Properties

Label 432.2.y.e.37.8
Level $432$
Weight $2$
Character 432.37
Analytic conductor $3.450$
Analytic rank $0$
Dimension $72$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [432,2,Mod(37,432)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(432, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([0, 3, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("432.37");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 432 = 2^{4} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 432.y (of order \(12\), degree \(4\), 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: \(3.44953736732\)
Analytic rank: \(0\)
Dimension: \(72\)
Relative dimension: \(18\) over \(\Q(\zeta_{12})\)
Twist minimal: no (minimal twist has level 144)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 37.8
Character \(\chi\) \(=\) 432.37
Dual form 432.2.y.e.397.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.268956 - 1.38840i) q^{2} +(-1.85533 + 0.746838i) q^{4} +(-2.97932 + 0.798307i) q^{5} +(1.78208 - 1.02889i) q^{7} +(1.53591 + 2.37507i) q^{8} +O(q^{10})\) \(q+(-0.268956 - 1.38840i) q^{2} +(-1.85533 + 0.746838i) q^{4} +(-2.97932 + 0.798307i) q^{5} +(1.78208 - 1.02889i) q^{7} +(1.53591 + 2.37507i) q^{8} +(1.90968 + 3.92179i) q^{10} +(-0.119598 + 0.446347i) q^{11} +(1.52075 + 5.67550i) q^{13} +(-1.90781 - 2.19752i) q^{14} +(2.88447 - 2.77126i) q^{16} -0.0443921 q^{17} +(-1.10726 + 1.10726i) q^{19} +(4.93140 - 3.70619i) q^{20} +(0.651876 + 0.0460030i) q^{22} +(7.89263 + 4.55681i) q^{23} +(3.90893 - 2.25682i) q^{25} +(7.47087 - 3.63787i) q^{26} +(-2.53793 + 3.23984i) q^{28} +(6.95662 + 1.86402i) q^{29} +(0.542236 - 0.939180i) q^{31} +(-4.62341 - 3.25946i) q^{32} +(0.0119395 + 0.0616341i) q^{34} +(-4.48803 + 4.48803i) q^{35} +(-0.769054 - 0.769054i) q^{37} +(1.83513 + 1.23952i) q^{38} +(-6.47201 - 5.84998i) q^{40} +(-5.77193 - 3.33242i) q^{41} +(-2.96351 + 11.0600i) q^{43} +(-0.111455 - 0.917439i) q^{44} +(4.20392 - 12.1837i) q^{46} +(1.22453 + 2.12095i) q^{47} +(-1.38279 + 2.39506i) q^{49} +(-4.18471 - 4.82019i) q^{50} +(-7.06016 - 9.39416i) q^{52} +(-2.44801 - 2.44801i) q^{53} -1.42529i q^{55} +(5.18080 + 2.65230i) q^{56} +(0.716989 - 10.1599i) q^{58} +(-3.59122 + 0.962265i) q^{59} +(-1.18758 - 0.318210i) q^{61} +(-1.44980 - 0.500244i) q^{62} +(-3.28195 + 7.29581i) q^{64} +(-9.06158 - 15.6951i) q^{65} +(1.48102 + 5.52723i) q^{67} +(0.0823618 - 0.0331537i) q^{68} +(7.43827 + 5.02411i) q^{70} +6.88571i q^{71} -13.1963i q^{73} +(-0.860915 + 1.27460i) q^{74} +(1.22738 - 2.88127i) q^{76} +(0.246106 + 0.918480i) q^{77} +(3.46441 + 6.00054i) q^{79} +(-6.38144 + 10.5591i) q^{80} +(-3.07435 + 8.91003i) q^{82} +(0.588112 + 0.157584i) q^{83} +(0.132258 - 0.0354385i) q^{85} +(16.1528 + 1.13991i) q^{86} +(-1.24380 + 0.401495i) q^{88} +5.30004i q^{89} +(8.54954 + 8.54954i) q^{91} +(-18.0466 - 2.55985i) q^{92} +(2.61539 - 2.27059i) q^{94} +(2.41495 - 4.18282i) q^{95} +(-5.88304 - 10.1897i) q^{97} +(3.69722 + 1.27570i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 72 q - 4 q^{2} - 2 q^{4} - 4 q^{5} + 8 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 72 q - 4 q^{2} - 2 q^{4} - 4 q^{5} + 8 q^{8} - 20 q^{10} + 2 q^{11} - 16 q^{13} + 4 q^{14} - 10 q^{16} + 16 q^{17} + 28 q^{19} - 12 q^{20} - 8 q^{22} + 4 q^{26} - 16 q^{28} - 4 q^{29} + 28 q^{31} + 46 q^{32} - 14 q^{34} + 16 q^{35} + 16 q^{37} - 2 q^{38} - 10 q^{40} - 10 q^{43} - 60 q^{44} + 20 q^{46} + 56 q^{47} + 4 q^{49} + 36 q^{50} + 6 q^{52} + 8 q^{53} - 52 q^{56} - 14 q^{58} + 14 q^{59} - 32 q^{61} - 16 q^{62} - 44 q^{64} + 64 q^{65} - 18 q^{67} - 16 q^{68} + 14 q^{70} - 38 q^{74} + 10 q^{76} + 36 q^{77} + 44 q^{79} - 144 q^{80} - 88 q^{82} - 20 q^{83} - 8 q^{85} - 76 q^{86} - 42 q^{88} - 80 q^{91} + 68 q^{92} + 20 q^{94} - 48 q^{95} + 40 q^{97} - 88 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/432\mathbb{Z}\right)^\times\).

\(n\) \(271\) \(325\) \(353\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{4}\right)\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.268956 1.38840i −0.190180 0.981749i
\(3\) 0 0
\(4\) −1.85533 + 0.746838i −0.927663 + 0.373419i
\(5\) −2.97932 + 0.798307i −1.33239 + 0.357014i −0.853607 0.520918i \(-0.825590\pi\)
−0.478786 + 0.877932i \(0.658923\pi\)
\(6\) 0 0
\(7\) 1.78208 1.02889i 0.673564 0.388882i −0.123862 0.992299i \(-0.539528\pi\)
0.797426 + 0.603417i \(0.206195\pi\)
\(8\) 1.53591 + 2.37507i 0.543027 + 0.839715i
\(9\) 0 0
\(10\) 1.90968 + 3.92179i 0.603893 + 1.24018i
\(11\) −0.119598 + 0.446347i −0.0360602 + 0.134579i −0.981609 0.190901i \(-0.938859\pi\)
0.945549 + 0.325480i \(0.105526\pi\)
\(12\) 0 0
\(13\) 1.52075 + 5.67550i 0.421779 + 1.57410i 0.770857 + 0.637008i \(0.219828\pi\)
−0.349078 + 0.937094i \(0.613505\pi\)
\(14\) −1.90781 2.19752i −0.509883 0.587313i
\(15\) 0 0
\(16\) 2.88447 2.77126i 0.721117 0.692814i
\(17\) −0.0443921 −0.0107667 −0.00538333 0.999986i \(-0.501714\pi\)
−0.00538333 + 0.999986i \(0.501714\pi\)
\(18\) 0 0
\(19\) −1.10726 + 1.10726i −0.254023 + 0.254023i −0.822618 0.568595i \(-0.807487\pi\)
0.568595 + 0.822618i \(0.307487\pi\)
\(20\) 4.93140 3.70619i 1.10270 0.828729i
\(21\) 0 0
\(22\) 0.651876 + 0.0460030i 0.138980 + 0.00980788i
\(23\) 7.89263 + 4.55681i 1.64573 + 0.950161i 0.978743 + 0.205089i \(0.0657485\pi\)
0.666984 + 0.745072i \(0.267585\pi\)
\(24\) 0 0
\(25\) 3.90893 2.25682i 0.781786 0.451364i
\(26\) 7.47087 3.63787i 1.46516 0.713445i
\(27\) 0 0
\(28\) −2.53793 + 3.23984i −0.479624 + 0.612273i
\(29\) 6.95662 + 1.86402i 1.29181 + 0.346140i 0.838349 0.545134i \(-0.183521\pi\)
0.453464 + 0.891275i \(0.350188\pi\)
\(30\) 0 0
\(31\) 0.542236 0.939180i 0.0973884 0.168682i −0.813214 0.581964i \(-0.802284\pi\)
0.910603 + 0.413282i \(0.135618\pi\)
\(32\) −4.62341 3.25946i −0.817312 0.576196i
\(33\) 0 0
\(34\) 0.0119395 + 0.0616341i 0.00204761 + 0.0105702i
\(35\) −4.48803 + 4.48803i −0.758615 + 0.758615i
\(36\) 0 0
\(37\) −0.769054 0.769054i −0.126432 0.126432i 0.641060 0.767491i \(-0.278495\pi\)
−0.767491 + 0.641060i \(0.778495\pi\)
\(38\) 1.83513 + 1.23952i 0.297697 + 0.201077i
\(39\) 0 0
\(40\) −6.47201 5.84998i −1.02332 0.924962i
\(41\) −5.77193 3.33242i −0.901423 0.520437i −0.0237617 0.999718i \(-0.507564\pi\)
−0.877662 + 0.479281i \(0.840898\pi\)
\(42\) 0 0
\(43\) −2.96351 + 11.0600i −0.451932 + 1.68663i 0.245023 + 0.969517i \(0.421204\pi\)
−0.696955 + 0.717115i \(0.745462\pi\)
\(44\) −0.111455 0.917439i −0.0168025 0.138309i
\(45\) 0 0
\(46\) 4.20392 12.1837i 0.619835 1.79639i
\(47\) 1.22453 + 2.12095i 0.178617 + 0.309373i 0.941407 0.337273i \(-0.109504\pi\)
