Properties

Label 625.2.h.a.274.6
Level $625$
Weight $2$
Character 625.274
Analytic conductor $4.991$
Analytic rank $0$
Dimension $240$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [625,2,Mod(24,625)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(625, base_ring=CyclotomicField(50))
 
chi = DirichletCharacter(H, H._module([11]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("625.24");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 625 = 5^{4} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 625.h (of order \(50\), degree \(20\), not 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: \(4.99065012633\)
Analytic rank: \(0\)
Dimension: \(240\)
Relative dimension: \(12\) over \(\Q(\zeta_{50})\)
Twist minimal: no (minimal twist has level 125)
Sato-Tate group: $\mathrm{SU}(2)[C_{50}]$

Embedding invariants

Embedding label 274.6
Character \(\chi\) \(=\) 625.274
Dual form 625.2.h.a.349.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.0406317 - 0.158250i) q^{2} +(-1.60542 + 0.306251i) q^{3} +(1.72922 - 0.950647i) q^{4} +(0.113695 + 0.241615i) q^{6} +(-0.875585 + 1.20514i) q^{7} +(-0.444388 - 0.473226i) q^{8} +(-0.305740 + 0.121051i) q^{9} +O(q^{10})\) \(q+(-0.0406317 - 0.158250i) q^{2} +(-1.60542 + 0.306251i) q^{3} +(1.72922 - 0.950647i) q^{4} +(0.113695 + 0.241615i) q^{6} +(-0.875585 + 1.20514i) q^{7} +(-0.444388 - 0.473226i) q^{8} +(-0.305740 + 0.121051i) q^{9} +(-4.14806 + 1.06504i) q^{11} +(-2.48499 + 2.05576i) q^{12} +(-1.43255 - 3.61820i) q^{13} +(0.226290 + 0.0895946i) q^{14} +(2.05787 - 3.24268i) q^{16} +(-1.44547 + 2.62930i) q^{17} +(0.0315791 + 0.0434649i) q^{18} +(-0.997848 + 5.23090i) q^{19} +(1.03661 - 2.20291i) q^{21} +(0.337085 + 0.613156i) q^{22} +(-2.26254 - 0.142347i) q^{23} +(0.858356 + 0.623632i) q^{24} +(-0.514374 + 0.373715i) q^{26} +(4.59360 - 2.91519i) q^{27} +(-0.368418 + 2.91633i) q^{28} +(-4.03691 - 0.509980i) q^{29} +(-7.84067 - 4.31044i) q^{31} +(-1.83157 - 0.595112i) q^{32} +(6.33321 - 2.98018i) q^{33} +(0.474819 + 0.121913i) q^{34} +(-0.413616 + 0.499975i) q^{36} +(5.64154 + 3.58023i) q^{37} +(0.868336 - 0.0546310i) q^{38} +(3.40792 + 5.37002i) q^{39} +(-0.106594 - 1.69427i) q^{41} +(-0.390729 - 0.0745356i) q^{42} +(-3.75815 + 1.22110i) q^{43} +(-6.16043 + 5.78503i) q^{44} +(0.0694046 + 0.363831i) q^{46} +(-8.41038 + 8.95615i) q^{47} +(-2.31067 + 5.83610i) q^{48} +(1.47741 + 4.54699i) q^{49} +(1.51536 - 4.66381i) q^{51} +(-5.91683 - 4.89482i) q^{52} +(-8.78940 - 4.13598i) q^{53} +(-0.647976 - 0.608490i) q^{54} +(0.959402 - 0.121201i) q^{56} -8.70340i q^{57} +(0.0833222 + 0.659563i) q^{58} +(2.23942 + 2.70700i) q^{59} +(0.0370600 - 0.589052i) q^{61} +(-0.363548 + 1.41593i) q^{62} +(0.121818 - 0.474450i) q^{63} +(0.462543 - 7.35191i) q^{64} +(-0.728944 - 0.881141i) q^{66} +(0.458471 + 3.62917i) q^{67} +5.92077i q^{68} +(3.67593 - 0.464378i) q^{69} +(0.992574 + 0.932089i) q^{71} +(0.193152 + 0.0908904i) q^{72} +(-3.33869 - 2.76201i) q^{73} +(0.337346 - 1.03825i) q^{74} +(3.24724 + 9.99399i) q^{76} +(2.34845 - 5.93152i) q^{77} +(0.711337 - 0.757497i) q^{78} +(-2.80389 - 14.6985i) q^{79} +(-5.76277 + 5.41160i) q^{81} +(-0.263787 + 0.0857097i) q^{82} +(-2.85082 - 0.543823i) q^{83} +(-0.301661 - 4.79476i) q^{84} +(0.345939 + 0.545113i) q^{86} +(6.63712 - 0.417572i) q^{87} +(2.34735 + 1.48967i) q^{88} +(0.276132 - 0.333786i) q^{89} +(5.61476 + 1.44162i) q^{91} +(-4.04776 + 1.90473i) q^{92} +(13.9076 + 4.51887i) q^{93} +(1.75904 + 0.967041i) q^{94} +(3.12269 + 0.394488i) q^{96} +(1.52301 - 12.0559i) q^{97} +(0.659533 - 0.418552i) q^{98} +(1.13930 - 0.827752i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 240 q + 20 q^{2} + 20 q^{3} - 20 q^{4} - 20 q^{6} + 25 q^{7} + 35 q^{8} - 20 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 240 q + 20 q^{2} + 20 q^{3} - 20 q^{4} - 20 q^{6} + 25 q^{7} + 35 q^{8} - 20 q^{9} - 25 q^{11} - 60 q^{12} + 20 q^{13} - 30 q^{14} - 40 q^{16} + 15 q^{17} + 25 q^{18} - 10 q^{19} - 35 q^{21} + 25 q^{22} - 70 q^{23} + 15 q^{24} - 45 q^{26} + 20 q^{27} + 10 q^{28} - 10 q^{29} - 30 q^{31} + 25 q^{32} + 35 q^{33} - 20 q^{34} + 170 q^{36} + 55 q^{37} + 40 q^{38} - 35 q^{41} + 10 q^{42} + 25 q^{43} + 15 q^{44} - 40 q^{46} - 100 q^{47} - 5 q^{48} + 35 q^{49} - 55 q^{51} + 15 q^{52} + 15 q^{53} + 30 q^{54} + 65 q^{56} - 255 q^{58} + 5 q^{59} - 40 q^{61} - 5 q^{62} + 35 q^{63} + 25 q^{64} - 95 q^{66} - 105 q^{67} - 10 q^{69} + 45 q^{71} + 30 q^{72} + 40 q^{73} + 35 q^{74} - 65 q^{76} + 35 q^{77} - 100 q^{78} - 95 q^{81} - 175 q^{82} - 20 q^{83} + 45 q^{84} - 80 q^{86} + 5 q^{87} + 5 q^{88} + 30 q^{89} + 65 q^{91} + 55 q^{92} - 275 q^{93} + 60 q^{94} - 135 q^{96} - 35 q^{97} + 15 q^{98} + 45 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/625\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{21}{50}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.0406317 0.158250i −0.0287310 0.111900i 0.952600 0.304225i \(-0.0983973\pi\)
−0.981331 + 0.192325i \(0.938397\pi\)
\(3\) −1.60542 + 0.306251i −0.926891 + 0.176814i −0.628660 0.777680i \(-0.716396\pi\)
−0.298230 + 0.954494i \(0.596396\pi\)
\(4\) 1.72922 0.950647i 0.864611 0.475324i
\(5\) 0 0
\(6\) 0.113695 + 0.241615i 0.0464159 + 0.0986388i
\(7\) −0.875585 + 1.20514i −0.330940 + 0.455500i −0.941768 0.336264i \(-0.890837\pi\)
0.610828 + 0.791763i \(0.290837\pi\)
\(8\) −0.444388 0.473226i −0.157115 0.167310i
\(9\) −0.305740 + 0.121051i −0.101913 + 0.0403504i
\(10\) 0 0
\(11\) −4.14806 + 1.06504i −1.25069 + 0.321122i −0.815256 0.579101i \(-0.803404\pi\)
−0.435430 + 0.900223i \(0.643404\pi\)
\(12\) −2.48499 + 2.05576i −0.717356 + 0.593448i
\(13\) −1.43255 3.61820i −0.397317 1.00351i −0.981427 0.191834i \(-0.938556\pi\)
0.584110 0.811674i \(-0.301444\pi\)
\(14\) 0.226290 + 0.0895946i 0.0604786 + 0.0239452i
\(15\) 0 0
\(16\) 2.05787 3.24268i 0.514467 0.810671i
\(17\) −1.44547 + 2.62930i −0.350578 + 0.637699i −0.991529 0.129883i \(-0.958540\pi\)
0.640952 + 0.767581i \(0.278540\pi\)
\(18\) 0.0315791 + 0.0434649i 0.00744327 + 0.0102448i
\(19\) −0.997848 + 5.23090i −0.228922 + 1.20005i 0.663265 + 0.748385i \(0.269170\pi\)
−0.892187 + 0.451667i \(0.850830\pi\)
\(20\) 0 0
\(21\) 1.03661 2.20291i 0.226207 0.480713i
\(22\) 0.337085 + 0.613156i 0.0718668 + 0.130725i
\(23\) −2.26254 0.142347i −0.471773 0.0296814i −0.174875 0.984591i \(-0.555952\pi\)
−0.296898 + 0.954909i \(0.595952\pi\)
\(24\) 0.858356 + 0.623632i 0.175211 + 0.127298i
\(25\) 0 0
\(26\) −0.514374 + 0.373715i −0.100877 + 0.0732915i
\(27\) 4.59360 2.91519i 0.884040 0.561029i
\(28\) −0.368418 + 2.91633i −0.0696244 + 0.551134i
\(29\) −4.03691 0.509980i −0.749635 0.0947009i −0.258773 0.965938i \(-0.583318\pi\)
−0.490862 + 0.871237i \(0.663318\pi\)
\(30\) 0 0
\(31\) −7.84067 4.31044i −1.40823 0.774178i −0.417322 0.908758i \(-0.637031\pi\)
−0.990903 + 0.134580i \(0.957031\pi\)
\(32\) −1.83157 0.595112i −0.323778 0.105202i
\(33\) 6.33321 2.98018i 1.10247 0.518783i
\(34\) 0.474819 + 0.121913i 0.0814308 + 0.0209079i
\(35\) 0 0
\(36\) −0.413616 + 0.499975i −0.0689359 + 0.0833292i
\(37\) 5.64154 + 3.58023i 0.927463 + 0.588586i 0.911506 0.411287i \(-0.134920\pi\)
0.0159571 + 0.999873i \(0.494920\pi\)
\(38\) 0.868336 0.0546310i 0.140863 0.00886233i
\(39\) 3.40792 + 5.37002i 0.545704 + 0.859892i
\(40\) 0 0
\(41\) −0.106594 1.69427i −0.0166473 0.264600i −0.997543 0.0700639i \(-0.977680\pi\)
