Properties

Label 72.2.i.b.49.2
Level $72$
Weight $2$
Character 72.49
Analytic conductor $0.575$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [72,2,Mod(25,72)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(72, 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("72.25");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 72 = 2^{3} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 72.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: \(0.574922894553\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{-11})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{3} - 2x^{2} - 3x + 9 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 49.2
Root \(1.68614 + 0.396143i\) of defining polynomial
Character \(\chi\) \(=\) 72.49
Dual form 72.2.i.b.25.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.68614 + 0.396143i) q^{3} +(-1.18614 + 2.05446i) q^{5} +(-2.18614 - 3.78651i) q^{7} +(2.68614 + 1.33591i) q^{9} +O(q^{10})\) \(q+(1.68614 + 0.396143i) q^{3} +(-1.18614 + 2.05446i) q^{5} +(-2.18614 - 3.78651i) q^{7} +(2.68614 + 1.33591i) q^{9} +(-0.500000 - 0.866025i) q^{11} +(0.186141 - 0.322405i) q^{13} +(-2.81386 + 2.99422i) q^{15} -5.37228 q^{17} +0.627719 q^{19} +(-2.18614 - 7.25061i) q^{21} +(0.186141 - 0.322405i) q^{23} +(-0.313859 - 0.543620i) q^{25} +(4.00000 + 3.31662i) q^{27} +(2.18614 + 3.78651i) q^{29} +(-3.18614 + 5.51856i) q^{31} +(-0.500000 - 1.65831i) q^{33} +10.3723 q^{35} +8.74456 q^{37} +(0.441578 - 0.469882i) q^{39} +(5.87228 - 10.1711i) q^{41} +(0.872281 + 1.51084i) q^{43} +(-5.93070 + 3.93398i) q^{45} +(-2.18614 - 3.78651i) q^{47} +(-6.05842 + 10.4935i) q^{49} +(-9.05842 - 2.12819i) q^{51} +0.744563 q^{53} +2.37228 q^{55} +(1.05842 + 0.248667i) q^{57} +(-3.50000 + 6.06218i) q^{59} +(-1.18614 - 2.05446i) q^{61} +(-0.813859 - 13.0916i) q^{63} +(0.441578 + 0.764836i) q^{65} +(1.87228 - 3.24289i) q^{67} +(0.441578 - 0.469882i) q^{69} -4.00000 q^{71} -12.1168 q^{73} +(-0.313859 - 1.04095i) q^{75} +(-2.18614 + 3.78651i) q^{77} +(3.18614 + 5.51856i) q^{79} +(5.43070 + 7.17687i) q^{81} +(-4.81386 - 8.33785i) q^{83} +(6.37228 - 11.0371i) q^{85} +(2.18614 + 7.25061i) q^{87} +6.00000 q^{89} -1.62772 q^{91} +(-7.55842 + 8.04290i) q^{93} +(-0.744563 + 1.28962i) q^{95} +(-0.872281 - 1.51084i) q^{97} +(-0.186141 - 2.99422i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + q^{3} + q^{5} - 3 q^{7} + 5 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + q^{3} + q^{5} - 3 q^{7} + 5 q^{9} - 2 q^{11} - 5 q^{13} - 17 q^{15} - 10 q^{17} + 14 q^{19} - 3 q^{21} - 5 q^{23} - 7 q^{25} + 16 q^{27} + 3 q^{29} - 7 q^{31} - 2 q^{33} + 30 q^{35} + 12 q^{37} + 19 q^{39} + 12 q^{41} - 8 q^{43} + 5 q^{45} - 3 q^{47} - 7 q^{49} - 19 q^{51} - 20 q^{53} - 2 q^{55} - 13 q^{57} - 14 q^{59} + q^{61} - 9 q^{63} + 19 q^{65} - 4 q^{67} + 19 q^{69} - 16 q^{71} - 14 q^{73} - 7 q^{75} - 3 q^{77} + 7 q^{79} - 7 q^{81} - 25 q^{83} + 14 q^{85} + 3 q^{87} + 24 q^{89} - 18 q^{91} - 13 q^{93} + 20 q^{95} + 8 q^{97} + 5 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/72\mathbb{Z}\right)^\times\).

\(n\) \(37\) \(55\) \(65\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\)

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
\(3\) 1.68614 + 0.396143i 0.973494 + 0.228714i
\(4\) 0 0
\(5\) −1.18614 + 2.05446i −0.530458 + 0.918781i 0.468910 + 0.883246i \(0.344647\pi\)
−0.999368 + 0.0355348i \(0.988687\pi\)
\(6\) 0 0
\(7\) −2.18614 3.78651i −0.826284 1.43117i −0.900934 0.433955i \(-0.857118\pi\)
0.0746509 0.997210i \(-0.476216\pi\)
\(8\) 0 0
\(9\) 2.68614 + 1.33591i 0.895380 + 0.445302i
\(10\) 0 0
\(11\) −0.500000 0.866025i −0.150756 0.261116i 0.780750 0.624844i \(-0.214837\pi\)
−0.931505 + 0.363727i \(0.881504\pi\)
\(12\) 0 0
\(13\) 0.186141 0.322405i 0.0516261 0.0894191i −0.839057 0.544043i \(-0.816893\pi\)
0.890684 + 0.454624i \(0.150226\pi\)
\(14\) 0 0
\(15\) −2.81386 + 2.99422i −0.726535 + 0.773104i
\(16\) 0 0
\(17\) −5.37228 −1.30297 −0.651485 0.758662i \(-0.725854\pi\)
−0.651485 + 0.758662i \(0.725854\pi\)
\(18\) 0 0
\(19\) 0.627719 0.144009 0.0720043 0.997404i \(-0.477060\pi\)
0.0720043 + 0.997404i \(0.477060\pi\)
\(20\) 0 0
\(21\) −2.18614 7.25061i −0.477055 1.58221i
\(22\) 0 0
\(23\) 0.186141 0.322405i 0.0388130 0.0672261i −0.845966 0.533236i \(-0.820976\pi\)
0.884779 + 0.466010i \(0.154309\pi\)
\(24\) 0 0
\(25\) −0.313859 0.543620i −0.0627719 0.108724i
