Properties

Label 804.2.c.b.671.11
Level $804$
Weight $2$
Character 804.671
Analytic conductor $6.420$
Analytic rank $0$
Dimension $128$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [804,2,Mod(671,804)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(804, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("804.671");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 804.c (of order \(2\), degree \(1\), 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: \(6.41997232251\)
Analytic rank: \(0\)
Dimension: \(128\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 671.11
Character \(\chi\) \(=\) 804.671
Dual form 804.2.c.b.671.12

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.37515 - 0.330103i) q^{2} +(0.355099 + 1.69526i) q^{3} +(1.78206 + 0.907880i) q^{4} +0.0453328i q^{5} +(0.0712965 - 2.44845i) q^{6} +2.82199i q^{7} +(-2.15091 - 1.83673i) q^{8} +(-2.74781 + 1.20397i) q^{9} +O(q^{10})\) \(q+(-1.37515 - 0.330103i) q^{2} +(0.355099 + 1.69526i) q^{3} +(1.78206 + 0.907880i) q^{4} +0.0453328i q^{5} +(0.0712965 - 2.44845i) q^{6} +2.82199i q^{7} +(-2.15091 - 1.83673i) q^{8} +(-2.74781 + 1.20397i) q^{9} +(0.0149645 - 0.0623394i) q^{10} +3.33857 q^{11} +(-0.906284 + 3.34345i) q^{12} -5.31881 q^{13} +(0.931548 - 3.88066i) q^{14} +(-0.0768509 + 0.0160976i) q^{15} +(2.35151 + 3.23580i) q^{16} +0.0462961i q^{17} +(4.17608 - 0.748576i) q^{18} +3.00472i q^{19} +(-0.0411568 + 0.0807860i) q^{20} +(-4.78401 + 1.00209i) q^{21} +(-4.59103 - 1.10207i) q^{22} -8.74554 q^{23} +(2.34996 - 4.29857i) q^{24} +4.99794 q^{25} +(7.31415 + 1.75575i) q^{26} +(-3.01678 - 4.23072i) q^{27} +(-2.56203 + 5.02897i) q^{28} +3.33779i q^{29} +(0.110995 + 0.00323207i) q^{30} +1.84815i q^{31} +(-2.16552 - 5.22595i) q^{32} +(1.18552 + 5.65975i) q^{33} +(0.0152825 - 0.0636640i) q^{34} -0.127929 q^{35} +(-5.98983 - 0.349132i) q^{36} +0.528333 q^{37} +(0.991868 - 4.13194i) q^{38} +(-1.88870 - 9.01677i) q^{39} +(0.0832644 - 0.0975068i) q^{40} -4.07375i q^{41} +(6.90952 + 0.201198i) q^{42} +0.346936i q^{43} +(5.94955 + 3.03102i) q^{44} +(-0.0545793 - 0.124566i) q^{45} +(12.0264 + 2.88693i) q^{46} -0.457301 q^{47} +(-4.65051 + 5.13544i) q^{48} -0.963647 q^{49} +(-6.87291 - 1.64984i) q^{50} +(-0.0784839 + 0.0164397i) q^{51} +(-9.47846 - 4.82884i) q^{52} -2.89403i q^{53} +(2.75195 + 6.81372i) q^{54} +0.151347i q^{55} +(5.18325 - 6.06985i) q^{56} +(-5.09379 + 1.06697i) q^{57} +(1.10182 - 4.58996i) q^{58} -0.226764 q^{59} +(-0.151568 - 0.0410844i) q^{60} -6.11785 q^{61} +(0.610078 - 2.54147i) q^{62} +(-3.39759 - 7.75430i) q^{63} +(1.25281 + 7.90129i) q^{64} -0.241117i q^{65} +(0.238029 - 8.17433i) q^{66} -1.00000i q^{67} +(-0.0420313 + 0.0825027i) q^{68} +(-3.10553 - 14.8260i) q^{69} +(0.175921 + 0.0422297i) q^{70} -7.18463 q^{71} +(8.12166 + 2.45737i) q^{72} -5.00203 q^{73} +(-0.726537 - 0.174404i) q^{74} +(1.77476 + 8.47281i) q^{75} +(-2.72793 + 5.35461i) q^{76} +9.42143i q^{77} +(-0.379213 + 13.0229i) q^{78} +15.3051i q^{79} +(-0.146688 + 0.106600i) q^{80} +(6.10092 - 6.61656i) q^{81} +(-1.34476 + 5.60201i) q^{82} -14.2834 q^{83} +(-9.43519 - 2.55753i) q^{84} -0.00209873 q^{85} +(0.114525 - 0.477088i) q^{86} +(-5.65843 + 1.18525i) q^{87} +(-7.18096 - 6.13207i) q^{88} -0.699578i q^{89} +(0.0339351 + 0.189313i) q^{90} -15.0097i q^{91} +(-15.5851 - 7.93990i) q^{92} +(-3.13309 + 0.656274i) q^{93} +(0.628857 + 0.150956i) q^{94} -0.136213 q^{95} +(8.09036 - 5.52685i) q^{96} +2.90757 q^{97} +(1.32516 + 0.318103i) q^{98} +(-9.17376 + 4.01954i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 128 q + 4 q^{4} - 6 q^{6} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 128 q + 4 q^{4} - 6 q^{6} - 4 q^{9} - 4 q^{10} + 4 q^{12} - 8 q^{13} - 4 q^{16} + 18 q^{18} - 8 q^{21} - 8 q^{22} - 24 q^{24} - 136 q^{25} + 14 q^{30} - 32 q^{33} + 34 q^{36} - 48 q^{37} + 16 q^{40} - 28 q^{42} - 16 q^{45} - 28 q^{46} - 22 q^{48} - 152 q^{49} + 8 q^{52} - 16 q^{54} - 32 q^{57} - 20 q^{58} - 14 q^{60} + 8 q^{61} + 16 q^{64} + 14 q^{66} + 56 q^{69} - 4 q^{70} - 8 q^{72} - 48 q^{73} - 36 q^{76} + 40 q^{78} + 44 q^{81} + 60 q^{82} + 46 q^{84} + 64 q^{85} - 28 q^{88} - 14 q^{90} + 32 q^{93} - 8 q^{96} + 64 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/804\mathbb{Z}\right)^\times\).

\(n\) \(269\) \(337\) \(403\)
\(\chi(n)\) \(-1\) \(1\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.37515 0.330103i −0.972377 0.233418i
\(3\) 0.355099 + 1.69526i 0.205016 + 0.978759i
\(4\) 1.78206 + 0.907880i 0.891032 + 0.453940i
\(5\) 0.0453328i 0.0202735i 0.999949 + 0.0101367i \(0.00322668\pi\)
−0.999949 + 0.0101367i \(0.996773\pi\)
\(6\) 0.0712965 2.44845i 0.0291067 0.999576i
\(7\) 2.82199i 1.06661i 0.845922 + 0.533307i \(0.179051\pi\)
−0.845922 + 0.533307i \(0.820949\pi\)
\(8\) −2.15091 1.83673i −0.760461 0.649384i
\(9\) −2.74781 + 1.20397i −0.915937 + 0.401323i
\(10\) 0.0149645 0.0623394i 0.00473219 0.0197134i
\(11\) 3.33857 1.00662 0.503309 0.864107i \(-0.332116\pi\)
0.503309 + 0.864107i \(0.332116\pi\)
\(12\) −0.906284 + 3.34345i −0.261622 + 0.965171i
\(13\) −5.31881 −1.47517 −0.737586 0.675253i \(-0.764035\pi\)
−0.737586 + 0.675253i \(0.764035\pi\)
\(14\) 0.931548 3.88066i 0.248967 1.03715i
\(15\) −0.0768509 + 0.0160976i −0.0198428 + 0.00415639i
\(16\) 2.35151 + 3.23580i 0.587877 + 0.808951i
\(17\) 0.0462961i 0.0112285i 0.999984 + 0.00561423i \(0.00178707\pi\)
−0.999984 + 0.00561423i \(0.998213\pi\)
\(18\) 4.17608 0.748576i 0.984311 0.176441i
\(19\) 3.00472i 0.689331i 0.938726 + 0.344666i \(0.112008\pi\)
−0.938726 + 0.344666i \(0.887992\pi\)
\(20\) −0.0411568 + 0.0807860i −0.00920294 + 0.0180643i
\(21\) −4.78401 + 1.00209i −1.04396 + 0.218673i
\(22\) −4.59103 1.10207i −0.978811 0.234963i
\(23\) −8.74554 −1.82357 −0.911786 0.410666i \(-0.865296\pi\)
−0.911786 + 0.410666i \(0.865296\pi\)
\(24\) 2.34996 4.29857i 0.479683 0.877442i
\(25\) 4.99794 0.999589
\(26\) 7.31415 + 1.75575i 1.43442 + 0.344332i
\(27\) −3.01678 4.23072i −0.580580 0.814203i
\(28\) −2.56203 + 5.02897i −0.484179 + 0.950387i
\(29\) 3.33779i 0.619813i 0.950767 + 0.309906i \(0.100298\pi\)
−0.950767 + 0.309906i \(0.899702\pi\)
\(30\) 0.110995 + 0.00323207i 0.0202649 + 0.000590093i
\(31\) 1.84815i 0.331937i 0.986131 + 0.165968i \(0.0530750\pi\)
−0.986131 + 0.165968i \(0.946925\pi\)
\(32\) −2.16552 5.22595i −0.382814 0.923825i
\(33\) 1.18552 + 5.65975i 0.206373 + 0.985235i
\(34\) 0.0152825 0.0636640i 0.00262092 0.0109183i
\(35\) −0.127929 −0.0216239
\(36\) −5.98983 0.349132i −0.998306 0.0581887i
\(37\) 0.528333 0.0868575 0.0434287 0.999057i \(-0.486172\pi\)
0.0434287 + 0.999057i \(0.486172\pi\)
\(38\) 0.991868 4.13194i 0.160902 0.670289i
\(39\) −1.88870 9.01677i −0.302435 1.44384i
\(40\) 0.0832644 0.0975068i 0.0131653 0.0154172i
\(41\) 4.07375i 0.636213i −0.948055 0.318107i \(-0.896953\pi\)
0.948055 0.318107i \(-0.103047\pi\)
\(42\) 6.90952 + 0.201198i 1.06616 + 0.0310456i
\(43\) 0.346936i 0.0529073i 0.999650 + 0.0264536i \(0.00842143\pi\)
−0.999650 + 0.0264536i \(0.991579\pi\)
\(44\) 5.94955 + 3.03102i 0.896929 + 0.456944i
\(45\) −0.0545793 0.124566i −0.00813621 0.0185692i
\(46\) 12.0264 + 2.88693i 1.77320 + 0.425654i
\(47\) −0.457301 −0.0667042 −0.0333521 0.999444i \(-0.510618\pi\)
−0.0333521 + 0.999444i \(0.510618\pi\)
\(48\) −4.65051 + 5.13544i −0.671243 + 0.741237i
\(49\) −0.963647 −0.137664
\(50\) −6.87291 1.64984i −0.971977 0.233322i
