Properties

Label 84.2.e.a.71.7
Level $84$
Weight $2$
Character 84.71
Analytic conductor $0.671$
Analytic rank $0$
Dimension $12$
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] = [84,2,Mod(71,84)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(84, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("84.71");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 84 = 2^{2} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 84.e (of order \(2\), degree \(1\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(0.670743376979\)
Analytic rank: \(0\)
Dimension: \(12\)
Coefficient field: 12.0.2593100598870016.2
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 2x^{10} + x^{8} + 4x^{6} + 4x^{4} - 32x^{2} + 64 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 71.7
Root \(1.37027 + 0.349801i\) of defining polynomial
Character \(\chi\) \(=\) 84.71
Dual form 84.2.e.a.71.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.349801 - 1.37027i) q^{2} +(-1.72007 - 0.203364i) q^{3} +(-1.75528 - 0.958643i) q^{4} -2.27740i q^{5} +(-0.880346 + 2.28582i) q^{6} -1.00000i q^{7} +(-1.92760 + 2.06987i) q^{8} +(2.91729 + 0.699602i) q^{9} +O(q^{10})\) \(q+(0.349801 - 1.37027i) q^{2} +(-1.72007 - 0.203364i) q^{3} +(-1.75528 - 0.958643i) q^{4} -2.27740i q^{5} +(-0.880346 + 2.28582i) q^{6} -1.00000i q^{7} +(-1.92760 + 2.06987i) q^{8} +(2.91729 + 0.699602i) q^{9} +(-3.12065 - 0.796636i) q^{10} +4.31834 q^{11} +(2.82425 + 2.00589i) q^{12} -0.406728 q^{13} +(-1.37027 - 0.349801i) q^{14} +(-0.463141 + 3.91729i) q^{15} +(2.16201 + 3.36537i) q^{16} +4.31834i q^{17} +(1.97911 - 3.75275i) q^{18} -5.42784i q^{19} +(-2.18321 + 3.99747i) q^{20} +(-0.203364 + 1.72007i) q^{21} +(1.51056 - 5.91729i) q^{22} +1.16274 q^{23} +(3.73654 - 3.16832i) q^{24} -0.186543 q^{25} +(-0.142274 + 0.557328i) q^{26} +(-4.87566 - 1.79664i) q^{27} +(-0.958643 + 1.75528i) q^{28} -3.72469i q^{29} +(5.20573 + 2.00490i) q^{30} +5.83457i q^{31} +(5.36774 - 1.78532i) q^{32} +(-7.42784 - 0.878195i) q^{33} +(5.91729 + 1.51056i) q^{34} -2.27740 q^{35} +(-4.44998 - 4.02463i) q^{36} -7.83457 q^{37} +(-7.43761 - 1.89866i) q^{38} +(0.699602 + 0.0827140i) q^{39} +(4.71392 + 4.38991i) q^{40} +2.56195i q^{41} +(2.28582 + 0.880346i) q^{42} +11.0211i q^{43} +(-7.57988 - 4.13974i) q^{44} +(1.59327 - 6.64382i) q^{45} +(0.406728 - 1.59327i) q^{46} +2.32549 q^{47} +(-3.03441 - 6.22835i) q^{48} -1.00000 q^{49} +(-0.0652529 + 0.255614i) q^{50} +(0.878195 - 7.42784i) q^{51} +(0.713922 + 0.389907i) q^{52} -5.48108i q^{53} +(-4.16739 + 6.05251i) q^{54} -9.83457i q^{55} +(2.06987 + 1.92760i) q^{56} +(-1.10383 + 9.33627i) q^{57} +(-5.10383 - 1.30290i) q^{58} +3.91306 q^{59} +(4.56822 - 6.43194i) q^{60} +10.4490 q^{61} +(7.99494 + 2.04094i) q^{62} +(0.699602 - 2.91729i) q^{63} +(-0.568736 - 7.97976i) q^{64} +0.926283i q^{65} +(-3.80163 + 9.87096i) q^{66} +7.83457i q^{67} +(4.13974 - 7.57988i) q^{68} +(-2.00000 - 0.236460i) q^{69} +(-0.796636 + 3.12065i) q^{70} -4.88743 q^{71} +(-7.07144 + 4.68986i) q^{72} +2.81346 q^{73} +(-2.74054 + 10.7355i) q^{74} +(0.320867 + 0.0379362i) q^{75} +(-5.20336 + 9.52738i) q^{76} -4.31834i q^{77} +(0.358062 - 0.929710i) q^{78} -4.00000i q^{79} +(7.66429 - 4.92375i) q^{80} +(8.02112 + 4.08188i) q^{81} +(3.51056 + 0.896171i) q^{82} +0.641735 q^{83} +(2.00589 - 2.82425i) q^{84} +9.83457 q^{85} +(15.1019 + 3.85520i) q^{86} +(-0.757468 + 6.40673i) q^{87} +(-8.32401 + 8.93840i) q^{88} +13.9970i q^{89} +(-8.54650 - 4.50723i) q^{90} +0.406728i q^{91} +(-2.04094 - 1.11466i) q^{92} +(1.18654 - 10.0359i) q^{93} +(0.813457 - 3.18654i) q^{94} -12.3614 q^{95} +(-9.59596 + 1.97928i) q^{96} -2.00000 q^{97} +(-0.349801 + 1.37027i) q^{98} +(12.5978 + 3.02112i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 4 q^{4} - 6 q^{6} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q - 4 q^{4} - 6 q^{6} - 4 q^{9} + 4 q^{10} - 6 q^{12} + 4 q^{16} - 8 q^{18} - 16 q^{22} + 2 q^{24} - 12 q^{25} + 8 q^{28} + 20 q^{30} - 16 q^{33} + 32 q^{34} - 20 q^{36} - 16 q^{37} + 20 q^{40} + 10 q^{42} + 24 q^{45} + 46 q^{48} - 12 q^{49} - 28 q^{52} + 10 q^{54} + 16 q^{57} - 32 q^{58} + 28 q^{60} - 16 q^{61} + 20 q^{64} - 12 q^{66} - 24 q^{69} - 12 q^{70} - 32 q^{72} + 24 q^{73} - 60 q^{76} + 20 q^{78} + 28 q^{81} + 8 q^{82} - 14 q^{84} + 40 q^{85} - 56 q^{88} - 80 q^{90} + 24 q^{93} - 34 q^{96} - 24 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/84\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(43\) \(73\)
\(\chi(n)\) \(-1\) \(-1\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.349801 1.37027i 0.247347 0.968927i
\(3\) −1.72007 0.203364i −0.993083 0.117412i
\(4\) −1.75528 0.958643i −0.877639 0.479321i
\(5\) 2.27740i 1.01848i −0.860624 0.509242i \(-0.829926\pi\)
0.860624 0.509242i \(-0.170074\pi\)
\(6\) −0.880346 + 2.28582i −0.359400 + 0.933184i
\(7\) 1.00000i 0.377964i
\(8\) −1.92760 + 2.06987i −0.681509 + 0.731810i
\(9\) 2.91729 + 0.699602i 0.972429 + 0.233201i
\(10\) −3.12065 0.796636i −0.986836 0.251918i
\(11\) 4.31834 1.30203 0.651014 0.759066i \(-0.274344\pi\)
0.651014 + 0.759066i \(0.274344\pi\)
\(12\) 2.82425 + 2.00589i 0.815291 + 0.579052i
\(13\) −0.406728 −0.112806 −0.0564031 0.998408i \(-0.517963\pi\)
−0.0564031 + 0.998408i \(0.517963\pi\)
\(14\) −1.37027 0.349801i −0.366220 0.0934882i
\(15\) −0.463141 + 3.91729i −0.119583 + 1.01144i
\(16\) 2.16201 + 3.36537i 0.540502 + 0.841343i
\(17\) 4.31834i 1.04735i 0.851918 + 0.523675i \(0.175439\pi\)
−0.851918 + 0.523675i \(0.824561\pi\)
\(18\) 1.97911 3.75275i 0.466481 0.884531i
\(19\) 5.42784i 1.24523i −0.782527 0.622616i \(-0.786070\pi\)
0.782527 0.622616i \(-0.213930\pi\)
\(20\) −2.18321 + 3.99747i −0.488181 + 0.893861i
\(21\) −0.203364 + 1.72007i −0.0443777 + 0.375350i
\(22\) 1.51056 5.91729i 0.322052 1.26157i
\(23\) 1.16274 0.242449 0.121224 0.992625i \(-0.461318\pi\)
0.121224 + 0.992625i \(0.461318\pi\)
\(24\) 3.73654 3.16832i 0.762718 0.646731i
\(25\) −0.186543 −0.0373086
\(26\) −0.142274 + 0.557328i −0.0279022 + 0.109301i
\(27\) −4.87566 1.79664i −0.938322 0.345763i
\(28\) −0.958643 + 1.75528i −0.181166 + 0.331717i
\(29\) 3.72469i 0.691657i −0.938298 0.345829i \(-0.887598\pi\)
0.938298 0.345829i \(-0.112402\pi\)
\(30\) 5.20573 + 2.00490i 0.950432 + 0.366043i
\(31\) 5.83457i 1.04792i 0.851743 + 0.523960i \(0.175546\pi\)
−0.851743 + 0.523960i \(0.824454\pi\)
\(32\) 5.36774 1.78532i 0.948891 0.315604i
\(33\) −7.42784 0.878195i −1.29302 0.152874i
\(34\) 5.91729 + 1.51056i 1.01481 + 0.259058i
\(35\) −2.27740 −0.384951
\(36\) −4.44998 4.02463i −0.741664 0.670772i
\(37\) −7.83457 −1.28800 −0.643998 0.765027i \(-0.722725\pi\)
−0.643998 + 0.765027i \(0.722725\pi\)
\(38\) −7.43761 1.89866i −1.20654 0.308004i
\(39\) 0.699602 + 0.0827140i 0.112026 + 0.0132448i
\(40\) 4.71392 + 4.38991i 0.745336 + 0.694105i
\(41\) 2.56195i 0.400109i 0.979785 + 0.200054i \(0.0641119\pi\)
−0.979785 + 0.200054i \(0.935888\pi\)
\(42\) 2.28582 + 0.880346i 0.352710 + 0.135840i
\(43\) 11.0211i 1.68070i 0.542041 + 0.840352i \(0.317652\pi\)
−0.542041 + 0.840352i \(0.682348\pi\)
\(44\) −7.57988 4.13974i −1.14271 0.624090i
\(45\) 1.59327 6.64382i 0.237511 0.990403i
\(46\) 0.406728 1.59327i 0.0599688 0.234915i
\(47\) 2.32549 0.339207 0.169603 0.985512i \(-0.445751\pi\)
0.169603 + 0.985512i \(0.445751\pi\)
\(48\) −3.03441 6.22835i −0.437979 0.898985i
\(49\) −1.00000 −0.142857
\(50\) −0.0652529 + 0.255614i −0.00922816 + 0.0361493i
\(51\) 0.878195 7.42784i 0.122972 1.04011i
