.i.529.6
Level $2640$
Weight $2$
Character 2640.529
Analytic conductor $21.081$
Analytic rank $0$
Dimension $6$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [2640,2,Mod(529,2640)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2640, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0, 1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("2640.529");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2640 = 2^{4} \cdot 3 \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2640.d (of order \(2\), degree \(1\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(21.0805061336\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: 6.0.350464.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 4x^{2} - 4x + 2 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 165)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 529.6
Root \(-0.854638 - 0.854638i\) of defining polynomial
Character \(\chi\) \(=\) 2640.529
Dual form 2640.2.d.i.529.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000i q^{3} +(2.17009 + 0.539189i) q^{5} +0.290725i q^{7} -1.00000 q^{9} +O(q^{10})\) \(q+1.00000i q^{3} +(2.17009 + 0.539189i) q^{5} +0.290725i q^{7} -1.00000 q^{9} +1.00000 q^{11} +6.97107i q^{13} +(-0.539189 + 2.17009i) q^{15} -4.78765i q^{17} +7.75872 q^{19} -0.290725 q^{21} -4.00000i q^{23} +(4.41855 + 2.34017i) q^{25} -1.00000i q^{27} +7.41855 q^{29} -6.34017 q^{31} +1.00000i q^{33} +(-0.156755 + 0.630898i) q^{35} +3.41855i q^{37} -6.97107 q^{39} -7.41855 q^{41} -0.290725i q^{43} +(-2.17009 - 0.539189i) q^{45} +5.26180i q^{47} +6.91548 q^{49} +4.78765 q^{51} +5.75872i q^{53} +(2.17009 + 0.539189i) q^{55} +7.75872i q^{57} +3.60197 q^{59} -6.68035 q^{61} -0.290725i q^{63} +(-3.75872 + 15.1278i) q^{65} +6.15676i q^{67} +4.00000 q^{69} +5.07838 q^{71} -1.12783i q^{73} +(-2.34017 + 4.41855i) q^{75} +0.290725i q^{77} -0.921622 q^{79} +1.00000 q^{81} -1.70928i q^{83} +(2.58145 - 10.3896i) q^{85} +7.41855i q^{87} -4.34017 q^{89} -2.02666 q^{91} -6.34017i q^{93} +(16.8371 + 4.18342i) q^{95} -4.68035i q^{97} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + 2 q^{5} - 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q + 2 q^{5} - 6 q^{9} + 6 q^{11} - 4 q^{19} - 16 q^{21} - 2 q^{25} + 16 q^{29} - 16 q^{31} + 12 q^{35} - 12 q^{39} - 16 q^{41} - 2 q^{45} - 22 q^{49} + 8 q^{51} + 2 q^{55} - 16 q^{59} + 4 q^{61} + 28 q^{65} + 24 q^{69} + 24 q^{71} + 8 q^{75} - 12 q^{79} + 6 q^{81} + 44 q^{85} - 4 q^{89} - 16 q^{91} + 44 q^{95} - 6 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2640\mathbb{Z}\right)^\times\).

\(n\) \(661\) \(881\) \(991\) \(1057\) \(1201\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(-1\) \(1\)

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
\(3\) 1.00000i 0.577350i
\(4\) 0 0
\(5\) 2.17009 + 0.539189i 0.970492 + 0.241133i
\(6\) 0 0
\(7\) 0.290725i 0.109884i 0.998490 + 0.0549418i \(0.0174973\pi\)
−0.998490 + 0.0549418i \(0.982503\pi\)
\(8\) 0 0
\(9\) −1.00000 −0.333333
\(10\) 0 0
\(11\) 1.00000 0.301511
\(12\) 0 0
\(13\) 6.97107i 1.93343i 0.255861 + 0.966714i \(0.417641\pi\)
−0.255861 + 0.966714i \(0.582359\pi\)
\(14\) 0 0
\(15\) −0.539189 + 2.17009i −0.139218 + 0.560314i
\(16\) 0 0
\(17\) 4.78765i 1.16118i −0.814197 0.580588i \(-0.802823\pi\)
0.814197 0.580588i \(-0.197177\pi\)
\(18\) 0 0
\(19\) 7.75872 1.77997 0.889987 0.455987i \(-0.150714\pi\)
0.889987 + 0.455987i \(0.150714\pi\)
\(20\) 0 0
\(21\) −0.290725 −0.0634413
\(22\) 0 0
\(23\) 4.00000i 0.834058i −0.908893 0.417029i \(-0.863071\pi\)
0.908893 0.417029i \(-0.136929\pi\)
\(24\) 0 0
\(25\) 4.41855 + 2.34017i 0.883710 + 0.468035i
\(26\) 0 0
\(27\) 1.00000i 0.192450i
\(28\) 0 0
\(29\) 7.41855 1.37759 0.688795 0.724956i \(-0.258140\pi\)
