Properties

Label 546.2.bw.a.11.13
Level $546$
Weight $2$
Character 546.11
Analytic conductor $4.360$
Analytic rank $0$
Dimension $152$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [546,2,Mod(11,546)]
 
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, 8, 7]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("546.11");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 546.bw (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: \(152\)
Relative dimension: \(38\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 11.13
Character \(\chi\) \(=\) 546.11
Dual form 546.2.bw.a.149.13

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.258819 - 0.965926i) q^{2} +(0.770566 + 1.55120i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(-1.57124 - 0.421014i) q^{5} +(1.29891 - 1.14579i) q^{6} +(0.222219 - 2.63640i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-1.81246 + 2.39061i) q^{9} +O(q^{10})\) \(q+(-0.258819 - 0.965926i) q^{2} +(0.770566 + 1.55120i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(-1.57124 - 0.421014i) q^{5} +(1.29891 - 1.14579i) q^{6} +(0.222219 - 2.63640i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-1.81246 + 2.39061i) q^{9} +1.62667i q^{10} +(3.58913 + 3.58913i) q^{11} +(-1.44293 - 0.958098i) q^{12} +(3.58027 - 0.426188i) q^{13} +(-2.60408 + 0.467704i) q^{14} +(-0.557670 - 2.76174i) q^{15} +(0.500000 - 0.866025i) q^{16} +(0.426717 + 0.739096i) q^{17} +(2.77825 + 1.13196i) q^{18} +(3.96078 + 3.96078i) q^{19} +(1.57124 - 0.421014i) q^{20} +(4.26083 - 1.68682i) q^{21} +(2.53789 - 4.39576i) q^{22} +(-1.24829 + 2.16211i) q^{23} +(-0.551993 + 1.64174i) q^{24} +(-2.03857 - 1.17697i) q^{25} +(-1.33831 - 3.34797i) q^{26} +(-5.10493 - 0.969366i) q^{27} +(1.12575 + 2.39430i) q^{28} +(4.98976 - 2.88084i) q^{29} +(-2.52330 + 1.25346i) q^{30} +(5.51999 - 1.47908i) q^{31} +(-0.965926 - 0.258819i) q^{32} +(-2.80180 + 8.33312i) q^{33} +(0.603469 - 0.603469i) q^{34} +(-1.45912 + 4.04888i) q^{35} +(0.374330 - 2.97655i) q^{36} +(1.42237 + 5.30835i) q^{37} +(2.80069 - 4.85094i) q^{38} +(3.41994 + 5.22532i) q^{39} +(-0.813336 - 1.40874i) q^{40} +(2.07420 + 0.555780i) q^{41} +(-2.73212 - 3.67906i) q^{42} +(11.2486 + 6.49440i) q^{43} +(-4.90284 - 1.31371i) q^{44} +(3.85429 - 2.99316i) q^{45} +(2.41152 + 0.646164i) q^{46} +(-1.93794 + 7.23248i) q^{47} +(1.72866 + 0.108271i) q^{48} +(-6.90124 - 1.17172i) q^{49} +(-0.609244 + 2.27373i) q^{50} +(-0.817673 + 1.23145i) q^{51} +(-2.88751 + 2.15923i) q^{52} +(-9.96523 - 5.75343i) q^{53} +(0.384918 + 5.18188i) q^{54} +(-4.12832 - 7.15047i) q^{55} +(2.02135 - 1.70709i) q^{56} +(-3.09193 + 9.19601i) q^{57} +(-4.07412 - 4.07412i) q^{58} +(-0.213668 + 0.797418i) q^{59} +(1.86382 + 2.11290i) q^{60} +5.85386 q^{61} +(-2.85736 - 4.94909i) q^{62} +(5.89984 + 5.30960i) q^{63} +1.00000i q^{64} +(-5.80492 - 0.837699i) q^{65} +(8.77433 + 0.549563i) q^{66} +(-8.67051 - 8.67051i) q^{67} +(-0.739096 - 0.426717i) q^{68} +(-4.31576 - 0.270309i) q^{69} +(4.28856 + 0.361477i) q^{70} +(-3.90925 - 14.5895i) q^{71} +(-2.97201 + 0.408814i) q^{72} +(2.83040 + 10.5632i) q^{73} +(4.75933 - 2.74780i) q^{74} +(0.254864 - 4.06917i) q^{75} +(-5.41052 - 1.44975i) q^{76} +(10.2600 - 8.66481i) q^{77} +(4.16213 - 4.65582i) q^{78} +(-6.03981 - 10.4613i) q^{79} +(-1.15023 + 1.15023i) q^{80} +(-2.43000 - 8.66574i) q^{81} -2.14737i q^{82} +(3.18424 - 3.18424i) q^{83} +(-2.84658 + 3.59124i) q^{84} +(-0.359308 - 1.34095i) q^{85} +(3.36175 - 12.5462i) q^{86} +(8.31371 + 5.52025i) q^{87} +5.07579i q^{88} +(6.85883 - 1.83782i) q^{89} +(-3.88873 - 2.94827i) q^{90} +(-0.327998 - 9.53375i) q^{91} -2.49659i q^{92} +(6.54787 + 7.42290i) q^{93} +7.48762 q^{94} +(-4.55581 - 7.89089i) q^{95} +(-0.342829 - 1.69778i) q^{96} +(-14.9348 + 4.00176i) q^{97} +(0.654380 + 6.96935i) q^{98} +(-15.0853 + 2.07506i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 152 q + 12 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 152 q + 12 q^{7} + 76 q^{16} - 8 q^{18} + 12 q^{19} + 8 q^{21} + 24 q^{27} + 16 q^{28} - 12 q^{31} - 48 q^{33} + 24 q^{36} - 36 q^{37} - 8 q^{39} + 84 q^{43} - 40 q^{45} - 16 q^{46} - 28 q^{49} + 4 q^{52} + 24 q^{54} + 16 q^{55} - 8 q^{57} - 16 q^{58} + 64 q^{61} - 100 q^{63} + 16 q^{66} - 112 q^{67} + 84 q^{69} + 16 q^{72} - 120 q^{73} - 48 q^{76} - 8 q^{78} + 32 q^{79} + 48 q^{81} - 8 q^{84} - 152 q^{85} + 48 q^{87} + 16 q^{91} - 12 q^{93} - 64 q^{94} - 100 q^{97} + 16 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(157\) \(365\) \(379\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(-1\) \(e\left(\frac{7}{12}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.258819 0.965926i −0.183013 0.683013i
\(3\) 0.770566 + 1.55120i 0.444886 + 0.895587i
\(4\) −0.866025 + 0.500000i −0.433013 + 0.250000i
\(5\) −1.57124 0.421014i −0.702682 0.188283i −0.110250 0.993904i \(-0.535165\pi\)
−0.592432 + 0.805621i \(0.701832\pi\)
\(6\) 1.29891 1.14579i 0.530277 0.467767i
\(7\) 0.222219 2.63640i 0.0839908 0.996467i
\(8\) 0.707107 + 0.707107i 0.250000 + 0.250000i
\(9\) −1.81246 + 2.39061i −0.604152 + 0.796869i
\(10\) 1.62667i 0.514399i
\(11\) 3.58913 + 3.58913i 1.08216 + 1.08216i 0.996308 + 0.0858544i \(0.0273620\pi\)
0.0858544 + 0.996308i \(0.472638\pi\)
\(12\) −1.44293 0.958098i −0.416538 0.276579i
\(13\) 3.58027 0.426188i 0.992989 0.118203i
\(14\) −2.60408 + 0.467704i −0.695971 + 0.124999i
\(15\) −0.557670 2.76174i −0.143990 0.713077i
\(16\) 0.500000 0.866025i 0.125000 0.216506i
\(17\) 0.426717 + 0.739096i 0.103494 + 0.179257i 0.913122 0.407687i \(-0.133664\pi\)
−0.809628 + 0.586944i \(0.800331\pi\)
\(18\) 2.77825 + 1.13196i 0.654839 + 0.266806i
\(19\) 3.96078 + 3.96078i 0.908665 + 0.908665i 0.996165 0.0874998i \(-0.0278877\pi\)
−0.0874998 + 0.996165i \(0.527888\pi\)
\(20\) 1.57124 0.421014i 0.351341 0.0941415i
\(21\) 4.26083 1.68682i 0.929789 0.368093i
\(22\) 2.53789 4.39576i 0.541081 0.937180i
\(23\) −1.24829 + 2.16211i −0.260287 + 0.450831i −0.966318 0.257350i \(-0.917151\pi\)
