Properties

Label 90.2.l.b.77.3
Level $90$
Weight $2$
Character 90.77
Analytic conductor $0.719$
Analytic rank $0$
Dimension $16$
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] = [90,2,Mod(23,90)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(90, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([10, 9]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("90.23");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 90 = 2 \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 90.l (of order \(12\), degree \(4\), 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: \(0.718653618192\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(4\) over \(\Q(\zeta_{12})\)
Coefficient field: 16.0.9349208943630483456.9
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 8 x^{15} + 48 x^{14} - 196 x^{13} + 642 x^{12} - 1668 x^{11} + 3580 x^{10} - 6328 x^{9} + 9297 x^{8} - 11276 x^{7} + 11224 x^{6} - 9024 x^{5} + 5736 x^{4} - 2780 x^{3} + \cdots + 25 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 77.3
Root \(0.500000 - 0.331082i\) of defining polynomial
Character \(\chi\) \(=\) 90.77
Dual form 90.2.l.b.83.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.965926 + 0.258819i) q^{2} +(-0.933998 + 1.45865i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-0.847015 + 2.06944i) q^{5} +(-1.27970 + 1.16721i) q^{6} +(0.686453 - 2.56188i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-1.25529 - 2.72474i) q^{9} +O(q^{10})\) \(q+(0.965926 + 0.258819i) q^{2} +(-0.933998 + 1.45865i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-0.847015 + 2.06944i) q^{5} +(-1.27970 + 1.16721i) q^{6} +(0.686453 - 2.56188i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-1.25529 - 2.72474i) q^{9} +(-1.35376 + 1.77970i) q^{10} +(4.15512 - 2.39896i) q^{11} +(-1.53819 + 0.796225i) q^{12} +(-0.155903 - 0.581838i) q^{13} +(1.32613 - 2.29692i) q^{14} +(-2.22746 - 3.16834i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-4.40865 + 4.40865i) q^{17} +(-0.507306 - 2.95680i) q^{18} -5.19145i q^{19} +(-1.76825 + 1.36868i) q^{20} +(3.09573 + 3.39408i) q^{21} +(4.63444 - 1.24179i) q^{22} +(-2.54237 + 0.681226i) q^{23} +(-1.69185 + 0.370982i) q^{24} +(-3.56513 - 3.50569i) q^{25} -0.602363i q^{26} +(5.14688 + 0.713876i) q^{27} +(1.87542 - 1.87542i) q^{28} +(0.920201 + 1.59383i) q^{29} +(-1.33154 - 3.63690i) q^{30} +(-2.03888 + 3.53145i) q^{31} +(0.258819 + 0.965926i) q^{32} +(-0.381642 + 8.30148i) q^{33} +(-5.39948 + 3.11739i) q^{34} +(4.72021 + 3.59052i) q^{35} +(0.275255 - 2.98735i) q^{36} +(0.632057 + 0.632057i) q^{37} +(1.34365 - 5.01456i) q^{38} +(0.994309 + 0.316029i) q^{39} +(-2.06224 + 0.864382i) q^{40} +(-5.58550 - 3.22479i) q^{41} +(2.11179 + 4.07966i) q^{42} +(2.40501 + 0.644420i) q^{43} +4.79792 q^{44} +(6.70194 - 0.289853i) q^{45} -2.63206 q^{46} +(-3.82678 - 1.02538i) q^{47} +(-1.73022 - 0.0795432i) q^{48} +(-0.0298240 - 0.0172189i) q^{49} +(-2.53631 - 4.30896i) q^{50} +(-2.31299 - 10.5483i) q^{51} +(0.155903 - 0.581838i) q^{52} +(1.31215 + 1.31215i) q^{53} +(4.78674 + 2.02166i) q^{54} +(1.44505 + 10.6307i) q^{55} +(2.29692 - 1.32613i) q^{56} +(7.57249 + 4.84881i) q^{57} +(0.476331 + 1.77769i) q^{58} +(0.0645473 - 0.111799i) q^{59} +(-0.344868 - 3.85760i) q^{60} +(6.27251 + 10.8643i) q^{61} +(-2.88341 + 2.88341i) q^{62} +(-7.84217 + 1.34550i) q^{63} +1.00000i q^{64} +(1.33613 + 0.170194i) q^{65} +(-2.51722 + 7.91984i) q^{66} +(-10.6655 + 2.85782i) q^{67} +(-6.02233 + 1.61368i) q^{68} +(1.38090 - 4.34468i) q^{69} +(3.63008 + 4.68986i) q^{70} -10.4203i q^{71} +(1.03906 - 2.81431i) q^{72} +(3.30021 - 3.30021i) q^{73} +(0.446932 + 0.774109i) q^{74} +(8.44338 - 1.92596i) q^{75} +(2.59573 - 4.49593i) q^{76} +(-3.29355 - 12.2917i) q^{77} +(0.878635 + 0.562606i) q^{78} +(-3.62792 + 2.09458i) q^{79} +(-2.21569 + 0.301182i) q^{80} +(-5.84847 + 6.84072i) q^{81} +(-4.56054 - 4.56054i) q^{82} +(2.97686 - 11.1098i) q^{83} +(0.983937 + 4.48722i) q^{84} +(-5.38923 - 12.8576i) q^{85} +(2.15627 + 1.24492i) q^{86} +(-3.18431 - 0.146391i) q^{87} +(4.63444 + 1.24179i) q^{88} -2.04989 q^{89} +(6.54860 + 1.45461i) q^{90} -1.59762 q^{91} +(-2.54237 - 0.681226i) q^{92} +(-3.24682 - 6.27237i) q^{93} +(-3.43100 - 1.98089i) q^{94} +(10.7434 + 4.39724i) q^{95} +(-1.65068 - 0.524648i) q^{96} +(4.47782 - 16.7115i) q^{97} +(-0.0243512 - 0.0243512i) q^{98} +(-11.7525 - 8.31025i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 12 q^{5} + 8 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 12 q^{5} + 8 q^{7} - 8 q^{10} - 24 q^{15} + 8 q^{16} - 12 q^{20} + 24 q^{21} + 8 q^{22} - 24 q^{23} - 16 q^{25} - 16 q^{28} - 12 q^{30} - 8 q^{31} + 24 q^{36} + 24 q^{38} - 4 q^{40} + 24 q^{41} + 24 q^{42} + 36 q^{45} - 32 q^{46} + 48 q^{47} + 24 q^{50} - 48 q^{51} + 24 q^{55} + 24 q^{56} + 24 q^{57} + 16 q^{58} + 12 q^{60} - 24 q^{61} - 48 q^{63} - 48 q^{66} - 16 q^{67} - 24 q^{68} + 16 q^{70} - 24 q^{72} + 16 q^{73} + 16 q^{76} - 72 q^{77} + 24 q^{81} - 16 q^{82} + 48 q^{83} - 4 q^{85} - 48 q^{86} - 48 q^{87} + 8 q^{88} + 12 q^{90} - 24 q^{92} + 72 q^{93} + 84 q^{95} - 48 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/90\mathbb{Z}\right)^\times\).

\(n\) \(11\) \(37\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{4}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.965926 + 0.258819i 0.683013 + 0.183013i
\(3\) −0.933998 + 1.45865i −0.539244 + 0.842150i
\(4\) 0.866025 + 0.500000i 0.433013 + 0.250000i
\(5\) −0.847015 + 2.06944i −0.378797 + 0.925480i
\(6\) −1.27970 + 1.16721i −0.522435 + 0.476510i
\(7\) 0.686453 2.56188i 0.259455 0.968299i −0.706103 0.708109i \(-0.749548\pi\)
0.965558 0.260189i \(-0.0837850\pi\)
\(8\) 0.707107 + 0.707107i 0.250000 + 0.250000i
\(9\) −1.25529 2.72474i −0.418432 0.908248i
\(10\) −1.35376 + 1.77970i −0.428097 + 0.562790i
\(11\) 4.15512 2.39896i 1.25282 0.723314i 0.281149 0.959664i \(-0.409285\pi\)
0.971668 + 0.236350i \(0.0759512\pi\)
\(12\) −1.53819 + 0.796225i −0.444037 + 0.229850i
\(13\) −0.155903 0.581838i −0.0432397 0.161373i 0.940930 0.338601i \(-0.109954\pi\)
−0.984170 + 0.177228i \(0.943287\pi\)
\(14\) 1.32613 2.29692i 0.354422 0.613877i
\(15\) −2.22746 3.16834i −0.575129 0.818063i
\(16\) 0.500000 + 0.866025i 0.125000 + 0.216506i
\(17\) −4.40865 + 4.40865i −1.06926 + 1.06926i −0.0718393 + 0.997416i \(0.522887\pi\)
−0.997416 + 0.0718393i \(0.977113\pi\)
\(18\) −0.507306 2.95680i −0.119573 0.696923i
\(19\) 5.19145i 1.19100i −0.803355 0.595501i \(-0.796954\pi\)
0.803355 0.595501i \(-0.203046\pi\)
\(20\) −1.76825 + 1.36868i −0.395394 + 0.306045i
\(21\) 3.09573 + 3.39408i 0.675543 + 0.740649i
\(22\) 4.63444 1.24179i 0.988065 0.264751i
\(23\) −2.54237 + 0.681226i −0.530121 + 0.142046i −0.513944 0.857824i \(-0.671816\pi\)
−0.0161770 + 0.999869i \(0.505150\pi\)
\(24\) −1.69185 + 0.370982i −0.345348 + 0.0757264i
\(25\) −3.56513 3.50569i −0.713026 0.701137i
\(26\) 0.602363i 0.118133i
\(27\) 5.14688 + 0.713876i 0.990518 + 0.137386i
\(28\) 1.87542 1.87542i 0.354422 0.354422i
\(29\) 0.920201 + 1.59383i 0.170877 + 0.295968i 0.938727 0.344662i \(-0.112007\pi\)
−0.767850 + 0.640630i \(0.778673\pi\)
\(30\) −1.33154 3.63690i −0.243104 0.664003i
\(31\) −2.03888 + 3.53145i −0.366194 + 0.634266i −0.988967 0.148136i \(-0.952673\pi\)
0.622773 + 0.782402i \(0.286006\pi\)
\(32\) 0.258819 + 0.965926i 0.0457532 + 0.170753i
\(33\) −0.381642 + 8.30148i −0.0664354 + 1.44510i
\(34\) −5.39948 + 3.11739i −0.926002 + 0.534628i
\(35\) 4.72021 + 3.59052i 0.797861 + 0.606909i
\(36\) 0.275255 2.98735i 0.0458759 0.497891i
\(37\) 0.632057 + 0.632057i 0.103910 + 0.103910i 0.757150 0.653241i \(-0.226591\pi\)
−0.653241 + 0.757150i \(0.726591\pi\)
\(38\) 1.34365 5.01456i 0.217968 0.813469i
\(39\) 0.994309 + 0.316029i 0.159217 + 0.0506051i
\(40\) −2.06224 + 0.864382i −0.326069 + 0.136671i
\(41\) −5.58550 3.22479i −0.872309 0.503628i −0.00419400 0.999991i \(-0.501335\pi\)
−0.868115 + 0.496363i \(0.834668\pi\)
\(42\) 2.11179 + 4.07966i 0.325856 + 0.629506i
\(43\) 2.40501 + 0.644420i 0.366760 + 0.0982731i 0.437492 0.899222i \(-0.355867\pi\)
−0.0707320 + 0.997495i \(0.522534\pi\)
\(44\) 4.79792 0.723314
\(45\) 6.70194 0.289853i 0.999066 0.0432088i
\(46\) −2.63206 −0.388076