\(51\) −0.0784839 + 0.0164397i −0.0109899 + 0.00230202i
\(52\) −9.47846 4.82884i −1.31443 0.669640i
\(53\) 2.89403i 0.397526i −0.980048 0.198763i \(-0.936308\pi\)
0.980048 0.198763i \(-0.0636924\pi\)
\(54\) 2.75195 + 6.81372i 0.374493 + 0.927230i
\(55\) 0.151347i 0.0204076i
\(56\) 5.18325 6.06985i 0.692641 0.811118i
\(57\) −5.09379 + 1.06697i −0.674689 + 0.141324i
\(58\) 1.10182 4.58996i 0.144675 0.602691i
\(59\) −0.226764 −0.0295222 −0.0147611 0.999891i \(-0.504699\pi\)
−0.0147611 + 0.999891i \(0.504699\pi\)
\(60\) −0.151568 0.0410844i −0.0195673 0.00530398i
\(61\) −6.11785 −0.783310 −0.391655 0.920112i \(-0.628097\pi\)
−0.391655 + 0.920112i \(0.628097\pi\)
\(62\) 0.610078 2.54147i 0.0774800 0.322767i
\(63\) −3.39759 7.75430i −0.428056 0.976950i
\(64\) 1.25281 + 7.90129i 0.156602 + 0.987662i
\(65\) 0.241117i 0.0299069i
\(66\) 0.238029 8.17433i 0.0292993 1.00619i
\(67\) 1.00000i 0.122169i
\(68\) −0.0420313 + 0.0825027i −0.00509705 + 0.0100049i
\(69\) −3.10553 14.8260i −0.373862 1.78484i
\(70\) 0.175921 + 0.0422297i 0.0210266 + 0.00504741i
\(71\) −7.18463 −0.852659 −0.426329 0.904568i \(-0.640194\pi\)
−0.426329 + 0.904568i \(0.640194\pi\)
\(72\) 8.12166 + 2.45737i 0.957147 + 0.289604i
\(73\) −5.00203 −0.585443 −0.292722 0.956198i \(-0.594561\pi\)
−0.292722 + 0.956198i \(0.594561\pi\)
\(74\) −0.726537 0.174404i −0.0844582 0.0202741i
\(75\) 1.77476 + 8.47281i 0.204932 + 0.978356i
\(76\) −2.72793 + 5.35461i −0.312915 + 0.614216i
\(77\) 9.42143i 1.07367i
\(78\) −0.379213 + 13.0229i −0.0429374 + 1.47455i
\(79\) 15.3051i 1.72196i 0.508640 + 0.860979i \(0.330148\pi\)
−0.508640 + 0.860979i \(0.669852\pi\)
\(80\) −0.146688 + 0.106600i −0.0164002 + 0.0119183i
\(81\) 6.10092 6.61656i 0.677880 0.735173i
\(82\) −1.34476 + 5.60201i −0.148504 + 0.618639i
\(83\) −14.2834 −1.56781 −0.783904 0.620881i \(-0.786775\pi\)
−0.783904 + 0.620881i \(0.786775\pi\)
\(84\) −9.43519 2.55753i −1.02946 0.279049i
\(85\) −0.00209873 −0.000227640
\(86\) 0.114525 0.477088i 0.0123495 0.0514458i
\(87\) −5.65843 + 1.18525i −0.606647 + 0.127072i
\(88\) −7.18096 6.13207i −0.765493 0.653681i
\(89\) 0.699578i 0.0741551i −0.999312 0.0370776i \(-0.988195\pi\)
0.999312 0.0370776i \(-0.0118049\pi\)
\(90\) 0.0339351 + 0.189313i 0.00357707 + 0.0199554i
\(91\) 15.0097i 1.57344i
\(92\) −15.5851 7.93990i −1.62486 0.827792i
\(93\) −3.13309 + 0.656274i −0.324886 + 0.0680524i
\(94\) 0.628857 + 0.150956i 0.0648616 + 0.0155700i
\(95\) −0.136213 −0.0139751
\(96\) 8.09036 5.52685i 0.825719 0.564082i
\(97\) 2.90757 0.295219 0.147610 0.989046i \(-0.452842\pi\)
0.147610 + 0.989046i \(0.452842\pi\)
\(98\) 1.32516 + 0.318103i 0.133861 + 0.0321332i
\(99\) −9.17376 + 4.01954i −0.921998 + 0.403979i
\(100\) 8.90666 + 4.53754i 0.890666 + 0.453754i
\(101\) 18.8879i 1.87941i 0.341982 + 0.939706i \(0.388902\pi\)
−0.341982 + 0.939706i \(0.611098\pi\)
\(102\) 0.113354 + 0.00330075i 0.0112237 + 0.000326823i
\(103\) 14.3849i 1.41739i −0.705516 0.708694i \(-0.749285\pi\)
0.705516 0.708694i \(-0.250715\pi\)
\(104\) 11.4403 + 9.76924i 1.12181 + 0.957953i
\(105\) −0.0454274 0.216873i −0.00443326 0.0211646i
\(106\) −0.955328 + 3.97972i −0.0927897 + 0.386545i
\(107\) −0.659701 −0.0637757 −0.0318878 0.999491i \(-0.510152\pi\)
−0.0318878 + 0.999491i \(0.510152\pi\)
\(108\) −1.53511 10.2783i −0.147716 0.989030i
\(109\) 11.4114 1.09301 0.546505 0.837456i \(-0.315958\pi\)
0.546505 + 0.837456i \(0.315958\pi\)
\(110\) 0.0499600 0.208124i 0.00476350 0.0198439i
\(111\) 0.187610 + 0.895662i 0.0178072 + 0.0850125i
\(112\) −9.13141 + 6.63594i −0.862837 + 0.627037i
\(113\) 9.58855i 0.902015i 0.892520 + 0.451007i \(0.148935\pi\)
−0.892520 + 0.451007i \(0.851065\pi\)
\(114\) 7.35692 + 0.214226i 0.689039 + 0.0200641i
\(115\) 0.396460i 0.0369701i
\(116\) −3.03032 + 5.94816i −0.281358 + 0.552273i
\(117\) 14.6151 6.40368i 1.35116 0.592021i
\(118\) 0.311834 + 0.0748555i 0.0287067 + 0.00689101i
\(119\) −0.130647 −0.0119764
\(120\) 0.194866 + 0.106530i 0.0177888 + 0.00972483i
\(121\) 0.146066 0.0132787
\(122\) 8.41295 + 2.01952i 0.761673 + 0.182839i
\(123\) 6.90607 1.44658i 0.622699 0.130434i
\(124\) −1.67789 + 3.29351i −0.150679 + 0.295766i
\(125\) 0.453235i 0.0405386i
\(126\) 2.11248 + 11.7849i 0.188194 + 1.04988i
\(127\) 6.92851i 0.614806i 0.951579 + 0.307403i \(0.0994600\pi\)
−0.951579 + 0.307403i \(0.900540\pi\)
\(128\) 0.885434 11.2790i 0.0782620 0.996933i
\(129\) −0.588147 + 0.123197i −0.0517834 + 0.0108469i
\(130\) −0.0795933 + 0.331571i −0.00698080 + 0.0290807i
\(131\) 0.832599 0.0727445 0.0363723 0.999338i \(-0.488420\pi\)
0.0363723 + 0.999338i \(0.488420\pi\)
\(132\) −3.02570 + 11.1623i −0.263353 + 0.971557i
\(133\) −8.47931 −0.735250
\(134\) −0.330103 + 1.37515i −0.0285165 + 0.118795i
\(135\) 0.191791 0.136759i 0.0165067 0.0117704i
\(136\) 0.0850337 0.0995787i 0.00729158 0.00853880i
\(137\) 4.92259i 0.420565i 0.977641 + 0.210282i \(0.0674384\pi\)
−0.977641 + 0.210282i \(0.932562\pi\)
\(138\) −0.623527 + 21.4130i −0.0530781 + 1.82280i
\(139\) 6.30934i 0.535151i 0.963537 + 0.267576i \(0.0862225\pi\)
−0.963537 + 0.267576i \(0.913777\pi\)
\(140\) −0.227978 0.116144i −0.0192676 0.00981598i
\(141\) −0.162387 0.775244i −0.0136755 0.0652873i
\(142\) 9.87993 + 2.37167i 0.829105 + 0.199026i
\(143\) −17.7572 −1.48493
\(144\) −10.3573 6.06023i −0.863108 0.505019i
\(145\) −0.151312 −0.0125658
\(146\) 6.87853 + 1.65118i 0.569271 + 0.136653i
\(147\) −0.342190 1.63363i −0.0282233 0.134740i
\(148\) 0.941524 + 0.479663i 0.0773928 + 0.0394281i
\(149\) 17.5015i 1.43378i 0.697187 + 0.716889i \(0.254435\pi\)
−0.697187 + 0.716889i \(0.745565\pi\)
\(150\) 0.356336 12.2372i 0.0290947 0.999165i
\(151\) 14.7325i 1.19891i 0.800408 + 0.599455i \(0.204616\pi\)
−0.800408 + 0.599455i \(0.795384\pi\)
\(152\) 5.51888 6.46289i 0.447640 0.524209i
\(153\) −0.0557391 0.127213i −0.00450624 0.0102846i
\(154\) 3.11004 12.9559i 0.250614 1.04401i
\(155\) −0.0837817 −0.00672951
\(156\) 4.82035 17.7832i 0.385937 1.42379i
\(157\) 12.3226 0.983451 0.491726 0.870750i \(-0.336366\pi\)
0.491726 + 0.870750i \(0.336366\pi\)
\(158\) 5.05226 21.0468i 0.401936 1.67439i
\(159\) 4.90614 1.02767i 0.389082 0.0814993i
\(160\) 0.236907 0.0981693i 0.0187291 0.00776096i
\(161\) 24.6799i 1.94505i
\(162\) −10.5738 + 7.08481i −0.830757 + 0.556636i
\(163\) 21.0635i 1.64982i −0.565261 0.824912i \(-0.691225\pi\)
0.565261 0.824912i \(-0.308775\pi\)
\(164\) 3.69848 7.25969i 0.288803 0.566887i
\(165\) −0.256572 + 0.0537431i −0.0199741 + 0.00418390i
\(166\) 19.6418 + 4.71500i 1.52450 + 0.365955i
\(167\) 21.7501 1.68308 0.841538 0.540198i \(-0.181651\pi\)
0.841538 + 0.540198i \(0.181651\pi\)
\(168\) 12.1305 + 6.63156i 0.935891 + 0.511636i
\(169\) 15.2898 1.17614
\(170\) 0.00288607 0.000692798i 0.000221351 5.31352e-5i
\(171\) −3.61760 8.25641i −0.276644 0.631384i
\(172\) −0.314976 + 0.618262i −0.0240167 + 0.0471421i
\(173\) 25.8893i 1.96833i −0.177259 0.984164i \(-0.556723\pi\)
0.177259 0.984164i \(-0.443277\pi\)
\(174\) 8.17243 + 0.237973i 0.619550 + 0.0180407i
\(175\) 14.1042i 1.06617i
\(176\) 7.85067 + 10.8030i 0.591767 + 0.814304i
\(177\) −0.0805237 0.384424i −0.00605253 0.0288951i
\(178\) −0.230933 + 0.962023i −0.0173091 + 0.0721067i
\(179\) 1.87615 0.140230 0.0701149 0.997539i \(-0.477663\pi\)
0.0701149 + 0.997539i \(0.477663\pi\)
\(180\) 0.0158272 0.271536i 0.00117969 0.0202391i
\(181\) 10.8705 0.808001 0.404000 0.914759i \(-0.367619\pi\)
