Properties

Label 231.2.n.a.89.20
Level $231$
Weight $2$
Character 231.89
Analytic conductor $1.845$
Analytic rank $0$
Dimension $52$
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] = [231,2,Mod(89,231)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(231, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 5, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("231.89");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 231 = 3 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 231.n (of order \(6\), degree \(2\), 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: \(1.84454428669\)
Analytic rank: \(0\)
Dimension: \(52\)
Relative dimension: \(26\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 89.20
Character \(\chi\) \(=\) 231.89
Dual form 231.2.n.a.122.20

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.33690 + 0.771860i) q^{2} +(1.06526 + 1.36573i) q^{3} +(0.191534 + 0.331747i) q^{4} +(0.895146 - 1.55044i) q^{5} +(0.369997 + 2.64808i) q^{6} +(-0.181616 + 2.63951i) q^{7} -2.49609i q^{8} +(-0.730435 + 2.90972i) q^{9} +O(q^{10})\) \(q+(1.33690 + 0.771860i) q^{2} +(1.06526 + 1.36573i) q^{3} +(0.191534 + 0.331747i) q^{4} +(0.895146 - 1.55044i) q^{5} +(0.369997 + 2.64808i) q^{6} +(-0.181616 + 2.63951i) q^{7} -2.49609i q^{8} +(-0.730435 + 2.90972i) q^{9} +(2.39344 - 1.38185i) q^{10} +(-0.866025 + 0.500000i) q^{11} +(-0.249043 + 0.614981i) q^{12} -0.312651i q^{13} +(-2.28013 + 3.38858i) q^{14} +(3.07104 - 0.429095i) q^{15} +(2.30970 - 4.00051i) q^{16} +(-2.01601 - 3.49184i) q^{17} +(-3.22241 + 3.32621i) q^{18} +(-2.64410 - 1.52657i) q^{19} +0.685804 q^{20} +(-3.79833 + 2.56373i) q^{21} -1.54372 q^{22} +(1.00775 + 0.581827i) q^{23} +(3.40898 - 2.65899i) q^{24} +(0.897428 + 1.55439i) q^{25} +(0.241323 - 0.417983i) q^{26} +(-4.75199 + 2.10203i) q^{27} +(-0.910436 + 0.445306i) q^{28} -8.12603i q^{29} +(4.43688 + 1.79676i) q^{30} +(-7.71143 + 4.45219i) q^{31} +(1.85232 - 1.06944i) q^{32} +(-1.60541 - 0.650126i) q^{33} -6.22432i q^{34} +(3.92982 + 2.64433i) q^{35} +(-1.10519 + 0.314991i) q^{36} +(-0.101409 + 0.175646i) q^{37} +(-2.35660 - 4.08175i) q^{38} +(0.426997 - 0.333055i) q^{39} +(-3.87003 - 2.23436i) q^{40} -1.11154 q^{41} +(-7.05682 + 0.495677i) q^{42} +9.88060 q^{43} +(-0.331747 - 0.191534i) q^{44} +(3.85749 + 3.73712i) q^{45} +(0.898177 + 1.55569i) q^{46} +(3.16903 - 5.48892i) q^{47} +(7.92405 - 1.10717i) q^{48} +(-6.93403 - 0.958754i) q^{49} +2.77075i q^{50} +(2.62133 - 6.47305i) q^{51} +(0.103721 - 0.0598834i) q^{52} +(6.82866 - 3.94253i) q^{53} +(-7.97542 - 0.857662i) q^{54} +1.79029i q^{55} +(6.58845 + 0.453329i) q^{56} +(-0.731775 - 5.23733i) q^{57} +(6.27216 - 10.8637i) q^{58} +(4.80421 + 8.32114i) q^{59} +(0.730561 + 0.936623i) q^{60} +(-1.71488 - 0.990087i) q^{61} -13.7459 q^{62} +(-7.54757 - 2.45644i) q^{63} -5.93697 q^{64} +(-0.484746 - 0.279868i) q^{65} +(-1.64446 - 2.10830i) q^{66} +(6.00058 + 10.3933i) q^{67} +(0.772271 - 1.33761i) q^{68} +(0.278903 + 1.99612i) q^{69} +(3.21273 + 6.56848i) q^{70} +11.0049i q^{71} +(7.26291 + 1.82323i) q^{72} +(-8.06212 + 4.65466i) q^{73} +(-0.271148 + 0.156547i) q^{74} +(-1.16688 + 2.88148i) q^{75} -1.16957i q^{76} +(-1.16247 - 2.37669i) q^{77} +(0.827924 - 0.115680i) q^{78} +(1.32894 - 2.30180i) q^{79} +(-4.13503 - 7.16209i) q^{80} +(-7.93293 - 4.25072i) q^{81} +(-1.48602 - 0.857954i) q^{82} -12.5950 q^{83} +(-1.57802 - 0.769041i) q^{84} -7.21850 q^{85} +(13.2094 + 7.62643i) q^{86} +(11.0980 - 8.65635i) q^{87} +(1.24804 + 2.16168i) q^{88} +(4.29818 - 7.44467i) q^{89} +(2.27255 + 7.97359i) q^{90} +(0.825246 + 0.0567824i) q^{91} +0.445759i q^{92} +(-14.2952 - 5.78897i) q^{93} +(8.47336 - 4.89210i) q^{94} +(-4.73372 + 2.73301i) q^{95} +(3.43377 + 1.39054i) q^{96} +5.61659i q^{97} +(-8.53008 - 6.63386i) q^{98} +(-0.822284 - 2.88511i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 52 q + 24 q^{4} - 6 q^{7} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 52 q + 24 q^{4} - 6 q^{7} - 4 q^{9} - 30 q^{12} - 4 q^{15} - 20 q^{16} - 18 q^{18} + 6 q^{19} - 2 q^{21} + 36 q^{24} - 22 q^{25} - 40 q^{28} - 20 q^{30} - 54 q^{31} + 36 q^{36} + 2 q^{37} + 20 q^{39} + 60 q^{40} - 36 q^{42} + 36 q^{43} - 54 q^{45} + 4 q^{46} + 22 q^{49} - 16 q^{51} + 12 q^{52} + 66 q^{54} - 44 q^{57} - 16 q^{58} + 20 q^{60} - 36 q^{61} - 24 q^{63} - 48 q^{64} - 30 q^{66} - 6 q^{67} - 116 q^{70} + 36 q^{72} - 6 q^{73} + 72 q^{75} + 112 q^{78} + 14 q^{79} + 52 q^{81} - 84 q^{82} + 8 q^{84} + 8 q^{85} + 18 q^{87} - 12 q^{88} + 46 q^{91} + 6 q^{93} + 48 q^{94} - 18 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/231\mathbb{Z}\right)^\times\).

\(n\) \(155\) \(199\) \(211\)
\(\chi(n)\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.33690 + 0.771860i 0.945331 + 0.545787i 0.891627 0.452770i \(-0.149564\pi\)
0.0537036 + 0.998557i \(0.482897\pi\)
\(3\) 1.06526 + 1.36573i 0.615029 + 0.788504i
\(4\) 0.191534 + 0.331747i 0.0957671 + 0.165874i
\(5\) 0.895146 1.55044i 0.400321 0.693377i −0.593443 0.804876i \(-0.702232\pi\)
0.993765 + 0.111499i \(0.0355652\pi\)
\(6\) 0.369997 + 2.64808i 0.151051 + 1.08107i
\(7\) −0.181616 + 2.63951i −0.0686444 + 0.997641i
\(8\) 2.49609i 0.882500i
\(9\) −0.730435 + 2.90972i −0.243478 + 0.969906i
\(10\) 2.39344 1.38185i 0.756872 0.436980i
\(11\) −0.866025 + 0.500000i −0.261116 + 0.150756i
\(12\) −0.249043 + 0.614981i −0.0718924 + 0.177530i
\(13\) 0.312651i 0.0867138i −0.999060 0.0433569i \(-0.986195\pi\)
0.999060 0.0433569i \(-0.0138053\pi\)
\(14\) −2.28013 + 3.38858i −0.609391 + 0.905636i
\(15\) 3.07104 0.429095i 0.792940 0.110792i
\(16\) 2.30970 4.00051i 0.577424 1.00013i
\(17\) −2.01601 3.49184i −0.488955 0.846895i 0.510964 0.859602i \(-0.329289\pi\)
−0.999919 + 0.0127068i \(0.995955\pi\)
\(18\) −3.22241 + 3.32621i −0.759530 + 0.783995i
\(19\) −2.64410 1.52657i −0.606599 0.350220i 0.165034 0.986288i \(-0.447227\pi\)
−0.771633 + 0.636068i \(0.780560\pi\)
\(20\) 0.685804 0.153350
\(21\) −3.79833 + 2.56373i −0.828863 + 0.559452i
\(22\) −1.54372 −0.329122
\(23\) 1.00775 + 0.581827i 0.210131 + 0.121319i 0.601372 0.798969i \(-0.294621\pi\)
−0.391241 + 0.920288i \(0.627954\pi\)
\(24\) 3.40898 2.65899i 0.695855 0.542763i
\(25\) 0.897428 + 1.55439i 0.179486 + 0.310878i
\(26\) 0.241323 0.417983i 0.0473273 0.0819733i
\(27\) −4.75199 + 2.10203i −0.914522 + 0.404537i
\(28\) −0.910436 + 0.445306i −0.172056 + 0.0841549i
\(29\) 8.12603i 1.50897i −0.656319 0.754483i \(-0.727888\pi\)
0.656319 0.754483i \(-0.272112\pi\)
\(30\) 4.43688 + 1.79676i 0.810059 + 0.328041i
\(31\) −7.71143 + 4.45219i −1.38501 + 0.799638i −0.992748 0.120215i \(-0.961642\pi\)
−0.392265 + 0.919852i \(0.628308\pi\)
\(32\) 1.85232 1.06944i 0.327447 0.189051i
\(33\) −1.60541 0.650126i −0.279466 0.113172i
\(34\) 6.22432i 1.06746i
\(35\) 3.92982 + 2.64433i 0.664262 + 0.446973i
\(36\) −1.10519 + 0.314991i −0.184199 + 0.0524985i
\(37\) −0.101409 + 0.175646i −0.0166716 + 0.0288760i −0.874241 0.485493i \(-0.838640\pi\)
0.857569 + 0.514369i \(0.171974\pi\)
\(38\) −2.35660 4.08175i −0.382291 0.662148i
\(39\) 0.426997 0.333055i 0.0683742 0.0533315i
\(40\) −3.87003 2.23436i −0.611905 0.353284i
\(41\) −1.11154 −0.173594 −0.0867968 0.996226i \(-0.527663\pi\)
−0.0867968 + 0.996226i \(0.527663\pi\)
\(42\) −7.05682 + 0.495677i −1.08889 + 0.0764847i
\(43\) 9.88060 1.50678 0.753388 0.657576i \(-0.228418\pi\)
0.753388 + 0.657576i \(0.228418\pi\)
\(44\) −0.331747 0.191534i −0.0500128 0.0288749i
\(45\) 3.85749 + 3.73712i 0.575041 + 0.557096i
\(46\) 0.898177 + 1.55569i 0.132429 + 0.229374i
\(47\) 3.16903 5.48892i 0.462251 0.800642i −0.536822 0.843696i \(-0.680375\pi\)
0.999073 + 0.0430536i \(0.0137086\pi\)
\(48\) 7.92405 1.10717i 1.14374 0.159806i
