Properties

Label 72.2.i.b.25.1
Level $72$
Weight $2$
Character 72.25
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 25.1
Root \(-1.18614 + 1.26217i\) of defining polynomial
Character \(\chi\) \(=\) 72.25
Dual form 72.2.i.b.49.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.18614 + 1.26217i) q^{3} +(1.68614 + 2.92048i) q^{5} +(0.686141 - 1.18843i) q^{7} +(-0.186141 - 2.99422i) q^{9} +O(q^{10})\) \(q+(-1.18614 + 1.26217i) q^{3} +(1.68614 + 2.92048i) q^{5} +(0.686141 - 1.18843i) q^{7} +(-0.186141 - 2.99422i) q^{9} +(-0.500000 + 0.866025i) q^{11} +(-2.68614 - 4.65253i) q^{13} +(-5.68614 - 1.33591i) q^{15} +0.372281 q^{17} +6.37228 q^{19} +(0.686141 + 2.27567i) q^{21} +(-2.68614 - 4.65253i) q^{23} +(-3.18614 + 5.51856i) q^{25} +(4.00000 + 3.31662i) q^{27} +(-0.686141 + 1.18843i) q^{29} +(-0.313859 - 0.543620i) q^{31} +(-0.500000 - 1.65831i) q^{33} +4.62772 q^{35} -2.74456 q^{37} +(9.05842 + 2.12819i) q^{39} +(0.127719 + 0.221215i) q^{41} +(-4.87228 + 8.43904i) q^{43} +(8.43070 - 5.59230i) q^{45} +(0.686141 - 1.18843i) q^{47} +(2.55842 + 4.43132i) q^{49} +(-0.441578 + 0.469882i) q^{51} -10.7446 q^{53} -3.37228 q^{55} +(-7.55842 + 8.04290i) q^{57} +(-3.50000 - 6.06218i) q^{59} +(1.68614 - 2.92048i) q^{61} +(-3.68614 - 1.83324i) q^{63} +(9.05842 - 15.6896i) q^{65} +(-3.87228 - 6.70699i) q^{67} +(9.05842 + 2.12819i) q^{69} -4.00000 q^{71} +5.11684 q^{73} +(-3.18614 - 10.5672i) q^{75} +(0.686141 + 1.18843i) q^{77} +(0.313859 - 0.543620i) q^{79} +(-8.93070 + 1.11469i) q^{81} +(-7.68614 + 13.3128i) q^{83} +(0.627719 + 1.08724i) q^{85} +(-0.686141 - 2.27567i) q^{87} +6.00000 q^{89} -7.37228 q^{91} +(1.05842 + 0.248667i) q^{93} +(10.7446 + 18.6101i) q^{95} +(4.87228 - 8.43904i) q^{97} +(2.68614 + 1.33591i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + q^{3} + q^{5} - 3 q^{7} + 5 q^{9}+O(q^{10}) \) 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 \(\left(\mathbb{Z}/72\mathbb{Z}\right)^\times\).

\(n\) \(37\) \(55\) \(65\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

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
\(3\) −1.18614 + 1.26217i −0.684819 + 0.728714i
\(4\) 0 0
\(5\) 1.68614 + 2.92048i 0.754065 + 1.30608i 0.945838 + 0.324640i \(0.105243\pi\)
−0.191773 + 0.981439i \(0.561424\pi\)
\(6\) 0 0
\(7\) 0.686141 1.18843i 0.259337 0.449185i −0.706728 0.707486i \(-0.749829\pi\)
0.966064 + 0.258301i \(0.0831627\pi\)
\(8\) 0 0
\(9\) −0.186141 2.99422i −0.0620469 0.998073i
\(10\) 0 0
\(11\) −0.500000 + 0.866025i −0.150756 + 0.261116i −0.931505 0.363727i \(-0.881504\pi\)
0.780750 + 0.624844i \(0.214837\pi\)
\(12\) 0 0
\(13\) −2.68614 4.65253i −0.745001 1.29038i −0.950194 0.311659i \(-0.899115\pi\)
0.205193 0.978722i \(-0.434218\pi\)
\(14\) 0 0
\(15\) −5.68614 1.33591i −1.46816 0.344930i
\(16\) 0 0
\(17\) 0.372281 0.0902915 0.0451457 0.998980i \(-0.485625\pi\)
0.0451457 + 0.998980i \(0.485625\pi\)
\(18\) 0 0
\(19\) 6.37228 1.46190 0.730951 0.682430i \(-0.239077\pi\)
0.730951 + 0.682430i \(0.239077\pi\)
\(20\) 0 0
\(21\) 0.686141 + 2.27567i 0.149728 + 0.496592i
\(22\) 0 0
\(23\) −2.68614 4.65253i −0.560099 0.970120i −0.997487 0.0708472i \(-0.977430\pi\)
0.437388 0.899273i \(-0.355904\pi\)
\(24\) 0 0
\(25\) −3.18614 + 5.51856i −0.637228 + 1.10371i
\(26\) 0 0
\(27\) 4.00000 + 3.31662i 0.769800 + 0.638285i
\(28\) 0 0
\(29\) −0.686141 + 1.18843i −0.127413 + 0.220686i −0.922674 0.385582i \(-0.874001\pi\)
0.795261 + 0.606268i \(0.207334\pi\)
\(30\) 0 0
\(31\) −0.313859 0.543620i −0.0563708 0.0976371i 0.836463 0.548023i \(-0.184620\pi\)
−0.892834 + 0.450386i \(0.851286\pi\)
\(32\) 0 0
\(33\) −0.500000 1.65831i −0.0870388 0.288675i
\(34\) 0 0
\(35\) 4.62772 0.782227
\(36\) 0 0
\(37\) −2.74456 −0.451203 −0.225602 0.974220i \(-0.572435\pi\)
−0.225602 + 0.974220i \(0.572435\pi\)
\(38\) 0 0
\(39\) 9.05842 + 2.12819i 1.45051 + 0.340784i
\(40\) 0 0
\(41\) 0.127719 + 0.221215i 0.0199463 + 0.0345480i 0.875826 0.482627i \(-0.160317\pi\)
−0.855880 + 0.517175i \(0.826984\pi\)
\(42\) 0 0
\(43\) −4.87228 + 8.43904i −0.743016 + 1.28694i 0.208100 + 0.978108i \(0.433272\pi\)
−0.951116 + 0.308834i \(0.900061\pi\)
\(44\) 0 0
\(45\) 8.43070 5.59230i 1.25678 0.833650i
\(46\) 0 0
\(47\) 0.686141 1.18843i 0.100084 0.173350i −0.811635 0.584165i \(-0.801422\pi\)
