Properties

Label 441.2.i.b.227.4
Level $441$
Weight $2$
Character 441.227
Analytic conductor $3.521$
Analytic rank $0$
Dimension $10$
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] = [441,2,Mod(68,441)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(441, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([5, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("441.68");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 441.i (of order \(6\), degree \(2\), 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: \(3.52140272914\)
Analytic rank: \(0\)
Dimension: \(10\)
Relative dimension: \(5\) over \(\Q(\zeta_{6})\)
Coefficient field: 10.0.288778218147.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{10} - x^{9} + 7x^{8} - 4x^{7} + 34x^{6} - 19x^{5} + 64x^{4} - x^{3} + 64x^{2} - 21x + 9 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 63)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 227.4
Root \(-1.04536 - 1.81062i\) of defining polynomial
Character \(\chi\) \(=\) 441.227
Dual form 441.2.i.b.68.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.51009i q^{2} +(-0.811070 + 1.53041i) q^{3} -0.280386 q^{4} +(0.387938 - 0.671929i) q^{5} +(-2.31107 - 1.22479i) q^{6} +2.59678i q^{8} +(-1.68433 - 2.48254i) q^{9} +O(q^{10})\) \(q+1.51009i q^{2} +(-0.811070 + 1.53041i) q^{3} -0.280386 q^{4} +(0.387938 - 0.671929i) q^{5} +(-2.31107 - 1.22479i) q^{6} +2.59678i q^{8} +(-1.68433 - 2.48254i) q^{9} +(1.01468 + 0.585823i) q^{10} +(-3.32830 + 1.92159i) q^{11} +(0.227413 - 0.429107i) q^{12} +(-2.54198 + 1.46761i) q^{13} +(0.713684 + 1.13869i) q^{15} -4.48216 q^{16} +(-2.69901 + 4.67482i) q^{17} +(3.74888 - 2.54350i) q^{18} +(0.376551 - 0.217402i) q^{19} +(-0.108773 + 0.188400i) q^{20} +(-2.90179 - 5.02605i) q^{22} +(-0.0482537 - 0.0278593i) q^{23} +(-3.97415 - 2.10617i) q^{24} +(2.19901 + 3.80879i) q^{25} +(-2.21624 - 3.83863i) q^{26} +(5.16543 - 0.564208i) q^{27} +(-0.187994 - 0.108538i) q^{29} +(-1.71953 + 1.07773i) q^{30} -6.55646i q^{31} -1.57492i q^{32} +(-0.241352 - 6.65222i) q^{33} +(-7.05942 - 4.07576i) q^{34} +(0.472264 + 0.696071i) q^{36} +(3.14698 + 5.45073i) q^{37} +(0.328298 + 0.568628i) q^{38} +(-0.184332 - 5.08062i) q^{39} +(1.74485 + 1.00739i) q^{40} +(3.78757 + 6.56026i) q^{41} +(6.42703 - 11.1319i) q^{43} +(0.933209 - 0.538789i) q^{44} +(-2.32151 + 0.168677i) q^{45} +(0.0420702 - 0.0728677i) q^{46} -0.965544 q^{47} +(3.63534 - 6.85955i) q^{48} +(-5.75164 + 3.32071i) q^{50} +(-4.96532 - 7.92220i) q^{51} +(0.712737 - 0.411499i) q^{52} +(6.46438 + 3.73221i) q^{53} +(0.852008 + 7.80029i) q^{54} +2.98184i q^{55} +(0.0273056 + 0.752608i) q^{57} +(0.163903 - 0.283889i) q^{58} +3.12439 q^{59} +(-0.200107 - 0.319272i) q^{60} -3.48424i q^{61} +9.90087 q^{62} -6.58603 q^{64} +2.27737i q^{65} +(10.0455 - 0.364464i) q^{66} -4.20177 q^{67} +(0.756765 - 1.31076i) q^{68} +(0.0817733 - 0.0512523i) q^{69} +3.50812i q^{71} +(6.44662 - 4.37384i) q^{72} +(7.05942 + 4.07576i) q^{73} +(-8.23112 + 4.75224i) q^{74} +(-7.61258 + 0.276195i) q^{75} +(-0.105580 + 0.0609566i) q^{76} +(7.67222 - 0.278359i) q^{78} -4.96220 q^{79} +(-1.73880 + 3.01169i) q^{80} +(-3.32605 + 8.36286i) q^{81} +(-9.90662 + 5.71959i) q^{82} +(-4.31033 + 7.46571i) q^{83} +(2.09410 + 3.62708i) q^{85} +(16.8103 + 9.70542i) q^{86} +(0.318585 - 0.199676i) q^{87} +(-4.98996 - 8.64286i) q^{88} +(7.82041 + 13.5453i) q^{89} +(-0.254718 - 3.50570i) q^{90} +(0.0135297 + 0.00781136i) q^{92} +(10.0341 + 5.31775i) q^{93} -1.45806i q^{94} -0.337354i q^{95} +(2.41028 + 1.27737i) q^{96} +(1.24162 + 0.716849i) q^{97} +(10.3764 + 5.02605i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q + 3 q^{3} - 8 q^{4} - 12 q^{6} + 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 10 q + 3 q^{3} - 8 q^{4} - 12 q^{6} + 3 q^{9} + 15 q^{10} - 12 q^{11} + 12 q^{12} + 6 q^{13} - 3 q^{15} + 12 q^{16} - 12 q^{17} + 24 q^{18} - 3 q^{19} - 3 q^{20} + 5 q^{22} - 15 q^{23} + 7 q^{25} + 3 q^{26} + 27 q^{27} - 15 q^{29} + 6 q^{30} + 3 q^{34} - 18 q^{36} + 6 q^{37} - 18 q^{38} + 18 q^{39} - 15 q^{40} - 9 q^{41} + 3 q^{43} - 24 q^{44} - 30 q^{45} - 13 q^{46} - 30 q^{47} - 15 q^{48} + 3 q^{50} + 21 q^{51} + 12 q^{52} + 9 q^{53} - 9 q^{54} - 36 q^{57} + 8 q^{58} + 36 q^{59} - 48 q^{60} + 12 q^{62} + 6 q^{64} + 39 q^{66} + 20 q^{67} + 27 q^{68} - 3 q^{69} - 30 q^{72} - 3 q^{73} - 30 q^{74} - 6 q^{75} + 9 q^{76} + 24 q^{78} - 40 q^{79} - 30 q^{80} + 15 q^{81} - 9 q^{82} - 15 q^{83} + 18 q^{85} + 54 q^{86} - 6 q^{87} - 8 q^{88} + 24 q^{89} + 24 q^{90} + 39 q^{92} + 36 q^{93} - 33 q^{96} + 6 q^{97} + 21 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(344\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.51009i 1.06780i 0.845548 + 0.533899i \(0.179274\pi\)
−0.845548 + 0.533899i \(0.820726\pi\)
\(3\) −0.811070 + 1.53041i −0.468271 + 0.883585i
\(4\) −0.280386 −0.140193
\(5\) 0.387938 0.671929i 0.173491 0.300496i −0.766147 0.642666i \(-0.777829\pi\)
0.939638 + 0.342170i \(0.111162\pi\)
\(6\) −2.31107 1.22479i −0.943490 0.500019i
\(7\) 0 0
\(8\) 2.59678i 0.918100i
\(9\) −1.68433 2.48254i −0.561444 0.827515i
\(10\) 1.01468 + 0.585823i 0.320869 + 0.185254i
\(11\) −3.32830 + 1.92159i −1.00352 + 0.579382i −0.909288 0.416168i \(-0.863373\pi\)
−0.0942318 + 0.995550i \(0.530039\pi\)
\(12\) 0.227413 0.429107i 0.0656484 0.123873i
\(13\) −2.54198 + 1.46761i −0.705019 + 0.407043i −0.809214 0.587514i \(-0.800107\pi\)
0.104195 + 0.994557i \(0.466773\pi\)
\(14\) 0 0
\(15\) 0.713684 + 1.13869i 0.184272 + 0.294008i
\(16\) −4.48216 −1.12054
\(17\) −2.69901 + 4.67482i −0.654606 + 1.13381i 0.327387 + 0.944890i \(0.393832\pi\)
−0.981993 + 0.188920i \(0.939501\pi\)
\(18\) 3.74888 2.54350i 0.883619 0.599509i
\(19\) 0.376551 0.217402i 0.0863868 0.0498755i −0.456184 0.889885i \(-0.650784\pi\)
0.542571 + 0.840010i \(0.317451\pi\)
\(20\) −0.108773 + 0.188400i −0.0243223 + 0.0421274i
\(21\) 0 0
\(22\) −2.90179 5.02605i −0.618663 1.07156i
\(23\) −0.0482537 0.0278593i −0.0100616 0.00580906i 0.494961 0.868915i \(-0.335182\pi\)
−0.505022 + 0.863106i \(0.668516\pi\)
\(24\) −3.97415 2.10617i −0.811219 0.429920i
\(25\) 2.19901 + 3.80879i 0.439802 + 0.761759i
\(26\) −2.21624 3.83863i −0.434640 0.752818i
\(27\) 5.16543 0.564208i 0.994088 0.108582i
\(28\) 0 0
\(29\) −0.187994 0.108538i −0.0349096 0.0201551i 0.482444 0.875927i \(-0.339749\pi\)
−0.517353 + 0.855772i \(0.673083\pi\)
\(30\) −1.71953 + 1.07773i −0.313941 + 0.196766i
\(31\) 6.55646i 1.17757i −0.808288 0.588787i \(-0.799606\pi\)
0.808288 0.588787i \(-0.200394\pi\)
\(32\) 1.57492i 0.278409i
\(33\) −0.241352 6.65222i −0.0420139 1.15800i
\(34\) −7.05942 4.07576i −1.21068 0.698987i
\(35\) 0 0
\(36\) 0.472264 + 0.696071i 0.0787106 + 0.116012i
\(37\) 3.14698 + 5.45073i 0.517361 + 0.896095i 0.999797 + 0.0201636i \(0.00641872\pi\)
−0.482436 + 0.875931i \(0.660248\pi\)
\(38\) 0.328298 + 0.568628i 0.0532569 + 0.0922437i
\(39\) −0.184332 5.08062i −0.0295167 0.813550i
\(40\) 1.74485 + 1.00739i 0.275885 + 0.159282i
\(41\) 3.78757 + 6.56026i 0.591519 + 1.02454i 0.994028 + 0.109125i \(0.0348049\pi\)
−0.402509 + 0.915416i \(0.631862\pi\)
\(42\) 0 0
\(43\) 6.42703 11.1319i 0.980112 1.69760i 0.318198 0.948024i \(-0.396922\pi\)
0.661914 0.749580i \(-0.269745\pi\)
\(44\) 0.933209 0.538789i 0.140687 0.0812254i
\(45\) −2.32151 + 0.168677i −0.346070 + 0.0251449i
