Properties

Label 546.2.bv.a.317.35
Level $546$
Weight $2$
Character 546.317
Analytic conductor $4.360$
Analytic rank $0$
Dimension $144$
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] = [546,2,Mod(317,546)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(546, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([6, 4, 9]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("546.317");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 546.bv (of order \(12\), degree \(4\), 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: \(4.35983195036\)
Analytic rank: \(0\)
Dimension: \(144\)
Relative dimension: \(36\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 317.35
Character \(\chi\) \(=\) 546.317
Dual form 546.2.bv.a.515.35

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.965926 - 0.258819i) q^{2} +(1.64650 + 0.537619i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-3.24035 + 0.868248i) q^{5} +(1.72954 + 0.0931546i) q^{6} +(-1.25441 + 2.32948i) q^{7} +(0.707107 - 0.707107i) q^{8} +(2.42193 + 1.77038i) q^{9} +O(q^{10})\) \(q+(0.965926 - 0.258819i) q^{2} +(1.64650 + 0.537619i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-3.24035 + 0.868248i) q^{5} +(1.72954 + 0.0931546i) q^{6} +(-1.25441 + 2.32948i) q^{7} +(0.707107 - 0.707107i) q^{8} +(2.42193 + 1.77038i) q^{9} +(-2.90521 + 1.67733i) q^{10} +(6.11240 + 1.63781i) q^{11} +(1.69472 - 0.357658i) q^{12} +(-0.0266902 + 3.60545i) q^{13} +(-0.608755 + 2.57477i) q^{14} +(-5.80202 - 0.312501i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-2.03425 - 3.52342i) q^{17} +(2.79761 + 1.08322i) q^{18} +(0.600144 + 2.23977i) q^{19} +(-2.37210 + 2.37210i) q^{20} +(-3.31776 + 3.16109i) q^{21} +6.32802 q^{22} +(2.74170 - 4.74876i) q^{23} +(1.54441 - 0.784098i) q^{24} +(5.41586 - 3.12685i) q^{25} +(0.907379 + 3.48951i) q^{26} +(3.03592 + 4.21701i) q^{27} +(0.0783861 + 2.64459i) q^{28} +0.127692i q^{29} +(-5.68520 + 1.19982i) q^{30} +(1.65420 + 0.443241i) q^{31} +(0.258819 - 0.965926i) q^{32} +(9.18355 + 5.98280i) q^{33} +(-2.87686 - 2.87686i) q^{34} +(2.04216 - 8.63745i) q^{35} +(2.98264 + 0.322230i) q^{36} +(-7.58283 + 2.03181i) q^{37} +(1.15939 + 2.00812i) q^{38} +(-1.98231 + 5.92203i) q^{39} +(-1.67733 + 2.90521i) q^{40} +(-7.12298 - 7.12298i) q^{41} +(-2.38656 + 3.91208i) q^{42} -2.56093i q^{43} +(6.11240 - 1.63781i) q^{44} +(-9.38502 - 3.63381i) q^{45} +(1.41921 - 5.29656i) q^{46} +(-2.54114 - 9.48367i) q^{47} +(1.28884 - 1.15710i) q^{48} +(-3.85291 - 5.84424i) q^{49} +(4.42203 - 4.42203i) q^{50} +(-1.45513 - 6.89496i) q^{51} +(1.77961 + 3.13576i) q^{52} +(-2.68874 + 1.55235i) q^{53} +(4.02392 + 3.28757i) q^{54} -21.2283 q^{55} +(0.760185 + 2.53419i) q^{56} +(-0.216005 + 4.01043i) q^{57} +(0.0330492 + 0.123341i) q^{58} +(6.18587 + 1.65750i) q^{59} +(-5.18095 + 2.63038i) q^{60} +(1.79532 - 3.10959i) q^{61} +1.71255 q^{62} +(-7.16216 + 3.42104i) q^{63} -1.00000i q^{64} +(-3.04394 - 11.7061i) q^{65} +(10.4191 + 3.40207i) q^{66} +(3.15651 + 0.845785i) q^{67} +(-3.52342 - 2.03425i) q^{68} +(7.06724 - 6.34485i) q^{69} +(-0.262958 - 8.87168i) q^{70} +(8.71117 + 8.71117i) q^{71} +(2.96441 - 0.460715i) q^{72} +(1.09357 - 4.08124i) q^{73} +(-6.79858 + 3.92516i) q^{74} +(10.5983 - 2.23669i) q^{75} +(1.63962 + 1.63962i) q^{76} +(-11.4827 + 12.1842i) q^{77} +(-0.382026 + 6.23330i) q^{78} +(3.01834 - 5.22792i) q^{79} +(-0.868248 + 3.24035i) q^{80} +(2.73150 + 8.57548i) q^{81} +(-8.72383 - 5.03671i) q^{82} +(0.395201 + 0.395201i) q^{83} +(-1.29272 + 4.39646i) q^{84} +(9.65087 + 9.65087i) q^{85} +(-0.662816 - 2.47366i) q^{86} +(-0.0686499 + 0.210246i) q^{87} +(5.48023 - 3.16401i) q^{88} +(0.836494 + 3.12184i) q^{89} +(-10.0057 - 1.08097i) q^{90} +(-8.36533 - 4.58489i) q^{91} -5.48340i q^{92} +(2.48534 + 1.61912i) q^{93} +(-4.90911 - 8.50283i) q^{94} +(-3.88935 - 6.73655i) q^{95} +(0.945446 - 1.45125i) q^{96} +(2.43118 - 2.43118i) q^{97} +(-5.23422 - 4.64789i) q^{98} +(11.9043 + 14.7879i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 144 q - 16 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 144 q - 16 q^{7} + 72 q^{16} + 16 q^{18} + 8 q^{19} + 8 q^{21} + 24 q^{27} - 8 q^{28} - 8 q^{31} + 12 q^{33} - 8 q^{37} + 16 q^{39} - 40 q^{45} + 8 q^{46} + 8 q^{52} - 12 q^{54} - 32 q^{55} + 16 q^{57} + 8 q^{58} - 32 q^{61} - 40 q^{63} - 32 q^{66} - 8 q^{67} + 16 q^{72} + 80 q^{73} - 16 q^{76} + 16 q^{78} - 112 q^{79} - 48 q^{81} + 16 q^{84} - 80 q^{85} + 96 q^{87} - 32 q^{91} + 36 q^{93} - 64 q^{94} - 144 q^{97} - 32 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).

\(n\) \(157\) \(365\) \(379\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(-1\) \(e\left(\frac{3}{4}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.965926 0.258819i 0.683013 0.183013i
\(3\) 1.64650 + 0.537619i 0.950608 + 0.310395i
\(4\) 0.866025 0.500000i 0.433013 0.250000i
\(5\) −3.24035 + 0.868248i −1.44913 + 0.388292i −0.895720 0.444619i \(-0.853339\pi\)
−0.553407 + 0.832911i \(0.686673\pi\)
\(6\) 1.72954 + 0.0931546i 0.706083 + 0.0380302i
\(7\) −1.25441 + 2.32948i −0.474123 + 0.880459i
\(8\) 0.707107 0.707107i 0.250000 0.250000i
\(9\) 2.42193 + 1.77038i 0.807310 + 0.590127i
\(10\) −2.90521 + 1.67733i −0.918710 + 0.530417i
\(11\) 6.11240 + 1.63781i 1.84296 + 0.493819i 0.999087 0.0427270i \(-0.0136046\pi\)
0.843871 + 0.536546i \(0.180271\pi\)
\(12\) 1.69472 0.357658i 0.489224 0.103247i
\(13\) −0.0266902 + 3.60545i −0.00740253 + 0.999973i
\(14\) −0.608755 + 2.57477i −0.162697 + 0.688135i
\(15\) −5.80202 0.312501i −1.49808 0.0806875i
\(16\) 0.500000 0.866025i 0.125000 0.216506i
\(17\) −2.03425 3.52342i −0.493377 0.854555i 0.506594 0.862185i \(-0.330904\pi\)
−0.999971 + 0.00763036i \(0.997571\pi\)
\(18\) 2.79761 + 1.08322i 0.659404 + 0.255316i
\(19\) 0.600144 + 2.23977i 0.137683 + 0.513838i 0.999972 + 0.00742326i \(0.00236292\pi\)
−0.862290 + 0.506415i \(0.830970\pi\)
\(20\) −2.37210 + 2.37210i −0.530417 + 0.530417i
\(21\) −3.31776 + 3.16109i −0.723994 + 0.689806i
\(22\) 6.32802 1.34914
\(23\) 2.74170 4.74876i 0.571684 0.990185i −0.424709 0.905330i \(-0.639624\pi\)
0.996393 0.0848557i \(-0.0270429\pi\)
\(24\) 1.54441 0.784098i 0.315251 0.160053i
\(25\) 5.41586 3.12685i 1.08317 0.625370i
\(26\) 0.907379 + 3.48951i 0.177952 + 0.684349i
\(27\) 3.03592 + 4.21701i 0.584263 + 0.811564i
\(28\) 0.0783861 + 2.64459i 0.0148136 + 0.499781i
\(29\) 0.127692i 0.0237119i 0.999930 + 0.0118559i \(0.00377395\pi\)
−0.999930 + 0.0118559i \(0.996226\pi\)
\(30\) −5.68520 + 1.19982i −1.03797 + 0.219056i
\(31\) 1.65420 + 0.443241i 0.297103 + 0.0796084i 0.404291 0.914630i \(-0.367518\pi\)
−0.107189 + 0.994239i \(0.534185\pi\)
\(32\) 0.258819 0.965926i 0.0457532 0.170753i
\(33\) 9.18355 + 5.98280i 1.59865 + 1.04147i
\(34\) −2.87686 2.87686i −0.493377 0.493377i
\(35\) 2.04216 8.63745i 0.345188 1.45999i
\(36\) 2.98264 + 0.322230i 0.497107 + 0.0537050i
\(37\) −7.58283 + 2.03181i −1.24661 + 0.334028i −0.821026 0.570891i \(-0.806598\pi\)
−0.425584 + 0.904919i \(0.639931\pi\)
\(38\) 1.15939 + 2.00812i 0.188078 + 0.325760i
\(39\) −1.98231 + 5.92203i −0.317423 + 0.948284i
\(40\) −1.67733 + 2.90521i −0.265209 + 0.459355i
\(41\) −7.12298 7.12298i −1.11242 1.11242i −0.992822 0.119600i \(-0.961839\pi\)
−0.119600 0.992822i \(-0.538161\pi\)
\(42\) −2.38656 + 3.91208i −0.368254 + 0.603646i
\(43\) 2.56093i 0.390538i −0.980750 0.195269i \(-0.937442\pi\)
0.980750 0.195269i \(-0.0625579\pi\)
\(44\) 6.11240 1.63781i 0.921479 0.246910i
\(45\) −9.38502 3.63381i −1.39904 0.541697i
\(46\) 1.41921 5.29656i 0.209251 0.780935i
\(47\) −2.54114 9.48367i −0.370664 1.38334i −0.859578 0.511004i \(-0.829274\pi\)
0.488914 0.872332i \(-0.337393\pi\)
\(48\) 1.28884 1.15710i 0.186028 0.167013i
\(49\) −3.85291 5.84424i −0.550415 0.834891i
\(50\) 4.42203 4.42203i 0.625370 0.625370i
\(51\) −1.45513 6.89496i −0.203759 0.965488i
\(52\) 1.77961 + 3.13576i 0.246788 + 0.434851i
\(53\) −2.68874 + 1.55235i −0.369327 + 0.213231i −0.673165 0.739493i \(-0.735065\pi\)