0.404000 + 0.914759i \(0.367619\pi\)
\(182\) −4.95473 + 20.6405i −0.367269 + 1.52998i
\(183\) −2.17244 10.3713i −0.160591 0.766672i
\(184\) 18.8109 + 16.0632i 1.38675 + 1.18420i
\(185\) 0.0239508i 0.00176090i
\(186\) 4.52510 + 0.131766i 0.331796 + 0.00966158i
\(187\) 0.154563i 0.0113028i
\(188\) −0.814940 0.415175i −0.0594356 0.0302797i
\(189\) 11.9391 8.51334i 0.868440 0.619255i
\(190\) 0.187313 + 0.0449642i 0.0135891 + 0.00326204i
\(191\) −4.00209 −0.289581 −0.144791 0.989462i \(-0.546251\pi\)
−0.144791 + 0.989462i \(0.546251\pi\)
\(192\) −12.9499 + 4.92959i −0.934577 + 0.355762i
\(193\) 19.1089 1.37549 0.687743 0.725954i \(-0.258602\pi\)
0.687743 + 0.725954i \(0.258602\pi\)
\(194\) −3.99834 0.959798i −0.287064 0.0689094i
\(195\) 0.408756 0.0856203i 0.0292716 0.00613139i
\(196\) −1.71728 0.874876i −0.122663 0.0624911i
\(197\) 3.18758i 0.227105i 0.993532 + 0.113553i \(0.0362231\pi\)
−0.993532 + 0.113553i \(0.963777\pi\)
\(198\) 13.9421 2.49918i 0.990825 0.177609i
\(199\) 17.5383i 1.24326i −0.783313 0.621628i \(-0.786472\pi\)
0.783313 0.621628i \(-0.213528\pi\)
\(200\) −10.7501 9.17990i −0.760148 0.649117i
\(201\) 1.69526 0.355099i 0.119574 0.0250467i
\(202\) 6.23494 25.9736i 0.438689 1.82750i
\(203\) −9.41923 −0.661101
\(204\) −0.154789 0.0419574i −0.0108374 0.00293761i
\(205\) 0.184675 0.0128982
\(206\) −4.74850 + 19.7814i −0.330844 + 1.37824i
\(207\) 24.0311 10.5294i 1.67028 0.731841i
\(208\) −12.5072 17.2106i −0.867220 1.19334i
\(209\) 10.0315i 0.693893i
\(210\) −0.00912089 + 0.313228i −0.000629401 + 0.0216148i
\(211\) 3.20034i 0.220321i 0.993914 + 0.110160i \(0.0351364\pi\)
−0.993914 + 0.110160i \(0.964864\pi\)
\(212\) 2.62744 5.15735i 0.180453 0.354208i
\(213\) −2.55125 12.1798i −0.174809 0.834547i
\(214\) 0.907186 + 0.217769i 0.0620140 + 0.0148864i
\(215\) −0.0157276 −0.00107261
\(216\) −1.28189 + 14.6409i −0.0872214 + 0.996189i
\(217\) −5.21545 −0.354048
\(218\) −15.6923 3.76692i −1.06282 0.255128i
\(219\) −1.77621 8.47974i −0.120025 0.573008i
\(220\) −0.137405 + 0.269710i −0.00926384 + 0.0181838i
\(221\) 0.246240i 0.0165639i
\(222\) 0.0376683 1.29360i 0.00252813 0.0868207i
\(223\) 23.6656i 1.58476i 0.610026 + 0.792382i \(0.291159\pi\)
−0.610026 + 0.792382i \(0.708841\pi\)
\(224\) 14.7476 6.11109i 0.985365 0.408314i
\(225\) −13.7334 + 6.01737i −0.915560 + 0.401158i
\(226\) 3.16521 13.1857i 0.210546 0.877098i
\(227\) 25.7062 1.70618 0.853091 0.521762i \(-0.174725\pi\)
0.853091 + 0.521762i \(0.174725\pi\)
\(228\) −10.0461 2.72313i −0.665322 0.180344i
\(229\) −11.9383 −0.788906 −0.394453 0.918916i \(-0.629066\pi\)
−0.394453 + 0.918916i \(0.629066\pi\)
\(230\) −0.130873 + 0.545191i −0.00862948 + 0.0359489i
\(231\) −15.9718 + 3.34554i −1.05087 + 0.220120i
\(232\) 6.13064 7.17929i 0.402496 0.471344i
\(233\) 17.8239i 1.16769i 0.811867 + 0.583843i \(0.198452\pi\)
−0.811867 + 0.583843i \(0.801548\pi\)
\(234\) −22.2118 + 3.98153i −1.45203 + 0.260281i
\(235\) 0.0207308i 0.00135233i
\(236\) −0.404108 0.205875i −0.0263052 0.0134013i
\(237\) −25.9461 + 5.43482i −1.68538 + 0.353030i
\(238\) 0.179659 + 0.0431270i 0.0116456 + 0.00279551i
\(239\) 22.2718 1.44064 0.720320 0.693642i \(-0.243995\pi\)
0.720320 + 0.693642i \(0.243995\pi\)
\(240\) −0.232804 0.210821i −0.0150274 0.0136084i
\(241\) 19.3681 1.24761 0.623804 0.781580i \(-0.285586\pi\)
0.623804 + 0.781580i \(0.285586\pi\)
\(242\) −0.200863 0.0482169i −0.0129119 0.00309950i
\(243\) 13.3832 + 7.99311i 0.858533 + 0.512758i
\(244\) −10.9024 5.55428i −0.697955 0.355576i
\(245\) 0.0436848i 0.00279092i
\(246\) −9.97439 0.290445i −0.635944 0.0185181i
\(247\) 15.9816i 1.01688i
\(248\) 3.39455 3.97519i 0.215554 0.252425i
\(249\) −5.07202 24.2141i −0.321426 1.53451i
\(250\) 0.149614 0.623265i 0.00946243 0.0394188i
\(251\) −12.1468 −0.766701 −0.383350 0.923603i \(-0.625230\pi\)
−0.383350 + 0.923603i \(0.625230\pi\)
\(252\) 0.985249 16.9033i 0.0620649 1.06481i
\(253\) −29.1976 −1.83564
\(254\) 2.28712 9.52773i 0.143507 0.597823i
\(255\) −0.000745258 0.00355790i −4.66699e−5 0.000222804i
\(256\) −4.94083 + 15.2180i −0.308802 + 0.951126i
\(257\) 22.4036i 1.39750i 0.715367 + 0.698748i \(0.246259\pi\)
−0.715367 + 0.698748i \(0.753741\pi\)
\(258\) 0.849456 + 0.0247353i 0.0528848 + 0.00153996i
\(259\) 1.49095i 0.0926433i
\(260\) 0.218905 0.429686i 0.0135759 0.0266480i
\(261\) −4.01860 9.17162i −0.248745 0.567709i
\(262\) −1.14495 0.274843i −0.0707351 0.0169799i
\(263\) 26.2457 1.61838 0.809189 0.587548i \(-0.199907\pi\)
0.809189 + 0.587548i \(0.199907\pi\)
\(264\) 7.84550 14.3511i 0.482857 0.883248i
\(265\) 0.131195 0.00805923
\(266\) 11.6603 + 2.79904i 0.714940 + 0.171620i
\(267\) 1.18597 0.248419i 0.0725800 0.0152030i
\(268\) 0.907880 1.78206i 0.0554576 0.108857i
\(269\) 16.0941i 0.981276i −0.871364 0.490638i \(-0.836764\pi\)
0.871364 0.490638i \(-0.163236\pi\)
\(270\) −0.308885 + 0.124754i −0.0187982 + 0.00759227i
\(271\) 13.4888i 0.819383i 0.912224 + 0.409692i \(0.134364\pi\)
−0.912224 + 0.409692i \(0.865636\pi\)
\(272\) −0.149805 + 0.108866i −0.00908327 + 0.00660095i
\(273\) 25.4453 5.32991i 1.54002 0.322581i
\(274\) 1.62496 6.76928i 0.0981674 0.408947i
\(275\) 16.6860 1.00620
\(276\) 7.92594 29.2403i 0.477086 1.76006i
\(277\) −13.5911 −0.816609 −0.408304 0.912846i \(-0.633880\pi\)
−0.408304 + 0.912846i \(0.633880\pi\)
\(278\) 2.08273 8.67628i 0.124914 0.520369i
\(279\) −2.22511 5.07835i −0.133214 0.304033i
\(280\) 0.275163 + 0.234971i 0.0164442 + 0.0140422i
\(281\) 14.2655i 0.851007i 0.904957 + 0.425504i \(0.139903\pi\)
−0.904957 + 0.425504i \(0.860097\pi\)
\(282\) −0.0326040 + 1.11968i −0.00194154 + 0.0666760i
\(283\) 2.05619i 0.122228i 0.998131 + 0.0611138i \(0.0194653\pi\)
−0.998131 + 0.0611138i \(0.980535\pi\)
\(284\) −12.8035 6.52278i −0.759746 0.387056i
\(285\) −0.0483689 0.230916i −0.00286513 0.0136783i
\(286\) 24.4188 + 5.86171i 1.44392 + 0.346610i
\(287\) 11.4961 0.678594
\(288\) 12.2423 + 11.7527i 0.721386 + 0.692534i
\(289\) 16.9979 0.999874
\(290\) 0.208076 + 0.0499484i 0.0122186 + 0.00293307i
\(291\) 1.03248 + 4.92909i 0.0605248 + 0.288948i
\(292\) −8.91394 4.54124i −0.521649 0.265756i
\(293\) 30.5801i 1.78651i 0.449554 + 0.893253i \(0.351583\pi\)
−0.449554 + 0.893253i \(0.648417\pi\)
\(294\) −0.0687047 + 2.35944i −0.00400694 + 0.137606i
\(295\) 0.0102799i 0.000598517i
\(296\) −1.13640 0.970408i −0.0660517 0.0564038i
\(297\) −10.0718 14.1246i −0.584422 0.819591i
\(298\) 5.77729 24.0671i 0.334669 1.39417i
\(299\) 46.5159 2.69008
\(300\) −4.52956 + 16.7104i −0.261514 + 0.964774i
\(301\) −0.979051 −0.0564316
\(302\) 4.86322 20.2593i 0.279847 1.16579i
\(303\) −32.0198 + 6.70706i −1.83949 + 0.385310i
\(304\) −9.72270 + 7.06563i −0.557635 + 0.405242i
\(305\) 0.277339i 0.0158804i
\(306\) 0.0346562 + 0.193336i 0.00198116 + 0.0110523i
\(307\) 17.9892i 1.02670i −0.858181 0.513348i \(-0.828405\pi\)
0.858181 0.513348i \(-0.171595\pi\)
\(308\) −8.55353 + 16.7896i −0.487383 + 0.956676i
\(309\) 24.3862 5.10807i 1.38728 0.290588i
\(310\) 0.115212 + 0.0276566i 0.00654361 + 0.00157079i
\(311\) −26.8825 −1.52436 −0.762182 0.647363i \(-0.775872\pi\)
−0.762182 + 0.647363i \(0.775872\pi\)
\(312\) −12.4990 + 22.8633i −0.707615 + 1.29438i
\(313\) −14.6195 −0.826344 −0.413172 0.910653i \(-0.635579\pi\)
−0.413172 + 0.910653i \(0.635579\pi\)
\(314\) −16.9454 4.06773i −0.956285 0.229555i
\(315\) 0.351524 0.154022i 0.0198062 0.00867818i
