Properties

Label 288.2.bc.a.13.14
Level $288$
Weight $2$
Character 288.13
Analytic conductor $2.300$
Analytic rank $0$
Dimension $368$
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] = [288,2,Mod(13,288)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(288, base_ring=CyclotomicField(24))
 
chi = DirichletCharacter(H, H._module([0, 21, 8]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("288.13");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 288 = 2^{5} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 288.bc (of order \(24\), degree \(8\), 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: \(2.29969157821\)
Analytic rank: \(0\)
Dimension: \(368\)
Relative dimension: \(46\) over \(\Q(\zeta_{24})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label 13.14
Character \(\chi\) \(=\) 288.13
Dual form 288.2.bc.a.133.14

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.897888 + 1.09261i) q^{2} +(-0.186796 - 1.72195i) q^{3} +(-0.387596 - 1.96208i) q^{4} +(-0.364708 + 2.77023i) q^{5} +(2.04914 + 1.34202i) q^{6} +(1.49458 + 0.400471i) q^{7} +(2.49181 + 1.33824i) q^{8} +(-2.93021 + 0.643306i) q^{9} +O(q^{10})\) \(q+(-0.897888 + 1.09261i) q^{2} +(-0.186796 - 1.72195i) q^{3} +(-0.387596 - 1.96208i) q^{4} +(-0.364708 + 2.77023i) q^{5} +(2.04914 + 1.34202i) q^{6} +(1.49458 + 0.400471i) q^{7} +(2.49181 + 1.33824i) q^{8} +(-2.93021 + 0.643306i) q^{9} +(-2.69932 - 2.88584i) q^{10} +(0.959786 - 1.25082i) q^{11} +(-3.30620 + 1.03393i) q^{12} +(3.24500 - 2.48998i) q^{13} +(-1.77952 + 1.27341i) q^{14} +(4.83833 + 0.110541i) q^{15} +(-3.69954 + 1.52099i) q^{16} +5.91726i q^{17} +(1.92812 - 3.77920i) q^{18} +(4.77806 + 1.97914i) q^{19} +(5.57679 - 0.358144i) q^{20} +(0.410410 - 2.64839i) q^{21} +(0.504877 + 2.17177i) q^{22} +(5.90684 - 1.58273i) q^{23} +(1.83892 - 4.54075i) q^{24} +(-2.71155 - 0.726558i) q^{25} +(-0.193071 + 5.78124i) q^{26} +(1.65509 + 4.92551i) q^{27} +(0.206465 - 3.08771i) q^{28} +(7.62066 - 1.00328i) q^{29} +(-4.46505 + 5.18715i) q^{30} +(0.188789 - 0.326992i) q^{31} +(1.65992 - 5.40783i) q^{32} +(-2.33313 - 1.41905i) q^{33} +(-6.46526 - 5.31303i) q^{34} +(-1.65448 + 3.99428i) q^{35} +(2.39796 + 5.49998i) q^{36} +(-5.26075 + 2.17907i) q^{37} +(-6.45258 + 3.44351i) q^{38} +(-4.89376 - 5.12261i) q^{39} +(-4.61602 + 6.41483i) q^{40} +(-7.61220 + 2.03968i) q^{41} +(2.52516 + 2.82638i) q^{42} +(0.280120 - 0.365060i) q^{43} +(-2.82622 - 1.39837i) q^{44} +(-0.713434 - 8.35200i) q^{45} +(-3.57437 + 7.87500i) q^{46} +(-3.08436 + 1.78075i) q^{47} +(3.31013 + 6.08630i) q^{48} +(-3.98879 - 2.30293i) q^{49} +(3.22851 - 2.31030i) q^{50} +(10.1892 - 1.10532i) q^{51} +(-6.14329 - 5.40185i) q^{52} +(-5.04865 - 12.1885i) q^{53} +(-6.86775 - 2.61419i) q^{54} +(3.11501 + 3.11501i) q^{55} +(3.18828 + 2.99800i) q^{56} +(2.51545 - 8.59726i) q^{57} +(-5.74630 + 9.22724i) q^{58} +(-0.130437 + 0.990764i) q^{59} +(-1.65843 - 9.53604i) q^{60} +(7.30369 - 0.961548i) q^{61} +(0.187764 + 0.499875i) q^{62} +(-4.63706 - 0.211995i) q^{63} +(4.41824 + 6.66927i) q^{64} +(5.71434 + 9.89752i) q^{65} +(3.64536 - 1.27505i) q^{66} +(-1.06190 - 1.38389i) q^{67} +(11.6101 - 2.29350i) q^{68} +(-3.82876 - 9.87563i) q^{69} +(-2.87865 - 5.39412i) q^{70} +(-6.27993 + 6.27993i) q^{71} +(-8.16244 - 2.31833i) q^{72} +(2.94945 + 2.94945i) q^{73} +(2.34268 - 7.70452i) q^{74} +(-0.744589 + 4.80487i) q^{75} +(2.03127 - 10.1420i) q^{76} +(1.93539 - 1.48508i) q^{77} +(9.99106 - 0.747454i) q^{78} +(-3.09758 + 1.78839i) q^{79} +(-2.86425 - 10.8033i) q^{80} +(8.17232 - 3.77005i) q^{81} +(4.60632 - 10.1486i) q^{82} +(-1.37237 - 10.4242i) q^{83} +(-5.35544 + 0.221249i) q^{84} +(-16.3922 - 2.15807i) q^{85} +(0.147352 + 0.633846i) q^{86} +(-3.15110 - 12.9350i) q^{87} +(4.06550 - 1.83238i) q^{88} +(-12.0893 + 12.0893i) q^{89} +(9.76606 + 6.71965i) q^{90} +(5.84707 - 2.42194i) q^{91} +(-5.39492 - 10.9763i) q^{92} +(-0.598328 - 0.264004i) q^{93} +(0.823735 - 4.96892i) q^{94} +(-7.22526 + 12.5145i) q^{95} +(-9.62208 - 1.84813i) q^{96} +(-2.26176 - 3.91749i) q^{97} +(6.09769 - 2.29042i) q^{98} +(-2.00772 + 4.28260i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 368 q - 4 q^{2} - 8 q^{3} - 4 q^{4} - 4 q^{5} - 8 q^{6} - 4 q^{7} - 16 q^{8} - 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 368 q - 4 q^{2} - 8 q^{3} - 4 q^{4} - 4 q^{5} - 8 q^{6} - 4 q^{7} - 16 q^{8} - 8 q^{9} - 16 q^{10} - 4 q^{11} - 8 q^{12} - 4 q^{13} - 4 q^{14} - 4 q^{16} - 8 q^{18} - 16 q^{19} - 4 q^{20} - 8 q^{21} - 4 q^{22} - 4 q^{23} - 48 q^{24} - 4 q^{25} - 16 q^{26} - 32 q^{27} - 16 q^{28} - 4 q^{29} + 24 q^{30} - 8 q^{31} - 4 q^{32} - 16 q^{33} + 4 q^{34} - 16 q^{35} + 20 q^{36} - 16 q^{37} - 60 q^{38} - 32 q^{39} - 4 q^{40} - 4 q^{41} - 88 q^{42} - 4 q^{43} - 104 q^{44} - 8 q^{45} - 16 q^{46} - 60 q^{48} + 48 q^{50} + 16 q^{51} - 4 q^{52} - 16 q^{53} - 52 q^{54} - 16 q^{55} - 84 q^{56} - 8 q^{57} - 40 q^{58} - 4 q^{59} - 52 q^{60} - 4 q^{61} - 24 q^{62} - 16 q^{63} - 16 q^{64} - 8 q^{65} + 64 q^{66} - 4 q^{67} + 12 q^{68} - 8 q^{69} - 4 q^{70} - 16 q^{71} - 68 q^{72} - 16 q^{73} - 4 q^{74} - 28 q^{75} + 20 q^{76} - 4 q^{77} - 72 q^{78} + 48 q^{80} - 16 q^{82} + 36 q^{83} + 200 q^{84} + 16 q^{85} + 100 q^{86} - 64 q^{87} - 4 q^{88} - 16 q^{89} + 4 q^{90} - 16 q^{91} - 80 q^{92} + 4 q^{93} - 20 q^{94} - 136 q^{95} + 28 q^{96} - 8 q^{97} + 104 q^{98} - 72 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/288\mathbb{Z}\right)^\times\).

\(n\) \(37\) \(65\) \(127\)
\(\chi(n)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.897888 + 1.09261i −0.634902 + 0.772592i
\(3\) −0.186796 1.72195i −0.107847 0.994168i
\(4\) −0.387596 1.96208i −0.193798 0.981041i
\(5\) −0.364708 + 2.77023i −0.163102 + 1.23889i 0.692563 + 0.721357i \(0.256481\pi\)
−0.855666 + 0.517529i \(0.826852\pi\)
\(6\) 2.04914 + 1.34202i 0.836558 + 0.547878i
\(7\) 1.49458 + 0.400471i 0.564898 + 0.151364i 0.529955 0.848025i \(-0.322209\pi\)
0.0349422 + 0.999389i \(0.488875\pi\)
\(8\) 2.49181 + 1.33824i 0.880988 + 0.473139i
\(9\) −2.93021 + 0.643306i −0.976738 + 0.214435i
\(10\) −2.69932 2.88584i −0.853600 0.912583i
\(11\) 0.959786 1.25082i 0.289386 0.377136i −0.625925 0.779884i \(-0.715278\pi\)
0.915311 + 0.402748i \(0.131945\pi\)
\(12\) −3.30620 + 1.03393i −0.954419 + 0.298470i
\(13\) 3.24500 2.48998i 0.900001 0.690595i −0.0513578 0.998680i \(-0.516355\pi\)
0.951359 + 0.308085i \(0.0996882\pi\)
\(14\) −1.77952 + 1.27341i −0.475597 + 0.340334i
\(15\) 4.83833 + 0.110541i 1.24925 + 0.0285414i
\(16\) −3.69954 + 1.52099i −0.924885 + 0.380248i
\(17\) 5.91726i 1.43515i 0.696484 + 0.717573i \(0.254747\pi\)
−0.696484 + 0.717573i \(0.745253\pi\)
\(18\) 1.92812 3.77920i 0.454462 0.890766i
\(19\) 4.77806 + 1.97914i 1.09616 + 0.454045i 0.856151 0.516725i \(-0.172849\pi\)
0.240010 + 0.970770i \(0.422849\pi\)
\(20\) 5.57679 0.358144i 1.24701 0.0800833i
\(21\) 0.410410 2.64839i 0.0895587 0.577927i
\(22\) 0.504877 + 2.17177i 0.107640 + 0.463022i
\(23\) 5.90684 1.58273i 1.23166 0.330023i 0.416435 0.909165i \(-0.363279\pi\)
0.815226 + 0.579142i \(0.196613\pi\)
\(24\) 1.83892 4.54075i 0.375368 0.926876i
\(25\) −2.71155 0.726558i −0.542310 0.145312i
\(26\) −0.193071 + 5.78124i −0.0378643 + 1.13379i
\(27\) 1.65509 + 4.92551i 0.318523 + 0.947915i
\(28\) 0.206465 3.08771i 0.0390182 0.583522i
\(29\) 7.62066 1.00328i 1.41512 0.186304i 0.616129 0.787646i \(-0.288700\pi\)
0.798992 + 0.601341i \(0.205367\pi\)
\(30\) −4.46505 + 5.18715i −0.815203 + 0.947040i
\(31\) 0.188789 0.326992i 0.0339075 0.0587295i −0.848574 0.529077i \(-0.822538\pi\)
0.882481 + 0.470348i \(0.155872\pi\)
\(32\) 1.65992 5.40783i 0.293435 0.955979i
\(33\) −2.33313 1.41905i −0.406145 0.247026i
\(34\) −6.46526 5.31303i −1.10878 0.911177i
\(35\) −1.65448 + 3.99428i −0.279659 + 0.675156i
\(36\) 2.39796 + 5.49998i 0.399660 + 0.916664i
\(37\) −5.26075 + 2.17907i −0.864862 + 0.358238i −0.770607 0.637310i \(-0.780047\pi\)
−0.0942551 + 0.995548i \(0.530047\pi\)
\(38\) −6.45258 + 3.44351i −1.04675 + 0.558612i
\(39\) −4.89376 5.12261i −0.783629 0.820273i
\(40\) −4.61602 + 6.41483i −0.729856 + 1.01427i
\(41\) −7.61220 + 2.03968i −1.18883 + 0.318545i −0.798421 0.602099i \(-0.794331\pi\)
−0.390404 + 0.920644i \(0.627665\pi\)
