Properties

Label 280.2.n.b.139.12
Level $280$
Weight $2$
Character 280.139
Analytic conductor $2.236$
Analytic rank $0$
Dimension $40$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [280,2,Mod(139,280)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(280, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1, 1, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("280.139");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 280.n (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: \(2.23581125660\)
Analytic rank: \(0\)
Dimension: \(40\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 139.12
Character \(\chi\) \(=\) 280.139
Dual form 280.2.n.b.139.10

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.918230 + 1.07557i) q^{2} +1.19038 q^{3} +(-0.313707 - 1.97524i) q^{4} +(-2.22369 - 0.234978i) q^{5} +(-1.09304 + 1.28034i) q^{6} +(-2.11797 + 1.58562i) q^{7} +(2.41257 + 1.47631i) q^{8} -1.58299 q^{9} +O(q^{10})\) \(q+(-0.918230 + 1.07557i) q^{2} +1.19038 q^{3} +(-0.313707 - 1.97524i) q^{4} +(-2.22369 - 0.234978i) q^{5} +(-1.09304 + 1.28034i) q^{6} +(-2.11797 + 1.58562i) q^{7} +(2.41257 + 1.47631i) q^{8} -1.58299 q^{9} +(2.29459 - 2.17597i) q^{10} -3.65078 q^{11} +(-0.373431 - 2.35130i) q^{12} +5.56044i q^{13} +(0.239337 - 3.73399i) q^{14} +(-2.64704 - 0.279713i) q^{15} +(-3.80318 + 1.23930i) q^{16} -0.808468 q^{17} +(1.45355 - 1.70262i) q^{18} +4.54845i q^{19} +(0.233448 + 4.46604i) q^{20} +(-2.52120 + 1.88750i) q^{21} +(3.35225 - 3.92667i) q^{22} +1.75488 q^{23} +(2.87188 + 1.75738i) q^{24} +(4.88957 + 1.04503i) q^{25} +(-5.98065 - 5.10576i) q^{26} -5.45551 q^{27} +(3.79641 + 3.68609i) q^{28} -8.36272i q^{29} +(2.73144 - 2.59024i) q^{30} +4.73282 q^{31} +(2.15924 - 5.22855i) q^{32} -4.34582 q^{33} +(0.742360 - 0.869565i) q^{34} +(5.08229 - 3.02825i) q^{35} +(0.496595 + 3.12679i) q^{36} -6.15399 q^{37} +(-4.89218 - 4.17652i) q^{38} +6.61905i q^{39} +(-5.01790 - 3.84976i) q^{40} -7.65085i q^{41} +(0.284902 - 4.44488i) q^{42} -2.66483i q^{43} +(1.14527 + 7.21117i) q^{44} +(3.52008 + 0.371968i) q^{45} +(-1.61138 + 1.88750i) q^{46} +4.79391i q^{47} +(-4.52723 + 1.47524i) q^{48} +(1.97161 - 6.71660i) q^{49} +(-5.61376 + 4.29950i) q^{50} -0.962386 q^{51} +(10.9832 - 1.74435i) q^{52} -2.98963 q^{53} +(5.00941 - 5.86779i) q^{54} +(8.11818 + 0.857851i) q^{55} +(-7.45063 + 0.698632i) q^{56} +5.41439i q^{57} +(8.99470 + 7.67890i) q^{58} +8.92626i q^{59} +(0.277892 + 5.31629i) q^{60} -4.08673 q^{61} +(-4.34582 + 5.09049i) q^{62} +(3.35273 - 2.51002i) q^{63} +(3.64099 + 7.12342i) q^{64} +(1.30658 - 12.3647i) q^{65} +(3.99046 - 4.67424i) q^{66} +11.7723i q^{67} +(0.253622 + 1.59692i) q^{68} +2.08897 q^{69} +(-1.40962 + 8.24700i) q^{70} +8.17275i q^{71} +(-3.81908 - 2.33699i) q^{72} +15.1783 q^{73} +(5.65078 - 6.61905i) q^{74} +(5.82046 + 1.24399i) q^{75} +(8.98430 - 1.42688i) q^{76} +(7.73224 - 5.78875i) q^{77} +(-7.11926 - 6.07781i) q^{78} +2.49307i q^{79} +(8.74828 - 1.86214i) q^{80} -1.74517 q^{81} +(8.22903 + 7.02524i) q^{82} -5.75885 q^{83} +(4.51918 + 4.38786i) q^{84} +(1.79778 + 0.189972i) q^{85} +(2.86621 + 2.44692i) q^{86} -9.95483i q^{87} +(-8.80775 - 5.38969i) q^{88} +4.95764i q^{89} +(-3.63232 + 3.44454i) q^{90} +(-8.81676 - 11.7769i) q^{91} +(-0.550517 - 3.46631i) q^{92} +5.63387 q^{93} +(-5.15619 - 4.40191i) q^{94} +(1.06878 - 10.1143i) q^{95} +(2.57032 - 6.22397i) q^{96} -11.7195 q^{97} +(5.41379 + 8.28799i) q^{98} +5.77914 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40 q - 12 q^{4} + 40 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 40 q - 12 q^{4} + 40 q^{9} - 12 q^{14} - 28 q^{16} + 16 q^{25} - 28 q^{30} + 16 q^{35} - 28 q^{36} - 8 q^{44} - 32 q^{46} + 8 q^{49} + 4 q^{50} - 32 q^{51} - 4 q^{56} + 12 q^{60} - 84 q^{64} - 24 q^{65} + 40 q^{70} + 80 q^{74} - 72 q^{81} - 8 q^{84} + 80 q^{86} - 128 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/280\mathbb{Z}\right)^\times\).

\(n\) \(57\) \(71\) \(141\) \(241\)
\(\chi(n)\) \(-1\) \(-1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.918230 + 1.07557i −0.649287 + 0.760544i
\(3\) 1.19038 0.687268 0.343634 0.939104i \(-0.388342\pi\)
0.343634 + 0.939104i \(0.388342\pi\)
\(4\) −0.313707 1.97524i −0.156854 0.987622i
\(5\) −2.22369 0.234978i −0.994463 0.105085i
\(6\) −1.09304 + 1.28034i −0.446234 + 0.522697i
\(7\) −2.11797 + 1.58562i −0.800518 + 0.599309i
\(8\) 2.41257 + 1.47631i 0.852973 + 0.521956i
\(9\) −1.58299 −0.527663
\(10\) 2.29459 2.17597i 0.725614 0.688102i
\(11\) −3.65078 −1.10075 −0.550375 0.834917i \(-0.685515\pi\)
−0.550375 + 0.834917i \(0.685515\pi\)
\(12\) −0.373431 2.35130i −0.107800 0.678760i
\(13\) 5.56044i 1.54219i 0.636721 + 0.771095i \(0.280290\pi\)
−0.636721 + 0.771095i \(0.719710\pi\)
\(14\) 0.239337 3.73399i 0.0639654 0.997952i
\(15\) −2.64704 0.279713i −0.683462 0.0722217i
\(16\) −3.80318 + 1.23930i −0.950794 + 0.309824i
\(17\) −0.808468 −0.196082 −0.0980411 0.995182i \(-0.531258\pi\)
−0.0980411 + 0.995182i \(0.531258\pi\)
\(18\) 1.45355 1.70262i 0.342605 0.401311i
\(19\) 4.54845i 1.04349i 0.853103 + 0.521743i \(0.174718\pi\)
−0.853103 + 0.521743i \(0.825282\pi\)
\(20\) 0.233448 + 4.46604i 0.0522005 + 0.998637i
\(21\) −2.52120 + 1.88750i −0.550170 + 0.411885i
\(22\) 3.35225 3.92667i 0.714703 0.837169i
\(23\) 1.75488 0.365917 0.182959 0.983121i \(-0.441433\pi\)
0.182959 + 0.983121i \(0.441433\pi\)
\(24\) 2.87188 + 1.75738i 0.586220 + 0.358723i
\(25\) 4.88957 + 1.04503i 0.977914 + 0.209007i
\(26\) −5.98065 5.10576i −1.17290 1.00132i
\(27\) −5.45551 −1.04991
\(28\) 3.79641 + 3.68609i 0.717454 + 0.696606i
\(29\) 8.36272i 1.55292i −0.630168 0.776459i \(-0.717014\pi\)
0.630168 0.776459i \(-0.282986\pi\)
\(30\) 2.73144 2.59024i 0.498691 0.472910i
\(31\) 4.73282 0.850040 0.425020 0.905184i \(-0.360267\pi\)
0.425020 + 0.905184i \(0.360267\pi\)
\(32\) 2.15924 5.22855i 0.381703 0.924285i
\(33\) −4.34582 −0.756510
\(34\) 0.742360 0.869565i 0.127314 0.149129i
\(35\) 5.08229 3.02825i 0.859064 0.511868i
\(36\) 0.496595 + 3.12679i 0.0827659 + 0.521132i
\(37\) −6.15399 −1.01171 −0.505855 0.862619i \(-0.668823\pi\)
−0.505855 + 0.862619i \(0.668823\pi\)
\(38\) −4.89218 4.17652i −0.793617 0.677521i
\(39\) 6.61905i 1.05990i
\(40\) −5.01790 3.84976i −0.793400 0.608701i
\(41\) 7.65085i 1.19486i −0.801920 0.597431i \(-0.796188\pi\)
0.801920 0.597431i \(-0.203812\pi\)
\(42\) 0.284902 4.44488i 0.0439613 0.685860i
\(43\) 2.66483i 0.406382i −0.979139 0.203191i \(-0.934869\pi\)
0.979139 0.203191i \(-0.0651312\pi\)
\(44\) 1.14527 + 7.21117i 0.172657 + 1.08713i
\(45\) 3.52008 + 0.371968i 0.524742 + 0.0554497i
\(46\) −1.61138 + 1.88750i −0.237585 + 0.278296i
\(47\) 4.79391i 0.699263i 0.936887 + 0.349632i \(0.113693\pi\)
−0.936887 + 0.349632i \(0.886307\pi\)
\(48\) −4.52723 + 1.47524i −0.653450 + 0.212932i
\(49\) 1.97161 6.71660i 0.281658 0.959515i
\(50\) −5.61376 + 4.29950i −0.793906 + 0.608041i
\(51\) −0.962386 −0.134761
\(52\) 10.9832 1.74435i 1.52310 0.241898i
\(53\) −2.98963 −0.410658 −0.205329 0.978693i \(-0.565826\pi\)
−0.205329 + 0.978693i \(0.565826\pi\)
\(54\) 5.00941 5.86779i 0.681695 0.798505i
\(55\) 8.11818 + 0.857851i 1.09466 + 0.115673i
\(56\) −7.45063 + 0.698632i −0.995633 + 0.0933587i
\(57\) 5.41439i 0.717154i
\(58\) 8.99470 + 7.67890i 1.18106 + 1.00829i