0.303837 + 0.952724i \(0.401732\pi\)
\(54\) 4.02392 + 3.28757i 0.547586 + 0.447381i
\(55\) −21.2283 −2.86243
\(56\) 0.760185 + 2.53419i 0.101584 + 0.338645i
\(57\) −0.216005 + 4.01043i −0.0286106 + 0.531195i
\(58\) 0.0330492 + 0.123341i 0.00433957 + 0.0161955i
\(59\) 6.18587 + 1.65750i 0.805332 + 0.215788i 0.637924 0.770100i \(-0.279793\pi\)
0.167408 + 0.985888i \(0.446460\pi\)
\(60\) −5.18095 + 2.63038i −0.668857 + 0.339580i
\(61\) 1.79532 3.10959i 0.229867 0.398142i −0.727901 0.685682i \(-0.759504\pi\)
0.957769 + 0.287540i \(0.0928374\pi\)
\(62\) 1.71255 0.217494
\(63\) −7.16216 + 3.42104i −0.902347 + 0.431011i
\(64\) 1.00000i 0.125000i
\(65\) −3.04394 11.7061i −0.377555 1.45196i
\(66\) 10.4191 + 3.40207i 1.28250 + 0.418766i
\(67\) 3.15651 + 0.845785i 0.385629 + 0.103329i 0.446425 0.894821i \(-0.352697\pi\)
−0.0607954 + 0.998150i \(0.519364\pi\)
\(68\) −3.52342 2.03425i −0.427277 0.246689i
\(69\) 7.06724 6.34485i 0.850795 0.763830i
\(70\) −0.262958 8.87168i −0.0314295 1.06037i
\(71\) 8.71117 + 8.71117i 1.03383 + 1.03383i 0.999408 + 0.0344187i \(0.0109580\pi\)
0.0344187 + 0.999408i \(0.489042\pi\)
\(72\) 2.96441 0.460715i 0.349359 0.0542958i
\(73\) 1.09357 4.08124i 0.127992 0.477673i −0.871937 0.489619i \(-0.837136\pi\)
0.999929 + 0.0119458i \(0.00380255\pi\)
\(74\) −6.79858 + 3.92516i −0.790319 + 0.456291i
\(75\) 10.5983 2.23669i 1.22378 0.258270i
\(76\) 1.63962 + 1.63962i 0.188078 + 0.188078i
\(77\) −11.4827 + 12.1842i −1.30858 + 1.38852i
\(78\) −0.382026 + 6.23330i −0.0432560 + 0.705782i
\(79\) 3.01834 5.22792i 0.339590 0.588187i −0.644766 0.764380i \(-0.723045\pi\)
0.984356 + 0.176193i \(0.0563784\pi\)
\(80\) −0.868248 + 3.24035i −0.0970731 + 0.362282i
\(81\) 2.73150 + 8.57548i 0.303500 + 0.952832i
\(82\) −8.72383 5.03671i −0.963386 0.556211i
\(83\) 0.395201 + 0.395201i 0.0433790 + 0.0433790i 0.728464 0.685085i \(-0.240235\pi\)
−0.685085 + 0.728464i \(0.740235\pi\)
\(84\) −1.29272 + 4.39646i −0.141047 + 0.479693i
\(85\) 9.65087 + 9.65087i 1.04678 + 1.04678i
\(86\) −0.662816 2.47366i −0.0714733 0.266742i
\(87\) −0.0686499 + 0.210246i −0.00736004 + 0.0225407i
\(88\) 5.48023 3.16401i 0.584194 0.337285i
\(89\) 0.836494 + 3.12184i 0.0886682 + 0.330914i 0.995984 0.0895366i \(-0.0285386\pi\)
−0.907315 + 0.420451i \(0.861872\pi\)
\(90\) −10.0057 1.08097i −1.05470 0.113944i
\(91\) −8.36533 4.58489i −0.876925 0.480627i
\(92\) 5.48340i 0.571684i
\(93\) 2.48534 + 1.61912i 0.257718 + 0.167895i
\(94\) −4.90911 8.50283i −0.506336 0.877000i
\(95\) −3.88935 6.73655i −0.399039 0.691156i
\(96\) 0.945446 1.45125i 0.0964942 0.148118i
\(97\) 2.43118 2.43118i 0.246849 0.246849i −0.572827 0.819676i \(-0.694153\pi\)
0.819676 + 0.572827i \(0.194153\pi\)
\(98\) −5.23422 4.64789i −0.528736 0.469508i
\(99\) 11.9043 + 14.7879i 1.19642 + 1.48624i
\(100\) 3.12685 5.41586i 0.312685 0.541586i
\(101\) −0.867612 1.50275i −0.0863306 0.149529i 0.819627 0.572898i \(-0.194181\pi\)
−0.905957 + 0.423369i \(0.860847\pi\)
\(102\) −3.19010 6.28341i −0.315867 0.622150i
\(103\) 11.0778 + 6.39579i 1.09153 + 0.630196i 0.933984 0.357315i \(-0.116308\pi\)
0.157548 + 0.987511i \(0.449641\pi\)
\(104\) 2.53057 + 2.56831i 0.248143 + 0.251844i
\(105\) 8.00608 13.1237i 0.781313 1.28074i
\(106\) −2.19535 + 2.19535i −0.213231 + 0.213231i
\(107\) −15.1052 8.72097i −1.46027 0.843088i −0.461248 0.887271i \(-0.652598\pi\)
−0.999023 + 0.0441826i \(0.985932\pi\)
\(108\) 4.73769 + 2.13408i 0.455884 + 0.205352i
\(109\) 5.10102 + 1.36681i 0.488589 + 0.130917i 0.494699 0.869064i \(-0.335278\pi\)
−0.00611014 + 0.999981i \(0.501945\pi\)
\(110\) −20.5050 + 5.49429i −1.95507 + 0.523860i
\(111\) −13.5775 0.731294i −1.28872 0.0694114i
\(112\) 1.39018 + 2.25109i 0.131360 + 0.212708i
\(113\) 0.606621i 0.0570661i −0.999593 0.0285331i \(-0.990916\pi\)
0.999593 0.0285331i \(-0.00908359\pi\)
\(114\) 0.829331 + 3.92968i 0.0776740 + 0.368049i
\(115\) −4.76095 + 17.7681i −0.443961 + 1.65688i
\(116\) 0.0638462 + 0.110585i 0.00592797 + 0.0102675i
\(117\) −6.44767 + 8.68490i −0.596087 + 0.802920i
\(118\) 6.40409 0.589544
\(119\) 10.7595 0.318913i 0.986322 0.0292347i
\(120\) −4.32362 + 3.88168i −0.394691 + 0.354347i
\(121\) 25.1527 + 14.5219i 2.28661 + 1.32018i
\(122\) 0.929327 3.46830i 0.0841373 0.314005i
\(123\) −7.89854 15.5574i −0.712187 1.40277i
\(124\) 1.65420 0.443241i 0.148551 0.0398042i
\(125\) −2.97389 + 2.97389i −0.265993 + 0.265993i
\(126\) −6.03268 + 5.15818i −0.537434 + 0.459527i
\(127\) 20.5110i 1.82006i −0.414543 0.910030i \(-0.636059\pi\)
0.414543 0.910030i \(-0.363941\pi\)
\(128\) −0.258819 0.965926i −0.0228766 0.0853766i
\(129\) 1.37680 4.21657i 0.121221 0.371248i
\(130\) −5.96998 10.5194i −0.523602 0.922611i
\(131\) 3.33860 + 1.92754i 0.291695 + 0.168410i 0.638706 0.769451i \(-0.279470\pi\)
−0.347011 + 0.937861i \(0.612803\pi\)
\(132\) 10.9446 + 0.589485i 0.952604 + 0.0513080i
\(133\) −5.97031 1.41157i −0.517692 0.122399i
\(134\) 3.26786 0.282300
\(135\) −13.4988 11.0286i −1.16180 0.949195i
\(136\) −3.92986 1.05300i −0.336983 0.0902943i
\(137\) 2.36895 + 0.634758i 0.202393 + 0.0542311i 0.358591 0.933495i \(-0.383257\pi\)
−0.156198 + 0.987726i \(0.549924\pi\)
\(138\) 5.18426 7.95779i 0.441313 0.677412i
\(139\) 17.2879 1.46634 0.733171 0.680044i \(-0.238039\pi\)
0.733171 + 0.680044i \(0.238039\pi\)
\(140\) −2.55016 8.50133i −0.215528 0.718493i
\(141\) 0.914613 16.9810i 0.0770243 1.43006i
\(142\) 10.6690 + 6.15973i 0.895320 + 0.516913i
\(143\) −6.06820 + 21.9943i −0.507448 + 1.83925i
\(144\) 2.74416 1.21226i 0.228680 0.101022i
\(145\) −0.110869 0.413767i −0.00920714 0.0343615i
\(146\) 4.22521i 0.349681i
\(147\) −3.20184 11.6939i −0.264083 0.964500i
\(148\) −5.55102 + 5.55102i −0.456291 + 0.456291i
\(149\) −5.67339 + 1.52018i −0.464783 + 0.124538i −0.483608 0.875285i \(-0.660674\pi\)
0.0188255 + 0.999823i \(0.494007\pi\)
\(150\) 9.65825 4.90351i 0.788593 0.400370i
\(151\) −2.81919 + 10.5214i −0.229423 + 0.856217i 0.751162 + 0.660118i \(0.229494\pi\)
−0.980584 + 0.196098i \(0.937173\pi\)
\(152\) 2.00812 + 1.15939i 0.162880 + 0.0940389i
\(153\) 1.31099 12.1349i 0.105987 0.981046i
\(154\) −7.93794 + 14.7410i −0.639657 + 1.18786i
\(155\) −5.74501 −0.461451
\(156\) 1.24429 + 6.11978i 0.0996228 + 0.489975i
\(157\) −3.72889 6.45864i −0.297598 0.515455i 0.677988 0.735073i \(-0.262852\pi\)
−0.975586 + 0.219618i \(0.929519\pi\)
\(158\) 1.56241 5.83099i 0.124298 0.463888i
\(159\) −5.26159 + 1.11042i −0.417271 + 0.0880620i
\(160\) 3.35465i 0.265209i
\(161\) 7.62291 + 12.3436i 0.600769 + 0.972813i
\(162\) 4.85792 + 7.57632i 0.381674 + 0.595252i
\(163\) −8.96107 + 2.40111i −0.701885 + 0.188070i −0.592075 0.805883i \(-0.701691\pi\)
−0.109810 + 0.993953i \(0.535024\pi\)
\(164\) −9.73017 2.60719i −0.759799 0.203587i
\(165\) −34.9524 11.4128i −2.72104 0.888482i
\(166\) 0.484021 + 0.279450i 0.0375673 + 0.0216895i
\(167\) −7.85626 + 7.85626i −0.607935 + 0.607935i −0.942406 0.334471i \(-0.891442\pi\)
0.334471 + 0.942406i \(0.391442\pi\)
\(168\) −0.110784 + 4.58124i −0.00854714 + 0.353450i
\(169\) −12.9986 0.192461i −0.999890 0.0148047i
\(170\) 11.8198 + 6.82419i 0.906541 + 0.523392i
\(171\) −2.51174 + 6.48705i −0.192077 + 0.496077i
\(172\) −1.28046 2.21783i −0.0976344 0.169108i
\(173\) 7.45262 12.9083i 0.566612 0.981401i −0.430286 0.902693i \(-0.641587\pi\)
0.996898 0.0787079i \(-0.0250794\pi\)
\(174\) −0.0118951 + 0.220850i −0.000901768 + 0.0167426i
\(175\) 0.490203 + 16.5385i 0.0370559 + 1.25019i
\(176\) 4.47459 4.47459i 0.337285 0.337285i
\(177\) 9.29394 + 6.05472i 0.698576 + 0.455101i
\(178\) 1.61598 + 2.79896i 0.121123 + 0.209791i
\(179\) −4.86804 8.43169i −0.363854 0.630214i 0.624737 0.780835i \(-0.285206\pi\)
−0.988592 + 0.150621i \(0.951873\pi\)
\(180\) −9.94458 + 1.54554i −0.741225 + 0.115198i
\(181\) 0.413098i 0.0307053i 0.999882 + 0.0153527i \(0.00488710\pi\)
−0.999882 + 0.0153527i \(0.995113\pi\)
\(182\) −9.26695 2.26356i −0.686912 0.167786i
\(183\) 4.62777 4.15474i 0.342095 0.307127i
\(184\) −1.41921 5.29656i −0.104625 0.390467i