\(52\) 0.713922 + 0.389907i 0.0990031 + 0.0540704i
\(53\) 5.48108i 0.752884i −0.926440 0.376442i \(-0.877147\pi\)
0.926440 0.376442i \(-0.122853\pi\)
\(54\) −4.16739 + 6.05251i −0.567110 + 0.823642i
\(55\) 9.83457i 1.32609i
\(56\) 2.06987 + 1.92760i 0.276598 + 0.257586i
\(57\) −1.10383 + 9.33627i −0.146206 + 1.23662i
\(58\) −5.10383 1.30290i −0.670166 0.171079i
\(59\) 3.91306 0.509437 0.254719 0.967015i \(-0.418017\pi\)
0.254719 + 0.967015i \(0.418017\pi\)
\(60\) 4.56822 6.43194i 0.589755 0.830360i
\(61\) 10.4490 1.33785 0.668926 0.743329i \(-0.266754\pi\)
0.668926 + 0.743329i \(0.266754\pi\)
\(62\) 7.99494 + 2.04094i 1.01536 + 0.259199i
\(63\) 0.699602 2.91729i 0.0881415 0.367543i
\(64\) −0.568736 7.97976i −0.0710920 0.997470i
\(65\) 0.926283i 0.114891i
\(66\) −3.80163 + 9.87096i −0.467948 + 1.21503i
\(67\) 7.83457i 0.957145i 0.878048 + 0.478573i \(0.158846\pi\)
−0.878048 + 0.478573i \(0.841154\pi\)
\(68\) 4.13974 7.57988i 0.502018 0.919196i
\(69\) −2.00000 0.236460i −0.240772 0.0284665i
\(70\) −0.796636 + 3.12065i −0.0952162 + 0.372989i
\(71\) −4.88743 −0.580031 −0.290016 0.957022i \(-0.593661\pi\)
−0.290016 + 0.957022i \(0.593661\pi\)
\(72\) −7.07144 + 4.68986i −0.833377 + 0.552705i
\(73\) 2.81346 0.329290 0.164645 0.986353i \(-0.447352\pi\)
0.164645 + 0.986353i \(0.447352\pi\)
\(74\) −2.74054 + 10.7355i −0.318581 + 1.24797i
\(75\) 0.320867 + 0.0379362i 0.0370506 + 0.00438050i
\(76\) −5.20336 + 9.52738i −0.596867 + 1.09287i
\(77\) 4.31834i 0.492120i
\(78\) 0.358062 0.929710i 0.0405425 0.105269i
\(79\) 4.00000i 0.450035i −0.974355 0.225018i \(-0.927756\pi\)
0.974355 0.225018i \(-0.0722440\pi\)
\(80\) 7.66429 4.92375i 0.856894 0.550492i
\(81\) 8.02112 + 4.08188i 0.891235 + 0.453542i
\(82\) 3.51056 + 0.896171i 0.387676 + 0.0989655i
\(83\) 0.641735 0.0704395 0.0352198 0.999380i \(-0.488787\pi\)
0.0352198 + 0.999380i \(0.488787\pi\)
\(84\) 2.00589 2.82425i 0.218861 0.308151i
\(85\) 9.83457 1.06671
\(86\) 15.1019 + 3.85520i 1.62848 + 0.415716i
\(87\) −0.757468 + 6.40673i −0.0812091 + 0.686873i
\(88\) −8.32401 + 8.93840i −0.887343 + 0.952837i
\(89\) 13.9970i 1.48368i 0.670576 + 0.741841i \(0.266047\pi\)
−0.670576 + 0.741841i \(0.733953\pi\)
\(90\) −8.54650 4.50723i −0.900880 0.475103i
\(91\) 0.406728i 0.0426367i
\(92\) −2.04094 1.11466i −0.212782 0.116211i
\(93\) 1.18654 10.0359i 0.123039 1.04067i
\(94\) 0.813457 3.18654i 0.0839017 0.328667i
\(95\) −12.3614 −1.26825
\(96\) −9.59596 + 1.97928i −0.979384 + 0.202009i
\(97\) −2.00000 −0.203069 −0.101535 0.994832i \(-0.532375\pi\)
−0.101535 + 0.994832i \(0.532375\pi\)
\(98\) −0.349801 + 1.37027i −0.0353352 + 0.138418i
\(99\) 12.5978 + 3.02112i 1.26613 + 0.303633i
\(100\) 0.327435 + 0.178828i 0.0327435 + 0.0178828i
\(101\) 8.68476i 0.864166i 0.901834 + 0.432083i \(0.142221\pi\)
−0.901834 + 0.432083i \(0.857779\pi\)
\(102\) −9.87096 3.80163i −0.977370 0.376417i
\(103\) 10.6480i 1.04918i −0.851355 0.524591i \(-0.824218\pi\)
0.851355 0.524591i \(-0.175782\pi\)
\(104\) 0.784009 0.841876i 0.0768784 0.0825527i
\(105\) 3.91729 + 0.463141i 0.382288 + 0.0451980i
\(106\) −7.51056 1.91729i −0.729490 0.186223i
\(107\) −8.40021 −0.812079 −0.406040 0.913855i \(-0.633090\pi\)
−0.406040 + 0.913855i \(0.633090\pi\)
\(108\) 6.83582 + 7.82762i 0.657777 + 0.753213i
\(109\) −10.4826 −1.00405 −0.502026 0.864853i \(-0.667412\pi\)
−0.502026 + 0.864853i \(0.667412\pi\)
\(110\) −13.4760 3.44014i −1.28489 0.328005i
\(111\) 13.4760 + 1.59327i 1.27909 + 0.151227i
\(112\) 3.36537 2.16201i 0.317998 0.204290i
\(113\) 9.56296i 0.899607i −0.893128 0.449804i \(-0.851494\pi\)
0.893128 0.449804i \(-0.148506\pi\)
\(114\) 12.4071 + 4.77838i 1.16203 + 0.447536i
\(115\) 2.64803i 0.246930i
\(116\) −3.57065 + 6.53787i −0.331526 + 0.607026i
\(117\) −1.18654 0.284548i −0.109696 0.0263065i
\(118\) 1.36879 5.36195i 0.126008 0.493608i
\(119\) 4.31834 0.395861
\(120\) −7.21553 8.50959i −0.658685 0.776816i
\(121\) 7.64803 0.695275
\(122\) 3.65505 14.3179i 0.330913 1.29628i
\(123\) 0.521008 4.40673i 0.0469777 0.397341i
\(124\) 5.59327 10.2413i 0.502291 0.919696i
\(125\) 10.9622i 0.980485i
\(126\) −3.75275 1.97911i −0.334321 0.176313i
\(127\) 6.20766i 0.550841i −0.961324 0.275420i \(-0.911183\pi\)
0.961324 0.275420i \(-0.0888170\pi\)
\(128\) −11.1334 2.01200i −0.984060 0.177838i
\(129\) 2.24130 18.9571i 0.197335 1.66908i
\(130\) 1.26926 + 0.324014i 0.111321 + 0.0284179i
\(131\) −14.4023 −1.25833 −0.629167 0.777270i \(-0.716604\pi\)
−0.629167 + 0.777270i \(0.716604\pi\)
\(132\) 12.1961 + 8.66213i 1.06153 + 0.753941i
\(133\) −5.42784 −0.470654
\(134\) 10.7355 + 2.74054i 0.927404 + 0.236747i
\(135\) −4.09166 + 11.1038i −0.352154 + 0.955665i
\(136\) −8.93840 8.32401i −0.766462 0.713778i
\(137\) 2.32549i 0.198680i −0.995054 0.0993398i \(-0.968327\pi\)
0.995054 0.0993398i \(-0.0316731\pi\)
\(138\) −1.02362 + 2.65783i −0.0871360 + 0.226249i
\(139\) 9.22019i 0.782046i 0.920381 + 0.391023i \(0.127879\pi\)
−0.920381 + 0.391023i \(0.872121\pi\)
\(140\) 3.99747 + 2.18321i 0.337848 + 0.184515i
\(141\) −4.00000 0.472921i −0.336861 0.0398271i
\(142\) −1.70963 + 6.69710i −0.143469 + 0.562008i
\(143\) −1.75639 −0.146877
\(144\) 3.95277 + 11.3303i 0.329398 + 0.944191i
\(145\) −8.48260 −0.704442
\(146\) 0.984149 3.85520i 0.0814488 0.319058i
\(147\) 1.72007 + 0.203364i 0.141869 + 0.0167732i
\(148\) 13.7519 + 7.51056i 1.13040 + 0.617364i
\(149\) 17.3891i 1.42457i 0.701891 + 0.712284i \(0.252339\pi\)
−0.701891 + 0.712284i \(0.747661\pi\)
\(150\) 0.164223 0.426405i 0.0134087 0.0348158i
\(151\) 4.16543i 0.338978i −0.985532 0.169489i \(-0.945788\pi\)
0.985532 0.169489i \(-0.0542117\pi\)
\(152\) 11.2349 + 10.4627i 0.911274 + 0.848637i
\(153\) −3.02112 + 12.5978i −0.244243 + 1.01847i
\(154\) −5.91729 1.51056i −0.476828 0.121724i
\(155\) 13.2876 1.06729
\(156\) −1.14870 0.815854i −0.0919698 0.0653206i
\(157\) −19.2624 −1.53731 −0.768654 0.639665i \(-0.779073\pi\)
−0.768654 + 0.639665i \(0.779073\pi\)
\(158\) −5.48108 1.39920i −0.436051 0.111315i
\(159\) −1.11466 + 9.42784i −0.0883979 + 0.747677i
\(160\) −4.06589 12.2245i −0.321437 0.966430i
\(161\) 1.16274i 0.0916370i
\(162\) 8.39906 9.56325i 0.659893 0.751360i
\(163\) 8.64803i 0.677366i 0.940901 + 0.338683i \(0.109981\pi\)
−0.940901 + 0.338683i \(0.890019\pi\)
\(164\) 2.45599 4.49693i 0.191781 0.351151i
\(165\) −2.00000 + 16.9162i −0.155700 + 1.31692i
\(166\) 0.224479 0.879350i 0.0174230 0.0682508i
\(167\) −1.75639 −0.135914 −0.0679568 0.997688i \(-0.521648\pi\)
−0.0679568 + 0.997688i \(0.521648\pi\)
\(168\) −3.16832 3.73654i −0.244441 0.288280i
\(169\) −12.8346 −0.987275
\(170\) 3.44014 13.4760i 0.263847 1.03356i
\(171\) 3.79733 15.8346i 0.290389 1.21090i
\(172\) 10.5653 19.3451i 0.805598 1.47505i
\(173\) 7.87421i 0.598665i −0.954149 0.299333i \(-0.903236\pi\)
0.954149 0.299333i \(-0.0967640\pi\)
\(174\) 8.51398 + 3.27902i 0.645443 + 0.248581i
\(175\) 0.186543i 0.0141013i
\(176\) 9.33627 + 14.5328i 0.703748 + 1.09545i
\(177\) −6.73074 0.795777i −0.505914 0.0598142i
\(178\) 19.1797 + 4.89617i 1.43758 + 0.366984i
\(179\) −9.34605 −0.698557 −0.349278 0.937019i \(-0.613573\pi\)
−0.349278 + 0.937019i \(0.613573\pi\)
\(180\) −9.16569 + 10.1344i −0.683170 + 0.755372i
\(181\) 16.8893 1.25537 0.627687 0.778466i \(-0.284002\pi\)
0.627687 + 0.778466i \(0.284002\pi\)
\(182\) 0.557328 + 0.142274i 0.0413119 + 0.0105460i
\(183\) −17.9729 2.12494i −1.32860 0.157080i
\(184\) −2.24130 + 2.40673i −0.165231 + 0.177426i
\(185\) 17.8424i 1.31180i