\(49\) −6.93403 0.958754i −0.990576 0.136965i
\(50\) 2.77075i 0.391844i
\(51\) 2.62133 6.47305i 0.367059 0.906409i
\(52\) 0.103721 0.0598834i 0.0143835 0.00830434i
\(53\) 6.82866 3.94253i 0.937988 0.541548i 0.0486590 0.998815i \(-0.484505\pi\)
0.889329 + 0.457268i \(0.151172\pi\)
\(54\) −7.97542 0.857662i −1.08532 0.116713i
\(55\) 1.79029i 0.241403i
\(56\) 6.58845 + 0.453329i 0.880419 + 0.0605787i
\(57\) −0.731775 5.23733i −0.0969259 0.693702i
\(58\) 6.27216 10.8637i 0.823574 1.42647i
\(59\) 4.80421 + 8.32114i 0.625455 + 1.08332i 0.988453 + 0.151530i \(0.0484199\pi\)
−0.362998 + 0.931790i \(0.618247\pi\)
\(60\) 0.730561 + 0.936623i 0.0943150 + 0.120918i
\(61\) −1.71488 0.990087i −0.219568 0.126768i 0.386182 0.922423i \(-0.373794\pi\)
−0.605750 + 0.795655i \(0.707127\pi\)
\(62\) −13.7459 −1.74573
\(63\) −7.54757 2.45644i −0.950905 0.309483i
\(64\) −5.93697 −0.742121
\(65\) −0.484746 0.279868i −0.0601254 0.0347134i
\(66\) −1.64446 2.10830i −0.202420 0.259514i
\(67\) 6.00058 + 10.3933i 0.733087 + 1.26974i 0.955557 + 0.294805i \(0.0952547\pi\)
−0.222470 + 0.974939i \(0.571412\pi\)
\(68\) 0.772271 1.33761i 0.0936517 0.162209i
\(69\) 0.278903 + 1.99612i 0.0335760 + 0.240304i
\(70\) 3.21273 + 6.56848i 0.383995 + 0.785083i
\(71\) 11.0049i 1.30604i 0.757340 + 0.653021i \(0.226499\pi\)
−0.757340 + 0.653021i \(0.773501\pi\)
\(72\) 7.26291 + 1.82323i 0.855943 + 0.214870i
\(73\) −8.06212 + 4.65466i −0.943599 + 0.544787i −0.891087 0.453833i \(-0.850056\pi\)
−0.0525125 + 0.998620i \(0.516723\pi\)
\(74\) −0.271148 + 0.156547i −0.0315203 + 0.0181982i
\(75\) −1.16688 + 2.88148i −0.134740 + 0.332724i
\(76\) 1.16957i 0.134158i
\(77\) −1.16247 2.37669i −0.132476 0.270849i
\(78\) 0.827924 0.115680i 0.0937440 0.0130982i
\(79\) 1.32894 2.30180i 0.149518 0.258973i −0.781531 0.623866i \(-0.785561\pi\)
0.931049 + 0.364893i \(0.118895\pi\)
\(80\) −4.13503 7.16209i −0.462311 0.800745i
\(81\) −7.93293 4.25072i −0.881436 0.472303i
\(82\) −1.48602 0.857954i −0.164103 0.0947452i
\(83\) −12.5950 −1.38248 −0.691238 0.722627i \(-0.742935\pi\)
−0.691238 + 0.722627i \(0.742935\pi\)
\(84\) −1.57802 0.769041i −0.172176 0.0839093i
\(85\) −7.21850 −0.782957
\(86\) 13.2094 + 7.62643i 1.42440 + 0.822379i
\(87\) 11.0980 8.65635i 1.18983 0.928058i
\(88\) 1.24804 + 2.16168i 0.133042 + 0.230435i
\(89\) 4.29818 7.44467i 0.455606 0.789133i −0.543117 0.839657i \(-0.682756\pi\)
0.998723 + 0.0505241i \(0.0160892\pi\)
\(90\) 2.27255 + 7.97359i 0.239548 + 0.840491i
\(91\) 0.825246 + 0.0567824i 0.0865093 + 0.00595242i
\(92\) 0.445759i 0.0464736i
\(93\) −14.2952 5.78897i −1.48234 0.600288i
\(94\) 8.47336 4.89210i 0.873960 0.504581i
\(95\) −4.73372 + 2.73301i −0.485669 + 0.280401i
\(96\) 3.43377 + 1.39054i 0.350457 + 0.141921i
\(97\) 5.61659i 0.570279i 0.958486 + 0.285139i \(0.0920399\pi\)
−0.958486 + 0.285139i \(0.907960\pi\)
\(98\) −8.53008 6.63386i −0.861668 0.670121i
\(99\) −0.822284 2.88511i −0.0826426 0.289964i
\(100\) −0.343777 + 0.595439i −0.0343777 + 0.0595439i
\(101\) 5.74083 + 9.94341i 0.571234 + 0.989406i 0.996440 + 0.0843093i \(0.0268684\pi\)
−0.425206 + 0.905097i \(0.639798\pi\)
\(102\) 8.50074 6.63053i 0.841698 0.656520i
\(103\) −3.35333 1.93605i −0.330414 0.190764i 0.325611 0.945504i \(-0.394430\pi\)
−0.656025 + 0.754739i \(0.727763\pi\)
\(104\) −0.780405 −0.0765250
\(105\) 0.574850 + 8.18398i 0.0560996 + 0.798675i
\(106\) 12.1723 1.18228
\(107\) −5.77236 3.33267i −0.558035 0.322182i 0.194321 0.980938i \(-0.437750\pi\)
−0.752357 + 0.658756i \(0.771083\pi\)
\(108\) −1.60751 1.17385i −0.154683 0.112954i
\(109\) 5.82190 + 10.0838i 0.557637 + 0.965855i 0.997693 + 0.0678848i \(0.0216250\pi\)
−0.440057 + 0.897970i \(0.645042\pi\)
\(110\) −1.38185 + 2.39344i −0.131755 + 0.228206i
\(111\) −0.347912 + 0.0486112i −0.0330223 + 0.00461398i
\(112\) 10.1399 + 6.82303i 0.958132 + 0.644716i
\(113\) 6.10224i 0.574050i 0.957923 + 0.287025i \(0.0926663\pi\)
−0.957923 + 0.287025i \(0.907334\pi\)
\(114\) 3.06418 7.56662i 0.286986 0.708679i
\(115\) 1.80417 1.04164i 0.168240 0.0971333i
\(116\) 2.69579 1.55641i 0.250298 0.144509i
\(117\) 0.909727 + 0.228371i 0.0841043 + 0.0211130i
\(118\) 14.8327i 1.36546i
\(119\) 9.58289 4.68712i 0.878462 0.429667i
\(120\) −1.07106 7.66559i −0.0977738 0.699770i
\(121\) 0.500000 0.866025i 0.0454545 0.0787296i
\(122\) −1.52842 2.64730i −0.138376 0.239675i
\(123\) −1.18408 1.51807i −0.106765 0.136879i
\(124\) −2.95400 1.70550i −0.265277 0.153158i
\(125\) 12.1648 1.08805
\(126\) −8.19432 9.10969i −0.730008 0.811555i
\(127\) 3.51847 0.312213 0.156107 0.987740i \(-0.450106\pi\)
0.156107 + 0.987740i \(0.450106\pi\)
\(128\) −11.6418 6.72138i −1.02900 0.594092i
\(129\) 10.5254 + 13.4942i 0.926712 + 1.18810i
\(130\) −0.432038 0.748312i −0.0378923 0.0656313i
\(131\) −3.14034 + 5.43923i −0.274373 + 0.475228i −0.969977 0.243198i \(-0.921804\pi\)
0.695604 + 0.718426i \(0.255137\pi\)
\(132\) −0.0918134 0.657111i −0.00799133 0.0571942i
\(133\) 4.50962 6.70189i 0.391034 0.581128i
\(134\) 18.5264i 1.60044i
\(135\) −0.994653 + 9.24930i −0.0856061 + 0.796053i
\(136\) −8.71594 + 5.03215i −0.747385 + 0.431503i
\(137\) −9.72336 + 5.61379i −0.830723 + 0.479618i −0.854100 0.520109i \(-0.825891\pi\)
0.0233773 + 0.999727i \(0.492558\pi\)
\(138\) −1.16786 + 2.88388i −0.0994145 + 0.245492i
\(139\) 19.6324i 1.66520i −0.553878 0.832598i \(-0.686852\pi\)
0.553878 0.832598i \(-0.313148\pi\)
\(140\) −0.124553 + 1.81019i −0.0105266 + 0.152989i
\(141\) 10.8722 1.51910i 0.915607 0.127931i
\(142\) −8.49424 + 14.7125i −0.712821 + 1.23464i
\(143\) 0.156326 + 0.270764i 0.0130726 + 0.0226424i
\(144\) 9.95329 + 9.64269i 0.829441 + 0.803557i
\(145\) −12.5989 7.27398i −1.04628 0.604071i
\(146\) −14.3710 −1.18935
\(147\) −6.07716 10.4913i −0.501236 0.865311i
\(148\) −0.0776933 −0.00638635
\(149\) −3.32787 1.92135i −0.272630 0.157403i 0.357452 0.933931i \(-0.383645\pi\)
−0.630082 + 0.776528i \(0.716979\pi\)
\(150\) −3.78410 + 2.95158i −0.308971 + 0.240995i
\(151\) 9.15015 + 15.8485i 0.744629 + 1.28974i 0.950368 + 0.311128i \(0.100707\pi\)
−0.205739 + 0.978607i \(0.565960\pi\)
\(152\) −3.81046 + 6.59992i −0.309069 + 0.535324i
\(153\) 11.6328 3.31547i 0.940459 0.268040i
\(154\) 0.280364 4.07466i 0.0225924 0.328346i
\(155\) 15.9414i 1.28045i
\(156\) 0.192275 + 0.0778635i 0.0153943 + 0.00623407i
\(157\) −14.2725 + 8.24021i −1.13907 + 0.657641i −0.946199 0.323584i \(-0.895112\pi\)
−0.192868 + 0.981225i \(0.561779\pi\)
\(158\) 3.55333 2.05152i 0.282688 0.163210i
\(159\) 12.6587 + 5.12628i 1.00390 + 0.406540i
\(160\) 3.82921i 0.302725i
\(161\) −1.71876 + 2.55431i −0.135457 + 0.201308i
\(162\) −7.32457 11.8059i −0.575473 0.927559i
\(163\) 11.9353 20.6726i 0.934846 1.61920i 0.159938 0.987127i \(-0.448871\pi\)
0.774908 0.632074i \(-0.217796\pi\)
\(164\) −0.212898 0.368751i −0.0166246 0.0287946i
\(165\) −2.44505 + 1.90713i −0.190347 + 0.148470i
\(166\) −16.8382 9.72154i −1.30690 0.754538i
\(167\) 18.9731 1.46818 0.734091 0.679052i \(-0.237609\pi\)
0.734091 + 0.679052i \(0.237609\pi\)
\(168\) 6.39930 + 9.48096i 0.493717 + 0.731472i
\(169\) 12.9022 0.992481
\(170\) −9.65042 5.57167i −0.740153 0.427328i
\(171\) 6.37325 6.57854i 0.487375 0.503073i
\(172\) 1.89247 + 3.27786i 0.144300 + 0.249934i
\(173\) 1.92741 3.33838i 0.146539 0.253812i −0.783407 0.621509i \(-0.786520\pi\)
0.929946 + 0.367696i \(0.119853\pi\)
\(174\) 21.5184 3.00661i 1.63130 0.227930i
\(175\) −4.26582 + 2.08647i −0.322466 + 0.157722i
\(176\) 4.61940i 0.348200i
\(177\) −6.24668 + 15.4254i −0.469529 + 1.15945i
\(178\) 11.4925 6.63518i 0.861397 0.497328i
\(179\) −0.262573 + 0.151597i −0.0196256 + 0.0113309i −0.509781 0.860304i \(-0.670273\pi\)
0.490155 + 0.871635i \(0.336940\pi\)