\(42\) 2.52516 + 2.82638i 0.389641 + 0.436120i
\(43\) 0.280120 0.365060i 0.0427180 0.0556711i −0.771506 0.636222i \(-0.780496\pi\)
0.814224 + 0.580551i \(0.197163\pi\)
\(44\) −2.82622 1.39837i −0.426068 0.210812i
\(45\) −0.713434 8.35200i −0.106352 1.24504i
\(46\) −3.57437 + 7.87500i −0.527012 + 1.16110i
\(47\) −3.08436 + 1.78075i −0.449900 + 0.259750i −0.707788 0.706425i \(-0.750307\pi\)
0.257888 + 0.966175i \(0.416973\pi\)
\(48\) 3.31013 + 6.08630i 0.477776 + 0.878482i
\(49\) −3.98879 2.30293i −0.569827 0.328990i
\(50\) 3.22851 2.31030i 0.456581 0.326726i
\(51\) 10.1892 1.10532i 1.42677 0.154776i
\(52\) −6.14329 5.40185i −0.851921 0.749102i
\(53\) −5.04865 12.1885i −0.693485 1.67422i −0.737638 0.675197i \(-0.764059\pi\)
0.0441524 0.999025i \(-0.485941\pi\)
\(54\) −6.86775 2.61419i −0.934583 0.355746i
\(55\) 3.11501 + 3.11501i 0.420028 + 0.420028i
\(56\) 3.18828 + 2.99800i 0.426052 + 0.400625i
\(57\) 2.51545 8.59726i 0.333179 1.13874i
\(58\) −5.74630 + 9.22724i −0.754526 + 1.21160i
\(59\) −0.130437 + 0.990764i −0.0169814 + 0.128987i −0.997836 0.0657565i \(-0.979054\pi\)
0.980854 + 0.194743i \(0.0623873\pi\)
\(60\) −1.65843 9.53604i −0.214102 1.23110i
\(61\) 7.30369 0.961548i 0.935141 0.123114i 0.352471 0.935823i \(-0.385341\pi\)
0.582670 + 0.812709i \(0.302008\pi\)
\(62\) 0.187764 + 0.499875i 0.0238460 + 0.0634842i
\(63\) −4.63706 0.211995i −0.584215 0.0267089i
\(64\) 4.41824 + 6.66927i 0.552279 + 0.833659i
\(65\) 5.71434 + 9.89752i 0.708776 + 1.22764i
\(66\) 3.64536 1.27505i 0.448713 0.156948i
\(67\) −1.06190 1.38389i −0.129732 0.169070i 0.723971 0.689830i \(-0.242315\pi\)
−0.853703 + 0.520761i \(0.825648\pi\)
\(68\) 11.6101 2.29350i 1.40794 0.278128i
\(69\) −3.82876 9.87563i −0.460929 1.18889i
\(70\) −2.87865 5.39412i −0.344064 0.644720i
\(71\) −6.27993 + 6.27993i −0.745291 + 0.745291i −0.973591 0.228300i \(-0.926683\pi\)
0.228300 + 0.973591i \(0.426683\pi\)
\(72\) −8.16244 2.31833i −0.961952 0.273218i
\(73\) 2.94945 + 2.94945i 0.345207 + 0.345207i 0.858321 0.513114i \(-0.171508\pi\)
−0.513114 + 0.858321i \(0.671508\pi\)
\(74\) 2.34268 7.70452i 0.272331 0.895632i
\(75\) −0.744589 + 4.80487i −0.0859777 + 0.554819i
\(76\) 2.03127 10.1420i 0.233003 1.16337i
\(77\) 1.93539 1.48508i 0.220558 0.169240i
\(78\) 9.99106 0.747454i 1.13126 0.0846325i
\(79\) −3.09758 + 1.78839i −0.348505 + 0.201210i −0.664027 0.747709i \(-0.731154\pi\)
0.315521 + 0.948918i \(0.397821\pi\)
\(80\) −2.86425 10.8033i −0.320233 1.20785i
\(81\) 8.17232 3.77005i 0.908035 0.418894i
\(82\) 4.60632 10.1486i 0.508683 1.12072i
\(83\) −1.37237 10.4242i −0.150638 1.14421i −0.885048 0.465500i \(-0.845875\pi\)
0.734410 0.678706i \(-0.237459\pi\)
\(84\) −5.35544 + 0.221249i −0.584327 + 0.0241402i
\(85\) −16.3922 2.15807i −1.77798 0.234076i
\(86\) 0.147352 + 0.633846i 0.0158894 + 0.0683493i
\(87\) −3.15110 12.9350i −0.337834 1.38677i
\(88\) 4.06550 1.83238i 0.433383 0.195332i
\(89\) −12.0893 + 12.0893i −1.28147 + 1.28147i −0.341635 + 0.939833i \(0.610981\pi\)
−0.939833 + 0.341635i \(0.889019\pi\)
\(90\) 9.76606 + 6.71965i 1.02943 + 0.708313i
\(91\) 5.84707 2.42194i 0.612940 0.253888i
\(92\) −5.39492 10.9763i −0.562460 1.14435i
\(93\) −0.598328 0.264004i −0.0620438 0.0273759i
\(94\) 0.823735 4.96892i 0.0849618 0.512505i
\(95\) −7.22526 + 12.5145i −0.741296 + 1.28396i
\(96\) −9.62208 1.84813i −0.982049 0.188624i
\(97\) −2.26176 3.91749i −0.229647 0.397760i 0.728056 0.685517i \(-0.240424\pi\)
−0.957704 + 0.287757i \(0.907091\pi\)
\(98\) 6.09769 2.29042i 0.615960 0.231368i
\(99\) −2.00772 + 4.28260i −0.201784 + 0.430417i
\(100\) −0.374581 + 5.60190i −0.0374581 + 0.560190i
\(101\) 11.4186 + 8.76178i 1.13619 + 0.871829i 0.993029 0.117870i \(-0.0376067\pi\)
0.143161 + 0.989699i \(0.454273\pi\)
\(102\) −7.94108 + 12.1253i −0.786284 + 1.20058i
\(103\) −1.68601 6.29229i −0.166128 0.619998i −0.997894 0.0648711i \(-0.979336\pi\)
0.831766 0.555127i \(-0.187330\pi\)
\(104\) 11.4181 1.86196i 1.11964 0.182581i
\(105\) 7.18699 + 2.10282i 0.701378 + 0.205214i
\(106\) 17.8504 + 5.42771i 1.73379 + 0.527186i
\(107\) −2.47568 5.97681i −0.239333 0.577800i 0.757881 0.652392i \(-0.226235\pi\)
−0.997214 + 0.0745920i \(0.976235\pi\)
\(108\) 9.02276 5.15654i 0.868215 0.496188i
\(109\) −6.91502 2.86430i −0.662339 0.274350i 0.0260833 0.999660i \(-0.491696\pi\)
−0.688423 + 0.725310i \(0.741696\pi\)
\(110\) −6.20043 + 0.606565i −0.591188 + 0.0578337i
\(111\) 4.73494 + 8.65170i 0.449421 + 0.821183i
\(112\) −6.13836 + 0.791682i −0.580021 + 0.0748069i
\(113\) −8.22523 4.74884i −0.773765 0.446733i 0.0604513 0.998171i \(-0.480746\pi\)
−0.834216 + 0.551438i \(0.814079\pi\)
\(114\) 7.13487 + 10.4678i 0.668242 + 0.980398i
\(115\) 2.23027 + 16.9406i 0.207974 + 1.57972i
\(116\) −4.92225 14.5635i −0.457020 1.35219i
\(117\) −7.90673 + 9.38369i −0.730977 + 0.867522i
\(118\) −0.965402 1.03211i −0.0888725 0.0950136i
\(119\) −2.36969 + 8.84380i −0.217229 + 0.810710i
\(120\) 11.9083 + 6.75028i 1.08707 + 0.616213i
\(121\) 2.20365 + 8.22415i 0.200332 + 0.747650i
\(122\) −5.50729 + 8.84345i −0.498607 + 0.800648i
\(123\) 4.93415 + 12.7268i 0.444898 + 1.14754i
\(124\) −0.714759 0.243679i −0.0641873 0.0218830i
\(125\) −2.34469 + 5.66058i −0.209716 + 0.506298i
\(126\) 4.39519 4.87615i 0.391554 0.434402i
\(127\) 17.9616 1.59383 0.796916 0.604090i \(-0.206463\pi\)
0.796916 + 0.604090i \(0.206463\pi\)
\(128\) −11.2540 1.16084i −0.994722 0.102605i
\(129\) −0.680940 0.414161i −0.0599534 0.0364649i
\(130\) −15.9450 2.64332i −1.39847 0.231834i
\(131\) −8.72417 11.3696i −0.762234 0.993363i −0.999758 0.0219814i \(-0.993003\pi\)
0.237524 0.971382i \(-0.423664\pi\)
\(132\) −1.87999 + 5.12781i −0.163632 + 0.446319i
\(133\) 6.34859 + 4.87145i 0.550493 + 0.422408i
\(134\) 2.46552 + 0.0823388i 0.212989 + 0.00711299i
\(135\) −14.2484 + 2.78862i −1.22631 + 0.240006i
\(136\) −7.91870 + 14.7447i −0.679023 + 1.26435i
\(137\) −0.314725 + 1.17457i −0.0268887 + 0.100350i −0.978066 0.208295i \(-0.933209\pi\)
0.951177 + 0.308645i \(0.0998754\pi\)
\(138\) 14.2280 + 4.68386i 1.21117 + 0.398717i
\(139\) 20.1634 + 2.65457i 1.71024 + 0.225157i 0.921174 0.389151i \(-0.127232\pi\)
0.789066 + 0.614308i \(0.210565\pi\)
\(140\) 8.47837 + 1.69807i 0.716553 + 0.143513i
\(141\) 3.64251 + 4.97847i 0.306755 + 0.419263i
\(142\) −1.22285 12.5002i −0.102619 1.04899i
\(143\) 6.44875i 0.539271i
\(144\) 9.86198 6.83676i 0.821832 0.569730i
\(145\) 21.4769i 1.78356i
\(146\) −5.87087 + 0.574325i −0.485876 + 0.0475315i
\(147\) −3.22044 + 7.29867i −0.265617 + 0.601984i
\(148\) 6.31457 + 9.47743i 0.519055 + 0.779040i
\(149\) −4.47134 0.588662i −0.366306 0.0482251i −0.0548734 0.998493i \(-0.517476\pi\)
−0.311433 + 0.950268i \(0.600809\pi\)
\(150\) −4.58129 5.12778i −0.374061 0.418681i
\(151\) 2.67818 9.99510i 0.217947 0.813389i −0.767161 0.641454i \(-0.778331\pi\)
0.985108 0.171935i \(-0.0550020\pi\)
\(152\) 9.25745 + 11.3258i 0.750879 + 0.918644i
\(153\) −3.80660 17.3388i −0.307746 1.40176i
\(154\) −0.115152 + 3.44806i −0.00927920 + 0.277853i
\(155\) 0.836991 + 0.642246i 0.0672288 + 0.0515864i
\(156\) −8.15417 + 11.5875i −0.652856 + 0.927740i
\(157\) −6.44211 8.39552i −0.514136 0.670036i 0.462079 0.886839i \(-0.347104\pi\)
−0.976215 + 0.216803i \(0.930437\pi\)
\(158\) 0.827267 4.99023i 0.0658138 0.397001i
\(159\) −20.0449 + 10.9703i −1.58967 + 0.870000i
\(160\) 14.3756 + 6.57064i 1.13649 + 0.519455i
\(161\) 9.46208 0.745716
\(162\) −3.21863 + 12.3142i −0.252879 + 0.967498i
\(163\) 6.93912 16.7525i 0.543514 1.31216i −0.378715 0.925513i \(-0.623634\pi\)
0.922229 0.386645i \(-0.126366\pi\)
\(164\) 6.95248 + 14.1452i 0.542898 + 1.10455i
\(165\) 4.78202 5.94577i 0.372280 0.462877i
\(166\) 12.6218 + 7.86030i 0.979645 + 0.610077i
\(167\) −5.62955 21.0098i −0.435628 1.62578i −0.739560 0.673091i \(-0.764966\pi\)
0.303933 0.952694i \(-0.401700\pi\)
\(168\) 4.56685 6.05007i 0.352340 0.466773i
\(169\) 0.965395 3.60290i 0.0742612 0.277146i
\(170\) 17.0763 15.9726i 1.30969 1.22504i
\(171\) −15.2739 2.72554i −1.16803 0.208427i
\(172\) −0.824852 0.408124i −0.0628944 0.0311192i
\(173\) −0.650095 4.93796i −0.0494258 0.375426i −0.998225 0.0595478i \(-0.981034\pi\)
0.948800 0.315879i \(-0.102299\pi\)
\(174\) 16.9622 + 8.17123i 1.28590 + 0.619459i
