Properties

Label 216.2.t.a.85.25
Level $216$
Weight $2$
Character 216.85
Analytic conductor $1.725$
Analytic rank $0$
Dimension $204$
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] = [216,2,Mod(13,216)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(216, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([0, 9, 8]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("216.13");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 216 = 2^{3} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 216.t (of order \(18\), degree \(6\), 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: \(1.72476868366\)
Analytic rank: \(0\)
Dimension: \(204\)
Relative dimension: \(34\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 85.25
Character \(\chi\) \(=\) 216.85
Dual form 216.2.t.a.61.25

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.841104 - 1.13690i) q^{2} +(-1.24334 + 1.20586i) q^{3} +(-0.585087 - 1.91250i) q^{4} +(-0.528590 - 0.0932048i) q^{5} +(0.325159 + 2.42781i) q^{6} +(3.53662 - 2.96758i) q^{7} +(-2.66645 - 0.943430i) q^{8} +(0.0918112 - 2.99859i) q^{9} +O(q^{10})\) \(q+(0.841104 - 1.13690i) q^{2} +(-1.24334 + 1.20586i) q^{3} +(-0.585087 - 1.91250i) q^{4} +(-0.528590 - 0.0932048i) q^{5} +(0.325159 + 2.42781i) q^{6} +(3.53662 - 2.96758i) q^{7} +(-2.66645 - 0.943430i) q^{8} +(0.0918112 - 2.99859i) q^{9} +(-0.550564 + 0.522560i) q^{10} +(3.21180 - 0.566327i) q^{11} +(3.03367 + 1.67237i) q^{12} +(-1.23149 - 3.38349i) q^{13} +(-0.399175 - 6.51684i) q^{14} +(0.769612 - 0.521520i) q^{15} +(-3.31535 + 2.23796i) q^{16} +(-1.95280 + 3.38235i) q^{17} +(-3.33188 - 2.62651i) q^{18} +(-0.429657 + 0.248062i) q^{19} +(0.131017 + 1.06546i) q^{20} +(-0.818761 + 7.95439i) q^{21} +(2.05760 - 4.12783i) q^{22} +(5.76013 + 4.83332i) q^{23} +(4.45295 - 2.04235i) q^{24} +(-4.42774 - 1.61157i) q^{25} +(-4.88250 - 1.44579i) q^{26} +(3.50173 + 3.83900i) q^{27} +(-7.74474 - 5.02752i) q^{28} +(-0.222837 + 0.612239i) q^{29} +(0.0544077 - 1.31362i) q^{30} +(1.23894 + 1.03959i) q^{31} +(-0.244209 + 5.65158i) q^{32} +(-3.31046 + 4.57711i) q^{33} +(2.20289 + 5.06505i) q^{34} +(-2.14602 + 1.23900i) q^{35} +(-5.78854 + 1.57885i) q^{36} +(5.48132 + 3.16464i) q^{37} +(-0.0793637 + 0.697123i) q^{38} +(5.61117 + 2.72184i) q^{39} +(1.32153 + 0.747213i) q^{40} +(-6.37217 + 2.31928i) q^{41} +(8.35469 + 7.62132i) q^{42} +(-0.975843 + 0.172067i) q^{43} +(-2.96228 - 5.81123i) q^{44} +(-0.328014 + 1.57647i) q^{45} +(10.3399 - 2.48337i) q^{46} +(-3.76949 + 3.16298i) q^{47} +(1.42345 - 6.78040i) q^{48} +(2.48564 - 14.0968i) q^{49} +(-5.55638 + 3.67841i) q^{50} +(-1.65063 - 6.56022i) q^{51} +(-5.75041 + 4.33486i) q^{52} -3.01668i q^{53} +(7.30988 - 0.752120i) q^{54} -1.75051 q^{55} +(-12.2299 + 4.57634i) q^{56} +(0.235083 - 0.826532i) q^{57} +(0.508626 + 0.768300i) q^{58} +(3.23871 + 0.571073i) q^{59} +(-1.44770 - 1.16675i) q^{60} +(7.64643 + 9.11267i) q^{61} +(2.22398 - 0.534143i) q^{62} +(-8.57387 - 10.8774i) q^{63} +(6.21988 + 5.03121i) q^{64} +(0.335596 + 1.90326i) q^{65} +(2.41928 + 7.61349i) q^{66} +(-4.90853 - 13.4861i) q^{67} +(7.61131 + 1.75577i) q^{68} +(-12.9901 + 0.936415i) q^{69} +(-0.396400 + 3.48194i) q^{70} +(2.84000 - 4.91903i) q^{71} +(-3.07377 + 7.90898i) q^{72} +(7.83610 + 13.5725i) q^{73} +(8.20825 - 3.56993i) q^{74} +(7.44853 - 3.33550i) q^{75} +(0.725807 + 0.676582i) q^{76} +(9.67830 - 11.5342i) q^{77} +(7.81405 - 4.09000i) q^{78} +(7.15768 + 2.60518i) q^{79} +(1.96105 - 0.873960i) q^{80} +(-8.98314 - 0.550609i) q^{81} +(-2.72287 + 9.19529i) q^{82} +(-5.22327 + 14.3508i) q^{83} +(15.6919 - 3.08813i) q^{84} +(1.34748 - 1.60587i) q^{85} +(-0.625162 + 1.25416i) q^{86} +(-0.461211 - 1.02993i) q^{87} +(-9.09838 - 1.52002i) q^{88} +(-1.47797 - 2.55991i) q^{89} +(1.51640 + 1.69890i) q^{90} +(-14.3961 - 8.31159i) q^{91} +(5.87357 - 13.8442i) q^{92} +(-2.79402 + 0.201412i) q^{93} +(0.425458 + 6.94594i) q^{94} +(0.250233 - 0.0910774i) q^{95} +(-6.51137 - 7.32134i) q^{96} +(-0.656997 - 3.72601i) q^{97} +(-13.9360 - 14.6828i) q^{98} +(-1.40330 - 9.68287i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 204 q - 6 q^{2} - 6 q^{4} - 6 q^{6} - 12 q^{7} - 3 q^{8} - 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 204 q - 6 q^{2} - 6 q^{4} - 6 q^{6} - 12 q^{7} - 3 q^{8} - 12 q^{9} - 3 q^{10} + 3 q^{12} - 21 q^{14} - 12 q^{15} - 6 q^{16} - 6 q^{17} - 27 q^{18} + 15 q^{20} - 6 q^{22} - 12 q^{23} - 12 q^{25} - 30 q^{26} - 12 q^{28} - 39 q^{30} - 12 q^{31} - 36 q^{32} - 36 q^{36} - 42 q^{38} - 12 q^{39} - 21 q^{40} - 24 q^{41} - 66 q^{42} + 21 q^{44} - 3 q^{46} - 12 q^{47} + 51 q^{48} - 12 q^{49} - 99 q^{50} - 33 q^{52} - 90 q^{54} - 24 q^{55} + 99 q^{56} - 30 q^{57} + 21 q^{58} + 102 q^{60} - 36 q^{62} - 72 q^{63} - 3 q^{64} - 12 q^{65} - 9 q^{66} + 75 q^{68} + 9 q^{70} - 90 q^{71} + 60 q^{72} - 6 q^{73} + 9 q^{74} - 18 q^{76} + 12 q^{78} - 12 q^{79} + 78 q^{80} - 12 q^{81} - 12 q^{82} + 102 q^{84} - 30 q^{86} - 48 q^{87} - 30 q^{88} - 6 q^{89} + 6 q^{90} + 111 q^{92} - 33 q^{94} - 42 q^{95} + 126 q^{96} - 12 q^{97} + 54 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/216\mathbb{Z}\right)^\times\).

\(n\) \(55\) \(109\) \(137\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{1}{9}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.841104 1.13690i 0.594751 0.803910i
\(3\) −1.24334 + 1.20586i −0.717845 + 0.696203i
\(4\) −0.585087 1.91250i −0.292544 0.956252i
\(5\) −0.528590 0.0932048i −0.236393 0.0416824i 0.0541965 0.998530i \(-0.482740\pi\)
−0.290589 + 0.956848i \(0.593851\pi\)
\(6\) 0.325159 + 2.42781i 0.132746 + 0.991150i
\(7\) 3.53662 2.96758i 1.33672 1.12164i 0.354262 0.935146i \(-0.384732\pi\)
0.982456 0.186494i \(-0.0597124\pi\)
\(8\) −2.66645 0.943430i −0.942731 0.333553i
\(9\) 0.0918112 2.99859i 0.0306037 0.999532i
\(10\) −0.550564 + 0.522560i −0.174104 + 0.165248i
\(11\) 3.21180 0.566327i 0.968393 0.170754i 0.332987 0.942932i \(-0.391944\pi\)
0.635407 + 0.772178i \(0.280832\pi\)
\(12\) 3.03367 + 1.67237i 0.875746 + 0.482772i
\(13\) −1.23149 3.38349i −0.341554 0.938411i −0.984944 0.172873i \(-0.944695\pi\)
0.643390 0.765538i \(-0.277527\pi\)
\(14\) −0.399175 6.51684i −0.106684 1.74170i
\(15\) 0.769612 0.521520i 0.198713 0.134656i
\(16\) −3.31535 + 2.23796i −0.828837 + 0.559491i
\(17\) −1.95280 + 3.38235i −0.473623 + 0.820340i −0.999544 0.0301939i \(-0.990388\pi\)
0.525921 + 0.850534i \(0.323721\pi\)
\(18\) −3.33188 2.62651i −0.785332 0.619075i
\(19\) −0.429657 + 0.248062i −0.0985700 + 0.0569094i −0.548475 0.836167i \(-0.684791\pi\)
0.449905 + 0.893077i \(0.351458\pi\)
\(20\) 0.131017 + 1.06546i 0.0292963 + 0.238245i
\(21\) −0.818761 + 7.95439i −0.178668 + 1.73579i
\(22\) 2.05760 4.12783i 0.438682 0.880057i
\(23\) 5.76013 + 4.83332i 1.20107 + 1.00782i 0.999599 + 0.0283221i \(0.00901640\pi\)
0.201470 + 0.979495i \(0.435428\pi\)
\(24\) 4.45295 2.04235i 0.908956 0.416893i
\(25\) −4.42774 1.61157i −0.885548 0.322313i
\(26\) −4.88250 1.44579i −0.957538 0.283542i
\(27\) 3.50173 + 3.83900i 0.673908 + 0.738815i
\(28\) −7.74474 5.02752i −1.46362 0.950111i
\(29\) −0.222837 + 0.612239i −0.0413797 + 0.113690i −0.958662 0.284549i \(-0.908156\pi\)
0.917282 + 0.398239i \(0.130378\pi\)
\(30\) 0.0544077 1.31362i 0.00993344 0.239834i
\(31\) 1.23894 + 1.03959i 0.222519 + 0.186716i 0.747232 0.664564i \(-0.231383\pi\)
−0.524712 + 0.851280i \(0.675827\pi\)
\(32\) −0.244209 + 5.65158i −0.0431705 + 0.999068i
\(33\) −3.31046 + 4.57711i −0.576277 + 0.796773i
\(34\) 2.20289 + 5.06505i 0.377792 + 0.868648i
\(35\) −2.14602 + 1.23900i −0.362743 + 0.209430i
\(36\) −5.78854 + 1.57885i −0.964757 + 0.263142i
\(37\) 5.48132 + 3.16464i 0.901124 + 0.520264i 0.877565 0.479458i \(-0.159167\pi\)
0.0235593 + 0.999722i \(0.492500\pi\)
\(38\) −0.0793637 + 0.697123i −0.0128745 + 0.113088i
\(39\) 5.61117 + 2.72184i 0.898507 + 0.435843i
\(40\) 1.32153 + 0.747213i 0.208952 + 0.118145i
\(41\) −6.37217 + 2.31928i −0.995166 + 0.362211i −0.787719 0.616035i \(-0.788738\pi\)
−0.207448 + 0.978246i \(0.566516\pi\)
\(42\) 8.35469 + 7.62132i 1.28916 + 1.17600i
\(43\) −0.975843 + 0.172067i −0.148815 + 0.0262400i −0.247559 0.968873i \(-0.579628\pi\)
0.0987445 + 0.995113i \(0.468517\pi\)
\(44\) −2.96228 5.81123i −0.446581 0.876075i