0.688795 + 0.724956i \(0.258140\pi\)
\(30\) 0 0
\(31\) −6.34017 −1.13873 −0.569364 0.822085i \(-0.692811\pi\)
−0.569364 + 0.822085i \(0.692811\pi\)
\(32\) 0 0
\(33\) 1.00000i 0.174078i
\(34\) 0 0
\(35\) −0.156755 + 0.630898i −0.0264965 + 0.106641i
\(36\) 0 0
\(37\) 3.41855i 0.562006i 0.959707 + 0.281003i \(0.0906671\pi\)
−0.959707 + 0.281003i \(0.909333\pi\)
\(38\) 0 0
\(39\) −6.97107 −1.11626
\(40\) 0 0
\(41\) −7.41855 −1.15858 −0.579291 0.815120i \(-0.696671\pi\)
−0.579291 + 0.815120i \(0.696671\pi\)
\(42\) 0 0
\(43\) 0.290725i 0.0443351i −0.999754 0.0221675i \(-0.992943\pi\)
0.999754 0.0221675i \(-0.00705673\pi\)
\(44\) 0 0
\(45\) −2.17009 0.539189i −0.323497 0.0803775i
\(46\) 0 0
\(47\) 5.26180i 0.767512i 0.923435 + 0.383756i \(0.125370\pi\)
−0.923435 + 0.383756i \(0.874630\pi\)
\(48\) 0 0
\(49\) 6.91548 0.987926
\(50\) 0 0
\(51\) 4.78765 0.670406
\(52\) 0 0
\(53\) 5.75872i 0.791022i 0.918461 + 0.395511i \(0.129432\pi\)
−0.918461 + 0.395511i \(0.870568\pi\)
\(54\) 0 0
\(55\) 2.17009 + 0.539189i 0.292614 + 0.0727042i
\(56\) 0 0
\(57\) 7.75872i 1.02767i
\(58\) 0 0
\(59\) 3.60197 0.468936 0.234468 0.972124i \(-0.424665\pi\)
0.234468 + 0.972124i \(0.424665\pi\)
\(60\) 0 0
\(61\) −6.68035 −0.855331 −0.427665 0.903937i \(-0.640664\pi\)
−0.427665 + 0.903937i \(0.640664\pi\)
\(62\) 0 0
\(63\) 0.290725i 0.0366279i
\(64\) 0 0
\(65\) −3.75872 + 15.1278i −0.466212 + 1.87638i
\(66\) 0 0
\(67\) 6.15676i 0.752167i 0.926586 + 0.376084i \(0.122729\pi\)
−0.926586 + 0.376084i \(0.877271\pi\)
\(68\) 0 0
\(69\) 4.00000 0.481543
\(70\) 0 0
\(71\) 5.07838 0.602693 0.301346 0.953515i \(-0.402564\pi\)
0.301346 + 0.953515i \(0.402564\pi\)
\(72\) 0 0
\(73\) 1.12783i 0.132002i −0.997820 0.0660010i \(-0.978976\pi\)
0.997820 0.0660010i \(-0.0210241\pi\)
\(74\) 0 0
\(75\) −2.34017 + 4.41855i −0.270220 + 0.510210i
\(76\) 0 0
\(77\) 0.290725i 0.0331311i
\(78\) 0 0
\(79\) −0.921622 −0.103691 −0.0518453 0.998655i \(-0.516510\pi\)
−0.0518453 + 0.998655i \(0.516510\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) 1.70928i 0.187617i −0.995590 0.0938087i \(-0.970096\pi\)
0.995590 0.0938087i \(-0.0299042\pi\)
\(84\) 0 0
\(85\) 2.58145 10.3896i 0.279997 1.12691i
\(86\) 0 0
\(87\) 7.41855i 0.795352i
\(88\) 0 0
\(89\) −4.34017 −0.460057 −0.230029 0.973184i \(-0.573882\pi\)
−0.230029 + 0.973184i \(0.573882\pi\)
\(90\) 0 0
\(91\) −2.02666 −0.212452
\(92\) 0 0
\(93\) 6.34017i 0.657445i
\(94\) 0 0
\(95\) 16.8371 + 4.18342i 1.72745 + 0.429210i
\(96\) 0 0
\(97\) 4.68035i 0.475217i −0.971361 0.237609i \(-0.923636\pi\)
0.971361 0.237609i \(-0.0763635\pi\)
\(98\) 0 0
\(99\) −1.00000 −0.100504
\(100\) 0 0
\(101\) −8.58145 −0.853886 −0.426943 0.904279i \(-0.640410\pi\)
−0.426943 + 0.904279i \(0.640410\pi\)
\(102\) 0 0
\(103\) 6.73820i 0.663935i −0.943291 0.331968i \(-0.892288\pi\)
0.943291 0.331968i \(-0.107712\pi\)
\(104\) 0 0
\(105\) −0.630898 0.156755i −0.0615693 0.0152978i
\(106\) 0 0
\(107\) 12.2329i 1.18260i 0.806453 + 0.591298i \(0.201384\pi\)
−0.806453 + 0.591298i \(0.798616\pi\)
\(108\) 0 0
\(109\) 6.31351 0.604725 0.302362 0.953193i \(-0.402225\pi\)
0.302362 + 0.953193i \(0.402225\pi\)
\(110\) 0 0
\(111\) −3.41855 −0.324474
\(112\) 0 0
\(113\) 16.4969i 1.55190i −0.630794 0.775950i \(-0.717271\pi\)
0.630794 0.775950i \(-0.282729\pi\)
\(114\) 0 0
\(115\) 2.15676 8.68035i 0.201118 0.809446i
\(116\) 0 0
\(117\) 6.97107i 0.644476i
\(118\) 0 0
\(119\) 1.39189 0.127594
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) 0 0
\(123\) 7.41855i 0.668908i
\(124\) 0 0
\(125\) 8.32684 + 7.46081i 0.744775 + 0.667315i
\(126\) 0 0
\(127\) 4.87217i 0.432336i 0.976356 + 0.216168i \(0.0693558\pi\)
−0.976356 + 0.216168i \(0.930644\pi\)
\(128\) 0 0
\(129\) 0.290725 0.0255969
\(130\) 0 0