−0.762790 + 0.646646i \(0.776171\pi\)
\(48\) 0 0
\(49\) −1.38279 + 2.39506i −0.197541 + 0.342151i
\(50\) −4.18471 4.82019i −0.591807 0.681677i
\(51\) 0 0
\(52\) −7.06016 9.39416i −0.979068 1.30274i
\(53\) −2.44801 2.44801i −0.336260 0.336260i 0.518698 0.854958i \(-0.326417\pi\)
−0.854958 + 0.518698i \(0.826417\pi\)
\(54\) 0 0
\(55\) 1.42529i 0.192186i
\(56\) 5.18080 + 2.65230i 0.692314 + 0.354428i
\(57\) 0 0
\(58\) 0.716989 10.1599i 0.0941453 1.33407i
\(59\) −3.59122 + 0.962265i −0.467537 + 0.125276i −0.484894 0.874573i \(-0.661142\pi\)
0.0173563 + 0.999849i \(0.494475\pi\)
\(60\) 0 0
\(61\) −1.18758 0.318210i −0.152054 0.0407426i 0.181989 0.983301i \(-0.441746\pi\)
−0.334043 + 0.942558i \(0.608413\pi\)
\(62\) −1.44980 0.500244i −0.184124 0.0635310i
\(63\) 0 0
\(64\) −3.28195 + 7.29581i −0.410243 + 0.911976i
\(65\) −9.06158 15.6951i −1.12395 1.94674i
\(66\) 0 0
\(67\) 1.48102 + 5.52723i 0.180935 + 0.675258i 0.995464 + 0.0951361i \(0.0303286\pi\)
−0.814529 + 0.580122i \(0.803005\pi\)
\(68\) 0.0823618 0.0331537i 0.00998783 0.00402048i
\(69\) 0 0
\(70\) 7.43827 + 5.02411i 0.889044 + 0.600496i
\(71\) 6.88571i 0.817184i 0.912717 + 0.408592i \(0.133980\pi\)
−0.912717 + 0.408592i \(0.866020\pi\)
\(72\) 0 0
\(73\) 13.1963i 1.54451i −0.635312 0.772255i \(-0.719129\pi\)
0.635312 0.772255i \(-0.280871\pi\)
\(74\) −0.860915 + 1.27460i −0.100079 + 0.148169i
\(75\) 0 0
\(76\) 1.22738 2.88127i 0.140791 0.330505i
\(77\) 0.246106 + 0.918480i 0.0280464 + 0.104670i
\(78\) 0 0
\(79\) 3.46441 + 6.00054i 0.389777 + 0.675113i 0.992419 0.122898i \(-0.0392188\pi\)
−0.602643 + 0.798011i \(0.705885\pi\)
\(80\) −6.38144 + 10.5591i −0.713466 + 1.18055i
\(81\) 0 0
\(82\) −3.07435 + 8.91003i −0.339506 + 0.983949i
\(83\) 0.588112 + 0.157584i 0.0645537 + 0.0172971i 0.290951 0.956738i \(-0.406028\pi\)
−0.226398 + 0.974035i \(0.572695\pi\)
\(84\) 0 0
\(85\) 0.132258 0.0354385i 0.0143454 0.00384385i
\(86\) 16.1528 + 1.13991i 1.74180 + 0.122919i
\(87\) 0 0
\(88\) −1.24380 + 0.401495i −0.132589 + 0.0427995i
\(89\) 5.30004i 0.561803i 0.959737 + 0.280902i \(0.0906335\pi\)
−0.959737 + 0.280902i \(0.909367\pi\)
\(90\) 0 0
\(91\) 8.54954 + 8.54954i 0.896235 + 0.896235i
\(92\) −18.0466 2.55985i −1.88149 0.266883i
\(93\) 0 0
\(94\) 2.61539 2.27059i 0.269757 0.234193i
\(95\) 2.41495 4.18282i 0.247769 0.429148i
\(96\) 0 0
\(97\) −5.88304 10.1897i −0.597333 1.03461i −0.993213 0.116309i \(-0.962894\pi\)
0.395880 0.918302i \(-0.370439\pi\)
\(98\) 3.69722 + 1.27570i 0.373475 + 0.128865i
\(99\) 0 0
\(100\) −5.56686 + 7.10648i −0.556686 + 0.710648i
\(101\) −1.51464 + 5.65271i −0.150712 + 0.562466i 0.848722 + 0.528839i \(0.177372\pi\)
−0.999434 + 0.0336269i \(0.989294\pi\)
\(102\) 0 0
\(103\) 1.13680 + 0.656334i 0.112013 + 0.0646705i 0.554960 0.831877i \(-0.312734\pi\)
−0.442947 + 0.896548i \(0.646067\pi\)
\(104\) −11.1440 + 12.3290i −1.09276 + 1.20895i
\(105\) 0 0
\(106\) −2.74042 + 4.05723i −0.266173 + 0.394073i
\(107\) 2.92966 + 2.92966i 0.283221 + 0.283221i 0.834392 0.551171i \(-0.185819\pi\)
−0.551171 + 0.834392i \(0.685819\pi\)
\(108\) 0 0
\(109\) 11.5193 11.5193i 1.10335 1.10335i 0.109344 0.994004i \(-0.465125\pi\)
0.994004 0.109344i \(-0.0348750\pi\)
\(110\) −1.97887 + 0.383339i −0.188678 + 0.0365499i
\(111\) 0 0
\(112\) 2.28905 7.90639i 0.216295 0.747084i
\(113\) −3.79250 + 6.56880i −0.356768 + 0.617941i −0.987419 0.158126i \(-0.949455\pi\)
0.630651 + 0.776067i \(0.282788\pi\)
\(114\) 0 0
\(115\) −27.1524 7.27547i −2.53198 0.678441i
\(116\) −14.2989 + 1.73710i −1.32762 + 0.161286i
\(117\) 0 0
\(118\) 2.30189 + 4.72726i 0.211906 + 0.435179i
\(119\) −0.0791104 + 0.0456744i −0.00725204 + 0.00418696i
\(120\) 0 0
\(121\) 9.34136 + 5.39324i 0.849214 + 0.490294i
\(122\) −0.122398 + 1.73442i −0.0110814 + 0.157027i
\(123\) 0 0
\(124\) −0.304609 + 2.14745i −0.0273547 + 0.192846i
\(125\) 1.06075 1.06075i 0.0948761 0.0948761i
\(126\) 0 0
\(127\) −10.6374 −0.943915 −0.471958 0.881621i \(-0.656452\pi\)
−0.471958 + 0.881621i \(0.656452\pi\)
\(128\) 11.0122 + 2.59441i 0.973352 + 0.229316i
\(129\) 0 0
\(130\) −19.3540 + 16.8024i −1.69746 + 1.47367i
\(131\) −4.98338 18.5982i −0.435400 1.62493i −0.740108 0.672488i \(-0.765226\pi\)
0.304708 0.952446i \(-0.401441\pi\)
\(132\) 0 0
\(133\) −0.833985 + 3.11247i −0.0723157 + 0.269886i
\(134\) 7.27569 3.54283i 0.628524 0.306054i
\(135\) 0 0
\(136\) −0.0681824 0.105434i −0.00584659 0.00904093i
\(137\) 8.30213 4.79324i 0.709299 0.409514i −0.101502 0.994835i \(-0.532365\pi\)
0.810802 + 0.585321i \(0.199032\pi\)
\(138\) 0 0
\(139\) 6.81465 1.82598i 0.578011 0.154878i 0.0420428 0.999116i \(-0.486613\pi\)
0.535968 + 0.844238i \(0.319947\pi\)
\(140\) 4.97492 11.6786i 0.420458 0.987020i
\(141\) 0 0
\(142\) 9.56014 1.85195i 0.802270 0.155412i
\(143\) −2.71512 −0.227050
\(144\) 0 0
\(145\) −22.2141 −1.84478
\(146\) −18.3218 + 3.54922i −1.51632 + 0.293736i
\(147\) 0 0
\(148\) 2.00120 + 0.852487i 0.164498 + 0.0700740i
\(149\) −19.4991 + 5.22476i −1.59743 + 0.428029i −0.944264 0.329189i \(-0.893225\pi\)
−0.653162 + 0.757218i \(0.726558\pi\)
\(150\) 0 0
\(151\) 3.86699 2.23261i 0.314691 0.181687i −0.334333 0.942455i \(-0.608511\pi\)
0.649024 + 0.760768i \(0.275178\pi\)
\(152\) −4.33048 0.929169i −0.351248 0.0753656i
\(153\) 0 0
\(154\) 1.20903 0.588725i 0.0974263 0.0474408i
\(155\) −0.865741 + 3.23099i −0.0695380 + 0.259519i
\(156\) 0 0
\(157\) −4.26421 15.9143i −0.340321 1.27010i −0.897984 0.440029i \(-0.854968\pi\)
0.557662 0.830068i \(-0.311698\pi\)
\(158\) 7.39939 6.42388i 0.588664 0.511056i
\(159\) 0 0
\(160\) 16.3767 + 6.02006i 1.29469 + 0.475928i
\(161\) 18.7538 1.47800
\(162\) 0 0
\(163\) 5.24124 5.24124i 0.410525 0.410525i −0.471396 0.881922i \(-0.656250\pi\)
0.881922 + 0.471396i \(0.156250\pi\)
\(164\) 13.1976 + 1.87204i 1.03056 + 0.146181i
\(165\) 0 0
\(166\) 0.0606142 0.858920i 0.00470457 0.0666651i
\(167\) 11.2974 + 6.52257i 0.874220 + 0.504731i 0.868748 0.495254i \(-0.164925\pi\)
0.00547195 + 0.999985i \(0.498258\pi\)
\(168\) 0 0
\(169\) −18.6403 + 10.7620i −1.43387 + 0.827847i
\(170\) −0.0847745 0.174096i −0.00650191 0.0133526i
\(171\) 0 0
\(172\) −2.76173 22.7331i −0.210580 1.73339i
\(173\) −1.38769 0.371831i −0.105504 0.0282698i 0.205681 0.978619i \(-0.434059\pi\)
−0.311185 + 0.950349i \(0.600726\pi\)
\(174\) 0 0
\(175\) 4.64402 8.04369i 0.351055 0.608046i
\(176\) 0.891964 + 1.61891i 0.0672343 + 0.122030i
\(177\) 0 0
\(178\) 7.35859 1.42548i 0.551550 0.106844i
\(179\) 2.50772 2.50772i 0.187436 0.187436i −0.607151 0.794587i \(-0.707688\pi\)