\(186\) −13.3368 5.13644i −0.977902 0.376622i
\(187\) 18.6480i 1.36368i
\(188\) −4.08188 2.22931i −0.297701 0.162589i
\(189\) −1.79664 + 4.87566i −0.130686 + 0.354652i
\(190\) −4.32401 + 16.9384i −0.313697 + 1.22884i
\(191\) 20.3082 1.46945 0.734725 0.678365i \(-0.237311\pi\)
0.734725 + 0.678365i \(0.237311\pi\)
\(192\) −0.644532 + 13.8414i −0.0465151 + 0.998918i
\(193\) 6.85569 0.493483 0.246742 0.969081i \(-0.420640\pi\)
0.246742 + 0.969081i \(0.420640\pi\)
\(194\) −0.699602 + 2.74054i −0.0502285 + 0.196759i
\(195\) 0.188373 1.59327i 0.0134897 0.114097i
\(196\) 1.75528 + 0.958643i 0.125377 + 0.0684745i
\(197\) 1.96830i 0.140235i 0.997539 + 0.0701177i \(0.0223375\pi\)
−0.997539 + 0.0701177i \(0.977662\pi\)
\(198\) 8.54647 16.2056i 0.607371 1.15168i
\(199\) 6.37309i 0.451776i −0.974153 0.225888i \(-0.927472\pi\)
0.974153 0.225888i \(-0.0725284\pi\)
\(200\) 0.359580 0.386120i 0.0254262 0.0273028i
\(201\) 1.59327 13.4760i 0.112381 0.950525i
\(202\) 11.9005 + 3.03794i 0.837314 + 0.213748i
\(203\) −3.72469 −0.261422
\(204\) −8.66213 + 12.1961i −0.606470 + 0.853895i
\(205\) 5.83457 0.407504
\(206\) −14.5907 3.72469i −1.01658 0.259511i
\(207\) 3.39205 + 0.813457i 0.235764 + 0.0565392i
\(208\) −0.879350 1.36879i −0.0609719 0.0949087i
\(209\) 23.4393i 1.62133i
\(210\) 2.00490 5.20573i 0.138351 0.359230i
\(211\) 25.1306i 1.73006i −0.501717 0.865032i \(-0.667298\pi\)
0.501717 0.865032i \(-0.332702\pi\)
\(212\) −5.25440 + 9.62082i −0.360874 + 0.660761i
\(213\) 8.40673 + 0.993929i 0.576020 + 0.0681029i
\(214\) −2.93840 + 11.5106i −0.200865 + 0.786846i
\(215\) 25.0995 1.71177
\(216\) 13.1171 6.62881i 0.892507 0.451033i
\(217\) 5.83457 0.396077
\(218\) −3.66682 + 14.3640i −0.248349 + 0.972852i
\(219\) −4.83934 0.572156i −0.327013 0.0386627i
\(220\) −9.42784 + 17.2624i −0.635625 + 1.16383i
\(221\) 1.75639i 0.118148i
\(222\) 6.89713 17.9085i 0.462905 1.20194i
\(223\) 9.22877i 0.618004i 0.951061 + 0.309002i \(0.0999950\pi\)
−0.951061 + 0.309002i \(0.900005\pi\)
\(224\) −1.78532 5.36774i −0.119287 0.358647i
\(225\) −0.544200 0.130506i −0.0362800 0.00870039i
\(226\) −13.1038 3.34513i −0.871654 0.222515i
\(227\) 19.5262 1.29600 0.647999 0.761641i \(-0.275606\pi\)
0.647999 + 0.761641i \(0.275606\pi\)
\(228\) 10.8877 15.3296i 0.721054 1.01523i
\(229\) 2.03364 0.134387 0.0671934 0.997740i \(-0.478596\pi\)
0.0671934 + 0.997740i \(0.478596\pi\)
\(230\) −3.62851 0.926283i −0.239257 0.0610773i
\(231\) −0.878195 + 7.42784i −0.0577810 + 0.488716i
\(232\) 7.70963 + 7.17970i 0.506162 + 0.471370i
\(233\) 3.27133i 0.214312i −0.994242 0.107156i \(-0.965826\pi\)
0.994242 0.107156i \(-0.0341744\pi\)
\(234\) −0.804961 + 1.52635i −0.0526220 + 0.0997806i
\(235\) 5.29606i 0.345477i
\(236\) −6.86851 3.75123i −0.447102 0.244184i
\(237\) −0.813457 + 6.88028i −0.0528397 + 0.446922i
\(238\) 1.51056 5.91729i 0.0979149 0.383561i
\(239\) −24.5058 −1.58515 −0.792575 0.609775i \(-0.791260\pi\)
−0.792575 + 0.609775i \(0.791260\pi\)
\(240\) −14.1844 + 6.91056i −0.915601 + 0.446075i
\(241\) 18.4153 1.18623 0.593117 0.805116i \(-0.297897\pi\)
0.593117 + 0.805116i \(0.297897\pi\)
\(242\) 2.67529 10.4799i 0.171974 0.673671i
\(243\) −12.9668 8.65232i −0.831819 0.555047i
\(244\) −18.3408 10.0168i −1.17415 0.641261i
\(245\) 2.27740i 0.145498i
\(246\) −5.85616 2.25540i −0.373375 0.143799i
\(247\) 2.20766i 0.140470i
\(248\) −12.0768 11.2467i −0.766878 0.714167i
\(249\) −1.10383 0.130506i −0.0699523 0.00827047i
\(250\) −15.0211 3.83457i −0.950019 0.242520i
\(251\) −15.4443 −0.974837 −0.487418 0.873169i \(-0.662061\pi\)
−0.487418 + 0.873169i \(0.662061\pi\)
\(252\) −4.02463 + 4.44998i −0.253528 + 0.280323i
\(253\) 5.02112 0.315675
\(254\) −8.50617 2.17144i −0.533724 0.136249i
\(255\) −16.9162 2.00000i −1.05933 0.125245i
\(256\) −6.65145 + 14.5519i −0.415716 + 0.909495i
\(257\) 8.96931i 0.559490i −0.960074 0.279745i \(-0.909750\pi\)
0.960074 0.279745i \(-0.0902499\pi\)
\(258\) −25.1923 9.70239i −1.56841 0.604045i
\(259\) 7.83457i 0.486817i
\(260\) 0.887974 1.62588i 0.0550698 0.100833i
\(261\) 2.60580 10.8660i 0.161295 0.672587i
\(262\) −5.03794 + 19.7350i −0.311245 + 1.21923i
\(263\) 19.3624 1.19393 0.596967 0.802265i \(-0.296372\pi\)
0.596967 + 0.802265i \(0.296372\pi\)
\(264\) 16.1356 13.6819i 0.993080 0.842061i
\(265\) −12.4826 −0.766800
\(266\) −1.89866 + 7.43761i −0.116415 + 0.456029i
\(267\) 2.84649 24.0759i 0.174203 1.47342i
\(268\) 7.51056 13.7519i 0.458780 0.840028i
\(269\) 0.0480876i 0.00293195i 0.999999 + 0.00146598i \(0.000466635\pi\)
−0.999999 + 0.00146598i \(0.999533\pi\)
\(270\) 13.7840 + 9.49080i 0.838866 + 0.577592i
\(271\) 19.8768i 1.20743i 0.797200 + 0.603715i \(0.206313\pi\)
−0.797200 + 0.603715i \(0.793687\pi\)
\(272\) −14.5328 + 9.33627i −0.881181 + 0.566095i
\(273\) 0.0827140 0.699602i 0.00500608 0.0423418i
\(274\) −3.18654 0.813457i −0.192506 0.0491427i
\(275\) −0.805556 −0.0485769
\(276\) 3.28388 + 2.33234i 0.197666 + 0.140390i
\(277\) 10.2749 0.617361 0.308681 0.951166i \(-0.400113\pi\)
0.308681 + 0.951166i \(0.400113\pi\)
\(278\) 12.6341 + 3.22523i 0.757745 + 0.193436i
\(279\) −4.08188 + 17.0211i −0.244376 + 1.01903i
\(280\) 4.38991 4.71392i 0.262347 0.281711i
\(281\) 6.78411i 0.404706i −0.979313 0.202353i \(-0.935141\pi\)
0.979313 0.202353i \(-0.0648588\pi\)
\(282\) −2.04723 + 5.31565i −0.121911 + 0.316542i
\(283\) 5.42784i 0.322652i 0.986901 + 0.161326i \(0.0515770\pi\)
−0.986901 + 0.161326i \(0.948423\pi\)
\(284\) 8.57881 + 4.68530i 0.509058 + 0.278022i
\(285\) 21.2624 + 2.51386i 1.25948 + 0.148908i
\(286\) −0.614387 + 2.40673i −0.0363294 + 0.142313i
\(287\) 2.56195 0.151227
\(288\) 16.9082 1.45302i 0.996328 0.0856201i
\(289\) −1.64803 −0.0969429
\(290\) −2.96722 + 11.6235i −0.174241 + 0.682553i
\(291\) 3.44014 + 0.406728i 0.201665 + 0.0238428i
\(292\) −4.93840 2.69710i −0.288998 0.157836i
\(293\) 28.1874i 1.64673i 0.567515 + 0.823363i \(0.307905\pi\)
−0.567515 + 0.823363i \(0.692095\pi\)
\(294\) 0.880346 2.28582i 0.0513428 0.133312i
\(295\) 8.91160i 0.518853i
\(296\) 15.1019 16.2166i 0.877780 0.942568i
\(297\) −21.0548 7.75848i −1.22172 0.450193i
\(298\) 23.8277 + 6.08271i 1.38030 + 0.352362i
\(299\) −0.472921 −0.0273497
\(300\) −0.526844 0.374186i −0.0304174 0.0216036i
\(301\) 11.0211 0.635247
\(302\) −5.70776 1.45707i −0.328445 0.0838450i
\(303\) 1.76617 14.9384i 0.101464 0.858189i
\(304\) 18.2667 11.7350i 1.04767 0.673051i
\(305\) 23.7964i 1.36258i
\(306\) 16.2056 + 8.54647i 0.926414 + 0.488569i
\(307\) 2.24130i 0.127918i 0.997953 + 0.0639589i \(0.0203727\pi\)
−0.997953 + 0.0639589i \(0.979627\pi\)
\(308\) −4.13974 + 7.57988i −0.235884 + 0.431904i
\(309\) −2.16543 + 18.3154i −0.123187 + 1.04192i
\(310\) 4.64803 18.2077i 0.263990 1.03413i
\(311\) −26.4791 −1.50149 −0.750746 0.660591i \(-0.770306\pi\)
−0.750746 + 0.660591i \(0.770306\pi\)
\(312\) −1.51976 + 1.28865i −0.0860393 + 0.0729552i
\(313\) 0.440371 0.0248912 0.0124456 0.999923i \(-0.496038\pi\)
0.0124456 + 0.999923i \(0.496038\pi\)
\(314\) −6.73801 + 26.3947i −0.380248 + 1.48954i
\(315\) −6.64382 1.59327i −0.374337 0.0897707i
\(316\) −3.83457 + 7.02112i −0.215712 + 0.394969i
\(317\) 11.7923i 0.662320i 0.943575 + 0.331160i \(0.107440\pi\)
−0.943575 + 0.331160i \(0.892560\pi\)
\(318\) 12.5288 + 4.82525i 0.702579 + 0.270586i
\(319\) 16.0845i 0.900557i
\(320\) −18.1731 + 1.29524i −1.01591 + 0.0724060i
\(321\) 14.4490 + 1.70830i 0.806462 + 0.0953482i
\(322\) −1.59327 0.406728i −0.0887896 0.0226661i