\(180\) −0.500936 + 1.99550i −0.0373375 + 0.148736i
\(181\) 13.6432i 1.01409i −0.861920 0.507044i \(-0.830738\pi\)
0.861920 0.507044i \(-0.169262\pi\)
\(182\) 1.05944 + 0.712887i 0.0785312 + 0.0528427i
\(183\) −0.474606 3.39677i −0.0350839 0.251096i
\(184\) 1.45229 2.51544i 0.107064 0.185441i
\(185\) 0.181552 + 0.314457i 0.0133480 + 0.0231194i
\(186\) −14.6429 18.7731i −1.07367 1.37651i
\(187\) 3.49184 + 2.01601i 0.255349 + 0.147426i
\(188\) 2.42791 0.177074
\(189\) −4.68530 12.9247i −0.340806 0.940134i
\(190\) −8.43801 −0.612157
\(191\) 9.69981 + 5.60019i 0.701854 + 0.405216i 0.808038 0.589131i \(-0.200530\pi\)
−0.106184 + 0.994347i \(0.533863\pi\)
\(192\) −6.32443 8.10830i −0.456426 0.585166i
\(193\) −10.9724 19.0047i −0.789809 1.36799i −0.926083 0.377319i \(-0.876846\pi\)
0.136274 0.990671i \(-0.456487\pi\)
\(194\) −4.33522 + 7.50882i −0.311251 + 0.539102i
\(195\) −0.134157 0.960165i −0.00960718 0.0687589i
\(196\) −1.01004 2.48398i −0.0721458 0.177427i
\(197\) 1.71509i 0.122195i −0.998132 0.0610974i \(-0.980540\pi\)
0.998132 0.0610974i \(-0.0194600\pi\)
\(198\) 1.12759 4.49179i 0.0801341 0.319218i
\(199\) 12.7029 7.33400i 0.900482 0.519893i 0.0231253 0.999733i \(-0.492638\pi\)
0.877356 + 0.479839i \(0.159305\pi\)
\(200\) 3.87990 2.24006i 0.274350 0.158396i
\(201\) −7.80226 + 19.2668i −0.550329 + 1.35897i
\(202\) 17.7245i 1.24709i
\(203\) 21.4487 + 1.47582i 1.50541 + 0.103582i
\(204\) 2.64949 0.370194i 0.185501 0.0259188i
\(205\) −0.994992 + 1.72338i −0.0694932 + 0.120366i
\(206\) −2.98871 5.17660i −0.208233 0.360671i
\(207\) −2.42905 + 2.50729i −0.168831 + 0.174269i
\(208\) −1.25077 0.722130i −0.0867250 0.0500707i
\(209\) 3.05315 0.211191
\(210\) −5.54837 + 11.3849i −0.382874 + 0.785630i
\(211\) −17.1239 −1.17886 −0.589429 0.807820i \(-0.700647\pi\)
−0.589429 + 0.807820i \(0.700647\pi\)
\(212\) 2.61584 + 1.51026i 0.179657 + 0.103725i
\(213\) −15.0297 + 11.7231i −1.02982 + 0.803254i
\(214\) −5.14471 8.91090i −0.351685 0.609137i
\(215\) 8.84457 15.3192i 0.603195 1.04476i
\(216\) 5.24686 + 11.8614i 0.357004 + 0.807066i
\(217\) −10.3511 21.1630i −0.702678 1.43664i
\(218\) 17.9747i 1.21740i
\(219\) −14.9453 6.05224i −1.00991 0.408972i
\(220\) −0.593924 + 0.342902i −0.0400423 + 0.0231185i
\(221\) −1.09173 + 0.630309i −0.0734375 + 0.0423992i
\(222\) −0.502645 0.203551i −0.0337353 0.0136614i
\(223\) 5.84935i 0.391701i −0.980634 0.195851i \(-0.937253\pi\)
0.980634 0.195851i \(-0.0627468\pi\)
\(224\) 2.48638 + 5.08344i 0.166128 + 0.339652i
\(225\) −5.17836 + 1.47588i −0.345224 + 0.0983921i
\(226\) −4.71007 + 8.15808i −0.313309 + 0.542667i
\(227\) −11.2674 19.5156i −0.747841 1.29530i −0.948856 0.315711i \(-0.897757\pi\)
0.201014 0.979588i \(-0.435576\pi\)
\(228\) 1.59731 1.24589i 0.105784 0.0825113i
\(229\) 24.1747 + 13.9573i 1.59751 + 0.922324i 0.991965 + 0.126513i \(0.0403787\pi\)
0.605546 + 0.795810i \(0.292955\pi\)
\(230\) 3.21600 0.212056
\(231\) 2.00758 4.11942i 0.132089 0.271038i
\(232\) −20.2833 −1.33166
\(233\) −22.1542 12.7908i −1.45137 0.837950i −0.452813 0.891606i \(-0.649579\pi\)
−0.998559 + 0.0536557i \(0.982913\pi\)
\(234\) 1.03994 + 1.00749i 0.0679832 + 0.0658618i
\(235\) −5.67349 9.82677i −0.370098 0.641028i
\(236\) −1.84034 + 3.18757i −0.119796 + 0.207493i
\(237\) 4.55931 0.637039i 0.296159 0.0413802i
\(238\) 16.4292 + 1.13044i 1.06494 + 0.0732752i
\(239\) 18.8848i 1.22156i −0.791802 0.610778i \(-0.790857\pi\)
0.791802 0.610778i \(-0.209143\pi\)
\(240\) 5.37658 13.2768i 0.347057 0.857016i
\(241\) −9.47018 + 5.46761i −0.610028 + 0.352200i −0.772976 0.634435i \(-0.781233\pi\)
0.162949 + 0.986635i \(0.447900\pi\)
\(242\) 1.33690 0.771860i 0.0859392 0.0496170i
\(243\) −2.64531 15.3624i −0.169696 0.985496i
\(244\) 0.758543i 0.0485607i
\(245\) −7.69346 + 9.89256i −0.491517 + 0.632012i
\(246\) −0.411267 2.94345i −0.0262214 0.187667i
\(247\) −0.477285 + 0.826682i −0.0303689 + 0.0526005i
\(248\) 11.1131 + 19.2484i 0.705680 + 1.22227i
\(249\) −13.4169 17.2013i −0.850263 1.09009i
\(250\) 16.2631 + 9.38950i 1.02857 + 0.593844i
\(251\) −7.68374 −0.484993 −0.242497 0.970152i \(-0.577966\pi\)
−0.242497 + 0.970152i \(0.577966\pi\)
\(252\) −0.630701 2.97438i −0.0397305 0.187368i
\(253\) −1.16365 −0.0731582
\(254\) 4.70384 + 2.71576i 0.295145 + 0.170402i
\(255\) −7.68960 9.85853i −0.481541 0.617365i
\(256\) −4.43895 7.68849i −0.277435 0.480531i
\(257\) −1.21453 + 2.10363i −0.0757604 + 0.131221i −0.901417 0.432953i \(-0.857472\pi\)
0.825656 + 0.564173i \(0.190805\pi\)
\(258\) 3.65579 + 26.1646i 0.227599 + 1.62894i
\(259\) −0.445201 0.299571i −0.0276635 0.0186144i
\(260\) 0.214418i 0.0132976i
\(261\) 23.6445 + 5.93554i 1.46356 + 0.367401i
\(262\) −8.39665 + 4.84781i −0.518747 + 0.299499i
\(263\) −15.4952 + 8.94617i −0.955477 + 0.551645i −0.894778 0.446511i \(-0.852666\pi\)
−0.0606987 + 0.998156i \(0.519333\pi\)
\(264\) −1.62277 + 4.00724i −0.0998747 + 0.246629i
\(265\) 14.1165i 0.867172i
\(266\) 11.2018 5.47896i 0.686828 0.335937i
\(267\) 14.7461 2.06037i 0.902446 0.126092i
\(268\) −2.29863 + 3.98135i −0.140411 + 0.243200i
\(269\) −5.15486 8.92847i −0.314297 0.544379i 0.664991 0.746852i \(-0.268435\pi\)
−0.979288 + 0.202473i \(0.935102\pi\)
\(270\) −8.46891 + 11.5977i −0.515402 + 0.705811i
\(271\) 12.7191 + 7.34338i 0.772631 + 0.446078i 0.833812 0.552048i \(-0.186154\pi\)
−0.0611817 + 0.998127i \(0.519487\pi\)
\(272\) −18.6255 −1.12934
\(273\) 0.801554 + 1.18755i 0.0485122 + 0.0718739i
\(274\) −17.3322 −1.04708
\(275\) −1.55439 0.897428i −0.0937333 0.0541170i
\(276\) −0.608786 + 0.474850i −0.0366446 + 0.0285826i
\(277\) 4.89785 + 8.48332i 0.294283 + 0.509714i 0.974818 0.223002i \(-0.0715858\pi\)
−0.680535 + 0.732716i \(0.738252\pi\)
\(278\) 15.1534 26.2465i 0.908843 1.57416i
\(279\) −7.32193 25.6901i −0.438353 1.53803i
\(280\) 6.60048 9.80919i 0.394454 0.586211i
\(281\) 14.9221i 0.890176i −0.895487 0.445088i \(-0.853172\pi\)
0.895487 0.445088i \(-0.146828\pi\)
\(282\) 15.7076 + 6.36096i 0.935375 + 0.378789i
\(283\) 22.0773 12.7463i 1.31236 0.757691i 0.329873 0.944025i \(-0.392994\pi\)
0.982486 + 0.186334i \(0.0596607\pi\)
\(284\) −3.65085 + 2.10782i −0.216638 + 0.125076i
\(285\) −8.77520 3.55360i −0.519798 0.210497i
\(286\) 0.482646i 0.0285394i
\(287\) 0.201874 2.93393i 0.0119162 0.173184i
\(288\) 1.75876 + 6.17088i 0.103636 + 0.363623i
\(289\) 0.371375 0.643241i 0.0218456 0.0378377i
\(290\) −11.2290 19.4492i −0.659389 1.14209i
\(291\) −7.67075 + 5.98314i −0.449667 + 0.350738i
\(292\) −3.08834 1.78306i −0.180732 0.104345i
\(293\) −3.58027 −0.209162 −0.104581 0.994516i \(-0.533350\pi\)
−0.104581 + 0.994516i \(0.533350\pi\)
\(294\) −0.0267138 18.7166i −0.00155798 1.09157i
\(295\) 17.2019 1.00153
\(296\) 0.438427 + 0.253126i 0.0254831 + 0.0147127i
\(297\) 3.06433 4.19641i 0.177810 0.243501i
\(298\) −2.96602 5.13730i −0.171817 0.297596i
\(299\) 0.181909 0.315075i 0.0105201 0.0182213i
\(300\) −1.17942 + 0.164792i −0.0680939 + 0.00951427i
\(301\) −1.79447 + 26.0799i −0.103432 + 1.50322i
\(302\) 28.2505i 1.62564i
\(303\) −7.46452 + 18.4328i −0.428826 + 1.05893i
\(304\) −12.2142 + 7.05185i −0.700530 + 0.404451i
\(305\) −3.07014 + 1.77254i −0.175796 + 0.101496i
\(306\) 18.1110 + 4.54646i 1.03534 + 0.259904i
\(307\) 25.2153i 1.43912i 0.694433 + 0.719558i \(0.255655\pi\)
−0.694433 + 0.719558i \(0.744345\pi\)
\(308\) 0.565807 0.840864i 0.0322399 0.0479127i
\(309\) −0.928059 6.64214i −0.0527954 0.377858i
\(310\) −12.3046 + 21.3121i −0.698852 + 1.21045i
\(311\) 2.56317 + 4.43953i 0.145344 + 0.251743i 0.929501 0.368819i \(-0.120238\pi\)
−0.784157 + 0.620562i \(0.786905\pi\)
\(312\) −0.831335 1.06582i −0.0470651 0.0603403i
\(313\) 6.18073 + 3.56844i 0.349355 + 0.201700i 0.664401 0.747376i \(-0.268687\pi\)