0.794587 + 0.607151i \(0.207688\pi\)
\(180\) 0 0
\(181\) 10.8795 + 10.8795i 0.808666 + 0.808666i 0.984432 0.175766i \(-0.0562403\pi\)
−0.175766 + 0.984432i \(0.556240\pi\)
\(182\) 9.57076 14.1697i 0.709432 1.05032i
\(183\) 0 0
\(184\) 1.29963 + 25.7444i 0.0958098 + 1.89791i
\(185\) 2.90520 + 1.67732i 0.213594 + 0.123319i
\(186\) 0 0
\(187\) 0.00530922 0.0198143i 0.000388248 0.00144896i
\(188\) −3.85592 3.02053i −0.281222 0.220295i
\(189\) 0 0
\(190\) −6.45695 2.22793i −0.468436 0.161631i
\(191\) 6.59227 + 11.4182i 0.477000 + 0.826188i 0.999653 0.0263575i \(-0.00839081\pi\)
−0.522653 + 0.852546i \(0.675057\pi\)
\(192\) 0 0
\(193\) 8.71808 15.1002i 0.627541 1.08693i −0.360503 0.932758i \(-0.617395\pi\)
0.988044 0.154175i \(-0.0492718\pi\)
\(194\) −12.5652 + 10.9086i −0.902127 + 0.783194i
\(195\) 0 0
\(196\) 0.776801 5.47633i 0.0554858 0.391167i
\(197\) 8.36275 + 8.36275i 0.595822 + 0.595822i 0.939198 0.343376i \(-0.111571\pi\)
−0.343376 + 0.939198i \(0.611571\pi\)
\(198\) 0 0
\(199\) 15.6420i 1.10883i −0.832240 0.554416i \(-0.812942\pi\)
0.832240 0.554416i \(-0.187058\pi\)
\(200\) 11.3639 + 5.81772i 0.803549 + 0.411375i
\(201\) 0 0
\(202\) 8.25561 + 0.582601i 0.580863 + 0.0409916i
\(203\) 14.3151 3.83573i 1.00473 0.269216i
\(204\) 0 0
\(205\) 19.8567 + 5.32059i 1.38685 + 0.371606i
\(206\) 0.605506 1.75487i 0.0421876 0.122267i
\(207\) 0 0
\(208\) 20.1148 + 12.1564i 1.39471 + 0.842896i
\(209\) −0.361796 0.626649i −0.0250259 0.0433462i
\(210\) 0 0
\(211\) 5.00865 + 18.6925i 0.344810 + 1.28685i 0.892834 + 0.450386i \(0.148713\pi\)
−0.548024 + 0.836462i \(0.684620\pi\)
\(212\) 6.37012 + 2.71359i 0.437502 + 0.186370i
\(213\) 0 0
\(214\) 3.27960 4.85550i 0.224189 0.331915i
\(215\) 35.3170i 2.40860i
\(216\) 0 0
\(217\) 2.23159i 0.151491i
\(218\) −19.0916 12.8952i −1.29305 0.873376i
\(219\) 0 0
\(220\) 1.06446 + 2.64437i 0.0717657 + 0.178283i
\(221\) −0.0675091 0.251948i −0.00454116 0.0169478i
\(222\) 0 0
\(223\) −2.07790 3.59904i −0.139147 0.241009i 0.788027 0.615641i \(-0.211103\pi\)
−0.927174 + 0.374631i \(0.877769\pi\)
\(224\) −11.5929 1.05166i −0.774584 0.0702667i
\(225\) 0 0
\(226\) 10.1402 + 3.49880i 0.674513 + 0.232737i
\(227\) −6.22983 1.66928i −0.413488 0.110794i 0.0460768 0.998938i \(-0.485328\pi\)
−0.459565 + 0.888144i \(0.651995\pi\)
\(228\) 0 0
\(229\) −9.37974 + 2.51329i −0.619831 + 0.166083i −0.555051 0.831816i \(-0.687301\pi\)
−0.0647799 + 0.997900i \(0.520635\pi\)
\(230\) −2.79848 + 39.6553i −0.184526 + 2.61479i
\(231\) 0 0
\(232\) 6.25758 + 19.3855i 0.410830 + 1.27272i
\(233\) 22.2096i 1.45500i −0.686108 0.727499i \(-0.740682\pi\)
0.686108 0.727499i \(-0.259318\pi\)
\(234\) 0 0
\(235\) −5.34145 5.34145i −0.348438 0.348438i
\(236\) 5.94423 4.46738i 0.386937 0.290801i
\(237\) 0 0
\(238\) 0.0846917 + 0.0975527i 0.00548974 + 0.00632340i
\(239\) 4.02723 6.97537i 0.260500 0.451199i −0.705875 0.708337i \(-0.749446\pi\)
0.966375 + 0.257137i \(0.0827792\pi\)
\(240\) 0 0
\(241\) 5.07653 + 8.79280i 0.327008 + 0.566394i 0.981917 0.189314i \(-0.0606263\pi\)
−0.654909 + 0.755708i \(0.727293\pi\)
\(242\) 4.97557 14.4201i 0.319842 0.926960i
\(243\) 0 0
\(244\) 2.44099 0.296544i 0.156268 0.0189843i
\(245\) 2.20778 8.23954i 0.141050 0.526405i
\(246\) 0 0
\(247\) −7.96812 4.60040i −0.507000 0.292716i
\(248\) 3.06345 0.154649i 0.194529 0.00982020i
\(249\) 0 0
\(250\) −1.75804 1.18745i −0.111188 0.0751010i
\(251\) −11.0682 11.0682i −0.698617 0.698617i 0.265495 0.964112i \(-0.414465\pi\)
−0.964112 + 0.265495i \(0.914465\pi\)
\(252\) 0 0
\(253\) −2.97786 + 2.97786i −0.187217 + 0.187217i
\(254\) 2.86099 + 14.7690i 0.179514 + 0.926688i
\(255\) 0 0
\(256\) 0.640289 15.9872i 0.0400181 0.999199i
\(257\) 10.3807 17.9800i 0.647533 1.12156i −0.336177 0.941799i \(-0.609134\pi\)
0.983710 0.179761i \(-0.0575326\pi\)
\(258\) 0 0
\(259\) −2.16179 0.579249i −0.134327 0.0359928i
\(260\) 28.5339 + 22.3520i 1.76960 + 1.38621i
\(261\) 0 0
\(262\) −24.4815 + 11.9210i −1.51247 + 0.736484i
\(263\) 9.13436 5.27373i 0.563249 0.325192i −0.191200 0.981551i \(-0.561238\pi\)
0.754448 + 0.656359i \(0.227904\pi\)
\(264\) 0 0
\(265\) 9.24767 + 5.33914i 0.568080 + 0.327981i
\(266\) 4.54567 + 0.320789i 0.278713 + 0.0196689i
\(267\) 0 0
\(268\) −6.87571 9.14873i −0.420001 0.558848i
\(269\) 0.529850 0.529850i 0.0323055 0.0323055i −0.690770 0.723075i \(-0.742728\pi\)
0.723075 + 0.690770i \(0.242728\pi\)
\(270\) 0 0
\(271\) 14.3682 0.872804 0.436402 0.899752i \(-0.356253\pi\)
0.436402 + 0.899752i \(0.356253\pi\)
\(272\) −0.128047 + 0.123022i −0.00776402 + 0.00745929i
\(273\) 0 0
\(274\) −8.88786 10.2375i −0.536935 0.618472i
\(275\) 0.539824 + 2.01465i 0.0325526 + 0.121488i
\(276\) 0 0
\(277\) 2.19602 8.19567i 0.131946 0.492430i −0.868046 0.496485i \(-0.834624\pi\)
0.999992 + 0.00405455i \(0.00129061\pi\)
\(278\) −4.36803 8.97037i −0.261977 0.538007i
\(279\) 0 0
\(280\) −17.5526 3.76618i −1.04897 0.225072i
\(281\) −6.21827 + 3.59012i −0.370951 + 0.214169i −0.673874 0.738847i \(-0.735371\pi\)
0.302923 + 0.953015i \(0.402038\pi\)
\(282\) 0 0
\(283\) −14.8817 + 3.98753i −0.884623 + 0.237034i −0.672401 0.740187i \(-0.734737\pi\)
−0.212222 + 0.977221i \(0.568070\pi\)
\(284\) −5.14251 12.7752i −0.305152 0.758071i
\(285\) 0 0
\(286\) 0.730248 + 3.76968i 0.0431805 + 0.222906i
\(287\) −13.7147 −0.809555
\(288\) 0 0
\(289\) −16.9980 −0.999884
\(290\) 5.97460 + 30.8421i 0.350841 + 1.81111i
\(291\) 0 0
\(292\) 9.85550 + 24.4834i 0.576750 + 1.43278i
\(293\) 15.3492 4.11281i 0.896711 0.240273i 0.219108 0.975701i \(-0.429685\pi\)
0.677603 + 0.735428i \(0.263019\pi\)
\(294\) 0 0
\(295\) 9.93122 5.73379i 0.578218 0.333834i
\(296\) 0.645360 3.00776i 0.0375108 0.174822i
\(297\) 0 0
\(298\) 12.4985 + 25.6673i 0.724016 + 1.48687i
\(299\) −13.8595 + 51.7244i −0.801517 + 2.99130i
\(300\) 0 0
\(301\) 6.09824 + 22.7589i 0.351496 + 1.31180i
\(302\) −4.13981 4.76846i −0.238219 0.274394i
\(303\) 0 0
\(304\) −0.125354 + 6.26236i −0.00718954 + 0.359171i
\(305\) 3.79220 0.217141
\(306\) 0 0
\(307\) 7.37130 7.37130i 0.420702 0.420702i −0.464743 0.885446i \(-0.653853\pi\)
0.885446 + 0.464743i \(0.153853\pi\)
\(308\) −1.14256 1.52028i −0.0651035 0.0866259i
\(309\) 0 0
\(310\) 4.71876 + 0.333004i 0.268008 + 0.0189134i
\(311\) 6.23360 + 3.59897i 0.353475 + 0.204079i 0.666215 0.745760i \(-0.267913\pi\)
−0.312740 + 0.949839i \(0.601247\pi\)
\(312\) 0 0
\(313\) −9.23161 + 5.32987i −0.521801 + 0.301262i −0.737671 0.675160i \(-0.764075\pi\)
0.215870 + 0.976422i \(0.430741\pi\)
\(314\) −20.9485 + 10.2007i −1.18219 + 0.575658i
\(315\) 0 0
\(316\) −10.9090 8.54560i −0.613681 0.480727i