\(316\) −13.8952 + 27.2747i −0.781666 + 1.53432i
\(317\) 16.4279i 0.922683i 0.887223 + 0.461341i \(0.152632\pi\)
−0.887223 + 0.461341i \(0.847368\pi\)
\(318\) −7.08590 0.206335i −0.397358 0.0115707i
\(319\) 11.1435i 0.623914i
\(320\) −0.358188 + 0.0567936i −0.0200233 + 0.00317486i
\(321\) −0.234259 1.11836i −0.0130751 0.0624210i
\(322\) −8.14689 + 33.9385i −0.454008 + 1.89132i
\(323\) −0.139107 −0.00774013
\(324\) 16.8793 6.25222i 0.937737 0.347346i
\(325\) −26.5831 −1.47457
\(326\) −6.95313 + 28.9655i −0.385098 + 1.60425i
\(327\) 4.05216 + 19.3452i 0.224085 + 1.06979i
\(328\) −7.48240 + 8.76227i −0.413147 + 0.483815i
\(329\) 1.29050i 0.0711476i
\(330\) 0.370566 + 0.0107905i 0.0203990 + 0.000593998i
\(331\) 18.0323i 0.991146i −0.868566 0.495573i \(-0.834958\pi\)
0.868566 0.495573i \(-0.165042\pi\)
\(332\) −25.4540 12.9676i −1.39697 0.711691i
\(333\) −1.45176 + 0.636097i −0.0795559 + 0.0348579i
\(334\) −29.9097 7.17978i −1.63658 0.392860i
\(335\) 0.0453328 0.00247680
\(336\) −14.4922 13.1237i −0.790614 0.715957i
\(337\) 21.9123 1.19364 0.596821 0.802375i \(-0.296430\pi\)
0.596821 + 0.802375i \(0.296430\pi\)
\(338\) −21.0257 5.04719i −1.14365 0.274531i
\(339\) −16.2551 + 3.40488i −0.882855 + 0.184928i
\(340\) −0.00374008 0.00190540i −0.000202834 0.000103335i
\(341\) 6.17017i 0.334133i
\(342\) 2.24926 + 12.5480i 0.121626 + 0.678516i
\(343\) 17.0345i 0.919779i
\(344\) 0.637229 0.746228i 0.0343571 0.0402339i
\(345\) 0.672103 0.140782i 0.0361848 0.00757947i
\(346\) −8.54614 + 35.6016i −0.459443 + 1.91396i
\(347\) −8.77121 −0.470863 −0.235432 0.971891i \(-0.575650\pi\)
−0.235432 + 0.971891i \(0.575650\pi\)
\(348\) −11.1597 3.02499i −0.598225 0.162156i
\(349\) −24.2036 −1.29559 −0.647794 0.761815i \(-0.724308\pi\)
−0.647794 + 0.761815i \(0.724308\pi\)
\(350\) 4.65582 19.3953i 0.248864 1.03672i
\(351\) 16.0457 + 22.5024i 0.856456 + 1.20109i
\(352\) −7.22975 17.4472i −0.385347 0.929939i
\(353\) 30.4426i 1.62030i 0.586225 + 0.810148i \(0.300613\pi\)
−0.586225 + 0.810148i \(0.699387\pi\)
\(354\) −0.0161675 + 0.555221i −0.000859293 + 0.0295097i
\(355\) 0.325700i 0.0172863i
\(356\) 0.635133 1.24669i 0.0336620 0.0660746i
\(357\) −0.0463927 0.221481i −0.00245536 0.0117220i
\(358\) −2.57998 0.619322i −0.136356 0.0327322i
\(359\) 17.3593 0.916188 0.458094 0.888904i \(-0.348532\pi\)
0.458094 + 0.888904i \(0.348532\pi\)
\(360\) −0.111400 + 0.368178i −0.00587127 + 0.0194047i
\(361\) 9.97163 0.524823
\(362\) −14.9486 3.58840i −0.785681 0.188602i
\(363\) 0.0518679 + 0.247620i 0.00272236 + 0.0129967i
\(364\) 13.6270 26.7482i 0.714247 1.40198i
\(365\) 0.226756i 0.0118690i
\(366\) −0.436182 + 14.9793i −0.0227996 + 0.782978i
\(367\) 20.2091i 1.05491i 0.849584 + 0.527453i \(0.176853\pi\)
−0.849584 + 0.527453i \(0.823147\pi\)
\(368\) −20.5652 28.2988i −1.07203 1.47518i
\(369\) 4.90467 + 11.1939i 0.255327 + 0.582731i
\(370\) 0.00790624 0.0329360i 0.000411026 0.00171226i
\(371\) 8.16694 0.424007
\(372\) −6.17918 1.67494i −0.320376 0.0868418i
\(373\) −9.05088 −0.468637 −0.234318 0.972160i \(-0.575286\pi\)
−0.234318 + 0.972160i \(0.575286\pi\)
\(374\) 0.0510217 0.212547i 0.00263827 0.0109905i
\(375\) −0.768351 + 0.160943i −0.0396775 + 0.00831107i
\(376\) 0.983613 + 0.839941i 0.0507260 + 0.0433166i
\(377\) 17.7531i 0.914331i
\(378\) −19.2283 + 7.76599i −0.988996 + 0.399439i
\(379\) 21.7509i 1.11727i 0.829415 + 0.558634i \(0.188674\pi\)
−0.829415 + 0.558634i \(0.811326\pi\)
\(380\) −0.242740 0.123665i −0.0124523 0.00634387i
\(381\) −11.7456 + 2.46031i −0.601747 + 0.126045i
\(382\) 5.50347 + 1.32110i 0.281582 + 0.0675934i
\(383\) 14.9683 0.764845 0.382423 0.923987i \(-0.375090\pi\)
0.382423 + 0.923987i \(0.375090\pi\)
\(384\) 19.4353 2.50412i 0.991802 0.127788i
\(385\) −0.427100 −0.0217670
\(386\) −26.2775 6.30789i −1.33749 0.321063i
\(387\) −0.417700 0.953314i −0.0212329 0.0484597i
\(388\) 5.18148 + 2.63973i 0.263050 + 0.134012i
\(389\) 26.1553i 1.32613i −0.748564 0.663063i \(-0.769256\pi\)
0.748564 0.663063i \(-0.230744\pi\)
\(390\) −0.590363 0.0171908i −0.0298942 0.000870490i
\(391\) 0.404885i 0.0204759i
\(392\) 2.07272 + 1.76996i 0.104688 + 0.0893966i
\(393\) 0.295655 + 1.41147i 0.0149138 + 0.0711993i
\(394\) 1.05223 4.38339i 0.0530105 0.220832i
\(395\) −0.693823 −0.0349100
\(396\) −19.9975 1.16560i −1.00491 0.0585738i
\(397\) −21.6228 −1.08522 −0.542610 0.839985i \(-0.682564\pi\)
−0.542610 + 0.839985i \(0.682564\pi\)
\(398\) −5.78944 + 24.1177i −0.290198 + 1.20891i
\(399\) −3.01099 14.3746i −0.150738 0.719632i
\(400\) 11.7527 + 16.1724i 0.587635 + 0.808618i
\(401\) 30.4479i 1.52050i 0.649633 + 0.760248i \(0.274923\pi\)
−0.649633 + 0.760248i \(0.725077\pi\)
\(402\) −2.44845 0.0712965i −0.122118 0.00355595i
\(403\) 9.82994i 0.489664i
\(404\) −17.1479 + 33.6594i −0.853141 + 1.67462i
\(405\) 0.299947 + 0.276572i 0.0149045 + 0.0137430i
\(406\) 12.9528 + 3.10932i 0.642839 + 0.154313i
\(407\) 1.76388 0.0874322
\(408\) 0.199007 + 0.108794i 0.00985232 + 0.00538610i
\(409\) −9.38435 −0.464026 −0.232013 0.972713i \(-0.574531\pi\)
−0.232013 + 0.972713i \(0.574531\pi\)
\(410\) −0.253955 0.0609617i −0.0125420 0.00301068i
\(411\) −8.34506 + 1.74800i −0.411631 + 0.0862227i
\(412\) 13.0598 25.6349i 0.643410 1.26294i
\(413\) 0.639927i 0.0314888i
\(414\) −36.5221 + 6.54670i −1.79496 + 0.321753i
\(415\) 0.647508i 0.0317849i
\(416\) 11.5180 + 27.7958i 0.564717 + 1.36280i
\(417\) −10.6960 + 2.24044i −0.523784 + 0.109715i
\(418\) 3.31142 13.7948i 0.161967 0.674725i
\(419\) 14.5317 0.709920 0.354960 0.934881i \(-0.384494\pi\)
0.354960 + 0.934881i \(0.384494\pi\)
\(420\) 0.115940 0.427724i 0.00565729 0.0208708i
\(421\) 7.75853 0.378127 0.189064 0.981965i \(-0.439455\pi\)
0.189064 + 0.981965i \(0.439455\pi\)
\(422\) 1.05644 4.40095i 0.0514268 0.214235i
\(423\) 1.25658 0.550576i 0.0610969 0.0267699i
\(424\) −5.31557 + 6.22480i −0.258147 + 0.302303i
\(425\) 0.231385i 0.0112238i
\(426\) −0.512239 + 17.5912i −0.0248181 + 0.852297i
\(427\) 17.2645i 0.835489i
\(428\) −1.17563 0.598929i −0.0568262 0.0289503i
\(429\) −6.30557 30.1031i −0.304436 1.45339i
\(430\) 0.0216278 + 0.00519172i 0.00104298 + 0.000250367i
\(431\) −24.2429 −1.16774 −0.583869 0.811848i \(-0.698462\pi\)
−0.583869 + 0.811848i \(0.698462\pi\)
\(432\) 6.59580 19.7103i 0.317340 0.948312i
\(433\) 30.8720 1.48361 0.741806 0.670614i \(-0.233969\pi\)
0.741806 + 0.670614i \(0.233969\pi\)
\(434\) 7.17202 + 1.72164i 0.344268 + 0.0826412i
\(435\) −0.0537306 0.256513i −0.00257618 0.0122988i
\(436\) 20.3358 + 10.3602i 0.973907 + 0.496161i
\(437\) 26.2779i 1.25704i
\(438\) −0.356627 + 12.2472i −0.0170403 + 0.585195i
\(439\) 36.8150i 1.75708i −0.477665 0.878542i \(-0.658517\pi\)
0.477665 0.878542i \(-0.341483\pi\)
\(440\) 0.277984 0.325533i 0.0132524 0.0155192i
\(441\) 2.64792 1.16020i 0.126091 0.0552477i
\(442\) −0.0812846 + 0.338617i −0.00386631 + 0.0161064i
\(443\) −20.0252 −0.951425 −0.475712 0.879601i \(-0.657810\pi\)
−0.475712 + 0.879601i \(0.657810\pi\)
\(444\) −0.478820 + 1.76646i −0.0227238 + 0.0838323i
\(445\) 0.0317139 0.00150338
\(446\) 7.81207 32.5436i 0.369912 1.54099i
\(447\) −29.6696 + 6.21476i −1.40332 + 0.293948i
\(448\) −22.2974 + 3.53543i −1.05345 + 0.167034i
\(449\) 19.0841i 0.900634i −0.892869 0.450317i \(-0.851311\pi\)
0.892869 0.450317i \(-0.148689\pi\)
\(450\) 20.8718 3.74134i 0.983907 0.176369i
\(451\) 13.6005i 0.640424i