\(175\) −3.76166 2.17180i −0.284355 0.164172i
\(176\) −1.64828 + 6.08727i −0.124244 + 0.458845i
\(177\) 1.73041 + 0.0395344i 0.130066 + 0.00297159i
\(178\) −2.35407 24.0638i −0.176445 1.80366i
\(179\) 2.84085 + 1.17672i 0.212335 + 0.0879520i 0.486316 0.873783i \(-0.338340\pi\)
−0.273981 + 0.961735i \(0.588340\pi\)
\(180\) −16.1108 + 4.63702i −1.20083 + 0.345623i
\(181\) 4.76586 + 11.5058i 0.354244 + 0.855220i 0.996087 + 0.0883835i \(0.0281701\pi\)
−0.641843 + 0.766836i \(0.721830\pi\)
\(182\) −2.60378 + 8.56320i −0.193005 + 0.634746i
\(183\) −3.02004 12.3970i −0.223247 0.916410i
\(184\) 16.8368 + 3.96089i 1.24123 + 0.292001i
\(185\) −4.11791 15.3682i −0.302755 1.12990i
\(186\) 0.825685 0.416694i 0.0605422 0.0305535i
\(187\) 7.40141 + 5.67930i 0.541244 + 0.415311i
\(188\) 4.68947 + 5.36155i 0.342015 + 0.391031i
\(189\) 0.501139 + 8.02438i 0.0364525 + 0.583688i
\(190\) −7.18603 19.1310i −0.521329 1.38791i
\(191\) −4.26215 7.38226i −0.308398 0.534162i 0.669614 0.742709i \(-0.266460\pi\)
−0.978012 + 0.208548i \(0.933126\pi\)
\(192\) 10.6588 8.85377i 0.769235 0.638966i
\(193\) −13.4850 + 23.3567i −0.970673 + 1.68125i −0.277140 + 0.960830i \(0.589387\pi\)
−0.693533 + 0.720425i \(0.743947\pi\)
\(194\) 6.31110 + 1.04624i 0.453110 + 0.0751155i
\(195\) 15.9756 11.6886i 1.14404 0.837039i
\(196\) −2.97250 + 8.71894i −0.212321 + 0.622782i
\(197\) 7.69679 3.18811i 0.548373 0.227144i −0.0912556 0.995828i \(-0.529088\pi\)
0.639629 + 0.768684i \(0.279088\pi\)
\(198\) −2.87651 6.03895i −0.204424 0.429169i
\(199\) 5.67075 5.67075i 0.401989 0.401989i −0.476945 0.878933i \(-0.658256\pi\)
0.878933 + 0.476945i \(0.158256\pi\)
\(200\) −5.78436 5.43915i −0.409016 0.384606i
\(201\) −2.18464 + 2.08704i −0.154092 + 0.147209i
\(202\) −19.8258 + 4.60896i −1.39494 + 0.324285i
\(203\) 11.7915 + 1.55237i 0.827598 + 0.108955i
\(204\) −6.11802 19.5637i −0.428347 1.36973i
\(205\) −2.87416 21.8314i −0.200740 1.52477i
\(206\) 8.38888 + 3.80761i 0.584481 + 0.265289i
\(207\) −16.2901 + 8.43766i −1.13224 + 0.586458i
\(208\) −8.21777 + 14.1474i −0.569800 + 0.980944i
\(209\) 7.06145 4.07693i 0.488451 0.282007i
\(210\) −8.75067 + 5.96448i −0.603854 + 0.411589i
\(211\) −20.6396 + 15.8374i −1.42089 + 1.09029i −0.439506 + 0.898240i \(0.644847\pi\)
−0.981385 + 0.192049i \(0.938487\pi\)
\(212\) −21.9580 + 14.6301i −1.50808 + 1.00480i
\(213\) 11.9868 + 9.64065i 0.821321 + 0.660567i
\(214\) 8.75321 + 2.66156i 0.598357 + 0.181940i
\(215\) 0.909140 + 0.909140i 0.0620028 + 0.0620028i
\(216\) −2.46734 + 14.4883i −0.167881 + 0.985807i
\(217\) 0.413111 0.413111i 0.0280438 0.0280438i
\(218\) 9.33848 4.98361i 0.632481 0.337533i
\(219\) 4.52785 5.62974i 0.305964 0.380423i
\(220\) 4.90455 7.31928i 0.330665 0.493466i
\(221\) 14.7338 + 19.2015i 0.991104 + 1.29163i
\(222\) −13.7044 2.59481i −0.919778 0.174152i
\(223\) −8.09072 14.0135i −0.541795 0.938416i −0.998801 0.0489528i \(-0.984412\pi\)
0.457006 0.889464i \(-0.348922\pi\)
\(224\) 4.64656 7.41768i 0.310461 0.495615i
\(225\) 8.41283 + 0.384614i 0.560855 + 0.0256409i
\(226\) 12.5740 4.72305i 0.836408 0.314173i
\(227\) −14.9250 + 1.96491i −0.990604 + 0.130416i −0.608373 0.793651i \(-0.708178\pi\)
−0.382231 + 0.924067i \(0.624844\pi\)
\(228\) −17.8435 1.60326i −1.18172 0.106178i
\(229\) 0.306088 2.32497i 0.0202268 0.153638i −0.978351 0.206953i \(-0.933645\pi\)
0.998578 + 0.0533147i \(0.0169787\pi\)
\(230\) −20.5120 12.7739i −1.35252 0.842287i
\(231\) −2.91875 3.05524i −0.192040 0.201020i
\(232\) 20.3319 + 7.69828i 1.33485 + 0.505417i
\(233\) 1.12782 + 1.12782i 0.0738862 + 0.0738862i 0.743084 0.669198i \(-0.233362\pi\)
−0.669198 + 0.743084i \(0.733362\pi\)
\(234\) −3.15337 17.0645i −0.206142 1.11554i
\(235\) −3.80822 9.19385i −0.248421 0.599740i
\(236\) 1.99452 0.128089i 0.129832 0.00833787i
\(237\) 3.65813 + 4.99982i 0.237621 + 0.324773i
\(238\) −7.53512 10.5299i −0.488429 0.682551i
\(239\) −3.90883 2.25677i −0.252841 0.145978i 0.368223 0.929737i \(-0.379966\pi\)
−0.621065 + 0.783759i \(0.713300\pi\)
\(240\) −18.0677 + 6.95010i −1.16627 + 0.448627i
\(241\) 12.3078 7.10592i 0.792816 0.457732i −0.0481373 0.998841i \(-0.515328\pi\)
0.840953 + 0.541108i \(0.181995\pi\)
\(242\) −10.9644 4.97663i −0.704820 0.319910i
\(243\) −8.01838 13.3681i −0.514380 0.857563i
\(244\) −4.71752 13.9577i −0.302008 0.893553i
\(245\) 7.83439 10.2100i 0.500521 0.652292i
\(246\) −18.3358 6.03613i −1.16905 0.384850i
\(247\) 20.4328 5.47495i 1.30011 0.348363i
\(248\) 0.908019 0.562157i 0.0576593 0.0356970i
\(249\) −17.6936 + 4.31036i −1.12129 + 0.273158i
\(250\) −4.07955 7.64440i −0.258013 0.483474i
\(251\) 0.883121 0.365801i 0.0557421 0.0230891i −0.354638 0.935004i \(-0.615396\pi\)
0.410380 + 0.911914i \(0.365396\pi\)
\(252\) 1.38135 + 9.18047i 0.0870171 + 0.578315i
\(253\) 3.68959 8.90747i 0.231963 0.560008i
\(254\) −16.1275 + 19.6250i −1.01193 + 1.23138i
\(255\) −0.654097 + 28.6296i −0.0409611 + 1.79286i
\(256\) 11.3732 11.2539i 0.710823 0.703370i
\(257\) 2.46613 4.27147i 0.153833 0.266447i −0.778800 0.627272i \(-0.784171\pi\)
0.932634 + 0.360825i \(0.117505\pi\)
\(258\) 1.06392 0.372132i 0.0662371 0.0231679i
\(259\) −8.73526 + 1.15002i −0.542783 + 0.0714587i
\(260\) 17.2049 15.0482i 1.06700 0.933252i
\(261\) −21.6848 + 7.84224i −1.34225 + 0.485422i
\(262\) 20.2558 + 0.676465i 1.25141 + 0.0417922i
\(263\) 16.0761 + 4.30758i 0.991295 + 0.265617i 0.717795 0.696255i \(-0.245152\pi\)
0.273501 + 0.961872i \(0.411818\pi\)
\(264\) −3.91468 6.65830i −0.240932 0.409790i
\(265\) 35.6063 9.54068i 2.18728 0.586080i
\(266\) −11.0229 + 2.56253i −0.675859 + 0.157119i
\(267\) 23.0755 + 18.5590i 1.41220 + 1.13579i
\(268\) −2.30373 + 2.61993i −0.140722 + 0.160037i
\(269\) 17.5062 + 7.25129i 1.06737 + 0.442119i 0.846062 0.533085i \(-0.178967\pi\)
0.221308 + 0.975204i \(0.428967\pi\)
\(270\) 9.74663 18.0719i 0.593161 1.09982i
\(271\) 0.969626i 0.0589006i 0.999566 + 0.0294503i \(0.00937567\pi\)
−0.999566 + 0.0294503i \(0.990624\pi\)
\(272\) −9.00009 21.8911i −0.545711 1.32734i
\(273\) −5.26266 9.61595i −0.318511 0.581984i
\(274\) −1.00076 1.39850i −0.0604580 0.0844866i
\(275\) −3.51130 + 2.69432i −0.211739 + 0.162473i
\(276\) −17.8928 + 11.3401i −1.07702 + 0.682594i
\(277\) 2.09228 2.72671i 0.125713 0.163832i −0.726257 0.687424i \(-0.758742\pi\)
0.851969 + 0.523592i \(0.175408\pi\)
\(278\) −21.0049 + 19.6473i −1.25979 + 1.17837i
\(279\) −0.342836 + 1.07961i −0.0205251 + 0.0646343i
\(280\) −9.46795 + 7.73889i −0.565818 + 0.462487i
\(281\) −13.4966 3.61641i −0.805142 0.215737i −0.167301 0.985906i \(-0.553505\pi\)
−0.637840 + 0.770169i \(0.720172\pi\)
\(282\) −8.71009 0.490255i −0.518679 0.0291943i
\(283\) −3.37980 + 25.6721i −0.200908 + 1.52605i 0.532599 + 0.846368i \(0.321216\pi\)
−0.733507 + 0.679682i \(0.762118\pi\)
\(284\) 14.7558 + 9.88767i 0.875597 + 0.586725i
\(285\) 22.8990 + 10.1039i 1.35642 + 0.598502i
\(286\) 7.04597 + 5.79025i 0.416637 + 0.342385i
\(287\) −12.1939 −0.719781
\(288\) −1.38503 + 16.9139i −0.0816136 + 0.996664i
\(289\) −18.0139 −1.05964
\(290\) −23.4659 19.2838i −1.37796 1.13239i
\(291\) −6.32322 + 4.62641i −0.370674 + 0.271205i
\(292\) 4.64387 6.93025i 0.271762 0.405562i
\(293\) 0.397408 3.01861i 0.0232168 0.176349i −0.975908 0.218183i \(-0.929987\pi\)
0.999125 + 0.0418344i \(0.0133202\pi\)
\(294\) −5.08301 10.0721i −0.296447 0.587415i
\(295\) −2.69708 0.722680i −0.157030 0.0420760i
\(296\) −16.0249 1.61030i −0.931429 0.0935968i
\(297\) 7.74945 + 2.65722i 0.449669 + 0.154188i
\(298\) 4.65793 4.35688i 0.269827 0.252387i
\(299\) 15.2267 19.8439i 0.880585 1.14760i
\(300\) 9.71615 0.401403i 0.560962 0.0231750i
\(301\) 0.564858 0.433431i 0.0325579 0.0249825i
\(302\) 8.51605 + 11.9007i 0.490043 + 0.684807i
\(303\) 12.9544 21.2989i 0.744210 1.22359i
\(304\) −20.6869 0.0545104i −1.18647 0.00312639i
\(305\) 20.5836i 1.17861i
\(306\) 22.3625 + 11.4092i 1.27838 + 0.652219i
\(307\) −30.5109 12.6380i −1.74135 0.721291i −0.998665 0.0516513i \(-0.983552\pi\)
−0.742686 0.669640i \(-0.766448\pi\)
\(308\) −3.66400 3.22179i −0.208776 0.183578i
\(309\) −10.5201 + 4.07861i −0.598466 + 0.232024i
\(310\) −1.45325 + 0.337841i −0.0825390 + 0.0191881i
\(311\) 6.28426 1.68386i 0.356348 0.0954831i −0.0762039 0.997092i \(-0.524280\pi\)