\(317\) −14.5196 3.89052i −0.815503 0.218513i −0.173123 0.984900i \(-0.555386\pi\)
−0.642379 + 0.766387i \(0.722053\pi\)
\(318\) 0 0
\(319\) −1.66400 + 2.88213i −0.0931662 + 0.161369i
\(320\) 3.95367 24.3566i 0.221017 1.36157i
\(321\) 0 0
\(322\) −5.04393 26.0378i −0.281087 1.45103i
\(323\) 0.0491536 0.0491536i 0.00273498 0.00273498i
\(324\) 0 0
\(325\) 18.7531 + 18.7531i 1.04023 + 1.04023i
\(326\) −8.68661 5.86729i −0.481107 0.324959i
\(327\) 0 0
\(328\) −0.950425 18.8271i −0.0524785 1.03955i
\(329\) 4.36444 + 2.51981i 0.240619 + 0.138922i
\(330\) 0 0
\(331\) 6.53309 24.3818i 0.359091 1.34015i −0.516166 0.856488i \(-0.672641\pi\)
0.875257 0.483658i \(-0.160692\pi\)
\(332\) −1.20883 + 0.146855i −0.0663431 + 0.00805969i
\(333\) 0 0
\(334\) 6.01745 17.4396i 0.329260 0.954255i
\(335\) −8.82485 15.2851i −0.482153 0.835113i
\(336\) 0 0
\(337\) 1.80217 3.12146i 0.0981707 0.170037i −0.812757 0.582603i \(-0.802034\pi\)
0.910928 + 0.412566i \(0.135368\pi\)
\(338\) 19.9554 + 22.9858i 1.08543 + 1.25026i
\(339\) 0 0
\(340\) −0.218915 + 0.164525i −0.0118724 + 0.00892265i
\(341\) 0.354350 + 0.354350i 0.0191891 + 0.0191891i
\(342\) 0 0
\(343\) 20.0953i 1.08505i
\(344\) −30.8200 + 9.94861i −1.66170 + 0.536393i
\(345\) 0 0
\(346\) −0.143023 + 2.02668i −0.00768899 + 0.108955i
\(347\) −15.4243 + 4.13293i −0.828020 + 0.221867i −0.647850 0.761768i \(-0.724331\pi\)
−0.180170 + 0.983635i \(0.557665\pi\)
\(348\) 0 0
\(349\) −15.1326 4.05477i −0.810029 0.217047i −0.170047 0.985436i \(-0.554392\pi\)
−0.639983 + 0.768389i \(0.721058\pi\)
\(350\) −12.4169 4.28438i −0.663712 0.229010i
\(351\) 0 0
\(352\) 2.00780 1.67382i 0.107016 0.0892149i
\(353\) −2.05577 3.56070i −0.109418 0.189517i 0.806117 0.591756i \(-0.201565\pi\)
−0.915534 + 0.402239i \(0.868232\pi\)
\(354\) 0 0
\(355\) −5.49691 20.5147i −0.291746 1.08881i
\(356\) −3.95827 9.83330i −0.209788 0.521164i
\(357\) 0 0
\(358\) −4.15619 2.80726i −0.219662 0.148368i
\(359\) 20.1902i 1.06560i 0.846242 + 0.532800i \(0.178860\pi\)
−0.846242 + 0.532800i \(0.821140\pi\)
\(360\) 0 0
\(361\) 16.5479i 0.870945i
\(362\) 12.1790 18.0312i 0.640114 0.947699i
\(363\) 0 0
\(364\) −22.2473 9.47706i −1.16608 0.496733i
\(365\) 10.5347 + 39.3160i 0.551411 + 2.05789i
\(366\) 0 0
\(367\) 11.2398 + 19.4679i 0.586714 + 1.01622i 0.994659 + 0.103212i \(0.0329120\pi\)
−0.407946 + 0.913006i \(0.633755\pi\)
\(368\) 35.3941 8.72852i 1.84505 0.455006i
\(369\) 0 0
\(370\) 1.54742 4.48471i 0.0804466 0.233149i
\(371\) −6.88128 1.84383i −0.357258 0.0957270i
\(372\) 0 0
\(373\) −25.6543 + 6.87405i −1.32833 + 0.355925i −0.852092 0.523392i \(-0.824666\pi\)
−0.476237 + 0.879317i \(0.658000\pi\)
\(374\) −0.0289381 0.00204217i −0.00149636 0.000105598i
\(375\) 0 0
\(376\) −3.15665 + 6.16596i −0.162792 + 0.317985i
\(377\) 42.3171i 2.17944i
\(378\) 0 0
\(379\) −6.62881 6.62881i −0.340499 0.340499i 0.516056 0.856555i \(-0.327400\pi\)
−0.856555 + 0.516056i \(0.827400\pi\)
\(380\) −1.35663 + 9.56407i −0.0695938 + 0.490626i
\(381\) 0 0
\(382\) 14.0800 12.2237i 0.720394 0.625419i
\(383\) −1.98902 + 3.44509i −0.101634 + 0.176036i −0.912358 0.409393i \(-0.865741\pi\)
0.810724 + 0.585429i \(0.199074\pi\)
\(384\) 0 0
\(385\) −1.46646 2.53998i −0.0747376 0.129449i
\(386\) −23.3099 8.04293i −1.18644 0.409374i
\(387\) 0 0
\(388\) 18.5250 + 14.5116i 0.940467 + 0.736714i
\(389\) −1.21847 + 4.54738i −0.0617787 + 0.230561i −0.989911 0.141688i \(-0.954747\pi\)
0.928133 + 0.372250i \(0.121414\pi\)
\(390\) 0 0
\(391\) −0.350370 0.202286i −0.0177190 0.0102301i
\(392\) −7.81228 + 0.394379i −0.394580 + 0.0199191i
\(393\) 0 0
\(394\) 9.36166 13.8601i 0.471634 0.698261i
\(395\) −15.1119 15.1119i −0.760360 0.760360i
\(396\) 0 0
\(397\) −18.1361 + 18.1361i −0.910223 + 0.910223i −0.996289 0.0860661i \(-0.972570\pi\)
0.0860661 + 0.996289i \(0.472570\pi\)
\(398\) −21.7174 + 4.20700i −1.08859 + 0.210878i
\(399\) 0 0
\(400\) 5.02095 17.3424i 0.251047 0.867119i
\(401\) 2.47526 4.28727i 0.123608 0.214096i −0.797580 0.603214i \(-0.793887\pi\)
0.921188 + 0.389118i \(0.127220\pi\)
\(402\) 0 0
\(403\) 6.15492 + 1.64921i 0.306599 + 0.0821528i
\(404\) −1.41151 11.6188i −0.0702253 0.578057i
\(405\) 0 0
\(406\) −9.17568 18.8435i −0.455381 0.935189i
\(407\) 0.435242 0.251287i 0.0215742 0.0124558i
\(408\) 0 0
\(409\) −12.4390 7.18164i −0.615067 0.355109i 0.159879 0.987137i \(-0.448890\pi\)
−0.774946 + 0.632027i \(0.782223\pi\)
\(410\) 2.04655 29.0001i 0.101072 1.43221i
\(411\) 0 0
\(412\) −2.59931 0.368705i −0.128059 0.0181648i
\(413\) −5.40979 + 5.40979i −0.266199 + 0.266199i
\(414\) 0 0
\(415\) −1.87798 −0.0921862
\(416\) 11.4680 31.1970i 0.562266 1.52956i
\(417\) 0 0
\(418\) −0.772734 + 0.670859i −0.0377956 + 0.0328128i
\(419\) 6.54483 + 24.4257i 0.319736 + 1.19327i 0.919499 + 0.393093i \(0.128595\pi\)
−0.599763 + 0.800178i \(0.704738\pi\)
\(420\) 0 0
\(421\) 1.33131 4.96853i 0.0648842 0.242151i −0.925865 0.377853i \(-0.876662\pi\)
0.990750 + 0.135702i \(0.0433290\pi\)
\(422\) 24.6057 11.9815i 1.19779 0.583250i
\(423\) 0 0
\(424\) 2.05427 9.57413i 0.0997643 0.464961i
\(425\) −0.173526 + 0.100185i −0.00841723 + 0.00485969i
\(426\) 0 0
\(427\) −2.44376 + 0.654803i −0.118262 + 0.0316882i
\(428\) −7.62346 3.24749i −0.368494 0.156974i
\(429\) 0 0
\(430\) −49.0343 + 9.49872i −2.36464 + 0.458069i
\(431\) −20.0912 −0.967760 −0.483880 0.875134i \(-0.660773\pi\)
−0.483880 + 0.875134i \(0.660773\pi\)
\(432\) 0 0
\(433\) 21.8262 1.04890 0.524449 0.851442i \(-0.324271\pi\)
0.524449 + 0.851442i \(0.324271\pi\)
\(434\) −3.09835 + 0.600200i −0.148726 + 0.0288105i
\(435\) 0 0
\(436\) −12.7690 + 29.9751i −0.611524 + 1.43555i
\(437\) −13.7848 + 3.69362i −0.659415 + 0.176690i
\(438\) 0 0
\(439\) 25.7554 14.8699i 1.22924 0.709700i 0.262367 0.964968i \(-0.415497\pi\)
0.966870 + 0.255268i \(0.0821636\pi\)
\(440\) 3.38516 2.18912i 0.161381 0.104362i
\(441\) 0 0
\(442\) −0.331648 + 0.161493i −0.0157749 + 0.00768142i
\(443\) 9.06164 33.8185i 0.430532 1.60677i −0.321007 0.947077i \(-0.604021\pi\)
0.751539 0.659689i \(-0.229312\pi\)
\(444\) 0 0
\(445\) −4.23106 15.7905i −0.200571 0.748543i
\(446\) −4.43805 + 3.85295i −0.210148 + 0.182442i
\(447\) 0 0
\(448\) 1.65786 + 16.3785i 0.0783264 + 0.773810i
\(449\) −27.6805 −1.30633 −0.653163 0.757217i \(-0.726558\pi\)
−0.653163 + 0.757217i \(0.726558\pi\)
\(450\) 0 0
\(451\) 2.17773 2.17773i 0.102545 0.102545i
\(452\) 2.13049 15.0196i 0.100210 0.706465i
\(453\) 0 0
\(454\) −0.642082 + 9.09848i −0.0301344 + 0.427013i
\(455\) −32.2970 18.6467i −1.51411 0.874169i
\(456\) 0 0