\(59\) 8.92626i 1.16210i 0.813868 + 0.581050i \(0.197358\pi\)
−0.813868 + 0.581050i \(0.802642\pi\)
\(60\) 0.277892 + 5.31629i 0.0358757 + 0.686331i
\(61\) −4.08673 −0.523253 −0.261626 0.965169i \(-0.584259\pi\)
−0.261626 + 0.965169i \(0.584259\pi\)
\(62\) −4.34582 + 5.09049i −0.551919 + 0.646492i
\(63\) 3.35273 2.51002i 0.422404 0.316233i
\(64\) 3.64099 + 7.12342i 0.455124 + 0.890428i
\(65\) 1.30658 12.3647i 0.162061 1.53365i
\(66\) 3.99046 4.67424i 0.491192 0.575359i
\(67\) 11.7723i 1.43821i 0.694901 + 0.719105i \(0.255448\pi\)
−0.694901 + 0.719105i \(0.744552\pi\)
\(68\) 0.253622 + 1.59692i 0.0307562 + 0.193655i
\(69\) 2.08897 0.251483
\(70\) −1.40962 + 8.24700i −0.168481 + 0.985705i
\(71\) 8.17275i 0.969927i 0.874534 + 0.484963i \(0.161167\pi\)
−0.874534 + 0.484963i \(0.838833\pi\)
\(72\) −3.81908 2.33699i −0.450082 0.275417i
\(73\) 15.1783 1.77648 0.888241 0.459378i \(-0.151928\pi\)
0.888241 + 0.459378i \(0.151928\pi\)
\(74\) 5.65078 6.61905i 0.656889 0.769449i
\(75\) 5.82046 + 1.24399i 0.672089 + 0.143644i
\(76\) 8.98430 1.42688i 1.03057 0.163674i
\(77\) 7.73224 5.78875i 0.881170 0.659689i
\(78\) −7.11926 6.07781i −0.806098 0.688177i
\(79\) 2.49307i 0.280492i 0.990117 + 0.140246i \(0.0447893\pi\)
−0.990117 + 0.140246i \(0.955211\pi\)
\(80\) 8.74828 1.86214i 0.978088 0.208194i
\(81\) −1.74517 −0.193908
\(82\) 8.22903 + 7.02524i 0.908745 + 0.775808i
\(83\) −5.75885 −0.632116 −0.316058 0.948740i \(-0.602359\pi\)
−0.316058 + 0.948740i \(0.602359\pi\)
\(84\) 4.51918 + 4.38786i 0.493083 + 0.478754i
\(85\) 1.79778 + 0.189972i 0.194997 + 0.0206054i
\(86\) 2.86621 + 2.44692i 0.309071 + 0.263858i
\(87\) 9.95483i 1.06727i
\(88\) −8.80775 5.38969i −0.938910 0.574543i
\(89\) 4.95764i 0.525509i 0.964863 + 0.262755i \(0.0846310\pi\)
−0.964863 + 0.262755i \(0.915369\pi\)
\(90\) −3.63232 + 3.44454i −0.382880 + 0.363086i
\(91\) −8.81676 11.7769i −0.924247 1.23455i
\(92\) −0.550517 3.46631i −0.0573954 0.361388i
\(93\) 5.63387 0.584205
\(94\) −5.15619 4.40191i −0.531820 0.454022i
\(95\) 1.06878 10.1143i 0.109655 1.03771i
\(96\) 2.57032 6.22397i 0.262332 0.635231i
\(97\) −11.7195 −1.18993 −0.594967 0.803750i \(-0.702835\pi\)
−0.594967 + 0.803750i \(0.702835\pi\)
\(98\) 5.41379 + 8.28799i 0.546876 + 0.837214i
\(99\) 5.77914 0.580826
\(100\) 0.530305 9.98593i 0.0530305 0.998593i
\(101\) −7.10724 −0.707197 −0.353598 0.935397i \(-0.615042\pi\)
−0.353598 + 0.935397i \(0.615042\pi\)
\(102\) 0.883692 1.03511i 0.0874985 0.102492i
\(103\) 5.06789i 0.499354i 0.968329 + 0.249677i \(0.0803244\pi\)
−0.968329 + 0.249677i \(0.919676\pi\)
\(104\) −8.20896 + 13.4150i −0.804955 + 1.31544i
\(105\) 6.04987 3.60478i 0.590407 0.351790i
\(106\) 2.74517 3.21556i 0.266635 0.312323i
\(107\) 10.8670i 1.05056i 0.850931 + 0.525278i \(0.176039\pi\)
−0.850931 + 0.525278i \(0.823961\pi\)
\(108\) 1.71143 + 10.7760i 0.164683 + 1.03692i
\(109\) 7.15158i 0.684997i 0.939518 + 0.342498i \(0.111273\pi\)
−0.939518 + 0.342498i \(0.888727\pi\)
\(110\) −8.37704 + 7.94398i −0.798719 + 0.757429i
\(111\) −7.32560 −0.695315
\(112\) 6.08997 8.65519i 0.575448 0.817839i
\(113\) 0.0847428i 0.00797193i −0.999992 0.00398597i \(-0.998731\pi\)
0.999992 0.00398597i \(-0.00126878\pi\)
\(114\) −5.82357 4.97166i −0.545427 0.465638i
\(115\) −3.90230 0.412357i −0.363891 0.0384525i
\(116\) −16.5184 + 2.62344i −1.53370 + 0.243581i
\(117\) 8.80212i 0.813757i
\(118\) −9.60083 8.19636i −0.883828 0.754536i
\(119\) 1.71231 1.28192i 0.156967 0.117514i
\(120\) −5.97322 4.58269i −0.545278 0.418340i
\(121\) 2.32816 0.211651
\(122\) 3.75256 4.39557i 0.339741 0.397956i
\(123\) 9.10743i 0.821190i
\(124\) −1.48472 9.34847i −0.133332 0.839518i
\(125\) −10.6273 3.47277i −0.950536 0.310614i
\(126\) −0.378867 + 5.91088i −0.0337522 + 0.526583i
\(127\) 5.93446 0.526598 0.263299 0.964714i \(-0.415189\pi\)
0.263299 + 0.964714i \(0.415189\pi\)
\(128\) −11.0050 2.62479i −0.972716 0.232001i
\(129\) 3.17216i 0.279293i
\(130\) 12.0994 + 12.7589i 1.06118 + 1.11903i
\(131\) 17.2792i 1.50969i 0.655905 + 0.754844i \(0.272287\pi\)
−0.655905 + 0.754844i \(0.727713\pi\)
\(132\) 1.36331 + 8.58405i 0.118661 + 0.747146i
\(133\) −7.21212 9.63349i −0.625370 0.835329i
\(134\) −12.6619 10.8096i −1.09382 0.933811i
\(135\) 12.1313 + 1.28192i 1.04410 + 0.110330i
\(136\) −1.95049 1.19355i −0.167253 0.102346i
\(137\) 6.59924i 0.563811i 0.959442 + 0.281906i \(0.0909665\pi\)
−0.959442 + 0.281906i \(0.909033\pi\)
\(138\) −1.91816 + 2.24684i −0.163285 + 0.191264i
\(139\) 6.37544i 0.540757i −0.962754 0.270379i \(-0.912851\pi\)
0.962754 0.270379i \(-0.0871489\pi\)
\(140\) −7.57588 9.08878i −0.640279 0.768142i
\(141\) 5.70658i 0.480581i
\(142\) −8.79037 7.50446i −0.737672 0.629760i
\(143\) 20.2999i 1.69756i
\(144\) 6.02039 1.96179i 0.501699 0.163483i
\(145\) −1.96505 + 18.5961i −0.163189 + 1.54432i
\(146\) −13.9371 + 16.3253i −1.15345 + 1.35109i
\(147\) 2.34697 7.99533i 0.193575 0.659443i
\(148\) 1.93055 + 12.1556i 0.158690 + 0.999186i
\(149\) 17.0131i 1.39377i −0.717184 0.696883i \(-0.754569\pi\)
0.717184 0.696883i \(-0.245431\pi\)
\(150\) −6.68252 + 5.11805i −0.545626 + 0.417887i
\(151\) 14.7918i 1.20374i −0.798594 0.601870i \(-0.794423\pi\)
0.798594 0.601870i \(-0.205577\pi\)
\(152\) −6.71494 + 10.9735i −0.544653 + 0.890065i
\(153\) 1.27980 0.103465
\(154\) −0.873764 + 13.6320i −0.0704099 + 1.09850i
\(155\) −10.5243 1.11211i −0.845333 0.0893267i
\(156\) 13.0742 2.07644i 1.04678 0.166248i
\(157\) 16.6742i 1.33075i 0.746510 + 0.665374i \(0.231728\pi\)
−0.746510 + 0.665374i \(0.768272\pi\)
\(158\) −2.68147 2.28921i −0.213326 0.182120i
\(159\) −3.55881 −0.282232
\(160\) −6.03007 + 11.1193i −0.476719 + 0.879056i
\(161\) −3.71678 + 2.78257i −0.292923 + 0.219297i
\(162\) 1.60247 1.87706i 0.125902 0.147476i
\(163\) 10.8670i 0.851172i −0.904918 0.425586i \(-0.860068\pi\)
0.904918 0.425586i \(-0.139932\pi\)
\(164\) −15.1123 + 2.40012i −1.18007 + 0.187418i
\(165\) 9.66374 + 1.02117i 0.752321 + 0.0794981i
\(166\) 5.28795 6.19406i 0.410425 0.480752i
\(167\) 5.06789i 0.392165i −0.980587 0.196082i \(-0.937178\pi\)
0.980587 0.196082i \(-0.0628220\pi\)
\(168\) −8.86910 + 0.831640i −0.684266 + 0.0641624i
\(169\) −17.9185 −1.37835
\(170\) −1.85510 + 1.75920i −0.142280 + 0.134925i
\(171\) 7.20015i 0.550609i
\(172\) −5.26368 + 0.835974i −0.401352 + 0.0637424i
\(173\) 3.71164i 0.282191i −0.989996 0.141095i \(-0.954938\pi\)
0.989996 0.141095i \(-0.0450624\pi\)
\(174\) 10.7071 + 9.14083i 0.811706 + 0.692964i
\(175\) −12.0130 + 5.53965i −0.908098 + 0.418759i
\(176\) 13.8845 4.52439i 1.04659 0.341039i
\(177\) 10.6257i 0.798674i
\(178\) −5.33230 4.55226i −0.399673 0.341206i
\(179\) 7.26949 0.543347 0.271673 0.962390i \(-0.412423\pi\)
0.271673 + 0.962390i \(0.412423\pi\)
\(180\) −0.369546 7.06970i −0.0275443 0.526944i
\(181\) 18.2341 1.35533 0.677666 0.735370i \(-0.262992\pi\)
0.677666 + 0.735370i \(0.262992\pi\)
\(182\) 20.7627 + 1.33082i 1.53903 + 0.0986467i
\(183\) −4.86477 −0.359614
\(184\) 4.23377 + 2.59075i 0.312117 + 0.190993i
\(185\) 13.6845 + 1.44605i 1.00611 + 0.106316i
\(186\) −5.17318 + 6.05962i −0.379316 + 0.444313i
\(187\) 2.95153 0.215838
\(188\) 9.46913 1.50388i 0.690608 0.109682i
\(189\) 11.5546 8.65037i 0.840475 0.629222i
\(190\) 9.89729 + 10.4368i 0.718025 + 0.757168i