0.911719 + 0.410814i \(0.134756\pi\)
\(48\) 0 0
\(49\) 2.55842 + 4.43132i 0.365489 + 0.633045i
\(50\) 0 0
\(51\) −0.441578 + 0.469882i −0.0618333 + 0.0657966i
\(52\) 0 0
\(53\) −10.7446 −1.47588 −0.737940 0.674867i \(-0.764201\pi\)
−0.737940 + 0.674867i \(0.764201\pi\)
\(54\) 0 0
\(55\) −3.37228 −0.454718
\(56\) 0 0
\(57\) −7.55842 + 8.04290i −1.00114 + 1.06531i
\(58\) 0 0
\(59\) −3.50000 6.06218i −0.455661 0.789228i 0.543065 0.839691i \(-0.317264\pi\)
−0.998726 + 0.0504625i \(0.983930\pi\)
\(60\) 0 0
\(61\) 1.68614 2.92048i 0.215888 0.373929i −0.737659 0.675174i \(-0.764069\pi\)
0.953547 + 0.301244i \(0.0974020\pi\)
\(62\) 0 0
\(63\) −3.68614 1.83324i −0.464410 0.230967i
\(64\) 0 0
\(65\) 9.05842 15.6896i 1.12356 1.94606i
\(66\) 0 0
\(67\) −3.87228 6.70699i −0.473074 0.819389i 0.526451 0.850206i \(-0.323523\pi\)
−0.999525 + 0.0308167i \(0.990189\pi\)
\(68\) 0 0
\(69\) 9.05842 + 2.12819i 1.09051 + 0.256204i
\(70\) 0 0
\(71\) −4.00000 −0.474713 −0.237356 0.971423i \(-0.576281\pi\)
−0.237356 + 0.971423i \(0.576281\pi\)
\(72\) 0 0
\(73\) 5.11684 0.598881 0.299441 0.954115i \(-0.403200\pi\)
0.299441 + 0.954115i \(0.403200\pi\)
\(74\) 0 0
\(75\) −3.18614 10.5672i −0.367904 1.22020i
\(76\) 0 0
\(77\) 0.686141 + 1.18843i 0.0781930 + 0.135434i
\(78\) 0 0
\(79\) 0.313859 0.543620i 0.0353119 0.0611621i −0.847829 0.530269i \(-0.822091\pi\)
0.883141 + 0.469107i \(0.155424\pi\)
\(80\) 0 0
\(81\) −8.93070 + 1.11469i −0.992300 + 0.123855i
\(82\) 0 0
\(83\) −7.68614 + 13.3128i −0.843664 + 1.46127i 0.0431132 + 0.999070i \(0.486272\pi\)
−0.886777 + 0.462198i \(0.847061\pi\)
\(84\) 0 0
\(85\) 0.627719 + 1.08724i 0.0680856 + 0.117928i
\(86\) 0 0
\(87\) −0.686141 2.27567i −0.0735620 0.243978i
\(88\) 0 0
\(89\) 6.00000 0.635999 0.317999 0.948091i \(-0.396989\pi\)
0.317999 + 0.948091i \(0.396989\pi\)
\(90\) 0 0
\(91\) −7.37228 −0.772825
\(92\) 0 0
\(93\) 1.05842 + 0.248667i 0.109753 + 0.0257855i
\(94\) 0 0
\(95\) 10.7446 + 18.6101i 1.10237 + 1.90936i
\(96\) 0 0
\(97\) 4.87228 8.43904i 0.494705 0.856855i −0.505276 0.862958i \(-0.668609\pi\)
0.999981 + 0.00610314i \(0.00194270\pi\)
\(98\) 0 0
\(99\) 2.68614 + 1.33591i 0.269967 + 0.134264i
\(100\) 0 0
\(101\) −5.05842 + 8.76144i −0.503332 + 0.871796i 0.496661 + 0.867945i \(0.334559\pi\)
−0.999993 + 0.00385151i \(0.998774\pi\)
\(102\) 0 0
\(103\) 3.31386 + 5.73977i 0.326524 + 0.565557i 0.981820 0.189816i \(-0.0607892\pi\)
−0.655295 + 0.755373i \(0.727456\pi\)
\(104\) 0 0
\(105\) −5.48913 + 5.84096i −0.535684 + 0.570020i
\(106\) 0 0
\(107\) 15.8614 1.53338 0.766690 0.642017i \(-0.221902\pi\)
0.766690 + 0.642017i \(0.221902\pi\)
\(108\) 0 0
\(109\) 6.74456 0.646012 0.323006 0.946397i \(-0.395307\pi\)
0.323006 + 0.946397i \(0.395307\pi\)
\(110\) 0 0
\(111\) 3.25544 3.46410i 0.308992 0.328798i
\(112\) 0 0
\(113\) −0.686141 1.18843i −0.0645467 0.111798i 0.831946 0.554856i \(-0.187227\pi\)
−0.896493 + 0.443058i \(0.853893\pi\)
\(114\) 0 0
\(115\) 9.05842 15.6896i 0.844702 1.46307i
\(116\) 0 0
\(117\) −13.4307 + 8.90892i −1.24167 + 0.823630i
\(118\) 0 0
\(119\) 0.255437 0.442430i 0.0234159 0.0405575i
\(120\) 0 0
\(121\) 5.00000 + 8.66025i 0.454545 + 0.787296i
\(122\) 0 0
\(123\) −0.430703 0.101190i −0.0388352 0.00912398i
\(124\) 0 0
\(125\) −4.62772 −0.413916
\(126\) 0 0
\(127\) −4.74456 −0.421012 −0.210506 0.977593i \(-0.567511\pi\)
−0.210506 + 0.977593i \(0.567511\pi\)
\(128\) 0 0
\(129\) −4.87228 16.1595i −0.428980 1.42277i
\(130\) 0 0
\(131\) −6.31386 10.9359i −0.551644 0.955476i −0.998156 0.0606984i \(-0.980667\pi\)
0.446512 0.894778i \(-0.352666\pi\)
\(132\) 0 0
\(133\) 4.37228 7.57301i 0.379125 0.656664i
\(134\) 0 0
\(135\) −2.94158 + 17.2742i −0.253171 + 1.48673i
\(136\) 0 0
\(137\) −3.12772 + 5.41737i −0.267219 + 0.462837i −0.968143 0.250399i \(-0.919438\pi\)
0.700924 + 0.713236i \(0.252771\pi\)
\(138\) 0 0
\(139\) 2.87228 + 4.97494i 0.243624 + 0.421969i 0.961744 0.273951i \(-0.0883305\pi\)
−0.718120 + 0.695919i \(0.754997\pi\)
\(140\) 0 0
\(141\) 0.686141 + 2.27567i 0.0577835 + 0.191646i
\(142\) 0 0
\(143\) 5.37228 0.449253
\(144\) 0 0
\(145\) −4.62772 −0.384311
\(146\) 0 0
\(147\) −8.62772 2.02700i −0.711602 0.167185i
\(148\) 0 0