\(47\) −3.82678 1.02538i −0.558194 0.149568i −0.0313173 0.999509i \(-0.509970\pi\)
−0.526876 + 0.849942i \(0.676637\pi\)
\(48\) −1.73022 0.0795432i −0.249736 0.0114811i
\(49\) −0.0298240 0.0172189i −0.00426058 0.00245984i
\(50\) −2.53631 4.30896i −0.358689 0.609379i
\(51\) −2.31299 10.5483i −0.323883 1.47706i
\(52\) 0.155903 0.581838i 0.0216199 0.0806865i
\(53\) 1.31215 + 1.31215i 0.180237 + 0.180237i 0.791459 0.611222i \(-0.209322\pi\)
−0.611222 + 0.791459i \(0.709322\pi\)
\(54\) 4.78674 + 2.02166i 0.651393 + 0.275113i
\(55\) 1.44505 + 10.6307i 0.194850 + 1.43345i
\(56\) 2.29692 1.32613i 0.306938 0.177211i
\(57\) 7.57249 + 4.84881i 1.00300 + 0.642240i
\(58\) 0.476331 + 1.77769i 0.0625453 + 0.233422i
\(59\) 0.0645473 0.111799i 0.00840334 0.0145550i −0.861793 0.507260i \(-0.830658\pi\)
0.870196 + 0.492705i \(0.163992\pi\)
\(60\) −0.344868 3.85760i −0.0445223 0.498014i
\(61\) 6.27251 + 10.8643i 0.803113 + 1.39103i 0.917558 + 0.397603i \(0.130158\pi\)
−0.114445 + 0.993430i \(0.536509\pi\)
\(62\) −2.88341 + 2.88341i −0.366194 + 0.366194i
\(63\) −7.84217 + 1.34550i −0.988020 + 0.169517i
\(64\) 1.00000i 0.125000i
\(65\) 1.33613 + 0.170194i 0.165726 + 0.0211100i
\(66\) −2.51722 + 7.91984i −0.309848 + 0.974864i
\(67\) −10.6655 + 2.85782i −1.30300 + 0.349138i −0.842584 0.538566i \(-0.818966\pi\)
−0.460416 + 0.887703i \(0.652300\pi\)
\(68\) −6.02233 + 1.61368i −0.730315 + 0.195687i
\(69\) 1.38090 4.34468i 0.166241 0.523039i
\(70\) 3.63008 + 4.68986i 0.433877 + 0.560545i
\(71\) 10.4203i 1.23666i −0.785919 0.618329i \(-0.787810\pi\)
0.785919 0.618329i \(-0.212190\pi\)
\(72\) 1.03906 2.81431i 0.122454 0.331670i
\(73\) 3.30021 3.30021i 0.386261 0.386261i −0.487091 0.873351i \(-0.661942\pi\)
0.873351 + 0.487091i \(0.161942\pi\)
\(74\) 0.446932 + 0.774109i 0.0519548 + 0.0899883i
\(75\) 8.44338 1.92596i 0.974958 0.222391i
\(76\) 2.59573 4.49593i 0.297750 0.515719i
\(77\) −3.29355 12.2917i −0.375335 1.40077i
\(78\) 0.878635 + 0.562606i 0.0994858 + 0.0637026i
\(79\) −3.62792 + 2.09458i −0.408173 + 0.235659i −0.690004 0.723805i \(-0.742391\pi\)
0.281832 + 0.959464i \(0.409058\pi\)
\(80\) −2.21569 + 0.301182i −0.247722 + 0.0336731i
\(81\) −5.84847 + 6.84072i −0.649830 + 0.760080i
\(82\) −4.56054 4.56054i −0.503628 0.503628i
\(83\) 2.97686 11.1098i 0.326753 1.21946i −0.585785 0.810466i \(-0.699214\pi\)
0.912538 0.408992i \(-0.134119\pi\)
\(84\) 0.983937 + 4.48722i 0.107356 + 0.489596i
\(85\) −5.38923 12.8576i −0.584544 1.39460i
\(86\) 2.15627 + 1.24492i 0.232517 + 0.134243i
\(87\) −3.18431 0.146391i −0.341393 0.0156948i
\(88\) 4.63444 + 1.24179i 0.494033 + 0.132376i
\(89\) −2.04989 −0.217288 −0.108644 0.994081i \(-0.534651\pi\)
−0.108644 + 0.994081i \(0.534651\pi\)
\(90\) 6.54860 + 1.45461i 0.690283 + 0.153330i
\(91\) −1.59762 −0.167476
\(92\) −2.54237 0.681226i −0.265061 0.0710228i
\(93\) −3.24682 6.27237i −0.336679 0.650414i
\(94\) −3.43100 1.98089i −0.353881 0.204313i
\(95\) 10.7434 + 4.39724i 1.10225 + 0.451147i
\(96\) −1.65068 0.524648i −0.168472 0.0535466i
\(97\) 4.47782 16.7115i 0.454654 1.69679i −0.234450 0.972128i \(-0.575329\pi\)
0.689104 0.724663i \(-0.258004\pi\)
\(98\) −0.0243512 0.0243512i −0.00245984 0.00245984i
\(99\) −11.7525 8.31025i −1.18117 0.835211i
\(100\) −1.33465 4.81858i −0.133465 0.481858i
\(101\) −10.3594 + 5.98097i −1.03079 + 0.595129i −0.917212 0.398399i \(-0.869566\pi\)
−0.113582 + 0.993529i \(0.536232\pi\)
\(102\) 0.495934 10.7876i 0.0491048 1.06813i
\(103\) 2.78816 + 10.4055i 0.274725 + 1.02529i 0.956025 + 0.293285i \(0.0947483\pi\)
−0.681300 + 0.732004i \(0.738585\pi\)
\(104\) 0.301182 0.521662i 0.0295333 0.0511532i
\(105\) −9.64596 + 3.53157i −0.941349 + 0.344646i
\(106\) 0.927828 + 1.60704i 0.0901186 + 0.156090i
\(107\) −4.35367 + 4.35367i −0.420885 + 0.420885i −0.885508 0.464623i \(-0.846190\pi\)
0.464623 + 0.885508i \(0.346190\pi\)
\(108\) 4.10039 + 3.19168i 0.394560 + 0.307119i
\(109\) 15.4546i 1.48028i 0.672452 + 0.740141i \(0.265241\pi\)
−0.672452 + 0.740141i \(0.734759\pi\)
\(110\) −1.35562 + 10.6425i −0.129254 + 1.01472i
\(111\) −1.51229 + 0.331607i −0.143540 + 0.0314748i
\(112\) 2.56188 0.686453i 0.242075 0.0648637i
\(113\) 5.73124 1.53568i 0.539150 0.144465i 0.0210396 0.999779i \(-0.493302\pi\)
0.518110 + 0.855314i \(0.326636\pi\)
\(114\) 6.05950 + 6.64349i 0.567524 + 0.622220i
\(115\) 0.743672 5.83829i 0.0693478 0.544423i
\(116\) 1.84040i 0.170877i
\(117\) −1.38966 + 1.15518i −0.128474 + 0.106796i
\(118\) 0.0912837 0.0912837i 0.00840334 0.00840334i
\(119\) 8.26810 + 14.3208i 0.757935 + 1.31278i
\(120\) 0.665303 3.81541i 0.0607336 0.348298i
\(121\) 6.01003 10.4097i 0.546367 0.946335i
\(122\) 3.24689 + 12.1176i 0.293960 + 1.09707i
\(123\) 9.92068 5.13532i 0.894517 0.463036i
\(124\) −3.53145 + 2.03888i −0.317133 + 0.183097i
\(125\) 10.2745 4.40844i 0.918980 0.394303i
\(126\) −7.92319 0.730046i −0.705854 0.0650377i
\(127\) 2.51837 + 2.51837i 0.223469 + 0.223469i 0.809957 0.586489i \(-0.199490\pi\)
−0.586489 + 0.809957i \(0.699490\pi\)
\(128\) −0.258819 + 0.965926i −0.0228766 + 0.0853766i
\(129\) −3.18625 + 2.90617i −0.280534 + 0.255874i
\(130\) 1.24655 + 0.510211i 0.109330 + 0.0447484i
\(131\) 11.3102 + 6.52997i 0.988181 + 0.570526i 0.904730 0.425985i \(-0.140073\pi\)
0.0834508 + 0.996512i \(0.473406\pi\)
\(132\) −4.48125 + 6.99847i −0.390043 + 0.609139i
\(133\) −13.2999 3.56369i −1.15325 0.309011i
\(134\) −11.0417 −0.953862
\(135\) −5.83681 + 10.0465i −0.502352 + 0.864663i
\(136\) −6.23478 −0.534628
\(137\) 3.13844 + 0.840942i 0.268135 + 0.0718465i 0.390381 0.920653i \(-0.372343\pi\)
−0.122246 + 0.992500i \(0.539010\pi\)
\(138\) 2.45834 3.83924i 0.209267 0.326818i
\(139\) 19.0478 + 10.9973i 1.61561 + 0.932775i 0.988036 + 0.154221i \(0.0492868\pi\)
0.627578 + 0.778554i \(0.284047\pi\)
\(140\) 2.29256 + 5.46959i 0.193757 + 0.462264i
\(141\) 5.06988 4.62421i 0.426961 0.389429i
\(142\) 2.69696 10.0652i 0.226324 0.844653i
\(143\) −2.04360 2.04360i −0.170895 0.170895i
\(144\) 1.73205 2.44949i 0.144338 0.204124i
\(145\) −4.07776 + 0.554295i −0.338640 + 0.0460317i
\(146\) 4.04192 2.33360i 0.334512 0.193130i
\(147\) 0.0529719 0.0274203i 0.00436905 0.00226159i
\(148\) 0.231349 + 0.863406i 0.0190168 + 0.0709715i
\(149\) −6.56668 + 11.3738i −0.537964 + 0.931780i 0.461050 + 0.887374i \(0.347473\pi\)
−0.999014 + 0.0444061i \(0.985860\pi\)
\(150\) 8.65415 + 0.324973i 0.706609 + 0.0265340i
\(151\) −0.167899 0.290810i −0.0136634 0.0236658i 0.859113 0.511786i \(-0.171016\pi\)
−0.872776 + 0.488120i \(0.837683\pi\)
\(152\) 3.67091 3.67091i 0.297750 0.297750i
\(153\) 17.5466 + 6.47830i 1.41856 + 0.523739i
\(154\) 12.7253i 1.02543i
\(155\) −5.58114 7.21052i −0.448288 0.579163i
\(156\) 0.703083 + 0.770843i 0.0562917 + 0.0617169i
\(157\) 4.40352 1.17992i 0.351439 0.0941678i −0.0787808 0.996892i \(-0.525103\pi\)
0.430220 + 0.902724i \(0.358436\pi\)
\(158\) −4.04642 + 1.08423i −0.321916 + 0.0862571i
\(159\) −3.13950 + 0.688415i −0.248979 + 0.0545948i
\(160\) −2.21815 0.282544i −0.175360 0.0223371i
\(161\) 6.98088i 0.550170i
\(162\) −7.41970 + 5.09393i −0.582946 + 0.400217i
\(163\) 9.01496 9.01496i 0.706106 0.706106i −0.259608 0.965714i \(-0.583593\pi\)
0.965714 + 0.259608i \(0.0835932\pi\)
\(164\) −3.22479 5.58550i −0.251814 0.436154i
\(165\) −16.8561 7.82126i −1.31225 0.608884i
\(166\) 5.75085 9.96076i 0.446353 0.773105i
\(167\) −0.00229992 0.00858342i −0.000177973 0.000664205i 0.965837 0.259151i \(-0.0834428\pi\)
−0.966015 + 0.258487i \(0.916776\pi\)
\(168\) −0.210969 + 4.58899i −0.0162766 + 0.354048i
\(169\) 10.9441 6.31858i 0.841854 0.486045i
\(170\) −1.87780 13.8143i −0.144021 1.05951i
\(171\) −14.1454 + 6.51681i −1.08172 + 0.498353i
\(172\) 1.76059 + 1.76059i 0.134243 + 0.134243i
\(173\) −2.68729 + 10.0291i −0.204311 + 0.762500i 0.785347 + 0.619056i \(0.212484\pi\)
−0.989658 + 0.143444i \(0.954182\pi\)
\(174\) −3.03791 0.965562i −0.230304 0.0731991i
\(175\) −11.4284 + 6.72694i −0.863909 + 0.508509i
\(176\) 4.15512 + 2.39896i 0.313204 + 0.180829i
\(177\) 0.102788 + 0.198572i 0.00772605 + 0.0149256i
\(178\) −1.98004 0.530550i −0.148410 0.0397664i
\(179\) −1.46292 −0.109343 −0.0546717 0.998504i \(-0.517411\pi\)
−0.0546717 + 0.998504i \(0.517411\pi\)