\(45\) −0.328014 + 1.57647i −0.0488974 + 0.235006i
\(46\) 10.3399 2.48337i 1.52453 0.366152i
\(47\) −3.76949 + 3.16298i −0.549837 + 0.461368i −0.874886 0.484329i \(-0.839064\pi\)
0.325049 + 0.945697i \(0.394619\pi\)
\(48\) 1.42345 6.78040i 0.205457 0.978666i
\(49\) 2.48564 14.0968i 0.355092 2.01383i
\(50\) −5.55638 + 3.67841i −0.785791 + 0.520206i
\(51\) −1.65063 6.56022i −0.231134 0.918615i
\(52\) −5.75041 + 4.33486i −0.797438 + 0.601138i
\(53\) 3.01668i 0.414372i −0.978302 0.207186i \(-0.933569\pi\)
0.978302 0.207186i \(-0.0664306\pi\)
\(54\) 7.30988 0.752120i 0.994748 0.102351i
\(55\) −1.75051 −0.236039
\(56\) −12.2299 + 4.57634i −1.63429 + 0.611539i
\(57\) 0.235083 0.826532i 0.0311375 0.109477i
\(58\) 0.508626 + 0.768300i 0.0667859 + 0.100883i
\(59\) 3.23871 + 0.571073i 0.421645 + 0.0743473i 0.380445 0.924804i \(-0.375771\pi\)
0.0411997 + 0.999151i \(0.486882\pi\)
\(60\) −1.44770 1.16675i −0.186897 0.150627i
\(61\) 7.64643 + 9.11267i 0.979026 + 1.16676i 0.985994 + 0.166781i \(0.0533374\pi\)
−0.00696835 + 0.999976i \(0.502218\pi\)
\(62\) 2.22398 0.534143i 0.282446 0.0678362i
\(63\) −8.57387 10.8774i −1.08021 1.37042i
\(64\) 6.21988 + 5.03121i 0.777485 + 0.628901i
\(65\) 0.335596 + 1.90326i 0.0416256 + 0.236070i
\(66\) 2.41928 + 7.61349i 0.297793 + 0.937156i
\(67\) −4.90853 13.4861i −0.599672 1.64759i −0.751929 0.659244i \(-0.770876\pi\)
0.152257 0.988341i \(-0.451346\pi\)
\(68\) 7.61131 + 1.75577i 0.923007 + 0.212918i
\(69\) −12.9901 + 0.936415i −1.56383 + 0.112731i
\(70\) −0.396400 + 3.48194i −0.0473789 + 0.416172i
\(71\) 2.84000 4.91903i 0.337046 0.583781i −0.646830 0.762635i \(-0.723905\pi\)
0.983876 + 0.178853i \(0.0572388\pi\)
\(72\) −3.07377 + 7.90898i −0.362248 + 0.932082i
\(73\) 7.83610 + 13.5725i 0.917146 + 1.58854i 0.803728 + 0.594997i \(0.202847\pi\)
0.113419 + 0.993547i \(0.463820\pi\)
\(74\) 8.20825 3.56993i 0.954190 0.414995i
\(75\) 7.44853 3.33550i 0.860082 0.385150i
\(76\) 0.725807 + 0.676582i 0.0832558 + 0.0776093i
\(77\) 9.67830 11.5342i 1.10294 1.31444i
\(78\) 7.81405 4.09000i 0.884767 0.463101i
\(79\) 7.15768 + 2.60518i 0.805302 + 0.293106i 0.711682 0.702502i \(-0.247934\pi\)
0.0936200 + 0.995608i \(0.470156\pi\)
\(80\) 1.96105 0.873960i 0.219252 0.0977117i
\(81\) −8.98314 0.550609i −0.998127 0.0611788i
\(82\) −2.72287 + 9.19529i −0.300691 + 1.01545i
\(83\) −5.22327 + 14.3508i −0.573328 + 1.57521i 0.225882 + 0.974155i \(0.427474\pi\)
−0.799210 + 0.601052i \(0.794749\pi\)
\(84\) 15.6919 3.08813i 1.71212 0.336942i
\(85\) 1.34748 1.60587i 0.146155 0.174181i
\(86\) −0.625162 + 1.25416i −0.0674129 + 0.135240i
\(87\) −0.461211 1.02993i −0.0494470 0.110420i
\(88\) −9.09838 1.52002i −0.969890 0.162035i
\(89\) −1.47797 2.55991i −0.156664 0.271350i 0.777000 0.629501i \(-0.216741\pi\)
−0.933664 + 0.358151i \(0.883407\pi\)
\(90\) 1.51640 + 1.69890i 0.159842 + 0.179079i
\(91\) −14.3961 8.31159i −1.50912 0.871291i
\(92\) 5.87357 13.8442i 0.612362 1.44336i
\(93\) −2.79402 + 0.201412i −0.289727 + 0.0208854i
\(94\) 0.425458 + 6.94594i 0.0438827 + 0.716419i
\(95\) 0.250233 0.0910774i 0.0256734 0.00934434i
\(96\) −6.51137 7.32134i −0.664564 0.747231i
\(97\) −0.656997 3.72601i −0.0667079 0.378319i −0.999824 0.0187449i \(-0.994033\pi\)
0.933116 0.359574i \(-0.117078\pi\)
\(98\) −13.9360 14.6828i −1.40774 1.48319i
\(99\) −1.40330 9.68287i −0.141037 0.973165i
\(100\) −0.491513 + 9.41098i −0.0491513 + 0.941098i
\(101\) −7.01349 8.35836i −0.697869 0.831687i 0.294415 0.955678i \(-0.404875\pi\)
−0.992283 + 0.123990i \(0.960431\pi\)
\(102\) −8.84667 3.64123i −0.875951 0.360535i
\(103\) −0.992120 + 5.62659i −0.0977565 + 0.554405i 0.896111 + 0.443829i \(0.146380\pi\)
−0.993868 + 0.110575i \(0.964731\pi\)
\(104\) 0.0916177 + 10.1837i 0.00898385 + 0.998596i
\(105\) 1.17418 4.12830i 0.114588 0.402881i
\(106\) −3.42966 2.53734i −0.333118 0.246448i
\(107\) 10.9720i 1.06070i 0.847778 + 0.530352i \(0.177940\pi\)
−0.847778 + 0.530352i \(0.822060\pi\)
\(108\) 5.29328 8.94322i 0.509346 0.860562i
\(109\) 10.8514i 1.03938i −0.854356 0.519688i \(-0.826048\pi\)
0.854356 0.519688i \(-0.173952\pi\)
\(110\) −1.47236 + 1.99016i −0.140384 + 0.189754i
\(111\) −10.6313 + 2.67496i −1.00908 + 0.253896i
\(112\) −5.08380 + 17.7534i −0.480374 + 1.67754i
\(113\) −0.590124 + 3.34676i −0.0555142 + 0.314837i −0.999902 0.0139970i \(-0.995544\pi\)
0.944388 + 0.328834i \(0.106656\pi\)
\(114\) −0.741956 0.962466i −0.0694905 0.0901432i
\(115\) −2.59426 3.09172i −0.241916 0.288304i
\(116\) 1.30129 + 0.0679631i 0.120822 + 0.00631022i
\(117\) −10.2588 + 3.38210i −0.948424 + 0.312675i
\(118\) 3.37335 3.20176i 0.310542 0.294746i
\(119\) 3.13107 + 17.7572i 0.287025 + 1.62780i
\(120\) −2.54415 + 0.664530i −0.232248 + 0.0606630i
\(121\) −0.341702 + 0.124369i −0.0310639 + 0.0113063i
\(122\) 16.7916 1.02854i 1.52024 0.0931192i
\(123\) 5.12608 10.5676i 0.462203 0.952849i
\(124\) 1.26334 2.97772i 0.113451 0.267407i
\(125\) 4.51443 + 2.60641i 0.403783 + 0.233124i
\(126\) −19.5780 + 0.598644i −1.74415 + 0.0533315i
\(127\) −0.235764 0.408356i −0.0209207 0.0362357i 0.855376 0.518008i \(-0.173326\pi\)
−0.876296 + 0.481773i \(0.839993\pi\)
\(128\) 10.9516 2.83962i 0.967990 0.250989i
\(129\) 1.00582 1.39067i 0.0885575 0.122441i
\(130\) 2.44609 + 1.21930i 0.214536 + 0.106940i
\(131\) 8.89337 10.5987i 0.777017 0.926013i −0.221777 0.975097i \(-0.571186\pi\)
0.998795 + 0.0490841i \(0.0156302\pi\)
\(132\) 10.6907 + 3.65326i 0.930502 + 0.317976i
\(133\) −0.783389 + 2.15234i −0.0679285 + 0.186632i
\(134\) −19.4609 5.76268i −1.68117 0.497820i
\(135\) −1.49317 2.35564i −0.128511 0.202741i
\(136\) 8.39804 7.17652i 0.720126 0.615382i
\(137\) −10.3040 3.75036i −0.880332 0.320415i −0.137988 0.990434i \(-0.544064\pi\)
−0.742344 + 0.670019i \(0.766286\pi\)
\(138\) −9.86143 + 15.5561i −0.839461 + 1.32422i
\(139\) −1.01062 + 1.20441i −0.0857193 + 0.102156i −0.807199 0.590279i \(-0.799018\pi\)
0.721480 + 0.692435i \(0.243462\pi\)
\(140\) 3.62521 + 3.37934i 0.306386 + 0.285607i
\(141\) 0.872672 8.47815i 0.0734923 0.713989i
\(142\) −3.20371 7.36622i −0.268849 0.618159i
\(143\) −5.87145 10.1697i −0.490996 0.850429i
\(144\) 6.40636 + 10.1468i 0.533863 + 0.845571i
\(145\) 0.174853 0.302854i 0.0145207 0.0251507i
\(146\) 22.0216 + 2.50704i 1.82252 + 0.207484i
\(147\) 13.9082 + 20.5245i 1.14713 + 1.69283i
\(148\) 2.84534 12.3346i 0.233886 1.01390i
\(149\) −2.56998 7.06096i −0.210541 0.578456i 0.788804 0.614645i \(-0.210701\pi\)
−0.999345 + 0.0361885i \(0.988478\pi\)
\(150\) 2.47286 11.2737i 0.201908 0.920497i
\(151\) −1.19497 6.77702i −0.0972455 0.551506i −0.994036 0.109051i \(-0.965219\pi\)
0.896791 0.442455i \(-0.145892\pi\)
\(152\) 1.37969 0.256094i 0.111907 0.0207720i
\(153\) 9.96300 + 6.16619i 0.805461 + 0.498507i
\(154\) −4.97273 20.7047i −0.400714 1.66843i
\(155\) −0.557995 0.664992i −0.0448192 0.0534135i
\(156\) 1.92251 12.3239i 0.153924 0.986702i
\(157\) 5.91336 + 1.04268i 0.471937 + 0.0832153i 0.404558 0.914512i \(-0.367425\pi\)
0.0673790 + 0.997727i \(0.478536\pi\)
\(158\) 8.98219 5.94634i 0.714584 0.473065i
\(159\) 3.63768 + 3.75077i 0.288487 + 0.297455i
\(160\) 0.655841 2.96461i 0.0518488 0.234373i
\(161\) 34.7147 2.73590
\(162\) −8.18175 + 9.74982i −0.642819 + 0.766018i
\(163\) 23.2811i 1.82351i 0.410732 + 0.911756i \(0.365273\pi\)
−0.410732 + 0.911756i \(0.634727\pi\)
\(164\) 8.16391 + 10.8298i 0.637495 + 0.845668i
\(165\) 2.17649 2.11087i 0.169439 0.164331i
\(166\) 11.9221 + 18.0089i 0.925337 + 1.39776i
\(167\) 3.63941 20.6401i 0.281626 1.59718i −0.435469 0.900204i \(-0.643418\pi\)
0.717095 0.696975i \(-0.245471\pi\)
\(168\) 9.68759 20.4375i 0.747414 1.57679i
\(169\) 0.0271444 0.0227769i 0.00208803 0.00175207i
\(170\) −0.692338 2.88265i −0.0530999 0.221089i
\(171\) 0.704391 + 1.31114i 0.0538661 + 0.100265i
\(172\) 0.900033 + 1.76563i 0.0686268 + 0.134628i
\(173\) −6.07203 + 1.07066i −0.461648 + 0.0814009i −0.399635 0.916674i \(-0.630863\pi\)
−0.0620128 + 0.998075i \(0.519752\pi\)
\(174\) −1.55886 0.341931i −0.118177 0.0259217i
\(175\) −20.4417 + 7.44018i −1.54525 + 0.562424i
\(176\) −9.38080 + 9.06545i −0.707105 + 0.683334i
\(177\) −4.71547 + 3.19539i −0.354436 + 0.240180i
\(178\) −4.15349 0.472853i −0.311317 0.0354418i