\(452\) −8.70526 + 17.0874i −0.409461 + 0.803724i
\(453\) −24.9753 + 5.23148i −1.17344 + 0.245796i
\(454\) −35.3499 8.48570i −1.65905 0.398253i
\(455\) 0.680430 0.0318991
\(456\) 12.9160 + 7.06097i 0.604848 + 0.330660i
\(457\) −14.3677 −0.672092 −0.336046 0.941846i \(-0.609090\pi\)
−0.336046 + 0.941846i \(0.609090\pi\)
\(458\) 16.4170 + 3.94087i 0.767114 + 0.184145i
\(459\) 0.195866 0.139665i 0.00914224 0.00651902i
\(460\) 0.359938 0.706517i 0.0167822 0.0329415i
\(461\) 24.9347i 1.16132i −0.814145 0.580661i \(-0.802794\pi\)
0.814145 0.580661i \(-0.197206\pi\)
\(462\) 23.0679 + 0.671715i 1.07322 + 0.0312510i
\(463\) 15.6605i 0.727807i 0.931437 + 0.363904i \(0.118556\pi\)
−0.931437 + 0.363904i \(0.881444\pi\)
\(464\) −10.8004 + 7.84885i −0.501398 + 0.364374i
\(465\) −0.0297508 0.142032i −0.00137966 0.00658656i
\(466\) 5.88373 24.5106i 0.272559 1.13543i
\(467\) −0.0672601 −0.00311243 −0.00155621 0.999999i \(-0.500495\pi\)
−0.00155621 + 0.999999i \(0.500495\pi\)
\(468\) 31.8588 + 1.85697i 1.47267 + 0.0858384i
\(469\) 2.82199 0.130308
\(470\) −0.00684328 + 0.0285079i −0.000315657 + 0.00131497i
\(471\) 4.37574 + 20.8900i 0.201624 + 0.962561i
\(472\) 0.487749 + 0.416506i 0.0224505 + 0.0191712i
\(473\) 1.15827i 0.0532574i
\(474\) 37.4738 + 1.09120i 1.72123 + 0.0501205i
\(475\) 15.0174i 0.689048i
\(476\) −0.232822 0.118612i −0.0106714 0.00543658i
\(477\) 3.48433 + 7.95225i 0.159536 + 0.364109i
\(478\) −30.6270 7.35197i −1.40085 0.336271i
\(479\) 10.4537 0.477640 0.238820 0.971064i \(-0.423239\pi\)
0.238820 + 0.971064i \(0.423239\pi\)
\(480\) 0.250548 + 0.366759i 0.0114359 + 0.0167402i
\(481\) −2.81011 −0.128130
\(482\) −26.6340 6.39346i −1.21315 0.291214i
\(483\) 41.8388 8.76379i 1.90373 0.398766i
\(484\) 0.260299 + 0.132611i 0.0118318 + 0.00602776i
\(485\) 0.131808i 0.00598511i
\(486\) −15.7653 15.4095i −0.715131 0.698991i
\(487\) 23.8327i 1.07996i 0.841677 + 0.539982i \(0.181569\pi\)
−0.841677 + 0.539982i \(0.818431\pi\)
\(488\) 13.1589 + 11.2369i 0.595677 + 0.508669i
\(489\) 35.7082 7.47964i 1.61478 0.338241i
\(490\) −0.0144205 + 0.0600731i −0.000651451 + 0.00271383i
\(491\) −29.4130 −1.32739 −0.663694 0.748004i \(-0.731012\pi\)
−0.663694 + 0.748004i \(0.731012\pi\)
\(492\) 13.6204 + 3.69198i 0.614054 + 0.166447i
\(493\) −0.154527 −0.00695954
\(494\) −5.27556 + 21.9770i −0.237359 + 0.988793i
\(495\) −0.182217 0.415873i −0.00819005 0.0186921i
\(496\) −5.98023 + 4.34593i −0.268520 + 0.195138i
\(497\) 20.2750i 0.909457i
\(498\) −1.01836 + 34.9723i −0.0456337 + 1.56714i
\(499\) 39.5774i 1.77173i −0.463946 0.885864i \(-0.653567\pi\)
0.463946 0.885864i \(-0.346433\pi\)
\(500\) −0.411483 + 0.807694i −0.0184021 + 0.0361212i
\(501\) 7.72344 + 36.8721i 0.345058 + 1.64732i
\(502\) 16.7037 + 4.00970i 0.745522 + 0.178962i
\(503\) −6.34209 −0.282780 −0.141390 0.989954i \(-0.545157\pi\)
−0.141390 + 0.989954i \(0.545157\pi\)
\(504\) −6.93468 + 22.9193i −0.308895 + 1.02091i
\(505\) −0.856240 −0.0381022
\(506\) 40.1511 + 9.63822i 1.78493 + 0.428471i
\(507\) 5.42937 + 25.9201i 0.241127 + 1.15115i
\(508\) −6.29026 + 12.3471i −0.279085 + 0.547812i
\(509\) 27.5700i 1.22202i −0.791623 0.611009i \(-0.790764\pi\)
0.791623 0.611009i \(-0.209236\pi\)
\(510\) −0.000149632 0.00513865i −6.62584e−6 0.000227543i
\(511\) 14.1157i 0.624441i
\(512\) 11.8179 19.2960i 0.522282 0.852773i
\(513\) 12.7122 9.06460i 0.561255 0.400212i
\(514\) 7.39548 30.8082i 0.326201 1.35889i
\(515\) 0.652109 0.0287354
\(516\) −1.15996 0.314423i −0.0510645 0.0138417i
\(517\) −1.52673 −0.0671456
\(518\) 0.492168 2.05028i 0.0216246 0.0900842i
\(519\) 43.8891 9.19326i 1.92652 0.403539i
\(520\) −0.442867 + 0.518620i −0.0194210 + 0.0227430i
\(521\) 27.0474i 1.18497i −0.805581 0.592485i \(-0.798147\pi\)
0.805581 0.592485i \(-0.201853\pi\)
\(522\) 2.49859 + 13.9389i 0.109360 + 0.610089i
\(523\) 5.32931i 0.233035i 0.993189 + 0.116517i \(0.0371730\pi\)
−0.993189 + 0.116517i \(0.962827\pi\)
\(524\) 1.48375 + 0.755901i 0.0648177 + 0.0330217i
\(525\) −23.9102 + 5.00837i −1.04353 + 0.218583i
\(526\) −36.0917 8.66378i −1.57367 0.377759i
\(527\) −0.0855620 −0.00372714
\(528\) −15.5261 + 17.1450i −0.675685 + 0.746142i
\(529\) 53.4845 2.32541
\(530\) −0.180412 0.0433077i −0.00783660 0.00188117i
\(531\) 0.623105 0.273017i 0.0270405 0.0118479i
\(532\) −15.1107 7.69820i −0.655131 0.333759i
\(533\) 21.6675i 0.938525i
\(534\) −1.71288 0.0498775i −0.0741237 0.00215841i
\(535\) 0.0299061i 0.00129295i
\(536\) −1.83673 + 2.15091i −0.0793348 + 0.0929051i
\(537\) 0.666218 + 3.18056i 0.0287494 + 0.137251i
\(538\) −5.31271 + 22.1318i −0.229047 + 0.954170i
\(539\) −3.21721 −0.138575
\(540\) 0.465944 0.0695910i 0.0200511 0.00299472i
\(541\) −18.5591 −0.797920 −0.398960 0.916968i \(-0.630629\pi\)
−0.398960 + 0.916968i \(0.630629\pi\)
\(542\) 4.45267 18.5490i 0.191259 0.796749i
\(543\) 3.86012 + 18.4284i 0.165653 + 0.790838i
\(544\) 0.241941 0.100255i 0.0103731 0.00429841i
\(545\) 0.517309i 0.0221591i
\(546\) −36.7504 1.07014i −1.57277 0.0457976i
\(547\) 16.1107i 0.688845i 0.938815 + 0.344423i \(0.111925\pi\)
−0.938815 + 0.344423i \(0.888075\pi\)
\(548\) −4.46912 + 8.77236i −0.190911 + 0.374737i
\(549\) 16.8107 7.36570i 0.717463 0.314360i
\(550\) −22.9457 5.50810i −0.978409 0.234866i
\(551\) −10.0292 −0.427256
\(552\) −20.5516 + 37.5933i −0.874736 + 1.60008i
\(553\) −43.1909 −1.83666
\(554\) 18.6897 + 4.48645i 0.794051 + 0.190611i
\(555\) −0.0406029 + 0.00850491i −0.00172350 + 0.000361014i
\(556\) −5.72813 + 11.2437i −0.242927 + 0.476837i
\(557\) 0.882960i 0.0374122i 0.999825 + 0.0187061i \(0.00595469\pi\)
−0.999825 + 0.0187061i \(0.994045\pi\)
\(558\) 1.38348 + 7.71800i 0.0585673 + 0.326729i
\(559\) 1.84529i 0.0780473i
\(560\) −0.300826 0.413953i −0.0127122 0.0174927i
\(561\) −0.262024 + 0.0548851i −0.0110627 + 0.00231725i
\(562\) 4.70908 19.6172i 0.198640 0.827500i
\(563\) 4.74187 0.199846 0.0999230 0.994995i \(-0.468140\pi\)
0.0999230 + 0.994995i \(0.468140\pi\)
\(564\) 0.414445 1.52896i 0.0174513 0.0643810i
\(565\) −0.434676 −0.0182870
\(566\) 0.678753 2.82756i 0.0285301 0.118851i
\(567\) 18.6719 + 17.2167i 0.784145 + 0.723035i
\(568\) 15.4535 + 13.1963i 0.648414 + 0.553702i
\(569\) 29.6251i 1.24195i −0.783830 0.620975i \(-0.786737\pi\)
0.783830 0.620975i \(-0.213263\pi\)
\(570\) −0.00971149 + 0.333510i −0.000406770 + 0.0139692i
\(571\) 7.09982i 0.297118i −0.988904 0.148559i \(-0.952536\pi\)
0.988904 0.148559i \(-0.0474635\pi\)
\(572\) −31.6445 16.1214i −1.32312 0.674072i
\(573\) −1.42114 6.78458i −0.0593689 0.283430i
\(574\) −15.8088 3.79490i −0.659849 0.158396i
\(575\) −43.7097 −1.82282
\(576\) −12.9554 20.2029i −0.539809 0.841788i
\(577\) −45.0273 −1.87451 −0.937256 0.348641i \(-0.886643\pi\)
−0.937256 + 0.348641i \(0.886643\pi\)
\(578\) −23.3746 5.61104i −0.972254 0.233388i
\(579\) 6.78553 + 32.3945i 0.281997 + 1.34627i
\(580\) −0.269647 0.137373i −0.0111965 0.00570410i
\(581\) 40.3077i 1.67225i
\(582\) 0.207300 7.11905i 0.00859285 0.295094i
\(583\) 9.66194i 0.400157i
\(584\) 10.7589 + 9.18740i 0.445207 + 0.380177i
\(585\) 0.290297 + 0.662543i 0.0120023 + 0.0273928i
\(586\) 10.0946 42.0521i 0.417003 1.73716i
\(587\) 34.7911 1.43598 0.717990 0.696053i \(-0.245062\pi\)
0.717990 + 0.696053i \(0.245062\pi\)
\(588\) 0.873338 3.22190i 0.0360158 0.132869i
\(589\) −5.55317 −0.228814
\(590\) −0.00339341 + 0.0141363i −0.000139705 + 0.000581984i