0.980895 0.194537i \(-0.0623203\pi\)
\(42\) −0.390729 0.0745356i −0.0602908 0.0115011i
\(43\) −3.75815 + 1.22110i −0.573113 + 0.186216i −0.581213 0.813752i \(-0.697422\pi\)
0.00810001 + 0.999967i \(0.497422\pi\)
\(44\) −6.16043 + 5.78503i −0.928719 + 0.872126i
\(45\) 0 0
\(46\) 0.0694046 + 0.363831i 0.0102331 + 0.0536440i
\(47\) −8.41038 + 8.95615i −1.22678 + 1.30639i −0.289766 + 0.957097i \(0.593578\pi\)
−0.937014 + 0.349291i \(0.886422\pi\)
\(48\) −2.31067 + 5.83610i −0.333517 + 0.842368i
\(49\) 1.47741 + 4.54699i 0.211058 + 0.649570i
\(50\) 0 0
\(51\) 1.51536 4.66381i 0.212193 0.653064i
\(52\) −5.91683 4.89482i −0.820516 0.678790i
\(53\) −8.78940 4.13598i −1.20732 0.568120i −0.286486 0.958084i \(-0.592487\pi\)
−0.920830 + 0.389964i \(0.872487\pi\)
\(54\) −0.647976 0.608490i −0.0881783 0.0828049i
\(55\) 0 0
\(56\) 0.959402 0.121201i 0.128206 0.0161961i
\(57\) 8.70340i 1.15279i
\(58\) 0.0833222 + 0.659563i 0.0109407 + 0.0866048i
\(59\) 2.23942 + 2.70700i 0.291548 + 0.352421i 0.895868 0.444321i \(-0.146555\pi\)
−0.604320 + 0.796742i \(0.706555\pi\)
\(60\) 0 0
\(61\) 0.0370600 0.589052i 0.00474505 0.0754204i −0.994942 0.100456i \(-0.967970\pi\)
0.999687 + 0.0250355i \(0.00796988\pi\)
\(62\) −0.363548 + 1.41593i −0.0461707 + 0.179823i
\(63\) 0.121818 0.474450i 0.0153476 0.0597751i
\(64\) 0.462543 7.35191i 0.0578179 0.918989i
\(65\) 0 0
\(66\) −0.728944 0.881141i −0.0897268 0.108461i
\(67\) 0.458471 + 3.62917i 0.0560111 + 0.443374i 0.995035 + 0.0995226i \(0.0317316\pi\)
−0.939024 + 0.343851i \(0.888268\pi\)
\(68\) 5.92077i 0.717999i
\(69\) 3.67593 0.464378i 0.442530 0.0559045i
\(70\) 0 0
\(71\) 0.992574 + 0.932089i 0.117797 + 0.110619i 0.741207 0.671276i \(-0.234253\pi\)
−0.623411 + 0.781895i \(0.714253\pi\)
\(72\) 0.193152 + 0.0908904i 0.0227632 + 0.0107115i
\(73\) −3.33869 2.76201i −0.390765 0.323269i 0.421208 0.906964i \(-0.361606\pi\)
−0.811973 + 0.583695i \(0.801606\pi\)
\(74\) 0.337346 1.03825i 0.0392157 0.120694i
\(75\) 0 0
\(76\) 3.24724 + 9.99399i 0.372484 + 1.14639i
\(77\) 2.34845 5.93152i 0.267631 0.675959i
\(78\) 0.711337 0.757497i 0.0805431 0.0857697i
\(79\) −2.80389 14.6985i −0.315463 1.65371i −0.688011 0.725701i \(-0.741516\pi\)
0.372548 0.928013i \(-0.378484\pi\)
\(80\) 0 0
\(81\) −5.76277 + 5.41160i −0.640308 + 0.601289i
\(82\) −0.263787 + 0.0857097i −0.0291304 + 0.00946505i
\(83\) −2.85082 0.543823i −0.312918 0.0596924i 0.0285299 0.999593i \(-0.490917\pi\)
−0.341448 + 0.939901i \(0.610917\pi\)
\(84\) −0.301661 4.79476i −0.0329139 0.523151i
\(85\) 0 0
\(86\) 0.345939 + 0.545113i 0.0373036 + 0.0587810i
\(87\) 6.63712 0.417572i 0.711574 0.0447685i
\(88\) 2.34735 + 1.48967i 0.250228 + 0.158800i
\(89\) 0.276132 0.333786i 0.0292699 0.0353812i −0.755675 0.654947i \(-0.772691\pi\)
0.784945 + 0.619565i \(0.212691\pi\)
\(90\) 0 0
\(91\) 5.61476 + 1.44162i 0.588586 + 0.151123i
\(92\) −4.04776 + 1.90473i −0.422008 + 0.198582i
\(93\) 13.9076 + 4.51887i 1.44216 + 0.468585i
\(94\) 1.75904 + 0.967041i 0.181431 + 0.0997426i
\(95\) 0 0
\(96\) 3.12269 + 0.394488i 0.318708 + 0.0402622i
\(97\) 1.52301 12.0559i 0.154639 1.22409i −0.703509 0.710687i \(-0.748384\pi\)
0.858147 0.513404i \(-0.171616\pi\)
\(98\) 0.659533 0.418552i 0.0666229 0.0422802i
\(99\) 1.13930 0.827752i 0.114504 0.0831922i
\(100\) 0 0
\(101\) 11.0928 + 8.05937i 1.10377 + 0.801937i 0.981672 0.190580i \(-0.0610370\pi\)
0.122100 + 0.992518i \(0.461037\pi\)
\(102\) −0.799621 0.0503079i −0.0791742 0.00498122i
\(103\) 0.304120 + 0.553192i 0.0299658 + 0.0545077i 0.890866 0.454267i \(-0.150099\pi\)
−0.860900 + 0.508774i \(0.830099\pi\)
\(104\) −1.07562 + 2.28580i −0.105473 + 0.224142i
\(105\) 0 0
\(106\) −0.297390 + 1.55898i −0.0288851 + 0.151421i
\(107\) 6.29302 + 8.66160i 0.608369 + 0.837348i 0.996442 0.0842806i \(-0.0268592\pi\)
−0.388073 + 0.921629i \(0.626859\pi\)
\(108\) 5.17204 9.40791i 0.497680 0.905276i
\(109\) 4.27860 6.74200i 0.409816 0.645767i −0.575243 0.817982i \(-0.695093\pi\)
0.985059 + 0.172216i \(0.0550926\pi\)
\(110\) 0 0
\(111\) −10.1535 4.02005i −0.963727 0.381567i
\(112\) 2.10604 + 5.31926i 0.199003 + 0.502623i
\(113\) 10.3271 8.54330i 0.971489 0.803686i −0.00905990 0.999959i \(-0.502884\pi\)
0.980549 + 0.196273i \(0.0628839\pi\)
\(114\) −1.37731 + 0.353634i −0.128997 + 0.0331209i
\(115\) 0 0
\(116\) −7.46552 + 2.95581i −0.693156 + 0.274440i
\(117\) 0.875975 + 0.932818i 0.0809839 + 0.0862391i
\(118\) 0.337391 0.464379i 0.0310594 0.0427496i
\(119\) −1.90304 4.04417i −0.174451 0.370728i
\(120\) 0 0
\(121\) 6.43268 3.53640i 0.584789 0.321490i
\(122\) −0.0947234 + 0.0180695i −0.00857585 + 0.00163593i
\(123\) 0.690000 + 2.68737i 0.0622152 + 0.242312i
\(124\) −17.6560 −1.58555
\(125\) 0 0
\(126\) −0.0800315 −0.00712977
\(127\) 1.30444 + 5.08048i 0.115751 + 0.450819i 0.999865 0.0164521i \(-0.00523709\pi\)
−0.884114 + 0.467271i \(0.845237\pi\)
\(128\) −4.96566 + 0.947250i −0.438906 + 0.0837259i
\(129\) 5.65946 3.11131i 0.498287 0.273936i
\(130\) 0 0
\(131\) 6.02713 + 12.8083i 0.526593 + 1.11907i 0.974376 + 0.224925i \(0.0722137\pi\)
−0.447783 + 0.894142i \(0.647786\pi\)
\(132\) 8.11842 11.1740i 0.706617 0.972576i
\(133\) −5.43027 5.78265i −0.470864 0.501419i
\(134\) 0.555688 0.220013i 0.0480042 0.0190062i
\(135\) 0 0
\(136\) 1.88660 0.484397i 0.161775 0.0415367i
\(137\) 9.22019 7.62761i 0.787734 0.651670i −0.153984 0.988073i \(-0.549210\pi\)
0.941718 + 0.336403i \(0.109210\pi\)
\(138\) −0.222847 0.562848i −0.0189700 0.0479128i
\(139\) 21.4738 + 8.50210i 1.82139 + 0.721138i 0.984893 + 0.173163i \(0.0553989\pi\)
0.836495 + 0.547975i \(0.184601\pi\)
\(140\) 0 0
\(141\) 10.7594 16.9541i 0.906104 1.42779i
\(142\) 0.107173 0.194947i 0.00899378 0.0163596i
\(143\) 9.79582 + 13.4828i 0.819167 + 1.12749i
\(144\) −0.236643 + 1.24053i −0.0197202 + 0.103377i
\(145\) 0 0
\(146\) −0.301431 + 0.640574i −0.0249466 + 0.0530143i
\(147\) −3.76438 6.84738i −0.310481 0.564763i
\(148\) 13.1590 + 0.827894i 1.08166 + 0.0680525i
\(149\) −17.8909 12.9985i −1.46568 1.06488i −0.981838 0.189719i \(-0.939242\pi\)
−0.483839 0.875157i \(-0.660758\pi\)
\(150\) 0 0
\(151\) −2.95732 + 2.14862i −0.240663 + 0.174852i −0.701579 0.712592i \(-0.747521\pi\)
0.460915 + 0.887444i \(0.347521\pi\)
\(152\) 2.91883 1.85234i 0.236748 0.150245i
\(153\) 0.123659 0.978858i 0.00999720 0.0791360i
\(154\) −1.03409 0.130635i −0.0833290 0.0105269i
\(155\) 0 0
\(156\) 10.9980 + 6.04623i 0.880548 + 0.484085i
\(157\) 10.9673 + 3.56350i 0.875288 + 0.284398i 0.712000 0.702180i \(-0.247790\pi\)
0.163289 + 0.986578i \(0.447790\pi\)
\(158\) −2.21212 + 1.04094i −0.175987 + 0.0828130i
\(159\) 15.3773 + 3.94823i 1.21950 + 0.313115i
\(160\) 0 0
\(161\) 2.15260 2.60204i 0.169648 0.205070i
\(162\) 1.09054 + 0.692077i 0.0856808 + 0.0543747i
\(163\) 17.4902 1.10039i 1.36994 0.0861893i 0.639302 0.768956i \(-0.279223\pi\)
0.730637 + 0.682766i \(0.239223\pi\)
\(164\) −1.79498 2.82843i −0.140164 0.220864i
\(165\) 0 0
\(166\) 0.0297737 + 0.473240i 0.00231089 + 0.0367305i
\(167\) −6.43823 1.22816i −0.498205 0.0950377i −0.0678467 0.997696i \(-0.521613\pi\)
−0.430359 + 0.902658i \(0.641613\pi\)
\(168\) −1.50313 + 0.488396i −0.115969 + 0.0376806i
\(169\) −1.56260 + 1.46738i −0.120200 + 0.112876i
\(170\) 0 0
\(171\) −0.328124 1.72009i −0.0250923 0.131538i
\(172\) −5.33784 + 5.68423i −0.407007 + 0.433418i
