Properties

Label 144.2.x.e.133.2
Level $144$
Weight $2$
Character 144.133
Analytic conductor $1.150$
Analytic rank $0$
Dimension $72$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [144,2,Mod(13,144)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(144, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([0, 9, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("144.13");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 144 = 2^{4} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 144.x (of order \(12\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(1.14984578911\)
Analytic rank: \(0\)
Dimension: \(72\)
Relative dimension: \(18\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 133.2
Character \(\chi\) \(=\) 144.133
Dual form 144.2.x.e.13.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.31447 - 0.521699i) q^{2} +(0.241506 - 1.71513i) q^{3} +(1.45566 + 1.37152i) q^{4} +(0.531653 - 1.98415i) q^{5} +(-1.21223 + 2.12849i) q^{6} +(1.54969 + 0.894715i) q^{7} +(-1.19790 - 2.56223i) q^{8} +(-2.88335 - 0.828427i) q^{9} +O(q^{10})\) \(q+(-1.31447 - 0.521699i) q^{2} +(0.241506 - 1.71513i) q^{3} +(1.45566 + 1.37152i) q^{4} +(0.531653 - 1.98415i) q^{5} +(-1.21223 + 2.12849i) q^{6} +(1.54969 + 0.894715i) q^{7} +(-1.19790 - 2.56223i) q^{8} +(-2.88335 - 0.828427i) q^{9} +(-1.73397 + 2.33075i) q^{10} +(2.58637 - 0.693015i) q^{11} +(2.70388 - 2.16542i) q^{12} +(-4.63944 - 1.24314i) q^{13} +(-1.57025 - 1.98455i) q^{14} +(-3.27469 - 1.39104i) q^{15} +(0.237889 + 3.99292i) q^{16} -3.58889 q^{17} +(3.35789 + 2.59318i) q^{18} +(4.85244 - 4.85244i) q^{19} +(3.49520 - 2.15908i) q^{20} +(1.90881 - 2.44185i) q^{21} +(-3.76124 - 0.438359i) q^{22} +(-0.446082 + 0.257545i) q^{23} +(-4.68386 + 1.43576i) q^{24} +(0.675912 + 0.390238i) q^{25} +(5.44986 + 4.05446i) q^{26} +(-2.11721 + 4.74525i) q^{27} +(1.02871 + 3.42783i) q^{28} +(1.72815 + 6.44956i) q^{29} +(3.57877 + 3.53688i) q^{30} +(4.05128 + 7.01703i) q^{31} +(1.77041 - 5.37268i) q^{32} +(-0.563989 - 4.60332i) q^{33} +(4.71749 + 1.87232i) q^{34} +(2.59915 - 2.59915i) q^{35} +(-3.06097 - 5.16047i) q^{36} +(1.25948 + 1.25948i) q^{37} +(-8.90990 + 3.84687i) q^{38} +(-3.25259 + 7.65703i) q^{39} +(-5.72073 + 1.01460i) q^{40} +(4.07959 - 2.35535i) q^{41} +(-3.78299 + 2.21391i) q^{42} +(6.57670 - 1.76222i) q^{43} +(4.71535 + 2.53845i) q^{44} +(-3.17667 + 5.28058i) q^{45} +(0.720722 - 0.105815i) q^{46} +(-3.48945 + 6.04391i) q^{47} +(6.90583 + 0.556302i) q^{48} +(-1.89897 - 3.28911i) q^{49} +(-0.684879 - 0.865579i) q^{50} +(-0.866737 + 6.15542i) q^{51} +(-5.04847 - 8.17265i) q^{52} +(5.26302 + 5.26302i) q^{53} +(5.25860 - 5.13295i) q^{54} -5.50019i q^{55} +(0.436091 - 5.04245i) q^{56} +(-7.15068 - 9.49446i) q^{57} +(1.09313 - 9.37932i) q^{58} +(-1.81387 + 6.76946i) q^{59} +(-2.85900 - 6.51616i) q^{60} +(-1.55082 - 5.78773i) q^{61} +(-1.66451 - 11.3372i) q^{62} +(-3.72710 - 3.86359i) q^{63} +(-5.13007 + 6.13860i) q^{64} +(-4.93314 + 8.54446i) q^{65} +(-1.66020 + 6.34516i) q^{66} +(1.69184 + 0.453328i) q^{67} +(-5.22420 - 4.92222i) q^{68} +(0.333993 + 0.827288i) q^{69} +(-4.77248 + 2.06053i) q^{70} -7.58339i q^{71} +(1.33134 + 8.38019i) q^{72} -12.5473i q^{73} +(-0.998475 - 2.31261i) q^{74} +(0.832546 - 1.06503i) q^{75} +(13.7187 - 0.408302i) q^{76} +(4.62812 + 1.24010i) q^{77} +(8.27010 - 8.36806i) q^{78} +(-4.01735 + 6.95825i) q^{79} +(8.04904 + 1.65084i) q^{80} +(7.62742 + 4.77729i) q^{81} +(-6.59129 + 0.967720i) q^{82} +(-2.14313 - 7.99826i) q^{83} +(6.12761 - 0.936530i) q^{84} +(-1.90804 + 7.12091i) q^{85} +(-9.56422 - 1.11467i) q^{86} +(11.4792 - 1.40641i) q^{87} +(-4.87387 - 5.79671i) q^{88} +16.5414i q^{89} +(6.93051 - 5.28389i) q^{90} +(-6.07746 - 6.07746i) q^{91} +(-1.00257 - 0.236910i) q^{92} +(13.0135 - 5.25383i) q^{93} +(7.73988 - 6.12409i) q^{94} +(-7.04818 - 12.2078i) q^{95} +(-8.78728 - 4.33401i) q^{96} +(-4.15739 + 7.20082i) q^{97} +(0.780209 + 5.31413i) q^{98} +(-8.03151 - 0.144412i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 72 q + 4 q^{2} + 2 q^{3} - 2 q^{4} + 4 q^{5} - 28 q^{6} - 8 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 72 q + 4 q^{2} + 2 q^{3} - 2 q^{4} + 4 q^{5} - 28 q^{6} - 8 q^{8} - 20 q^{10} - 2 q^{11} + 8 q^{12} - 16 q^{13} - 4 q^{14} - 20 q^{15} - 10 q^{16} - 16 q^{17} + 28 q^{19} + 12 q^{20} - 16 q^{21} - 8 q^{22} - 40 q^{24} - 4 q^{26} + 8 q^{27} - 16 q^{28} + 4 q^{29} + 18 q^{30} + 28 q^{31} - 46 q^{32} - 32 q^{33} - 14 q^{34} - 16 q^{35} + 14 q^{36} + 16 q^{37} + 2 q^{38} - 10 q^{40} + 26 q^{42} - 10 q^{43} + 60 q^{44} + 40 q^{45} + 20 q^{46} - 56 q^{47} + 2 q^{48} + 4 q^{49} - 36 q^{50} - 54 q^{51} + 6 q^{52} - 8 q^{53} + 92 q^{54} + 52 q^{56} - 14 q^{58} - 14 q^{59} + 18 q^{60} - 32 q^{61} + 16 q^{62} - 108 q^{63} - 44 q^{64} - 64 q^{65} + 26 q^{66} - 18 q^{67} + 16 q^{68} + 32 q^{69} + 14 q^{70} + 114 q^{72} + 38 q^{74} + 86 q^{75} + 10 q^{76} - 36 q^{77} + 16 q^{78} + 44 q^{79} + 144 q^{80} - 44 q^{81} - 88 q^{82} + 20 q^{83} - 58 q^{84} - 8 q^{85} + 76 q^{86} - 42 q^{88} - 80 q^{91} - 68 q^{92} - 4 q^{93} + 20 q^{94} + 48 q^{95} + 94 q^{96} + 40 q^{97} + 88 q^{98} + 28 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/144\mathbb{Z}\right)^\times\).

\(n\) \(37\) \(65\) \(127\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(e\left(\frac{2}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.31447 0.521699i −0.929470 0.368897i
\(3\) 0.241506 1.71513i 0.139433 0.990231i
\(4\) 1.45566 + 1.37152i 0.727830 + 0.685758i
\(5\) 0.531653 1.98415i 0.237762 0.887341i −0.739122 0.673572i \(-0.764759\pi\)
0.976884 0.213769i \(-0.0685741\pi\)
\(6\) −1.21223 + 2.12849i −0.494893 + 0.868954i
\(7\) 1.54969 + 0.894715i 0.585729 + 0.338171i 0.763407 0.645918i \(-0.223525\pi\)
−0.177678 + 0.984089i \(0.556859\pi\)
\(8\) −1.19790 2.56223i −0.423522 0.905886i
\(9\) −2.88335 0.828427i −0.961117 0.276142i
\(10\) −1.73397 + 2.33075i −0.548331 + 0.737047i
\(11\) 2.58637 0.693015i 0.779819 0.208952i 0.153114 0.988209i \(-0.451070\pi\)
0.626705 + 0.779257i \(0.284403\pi\)
\(12\) 2.70388 2.16542i 0.780543 0.625102i
\(13\) −4.63944 1.24314i −1.28675 0.344784i −0.450325 0.892865i \(-0.648692\pi\)
−0.836425 + 0.548081i \(0.815359\pi\)
\(14\) −1.57025 1.98455i −0.419667 0.530393i
\(15\) −3.27469 1.39104i −0.845521 0.359165i
\(16\) 0.237889 + 3.99292i 0.0594722 + 0.998230i
\(17\) −3.58889 −0.870434 −0.435217 0.900326i \(-0.643328\pi\)
−0.435217 + 0.900326i \(0.643328\pi\)
\(18\) 3.35789 + 2.59318i 0.791461 + 0.611219i
\(19\) 4.85244 4.85244i 1.11323 1.11323i 0.120514 0.992712i \(-0.461546\pi\)
0.992712 0.120514i \(-0.0384543\pi\)
\(20\) 3.49520 2.15908i 0.781551 0.482786i
\(21\) 1.90881 2.44185i 0.416537 0.532855i
\(22\) −3.76124 0.438359i −0.801900 0.0934584i
\(23\) −0.446082 + 0.257545i −0.0930145 + 0.0537019i −0.545786 0.837925i \(-0.683769\pi\)
0.452771 + 0.891627i \(0.350435\pi\)
\(24\) −4.68386 + 1.43576i −0.956090 + 0.293074i
\(25\) 0.675912 + 0.390238i 0.135182 + 0.0780476i
\(26\) 5.44986 + 4.05446i 1.06881 + 0.795145i
\(27\) −2.11721 + 4.74525i −0.407457 + 0.913225i
\(28\) 1.02871 + 3.42783i 0.194408 + 0.647799i
\(29\) 1.72815 + 6.44956i 0.320910 + 1.19765i 0.918360 + 0.395746i \(0.129514\pi\)
−0.597450 + 0.801906i \(0.703819\pi\)
\(30\) 3.57877 + 3.53688i 0.653392 + 0.645743i
\(31\) 4.05128 + 7.01703i 0.727632 + 1.26030i 0.957881 + 0.287164i \(0.0927125\pi\)
−0.230249 + 0.973132i \(0.573954\pi\)
\(32\) 1.77041 5.37268i 0.312967 0.949764i
\(33\) −0.563989 4.60332i −0.0981779 0.801336i
\(34\) 4.71749 + 1.87232i 0.809042 + 0.321101i
\(35\) 2.59915 2.59915i 0.439337 0.439337i
\(36\) −3.06097 5.16047i −0.510162 0.860078i
\(37\) 1.25948 + 1.25948i 0.207057 + 0.207057i 0.803015 0.595959i \(-0.203228\pi\)
−0.595959 + 0.803015i \(0.703228\pi\)
\(38\) −8.90990 + 3.84687i −1.44538 + 0.624044i
\(39\) −3.25259 + 7.65703i −0.520831 + 1.22611i
\(40\) −5.72073 + 1.01460i −0.904527 + 0.160423i
\(41\) 4.07959 2.35535i 0.637126 0.367845i −0.146381 0.989228i \(-0.546762\pi\)
0.783506 + 0.621384i \(0.213429\pi\)
\(42\) −3.78299 + 2.21391i −0.583728 + 0.341613i
\(43\) 6.57670 1.76222i 1.00294 0.268736i 0.280262 0.959924i \(-0.409579\pi\)
0.722676 + 0.691187i \(0.242912\pi\)