−0.315046 + 0.949076i \(0.602020\pi\)
\(314\) −25.4412 −1.43573
\(315\) −10.5647 + 9.50317i −0.595256 + 0.535443i
\(316\) 1.01815 0.0572756
\(317\) −9.84764 5.68554i −0.553099 0.319332i 0.197272 0.980349i \(-0.436792\pi\)
−0.750371 + 0.661017i \(0.770125\pi\)
\(318\) 12.9667 + 16.6241i 0.727136 + 0.932232i
\(319\) 4.06302 + 7.03735i 0.227485 + 0.394016i
\(320\) −5.31445 + 9.20491i −0.297087 + 0.514570i
\(321\) −1.59754 11.4337i −0.0891661 0.638164i
\(322\) −4.26938 + 2.08821i −0.237923 + 0.116371i
\(323\) 12.3104i 0.684968i
\(324\) −0.109263 3.44588i −0.00607015 0.191438i
\(325\) 0.485982 0.280582i 0.0269575 0.0155639i
\(326\) 31.9126 18.4248i 1.76748 1.02045i
\(327\) −7.56993 + 18.6930i −0.418618 + 1.03373i
\(328\) 2.77451i 0.153196i
\(329\) 13.9125 + 9.36157i 0.767022 + 0.516120i
\(330\) −4.74083 + 0.662402i −0.260974 + 0.0364640i
\(331\) −9.99224 + 17.3071i −0.549223 + 0.951282i 0.449105 + 0.893479i \(0.351743\pi\)
−0.998328 + 0.0578032i \(0.981590\pi\)
\(332\) −2.41237 4.17834i −0.132396 0.229316i
\(333\) −0.437007 0.423370i −0.0239478 0.0232005i
\(334\) 25.3651 + 14.6446i 1.38792 + 0.801314i
\(335\) 21.4856 1.17388
\(336\) 1.48326 + 21.1167i 0.0809182 + 1.15201i
\(337\) −6.65968 −0.362776 −0.181388 0.983412i \(-0.558059\pi\)
−0.181388 + 0.983412i \(0.558059\pi\)
\(338\) 17.2490 + 9.95872i 0.938223 + 0.541683i
\(339\) −8.33401 + 6.50048i −0.452641 + 0.353058i
\(340\) −1.38259 2.39472i −0.0749815 0.129872i
\(341\) 4.45219 7.71143i 0.241100 0.417597i
\(342\) 13.5981 3.87559i 0.735301 0.209568i
\(343\) 3.78997 18.1283i 0.204639 0.978837i
\(344\) 24.6628i 1.32973i
\(345\) 3.34451 + 1.35439i 0.180062 + 0.0729181i
\(346\) 5.15352 2.97539i 0.277055 0.159958i
\(347\) 22.7713 13.1470i 1.22243 0.705769i 0.256993 0.966413i \(-0.417268\pi\)
0.965435 + 0.260644i \(0.0839349\pi\)
\(348\) 4.99736 + 2.02373i 0.267887 + 0.108483i
\(349\) 1.27938i 0.0684836i −0.999414 0.0342418i \(-0.989098\pi\)
0.999414 0.0342418i \(-0.0109016\pi\)
\(350\) −7.31344 0.503213i −0.390920 0.0268979i
\(351\) 0.657204 + 1.48572i 0.0350789 + 0.0793017i
\(352\) −1.06944 + 1.85232i −0.0570012 + 0.0987289i
\(353\) −4.32979 7.49941i −0.230451 0.399154i 0.727490 0.686119i \(-0.240687\pi\)
−0.957941 + 0.286965i \(0.907354\pi\)
\(354\) −20.2575 + 15.8007i −1.07667 + 0.839798i
\(355\) 17.0624 + 9.85100i 0.905579 + 0.522837i
\(356\) 3.29300 0.174528
\(357\) 16.6096 + 8.09463i 0.879074 + 0.428413i
\(358\) −0.468046 −0.0247370
\(359\) 12.2684 + 7.08314i 0.647499 + 0.373834i 0.787497 0.616318i \(-0.211376\pi\)
−0.139998 + 0.990152i \(0.544710\pi\)
\(360\) 9.32817 9.62864i 0.491638 0.507474i
\(361\) −4.83914 8.38164i −0.254692 0.441139i
\(362\) 10.5306 18.2396i 0.553477 0.958650i
\(363\) 1.71539 0.239679i 0.0900345 0.0125799i
\(364\) 0.139226 + 0.284649i 0.00729740 + 0.0149196i
\(365\) 16.6664i 0.872360i
\(366\) 1.98733 4.90747i 0.103879 0.256517i
\(367\) −3.16709 + 1.82852i −0.165321 + 0.0954480i −0.580378 0.814347i \(-0.697095\pi\)
0.415057 + 0.909796i \(0.363762\pi\)
\(368\) 4.65521 2.68769i 0.242670 0.140105i
\(369\) 0.811909 3.23427i 0.0422663 0.168370i
\(370\) 0.560530i 0.0291406i
\(371\) 9.16615 + 18.7403i 0.475883 + 0.972950i
\(372\) −0.817542 5.85117i −0.0423876 0.303369i
\(373\) −7.87880 + 13.6465i −0.407949 + 0.706588i −0.994660 0.103208i \(-0.967089\pi\)
0.586711 + 0.809797i \(0.300423\pi\)
\(374\) 3.11216 + 5.39042i 0.160926 + 0.278732i
\(375\) 12.9587 + 16.6138i 0.669183 + 0.857933i
\(376\) −13.7008 7.91018i −0.706567 0.407937i
\(377\) −2.54061 −0.130848
\(378\) 3.71227 20.8954i 0.190939 1.07474i
\(379\) 0.666396 0.0342305 0.0171152 0.999854i \(-0.494552\pi\)
0.0171152 + 0.999854i \(0.494552\pi\)
\(380\) −1.81334 1.04693i −0.0930223 0.0537064i
\(381\) 3.74809 + 4.80528i 0.192020 + 0.246182i
\(382\) 8.64512 + 14.9738i 0.442323 + 0.766126i
\(383\) 4.36293 7.55682i 0.222935 0.386135i −0.732763 0.680484i \(-0.761769\pi\)
0.955698 + 0.294349i \(0.0951028\pi\)
\(384\) −3.22194 23.0595i −0.164419 1.17675i
\(385\) −4.72549 0.325145i −0.240833 0.0165709i
\(386\) 33.8765i 1.72427i
\(387\) −7.21714 + 28.7498i −0.366868 + 1.46143i
\(388\) −1.86329 + 1.07577i −0.0945941 + 0.0546140i
\(389\) −8.77007 + 5.06340i −0.444660 + 0.256725i −0.705572 0.708638i \(-0.749310\pi\)
0.260912 + 0.965363i \(0.415977\pi\)
\(390\) 0.561758 1.38720i 0.0284457 0.0702434i
\(391\) 4.69188i 0.237279i
\(392\) −2.39314 + 17.3080i −0.120872 + 0.874184i
\(393\) −10.7738 + 1.50535i −0.543467 + 0.0759347i
\(394\) 1.32381 2.29290i 0.0666923 0.115515i
\(395\) −2.37920 4.12089i −0.119710 0.207344i
\(396\) 0.799631 0.825387i 0.0401830 0.0414773i
\(397\) 5.02915 + 2.90358i 0.252406 + 0.145727i 0.620865 0.783917i \(-0.286781\pi\)
−0.368460 + 0.929644i \(0.620115\pi\)
\(398\) 22.6433 1.13500
\(399\) 13.9569 0.980344i 0.698719 0.0490786i
\(400\) 8.29115 0.414558
\(401\) 11.9652 + 6.90811i 0.597513 + 0.344975i 0.768063 0.640375i \(-0.221221\pi\)
−0.170549 + 0.985349i \(0.554554\pi\)
\(402\) −25.3021 + 19.7355i −1.26195 + 0.984316i
\(403\) 1.39198 + 2.41099i 0.0693396 + 0.120100i
\(404\) −2.19913 + 3.80901i −0.109411 + 0.189505i
\(405\) −13.6916 + 8.49450i −0.680341 + 0.422095i
\(406\) 27.5357 + 18.5284i 1.36657 + 0.919551i
\(407\) 0.202818i 0.0100533i
\(408\) −16.1573 6.54306i −0.799906 0.323930i
\(409\) 6.05430 3.49545i 0.299366 0.172839i −0.342792 0.939411i \(-0.611373\pi\)
0.642158 + 0.766572i \(0.278039\pi\)
\(410\) −2.66041 + 1.53599i −0.131388 + 0.0758570i
\(411\) −18.0248 7.29933i −0.889100 0.360050i
\(412\) 1.48328i 0.0730758i
\(413\) −22.8362 + 11.1695i −1.12370 + 0.549616i
\(414\) −5.18267 + 1.47711i −0.254715 + 0.0725961i
\(415\) −11.2743 + 19.5277i −0.553435 + 0.958577i
\(416\) −0.334361 0.579130i −0.0163934 0.0283942i
\(417\) 26.8125 20.9136i 1.31301 1.02414i
\(418\) 4.08175 + 2.35660i 0.199645 + 0.115265i
\(419\) −40.7516 −1.99084 −0.995422 0.0955780i \(-0.969530\pi\)
−0.995422 + 0.0955780i \(0.969530\pi\)
\(420\) −2.60491 + 1.75822i −0.127107 + 0.0857922i
\(421\) 39.4303 1.92171 0.960857 0.277044i \(-0.0893547\pi\)
0.960857 + 0.277044i \(0.0893547\pi\)
\(422\) −22.8929 13.2172i −1.11441 0.643405i
\(423\) 13.6565 + 13.2303i 0.664000 + 0.643279i
\(424\) −9.84089 17.0449i −0.477916 0.827775i
\(425\) 3.61846 6.26735i 0.175521 0.304011i
\(426\) −29.1418 + 4.07178i −1.41193 + 0.197278i
\(427\) 2.92480 4.34663i 0.141541 0.210348i
\(428\) 2.55329i 0.123418i
\(429\) −0.203263 + 0.501933i −0.00981361 + 0.0242335i
\(430\) 23.6486 13.6535i 1.14044 0.658432i
\(431\) 6.17078 3.56270i 0.297236 0.171609i −0.343965 0.938983i \(-0.611770\pi\)
0.641201 + 0.767373i \(0.278437\pi\)
\(432\) −2.56645 + 23.8655i −0.123478 + 1.14823i
\(433\) 1.71069i 0.0822107i −0.999155 0.0411054i \(-0.986912\pi\)
0.999155 0.0411054i \(-0.0130879\pi\)
\(434\) 2.49647 36.2824i 0.119834 1.74161i
\(435\) −3.48684 24.9554i −0.167181 1.19652i
\(436\) −2.23019 + 3.86279i −0.106807 + 0.184994i
\(437\) −1.77640 3.07682i −0.0849769 0.147184i
\(438\) −15.3089 19.6269i −0.731486 0.937809i
\(439\) −13.9071 8.02929i −0.663752 0.383217i 0.129953 0.991520i \(-0.458517\pi\)
−0.793705 + 0.608303i \(0.791851\pi\)
\(440\) 4.46872 0.213038
\(441\) 7.85457 19.4758i 0.374027 0.927418i
\(442\) −1.94604 −0.0925637
\(443\) 22.0981 + 12.7583i 1.04991 + 0.606167i 0.922625 0.385699i \(-0.126040\pi\)
0.127287 + 0.991866i \(0.459373\pi\)
\(444\) −0.0827637 0.106108i −0.00392779 0.00503567i
\(445\) −7.69500 13.3281i −0.364778 0.631814i
\(446\) 4.51488 7.81999i 0.213786 0.370287i
\(447\) −0.921013 6.59171i −0.0435624 0.311777i
\(448\) 1.07825 15.6707i 0.0509425 0.740371i
\(449\) 27.3754i 1.29192i −0.763370 0.645961i \(-0.776457\pi\)
0.763370 0.645961i \(-0.223543\pi\)