\(46\) 0.0420702 0.0728677i 0.00620291 0.0107437i
\(47\) −0.965544 −0.140839 −0.0704195 0.997517i \(-0.522434\pi\)
−0.0704195 + 0.997517i \(0.522434\pi\)
\(48\) 3.63534 6.85955i 0.524716 0.990091i
\(49\) 0 0
\(50\) −5.75164 + 3.32071i −0.813405 + 0.469619i
\(51\) −4.96532 7.92220i −0.695284 1.10933i
\(52\) 0.712737 0.411499i 0.0988388 0.0570646i
\(53\) 6.46438 + 3.73221i 0.887950 + 0.512658i 0.873272 0.487234i \(-0.161994\pi\)
0.0146788 + 0.999892i \(0.495327\pi\)
\(54\) 0.852008 + 7.80029i 0.115944 + 1.06148i
\(55\) 2.98184i 0.402071i
\(56\) 0 0
\(57\) 0.0273056 + 0.752608i 0.00361672 + 0.0996853i
\(58\) 0.163903 0.283889i 0.0215215 0.0372764i
\(59\) 3.12439 0.406760 0.203380 0.979100i \(-0.434807\pi\)
0.203380 + 0.979100i \(0.434807\pi\)
\(60\) −0.200107 0.319272i −0.0258337 0.0412179i
\(61\) 3.48424i 0.446111i −0.974806 0.223055i \(-0.928397\pi\)
0.974806 0.223055i \(-0.0716031\pi\)
\(62\) 9.90087 1.25741
\(63\) 0 0
\(64\) −6.58603 −0.823254
\(65\) 2.27737i 0.282473i
\(66\) 10.0455 0.364464i 1.23651 0.0448624i
\(67\) −4.20177 −0.513328 −0.256664 0.966501i \(-0.582623\pi\)
−0.256664 + 0.966501i \(0.582623\pi\)
\(68\) 0.756765 1.31076i 0.0917712 0.158952i
\(69\) 0.0817733 0.0512523i 0.00984435 0.00617005i
\(70\) 0 0
\(71\) 3.50812i 0.416337i 0.978093 + 0.208169i \(0.0667503\pi\)
−0.978093 + 0.208169i \(0.933250\pi\)
\(72\) 6.44662 4.37384i 0.759742 0.515462i
\(73\) 7.05942 + 4.07576i 0.826243 + 0.477031i 0.852564 0.522622i \(-0.175046\pi\)
−0.0263219 + 0.999654i \(0.508379\pi\)
\(74\) −8.23112 + 4.75224i −0.956848 + 0.552437i
\(75\) −7.61258 + 0.276195i −0.879025 + 0.0318922i
\(76\) −0.105580 + 0.0609566i −0.0121108 + 0.00699220i
\(77\) 0 0
\(78\) 7.67222 0.278359i 0.868708 0.0315179i
\(79\) −4.96220 −0.558291 −0.279145 0.960249i \(-0.590051\pi\)
−0.279145 + 0.960249i \(0.590051\pi\)
\(80\) −1.73880 + 3.01169i −0.194404 + 0.336717i
\(81\) −3.32605 + 8.36286i −0.369561 + 0.929206i
\(82\) −9.90662 + 5.71959i −1.09400 + 0.631623i
\(83\) −4.31033 + 7.46571i −0.473120 + 0.819469i −0.999527 0.0307645i \(-0.990206\pi\)
0.526406 + 0.850233i \(0.323539\pi\)
\(84\) 0 0
\(85\) 2.09410 + 3.62708i 0.227137 + 0.393412i
\(86\) 16.8103 + 9.70542i 1.81270 + 1.04656i
\(87\) 0.318585 0.199676i 0.0341559 0.0214075i
\(88\) −4.98996 8.64286i −0.531931 0.921332i
\(89\) 7.82041 + 13.5453i 0.828962 + 1.43580i 0.898853 + 0.438249i \(0.144401\pi\)
−0.0698916 + 0.997555i \(0.522265\pi\)
\(90\) −0.254718 3.50570i −0.0268497 0.369533i
\(91\) 0 0
\(92\) 0.0135297 + 0.00781136i 0.00141057 + 0.000814391i
\(93\) 10.0341 + 5.31775i 1.04049 + 0.551424i
\(94\) 1.45806i 0.150388i
\(95\) 0.337354i 0.0346118i
\(96\) 2.41028 + 1.27737i 0.245998 + 0.130371i
\(97\) 1.24162 + 0.716849i 0.126067 + 0.0727850i 0.561708 0.827336i \(-0.310145\pi\)
−0.435640 + 0.900121i \(0.643478\pi\)
\(98\) 0 0
\(99\) 10.3764 + 5.02605i 1.04287 + 0.505137i
\(100\) −0.616572 1.06793i −0.0616572 0.106793i
\(101\) −8.01096 13.8754i −0.797120 1.38065i −0.921484 0.388416i \(-0.873023\pi\)
0.124364 0.992237i \(-0.460311\pi\)
\(102\) 11.9633 7.49811i 1.18454 0.742423i
\(103\) 14.6064 + 8.43299i 1.43921 + 0.830928i 0.997795 0.0663758i \(-0.0211436\pi\)
0.441414 + 0.897303i \(0.354477\pi\)
\(104\) −3.81107 6.60097i −0.373706 0.647278i
\(105\) 0 0
\(106\) −5.63599 + 9.76182i −0.547416 + 0.948152i
\(107\) 3.36444 1.94246i 0.325253 0.187785i −0.328479 0.944511i \(-0.606536\pi\)
0.653731 + 0.756727i \(0.273203\pi\)
\(108\) −1.44832 + 0.158196i −0.139364 + 0.0152224i
\(109\) 1.28254 2.22143i 0.122845 0.212774i −0.798043 0.602600i \(-0.794131\pi\)
0.920889 + 0.389826i \(0.127465\pi\)
\(110\) −4.50286 −0.429331
\(111\) −10.8943 + 0.395260i −1.03404 + 0.0375164i
\(112\) 0 0
\(113\) −9.79043 + 5.65251i −0.921006 + 0.531743i −0.883956 0.467570i \(-0.845129\pi\)
−0.0370501 + 0.999313i \(0.511796\pi\)
\(114\) −1.13651 + 0.0412341i −0.106444 + 0.00386193i
\(115\) −0.0374389 + 0.0216154i −0.00349120 + 0.00201564i
\(116\) 0.0527109 + 0.0304327i 0.00489408 + 0.00282560i
\(117\) 7.92496 + 3.83863i 0.732663 + 0.354882i
\(118\) 4.71812i 0.434338i
\(119\) 0 0
\(120\) −2.95692 + 1.85328i −0.269929 + 0.169181i
\(121\) 1.88504 3.26499i 0.171368 0.296817i
\(122\) 5.26153 0.476356
\(123\) −13.1119 + 0.475718i −1.18226 + 0.0428940i
\(124\) 1.83834i 0.165088i
\(125\) 7.29170 0.652189
\(126\) 0 0
\(127\) 2.65660 0.235735 0.117867 0.993029i \(-0.462394\pi\)
0.117867 + 0.993029i \(0.462394\pi\)
\(128\) 13.0954i 1.15748i
\(129\) 11.8237 + 18.8648i 1.04102 + 1.66095i
\(130\) −3.43905 −0.301625
\(131\) 4.11811 7.13278i 0.359801 0.623194i −0.628126 0.778111i \(-0.716178\pi\)
0.987927 + 0.154918i \(0.0495112\pi\)
\(132\) 0.0676717 + 1.86519i 0.00589006 + 0.162344i
\(133\) 0 0
\(134\) 6.34507i 0.548131i
\(135\) 1.62476 3.68968i 0.139837 0.317557i
\(136\) −12.1395 7.00873i −1.04095 0.600994i
\(137\) 15.0058 8.66359i 1.28203 0.740180i 0.304811 0.952413i \(-0.401407\pi\)
0.977219 + 0.212233i \(0.0680735\pi\)
\(138\) 0.0773958 + 0.123485i 0.00658837 + 0.0105118i
\(139\) −5.47677 + 3.16201i −0.464533 + 0.268198i −0.713949 0.700198i \(-0.753095\pi\)
0.249415 + 0.968397i \(0.419762\pi\)
\(140\) 0 0
\(141\) 0.783123 1.47768i 0.0659509 0.124443i
\(142\) −5.29759 −0.444564
\(143\) 5.64031 9.76931i 0.471667 0.816951i
\(144\) 7.54944 + 11.1272i 0.629120 + 0.927263i
\(145\) −0.145860 + 0.0842123i −0.0121130 + 0.00699345i
\(146\) −6.15478 + 10.6604i −0.509373 + 0.882260i
\(147\) 0 0
\(148\) −0.882370 1.52831i −0.0725304 0.125626i
\(149\) −11.1061 6.41211i −0.909847 0.525300i −0.0294650 0.999566i \(-0.509380\pi\)
−0.880382 + 0.474265i \(0.842714\pi\)
\(150\) −0.417080 11.4957i −0.0340545 0.938621i
\(151\) −2.62759 4.55111i −0.213830 0.370364i 0.739080 0.673618i \(-0.235260\pi\)
−0.952910 + 0.303253i \(0.901927\pi\)
\(152\) 0.564545 + 0.977821i 0.0457907 + 0.0793118i
\(153\) 16.1515 1.17354i 1.30577 0.0948751i
\(154\) 0 0
\(155\) −4.40547 2.54350i −0.353856 0.204299i
\(156\) 0.0516841 + 1.42454i 0.00413804 + 0.114054i
\(157\) 7.98815i 0.637523i 0.947835 + 0.318762i \(0.103267\pi\)
−0.947835 + 0.318762i \(0.896733\pi\)
\(158\) 7.49339i 0.596142i
\(159\) −10.9549 + 6.86609i −0.868779 + 0.544516i
\(160\) −1.05823 0.610972i −0.0836608 0.0483016i
\(161\) 0 0
\(162\) −12.6287 5.02265i −0.992205 0.394617i
\(163\) 5.75231 + 9.96329i 0.450556 + 0.780385i 0.998421 0.0561817i \(-0.0178926\pi\)
−0.547865 + 0.836567i \(0.684559\pi\)
\(164\) −1.06198 1.83941i −0.0829269 0.143634i
\(165\) −4.56345 2.41848i −0.355264 0.188278i
\(166\) −11.2739 6.50901i −0.875027 0.505197i
\(167\) −8.38240 14.5187i −0.648650 1.12349i −0.983446 0.181204i \(-0.942001\pi\)
0.334796 0.942291i \(-0.391333\pi\)
\(168\) 0 0
\(169\) −2.19222 + 3.79704i −0.168632 + 0.292080i
\(170\) −5.47724 + 3.16228i −0.420085 + 0.242536i
\(171\) −1.17395 0.568628i −0.0897740 0.0434841i
\(172\) −1.80205 + 3.12124i −0.137405 + 0.237992i
\(173\) −1.71279 −0.130221 −0.0651106 0.997878i \(-0.520740\pi\)
−0.0651106 + 0.997878i \(0.520740\pi\)
\(174\) 0.301530 + 0.481093i 0.0228589 + 0.0364716i
\(175\) 0 0
\(176\) 14.9180 8.61288i 1.12448 0.649220i
\(177\) −2.53409 + 4.78160i −0.190474 + 0.359407i
\(178\) −20.4548 + 11.8096i −1.53315 + 0.885164i
\(179\) 12.4141 + 7.16731i 0.927877 + 0.535710i 0.886139 0.463419i \(-0.153377\pi\)
0.0417372 + 0.999129i \(0.486711\pi\)
\(180\) 0.650919 0.0472948i 0.0485167 0.00352514i