\(180\) 5.94898 + 3.09995i 0.443410 + 0.231057i
\(181\) −8.68576 −0.645607 −0.322804 0.946466i \(-0.604625\pi\)
−0.322804 + 0.946466i \(0.604625\pi\)
\(182\) −1.54318 0.413494i −0.114388 0.0306502i
\(183\) −21.7057 0.997872i −1.60453 0.0737648i
\(184\) −2.27943 1.31603i −0.168042 0.0970189i
\(185\) −1.84336 + 0.772640i −0.135527 + 0.0568056i
\(186\) −1.51278 6.89898i −0.110922 0.505858i
\(187\) −7.74231 + 28.8947i −0.566174 + 2.11299i
\(188\) −2.80140 2.80140i −0.204313 0.204313i
\(189\) 5.36196 12.6956i 0.390025 0.923472i
\(190\) 9.23922 + 7.02800i 0.670284 + 0.509865i
\(191\) −4.33795 + 2.50452i −0.313883 + 0.181220i −0.648663 0.761076i \(-0.724671\pi\)
0.334780 + 0.942296i \(0.391338\pi\)
\(192\) −1.45865 0.933998i −0.105269 0.0674055i
\(193\) 0.871785 + 3.25355i 0.0627524 + 0.234195i 0.990178 0.139812i \(-0.0446500\pi\)
−0.927426 + 0.374008i \(0.877983\pi\)
\(194\) 8.65048 14.9831i 0.621069 1.07572i
\(195\) −1.49620 + 1.78998i −0.107145 + 0.128183i
\(196\) −0.0172189 0.0298240i −0.00122992 0.00213029i
\(197\) 15.5027 15.5027i 1.10452 1.10452i 0.110665 0.993858i \(-0.464702\pi\)
0.993858 0.110665i \(-0.0352980\pi\)
\(198\) −9.20116 11.0688i −0.653898 0.786628i
\(199\) 18.4607i 1.30864i −0.756217 0.654321i \(-0.772955\pi\)
0.756217 0.654321i \(-0.227045\pi\)
\(200\) −0.0420344 4.99982i −0.00297228 0.353541i
\(201\) 5.79303 18.2264i 0.408609 1.28559i
\(202\) −11.5544 + 3.09598i −0.812962 + 0.217832i
\(203\) 4.71488 1.26335i 0.330920 0.0886697i
\(204\) 3.27106 10.2916i 0.229020 0.720558i
\(205\) 11.4045 8.82739i 0.796525 0.616532i
\(206\) 10.7726i 0.750564i
\(207\) 5.04759 + 6.07217i 0.350832 + 0.422045i
\(208\) 0.425935 0.425935i 0.0295333 0.0295333i
\(209\) −12.4541 21.5711i −0.861468 1.49211i
\(210\) −10.2313 + 0.914678i −0.706028 + 0.0631187i
\(211\) 0.654465 1.13357i 0.0450552 0.0780380i −0.842618 0.538511i \(-0.818987\pi\)
0.887674 + 0.460473i \(0.152320\pi\)
\(212\) 0.480279 + 1.79243i 0.0329857 + 0.123104i
\(213\) 15.1995 + 9.73251i 1.04145 + 0.666860i
\(214\) −5.33213 + 3.07851i −0.364497 + 0.210442i
\(215\) −3.37066 + 4.43117i −0.229877 + 0.302204i
\(216\) 3.13461 + 4.14418i 0.213283 + 0.281976i
\(217\) 7.64754 + 7.64754i 0.519149 + 0.519149i
\(218\) −3.99994 + 14.9280i −0.270910 + 1.01105i
\(219\) 1.73145 + 7.89624i 0.117001 + 0.533578i
\(220\) −4.06391 + 9.92900i −0.273989 + 0.669413i
\(221\) 3.25245 + 1.87780i 0.218783 + 0.126315i
\(222\) −1.54658 0.0711008i −0.103800 0.00477197i
\(223\) −20.2614 5.42903i −1.35681 0.363555i −0.494163 0.869369i \(-0.664526\pi\)
−0.862643 + 0.505814i \(0.831192\pi\)
\(224\) 2.65225 0.177211
\(225\) −5.07681 + 14.1147i −0.338454 + 0.940983i
\(226\) 5.93342 0.394685
\(227\) 5.75206 + 1.54126i 0.381778 + 0.102297i 0.444604 0.895727i \(-0.353345\pi\)
−0.0628257 + 0.998025i \(0.520011\pi\)
\(228\) 4.13357 + 7.98544i 0.273752 + 0.528848i
\(229\) −10.1822 5.87872i −0.672862 0.388477i 0.124298 0.992245i \(-0.460332\pi\)
−0.797160 + 0.603768i \(0.793665\pi\)
\(230\) 2.22939 5.44687i 0.147002 0.359156i
\(231\) 21.0054 + 6.67630i 1.38205 + 0.439268i
\(232\) −0.476331 + 1.77769i −0.0312727 + 0.116711i
\(233\) −13.4322 13.4322i −0.879973 0.879973i 0.113558 0.993531i \(-0.463775\pi\)
−0.993531 + 0.113558i \(0.963775\pi\)
\(234\) −1.64129 + 0.756144i −0.107294 + 0.0494307i
\(235\) 5.36331 7.05077i 0.349864 0.459941i
\(236\) 0.111799 0.0645473i 0.00727751 0.00420167i
\(237\) 0.333219 7.24818i 0.0216449 0.470820i
\(238\) 4.27988 + 15.9727i 0.277424 + 1.03536i
\(239\) 2.27943 3.94809i 0.147444 0.255380i −0.782838 0.622225i \(-0.786229\pi\)
0.930282 + 0.366845i \(0.119562\pi\)
\(240\) 1.63013 3.51321i 0.105225 0.226777i
\(241\) 8.03104 + 13.9102i 0.517325 + 0.896032i 0.999798 + 0.0201215i \(0.00640532\pi\)
−0.482473 + 0.875911i \(0.660261\pi\)
\(242\) 8.49947 8.49947i 0.546367 0.546367i
\(243\) −4.51572 14.9201i −0.289684 0.957122i
\(244\) 12.5450i 0.803113i
\(245\) 0.0608948 0.0471343i 0.00389043 0.00301130i
\(246\) 10.9118 2.39268i 0.695708 0.152552i
\(247\) −3.02059 + 0.809364i −0.192195 + 0.0514986i
\(248\) −3.93882 + 1.05540i −0.250115 + 0.0670181i
\(249\) 13.4249 + 14.7187i 0.850766 + 0.932760i
\(250\) 11.0654 1.59899i 0.699838 0.101129i
\(251\) 18.9981i 1.19915i −0.800319 0.599574i \(-0.795337\pi\)
0.800319 0.599574i \(-0.204663\pi\)
\(252\) −7.46427 2.75584i −0.470205 0.173602i
\(253\) −8.92963 + 8.92963i −0.561401 + 0.561401i
\(254\) 1.78075 + 3.08436i 0.111734 + 0.193530i
\(255\) 23.7882 + 4.14801i 1.48968 + 0.259759i
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 0.867374 + 3.23709i 0.0541053 + 0.201924i 0.987688 0.156439i \(-0.0500016\pi\)
−0.933582 + 0.358363i \(0.883335\pi\)
\(258\) −3.82985 + 1.98248i −0.238436 + 0.123424i
\(259\) 2.05313 1.18538i 0.127575 0.0736557i
\(260\) 1.07203 + 0.815457i 0.0664842 + 0.0505725i
\(261\) 3.18767 4.50804i 0.197312 0.279041i
\(262\) 9.23478 + 9.23478i 0.570526 + 0.570526i
\(263\) −4.33402 + 16.1748i −0.267247 + 0.997380i 0.693614 + 0.720347i \(0.256018\pi\)
−0.960861 + 0.277032i \(0.910649\pi\)
\(264\) −6.13989 + 5.60017i −0.377884 + 0.344667i
\(265\) −3.82681 + 1.60400i −0.235079 + 0.0985327i
\(266\) −11.9243 6.88452i −0.731128 0.422117i
\(267\) 1.91459 2.99006i 0.117171 0.182989i
\(268\) −10.6655 2.85782i −0.651500 0.174569i
\(269\) −0.535741 −0.0326647 −0.0163324 0.999867i \(-0.505199\pi\)
−0.0163324 + 0.999867i \(0.505199\pi\)
\(270\) −8.23814 + 8.19348i −0.501357 + 0.498639i
\(271\) −15.5412 −0.944063 −0.472032 0.881582i \(-0.656479\pi\)
−0.472032 + 0.881582i \(0.656479\pi\)
\(272\) −6.02233 1.61368i −0.365158 0.0978437i
\(273\) 1.49217 2.33036i 0.0903104 0.141040i
\(274\) 2.81385 + 1.62458i 0.169991 + 0.0981442i
\(275\) −23.2236 6.01394i −1.40043 0.362654i
\(276\) 3.36824 3.07216i 0.202744 0.184922i
\(277\) −4.48011 + 16.7200i −0.269184 + 1.00461i 0.690456 + 0.723374i \(0.257410\pi\)
−0.959640 + 0.281232i \(0.909257\pi\)
\(278\) 15.5525 + 15.5525i 0.932775 + 0.932775i
\(279\) 12.1817 + 1.12242i 0.729298 + 0.0671978i
\(280\) 0.798810 + 5.87657i 0.0477380 + 0.351192i
\(281\) −20.8909 + 12.0613i −1.24624 + 0.719519i −0.970358 0.241671i \(-0.922304\pi\)
−0.275886 + 0.961190i \(0.588971\pi\)
\(282\) 6.09396 3.15447i 0.362890 0.187846i
\(283\) −4.28387 15.9876i −0.254649 0.950365i −0.968285 0.249848i \(-0.919619\pi\)
0.713636 0.700517i \(-0.247047\pi\)
\(284\) 5.21013 9.02421i 0.309164 0.535489i
\(285\) −16.4483 + 11.5638i −0.974314 + 0.684979i
\(286\) −1.44505 2.50289i −0.0854474 0.147999i
\(287\) −12.0957 + 12.0957i −0.713987 + 0.713987i
\(288\) 2.30701 1.91774i 0.135942 0.113004i
\(289\) 21.8725i 1.28661i
\(290\) −4.08228 0.519994i −0.239720 0.0305351i
\(291\) 20.1938 + 22.1400i 1.18378 + 1.29787i
\(292\) 4.50818 1.20796i 0.263821 0.0706906i
\(293\) 15.6012 4.18032i 0.911431 0.244217i 0.227512 0.973775i \(-0.426941\pi\)
0.683919 + 0.729558i \(0.260274\pi\)
\(294\) 0.0582638 0.0127758i 0.00339801 0.000745100i
\(295\) 0.176689 + 0.228272i 0.0102872 + 0.0132905i
\(296\) 0.893864i 0.0519548i
\(297\) 23.0985 9.38093i 1.34031 0.544337i
\(298\) −9.28669 + 9.28669i −0.537964 + 0.537964i
\(299\) 0.792727 + 1.37304i 0.0458446 + 0.0794052i
\(300\) 8.27516 + 2.55376i 0.477767 + 0.147441i
\(301\) 3.30185 5.71897i 0.190315 0.329636i
\(302\) −0.0869109 0.324356i −0.00500116 0.0186646i
\(303\) 0.951492 20.6968i 0.0546618 1.18900i
\(304\) 4.49593 2.59573i 0.257859 0.148875i
\(305\) −27.7959 + 3.77833i −1.59159 + 0.216347i
\(306\) 15.2720 + 10.7990i 0.873043 + 0.617335i
\(307\) −1.45642 1.45642i −0.0831222 0.0831222i 0.664323 0.747445i \(-0.268720\pi\)
−0.747445 + 0.664323i \(0.768720\pi\)
\(308\) 3.29355 12.2917i 0.187667 0.700384i
\(309\) −17.7821 5.65183i −1.01159 0.321521i
\(310\) −3.52475 8.40933i −0.200192 0.477618i
\(311\) −1.81462 1.04767i −0.102898 0.0594081i 0.447668 0.894200i \(-0.352255\pi\)
−0.550566 + 0.834792i \(0.685588\pi\)
\(312\) 0.479617 + 0.926549i 0.0271530 + 0.0524555i
\(313\) 19.0789 + 5.11217i 1.07840 + 0.288957i 0.753941 0.656942i \(-0.228150\pi\)
0.324461 + 0.945899i \(0.394817\pi\)
\(314\) 4.55886 0.257271
\(315\) 3.85800 17.3685i 0.217374 0.978605i
\(316\) −4.18916 −0.235659
\(317\) 32.9248 + 8.82217i 1.84924 + 0.495503i 0.999498 0.0316937i \(-0.0100901\pi\)