\(26\) 0 0
\(27\) 4.00000 + 3.31662i 0.769800 + 0.638285i
\(28\) 0 0
\(29\) 2.18614 + 3.78651i 0.405956 + 0.703137i 0.994432 0.105378i \(-0.0336052\pi\)
−0.588476 + 0.808515i \(0.700272\pi\)
\(30\) 0 0
\(31\) −3.18614 + 5.51856i −0.572248 + 0.991162i 0.424087 + 0.905621i \(0.360595\pi\)
−0.996335 + 0.0855407i \(0.972738\pi\)
\(32\) 0 0
\(33\) −0.500000 1.65831i −0.0870388 0.288675i
\(34\) 0 0
\(35\) 10.3723 1.75324
\(36\) 0 0
\(37\) 8.74456 1.43760 0.718799 0.695218i \(-0.244692\pi\)
0.718799 + 0.695218i \(0.244692\pi\)
\(38\) 0 0
\(39\) 0.441578 0.469882i 0.0707091 0.0752413i
\(40\) 0 0
\(41\) 5.87228 10.1711i 0.917096 1.58846i 0.113293 0.993562i \(-0.463860\pi\)
0.803803 0.594896i \(-0.202807\pi\)
\(42\) 0 0
\(43\) 0.872281 + 1.51084i 0.133022 + 0.230400i 0.924840 0.380356i \(-0.124199\pi\)
−0.791818 + 0.610757i \(0.790865\pi\)
\(44\) 0 0
\(45\) −5.93070 + 3.93398i −0.884097 + 0.586444i
\(46\) 0 0
\(47\) −2.18614 3.78651i −0.318881 0.552319i 0.661374 0.750057i \(-0.269974\pi\)
−0.980255 + 0.197738i \(0.936640\pi\)
\(48\) 0 0
\(49\) −6.05842 + 10.4935i −0.865489 + 1.49907i
\(50\) 0 0
\(51\) −9.05842 2.12819i −1.26843 0.298007i
\(52\) 0 0
\(53\) 0.744563 0.102274 0.0511368 0.998692i \(-0.483716\pi\)
0.0511368 + 0.998692i \(0.483716\pi\)
\(54\) 0 0
\(55\) 2.37228 0.319878
\(56\) 0 0
\(57\) 1.05842 + 0.248667i 0.140191 + 0.0329367i
\(58\) 0 0
\(59\) −3.50000 + 6.06218i −0.455661 + 0.789228i −0.998726 0.0504625i \(-0.983930\pi\)
0.543065 + 0.839691i \(0.317264\pi\)
\(60\) 0 0
\(61\) −1.18614 2.05446i −0.151870 0.263046i 0.780045 0.625723i \(-0.215196\pi\)
−0.931915 + 0.362677i \(0.881863\pi\)
\(62\) 0 0
\(63\) −0.813859 13.0916i −0.102537 1.64938i
\(64\) 0 0
\(65\) 0.441578 + 0.764836i 0.0547710 + 0.0948662i
\(66\) 0 0
\(67\) 1.87228 3.24289i 0.228736 0.396182i −0.728698 0.684835i \(-0.759874\pi\)
0.957434 + 0.288653i \(0.0932076\pi\)
\(68\) 0 0
\(69\) 0.441578 0.469882i 0.0531597 0.0565671i
\(70\) 0 0
\(71\) −4.00000 −0.474713 −0.237356 0.971423i \(-0.576281\pi\)
−0.237356 + 0.971423i \(0.576281\pi\)
\(72\) 0 0
\(73\) −12.1168 −1.41817 −0.709085 0.705123i \(-0.750892\pi\)
−0.709085 + 0.705123i \(0.750892\pi\)
\(74\) 0 0
\(75\) −0.313859 1.04095i −0.0362414 0.120199i
\(76\) 0 0
\(77\) −2.18614 + 3.78651i −0.249134 + 0.431512i
\(78\) 0 0
\(79\) 3.18614 + 5.51856i 0.358469 + 0.620886i 0.987705 0.156328i \(-0.0499656\pi\)
−0.629236 + 0.777214i \(0.716632\pi\)
\(80\) 0 0
\(81\) 5.43070 + 7.17687i 0.603411 + 0.797430i
\(82\) 0 0
\(83\) −4.81386 8.33785i −0.528390 0.915198i −0.999452 0.0330979i \(-0.989463\pi\)
0.471062 0.882100i \(-0.343871\pi\)
\(84\) 0 0
\(85\) 6.37228 11.0371i 0.691171 1.19714i
\(86\) 0 0
\(87\) 2.18614 + 7.25061i 0.234379 + 0.777347i
\(88\) 0 0
\(89\) 6.00000 0.635999 0.317999 0.948091i \(-0.396989\pi\)
0.317999 + 0.948091i \(0.396989\pi\)
\(90\) 0 0
\(91\) −1.62772 −0.170631
\(92\) 0 0
\(93\) −7.55842 + 8.04290i −0.783772 + 0.834009i
\(94\) 0 0
\(95\) −0.744563 + 1.28962i −0.0763905 + 0.132312i
\(96\) 0 0
\(97\) −0.872281 1.51084i −0.0885667 0.153402i 0.818339 0.574736i \(-0.194895\pi\)
−0.906906 + 0.421334i \(0.861562\pi\)
\(98\) 0 0
\(99\) −0.186141 2.99422i −0.0187078 0.300930i
\(100\) 0 0
\(101\) 3.55842 + 6.16337i 0.354076 + 0.613278i 0.986959 0.160969i \(-0.0514620\pi\)
−0.632883 + 0.774247i \(0.718129\pi\)
\(102\) 0 0
\(103\) 6.18614 10.7147i 0.609539 1.05575i −0.381778 0.924254i \(-0.624688\pi\)
0.991316 0.131498i \(-0.0419786\pi\)
\(104\) 0 0
\(105\) 17.4891 + 4.10891i 1.70676 + 0.400989i
\(106\) 0 0
\(107\) −12.8614 −1.24336 −0.621680 0.783272i \(-0.713549\pi\)
−0.621680 + 0.783272i \(0.713549\pi\)
\(108\) 0 0
\(109\) −4.74456 −0.454447 −0.227223 0.973843i \(-0.572965\pi\)
−0.227223 + 0.973843i \(0.572965\pi\)
\(110\) 0 0
\(111\) 14.7446 + 3.46410i 1.39949 + 0.328798i
\(112\) 0 0
\(113\) 2.18614 3.78651i 0.205655 0.356205i −0.744686 0.667415i \(-0.767401\pi\)
0.950341 + 0.311210i \(0.100734\pi\)
\(114\) 0 0
\(115\) 0.441578 + 0.764836i 0.0411774 + 0.0713213i
\(116\) 0 0
\(117\) 0.930703 0.617359i 0.0860436 0.0570748i
\(118\) 0 0
\(119\) 11.7446 + 20.3422i 1.07662 + 1.86476i
\(120\) 0 0
\(121\) 5.00000 8.66025i 0.454545 0.787296i
\(122\) 0 0
\(123\) 13.9307 14.8236i 1.25609 1.33660i
\(124\) 0 0
\(125\) −10.3723 −0.927725
\(126\) 0 0
\(127\) 6.74456 0.598483 0.299242 0.954177i \(-0.403266\pi\)
0.299242 + 0.954177i \(0.403266\pi\)