\(179\) 17.5322 + 10.1222i 1.31041 + 0.756568i 0.982165 0.188023i \(-0.0602078\pi\)
0.328250 + 0.944591i \(0.393541\pi\)
\(180\) 3.20693 0.295045i 0.239030 0.0219914i
\(181\) −13.8486 + 7.99549i −1.02936 + 0.594300i −0.916801 0.399345i \(-0.869237\pi\)
−0.112557 + 0.993645i \(0.535904\pi\)
\(182\) −21.5581 + 9.37602i −1.59799 + 0.694997i
\(183\) −20.4957 2.10967i −1.51509 0.155951i
\(184\) −10.7992 18.3221i −0.796126 1.35072i
\(185\) −2.60242 2.18369i −0.191333 0.160548i
\(186\) −2.12108 + 3.34593i −0.155525 + 0.245336i
\(187\) −4.35648 + 11.9693i −0.318578 + 0.875284i
\(188\) 8.25469 + 5.35855i 0.602035 + 0.390813i
\(189\) 23.7768 + 3.18544i 1.72951 + 0.231706i
\(190\) 0.106926 0.361096i 0.00775724 0.0261966i
\(191\) 4.78680 + 1.74225i 0.346361 + 0.126065i 0.509342 0.860564i \(-0.329889\pi\)
−0.162981 + 0.986629i \(0.552111\pi\)
\(192\) −13.8004 + 1.24477i −0.995957 + 0.0898334i
\(193\) 7.42183 + 6.22766i 0.534235 + 0.448277i 0.869561 0.493826i \(-0.164402\pi\)
−0.335326 + 0.942102i \(0.608846\pi\)
\(194\) −4.78871 2.38703i −0.343809 0.171378i
\(195\) −2.71232 1.96173i −0.194234 0.140482i
\(196\) −28.4145 + 3.49404i −2.02961 + 0.249574i
\(197\) −9.25222 + 5.34177i −0.659194 + 0.380586i −0.791970 0.610560i \(-0.790944\pi\)
0.132776 + 0.991146i \(0.457611\pi\)
\(198\) −12.1888 6.54889i −0.866220 0.465409i
\(199\) −2.67611 + 4.63515i −0.189704 + 0.328577i −0.945152 0.326632i \(-0.894086\pi\)
0.755447 + 0.655209i \(0.227420\pi\)
\(200\) 10.2859 + 8.47442i 0.727326 + 0.599232i
\(201\) 22.3653 + 10.8488i 1.57753 + 0.765218i
\(202\) −15.4017 + 0.943398i −1.08366 + 0.0663772i
\(203\) 1.02878 + 2.82655i 0.0722061 + 0.198385i
\(204\) −11.5807 + 6.99514i −0.810811 + 0.489758i
\(205\) 3.58444 0.632033i 0.250348 0.0441431i
\(206\) 5.56240 + 5.86049i 0.387551 + 0.408320i
\(207\) 15.0220 16.8285i 1.04410 1.16966i
\(208\) 11.6549 + 8.46141i 0.808125 + 0.586693i
\(209\) −1.23949 + 1.04005i −0.0857370 + 0.0719419i
\(210\) −3.70587 4.80726i −0.255729 0.331732i
\(211\) −6.14229 1.08305i −0.422853 0.0745603i −0.0418271 0.999125i \(-0.513318\pi\)
−0.381025 + 0.924565i \(0.624429\pi\)
\(212\) −5.76941 + 1.76502i −0.396244 + 0.121222i
\(213\) 2.40055 + 9.54069i 0.164483 + 0.653717i
\(214\) 12.4741 + 9.22860i 0.852711 + 0.630854i
\(215\) 0.531859 0.0362725
\(216\) −5.71535 13.5401i −0.388880 0.921288i
\(217\) 7.46672 0.506874
\(218\) −12.3370 9.12717i −0.835566 0.618170i
\(219\) −26.1095 7.42610i −1.76432 0.501809i
\(220\) 1.02420 + 3.34786i 0.0690516 + 0.225713i
\(221\) 13.8490 + 2.44195i 0.931584 + 0.164263i
\(222\) −5.90086 + 14.3366i −0.396040 + 0.962212i
\(223\) −3.33662 + 2.79976i −0.223437 + 0.187486i −0.747634 0.664111i \(-0.768810\pi\)
0.524197 + 0.851597i \(0.324366\pi\)
\(224\) 15.9078 + 20.7122i 1.06289 + 1.38389i
\(225\) −5.23895 + 13.1290i −0.349263 + 0.875270i
\(226\) 3.30858 + 3.48589i 0.220083 + 0.231878i
\(227\) −8.75242 + 1.54329i −0.580919 + 0.102432i −0.456383 0.889783i \(-0.650855\pi\)
−0.124536 + 0.992215i \(0.539744\pi\)
\(228\) −1.71829 + 0.0339958i −0.113797 + 0.00225142i
\(229\) −5.45148 14.9778i −0.360244 0.989762i −0.978943 0.204134i \(-0.934562\pi\)
0.618699 0.785628i \(-0.287660\pi\)
\(230\) −5.69702 + 0.348958i −0.375650 + 0.0230096i
\(231\) 1.87509 + 26.0116i 0.123372 + 1.71144i
\(232\) 1.17179 1.42227i 0.0769316 0.0933767i
\(233\) 5.28886 9.16058i 0.346485 0.600129i −0.639138 0.769092i \(-0.720709\pi\)
0.985622 + 0.168963i \(0.0540419\pi\)
\(234\) −4.78359 + 14.5079i −0.312713 + 0.948412i
\(235\) 2.28732 1.32059i 0.149208 0.0861456i
\(236\) −0.802751 6.52818i −0.0522546 0.424948i
\(237\) −12.0409 + 5.39201i −0.782143 + 0.350248i
\(238\) 22.8217 + 11.3759i 1.47931 + 0.737392i
\(239\) −18.6662 15.6628i −1.20742 1.01314i −0.999387 0.0350216i \(-0.988850\pi\)
−0.208031 0.978122i \(-0.566706\pi\)
\(240\) −1.38439 + 3.45138i −0.0893618 + 0.222786i
\(241\) −11.3590 4.13433i −0.731696 0.266316i −0.0508137 0.998708i \(-0.516181\pi\)
−0.680883 + 0.732392i \(0.738404\pi\)
\(242\) −0.146012 + 0.493089i −0.00938598 + 0.0316970i
\(243\) 11.8331 10.1478i 0.759093 0.650982i
\(244\) 12.9542 19.9555i 0.829306 1.27752i
\(245\) −2.62777 + 7.21975i −0.167882 + 0.461253i
\(246\) −7.70275 14.7163i −0.491109 0.938277i
\(247\) 1.36843 + 1.14825i 0.0870714 + 0.0730615i
\(248\) −2.32278 3.94086i −0.147496 0.250245i
\(249\) −10.8107 24.1415i −0.685102 1.52991i
\(250\) 6.76033 2.94020i 0.427561 0.185955i
\(251\) −18.3953 + 10.6206i −1.16110 + 0.670363i −0.951568 0.307438i \(-0.900528\pi\)
−0.209535 + 0.977801i \(0.567195\pi\)
\(252\) −15.7865 + 22.7618i −0.994459 + 1.43386i
\(253\) 21.2376 + 12.2615i 1.33520 + 0.770876i
\(254\) −0.662563 0.0754292i −0.0415729 0.00473285i
\(255\) 0.261063 + 3.62152i 0.0163484 + 0.226788i
\(256\) 5.98304 14.8392i 0.373940 0.927453i
\(257\) −7.46449 + 2.71685i −0.465622 + 0.169473i −0.564168 0.825660i \(-0.690803\pi\)
0.0985460 + 0.995132i \(0.468581\pi\)
\(258\) −0.735051 2.31321i −0.0457623 0.144014i
\(259\) 28.7767 5.07411i 1.78810 0.315290i
\(260\) 3.44364 1.75540i 0.213566 0.108865i
\(261\) 1.81540 + 0.724408i 0.112370 + 0.0448397i
\(262\) −4.56943 19.0255i −0.282300 1.17540i
\(263\) 1.51853 1.27420i 0.0936365 0.0785703i −0.594768 0.803898i \(-0.702756\pi\)
0.688404 + 0.725327i \(0.258312\pi\)
\(264\) 13.1454 9.08144i 0.809040 0.558924i
\(265\) −0.281169 + 1.59459i −0.0172720 + 0.0979546i
\(266\) 1.78809 + 2.70098i 0.109635 + 0.165608i
\(267\) 4.92452 + 1.40064i 0.301375 + 0.0857175i
\(268\) −22.9202 + 17.2781i −1.40008 + 1.05543i
\(269\) 10.8443i 0.661189i −0.943773 0.330594i \(-0.892751\pi\)
0.943773 0.330594i \(-0.107249\pi\)
\(270\) −3.93403 0.283752i −0.239418 0.0172686i
\(271\) 10.0732 0.611902 0.305951 0.952047i \(-0.401026\pi\)
0.305951 + 0.952047i \(0.401026\pi\)
\(272\) −1.09536 15.5839i −0.0664163 0.944915i
\(273\) 27.9219 7.02548i 1.68991 0.425201i
\(274\) −12.9305 + 8.56021i −0.781163 + 0.517141i
\(275\) −15.1337 2.66848i −0.912595 0.160915i
\(276\) 9.39125 + 24.2958i 0.565287 + 1.46243i
\(277\) 15.2273 + 18.1472i 0.914919 + 1.09036i 0.995608 + 0.0936189i \(0.0298435\pi\)
−0.0806889 + 0.996739i \(0.525712\pi\)
\(278\) 0.519256 + 2.16200i 0.0311429 + 0.129668i
\(279\) 3.23106 3.61962i 0.193438 0.216701i
\(280\) 6.89116 1.27912i 0.411826 0.0764422i
\(281\) −2.96256 16.8015i −0.176732 1.00229i −0.936126 0.351664i \(-0.885616\pi\)
0.759394 0.650630i \(-0.225495\pi\)
\(282\) −8.90481 8.12315i −0.530273 0.483726i
\(283\) 1.72127 + 4.72914i 0.102319 + 0.281118i 0.980280 0.197613i \(-0.0633190\pi\)
−0.877961 + 0.478731i \(0.841097\pi\)
\(284\) −11.0693 2.55346i −0.656843 0.151520i
\(285\) −0.201299 + 0.414986i −0.0119239 + 0.0245817i
\(286\) −16.5004 1.87848i −0.975689 0.111077i
\(287\) −15.6533 + 27.1124i −0.923987 + 1.60039i
\(288\) 16.9244 + 1.25116i 0.997279 + 0.0737255i
\(289\) 0.873152 + 1.51234i 0.0513619 + 0.0889614i
\(290\) −0.197246 0.453523i −0.0115827 0.0266318i
\(291\) 5.30992 + 3.84047i 0.311273 + 0.225133i
\(292\) 21.3727 22.9277i 1.25074 1.34174i
\(293\) −11.6931 + 13.9353i −0.683117 + 0.814108i −0.990505 0.137477i \(-0.956101\pi\)
0.307388 + 0.951584i \(0.400545\pi\)
\(294\) 35.0326 + 1.45098i 2.04314 + 0.0846228i
\(295\) −1.65873 0.603727i −0.0965748 0.0351503i
\(296\) −11.6300 13.6096i −0.675982 0.791042i
\(297\) 13.4210 + 10.3470i 0.778763 + 0.600392i
\(298\) −10.1892 3.01719i −0.590246 0.174781i
\(299\) 9.25995 25.4415i 0.535517 1.47132i
\(300\) −10.7372 12.2938i −0.619912 0.709782i
\(301\) −2.94057 + 3.50443i −0.169491 + 0.201992i
\(302\) −8.70990 4.34162i −0.501199 0.249832i
\(303\) 18.7992 + 1.93504i 1.07998 + 0.111165i
\(304\) 0.869306 1.78397i 0.0498581 0.102318i
\(305\) −3.19249 5.52955i −0.182801 0.316621i
\(306\) 15.3903 6.14053i 0.879803 0.351031i
\(307\) −4.06142 2.34486i −0.231797 0.133828i 0.379604 0.925149i \(-0.376060\pi\)
−0.611401 + 0.791321i \(0.709394\pi\)
\(308\) −27.7218 11.7613i −1.57959 0.670163i
\(309\) −5.55133 8.19215i −0.315804 0.466035i
\(310\) −1.22536 + 0.0750569i −0.0695959 + 0.00426294i
\(311\) 23.8183 8.66914i 1.35061 0.491582i 0.437472 0.899232i \(-0.355874\pi\)
0.913138 + 0.407650i \(0.133652\pi\)
\(312\) −12.3940 12.5514i −0.701674 0.710583i
\(313\) −0.898635 5.09641i −0.0507938 0.288066i 0.948821 0.315814i \(-0.102278\pi\)