\(173\) −4.50909 + 11.3887i −0.342820 + 0.865863i 0.651423 + 0.758714i \(0.274172\pi\)
−0.994243 + 0.107149i \(0.965828\pi\)
\(174\) −0.335759 1.03336i −0.0254538 0.0783387i
\(175\) 0 0
\(176\) −5.08257 + 15.6425i −0.383113 + 1.17910i
\(177\) −4.42424 3.66005i −0.332546 0.275106i
\(178\) −0.0640414 0.0301356i −0.00480010 0.00225876i
\(179\) −1.50281 1.41123i −0.112325 0.105481i 0.626350 0.779542i \(-0.284548\pi\)
−0.738675 + 0.674062i \(0.764548\pi\)
\(180\) 0 0
\(181\) −10.6567 + 1.34626i −0.792108 + 0.100067i −0.510968 0.859600i \(-0.670713\pi\)
−0.281141 + 0.959667i \(0.590713\pi\)
\(182\) 0.947112i 0.0702046i
\(183\) 0.120901 + 0.957026i 0.00893723 + 0.0707454i
\(184\) 0.938085 + 1.13395i 0.0691565 + 0.0835959i
\(185\) 0 0
\(186\) 0.150020 2.38450i 0.0110000 0.174840i
\(187\) 3.19558 12.4460i 0.233684 0.910139i
\(188\) −6.02927 + 23.4825i −0.439730 + 1.71264i
\(189\) −0.508881 + 8.08843i −0.0370156 + 0.588347i
\(190\) 0 0
\(191\) −7.80278 9.43194i −0.564589 0.682471i 0.408538 0.912742i \(-0.366039\pi\)
−0.973127 + 0.230271i \(0.926039\pi\)
\(192\) 1.50895 + 11.9446i 0.108899 + 0.862025i
\(193\) 19.8655i 1.42995i −0.699149 0.714976i \(-0.746438\pi\)
0.699149 0.714976i \(-0.253562\pi\)
\(194\) −1.96973 + 0.248835i −0.141418 + 0.0178653i
\(195\) 0 0
\(196\) 6.87735 + 6.45826i 0.491239 + 0.461304i
\(197\) −23.8669 11.2309i −1.70044 0.800169i −0.995895 0.0905141i \(-0.971149\pi\)
−0.704550 0.709655i \(-0.748851\pi\)
\(198\) −0.177284 0.146662i −0.0125990 0.0104228i
\(199\) −1.78603 + 5.49684i −0.126609 + 0.389661i −0.994191 0.107633i \(-0.965673\pi\)
0.867582 + 0.497294i \(0.165673\pi\)
\(200\) 0 0
\(201\) −1.84747 5.68594i −0.130311 0.401055i
\(202\) 0.824678 2.08290i 0.0580242 0.146552i
\(203\) 4.14925 4.41851i 0.291221 0.310118i
\(204\) −1.81324 9.50533i −0.126952 0.665507i
\(205\) 0 0
\(206\) 0.0751859 0.0706042i 0.00523845 0.00491923i
\(207\) 0.708981 0.230362i 0.0492776 0.0160113i
\(208\) −14.6807 2.80049i −1.01792 0.194179i
\(209\) −1.43199 22.7608i −0.0990528 1.57440i
\(210\) 0 0
\(211\) −9.13143 14.3888i −0.628633 0.990567i −0.998118 0.0613305i \(-0.980466\pi\)
0.369484 0.929237i \(-0.379534\pi\)
\(212\) −19.1307 + 1.20360i −1.31390 + 0.0826635i
\(213\) −1.87895 1.19242i −0.128744 0.0817032i
\(214\) 1.11500 1.34781i 0.0762200 0.0921342i
\(215\) 0 0
\(216\) −3.42089 0.878334i −0.232762 0.0597631i
\(217\) 12.0599 5.67494i 0.818676 0.385240i
\(218\) −1.24077 0.403151i −0.0840355 0.0273048i
\(219\) 6.20588 + 3.41171i 0.419354 + 0.230542i
\(220\) 0 0
\(221\) 11.5840 + 1.46340i 0.779227 + 0.0984392i
\(222\) −0.223620 + 1.77013i −0.0150084 + 0.118804i
\(223\) −13.2626 + 8.41669i −0.888128 + 0.563623i −0.899797 0.436309i \(-0.856286\pi\)
0.0116690 + 0.999932i \(0.496286\pi\)
\(224\) 2.32089 1.68622i 0.155071 0.112665i
\(225\) 0 0
\(226\) −1.77159 1.28713i −0.117844 0.0856188i
\(227\) −24.4170 1.53619i −1.62062 0.101961i −0.773652 0.633611i \(-0.781572\pi\)
−0.846964 + 0.531650i \(0.821572\pi\)
\(228\) −8.27386 15.0501i −0.547950 0.996717i
\(229\) −11.9652 + 25.4274i −0.790685 + 1.68029i −0.0593840 + 0.998235i \(0.518914\pi\)
−0.731301 + 0.682055i \(0.761086\pi\)
\(230\) 0 0
\(231\) −1.95373 + 10.2418i −0.128546 + 0.673861i
\(232\) 1.55262 + 2.13700i 0.101934 + 0.140301i
\(233\) −3.85827 + 7.01816i −0.252764 + 0.459775i −0.971997 0.234993i \(-0.924493\pi\)
0.719233 + 0.694768i \(0.244493\pi\)
\(234\) 0.112026 0.176525i 0.00732339 0.0115398i
\(235\) 0 0
\(236\) 6.44586 + 2.55210i 0.419590 + 0.166127i
\(237\) 9.00286 + 22.7386i 0.584799 + 1.47703i
\(238\) −0.562666 + 0.465478i −0.0364722 + 0.0301725i
\(239\) −4.63146 + 1.18916i −0.299584 + 0.0769202i −0.395490 0.918470i \(-0.629425\pi\)
0.0959058 + 0.995390i \(0.469425\pi\)
\(240\) 0 0
\(241\) −12.0650 + 4.77686i −0.777174 + 0.307705i −0.723019 0.690828i \(-0.757246\pi\)
−0.0541544 + 0.998533i \(0.517246\pi\)
\(242\) −0.821006 0.874283i −0.0527763 0.0562010i
\(243\) −1.99925 + 2.75173i −0.128252 + 0.176524i
\(244\) −0.495896 1.05383i −0.0317465 0.0674647i
\(245\) 0 0
\(246\) 0.397241 0.218385i 0.0253272 0.0139237i
\(247\) 20.3559 3.88310i 1.29522 0.247076i
\(248\) 1.44449 + 5.62591i 0.0917251 + 0.357246i
\(249\) 4.74332 0.300596
\(250\) 0 0
\(251\) −8.42741 −0.531934 −0.265967 0.963982i \(-0.585691\pi\)
−0.265967 + 0.963982i \(0.585691\pi\)
\(252\) −0.240384 0.936235i −0.0151428 0.0589773i
\(253\) 9.53675 1.81923i 0.599571 0.114374i
\(254\) 0.750984 0.412857i 0.0471210 0.0259050i
\(255\) 0 0
\(256\) −5.92130 12.5834i −0.370081 0.786462i
\(257\) 13.4657 18.5339i 0.839964 1.15611i −0.146021 0.989281i \(-0.546647\pi\)
0.985986 0.166830i \(-0.0533532\pi\)
\(258\) −0.722320 0.769192i −0.0449696 0.0478878i
\(259\) −9.25432 + 3.66404i −0.575036 + 0.227673i
\(260\) 0 0
\(261\) 1.29598 0.332751i 0.0802191 0.0205968i
\(262\) 1.78202 1.47422i 0.110094 0.0910776i
\(263\) 2.61528 + 6.60545i 0.161265 + 0.407309i 0.987831 0.155531i \(-0.0497087\pi\)
−0.826566 + 0.562840i \(0.809709\pi\)
\(264\) −4.22470 1.67268i −0.260012 0.102946i
\(265\) 0 0
\(266\) −0.694464 + 1.09430i −0.0425803 + 0.0670958i
\(267\) −0.341086 + 0.620432i −0.0208741 + 0.0379699i
\(268\) 4.24286 + 5.83979i 0.259174 + 0.356722i
\(269\) −0.533159 + 2.79492i −0.0325073 + 0.170409i −0.994839 0.101471i \(-0.967645\pi\)
0.962331 + 0.271880i \(0.0876452\pi\)
\(270\) 0 0
\(271\) −0.585443 + 1.24413i −0.0355632 + 0.0755756i −0.921819 0.387620i \(-0.873297\pi\)
0.886256 + 0.463196i \(0.153297\pi\)
\(272\) 5.55140 + 10.0980i 0.336603 + 0.612278i
\(273\) −9.45555 0.594893i −0.572276 0.0360045i
\(274\) −1.58170 1.14917i −0.0955541 0.0694241i
\(275\) 0 0
\(276\) 5.91503 4.29752i 0.356043 0.258680i
\(277\) 5.21615 3.31027i 0.313408 0.198895i −0.369813 0.929106i \(-0.620578\pi\)
0.683221 + 0.730211i \(0.260578\pi\)
\(278\) 0.472939 3.74369i 0.0283650 0.224532i
\(279\) 2.91899 + 0.368754i 0.174755 + 0.0220767i
\(280\) 0 0
\(281\) 5.60578 + 3.08180i 0.334413 + 0.183845i 0.640109 0.768284i \(-0.278889\pi\)
−0.305696 + 0.952129i \(0.598889\pi\)
\(282\) −3.12016 1.01380i −0.185803 0.0603710i
\(283\) 13.4216 6.31571i 0.797829 0.375430i 0.0167483 0.999860i \(-0.494669\pi\)
0.781081 + 0.624430i \(0.214669\pi\)
\(284\) 2.60247 + 0.668200i 0.154428 + 0.0396504i
\(285\) 0 0
\(286\) 1.73563 2.09802i 0.102630 0.124058i
\(287\) 2.13516 + 1.35502i 0.126035 + 0.0799841i
\(288\) 0.632023 0.0397635i 0.0372423 0.00234309i
\(289\) 4.28522 + 6.75243i 0.252072 + 0.397202i
\(290\) 0 0
\(291\) 1.24705 + 19.8212i 0.0731031 + 1.16194i
\(292\) −8.39904 1.60220i −0.491516 0.0937618i
\(293\) −0.717265 + 0.233053i −0.0419031 + 0.0136151i −0.329894 0.944018i \(-0.607013\pi\)
0.287990 + 0.957633i \(0.407013\pi\)
\(294\) −0.930646 + 0.873935i −0.0542764 + 0.0509689i
\(295\) 0 0
\(296\) −0.812778 4.26073i −0.0472418 0.247650i
\(297\) −15.9497 + 16.9847i −0.925497 + 0.985555i
\(298\) −1.33007 + 3.35938i −0.0770491 + 0.194604i
\(299\) 2.72616 + 8.39025i 0.157658 + 0.485221i
\(300\) 0 0
\(301\) 1.81899 5.59827i 0.104845 0.322679i
\(302\) 0.460180 + 0.380694i 0.0264804 + 0.0219065i
\(303\) −20.2768 9.54152i −1.16487 0.548146i
\(304\) 14.9087 + 14.0002i 0.855073 + 0.802967i
\(305\) 0 0
\(306\) −0.159929 + 0.0202037i −0.00914253 + 0.00115497i
\(307\) 24.1926i 1.38074i 0.723455 + 0.690372i \(0.242553\pi\)
−0.723455 + 0.690372i \(0.757447\pi\)
\(308\) −1.57779 12.4895i −0.0899027 0.711653i