\(128\) 0 0
\(129\) 0.872281 + 2.89303i 0.0768001 + 0.254717i
\(130\) 0 0
\(131\) −9.18614 + 15.9109i −0.802597 + 1.39014i 0.115305 + 0.993330i \(0.463216\pi\)
−0.917901 + 0.396808i \(0.870118\pi\)
\(132\) 0 0
\(133\) −1.37228 2.37686i −0.118992 0.206100i
\(134\) 0 0
\(135\) −11.5584 + 4.28384i −0.994791 + 0.368694i
\(136\) 0 0
\(137\) −8.87228 15.3672i −0.758010 1.31291i −0.943864 0.330335i \(-0.892838\pi\)
0.185854 0.982577i \(-0.440495\pi\)
\(138\) 0 0
\(139\) −2.87228 + 4.97494i −0.243624 + 0.421969i −0.961744 0.273951i \(-0.911670\pi\)
0.718120 + 0.695919i \(0.245003\pi\)
\(140\) 0 0
\(141\) −2.18614 7.25061i −0.184106 0.610611i
\(142\) 0 0
\(143\) −0.372281 −0.0311317
\(144\) 0 0
\(145\) −10.3723 −0.861371
\(146\) 0 0
\(147\) −14.3723 + 15.2935i −1.18541 + 1.26139i
\(148\) 0 0
\(149\) 4.18614 7.25061i 0.342942 0.593993i −0.642036 0.766675i \(-0.721910\pi\)
0.984978 + 0.172682i \(0.0552432\pi\)
\(150\) 0 0
\(151\) −0.186141 0.322405i −0.0151479 0.0262370i 0.858352 0.513061i \(-0.171489\pi\)
−0.873500 + 0.486824i \(0.838155\pi\)
\(152\) 0 0
\(153\) −14.4307 7.17687i −1.16665 0.580216i
\(154\) 0 0
\(155\) −7.55842 13.0916i −0.607107 1.05154i
\(156\) 0 0
\(157\) 1.55842 2.69927i 0.124376 0.215425i −0.797113 0.603830i \(-0.793641\pi\)
0.921489 + 0.388405i \(0.126974\pi\)
\(158\) 0 0
\(159\) 1.25544 + 0.294954i 0.0995627 + 0.0233913i
\(160\) 0 0
\(161\) −1.62772 −0.128282
\(162\) 0 0
\(163\) −12.0000 −0.939913 −0.469956 0.882690i \(-0.655730\pi\)
−0.469956 + 0.882690i \(0.655730\pi\)
\(164\) 0 0
\(165\) 4.00000 + 0.939764i 0.311400 + 0.0731605i
\(166\) 0 0
\(167\) 9.55842 16.5557i 0.739653 1.28112i −0.212999 0.977052i \(-0.568323\pi\)
0.952652 0.304064i \(-0.0983436\pi\)
\(168\) 0 0
\(169\) 6.43070 + 11.1383i 0.494669 + 0.856793i
\(170\) 0 0
\(171\) 1.68614 + 0.838574i 0.128942 + 0.0641274i
\(172\) 0 0
\(173\) 8.18614 + 14.1788i 0.622381 + 1.07800i 0.989041 + 0.147640i \(0.0471678\pi\)
−0.366660 + 0.930355i \(0.619499\pi\)
\(174\) 0 0
\(175\) −1.37228 + 2.37686i −0.103735 + 0.179674i
\(176\) 0 0
\(177\) −8.30298 + 8.83518i −0.624091 + 0.664093i
\(178\) 0 0
\(179\) 22.9783 1.71748 0.858738 0.512416i \(-0.171249\pi\)
0.858738 + 0.512416i \(0.171249\pi\)
\(180\) 0 0
\(181\) −0.510875 −0.0379730 −0.0189865 0.999820i \(-0.506044\pi\)
−0.0189865 + 0.999820i \(0.506044\pi\)
\(182\) 0 0
\(183\) −1.18614 3.93398i −0.0876820 0.290808i
\(184\) 0 0
\(185\) −10.3723 + 17.9653i −0.762585 + 1.32084i
\(186\) 0 0
\(187\) 2.68614 + 4.65253i 0.196430 + 0.340227i
\(188\) 0 0
\(189\) 3.81386 22.3966i 0.277417 1.62912i
\(190\) 0 0
\(191\) −4.93070 8.54023i −0.356773 0.617949i 0.630647 0.776070i \(-0.282790\pi\)
−0.987420 + 0.158121i \(0.949456\pi\)
\(192\) 0 0
\(193\) −0.872281 + 1.51084i −0.0627882 + 0.108752i −0.895711 0.444637i \(-0.853333\pi\)
0.832923 + 0.553390i \(0.186666\pi\)
\(194\) 0 0
\(195\) 0.441578 + 1.46455i 0.0316221 + 0.104879i
\(196\) 0 0
\(197\) 15.2554 1.08690 0.543452 0.839440i \(-0.317117\pi\)
0.543452 + 0.839440i \(0.317117\pi\)
\(198\) 0 0
\(199\) −16.2337 −1.15078 −0.575388 0.817881i \(-0.695149\pi\)
−0.575388 + 0.817881i \(0.695149\pi\)
\(200\) 0 0
\(201\) 4.44158 4.72627i 0.313285 0.333365i
\(202\) 0 0
\(203\) 9.55842 16.5557i 0.670870 1.16198i
\(204\) 0 0
\(205\) 13.9307 + 24.1287i 0.972963 + 1.68522i
\(206\) 0 0
\(207\) 0.930703 0.617359i 0.0646884 0.0429094i
\(208\) 0 0
\(209\) −0.313859 0.543620i −0.0217101 0.0376030i
\(210\) 0 0
\(211\) 4.81386 8.33785i 0.331400 0.574001i −0.651387 0.758746i \(-0.725812\pi\)
0.982787 + 0.184745i \(0.0591458\pi\)
\(212\) 0 0
\(213\) −6.74456 1.58457i −0.462130 0.108573i
\(214\) 0 0
\(215\) −4.13859 −0.282250
\(216\) 0 0
\(217\) 27.8614 1.89136
\(218\) 0 0
\(219\) −20.4307 4.80001i −1.38058 0.324355i
\(220\) 0 0
\(221\) −1.00000 + 1.73205i −0.0672673 + 0.116510i
\(222\) 0 0
\(223\) 7.30298 + 12.6491i 0.489044 + 0.847049i 0.999921 0.0126050i \(-0.00401240\pi\)
−0.510877 + 0.859654i \(0.670679\pi\)
\(224\) 0 0
\(225\) −0.116844 1.87953i −0.00778960 0.125302i
\(226\) 0 0
\(227\) 7.50000 + 12.9904i 0.497792 + 0.862202i 0.999997 0.00254715i \(-0.000810783\pi\)
−0.502204 + 0.864749i \(0.667477\pi\)
\(228\) 0 0
\(229\) −11.3030 + 19.5773i −0.746922 + 1.29371i 0.202369 + 0.979309i \(0.435136\pi\)
−0.949291 + 0.314398i \(0.898197\pi\)
\(230\) 0 0
\(231\) −5.18614 + 5.51856i −0.341223 + 0.363094i
\(232\) 0 0