0.849743 + 0.527196i \(0.176757\pi\)
\(318\) −3.21070 0.147605i −0.180047 0.00827727i
\(319\) 7.64709 + 4.41505i 0.428155 + 0.247195i
\(320\) −2.06944 0.847015i −0.115685 0.0473496i
\(321\) −2.28414 10.4168i −0.127488 0.581408i
\(322\) −1.80678 + 6.74301i −0.100688 + 0.375773i
\(323\) 22.8873 + 22.8873i 1.27348 + 1.27348i
\(324\) −8.48528 + 3.00000i −0.471405 + 0.166667i
\(325\) −1.48393 + 2.62088i −0.0823135 + 0.145380i
\(326\) 11.0410 6.37454i 0.611506 0.353053i
\(327\) −22.5428 14.4346i −1.24662 0.798233i
\(328\) −1.66927 6.22982i −0.0921703 0.343984i
\(329\) −5.25381 + 9.09987i −0.289652 + 0.501692i
\(330\) −14.2575 11.9174i −0.784848 0.656034i
\(331\) −12.0140 20.8088i −0.660348 1.14376i −0.980524 0.196399i \(-0.937075\pi\)
0.320176 0.947358i \(-0.396258\pi\)
\(332\) 8.13293 8.13293i 0.446353 0.446353i
\(333\) 0.928776 2.51561i 0.0508966 0.137855i
\(334\) 0.00888621i 0.000486232i
\(335\) 3.11978 24.4922i 0.170452 1.33815i
\(336\) −1.39150 + 4.37802i −0.0759124 + 0.238841i
\(337\) −11.8340 + 3.17090i −0.644637 + 0.172730i −0.566303 0.824197i \(-0.691627\pi\)
−0.0783338 + 0.996927i \(0.524960\pi\)
\(338\) 12.2066 3.27074i 0.663949 0.177905i
\(339\) −3.11295 + 9.79417i −0.169072 + 0.531947i
\(340\) 1.76160 13.8296i 0.0955361 0.750018i
\(341\) 19.5648i 1.05949i
\(342\) −15.3501 + 2.63366i −0.830037 + 0.142412i
\(343\) 13.0634 13.0634i 0.705357 0.705357i
\(344\) 1.24492 + 2.15627i 0.0671217 + 0.116258i
\(345\) 7.82140 + 6.53770i 0.421090 + 0.351978i
\(346\) −5.19145 + 8.99186i −0.279094 + 0.483405i
\(347\) −4.81127 17.9559i −0.258283 0.963924i −0.966235 0.257663i \(-0.917047\pi\)
0.707952 0.706260i \(-0.249619\pi\)
\(348\) −2.68449 1.71893i −0.143904 0.0921444i
\(349\) −27.2305 + 15.7215i −1.45761 + 0.841553i −0.998894 0.0470278i \(-0.985025\pi\)
−0.458720 + 0.888581i \(0.651692\pi\)
\(350\) −12.7801 + 3.53983i −0.683124 + 0.189212i
\(351\) −0.387054 3.10595i −0.0206594 0.165783i
\(352\) 3.39264 + 3.39264i 0.180829 + 0.180829i
\(353\) 3.14681 11.7440i 0.167488 0.625073i −0.830222 0.557433i \(-0.811786\pi\)
0.997710 0.0676398i \(-0.0215469\pi\)
\(354\) 0.0478918 + 0.218409i 0.00254542 + 0.0116083i
\(355\) 21.5641 + 8.82612i 1.14450 + 0.468442i
\(356\) −1.77526 1.02494i −0.0940883 0.0543219i
\(357\) −28.6113 1.31534i −1.51427 0.0696153i
\(358\) −1.41307 0.378631i −0.0746830 0.0200112i
\(359\) 4.31606 0.227793 0.113896 0.993493i \(-0.463667\pi\)
0.113896 + 0.993493i \(0.463667\pi\)
\(360\) 4.94394 + 4.53403i 0.260569 + 0.238964i
\(361\) −7.95119 −0.418484
\(362\) −8.38980 2.24804i −0.440958 0.118154i
\(363\) 9.57068 + 18.4891i 0.502330 + 0.970428i
\(364\) −1.38358 0.798810i −0.0725192 0.0418690i
\(365\) 4.03425 + 9.62491i 0.211162 + 0.503791i
\(366\) −20.7078 6.58172i −1.08242 0.344032i
\(367\) 5.14485 19.2008i 0.268559 1.00228i −0.691477 0.722399i \(-0.743040\pi\)
0.960036 0.279877i \(-0.0902938\pi\)
\(368\) −1.86115 1.86115i −0.0970189 0.0970189i
\(369\) −1.77528 + 19.2671i −0.0924174 + 1.00301i
\(370\) −1.98053 + 0.269215i −0.102963 + 0.0139958i
\(371\) 4.26229 2.46083i 0.221287 0.127760i
\(372\) 0.324358 7.05544i 0.0168172 0.365807i
\(373\) −0.680056 2.53800i −0.0352120 0.131413i 0.946082 0.323926i \(-0.105003\pi\)
−0.981294 + 0.192513i \(0.938336\pi\)
\(374\) −14.9570 + 25.9063i −0.773408 + 1.33958i
\(375\) −3.16602 + 19.1044i −0.163492 + 0.986545i
\(376\) −1.98089 3.43100i −0.102157 0.176940i
\(377\) 0.783892 0.783892i 0.0403725 0.0403725i
\(378\) 8.46512 10.8753i 0.435399 0.559363i
\(379\) 3.03124i 0.155705i −0.996965 0.0778523i \(-0.975194\pi\)
0.996965 0.0778523i \(-0.0248063\pi\)
\(380\) 7.10542 + 9.17981i 0.364500 + 0.470914i
\(381\) −6.02555 + 1.32125i −0.308698 + 0.0676899i
\(382\) −4.83835 + 1.29643i −0.247552 + 0.0663313i
\(383\) −22.9416 + 6.14717i −1.17226 + 0.314106i −0.791852 0.610713i \(-0.790883\pi\)
−0.380407 + 0.924819i \(0.624216\pi\)
\(384\) −1.16721 1.27970i −0.0595638 0.0653043i
\(385\) 28.2266 + 3.59546i 1.43856 + 0.183241i
\(386\) 3.36832i 0.171443i
\(387\) −1.26311 7.36197i −0.0642077 0.374230i
\(388\) 12.2336 12.2336i 0.621069 0.621069i
\(389\) −3.33254 5.77213i −0.168966 0.292659i 0.769090 0.639140i \(-0.220710\pi\)
−0.938057 + 0.346482i \(0.887376\pi\)
\(390\) −1.90849 + 1.34174i −0.0966404 + 0.0679418i
\(391\) 8.20515 14.2117i 0.414952 0.718718i
\(392\) −0.00891317 0.0332644i −0.000450183 0.00168011i
\(393\) −20.0887 + 10.3987i −1.01334 + 0.524543i
\(394\) 18.9869 10.9621i 0.956545 0.552261i
\(395\) −1.26170 9.28189i −0.0634829 0.467022i
\(396\) −6.02281 13.0731i −0.302658 0.656949i
\(397\) −13.2242 13.2242i −0.663703 0.663703i 0.292548 0.956251i \(-0.405497\pi\)
−0.956251 + 0.292548i \(0.905497\pi\)
\(398\) 4.77797 17.8316i 0.239498 0.893819i
\(399\) 17.6202 16.0713i 0.882114 0.804572i
\(400\) 1.25345 4.84034i 0.0626724 0.242017i
\(401\) 4.66934 + 2.69585i 0.233176 + 0.134624i 0.612036 0.790830i \(-0.290351\pi\)
−0.378860 + 0.925454i \(0.623684\pi\)
\(402\) 10.3130 16.1060i 0.514364 0.803294i
\(403\) 2.37260 + 0.635736i 0.118188 + 0.0316683i
\(404\) −11.9619 −0.595129
\(405\) −9.20269 17.8972i −0.457285 0.889320i
\(406\) 4.88121 0.242250
\(407\) 4.14256 + 1.10999i 0.205339 + 0.0550204i
\(408\) 5.82327 9.09433i 0.288295 0.450237i
\(409\) 7.43574 + 4.29303i 0.367674 + 0.212277i 0.672442 0.740150i \(-0.265246\pi\)
−0.304768 + 0.952427i \(0.598579\pi\)
\(410\) 13.3006 5.57490i 0.656870 0.275325i
\(411\) −4.15793 + 3.79243i −0.205096 + 0.187067i
\(412\) −2.78816 + 10.4055i −0.137363 + 0.512644i
\(413\) −0.242107 0.242107i −0.0119133 0.0119133i
\(414\) 3.30401 + 7.17168i 0.162383 + 0.352469i
\(415\) 20.4696 + 15.5706i 1.00481 + 0.764329i
\(416\) 0.521662 0.301182i 0.0255766 0.0147666i
\(417\) −33.8317 + 17.5126i −1.65675 + 0.857595i
\(418\) −6.44672 24.0595i −0.315319 1.17679i
\(419\) −7.72749 + 13.3844i −0.377512 + 0.653871i −0.990700 0.136067i \(-0.956554\pi\)
0.613187 + 0.789938i \(0.289887\pi\)
\(420\) −10.1194 1.76455i −0.493778 0.0861012i
\(421\) 9.45129 + 16.3701i 0.460628 + 0.797831i 0.998992 0.0448812i \(-0.0142909\pi\)
−0.538364 + 0.842712i \(0.680958\pi\)
\(422\) 0.925553 0.925553i 0.0450552 0.0450552i
\(423\) 2.00983 + 11.7142i 0.0977214 + 0.569562i
\(424\) 1.85566i 0.0901186i
\(425\) 31.1728 0.262075i 1.51210 0.0127125i
\(426\) 12.1626 + 13.3348i 0.589280 + 0.646073i
\(427\) 32.1388 8.61157i 1.55531 0.416743i
\(428\) −5.94722 + 1.59355i −0.287470 + 0.0770273i
\(429\) 4.88962 1.07217i 0.236073 0.0517650i
\(430\) −4.40268 + 3.40779i −0.212316 + 0.164338i
\(431\) 3.91428i 0.188544i 0.995546 + 0.0942720i \(0.0300523\pi\)
−0.995546 + 0.0942720i \(0.969948\pi\)
\(432\) 1.95521 + 4.81427i 0.0940699 + 0.231627i
\(433\) −27.2049 + 27.2049i −1.30738 + 1.30738i −0.384086 + 0.923297i \(0.625483\pi\)
−0.923297 + 0.384086i \(0.874517\pi\)
\(434\) 5.40762 + 9.36628i 0.259574 + 0.449596i
\(435\) 3.00010 6.46572i 0.143844 0.310008i
\(436\) −7.72730 + 13.3841i −0.370070 + 0.640981i
\(437\) 3.53656 + 13.1986i 0.169176 + 0.631375i
\(438\) −0.371245 + 8.07531i −0.0177388 + 0.385853i
\(439\) 13.2725 7.66286i 0.633460 0.365728i −0.148631 0.988893i \(-0.547487\pi\)
0.782091 + 0.623164i \(0.214153\pi\)
\(440\) −6.49525 + 8.53886i −0.309649 + 0.407074i
\(441\) −0.00947919 + 0.102878i −0.000451390 + 0.00489894i
\(442\) 2.65561 + 2.65561i 0.126315 + 0.126315i
\(443\) −7.20031 + 26.8719i −0.342097 + 1.27672i 0.553870 + 0.832603i \(0.313150\pi\)
−0.895967 + 0.444120i \(0.853516\pi\)
\(444\) −1.47548 0.468963i −0.0700233 0.0222560i
\(445\) 1.73629 4.24211i 0.0823078 0.201095i
\(446\) −18.1659 10.4881i −0.860180 0.496625i
\(447\) −10.4571 20.2016i −0.494605 0.955503i
\(448\) 2.56188 + 0.686453i 0.121037 + 0.0324319i
\(449\) 24.3627 1.14975 0.574874 0.818242i \(-0.305051\pi\)
0.574874 + 0.818242i \(0.305051\pi\)
\(450\) −8.55699 + 12.3198i −0.403380 + 0.580762i
\(451\) −30.9446 −1.45712
\(452\) 5.73124 + 1.53568i 0.269575 + 0.0722324i
\(453\) 0.581006 + 0.0267105i 0.0272980 + 0.00125497i
\(454\) 5.15716 + 2.97749i 0.242037 + 0.139740i
\(455\) 1.35321 3.30617i 0.0634393 0.154996i
\(456\) 1.92594 + 8.78319i 0.0901902 + 0.411310i
\(457\) 3.39506 12.6705i 0.158814 0.592702i −0.839935 0.542688i \(-0.817407\pi\)
0.998749 0.0500141i \(-0.0159266\pi\)