−0.999615 + 0.0277478i \(0.991166\pi\)
\(314\) 6.15918 5.84590i 0.347583 0.329903i
\(315\) 3.51824 + 6.54880i 0.198231 + 0.368983i
\(316\) 0.794556 15.2133i 0.0446973 0.855818i
\(317\) −8.10759 9.66225i −0.455368 0.542686i 0.488694 0.872455i \(-0.337473\pi\)
−0.944062 + 0.329769i \(0.893029\pi\)
\(318\) 7.32392 0.980899i 0.410705 0.0550061i
\(319\) −0.368979 + 2.09259i −0.0206589 + 0.117162i
\(320\) −2.81884 3.23917i −0.157578 0.181075i
\(321\) −13.2307 13.6420i −0.738465 0.761421i
\(322\) 29.1987 39.4671i 1.62718 2.19942i
\(323\) 1.93766i 0.107814i
\(324\) 4.20288 + 17.5025i 0.233493 + 0.972358i
\(325\) 16.9658i 0.941096i
\(326\) 26.4682 + 19.5818i 1.46594 + 1.08454i
\(327\) 13.0853 + 13.4920i 0.723617 + 0.746112i
\(328\) 19.1791 0.172545i 1.05899 0.00952720i
\(329\) −3.94488 + 22.3725i −0.217488 + 1.23344i
\(330\) −0.569194 4.24991i −0.0313331 0.233950i
\(331\) −8.45285 10.0737i −0.464611 0.553701i 0.481962 0.876192i \(-0.339924\pi\)
−0.946573 + 0.322491i \(0.895480\pi\)
\(332\) 30.5021 + 1.59305i 1.67402 + 0.0874299i
\(333\) 9.99273 16.1457i 0.547598 0.884780i
\(334\) −20.4046 21.4981i −1.11649 1.17632i
\(335\) 1.33764 + 7.58611i 0.0730828 + 0.414473i
\(336\) −15.0872 28.2039i −0.823072 1.53865i
\(337\) −12.3641 + 4.50015i −0.673513 + 0.245139i −0.656060 0.754709i \(-0.727778\pi\)
−0.0174532 + 0.999848i \(0.505556\pi\)
\(338\) −0.00306376 0.0500183i −0.000166647 0.00272064i
\(339\) −3.30199 4.87278i −0.179340 0.264653i
\(340\) −3.85962 1.63749i −0.209317 0.0888055i
\(341\) 4.56796 + 2.63731i 0.247369 + 0.142818i
\(342\) 2.08310 + 0.301983i 0.112641 + 0.0163294i
\(343\) −16.8840 29.2439i −0.911649 1.57902i
\(344\) 2.76437 + 0.461830i 0.149045 + 0.0249002i
\(345\) 6.95373 + 0.715761i 0.374376 + 0.0385353i
\(346\) −3.88997 + 7.80383i −0.209126 + 0.419537i
\(347\) −14.5614 + 17.3536i −0.781698 + 0.931591i −0.999009 0.0445115i \(-0.985827\pi\)
0.217311 + 0.976102i \(0.430271\pi\)
\(348\) −1.69990 + 1.48467i −0.0911244 + 0.0795866i
\(349\) 9.93430 27.2943i 0.531771 1.46103i −0.325191 0.945648i \(-0.605428\pi\)
0.856962 0.515380i \(-0.172349\pi\)
\(350\) −8.73487 + 29.4982i −0.466899 + 1.57674i
\(351\) 8.67687 16.5757i 0.463137 0.884748i
\(352\) 2.41629 + 18.2900i 0.128789 + 0.974862i
\(353\) −6.27092 2.28243i −0.333767 0.121481i 0.169700 0.985496i \(-0.445720\pi\)
−0.503467 + 0.864014i \(0.667942\pi\)
\(354\) −0.333360 + 8.04868i −0.0177179 + 0.427782i
\(355\) −1.95967 + 2.33545i −0.104009 + 0.123953i
\(356\) −4.03111 + 4.32439i −0.213648 + 0.229192i
\(357\) −25.3056 18.3027i −1.33932 0.968680i
\(358\) 26.2543 11.4185i 1.38758 0.603486i
\(359\) −12.8148 22.1959i −0.676339 1.17145i −0.976076 0.217431i \(-0.930232\pi\)
0.299737 0.954022i \(-0.403101\pi\)
\(360\) 2.36192 3.89412i 0.124484 0.205238i
\(361\) −9.37693 + 16.2413i −0.493523 + 0.854806i
\(362\) −2.55803 + 22.4695i −0.134447 + 1.18097i
\(363\) 0.274882 0.566679i 0.0144276 0.0297429i
\(364\) −7.47298 + 32.3956i −0.391691 + 1.69799i
\(365\) −2.87707 7.90467i −0.150592 0.413749i
\(366\) −19.6375 + 21.5272i −1.02647 + 1.12524i
\(367\) 1.41593 + 8.03017i 0.0739112 + 0.419171i 0.999203 + 0.0399154i \(0.0127089\pi\)
−0.925292 + 0.379256i \(0.876180\pi\)
\(368\) −29.9136 3.13317i −1.55935 0.163328i
\(369\) 6.36955 + 19.3205i 0.331585 + 1.00579i
\(370\) −4.67154 + 1.12198i −0.242862 + 0.0583290i
\(371\) −8.95223 10.6688i −0.464777 0.553899i
\(372\) 2.01995 + 5.22574i 0.104729 + 0.270942i
\(373\) −2.11412 0.372777i −0.109465 0.0193017i 0.118647 0.992936i \(-0.462144\pi\)
−0.228112 + 0.973635i \(0.573255\pi\)
\(374\) 9.94369 + 15.0203i 0.514176 + 0.776684i
\(375\) −8.75595 + 2.20310i −0.452155 + 0.113768i
\(376\) 13.0352 4.87767i 0.672239 0.251547i
\(377\) 2.34593 0.120821
\(378\) 23.6203 24.3526i 1.21490 1.25256i
\(379\) 15.6848i 0.805674i −0.915272 0.402837i \(-0.868024\pi\)
0.915272 0.402837i \(-0.131976\pi\)
\(380\) −0.320594 0.425283i −0.0164461 0.0218166i
\(381\) 0.785556 + 0.223429i 0.0402453 + 0.0114466i
\(382\) 6.00697 3.97670i 0.307343 0.203466i
\(383\) 0.108638 0.616115i 0.00555113 0.0314820i −0.981906 0.189367i \(-0.939356\pi\)
0.987458 + 0.157885i \(0.0504675\pi\)
\(384\) −10.1924 + 16.7366i −0.520128 + 0.854088i
\(385\) −6.19090 + 5.19478i −0.315517 + 0.264750i
\(386\) 13.3228 3.19978i 0.678111 0.162865i
\(387\) 0.426367 + 2.94195i 0.0216735 + 0.149548i
\(388\) −6.74162 + 3.43655i −0.342254 + 0.174464i
\(389\) −9.02471 + 1.59130i −0.457571 + 0.0806821i −0.397683 0.917523i \(-0.630186\pi\)
−0.0598882 + 0.998205i \(0.519074\pi\)
\(390\) −4.51164 + 1.43363i −0.228456 + 0.0725945i
\(391\) −27.5963 + 10.0442i −1.39561 + 0.507959i
\(392\) −19.9272 + 35.2433i −1.00647 + 1.78006i
\(393\) 1.72302 + 23.9020i 0.0869146 + 1.20570i
\(394\) −1.70902 + 15.0119i −0.0860991 + 0.756286i
\(395\) −3.54066 2.04420i −0.178150 0.102855i
\(396\) −17.6975 + 8.34915i −0.889332 + 0.419561i
\(397\) 1.59689 0.921968i 0.0801459 0.0462722i −0.459392 0.888234i \(-0.651932\pi\)
0.539537 + 0.841962i \(0.318599\pi\)
\(398\) 3.01882 + 6.94111i 0.151320 + 0.347927i
\(399\) −1.62140 3.62076i −0.0811715 0.181265i
\(400\) 18.2861 4.56623i 0.914306 0.228311i
\(401\) −23.3364 19.5816i −1.16537 0.977858i −0.165401 0.986226i \(-0.552892\pi\)
−0.999965 + 0.00836797i \(0.997336\pi\)
\(402\) 31.1456 16.3021i 1.55340 0.813075i
\(403\) 1.99171 5.47217i 0.0992140 0.272588i
\(404\) −11.8819 + 18.3037i −0.591146 + 0.910643i
\(405\) 4.69708 + 1.12832i 0.233400 + 0.0560666i
\(406\) 4.07881 + 1.20780i 0.202428 + 0.0599421i
\(407\) 19.3971 + 7.05998i 0.961480 + 0.349950i
\(408\) −1.78779 + 19.0497i −0.0885088 + 0.943103i
\(409\) −20.2699 17.0085i −1.00228 0.841015i −0.0149837 0.999888i \(-0.504770\pi\)
−0.987299 + 0.158873i \(0.949214\pi\)
\(410\) 2.29633 4.60676i 0.113408 0.227512i
\(411\) 17.3339 7.76221i 0.855016 0.382881i
\(412\) 11.3414 1.39461i 0.558749 0.0687077i
\(413\) 13.1488 7.59147i 0.647011 0.373552i
\(414\) −6.49729 31.2331i −0.319325 1.53502i
\(415\) 4.09853 7.09887i 0.201189 0.348470i
\(416\) 19.4228 6.13358i 0.952281 0.300724i
\(417\) −0.195798 2.71615i −0.00958828 0.133010i
\(418\) 0.139899 + 2.28396i 0.00684270 + 0.111712i
\(419\) −10.2786 28.2402i −0.502142 1.37962i −0.889179 0.457560i \(-0.848723\pi\)
0.387036 0.922064i \(-0.373499\pi\)
\(420\) −8.58240 + 0.169800i −0.418778 + 0.00828537i
\(421\) −26.1531 + 4.61150i −1.27463 + 0.224751i −0.769697 0.638410i \(-0.779593\pi\)
−0.504929 + 0.863161i \(0.668481\pi\)
\(422\) −6.39763 + 6.07221i −0.311432 + 0.295591i
\(423\) 9.13841 + 11.5936i 0.444325 + 0.563699i
\(424\) −2.84602 + 8.04381i −0.138215 + 0.390642i
\(425\) 14.0974 11.8291i 0.683823 0.573795i
\(426\) 12.8659 + 5.29552i 0.623356 + 0.256569i
\(427\) 54.0851 + 9.53667i 2.61736 + 0.461512i
\(428\) 20.9840 6.41958i 1.01430 0.310302i
\(429\) 19.5634 + 5.56424i 0.944530 + 0.268644i
\(430\) 0.447349 0.604671i 0.0215731 0.0291598i
\(431\) 7.75377 0.373486 0.186743 0.982409i \(-0.440207\pi\)
0.186743 + 0.982409i \(0.440207\pi\)
\(432\) −20.2010 4.89087i −0.971920 0.235312i
\(433\) 4.34697 0.208902 0.104451 0.994530i \(-0.466691\pi\)
0.104451 + 0.994530i \(0.466691\pi\)
\(434\) 6.28029 8.48892i 0.301463 0.407481i
\(435\) 0.147797 + 0.587400i 0.00708632 + 0.0281637i
\(436\) −20.7534 + 6.34902i −0.993906 + 0.304063i
\(437\) −3.67384 0.647797i −0.175744 0.0309883i
\(438\) −30.4036 + 23.4378i −1.45274 + 1.11990i
\(439\) 25.7453 21.6028i 1.22875 1.03105i 0.230435 0.973088i \(-0.425985\pi\)
0.998319 0.0579596i \(-0.0184595\pi\)
\(440\) 4.66764 + 1.65148i 0.222521 + 0.0787313i
\(441\) −42.0423 8.74768i −2.00202 0.416556i
\(442\) 14.4247 13.6910i 0.686113 0.651214i
\(443\) 4.51691 0.796453i 0.214605 0.0378406i −0.0653119 0.997865i \(-0.520804\pi\)
0.279917 + 0.960024i \(0.409693\pi\)
\(444\) 11.3361 + 18.7673i 0.537987 + 0.890657i
\(445\) 0.542643 + 1.49090i 0.0257237 + 0.0706754i
\(446\) 0.376601 + 6.14830i 0.0178326 + 0.291130i
\(447\) 11.7099 + 5.68017i 0.553858 + 0.268663i
\(448\) 36.9279 0.664496i 1.74468 0.0313945i
\(449\) −16.9308 + 29.3250i −0.799013 + 1.38393i 0.121246 + 0.992622i \(0.461311\pi\)
−0.920259 + 0.391309i \(0.872022\pi\)
\(450\) 10.5199 + 16.9991i 0.495914 + 0.801344i
\(451\) −19.1527 + 11.0578i −0.901864 + 0.520691i