\(233\) 5.37228 0.351950 0.175975 0.984395i \(-0.443692\pi\)
0.175975 + 0.984395i \(0.443692\pi\)
\(234\) 0 0
\(235\) 10.3723 0.676613
\(236\) 0 0
\(237\) 3.18614 + 10.5672i 0.206962 + 0.686416i
\(238\) 0 0
\(239\) 6.93070 12.0043i 0.448310 0.776496i −0.549966 0.835187i \(-0.685359\pi\)
0.998276 + 0.0586913i \(0.0186928\pi\)
\(240\) 0 0
\(241\) −2.87228 4.97494i −0.185020 0.320464i 0.758563 0.651599i \(-0.225902\pi\)
−0.943583 + 0.331135i \(0.892568\pi\)
\(242\) 0 0
\(243\) 6.31386 + 14.2525i 0.405034 + 0.914302i
\(244\) 0 0
\(245\) −14.3723 24.8935i −0.918211 1.59039i
\(246\) 0 0
\(247\) 0.116844 0.202380i 0.00743460 0.0128771i
\(248\) 0 0
\(249\) −4.81386 15.9658i −0.305066 1.01179i
\(250\) 0 0
\(251\) 9.88316 0.623819 0.311910 0.950112i \(-0.399031\pi\)
0.311910 + 0.950112i \(0.399031\pi\)
\(252\) 0 0
\(253\) −0.372281 −0.0234051
\(254\) 0 0
\(255\) 15.1168 16.0858i 0.946653 1.00733i
\(256\) 0 0
\(257\) −2.24456 + 3.88770i −0.140012 + 0.242508i −0.927501 0.373821i \(-0.878047\pi\)
0.787489 + 0.616329i \(0.211381\pi\)
\(258\) 0 0
\(259\) −19.1168 33.1113i −1.18786 2.05744i
\(260\) 0 0
\(261\) 0.813859 + 13.0916i 0.0503766 + 0.810348i
\(262\) 0 0
\(263\) 10.5584 + 18.2877i 0.651060 + 1.12767i 0.982866 + 0.184322i \(0.0590088\pi\)
−0.331806 + 0.943348i \(0.607658\pi\)
\(264\) 0 0
\(265\) −0.883156 + 1.52967i −0.0542518 + 0.0939669i
\(266\) 0 0
\(267\) 10.1168 + 2.37686i 0.619141 + 0.145462i
\(268\) 0 0
\(269\) −12.7446 −0.777050 −0.388525 0.921438i \(-0.627015\pi\)
−0.388525 + 0.921438i \(0.627015\pi\)
\(270\) 0 0
\(271\) −21.4891 −1.30537 −0.652686 0.757629i \(-0.726358\pi\)
−0.652686 + 0.757629i \(0.726358\pi\)
\(272\) 0 0
\(273\) −2.74456 0.644810i −0.166108 0.0390257i
\(274\) 0 0
\(275\) −0.313859 + 0.543620i −0.0189264 + 0.0327815i
\(276\) 0 0
\(277\) −14.5584 25.2159i −0.874731 1.51508i −0.857049 0.515235i \(-0.827705\pi\)
−0.0176816 0.999844i \(-0.505629\pi\)
\(278\) 0 0
\(279\) −15.9307 + 10.5672i −0.953746 + 0.632644i
\(280\) 0 0
\(281\) 6.93070 + 12.0043i 0.413451 + 0.716118i 0.995264 0.0972040i \(-0.0309899\pi\)
−0.581813 + 0.813322i \(0.697657\pi\)
\(282\) 0 0
\(283\) −11.9307 + 20.6646i −0.709207 + 1.22838i 0.255945 + 0.966691i \(0.417613\pi\)
−0.965152 + 0.261691i \(0.915720\pi\)
\(284\) 0 0
\(285\) −1.76631 + 1.87953i −0.104627 + 0.111334i
\(286\) 0 0
\(287\) −51.3505 −3.03113
\(288\) 0 0
\(289\) 11.8614 0.697730
\(290\) 0 0
\(291\) −0.872281 2.89303i −0.0511340 0.169592i
\(292\) 0 0
\(293\) −9.81386 + 16.9981i −0.573332 + 0.993040i 0.422889 + 0.906182i \(0.361016\pi\)
−0.996221 + 0.0868582i \(0.972317\pi\)
\(294\) 0 0
\(295\) −8.30298 14.3812i −0.483418 0.837305i
\(296\) 0 0
\(297\) 0.872281 5.12241i 0.0506149 0.297233i
\(298\) 0 0
\(299\) −0.0692967 0.120025i −0.00400753 0.00694125i
\(300\) 0 0
\(301\) 3.81386 6.60580i 0.219827 0.380752i
\(302\) 0 0
\(303\) 3.55842 + 11.8020i 0.204426 + 0.678004i
\(304\) 0 0
\(305\) 5.62772 0.322242
\(306\) 0 0
\(307\) 31.3723 1.79051 0.895255 0.445553i \(-0.146993\pi\)
0.895255 + 0.445553i \(0.146993\pi\)
\(308\) 0 0
\(309\) 14.6753 15.6159i 0.834847 0.888358i
\(310\) 0 0
\(311\) 5.44158 9.42509i 0.308564 0.534448i −0.669485 0.742826i \(-0.733485\pi\)
0.978048 + 0.208378i \(0.0668184\pi\)
\(312\) 0 0
\(313\) −5.61684 9.72866i −0.317483 0.549896i 0.662479 0.749080i \(-0.269504\pi\)
−0.979962 + 0.199184i \(0.936171\pi\)
\(314\) 0 0
\(315\) 27.8614 + 13.8564i 1.56981 + 0.780720i
\(316\) 0 0
\(317\) −15.3030 26.5055i −0.859501 1.48870i −0.872405 0.488783i \(-0.837441\pi\)
0.0129041 0.999917i \(-0.495892\pi\)
\(318\) 0 0
\(319\) 2.18614 3.78651i 0.122400 0.212004i
\(320\) 0 0
\(321\) −21.6861 5.09496i −1.21040 0.284373i
\(322\) 0 0
\(323\) −3.37228 −0.187639
\(324\) 0 0
\(325\) −0.233688 −0.0129627
\(326\) 0 0
\(327\) −8.00000 1.87953i −0.442401 0.103938i
\(328\) 0 0
\(329\) −9.55842 + 16.5557i −0.526973 + 0.912744i
\(330\) 0 0
\(331\) 15.9307 + 27.5928i 0.875631 + 1.51664i 0.856089 + 0.516828i \(0.172887\pi\)
0.0195412 + 0.999809i \(0.493779\pi\)
\(332\) 0 0
\(333\) 23.4891 + 11.6819i 1.28720 + 0.640166i
\(334\) 0 0
\(335\) 4.44158 + 7.69304i 0.242669 + 0.420316i
\(336\) 0 0
\(337\) 9.98913 17.3017i 0.544142 0.942482i −0.454518 0.890738i \(-0.650188\pi\)
0.998660 0.0517446i \(-0.0164782\pi\)
\(338\) 0 0
\(339\) 5.18614 5.51856i 0.281672 0.299727i
\(340\) 0 0
\(341\) 6.37228 0.345078
\(342\) 0 0
\(343\) 22.3723 1.20799
\(344\) 0 0