\(323\) 23.4393 1.30419
\(324\) −10.1662 14.8542i −0.564791 0.825234i
\(325\) 0.0758724 0.00420864
\(326\) 11.8501 + 3.02509i 0.656318 + 0.167544i
\(327\) 18.0308 + 2.13179i 0.997106 + 0.117888i
\(328\) −5.30290 4.93840i −0.292804 0.272678i
\(329\) 2.32549i 0.128208i
\(330\) 22.4801 + 8.65783i 1.23749 + 0.476598i
\(331\) 1.30974i 0.0719899i 0.999352 + 0.0359949i \(0.0114600\pi\)
−0.999352 + 0.0359949i \(0.988540\pi\)
\(332\) −1.12642 0.615195i −0.0618205 0.0337632i
\(333\) −22.8557 5.48108i −1.25248 0.300361i
\(334\) −0.614387 + 2.40673i −0.0336177 + 0.131690i
\(335\) 17.8424 0.974837
\(336\) −6.22835 + 3.03441i −0.339784 + 0.165541i
\(337\) −15.4615 −0.842241 −0.421120 0.907005i \(-0.638363\pi\)
−0.421120 + 0.907005i \(0.638363\pi\)
\(338\) −4.48954 + 17.5868i −0.244199 + 0.956597i
\(339\) −1.94476 + 16.4490i −0.105625 + 0.893385i
\(340\) −17.2624 9.42784i −0.936186 0.511297i
\(341\) 25.1956i 1.36442i
\(342\) −20.3693 10.7423i −1.10145 0.580878i
\(343\) 1.00000i 0.0539949i
\(344\) −22.8123 21.2443i −1.22996 1.14541i
\(345\) −0.538514 + 4.55480i −0.0289926 + 0.245222i
\(346\) −10.7898 2.75441i −0.580063 0.148078i
\(347\) 27.6614 1.48494 0.742471 0.669878i \(-0.233654\pi\)
0.742471 + 0.669878i \(0.233654\pi\)
\(348\) 7.47133 10.5195i 0.400506 0.563902i
\(349\) −18.9316 −1.01338 −0.506692 0.862127i \(-0.669132\pi\)
−0.506692 + 0.862127i \(0.669132\pi\)
\(350\) 0.255614 + 0.0652529i 0.0136632 + 0.00348792i
\(351\) 1.98307 + 0.730743i 0.105849 + 0.0390042i
\(352\) 23.1797 7.70963i 1.23548 0.410925i
\(353\) 1.99285i 0.106069i 0.998593 + 0.0530344i \(0.0168893\pi\)
−0.998593 + 0.0530344i \(0.983111\pi\)
\(354\) −3.44485 + 8.94457i −0.183092 + 0.475399i
\(355\) 11.1306i 0.590752i
\(356\) 13.4182 24.5687i 0.711161 1.30214i
\(357\) −7.42784 0.878195i −0.393123 0.0464790i
\(358\) −3.26926 + 12.8066i −0.172786 + 0.676851i
\(359\) −2.35004 −0.124030 −0.0620151 0.998075i \(-0.519753\pi\)
−0.0620151 + 0.998075i \(0.519753\pi\)
\(360\) 10.6807 + 16.1045i 0.562921 + 0.848781i
\(361\) −10.4615 −0.550605
\(362\) 5.90790 23.1429i 0.310512 1.21637i
\(363\) −13.1551 1.55534i −0.690466 0.0816339i
\(364\) 0.389907 0.713922i 0.0204367 0.0374197i
\(365\) 6.40736i 0.335377i
\(366\) −9.19870 + 23.8845i −0.480824 + 1.24846i
\(367\) 34.1940i 1.78491i −0.451135 0.892455i \(-0.648981\pi\)
0.451135 0.892455i \(-0.351019\pi\)
\(368\) 2.51386 + 3.91306i 0.131044 + 0.203982i
\(369\) −1.79234 + 7.47393i −0.0933056 + 0.389077i
\(370\) 24.4490 + 6.24130i 1.27104 + 0.324470i
\(371\) −5.48108 −0.284563
\(372\) −11.7035 + 16.4783i −0.606800 + 0.854359i
\(373\) −17.6691 −0.914874 −0.457437 0.889242i \(-0.651232\pi\)
−0.457437 + 0.889242i \(0.651232\pi\)
\(374\) 25.5528 + 6.52310i 1.32131 + 0.337301i
\(375\) −2.22931 + 18.8557i −0.115121 + 0.973703i
\(376\) −4.48260 + 4.81346i −0.231172 + 0.248235i
\(377\) 1.51494i 0.0780232i
\(378\) 6.05251 + 4.16739i 0.311308 + 0.214347i
\(379\) 5.39420i 0.277082i 0.990357 + 0.138541i \(0.0442412\pi\)
−0.990357 + 0.138541i \(0.955759\pi\)
\(380\) 21.6976 + 11.8501i 1.11307 + 0.607899i
\(381\) −1.26242 + 10.6776i −0.0646755 + 0.547031i
\(382\) 7.10383 27.8277i 0.363464 1.42379i
\(383\) 1.85257 0.0946617 0.0473308 0.998879i \(-0.484928\pi\)
0.0473308 + 0.998879i \(0.484928\pi\)
\(384\) 18.7410 + 5.72492i 0.956373 + 0.292149i
\(385\) −9.83457 −0.501216
\(386\) 2.39812 9.39414i 0.122061 0.478149i
\(387\) −7.71039 + 32.1517i −0.391941 + 1.63437i
\(388\) 3.51056 + 1.91729i 0.178222 + 0.0973354i
\(389\) 5.38490i 0.273025i −0.990638 0.136513i \(-0.956411\pi\)
0.990638 0.136513i \(-0.0435895\pi\)
\(390\) −2.11732 0.815449i −0.107215 0.0412919i
\(391\) 5.02112i 0.253929i
\(392\) 1.92760 2.06987i 0.0973584 0.104544i
\(393\) 24.7730 + 2.92891i 1.24963 + 0.147744i
\(394\) 2.69710 + 0.688513i 0.135878 + 0.0346868i
\(395\) −9.10959 −0.458353
\(396\) −19.2165 17.3797i −0.965666 0.873363i
\(397\) −21.6355 −1.08585 −0.542927 0.839780i \(-0.682684\pi\)
−0.542927 + 0.839780i \(0.682684\pi\)
\(398\) −8.73285 2.22931i −0.437738 0.111745i
\(399\) 9.33627 + 1.10383i 0.467398 + 0.0552606i
\(400\) −0.403308 0.627787i −0.0201654 0.0313893i
\(401\) 38.2714i 1.91118i −0.294697 0.955591i \(-0.595219\pi\)
0.294697 0.955591i \(-0.404781\pi\)
\(402\) −17.9085 6.89713i −0.893192 0.343998i
\(403\) 2.37309i 0.118212i
\(404\) 8.32558 15.2442i 0.414213 0.758426i
\(405\) 9.29606 18.2673i 0.461925 0.907708i
\(406\) −1.30290 + 5.10383i −0.0646618 + 0.253299i
\(407\) −33.8323 −1.67701
\(408\) 13.6819 + 16.1356i 0.677354 + 0.798833i
\(409\) 4.77123 0.235922 0.117961 0.993018i \(-0.462364\pi\)
0.117961 + 0.993018i \(0.462364\pi\)
\(410\) 2.04094 7.99494i 0.100795 0.394842i
\(411\) −0.472921 + 4.00000i −0.0233275 + 0.197305i
\(412\) −10.2077 + 18.6903i −0.502895 + 0.920803i
\(413\) 3.91306i 0.192549i
\(414\) 2.30120 4.36348i 0.113098 0.214453i
\(415\) 1.46149i 0.0717415i
\(416\) −2.18321 + 0.726142i −0.107041 + 0.0356020i
\(417\) 1.87506 15.8594i 0.0918219 0.776637i
\(418\) −32.1181 8.19907i −1.57095 0.401030i
\(419\) −8.33257 −0.407072 −0.203536 0.979067i \(-0.565243\pi\)
−0.203536 + 0.979067i \(0.565243\pi\)
\(420\) −6.43194 4.56822i −0.313847 0.222906i
\(421\) −20.7325 −1.01044 −0.505220 0.862991i \(-0.668589\pi\)
−0.505220 + 0.862991i \(0.668589\pi\)
\(422\) −34.4357 8.79071i −1.67631 0.427925i
\(423\) 6.78411 + 1.62691i 0.329855 + 0.0791033i
\(424\) 11.3451 + 10.5653i 0.550968 + 0.513097i
\(425\) 0.805556i 0.0390752i
\(426\) 4.30263 11.1718i 0.208463 0.541276i
\(427\) 10.4490i 0.505661i
\(428\) 14.7447 + 8.05280i 0.712713 + 0.389247i
\(429\) 3.02112 + 0.357187i 0.145861 + 0.0172451i
\(430\) 8.77981 34.3930i 0.423400 1.65858i
\(431\) −34.9951 −1.68565 −0.842826 0.538186i \(-0.819110\pi\)
−0.842826 + 0.538186i \(0.819110\pi\)
\(432\) −4.49487 20.2928i −0.216260 0.976336i
\(433\) 17.3383 0.833225 0.416612 0.909084i \(-0.363217\pi\)
0.416612 + 0.909084i \(0.363217\pi\)
\(434\) 2.04094 7.99494i 0.0979682 0.383769i
\(435\) 14.5907 + 1.72506i 0.699569 + 0.0827102i
\(436\) 18.3999 + 10.0491i 0.881195 + 0.481263i
\(437\) 6.31119i 0.301905i
\(438\) −2.47682 + 6.43107i −0.118347 + 0.307288i
\(439\) 33.2961i 1.58913i −0.607176 0.794567i \(-0.707698\pi\)
0.607176 0.794567i \(-0.292302\pi\)
\(440\) 20.3563 + 18.9571i 0.970449 + 0.903744i
\(441\) −2.91729 0.699602i −0.138918 0.0333144i
\(442\) −2.40673 0.614387i −0.114476 0.0292234i
\(443\) −8.87313 −0.421575 −0.210788 0.977532i \(-0.567603\pi\)
−0.210788 + 0.977532i \(0.567603\pi\)
\(444\) −22.1268 15.7153i −1.05009 0.745816i
\(445\) 31.8768 1.51111
\(446\) 12.6459 + 3.22823i 0.598801 + 0.152861i
\(447\) 3.53632 29.9104i 0.167262 1.41472i
\(448\) −7.97976 + 0.568736i −0.377008 + 0.0268702i
\(449\) 26.3829i 1.24509i 0.782585 + 0.622544i \(0.213901\pi\)
−0.782585 + 0.622544i \(0.786099\pi\)
\(450\) −0.369190 + 0.700049i −0.0174038 + 0.0330006i
\(451\) 11.0633i 0.520953i
\(452\) −9.16746 + 16.7857i −0.431201 + 0.789531i
\(453\) −0.847099 + 7.16483i −0.0398002 + 0.336633i
\(454\) 6.83028 26.7562i 0.320561 1.25573i
\(455\) 0.926283 0.0434248
\(456\) −17.1971 20.2814i −0.805330 0.949762i
\(457\) 30.2499 1.41503 0.707515 0.706698i \(-0.249816\pi\)
0.707515 + 0.706698i \(0.249816\pi\)
\(458\) 0.711370 2.78664i 0.0332401 0.130211i
\(459\) 7.75848 21.0548i 0.362135 0.982752i
\(460\) −2.53851 + 4.64803i −0.118359 + 0.216715i
\(461\) 1.56302i 0.0727973i 0.999337 + 0.0363987i \(0.0115886\pi\)
−0.999337 + 0.0363987i \(0.988411\pi\)
\(462\) 9.87096 + 3.80163i 0.459238 + 0.176868i
