Properties

Label 165.2.p.b.101.2
Level $165$
Weight $2$
Character 165.101
Analytic conductor $1.318$
Analytic rank $0$
Dimension $48$
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] = [165,2,Mod(41,165)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(165, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([5, 0, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("165.41");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 165 = 3 \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 165.p (of order \(10\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(1.31753163335\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(12\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 101.2
Character \(\chi\) \(=\) 165.101
Dual form 165.2.p.b.116.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.664086 + 2.04385i) q^{2} +(1.72041 + 0.200478i) q^{3} +(-2.11826 - 1.53901i) q^{4} +(0.951057 - 0.309017i) q^{5} +(-1.55225 + 3.38312i) q^{6} +(-1.16392 + 1.60200i) q^{7} +(1.07501 - 0.781038i) q^{8} +(2.91962 + 0.689809i) q^{9} +O(q^{10})\) \(q+(-0.664086 + 2.04385i) q^{2} +(1.72041 + 0.200478i) q^{3} +(-2.11826 - 1.53901i) q^{4} +(0.951057 - 0.309017i) q^{5} +(-1.55225 + 3.38312i) q^{6} +(-1.16392 + 1.60200i) q^{7} +(1.07501 - 0.781038i) q^{8} +(2.91962 + 0.689809i) q^{9} +2.14903i q^{10} +(-3.11285 + 1.14463i) q^{11} +(-3.33574 - 3.07239i) q^{12} +(5.55519 + 1.80499i) q^{13} +(-2.50130 - 3.44275i) q^{14} +(1.69816 - 0.340970i) q^{15} +(-0.735784 - 2.26451i) q^{16} +(-0.00961787 - 0.0296008i) q^{17} +(-3.34874 + 5.50916i) q^{18} +(-3.10262 - 4.27039i) q^{19} +(-2.49017 - 0.809105i) q^{20} +(-2.32359 + 2.52276i) q^{21} +(-0.272240 - 7.12232i) q^{22} -8.23244i q^{23} +(2.00603 - 1.12819i) q^{24} +(0.809017 - 0.587785i) q^{25} +(-7.37825 + 10.1553i) q^{26} +(4.88464 + 1.77207i) q^{27} +(4.93099 - 1.60218i) q^{28} +(-0.972361 - 0.706461i) q^{29} +(-0.430833 + 3.69721i) q^{30} +(0.153421 - 0.472180i) q^{31} +7.77450 q^{32} +(-5.58485 + 1.34517i) q^{33} +0.0668865 q^{34} +(-0.611911 + 1.88327i) q^{35} +(-5.12290 - 5.95451i) q^{36} +(2.98318 + 2.16741i) q^{37} +(10.7884 - 3.50537i) q^{38} +(9.19534 + 4.21902i) q^{39} +(0.781038 - 1.07501i) q^{40} +(2.54451 - 1.84869i) q^{41} +(-3.61307 - 6.42440i) q^{42} -2.79044i q^{43} +(8.35542 + 2.36608i) q^{44} +(2.98988 - 0.246164i) q^{45} +(16.8258 + 5.46705i) q^{46} +(0.700301 + 0.963882i) q^{47} +(-0.811865 - 4.04340i) q^{48} +(0.951421 + 2.92817i) q^{49} +(0.664086 + 2.04385i) q^{50} +(-0.0106124 - 0.0528536i) q^{51} +(-8.98946 - 12.3729i) q^{52} +(-9.74834 - 3.16743i) q^{53} +(-6.86567 + 8.80665i) q^{54} +(-2.60679 + 2.05053i) q^{55} +2.63123i q^{56} +(-4.48166 - 7.96883i) q^{57} +(2.08963 - 1.51820i) q^{58} +(1.78927 - 2.46272i) q^{59} +(-4.12190 - 1.89122i) q^{60} +(-8.33893 + 2.70948i) q^{61} +(0.863180 + 0.627137i) q^{62} +(-4.50329 + 3.87435i) q^{63} +(-3.69137 + 11.3609i) q^{64} +5.84107 q^{65} +(0.959505 - 12.3079i) q^{66} +6.68562 q^{67} +(-0.0251826 + 0.0775042i) q^{68} +(1.65042 - 14.1632i) q^{69} +(-3.44275 - 2.50130i) q^{70} +(-0.561251 + 0.182361i) q^{71} +(3.67737 - 1.53878i) q^{72} +(-2.63362 + 3.62486i) q^{73} +(-6.41094 + 4.65782i) q^{74} +(1.50968 - 0.849041i) q^{75} +13.8208i q^{76} +(1.78943 - 6.31905i) q^{77} +(-14.7295 + 15.9921i) q^{78} +(-16.4103 - 5.33204i) q^{79} +(-1.39955 - 1.92631i) q^{80} +(8.04833 + 4.02796i) q^{81} +(2.08867 + 6.42827i) q^{82} +(3.17214 + 9.76284i) q^{83} +(8.80453 - 1.76784i) q^{84} +(-0.0182943 - 0.0251799i) q^{85} +(5.70322 + 1.85309i) q^{86} +(-1.53123 - 1.41034i) q^{87} +(-2.45234 + 3.66173i) q^{88} -1.78657i q^{89} +(-1.48242 + 6.27434i) q^{90} +(-9.35742 + 6.79857i) q^{91} +(-12.6698 + 17.4385i) q^{92} +(0.358608 - 0.781586i) q^{93} +(-2.43509 + 0.791207i) q^{94} +(-4.27039 - 3.10262i) q^{95} +(13.3753 + 1.55862i) q^{96} +(-5.65837 + 17.4147i) q^{97} -6.61656 q^{98} +(-9.87790 + 1.19460i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q - 4 q^{3} - 4 q^{4} - 20 q^{6} + 10 q^{7} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 48 q - 4 q^{3} - 4 q^{4} - 20 q^{6} + 10 q^{7} + 2 q^{9} + 8 q^{12} + 6 q^{15} + 32 q^{16} - 30 q^{18} - 100 q^{19} - 82 q^{22} + 100 q^{24} + 12 q^{25} + 14 q^{27} + 30 q^{28} + 10 q^{30} + 10 q^{31} - 46 q^{33} - 28 q^{34} + 14 q^{36} + 6 q^{37} - 50 q^{40} - 52 q^{42} + 32 q^{45} + 20 q^{46} - 80 q^{48} - 26 q^{49} - 30 q^{51} + 40 q^{52} + 6 q^{55} - 70 q^{57} + 92 q^{58} + 44 q^{60} + 70 q^{61} - 20 q^{63} + 18 q^{64} + 76 q^{66} + 20 q^{67} + 42 q^{69} - 4 q^{70} - 80 q^{72} + 90 q^{73} - 6 q^{75} - 108 q^{78} - 100 q^{79} + 38 q^{81} - 34 q^{82} + 70 q^{84} + 20 q^{85} + 74 q^{88} + 20 q^{90} - 86 q^{91} + 76 q^{93} + 10 q^{94} - 30 q^{96} + 6 q^{97} - 28 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/165\mathbb{Z}\right)^\times\).

\(n\) \(46\) \(56\) \(67\)
\(\chi(n)\) \(e\left(\frac{1}{10}\right)\) \(-1\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.664086 + 2.04385i −0.469580 + 1.44522i 0.383551 + 0.923520i \(0.374701\pi\)
−0.853130 + 0.521698i \(0.825299\pi\)
\(3\) 1.72041 + 0.200478i 0.993279 + 0.115746i
\(4\) −2.11826 1.53901i −1.05913 0.769504i
\(5\) 0.951057 0.309017i 0.425325 0.138197i
\(6\) −1.55225 + 3.38312i −0.633702 + 1.38115i
\(7\) −1.16392 + 1.60200i −0.439922 + 0.605501i −0.970195 0.242326i \(-0.922089\pi\)
0.530273 + 0.847827i \(0.322089\pi\)
\(8\) 1.07501 0.781038i 0.380072 0.276139i
\(9\) 2.91962 + 0.689809i 0.973206 + 0.229936i
\(10\) 2.14903i 0.679582i
\(11\) −3.11285 + 1.14463i −0.938559 + 0.345118i
\(12\) −3.33574 3.07239i −0.962946 0.886923i
\(13\) 5.55519 + 1.80499i 1.54073 + 0.500614i 0.951578 0.307406i \(-0.0994609\pi\)
0.589155 + 0.808020i \(0.299461\pi\)
\(14\) −2.50130 3.44275i −0.668502 0.920114i
\(15\) 1.69816 0.340970i 0.438462 0.0880380i
\(16\) −0.735784 2.26451i −0.183946 0.566128i
\(17\) −0.00961787 0.0296008i −0.00233268 0.00717924i 0.949883 0.312604i \(-0.101201\pi\)
−0.952216 + 0.305425i \(0.901201\pi\)
\(18\) −3.34874 + 5.50916i −0.789306 + 1.29852i
\(19\) −3.10262 4.27039i −0.711790 0.979695i −0.999757 0.0220545i \(-0.992979\pi\)
0.287967 0.957640i \(-0.407021\pi\)
\(20\) −2.49017 0.809105i −0.556818 0.180921i
\(21\) −2.32359 + 2.52276i −0.507049 + 0.550512i
\(22\) −0.272240 7.12232i −0.0580417 1.51848i
\(23\) 8.23244i 1.71658i −0.513163 0.858291i \(-0.671526\pi\)
0.513163 0.858291i \(-0.328474\pi\)
\(24\) 2.00603 1.12819i 0.409480 0.230291i
\(25\) 0.809017 0.587785i 0.161803 0.117557i
\(26\) −7.37825 + 10.1553i −1.44699 + 1.99162i
\(27\) 4.88464 + 1.77207i 0.940050 + 0.341036i
\(28\) 4.93099 1.60218i 0.931870 0.302783i
\(29\) −0.972361 0.706461i −0.180563 0.131187i 0.493832 0.869557i \(-0.335596\pi\)
−0.674395 + 0.738370i \(0.735596\pi\)
\(30\) −0.430833 + 3.69721i −0.0786590 + 0.675014i
\(31\) 0.153421 0.472180i 0.0275552 0.0848061i −0.936333 0.351113i \(-0.885803\pi\)
0.963888 + 0.266307i \(0.0858034\pi\)
\(32\) 7.77450 1.37435
\(33\) −5.58485 + 1.34517i −0.972197 + 0.234163i
\(34\) 0.0668865 0.0114709
\(35\) −0.611911 + 1.88327i −0.103432 + 0.318330i
\(36\) −5.12290 5.95451i −0.853816 0.992419i
\(37\) 2.98318 + 2.16741i 0.490432 + 0.356320i 0.805350 0.592799i \(-0.201977\pi\)
−0.314918 + 0.949119i \(0.601977\pi\)
\(38\) 10.7884 3.50537i 1.75011 0.568647i
\(39\) 9.19534 + 4.21902i 1.47243 + 0.675584i
\(40\) 0.781038 1.07501i 0.123493 0.169973i
\(41\) 2.54451 1.84869i 0.397385 0.288717i −0.371090 0.928597i \(-0.621016\pi\)
0.768475 + 0.639880i \(0.221016\pi\)
\(42\) −3.61307 6.42440i −0.557509 0.991306i
\(43\) 2.79044i 0.425538i −0.977103 0.212769i \(-0.931752\pi\)
0.977103 0.212769i \(-0.0682481\pi\)
\(44\) 8.35542 + 2.36608i 1.25963 + 0.356700i
\(45\) 2.98988 0.246164i 0.445706 0.0366959i
\(46\) 16.8258 + 5.46705i 2.48083 + 0.806072i
\(47\) 0.700301 + 0.963882i 0.102149 + 0.140597i 0.857032 0.515264i \(-0.172306\pi\)
−0.754882 + 0.655860i \(0.772306\pi\)
\(48\) −0.811865 4.04340i −0.117183 0.583614i
\(49\) 0.951421 + 2.92817i 0.135917 + 0.418311i