\(345\) 0.441578 + 1.46455i 0.0237738 + 0.0788486i
\(346\) 0 0
\(347\) −14.3614 + 24.8747i −0.770961 + 1.33534i 0.166076 + 0.986113i \(0.446890\pi\)
−0.937037 + 0.349230i \(0.886443\pi\)
\(348\) 0 0
\(349\) −8.44158 14.6212i −0.451867 0.782657i 0.546635 0.837371i \(-0.315909\pi\)
−0.998502 + 0.0547140i \(0.982575\pi\)
\(350\) 0 0
\(351\) 1.81386 0.672262i 0.0968166 0.0358827i
\(352\) 0 0
\(353\) 11.9891 + 20.7658i 0.638117 + 1.10525i 0.985846 + 0.167656i \(0.0536196\pi\)
−0.347729 + 0.937595i \(0.613047\pi\)
\(354\) 0 0
\(355\) 4.74456 8.21782i 0.251815 0.436157i
\(356\) 0 0
\(357\) 11.7446 + 38.9523i 0.621588 + 2.06157i
\(358\) 0 0
\(359\) 20.2337 1.06789 0.533947 0.845518i \(-0.320708\pi\)
0.533947 + 0.845518i \(0.320708\pi\)
\(360\) 0 0
\(361\) −18.6060 −0.979262
\(362\) 0 0
\(363\) 11.8614 12.6217i 0.622562 0.662467i
\(364\) 0 0
\(365\) 14.3723 24.8935i 0.752280 1.30299i
\(366\) 0 0
\(367\) −8.81386 15.2661i −0.460080 0.796881i 0.538885 0.842380i \(-0.318846\pi\)
−0.998964 + 0.0454981i \(0.985513\pi\)
\(368\) 0 0
\(369\) 29.3614 19.4762i 1.52849 1.01389i
\(370\) 0 0
\(371\) −1.62772 2.81929i −0.0845069 0.146370i
\(372\) 0 0
\(373\) −10.5584 + 18.2877i −0.546694 + 0.946902i 0.451804 + 0.892117i \(0.350781\pi\)
−0.998498 + 0.0547851i \(0.982553\pi\)
\(374\) 0 0
\(375\) −17.4891 4.10891i −0.903135 0.212183i
\(376\) 0 0
\(377\) 1.62772 0.0838318
\(378\) 0 0
\(379\) −5.88316 −0.302197 −0.151099 0.988519i \(-0.548281\pi\)
−0.151099 + 0.988519i \(0.548281\pi\)
\(380\) 0 0
\(381\) 11.3723 + 2.67181i 0.582620 + 0.136881i
\(382\) 0 0
\(383\) −10.6753 + 18.4901i −0.545481 + 0.944800i 0.453096 + 0.891462i \(0.350320\pi\)
−0.998576 + 0.0533383i \(0.983014\pi\)
\(384\) 0 0
\(385\) −5.18614 8.98266i −0.264310 0.457799i
\(386\) 0 0
\(387\) 0.324734 + 5.22360i 0.0165072 + 0.265531i
\(388\) 0 0
\(389\) −5.30298 9.18504i −0.268872 0.465700i 0.699699 0.714438i \(-0.253318\pi\)
−0.968571 + 0.248738i \(0.919984\pi\)
\(390\) 0 0
\(391\) −1.00000 + 1.73205i −0.0505722 + 0.0875936i
\(392\) 0 0
\(393\) −21.7921 + 23.1889i −1.09927 + 1.16973i
\(394\) 0 0
\(395\) −15.1168 −0.760611
\(396\) 0 0
\(397\) −18.2337 −0.915123 −0.457561 0.889178i \(-0.651277\pi\)
−0.457561 + 0.889178i \(0.651277\pi\)
\(398\) 0 0
\(399\) −1.37228 4.55134i −0.0687000 0.227852i
\(400\) 0 0
\(401\) 8.61684 14.9248i 0.430305 0.745310i −0.566595 0.823997i \(-0.691739\pi\)
0.996899 + 0.0786871i \(0.0250728\pi\)
\(402\) 0 0
\(403\) 1.18614 + 2.05446i 0.0590859 + 0.102340i
\(404\) 0 0
\(405\) −21.1861 + 2.64436i −1.05275 + 0.131399i
\(406\) 0 0
\(407\) −4.37228 7.57301i −0.216726 0.375380i
\(408\) 0 0
\(409\) −2.87228 + 4.97494i −0.142025 + 0.245995i −0.928259 0.371934i \(-0.878695\pi\)
0.786234 + 0.617929i \(0.212028\pi\)
\(410\) 0 0
\(411\) −8.87228 29.4260i −0.437637 1.45148i
\(412\) 0 0
\(413\) 30.6060 1.50602
\(414\) 0 0
\(415\) 22.8397 1.12115
\(416\) 0 0
\(417\) −6.81386 + 7.25061i −0.333676 + 0.355064i
\(418\) 0 0
\(419\) 6.30298 10.9171i 0.307921 0.533335i −0.669986 0.742373i \(-0.733700\pi\)
0.977907 + 0.209039i \(0.0670334\pi\)
\(420\) 0 0
\(421\) 17.5584 + 30.4121i 0.855745 + 1.48219i 0.875952 + 0.482398i \(0.160234\pi\)
−0.0202069 + 0.999796i \(0.506432\pi\)
\(422\) 0 0
\(423\) −0.813859 13.0916i −0.0395712 0.636534i
\(424\) 0 0
\(425\) 1.68614 + 2.92048i 0.0817898 + 0.141664i
\(426\) 0 0
\(427\) −5.18614 + 8.98266i −0.250975 + 0.434701i
\(428\) 0 0
\(429\) −0.627719 0.147477i −0.0303065 0.00712025i
\(430\) 0 0
\(431\) −1.25544 −0.0604723 −0.0302361 0.999543i \(-0.509626\pi\)
−0.0302361 + 0.999543i \(0.509626\pi\)
\(432\) 0 0
\(433\) 32.1168 1.54344 0.771719 0.635964i \(-0.219397\pi\)
0.771719 + 0.635964i \(0.219397\pi\)
\(434\) 0 0
\(435\) −17.4891 4.10891i −0.838539 0.197007i
\(436\) 0 0
\(437\) 0.116844 0.202380i 0.00558941 0.00968113i
\(438\) 0 0
\(439\) −3.55842 6.16337i −0.169834 0.294161i 0.768527 0.639817i \(-0.220990\pi\)
−0.938361 + 0.345656i \(0.887657\pi\)
\(440\) 0 0
\(441\) −30.2921 + 20.0935i −1.44248 + 0.956834i
\(442\) 0 0
\(443\) −15.3614 26.6067i −0.729842 1.26412i −0.956950 0.290254i \(-0.906260\pi\)
0.227107 0.973870i \(-0.427073\pi\)
\(444\) 0 0
\(445\) −7.11684 + 12.3267i −0.337371 + 0.584343i
\(446\) 0 0
\(447\) 9.93070 10.5672i 0.469706 0.499813i
\(448\) 0 0
\(449\) −15.8832 −0.749572 −0.374786 0.927111i \(-0.622284\pi\)
−0.374786 + 0.927111i \(0.622284\pi\)
\(450\) 0 0