0.432552 + 0.901609i \(0.357613\pi\)
\(312\) −5.33906 19.3136i −0.302265 1.09342i
\(313\) −7.49566 2.00846i −0.423680 0.113525i 0.0406782 0.999172i \(-0.487048\pi\)
−0.464358 + 0.885648i \(0.653715\pi\)
\(314\) 14.9573 + 0.499516i 0.844091 + 0.0281893i
\(315\) 2.27845 12.7684i 0.128376 0.719419i
\(316\) 4.70958 + 5.38454i 0.264935 + 0.302904i
\(317\) −8.02205 + 1.05612i −0.450563 + 0.0593178i −0.352393 0.935852i \(-0.614632\pi\)
−0.0981696 + 0.995170i \(0.531299\pi\)
\(318\) 6.01185 31.7514i 0.337128 1.78053i
\(319\) 6.05928 10.4950i 0.339255 0.587606i
\(320\) −20.0868 + 9.80721i −1.12289 + 0.548239i
\(321\) −9.82932 + 5.37943i −0.548619 + 0.300251i
\(322\) −8.49588 + 10.3384i −0.473457 + 0.576135i
\(323\) −11.7111 + 28.2730i −0.651620 + 1.57315i
\(324\) −10.5647 14.5735i −0.586928 0.809639i
\(325\) −10.6081 + 4.39402i −0.588431 + 0.243736i
\(326\) 12.0734 + 22.6236i 0.668685 + 1.25301i
\(327\) −3.64047 + 12.4424i −0.201319 + 0.688064i
\(328\) −21.6977 5.10443i −1.19806 0.281845i
\(329\) −5.32296 + 1.42628i −0.293464 + 0.0786335i
\(330\) 2.20269 + 10.5635i 0.121254 + 0.581503i
\(331\) −2.33281 + 3.04017i −0.128223 + 0.167103i −0.853053 0.521825i \(-0.825252\pi\)
0.724830 + 0.688928i \(0.241918\pi\)
\(332\) −19.9212 + 6.73309i −1.09332 + 0.369526i
\(333\) 14.0133 9.76943i 0.767925 0.535361i
\(334\) 28.0102 + 12.7135i 1.53265 + 0.695652i
\(335\) 4.22099 2.43699i 0.230617 0.133147i
\(336\) 2.50986 + 10.4221i 0.136924 + 0.568570i
\(337\) 12.2682 + 7.08303i 0.668289 + 0.385837i 0.795428 0.606048i \(-0.207246\pi\)
−0.127139 + 0.991885i \(0.540579\pi\)
\(338\) 3.06975 + 4.28980i 0.166973 + 0.233335i
\(339\) −6.64082 + 15.0505i −0.360680 + 0.817430i
\(340\) 2.11923 + 32.9993i 0.114931 + 1.78964i
\(341\) −0.227810 0.549983i −0.0123366 0.0297832i
\(342\) 16.6922 14.2412i 0.902612 0.770077i
\(343\) −12.6981 12.6981i −0.685631 0.685631i
\(344\) 1.18654 0.534793i 0.0639742 0.0288341i
\(345\) 28.7542 7.00484i 1.54807 0.377128i
\(346\) 5.97898 + 3.72343i 0.321432 + 0.200173i
\(347\) 3.94361 29.9547i 0.211704 1.60805i −0.474238 0.880397i \(-0.657276\pi\)
0.685942 0.727656i \(-0.259390\pi\)
\(348\) −24.1581 + 11.1963i −1.29501 + 0.600183i
\(349\) −23.6392 + 3.11216i −1.26538 + 0.166590i −0.733182 0.680033i \(-0.761966\pi\)
−0.532194 + 0.846623i \(0.678632\pi\)
\(350\) 5.75048 2.16000i 0.307376 0.115457i
\(351\) 17.6352 + 11.8621i 0.941296 + 0.633155i
\(352\) −5.17105 7.26662i −0.275618 0.387312i
\(353\) 15.1147 + 26.1794i 0.804473 + 1.39339i 0.916646 + 0.399700i \(0.130886\pi\)
−0.112173 + 0.993689i \(0.535781\pi\)
\(354\) −1.59691 + 1.85517i −0.0848748 + 0.0986010i
\(355\) −15.1065 19.6872i −0.801771 1.04489i
\(356\) 28.4061 + 19.0345i 1.50552 + 1.00883i
\(357\) 15.6712 + 2.42850i 0.829409 + 0.128530i
\(358\) −3.83646 + 2.04738i −0.202763 + 0.108207i
\(359\) 11.2746 11.2746i 0.595050 0.595050i −0.343942 0.938991i \(-0.611762\pi\)
0.938991 + 0.343942i \(0.111762\pi\)
\(360\) 9.39922 21.7663i 0.495382 1.14719i
\(361\) 5.47782 + 5.47782i 0.288306 + 0.288306i
\(362\) −16.8506 5.12369i −0.885646 0.269295i
\(363\) 13.7499 5.33082i 0.721684 0.279795i
\(364\) −7.01834 10.5337i −0.367861 0.552116i
\(365\) −9.24634 + 7.09497i −0.483976 + 0.371368i
\(366\) 16.2567 + 7.83135i 0.849751 + 0.409351i
\(367\) 0.271211 0.156584i 0.0141571 0.00817360i −0.492905 0.870083i \(-0.664065\pi\)
0.507062 + 0.861910i \(0.330732\pi\)
\(368\) −19.4453 + 14.8396i −1.01365 + 0.773570i
\(369\) 20.9932 10.8737i 1.09286 0.566061i
\(370\) 20.4889 + 9.29968i 1.06517 + 0.483467i
\(371\) −2.66445 20.2385i −0.138332 1.05073i
\(372\) −0.286088 + 1.27630i −0.0148330 + 0.0661729i
\(373\) −12.1854 1.60424i −0.630936 0.0830642i −0.191725 0.981449i \(-0.561408\pi\)
−0.439210 + 0.898384i \(0.644742\pi\)
\(374\) −12.8509 + 2.98748i −0.664504 + 0.154479i
\(375\) 10.1852 + 2.98006i 0.525962 + 0.153890i
\(376\) −10.0687 + 0.309697i −0.519254 + 0.0159714i
\(377\) 22.2309 22.2309i 1.14495 1.14495i
\(378\) −9.21749 6.65744i −0.474097 0.342422i
\(379\) −28.6291 + 11.8585i −1.47058 + 0.609133i −0.966990 0.254813i \(-0.917986\pi\)
−0.503586 + 0.863945i \(0.667986\pi\)
\(380\) 27.3550 + 9.32599i 1.40328 + 0.478413i
\(381\) −3.35515 30.9289i −0.171889 1.58454i
\(382\) 11.8929 + 1.97157i 0.608492 + 0.100874i
\(383\) −1.45576 + 2.52144i −0.0743857 + 0.128840i −0.900819 0.434195i \(-0.857033\pi\)
0.826433 + 0.563035i \(0.190366\pi\)
\(384\) 0.103285 + 19.5956i 0.00527072 + 0.999986i
\(385\) 3.40816 + 5.90311i 0.173696 + 0.300850i
\(386\) −13.4118 35.7056i −0.682642 1.81737i
\(387\) −0.585968 + 1.24991i −0.0297864 + 0.0635364i
\(388\) −6.80978 + 5.95617i −0.345714 + 0.302379i
\(389\) 6.63121 + 5.08831i 0.336216 + 0.257988i 0.763046 0.646344i \(-0.223703\pi\)
−0.426830 + 0.904332i \(0.640370\pi\)
\(390\) −1.57320 + 27.9502i −0.0796621 + 1.41531i
\(391\) 9.36544 + 34.9523i 0.473631 + 1.76761i
\(392\) −6.85744 11.0764i −0.346353 0.559443i
\(393\) −17.9482 + 17.1464i −0.905365 + 0.864919i
\(394\) −3.42748 + 11.2722i −0.172674 + 0.567883i
\(395\) −3.82455 9.23327i −0.192434 0.464576i
\(396\) 9.18100 + 2.27940i 0.461363 + 0.114544i
\(397\) 7.02978 + 2.91183i 0.352814 + 0.146141i 0.552050 0.833811i \(-0.313846\pi\)
−0.199235 + 0.979952i \(0.563846\pi\)
\(398\) 1.10423 + 11.2876i 0.0553498 + 0.565797i
\(399\) 7.20249 11.8419i 0.360576 0.592838i
\(400\) 11.1366 1.43631i 0.556829 0.0718157i
\(401\) −1.52697 0.881597i −0.0762533 0.0440248i 0.461389 0.887198i \(-0.347351\pi\)
−0.537642 + 0.843173i \(0.680685\pi\)
\(402\) −0.318766 4.26088i −0.0158986 0.212514i
\(403\) −0.201582 1.53117i −0.0100415 0.0762729i
\(404\) 12.7655 25.8002i 0.635109 1.28361i
\(405\) 7.46340 + 24.0142i 0.370859 + 1.19327i
\(406\) −12.2835 + 11.4896i −0.609622 + 0.570220i
\(407\) −2.32357 + 8.67169i −0.115175 + 0.429839i
\(408\) 26.8688 + 10.8813i 1.33020 + 0.538707i
\(409\) −4.44312 16.5820i −0.219698 0.819925i −0.984460 0.175611i \(-0.943810\pi\)
0.764761 0.644314i \(-0.222857\pi\)
\(410\) 26.4339 + 16.4618i 1.30548 + 0.812992i
\(411\) 2.08134 + 0.322535i 0.102665 + 0.0159095i
\(412\) −11.6925 + 5.74697i −0.576049 + 0.283133i
\(413\) −0.591720 + 1.42854i −0.0291167 + 0.0702938i
\(414\) 5.40764 25.3748i 0.265771 1.24711i
\(415\) 29.3780 1.44211
\(416\) −8.07894 21.6816i −0.396103 1.06303i
\(417\) 0.804581 35.2163i 0.0394005 1.72455i
\(418\) −1.88589 + 11.3760i −0.0922419 + 0.556420i
\(419\) −4.98049 6.49070i −0.243313 0.317091i 0.655694 0.755027i \(-0.272376\pi\)
−0.899006 + 0.437936i \(0.855710\pi\)
\(420\) 1.34026 14.9165i 0.0653981 0.727851i
\(421\) −2.09123 1.60466i −0.101920 0.0782063i 0.556544 0.830818i \(-0.312127\pi\)
−0.658464 + 0.752612i \(0.728794\pi\)
\(422\) 1.22802 36.7713i 0.0597789 1.79000i
\(423\) 7.89226 7.20218i 0.383735 0.350182i
\(424\) 3.73087 37.1278i 0.181187 1.80308i
\(425\) 4.29923 16.0449i 0.208543 0.778294i
\(426\) −21.2963 + 4.44066i −1.03181 + 0.215151i
\(427\) 11.3010 + 1.48781i 0.546894 + 0.0720000i
\(428\) −10.7674 + 7.17407i −0.520464 + 0.346772i
\(429\) −11.1044 + 1.20460i −0.536126 + 0.0581586i
\(430\) −1.80964 + 0.177030i −0.0872686 + 0.00853717i
\(431\) 17.7118i 0.853148i 0.904453 + 0.426574i \(0.140280\pi\)
−0.904453 + 0.426574i \(0.859720\pi\)
\(432\) −13.6147 15.7047i −0.655039 0.755595i
\(433\) 17.0411i 0.818943i −0.912323 0.409472i \(-0.865713\pi\)
0.912323 0.409472i \(-0.134287\pi\)
\(434\) 0.0804422 + 0.822296i 0.00386135 + 0.0394715i
\(435\) 36.9821 4.01180i 1.77316 0.192351i
\(436\) −2.93975 + 14.6780i −0.140789 + 0.702951i
\(437\) 31.3557 + 4.12805i 1.49995 + 0.197472i
\(438\) 2.08561 + 10.0021i 0.0996544 + 0.477916i
\(439\) −8.65547 + 32.3026i −0.413103 + 1.54172i 0.375503 + 0.926821i \(0.377470\pi\)
−0.788605 + 0.614900i \(0.789197\pi\)
\(440\) 3.59339 + 11.9307i 0.171308 + 0.568772i
\(441\) 13.1695 + 4.18206i 0.627119 + 0.199146i
\(442\) −34.2091 1.14245i −1.62716 0.0543408i
\(443\) −24.2055 18.5735i −1.15004 0.882456i −0.155605 0.987819i \(-0.549733\pi\)
−0.994434 + 0.105364i \(0.966399\pi\)
\(444\) 15.1401 12.6437i 0.718518 0.600044i
\(445\) −29.0812 37.8994i −1.37858 1.79660i
\(446\) 22.5759 + 3.74258i 1.06900 + 0.177216i
\(447\) −0.178420 + 7.80937i −0.00843896 + 0.369370i
\(448\) 3.93255 + 11.7371i 0.185796 + 0.554527i