\(463\) 33.2961i 1.54740i 0.633553 + 0.773700i \(0.281596\pi\)
−0.633553 + 0.773700i \(0.718404\pi\)
\(464\) 12.5350 8.05280i 0.581921 0.373842i
\(465\) −22.8557 2.70223i −1.05991 0.125313i
\(466\) −4.48260 1.14431i −0.207652 0.0530093i
\(467\) −17.2969 −0.800404 −0.400202 0.916427i \(-0.631060\pi\)
−0.400202 + 0.916427i \(0.631060\pi\)
\(468\) 1.80993 + 1.63693i 0.0836642 + 0.0756672i
\(469\) 7.83457 0.361767
\(470\) −7.25703 1.85257i −0.334742 0.0854525i
\(471\) 33.1327 + 3.91729i 1.52667 + 0.180499i
\(472\) −7.54281 + 8.09954i −0.347186 + 0.372811i
\(473\) 47.5929i 2.18832i
\(474\) 9.14330 + 3.52138i 0.419965 + 0.161743i
\(475\) 1.01253i 0.0464579i
\(476\) −7.57988 4.13974i −0.347423 0.189745i
\(477\) 3.83457 15.9899i 0.175573 0.732126i
\(478\) −8.57216 + 33.5796i −0.392081 + 1.53589i
\(479\) 16.6081 0.758842 0.379421 0.925224i \(-0.376123\pi\)
0.379421 + 0.925224i \(0.376123\pi\)
\(480\) 4.50760 + 21.8538i 0.205743 + 0.997486i
\(481\) 3.18654 0.145294
\(482\) 6.44169 25.2340i 0.293411 1.14938i
\(483\) −0.236460 + 2.00000i −0.0107593 + 0.0910032i
\(484\) −13.4244 7.33173i −0.610201 0.333260i
\(485\) 4.55480i 0.206823i
\(486\) −16.3918 + 14.7414i −0.743547 + 0.668683i
\(487\) 24.2499i 1.09887i 0.835537 + 0.549434i \(0.185156\pi\)
−0.835537 + 0.549434i \(0.814844\pi\)
\(488\) −20.1414 + 21.6280i −0.911758 + 0.979054i
\(489\) 1.75870 14.8752i 0.0795311 0.672681i
\(490\) 3.12065 + 0.796636i 0.140977 + 0.0359883i
\(491\) 20.3082 0.916497 0.458248 0.888824i \(-0.348477\pi\)
0.458248 + 0.888824i \(0.348477\pi\)
\(492\) −5.13899 + 7.23558i −0.231684 + 0.326205i
\(493\) 16.0845 0.724408
\(494\) 3.02509 + 0.772241i 0.136105 + 0.0347447i
\(495\) 6.88028 28.6903i 0.309246 1.28953i
\(496\) −19.6355 + 12.6144i −0.881660 + 0.566403i
\(497\) 4.88743i 0.219231i
\(498\) −0.564949 + 1.46689i −0.0253160 + 0.0657330i
\(499\) 10.5385i 0.471769i −0.971781 0.235884i \(-0.924201\pi\)
0.971781 0.235884i \(-0.0757987\pi\)
\(500\) −10.5088 + 19.2416i −0.469968 + 0.860512i
\(501\) 3.02112 + 0.357187i 0.134973 + 0.0159579i
\(502\) −5.40243 + 21.1629i −0.241122 + 0.944546i
\(503\) 27.6664 1.23358 0.616792 0.787126i \(-0.288432\pi\)
0.616792 + 0.787126i \(0.288432\pi\)
\(504\) 4.68986 + 7.07144i 0.208903 + 0.314987i
\(505\) 19.7787 0.880139
\(506\) 1.75639 6.88028i 0.0780811 0.305866i
\(507\) 22.0764 + 2.61009i 0.980446 + 0.115918i
\(508\) −5.95093 + 10.8962i −0.264030 + 0.483439i
\(509\) 28.1874i 1.24939i −0.780871 0.624693i \(-0.785224\pi\)
0.780871 0.624693i \(-0.214776\pi\)
\(510\) −8.65783 + 22.4801i −0.383375 + 0.995436i
\(511\) 2.81346i 0.124460i
\(512\) 17.6134 + 14.2046i 0.778408 + 0.627758i
\(513\) −9.75186 + 26.4643i −0.430555 + 1.16843i
\(514\) −12.2904 3.13747i −0.542105 0.138388i
\(515\) −24.2498 −1.06857
\(516\) −22.1072 + 31.1264i −0.973215 + 1.37026i
\(517\) 10.0422 0.441657
\(518\) 10.7355 + 2.74054i 0.471690 + 0.120412i
\(519\) −1.60133 + 13.5442i −0.0702907 + 0.594524i
\(520\) −1.91729 1.78550i −0.0840786 0.0782994i
\(521\) 24.0133i 1.05204i −0.850471 0.526022i \(-0.823683\pi\)
0.850471 0.526022i \(-0.176317\pi\)
\(522\) −13.9778 7.37158i −0.611793 0.322645i
\(523\) 2.77981i 0.121553i −0.998151 0.0607764i \(-0.980642\pi\)
0.998151 0.0607764i \(-0.0193577\pi\)
\(524\) 25.2801 + 13.8067i 1.10436 + 0.603147i
\(525\) 0.0379362 0.320867i 0.00165567 0.0140038i
\(526\) 6.77297 26.5317i 0.295316 1.15684i
\(527\) −25.1956 −1.09754
\(528\) −13.1036 26.8961i −0.570261 1.17050i
\(529\) −21.6480 −0.941219
\(530\) −4.36642 + 17.1045i −0.189665 + 0.742973i
\(531\) 11.4155 + 2.73758i 0.495391 + 0.118801i
\(532\) 9.52738 + 5.20336i 0.413064 + 0.225594i
\(533\) 1.04202i 0.0451347i
\(534\) −31.9947 12.3222i −1.38455 0.533235i
\(535\) 19.1306i 0.827089i
\(536\) −16.2166 15.1019i −0.700449 0.652303i
\(537\) 16.0759 + 1.90065i 0.693725 + 0.0820192i
\(538\) 0.0658929 + 0.0168211i 0.00284085 + 0.000725208i
\(539\) −4.31834 −0.186004
\(540\) 17.8266 15.5679i 0.767135 0.669935i
\(541\) 8.31717 0.357583 0.178792 0.983887i \(-0.442781\pi\)
0.178792 + 0.983887i \(0.442781\pi\)
\(542\) 27.2366 + 6.95292i 1.16991 + 0.298654i
\(543\) −29.0508 3.43469i −1.24669 0.147396i
\(544\) 7.70963 + 23.1797i 0.330548 + 0.993822i
\(545\) 23.8731i 1.02261i
\(546\) −0.929710 0.358062i −0.0397879 0.0153236i
\(547\) 15.4364i 0.660014i 0.943978 + 0.330007i \(0.107051\pi\)
−0.943978 + 0.330007i \(0.892949\pi\)
\(548\) −2.22931 + 4.08188i −0.0952314 + 0.174369i
\(549\) 30.4826 + 7.31011i 1.30097 + 0.311988i
\(550\) −0.281784 + 1.10383i −0.0120153 + 0.0470674i
\(551\) −20.2170 −0.861274
\(552\) 4.34464 3.68394i 0.184920 0.156799i
\(553\) −4.00000 −0.170097
\(554\) 3.59418 14.0794i 0.152702 0.598178i
\(555\) 3.62851 30.6903i 0.154022 1.30273i
\(556\) 8.83887 16.1840i 0.374851 0.686354i
\(557\) 13.4525i 0.570000i 0.958528 + 0.285000i \(0.0919936\pi\)
−0.958528 + 0.285000i \(0.908006\pi\)
\(558\) 21.8957 + 11.5473i 0.926918 + 0.488835i
\(559\) 4.48260i 0.189594i
\(560\) −4.92375 7.66429i −0.208066 0.323875i
\(561\) 3.79234 32.0759i 0.160113 1.35425i
\(562\) −9.29606 2.37309i −0.392131 0.100103i
\(563\) 34.0011 1.43298 0.716488 0.697599i \(-0.245748\pi\)
0.716488 + 0.697599i \(0.245748\pi\)
\(564\) 6.56775 + 4.66468i 0.276552 + 0.196418i
\(565\) −21.7787 −0.916235
\(566\) 7.43761 + 1.89866i 0.312626 + 0.0798068i
\(567\) 4.08188 8.02112i 0.171423 0.336855i
\(568\) 9.42100 10.1164i 0.395296 0.424473i
\(569\) 26.5948i 1.11491i 0.830206 + 0.557457i \(0.188223\pi\)
−0.830206 + 0.557457i \(0.811777\pi\)
\(570\) 10.8823 28.2559i 0.455808 1.18351i
\(571\) 8.23271i 0.344528i −0.985051 0.172264i \(-0.944892\pi\)
0.985051 0.172264i \(-0.0551083\pi\)
\(572\) 3.08295 + 1.68375i 0.128905 + 0.0704012i
\(573\) −34.9316 4.12996i −1.45929 0.172532i
\(574\) 0.896171 3.51056i 0.0374054 0.146528i
\(575\) −0.216902 −0.00904543
\(576\) 3.92349 23.6771i 0.163479 0.986547i
\(577\) 1.58468 0.0659712 0.0329856 0.999456i \(-0.489498\pi\)
0.0329856 + 0.999456i \(0.489498\pi\)
\(578\) −0.576482 + 2.25824i −0.0239785 + 0.0939306i
\(579\) −11.7923 1.39420i −0.490070 0.0579410i
\(580\) 14.8893 + 8.13179i 0.618246 + 0.337654i
\(581\) 0.641735i 0.0266236i
\(582\) 1.76069 4.57165i 0.0729830 0.189501i
\(583\) 23.6691i 0.980276i
\(584\) −5.42321 + 5.82349i −0.224414 + 0.240978i
\(585\) −0.648029 + 2.70223i −0.0267927 + 0.111724i
\(586\) 38.6244 + 9.85998i 1.59556 + 0.407312i
\(587\) −30.8651 −1.27394 −0.636969 0.770889i \(-0.719812\pi\)
−0.636969 + 0.770889i \(0.719812\pi\)
\(588\) −2.82425 2.00589i −0.116470 0.0827217i
\(589\) 31.6691 1.30490
\(590\) −12.2113 3.11729i −0.502731 0.128337i
\(591\) 0.400282 3.38561i 0.0164654 0.139266i
\(592\) −16.9384 26.3662i −0.696164 1.08365i
\(593\) 6.45147i 0.264930i −0.991188 0.132465i \(-0.957711\pi\)
0.991188 0.132465i \(-0.0422892\pi\)
\(594\) −17.9962 + 26.1368i −0.738392 + 1.07240i
\(595\) 9.83457i 0.403178i
\(596\) 16.6699 30.5227i 0.682826 1.25026i
\(597\) −1.29606 + 10.9622i −0.0530441 + 0.448651i
\(598\) −0.165428 + 0.648029i −0.00676485 + 0.0264999i
\(599\) 12.8097 0.523391 0.261696 0.965150i \(-0.415718\pi\)
0.261696 + 0.965150i \(0.415718\pi\)
\(600\) −0.697026 + 0.591029i −0.0284560 + 0.0241286i
\(601\) −37.2710 −1.52032 −0.760158 0.649738i \(-0.774878\pi\)
−0.760158 + 0.649738i \(0.774878\pi\)
\(602\) 3.85520 15.1019i 0.157126 0.615508i
\(603\) −5.48108 + 22.8557i −0.223207 + 0.930756i
\(604\) −3.99316 + 7.31149i −0.162479 + 0.297500i
\(605\) 17.4176i 0.708126i