\(458\) −8.31377 8.31377i −0.388477 0.388477i
\(459\) −25.8380 + 19.5436i −1.20602 + 0.912216i
\(460\) 3.56318 4.68427i 0.166134 0.218405i
\(461\) 34.7684 20.0736i 1.61933 0.934919i 0.632233 0.774778i \(-0.282139\pi\)
0.987094 0.160141i \(-0.0511948\pi\)
\(462\) 18.5617 + 11.8854i 0.863569 + 0.552959i
\(463\) 3.09986 + 11.5688i 0.144063 + 0.537649i 0.999795 + 0.0202307i \(0.00644006\pi\)
−0.855733 + 0.517418i \(0.826893\pi\)
\(464\) −0.920201 + 1.59383i −0.0427192 + 0.0739919i
\(465\) 15.7304 1.40629i 0.729478 0.0652152i
\(466\) −9.49800 16.4510i −0.439986 0.762079i
\(467\) −8.63124 + 8.63124i −0.399406 + 0.399406i −0.878024 0.478617i \(-0.841138\pi\)
0.478617 + 0.878024i \(0.341138\pi\)
\(468\) −1.78107 + 0.305583i −0.0823298 + 0.0141256i
\(469\) 29.2855i 1.35228i
\(470\) 7.00543 5.42239i 0.323136 0.250116i
\(471\) −2.39179 + 7.52521i −0.110208 + 0.346744i
\(472\) 0.124696 0.0334121i 0.00573959 0.00153792i
\(473\) 11.5390 3.09188i 0.530565 0.142165i
\(474\) 2.19783 6.91496i 0.100950 0.317615i
\(475\) −18.1996 + 18.5082i −0.835055 + 0.849215i
\(476\) 16.5362i 0.757935i
\(477\) 1.92813 5.22240i 0.0882832 0.239117i
\(478\) 3.22360 3.22360i 0.147444 0.147444i
\(479\) −5.13488 8.89388i −0.234619 0.406372i 0.724543 0.689230i \(-0.242051\pi\)
−0.959162 + 0.282858i \(0.908718\pi\)
\(480\) 2.48388 2.97159i 0.113373 0.135634i
\(481\) 0.269215 0.466295i 0.0122752 0.0212612i
\(482\) 4.15717 + 15.5148i 0.189354 + 0.706678i
\(483\) −10.1826 6.52013i −0.463326 0.296676i
\(484\) 10.4097 6.01003i 0.473167 0.273183i
\(485\) 30.7905 + 23.4214i 1.39812 + 1.06351i
\(486\) −0.500258 15.5804i −0.0226921 0.706743i
\(487\) 17.5218 + 17.5218i 0.793987 + 0.793987i 0.982140 0.188153i \(-0.0602500\pi\)
−0.188153 + 0.982140i \(0.560250\pi\)
\(488\) −3.24689 + 12.1176i −0.146980 + 0.548536i
\(489\) 4.72968 + 21.5696i 0.213884 + 0.975411i
\(490\) 0.0710191 0.0297675i 0.00320832 0.00134476i
\(491\) −7.70100 4.44617i −0.347541 0.200653i 0.316061 0.948739i \(-0.397640\pi\)
−0.663602 + 0.748086i \(0.730973\pi\)
\(492\) 11.1592 + 0.513021i 0.503096 + 0.0231288i
\(493\) −11.0835 2.96982i −0.499176 0.133754i
\(494\) −3.12714 −0.140697
\(495\) 27.1520 17.2821i 1.22039 0.776771i
\(496\) −4.07776 −0.183097
\(497\) −26.6954 7.15302i −1.19745 0.320857i
\(498\) 9.15794 + 17.6918i 0.410377 + 0.792788i
\(499\) −25.4186 14.6754i −1.13789 0.656963i −0.191985 0.981398i \(-0.561493\pi\)
−0.945908 + 0.324435i \(0.894826\pi\)
\(500\) 11.1022 + 1.31943i 0.496506 + 0.0590068i
\(501\) 0.0146683 + 0.00466213i 0.000655331 + 0.000208288i
\(502\) 4.91707 18.3507i 0.219459 0.819034i
\(503\) −10.0766 10.0766i −0.449293 0.449293i 0.445826 0.895120i \(-0.352910\pi\)
−0.895120 + 0.445826i \(0.852910\pi\)
\(504\) −6.49666 4.59383i −0.289384 0.204626i
\(505\) −3.60272 26.5040i −0.160319 1.17941i
\(506\) −10.9365 + 6.31420i −0.486188 + 0.280701i
\(507\) −1.00520 + 21.8651i −0.0446425 + 0.971063i
\(508\) 0.921786 + 3.44015i 0.0408976 + 0.152632i
\(509\) 15.0024 25.9849i 0.664970 1.15176i −0.314323 0.949316i \(-0.601777\pi\)
0.979293 0.202446i \(-0.0648892\pi\)
\(510\) 21.9041 + 10.1635i 0.969930 + 0.450048i
\(511\) −6.18930 10.7202i −0.273799 0.474233i
\(512\) −0.707107 + 0.707107i −0.0312500 + 0.0312500i
\(513\) 3.70605 26.7198i 0.163626 1.17971i
\(514\) 3.35128i 0.147819i
\(515\) −23.8952 3.04374i −1.05295 0.134123i
\(516\) −4.21246 + 0.923688i −0.185443 + 0.0406631i
\(517\) −18.3606 + 4.91971i −0.807499 + 0.216369i
\(518\) 2.28997 0.613596i 0.100615 0.0269598i
\(519\) −12.1190 13.2870i −0.531965 0.583234i
\(520\) 0.824441 + 1.06513i 0.0361541 + 0.0467091i
\(521\) 6.40485i 0.280602i 0.990109 + 0.140301i \(0.0448070\pi\)
−0.990109 + 0.140301i \(0.955193\pi\)
\(522\) 4.24582 3.52941i 0.185834 0.154478i
\(523\) 16.0596 16.0596i 0.702237 0.702237i −0.262653 0.964890i \(-0.584597\pi\)
0.964890 + 0.262653i \(0.0845974\pi\)
\(524\) 6.52997 + 11.3102i 0.285263 + 0.494090i
\(525\) 0.861911 22.9530i 0.0376169 1.00175i
\(526\) −8.37268 + 14.5019i −0.365066 + 0.632313i
\(527\) −6.58020 24.5576i −0.286638 1.06975i
\(528\) −7.38011 + 3.82023i −0.321178 + 0.166254i
\(529\) −13.9190 + 8.03614i −0.605174 + 0.349397i
\(530\) −4.11156 + 0.558889i −0.178595 + 0.0242766i
\(531\) −0.385650 0.0355339i −0.0167358 0.00154204i
\(532\) −9.73618 9.73618i −0.422117 0.422117i
\(533\) −1.00551 + 3.75261i −0.0435535 + 0.162544i
\(534\) 2.62324 2.39264i 0.113519 0.103540i
\(535\) −5.32202 12.6973i −0.230091 0.548950i
\(536\) −9.56244 5.52087i −0.413034 0.238465i
\(537\) 1.36636 2.13388i 0.0589628 0.0920836i
\(538\) −0.517486 0.138660i −0.0223104 0.00597806i
\(539\) −0.165230 −0.00711696
\(540\) −10.0781 + 5.78210i −0.433691 + 0.248822i
\(541\) 44.6389 1.91917 0.959587 0.281412i \(-0.0908026\pi\)
0.959587 + 0.281412i \(0.0908026\pi\)
\(542\) −15.0117 4.02237i −0.644807 0.172776i
\(543\) 8.11248 12.6694i 0.348140 0.543698i
\(544\) −5.39948 3.11739i −0.231501 0.133657i
\(545\) −31.9823 13.0903i −1.36997 0.560725i
\(546\) 2.04447 1.86475i 0.0874953 0.0798040i
\(547\) −1.38008 + 5.15053i −0.0590080 + 0.220221i −0.989133 0.147022i \(-0.953031\pi\)
0.930125 + 0.367242i \(0.119698\pi\)
\(548\) 2.29750 + 2.29750i 0.0981442 + 0.0981442i
\(549\) 21.7286 30.7289i 0.927355 1.31148i
\(550\) −20.8757 11.8197i −0.890144 0.503995i
\(551\) 8.27432 4.77718i 0.352498 0.203515i
\(552\) 4.04860 2.09571i 0.172320 0.0891994i
\(553\) 2.87566 + 10.7321i 0.122286 + 0.456376i
\(554\) −8.65490 + 14.9907i −0.367712 + 0.636895i
\(555\) 0.594690 3.41046i 0.0252432 0.144766i
\(556\) 10.9973 + 19.0478i 0.466388 + 0.807807i
\(557\) −4.10329 + 4.10329i −0.173862 + 0.173862i −0.788674 0.614812i \(-0.789232\pi\)
0.614812 + 0.788674i \(0.289232\pi\)
\(558\) 11.4761 + 4.23703i 0.485822 + 0.179368i
\(559\) 1.49979i 0.0634344i
\(560\) −0.749378 + 5.88308i −0.0316670 + 0.248605i
\(561\) −34.9158 38.2809i −1.47415 1.61622i
\(562\) −23.3007 + 6.24341i −0.982882 + 0.263362i
\(563\) 5.73047 1.53547i 0.241510 0.0647125i −0.136033 0.990704i \(-0.543435\pi\)
0.377544 + 0.925992i \(0.376769\pi\)
\(564\) 6.70275 1.46975i 0.282237 0.0618875i
\(565\) −1.67645 + 13.1612i −0.0705288 + 0.553695i
\(566\) 16.5516i 0.695715i
\(567\) 13.5104 + 19.6789i 0.567383 + 0.826436i
\(568\) 7.36824 7.36824i 0.309164 0.309164i
\(569\) −17.6714 30.6077i −0.740822 1.28314i −0.952122 0.305720i \(-0.901103\pi\)
0.211300 0.977421i \(-0.432230\pi\)
\(570\) −18.8808 + 6.91261i −0.790829 + 0.289538i
\(571\) 1.50529 2.60725i 0.0629946 0.109110i −0.832808 0.553562i \(-0.813268\pi\)
0.895803 + 0.444452i \(0.146602\pi\)
\(572\) −0.748011 2.79162i −0.0312759 0.116723i
\(573\) 0.398435 8.66674i 0.0166448 0.362058i
\(574\) −14.8142 + 8.55296i −0.618331 + 0.356993i
\(575\) 11.4521 + 6.48410i 0.477584 + 0.270405i
\(576\) 2.72474 1.25529i 0.113531 0.0523040i
\(577\) −11.5350 11.5350i −0.480208 0.480208i 0.424990 0.905198i \(-0.360278\pi\)
−0.905198 + 0.424990i \(0.860278\pi\)
\(578\) 5.66101 21.1272i 0.235467 0.878774i
\(579\) −5.56002 1.76718i −0.231066 0.0734415i
\(580\) −3.80859 1.55885i −0.158143 0.0647276i
\(581\) −26.4185 15.2527i −1.09602 0.632789i
\(582\) 13.7755 + 26.6122i 0.571011 + 1.10311i
\(583\) 8.59992 + 2.30434i 0.356172 + 0.0954361i
\(584\) 4.66721 0.193130
\(585\) −1.21350 3.85426i −0.0501721 0.159354i
\(586\) 16.1515 0.667214
\(587\) −11.0157 2.95165i −0.454666 0.121828i 0.0242156 0.999707i \(-0.492291\pi\)
−0.478882 + 0.877879i \(0.658958\pi\)
\(588\) 0.0595851 + 0.00273930i 0.00245725 + 0.000112967i
\(589\) 18.3333 + 10.5848i 0.755412 + 0.436137i
\(590\) 0.111587 + 0.266224i 0.00459397 + 0.0109603i
\(591\) 8.13346 + 37.0925i 0.334566 + 1.52578i
\(592\) −0.231349 + 0.863406i −0.00950838 + 0.0354858i
\(593\) −23.4664 23.4664i −0.963651 0.963651i 0.0357109 0.999362i \(-0.488630\pi\)
−0.999362 + 0.0357109i \(0.988630\pi\)
\(594\) 24.7394 3.08295i 1.01507 0.126495i
\(595\) −36.6391 + 4.98040i −1.50206 + 0.204177i
\(596\) −11.3738 + 6.56668i −0.465890 + 0.268982i
\(597\) 26.9276 + 17.2422i 1.10207 + 0.705678i
\(598\) 0.410346 + 1.53143i 0.0167803 + 0.0626249i
\(599\) 17.2683 29.9097i 0.705566 1.22208i −0.260922 0.965360i \(-0.584026\pi\)
0.966487 0.256715i \(-0.0826403\pi\)
\(600\) 7.33223 + 4.60851i 0.299337 + 0.188142i