\(191\) 2.49307i 0.180392i −0.995924 0.0901960i \(-0.971251\pi\)
0.995924 0.0901960i \(-0.0287494\pi\)
\(192\) 4.33417 + 8.47960i 0.312792 + 0.611962i
\(193\) 14.0190i 1.00911i −0.863380 0.504554i \(-0.831657\pi\)
0.863380 0.504554i \(-0.168343\pi\)
\(194\) 10.7612 12.6051i 0.772608 0.904997i
\(195\) 1.55533 14.7187i 0.111380 1.05403i
\(196\) −13.8854 1.78736i −0.991817 0.127669i
\(197\) 8.27025 0.589231 0.294615 0.955616i \(-0.404808\pi\)
0.294615 + 0.955616i \(0.404808\pi\)
\(198\) −5.30658 + 6.21588i −0.377122 + 0.441743i
\(199\) −27.1530 −1.92483 −0.962413 0.271592i \(-0.912450\pi\)
−0.962413 + 0.271592i \(0.912450\pi\)
\(200\) 10.2536 + 9.73976i 0.725042 + 0.688705i
\(201\) 14.0135i 0.988435i
\(202\) 6.52608 7.64434i 0.459174 0.537854i
\(203\) 13.2601 + 17.7120i 0.930677 + 1.24314i
\(204\) 0.301907 + 1.90095i 0.0211377 + 0.133093i
\(205\) −1.79778 + 17.0131i −0.125562 + 1.18825i
\(206\) −5.45087 4.65349i −0.379780 0.324224i
\(207\) −2.77795 −0.193081
\(208\) −6.89103 21.1473i −0.477807 1.46630i
\(209\) 16.6054i 1.14862i
\(210\) −1.67798 + 9.81708i −0.115792 + 0.677443i
\(211\) 20.1183 1.38500 0.692501 0.721417i \(-0.256509\pi\)
0.692501 + 0.721417i \(0.256509\pi\)
\(212\) 0.937869 + 5.90526i 0.0644131 + 0.405575i
\(213\) 9.72869i 0.666599i
\(214\) −11.6883 9.97844i −0.798994 0.682112i
\(215\) −0.626175 + 5.92574i −0.0427048 + 0.404132i
\(216\) −13.1618 8.05405i −0.895547 0.548008i
\(217\) −10.0240 + 7.50446i −0.680472 + 0.509436i
\(218\) −7.69203 6.56679i −0.520970 0.444759i
\(219\) 18.0679 1.22092
\(220\) −0.852265 16.3045i −0.0574597 1.09925i
\(221\) 4.49544i 0.302396i
\(222\) 6.72658 7.87920i 0.451459 0.528817i
\(223\) 15.7322i 1.05350i 0.850019 + 0.526752i \(0.176590\pi\)
−0.850019 + 0.526752i \(0.823410\pi\)
\(224\) 3.71728 + 14.4976i 0.248372 + 0.968665i
\(225\) −7.74014 1.65428i −0.516009 0.110285i
\(226\) 0.0911469 + 0.0778134i 0.00606300 + 0.00517607i
\(227\) −17.5252 −1.16319 −0.581595 0.813478i \(-0.697571\pi\)
−0.581595 + 0.813478i \(0.697571\pi\)
\(228\) 10.6947 1.69853i 0.708277 0.112488i
\(229\) 16.5729 1.09517 0.547583 0.836751i \(-0.315548\pi\)
0.547583 + 0.836751i \(0.315548\pi\)
\(230\) 4.02673 3.81856i 0.265515 0.251788i
\(231\) 9.20432 6.89082i 0.605600 0.453383i
\(232\) 12.3460 20.1757i 0.810555 1.32460i
\(233\) 14.1037i 0.923964i 0.886889 + 0.461982i \(0.152862\pi\)
−0.886889 + 0.461982i \(0.847138\pi\)
\(234\) 9.46731 + 8.08238i 0.618898 + 0.528361i
\(235\) 1.12646 10.6602i 0.0734823 0.695392i
\(236\) 17.6315 2.80023i 1.14772 0.182279i
\(237\) 2.96770i 0.192773i
\(238\) −0.193496 + 3.01882i −0.0125425 + 0.195681i
\(239\) 22.7217i 1.46975i 0.678205 + 0.734873i \(0.262758\pi\)
−0.678205 + 0.734873i \(0.737242\pi\)
\(240\) 10.4138 2.21666i 0.672208 0.143085i
\(241\) 15.0216i 0.967629i 0.875171 + 0.483814i \(0.160749\pi\)
−0.875171 + 0.483814i \(0.839251\pi\)
\(242\) −2.13779 + 2.50410i −0.137422 + 0.160970i
\(243\) 14.2891 0.916647
\(244\) 1.28204 + 8.07229i 0.0820740 + 0.516776i
\(245\) −5.96249 + 14.4723i −0.380930 + 0.924604i
\(246\) 9.79569 + 8.36272i 0.624551 + 0.533188i
\(247\) −25.2914 −1.60925
\(248\) 11.4183 + 6.98713i 0.725061 + 0.443683i
\(249\) −6.85524 −0.434433
\(250\) 13.4935 8.24163i 0.853406 0.521247i
\(251\) 15.4522i 0.975332i −0.873030 0.487666i \(-0.837848\pi\)
0.873030 0.487666i \(-0.162152\pi\)
\(252\) −6.00968 5.83504i −0.378574 0.367573i
\(253\) −6.40666 −0.402783
\(254\) −5.44920 + 6.38293i −0.341913 + 0.400501i
\(255\) 2.14005 + 0.226139i 0.134015 + 0.0141614i
\(256\) 12.9283 9.42652i 0.808018 0.589157i
\(257\) −19.9954 −1.24728 −0.623640 0.781712i \(-0.714347\pi\)
−0.623640 + 0.781712i \(0.714347\pi\)
\(258\) 3.41188 + 2.91277i 0.212415 + 0.181341i
\(259\) 13.0340 9.75789i 0.809891 0.606326i
\(260\) −24.8331 + 1.29807i −1.54009 + 0.0805031i
\(261\) 13.2381i 0.819418i
\(262\) −18.5850 15.8662i −1.14818 0.980220i
\(263\) 3.10990 0.191764 0.0958822 0.995393i \(-0.469433\pi\)
0.0958822 + 0.995393i \(0.469433\pi\)
\(264\) −10.4846 6.41579i −0.645282 0.394865i
\(265\) 6.64801 + 0.702498i 0.408384 + 0.0431541i
\(266\) 16.9839 + 1.08861i 1.04135 + 0.0667470i
\(267\) 5.90149i 0.361165i
\(268\) 23.2531 3.69304i 1.42041 0.225588i
\(269\) 11.2181 0.683980 0.341990 0.939704i \(-0.388899\pi\)
0.341990 + 0.939704i \(0.388899\pi\)
\(270\) −12.5182 + 11.8710i −0.761832 + 0.722448i
\(271\) 6.60431 0.401183 0.200592 0.979675i \(-0.435714\pi\)
0.200592 + 0.979675i \(0.435714\pi\)
\(272\) 3.07475 1.00193i 0.186434 0.0607510i
\(273\) −10.4953 14.0190i −0.635205 0.848466i
\(274\) −7.09796 6.05962i −0.428803 0.366075i
\(275\) −17.8507 3.81519i −1.07644 0.230064i
\(276\) −0.655326 4.12623i −0.0394460 0.248370i
\(277\) −16.0704 −0.965577 −0.482789 0.875737i \(-0.660376\pi\)
−0.482789 + 0.875737i \(0.660376\pi\)
\(278\) 6.85724 + 5.85412i 0.411270 + 0.351107i
\(279\) −7.49201 −0.448535
\(280\) 16.7320 + 0.197193i 0.999931 + 0.0117846i
\(281\) 21.1540 1.26194 0.630972 0.775806i \(-0.282656\pi\)
0.630972 + 0.775806i \(0.282656\pi\)
\(282\) −6.13784 5.23996i −0.365503 0.312035i
\(283\) −24.7231 −1.46964 −0.734819 0.678263i \(-0.762733\pi\)
−0.734819 + 0.678263i \(0.762733\pi\)
\(284\) 16.1432 2.56385i 0.957921 0.152136i
\(285\) 1.27226 12.0399i 0.0753623 0.713183i
\(286\) 21.8340 + 18.6400i 1.29107 + 1.10221i
\(287\) 12.1313 + 16.2043i 0.716091 + 0.956508i
\(288\) −3.41806 + 8.27674i −0.201411 + 0.487711i
\(289\) −16.3464 −0.961552
\(290\) −18.1970 19.1890i −1.06857 1.12682i
\(291\) −13.9507 −0.817803
\(292\) −4.76153 29.9808i −0.278647 1.75449i
\(293\) 11.4011i 0.666060i 0.942916 + 0.333030i \(0.108071\pi\)
−0.942916 + 0.333030i \(0.891929\pi\)
\(294\) 6.44449 + 9.86588i 0.375850 + 0.575390i
\(295\) 2.09747 19.8492i 0.122120 1.15567i
\(296\) −14.8469 9.08522i −0.862960 0.528067i
\(297\) 19.9168 1.15569
\(298\) 18.2988 + 15.6219i 1.06002 + 0.904954i
\(299\) 9.75789i 0.564314i
\(300\) 0.631266 11.8871i 0.0364462 0.686300i
\(301\) 4.22540 + 5.64402i 0.243548 + 0.325316i
\(302\) 15.9096 + 13.5823i 0.915496 + 0.781572i
\(303\) −8.46033 −0.486034
\(304\) −5.63687 17.2986i −0.323297 0.992140i
\(305\) 9.08762 + 0.960292i 0.520355 + 0.0549861i
\(306\) −1.17515 + 1.37651i −0.0671787 + 0.0786900i
\(307\) −0.426554 −0.0243447 −0.0121723 0.999926i \(-0.503875\pi\)
−0.0121723 + 0.999926i \(0.503875\pi\)
\(308\) −13.8598 13.4571i −0.789738 0.766789i
\(309\) 6.03272i 0.343190i
\(310\) 10.8599 10.2985i 0.616800 0.584914i
\(311\) 0.586913 0.0332808 0.0166404 0.999862i \(-0.494703\pi\)
0.0166404 + 0.999862i \(0.494703\pi\)
\(312\) −9.77180 + 15.9689i −0.553219 + 0.904063i
\(313\) 6.45704 0.364973 0.182487 0.983208i \(-0.441585\pi\)
0.182487 + 0.983208i \(0.441585\pi\)
\(314\) −17.9343 15.3108i −1.01209 0.864038i
\(315\) −8.04522 + 4.79369i −0.453297 + 0.270094i
\(316\) 4.92442 0.782093i 0.277020 0.0439962i
\(317\) −10.3086 −0.578986 −0.289493 0.957180i \(-0.593487\pi\)
−0.289493 + 0.957180i \(0.593487\pi\)
\(318\) 3.26780 3.82775i 0.183249 0.214650i
\(319\) 30.5304i 1.70937i
\(320\) −6.42259 16.6958i −0.359033 0.933325i
\(321\) 12.9359i 0.722013i
\(322\) 0.420006 6.55270i 0.0234060 0.365168i
\(323\) 3.67728i 0.204609i
\(324\) 0.547473 + 3.44714i 0.0304151 + 0.191508i
\(325\) −5.81085 + 27.1882i −0.322328 + 1.50813i