\(606\) −19.8518 7.64559i −0.806426 0.310581i
\(607\) 20.8135i 0.844792i 0.906411 + 0.422396i \(0.138811\pi\)
−0.906411 + 0.422396i \(0.861189\pi\)
\(608\) −9.69046 29.1352i −0.393000 1.18159i
\(609\) 6.40673 + 0.757468i 0.259614 + 0.0306942i
\(610\) −32.6075 8.32401i −1.32024 0.337029i
\(611\) −0.945841 −0.0382646
\(612\) 17.3797 19.2165i 0.702533 0.776782i
\(613\) 19.2288 0.776643 0.388321 0.921524i \(-0.373055\pi\)
0.388321 + 0.921524i \(0.373055\pi\)
\(614\) 3.07119 + 0.784009i 0.123943 + 0.0316400i
\(615\) −10.0359 1.18654i −0.404686 0.0478460i
\(616\) 8.93840 + 8.32401i 0.360138 + 0.335384i
\(617\) 29.3933i 1.18333i −0.806185 0.591664i \(-0.798471\pi\)
0.806185 0.591664i \(-0.201529\pi\)
\(618\) 24.3395 + 9.37395i 0.979079 + 0.377076i
\(619\) 19.9241i 0.800818i 0.916336 + 0.400409i \(0.131132\pi\)
−0.916336 + 0.400409i \(0.868868\pi\)
\(620\) −23.3235 12.7381i −0.936695 0.511575i
\(621\) −5.66914 2.08903i −0.227495 0.0838297i
\(622\) −9.26242 + 36.2835i −0.371389 + 1.45484i
\(623\) 13.9970 0.560779
\(624\) 1.23418 + 2.53325i 0.0494068 + 0.101411i
\(625\) −25.8979 −1.03592
\(626\) 0.154042 0.603426i 0.00615676 0.0241178i
\(627\) −4.76671 + 40.3172i −0.190364 + 1.61011i
\(628\) 33.8109 + 18.4658i 1.34920 + 0.736865i
\(629\) 33.8323i 1.34898i
\(630\) −4.50723 + 8.54650i −0.179572 + 0.340501i
\(631\) 17.6269i 0.701716i 0.936429 + 0.350858i \(0.114110\pi\)
−0.936429 + 0.350858i \(0.885890\pi\)
\(632\) 8.27949 + 7.71039i 0.329340 + 0.306703i
\(633\) −5.11067 + 43.2265i −0.203131 + 1.71810i
\(634\) 16.1586 + 4.12494i 0.641739 + 0.163822i
\(635\) −14.1373 −0.561022
\(636\) 10.9945 15.4799i 0.435959 0.613819i
\(637\) 0.406728 0.0161152
\(638\) −22.0401 5.62636i −0.872574 0.222750i
\(639\) −14.2580 3.41926i −0.564039 0.135264i
\(640\) −4.58214 + 25.3551i −0.181125 + 1.00225i
\(641\) 21.9439i 0.866731i 0.901218 + 0.433365i \(0.142674\pi\)
−0.901218 + 0.433365i \(0.857326\pi\)
\(642\) 7.39509 19.2014i 0.291861 0.757819i
\(643\) 49.5796i 1.95523i −0.210406 0.977614i \(-0.567479\pi\)
0.210406 0.977614i \(-0.432521\pi\)
\(644\) −1.11466 + 2.04094i −0.0439236 + 0.0804242i
\(645\) −43.1729 5.10433i −1.69993 0.200983i
\(646\) 8.19907 32.1181i 0.322588 1.26367i
\(647\) −23.9122 −0.940085 −0.470042 0.882644i \(-0.655761\pi\)
−0.470042 + 0.882644i \(0.655761\pi\)
\(648\) −23.9104 + 8.73446i −0.939291 + 0.343122i
\(649\) 16.8979 0.663301
\(650\) 0.0265402 0.103966i 0.00104099 0.00407787i
\(651\) −10.0359 1.18654i −0.393337 0.0465043i
\(652\) 8.29037 15.1797i 0.324676 0.594483i
\(653\) 46.6666i 1.82621i −0.407730 0.913103i \(-0.633680\pi\)
0.407730 0.913103i \(-0.366320\pi\)
\(654\) 9.22832 23.9614i 0.360856 0.936964i
\(655\) 32.7998i 1.28159i
\(656\) −8.62190 + 5.53895i −0.336629 + 0.216260i
\(657\) 8.20766 + 1.96830i 0.320211 + 0.0767907i
\(658\) −3.18654 0.813457i −0.124224 0.0317118i
\(659\) 30.4598 1.18655 0.593273 0.805001i \(-0.297835\pi\)
0.593273 + 0.805001i \(0.297835\pi\)
\(660\) 19.7271 27.7753i 0.767877 1.08115i
\(661\) −49.3046 −1.91773 −0.958864 0.283865i \(-0.908383\pi\)
−0.958864 + 0.283865i \(0.908383\pi\)
\(662\) 1.79470 + 0.458148i 0.0697529 + 0.0178064i
\(663\) −0.357187 + 3.02112i −0.0138720 + 0.117330i
\(664\) −1.23701 + 1.32831i −0.0480052 + 0.0515484i
\(665\) 12.3614i 0.479353i
\(666\) −15.5055 + 29.4012i −0.600826 + 1.13927i
\(667\) 4.33086i 0.167691i
\(668\) 3.08295 + 1.68375i 0.119283 + 0.0651463i
\(669\) 1.87680 15.8741i 0.0725614 0.613730i
\(670\) 6.24130 24.4490i 0.241122 0.944546i
\(671\) 45.1221 1.74192
\(672\) 1.97928 + 9.59596i 0.0763523 + 0.370172i
\(673\) −19.4364 −0.749219 −0.374610 0.927183i \(-0.622223\pi\)
−0.374610 + 0.927183i \(0.622223\pi\)
\(674\) −5.40844 + 21.1864i −0.208325 + 0.816070i
\(675\) 0.909522 + 0.335150i 0.0350075 + 0.0128999i
\(676\) 22.5283 + 12.3038i 0.866471 + 0.473222i
\(677\) 9.96823i 0.383110i −0.981482 0.191555i \(-0.938647\pi\)
0.981482 0.191555i \(-0.0613531\pi\)
\(678\) 21.8592 + 8.41871i 0.839499 + 0.323319i
\(679\) 2.00000i 0.0767530i
\(680\) −18.9571 + 20.3563i −0.726971 + 0.780628i
\(681\) −33.5864 3.97093i −1.28703 0.152166i
\(682\) 34.5248 + 8.81346i 1.32202 + 0.337485i
\(683\) 29.6102 1.13300 0.566501 0.824061i \(-0.308297\pi\)
0.566501 + 0.824061i \(0.308297\pi\)
\(684\) −21.8451 + 24.1538i −0.835267 + 0.923544i
\(685\) −5.29606 −0.202352
\(686\) 1.37027 + 0.349801i 0.0523171 + 0.0133555i
\(687\) −3.49801 0.413570i −0.133457 0.0157787i
\(688\) −37.0901 + 23.8277i −1.41405 + 0.908424i
\(689\) 2.22931i 0.0849300i
\(690\) 6.05293 + 2.33118i 0.230431 + 0.0887466i
\(691\) 44.1603i 1.67994i −0.542634 0.839969i \(-0.682573\pi\)
0.542634 0.839969i \(-0.317427\pi\)
\(692\) −7.54856 + 13.8214i −0.286953 + 0.525412i
\(693\) 3.02112 12.5978i 0.114763 0.478552i
\(694\) 9.67599 37.9036i 0.367295 1.43880i
\(695\) 20.9980 0.796501
\(696\) −11.8010 13.9175i −0.447316 0.527540i
\(697\) −11.0633 −0.419054
\(698\) −6.62227 + 25.9413i −0.250657 + 0.981894i
\(699\) −0.665271 + 5.62691i −0.0251629 + 0.212829i
\(700\) 0.178828 0.327435i 0.00675907 0.0123759i
\(701\) 38.2714i 1.44549i 0.691115 + 0.722745i \(0.257120\pi\)
−0.691115 + 0.722745i \(0.742880\pi\)
\(702\) 1.69499 2.46173i 0.0639735 0.0929119i
\(703\) 42.5248i 1.60385i
\(704\) −2.45599 34.4593i −0.0925637 1.29873i
\(705\) −1.07703 + 9.10959i −0.0405632 + 0.343087i
\(706\) 2.73074 + 0.697101i 0.102773 + 0.0262357i
\(707\) 8.68476 0.326624
\(708\) 11.0515 + 7.84919i 0.415339 + 0.294991i
\(709\) 6.89792 0.259057 0.129528 0.991576i \(-0.458654\pi\)
0.129528 + 0.991576i \(0.458654\pi\)
\(710\) 15.2520 + 3.89350i 0.572396 + 0.146121i
\(711\) 2.79841 11.6691i 0.104948 0.437627i
\(712\) −28.9720 26.9806i −1.08577 1.01114i
\(713\) 6.78411i 0.254067i
\(714\) −3.80163 + 9.87096i −0.142272 + 0.369411i
\(715\) 4.00000i 0.149592i
\(716\) 16.4049 + 8.95953i 0.613081 + 0.334833i
\(717\) 42.1517 + 4.98361i 1.57419 + 0.186116i
\(718\) −0.822045 + 3.22019i −0.0306784 + 0.120176i
\(719\) 28.2355 1.05301 0.526503 0.850173i \(-0.323503\pi\)
0.526503 + 0.850173i \(0.323503\pi\)
\(720\) 25.8036 9.00204i 0.961643 0.335486i
\(721\) −10.6480 −0.396553
\(722\) −3.65944 + 14.3351i −0.136190 + 0.533496i
\(723\) −31.6756 3.74502i −1.17803 0.139279i
\(724\) −29.6455 16.1908i −1.10177 0.601728i
\(725\) 0.694815i 0.0258048i
\(726\) −6.73291 + 17.4820i −0.249882 + 0.648820i
\(727\) 27.3942i 1.01599i −0.861359 0.507997i \(-0.830386\pi\)
0.861359 0.507997i \(-0.169614\pi\)
\(728\) −0.841876 0.784009i −0.0312020 0.0290573i
\(729\) 20.5442 + 17.5196i 0.760896 + 0.648874i
\(730\) −8.77981 2.24130i −0.324956 0.0829543i
\(731\) −47.5929 −1.76029
\(732\) 29.5105 + 20.9595i 1.09074 + 0.774686i
\(733\) −29.7028 −1.09710 −0.548549 0.836119i \(-0.684819\pi\)
−0.548549 + 0.836119i \(0.684819\pi\)
\(734\) −46.8550 11.9611i −1.72945 0.441492i
\(735\) 0.463141 3.91729i 0.0170832 0.144491i
\(736\) 6.24130 2.07587i 0.230057 0.0765177i
\(737\) 33.8323i 1.24623i
\(738\) 9.61434 + 5.07038i 0.353909 + 0.186643i
\(739\) 27.4364i 1.00927i −0.863334 0.504633i \(-0.831628\pi\)
0.863334 0.504633i \(-0.168372\pi\)
\(740\) 17.1045 31.3185i 0.628775 1.15129i
\(741\) 0.448959 3.79733i 0.0164929 0.139498i
\(742\) −1.91729 + 7.51056i −0.0703858 + 0.275721i
\(743\) −2.30093 −0.0844131 −0.0422065 0.999109i \(-0.513439\pi\)
−0.0422065 + 0.999109i \(0.513439\pi\)
\(744\) 18.4858 + 21.8011i 0.677722 + 0.799268i
\(745\) 39.6019 1.45090
\(746\) −6.18068 + 24.2115i −0.226291 + 0.886446i
\(747\) 1.87212 + 0.448959i 0.0684974 + 0.0164265i