\(181\) 4.83147i 0.359121i −0.983747 0.179560i \(-0.942532\pi\)
0.983747 0.179560i \(-0.0574675\pi\)
\(182\) 0 0
\(183\) 5.33232 + 2.82596i 0.394177 + 0.208901i
\(184\) 0.0723444 0.125304i 0.00533330 0.00923755i
\(185\) 4.88334 0.359030
\(186\) −8.03030 + 15.1524i −0.588810 + 1.11103i
\(187\) 20.7456i 1.51707i
\(188\) 0.270725 0.0197447
\(189\) 0 0
\(190\) 0.509437 0.0369584
\(191\) 3.14210i 0.227355i −0.993518 0.113677i \(-0.963737\pi\)
0.993518 0.113677i \(-0.0362630\pi\)
\(192\) 5.34173 10.0794i 0.385506 0.727415i
\(193\) 6.01017 0.432621 0.216311 0.976325i \(-0.430598\pi\)
0.216311 + 0.976325i \(0.430598\pi\)
\(194\) −1.08251 + 1.87496i −0.0777197 + 0.134615i
\(195\) −3.48532 1.84711i −0.249589 0.132274i
\(196\) 0 0
\(197\) 14.0902i 1.00388i −0.864901 0.501942i \(-0.832619\pi\)
0.864901 0.501942i \(-0.167381\pi\)
\(198\) −7.58980 + 15.6693i −0.539384 + 1.11357i
\(199\) 6.84234 + 3.95043i 0.485041 + 0.280038i 0.722515 0.691355i \(-0.242986\pi\)
−0.237474 + 0.971394i \(0.576319\pi\)
\(200\) −9.89060 + 5.71034i −0.699371 + 0.403782i
\(201\) 3.40793 6.43045i 0.240377 0.453569i
\(202\) 20.9531 12.0973i 1.47426 0.851163i
\(203\) 0 0
\(204\) 1.39221 + 2.22128i 0.0974741 + 0.155520i
\(205\) 5.87737 0.410493
\(206\) −12.7346 + 22.0570i −0.887263 + 1.53678i
\(207\) 0.0121133 + 0.166716i 0.000841935 + 0.0115876i
\(208\) 11.3936 6.57807i 0.790001 0.456107i
\(209\) −0.835517 + 1.44716i −0.0577939 + 0.100102i
\(210\) 0 0
\(211\) 2.57821 + 4.46559i 0.177491 + 0.307424i 0.941021 0.338349i \(-0.109868\pi\)
−0.763529 + 0.645773i \(0.776535\pi\)
\(212\) −1.81252 1.04646i −0.124485 0.0718712i
\(213\) −5.36887 2.84533i −0.367869 0.194959i
\(214\) 2.93330 + 5.08062i 0.200516 + 0.347304i
\(215\) −4.98658 8.63701i −0.340082 0.589039i
\(216\) 1.46512 + 13.4135i 0.0996891 + 0.912672i
\(217\) 0 0
\(218\) 3.35457 + 1.93676i 0.227200 + 0.131174i
\(219\) −11.9633 + 7.49811i −0.808403 + 0.506675i
\(220\) 0.836067i 0.0563676i
\(221\) 15.8444i 1.06581i
\(222\) −0.596880 16.4514i −0.0400600 1.10415i
\(223\) 3.79823 + 2.19291i 0.254348 + 0.146848i 0.621754 0.783213i \(-0.286420\pi\)
−0.367405 + 0.930061i \(0.619754\pi\)
\(224\) 0 0
\(225\) 5.75164 11.8744i 0.383443 0.791627i
\(226\) −8.53582 14.7845i −0.567794 0.983449i
\(227\) −4.83697 8.37788i −0.321041 0.556059i 0.659662 0.751562i \(-0.270699\pi\)
−0.980703 + 0.195503i \(0.937366\pi\)
\(228\) −0.00765613 0.211021i −0.000507039 0.0139752i
\(229\) −7.66705 4.42657i −0.506653 0.292516i 0.224804 0.974404i \(-0.427826\pi\)
−0.731457 + 0.681888i \(0.761159\pi\)
\(230\) −0.0326412 0.0565363i −0.00215230 0.00372789i
\(231\) 0 0
\(232\) 0.281850 0.488179i 0.0185044 0.0320505i
\(233\) −11.1612 + 6.44391i −0.731194 + 0.422155i −0.818859 0.573995i \(-0.805393\pi\)
0.0876651 + 0.996150i \(0.472059\pi\)
\(234\) −5.79670 + 11.9674i −0.378942 + 0.782336i
\(235\) −0.374571 + 0.648777i −0.0244343 + 0.0423215i
\(236\) −0.876035 −0.0570250
\(237\) 4.02469 7.59421i 0.261432 0.493297i
\(238\) 0 0
\(239\) 4.18421 2.41575i 0.270654 0.156262i −0.358531 0.933518i \(-0.616722\pi\)
0.629185 + 0.777256i \(0.283389\pi\)
\(240\) −3.19884 5.10377i −0.206484 0.329447i
\(241\) 8.68938 5.01681i 0.559732 0.323161i −0.193306 0.981139i \(-0.561921\pi\)
0.753038 + 0.657977i \(0.228588\pi\)
\(242\) 4.93045 + 2.84659i 0.316941 + 0.182986i
\(243\) −10.1010 11.8731i −0.647978 0.761659i
\(244\) 0.976932i 0.0625417i
\(245\) 0 0
\(246\) −0.718379 19.8002i −0.0458022 1.26242i
\(247\) −0.638125 + 1.10526i −0.0406029 + 0.0703263i
\(248\) 17.0257 1.08113
\(249\) −7.92965 12.6518i −0.502521 0.801776i
\(250\) 11.0112i 0.696407i
\(251\) −7.98203 −0.503821 −0.251911 0.967751i \(-0.581059\pi\)
−0.251911 + 0.967751i \(0.581059\pi\)
\(252\) 0 0
\(253\) 0.214137 0.0134627
\(254\) 4.01171i 0.251717i
\(255\) −7.24939 + 0.263018i −0.453975 + 0.0164708i
\(256\) 6.60319 0.412700
\(257\) 1.34115 2.32294i 0.0836585 0.144901i −0.821160 0.570698i \(-0.806673\pi\)
0.904819 + 0.425797i \(0.140006\pi\)
\(258\) −28.4876 + 17.8549i −1.77356 + 1.11160i
\(259\) 0 0
\(260\) 0.638544i 0.0396008i
\(261\) 0.0471929 + 0.649518i 0.00292117 + 0.0402041i
\(262\) 10.7712 + 6.21874i 0.665445 + 0.384195i
\(263\) −20.2961 + 11.7179i −1.25151 + 0.722560i −0.971409 0.237411i \(-0.923701\pi\)
−0.280101 + 0.959971i \(0.590368\pi\)
\(264\) 17.2743 0.626737i 1.06316 0.0385730i
\(265\) 5.01556 2.89573i 0.308103 0.177883i
\(266\) 0 0
\(267\) −27.0729 + 0.982241i −1.65683 + 0.0601122i
\(268\) 1.17812 0.0719651
\(269\) −1.98955 + 3.44600i −0.121305 + 0.210106i −0.920283 0.391254i \(-0.872041\pi\)
0.798978 + 0.601361i \(0.205375\pi\)
\(270\) 5.57176 + 2.45354i 0.339087 + 0.149318i
\(271\) −10.8303 + 6.25288i −0.657895 + 0.379836i −0.791474 0.611202i \(-0.790686\pi\)
0.133580 + 0.991038i \(0.457353\pi\)
\(272\) 12.0974 20.9533i 0.733511 1.27048i
\(273\) 0 0
\(274\) 13.0828 + 22.6601i 0.790363 + 1.36895i
\(275\) −14.6379 8.45120i −0.882699 0.509626i
\(276\) −0.0229281 + 0.0143704i −0.00138011 + 0.000864999i
\(277\) 9.84547 + 17.0529i 0.591557 + 1.02461i 0.994023 + 0.109172i \(0.0348199\pi\)
−0.402466 + 0.915435i \(0.631847\pi\)
\(278\) −4.77494 8.27044i −0.286382 0.496028i
\(279\) −16.2767 + 11.0433i −0.974460 + 0.661142i
\(280\) 0 0
\(281\) 7.03456 + 4.06141i 0.419647 + 0.242283i 0.694926 0.719081i \(-0.255437\pi\)
−0.275279 + 0.961364i \(0.588770\pi\)
\(282\) 2.23144 + 1.18259i 0.132880 + 0.0704222i
\(283\) 1.34396i 0.0798899i −0.999202 0.0399450i \(-0.987282\pi\)
0.999202 0.0399450i \(-0.0127183\pi\)
\(284\) 0.983629i 0.0583676i
\(285\) 0.516292 + 0.273618i 0.0305825 + 0.0162077i
\(286\) 14.7526 + 8.51741i 0.872339 + 0.503645i
\(287\) 0 0
\(288\) −3.90981 + 2.65269i −0.230388 + 0.156311i
\(289\) −6.06929 10.5123i −0.357017 0.618371i
\(290\) −0.127169 0.220262i −0.00746760 0.0129343i
\(291\) −2.10412 + 1.31878i −0.123345 + 0.0773081i
\(292\) −1.97936 1.14279i −0.115834 0.0668765i
\(293\) −10.6300 18.4117i −0.621012 1.07562i −0.989298 0.145912i \(-0.953388\pi\)
0.368285 0.929713i \(-0.379945\pi\)
\(294\) 0 0
\(295\) 1.21207 2.09936i 0.0705693 0.122230i
\(296\) −14.1543 + 8.17202i −0.822705 + 0.474989i
\(297\) −16.1079 + 11.8037i −0.934676 + 0.684921i
\(298\) 9.68289 16.7713i 0.560915 0.971533i
\(299\) 0.163547 0.00945815
\(300\) 2.13446 0.0774412i 0.123233 0.00447107i
\(301\) 0 0
\(302\) 6.87261 3.96790i 0.395474 0.228327i
\(303\) 27.7325 1.00617i 1.59319 0.0578032i
\(304\) −1.68776 + 0.974430i −0.0967998 + 0.0558874i
\(305\) −2.34116 1.35167i −0.134054 0.0773963i
\(306\) 1.77216 + 24.3903i 0.101307 + 1.39430i
\(307\) 13.2098i 0.753925i −0.926229 0.376962i \(-0.876969\pi\)
0.926229 0.376962i \(-0.123031\pi\)
\(308\) 0 0
\(309\) −24.7528 + 15.5140i −1.40814 + 0.882563i
\(310\) 3.84093 6.65268i 0.218150 0.377847i
\(311\) −20.5373 −1.16457 −0.582283 0.812986i \(-0.697840\pi\)
−0.582283 + 0.812986i \(0.697840\pi\)
\(312\) 13.1933 0.478669i 0.746921 0.0270993i
\(313\) 16.5094i 0.933168i 0.884477 + 0.466584i \(0.154515\pi\)
−0.884477 + 0.466584i \(0.845485\pi\)
\(314\) −12.0629 −0.680746
\(315\) 0 0
\(316\) 1.39133 0.0782685
\(317\) 9.36591i 0.526042i 0.964790 + 0.263021i \(0.0847188\pi\)
−0.964790 + 0.263021i \(0.915281\pi\)
\(318\) −10.3684 16.5429i −0.581433 0.927680i
\(319\) 0.834266 0.0467099
\(320\) −2.55497 + 4.42534i −0.142827 + 0.247384i
\(321\) 0.243972 + 6.72445i 0.0136172 + 0.375322i
\(322\) 0 0