0.706031 + 0.708181i \(0.250484\pi\)
\(24\) −0.551993 + 1.64174i −0.112675 + 0.335118i
\(25\) −2.03857 1.17697i −0.407714 0.235394i
\(26\) −1.33831 3.34797i −0.262464 0.656592i
\(27\) −5.10493 0.969366i −0.982445 0.186555i
\(28\) 1.12575 + 2.39430i 0.212748 + 0.452480i
\(29\) 4.98976 2.88084i 0.926576 0.534959i 0.0408488 0.999165i \(-0.486994\pi\)
0.885727 + 0.464207i \(0.153660\pi\)
\(30\) −2.52330 + 1.25346i −0.460689 + 0.228849i
\(31\) 5.51999 1.47908i 0.991420 0.265650i 0.273573 0.961851i \(-0.411794\pi\)
0.717847 + 0.696201i \(0.245128\pi\)
\(32\) −0.965926 0.258819i −0.170753 0.0457532i
\(33\) −2.80180 + 8.33312i −0.487731 + 1.45061i
\(34\) 0.603469 0.603469i 0.103494 0.103494i
\(35\) −1.45912 + 4.04888i −0.246637 + 0.684385i
\(36\) 0.374330 2.97655i 0.0623883 0.496092i
\(37\) 1.42237 + 5.30835i 0.233836 + 0.872687i 0.978670 + 0.205437i \(0.0658617\pi\)
−0.744835 + 0.667249i \(0.767472\pi\)
\(38\) 2.80069 4.85094i 0.454332 0.786927i
\(39\) 3.41994 + 5.22532i 0.547629 + 0.836721i
\(40\) −0.813336 1.40874i −0.128600 0.222741i
\(41\) 2.07420 + 0.555780i 0.323935 + 0.0867982i 0.417122 0.908850i \(-0.363039\pi\)
−0.0931868 + 0.995649i \(0.529705\pi\)
\(42\) −2.73212 3.67906i −0.421576 0.567692i
\(43\) 11.2486 + 6.49440i 1.71540 + 0.990386i 0.926865 + 0.375395i \(0.122493\pi\)
0.788534 + 0.614991i \(0.210841\pi\)
\(44\) −4.90284 1.31371i −0.739130 0.198049i
\(45\) 3.85429 2.99316i 0.574564 0.446194i
\(46\) 2.41152 + 0.646164i 0.355559 + 0.0952717i
\(47\) −1.93794 + 7.23248i −0.282677 + 1.05497i 0.667843 + 0.744303i \(0.267218\pi\)
−0.950520 + 0.310664i \(0.899449\pi\)
\(48\) 1.72866 + 0.108271i 0.249511 + 0.0156276i
\(49\) −6.90124 1.17172i −0.985891 0.167388i
\(50\) −0.609244 + 2.27373i −0.0861601 + 0.321554i
\(51\) −0.817673 + 1.23145i −0.114497 + 0.172437i
\(52\) −2.88751 + 2.15923i −0.400426 + 0.299431i
\(53\) −9.96523 5.75343i −1.36883 0.790294i −0.378051 0.925785i \(-0.623406\pi\)
−0.990779 + 0.135490i \(0.956739\pi\)
\(54\) 0.384918 + 5.18188i 0.0523807 + 0.705164i
\(55\) −4.12832 7.15047i −0.556663 0.964169i
\(56\) 2.02135 1.70709i 0.270114 0.228119i
\(57\) −3.09193 + 9.19601i −0.409536 + 1.21804i
\(58\) −4.07412 4.07412i −0.534959 0.534959i
\(59\) −0.213668 + 0.797418i −0.0278172 + 0.103815i −0.978439 0.206538i \(-0.933780\pi\)
0.950622 + 0.310353i \(0.100447\pi\)
\(60\) 1.86382 + 2.11290i 0.240619 + 0.272774i
\(61\) 5.85386 0.749510 0.374755 0.927124i \(-0.377727\pi\)
0.374755 + 0.927124i \(0.377727\pi\)
\(62\) −2.85736 4.94909i −0.362885 0.628535i
\(63\) 5.89984 + 5.30960i 0.743310 + 0.668947i
\(64\) 1.00000i 0.125000i
\(65\) −5.80492 0.837699i −0.720011 0.103904i
\(66\) 8.77433 + 0.549563i 1.08005 + 0.0676465i
\(67\) −8.67051 8.67051i −1.05927 1.05927i −0.998129 0.0611424i \(-0.980526\pi\)
−0.0611424 0.998129i \(-0.519474\pi\)
\(68\) −0.739096 0.426717i −0.0896285 0.0517471i
\(69\) −4.31576 0.270309i −0.519556 0.0325414i
\(70\) 4.28856 + 0.361477i 0.512581 + 0.0432048i
\(71\) −3.90925 14.5895i −0.463942 1.73146i −0.660373 0.750938i \(-0.729602\pi\)
0.196431 0.980518i \(-0.437065\pi\)
\(72\) −2.97201 + 0.408814i −0.350255 + 0.0481792i
\(73\) 2.83040 + 10.5632i 0.331273 + 1.23633i 0.907853 + 0.419288i \(0.137720\pi\)
−0.576580 + 0.817040i \(0.695613\pi\)
\(74\) 4.75933 2.74780i 0.553261 0.319425i
\(75\) 0.254864 4.06917i 0.0294292 0.469867i
\(76\) −5.41052 1.44975i −0.620630 0.166297i
\(77\) 10.2600 8.66481i 1.16923 0.987447i
\(78\) 4.16213 4.65582i 0.471268 0.527168i
\(79\) −6.03981 10.4613i −0.679532 1.17698i −0.975122 0.221669i \(-0.928850\pi\)
0.295590 0.955315i \(-0.404484\pi\)
\(80\) −1.15023 + 1.15023i −0.128600 + 0.128600i
\(81\) −2.43000 8.66574i −0.270000 0.962860i
\(82\) 2.14737i 0.237137i
\(83\) 3.18424 3.18424i 0.349516 0.349516i −0.510413 0.859929i \(-0.670508\pi\)
0.859929 + 0.510413i \(0.170508\pi\)
\(84\) −2.84658 + 3.59124i −0.310587 + 0.391836i
\(85\) −0.359308 1.34095i −0.0389724 0.145447i
\(86\) 3.36175 12.5462i 0.362506 1.35289i
\(87\) 8.31371 + 5.52025i 0.891323 + 0.591833i
\(88\) 5.07579i 0.541081i
\(89\) 6.85883 1.83782i 0.727034 0.194808i 0.123726 0.992316i \(-0.460516\pi\)
0.603308 + 0.797508i \(0.293849\pi\)
\(90\) −3.88873 2.94827i −0.409909 0.310775i
\(91\) −0.327998 9.53375i −0.0343835 0.999409i
\(92\) 2.49659i 0.260287i
\(93\) 6.54787 + 7.42290i 0.678982 + 0.769719i
\(94\) 7.48762 0.772289
\(95\) −4.55581 7.89089i −0.467416 0.809588i
\(96\) −0.342829 1.69778i −0.0349898 0.173279i
\(97\) −14.9348 + 4.00176i −1.51640 + 0.406317i −0.918554 0.395296i \(-0.870642\pi\)
−0.597843 + 0.801613i \(0.703975\pi\)
\(98\) 0.654380 + 6.96935i 0.0661024 + 0.704010i
\(99\) −15.0853 + 2.07506i −1.51613 + 0.208551i
\(100\) 2.35394 0.235394
\(101\) 2.12057 0.211005 0.105502 0.994419i \(-0.466355\pi\)
0.105502 + 0.994419i \(0.466355\pi\)
\(102\) 1.40112 + 0.471090i 0.138731 + 0.0466449i
\(103\) −2.43480 + 1.40573i −0.239908 + 0.138511i −0.615135 0.788422i \(-0.710898\pi\)
0.375226 + 0.926933i \(0.377565\pi\)
\(104\) 2.83300 + 2.23028i 0.277798 + 0.218697i
\(105\) −7.40498 + 0.856533i −0.722652 + 0.0835891i
\(106\) −2.97819 + 11.1148i −0.289268 + 1.07956i
\(107\) −10.5143 6.07045i −1.01646 0.586852i −0.103382 0.994642i \(-0.532966\pi\)
−0.913076 + 0.407790i \(0.866300\pi\)
\(108\) 4.90568 1.71297i 0.472050 0.164831i
\(109\) −6.99713 + 1.87488i −0.670204 + 0.179581i −0.577847 0.816145i \(-0.696107\pi\)
−0.0923571 + 0.995726i \(0.529440\pi\)
\(110\) −5.83833 + 5.83833i −0.556663 + 0.556663i
\(111\) −7.13829 + 6.29681i −0.677536 + 0.597667i
\(112\) −2.17208 1.51065i −0.205242 0.142743i
\(113\) −9.65602 5.57491i −0.908362 0.524443i −0.0284582 0.999595i \(-0.509060\pi\)
−0.879904 + 0.475152i \(0.842393\pi\)
\(114\) 9.68291 + 0.606470i 0.906888 + 0.0568011i
\(115\) 2.87165 2.87165i 0.267783 0.267783i
\(116\) −2.88084 + 4.98976i −0.267479 + 0.463288i
\(117\) −5.47024 + 9.33148i −0.505724 + 0.862695i
\(118\) 0.825548 0.0759979
\(119\) 2.04338 0.960757i 0.187316 0.0880725i