\(149\) 1.31386 + 2.27567i 0.107636 + 0.186430i 0.914812 0.403880i \(-0.132339\pi\)
−0.807176 + 0.590310i \(0.799005\pi\)
\(150\) 0 0
\(151\) 2.68614 4.65253i 0.218595 0.378618i −0.735784 0.677217i \(-0.763186\pi\)
0.954379 + 0.298599i \(0.0965193\pi\)
\(152\) 0 0
\(153\) −0.0692967 1.11469i −0.00560231 0.0901175i
\(154\) 0 0
\(155\) 1.05842 1.83324i 0.0850145 0.147249i
\(156\) 0 0
\(157\) −7.05842 12.2255i −0.563323 0.975705i −0.997203 0.0747341i \(-0.976189\pi\)
0.433880 0.900971i \(-0.357144\pi\)
\(158\) 0 0
\(159\) 12.7446 13.5615i 1.01071 1.07549i
\(160\) 0 0
\(161\) −7.37228 −0.581017
\(162\) 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 4.25639i 0.311400 0.331359i
\(166\) 0 0
\(167\) 0.941578 + 1.63086i 0.0728615 + 0.126200i 0.900154 0.435571i \(-0.143454\pi\)
−0.827293 + 0.561771i \(0.810120\pi\)
\(168\) 0 0
\(169\) −7.93070 + 13.7364i −0.610054 + 1.05664i
\(170\) 0 0
\(171\) −1.18614 19.0800i −0.0907064 1.45908i
\(172\) 0 0
\(173\) 5.31386 9.20387i 0.404005 0.699758i −0.590200 0.807257i \(-0.700951\pi\)
0.994205 + 0.107500i \(0.0342844\pi\)
\(174\) 0 0
\(175\) 4.37228 + 7.57301i 0.330513 + 0.572466i
\(176\) 0 0
\(177\) 11.8030 + 2.77300i 0.887167 + 0.208432i
\(178\) 0 0
\(179\) −22.9783 −1.71748 −0.858738 0.512416i \(-0.828751\pi\)
−0.858738 + 0.512416i \(0.828751\pi\)
\(180\) 0 0
\(181\) −23.4891 −1.74593 −0.872966 0.487780i \(-0.837807\pi\)
−0.872966 + 0.487780i \(0.837807\pi\)
\(182\) 0 0
\(183\) 1.68614 + 5.59230i 0.124643 + 0.413394i
\(184\) 0 0
\(185\) −4.62772 8.01544i −0.340237 0.589307i
\(186\) 0 0
\(187\) −0.186141 + 0.322405i −0.0136120 + 0.0235766i
\(188\) 0 0
\(189\) 6.68614 2.47805i 0.486345 0.180252i
\(190\) 0 0
\(191\) 9.43070 16.3345i 0.682382 1.18192i −0.291870 0.956458i \(-0.594278\pi\)
0.974252 0.225462i \(-0.0723891\pi\)
\(192\) 0 0
\(193\) 4.87228 + 8.43904i 0.350714 + 0.607455i 0.986375 0.164514i \(-0.0526054\pi\)
−0.635660 + 0.771969i \(0.719272\pi\)
\(194\) 0 0
\(195\) 9.05842 + 30.0434i 0.648687 + 2.15145i
\(196\) 0 0
\(197\) 26.7446 1.90547 0.952736 0.303801i \(-0.0982557\pi\)
0.952736 + 0.303801i \(0.0982557\pi\)
\(198\) 0 0
\(199\) 18.2337 1.29255 0.646276 0.763104i \(-0.276326\pi\)
0.646276 + 0.763104i \(0.276326\pi\)
\(200\) 0 0
\(201\) 13.0584 + 3.06796i 0.921070 + 0.216397i
\(202\) 0 0
\(203\) 0.941578 + 1.63086i 0.0660858 + 0.114464i
\(204\) 0 0
\(205\) −0.430703 + 0.746000i −0.0300816 + 0.0521029i
\(206\) 0 0
\(207\) −13.4307 + 8.90892i −0.933498 + 0.619213i
\(208\) 0 0
\(209\) −3.18614 + 5.51856i −0.220390 + 0.381727i
\(210\) 0 0
\(211\) 7.68614 + 13.3128i 0.529136 + 0.916490i 0.999423 + 0.0339764i \(0.0108171\pi\)
−0.470287 + 0.882514i \(0.655850\pi\)
\(212\) 0 0
\(213\) 4.74456 5.04868i 0.325092 0.345930i
\(214\) 0 0
\(215\) −32.8614 −2.24113
\(216\) 0 0
\(217\) −0.861407 −0.0584761
\(218\) 0 0
\(219\) −6.06930 + 6.45832i −0.410125 + 0.436413i
\(220\) 0 0
\(221\) −1.00000 1.73205i −0.0672673 0.116510i
\(222\) 0 0
\(223\) −12.8030 + 22.1754i −0.857351 + 1.48498i 0.0170952 + 0.999854i \(0.494558\pi\)
−0.874446 + 0.485122i \(0.838775\pi\)
\(224\) 0 0
\(225\) 17.1168 + 8.51278i 1.14112 + 0.567518i
\(226\) 0 0
\(227\) 7.50000 12.9904i 0.497792 0.862202i −0.502204 0.864749i \(-0.667477\pi\)
0.999997 + 0.00254715i \(0.000810783\pi\)
\(228\) 0 0
\(229\) 8.80298 + 15.2472i 0.581718 + 1.00756i 0.995276 + 0.0970868i \(0.0309524\pi\)
−0.413558 + 0.910478i \(0.635714\pi\)
\(230\) 0 0
\(231\) −2.31386 0.543620i −0.152241 0.0357676i
\(232\) 0 0
\(233\) −0.372281 −0.0243890 −0.0121945 0.999926i \(-0.503882\pi\)
−0.0121945 + 0.999926i \(0.503882\pi\)
\(234\) 0 0
\(235\) 4.62772 0.301879
\(236\) 0 0
\(237\) 0.313859 + 1.04095i 0.0203874 + 0.0676172i
\(238\) 0 0
\(239\) −7.43070 12.8704i −0.480652 0.832514i 0.519101 0.854713i \(-0.326267\pi\)
−0.999754 + 0.0221986i \(0.992933\pi\)
\(240\) 0 0
\(241\) 2.87228 4.97494i 0.185020 0.320464i −0.758563 0.651599i \(-0.774098\pi\)
0.943583 + 0.331135i \(0.107432\pi\)
\(242\) 0 0
\(243\) 9.18614 12.5942i 0.589291 0.807921i
\(244\) 0 0
\(245\) −8.62772 + 14.9436i −0.551205 + 0.954715i
\(246\) 0 0
\(247\) −17.1168 29.6472i −1.08912 1.88641i
\(248\) 0 0
\(249\) −7.68614 25.4920i −0.487089 1.61549i
\(250\) 0 0
\(251\) 27.1168 1.71160 0.855800 0.517307i \(-0.173065\pi\)