\(449\) −14.4794 −0.683323 −0.341661 0.939823i \(-0.610990\pi\)
−0.341661 + 0.939823i \(0.610990\pi\)
\(450\) −7.97400 + 8.84660i −0.375898 + 0.417033i
\(451\) −4.75481 + 11.4791i −0.223895 + 0.540531i
\(452\) −6.12955 + 17.9792i −0.288310 + 0.845671i
\(453\) −17.7113 2.74464i −0.832150 0.128955i
\(454\) 11.2541 18.0714i 0.528179 0.848135i
\(455\) 4.57685 + 17.0810i 0.214566 + 0.800772i
\(456\) 17.7732 18.0565i 0.832307 0.845572i
\(457\) 2.16499 8.07985i 0.101274 0.377959i −0.896622 0.442797i \(-0.853986\pi\)
0.997896 + 0.0648376i \(0.0206529\pi\)
\(458\) 2.26545 + 2.42199i 0.105858 + 0.113172i
\(459\) −29.1455 + 9.79360i −1.36040 + 0.457126i
\(460\) 32.3744 10.9421i 1.50946 0.510176i
\(461\) −4.11394 31.2485i −0.191605 1.45539i −0.769171 0.639043i \(-0.779331\pi\)
0.577565 0.816344i \(-0.304003\pi\)
\(462\) 5.95890 0.445798i 0.277233 0.0207404i
\(463\) −17.6385 10.1836i −0.819730 0.473271i 0.0305934 0.999532i \(-0.490260\pi\)
−0.850323 + 0.526261i \(0.823594\pi\)
\(464\) −26.6669 + 15.3026i −1.23798 + 0.710406i
\(465\) 0.949568 1.56122i 0.0440352 0.0724001i
\(466\) −2.24493 + 0.219613i −0.103994 + 0.0101734i
\(467\) 30.6247 + 12.6852i 1.41714 + 0.586999i 0.954141 0.299359i \(-0.0967728\pi\)
0.463001 + 0.886358i \(0.346773\pi\)
\(468\) 21.4762 + 11.8766i 0.992737 + 0.548995i
\(469\) −1.03288 2.49360i −0.0476941 0.115144i
\(470\) 13.4646 + 4.09414i 0.621078 + 0.188849i
\(471\) −13.2533 + 12.6612i −0.610680 + 0.583399i
\(472\) −1.65090 + 2.29424i −0.0759889 + 0.105601i
\(473\) −0.187768 0.700759i −0.00863358 0.0322209i
\(474\) −8.74744 0.492358i −0.401783 0.0226147i
\(475\) −11.5180 8.83806i −0.528482 0.405518i
\(476\) 18.2708 + 1.22171i 0.837439 + 0.0559968i
\(477\) 22.6346 + 32.4671i 1.03637 + 1.48657i
\(478\) 5.97546 2.24451i 0.273311 0.102662i
\(479\) 17.8654 + 30.9438i 0.816292 + 1.41386i 0.908397 + 0.418109i \(0.137307\pi\)
−0.0921049 + 0.995749i \(0.529360\pi\)
\(480\) 8.62901 25.9814i 0.393859 1.18588i
\(481\) −11.6453 + 20.1702i −0.530980 + 0.919684i
\(482\) −3.28703 + 19.8280i −0.149720 + 0.903139i
\(483\) −1.76748 16.2932i −0.0804230 0.741367i
\(484\) 15.2823 7.51140i 0.694652 0.341427i
\(485\) 11.6772 4.83687i 0.530236 0.219631i
\(486\) 21.8057 + 3.24206i 0.989127 + 0.147063i
\(487\) −4.76754 + 4.76754i −0.216038 + 0.216038i −0.806826 0.590789i \(-0.798817\pi\)
0.590789 + 0.806826i \(0.298817\pi\)
\(488\) 19.4862 + 7.37808i 0.882098 + 0.333990i
\(489\) −30.1432 8.81951i −1.36312 0.398832i
\(490\) 4.12113 + 17.7274i 0.186174 + 0.800840i
\(491\) −14.5605 1.91693i −0.657107 0.0865098i −0.205403 0.978678i \(-0.565850\pi\)
−0.451704 + 0.892168i \(0.649184\pi\)
\(492\) 23.0586 14.6141i 1.03956 0.658854i
\(493\) 5.93666 + 45.0934i 0.267374 + 2.03090i
\(494\) −12.3644 + 27.2410i −0.556299 + 1.22563i
\(495\) −11.1316 7.12375i −0.500327 0.320189i
\(496\) −0.201080 + 1.49687i −0.00902877 + 0.0672113i
\(497\) −11.9008 + 6.87092i −0.533823 + 0.308203i
\(498\) 11.1773 23.2024i 0.500868 1.03973i
\(499\) 12.5551 9.63386i 0.562043 0.431271i −0.288269 0.957549i \(-0.593080\pi\)
0.850312 + 0.526278i \(0.176413\pi\)
\(500\) 12.0153 + 2.40646i 0.537342 + 0.107620i
\(501\) −35.1262 + 13.6183i −1.56932 + 0.608422i
\(502\) −0.393266 + 1.29336i −0.0175523 + 0.0577253i
\(503\) 4.11740 + 4.11740i 0.183586 + 0.183586i 0.792916 0.609330i \(-0.208562\pi\)
−0.609330 + 0.792916i \(0.708562\pi\)
\(504\) −11.2710 6.73375i −0.502049 0.299945i
\(505\) −28.4366 + 28.4366i −1.26541 + 1.26541i
\(506\) 6.41955 + 12.0292i 0.285384 + 0.534763i
\(507\) −6.38435 0.989353i −0.283539 0.0439387i
\(508\) −6.96183 35.2421i −0.308881 1.56361i
\(509\) 4.17050 + 5.43510i 0.184854 + 0.240907i 0.876583 0.481251i \(-0.159817\pi\)
−0.691729 + 0.722157i \(0.743151\pi\)
\(510\) −30.6937 26.4208i −1.35914 1.16993i
\(511\) 3.22701 + 5.58935i 0.142755 + 0.247258i
\(512\) 2.08433 + 22.5312i 0.0921152 + 0.995748i
\(513\) −1.84014 + 26.8100i −0.0812440 + 1.18369i
\(514\) 2.45274 + 6.52982i 0.108186 + 0.288018i
\(515\) 18.0460 2.37580i 0.795203 0.104690i
\(516\) −0.548689 + 1.49659i −0.0241547 + 0.0658836i
\(517\) −0.732924 + 5.56711i −0.0322340 + 0.244841i
\(518\) 6.58676 10.5768i 0.289406 0.464719i
\(519\) −8.38148 + 2.04182i −0.367906 + 0.0896260i
\(520\) 0.993799 + 32.3099i 0.0435810 + 1.41688i
\(521\) −25.7080 25.7080i −1.12629 1.12629i −0.990776 0.135511i \(-0.956732\pi\)
−0.135511 0.990776i \(-0.543268\pi\)
\(522\) 10.9020 30.7344i 0.477166 1.34521i
\(523\) 2.18896 + 5.28462i 0.0957166 + 0.231080i 0.964485 0.264139i \(-0.0850878\pi\)
−0.868768 + 0.495219i \(0.835088\pi\)
\(524\) −18.9266 + 21.5243i −0.826811 + 0.940295i
\(525\) −3.03706 + 6.88307i −0.132548 + 0.300402i
\(526\) −19.1410 + 13.6972i −0.834589 + 0.597227i
\(527\) 1.93490 + 1.11711i 0.0842854 + 0.0486622i
\(528\) 10.7899 + 1.70118i 0.469569 + 0.0740345i
\(529\) 12.4672 7.19792i 0.542050 0.312953i
\(530\) −21.5462 + 47.4703i −0.935908 + 2.06198i
\(531\) −0.255157 2.98706i −0.0110729 0.129627i
\(532\) 7.09750 14.3446i 0.307715 0.621918i
\(533\) −19.6228 + 25.5730i −0.849958 + 1.10769i
\(534\) −40.9969 + 8.54862i −1.77411 + 0.369935i
\(535\) 17.4601 4.67841i 0.754865 0.202265i
\(536\) −0.794071 4.86947i −0.0342986 0.210329i
\(537\) 1.49559 5.11160i 0.0645394 0.220582i
\(538\) −23.6414 + 12.6166i −1.01925 + 0.543939i
\(539\) −6.70893 + 2.77893i −0.288974 + 0.119697i
\(540\) 10.9941 + 26.8758i 0.473112 + 1.15655i
\(541\) 5.88959 14.2187i 0.253213 0.611311i −0.745246 0.666789i \(-0.767668\pi\)
0.998460 + 0.0554777i \(0.0176682\pi\)
\(542\) −1.05942 0.870615i −0.0455061 0.0373961i
\(543\) 18.9222 10.3558i 0.812028 0.444410i
\(544\) 31.9995 + 9.82217i 1.37197 + 0.421122i
\(545\) 10.4567 18.1116i 0.447917 0.775816i
\(546\) 15.2318 + 2.88400i 0.651859 + 0.123424i
\(547\) −40.6674 + 5.35396i −1.73881 + 0.228919i −0.932144 0.362088i \(-0.882064\pi\)
−0.806667 + 0.591007i \(0.798731\pi\)
\(548\) 2.42659 + 0.162258i 0.103659 + 0.00693131i
\(549\) −20.7828 + 7.51605i −0.886988 + 0.320777i
\(550\) 0.208915 6.25568i 0.00890817 0.266743i
\(551\) 38.3976 + 10.2886i 1.63579 + 0.438309i
\(552\) 3.67541 29.7320i 0.156436 1.26548i
\(553\) −5.34578 + 1.43240i −0.227326 + 0.0609117i
\(554\) 1.10060 + 4.73433i 0.0467601 + 0.201142i
\(555\) −25.6941 + 9.96155i −1.09065 + 0.422844i
\(556\) −2.60679 40.5912i −0.110552 1.72145i
\(557\) −21.2463 8.80052i −0.900237 0.372890i −0.115925 0.993258i \(-0.536983\pi\)
−0.784311 + 0.620368i \(0.786983\pi\)
\(558\) −0.871760 1.34395i −0.0369046 0.0568940i
\(559\) 1.88211i 0.0796049i
\(560\) 0.0455687 17.2934i 0.00192563 0.730781i
\(561\) 8.39691 13.8057i 0.354518 0.582878i
\(562\) 16.0698 11.4994i 0.677863 0.485074i
\(563\) 6.79239 5.21198i 0.286265 0.219659i −0.455640 0.890164i \(-0.650589\pi\)
0.741905 + 0.670505i \(0.233923\pi\)
\(564\) 8.35634 9.07655i 0.351866 0.382192i
\(565\) 16.1552 21.0539i 0.679654 0.885743i
\(566\) −25.0150 26.7435i −1.05146 1.12411i
\(567\) 13.7240 2.36186i 0.576352 0.0991887i
\(568\) −24.0524 + 7.24435i −1.00922 + 0.303966i
\(569\) −16.2769 4.36139i −0.682365 0.182839i −0.0990464 0.995083i \(-0.531579\pi\)
−0.583318 + 0.812244i \(0.698246\pi\)
\(570\) −31.6003 + 15.9476i −1.32359 + 0.667970i
\(571\) −1.10097 + 8.36268i −0.0460741 + 0.349967i 0.952844 + 0.303461i \(0.0981422\pi\)
−0.998918 + 0.0465065i \(0.985191\pi\)
\(572\) −12.6530 + 2.49951i −0.529047 + 0.104510i
\(573\) −11.9157 + 8.71818i −0.497786 + 0.364207i
\(574\) 10.9487 13.3231i 0.456991 0.556097i
\(575\) −17.1667 −0.715899
\(576\) −17.2368 16.7001i −0.718198 0.695838i
\(577\) 20.2260 0.842018 0.421009 0.907056i \(-0.361676\pi\)
0.421009 + 0.907056i \(0.361676\pi\)
\(578\) 16.1745 19.6822i 0.672769 0.818671i
\(579\) 42.7380 + 18.8576i 1.77613 + 0.783694i
\(580\) 42.1395 8.32436i 1.74975 0.345650i
\(581\) 2.12348 16.1294i 0.0880966 0.669160i
\(582\) 0.622680 11.0628i 0.0258109 0.458568i
\(583\) −20.0912 5.38343i −0.832094 0.222959i
\(584\) 3.40240 + 11.2965i 0.140792 + 0.467453i
\(585\) −23.1114 25.3258i −0.955537 1.04709i
\(586\) 2.94134 + 3.14458i 0.121506 + 0.129902i
\(587\) 12.4270 16.1951i 0.512916 0.668445i −0.463059 0.886327i \(-0.653248\pi\)
0.975975 + 0.217883i \(0.0699150\pi\)
\(588\) 15.5688 + 3.48983i 0.642047 + 0.143918i
\(589\) 1.54921 1.18875i 0.0638339 0.0489815i