\(44\) 4.71535 + 2.53845i 0.710865 + 0.382685i
\(45\) −3.17667 + 5.28058i −0.473550 + 0.787182i
\(46\) 0.720722 0.105815i 0.106265 0.0156016i
\(47\) −3.48945 + 6.04391i −0.508989 + 0.881595i 0.490957 + 0.871184i \(0.336647\pi\)
−0.999946 + 0.0104109i \(0.996686\pi\)
\(48\) 6.90583 + 0.556302i 0.996771 + 0.0802952i
\(49\) −1.89897 3.28911i −0.271281 0.469873i
\(50\) −0.684879 0.865579i −0.0968565 0.122411i
\(51\) −0.866737 + 6.15542i −0.121367 + 0.861931i
\(52\) −5.04847 8.17265i −0.700097 1.13334i
\(53\) 5.26302 + 5.26302i 0.722932 + 0.722932i 0.969201 0.246269i \(-0.0792048\pi\)
−0.246269 + 0.969201i \(0.579205\pi\)
\(54\) 5.25860 5.13295i 0.715605 0.698505i
\(55\) 5.50019i 0.741646i
\(56\) 0.436091 5.04245i 0.0582751 0.673826i
\(57\) −7.15068 9.49446i −0.947131 1.25757i
\(58\) 1.09313 9.37932i 0.143534 1.23157i
\(59\) −1.81387 + 6.76946i −0.236146 + 0.881308i 0.741483 + 0.670972i \(0.234123\pi\)
−0.977629 + 0.210337i \(0.932544\pi\)
\(60\) −2.85900 6.51616i −0.369095 0.841233i
\(61\) −1.55082 5.78773i −0.198562 0.741042i −0.991316 0.131501i \(-0.958020\pi\)
0.792754 0.609541i \(-0.208646\pi\)
\(62\) −1.66451 11.3372i −0.211393 1.43983i
\(63\) −3.72710 3.86359i −0.469570 0.486766i
\(64\) −5.13007 + 6.13860i −0.641258 + 0.767325i
\(65\) −4.93314 + 8.54446i −0.611881 + 1.05981i
\(66\) −1.66020 + 6.34516i −0.204357 + 0.781035i
\(67\) 1.69184 + 0.453328i 0.206692 + 0.0553829i 0.360679 0.932690i \(-0.382545\pi\)
−0.153988 + 0.988073i \(0.549212\pi\)
\(68\) −5.22420 4.92222i −0.633528 0.596907i
\(69\) 0.333993 + 0.827288i 0.0402080 + 0.0995937i
\(70\) −4.77248 + 2.06053i −0.570421 + 0.246280i
\(71\) 7.58339i 0.899983i −0.893033 0.449992i \(-0.851427\pi\)
0.893033 0.449992i \(-0.148573\pi\)
\(72\) 1.33134 + 8.38019i 0.156900 + 0.987614i
\(73\) 12.5473i 1.46855i −0.678854 0.734273i \(-0.737523\pi\)
0.678854 0.734273i \(-0.262477\pi\)
\(74\) −0.998475 2.31261i −0.116070 0.268836i
\(75\) 0.832546 1.06503i 0.0961341 0.122979i
\(76\) 13.7187 0.408302i 1.57364 0.0468355i
\(77\) 4.62812 + 1.24010i 0.527423 + 0.141323i
\(78\) 8.27010 8.36806i 0.936404 0.947496i
\(79\) −4.01735 + 6.95825i −0.451987 + 0.782864i −0.998509 0.0545802i \(-0.982618\pi\)
0.546523 + 0.837444i \(0.315951\pi\)
\(80\) 8.04904 + 1.65084i 0.899911 + 0.184569i
\(81\) 7.62742 + 4.77729i 0.847491 + 0.530810i
\(82\) −6.59129 + 0.967720i −0.727886 + 0.106867i
\(83\) −2.14313 7.99826i −0.235239 0.877923i −0.978041 0.208412i \(-0.933171\pi\)
0.742802 0.669511i \(-0.233496\pi\)
\(84\) 6.12761 0.936530i 0.668578 0.102184i
\(85\) −1.90804 + 7.12091i −0.206956 + 0.772371i
\(86\) −9.56422 1.11467i −1.03134 0.120198i
\(87\) 11.4792 1.40641i 1.23070 0.150783i
\(88\) −4.87387 5.79671i −0.519557 0.617931i
\(89\) 16.5414i 1.75339i 0.481047 + 0.876695i \(0.340257\pi\)
−0.481047 + 0.876695i \(0.659743\pi\)
\(90\) 6.93051 5.28389i 0.730540 0.556971i
\(91\) −6.07746 6.07746i −0.637091 0.637091i
\(92\) −1.00257 0.236910i −0.104525 0.0246996i
\(93\) 13.0135 5.25383i 1.34944 0.544797i
\(94\) 7.73988 6.12409i 0.798308 0.631651i
\(95\) −7.04818 12.2078i −0.723128 1.25249i
\(96\) −8.78728 4.33401i −0.896848 0.442338i
\(97\) −4.15739 + 7.20082i −0.422119 + 0.731132i −0.996147 0.0877040i \(-0.972047\pi\)
0.574027 + 0.818836i \(0.305380\pi\)
\(98\) 0.780209 + 5.31413i 0.0788130 + 0.536808i
\(99\) −8.03151 0.144412i −0.807197 0.0145140i
\(100\) 0.448680 + 1.49508i 0.0448680 + 0.149508i
\(101\) −4.70129 + 1.25971i −0.467796 + 0.125346i −0.485014 0.874506i \(-0.661186\pi\)
0.0172183 + 0.999852i \(0.494519\pi\)
\(102\) 4.35058 7.63893i 0.430771 0.756367i
\(103\) −6.13162 + 3.54009i −0.604166 + 0.348816i −0.770679 0.637224i \(-0.780083\pi\)
0.166512 + 0.986039i \(0.446749\pi\)
\(104\) 2.37239 + 13.3765i 0.232632 + 1.31167i
\(105\) −3.83018 5.08560i −0.373787 0.496303i
\(106\) −4.17237 9.66380i −0.405256 0.938631i
\(107\) 6.68494 + 6.68494i 0.646258 + 0.646258i 0.952087 0.305829i \(-0.0989335\pi\)
−0.305829 + 0.952087i \(0.598934\pi\)
\(108\) −9.59012 + 4.00369i −0.922810 + 0.385255i
\(109\) −11.6423 + 11.6423i −1.11513 + 1.11513i −0.122687 + 0.992445i \(0.539151\pi\)
−0.992445 + 0.122687i \(0.960849\pi\)
\(110\) −2.86945 + 7.22983i −0.273591 + 0.689338i
\(111\) 2.46434 1.85600i 0.233905 0.176163i
\(112\) −3.20387 + 6.40064i −0.302737 + 0.604804i
\(113\) 0.346060 + 0.599393i 0.0325545 + 0.0563861i 0.881844 0.471542i \(-0.156302\pi\)
−0.849289 + 0.527928i \(0.822969\pi\)
\(114\) 4.44609 + 16.2107i 0.416415 + 1.51827i
\(115\) 0.273849 + 1.02202i 0.0255366 + 0.0953039i
\(116\) −6.33007 + 11.7586i −0.587732 + 1.09175i
\(117\) 12.3473 + 7.42784i 1.14151 + 0.686704i
\(118\) 5.91590 7.95195i 0.544603 0.732036i
\(119\) −5.56168 3.21104i −0.509838 0.294355i
\(120\) 0.358589 + 10.0568i 0.0327345 + 0.918059i
\(121\) −3.31726 + 1.91522i −0.301569 + 0.174111i
\(122\) −0.980952 + 8.41685i −0.0888113 + 0.762026i
\(123\) −3.05450 7.56587i −0.275415 0.682192i
\(124\) −3.72668 + 15.7708i −0.334666 + 1.41626i
\(125\) 8.39615 8.39615i 0.750975 0.750975i
\(126\) 2.88353 + 7.02299i 0.256885 + 0.625658i
\(127\) 5.71585 0.507200 0.253600 0.967309i \(-0.418385\pi\)
0.253600 + 0.967309i \(0.418385\pi\)
\(128\) 9.94582 5.39265i 0.879095 0.476647i
\(129\) −1.43413 11.7055i −0.126268 1.03061i
\(130\) 10.9421 8.65781i 0.959686 0.759340i
\(131\) −8.83835 2.36823i −0.772210 0.206913i −0.148863 0.988858i \(-0.547561\pi\)
−0.623348 + 0.781945i \(0.714228\pi\)
\(132\) 5.49255 7.47439i 0.478065 0.650562i
\(133\) 11.8613 3.17824i 1.02851 0.275588i
\(134\) −1.98738 1.47852i −0.171683 0.127725i
\(135\) 8.28970 + 6.72369i 0.713464 + 0.578683i
\(136\) 4.29913 + 9.19557i 0.368648 + 0.788514i
\(137\) −0.535518 0.309181i −0.0457524 0.0264151i 0.476949 0.878931i \(-0.341743\pi\)
−0.522702 + 0.852516i \(0.675076\pi\)
\(138\) −0.00742822 1.26169i −0.000632332 0.107402i
\(139\) 4.94601 18.4588i 0.419515 1.56565i −0.356101 0.934447i \(-0.615894\pi\)
0.775616 0.631205i \(-0.217439\pi\)
\(140\) 7.34826 0.218702i 0.621041 0.0184837i
\(141\) 9.52338 + 7.44451i 0.802013 + 0.626941i
\(142\) −3.95625 + 9.96814i −0.332001 + 0.836508i
\(143\) −12.8608 −1.07547
\(144\) 2.62193 11.7101i 0.218494 0.975838i
\(145\) 13.7157 1.13903
\(146\) −6.54590 + 16.4930i −0.541743 + 1.36497i
\(147\) −6.09987 + 2.46264i −0.503109 + 0.203115i
\(148\) 0.105977 + 3.56076i 0.00871125 + 0.292693i
\(149\) 1.35719 5.06509i 0.111185 0.414948i −0.887788 0.460252i \(-0.847759\pi\)
0.998973 + 0.0453039i \(0.0144256\pi\)
\(150\) −1.64998 + 0.965615i −0.134721 + 0.0788421i
\(151\) 7.80108 + 4.50395i 0.634843 + 0.366527i 0.782625 0.622493i \(-0.213880\pi\)
−0.147782 + 0.989020i \(0.547214\pi\)
\(152\) −18.2458 6.62033i −1.47993 0.536980i
\(153\) 10.3480 + 2.97313i 0.836588 + 0.240364i
\(154\) −5.43656 4.04456i −0.438091 0.325920i
\(155\) 16.0767 4.30775i 1.29132 0.346007i
\(156\) −15.2364 + 6.68505i −1.21989 + 0.535232i
\(157\) −10.9432 2.93223i −0.873364 0.234017i −0.205822 0.978589i \(-0.565987\pi\)
−0.667542 + 0.744572i \(0.732653\pi\)
\(158\) 8.91079 7.05056i 0.708905 0.560912i
\(159\) 10.2978 7.75573i 0.816671 0.615069i
\(160\) −9.71898 6.36916i −0.768353 0.503526i
\(161\) −0.921720 −0.0726417
\(162\) −7.53369 10.2588i −0.591903 0.806009i
\(163\) −11.9073 + 11.9073i −0.932649 + 0.932649i −0.997871 0.0652222i \(-0.979224\pi\)
0.0652222 + 0.997871i \(0.479224\pi\)
\(164\) 9.16891 + 2.16663i 0.715971 + 0.169186i
\(165\) −9.43355 1.32833i −0.734401 0.103410i
\(166\) −1.35561 + 11.6315i −0.105216 + 0.902782i
\(167\) −8.19418 + 4.73091i −0.634085 + 0.366089i −0.782332 0.622861i \(-0.785970\pi\)
0.148248 + 0.988950i \(0.452637\pi\)
\(168\) −8.54315 1.96573i −0.659118 0.151660i
\(169\) 8.72072 + 5.03491i 0.670825 + 0.387301i
\(170\) 6.22304 8.36480i 0.477285 0.641551i
\(171\) −18.0112 + 9.97139i −1.37735 + 0.762531i
\(172\) 11.9903 + 6.45485i 0.914255 + 0.492178i
\(173\) −6.19263 23.1112i −0.470817 1.75711i −0.636846 0.770991i \(-0.719761\pi\)
0.166030 0.986121i \(-0.446905\pi\)
\(174\) −15.8228 4.14001i −1.19952 0.313853i
\(175\) 0.698304 + 1.20950i 0.0527868 + 0.0914295i
\(176\) 3.38242 + 10.1623i 0.254959 + 0.766011i
\(177\) 11.1724 + 4.74589i 0.839773 + 0.356723i
\(178\) 8.62966 21.7432i 0.646820 1.62972i