\(452\) 6.74597 0.829531i 0.317304 0.0390179i
\(453\) 9.65789 + 6.98521i 0.453767 + 0.328194i
\(454\) −5.60714 + 11.2487i −0.263156 + 0.527928i
\(455\) 6.83496 + 5.73521i 0.320428 + 0.268871i
\(456\) −1.40661 + 1.98212i −0.0658706 + 0.0928213i
\(457\) −19.2943 7.02257i −0.902551 0.328502i −0.151277 0.988491i \(-0.548338\pi\)
−0.751275 + 0.659990i \(0.770561\pi\)
\(458\) −21.6136 6.40011i −1.00994 0.299058i
\(459\) −19.8230 + 4.34727i −0.925258 + 0.202913i
\(460\) −4.39506 + 6.77046i −0.204921 + 0.315674i
\(461\) −3.85808 + 10.6000i −0.179689 + 0.493690i −0.996536 0.0831635i \(-0.973498\pi\)
0.816847 + 0.576854i \(0.195720\pi\)
\(462\) 31.1497 + 19.7467i 1.44922 + 0.918698i
\(463\) 25.0603 + 21.0281i 1.16465 + 0.977260i 0.999959 0.00908483i \(-0.00289183\pi\)
0.164694 + 0.986345i \(0.447336\pi\)
\(464\) −0.631388 2.52848i −0.0293114 0.117382i
\(465\) 1.49567 + 0.153952i 0.0693599 + 0.00713934i
\(466\) −5.96618 13.7179i −0.276378 0.635470i
\(467\) 11.9731 6.91266i 0.554048 0.319880i −0.196705 0.980463i \(-0.563024\pi\)
0.750753 + 0.660583i \(0.229691\pi\)
\(468\) 12.4706 + 17.6411i 0.576451 + 0.815462i
\(469\) −57.3806 33.1287i −2.64959 1.52974i
\(470\) 0.422501 3.71121i 0.0194885 0.171185i
\(471\) −8.60967 + 5.83426i −0.396713 + 0.268828i
\(472\) −8.09709 4.57823i −0.372699 0.210730i
\(473\) −3.03676 + 1.10529i −0.139630 + 0.0508213i
\(474\) −3.99751 + 18.2246i −0.183612 + 0.837083i
\(475\) 2.30218 0.405936i 0.105631 0.0186256i
\(476\) 32.1287 16.3777i 1.47262 0.750670i
\(477\) −9.04579 0.276965i −0.414178 0.0126813i
\(478\) −33.5073 + 8.04758i −1.53259 + 0.368088i
\(479\) −9.80478 + 8.22719i −0.447992 + 0.375910i −0.838690 0.544609i \(-0.816678\pi\)
0.390698 + 0.920519i \(0.372234\pi\)
\(480\) 2.75946 + 4.47688i 0.125952 + 0.204341i
\(481\) 3.95735 22.4432i 0.180439 1.02332i
\(482\) −14.2544 + 9.43663i −0.649271 + 0.429827i
\(483\) −43.1623 + 41.8610i −1.96395 + 1.90474i
\(484\) 0.437783 + 0.580740i 0.0198992 + 0.0263973i
\(485\) 2.03077i 0.0922125i
\(486\) −1.58417 21.9884i −0.0718596 0.997415i
\(487\) −36.3512 −1.64723 −0.823614 0.567150i \(-0.808046\pi\)
−0.823614 + 0.567150i \(0.808046\pi\)
\(488\) −11.7917 31.5123i −0.533783 1.42650i
\(489\) −28.0736 28.9464i −1.26953 1.30900i
\(490\) 5.99791 + 9.06008i 0.270958 + 0.409293i
\(491\) 33.3296 + 5.87690i 1.50414 + 0.265221i 0.864179 0.503184i \(-0.167838\pi\)
0.639964 + 0.768405i \(0.278949\pi\)
\(492\) −23.2098 3.62069i −1.04638 0.163233i
\(493\) −1.63565 1.94929i −0.0736659 0.0877917i
\(494\) 2.45644 0.589974i 0.110521 0.0265442i
\(495\) −0.160716 + 5.24907i −0.00722366 + 0.235928i
\(496\) −6.43406 0.673909i −0.288898 0.0302594i
\(497\) −4.55359 25.8247i −0.204256 1.15840i
\(498\) −36.5395 8.01482i −1.63737 0.359153i
\(499\) 5.51889 + 15.1630i 0.247059 + 0.678790i 0.999791 + 0.0204623i \(0.00651380\pi\)
−0.752731 + 0.658328i \(0.771264\pi\)
\(500\) 2.34343 10.1588i 0.104801 0.454317i
\(501\) 20.3640 + 30.0514i 0.909797 + 1.34260i
\(502\) −3.39788 + 29.8467i −0.151655 + 1.33212i
\(503\) −6.56294 + 11.3673i −0.292627 + 0.506845i −0.974430 0.224691i \(-0.927863\pi\)
0.681803 + 0.731536i \(0.261196\pi\)
\(504\) 12.5997 + 37.0928i 0.561237 + 1.65224i
\(505\) 2.92823 + 5.07184i 0.130304 + 0.225694i
\(506\) 31.8032 13.8318i 1.41382 0.614899i
\(507\) −0.00628419 + 0.0610519i −0.000279091 + 0.00271141i
\(508\) −0.643040 + 0.689824i −0.0285303 + 0.0306060i
\(509\) −8.94755 + 10.6633i −0.396593 + 0.472641i −0.926978 0.375116i \(-0.877603\pi\)
0.530385 + 0.847757i \(0.322047\pi\)
\(510\) 4.33689 + 2.74927i 0.192041 + 0.121740i
\(511\) 67.9909 + 24.7467i 3.00774 + 1.09473i
\(512\) −11.8384 19.2835i −0.523188 0.852217i
\(513\) −2.45685 0.780804i −0.108473 0.0344733i
\(514\) −3.18962 + 10.7715i −0.140688 + 0.475112i
\(515\) 1.04885 2.88169i 0.0462179 0.126983i
\(516\) −3.24815 1.10997i −0.142992 0.0488638i
\(517\) −10.3156 + 12.2936i −0.453678 + 0.540673i
\(518\) 18.4355 36.9841i 0.810008 1.62499i
\(519\) 6.25856 8.65321i 0.274720 0.379834i
\(520\) 0.900743 5.39156i 0.0395002 0.236435i
\(521\) 17.1853 + 29.7658i 0.752902 + 1.30406i 0.946411 + 0.322966i \(0.104680\pi\)
−0.193509 + 0.981099i \(0.561987\pi\)
\(522\) 2.35052 1.45462i 0.102879 0.0636672i
\(523\) 21.9893 + 12.6955i 0.961523 + 0.555136i 0.896642 0.442757i \(-0.146000\pi\)
0.0648818 + 0.997893i \(0.479333\pi\)
\(524\) −25.4735 10.8074i −1.11281 0.472125i
\(525\) 16.4443 33.9005i 0.717688 1.47954i
\(526\) −0.171395 2.79815i −0.00747316 0.122005i
\(527\) −5.93565 + 2.16040i −0.258561 + 0.0941084i
\(528\) 0.731915 22.5834i 0.0318525 0.982816i
\(529\) 5.82416 + 33.0305i 0.253224 + 1.43611i
\(530\) 1.57639 + 1.66087i 0.0684742 + 0.0721438i
\(531\) 2.00977 9.65916i 0.0872164 0.419172i
\(532\) 4.57472 + 0.238926i 0.198339 + 0.0103588i
\(533\) 15.6945 + 18.7040i 0.679806 + 0.810161i
\(534\) 5.73441 4.42060i 0.248152 0.191298i
\(535\) 1.02264 5.79970i 0.0442127 0.250743i
\(536\) 0.365174 + 40.5907i 0.0157731 + 1.75325i
\(537\) −34.0044 + 8.55592i −1.46740 + 0.369215i
\(538\) −12.3289 9.12119i −0.531536 0.393242i
\(539\) 46.6837i 2.01081i
\(540\) −3.63153 + 4.23394i −0.156276 + 0.182200i
\(541\) 16.9320i 0.727966i −0.931406 0.363983i \(-0.881417\pi\)
0.931406 0.363983i \(-0.118583\pi\)
\(542\) 8.47259 11.4522i 0.363929 0.491914i
\(543\) 7.57714 26.6406i 0.325166 1.14326i
\(544\) −18.6387 11.8624i −0.799128 0.508596i
\(545\) −1.01140 + 5.73595i −0.0433238 + 0.245701i
\(546\) 15.4980 37.6536i 0.663251 1.61143i
\(547\) −13.5017 16.0907i −0.577292 0.687990i 0.395819 0.918329i \(-0.370461\pi\)
−0.973110 + 0.230339i \(0.926016\pi\)
\(548\) −1.14382 + 21.9008i −0.0488618 + 0.935555i
\(549\) 28.0272 22.0919i 1.19617 0.942860i
\(550\) −15.7628 + 14.9610i −0.672128 + 0.637941i
\(551\) −0.0561302 0.318330i −0.00239123 0.0135613i
\(552\) 35.5209 + 9.75836i 1.51187 + 0.415343i
\(553\) 33.0451 12.0274i 1.40522 0.511458i
\(554\) 33.4393 2.04825i 1.42070 0.0870218i
\(555\) 5.86892 0.423071i 0.249122 0.0179583i
\(556\) 2.89473 + 1.22813i 0.122764 + 0.0520841i
\(557\) 37.8230 + 21.8371i 1.60261 + 0.925268i 0.990962 + 0.134140i \(0.0428271\pi\)
0.611650 + 0.791129i \(0.290506\pi\)
\(558\) −1.39749 6.71787i −0.0591605 0.284390i
\(559\) 1.78393 + 3.08985i 0.0754521 + 0.130687i
\(560\) 4.34195 8.91044i 0.183481 0.376535i
\(561\) −9.01672 20.1353i −0.380686 0.850113i
\(562\) −21.5935 10.7637i −0.910866 0.454039i
\(563\) 7.03271 8.38125i 0.296393 0.353228i −0.597210 0.802085i \(-0.703724\pi\)
0.893604 + 0.448857i \(0.148169\pi\)
\(564\) −16.7251 + 3.29147i −0.704253 + 0.138596i
\(565\) 0.623868 1.71406i 0.0262463 0.0721112i
\(566\) 6.82433 + 2.02079i 0.286848 + 0.0849402i
\(567\) −33.4040 + 24.7109i −1.40284 + 1.03776i
\(568\) −12.2135 + 10.4370i −0.512466 + 0.437926i
\(569\) 26.7673 + 9.74248i 1.12214 + 0.408426i 0.835433 0.549592i \(-0.185217\pi\)
0.286708 + 0.958018i \(0.407439\pi\)
\(570\) 0.302484 + 0.577904i 0.0126697 + 0.0242057i
\(571\) 1.75375 2.09003i 0.0733920 0.0874652i −0.728099 0.685472i \(-0.759596\pi\)
0.801491 + 0.598007i \(0.204040\pi\)
\(572\) −16.0142 + 17.1793i −0.669587 + 0.718303i
\(573\) −8.05255 + 3.60598i −0.336400 + 0.150642i
\(574\) 17.6580 + 40.6006i 0.737030 + 1.69464i
\(575\) −17.7151 30.6835i −0.738772 1.27959i
\(576\) 15.6576 18.1890i 0.652401 0.757874i
\(577\) −6.17552 + 10.6963i −0.257090 + 0.445293i −0.965461 0.260547i \(-0.916097\pi\)
0.708371 + 0.705840i \(0.249430\pi\)
\(578\) 2.45380 + 0.279351i 0.102064 + 0.0116195i
\(579\) −16.7376 + 1.20656i −0.695590 + 0.0501428i
\(580\) −0.681514 0.157211i −0.0282983 0.00652783i
\(581\) 24.1145 + 66.2539i 1.00044 + 2.74868i
\(582\) 8.83243 2.80661i 0.366116 0.116338i
\(583\) −1.70842 9.68895i −0.0707557 0.401275i
\(584\) −8.08983 43.5832i −0.334760 1.80349i
\(585\) 5.73792 0.831577i 0.237234 0.0343815i
\(586\) 6.00792 + 25.0149i 0.248185 + 1.03336i
\(587\) 5.44737 + 6.49192i 0.224837 + 0.267950i 0.866656 0.498906i \(-0.166265\pi\)
−0.641819 + 0.766856i \(0.721820\pi\)
\(588\) 31.1157 38.6081i 1.28319 1.59217i
\(589\) −0.790200 0.139334i −0.0325596 0.00574114i
\(590\) −2.08154 + 1.37801i −0.0856956 + 0.0567318i
\(591\) 5.06228 17.7985i 0.208234 0.732134i
\(592\) −25.2548 + 1.77511i −1.03797 + 0.0729567i
\(593\) 14.9671 0.614625 0.307312 0.951609i \(-0.400570\pi\)