\(120\) 1.55851 2.34718i 0.142272 0.214267i
\(121\) 14.7636i 1.34215i
\(122\) −1.51509 5.65440i −0.137170 0.511925i
\(123\) 0.736180 + 3.64577i 0.0663791 + 0.328728i
\(124\) −4.04092 + 4.04092i −0.362885 + 0.362885i
\(125\) 8.45873 + 8.45873i 0.756571 + 0.756571i
\(126\) 3.60169 7.07303i 0.320864 0.630116i
\(127\) 6.85083 3.95533i 0.607913 0.350979i −0.164235 0.986421i \(-0.552516\pi\)
0.772148 + 0.635442i \(0.219182\pi\)
\(128\) 0.965926 0.258819i 0.0853766 0.0228766i
\(129\) −1.40631 + 22.4532i −0.123819 + 1.97690i
\(130\) 0.693268 + 5.82393i 0.0608036 + 0.510793i
\(131\) 6.60251 3.81196i 0.576864 0.333053i −0.183022 0.983109i \(-0.558588\pi\)
0.759886 + 0.650056i \(0.225255\pi\)
\(132\) −1.74013 8.61759i −0.151459 0.750065i
\(133\) 11.3224 9.56204i 0.981773 0.829134i
\(134\) −6.13098 + 10.6192i −0.529636 + 0.917356i
\(135\) 7.61298 + 3.67236i 0.655221 + 0.316066i
\(136\) −0.220885 + 0.824354i −0.0189407 + 0.0706878i
\(137\) −1.87303 + 6.99026i −0.160024 + 0.597218i 0.838599 + 0.544750i \(0.183375\pi\)
−0.998623 + 0.0524680i \(0.983291\pi\)
\(138\) 0.855902 + 4.23867i 0.0728592 + 0.360819i
\(139\) 2.22956 3.86172i 0.189109 0.327547i −0.755844 0.654751i \(-0.772773\pi\)
0.944953 + 0.327205i \(0.106107\pi\)
\(140\) −0.760801 4.23599i −0.0642995 0.358007i
\(141\) −12.7124 + 2.56697i −1.07057 + 0.216178i
\(142\) −13.0806 + 7.55208i −1.09770 + 0.633757i
\(143\) 14.3797 + 11.3204i 1.20249 + 0.946660i
\(144\) 1.16410 + 2.76494i 0.0970082 + 0.230411i
\(145\) −9.05301 + 2.42575i −0.751812 + 0.201447i
\(146\) 9.47070 5.46791i 0.783801 0.452527i
\(147\) −3.50029 11.6081i −0.288699 0.957420i
\(148\) −3.88598 3.88598i −0.319425 0.319425i
\(149\) 8.68358 8.68358i 0.711387 0.711387i −0.255439 0.966825i \(-0.582220\pi\)
0.966825 + 0.255439i \(0.0822199\pi\)
\(150\) −3.99648 + 0.806998i −0.326311 + 0.0658911i
\(151\) 0.0146551 + 0.0546937i 0.00119262 + 0.00445091i 0.966520 0.256593i \(-0.0826000\pi\)
−0.965327 + 0.261044i \(0.915933\pi\)
\(152\) 5.60139i 0.454332i
\(153\) −2.54029 0.319466i −0.205371 0.0258273i
\(154\) −11.0250 7.66773i −0.888422 0.617884i
\(155\) −9.29597 −0.746671
\(156\) −5.57442 2.81529i −0.446311 0.225404i
\(157\) −2.03262 + 3.52061i −0.162221 + 0.280975i −0.935665 0.352890i \(-0.885199\pi\)
0.773444 + 0.633865i \(0.218532\pi\)
\(158\) −8.54158 + 8.54158i −0.679532 + 0.679532i
\(159\) 1.24586 19.8915i 0.0988035 1.57750i
\(160\) 1.40874 + 0.813336i 0.111371 + 0.0642999i
\(161\) 5.42279 + 3.77147i 0.427376 + 0.297233i
\(162\) −7.74153 + 4.59006i −0.608232 + 0.360629i
\(163\) −7.19966 + 7.19966i −0.563921 + 0.563921i −0.930419 0.366498i \(-0.880557\pi\)
0.366498 + 0.930419i \(0.380557\pi\)
\(164\) −2.07420 + 0.555780i −0.161968 + 0.0433991i
\(165\) 7.91067 11.9138i 0.615845 0.927486i
\(166\) −3.89989 2.25160i −0.302690 0.174758i
\(167\) 2.89910 10.8196i 0.224339 0.837245i −0.758329 0.651872i \(-0.773984\pi\)
0.982668 0.185373i \(-0.0593493\pi\)
\(168\) 4.20562 + 1.82010i 0.324471 + 0.140424i
\(169\) 12.6367 3.05174i 0.972056 0.234749i
\(170\) −1.20227 + 0.694129i −0.0922096 + 0.0532373i
\(171\) −16.6474 + 2.28993i −1.27306 + 0.175115i
\(172\) −12.9888 −0.990386
\(173\) −11.9430 −0.908013 −0.454007 0.890998i \(-0.650006\pi\)
−0.454007 + 0.890998i \(0.650006\pi\)
\(174\) 3.18041 9.45917i 0.241106 0.717098i
\(175\) −3.55597 + 5.11295i −0.268806 + 0.386502i
\(176\) 4.90284 1.31371i 0.369565 0.0990247i
\(177\) −1.40160 + 0.283022i −0.105351 + 0.0212732i
\(178\) −3.55039 6.14945i −0.266113 0.460921i
\(179\) −17.0979 −1.27796 −0.638980 0.769223i \(-0.720643\pi\)
−0.638980 + 0.769223i \(0.720643\pi\)
\(180\) −1.84133 + 4.51930i −0.137245 + 0.336849i
\(181\) 10.3755i 0.771203i 0.922665 + 0.385602i \(0.126006\pi\)
−0.922665 + 0.385602i \(0.873994\pi\)
\(182\) −9.12400 + 2.78434i −0.676316 + 0.206389i
\(183\) 4.51079 + 9.08053i 0.333447 + 0.671252i
\(184\) −2.41152 + 0.646164i −0.177780 + 0.0476359i
\(185\) 8.93954i 0.657248i
\(186\) 5.47526 8.24594i 0.401465 0.604622i
\(187\) −1.12117 + 4.18425i −0.0819878 + 0.305983i
\(188\) −1.93794 7.23248i −0.141339 0.527483i
\(189\) −3.69005 + 13.2432i −0.268412 + 0.963304i
\(190\) −6.44289 + 6.44289i −0.467416 + 0.467416i
\(191\) 10.4796i 0.758275i 0.925340 + 0.379138i \(0.123779\pi\)
−0.925340 + 0.379138i \(0.876221\pi\)
\(192\) −1.55120 + 0.770566i −0.111948 + 0.0556108i
\(193\) 2.15847 2.15847i 0.155370 0.155370i −0.625141 0.780512i \(-0.714959\pi\)
0.780512 + 0.625141i \(0.214959\pi\)
\(194\) 7.73081 + 13.3902i 0.555040 + 0.961357i
\(195\) −3.17363 9.65010i −0.227268 0.691058i
\(196\) 6.56251 2.43588i 0.468750 0.173992i
\(197\) 21.4008 + 5.73433i 1.52474 + 0.408554i 0.921301 0.388851i \(-0.127128\pi\)
0.603444 + 0.797405i \(0.293795\pi\)
\(198\) 5.90872 + 14.0342i 0.419914 + 0.997370i
\(199\) 4.29390 2.47908i 0.304386 0.175737i −0.340025 0.940416i \(-0.610436\pi\)
0.644412 + 0.764679i \(0.277102\pi\)
\(200\) −0.609244 2.27373i −0.0430801 0.160777i
\(201\) 6.76852 20.1309i 0.477414 1.41993i
\(202\) −0.548845 2.04832i −0.0386166 0.144119i
\(203\) −6.48624 13.7952i −0.455245 0.968233i
\(204\) 0.0924026 1.47530i 0.00646947 0.103292i
\(205\) −3.02508 1.74653i −0.211281 0.121983i
\(206\) 1.98801 + 1.98801i 0.138511 + 0.138511i
\(207\) −2.90627 6.90291i −0.202000 0.479785i
\(208\) 1.42105 3.31370i 0.0985319 0.229764i
\(209\) 28.4315i 1.96664i
\(210\) 2.74390 + 6.93097i 0.189347 + 0.478282i
\(211\) −2.66289 4.61226i −0.183321 0.317521i 0.759689 0.650287i \(-0.225351\pi\)
−0.943009 + 0.332766i \(0.892018\pi\)
\(212\) 11.5069 0.790294
\(213\) 19.6189 17.3062i 1.34427 1.18580i
\(214\) −3.14229 + 11.7272i −0.214803 + 0.801655i
\(215\) −14.9401 14.9401i −1.01891 1.01891i
\(216\) −2.92429 4.29518i −0.198973 0.292250i
\(217\) −2.67280 14.8816i −0.181441 1.01023i
\(218\) 3.62198 + 6.27346i 0.245312 + 0.424892i
\(219\) −14.2046 + 12.5302i −0.959860 + 0.846709i
\(220\) 7.15047 + 4.12832i 0.482084 + 0.278331i
\(221\) 1.84276 + 2.46430i 0.123957 + 0.165767i