\(326\) 11.6883 + 9.97844i 0.647354 + 0.552655i
\(327\) 8.51311i 0.470776i
\(328\) 11.2951 18.4582i 0.623665 1.01918i
\(329\) −7.60132 10.1534i −0.419074 0.559773i
\(330\) −9.97188 + 9.45637i −0.548934 + 0.520556i
\(331\) 8.02828 0.441274 0.220637 0.975356i \(-0.429186\pi\)
0.220637 + 0.975356i \(0.429186\pi\)
\(332\) 1.80659 + 11.3751i 0.0991497 + 0.624292i
\(333\) 9.74170 0.533842
\(334\) 5.45087 + 4.65349i 0.298259 + 0.254627i
\(335\) 2.76622 26.1778i 0.151135 1.43025i
\(336\) 7.24939 10.3030i 0.395486 0.562074i
\(337\) 33.3339i 1.81582i −0.419170 0.907908i \(-0.637679\pi\)
0.419170 0.907908i \(-0.362321\pi\)
\(338\) 16.4533 19.2726i 0.894942 1.04829i
\(339\) 0.100876i 0.00547885i
\(340\) −0.188735 3.61065i −0.0102356 0.195815i
\(341\) −17.2785 −0.935681
\(342\) 7.74427 + 6.61139i 0.418762 + 0.357503i
\(343\) 6.47418 + 17.3518i 0.349573 + 0.936909i
\(344\) 3.93412 6.42908i 0.212113 0.346633i
\(345\) −4.64523 0.490863i −0.250091 0.0264272i
\(346\) 3.99213 + 3.40814i 0.214618 + 0.183223i
\(347\) 16.7685i 0.900182i −0.892983 0.450091i \(-0.851392\pi\)
0.892983 0.450091i \(-0.148608\pi\)
\(348\) −19.6632 + 3.12290i −1.05406 + 0.167405i
\(349\) −0.234376 −0.0125458 −0.00627292 0.999980i \(-0.501997\pi\)
−0.00627292 + 0.999980i \(0.501997\pi\)
\(350\) 5.07241 18.0075i 0.271132 0.962542i
\(351\) 30.3350i 1.61916i
\(352\) −7.88290 + 19.0882i −0.420160 + 1.01741i
\(353\) −14.2235 −0.757039 −0.378519 0.925593i \(-0.623567\pi\)
−0.378519 + 0.925593i \(0.623567\pi\)
\(354\) −11.4287 9.75680i −0.607426 0.518568i
\(355\) 1.92041 18.1736i 0.101925 0.964556i
\(356\) 9.79256 1.55525i 0.519004 0.0824280i
\(357\) 2.03831 1.52598i 0.107879 0.0807634i
\(358\) −6.67506 + 7.81885i −0.352788 + 0.413239i
\(359\) 14.2398i 0.751549i −0.926711 0.375774i \(-0.877377\pi\)
0.926711 0.375774i \(-0.122623\pi\)
\(360\) 7.94329 + 6.09413i 0.418648 + 0.321189i
\(361\) −1.68839 −0.0888626
\(362\) −16.7431 + 19.6121i −0.879999 + 1.03079i
\(363\) 2.77140 0.145461
\(364\) −20.4963 + 21.1097i −1.07430 + 1.10645i
\(365\) −33.7517 3.56656i −1.76665 0.186682i
\(366\) 4.46698 5.23241i 0.233493 0.273503i
\(367\) 5.09891i 0.266161i −0.991105 0.133080i \(-0.957513\pi\)
0.991105 0.133080i \(-0.0424868\pi\)
\(368\) −6.67411 + 2.17481i −0.347912 + 0.113370i
\(369\) 12.1112i 0.630485i
\(370\) −14.1209 + 13.3909i −0.734110 + 0.696159i
\(371\) 6.33196 4.74043i 0.328739 0.246111i
\(372\) −1.76738 11.1283i −0.0916346 0.576973i
\(373\) 25.1282 1.30109 0.650545 0.759468i \(-0.274541\pi\)
0.650545 + 0.759468i \(0.274541\pi\)
\(374\) −2.71019 + 3.17459i −0.140140 + 0.164154i
\(375\) −12.6506 4.13393i −0.653273 0.213475i
\(376\) −7.07731 + 11.5656i −0.364984 + 0.596452i
\(377\) 46.5004 2.39489
\(378\) −1.30570 + 20.3708i −0.0671581 + 1.04776i
\(379\) −5.77914 −0.296855 −0.148427 0.988923i \(-0.547421\pi\)
−0.148427 + 0.988923i \(0.547421\pi\)
\(380\) −20.3136 + 1.06183i −1.04206 + 0.0544705i
\(381\) 7.06428 0.361914
\(382\) 2.68147 + 2.28921i 0.137196 + 0.117126i
\(383\) 24.8199i 1.26824i 0.773237 + 0.634118i \(0.218636\pi\)
−0.773237 + 0.634118i \(0.781364\pi\)
\(384\) −13.1002 3.12451i −0.668516 0.159447i
\(385\) −18.5543 + 11.0555i −0.945615 + 0.563438i
\(386\) 15.0784 + 12.8726i 0.767470 + 0.655200i
\(387\) 4.21839i 0.214433i
\(388\) 3.67649 + 23.1488i 0.186645 + 1.17520i
\(389\) 7.34694i 0.372505i 0.982502 + 0.186252i \(0.0596342\pi\)
−0.982502 + 0.186252i \(0.940366\pi\)
\(390\) 14.4029 + 15.1880i 0.729317 + 0.769075i
\(391\) −1.41876 −0.0717499
\(392\) 14.6725 13.2936i 0.741071 0.671426i
\(393\) 20.5688i 1.03756i
\(394\) −7.59399 + 8.89524i −0.382580 + 0.448136i
\(395\) 0.585816 5.54380i 0.0294756 0.278939i
\(396\) −1.81296 11.4152i −0.0911045 0.573636i
\(397\) 10.0197i 0.502872i −0.967874 0.251436i \(-0.919097\pi\)
0.967874 0.251436i \(-0.0809029\pi\)
\(398\) 24.9327 29.2050i 1.24976 1.46391i
\(399\) −8.58518 11.4675i −0.429796 0.574095i
\(400\) −19.8910 + 2.08517i −0.994550 + 0.104259i
\(401\) 11.7525 0.586893 0.293447 0.955975i \(-0.405198\pi\)
0.293447 + 0.955975i \(0.405198\pi\)
\(402\) −15.0725 12.8676i −0.751748 0.641778i
\(403\) 26.3166i 1.31092i
\(404\) 2.22959 + 14.0385i 0.110926 + 0.698443i
\(405\) 3.88072 + 0.410077i 0.192834 + 0.0203769i
\(406\) −31.2264 2.00150i −1.54974 0.0993330i
\(407\) 22.4668 1.11364
\(408\) −2.32182 1.42078i −0.114947 0.0703393i
\(409\) 4.67758i 0.231292i 0.993291 + 0.115646i \(0.0368938\pi\)
−0.993291 + 0.115646i \(0.963106\pi\)
\(410\) −16.6480 17.5556i −0.822187 0.867008i
\(411\) 7.85562i 0.387489i
\(412\) 10.0103 1.58983i 0.493173 0.0783254i
\(413\) −14.1537 18.9056i −0.696457 0.930282i
\(414\) 2.55080 2.98789i 0.125365 0.146847i
\(415\) 12.8059 + 1.35320i 0.628616 + 0.0664261i
\(416\) 29.0730 + 12.0063i 1.42542 + 0.588659i
\(417\) 7.58921i 0.371645i
\(418\) 17.8603 + 15.2475i 0.873574 + 0.745782i
\(419\) 21.7400i 1.06207i 0.847351 + 0.531034i \(0.178196\pi\)
−0.847351 + 0.531034i \(0.821804\pi\)
\(420\) −9.01820 10.8191i −0.440043 0.527919i
\(421\) 9.76923i 0.476123i −0.971250 0.238062i \(-0.923488\pi\)
0.971250 0.238062i \(-0.0765120\pi\)
\(422\) −18.4732 + 21.6387i −0.899263 + 1.05335i
\(423\) 7.58871i 0.368976i
\(424\) −7.21270 4.41364i −0.350280 0.214345i
\(425\) −3.95306 0.844877i −0.191752 0.0409826i
\(426\) −10.4639 8.93318i −0.506978 0.432814i
\(427\) 8.65559 6.48001i 0.418873 0.313590i
\(428\) 21.4651 3.40907i 1.03755 0.164783i
\(429\) 24.1647i 1.16668i
\(430\) −5.79858 6.11469i −0.279632 0.294876i
\(431\) 2.12901i 0.102551i −0.998685 0.0512753i \(-0.983671\pi\)
0.998685 0.0512753i \(-0.0163286\pi\)
\(432\) 20.7483 6.76099i 0.998251 0.325288i
\(433\) −1.12265 −0.0539513 −0.0269756 0.999636i \(-0.508588\pi\)
−0.0269756 + 0.999636i \(0.508588\pi\)
\(434\) 1.13274 17.6723i 0.0543731 0.848299i
\(435\) −2.33917 + 22.1364i −0.112154 + 1.06136i
\(436\) 14.1261 2.24350i 0.676518 0.107444i
\(437\) 7.98197i 0.381829i
\(438\) −16.5905 + 19.4334i −0.792726 + 0.928562i
\(439\) −17.9973 −0.858964 −0.429482 0.903075i \(-0.641304\pi\)
−0.429482 + 0.903075i \(0.641304\pi\)
\(440\) 18.3192 + 14.0546i 0.873335 + 0.670027i
\(441\) −3.12104 + 10.6323i −0.148621 + 0.506301i
\(442\) 4.83516 + 4.12785i 0.229985 + 0.196342i
\(443\) 10.1199i 0.480810i −0.970673 0.240405i \(-0.922720\pi\)
0.970673 0.240405i \(-0.0772803\pi\)
\(444\) 2.29809 + 14.4698i 0.109063 + 0.686708i
\(445\) 1.16494 11.0243i 0.0552233 0.522600i
\(446\) −16.9211 14.4457i −0.801235 0.684026i
\(447\) 20.2521i 0.957891i
\(448\) −19.0066 9.31397i −0.897976 0.440044i
\(449\) 0.750627 0.0354243 0.0177121 0.999843i \(-0.494362\pi\)
0.0177121 + 0.999843i \(0.494362\pi\)
\(450\) 8.88653 6.80607i 0.418915 0.320841i
\(451\) 27.9315i 1.31524i
\(452\) −0.167388 + 0.0265844i −0.00787325 + 0.00125043i
\(453\) 17.6079i 0.827291i
\(454\) 16.0922 18.8496i 0.755244 0.884657i
\(455\) 16.8384 + 28.2598i 0.789397 + 1.32484i
\(456\) −7.99334 + 13.0626i −0.374323 + 0.611713i
\(457\) 20.4998i 0.958941i 0.877558 + 0.479471i \(0.159171\pi\)
−0.877558 + 0.479471i \(0.840829\pi\)
\(458\) −15.2177 + 17.8253i −0.711077 + 0.832922i
\(459\) 4.41060 0.205869
\(460\) 0.409672 + 7.83735i 0.0191011 + 0.365418i
\(461\) −14.9599 −0.696752 −0.348376 0.937355i \(-0.613267\pi\)
−0.348376 + 0.937355i \(0.613267\pi\)
\(462\) −1.04011 + 16.2273i −0.0483904 + 0.754961i