\(179\) 11.6334 11.6334i 0.869521 0.869521i −0.122898 0.992419i \(-0.539219\pi\)
0.992419 + 0.122898i \(0.0392188\pi\)
\(180\) −11.8665 + 3.32987i −0.884480 + 0.248194i
\(181\) −10.9379 10.9379i −0.813010 0.813010i 0.172074 0.985084i \(-0.444953\pi\)
−0.985084 + 0.172074i \(0.944953\pi\)
\(182\) 4.81803 + 11.1592i 0.357136 + 0.827178i
\(183\) −10.3012 + 1.26209i −0.761490 + 0.0932961i
\(184\) 1.19425 + 0.834451i 0.0880415 + 0.0615166i
\(185\) 3.16860 1.82939i 0.232960 0.134500i
\(186\) −19.8468 + 0.116849i −1.45524 + 0.00856775i
\(187\) −9.28218 + 2.48715i −0.678780 + 0.181879i
\(188\) −13.3688 + 4.01203i −0.975018 + 0.292608i
\(189\) −7.52667 + 5.45939i −0.547485 + 0.397112i
\(190\) 2.89581 + 19.7238i 0.210084 + 1.43092i
\(191\) 3.34360 5.79129i 0.241934 0.419043i −0.719331 0.694668i \(-0.755551\pi\)
0.961265 + 0.275625i \(0.0888848\pi\)
\(192\) 9.28956 + 10.2812i 0.670417 + 0.741985i
\(193\) −0.468469 0.811411i −0.0337211 0.0584067i 0.848672 0.528919i \(-0.177402\pi\)
−0.882393 + 0.470512i \(0.844069\pi\)
\(194\) 9.22143 7.29634i 0.662060 0.523847i
\(195\) 13.4635 + 10.5245i 0.964140 + 0.753677i
\(196\) 1.74682 7.39229i 0.124773 0.528021i
\(197\) −14.7962 14.7962i −1.05419 1.05419i −0.998445 0.0557400i \(-0.982248\pi\)
−0.0557400 0.998445i \(-0.517752\pi\)
\(198\) 10.4818 + 4.37986i 0.744911 + 0.311263i
\(199\) 2.36977i 0.167988i −0.996466 0.0839942i \(-0.973232\pi\)
0.996466 0.0839942i \(-0.0267677\pi\)
\(200\) 0.190205 2.19931i 0.0134495 0.155515i
\(201\) 1.18611 2.79225i 0.0836616 0.196950i
\(202\) 6.83689 + 0.796814i 0.481042 + 0.0560637i
\(203\) −3.09241 + 11.5410i −0.217045 + 0.810022i
\(204\) −9.70393 + 7.77145i −0.679411 + 0.544110i
\(205\) −2.50446 9.34678i −0.174919 0.652807i
\(206\) 9.90669 1.45448i 0.690232 0.101338i
\(207\) 1.49957 0.373047i 0.104227 0.0259286i
\(208\) 3.86007 18.8207i 0.267647 1.30498i
\(209\) 9.18737 15.9130i 0.635504 1.10072i
\(210\) 2.38150 + 8.68306i 0.164339 + 0.599188i
\(211\) 1.94786 + 0.521927i 0.134096 + 0.0359309i 0.325243 0.945631i \(-0.394554\pi\)
−0.191147 + 0.981561i \(0.561221\pi\)
\(212\) 0.442850 + 14.8795i 0.0304151 + 1.02193i
\(213\) −13.0065 1.83143i −0.891192 0.125488i
\(214\) −5.29962 12.2747i −0.362275 0.839080i
\(215\) 13.9861i 0.953842i
\(216\) 14.6946 0.259569i 0.999844 0.0176614i
\(217\) 14.4990i 0.984255i
\(218\) 21.3773 9.22968i 1.44785 0.625113i
\(219\) −21.5202 3.03023i −1.45420 0.204764i
\(220\) 7.54360 8.00641i 0.508589 0.539792i
\(221\) 16.6505 + 4.46148i 1.12003 + 0.300111i
\(222\) −4.20757 + 1.15401i −0.282393 + 0.0774519i
\(223\) 5.55008 9.61302i 0.371661 0.643735i −0.618160 0.786052i \(-0.712122\pi\)
0.989821 + 0.142317i \(0.0454551\pi\)
\(224\) 7.55060 6.74199i 0.504496 0.450468i
\(225\) −1.62561 1.68514i −0.108374 0.112342i
\(226\) −0.142182 0.968422i −0.00945780 0.0644185i
\(227\) 4.49779 + 16.7860i 0.298529 + 1.11412i 0.938374 + 0.345621i \(0.112332\pi\)
−0.639845 + 0.768504i \(0.721002\pi\)
\(228\) 2.61285 23.6280i 0.173040 1.56480i
\(229\) −4.14447 + 15.4674i −0.273874 + 1.02211i 0.682718 + 0.730682i \(0.260798\pi\)
−0.956592 + 0.291430i \(0.905869\pi\)
\(230\) 0.173221 1.48628i 0.0114218 0.0980025i
\(231\) 3.24465 7.63835i 0.213483 0.502566i
\(232\) 14.4551 12.1539i 0.949024 0.797940i
\(233\) 25.2041i 1.65118i 0.564273 + 0.825588i \(0.309156\pi\)
−0.564273 + 0.825588i \(0.690844\pi\)
\(234\) −12.3550 16.2052i −0.807674 1.05937i
\(235\) 10.1369 + 10.1369i 0.661257 + 0.661257i
\(236\) −11.9248 + 7.36627i −0.776238 + 0.479504i
\(237\) 10.9641 + 8.57073i 0.712195 + 0.556729i
\(238\) 5.63546 + 7.12233i 0.365292 + 0.461672i
\(239\) 4.14085 + 7.17217i 0.267850 + 0.463929i 0.968306 0.249766i \(-0.0803537\pi\)
−0.700457 + 0.713695i \(0.747020\pi\)
\(240\) 4.77529 13.4065i 0.308244 0.865385i
\(241\) −6.40038 + 11.0858i −0.412285 + 0.714098i −0.995139 0.0984784i \(-0.968602\pi\)
0.582854 + 0.812577i \(0.301936\pi\)
\(242\) 5.35961 0.786887i 0.344529 0.0505830i
\(243\) 10.0357 11.9283i 0.643793 0.765199i
\(244\) 5.68050 10.5519i 0.363657 0.675518i
\(245\) −7.53570 + 2.01918i −0.481438 + 0.129001i
\(246\) 0.0679340 + 11.5386i 0.00433131 + 0.735677i
\(247\) −28.5449 + 16.4804i −1.81627 + 1.04862i
\(248\) 13.1262 18.7860i 0.833516 1.19291i
\(249\) −14.2356 + 1.74412i −0.902147 + 0.110529i
\(250\) −15.4168 + 6.65622i −0.975041 + 0.420976i
\(251\) −13.9414 13.9414i −0.879976 0.879976i 0.113556 0.993532i \(-0.463776\pi\)
−0.993532 + 0.113556i \(0.963776\pi\)
\(252\) −0.126419 10.7358i −0.00796367 0.676294i
\(253\) −0.975248 + 0.975248i −0.0613133 + 0.0613133i
\(254\) −7.51332 2.98196i −0.471427 0.187105i
\(255\) 11.7525 + 4.99228i 0.735970 + 0.312629i
\(256\) −15.8868 + 1.89974i −0.992926 + 0.118734i
\(257\) −3.51445 6.08720i −0.219225 0.379709i 0.735346 0.677692i \(-0.237020\pi\)
−0.954571 + 0.297983i \(0.903686\pi\)
\(258\) −4.22162 + 16.1347i −0.262827 + 1.00450i
\(259\) 0.824928 + 3.07867i 0.0512585 + 0.191299i
\(260\) −18.8998 + 5.67193i −1.17212 + 0.351758i
\(261\) 0.360117 20.0280i 0.0222907 1.23970i
\(262\) 10.3822 + 7.72393i 0.641417 + 0.477186i
\(263\) 15.1779 + 8.76296i 0.935909 + 0.540348i 0.888676 0.458536i \(-0.151626\pi\)
0.0472338 + 0.998884i \(0.484959\pi\)
\(264\) −11.1192 + 6.95940i −0.684338 + 0.428321i
\(265\) 13.2408 7.64455i 0.813373 0.469601i
\(266\) −17.2495 2.01036i −1.05763 0.123263i
\(267\) 28.3707 + 3.99485i 1.73626 + 0.244481i
\(268\) 1.84100 + 2.98028i 0.112457 + 0.182050i
\(269\) −0.311911 + 0.311911i −0.0190176 + 0.0190176i −0.716552 0.697534i \(-0.754281\pi\)
0.697534 + 0.716552i \(0.254281\pi\)
\(270\) −7.38881 13.1628i −0.449669 0.801064i
\(271\) 7.46993 0.453766 0.226883 0.973922i \(-0.427147\pi\)
0.226883 + 0.973922i \(0.427147\pi\)
\(272\) −0.853757 14.3302i −0.0517666 0.868893i
\(273\) −11.8914 + 8.95590i −0.719699 + 0.542036i
\(274\) 0.542622 + 0.685789i 0.0327810 + 0.0414300i
\(275\) 2.01860 + 0.540881i 0.121726 + 0.0326164i
\(276\) −0.648458 + 1.66233i −0.0390326 + 0.100060i
\(277\) −10.1481 + 2.71916i −0.609737 + 0.163379i −0.550458 0.834863i \(-0.685547\pi\)
−0.0592792 + 0.998241i \(0.518880\pi\)
\(278\) −16.1313 + 21.6831i −0.967491 + 1.30047i
\(279\) −5.86817 23.5887i −0.351318 1.41222i
\(280\) −9.77316 3.54610i −0.584058 0.211920i
\(281\) −5.76358 3.32761i −0.343826 0.198508i 0.318136 0.948045i \(-0.396943\pi\)
−0.661963 + 0.749537i \(0.730276\pi\)
\(282\) −8.63439 14.7539i −0.514170 0.878583i
\(283\) 2.85005 10.6365i 0.169418 0.632275i −0.828018 0.560702i \(-0.810531\pi\)
0.997435 0.0715734i \(-0.0228020\pi\)
\(284\) 10.4007 11.0388i 0.617171 0.655034i
\(285\) −22.6402 + 9.14030i −1.34109 + 0.541424i
\(286\) 16.9051 + 6.70948i 0.999622 + 0.396740i
\(287\) 8.42949 0.497577
\(288\) −9.55557 + 14.0247i −0.563068 + 0.826411i
\(289\) −4.11987 −0.242345
\(290\) −18.0289 7.15547i −1.05869 0.420184i
\(291\) 11.3463 + 8.86951i 0.665133 + 0.519940i
\(292\) 17.2088 18.2645i 1.00707 1.06885i
\(293\) 0.739342 2.75926i 0.0431928 0.161198i −0.940961 0.338515i \(-0.890075\pi\)
0.984154 + 0.177318i \(0.0567420\pi\)
\(294\) 9.30285 0.0547707i 0.542553 0.00319429i
\(295\) 12.4673 + 7.19800i 0.725874 + 0.419084i
\(296\) 1.71834 4.73580i 0.0998766 0.275263i
\(297\) −2.18734 + 13.7402i −0.126922 + 0.797288i
\(298\) −4.42644 + 5.94986i −0.256416 + 0.344666i
\(299\) 2.38974 0.640328i 0.138202 0.0370311i
\(300\) 2.67261 0.408476i 0.154303 0.0235834i
\(301\) 11.7685 + 3.15337i 0.678328 + 0.181757i
\(302\) −7.90457 9.99013i −0.454857 0.574867i
\(303\) 1.02518 + 8.36756i 0.0588948 + 0.480704i
\(304\) 20.5297 + 18.2211i 1.17746 + 1.04505i
\(305\) −12.3082 −0.704768
\(306\) −12.0511 9.30665i −0.688915 0.532026i
\(307\) −8.15691 + 8.15691i −0.465540 + 0.465540i −0.900466 0.434926i \(-0.856774\pi\)
0.434926 + 0.900466i \(0.356774\pi\)
\(308\) 5.03615 + 8.15271i 0.286961 + 0.464544i
\(309\) 4.59090 + 11.3715i 0.261167 + 0.646901i
\(310\) −23.3797 2.72482i −1.32788 0.154760i
\(311\) 8.33416 4.81173i 0.472587 0.272848i −0.244735 0.969590i \(-0.578701\pi\)
0.717322 + 0.696742i \(0.245368\pi\)
\(312\) 23.5154 0.838469i 1.33130 0.0474690i
\(313\) 22.2531 + 12.8478i 1.25782 + 0.726202i 0.972650 0.232276i \(-0.0746172\pi\)
0.285168 + 0.958477i \(0.407951\pi\)
\(314\) 12.8548 + 9.56339i 0.725437 + 0.539693i