\(323\) 2.34708i 0.130595i
\(324\) 0.932579 2.34483i 0.0518100 0.130268i
\(325\) −11.1797 6.45459i −0.620137 0.358036i
\(326\) −15.0455 + 8.68653i −0.833294 + 0.481102i
\(327\) 2.35948 + 3.76456i 0.130479 + 0.208180i
\(328\) −17.0356 + 9.83548i −0.940631 + 0.543074i
\(329\) 0 0
\(330\) 3.65213 6.89124i 0.201043 0.379350i
\(331\) 28.8439 1.58540 0.792702 0.609609i \(-0.208674\pi\)
0.792702 + 0.609609i \(0.208674\pi\)
\(332\) 1.20856 2.09328i 0.0663282 0.114884i
\(333\) 8.23112 16.9934i 0.451063 0.931231i
\(334\) 21.9247 12.6582i 1.19967 0.692627i
\(335\) −1.63003 + 2.82329i −0.0890579 + 0.154253i
\(336\) 0 0
\(337\) −6.26205 10.8462i −0.341116 0.590829i 0.643525 0.765425i \(-0.277471\pi\)
−0.984640 + 0.174596i \(0.944138\pi\)
\(338\) −5.73388 3.31046i −0.311882 0.180065i
\(339\) −0.709953 19.5680i −0.0385594 1.06279i
\(340\) −0.587156 1.01698i −0.0318430 0.0551537i
\(341\) 12.5988 + 21.8218i 0.682266 + 1.18172i
\(342\) 0.858683 1.77277i 0.0464322 0.0958606i
\(343\) 0 0
\(344\) 28.9072 + 16.6896i 1.55857 + 0.899841i
\(345\) −0.00271488 0.0748286i −0.000146164 0.00402864i
\(346\) 2.58648i 0.139050i
\(347\) 28.7220i 1.54188i −0.636908 0.770939i \(-0.719787\pi\)
0.636908 0.770939i \(-0.280213\pi\)
\(348\) −0.0893268 + 0.0559865i −0.00478842 + 0.00300119i
\(349\) 11.0854 + 6.40017i 0.593389 + 0.342593i 0.766436 0.642320i \(-0.222028\pi\)
−0.173048 + 0.984913i \(0.555361\pi\)
\(350\) 0 0
\(351\) −12.3024 + 9.01506i −0.656653 + 0.481188i
\(352\) 3.02636 + 5.24181i 0.161305 + 0.279389i
\(353\) 13.4991 + 23.3811i 0.718485 + 1.24445i 0.961600 + 0.274455i \(0.0884975\pi\)
−0.243115 + 0.969998i \(0.578169\pi\)
\(354\) −7.22067 3.82672i −0.383774 0.203388i
\(355\) 2.35721 + 1.36093i 0.125108 + 0.0722309i
\(356\) −2.19274 3.79793i −0.116215 0.201290i
\(357\) 0 0
\(358\) −10.8233 + 18.7465i −0.572030 + 0.990785i
\(359\) 24.2669 14.0105i 1.28076 0.739445i 0.303770 0.952745i \(-0.401755\pi\)
0.976987 + 0.213300i \(0.0684212\pi\)
\(360\) −0.438017 6.02845i −0.0230855 0.317727i
\(361\) −9.40547 + 16.2908i −0.495025 + 0.857408i
\(362\) 7.29598 0.383468
\(363\) 3.46789 + 5.53303i 0.182017 + 0.290409i
\(364\) 0 0
\(365\) 5.47724 3.16228i 0.286692 0.165522i
\(366\) −4.26747 + 8.05232i −0.223064 + 0.420901i
\(367\) 28.9584 16.7191i 1.51161 0.872731i 0.511706 0.859160i \(-0.329014\pi\)
0.999908 0.0135705i \(-0.00431975\pi\)
\(368\) 0.216281 + 0.124870i 0.0112744 + 0.00650928i
\(369\) 9.90662 20.4525i 0.515718 1.06471i
\(370\) 7.37430i 0.383372i
\(371\) 0 0
\(372\) −2.81342 1.49102i −0.145869 0.0773059i
\(373\) 3.98403 6.90053i 0.206285 0.357296i −0.744256 0.667894i \(-0.767196\pi\)
0.950541 + 0.310598i \(0.100529\pi\)
\(374\) 31.3278 1.61992
\(375\) −5.91408 + 11.1593i −0.305402 + 0.576265i
\(376\) 2.50730i 0.129304i
\(377\) 0.637169 0.0328159
\(378\) 0 0
\(379\) 3.88714 0.199669 0.0998345 0.995004i \(-0.468169\pi\)
0.0998345 + 0.995004i \(0.468169\pi\)
\(380\) 0.0945895i 0.00485234i
\(381\) −2.15468 + 4.06569i −0.110388 + 0.208292i
\(382\) 4.74487 0.242769
\(383\) −6.34150 + 10.9838i −0.324036 + 0.561246i −0.981317 0.192399i \(-0.938373\pi\)
0.657281 + 0.753646i \(0.271706\pi\)
\(384\) 20.0413 + 10.6213i 1.02273 + 0.542014i
\(385\) 0 0
\(386\) 9.07592i 0.461952i
\(387\) −38.4608 + 2.79450i −1.95507 + 0.142052i
\(388\) −0.348133 0.200995i −0.0176738 0.0102040i
\(389\) 17.8067 10.2807i 0.902835 0.521252i 0.0247163 0.999695i \(-0.492132\pi\)
0.878119 + 0.478442i \(0.158798\pi\)
\(390\) 2.78931 5.26317i 0.141242 0.266511i
\(391\) 0.260474 0.150385i 0.0131727 0.00760529i
\(392\) 0 0
\(393\) 7.57603 + 12.0876i 0.382160 + 0.609739i
\(394\) 21.2775 1.07195
\(395\) −1.92503 + 3.33424i −0.0968586 + 0.167764i
\(396\) −2.90940 1.40923i −0.146203 0.0708167i
\(397\) −12.9646 + 7.48513i −0.650676 + 0.375668i −0.788715 0.614759i \(-0.789253\pi\)
0.138039 + 0.990427i \(0.455920\pi\)
\(398\) −5.96552 + 10.3326i −0.299025 + 0.517926i
\(399\) 0 0
\(400\) −9.85630 17.0716i −0.492815 0.853580i
\(401\) 8.93429 + 5.15821i 0.446157 + 0.257589i 0.706206 0.708007i \(-0.250405\pi\)
−0.260049 + 0.965595i \(0.583739\pi\)
\(402\) 9.71058 + 5.14629i 0.484320 + 0.256674i
\(403\) 9.62235 + 16.6664i 0.479323 + 0.830212i
\(404\) 2.24616 + 3.89047i 0.111751 + 0.193558i
\(405\) 4.32894 + 5.47914i 0.215107 + 0.272261i
\(406\) 0 0
\(407\) −20.9482 12.0944i −1.03836 0.599499i
\(408\) 20.5722 12.8939i 1.01848 0.638341i
\(409\) 18.5199i 0.915750i 0.889017 + 0.457875i \(0.151389\pi\)
−0.889017 + 0.457875i \(0.848611\pi\)
\(410\) 8.87539i 0.438324i
\(411\) 1.08814 + 29.9918i 0.0536742 + 1.47939i
\(412\) −4.09543 2.36450i −0.201767 0.116490i
\(413\) 0 0
\(414\) −0.251757 + 0.0182923i −0.0123732 + 0.000899017i
\(415\) 3.34429 + 5.79247i 0.164165 + 0.284341i
\(416\) 2.31138 + 4.00342i 0.113325 + 0.196284i
\(417\) −0.397148 10.9463i −0.0194484 0.536044i
\(418\) −2.18535 1.26171i −0.106889 0.0617122i
\(419\) 6.37677 + 11.0449i 0.311526 + 0.539578i 0.978693 0.205330i \(-0.0658267\pi\)
−0.667167 + 0.744908i \(0.732493\pi\)
\(420\) 0 0
\(421\) 6.78793 11.7570i 0.330824 0.573003i −0.651850 0.758348i \(-0.726007\pi\)
0.982674 + 0.185345i \(0.0593402\pi\)
\(422\) −6.74347 + 3.89334i −0.328267 + 0.189525i
\(423\) 1.62630 + 2.39701i 0.0790732 + 0.116546i
\(424\) −9.69173 + 16.7866i −0.470672 + 0.815227i
\(425\) −23.7406 −1.15159
\(426\) 4.29672 8.10751i 0.208177 0.392810i
\(427\) 0 0
\(428\) −0.943342 + 0.544639i −0.0455982 + 0.0263261i
\(429\) 10.3764 + 16.5556i 0.500977 + 0.799312i
\(430\) 13.0427 7.53020i 0.628975 0.363139i
\(431\) −31.3069 18.0750i −1.50800 0.870643i −0.999957 0.00931038i \(-0.997036\pi\)
−0.508041 0.861333i \(-0.669630\pi\)
\(432\) −23.1523 + 2.52887i −1.11391 + 0.121670i
\(433\) 33.0085i 1.58629i −0.609034 0.793144i \(-0.708443\pi\)
0.609034 0.793144i \(-0.291557\pi\)
\(434\) 0 0
\(435\) −0.0105770 0.291528i −0.000507130 0.0139777i
\(436\) −0.359608 + 0.622859i −0.0172221 + 0.0298295i
\(437\) −0.0242267 −0.00115892
\(438\) −11.3229 18.0657i −0.541027 0.863212i
\(439\) 30.5618i 1.45863i 0.684176 + 0.729317i \(0.260162\pi\)
−0.684176 + 0.729317i \(0.739838\pi\)
\(440\) −7.74318 −0.369141
\(441\) 0 0
\(442\) 23.9266 1.13807
\(443\) 20.7026i 0.983612i −0.870705 0.491806i \(-0.836337\pi\)
0.870705 0.491806i \(-0.163663\pi\)
\(444\) 3.05461 0.110825i 0.144965 0.00525955i
\(445\) 12.1353 0.575270
\(446\) −3.31150 + 5.73569i −0.156804 + 0.271593i
\(447\) 18.8210 11.7963i 0.890203 0.557944i
\(448\) 0 0
\(449\) 6.40243i 0.302150i 0.988522 + 0.151075i \(0.0482734\pi\)
−0.988522 + 0.151075i \(0.951727\pi\)
\(450\) 17.9315 + 8.68552i 0.845298 + 0.409439i
\(451\) −25.2123 14.5563i −1.18720 0.685431i
\(452\) 2.74510 1.58489i 0.129119 0.0745467i
\(453\) 9.09624 0.330024i 0.427379 0.0155059i
\(454\) 12.6514 7.30428i 0.593759 0.342807i
\(455\) 0 0
\(456\) −1.95436 + 0.0709067i −0.0915211 + 0.00332051i
\(457\) −3.14680 −0.147201 −0.0736007 0.997288i \(-0.523449\pi\)
−0.0736007 + 0.997288i \(0.523449\pi\)
\(458\) 6.68454 11.5780i 0.312348 0.541003i
\(459\) −11.3040 + 25.6703i −0.527624 + 1.19818i
\(460\) 0.0104974 0.00606065i 0.000489442 0.000282579i
\(461\) 7.44225 12.8904i 0.346620 0.600364i −0.639026 0.769185i \(-0.720663\pi\)
0.985647 + 0.168821i \(0.0539959\pi\)
\(462\) 0 0
\(463\) 13.3616 + 23.1429i 0.620964 + 1.07554i 0.989307 + 0.145851i \(0.0465921\pi\)
−0.368342 + 0.929690i \(0.620075\pi\)