\(309\) −0.657656 0.794970i −0.0374128 0.0452243i
\(310\) 0 0
\(311\) −0.656320 + 10.4319i −0.0372165 + 0.591540i 0.934585 + 0.355740i \(0.115771\pi\)
−0.971802 + 0.235800i \(0.924229\pi\)
\(312\) 1.02679 3.99909i 0.0581306 0.226404i
\(313\) 5.89068 22.9427i 0.332961 1.29680i −0.553055 0.833145i \(-0.686538\pi\)
0.886017 0.463654i \(-0.153462\pi\)
\(314\) 0.118303 1.88037i 0.00667623 0.106116i
\(315\) 0 0
\(316\) −18.8217 22.7515i −1.05880 1.27987i
\(317\) 3.74056 + 29.6096i 0.210091 + 1.66304i 0.646215 + 0.763155i \(0.276351\pi\)
−0.436124 + 0.899887i \(0.643649\pi\)
\(318\) 2.59389i 0.145458i
\(319\) 17.2885 2.18404i 0.967968 0.122283i
\(320\) 0 0
\(321\) −12.7556 11.9783i −0.711946 0.668562i
\(322\) −0.499237 0.234923i −0.0278214 0.0130918i
\(323\) −12.3112 10.1848i −0.685016 0.566695i
\(324\) −4.82058 + 14.8362i −0.267810 + 0.824234i
\(325\) 0 0
\(326\) −0.884795 2.72312i −0.0490043 0.150820i
\(327\) −4.80422 + 12.1341i −0.265674 + 0.671016i
\(328\) −0.754402 + 0.803357i −0.0416549 + 0.0443580i
\(329\) −3.42940 17.9776i −0.189069 0.991135i
\(330\) 0 0
\(331\) 9.02161 8.47186i 0.495873 0.465655i −0.395800 0.918337i \(-0.629533\pi\)
0.891672 + 0.452682i \(0.149533\pi\)
\(332\) −5.44669 + 1.76974i −0.298926 + 0.0971269i
\(333\) −2.15824 0.411705i −0.118271 0.0225613i
\(334\) 0.0672403 + 1.06875i 0.00367922 + 0.0584796i
\(335\) 0 0
\(336\) −5.01012 7.89468i −0.273324 0.430690i
\(337\) −25.7802 + 1.62195i −1.40434 + 0.0883534i −0.746790 0.665060i \(-0.768406\pi\)
−0.657547 + 0.753413i \(0.728406\pi\)
\(338\) 0.295705 + 0.187660i 0.0160842 + 0.0102074i
\(339\) −13.9629 + 16.8783i −0.758362 + 0.916702i
\(340\) 0 0
\(341\) 37.1143 + 9.52933i 2.00985 + 0.516042i
\(342\) −0.258872 + 0.121816i −0.0139982 + 0.00658705i
\(343\) −16.6904 5.42305i −0.901199 0.292817i
\(344\) 2.24793 + 1.23581i 0.121200 + 0.0666305i
\(345\) 0 0
\(346\) 1.98547 + 0.250823i 0.106739 + 0.0134843i
\(347\) 0.155697 1.23247i 0.00835824 0.0661623i −0.987384 0.158345i \(-0.949384\pi\)
0.995742 + 0.0921824i \(0.0293843\pi\)
\(348\) 11.0801 7.03164i 0.593955 0.376935i
\(349\) 4.49001 3.26218i 0.240344 0.174620i −0.461092 0.887352i \(-0.652542\pi\)
0.701437 + 0.712732i \(0.252542\pi\)
\(350\) 0 0
\(351\) −17.1283 12.4444i −0.914241 0.664235i
\(352\) 8.23126 + 0.517867i 0.438728 + 0.0276024i
\(353\) 13.1413 + 23.9040i 0.699443 + 1.27228i 0.952414 + 0.304808i \(0.0985924\pi\)
−0.252970 + 0.967474i \(0.581408\pi\)
\(354\) −0.399439 + 0.848851i −0.0212299 + 0.0451159i
\(355\) 0 0
\(356\) 0.160180 0.839693i 0.00848953 0.0445037i
\(357\) 4.29371 + 5.90979i 0.227247 + 0.312779i
\(358\) −0.162266 + 0.295161i −0.00857604 + 0.0155998i
\(359\) −9.41649 + 14.8380i −0.496983 + 0.783120i −0.996536 0.0831632i \(-0.973498\pi\)
0.499553 + 0.866284i \(0.333498\pi\)
\(360\) 0 0
\(361\) −8.70089 3.44493i −0.457942 0.181312i
\(362\) 0.646047 + 1.63173i 0.0339555 + 0.0857617i
\(363\) −9.24414 + 7.64742i −0.485192 + 0.401385i
\(364\) 11.0796 2.84477i 0.580730 0.149106i
\(365\) 0 0
\(366\) 0.146537 0.0580182i 0.00765962 0.00303266i
\(367\) 2.29930 + 2.44850i 0.120022 + 0.127811i 0.786173 0.618006i \(-0.212059\pi\)
−0.666151 + 0.745817i \(0.732059\pi\)
\(368\) −5.11760 + 7.04377i −0.266773 + 0.367182i
\(369\) 0.237683 + 0.505103i 0.0123733 + 0.0262946i
\(370\) 0 0
\(371\) 12.6803 6.97105i 0.658328 0.361919i
\(372\) 28.3453 5.40715i 1.46963 0.280347i
\(373\) −2.27628 8.86553i −0.117861 0.459040i 0.882066 0.471127i \(-0.156152\pi\)
−0.999927 + 0.0120870i \(0.996152\pi\)
\(374\) −2.09942 −0.108558
\(375\) 0 0
\(376\) 7.97575 0.411318
\(377\) 3.93785 + 15.3369i 0.202810 + 0.789892i
\(378\) 1.30067 0.248117i 0.0668994 0.0127617i
\(379\) −3.46106 + 1.90273i −0.177783 + 0.0977369i −0.568160 0.822918i \(-0.692345\pi\)
0.390377 + 0.920655i \(0.372345\pi\)
\(380\) 0 0
\(381\) −3.65008 7.75682i −0.186999 0.397394i
\(382\) −1.17557 + 1.61803i −0.0601472 + 0.0827855i
\(383\) 0.312583 + 0.332867i 0.0159722 + 0.0170087i 0.736905 0.675996i \(-0.236286\pi\)
−0.720933 + 0.693005i \(0.756286\pi\)
\(384\) 7.68188 3.04147i 0.392014 0.155209i
\(385\) 0 0
\(386\) −3.14372 + 0.807171i −0.160011 + 0.0410839i
\(387\) 1.00120 0.828267i 0.0508940 0.0421032i
\(388\) −8.82728 22.2952i −0.448137 1.13186i
\(389\) −4.37456 1.73201i −0.221799 0.0878165i 0.254597 0.967047i \(-0.418057\pi\)
−0.476396 + 0.879231i \(0.658057\pi\)
\(390\) 0 0
\(391\) 3.64471 5.74314i 0.184321 0.290443i
\(392\) 1.49521 2.71978i 0.0755195 0.137369i
\(393\) −13.5986 18.7169i −0.685961 0.944144i
\(394\) −0.807539 + 4.23327i −0.0406832 + 0.213269i
\(395\) 0 0
\(396\) 1.18321 2.51444i 0.0594584 0.126355i
\(397\) −12.3968 22.5497i −0.622177 1.13174i −0.980197 0.198022i \(-0.936548\pi\)
0.358020 0.933714i \(-0.383452\pi\)
\(398\) 0.942446 + 0.0592937i 0.0472406 + 0.00297212i
\(399\) 10.4888 + 7.62056i 0.525097 + 0.381505i
\(400\) 0 0
\(401\) 5.89068 4.27983i 0.294167 0.213725i −0.430906 0.902397i \(-0.641806\pi\)
0.725073 + 0.688672i \(0.241806\pi\)
\(402\) −0.824735 + 0.523393i −0.0411340 + 0.0261045i
\(403\) −4.36393 + 34.5440i −0.217383 + 1.72076i
\(404\) 26.8435 + 3.39112i 1.33551 + 0.168715i
\(405\) 0 0
\(406\) −0.867821 0.477089i −0.0430692 0.0236775i
\(407\) −27.2145 8.84253i −1.34897 0.438308i
\(408\) −2.88044 + 1.35543i −0.142603 + 0.0671040i
\(409\) −5.66370 1.45419i −0.280052 0.0719051i 0.106051 0.994361i \(-0.466179\pi\)
−0.386103 + 0.922456i \(0.626179\pi\)
\(410\) 0 0
\(411\) −12.4663 + 15.0692i −0.614919 + 0.743309i
\(412\) 1.05178 + 0.667481i 0.0518176 + 0.0328844i
\(413\) −5.22312 + 0.328611i −0.257013 + 0.0161699i
\(414\) −0.0652620 0.102836i −0.00320745 0.00505413i
\(415\) 0 0
\(416\) 0.470571 + 7.47951i 0.0230716 + 0.366713i
\(417\) −37.0783 7.07307i −1.81573 0.346370i
\(418\) −3.54372 + 1.15142i −0.173329 + 0.0563180i
\(419\) −11.2710 + 10.5841i −0.550622 + 0.517069i −0.909160 0.416446i \(-0.863275\pi\)
0.358538 + 0.933515i \(0.383275\pi\)
\(420\) 0 0
\(421\) 2.56790 + 13.4614i 0.125152 + 0.656069i 0.988471 + 0.151411i \(0.0483816\pi\)
−0.863319 + 0.504658i \(0.831618\pi\)
\(422\) −1.90601 + 2.02969i −0.0927830 + 0.0988039i
\(423\) 1.48724 3.75634i 0.0723121 0.182640i
\(424\) 1.94866 + 5.99735i 0.0946351 + 0.291257i
\(425\) 0 0
\(426\) −0.112355 + 0.345795i −0.00544364 + 0.0167538i
\(427\) 0.677441 + 0.560428i 0.0327836 + 0.0271210i
\(428\) 19.1161 + 8.99537i 0.924014 + 0.434808i
\(429\) −19.8555 18.6456i −0.958634 0.900217i
\(430\) 0 0
\(431\) −29.6109 + 3.74072i −1.42631 + 0.180184i −0.800284 0.599622i \(-0.795318\pi\)
−0.626021 + 0.779806i \(0.715318\pi\)
\(432\) 20.8947i 1.00530i
\(433\) 3.05601 + 24.1908i 0.146862 + 1.16254i 0.877433 + 0.479698i \(0.159254\pi\)
−0.730571 + 0.682837i \(0.760746\pi\)
\(434\) −1.38807 1.67789i −0.0666296 0.0805414i
\(435\) 0 0
\(436\) 0.989387 15.7259i 0.0473830 0.753132i
\(437\) 3.00228 11.6931i 0.143618 0.559357i
\(438\) 0.287748 1.12071i 0.0137491 0.0535494i
\(439\) 0.964622 15.3322i 0.0460389 0.731767i −0.905521 0.424302i \(-0.860519\pi\)
0.951559 0.307465i \(-0.0994806\pi\)
\(440\) 0 0
\(441\) −1.00212 1.21136i −0.0477201 0.0576836i
\(442\) −0.239096 1.89264i −0.0113726 0.0900236i
\(443\) 18.9603i 0.900830i 0.892819 + 0.450415i \(0.148724\pi\)
−0.892819 + 0.450415i \(0.851276\pi\)
\(444\) −21.3793 + 2.70083i −1.01462 + 0.128176i
\(445\) 0 0
\(446\) 1.87082 + 1.75682i 0.0885861 + 0.0831879i