\(50\) 0.664086 + 2.04385i 0.0939159 + 0.289044i
\(51\) −0.0106124 0.0528536i −0.00148603 0.00740099i
\(52\) −8.98946 12.3729i −1.24661 1.71582i
\(53\) −9.74834 3.16743i −1.33904 0.435080i −0.450047 0.893005i \(-0.648593\pi\)
−0.888991 + 0.457925i \(0.848593\pi\)
\(54\) −6.86567 + 8.80665i −0.934299 + 1.19843i
\(55\) −2.60679 + 2.05053i −0.351499 + 0.276493i
\(56\) 2.63123i 0.351613i
\(57\) −4.48166 7.96883i −0.593610 1.05550i
\(58\) 2.08963 1.51820i 0.274382 0.199350i
\(59\) 1.78927 2.46272i 0.232943 0.320619i −0.676503 0.736439i \(-0.736506\pi\)
0.909447 + 0.415821i \(0.136506\pi\)
\(60\) −4.12190 1.89122i −0.532135 0.244155i
\(61\) −8.33893 + 2.70948i −1.06769 + 0.346914i −0.789588 0.613638i \(-0.789706\pi\)
−0.278103 + 0.960551i \(0.589706\pi\)
\(62\) 0.863180 + 0.627137i 0.109624 + 0.0796464i
\(63\) −4.50329 + 3.87435i −0.567361 + 0.488123i
\(64\) −3.69137 + 11.3609i −0.461421 + 1.42011i
\(65\) 5.84107 0.724496
\(66\) 0.959505 12.3079i 0.118107 1.51499i
\(67\) 6.68562 0.816779 0.408389 0.912808i \(-0.366091\pi\)
0.408389 + 0.912808i \(0.366091\pi\)
\(68\) −0.0251826 + 0.0775042i −0.00305384 + 0.00939877i
\(69\) 1.65042 14.1632i 0.198688 1.70504i
\(70\) −3.44275 2.50130i −0.411487 0.298963i
\(71\) −0.561251 + 0.182361i −0.0666082 + 0.0216423i −0.342132 0.939652i \(-0.611149\pi\)
0.275523 + 0.961294i \(0.411149\pi\)
\(72\) 3.67737 1.53878i 0.433383 0.181347i
\(73\) −2.63362 + 3.62486i −0.308242 + 0.424258i −0.934832 0.355091i \(-0.884450\pi\)
0.626590 + 0.779349i \(0.284450\pi\)
\(74\) −6.41094 + 4.65782i −0.745257 + 0.541461i
\(75\) 1.50968 0.849041i 0.174323 0.0980388i
\(76\) 13.8208i 1.58535i
\(77\) 1.78943 6.31905i 0.203924 0.720123i
\(78\) −14.7295 + 15.9921i −1.66779 + 1.81075i
\(79\) −16.4103 5.33204i −1.84631 0.599902i −0.997457 0.0712699i \(-0.977295\pi\)
−0.848851 0.528632i \(-0.822705\pi\)
\(80\) −1.39955 1.92631i −0.156474 0.215368i
\(81\) 8.04833 + 4.02796i 0.894259 + 0.447551i
\(82\) 2.08867 + 6.42827i 0.230655 + 0.709884i
\(83\) 3.17214 + 9.76284i 0.348188 + 1.07161i 0.959855 + 0.280496i \(0.0904991\pi\)
−0.611667 + 0.791115i \(0.709501\pi\)
\(84\) 8.80453 1.76784i 0.960653 0.192888i
\(85\) −0.0182943 0.0251799i −0.00198429 0.00273115i
\(86\) 5.70322 + 1.85309i 0.614994 + 0.199824i
\(87\) −1.53123 1.41034i −0.164165 0.151204i
\(88\) −2.45234 + 3.66173i −0.261420 + 0.390342i
\(89\) 1.78657i 0.189376i −0.995507 0.0946882i \(-0.969815\pi\)
0.995507 0.0946882i \(-0.0301854\pi\)
\(90\) −1.48242 + 6.27434i −0.156261 + 0.661373i
\(91\) −9.35742 + 6.79857i −0.980925 + 0.712683i
\(92\) −12.6698 + 17.4385i −1.32092 + 1.81809i
\(93\) 0.358608 0.781586i 0.0371860 0.0810467i
\(94\) −2.43509 + 0.791207i −0.251160 + 0.0816068i
\(95\) −4.27039 3.10262i −0.438133 0.318322i
\(96\) 13.3753 + 1.55862i 1.36511 + 0.159076i
\(97\) −5.65837 + 17.4147i −0.574521 + 1.76819i 0.0632844 + 0.997996i \(0.479842\pi\)
−0.637805 + 0.770198i \(0.720158\pi\)
\(98\) −6.61656 −0.668374
\(99\) −9.87790 + 1.19460i −0.992766 + 0.120062i
\(100\) −2.61832 −0.261832
\(101\) 1.22660 3.77507i 0.122051 0.375634i −0.871301 0.490748i \(-0.836723\pi\)
0.993352 + 0.115114i \(0.0367235\pi\)
\(102\) 0.115072 + 0.0134093i 0.0113938 + 0.00132772i
\(103\) −12.5457 9.11498i −1.23616 0.898126i −0.238828 0.971062i \(-0.576763\pi\)
−0.997337 + 0.0729362i \(0.976763\pi\)
\(104\) 7.38163 2.39844i 0.723829 0.235186i
\(105\) −1.43029 + 3.11732i −0.139582 + 0.304219i
\(106\) 12.9475 17.8207i 1.25757 1.73090i
\(107\) 3.78361 2.74896i 0.365776 0.265752i −0.389681 0.920950i \(-0.627415\pi\)
0.755457 + 0.655198i \(0.227415\pi\)
\(108\) −7.61973 11.2712i −0.733209 1.08457i
\(109\) 8.55279i 0.819208i −0.912263 0.409604i \(-0.865667\pi\)
0.912263 0.409604i \(-0.134333\pi\)
\(110\) −2.45983 6.68960i −0.234536 0.637828i
\(111\) 4.69778 + 4.32689i 0.445893 + 0.410691i
\(112\) 4.48415 + 1.45699i 0.423713 + 0.137673i
\(113\) 6.87503 + 9.46267i 0.646748 + 0.890173i 0.998953 0.0457503i \(-0.0145679\pi\)
−0.352205 + 0.935923i \(0.614568\pi\)
\(114\) 19.2633 3.86783i 1.80417 0.362256i
\(115\) −2.54396 7.82951i −0.237226 0.730106i
\(116\) 0.972466 + 2.99294i 0.0902912 + 0.277888i
\(117\) 14.9739 + 9.10190i 1.38434 + 0.841471i
\(118\) 3.84519 + 5.29245i 0.353979 + 0.487210i
\(119\) 0.0586150 + 0.0190452i 0.00537323 + 0.00174587i
\(120\) 1.55922 1.69287i 0.142337 0.154537i
\(121\) 8.37966 7.12610i 0.761788 0.647827i
\(122\) 18.8428i 1.70595i
\(123\) 4.74821 2.67039i 0.428132 0.240781i
\(124\) −1.05168 + 0.764087i −0.0944432 + 0.0686170i
\(125\) 0.587785 0.809017i 0.0525731 0.0723607i
\(126\) −4.92801 11.7769i −0.439022 1.04917i
\(127\) 14.7022 4.77705i 1.30461 0.423894i 0.427429 0.904049i \(-0.359420\pi\)
0.877184 + 0.480155i \(0.159420\pi\)
\(128\) −8.18906 5.94970i −0.723817 0.525884i
\(129\) 0.559422 4.80069i 0.0492543 0.422678i
\(130\) −3.87898 + 11.9383i −0.340209 + 1.04705i
\(131\) −11.6784 −1.02035 −0.510175 0.860070i \(-0.670420\pi\)
−0.510175 + 0.860070i \(0.670420\pi\)
\(132\) 13.9004 + 5.74571i 1.20987 + 0.500100i
\(133\) 10.4524 0.906338
\(134\) −4.43983 + 13.6644i −0.383543 + 1.18042i
\(135\) 5.19317 + 0.175904i 0.446957 + 0.0151394i
\(136\) −0.0334586 0.0243091i −0.00286905 0.00208449i
\(137\) −3.41003 + 1.10798i −0.291338 + 0.0946615i −0.451040 0.892504i \(-0.648947\pi\)
0.159702 + 0.987165i \(0.448947\pi\)
\(138\) 27.8513 + 12.7788i 2.37086 + 1.08780i
\(139\) 2.96853 4.08583i 0.251787 0.346555i −0.664349 0.747422i \(-0.731291\pi\)
0.916136 + 0.400867i \(0.131291\pi\)
\(140\) 4.19455 3.04752i 0.354505 0.257563i
\(141\) 1.01157 + 1.79867i 0.0851893 + 0.151475i
\(142\) 1.26821i 0.106426i
\(143\) −19.3585 + 0.739950i −1.61884 + 0.0618777i
\(144\) −0.586128 7.11906i −0.0488440 0.593255i
\(145\) −1.14308 0.371409i −0.0949275 0.0308438i
\(146\) −5.65972 7.78993i −0.468401 0.644699i
\(147\) 1.04980 + 5.22840i 0.0865860 + 0.431231i
\(148\) −2.98351 9.18229i −0.245243 0.754779i
\(149\) 0.529308 + 1.62904i 0.0433626 + 0.133456i 0.970394 0.241527i \(-0.0776483\pi\)
−0.927031 + 0.374984i \(0.877648\pi\)
\(150\) 0.732753 + 3.64939i 0.0598290 + 0.297971i
\(151\) −2.41375 3.32225i −0.196429 0.270361i 0.699429 0.714702i \(-0.253438\pi\)
−0.895858 + 0.444341i \(0.853438\pi\)
\(152\) −6.67067 2.16743i −0.541063 0.175802i
\(153\) −0.00766163 0.0930574i −0.000619406 0.00752325i
\(154\) 11.7268 + 7.85370i 0.944976 + 0.632870i
\(155\) 0.496480i 0.0398782i
\(156\) −12.9851 23.0887i −1.03964 1.84858i
\(157\) −15.6147 + 11.3447i −1.24619 + 0.905408i −0.997994 0.0633033i \(-0.979836\pi\)
−0.248192 + 0.968711i \(0.579836\pi\)
\(158\) 21.7958 29.9993i 1.73398 2.38662i
\(159\) −16.1361 7.40361i −1.27968 0.587144i
\(160\) 7.39399 2.40245i 0.584546 0.189931i
\(161\) 13.1884 + 9.58193i 1.03939 + 0.755162i
\(162\) −13.5773 + 13.7746i −1.06673 + 1.08224i
\(163\) −5.84374 + 17.9852i −0.457717 + 1.40871i 0.410198 + 0.911997i \(0.365460\pi\)
−0.867915 + 0.496713i \(0.834540\pi\)
\(164\) −8.23509 −0.643052
\(165\) −4.89583 + 3.00514i −0.381140 + 0.233950i
\(166\) −22.0603 −1.71221
\(167\) −6.43029 + 19.7904i −0.497591 + 1.53143i 0.315289 + 0.948996i \(0.397899\pi\)
−0.812880 + 0.582432i \(0.802101\pi\)
\(168\) −0.527505 + 4.52680i −0.0406979 + 0.349250i
\(169\) 17.0849 + 12.4129i 1.31423 + 0.954841i
\(170\) 0.0636129 0.0206691i 0.00487888 0.00158525i
\(171\) −6.11271 14.6081i −0.467451 1.11711i
\(172\) −4.29451 + 5.91088i −0.327453 + 0.450700i
\(173\) 14.2850 10.3787i 1.08607 0.789075i 0.107338 0.994223i \(-0.465767\pi\)
0.978731 + 0.205147i \(0.0657674\pi\)
\(174\) 3.89938 2.19301i 0.295612 0.166252i
\(175\) 1.98019i 0.149688i
\(176\) 4.88241 + 6.20689i 0.368025 + 0.467862i
\(177\) 3.57200 3.87818i 0.268488 0.291502i
\(178\) 3.65148 + 1.18644i 0.273690 + 0.0889273i
\(179\) 8.36264 + 11.5102i 0.625053 + 0.860311i 0.997709 0.0676583i \(-0.0215528\pi\)
−0.372656 + 0.927970i \(0.621553\pi\)
\(180\) −6.71221 4.08002i −0.500299 0.304106i
\(181\) −1.33134 4.09745i −0.0989578 0.304561i 0.889307 0.457311i \(-0.151187\pi\)
−0.988265 + 0.152750i \(0.951187\pi\)