\(464\) 0.842618 + 0.486486i 0.0391175 + 0.0225845i
\(465\) 7.46575 4.67924i 0.346216 0.216995i
\(466\) −9.73092 16.8544i −0.450776 0.780767i
\(467\) −12.3967 21.4717i −0.573650 0.993591i −0.996187 0.0872454i \(-0.972194\pi\)
0.422537 0.906346i \(-0.361140\pi\)
\(468\) −2.22205 1.07630i −0.102714 0.0497520i
\(469\) 0 0
\(470\) −0.979714 0.565638i −0.0451908 0.0260909i
\(471\) −12.2252 6.47894i −0.563306 0.298534i
\(472\) 8.11334i 0.373447i
\(473\) 49.4005i 2.27144i
\(474\) 11.4680 + 6.07766i 0.526742 + 0.279156i
\(475\) 1.65608 + 0.956138i 0.0759861 + 0.0438706i
\(476\) 0 0
\(477\) −1.62278 22.3344i −0.0743020 1.02262i
\(478\) 3.64801 + 6.31855i 0.166856 + 0.289004i
\(479\) −6.26354 10.8488i −0.286189 0.495693i 0.686708 0.726933i \(-0.259055\pi\)
−0.972897 + 0.231240i \(0.925722\pi\)
\(480\) 1.79334 1.12400i 0.0818545 0.0513032i
\(481\) −15.9991 9.23711i −0.729498 0.421176i
\(482\) 7.57587 + 13.1218i 0.345071 + 0.597681i
\(483\) 0 0
\(484\) −0.528540 + 0.915459i −0.0240246 + 0.0416118i
\(485\) 0.963343 0.556187i 0.0437432 0.0252551i
\(486\) 17.9295 15.2534i 0.813299 0.691909i
\(487\) 1.69748 2.94012i 0.0769202 0.133230i −0.824999 0.565133i \(-0.808825\pi\)
0.901920 + 0.431904i \(0.142158\pi\)
\(488\) 9.04780 0.409575
\(489\) −19.9135 + 0.722488i −0.900519 + 0.0326720i
\(490\) 0 0
\(491\) 0.780171 0.450432i 0.0352086 0.0203277i −0.482292 0.876010i \(-0.660196\pi\)
0.517501 + 0.855683i \(0.326862\pi\)
\(492\) 3.67640 0.133385i 0.165745 0.00601345i
\(493\) 1.01479 0.585891i 0.0457040 0.0263872i
\(494\) −1.66905 0.963629i −0.0750943 0.0433557i
\(495\) 7.40255 5.02241i 0.332720 0.225740i
\(496\) 29.3871i 1.31952i
\(497\) 0 0
\(498\) 19.1054 11.9745i 0.856135 0.536591i
\(499\) −10.9344 + 18.9390i −0.489492 + 0.847825i −0.999927 0.0120916i \(-0.996151\pi\)
0.510435 + 0.859916i \(0.329484\pi\)
\(500\) −2.04449 −0.0914325
\(501\) 29.0184 1.05283i 1.29645 0.0470369i
\(502\) 12.0536i 0.537979i
\(503\) 42.9876 1.91672 0.958362 0.285557i \(-0.0921785\pi\)
0.958362 + 0.285557i \(0.0921785\pi\)
\(504\) 0 0
\(505\) −12.4310 −0.553173
\(506\) 0.323367i 0.0143754i
\(507\) −4.03299 6.43466i −0.179111 0.285773i
\(508\) −0.744873 −0.0330484
\(509\) 15.0416 26.0528i 0.666708 1.15477i −0.312111 0.950046i \(-0.601036\pi\)
0.978819 0.204727i \(-0.0656305\pi\)
\(510\) −0.397182 10.9473i −0.0175875 0.484753i
\(511\) 0 0
\(512\) 16.2193i 0.716799i
\(513\) 1.82239 1.33543i 0.0804605 0.0589606i
\(514\) 3.50785 + 2.02526i 0.154725 + 0.0893304i
\(515\) 11.3327 6.54296i 0.499380 0.288317i
\(516\) −3.31520 5.28943i −0.145944 0.232854i
\(517\) 3.21362 1.85538i 0.141335 0.0815997i
\(518\) 0 0
\(519\) 1.38919 2.62128i 0.0609789 0.115061i
\(520\) −5.91384 −0.259339
\(521\) 6.00837 10.4068i 0.263231 0.455930i −0.703867 0.710331i \(-0.748545\pi\)
0.967099 + 0.254401i \(0.0818784\pi\)
\(522\) −0.980833 + 0.0712658i −0.0429299 + 0.00311922i
\(523\) 16.1185 9.30602i 0.704813 0.406924i −0.104325 0.994543i \(-0.533268\pi\)
0.809137 + 0.587620i \(0.199935\pi\)
\(524\) −1.15466 + 1.99993i −0.0504417 + 0.0873675i
\(525\) 0 0
\(526\) −17.6952 30.6490i −0.771548 1.33636i
\(527\) 30.6503 + 17.6959i 1.33515 + 0.770847i
\(528\) 1.08178 + 29.8163i 0.0470782 + 1.29759i
\(529\) −11.4984 19.9159i −0.499933 0.865909i
\(530\) 4.37283 + 7.57397i 0.189944 + 0.328992i
\(531\) −5.26250 7.75642i −0.228373 0.336600i
\(532\) 0 0
\(533\) −19.2559 11.1174i −0.834064 0.481547i
\(534\) −1.48328 40.8826i −0.0641877 1.76916i
\(535\) 3.01422i 0.130316i
\(536\) 10.9111i 0.471286i
\(537\) −21.0377 + 13.1856i −0.907843 + 0.569000i
\(538\) −5.20379 3.00441i −0.224351 0.129529i
\(539\) 0 0
\(540\) −0.455560 + 1.03454i −0.0196042 + 0.0445193i
\(541\) −21.1242 36.5882i −0.908201 1.57305i −0.816562 0.577258i \(-0.804123\pi\)
−0.0916391 0.995792i \(-0.529211\pi\)
\(542\) −9.44245 16.3548i −0.405588 0.702499i
\(543\) 7.39415 + 3.91866i 0.317314 + 0.168166i
\(544\) 7.36247 + 4.25072i 0.315663 + 0.182248i
\(545\) −0.995095 1.72356i −0.0426252 0.0738290i
\(546\) 0 0
\(547\) −6.92349 + 11.9918i −0.296027 + 0.512734i −0.975223 0.221223i \(-0.928995\pi\)
0.679196 + 0.733957i \(0.262329\pi\)
\(548\) −4.20741 + 2.42915i −0.179732 + 0.103768i
\(549\) −8.64977 + 5.86861i −0.369163 + 0.250466i
\(550\) 12.7621 22.1046i 0.544178 0.942544i
\(551\) −0.0943858 −0.00402097
\(552\) 0.133091 + 0.212347i 0.00566473 + 0.00903810i
\(553\) 0 0
\(554\) −25.7514 + 14.8676i −1.09407 + 0.631664i
\(555\) −3.96073 + 7.47353i −0.168123 + 0.317234i
\(556\) 1.53561 0.886585i 0.0651244 0.0375996i
\(557\) 27.2305 + 15.7215i 1.15379 + 0.666143i 0.949809 0.312831i \(-0.101277\pi\)
0.203985 + 0.978974i \(0.434611\pi\)
\(558\) −16.6764 24.5794i −0.705967 1.04053i
\(559\) 37.7296i 1.59579i
\(560\) 0 0
\(561\) 31.7493 + 16.8261i 1.34046 + 0.710399i
\(562\) −6.13311 + 10.6229i −0.258710 + 0.448098i
\(563\) −34.1657 −1.43991 −0.719956 0.694019i \(-0.755838\pi\)
−0.719956 + 0.694019i \(0.755838\pi\)
\(564\) −0.219577 + 0.414322i −0.00924586 + 0.0174461i
\(565\) 8.77129i 0.369011i
\(566\) 2.02950 0.0853063
\(567\) 0 0
\(568\) −9.10981 −0.382239
\(569\) 22.7074i 0.951944i 0.879461 + 0.475972i \(0.157904\pi\)
−0.879461 + 0.475972i \(0.842096\pi\)
\(570\) −0.413189 + 0.779649i −0.0173066 + 0.0326559i
\(571\) −10.5986 −0.443538 −0.221769 0.975099i \(-0.571183\pi\)
−0.221769 + 0.975099i \(0.571183\pi\)
\(572\) −1.58147 + 2.73918i −0.0661245 + 0.114531i
\(573\) 4.80872 + 2.54846i 0.200887 + 0.106464i
\(574\) 0 0
\(575\) 0.245051i 0.0102193i
\(576\) 11.0931 + 16.3501i 0.462211 + 0.681255i
\(577\) 12.6222 + 7.28745i 0.525471 + 0.303381i 0.739170 0.673519i \(-0.235218\pi\)
−0.213699 + 0.976899i \(0.568551\pi\)
\(578\) 15.8746 9.16520i 0.660296 0.381222i
\(579\) −4.87467 + 9.19804i −0.202584 + 0.382258i
\(580\) 0.0408971 0.0236120i 0.00169816 0.000980434i
\(581\) 0 0
\(582\) −1.99148 3.17741i −0.0825494 0.131708i
\(583\) −28.6872 −1.18810
\(584\) −10.5838 + 18.3318i −0.437963 + 0.758574i
\(585\) 5.65368 3.83585i 0.233751 0.158593i
\(586\) 27.8035 16.0523i 1.14855 0.663116i
\(587\) −15.0927 + 26.1414i −0.622944 + 1.07897i 0.365991 + 0.930619i \(0.380730\pi\)
−0.988935 + 0.148352i \(0.952603\pi\)
\(588\) 0 0
\(589\) −1.42539 2.46884i −0.0587321 0.101727i
\(590\) 3.17024 + 1.83034i 0.130517 + 0.0753538i
\(591\) 21.5638 + 11.4281i 0.887016 + 0.470090i
\(592\) −14.1053 24.4310i −0.579723 1.00411i
\(593\) 15.2911 + 26.4850i 0.627930 + 1.08761i 0.987966 + 0.154669i \(0.0494310\pi\)
−0.360036 + 0.932938i \(0.617236\pi\)
\(594\) −17.8247 24.3245i −0.731357 0.998045i
\(595\) 0 0
\(596\) 3.11400 + 1.79787i 0.127554 + 0.0736435i
\(597\) −11.5954 + 7.26754i −0.474568 + 0.297441i
\(598\) 0.246971i 0.0100994i
\(599\) 2.70052i 0.110340i −0.998477 0.0551701i \(-0.982430\pi\)
0.998477 0.0551701i \(-0.0175701\pi\)
\(600\) −0.717217 19.7682i −0.0292803 0.807033i
\(601\) −21.0197 12.1357i −0.857411 0.495026i 0.00573343 0.999984i \(-0.498175\pi\)
−0.863144 + 0.504957i \(0.831508\pi\)
\(602\) 0 0
\(603\) 7.07717 + 10.4311i 0.288205 + 0.424786i
\(604\) 0.736739 + 1.27607i 0.0299775 + 0.0519225i
\(605\) −1.46256 2.53323i −0.0594616 0.102990i
\(606\) 1.51942 + 41.8787i 0.0617221 + 1.70121i
\(607\) −18.5486 10.7090i −0.752865 0.434667i 0.0738631 0.997268i \(-0.476467\pi\)
−0.826728 + 0.562601i \(0.809801\pi\)
\(608\) −0.342391 0.593039i −0.0138858 0.0240509i
\(609\) 0 0