\(457\) 13.8114 7.97402i 0.646070 0.373009i −0.140879 0.990027i \(-0.544993\pi\)
0.786949 + 0.617018i \(0.211659\pi\)
\(458\) 6.01220 + 12.3469i 0.280932 + 0.576932i
\(459\) 0 0
\(460\) 55.8102 6.78009i 2.60216 0.316123i
\(461\) 18.1773 + 4.87059i 0.846600 + 0.226846i 0.655943 0.754811i \(-0.272271\pi\)
0.190658 + 0.981657i \(0.438938\pi\)
\(462\) 0 0
\(463\) 6.07529 10.5227i 0.282343 0.489032i −0.689619 0.724173i \(-0.742222\pi\)
0.971961 + 0.235141i \(0.0755552\pi\)
\(464\) 25.2318 13.9019i 1.17136 0.645378i
\(465\) 0 0
\(466\) −30.8359 + 5.97340i −1.42844 + 0.276712i
\(467\) 15.9698 15.9698i 0.738992 0.738992i −0.233391 0.972383i \(-0.574982\pi\)
0.972383 + 0.233391i \(0.0749822\pi\)
\(468\) 0 0
\(469\) 8.32618 + 8.32618i 0.384467 + 0.384467i
\(470\) −5.97947 + 8.85270i −0.275812 + 0.408345i
\(471\) 0 0
\(472\) −7.80126 7.05146i −0.359082 0.324570i
\(473\) −4.58216 2.64551i −0.210688 0.121641i
\(474\) 0 0
\(475\) −1.82931 + 6.82710i −0.0839347 + 0.313249i
\(476\) 0.112664 0.143823i 0.00516395 0.00659214i
\(477\) 0 0
\(478\) −10.7678 3.71536i −0.492507 0.169936i
\(479\) 9.27240 + 16.0603i 0.423667 + 0.733813i 0.996295 0.0860026i \(-0.0274094\pi\)
−0.572628 + 0.819815i \(0.694076\pi\)
\(480\) 0 0
\(481\) 3.19523 5.53430i 0.145690 0.252343i
\(482\) 10.8426 9.41314i 0.493866 0.428757i
\(483\) 0 0
\(484\) −21.3591 3.02973i −0.970870 0.137715i
\(485\) 25.6620 + 25.6620i 1.16525 + 1.16525i
\(486\) 0 0
\(487\) 6.58835i 0.298547i 0.988796 + 0.149273i \(0.0476934\pi\)
−0.988796 + 0.149273i \(0.952307\pi\)
\(488\) −1.06824 3.30932i −0.0483570 0.149806i
\(489\) 0 0
\(490\) −12.0336 0.849214i −0.543623 0.0383636i
\(491\) 4.86361 1.30320i 0.219491 0.0588126i −0.147397 0.989077i \(-0.547090\pi\)
0.366889 + 0.930265i \(0.380423\pi\)
\(492\) 0 0
\(493\) −0.308819 0.0827478i −0.0139085 0.00372678i
\(494\) −4.24413 + 12.3003i −0.190953 + 0.553415i
\(495\) 0 0
\(496\) −1.03865 4.21171i −0.0466366 0.189111i
\(497\) 7.08461 + 12.2709i 0.317788 + 0.550425i
\(498\) 0 0
\(499\) 5.62008 + 20.9744i 0.251589 + 0.938944i 0.969956 + 0.243279i \(0.0782232\pi\)
−0.718367 + 0.695664i \(0.755110\pi\)
\(500\) −1.17583 + 2.76024i −0.0525845 + 0.123442i
\(501\) 0 0
\(502\) −12.3902 + 18.3439i −0.553003 + 0.818730i
\(503\) 9.04140i 0.403136i 0.979475 + 0.201568i \(0.0646037\pi\)
−0.979475 + 0.201568i \(0.935396\pi\)
\(504\) 0 0
\(505\) 18.0504i 0.803232i
\(506\) 4.93539 + 3.33356i 0.219405 + 0.148195i
\(507\) 0 0
\(508\) 19.7358 7.94440i 0.875635 0.352476i
\(509\) −3.80331 14.1941i −0.168579 0.629144i −0.997557 0.0698626i \(-0.977744\pi\)
0.828978 0.559281i \(-0.188923\pi\)
\(510\) 0 0
\(511\) −13.5775 23.5169i −0.600633 1.04033i
\(512\) −22.3689 + 3.41087i −0.988573 + 0.150740i
\(513\) 0 0
\(514\) −27.7554 9.57684i −1.22424 0.422416i
\(515\) −3.91086 1.04791i −0.172333 0.0461765i
\(516\) 0 0
\(517\) −1.09313 + 0.292904i −0.0480760 + 0.0128819i
\(518\) −0.222806 + 3.15722i −0.00978953 + 0.138720i
\(519\) 0 0
\(520\) 23.3593 45.6283i 1.02437 2.00093i
\(521\) 7.25761i 0.317962i 0.987282 + 0.158981i \(0.0508208\pi\)
−0.987282 + 0.158981i \(0.949179\pi\)
\(522\) 0 0
\(523\) −19.0736 19.0736i −0.834028 0.834028i 0.154037 0.988065i \(-0.450773\pi\)
−0.988065 + 0.154037i \(0.950773\pi\)
\(524\) 23.1356 + 30.7840i 1.01069 + 1.34480i
\(525\) 0 0
\(526\) −9.77879 11.2638i −0.426376 0.491124i
\(527\) −0.0240710 + 0.0416922i −0.00104855 + 0.00181614i
\(528\) 0 0
\(529\) 30.0291 + 52.0119i 1.30561 + 2.26139i
\(530\) 4.92567 14.2755i 0.213957 0.620087i
\(531\) 0 0
\(532\) −0.777200 6.39750i −0.0336959 0.277367i
\(533\) 10.1355 37.8264i 0.439019 1.63844i
\(534\) 0 0
\(535\) −11.0672 6.38963i −0.478476 0.276248i
\(536\) −10.8529 + 12.0069i −0.468772 + 0.518617i
\(537\) 0 0
\(538\) −0.878151 0.593139i −0.0378598 0.0255720i
\(539\) −0.903648 0.903648i −0.0389229 0.0389229i
\(540\) 0 0
\(541\) 12.1246 12.1246i 0.521279 0.521279i −0.396679 0.917957i \(-0.629837\pi\)
0.917957 + 0.396679i \(0.129837\pi\)
\(542\) −3.86440 19.9488i −0.165990 0.856875i
\(543\) 0 0
\(544\) 0.205243 + 0.144694i 0.00879972 + 0.00620371i
\(545\) −25.1237 + 43.5156i −1.07618 + 1.86400i
\(546\) 0 0
\(547\) 37.1224 + 9.94693i 1.58724 + 0.425300i 0.941158 0.337967i \(-0.109739\pi\)
0.646083 + 0.763267i \(0.276406\pi\)
\(548\) −11.8234 + 15.0934i −0.505070 + 0.644757i
\(549\) 0 0
\(550\) 2.65196 1.29135i 0.113080 0.0550632i
\(551\) −9.76675 + 5.63884i −0.416078 + 0.240223i
\(552\) 0 0
\(553\) 12.3477 + 7.12897i 0.525079 + 0.303155i
\(554\) −11.9695 0.844692i −0.508536 0.0358875i
\(555\) 0 0
\(556\) −11.2797 + 8.47722i −0.478365 + 0.359514i
\(557\) 7.00897 7.00897i 0.296979 0.296979i −0.542850 0.839830i \(-0.682655\pi\)
0.839830 + 0.542850i \(0.182655\pi\)
\(558\) 0 0
\(559\) −67.2778 −2.84555
\(560\) −0.508094 + 25.3830i −0.0214709 + 1.07263i
\(561\) 0 0
\(562\) 6.65697 + 7.66788i 0.280807 + 0.323450i
\(563\) −1.62398 6.06076i −0.0684424 0.255430i 0.923224 0.384262i \(-0.125544\pi\)
−0.991667 + 0.128831i \(0.958877\pi\)
\(564\) 0 0
\(565\) 6.05515 22.5981i 0.254742 0.950711i
\(566\) 9.53881 + 19.5893i 0.400946 + 0.823399i
\(567\) 0 0
\(568\) −16.3541 + 10.5759i −0.686202 + 0.443753i
\(569\) 5.33529 3.08033i 0.223667 0.129134i −0.383980 0.923341i \(-0.625447\pi\)
0.607647 + 0.794207i \(0.292113\pi\)
\(570\) 0 0
\(571\) 18.0529 4.83727i 0.755491 0.202433i 0.139539 0.990217i \(-0.455438\pi\)
0.615952 + 0.787783i \(0.288771\pi\)
\(572\) 5.03744 2.02776i 0.210626 0.0847847i
\(573\) 0 0
\(574\) 3.68866 + 19.0416i 0.153962 + 0.794780i
\(575\) 41.1357 1.71548
\(576\) 0 0
\(577\) 11.2964 0.470277 0.235138 0.971962i \(-0.424446\pi\)
0.235138 + 0.971962i \(0.424446\pi\)
\(578\) 4.57172 + 23.6001i 0.190158 + 0.981635i
\(579\) 0 0
\(580\) 41.2143 16.5903i 1.71133 0.688875i
\(581\) 1.21020 0.324272i 0.0502076 0.0134531i
\(582\) 0 0
\(583\) 1.38544 0.799884i 0.0573790 0.0331278i
\(584\) 31.3422 20.2684i 1.29695 0.838711i
\(585\) 0 0
\(586\) −9.83850 20.2047i −0.406425 0.834650i
\(587\) 9.93836 37.0905i 0.410200 1.53089i −0.384059 0.923309i \(-0.625474\pi\)
0.794259 0.607579i \(-0.207859\pi\)
\(588\) 0 0
\(589\) 0.439521 + 1.64031i 0.0181101 + 0.0675879i
\(590\) −10.6319 12.2464i −0.437707 0.504176i
\(591\) 0 0
\(592\) −4.34955 0.0870653i −0.178766 0.00357836i
\(593\) −7.39166 −0.303539 −0.151770 0.988416i \(-0.548497\pi\)
−0.151770 + 0.988416i \(0.548497\pi\)
\(594\) 0 0
\(595\) 0.199233 0.199233i 0.00816776 0.00816776i
\(596\) 32.2751 24.2563i 1.32204 0.993576i
\(597\) 0 0
\(598\) 75.5419 + 5.33101i 3.08914 + 0.218001i
\(599\) −22.9017 13.2223i −0.935739 0.540249i −0.0471171 0.998889i \(-0.515003\pi\)