\(748\) 17.8768 32.7325i 0.653641 1.19682i
\(749\) 8.40021i 0.306937i
\(750\) 25.0576 + 9.65049i 0.914973 + 0.352386i
\(751\) 19.4193i 0.708619i 0.935128 + 0.354309i \(0.115284\pi\)
−0.935128 + 0.354309i \(0.884716\pi\)
\(752\) 5.02772 + 7.82612i 0.183342 + 0.285389i
\(753\) 26.5653 + 3.14082i 0.968094 + 0.114458i
\(754\) 2.07587 + 0.529926i 0.0755988 + 0.0192988i
\(755\) −9.48634 −0.345243
\(756\) 7.82762 6.83582i 0.284688 0.248616i
\(757\) 13.9327 0.506393 0.253197 0.967415i \(-0.418518\pi\)
0.253197 + 0.967415i \(0.418518\pi\)
\(758\) 7.39151 + 1.88690i 0.268472 + 0.0685352i
\(759\) −8.63667 1.02112i −0.313491 0.0370641i
\(760\) 23.8277 25.5864i 0.864323 0.928117i
\(761\) 12.3859i 0.448989i 0.974475 + 0.224495i \(0.0720731\pi\)
−0.974475 + 0.224495i \(0.927927\pi\)
\(762\) 14.1896 + 5.46489i 0.514035 + 0.197972i
\(763\) 10.4826i 0.379496i
\(764\) −35.6466 19.4683i −1.28965 0.704339i
\(765\) 28.6903 + 6.88028i 1.03730 + 0.248757i
\(766\) 0.648029 2.53851i 0.0234142 0.0917203i
\(767\) −1.59155 −0.0574677
\(768\) 14.4003 23.6777i 0.519626 0.854394i
\(769\) 45.0074 1.62301 0.811505 0.584346i \(-0.198649\pi\)
0.811505 + 0.584346i \(0.198649\pi\)
\(770\) −3.44014 + 13.4760i −0.123974 + 0.485642i
\(771\) −1.82404 + 15.4278i −0.0656911 + 0.555620i
\(772\) −12.0336 6.57216i −0.433100 0.236537i
\(773\) 51.4814i 1.85166i −0.377944 0.925828i \(-0.623369\pi\)
0.377944 0.925828i \(-0.376631\pi\)
\(774\) 41.3595 + 21.8120i 1.48664 + 0.784017i
\(775\) 1.08840i 0.0390965i
\(776\) 3.85520 4.13974i 0.138393 0.148608i
\(777\) 1.59327 13.4760i 0.0571583 0.483449i
\(778\) −7.37877 1.88364i −0.264542 0.0675319i
\(779\) 13.9058 0.498229
\(780\) −1.85803 + 2.61605i −0.0665280 + 0.0936697i
\(781\) −21.1056 −0.755217
\(782\) 6.88028 + 1.75639i 0.246038 + 0.0628084i
\(783\) −6.69191 + 18.1603i −0.239149 + 0.648997i
\(784\) −2.16201 3.36537i −0.0772145 0.120192i
\(785\) 43.8682i 1.56572i
\(786\) 12.6790 32.9211i 0.452245 1.17426i
\(787\) 41.2202i 1.46934i −0.678424 0.734670i \(-0.737337\pi\)
0.678424 0.734670i \(-0.262663\pi\)
\(788\) 1.88690 3.45491i 0.0672179 0.123076i
\(789\) −33.3046 3.93761i −1.18568 0.140183i
\(790\) −3.18654 + 12.4826i −0.113372 + 0.444111i
\(791\) −9.56296 −0.340020
\(792\) −30.5369 + 20.2524i −1.08508 + 0.719637i
\(793\) −4.24989 −0.150918
\(794\) −7.56812 + 29.6465i −0.268582 + 1.05211i
\(795\) 21.4710 + 2.53851i 0.761496 + 0.0900318i
\(796\) −6.10951 + 11.1865i −0.216546 + 0.396497i
\(797\) 37.0164i 1.31119i 0.755113 + 0.655595i \(0.227582\pi\)
−0.755113 + 0.655595i \(0.772418\pi\)
\(798\) 4.77838 12.4071i 0.169153 0.439206i
\(799\) 10.0422i 0.355269i
\(800\) −1.00131 + 0.333040i −0.0354018 + 0.0117747i
\(801\) −9.79234 + 40.8333i −0.345995 + 1.44277i
\(802\) −52.4421 13.3874i −1.85180 0.472724i
\(803\) 12.1495 0.428745
\(804\) −15.7153 + 22.1268i −0.554237 + 0.780352i
\(805\) −2.64803 −0.0933308
\(806\) −3.25177 0.830108i −0.114539 0.0292393i
\(807\) 0.00977929 0.0827140i 0.000344247 0.00291167i
\(808\) −17.9763 16.7407i −0.632405 0.588937i
\(809\) 52.3125i 1.83921i −0.392844 0.919605i \(-0.628509\pi\)
0.392844 0.919605i \(-0.371491\pi\)
\(810\) −21.7793 19.1280i −0.765248 0.672090i
\(811\) 25.3719i 0.890929i 0.895300 + 0.445464i \(0.146961\pi\)
−0.895300 + 0.445464i \(0.853039\pi\)
\(812\) 6.53787 + 3.57065i 0.229434 + 0.125305i
\(813\) 4.04223 34.1895i 0.141767 1.19908i
\(814\) −11.8346 + 46.3594i −0.414802 + 1.62490i
\(815\) 19.6950 0.689886
\(816\) 26.8961 13.1036i 0.941552 0.458718i
\(817\) 59.8209 2.09287
\(818\) 1.66898 6.53787i 0.0583545 0.228591i
\(819\) −0.284548 + 1.18654i −0.00994291 + 0.0414612i
\(820\) −10.2413 5.59327i −0.357642 0.195326i
\(821\) 29.0656i 1.01440i −0.861829 0.507198i \(-0.830681\pi\)
0.861829 0.507198i \(-0.169319\pi\)
\(822\) 5.31565 + 2.04723i 0.185405 + 0.0714054i
\(823\) 28.6343i 0.998131i −0.866564 0.499065i \(-0.833677\pi\)
0.866564 0.499065i \(-0.166323\pi\)
\(824\) 22.0401 + 20.5251i 0.767802 + 0.715026i
\(825\) 1.38561 + 0.163821i 0.0482409 + 0.00570352i
\(826\) −5.36195 1.36879i −0.186566 0.0476264i
\(827\) 4.88743 0.169953 0.0849763 0.996383i \(-0.472919\pi\)
0.0849763 + 0.996383i \(0.472919\pi\)
\(828\) −5.17419 4.67961i −0.179815 0.162628i
\(829\) −38.9316 −1.35215 −0.676074 0.736833i \(-0.736320\pi\)
−0.676074 + 0.736833i \(0.736320\pi\)
\(830\) −2.00263 0.511229i −0.0695123 0.0177450i
\(831\) −17.6736 2.08956i −0.613091 0.0724859i
\(832\) 0.231321 + 3.24559i 0.00801961 + 0.112521i
\(833\) 4.31834i 0.149621i
\(834\) −21.0757 8.11695i −0.729793 0.281067i
\(835\) 4.00000i 0.138426i
\(836\) −22.4699 + 41.1424i −0.777137 + 1.42294i
\(837\) 10.4826 28.4474i 0.362332 0.983286i
\(838\) −2.91474 + 11.4179i −0.100688 + 0.394424i
\(839\) −49.3493 −1.70373 −0.851863 0.523765i \(-0.824527\pi\)
−0.851863 + 0.523765i \(0.824527\pi\)
\(840\) −8.50959 + 7.21553i −0.293609 + 0.248959i
\(841\) 15.1267 0.521610
\(842\) −7.25224 + 28.4091i −0.249929 + 0.979042i
\(843\) −1.37964 + 11.6691i −0.0475175 + 0.401907i
\(844\) −24.0913 + 44.1113i −0.829257 + 1.51837i
\(845\) 29.2294i 1.00552i
\(846\) 4.60240 8.72696i 0.158234 0.300039i
\(847\) 7.64803i 0.262789i
\(848\) 18.4459 11.8501i 0.633434 0.406935i
\(849\) 1.10383 9.33627i 0.0378833 0.320420i
\(850\) −1.10383 0.281784i −0.0378610 0.00966512i
\(851\) −9.10959 −0.312273
\(852\) −13.8033 9.80367i −0.472894 0.335868i
\(853\) 36.4912 1.24943 0.624717 0.780851i \(-0.285214\pi\)
0.624717 + 0.780851i \(0.285214\pi\)
\(854\) −14.3179 3.65505i −0.489948 0.125073i
\(855\) −36.0616 8.64803i −1.23328 0.295756i
\(856\) 16.1922 17.3874i 0.553439 0.594288i
\(857\) 36.4434i 1.24488i −0.782667 0.622441i \(-0.786141\pi\)
0.782667 0.622441i \(-0.213859\pi\)
\(858\) 1.54623 4.01480i 0.0527875 0.137063i
\(859\) 11.8682i 0.404938i −0.979289 0.202469i \(-0.935103\pi\)
0.979289 0.202469i \(-0.0648966\pi\)
\(860\) −44.0566 24.0614i −1.50232 0.820488i
\(861\) −4.40673 0.521008i −0.150181 0.0177559i
\(862\) −12.2413 + 47.9527i −0.416940 + 1.63327i
\(863\) 16.3225 0.555625 0.277812 0.960635i \(-0.410391\pi\)
0.277812 + 0.960635i \(0.410391\pi\)
\(864\) −29.3789 0.939234i −0.999489 0.0319534i
\(865\) −17.9327 −0.609731
\(866\) 6.06495 23.7581i 0.206095 0.807334i
\(867\) 2.83473 + 0.335150i 0.0962723 + 0.0113823i
\(868\) −10.2413 5.59327i −0.347612 0.189848i
\(869\) 17.2733i 0.585958i
\(870\) 7.46762 19.3897i 0.253176 0.657373i
\(871\) 3.18654i 0.107972i
\(872\) 20.2062 21.6976i 0.684269 0.734775i
\(873\) −5.83457 1.39920i −0.197470 0.0473559i
\(874\) −8.64803 2.20766i −0.292524 0.0746752i
\(875\) −10.9622 −0.370589
\(876\) 7.94591 + 5.64350i 0.268467 + 0.190676i
\(877\) 6.81346 0.230074 0.115037 0.993361i \(-0.463301\pi\)
0.115037 + 0.993361i \(0.463301\pi\)
\(878\) −45.6246 11.6470i −1.53976 0.393067i
\(879\) 5.73231 48.4843i 0.193346 1.63534i
\(880\) 33.0970 21.2624i 1.11570 0.716756i
\(881\) 10.1075i 0.340530i −0.985398 0.170265i \(-0.945538\pi\)
0.985398 0.170265i \(-0.0544624\pi\)
\(882\) −1.97911 + 3.75275i −0.0666402 + 0.126362i
\(883\) 29.4615i 0.991458i −0.868477 0.495729i \(-0.834901\pi\)
0.868477 0.495729i \(-0.165099\pi\)
\(884\) −1.68375 + 3.08295i −0.0566307 + 0.103691i
\(885\) −1.81230 + 15.3286i −0.0609198 + 0.515265i
\(886\) −3.10383 + 12.1586i −0.104275 + 0.408476i
\(887\) 44.4668 1.49305 0.746525 0.665357i \(-0.231721\pi\)
0.746525 + 0.665357i \(0.231721\pi\)
\(888\) −29.2742 + 24.8224i −0.982378 + 0.832986i
\(889\) −6.20766 −0.208198