\(601\) −1.57759 2.73247i −0.0643513 0.111460i 0.832055 0.554694i \(-0.187164\pi\)
−0.896406 + 0.443234i \(0.853831\pi\)
\(602\) 4.66952 4.66952i 0.190315 0.190315i
\(603\) 21.1752 + 25.4734i 0.862320 + 1.03736i
\(604\) 0.335798i 0.0136634i
\(605\) 16.4516 + 21.2545i 0.668852 + 0.864120i
\(606\) 6.27581 19.7454i 0.254937 0.802100i
\(607\) −4.92890 + 1.32070i −0.200058 + 0.0536054i −0.357456 0.933930i \(-0.616356\pi\)
0.157399 + 0.987535i \(0.449689\pi\)
\(608\) 5.01456 1.34365i 0.203367 0.0544921i
\(609\) −2.56091 + 8.05731i −0.103773 + 0.326499i
\(610\) −27.8267 3.54452i −1.12667 0.143513i
\(611\) 2.38643i 0.0965446i
\(612\) 11.9567 + 14.3837i 0.483320 + 0.581426i
\(613\) −9.09622 + 9.09622i −0.367393 + 0.367393i −0.866525 0.499133i \(-0.833652\pi\)
0.499133 + 0.866525i \(0.333652\pi\)
\(614\) −1.02984 1.78374i −0.0415611 0.0719859i
\(615\) 2.22426 + 24.8799i 0.0896907 + 1.00325i
\(616\) 6.36265 11.0204i 0.256358 0.444026i
\(617\) 6.24315 + 23.2998i 0.251340 + 0.938013i 0.970090 + 0.242745i \(0.0780477\pi\)
−0.718751 + 0.695268i \(0.755286\pi\)
\(618\) −15.7134 10.0616i −0.632087 0.404737i
\(619\) −26.9280 + 15.5469i −1.08233 + 0.624883i −0.931524 0.363680i \(-0.881520\pi\)
−0.150806 + 0.988563i \(0.548187\pi\)
\(620\) −1.22815 9.03506i −0.0493236 0.362857i
\(621\) −13.5716 + 1.69125i −0.544609 + 0.0678677i
\(622\) −1.48163 1.48163i −0.0594081 0.0594081i
\(623\) −1.40715 + 5.25156i −0.0563764 + 0.210399i
\(624\) 0.223466 + 1.01911i 0.00894580 + 0.0407971i
\(625\) 0.420329 + 24.9965i 0.0168132 + 0.999859i
\(626\) 17.1057 + 9.87595i 0.683679 + 0.394723i
\(627\) 43.0967 + 1.98128i 1.72112 + 0.0791246i
\(628\) 4.40352 + 1.17992i 0.175719 + 0.0470839i
\(629\) −5.57304 −0.222212
\(630\) 8.22184 15.7782i 0.327566 0.628618i
\(631\) 46.1604 1.83762 0.918809 0.394703i \(-0.129153\pi\)
0.918809 + 0.394703i \(0.129153\pi\)
\(632\) −4.04642 1.08423i −0.160958 0.0431285i
\(633\) 1.04220 + 2.01338i 0.0414239 + 0.0800247i
\(634\) 29.5196 + 17.0431i 1.17237 + 0.676869i
\(635\) −7.34469 + 3.07850i −0.291465 + 0.122167i
\(636\) −3.06309 0.973565i −0.121460 0.0386044i
\(637\) −0.00536896 + 0.0200372i −0.000212726 + 0.000793905i
\(638\) 6.24383 + 6.24383i 0.247195 + 0.247195i
\(639\) −28.3926 + 13.0805i −1.12319 + 0.517457i
\(640\) −1.77970 1.35376i −0.0703487 0.0535122i
\(641\) −3.41084 + 1.96925i −0.134720 + 0.0777808i −0.565845 0.824511i \(-0.691450\pi\)
0.431125 + 0.902292i \(0.358117\pi\)
\(642\) 0.489749 10.6530i 0.0193288 0.420441i
\(643\) 8.03625 + 29.9917i 0.316919 + 1.18276i 0.922190 + 0.386737i \(0.126398\pi\)
−0.605271 + 0.796019i \(0.706935\pi\)
\(644\) −3.49044 + 6.04562i −0.137543 + 0.238231i
\(645\) −3.31532 9.05531i −0.130541 0.356552i
\(646\) 16.1838 + 28.0311i 0.636742 + 1.10287i
\(647\) 18.0986 18.0986i 0.711531 0.711531i −0.255325 0.966855i \(-0.582182\pi\)
0.966855 + 0.255325i \(0.0821824\pi\)
\(648\) −8.97261 + 0.701625i −0.352477 + 0.0275624i
\(649\) 0.619386i 0.0243130i
\(650\) −2.11170 + 2.14750i −0.0828276 + 0.0842321i
\(651\) −18.2978 + 4.01226i −0.717149 + 0.157253i
\(652\) 12.3147 3.29971i 0.482280 0.129226i
\(653\) 13.5729 3.63685i 0.531148 0.142321i 0.0167299 0.999860i \(-0.494674\pi\)
0.514419 + 0.857539i \(0.328008\pi\)
\(654\) −18.0387 19.7772i −0.705369 0.773350i
\(655\) −23.0933 + 17.8748i −0.902330 + 0.698428i
\(656\) 6.44958i 0.251814i
\(657\) −13.1350 4.84950i −0.512444 0.189197i
\(658\) −7.43002 + 7.43002i −0.289652 + 0.289652i
\(659\) 18.2709 + 31.6462i 0.711734 + 1.23276i 0.964206 + 0.265155i \(0.0854233\pi\)
−0.252471 + 0.967604i \(0.581243\pi\)
\(660\) −10.6872 15.2015i −0.415999 0.591716i
\(661\) −17.9365 + 31.0670i −0.697650 + 1.20836i 0.271629 + 0.962402i \(0.412438\pi\)
−0.969279 + 0.245963i \(0.920896\pi\)
\(662\) −6.21890 23.2092i −0.241704 0.902053i
\(663\) −5.77683 + 2.99030i −0.224353 + 0.116134i
\(664\) 9.96076 5.75085i 0.386553 0.223176i
\(665\) 18.6400 24.5047i 0.722829 0.950253i
\(666\) 1.54822 2.18951i 0.0599922 0.0848418i
\(667\) −3.42525 3.42525i −0.132626 0.132626i
\(668\) 0.00229992 0.00858342i 8.89866e−5 0.000332102i
\(669\) 26.8432 24.4835i 1.03782 0.946588i
\(670\) 9.35253 22.8502i 0.361320 0.882780i
\(671\) 52.1261 + 30.0950i 2.01231 + 1.16181i
\(672\) −2.47720 + 3.86870i −0.0955600 + 0.149238i
\(673\) 24.2285 + 6.49200i 0.933939 + 0.250248i 0.693534 0.720424i \(-0.256053\pi\)
0.240406 + 0.970673i \(0.422720\pi\)
\(674\) −12.2514 −0.471907
\(675\) −15.8467 20.5884i −0.609939 0.792448i
\(676\) 12.6372 0.486045
\(677\) 5.23054 + 1.40152i 0.201026 + 0.0538647i 0.357927 0.933750i \(-0.383484\pi\)
−0.156901 + 0.987614i \(0.550150\pi\)
\(678\) −5.54180 + 8.65475i −0.212832 + 0.332384i
\(679\) −39.7389 22.9433i −1.52504 0.880481i
\(680\) 5.28095 12.9025i 0.202515 0.494787i
\(681\) −7.62057 + 6.95069i −0.292021 + 0.266351i
\(682\) −5.06374 + 18.8981i −0.193901 + 0.723647i
\(683\) −14.3302 14.3302i −0.548331 0.548331i 0.377627 0.925958i \(-0.376740\pi\)
−0.925958 + 0.377627i \(0.876740\pi\)
\(684\) −15.5087 1.42897i −0.592989 0.0546382i
\(685\) −4.39858 + 5.78251i −0.168061 + 0.220938i
\(686\) 15.9993 9.23721i 0.610857 0.352678i
\(687\) 18.0852 9.36157i 0.689992 0.357166i
\(688\) 0.644420 + 2.40501i 0.0245683 + 0.0916900i
\(689\) 0.558889 0.968025i 0.0212920 0.0368788i
\(690\) 5.86281 + 8.33926i 0.223193 + 0.317470i
\(691\) −5.85991 10.1497i −0.222921 0.386111i 0.732772 0.680474i \(-0.238226\pi\)
−0.955694 + 0.294363i \(0.904893\pi\)
\(692\) −7.34182 + 7.34182i −0.279094 + 0.279094i
\(693\) −29.3574 + 24.4038i −1.11519 + 0.927023i
\(694\) 18.5893i 0.705641i
\(695\) −38.8919 + 30.1034i −1.47525 + 1.14189i
\(696\) −2.14813 2.35516i −0.0814246 0.0892720i
\(697\) 38.8415 10.4076i 1.47123 0.394214i
\(698\) −30.3716 + 8.13805i −1.14958 + 0.308030i
\(699\) 32.1385 7.04717i 1.21559 0.266549i
\(700\) −13.2608 + 0.111486i −0.501211 + 0.00421377i
\(701\) 30.7235i 1.16041i −0.814471 0.580205i \(-0.802972\pi\)
0.814471 0.580205i \(-0.197028\pi\)
\(702\) 0.430013 3.10029i 0.0162298 0.117013i
\(703\) 3.28129 3.28129i 0.123756 0.123756i
\(704\) 2.39896 + 4.15512i 0.0904143 + 0.156602i
\(705\) 5.27525 + 14.4086i 0.198678 + 0.542658i
\(706\) 6.07917 10.5294i 0.228792 0.396280i
\(707\) 8.21132 + 30.6451i 0.308818 + 1.15253i
\(708\) −0.0102686 + 0.223362i −0.000385918 + 0.00839448i
\(709\) 27.4879 15.8701i 1.03233 0.596015i 0.114678 0.993403i \(-0.463416\pi\)
0.917651 + 0.397387i \(0.130083\pi\)
\(710\) 18.5449 + 14.1066i 0.695979 + 0.529410i
\(711\) 10.2613 + 7.25584i 0.384829 + 0.272115i
\(712\) −1.44949 1.44949i −0.0543219 0.0543219i
\(713\) 2.77788 10.3672i 0.104032 0.388254i
\(714\) −27.2960 8.67568i −1.02153 0.324679i
\(715\) 5.96007 2.49815i 0.222894 0.0934254i
\(716\) −1.26692 0.731458i −0.0473471 0.0273359i
\(717\) 3.62988 + 7.01238i 0.135560 + 0.261882i
\(718\) 4.16899 + 1.11708i 0.155585 + 0.0416890i
\(719\) 7.79879 0.290846 0.145423 0.989370i \(-0.453546\pi\)
0.145423 + 0.989370i \(0.453546\pi\)
\(720\) 3.60199 + 5.65912i 0.134238 + 0.210903i
\(721\) 28.5717 1.06407
\(722\) −7.68026 2.05792i −0.285830 0.0765878i
\(723\) −27.7910 1.27763i −1.03356 0.0475155i
\(724\) −7.52209 4.34288i −0.279556 0.161402i
\(725\) 2.30685 8.90816i 0.0856741 0.330841i
\(726\) 4.45923 + 20.3362i 0.165497 + 0.754747i
\(727\) 11.4645 42.7863i 0.425196 1.58685i −0.338297 0.941039i \(-0.609851\pi\)
0.763494 0.645815i \(-0.223482\pi\)
\(728\) −1.12969 1.12969i −0.0418690 0.0418690i
\(729\) 25.9808 + 7.34847i 0.962250 + 0.272166i
\(730\) 1.40568 + 10.3411i 0.0520265 + 0.382741i
\(731\) −13.4439 + 7.76182i −0.497239 + 0.287081i
\(732\) −18.2987 11.7170i −0.676341 0.433074i
\(733\) −7.21598 26.9304i −0.266528 0.994697i −0.961308 0.275475i \(-0.911165\pi\)
0.694780 0.719222i \(-0.255502\pi\)
\(734\) 9.93909 17.2150i 0.366858 0.635418i
\(735\) 0.0118765 + 0.132847i 0.000438072 + 0.00490015i
\(736\) −1.31603 2.27943i −0.0485095 0.0840208i
\(737\) −37.4607 + 37.4607i −1.37988 + 1.37988i
\(738\) −6.70149 + 18.1511i −0.246685 + 0.668153i
\(739\) 10.8068i 0.397536i 0.980047 + 0.198768i \(0.0636941\pi\)
−0.980047 + 0.198768i \(0.936306\pi\)
\(740\) −1.98272 0.252556i −0.0728862 0.00928414i
\(741\) 1.64065 5.16191i 0.0602707 0.189628i