\(590\) 3.21128 2.29797i 0.132206 0.0946059i
\(591\) −6.92750 12.6579i −0.284959 0.520678i
\(592\) 16.1480 16.0631i 0.663679 0.660190i
\(593\) 38.1910i 1.56832i 0.620560 + 0.784159i \(0.286905\pi\)
−0.620560 + 0.784159i \(0.713095\pi\)
\(594\) −9.86144 + 6.08125i −0.404620 + 0.249517i
\(595\) −23.6352 9.79000i −0.968947 0.401351i
\(596\) 0.578067 + 9.00129i 0.0236785 + 0.368707i
\(597\) −10.8240 8.70546i −0.442997 0.356291i
\(598\) 8.00972 + 34.4544i 0.327542 + 1.40895i
\(599\) 12.6251 3.38290i 0.515849 0.138221i 0.00850325 0.999964i \(-0.497293\pi\)
0.507346 + 0.861742i \(0.330627\pi\)
\(600\) −8.28544 + 10.9764i −0.338251 + 0.448109i
\(601\) 40.2934 + 10.7966i 1.64360 + 0.440402i 0.957811 0.287398i \(-0.0927903\pi\)
0.685790 + 0.727800i \(0.259457\pi\)
\(602\) −0.0336079 + 1.00634i −0.00136976 + 0.0410154i
\(603\) 4.00186 + 3.37198i 0.162968 + 0.137318i
\(604\) −20.6493 1.38075i −0.840206 0.0561819i
\(605\) −23.5865 + 3.10522i −0.958928 + 0.126245i
\(606\) 11.6398 + 33.2781i 0.472833 + 1.35183i
\(607\) 15.9905 27.6963i 0.649033 1.12416i −0.334321 0.942459i \(-0.608507\pi\)
0.983354 0.181699i \(-0.0581596\pi\)
\(608\) 18.6340 22.5537i 0.755710 0.914675i
\(609\) 0.470514 20.5943i 0.0190662 0.834522i
\(610\) −22.4899 18.4818i −0.910588 0.748304i
\(611\) −5.57470 + 13.4585i −0.225528 + 0.544474i
\(612\) −32.5448 + 14.1893i −1.31555 + 0.573570i
\(613\) −28.8640 + 11.9559i −1.16581 + 0.482892i −0.879804 0.475337i \(-0.842326\pi\)
−0.286002 + 0.958229i \(0.592326\pi\)
\(614\) 41.2038 21.9890i 1.66285 0.887405i
\(615\) −37.0558 + 9.02719i −1.49423 + 0.364011i
\(616\) 6.81002 1.11052i 0.274383 0.0447440i
\(617\) 15.5155 4.15737i 0.624631 0.167369i 0.0673990 0.997726i \(-0.478530\pi\)
0.557232 + 0.830357i \(0.311863\pi\)
\(618\) 4.98951 15.1565i 0.200707 0.609682i
\(619\) −4.72212 + 6.15399i −0.189798 + 0.247350i −0.878553 0.477644i \(-0.841491\pi\)
0.688755 + 0.724994i \(0.258157\pi\)
\(620\) 0.935726 1.89118i 0.0375796 0.0759515i
\(621\) 17.5721 + 26.4747i 0.705146 + 1.06239i
\(622\) −3.80275 + 8.37817i −0.152476 + 0.335934i
\(623\) −22.9099 + 13.2270i −0.917866 + 0.529930i
\(624\) 25.8961 + 11.5079i 1.03667 + 0.460685i
\(625\) −26.9816 15.5778i −1.07926 0.623113i
\(626\) 8.92472 6.38647i 0.356703 0.255255i
\(627\) −8.33931 11.3979i −0.333040 0.455188i
\(628\) −13.9758 + 15.8940i −0.557694 + 0.634241i
\(629\) −12.8941 31.1292i −0.514123 1.24120i
\(630\) 11.9051 + 13.9541i 0.474312 + 0.555943i
\(631\) −18.6638 18.6638i −0.742993 0.742993i 0.230160 0.973153i \(-0.426075\pi\)
−0.973153 + 0.230160i \(0.926075\pi\)
\(632\) −10.1119 + 0.311025i −0.402229 + 0.0123719i
\(633\) 31.1265 + 32.5821i 1.23717 + 1.29502i
\(634\) 6.04897 9.71325i 0.240235 0.385763i
\(635\) −6.55073 + 49.7577i −0.259958 + 1.97458i
\(636\) 29.2939 + 35.0778i 1.16158 + 1.39092i
\(637\) −18.6779 + 2.45899i −0.740044 + 0.0974286i
\(638\) 6.02638 + 16.0438i 0.238587 + 0.635178i
\(639\) 14.3616 22.4415i 0.568137 0.887770i
\(640\) 7.32024 30.7528i 0.289358 1.21561i
\(641\) −16.1318 27.9411i −0.637168 1.10361i −0.986051 0.166441i \(-0.946772\pi\)
0.348884 0.937166i \(-0.386561\pi\)
\(642\) 2.94800 15.5697i 0.116348 0.614489i
\(643\) 15.5838 + 20.3092i 0.614566 + 0.800918i 0.992149 0.125058i \(-0.0399116\pi\)
−0.377584 + 0.925976i \(0.623245\pi\)
\(644\) −3.66746 18.5654i −0.144518 0.731579i
\(645\) 1.39567 1.73532i 0.0549544 0.0683280i
\(646\) −20.3762 38.1816i −0.801689 1.50223i
\(647\) 28.0801 28.0801i 1.10394 1.10394i 0.110012 0.993930i \(-0.464911\pi\)
0.993930 0.110012i \(-0.0350890\pi\)
\(648\) 25.4091 + 1.54226i 0.998163 + 0.0605858i
\(649\) 1.11407 + 1.11407i 0.0437312 + 0.0437312i
\(650\) 4.72393 15.5358i 0.185288 0.609366i
\(651\) −0.788523 0.634188i −0.0309046 0.0248558i
\(652\) −35.5594 7.12192i −1.39261 0.278916i
\(653\) −5.08135 + 3.89906i −0.198849 + 0.152582i −0.703386 0.710808i \(-0.748330\pi\)
0.504538 + 0.863390i \(0.331663\pi\)
\(654\) −10.3259 15.1495i −0.403775 0.592391i
\(655\) 34.6781 20.0214i 1.35499 0.782301i
\(656\) 25.0593 19.1240i 0.978400 0.746665i
\(657\) −10.5399 6.74511i −0.411201 0.263152i
\(658\) 3.22105 7.09656i 0.125569 0.276653i
\(659\) 3.68351 + 27.9790i 0.143489 + 1.08991i 0.899989 + 0.435913i \(0.143575\pi\)
−0.756500 + 0.653994i \(0.773092\pi\)
\(660\) −13.5196 7.07817i −0.526249 0.275517i
\(661\) 23.0491 + 3.03448i 0.896508 + 0.118027i 0.564677 0.825312i \(-0.309001\pi\)
0.331830 + 0.943339i \(0.392334\pi\)
\(662\) −1.22713 5.27858i −0.0476937 0.205158i
\(663\) 30.3118 28.9576i 1.17721 1.12462i
\(664\) 10.5304 27.8117i 0.408658 1.07930i
\(665\) −15.8104 + 15.8104i −0.613102 + 0.613102i
\(666\) −1.90820 + 24.0830i −0.0739414 + 0.933195i
\(667\) 43.4261 17.9877i 1.68147 0.696486i
\(668\) −39.0409 + 19.1889i −1.51054 + 0.742442i
\(669\) −22.6193 + 16.5495i −0.874512 + 0.639840i
\(670\) −1.12729 + 6.80004i −0.0435512 + 0.262709i
\(671\) 5.80725 10.0585i 0.224187 0.388302i
\(672\) −13.6408 6.61555i −0.526206 0.255200i
\(673\) −3.07791 5.33110i −0.118645 0.205499i 0.800586 0.599218i \(-0.204522\pi\)
−0.919231 + 0.393719i \(0.871188\pi\)
\(674\) −18.7544 + 7.04456i −0.722393 + 0.271346i
\(675\) −0.909195 14.5583i −0.0349949 0.560349i
\(676\) −7.44338 0.497715i −0.286284 0.0191429i
\(677\) 7.94079 + 6.09318i 0.305189 + 0.234180i 0.749989 0.661450i \(-0.230059\pi\)
−0.444800 + 0.895630i \(0.646725\pi\)
\(678\) −10.4816 20.7695i −0.402544 0.797647i
\(679\) −1.81154 6.76076i −0.0695206 0.259454i
\(680\) −37.9582 27.3141i −1.45563 1.04745i
\(681\) 6.17139 + 25.3330i 0.236488 + 0.970762i
\(682\) 0.805465 + 0.244915i 0.0308429 + 0.00937827i
\(683\) −8.34055 20.1359i −0.319142 0.770478i −0.999300 0.0374119i \(-0.988089\pi\)
0.680158 0.733066i \(-0.261911\pi\)
\(684\) 0.572372 + 31.0251i 0.0218852 + 1.18627i
\(685\) −3.13905 1.30024i −0.119937 0.0496794i
\(686\) 25.2755 2.47260i 0.965021 0.0944045i
\(687\) −4.06065 0.0927731i −0.154923 0.00353951i
\(688\) −0.481064 + 1.77661i −0.0183404 + 0.0677328i
\(689\) −46.7320 26.9807i −1.78035 1.02788i
\(690\) −18.1645 + 37.7067i −0.691509 + 1.43547i
\(691\) −2.11438 16.0603i −0.0804348 0.610963i −0.983427 0.181306i \(-0.941968\pi\)
0.902992 0.429657i \(-0.141366\pi\)
\(692\) −9.43672 + 3.18947i −0.358730 + 0.121246i
\(693\) −4.71575 + 5.59665i −0.179137 + 0.212599i
\(694\) 29.1879 + 31.2048i 1.10796 + 1.18452i
\(695\) −14.7075 + 54.8893i −0.557889 + 2.08207i
\(696\) 9.45813 36.4484i 0.358510 1.38157i
\(697\) −12.0693 45.0433i −0.457158 1.70614i
\(698\) 17.8249 28.6228i 0.674684 1.08339i
\(699\) 1.73138 2.15273i 0.0654869 0.0814237i
\(700\) −2.80324 + 8.22247i −0.105952 + 0.310780i
\(701\) −3.55913 + 8.59250i −0.134427 + 0.324534i −0.976731 0.214467i \(-0.931198\pi\)
0.842305 + 0.539002i \(0.181198\pi\)
\(702\) −28.7951 + 8.61751i −1.08680 + 0.325247i
\(703\) −29.4489 −1.11068
\(704\) 12.5826 + 0.874667i 0.474225 + 0.0329653i
\(705\) −15.1200 + 8.27492i −0.569451 + 0.311652i
\(706\) −42.1752 6.99169i −1.58728 0.263136i
\(707\) 13.5571 + 17.6680i 0.509868 + 0.664472i
\(708\) −0.593130 3.41053i −0.0222912 0.128176i
\(709\) 33.4466 + 25.6645i 1.25611 + 0.963850i 0.999996 0.00279603i \(-0.000890006\pi\)
0.256117 + 0.966646i \(0.417557\pi\)
\(710\) 35.0744 + 1.17135i 1.31632 + 0.0439599i
\(711\) 7.92610 7.23306i 0.297252 0.271261i
\(712\) −46.3028 + 13.9459i −1.73527 + 0.522646i
\(713\) 0.597605 2.23029i 0.0223805 0.0835251i
\(714\) −16.7244 + 14.9420i −0.625895 + 0.559191i
\(715\) 17.8645 + 2.35191i 0.668096 + 0.0879564i
\(716\) 1.20772 6.03007i 0.0451345 0.225354i
\(717\) −3.15588 + 7.15236i −0.117859 + 0.267110i
\(718\) 2.19542 + 22.4420i 0.0819324 + 0.837529i
\(719\) 22.2302i 0.829046i 0.910039 + 0.414523i \(0.136052\pi\)
−0.910039 + 0.414523i \(0.863948\pi\)
\(720\) 15.3427 + 29.8134i 0.571788 + 1.11108i
\(721\) 10.0795i 0.375381i
\(722\) −10.9036 + 1.06666i −0.405789 + 0.0396969i
\(723\) −14.5351 19.8661i −0.540565 0.738827i
\(724\) 20.7281 13.8106i 0.770354 0.513267i
\(725\) −21.3927 2.81641i −0.794507 0.104599i
\(726\) −6.52138 + 19.8098i −0.242031 + 0.735210i
\(727\) −9.91513 + 37.0038i −0.367732 + 1.37239i 0.495948 + 0.868352i \(0.334821\pi\)
−0.863680 + 0.504041i \(0.831846\pi\)
\(728\) 17.8109 + 1.78977i 0.660116 + 0.0663333i
\(729\) −21.5213 + 16.3043i −0.797087 + 0.603865i