\(182\) −7.68109 23.6400i −0.569360 1.75231i
\(183\) −14.8896 + 2.98965i −1.10067 + 0.221001i
\(184\) −6.42985 8.84992i −0.474015 0.652425i
\(185\) 3.50694 + 1.13947i 0.257835 + 0.0837758i
\(186\) 1.35930 + 1.25198i 0.0996684 + 0.0917997i
\(187\) 0.0638208 + 0.0811339i 0.00466704 + 0.00593310i
\(188\) 3.11952i 0.227515i
\(189\) −8.52422 + 5.76266i −0.620046 + 0.419172i
\(190\) 9.17719 6.66762i 0.665783 0.483720i
\(191\) −8.93739 + 12.3013i −0.646687 + 0.890088i −0.998950 0.0458131i \(-0.985412\pi\)
0.352263 + 0.935901i \(0.385412\pi\)
\(192\) −8.62827 + 18.8053i −0.622691 + 1.35715i
\(193\) 2.69578 0.875912i 0.194047 0.0630495i −0.210381 0.977619i \(-0.567471\pi\)
0.404428 + 0.914570i \(0.367471\pi\)
\(194\) −31.8353 23.1297i −2.28564 1.66062i
\(195\) 10.0490 + 1.17101i 0.719627 + 0.0838576i
\(196\) 2.49112 7.66689i 0.177937 0.547635i
\(197\) −24.7092 −1.76046 −0.880229 0.474549i \(-0.842611\pi\)
−0.880229 + 0.474549i \(0.842611\pi\)
\(198\) 4.11820 20.9822i 0.292668 1.49114i
\(199\) 11.4443 0.811262 0.405631 0.914037i \(-0.367052\pi\)
0.405631 + 0.914037i \(0.367052\pi\)
\(200\) 0.410616 1.26375i 0.0290349 0.0893603i
\(201\) 11.5020 + 1.34032i 0.811289 + 0.0945390i
\(202\) 6.90111 + 5.01395i 0.485560 + 0.352780i
\(203\) 2.26351 0.735458i 0.158867 0.0516190i
\(204\) −0.0588624 + 0.128290i −0.00412119 + 0.00898213i
\(205\) 1.84869 2.54451i 0.129118 0.177716i
\(206\) 26.9610 19.5883i 1.87846 1.36478i
\(207\) 5.67881 24.0356i 0.394705 1.67059i
\(208\) 13.9079i 0.964338i
\(209\) 14.5460 + 9.74174i 1.00617 + 0.673851i
\(210\) −5.42148 4.99346i −0.374118 0.344582i
\(211\) −17.4201 5.66013i −1.19925 0.389660i −0.359765 0.933043i \(-0.617143\pi\)
−0.839485 + 0.543383i \(0.817143\pi\)
\(212\) 15.7749 + 21.7122i 1.08342 + 1.49120i
\(213\) −1.00214 + 0.201218i −0.0686655 + 0.0137872i
\(214\) 3.10580 + 9.55867i 0.212308 + 0.653417i
\(215\) −0.862292 2.65386i −0.0588079 0.180992i
\(216\) 6.63508 1.91010i 0.451460 0.129966i
\(217\) 0.577865 + 0.795363i 0.0392280 + 0.0539927i
\(218\) 17.4806 + 5.67979i 1.18393 + 0.384684i
\(219\) −5.25761 + 5.70827i −0.355276 + 0.385729i
\(220\) 8.67764 0.331690i 0.585046 0.0223625i
\(221\) 0.181798i 0.0122291i
\(222\) −11.9632 + 6.72810i −0.802920 + 0.451561i
\(223\) −4.51702 + 3.28181i −0.302482 + 0.219766i −0.728664 0.684871i \(-0.759858\pi\)
0.426182 + 0.904638i \(0.359858\pi\)
\(224\) −9.04893 + 12.4548i −0.604607 + 0.832170i
\(225\) 2.76748 1.15804i 0.184499 0.0772027i
\(226\) −23.9058 + 7.76748i −1.59019 + 0.516685i
\(227\) 9.76094 + 7.09174i 0.647856 + 0.470695i 0.862540 0.505988i \(-0.168872\pi\)
−0.214684 + 0.976684i \(0.568872\pi\)
\(228\) −2.77076 + 23.7774i −0.183498 + 1.57470i
\(229\) 3.18272 9.79542i 0.210320 0.647299i −0.789133 0.614223i \(-0.789470\pi\)
0.999453 0.0330764i \(-0.0105305\pi\)
\(230\) 17.6917 1.16656
\(231\) 4.34538 10.5126i 0.285905 0.691680i
\(232\) −1.59707 −0.104853
\(233\) −0.155167 + 0.477556i −0.0101654 + 0.0312858i −0.956011 0.293332i \(-0.905236\pi\)
0.945845 + 0.324618i \(0.105236\pi\)
\(234\) −28.5469 + 24.5600i −1.86617 + 1.60554i
\(235\) 0.963882 + 0.700301i 0.0628767 + 0.0456826i
\(236\) −7.58029 + 2.46299i −0.493435 + 0.160327i
\(237\) −27.1636 12.4632i −1.76446 0.809573i
\(238\) −0.0778508 + 0.107152i −0.00504632 + 0.00694566i
\(239\) 0.520067 0.377850i 0.0336403 0.0244411i −0.570838 0.821063i \(-0.693382\pi\)
0.604478 + 0.796622i \(0.293382\pi\)
\(240\) −2.02161 3.59462i −0.130494 0.232032i
\(241\) 17.0924i 1.10102i −0.834830 0.550508i \(-0.814434\pi\)
0.834830 0.550508i \(-0.185566\pi\)
\(242\) 8.99983 + 21.8591i 0.578531 + 1.40516i
\(243\) 13.0389 + 8.54325i 0.836446 + 0.548050i
\(244\) 21.8340 + 7.09429i 1.39778 + 0.454165i
\(245\) 1.80971 + 2.49085i 0.115618 + 0.159135i
\(246\) 2.30464 + 11.4780i 0.146939 + 0.731810i
\(247\) −9.52763 29.3230i −0.606229 1.86578i
\(248\) −0.203863 0.627424i −0.0129453 0.0398415i
\(249\) 3.50014 + 17.4320i 0.221813 + 1.10471i
\(250\) 1.26317 + 1.73860i 0.0798897 + 0.109959i
\(251\) 12.8145 + 4.16368i 0.808844 + 0.262809i 0.684108 0.729381i \(-0.260192\pi\)
0.124736 + 0.992190i \(0.460192\pi\)
\(252\) 15.5018 1.27630i 0.976522 0.0803993i
\(253\) 9.42306 + 25.6263i 0.592423 + 1.61111i
\(254\) 33.2215i 2.08450i
\(255\) −0.0264256 0.0469874i −0.00165484 0.00294246i
\(256\) −1.72974 + 1.25673i −0.108109 + 0.0785456i
\(257\) −0.141442 + 0.194679i −0.00882294 + 0.0121437i −0.813406 0.581697i \(-0.802389\pi\)
0.804583 + 0.593841i \(0.202389\pi\)
\(258\) 9.44038 + 4.33144i 0.587732 + 0.269664i
\(259\) −6.94439 + 2.25637i −0.431504 + 0.140204i
\(260\) −12.3729 8.98946i −0.767337 0.557503i
\(261\) −2.35160 2.73334i −0.145560 0.169189i
\(262\) 7.75549 23.8690i 0.479136 1.47463i
\(263\) −0.755445 −0.0465827 −0.0232914 0.999729i \(-0.507415\pi\)
−0.0232914 + 0.999729i \(0.507415\pi\)
\(264\) −4.95312 + 5.80804i −0.304844 + 0.357460i
\(265\) −10.2500 −0.629653
\(266\) −6.94129 + 21.3631i −0.425598 + 1.30986i
\(267\) 0.358169 3.07364i 0.0219196 0.188104i
\(268\) −14.1619 10.2892i −0.865076 0.628515i
\(269\) 23.4922 7.63308i 1.43234 0.465397i 0.512842 0.858483i \(-0.328593\pi\)
0.919502 + 0.393086i \(0.128593\pi\)
\(270\) −3.80823 + 10.4972i −0.231762 + 0.638841i
\(271\) −3.34507 + 4.60410i −0.203199 + 0.279679i −0.898439 0.439098i \(-0.855298\pi\)
0.695240 + 0.718777i \(0.255298\pi\)
\(272\) −0.0599546 + 0.0435596i −0.00363528 + 0.00264119i
\(273\) −17.4616 + 9.82036i −1.05682 + 0.594355i
\(274\) 7.70536i 0.465498i
\(275\) −1.84555 + 2.75571i −0.111291 + 0.166175i
\(276\) −25.2933 + 27.4613i −1.52248 + 1.65298i
\(277\) 14.5011 + 4.71169i 0.871286 + 0.283098i 0.710335 0.703864i \(-0.248544\pi\)
0.160952 + 0.986962i \(0.448544\pi\)
\(278\) 6.37944 + 8.78055i 0.382614 + 0.526622i
\(279\) 0.773644 1.27276i 0.0463169 0.0761979i
\(280\) 0.813096 + 2.50245i 0.0485918 + 0.149550i
\(281\) 0.414328 + 1.27517i 0.0247168 + 0.0760704i 0.962654 0.270735i \(-0.0872666\pi\)
−0.937937 + 0.346805i \(0.887267\pi\)
\(282\) −4.34796 + 0.873019i −0.258918 + 0.0519875i
\(283\) −0.978635 1.34698i −0.0581738 0.0800694i 0.778939 0.627100i \(-0.215758\pi\)
−0.837113 + 0.547030i \(0.815758\pi\)
\(284\) 1.46953 + 0.477480i 0.0872007 + 0.0283332i
\(285\) −6.72481 6.19390i −0.398344 0.366895i
\(286\) 11.3434 40.0572i 0.670748 2.36863i
\(287\) 6.22805i 0.367630i
\(288\) 22.6986 + 5.36292i 1.33753 + 0.316013i
\(289\) 13.7525 9.99178i 0.808971 0.587752i
\(290\) 1.51820 2.08963i 0.0891520 0.122707i
\(291\) −13.2260 + 28.8260i −0.775321 + 1.68981i
\(292\) 11.1574 3.62526i 0.652937 0.212152i
\(293\) −8.47130 6.15476i −0.494899 0.359565i 0.312166 0.950027i \(-0.398945\pi\)
−0.807065 + 0.590463i \(0.798945\pi\)
\(294\) −11.3832 1.32648i −0.663882 0.0773617i
\(295\) 0.940675 2.89510i 0.0547682 0.168559i
\(296\) 4.89977 0.284793
\(297\) −17.2335 + 0.0748932i −0.999991 + 0.00434575i
\(298\) −3.68102 −0.213235
\(299\) 14.8595 45.7328i 0.859346 2.64479i
\(300\) −4.50458 0.524915i −0.260072 0.0303060i
\(301\) 4.47029 + 3.24786i 0.257663 + 0.187203i
\(302\) 8.39310 2.72708i 0.482969 0.156926i
\(303\) 2.86707 6.24877i 0.164709 0.358982i
\(304\) −7.38749 + 10.1680i −0.423702 + 0.583175i
\(305\) −7.09352 + 5.15374i −0.406174 + 0.295102i
\(306\) 0.195283 + 0.0461389i 0.0111636 + 0.00263759i
\(307\) 9.83161i 0.561119i 0.959837 + 0.280560i \(0.0905201\pi\)
−0.959837 + 0.280560i \(0.909480\pi\)
\(308\) −13.5156 + 10.6315i −0.770120 + 0.605785i
\(309\) −19.7564 18.1966i −1.12390 1.03517i
\(310\) 1.01473 + 0.329705i 0.0576327 + 0.0187260i
\(311\) −19.6486 27.0440i −1.11417 1.53353i −0.815123 0.579288i \(-0.803331\pi\)
−0.299049 0.954238i \(-0.596669\pi\)
\(312\) 13.1803 2.64644i 0.746186 0.149825i
\(313\) −2.93316 9.02734i −0.165792 0.510255i 0.833302 0.552818i \(-0.186448\pi\)
−0.999094 + 0.0425630i \(0.986448\pi\)
\(314\) −12.8174 39.4479i −0.723327 2.22617i
\(315\) −3.08564 + 5.07632i −0.173856 + 0.286018i
\(316\) 26.5554 + 36.5503i 1.49386 + 2.05612i
\(317\) −2.35417 0.764916i −0.132223 0.0429619i 0.242158 0.970237i \(-0.422145\pi\)