\(222\) 7.92977 + 5.26532i 0.532212 + 0.353385i
\(223\) 2.72617 10.1742i 0.182558 0.681315i −0.812582 0.582846i \(-0.801939\pi\)
0.995140 0.0984687i \(-0.0313944\pi\)
\(224\) −0.896998 + 2.48905i −0.0599332 + 0.166307i
\(225\) 6.50849 2.74022i 0.433899 0.182681i
\(226\) −2.88578 + 10.7699i −0.191959 + 0.716403i
\(227\) 3.90354 + 1.04595i 0.259087 + 0.0694221i 0.386024 0.922489i \(-0.373848\pi\)
−0.126937 + 0.991911i \(0.540515\pi\)
\(228\) −1.92032 9.50994i −0.127176 0.629811i
\(229\) −5.91603 1.58519i −0.390942 0.104753i 0.0579930 0.998317i \(-0.481530\pi\)
−0.448935 + 0.893564i \(0.648197\pi\)
\(230\) −3.51704 2.03056i −0.231907 0.133891i
\(231\) 21.3468 + 9.23845i 1.40452 + 0.607846i
\(232\) 5.56536 + 1.49123i 0.365384 + 0.0979043i
\(233\) −6.28957 10.8939i −0.412044 0.713681i 0.583069 0.812422i \(-0.301852\pi\)
−0.995113 + 0.0987417i \(0.968518\pi\)
\(234\) 10.4293 + 2.86869i 0.681786 + 0.187532i
\(235\) 6.08995 10.5481i 0.397264 0.688082i
\(236\) −0.213668 0.797418i −0.0139086 0.0519075i
\(237\) 11.5735 17.4301i 0.751777 1.13220i
\(238\) −1.45689 1.72509i −0.0944359 0.111821i
\(239\) −14.2838 + 14.2838i −0.923944 + 0.923944i −0.997305 0.0733617i \(-0.976627\pi\)
0.0733617 + 0.997305i \(0.476627\pi\)
\(240\) −2.67057 0.897912i −0.172385 0.0579600i
\(241\) 22.8441 + 6.12107i 1.47152 + 0.394293i 0.903452 0.428689i \(-0.141024\pi\)
0.568068 + 0.822982i \(0.307691\pi\)
\(242\) 14.2606 3.82111i 0.916705 0.245630i
\(243\) 11.5698 10.4470i 0.742206 0.670172i
\(244\) −5.06959 + 2.92693i −0.324548 + 0.187378i
\(245\) 10.3502 + 4.74657i 0.661252 + 0.303247i
\(246\) 3.33100 1.65469i 0.212377 0.105499i
\(247\) 15.8687 + 12.4926i 1.00970 + 0.794887i
\(248\) 4.94909 + 2.85736i 0.314268 + 0.181442i
\(249\) 7.39307 + 2.48574i 0.468517 + 0.157527i
\(250\) 5.98122 10.3598i 0.378286 0.655210i
\(251\) −0.773364 + 1.33951i −0.0488143 + 0.0845489i −0.889400 0.457129i \(-0.848878\pi\)
0.840586 + 0.541678i \(0.182211\pi\)
\(252\) −7.76421 1.64833i −0.489099 0.103835i
\(253\) −12.2404 + 3.27979i −0.769545 + 0.206199i
\(254\) −5.59368 5.59368i −0.350979 0.350979i
\(255\) 1.80322 1.59065i 0.112922 0.0996105i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −3.44487 + 5.96669i −0.214885 + 0.372192i −0.953237 0.302224i \(-0.902271\pi\)
0.738352 + 0.674415i \(0.235604\pi\)
\(258\) 22.0522 4.45293i 1.37291 0.277227i
\(259\) 14.3110 2.57032i 0.889243 0.159712i
\(260\) 5.44606 2.17699i 0.337750 0.135011i
\(261\) −2.15677 + 17.1500i −0.133501 + 1.06156i
\(262\) −5.39093 5.39093i −0.333053 0.333053i
\(263\) 5.27945i 0.325545i −0.986664 0.162772i \(-0.947956\pi\)
0.986664 0.162772i \(-0.0520436\pi\)
\(264\) −7.87358 + 3.91123i −0.484585 + 0.240720i
\(265\) 13.2355 + 13.2355i 0.813053 + 0.813053i
\(266\) −12.1667 8.46172i −0.745986 0.518822i
\(267\) 8.13600 + 9.22327i 0.497915 + 0.564455i
\(268\) 11.8441 + 3.17363i 0.723496 + 0.193860i
\(269\) −16.4974 + 9.52479i −1.00587 + 0.580737i −0.909979 0.414655i \(-0.863902\pi\)
−0.0958873 + 0.995392i \(0.530569\pi\)
\(270\) 1.57684 8.30405i 0.0959635 0.505368i
\(271\) 0.0665053 + 0.248201i 0.00403991 + 0.0150772i 0.967916 0.251273i \(-0.0808491\pi\)
−0.963876 + 0.266350i \(0.914182\pi\)
\(272\) 0.853434 0.0517471
\(273\) 14.5360 7.85518i 0.879761 0.475417i
\(274\) 7.23685 0.437194
\(275\) −3.09239 11.5410i −0.186478 0.695947i
\(276\) 3.87271 1.92379i 0.233110 0.115798i
\(277\) −1.21697 + 0.702616i −0.0731204 + 0.0422161i −0.536114 0.844145i \(-0.680108\pi\)
0.462994 + 0.886361i \(0.346775\pi\)
\(278\) −4.30719 1.15411i −0.258328 0.0692187i
\(279\) −6.46885 + 15.8769i −0.387280 + 0.950525i
\(280\) −3.89474 + 1.83123i −0.232755 + 0.109437i
\(281\) 18.3020 + 18.3020i 1.09180 + 1.09180i 0.995336 + 0.0964690i \(0.0307548\pi\)
0.0964690 + 0.995336i \(0.469245\pi\)
\(282\) 5.76970 + 11.6148i 0.343581 + 0.691652i
\(283\) 24.0284i 1.42834i −0.699973 0.714169i \(-0.746805\pi\)
0.699973 0.714169i \(-0.253195\pi\)
\(284\) 10.6803 + 10.6803i 0.633757 + 0.633757i
\(285\) 8.72982 13.1474i 0.517110 0.778787i
\(286\) 7.21294 16.8197i 0.426510 0.994567i
\(287\) 1.92619 5.34492i 0.113699 0.315501i
\(288\) 2.36943 1.84005i 0.139620 0.108426i
\(289\) 8.13582 14.0917i 0.478578 0.828921i
\(290\) 4.68618 + 8.11671i 0.275182 + 0.476630i
\(291\) −17.7158 20.0832i −1.03852 1.17730i
\(292\) −7.73279 7.73279i −0.452527 0.452527i
\(293\) −12.2954 + 3.29454i −0.718304 + 0.192469i −0.599415 0.800439i \(-0.704600\pi\)
−0.118889 + 0.992908i \(0.537933\pi\)
\(294\) −10.3066 + 6.38542i −0.601094 + 0.372405i
\(295\) 0.671448 1.16298i 0.0390932 0.0677114i
\(296\) −2.74780 + 4.75933i −0.159713 + 0.276631i
\(297\) −14.8431 21.8014i −0.861282 1.26505i
\(298\) −10.6352 6.14022i −0.616079 0.355693i
\(299\) −3.54777 + 8.27295i −0.205173 + 0.478437i
\(300\) 1.81386 + 3.65143i 0.104724 + 0.210816i
\(301\) 19.6215 28.2127i 1.13096 1.62615i
\(302\) 0.0490370 0.0283115i 0.00282176 0.00162915i
\(303\) 1.63404 + 3.28944i 0.0938733 + 0.188973i
\(304\) 5.41052 1.44975i 0.310315 0.0831486i
\(305\) −9.19785 2.46456i −0.526667 0.141120i
\(306\) 0.348896 + 2.53642i 0.0199451 + 0.144997i
\(307\) 6.70956 6.70956i 0.382935 0.382935i −0.489223 0.872158i \(-0.662720\pi\)
0.872158 + 0.489223i \(0.162720\pi\)
\(308\) −4.55297 + 12.6339i −0.259430 + 0.719884i
\(309\) −4.05676 2.69366i −0.230781 0.153237i
\(310\) 2.40597 + 8.97922i 0.136650 + 0.509985i
\(311\) 6.66105 11.5373i 0.377714 0.654219i −0.613016 0.790071i \(-0.710044\pi\)
0.990729 + 0.135852i \(0.0433770\pi\)
\(312\) −1.27660 + 6.11312i −0.0722731 + 0.346088i
\(313\) 12.9713 + 22.4670i 0.733183 + 1.26991i 0.955516 + 0.294939i \(0.0952994\pi\)
−0.222333 + 0.974971i \(0.571367\pi\)
\(314\) 3.92673 + 1.05216i 0.221598 + 0.0593770i
\(315\) −7.03468 10.8266i −0.396359 0.610010i
\(316\) 10.4613 + 6.03981i 0.588492 + 0.339766i
\(317\) 5.29018 + 1.41750i 0.297126 + 0.0796148i 0.404303 0.914625i \(-0.367514\pi\)
−0.107176 + 0.994240i \(0.534181\pi\)
\(318\) −19.5362 + 3.94488i −1.09553 + 0.221218i