\(591\) −5.40377 + 1.13190i −0.222281 + 0.0465603i
\(592\) 1.24238 + 1.70958i 0.0510615 + 0.0702634i
\(593\) 22.8534i 0.938475i −0.883072 0.469237i \(-0.844529\pi\)
0.883072 0.469237i \(-0.155471\pi\)
\(594\) 9.18759 + 22.7481i 0.376971 + 0.933366i
\(595\) 0.00592261i 0.000242803i
\(596\) −15.8893 + 31.1888i −0.650850 + 1.27754i
\(597\) 29.7319 6.22782i 1.21685 0.254888i
\(598\) −63.9662 15.3550i −2.61577 0.627914i
\(599\) 27.3056 1.11568 0.557838 0.829950i \(-0.311631\pi\)
0.557838 + 0.829950i \(0.311631\pi\)
\(600\) 11.7450 21.4840i 0.479486 0.877081i
\(601\) 35.2624 1.43838 0.719192 0.694812i \(-0.244512\pi\)
0.719192 + 0.694812i \(0.244512\pi\)
\(602\) 1.34634 + 0.323188i 0.0548727 + 0.0131721i
\(603\) 1.20397 + 2.74781i 0.0490294 + 0.111899i
\(604\) −13.3753 + 26.2542i −0.544234 + 1.06827i
\(605\) 0.00662160i 0.000269206i
\(606\) 46.2460 + 1.34664i 1.87862 + 0.0547035i
\(607\) 23.8874i 0.969560i −0.874636 0.484780i \(-0.838900\pi\)
0.874636 0.484780i \(-0.161100\pi\)
\(608\) 15.7025 6.50680i 0.636822 0.263886i
\(609\) −3.34476 15.9680i −0.135536 0.647058i
\(610\) −0.0915505 + 0.381383i −0.00370677 + 0.0154417i
\(611\) 2.43230 0.0984003
\(612\) 0.0161635 0.277306i 0.000653370 0.0112094i
\(613\) −32.2630 −1.30309 −0.651545 0.758610i \(-0.725879\pi\)
−0.651545 + 0.758610i \(0.725879\pi\)
\(614\) −5.93827 + 24.7377i −0.239649 + 0.998334i
\(615\) 0.0655778 + 0.313072i 0.00264435 + 0.0126243i
\(616\) 17.3047 20.2646i 0.697225 0.816485i
\(617\) 42.1094i 1.69526i 0.530587 + 0.847630i \(0.321971\pi\)
−0.530587 + 0.847630i \(0.678029\pi\)
\(618\) −35.2208 1.02560i −1.41679 0.0412555i
\(619\) 8.85623i 0.355962i −0.984034 0.177981i \(-0.943043\pi\)
0.984034 0.177981i \(-0.0569566\pi\)
\(620\) −0.149304 0.0760637i −0.00599621 0.00305479i
\(621\) 26.3834 + 37.0000i 1.05873 + 1.48476i
\(622\) 36.9673 + 8.87397i 1.48226 + 0.355814i
\(623\) 1.97420 0.0790948
\(624\) 24.7352 27.3145i 0.990200 1.09345i
\(625\) 24.9692 0.998767
\(626\) 20.1040 + 4.82594i 0.803518 + 0.192884i
\(627\) −17.0060 + 3.56217i −0.679153 + 0.142259i
\(628\) 21.9597 + 11.1875i 0.876287 + 0.446428i
\(629\) 0.0244598i 0.000975275i
\(630\) −0.534241 + 0.0957645i −0.0212847 + 0.00381535i
\(631\) 45.1892i 1.79895i −0.436970 0.899476i \(-0.643949\pi\)
0.436970 0.899476i \(-0.356051\pi\)
\(632\) 28.1114 32.9199i 1.11821 1.30948i
\(633\) −5.42541 + 1.13644i −0.215641 + 0.0451694i
\(634\) 5.42290 22.5908i 0.215371 0.897195i
\(635\) −0.314089 −0.0124642
\(636\) 9.67605 + 2.62282i 0.383680 + 0.104001i
\(637\) 5.12546 0.203078
\(638\) 3.67849 15.3239i 0.145633 0.606680i
\(639\) 19.7420 8.65007i 0.780981 0.342191i
\(640\) 0.511309 + 0.0401392i 0.0202113 + 0.00158664i
\(641\) 15.8749i 0.627021i 0.949585 + 0.313510i \(0.101505\pi\)
−0.949585 + 0.313510i \(0.898495\pi\)
\(642\) −0.0470344 + 1.61525i −0.00185630 + 0.0637487i
\(643\) 11.1940i 0.441449i 0.975336 + 0.220725i \(0.0708422\pi\)
−0.975336 + 0.220725i \(0.929158\pi\)
\(644\) 22.4064 43.9811i 0.882934 1.73310i
\(645\) −0.00558485 0.0266624i −0.000219903 0.00104983i
\(646\) 0.191293 + 0.0459196i 0.00752632 + 0.00180668i
\(647\) 9.10556 0.357977 0.178988 0.983851i \(-0.442718\pi\)
0.178988 + 0.983851i \(0.442718\pi\)
\(648\) −25.2754 + 3.02584i −0.992910 + 0.118866i
\(649\) −0.757069 −0.0297176
\(650\) 36.5557 + 8.77516i 1.43383 + 0.344190i
\(651\) −1.85200 8.84155i −0.0725856 0.346528i
\(652\) 19.1232 37.5366i 0.748921 1.47005i
\(653\) 23.2914i 0.911461i 0.890118 + 0.455731i \(0.150622\pi\)
−0.890118 + 0.455731i \(0.849378\pi\)
\(654\) 0.813591 27.9402i 0.0318139 1.09255i
\(655\) 0.0377441i 0.00147478i
\(656\) 13.1819 9.57946i 0.514665 0.374015i
\(657\) 13.7446 6.02229i 0.536229 0.234952i
\(658\) −0.425998 + 1.77463i −0.0166071 + 0.0691823i
\(659\) −31.9785 −1.24571 −0.622853 0.782339i \(-0.714026\pi\)
−0.622853 + 0.782339i \(0.714026\pi\)
\(660\) −0.506021 0.137163i −0.0196968 0.00533908i
\(661\) 0.528143 0.0205424 0.0102712 0.999947i \(-0.496731\pi\)
0.0102712 + 0.999947i \(0.496731\pi\)
\(662\) −5.95252 + 24.7971i −0.231351 + 0.963767i
\(663\) 0.417441 0.0874396i 0.0162121 0.00339587i
\(664\) 30.7223 + 26.2348i 1.19226 + 1.01811i
\(665\) 0.384391i 0.0149061i
\(666\) 2.20636 0.395498i 0.0854948 0.0153252i
\(667\) 29.1908i 1.13027i
\(668\) 38.7601 + 19.7465i 1.49967 + 0.764016i
\(669\) −40.1193 + 8.40361i −1.55110 + 0.324902i
\(670\) −0.0623394 0.0149645i −0.00240838 0.000578129i
\(671\) −20.4249 −0.788494
\(672\) 15.5967 + 22.8309i 0.601657 + 0.880723i
\(673\) 14.1935 0.547121 0.273561 0.961855i \(-0.411799\pi\)
0.273561 + 0.961855i \(0.411799\pi\)
\(674\) −30.1327 7.23333i −1.16067 0.278617i
\(675\) −15.0777 21.1449i −0.580342 0.813868i
\(676\) 27.2473 + 13.8813i 1.04797 + 0.533895i
\(677\) 5.83261i 0.224165i 0.993699 + 0.112083i \(0.0357521\pi\)
−0.993699 + 0.112083i \(0.964248\pi\)
\(678\) 23.4771 + 0.683631i 0.901633 + 0.0262547i
\(679\) 8.20515i 0.314885i
\(680\) 0.00451418 + 0.00385482i 0.000173111 + 0.000147825i
\(681\) 9.12825 + 43.5787i 0.349795 + 1.66994i
\(682\) 2.03679 8.48489i 0.0779927 0.324903i
\(683\) 20.2308 0.774110 0.387055 0.922057i \(-0.373492\pi\)
0.387055 + 0.922057i \(0.373492\pi\)
\(684\) 1.04905 17.9978i 0.0401113 0.688163i
\(685\) −0.223155 −0.00852630
\(686\) 5.62315 23.4250i 0.214693 0.894372i
\(687\) −4.23928 20.2385i −0.161739 0.772149i
\(688\) −1.12262 + 0.815822i −0.0427994 + 0.0311029i
\(689\) 15.3928i 0.586420i
\(690\) −0.970714 0.0282662i −0.0369544 0.00107608i
\(691\) 27.2492i 1.03661i 0.855196 + 0.518305i \(0.173437\pi\)
−0.855196 + 0.518305i \(0.826563\pi\)
\(692\) 23.5044 46.1364i 0.893503 1.75384i
\(693\) −11.3431 25.8883i −0.430889 0.983415i
\(694\) 12.0617 + 2.89540i 0.457856 + 0.109908i
\(695\) −0.286020 −0.0108494
\(696\) 14.3477 + 7.84367i 0.543850 + 0.297314i
\(697\) 0.188599 0.00714370
\(698\) 33.2835 + 7.98967i 1.25980 + 0.302413i
\(699\) −30.2162 + 6.32926i −1.14288 + 0.239395i
\(700\) −12.8049 + 25.1345i −0.483980 + 0.949996i
\(701\) 1.36934i 0.0517193i −0.999666 0.0258596i \(-0.991768\pi\)
0.999666 0.0258596i \(-0.00823230\pi\)
\(702\) −14.6371 36.2409i −0.552442 1.36782i
\(703\) 1.58750i 0.0598735i
\(704\) 4.18261 + 26.3790i 0.157638 + 0.994198i
\(705\) 0.0351440 0.00736147i 0.00132360 0.000277249i
\(706\) 10.0492 41.8631i 0.378206 1.57554i
\(707\) −53.3014 −2.00461
\(708\) 0.205513 0.758175i 0.00772364 0.0284939i
\(709\) −9.08190 −0.341078 −0.170539 0.985351i \(-0.554551\pi\)
−0.170539 + 0.985351i \(0.554551\pi\)
\(710\) −0.107514 + 0.447885i −0.00403494 + 0.0168088i
\(711\) −18.4269 42.0555i −0.691061 1.57720i
\(712\) −1.28494 + 1.50473i −0.0481551 + 0.0563921i
\(713\) 16.1630i 0.605310i
\(714\) −0.00931470 + 0.319884i −0.000348594 + 0.0119713i
\(715\) 0.804986i 0.0301048i
\(716\) 3.34342 + 1.70332i 0.124949 + 0.0636560i
\(717\) 7.90868 + 37.7564i 0.295355 + 1.41004i
\(718\) −23.8716 5.73035i −0.890880 0.213855i
\(719\) −3.80251 −0.141810 −0.0709048 0.997483i \(-0.522589\pi\)
−0.0709048 + 0.997483i \(0.522589\pi\)
\(720\) 0.274727 0.469526i 0.0102385 0.0174982i
\(721\) 40.5942 1.51181
\(722\) −13.7125 3.29166i −0.510325 0.122503i
\(723\) 6.87759 + 32.8340i 0.255780 + 1.22111i
\(724\) 19.3720 + 9.86915i 0.719955 + 0.366784i
\(725\) 16.6821i 0.619558i
\(726\) 0.0104140 0.357636i 0.000386500 0.0132731i
\(727\) 7.17785i 0.266212i −0.991102 0.133106i \(-0.957505\pi\)
0.991102 0.133106i \(-0.0424950\pi\)
\(728\) −27.5687 + 32.2844i −1.02177 + 1.19654i