\(131\) 8.68035 0.758405 0.379203 0.925314i \(-0.376198\pi\)
0.379203 + 0.925314i \(0.376198\pi\)
\(132\) 0 0
\(133\) 2.25565i 0.195590i
\(134\) 0 0
\(135\) 0.539189 2.17009i 0.0464060 0.186771i
\(136\) 0 0
\(137\) 12.5958i 1.07613i 0.842902 + 0.538067i \(0.180845\pi\)
−0.842902 + 0.538067i \(0.819155\pi\)
\(138\) 0 0
\(139\) −9.91548 −0.841020 −0.420510 0.907288i \(-0.638149\pi\)
−0.420510 + 0.907288i \(0.638149\pi\)
\(140\) 0 0
\(141\) −5.26180 −0.443123
\(142\) 0 0
\(143\) 6.97107i 0.582950i
\(144\) 0 0
\(145\) 16.0989 + 4.00000i 1.33694 + 0.332182i
\(146\) 0 0
\(147\) 6.91548i 0.570379i
\(148\) 0 0
\(149\) 1.26180 0.103370 0.0516851 0.998663i \(-0.483541\pi\)
0.0516851 + 0.998663i \(0.483541\pi\)
\(150\) 0 0
\(151\) −1.60197 −0.130366 −0.0651832 0.997873i \(-0.520763\pi\)
−0.0651832 + 0.997873i \(0.520763\pi\)
\(152\) 0 0
\(153\) 4.78765i 0.387059i
\(154\) 0 0
\(155\) −13.7587 3.41855i −1.10513 0.274585i
\(156\) 0 0
\(157\) 7.10504i 0.567044i 0.958966 + 0.283522i \(0.0915029\pi\)
−0.958966 + 0.283522i \(0.908497\pi\)
\(158\) 0 0
\(159\) −5.75872 −0.456696
\(160\) 0 0
\(161\) 1.16290 0.0916492
\(162\) 0 0
\(163\) 22.9360i 1.79649i 0.439499 + 0.898243i \(0.355156\pi\)
−0.439499 + 0.898243i \(0.644844\pi\)
\(164\) 0 0
\(165\) −0.539189 + 2.17009i −0.0419758 + 0.168941i
\(166\) 0 0
\(167\) 4.81432i 0.372543i 0.982498 + 0.186271i \(0.0596404\pi\)
−0.982498 + 0.186271i \(0.940360\pi\)
\(168\) 0 0
\(169\) −35.5958 −2.73814
\(170\) 0 0
\(171\) −7.75872 −0.593324
\(172\) 0 0
\(173\) 12.8865i 0.979746i −0.871794 0.489873i \(-0.837043\pi\)
0.871794 0.489873i \(-0.162957\pi\)
\(174\) 0 0
\(175\) −0.680346 + 1.28458i −0.0514293 + 0.0971052i
\(176\) 0 0
\(177\) 3.60197i 0.270741i
\(178\) 0 0
\(179\) 1.84324 0.137771 0.0688853 0.997625i \(-0.478056\pi\)
0.0688853 + 0.997625i \(0.478056\pi\)
\(180\) 0 0
\(181\) 10.2823 0.764278 0.382139 0.924105i \(-0.375187\pi\)
0.382139 + 0.924105i \(0.375187\pi\)
\(182\) 0 0
\(183\) 6.68035i 0.493825i
\(184\) 0 0
\(185\) −1.84324 + 7.41855i −0.135518 + 0.545423i
\(186\) 0 0
\(187\) 4.78765i 0.350108i
\(188\) 0 0
\(189\) 0.290725 0.0211471
\(190\) 0 0
\(191\) 11.5174 0.833373 0.416687 0.909050i \(-0.363191\pi\)
0.416687 + 0.909050i \(0.363191\pi\)
\(192\) 0 0
\(193\) 3.86603i 0.278283i 0.990273 + 0.139141i \(0.0444343\pi\)
−0.990273 + 0.139141i \(0.955566\pi\)
\(194\) 0 0
\(195\) −15.1278 3.75872i −1.08333 0.269168i
\(196\) 0 0
\(197\) 8.57304i 0.610804i 0.952224 + 0.305402i \(0.0987908\pi\)
−0.952224 + 0.305402i \(0.901209\pi\)
\(198\) 0 0
\(199\) 8.31351 0.589329 0.294665 0.955601i \(-0.404792\pi\)
0.294665 + 0.955601i \(0.404792\pi\)
\(200\) 0 0
\(201\) −6.15676 −0.434264
\(202\) 0 0
\(203\) 2.15676i 0.151375i
\(204\) 0 0
\(205\) −16.0989 4.00000i −1.12440 0.279372i
\(206\) 0 0
\(207\) 4.00000i 0.278019i
\(208\) 0 0
\(209\) 7.75872 0.536682
\(210\) 0 0
\(211\) −25.9155 −1.78410 −0.892048 0.451941i \(-0.850732\pi\)
−0.892048 + 0.451941i \(0.850732\pi\)
\(212\) 0 0
\(213\) 5.07838i 0.347965i
\(214\) 0 0
\(215\) 0.156755 0.630898i 0.0106906 0.0430269i
\(216\) 0 0
\(217\) 1.84324i 0.125128i
\(218\) 0 0
\(219\) 1.12783 0.0762114
\(220\) 0 0
\(221\) 33.3751 2.24505
\(222\) 0 0
\(223\) 9.62863i 0.644781i 0.946607 + 0.322390i \(0.104486\pi\)
−0.946607 + 0.322390i \(0.895514\pi\)
\(224\) 0 0
\(225\) −4.41855 2.34017i −0.294570 0.156012i
\(226\) 0 0
\(227\) 18.3896i 1.22056i −0.792185 0.610281i \(-0.791057\pi\)
0.792185 0.610281i \(-0.208943\pi\)
\(228\) 0 0
\(229\) −17.1506 −1.13334 −0.566672 0.823943i \(-0.691769\pi\)
−0.566672 + 0.823943i \(0.691769\pi\)
\(230\) 0 0
\(231\) −0.290725 −0.0191283
\(232\) 0 0
\(233\) 4.10731i 0.269079i −0.990908 0.134539i \(-0.957045\pi\)
0.990908 0.134539i \(-0.0429555\pi\)
\(234\) 0 0