\(319\) 28.2486 + 7.56919i 1.58162 + 0.423793i
\(320\) 0.421014 1.57124i 0.0235354 0.0878352i
\(321\) 1.31451 20.9875i 0.0733689 1.17141i
\(322\) 2.23943 6.21414i 0.124799 0.346301i
\(323\) −1.23726 + 4.61753i −0.0688431 + 0.256926i
\(324\) 6.43732 + 6.28975i 0.357629 + 0.349431i
\(325\) −7.80025 3.34506i −0.432680 0.185550i
\(326\) 8.81774 + 5.09093i 0.488370 + 0.281960i
\(327\) −8.30006 9.40925i −0.458994 0.520333i
\(328\) 1.07368 + 1.85968i 0.0592843 + 0.102683i
\(329\) 18.6371 + 6.71638i 1.02750 + 0.370286i
\(330\) −13.5552 4.55761i −0.746192 0.250888i
\(331\) −1.71360 1.71360i −0.0941880 0.0941880i 0.658443 0.752631i \(-0.271215\pi\)
−0.752631 + 0.658443i \(0.771215\pi\)
\(332\) −1.16551 + 4.34976i −0.0639659 + 0.238724i
\(333\) −15.2681 6.22082i −0.836689 0.340899i
\(334\) −11.2013 −0.612906
\(335\) 9.97309 + 17.2739i 0.544888 + 0.943774i
\(336\) 0.669589 4.53339i 0.0365291 0.247317i
\(337\) 7.56541i 0.412114i −0.978540 0.206057i \(-0.933937\pi\)
0.978540 0.206057i \(-0.0660633\pi\)
\(338\) −6.21838 11.4163i −0.338235 0.620965i
\(339\) 1.20721 19.2743i 0.0655664 1.04683i
\(340\) 0.981647 + 0.981647i 0.0532373 + 0.0532373i
\(341\) 25.1205 + 14.5034i 1.36035 + 0.785401i
\(342\) 6.52056 + 15.4875i 0.352592 + 0.837467i
\(343\) −4.62270 + 17.9341i −0.249602 + 0.968348i
\(344\) 3.36175 + 12.5462i 0.181253 + 0.676446i
\(345\) 6.66731 + 2.24172i 0.358956 + 0.120690i
\(346\) 3.09109 + 11.5361i 0.166178 + 0.620184i
\(347\) −19.8047 + 11.4343i −1.06317 + 0.613824i −0.926309 0.376765i \(-0.877036\pi\)
−0.136866 + 0.990590i \(0.543703\pi\)
\(348\) −9.96001 0.623826i −0.533913 0.0334406i
\(349\) −14.5245 3.89183i −0.777480 0.208325i −0.151806 0.988410i \(-0.548509\pi\)
−0.625673 + 0.780085i \(0.715176\pi\)
\(350\) 5.85908 + 2.11148i 0.313181 + 0.112863i
\(351\) −18.6902 1.29494i −0.997608 0.0691186i
\(352\) −2.53789 4.39576i −0.135270 0.234295i
\(353\) 6.61649 6.61649i 0.352160 0.352160i −0.508752 0.860913i \(-0.669893\pi\)
0.860913 + 0.508752i \(0.169893\pi\)
\(354\) 0.636139 + 1.28059i 0.0338104 + 0.0680627i
\(355\) 24.5695i 1.30401i
\(356\) −5.02101 + 5.02101i −0.266113 + 0.266113i
\(357\) 3.06489 + 2.42937i 0.162211 + 0.128576i
\(358\) 4.42527 + 16.5153i 0.233883 + 0.872863i
\(359\) 9.54536 35.6238i 0.503785 1.88015i 0.0299221 0.999552i \(-0.490474\pi\)
0.473863 0.880599i \(-0.342859\pi\)
\(360\) 4.84188 + 0.608912i 0.255189 + 0.0320925i
\(361\) 12.3755i 0.651343i
\(362\) 10.0219 2.68537i 0.526741 0.141140i
\(363\) −22.9014 + 11.3764i −1.20201 + 0.597104i
\(364\) 5.05093 + 8.09247i 0.264741 + 0.424161i
\(365\) 17.7890i 0.931118i
\(366\) 7.60364 6.70730i 0.397448 0.350596i
\(367\) −33.7117 −1.75974 −0.879868 0.475218i \(-0.842369\pi\)
−0.879868 + 0.475218i \(0.842369\pi\)
\(368\) 1.24829 + 2.16211i 0.0650718 + 0.112708i
\(369\) −5.08805 + 3.95127i −0.264873 + 0.205695i
\(370\) −8.63494 + 2.31372i −0.448909 + 0.120285i
\(371\) −17.3828 + 24.9938i −0.902471 + 1.29762i
\(372\) −9.38207 3.15449i −0.486438 0.163552i
\(373\) −20.1797 −1.04486 −0.522432 0.852681i \(-0.674975\pi\)
−0.522432 + 0.852681i \(0.674975\pi\)
\(374\) 4.33185 0.223995
\(375\) −6.60319 + 19.6392i −0.340987 + 1.01416i
\(376\) −6.48447 + 3.74381i −0.334411 + 0.193072i
\(377\) 16.6369 12.4408i 0.856846 0.640733i
\(378\) 13.7470 + 0.136712i 0.707072 + 0.00703170i
\(379\) 2.45073 9.14625i 0.125886 0.469811i −0.873984 0.485954i \(-0.838472\pi\)
0.999870 + 0.0161431i \(0.00513874\pi\)
\(380\) 7.89089 + 4.55581i 0.404794 + 0.233708i
\(381\) 11.4145 + 7.57919i 0.584784 + 0.388293i
\(382\) 10.1225 2.71231i 0.517912 0.138774i
\(383\) 15.5349 15.5349i 0.793794 0.793794i −0.188314 0.982109i \(-0.560302\pi\)
0.982109 + 0.188314i \(0.0603024\pi\)
\(384\) 1.14579 + 1.29891i 0.0584709 + 0.0662847i
\(385\) −19.7689 + 9.29495i −1.00752 + 0.473715i
\(386\) −2.64358 1.52627i −0.134555 0.0776851i
\(387\) −35.9132 + 15.1202i −1.82557 + 0.768604i
\(388\) 10.9330 10.9330i 0.555040 0.555040i
\(389\) 1.09507 1.89671i 0.0555220 0.0961669i −0.836929 0.547312i \(-0.815651\pi\)
0.892451 + 0.451145i \(0.148984\pi\)
\(390\) −8.49989 + 5.56312i −0.430409 + 0.281700i
\(391\) −2.13067 −0.107753
\(392\) −4.05138 5.70844i −0.204626 0.288320i
\(393\) 11.0008 + 7.30446i 0.554917 + 0.368461i
\(394\) 22.1557i 1.11619i
\(395\) 5.08569 + 18.9800i 0.255889 + 0.954989i
\(396\) 12.0267 9.33971i 0.604367 0.469338i
\(397\) 7.44654 7.44654i 0.373731 0.373731i −0.495103 0.868834i \(-0.664870\pi\)
0.868834 + 0.495103i \(0.164870\pi\)
\(398\) −3.50595 3.50595i −0.175737 0.175737i
\(399\) 23.5573 + 10.1951i 1.17934 + 0.510393i
\(400\) −2.03857 + 1.17697i −0.101929 + 0.0588484i
\(401\) −23.6965 + 6.34945i −1.18335 + 0.317077i −0.796253 0.604964i \(-0.793187\pi\)
−0.387093 + 0.922041i \(0.626521\pi\)
\(402\) −21.1968 1.32762i −1.05720 0.0662156i
\(403\) 19.1327 7.64806i 0.953069 0.380977i
\(404\) −1.83647 + 1.06029i −0.0913678 + 0.0527512i
\(405\) 0.169735 + 14.6391i 0.00843418 + 0.727421i
\(406\) −11.6464 + 9.83569i −0.578000 + 0.488137i
\(407\) −13.9473 + 24.1574i −0.691340 + 1.19744i
\(408\) −1.44895 + 0.292582i −0.0717335 + 0.0144850i
\(409\) 1.20975 4.51486i 0.0598184 0.223245i −0.929545 0.368708i \(-0.879800\pi\)
0.989364 + 0.145462i \(0.0464670\pi\)
\(410\) −0.904072 + 3.37404i −0.0446489 + 0.166632i
\(411\) −12.2866 + 2.48100i −0.606053 + 0.122379i
\(412\) 1.40573 2.43480i 0.0692556 0.119954i
\(413\) 2.05483 + 0.740515i 0.101112 + 0.0364384i
\(414\) −5.91550 + 4.59385i −0.290731 + 0.225775i
\(415\) −6.34383 + 3.66261i −0.311407 + 0.179791i
\(416\) −3.56858 0.514977i −0.174964 0.0252488i
\(417\) 7.70833 + 0.482796i 0.377479 + 0.0236426i
\(418\) 27.4627 7.35860i 1.34324 0.359921i
\(419\) 17.5508 10.1330i 0.857413 0.495028i −0.00573204 0.999984i \(-0.501825\pi\)
0.863145 + 0.504956i \(0.168491\pi\)
\(420\) 5.98463 4.44427i 0.292020 0.216858i
\(421\) 6.81033 + 6.81033i 0.331915 + 0.331915i 0.853313 0.521398i \(-0.174589\pi\)
−0.521398 + 0.853313i \(0.674589\pi\)