\(185\) 22.8069 13.1676i 1.67679 0.968098i
\(186\) 2.81972 + 0.920700i 0.206752 + 0.0675090i
\(187\) −6.66343 24.8683i −0.487278 1.81855i
\(188\) −6.94253 6.94253i −0.506336 0.506336i
\(189\) −13.6317 + 1.78224i −0.991561 + 0.129639i
\(190\) −5.50037 5.50037i −0.399039 0.399039i
\(191\) −21.0580 12.1578i −1.52370 0.879711i −0.999606 0.0280531i \(-0.991069\pi\)
−0.524098 0.851658i \(-0.675597\pi\)
\(192\) 0.537619 1.64650i 0.0387993 0.118826i
\(193\) 0.225659 0.842169i 0.0162433 0.0606207i −0.957329 0.289002i \(-0.906677\pi\)
0.973572 + 0.228381i \(0.0733433\pi\)
\(194\) 1.71910 2.97758i 0.123424 0.213777i
\(195\) 1.28157 20.9106i 0.0917749 1.49744i
\(196\) −6.25883 3.13480i −0.447060 0.223915i
\(197\) 3.35030 + 3.35030i 0.238699 + 0.238699i 0.816311 0.577612i \(-0.196015\pi\)
−0.577612 + 0.816311i \(0.696015\pi\)
\(198\) 15.3260 + 11.2030i 1.08917 + 0.796163i
\(199\) −19.7369 + 11.3951i −1.39911 + 0.807778i −0.994300 0.106622i \(-0.965997\pi\)
−0.404813 + 0.914400i \(0.632663\pi\)
\(200\) 1.61858 6.04061i 0.114451 0.427135i
\(201\) 4.74249 + 3.08959i 0.334509 + 0.217923i
\(202\) −1.22699 1.22699i −0.0863306 0.0863306i
\(203\) −0.297456 0.160179i −0.0208773 0.0112423i
\(204\) −4.70766 5.24365i −0.329602 0.367129i
\(205\) 29.2654 + 16.8964i 2.04399 + 1.18010i
\(206\) 12.3557 + 3.31071i 0.860864 + 0.230668i
\(207\) 15.0473 6.64732i 1.04586 0.462021i
\(208\) 3.10907 + 1.82584i 0.215575 + 0.126599i
\(209\) 14.6733i 1.01497i
\(210\) 4.33663 14.7486i 0.299256 1.01775i
\(211\) 13.7192 0.944470 0.472235 0.881473i \(-0.343447\pi\)
0.472235 + 0.881473i \(0.343447\pi\)
\(212\) −1.55235 + 2.68874i −0.106616 + 0.184664i
\(213\) 9.65966 + 19.0263i 0.661869 + 1.30366i
\(214\) −16.8476 4.51431i −1.15168 0.308592i
\(215\) 2.22352 + 8.29829i 0.151643 + 0.565938i
\(216\) 5.12860 + 0.835158i 0.348957 + 0.0568253i
\(217\) −3.10756 + 3.29740i −0.210955 + 0.223842i
\(218\) 5.28096 0.357672
\(219\) 3.99471 6.13185i 0.269938 0.414352i
\(220\) −18.3843 + 10.6142i −1.23947 + 0.715606i
\(221\) 12.7578 7.24034i 0.858183 0.487038i
\(222\) −13.3041 + 2.80773i −0.892913 + 0.188443i
\(223\) −4.07576 + 4.07576i −0.272933 + 0.272933i −0.830280 0.557347i \(-0.811819\pi\)
0.557347 + 0.830280i \(0.311819\pi\)
\(224\) 1.92543 + 1.81458i 0.128649 + 0.121242i
\(225\) 18.6526 + 2.01513i 1.24350 + 0.134342i
\(226\) −0.157005 0.585951i −0.0104438 0.0389769i
\(227\) −4.41341 + 16.4711i −0.292928 + 1.09322i 0.649921 + 0.760002i \(0.274802\pi\)
−0.942849 + 0.333221i \(0.891865\pi\)
\(228\) 1.81815 + 3.58114i 0.120410 + 0.237167i
\(229\) 9.59834 2.57187i 0.634276 0.169954i 0.0726666 0.997356i \(-0.476849\pi\)
0.561609 + 0.827403i \(0.310182\pi\)
\(230\) 18.3949i 1.21292i
\(231\) −25.4567 + 13.8880i −1.67493 + 0.913761i
\(232\) 0.0902921 + 0.0902921i 0.00592797 + 0.00592797i
\(233\) 9.19291 15.9226i 0.602248 1.04312i −0.390232 0.920716i \(-0.627605\pi\)
0.992480 0.122407i \(-0.0390613\pi\)
\(234\) −3.98015 + 10.0578i −0.260191 + 0.657496i
\(235\) 16.4684 + 28.5240i 1.07428 + 1.86070i
\(236\) 6.18587 1.65750i 0.402666 0.107894i
\(237\) 7.78033 6.98505i 0.505387 0.453728i
\(238\) 10.3103 3.09281i 0.668320 0.200477i
\(239\) −3.07854 3.07854i −0.199134 0.199134i 0.600495 0.799629i \(-0.294970\pi\)
−0.799629 + 0.600495i \(0.794970\pi\)
\(240\) −3.17164 + 4.86845i −0.204729 + 0.314257i
\(241\) −4.61685 + 17.2303i −0.297397 + 1.10990i 0.641897 + 0.766791i \(0.278148\pi\)
−0.939295 + 0.343112i \(0.888519\pi\)
\(242\) 28.0542 + 7.51710i 1.80339 + 0.483218i
\(243\) −0.112933 + 15.5880i −0.00724462 + 0.999974i
\(244\) 3.59064i 0.229867i
\(245\) 17.5590 + 15.5921i 1.12180 + 0.996141i
\(246\) −11.6560 12.9830i −0.743157 0.827769i
\(247\) −8.09140 + 2.10401i −0.514843 + 0.133875i
\(248\) 1.48311 0.856275i 0.0941777 0.0543735i
\(249\) 0.438232 + 0.863167i 0.0277718 + 0.0547010i
\(250\) −2.10286 + 3.64226i −0.132997 + 0.230357i
\(251\) −25.3659 −1.60108 −0.800542 0.599276i \(-0.795455\pi\)
−0.800542 + 0.599276i \(0.795455\pi\)
\(252\) −4.49209 + 6.54379i −0.282975 + 0.412220i
\(253\) 24.5359 24.5359i 1.54256 1.54256i
\(254\) −5.30864 19.8121i −0.333094 1.24312i
\(255\) 10.7017 + 21.0787i 0.670164 + 1.32000i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −11.3035 + 19.5783i −0.705096 + 1.22126i 0.261561 + 0.965187i \(0.415763\pi\)
−0.966657 + 0.256075i \(0.917571\pi\)
\(258\) 0.238562 4.42923i 0.0148522 0.275752i
\(259\) 4.77892 20.2127i 0.296948 1.25596i
\(260\) −8.48917 8.61580i −0.526476 0.534329i
\(261\) −0.226064 + 0.309262i −0.0139930 + 0.0191428i
\(262\) 3.72373 + 0.997770i 0.230053 + 0.0616424i
\(263\) −16.2993 + 9.41043i −1.00506 + 0.580272i −0.909742 0.415175i \(-0.863720\pi\)
−0.0953187 + 0.995447i \(0.530387\pi\)
\(264\) 10.7242 2.26327i 0.660031 0.139295i
\(265\) 7.36464 7.36464i 0.452406 0.452406i
\(266\) −6.13222 + 0.181760i −0.375991 + 0.0111444i
\(267\) −0.301072 + 5.58982i −0.0184253 + 0.342092i
\(268\) 3.15651 0.845785i 0.192815 0.0516645i
\(269\) 4.49802 2.59693i 0.274249 0.158338i −0.356568 0.934269i \(-0.616053\pi\)
0.630817 + 0.775932i \(0.282720\pi\)
\(270\) −15.8933 7.15910i −0.967236 0.435689i
\(271\) −4.20199 + 1.12592i −0.255253 + 0.0683948i −0.384176 0.923260i \(-0.625515\pi\)
0.128923 + 0.991655i \(0.458848\pi\)
\(272\) −4.06849 −0.246689
\(273\) −11.3086 12.0464i −0.684428 0.729081i
\(274\) 2.45252 0.148162
\(275\) 38.2251 10.2424i 2.30506 0.617639i
\(276\) 2.94798 9.02842i 0.177448 0.543447i
\(277\) −6.13780 + 3.54366i −0.368785 + 0.212918i −0.672928 0.739708i \(-0.734963\pi\)
0.304143 + 0.952627i \(0.401630\pi\)
\(278\) 16.6989 4.47444i 1.00153 0.268359i
\(279\) 3.22165 + 4.00206i 0.192875 + 0.239597i
\(280\) −4.66357 7.55162i −0.278702 0.451296i
\(281\) −7.47121 + 7.47121i −0.445695 + 0.445695i −0.893920 0.448226i \(-0.852056\pi\)
0.448226 + 0.893920i \(0.352056\pi\)
\(282\) −3.51157 16.6392i −0.209111 0.990847i
\(283\) 10.1109 5.83755i 0.601033 0.347006i −0.168415 0.985716i \(-0.553865\pi\)
0.769448 + 0.638710i \(0.220532\pi\)
\(284\) 11.8997 + 3.18851i 0.706116 + 0.189203i
\(285\) −2.78212 13.1827i −0.164798 0.780878i
\(286\) −0.168896 + 22.8154i −0.00998704 + 1.34910i
\(287\) 25.5279 7.65766i 1.50687 0.452017i
\(288\) 2.33690 1.88120i 0.137703 0.110851i
\(289\) 0.223679 0.387423i 0.0131576 0.0227896i
\(290\) −0.214182 0.370974i −0.0125772 0.0217843i
\(291\) 5.30999 2.69589i 0.311277 0.158036i
\(292\) −1.09357 4.08124i −0.0639961 0.238837i
\(293\) 11.5897 11.5897i 0.677076 0.677076i −0.282261 0.959338i \(-0.591084\pi\)
0.959338 + 0.282261i \(0.0910845\pi\)
\(294\) −6.11936 10.4668i −0.356888 0.610435i
\(295\) −21.4835 −1.25082
\(296\) −3.92516 + 6.79858i −0.228145 + 0.395159i
\(297\) 11.6501 + 30.7483i 0.676006 + 1.78420i
\(298\) −5.08663 + 2.93676i −0.294660 + 0.170122i
\(299\) 17.0483 + 10.0118i 0.985926 + 0.578998i
\(300\) 8.06003 7.23617i 0.465346 0.417780i
\(301\) 5.96561 + 3.21245i 0.343852 + 0.185163i
\(302\) 10.8925i 0.626794i
\(303\) −0.620618 2.94072i −0.0356536 0.168940i
\(304\) 2.23977 + 0.600144i 0.128460 + 0.0344206i
\(305\) −3.11757 + 11.6349i −0.178512 + 0.666214i
\(306\) −1.87442 12.0607i −0.107153 0.689464i
\(307\) −18.6550 18.6550i −1.06469 1.06469i −0.997757 0.0669373i \(-0.978677\pi\)
−0.0669373 0.997757i \(-0.521323\pi\)
\(308\) −3.85222 + 16.2932i −0.219500 + 0.928390i
\(309\) 14.8012 + 16.4863i 0.842009 + 0.937875i
\(310\) −5.54926 + 1.48692i −0.315177 + 0.0844513i
\(311\) −6.40089 11.0867i −0.362961 0.628667i 0.625486 0.780236i \(-0.284901\pi\)
−0.988447 + 0.151569i \(0.951568\pi\)
\(312\) 2.78581 + 5.58921i 0.157715 + 0.316427i
\(313\) −8.15974 + 14.1331i −0.461216 + 0.798849i −0.999022 0.0442193i \(-0.985920\pi\)
0.537806 + 0.843069i \(0.319253\pi\)
\(314\) −5.27345 5.27345i −0.297598 0.297598i
\(315\) 20.2375 17.3039i 1.14026 0.974964i
\(316\) 6.03668i 0.339590i
\(317\) −0.351074 + 0.0940699i −0.0197183 + 0.00528349i −0.268665 0.963234i \(-0.586582\pi\)
0.248946 + 0.968517i \(0.419916\pi\)
\(318\) −4.79491 + 2.43438i −0.268885 + 0.136513i