\(447\) 32.7032 + 15.3889i 1.54681 + 0.727872i
\(448\) 8.45508 + 6.99465i 0.399465 + 0.330466i
\(449\) 8.44214 25.9822i 0.398409 1.22618i −0.527866 0.849328i \(-0.677008\pi\)
0.926275 0.376849i \(-0.122992\pi\)
\(450\) 0 0
\(451\) 2.24662 + 6.91440i 0.105789 + 0.325586i
\(452\) 9.73613 24.5907i 0.457949 1.15665i
\(453\) 4.08973 4.35512i 0.192152 0.204621i
\(454\) 0.749005 + 3.92642i 0.0351525 + 0.184276i
\(455\) 0 0
\(456\) −4.11867 + 3.86769i −0.192874 + 0.181121i
\(457\) −31.1582 + 10.1239i −1.45752 + 0.473576i −0.927311 0.374293i \(-0.877886\pi\)
−0.530206 + 0.847869i \(0.677886\pi\)
\(458\) 4.51006 + 0.860340i 0.210741 + 0.0402010i
\(459\) 1.02499 + 16.2918i 0.0478425 + 0.760435i
\(460\) 0 0
\(461\) 21.7088 + 34.2076i 1.01108 + 1.59320i 0.785386 + 0.619006i \(0.212464\pi\)
0.225692 + 0.974199i \(0.427536\pi\)
\(462\) 1.70015 0.106964i 0.0790981 0.00497643i
\(463\) −10.7975 6.85233i −0.501805 0.318455i 0.260720 0.965415i \(-0.416040\pi\)
−0.762524 + 0.646960i \(0.776040\pi\)
\(464\) −9.96113 + 12.0409i −0.462434 + 0.558987i
\(465\) 0 0
\(466\) 1.26739 + 0.325411i 0.0587109 + 0.0150744i
\(467\) 17.2207 8.10344i 0.796878 0.374983i 0.0161631 0.999869i \(-0.494855\pi\)
0.780715 + 0.624887i \(0.214855\pi\)
\(468\) 2.40154 + 0.780306i 0.111011 + 0.0360697i
\(469\) −4.77509 2.62513i −0.220493 0.121217i
\(470\) 0 0
\(471\) −18.6985 2.36217i −0.861582 0.108843i
\(472\) 0.285847 2.26271i 0.0131572 0.104150i
\(473\) 14.2885 9.06776i 0.656986 0.416936i
\(474\) 3.23259 2.34862i 0.148478 0.107875i
\(475\) 0 0
\(476\) −7.13535 5.18414i −0.327048 0.237615i
\(477\) 3.18794 + 0.200568i 0.145966 + 0.00918337i
\(478\) 0.376369 + 0.684612i 0.0172147 + 0.0313134i
\(479\) 8.33691 17.7168i 0.380923 0.809503i −0.618790 0.785556i \(-0.712377\pi\)
0.999713 0.0239463i \(-0.00762307\pi\)
\(480\) 0 0
\(481\) 4.87222 25.5411i 0.222154 1.16457i
\(482\) 1.24616 + 1.71519i 0.0567611 + 0.0781249i
\(483\) −2.65895 + 4.83661i −0.120986 + 0.220073i
\(484\) 7.76166 12.2304i 0.352803 0.555928i
\(485\) 0 0
\(486\) 0.516695 + 0.204574i 0.0234377 + 0.00927966i
\(487\) 1.62012 + 4.09195i 0.0734146 + 0.185424i 0.961850 0.273578i \(-0.0882071\pi\)
−0.888435 + 0.459002i \(0.848207\pi\)
\(488\) −0.295223 + 0.244230i −0.0133641 + 0.0110558i
\(489\) −27.7422 + 7.12298i −1.25454 + 0.322112i
\(490\) 0 0
\(491\) −30.1074 + 11.9204i −1.35873 + 0.537958i −0.930692 0.365803i \(-0.880794\pi\)
−0.428036 + 0.903762i \(0.640794\pi\)
\(492\) 3.74791 + 3.99112i 0.168969 + 0.179933i
\(493\) 7.17612 9.87708i 0.323196 0.444841i
\(494\) −1.44160 3.06355i −0.0648606 0.137836i
\(495\) 0 0
\(496\) −30.1125 + 16.5545i −1.35209 + 0.743317i
\(497\) −1.99238 + 0.380067i −0.0893704 + 0.0170483i
\(498\) −0.192729 0.750631i −0.00863641 0.0336366i
\(499\) 7.95945 0.356314 0.178157 0.984002i \(-0.442987\pi\)
0.178157 + 0.984002i \(0.442987\pi\)
\(500\) 0 0
\(501\) 10.7122 0.478586
\(502\) 0.342421 + 1.33364i 0.0152830 + 0.0595233i
\(503\) −18.1247 + 3.45746i −0.808139 + 0.154161i −0.574863 0.818250i \(-0.694945\pi\)
−0.233276 + 0.972411i \(0.574945\pi\)
\(504\) −0.278656 + 0.153193i −0.0124123 + 0.00682374i
\(505\) 0 0
\(506\) −0.675389 1.43527i −0.0300247 0.0638057i
\(507\) 2.05925 2.83431i 0.0914545 0.125876i
\(508\) 7.08541 + 7.54520i 0.314364 + 0.334764i
\(509\) −21.8248 + 8.64107i −0.967369 + 0.383009i −0.798076 0.602557i \(-0.794149\pi\)
−0.169294 + 0.985566i \(0.554149\pi\)
\(510\) 0 0
\(511\) 6.25192 1.60522i 0.276568 0.0710107i
\(512\) −9.54093 + 7.89294i −0.421654 + 0.348822i
\(513\) 10.6654 + 26.9376i 0.470887 + 1.18932i
\(514\) −3.48012 1.37788i −0.153502 0.0607756i
\(515\) 0 0
\(516\) 6.82869 10.7603i 0.300616 0.473696i
\(517\) 25.3481 46.1080i 1.11481 2.02783i
\(518\) 0.955855 + 1.31562i 0.0419979 + 0.0578051i
\(519\) 3.75120 19.6645i 0.164660 0.863176i
\(520\) 0 0
\(521\) 6.85648 14.5708i 0.300388 0.638356i −0.696469 0.717587i \(-0.745246\pi\)
0.996856 + 0.0792310i \(0.0252465\pi\)
\(522\) −0.105316 0.191569i −0.00460955 0.00838473i
\(523\) −12.7313 0.800988i −0.556703 0.0350248i −0.218052 0.975937i \(-0.569970\pi\)
−0.338650 + 0.940912i \(0.609970\pi\)
\(524\) 22.5984 + 16.4187i 0.987217 + 0.717255i
\(525\) 0 0
\(526\) 0.939050 0.682260i 0.0409445 0.0297479i
\(527\) 22.6669 14.3848i 0.987385 0.626614i
\(528\) 3.36913 26.6694i 0.146623 1.16064i
\(529\) −17.7198 2.23853i −0.770426 0.0973275i
\(530\) 0 0
\(531\) −1.01237 0.556554i −0.0439330 0.0241524i
\(532\) −14.8874 4.83721i −0.645450 0.209719i
\(533\) −5.97751 + 2.81280i −0.258915 + 0.121836i
\(534\) 0.112042 + 0.0287676i 0.00484855 + 0.00124490i
\(535\) 0 0
\(536\) 1.51368 1.82972i 0.0653809 0.0790319i
\(537\) 2.84484 + 1.80539i 0.122764 + 0.0779083i
\(538\) 0.463959 0.0291898i 0.0200027 0.00125846i
\(539\) −10.9711 17.2877i −0.472558 0.744633i
\(540\) 0 0
\(541\) 2.53120 + 40.2323i 0.108825 + 1.72972i 0.552483 + 0.833524i \(0.313680\pi\)
−0.443658 + 0.896196i \(0.646320\pi\)
\(542\) 0.220671 + 0.0420953i 0.00947865 + 0.00180815i
\(543\) 16.6962 5.42494i 0.716505 0.232806i
\(544\) 4.21220 3.95552i 0.180597 0.169592i
\(545\) 0 0
\(546\) 0.290053 + 1.52051i 0.0124131 + 0.0650720i
\(547\) −19.1239 + 20.3649i −0.817679 + 0.870740i −0.993518 0.113679i \(-0.963736\pi\)
0.175838 + 0.984419i \(0.443736\pi\)
\(548\) 8.69259 21.9550i 0.371329 0.937870i
\(549\) 0.0599747 + 0.184583i 0.00255966 + 0.00787781i
\(550\) 0 0
\(551\) 6.69588 20.6078i 0.285254 0.877922i
\(552\) −1.85329 1.53318i −0.0788815 0.0652564i
\(553\) 20.1688 + 9.49073i 0.857666 + 0.403587i
\(554\) −0.735792 0.690955i −0.0312608 0.0293558i
\(555\) 0 0
\(556\) 45.2155 5.71205i 1.91757 0.242245i
\(557\) 7.51870i 0.318578i −0.987232 0.159289i \(-0.949080\pi\)
0.987232 0.159289i \(-0.0509201\pi\)
\(558\) −0.0602482 0.476914i −0.00255051 0.0201894i
\(559\) 9.80191 + 11.8485i 0.414577 + 0.501137i
\(560\) 0 0
\(561\) −1.31867 + 20.9597i −0.0556743 + 0.884918i
\(562\) 0.259923 1.01233i 0.0109642 0.0427027i
\(563\) 3.00396 11.6997i 0.126602 0.493081i −0.873380 0.487039i \(-0.838077\pi\)
0.999982 0.00604197i \(-0.00192323\pi\)
\(564\) 2.48801 39.5457i 0.104764 1.66518i
\(565\) 0 0
\(566\) −1.54480 1.86735i −0.0649329 0.0784904i
\(567\) −1.47594 11.6833i −0.0619836 0.490651i
\(568\) 0.883921i 0.0370885i
\(569\) 17.6190 2.22580i 0.738628 0.0933104i 0.252988 0.967469i \(-0.418587\pi\)
0.485640 + 0.874159i \(0.338587\pi\)
\(570\) 0 0
\(571\) 18.2989 + 17.1838i 0.765783 + 0.719118i 0.965405 0.260755i \(-0.0839714\pi\)
−0.199622 + 0.979873i \(0.563971\pi\)
\(572\) 29.7565 + 14.0023i 1.24418 + 0.585468i
\(573\) 15.4153 + 12.7526i 0.643983 + 0.532749i
\(574\) 0.127676 0.392947i 0.00532910 0.0164013i
\(575\) 0 0
\(576\) 0.748539 + 2.30377i 0.0311891 + 0.0959903i
\(577\) −10.7087 + 27.0470i −0.445807 + 1.12598i 0.517047 + 0.855957i \(0.327031\pi\)
−0.962854 + 0.270023i \(0.912969\pi\)
\(578\) 0.894457 0.952500i 0.0372045 0.0396188i
\(579\) 6.08383 + 31.8925i 0.252835 + 1.32541i
\(580\) 0 0
\(581\) 3.15152 2.95947i 0.130747 0.122780i
\(582\) 3.08604 1.00272i 0.127921 0.0415639i
\(583\) 40.8639 + 7.79520i 1.69241 + 0.322844i
\(584\) 0.176624 + 2.80736i 0.00730876 + 0.116169i
\(585\) 0 0
\(586\) 0.0660245 + 0.104038i 0.00272745 + 0.00429777i
\(587\) −12.9475 + 0.814590i −0.534402 + 0.0336217i −0.327699 0.944782i \(-0.606273\pi\)
−0.206703 + 0.978404i \(0.566273\pi\)
