Properties

Label 240.2.bk.b.11.4
Level $240$
Weight $2$
Character 240.11
Analytic conductor $1.916$
Analytic rank $0$
Dimension $60$
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] = [240,2,Mod(11,240)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(240, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 1, 2, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("240.11");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 240.bk (of order \(4\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(1.91640964851\)
Analytic rank: \(0\)
Dimension: \(60\)
Relative dimension: \(30\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 11.4
Character \(\chi\) \(=\) 240.11
Dual form 240.2.bk.b.131.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.24180 - 0.676700i) q^{2} +(-0.861442 + 1.50264i) q^{3} +(1.08415 + 1.68066i) q^{4} +(0.707107 - 0.707107i) q^{5} +(2.08658 - 1.28304i) q^{6} +0.563322 q^{7} +(-0.209007 - 2.82069i) q^{8} +(-1.51583 - 2.58887i) q^{9} +O(q^{10})\) \(q+(-1.24180 - 0.676700i) q^{2} +(-0.861442 + 1.50264i) q^{3} +(1.08415 + 1.68066i) q^{4} +(0.707107 - 0.707107i) q^{5} +(2.08658 - 1.28304i) q^{6} +0.563322 q^{7} +(-0.209007 - 2.82069i) q^{8} +(-1.51583 - 2.58887i) q^{9} +(-1.35659 + 0.399589i) q^{10} +(3.95012 + 3.95012i) q^{11} +(-3.45935 + 0.181302i) q^{12} +(-2.81363 + 2.81363i) q^{13} +(-0.699535 - 0.381200i) q^{14} +(0.453393 + 1.67166i) q^{15} +(-1.64922 + 3.64418i) q^{16} +1.84903i q^{17} +(0.130482 + 4.24063i) q^{18} +(2.87523 + 2.87523i) q^{19} +(1.95502 + 0.421791i) q^{20} +(-0.485269 + 0.846468i) q^{21} +(-2.23223 - 7.57832i) q^{22} +4.28805i q^{23} +(4.41853 + 2.11580i) q^{24} -1.00000i q^{25} +(5.39796 - 1.58999i) q^{26} +(5.19593 - 0.0475870i) q^{27} +(0.610728 + 0.946751i) q^{28} +(-0.371339 - 0.371339i) q^{29} +(0.568184 - 2.38268i) q^{30} +1.24571i q^{31} +(4.51402 - 3.40934i) q^{32} +(-9.33840 + 2.53280i) q^{33} +(1.25124 - 2.29613i) q^{34} +(0.398329 - 0.398329i) q^{35} +(2.70760 - 5.35433i) q^{36} +(0.150367 + 0.150367i) q^{37} +(-1.62480 - 5.51614i) q^{38} +(-1.80408 - 6.65164i) q^{39} +(-2.14232 - 1.84674i) q^{40} +7.24837 q^{41} +(1.17541 - 0.722766i) q^{42} +(0.886832 - 0.886832i) q^{43} +(-2.35626 + 10.9213i) q^{44} +(-2.90246 - 0.758750i) q^{45} +(2.90173 - 5.32492i) q^{46} -12.4833 q^{47} +(-4.05518 - 5.61743i) q^{48} -6.68267 q^{49} +(-0.676700 + 1.24180i) q^{50} +(-2.77842 - 1.59283i) q^{51} +(-7.77915 - 1.67834i) q^{52} +(8.71705 - 8.71705i) q^{53} +(-6.48453 - 3.45699i) q^{54} +5.58632 q^{55} +(-0.117738 - 1.58896i) q^{56} +(-6.79727 + 1.84358i) q^{57} +(0.209845 + 0.712416i) q^{58} +(1.63588 + 1.63588i) q^{59} +(-2.31793 + 2.57433i) q^{60} +(0.657825 - 0.657825i) q^{61} +(0.842969 - 1.54692i) q^{62} +(-0.853902 - 1.45837i) q^{63} +(-7.91263 + 1.17909i) q^{64} +3.97907i q^{65} +(13.3104 + 3.17406i) q^{66} +(8.22317 + 8.22317i) q^{67} +(-3.10758 + 2.00463i) q^{68} +(-6.44339 - 3.69391i) q^{69} +(-0.764195 + 0.225097i) q^{70} -12.6995i q^{71} +(-6.98559 + 4.81680i) q^{72} -10.2509i q^{73} +(-0.0849732 - 0.288480i) q^{74} +(1.50264 + 0.861442i) q^{75} +(-1.71508 + 7.94947i) q^{76} +(2.22519 + 2.22519i) q^{77} +(-2.26084 + 9.48085i) q^{78} -13.0899i q^{79} +(1.41066 + 3.74300i) q^{80} +(-4.40449 + 7.84860i) q^{81} +(-9.00106 - 4.90497i) q^{82} +(-3.31432 + 3.31432i) q^{83} +(-1.94873 + 0.102131i) q^{84} +(1.30746 + 1.30746i) q^{85} +(-1.70139 + 0.501153i) q^{86} +(0.877875 - 0.238101i) q^{87} +(10.3165 - 11.9677i) q^{88} -14.1100 q^{89} +(3.09085 + 2.90632i) q^{90} +(-1.58498 + 1.58498i) q^{91} +(-7.20675 + 4.64891i) q^{92} +(-1.87184 - 1.07310i) q^{93} +(15.5018 + 8.44746i) q^{94} +4.06619 q^{95} +(1.23443 + 9.71989i) q^{96} +16.2142 q^{97} +(8.29857 + 4.52216i) q^{98} +(4.23862 - 16.2141i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 60 q + 4 q^{3} + 8 q^{4} + 8 q^{6} + 16 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 60 q + 4 q^{3} + 8 q^{4} + 8 q^{6} + 16 q^{7} + 4 q^{12} + 16 q^{13} - 52 q^{16} - 20 q^{18} + 20 q^{19} - 16 q^{21} - 24 q^{22} - 28 q^{24} - 20 q^{27} - 56 q^{28} - 12 q^{34} + 12 q^{36} + 24 q^{37} - 80 q^{39} - 8 q^{40} + 36 q^{42} - 8 q^{45} + 36 q^{46} + 56 q^{48} + 28 q^{49} - 36 q^{51} - 24 q^{52} + 92 q^{54} - 80 q^{58} + 28 q^{60} + 20 q^{61} - 64 q^{64} + 24 q^{66} - 40 q^{67} + 12 q^{69} - 16 q^{70} - 56 q^{72} + 4 q^{75} - 20 q^{76} - 8 q^{78} - 28 q^{81} - 32 q^{82} + 16 q^{84} - 20 q^{85} - 24 q^{87} + 8 q^{88} + 32 q^{90} - 16 q^{91} - 48 q^{93} + 28 q^{94} + 72 q^{96} - 8 q^{97} + 32 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/240\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(97\) \(161\) \(181\)
\(\chi(n)\) \(-1\) \(1\) \(-1\) \(e\left(\frac{1}{4}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.24180 0.676700i −0.878088 0.478499i
\(3\) −0.861442 + 1.50264i −0.497354 + 0.867548i
\(4\) 1.08415 + 1.68066i 0.542077 + 0.840329i
\(5\) 0.707107 0.707107i 0.316228 0.316228i
\(6\) 2.08658 1.28304i 0.851841 0.523800i
\(7\) 0.563322 0.212916 0.106458 0.994317i \(-0.466049\pi\)
0.106458 + 0.994317i \(0.466049\pi\)
\(8\) −0.209007 2.82069i −0.0738953 0.997266i
\(9\) −1.51583 2.58887i −0.505278 0.862957i
\(10\) −1.35659 + 0.399589i −0.428991 + 0.126361i
\(11\) 3.95012 + 3.95012i 1.19101 + 1.19101i 0.976785 + 0.214222i \(0.0687214\pi\)
0.214222 + 0.976785i \(0.431279\pi\)
\(12\) −3.45935 + 0.181302i −0.998629 + 0.0523373i
\(13\) −2.81363 + 2.81363i −0.780360 + 0.780360i −0.979891 0.199532i \(-0.936058\pi\)
0.199532 + 0.979891i \(0.436058\pi\)
\(14\) −0.699535 0.381200i −0.186959 0.101880i
\(15\) 0.453393 + 1.67166i 0.117066 + 0.431620i
\(16\) −1.64922 + 3.64418i −0.412304 + 0.911046i
\(17\) 1.84903i 0.448455i 0.974537 + 0.224228i \(0.0719859\pi\)
−0.974537 + 0.224228i \(0.928014\pi\)
\(18\) 0.130482 + 4.24063i 0.0307549 + 0.999527i
\(19\) 2.87523 + 2.87523i 0.659623 + 0.659623i 0.955291 0.295668i \(-0.0955422\pi\)
−0.295668 + 0.955291i \(0.595542\pi\)
\(20\) 1.95502 + 0.421791i 0.437155 + 0.0943153i
\(21\) −0.485269 + 0.846468i −0.105894 + 0.184714i
\(22\) −2.23223 7.57832i −0.475913 1.61570i
\(23\) 4.28805i 0.894121i 0.894504 + 0.447061i \(0.147529\pi\)
−0.894504 + 0.447061i \(0.852471\pi\)
\(24\) 4.41853 + 2.11580i 0.901928 + 0.431886i
\(25\) 1.00000i 0.200000i
\(26\) 5.39796 1.58999i 1.05863 0.311823i
\(27\) 5.19593 0.0475870i 0.999958 0.00915812i
\(28\) 0.610728 + 0.946751i 0.115417 + 0.178919i
\(29\) −0.371339 0.371339i −0.0689559 0.0689559i 0.671788 0.740744i \(-0.265527\pi\)
−0.740744 + 0.671788i \(0.765527\pi\)
\(30\) 0.568184 2.38268i 0.103736 0.435016i
\(31\) 1.24571i 0.223735i 0.993723 + 0.111868i \(0.0356833\pi\)
−0.993723 + 0.111868i \(0.964317\pi\)
\(32\) 4.51402 3.40934i 0.797974 0.602692i
\(33\) −9.33840 + 2.53280i −1.62561 + 0.440903i
\(34\) 1.25124 2.29613i 0.214585 0.393783i
\(35\) 0.398329 0.398329i 0.0673298 0.0673298i
\(36\) 2.70760 5.35433i 0.451267 0.892389i
\(37\) 0.150367 + 0.150367i 0.0247202 + 0.0247202i 0.719359 0.694639i \(-0.244436\pi\)
−0.694639 + 0.719359i \(0.744436\pi\)
\(38\) −1.62480 5.51614i −0.263578 0.894836i
\(39\) −1.80408 6.65164i −0.288884 1.06511i
\(40\) −2.14232 1.84674i −0.338731 0.291995i
\(41\) 7.24837 1.13201 0.566003 0.824403i \(-0.308489\pi\)
0.566003 + 0.824403i \(0.308489\pi\)
\(42\) 1.17541 0.722766i 0.181370 0.111525i
\(43\) 0.886832 0.886832i 0.135241 0.135241i −0.636246 0.771486i \(-0.719514\pi\)
0.771486 + 0.636246i \(0.219514\pi\)
\(44\) −2.35626 + 10.9213i −0.355219 + 1.64645i
\(45\) −2.90246 0.758750i −0.432674 0.113108i
\(46\) 2.90173 5.32492i 0.427836 0.785117i
\(47\) −12.4833 −1.82088 −0.910439 0.413643i \(-0.864256\pi\)
−0.910439 + 0.413643i \(0.864256\pi\)
\(48\) −4.05518 5.61743i −0.585315 0.810806i
\(49\) −6.68267 −0.954667
\(50\) −0.676700 + 1.24180i −0.0956998 + 0.175618i