\(730\) 0.550138 16.4731i 0.0203615 0.609698i
\(731\) 2.16015 + 1.65754i 0.0798962 + 0.0613065i
\(732\) −23.1533 + 10.7306i −0.855771 + 0.396613i
\(733\) 5.95661 + 7.76280i 0.220012 + 0.286726i 0.890299 0.455377i \(-0.150495\pi\)
−0.670287 + 0.742102i \(0.733829\pi\)
\(734\) −0.0724319 + 0.436922i −0.00267351 + 0.0161271i
\(735\) −19.0445 11.5832i −0.702467 0.427254i
\(736\) 1.24572 34.5704i 0.0459179 1.27428i
\(737\) −2.75019 −0.101305
\(738\) −6.96887 + 32.7008i −0.256527 + 1.20373i
\(739\) 3.92363 9.47249i 0.144333 0.348451i −0.835136 0.550043i \(-0.814611\pi\)
0.979470 + 0.201592i \(0.0646114\pi\)
\(740\) −28.5577 + 14.0363i −1.04980 + 0.515986i
\(741\) −13.2443 34.1615i −0.486543 1.25495i
\(742\) 24.5052 + 15.2607i 0.899615 + 0.560239i
\(743\) −11.5176 42.9843i −0.422540 1.57694i −0.769237 0.638963i \(-0.779364\pi\)
0.346697 0.937977i \(-0.387303\pi\)
\(744\) −1.13762 1.45855i −0.0417072 0.0534732i
\(745\) 3.26146 12.1720i 0.119491 0.445946i
\(746\) 12.6939 11.8735i 0.464757 0.434718i
\(747\) 10.7273 + 29.6623i 0.392491 + 1.08529i
\(748\) 8.27450 16.7234i 0.302546 0.611470i
\(749\) −1.30655 9.92426i −0.0477404 0.362624i
\(750\) −12.4012 + 8.45271i −0.452829 + 0.308649i
\(751\) 39.8107 + 22.9847i 1.45271 + 0.838724i 0.998635 0.0522371i \(-0.0166352\pi\)
0.454079 + 0.890962i \(0.349968\pi\)
\(752\) 8.70219 11.2793i 0.317336 0.411312i
\(753\) −0.794854 1.45236i −0.0289661 0.0529269i
\(754\) 4.32887 + 44.2506i 0.157648 + 1.61151i
\(755\) 26.7120 + 11.0645i 0.972149 + 0.402677i
\(756\) 15.5503 4.09349i 0.565558 0.148879i
\(757\) 14.1464 + 34.1525i 0.514160 + 1.24129i 0.941442 + 0.337174i \(0.109471\pi\)
−0.427282 + 0.904118i \(0.640529\pi\)
\(758\) 12.7489 41.9281i 0.463061 1.52290i
\(759\) −16.0274 4.68941i −0.581758 0.170215i
\(760\) −34.7514 + 21.5147i −1.26057 + 0.780420i
\(761\) 5.95991 + 22.2427i 0.216047 + 0.806297i 0.985796 + 0.167950i \(0.0537147\pi\)
−0.769749 + 0.638347i \(0.779619\pi\)
\(762\) 36.8058 + 24.1048i 1.33333 + 0.873225i
\(763\) −9.18798 7.05018i −0.332627 0.255234i
\(764\) −12.8326 + 11.2240i −0.464268 + 0.406071i
\(765\) 49.4209 4.22157i 1.78682 0.152631i
\(766\) −1.44785 3.85455i −0.0523130 0.139271i
\(767\) 2.04371 + 3.53981i 0.0737942 + 0.127815i
\(768\) −21.5031 17.4818i −0.775928 0.630821i
\(769\) 5.26497 9.11919i 0.189860 0.328846i −0.755344 0.655329i \(-0.772530\pi\)
0.945203 + 0.326482i \(0.105863\pi\)
\(770\) −9.50994 1.57653i −0.342715 0.0568143i
\(771\) −7.81592 3.44866i −0.281483 0.124201i
\(772\) 51.0546 + 17.4057i 1.83749 + 0.626447i
\(773\) 25.0978 10.3958i 0.902705 0.373912i 0.117445 0.993079i \(-0.462530\pi\)
0.785259 + 0.619167i \(0.212530\pi\)
\(774\) −0.839529 1.76251i −0.0301763 0.0633522i
\(775\) −0.749489 + 0.749489i −0.0269225 + 0.0269225i
\(776\) −0.393350 12.7884i −0.0141205 0.459077i
\(777\) 3.61199 + 14.8269i 0.129579 + 0.531911i
\(778\) −11.5136 + 2.67661i −0.412783 + 0.0959609i
\(779\) −40.4083 5.31986i −1.44778 0.190604i
\(780\) −29.1261 26.8150i −1.04288 0.960131i
\(781\) 1.82766 + 13.8824i 0.0653987 + 0.496753i
\(782\) −46.5984 21.1505i −1.66635 0.756339i
\(783\) 17.5546 + 35.8751i 0.627348 + 1.28207i
\(784\) 18.2594 + 2.45286i 0.652122 + 0.0876022i
\(785\) 25.6070 14.7842i 0.913955 0.527672i
\(786\) −2.61887 35.0059i −0.0934119 1.24862i
\(787\) 9.26181 7.10684i 0.330148 0.253331i −0.430364 0.902655i \(-0.641615\pi\)
0.760512 + 0.649324i \(0.224948\pi\)
\(788\) −9.23859 13.8660i −0.329111 0.493957i
\(789\) 4.41448 28.4869i 0.157160 1.01416i
\(790\) 13.5224 + 4.11170i 0.481105 + 0.146288i
\(791\) −10.3915 10.3915i −0.369479 0.369479i
\(792\) −10.7340 + 7.98462i −0.381416 + 0.283721i
\(793\) 21.3062 21.3062i 0.756606 0.756606i
\(794\) −9.49345 + 5.06632i −0.336910 + 0.179797i
\(795\) −23.0797 59.5301i −0.818552 2.11131i
\(796\) −13.3244 8.92852i −0.472272 0.316463i
\(797\) 0.0224506 + 0.0292583i 0.000795243 + 0.00103638i 0.793751 0.608243i \(-0.208125\pi\)
−0.792956 + 0.609279i \(0.791459\pi\)
\(798\) 6.47158 + 18.5022i 0.229091 + 0.654972i
\(799\) −10.5372 18.2509i −0.372779 0.645672i
\(800\) −8.43006 + 13.4576i −0.298048 + 0.475798i
\(801\) 27.6472 43.2015i 0.976867 1.52645i
\(802\) 2.33429 0.876809i 0.0824266 0.0309612i
\(803\) 6.52006 0.858382i 0.230088 0.0302916i
\(804\) 4.94170 + 3.47751i 0.174280 + 0.122642i
\(805\) −3.45090 + 26.2122i −0.121628 + 0.923858i
\(806\) 1.85397 + 1.15457i 0.0653033 + 0.0406679i
\(807\) 9.21627 31.4992i 0.324428 1.10883i
\(808\) 16.7276 + 37.1134i 0.588473 + 1.30565i
\(809\) −14.2848 14.2848i −0.502227 0.502227i 0.409903 0.912129i \(-0.365563\pi\)
−0.912129 + 0.409903i \(0.865563\pi\)
\(810\) −32.9395 13.4074i −1.15737 0.471090i
\(811\) 11.3483 + 27.3972i 0.398493 + 0.962046i 0.988024 + 0.154301i \(0.0493125\pi\)
−0.589531 + 0.807746i \(0.700688\pi\)
\(812\) −1.52443 23.7375i −0.0534971 0.833023i
\(813\) 1.66965 0.181122i 0.0585570 0.00635223i
\(814\) −7.38847 10.3250i −0.258966 0.361890i
\(815\) 43.8776 + 25.3328i 1.53697 + 0.887368i
\(816\) −36.0142 + 19.5869i −1.26075 + 0.685677i
\(817\) 2.06094 1.18988i 0.0721030 0.0416287i
\(818\) 22.1071 + 10.0341i 0.772955 + 0.350835i
\(819\) −15.5751 + 10.8582i −0.544239 + 0.379418i
\(820\) −41.7211 + 14.1011i −1.45696 + 0.492433i
\(821\) 3.58821 4.67625i 0.125229 0.163202i −0.726531 0.687134i \(-0.758869\pi\)
0.851760 + 0.523932i \(0.175535\pi\)
\(822\) −2.22121 + 1.98449i −0.0774736 + 0.0692170i
\(823\) −41.5975 + 11.1460i −1.45000 + 0.388526i −0.896023 0.444007i \(-0.853557\pi\)
−0.553976 + 0.832533i \(0.686890\pi\)
\(824\) 4.21936 17.9355i 0.146988 0.624812i
\(825\) 5.29537 + 5.54299i 0.184361 + 0.192982i
\(826\) −1.02954 1.92919i −0.0358222 0.0671250i
\(827\) 22.4652 9.30540i 0.781193 0.323581i 0.0437960 0.999040i \(-0.486055\pi\)
0.737397 + 0.675460i \(0.236055\pi\)
\(828\) 22.8694 + 28.6922i 0.794766 + 0.997123i
\(829\) 8.38388 20.2405i 0.291184 0.702981i −0.708813 0.705397i \(-0.750769\pi\)
0.999997 + 0.00241577i \(0.000768964\pi\)
\(830\) −26.3781 + 32.0987i −0.915599 + 1.11416i
\(831\) −5.08609 3.09346i −0.176434 0.107311i
\(832\) 30.9435 + 10.6405i 1.07277 + 0.368892i
\(833\) 13.6270 23.6027i 0.472148 0.817785i
\(834\) 37.7552 + 32.4993i 1.30736 + 1.12536i
\(835\) 60.2551 7.93273i 2.08521 0.274524i
\(836\) −10.7363 12.2749i −0.371321 0.424538i
\(837\) 1.92307 + 0.388680i 0.0664709 + 0.0134348i
\(838\) 11.5637 + 0.386183i 0.399462 + 0.0133405i
\(839\) 24.7076 + 6.62039i 0.853002 + 0.228561i 0.658723 0.752385i \(-0.271097\pi\)
0.194279 + 0.980946i \(0.437763\pi\)
\(840\) 15.0945 + 14.8577i 0.520811 + 0.512641i
\(841\) 29.0560 7.78554i 1.00193 0.268467i
\(842\) 3.63096 0.844100i 0.125131 0.0290896i
\(843\) −3.70616 + 23.9160i −0.127647 + 0.823712i
\(844\) 39.0740 + 34.3582i 1.34498 + 1.18266i
\(845\) 9.62880 + 3.98838i 0.331241 + 0.137204i
\(846\) 0.782815 + 15.0899i 0.0269137 + 0.518802i
\(847\) 13.1741i 0.452669i
\(848\) 37.2163 + 37.4129i 1.27801 + 1.28477i
\(849\) 44.8374 + 1.02439i 1.53882 + 0.0351571i
\(850\) 13.6706 + 19.1039i 0.468899 + 0.655260i
\(851\) −27.6255 + 21.1978i −0.946991 + 0.726652i
\(852\) 14.2697 27.2557i 0.488873 0.933766i
\(853\) 10.9704 14.2969i 0.375619 0.489517i −0.566844 0.823825i \(-0.691836\pi\)
0.942464 + 0.334308i \(0.108503\pi\)
\(854\) −11.7726 + 11.0117i −0.402851 + 0.376813i
\(855\) 13.1209 41.3183i 0.448726 1.41306i
\(856\) 1.82948 18.2061i 0.0625305 0.622273i
\(857\) 43.9763 + 11.7834i 1.50220 + 0.402513i 0.913836 0.406083i \(-0.133106\pi\)
0.588364 + 0.808596i \(0.299772\pi\)
\(858\) 8.65435 13.2144i 0.295455 0.451132i
\(859\) −4.25432 + 32.3147i −0.145155 + 1.10256i 0.751468 + 0.659770i \(0.229346\pi\)
−0.896623 + 0.442795i \(0.853987\pi\)
\(860\) 1.43143 2.13619i 0.0488113 0.0728433i
\(861\) 2.27776 + 20.9972i 0.0776259 + 0.715583i
\(862\) −19.3521 15.9032i −0.659135 0.541665i
\(863\) −19.9053 −0.677583 −0.338791 0.940862i \(-0.610018\pi\)
−0.338791 + 0.940862i \(0.610018\pi\)
\(864\) 29.3837 0.774508i 0.999653 0.0263493i
\(865\) 13.9164 0.473172
\(866\) 18.6193 + 15.3010i 0.632709 + 0.519949i
\(867\) 3.36492 + 31.0190i 0.114279 + 1.05346i
\(868\) −0.970678 0.650438i −0.0329469 0.0220773i
\(869\) −0.736067 + 5.59098i −0.0249694 + 0.189661i
\(870\) −28.8225 + 44.0092i −0.977173 + 1.49205i