−0.374381 + 0.927275i \(0.622145\pi\)
\(318\) 25.8476 28.0632i 1.44946 1.57370i
\(319\) 3.83545 + 1.08612i 0.214744 + 0.0608110i
\(320\) 11.9455i 0.667775i
\(321\) 7.06047 3.97080i 0.394077 0.221628i
\(322\) −28.3422 + 20.5918i −1.57945 + 1.14754i
\(323\) −0.0965663 + 0.132912i −0.00537309 + 0.00739542i
\(324\) −10.8494 20.9187i −0.602745 1.16215i
\(325\) 5.55519 1.80499i 0.308147 0.100123i
\(326\) −32.8782 23.8874i −1.82096 1.32300i
\(327\) 1.71465 14.7143i 0.0948202 0.813702i
\(328\) 1.29146 3.97471i 0.0713091 0.219467i
\(329\) −2.35924 −0.130069
\(330\) −2.89080 12.0020i −0.159133 0.660688i
\(331\) −1.15716 −0.0636035 −0.0318018 0.999494i \(-0.510125\pi\)
−0.0318018 + 0.999494i \(0.510125\pi\)
\(332\) 8.30567 25.5622i 0.455833 1.40291i
\(333\) 7.21465 + 8.38583i 0.395360 + 0.459541i
\(334\) −36.1783 26.2851i −1.97959 1.43825i
\(335\) 6.35840 2.06597i 0.347397 0.112876i
\(336\) 7.42249 + 3.40559i 0.404930 + 0.185790i
\(337\) 15.8295 21.7874i 0.862287 1.18684i −0.118732 0.992926i \(-0.537883\pi\)
0.981019 0.193910i \(-0.0621170\pi\)
\(338\) −36.7160 + 26.6757i −1.99709 + 1.45097i
\(339\) 9.93081 + 17.6580i 0.539367 + 0.959048i
\(340\) 0.0814928i 0.00441957i
\(341\) 0.0628943 + 1.64544i 0.00340592 + 0.0891054i
\(342\) 33.9161 2.79239i 1.83397 0.150995i
\(343\) −18.9812 6.16737i −1.02489 0.333007i
\(344\) −2.17944 2.99974i −0.117507 0.161735i
\(345\) −2.80701 13.9800i −0.151124 0.752657i
\(346\) 11.7259 + 36.0887i 0.630389 + 1.94014i
\(347\) 0.903532 + 2.78078i 0.0485041 + 0.149280i 0.972375 0.233424i \(-0.0749929\pi\)
−0.923871 + 0.382704i \(0.874993\pi\)
\(348\) 1.07302 + 5.34404i 0.0575199 + 0.286471i
\(349\) 15.4992 + 21.3328i 0.829652 + 1.14192i 0.987988 + 0.154533i \(0.0493874\pi\)
−0.158335 + 0.987385i \(0.550613\pi\)
\(350\) −4.04720 1.31501i −0.216332 0.0702904i
\(351\) 23.9366 + 18.6609i 1.27764 + 0.996048i
\(352\) −24.2008 + 8.89889i −1.28991 + 0.474313i
\(353\) 26.5862i 1.41504i −0.706694 0.707519i \(-0.749814\pi\)
0.706694 0.707519i \(-0.250186\pi\)
\(354\) 5.55428 + 9.87606i 0.295207 + 0.524907i
\(355\) −0.477428 + 0.346872i −0.0253393 + 0.0184101i
\(356\) −2.74955 + 3.78443i −0.145726 + 0.200575i
\(357\) 0.0970237 + 0.0445165i 0.00513504 + 0.00235606i
\(358\) −29.0786 + 9.44819i −1.53685 + 0.499353i
\(359\) 4.63117 + 3.36474i 0.244424 + 0.177584i 0.703252 0.710941i \(-0.251731\pi\)
−0.458828 + 0.888525i \(0.651731\pi\)
\(360\) 3.02188 2.59984i 0.159267 0.137024i
\(361\) −2.73866 + 8.42873i −0.144140 + 0.443617i
\(362\) 9.25868 0.486625
\(363\) 15.8451 10.5799i 0.831651 0.555299i
\(364\) 30.2845 1.58734
\(365\) −1.38457 + 4.26128i −0.0724720 + 0.223046i
\(366\) 3.77757 32.4174i 0.197457 1.69448i
\(367\) 18.7868 + 13.6494i 0.980663 + 0.712494i 0.957857 0.287246i \(-0.0927399\pi\)
0.0228065 + 0.999740i \(0.492740\pi\)
\(368\) −18.6425 + 6.05730i −0.971805 + 0.315759i
\(369\) 8.70423 3.64225i 0.453124 0.189608i
\(370\) −4.65782 + 6.41094i −0.242149 + 0.333289i
\(371\) 16.4206 11.9302i 0.852513 0.619387i
\(372\) −1.96249 + 1.10370i −0.101751 + 0.0572244i
\(373\) 2.67037i 0.138266i 0.997607 + 0.0691332i \(0.0220233\pi\)
−0.997607 + 0.0691332i \(0.977977\pi\)
\(374\) −0.208208 + 0.0765600i −0.0107662 + 0.00395883i
\(375\) 1.17342 1.27400i 0.0605952 0.0657892i
\(376\) 1.50566 + 0.489217i 0.0776483 + 0.0252295i
\(377\) −4.12649 5.67963i −0.212525 0.292516i
\(378\) −6.11718 21.2491i −0.314634 1.09294i
\(379\) 8.17873 + 25.1716i 0.420113 + 1.29298i 0.907596 + 0.419844i \(0.137915\pi\)
−0.487483 + 0.873132i \(0.662085\pi\)
\(380\) 4.27085 + 13.1443i 0.219090 + 0.674290i
\(381\) 26.2516 5.27100i 1.34491 0.270041i
\(382\) −19.2067 26.4357i −0.982700 1.35257i
\(383\) 14.5913 + 4.74102i 0.745583 + 0.242255i 0.657080 0.753821i \(-0.271792\pi\)
0.0885035 + 0.996076i \(0.471792\pi\)
\(384\) −12.8957 11.8776i −0.658083 0.606129i
\(385\) −0.250851 6.56274i −0.0127845 0.334468i
\(386\) 6.09144i 0.310046i
\(387\) 1.92487 8.14701i 0.0978466 0.414136i
\(388\) 38.7873 28.1806i 1.96913 1.43065i
\(389\) 1.58236 2.17793i 0.0802289 0.110426i −0.767016 0.641628i \(-0.778259\pi\)
0.847245 + 0.531202i \(0.178259\pi\)
\(390\) −9.06679 + 19.7610i −0.459115 + 1.00064i
\(391\) −0.243687 + 0.0791786i −0.0123238 + 0.00400423i
\(392\) 3.30980 + 2.40471i 0.167170 + 0.121456i
\(393\) −20.0917 2.34127i −1.01349 0.118102i
\(394\) 16.4090 50.5018i 0.826675 2.54425i
\(395\) −17.2549 −0.868186
\(396\) 22.7625 + 12.6717i 1.14386 + 0.636777i
\(397\) 5.48975 0.275523 0.137761 0.990465i \(-0.456009\pi\)
0.137761 + 0.990465i \(0.456009\pi\)
\(398\) −7.59998 + 23.3903i −0.380952 + 1.17245i
\(399\) 17.9824 + 2.09548i 0.900246 + 0.104905i
\(400\) −1.92631 1.39955i −0.0963154 0.0699773i
\(401\) −23.5129 + 7.63981i −1.17418 + 0.381514i −0.830201 0.557464i \(-0.811774\pi\)
−0.343978 + 0.938978i \(0.611774\pi\)
\(402\) −10.3777 + 22.6182i −0.517594 + 1.12810i
\(403\) 1.70456 2.34613i 0.0849103 0.116869i
\(404\) −8.40812 + 6.10886i −0.418320 + 0.303927i
\(405\) 8.89912 + 1.34374i 0.442201 + 0.0667712i
\(406\) 5.11467i 0.253837i
\(407\) −11.7671 3.33219i −0.583272 0.165171i
\(408\) −0.0526890 0.0485293i −0.00260850 0.00240256i
\(409\) −1.84816 0.600504i −0.0913857 0.0296930i 0.262967 0.964805i \(-0.415299\pi\)
−0.354353 + 0.935112i \(0.615299\pi\)
\(410\) 3.97289 + 5.46821i 0.196207 + 0.270056i
\(411\) −6.08877 + 1.22255i −0.300337 + 0.0603040i
\(412\) 12.5471 + 38.6159i 0.618149 + 1.90247i
\(413\) 1.86271 + 5.73284i 0.0916581 + 0.282094i
\(414\) 45.3538 + 27.5683i 2.22902 + 1.35491i
\(415\) 6.03377 + 8.30477i 0.296186 + 0.407665i
\(416\) 43.1888 + 14.0329i 2.11751 + 0.688020i
\(417\) 5.92620 6.43417i 0.290207 0.315083i
\(418\) −29.5704 + 23.2604i −1.44634 + 1.13770i
\(419\) 12.7547i 0.623109i 0.950228 + 0.311555i \(0.100850\pi\)
−0.950228 + 0.311555i \(0.899150\pi\)
\(420\) 7.82731 4.40207i 0.381934 0.214799i
\(421\) 27.8569 20.2392i 1.35766 0.986398i 0.359071 0.933310i \(-0.383094\pi\)
0.998590 0.0530880i \(-0.0169064\pi\)
\(422\) 23.1369 31.8452i 1.12629 1.55020i
\(423\) 1.37972 + 3.29724i 0.0670841 + 0.160317i
\(424\) −12.9534 + 4.20882i −0.629073 + 0.204398i
\(425\) −0.0251799 0.0182943i −0.00122141 0.000887403i
\(426\) 0.254249 2.18185i 0.0123184 0.105711i
\(427\) 5.36528 16.5126i 0.259644 0.799102i
\(428\) −12.2454 −0.591902
\(429\) −33.4529 2.60794i −1.61512 0.125913i
\(430\) 5.99672 0.289188
\(431\) 8.15148 25.0877i 0.392643 1.20843i −0.538139 0.842856i \(-0.680873\pi\)
0.930782 0.365575i \(-0.119127\pi\)
\(432\) 0.418835 12.3652i 0.0201512 0.594921i
\(433\) −7.51544 5.46029i −0.361169 0.262405i 0.392370 0.919807i \(-0.371655\pi\)
−0.753540 + 0.657403i \(0.771655\pi\)
\(434\) −2.00935 + 0.652878i −0.0964519 + 0.0313391i
\(435\) −1.89210 0.868137i −0.0907194 0.0416240i
\(436\) −13.1628 + 18.1171i −0.630384 + 0.867650i
\(437\) −35.1557 + 25.5421i −1.68173 + 1.22185i
\(438\) −8.17532 14.5365i −0.390632 0.694582i
\(439\) 7.50627i 0.358255i −0.983826 0.179127i \(-0.942673\pi\)
0.983826 0.179127i \(-0.0573274\pi\)
\(440\) −1.20077 + 4.24033i −0.0572446 + 0.202150i
\(441\) 0.757905 + 9.20545i 0.0360907 + 0.438355i
\(442\) 0.371567 + 0.120730i 0.0176737 + 0.00574252i
\(443\) 2.64876 + 3.64571i 0.125847 + 0.173213i 0.867291 0.497801i \(-0.165859\pi\)
−0.741445 + 0.671014i \(0.765859\pi\)
\(444\) −3.29200 16.3954i −0.156232 0.778092i
\(445\) −0.552082 1.69913i −0.0261712 0.0805466i
\(446\) −3.70782 11.4115i −0.175571 0.540351i
\(447\) 0.584039 + 2.90873i 0.0276241 + 0.137578i
\(448\) −13.9037 19.1368i −0.656887 0.904127i
\(449\) −36.6279 11.9011i −1.72858 0.561648i −0.735333 0.677706i \(-0.762974\pi\)
−0.993242 + 0.116058i \(0.962974\pi\)
\(450\) 0.529013 + 6.42534i 0.0249379 + 0.302893i
\(451\) −5.80460 + 8.66721i −0.273328 + 0.408123i
\(452\) 30.6251i 1.44049i
\(453\) −3.48661 6.19953i −0.163815 0.291279i
\(454\) −20.9765 + 15.2403i −0.984477 + 0.715265i
\(455\) −6.79857 + 9.35742i −0.318722 + 0.438683i
\(456\) −11.0418 5.06620i −0.517078 0.237246i
\(457\) −21.3393 + 6.93356i −0.998211 + 0.324338i −0.762150 0.647400i \(-0.775856\pi\)