\(51\) −2.77842 1.59283i −0.389056 0.223041i
\(52\) −7.77915 1.67834i −1.07877 0.232743i
\(53\) 8.71705 8.71705i 1.19738 1.19738i 0.222430 0.974949i \(-0.428601\pi\)
0.974949 0.222430i \(-0.0713990\pi\)
\(54\) −6.48453 3.45699i −0.882433 0.470437i
\(55\) 5.58632 0.753259
\(56\) −0.117738 1.58896i −0.0157335 0.212333i
\(57\) −6.79727 + 1.84358i −0.900320 + 0.244188i
\(58\) 0.209845 + 0.712416i 0.0275540 + 0.0935447i
\(59\) 1.63588 + 1.63588i 0.212974 + 0.212974i 0.805529 0.592556i \(-0.201881\pi\)
−0.592556 + 0.805529i \(0.701881\pi\)
\(60\) −2.31793 + 2.57433i −0.299244 + 0.332345i
\(61\) 0.657825 0.657825i 0.0842259 0.0842259i −0.663739 0.747965i \(-0.731031\pi\)
0.747965 + 0.663739i \(0.231031\pi\)
\(62\) 0.842969 1.54692i 0.107057 0.196459i
\(63\) −0.853902 1.45837i −0.107582 0.183737i
\(64\) −7.91263 + 1.17909i −0.989079 + 0.147387i
\(65\) 3.97907i 0.493543i
\(66\) 13.3104 + 3.17406i 1.63840 + 0.390699i
\(67\) 8.22317 + 8.22317i 1.00462 + 1.00462i 0.999989 + 0.00463097i \(0.00147409\pi\)
0.00463097 + 0.999989i \(0.498526\pi\)
\(68\) −3.10758 + 2.00463i −0.376850 + 0.243097i
\(69\) −6.44339 3.69391i −0.775693 0.444695i
\(70\) −0.764195 + 0.225097i −0.0913388 + 0.0269043i
\(71\) 12.6995i 1.50715i −0.657361 0.753575i \(-0.728327\pi\)
0.657361 0.753575i \(-0.271673\pi\)
\(72\) −6.98559 + 4.81680i −0.823260 + 0.567665i
\(73\) 10.2509i 1.19977i −0.800085 0.599887i \(-0.795212\pi\)
0.800085 0.599887i \(-0.204788\pi\)
\(74\) −0.0849732 0.288480i −0.00987794 0.0335352i
\(75\) 1.50264 + 0.861442i 0.173510 + 0.0994708i
\(76\) −1.71508 + 7.94947i −0.196733 + 0.911866i
\(77\) 2.22519 + 2.22519i 0.253584 + 0.253584i
\(78\) −2.26084 + 9.48085i −0.255990 + 1.07350i
\(79\) 13.0899i 1.47272i −0.676588 0.736362i \(-0.736542\pi\)
0.676588 0.736362i \(-0.263458\pi\)
\(80\) 1.41066 + 3.74300i 0.157716 + 0.418480i
\(81\) −4.40449 + 7.84860i −0.489388 + 0.872066i
\(82\) −9.00106 4.90497i −0.994001 0.541664i
\(83\) −3.31432 + 3.31432i −0.363794 + 0.363794i −0.865208 0.501414i \(-0.832813\pi\)
0.501414 + 0.865208i \(0.332813\pi\)
\(84\) −1.94873 + 0.102131i −0.212624 + 0.0111434i
\(85\) 1.30746 + 1.30746i 0.141814 + 0.141814i
\(86\) −1.70139 + 0.501153i −0.183466 + 0.0540407i
\(87\) 0.877875 0.238101i 0.0941181 0.0255271i
\(88\) 10.3165 11.9677i 1.09974 1.27576i
\(89\) −14.1100 −1.49565 −0.747827 0.663893i \(-0.768903\pi\)
−0.747827 + 0.663893i \(0.768903\pi\)
\(90\) 3.09085 + 2.90632i 0.325804 + 0.306353i
\(91\) −1.58498 + 1.58498i −0.166151 + 0.166151i
\(92\) −7.20675 + 4.64891i −0.751356 + 0.484683i
\(93\) −1.87184 1.07310i −0.194101 0.111276i
\(94\) 15.5018 + 8.44746i 1.59889 + 0.871289i
\(95\) 4.06619 0.417182
\(96\) 1.23443 + 9.71989i 0.125988 + 0.992032i
\(97\) 16.2142 1.64630 0.823151 0.567822i \(-0.192214\pi\)
0.823151 + 0.567822i \(0.192214\pi\)
\(98\) 8.29857 + 4.52216i 0.838282 + 0.456807i
\(99\) 4.23862 16.2141i 0.425997 1.62958i
\(100\) 1.68066 1.08415i 0.168066 0.108415i
\(101\) 10.9221 10.9221i 1.08679 1.08679i 0.0909318 0.995857i \(-0.471015\pi\)
0.995857 0.0909318i \(-0.0289845\pi\)
\(102\) 2.37238 + 3.85814i 0.234901 + 0.382013i
\(103\) 15.8806 1.56476 0.782381 0.622800i \(-0.214005\pi\)
0.782381 + 0.622800i \(0.214005\pi\)
\(104\) 8.52445 + 7.34831i 0.835891 + 0.720561i
\(105\) 0.255406 + 0.941680i 0.0249251 + 0.0918986i
\(106\) −16.7237 + 4.92604i −1.62435 + 0.478460i
\(107\) −0.181436 0.181436i −0.0175401 0.0175401i 0.698282 0.715822i \(-0.253948\pi\)
−0.715822 + 0.698282i \(0.753948\pi\)
\(108\) 5.71317 + 8.68099i 0.549750 + 0.835329i
\(109\) −2.42482 + 2.42482i −0.232256 + 0.232256i −0.813634 0.581378i \(-0.802514\pi\)
0.581378 + 0.813634i \(0.302514\pi\)
\(110\) −6.93711 3.78026i −0.661428 0.360434i
\(111\) −0.355480 + 0.0964147i −0.0337407 + 0.00915128i
\(112\) −0.929040 + 2.05285i −0.0877860 + 0.193976i
\(113\) 12.9498i 1.21822i −0.793087 0.609109i \(-0.791527\pi\)
0.793087 0.609109i \(-0.208473\pi\)
\(114\) 9.68843 + 2.31034i 0.907404 + 0.216383i
\(115\) 3.03211 + 3.03211i 0.282746 + 0.282746i
\(116\) 0.221505 1.02668i 0.0205662 0.0953251i
\(117\) 11.5491 + 3.01912i 1.06772 + 0.279118i
\(118\) −0.924444 3.13845i −0.0851020 0.288918i
\(119\) 1.04160i 0.0954831i
\(120\) 4.62047 1.62827i 0.421789 0.148640i
\(121\) 20.2069i 1.83699i
\(122\) −1.26204 + 0.371740i −0.114260 + 0.0336557i
\(123\) −6.24406 + 10.8917i −0.563008 + 0.982069i
\(124\) −2.09360 + 1.35054i −0.188011 + 0.121282i
\(125\) −0.707107 0.707107i −0.0632456 0.0632456i
\(126\) 0.0735033 + 2.38884i 0.00654819 + 0.212815i
\(127\) 3.31548i 0.294201i 0.989122 + 0.147100i \(0.0469941\pi\)
−0.989122 + 0.147100i \(0.953006\pi\)
\(128\) 10.6238 + 3.89027i 0.939023 + 0.343855i
\(129\) 0.568632 + 2.09654i 0.0500653 + 0.184590i
\(130\) 2.69264 4.94123i 0.236160 0.433374i
\(131\) −9.79209 + 9.79209i −0.855539 + 0.855539i −0.990809 0.135270i \(-0.956810\pi\)
0.135270 + 0.990809i \(0.456810\pi\)
\(132\) −14.3810 12.9487i −1.25171 1.12704i
\(133\) 1.61968 + 1.61968i 0.140444 + 0.140444i
\(134\) −4.64695 15.7762i −0.401435 1.36285i
\(135\) 3.64043 3.70773i 0.313318 0.319111i
\(136\) 5.21554 0.386461i 0.447229 0.0331387i
\(137\) −9.04142 −0.772460 −0.386230 0.922402i \(-0.626223\pi\)
−0.386230 + 0.922402i \(0.626223\pi\)
\(138\) 5.50176 + 8.94735i 0.468341 + 0.761649i
\(139\) −6.47740 + 6.47740i −0.549406 + 0.549406i −0.926269 0.376863i \(-0.877003\pi\)
0.376863 + 0.926269i \(0.377003\pi\)
\(140\) 1.10130 + 0.237604i 0.0930771 + 0.0200812i
\(141\) 10.7537 18.7579i 0.905621 1.57970i
\(142\) −8.59374 + 15.7703i −0.721170 + 1.32341i
\(143\) −22.2283 −1.85883
\(144\) 11.9343 1.25437i 0.994522 0.104531i
\(145\) −0.525153 −0.0436116
\(146\) −6.93677 + 12.7296i −0.574091 + 1.05351i
\(147\) 5.75673 10.0416i 0.474807 0.828219i
\(148\) −0.0896945 + 0.415737i −0.00737284 + 0.0341734i
\(149\) −1.99722 + 1.99722i −0.163618 + 0.163618i −0.784168 0.620549i \(-0.786910\pi\)
0.620549 + 0.784168i \(0.286910\pi\)
\(150\) −1.28304 2.08658i −0.104760 0.170368i
\(151\) −15.3318 −1.24769 −0.623843 0.781550i \(-0.714430\pi\)
−0.623843 + 0.781550i \(0.714430\pi\)
\(152\) 7.50920 8.71108i 0.609076 0.706562i
\(153\) 4.78689 2.80282i 0.386997 0.226595i
\(154\) −1.25746 4.26903i −0.101329 0.344009i
\(155\) 0.880847 + 0.880847i 0.0707513 + 0.0707513i
\(156\) 9.22322 10.2434i 0.738448 0.820132i
\(157\) 0.320523 0.320523i 0.0255805 0.0255805i −0.694201 0.719781i \(-0.744242\pi\)
0.719781 + 0.694201i \(0.244242\pi\)
\(158\) −8.85791 + 16.2550i −0.704697 + 1.29318i
\(159\) 5.58933 + 20.6078i 0.443262 + 1.63430i
\(160\) 0.781130 5.60266i 0.0617537 0.442929i
\(161\) 2.41555i 0.190372i
\(162\) 10.7807 6.76590i 0.847009 0.531579i
\(163\) −11.8288 11.8288i −0.926506 0.926506i 0.0709724 0.997478i \(-0.477390\pi\)
−0.997478 + 0.0709724i \(0.977390\pi\)
\(164\) 7.85836 + 12.1820i 0.613635 + 0.951257i
\(165\) −4.81229 + 8.39420i −0.374636 + 0.653488i
\(166\) 6.35854 1.87294i 0.493518 0.145368i
\(167\) 9.72409i 0.752473i 0.926524 + 0.376236i \(0.122782\pi\)
−0.926524 + 0.376236i \(0.877218\pi\)
\(168\) 2.48905 + 1.19188i 0.192035 + 0.0919554i
\(169\) 2.83300i 0.217923i
\(170\) −0.738851 2.50837i −0.0566673 0.192383i
\(171\) 3.08522 11.8020i 0.235933 0.902519i
\(172\) 2.45193 + 0.528998i 0.186958 + 0.0403357i
\(173\) 1.25519 + 1.25519i 0.0954304 + 0.0954304i 0.753210 0.657780i \(-0.228504\pi\)
−0.657780 + 0.753210i \(0.728504\pi\)
\(174\) −1.25127 0.298384i −0.0948586 0.0226204i
\(175\) 0.563322i 0.0425831i
\(176\) −20.9096 + 7.88037i −1.57612 + 0.594005i
\(177\) −3.86736 + 1.04892i −0.290688 + 0.0788416i
\(178\) 17.5218 + 9.54822i 1.31332 + 0.715669i
\(179\) 7.94161 7.94161i 0.593584 0.593584i −0.345014 0.938598i \(-0.612126\pi\)
0.938598 + 0.345014i \(0.112126\pi\)
\(180\) −1.87152 5.70065i −0.139495 0.424901i
\(181\) −8.15197 8.15197i −0.605931 0.605931i 0.335949 0.941880i \(-0.390943\pi\)