\(319\) −0.209136 + 0.780507i −0.0117094 + 0.0437000i
\(320\) 0.868248 + 3.24035i 0.0485365 + 0.181141i
\(321\) −20.1821 22.4799i −1.12646 1.25471i
\(322\) 10.5579 + 9.95007i 0.588370 + 0.554496i
\(323\) 6.67080 6.67080i 0.371173 0.371173i
\(324\) 6.65329 + 6.06084i 0.369627 + 0.336713i
\(325\) 11.1292 + 19.6101i 0.617334 + 1.08777i
\(326\) −8.03428 + 4.63859i −0.444977 + 0.256908i
\(327\) 7.66401 + 4.99287i 0.423821 + 0.276106i
\(328\) −10.0734 −0.556211
\(329\) 25.2796 + 5.97689i 1.39371 + 0.329517i
\(330\) −36.7153 1.97752i −2.02111 0.108859i
\(331\) −3.54154 13.2172i −0.194661 0.726484i −0.992354 0.123421i \(-0.960613\pi\)
0.797694 0.603063i \(-0.206053\pi\)
\(332\) 0.539855 + 0.144654i 0.0296284 + 0.00793891i
\(333\) −21.9622 8.50359i −1.20352 0.465994i
\(334\) −5.55521 + 9.62191i −0.303968 + 0.526487i
\(335\) −10.9625 −0.598948
\(336\) 1.07870 + 4.45381i 0.0588480 + 0.242975i
\(337\) 6.55986i 0.357338i 0.983909 + 0.178669i \(0.0571792\pi\)
−0.983909 + 0.178669i \(0.942821\pi\)
\(338\) −12.6055 + 3.17838i −0.685647 + 0.172881i
\(339\) 0.326131 0.998803i 0.0177130 0.0542475i
\(340\) 13.1833 + 3.53246i 0.714966 + 0.191575i
\(341\) 9.38517 + 5.41853i 0.508235 + 0.293430i
\(342\) −0.747180 + 6.91609i −0.0404029 + 0.373980i
\(343\) 18.4471 1.64418i 0.996051 0.0887774i
\(344\) −1.81085 1.81085i −0.0976344 0.0976344i
\(345\) −17.3914 + 26.6956i −0.936321 + 1.43724i
\(346\) 3.85776 14.3973i 0.207394 0.774006i
\(347\) −18.0884 + 10.4434i −0.971038 + 0.560629i −0.899553 0.436812i \(-0.856107\pi\)
−0.0714856 + 0.997442i \(0.522774\pi\)
\(348\) 0.0456702 + 0.216403i 0.00244818 + 0.0116004i
\(349\) 3.21831 + 3.21831i 0.172272 + 0.172272i 0.787977 0.615705i \(-0.211129\pi\)
−0.615705 + 0.787977i \(0.711129\pi\)
\(350\) 4.75397 + 15.8481i 0.254110 + 0.847114i
\(351\) −15.2853 + 10.8333i −0.815867 + 0.578239i
\(352\) 3.16401 5.48023i 0.168642 0.292097i
\(353\) 4.76936 17.7995i 0.253848 0.947372i −0.714880 0.699247i \(-0.753519\pi\)
0.968728 0.248125i \(-0.0798145\pi\)
\(354\) 10.5443 + 3.44296i 0.560425 + 0.182991i
\(355\) −35.7907 20.6638i −1.89957 1.09672i
\(356\) 2.28534 + 2.28534i 0.121123 + 0.121123i
\(357\) 17.8870 + 5.25942i 0.946679 + 0.278358i
\(358\) −6.88445 6.88445i −0.363854 0.363854i
\(359\) −2.23711 8.34901i −0.118070 0.440644i 0.881428 0.472318i \(-0.156583\pi\)
−0.999498 + 0.0316744i \(0.989916\pi\)
\(360\) −9.20571 + 4.06672i −0.485183 + 0.214335i
\(361\) 11.7981 6.81163i 0.620952 0.358507i
\(362\) 0.106918 + 0.399022i 0.00561947 + 0.0209721i
\(363\) 33.6067 + 37.4330i 1.76389 + 1.96472i
\(364\) −9.53704 + 0.212033i −0.499876 + 0.0111135i
\(365\) 14.1741i 0.741907i
\(366\) 3.39476 5.21093i 0.177447 0.272380i
\(367\) 12.2707 + 21.2535i 0.640527 + 1.10943i 0.985315 + 0.170745i \(0.0546174\pi\)
−0.344788 + 0.938680i \(0.612049\pi\)
\(368\) −2.74170 4.74876i −0.142921 0.247546i
\(369\) −4.64097 29.8617i −0.241599 1.55454i
\(370\) 18.6217 18.6217i 0.968098 0.968098i
\(371\) −0.243365 8.21064i −0.0126349 0.426275i
\(372\) 2.96193 + 0.159532i 0.153569 + 0.00827135i
\(373\) 0.647930 1.12225i 0.0335485 0.0581078i −0.848764 0.528772i \(-0.822652\pi\)
0.882312 + 0.470665i \(0.155986\pi\)
\(374\) −12.8728 22.2963i −0.665635 1.15291i
\(375\) −6.49534 + 3.29770i −0.335418 + 0.170292i
\(376\) −8.50283 4.90911i −0.438500 0.253168i
\(377\) −0.460389 0.00340814i −0.0237112 0.000175528i
\(378\) −12.7059 + 5.24965i −0.653523 + 0.270013i
\(379\) −20.8376 + 20.8376i −1.07035 + 1.07035i −0.0730241 + 0.997330i \(0.523265\pi\)
−0.997330 + 0.0730241i \(0.976735\pi\)
\(380\) −6.73655 3.88935i −0.345578 0.199519i
\(381\) 11.0271 33.7714i 0.564937 1.73016i
\(382\) −23.4872 6.29337i −1.20171 0.321997i
\(383\) 8.85758 2.37338i 0.452601 0.121274i −0.0253151 0.999680i \(-0.508059\pi\)
0.477916 + 0.878405i \(0.341392\pi\)
\(384\) 0.0931546 1.72954i 0.00475378 0.0882604i
\(385\) 26.6290 49.4508i 1.35714 2.52025i
\(386\) 0.871878i 0.0443774i
\(387\) 4.53382 6.20238i 0.230467 0.315285i
\(388\) 0.889874 3.32105i 0.0451765 0.168601i
\(389\) 17.7461 + 30.7371i 0.899761 + 1.55843i 0.827799 + 0.561025i \(0.189593\pi\)
0.0719626 + 0.997407i \(0.477074\pi\)
\(390\) −4.17415 20.5298i −0.211367 1.03956i
\(391\) −22.3092 −1.12822
\(392\) −6.85692 1.40808i −0.346327 0.0711189i
\(393\) 4.46073 + 4.96860i 0.225014 + 0.250633i
\(394\) 4.10326 + 2.36902i 0.206719 + 0.119349i
\(395\) −5.24134 + 19.5609i −0.263720 + 0.984217i
\(396\) 17.7034 + 6.85461i 0.889627 + 0.344457i
\(397\) 32.5233 8.71460i 1.63230 0.437373i 0.677718 0.735322i \(-0.262969\pi\)
0.954582 + 0.297949i \(0.0963026\pi\)
\(398\) −16.1151 + 16.1151i −0.807778 + 0.807778i
\(399\) −9.07124 5.53391i −0.454130 0.277042i
\(400\) 6.25370i 0.312685i
\(401\) 3.88669 + 14.5053i 0.194092 + 0.724362i 0.992500 + 0.122245i \(0.0390093\pi\)
−0.798408 + 0.602117i \(0.794324\pi\)
\(402\) 5.38054 + 1.75687i 0.268357 + 0.0876245i
\(403\) −1.64223 + 5.95230i −0.0818055 + 0.296505i
\(404\) −1.50275 0.867612i −0.0747645 0.0431653i
\(405\) −16.2966 25.4159i −0.809787 1.26293i
\(406\) −0.328778 0.0777334i −0.0163170 0.00385784i
\(407\) −49.6770 −2.46240
\(408\) −5.90441 3.84654i −0.292312 0.190432i
\(409\) −27.2465 7.30067i −1.34725 0.360995i −0.488131 0.872770i \(-0.662321\pi\)
−0.859119 + 0.511775i \(0.828988\pi\)
\(410\) 32.6413 + 8.74622i 1.61204 + 0.431945i
\(411\) 3.55922 + 2.31872i 0.175563 + 0.114374i
\(412\) 12.7916 0.630196
\(413\) −11.6207 + 12.3307i −0.571819 + 0.606752i
\(414\) 12.8141 10.3154i 0.629781 0.506972i
\(415\) −1.62372 0.937456i −0.0797054 0.0460179i
\(416\) 3.47569 + 0.958941i 0.170410 + 0.0470159i
\(417\) 28.4646 + 9.29432i 1.39392 + 0.455145i
\(418\) 3.79773 + 14.1733i 0.185753 + 0.693239i
\(419\) 22.9443i 1.12090i 0.828187 + 0.560451i \(0.189372\pi\)
−0.828187 + 0.560451i \(0.810628\pi\)
\(420\) 0.371641 15.3685i 0.0181342 0.749904i
\(421\) −17.8994 + 17.8994i −0.872363 + 0.872363i −0.992729 0.120367i \(-0.961593\pi\)
0.120367 + 0.992729i \(0.461593\pi\)
\(422\) 13.2518 3.55080i 0.645085 0.172850i
\(423\) 10.6353 27.4676i 0.517104 1.33552i
\(424\) −0.803554 + 2.99890i −0.0390240 + 0.145640i
\(425\) −22.0344 12.7216i −1.06883 0.617087i
\(426\) 14.2549 + 15.8778i 0.690651 + 0.769284i
\(427\) 4.99164 + 8.08286i 0.241562 + 0.391157i
\(428\) −17.4419 −0.843088
\(429\) −21.8158 + 32.9512i −1.05328 + 1.59090i
\(430\) 4.29551 + 7.44004i 0.207148 + 0.358791i
\(431\) 2.78931 10.4099i 0.134356 0.501425i −0.865643 0.500661i \(-0.833090\pi\)
1.00000 0.000763751i \(-0.000243109\pi\)
\(432\) 5.17000 0.520678i 0.248742 0.0250511i
\(433\) 30.1662i 1.44970i 0.688909 + 0.724848i \(0.258090\pi\)
−0.688909 + 0.724848i \(0.741910\pi\)
\(434\) −2.14824 + 3.98934i −0.103119 + 0.191495i
\(435\) 0.0399040 0.740874i 0.00191325 0.0355222i
\(436\) 5.10102 1.36681i 0.244294 0.0654585i
\(437\) 12.2815 + 3.29083i 0.587506 + 0.157422i
\(438\) 2.27156 6.95682i 0.108539 0.332410i
\(439\) 25.2577 + 14.5825i 1.20548 + 0.695986i 0.961769 0.273861i \(-0.0883007\pi\)
0.243714 + 0.969847i \(0.421634\pi\)
\(440\) −15.0107 + 15.0107i −0.715606 + 0.715606i
\(441\) 1.01505 20.9755i 0.0483358 0.998831i
\(442\) 10.4492 10.2956i 0.497016 0.489712i
\(443\) 12.2531 + 7.07436i 0.582165 + 0.336113i 0.761993 0.647585i \(-0.224221\pi\)
−0.179828 + 0.983698i \(0.557554\pi\)
\(444\) −12.1241 + 6.15542i −0.575384 + 0.292123i
\(445\) −5.42106 9.38955i −0.256983 0.445107i
\(446\) −2.88200 + 4.99176i −0.136466 + 0.236367i
\(447\) −10.1585 0.547147i −0.480482 0.0258791i
\(448\) 2.32948 + 1.25441i 0.110057 + 0.0592653i
\(449\) −16.7895 + 16.7895i −0.792348 + 0.792348i −0.981875 0.189528i \(-0.939304\pi\)
0.189528 + 0.981875i \(0.439304\pi\)
\(450\) 18.5385 2.88117i 0.873915 0.135820i
\(451\) −31.8724 55.2046i −1.50081 2.59948i
\(452\) −0.303311 0.525349i −0.0142665 0.0247104i
\(453\) −10.2983 + 15.8078i −0.483856 + 0.742715i
\(454\) 17.0521i 0.800295i
\(455\) 31.0874 + 7.59345i 1.45740 + 0.355987i
\(456\) 2.68306 + 2.98854i 0.125646 + 0.139951i