−0.236060 + 0.971738i \(0.575856\pi\)
\(458\) 17.9067 + 13.0100i 0.836726 + 0.607917i
\(459\) 0.00547484 0.161633i 0.000255544 0.00754437i
\(460\) −6.66090 + 20.5002i −0.310566 + 0.955825i
\(461\) 10.8954 0.507448 0.253724 0.967277i \(-0.418345\pi\)
0.253724 + 0.967277i \(0.418345\pi\)
\(462\) 18.6005 + 15.8626i 0.865372 + 0.737993i
\(463\) 6.54617 0.304226 0.152113 0.988363i \(-0.451392\pi\)
0.152113 + 0.988363i \(0.451392\pi\)
\(464\) −0.884342 + 2.72173i −0.0410546 + 0.126353i
\(465\) 0.0995334 0.854149i 0.00461575 0.0396102i
\(466\) −0.873007 0.634277i −0.0404413 0.0293823i
\(467\) 30.8859 10.0354i 1.42923 0.464384i 0.510706 0.859755i \(-0.329384\pi\)
0.918521 + 0.395371i \(0.129384\pi\)
\(468\) −17.7108 42.3252i −0.818683 1.95648i
\(469\) −7.78156 + 10.7104i −0.359319 + 0.494560i
\(470\) −2.07141 + 1.50497i −0.0955469 + 0.0694189i
\(471\) −29.1380 + 16.3872i −1.34261 + 0.755081i
\(472\) 4.04493i 0.186183i
\(473\) 3.19401 + 8.68621i 0.146861 + 0.399392i
\(474\) 43.5118 47.2415i 1.99856 2.16987i
\(475\) −5.02015 1.63114i −0.230340 0.0748420i
\(476\) −0.0948514 0.130552i −0.00434751 0.00598383i
\(477\) −26.2765 15.9722i −1.20312 0.731316i
\(478\) 0.426899 + 1.31386i 0.0195259 + 0.0600946i
\(479\) 6.40040 + 19.6984i 0.292442 + 0.900043i 0.984069 + 0.177788i \(0.0568942\pi\)
−0.691627 + 0.722255i \(0.743106\pi\)
\(480\) 13.2023 2.65087i 0.602601 0.120995i
\(481\) 12.6600 + 17.4250i 0.577246 + 0.794511i
\(482\) 34.9342 + 11.3508i 1.59121 + 0.517015i
\(483\) 20.7685 + 19.1288i 0.944998 + 0.870392i
\(484\) −28.7175 + 2.19858i −1.30534 + 0.0999353i
\(485\) 18.3109i 0.831454i
\(486\) −26.1200 + 20.9761i −1.18483 + 0.951493i
\(487\) −0.910597 + 0.661588i −0.0412631 + 0.0299794i −0.608226 0.793764i \(-0.708118\pi\)
0.566963 + 0.823744i \(0.308118\pi\)
\(488\) −6.84819 + 9.42573i −0.310003 + 0.426683i
\(489\) −13.6593 + 29.7704i −0.617694 + 1.34626i
\(490\) −6.29273 + 2.04463i −0.284276 + 0.0923670i
\(491\) 12.3640 + 8.98296i 0.557979 + 0.405395i 0.830719 0.556693i \(-0.187930\pi\)
−0.272740 + 0.962088i \(0.587930\pi\)
\(492\) −14.1677 1.65096i −0.638730 0.0744308i
\(493\) −0.0115598 + 0.0355773i −0.000520625 + 0.00160232i
\(494\) 66.2590 2.98113
\(495\) −9.02529 + 4.18857i −0.405657 + 0.188262i
\(496\) −1.18214 −0.0530798
\(497\) 0.361109 1.11138i 0.0161980 0.0498522i
\(498\) −37.9528 4.42261i −1.70071 0.198182i
\(499\) 9.10636 + 6.61616i 0.407657 + 0.296180i 0.772652 0.634829i \(-0.218930\pi\)
−0.364996 + 0.931009i \(0.618930\pi\)
\(500\) −2.49017 + 0.809105i −0.111364 + 0.0361843i
\(501\) −15.0303 + 32.7585i −0.671503 + 1.46354i
\(502\) −17.0199 + 23.4258i −0.759633 + 1.04555i
\(503\) 14.1300 10.2661i 0.630026 0.457741i −0.226383 0.974038i \(-0.572690\pi\)
0.856409 + 0.516297i \(0.172690\pi\)
\(504\) −1.81505 + 7.68219i −0.0808487 + 0.342192i
\(505\) 3.96935i 0.176634i
\(506\) −58.6340 + 2.24120i −2.60660 + 0.0996334i
\(507\) 26.9046 + 24.7805i 1.19487 + 1.10054i
\(508\) −38.4951 12.5078i −1.70794 0.554945i
\(509\) −1.60146 2.20422i −0.0709834 0.0977003i 0.772049 0.635563i \(-0.219232\pi\)
−0.843033 + 0.537863i \(0.819232\pi\)
\(510\) 0.113584 0.0228063i 0.00502958 0.00100988i
\(511\) −2.74172 8.43813i −0.121286 0.373281i
\(512\) −7.67575 23.6235i −0.339223 1.04402i
\(513\) −7.58775 26.3574i −0.335008 1.16371i
\(514\) −0.303964 0.418370i −0.0134073 0.0184535i
\(515\) −14.7483 4.79203i −0.649890 0.211162i
\(516\) −8.57331 + 9.30818i −0.377419 + 0.409770i
\(517\) −3.28322 2.19884i −0.144396 0.0967047i
\(518\) 15.6917i 0.689454i
\(519\) 26.6568 14.9917i 1.17010 0.658063i
\(520\) 6.27919 4.56210i 0.275361 0.200061i
\(521\) 0.277311 0.381686i 0.0121492 0.0167220i −0.802899 0.596115i \(-0.796710\pi\)
0.815048 + 0.579393i \(0.196710\pi\)
\(522\) 7.14819 2.99113i 0.312868 0.130918i
\(523\) 26.2068 8.51509i 1.14594 0.372339i 0.326329 0.945256i \(-0.394188\pi\)
0.819613 + 0.572917i \(0.194188\pi\)
\(524\) 24.7380 + 17.9732i 1.08069 + 0.785164i
\(525\) −0.396984 + 3.40673i −0.0173258 + 0.148682i
\(526\) 0.501680 1.54401i 0.0218743 0.0673222i
\(527\) −0.0154525 −0.000673121
\(528\) 7.15539 + 11.6572i 0.311398 + 0.507315i
\(529\) −44.7731 −1.94665
\(530\) 6.80689 20.9495i 0.295672 0.909986i
\(531\) 6.92279 5.95594i 0.300424 0.258466i
\(532\) −22.1409 16.0863i −0.959931 0.697431i
\(533\) 17.4721 5.67703i 0.756800 0.245899i
\(534\) 6.04419 + 2.77320i 0.261558 + 0.120008i
\(535\) 2.74896 3.78361i 0.118848 0.163580i
\(536\) 7.18709 5.22172i 0.310435 0.225544i
\(537\) 12.0796 + 21.4788i 0.521274 + 0.926877i
\(538\) 53.0834i 2.28859i
\(539\) −6.31330 8.02594i −0.271933 0.345702i
\(540\) −10.7298 8.36495i −0.461737 0.359970i
\(541\) −9.48950 3.08332i −0.407985 0.132562i 0.0978323 0.995203i \(-0.468809\pi\)
−0.505818 + 0.862640i \(0.668809\pi\)
\(542\) −7.18865 9.89433i −0.308779 0.424998i
\(543\) −1.46900 7.31619i −0.0630410 0.313968i
\(544\) −0.0747742 0.230131i −0.00320592 0.00986679i
\(545\) −2.64296 8.13418i −0.113212 0.348430i
\(546\) −8.47532 42.2103i −0.362710 1.80643i
\(547\) −1.68151 2.31440i −0.0718963 0.0989568i 0.771554 0.636163i \(-0.219480\pi\)
−0.843451 + 0.537207i \(0.819480\pi\)
\(548\) 8.92853 + 2.90105i 0.381408 + 0.123927i
\(549\) −26.2155 + 2.15838i −1.11885 + 0.0921175i
\(550\) −4.40664 5.60206i −0.187900 0.238872i
\(551\) 6.34424i 0.270274i
\(552\) −9.28775 16.5145i −0.395313 0.702905i
\(553\) 27.6424 20.0833i 1.17547 0.854031i
\(554\) −19.2599 + 26.5090i −0.818277 + 1.12626i
\(555\) 5.80493 + 2.66343i 0.246406 + 0.113056i
\(556\) −12.5762 + 4.08627i −0.533351 + 0.173296i
\(557\) −12.5736 9.13523i −0.532759 0.387072i 0.288630 0.957441i \(-0.406800\pi\)
−0.821389 + 0.570369i \(0.806800\pi\)
\(558\) 2.08755 + 2.42643i 0.0883730 + 0.102719i
\(559\) 5.03671 15.5014i 0.213030 0.655640i
\(560\) 4.71492 0.199242
\(561\) 0.0935323 + 0.152378i 0.00394894 + 0.00643341i
\(562\) −2.88140 −0.121545
\(563\) −14.0164 + 43.1381i −0.590721 + 1.81805i −0.0157560 + 0.999876i \(0.505016\pi\)
−0.574965 + 0.818178i \(0.694984\pi\)
\(564\) 0.625397 5.36686i 0.0263339 0.225986i
\(565\) 9.46267 + 6.87503i 0.398097 + 0.289235i
\(566\) 3.40291 1.10567i 0.143035 0.0464749i
\(567\) −15.8204 + 8.20522i −0.664396 + 0.344587i
\(568\) −0.460917 + 0.634398i −0.0193396 + 0.0266187i
\(569\) 2.86296 2.08006i 0.120021 0.0872007i −0.526155 0.850389i \(-0.676367\pi\)
0.646177 + 0.763188i \(0.276367\pi\)
\(570\) 17.1252 9.63120i 0.717297 0.403407i
\(571\) 30.7480i 1.28677i 0.765545 + 0.643383i \(0.222470\pi\)
−0.765545 + 0.643383i \(0.777530\pi\)
\(572\) 42.1452 + 28.2255i 1.76218 + 1.18017i
\(573\) −17.8421 + 19.3714i −0.745364 + 0.809254i
\(574\) −12.7292 4.13596i −0.531305 0.172632i
\(575\) −4.83891 6.66018i −0.201796 0.277749i
\(576\) −18.6142 + 30.6230i −0.775592 + 1.27596i
\(577\) −6.92177 21.3030i −0.288157 0.886857i −0.985435 0.170055i \(-0.945605\pi\)
0.697277 0.716801i \(-0.254395\pi\)
\(578\) 11.2888 + 34.7434i 0.469553 + 1.44514i
\(579\) 4.81345 0.966483i 0.200040 0.0401656i
\(580\) 1.84974 + 2.54595i 0.0768063 + 0.105715i
\(581\) −19.3322 6.28143i −0.802037 0.260598i
\(582\) −50.1327 46.1748i −2.07807 1.91401i
\(583\) 33.9707 1.29848i 1.40692 0.0537774i
\(584\) 5.95371i 0.246366i
\(585\) 17.0537 + 4.02923i 0.705084 + 0.166588i
\(586\) 18.2051 13.2267i 0.752044 0.546392i
\(587\) 1.62261 2.23334i 0.0669724 0.0921796i −0.774217 0.632920i \(-0.781856\pi\)
0.841189 + 0.540741i \(0.181856\pi\)
\(588\) 5.82280 12.6908i 0.240128 0.523359i
\(589\) −2.49240 + 0.809830i −0.102698 + 0.0333685i
\(590\) 5.29245 + 3.84519i 0.217887 + 0.158304i
\(591\) −42.5100 4.95366i −1.74863 0.203766i
\(592\) 2.71314 8.35020i 0.111510 0.343191i
\(593\) 23.1963 0.952558 0.476279 0.879294i \(-0.341985\pi\)
0.476279 + 0.879294i \(0.341985\pi\)
\(594\) 11.2915 35.2724i 0.463295 1.44724i
\(595\) 0.0616315 0.00252664
\(596\) 1.38590 4.26535i 0.0567685 0.174715i
\(597\) 19.6888 + 2.29433i 0.805810 + 0.0939005i
\(598\) 83.6028 + 60.7410i 3.41877 + 2.48388i