\(742\) 4.75396 1.27382i 0.174523 0.0467634i
\(743\) −21.4877 + 5.75762i −0.788309 + 0.211227i −0.630445 0.776234i \(-0.717127\pi\)
−0.157864 + 0.987461i \(0.550461\pi\)
\(744\) 2.13939 6.73108i 0.0784338 0.246773i
\(745\) −17.9753 23.2231i −0.658565 0.850830i
\(746\) 2.62754i 0.0962009i
\(747\) −34.0082 + 5.83488i −1.24429 + 0.213487i
\(748\) −21.1524 + 21.1524i −0.773408 + 0.773408i
\(749\) 8.16498 + 14.1422i 0.298342 + 0.516743i
\(750\) −8.00271 + 17.6340i −0.292218 + 0.643901i
\(751\) −20.6235 + 35.7209i −0.752561 + 1.30347i 0.194017 + 0.980998i \(0.437848\pi\)
−0.946578 + 0.322476i \(0.895485\pi\)
\(752\) −1.02538 3.82678i −0.0373919 0.139548i
\(753\) 27.7115 + 17.7442i 1.00986 + 0.646634i
\(754\) 0.960067 0.554295i 0.0349636 0.0201862i
\(755\) 0.744025 0.101136i 0.0270778 0.00368072i
\(756\) 10.9914 8.31377i 0.399754 0.302369i
\(757\) −20.5246 20.5246i −0.745978 0.745978i 0.227743 0.973721i \(-0.426865\pi\)
−0.973721 + 0.227743i \(0.926865\pi\)
\(758\) 0.784544 2.92796i 0.0284959 0.106348i
\(759\) −4.68491 21.3654i −0.170051 0.775516i
\(760\) 4.48740 + 10.7060i 0.162775 + 0.388349i
\(761\) 39.8188 + 22.9894i 1.44343 + 0.833365i 0.998077 0.0619904i \(-0.0197448\pi\)
0.445353 + 0.895355i \(0.353078\pi\)
\(762\) −6.16220 0.283294i −0.223233 0.0102626i
\(763\) 39.5928 + 10.6089i 1.43335 + 0.384066i
\(764\) −5.00903 −0.181220
\(765\) −28.2687 + 30.8244i −1.02206 + 1.11446i
\(766\) −23.7508 −0.858153
\(767\) −0.0751122 0.0201262i −0.00271214 0.000726717i
\(768\) −0.796225 1.53819i −0.0287313 0.0555046i
\(769\) −26.6702 15.3980i −0.961752 0.555268i −0.0650399 0.997883i \(-0.520717\pi\)
−0.896712 + 0.442615i \(0.854051\pi\)
\(770\) 26.3342 + 10.7785i 0.949018 + 0.388431i
\(771\) −5.53189 1.75824i −0.199226 0.0633215i
\(772\) −0.871785 + 3.25355i −0.0313762 + 0.117098i
\(773\) −29.6376 29.6376i −1.06599 1.06599i −0.997663 0.0683287i \(-0.978233\pi\)
−0.0683287 0.997663i \(-0.521767\pi\)
\(774\) 0.685343 7.43803i 0.0246341 0.267354i
\(775\) 19.6490 5.44239i 0.705814 0.195496i
\(776\) 14.9831 8.65048i 0.537861 0.310534i
\(777\) −0.188577 + 4.10193i −0.00676517 + 0.147156i
\(778\) −1.72505 6.43797i −0.0618460 0.230813i
\(779\) −16.7414 + 28.9969i −0.599821 + 1.03892i
\(780\) −2.19073 + 0.802069i −0.0784408 + 0.0287187i
\(781\) −24.9978 43.2975i −0.894492 1.54931i
\(782\) 11.6038 11.6038i 0.414952 0.414952i
\(783\) 3.59836 + 8.86018i 0.128595 + 0.316637i
\(784\) 0.0344378i 0.00122992i
\(785\) −1.28808 + 10.1122i −0.0459735 + 0.360920i
\(786\) −22.0955 + 4.84500i −0.788122 + 0.172816i
\(787\) 26.0615 6.98316i 0.928993 0.248923i 0.237568 0.971371i \(-0.423650\pi\)
0.691425 + 0.722448i \(0.256983\pi\)
\(788\) 21.1771 5.67439i 0.754403 0.202142i
\(789\) −19.5453 21.4290i −0.695831 0.762893i
\(790\) 1.18362 9.29217i 0.0421114 0.330600i
\(791\) 15.7369i 0.559540i
\(792\) −2.43401 14.1865i −0.0864890 0.504095i
\(793\) 5.34337 5.34337i 0.189749 0.189749i
\(794\) −9.35091 16.1963i −0.331852 0.574784i
\(795\) 1.23457 7.08009i 0.0437858 0.251105i
\(796\) 9.23033 15.9874i 0.327161 0.566659i
\(797\) 1.68322 + 6.28188i 0.0596228 + 0.222515i 0.989308 0.145839i \(-0.0465880\pi\)
−0.929686 + 0.368354i \(0.879921\pi\)
\(798\) 21.1794 10.9633i 0.749742 0.388095i
\(799\) 21.3915 12.3504i 0.756778 0.436926i
\(800\) 2.46351 4.35099i 0.0870982 0.153831i
\(801\) 2.57321 + 5.58542i 0.0909200 + 0.197351i
\(802\) 3.81250 + 3.81250i 0.134624 + 0.134624i
\(803\) 5.79571 21.6299i 0.204526 0.763302i
\(804\) 14.1301 12.8880i 0.498330 0.454525i
\(805\) −14.4465 5.91291i −0.509171 0.208403i
\(806\) 2.12721 + 1.22815i 0.0749279 + 0.0432596i
\(807\) 0.500381 0.781457i 0.0176143 0.0275086i
\(808\) −11.5544 3.09598i −0.406481 0.108916i
\(809\) 5.79431 0.203717 0.101859 0.994799i \(-0.467521\pi\)
0.101859 + 0.994799i \(0.467521\pi\)
\(810\) −4.25697 19.6692i −0.149575 0.691106i
\(811\) 1.90498 0.0668929 0.0334465 0.999441i \(-0.489352\pi\)
0.0334465 + 0.999441i \(0.489352\pi\)
\(812\) 4.71488 + 1.26335i 0.165460 + 0.0443349i
\(813\) 14.5155 22.6692i 0.509080 0.795042i
\(814\) 3.71411 + 2.14434i 0.130180 + 0.0751592i
\(815\) 11.0201 + 26.2917i 0.386017 + 0.920958i
\(816\) 7.97863 7.27728i 0.279308 0.254756i
\(817\) 3.34547 12.4855i 0.117043 0.436812i
\(818\) 6.07126 + 6.07126i 0.212277 + 0.212277i
\(819\) 2.00548 + 4.35310i 0.0700773 + 0.152110i
\(820\) 14.2903 1.94250i 0.499038 0.0678349i
\(821\) −33.4503 + 19.3125i −1.16742 + 0.674012i −0.953072 0.302745i \(-0.902097\pi\)
−0.214351 + 0.976757i \(0.568764\pi\)
\(822\) −4.99781 + 2.58706i −0.174319 + 0.0902339i
\(823\) −5.53879 20.6711i −0.193070 0.720548i −0.992758 0.120132i \(-0.961668\pi\)
0.799688 0.600416i \(-0.204998\pi\)
\(824\) −5.38631 + 9.32936i −0.187641 + 0.325004i
\(825\) 30.4630 28.2579i 1.06058 0.983815i
\(826\) −0.171196 0.296520i −0.00595666 0.0103172i
\(827\) −23.1603 + 23.1603i −0.805364 + 0.805364i −0.983928 0.178564i \(-0.942855\pi\)
0.178564 + 0.983928i \(0.442855\pi\)
\(828\) 1.33526 + 7.78245i 0.0464034 + 0.270459i
\(829\) 34.1116i 1.18475i 0.805664 + 0.592373i \(0.201809\pi\)
−0.805664 + 0.592373i \(0.798191\pi\)
\(830\) 15.7421 + 20.3379i 0.546417 + 0.705940i
\(831\) −20.2041 22.1513i −0.700873 0.768421i
\(832\) 0.581838 0.155903i 0.0201716 0.00540497i
\(833\) 0.207396 0.0555716i 0.00718585 0.00192544i
\(834\) −37.2115 + 8.15957i −1.28853 + 0.282543i
\(835\) 0.0197109 + 0.00251074i 0.000682124 + 8.68879e-5i
\(836\) 24.9082i 0.861468i
\(837\) −13.0149 + 16.7204i −0.449860 + 0.577942i
\(838\) −10.9283 + 10.9283i −0.377512 + 0.377512i
\(839\) −18.8058 32.5726i −0.649249 1.12453i −0.983303 0.181978i \(-0.941750\pi\)
0.334054 0.942554i \(-0.391583\pi\)
\(840\) −9.31792 4.32353i −0.321499 0.149176i
\(841\) 12.8065 22.1814i 0.441602 0.764877i
\(842\) 4.89235 + 18.2585i 0.168602 + 0.629229i
\(843\) 1.91880 41.7376i 0.0660868 1.43752i
\(844\) 1.13357 0.654465i 0.0390190 0.0225276i
\(845\) 3.80608 + 28.0000i 0.130933 + 0.963231i
\(846\) −1.09050 + 11.8352i −0.0374921 + 0.406903i
\(847\) −22.5427 22.5427i −0.774577 0.774577i
\(848\) −0.480279 + 1.79243i −0.0164928 + 0.0615521i
\(849\) 27.3214 + 8.68375i 0.937667 + 0.298026i
\(850\) 30.1784 + 7.81497i 1.03511 + 0.268051i
\(851\) −2.03750 1.17635i −0.0698445 0.0403248i
\(852\) 8.29688 + 16.0283i 0.284246 + 0.549122i
\(853\) 7.41714 + 1.98742i 0.253958 + 0.0680478i 0.383552 0.923519i \(-0.374701\pi\)
−0.129594 + 0.991567i \(0.541367\pi\)
\(854\) 33.2726 1.13856
\(855\) −1.50476 34.7928i −0.0514617 1.18989i
\(856\) −6.15702 −0.210442
\(857\) 7.00264 + 1.87635i 0.239206 + 0.0640949i 0.376430 0.926445i \(-0.377152\pi\)
−0.137224 + 0.990540i \(0.543818\pi\)
\(858\) 5.00051 + 0.229887i 0.170714 + 0.00784823i
\(859\) 1.50446 + 0.868601i 0.0513316 + 0.0296363i 0.525446 0.850827i \(-0.323898\pi\)
−0.474115 + 0.880463i \(0.657232\pi\)
\(860\) −5.13467 + 2.15218i −0.175091 + 0.0733887i
\(861\) −6.34598 28.9407i −0.216271 0.986297i
\(862\) −1.01309 + 3.78090i −0.0345060 + 0.128778i
\(863\) 36.4612 + 36.4612i 1.24115 + 1.24115i 0.959523 + 0.281630i \(0.0908751\pi\)
0.281630 + 0.959523i \(0.409125\pi\)
\(864\) 0.642559 + 5.15627i 0.0218603 + 0.175420i
\(865\) −18.4784 14.0560i −0.628286 0.477918i
\(866\) −33.3190 + 19.2368i −1.13223 + 0.653692i
\(867\) 31.9042 + 20.4288i 1.08352 + 0.693799i
\(868\) 2.79919 + 10.4467i 0.0950108 + 0.354585i
\(869\) −10.0496 + 17.4065i −0.340911 + 0.590474i
\(870\) 4.57133 5.46892i 0.154983 0.185414i
\(871\) 3.32557 + 5.76006i 0.112683 + 0.195172i
\(872\) −10.9280 + 10.9280i −0.370070 + 0.370070i
\(873\) −51.1554 + 8.77688i −1.73135 + 0.297052i
\(874\) 13.6642i 0.462199i
\(875\) −4.24093 29.3482i −0.143369 0.992152i
\(876\) −2.44864 + 7.70407i −0.0827318 + 0.260296i
\(877\) −10.0092 + 2.68194i −0.337985 + 0.0905628i −0.423820 0.905747i \(-0.639311\pi\)
0.0858347 + 0.996309i \(0.472644\pi\)
\(878\) 14.8035 3.96659i 0.499594 0.133866i
\(879\) −8.47386 + 26.6610i −0.285816 + 0.899254i
\(880\) −8.48395 + 6.56681i −0.285994 + 0.221367i
\(881\) 1.17719i 0.0396604i 0.999803 + 0.0198302i \(0.00631257\pi\)
−0.999803 + 0.0198302i \(0.993687\pi\)
\(882\) −0.0357829 + 0.0969188i −0.00120487 + 0.00326343i
\(883\) −22.1929 + 22.1929i −0.746850 + 0.746850i −0.973886 0.227036i \(-0.927097\pi\)