−0.888622 + 0.458640i \(0.848337\pi\)
\(600\) 0 0
\(601\) −33.6284 + 19.4154i −1.37173 + 0.791970i −0.991146 0.132775i \(-0.957611\pi\)
−0.380587 + 0.924745i \(0.624278\pi\)
\(602\) 29.9584 14.5880i 1.22101 0.594561i
\(603\) 0 0
\(604\) −5.50713 + 7.03022i −0.224082 + 0.286056i
\(605\) −32.1364 8.61091i −1.30653 0.350083i
\(606\) 0 0
\(607\) 1.86964 3.23831i 0.0758863 0.131439i −0.825585 0.564278i \(-0.809155\pi\)
0.901471 + 0.432839i \(0.142488\pi\)
\(608\) 8.72839 1.51026i 0.353983 0.0612489i
\(609\) 0 0
\(610\) −1.01993 5.26510i −0.0412959 0.213178i
\(611\) −10.1753 + 10.1753i −0.411648 + 0.411648i
\(612\) 0 0
\(613\) −4.21378 4.21378i −0.170193 0.170193i 0.616871 0.787064i \(-0.288400\pi\)
−0.787064 + 0.616871i \(0.788400\pi\)
\(614\) −12.2169 8.25178i −0.493034 0.333015i
\(615\) 0 0
\(616\) −1.80346 + 1.99522i −0.0726635 + 0.0803899i
\(617\) 19.3833 + 11.1910i 0.780343 + 0.450531i 0.836552 0.547888i \(-0.184568\pi\)
−0.0562088 + 0.998419i \(0.517901\pi\)
\(618\) 0 0
\(619\) −4.10361 + 15.3149i −0.164938 + 0.615557i 0.833110 + 0.553107i \(0.186558\pi\)
−0.998048 + 0.0624496i \(0.980109\pi\)
\(620\) −0.806794 6.64110i −0.0324016 0.266713i
\(621\) 0 0
\(622\) 3.32026 9.62271i 0.133130 0.385836i
\(623\) 5.45314 + 9.44511i 0.218475 + 0.378410i
\(624\) 0 0
\(625\) −13.5976 + 23.5518i −0.543905 + 0.942071i
\(626\) 9.88290 + 11.3837i 0.395000 + 0.454984i
\(627\) 0 0
\(628\) 19.7969 + 26.3415i 0.789982 + 1.05114i
\(629\) 0.0341399 + 0.0341399i 0.00136125 + 0.00136125i
\(630\) 0 0
\(631\) 38.2887i 1.52425i 0.647429 + 0.762125i \(0.275844\pi\)
−0.647429 + 0.762125i \(0.724156\pi\)
\(632\) −8.93068 + 17.4445i −0.355243 + 0.693906i
\(633\) 0 0
\(634\) −1.49647 + 21.2054i −0.0594326 + 0.842176i
\(635\) 31.6922 8.49189i 1.25767 0.336990i
\(636\) 0 0
\(637\) −15.6960 4.20574i −0.621900 0.166638i
\(638\) 4.44911 + 1.53514i 0.176142 + 0.0607767i
\(639\) 0 0
\(640\) −34.8801 + 1.06154i −1.37876 + 0.0419611i
\(641\) 8.82135 + 15.2790i 0.348422 + 0.603485i 0.985969 0.166926i \(-0.0533841\pi\)
−0.637547 + 0.770412i \(0.720051\pi\)
\(642\) 0 0
\(643\) 7.49737 + 27.9805i 0.295667 + 1.10345i 0.940686 + 0.339278i \(0.110183\pi\)
−0.645019 + 0.764167i \(0.723150\pi\)
\(644\) −34.7943 + 14.0060i −1.37109 + 0.551914i
\(645\) 0 0
\(646\) −0.0814652 0.0550249i −0.00320520 0.00216492i
\(647\) 5.73725i 0.225555i 0.993620 + 0.112777i \(0.0359747\pi\)
−0.993620 + 0.112777i \(0.964025\pi\)
\(648\) 0 0
\(649\) 1.71802i 0.0674380i
\(650\) 20.9931 31.0806i 0.823417 1.21908i
\(651\) 0 0
\(652\) −5.80985 + 13.6386i −0.227531 + 0.534127i
\(653\) −10.0743 37.5980i −0.394239 1.47132i −0.823072 0.567938i \(-0.807741\pi\)
0.428832 0.903384i \(-0.358925\pi\)
\(654\) 0 0
\(655\) 29.6942 + 51.4318i 1.16025 + 2.00961i
\(656\) −25.8839 + 6.38322i −1.01060 + 0.249223i
\(657\) 0 0
\(658\) 2.32467 6.73732i 0.0906251 0.262648i
\(659\) 38.3072 + 10.2644i 1.49224 + 0.399844i 0.910492 0.413528i \(-0.135703\pi\)
0.581745 + 0.813371i \(0.302370\pi\)
\(660\) 0 0
\(661\) 5.49909 1.47348i 0.213890 0.0573116i −0.150283 0.988643i \(-0.548018\pi\)
0.364173 + 0.931331i \(0.381352\pi\)
\(662\) −35.6089 2.51293i −1.38398 0.0976678i
\(663\) 0 0
\(664\) 0.529015 + 1.63885i 0.0205298 + 0.0635995i
\(665\) 9.93883i 0.385411i
\(666\) 0 0
\(667\) 46.4121 + 46.4121i 1.79708 + 1.79708i
\(668\) −25.8317 3.66415i −0.999458 0.141770i
\(669\) 0 0
\(670\) −18.8484 + 16.3635i −0.728176 + 0.632175i
\(671\) 0.284064 0.492013i 0.0109662 0.0189940i
\(672\) 0 0
\(673\) −2.23206 3.86604i −0.0860396 0.149025i 0.819794 0.572658i \(-0.194088\pi\)
−0.905834 + 0.423633i \(0.860754\pi\)
\(674\) −4.81855 1.66261i −0.185604 0.0640414i
\(675\) 0 0
\(676\) 26.5464 33.8883i 1.02102 1.30340i
\(677\) −2.16066 + 8.06369i −0.0830409 + 0.309913i −0.994936 0.100511i \(-0.967952\pi\)
0.911895 + 0.410423i \(0.134619\pi\)
\(678\) 0 0
\(679\) −20.9681 12.1060i −0.804683 0.464584i
\(680\) 0.287306 + 0.259693i 0.0110177 + 0.00995876i
\(681\) 0 0
\(682\) 0.396676 0.587284i 0.0151895 0.0224883i
\(683\) −3.00972 3.00972i −0.115164 0.115164i 0.647177 0.762340i \(-0.275950\pi\)
−0.762340 + 0.647177i \(0.775950\pi\)
\(684\) 0 0
\(685\) −20.9082 + 20.9082i −0.798863 + 0.798863i
\(686\) 27.9004 5.40475i 1.06524 0.206354i
\(687\) 0 0
\(688\) 22.1019 + 40.1148i 0.842627 + 1.52936i
\(689\) 10.1709 17.6165i 0.387480 0.671135i
\(690\) 0 0
\(691\) −28.5847 7.65924i −1.08741 0.291371i −0.329783 0.944057i \(-0.606976\pi\)
−0.757629 + 0.652686i \(0.773642\pi\)
\(692\) 2.85232 0.346514i 0.108429 0.0131725i
\(693\) 0 0
\(694\) 9.88662 + 20.3036i 0.375291 + 0.770713i
\(695\) −18.8453 + 10.8804i −0.714844 + 0.412715i
\(696\) 0 0
\(697\) 0.256228 + 0.147933i 0.00970532 + 0.00560337i
\(698\) −1.55965 + 22.1007i −0.0590337 + 0.836524i
\(699\) 0 0
\(700\) −2.60885 + 18.3920i −0.0986052 + 0.695152i
\(701\) 1.29990 1.29990i 0.0490966 0.0490966i −0.682132 0.731229i \(-0.738947\pi\)
0.731229 + 0.682132i \(0.238947\pi\)
\(702\) 0 0
\(703\) 1.70309 0.0642331
\(704\) −2.86395 2.33745i −0.107939 0.0880960i
\(705\) 0 0
\(706\) −4.39077 + 3.81191i −0.165249 + 0.143463i
\(707\) 3.11678 + 11.6320i 0.117219 + 0.437466i
\(708\) 0 0
\(709\) 9.80720 36.6010i 0.368317 1.37458i −0.494551 0.869149i \(-0.664667\pi\)
0.862868 0.505429i \(-0.168666\pi\)
\(710\) −27.0043 + 13.1495i −1.01345 + 0.493491i
\(711\) 0 0
\(712\) −12.5880 + 8.14040i −0.471755 + 0.305074i
\(713\) 8.55933 4.94173i 0.320550 0.185069i
\(714\) 0 0
\(715\) 8.08922 2.16750i 0.302520 0.0810599i
\(716\) −2.77978 + 6.52550i −0.103885 + 0.243869i
\(717\) 0 0
\(718\) 28.0322 5.43028i 1.04615 0.202656i
\(719\) −5.11125 −0.190617 −0.0953087 0.995448i \(-0.530384\pi\)
−0.0953087 + 0.995448i \(0.530384\pi\)
\(720\) 0 0
\(721\) 2.70117 0.100597
\(722\) 22.9752 4.45067i 0.855049 0.165637i
\(723\) 0 0
\(724\) −28.3102 12.0598i −1.05214 0.448198i
\(725\) 31.3997 8.41353i 1.16616 0.312471i
\(726\) 0 0
\(727\) −18.6355 + 10.7592i −0.691154 + 0.399038i −0.804044 0.594570i \(-0.797322\pi\)
0.112890 + 0.993607i \(0.463989\pi\)
\(728\) −7.17444 + 33.4371i −0.265902 + 1.23926i
\(729\) 0 0
\(730\) 51.7531 25.2007i 1.91547 0.932719i
\(731\) 0.131557 0.490976i 0.00486580 0.0181594i
\(732\) 0 0
\(733\) −0.799079 2.98220i −0.0295147 0.110150i 0.949597 0.313473i \(-0.101493\pi\)
−0.979112 + 0.203323i \(0.934826\pi\)
\(734\) 24.0063 20.8414i 0.886090 0.769271i
\(735\) 0 0
\(736\) −21.6382 46.7937i −0.797593 1.72484i
\(737\) −2.64419 −0.0973999
\(738\) 0 0
\(739\) 23.9990 23.9990i 0.882818 0.882818i −0.111002 0.993820i \(-0.535406\pi\)