\(599\) −5.01169 + 1.62840i −0.204772 + 0.0665345i −0.409607 0.912262i \(-0.634334\pi\)
0.204835 + 0.978797i \(0.434334\pi\)
\(600\) 0.959781 2.09184i 0.0391829 0.0853990i
\(601\) 7.05506 9.71046i 0.287782 0.396098i −0.640510 0.767950i \(-0.721277\pi\)
0.928292 + 0.371852i \(0.121277\pi\)
\(602\) −9.60678 + 6.97973i −0.391543 + 0.284473i
\(603\) 19.5195 + 4.61180i 0.794894 + 0.187807i
\(604\) 10.7522i 0.437500i
\(605\) 5.76745 9.36678i 0.234480 0.380814i
\(606\) 10.8675 + 10.0096i 0.441464 + 0.406611i
\(607\) −2.99925 0.974515i −0.121736 0.0395544i 0.247516 0.968884i \(-0.420386\pi\)
−0.369251 + 0.929330i \(0.620386\pi\)
\(608\) −24.1213 33.2002i −0.978249 1.34644i
\(609\) 4.04160 0.811505i 0.163774 0.0328839i
\(610\) −5.82275 17.9206i −0.235756 0.725583i
\(611\) 2.15051 + 6.61859i 0.0870003 + 0.267759i
\(612\) −0.126987 + 0.208911i −0.00513314 + 0.00844474i
\(613\) 5.53546 + 7.61890i 0.223575 + 0.307725i 0.906039 0.423195i \(-0.139091\pi\)
−0.682464 + 0.730920i \(0.739091\pi\)
\(614\) −20.0943 6.52903i −0.810940 0.263490i
\(615\) 3.69063 4.00697i 0.148820 0.161577i
\(616\) −3.01178 8.19063i −0.121348 0.330010i
\(617\) 0.387728i 0.0156093i −0.999970 0.00780467i \(-0.997516\pi\)
0.999970 0.00780467i \(-0.00248433\pi\)
\(618\) 50.3111 28.2949i 2.02381 1.13819i
\(619\) −19.2084 + 13.9557i −0.772051 + 0.560928i −0.902583 0.430516i \(-0.858332\pi\)
0.130531 + 0.991444i \(0.458332\pi\)
\(620\) −0.764087 + 1.05168i −0.0306865 + 0.0422363i
\(621\) 14.5885 40.2125i 0.585416 1.61367i
\(622\) 68.3222 22.1992i 2.73947 0.890108i
\(623\) 2.86210 + 2.07944i 0.114668 + 0.0833109i
\(624\) 2.78823 23.9273i 0.111618 0.957857i
\(625\) 0.309017 0.951057i 0.0123607 0.0380423i
\(626\) 20.3984 0.815283
\(627\) 23.0721 + 19.6759i 0.921409 + 0.785781i
\(628\) 50.5356 2.01659
\(629\) 0.0354651 0.109150i 0.00141409 0.00435211i
\(630\) −8.32609 9.67769i −0.331719 0.385568i
\(631\) −22.7414 16.5226i −0.905321 0.657754i 0.0345063 0.999404i \(-0.489014\pi\)
−0.939827 + 0.341650i \(0.889014\pi\)
\(632\) −21.8058 + 7.08512i −0.867386 + 0.281831i
\(633\) −28.8350 13.2301i −1.14609 0.525849i
\(634\) 3.12674 4.30359i 0.124179 0.170917i
\(635\) 12.5065 9.08648i 0.496304 0.360586i
\(636\) 22.7864 + 40.5164i 0.903539 + 1.60658i
\(637\) 17.9839i 0.712547i
\(638\) −4.76692 + 7.11779i −0.188724 + 0.281796i
\(639\) −1.76443 + 0.145270i −0.0697998 + 0.00574678i
\(640\) −9.62682 3.12794i −0.380533 0.123643i
\(641\) 14.2598 + 19.6270i 0.563229 + 0.775218i 0.991733 0.128322i \(-0.0409591\pi\)
−0.428504 + 0.903540i \(0.640959\pi\)
\(642\) 3.42694 + 17.0675i 0.135251 + 0.673599i
\(643\) 3.01021 + 9.26448i 0.118711 + 0.365355i 0.992703 0.120585i \(-0.0384771\pi\)
−0.873992 + 0.485941i \(0.838477\pi\)
\(644\) −13.1898 40.5941i −0.519752 1.59963i
\(645\) −0.951454 4.73860i −0.0374635 0.186582i
\(646\) −0.207523 0.285632i −0.00816490 0.0112380i
\(647\) −28.4278 9.23675i −1.11761 0.363134i −0.308756 0.951141i \(-0.599913\pi\)
−0.808856 + 0.588007i \(0.799913\pi\)
\(648\) 11.7980 1.95597i 0.463469 0.0768377i
\(649\) −2.75084 + 9.71412i −0.107980 + 0.381313i
\(650\) 12.5526i 0.492355i
\(651\) 0.834711 + 1.48420i 0.0327149 + 0.0581703i
\(652\) 40.0580 29.1038i 1.56879 1.13979i
\(653\) −16.5857 + 22.8283i −0.649050 + 0.893340i −0.999057 0.0434064i \(-0.986179\pi\)
0.350008 + 0.936747i \(0.386179\pi\)
\(654\) 28.9351 + 13.2760i 1.13145 + 0.519134i
\(655\) −11.1069 + 3.60884i −0.433981 + 0.141009i
\(656\) −6.05859 4.40183i −0.236548 0.171862i
\(657\) −10.1896 + 8.76652i −0.397535 + 0.342015i
\(658\) 1.56674 4.82192i 0.0610778 0.187978i
\(659\) 28.6675 1.11673 0.558363 0.829596i \(-0.311429\pi\)
0.558363 + 0.829596i \(0.311429\pi\)
\(660\) 14.9956 + 1.16904i 0.583703 + 0.0455046i
\(661\) −8.42019 −0.327507 −0.163754 0.986501i \(-0.552360\pi\)
−0.163754 + 0.986501i \(0.552360\pi\)
\(662\) 0.768457 2.36507i 0.0298669 0.0919209i
\(663\) 0.0364466 0.312767i 0.00141547 0.0121469i
\(664\) 11.0352 + 8.01756i 0.428250 + 0.311142i
\(665\) 9.94082 3.22997i 0.385488 0.125253i
\(666\) −21.9305 + 9.17673i −0.849789 + 0.355591i
\(667\) −5.81590 + 8.00490i −0.225193 + 0.309951i
\(668\) 44.0787 32.0250i 1.70545 1.23909i
\(669\) −8.42906 + 4.74049i −0.325886 + 0.183278i
\(670\) 14.3676i 0.555068i
\(671\) 22.8565 17.9792i 0.882365 0.694078i
\(672\) −18.0648 + 19.6132i −0.696864 + 0.756596i
\(673\) −43.6567 14.1849i −1.68284 0.546789i −0.697383 0.716698i \(-0.745653\pi\)
−0.985460 + 0.169909i \(0.945653\pi\)
\(674\) 34.0180 + 46.8218i 1.31032 + 1.80351i
\(675\) 4.99336 1.43748i 0.192194 0.0553288i
\(676\) −17.0868 52.5877i −0.657184 2.02261i
\(677\) −3.84028 11.8192i −0.147594 0.454247i 0.849742 0.527199i \(-0.176758\pi\)
−0.997335 + 0.0729523i \(0.976758\pi\)
\(678\) −42.6850 + 8.57065i −1.63931 + 0.329154i
\(679\) −21.3125 29.3341i −0.817898 1.12574i
\(680\) −0.0393329 0.0127800i −0.00150835 0.000490092i
\(681\) 15.3711 + 14.1575i 0.589021 + 0.542518i
\(682\) −3.40479 0.964165i −0.130376 0.0369198i
\(683\) 29.7836i 1.13964i −0.821770 0.569819i \(-0.807013\pi\)
0.821770 0.569819i \(-0.192987\pi\)
\(684\) −9.53369 + 40.3514i −0.364530 + 1.54287i
\(685\) −2.90074 + 2.10751i −0.110832 + 0.0805239i
\(686\) 25.2103 34.6990i 0.962534 1.32481i
\(687\) 7.43936 16.2141i 0.283829 0.618605i
\(688\) −6.31898 + 2.05316i −0.240909 + 0.0782760i
\(689\) −48.4367 35.1914i −1.84529 1.34068i
\(690\) 30.4370 + 3.54681i 1.15872 + 0.135025i
\(691\) 6.39147 19.6709i 0.243143 0.748318i −0.752793 0.658257i \(-0.771294\pi\)
0.995936 0.0900605i \(-0.0287060\pi\)
\(692\) −46.2323 −1.75749
\(693\) 9.58338 17.2149i 0.364042 0.653938i
\(694\) −6.28352 −0.238519
\(695\) 1.56065 4.80318i 0.0591987 0.182195i
\(696\) −2.74761 0.320177i −0.104148 0.0121363i
\(697\) −0.0791955 0.0575389i −0.00299974 0.00217944i
\(698\) −53.8938 + 17.5111i −2.03991 + 0.662807i
\(699\) −0.362691 + 0.790485i −0.0137182 + 0.0298989i
\(700\) 3.04752 4.19455i 0.115186 0.158539i
\(701\) −8.11952 + 5.89918i −0.306670 + 0.222809i −0.730466 0.682949i \(-0.760697\pi\)
0.423796 + 0.905758i \(0.360697\pi\)
\(702\) −54.0360 + 36.5302i −2.03946 + 1.37874i
\(703\) 19.4640i 0.734099i
\(704\) −1.51326 39.5899i −0.0570333 1.49210i
\(705\) 1.51788 + 1.39804i 0.0571665 + 0.0526533i
\(706\) 54.3380 + 17.6555i 2.04504 + 0.664473i
\(707\) 4.62002 + 6.35891i 0.173754 + 0.239151i
\(708\) −13.5350 + 2.71766i −0.508676 + 0.102136i
\(709\) 7.88302 + 24.2614i 0.296053 + 0.911157i 0.982866 + 0.184323i \(0.0590092\pi\)
−0.686813 + 0.726834i \(0.740991\pi\)
\(710\) −0.391900 1.20614i −0.0147077 0.0452657i
\(711\) −44.2338 26.8875i −1.65890 1.00836i
\(712\) −1.39538 1.92058i −0.0522942 0.0719767i
\(713\) −3.88720 1.26303i −0.145577 0.0473007i
\(714\) −0.155417 + 0.168739i −0.00581634 + 0.00631489i
\(715\) −18.1824 + 6.68584i −0.679983 + 0.250036i
\(716\) 37.2518i 1.39216i
\(717\) 0.970478 0.545796i 0.0362432 0.0203831i
\(718\) −9.95251 + 7.23092i −0.371424 + 0.269856i
\(719\) −11.8237 + 16.2739i −0.440949 + 0.606915i −0.970423 0.241412i \(-0.922390\pi\)
0.529473 + 0.848327i \(0.322390\pi\)
\(720\) −2.75735 6.58950i −0.102760 0.245576i
\(721\) 29.2045 9.48911i 1.08763 0.353393i
\(722\) −15.4083 11.1948i −0.573438 0.416627i
\(723\) 3.42665 29.4059i 0.127438 1.09362i
\(724\) −3.48587 + 10.7284i −0.129552 + 0.398719i
\(725\) −1.20190 −0.0446376
\(726\) 11.1011 + 39.4108i 0.412001 + 1.46267i
\(727\) −22.2725 −0.826043 −0.413021 0.910721i \(-0.635527\pi\)
−0.413021 + 0.910721i \(0.635527\pi\)
\(728\) −4.74935 + 14.6170i −0.176023 + 0.541742i
\(729\) 20.7195 + 17.3119i 0.767389 + 0.641181i
\(730\) −7.78993 5.65972i −0.288318 0.209476i
\(731\) −0.0825991 + 0.0268381i −0.00305504 + 0.000992642i
\(732\) 36.1411 + 16.5823i 1.33581 + 0.612900i
\(733\) 18.1286 24.9519i 0.669596 0.921620i −0.330155 0.943927i \(-0.607101\pi\)
0.999751 + 0.0223067i \(0.00710103\pi\)
\(734\) −40.3734 + 29.3330i −1.49021 + 1.08270i
\(735\) 2.61408 + 4.64810i 0.0964219 + 0.171448i
\(736\) 64.0031i 2.35919i
\(737\) −20.8113 + 7.65254i −0.766595 + 0.281885i
\(738\) 1.66384 + 20.2089i 0.0612469 + 0.743899i