\(315\) −9.64747 + 5.34106i −0.543573 + 0.300934i
\(316\) −15.3912 + 4.61899i −0.865825 + 0.259838i
\(317\) −4.18167 15.6062i −0.234866 0.876532i −0.978209 0.207622i \(-0.933428\pi\)
0.743343 0.668910i \(-0.233239\pi\)
\(318\) −17.5823 + 4.82230i −0.985968 + 0.270421i
\(319\) 8.93928 + 15.4833i 0.500503 + 0.866897i
\(320\) 9.45252 + 13.4424i 0.528412 + 0.751456i
\(321\) 13.0800 9.85110i 0.730055 0.549835i
\(322\) 1.21157 + 0.480861i 0.0675183 + 0.0267973i
\(323\) −17.4149 + 17.4149i −0.968989 + 0.968989i
\(324\) 4.55079 + 17.4152i 0.252822 + 0.967513i
\(325\) −2.65074 2.65074i −0.147036 0.147036i
\(326\) 21.8637 9.43972i 1.21092 0.522818i
\(327\) 17.1564 + 22.7798i 0.948752 + 1.25973i
\(328\) −10.9219 7.63139i −0.603062 0.421373i
\(329\) −10.8152 + 6.24413i −0.596259 + 0.344250i
\(330\) 11.7071 + 6.66752i 0.644456 + 0.367035i
\(331\) −19.6090 + 5.25422i −1.07781 + 0.288798i −0.753698 0.657221i \(-0.771732\pi\)
−0.324111 + 0.946019i \(0.605065\pi\)
\(332\) 7.85007 14.5821i 0.430829 0.800295i
\(333\) −2.58813 4.67489i −0.141828 0.256183i
\(334\) 13.2391 1.94374i 0.724412 0.106357i
\(335\) 1.79895 3.11587i 0.0982870 0.170238i
\(336\) 10.2042 + 7.04085i 0.556684 + 0.384110i
\(337\) 1.04249 + 1.80564i 0.0567879 + 0.0983595i 0.893022 0.450013i \(-0.148581\pi\)
−0.836234 + 0.548373i \(0.815247\pi\)
\(338\) −8.83641 11.1678i −0.480637 0.607450i
\(339\) 1.11161 0.448781i 0.0603745 0.0243744i
\(340\) −12.5439 + 7.74871i −0.680289 + 0.420233i
\(341\) 15.3410 + 15.3410i 0.830762 + 0.830762i
\(342\) 28.8772 3.71067i 1.56150 0.200650i
\(343\) 19.3222i 1.04330i
\(344\) −12.3935 14.7401i −0.668210 0.794731i
\(345\) 1.81903 0.222864i 0.0979335 0.0119986i
\(346\) −3.91708 + 33.6096i −0.210583 + 1.80687i
\(347\) −2.18722 + 8.16281i −0.117416 + 0.438203i −0.999456 0.0329715i \(-0.989503\pi\)
0.882040 + 0.471174i \(0.156170\pi\)
\(348\) 18.6387 + 13.6967i 0.999140 + 0.734218i
\(349\) 0.403839 + 1.50715i 0.0216170 + 0.0806758i 0.975892 0.218255i \(-0.0700366\pi\)
−0.954275 + 0.298931i \(0.903370\pi\)
\(350\) −0.286905 1.95415i −0.0153357 0.104454i
\(351\) 15.7217 19.3834i 0.839160 1.03461i
\(352\) 0.855574 15.1226i 0.0456023 0.806039i
\(353\) −8.13441 + 14.0892i −0.432951 + 0.749893i −0.997126 0.0757623i \(-0.975861\pi\)
0.564175 + 0.825655i \(0.309194\pi\)
\(354\) −12.2099 12.0670i −0.648950 0.641353i
\(355\) −15.0466 4.03173i −0.798592 0.213982i
\(356\) −22.6869 + 24.0787i −1.20240 + 1.27617i
\(357\) −6.85052 + 8.76352i −0.362568 + 0.463815i
\(358\) −21.3609 + 9.22261i −1.12896 + 0.487430i
\(359\) 3.08148i 0.162634i −0.996688 0.0813172i \(-0.974087\pi\)
0.996688 0.0813172i \(-0.0259127\pi\)
\(360\) 17.3354 + 1.81375i 0.913656 + 0.0955933i
\(361\) 28.0923i 1.47854i
\(362\) 8.67126 + 20.0839i 0.455751 + 1.05559i
\(363\) 2.48372 + 6.15208i 0.130362 + 0.322900i
\(364\) −0.511380 17.1820i −0.0268036 0.900584i
\(365\) −24.8957 6.67079i −1.30310 0.349165i
\(366\) 14.1991 + 3.71518i 0.742199 + 0.194195i
\(367\) −1.38231 + 2.39424i −0.0721562 + 0.124978i −0.899846 0.436208i \(-0.856321\pi\)
0.827690 + 0.561186i \(0.189655\pi\)
\(368\) −1.13448 1.71990i −0.0591387 0.0896561i
\(369\) −13.7141 + 3.41167i −0.713930 + 0.177604i
\(370\) −5.11942 + 0.751623i −0.266146 + 0.0390750i
\(371\) 3.44716 + 12.8650i 0.178968 + 0.667916i
\(372\) 26.1490 + 10.2005i 1.35576 + 0.528870i
\(373\) 6.06106 22.6202i 0.313830 1.17123i −0.611244 0.791442i \(-0.709331\pi\)
0.925074 0.379787i \(-0.124003\pi\)
\(374\) 13.4987 + 1.57322i 0.698001 + 0.0813494i
\(375\) −12.3728 16.4282i −0.638928 0.848350i
\(376\) 19.6659 + 1.70078i 1.01419 + 0.0877112i
\(377\) 32.0707i 1.65172i
\(378\) 12.7417 3.24954i 0.655364 0.167138i
\(379\) 4.70551 + 4.70551i 0.241706 + 0.241706i 0.817555 0.575850i \(-0.195329\pi\)
−0.575850 + 0.817555i \(0.695329\pi\)
\(380\) 6.48345 27.4371i 0.332594 1.40749i
\(381\) 1.38041 9.80344i 0.0707206 0.502245i
\(382\) −7.41637 + 5.86811i −0.379455 + 0.300239i
\(383\) 18.3311 + 31.7505i 0.936678 + 1.62237i 0.771614 + 0.636091i \(0.219450\pi\)
0.165063 + 0.986283i \(0.447217\pi\)
\(384\) −6.84713 18.3607i −0.349416 0.936968i
\(385\) 4.92111 8.52361i 0.250803 0.434403i
\(386\) 0.192475 + 1.31098i 0.00979671 + 0.0667269i
\(387\) −20.4228 0.367216i −1.03815 0.0186666i
\(388\) −15.9278 + 4.78001i −0.808611 + 0.242668i
\(389\) 2.82758 0.757647i 0.143364 0.0384142i −0.186423 0.982469i \(-0.559690\pi\)
0.329787 + 0.944055i \(0.393023\pi\)
\(390\) −12.2067 20.8581i −0.618110 1.05619i
\(391\) 1.60094 0.924302i 0.0809630 0.0467440i
\(392\) −6.15269 + 8.80563i −0.310758 + 0.444751i
\(393\) −6.19634 + 14.5870i −0.312564 + 0.735817i
\(394\) 11.7300 + 27.1683i 0.590948 + 1.36872i
\(395\) 11.6704 + 11.6704i 0.587202 + 0.587202i
\(396\) −11.4931 11.2256i −0.577549 0.564105i
\(397\) 13.3392 13.3392i 0.669474 0.669474i −0.288120 0.957594i \(-0.593030\pi\)
0.957594 + 0.288120i \(0.0930302\pi\)
\(398\) −1.23631 + 3.11499i −0.0619705 + 0.156140i
\(399\) −2.58651 21.1113i −0.129488 1.05689i
\(400\) −1.39740 + 2.79170i −0.0698699 + 0.139585i
\(401\) −4.84547 8.39261i −0.241971 0.419107i 0.719304 0.694695i \(-0.244461\pi\)
−0.961276 + 0.275588i \(0.911127\pi\)
\(402\) −3.01582 + 3.05154i −0.150415 + 0.152197i
\(403\) −10.0726 37.5914i −0.501751 1.87256i
\(404\) −8.57119 4.61419i −0.426433 0.229565i
\(405\) 13.5340 12.5941i 0.672511 0.625807i
\(406\) 10.0858 13.5570i 0.500551 0.672824i
\(407\) 4.13030 + 2.38463i 0.204731 + 0.118202i
\(408\) 16.8099 5.15280i 0.832213 0.255102i
\(409\) 6.19403 3.57613i 0.306275 0.176828i −0.338983 0.940792i \(-0.610083\pi\)
0.645258 + 0.763964i \(0.276750\pi\)
\(410\) −1.58417 + 13.5926i −0.0782366 + 0.671292i
\(411\) −0.659617 + 0.843814i −0.0325365 + 0.0416223i
\(412\) −13.7808 3.25644i −0.678933 0.160434i
\(413\) −8.86768 + 8.86768i −0.436350 + 0.436350i
\(414\) −2.16575 0.291964i −0.106441 0.0143493i
\(415\) −17.0092 −0.834948
\(416\) −14.8927 + 22.7254i −0.730173 + 1.11420i
\(417\) −30.4647 12.9410i −1.49186 0.633721i
\(418\) −20.3783 + 16.1241i −0.996736 + 0.788655i
\(419\) 17.9404 + 4.80711i 0.876445 + 0.234843i 0.668873 0.743377i \(-0.266777\pi\)
0.207572 + 0.978220i \(0.433444\pi\)
\(420\) 1.39954 12.6560i 0.0682906 0.617552i
\(421\) 1.97005 0.527873i 0.0960144 0.0257270i −0.210492 0.977596i \(-0.567507\pi\)
0.306506 + 0.951869i \(0.400840\pi\)
\(422\) −2.28811 1.70225i −0.111383 0.0828644i
\(423\) 15.0683 14.5359i 0.732644 0.706762i
\(424\) 7.18051 19.7897i 0.348716 0.961071i
\(425\) −2.42577 1.40052i −0.117667 0.0679353i
\(426\) 16.1412 + 9.19285i 0.782044 + 0.445395i
\(427\) 2.77508 10.3567i 0.134295 0.501198i
\(428\) 0.562495 + 18.8995i 0.0271892 + 0.913542i
\(429\) −3.10596 + 22.0580i −0.149957 + 1.06497i
\(430\) −7.29653 + 18.3843i −0.351870 + 0.886568i
\(431\) −19.8202 −0.954707 −0.477354 0.878711i \(-0.658404\pi\)
−0.477354 + 0.878711i \(0.658404\pi\)
\(432\) −19.4511 7.32499i −0.935840 0.352424i
\(433\) 23.7342 1.14060 0.570298 0.821438i \(-0.306828\pi\)
0.570298 + 0.821438i \(0.306828\pi\)
\(434\) 7.56411 19.0585i 0.363089 0.914836i
\(435\) 3.31242 23.5242i 0.158818 1.12790i
\(436\) −32.9149 + 0.979628i −1.57634 + 0.0469156i
\(437\) −0.914861 + 3.41431i −0.0437637 + 0.163329i
\(438\) 26.7068 + 15.2102i 1.27610 + 0.726773i
\(439\) −19.0949 11.0245i −0.911350 0.526168i −0.0304850 0.999535i \(-0.509705\pi\)
−0.880865 + 0.473367i \(0.843039\pi\)
\(440\) −14.0928 + 6.58868i −0.671846 + 0.314103i
\(441\) 2.75060 + 11.0568i 0.130981 + 0.526515i
\(442\) −19.5590 14.5510i −0.930325 0.692121i
\(443\) −9.71199 + 2.60232i −0.461431 + 0.123640i −0.482043 0.876148i \(-0.660105\pi\)
0.0206123 + 0.999788i \(0.493438\pi\)
\(444\) 6.13276 + 0.678179i 0.291048 + 0.0321849i
\(445\) 32.8208 + 8.79430i 1.55585 + 0.416890i
\(446\) −12.3105 + 9.74054i −0.582920 + 0.461228i
\(447\) −8.35953 3.55100i −0.395392 0.167957i
\(448\) −13.4423 + 4.92299i −0.635090 + 0.232590i
\(449\) 24.6980 1.16557 0.582786 0.812626i \(-0.301963\pi\)
0.582786 + 0.812626i \(0.301963\pi\)
\(450\) 1.25768 + 3.06314i 0.0592874 + 0.144398i
\(451\) 8.91903 8.91903i 0.419981 0.419981i
\(452\) −0.318332 + 1.34714i −0.0149731 + 0.0633640i
\(453\) 9.60887 12.2921i 0.451464 0.577535i