\(457\) −9.97842 37.2400i −0.466771 1.74201i −0.650950 0.759120i \(-0.725629\pi\)
0.184179 0.982893i \(-0.441037\pi\)
\(458\) 8.60563 4.96846i 0.402115 0.232161i
\(459\) 8.68249 19.2753i 0.405264 0.899692i
\(460\) 4.76095 + 17.7681i 0.221980 + 0.828442i
\(461\) 2.27891 + 2.27891i 0.106140 + 0.106140i 0.758182 0.652043i \(-0.226088\pi\)
−0.652043 + 0.758182i \(0.726088\pi\)
\(462\) −20.9949 + 20.0034i −0.976769 + 0.930644i
\(463\) 10.4036 + 10.4036i 0.483497 + 0.483497i 0.906247 0.422749i \(-0.138935\pi\)
−0.422749 + 0.906247i \(0.638935\pi\)
\(464\) 0.110585 + 0.0638462i 0.00513377 + 0.00296398i
\(465\) −9.45917 3.08863i −0.438659 0.143232i
\(466\) 4.75860 17.7593i 0.220438 0.822685i
\(467\) 0.964739 1.67098i 0.0446428 0.0773236i −0.842841 0.538163i \(-0.819118\pi\)
0.887483 + 0.460840i \(0.152452\pi\)
\(468\) −1.24139 + 10.7452i −0.0573834 + 0.496696i
\(469\) −5.92980 + 6.29206i −0.273813 + 0.290540i
\(470\) 23.2898 + 23.2898i 1.07428 + 1.07428i
\(471\) −2.66734 12.6389i −0.122905 0.582369i
\(472\) 5.54610 3.20204i 0.255280 0.147386i
\(473\) 4.19432 15.6534i 0.192855 0.719744i
\(474\) 5.70736 8.76074i 0.262148 0.402394i
\(475\) 10.2537 + 10.2537i 0.470473 + 0.470473i
\(476\) 9.15854 5.65594i 0.419781 0.259239i
\(477\) −9.26020 1.00043i −0.423995 0.0458063i
\(478\) −3.77043 2.17686i −0.172455 0.0995672i
\(479\) −4.55727 1.22112i −0.208227 0.0557942i 0.153198 0.988196i \(-0.451043\pi\)
−0.361425 + 0.932401i \(0.617710\pi\)
\(480\) −1.80353 + 5.52344i −0.0823193 + 0.252109i
\(481\) −7.12322 27.3938i −0.324791 1.24905i
\(482\) 17.8381i 0.812505i
\(483\) 5.91496 + 24.4220i 0.269140 + 1.11124i
\(484\) 29.0439 1.32018
\(485\) −5.76700 + 9.98873i −0.261866 + 0.453565i
\(486\) 3.92540 + 15.0861i 0.178060 + 0.684321i
\(487\) −16.5087 4.42349i −0.748081 0.200448i −0.135414 0.990789i \(-0.543236\pi\)
−0.612667 + 0.790342i \(0.709903\pi\)
\(488\) −0.929327 3.46830i −0.0420687 0.157002i
\(489\) −16.0453 0.864212i −0.725593 0.0390810i
\(490\) 20.9962 + 10.5162i 0.948512 + 0.475072i
\(491\) 24.8371 1.12088 0.560442 0.828194i \(-0.310631\pi\)
0.560442 + 0.828194i \(0.310631\pi\)
\(492\) −14.6191 9.52387i −0.659078 0.429369i
\(493\) 0.449914 0.259758i 0.0202631 0.0116989i
\(494\) −7.27113 + 4.12653i −0.327144 + 0.185661i
\(495\) −51.4135 37.5822i −2.31087 1.68920i
\(496\) 1.21096 1.21096i 0.0543735 0.0543735i
\(497\) −31.2199 + 9.36507i −1.40040 + 0.420081i
\(498\) 0.646703 + 0.720333i 0.0289795 + 0.0322789i
\(499\) 7.15652 + 26.7085i 0.320370 + 1.19564i 0.918885 + 0.394525i \(0.129091\pi\)
−0.598516 + 0.801111i \(0.704243\pi\)
\(500\) −1.08852 + 4.06241i −0.0486801 + 0.181677i
\(501\) −17.1590 + 8.71166i −0.766608 + 0.389208i
\(502\) −24.5016 + 6.56519i −1.09356 + 0.293019i
\(503\) 27.6359i 1.23222i −0.787658 0.616112i \(-0.788707\pi\)
0.787658 0.616112i \(-0.211293\pi\)
\(504\) −2.64537 + 7.48345i −0.117834 + 0.333339i
\(505\) 4.11612 + 4.11612i 0.183165 + 0.183165i
\(506\) 17.3495 30.0503i 0.771281 1.33590i
\(507\) −21.2987 7.30517i −0.945908 0.324434i
\(508\) −10.2555 17.7631i −0.455015 0.788109i
\(509\) −3.42423 + 0.917520i −0.151776 + 0.0406684i −0.333907 0.942606i \(-0.608367\pi\)
0.182131 + 0.983274i \(0.441701\pi\)
\(510\) 15.7926 + 17.5906i 0.699307 + 0.778926i
\(511\) 8.13537 + 7.66699i 0.359888 + 0.339167i
\(512\) −0.707107 0.707107i −0.0312500 0.0312500i
\(513\) −7.62314 + 9.33057i −0.336570 + 0.411955i
\(514\) −5.85115 + 21.8368i −0.258083 + 0.963179i
\(515\) −41.4492 11.1063i −1.82647 0.489401i
\(516\) −0.915937 4.34006i −0.0403219 0.191060i
\(517\) 62.1299i 2.73247i
\(518\) −0.615356 20.7609i −0.0270372 0.912181i
\(519\) 19.2105 17.2469i 0.843247 0.757054i
\(520\) −10.4298 6.12506i −0.457379 0.268602i
\(521\) −4.31187 + 2.48946i −0.188906 + 0.109065i −0.591471 0.806327i \(-0.701452\pi\)
0.402564 + 0.915392i \(0.368119\pi\)
\(522\) −0.138318 + 0.357234i −0.00605403 + 0.0156357i
\(523\) −0.204767 + 0.354667i −0.00895385 + 0.0155085i −0.870468 0.492226i \(-0.836183\pi\)
0.861514 + 0.507734i \(0.169517\pi\)
\(524\) 3.85509 0.168410
\(525\) −8.08428 + 27.4941i −0.352827 + 1.19994i
\(526\) −13.3084 + 13.3084i −0.580272 + 0.580272i
\(527\) −1.80332 6.73009i −0.0785540 0.293167i
\(528\) 9.77304 4.96179i 0.425317 0.215934i
\(529\) −3.53383 6.12077i −0.153645 0.266121i
\(530\) 5.20758 9.01980i 0.226203 0.391795i
\(531\) 12.0474 + 14.9657i 0.522810 + 0.649456i
\(532\) −5.87623 + 1.76270i −0.254767 + 0.0764228i
\(533\) 25.8717 25.4914i 1.12063 1.10416i
\(534\) 1.15594 + 5.47728i 0.0500224 + 0.237025i
\(535\) 56.5179 + 15.1439i 2.44348 + 0.654730i
\(536\) 2.83005 1.63393i 0.122240 0.0705751i
\(537\) −3.48219 16.4999i −0.150268 0.712025i
\(538\) 3.67262 3.67262i 0.158338 0.158338i
\(539\) −13.9787 42.0326i −0.602107 1.81047i
\(540\) −17.2047 2.80167i −0.740371 0.120565i
\(541\) −29.7273 + 7.96540i −1.27807 + 0.342459i −0.833119 0.553094i \(-0.813447\pi\)
−0.444956 + 0.895553i \(0.646781\pi\)
\(542\) −3.76740 + 2.17511i −0.161824 + 0.0934290i
\(543\) −0.222090 + 0.680166i −0.00953077 + 0.0291887i
\(544\) −3.92986 + 1.05300i −0.168492 + 0.0451472i
\(545\) −17.7158 −0.758862
\(546\) −14.0411 8.70904i −0.600904 0.372713i
\(547\) 11.8216 0.505453 0.252727 0.967538i \(-0.418673\pi\)
0.252727 + 0.967538i \(0.418673\pi\)
\(548\) 2.36895 0.634758i 0.101197 0.0271155i
\(549\) 9.85330 4.35280i 0.420529 0.185773i
\(550\) 34.2717 19.7868i 1.46135 0.843711i
\(551\) −0.286001 + 0.0766338i −0.0121841 + 0.00326471i
\(552\) 0.510804 9.48378i 0.0217413 0.403656i
\(553\) 8.39207 + 13.5891i 0.356867 + 0.577867i
\(554\) −5.01150 + 5.01150i −0.212918 + 0.212918i
\(555\) 44.6307 9.41897i 1.89447 0.399813i
\(556\) 14.9718 8.64396i 0.634945 0.366586i
\(557\) −10.5106 2.81630i −0.445347 0.119330i 0.0291745 0.999574i \(-0.490712\pi\)
−0.474521 + 0.880244i \(0.657379\pi\)
\(558\) 4.14768 + 3.03187i 0.175585 + 0.128349i
\(559\) 9.23330 + 0.0683516i 0.390527 + 0.00289097i
\(560\) −6.45917 6.08729i −0.272950 0.257235i
\(561\) 2.39831 44.5280i 0.101257 1.87997i
\(562\) −5.28294 + 9.15032i −0.222847 + 0.385983i
\(563\) 10.7017 + 18.5359i 0.451024 + 0.781196i 0.998450 0.0556577i \(-0.0177256\pi\)
−0.547426 + 0.836854i \(0.684392\pi\)
\(564\) −7.69845 15.1633i −0.324163 0.638491i
\(565\) 0.526698 + 1.96566i 0.0221583 + 0.0826961i
\(566\) 8.25554 8.25554i 0.347006 0.347006i
\(567\) −23.4028 4.39422i −0.982825 0.184540i
\(568\) 12.3195 0.516913
\(569\) 6.50476 11.2666i 0.272694 0.472319i −0.696857 0.717210i \(-0.745419\pi\)
0.969551 + 0.244891i \(0.0787521\pi\)
\(570\) −6.09926 12.0135i −0.255470 0.503189i
\(571\) −30.0569 + 17.3534i −1.25784 + 0.726216i −0.972655 0.232256i \(-0.925389\pi\)
−0.285188 + 0.958472i \(0.592056\pi\)
\(572\) 5.74191 + 22.0817i 0.240081 + 0.923281i
\(573\) −28.1357 31.3391i −1.17539 1.30921i
\(574\) 22.6761 14.0038i 0.946484 0.584509i
\(575\) 34.2915i 1.43006i
\(576\) 1.77038 2.42193i 0.0737659 0.100914i
\(577\) −39.1973 10.5029i −1.63180 0.437240i −0.677364 0.735648i \(-0.736878\pi\)
−0.954439 + 0.298407i \(0.903545\pi\)
\(578\) 0.115785 0.432114i 0.00481600 0.0179736i
\(579\) 0.824314 1.26531i 0.0342573 0.0525847i
\(580\) −0.302899 0.302899i −0.0125772 0.0125772i
\(581\) −1.41636 + 0.424867i −0.0587604 + 0.0176265i
\(582\) 4.43131 3.97836i 0.183684 0.164908i
\(583\) −18.9771 + 5.08491i −0.785952 + 0.210595i
\(584\) −2.11261 3.65914i −0.0874203 0.151416i
\(585\) 13.3520 33.7403i 0.552038 1.39499i
\(586\) 8.19514 14.1944i 0.338538 0.586365i
\(587\) −11.6106 11.6106i −0.479223 0.479223i 0.425660 0.904883i \(-0.360042\pi\)
−0.904883 + 0.425660i \(0.860042\pi\)
\(588\) −8.61985 8.52633i −0.355476 0.351620i
\(589\) 3.97103i 0.163623i
\(590\) −20.7515 + 5.56034i −0.854324 + 0.228915i
\(591\) 3.71509 + 7.31746i 0.152818 + 0.301000i
\(592\) −2.03181 + 7.58283i −0.0835070 + 0.311652i
\(593\) −9.64729 36.0042i −0.396167 1.47851i −0.819784 0.572673i \(-0.805906\pi\)
0.423617 0.905841i \(-0.360760\pi\)
\(594\) 19.2114 + 26.6853i 0.788252 + 1.09491i
\(595\) −34.5876 + 10.3753i −1.41795 + 0.425346i