\(463\) −23.1072 −1.07388 −0.536941 0.843619i \(-0.680420\pi\)
−0.536941 + 0.843619i \(0.680420\pi\)
\(464\) 10.3639 + 31.8049i 0.481131 + 1.47651i
\(465\) −12.5280 1.32383i −0.580970 0.0613913i
\(466\) −15.1695 12.9504i −0.702715 0.599918i
\(467\) 22.3760 1.03544 0.517720 0.855550i \(-0.326781\pi\)
0.517720 + 0.855550i \(0.326781\pi\)
\(468\) −17.3863 + 2.76129i −0.803684 + 0.127641i
\(469\) −18.6663 24.9333i −0.861932 1.15131i
\(470\) 10.4314 + 11.0001i 0.481165 + 0.507395i
\(471\) 19.8487i 0.914580i
\(472\) −13.1780 + 21.5352i −0.606565 + 0.991239i
\(473\) 9.72868i 0.447325i
\(474\) −3.19198 2.72503i −0.146612 0.125165i
\(475\) −4.75329 + 22.2400i −0.218096 + 1.02044i
\(476\) −3.06928 2.98009i −0.140680 0.136592i
\(477\) 4.73256 0.216689
\(478\) −24.4388 20.8638i −1.11781 0.954287i
\(479\) 32.6071 1.48986 0.744928 0.667145i \(-0.232484\pi\)
0.744928 + 0.667145i \(0.232484\pi\)
\(480\) −7.17808 + 13.2362i −0.327633 + 0.604147i
\(481\) 34.2189i 1.56025i
\(482\) −16.1568 13.7933i −0.735924 0.628268i
\(483\) −4.42439 + 3.31232i −0.201317 + 0.150716i
\(484\) −0.730361 4.59869i −0.0331982 0.209031i
\(485\) 26.0605 + 2.75382i 1.18335 + 0.125045i
\(486\) −13.1207 + 15.3690i −0.595167 + 0.697150i
\(487\) 3.90400 0.176907 0.0884536 0.996080i \(-0.471808\pi\)
0.0884536 + 0.996080i \(0.471808\pi\)
\(488\) −9.85953 6.03330i −0.446320 0.273115i
\(489\) 12.9359i 0.584983i
\(490\) −10.0911 19.7020i −0.455869 0.890047i
\(491\) −20.5527 −0.927532 −0.463766 0.885958i \(-0.653502\pi\)
−0.463766 + 0.885958i \(0.653502\pi\)
\(492\) −17.9894 + 2.85707i −0.811025 + 0.128806i
\(493\) 6.76099i 0.304500i
\(494\) 23.2233 27.2027i 1.04487 1.22391i
\(495\) −12.8510 1.35797i −0.577610 0.0610362i
\(496\) −17.9997 + 5.86536i −0.808213 + 0.263363i
\(497\) −12.9589 17.3096i −0.581285 0.776444i
\(498\) 6.29468 7.37329i 0.282072 0.330405i
\(499\) −25.8654 −1.15789 −0.578947 0.815365i \(-0.696536\pi\)
−0.578947 + 0.815365i \(0.696536\pi\)
\(500\) −3.52571 + 22.0810i −0.157674 + 0.987491i
\(501\) 6.03272i 0.269522i
\(502\) 16.6199 + 14.1886i 0.741783 + 0.633270i
\(503\) 31.0150i 1.38289i −0.722428 0.691446i \(-0.756974\pi\)
0.722428 0.691446i \(-0.243026\pi\)
\(504\) 11.7943 1.10593i 0.525359 0.0492620i
\(505\) 15.8043 + 1.67004i 0.703281 + 0.0743160i
\(506\) 5.88279 6.89082i 0.261522 0.306334i
\(507\) −21.3299 −0.947293
\(508\) −1.86168 11.7220i −0.0825988 0.520080i
\(509\) −14.2066 −0.629695 −0.314847 0.949142i \(-0.601953\pi\)
−0.314847 + 0.949142i \(0.601953\pi\)
\(510\) −2.20828 + 2.09412i −0.0977844 + 0.0927293i
\(511\) −32.1471 + 24.0670i −1.42211 + 1.06466i
\(512\) −1.73225 + 22.5610i −0.0765556 + 0.997065i
\(513\) 24.8141i 1.09557i
\(514\) 18.3604 21.5065i 0.809842 0.948611i
\(515\) 1.19084 11.2694i 0.0524747 0.496589i
\(516\) −6.26579 + 0.995129i −0.275836 + 0.0438081i
\(517\) 17.5015i 0.769714i
\(518\) −1.47287 + 22.9790i −0.0647144 + 1.00964i
\(519\) 4.41827i 0.193940i
\(520\) 21.4064 27.9017i 0.938732 1.22357i
\(521\) 37.9559i 1.66288i −0.555617 0.831438i \(-0.687518\pi\)
0.555617 0.831438i \(-0.312482\pi\)
\(522\) −14.2385 12.1556i −0.623203 0.532037i
\(523\) 20.8846 0.913219 0.456609 0.889667i \(-0.349064\pi\)
0.456609 + 0.889667i \(0.349064\pi\)
\(524\) 34.1305 5.42059i 1.49100 0.236800i
\(525\) −14.3001 + 6.59431i −0.624106 + 0.287799i
\(526\) −2.85560 + 3.34492i −0.124510 + 0.145845i
\(527\) −3.82633 −0.166678
\(528\) 16.5279 5.38575i 0.719285 0.234385i
\(529\) −19.9204 −0.866105
\(530\) −6.85999 + 6.50536i −0.297979 + 0.282575i
\(531\) 14.1302i 0.613198i
\(532\) −16.7660 + 17.2678i −0.726898 + 0.748653i
\(533\) 42.5421 1.84270
\(534\) −6.34747 5.41893i −0.274682 0.234500i
\(535\) 2.55351 24.1649i 0.110398 1.04474i
\(536\) −17.3795 + 28.4014i −0.750682 + 1.22675i
\(537\) 8.65347 0.373425
\(538\) −10.3008 + 12.0659i −0.444099 + 0.520196i
\(539\) −7.19790 + 24.5208i −0.310036 + 1.05619i
\(540\) −1.27358 24.3645i −0.0548060 1.04848i
\(541\) 1.19268i 0.0512773i −0.999671 0.0256387i \(-0.991838\pi\)
0.999671 0.0256387i \(-0.00816194\pi\)
\(542\) −6.06428 + 7.10341i −0.260483 + 0.305118i
\(543\) 21.7056 0.931476
\(544\) −1.74568 + 4.22711i −0.0748452 + 0.181236i
\(545\) 1.68046 15.9029i 0.0719831 0.681204i
\(546\) 24.7155 + 1.58418i 1.05773 + 0.0677967i
\(547\) 15.5500i 0.664872i −0.943126 0.332436i \(-0.892129\pi\)
0.943126 0.332436i \(-0.107871\pi\)
\(548\) 13.0351 2.07023i 0.556833 0.0884358i
\(549\) 6.46926 0.276101
\(550\) 20.4946 15.6965i 0.873892 0.669301i
\(551\) 38.0374 1.62045
\(552\) 5.03980 + 3.08398i 0.214508 + 0.131263i
\(553\) −3.95306 5.28025i −0.168101 0.224539i
\(554\) 14.7563 17.2849i 0.626936 0.734364i
\(555\) 16.2898 + 1.72135i 0.691465 + 0.0730674i
\(556\) −12.5930 + 2.00002i −0.534064 + 0.0848197i
\(557\) 31.9739 1.35478 0.677390 0.735624i \(-0.263111\pi\)
0.677390 + 0.735624i \(0.263111\pi\)
\(558\) 6.87939 8.05819i 0.291228 0.341130i
\(559\) 14.8176 0.626718
\(560\) −15.5760 + 17.8154i −0.658204 + 0.752839i
\(561\) 3.51345 0.148338
\(562\) −19.4243 + 22.7527i −0.819363 + 0.959763i
\(563\) −6.48451 −0.273290 −0.136645 0.990620i \(-0.543632\pi\)
−0.136645 + 0.990620i \(0.543632\pi\)
\(564\) 11.2719 1.79019i 0.474632 0.0753808i
\(565\) −0.0199127 + 0.188441i −0.000837733 + 0.00792779i
\(566\) 22.7015 26.5915i 0.954217 1.11772i
\(567\) 3.69622 2.76718i 0.155227 0.116211i
\(568\) −12.0655 + 19.7173i −0.506259 + 0.827321i
\(569\) 36.4610 1.52853 0.764263 0.644905i \(-0.223103\pi\)
0.764263 + 0.644905i \(0.223103\pi\)
\(570\) 11.7816 + 12.4238i 0.493475 + 0.520377i
\(571\) 24.9527 1.04424 0.522119 0.852872i \(-0.325142\pi\)
0.522119 + 0.852872i \(0.325142\pi\)
\(572\) −40.0973 + 6.36823i −1.67655 + 0.266269i
\(573\) 2.96770i 0.123978i
\(574\) −28.5682 1.83113i −1.19241 0.0764298i
\(575\) 8.58060 + 1.83391i 0.357836 + 0.0764792i
\(576\) −5.76366 11.2763i −0.240152 0.469846i
\(577\) 21.7435 0.905192 0.452596 0.891716i \(-0.350498\pi\)
0.452596 + 0.891716i \(0.350498\pi\)
\(578\) 15.0097 17.5817i 0.624323 0.731302i
\(579\) 16.6879i 0.693526i
\(580\) 37.3482 1.95226i 1.55080 0.0810631i
\(581\) 12.1971 9.13136i 0.506020 0.378833i
\(582\) 12.8099 15.0049i 0.530988 0.621975i
\(583\) 10.9145 0.452032
\(584\) 36.6186 + 22.4079i 1.51529 + 0.927245i
\(585\) −2.06830 + 19.5732i −0.0855139 + 0.809251i
\(586\) −12.2627 10.4688i −0.506568 0.432464i
\(587\) 24.7885 1.02313 0.511565 0.859245i \(-0.329066\pi\)
0.511565 + 0.859245i \(0.329066\pi\)
\(588\) −16.5290 2.12764i −0.681644 0.0877426i
\(589\) 21.5270i 0.887004i
\(590\) 19.4233 + 20.4821i 0.799644 + 0.843236i
\(591\) 9.84476 0.404959
\(592\) 23.4047 7.62661i 0.961927 0.313452i
\(593\) −41.5751 −1.70728 −0.853642 0.520860i \(-0.825611\pi\)
−0.853642 + 0.520860i \(0.825611\pi\)
\(594\) −18.2882 + 21.4220i −0.750376 + 0.878955i
\(595\) −4.10887 + 2.44824i −0.168447 + 0.100368i
\(596\) −33.6050 + 5.33713i −1.37651 + 0.218617i
\(597\) −32.3224 −1.32287
\(598\) −10.4953 8.95999i −0.429185 0.366401i
\(599\) 38.2863i 1.56434i 0.623068 + 0.782168i \(0.285886\pi\)
−0.623068 + 0.782168i \(0.714114\pi\)
\(600\) 12.2057 + 11.5940i 0.498297 + 0.473325i
\(601\) 22.8512i 0.932121i 0.884753 + 0.466060i \(0.154327\pi\)
−0.884753 + 0.466060i \(0.845673\pi\)
\(602\) −9.95044 0.637790i −0.405550 0.0259944i