0.855800 + 0.517307i \(0.173065\pi\)
\(252\) 0 0
\(253\) 5.37228 0.337752
\(254\) 0 0
\(255\) −2.11684 0.497333i −0.132562 0.0311442i
\(256\) 0 0
\(257\) 9.24456 + 16.0121i 0.576660 + 0.998804i 0.995859 + 0.0909101i \(0.0289776\pi\)
−0.419199 + 0.907894i \(0.637689\pi\)
\(258\) 0 0
\(259\) −1.88316 + 3.26172i −0.117014 + 0.202674i
\(260\) 0 0
\(261\) 3.68614 + 1.83324i 0.228166 + 0.113475i
\(262\) 0 0
\(263\) 1.94158 3.36291i 0.119723 0.207366i −0.799935 0.600087i \(-0.795133\pi\)
0.919658 + 0.392721i \(0.128466\pi\)
\(264\) 0 0
\(265\) −18.1168 31.3793i −1.11291 1.92761i
\(266\) 0 0
\(267\) −7.11684 + 7.57301i −0.435544 + 0.463461i
\(268\) 0 0
\(269\) −1.25544 −0.0765454 −0.0382727 0.999267i \(-0.512186\pi\)
−0.0382727 + 0.999267i \(0.512186\pi\)
\(270\) 0 0
\(271\) 1.48913 0.0904579 0.0452290 0.998977i \(-0.485598\pi\)
0.0452290 + 0.998977i \(0.485598\pi\)
\(272\) 0 0
\(273\) 8.74456 9.30506i 0.529245 0.563168i
\(274\) 0 0
\(275\) −3.18614 5.51856i −0.192132 0.332782i
\(276\) 0 0
\(277\) −5.94158 + 10.2911i −0.356995 + 0.618333i −0.987457 0.157887i \(-0.949532\pi\)
0.630462 + 0.776220i \(0.282865\pi\)
\(278\) 0 0
\(279\) −1.56930 + 1.04095i −0.0939513 + 0.0623203i
\(280\) 0 0
\(281\) −7.43070 + 12.8704i −0.443279 + 0.767781i −0.997931 0.0643014i \(-0.979518\pi\)
0.554652 + 0.832082i \(0.312851\pi\)
\(282\) 0 0
\(283\) 2.43070 + 4.21010i 0.144490 + 0.250265i 0.929183 0.369621i \(-0.120512\pi\)
−0.784692 + 0.619885i \(0.787179\pi\)
\(284\) 0 0
\(285\) −36.2337 8.51278i −2.14630 0.504253i
\(286\) 0 0
\(287\) 0.350532 0.0206912
\(288\) 0 0
\(289\) −16.8614 −0.991847
\(290\) 0 0
\(291\) 4.87228 + 16.1595i 0.285618 + 0.947288i
\(292\) 0 0
\(293\) −12.6861 21.9730i −0.741132 1.28368i −0.951980 0.306160i \(-0.900956\pi\)
0.210848 0.977519i \(-0.432378\pi\)
\(294\) 0 0
\(295\) 11.8030 20.4434i 0.687196 1.19026i
\(296\) 0 0
\(297\) −4.87228 + 1.80579i −0.282718 + 0.104783i
\(298\) 0 0
\(299\) −14.4307 + 24.9947i −0.834549 + 1.44548i
\(300\) 0 0
\(301\) 6.68614 + 11.5807i 0.385383 + 0.667502i
\(302\) 0 0
\(303\) −5.05842 16.7769i −0.290599 0.963807i
\(304\) 0 0
\(305\) 11.3723 0.651175
\(306\) 0 0
\(307\) 25.6277 1.46265 0.731326 0.682029i \(-0.238902\pi\)
0.731326 + 0.682029i \(0.238902\pi\)
\(308\) 0 0
\(309\) −11.1753 2.62553i −0.635739 0.149361i
\(310\) 0 0
\(311\) 14.0584 + 24.3499i 0.797180 + 1.38076i 0.921446 + 0.388507i \(0.127009\pi\)
−0.124266 + 0.992249i \(0.539658\pi\)
\(312\) 0 0
\(313\) 11.6168 20.1210i 0.656623 1.13730i −0.324861 0.945762i \(-0.605318\pi\)
0.981484 0.191543i \(-0.0613490\pi\)
\(314\) 0 0
\(315\) −0.861407 13.8564i −0.0485348 0.780720i
\(316\) 0 0
\(317\) 4.80298 8.31901i 0.269762 0.467242i −0.699038 0.715085i \(-0.746388\pi\)
0.968800 + 0.247842i \(0.0797215\pi\)
\(318\) 0 0
\(319\) −0.686141 1.18843i −0.0384165 0.0665393i
\(320\) 0 0
\(321\) −18.8139 + 20.0198i −1.05009 + 1.11739i
\(322\) 0 0
\(323\) 2.37228 0.131997
\(324\) 0 0
\(325\) 34.2337 1.89894
\(326\) 0 0
\(327\) −8.00000 + 8.51278i −0.442401 + 0.470758i
\(328\) 0 0
\(329\) −0.941578 1.63086i −0.0519109 0.0899123i
\(330\) 0 0
\(331\) 1.56930 2.71810i 0.0862563 0.149400i −0.819670 0.572837i \(-0.805843\pi\)
0.905926 + 0.423436i \(0.139176\pi\)
\(332\) 0 0
\(333\) 0.510875 + 8.21782i 0.0279958 + 0.450334i
\(334\) 0 0
\(335\) 13.0584 22.6179i 0.713458 1.23575i
\(336\) 0 0
\(337\) −12.9891 22.4978i −0.707563 1.22553i −0.965759 0.259442i \(-0.916461\pi\)
0.258196 0.966093i \(-0.416872\pi\)
\(338\) 0 0
\(339\) 2.31386 + 0.543620i 0.125672 + 0.0295254i
\(340\) 0 0
\(341\) 0.627719 0.0339929
\(342\) 0 0
\(343\) 16.6277 0.897812
\(344\) 0 0
\(345\) 9.05842 + 30.0434i 0.487689 + 1.61748i
\(346\) 0 0
\(347\) 14.3614 + 24.8747i 0.770961 + 1.33534i 0.937037 + 0.349230i \(0.113557\pi\)
−0.166076 + 0.986113i \(0.553110\pi\)
\(348\) 0 0
\(349\) −17.0584 + 29.5461i −0.913116 + 1.58156i −0.103481 + 0.994631i \(0.532998\pi\)
−0.809636 + 0.586933i \(0.800335\pi\)
\(350\) 0 0
\(351\) 4.68614 27.5190i 0.250128 1.46886i
\(352\) 0 0
\(353\) −10.9891 + 19.0337i −0.584892 + 1.01306i 0.409997 + 0.912087i \(0.365530\pi\)
−0.994889 + 0.100976i \(0.967804\pi\)
\(354\) 0 0
\(355\) −6.74456 11.6819i −0.357964 0.620012i
\(356\) 0 0