\(739\) 4.46928 + 1.45216i 0.164405 + 0.0534184i 0.390063 0.920788i \(-0.372453\pi\)
−0.225658 + 0.974207i \(0.572453\pi\)
\(740\) −5.67496 7.81092i −0.208616 0.287135i
\(741\) −10.5128 52.3577i −0.386197 1.92341i
\(742\) 13.4789 + 41.4838i 0.494826 + 1.52292i
\(743\) −11.4594 35.2684i −0.420404 1.29387i −0.907327 0.420426i \(-0.861881\pi\)
0.486923 0.873445i \(-0.338119\pi\)
\(744\) −0.224942 1.12030i −0.00824678 0.0410721i
\(745\) 1.00680 + 1.38575i 0.0368864 + 0.0507698i
\(746\) −5.45782 1.77335i −0.199825 0.0649270i
\(747\) 2.52694 + 30.6919i 0.0924558 + 1.12296i
\(748\) −0.0103235 0.270084i −0.000377466 0.00987524i
\(749\) 9.26094i 0.338387i
\(750\) 1.82461 + 3.24434i 0.0666254 + 0.118467i
\(751\) −40.1062 + 29.1389i −1.46350 + 1.06329i −0.481062 + 0.876686i \(0.659749\pi\)
−0.982435 + 0.186606i \(0.940251\pi\)
\(752\) 1.66745 2.29505i 0.0608057 0.0836918i
\(753\) 21.2115 + 9.73227i 0.772989 + 0.354664i
\(754\) 14.3486 4.66215i 0.522547 0.169786i
\(755\) −3.32225 2.41375i −0.120909 0.0878455i
\(756\) 26.9253 + 0.912017i 0.979265 + 0.0331697i
\(757\) −3.05608 + 9.40565i −0.111075 + 0.341854i −0.991108 0.133058i \(-0.957520\pi\)
0.880033 + 0.474912i \(0.157520\pi\)
\(758\) −56.8782 −2.06591
\(759\) 11.0740 + 45.9769i 0.401961 + 1.66886i
\(760\) −7.01396 −0.254423
\(761\) −7.88949 + 24.2814i −0.285994 + 0.880198i 0.700105 + 0.714040i \(0.253136\pi\)
−0.986099 + 0.166159i \(0.946864\pi\)
\(762\) −6.66018 + 57.1545i −0.241273 + 2.07049i
\(763\) 13.7016 + 9.95479i 0.496031 + 0.360388i
\(764\) 37.8635 12.3026i 1.36985 0.445092i
\(765\) −0.0360430 0.0861353i −0.00130314 0.00311423i
\(766\) −19.3798 + 26.6740i −0.700221 + 0.963772i
\(767\) 14.3849 10.4513i 0.519410 0.377373i
\(768\) −3.22781 + 1.81531i −0.116473 + 0.0655045i
\(769\) 39.4758i 1.42353i −0.702416 0.711767i \(-0.747895\pi\)
0.702416 0.711767i \(-0.252105\pi\)
\(770\) 13.5798 + 3.84552i 0.489383 + 0.138583i
\(771\) −0.282368 + 0.306571i −0.0101692 + 0.0110409i
\(772\) −7.05841 2.29342i −0.254038 0.0825419i
\(773\) 13.5974 + 18.7152i 0.489065 + 0.673140i 0.980215 0.197935i \(-0.0634235\pi\)
−0.491151 + 0.871075i \(0.663423\pi\)
\(774\) 15.3730 + 9.34445i 0.552569 + 0.335879i
\(775\) −0.153421 0.472180i −0.00551104 0.0169612i
\(776\) 7.51874 + 23.1403i 0.269907 + 0.830688i
\(777\) −12.3996 + 2.48968i −0.444832 + 0.0893168i
\(778\) 3.40054 + 4.68044i 0.121915 + 0.167802i
\(779\) −15.7893 5.13025i −0.565709 0.183810i
\(780\) −19.4843 17.9461i −0.697651 0.642572i
\(781\) 1.53835 1.21009i 0.0550466 0.0433003i
\(782\) 0.550639i 0.0196908i
\(783\) −3.49773 5.17391i −0.124999 0.184900i
\(784\) 5.93084 4.30901i 0.211816 0.153893i
\(785\) −11.3447 + 15.6147i −0.404911 + 0.557312i
\(786\) 18.1278 39.5096i 0.646598 1.40926i
\(787\) 12.3336 4.00742i 0.439644 0.142849i −0.0808275 0.996728i \(-0.525756\pi\)
0.520471 + 0.853879i \(0.325756\pi\)
\(788\) 52.3406 + 38.0277i 1.86456 + 1.35468i
\(789\) −1.29967 0.151450i −0.0462697 0.00539177i
\(790\) 11.4587 35.2663i 0.407683 1.25472i
\(791\) −23.1612 −0.823519
\(792\) −9.68578 + 8.99921i −0.344169 + 0.319773i
\(793\) −51.2149 −1.81870
\(794\) −3.64567 + 11.2202i −0.129380 + 0.398190i
\(795\) −17.6342 2.05490i −0.625421 0.0728799i
\(796\) −24.2420 17.6128i −0.859234 0.624270i
\(797\) 24.3406 7.90875i 0.862189 0.280142i 0.155647 0.987813i \(-0.450254\pi\)
0.706543 + 0.707671i \(0.250254\pi\)
\(798\) −16.2247 + 35.3617i −0.574348 + 1.25179i
\(799\) 0.0217962 0.0299999i 0.000771095 0.00106132i
\(800\) 6.28970 4.56974i 0.222375 0.161565i
\(801\) 1.23240 5.21611i 0.0435445 0.184302i
\(802\) 53.1303i 1.87609i
\(803\) 4.04894 14.2982i 0.142884 0.504571i
\(804\) −22.3015 20.5408i −0.786514 0.724419i
\(805\) 15.5039 + 5.03752i 0.546440 + 0.177549i
\(806\) 3.66315 + 5.04190i 0.129029 + 0.177593i
\(807\) 41.9464 8.42234i 1.47658 0.296481i
\(808\) −1.62988 5.01625i −0.0573389 0.176471i
\(809\) 7.33409 + 22.5720i 0.257853 + 0.793589i 0.993254 + 0.115957i \(0.0369936\pi\)
−0.735401 + 0.677632i \(0.763006\pi\)
\(810\) −8.65619 + 17.2961i −0.304147 + 0.607722i
\(811\) 25.8764 + 35.6158i 0.908642 + 1.25064i 0.967628 + 0.252380i \(0.0812132\pi\)
−0.0589862 + 0.998259i \(0.518787\pi\)
\(812\) −5.92658 1.92566i −0.207982 0.0675775i
\(813\) −6.67792 + 7.25032i −0.234205 + 0.254280i
\(814\) 14.6248 21.8372i 0.512600 0.765394i
\(815\) 18.9108i 0.662415i
\(816\) −0.111879 + 0.0629207i −0.00391656 + 0.00220267i
\(817\) −11.9163 + 8.65767i −0.416897 + 0.302893i
\(818\) 2.45468 3.37857i 0.0858257 0.118129i
\(819\) −32.0098 + 13.3944i −1.11851 + 0.468037i
\(820\) −7.83203 + 2.54478i −0.273506 + 0.0888676i
\(821\) 23.8573 + 17.3334i 0.832626 + 0.604938i 0.920301 0.391211i \(-0.127944\pi\)
−0.0876748 + 0.996149i \(0.527944\pi\)
\(822\) 1.54476 13.2564i 0.0538796 0.462369i
\(823\) 8.56184 26.3506i 0.298447 0.918525i −0.683595 0.729862i \(-0.739584\pi\)
0.982042 0.188663i \(-0.0604155\pi\)
\(824\) −20.6058 −0.717839
\(825\) −3.72757 + 4.37095i −0.129777 + 0.152177i
\(826\) −12.9540 −0.450729
\(827\) −4.25666 + 13.1007i −0.148019 + 0.455554i −0.997387 0.0722463i \(-0.976983\pi\)
0.849368 + 0.527801i \(0.176983\pi\)
\(828\) −49.0202 + 42.1739i −1.70357 + 1.46565i
\(829\) −6.39438 4.64579i −0.222086 0.161355i 0.471179 0.882038i \(-0.343829\pi\)
−0.693265 + 0.720683i \(0.743829\pi\)
\(830\) −20.9806 + 6.81702i −0.728248 + 0.236622i
\(831\) 24.0032 + 11.0132i 0.832663 + 0.382043i
\(832\) −41.0125 + 56.4489i −1.42185 + 1.95701i
\(833\) 0.0775256 0.0563256i 0.00268610 0.00195157i
\(834\) 9.21495 + 16.3851i 0.319088 + 0.567369i
\(835\) 20.8089i 0.720121i
\(836\) −15.8196 43.0220i −0.547133 1.48795i
\(837\) 1.58614 2.03456i 0.0548252 0.0703247i
\(838\) −26.0687 8.47023i −0.900528 0.292599i
\(839\) −3.95639 5.44550i −0.136590 0.187999i 0.735243 0.677804i \(-0.237068\pi\)
−0.871832 + 0.489804i \(0.837068\pi\)
\(840\) 0.897171 + 4.46825i 0.0309553 + 0.154169i
\(841\) −8.51510 26.2068i −0.293624 0.903682i
\(842\) 22.8665 + 70.3757i 0.788030 + 2.42531i
\(843\) 0.457170 + 2.27688i 0.0157458 + 0.0784200i
\(844\) 28.1894 + 38.7993i 0.970318 + 1.33553i
\(845\) 20.0846 + 6.52587i 0.690930 + 0.224497i
\(846\) −7.65530 + 0.630278i −0.263195 + 0.0216694i
\(847\) 1.66274 + 21.7185i 0.0571325 + 0.746256i
\(848\) 24.4058i 0.838098i
\(849\) −1.41361 2.51354i −0.0485151 0.0862646i
\(850\) 0.0541123 0.0393149i 0.00185604 0.00134849i
\(851\) 17.8431 24.5589i 0.611652 0.841867i
\(852\) 2.43247 + 1.11607i 0.0833352 + 0.0382359i
\(853\) 16.5336 5.37211i 0.566101 0.183937i −0.0119634 0.999928i \(-0.503808\pi\)
0.578065 + 0.815991i \(0.303808\pi\)
\(854\) 30.1863 + 21.9316i 1.03295 + 0.750484i
\(855\) −10.3277 12.0042i −0.353200 0.410536i
\(856\) 1.92037 5.91029i 0.0656369 0.202010i
\(857\) −1.61379 −0.0551259 −0.0275630 0.999620i \(-0.508775\pi\)
−0.0275630 + 0.999620i \(0.508775\pi\)
\(858\) 27.5458 66.6407i 0.940400 2.27508i
\(859\) −7.55567 −0.257796 −0.128898 0.991658i \(-0.541144\pi\)
−0.128898 + 0.991658i \(0.541144\pi\)
\(860\) −2.25776 + 6.94866i −0.0769888 + 0.236947i
\(861\) −1.24859 + 10.7148i −0.0425517 + 0.365159i
\(862\) 45.8621 + 33.3207i 1.56207 + 1.13491i
\(863\) −37.9258 + 12.3228i −1.29101 + 0.419475i −0.872445 0.488712i \(-0.837467\pi\)
−0.418565 + 0.908187i \(0.637467\pi\)
\(864\) 37.9757 + 13.7770i 1.29196 + 0.468703i
\(865\) 10.3787 14.2850i 0.352885 0.485705i
\(866\) 16.1509 11.7343i 0.548830 0.398748i
\(867\) 25.6631 14.4329i 0.871564 0.490166i
\(868\) 2.57413i 0.0873716i
\(869\) 57.1861 2.18585i 1.93991 0.0741500i
\(870\) 3.03086 3.29065i 0.102756 0.111564i
\(871\) 37.1399 + 12.0675i 1.25844 + 0.408891i
\(872\) −6.68005 9.19430i −0.226215 0.311358i
\(873\) −28.5331 + 46.9410i −0.965699 + 1.58871i
\(874\) −28.8578 88.8151i −0.976129 3.00421i
\(875\) 0.611911 + 1.88327i 0.0206864 + 0.0636661i
\(876\) 19.9221 4.00011i 0.673104 0.135151i
\(877\) 22.3509 + 30.7634i 0.754738 + 1.03881i 0.997634 + 0.0687551i \(0.0219027\pi\)
−0.242896 + 0.970052i \(0.578097\pi\)
\(878\) 15.3417 + 4.98481i 0.517756 + 0.168229i