\(451\) −11.7446 −0.553030
\(452\) 0 0
\(453\) −0.186141 0.617359i −0.00874565 0.0290060i
\(454\) 0 0
\(455\) 1.93070 3.34408i 0.0905128 0.156773i
\(456\) 0 0
\(457\) 1.87228 + 3.24289i 0.0875816 + 0.151696i 0.906488 0.422231i \(-0.138753\pi\)
−0.818907 + 0.573927i \(0.805419\pi\)
\(458\) 0 0
\(459\) −21.4891 17.8178i −1.00303 0.831666i
\(460\) 0 0
\(461\) 3.44158 + 5.96099i 0.160290 + 0.277631i 0.934973 0.354720i \(-0.115424\pi\)
−0.774682 + 0.632350i \(0.782090\pi\)
\(462\) 0 0
\(463\) −20.6753 + 35.8106i −0.960861 + 1.66426i −0.240515 + 0.970645i \(0.577316\pi\)
−0.720346 + 0.693615i \(0.756017\pi\)
\(464\) 0 0
\(465\) −7.55842 25.0684i −0.350513 1.16252i
\(466\) 0 0
\(467\) 7.37228 0.341148 0.170574 0.985345i \(-0.445438\pi\)
0.170574 + 0.985345i \(0.445438\pi\)
\(468\) 0 0
\(469\) −16.3723 −0.756002
\(470\) 0 0
\(471\) 3.69702 3.93398i 0.170349 0.181268i
\(472\) 0 0
\(473\) 0.872281 1.51084i 0.0401075 0.0694683i
\(474\) 0 0
\(475\) −0.197015 0.341241i −0.00903969 0.0156572i
\(476\) 0 0
\(477\) 2.00000 + 0.994667i 0.0915737 + 0.0455427i
\(478\) 0 0
\(479\) 5.30298 + 9.18504i 0.242300 + 0.419675i 0.961369 0.275263i \(-0.0887650\pi\)
−0.719069 + 0.694938i \(0.755432\pi\)
\(480\) 0 0
\(481\) 1.62772 2.81929i 0.0742176 0.128549i
\(482\) 0 0
\(483\) −2.74456 0.644810i −0.124882 0.0293399i
\(484\) 0 0
\(485\) 4.13859 0.187924
\(486\) 0 0
\(487\) 6.74456 0.305625 0.152813 0.988255i \(-0.451167\pi\)
0.152813 + 0.988255i \(0.451167\pi\)
\(488\) 0 0
\(489\) −20.2337 4.75372i −0.914999 0.214971i
\(490\) 0 0
\(491\) −0.127719 + 0.221215i −0.00576386 + 0.00998330i −0.868893 0.495000i \(-0.835168\pi\)
0.863129 + 0.504983i \(0.168501\pi\)
\(492\) 0 0
\(493\) −11.7446 20.3422i −0.528948 0.916166i
\(494\) 0 0
\(495\) 6.37228 + 3.16915i 0.286413 + 0.142443i
\(496\) 0 0
\(497\) 8.74456 + 15.1460i 0.392247 + 0.679392i
\(498\) 0 0
\(499\) 9.98913 17.3017i 0.447175 0.774529i −0.551026 0.834488i \(-0.685764\pi\)
0.998201 + 0.0599587i \(0.0190969\pi\)
\(500\) 0 0
\(501\) 22.6753 24.1287i 1.01306 1.07799i
\(502\) 0 0
\(503\) 6.51087 0.290306 0.145153 0.989409i \(-0.453633\pi\)
0.145153 + 0.989409i \(0.453633\pi\)
\(504\) 0 0
\(505\) −16.8832 −0.751291
\(506\) 0 0
\(507\) 6.43070 + 21.3282i 0.285598 + 0.947220i
\(508\) 0 0
\(509\) 15.5584 26.9480i 0.689615 1.19445i −0.282348 0.959312i \(-0.591113\pi\)
0.971962 0.235136i \(-0.0755535\pi\)
\(510\) 0 0
\(511\) 26.4891 + 45.8805i 1.17181 + 2.02963i
\(512\) 0 0
\(513\) 2.51087 + 2.08191i 0.110858 + 0.0919185i
\(514\) 0 0
\(515\) 14.6753 + 25.4183i 0.646669 + 1.12006i
\(516\) 0 0
\(517\) −2.18614 + 3.78651i −0.0961464 + 0.166530i
\(518\) 0 0
\(519\) 8.18614 + 27.1504i 0.359332 + 1.19177i
\(520\) 0 0
\(521\) 12.1168 0.530849 0.265424 0.964132i \(-0.414488\pi\)
0.265424 + 0.964132i \(0.414488\pi\)
\(522\) 0 0
\(523\) −13.4891 −0.589838 −0.294919 0.955522i \(-0.595293\pi\)
−0.294919 + 0.955522i \(0.595293\pi\)
\(524\) 0 0
\(525\) −3.25544 + 3.46410i −0.142079 + 0.151186i
\(526\) 0 0
\(527\) 17.1168 29.6472i 0.745621 1.29145i
\(528\) 0 0
\(529\) 11.4307 + 19.7986i 0.496987 + 0.860807i
\(530\) 0 0
\(531\) −17.5000 + 11.6082i −0.759435 + 0.503752i
\(532\) 0 0
\(533\) −2.18614 3.78651i −0.0946923 0.164012i
\(534\) 0 0
\(535\) 15.2554 26.4232i 0.659550 1.14237i
\(536\) 0 0
\(537\) 38.7446 + 9.10268i 1.67195 + 0.392810i
\(538\) 0 0
\(539\) 12.1168 0.521909
\(540\) 0 0
\(541\) 2.23369 0.0960337 0.0480169 0.998847i \(-0.484710\pi\)
0.0480169 + 0.998847i \(0.484710\pi\)
\(542\) 0 0
\(543\) −0.861407 0.202380i −0.0369665 0.00868494i
\(544\) 0 0
\(545\) 5.62772 9.74749i 0.241065 0.417537i
\(546\) 0 0
\(547\) 8.12772 + 14.0776i 0.347516 + 0.601916i 0.985808 0.167879i \(-0.0536918\pi\)
−0.638291 + 0.769795i \(0.720359\pi\)
\(548\) 0 0
\(549\) −0.441578 7.10313i −0.0188461 0.303154i
\(550\) 0 0
\(551\) 1.37228 + 2.37686i 0.0584611 + 0.101258i
\(552\) 0 0
\(553\) 13.9307 24.1287i 0.592394 1.02606i
\(554\) 0 0
\(555\) −24.6060 + 26.1831i −1.04447 + 1.11141i
\(556\) 0 0
\(557\) −14.0000 −0.593199 −0.296600 0.955002i \(-0.595853\pi\)
−0.296600 + 0.955002i \(0.595853\pi\)
\(558\) 0 0
\(559\) 0.649468 0.0274696
\(560\) 0 0
\(561\) 2.68614 + 8.90892i 0.113409 + 0.376135i
\(562\) 0 0
\(563\) −4.87228 + 8.43904i −0.205342 + 0.355663i −0.950242 0.311514i \(-0.899164\pi\)
0.744900 + 0.667177i \(0.232497\pi\)
\(564\) 0 0
\(565\) 5.18614 + 8.98266i 0.218183 + 0.377903i