0.307312 + 0.951609i \(0.400570\pi\)
\(594\) 23.0519 6.55543i 0.945831 0.268973i
\(595\) 9.67811i 0.396764i
\(596\) −12.0004 + 9.04637i −0.491558 + 0.370554i
\(597\) −2.26201 8.99010i −0.0925781 0.367940i
\(598\) −21.1359 31.9266i −0.864311 1.30558i
\(599\) −2.34457 + 13.2967i −0.0957965 + 0.543289i 0.898704 + 0.438556i \(0.144510\pi\)
−0.994500 + 0.104733i \(0.966601\pi\)
\(600\) −23.0079 + 1.86677i −0.939294 + 0.0762104i
\(601\) −7.15855 + 6.00673i −0.292003 + 0.245020i −0.777007 0.629493i \(-0.783263\pi\)
0.485003 + 0.874512i \(0.338818\pi\)
\(602\) 1.51087 + 6.29072i 0.0615783 + 0.256391i
\(603\) −40.8899 + 13.4805i −1.66517 + 0.548969i
\(604\) −12.2619 + 6.25054i −0.498931 + 0.254331i
\(605\) 0.192212 0.0338922i 0.00781455 0.00137792i
\(606\) 18.0120 19.7452i 0.731688 0.802095i
\(607\) 13.4916 4.91054i 0.547607 0.199313i −0.0533761 0.998574i \(-0.516998\pi\)
0.600983 + 0.799262i \(0.294776\pi\)
\(608\) −1.29702 2.48882i −0.0526010 0.100935i
\(609\) −4.68754 2.27381i −0.189949 0.0921394i
\(610\) −8.97177 1.02139i −0.363256 0.0413548i
\(611\) 15.3440 + 8.85886i 0.620752 + 0.358391i
\(612\) 5.96364 22.6620i 0.241066 0.916059i
\(613\) 28.4032 16.3986i 1.14719 0.662333i 0.198993 0.980001i \(-0.436233\pi\)
0.948202 + 0.317668i \(0.102900\pi\)
\(614\) −6.08195 + 2.64516i −0.245448 + 0.106750i
\(615\) −3.69455 + 5.10816i −0.148979 + 0.205981i
\(616\) −36.6883 + 21.6244i −1.47822 + 0.871272i
\(617\) 14.6067 + 12.2565i 0.588045 + 0.493428i 0.887578 0.460658i \(-0.152386\pi\)
−0.299533 + 0.954086i \(0.596831\pi\)
\(618\) −13.9829 0.579144i −0.562475 0.0232966i
\(619\) −11.9921 + 32.9481i −0.482004 + 1.32430i 0.425768 + 0.904832i \(0.360004\pi\)
−0.907772 + 0.419464i \(0.862218\pi\)
\(620\) −0.945325 + 1.45625i −0.0379652 + 0.0584842i
\(621\) 1.61529 + 39.0381i 0.0648193 + 1.56654i
\(622\) 10.1777 34.3707i 0.408088 1.37814i
\(623\) −12.8238 4.66747i −0.513773 0.186998i
\(624\) −24.6944 + 3.53376i −0.988566 + 0.141464i
\(625\) 15.9043 + 13.3453i 0.636172 + 0.533811i
\(626\) −6.54996 3.26495i −0.261789 0.130494i
\(627\) 0.286952 2.78779i 0.0114598 0.111333i
\(628\) −1.46569 11.9194i −0.0584874 0.475635i
\(629\) −21.4078 + 12.3598i −0.853587 + 0.492819i
\(630\) 10.4045 + 1.50833i 0.414527 + 0.0600931i
\(631\) 20.4300 35.3858i 0.813306 1.40869i −0.0972326 0.995262i \(-0.530999\pi\)
0.910538 0.413425i \(-0.135668\pi\)
\(632\) −16.6278 13.6993i −0.661417 0.544931i
\(633\) 8.94299 6.06013i 0.355452 0.240868i
\(634\) −17.8043 + 1.09057i −0.707101 + 0.0433119i
\(635\) 0.0865621 + 0.237827i 0.00343511 + 0.00943790i
\(636\) 5.04500 9.15161i 0.200047 0.362885i
\(637\) −50.7573 + 8.94989i −2.01108 + 0.354608i
\(638\) 2.06871 + 2.17958i 0.0819011 + 0.0862902i
\(639\) −14.4894 8.96764i −0.573193 0.354754i
\(640\) −6.05355 + 0.480257i −0.239288 + 0.0189838i
\(641\) 14.9231 12.5220i 0.589427 0.494588i −0.298601 0.954378i \(-0.596520\pi\)
0.888027 + 0.459790i \(0.152075\pi\)
\(642\) −26.6380 + 3.56765i −1.05132 + 0.140804i
\(643\) −16.5399 2.91644i −0.652271 0.115013i −0.162286 0.986744i \(-0.551887\pi\)
−0.489985 + 0.871731i \(0.662998\pi\)
\(644\) −20.3111 66.3919i −0.800370 2.61621i
\(645\) −0.661284 + 0.641346i −0.0260380 + 0.0252530i
\(646\) −2.20293 1.62978i −0.0866732 0.0641227i
\(647\) 10.1590 0.399390 0.199695 0.979858i \(-0.436005\pi\)
0.199695 + 0.979858i \(0.436005\pi\)
\(648\) 23.4336 + 9.94313i 0.920559 + 0.390603i
\(649\) 10.7255 0.421013
\(650\) 19.2885 + 14.2700i 0.756557 + 0.559717i
\(651\) −9.28370 + 9.00380i −0.363857 + 0.352887i
\(652\) 44.5251 13.6214i 1.74374 0.533457i
\(653\) −19.0284 3.35522i −0.744640 0.131300i −0.211560 0.977365i \(-0.567854\pi\)
−0.533080 + 0.846065i \(0.678965\pi\)
\(654\) 26.3452 3.52843i 1.03018 0.137973i
\(655\) −5.68880 + 4.77347i −0.222280 + 0.186515i
\(656\) 15.9355 21.9499i 0.622177 0.857000i
\(657\) 41.4180 22.2512i 1.61587 0.868101i
\(658\) 22.1173 + 23.3026i 0.862222 + 0.908429i
\(659\) 8.13980 1.43527i 0.317082 0.0559101i −0.0128424 0.999918i \(-0.504088\pi\)
0.329924 + 0.944007i \(0.392977\pi\)
\(660\) −5.31048 2.92750i −0.206710 0.113953i
\(661\) −3.58357 9.84578i −0.139385 0.382957i 0.850285 0.526323i \(-0.176430\pi\)
−0.989670 + 0.143366i \(0.954207\pi\)
\(662\) −18.5625 + 1.13701i −0.721454 + 0.0441911i
\(663\) −20.1637 + 13.6637i −0.783093 + 0.530655i
\(664\) 27.4666 33.3379i 1.06591 1.29376i
\(665\) 0.614701 1.06469i 0.0238371 0.0412870i
\(666\) −9.95115 24.9410i −0.385599 0.966443i
\(667\) −4.24271 + 2.44953i −0.164279 + 0.0948463i
\(668\) −41.6037 + 5.11588i −1.60969 + 0.197939i
\(669\) 0.772459 7.50456i 0.0298650 0.290143i
\(670\) 9.74974 + 4.85995i 0.376665 + 0.187756i
\(671\) 29.7195 + 24.9377i 1.14731 + 0.962707i
\(672\) −44.7549 6.56983i −1.72646 0.253437i
\(673\) 1.15505 + 0.420402i 0.0445238 + 0.0162053i 0.364186 0.931326i \(-0.381347\pi\)
−0.319662 + 0.947532i \(0.603569\pi\)
\(674\) −5.28324 + 17.8418i −0.203503 + 0.687240i
\(675\) −9.31795 22.6414i −0.358648 0.871466i
\(676\) −0.0594428 0.0385874i −0.00228626 0.00148413i
\(677\) 15.0146 41.2524i 0.577059 1.58546i −0.216053 0.976382i \(-0.569318\pi\)
0.793112 0.609076i \(-0.208459\pi\)
\(678\) −8.31719 0.344481i −0.319420 0.0132297i
\(679\) −13.3808 11.2278i −0.513508 0.430884i
\(680\) −5.10801 + 3.01070i −0.195883 + 0.115455i
\(681\) 9.02129 12.4730i 0.345697 0.477967i
\(682\) 6.84049 2.97506i 0.261936 0.113921i
\(683\) −13.7607 + 7.94474i −0.526539 + 0.303997i −0.739606 0.673040i \(-0.764988\pi\)
0.213067 + 0.977038i \(0.431655\pi\)
\(684\) 2.09543 2.11428i 0.0801209 0.0808416i
\(685\) 5.09706 + 2.94279i 0.194749 + 0.112438i
\(686\) −47.4486 5.40176i −1.81160 0.206240i
\(687\) 24.8392 + 12.0489i 0.947674 + 0.459693i
\(688\) 2.85018 2.75436i 0.108662 0.105009i
\(689\) −10.2069 + 3.71500i −0.388852 + 0.141530i
\(690\) 6.66256 7.30367i 0.253639 0.278046i
\(691\) 40.8059 7.19518i 1.55233 0.273717i 0.669284 0.743007i \(-0.266601\pi\)
0.883045 + 0.469289i \(0.155490\pi\)
\(692\) 5.60031 + 10.9863i 0.212892 + 0.417638i
\(693\) −33.6977 30.0803i −1.28007 1.14265i
\(694\) 7.48167 + 31.1511i 0.284000 + 1.18248i
\(695\) 0.646458 0.542443i 0.0245216 0.0205760i
\(696\) 0.258124 + 3.18138i 0.00978417 + 0.120590i
\(697\) 4.59896 26.0820i 0.174198 0.987926i
\(698\) −22.6751 34.2516i −0.858265 1.29644i
\(699\) 4.47048 + 17.7674i 0.169089 + 0.672024i
\(700\) 26.1896 + 34.7417i 0.989872 + 1.31311i
\(701\) 4.82376i 0.182191i 0.995842 + 0.0910955i \(0.0290368\pi\)
−0.995842 + 0.0910955i \(0.970963\pi\)
\(702\) −11.5468 23.8067i −0.435807 0.898525i
\(703\) −3.14012 −0.118432
\(704\) 22.8263 + 12.6367i 0.860299 + 0.476265i
\(705\) −1.25149 + 4.40013i −0.0471338 + 0.165719i
\(706\) −7.86939 + 5.20965i −0.296168 + 0.196068i
\(707\) −49.6082 8.74726i −1.86571 0.328975i
\(708\) 8.87016 + 7.14877i 0.333361 + 0.268667i
\(709\) 5.87727 + 7.00426i 0.220726 + 0.263051i 0.865032 0.501717i \(-0.167298\pi\)
−0.644306 + 0.764768i \(0.722854\pi\)
\(710\) 1.00688 + 4.19231i 0.0377877 + 0.157335i
\(711\) 8.46904 21.2238i 0.317614 0.795954i
\(712\) 1.52582 + 8.22023i 0.0571826 + 0.308066i
\(713\) 2.11175 + 11.9763i 0.0790857 + 0.448517i
\(714\) −42.0930 + 13.3756i −1.57529 + 0.500568i
\(715\) 2.15573 + 5.92283i 0.0806199 + 0.221501i
\(716\) 9.10090 39.4527i 0.340117 1.47442i
\(717\) 42.0957 3.03454i 1.57209 0.113327i
\(718\) −36.0131 4.09989i −1.34400 0.153007i
\(719\) −12.3655 + 21.4178i −0.461157 + 0.798747i −0.999019 0.0442856i \(-0.985899\pi\)
0.537862 + 0.843033i \(0.319232\pi\)
\(720\) −2.44061 5.96063i −0.0909560 0.222140i
\(721\) 13.1886 + 22.8433i 0.491170 + 0.850731i
\(722\) 10.5778 + 24.3213i 0.393665 + 0.905144i
\(723\) 19.1085 8.55693i 0.710655 0.318236i
\(724\) 23.3940 + 21.8074i 0.869432 + 0.810467i
\(725\) 1.97333 2.35172i 0.0732875 0.0873407i
\(726\) −0.413053 0.789149i −0.0153298 0.0292881i
\(727\) −21.2835 7.74655i −0.789360 0.287304i −0.0842902 0.996441i \(-0.526862\pi\)
−0.705070 + 0.709138i \(0.749084\pi\)
\(728\) 30.5450 + 35.7441i 1.13207 + 1.32476i
\(729\) −2.47581 + 26.8862i −0.0916965 + 0.995787i
\(730\) −11.4067 3.37772i −0.422182 0.125015i
\(731\) 1.32363 3.63665i 0.0489563 0.134506i
\(732\) 7.95705 + 40.4325i 0.294101 + 1.49443i