\(422\) −3.76589 + 3.76589i −0.183321 + 0.183321i
\(423\) −13.7776 17.7414i −0.669890 0.862617i
\(424\) −2.97819 11.1148i −0.144634 0.539781i
\(425\) 2.00893i 0.0974475i
\(426\) −21.7943 14.4713i −1.05594 0.701135i
\(427\) 1.30084 15.4331i 0.0629520 0.746862i
\(428\) 12.1409 0.586852
\(429\) −6.47975 + 31.0289i −0.312845 + 1.49809i
\(430\) −10.5643 + 18.2978i −0.509453 + 0.882399i
\(431\) −4.02736 + 4.02736i −0.193991 + 0.193991i −0.797418 0.603427i \(-0.793801\pi\)
0.603427 + 0.797418i \(0.293801\pi\)
\(432\) −3.39196 + 3.93632i −0.163196 + 0.189386i
\(433\) −29.1233 16.8144i −1.39958 0.808047i −0.405230 0.914215i \(-0.632808\pi\)
−0.994348 + 0.106168i \(0.966142\pi\)
\(434\) −13.6828 + 6.43337i −0.656793 + 0.308812i
\(435\) −10.7388 12.1739i −0.514884 0.583692i
\(436\) 5.12226 5.12226i 0.245312 0.245312i
\(437\) −13.5078 + 3.61942i −0.646168 + 0.173140i
\(438\) 15.7796 + 10.4776i 0.753980 + 0.500638i
\(439\) −1.21368 0.700720i −0.0579259 0.0334436i 0.470757 0.882263i \(-0.343981\pi\)
−0.528683 + 0.848819i \(0.677314\pi\)
\(440\) 2.13698 7.97531i 0.101876 0.380208i
\(441\) 15.3093 14.3745i 0.729015 0.684498i
\(442\) 1.90339 2.41778i 0.0905352 0.115002i
\(443\) −16.1647 + 9.33267i −0.768007 + 0.443409i −0.832163 0.554531i \(-0.812898\pi\)
0.0641565 + 0.997940i \(0.479564\pi\)
\(444\) 3.03354 9.02234i 0.143965 0.428181i
\(445\) −11.5506 −0.547553
\(446\) −10.5331 −0.498757
\(447\) 20.1613 + 6.77872i 0.953595 + 0.320622i
\(448\) 2.63640 + 0.222219i 0.124558 + 0.0104989i
\(449\) 13.6899 3.66820i 0.646066 0.173113i 0.0791167 0.996865i \(-0.474790\pi\)
0.566950 + 0.823752i \(0.308123\pi\)
\(450\) −4.33137 5.57750i −0.204183 0.262926i
\(451\) 5.44980 + 9.43932i 0.256621 + 0.444480i
\(452\) 11.1498 0.524443
\(453\) −0.0735482 + 0.0648781i −0.00345560 + 0.00304824i
\(454\) 4.04124i 0.189665i
\(455\) −3.49848 + 15.1179i −0.164011 + 0.708740i
\(456\) −8.68888 + 4.31624i −0.406894 + 0.202126i
\(457\) 1.91652 0.513530i 0.0896510 0.0240219i −0.213715 0.976896i \(-0.568556\pi\)
0.303366 + 0.952874i \(0.401890\pi\)
\(458\) 6.12472i 0.286190i
\(459\) −1.46191 4.18668i −0.0682360 0.195417i
\(460\) −1.05110 + 3.92275i −0.0490077 + 0.182899i
\(461\) 3.48234 + 12.9963i 0.162189 + 0.605297i 0.998382 + 0.0568621i \(0.0181095\pi\)
−0.836193 + 0.548435i \(0.815224\pi\)
\(462\) 3.39869 23.0106i 0.158121 1.07055i
\(463\) −25.6449 + 25.6449i −1.19182 + 1.19182i −0.215266 + 0.976555i \(0.569062\pi\)
−0.976555 + 0.215266i \(0.930938\pi\)
\(464\) 5.76168i 0.267479i
\(465\) −7.16316 14.4199i −0.332184 0.668708i
\(466\) −8.89480 + 8.89480i −0.412044 + 0.412044i
\(467\) −5.68598 9.84841i −0.263116 0.455730i 0.703952 0.710247i \(-0.251417\pi\)
−0.967068 + 0.254517i \(0.918083\pi\)
\(468\) 0.0716318 10.8164i 0.00331118 0.499989i
\(469\) −24.7857 + 20.9322i −1.14450 + 0.966559i
\(470\) −11.7649 3.15239i −0.542673 0.145409i
\(471\) −7.02744 0.440150i −0.323807 0.0202810i
\(472\) −0.714946 + 0.412774i −0.0329080 + 0.0189995i
\(473\) 17.0635 + 63.6819i 0.784581 + 2.92810i
\(474\) −19.8316 6.66787i −0.910894 0.306265i
\(475\) −3.41261 12.7360i −0.156581 0.584369i
\(476\) −1.28924 + 1.85373i −0.0590922 + 0.0849656i
\(477\) 31.8157 13.3951i 1.45674 0.613320i
\(478\) 17.4940 + 10.1002i 0.800159 + 0.461972i
\(479\) −3.25970 3.25970i −0.148939 0.148939i 0.628705 0.777644i \(-0.283585\pi\)
−0.777644 + 0.628705i \(0.783585\pi\)
\(480\) −0.176122 + 2.81197i −0.00803884 + 0.128348i
\(481\) 7.35481 + 18.3991i 0.335351 + 0.838928i
\(482\) 23.6500i 1.07723i
\(483\) −1.67169 + 11.3180i −0.0760644 + 0.514987i
\(484\) −7.38182 12.7857i −0.335537 0.581168i
\(485\) 25.1510 1.14205
\(486\) −13.0855 8.47174i −0.593569 0.384286i
\(487\) 2.40006 8.95714i 0.108757 0.405887i −0.889987 0.455985i \(-0.849287\pi\)
0.998744 + 0.0500987i \(0.0159536\pi\)
\(488\) 4.13931 + 4.13931i 0.187378 + 0.187378i
\(489\) −16.7159 5.62031i −0.755921 0.254159i
\(490\) 1.90600 11.2261i 0.0861043 0.507141i
\(491\) −13.9676 24.1925i −0.630347 1.09179i −0.987481 0.157739i \(-0.949579\pi\)
0.357134 0.934053i \(-0.383754\pi\)
\(492\) −2.46043 2.78924i −0.110925 0.125748i
\(493\) 4.25844 + 2.45861i 0.191790 + 0.110730i
\(494\) 7.95984 18.5613i 0.358130 0.835113i
\(495\) 24.5764 + 3.09071i 1.10463 + 0.138917i
\(496\) 1.47908 5.51999i 0.0664126 0.247855i
\(497\) −39.3325 + 7.06428i −1.76430 + 0.316876i
\(498\) 0.487568 7.78452i 0.0218484 0.348833i
\(499\) 1.30997 4.88887i 0.0586423 0.218856i −0.930386 0.366581i \(-0.880528\pi\)
0.989029 + 0.147725i \(0.0471950\pi\)
\(500\) −11.5548 3.09611i −0.516748 0.138462i
\(501\) 19.0173 3.84012i 0.849631 0.171564i
\(502\) 1.49403 + 0.400323i 0.0666816 + 0.0178673i
\(503\) 19.2261 + 11.1002i 0.857248 + 0.494932i 0.863090 0.505051i \(-0.168526\pi\)
−0.00584193 + 0.999983i \(0.501860\pi\)
\(504\) 0.417361 + 7.92627i 0.0185907 + 0.353064i
\(505\) −3.33194 0.892791i −0.148269 0.0397287i
\(506\) 6.33608 + 10.9744i 0.281673 + 0.487872i
\(507\) 14.4713 + 17.2506i 0.642693 + 0.766124i
\(508\) −3.95533 + 6.85083i −0.175489 + 0.303957i
\(509\) −6.72166 25.0856i −0.297932 1.11190i −0.938861 0.344298i \(-0.888117\pi\)
0.640928 0.767601i \(-0.278550\pi\)
\(510\) −2.00316 1.33009i −0.0887014 0.0588972i
\(511\) 28.4778 5.11473i 1.25978 0.226262i
\(512\) −0.707107 + 0.707107i −0.0312500 + 0.0312500i
\(513\) −16.3801 24.0589i −0.723197 1.06223i
\(514\) 6.65497 + 1.78319i 0.293538 + 0.0786533i
\(515\) 4.41751 1.18367i 0.194659 0.0521586i
\(516\) −10.0087 20.1482i −0.440609 0.886977i
\(517\) −32.9138 + 19.0028i −1.44755 + 0.835742i
\(518\) −6.18670 13.1581i −0.271828 0.578135i
\(519\) −9.20291 18.5261i −0.403963 0.813205i
\(520\) −3.51235 4.69704i −0.154027 0.205979i
\(521\) −24.5520 14.1751i −1.07564 0.621021i −0.145923 0.989296i \(-0.546615\pi\)
−0.929717 + 0.368275i \(0.879949\pi\)
\(522\) 17.1238 2.35546i 0.749489 0.103096i
\(523\) 21.0465 36.4536i 0.920299 1.59400i 0.121346 0.992610i \(-0.461279\pi\)
0.798953 0.601394i \(-0.205388\pi\)