0.993820 + 0.111002i \(0.0354060\pi\)
\(740\) −6.64277 0.942257i −0.244193 0.0346381i
\(741\) 0 0
\(742\) −0.709223 + 10.0499i −0.0260364 + 0.368943i
\(743\) −14.4499 8.34266i −0.530116 0.306062i 0.210948 0.977497i \(-0.432345\pi\)
−0.741064 + 0.671435i \(0.765678\pi\)
\(744\) 0 0
\(745\) 53.9230 31.1325i 1.97559 1.14061i
\(746\) 16.4438 + 33.7697i 0.602051 + 1.23640i
\(747\) 0 0
\(748\) 0.00494772 + 0.0407271i 0.000180907 + 0.00148913i
\(749\) 8.23519 + 2.20661i 0.300907 + 0.0806278i
\(750\) 0 0
\(751\) 17.1635 29.7281i 0.626305 1.08479i −0.361982 0.932185i \(-0.617900\pi\)
0.988287 0.152607i \(-0.0487669\pi\)
\(752\) 9.40983 + 2.72433i 0.343141 + 0.0993460i
\(753\) 0 0
\(754\) 58.7531 11.3814i 2.13966 0.414487i
\(755\) −9.73869 + 9.73869i −0.354427 + 0.354427i
\(756\) 0 0
\(757\) −24.0162 24.0162i −0.872884 0.872884i 0.119902 0.992786i \(-0.461742\pi\)
−0.992786 + 0.119902i \(0.961742\pi\)
\(758\) −7.42061 + 10.9863i −0.269529 + 0.399041i
\(759\) 0 0
\(760\) 13.6437 0.688757i 0.494907 0.0249838i
\(761\) −13.2713 7.66221i −0.481086 0.277755i 0.239783 0.970826i \(-0.422924\pi\)
−0.720869 + 0.693072i \(0.756257\pi\)
\(762\) 0 0
\(763\) 8.67629 32.3804i 0.314103 1.17225i
\(764\) −20.7583 16.2610i −0.751010 0.588303i
\(765\) 0 0
\(766\) 5.31813 + 1.83499i 0.192152 + 0.0663009i
\(767\) −10.9227 18.9186i −0.394395 0.683112i
\(768\) 0 0
\(769\) 20.6394 35.7485i 0.744276 1.28912i −0.206256 0.978498i \(-0.566128\pi\)
0.950532 0.310626i \(-0.100539\pi\)
\(770\) −3.13210 + 2.71917i −0.112873 + 0.0979923i
\(771\) 0 0
\(772\) −4.89750 + 34.5267i −0.176265 + 1.24264i
\(773\) −36.3711 36.3711i −1.30818 1.30818i −0.922730 0.385448i \(-0.874047\pi\)
−0.385448 0.922730i \(-0.625953\pi\)
\(774\) 0 0
\(775\) 4.89492i 0.175831i
\(776\) 15.1655 29.6232i 0.544410 1.06341i
\(777\) 0 0
\(778\) 6.64131 + 0.468679i 0.238103 + 0.0168030i
\(779\) 10.0809 2.70117i 0.361185 0.0967793i
\(780\) 0 0
\(781\) −3.07342 0.823519i −0.109975 0.0294678i
\(782\) −0.186621 + 0.540861i −0.00667355 + 0.0193412i
\(783\) 0 0
\(784\) 2.64872 + 10.7405i 0.0945970 + 0.383590i
\(785\) 25.4089 + 44.0096i 0.906883 + 1.57077i
\(786\) 0 0
\(787\) −7.98650 29.8060i −0.284688 1.06247i −0.949067 0.315074i \(-0.897971\pi\)
0.664379 0.747396i \(-0.268696\pi\)
\(788\) −21.7613 9.27001i −0.775213 0.330230i
\(789\) 0 0
\(790\) −16.9169 + 25.0458i −0.601877 + 0.891089i
\(791\) 15.6082i 0.554963i
\(792\) 0 0
\(793\) 7.22401i 0.256532i
\(794\) 30.0580 + 20.3024i 1.06672 + 0.720504i
\(795\) 0 0
\(796\) 11.6820 + 29.0210i 0.414059 + 1.02862i
\(797\) −6.90917 25.7854i −0.244735 0.913364i −0.973516 0.228617i \(-0.926580\pi\)
0.728781 0.684747i \(-0.240087\pi\)
\(798\) 0 0
\(799\) −0.0543596 0.0941536i −0.00192311 0.00333092i
\(800\) −25.4286 2.30677i −0.899037 0.0815566i
\(801\) 0 0
\(802\) −6.61819 2.28357i −0.233697 0.0806356i
\(803\) 5.89013 + 1.57826i 0.207858 + 0.0556954i
\(804\) 0 0
\(805\) −55.8735 + 14.9712i −1.96928 + 0.527667i
\(806\) 0.634361 8.98908i 0.0223444 0.316627i
\(807\) 0 0
\(808\) −15.7520 + 5.08469i −0.554152 + 0.178879i
\(809\) 41.9379i 1.47446i −0.675644 0.737228i \(-0.736134\pi\)
0.675644 0.737228i \(-0.263866\pi\)
\(810\) 0 0
\(811\) 0.250947 + 0.250947i 0.00881196 + 0.00881196i 0.711499 0.702687i \(-0.248017\pi\)
−0.702687 + 0.711499i \(0.748017\pi\)
\(812\) −23.6946 + 17.8076i −0.831517 + 0.624925i
\(813\) 0 0
\(814\) −0.465949 0.536706i −0.0163315 0.0188116i
\(815\) −11.4312 + 19.7994i −0.400418 + 0.693544i
\(816\) 0 0
\(817\) −8.96490 15.5277i −0.313642 0.543244i
\(818\) −6.62548 + 19.2018i −0.231654 + 0.671377i
\(819\) 0 0
\(820\) −40.8143 + 4.95832i −1.42530 + 0.173152i
\(821\) 5.03635 18.7959i 0.175770 0.655982i −0.820650 0.571432i \(-0.806388\pi\)
0.996419 0.0845497i \(-0.0269452\pi\)
\(822\) 0 0
\(823\) −34.7295 20.0511i −1.21059 0.698936i −0.247705 0.968836i \(-0.579676\pi\)
−0.962889 + 0.269899i \(0.913010\pi\)
\(824\) 0.187190 + 3.70806i 0.00652107 + 0.129176i
\(825\) 0 0
\(826\) 8.96597 + 6.05598i 0.311966 + 0.210714i
\(827\) 39.0429 + 39.0429i 1.35765 + 1.35765i 0.876801 + 0.480853i \(0.159673\pi\)
0.480853 + 0.876801i \(0.340327\pi\)
\(828\) 0 0
\(829\) −18.5103 + 18.5103i −0.642891 + 0.642891i −0.951265 0.308374i \(-0.900215\pi\)
0.308374 + 0.951265i \(0.400215\pi\)
\(830\) 0.505092 + 2.60739i 0.0175320 + 0.0905037i
\(831\) 0 0
\(832\) −46.3984 7.53161i −1.60858 0.261112i
\(833\) 0.0613849 0.106322i 0.00212686 0.00368383i
\(834\) 0 0
\(835\) −38.8656 10.4140i −1.34500 0.360392i
\(836\) 1.13925 + 0.892435i 0.0394019 + 0.0308655i
\(837\) 0 0
\(838\) 32.1524 15.6563i 1.11069 0.540837i
\(839\) −9.12331 + 5.26735i −0.314972 + 0.181849i −0.649149 0.760661i \(-0.724875\pi\)
0.334177 + 0.942510i \(0.391542\pi\)
\(840\) 0 0
\(841\) 19.8053 + 11.4346i 0.682942 + 0.394297i
\(842\) −7.25638 0.512085i −0.250072 0.0176476i
\(843\) 0 0
\(844\) −23.2530 30.9401i −0.800401 1.06500i
\(845\) 46.9442 46.9442i 1.61493 1.61493i
\(846\) 0 0
\(847\) 22.1961 0.762667
\(848\) −13.8453 0.277141i −0.475448 0.00951707i
\(849\) 0 0
\(850\) 0.185768 + 0.213978i 0.00637179 + 0.00733939i
\(851\) −2.56542 9.57429i −0.0879416 0.328203i
\(852\) 0 0
\(853\) 8.50035 31.7237i 0.291046 1.08620i −0.653260 0.757133i \(-0.726599\pi\)
0.944307 0.329067i \(-0.106734\pi\)
\(854\) 1.56639 + 3.21681i 0.0536009 + 0.110077i
\(855\) 0 0
\(856\) −2.45846 + 11.4579i −0.0840283 + 0.391622i
\(857\) −32.9302 + 19.0123i −1.12487 + 0.649447i −0.942641 0.333808i \(-0.891666\pi\)
−0.182234 + 0.983255i \(0.558333\pi\)
\(858\) 0 0
\(859\) −41.8849 + 11.2230i −1.42910 + 0.382925i −0.888701 0.458487i \(-0.848392\pi\)
−0.540395 + 0.841412i \(0.681725\pi\)
\(860\) 26.3761 + 65.5246i 0.899418 + 2.23437i
\(861\) 0 0
\(862\) 5.40365 + 27.8947i 0.184049 + 0.950097i
\(863\) 19.8437 0.675487 0.337744 0.941238i \(-0.390336\pi\)
0.337744 + 0.941238i \(0.390336\pi\)
\(864\) 0 0
\(865\) 4.43121 0.150666
\(866\) −5.87027 30.3035i −0.199480 1.02975i
\(867\) 0 0
\(868\) 1.66664 + 4.14033i 0.0565694 + 0.140532i
\(869\) −3.09266 + 0.828675i −0.104911 + 0.0281109i
\(870\) 0 0
\(871\) −29.1176 + 16.8110i −0.986611 + 0.569620i
\(872\) 45.0518 + 9.66654i 1.52565 + 0.327350i
\(873\) 0 0
\(874\) 8.83573 + 18.1454i 0.298873 + 0.613778i
\(875\) 0.798951 2.98173i 0.0270095 0.100801i
\(876\) 0 0
\(877\) −13.2670 49.5131i −0.447995 1.67194i −0.707906 0.706307i \(-0.750360\pi\)
0.259911 0.965633i \(-0.416307\pi\)
\(878\) −27.5724 31.7595i −0.930525 1.07183i
\(879\) 0 0
\(880\) −3.94983 4.11119i −0.133149 0.138588i
\(881\) 31.7902 1.07104 0.535519 0.844523i \(-0.320116\pi\)
0.535519 + 0.844523i \(0.320116\pi\)