−0.941880 + 0.335949i \(0.890943\pi\)
\(182\) 3.04079 0.895678i 0.225398 0.0663920i
\(183\) 0.421794 + 1.55515i 0.0311799 + 0.114960i
\(184\) 12.0953 0.896235i 0.891677 0.0660714i
\(185\) 0.212652 0.0156345
\(186\) 1.59829 + 2.59926i 0.117193 + 0.190587i
\(187\) −7.30388 + 7.30388i −0.534113 + 0.534113i
\(188\) −13.5338 20.9802i −0.987057 1.53014i
\(189\) 2.92698 0.0268068i 0.212907 0.00194991i
\(190\) −5.04941 2.75159i −0.366323 0.199621i
\(191\) 1.84103 0.133212 0.0666062 0.997779i \(-0.478783\pi\)
0.0666062 + 0.997779i \(0.478783\pi\)
\(192\) 5.04453 12.9055i 0.364057 0.931377i
\(193\) 18.8569 1.35735 0.678674 0.734439i \(-0.262555\pi\)
0.678674 + 0.734439i \(0.262555\pi\)
\(194\) −20.1349 10.9721i −1.44560 0.787754i
\(195\) −5.97910 3.42774i −0.428172 0.245466i
\(196\) −7.24505 11.2313i −0.517503 0.802234i
\(197\) 1.71665 1.71665i 0.122306 0.122306i −0.643304 0.765611i \(-0.722437\pi\)
0.765611 + 0.643304i \(0.222437\pi\)
\(198\) −16.2356 + 17.2664i −1.15381 + 1.22707i
\(199\) −14.1146 −1.00056 −0.500279 0.865864i \(-0.666769\pi\)
−0.500279 + 0.865864i \(0.666769\pi\)
\(200\) −2.82069 + 0.209007i −0.199453 + 0.0147791i
\(201\) −19.4402 + 5.27265i −1.37121 + 0.371904i
\(202\) −20.9541 + 6.17212i −1.47432 + 0.434269i
\(203\) −0.209183 0.209183i −0.0146818 0.0146818i
\(204\) −0.335232 6.39644i −0.0234709 0.447840i
\(205\) 5.12537 5.12537i 0.357972 0.357972i
\(206\) −19.7206 10.7464i −1.37400 0.748737i
\(207\) 11.1012 6.49998i 0.771588 0.451780i
\(208\) −5.61310 14.8937i −0.389198 1.03269i
\(209\) 22.7150i 1.57123i
\(210\) 0.320070 1.34222i 0.0220870 0.0926217i
\(211\) −0.0697389 0.0697389i −0.00480102 0.00480102i 0.704702 0.709503i \(-0.251081\pi\)
−0.709503 + 0.704702i \(0.751081\pi\)
\(212\) 24.1010 + 5.19974i 1.65526 + 0.357120i
\(213\) 19.0827 + 10.9399i 1.30753 + 0.749587i
\(214\) 0.102530 + 0.348086i 0.00700884 + 0.0237947i
\(215\) 1.25417i 0.0855337i
\(216\) −1.22022 14.6462i −0.0830253 0.996547i
\(217\) 0.701733i 0.0476367i
\(218\) 4.65203 1.37028i 0.315075 0.0928069i
\(219\) 15.4033 + 8.83054i 1.04086 + 0.596712i
\(220\) 6.05643 + 9.38868i 0.408325 + 0.632985i
\(221\) −5.20248 5.20248i −0.349956 0.349956i
\(222\) 0.506681 + 0.120825i 0.0340062 + 0.00810926i
\(223\) 25.8137i 1.72862i −0.502963 0.864308i \(-0.667757\pi\)
0.502963 0.864308i \(-0.332243\pi\)
\(224\) 2.54285 1.92055i 0.169901 0.128322i
\(225\) −2.58887 + 1.51583i −0.172591 + 0.101056i
\(226\) −8.76315 + 16.0811i −0.582916 + 1.06970i
\(227\) −5.95912 + 5.95912i −0.395521 + 0.395521i −0.876650 0.481129i \(-0.840227\pi\)
0.481129 + 0.876650i \(0.340227\pi\)
\(228\) −10.4677 9.42515i −0.693242 0.624196i
\(229\) −6.68020 6.68020i −0.441440 0.441440i 0.451056 0.892496i \(-0.351048\pi\)
−0.892496 + 0.451056i \(0.851048\pi\)
\(230\) −1.71346 5.81712i −0.112982 0.383569i
\(231\) −5.26052 + 1.42678i −0.346117 + 0.0938752i
\(232\) −0.969821 + 1.12505i −0.0636719 + 0.0738629i
\(233\) 27.1041 1.77565 0.887824 0.460183i \(-0.152216\pi\)
0.887824 + 0.460183i \(0.152216\pi\)
\(234\) −12.2987 11.5644i −0.803991 0.755991i
\(235\) −8.82704 + 8.82704i −0.575812 + 0.575812i
\(236\) −0.975808 + 4.52291i −0.0635197 + 0.294416i
\(237\) 19.6693 + 11.2762i 1.27766 + 0.732465i
\(238\) 0.704849 1.29346i 0.0456886 0.0838425i
\(239\) 11.6534 0.753798 0.376899 0.926254i \(-0.376990\pi\)
0.376899 + 0.926254i \(0.376990\pi\)
\(240\) −6.83957 1.10468i −0.441492 0.0713065i
\(241\) 5.37109 0.345982 0.172991 0.984923i \(-0.444657\pi\)
0.172991 + 0.984923i \(0.444657\pi\)
\(242\) 13.6740 25.0930i 0.879000 1.61304i
\(243\) −7.99937 13.3795i −0.513160 0.858293i
\(244\) 1.81876 + 0.392394i 0.116434 + 0.0251205i
\(245\) −4.72536 + 4.72536i −0.301892 + 0.301892i
\(246\) 15.1243 9.29997i 0.964289 0.592945i
\(247\) −16.1796 −1.02949
\(248\) 3.51375 0.260362i 0.223124 0.0165330i
\(249\) −2.12512 7.83532i −0.134674 0.496543i
\(250\) 0.399589 + 1.35659i 0.0252722 + 0.0857981i
\(251\) 0.545120 + 0.545120i 0.0344077 + 0.0344077i 0.724101 0.689694i \(-0.242255\pi\)
−0.689694 + 0.724101i \(0.742255\pi\)
\(252\) 1.52525 3.01621i 0.0960818 0.190003i
\(253\) −16.9383 + 16.9383i −1.06490 + 1.06490i
\(254\) 2.24358 4.11717i 0.140775 0.258334i
\(255\) −3.09094 + 0.838336i −0.193562 + 0.0524986i
\(256\) −10.5602 12.0201i −0.660010 0.751256i
\(257\) 9.93444i 0.619693i −0.950787 0.309847i \(-0.899722\pi\)
0.950787 0.309847i \(-0.100278\pi\)
\(258\) 0.712600 2.98829i 0.0443645 0.186043i
\(259\) 0.0847052 + 0.0847052i 0.00526332 + 0.00526332i
\(260\) −6.68745 + 4.31393i −0.414738 + 0.267538i
\(261\) −0.398460 + 1.52424i −0.0246640 + 0.0943479i
\(262\) 18.7862 5.53355i 1.16061 0.341864i
\(263\) 4.61484i 0.284563i 0.989826 + 0.142282i \(0.0454439\pi\)
−0.989826 + 0.142282i \(0.954556\pi\)
\(264\) 9.09604 + 25.8114i 0.559823 + 1.58858i
\(265\) 12.3278i 0.757289i
\(266\) −0.915287 3.10736i −0.0561199 0.190524i
\(267\) 12.1549 21.2022i 0.743870 1.29755i
\(268\) −4.90514 + 22.7355i −0.299629 + 1.38879i
\(269\) 3.61458 + 3.61458i 0.220385 + 0.220385i 0.808660 0.588276i \(-0.200193\pi\)
−0.588276 + 0.808660i \(0.700193\pi\)
\(270\) −7.02972 + 2.14079i −0.427815 + 0.130285i
\(271\) 4.40776i 0.267752i −0.990998 0.133876i \(-0.957258\pi\)
0.990998 0.133876i \(-0.0427425\pi\)
\(272\) −6.73820 3.04945i −0.408563 0.184900i
\(273\) −1.01628 3.74701i −0.0615080 0.226779i
\(274\) 11.2277 + 6.11833i 0.678288 + 0.369622i
\(275\) 3.95012 3.95012i 0.238201 0.238201i
\(276\) −0.777432 14.8339i −0.0467959 0.892896i
\(277\) −7.48938 7.48938i −0.449993 0.449993i 0.445359 0.895352i \(-0.353076\pi\)
−0.895352 + 0.445359i \(0.853076\pi\)
\(278\) 12.4269 3.66041i 0.745317 0.219537i
\(279\) 3.22497 1.88828i 0.193074 0.113049i
\(280\) −1.20682 1.04031i −0.0721211 0.0621704i
\(281\) 22.1310 1.32023 0.660113 0.751166i \(-0.270508\pi\)
0.660113 + 0.751166i \(0.270508\pi\)
\(282\) −26.0474 + 16.0166i −1.55110 + 0.953776i
\(283\) −13.2776 + 13.2776i −0.789273 + 0.789273i −0.981375 0.192102i \(-0.938470\pi\)
0.192102 + 0.981375i \(0.438470\pi\)
\(284\) 21.3435 13.7682i 1.26650 0.816992i
\(285\) −3.50279 + 6.11000i −0.207487 + 0.361925i
\(286\) 27.6033 + 15.0419i 1.63221 + 0.889447i
\(287\) 4.08317 0.241022
\(288\) −15.6688 6.51822i −0.923296 0.384090i
\(289\) 13.5811 0.798888
\(290\) 0.652137 + 0.355371i 0.0382948 + 0.0208681i
\(291\) −13.9676 + 24.3640i −0.818795 + 1.42825i
\(292\) 17.2282 11.1135i 1.00820 0.650370i
\(293\) −16.1594 + 16.1594i −0.944044 + 0.944044i −0.998515 0.0544714i \(-0.982653\pi\)
0.0544714 + 0.998515i \(0.482653\pi\)
\(294\) −13.9439 + 8.57415i −0.813225 + 0.500055i
\(295\) 2.31349 0.134696
\(296\) 0.392712 0.455568i 0.0228259 0.0264794i
\(297\) 20.7126 + 20.3366i 1.20186 + 1.18005i
\(298\) 3.83167 1.12864i 0.221962 0.0653801i
\(299\) −12.0650 12.0650i −0.697736 0.697736i
\(300\) 0.181302 + 3.45935i 0.0104675 + 0.199726i
\(301\) 0.499572 0.499572i 0.0287948 0.0287948i
\(302\) 19.0391 + 10.3750i 1.09558 + 0.597017i
\(303\) 7.00319 + 25.8207i 0.402323 + 1.48336i
\(304\) −15.2197 + 5.73599i −0.872912 + 0.328982i
\(305\) 0.930305i 0.0532691i
\(306\) −7.84105 + 0.241265i −0.448243 + 0.0137922i
\(307\) 14.4031 + 14.4031i 0.822030 + 0.822030i 0.986399 0.164369i \(-0.0525588\pi\)
−0.164369 + 0.986399i \(0.552559\pi\)
\(308\) −1.32733 + 6.15223i −0.0756317 + 0.350556i
\(309\) −13.6802 + 23.8628i −0.778241 + 1.35751i
\(310\) −0.497770 1.68991i −0.0282715 0.0959803i
\(311\) 10.8212i 0.613613i 0.951772 + 0.306806i \(0.0992604\pi\)
−0.951772 + 0.306806i \(0.900740\pi\)
\(312\) −18.3852 + 6.47901i −1.04086 + 0.366802i
\(313\) 12.5581i 0.709825i −0.934900 0.354912i \(-0.884511\pi\)
0.934900 0.354912i \(-0.115489\pi\)
\(314\) −0.614925 + 0.181129i −0.0347022 + 0.0102217i
\(315\) −1.63502 0.427421i −0.0921230 0.0240824i
\(316\) 21.9996 14.1914i 1.23757 0.798331i