\(450\) −8.06212 2.02386i −0.380052 0.0954055i
\(451\) 0.962623 0.555771i 0.0453282 0.0261702i
\(452\) −2.02440 + 1.16879i −0.0952197 + 0.0549751i
\(453\) −11.8975 + 29.3795i −0.558993 + 1.38037i
\(454\) 34.7873i 1.63265i
\(455\) 0.826753 1.22866i 0.0387588 0.0576007i
\(456\) −13.0728 + 1.82657i −0.612192 + 0.0855372i
\(457\) −5.64235 + 9.77284i −0.263938 + 0.457154i −0.967285 0.253693i \(-0.918355\pi\)
0.703347 + 0.710847i \(0.251688\pi\)
\(458\) 21.5461 + 37.3190i 1.00678 + 1.74380i
\(459\) 16.9201 + 12.3555i 0.789760 + 0.576704i
\(460\) 0.691121 + 0.399019i 0.0322237 + 0.0186044i
\(461\) −18.5685 −0.864820 −0.432410 0.901677i \(-0.642337\pi\)
−0.432410 + 0.901677i \(0.642337\pi\)
\(462\) 5.86355 3.95768i 0.272797 0.184128i
\(463\) −29.3017 −1.36177 −0.680883 0.732392i \(-0.738404\pi\)
−0.680883 + 0.732392i \(0.738404\pi\)
\(464\) −32.5083 18.7687i −1.50916 0.871314i
\(465\) −21.7717 + 16.9818i −1.00964 + 0.787513i
\(466\) −19.7453 34.1999i −0.914685 1.58428i
\(467\) −16.3374 + 28.2972i −0.756004 + 1.30944i 0.188869 + 0.982002i \(0.439518\pi\)
−0.944874 + 0.327436i \(0.893816\pi\)
\(468\) 0.0984823 + 0.345540i 0.00455235 + 0.0159726i
\(469\) −28.5230 + 13.9510i −1.31707 + 0.644197i
\(470\) 17.5166i 0.807978i
\(471\) −26.4578 10.7144i −1.21911 0.493691i
\(472\) 20.7703 11.9917i 0.956030 0.551964i
\(473\) −8.55685 + 4.94030i −0.393444 + 0.227155i
\(474\) 6.58704 + 2.66749i 0.302553 + 0.122522i
\(475\) 5.47996i 0.251438i
\(476\) 3.39039 + 2.28135i 0.155398 + 0.104566i
\(477\) 6.48375 + 22.7492i 0.296871 + 1.04162i
\(478\) 14.5764 25.2471i 0.666709 1.15477i
\(479\) 0.509331 + 0.882188i 0.0232719 + 0.0403082i 0.877427 0.479710i \(-0.159258\pi\)
−0.854155 + 0.520019i \(0.825925\pi\)
\(480\) 5.22966 4.07911i 0.238700 0.186185i
\(481\) 0.0549159 + 0.0317057i 0.00250395 + 0.00144566i
\(482\) −16.8809 −0.768904
\(483\) −5.31942 + 0.373641i −0.242042 + 0.0170012i
\(484\) 0.383069 0.0174122
\(485\) 8.70818 + 5.02767i 0.395418 + 0.228295i
\(486\) 8.32108 22.5798i 0.377452 1.02424i
\(487\) −20.2114 35.0072i −0.915866 1.58633i −0.805628 0.592421i \(-0.798172\pi\)
−0.110238 0.993905i \(-0.535161\pi\)
\(488\) −2.47134 + 4.28049i −0.111873 + 0.193769i
\(489\) 40.9474 5.72128i 1.85170 0.258725i
\(490\) −17.9210 + 7.28709i −0.809590 + 0.329197i
\(491\) 0.0334935i 0.00151154i −1.00000 0.000755769i \(-0.999759\pi\)
1.00000 0.000755769i \(-0.000240569\pi\)
\(492\) 0.276821 0.683578i 0.0124801 0.0308181i
\(493\) −28.3748 + 16.3822i −1.27794 + 0.737817i
\(494\) −1.27617 + 0.736794i −0.0574174 + 0.0331499i
\(495\) −5.20924 1.30769i −0.234138 0.0587764i
\(496\) 41.1329i 1.84692i
\(497\) −29.0476 1.99867i −1.30296 0.0896525i
\(498\) −4.66009 33.3524i −0.208824 1.49456i
\(499\) 2.71651 4.70513i 0.121608 0.210630i −0.798794 0.601604i \(-0.794528\pi\)
0.920402 + 0.390974i \(0.127862\pi\)
\(500\) 2.32997 + 4.03563i 0.104199 + 0.180479i
\(501\) 20.2113 + 25.9121i 0.902974 + 1.15767i
\(502\) −10.2724 5.93077i −0.458479 0.264703i
\(503\) −22.4949 −1.00300 −0.501499 0.865158i \(-0.667218\pi\)
−0.501499 + 0.865158i \(0.667218\pi\)
\(504\) −6.13150 + 18.8394i −0.273119 + 0.839174i
\(505\) 20.5555 0.914708
\(506\) −1.55569 0.898177i −0.0691588 0.0399288i
\(507\) 13.7443 + 17.6210i 0.610405 + 0.782575i
\(508\) 0.673907 + 1.16724i 0.0298998 + 0.0517880i
\(509\) −1.18805 + 2.05777i −0.0526595 + 0.0912090i −0.891154 0.453702i \(-0.850103\pi\)
0.838494 + 0.544911i \(0.183436\pi\)
\(510\) −2.67082 19.1152i −0.118266 0.846433i
\(511\) −10.8218 22.1254i −0.478729 0.978770i
\(512\) 13.1805i 0.582503i
\(513\) 15.7737 + 1.69627i 0.696425 + 0.0748923i
\(514\) −3.24742 + 1.87490i −0.143237 + 0.0826982i
\(515\) −6.00344 + 3.46609i −0.264543 + 0.152734i
\(516\) −2.46069 + 6.07638i −0.108326 + 0.267498i
\(517\) 6.33806i 0.278748i
\(518\) −0.363963 0.744129i −0.0159916 0.0326951i
\(519\) 6.61252 0.923920i 0.290258 0.0405556i
\(520\) −0.698576 + 1.20997i −0.0306346 + 0.0530607i
\(521\) −9.31600 16.1358i −0.408141 0.706922i 0.586540 0.809920i \(-0.300490\pi\)
−0.994682 + 0.102999i \(0.967156\pi\)
\(522\) 27.0289 + 26.1854i 1.18302 + 1.14611i
\(523\) −2.07027 1.19527i −0.0905268 0.0522657i 0.454053 0.890975i \(-0.349978\pi\)
−0.544580 + 0.838709i \(0.683311\pi\)
\(524\) −2.40593 −0.105104
\(525\) −7.39377 3.60332i −0.322690 0.157262i
\(526\) −27.6208 −1.20432
\(527\) 31.0927 + 17.9514i 1.35442 + 0.781974i
\(528\) −6.30885 + 4.92086i −0.274557 + 0.214153i
\(529\) −10.8230 18.7459i −0.470563 0.815040i
\(530\) 10.8960 18.8724i 0.473291 0.819765i
\(531\) −27.7213 + 7.90085i −1.20300 + 0.342868i
\(532\) 3.08708 + 0.212412i 0.133842 + 0.00920921i
\(533\) 0.347525i 0.0150530i
\(534\) 21.3044 + 8.62741i 0.921930 + 0.373344i
\(535\) −10.3342 + 5.96646i −0.446787 + 0.257952i
\(536\) 25.9426 14.9780i 1.12055 0.646950i
\(537\) −0.486749 0.197114i −0.0210048 0.00850609i
\(538\) 15.9153i 0.686157i
\(539\) 6.48442 2.63671i 0.279304 0.113571i
\(540\) −3.25894 + 1.44158i −0.140242 + 0.0620359i
\(541\) 10.0844 17.4668i 0.433564 0.750954i −0.563613 0.826039i \(-0.690589\pi\)
0.997177 + 0.0750842i \(0.0239226\pi\)
\(542\) 11.3361 + 19.6347i 0.486928 + 0.843384i
\(543\) 18.6329 14.5335i 0.799614 0.623694i
\(544\) −7.46860 4.31200i −0.320214 0.184875i
\(545\) 20.8458 0.892935
\(546\) 0.154974 + 2.20632i 0.00663228 + 0.0944220i
\(547\) −32.5957 −1.39369 −0.696845 0.717221i \(-0.745414\pi\)
−0.696845 + 0.717221i \(0.745414\pi\)
\(548\) −3.72471 2.15046i −0.159112 0.0918633i
\(549\) 4.13349 4.26663i 0.176413 0.182095i
\(550\) −1.38538 2.39954i −0.0590727 0.102317i
\(551\) −12.4050 + 21.4861i −0.528470 + 0.915338i
\(552\) 4.98248 0.696166i 0.212068 0.0296308i
\(553\) 5.83426 + 3.92581i 0.248098 + 0.166942i
\(554\) 15.1218i 0.642464i
\(555\) −0.236063 + 0.582930i −0.0100203 + 0.0247440i
\(556\) 6.51298 3.76027i 0.276212 0.159471i
\(557\) 12.8239 7.40386i 0.543365 0.313712i −0.203077 0.979163i \(-0.565094\pi\)
0.746441 + 0.665451i \(0.231761\pi\)
\(558\) 10.0405 39.9966i 0.425047 1.69319i
\(559\) 3.08918i 0.130658i
\(560\) 19.6554 9.61371i 0.830592 0.406253i
\(561\) 0.966392 + 6.91649i 0.0408011 + 0.292014i
\(562\) 11.5177 19.9493i 0.485847 0.841511i
\(563\) −3.43208 5.94453i −0.144645 0.250532i 0.784596 0.620008i \(-0.212871\pi\)
−0.929240 + 0.369476i \(0.879537\pi\)
\(564\) 2.58636 + 3.31587i 0.108906 + 0.139623i
\(565\) 9.46114 + 5.46239i 0.398033 + 0.229805i
\(566\) 39.3535 1.65415
\(567\) 12.6606 20.1670i 0.531694 0.846936i
\(568\) 27.4692 1.15258
\(569\) 15.8236 + 9.13577i 0.663360 + 0.382991i 0.793556 0.608497i \(-0.208227\pi\)
−0.130196 + 0.991488i \(0.541561\pi\)
\(570\) −8.98868 11.5240i −0.376495 0.482689i
\(571\) 11.1175 + 19.2560i 0.465252 + 0.805840i 0.999213 0.0396695i \(-0.0126305\pi\)
−0.533961 + 0.845509i \(0.679297\pi\)
\(572\) −0.0598834 + 0.103721i −0.00250385 + 0.00433680i
\(573\) 2.68449 + 19.2130i 0.112146 + 0.802634i
\(574\) 2.53446 3.76655i 0.105786 0.157213i
\(575\) 2.08859i 0.0871003i
\(576\) 4.33657 17.2749i 0.180691 0.719788i
\(577\) −18.2247 + 10.5220i −0.758705 + 0.438039i −0.828831 0.559500i \(-0.810993\pi\)
0.0701256 + 0.997538i \(0.477660\pi\)
\(578\) 0.992983 0.573299i 0.0413027 0.0238461i
\(579\) 14.2669 35.2303i 0.592910 1.46412i
\(580\) 5.57287i 0.231401i
\(581\) 2.28745 33.2445i 0.0948992 1.37922i
\(582\) −14.8732 + 2.07812i −0.616513 + 0.0861409i
\(583\) −3.94253 + 6.82866i −0.163283 + 0.282814i
\(584\) 11.6185 + 20.1237i 0.480775 + 0.832727i
\(585\) 1.16841 1.20605i 0.0483080 0.0498640i
\(586\) −4.78647 2.76347i −0.197727 0.114158i
\(587\) −3.18901 −0.131625 −0.0658123 0.997832i \(-0.520964\pi\)
−0.0658123 + 0.997832i \(0.520964\pi\)
\(588\) 2.31649 4.02553i 0.0955303 0.166010i