\(733\) −14.8278 + 17.6710i −0.547676 + 0.652695i −0.966890 0.255192i \(-0.917861\pi\)
0.419214 + 0.907887i \(0.362306\pi\)
\(734\) 10.3205 + 5.14443i 0.380935 + 0.189884i
\(735\) −5.43877 12.1454i −0.200612 0.447988i
\(736\) −28.7226 + 31.3735i −1.05873 + 1.15644i
\(737\) −23.4027 40.5347i −0.862050 1.49311i
\(738\) 27.3230 + 9.00901i 1.00577 + 0.331626i
\(739\) 37.0237 + 21.3756i 1.36194 + 0.786316i 0.989882 0.141894i \(-0.0453192\pi\)
0.372057 + 0.928210i \(0.378653\pi\)
\(740\) −2.65367 + 6.25478i −0.0975508 + 0.229930i
\(741\) −3.08606 + 0.222464i −0.113369 + 0.00817243i
\(742\) −19.6592 + 1.20418i −0.721711 + 0.0442069i
\(743\) 16.9810 6.18057i 0.622972 0.226743i −0.0111976 0.999937i \(-0.503564\pi\)
0.634169 + 0.773194i \(0.281342\pi\)
\(744\) 7.64013 + 2.09891i 0.280101 + 0.0769497i
\(745\) 0.700351 + 3.97189i 0.0256589 + 0.145519i
\(746\) −2.20201 + 2.09001i −0.0806213 + 0.0765205i
\(747\) 42.5527 + 16.9800i 1.55692 + 0.621267i
\(748\) 25.4403 + 1.32869i 0.930191 + 0.0485816i
\(749\) 32.5603 + 38.8039i 1.18973 + 1.41786i
\(750\) −4.85996 + 11.8077i −0.177461 + 0.431156i
\(751\) −7.28217 + 41.2992i −0.265730 + 1.50703i 0.501218 + 0.865321i \(0.332885\pi\)
−0.766948 + 0.641709i \(0.778226\pi\)
\(752\) 5.41854 18.9224i 0.197594 0.690027i
\(753\) 10.0649 35.3872i 0.366784 1.28958i
\(754\) 1.97317 2.66708i 0.0718585 0.0971295i
\(755\) 3.69365i 0.134426i
\(756\) −7.81936 47.3370i −0.284387 1.72163i
\(757\) 16.7039i 0.607113i 0.952813 + 0.303557i \(0.0981741\pi\)
−0.952813 + 0.303557i \(0.901826\pi\)
\(758\) −17.8321 13.1926i −0.647690 0.479175i
\(759\) −41.1913 + 10.3642i −1.49515 + 0.376197i
\(760\) −0.753158 + 0.00677577i −0.0273199 + 0.000245783i
\(761\) 3.87296 21.9646i 0.140395 0.796217i −0.830556 0.556936i \(-0.811977\pi\)
0.970950 0.239282i \(-0.0769119\pi\)
\(762\) 0.914751 0.705172i 0.0331379 0.0255457i
\(763\) −32.2024 38.3774i −1.16581 1.38935i
\(764\) 0.531371 10.1741i 0.0192243 0.368088i
\(765\) −4.69163 4.18799i −0.169626 0.151417i
\(766\) −0.609086 0.641728i −0.0220072 0.0231866i
\(767\) −2.05622 11.6614i −0.0742459 0.421069i
\(768\) 10.4551 + 25.6650i 0.377264 + 0.926106i
\(769\) 2.44160 0.888671i 0.0880465 0.0320463i −0.297621 0.954684i \(-0.596193\pi\)
0.385668 + 0.922638i \(0.373971\pi\)
\(770\) 0.698759 + 11.4078i 0.0251815 + 0.411108i
\(771\) 6.00480 12.3791i 0.216257 0.445823i
\(772\) 7.56800 17.8380i 0.272378 0.642004i
\(773\) −42.1331 24.3256i −1.51542 0.874929i −0.999836 0.0180914i \(-0.994241\pi\)
−0.515586 0.856838i \(-0.672426\pi\)
\(774\) 3.70333 + 1.98975i 0.133113 + 0.0715202i
\(775\) −3.81032 6.59966i −0.136871 0.237067i
\(776\) −1.76338 + 10.5550i −0.0633018 + 0.378904i
\(777\) −29.6607 + 41.0095i −1.06407 + 1.47121i
\(778\) −5.78157 + 11.5987i −0.207279 + 0.415832i
\(779\) 2.16252 2.57719i 0.0774803 0.0923375i
\(780\) −2.16487 + 6.33511i −0.0775146 + 0.226833i
\(781\) 6.33573 17.4073i 0.226710 0.622882i
\(782\) −11.7921 + 39.8225i −0.421684 + 1.42405i
\(783\) −3.13070 + 1.28842i −0.111882 + 0.0460445i
\(784\) 23.3073 + 52.2985i 0.832404 + 1.86780i
\(785\) −3.02856 1.10231i −0.108094 0.0393430i
\(786\) 28.6234 + 18.1452i 1.02096 + 0.647217i
\(787\) −3.32622 + 3.96404i −0.118567 + 0.141303i −0.822063 0.569397i \(-0.807177\pi\)
0.703496 + 0.710699i \(0.251621\pi\)
\(788\) 15.6295 + 14.5695i 0.556779 + 0.519018i
\(789\) −0.351553 + 3.41540i −0.0125156 + 0.121591i
\(790\) −5.30212 + 2.30600i −0.188641 + 0.0820437i
\(791\) 7.84473 + 13.5875i 0.278927 + 0.483115i
\(792\) −5.39327 + 27.1428i −0.191642 + 0.964477i
\(793\) 21.4161 37.0938i 0.760508 1.31724i
\(794\) 0.294969 2.59098i 0.0104681 0.0919505i
\(795\) −1.57326 2.32167i −0.0557976 0.0823411i
\(796\) 10.4305 + 2.40610i 0.369699 + 0.0852819i
\(797\) −6.96026 19.1232i −0.246545 0.677377i −0.999807 0.0196562i \(-0.993743\pi\)
0.753262 0.657721i \(-0.228479\pi\)
\(798\) −5.48021 1.20207i −0.193997 0.0425527i
\(799\) −3.33723 18.9264i −0.118063 0.669568i
\(800\) 10.1892 24.6302i 0.360242 0.870808i
\(801\) −7.81184 + 4.19679i −0.276018 + 0.148286i
\(802\) −41.8907 + 10.0611i −1.47921 + 0.355268i
\(803\) 32.8545 + 39.1544i 1.15941 + 1.38173i
\(804\) 7.66282 49.1212i 0.270247 1.73237i
\(805\) −18.3498 3.23557i −0.646747 0.114039i
\(806\) −4.54608 6.86704i −0.160129 0.241881i
\(807\) 13.0767 + 13.4832i 0.460321 + 0.474631i
\(808\) 10.8156 + 28.9039i 0.380491 + 1.01683i
\(809\) 2.34311 0.0823792 0.0411896 0.999151i \(-0.486885\pi\)
0.0411896 + 0.999151i \(0.486885\pi\)
\(810\) 5.23352 4.39109i 0.183887 0.154287i
\(811\) 19.7047i 0.691926i −0.938248 0.345963i \(-0.887552\pi\)
0.938248 0.345963i \(-0.112448\pi\)
\(812\) 4.80386 3.62132i 0.168582 0.127083i
\(813\) −12.5244 + 12.1468i −0.439251 + 0.426008i
\(814\) 24.3415 16.1144i 0.853169 0.564810i
\(815\) 2.16990 12.3061i 0.0760084 0.431065i
\(816\) 20.1539 + 18.0554i 0.705529 + 0.632064i
\(817\) 0.376594 0.316000i 0.0131753 0.0110554i
\(818\) −36.3861 + 8.73898i −1.27221 + 0.305551i
\(819\) −26.2448 + 42.4049i −0.917068 + 1.48175i
\(820\) −3.30598 6.48546i −0.115450 0.226482i
\(821\) 20.1348 3.55031i 0.702710 0.123907i 0.189135 0.981951i \(-0.439432\pi\)
0.513576 + 0.858044i \(0.328321\pi\)
\(822\) 5.75472 26.2357i 0.200719 0.915075i
\(823\) 25.4915 9.27816i 0.888579 0.323416i 0.142913 0.989735i \(-0.454353\pi\)
0.745667 + 0.666319i \(0.232131\pi\)
\(824\) 7.95373 14.0670i 0.277081 0.490048i
\(825\) 22.0342 14.9312i 0.767132 0.519839i
\(826\) 2.42877 21.3341i 0.0845079 0.742309i
\(827\) −22.8752 13.2070i −0.795450 0.459253i 0.0464278 0.998922i \(-0.485216\pi\)
−0.841878 + 0.539669i \(0.818550\pi\)
\(828\) −40.9738 18.8835i −1.42394 0.656247i
\(829\) 33.7637 19.4935i 1.17266 0.677037i 0.218356 0.975869i \(-0.429931\pi\)
0.954306 + 0.298833i \(0.0965972\pi\)
\(830\) −4.62342 10.6305i −0.160481 0.368991i
\(831\) −40.8157 4.20124i −1.41588 0.145739i
\(832\) 9.36333 27.2408i 0.324615 0.944404i
\(833\) 42.8262 + 35.9355i 1.48384 + 1.24509i
\(834\) −3.25268 2.06196i −0.112631 0.0713999i
\(835\) −3.84751 + 10.5710i −0.133149 + 0.365823i
\(836\) 2.71431 + 1.76200i 0.0938764 + 0.0609401i
\(837\) 0.347430 + 8.39663i 0.0120089 + 0.290230i
\(838\) −40.7517 12.0672i −1.40774 0.416855i
\(839\) −4.97178 1.80958i −0.171645 0.0624736i 0.254768 0.967002i \(-0.418001\pi\)
−0.426413 + 0.904529i \(0.640223\pi\)
\(840\) −7.02564 + 9.90015i −0.242408 + 0.341588i
\(841\) 21.8901 + 18.3680i 0.754831 + 0.633379i
\(842\) −16.7547 + 33.6123i −0.577405 + 1.15836i
\(843\) 23.9437 + 17.3177i 0.824666 + 0.596452i
\(844\) 1.52243 + 12.3808i 0.0524043 + 0.426166i
\(845\) −0.0164712 + 0.00950966i −0.000566627 + 0.000327142i
\(846\) 20.8671 0.638062i 0.717426 0.0219370i
\(847\) −0.839397 + 1.45388i −0.0288420 + 0.0499558i
\(848\) 6.75121 + 10.0013i 0.231838 + 0.343447i
\(849\) −7.84280 3.80435i −0.269164 0.130565i
\(850\) −1.59115 25.9768i −0.0545761 0.890997i
\(851\) 16.2774 + 44.7217i 0.557981 + 1.53304i
\(852\) 16.8421 10.1732i 0.577000 0.348528i
\(853\) −1.23616 + 0.217968i −0.0423252 + 0.00746308i −0.194771 0.980849i \(-0.562396\pi\)
0.152445 + 0.988312i \(0.451285\pi\)
\(854\) 56.3335 53.4681i 1.92769 1.82964i
\(855\) −0.250130 0.758709i −0.00855426 0.0259473i
\(856\) 10.3513 29.2563i 0.353801 0.999959i
\(857\) −27.5447 + 23.1128i −0.940910 + 0.789517i −0.977743 0.209804i \(-0.932717\pi\)
0.0368333 + 0.999321i \(0.488273\pi\)
\(858\) 22.7809 17.5615i 0.777726 0.599541i
\(859\) −32.8367 5.79000i −1.12037 0.197552i −0.417369 0.908737i \(-0.637048\pi\)
−0.703005 + 0.711185i \(0.748159\pi\)
\(860\) −0.311184 1.01718i −0.0106113 0.0346856i
\(861\) −13.2312 52.5857i −0.450918 1.79212i
\(862\) 6.52173 8.81526i 0.222131 0.300249i
\(863\) −42.4495 −1.44500 −0.722499 0.691372i \(-0.757007\pi\)
−0.722499 + 0.691372i \(0.757007\pi\)
\(864\) −22.5516 + 18.8528i −0.767220 + 0.641385i
\(865\) 3.30941 0.112523
\(866\) 3.65625 4.94207i 0.124245 0.167939i
\(867\) −2.90930 0.827467i −0.0988050 0.0281022i
\(868\) −4.36868 14.2801i −0.148283 0.484699i
\(869\) 24.4644 + 4.31373i 0.829898 + 0.146333i
\(870\) 0.792128 + 0.326034i 0.0268557 + 0.0110536i
\(871\) −39.5852 + 33.2159i −1.34129 + 1.12548i
\(872\) −10.2375 + 28.9347i −0.346687 + 0.979853i
\(873\) −11.2331 + 1.62798i −0.380184 + 0.0550987i
\(874\) −3.82656 + 3.63193i −0.129435 + 0.122852i