\(317\) 0.917933 + 0.917933i 0.0515563 + 0.0515563i 0.732415 0.680859i \(-0.238393\pi\)
−0.680859 + 0.732415i \(0.738393\pi\)
\(318\) 7.00445 29.3731i 0.392790 1.64716i
\(319\) 2.93367i 0.164254i
\(320\) −4.76133 + 6.42882i −0.266167 + 0.359382i
\(321\) 0.428930 0.116336i 0.0239405 0.00649324i
\(322\) 1.63460 2.99964i 0.0910930 0.167164i
\(323\) −5.31638 + 5.31638i −0.295811 + 0.295811i
\(324\) −17.9659 + 1.10665i −0.998108 + 0.0614807i
\(325\) 2.81363 + 2.81363i 0.156072 + 0.156072i
\(326\) 6.68453 + 22.6937i 0.370222 + 1.25689i
\(327\) −1.55478 5.73247i −0.0859797 0.317006i
\(328\) −1.51496 20.4454i −0.0836499 1.12891i
\(329\) −7.03212 −0.387693
\(330\) 11.6563 7.16748i 0.641657 0.394557i
\(331\) 17.2545 17.2545i 0.948393 0.948393i −0.0503389 0.998732i \(-0.516030\pi\)
0.998732 + 0.0503389i \(0.0160302\pi\)
\(332\) −9.16347 1.97700i −0.502911 0.108502i
\(333\) 0.161349 0.617214i 0.00884190 0.0338231i
\(334\) 6.58029 12.0754i 0.360057 0.660737i
\(335\) 11.6293 0.635378
\(336\) −2.28437 3.16442i −0.124623 0.172633i
\(337\) −15.5726 −0.848293 −0.424146 0.905594i \(-0.639426\pi\)
−0.424146 + 0.905594i \(0.639426\pi\)
\(338\) −1.91709 + 3.51803i −0.104276 + 0.191356i
\(339\) 19.4589 + 11.1555i 1.05686 + 0.605885i
\(340\) −0.779903 + 3.61488i −0.0422962 + 0.196044i
\(341\) −4.92069 + 4.92069i −0.266470 + 0.266470i
\(342\) −11.8176 + 12.5680i −0.639024 + 0.679597i
\(343\) −7.70774 −0.416179
\(344\) −2.68684 2.31613i −0.144865 0.124877i
\(345\) −7.16815 + 1.94417i −0.385920 + 0.104671i
\(346\) −0.709313 2.40809i −0.0381329 0.129460i
\(347\) 2.06101 + 2.06101i 0.110641 + 0.110641i 0.760260 0.649619i \(-0.225072\pi\)
−0.649619 + 0.760260i \(0.725072\pi\)
\(348\) 1.35192 + 1.21727i 0.0724704 + 0.0652525i
\(349\) −11.9252 + 11.9252i −0.638341 + 0.638341i −0.950146 0.311805i \(-0.899066\pi\)
0.311805 + 0.950146i \(0.399066\pi\)
\(350\) −0.381200 + 0.699535i −0.0203760 + 0.0373917i
\(351\) −14.4855 + 14.7533i −0.773181 + 0.787474i
\(352\) 31.2982 + 4.36364i 1.66820 + 0.232583i
\(353\) 3.31846i 0.176624i 0.996093 + 0.0883118i \(0.0281472\pi\)
−0.996093 + 0.0883118i \(0.971853\pi\)
\(354\) 5.51230 + 1.31449i 0.292976 + 0.0698642i
\(355\) −8.97989 8.97989i −0.476603 0.476603i
\(356\) −15.2974 23.7140i −0.810761 1.25684i
\(357\) −1.56514 0.897276i −0.0828361 0.0474889i
\(358\) −15.2360 + 4.48784i −0.805248 + 0.237190i
\(359\) 13.4809i 0.711495i −0.934582 0.355747i \(-0.884226\pi\)
0.934582 0.355747i \(-0.115774\pi\)
\(360\) −1.53357 + 8.34555i −0.0808260 + 0.439849i
\(361\) 2.46612i 0.129796i
\(362\) 4.60671 + 15.6396i 0.242124 + 0.821999i
\(363\) −30.3637 17.4071i −1.59368 0.913636i
\(364\) −4.38216 0.945443i −0.229688 0.0495547i
\(365\) −7.24846 7.24846i −0.379402 0.379402i
\(366\) 0.528585 2.21662i 0.0276296 0.115865i
\(367\) 0.873241i 0.0455828i 0.999740 + 0.0227914i \(0.00725536\pi\)
−0.999740 + 0.0227914i \(0.992745\pi\)
\(368\) −15.6265 7.07193i −0.814586 0.368650i
\(369\) −10.9873 18.7651i −0.571978 0.976872i
\(370\) −0.264072 0.143901i −0.0137284 0.00748107i
\(371\) 4.91050 4.91050i 0.254941 0.254941i
\(372\) −0.225849 4.30934i −0.0117097 0.223429i
\(373\) 24.0709 + 24.0709i 1.24635 + 1.24635i 0.957322 + 0.289023i \(0.0933305\pi\)
0.289023 + 0.957322i \(0.406670\pi\)
\(374\) 14.0125 4.12746i 0.724571 0.213426i
\(375\) 1.67166 0.453393i 0.0863240 0.0234131i
\(376\) 2.60911 + 35.2116i 0.134554 + 1.81590i
\(377\) 2.08962 0.107621
\(378\) −3.65288 1.94740i −0.187884 0.100163i
\(379\) 19.8062 19.8062i 1.01738 1.01738i 0.0175304 0.999846i \(-0.494420\pi\)
0.999846 0.0175304i \(-0.00558039\pi\)
\(380\) 4.40838 + 6.83387i 0.226145 + 0.350570i
\(381\) −4.98196 2.85609i −0.255233 0.146322i
\(382\) −2.28620 1.24583i −0.116972 0.0637420i
\(383\) 12.6693 0.647369 0.323684 0.946165i \(-0.395078\pi\)
0.323684 + 0.946165i \(0.395078\pi\)
\(384\) −14.9975 + 12.6125i −0.765337 + 0.643629i
\(385\) 3.14689 0.160381
\(386\) −23.4166 12.7605i −1.19187 0.649490i
\(387\) −3.64018 0.951602i −0.185041 0.0483727i
\(388\) 17.5787 + 27.2505i 0.892423 + 1.38343i
\(389\) −1.23680 + 1.23680i −0.0627081 + 0.0627081i −0.737765 0.675057i \(-0.764119\pi\)
0.675057 + 0.737765i \(0.264119\pi\)
\(390\) 5.10532 + 8.30263i 0.258518 + 0.420420i
\(391\) −7.92873 −0.400973
\(392\) 1.39673 + 18.8498i 0.0705454 + 0.952057i
\(393\) −6.27863 23.1493i −0.316715 1.16773i
\(394\) −3.29340 + 0.970086i −0.165919 + 0.0488722i
\(395\) −9.25593 9.25593i −0.465716 0.465716i
\(396\) 31.8456 10.4549i 1.60030 0.525379i
\(397\) 5.66025 5.66025i 0.284080 0.284080i −0.550654 0.834734i \(-0.685622\pi\)
0.834734 + 0.550654i \(0.185622\pi\)
\(398\) 17.5276 + 9.55135i 0.878578 + 0.478766i
\(399\) −3.82905 + 1.03853i −0.191692 + 0.0519915i
\(400\) 3.64418 + 1.64922i 0.182209 + 0.0824608i
\(401\) 30.0565i 1.50095i −0.660898 0.750476i \(-0.729824\pi\)
0.660898 0.750476i \(-0.270176\pi\)
\(402\) 27.7090 + 6.60760i 1.38200 + 0.329557i
\(403\) −3.50495 3.50495i −0.174594 0.174594i
\(404\) 30.1975 + 6.51505i 1.50238 + 0.324136i
\(405\) 2.43535 + 8.66424i 0.121013 + 0.430530i
\(406\) 0.118210 + 0.401319i 0.00586668 + 0.0199171i
\(407\) 1.18794i 0.0588839i
\(408\) −3.91218 + 8.16998i −0.193682 + 0.404474i
\(409\) 29.4758i 1.45748i 0.684788 + 0.728742i \(0.259895\pi\)
−0.684788 + 0.728742i \(0.740105\pi\)
\(410\) −9.83305 + 2.89637i −0.485620 + 0.143042i
\(411\) 7.78866 13.5860i 0.384186 0.670146i
\(412\) 17.2170 + 26.6899i 0.848222 + 1.31491i
\(413\) 0.921528 + 0.921528i 0.0453454 + 0.0453454i
\(414\) −18.1841 + 0.559514i −0.893698 + 0.0274986i
\(415\) 4.68716i 0.230084i
\(416\) −3.10817 + 22.2934i −0.152391 + 1.09302i
\(417\) −4.15328 15.3131i −0.203387 0.749885i
\(418\) 15.3712 28.2076i 0.751832 1.37968i
\(419\) 3.58840 3.58840i 0.175305 0.175305i −0.614001 0.789306i \(-0.710441\pi\)
0.789306 + 0.614001i \(0.210441\pi\)
\(420\) −1.30574 + 1.45018i −0.0637137 + 0.0707614i
\(421\) −26.8679 26.8679i −1.30946 1.30946i −0.921802 0.387661i \(-0.873283\pi\)
−0.387661 0.921802i \(-0.626717\pi\)
\(422\) 0.0394097 + 0.133794i 0.00191844 + 0.00651301i
\(423\) 18.9226 + 32.3177i 0.920050 + 1.57134i
\(424\) −26.4101 22.7662i −1.28259 1.10562i
\(425\) 1.84903 0.0896910
\(426\) −16.2940 26.4984i −0.789446 1.28385i
\(427\) 0.370567 0.370567i 0.0179330 0.0179330i
\(428\) 0.108227 0.501638i 0.00523136 0.0242476i
\(429\) 19.1484 33.4011i 0.924495 1.61262i
\(430\) −0.848697 + 1.55743i −0.0409278 + 0.0751061i
\(431\) 5.50470 0.265152 0.132576 0.991173i \(-0.457675\pi\)
0.132576 + 0.991173i \(0.457675\pi\)
\(432\) −8.39581 + 19.0134i −0.403943 + 0.914784i
\(433\) −12.0995 −0.581463 −0.290731 0.956805i \(-0.593899\pi\)
−0.290731 + 0.956805i \(0.593899\pi\)
\(434\) 0.474862 0.871415i 0.0227941 0.0418292i
\(435\) 0.452389 0.789114i 0.0216904 0.0378351i
\(436\) −6.70418 1.44641i −0.321072 0.0692706i
\(437\) −12.3291 + 12.3291i −0.589783 + 0.589783i
\(438\) −13.1523 21.3892i −0.628442 1.02202i
\(439\) 31.4223 1.49970 0.749852 0.661606i \(-0.230125\pi\)
0.749852 + 0.661606i \(0.230125\pi\)
\(440\) −1.16758 15.7573i −0.0556623 0.751199i
\(441\) 10.1298 + 17.3006i 0.482372 + 0.823836i
\(442\) 2.93994 + 9.98097i 0.139839 + 0.474746i
\(443\) −3.58925 3.58925i −0.170530 0.170530i 0.616682 0.787212i \(-0.288476\pi\)
−0.787212 + 0.616682i \(0.788476\pi\)
\(444\) −0.547436 0.492912i −0.0259802 0.0233926i
\(445\) −9.97726 + 9.97726i −0.472968 + 0.472968i
\(446\) −17.4681 + 32.0556i −0.827141 + 1.51788i
\(447\) −1.28060 4.72158i −0.0605705 0.223323i
\(448\) −4.45736 + 0.664208i −0.210590 + 0.0313809i
\(449\) 22.3166i 1.05318i −0.850118 0.526592i \(-0.823470\pi\)
0.850118 0.526592i \(-0.176530\pi\)
\(450\) 4.24063 0.130482i 0.199905 0.00615098i
\(451\) 28.6320 + 28.6320i 1.34823 + 1.34823i
\(452\) 21.7642 14.0396i 1.02370 0.660368i
\(453\) 13.2075 23.0382i 0.620542 1.08243i