\(589\) 27.1864 1.12020
\(590\) 22.9972 + 13.2774i 0.946779 + 0.546623i
\(591\) 2.34234 1.82702i 0.0963511 0.0751534i
\(592\) 0.468449 + 0.811377i 0.0192531 + 0.0333474i
\(593\) 3.36000 5.81969i 0.137979 0.238986i −0.788753 0.614711i \(-0.789273\pi\)
0.926731 + 0.375725i \(0.122606\pi\)
\(594\) 7.33574 3.24495i 0.300989 0.133142i
\(595\) 1.31100 19.0533i 0.0537456 0.781110i
\(596\) 1.47202i 0.0602961i
\(597\) 23.5481 + 9.53604i 0.963761 + 0.390284i
\(598\) 0.486388 0.280816i 0.0198899 0.0114834i
\(599\) −10.8020 + 6.23656i −0.441359 + 0.254819i −0.704174 0.710027i \(-0.748683\pi\)
0.262815 + 0.964846i \(0.415349\pi\)
\(600\) 7.19242 + 2.91264i 0.293629 + 0.118908i
\(601\) 11.5194i 0.469886i 0.972009 + 0.234943i \(0.0754904\pi\)
−0.972009 + 0.234943i \(0.924510\pi\)
\(602\) −22.5291 + 33.4812i −0.918217 + 1.36459i
\(603\) −34.6246 + 9.86836i −1.41002 + 0.401871i
\(604\) −3.50514 + 6.07107i −0.142622 + 0.247028i
\(605\) −0.895146 1.55044i −0.0363928 0.0630343i
\(606\) −24.2068 + 18.8812i −0.983335 + 0.766996i
\(607\) 32.5338 + 18.7834i 1.32051 + 0.762395i 0.983809 0.179218i \(-0.0573568\pi\)
0.336697 + 0.941613i \(0.390690\pi\)
\(608\) −6.53030 −0.264839
\(609\) 20.8330 + 30.8653i 0.844194 + 1.25073i
\(610\) −5.47262 −0.221580
\(611\) −1.71612 0.990802i −0.0694267 0.0400835i
\(612\) 3.32798 + 3.22413i 0.134526 + 0.130328i
\(613\) 10.1988 + 17.6649i 0.411927 + 0.713478i 0.995100 0.0988694i \(-0.0315226\pi\)
−0.583174 + 0.812348i \(0.698189\pi\)
\(614\) −19.4627 + 33.7104i −0.785451 + 1.36044i
\(615\) −3.41359 + 0.476957i −0.137649 + 0.0192328i
\(616\) −5.93243 + 2.90163i −0.239024 + 0.116910i
\(617\) 0.725688i 0.0292151i −0.999893 0.0146076i \(-0.995350\pi\)
0.999893 0.0146076i \(-0.00464989\pi\)
\(618\) 3.88608 9.59621i 0.156321 0.386016i
\(619\) −2.37483 + 1.37111i −0.0954527 + 0.0551096i −0.546966 0.837155i \(-0.684217\pi\)
0.451514 + 0.892264i \(0.350884\pi\)
\(620\) −5.28853 + 3.05333i −0.212392 + 0.122625i
\(621\) −6.01186 0.646504i −0.241247 0.0259433i
\(622\) 7.91362i 0.317307i
\(623\) 18.8697 + 12.6972i 0.755997 + 0.508701i
\(624\) −0.346158 2.47746i −0.0138574 0.0991780i
\(625\) 6.40210 11.0888i 0.256084 0.443551i
\(626\) 5.50868 + 9.54131i 0.220171 + 0.381347i
\(627\) 3.25240 + 4.16978i 0.129888 + 0.166525i
\(628\) −5.46733 3.15657i −0.218170 0.125961i
\(629\) 0.817769 0.0326066
\(630\) −21.4591 + 4.55029i −0.854952 + 0.181288i
\(631\) 2.29831 0.0914942 0.0457471 0.998953i \(-0.485433\pi\)
0.0457471 + 0.998953i \(0.485433\pi\)
\(632\) −5.74549 3.31716i −0.228543 0.131950i
\(633\) −18.2414 23.3866i −0.725031 0.929534i
\(634\) −8.77687 15.2020i −0.348574 0.603748i
\(635\) 3.14954 5.45516i 0.124986 0.216482i
\(636\) 0.723953 + 5.18135i 0.0287066 + 0.205454i
\(637\) −0.299756 + 2.16793i −0.0118768 + 0.0858966i
\(638\) 12.5443i 0.496634i
\(639\) −32.0212 8.03837i −1.26674 0.317993i
\(640\) −20.8422 + 12.0332i −0.823859 + 0.475655i
\(641\) −17.3791 + 10.0338i −0.686431 + 0.396311i −0.802274 0.596956i \(-0.796377\pi\)
0.115842 + 0.993268i \(0.463043\pi\)
\(642\) 6.68942 16.5187i 0.264010 0.651942i
\(643\) 37.7708i 1.48953i 0.667325 + 0.744767i \(0.267439\pi\)
−0.667325 + 0.744767i \(0.732561\pi\)
\(644\) −1.17659 0.0809569i −0.0463640 0.00319015i
\(645\) 30.3437 4.23971i 1.19478 0.166939i
\(646\) −9.50188 + 16.4577i −0.373847 + 0.647521i
\(647\) −12.2754 21.2617i −0.482597 0.835882i 0.517204 0.855862i \(-0.326973\pi\)
−0.999800 + 0.0199804i \(0.993640\pi\)
\(648\) −10.6102 + 19.8013i −0.416807 + 0.777868i
\(649\) −8.32114 4.80421i −0.326633 0.188582i
\(650\) 0.866280 0.0339783
\(651\) 17.8763 36.6809i 0.700627 1.43764i
\(652\) 9.14409 0.358110
\(653\) −35.0696 20.2474i −1.37238 0.792343i −0.381152 0.924513i \(-0.624472\pi\)
−0.991227 + 0.132169i \(0.957806\pi\)
\(654\) −24.5486 + 19.1478i −0.959928 + 0.748738i
\(655\) 5.62213 + 9.73781i 0.219675 + 0.380488i
\(656\) −2.56733 + 4.44674i −0.100237 + 0.173616i
\(657\) −7.65491 26.8584i −0.298647 1.04785i
\(658\) 11.3738 + 23.2540i 0.443398 + 0.906535i
\(659\) 45.5163i 1.77306i 0.462670 + 0.886531i \(0.346892\pi\)
−0.462670 + 0.886531i \(0.653108\pi\)
\(660\) −1.10100 0.445859i −0.0428562 0.0173550i
\(661\) 36.6307 21.1487i 1.42477 0.822590i 0.428067 0.903747i \(-0.359195\pi\)
0.996701 + 0.0811565i \(0.0258614\pi\)
\(662\) −26.7172 + 15.4252i −1.03840 + 0.599518i
\(663\) −2.02381 0.819561i −0.0785982 0.0318291i
\(664\) 31.4381i 1.22004i
\(665\) −6.35410 12.9911i −0.246401 0.503771i
\(666\) −0.257453 0.903312i −0.00997608 0.0350026i
\(667\) 4.72794 8.18903i 0.183067 0.317081i
\(668\) 3.63400 + 6.29426i 0.140603 + 0.243532i
\(669\) 7.98863 6.23109i 0.308858 0.240908i
\(670\) 28.7241 + 16.5838i 1.10971 + 0.640690i
\(671\) 1.98017 0.0764438
\(672\) −4.29396 + 8.81092i −0.165643 + 0.339888i
\(673\) 6.17411 0.237994 0.118997 0.992895i \(-0.462032\pi\)
0.118997 + 0.992895i \(0.462032\pi\)
\(674\) −8.90333 5.14034i −0.342943 0.197998i
\(675\) −7.53196 5.50003i −0.289905 0.211696i
\(676\) 2.47122 + 4.28028i 0.0950470 + 0.164626i
\(677\) −18.2098 + 31.5403i −0.699859 + 1.21219i 0.268656 + 0.963236i \(0.413421\pi\)
−0.968515 + 0.248955i \(0.919913\pi\)
\(678\) −16.1592 + 2.25781i −0.620590 + 0.0867106i
\(679\) −14.8251 1.02006i −0.568934 0.0391464i
\(680\) 18.0180i 0.690960i
\(681\) 14.6504 36.1774i 0.561405 1.38632i
\(682\) 11.9043 6.87294i 0.455838 0.263178i
\(683\) −10.5489 + 6.09040i −0.403642 + 0.233043i −0.688054 0.725659i \(-0.741535\pi\)
0.284412 + 0.958702i \(0.408202\pi\)
\(684\) 3.40311 + 0.854292i 0.130121 + 0.0326647i
\(685\) 20.1006i 0.768005i
\(686\) 19.0593 21.3104i 0.727689 0.813636i
\(687\) 6.69053 + 47.8843i 0.255260 + 1.82690i
\(688\) 22.8212 39.5275i 0.870050 1.50697i
\(689\) −1.23264 2.13499i −0.0469597 0.0813365i
\(690\) 3.42588 + 4.39218i 0.130421 + 0.167207i
\(691\) −32.3287 18.6650i −1.22984 0.710049i −0.262844 0.964838i \(-0.584661\pi\)
−0.966997 + 0.254789i \(0.917994\pi\)
\(692\) 1.47666 0.0561343
\(693\) 7.76461 1.64645i 0.294953 0.0625433i
\(694\) 40.5906 1.54080
\(695\) −30.4388 17.5738i −1.15461 0.666614i
\(696\) −21.6070 27.7015i −0.819012 1.05002i
\(697\) 2.24088 + 3.88132i 0.0848795 + 0.147016i
\(698\) 0.987501 1.71040i 0.0373775 0.0647397i
\(699\) −6.13134 43.8822i −0.231909 1.65978i
\(700\) −1.50923 1.01554i −0.0570436 0.0383839i
\(701\) 18.4732i 0.697723i −0.937174 0.348861i \(-0.886568\pi\)
0.937174 0.348861i \(-0.113432\pi\)
\(702\) −0.268149 + 2.49352i −0.0101206 + 0.0941120i
\(703\) 0.536273 0.309617i 0.0202259 0.0116774i
\(704\) 5.14157 2.96849i 0.193780 0.111879i
\(705\) 7.37697 18.2165i 0.277833 0.686075i
\(706\) 13.3680i 0.503110i
\(707\) −27.2884 + 13.3471i −1.02628 + 0.501969i
\(708\) −6.31380 + 0.882182i −0.237287 + 0.0331544i
\(709\) −8.88722 + 15.3931i −0.333767 + 0.578101i −0.983247 0.182277i \(-0.941653\pi\)
0.649480 + 0.760378i \(0.274986\pi\)
\(710\) 15.2072 + 26.3396i 0.570715 + 0.988507i
\(711\) 5.72688 + 5.54817i 0.214775 + 0.208073i
\(712\) −18.5825 10.7286i −0.696410 0.402073i
\(713\) −10.3616 −0.388046
\(714\) 15.9575 + 23.6420i 0.597194 + 0.884779i
\(715\) 0.559737 0.0209330
\(716\) −0.100584 0.0580719i −0.00375898 0.00217025i
\(717\) 25.7915 20.1172i 0.963202 0.751292i
\(718\) 10.9344 + 18.9389i 0.408067 + 0.706793i
\(719\) −4.23559 + 7.33627i −0.157961 + 0.273597i −0.934133 0.356924i \(-0.883825\pi\)
0.776172 + 0.630521i \(0.217159\pi\)
\(720\) 23.8600 6.80034i 0.889211 0.253434i
\(721\) 5.71923 8.49954i 0.212995 0.316539i
\(722\) 14.9406i 0.556030i
\(723\) −17.5555 7.10927i −0.652896 0.264397i
\(724\) 4.52608 2.61313i 0.168211 0.0971164i
\(725\) 12.6310 7.29253i 0.469105 0.270838i
\(726\) 2.47830 + 1.00361i 0.0919783 + 0.0372475i