\(357\) 0.255437 + 0.847190i 0.0135192 + 0.0448380i
\(358\) 0 0
\(359\) −14.2337 −0.751225 −0.375613 0.926777i \(-0.622568\pi\)
−0.375613 + 0.926777i \(0.622568\pi\)
\(360\) 0 0
\(361\) 21.6060 1.13716
\(362\) 0 0
\(363\) −16.8614 3.96143i −0.884994 0.207921i
\(364\) 0 0
\(365\) 8.62772 + 14.9436i 0.451595 + 0.782186i
\(366\) 0 0
\(367\) −11.6861 + 20.2410i −0.610012 + 1.05657i 0.381226 + 0.924482i \(0.375502\pi\)
−0.991238 + 0.132089i \(0.957831\pi\)
\(368\) 0 0
\(369\) 0.638593 0.423595i 0.0332438 0.0220515i
\(370\) 0 0
\(371\) −7.37228 + 12.7692i −0.382750 + 0.662942i
\(372\) 0 0
\(373\) −1.94158 3.36291i −0.100531 0.174125i 0.811372 0.584529i \(-0.198721\pi\)
−0.911904 + 0.410404i \(0.865388\pi\)
\(374\) 0 0
\(375\) 5.48913 5.84096i 0.283457 0.301626i
\(376\) 0 0
\(377\) 7.37228 0.379692
\(378\) 0 0
\(379\) −23.1168 −1.18743 −0.593716 0.804674i \(-0.702340\pi\)
−0.593716 + 0.804674i \(0.702340\pi\)
\(380\) 0 0
\(381\) 5.62772 5.98844i 0.288317 0.306797i
\(382\) 0 0
\(383\) 15.1753 + 26.2843i 0.775420 + 1.34307i 0.934558 + 0.355810i \(0.115795\pi\)
−0.159138 + 0.987256i \(0.550872\pi\)
\(384\) 0 0
\(385\) −2.31386 + 4.00772i −0.117925 + 0.204252i
\(386\) 0 0
\(387\) 26.1753 + 13.0178i 1.33056 + 0.661734i
\(388\) 0 0
\(389\) 14.8030 25.6395i 0.750541 1.29998i −0.197020 0.980400i \(-0.563126\pi\)
0.947561 0.319576i \(-0.103540\pi\)
\(390\) 0 0
\(391\) −1.00000 1.73205i −0.0505722 0.0875936i
\(392\) 0 0
\(393\) 21.2921 + 5.00239i 1.07404 + 0.252337i
\(394\) 0 0
\(395\) 2.11684 0.106510
\(396\) 0 0
\(397\) 16.2337 0.814745 0.407373 0.913262i \(-0.366445\pi\)
0.407373 + 0.913262i \(0.366445\pi\)
\(398\) 0 0
\(399\) 4.37228 + 14.5012i 0.218888 + 0.725969i
\(400\) 0 0
\(401\) −8.61684 14.9248i −0.430305 0.745310i 0.566595 0.823997i \(-0.308261\pi\)
−0.996899 + 0.0786871i \(0.974927\pi\)
\(402\) 0 0
\(403\) −1.68614 + 2.92048i −0.0839926 + 0.145480i
\(404\) 0 0
\(405\) −18.3139 24.2024i −0.910023 1.20263i
\(406\) 0 0
\(407\) 1.37228 2.37686i 0.0680215 0.117817i
\(408\) 0 0
\(409\) 2.87228 + 4.97494i 0.142025 + 0.245995i 0.928259 0.371934i \(-0.121305\pi\)
−0.786234 + 0.617929i \(0.787972\pi\)
\(410\) 0 0
\(411\) −3.12772 10.3735i −0.154279 0.511686i
\(412\) 0 0
\(413\) −9.60597 −0.472679
\(414\) 0 0
\(415\) −51.8397 −2.54471
\(416\) 0 0
\(417\) −9.68614 2.27567i −0.474332 0.111440i
\(418\) 0 0
\(419\) −13.8030 23.9075i −0.674320 1.16796i −0.976667 0.214759i \(-0.931104\pi\)
0.302347 0.953198i \(-0.402230\pi\)
\(420\) 0 0
\(421\) 8.94158 15.4873i 0.435786 0.754803i −0.561574 0.827427i \(-0.689804\pi\)
0.997359 + 0.0726236i \(0.0231372\pi\)
\(422\) 0 0
\(423\) −3.68614 1.83324i −0.179226 0.0891352i
\(424\) 0 0
\(425\) −1.18614 + 2.05446i −0.0575363 + 0.0996557i
\(426\) 0 0
\(427\) −2.31386 4.00772i −0.111976 0.193947i
\(428\) 0 0
\(429\) −6.37228 + 6.78073i −0.307657 + 0.327377i
\(430\) 0 0
\(431\) −12.7446 −0.613884 −0.306942 0.951728i \(-0.599306\pi\)
−0.306942 + 0.951728i \(0.599306\pi\)
\(432\) 0 0
\(433\) 14.8832 0.715239 0.357619 0.933867i \(-0.383589\pi\)
0.357619 + 0.933867i \(0.383589\pi\)
\(434\) 0 0
\(435\) 5.48913 5.84096i 0.263183 0.280053i
\(436\) 0 0
\(437\) −17.1168 29.6472i −0.818810 1.41822i
\(438\) 0 0
\(439\) 5.05842 8.76144i 0.241425 0.418161i −0.719695 0.694290i \(-0.755718\pi\)
0.961121 + 0.276129i \(0.0890518\pi\)
\(440\) 0 0
\(441\) 12.7921 8.48533i 0.609148 0.404063i
\(442\) 0 0
\(443\) 13.3614 23.1426i 0.634820 1.09954i −0.351734 0.936100i \(-0.614408\pi\)
0.986553 0.163440i \(-0.0522589\pi\)
\(444\) 0 0
\(445\) 10.1168 + 17.5229i 0.479584 + 0.830665i
\(446\) 0 0
\(447\) −4.43070 1.04095i −0.209565 0.0492354i
\(448\) 0 0
\(449\) −33.1168 −1.56288 −0.781440 0.623980i \(-0.785515\pi\)
−0.781440 + 0.623980i \(0.785515\pi\)
\(450\) 0 0
\(451\) −0.255437 −0.0120281
\(452\) 0 0
\(453\) 2.68614 + 8.90892i 0.126206 + 0.418578i
\(454\) 0 0
\(455\) −12.4307 21.5306i −0.582760 1.00937i
\(456\) 0 0
\(457\) −3.87228 + 6.70699i −0.181138 + 0.313740i −0.942268 0.334859i \(-0.891311\pi\)
0.761131 + 0.648599i \(0.224645\pi\)
\(458\) 0 0
\(459\) 1.48913 + 1.23472i 0.0695064 + 0.0576317i
\(460\) 0 0
\(461\) 12.0584 20.8858i 0.561617 0.972749i −0.435739 0.900073i \(-0.643513\pi\)
0.997356 0.0726756i \(-0.0231538\pi\)