\(596\) −4.15321 + 4.15321i −0.170122 + 0.170122i
\(597\) −38.6231 + 8.15111i −1.58074 + 0.333603i
\(598\) 19.0586 + 5.25825i 0.779364 + 0.215026i
\(599\) 36.8375 21.2681i 1.50514 0.868993i 0.505157 0.863027i \(-0.331435\pi\)
0.999982 0.00596522i \(-0.00189880\pi\)
\(600\) 5.91254 9.07569i 0.241378 0.370513i
\(601\) −16.3118 −0.665372 −0.332686 0.943038i \(-0.607955\pi\)
−0.332686 + 0.943038i \(0.607955\pi\)
\(602\) 6.59378 + 1.55898i 0.268743 + 0.0635391i
\(603\) 6.14749 + 7.63666i 0.250345 + 0.310989i
\(604\) 2.81919 + 10.5214i 0.114711 + 0.428108i
\(605\) −94.1122 25.2173i −3.82620 1.02523i
\(606\) −1.36059 2.67989i −0.0552700 0.108863i
\(607\) −1.43203 + 2.48035i −0.0581243 + 0.100674i −0.893623 0.448818i \(-0.851845\pi\)
0.835499 + 0.549492i \(0.185179\pi\)
\(608\) 2.31878 0.0940389
\(609\) −0.403647 0.423652i −0.0163566 0.0171673i
\(610\) 12.0454i 0.487703i
\(611\) 34.2608 8.90885i 1.38604 0.360413i
\(612\) −4.93208 11.1646i −0.199368 0.451302i
\(613\) −19.0273 5.09834i −0.768504 0.205920i −0.146794 0.989167i \(-0.546895\pi\)
−0.621711 + 0.783247i \(0.713562\pi\)
\(614\) −22.8476 13.1910i −0.922052 0.532347i
\(615\) 39.1017 + 43.5536i 1.57673 + 1.75625i
\(616\) 0.496029 + 16.7350i 0.0199856 + 0.674273i
\(617\) −24.8368 24.8368i −0.999893 0.999893i 0.000106988 1.00000i \(-0.499966\pi\)
−1.00000 0.000106988i \(0.999966\pi\)
\(618\) 18.5638 + 12.0938i 0.746746 + 0.486482i
\(619\) 10.4779 39.1040i 0.421142 1.57172i −0.351063 0.936352i \(-0.614180\pi\)
0.772206 0.635373i \(-0.219153\pi\)
\(620\) −4.97533 + 2.87251i −0.199814 + 0.115363i
\(621\) 28.3492 2.85508i 1.13761 0.114571i
\(622\) −9.05222 9.05222i −0.362961 0.362961i
\(623\) −8.32155 1.96747i −0.333396 0.0788252i
\(624\) 4.13748 + 4.67774i 0.165632 + 0.187260i
\(625\) −8.57988 + 14.8608i −0.343195 + 0.594431i
\(626\) −4.22379 + 15.7634i −0.168817 + 0.630033i
\(627\) −7.88864 + 24.1596i −0.315042 + 0.964841i
\(628\) −6.45864 3.72889i −0.257728 0.148799i
\(629\) 22.5843 + 22.5843i 0.900494 + 0.900494i
\(630\) 15.0694 21.9521i 0.600379 0.874594i
\(631\) −12.0035 12.0035i −0.477850 0.477850i 0.426593 0.904444i \(-0.359714\pi\)
−0.904444 + 0.426593i \(0.859714\pi\)
\(632\) −1.56241 5.83099i −0.0621492 0.231944i
\(633\) 22.5887 + 7.37572i 0.897821 + 0.293159i
\(634\) −0.314764 + 0.181729i −0.0125009 + 0.00721738i
\(635\) 17.8087 + 66.4628i 0.706715 + 2.63750i
\(636\) −4.00146 + 3.59245i −0.158668 + 0.142450i
\(637\) 21.1740 13.7355i 0.838943 0.544220i
\(638\) 0.808040i 0.0319906i
\(639\) 5.67576 + 36.5200i 0.224530 + 1.44471i
\(640\) 1.67733 + 2.90521i 0.0663022 + 0.114839i
\(641\) 12.8018 + 22.1734i 0.505641 + 0.875795i 0.999979 + 0.00652568i \(0.00207720\pi\)
−0.494338 + 0.869270i \(0.664589\pi\)
\(642\) −25.3127 16.4904i −0.999011 0.650825i
\(643\) 0.384715 0.384715i 0.0151717 0.0151717i −0.699480 0.714652i \(-0.746585\pi\)
0.714652 + 0.699480i \(0.246585\pi\)
\(644\) 12.7734 + 6.87843i 0.503344 + 0.271048i
\(645\) −0.800293 + 14.8585i −0.0315115 + 0.585055i
\(646\) 4.71697 8.17003i 0.185587 0.321446i
\(647\) −0.186170 0.322457i −0.00731911 0.0126771i 0.862343 0.506325i \(-0.168996\pi\)
−0.869662 + 0.493648i \(0.835663\pi\)
\(648\) 7.99524 + 4.13232i 0.314083 + 0.162333i
\(649\) 35.0959 + 20.2626i 1.37763 + 0.795377i
\(650\) 15.8254 + 16.0615i 0.620723 + 0.629982i
\(651\) −6.88935 + 3.75850i −0.270015 + 0.147307i
\(652\) −6.55996 + 6.55996i −0.256908 + 0.256908i
\(653\) 6.47137 + 3.73625i 0.253244 + 0.146211i 0.621249 0.783613i \(-0.286626\pi\)
−0.368005 + 0.929824i \(0.619959\pi\)
\(654\) 8.69511 + 2.83915i 0.340006 + 0.111019i
\(655\) −12.4918 3.34717i −0.488096 0.130785i
\(656\) −9.73017 + 2.60719i −0.379899 + 0.101794i
\(657\) 9.87389 7.94846i 0.385217 0.310099i
\(658\) 25.9652 0.769612i 1.01223 0.0300026i
\(659\) 32.4190i 1.26286i 0.775431 + 0.631432i \(0.217532\pi\)
−0.775431 + 0.631432i \(0.782468\pi\)
\(660\) −35.9761 + 7.59249i −1.40037 + 0.295537i
\(661\) 5.61492 20.9552i 0.218395 0.815061i −0.766549 0.642186i \(-0.778028\pi\)
0.984944 0.172875i \(-0.0553057\pi\)
\(662\) −6.84173 11.8502i −0.265911 0.460572i
\(663\) 24.8983 5.06238i 0.966970 0.196606i
\(664\) 0.558899 0.0216895
\(665\) 20.5715 0.609742i 0.797727 0.0236448i
\(666\) −23.4147 2.52961i −0.907302 0.0980204i
\(667\) 0.606381 + 0.350094i 0.0234792 + 0.0135557i
\(668\) −2.87559 + 10.7318i −0.111260 + 0.415228i
\(669\) −8.90194 + 4.51953i −0.344169 + 0.174735i
\(670\) −10.5890 + 2.83732i −0.409089 + 0.109615i
\(671\) 16.0666 16.0666i 0.620246 0.620246i
\(672\) 2.19468 + 4.02286i 0.0846615 + 0.155185i
\(673\) 22.3366i 0.861014i 0.902587 + 0.430507i \(0.141665\pi\)
−0.902587 + 0.430507i \(0.858335\pi\)
\(674\) 1.69782 + 6.33634i 0.0653975 + 0.244067i
\(675\) 29.6281 + 13.3459i 1.14039 + 0.513683i
\(676\) −11.3533 + 6.33261i −0.436666 + 0.243562i
\(677\) 21.2839 + 12.2883i 0.818006 + 0.472276i 0.849728 0.527221i \(-0.176766\pi\)
−0.0317225 + 0.999497i \(0.510099\pi\)
\(678\) 0.0565096 1.04918i 0.00217024 0.0402934i
\(679\) 2.61368 + 8.71307i 0.100304 + 0.334377i
\(680\) 13.6484 0.523392
\(681\) −16.1218 + 24.7469i −0.617790 + 0.948303i
\(682\) 10.4678 + 2.80484i 0.400833 + 0.107403i
\(683\) 30.6088 + 8.20161i 1.17121 + 0.313826i 0.791436 0.611252i \(-0.209334\pi\)
0.379778 + 0.925078i \(0.376000\pi\)
\(684\) 1.06830 + 6.87382i 0.0408473 + 0.262827i
\(685\) −8.22735 −0.314351
\(686\) 17.3930 6.36263i 0.664068 0.242926i
\(687\) 17.1864 + 0.925671i 0.655700 + 0.0353165i
\(688\) −2.21783 1.28046i −0.0845539 0.0488172i
\(689\) −5.52515 9.73557i −0.210491 0.370896i
\(690\) −9.88945 + 30.2872i −0.376485 + 1.15301i
\(691\) −2.97064 11.0866i −0.113008 0.421753i 0.886122 0.463453i \(-0.153390\pi\)
−0.999130 + 0.0416992i \(0.986723\pi\)
\(692\) 14.9052i 0.566612i
\(693\) −49.3810 + 9.18051i −1.87583 + 0.348739i
\(694\) −14.7691 + 14.7691i −0.560629 + 0.560629i
\(695\) −56.0189 + 15.0102i −2.12492 + 0.569370i
\(696\) 0.100123 + 0.197209i 0.00379516 + 0.00747518i
\(697\) −10.6073 + 39.5871i −0.401782 + 1.49947i
\(698\) 3.94161 + 2.27569i 0.149192 + 0.0861360i
\(699\) 23.6964 21.2743i 0.896281 0.804667i
\(700\) 8.69376 + 14.0776i 0.328593 + 0.532084i
\(701\) −10.1192 −0.382196 −0.191098 0.981571i \(-0.561205\pi\)
−0.191098 + 0.981571i \(0.561205\pi\)
\(702\) −11.9606 + 14.4203i −0.451422 + 0.544259i
\(703\) −9.10158 15.7644i −0.343273 0.594566i
\(704\) 1.63781 6.11240i 0.0617274 0.230370i
\(705\) 11.7801 + 55.8186i 0.443664 + 2.10225i
\(706\) 18.4274i 0.693525i
\(707\) 4.58896 0.136017i 0.172585 0.00511546i
\(708\) 11.0762 + 0.596570i 0.416267 + 0.0224205i
\(709\) 28.3531 7.59719i 1.06482 0.285318i 0.316459 0.948606i \(-0.397506\pi\)
0.748364 + 0.663288i \(0.230840\pi\)
\(710\) −39.9193 10.6963i −1.49815 0.401427i
\(711\) 16.5656 7.31804i 0.621259 0.274448i
\(712\) 2.79896 + 1.61598i 0.104896 + 0.0605615i
\(713\) 6.64016 6.64016i 0.248676 0.248676i
\(714\) 18.6387 + 0.450723i 0.697537 + 0.0168679i
\(715\) 0.566588 76.5377i 0.0211892 2.86235i
\(716\) −8.43169 4.86804i −0.315107 0.181927i
\(717\) −3.41374 6.72391i −0.127488 0.251109i
\(718\) −4.32177 7.48552i −0.161287 0.279357i
\(719\) −20.6861 + 35.8293i −0.771460 + 1.33621i 0.165302 + 0.986243i \(0.447140\pi\)
−0.936763 + 0.349966i \(0.886193\pi\)
\(720\) −7.83949 + 6.31076i −0.292160 + 0.235188i
\(721\) −28.7950 + 17.7826i −1.07238 + 0.662259i
\(722\) 9.63310 9.63310i 0.358507 0.358507i
\(723\) −16.8650 + 25.8876i −0.627216 + 0.962771i
\(724\) 0.206549 + 0.357753i 0.00767633 + 0.0132958i
\(725\) 0.399275 + 0.691564i 0.0148287 + 0.0256840i
\(726\) 42.1499 + 27.4594i 1.56433 + 1.01911i
\(727\) 3.12755i 0.115995i −0.998317 0.0579973i \(-0.981529\pi\)
0.998317 0.0579973i \(-0.0184715\pi\)
\(728\) −9.15719 + 2.67317i −0.339388 + 0.0990744i
\(729\) −8.56638 + 25.6050i −0.317273 + 0.948334i
\(730\) 3.66853 + 13.6911i 0.135778 + 0.506732i
\(731\) −9.02321 + 5.20956i −0.333736 + 0.192682i
\(732\) 1.93040 5.91200i 0.0713496 0.218514i
\(733\) 2.38043 + 8.88387i 0.0879230 + 0.328133i 0.995852 0.0909916i \(-0.0290036\pi\)