\(235\) −2.83710 + 11.4186i −0.185072 + 0.744864i
\(236\) 0 0
\(237\) 0.921622i 0.0598658i
\(238\) 0 0
\(239\) −4.36683 −0.282467 −0.141234 0.989976i \(-0.545107\pi\)
−0.141234 + 0.989976i \(0.545107\pi\)
\(240\) 0 0
\(241\) −5.20394 −0.335215 −0.167608 0.985854i \(-0.553604\pi\)
−0.167608 + 0.985854i \(0.553604\pi\)
\(242\) 0 0
\(243\) 1.00000i 0.0641500i
\(244\) 0 0
\(245\) 15.0072 + 3.72875i 0.958774 + 0.238221i
\(246\) 0 0
\(247\) 54.0866i 3.44145i
\(248\) 0 0
\(249\) 1.70928 0.108321
\(250\) 0 0
\(251\) 8.28231 0.522775 0.261388 0.965234i \(-0.415820\pi\)
0.261388 + 0.965234i \(0.415820\pi\)
\(252\) 0 0
\(253\) 4.00000i 0.251478i
\(254\) 0 0
\(255\) 10.3896 + 2.58145i 0.650623 + 0.161657i
\(256\) 0 0
\(257\) 11.0205i 0.687441i −0.939072 0.343721i \(-0.888313\pi\)
0.939072 0.343721i \(-0.111687\pi\)
\(258\) 0 0
\(259\) −0.993857 −0.0617553
\(260\) 0 0
\(261\) −7.41855 −0.459197
\(262\) 0 0
\(263\) 2.97107i 0.183204i 0.995796 + 0.0916020i \(0.0291988\pi\)
−0.995796 + 0.0916020i \(0.970801\pi\)
\(264\) 0 0
\(265\) −3.10504 + 12.4969i −0.190741 + 0.767680i
\(266\) 0 0
\(267\) 4.34017i 0.265614i
\(268\) 0 0
\(269\) 15.8432 0.965980 0.482990 0.875626i \(-0.339551\pi\)
0.482990 + 0.875626i \(0.339551\pi\)
\(270\) 0 0
\(271\) 6.28231 0.381623 0.190812 0.981627i \(-0.438888\pi\)
0.190812 + 0.981627i \(0.438888\pi\)
\(272\) 0 0
\(273\) 2.02666i 0.122659i
\(274\) 0 0
\(275\) 4.41855 + 2.34017i 0.266449 + 0.141118i
\(276\) 0 0
\(277\) 5.12783i 0.308101i −0.988063 0.154051i \(-0.950768\pi\)
0.988063 0.154051i \(-0.0492319\pi\)
\(278\) 0 0
\(279\) 6.34017 0.379576
\(280\) 0 0
\(281\) 21.8888 1.30578 0.652889 0.757454i \(-0.273557\pi\)
0.652889 + 0.757454i \(0.273557\pi\)
\(282\) 0 0
\(283\) 25.9649i 1.54345i −0.635954 0.771727i \(-0.719393\pi\)
0.635954 0.771727i \(-0.280607\pi\)
\(284\) 0 0
\(285\) −4.18342 + 16.8371i −0.247804 + 0.997344i
\(286\) 0 0
\(287\) 2.15676i 0.127309i
\(288\) 0 0
\(289\) −5.92162 −0.348331
\(290\) 0 0
\(291\) 4.68035 0.274367
\(292\) 0 0
\(293\) 10.4163i 0.608526i 0.952588 + 0.304263i \(0.0984101\pi\)
−0.952588 + 0.304263i \(0.901590\pi\)
\(294\) 0 0
\(295\) 7.81658 + 1.94214i 0.455099 + 0.113076i
\(296\) 0 0
\(297\) 1.00000i 0.0580259i
\(298\) 0 0
\(299\) 27.8843 1.61259
\(300\) 0 0
\(301\) 0.0845208 0.00487170
\(302\) 0 0
\(303\) 8.58145i 0.492991i
\(304\) 0 0
\(305\) −14.4969 3.60197i −0.830092 0.206248i
\(306\) 0 0
\(307\) 29.0700i 1.65911i −0.558425 0.829555i \(-0.688594\pi\)
0.558425 0.829555i \(-0.311406\pi\)
\(308\) 0 0
\(309\) 6.73820 0.383323
\(310\) 0 0
\(311\) −5.44521 −0.308770 −0.154385 0.988011i \(-0.549340\pi\)
−0.154385 + 0.988011i \(0.549340\pi\)
\(312\) 0 0
\(313\) 25.0928i 1.41833i 0.705044 + 0.709163i \(0.250927\pi\)
−0.705044 + 0.709163i \(0.749073\pi\)
\(314\) 0 0
\(315\) 0.156755 0.630898i 0.00883217 0.0355471i
\(316\) 0 0
\(317\) 21.1773i 1.18943i −0.803935 0.594717i \(-0.797264\pi\)
0.803935 0.594717i \(-0.202736\pi\)
\(318\) 0 0
\(319\) 7.41855 0.415359
\(320\) 0 0
\(321\) −12.2329 −0.682772
\(322\) 0 0
\(323\) 37.1461i 2.06686i
\(324\) 0 0
\(325\) −16.3135 + 30.8020i −0.904911 + 1.70859i
\(326\) 0 0
\(327\) 6.31351i 0.349138i
\(328\) 0 0
\(329\) −1.52973 −0.0843369
\(330\) 0 0
\(331\) 6.70701 0.368650 0.184325 0.982865i \(-0.440990\pi\)
0.184325 + 0.982865i \(0.440990\pi\)
\(332\) 0 0
\(333\) 3.41855i 0.187335i
\(334\) 0 0
\(335\) −3.31965 + 13.3607i −0.181372 + 0.729973i
\(336\) 0 0
\(337\) 23.7503i 1.29376i −0.762591 0.646881i \(-0.776073\pi\)
0.762591 0.646881i \(-0.223927\pi\)
\(338\) 0 0
\(339\) 16.4969 0.895990
\(340\) 0 0
\(341\) −6.34017 −0.343340
\(342\) 0 0
\(343\) 4.04557i 0.218440i
\(344\) 0 0
\(345\) 8.68035 + 2.15676i 0.467334 + 0.116116i
\(346\) 0 0