\(454\) 11.4326 3.36753i 0.536559 0.158046i
\(455\) 2.24150i 0.105083i
\(456\) 6.62086 + 18.7877i 0.310050 + 0.879814i
\(457\) 22.4547i 1.05039i −0.850983 0.525193i \(-0.823993\pi\)
0.850983 0.525193i \(-0.176007\pi\)
\(458\) 3.77501 + 12.8160i 0.176395 + 0.598852i
\(459\) 0.0879896 + 9.60743i 0.00410700 + 0.448436i
\(460\) −1.80866 + 8.38322i −0.0843293 + 0.390870i
\(461\) 21.1543 + 21.1543i 0.985252 + 0.985252i 0.999893 0.0146408i \(-0.00466046\pi\)
−0.0146408 + 0.999893i \(0.504660\pi\)
\(462\) 7.49804 + 1.78801i 0.348840 + 0.0831860i
\(463\) 2.14084i 0.0994931i −0.998762 0.0497466i \(-0.984159\pi\)
0.998762 0.0497466i \(-0.0158414\pi\)
\(464\) 1.96565 0.740810i 0.0912529 0.0343912i
\(465\) −2.08239 + 0.564794i −0.0965686 + 0.0261917i
\(466\) −33.6580 18.3413i −1.55918 0.849646i
\(467\) −6.25077 + 6.25077i −0.289251 + 0.289251i −0.836784 0.547533i \(-0.815567\pi\)
0.547533 + 0.836784i \(0.315567\pi\)
\(468\) 7.44691 + 22.6833i 0.344234 + 1.04854i
\(469\) 4.63229 + 4.63229i 0.213899 + 0.213899i
\(470\) 16.9347 4.98820i 0.781140 0.230088i
\(471\) 0.205518 + 0.757742i 0.00946976 + 0.0349149i
\(472\) 4.27241 4.95624i 0.196654 0.228129i
\(473\) 7.00619 0.322145
\(474\) −16.7948 27.3130i −0.771413 1.25453i
\(475\) 2.87523 2.87523i 0.131925 0.131925i
\(476\) −1.75057 + 1.12925i −0.0802372 + 0.0517592i
\(477\) −35.7809 9.35370i −1.63830 0.428277i
\(478\) −14.4713 7.88587i −0.661901 0.360691i
\(479\) 30.9971 1.41629 0.708147 0.706065i \(-0.249531\pi\)
0.708147 + 0.706065i \(0.249531\pi\)
\(480\) 7.74587 + 6.00013i 0.353549 + 0.273867i
\(481\) −0.846156 −0.0385814
\(482\) −6.66984 3.63461i −0.303803 0.165552i
\(483\) −3.62970 2.08086i −0.165157 0.0946824i
\(484\) −33.9609 + 21.9074i −1.54368 + 0.995793i
\(485\) 11.4652 11.4652i 0.520606 0.520606i
\(486\) 0.879775 + 22.0278i 0.0399074 + 0.999203i
\(487\) −23.8317 −1.07992 −0.539959 0.841691i \(-0.681560\pi\)
−0.539959 + 0.841691i \(0.681560\pi\)
\(488\) −1.99301 1.71803i −0.0902195 0.0777717i
\(489\) 27.9643 7.58458i 1.26459 0.342987i
\(490\) 9.06562 2.67032i 0.409543 0.120633i
\(491\) 10.5656 + 10.5656i 0.476819 + 0.476819i 0.904113 0.427294i \(-0.140533\pi\)
−0.427294 + 0.904113i \(0.640533\pi\)
\(492\) −25.0747 + 1.31414i −1.13045 + 0.0592461i
\(493\) 0.686616 0.686616i 0.0309236 0.0309236i
\(494\) 20.0919 + 10.9488i 0.903980 + 0.492608i
\(495\) −8.46793 14.4622i −0.380605 0.650030i
\(496\) −4.53958 2.05444i −0.203833 0.0922470i
\(497\) 7.15389i 0.320896i
\(498\) −2.66317 + 11.1680i −0.119339 + 0.500450i
\(499\) 5.65208 + 5.65208i 0.253022 + 0.253022i 0.822208 0.569187i \(-0.192742\pi\)
−0.569187 + 0.822208i \(0.692742\pi\)
\(500\) 0.421791 1.95502i 0.0188631 0.0874310i
\(501\) −14.6118 8.37674i −0.652806 0.374245i
\(502\) −0.308050 1.04582i −0.0137489 0.0466770i
\(503\) 2.22054i 0.0990088i 0.998774 + 0.0495044i \(0.0157642\pi\)
−0.998774 + 0.0495044i \(0.984236\pi\)
\(504\) −3.93513 + 2.71341i −0.175285 + 0.120865i
\(505\) 15.4462i 0.687346i
\(506\) 32.4963 9.57193i 1.44464 0.425524i
\(507\) 4.25697 + 2.44047i 0.189059 + 0.108385i
\(508\) −5.57218 + 3.59449i −0.247225 + 0.159480i
\(509\) −14.6006 14.6006i −0.647161 0.647161i 0.305145 0.952306i \(-0.401295\pi\)
−0.952306 + 0.305145i \(0.901295\pi\)
\(510\) 4.40564 + 1.05059i 0.195085 + 0.0465208i
\(511\) 5.77454i 0.255451i
\(512\) 4.97966 + 22.0727i 0.220072 + 0.975484i
\(513\) 15.0763 + 14.8027i 0.665636 + 0.653554i
\(514\) −6.72263 + 12.3366i −0.296523 + 0.544145i
\(515\) 11.2293 11.2293i 0.494821 0.494821i
\(516\) −2.90708 + 3.22865i −0.127977 + 0.142133i
\(517\) −49.3106 49.3106i −2.16868 2.16868i
\(518\) −0.0478673 0.162507i −0.00210317 0.00714016i
\(519\) −2.96737 + 0.804821i −0.130253 + 0.0353277i
\(520\) 11.2237 0.831656i 0.492194 0.0364705i
\(521\) −17.9574 −0.786728 −0.393364 0.919383i \(-0.628689\pi\)
−0.393364 + 0.919383i \(0.628689\pi\)
\(522\) 1.52626 1.62317i 0.0668026 0.0710441i
\(523\) −15.8724 + 15.8724i −0.694051 + 0.694051i −0.963121 0.269070i \(-0.913284\pi\)
0.269070 + 0.963121i \(0.413284\pi\)
\(524\) −27.0733 5.84100i −1.18270 0.255165i
\(525\) 0.846468 + 0.485269i 0.0369429 + 0.0211789i
\(526\) 3.12286 5.73073i 0.136163 0.249872i
\(527\) −2.30334 −0.100335
\(528\) 6.17107 38.2080i 0.268561 1.66279i
\(529\) 4.61259 0.200547
\(530\) −8.34220 + 15.3087i −0.362362 + 0.664966i
\(531\) 1.75536 6.71481i 0.0761761 0.291398i
\(532\) −0.966142 + 4.47811i −0.0418876 + 0.194151i
\(533\) −20.3942 + 20.3942i −0.883372 + 0.883372i
\(534\) −29.4415 + 18.1037i −1.27406 + 0.783424i
\(535\) −0.256590 −0.0110933
\(536\) 21.4763 24.9138i 0.927637 1.07611i
\(537\) 5.09211 + 18.7746i 0.219741 + 0.810183i
\(538\) −2.04261 6.93458i −0.0880633 0.298971i
\(539\) −26.3974 26.3974i −1.13701 1.13701i
\(540\) 10.1782 + 2.09856i 0.438001 + 0.0903078i
\(541\) −4.11204 + 4.11204i −0.176791 + 0.176791i −0.789955 0.613165i \(-0.789896\pi\)
0.613165 + 0.789955i \(0.289896\pi\)
\(542\) −2.98273 + 5.47358i −0.128119 + 0.235110i
\(543\) 19.2719 5.22700i 0.827037 0.224312i
\(544\) 6.30396 + 8.34655i 0.270280 + 0.357856i
\(545\) 3.42922i 0.146892i
\(546\) −1.27358 + 5.34077i −0.0545043 + 0.228564i
\(547\) −14.7651 14.7651i −0.631309 0.631309i 0.317087 0.948396i \(-0.397295\pi\)
−0.948396 + 0.317087i \(0.897295\pi\)
\(548\) −9.80230 15.1955i −0.418733 0.649121i
\(549\) −2.70018 0.705870i −0.115241 0.0301258i
\(550\) −7.57832 + 2.23223i −0.323141 + 0.0951826i
\(551\) 2.13537i 0.0909698i
\(552\) −9.07268 + 18.9469i −0.386159 + 0.806433i
\(553\) 7.37380i 0.313566i
\(554\) 4.23228 + 14.3684i 0.179812 + 0.610455i
\(555\) −0.183187 + 0.319538i −0.00777586 + 0.0135636i
\(556\) −17.9088 3.86379i −0.759502 0.163861i
\(557\) −14.6624 14.6624i −0.621264 0.621264i 0.324591 0.945855i \(-0.394773\pi\)
−0.945855 + 0.324591i \(0.894773\pi\)
\(558\) −5.28258 + 0.162542i −0.223629 + 0.00688095i
\(559\) 4.99043i 0.211073i
\(560\) 0.794653 + 2.10851i 0.0335802 + 0.0891009i
\(561\) −4.68321 17.2670i −0.197725 0.729012i
\(562\) −27.4824 14.9761i −1.15928 0.631727i
\(563\) −2.01094 + 2.01094i −0.0847511 + 0.0847511i −0.748211 0.663460i \(-0.769087\pi\)
0.663460 + 0.748211i \(0.269087\pi\)
\(564\) 43.1842 2.26325i 1.81838 0.0952999i
\(565\) −9.15691 9.15691i −0.385234 0.385234i
\(566\) 25.4732 7.50324i 1.07072 0.315385i
\(567\) −2.48115 + 4.42128i −0.104198 + 0.185676i
\(568\) −35.8213 + 2.65429i −1.50303 + 0.111371i
\(569\) −30.4097 −1.27484 −0.637420 0.770516i \(-0.719998\pi\)
−0.637420 + 0.770516i \(0.719998\pi\)
\(570\) 8.48441 5.21709i 0.355373 0.218520i
\(571\) −6.43255 + 6.43255i −0.269194 + 0.269194i −0.828775 0.559581i \(-0.810962\pi\)
0.559581 + 0.828775i \(0.310962\pi\)
\(572\) −24.0990 37.3582i −1.00763 1.56203i
\(573\) −1.58594 + 2.76640i −0.0662537 + 0.115568i
\(574\) −5.07049 2.76308i −0.211638 0.115329i
\(575\) 4.28805 0.178824
\(576\) 15.0468 + 18.6975i 0.626948 + 0.779061i
\(577\) 4.57889 0.190622 0.0953108 0.995448i \(-0.469616\pi\)
0.0953108 + 0.995448i \(0.469616\pi\)
\(578\) −16.8651 9.19033i −0.701494 0.382267i
\(579\) −16.2441 + 28.3351i −0.675083 + 1.17756i
\(580\) −0.569347 0.882602i −0.0236408 0.0366480i
\(581\) −1.86703 + 1.86703i −0.0774574 + 0.0774574i
\(582\) 33.8322 20.8035i 1.40239 0.862333i
\(583\) 68.8668 2.85217
\(584\) −28.9146 + 2.14251i −1.19649 + 0.0886577i
\(585\) 10.3013 6.03161i 0.425906 0.249376i
\(586\) 31.0019 9.13176i 1.28068 0.377230i
\(587\) −7.23894 7.23894i −0.298783 0.298783i 0.541754 0.840537i \(-0.317760\pi\)
−0.840537 + 0.541754i \(0.817760\pi\)
\(588\) 23.1177 1.21158i 0.953359 0.0499647i
\(589\) −3.58169 + 3.58169i −0.147581 + 0.147581i
\(590\) −2.87290 1.56554i −0.118275 0.0644521i
\(591\) 1.10071 + 4.05830i 0.0452770 + 0.166936i
\(592\) −0.795955 + 0.299978i −0.0327135 + 0.0123290i
\(593\) 16.5711i 0.680494i −0.940336 0.340247i \(-0.889489\pi\)