\(610\) 2.04115 3.53537i 0.0826437 0.143143i
\(611\) 2.45439 1.41705i 0.0992942 0.0573275i
\(612\) −4.52865 + 0.329044i −0.183060 + 0.0133008i
\(613\) −2.95306 + 5.11485i −0.119273 + 0.206587i −0.919480 0.393137i \(-0.871390\pi\)
0.800207 + 0.599724i \(0.204723\pi\)
\(614\) 19.9481 0.805039
\(615\) −4.76696 + 8.99481i −0.192222 + 0.362706i
\(616\) 0 0
\(617\) −1.19246 + 0.688465i −0.0480065 + 0.0277166i −0.523811 0.851834i \(-0.675490\pi\)
0.475805 + 0.879551i \(0.342157\pi\)
\(618\) −23.4277 37.3790i −0.942400 1.50360i
\(619\) −29.2918 + 16.9116i −1.17734 + 0.679736i −0.955397 0.295324i \(-0.904572\pi\)
−0.221941 + 0.975060i \(0.571239\pi\)
\(620\) 1.23523 + 0.713163i 0.0496082 + 0.0286413i
\(621\) −0.264970 0.116680i −0.0106329 0.00468221i
\(622\) 31.0133i 1.24352i
\(623\) 0 0
\(624\) 0.826204 + 22.7721i 0.0330746 + 0.911615i
\(625\) −8.16631 + 14.1445i −0.326652 + 0.565779i
\(626\) −24.9308 −0.996435
\(627\) −1.53709 2.45243i −0.0613854 0.0979407i
\(628\) 2.23977i 0.0893764i
\(629\) −33.9749 −1.35467
\(630\) 0 0
\(631\) −25.0205 −0.996049 −0.498024 0.867163i \(-0.665941\pi\)
−0.498024 + 0.867163i \(0.665941\pi\)
\(632\) 12.8857i 0.512567i
\(633\) −8.92531 + 0.323823i −0.354749 + 0.0128708i
\(634\) −14.1434 −0.561707
\(635\) 1.03059 1.78504i 0.0408979 0.0708373i
\(636\) 3.07160 1.92516i 0.121797 0.0763374i
\(637\) 0 0
\(638\) 1.25982i 0.0498768i
\(639\) 8.70906 5.90884i 0.344525 0.233750i
\(640\) −8.79916 5.08020i −0.347817 0.200812i
\(641\) 9.25173 5.34149i 0.365421 0.210976i −0.306035 0.952020i \(-0.599002\pi\)
0.671456 + 0.741044i \(0.265669\pi\)
\(642\) −10.1546 + 0.368421i −0.400769 + 0.0145404i
\(643\) −38.1128 + 22.0044i −1.50302 + 0.867771i −0.503029 + 0.864270i \(0.667781\pi\)
−0.999994 + 0.00350106i \(0.998886\pi\)
\(644\) 0 0
\(645\) 17.2627 0.626313i 0.679716 0.0246610i
\(646\) −3.54431 −0.139449
\(647\) 23.5043 40.7107i 0.924050 1.60050i 0.130968 0.991387i \(-0.458192\pi\)
0.793082 0.609115i \(-0.208475\pi\)
\(648\) −21.7165 8.63702i −0.853105 0.339294i
\(649\) −10.3989 + 6.00380i −0.408192 + 0.235670i
\(650\) 9.74704 16.8824i 0.382310 0.662181i
\(651\) 0 0
\(652\) −1.61287 2.79357i −0.0631648 0.109405i
\(653\) −29.3918 16.9694i −1.15019 0.664063i −0.201257 0.979538i \(-0.564503\pi\)
−0.948934 + 0.315475i \(0.897836\pi\)
\(654\) −5.68484 + 3.56303i −0.222295 + 0.139326i
\(655\) −3.19515 5.53416i −0.124845 0.216237i
\(656\) −16.9765 29.4041i −0.662820 1.14804i
\(657\) −1.77216 24.3903i −0.0691384 0.951554i
\(658\) 0 0
\(659\) −1.36652 0.788962i −0.0532322 0.0307336i 0.473148 0.880983i \(-0.343118\pi\)
−0.526380 + 0.850249i \(0.676451\pi\)
\(660\) 1.27953 + 0.678108i 0.0498055 + 0.0263953i
\(661\) 2.40720i 0.0936293i −0.998904 0.0468147i \(-0.985093\pi\)
0.998904 0.0468147i \(-0.0149070\pi\)
\(662\) 43.5570i 1.69289i
\(663\) 24.2485 + 12.8509i 0.941733 + 0.499088i
\(664\) −19.3868 11.1930i −0.752354 0.434372i
\(665\) 0 0
\(666\) 25.6616 + 12.4298i 0.994366 + 0.481644i
\(667\) 0.00604760 + 0.0104747i 0.000234164 + 0.000405584i
\(668\) 2.35031 + 4.07086i 0.0909363 + 0.157506i
\(669\) −6.43669 + 4.03426i −0.248857 + 0.155974i
\(670\) −4.26344 2.46150i −0.164711 0.0950959i
\(671\) 6.69529 + 11.5966i 0.258469 + 0.447681i
\(672\) 0 0
\(673\) 12.1767 21.0906i 0.469377 0.812984i −0.530010 0.847991i \(-0.677812\pi\)
0.999387 + 0.0350069i \(0.0111453\pi\)
\(674\) 16.3788 9.45629i 0.630887 0.364243i
\(675\) 13.5078 + 18.4334i 0.519914 + 0.709500i
\(676\) 0.614668 1.06464i 0.0236411 0.0409476i
\(677\) 9.67694 0.371915 0.185958 0.982558i \(-0.440461\pi\)
0.185958 + 0.982558i \(0.440461\pi\)
\(678\) 29.5495 1.07210i 1.13484 0.0411736i
\(679\) 0 0
\(680\) −9.41873 + 5.43791i −0.361192 + 0.208534i
\(681\) 16.7447 0.607522i 0.641660 0.0232803i
\(682\) −32.9531 + 19.0255i −1.26184 + 0.728522i
\(683\) −18.6341 10.7584i −0.713012 0.411658i 0.0991632 0.995071i \(-0.468383\pi\)
−0.812175 + 0.583413i \(0.801717\pi\)
\(684\) 0.329159 + 0.159436i 0.0125857 + 0.00609617i
\(685\) 13.4437i 0.513659i
\(686\) 0 0
\(687\) 12.9930 8.14349i 0.495714 0.310694i
\(688\) −28.8069 + 49.8951i −1.09825 + 1.90223i
\(689\) −21.9098 −0.834696
\(690\) 0.112998 0.00409973i 0.00430177 0.000156074i
\(691\) 29.4425i 1.12005i −0.828477 0.560023i \(-0.810792\pi\)
0.828477 0.560023i \(-0.189208\pi\)
\(692\) 0.480244 0.0182561
\(693\) 0 0
\(694\) 43.3730 1.64642
\(695\) 4.90666i 0.186120i
\(696\) 0.518515 + 0.827294i 0.0196543 + 0.0313585i
\(697\) −40.8907 −1.54885
\(698\) −9.66486 + 16.7400i −0.365820 + 0.633619i
\(699\) −0.809354 22.3077i −0.0306126 0.843754i
\(700\) 0 0
\(701\) 40.4325i 1.52712i 0.645740 + 0.763558i \(0.276549\pi\)
−0.645740 + 0.763558i \(0.723451\pi\)
\(702\) −13.6136 18.5778i −0.513812 0.701173i
\(703\) 2.37000 + 1.36832i 0.0893863 + 0.0516072i
\(704\) 21.9203 12.6557i 0.826151 0.476979i
\(705\) −0.689093 1.09945i −0.0259527 0.0414078i
\(706\) −35.3077 + 20.3849i −1.32882 + 0.767197i
\(707\) 0 0
\(708\) 0.710525 1.34070i 0.0267032 0.0503864i
\(709\) −15.9023 −0.597223 −0.298611 0.954375i \(-0.596523\pi\)
−0.298611 + 0.954375i \(0.596523\pi\)
\(710\) −2.05514 + 3.55960i −0.0771280 + 0.133590i
\(711\) 8.35799 + 12.3189i 0.313449 + 0.461994i
\(712\) −35.1743 + 20.3079i −1.31821 + 0.761070i
\(713\) −0.182658 + 0.316373i −0.00684061 + 0.0118483i
\(714\) 0 0
\(715\) −4.37619 7.57978i −0.163660 0.283468i
\(716\) −3.48076 2.00962i −0.130082 0.0751028i
\(717\) 0.303418 + 8.36291i 0.0113313 + 0.312319i
\(718\) 21.1572 + 36.6453i 0.789578 + 1.36759i
\(719\) −13.0488 22.6012i −0.486638 0.842883i 0.513244 0.858243i \(-0.328444\pi\)
−0.999882 + 0.0153605i \(0.995110\pi\)
\(720\) 10.4054 0.756037i 0.387785 0.0281758i
\(721\) 0 0
\(722\) −24.6006 14.2032i −0.915539 0.528587i
\(723\) 0.630111 + 17.3673i 0.0234341 + 0.645898i
\(724\) 1.35468i 0.0503463i
\(725\) 0.954706i 0.0354569i
\(726\) −8.35540 + 5.23684i −0.310098 + 0.194357i
\(727\) 3.74533 + 2.16237i 0.138907 + 0.0801977i 0.567843 0.823137i \(-0.307778\pi\)
−0.428936 + 0.903335i \(0.641111\pi\)
\(728\) 0 0
\(729\) 26.3633 5.82876i 0.976420 0.215880i
\(730\) 4.77535 + 8.27115i 0.176744 + 0.306129i
\(731\) 34.6932 + 60.0904i 1.28317 + 2.22252i
\(732\) −1.49511 0.792360i −0.0552609 0.0292865i
\(733\) 36.6480 + 21.1587i 1.35362 + 0.781515i 0.988755 0.149544i \(-0.0477805\pi\)
0.364869 + 0.931059i \(0.381114\pi\)
\(734\) 25.2475 + 43.7299i 0.931901 + 1.61410i
\(735\) 0 0
\(736\) −0.0438762 + 0.0759958i −0.00161730 + 0.00280124i
\(737\) 13.9847 8.07409i 0.515135 0.297413i
\(738\) 30.8852 + 14.9599i 1.13690 + 0.550683i
\(739\) 1.62120 2.80801i 0.0596369 0.103294i −0.834666 0.550757i \(-0.814339\pi\)
0.894302 + 0.447463i \(0.147672\pi\)
\(740\) −1.36922 −0.0503336
\(741\) −1.17395 1.87304i −0.0431261 0.0688079i
\(742\) 0 0
\(743\) 5.41770 3.12791i 0.198756 0.114752i −0.397319 0.917681i \(-0.630059\pi\)
0.596075 + 0.802929i \(0.296726\pi\)
\(744\) −13.8090 + 26.0563i −0.506263 + 0.955271i
\(745\) −8.61696 + 4.97500i −0.315701 + 0.182270i
\(746\) 10.4205 + 6.01626i 0.381520 + 0.220271i
\(747\) 25.7940 1.87415i 0.943753 0.0685716i
\(748\) 5.81678i 0.212682i
\(749\) 0 0
\(750\) −16.8516 8.93082i −0.615334 0.326107i
\(751\) 9.45315 16.3733i 0.344950 0.597471i −0.640395 0.768046i \(-0.721229\pi\)
0.985345 + 0.170575i \(0.0545625\pi\)
\(752\) 4.32772 0.157816
\(753\) 6.47398 12.2158i 0.235925 0.445169i
\(754\) 0.962186i 0.0350407i