\(347\) 31.1689i 1.67323i −0.547790 0.836616i \(-0.684531\pi\)
0.547790 0.836616i \(-0.315469\pi\)
\(348\) 0 0
\(349\) −11.0472 −0.591342 −0.295671 0.955290i \(-0.595543\pi\)
−0.295671 + 0.955290i \(0.595543\pi\)
\(350\) 0 0
\(351\) 6.97107 0.372088
\(352\) 0 0
\(353\) 27.4329i 1.46011i −0.683390 0.730054i \(-0.739495\pi\)
0.683390 0.730054i \(-0.260505\pi\)
\(354\) 0 0
\(355\) 11.0205 + 2.73820i 0.584908 + 0.145329i
\(356\) 0 0
\(357\) 1.39189i 0.0736666i
\(358\) 0 0
\(359\) −19.1506 −1.01073 −0.505365 0.862905i \(-0.668642\pi\)
−0.505365 + 0.862905i \(0.668642\pi\)
\(360\) 0 0
\(361\) 41.1978 2.16830
\(362\) 0 0
\(363\) 1.00000i 0.0524864i
\(364\) 0 0
\(365\) 0.608111 2.44748i 0.0318300 0.128107i
\(366\) 0 0
\(367\) 14.5692i 0.760504i −0.924883 0.380252i \(-0.875837\pi\)
0.924883 0.380252i \(-0.124163\pi\)
\(368\) 0 0
\(369\) 7.41855 0.386194
\(370\) 0 0
\(371\) −1.67420 −0.0869203
\(372\) 0 0
\(373\) 8.81432i 0.456388i −0.973616 0.228194i \(-0.926718\pi\)
0.973616 0.228194i \(-0.0732820\pi\)
\(374\) 0 0
\(375\) −7.46081 + 8.32684i −0.385275 + 0.429996i
\(376\) 0 0
\(377\) 51.7152i 2.66347i
\(378\) 0 0
\(379\) −23.5174 −1.20801 −0.604005 0.796980i \(-0.706429\pi\)
−0.604005 + 0.796980i \(0.706429\pi\)
\(380\) 0 0
\(381\) −4.87217 −0.249609
\(382\) 0 0
\(383\) 19.3028i 0.986329i 0.869936 + 0.493164i \(0.164160\pi\)
−0.869936 + 0.493164i \(0.835840\pi\)
\(384\) 0 0
\(385\) −0.156755 + 0.630898i −0.00798900 + 0.0321535i
\(386\) 0 0
\(387\) 0.290725i 0.0147784i
\(388\) 0 0
\(389\) 20.0410 1.01612 0.508060 0.861321i \(-0.330363\pi\)
0.508060 + 0.861321i \(0.330363\pi\)
\(390\) 0 0
\(391\) −19.1506 −0.968488
\(392\) 0 0
\(393\) 8.68035i 0.437866i
\(394\) 0 0
\(395\) −2.00000 0.496928i −0.100631 0.0250032i
\(396\) 0 0
\(397\) 33.3607i 1.67433i 0.546954 + 0.837163i \(0.315787\pi\)
−0.546954 + 0.837163i \(0.684213\pi\)
\(398\) 0 0
\(399\) −2.25565 −0.112924
\(400\) 0 0
\(401\) −37.6475 −1.88003 −0.940014 0.341135i \(-0.889189\pi\)
−0.940014 + 0.341135i \(0.889189\pi\)
\(402\) 0 0
\(403\) 44.1978i 2.20165i
\(404\) 0 0
\(405\) 2.17009 + 0.539189i 0.107832 + 0.0267925i
\(406\) 0 0
\(407\) 3.41855i 0.169451i
\(408\) 0 0
\(409\) 25.2039 1.24625 0.623127 0.782120i \(-0.285862\pi\)
0.623127 + 0.782120i \(0.285862\pi\)
\(410\) 0 0
\(411\) −12.5958 −0.621306
\(412\) 0 0
\(413\) 1.04718i 0.0515284i
\(414\) 0 0
\(415\) 0.921622 3.70928i 0.0452407 0.182081i
\(416\) 0 0
\(417\) 9.91548i 0.485563i
\(418\) 0 0
\(419\) 17.8432 0.871700 0.435850 0.900019i \(-0.356448\pi\)
0.435850 + 0.900019i \(0.356448\pi\)
\(420\) 0 0
\(421\) −11.8120 −0.575684 −0.287842 0.957678i \(-0.592938\pi\)
−0.287842 + 0.957678i \(0.592938\pi\)
\(422\) 0 0
\(423\) 5.26180i 0.255837i
\(424\) 0 0
\(425\) 11.2039 21.1545i 0.543471 1.02614i
\(426\) 0 0
\(427\) 1.94214i 0.0939868i
\(428\) 0 0
\(429\) −6.97107 −0.336566
\(430\) 0 0
\(431\) −16.6803 −0.803464 −0.401732 0.915757i \(-0.631592\pi\)
−0.401732 + 0.915757i \(0.631592\pi\)
\(432\) 0 0
\(433\) 28.3135i 1.36066i −0.732906 0.680330i \(-0.761836\pi\)
0.732906 0.680330i \(-0.238164\pi\)
\(434\) 0 0
\(435\) −4.00000 + 16.0989i −0.191785 + 0.771883i
\(436\) 0 0
\(437\) 31.0349i 1.48460i
\(438\) 0 0
\(439\) −27.4452 −1.30989 −0.654944 0.755677i \(-0.727308\pi\)
−0.654944 + 0.755677i \(0.727308\pi\)
\(440\) 0 0
\(441\) −6.91548 −0.329309
\(442\) 0 0
\(443\) 0.412408i 0.0195941i −0.999952 0.00979704i \(-0.996881\pi\)
0.999952 0.00979704i \(-0.00311854\pi\)
\(444\) 0 0
\(445\) −9.41855 2.34017i −0.446482 0.110935i
\(446\) 0 0
\(447\) 1.26180i 0.0596809i
\(448\) 0 0
\(449\) −1.33403 −0.0629568 −0.0314784 0.999504i \(-0.510022\pi\)
−0.0314784 + 0.999504i \(0.510022\pi\)
\(450\) 0 0
\(451\) −7.41855 −0.349326
\(452\) 0 0
\(453\) 1.60197i 0.0752670i
\(454\) 0 0