\(882\) 0 0
\(883\) 28.7423 28.7423i 0.967255 0.967255i −0.0322259 0.999481i \(-0.510260\pi\)
0.999481 + 0.0322259i \(0.0102596\pi\)
\(884\) 0.313415 + 0.417026i 0.0105413 + 0.0140261i
\(885\) 0 0
\(886\) −49.3909 3.48553i −1.65932 0.117099i
\(887\) 23.1996 + 13.3943i 0.778966 + 0.449736i 0.836064 0.548632i \(-0.184851\pi\)
−0.0570976 + 0.998369i \(0.518185\pi\)
\(888\) 0 0
\(889\) −18.9567 + 10.9447i −0.635787 + 0.367072i
\(890\) −20.7856 + 10.1214i −0.696736 + 0.339269i
\(891\) 0 0
\(892\) 6.54309 + 5.12553i 0.219079 + 0.171615i
\(893\) −3.70433 0.992572i −0.123961 0.0332151i
\(894\) 0 0
\(895\) −5.46938 + 9.47324i −0.182821 + 0.316655i
\(896\) 22.2940 6.70686i 0.744792 0.224060i
\(897\) 0 0
\(898\) 7.44484 + 38.4318i 0.248438 + 1.28248i
\(899\) 5.52278 5.52278i 0.184195 0.184195i
\(900\) 0 0
\(901\) 0.108672 + 0.108672i 0.00362040 + 0.00362040i
\(902\) −3.60928 2.43785i −0.120176 0.0811716i
\(903\) 0 0
\(904\) −21.4263 + 1.08164i −0.712629 + 0.0359749i
\(905\) −41.0986 23.7283i −1.36616 0.788756i
\(906\) 0 0
\(907\) 4.28704 15.9995i 0.142349 0.531253i −0.857510 0.514467i \(-0.827990\pi\)
0.999859 0.0167863i \(-0.00534350\pi\)
\(908\) 12.8050 1.55562i 0.424950 0.0516251i
\(909\) 0 0
\(910\) −17.2026 + 49.8563i −0.570262 + 1.65272i
\(911\) −0.940538 1.62906i −0.0311614 0.0539731i 0.850024 0.526744i \(-0.176587\pi\)
−0.881186 + 0.472771i \(0.843254\pi\)
\(912\) 0 0
\(913\) −0.140674 + 0.243655i −0.00465564 + 0.00806381i
\(914\) −14.7858 17.0311i −0.489071 0.563340i
\(915\) 0 0
\(916\) 15.5254 11.6681i 0.512975 0.385526i
\(917\) −28.0162 28.0162i −0.925177 0.925177i
\(918\) 0 0
\(919\) 58.7898i 1.93930i 0.244501 + 0.969649i \(0.421376\pi\)
−0.244501 + 0.969649i \(0.578624\pi\)
\(920\) −24.4240 75.6635i −0.805234 2.49455i
\(921\) 0 0
\(922\) 1.87345 26.5474i 0.0616989 0.874291i
\(923\) −39.0799 + 10.4714i −1.28633 + 0.344671i
\(924\) 0 0
\(925\) −4.74180 1.27056i −0.155909 0.0417758i
\(926\) −16.2437 5.60480i −0.533802 0.184185i
\(927\) 0 0
\(928\) −26.0876 31.2930i −0.856369 1.02724i
\(929\) −17.0265 29.4908i −0.558622 0.967562i −0.997612 0.0690699i \(-0.977997\pi\)
0.438990 0.898492i \(-0.355336\pi\)
\(930\) 0 0
\(931\) −1.12085 4.18306i −0.0367343 0.137094i
\(932\) 16.5870 + 41.2060i 0.543324 + 1.34975i
\(933\) 0 0
\(934\) −26.4676 17.8773i −0.866047 0.584963i
\(935\) 0.0632715i 0.00206920i
\(936\) 0 0
\(937\) 23.8098i 0.777833i −0.921273 0.388916i \(-0.872849\pi\)
0.921273 0.388916i \(-0.127151\pi\)
\(938\) 9.32072 13.7995i 0.304332 0.450569i
\(939\) 0 0
\(940\) 13.8993 + 5.92093i 0.453346 + 0.193120i
\(941\) −3.51153 13.1052i −0.114473 0.427217i 0.884774 0.466020i \(-0.154312\pi\)
−0.999247 + 0.0388023i \(0.987646\pi\)
\(942\) 0 0
\(943\) −30.3705 52.6032i −0.988998 1.71300i
\(944\) −7.69208 + 12.7278i −0.250356 + 0.414255i
\(945\) 0 0
\(946\) −2.44064 + 7.07341i −0.0793519 + 0.229976i
\(947\) 19.1830 + 5.14006i 0.623363 + 0.167030i 0.556656 0.830743i \(-0.312084\pi\)
0.0667069 + 0.997773i \(0.478751\pi\)
\(948\) 0 0
\(949\) 74.8957 20.0682i 2.43122 0.651442i
\(950\) 9.97076 + 0.703639i 0.323494 + 0.0228291i
\(951\) 0 0
\(952\) −0.229987 0.117741i −0.00745391 0.00381601i
\(953\) 13.2336i 0.428678i −0.976759 0.214339i \(-0.931240\pi\)
0.976759 0.214339i \(-0.0687598\pi\)
\(954\) 0 0
\(955\) −28.7557 28.7557i −0.930512 0.930512i
\(956\) −2.26236 + 15.9493i −0.0731698 + 0.515837i
\(957\) 0 0
\(958\) 19.8043 17.1933i 0.639847 0.555492i
\(959\) 9.86339 17.0839i 0.318506 0.551668i
\(960\) 0 0
\(961\) 14.9120 + 25.8283i 0.481031 + 0.833170i
\(962\) −8.54322 2.94779i −0.275444 0.0950404i
\(963\) 0 0
\(964\) −15.9854 12.5222i −0.514855 0.403312i
\(965\) −13.9194 + 51.9479i −0.448081 + 1.67226i
\(966\) 0 0
\(967\) 45.2656 + 26.1341i 1.45564 + 0.840417i 0.998793 0.0491262i \(-0.0156437\pi\)
0.456852 + 0.889543i \(0.348977\pi\)
\(968\) 1.53818 + 30.4699i 0.0494390 + 0.979341i
\(969\) 0 0
\(970\) 28.7273 42.5312i 0.922377 1.36559i
\(971\) 33.2081 + 33.2081i 1.06570 + 1.06570i 0.997684 + 0.0680139i \(0.0216662\pi\)
0.0680139 + 0.997684i \(0.478334\pi\)
\(972\) 0 0
\(973\) 10.2655 10.2655i 0.329098 0.329098i
\(974\) 9.14728 1.77197i 0.293098 0.0567777i
\(975\) 0 0
\(976\) −4.30736 + 2.37321i −0.137875 + 0.0759646i
\(977\) −15.0366 + 26.0441i −0.481063 + 0.833226i −0.999764 0.0217300i \(-0.993083\pi\)
0.518701 + 0.854956i \(0.326416\pi\)
\(978\) 0 0
\(979\) −2.36566 0.633876i −0.0756067 0.0202588i
\(980\) 2.05745 + 16.9359i 0.0657230 + 0.540997i
\(981\) 0 0
\(982\) −3.11746 6.40214i −0.0994822 0.204301i
\(983\) 18.8575 10.8874i 0.601460 0.347253i −0.168155 0.985760i \(-0.553781\pi\)
0.769616 + 0.638507i \(0.220448\pi\)
\(984\) 0 0
\(985\) −31.5914 18.2393i −1.00658 0.581152i
\(986\) −0.0318287 + 0.451021i −0.00101363 + 0.0143634i
\(987\) 0 0
\(988\) 18.2192 + 2.58434i 0.579631 + 0.0822188i
\(989\) −73.7882 + 73.7882i −2.34633 + 2.34633i
\(990\) 0 0
\(991\) 21.5288 0.683884 0.341942 0.939721i \(-0.388915\pi\)
0.341942 + 0.939721i \(0.388915\pi\)
\(992\) −5.56820 + 2.57482i −0.176790 + 0.0817507i
\(993\) 0 0
\(994\) 15.1315 13.1366i 0.479943 0.416669i
\(995\) 12.4871 + 46.6025i 0.395868 + 1.47740i
\(996\) 0 0
\(997\) −8.21836 + 30.6713i −0.260278 + 0.971371i 0.704799 + 0.709407i \(0.251037\pi\)
−0.965078 + 0.261964i \(0.915630\pi\)
\(998\) 27.6094 13.4441i 0.873960 0.425566i
\(999\) 0 0
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 432.2.y.e.37.8 72
3.2 odd 2 144.2.x.e.85.11 yes 72
4.3 odd 2 1728.2.bc.e.1009.3 72
9.2 odd 6 144.2.x.e.133.14 yes 72
9.7 even 3 inner 432.2.y.e.181.5 72
12.11 even 2 576.2.bb.e.49.9 72
16.3 odd 4 1728.2.bc.e.145.16 72
16.13 even 4 inner 432.2.y.e.253.5 72
36.7 odd 6 1728.2.bc.e.1585.16 72
36.11 even 6 576.2.bb.e.241.2 72
48.29 odd 4 144.2.x.e.13.14 72
48.35 even 4 576.2.bb.e.337.2 72
144.29 odd 12 144.2.x.e.61.11 yes 72
144.61 even 12 inner 432.2.y.e.397.8 72
144.83 even 12 576.2.bb.e.529.9 72
144.115 odd 12 1728.2.bc.e.721.3 72
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
144.2.x.e.13.14 72 48.29 odd 4
144.2.x.e.61.11 yes 72 144.29 odd 12
144.2.x.e.85.11 yes 72 3.2 odd 2
144.2.x.e.133.14 yes 72 9.2 odd 6
432.2.y.e.37.8 72 1.1 even 1 trivial
432.2.y.e.181.5 72 9.7 even 3 inner
432.2.y.e.253.5 72 16.13 even 4 inner
432.2.y.e.397.8 72 144.61 even 12 inner
576.2.bb.e.49.9 72 12.11 even 2
576.2.bb.e.241.2 72 36.11 even 6
576.2.bb.e.337.2 72 48.35 even 4
576.2.bb.e.529.9 72 144.83 even 12
1728.2.bc.e.145.16 72 16.3 odd 4
1728.2.bc.e.721.3 72 144.115 odd 12
1728.2.bc.e.1009.3 72 4.3 odd 2
1728.2.bc.e.1585.16 72 36.7 odd 6