\(603\) 18.6354i 0.758891i
\(604\) −29.2174 + 4.64029i −1.18884 + 0.188811i
\(605\) −5.17710 0.547067i −0.210479 0.0222414i
\(606\) 7.76853 9.09969i 0.315575 0.369650i
\(607\) 3.04718i 0.123681i −0.998086 0.0618407i \(-0.980303\pi\)
0.998086 0.0618407i \(-0.0196971\pi\)
\(608\) 23.7818 + 9.82119i 0.964478 + 0.398302i
\(609\) 15.7846 + 21.0841i 0.639624 + 0.854369i
\(610\) −9.37739 + 8.89261i −0.379679 + 0.360051i
\(611\) −26.6562 −1.07840
\(612\) −0.401481 2.52791i −0.0162289 0.102185i
\(613\) −36.3023 −1.46624 −0.733118 0.680101i \(-0.761936\pi\)
−0.733118 + 0.680101i \(0.761936\pi\)
\(614\) 0.391674 0.458789i 0.0158067 0.0185152i
\(615\) −2.14005 + 20.2521i −0.0862950 + 0.816643i
\(616\) 27.2006 2.55055i 1.09594 0.102765i
\(617\) 15.0501i 0.605894i −0.953007 0.302947i \(-0.902029\pi\)
0.953007 0.302947i \(-0.0979705\pi\)
\(618\) −6.48862 5.53943i −0.261011 0.222828i
\(619\) 1.73303i 0.0696563i 0.999393 + 0.0348281i \(0.0110884\pi\)
−0.999393 + 0.0348281i \(0.988912\pi\)
\(620\) 1.10487 + 21.1370i 0.0443725 + 0.848881i
\(621\) −9.57375 −0.384181
\(622\) −0.538921 + 0.631267i −0.0216088 + 0.0253115i
\(623\) −7.86095 10.5002i −0.314942 0.420680i
\(624\) −8.20296 25.1734i −0.328381 1.00774i
\(625\) 22.8158 + 10.2195i 0.912632 + 0.408782i
\(626\) −5.92904 + 6.94500i −0.236972 + 0.277578i
\(627\) 19.7667i 0.789407i
\(628\) 32.9357 5.23082i 1.31428 0.208733i
\(629\) 4.97530 0.198378
\(630\) 2.23141 13.0549i 0.0889014 0.520120i
\(631\) 19.5984i 0.780202i 0.920772 + 0.390101i \(0.127560\pi\)
−0.920772 + 0.390101i \(0.872440\pi\)
\(632\) −3.68055 + 6.01470i −0.146404 + 0.239252i
\(633\) 23.9485 0.951866
\(634\) 9.46563 11.0876i 0.375928 0.440344i
\(635\) −13.1964 1.39447i −0.523682 0.0553377i
\(636\) 1.11642 + 7.02951i 0.0442690 + 0.278738i
\(637\) 37.3473 + 10.9630i 1.47975 + 0.434371i
\(638\) −32.8376 28.0339i −1.30005 1.10987i
\(639\) 12.9374i 0.511795i
\(640\) 23.8550 + 8.42266i 0.942950 + 0.332935i
\(641\) 5.76448 0.227683 0.113842 0.993499i \(-0.463684\pi\)
0.113842 + 0.993499i \(0.463684\pi\)
\(642\) −13.9135 11.8782i −0.549123 0.468794i
\(643\) 12.8313 0.506017 0.253009 0.967464i \(-0.418580\pi\)
0.253009 + 0.967464i \(0.418580\pi\)
\(644\) 6.66224 + 6.46864i 0.262529 + 0.254900i
\(645\) −0.745388 + 7.05389i −0.0293496 + 0.277747i
\(646\) 3.95517 + 3.37658i 0.155614 + 0.132850i
\(647\) 1.42452i 0.0560037i −0.999608 0.0280018i \(-0.991086\pi\)
0.999608 0.0280018i \(-0.00891443\pi\)
\(648\) −4.21035 2.57642i −0.165398 0.101211i
\(649\) 32.5878i 1.27918i
\(650\) −23.9071 31.2150i −0.937714 1.22435i
\(651\) −11.9324 + 8.93318i −0.467666 + 0.350119i
\(652\) −21.4651 + 3.40907i −0.840636 + 0.133509i
\(653\) −29.1628 −1.14123 −0.570615 0.821218i \(-0.693295\pi\)
−0.570615 + 0.821218i \(0.693295\pi\)
\(654\) −9.15646 7.81699i −0.358046 0.305669i
\(655\) 4.06022 38.4234i 0.158646 1.50133i
\(656\) 9.48166 + 29.0975i 0.370197 + 1.13607i
\(657\) −24.0270 −0.937384
\(658\) 17.9004 + 1.14736i 0.697831 + 0.0447286i
\(659\) −7.06968 −0.275396 −0.137698 0.990474i \(-0.543970\pi\)
−0.137698 + 0.990474i \(0.543970\pi\)
\(660\) −1.01452 19.4086i −0.0394902 0.755478i
\(661\) 3.04463 0.118423 0.0592113 0.998245i \(-0.481141\pi\)
0.0592113 + 0.998245i \(0.481141\pi\)
\(662\) −7.37181 + 8.63498i −0.286513 + 0.335608i
\(663\) 5.35129i 0.207827i
\(664\) −13.8936 8.50188i −0.539178 0.329937i
\(665\) 13.7738 + 23.1166i 0.534127 + 0.896421i
\(666\) −8.94512 + 10.4779i −0.346616 + 0.406010i
\(667\) 14.6755i 0.568239i
\(668\) −10.0103 + 1.58983i −0.387311 + 0.0615124i
\(669\) 18.7273i 0.724038i
\(670\) 25.6161 + 27.0125i 0.989636 + 1.04359i
\(671\) 14.9197 0.575970
\(672\) 4.42499 + 17.2577i 0.170698 + 0.665732i
\(673\) 45.1287i 1.73958i 0.493420 + 0.869791i \(0.335747\pi\)
−0.493420 + 0.869791i \(0.664253\pi\)
\(674\) 35.8530 + 30.6082i 1.38101 + 1.17898i
\(675\) −26.6751 5.70120i −1.02673 0.219439i
\(676\) 5.62116 + 35.3934i 0.216199 + 1.36129i
\(677\) 3.41915i 0.131408i −0.997839 0.0657042i \(-0.979071\pi\)
0.997839 0.0657042i \(-0.0209294\pi\)
\(678\) 0.108500 + 0.0926277i 0.00416690 + 0.00355734i
\(679\) 24.8215 18.5827i 0.952563 0.713138i
\(680\) 4.05681 + 3.11241i 0.155572 + 0.119355i
\(681\) −20.8617 −0.799423
\(682\) 15.8656 18.5842i 0.607526 0.711627i
\(683\) 52.1925i 1.99709i 0.0539068 + 0.998546i \(0.482833\pi\)
−0.0539068 + 0.998546i \(0.517167\pi\)
\(684\) −14.2221 + 2.25874i −0.543794 + 0.0863650i
\(685\) 1.55068 14.6747i 0.0592483 0.560690i
\(686\) −24.6079 8.96951i −0.939533 0.342457i
\(687\) 19.7281 0.752673
\(688\) 3.30251 + 10.1348i 0.125907 + 0.386386i
\(689\) 16.6237i 0.633312i
\(690\) 4.79335 4.54555i 0.182480 0.173046i
\(691\) 22.1744i 0.843554i −0.906700 0.421777i \(-0.861406\pi\)
0.906700 0.421777i \(-0.138594\pi\)
\(692\) −7.33139 + 1.16437i −0.278698 + 0.0442626i
\(693\) −12.2401 + 9.16353i −0.464961 + 0.348094i
\(694\) 18.0357 + 15.3974i 0.684628 + 0.584476i
\(695\) −1.49809 + 14.1770i −0.0568256 + 0.537763i
\(696\) 14.6965 24.0167i 0.557068 0.910352i
\(697\) 6.18546i 0.234291i
\(698\) 0.215211 0.252088i 0.00814585 0.00954166i
\(699\) 16.7888i 0.635011i
\(700\) 14.7107 + 21.9908i 0.556013 + 0.831173i
\(701\) 17.3192i 0.654138i 0.945001 + 0.327069i \(0.106061\pi\)
−0.945001 + 0.327069i \(0.893939\pi\)
\(702\) 32.6275 + 27.8546i 1.23145 + 1.05130i
\(703\) 27.9911i 1.05570i
\(704\) −13.2925 26.0060i −0.500978 0.980139i
\(705\) 1.34092 12.6897i 0.0505020 0.477920i
\(706\) 13.0604 15.2983i 0.491535 0.575761i
\(707\) 15.0529 11.2694i 0.566124 0.423829i
\(708\) 20.9883 3.33334i 0.788788 0.125275i
\(709\) 3.57195i 0.134147i −0.997748 0.0670737i \(-0.978634\pi\)
0.997748 0.0670737i \(-0.0213663\pi\)
\(710\) 17.7837 + 18.7531i 0.667409 + 0.703792i
\(711\) 3.94650i 0.148005i
\(712\) −7.31904 + 11.9607i −0.274293 + 0.448245i
\(713\) 8.30552 0.311044
\(714\) −0.230334 + 3.59354i −0.00862004 + 0.134485i
\(715\) −4.77003 + 45.1407i −0.178389 + 1.68817i
\(716\) −2.28049 14.3590i −0.0852259 0.536621i
\(717\) 27.0475i 1.01011i
\(718\) 15.3159 + 13.0754i 0.571586 + 0.487971i
\(719\) 1.20606 0.0449783 0.0224891 0.999747i \(-0.492841\pi\)
0.0224891 + 0.999747i \(0.492841\pi\)
\(720\) −13.8484 + 2.94776i −0.516101 + 0.109856i
\(721\) −8.03575 10.7336i −0.299267 0.399742i
\(722\) 1.55033 1.81598i 0.0576973 0.0675839i
\(723\) 17.8815i 0.665020i
\(724\) −5.72017 36.0168i −0.212589 1.33856i
\(725\) 8.73933 40.8901i 0.324571 1.51862i
\(726\) −2.54479 + 2.98084i −0.0944458 + 0.110629i
\(727\) 28.9323i 1.07304i 0.843888 + 0.536520i \(0.180261\pi\)
−0.843888 + 0.536520i \(0.819739\pi\)
\(728\) −3.88471 41.4288i −0.143977 1.53545i
\(729\) 22.2450 0.823890
\(730\) 34.8279 33.0275i 1.28904 1.22240i
\(731\) 2.15443i 0.0796843i
\(732\) 1.52611 + 9.60912i 0.0564068 + 0.355163i
\(733\) 11.5527i 0.426710i −0.976975 0.213355i \(-0.931561\pi\)
0.976975 0.213355i \(-0.0684391\pi\)
\(734\) 5.48424 + 4.68197i 0.202427 + 0.172815i
\(735\) −7.09765 + 17.2276i −0.261801 + 0.635450i
\(736\) 3.78920 9.17546i 0.139672 0.338212i
\(737\) 42.9779i 1.58311i
\(738\) −13.0265 11.1209i −0.479511 0.409365i
\(739\) −11.3868 −0.418869 −0.209434 0.977823i \(-0.567162\pi\)
−0.209434 + 0.977823i \(0.567162\pi\)
\(740\) −1.43663 27.4839i −0.0528117 1.01033i
\(741\) −30.1064 −1.10599
\(742\) −0.715529 + 11.1633i −0.0262679 + 0.409817i