\(455\) −4.39803 1.09275i −0.206183 0.0512291i
\(456\) 0 0
\(457\) 11.6514i 0.545030i −0.962151 0.272515i \(-0.912145\pi\)
0.962151 0.272515i \(-0.0878555\pi\)
\(458\) 0 0
\(459\) −4.78765 −0.223469
\(460\) 0 0
\(461\) −2.05786 −0.0958440 −0.0479220 0.998851i \(-0.515260\pi\)
−0.0479220 + 0.998851i \(0.515260\pi\)
\(462\) 0 0
\(463\) 28.7792i 1.33748i −0.743494 0.668742i \(-0.766833\pi\)
0.743494 0.668742i \(-0.233167\pi\)
\(464\) 0 0
\(465\) 3.41855 13.7587i 0.158531 0.638046i
\(466\) 0 0
\(467\) 1.84324i 0.0852952i 0.999090 + 0.0426476i \(0.0135793\pi\)
−0.999090 + 0.0426476i \(0.986421\pi\)
\(468\) 0 0
\(469\) −1.78992 −0.0826509
\(470\) 0 0
\(471\) −7.10504 −0.327383
\(472\) 0 0
\(473\) 0.290725i 0.0133675i
\(474\) 0 0
\(475\) 34.2823 + 18.1568i 1.57298 + 0.833089i
\(476\) 0 0
\(477\) 5.75872i 0.263674i
\(478\) 0 0
\(479\) 26.8371 1.22622 0.613109 0.789998i \(-0.289919\pi\)
0.613109 + 0.789998i \(0.289919\pi\)
\(480\) 0 0
\(481\) −23.8310 −1.08660
\(482\) 0 0
\(483\) 1.16290i 0.0529137i
\(484\) 0 0
\(485\) 2.52359 10.1568i 0.114590 0.461195i
\(486\) 0 0
\(487\) 28.5646i 1.29439i 0.762326 + 0.647193i \(0.224057\pi\)
−0.762326 + 0.647193i \(0.775943\pi\)
\(488\) 0 0
\(489\) −22.9360 −1.03720
\(490\) 0 0
\(491\) −25.9877 −1.17281 −0.586405 0.810018i \(-0.699457\pi\)
−0.586405 + 0.810018i \(0.699457\pi\)
\(492\) 0 0
\(493\) 35.5174i 1.59963i
\(494\) 0 0
\(495\) −2.17009 0.539189i −0.0975381 0.0242347i
\(496\) 0 0
\(497\) 1.47641i 0.0662260i
\(498\) 0 0
\(499\) −27.5174 −1.23185 −0.615925 0.787805i \(-0.711218\pi\)
−0.615925 + 0.787805i \(0.711218\pi\)
\(500\) 0 0
\(501\) −4.81432 −0.215088
\(502\) 0 0
\(503\) 22.6576i 1.01025i −0.863046 0.505125i \(-0.831446\pi\)
0.863046 0.505125i \(-0.168554\pi\)
\(504\) 0 0
\(505\) −18.6225 4.62702i −0.828690 0.205900i
\(506\) 0 0
\(507\) 35.5958i 1.58087i
\(508\) 0 0
\(509\) 27.8432 1.23413 0.617065 0.786912i \(-0.288322\pi\)
0.617065 + 0.786912i \(0.288322\pi\)
\(510\) 0 0
\(511\) 0.327887 0.0145049
\(512\) 0 0
\(513\) 7.75872i 0.342556i
\(514\) 0 0
\(515\) 3.63317 14.6225i 0.160096 0.644344i
\(516\) 0 0
\(517\) 5.26180i 0.231413i
\(518\) 0 0
\(519\) 12.8865 0.565657
\(520\) 0 0
\(521\) 29.7009 1.30122 0.650609 0.759413i \(-0.274514\pi\)
0.650609 + 0.759413i \(0.274514\pi\)
\(522\) 0 0
\(523\) 24.7565i 1.08252i −0.840854 0.541262i \(-0.817947\pi\)
0.840854 0.541262i \(-0.182053\pi\)
\(524\) 0 0
\(525\) −1.28458 0.680346i −0.0560637 0.0296927i
\(526\) 0 0
\(527\) 30.3545i 1.32226i
\(528\) 0 0
\(529\) 7.00000 0.304348
\(530\) 0 0
\(531\) −3.60197 −0.156312
\(532\) 0 0
\(533\) 51.7152i 2.24004i
\(534\) 0 0
\(535\) −6.59583 + 26.5464i −0.285162 + 1.14770i
\(536\) 0 0
\(537\) 1.84324i 0.0795419i
\(538\) 0 0
\(539\) 6.91548 0.297871
\(540\) 0 0
\(541\) −12.5236 −0.538431 −0.269216 0.963080i \(-0.586764\pi\)
−0.269216 + 0.963080i \(0.586764\pi\)
\(542\) 0 0
\(543\) 10.2823i 0.441256i
\(544\) 0 0
\(545\) 13.7009 + 3.40417i 0.586881 + 0.145819i
\(546\) 0 0
\(547\) 14.2784i 0.610502i −0.952272 0.305251i \(-0.901260\pi\)
0.952272 0.305251i \(-0.0987404\pi\)
\(548\) 0 0
\(549\) 6.68035 0.285110
\(550\) 0 0
\(551\) 57.5585 2.45207
\(552\) 0 0
\(553\) 0.267938i 0.0113939i
\(554\) 0 0
\(555\) −7.41855 1.84324i −0.314900 0.0782414i
\(556\) 0 0
\(557\) 3.57918i 0.151655i 0.997121 + 0.0758274i \(0.0241598\pi\)
−0.997121 + 0.0758274i \(0.975840\pi\)
\(558\) 0 0
\(559\) 2.02666 0.0857187
\(560\) 0 0
\(561\) 4.78765 0.202135
\(562\) 0 0
\(563\) 28.9588i 1.22047i −0.792222 0.610234i \(-0.791076\pi\)
0.792222 0.610234i \(-0.208924\pi\)
\(564\) 0 0
\(565\) 8.89496 35.7998i 0.374214 1.50611i
\(566\) 0 0
\(567\) 0.290725i 0.0122093i
\(568\) 0 0
\(569\) 25.8264 1.08270 0.541350 0.840797i \(-0.317913\pi\)
0.541350 + 0.840797i \(0.317913\pi\)