−0.907929 + 0.419125i \(0.862337\pi\)
\(734\) 17.3534 + 17.3534i 0.640527 + 0.640527i
\(735\) 20.5283 + 35.1124i 0.757198 + 1.29514i
\(736\) −3.87735 3.87735i −0.142921 0.142921i
\(737\) 17.9086 + 10.3396i 0.659673 + 0.380862i
\(738\) −12.2116 27.6431i −0.449516 1.01756i
\(739\) 9.16774 34.2145i 0.337241 1.25860i −0.564179 0.825653i \(-0.690807\pi\)
0.901420 0.432947i \(-0.142526\pi\)
\(740\) 13.1676 22.8069i 0.484049 0.838397i
\(741\) −14.4537 0.885835i −0.530968 0.0325420i
\(742\) −2.36014 7.86788i −0.0866435 0.288839i
\(743\) −1.93223 1.93223i −0.0708866 0.0708866i 0.670775 0.741661i \(-0.265962\pi\)
−0.741661 + 0.670775i \(0.765962\pi\)
\(744\) 2.90230 0.612508i 0.106403 0.0224556i
\(745\) 17.0639 9.85183i 0.625172 0.360943i
\(746\) 0.335393 1.25170i 0.0122796 0.0458282i
\(747\) 0.257493 + 1.65681i 0.00942118 + 0.0606194i
\(748\) −18.2048 18.2048i −0.665635 0.665635i
\(749\) 39.2634 24.2474i 1.43465 0.885982i
\(750\) −5.42051 + 4.86645i −0.197929 + 0.177698i
\(751\) −44.5053 25.6951i −1.62402 0.937628i −0.985830 0.167750i \(-0.946350\pi\)
−0.638190 0.769879i \(-0.720317\pi\)
\(752\) −9.48367 2.54114i −0.345834 0.0926659i
\(753\) −41.7651 13.6372i −1.52200 0.496968i
\(754\) −0.445583 + 0.115865i −0.0162272 + 0.00421957i
\(755\) 36.5406i 1.32985i
\(756\) −10.9143 + 8.35932i −0.396949 + 0.304025i
\(757\) 10.1111 0.367493 0.183746 0.982974i \(-0.441178\pi\)
0.183746 + 0.982974i \(0.441178\pi\)
\(758\) −14.7344 + 25.5207i −0.535177 + 0.926954i
\(759\) 53.5895 27.2075i 1.94517 0.987568i
\(760\) −7.51365 2.01328i −0.272549 0.0730292i
\(761\) −8.27536 30.8841i −0.299981 1.11955i −0.937180 0.348846i \(-0.886573\pi\)
0.637198 0.770700i \(-0.280093\pi\)
\(762\) 1.91070 35.4747i 0.0692173 1.28511i
\(763\) −9.58273 + 10.1682i −0.346918 + 0.368112i
\(764\) −24.3157 −0.879711
\(765\) 6.28801 + 40.4594i 0.227344 + 1.46281i
\(766\) 7.94149 4.58502i 0.286938 0.165664i
\(767\) −6.14114 + 22.2586i −0.221744 + 0.803713i
\(768\) −0.357658 1.69472i −0.0129059 0.0611530i
\(769\) −15.3274 + 15.3274i −0.552718 + 0.552718i −0.927224 0.374506i \(-0.877812\pi\)
0.374506 + 0.927224i \(0.377812\pi\)
\(770\) 12.9228 54.6579i 0.465707 1.96974i
\(771\) −29.1370 + 26.1587i −1.04934 + 0.942083i
\(772\) −0.225659 0.842169i −0.00812163 0.0303103i
\(773\) 5.09546 19.0165i 0.183271 0.683977i −0.811723 0.584043i \(-0.801470\pi\)
0.994994 0.0999342i \(-0.0318632\pi\)
\(774\) 2.77403 7.16448i 0.0997106 0.257522i
\(775\) 10.3448 2.77189i 0.371598 0.0995694i
\(776\) 3.43821i 0.123424i
\(777\) 18.7353 30.7111i 0.672124 1.10175i
\(778\) 25.0967 + 25.0967i 0.899761 + 0.899761i
\(779\) 11.6790 20.2286i 0.418444 0.724766i
\(780\) −9.34541 18.7499i −0.334620 0.671353i
\(781\) 38.9789 + 67.5134i 1.39477 + 2.41582i
\(782\) −21.5490 + 5.77404i −0.770591 + 0.206479i
\(783\) −0.538480 + 0.387664i −0.0192437 + 0.0138540i
\(784\) −6.98771 + 0.414598i −0.249561 + 0.0148071i
\(785\) 17.6906 + 17.6906i 0.631405 + 0.631405i
\(786\) 5.59470 + 3.64478i 0.199556 + 0.130005i
\(787\) 1.07436 4.00955i 0.0382966 0.142925i −0.944130 0.329572i \(-0.893095\pi\)
0.982427 + 0.186647i \(0.0597621\pi\)
\(788\) 4.57659 + 1.22629i 0.163034 + 0.0436849i
\(789\) −31.8961 + 6.73144i −1.13553 + 0.239646i
\(790\) 20.2510i 0.720497i
\(791\) 1.41311 + 0.760952i 0.0502444 + 0.0270563i
\(792\) 18.8742 + 2.03908i 0.670667 + 0.0724555i
\(793\) 11.1636 + 6.55594i 0.396430 + 0.232808i
\(794\) 29.1596 16.8353i 1.03484 0.597463i
\(795\) 16.0853 8.16651i 0.570485 0.289636i
\(796\) −11.3951 + 19.7369i −0.403889 + 0.699556i
\(797\) −21.8139 −0.772687 −0.386344 0.922355i \(-0.626262\pi\)
−0.386344 + 0.922355i \(0.626262\pi\)
\(798\) −10.1944 2.99753i −0.360879 0.106111i
\(799\) −28.2456 + 28.2456i −0.999259 + 0.999259i
\(800\) −1.61858 6.04061i −0.0572253 0.213568i
\(801\) −3.50091 + 9.04179i −0.123699 + 0.319476i
\(802\) 7.50852 + 13.0051i 0.265135 + 0.459227i
\(803\) 13.3686 23.1551i 0.471768 0.817127i
\(804\) 5.65191 + 0.304416i 0.199328 + 0.0107359i
\(805\) −35.4182 33.3790i −1.24833 1.17646i
\(806\) −0.0457083 + 6.17452i −0.00161001 + 0.217488i
\(807\) 8.80215 1.85763i 0.309850 0.0653916i
\(808\) −1.67610 0.449109i −0.0589649 0.0157996i
\(809\) 8.41983 4.86119i 0.296026 0.170910i −0.344631 0.938738i \(-0.611996\pi\)
0.640656 + 0.767828i \(0.278662\pi\)
\(810\) −22.3195 20.3320i −0.784226 0.714394i
\(811\) 20.2937 20.2937i 0.712607 0.712607i −0.254473 0.967080i \(-0.581902\pi\)
0.967080 + 0.254473i \(0.0819020\pi\)
\(812\) −0.337694 + 0.0100093i −0.0118507 + 0.000351258i
\(813\) −7.52390 0.405243i −0.263875 0.0142125i
\(814\) −47.9843 + 12.8574i −1.68185 + 0.450650i
\(815\) 26.9522 15.5609i 0.944095 0.545073i
\(816\) −6.69878 2.18730i −0.234504 0.0765709i
\(817\) 5.73588 1.53692i 0.200673 0.0537702i
\(818\) −28.2076 −0.986256
\(819\) −12.1432 25.9141i −0.424319 0.905513i
\(820\) 33.7928 1.18010
\(821\) −47.1195 + 12.6256i −1.64448 + 0.440638i −0.958060 0.286566i \(-0.907486\pi\)
−0.686421 + 0.727204i \(0.740819\pi\)
\(822\) 4.03807 + 1.31852i 0.140844 + 0.0459887i
\(823\) 18.1900 10.5020i 0.634062 0.366076i −0.148262 0.988948i \(-0.547368\pi\)
0.782323 + 0.622872i \(0.214034\pi\)
\(824\) 12.3557 3.31071i 0.430432 0.115334i
\(825\) 68.4442 + 3.68646i 2.38292 + 0.128346i
\(826\) −8.03336 + 14.9182i −0.279516 + 0.519069i
\(827\) −22.1257 + 22.1257i −0.769387 + 0.769387i −0.977999 0.208612i \(-0.933105\pi\)
0.208612 + 0.977999i \(0.433105\pi\)
\(828\) 9.70771 13.2804i 0.337366 0.461526i
\(829\) −7.06627 + 4.07971i −0.245422 + 0.141694i −0.617666 0.786440i \(-0.711922\pi\)
0.372244 + 0.928135i \(0.378588\pi\)
\(830\) −1.81103 0.485263i −0.0628617 0.0168437i
\(831\) −12.0110 + 2.53484i −0.416658 + 0.0879327i
\(832\) 3.60545 + 0.0266902i 0.124997 + 0.000925316i
\(833\) −12.7539 + 25.4640i −0.441897 + 0.882276i
\(834\) 29.9002 + 1.61045i 1.03536 + 0.0557653i
\(835\) 18.6358 32.2782i 0.644919 1.11703i
\(836\) 7.33664 + 12.7074i 0.253743 + 0.439496i
\(837\) 3.15286 + 8.32141i 0.108979 + 0.287630i
\(838\) 5.93842 + 22.1625i 0.205139 + 0.765591i
\(839\) 35.7272 35.7272i 1.23344 1.23344i 0.270806 0.962634i \(-0.412710\pi\)
0.962634 0.270806i \(-0.0872901\pi\)
\(840\) −3.61867 14.9410i −0.124856 0.515513i
\(841\) 28.9837 0.999438
\(842\) −12.6568 + 21.9222i −0.436181 + 0.755488i
\(843\) −16.3180 + 8.28469i −0.562022 + 0.285340i
\(844\) 11.8812 6.85961i 0.408968 0.236118i
\(845\) 42.2870 10.6623i 1.45472 0.366796i
\(846\) 3.16373 29.2843i 0.108771 1.00681i
\(847\) −65.3803 + 40.3762i −2.24649 + 1.38734i
\(848\) 3.10469i 0.106616i
\(849\) 19.7860 4.17570i 0.679055 0.143310i
\(850\) −24.5762 6.58517i −0.842956 0.225869i
\(851\) −11.1412 + 41.5797i −0.381917 + 1.42533i
\(852\) 17.8786 + 11.6474i 0.612512 + 0.399033i
\(853\) 32.5674 + 32.5674i 1.11509 + 1.11509i 0.992452 + 0.122634i \(0.0391343\pi\)
0.122634 + 0.992452i \(0.460866\pi\)
\(854\) 6.91355 + 6.51551i 0.236577 + 0.222956i
\(855\) 2.50653 23.2011i 0.0857216 0.793461i
\(856\) −16.8476 + 4.51431i −0.575840 + 0.154296i
\(857\) −9.66161 16.7344i −0.330034 0.571636i 0.652484 0.757803i \(-0.273727\pi\)
−0.982518 + 0.186166i \(0.940394\pi\)
\(858\) −12.5441 + 37.4747i −0.428248 + 1.27937i
\(859\) 23.7519 41.1395i 0.810404 1.40366i −0.102178 0.994766i \(-0.532581\pi\)
0.912582 0.408895i \(-0.134086\pi\)
\(860\) 6.07477 + 6.07477i 0.207148 + 0.207148i
\(861\) 46.1487 + 1.11597i 1.57274 + 0.0380321i
\(862\) 10.7771i 0.367069i
\(863\) −7.73101 + 2.07152i −0.263167 + 0.0705153i −0.387990 0.921664i \(-0.626830\pi\)
0.124823 + 0.992179i \(0.460164\pi\)
\(864\) 4.85907 1.84103i 0.165309 0.0626331i
\(865\) −12.9414 + 48.2981i −0.440022 + 1.64219i
\(866\) 7.80759 + 29.1383i 0.265313 + 0.990160i
\(867\) 0.576573 0.517638i 0.0195814 0.0175799i
\(868\) −1.04252 + 4.40942i −0.0353856 + 0.149665i
\(869\) 27.0116 27.0116i 0.916307 0.916307i
\(870\) −0.153208 0.725957i −0.00519423 0.0246122i
\(871\) −3.13369 + 11.3581i −0.106181 + 0.384854i
\(872\) 4.57345 2.64048i 0.154877 0.0894180i