\(743\) −48.8376 −1.79168 −0.895840 0.444377i \(-0.853425\pi\)
−0.895840 + 0.444377i \(0.853425\pi\)
\(744\) 13.5921 + 8.31735i 0.498311 + 0.304929i
\(745\) −3.99770 + 37.8318i −0.146464 + 1.38605i
\(746\) −23.0735 + 27.0272i −0.844780 + 0.989536i
\(747\) 9.11621 0.333545
\(748\) −0.925917 5.83000i −0.0338549 0.213166i
\(749\) −17.2310 23.0161i −0.629607 0.840989i
\(750\) 16.0625 9.81069i 0.586518 0.358236i
\(751\) 0.434842i 0.0158676i −0.999969 0.00793381i \(-0.997475\pi\)
0.999969 0.00793381i \(-0.00252544\pi\)
\(752\) −5.94107 18.2321i −0.216648 0.664855i
\(753\) 18.3940i 0.670314i
\(754\) −42.6981 + 50.0145i −1.55497 + 1.82142i
\(755\) −3.47575 + 32.8923i −0.126495 + 1.19707i
\(756\) −20.7114 20.1095i −0.753265 0.731375i
\(757\) −13.5346 −0.491923 −0.245962 0.969280i \(-0.579104\pi\)
−0.245962 + 0.969280i \(0.579104\pi\)
\(758\) 5.30658 6.21588i 0.192744 0.225771i
\(759\) −7.62638 −0.276820
\(760\) 17.5104 22.8237i 0.635171 0.827902i
\(761\) 28.4347i 1.03076i −0.856963 0.515378i \(-0.827651\pi\)
0.856963 0.515378i \(-0.172349\pi\)
\(762\) −6.48663 + 7.59813i −0.234986 + 0.275251i
\(763\) −11.3397 15.1468i −0.410524 0.548352i
\(764\) −4.92442 + 0.782093i −0.178159 + 0.0282951i
\(765\) −2.84587 0.300724i −0.102893 0.0108727i
\(766\) −26.6955 22.7903i −0.964548 0.823448i
\(767\) −49.6339 −1.79218
\(768\) 15.3896 11.2212i 0.555325 0.404909i
\(769\) 37.6894i 1.35912i 0.733622 + 0.679558i \(0.237828\pi\)
−0.733622 + 0.679558i \(0.762172\pi\)
\(770\) 5.14619 30.1079i 0.185456 1.08501i
\(771\) −23.8022 −0.857215
\(772\) −27.6909 + 4.39785i −0.996616 + 0.158282i
\(773\) 8.24274i 0.296471i 0.988952 + 0.148235i \(0.0473593\pi\)
−0.988952 + 0.148235i \(0.952641\pi\)
\(774\) −4.53718 3.87345i −0.163086 0.139228i
\(775\) 23.1415 + 4.94596i 0.831266 + 0.177664i
\(776\) −28.2741 17.3016i −1.01498 0.621093i
\(777\) 15.5154 11.6156i 0.556612 0.416708i
\(778\) −7.90216 6.74618i −0.283306 0.241862i
\(779\) 34.7995 1.24682
\(780\) −29.5609 + 1.54520i −1.05845 + 0.0553271i
\(781\) 29.8369i 1.06765i
\(782\) 1.30275 1.52598i 0.0465862 0.0545689i
\(783\) 45.6229i 1.63043i
\(784\) 0.825482 + 27.9878i 0.0294815 + 0.999565i
\(785\) 3.91808 37.0783i 0.139842 1.32338i
\(786\) −22.1232 18.8869i −0.789109 0.673673i
\(787\) 22.9785 0.819095 0.409547 0.912289i \(-0.365687\pi\)
0.409547 + 0.912289i \(0.365687\pi\)
\(788\) −2.59444 16.3358i −0.0924230 0.581937i
\(789\) 3.70197 0.131793
\(790\) 5.42484 + 5.72057i 0.193007 + 0.203529i
\(791\) 0.134370 + 0.179483i 0.00477765 + 0.00638167i
\(792\) 13.9426 + 8.53183i 0.495428 + 0.303165i
\(793\) 22.7240i 0.806954i
\(794\) 10.7769 + 9.20035i 0.382456 + 0.326508i
\(795\) 7.91367 + 0.836241i 0.280669 + 0.0296584i
\(796\) 8.51809 + 53.6338i 0.301916 + 1.90100i
\(797\) 33.7838i 1.19668i 0.801241 + 0.598341i \(0.204173\pi\)
−0.801241 + 0.598341i \(0.795827\pi\)
\(798\) 20.2173 + 1.29586i 0.715685 + 0.0458730i
\(799\) 3.87572i 0.137113i
\(800\) 16.0218 23.3089i 0.566455 0.824093i
\(801\) 7.84790i 0.277292i
\(802\) −10.7915 + 12.6407i −0.381062 + 0.446358i
\(803\) −55.4124 −1.95546
\(804\) 27.6801 4.39613i 0.976200 0.155040i
\(805\) 8.91880 5.31421i 0.314346 0.187301i
\(806\) −28.3053 24.1647i −0.997013 0.851164i
\(807\) 13.3538 0.470077
\(808\) −17.1467 10.4925i −0.603220 0.369126i
\(809\) 20.4803 0.720049 0.360024 0.932943i \(-0.382768\pi\)
0.360024 + 0.932943i \(0.382768\pi\)
\(810\) −4.00446 + 3.79744i −0.140702 + 0.133429i
\(811\) 12.3156i 0.432460i 0.976342 + 0.216230i \(0.0693762\pi\)
−0.976342 + 0.216230i \(0.930624\pi\)
\(812\) 30.8257 31.7483i 1.08177 1.11415i
\(813\) 7.86166 0.275720
\(814\) −20.6297 + 24.1647i −0.723071 + 0.846971i
\(815\) −2.55351 + 24.1649i −0.0894457 + 0.846459i
\(816\) 3.66012 1.19268i 0.128130 0.0417522i
\(817\) 12.1208 0.424054
\(818\) −5.03108 4.29510i −0.175907 0.150175i
\(819\) 13.9568 + 18.6427i 0.487691 + 0.651427i
\(820\) 34.1690 1.78607i 1.19323 0.0623724i
\(821\) 26.8208i 0.936053i 0.883715 + 0.468026i \(0.155035\pi\)
−0.883715 + 0.468026i \(0.844965\pi\)
\(822\) −8.44928 7.21327i −0.294703 0.251592i
\(823\) 26.3764 0.919425 0.459712 0.888068i \(-0.347953\pi\)
0.459712 + 0.888068i \(0.347953\pi\)
\(824\) −7.48179 + 12.2266i −0.260641 + 0.425935i
\(825\) −21.2492 4.54153i −0.739802 0.158116i
\(826\) 33.3306 + 2.13638i 1.15972 + 0.0743342i
\(827\) 13.0913i 0.455228i −0.973751 0.227614i \(-0.926908\pi\)
0.973751 0.227614i \(-0.0730924\pi\)
\(828\) 0.871464 + 5.48714i 0.0302855 + 0.190691i
\(829\) −13.7348 −0.477030 −0.238515 0.971139i \(-0.576661\pi\)
−0.238515 + 0.971139i \(0.576661\pi\)
\(830\) −13.2142 + 12.5311i −0.458672 + 0.434961i
\(831\) −19.1299 −0.663610
\(832\) −39.6094 + 20.2455i −1.37321 + 0.701888i
\(833\) −1.59398 + 5.43016i −0.0552282 + 0.188144i
\(834\) 8.16273 + 6.96864i 0.282652 + 0.241304i
\(835\) −1.19084 + 11.2694i −0.0412108 + 0.389994i
\(836\) −32.7996 + 5.20922i −1.13440 + 0.180165i
\(837\) −25.8200 −0.892468
\(838\) −23.3829 19.9623i −0.807749 0.689586i
\(839\) −25.7342 −0.888445 −0.444222 0.895917i \(-0.646520\pi\)
−0.444222 + 0.895917i \(0.646520\pi\)
\(840\) 19.9175 + 0.234735i 0.687220 + 0.00809914i
\(841\) −40.9351 −1.41155
\(842\) 10.5075 + 8.97040i 0.362112 + 0.309140i
\(843\) 25.1814 0.867293
\(844\) −6.31125 39.7386i −0.217242 1.36786i
\(845\) 39.8452 + 4.21045i 1.37072 + 0.144844i
\(846\) 8.16220 + 6.96818i 0.280622 + 0.239571i
\(847\) −4.93098 + 3.69158i −0.169431 + 0.126844i
\(848\) 11.3701 3.70504i 0.390451 0.127232i
\(849\) −29.4300 −1.01003
\(850\) 4.53854 3.47601i 0.155671 0.119226i
\(851\) −10.7995 −0.370202
\(852\) 19.2165 3.05196i 0.658348 0.104558i
\(853\) 8.40578i 0.287808i 0.989592 + 0.143904i \(0.0459657\pi\)
−0.989592 + 0.143904i \(0.954034\pi\)
\(854\) −0.978104 + 15.2598i −0.0334700 + 0.522181i
\(855\) −1.69188 + 16.0109i −0.0578609 + 0.547561i
\(856\) −16.0432 + 26.2175i −0.548344 + 0.896096i
\(857\) −25.2022 −0.860892 −0.430446 0.902616i \(-0.641644\pi\)
−0.430446 + 0.902616i \(0.641644\pi\)
\(858\) 25.9908 + 22.1887i 0.887312 + 0.757511i
\(859\) 44.9663i 1.53423i −0.641510 0.767114i \(-0.721692\pi\)
0.641510 0.767114i \(-0.278308\pi\)
\(860\) 11.9012 0.622098i 0.405828 0.0212133i
\(861\) 14.4409 + 19.2893i 0.492146 + 0.657377i
\(862\) 2.28990 + 1.95492i 0.0779942 + 0.0665847i
\(863\) 21.2327 0.722768 0.361384 0.932417i \(-0.382304\pi\)
0.361384 + 0.932417i \(0.382304\pi\)
\(864\) −11.7798 + 28.5244i −0.400755 + 0.970419i
\(865\) −0.872153 + 8.25352i −0.0296541 + 0.280628i
\(866\) 1.03085 1.20749i 0.0350299 0.0410323i
\(867\) −19.4584 −0.660843
\(868\) 17.9677 + 17.4456i 0.609865 + 0.592142i
\(869\) 9.10163i 0.308752i
\(870\) −21.6614 22.8423i −0.734391 0.774426i
\(871\) −65.4590 −2.21799
\(872\) −10.5580 + 17.2537i −0.357538 + 0.584283i
\(873\) 18.5518 0.627884
\(874\) −8.58518 7.32929i −0.290398 0.247917i
\(875\) 28.0149 9.49567i 0.947075 0.321012i
\(876\) −5.66804 35.6886i −0.191505 1.20581i
\(877\) 23.4510 0.791884 0.395942 0.918275i \(-0.370418\pi\)
0.395942 + 0.918275i \(0.370418\pi\)
\(878\) 16.5257 19.3574i 0.557714 0.653280i
\(879\) 13.5717i 0.457762i
\(880\) −31.9380 + 6.79827i −1.07663 + 0.229170i
\(881\) 30.2220i 1.01821i 0.860706 + 0.509103i \(0.170023\pi\)
−0.860706 + 0.509103i \(0.829977\pi\)