\(570\) 0 0
\(571\) −17.1194 −0.716425 −0.358213 0.933640i \(-0.616614\pi\)
−0.358213 + 0.933640i \(0.616614\pi\)
\(572\) 0 0
\(573\) 11.5174i 0.481148i
\(574\) 0 0
\(575\) 9.36069 17.6742i 0.390368 0.737065i
\(576\) 0 0
\(577\) 22.5692i 0.939567i −0.882782 0.469783i \(-0.844332\pi\)
0.882782 0.469783i \(-0.155668\pi\)
\(578\) 0 0
\(579\) −3.86603 −0.160667
\(580\) 0 0
\(581\) 0.496928 0.0206161
\(582\) 0 0
\(583\) 5.75872i 0.238502i
\(584\) 0 0
\(585\) 3.75872 15.1278i 0.155404 0.625459i
\(586\) 0 0
\(587\) 3.63317i 0.149957i 0.997185 + 0.0749784i \(0.0238888\pi\)
−0.997185 + 0.0749784i \(0.976111\pi\)
\(588\) 0 0
\(589\) −49.1917 −2.02691
\(590\) 0 0
\(591\) −8.57304 −0.352648
\(592\) 0 0
\(593\) 12.3051i 0.505310i 0.967556 + 0.252655i \(0.0813037\pi\)
−0.967556 + 0.252655i \(0.918696\pi\)
\(594\) 0 0
\(595\) 3.02052 + 0.750491i 0.123829 + 0.0307671i
\(596\) 0 0
\(597\) 8.31351i 0.340249i
\(598\) 0 0
\(599\) 19.6865 0.804368 0.402184 0.915559i \(-0.368251\pi\)
0.402184 + 0.915559i \(0.368251\pi\)
\(600\) 0 0
\(601\) 25.8843 1.05584 0.527921 0.849294i \(-0.322972\pi\)
0.527921 + 0.849294i \(0.322972\pi\)
\(602\) 0 0
\(603\) 6.15676i 0.250722i
\(604\) 0 0
\(605\) 2.17009 + 0.539189i 0.0882266 + 0.0219211i
\(606\) 0 0
\(607\) 41.5357i 1.68588i −0.538006 0.842941i \(-0.680822\pi\)
0.538006 0.842941i \(-0.319178\pi\)
\(608\) 0 0
\(609\) −2.15676 −0.0873961
\(610\) 0 0
\(611\) −36.6803 −1.48393
\(612\) 0 0
\(613\) 20.6453i 0.833855i −0.908940 0.416927i \(-0.863107\pi\)
0.908940 0.416927i \(-0.136893\pi\)
\(614\) 0 0
\(615\) 4.00000 16.0989i 0.161296 0.649170i
\(616\) 0 0
\(617\) 8.69472i 0.350036i −0.984565 0.175018i \(-0.944002\pi\)
0.984565 0.175018i \(-0.0559984\pi\)
\(618\) 0 0
\(619\) 2.65368 0.106661 0.0533303 0.998577i \(-0.483016\pi\)
0.0533303 + 0.998577i \(0.483016\pi\)
\(620\) 0 0
\(621\) −4.00000 −0.160514
\(622\) 0 0
\(623\) 1.26180i 0.0505528i
\(624\) 0 0
\(625\) 14.0472 + 20.6803i 0.561887 + 0.827214i
\(626\) 0 0
\(627\) 7.75872i 0.309854i
\(628\) 0 0
\(629\) 16.3668 0.652588
\(630\) 0 0
\(631\) 10.6393 0.423544 0.211772 0.977319i \(-0.432077\pi\)
0.211772 + 0.977319i \(0.432077\pi\)
\(632\) 0 0
\(633\) 25.9155i 1.03005i
\(634\) 0 0
\(635\) −2.62702 + 10.5730i −0.104250 + 0.419578i
\(636\) 0 0
\(637\) 48.2083i 1.91008i
\(638\) 0 0
\(639\) −5.07838 −0.200898
\(640\) 0 0
\(641\) −35.8576 −1.41629 −0.708145 0.706067i \(-0.750468\pi\)
−0.708145 + 0.706067i \(0.750468\pi\)
\(642\) 0 0
\(643\) 12.2146i 0.481697i −0.970563 0.240849i \(-0.922574\pi\)
0.970563 0.240849i \(-0.0774258\pi\)
\(644\) 0 0
\(645\) 0.630898 + 0.156755i 0.0248416 + 0.00617224i
\(646\) 0 0
\(647\) 25.9421i 1.01989i 0.860207 + 0.509945i \(0.170334\pi\)
−0.860207 + 0.509945i \(0.829666\pi\)
\(648\) 0 0
\(649\) 3.60197 0.141390
\(650\) 0 0
\(651\) 1.84324 0.0722424
\(652\) 0 0
\(653\) 14.3402i 0.561174i −0.959829 0.280587i \(-0.909471\pi\)
0.959829 0.280587i \(-0.0905292\pi\)
\(654\) 0 0
\(655\) 18.8371 + 4.68035i 0.736026 + 0.182876i
\(656\) 0 0
\(657\) 1.12783i 0.0440007i
\(658\) 0 0
\(659\) 6.52359 0.254123 0.127062 0.991895i \(-0.459445\pi\)
0.127062 + 0.991895i \(0.459445\pi\)
\(660\) 0 0
\(661\) 3.16290 0.123022 0.0615112 0.998106i \(-0.480408\pi\)
0.0615112 + 0.998106i \(0.480408\pi\)
\(662\) 0 0
\(663\) 33.3751i 1.29618i
\(664\) 0 0
\(665\) −1.21622 + 4.89496i −0.0471631 + 0.189818i
\(666\) 0 0
\(667\) 29.6742i 1.14899i
\(668\) 0 0
\(669\) −9.62863 −0.372264
\(670\) 0 0
\(671\) −6.68035 −0.257892
\(672\) 0 0
\(673\) 18.4885i 0.712680i −0.934356 0.356340i \(-0.884024\pi\)
0.934356 0.356340i \(-0.115976\pi\)
\(674\) 0 0
\(675\) 2.34017 4.41855i 0.0900733 0.170070i
\(676\) 0 0
\(677\) 15.0966i 0.580211i −0.956995 0.290105i \(-0.906310\pi\)