\(727\) 13.3978i 0.496897i −0.968645 0.248448i \(-0.920079\pi\)
0.968645 0.248448i \(-0.0799206\pi\)
\(728\) 0.141734 2.05989i 0.00525301 0.0763445i
\(729\) 18.1629 19.9777i 0.672700 0.739915i
\(730\) −12.8641 + 22.2813i −0.476123 + 0.824669i
\(731\) −19.9194 34.5014i −0.736746 1.27608i
\(732\) 1.03596 0.808046i 0.0382903 0.0298662i
\(733\) 25.9002 + 14.9535i 0.956646 + 0.552320i 0.895139 0.445787i \(-0.147076\pi\)
0.0615067 + 0.998107i \(0.480409\pi\)
\(734\) −5.64545 −0.208377
\(735\) −21.7061 + 0.0309807i −0.800642 + 0.00114274i
\(736\) 2.48891 0.0917423
\(737\) −10.3933 6.00058i −0.382842 0.221034i
\(738\) 3.58185 3.69722i 0.131850 0.136097i
\(739\) 17.0158 + 29.4722i 0.625935 + 1.08415i 0.988359 + 0.152139i \(0.0486160\pi\)
−0.362424 + 0.932013i \(0.618051\pi\)
\(740\) −0.0695468 + 0.120459i −0.00255659 + 0.00442815i
\(741\) −1.63746 + 0.228790i −0.0601535 + 0.00840482i
\(742\) −2.21068 + 32.1289i −0.0811568 + 1.17949i
\(743\) 20.5928i 0.755477i −0.925912 0.377738i \(-0.876702\pi\)
0.925912 0.377738i \(-0.123298\pi\)
\(744\) −14.4498 + 35.6820i −0.529755 + 1.30817i
\(745\) −5.95786 + 3.43977i −0.218279 + 0.126024i
\(746\) −21.0663 + 12.1627i −0.771294 + 0.445307i
\(747\) 9.19981 36.6478i 0.336603 1.34087i
\(748\) 1.54454i 0.0564741i
\(749\) 9.84498 14.6309i 0.359728 0.534603i
\(750\) 4.50093 + 32.2132i 0.164351 + 1.17626i
\(751\) −8.54159 + 14.7945i −0.311687 + 0.539858i −0.978728 0.205164i \(-0.934227\pi\)
0.667041 + 0.745021i \(0.267561\pi\)
\(752\) −14.6390 25.3555i −0.533830 0.924620i
\(753\) −8.18519 10.4939i −0.298285 0.382419i
\(754\) −3.39655 1.96100i −0.123695 0.0714153i
\(755\) 32.7629 1.19236
\(756\) 3.39034 4.02986i 0.123305 0.146565i
\(757\) 28.9720 1.05301 0.526503 0.850173i \(-0.323503\pi\)
0.526503 + 0.850173i \(0.323503\pi\)
\(758\) 0.890905 + 0.514364i 0.0323591 + 0.0186826i
\(759\) −1.23959 1.58924i −0.0449944 0.0576856i
\(760\) 6.82184 + 11.8158i 0.247454 + 0.428603i
\(761\) −1.91120 + 3.31030i −0.0692810 + 0.119998i −0.898585 0.438799i \(-0.855404\pi\)
0.829304 + 0.558798i \(0.188737\pi\)
\(762\) 1.30182 + 9.31717i 0.0471600 + 0.337525i
\(763\) −27.6737 + 13.5356i −1.00186 + 0.490021i
\(764\) 4.29051i 0.155225i
\(765\) 5.27265 21.0038i 0.190633 0.759395i
\(766\) 11.6656 6.73514i 0.421495 0.243351i
\(767\) 2.60161 1.50204i 0.0939388 0.0542356i
\(768\) 5.77176 14.2527i 0.208270 0.514299i
\(769\) 8.34488i 0.300924i −0.988616 0.150462i \(-0.951924\pi\)
0.988616 0.150462i \(-0.0480762\pi\)
\(770\) −6.06654 4.08210i −0.218623 0.147109i
\(771\) −4.16679 + 0.582195i −0.150063 + 0.0209673i
\(772\) 4.20317 7.28011i 0.151276 0.262017i
\(773\) 20.3174 + 35.1908i 0.730766 + 1.26572i 0.956556 + 0.291548i \(0.0941703\pi\)
−0.225790 + 0.974176i \(0.572496\pi\)
\(774\) −31.8394 + 32.8649i −1.14444 + 1.18131i
\(775\) −13.8409 7.99105i −0.497180 0.287047i
\(776\) 14.0195 0.503271
\(777\) −0.0651235 0.927146i −0.00233629 0.0332612i
\(778\) −15.6329 −0.560468
\(779\) 2.93903 + 1.69685i 0.105302 + 0.0607960i
\(780\) 0.292836 0.228411i 0.0104852 0.00817842i
\(781\) −5.50245 9.53053i −0.196893 0.341029i
\(782\) 3.62147 6.27258i 0.129504 0.224307i
\(783\) 17.0812 + 38.6149i 0.610432 + 1.37998i
\(784\) −19.8510 + 25.5253i −0.708965 + 0.911616i
\(785\) 29.5048i 1.05307i
\(786\) −15.5654 6.30337i −0.555200 0.224834i
\(787\) 10.5537 6.09321i 0.376201 0.217199i −0.299963 0.953951i \(-0.596974\pi\)
0.676164 + 0.736751i \(0.263641\pi\)
\(788\) 0.568975 0.328498i 0.0202689 0.0117022i
\(789\) −28.7245 11.6323i −1.02262 0.414120i
\(790\) 7.34562i 0.261346i
\(791\) −16.1069 1.10826i −0.572696 0.0394053i
\(792\) −7.20148 + 2.05249i −0.255894 + 0.0729322i
\(793\) −0.309552 + 0.536160i −0.0109925 + 0.0190396i
\(794\) 4.48231 + 7.76359i 0.159071 + 0.275520i
\(795\) 19.2794 15.0378i 0.683769 0.533336i
\(796\) 4.86607 + 2.80942i 0.172473 + 0.0995774i
\(797\) 49.0317 1.73679 0.868397 0.495870i \(-0.165151\pi\)
0.868397 + 0.495870i \(0.165151\pi\)
\(798\) 19.4157 + 9.46214i 0.687307 + 0.334956i
\(799\) −25.5553 −0.904080
\(800\) 3.32465 + 1.91949i 0.117544 + 0.0678641i
\(801\) 18.5223 + 17.9443i 0.654455 + 0.634032i
\(802\) 10.6642 + 18.4709i 0.376565 + 0.652230i
\(803\) 4.65466 8.06212i 0.164260 0.284506i
\(804\) −7.88609 + 1.10187i −0.278121 + 0.0388598i
\(805\) 2.42175 + 4.95131i 0.0853555 + 0.174511i
\(806\) 4.29766i 0.151379i
\(807\) 6.70261 16.5513i 0.235943 0.582633i
\(808\) 24.8196 14.3296i 0.873151 0.504114i
\(809\) −12.8480 + 7.41778i −0.451711 + 0.260795i −0.708553 0.705658i \(-0.750651\pi\)
0.256842 + 0.966454i \(0.417318\pi\)
\(810\) −24.8609 + 0.788293i −0.873522 + 0.0276978i
\(811\) 24.0392i 0.844129i 0.906566 + 0.422065i \(0.138694\pi\)
−0.906566 + 0.422065i \(0.861306\pi\)
\(812\) 3.61857 + 7.39823i 0.126987 + 0.259627i
\(813\) 3.52010 + 25.1935i 0.123455 + 0.883574i
\(814\) 0.156547 0.271148i 0.00548698 0.00950373i
\(815\) −21.3677 37.0099i −0.748478 1.29640i
\(816\) −19.8411 25.4374i −0.694576 0.890489i
\(817\) −26.1253 15.0835i −0.914009 0.527704i
\(818\) 10.7920 0.377333
\(819\) −0.768010 + 2.35976i −0.0268364 + 0.0824566i
\(820\) −0.762300 −0.0266207
\(821\) 20.3571 + 11.7532i 0.710466 + 0.410188i 0.811234 0.584722i \(-0.198796\pi\)
−0.100767 + 0.994910i \(0.532130\pi\)
\(822\) −18.4633 23.6711i −0.643983 0.825625i
\(823\) −1.08860 1.88551i −0.0379461 0.0657246i 0.846429 0.532502i \(-0.178748\pi\)
−0.884375 + 0.466778i \(0.845415\pi\)
\(824\) −4.83254 + 8.37021i −0.168350 + 0.291590i
\(825\) −0.430189 3.07887i −0.0149773 0.107193i
\(826\) −39.1511 2.69386i −1.36224 0.0937312i
\(827\) 35.0853i 1.22003i 0.792388 + 0.610017i \(0.208838\pi\)
−0.792388 + 0.610017i \(0.791162\pi\)
\(828\) −1.29703 0.325598i −0.0450750 0.0113153i
\(829\) 19.1964 11.0831i 0.666719 0.384931i −0.128113 0.991760i \(-0.540892\pi\)
0.794832 + 0.606829i \(0.207559\pi\)
\(830\) −30.1453 + 17.4044i −1.04636 + 0.604115i
\(831\) −6.36844 + 15.7261i −0.220919 + 0.545532i
\(832\) 1.85620i 0.0643522i
\(833\) 10.6313 + 26.1454i 0.368352 + 0.905884i
\(834\) 51.9880 7.26391i 1.80020 0.251529i
\(835\) 16.9837 29.4166i 0.587744 1.01800i
\(836\) 0.584783 + 1.01287i 0.0202251 + 0.0350309i
\(837\) 27.2860 37.3665i 0.943142 1.29157i
\(838\) −54.4808 31.4545i −1.88201 1.08658i
\(839\) 40.1944 1.38767 0.693833 0.720136i \(-0.255921\pi\)
0.693833 + 0.720136i \(0.255921\pi\)
\(840\) 20.4279 1.43488i 0.704831 0.0495079i
\(841\) −37.0324 −1.27698
\(842\) 52.7143 + 30.4346i 1.81666 + 1.04885i
\(843\) 20.3795 15.8959i 0.701908 0.547484i
\(844\) −3.27981 5.68080i −0.112896 0.195541i
\(845\) 11.5494 20.0041i 0.397311 0.688163i
\(846\) 8.04538 + 28.2284i 0.276606 + 0.970514i
\(847\) 2.19508 + 1.47704i 0.0754237 + 0.0507517i
\(848\) 36.4242i 1.25081i
\(849\) 40.9262 + 16.5734i 1.40458 + 0.568799i
\(850\) 9.67503 5.58588i 0.331851 0.191594i
\(851\) −0.204391 + 0.118005i −0.00700643 + 0.00404516i
\(852\) −6.76781 2.74069i −0.231861 0.0938946i
\(853\) 8.08491i 0.276822i 0.990375 + 0.138411i \(0.0441995\pi\)
−0.990375 + 0.138411i \(0.955800\pi\)
\(854\) 7.26515 3.55348i 0.248608 0.121598i
\(855\) −4.49462 15.7701i −0.153713 0.539325i
\(856\) −8.31865 + 14.4083i −0.284326 + 0.492466i
\(857\) −25.0629 43.4103i −0.856134 1.48287i −0.875589 0.483057i \(-0.839526\pi\)
0.0194549 0.999811i \(-0.493807\pi\)
\(858\) −0.659163 + 0.514144i −0.0225035 + 0.0175526i
\(859\) 6.95960 + 4.01813i 0.237459 + 0.137097i 0.614008 0.789300i \(-0.289556\pi\)
−0.376550 + 0.926396i \(0.622890\pi\)
\(860\) 6.77615 0.231065
\(861\) 4.22200 2.84969i 0.143885 0.0971173i
\(862\) 10.9996 0.374649
\(863\) −38.9633 22.4955i −1.32633 0.765755i −0.341597 0.939847i \(-0.610968\pi\)
−0.984729 + 0.174092i \(0.944301\pi\)
\(864\) −6.55421 + 8.97559i −0.222979 + 0.305356i