0.940336 0.340247i \(-0.110511\pi\)
\(594\) −11.9592 39.2703i −0.490690 1.61128i
\(595\) 0.736521 + 0.736521i 0.0301944 + 0.0301944i
\(596\) −5.52193 1.19134i −0.226187 0.0487994i
\(597\) 12.1589 21.2091i 0.497631 0.868032i
\(598\) 6.81798 + 23.1467i 0.278808 + 0.946540i
\(599\) 43.9020i 1.79379i 0.442248 + 0.896893i \(0.354181\pi\)
−0.442248 + 0.896893i \(0.645819\pi\)
\(600\) 2.11580 4.41853i 0.0863773 0.180386i
\(601\) 44.3616i 1.80955i 0.425891 + 0.904775i \(0.359961\pi\)
−0.425891 + 0.904775i \(0.640039\pi\)
\(602\) −0.958431 + 0.282310i −0.0390627 + 0.0115061i
\(603\) 8.82375 33.7537i 0.359331 1.37456i
\(604\) −16.6221 25.7675i −0.676343 1.04847i
\(605\) 14.2885 + 14.2885i 0.580908 + 0.580908i
\(606\) 8.77627 36.8033i 0.356512 1.49503i
\(607\) 23.3252i 0.946742i 0.880863 + 0.473371i \(0.156963\pi\)
−0.880863 + 0.473371i \(0.843037\pi\)
\(608\) 22.7815 + 3.17622i 0.923911 + 0.128813i
\(609\) 0.494526 0.134127i 0.0200392 0.00543511i
\(610\) −0.629537 + 1.15526i −0.0254892 + 0.0467750i
\(611\) 35.1234 35.1234i 1.42094 1.42094i
\(612\) 9.90031 + 5.00643i 0.400196 + 0.202373i
\(613\) 13.5475 + 13.5475i 0.547179 + 0.547179i 0.925624 0.378445i \(-0.123541\pi\)
−0.378445 + 0.925624i \(0.623541\pi\)
\(614\) −8.13927 27.6324i −0.328474 1.11515i
\(615\) 3.28636 + 12.1168i 0.132519 + 0.488596i
\(616\) 5.81150 6.74166i 0.234152 0.271629i
\(617\) −11.2760 −0.453955 −0.226977 0.973900i \(-0.572884\pi\)
−0.226977 + 0.973900i \(0.572884\pi\)
\(618\) 33.1361 20.3755i 1.33293 0.819623i
\(619\) 9.25371 9.25371i 0.371938 0.371938i −0.496245 0.868183i \(-0.665288\pi\)
0.868183 + 0.496245i \(0.165288\pi\)
\(620\) −0.525427 + 2.43538i −0.0211017 + 0.0978070i
\(621\) 0.204056 + 22.2804i 0.00818847 + 0.894084i
\(622\) 7.32269 13.4378i 0.293613 0.538806i
\(623\) −7.94846 −0.318448
\(624\) 27.2151 + 4.39558i 1.08948 + 0.175964i
\(625\) −1.00000 −0.0400000
\(626\) −8.49805 + 15.5947i −0.339650 + 0.623288i
\(627\) −34.1324 19.5677i −1.36312 0.781457i
\(628\) 0.886187 + 0.191193i 0.0353627 + 0.00762943i
\(629\) −0.278033 + 0.278033i −0.0110859 + 0.0110859i
\(630\) 1.74114 + 1.63719i 0.0693687 + 0.0652272i
\(631\) −14.7105 −0.585616 −0.292808 0.956171i \(-0.594590\pi\)
−0.292808 + 0.956171i \(0.594590\pi\)
\(632\) −36.9225 + 2.73588i −1.46870 + 0.108827i
\(633\) 0.164868 0.0447162i 0.00655292 0.00177731i
\(634\) −0.518728 1.76106i −0.0206013 0.0699406i
\(635\) 2.34440 + 2.34440i 0.0930345 + 0.0930345i
\(636\) −28.5749 + 31.7358i −1.13307 + 1.25841i
\(637\) 18.8025 18.8025i 0.744984 0.744984i
\(638\) −1.98521 + 3.64304i −0.0785954 + 0.144229i
\(639\) −32.8773 + 19.2503i −1.30061 + 0.761530i
\(640\) 10.2630 4.76134i 0.405682 0.188209i
\(641\) 3.29813i 0.130268i 0.997877 + 0.0651342i \(0.0207475\pi\)
−0.997877 + 0.0651342i \(0.979252\pi\)
\(642\) −0.611372 0.145790i −0.0241289 0.00575388i
\(643\) −2.22462 2.22462i −0.0877303 0.0877303i 0.661880 0.749610i \(-0.269759\pi\)
−0.749610 + 0.661880i \(0.769759\pi\)
\(644\) −4.05972 + 2.61883i −0.159975 + 0.103197i
\(645\) 1.88456 + 1.08040i 0.0742046 + 0.0425405i
\(646\) 10.1995 3.00431i 0.401294 0.118203i
\(647\) 35.7052i 1.40372i −0.712316 0.701858i \(-0.752354\pi\)
0.712316 0.701858i \(-0.247646\pi\)
\(648\) 23.0591 + 10.7833i 0.905845 + 0.423608i
\(649\) 12.9239i 0.507306i
\(650\) −1.58999 5.39796i −0.0623647 0.211725i
\(651\) −1.05445 0.604502i −0.0413271 0.0236923i
\(652\) 7.05593 32.7045i 0.276331 1.28081i
\(653\) −6.79809 6.79809i −0.266030 0.266030i 0.561468 0.827498i \(-0.310237\pi\)
−0.827498 + 0.561468i \(0.810237\pi\)
\(654\) −1.94843 + 8.17073i −0.0761895 + 0.319501i
\(655\) 13.8481i 0.541090i
\(656\) −11.9541 + 26.4144i −0.466731 + 1.03131i
\(657\) −26.5382 + 15.5386i −1.03535 + 0.606220i
\(658\) 8.73252 + 4.75863i 0.340429 + 0.185511i
\(659\) −28.5628 + 28.5628i −1.11265 + 1.11265i −0.119857 + 0.992791i \(0.538244\pi\)
−0.992791 + 0.119857i \(0.961756\pi\)
\(660\) −19.3250 + 1.01281i −0.752226 + 0.0394235i
\(661\) 22.5826 + 22.5826i 0.878362 + 0.878362i 0.993365 0.115003i \(-0.0366878\pi\)
−0.115003 + 0.993365i \(0.536688\pi\)
\(662\) −33.1028 + 9.75059i −1.28658 + 0.378968i
\(663\) 12.2991 3.33580i 0.477656 0.129552i
\(664\) 10.0414 + 8.65597i 0.389682 + 0.335917i
\(665\) 2.29057 0.0888245
\(666\) −0.618033 + 0.657273i −0.0239483 + 0.0254688i
\(667\) 1.59232 1.59232i 0.0616550 0.0616550i
\(668\) −16.3429 + 10.5424i −0.632324 + 0.407898i
\(669\) 38.7887 + 22.2370i 1.49966 + 0.859734i
\(670\) −14.4413 7.86956i −0.557918 0.304028i
\(671\) 5.19698 0.200627
\(672\) 0.695380 + 5.47542i 0.0268249 + 0.211219i
\(673\) −18.0179 −0.694540 −0.347270 0.937765i \(-0.612891\pi\)
−0.347270 + 0.937765i \(0.612891\pi\)
\(674\) 19.3381 + 10.5380i 0.744876 + 0.405907i
\(675\) −0.0475870 5.19593i −0.00183162 0.199992i
\(676\) 4.76130 3.07141i 0.183127 0.118131i
\(677\) −6.22469 + 6.22469i −0.239234 + 0.239234i −0.816533 0.577299i \(-0.804107\pi\)
0.577299 + 0.816533i \(0.304107\pi\)
\(678\) −16.6152 27.0208i −0.638102 1.03773i
\(679\) 9.13381 0.350523
\(680\) 3.41468 3.96121i 0.130947 0.151906i
\(681\) −3.82096 14.0878i −0.146419 0.539847i
\(682\) 9.44036 2.78070i 0.361490 0.106479i
\(683\) 20.9599 + 20.9599i 0.802009 + 0.802009i 0.983409 0.181400i \(-0.0580629\pi\)
−0.181400 + 0.983409i \(0.558063\pi\)
\(684\) 23.1799 7.60995i 0.886306 0.290974i
\(685\) −6.39325 + 6.39325i −0.244273 + 0.244273i
\(686\) 9.57151 + 5.21583i 0.365442 + 0.199141i
\(687\) 15.7925 4.28331i 0.602522 0.163418i
\(688\) 1.76920 + 4.69436i 0.0674502 + 0.178971i
\(689\) 49.0531i 1.86877i
\(690\) 10.2171 + 2.43640i 0.388957 + 0.0927523i
\(691\) 10.1569 + 10.1569i 0.386387 + 0.386387i 0.873397 0.487010i \(-0.161912\pi\)
−0.487010 + 0.873397i \(0.661912\pi\)
\(692\) −0.748724 + 3.47037i −0.0284622 + 0.131923i
\(693\) 2.38771 9.13374i 0.0907015 0.346962i
\(694\) −1.16468 3.95405i −0.0442108 0.150094i
\(695\) 9.16043i 0.347475i
\(696\) −0.855091 2.42645i −0.0324122 0.0919744i
\(697\) 13.4024i 0.507654i
\(698\) 22.8785 6.73897i 0.865965 0.255074i
\(699\) −23.3486 + 40.7276i −0.883126 + 1.54046i
\(700\) 0.946751 0.610728i 0.0357838 0.0230833i
\(701\) 23.2304 + 23.2304i 0.877402 + 0.877402i 0.993265 0.115863i \(-0.0369634\pi\)
−0.115863 + 0.993265i \(0.536963\pi\)
\(702\) 27.9718 8.51837i 1.05573 0.321505i
\(703\) 0.864681i 0.0326121i
\(704\) −35.9134 26.5983i −1.35354 1.00246i
\(705\) −5.65985 20.8678i −0.213162 0.785927i
\(706\) 2.24560 4.12087i 0.0845142 0.155091i
\(707\) 6.15265 6.15265i 0.231394 0.231394i
\(708\) −5.95569 5.36251i −0.223828 0.201535i
\(709\) 5.27993 + 5.27993i 0.198292 + 0.198292i 0.799267 0.600976i \(-0.205221\pi\)
−0.600976 + 0.799267i \(0.705221\pi\)
\(710\) 5.07457 + 17.2280i 0.190445 + 0.646553i
\(711\) −33.8879 + 19.8421i −1.27090 + 0.744135i
\(712\) 2.94909 + 39.7999i 0.110522 + 1.49157i
\(713\) −5.34165 −0.200046
\(714\) 1.33641 + 2.17337i 0.0500140 + 0.0813364i
\(715\) −15.7178 + 15.7178i −0.587813 + 0.587813i
\(716\) 21.9570 + 4.73719i 0.820573 + 0.177037i
\(717\) −10.0388 + 17.5109i −0.374904 + 0.653955i
\(718\) −9.12252 + 16.7406i −0.340449 + 0.624755i
\(719\) −9.22912 −0.344188 −0.172094 0.985081i \(-0.555053\pi\)
−0.172094 + 0.985081i \(0.555053\pi\)
\(720\) 7.55182 9.32577i 0.281440 0.347551i
\(721\) 8.94589 0.333162
\(722\) −1.66882 + 3.06244i −0.0621072 + 0.113972i
\(723\) −4.62688 + 8.07079i −0.172076 + 0.300156i
\(724\) 4.86267 22.5387i 0.180720 0.837643i
\(725\) −0.371339 + 0.371339i −0.0137912 + 0.0137912i
\(726\) 25.9264 + 42.1633i 0.962217 + 1.56483i
\(727\) 28.4964 1.05687 0.528437 0.848973i \(-0.322778\pi\)
0.528437 + 0.848973i \(0.322778\pi\)
\(728\) 4.80201 + 4.13946i 0.177974 + 0.153419i
\(729\) 26.9955 0.494518i 0.999832 0.0183155i
\(730\) 4.09614 + 13.9062i 0.151605 + 0.514692i
\(731\) 1.63978 + 1.63978i 0.0606494 + 0.0606494i