\(882\) −8.56998 13.1198i −0.288566 0.441767i
\(883\) 55.2980i 1.86092i −0.366387 0.930462i \(-0.619405\pi\)
0.366387 0.930462i \(-0.380595\pi\)
\(884\) −8.87959 + 1.41025i −0.298653 + 0.0474319i
\(885\) 2.49680 23.6281i 0.0839289 0.794252i
\(886\) 10.8847 + 9.29238i 0.365677 + 0.312184i
\(887\) 8.28733i 0.278261i 0.990274 + 0.139131i \(0.0444308\pi\)
−0.990274 + 0.139131i \(0.955569\pi\)
\(888\) −17.6735 10.8149i −0.593084 0.362924i
\(889\) −12.5690 + 9.40981i −0.421551 + 0.315595i
\(890\) 10.7877 + 11.3758i 0.361604 + 0.381317i
\(891\) 6.37123 0.213444
\(892\) 31.0748 4.93529i 1.04046 0.165246i
\(893\) −21.8048 −0.729671
\(894\) 21.7826 + 18.5961i 0.728518 + 0.621946i
\(895\) −16.1651 1.70817i −0.540338 0.0570978i
\(896\) 27.4702 11.8906i 0.917717 0.397236i
\(897\) 11.6156i 0.387834i
\(898\) −0.689248 + 0.807352i −0.0230005 + 0.0269417i
\(899\) 39.5793i 1.32004i
\(900\) −0.839468 + 15.8076i −0.0279823 + 0.526921i
\(901\) 2.41702 0.0805227
\(902\) −30.0423 25.6476i −1.00030 0.853971i
\(903\) 5.02985 + 6.71855i 0.167383 + 0.223579i
\(904\) 0.125107 0.204448i 0.00416100 0.00679984i
\(905\) −40.5470 4.28462i −1.34783 0.142425i
\(906\) 18.9385 + 16.1681i 0.629191 + 0.537149i
\(907\) 18.0875i 0.600587i 0.953847 + 0.300293i \(0.0970845\pi\)
−0.953847 + 0.300293i \(0.902915\pi\)
\(908\) 5.49779 + 34.6166i 0.182451 + 1.14879i
\(909\) 11.2507 0.373162
\(910\) −45.8570 7.83809i −1.52014 0.259830i
\(911\) 6.16833i 0.204366i −0.994766 0.102183i \(-0.967417\pi\)
0.994766 0.102183i \(-0.0325827\pi\)
\(912\) −6.71003 20.5919i −0.222191 0.681866i
\(913\) 21.0243 0.695802
\(914\) −22.0490 18.8236i −0.729317 0.622628i
\(915\) 10.8177 + 1.14311i 0.357623 + 0.0377902i
\(916\) −5.19903 32.7355i −0.171781 1.08161i
\(917\) −27.3982 36.5968i −0.904768 1.20853i
\(918\) −4.04995 + 4.74392i −0.133668 + 0.156573i
\(919\) 55.8085i 1.84095i −0.390797 0.920477i \(-0.627801\pi\)
0.390797 0.920477i \(-0.372199\pi\)
\(920\) −8.80580 6.75586i −0.290319 0.222734i
\(921\) −0.507762 −0.0167313
\(922\) 13.7366 16.0904i 0.452392 0.529910i
\(923\) −45.4441 −1.49581
\(924\) −16.4985 16.0191i −0.542761 0.526989i
\(925\) −30.0904 6.43113i −0.989365 0.211454i
\(926\) 21.2177 24.8534i 0.697258 0.816735i
\(927\) 8.02241i 0.263491i
\(928\) −43.7249 18.0571i −1.43534 0.592754i
\(929\) 14.2579i 0.467787i 0.972262 + 0.233894i \(0.0751467\pi\)
−0.972262 + 0.233894i \(0.924853\pi\)
\(930\) 12.9274 12.2591i 0.423907 0.401993i
\(931\) 30.5501 + 8.96776i 1.00124 + 0.293907i
\(932\) 27.8583 4.42443i 0.912528 0.144927i
\(933\) 0.698651 0.0228728
\(934\) −20.5464 + 24.0670i −0.672297 + 0.787497i
\(935\) −6.56329 0.693545i −0.214643 0.0226814i
\(936\) 12.9947 21.2357i 0.424745 0.694112i
\(937\) −22.5672 −0.737237 −0.368618 0.929581i \(-0.620169\pi\)
−0.368618 + 0.929581i \(0.620169\pi\)
\(938\) 43.9576 + 2.81753i 1.43526 + 0.0919957i
\(939\) 7.68634 0.250834
\(940\) −21.4098 + 1.11913i −0.698310 + 0.0365019i
\(941\) −12.3410 −0.402307 −0.201153 0.979560i \(-0.564469\pi\)
−0.201153 + 0.979560i \(0.564469\pi\)
\(942\) −21.3487 18.2257i −0.695578 0.593825i
\(943\) 13.4263i 0.437220i
\(944\) −11.0623 33.9481i −0.360046 1.10492i
\(945\) −27.7265 + 16.5206i −0.901943 + 0.537417i
\(946\) −10.4639 8.93317i −0.340210 0.290442i
\(947\) 38.9941i 1.26714i 0.773687 + 0.633568i \(0.218410\pi\)
−0.773687 + 0.633568i \(0.781590\pi\)
\(948\) 5.86194 0.930989i 0.190387 0.0302371i
\(949\) 84.3979i 2.73967i
\(950\) −19.5561 25.5339i −0.634482 0.828429i
\(951\) −12.2711 −0.397918
\(952\) 6.02360 0.564822i 0.195226 0.0183060i
\(953\) 57.1070i 1.84988i 0.380117 + 0.924938i \(0.375884\pi\)
−0.380117 + 0.924938i \(0.624116\pi\)
\(954\) −4.34558 + 5.09021i −0.140693 + 0.164802i
\(955\) −0.585816 + 5.54380i −0.0189565 + 0.179393i
\(956\) 44.8809 7.12796i 1.45155 0.230535i
\(957\) 36.3429i 1.17480i
\(958\) −29.9408 + 35.0713i −0.967344 + 1.13310i
\(959\) −10.4639 13.9770i −0.337897 0.451341i
\(960\) −7.64533 19.8744i −0.246752 0.641444i
\(961\) −8.60041 −0.277433
\(962\) 36.8048 + 31.4208i 1.18664 + 1.01305i
\(963\) 17.2024i 0.554340i
\(964\) 29.6714 4.71239i 0.955651 0.151776i
\(965\) −3.29415 + 31.1738i −0.106042 + 1.00352i
\(966\) 0.499968 7.80022i 0.0160862 0.250968i
\(967\) 11.1371 0.358146 0.179073 0.983836i \(-0.442690\pi\)
0.179073 + 0.983836i \(0.442690\pi\)
\(968\) 5.61686 + 3.43710i 0.180533 + 0.110473i
\(969\) 4.37736i 0.140621i
\(970\) −26.8914 + 25.5013i −0.863432 + 0.818796i
\(971\) 7.38403i 0.236965i −0.992956 0.118482i \(-0.962197\pi\)
0.992956 0.118482i \(-0.0378029\pi\)
\(972\) −4.48259 28.2245i −0.143779 0.905300i
\(973\) 10.1090 + 13.5030i 0.324081 + 0.432886i
\(974\) −3.58477 + 4.19903i −0.114863 + 0.134546i
\(975\) −6.91714 + 32.3643i −0.221526 + 1.03649i
\(976\) 15.5426 5.06467i 0.497505 0.162116i
\(977\) 23.4951i 0.751675i 0.926686 + 0.375838i \(0.122645\pi\)
−0.926686 + 0.375838i \(0.877355\pi\)
\(978\) 13.9135 + 11.8782i 0.444905 + 0.379822i
\(979\) 18.0992i 0.578454i
\(980\) 30.4569 + 7.23731i 0.972909 + 0.231187i
\(981\) 11.3209i 0.361448i
\(982\) 18.8721 22.1059i 0.602234 0.705429i
\(983\) 60.7158i 1.93653i 0.249918 + 0.968267i \(0.419596\pi\)
−0.249918 + 0.968267i \(0.580404\pi\)
\(984\) 13.4454 21.9723i 0.428625 0.700452i
\(985\) −18.3905 1.94333i −0.585969 0.0619195i
\(986\) −7.27193 6.20814i −0.231585 0.197708i
\(987\) −9.04848 12.0864i −0.288016 0.384714i
\(988\) 7.93409 + 49.9567i 0.252417 + 1.58933i
\(989\) 4.67644i 0.148702i
\(990\) 13.2608 12.5752i 0.421455 0.399667i
\(991\) 8.22655i 0.261325i 0.991427 + 0.130663i \(0.0417104\pi\)
−0.991427 + 0.130663i \(0.958290\pi\)
\(992\) 10.2193 24.7458i 0.324463 0.785679i
\(993\) 9.55672 0.303273
\(994\) 30.5170 + 1.95604i 0.967940 + 0.0620417i
\(995\) 60.3798 + 6.38035i 1.91417 + 0.202271i
\(996\) 2.15054 + 13.5408i 0.0681423 + 0.429055i
\(997\) 49.5766i 1.57011i −0.619428 0.785054i \(-0.712635\pi\)
0.619428 0.785054i \(-0.287365\pi\)
\(998\) 23.7504 27.8201i 0.751805 0.880629i
\(999\) 33.5731 1.06221
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 280.2.n.b.139.12 yes 40
4.3 odd 2 1120.2.n.b.559.14 40
5.4 even 2 inner 280.2.n.b.139.29 yes 40
7.6 odd 2 inner 280.2.n.b.139.11 yes 40
8.3 odd 2 inner 280.2.n.b.139.32 yes 40
8.5 even 2 1120.2.n.b.559.13 40
20.19 odd 2 1120.2.n.b.559.28 40
28.27 even 2 1120.2.n.b.559.27 40
35.34 odd 2 inner 280.2.n.b.139.30 yes 40
40.19 odd 2 inner 280.2.n.b.139.9 40
40.29 even 2 1120.2.n.b.559.26 40
56.13 odd 2 1120.2.n.b.559.25 40
56.27 even 2 inner 280.2.n.b.139.31 yes 40
140.139 even 2 1120.2.n.b.559.16 40
280.69 odd 2 1120.2.n.b.559.15 40
280.139 even 2 inner 280.2.n.b.139.10 yes 40
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
280.2.n.b.139.9 40 40.19 odd 2 inner
280.2.n.b.139.10 yes 40 280.139 even 2 inner
280.2.n.b.139.11 yes 40 7.6 odd 2 inner
280.2.n.b.139.12 yes 40 1.1 even 1 trivial
280.2.n.b.139.29 yes 40 5.4 even 2 inner
280.2.n.b.139.30 yes 40 35.34 odd 2 inner
280.2.n.b.139.31 yes 40 56.27 even 2 inner
280.2.n.b.139.32 yes 40 8.3 odd 2 inner
1120.2.n.b.559.13 40 8.5 even 2
1120.2.n.b.559.14 40 4.3 odd 2
1120.2.n.b.559.15 40 280.69 odd 2
1120.2.n.b.559.16 40 140.139 even 2
1120.2.n.b.559.25 40 56.13 odd 2
1120.2.n.b.559.26 40 40.29 even 2
1120.2.n.b.559.27 40 28.27 even 2
1120.2.n.b.559.28 40 20.19 odd 2