\(865\) −3.45063 5.97667i −0.117325 0.203213i
\(866\) 1.32042 2.28703i 0.0448696 0.0777163i
\(867\) 1.27411 0.178022i 0.0432709 0.00604593i
\(868\) 5.03817 7.48738i 0.171007 0.254138i
\(869\) 2.65789i 0.0901627i
\(870\) 14.6005 36.0542i 0.495004 1.22235i
\(871\) 3.24948 1.87609i 0.110104 0.0635688i
\(872\) 25.1701 14.5320i 0.852367 0.492114i
\(873\) −16.3427 4.10256i −0.553117 0.138851i
\(874\) 5.48453i 0.185517i
\(875\) −2.20932 + 32.1090i −0.0746885 + 1.08548i
\(876\) −0.854721 6.11726i −0.0288784 0.206683i
\(877\) 18.1552 31.4456i 0.613056 1.06184i −0.377666 0.925942i \(-0.623273\pi\)
0.990722 0.135902i \(-0.0433933\pi\)
\(878\) −12.3950 21.4687i −0.418310 0.724534i
\(879\) −3.81393 4.88968i −0.128641 0.164925i
\(880\) 7.16209 + 4.13503i 0.241434 + 0.139392i
\(881\) 51.6009 1.73848 0.869240 0.494391i \(-0.164609\pi\)
0.869240 + 0.494391i \(0.164609\pi\)
\(882\) 25.5333 19.9745i 0.859752 0.672578i
\(883\) −46.1132 −1.55183 −0.775916 0.630836i \(-0.782712\pi\)
−0.775916 + 0.630836i \(0.782712\pi\)
\(884\) −0.418206 0.241452i −0.0140658 0.00812090i
\(885\) 18.3245 + 23.4931i 0.615971 + 0.789712i
\(886\) 19.6953 + 34.1132i 0.661676 + 1.14606i
\(887\) −15.9647 + 27.6517i −0.536042 + 0.928452i 0.463070 + 0.886322i \(0.346748\pi\)
−0.999112 + 0.0421303i \(0.986586\pi\)
\(888\) 0.121338 + 0.868419i 0.00407183 + 0.0291422i
\(889\) −0.639010 + 9.28703i −0.0214317 + 0.311477i
\(890\) 23.7578i 0.796364i
\(891\) 8.99548 0.285230i 0.301360 0.00955557i
\(892\) 1.94050 1.12035i 0.0649729 0.0375121i
\(893\) −16.7585 + 9.67553i −0.560802 + 0.323779i
\(894\) 3.85657 9.52335i 0.128983 0.318509i
\(895\) 0.542805i 0.0181440i
\(896\) 19.8555 29.5079i 0.663325 0.985789i
\(897\) 0.624088 0.0871993i 0.0208377 0.00291150i
\(898\) 21.1299 36.5981i 0.705115 1.22129i
\(899\) 36.1787 + 62.6633i 1.20663 + 2.08994i
\(900\) −1.48145 1.43522i −0.0493817 0.0478408i
\(901\) −27.5333 15.8964i −0.917268 0.529585i
\(902\) 1.71591 0.0571335
\(903\) −37.5297 + 25.3312i −1.24891 + 0.842969i
\(904\) 15.2317 0.506600
\(905\) −21.1529 12.2126i −0.703146 0.405961i
\(906\) −38.5826 + 30.0942i −1.28182 + 0.999813i
\(907\) −6.26921 10.8586i −0.208166 0.360554i 0.742971 0.669324i \(-0.233416\pi\)
−0.951137 + 0.308770i \(0.900083\pi\)
\(908\) 4.31617 7.47583i 0.143237 0.248094i
\(909\) −33.1258 + 9.44118i −1.09871 + 0.313144i
\(910\) 2.05364 1.00446i 0.0680776 0.0332977i
\(911\) 8.83725i 0.292791i −0.989226 0.146396i \(-0.953233\pi\)
0.989226 0.146396i \(-0.0467672\pi\)
\(912\) −22.6422 9.16918i −0.749758 0.303622i
\(913\) 10.9076 6.29748i 0.360987 0.208416i
\(914\) −15.0865 + 8.71021i −0.499018 + 0.288108i
\(915\) −5.69132 2.30475i −0.188149 0.0761928i
\(916\) 10.6932i 0.353313i
\(917\) −13.7866 9.27682i −0.455273 0.306348i
\(918\) 13.0837 + 29.5779i 0.431828 + 0.976217i
\(919\) −13.3221 + 23.0745i −0.439455 + 0.761158i −0.997647 0.0685537i \(-0.978162\pi\)
0.558193 + 0.829711i \(0.311495\pi\)
\(920\) −2.60002 4.50337i −0.0857202 0.148472i
\(921\) −34.4373 + 26.8609i −1.13475 + 0.885098i
\(922\) −24.8242 14.3323i −0.817541 0.472008i
\(923\) 3.44070 0.113252
\(924\) 1.75113 0.123001i 0.0576078 0.00404642i
\(925\) −0.364030 −0.0119692
\(926\) −39.1735 22.6168i −1.28732 0.743234i
\(927\) 8.08274 8.34309i 0.265472 0.274023i
\(928\) −8.69028 15.0520i −0.285272 0.494106i
\(929\) 3.19802 5.53914i 0.104924 0.181733i −0.808783 0.588107i \(-0.799873\pi\)
0.913707 + 0.406373i \(0.133207\pi\)
\(930\) −42.2142 + 5.89828i −1.38426 + 0.193412i
\(931\) 16.8707 + 13.1204i 0.552915 + 0.430002i
\(932\) 9.79947i 0.320992i
\(933\) −3.33276 + 8.22986i −0.109110 + 0.269433i
\(934\) −43.6829 + 25.2203i −1.42935 + 0.825235i
\(935\) 6.25141 3.60925i 0.204443 0.118035i
\(936\) 0.570035 2.27076i 0.0186322 0.0742221i
\(937\) 22.1666i 0.724153i −0.932148 0.362076i \(-0.882068\pi\)
0.932148 0.362076i \(-0.117932\pi\)
\(938\) −48.9007 3.36469i −1.59666 0.109861i
\(939\) 1.71056 + 12.2425i 0.0558220 + 0.399520i
\(940\) 2.17334 3.76433i 0.0708864 0.122779i
\(941\) −4.80357 8.32003i −0.156592 0.271225i 0.777046 0.629444i \(-0.216717\pi\)
−0.933638 + 0.358219i \(0.883384\pi\)
\(942\) −27.1015 34.7457i −0.883014 1.13208i
\(943\) −1.12016 0.646724i −0.0364774 0.0210602i
\(944\) 44.3851 1.44461
\(945\) −24.2330 4.30522i −0.788299 0.140049i
\(946\) −15.2529 −0.495913
\(947\) 52.1892 + 30.1315i 1.69592 + 0.979141i 0.949552 + 0.313609i \(0.101538\pi\)
0.746370 + 0.665532i \(0.231795\pi\)
\(948\) 1.08460 + 1.39052i 0.0352262 + 0.0451621i
\(949\) 1.45529 + 2.52063i 0.0472406 + 0.0818231i
\(950\) 4.22976 7.32616i 0.137232 0.237692i
\(951\) −2.72541 19.5058i −0.0883773 0.632519i
\(952\) −11.6995 23.9197i −0.379182 0.775243i
\(953\) 26.7268i 0.865766i −0.901450 0.432883i \(-0.857496\pi\)
0.901450 0.432883i \(-0.142504\pi\)
\(954\) −8.89108 + 35.4180i −0.287859 + 1.14670i
\(955\) 17.3655 10.0260i 0.561934 0.324433i
\(956\) 6.26498 3.61709i 0.202624 0.116985i
\(957\) −5.28294 + 13.0456i −0.170773 + 0.421704i
\(958\) 1.57253i 0.0508061i
\(959\) −13.0517 26.6845i −0.421462 0.861686i
\(960\) −18.2327 + 2.54752i −0.588458 + 0.0822210i
\(961\) 24.1441 41.8187i 0.778840 1.34899i
\(962\) 0.0489447 + 0.0847747i 0.00157804 + 0.00273325i
\(963\) 13.9135 14.3616i 0.448356 0.462798i
\(964\) −3.62773 2.09447i −0.116841 0.0674583i
\(965\) −39.2875 −1.26471
\(966\) −7.39993 3.60633i −0.238089 0.116032i
\(967\) −28.3729 −0.912411 −0.456206 0.889874i \(-0.650792\pi\)
−0.456206 + 0.889874i \(0.650792\pi\)
\(968\) −2.16168 1.24804i −0.0694789 0.0401137i
\(969\) −16.8127 + 13.1138i −0.540100 + 0.421275i
\(970\) 7.76131 + 13.4430i 0.249201 + 0.431628i
\(971\) 25.4870 44.1447i 0.817916 1.41667i −0.0892993 0.996005i \(-0.528463\pi\)
0.907215 0.420667i \(-0.138204\pi\)
\(972\) 4.58975 3.81999i 0.147216 0.122526i
\(973\) 51.8199 + 3.56555i 1.66127 + 0.114306i
\(974\) 62.4015i 1.99947i
\(975\) 0.900898 + 0.364827i 0.0288518 + 0.0116838i
\(976\) −7.92172 + 4.57360i −0.253568 + 0.146398i
\(977\) −5.52362 + 3.18906i −0.176716 + 0.102027i −0.585749 0.810493i \(-0.699200\pi\)
0.409033 + 0.912520i \(0.365866\pi\)
\(978\) 59.1586 + 23.9568i 1.89168 + 0.766055i
\(979\) 8.59636i 0.274741i
\(980\) −4.75539 0.657518i −0.151905 0.0210036i
\(981\) −33.5936 + 9.57450i −1.07256 + 0.305690i
\(982\) 0.0258522 0.0447774i 0.000824978 0.00142890i
\(983\) 20.2941 + 35.1504i 0.647281 + 1.12112i 0.983770 + 0.179436i \(0.0574273\pi\)
−0.336489 + 0.941688i \(0.609239\pi\)
\(984\) −3.78923 + 2.95557i −0.120796 + 0.0942203i
\(985\) −2.65913 1.53525i −0.0847270 0.0489172i
\(986\) −50.5790 −1.61076
\(987\) 2.03511 + 28.9733i 0.0647782 + 0.922229i
\(988\) −0.365666 −0.0116334
\(989\) 9.95720 + 5.74879i 0.316621 + 0.182801i
\(990\) −5.95488 5.76906i −0.189259 0.183353i
\(991\) 5.88123 + 10.1866i 0.186823 + 0.323588i 0.944189 0.329403i \(-0.106847\pi\)
−0.757366 + 0.652991i \(0.773514\pi\)
\(992\) −9.52268 + 16.4938i −0.302345 + 0.523677i
\(993\) −34.2811 + 4.78985i −1.08788 + 0.152001i
\(994\) −37.2910 25.0927i −1.18280 0.795891i
\(995\) 26.2600i 0.832498i
\(996\) 3.13668 7.74567i 0.0993896 0.245431i
\(997\) −18.7096 + 10.8020i −0.592539 + 0.342103i −0.766101 0.642720i \(-0.777806\pi\)
0.173562 + 0.984823i \(0.444472\pi\)
\(998\) 7.26340 4.19352i 0.229919 0.132744i
\(999\) 0.112682 1.04783i 0.00356511 0.0331520i
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 231.2.n.a.89.20 yes 52
3.2 odd 2 inner 231.2.n.a.89.7 52
7.3 odd 6 inner 231.2.n.a.122.7 yes 52
21.17 even 6 inner 231.2.n.a.122.20 yes 52
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
231.2.n.a.89.7 52 3.2 odd 2 inner
231.2.n.a.89.20 yes 52 1.1 even 1 trivial
231.2.n.a.122.7 yes 52 7.3 odd 6 inner
231.2.n.a.122.20 yes 52 21.17 even 6 inner