\(873\) 10.1923 1.58403i 0.344956 0.0536114i
\(874\) 12.7148 0.430084
\(875\) −3.19713 10.6581i −0.108083 0.360309i
\(876\) 0.393598 7.30769i 0.0132984 0.246904i
\(877\) 6.00003 + 22.3924i 0.202607 + 0.756138i 0.990166 + 0.139899i \(0.0446778\pi\)
−0.787559 + 0.616239i \(0.788655\pi\)
\(878\) 28.1713 + 7.54848i 0.950735 + 0.254749i
\(879\) 25.3133 12.8516i 0.853795 0.433473i
\(880\) −10.6142 + 18.3843i −0.357803 + 0.619733i
\(881\) 17.8123 0.600111 0.300056 0.953922i \(-0.402995\pi\)
0.300056 + 0.953922i \(0.402995\pi\)
\(882\) −4.44838 20.5234i −0.149785 0.691060i
\(883\) 13.4521i 0.452701i −0.974046 0.226350i \(-0.927321\pi\)
0.974046 0.226350i \(-0.0726794\pi\)
\(884\) 7.42842 12.6492i 0.249845 0.425439i
\(885\) −35.3726 11.5499i −1.18904 0.388247i
\(886\) 13.6666 + 3.66196i 0.459139 + 0.123026i
\(887\) −13.0811 7.55237i −0.439220 0.253584i 0.264047 0.964510i \(-0.414943\pi\)
−0.703267 + 0.710926i \(0.748276\pi\)
\(888\) −10.1178 + 9.08362i −0.339532 + 0.304826i
\(889\) 47.7799 + 25.7292i 1.60249 + 0.862931i
\(890\) −7.66654 7.66654i −0.256983 0.256983i
\(891\) 2.65097 + 56.8905i 0.0888109 + 1.90590i
\(892\) −1.49183 + 5.56759i −0.0499502 + 0.186417i
\(893\) 19.7162 11.3831i 0.659777 0.380922i
\(894\) −9.95400 + 2.10072i −0.332911 + 0.0702585i
\(895\) 23.0949 + 23.0949i 0.771979 + 0.771979i
\(896\) 2.57477 + 0.608755i 0.0860169 + 0.0203371i
\(897\) 22.6874 + 25.6499i 0.757511 + 0.856426i
\(898\) −11.8720 + 20.5629i −0.396174 + 0.686193i
\(899\) −0.0565985 + 0.211228i −0.00188766 + 0.00704486i
\(900\) 17.1612 7.58113i 0.572038 0.252704i
\(901\) 10.9391 + 6.31571i 0.364435 + 0.210407i
\(902\) −45.0744 45.0744i −1.50081 1.50081i
\(903\) 8.09531 + 8.49653i 0.269395 + 0.282747i
\(904\) −0.428946 0.428946i −0.0142665 0.0142665i
\(905\) −0.358672 1.33858i −0.0119226 0.0444959i
\(906\) −5.85603 + 17.9345i −0.194554 + 0.595835i
\(907\) −25.5184 + 14.7331i −0.847326 + 0.489204i −0.859748 0.510719i \(-0.829379\pi\)
0.0124219 + 0.999923i \(0.496046\pi\)
\(908\) 4.41341 + 16.4711i 0.146464 + 0.546611i
\(909\) 0.559141 5.17556i 0.0185456 0.171662i
\(910\) 31.9934 0.711296i 1.06057 0.0235792i
\(911\) 43.7241i 1.44864i 0.689462 + 0.724322i \(0.257847\pi\)
−0.689462 + 0.724322i \(0.742153\pi\)
\(912\) 3.36513 + 2.19228i 0.111431 + 0.0725937i
\(913\) 1.76836 + 3.06289i 0.0585243 + 0.101367i
\(914\) −19.2768 33.3885i −0.637621 1.10439i
\(915\) −11.3882 + 17.4809i −0.376484 + 0.577899i
\(916\) 7.02647 7.02647i 0.232161 0.232161i
\(917\) −8.67814 + 5.35926i −0.286578 + 0.176978i
\(918\) 3.39784 20.8657i 0.112145 0.688670i
\(919\) 5.43311 9.41042i 0.179222 0.310421i −0.762392 0.647115i \(-0.775975\pi\)
0.941614 + 0.336694i \(0.109309\pi\)
\(920\) 9.19745 + 15.9305i 0.303231 + 0.525211i
\(921\) −20.6861 40.7447i −0.681631 1.34258i
\(922\) 2.79109 + 1.61144i 0.0919196 + 0.0530698i
\(923\) −31.6402 + 31.1752i −1.04145 + 1.02614i
\(924\) −15.1022 + 24.7557i −0.496826 + 0.814403i
\(925\) −34.7144 + 34.7144i −1.14140 + 1.14140i
\(926\) 12.7418 + 7.35647i 0.418721 + 0.241749i
\(927\) 15.5068 + 35.1022i 0.509309 + 1.15291i
\(928\) 0.123341 + 0.0330492i 0.00404888 + 0.00108489i
\(929\) −20.3377 + 5.44946i −0.667257 + 0.178791i −0.576519 0.817084i \(-0.695589\pi\)
−0.0907383 + 0.995875i \(0.528923\pi\)
\(930\) −9.93625 0.535175i −0.325823 0.0175491i
\(931\) 10.7774 12.1370i 0.353216 0.397774i
\(932\) 18.3858i 0.602248i
\(933\) −4.57866 21.6954i −0.149899 0.710277i
\(934\) 0.499386 1.86373i 0.0163404 0.0609832i
\(935\) 43.1836 + 74.7963i 1.41226 + 2.44610i
\(936\) 1.58196 + 10.7003i 0.0517081 + 0.349752i
\(937\) 40.3453 1.31802 0.659012 0.752133i \(-0.270975\pi\)
0.659012 + 0.752133i \(0.270975\pi\)
\(938\) −4.09924 + 7.61240i −0.133845 + 0.248554i
\(939\) −21.0332 + 18.8833i −0.686394 + 0.616233i
\(940\) 28.5240 + 16.4684i 0.930352 + 0.537139i
\(941\) 4.03518 15.0595i 0.131543 0.490926i −0.868445 0.495786i \(-0.834880\pi\)
0.999988 + 0.00485964i \(0.00154688\pi\)
\(942\) −5.84764 11.5179i −0.190526 0.375272i
\(943\) −53.3544 + 14.2963i −1.73746 + 0.465551i
\(944\) 4.52837 4.52837i 0.147386 0.147386i
\(945\) 42.6241 17.6108i 1.38656 0.572878i
\(946\) 16.2056i 0.526889i
\(947\) −11.0500 41.2392i −0.359077 1.34009i −0.875275 0.483625i \(-0.839320\pi\)
0.516198 0.856469i \(-0.327347\pi\)
\(948\) 3.24544 9.93940i 0.105407 0.322817i
\(949\) 14.6855 + 4.05173i 0.476713 + 0.131525i
\(950\) 12.5582 + 7.25047i 0.407441 + 0.235236i
\(951\) −0.628617 0.0338578i −0.0203843 0.00109791i
\(952\) 7.38261 7.83362i 0.239272 0.253889i
\(953\) −24.5509 −0.795283 −0.397641 0.917541i \(-0.630171\pi\)
−0.397641 + 0.917541i \(0.630171\pi\)
\(954\) −9.20359 + 1.43038i −0.297977 + 0.0463102i
\(955\) 78.7913 + 21.1121i 2.54963 + 0.683170i
\(956\) −4.20537 1.12682i −0.136011 0.0364441i
\(957\) −0.763958 + 1.17267i −0.0246953 + 0.0379070i
\(958\) −4.71803 −0.152433
\(959\) −4.45029 + 4.72216i −0.143707 + 0.152487i
\(960\) −0.312501 + 5.80202i −0.0100859 + 0.187259i
\(961\) −24.3069 14.0336i −0.784093 0.452696i
\(962\) −13.9705 24.6167i −0.450428 0.793675i
\(963\) −21.1442 47.8635i −0.681363 1.54238i
\(964\) 4.61685 + 17.2303i 0.148699 + 0.554951i
\(965\) 2.92485i 0.0941542i
\(966\) 12.0343 + 22.0589i 0.387197 + 0.709735i
\(967\) 2.78613 2.78613i 0.0895958 0.0895958i −0.660888 0.750484i \(-0.729820\pi\)
0.750484 + 0.660888i \(0.229820\pi\)
\(968\) 28.0542 7.51710i 0.901697 0.241609i
\(969\) 14.5698 7.39713i 0.468051 0.237630i
\(970\) −2.98522 + 11.1410i −0.0958496 + 0.357715i
\(971\) 17.9367 + 10.3557i 0.575615 + 0.332332i 0.759389 0.650637i \(-0.225498\pi\)
−0.183774 + 0.982969i \(0.558831\pi\)
\(972\) 7.69622 + 13.5561i 0.246856 + 0.434812i
\(973\) −21.6862 + 40.2718i −0.695226 + 1.29105i
\(974\) −17.0911 −0.547633
\(975\) 7.78140 + 38.2713i 0.249204 + 1.22566i
\(976\) −1.79532 3.10959i −0.0574669 0.0995355i
\(977\) 4.50162 16.8003i 0.144020 0.537489i −0.855777 0.517344i \(-0.826921\pi\)
0.999797 0.0201445i \(-0.00641264\pi\)
\(978\) −15.7222 + 3.31806i −0.502742 + 0.106100i
\(979\) 20.4519i 0.653647i
\(980\) 23.0026 + 4.72363i 0.734790 + 0.150891i
\(981\) 9.93453 + 12.3411i 0.317185 + 0.394020i
\(982\) 23.9908 6.42832i 0.765578 0.205136i
\(983\) −13.4884 3.61420i −0.430212 0.115275i 0.0372135 0.999307i \(-0.488152\pi\)
−0.467426 + 0.884032i \(0.654819\pi\)
\(984\) −16.5859 5.41566i −0.528739 0.172645i
\(985\) −13.7650 7.94724i −0.438590 0.253220i
\(986\) 0.367353 0.367353i 0.0116989 0.0116989i
\(987\) 38.4096 + 23.4318i 1.22259 + 0.745842i
\(988\) −5.95535 + 5.86783i −0.189465 + 0.186680i
\(989\) −12.1612 7.02129i −0.386705 0.223264i
\(990\) −59.3886 22.9948i −1.88749 0.730824i
\(991\) 1.69315 + 2.93263i 0.0537848 + 0.0931580i 0.891664 0.452697i \(-0.149538\pi\)
−0.837879 + 0.545855i \(0.816205\pi\)
\(992\) 0.856275 1.48311i 0.0271868 0.0470889i
\(993\) 1.27468 23.6662i 0.0404507 0.751023i
\(994\) −27.7322 + 17.1263i −0.879612 + 0.543212i
\(995\) 54.0606 54.0606i 1.71384 1.71384i
\(996\) 0.811103 + 0.528409i 0.0257008 + 0.0167433i
\(997\) −18.3914 31.8548i −0.582461 1.00885i −0.995187 0.0979970i \(-0.968756\pi\)
0.412725 0.910855i \(-0.364577\pi\)
\(998\) 13.8253 + 23.9462i 0.437633 + 0.758003i
\(999\) −31.5890 25.8085i −0.999433 0.816544i
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 546.2.bv.a.317.35 yes 144
3.2 odd 2 inner 546.2.bv.a.317.8 144
7.4 even 3 inner 546.2.bv.a.473.8 yes 144
13.8 odd 4 inner 546.2.bv.a.359.35 yes 144
21.11 odd 6 inner 546.2.bv.a.473.35 yes 144
39.8 even 4 inner 546.2.bv.a.359.8 yes 144
91.60 odd 12 inner 546.2.bv.a.515.8 yes 144
273.242 even 12 inner 546.2.bv.a.515.35 yes 144
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
546.2.bv.a.317.8 144 3.2 odd 2 inner
546.2.bv.a.317.35 yes 144 1.1 even 1 trivial
546.2.bv.a.359.8 yes 144 39.8 even 4 inner
546.2.bv.a.359.35 yes 144 13.8 odd 4 inner
546.2.bv.a.473.8 yes 144 7.4 even 3 inner
546.2.bv.a.473.35 yes 144 21.11 odd 6 inner
546.2.bv.a.515.8 yes 144 91.60 odd 12 inner
546.2.bv.a.515.35 yes 144 273.242 even 12 inner