\(890\) 11.1505 43.6798i 0.373767 1.46415i
\(891\) 34.6379 + 17.6269i 1.16041 + 0.590524i
\(892\) 8.84710 16.1991i 0.296223 0.542385i
\(893\) 12.6224i 0.422392i
\(894\) −39.7484 15.3084i −1.32938 0.511990i
\(895\) 21.2847i 0.711469i
\(896\) −2.01200 + 11.1334i −0.0672164 + 0.371940i
\(897\) 0.813457 + 0.0961751i 0.0271605 + 0.00321119i
\(898\) 36.1517 + 9.22877i 1.20640 + 0.307968i
\(899\) 21.7320 0.724802
\(900\) 0.830114 + 0.750767i 0.0276705 + 0.0250256i
\(901\) 23.6691 0.788534
\(902\) 15.1598 + 3.86997i 0.504765 + 0.128856i
\(903\) −18.9571 2.24130i −0.630853 0.0745858i
\(904\) 19.7941 + 18.4335i 0.658342 + 0.613090i
\(905\) 38.4637i 1.27858i
\(906\) 9.52144 + 3.66702i 0.316328 + 0.121829i
\(907\) 55.9190i 1.85676i 0.371631 + 0.928380i \(0.378799\pi\)
−0.371631 + 0.928380i \(0.621201\pi\)
\(908\) −34.2739 18.7186i −1.13742 0.621200i
\(909\) −6.07587 + 25.3359i −0.201524 + 0.840340i
\(910\) 0.324014 1.26926i 0.0107410 0.0420755i
\(911\) −7.71538 −0.255622 −0.127811 0.991799i \(-0.540795\pi\)
−0.127811 + 0.991799i \(0.540795\pi\)
\(912\) −33.8065 + 16.4703i −1.11945 + 0.545386i
\(913\) 2.77123 0.0917142
\(914\) 10.5814 41.4505i 0.350003 1.37106i
\(915\) −4.83934 + 40.9316i −0.159984 + 1.35316i
\(916\) −3.56961 1.94954i −0.117943 0.0644145i
\(917\) 14.4023i 0.475606i
\(918\) −26.1368 17.9962i −0.862642 0.593962i
\(919\) 10.0422i 0.331263i 0.986188 + 0.165631i \(0.0529662\pi\)
−0.986188 + 0.165631i \(0.947034\pi\)
\(920\) 5.48108 + 5.10433i 0.180706 + 0.168285i
\(921\) 0.455800 3.85520i 0.0150191 0.127033i
\(922\) 2.14177 + 0.546747i 0.0705353 + 0.0180062i
\(923\) 1.98786 0.0654311
\(924\) 8.66213 12.1961i 0.284963 0.401221i
\(925\) 1.46149 0.0480534
\(926\) 45.6246 + 11.6470i 1.49932 + 0.382744i
\(927\) 7.44938 31.0633i 0.244670 1.02025i
\(928\) −6.64978 19.9932i −0.218290 0.656308i
\(929\) 3.13104i 0.102726i 0.998680 + 0.0513631i \(0.0163566\pi\)
−0.998680 + 0.0513631i \(0.983643\pi\)
\(930\) −11.6977 + 30.3732i −0.383583 + 0.995977i
\(931\) 5.42784i 0.177890i
\(932\) −3.13603 + 5.74209i −0.102724 + 0.188088i
\(933\) 45.5459 + 5.38490i 1.49111 + 0.176294i
\(934\) −6.05046 + 23.7014i −0.197977 + 0.775533i
\(935\) 42.4690 1.38888
\(936\) 2.87616 1.90750i 0.0940101 0.0623485i
\(937\) −47.0325 −1.53648 −0.768242 0.640159i \(-0.778868\pi\)
−0.768242 + 0.640159i \(0.778868\pi\)
\(938\) 2.74054 10.7355i 0.0894818 0.350526i
\(939\) −0.757468 0.0895556i −0.0247190 0.00292254i
\(940\) −5.07703 + 9.29606i −0.165594 + 0.303204i
\(941\) 22.2530i 0.725426i 0.931901 + 0.362713i \(0.118150\pi\)
−0.931901 + 0.362713i \(0.881850\pi\)
\(942\) 16.9576 44.0305i 0.552508 1.43459i
\(943\) 2.97888i 0.0970058i
\(944\) 8.46007 + 13.1689i 0.275352 + 0.428611i
\(945\) 11.1038 + 4.09166i 0.361208 + 0.133102i
\(946\) 65.2151 + 16.6480i 2.12033 + 0.541274i
\(947\) −33.9335 −1.10269 −0.551345 0.834277i \(-0.685885\pi\)
−0.551345 + 0.834277i \(0.685885\pi\)
\(948\) 8.02358 11.2970i 0.260594 0.366909i
\(949\) −1.14431 −0.0371460
\(950\) 1.38744 + 0.354183i 0.0450143 + 0.0114912i
\(951\) 2.39812 20.2835i 0.0777645 0.657739i
\(952\) −8.32401 + 8.93840i −0.269783 + 0.289695i
\(953\) 20.2641i 0.656419i 0.944605 + 0.328209i \(0.106445\pi\)
−0.944605 + 0.328209i \(0.893555\pi\)
\(954\) −20.5691 10.8477i −0.665949 0.351206i
\(955\) 46.2499i 1.49661i
\(956\) 43.0145 + 23.4923i 1.39119 + 0.759796i
\(957\) −3.27100 + 27.6664i −0.105737 + 0.894328i
\(958\) 5.80952 22.7575i 0.187697 0.735263i
\(959\) −2.32549 −0.0750939
\(960\) 31.5224 + 1.46786i 1.01738 + 0.0473748i
\(961\) −3.04223 −0.0981365
\(962\) 1.11466 4.36642i 0.0359379 0.140779i
\(963\) −24.5058 5.87680i −0.789689 0.189377i
\(964\) −32.3240 17.6537i −1.04109 0.568588i
\(965\) 15.6131i 0.502604i
\(966\) 2.65783 + 1.02362i 0.0855141 + 0.0329343i
\(967\) 43.5882i 1.40170i −0.713308 0.700851i \(-0.752804\pi\)
0.713308 0.700851i \(-0.247196\pi\)
\(968\) −14.7423 + 15.8304i −0.473836 + 0.508810i
\(969\) −40.3172 4.76671i −1.29517 0.153129i
\(970\) 6.24130 + 1.59327i 0.200396 + 0.0511569i
\(971\) 3.67161 0.117828 0.0589138 0.998263i \(-0.481236\pi\)
0.0589138 + 0.998263i \(0.481236\pi\)
\(972\) 14.4658 + 27.6177i 0.463991 + 0.885840i
\(973\) 9.22019 0.295586
\(974\) 33.2289 + 8.48263i 1.06472 + 0.271801i
\(975\) −0.130506 0.0154297i −0.00417953 0.000494147i
\(976\) 22.5907 + 35.1646i 0.723111 + 1.12559i
\(977\) 34.0738i 1.09012i 0.838398 + 0.545058i \(0.183492\pi\)
−0.838398 + 0.545058i \(0.816508\pi\)
\(978\) −19.7679 7.61326i −0.632107 0.243445i
\(979\) 60.4439i 1.93179i
\(980\) 2.18321 3.99747i 0.0697401 0.127694i
\(981\) −30.5807 7.33364i −0.976368 0.234145i
\(982\) 7.10383 27.8277i 0.226692 0.888019i
\(983\) −54.2808 −1.73129 −0.865645 0.500659i \(-0.833091\pi\)
−0.865645 + 0.500659i \(0.833091\pi\)
\(984\) 8.11707 + 9.57282i 0.258763 + 0.305170i
\(985\) 4.48260 0.142828
\(986\) 5.62636 22.0401i 0.179180 0.701898i
\(987\) −0.472921 + 4.00000i −0.0150532 + 0.127321i
\(988\) 2.11636 3.87506i 0.0673303 0.123282i
\(989\) 12.8147i 0.407485i
\(990\) −36.9067 19.4637i −1.17297 0.618598i
\(991\) 10.5077i 0.333787i 0.985975 + 0.166893i \(0.0533736\pi\)
−0.985975 + 0.166893i \(0.946626\pi\)
\(992\) 10.4166 + 31.3185i 0.330727 + 0.994362i
\(993\) 0.266354 2.25285i 0.00845250 0.0714919i
\(994\) 6.69710 + 1.70963i 0.212419 + 0.0542261i
\(995\) −14.5141 −0.460127
\(996\) 1.81242 + 1.28725i 0.0574287 + 0.0407881i
\(997\) 21.4564 0.679531 0.339765 0.940510i \(-0.389652\pi\)
0.339765 + 0.940510i \(0.389652\pi\)
\(998\) −14.4406 3.68638i −0.457109 0.116690i
\(999\) 38.1987 + 14.0759i 1.20855 + 0.445341i
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 84.2.e.a.71.7 yes 12
3.2 odd 2 inner 84.2.e.a.71.6 yes 12
4.3 odd 2 inner 84.2.e.a.71.5 12
7.2 even 3 588.2.n.f.263.2 24
7.3 odd 6 588.2.n.g.275.9 24
7.4 even 3 588.2.n.f.275.9 24
7.5 odd 6 588.2.n.g.263.2 24
7.6 odd 2 588.2.e.c.491.7 12
8.3 odd 2 1344.2.h.h.575.1 12
8.5 even 2 1344.2.h.h.575.12 12
12.11 even 2 inner 84.2.e.a.71.8 yes 12
21.2 odd 6 588.2.n.f.263.11 24
21.5 even 6 588.2.n.g.263.11 24
21.11 odd 6 588.2.n.f.275.4 24
21.17 even 6 588.2.n.g.275.4 24
21.20 even 2 588.2.e.c.491.6 12
24.5 odd 2 1344.2.h.h.575.2 12
24.11 even 2 1344.2.h.h.575.11 12
28.3 even 6 588.2.n.g.275.11 24
28.11 odd 6 588.2.n.f.275.11 24
28.19 even 6 588.2.n.g.263.4 24
28.23 odd 6 588.2.n.f.263.4 24
28.27 even 2 588.2.e.c.491.5 12
84.11 even 6 588.2.n.f.275.2 24
84.23 even 6 588.2.n.f.263.9 24
84.47 odd 6 588.2.n.g.263.9 24
84.59 odd 6 588.2.n.g.275.2 24
84.83 odd 2 588.2.e.c.491.8 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
84.2.e.a.71.5 12 4.3 odd 2 inner
84.2.e.a.71.6 yes 12 3.2 odd 2 inner
84.2.e.a.71.7 yes 12 1.1 even 1 trivial
84.2.e.a.71.8 yes 12 12.11 even 2 inner
588.2.e.c.491.5 12 28.27 even 2
588.2.e.c.491.6 12 21.20 even 2
588.2.e.c.491.7 12 7.6 odd 2
588.2.e.c.491.8 12 84.83 odd 2
588.2.n.f.263.2 24 7.2 even 3
588.2.n.f.263.4 24 28.23 odd 6
588.2.n.f.263.9 24 84.23 even 6
588.2.n.f.263.11 24 21.2 odd 6
588.2.n.f.275.2 24 84.11 even 6
588.2.n.f.275.4 24 21.11 odd 6
588.2.n.f.275.9 24 7.4 even 3
588.2.n.f.275.11 24 28.11 odd 6
588.2.n.g.263.2 24 7.5 odd 6
588.2.n.g.263.4 24 28.19 even 6
588.2.n.g.263.9 24 84.47 odd 6
588.2.n.g.263.11 24 21.5 even 6
588.2.n.g.275.2 24 84.59 odd 6
588.2.n.g.275.4 24 21.17 even 6
588.2.n.g.275.9 24 7.3 odd 6
588.2.n.g.275.11 24 28.3 even 6
1344.2.h.h.575.1 12 8.3 odd 2
1344.2.h.h.575.2 12 24.5 odd 2
1344.2.h.h.575.11 12 24.11 even 2
1344.2.h.h.575.12 12 8.5 even 2