0.956995 0.290105i \(-0.0936903\pi\)
\(678\) 0 0
\(679\) 1.36069 0.0522186
\(680\) 0 0
\(681\) 18.3896 0.704692
\(682\) 0 0
\(683\) 12.4657i 0.476988i 0.971144 + 0.238494i \(0.0766537\pi\)
−0.971144 + 0.238494i \(0.923346\pi\)
\(684\) 0 0
\(685\) −6.79153 + 27.3340i −0.259491 + 1.04438i
\(686\) 0 0
\(687\) 17.1506i 0.654337i
\(688\) 0 0
\(689\) −40.1445 −1.52938
\(690\) 0 0
\(691\) 30.7214 1.16870 0.584348 0.811503i \(-0.301350\pi\)
0.584348 + 0.811503i \(0.301350\pi\)
\(692\) 0 0
\(693\) 0.290725i 0.0110437i
\(694\) 0 0
\(695\) −21.5174 5.34632i −0.816203 0.202797i
\(696\) 0 0
\(697\) 35.5174i 1.34532i
\(698\) 0 0
\(699\) 4.10731 0.155353
\(700\) 0 0
\(701\) 17.9955 0.679679 0.339840 0.940483i \(-0.389627\pi\)
0.339840 + 0.940483i \(0.389627\pi\)
\(702\) 0 0
\(703\) 26.5236i 1.00036i
\(704\) 0 0
\(705\) −11.4186 2.83710i −0.430047 0.106851i
\(706\) 0 0
\(707\) 2.49484i 0.0938281i
\(708\) 0 0
\(709\) −23.5897 −0.885929 −0.442965 0.896539i \(-0.646073\pi\)
−0.442965 + 0.896539i \(0.646073\pi\)
\(710\) 0 0
\(711\) 0.921622 0.0345635
\(712\) 0 0
\(713\) 25.3607i 0.949765i
\(714\) 0 0
\(715\) −3.75872 + 15.1278i −0.140568 + 0.565749i
\(716\) 0 0
\(717\) 4.36683i 0.163082i
\(718\) 0 0
\(719\) 24.5646 0.916106 0.458053 0.888925i \(-0.348547\pi\)
0.458053 + 0.888925i \(0.348547\pi\)
\(720\) 0 0
\(721\) 1.95896 0.0729556
\(722\) 0 0
\(723\) 5.20394i 0.193536i
\(724\) 0 0
\(725\) 32.7792 + 17.3607i 1.21739 + 0.644760i
\(726\) 0 0
\(727\) 8.51130i 0.315667i 0.987466 + 0.157833i \(0.0504509\pi\)
−0.987466 + 0.157833i \(0.949549\pi\)
\(728\) 0 0
\(729\) −1.00000 −0.0370370
\(730\) 0 0
\(731\) −1.39189 −0.0514809
\(732\) 0 0
\(733\) 29.8615i 1.10296i −0.834188 0.551480i \(-0.814063\pi\)
0.834188 0.551480i \(-0.185937\pi\)
\(734\) 0 0
\(735\) −3.72875 + 15.0072i −0.137537 + 0.553548i
\(736\) 0 0
\(737\) 6.15676i 0.226787i
\(738\) 0 0
\(739\) −36.7526 −1.35197 −0.675983 0.736917i \(-0.736281\pi\)
−0.675983 + 0.736917i \(0.736281\pi\)
\(740\) 0 0
\(741\) −54.0866 −1.98692
\(742\) 0 0
\(743\) 2.17501i 0.0797933i 0.999204 + 0.0398966i \(0.0127029\pi\)
−0.999204 + 0.0398966i \(0.987297\pi\)
\(744\) 0 0
\(745\) 2.73820 + 0.680346i 0.100320 + 0.0249259i
\(746\) 0 0
\(747\) 1.70928i 0.0625391i
\(748\) 0 0
\(749\) −3.55640 −0.129948
\(750\) 0 0
\(751\) 44.4580 1.62229 0.811147 0.584842i \(-0.198843\pi\)
0.811147 + 0.584842i \(0.198843\pi\)
\(752\) 0 0
\(753\) 8.28231i 0.301824i
\(754\) 0 0
\(755\) −3.47641 0.863763i −0.126519 0.0314356i
\(756\) 0 0
\(757\) 26.4247i 0.960422i 0.877153 + 0.480211i \(0.159440\pi\)
−0.877153 + 0.480211i \(0.840560\pi\)
\(758\) 0 0
\(759\) 4.00000 0.145191
\(760\) 0 0
\(761\) −27.6163 −1.00109 −0.500546 0.865710i \(-0.666867\pi\)
−0.500546 + 0.865710i \(0.666867\pi\)
\(762\) 0 0
\(763\) 1.83549i 0.0664493i
\(764\) 0 0
\(765\) −2.58145 + 10.3896i −0.0933325 + 0.375638i
\(766\) 0 0
\(767\) 25.1096i 0.906654i
\(768\) 0 0
\(769\) −27.8432 −1.00405 −0.502027 0.864852i \(-0.667412\pi\)
−0.502027 + 0.864852i \(0.667412\pi\)
\(770\) 0 0
\(771\) 11.0205 0.396894
\(772\) 0 0
\(773\) 18.0267i 0.648374i −0.945993 0.324187i \(-0.894909\pi\)
0.945993 0.324187i \(-0.105091\pi\)
\(774\) 0 0
\(775\) −28.0144 14.8371i −1.00631 0.532964i
\(776\) 0 0
\(777\) 0.993857i 0.0356544i
\(778\) 0 0
\(779\) −57.5585 −2.06225
\(780\) 0 0
\(781\) 5.07838 0.181719
\(782\) 0 0
\(783\) 7.41855i 0.265117i
\(784\) 0 0
\(785\) −3.83096 + 15.4186i −0.136733 + 0.550312i
\(786\) 0 0
\(787\) 35.6391i 1.27040i 0.772349 + 0.635199i \(0.219082\pi\)
−0.772349 + 0.635199i \(0.780918\pi\)
\(788\) 0 0
\(789\) −2.97107 −0.105773
\(790\) 0 0
\(791\) 4.79606 0.170528
\(792\) 0 0
\(793\) 46.5692i 1.65372i
\(794\) 0 0
\(795\) −12.4969 3.10504i −0.443220 0.110124i
\(796\) 0 0