\(871\) −6.89172 1.84663i −0.233517 0.0625707i
\(872\) −13.3978 16.3912i −0.453707 0.555077i
\(873\) 9.14759 + 10.0241i 0.309599 + 0.339263i
\(874\) −32.6642 + 30.5530i −1.10488 + 1.03347i
\(875\) −5.77123 + 7.52121i −0.195103 + 0.254263i
\(876\) −12.8010 6.70195i −0.432505 0.226438i
\(877\) −2.67560 + 2.05306i −0.0903484 + 0.0693268i −0.652948 0.757403i \(-0.726468\pi\)
0.562600 + 0.826730i \(0.309801\pi\)
\(878\) −27.5226 38.4612i −0.928842 1.29800i
\(879\) −5.27213 0.120452i −0.177824 0.00406273i
\(880\) −16.2620 6.78621i −0.548193 0.228763i
\(881\) 11.8754i 0.400091i 0.979787 + 0.200045i \(0.0641090\pi\)
−0.979787 + 0.200045i \(0.935891\pi\)
\(882\) −16.3941 + 10.6341i −0.552018 + 0.358069i
\(883\) 2.03653 + 0.843558i 0.0685347 + 0.0283880i 0.416687 0.909050i \(-0.363191\pi\)
−0.348153 + 0.937438i \(0.613191\pi\)
\(884\) 31.9641 36.3514i 1.07507 1.22263i
\(885\) −0.740614 + 4.77922i −0.0248955 + 0.160652i
\(886\) 42.0275 9.77025i 1.41194 0.328238i
\(887\) −4.06167 + 1.08832i −0.136378 + 0.0365423i −0.326362 0.945245i \(-0.605823\pi\)
0.189985 + 0.981787i \(0.439156\pi\)
\(888\) 0.220535 + 27.8949i 0.00740067 + 0.936091i
\(889\) 26.8450 + 7.19309i 0.900352 + 0.241248i
\(890\) 67.5209 + 2.25493i 2.26331 + 0.0755856i
\(891\) 3.12803 13.8405i 0.104793 0.463675i
\(892\) −24.3598 + 21.3063i −0.815627 + 0.713386i
\(893\) −18.2616 + 2.40418i −0.611101 + 0.0804530i
\(894\) −8.37240 7.20688i −0.280015 0.241034i
\(895\) −4.29586 + 7.44065i −0.143595 + 0.248714i
\(896\) −16.3551 6.24187i −0.546385 0.208526i
\(897\) −37.0144 22.5129i −1.23588 0.751684i
\(898\) 13.0008 15.8203i 0.433843 0.527930i
\(899\) 1.11063 2.68130i 0.0370416 0.0894265i
\(900\) −2.50613 16.6557i −0.0835377 0.555191i
\(901\) 72.1226 29.8741i 2.40275 0.995252i
\(902\) −8.27293 15.5021i −0.275458 0.516164i
\(903\) −0.851859 0.891694i −0.0283481 0.0296737i
\(904\) −14.1406 22.8405i −0.470311 0.759665i
\(905\) −33.6119 + 9.00628i −1.11730 + 0.299379i
\(906\) 18.9016 16.8872i 0.627963 0.561039i
\(907\) 0.00312197 0.00406863i 0.000103663 0.000135097i −0.793302 0.608829i \(-0.791640\pi\)
0.793405 + 0.608694i \(0.208306\pi\)
\(908\) 9.64017 + 28.5224i 0.319920 + 0.946550i
\(909\) −39.0954 18.3283i −1.29671 0.607910i
\(910\) −22.7724 10.3361i −0.754899 0.342640i
\(911\) 0.0594090 0.0342998i 0.00196831 0.00113640i −0.499016 0.866593i \(-0.666305\pi\)
0.500984 + 0.865457i \(0.332972\pi\)
\(912\) 3.77035 + 35.6319i 0.124849 + 1.17989i
\(913\) −14.3560 8.28842i −0.475113 0.274307i
\(914\) 6.88421 + 9.62028i 0.227709 + 0.318211i
\(915\) 35.4439 3.84493i 1.17174 0.127109i
\(916\) −4.68042 + 0.300578i −0.154645 + 0.00993138i
\(917\) −8.48578 20.4865i −0.280225 0.676523i
\(918\) 15.4688 40.6382i 0.510547 1.34126i
\(919\) −18.1802 18.1802i −0.599710 0.599710i 0.340525 0.940235i \(-0.389395\pi\)
−0.940235 + 0.340525i \(0.889395\pi\)
\(920\) −17.1131 + 45.1973i −0.564203 + 1.49011i
\(921\) −16.0627 + 54.8990i −0.529285 + 1.80898i
\(922\) 37.8363 + 23.5627i 1.24607 + 0.775996i
\(923\) −4.74150 + 36.0152i −0.156068 + 1.18546i
\(924\) −4.86334 + 6.91103i −0.159992 + 0.227356i
\(925\) 15.8480 2.08643i 0.521080 0.0686014i
\(926\) 26.9641 10.1283i 0.886094 0.332836i
\(927\) 8.98825 + 17.3531i 0.295213 + 0.569952i
\(928\) 7.22411 42.8766i 0.237143 1.40749i
\(929\) 0.903501 + 1.56491i 0.0296429 + 0.0513430i 0.880466 0.474109i \(-0.157230\pi\)
−0.850823 + 0.525452i \(0.823896\pi\)
\(930\) 0.853206 + 2.43931i 0.0279777 + 0.0799882i
\(931\) −14.5009 18.8979i −0.475246 0.619353i
\(932\) 1.77574 2.65003i 0.0581665 0.0868045i
\(933\) −4.07340 10.5066i −0.133357 0.343972i
\(934\) −41.3575 + 22.0710i −1.35326 + 0.722185i
\(935\) −18.4323 + 18.4323i −0.602802 + 0.602802i
\(936\) −32.2597 + 12.8013i −1.05444 + 0.418423i
\(937\) 11.6502 + 11.6502i 0.380596 + 0.380596i 0.871317 0.490721i \(-0.163267\pi\)
−0.490721 + 0.871317i \(0.663267\pi\)
\(938\) 3.65194 + 1.11043i 0.119240 + 0.0362569i
\(939\) −2.05830 + 13.2823i −0.0671701 + 0.433452i
\(940\) −16.5630 + 11.0355i −0.540227 + 0.359939i
\(941\) −17.9330 + 13.7605i −0.584600 + 0.448579i −0.858237 0.513254i \(-0.828440\pi\)
0.273637 + 0.961833i \(0.411773\pi\)
\(942\) −1.93383 25.8491i −0.0630075 0.842208i
\(943\) −41.7358 + 24.0962i −1.35910 + 0.784679i
\(944\) −1.02439 3.86376i −0.0333410 0.125755i
\(945\) −22.4122 1.53829i −0.729068 0.0500404i
\(946\) 0.934251 + 0.424046i 0.0303751 + 0.0137869i
\(947\) −5.14099 39.0497i −0.167060 1.26894i −0.845375 0.534173i \(-0.820623\pi\)
0.678315 0.734771i \(-0.262710\pi\)
\(948\) 8.39218 9.11547i 0.272565 0.296057i
\(949\) 16.9150 + 2.22690i 0.549084 + 0.0722883i
\(950\) 19.9984 4.64909i 0.648834 0.150836i
\(951\) 3.31707 + 13.6163i 0.107564 + 0.441538i
\(952\) −17.7399 + 18.8659i −0.574955 + 0.611446i
\(953\) −27.0577 + 27.0577i −0.876485 + 0.876485i −0.993169 0.116684i \(-0.962774\pi\)
0.116684 + 0.993169i \(0.462774\pi\)
\(954\) −55.7972 4.42107i −1.80650 0.143138i
\(955\) 22.0050 9.11478i 0.712066 0.294947i
\(956\) −2.91291 + 8.54417i −0.0942104 + 0.276338i
\(957\) −19.2037 8.47335i −0.620767 0.273905i
\(958\) −49.8507 8.26412i −1.61060 0.267002i
\(959\) −0.940761 + 1.62945i −0.0303788 + 0.0526176i
\(960\) 20.6396 + 32.7565i 0.666141 + 1.05721i
\(961\) 15.4287 + 26.7233i 0.497701 + 0.862043i
\(962\) −11.5821 30.8344i −0.373420 0.994140i
\(963\) 11.0992 + 15.9207i 0.357666 + 0.513038i
\(964\) −18.7129 21.3947i −0.602700 0.689077i
\(965\) −59.7855 45.8750i −1.92456 1.47677i
\(966\) 19.3891 + 12.6983i 0.623835 + 0.408561i
\(967\) 15.7919 + 58.9361i 0.507833 + 1.89526i 0.441032 + 0.897491i \(0.354612\pi\)
0.0668005 + 0.997766i \(0.478721\pi\)
\(968\) −5.51479 + 23.4420i −0.177252 + 0.753456i
\(969\) 50.8722 + 14.8846i 1.63425 + 0.478161i
\(970\) −5.20003 + 17.1016i −0.166963 + 0.549100i
\(971\) −12.5728 30.3535i −0.403481 0.974089i −0.986814 0.161856i \(-0.948252\pi\)
0.583333 0.812233i \(-0.301748\pi\)
\(972\) −23.1214 + 20.9141i −0.741619 + 0.670822i
\(973\) 29.0728 + 12.0423i 0.932030 + 0.386059i
\(974\) −0.928350 9.48978i −0.0297463 0.304072i
\(975\) 9.54782 + 17.4458i 0.305775 + 0.558713i
\(976\) −25.5578 + 14.6661i −0.818084 + 0.469451i
\(977\) 32.2122 + 18.5977i 1.03056 + 0.594995i 0.917145 0.398553i \(-0.130488\pi\)
0.113416 + 0.993548i \(0.463821\pi\)
\(978\) 36.7015 25.0158i 1.17358 0.799918i
\(979\) 3.51838 + 26.7247i 0.112448 + 0.854126i
\(980\) −23.0694 11.4144i −0.736925 0.364619i
\(981\) 22.1051 + 3.94453i 0.705762 + 0.125939i
\(982\) 15.1682 14.1878i 0.484036 0.452751i
\(983\) 0.771733 2.88015i 0.0246145 0.0918624i −0.952526 0.304457i \(-0.901525\pi\)
0.977140 + 0.212595i \(0.0681915\pi\)
\(984\) −4.73653 + 38.3159i −0.150995 + 1.22147i
\(985\) 6.02474 + 22.4846i 0.191964 + 0.716420i
\(986\) −54.6000 34.0023i −1.73882 1.08285i
\(987\) 3.45029 + 8.89943i 0.109824 + 0.283272i
\(988\) −18.6620 37.9688i −0.593716 1.20795i
\(989\) 1.07683 2.59971i 0.0342414 0.0826659i
\(990\) 17.7784 5.76614i 0.565034 0.183260i
\(991\) 17.8473 0.566938 0.283469 0.958981i \(-0.408515\pi\)
0.283469 + 0.958981i \(0.408515\pi\)
\(992\) −1.45494 1.56372i −0.0461945 0.0496481i
\(993\) 5.67078 + 3.44908i 0.179957 + 0.109453i
\(994\) 3.17832 19.1722i 0.100810 0.608106i
\(995\) 13.6411 + 17.7775i 0.432453 + 0.563583i
\(996\) 15.3152 + 33.0456i 0.485282 + 1.04709i
\(997\) −28.6012 21.9465i −0.905809 0.695052i 0.0469118 0.998899i \(-0.485062\pi\)
−0.952721 + 0.303847i \(0.901729\pi\)
\(998\) −0.747002 + 22.3680i −0.0236459 + 0.708045i
\(999\) −19.4401 22.3053i −0.615057 0.705709i
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 288.2.bc.a.13.14 368
3.2 odd 2 864.2.bk.a.685.33 368
9.2 odd 6 864.2.bk.a.397.3 368
9.7 even 3 inner 288.2.bc.a.205.44 yes 368
32.5 even 8 inner 288.2.bc.a.229.44 yes 368
96.5 odd 8 864.2.bk.a.37.3 368
288.101 odd 24 864.2.bk.a.613.33 368
288.133 even 24 inner 288.2.bc.a.133.14 yes 368
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
288.2.bc.a.13.14 368 1.1 even 1 trivial
288.2.bc.a.133.14 yes 368 288.133 even 24 inner
288.2.bc.a.205.44 yes 368 9.7 even 3 inner
288.2.bc.a.229.44 yes 368 32.5 even 8 inner
864.2.bk.a.37.3 368 96.5 odd 8
864.2.bk.a.397.3 368 9.2 odd 6
864.2.bk.a.613.33 368 288.101 odd 24
864.2.bk.a.685.33 368 3.2 odd 2