\(755\) −4.07736 −0.148390
\(756\) 0 0
\(757\) −40.7873 −1.48244 −0.741220 0.671262i \(-0.765752\pi\)
−0.741220 + 0.671262i \(0.765752\pi\)
\(758\) 5.86995i 0.213206i
\(759\) −0.173680 + 0.327718i −0.00630418 + 0.0118954i
\(760\) 0.876035 0.0317771
\(761\) 21.3106 36.9110i 0.772508 1.33802i −0.163676 0.986514i \(-0.552335\pi\)
0.936184 0.351509i \(-0.114331\pi\)
\(762\) −6.13958 3.25378i −0.222413 0.117872i
\(763\) 0 0
\(764\) 0.881003i 0.0318736i
\(765\) 5.47724 11.3079i 0.198030 0.408838i
\(766\) −16.5866 9.57627i −0.599298 0.346005i
\(767\) −7.94213 + 4.58539i −0.286774 + 0.165569i
\(768\) −5.35565 + 10.1056i −0.193255 + 0.364655i
\(769\) −0.932209 + 0.538211i −0.0336163 + 0.0194084i −0.516714 0.856158i \(-0.672845\pi\)
0.483098 + 0.875566i \(0.339512\pi\)
\(770\) 0 0
\(771\) 2.46729 + 3.93658i 0.0888573 + 0.141772i
\(772\) −1.68517 −0.0606506
\(773\) 2.96855 5.14169i 0.106771 0.184934i −0.807689 0.589609i \(-0.799282\pi\)
0.914461 + 0.404675i \(0.132615\pi\)
\(774\) −4.21996 58.0794i −0.151683 2.08762i
\(775\) 24.9722 14.4177i 0.897028 0.517899i
\(776\) −1.86150 + 3.22421i −0.0668240 + 0.115742i
\(777\) 0 0
\(778\) 15.5248 + 26.8898i 0.556592 + 0.964046i
\(779\) 2.85243 + 1.64685i 0.102199 + 0.0590046i
\(780\) 0.977237 + 0.517904i 0.0349907 + 0.0185439i
\(781\) −6.74118 11.6761i −0.241218 0.417802i
\(782\) 0.227095 + 0.393341i 0.00812091 + 0.0140658i
\(783\) −1.03231 0.454579i −0.0368917 0.0162453i
\(784\) 0 0
\(785\) 5.36746 + 3.09891i 0.191573 + 0.110605i
\(786\) −18.2534 + 11.4405i −0.651078 + 0.408070i
\(787\) 8.83847i 0.315057i 0.987514 + 0.157529i \(0.0503527\pi\)
−0.987514 + 0.157529i \(0.949647\pi\)
\(788\) 3.95069i 0.140738i
\(789\) −1.47177 40.5655i −0.0523964 1.44417i
\(790\) −5.03502 2.90697i −0.179138 0.103425i
\(791\) 0 0
\(792\) −13.0515 + 26.9452i −0.463766 + 0.957457i
\(793\) 5.11351 + 8.85687i 0.181586 + 0.314517i
\(794\) −11.3033 19.5778i −0.401138 0.694791i
\(795\) 0.363703 + 10.0245i 0.0128992 + 0.355533i
\(796\) −1.91850 1.10765i −0.0679994 0.0392595i
\(797\) 19.0123 + 32.9303i 0.673450 + 1.16645i 0.976919 + 0.213609i \(0.0685218\pi\)
−0.303469 + 0.952841i \(0.598145\pi\)
\(798\) 0 0
\(799\) 2.60601 4.51374i 0.0921940 0.159685i
\(800\) 5.99855 3.46326i 0.212081 0.122445i
\(801\) 20.4548 42.2294i 0.722733 1.49210i
\(802\) −7.78939 + 13.4916i −0.275053 + 0.476406i
\(803\) −31.3278 −1.10553
\(804\) −0.955536 + 1.80301i −0.0336992 + 0.0635872i
\(805\) 0 0
\(806\) −25.1678 + 14.5307i −0.886499 + 0.511821i
\(807\) −3.66014 5.83978i −0.128843 0.205570i
\(808\) 36.0313 20.8027i 1.26758 0.731836i
\(809\) −14.6570 8.46222i −0.515312 0.297516i 0.219702 0.975567i \(-0.429491\pi\)
−0.735015 + 0.678051i \(0.762825\pi\)
\(810\) −8.27402 + 6.53711i −0.290720 + 0.229691i
\(811\) 26.9840i 0.947536i −0.880650 0.473768i \(-0.842894\pi\)
0.880650 0.473768i \(-0.157106\pi\)
\(812\) 0 0
\(813\) −0.785360 21.6464i −0.0275438 0.759172i
\(814\) 18.2637 31.6337i 0.640144 1.10876i
\(815\) 8.92616 0.312670
\(816\) 22.2554 + 35.5085i 0.779093 + 1.24305i
\(817\) 5.58899i 0.195534i
\(818\) −27.9668 −0.977836
\(819\) 0 0
\(820\) −1.64793 −0.0575484
\(821\) 32.0512i 1.11859i 0.828967 + 0.559297i \(0.188929\pi\)
−0.828967 + 0.559297i \(0.811071\pi\)
\(822\) −45.2905 + 1.64320i −1.57969 + 0.0573132i
\(823\) 20.7948 0.724863 0.362431 0.932011i \(-0.381947\pi\)
0.362431 + 0.932011i \(0.381947\pi\)
\(824\) −21.8986 + 37.9295i −0.762875 + 1.32134i
\(825\) 24.8062 15.5475i 0.863641 0.541296i
\(826\) 0 0
\(827\) 34.0792i 1.18505i −0.805552 0.592525i \(-0.798131\pi\)
0.805552 0.592525i \(-0.201869\pi\)
\(828\) −0.00339641 0.0467449i −0.000118033 0.00162450i
\(829\) 29.3229 + 16.9296i 1.01843 + 0.587988i 0.913648 0.406507i \(-0.133253\pi\)
0.104778 + 0.994496i \(0.466587\pi\)
\(830\) −8.74718 + 5.05019i −0.303619 + 0.175295i
\(831\) −34.0833 + 1.23659i −1.18234 + 0.0428968i
\(832\) 16.7416 9.66575i 0.580410 0.335100i
\(833\) 0 0
\(834\) 16.5300 0.599731i 0.572387 0.0207670i
\(835\) −13.0074 −0.450140
\(836\) 0.234267 0.405763i 0.00810231 0.0140336i
\(837\) −3.69921 33.8669i −0.127863 1.17061i
\(838\) −16.6788 + 9.62953i −0.576161 + 0.332647i
\(839\) 11.7633 20.3747i 0.406115 0.703412i −0.588335 0.808617i \(-0.700216\pi\)
0.994451 + 0.105205i \(0.0335498\pi\)
\(840\) 0 0
\(841\) −14.4764 25.0739i −0.499188 0.864618i
\(842\) 17.7542 + 10.2504i 0.611852 + 0.353253i
\(843\) −11.9212 + 7.47171i −0.410586 + 0.257339i
\(844\) −0.722895 1.25209i −0.0248831 0.0430987i
\(845\) 1.70089 + 2.94603i 0.0585124 + 0.101347i
\(846\) −3.61971 + 2.45586i −0.124448 + 0.0844343i
\(847\) 0 0
\(848\) −28.9743 16.7283i −0.994983 0.574454i
\(849\) 2.05681 + 1.09004i 0.0705895 + 0.0374102i
\(850\) 35.8505i 1.22966i
\(851\) 0.350691i 0.0120215i
\(852\) 1.50536 + 0.797791i 0.0515727 + 0.0273319i
\(853\) 39.7270 + 22.9364i 1.36023 + 0.785328i 0.989654 0.143475i \(-0.0458277\pi\)
0.370574 + 0.928803i \(0.379161\pi\)
\(854\) 0 0
\(855\) −0.837497 + 0.568217i −0.0286418 + 0.0194326i
\(856\) 5.04414 + 8.73670i 0.172405 + 0.298614i
\(857\) −9.12274 15.8010i −0.311627 0.539753i 0.667088 0.744979i \(-0.267540\pi\)
−0.978715 + 0.205226i \(0.934207\pi\)
\(858\) −25.0005 + 15.6693i −0.853504 + 0.534943i
\(859\) 5.03737 + 2.90833i 0.171873 + 0.0992309i 0.583469 0.812136i \(-0.301695\pi\)
−0.411596 + 0.911367i \(0.635028\pi\)
\(860\) 1.39817 + 2.42170i 0.0476771 + 0.0825792i
\(861\) 0 0
\(862\) 27.2950 47.2763i 0.929671 1.61024i
\(863\) 27.7060 15.9961i 0.943123 0.544513i 0.0521854 0.998637i \(-0.483381\pi\)
0.890938 + 0.454125i \(0.150048\pi\)
\(864\) −0.888583 8.13515i −0.0302302 0.276763i
\(865\) −0.664458 + 1.15087i −0.0225922 + 0.0391309i
\(866\) 49.8460 1.69384
\(867\) 21.0108 0.762301i 0.713564 0.0258891i
\(868\) 0 0
\(869\) 16.5157 9.53533i 0.560256 0.323464i
\(870\) 0.440235 0.0159723i 0.0149254 0.000541513i
\(871\) 10.6808 6.16658i 0.361906 0.208946i
\(872\) 5.76857 + 3.33048i 0.195348 + 0.112784i
\(873\) −0.311689 4.28979i −0.0105491 0.145187i
\(874\) 0.0365846i 0.00123749i
\(875\) 0 0
\(876\) 3.35434 2.10237i 0.113333 0.0710324i
\(877\) 24.1949 41.9068i 0.817004 1.41509i −0.0908756 0.995862i \(-0.528967\pi\)
0.907880 0.419231i \(-0.137700\pi\)
\(878\) −46.1512 −1.55753
\(879\) 36.7992 1.33513i 1.24121 0.0450327i
\(880\) 13.3651i 0.450536i
\(881\) 26.6822 0.898946 0.449473 0.893294i \(-0.351612\pi\)
0.449473 + 0.893294i \(0.351612\pi\)
\(882\) 0 0
\(883\) 35.0484 1.17947 0.589737 0.807595i \(-0.299231\pi\)
0.589737 + 0.807595i \(0.299231\pi\)
\(884\) 4.44255i 0.149419i
\(885\) 2.22982 + 3.55770i 0.0749547 + 0.119591i
\(886\) 31.2629 1.05030
\(887\) −6.48380 + 11.2303i −0.217705 + 0.377076i −0.954106 0.299469i \(-0.903190\pi\)
0.736401 + 0.676545i \(0.236524\pi\)
\(888\) −1.02640 28.2901i −0.0344438 0.949353i
\(889\) 0 0
\(890\) 18.3255i 0.614273i
\(891\) −4.99992 34.2254i −0.167504 1.14659i
\(892\) −1.06497 0.614862i −0.0356579 0.0205871i
\(893\) −0.363577 + 0.209911i −0.0121666 + 0.00702441i
\(894\) 17.8135 + 28.4215i 0.595771 + 0.950557i
\(895\) 9.63184 5.56095i 0.321957 0.185882i
\(896\) 0 0
\(897\) −0.132648 + 0.250294i −0.00442898 + 0.00835708i
\(898\) −9.66828 −0.322635
\(899\) −0.711627 + 1.23257i −0.0237341 + 0.0411086i
\(900\) −1.61268 + 3.32942i −0.0537560 + 0.110981i
\(901\) −34.8948 + 20.1465i −1.16251 + 0.671178i
\(902\) 21.9815 38.0730i 0.731902 1.26769i