\(732\) −2.15639 + 2.39492i −0.0797023 + 0.0885186i
\(733\) −16.5785 + 16.5785i −0.612342 + 0.612342i −0.943556 0.331214i \(-0.892542\pi\)
0.331214 + 0.943556i \(0.392542\pi\)
\(734\) 0.590922 1.08439i 0.0218113 0.0400257i
\(735\) −3.02988 11.1711i −0.111759 0.412053i
\(736\) 14.6194 + 19.3564i 0.538879 + 0.713486i
\(737\) 64.9651i 2.39302i
\(738\) 0.945782 + 30.7377i 0.0348147 + 1.13147i
\(739\) −10.4505 10.4505i −0.384429 0.384429i 0.488266 0.872695i \(-0.337630\pi\)
−0.872695 + 0.488266i \(0.837630\pi\)
\(740\) 0.230547 + 0.357394i 0.00847508 + 0.0131381i
\(741\) 13.9378 24.3121i 0.512019 0.893128i
\(742\) −9.42082 + 2.77495i −0.345849 + 0.101871i
\(743\) 23.0782i 0.846657i −0.905976 0.423328i \(-0.860862\pi\)
0.905976 0.423328i \(-0.139138\pi\)
\(744\) −2.63567 + 5.50418i −0.0966282 + 0.201793i
\(745\) 2.82449i 0.103481i
\(746\) −13.6026 46.1802i −0.498026 1.69078i
\(747\) 13.6043 + 3.55638i 0.497756 + 0.130121i
\(748\) −20.1939 4.35678i −0.738361 0.159300i
\(749\) −0.102207 0.102207i −0.00373456 0.00373456i
\(750\) −2.38268 0.568184i −0.0870032 0.0207472i
\(751\) 20.5355i 0.749351i −0.927156 0.374675i \(-0.877754\pi\)
0.927156 0.374675i \(-0.122246\pi\)
\(752\) 20.5877 45.4915i 0.750756 1.65890i
\(753\) −1.28871 + 0.349528i −0.0469631 + 0.0127375i
\(754\) −2.59490 1.41405i −0.0945006 0.0514965i
\(755\) −10.8412 + 10.8412i −0.394553 + 0.394553i
\(756\) 3.21835 + 4.89019i 0.117050 + 0.177855i
\(757\) 30.5550 + 30.5550i 1.11054 + 1.11054i 0.993077 + 0.117461i \(0.0374756\pi\)
0.117461 + 0.993077i \(0.462524\pi\)
\(758\) −37.9983 + 11.1926i −1.38016 + 0.406533i
\(759\) −10.8608 40.0436i −0.394221 1.45349i
\(760\) −0.849864 11.4695i −0.0308278 0.416041i
\(761\) −33.9032 −1.22899 −0.614495 0.788921i \(-0.710640\pi\)
−0.614495 + 0.788921i \(0.710640\pi\)
\(762\) 4.25390 + 6.91799i 0.154102 + 0.250612i
\(763\) −1.36596 + 1.36596i −0.0494509 + 0.0494509i
\(764\) 1.99596 + 3.09414i 0.0722114 + 0.111942i
\(765\) 1.40295 5.36674i 0.0507238 0.194035i
\(766\) −15.7327 8.57328i −0.568447 0.309765i
\(767\) −9.20553 −0.332392
\(768\) 27.1588 5.51347i 0.980010 0.198950i
\(769\) 28.2935 1.02029 0.510145 0.860088i \(-0.329592\pi\)
0.510145 + 0.860088i \(0.329592\pi\)
\(770\) −3.90782 2.12950i −0.140828 0.0767419i
\(771\) 14.9279 + 8.55794i 0.537613 + 0.308207i
\(772\) 20.4438 + 31.6920i 0.735788 + 1.14062i
\(773\) −32.9604 + 32.9604i −1.18550 + 1.18550i −0.207205 + 0.978298i \(0.566437\pi\)
−0.978298 + 0.207205i \(0.933563\pi\)
\(774\) 3.87645 + 3.64502i 0.139336 + 0.131017i
\(775\) 1.24571 0.0447471
\(776\) −3.38889 45.7353i −0.121654 1.64180i
\(777\) −0.200250 + 0.0543125i −0.00718392 + 0.00194845i
\(778\) 2.37280 0.698919i 0.0850690 0.0250575i
\(779\) 20.8407 + 20.8407i 0.746697 + 0.746697i
\(780\) −0.721412 13.7650i −0.0258307 0.492867i
\(781\) 50.1645 50.1645i 1.79503 1.79503i
\(782\) 9.84593 + 5.36537i 0.352090 + 0.191865i
\(783\) −1.94712 1.91178i −0.0695846 0.0683215i
\(784\) 11.0212 24.3529i 0.393613 0.869746i
\(785\) 0.453288i 0.0161786i
\(786\) −7.86827 + 32.9956i −0.280652 + 1.17691i
\(787\) −4.79088 4.79088i −0.170776 0.170776i 0.616544 0.787320i \(-0.288532\pi\)
−0.787320 + 0.616544i \(0.788532\pi\)
\(788\) 4.74621 + 1.02399i 0.169077 + 0.0364780i
\(789\) −6.93443 3.97542i −0.246872 0.141529i
\(790\) 5.23057 + 17.7575i 0.186095 + 0.631785i
\(791\) 7.29492i 0.259377i
\(792\) −46.6209 8.56699i −1.65660 0.304415i
\(793\) 3.70175i 0.131453i
\(794\) −10.8592 + 3.19863i −0.385379 + 0.113515i
\(795\) 18.5242 + 10.6197i 0.656984 + 0.376641i
\(796\) −15.3024 23.7218i −0.542380 0.840797i
\(797\) 1.19187 + 1.19187i 0.0422181 + 0.0422181i 0.727901 0.685683i \(-0.240496\pi\)
−0.685683 + 0.727901i \(0.740496\pi\)
\(798\) 5.45770 + 1.30147i 0.193200 + 0.0460714i
\(799\) 23.0820i 0.816582i
\(800\) −3.40934 4.51402i −0.120538 0.159595i
\(801\) 21.3884 + 36.5289i 0.755722 + 1.29069i
\(802\) −20.3393 + 37.3243i −0.718204 + 1.31797i
\(803\) 40.4922 40.4922i 1.42894 1.42894i
\(804\) −29.9377 26.9560i −1.05582 0.950664i
\(805\) 1.70805 + 1.70805i 0.0602010 + 0.0602010i
\(806\) 1.98066 + 6.72426i 0.0697659 + 0.236852i
\(807\) −8.54515 + 2.31765i −0.300803 + 0.0815851i
\(808\) −33.0907 28.5251i −1.16413 1.00351i
\(809\) 32.3957 1.13897 0.569486 0.822001i \(-0.307142\pi\)
0.569486 + 0.822001i \(0.307142\pi\)
\(810\) 2.83886 12.4073i 0.0997475 0.435948i
\(811\) 28.8320 28.8320i 1.01243 1.01243i 0.0125060 0.999922i \(-0.496019\pi\)
0.999922 0.0125060i \(-0.00398088\pi\)
\(812\) 0.124778 0.578353i 0.00437886 0.0202962i
\(813\) 6.62326 + 3.79703i 0.232288 + 0.133168i
\(814\) 0.803878 1.47519i 0.0281759 0.0517053i
\(815\) −16.7285 −0.585974
\(816\) 10.3868 7.49814i 0.363610 0.262487i
\(817\) 5.09969 0.178416
\(818\) 19.9463 36.6032i 0.697405 1.27980i
\(819\) 6.50586 + 1.70074i 0.227333 + 0.0594285i
\(820\) 14.1707 + 3.05730i 0.494862 + 0.106765i
\(821\) 11.4197 11.4197i 0.398551 0.398551i −0.479170 0.877722i \(-0.659062\pi\)
0.877722 + 0.479170i \(0.159062\pi\)
\(822\) −18.8656 + 11.6005i −0.658014 + 0.404615i
\(823\) −21.8579 −0.761919 −0.380960 0.924592i \(-0.624406\pi\)
−0.380960 + 0.924592i \(0.624406\pi\)
\(824\) −3.31917 44.7943i −0.115629 1.56048i
\(825\) 2.53280 + 9.33840i 0.0881807 + 0.325121i
\(826\) −0.520760 1.76796i −0.0181195 0.0615150i
\(827\) −18.0378 18.0378i −0.627236 0.627236i 0.320136 0.947372i \(-0.396272\pi\)
−0.947372 + 0.320136i \(0.896272\pi\)
\(828\) 22.9597 + 11.6103i 0.797904 + 0.403488i
\(829\) −14.4922 + 14.4922i −0.503335 + 0.503335i −0.912473 0.409138i \(-0.865830\pi\)
0.409138 + 0.912473i \(0.365830\pi\)
\(830\) 3.17180 5.82053i 0.110095 0.202034i
\(831\) 17.7055 4.80215i 0.614196 0.166585i
\(832\) 18.9457 25.5807i 0.656823 0.886852i
\(833\) 12.3564i 0.428125i
\(834\) −5.20481 + 21.8264i −0.180228 + 0.755786i
\(835\) 6.87597 + 6.87597i 0.237953 + 0.237953i
\(836\) −38.1761 + 24.6266i −1.32035 + 0.851728i
\(837\) 0.0592793 + 6.47260i 0.00204899 + 0.223726i
\(838\) −6.88436 + 2.02782i −0.237816 + 0.0700499i
\(839\) 17.7483i 0.612739i 0.951913 + 0.306369i \(0.0991143\pi\)
−0.951913 + 0.306369i \(0.900886\pi\)
\(840\) 2.60281 0.917241i 0.0898055 0.0316478i
\(841\) 28.7242i 0.990490i
\(842\) 15.1832 + 51.5462i 0.523247 + 1.77640i
\(843\) −19.0646 + 33.2549i −0.656620 + 1.14536i
\(844\) 0.0415994 0.192815i 0.00143191 0.00663696i
\(845\) −2.00323 2.00323i −0.0689133 0.0689133i
\(846\) −1.62885 52.9372i −0.0560009 1.82002i
\(847\) 11.3830i 0.391125i
\(848\) 17.3902 + 46.1429i 0.597183 + 1.58455i
\(849\) −8.51354 31.3894i −0.292184 1.07728i
\(850\) −2.29613 1.25124i −0.0787566 0.0429171i
\(851\) −0.644783 + 0.644783i −0.0221029 + 0.0221029i
\(852\) 2.30244 + 43.9320i 0.0788802 + 1.50509i
\(853\) −1.65838 1.65838i −0.0567818 0.0567818i 0.678146 0.734927i \(-0.262784\pi\)
−0.734927 + 0.678146i \(0.762784\pi\)
\(854\) −0.710935 + 0.209409i −0.0243277 + 0.00716583i
\(855\) −6.16367 10.5268i −0.210793 0.360010i
\(856\) −0.473855 + 0.549698i −0.0161960 + 0.0187883i
\(857\) 9.06031 0.309494 0.154747 0.987954i \(-0.450544\pi\)
0.154747 + 0.987954i \(0.450544\pi\)
\(858\) −46.3811 + 28.5199i −1.58343 + 0.973654i
\(859\) 13.5598 13.5598i 0.462656 0.462656i −0.436869 0.899525i \(-0.643913\pi\)
0.899525 + 0.436869i \(0.143913\pi\)
\(860\) 2.10783 1.35971i 0.0718764 0.0463659i
\(861\) −3.51741 + 6.13552i −0.119873 + 0.209098i
\(862\) −6.83575 3.72503i −0.232827 0.126875i
\(863\) −13.9970 −0.476464 −0.238232 0.971208i \(-0.576568\pi\)
−0.238232 + 0.971208i \(0.576568\pi\)
\(864\) 23.2923 17.9295i 0.792421 0.609974i
\(865\) 1.77511 0.0603555
\(866\) 15.0252 + 8.18770i 0.510576 + 0.278229i
\(867\) −11.6993 + 20.4075i −0.397330 + 0.693074i
\(868\) −1.17937 + 0.760787i −0.0400305 + 0.0258228i
\(869\) 51.7065 51.7065i 1.75402 1.75402i
\(870\) −1.09577 + 0.673793i −0.0371501 + 0.0228437i