\(524\) −3.81196 + 6.60251i −0.166526 + 0.288432i
\(525\) −10.6713 1.57617i −0.465735 0.0687897i
\(526\) −5.09956 + 1.36642i −0.222351 + 0.0595788i
\(527\) 3.44866 + 3.44866i 0.150226 + 0.150226i
\(528\) 5.81579 + 6.59299i 0.253100 + 0.286923i
\(529\) 8.38353 + 14.5207i 0.364501 + 0.631334i
\(530\) 9.35894 16.2102i 0.406527 0.704125i
\(531\) −1.51905 1.95608i −0.0659212 0.0848867i
\(532\) −5.02443 + 13.9422i −0.217837 + 0.604469i
\(533\) 7.66307 + 1.10585i 0.331924 + 0.0478995i
\(534\) 6.80324 10.2459i 0.294405 0.443385i
\(535\) 13.9648 + 13.9648i 0.603752 + 0.603752i
\(536\) 12.2620i 0.529636i
\(537\) −13.1751 26.5224i −0.568547 1.14452i
\(538\) 13.4701 + 13.4701i 0.580737 + 0.580737i
\(539\) −20.5640 28.9748i −0.885753 1.24804i
\(540\) −8.42921 + 0.626135i −0.362736 + 0.0269446i
\(541\) 0.688861 + 0.184580i 0.0296164 + 0.00793570i 0.273597 0.961844i \(-0.411787\pi\)
−0.243980 + 0.969780i \(0.578453\pi\)
\(542\) 0.222531 0.128478i 0.00955853 0.00551862i
\(543\) −16.0945 + 7.99499i −0.690679 + 0.343098i
\(544\) −0.220885 0.824354i −0.00947037 0.0353439i
\(545\) 11.7836 0.504752
\(546\) −11.3497 12.0077i −0.485723 0.513880i
\(547\) 3.36783 0.143998 0.0719990 0.997405i \(-0.477062\pi\)
0.0719990 + 0.997405i \(0.477062\pi\)
\(548\) −1.87303 6.99026i −0.0800120 0.298609i
\(549\) −10.6099 + 13.9943i −0.452818 + 0.597262i
\(550\) −10.3474 + 5.97405i −0.441213 + 0.254734i
\(551\) 31.1737 + 8.35297i 1.32804 + 0.355849i
\(552\) −2.86057 3.24284i −0.121754 0.138024i
\(553\) −28.9223 + 13.5987i −1.22990 + 0.578275i
\(554\) 0.993649 + 0.993649i 0.0422161 + 0.0422161i
\(555\) 13.8670 6.88851i 0.588623 0.292401i
\(556\) 4.45913i 0.189109i
\(557\) −1.12258 1.12258i −0.0475654 0.0475654i 0.682924 0.730489i \(-0.260708\pi\)
−0.730489 + 0.682924i \(0.760708\pi\)
\(558\) 17.0102 + 2.13919i 0.720098 + 0.0905591i
\(559\) 43.0410 + 18.4577i 1.82044 + 0.780677i
\(560\) 2.77687 + 3.28807i 0.117344 + 0.138947i
\(561\) −7.35455 + 1.48508i −0.310509 + 0.0627003i
\(562\) 12.9415 22.4153i 0.545902 0.945531i
\(563\) 4.86152 + 8.42039i 0.204889 + 0.354877i 0.950097 0.311954i \(-0.100983\pi\)
−0.745209 + 0.666831i \(0.767650\pi\)
\(564\) 9.72573 8.57924i 0.409527 0.361251i
\(565\) 12.8249 + 12.8249i 0.539546 + 0.539546i
\(566\) −23.2096 + 6.21900i −0.975573 + 0.261404i
\(567\) −23.3864 + 4.48078i −0.982136 + 0.188175i
\(568\) 7.55208 13.0806i 0.316878 0.548849i
\(569\) 11.1191 19.2589i 0.466138 0.807374i −0.533114 0.846043i \(-0.678978\pi\)
0.999252 + 0.0386691i \(0.0123118\pi\)
\(570\) −14.9589 5.02955i −0.626559 0.210665i
\(571\) 0.631338 + 0.364503i 0.0264207 + 0.0152540i 0.513152 0.858298i \(-0.328478\pi\)
−0.486731 + 0.873552i \(0.661811\pi\)
\(572\) −18.1134 2.61392i −0.757359 0.109293i
\(573\) −16.2559 + 8.07520i −0.679101 + 0.337346i
\(574\) −5.66133 0.477186i −0.236299 0.0199174i
\(575\) 5.08947 2.93841i 0.212246 0.122540i
\(576\) −2.39061 1.81246i −0.0996086 0.0755190i
\(577\) −40.9337 + 10.9682i −1.70409 + 0.456610i −0.973965 0.226700i \(-0.927206\pi\)
−0.730128 + 0.683310i \(0.760540\pi\)
\(578\) −15.7172 4.21141i −0.653750 0.175172i
\(579\) 5.01147 + 1.68498i 0.208270 + 0.0700254i
\(580\) 6.62726 6.62726i 0.275182 0.275182i
\(581\) −7.68735 9.10255i −0.318925 0.377637i
\(582\) −14.8137 + 22.3101i −0.614049 + 0.924781i
\(583\) −15.1167 56.4163i −0.626069 2.33652i
\(584\) −5.46791 + 9.47070i −0.226264 + 0.391900i
\(585\) 12.5238 12.3590i 0.517794 0.510981i
\(586\) 6.36456 + 11.0237i 0.262918 + 0.455387i
\(587\) 26.7015 + 7.15465i 1.10209 + 0.295304i 0.763615 0.645672i \(-0.223422\pi\)
0.338474 + 0.940976i \(0.390089\pi\)
\(588\) 8.83539 + 8.30277i 0.364365 + 0.342400i
\(589\) 27.7218 + 16.0052i 1.14226 + 0.659482i
\(590\) −1.29714 0.347567i −0.0534023 0.0143091i
\(591\) 7.59563 + 37.6157i 0.312442 + 1.54730i
\(592\) 5.30835 + 1.42237i 0.218172 + 0.0584589i
\(593\) −6.42316 + 23.9716i −0.263768 + 0.984394i 0.699233 + 0.714894i \(0.253525\pi\)
−0.963000 + 0.269500i \(0.913142\pi\)
\(594\) −17.2169 + 19.9799i −0.706417 + 0.819786i
\(595\) −3.61514 + 0.649294i −0.148206 + 0.0266185i
\(596\) −3.17841 + 11.8620i −0.130193 + 0.485886i
\(597\) 7.15429 + 4.75041i 0.292806 + 0.194421i
\(598\) 8.90929 + 1.28569i 0.364328 + 0.0525756i
\(599\) −13.1943 7.61771i −0.539103 0.311251i 0.205612 0.978634i \(-0.434081\pi\)
−0.744715 + 0.667382i \(0.767415\pi\)
\(600\) 3.05755 2.69712i 0.124824 0.110109i
\(601\) 4.51090 + 7.81311i 0.184004 + 0.318703i 0.943240 0.332111i \(-0.107761\pi\)
−0.759237 + 0.650815i \(0.774428\pi\)
\(602\) −32.3298 11.6509i −1.31766 0.474856i
\(603\) 36.4427 5.01286i 1.48406 0.204140i
\(604\) −0.0400385 0.0400385i −0.00162915 0.00162915i
\(605\) 6.21570 23.1973i 0.252704 0.943104i
\(606\) 2.75443 2.42973i 0.111891 0.0987011i
\(607\) −36.4750 −1.48047 −0.740237 0.672347i \(-0.765286\pi\)
−0.740237 + 0.672347i \(0.765286\pi\)
\(608\) −2.80069 4.85094i −0.113583 0.196732i
\(609\) 16.4011 20.6916i 0.664605 0.838465i
\(610\) 9.52232i 0.385547i
\(611\) −3.85595 + 26.7202i −0.155995 + 1.08098i
\(612\) 2.35969 0.993481i 0.0953849 0.0401591i
\(613\) −3.60295 3.60295i −0.145522 0.145522i 0.630592 0.776114i \(-0.282812\pi\)
−0.776114 + 0.630592i \(0.782812\pi\)
\(614\) −8.21750 4.74438i −0.331632 0.191468i
\(615\) 0.378199 6.03833i 0.0152505 0.243489i
\(616\) 13.3818 + 1.12794i 0.539169 + 0.0454459i
\(617\) −0.366038 1.36607i −0.0147361 0.0549960i 0.958166 0.286212i \(-0.0923962\pi\)
−0.972902 + 0.231216i \(0.925730\pi\)
\(618\) −1.55191 + 4.61570i −0.0624271 + 0.185671i
\(619\) −0.0248681 0.0928089i −0.000999532 0.00373031i 0.965424 0.260684i \(-0.0839480\pi\)
−0.966424 + 0.256953i \(0.917281\pi\)
\(620\) 8.05055 4.64799i 0.323318 0.186668i
\(621\) 8.46833 9.82736i 0.339822 0.394358i
\(622\) −12.8682 3.44801i −0.515966 0.138253i
\(623\) −3.32106 18.4910i −0.133056 0.740827i
\(624\) 6.23523 0.349094i 0.249609 0.0139749i
\(625\) −3.84464 6.65912i −0.153786 0.266365i
\(626\) 18.3442 18.3442i 0.733183 0.733183i