\(566\) 0 0
\(567\) 15.3030 36.2530i 0.642665 1.52248i
\(568\) 0 0
\(569\) −13.6168 23.5851i −0.570848 0.988737i −0.996479 0.0838407i \(-0.973281\pi\)
0.425631 0.904897i \(-0.360052\pi\)
\(570\) 0 0
\(571\) 13.2446 22.9403i 0.554268 0.960020i −0.443692 0.896179i \(-0.646332\pi\)
0.997960 0.0638407i \(-0.0203349\pi\)
\(572\) 0 0
\(573\) −4.93070 16.3533i −0.205983 0.683169i
\(574\) 0 0
\(575\) −0.233688 −0.00974546
\(576\) 0 0
\(577\) 14.8614 0.618688 0.309344 0.950950i \(-0.399890\pi\)
0.309344 + 0.950950i \(0.399890\pi\)
\(578\) 0 0
\(579\) −2.06930 + 2.20193i −0.0859970 + 0.0915092i
\(580\) 0 0
\(581\) −21.0475 + 36.4554i −0.873199 + 1.51243i
\(582\) 0 0
\(583\) −0.372281 0.644810i −0.0154183 0.0267053i
\(584\) 0 0
\(585\) 0.164391 + 2.64436i 0.00679674 + 0.109331i
\(586\) 0 0
\(587\) −4.61684 7.99661i −0.190558 0.330055i 0.754878 0.655866i \(-0.227696\pi\)
−0.945435 + 0.325810i \(0.894363\pi\)
\(588\) 0 0
\(589\) −2.00000 + 3.46410i −0.0824086 + 0.142736i
\(590\) 0 0
\(591\) 25.7228 + 6.04334i 1.05810 + 0.248590i
\(592\) 0 0
\(593\) −26.0000 −1.06769 −0.533846 0.845582i \(-0.679254\pi\)
−0.533846 + 0.845582i \(0.679254\pi\)
\(594\) 0 0
\(595\) −55.7228 −2.28441
\(596\) 0 0
\(597\) −27.3723 6.43087i −1.12027 0.263198i
\(598\) 0 0
\(599\) −19.9307 + 34.5210i −0.814346 + 1.41049i 0.0954498 + 0.995434i \(0.469571\pi\)
−0.909796 + 0.415055i \(0.863762\pi\)
\(600\) 0 0
\(601\) −2.98913 5.17732i −0.121929 0.211187i 0.798599 0.601863i \(-0.205575\pi\)
−0.920528 + 0.390676i \(0.872241\pi\)
\(602\) 0 0
\(603\) 9.36141 6.20965i 0.381226 0.252877i
\(604\) 0 0
\(605\) 11.8614 + 20.5446i 0.482235 + 0.835255i
\(606\) 0 0
\(607\) 5.55842 9.62747i 0.225609 0.390767i −0.730893 0.682492i \(-0.760896\pi\)
0.956502 + 0.291725i \(0.0942294\pi\)
\(608\) 0 0
\(609\) 22.6753 24.1287i 0.918848 0.977744i
\(610\) 0 0
\(611\) −1.62772 −0.0658504
\(612\) 0 0
\(613\) −12.7446 −0.514748 −0.257374 0.966312i \(-0.582857\pi\)
−0.257374 + 0.966312i \(0.582857\pi\)
\(614\) 0 0
\(615\) 13.9307 + 46.2029i 0.561740 + 1.86308i
\(616\) 0 0
\(617\) −18.9891 + 32.8901i −0.764473 + 1.32411i 0.176051 + 0.984381i \(0.443668\pi\)
−0.940525 + 0.339726i \(0.889666\pi\)
\(618\) 0 0
\(619\) −10.6168 18.3889i −0.426727 0.739113i 0.569853 0.821747i \(-0.307000\pi\)
−0.996580 + 0.0826338i \(0.973667\pi\)
\(620\) 0 0
\(621\) 1.81386 0.672262i 0.0727877 0.0269769i
\(622\) 0 0
\(623\) −13.1168 22.7190i −0.525515 0.910219i
\(624\) 0 0
\(625\) 13.8723 24.0275i 0.554891 0.961100i
\(626\) 0 0
\(627\) −0.313859 1.04095i −0.0125343 0.0415717i
\(628\) 0 0
\(629\) −46.9783 −1.87315
\(630\) 0 0
\(631\) −32.0000 −1.27390 −0.636950 0.770905i \(-0.719804\pi\)
−0.636950 + 0.770905i \(0.719804\pi\)
\(632\) 0 0
\(633\) 11.4198 12.1518i 0.453897 0.482991i
\(634\) 0 0
\(635\) −8.00000 + 13.8564i −0.317470 + 0.549875i
\(636\) 0 0
\(637\) 2.25544 + 3.90653i 0.0893637 + 0.154782i
\(638\) 0 0
\(639\) −10.7446 5.34363i −0.425048 0.211391i
\(640\) 0 0
\(641\) −1.61684 2.80046i −0.0638615 0.110611i 0.832327 0.554285i \(-0.187008\pi\)
−0.896188 + 0.443674i \(0.853675\pi\)
\(642\) 0 0
\(643\) −1.50000 + 2.59808i −0.0591542 + 0.102458i −0.894086 0.447895i \(-0.852174\pi\)
0.834932 + 0.550353i \(0.185507\pi\)
\(644\) 0 0
\(645\) −6.97825 1.63948i −0.274768 0.0645543i
\(646\) 0 0
\(647\) 33.7228 1.32578 0.662890 0.748717i \(-0.269330\pi\)
0.662890 + 0.748717i \(0.269330\pi\)
\(648\) 0 0
\(649\) 7.00000 0.274774
\(650\) 0 0
\(651\) 46.9783 + 11.0371i 1.84122 + 0.432579i
\(652\) 0 0
\(653\) 11.4416 19.8174i 0.447744 0.775515i −0.550495 0.834838i \(-0.685561\pi\)
0.998239 + 0.0593237i \(0.0188944\pi\)
\(654\) 0 0
\(655\) −21.7921 37.7450i −0.851488 1.47482i
\(656\) 0 0
\(657\) −32.5475 16.1870i −1.26980 0.631514i
\(658\) 0 0
\(659\) −9.55842 16.5557i −0.372343 0.644917i 0.617582 0.786506i \(-0.288112\pi\)
−0.989926 + 0.141589i \(0.954779\pi\)
\(660\) 0 0
\(661\) 23.0475 39.9195i 0.896446 1.55269i 0.0644406 0.997922i \(-0.479474\pi\)
0.832005 0.554768i \(-0.187193\pi\)
\(662\) 0 0
\(663\) −2.37228 + 2.52434i −0.0921318 + 0.0980372i
\(664\) 0 0
\(665\) 6.51087 0.252481
\(666\) 0 0
\(667\) 1.62772 0.0630255
\(668\) 0 0
\(669\) 7.30298 + 24.2213i 0.282350 + 0.936448i
\(670\) 0 0
\(671\) −1.18614 + 2.05446i −0.0457905 + 0.0793114i
\(672\) 0 0
\(673\) 0.186141 + 0.322405i 0.00717520 + 0.0124278i 0.869591 0.493773i \(-0.164383\pi\)