\(871\) −46.2739 −1.56793
\(872\) 7.34649 + 6.33288i 0.248784 + 0.214458i
\(873\) −24.5780 41.9764i −0.831841 1.42069i
\(874\) 23.6535 6.96725i 0.800091 0.235671i
\(875\) −0.398329 0.398329i −0.0134660 0.0134660i
\(876\) 1.85850 + 35.4614i 0.0627930 + 1.19813i
\(877\) 34.4386 34.4386i 1.16291 1.16291i 0.179074 0.983836i \(-0.442690\pi\)
0.983836 0.179074i \(-0.0573100\pi\)
\(878\) −39.0203 21.2634i −1.31687 0.717606i
\(879\) −10.3613 38.2022i −0.349479 1.28853i
\(880\) −9.21305 + 20.3576i −0.310572 + 0.686254i
\(881\) 17.0679i 0.575031i 0.957776 + 0.287516i \(0.0928293\pi\)
−0.957776 + 0.287516i \(0.907171\pi\)
\(882\) −0.871968 28.3388i −0.0293607 0.954215i
\(883\) 13.8084 + 13.8084i 0.464690 + 0.464690i 0.900189 0.435499i \(-0.143428\pi\)
−0.435499 + 0.900189i \(0.643428\pi\)
\(884\) 3.10329 14.3839i 0.104375 0.483782i
\(885\) −1.99294 + 3.47633i −0.0669918 + 0.116856i
\(886\) 2.02830 + 6.88599i 0.0681421 + 0.231339i
\(887\) 1.71376i 0.0575425i −0.999586 0.0287712i \(-0.990841\pi\)
0.999586 0.0287712i \(-0.00915944\pi\)
\(888\) 0.346255 + 0.982550i 0.0116195 + 0.0329722i
\(889\) 1.86768i 0.0626399i
\(890\) 19.1414 5.63819i 0.641622 0.188993i
\(891\) −48.4012 + 13.6046i −1.62150 + 0.455772i
\(892\) 43.3840 27.9861i 1.45260 0.937043i
\(893\) −35.8924 35.8924i −1.20109 1.20109i
\(894\) −1.60483 + 6.72986i −0.0536736 + 0.225080i
\(895\) 11.2311i 0.375415i
\(896\) 5.98463 + 2.19148i 0.199933 + 0.0732121i
\(897\) 28.5226 7.73600i 0.952341 0.258298i
\(898\) −15.1016 + 27.7128i −0.503947 + 0.924788i
\(899\) 0.462579 0.462579i 0.0154279 0.0154279i
\(900\) −5.35433 2.70760i −0.178478 0.0902534i
\(901\) 16.1181 + 16.1181i 0.536971 + 0.536971i
\(902\) −16.1800 54.9305i −0.538737 1.82899i
\(903\) 0.320323 + 1.18103i 0.0106597 + 0.0393021i
\(904\) −36.5275 + 2.70661i −1.21489 + 0.0900205i
\(905\) −11.5286 −0.383225
\(906\) −31.9910 + 19.6714i −1.06283 + 0.653538i
\(907\) −22.7653 + 22.7653i −0.755908 + 0.755908i −0.975575 0.219667i \(-0.929503\pi\)
0.219667 + 0.975575i \(0.429503\pi\)
\(908\) −16.4759 3.55463i −0.546771 0.117965i
\(909\) −44.8320 11.7198i −1.48698 0.388721i
\(910\) 1.51682 2.78350i 0.0502821 0.0922721i
\(911\) −16.6383 −0.551251 −0.275626 0.961265i \(-0.588885\pi\)
−0.275626 + 0.961265i \(0.588885\pi\)
\(912\) 4.49182 27.8110i 0.148739 0.920913i
\(913\) −26.1839 −0.866562
\(914\) −15.1951 + 27.8843i −0.502609 + 0.922332i
\(915\) 1.39791 + 0.801404i 0.0462135 + 0.0264936i
\(916\) 3.98475 18.4695i 0.131660 0.610249i
\(917\) −5.51609 + 5.51609i −0.182157 + 0.182157i
\(918\) 6.39208 11.9901i 0.210970 0.395732i
\(919\) −44.9016 −1.48117 −0.740584 0.671964i \(-0.765451\pi\)
−0.740584 + 0.671964i \(0.765451\pi\)
\(920\) 7.91893 9.18640i 0.261079 0.302866i
\(921\) −34.0501 + 9.23520i −1.12199 + 0.304310i
\(922\) −11.9544 40.5845i −0.393696 1.33658i
\(923\) 35.7316 + 35.7316i 1.17612 + 1.17612i
\(924\) −8.10115 7.29429i −0.266508 0.239964i
\(925\) 0.150367 0.150367i 0.00494405 0.00494405i
\(926\) −1.44870 + 2.65850i −0.0476074 + 0.0873637i
\(927\) −24.0724 41.1128i −0.790640 1.35032i
\(928\) −2.94225 0.410213i −0.0965842 0.0134659i
\(929\) 19.2949i 0.633046i 0.948585 + 0.316523i \(0.102516\pi\)
−0.948585 + 0.316523i \(0.897484\pi\)
\(930\) 2.96812 + 0.707790i 0.0973284 + 0.0232094i
\(931\) −19.2142 19.2142i −0.629720 0.629720i
\(932\) 29.3850 + 45.5527i 0.962539 + 1.49213i
\(933\) −16.2603 9.32182i −0.532338 0.305183i
\(934\) 11.9921 3.53233i 0.392394 0.115582i
\(935\) 10.3293i 0.337803i
\(936\) 6.10217 33.2075i 0.199456 1.08542i
\(937\) 15.9035i 0.519545i −0.965670 0.259772i \(-0.916353\pi\)
0.965670 0.259772i \(-0.0836475\pi\)
\(938\) −2.61773 8.88707i −0.0854718 0.290173i
\(939\) 18.8702 + 10.8181i 0.615807 + 0.353034i
\(940\) −24.4051 5.26535i −0.796006 0.171737i
\(941\) −23.7121 23.7121i −0.772993 0.772993i 0.205635 0.978629i \(-0.434074\pi\)
−0.978629 + 0.205635i \(0.934074\pi\)
\(942\) 0.257551 1.08004i 0.00839148 0.0351897i
\(943\) 31.0814i 1.01215i
\(944\) −8.65938 + 3.26353i −0.281839 + 0.106219i
\(945\) 2.05073 2.08864i 0.0667104 0.0679436i
\(946\) −8.70032 4.74109i −0.282872 0.154146i
\(947\) −1.00185 + 1.00185i −0.0325558 + 0.0325558i −0.723197 0.690642i \(-0.757328\pi\)
0.690642 + 0.723197i \(0.257328\pi\)
\(948\) 2.37321 + 45.2825i 0.0770784 + 1.47071i
\(949\) 28.8421 + 28.8421i 0.936256 + 0.936256i
\(950\) −5.51614 + 1.62480i −0.178967 + 0.0527156i
\(951\) −2.17007 + 0.588574i −0.0703692 + 0.0190858i
\(952\) 2.93803 0.217702i 0.0952220 0.00705575i
\(953\) 10.9149 0.353567 0.176784 0.984250i \(-0.443431\pi\)
0.176784 + 0.984250i \(0.443431\pi\)
\(954\) 38.1032 + 35.8284i 1.23364 + 1.15999i
\(955\) 1.30181 1.30181i 0.0421254 0.0421254i
\(956\) 12.6341 + 19.5854i 0.408617 + 0.633438i
\(957\) 4.40824 + 2.52719i 0.142498 + 0.0816924i
\(958\) −38.4923 20.9757i −1.24363 0.677695i
\(959\) −5.09323 −0.164469
\(960\) −5.55857 12.6926i −0.179402 0.409652i
\(961\) 29.4482 0.949943
\(962\) 1.05076 + 0.572593i 0.0338778 + 0.0184611i
\(963\) −0.194688 + 0.744743i −0.00627372 + 0.0239990i
\(964\) 5.82309 + 9.02695i 0.187549 + 0.290739i
\(965\) 13.3338 13.3338i 0.429231 0.429231i
\(966\) 3.09926 + 5.04024i 0.0997170 + 0.162167i
\(967\) −21.2688 −0.683958 −0.341979 0.939708i \(-0.611097\pi\)
−0.341979 + 0.939708i \(0.611097\pi\)
\(968\) 56.9976 4.22340i 1.83197 0.135745i
\(969\) −3.40883 12.5683i −0.109507 0.403753i
\(970\) −21.9960 + 6.47902i −0.706248 + 0.208029i
\(971\) 16.7603 + 16.7603i 0.537865 + 0.537865i 0.922901 0.385037i \(-0.125811\pi\)
−0.385037 + 0.922901i \(0.625811\pi\)
\(972\) 13.8137 27.9496i 0.443076 0.896484i
\(973\) −3.64886 + 3.64886i −0.116977 + 0.116977i
\(974\) 29.5943 + 16.1269i 0.948263 + 0.516739i
\(975\) −6.65164 + 1.80408i −0.213023 + 0.0577769i
\(976\) 1.31234 + 3.48213i 0.0420070 + 0.111460i
\(977\) 47.4863i 1.51922i −0.650378 0.759611i \(-0.725389\pi\)
0.650378 0.759611i \(-0.274611\pi\)
\(978\) −39.8587 9.50487i −1.27454 0.303932i
\(979\) −55.7361 55.7361i −1.78133 1.78133i
\(980\) −13.0647 2.81869i −0.417338 0.0900397i
\(981\) 9.95318 + 2.60192i 0.317781 + 0.0830729i
\(982\) −5.97067 20.2701i −0.190532 0.646846i
\(983\) 57.1239i 1.82197i −0.412442 0.910984i \(-0.635324\pi\)
0.412442 0.910984i \(-0.364676\pi\)
\(984\) 32.0271 + 15.3361i 1.02099 + 0.488898i
\(985\) 2.42771i 0.0773533i
\(986\) −1.31728 + 0.388010i −0.0419506 + 0.0123567i
\(987\) 6.05777 10.5667i 0.192821 0.336343i
\(988\) −17.5412 27.1924i −0.558061 0.865107i
\(989\) 3.80279 + 3.80279i 0.120922 + 0.120922i
\(990\) 0.728913 + 23.6895i 0.0231664 + 0.752902i
\(991\) 25.2736i 0.802843i 0.915893 + 0.401421i \(0.131484\pi\)
−0.915893 + 0.401421i \(0.868516\pi\)
\(992\) 4.24703 + 5.62314i 0.134843 + 0.178535i
\(993\) 11.0635 + 40.7910i 0.351089 + 1.29446i
\(994\) −4.84104 + 8.88373i −0.153548 + 0.281775i
\(995\) −9.98053 + 9.98053i −0.316404 + 0.316404i
\(996\) 10.8645 12.0663i 0.344255 0.382335i
\(997\) 29.8735 + 29.8735i 0.946103 + 0.946103i 0.998620 0.0525166i \(-0.0167242\pi\)
−0.0525166 + 0.998620i \(0.516724\pi\)
\(998\) −3.19402 10.8435i −0.101105 0.343246i
\(999\) 0.788455 + 0.774143i 0.0249456 + 0.0244928i
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 240.2.bk.b.11.4 60
3.2 odd 2 inner 240.2.bk.b.11.27 yes 60
4.3 odd 2 960.2.bk.b.911.21 60
12.11 even 2 960.2.bk.b.911.5 60
16.3 odd 4 inner 240.2.bk.b.131.27 yes 60
16.13 even 4 960.2.bk.b.431.5 60
48.29 odd 4 960.2.bk.b.431.21 60
48.35 even 4 inner 240.2.bk.b.131.4 yes 60
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
240.2.bk.b.11.4 60 1.1 even 1 trivial
240.2.bk.b.11.27 yes 60 3.2 odd 2 inner
240.2.bk.b.131.4 yes 60 48.35 even 4 inner
240.2.bk.b.131.27 yes 60 16.3 odd 4 inner
960.2.bk.b.431.5 60 16.13 even 4
960.2.bk.b.431.21 60 48.29 odd 4
960.2.bk.b.911.5 60 12.11 even 2
960.2.bk.b.911.21 60 4.3 odd 2