\(462\) 0 0
\(463\) 5.17527 + 8.96382i 0.240515 + 0.416584i 0.960861 0.277031i \(-0.0893503\pi\)
−0.720346 + 0.693615i \(0.756017\pi\)
\(464\) 0 0
\(465\) 1.05842 + 3.51039i 0.0490831 + 0.162790i
\(466\) 0 0
\(467\) 1.62772 0.0753218 0.0376609 0.999291i \(-0.488009\pi\)
0.0376609 + 0.999291i \(0.488009\pi\)
\(468\) 0 0
\(469\) −10.6277 −0.490742
\(470\) 0 0
\(471\) 23.8030 + 5.59230i 1.09678 + 0.257679i
\(472\) 0 0
\(473\) −4.87228 8.43904i −0.224028 0.388027i
\(474\) 0 0
\(475\) −20.3030 + 35.1658i −0.931565 + 1.61352i
\(476\) 0 0
\(477\) 2.00000 + 32.1716i 0.0915737 + 1.47304i
\(478\) 0 0
\(479\) −14.8030 + 25.6395i −0.676366 + 1.17150i 0.299702 + 0.954033i \(0.403113\pi\)
−0.976068 + 0.217467i \(0.930221\pi\)
\(480\) 0 0
\(481\) 7.37228 + 12.7692i 0.336147 + 0.582224i
\(482\) 0 0
\(483\) 8.74456 9.30506i 0.397891 0.423395i
\(484\) 0 0
\(485\) 32.8614 1.49216
\(486\) 0 0
\(487\) −4.74456 −0.214997 −0.107498 0.994205i \(-0.534284\pi\)
−0.107498 + 0.994205i \(0.534284\pi\)
\(488\) 0 0
\(489\) 14.2337 15.1460i 0.643670 0.684927i
\(490\) 0 0
\(491\) −5.87228 10.1711i −0.265012 0.459015i 0.702555 0.711630i \(-0.252043\pi\)
−0.967567 + 0.252615i \(0.918709\pi\)
\(492\) 0 0
\(493\) −0.255437 + 0.442430i −0.0115043 + 0.0199261i
\(494\) 0 0
\(495\) 0.627719 + 10.0974i 0.0282139 + 0.453842i
\(496\) 0 0
\(497\) −2.74456 + 4.75372i −0.123110 + 0.213234i
\(498\) 0 0
\(499\) −12.9891 22.4978i −0.581473 1.00714i −0.995305 0.0967877i \(-0.969143\pi\)
0.413832 0.910353i \(-0.364190\pi\)
\(500\) 0 0
\(501\) −3.17527 0.746000i −0.141860 0.0333288i
\(502\) 0 0
\(503\) 29.4891 1.31486 0.657428 0.753518i \(-0.271645\pi\)
0.657428 + 0.753518i \(0.271645\pi\)
\(504\) 0 0
\(505\) −34.1168 −1.51818
\(506\) 0 0
\(507\) −7.93070 26.3032i −0.352215 1.16816i
\(508\) 0 0
\(509\) 6.94158 + 12.0232i 0.307680 + 0.532917i 0.977854 0.209286i \(-0.0671140\pi\)
−0.670174 + 0.742204i \(0.733781\pi\)
\(510\) 0 0
\(511\) 3.51087 6.08101i 0.155312 0.269008i
\(512\) 0 0
\(513\) 25.4891 + 21.1345i 1.12537 + 0.933109i
\(514\) 0 0
\(515\) −11.1753 + 19.3561i −0.492441 + 0.852933i
\(516\) 0 0
\(517\) 0.686141 + 1.18843i 0.0301764 + 0.0522671i
\(518\) 0 0
\(519\) 5.31386 + 17.6241i 0.233253 + 0.773611i
\(520\) 0 0
\(521\) −5.11684 −0.224173 −0.112087 0.993698i \(-0.535753\pi\)
−0.112087 + 0.993698i \(0.535753\pi\)
\(522\) 0 0
\(523\) 9.48913 0.414930 0.207465 0.978242i \(-0.433479\pi\)
0.207465 + 0.978242i \(0.433479\pi\)
\(524\) 0 0
\(525\) −14.7446 3.46410i −0.643505 0.151186i
\(526\) 0 0
\(527\) −0.116844 0.202380i −0.00508980 0.00881580i
\(528\) 0 0
\(529\) −2.93070 + 5.07613i −0.127422 + 0.220701i
\(530\) 0 0
\(531\) −17.5000 + 11.6082i −0.759435 + 0.503752i
\(532\) 0 0
\(533\) 0.686141 1.18843i 0.0297201 0.0514766i
\(534\) 0 0
\(535\) 26.7446 + 46.3229i 1.15627 + 2.00272i
\(536\) 0 0
\(537\) 27.2554 29.0024i 1.17616 1.25155i
\(538\) 0 0
\(539\) −5.11684 −0.220398
\(540\) 0 0
\(541\) −32.2337 −1.38583 −0.692917 0.721017i \(-0.743675\pi\)
−0.692917 + 0.721017i \(0.743675\pi\)
\(542\) 0 0
\(543\) 27.8614 29.6472i 1.19565 1.27228i
\(544\) 0 0
\(545\) 11.3723 + 19.6974i 0.487135 + 0.843743i
\(546\) 0 0
\(547\) 13.8723 24.0275i 0.593136 1.02734i −0.400671 0.916222i \(-0.631223\pi\)
0.993807 0.111120i \(-0.0354437\pi\)
\(548\) 0 0
\(549\) −9.05842 4.50506i −0.386604 0.192271i
\(550\) 0 0
\(551\) −4.37228 + 7.57301i −0.186265 + 0.322621i
\(552\) 0 0
\(553\) −0.430703 0.746000i −0.0183154 0.0317231i
\(554\) 0 0
\(555\) 15.6060 + 3.66648i 0.662437 + 0.155633i
\(556\) 0 0
\(557\) −14.0000 −0.593199 −0.296600 0.955002i \(-0.595853\pi\)
−0.296600 + 0.955002i \(0.595853\pi\)
\(558\) 0 0
\(559\) 52.3505 2.21419
\(560\) 0 0
\(561\) −0.186141 0.617359i −0.00785886 0.0260649i
\(562\) 0 0
\(563\) 0.872281 + 1.51084i 0.0367623 + 0.0636741i 0.883821 0.467825i \(-0.154962\pi\)
−0.847059 + 0.531499i \(0.821629\pi\)
\(564\) 0 0
\(565\) 2.31386 4.00772i 0.0973448 0.168606i
\(566\) 0 0
\(567\) −4.80298 + 11.3784i −0.201706 + 0.477846i
\(568\) 0 0
\(569\) 3.61684 6.26456i 0.151626 0.262624i −0.780199 0.625531i \(-0.784882\pi\)
0.931825 + 0.362907i \(0.118216\pi\)
\(570\) 0 0
\(571\) 1.75544 + 3.04051i 0.0734628 + 0.127241i 0.900417 0.435028i \(-0.143262\pi\)