\(879\) −13.3402 12.2870i −0.449954 0.414431i
\(880\) 6.56148 + 4.39435i 0.221187 + 0.148134i
\(881\) 35.8747i 1.20865i −0.796738 0.604324i \(-0.793443\pi\)
0.796738 0.604324i \(-0.206557\pi\)
\(882\) −19.3178 4.56416i −0.650465 0.153683i
\(883\) −27.0229 + 19.6333i −0.909394 + 0.660713i −0.940861 0.338792i \(-0.889982\pi\)
0.0314677 + 0.999505i \(0.489982\pi\)
\(884\) −0.279789 + 0.385096i −0.00941032 + 0.0129522i
\(885\) 2.19875 4.79217i 0.0739102 0.161087i
\(886\) −9.21028 + 2.99260i −0.309425 + 0.100538i
\(887\) 32.8038 + 23.8333i 1.10144 + 0.800245i 0.981295 0.192511i \(-0.0616631\pi\)
0.120148 + 0.992756i \(0.461663\pi\)
\(888\) 8.42961 + 0.982297i 0.282879 + 0.0329637i
\(889\) −9.45944 + 29.1132i −0.317259 + 0.976424i
\(890\) 3.83940 0.128697
\(891\) −29.6637 3.32610i −0.993772 0.111428i
\(892\) 14.6190 0.489480
\(893\) 1.94338 5.98112i 0.0650328 0.200151i
\(894\) −6.33285 0.737963i −0.211802 0.0246812i
\(895\) 11.5102 + 8.36264i 0.384743 + 0.279532i
\(896\) 19.0629 6.19391i 0.636846 0.206924i
\(897\) 34.7328 75.7001i 1.15969 2.52755i
\(898\) 48.6481 66.9583i 1.62341 2.23443i
\(899\) −0.482757 + 0.350744i −0.0161009 + 0.0116980i
\(900\) −7.64448 1.80614i −0.254816 0.0602046i
\(901\) 0.319022i 0.0106282i
\(902\) −13.8597 17.6195i −0.461477 0.586665i
\(903\) 7.03961 + 6.48384i 0.234263 + 0.215769i
\(904\) 14.7814 + 4.80277i 0.491622 + 0.159738i
\(905\) −2.53236 3.48550i −0.0841786 0.115862i
\(906\) 14.9863 3.00907i 0.497886 0.0999696i
\(907\) 4.39617 + 13.5300i 0.145972 + 0.449257i 0.997135 0.0756458i \(-0.0241018\pi\)
−0.851162 + 0.524902i \(0.824102\pi\)
\(908\) −9.76200 30.0443i −0.323963 0.997056i
\(909\) 6.18527 10.1757i 0.205152 0.337505i
\(910\) −14.6103 20.1094i −0.484327 0.666619i
\(911\) −7.30632 2.37397i −0.242069 0.0786531i 0.185470 0.982650i \(-0.440619\pi\)
−0.427539 + 0.903997i \(0.640619\pi\)
\(912\) −14.7480 + 16.0121i −0.488354 + 0.530214i
\(913\) −21.0492 26.7593i −0.696627 0.885605i
\(914\) 48.2188i 1.59493i
\(915\) −13.2370 + 7.44445i −0.437601 + 0.246106i
\(916\) −21.8171 + 15.8510i −0.720856 + 0.523733i
\(917\) 13.5928 18.7089i 0.448875 0.617823i
\(918\) 0.326717 + 0.118528i 0.0107833 + 0.00391200i
\(919\) 39.4844 12.8293i 1.30247 0.423199i 0.426031 0.904709i \(-0.359912\pi\)
0.876441 + 0.481510i \(0.159912\pi\)
\(920\) −8.84992 6.42985i −0.291773 0.211986i
\(921\) −1.97102 + 16.9144i −0.0649474 + 0.557348i
\(922\) −7.23546 + 22.2685i −0.238287 + 0.733373i
\(923\) −3.44702 −0.113460
\(924\) −25.3837 + 15.5809i −0.835061 + 0.512575i
\(925\) 3.68742 0.121241
\(926\) −4.34722 + 13.3794i −0.142858 + 0.439673i
\(927\) −30.3410 35.2664i −0.996530 1.15830i
\(928\) −7.55962 5.49238i −0.248157 0.180296i
\(929\) −25.9678 + 8.43744i −0.851974 + 0.276823i −0.702273 0.711908i \(-0.747831\pi\)
−0.149702 + 0.988731i \(0.547831\pi\)
\(930\) 1.67965 + 0.770659i 0.0550779 + 0.0252709i
\(931\) 9.55255 13.1480i 0.313072 0.430907i
\(932\) 1.06365 0.772786i 0.0348410 0.0253135i
\(933\) −28.3820 50.4659i −0.929183 1.65218i
\(934\) 69.7903i 2.28361i
\(935\) 0.0857689 + 0.0574412i 0.00280494 + 0.00187853i
\(936\) 23.2060 1.91060i 0.758512 0.0624500i
\(937\) 32.9847 + 10.7174i 1.07756 + 0.350122i 0.793429 0.608663i \(-0.208294\pi\)
0.284135 + 0.958784i \(0.408294\pi\)
\(938\) −16.7228 23.0169i −0.546018 0.751529i
\(939\) −3.23645 16.1188i −0.105618 0.526016i
\(940\) −0.963986 2.96684i −0.0314418 0.0967678i
\(941\) 8.45885 + 26.0337i 0.275751 + 0.848673i 0.989020 + 0.147783i \(0.0472138\pi\)
−0.713269 + 0.700890i \(0.752786\pi\)
\(942\) −14.1427 70.4361i −0.460795 2.29493i
\(943\) −15.2192 20.9475i −0.495607 0.682144i
\(944\) −6.89338 2.23979i −0.224360 0.0728991i
\(945\) −6.32626 + 8.11475i −0.205793 + 0.263973i
\(946\) −19.8744 + 0.759668i −0.646172 + 0.0246989i
\(947\) 44.8877i 1.45865i 0.684166 + 0.729327i \(0.260166\pi\)
−0.684166 + 0.729327i \(0.739834\pi\)
\(948\) 38.3586 + 68.2053i 1.24583 + 2.21521i
\(949\) −21.1731 + 15.3832i −0.687308 + 0.499358i
\(950\) 6.66762 9.17719i 0.216326 0.297747i
\(951\) −3.89678 1.78793i −0.126362 0.0579775i
\(952\) 0.0778865 0.0253069i 0.00252432 0.000820200i
\(953\) 46.6386 + 33.8849i 1.51077 + 1.09764i 0.965833 + 0.259165i \(0.0834475\pi\)
0.544940 + 0.838475i \(0.316553\pi\)
\(954\) 50.0945 43.0983i 1.62187 1.39536i
\(955\) −4.69866 + 14.4610i −0.152045 + 0.467947i
\(956\) −1.68315 −0.0544371
\(957\) 6.38079 + 2.63749i 0.206262 + 0.0852580i
\(958\) −44.5109 −1.43808
\(959\) 2.19401 6.75248i 0.0708484 0.218049i
\(960\) −2.39481 + 20.5512i −0.0772923 + 0.663286i
\(961\) 24.8801 + 18.0765i 0.802584 + 0.583112i
\(962\) −44.0213 + 14.3034i −1.41930 + 0.461160i
\(963\) 12.9430 5.41593i 0.417081 0.174526i
\(964\) −26.3053 + 36.2061i −0.847237 + 1.16612i
\(965\) 2.29317 1.66608i 0.0738197 0.0536331i
\(966\) −52.8884 + 29.7444i −1.70166 + 0.957010i
\(967\) 22.2716i 0.716207i −0.933682 0.358104i \(-0.883423\pi\)
0.933682 0.358104i \(-0.116577\pi\)
\(968\) 3.44244 14.2054i 0.110644 0.456580i
\(969\) −0.192779 + 0.209304i −0.00619297 + 0.00672380i
\(970\) −37.4246 12.1600i −1.20163 0.390434i
\(971\) 13.3684 + 18.4000i 0.429012 + 0.590485i 0.967726 0.252004i \(-0.0810896\pi\)
−0.538714 + 0.842489i \(0.681090\pi\)
\(972\) −14.4717 38.1638i −0.464180 1.22411i
\(973\) 3.09037 + 9.51118i 0.0990727 + 0.304915i
\(974\) −0.747469 2.30047i −0.0239504 0.0737119i
\(975\) 9.91907 1.99163i 0.317664 0.0637832i
\(976\) 12.2713 + 16.8900i 0.392795 + 0.540636i
\(977\) 23.0660 + 7.49460i 0.737947 + 0.239774i 0.653787 0.756679i \(-0.273179\pi\)
0.0841602 + 0.996452i \(0.473179\pi\)
\(978\) −51.7751 47.6875i −1.65559 1.52488i
\(979\) 2.04496 + 5.56134i 0.0653572 + 0.177741i
\(980\) 8.06144i 0.257513i
\(981\) 5.89979 24.9709i 0.188366 0.797258i
\(982\) −26.5705 + 19.3046i −0.847900 + 0.616035i
\(983\) −21.5454 + 29.6547i −0.687192 + 0.945839i −0.999992 0.00398035i \(-0.998733\pi\)
0.312800 + 0.949819i \(0.398733\pi\)
\(984\) 3.01869 6.57922i 0.0962322 0.209738i
\(985\) −23.4999 + 7.63557i −0.748768 + 0.243289i
\(986\) −0.0650378 0.0472527i −0.00207123 0.00150483i
\(987\) −4.05886 0.472976i −0.129195 0.0150550i
\(988\) −24.9464 + 76.7770i −0.793650 + 2.44260i
\(989\) −22.9721 −0.730470
\(990\) −2.56722 21.2279i −0.0815917 0.674666i
\(991\) −15.4812 −0.491778 −0.245889 0.969298i \(-0.579080\pi\)
−0.245889 + 0.969298i \(0.579080\pi\)
\(992\) 1.19277 3.67097i 0.0378705 0.116553i
\(993\) −1.99080 0.231986i −0.0631760 0.00736186i
\(994\) 2.03168 + 1.47610i 0.0644411 + 0.0468192i
\(995\) 10.8841 3.53647i 0.345051 0.112114i
\(996\) 19.4138 42.3124i 0.615150 1.34072i
\(997\) 10.4160 14.3364i 0.329878 0.454039i −0.611573 0.791188i \(-0.709463\pi\)
0.941451 + 0.337150i \(0.109463\pi\)
\(998\) −19.5698 + 14.2183i −0.619471 + 0.450072i
\(999\) 10.7310 + 15.8734i 0.339513 + 0.502213i
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 165.2.p.b.101.2 48
3.2 odd 2 inner 165.2.p.b.101.11 yes 48
5.2 odd 4 825.2.bs.h.299.1 48
5.3 odd 4 825.2.bs.g.299.12 48
5.4 even 2 825.2.bi.e.101.11 48
11.6 odd 10 inner 165.2.p.b.116.11 yes 48
15.2 even 4 825.2.bs.g.299.11 48
15.8 even 4 825.2.bs.h.299.2 48
15.14 odd 2 825.2.bi.e.101.2 48
33.17 even 10 inner 165.2.p.b.116.2 yes 48
55.17 even 20 825.2.bs.h.149.2 48
55.28 even 20 825.2.bs.g.149.11 48
55.39 odd 10 825.2.bi.e.776.2 48
165.17 odd 20 825.2.bs.g.149.12 48
165.83 odd 20 825.2.bs.h.149.1 48
165.149 even 10 825.2.bi.e.776.11 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
165.2.p.b.101.2 48 1.1 even 1 trivial
165.2.p.b.101.11 yes 48 3.2 odd 2 inner
165.2.p.b.116.2 yes 48 33.17 even 10 inner
165.2.p.b.116.11 yes 48 11.6 odd 10 inner
825.2.bi.e.101.2 48 15.14 odd 2
825.2.bi.e.101.11 48 5.4 even 2
825.2.bi.e.776.2 48 55.39 odd 10
825.2.bi.e.776.11 48 165.149 even 10
825.2.bs.g.149.11 48 55.28 even 20
825.2.bs.g.149.12 48 165.17 odd 20
825.2.bs.g.299.11 48 15.2 even 4
825.2.bs.g.299.12 48 5.3 odd 4
825.2.bs.h.149.1 48 165.83 odd 20
825.2.bs.h.149.2 48 55.17 even 20
825.2.bs.h.299.1 48 5.2 odd 4
825.2.bs.h.299.2 48 15.8 even 4