−0.862416 + 0.506201i \(0.831049\pi\)
\(674\) 0 0
\(675\) 0.547547 3.21543i 0.0210751 0.123762i
\(676\) 0 0
\(677\) 10.3030 + 17.8453i 0.395976 + 0.685850i 0.993225 0.116205i \(-0.0370731\pi\)
−0.597249 + 0.802056i \(0.703740\pi\)
\(678\) 0 0
\(679\) −3.81386 + 6.60580i −0.146362 + 0.253507i
\(680\) 0 0
\(681\) 7.50000 + 24.8747i 0.287401 + 0.953200i
\(682\) 0 0
\(683\) −15.3723 −0.588204 −0.294102 0.955774i \(-0.595021\pi\)
−0.294102 + 0.955774i \(0.595021\pi\)
\(684\) 0 0
\(685\) 42.0951 1.60837
\(686\) 0 0
\(687\) −26.8139 + 28.5326i −1.02301 + 1.08858i
\(688\) 0 0
\(689\) 0.138593 0.240051i 0.00527999 0.00914521i
\(690\) 0 0
\(691\) −7.55842 13.0916i −0.287536 0.498027i 0.685685 0.727898i \(-0.259503\pi\)
−0.973221 + 0.229872i \(0.926169\pi\)
\(692\) 0 0
\(693\) −10.9307 + 7.25061i −0.415223 + 0.275428i
\(694\) 0 0
\(695\) −6.81386 11.8020i −0.258464 0.447674i
\(696\) 0 0
\(697\) −31.5475 + 54.6420i −1.19495 + 2.06971i
\(698\) 0 0
\(699\) 9.05842 + 2.12819i 0.342621 + 0.0804957i
\(700\) 0 0
\(701\) −35.4891 −1.34041 −0.670203 0.742178i \(-0.733793\pi\)
−0.670203 + 0.742178i \(0.733793\pi\)
\(702\) 0 0
\(703\) 5.48913 0.207026
\(704\) 0 0
\(705\) 17.4891 + 4.10891i 0.658679 + 0.154751i
\(706\) 0 0
\(707\) 15.5584 26.9480i 0.585135 1.01348i
\(708\) 0 0
\(709\) 14.3030 + 24.7735i 0.537160 + 0.930388i 0.999055 + 0.0434539i \(0.0138361\pi\)
−0.461896 + 0.886934i \(0.652831\pi\)
\(710\) 0 0
\(711\) 1.18614 + 19.0800i 0.0444838 + 0.715556i
\(712\) 0 0
\(713\) 1.18614 + 2.05446i 0.0444213 + 0.0769400i
\(714\) 0 0
\(715\) 0.441578 0.764836i 0.0165141 0.0286032i
\(716\) 0 0
\(717\) 16.4416 17.4954i 0.614022 0.653379i
\(718\) 0 0
\(719\) 45.4891 1.69646 0.848229 0.529630i \(-0.177669\pi\)
0.848229 + 0.529630i \(0.177669\pi\)
\(720\) 0 0
\(721\) −54.0951 −2.01461
\(722\) 0 0
\(723\) −2.87228 9.52628i −0.106821 0.354286i
\(724\) 0 0
\(725\) 1.37228 2.37686i 0.0509652 0.0882744i
\(726\) 0 0
\(727\) −5.44158 9.42509i −0.201817 0.349557i 0.747297 0.664490i \(-0.231351\pi\)
−0.949114 + 0.314933i \(0.898018\pi\)
\(728\) 0 0
\(729\) 5.00000 + 26.5330i 0.185185 + 0.982704i
\(730\) 0 0
\(731\) −4.68614 8.11663i −0.173323 0.300205i
\(732\) 0 0
\(733\) 18.9307 32.7889i 0.699221 1.21109i −0.269515 0.962996i \(-0.586863\pi\)
0.968737 0.248091i \(-0.0798032\pi\)
\(734\) 0 0
\(735\) −14.3723 47.6675i −0.530130 1.75824i
\(736\) 0 0
\(737\) −3.74456 −0.137933
\(738\) 0 0
\(739\) 42.1168 1.54929 0.774647 0.632394i \(-0.217928\pi\)
0.774647 + 0.632394i \(0.217928\pi\)
\(740\) 0 0
\(741\) 0.277187 0.294954i 0.0101827 0.0108354i
\(742\) 0 0
\(743\) −17.8139 + 30.8545i −0.653527 + 1.13194i 0.328734 + 0.944423i \(0.393378\pi\)
−0.982261 + 0.187520i \(0.939955\pi\)
\(744\) 0 0
\(745\) 9.93070 + 17.2005i 0.363833 + 0.630177i
\(746\) 0 0
\(747\) −1.79211 28.8275i −0.0655699 1.05474i
\(748\) 0 0
\(749\) 28.1168 + 48.6998i 1.02737 + 1.77945i
\(750\) 0 0
\(751\) 18.8139 32.5866i 0.686527 1.18910i −0.286427 0.958102i \(-0.592467\pi\)
0.972954 0.230998i \(-0.0741992\pi\)
\(752\) 0 0
\(753\) 16.6644 + 3.91515i 0.607284 + 0.142676i
\(754\) 0 0
\(755\) 0.883156 0.0321413
\(756\) 0 0
\(757\) 8.51087 0.309333 0.154667 0.987967i \(-0.450570\pi\)
0.154667 + 0.987967i \(0.450570\pi\)
\(758\) 0 0
\(759\) −0.627719 0.147477i −0.0227847 0.00535307i
\(760\) 0 0
\(761\) 9.67527 16.7581i 0.350728 0.607479i −0.635649 0.771978i \(-0.719267\pi\)
0.986377 + 0.164499i \(0.0526008\pi\)
\(762\) 0 0
\(763\) 10.3723 + 17.9653i 0.375502 + 0.650388i
\(764\) 0 0
\(765\) 31.8614 21.1345i 1.15195 0.764118i
\(766\) 0 0
\(767\) 1.30298 + 2.25684i 0.0470480 + 0.0814896i
\(768\) 0 0
\(769\) −16.5584 + 28.6800i −0.597112 + 1.03423i 0.396133 + 0.918193i \(0.370352\pi\)
−0.993245 + 0.116035i \(0.962981\pi\)
\(770\) 0 0
\(771\) −5.32473 + 5.66603i −0.191766 + 0.204057i
\(772\) 0 0
\(773\) 28.9783 1.04228 0.521138 0.853473i \(-0.325508\pi\)
0.521138 + 0.853473i \(0.325508\pi\)
\(774\) 0 0
\(775\) 4.00000 0.143684
\(776\) 0 0
\(777\) −19.1168 63.4034i −0.685813 2.27458i
\(778\) 0 0
\(779\) 3.68614 6.38458i 0.132070 0.228751i
\(780\) 0 0
\(781\) 2.00000 + 3.46410i 0.0715656 + 0.123955i
\(782\) 0 0
\(783\) −3.81386 + 22.3966i −0.136296 + 0.800390i
\(784\) 0 0
\(785\) 3.69702 + 6.40342i 0.131952 + 0.228548i
\(786\) 0 0
\(787\) −21.4198 + 37.1002i −0.763534 + 1.32248i 0.177484 + 0.984124i \(0.443204\pi\)
−0.941018 + 0.338357i \(0.890129\pi\)
\(788\) 0