\(903\) 0 0
\(904\) −14.6783 25.4236i −0.488193 0.845576i
\(905\) −3.24641 1.87431i −0.107914 0.0623043i
\(906\) 0.498368 + 13.7362i 0.0165572 + 0.456354i
\(907\) 4.56307 + 7.90346i 0.151514 + 0.262430i 0.931784 0.363012i \(-0.118252\pi\)
−0.780270 + 0.625443i \(0.784918\pi\)
\(908\) 1.35622 + 2.34904i 0.0450077 + 0.0779557i
\(909\) −20.9531 + 43.2583i −0.694972 + 1.43479i
\(910\) 0 0
\(911\) 41.5720 + 24.0016i 1.37734 + 0.795209i 0.991839 0.127498i \(-0.0406947\pi\)
0.385503 + 0.922707i \(0.374028\pi\)
\(912\) −0.122388 3.37331i −0.00405268 0.111701i
\(913\) 33.1308i 1.09647i
\(914\) 4.75197i 0.157181i
\(915\) 3.96746 2.48664i 0.131160 0.0822059i
\(916\) 2.14973 + 1.24115i 0.0710292 + 0.0410087i
\(917\) 0 0
\(918\) −38.7645 17.0701i −1.27942 0.563396i
\(919\) 19.8096 + 34.3113i 0.653459 + 1.13182i 0.982278 + 0.187432i \(0.0600163\pi\)
−0.328818 + 0.944393i \(0.606650\pi\)
\(920\) −0.0561303 0.0972206i −0.00185056 0.00320527i
\(921\) 20.2165 + 10.7141i 0.666156 + 0.353041i
\(922\) 19.4657 + 11.2385i 0.641068 + 0.370121i
\(923\) −5.14856 8.91757i −0.169467 0.293526i
\(924\) 0 0
\(925\) −13.8405 + 23.9724i −0.455072 + 0.788208i
\(926\) −34.9480 + 20.1772i −1.14846 + 0.663065i
\(927\) −3.66670 50.4649i −0.120430 1.65749i
\(928\) −0.170939 + 0.296076i −0.00561136 + 0.00971915i
\(929\) 23.5795 0.773618 0.386809 0.922160i \(-0.373577\pi\)
0.386809 + 0.922160i \(0.373577\pi\)
\(930\) 7.06609 + 11.2740i 0.231706 + 0.369689i
\(931\) 0 0
\(932\) 3.12944 1.80679i 0.102508 0.0591832i
\(933\) 16.6572 31.4306i 0.545333 1.02899i
\(934\) 32.4243 18.7202i 1.06096 0.612543i
\(935\) −13.9396 8.04801i −0.455872 0.263198i
\(936\) −9.96808 + 20.5794i −0.325817 + 0.672658i
\(937\) 52.5144i 1.71557i 0.514007 + 0.857786i \(0.328160\pi\)
−0.514007 + 0.857786i \(0.671840\pi\)
\(938\) 0 0
\(939\) −25.2662 13.3903i −0.824533 0.436976i
\(940\) 0.105025 0.181908i 0.00342553 0.00593319i
\(941\) 49.1425 1.60200 0.801000 0.598664i \(-0.204302\pi\)
0.801000 + 0.598664i \(0.204302\pi\)
\(942\) 9.78382 18.4612i 0.318774 0.601497i
\(943\) 0.422076i 0.0137447i
\(944\) −14.0040 −0.455791
\(945\) 0 0
\(946\) −74.5995 −2.42544
\(947\) 9.29426i 0.302023i 0.988532 + 0.151012i \(0.0482531\pi\)
−0.988532 + 0.151012i \(0.951747\pi\)
\(948\) −1.12847 + 2.12931i −0.0366509 + 0.0691569i
\(949\) −23.9266 −0.776689
\(950\) −1.44386 + 2.50084i −0.0468450 + 0.0811379i
\(951\) −14.3337 7.59641i −0.464803 0.246330i
\(952\) 0 0
\(953\) 40.3761i 1.30791i 0.756534 + 0.653955i \(0.226891\pi\)
−0.756534 + 0.653955i \(0.773109\pi\)
\(954\) 33.7270 2.45055i 1.09195 0.0793395i
\(955\) −2.11127 1.21894i −0.0683191 0.0394440i
\(956\) −1.17319 + 0.677344i −0.0379438 + 0.0219069i
\(957\) −0.676648 + 1.27677i −0.0218729 + 0.0412722i
\(958\) 16.3827 9.45854i 0.529300 0.305592i
\(959\) 0 0
\(960\) −4.70034 7.49943i −0.151703 0.242043i
\(961\) −11.9872 −0.386682
\(962\) 13.9489 24.1602i 0.449731 0.778957i
\(963\) −10.4891 5.08062i −0.338006 0.163721i
\(964\) −2.43638 + 1.40665i −0.0784706 + 0.0453050i
\(965\) 2.33157 4.03840i 0.0750560 0.130001i
\(966\) 0 0
\(967\) 8.78620 + 15.2181i 0.282545 + 0.489383i 0.972011 0.234936i \(-0.0754879\pi\)
−0.689466 + 0.724318i \(0.742155\pi\)
\(968\) 8.47846 + 4.89504i 0.272508 + 0.157333i
\(969\) −3.59200 1.90365i −0.115392 0.0611539i
\(970\) 0.839894 + 1.45474i 0.0269674 + 0.0467089i
\(971\) −20.1321 34.8697i −0.646068 1.11902i −0.984054 0.177872i \(-0.943079\pi\)
0.337985 0.941151i \(-0.390255\pi\)
\(972\) 2.83217 + 3.32905i 0.0908420 + 0.106779i
\(973\) 0 0
\(974\) 4.43986 + 2.56336i 0.142262 + 0.0821353i
\(975\) 18.9457 11.8744i 0.606748 0.380285i
\(976\) 15.6169i 0.499885i
\(977\) 26.5109i 0.848159i 0.905625 + 0.424080i \(0.139402\pi\)
−0.905625 + 0.424080i \(0.860598\pi\)
\(978\) −1.09103 30.0712i −0.0348872 0.961572i
\(979\) −52.0573 30.0553i −1.66376 0.960572i
\(980\) 0 0
\(981\) −7.67503 + 0.557655i −0.245045 + 0.0178046i
\(982\) 0.680195 + 1.17813i 0.0217059 + 0.0375957i
\(983\) 19.1357 + 33.1440i 0.610334 + 1.05713i 0.991184 + 0.132493i \(0.0422982\pi\)
−0.380850 + 0.924637i \(0.624368\pi\)
\(984\) −1.23533 34.0487i −0.0393810 1.08543i
\(985\) −9.46759 5.46612i −0.301663 0.174165i
\(986\) 0.884752 + 1.53243i 0.0281762 + 0.0488027i
\(987\) 0 0
\(988\) 0.178921 0.309901i 0.00569225 0.00985926i
\(989\) −0.620255 + 0.358105i −0.0197230 + 0.0113871i
\(990\) 7.58431 + 11.1785i 0.241045 + 0.355277i
\(991\) 30.4509 52.7425i 0.967305 1.67542i 0.264016 0.964518i \(-0.414953\pi\)
0.703289 0.710904i \(-0.251714\pi\)
\(992\) −10.3259 −0.327848
\(993\) −23.3944 + 44.1431i −0.742399 + 1.40084i
\(994\) 0 0
\(995\) 5.30881 3.06504i 0.168301 0.0971684i
\(996\) 2.22337 + 3.54739i 0.0704500 + 0.112403i
\(997\) −12.4807 + 7.20573i −0.395267 + 0.228208i −0.684440 0.729069i \(-0.739953\pi\)
0.289173 + 0.957277i \(0.406620\pi\)
\(998\) −28.5996 16.5120i −0.905306 0.522679i
\(999\) 19.3309 + 26.3798i 0.611601 + 0.834621i
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 441.2.i.b.227.4 10
3.2 odd 2 1323.2.i.b.521.2 10
7.2 even 3 63.2.s.b.47.4 yes 10
7.3 odd 6 441.2.o.d.146.2 10
7.4 even 3 441.2.o.c.146.2 10
7.5 odd 6 441.2.s.b.362.4 10
7.6 odd 2 63.2.i.b.38.4 yes 10
9.4 even 3 1323.2.s.b.962.2 10
9.5 odd 6 441.2.s.b.374.4 10
21.2 odd 6 189.2.s.b.89.2 10
21.5 even 6 1323.2.s.b.656.2 10
21.11 odd 6 1323.2.o.d.440.4 10
21.17 even 6 1323.2.o.c.440.4 10
21.20 even 2 189.2.i.b.143.2 10
28.23 odd 6 1008.2.df.b.929.4 10
28.27 even 2 1008.2.ca.b.353.2 10
63.2 odd 6 567.2.p.d.404.4 10
63.4 even 3 1323.2.o.c.881.4 10
63.5 even 6 inner 441.2.i.b.68.2 10
63.13 odd 6 189.2.s.b.17.2 10
63.16 even 3 567.2.p.c.404.2 10
63.20 even 6 567.2.p.c.80.2 10
63.23 odd 6 63.2.i.b.5.2 10
63.31 odd 6 1323.2.o.d.881.4 10
63.32 odd 6 441.2.o.d.293.2 10
63.34 odd 6 567.2.p.d.80.4 10
63.40 odd 6 1323.2.i.b.1097.4 10
63.41 even 6 63.2.s.b.59.4 yes 10
63.58 even 3 189.2.i.b.152.4 10
63.59 even 6 441.2.o.c.293.2 10
84.23 even 6 3024.2.df.b.1601.3 10
84.83 odd 2 3024.2.ca.b.2033.3 10
252.23 even 6 1008.2.ca.b.257.2 10
252.139 even 6 3024.2.df.b.17.3 10
252.167 odd 6 1008.2.df.b.689.4 10
252.247 odd 6 3024.2.ca.b.2609.3 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
63.2.i.b.5.2 10 63.23 odd 6
63.2.i.b.38.4 yes 10 7.6 odd 2
63.2.s.b.47.4 yes 10 7.2 even 3
63.2.s.b.59.4 yes 10 63.41 even 6
189.2.i.b.143.2 10 21.20 even 2
189.2.i.b.152.4 10 63.58 even 3
189.2.s.b.17.2 10 63.13 odd 6
189.2.s.b.89.2 10 21.2 odd 6
441.2.i.b.68.2 10 63.5 even 6 inner
441.2.i.b.227.4 10 1.1 even 1 trivial
441.2.o.c.146.2 10 7.4 even 3
441.2.o.c.293.2 10 63.59 even 6
441.2.o.d.146.2 10 7.3 odd 6
441.2.o.d.293.2 10 63.32 odd 6
441.2.s.b.362.4 10 7.5 odd 6
441.2.s.b.374.4 10 9.5 odd 6
567.2.p.c.80.2 10 63.20 even 6
567.2.p.c.404.2 10 63.16 even 3
567.2.p.d.80.4 10 63.34 odd 6
567.2.p.d.404.4 10 63.2 odd 6
1008.2.ca.b.257.2 10 252.23 even 6
1008.2.ca.b.353.2 10 28.27 even 2
1008.2.df.b.689.4 10 252.167 odd 6
1008.2.df.b.929.4 10 28.23 odd 6
1323.2.i.b.521.2 10 3.2 odd 2
1323.2.i.b.1097.4 10 63.40 odd 6
1323.2.o.c.440.4 10 21.17 even 6
1323.2.o.c.881.4 10 63.4 even 3
1323.2.o.d.440.4 10 21.11 odd 6
1323.2.o.d.881.4 10 63.31 odd 6
1323.2.s.b.656.2 10 21.5 even 6
1323.2.s.b.962.2 10 9.4 even 3
3024.2.ca.b.2033.3 10 84.83 odd 2
3024.2.ca.b.2609.3 10 252.247 odd 6
3024.2.df.b.17.3 10 252.139 even 6
3024.2.df.b.1601.3 10 84.23 even 6