\(729\) −8.79803 + 25.5264i −0.325853 + 0.945420i
\(730\) −0.0748528 + 0.311823i −0.00277043 + 0.0115411i
\(731\) −0.0160618 −0.000594067
\(732\) 5.54451 20.4547i 0.204931 0.756028i
\(733\) −2.44611 −0.0903492 −0.0451746 0.998979i \(-0.514384\pi\)
−0.0451746 + 0.998979i \(0.514384\pi\)
\(734\) 6.67107 27.7905i 0.246234 1.02576i
\(735\) 0.0740571 0.0155124i 0.00273164 0.000572185i
\(736\) 18.9387 + 45.7037i 0.698088 + 1.68466i
\(737\) 3.33857i 0.122978i
\(738\) −3.04951 17.0123i −0.112254 0.626232i
\(739\) 49.4937i 1.82065i 0.413890 + 0.910327i \(0.364170\pi\)
−0.413890 + 0.910327i \(0.635830\pi\)
\(740\) −0.0217445 + 0.0426819i −0.000799344 + 0.00156902i
\(741\) 27.0929 5.67503i 0.995283 0.208478i
\(742\) −11.2308 2.69593i −0.412294 0.0989707i
\(743\) −47.0335 −1.72549 −0.862746 0.505638i \(-0.831257\pi\)
−0.862746 + 0.505638i \(0.831257\pi\)
\(744\) 7.94438 + 4.34306i 0.291255 + 0.159224i
\(745\) −0.793392 −0.0290676
\(746\) 12.4463 + 2.98772i 0.455691 + 0.109388i
\(747\) 39.2481 17.1968i 1.43601 0.629198i
\(748\) −0.140325 + 0.275441i −0.00513078 + 0.0100711i
\(749\) 1.86167i 0.0680240i
\(750\) 1.10972 + 0.0323141i 0.0405214 + 0.00117994i
\(751\) 43.9718i 1.60455i −0.596952 0.802277i \(-0.703622\pi\)
0.596952 0.802277i \(-0.296378\pi\)
\(752\) −1.07535 1.47974i −0.0392139 0.0539604i
\(753\) −4.31332 20.5920i −0.157186 0.750415i
\(754\) −5.86035 + 24.4131i −0.213421 + 0.889074i
\(755\) −0.667864 −0.0243061
\(756\) 29.0053 4.33208i 1.05491 0.157556i
\(757\) 18.1609 0.660068 0.330034 0.943969i \(-0.392940\pi\)
0.330034 + 0.943969i \(0.392940\pi\)
\(758\) 7.18002 29.9107i 0.260790 1.08640i
\(759\) −10.3680 49.4975i −0.376336 1.79665i
\(760\) 0.292981 + 0.250186i 0.0106275 + 0.00907522i
\(761\) 33.2514i 1.20536i 0.797982 + 0.602681i \(0.205901\pi\)
−0.797982 + 0.602681i \(0.794099\pi\)
\(762\) 16.9641 + 0.493979i 0.614546 + 0.0178950i
\(763\) 32.2028i 1.16582i
\(764\) −7.13198 3.63342i −0.258026 0.131453i
\(765\) 0.00576692 0.00252681i 0.000208504 9.13570e-5i
\(766\) −20.5837 4.94108i −0.743718 0.178529i
\(767\) 1.20612 0.0435503
\(768\) −27.5530 2.97210i −0.994232 0.107246i
\(769\) −43.4416 −1.56655 −0.783273 0.621678i \(-0.786451\pi\)
−0.783273 + 0.621678i \(0.786451\pi\)
\(770\) 0.587326 + 0.140987i 0.0211658 + 0.00508082i
\(771\) −37.9799 + 7.95548i −1.36781 + 0.286510i
\(772\) 34.0532 + 17.3486i 1.22560 + 0.624388i
\(773\) 6.95049i 0.249992i −0.992157 0.124996i \(-0.960108\pi\)
0.992157 0.124996i \(-0.0398918\pi\)
\(774\) 0.259708 + 1.44883i 0.00933501 + 0.0520772i
\(775\) 9.23693i 0.331800i
\(776\) −6.25392 5.34044i −0.224503 0.191711i
\(777\) −2.52755 + 0.529436i −0.0906754 + 0.0189934i
\(778\) −8.63393 + 35.9674i −0.309541 + 1.28949i
\(779\) 12.2405 0.438562
\(780\) 0.806162 + 0.218520i 0.0288652 + 0.00782428i
\(781\) −23.9864 −0.858301
\(782\) −0.133654 + 0.556776i −0.00477944 + 0.0199103i
\(783\) 14.1213 10.0694i 0.504654 0.359851i
\(784\) −2.26602 3.11817i −0.0809294 0.111363i
\(785\) 0.558619i 0.0199380i
\(786\) 0.0593615 2.03858i 0.00211735 0.0727137i
\(787\) 6.96183i 0.248162i 0.992272 + 0.124081i \(0.0395983\pi\)
−0.992272 + 0.124081i \(0.960402\pi\)
\(788\) −2.89394 + 5.68047i −0.103092 + 0.202358i
\(789\) 9.31981 + 44.4933i 0.331794 + 1.58400i
\(790\) 0.954110 + 0.229033i 0.0339457 + 0.00814863i
\(791\) −27.0588 −0.962101
\(792\) 27.1147 + 8.20411i 0.963481 + 0.291520i
\(793\) 32.5397 1.15552
\(794\) 29.7346 + 7.13776i 1.05524 + 0.253310i
\(795\) 0.0465871 + 0.222409i 0.00165227 + 0.00788804i
\(796\) 15.9227 31.2543i 0.564364 1.10778i
\(797\) 39.3251i 1.39297i −0.717574 0.696483i \(-0.754747\pi\)
0.717574 0.696483i \(-0.245253\pi\)
\(798\) −0.604546 + 20.7612i −0.0214007 + 0.734938i
\(799\) 0.0211713i 0.000748986i
\(800\) −10.8232 26.1190i −0.382657 0.923446i
\(801\) 0.842270 + 1.92231i 0.0297602 + 0.0679214i
\(802\) 10.0509 41.8704i 0.354911 1.47849i
\(803\) −16.6996 −0.589317
\(804\) 3.34345 + 0.906284i 0.117914 + 0.0319622i
\(805\) 1.11881 0.0394328
\(806\) −3.24489 + 13.5176i −0.114296 + 0.476138i
\(807\) 27.2837 5.71500i 0.960432 0.201178i
\(808\) 34.6920 40.6261i 1.22046 1.42922i
\(809\) 1.17193i 0.0412029i −0.999788 0.0206014i \(-0.993442\pi\)
0.999788 0.0206014i \(-0.00655811\pi\)
\(810\) −0.321175 0.479341i −0.0112849 0.0168423i
\(811\) 18.4901i 0.649274i −0.945839 0.324637i \(-0.894758\pi\)
0.945839 0.324637i \(-0.105242\pi\)
\(812\) −16.7857 8.55154i −0.589062 0.300100i
\(813\) −22.8669 + 4.78984i −0.801978 + 0.167987i
\(814\) −2.42559 0.582261i −0.0850171 0.0204083i
\(815\) 0.954870 0.0334476
\(816\) −0.237751 0.215300i −0.00832295 0.00753702i
\(817\) −1.04245 −0.0364706
\(818\) 12.9049 + 3.09780i 0.451208 + 0.108312i
\(819\) 18.0712 + 41.2437i 0.631457 + 1.44117i
\(820\) 0.329102 + 0.167663i 0.0114928 + 0.00585503i
\(821\) 21.7270i 0.758278i 0.925340 + 0.379139i \(0.123780\pi\)
−0.925340 + 0.379139i \(0.876220\pi\)
\(822\) 12.0527 + 0.350963i 0.420387 + 0.0122413i
\(823\) 4.79475i 0.167135i −0.996502 0.0835673i \(-0.973369\pi\)
0.996502 0.0835673i \(-0.0266314\pi\)
\(824\) −26.4213 + 30.9407i −0.920429 + 1.07787i
\(825\) 5.92518 + 28.2871i 0.206288 + 0.984831i
\(826\) −0.211242 + 0.879995i −0.00735004 + 0.0306189i
\(827\) −54.0235 −1.87858 −0.939290 0.343124i \(-0.888515\pi\)
−0.939290 + 0.343124i \(0.888515\pi\)
\(828\) 52.3843 + 3.05335i 1.82048 + 0.106111i
\(829\) 2.34284 0.0813702 0.0406851 0.999172i \(-0.487046\pi\)
0.0406851 + 0.999172i \(0.487046\pi\)
\(830\) −0.213744 + 0.890419i −0.00741917 + 0.0309069i
\(831\) −4.82617 23.0404i −0.167418 0.799263i
\(832\) −6.66348 42.0255i −0.231015 1.45697i
\(833\) 0.0446131i 0.00154575i
\(834\) 15.4481 + 0.449834i 0.534925 + 0.0155765i
\(835\) 0.985995i 0.0341218i
\(836\) −9.10739 + 17.8768i −0.314986 + 0.618281i
\(837\) 7.81899 5.57545i 0.270264 0.192716i
\(838\) −19.9832 4.79696i −0.690310 0.165708i
\(839\) 16.2551 0.561190 0.280595 0.959826i \(-0.409468\pi\)
0.280595 + 0.959826i \(0.409468\pi\)
\(840\) −0.300627 + 0.549912i −0.0103726 + 0.0189738i
\(841\) 17.8591 0.615832
\(842\) −10.6691 2.56111i −0.367682 0.0882617i
\(843\) −24.1837 + 5.06566i −0.832931 + 0.174470i
\(844\) −2.90553 + 5.70322i −0.100012 + 0.196313i
\(845\) 0.693128i 0.0238443i
\(846\) −1.90973 + 0.342325i −0.0656577 + 0.0117694i
\(847\) 0.412198i 0.0141633i
\(848\) 9.36452 6.80534i 0.321579 0.233696i
\(849\) −3.48577 + 0.730149i −0.119631 + 0.0250587i
\(850\) 0.0763810 0.318189i 0.00261985 0.0109138i
\(851\) −4.62056 −0.158391
\(852\) 6.51131 24.0214i 0.223074 0.822961i
\(853\) 43.8622 1.50181 0.750906 0.660409i \(-0.229617\pi\)
0.750906 + 0.660409i \(0.229617\pi\)
\(854\) −5.69907 + 23.7413i −0.195018 + 0.812410i
\(855\) 0.374287 0.163996i 0.0128003 0.00560854i
\(856\) 1.41896 + 1.21170i 0.0484989 + 0.0414149i
\(857\) 4.50112i 0.153755i −0.997041 0.0768777i \(-0.975505\pi\)
0.997041 0.0768777i \(-0.0244951\pi\)
\(858\) −1.26603 + 43.4777i −0.0432215 + 1.48431i
\(859\) 4.27027i 0.145700i −0.997343 0.0728499i \(-0.976791\pi\)
0.997343 0.0728499i \(-0.0232094\pi\)
\(860\) −0.0280276 0.0142788i −0.000955733 0.000486902i
\(861\) 4.08225 + 19.4889i 0.139123 + 0.664179i
\(862\) 33.3375 + 8.00264i 1.13548 + 0.272571i
\(863\) 11.8273 0.402606 0.201303 0.979529i \(-0.435482\pi\)
0.201303 + 0.979529i \(0.435482\pi\)
\(864\) −15.5766 + 24.9273i −0.529927 + 0.848043i
\(865\) 1.17364 0.0399048