−0.826954 + 0.562270i \(0.809928\pi\)
\(572\) 0 0
\(573\) 9.43070 + 31.2781i 0.393973 + 1.30666i
\(574\) 0 0
\(575\) 34.2337 1.42764
\(576\) 0 0
\(577\) −13.8614 −0.577058 −0.288529 0.957471i \(-0.593166\pi\)
−0.288529 + 0.957471i \(0.593166\pi\)
\(578\) 0 0
\(579\) −16.4307 3.86025i −0.682837 0.160426i
\(580\) 0 0
\(581\) 10.5475 + 18.2689i 0.437586 + 0.757921i
\(582\) 0 0
\(583\) 5.37228 9.30506i 0.222497 0.385376i
\(584\) 0 0
\(585\) −48.6644 24.2024i −2.01202 1.00065i
\(586\) 0 0
\(587\) 12.6168 21.8530i 0.520753 0.901970i −0.478956 0.877839i \(-0.658985\pi\)
0.999709 0.0241315i \(-0.00768204\pi\)
\(588\) 0 0
\(589\) −2.00000 3.46410i −0.0824086 0.142736i
\(590\) 0 0
\(591\) −31.7228 + 33.7562i −1.30490 + 1.38854i
\(592\) 0 0
\(593\) −26.0000 −1.06769 −0.533846 0.845582i \(-0.679254\pi\)
−0.533846 + 0.845582i \(0.679254\pi\)
\(594\) 0 0
\(595\) 1.72281 0.0706285
\(596\) 0 0
\(597\) −21.6277 + 23.0140i −0.885164 + 0.941900i
\(598\) 0 0
\(599\) −5.56930 9.64630i −0.227555 0.394137i 0.729528 0.683951i \(-0.239740\pi\)
−0.957083 + 0.289814i \(0.906407\pi\)
\(600\) 0 0
\(601\) 19.9891 34.6222i 0.815373 1.41227i −0.0936860 0.995602i \(-0.529865\pi\)
0.909059 0.416666i \(-0.136802\pi\)
\(602\) 0 0
\(603\) −19.3614 + 12.8429i −0.788457 + 0.523003i
\(604\) 0 0
\(605\) −16.8614 + 29.2048i −0.685514 + 1.18734i
\(606\) 0 0
\(607\) −3.05842 5.29734i −0.124138 0.215012i 0.797258 0.603639i \(-0.206283\pi\)
−0.921395 + 0.388626i \(0.872950\pi\)
\(608\) 0 0
\(609\) −3.17527 0.746000i −0.128668 0.0302294i
\(610\) 0 0
\(611\) −7.37228 −0.298251
\(612\) 0 0
\(613\) −1.25544 −0.0507066 −0.0253533 0.999679i \(-0.508071\pi\)
−0.0253533 + 0.999679i \(0.508071\pi\)
\(614\) 0 0
\(615\) −0.430703 1.42848i −0.0173676 0.0576019i
\(616\) 0 0
\(617\) 3.98913 + 6.90937i 0.160596 + 0.278161i 0.935083 0.354430i \(-0.115325\pi\)
−0.774487 + 0.632590i \(0.781992\pi\)
\(618\) 0 0
\(619\) 6.61684 11.4607i 0.265953 0.460645i −0.701860 0.712315i \(-0.747647\pi\)
0.967813 + 0.251671i \(0.0809799\pi\)
\(620\) 0 0
\(621\) 4.68614 27.5190i 0.188048 1.10430i
\(622\) 0 0
\(623\) 4.11684 7.13058i 0.164938 0.285681i
\(624\) 0 0
\(625\) 8.12772 + 14.0776i 0.325109 + 0.563105i
\(626\) 0 0
\(627\) −3.18614 10.5672i −0.127242 0.422015i
\(628\) 0 0
\(629\) −1.02175 −0.0407398
\(630\) 0 0
\(631\) −32.0000 −1.27390 −0.636950 0.770905i \(-0.719804\pi\)
−0.636950 + 0.770905i \(0.719804\pi\)
\(632\) 0 0
\(633\) −25.9198 6.08963i −1.03022 0.242041i
\(634\) 0 0
\(635\) −8.00000 13.8564i −0.317470 0.549875i
\(636\) 0 0
\(637\) 13.7446 23.8063i 0.544579 0.943239i
\(638\) 0 0
\(639\) 0.744563 + 11.9769i 0.0294544 + 0.473798i
\(640\) 0 0
\(641\) 15.6168 27.0492i 0.616828 1.06838i −0.373233 0.927738i \(-0.621751\pi\)
0.990061 0.140640i \(-0.0449160\pi\)
\(642\) 0 0
\(643\) −1.50000 2.59808i −0.0591542 0.102458i 0.834932 0.550353i \(-0.185507\pi\)
−0.894086 + 0.447895i \(0.852174\pi\)
\(644\) 0 0
\(645\) 38.9783 41.4766i 1.53477 1.63314i
\(646\) 0 0
\(647\) −23.7228 −0.932640 −0.466320 0.884616i \(-0.654420\pi\)
−0.466320 + 0.884616i \(0.654420\pi\)
\(648\) 0 0
\(649\) 7.00000 0.274774
\(650\) 0 0
\(651\) 1.02175 1.08724i 0.0400455 0.0426123i
\(652\) 0 0
\(653\) 20.0584 + 34.7422i 0.784947 + 1.35957i 0.929031 + 0.370002i \(0.120643\pi\)
−0.144084 + 0.989565i \(0.546024\pi\)
\(654\) 0 0
\(655\) 21.2921 36.8790i 0.831952 1.44098i
\(656\) 0 0
\(657\) −0.952453 15.3210i −0.0371587 0.597727i
\(658\) 0 0
\(659\) −0.941578 + 1.63086i −0.0366787 + 0.0635293i −0.883782 0.467899i \(-0.845011\pi\)
0.847103 + 0.531428i \(0.178344\pi\)
\(660\) 0 0
\(661\) −8.54755 14.8048i −0.332461 0.575839i 0.650533 0.759478i \(-0.274546\pi\)
−0.982994 + 0.183639i \(0.941212\pi\)
\(662\) 0 0
\(663\) 3.37228 + 0.792287i 0.130969 + 0.0307699i
\(664\) 0 0
\(665\) 29.4891 1.14354
\(666\) 0 0
\(667\) 7.37228 0.285456
\(668\) 0 0
\(669\) −12.8030 42.4627i −0.494992 1.64170i
\(670\) 0 0
\(671\) 1.68614 + 2.92048i 0.0650927 + 0.112744i
\(672\) 0 0
\(673\) −2.68614 + 4.65253i −0.103543 + 0.179342i −0.913142 0.407642i \(-0.866351\pi\)
0.809599 + 0.586983i \(0.199685\pi\)
\(674\) 0 0
\(675\) −31.0475 + 11.5070i −1.19502 + 0.442905i
\(676\) 0 0
\(677\) −9.80298 + 16.9793i −0.376759 + 0.652566i −0.990589 0.136872i \(-0.956295\pi\)