\(588\) −13.0189 8.26204i −0.536890 0.340721i
\(589\) 30.3713 36.7126i 1.25143 1.51272i
\(590\) 0 0
\(591\) 41.7559 + 10.7211i 1.71761 + 0.441007i
\(592\) 23.2191 10.9261i 0.954299 0.449059i
\(593\) −0.398461 0.129468i −0.0163628 0.00531660i 0.300824 0.953680i \(-0.402738\pi\)
−0.317187 + 0.948363i \(0.602738\pi\)
\(594\) 3.33590 + 1.83393i 0.136874 + 0.0752470i
\(595\) 0 0
\(596\) −43.2942 5.46933i −1.77340 0.224033i
\(597\) 1.18392 9.37173i 0.0484548 0.383559i
\(598\) 1.21699 0.772326i 0.0497664 0.0315827i
\(599\) 23.1159 16.7947i 0.944491 0.686213i −0.00500643 0.999987i \(-0.501594\pi\)
0.949498 + 0.313775i \(0.101594\pi\)
\(600\) 0 0
\(601\) 14.3573 + 10.4312i 0.585646 + 0.425496i 0.840755 0.541416i \(-0.182111\pi\)
−0.255109 + 0.966912i \(0.582111\pi\)
\(602\) −0.959836 0.0603878i −0.0391200 0.00246122i
\(603\) −0.579488 1.05408i −0.0235986 0.0429257i
\(604\) −3.07128 + 6.52681i −0.124969 + 0.265572i
\(605\) 0 0
\(606\) −0.686067 + 3.59649i −0.0278696 + 0.146097i
\(607\) 25.0852 + 34.5268i 1.01817 + 1.40140i 0.913476 + 0.406894i \(0.133388\pi\)
0.104699 + 0.994504i \(0.466612\pi\)
\(608\) 4.94060 8.98692i 0.200368 0.364468i
\(609\) −5.30813 + 8.36428i −0.215096 + 0.338938i
\(610\) 0 0
\(611\) 44.4534 + 17.6004i 1.79839 + 0.712034i
\(612\) −0.716716 1.81022i −0.0289715 0.0731737i
\(613\) −19.8887 + 16.4534i −0.803299 + 0.664546i −0.945620 0.325274i \(-0.894543\pi\)
0.142321 + 0.989821i \(0.454543\pi\)
\(614\) 3.82848 0.982986i 0.154505 0.0396701i
\(615\) 0 0
\(616\) −3.85057 + 1.52455i −0.155144 + 0.0614258i
\(617\) −25.2971 26.9387i −1.01842 1.08451i −0.996402 0.0847527i \(-0.972990\pi\)
−0.0220209 0.999758i \(-0.507010\pi\)
\(618\) −0.0990824 + 0.136375i −0.00398568 + 0.00548582i
\(619\) −15.7832 33.5410i −0.634379 1.34812i −0.920805 0.390022i \(-0.872467\pi\)
0.286426 0.958102i \(-0.407533\pi\)
\(620\) 0 0
\(621\) −10.8082 + 5.94185i −0.433718 + 0.238438i
\(622\) 1.67752 0.320004i 0.0672624 0.0128310i
\(623\) 0.160482 + 0.625035i 0.00642956 + 0.0250415i
\(624\) 24.4263 0.977836
\(625\) 0 0
\(626\) −3.87004 −0.154678
\(627\) 9.26946 + 36.1022i 0.370187 + 1.44178i
\(628\) 22.3526 4.26398i 0.891965 0.170151i
\(629\) −17.5682 + 9.65818i −0.700489 + 0.385097i
\(630\) 0 0
\(631\) −4.30633 9.15142i −0.171432 0.364312i 0.800586 0.599218i \(-0.204522\pi\)
−0.972018 + 0.234906i \(0.924522\pi\)
\(632\) −5.70970 + 7.85873i −0.227120 + 0.312603i
\(633\) 19.0664 + 20.3036i 0.757820 + 0.806997i
\(634\) 4.53374 1.79504i 0.180058 0.0712900i
\(635\) 0 0
\(636\) 30.3442 7.79106i 1.20322 0.308936i
\(637\) 14.3355 11.8593i 0.567992 0.469884i
\(638\) −1.04809 2.64716i −0.0414941 0.104802i
\(639\) −0.416300 0.164825i −0.0164686 0.00652037i
\(640\) 0 0
\(641\) 10.9559 17.2638i 0.432734 0.681879i −0.556064 0.831139i \(-0.687689\pi\)
0.988798 + 0.149260i \(0.0476892\pi\)
\(642\) −1.37728 + 2.50527i −0.0543570 + 0.0988751i
\(643\) −13.1357 18.0798i −0.518022 0.712997i 0.467224 0.884139i \(-0.345254\pi\)
−0.985246 + 0.171142i \(0.945254\pi\)
\(644\) 1.24869 6.54586i 0.0492053 0.257943i
\(645\) 0 0
\(646\) −1.11151 + 2.36208i −0.0437318 + 0.0929349i
\(647\) 0.328412 + 0.597379i 0.0129112 + 0.0234854i 0.882684 0.469968i \(-0.155734\pi\)
−0.869772 + 0.493453i \(0.835734\pi\)
\(648\) 5.12181 + 0.322237i 0.201204 + 0.0126587i
\(649\) −12.1723 8.84371i −0.477805 0.347146i
\(650\) 0 0
\(651\) −17.6232 + 12.8040i −0.690708 + 0.501828i
\(652\) 29.1984 18.5298i 1.14350 0.725685i
\(653\) 2.47685 19.6063i 0.0969268 0.767254i −0.866480 0.499211i \(-0.833623\pi\)
0.963407 0.268043i \(-0.0863769\pi\)
\(654\) 2.11542 + 0.267240i 0.0827196 + 0.0104499i
\(655\) 0 0
\(656\) −5.71334 3.14093i −0.223068 0.122633i
\(657\) 1.35512 + 0.440304i 0.0528682 + 0.0171779i
\(658\) −2.70561 + 1.27316i −0.105476 + 0.0496331i
\(659\) −39.1292 10.0467i −1.52426 0.391363i −0.608651 0.793438i \(-0.708289\pi\)
−0.915607 + 0.402075i \(0.868289\pi\)
\(660\) 0 0
\(661\) −2.47526 + 2.99208i −0.0962765 + 0.116378i −0.816451 0.577415i \(-0.804062\pi\)
0.720175 + 0.693793i \(0.244062\pi\)
\(662\) −1.70724 1.08345i −0.0663536 0.0421093i
\(663\) −19.0454 + 1.19824i −0.739663 + 0.0465357i
\(664\) 1.00952 + 1.59075i 0.0391770 + 0.0617331i
\(665\) 0 0
\(666\) 0.0225404 + 0.358269i 0.000873423 + 0.0138827i
\(667\) 9.06108 + 1.72849i 0.350846 + 0.0669275i
\(668\) −12.3007 + 3.99673i −0.475927 + 0.154638i
\(669\) 18.7144 17.5740i 0.723541 0.679450i
\(670\) 0 0
\(671\) 0.473637 + 2.48289i 0.0182845 + 0.0958509i
\(672\) −3.20959 + 3.41787i −0.123813 + 0.131847i
\(673\) 10.6297 26.8475i 0.409744 1.03489i −0.567613 0.823296i \(-0.692133\pi\)
0.977357 0.211599i \(-0.0678670\pi\)
\(674\) 1.30417 + 4.01382i 0.0502347 + 0.154607i
\(675\) 0 0
\(676\) −1.30712 + 4.02291i −0.0502740 + 0.154727i
\(677\) −10.0730 8.33315i −0.387139 0.320269i 0.423412 0.905937i \(-0.360832\pi\)
−0.810551 + 0.585668i \(0.800832\pi\)
\(678\) 3.23833 + 1.52384i 0.124367 + 0.0585228i
\(679\) 13.1955 + 12.3914i 0.506397 + 0.475538i
\(680\) 0 0
\(681\) 39.6701 5.01150i 1.52016 0.192041i
\(682\) 6.26054i 0.239728i
\(683\) −1.06316 8.41581i −0.0406809 0.322022i −0.999303 0.0373394i \(-0.988112\pi\)
0.958622 0.284683i \(-0.0918883\pi\)
\(684\) −2.20260 2.66248i −0.0842184 0.101803i
\(685\) 0 0
\(686\) −0.180037 + 2.86161i −0.00687386 + 0.109257i
\(687\) 11.4221 44.4861i 0.435780 1.69725i
\(688\) −3.77415 + 14.6994i −0.143888 + 0.560408i
\(689\) −2.37357 + 37.7268i −0.0904258 + 1.43728i
\(690\) 0 0
\(691\) −2.26217 2.73449i −0.0860570 0.104025i 0.725727 0.687983i \(-0.241503\pi\)
−0.811784 + 0.583958i \(0.801503\pi\)
\(692\) 3.02939 + 23.9801i 0.115160 + 0.911585i
\(693\) 2.09779i 0.0796883i
\(694\) −0.201364 + 0.0254382i −0.00764369 + 0.000965622i
\(695\) 0 0
\(696\) −3.14707 2.95529i −0.119289 0.112020i
\(697\) 4.60882 + 2.16875i 0.174572 + 0.0821471i
\(698\) −0.698677 0.577996i −0.0264453 0.0218775i
\(699\) 4.04483 12.4487i 0.152990 0.470853i
\(700\) 0 0
\(701\) −6.48442 19.9570i −0.244913 0.753765i −0.995651 0.0931648i \(-0.970302\pi\)
0.750737 0.660601i \(-0.229698\pi\)
\(702\) −1.27338 + 3.21620i −0.0480607 + 0.121388i
\(703\) −24.3572 + 25.9378i −0.918650 + 0.978263i
\(704\) 5.91142 + 30.9888i 0.222795 + 1.16793i
\(705\) 0 0
\(706\) 3.24886 3.05088i 0.122272 0.114821i
\(707\) −19.4253 + 6.31167i −0.730565 + 0.237375i
\(708\) −11.1299 2.12314i −0.418288 0.0797926i
\(709\) 1.43737 + 22.8463i 0.0539815 + 0.858011i 0.928108 + 0.372312i \(0.121435\pi\)
−0.874126 + 0.485699i \(0.838565\pi\)
\(710\) 0 0
\(711\) 2.63654 + 4.15452i 0.0988778 + 0.155807i
\(712\) −0.280666 + 0.0176580i −0.0105184 + 0.000661761i
\(713\) 17.1263 + 10.8687i 0.641383 + 0.407034i
\(714\) 0.760764 0.919605i 0.0284709 0.0344154i
\(715\) 0 0
\(716\) −3.94028 1.01169i −0.147255 0.0378087i
\(717\) 7.07127 3.32749i 0.264081 0.124267i
\(718\) 2.73073 + 0.887267i 0.101910 + 0.0331125i
\(719\) −9.61148 5.28396i −0.358448 0.197058i 0.292347 0.956312i \(-0.405564\pi\)
−0.650794 + 0.759254i \(0.725564\pi\)
\(720\) 0 0
\(721\) −0.932957 0.117860i −0.0347451 0.00438933i
\(722\) −0.191628 + 1.51689i −0.00713165 + 0.0564528i
\(723\) 17.9065 11.3638i 0.665949 0.422624i
\(724\) −17.1480 + 12.4588i −0.637301 + 0.463026i
\(725\) 0 0
\(726\) 1.58581 + 1.15216i 0.0588550 + 0.0427606i
\(727\) −48.7342 3.06610i −1.80745 0.113715i −0.877083 0.480340i \(-0.840513\pi\)
−0.930369 + 0.366624i \(0.880513\pi\)