\(454\) 2.84503 24.4112i 0.133524 1.14567i
\(455\) −15.2897 + 8.82752i −0.716793 + 0.413841i
\(456\) −15.7612 + 29.6951i −0.738086 + 1.39060i
\(457\) −27.1171 15.6561i −1.26849 0.732360i −0.293784 0.955872i \(-0.594915\pi\)
−0.974701 + 0.223511i \(0.928248\pi\)
\(458\) 13.5171 18.1692i 0.631612 0.848992i
\(459\) 7.59842 17.0302i 0.354664 0.794902i
\(460\) −1.00309 + 1.86330i −0.0467691 + 0.0868769i
\(461\) 3.17103 + 11.8344i 0.147689 + 0.551185i 0.999621 + 0.0275314i \(0.00876461\pi\)
−0.851931 + 0.523653i \(0.824569\pi\)
\(462\) −8.24992 + 8.34764i −0.383821 + 0.388367i
\(463\) −12.7250 22.0403i −0.591379 1.02430i −0.994047 0.108953i \(-0.965250\pi\)
0.402668 0.915346i \(-0.368083\pi\)
\(464\) −25.3415 + 8.43466i −1.17645 + 0.391569i
\(465\) −3.50574 28.6141i −0.162575 1.32695i
\(466\) 13.1490 33.1300i 0.609114 1.53472i
\(467\) −6.28473 + 6.28473i −0.290822 + 0.290822i −0.837405 0.546583i \(-0.815928\pi\)
0.546583 + 0.837405i \(0.315928\pi\)
\(468\) 7.78606 + 27.7469i 0.359911 + 1.28260i
\(469\) 2.21624 + 2.21624i 0.102336 + 0.102336i
\(470\) −8.03621 18.6130i −0.370683 0.858554i
\(471\) −7.67200 + 18.0609i −0.353507 + 0.832203i
\(472\) 19.5178 3.46158i 0.898378 0.159332i
\(473\) 15.7885 9.11550i 0.725956 0.419131i
\(474\) −9.94063 16.9859i −0.456588 0.780190i
\(475\) 5.17343 1.38622i 0.237373 0.0636040i
\(476\) −3.69192 12.3021i −0.169219 0.563866i
\(477\) −10.8151 19.5352i −0.495190 0.894454i
\(478\) −1.70131 11.5879i −0.0778161 0.530017i
\(479\) −1.61178 + 2.79169i −0.0736442 + 0.127555i −0.900496 0.434865i \(-0.856796\pi\)
0.826852 + 0.562420i \(0.190130\pi\)
\(480\) −13.2711 + 15.1311i −0.605741 + 0.690639i
\(481\) −4.27757 7.40897i −0.195040 0.337820i
\(482\) 14.1966 11.2329i 0.646635 0.511642i
\(483\) −0.222600 + 1.58087i −0.0101287 + 0.0719321i
\(484\) −7.45556 1.76177i −0.338889 0.0800803i
\(485\) 12.0772 + 12.0772i 0.548399 + 0.548399i
\(486\) −19.4147 + 10.4437i −0.880667 + 0.473736i
\(487\) 11.2953i 0.511838i 0.966698 + 0.255919i \(0.0823780\pi\)
−0.966698 + 0.255919i \(0.917622\pi\)
\(488\) −12.9718 + 10.9067i −0.587205 + 0.493722i
\(489\) 17.5468 + 23.2982i 0.793496 + 1.05358i
\(490\) 10.9588 + 1.27721i 0.495070 + 0.0576986i
\(491\) 7.32459 27.3357i 0.330554 1.23364i −0.578055 0.815998i \(-0.696188\pi\)
0.908609 0.417647i \(-0.137145\pi\)
\(492\) 5.93040 15.2026i 0.267363 0.685387i
\(493\) −6.20215 23.1468i −0.279331 1.04248i
\(494\) 46.1191 6.77112i 2.07500 0.304647i
\(495\) −4.55651 + 15.8590i −0.204800 + 0.712808i
\(496\) −27.0547 + 17.8457i −1.21479 + 0.801297i
\(497\) 6.78498 11.7519i 0.304348 0.527146i
\(498\) 19.6222 + 5.13413i 0.879292 + 0.230066i
\(499\) 16.8830 + 4.52377i 0.755785 + 0.202512i 0.616082 0.787682i \(-0.288719\pi\)
0.139702 + 0.990194i \(0.455385\pi\)
\(500\) 23.7374 0.706483i 1.06157 0.0315949i
\(501\) 6.13520 + 15.1966i 0.274100 + 0.678936i
\(502\) 11.0524 + 25.5988i 0.493291 + 1.14253i
\(503\) 14.1184i 0.629509i 0.949173 + 0.314754i \(0.101922\pi\)
−0.949173 + 0.314754i \(0.898078\pi\)
\(504\) −5.43471 + 14.1779i −0.242081 + 0.631533i
\(505\) 9.99782i 0.444897i
\(506\) 1.79072 0.773147i 0.0796072 0.0343706i
\(507\) 10.7416 13.7412i 0.477053 0.610269i
\(508\) 8.32034 + 7.83938i 0.369155 + 0.347816i
\(509\) 29.4208 + 7.88327i 1.30405 + 0.349420i 0.842981 0.537943i \(-0.180798\pi\)
0.461072 + 0.887363i \(0.347465\pi\)
\(510\) −12.8438 12.6935i −0.568734 0.562077i
\(511\) 11.2262 19.4444i 0.496619 0.860170i
\(512\) 21.8738 + 5.79099i 0.966696 + 0.255928i
\(513\) 12.7524 + 33.2997i 0.563034 + 1.47022i
\(514\) 1.44394 + 9.83492i 0.0636896 + 0.433800i
\(515\) 3.76420 + 14.0482i 0.165870 + 0.619037i
\(516\) 13.9667 19.0061i 0.614848 0.836699i
\(517\) −4.83648 + 18.0500i −0.212708 + 0.793838i
\(518\) 0.521799 4.47719i 0.0229265 0.196716i
\(519\) −41.1343 + 5.03969i −1.80559 + 0.221218i
\(520\) 27.8023 + 2.40445i 1.21921 + 0.105442i
\(521\) 8.75761i 0.383678i −0.981426 0.191839i \(-0.938555\pi\)
0.981426 0.191839i \(-0.0614451\pi\)
\(522\) −10.9220 + 26.1383i −0.478041 + 1.14404i
\(523\) 21.3424 + 21.3424i 0.933236 + 0.933236i 0.997907 0.0646706i \(-0.0205997\pi\)
−0.0646706 + 0.997907i \(0.520600\pi\)
\(524\) −9.61757 15.5693i −0.420145 0.680147i
\(525\) 2.24309 0.905583i 0.0978966 0.0395229i
\(526\) −15.3793 19.4370i −0.670567 0.847491i
\(527\) −14.5396 25.1834i −0.633356 1.09700i
\(528\) 18.2465 3.34704i 0.794078 0.145661i
\(529\) −11.3673 + 19.6888i −0.494232 + 0.856035i
\(530\) −21.3927 + 3.14084i −0.929241 + 0.136429i
\(531\) 10.8380 18.0161i 0.470330 0.781830i
\(532\) 21.6251 + 11.6416i 0.937566 + 0.504727i
\(533\) −21.8551 + 5.85605i −0.946648 + 0.253654i
\(534\) −35.2084 20.0521i −1.52361 0.867740i
\(535\) 16.8180 9.70989i 0.727107 0.419795i
\(536\) −0.865129 4.87794i −0.0373679 0.210695i
\(537\) −17.1433 22.7623i −0.739787 0.982268i
\(538\) 0.572721 0.247274i 0.0246918 0.0106607i
\(539\) −7.19083 7.19083i −0.309731 0.309731i
\(540\) 2.84533 + 21.1569i 0.122444 + 0.910446i
\(541\) −25.1121 + 25.1121i −1.07965 + 1.07965i −0.0831121 + 0.996540i \(0.526486\pi\)
−0.996540 + 0.0831121i \(0.973514\pi\)
\(542\) −9.81899 3.89706i −0.421762 0.167393i
\(543\) −21.4016 + 16.1184i −0.918429 + 0.691707i
\(544\) −6.35379 + 19.2819i −0.272417 + 0.826707i
\(545\) 16.9105 + 29.2898i 0.724366 + 1.25464i
\(546\) 20.3031 5.56853i 0.868894 0.238311i
\(547\) 1.42764 + 5.32802i 0.0610414 + 0.227810i 0.989707 0.143108i \(-0.0457098\pi\)
−0.928666 + 0.370918i \(0.879043\pi\)
\(548\) −0.355484 1.18453i −0.0151855 0.0506008i
\(549\) −0.323163 + 17.9728i −0.0137923 + 0.767060i
\(550\) −2.37121 1.76407i −0.101109 0.0752203i
\(551\) 39.6818 + 22.9103i 1.69050 + 0.976013i
\(552\) 1.71961 1.84678i 0.0731916 0.0786040i
\(553\) −12.4513 + 7.18876i −0.529483 + 0.305697i
\(554\) 14.7579 + 1.71998i 0.627003 + 0.0730748i
\(555\) −2.37241 5.87637i −0.100703 0.249438i
\(556\) 32.5162 20.0861i 1.37899 0.851842i
\(557\) −15.4160 + 15.4160i −0.653197 + 0.653197i −0.953761 0.300565i \(-0.902825\pi\)
0.300565 + 0.953761i \(0.402825\pi\)
\(558\) −4.59270 + 34.0681i −0.194425 + 1.44222i
\(559\) −32.7029 −1.38319
\(560\) 10.9965 + 9.75989i 0.464688 + 0.412431i
\(561\) 2.02410 + 16.5208i 0.0854574 + 0.697510i
\(562\) 5.84004 + 7.38089i 0.246347 + 0.311344i
\(563\) −15.9692 4.27894i −0.673022 0.180336i −0.0939062 0.995581i \(-0.529935\pi\)
−0.579116 + 0.815245i \(0.696602\pi\)
\(564\) 3.65253 + 23.8981i 0.153799 + 1.00629i
\(565\) 1.37327 0.367967i 0.0577740 0.0154805i
\(566\) −9.29536 + 12.4945i −0.390713 + 0.525183i
\(567\) 7.54583 + 14.2277i 0.316895 + 0.597507i
\(568\) −19.4304 + 9.08415i −0.815282 + 0.381163i
\(569\) −9.85656 5.69069i −0.413208 0.238566i 0.278959 0.960303i \(-0.410011\pi\)
−0.692167 + 0.721737i \(0.743344\pi\)
\(570\) 34.5283 0.203286i 1.44623 0.00851471i
\(571\) −3.18813 + 11.8982i −0.133419 + 0.497926i −0.999999 0.00111115i \(-0.999646\pi\)
0.866580 + 0.499037i \(0.166313\pi\)
\(572\) −18.7210 17.6388i −0.782762 0.737515i
\(573\) −9.12532 7.13334i −0.381216 0.298000i
\(574\) −11.0803 4.39766i −0.462483 0.183555i
\(575\) −0.402016 −0.0167652
\(576\) 19.8772 13.4498i 0.828215 0.560410i
\(577\) 21.7471 0.905342 0.452671 0.891678i \(-0.350471\pi\)
0.452671 + 0.891678i \(0.350471\pi\)
\(578\) 5.41544 + 2.14933i 0.225253 + 0.0894004i
\(579\) −1.50481 + 0.607525i −0.0625380 + 0.0252479i
\(580\) 19.9654 + 18.8113i 0.829018 + 0.781097i
\(581\) 3.83498 14.3123i 0.159102 0.593775i
\(582\) −10.2872 17.5781i −0.426417 0.728634i
\(583\) 17.2595 + 9.96475i 0.714814 + 0.412698i
\(584\) −32.1490 + 15.0304i −1.33034 + 0.621961i
\(585\) 21.3024 20.5499i 0.880748 0.849634i
\(586\) −2.41135 + 3.24125i −0.0996118 + 0.133895i
\(587\) −15.2163 + 4.07718i −0.628042 + 0.168283i −0.558781 0.829315i \(-0.688731\pi\)
−0.0692610 + 0.997599i \(0.522064\pi\)
\(588\) −12.2569 4.78130i −0.505465 0.197177i
\(589\) 53.7083 + 14.3911i 2.21301 + 0.592975i
\(590\) −12.6327 15.9657i −0.520080 0.657299i
\(591\) −28.9508 + 21.8041i −1.19088 + 0.896899i
\(592\) −4.72937 + 5.32860i −0.194376 + 0.219004i
\(593\) 10.1125 0.415270 0.207635 0.978206i \(-0.433423\pi\)
0.207635 + 0.978206i \(0.433423\pi\)
\(594\) 10.0435 16.9200i 0.412088 0.694234i
\(595\) −9.32807 + 9.32807i −0.382414 + 0.382414i