0.613829 + 0.789439i \(0.289628\pi\)
\(678\) 0 0
\(679\) −6.68614 11.5807i −0.256591 0.444428i
\(680\) 0 0
\(681\) 7.50000 + 24.8747i 0.287401 + 0.953200i
\(682\) 0 0
\(683\) −9.62772 −0.368394 −0.184197 0.982889i \(-0.558969\pi\)
−0.184197 + 0.982889i \(0.558969\pi\)
\(684\) 0 0
\(685\) −21.0951 −0.806002
\(686\) 0 0
\(687\) −29.6861 6.97449i −1.13260 0.266093i
\(688\) 0 0
\(689\) 28.8614 + 49.9894i 1.09953 + 1.90445i
\(690\) 0 0
\(691\) 1.05842 1.83324i 0.0402643 0.0697398i −0.845191 0.534464i \(-0.820513\pi\)
0.885455 + 0.464725i \(0.153847\pi\)
\(692\) 0 0
\(693\) 3.43070 2.27567i 0.130322 0.0864456i
\(694\) 0 0
\(695\) −9.68614 + 16.7769i −0.367416 + 0.636384i
\(696\) 0 0
\(697\) 0.0475473 + 0.0823543i 0.00180098 + 0.00311939i
\(698\) 0 0
\(699\) 0.441578 0.469882i 0.0167020 0.0177726i
\(700\) 0 0
\(701\) −12.5109 −0.472529 −0.236265 0.971689i \(-0.575923\pi\)
−0.236265 + 0.971689i \(0.575923\pi\)
\(702\) 0 0
\(703\) −17.4891 −0.659615
\(704\) 0 0
\(705\) −5.48913 + 5.84096i −0.206732 + 0.219983i
\(706\) 0 0
\(707\) 6.94158 + 12.0232i 0.261065 + 0.452178i
\(708\) 0 0
\(709\) −5.80298 + 10.0511i −0.217936 + 0.377476i −0.954177 0.299244i \(-0.903266\pi\)
0.736241 + 0.676719i \(0.236599\pi\)
\(710\) 0 0
\(711\) −1.68614 0.838574i −0.0632352 0.0314490i
\(712\) 0 0
\(713\) −1.68614 + 2.92048i −0.0631465 + 0.109373i
\(714\) 0 0
\(715\) 9.05842 + 15.6896i 0.338766 + 0.586760i
\(716\) 0 0
\(717\) 25.0584 + 5.88725i 0.935824 + 0.219863i
\(718\) 0 0
\(719\) 22.5109 0.839514 0.419757 0.907637i \(-0.362115\pi\)
0.419757 + 0.907637i \(0.362115\pi\)
\(720\) 0 0
\(721\) 9.09509 0.338719
\(722\) 0 0
\(723\) 2.87228 + 9.52628i 0.106821 + 0.354286i
\(724\) 0 0
\(725\) −4.37228 7.57301i −0.162382 0.281255i
\(726\) 0 0
\(727\) −14.0584 + 24.3499i −0.521398 + 0.903088i 0.478292 + 0.878201i \(0.341256\pi\)
−0.999690 + 0.0248871i \(0.992077\pi\)
\(728\) 0 0
\(729\) 5.00000 + 26.5330i 0.185185 + 0.982704i
\(730\) 0 0
\(731\) −1.81386 + 3.14170i −0.0670880 + 0.116200i
\(732\) 0 0
\(733\) 4.56930 + 7.91425i 0.168771 + 0.292320i 0.937988 0.346668i \(-0.112687\pi\)
−0.769217 + 0.638987i \(0.779354\pi\)
\(734\) 0 0
\(735\) −8.62772 28.6149i −0.318238 1.05548i
\(736\) 0 0
\(737\) 7.74456 0.285275
\(738\) 0 0
\(739\) 24.8832 0.915342 0.457671 0.889122i \(-0.348684\pi\)
0.457671 + 0.889122i \(0.348684\pi\)
\(740\) 0 0
\(741\) 57.7228 + 13.5615i 2.12050 + 0.498192i
\(742\) 0 0
\(743\) −20.6861 35.8294i −0.758901 1.31445i −0.943412 0.331624i \(-0.892403\pi\)
0.184511 0.982831i \(-0.440930\pi\)
\(744\) 0 0
\(745\) −4.43070 + 7.67420i −0.162328 + 0.281161i
\(746\) 0 0
\(747\) 41.2921 + 20.5359i 1.51080 + 0.751371i
\(748\) 0 0
\(749\) 10.8832 18.8502i 0.397662 0.688771i
\(750\) 0 0
\(751\) 21.6861 + 37.5615i 0.791339 + 1.37064i 0.925138 + 0.379630i \(0.123949\pi\)
−0.133800 + 0.991008i \(0.542718\pi\)
\(752\) 0 0
\(753\) −32.1644 + 34.2260i −1.17214 + 1.24727i
\(754\) 0 0
\(755\) 18.1168 0.659339
\(756\) 0 0
\(757\) 31.4891 1.14449 0.572246 0.820082i \(-0.306072\pi\)
0.572246 + 0.820082i \(0.306072\pi\)
\(758\) 0 0
\(759\) −6.37228 + 6.78073i −0.231299 + 0.246125i
\(760\) 0 0
\(761\) −16.1753 28.0164i −0.586353 1.01559i −0.994705 0.102769i \(-0.967230\pi\)
0.408352 0.912824i \(-0.366103\pi\)
\(762\) 0 0
\(763\) 4.62772 8.01544i 0.167535 0.290179i
\(764\) 0 0
\(765\) 3.13859 2.08191i 0.113476 0.0752715i
\(766\) 0 0
\(767\) −18.8030 + 32.5677i −0.678936 + 1.17595i
\(768\) 0 0
\(769\) −7.94158 13.7552i −0.286381 0.496026i 0.686562 0.727071i \(-0.259119\pi\)
−0.972943 + 0.231045i \(0.925786\pi\)
\(770\) 0 0
\(771\) −31.1753 7.32435i −1.12275 0.263780i
\(772\) 0 0
\(773\) −16.9783 −0.610665 −0.305333 0.952246i \(-0.598768\pi\)
−0.305333 + 0.952246i \(0.598768\pi\)
\(774\) 0 0
\(775\) 4.00000 0.143684
\(776\) 0 0
\(777\) −1.88316 6.24572i −0.0675578 0.224064i
\(778\) 0 0
\(779\) 0.813859 + 1.40965i 0.0291595 + 0.0505058i
\(780\) 0 0
\(781\) 2.00000 3.46410i 0.0715656 0.123955i
\(782\) 0 0
\(783\) −6.68614 + 2.47805i −0.238943 + 0.0885583i
\(784\) 0 0
\(785\) 23.8030 41.2280i 0.849565 1.47149i
\(786\) 0 0
\(787\) 15.9198 + 27.5740i 0.567481 + 0.982905i 0.996814 + 0.0797592i \(0.0254151\pi\)
−0.429334 + 0.903146i \(0.641252\pi\)
\(788\) 0