\(866\) −42.4535 10.1909i −1.44263 0.346302i
\(867\) 6.03592 + 28.8158i 0.204990 + 0.978635i
\(868\) −9.29427 4.73501i −0.315468 0.160717i
\(869\) 51.0972i 1.73335i
\(870\) −0.0107880 + 0.370479i −0.000365747 + 0.0125604i
\(871\) 5.31881i 0.180221i
\(872\) −24.5448 20.9596i −0.831192 0.709783i
\(873\) −7.98945 + 3.50063i −0.270402 + 0.118478i
\(874\) −8.67442 + 36.1361i −0.293417 + 1.22232i
\(875\) −1.27903 −0.0432390
\(876\) 4.53326 16.7240i 0.153165 0.565052i
\(877\) 37.0994 1.25276 0.626380 0.779518i \(-0.284536\pi\)
0.626380 + 0.779518i \(0.284536\pi\)
\(878\) −12.1527 + 50.6261i −0.410135 + 1.70855i
\(879\) −51.8411 + 10.8589i −1.74856 + 0.366263i
\(880\) −0.489729 + 0.355893i −0.0165088 + 0.0119972i
\(881\) 6.46201i 0.217711i 0.994058 + 0.108855i \(0.0347185\pi\)
−0.994058 + 0.108855i \(0.965281\pi\)
\(882\) −4.02427 + 0.721363i −0.135504 + 0.0242896i
\(883\) 18.6252i 0.626789i −0.949623 0.313395i \(-0.898534\pi\)
0.949623 0.313395i \(-0.101466\pi\)
\(884\) 0.223557 0.438816i 0.00751903 0.0147590i
\(885\) 0.0174270 0.00365037i 0.000585804 0.000122706i
\(886\) 27.5376 + 6.61037i 0.925143 + 0.222080i
\(887\) −3.54980 −0.119190 −0.0595952 0.998223i \(-0.518981\pi\)
−0.0595952 + 0.998223i \(0.518981\pi\)
\(888\) 1.24156 2.27108i 0.0416640 0.0762124i
\(889\) −19.5522 −0.655760
\(890\) −0.0436112 0.0104688i −0.00146185 0.000350916i
\(891\) 20.3684 22.0899i 0.682366 0.740038i
\(892\) −21.4855 + 42.1735i −0.719388 + 1.41207i
\(893\) 1.37406i 0.0459813i
\(894\) 42.8516 + 1.24780i 1.43317 + 0.0417325i
\(895\) 0.0850511i 0.00284294i
\(896\) 31.8293 + 2.49869i 1.06334 + 0.0834753i
\(897\) 16.5177 + 78.8565i 0.551511 + 2.63294i
\(898\) −6.29971 + 26.2435i −0.210224 + 0.875756i
\(899\) −6.16873 −0.205739
\(900\) −29.9369 1.74494i −0.997895 0.0581648i
\(901\) 0.133982 0.00446360
\(902\) −4.48957 + 18.7027i −0.149486 + 0.622733i
\(903\) −0.347660 1.65975i −0.0115694 0.0552329i
\(904\) 17.6116 20.6241i 0.585754 0.685947i
\(905\) 0.492792i 0.0163810i
\(906\) 36.0717 + 1.05037i 1.19840 + 0.0348963i
\(907\) 18.7682i 0.623187i −0.950216 0.311593i \(-0.899137\pi\)
0.950216 0.311593i \(-0.100863\pi\)
\(908\) 45.8101 + 23.3382i 1.52026 + 0.774505i
\(909\) −22.7404 51.9003i −0.754252 1.72142i
\(910\) −0.935692 0.224612i −0.0310179 0.00744581i
\(911\) −18.4902 −0.612609 −0.306305 0.951934i \(-0.599093\pi\)
−0.306305 + 0.951934i \(0.599093\pi\)
\(912\) −15.4306 13.9735i −0.510958 0.462709i
\(913\) −47.6862 −1.57818
\(914\) 19.7577 + 4.74282i 0.653527 + 0.156878i
\(915\) 0.470162 0.0984829i 0.0155431 0.00325574i
\(916\) −21.2749 10.8386i −0.702941 0.358116i
\(917\) 2.34959i 0.0775903i
\(918\) −0.315449 + 0.127405i −0.0104114 + 0.00420498i
\(919\) 47.1741i 1.55613i 0.628183 + 0.778065i \(0.283799\pi\)
−0.628183 + 0.778065i \(0.716201\pi\)
\(920\) −0.728192 + 0.852749i −0.0240078 + 0.0281143i
\(921\) 30.4963 6.38793i 1.00489 0.210489i
\(922\) −8.23100 + 34.2888i −0.271074 + 1.12924i
\(923\) 38.2137 1.25782
\(924\) −31.5001 8.53849i −1.03628 0.280896i
\(925\) 2.64058 0.0868218
\(926\) 5.16959 21.5356i 0.169883 0.707703i
\(927\) 17.3190 + 39.5270i 0.568831 + 1.29824i
\(928\) 17.4431 7.22807i 0.572599 0.237273i
\(929\) 60.1181i 1.97241i −0.165522 0.986206i \(-0.552931\pi\)
0.165522 0.986206i \(-0.447069\pi\)
\(930\) −0.00597334 + 0.205135i −0.000195874 + 0.00672665i
\(931\) 2.89549i 0.0948960i
\(932\) −16.1820 + 31.7634i −0.530059 + 1.04045i
\(933\) −9.54592 45.5727i −0.312520 1.49198i
\(934\) 0.0924926 + 0.0222027i 0.00302645 + 0.000726496i
\(935\) −0.00700678 −0.000229146
\(936\) −43.1976 13.0703i −1.41196 0.427216i
\(937\) 12.3494 0.403438 0.201719 0.979443i \(-0.435347\pi\)
0.201719 + 0.979443i \(0.435347\pi\)
\(938\) −3.88066 0.931548i −0.126708 0.0304161i
\(939\) −5.19137 24.7839i −0.169414 0.808792i
\(940\) 0.0188210 0.0369435i 0.000613875 0.00120497i
\(941\) 24.8282i 0.809376i 0.914455 + 0.404688i \(0.132620\pi\)
−0.914455 + 0.404688i \(0.867380\pi\)
\(942\) 0.878559 30.1713i 0.0286250 0.983034i
\(943\) 35.6272i 1.16018i
\(944\) −0.533238 0.733764i −0.0173554 0.0238820i
\(945\) 0.385934 + 0.541232i 0.0125544 + 0.0176063i
\(946\) 0.382349 1.59279i 0.0124312 0.0517862i
\(947\) −11.3420 −0.368564 −0.184282 0.982873i \(-0.558996\pi\)
−0.184282 + 0.982873i \(0.558996\pi\)
\(948\) −51.1718 13.8708i −1.66198 0.450502i
\(949\) 26.6048 0.863630
\(950\) 4.95730 20.6512i 0.160836 0.670014i
\(951\) −27.8496 + 5.83353i −0.903084 + 0.189165i
\(952\) 0.281010 + 0.239964i 0.00910760 + 0.00777729i
\(953\) 29.4402i 0.953663i 0.878995 + 0.476831i \(0.158215\pi\)
−0.878995 + 0.476831i \(0.841785\pi\)
\(954\) −2.16640 12.0857i −0.0701399 0.391289i
\(955\) 0.181426i 0.00587081i
\(956\) 39.6897 + 20.2201i 1.28366 + 0.653965i
\(957\) −18.8911 + 3.95703i −0.610662 + 0.127913i
\(958\) −14.3753 3.45078i −0.464445 0.111490i
\(959\) −13.8915 −0.448580
\(960\) −0.223472 0.587054i −0.00721253 0.0189471i
\(961\) 27.5844 0.889818
\(962\) 3.86431 + 0.927624i 0.124590 + 0.0299078i
\(963\) 1.81273 0.794259i 0.0584145 0.0255947i
\(964\) 34.5152 + 17.5839i 1.11166 + 0.566340i
\(965\) 0.866259i 0.0278858i
\(966\) −60.4274 1.75959i −1.94422 0.0566138i
\(967\) 29.6692i 0.954097i −0.878877 0.477049i \(-0.841707\pi\)
0.878877 0.477049i \(-0.158293\pi\)
\(968\) −0.314175 0.268285i −0.0100980 0.00862300i
\(969\) −0.0493967 0.235823i −0.00158685 0.00757571i
\(970\) 0.0435103 0.181256i 0.00139703 0.00581978i
\(971\) 32.1612 1.03210 0.516050 0.856558i \(-0.327402\pi\)
0.516050 + 0.856558i \(0.327402\pi\)
\(972\) 16.5930 + 26.3946i 0.532219 + 0.846607i
\(973\) −17.8049 −0.570799
\(974\) 7.86725 32.7735i 0.252083 1.05013i
\(975\) −9.43964 45.0653i −0.302310 1.44324i
\(976\) −14.3862 19.7962i −0.460490 0.633659i
\(977\) 18.5520i 0.593531i 0.954950 + 0.296766i \(0.0959080\pi\)
−0.954950 + 0.296766i \(0.904092\pi\)
\(978\) −51.5731 1.50176i −1.64912 0.0480209i
\(979\) 2.33559i 0.0746458i
\(980\) 0.0396606 0.0778492i 0.00126691 0.00248680i
\(981\) −31.3563 + 13.7389i −1.00113 + 0.438650i
\(982\) 40.4472 + 9.70930i 1.29072 + 0.309836i
\(983\) −49.7253 −1.58599 −0.792995 0.609228i \(-0.791479\pi\)
−0.792995 + 0.609228i \(0.791479\pi\)
\(984\) −17.5113 9.57314i −0.558240 0.305181i
\(985\) −0.144502 −0.00460421
\(986\) 0.212497 + 0.0510098i 0.00676730 + 0.00162448i
\(987\) 2.18773 0.458255i 0.0696363 0.0145864i
\(988\) 14.5093 28.4802i 0.461604 0.906075i
\(989\) 3.03414i 0.0964801i
\(990\) 0.113295 + 0.632037i 0.00360074 + 0.0200874i
\(991\) 2.66567i 0.0846779i −0.999103 0.0423389i \(-0.986519\pi\)
0.999103 0.0423389i \(-0.0134809\pi\)
\(992\) 9.65831 4.00220i 0.306652 0.127070i
\(993\) 30.5695 6.40326i 0.970093 0.203201i
\(994\) −6.69283 + 27.8811i −0.212284 + 0.884335i
\(995\) 0.795060 0.0252051
\(996\) 12.9448 47.7559i 0.410173 1.51320i
\(997\) 11.0297 0.349315 0.174657 0.984629i \(-0.444118\pi\)
0.174657 + 0.984629i \(0.444118\pi\)
\(998\) −13.0646 + 54.4248i −0.413553 + 1.72279i
\(999\) −1.59387 2.23523i −0.0504277 0.0707196i
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 804.2.c.b.671.11 128
3.2 odd 2 inner 804.2.c.b.671.118 yes 128
4.3 odd 2 inner 804.2.c.b.671.117 yes 128
12.11 even 2 inner 804.2.c.b.671.12 yes 128
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
804.2.c.b.671.11 128 1.1 even 1 trivial
804.2.c.b.671.12 yes 128 12.11 even 2 inner
804.2.c.b.671.117 yes 128 4.3 odd 2 inner
804.2.c.b.671.118 yes 128 3.2 odd 2 inner