\(596\) 8.92245 5.51164i 0.365478 0.225766i
\(597\) −4.06446 0.572312i −0.166347 0.0234232i
\(598\) −3.47529 0.405032i −0.142115 0.0165630i
\(599\) 4.23917 2.44748i 0.173208 0.100002i −0.410890 0.911685i \(-0.634782\pi\)
0.584097 + 0.811684i \(0.301449\pi\)
\(600\) −3.72617 0.857372i −0.152120 0.0350021i
\(601\) −25.8322 14.9142i −1.05372 0.608364i −0.130030 0.991510i \(-0.541507\pi\)
−0.923688 + 0.383146i \(0.874841\pi\)
\(602\) −13.8243 10.2847i −0.563436 0.419171i
\(603\) −4.50263 2.70867i −0.183361 0.110306i
\(604\) 5.17847 + 17.2555i 0.210709 + 0.702117i
\(605\) 2.03647 + 7.60019i 0.0827941 + 0.308992i
\(606\) 3.01779 11.5337i 0.122589 0.468526i
\(607\) −8.48425 14.6952i −0.344365 0.596458i 0.640873 0.767647i \(-0.278572\pi\)
−0.985238 + 0.171189i \(0.945239\pi\)
\(608\) −17.4798 34.6614i −0.708900 1.40570i
\(609\) 19.0476 + 8.09112i 0.771846 + 0.327869i
\(610\) 16.1788 + 6.42120i 0.655061 + 0.259987i
\(611\) 23.7025 23.7025i 0.958901 0.958901i
\(612\) 10.9855 + 18.5204i 0.444063 + 0.748641i
\(613\) 30.2781 + 30.2781i 1.22292 + 1.22292i 0.966589 + 0.256332i \(0.0825140\pi\)
0.256332 + 0.966589i \(0.417486\pi\)
\(614\) 14.9775 6.46656i 0.604441 0.260969i
\(615\) −16.6358 + 2.03818i −0.670820 + 0.0821874i
\(616\) −2.36660 13.3438i −0.0953531 0.537639i
\(617\) −14.9377 + 8.62428i −0.601368 + 0.347200i −0.769580 0.638551i \(-0.779534\pi\)
0.168211 + 0.985751i \(0.446201\pi\)
\(618\) −0.102105 17.3425i −0.00410725 0.697619i
\(619\) −16.7334 + 4.48369i −0.672570 + 0.180215i −0.578912 0.815390i \(-0.696523\pi\)
−0.0936580 + 0.995604i \(0.529856\pi\)
\(620\) 29.3104 + 15.7789i 1.17713 + 0.633696i
\(621\) −0.277671 2.66205i −0.0111426 0.106824i
\(622\) −13.4653 + 1.97694i −0.539908 + 0.0792682i
\(623\) −14.7999 + 25.6341i −0.592945 + 1.02701i
\(624\) −31.3477 11.1658i −1.25491 0.446990i
\(625\) −10.2442 17.7435i −0.409770 0.709742i
\(626\) −22.5483 28.4975i −0.901211 1.13899i
\(627\) −25.0741 19.6006i −1.00136 0.782773i
\(628\) −11.9080 19.2771i −0.475181 0.769241i
\(629\) −4.52012 4.52012i −0.180229 0.180229i
\(630\) 15.4677 1.98757i 0.616249 0.0791868i
\(631\) 11.6246i 0.462766i −0.972863 0.231383i \(-0.925675\pi\)
0.972863 0.231383i \(-0.0743251\pi\)
\(632\) 22.6410 + 1.95808i 0.900612 + 0.0778884i
\(633\) 1.36559 3.21478i 0.0542774 0.127776i
\(634\) −2.64507 + 22.6955i −0.105049 + 0.901352i
\(635\) 3.03885 11.3411i 0.120593 0.450059i
\(636\) 25.6272 + 2.83393i 1.01619 + 0.112373i
\(637\) 4.72135 + 17.6203i 0.187067 + 0.698142i
\(638\) −3.67279 25.0159i −0.145407 0.990389i
\(639\) −6.28229 + 21.8656i −0.248524 + 0.864989i
\(640\) −5.41213 22.6011i −0.213933 0.893385i
\(641\) −3.04338 + 5.27129i −0.120206 + 0.208203i −0.919849 0.392273i \(-0.871689\pi\)
0.799643 + 0.600476i \(0.205022\pi\)
\(642\) −22.3326 + 6.12514i −0.881396 + 0.241740i
\(643\) 31.1326 + 8.34195i 1.22775 + 0.328974i 0.813702 0.581282i \(-0.197449\pi\)
0.414046 + 0.910256i \(0.364115\pi\)
\(644\) −1.34171 1.26415i −0.0528708 0.0498146i
\(645\) −23.9880 3.37771i −0.944525 0.132997i
\(646\) 31.9766 13.8060i 1.25810 0.543189i
\(647\) 13.1882i 0.518482i 0.965813 + 0.259241i \(0.0834724\pi\)
−0.965813 + 0.259241i \(0.916528\pi\)
\(648\) 3.10364 25.2659i 0.121923 0.992540i
\(649\) 18.7653i 0.736604i
\(650\) 2.10143 + 4.86720i 0.0824247 + 0.190907i
\(651\) 24.8677 + 3.50158i 0.974641 + 0.137238i
\(652\) −33.6639 + 1.00192i −1.31838 + 0.0392382i
\(653\) −15.2661 4.09053i −0.597407 0.160075i −0.0525710 0.998617i \(-0.516742\pi\)
−0.544836 + 0.838542i \(0.683408\pi\)
\(654\) −10.6674 38.8938i −0.417128 1.52087i
\(655\) −9.39787 + 16.2776i −0.367205 + 0.636018i
\(656\) 10.3752 + 15.7292i 0.405085 + 0.614121i
\(657\) −10.3945 + 36.1782i −0.405528 + 1.41144i
\(658\) 17.4738 2.56546i 0.681198 0.100012i
\(659\) −9.26579 34.5804i −0.360944 1.34706i −0.872837 0.488012i \(-0.837722\pi\)
0.511893 0.859049i \(-0.328944\pi\)
\(660\) −11.9102 14.8719i −0.463605 0.578886i
\(661\) 6.58569 24.5781i 0.256153 0.955978i −0.711292 0.702897i \(-0.751889\pi\)
0.967445 0.253081i \(-0.0814439\pi\)
\(662\) 28.5166 + 3.32350i 1.10833 + 0.129172i
\(663\) 11.6732 27.4802i 0.453349 1.06724i
\(664\) −17.9261 + 15.0723i −0.695669 + 0.584919i
\(665\) 25.2244i 0.978162i
\(666\) 0.963123 + 7.49523i 0.0373202 + 0.290434i
\(667\) −2.43195 2.43195i −0.0941656 0.0941656i
\(668\) −18.4165 4.35185i −0.712554 0.168378i
\(669\) −15.1472 11.8407i −0.585625 0.457788i
\(670\) −3.99021 + 3.15720i −0.154155 + 0.121973i
\(671\) −8.02196 13.8944i −0.309684 0.536389i
\(672\) −9.73988 14.5785i −0.375724 0.562378i
\(673\) −16.8241 + 29.1402i −0.648522 + 1.12327i 0.334954 + 0.942235i \(0.391279\pi\)
−0.983476 + 0.181039i \(0.942054\pi\)
\(674\) −0.428316 2.91732i −0.0164981 0.112371i
\(675\) −3.28282 + 2.38116i −0.126356 + 0.0916509i
\(676\) 5.78894 + 19.2897i 0.222652 + 0.741912i
\(677\) 35.5422 9.52351i 1.36600 0.366018i 0.499983 0.866035i \(-0.333340\pi\)
0.866015 + 0.500017i \(0.166673\pi\)
\(678\) −1.69531 + 0.00998117i −0.0651080 + 0.000383325i
\(679\) −12.8854 + 7.43937i −0.494495 + 0.285497i
\(680\) 20.5311 3.64130i 0.787331 0.139637i
\(681\) 29.8764 3.66039i 1.14487 0.140267i
\(682\) −12.1619 28.1687i −0.465703 1.07863i
\(683\) −0.339146 0.339146i −0.0129771 0.0129771i 0.700588 0.713566i \(-0.252921\pi\)
−0.713566 + 0.700588i \(0.752921\pi\)
\(684\) −39.8941 10.1877i −1.52539 0.389535i
\(685\) −0.898173 + 0.898173i −0.0343174 + 0.0343174i
\(686\) −10.0804 + 25.3984i −0.384870 + 0.969715i
\(687\) 25.5277 + 10.8438i 0.973941 + 0.413715i
\(688\) 8.60093 + 25.8410i 0.327907 + 0.985180i
\(689\) −17.8749 30.9602i −0.680978 1.17949i
\(690\) −2.50733 0.656041i −0.0954525 0.0249751i
\(691\) −4.63964 17.3154i −0.176500 0.658707i −0.996291 0.0860448i \(-0.972577\pi\)
0.819791 0.572663i \(-0.194089\pi\)
\(692\) 22.6830 42.1353i 0.862279 1.60174i
\(693\) −12.3172 7.40971i −0.467890 0.281472i
\(694\) 7.13356 9.58869i 0.270786 0.363982i
\(695\) −33.9955 19.6273i −1.28952 0.744506i
\(696\) −17.3545 27.7276i −0.657820 1.05101i
\(697\) −14.6412 + 8.45311i −0.554576 + 0.320184i
\(698\) 0.255444 2.19178i 0.00966871 0.0829602i
\(699\) 43.2284 + 6.08693i 1.63505 + 0.230229i
\(700\) −0.642353 + 2.71835i −0.0242787 + 0.102744i
\(701\) −14.5424 + 14.5424i −0.549258 + 0.549258i −0.926226 0.376968i \(-0.876967\pi\)
0.376968 + 0.926226i \(0.376967\pi\)
\(702\) −30.7779 + 17.2769i −1.16164 + 0.652073i
\(703\) 12.2231 0.461001
\(704\) −9.01409 + 19.4319i −0.339731 + 0.732366i
\(705\) 19.8342 14.9380i 0.746998 0.562596i
\(706\) 18.0428 14.2761i 0.679048 0.537289i
\(707\) −8.41264 2.25416i −0.316390 0.0847764i
\(708\) 9.75422 + 22.2316i 0.366586 + 0.835514i
\(709\) 32.2924 8.65273i 1.21277 0.324960i 0.404920 0.914352i \(-0.367299\pi\)
0.807847 + 0.589392i \(0.200633\pi\)
\(710\) 17.6750 + 13.1494i 0.663330 + 0.493488i
\(711\) 17.3478 16.7350i 0.650594 0.627611i
\(712\) 42.3830 19.8150i 1.58837 0.742599i
\(713\) −3.61441 2.08678i −0.135361 0.0781505i
\(714\) 13.5767 7.94547i 0.508096 0.297352i
\(715\) −6.83748 + 25.5178i −0.255707 + 0.954313i
\(716\) 32.8897 0.978877i 1.22914 0.0365824i
\(717\) 13.3012 5.36999i 0.496744 0.200546i
\(718\) −1.60761 + 4.05051i −0.0599954 + 0.151164i
\(719\) 38.7103 1.44365 0.721826 0.692075i \(-0.243303\pi\)
0.721826 + 0.692075i \(0.243303\pi\)
\(720\) −21.8406 11.4280i −0.813952 0.425896i
\(721\) −12.6695 −0.471837
\(722\) −14.6558 + 36.9265i −0.545431 + 1.37426i
\(723\) 17.4678 + 13.6548i 0.649636 + 0.507826i
\(724\) −0.920358 30.9234i −0.0342048 1.14926i
\(725\) −1.34878 + 5.03373i −0.0500925 + 0.186948i
\(726\) −0.0552395 9.38247i −0.00205013 0.348216i
\(727\) 24.4245 + 14.1015i 0.905853 + 0.522994i 0.879095 0.476647i \(-0.158148\pi\)
0.0267585 + 0.999642i \(0.491481\pi\)
\(728\) −8.29167 + 22.8521i −0.307310 + 0.846953i
\(729\) −18.0349 20.0934i −0.667958 0.744199i
\(730\) 29.2445 + 21.7566i 1.08239 + 0.805249i
\(731\) −23.6031 + 6.32442i −0.872990 + 0.233917i
\(732\) −16.7261 12.2911i −0.618213 0.454294i
\(733\) −7.28085 1.95090i −0.268924 0.0720580i 0.121837 0.992550i \(-0.461122\pi\)
−0.390761 + 0.920492i \(0.627788\pi\)
\(734\) 3.06608 2.42600i 0.113171 0.0895453i
\(735\) 1.64325 + 13.4123i 0.0606123 + 0.494722i