0.227036 + 0.973886i \(0.427097\pi\)
\(884\) 1.87780 + 3.25245i 0.0631573 + 0.109392i
\(885\) −0.497995 + 0.0445206i −0.0167399 + 0.00149654i
\(886\) −13.9099 + 24.0927i −0.467313 + 0.809410i
\(887\) 2.35927 + 8.80492i 0.0792166 + 0.295640i 0.994156 0.107950i \(-0.0344287\pi\)
−0.914940 + 0.403590i \(0.867762\pi\)
\(888\) −1.30383 0.834867i −0.0437537 0.0280163i
\(889\) 8.18049 4.72301i 0.274365 0.158405i
\(890\) 2.77506 3.64818i 0.0930203 0.122287i
\(891\) −7.89049 + 42.4543i −0.264341 + 1.42227i
\(892\) −14.8324 14.8324i −0.496625 0.496625i
\(893\) −5.32323 + 19.8666i −0.178135 + 0.664809i
\(894\) −4.87224 22.2197i −0.162952 0.743140i
\(895\) 1.23911 3.02741i 0.0414189 0.101195i
\(896\) 2.29692 + 1.32613i 0.0767346 + 0.0443028i
\(897\) −2.74319 0.126112i −0.0915925 0.00421076i
\(898\) 23.5326 + 6.30553i 0.785292 + 0.210418i
\(899\) −7.50472 −0.250296
\(900\) −11.4540 + 9.68532i −0.381801 + 0.322844i
\(901\) −11.5696 −0.385439
\(902\) −29.8902 8.00905i −0.995234 0.266672i
\(903\) 5.25803 + 10.1577i 0.174976 + 0.338028i
\(904\) 5.13849 + 2.96671i 0.170904 + 0.0986713i
\(905\) 7.35697 17.9746i 0.244554 0.597497i
\(906\) 0.554295 + 0.176176i 0.0184152 + 0.00585304i
\(907\) −1.96997 + 7.35203i −0.0654118 + 0.244120i −0.990889 0.134684i \(-0.956998\pi\)
0.925477 + 0.378804i \(0.123665\pi\)
\(908\) 4.21080 + 4.21080i 0.139740 + 0.139740i
\(909\) 29.3007 + 20.7187i 0.971842 + 0.687196i
\(910\) 2.16280 2.84328i 0.0716960 0.0942538i
\(911\) 39.2522 22.6623i 1.30048 0.750835i 0.319997 0.947418i \(-0.396318\pi\)
0.980487 + 0.196583i \(0.0629846\pi\)
\(912\) −0.412945 + 8.98237i −0.0136740 + 0.297436i
\(913\) −14.2827 53.3039i −0.472690 1.76410i
\(914\) 6.55874 11.3601i 0.216944 0.375758i
\(915\) 20.4501 44.0733i 0.676059 1.45702i
\(916\) −5.87872 10.1822i −0.194238 0.336431i
\(917\) 24.4930 24.4930i 0.808829 0.808829i
\(918\) −30.0159 + 12.1903i −0.990672 + 0.402339i
\(919\) 19.9726i 0.658836i 0.944184 + 0.329418i \(0.106852\pi\)
−0.944184 + 0.329418i \(0.893148\pi\)
\(920\) 4.65415 3.60244i 0.153443 0.118769i
\(921\) 3.48469 0.764106i 0.114824 0.0251782i
\(922\) 38.7791 10.3908i 1.27712 0.342204i
\(923\) −6.06291 + 1.62455i −0.199563 + 0.0534728i
\(924\) 14.8531 + 16.2845i 0.488630 + 0.535722i
\(925\) −0.0375730 4.46916i −0.00123539 0.146945i
\(926\) 11.9769i 0.393586i
\(927\) 24.8525 20.6590i 0.816263 0.678532i
\(928\) −1.30136 + 1.30136i −0.0427192 + 0.0427192i
\(929\) 24.8920 + 43.1142i 0.816681 + 1.41453i 0.908115 + 0.418721i \(0.137522\pi\)
−0.0914341 + 0.995811i \(0.529145\pi\)
\(930\) 15.5583 + 2.71295i 0.510178 + 0.0889610i
\(931\) −0.0893912 + 0.154830i −0.00292968 + 0.00507435i
\(932\) −4.91653 18.3487i −0.161046 0.601033i
\(933\) 3.22304 1.66837i 0.105518 0.0546199i
\(934\) −10.5711 + 6.10321i −0.345896 + 0.199703i
\(935\) −53.2379 40.4964i −1.74106 1.32438i
\(936\) −1.79947 0.165804i −0.0588174 0.00541946i
\(937\) 28.6750 + 28.6750i 0.936771 + 0.936771i 0.998117 0.0613453i \(-0.0195391\pi\)
−0.0613453 + 0.998117i \(0.519539\pi\)
\(938\) −7.57964 + 28.2876i −0.247484 + 0.923623i
\(939\) −25.2765 + 23.0546i −0.824867 + 0.752357i
\(940\) 8.17014 3.42449i 0.266481 0.111695i
\(941\) −42.4585 24.5134i −1.38411 0.799115i −0.391464 0.920193i \(-0.628031\pi\)
−0.992643 + 0.121078i \(0.961365\pi\)
\(942\) −4.25796 + 6.64976i −0.138732 + 0.216661i
\(943\) 16.3972 + 4.39363i 0.533967 + 0.143076i
\(944\) 0.129095 0.00420167
\(945\) 21.7312 + 21.8496i 0.706915 + 0.710768i
\(946\) 11.9461 0.388401
\(947\) 43.5407 + 11.6667i 1.41488 + 0.379117i 0.883665 0.468119i \(-0.155068\pi\)
0.531217 + 0.847236i \(0.321735\pi\)
\(948\) 3.91267 6.11050i 0.127078 0.198460i
\(949\) −2.43470 1.40568i −0.0790339 0.0456302i
\(950\) −22.3697 + 13.1672i −0.725770 + 0.427199i
\(951\) −43.6201 + 39.7857i −1.41448 + 1.29014i
\(952\) −4.27988 + 15.9727i −0.138712 + 0.517679i
\(953\) 2.71971 + 2.71971i 0.0881001 + 0.0881001i 0.749783 0.661683i \(-0.230158\pi\)
−0.661683 + 0.749783i \(0.730158\pi\)
\(954\) 3.21409 4.54541i 0.104060 0.147163i
\(955\) −1.50863 11.0985i −0.0488181 0.359138i
\(956\) 3.94809 2.27943i 0.127690 0.0737220i
\(957\) −13.5824 + 7.03075i −0.439056 + 0.227272i
\(958\) −2.65801 9.91983i −0.0858764 0.320495i
\(959\) 4.30878 7.46303i 0.139138 0.240994i
\(960\) 3.16834 2.22746i 0.102258 0.0718911i
\(961\) 7.18593 + 12.4464i 0.231804 + 0.401497i
\(962\) 0.380728 0.380728i 0.0122752 0.0122752i
\(963\) 17.3278 + 6.39750i 0.558380 + 0.206156i
\(964\) 16.0621i 0.517325i
\(965\) −7.47142 0.951698i −0.240513 0.0306362i
\(966\) −8.14813 8.93342i −0.262162 0.287428i
\(967\) −30.2627 + 8.10886i −0.973182 + 0.260763i −0.710171 0.704029i \(-0.751382\pi\)
−0.263011 + 0.964793i \(0.584716\pi\)
\(968\) 11.6105 3.11102i 0.373175 0.0999920i
\(969\) −54.7612 + 12.0078i −1.75918 + 0.385745i
\(970\) 23.6794 + 30.5925i 0.760301 + 0.982266i
\(971\) 31.9680i 1.02590i −0.858418 0.512951i \(-0.828552\pi\)
0.858418 0.512951i \(-0.171448\pi\)
\(972\) 3.54930 15.1790i 0.113844 0.486867i
\(973\) 41.2491 41.2491i 1.32238 1.32238i
\(974\) 12.3898 + 21.4597i 0.396993 + 0.687613i
\(975\) −2.43695 4.61242i −0.0780448 0.147716i
\(976\) −6.27251 + 10.8643i −0.200778 + 0.347758i
\(977\) −2.26667 8.45932i −0.0725171 0.270638i 0.920142 0.391585i \(-0.128073\pi\)
−0.992659 + 0.120948i \(0.961407\pi\)
\(978\) −1.01410 + 22.0588i −0.0324275 + 0.705361i
\(979\) −8.51754 + 4.91760i −0.272222 + 0.157167i
\(980\) 0.0763036 0.0103720i 0.00243743 0.000331323i
\(981\) 42.1098 19.4001i 1.34446 0.619397i
\(982\) −6.28784 6.28784i −0.200653 0.200653i
\(983\) 10.9162 40.7397i 0.348172 1.29940i −0.540691 0.841222i \(-0.681837\pi\)
0.888863 0.458174i \(-0.151496\pi\)
\(984\) 10.6462 + 3.38376i 0.339388 + 0.107870i
\(985\) 18.9508 + 45.2129i 0.603824 + 1.44060i
\(986\) −9.93720 5.73725i −0.316465 0.182711i
\(987\) −8.36644 16.1627i −0.266307 0.514465i
\(988\) −3.02059 0.809364i −0.0960977 0.0257493i
\(989\) −6.55342 −0.208387
\(990\) 30.6998 9.66573i 0.975703 0.307197i
\(991\) −13.9120 −0.441929 −0.220964 0.975282i \(-0.570920\pi\)
−0.220964 + 0.975282i \(0.570920\pi\)
\(992\) −3.93882 1.05540i −0.125058 0.0335091i
\(993\) 41.5738 + 1.91126i 1.31930 + 0.0606521i
\(994\) −23.9345 13.8186i −0.759156 0.438299i
\(995\) 38.2032 + 15.6365i 1.21112 + 0.495709i
\(996\) 4.26692 + 19.4592i 0.135203 + 0.616589i
\(997\) −7.83414 + 29.2374i −0.248110 + 0.925958i 0.723685 + 0.690130i \(0.242447\pi\)
−0.971795 + 0.235828i \(0.924220\pi\)
\(998\) −20.7542 20.7542i −0.656963 0.656963i
\(999\) 2.80191 + 3.70433i 0.0886486 + 0.117200i
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 90.2.l.b.77.3 yes 16
3.2 odd 2 270.2.m.b.17.1 16
4.3 odd 2 720.2.cu.b.257.3 16
5.2 odd 4 450.2.p.h.293.2 16
5.3 odd 4 inner 90.2.l.b.23.3 16
5.4 even 2 450.2.p.h.257.2 16
9.2 odd 6 inner 90.2.l.b.47.3 yes 16
9.4 even 3 810.2.f.c.647.4 16
9.5 odd 6 810.2.f.c.647.5 16
9.7 even 3 270.2.m.b.197.1 16
15.2 even 4 1350.2.q.h.1043.4 16
15.8 even 4 270.2.m.b.233.1 16
15.14 odd 2 1350.2.q.h.557.3 16
20.3 even 4 720.2.cu.b.113.4 16
36.11 even 6 720.2.cu.b.497.4 16
45.2 even 12 450.2.p.h.443.2 16
45.7 odd 12 1350.2.q.h.143.3 16
45.13 odd 12 810.2.f.c.323.5 16
45.23 even 12 810.2.f.c.323.4 16
45.29 odd 6 450.2.p.h.407.2 16
45.34 even 6 1350.2.q.h.1007.4 16
45.38 even 12 inner 90.2.l.b.83.3 yes 16
45.43 odd 12 270.2.m.b.143.1 16
180.83 odd 12 720.2.cu.b.353.3 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
90.2.l.b.23.3 16 5.3 odd 4 inner
90.2.l.b.47.3 yes 16 9.2 odd 6 inner
90.2.l.b.77.3 yes 16 1.1 even 1 trivial
90.2.l.b.83.3 yes 16 45.38 even 12 inner
270.2.m.b.17.1 16 3.2 odd 2
270.2.m.b.143.1 16 45.43 odd 12
270.2.m.b.197.1 16 9.7 even 3
270.2.m.b.233.1 16 15.8 even 4
450.2.p.h.257.2 16 5.4 even 2
450.2.p.h.293.2 16 5.2 odd 4
450.2.p.h.407.2 16 45.29 odd 6
450.2.p.h.443.2 16 45.2 even 12
720.2.cu.b.113.4 16 20.3 even 4
720.2.cu.b.257.3 16 4.3 odd 2
720.2.cu.b.353.3 16 180.83 odd 12
720.2.cu.b.497.4 16 36.11 even 6
810.2.f.c.323.4 16 45.23 even 12
810.2.f.c.323.5 16 45.13 odd 12
810.2.f.c.647.4 16 9.4 even 3
810.2.f.c.647.5 16 9.5 odd 6
1350.2.q.h.143.3 16 45.7 odd 12
1350.2.q.h.557.3 16 15.14 odd 2
1350.2.q.h.1007.4 16 45.34 even 6
1350.2.q.h.1043.4 16 15.2 even 4