\(875\) 23.7006 4.17905i 0.801225 0.141278i
\(876\) 1.07390 + 54.2795i 0.0362837 + 1.83393i
\(877\) 10.6705 + 29.3171i 0.360318 + 0.989967i 0.978917 + 0.204259i \(0.0654786\pi\)
−0.618598 + 0.785707i \(0.712299\pi\)
\(878\) −2.90584 47.4400i −0.0980672 1.60102i
\(879\) −2.26544 31.4266i −0.0764113 1.05999i
\(880\) 5.80355 3.91758i 0.195637 0.132061i
\(881\) −22.7011 + 39.3194i −0.764819 + 1.32471i 0.175523 + 0.984475i \(0.443838\pi\)
−0.940342 + 0.340230i \(0.889495\pi\)
\(882\) −45.3072 + 40.4402i −1.52557 + 1.36169i
\(883\) 14.2020 8.19952i 0.477935 0.275936i −0.241621 0.970371i \(-0.577679\pi\)
0.719555 + 0.694435i \(0.244346\pi\)
\(884\) −3.43262 27.9150i −0.115452 0.938883i
\(885\) 2.79038 1.24955i 0.0937975 0.0420031i
\(886\) 2.89371 5.80518i 0.0972159 0.195029i
\(887\) −6.88075 5.77363i −0.231033 0.193860i 0.519921 0.854214i \(-0.325961\pi\)
−0.750954 + 0.660355i \(0.770406\pi\)
\(888\) 30.8714 + 2.89724i 1.03598 + 0.0972249i
\(889\) −2.04564 0.744552i −0.0686086 0.0249715i
\(890\) 2.15142 + 0.637071i 0.0721159 + 0.0213547i
\(891\) −29.1639 + 3.31895i −0.977026 + 0.111189i
\(892\) 7.30677 + 4.74320i 0.244649 + 0.158814i
\(893\) 0.834971 2.29406i 0.0279412 0.0767679i
\(894\) 16.3070 8.53536i 0.545388 0.285465i
\(895\) −8.32389 6.98458i −0.278237 0.233469i
\(896\) 30.3048 42.5423i 1.01241 1.42124i
\(897\) 19.1655 + 42.7987i 0.639919 + 1.42901i
\(898\) 19.0990 + 43.9140i 0.637343 + 1.46543i
\(899\) −0.912558 + 0.526866i −0.0304355 + 0.0175720i
\(900\) 28.1746 + 2.33788i 0.939153 + 0.0779294i
\(901\) 10.2034 + 5.89096i 0.339926 + 0.196256i
\(902\) −3.53777 + 31.0754i −0.117795 + 1.03470i
\(903\) −0.569710 7.90312i −0.0189587 0.262999i
\(904\) 4.73097 8.36722i 0.157350 0.278290i
\(905\) 8.06545 2.93558i 0.268105 0.0975821i
\(906\) 16.0648 5.10478i 0.533717 0.169595i
\(907\) 16.7843 2.95952i 0.557312 0.0982691i 0.112104 0.993696i \(-0.464241\pi\)
0.445208 + 0.895427i \(0.353130\pi\)
\(908\) 8.07248 + 15.8361i 0.267895 + 0.525539i
\(909\) −25.7072 + 20.2632i −0.852655 + 0.672089i
\(910\) 12.2693 2.94676i 0.406723 0.0976841i
\(911\) −33.2666 + 27.9140i −1.10217 + 0.924831i −0.997569 0.0696828i \(-0.977801\pi\)
−0.104602 + 0.994514i \(0.533357\pi\)
\(912\) 1.07037 + 3.26635i 0.0354434 + 0.108160i
\(913\) −8.64883 + 49.0500i −0.286235 + 1.62332i
\(914\) −24.2125 + 16.0290i −0.800879 + 0.530194i
\(915\) 10.6372 + 3.02545i 0.351656 + 0.100018i
\(916\) −25.4556 + 19.1893i −0.841075 + 0.634033i
\(917\) 63.8754i 2.10935i
\(918\) −11.7308 + 26.1933i −0.387174 + 0.864507i
\(919\) 8.84543 0.291784 0.145892 0.989301i \(-0.453395\pi\)
0.145892 + 0.989301i \(0.453395\pi\)
\(920\) 4.00064 + 10.6914i 0.131897 + 0.352485i
\(921\) 7.87731 1.98203i 0.259566 0.0653100i
\(922\) 8.80608 + 13.3019i 0.290013 + 0.438076i
\(923\) −20.1409 3.55139i −0.662946 0.116895i
\(924\) 48.6502 18.8052i 1.60047 0.618644i
\(925\) −19.1699 22.8457i −0.630301 0.751163i
\(926\) 44.9853 10.8043i 1.47831 0.355051i
\(927\) 16.7808 + 3.49155i 0.551153 + 0.114678i
\(928\) −3.40570 1.40889i −0.111798 0.0462492i
\(929\) 0.469928 + 2.66510i 0.0154178 + 0.0874389i 0.991546 0.129758i \(-0.0414199\pi\)
−0.976128 + 0.217196i \(0.930309\pi\)
\(930\) 1.43304 1.57093i 0.0469912 0.0515130i
\(931\) 2.42891 + 6.67337i 0.0796042 + 0.218711i
\(932\) −20.6141 4.75523i −0.675237 0.155763i
\(933\) −19.1606 + 39.5002i −0.627289 + 1.29318i
\(934\) 2.21160 19.4265i 0.0723658 0.635654i
\(935\) 3.41839 5.92083i 0.111793 0.193632i
\(936\) 30.5453 + 0.660255i 0.998403 + 0.0215811i
\(937\) −24.1539 41.8358i −0.789074 1.36672i −0.926535 0.376209i \(-0.877227\pi\)
0.137460 0.990507i \(-0.456106\pi\)
\(938\) −85.9271 + 37.3714i −2.80562 + 1.22022i
\(939\) 7.26286 + 5.25297i 0.237015 + 0.171424i
\(940\) −3.86391 3.60186i −0.126027 0.117480i
\(941\) 5.97193 7.11707i 0.194679 0.232010i −0.659870 0.751380i \(-0.729389\pi\)
0.854550 + 0.519370i \(0.173833\pi\)
\(942\) −0.608661 + 14.6956i −0.0198312 + 0.478807i
\(943\) −47.9144 17.4394i −1.56031 0.567905i
\(944\) −12.0155 + 5.35482i −0.391071 + 0.174285i
\(945\) −12.2713 3.89990i −0.399186 0.126864i
\(946\) −1.29763 + 4.38216i −0.0421895 + 0.142476i
\(947\) 9.51429 26.1403i 0.309173 0.849446i −0.683645 0.729814i \(-0.739606\pi\)
0.992818 0.119631i \(-0.0381713\pi\)
\(948\) 17.3572 + 19.8736i 0.563737 + 0.645463i
\(949\) 36.2724 43.2278i 1.17745 1.40323i
\(950\) 1.47486 2.95878i 0.0478509 0.0959956i
\(951\) 21.7318 + 2.23690i 0.704703 + 0.0725364i
\(952\) 8.40382 50.3025i 0.272369 1.63031i
\(953\) 8.79617 + 15.2354i 0.284936 + 0.493523i 0.972594 0.232512i \(-0.0746943\pi\)
−0.687658 + 0.726035i \(0.741361\pi\)
\(954\) −7.92333 + 10.0512i −0.256527 + 0.325420i
\(955\) −2.36787 1.36709i −0.0766225 0.0442380i
\(956\) −19.0338 + 44.8634i −0.615599 + 1.45098i
\(957\) −2.06459 3.04674i −0.0667388 0.0984872i
\(958\) 1.10665 + 18.0670i 0.0357544 + 0.583718i
\(959\) −47.5710 + 17.3144i −1.53615 + 0.559112i
\(960\) 7.41077 + 0.628289i 0.239182 + 0.0202779i
\(961\) −4.92888 27.9531i −0.158996 0.901712i
\(962\) −22.1872 23.3762i −0.715343 0.753679i
\(963\) 32.9006 + 1.00735i 1.06021 + 0.0324615i
\(964\) −1.26093 + 24.1431i −0.0406119 + 0.777595i
\(965\) −3.34266 3.98363i −0.107604 0.128238i
\(966\) 11.2878 + 84.2807i 0.363179 + 2.71169i
\(967\) 6.34832 36.0031i 0.204148 1.15778i −0.694626 0.719371i \(-0.744430\pi\)
0.898774 0.438412i \(-0.144459\pi\)
\(968\) 1.02847 0.00925257i 0.0330561 0.000297389i
\(969\) 2.33655 + 2.40918i 0.0750607 + 0.0773941i
\(970\) 2.30878 + 1.70809i 0.0741306 + 0.0548435i
\(971\) 11.3272i 0.363508i −0.983344 0.181754i \(-0.941823\pi\)
0.983344 0.181754i \(-0.0581775\pi\)
\(972\) −26.3311 16.6935i −0.844571 0.535444i
\(973\) 7.25861i 0.232700i
\(974\) −30.5751 + 41.3277i −0.979690 + 1.32422i
\(975\) −20.4584 21.0944i −0.655193 0.675561i
\(976\) −45.7444 13.0992i −1.46424 0.419295i
\(977\) 0.542154 3.07471i 0.0173450 0.0983686i −0.974906 0.222616i \(-0.928540\pi\)
0.992251 + 0.124247i \(0.0396516\pi\)
\(978\) −56.5220 + 7.57004i −1.80737 + 0.242063i
\(979\) −6.19668 7.38491i −0.198047 0.236023i
\(980\) 15.3453 + 0.801447i 0.490187 + 0.0256013i
\(981\) −32.5390 0.996281i −1.03889 0.0318088i
\(982\) 34.7151 32.9493i 1.10780 1.05146i
\(983\) 0.180363 + 1.02289i 0.00575268 + 0.0326251i 0.987549 0.157312i \(-0.0502828\pi\)
−0.981796 + 0.189937i \(0.939172\pi\)
\(984\) −23.6382 + 23.3419i −0.753559 + 0.744112i
\(985\) 5.38852 1.96126i 0.171692 0.0624909i
\(986\) −3.59190 + 0.220014i −0.114389 + 0.00700668i
\(987\) −22.0733 32.5738i −0.702600 1.03683i
\(988\) 1.39538 3.28896i 0.0443931 0.104636i
\(989\) −6.45263 3.72543i −0.205182 0.118462i
\(990\) 5.83249 + 4.59773i 0.185369 + 0.146126i
\(991\) 16.7706 + 29.0475i 0.532734 + 0.922723i 0.999269 + 0.0382200i \(0.0121688\pi\)
−0.466535 + 0.884503i \(0.654498\pi\)
\(992\) −6.17789 + 6.74807i −0.196148 + 0.214251i
\(993\) 22.6573 + 2.33216i 0.719007 + 0.0740088i
\(994\) −33.1902 16.5443i −1.05273 0.524753i
\(995\) 1.84658 2.20067i 0.0585406 0.0697660i
\(996\) −39.8456 + 34.8005i −1.26255 + 1.10269i
\(997\) 14.5407 39.9502i 0.460508 1.26524i −0.464596 0.885523i \(-0.653800\pi\)
0.925104 0.379714i \(-0.123977\pi\)
\(998\) 21.8808 + 6.47926i 0.692625 + 0.205097i
\(999\) 7.04504 + 32.1245i 0.222895 + 1.01637i
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 216.2.t.a.85.25 yes 204
3.2 odd 2 648.2.t.a.469.10 204
4.3 odd 2 864.2.bf.a.625.25 204
8.3 odd 2 864.2.bf.a.625.10 204
8.5 even 2 inner 216.2.t.a.85.17 yes 204
24.5 odd 2 648.2.t.a.469.18 204
27.7 even 9 inner 216.2.t.a.61.17 204
27.20 odd 18 648.2.t.a.181.18 204
108.7 odd 18 864.2.bf.a.817.10 204
216.61 even 18 inner 216.2.t.a.61.25 yes 204
216.101 odd 18 648.2.t.a.181.10 204
216.115 odd 18 864.2.bf.a.817.25 204
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
216.2.t.a.61.17 204 27.7 even 9 inner
216.2.t.a.61.25 yes 204 216.61 even 18 inner
216.2.t.a.85.17 yes 204 8.5 even 2 inner
216.2.t.a.85.25 yes 204 1.1 even 1 trivial
648.2.t.a.181.10 204 216.101 odd 18
648.2.t.a.181.18 204 27.20 odd 18
648.2.t.a.469.10 204 3.2 odd 2
648.2.t.a.469.18 204 24.5 odd 2
864.2.bf.a.625.10 204 8.3 odd 2
864.2.bf.a.625.25 204 4.3 odd 2
864.2.bf.a.817.10 204 108.7 odd 18
864.2.bf.a.817.25 204 216.115 odd 18