\(736\) 0.593963 + 2.85261i 0.0218938 + 0.105149i
\(737\) 4.68989 0.172754
\(738\) 19.8067 + 2.67013i 0.729094 + 0.0982888i
\(739\) −16.1043 + 16.1043i −0.592407 + 0.592407i −0.938281 0.345874i \(-0.887583\pi\)
0.345874 + 0.938281i \(0.387583\pi\)
\(740\) 7.12144 + 1.68281i 0.261789 + 0.0618614i
\(741\) 21.3723 + 52.9383i 0.785130 + 1.94474i
\(742\) 2.18046 18.7090i 0.0800474 0.686829i
\(743\) −5.50307 + 3.17720i −0.201888 + 0.116560i −0.597536 0.801842i \(-0.703853\pi\)
0.395648 + 0.918402i \(0.370520\pi\)
\(744\) −29.0505 27.0501i −1.06504 0.991706i
\(745\) −9.32837 5.38574i −0.341765 0.197318i
\(746\) −19.7680 + 26.5715i −0.723759 + 0.972851i
\(747\) −0.446590 + 24.8372i −0.0163399 + 0.908746i
\(748\) −16.9229 9.11021i −0.618761 0.333102i
\(749\) 4.37848 + 16.3407i 0.159986 + 0.597077i
\(750\) 7.69306 + 28.0493i 0.280911 + 1.02421i
\(751\) 7.20371 + 12.4772i 0.262867 + 0.455299i 0.967003 0.254767i \(-0.0819986\pi\)
−0.704136 + 0.710066i \(0.748665\pi\)
\(752\) −24.9629 12.4953i −0.910305 0.455658i
\(753\) −27.2783 + 20.5445i −0.994077 + 0.748682i
\(754\) −16.7313 + 42.1559i −0.609317 + 1.53523i
\(755\) 13.0840 13.0840i 0.476176 0.476176i
\(756\) −18.4439 2.37594i −0.670798 0.0864121i
\(757\) −29.7018 29.7018i −1.07953 1.07953i −0.996551 0.0829799i \(-0.973556\pi\)
−0.0829799 0.996551i \(-0.526444\pi\)
\(758\) −3.73038 8.64010i −0.135494 0.313823i
\(759\) 1.43715 + 1.90821i 0.0521653 + 0.0692635i
\(760\) −22.8362 + 32.6828i −0.828356 + 1.18553i
\(761\) 21.6542 12.5021i 0.784965 0.453200i −0.0532222 0.998583i \(-0.516949\pi\)
0.838187 + 0.545383i \(0.183616\pi\)
\(762\) −6.92896 + 12.1662i −0.251010 + 0.440734i
\(763\) −28.4586 + 7.62545i −1.03027 + 0.276060i
\(764\) 12.8100 3.84434i 0.463449 0.139083i
\(765\) 11.4007 18.9514i 0.412194 0.685190i
\(766\) −7.53153 51.2984i −0.272125 1.85349i
\(767\) 16.8307 29.1516i 0.607721 1.05260i
\(768\) −0.578446 + 27.7068i −0.0208729 + 0.999782i
\(769\) −26.1481 45.2899i −0.942926 1.63320i −0.759851 0.650097i \(-0.774728\pi\)
−0.183076 0.983099i \(-0.558605\pi\)
\(770\) −10.9154 + 8.63668i −0.393364 + 0.311244i
\(771\) −11.2891 + 4.55764i −0.406567 + 0.164140i
\(772\) 0.430933 1.82365i 0.0155096 0.0656346i
\(773\) 0.679496 + 0.679496i 0.0244398 + 0.0244398i 0.719221 0.694781i \(-0.244499\pi\)
−0.694781 + 0.719221i \(0.744499\pi\)
\(774\) 26.6536 + 11.1373i 0.958043 + 0.400320i
\(775\) 6.32386i 0.227160i
\(776\) 23.4303 + 2.02634i 0.841099 + 0.0727415i
\(777\) 5.47955 0.671343i 0.196578 0.0240843i
\(778\) −4.11203 0.479241i −0.147423 0.0171816i
\(779\) 8.36677 31.2252i 0.299771 1.11876i
\(780\) 5.16370 + 33.7855i 0.184890 + 1.20972i
\(781\) −5.25540 19.6134i −0.188053 0.701824i
\(782\) −2.58659 + 0.379758i −0.0924964 + 0.0135801i
\(783\) −34.2637 5.45452i −1.22448 0.194929i
\(784\) 12.6814 8.36487i 0.452908 0.298745i
\(785\) −11.6360 + 20.1541i −0.415306 + 0.719331i
\(786\) 15.7549 15.9415i 0.561959 0.568616i
\(787\) 28.3085 + 7.58525i 1.00909 + 0.270385i 0.725249 0.688487i \(-0.241725\pi\)
0.283841 + 0.958871i \(0.408391\pi\)
\(788\) −1.24501 41.8314i −0.0443515 1.49018i
\(789\) 18.6952 23.9158i 0.665566 0.851425i
\(790\) −9.25195 21.4288i −0.329170 0.762404i
\(791\) 1.23850i 0.0440360i
\(792\) 9.25093 + 20.7516i 0.328718 + 0.737375i
\(793\) 28.7797i 1.02200i
\(794\) −24.4930 + 10.5749i −0.869223 + 0.375289i
\(795\) −9.91370 24.5558i −0.351603 0.870906i
\(796\) 3.25017 3.44958i 0.115199 0.122267i
\(797\) −21.0141 5.63071i −0.744357 0.199450i −0.133343 0.991070i \(-0.542571\pi\)
−0.611014 + 0.791620i \(0.709238\pi\)
\(798\) −7.61387 + 29.0996i −0.269528 + 1.03011i
\(799\) 12.5233 21.6909i 0.443041 0.767370i
\(800\) 3.29326 2.94058i 0.116434 0.103965i
\(801\) 13.7034 47.6948i 0.484185 1.68521i
\(802\) 1.99081 + 13.5597i 0.0702979 + 0.478810i
\(803\) −8.69544 32.4518i −0.306855 1.14520i
\(804\) 5.55619 2.43781i 0.195952 0.0859748i
\(805\) −0.490035 + 1.82883i −0.0172714 + 0.0644579i
\(806\) −6.37131 + 54.6676i −0.224420 + 1.92558i
\(807\) 0.459640 + 0.610297i 0.0161801 + 0.0214835i
\(808\) 8.85934 + 10.5368i 0.311671 + 0.370683i
\(809\) 12.5804i 0.442303i −0.975240 0.221151i \(-0.929019\pi\)
0.975240 0.221151i \(-0.0709815\pi\)
\(810\) −24.3604 + 9.49389i −0.855937 + 0.333581i
\(811\) 30.5378 + 30.5378i 1.07233 + 1.07233i 0.997172 + 0.0751549i \(0.0239451\pi\)
0.0751549 + 0.997172i \(0.476055\pi\)
\(812\) −20.3302 + 12.5585i −0.713451 + 0.440718i
\(813\) 1.80403 12.8119i 0.0632701 0.449333i
\(814\) −4.18509 5.28930i −0.146687 0.185390i
\(815\) 17.2953 + 29.9564i 0.605829 + 1.04933i
\(816\) −24.7843 1.99651i −0.867623 0.0698917i
\(817\) 23.3620 40.4641i 0.817331 1.41566i
\(818\) −10.0075 + 1.46929i −0.349905 + 0.0513723i
\(819\) 12.4887 + 22.5582i 0.436391 + 0.788246i
\(820\) 9.17361 17.0406i 0.320356 0.595085i
\(821\) 18.2160 4.88097i 0.635744 0.170347i 0.0734689 0.997298i \(-0.476593\pi\)
0.562275 + 0.826951i \(0.309926\pi\)
\(822\) 1.30726 0.765046i 0.0455961 0.0266840i
\(823\) 11.5958 6.69486i 0.404206 0.233368i −0.284091 0.958797i \(-0.591692\pi\)
0.688297 + 0.725429i \(0.258359\pi\)
\(824\) 16.4156 + 11.4700i 0.571865 + 0.399575i
\(825\) 1.41518 3.33153i 0.0492704 0.115989i
\(826\) 16.2826 7.03003i 0.566543 0.244606i
\(827\) −7.23348 7.23348i −0.251533 0.251533i 0.570066 0.821599i \(-0.306918\pi\)
−0.821599 + 0.570066i \(0.806918\pi\)
\(828\) 2.69450 + 1.51365i 0.0936404 + 0.0526030i
\(829\) −25.9641 + 25.9641i −0.901769 + 0.901769i −0.995589 0.0938197i \(-0.970092\pi\)
0.0938197 + 0.995589i \(0.470092\pi\)
\(830\) 22.3580 + 8.87368i 0.776059 + 0.308010i
\(831\) 2.21291 + 18.0619i 0.0767650 + 0.626561i
\(832\) 31.4318 22.1023i 1.08970 0.766260i
\(833\) 6.81519 + 11.8043i 0.236132 + 0.408993i
\(834\) 33.2936 + 32.9039i 1.15286 + 1.13937i
\(835\) 5.03040 + 18.7737i 0.174084 + 0.649691i
\(836\) 35.1986 10.5633i 1.21737 0.365338i
\(837\) −41.8750 + 4.36787i −1.44741 + 0.150976i
\(838\) −21.0742 15.6783i −0.727996 0.541597i
\(839\) −41.1955 23.7842i −1.42223 0.821123i −0.425738 0.904846i \(-0.639986\pi\)
−0.996489 + 0.0837230i \(0.973319\pi\)
\(840\) −8.44230 + 15.9058i −0.291287 + 0.548804i
\(841\) −13.4955 + 7.79166i −0.465364 + 0.268678i
\(842\) −2.86496 0.333901i −0.0987331 0.0115070i
\(843\) −7.09922 + 9.08166i −0.244510 + 0.312789i
\(844\) 2.11959 + 3.43127i 0.0729592 + 0.118109i
\(845\) 14.6264 14.6264i 0.503165 0.503165i
\(846\) −27.3902 + 11.2460i −0.941693 + 0.386644i
\(847\) −6.85431 −0.235517
\(848\) −19.7628 + 22.2668i −0.678658 + 0.764647i
\(849\) −17.5547 7.45698i −0.602477 0.255923i
\(850\) 2.45796 + 3.10647i 0.0843072 + 0.106551i
\(851\) −0.886202 0.237457i −0.0303786 0.00813992i
\(852\) −16.4212 20.5046i −0.562582 0.702475i
\(853\) −0.272071 + 0.0729011i −0.00931552 + 0.00249609i −0.263474 0.964667i \(-0.584868\pi\)
0.254158 + 0.967163i \(0.418202\pi\)
\(854\) −9.05086 + 12.1659i −0.309714 + 0.416307i
\(855\) 10.2091 + 41.0383i 0.349143 + 1.40348i
\(856\) 9.12048 25.1363i 0.311731 0.859140i
\(857\) 24.7820 + 14.3079i 0.846538 + 0.488749i 0.859481 0.511167i \(-0.170787\pi\)
−0.0129433 + 0.999916i \(0.504120\pi\)
\(858\) 15.5903 27.3742i 0.532245 0.934538i
\(859\) −0.282990 + 1.05613i −0.00965548 + 0.0360347i −0.970586 0.240757i \(-0.922604\pi\)
0.960930 + 0.276791i \(0.0892711\pi\)
\(860\) 19.1821 20.3590i 0.654105 0.694235i
\(861\) 2.03577 14.4577i 0.0693788 0.492716i
\(862\) 26.0531 + 10.3402i 0.887372 + 0.352189i
\(863\) 30.2887 1.03104 0.515520 0.856878i \(-0.327599\pi\)
0.515520 + 0.856878i \(0.327599\pi\)
\(864\) 21.7464 + 19.7761i 0.739828 + 0.672796i
\(865\) −49.1485 −1.67110
\(866\) −31.1979 12.3821i −1.06015 0.420762i
\(867\) −0.994970 + 7.06611i −0.0337910 + 0.239978i
\(868\) −19.8856 + 21.1056i −0.674961 + 0.716370i
\(869\) −5.56816 + 20.7807i −0.188887 + 0.704935i
\(870\) −16.6266 + 29.1938i −0.563696 + 0.989762i
\(871\) −7.28567 4.20638i −0.246865 0.142528i
\(872\) 43.7767 + 15.8840i 1.48247 + 0.537900i
\(873\) 17.9526 17.3184i 0.607603 0.586138i
\(874\) 2.98380 4.01072i 0.100929 0.135665i
\(875\) 20.5236 5.49929i 0.693825 0.185910i
\(876\) −27.1701 33.9263i −0.917992 1.14626i
\(877\) −23.3620 6.25984i −0.788880 0.211380i −0.158184 0.987410i \(-0.550564\pi\)
−0.630696 + 0.776030i \(0.717231\pi\)