\(728\) −1.81292 3.29769i −0.0671912 0.122220i
\(729\) 12.4648 26.4889i 0.461657 0.981072i
\(730\) 0 0
\(731\) 2.22166 11.6464i 0.0821712 0.430756i
\(732\) 1.11886 + 1.53998i 0.0413542 + 0.0569192i
\(733\) −21.2187 + 38.5967i −0.783730 + 1.42560i 0.117870 + 0.993029i \(0.462393\pi\)
−0.901600 + 0.432571i \(0.857607\pi\)
\(734\) 0.294051 0.463351i 0.0108536 0.0171026i
\(735\) 0 0
\(736\) 4.05928 + 1.60718i 0.149627 + 0.0592416i
\(737\) −5.76697 14.5657i −0.212429 0.536535i
\(738\) 0.0702751 0.0581367i 0.00258686 0.00214004i
\(739\) 9.86167 2.53205i 0.362767 0.0931428i −0.0629067 0.998019i \(-0.520037\pi\)
0.425674 + 0.904877i \(0.360037\pi\)
\(740\) 0 0
\(741\) −31.4906 + 12.4680i −1.15684 + 0.458025i
\(742\) −1.61839 1.72341i −0.0594130 0.0632685i
\(743\) 5.10593 7.02771i 0.187319 0.257822i −0.705021 0.709186i \(-0.749063\pi\)
0.892340 + 0.451364i \(0.149063\pi\)
\(744\) −4.04195 8.58959i −0.148185 0.314910i
\(745\) 0 0
\(746\) −1.31048 + 0.720443i −0.0479801 + 0.0263773i
\(747\) 0.937441 0.178827i 0.0342992 0.00654292i
\(748\) −6.30586 24.5597i −0.230565 0.897991i
\(749\) −15.9485 −0.582746
\(750\) 0 0
\(751\) −24.8544 −0.906949 −0.453474 0.891269i \(-0.649816\pi\)
−0.453474 + 0.891269i \(0.649816\pi\)
\(752\) 11.7345 + 45.7028i 0.427912 + 1.66661i
\(753\) 13.5296 2.58090i 0.493044 0.0940532i
\(754\) 2.26707 1.24633i 0.0825618 0.0453887i
\(755\) 0 0
\(756\) 6.80928 + 14.4705i 0.247651 + 0.526285i
\(757\) −2.91770 + 4.01587i −0.106046 + 0.145959i −0.858741 0.512409i \(-0.828753\pi\)
0.752696 + 0.658368i \(0.228753\pi\)
\(758\) 0.441737 + 0.470402i 0.0160446 + 0.0170858i
\(759\) −14.7534 + 5.84127i −0.535513 + 0.212025i
\(760\) 0 0
\(761\) −35.1478 + 9.02441i −1.27411 + 0.327135i −0.824382 0.566033i \(-0.808477\pi\)
−0.449723 + 0.893168i \(0.648477\pi\)
\(762\) −1.07921 + 0.892799i −0.0390956 + 0.0323427i
\(763\) 4.37877 + 11.0595i 0.158522 + 0.400381i
\(764\) −22.4592 8.89222i −0.812544 0.321709i
\(765\) 0 0
\(766\) 0.0399754 0.0629912i 0.00144437 0.00227597i
\(767\) 6.58639 11.9806i 0.237821 0.432594i
\(768\) 13.3599 + 18.3883i 0.482082 + 0.663529i
\(769\) −0.712846 + 3.73687i −0.0257059 + 0.134755i −0.992827 0.119562i \(-0.961851\pi\)
0.967121 + 0.254318i \(0.0818508\pi\)
\(770\) 0 0
\(771\) −15.9420 + 33.8786i −0.574138 + 1.22011i
\(772\) −18.8851 34.3519i −0.679690 1.23635i
\(773\) 40.1881 + 2.52842i 1.44546 + 0.0909409i 0.766034 0.642799i \(-0.222227\pi\)
0.679430 + 0.733740i \(0.262227\pi\)
\(774\) −0.171754 0.124787i −0.00617357 0.00448536i
\(775\) 0 0
\(776\) −6.38197 + 4.63677i −0.229099 + 0.166450i
\(777\) 13.7350 8.71648i 0.492739 0.312702i
\(778\) −0.0963451 + 0.762650i −0.00345414 + 0.0273423i
\(779\) 8.96893 + 1.13304i 0.321345 + 0.0405953i
\(780\) 0 0
\(781\) −5.10996 2.80923i −0.182849 0.100522i
\(782\) −1.05694 0.343422i −0.0377962 0.0122807i
\(783\) −20.0307 + 9.42571i −0.715837 + 0.336847i
\(784\) 17.7848 + 4.56635i 0.635170 + 0.163084i
\(785\) 0 0
\(786\) −2.40942 + 2.91249i −0.0859412 + 0.103885i
\(787\) 15.4253 + 9.78921i 0.549853 + 0.348948i 0.781552 0.623840i \(-0.214428\pi\)
−0.231699 + 0.972788i \(0.574428\pi\)
\(788\) −51.9477 + 3.26828i −1.85056 + 0.116427i
\(789\) −6.22155 9.80360i −0.221493 0.349017i
\(790\) 0 0
\(791\) 1.25363 + 19.9259i 0.0445741 + 0.708485i
\(792\) −0.898006 0.171304i −0.0319093 0.00608702i
\(793\) −2.18440 + 0.709754i −0.0775703 + 0.0252041i
\(794\) −3.06479 + 2.87803i −0.108765 + 0.102137i
\(795\) 0 0
\(796\) 2.13711 + 11.2031i 0.0757480 + 0.397085i
\(797\) 17.3622 18.4888i 0.615000 0.654908i −0.343783 0.939049i \(-0.611708\pi\)
0.958783 + 0.284141i \(0.0917084\pi\)
\(798\) 0.779777 1.96949i 0.0276038 0.0697193i
\(799\) −11.3914 35.0593i −0.403000 1.24031i
\(800\) 0 0
\(801\) −0.0440194 + 0.135478i −0.00155535 + 0.00478687i
\(802\) −0.916633 0.758305i −0.0323674 0.0267767i
\(803\) 16.7907 + 7.90112i 0.592532 + 0.278825i
\(804\) −8.60002 8.07595i −0.303299 0.284817i
\(805\) 0 0
\(806\) 5.64391 0.712992i 0.198798 0.0251141i
\(807\) 4.65030i 0.163698i
\(808\) −1.11560 8.83087i −0.0392466 0.310669i
\(809\) −0.815014 0.985183i −0.0286544 0.0346372i 0.755991 0.654582i \(-0.227155\pi\)
−0.784646 + 0.619944i \(0.787155\pi\)
\(810\) 0 0
\(811\) 2.03363 32.3236i 0.0714104 1.13504i −0.785258 0.619168i \(-0.787470\pi\)
0.856669 0.515867i \(-0.172530\pi\)
\(812\) 2.97454 11.5851i 0.104386 0.406556i
\(813\) 0.558868 2.17665i 0.0196004 0.0763383i
\(814\) −0.293559 + 4.66599i −0.0102892 + 0.163543i
\(815\) 0 0
\(816\) −12.0048 14.5114i −0.420253 0.507999i
\(817\) −2.63738 20.8770i −0.0922702 0.730394i
\(818\) 0.955367i 0.0334036i
\(819\) −1.89117 + 0.238910i −0.0660827 + 0.00834819i
\(820\) 0 0
\(821\) −29.3527 27.5640i −1.02442 0.961991i −0.0251272 0.999684i \(-0.507999\pi\)
−0.999289 + 0.0376931i \(0.987999\pi\)
\(822\) 2.89123 + 1.36051i 0.100843 + 0.0474533i
\(823\) −11.6096 9.60426i −0.404684 0.334783i 0.412711 0.910862i \(-0.364582\pi\)
−0.817394 + 0.576079i \(0.804582\pi\)
\(824\) 0.126637 0.389750i 0.00441162 0.0135776i
\(825\) 0 0
\(826\) 0.264227 + 0.813207i 0.00919364 + 0.0282951i
\(827\) −1.45717 + 3.68038i −0.0506707 + 0.127979i −0.952907 0.303262i \(-0.901924\pi\)
0.902237 + 0.431241i \(0.141924\pi\)
\(828\) 1.00699 1.07234i 0.0349954 0.0372663i
\(829\) 8.22262 + 43.1045i 0.285583 + 1.49708i 0.778855 + 0.627205i \(0.215801\pi\)
−0.493271 + 0.869876i \(0.664199\pi\)
\(830\) 0 0
\(831\) −7.36035 + 6.91183i −0.255328 + 0.239769i
\(832\) −27.2633 + 8.85839i −0.945186 + 0.307109i
\(833\) −14.0909 2.68799i −0.488222 0.0931334i
\(834\) 0.387243 + 6.15505i 0.0134091 + 0.213132i
\(835\) 0 0
\(836\) −24.1137 37.9972i −0.833991 1.31416i
\(837\) −48.5827 + 3.05656i −1.67926 + 0.105650i
\(838\) 2.13290 + 1.35358i 0.0736798 + 0.0467586i
\(839\) 4.22470 5.10678i 0.145853 0.176306i −0.692528 0.721391i \(-0.743503\pi\)
0.838380 + 0.545086i \(0.183503\pi\)
\(840\) 0 0
\(841\) −12.0524 3.09452i −0.415599 0.106708i
\(842\) 2.02593 0.953331i 0.0698182 0.0328540i
\(843\) −9.94344 3.23082i −0.342470 0.111275i
\(844\) −29.4690 16.2007i −1.01436 0.557651i
\(845\) 0 0
\(846\) −0.654871 0.0827294i −0.0225149 0.00284430i
\(847\) −1.37051 + 10.8487i −0.0470912 + 0.372765i
\(848\) −31.4991 + 19.9899i −1.08168 + 0.686457i
\(849\) −19.6131 + 14.2497i −0.673119 + 0.489050i
\(850\) 0 0
\(851\) −12.2546 8.90347i −0.420082 0.305207i
\(852\) −4.38269 0.275736i −0.150149 0.00944655i
\(853\) −7.19883 13.0946i −0.246483 0.448352i 0.723906 0.689899i \(-0.242345\pi\)
−0.970389 + 0.241547i \(0.922345\pi\)
\(854\) 0.0611622 0.129976i 0.00209293 0.00444770i
\(855\) 0 0
\(856\) 1.30234 6.82713i 0.0445132 0.233346i
\(857\) 24.9954 + 34.4032i 0.853825 + 1.17519i 0.983007 + 0.183568i \(0.0587649\pi\)
−0.129182 + 0.991621i \(0.541235\pi\)
\(858\) −2.14390 + 3.89974i −0.0731916 + 0.133135i
\(859\) −14.5992 + 23.0047i −0.498119 + 0.784910i −0.996635 0.0819707i \(-0.973879\pi\)
0.498516 + 0.866881i \(0.333879\pi\)
\(860\) 0 0
\(861\) −3.84281 1.52148i −0.130963 0.0518518i
\(862\) 1.79511 + 4.53393i 0.0611417 + 0.154426i
\(863\) −9.90696 + 8.19575i −0.337237 + 0.278987i −0.790592 0.612343i \(-0.790227\pi\)
0.453355 + 0.891330i \(0.350227\pi\)
\(864\) −10.1484 + 2.60566i −0.345254 + 0.0886462i
\(865\) 0 0
\(866\) 3.70403 1.46653i 0.125868 0.0498346i
\(867\) −8.94753 9.52815i −0.303874 0.323593i
\(868\) 15.4593 21.2779i 0.524722 0.722219i
\(869\) 27.2852 + 57.9840i 0.925588 + 1.96697i
\(870\) 0 0
\(871\) 12.4743 6.85780i 0.422675 0.232368i
\(872\) −5.09185 + 0.971322i −0.172432 + 0.0328931i
\(873\) 0.993733 + 3.87033i 0.0336328 + 0.130991i
\(874\) −1.97242 −0.0667182
\(875\) 0 0
\(876\) 13.9747 0.472160
\(877\) 8.87329 + 34.5592i 0.299630 + 1.16698i 0.922921 + 0.384990i \(0.125795\pi\)
−0.623291 + 0.781990i \(0.714205\pi\)
\(878\) −2.46552 + 0.470323i −0.0832073 + 0.0158726i
\(879\) 1.08014 0.593812i 0.0364322 0.0200288i
\(880\) 0 0
\(881\) 8.21754 + 17.4632i 0.276856 + 0.588349i 0.994099 0.108474i \(-0.0345964\pi\)
−0.717243 + 0.696823i \(0.754596\pi\)
\(882\) −0.150979 + 0.207805i −0.00508374 + 0.00699717i
\(883\) −1.25668 1.33823i −0.0422908 0.0450351i 0.707475 0.706738i \(-0.249834\pi\)
−0.749766 + 0.661703i \(0.769834\pi\)
\(884\) 21.4225 8.48179i 0.720518 0.285273i
\(885\) 0 0
\(886\) 3.00047 0.770389i 0.100803 0.0258817i
\(887\) −14.4627 + 11.9646i −0.485611 + 0.401732i −0.847754 0.530390i \(-0.822045\pi\)
0.362142 + 0.932123i \(0.382045\pi\)
\(888\) 2.60970 + 6.59136i 0.0875759 + 0.221191i
\(889\) −7.26483 2.87635i −0.243655 0.0964697i
\(890\) 0 0
\(891\) 18.1407 28.5852i 0.607737 0.957640i
\(892\) −14.9326 + 27.1624i −0.499981 + 0.909463i
\(893\) −38.4565 52.9308i −1.28690 1.77126i
\(894\) 1.10652 5.80056i 0.0370075 0.194000i
\(895\) 0 0
\(896\) 3.20629 6.81371i 0.107115 0.227630i
\(897\) −6.94615 12.6350i −0.231925 0.421871i
\(898\) −4.45471 0.280267i −0.148656 0.00935262i
\(899\) 29.4538 + 21.3994i 0.982340 + 0.713711i
\(900\) 0 0
\(901\) 23.5795 17.1315i 0.785548 0.570734i
\(902\) 1.00292 0.636473i 0.0333936 0.0211922i
\(903\) −1.20577 + 9.54465i −0.0401255 + 0.317626i
\(904\) −8.63214 1.09049i −0.287101 0.0362692i
\(905\) 0 0
\(906\) −0.855371 0.470244i −0.0284178 0.0156228i
\(907\) 2.98485 + 0.969836i 0.0991103 + 0.0322029i 0.358152 0.933663i \(-0.383407\pi\)
−0.259042 + 0.965866i \(0.583407\pi\)
\(908\) −43.6828 + 20.5556i −1.44967 + 0.682161i
\(909\) −4.36710 1.12128i −0.144848 0.0371906i
\(910\) 0 0
\(911\) 37.2809 45.0649i 1.23517 1.49307i 0.426851 0.904322i \(-0.359623\pi\)
0.808320 0.588743i \(-0.200377\pi\)
\(912\) −28.2223 17.9104i −0.934535 0.593074i
\(913\) 12.4046 0.780429i 0.410531 0.0258284i
\(914\) 2.86812 + 4.51943i 0.0948689 + 0.149490i
\(915\) 0 0
\(916\) 3.48197 + 55.3443i 0.115048 + 1.82863i
\(917\) −20.7131 3.95123i −0.684006 0.130481i
\(918\) 2.53653 0.824169i 0.0837180 0.0272016i
\(919\) 30.6984 28.8277i 1.01265 0.950939i 0.0138467 0.999904i \(-0.495592\pi\)
0.998800 + 0.0489651i \(0.0155923\pi\)
\(920\) 0 0
\(921\) −7.40899 38.8393i −0.244134 1.27980i
\(922\) 4.53129 4.82533i 0.149230 0.158914i
\(923\) 1.95058 4.92659i 0.0642040 0.162161i
\(924\) 6.35791 + 19.5676i 0.209160 + 0.643728i
\(925\) 0 0
\(926\) −0.645660 + 1.98714i −0.0212177 + 0.0653013i
\(927\) −0.159946 0.132319i −0.00525332 0.00434593i
\(928\) 7.09037 + 3.33648i 0.232753 + 0.109525i
\(929\) 10.3790 + 9.74654i 0.340524 + 0.319774i 0.835875 0.548919i \(-0.184961\pi\)
−0.495351 + 0.868693i \(0.664961\pi\)
\(930\) 0 0
\(931\) −25.2591 + 3.19097i −0.827834 + 0.104580i
\(932\) 15.8038i 0.517671i
\(933\) −2.14111 16.9486i −0.0700967 0.554873i
\(934\) −1.98208 2.39592i −0.0648556 0.0783969i
\(935\) 0 0
\(936\) 0.0521605 0.829067i 0.00170492 0.0270989i
\(937\) −5.78396 + 22.5271i −0.188954 + 0.735927i 0.801490 + 0.598009i \(0.204041\pi\)
−0.990444 + 0.137918i \(0.955959\pi\)
\(938\) −0.221407 + 0.862322i −0.00722918 + 0.0281558i
\(939\) −2.43082 + 38.6367i −0.0793267 + 1.26086i
\(940\) 0 0
\(941\) −17.0057 20.5564i −0.554370 0.670118i 0.416664 0.909061i \(-0.363199\pi\)
−0.971034 + 0.238943i \(0.923199\pi\)
\(942\) 0.385939 + 3.05502i 0.0125746 + 0.0995380i
\(943\) 3.84853i 0.125325i
\(944\) 13.3864 1.69109i 0.435690 0.0550404i
\(945\) 0 0
\(946\) −2.01554 1.89272i −0.0655309 0.0615376i
\(947\) 39.8945 + 18.7729i 1.29640 + 0.610038i 0.945270 0.326290i \(-0.105799\pi\)
0.351127 + 0.936328i \(0.385799\pi\)
\(948\) 37.1844 + 30.7616i 1.20769 + 0.999090i
\(949\) −5.21067 + 16.0368i −0.169145 + 0.520576i
\(950\) 0 0
\(951\) −15.0731 46.3904i −0.488780 1.50431i
\(952\) −1.06811 + 2.69775i −0.0346178 + 0.0874345i
\(953\) 16.0892 17.1333i 0.521180 0.555001i −0.413494 0.910507i \(-0.635692\pi\)
0.934674 + 0.355506i \(0.115692\pi\)
\(954\) −0.0977915 0.512641i −0.00316612 0.0165974i
\(955\) 0 0
\(956\) −6.87835 + 6.45920i −0.222462 + 0.208905i
\(957\) −27.0864 + 8.80091i −0.875580 + 0.284493i
\(958\) −3.14243 0.599451i −0.101527 0.0193674i
\(959\) 1.11927 + 17.7902i 0.0361430 + 0.574477i
\(960\) 0 0
\(961\) 26.2855 + 41.4193i 0.847919 + 1.33611i
\(962\) −4.23985 + 0.266749i −0.136698 + 0.00860032i
\(963\) −2.97252 1.88642i −0.0957882 0.0607891i
\(964\) −16.3219 + 19.7298i −0.525693 + 0.635454i
\(965\) 0 0
\(966\) 0.873432 + 0.224259i 0.0281022 + 0.00721542i
\(967\) 16.7480 7.88099i 0.538578 0.253436i −0.137197 0.990544i \(-0.543809\pi\)
0.675775 + 0.737108i \(0.263809\pi\)
\(968\) −4.53212 1.47258i −0.145668 0.0473304i
\(969\) 22.8838 + 12.5805i 0.735135 + 0.404144i
\(970\) 0 0
\(971\) 45.5963 + 5.76015i 1.46326 + 0.184852i 0.816279 0.577658i \(-0.196033\pi\)
0.646976 + 0.762510i \(0.276033\pi\)
\(972\) −0.841219 + 6.65893i −0.0269821 + 0.213585i
\(973\) −29.0484 + 18.4347i −0.931249 + 0.590988i
\(974\) 0.581724 0.422647i 0.0186396 0.0135425i
\(975\) 0 0
\(976\) −1.83384 1.33237i −0.0586999 0.0426480i
\(977\) 5.27063 + 0.331600i 0.168623 + 0.0106088i 0.146877 0.989155i \(-0.453078\pi\)
0.0217452 + 0.999764i \(0.493078\pi\)
\(978\) 2.25443 + 4.10078i 0.0720886 + 0.131129i
\(979\) −0.789914 + 1.67865i −0.0252458 + 0.0536500i
\(980\) 0 0
\(981\) −0.492014 + 2.57923i −0.0157088 + 0.0823485i
\(982\) 3.10972 + 4.28016i 0.0992350 + 0.136585i
\(983\) 6.55866 11.9302i 0.209189 0.380513i −0.750810 0.660519i \(-0.770336\pi\)
0.959998 + 0.280006i \(0.0903364\pi\)
\(984\) 0.965105 1.52076i 0.0307664 0.0484801i
\(985\) 0 0
\(986\) −1.85463 0.734299i −0.0590634 0.0233848i
\(987\) 11.0113 + 27.8113i 0.350493 + 0.885243i
\(988\) 31.5084 26.0661i 1.00242 0.829272i
\(989\) 8.67680 2.22782i 0.275906 0.0708406i
\(990\) 0 0
\(991\) −51.2918 + 20.3078i −1.62934 + 0.645100i −0.992086 0.125557i \(-0.959928\pi\)
−0.637250 + 0.770657i \(0.719928\pi\)
\(992\) 11.7955 + 12.5609i 0.374508 + 0.398810i
\(993\) −11.8890 + 16.3638i −0.377285 + 0.519289i
\(994\) 0.141099 + 0.299852i 0.00447540 + 0.00951072i
\(995\) 0 0
\(996\) 8.20225 4.50922i 0.259898 0.142880i
\(997\) −6.06499 + 1.15696i −0.192080 + 0.0366412i −0.282524 0.959260i \(-0.591172\pi\)
0.0904435 + 0.995902i \(0.471172\pi\)
\(998\) −0.323406 1.25958i −0.0102372 0.0398714i
\(999\) 36.3520 1.15013
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 625.2.h.a.274.6 240
5.2 odd 4 625.2.g.b.351.13 480
5.3 odd 4 625.2.g.b.351.12 480
5.4 even 2 125.2.h.a.104.7 240
125.6 even 25 125.2.h.a.119.7 yes 240
125.33 odd 100 625.2.g.b.276.12 480
125.92 odd 100 625.2.g.b.276.13 480
125.119 even 50 inner 625.2.h.a.349.6 240
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
125.2.h.a.104.7 240 5.4 even 2
125.2.h.a.119.7 yes 240 125.6 even 25
625.2.g.b.276.12 480 125.33 odd 100
625.2.g.b.276.13 480 125.92 odd 100
625.2.g.b.351.12 480 5.3 odd 4
625.2.g.b.351.13 480 5.2 odd 4
625.2.h.a.274.6 240 1.1 even 1 trivial
625.2.h.a.349.6 240 125.119 even 50 inner