\(878\) 19.3482 + 24.4531i 0.652971 + 0.825253i
\(879\) −4.55394 1.93444i −0.153601 0.0652472i
\(880\) 21.9618 1.30843i 0.740333 0.0441073i
\(881\) −10.3324 −0.348108 −0.174054 0.984736i \(-0.555687\pi\)
−0.174054 + 0.984736i \(0.555687\pi\)
\(882\) 2.15275 15.9688i 0.0724869 0.537699i
\(883\) 13.2455 13.2455i 0.445745 0.445745i −0.448192 0.893937i \(-0.647932\pi\)
0.893937 + 0.448192i \(0.147932\pi\)
\(884\) 18.1184 + 29.3307i 0.609388 + 0.986500i
\(885\) 15.3564 19.6447i 0.516201 0.660349i
\(886\) 14.1237 + 1.64607i 0.474497 + 0.0553008i
\(887\) 4.21020 2.43076i 0.141365 0.0816170i −0.427650 0.903945i \(-0.640658\pi\)
0.569014 + 0.822328i \(0.307325\pi\)
\(888\) −7.70752 4.09090i −0.258648 0.137282i
\(889\) 8.85782 + 5.11406i 0.297082 + 0.171520i
\(890\) −38.5539 28.6824i −1.29233 0.961437i
\(891\) 23.0380 + 7.06991i 0.771803 + 0.236851i
\(892\) 21.2634 6.38126i 0.711952 0.213660i
\(893\) 12.3953 + 46.2601i 0.414794 + 1.54803i
\(894\) 9.13579 + 9.02884i 0.305546 + 0.301970i
\(895\) −16.8975 29.2674i −0.564822 0.978301i
\(896\) 20.2378 + 0.541732i 0.676099 + 0.0180980i
\(897\) −0.521112 4.25335i −0.0173994 0.142015i
\(898\) −32.4648 12.8849i −1.08336 0.429976i
\(899\) −38.2555 + 38.2555i −1.27589 + 1.27589i
\(900\) −0.0551389 4.68253i −0.00183796 0.156084i
\(901\) −18.8884 18.8884i −0.629264 0.629264i
\(902\) −16.3768 + 7.07074i −0.545289 + 0.235430i
\(903\) 8.25062 19.4230i 0.274563 0.646358i
\(904\) 1.12124 1.60470i 0.0372918 0.0533715i
\(905\) −27.5177 + 15.8874i −0.914720 + 0.528114i
\(906\) −19.0434 + 11.1447i −0.632674 + 0.370258i
\(907\) −3.69290 + 0.989509i −0.122621 + 0.0328561i −0.319608 0.947550i \(-0.603551\pi\)
0.196987 + 0.980406i \(0.436884\pi\)
\(908\) −16.4750 + 30.6035i −0.546742 + 1.01561i
\(909\) 14.5990 + 0.262501i 0.484220 + 0.00870661i
\(910\) 24.7032 3.62687i 0.818902 0.120230i
\(911\) 24.1877 41.8944i 0.801376 1.38802i −0.117335 0.993092i \(-0.537435\pi\)
0.918711 0.394931i \(-0.129231\pi\)
\(912\) 36.2096 30.8107i 1.19902 1.02024i
\(913\) −11.0858 19.2012i −0.366887 0.635467i
\(914\) 27.4769 + 34.7264i 0.908854 + 1.14865i
\(915\) −2.97251 + 21.1102i −0.0982681 + 0.697883i
\(916\) −27.2467 + 16.8310i −0.900255 + 0.556112i
\(917\) −11.5778 11.5778i −0.382334 0.382334i
\(918\) −18.8725 + 18.4216i −0.622887 + 0.608003i
\(919\) 44.5150i 1.46841i −0.678926 0.734206i \(-0.737554\pi\)
0.678926 0.734206i \(-0.262446\pi\)
\(920\) 2.29061 1.92594i 0.0755191 0.0634965i
\(921\) 12.0202 + 15.9601i 0.396080 + 0.525904i
\(922\) 2.00580 17.2103i 0.0660575 0.566792i
\(923\) −9.42718 + 35.1827i −0.310299 + 1.15805i
\(924\) 15.1992 6.66874i 0.500018 0.219385i
\(925\) 0.359800 + 1.34279i 0.0118301 + 0.0441507i
\(926\) 5.22817 + 35.6099i 0.171808 + 1.17021i
\(927\) 20.6123 5.12773i 0.676997 0.168417i
\(928\) 37.7109 + 2.13353i 1.23792 + 0.0700364i
\(929\) 26.5718 46.0236i 0.871791 1.50999i 0.0116490 0.999932i \(-0.496292\pi\)
0.860142 0.510054i \(-0.170375\pi\)
\(930\) −10.3198 + 39.4413i −0.338398 + 1.29333i
\(931\) −25.1748 6.74558i −0.825072 0.221077i
\(932\) −34.5678 + 36.6886i −1.13231 + 1.20178i
\(933\) −6.24000 15.4562i −0.204288 0.506014i
\(934\) 11.5398 4.98234i 0.377594 0.163027i
\(935\) 19.7396i 0.645553i
\(936\) 4.24101 40.5344i 0.138622 1.32491i
\(937\) 2.96531i 0.0968724i −0.998826 0.0484362i \(-0.984576\pi\)
0.998826 0.0484362i \(-0.0154238\pi\)
\(938\) −1.75697 4.06939i −0.0573670 0.132870i
\(939\) 27.4099 35.0641i 0.894489 1.14427i
\(940\) 0.852954 + 28.6587i 0.0278203 + 0.934744i
\(941\) −45.6603 12.2347i −1.48848 0.398838i −0.579260 0.815143i \(-0.696658\pi\)
−0.909225 + 0.416305i \(0.863325\pi\)
\(942\) 19.5070 19.7380i 0.635571 0.643100i
\(943\) −1.21322 + 2.10136i −0.0395079 + 0.0684298i
\(944\) −27.4614 5.63226i −0.893793 0.183315i
\(945\) 6.83069 + 17.8366i 0.222203 + 0.580224i
\(946\) −25.5091 + 3.74519i −0.829371 + 0.121767i
\(947\) 8.31213 + 31.0213i 0.270108 + 1.00806i 0.959049 + 0.283239i \(0.0914090\pi\)
−0.688942 + 0.724817i \(0.741924\pi\)
\(948\) 4.20510 + 27.5135i 0.136575 + 0.893597i
\(949\) −15.5979 + 58.2123i −0.506331 + 1.88965i
\(950\) −7.52350 0.876836i −0.244095 0.0284483i
\(951\) −27.7766 + 3.40313i −0.900718 + 0.110354i
\(952\) −1.56508 + 18.0968i −0.0507246 + 0.586521i
\(953\) 14.4065i 0.466671i 0.972396 + 0.233336i \(0.0749641\pi\)
−0.972396 + 0.233336i \(0.925036\pi\)
\(954\) 4.02464 + 31.3206i 0.130303 + 1.01404i
\(955\) −9.71317 9.71317i −0.314311 0.314311i
\(956\) −3.80907 + 16.1195i −0.123194 + 0.521341i
\(957\) 28.7147 11.5927i 0.928216 0.374740i
\(958\) 3.57506 2.82872i 0.115505 0.0913918i
\(959\) −0.553259 0.958272i −0.0178656 0.0309442i
\(960\) 25.3384 12.9659i 0.817793 0.418472i
\(961\) −17.3258 + 30.0092i −0.558897 + 0.968038i
\(962\) 1.75748 + 11.9705i 0.0566634 + 0.385943i
\(963\) −13.7370 24.8130i −0.442670 0.799588i
\(964\) −24.5211 + 7.35890i −0.789772 + 0.237014i
\(965\) −1.85903 + 0.498125i −0.0598442 + 0.0160352i
\(966\) 1.11734 1.96187i 0.0359498 0.0631223i
\(967\) 46.2878 26.7243i 1.48852 0.859395i 0.488602 0.872507i \(-0.337507\pi\)
0.999914 + 0.0131113i \(0.00417357\pi\)
\(968\) 8.88099 + 6.20535i 0.285446 + 0.199447i
\(969\) 25.6630 + 34.0746i 0.824414 + 1.09463i
\(970\) −9.57448 22.1759i −0.307418 0.712024i
\(971\) −18.6508 18.6508i −0.598532 0.598532i 0.341389 0.939922i \(-0.389102\pi\)
−0.939922 + 0.341389i \(0.889102\pi\)
\(972\) 30.9684 3.59933i 0.993313 0.115448i
\(973\) 24.1801 24.1801i 0.775180 0.775180i
\(974\) 5.89274 14.8473i 0.188816 0.475738i
\(975\) −5.18653 + 3.90620i −0.166102 + 0.125098i
\(976\) 22.7410 7.56912i 0.727922 0.242282i
\(977\) 1.32572 + 2.29622i 0.0424136 + 0.0734624i 0.886453 0.462819i \(-0.153162\pi\)
−0.844039 + 0.536281i \(0.819829\pi\)
\(978\) −10.9101 39.7789i −0.348868 1.27199i
\(979\) 11.4635 + 42.7822i 0.366374 + 1.36733i
\(980\) −13.7387 7.39608i −0.438868 0.236259i
\(981\) 43.2137 23.9241i 1.37971 0.763837i
\(982\) −23.8890 + 32.1108i −0.762328 + 1.02470i
\(983\) −23.4130 13.5175i −0.746760 0.431142i 0.0777621 0.996972i \(-0.475223\pi\)
−0.824522 + 0.565830i \(0.808556\pi\)
\(984\) −15.7265 + 16.8895i −0.501344 + 0.538417i
\(985\) −37.2244 + 21.4915i −1.18607 + 0.684776i
\(986\) −3.92311 + 33.6614i −0.124937 + 1.07200i
\(987\) 8.09759 + 20.0574i 0.257749 + 0.638434i
\(988\) −64.1547 15.1599i −2.04103 0.482301i
\(989\) −2.47989 + 2.47989i −0.0788560 + 0.0788560i
\(990\) 14.2630 18.4690i 0.453308 0.586984i
\(991\) 5.32341 0.169104 0.0845519 0.996419i \(-0.473054\pi\)
0.0845519 + 0.996419i \(0.473054\pi\)
\(992\) 44.8727 9.34325i 1.42471 0.296648i
\(993\) 4.27599 + 34.9010i 0.135695 + 1.10755i
\(994\) −15.0496 + 11.9078i −0.477345 + 0.377693i
\(995\) −4.70199 1.25989i −0.149063 0.0399413i
\(996\) −23.1143 16.9856i −0.732405 0.538208i
\(997\) −5.87389 + 1.57391i −0.186028 + 0.0498461i −0.350630 0.936514i \(-0.614033\pi\)
0.164602 + 0.986360i \(0.447366\pi\)
\(998\) −19.8321 14.7542i −0.627773 0.467036i
\(999\) −8.64310 + 3.30996i −0.273456 + 0.104723i
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 144.2.x.e.133.2 yes 72
3.2 odd 2 432.2.y.e.181.17 72
4.3 odd 2 576.2.bb.e.241.10 72
9.4 even 3 inner 144.2.x.e.85.15 yes 72
9.5 odd 6 432.2.y.e.37.4 72
12.11 even 2 1728.2.bc.e.1585.5 72
16.3 odd 4 576.2.bb.e.529.1 72
16.13 even 4 inner 144.2.x.e.61.15 yes 72
36.23 even 6 1728.2.bc.e.1009.14 72
36.31 odd 6 576.2.bb.e.49.1 72
48.29 odd 4 432.2.y.e.397.4 72
48.35 even 4 1728.2.bc.e.721.14 72
144.13 even 12 inner 144.2.x.e.13.2 72
144.67 odd 12 576.2.bb.e.337.10 72
144.77 odd 12 432.2.y.e.253.17 72
144.131 even 12 1728.2.bc.e.145.5 72
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
144.2.x.e.13.2 72 144.13 even 12 inner
144.2.x.e.61.15 yes 72 16.13 even 4 inner
144.2.x.e.85.15 yes 72 9.4 even 3 inner
144.2.x.e.133.2 yes 72 1.1 even 1 trivial
432.2.y.e.37.4 72 9.5 odd 6
432.2.y.e.181.17 72 3.2 odd 2
432.2.y.e.253.17 72 144.77 odd 12
432.2.y.e.397.4 72 48.29 odd 4
576.2.bb.e.49.1 72 36.31 odd 6
576.2.bb.e.241.10 72 4.3 odd 2
576.2.bb.e.337.10 72 144.67 odd 12
576.2.bb.e.529.1 72 16.3 odd 4
1728.2.bc.e.145.5 72 144.131 even 12
1728.2.bc.e.721.14 72 48.35 even 4
1728.2.bc.e.1009.14 72 36.23 even 6
1728.2.bc.e.1585.5 72 12.11 even 2