\(627\) −44.1029 + 21.9083i −1.76130 + 0.874934i
\(628\) 4.06525i 0.162221i
\(629\) −3.31643 + 3.31643i −0.132235 + 0.132235i
\(630\) −8.63698 + 9.59711i −0.344106 + 0.382358i
\(631\) −2.23294 8.33346i −0.0888921 0.331750i 0.907131 0.420849i \(-0.138268\pi\)
−0.996023 + 0.0890992i \(0.971601\pi\)
\(632\) 3.12644 11.6680i 0.124363 0.464129i
\(633\) 5.10261 7.68473i 0.202811 0.305440i
\(634\) 5.47680i 0.217512i
\(635\) −12.4296 + 3.33050i −0.493253 + 0.132167i
\(636\) 8.86679 + 17.8495i 0.351591 + 0.707777i
\(637\) −25.2077 1.25384i −0.998765 0.0496791i
\(638\) 29.2451i 1.15782i
\(639\) 41.9631 + 17.0974i 1.66003 + 0.676361i
\(640\) −1.62667 −0.0642999
\(641\) −19.3095 33.4451i −0.762680 1.32100i −0.941465 0.337112i \(-0.890550\pi\)
0.178785 0.983888i \(-0.442783\pi\)
\(642\) −20.6126 + 4.16225i −0.813515 + 0.164271i
\(643\) −11.1923 + 2.99896i −0.441380 + 0.118268i −0.472663 0.881243i \(-0.656707\pi\)
0.0312830 + 0.999511i \(0.490041\pi\)
\(644\) −6.58201 0.554789i −0.259368 0.0218617i
\(645\) 11.6628 34.6875i 0.459222 1.36582i
\(646\) 4.78041 0.188083
\(647\) 45.7488 1.79857 0.899285 0.437363i \(-0.144087\pi\)
0.899285 + 0.437363i \(0.144087\pi\)
\(648\) 4.40933 7.84588i 0.173215 0.308215i
\(649\) −3.62891 + 2.09515i −0.142447 + 0.0822420i
\(650\) −1.21222 + 8.40023i −0.0475474 + 0.329484i
\(651\) 21.0248 15.6133i 0.824027 0.611934i
\(652\) 2.63526 9.83491i 0.103205 0.385165i
\(653\) 12.8154 + 7.39900i 0.501507 + 0.289545i 0.729336 0.684156i \(-0.239829\pi\)
−0.227829 + 0.973701i \(0.573163\pi\)
\(654\) −6.94042 + 10.4525i −0.271392 + 0.408727i
\(655\) −11.9791 + 3.20978i −0.468060 + 0.125416i
\(656\) 1.51842 1.51842i 0.0592843 0.0592843i
\(657\) −30.3824 12.3790i −1.18533 0.482949i
\(658\) 1.66389 19.7404i 0.0648652 0.769560i
\(659\) 32.1017 + 18.5340i 1.25051 + 0.721980i 0.971210 0.238225i \(-0.0765655\pi\)
0.279296 + 0.960205i \(0.409899\pi\)
\(660\) −0.893959 + 14.2730i −0.0347973 + 0.555574i
\(661\) −6.70536 + 6.70536i −0.260808 + 0.260808i −0.825382 0.564574i \(-0.809040\pi\)
0.564574 + 0.825382i \(0.309040\pi\)
\(662\) −1.21170 + 2.09872i −0.0470940 + 0.0815692i
\(663\) −2.40267 + 4.75740i −0.0933119 + 0.184762i
\(664\) 4.50320 0.174758
\(665\) −21.8160 + 10.2574i −0.845986 + 0.397766i
\(666\) −2.05717 + 16.3580i −0.0797136 + 0.633858i
\(667\) 14.3845i 0.556972i
\(668\) 2.89910 + 10.8196i 0.112170 + 0.418622i
\(669\) 17.8829 3.61105i 0.691394 0.139611i
\(670\) 14.1041 14.1041i 0.544888 0.544888i
\(671\) 21.0102 + 21.0102i 0.811092 + 0.811092i
\(672\) −4.55222 + 0.526555i −0.175606 + 0.0203123i
\(673\) −5.16640 + 2.98282i −0.199150 + 0.114979i −0.596259 0.802792i \(-0.703347\pi\)
0.397109 + 0.917772i \(0.370014\pi\)
\(674\) −7.30763 + 1.95807i −0.281479 + 0.0754221i
\(675\) 9.26585 + 7.98447i 0.356643 + 0.307322i
\(676\) −9.41786 + 8.96125i −0.362225 + 0.344663i
\(677\) 6.02868 3.48066i 0.231701 0.133773i −0.379655 0.925128i \(-0.623957\pi\)
0.611357 + 0.791355i \(0.290624\pi\)
\(678\) −18.9300 + 3.82248i −0.727001 + 0.146801i
\(679\) 7.23147 + 40.2634i 0.277518 + 1.54517i
\(680\) 0.694129 1.20227i 0.0266186 0.0461048i
\(681\) 1.38545 + 6.86115i 0.0530907 + 0.262920i
\(682\) 7.50749 28.0183i 0.287477 1.07288i
\(683\) 8.64501 32.2636i 0.330792 1.23453i −0.577567 0.816343i \(-0.695998\pi\)
0.908359 0.418190i \(-0.137335\pi\)
\(684\) 13.2721 10.3068i 0.507472 0.394092i
\(685\) 5.88599 10.1948i 0.224892 0.389524i
\(686\) 18.5194 0.176489i 0.707075 0.00673838i
\(687\) −2.09973 10.3985i −0.0801098 0.396726i
\(688\) 11.2486 6.49440i 0.428850 0.247597i
\(689\) −38.1303 16.3518i −1.45265 0.622954i
\(690\) 0.439704 7.02033i 0.0167393 0.267259i
\(691\) −20.4601 + 5.48228i −0.778341 + 0.208556i −0.626053 0.779780i \(-0.715331\pi\)
−0.152288 + 0.988336i \(0.548664\pi\)
\(692\) 10.3430 5.97152i 0.393181 0.227003i
\(693\) 2.11844 + 40.2321i 0.0804728 + 1.52829i
\(694\) 16.1705 + 16.1705i 0.613824 + 0.613824i
\(695\) −5.12903 + 5.12903i −0.194555 + 0.194555i
\(696\) 1.97527 + 9.78209i 0.0748725 + 0.370789i
\(697\) 0.474322 + 1.77019i 0.0179662 + 0.0670508i
\(698\) 15.0369i 0.569155i
\(699\) 12.0521 18.1508i 0.455850 0.686528i
\(700\) 0.523089 6.20593i 0.0197709 0.234562i
\(701\) −33.5732 −1.26804 −0.634021 0.773315i \(-0.718597\pi\)
−0.634021 + 0.773315i \(0.718597\pi\)
\(702\) 3.58656 + 18.3885i 0.135366 + 0.694029i
\(703\) −15.3915 + 26.6589i −0.580501 + 1.00546i
\(704\) −3.58913 + 3.58913i −0.135270 + 0.135270i
\(705\) 21.0549 + 1.31873i 0.792975 + 0.0496664i
\(706\) −8.10352 4.67857i −0.304980 0.176080i
\(707\) 0.471232 5.59069i 0.0177225 0.210259i
\(708\) 1.07231 0.945905i 0.0403000 0.0355493i
\(709\) −1.13202 + 1.13202i −0.0425140 + 0.0425140i −0.728044 0.685530i \(-0.759570\pi\)
0.685530 + 0.728044i \(0.259570\pi\)
\(710\) 23.7323 6.35906i 0.890659 0.238651i
\(711\) 35.9557 + 4.52176i 1.34844 + 0.169579i
\(712\) 6.14945 + 3.55039i 0.230461 + 0.133056i
\(713\) −3.69265 + 13.7811i −0.138291 + 0.516108i
\(714\) 1.55334 3.58922i 0.0581322 0.134323i
\(715\) −17.8280 23.8412i −0.666728 0.891610i
\(716\) 14.8072 8.54897i 0.553373 0.319490i
\(717\) −33.1637 11.1505i −1.23852 0.416422i
\(718\) −36.8804 −1.37637
\(719\) 49.0565 1.82950 0.914750 0.404021i \(-0.132388\pi\)
0.914750 + 0.404021i \(0.132388\pi\)
\(720\) −0.665007 4.83449i −0.0247833 0.180171i
\(721\) 3.16502 + 6.73150i 0.117872 + 0.250694i
\(722\) 11.9538 3.20302i 0.444876 0.119204i
\(723\) 8.10790 + 40.1526i 0.301536 + 1.49329i
\(724\) −5.18774 8.98543i −0.192801 0.333941i
\(725\) −13.5626 −0.503704
\(726\) 16.9160 + 19.1766i 0.627813 + 0.711712i
\(727\) 8.58214i 0.318294i −0.987255 0.159147i \(-0.949126\pi\)
0.987255 0.159147i \(-0.0508744\pi\)
\(728\) 6.50945 6.97331i 0.241256 0.258448i
\(729\) 25.1207 + 9.89709i 0.930395 + 0.366559i
\(730\) −17.1828 + 4.60413i −0.635966 + 0.170407i
\(731\) 11.0851i 0.409996i
\(732\) −8.44672 5.60857i −0.312200 0.207299i
\(733\) 11.5251 43.0122i 0.425689 1.58869i −0.336726 0.941603i \(-0.609319\pi\)
0.762414 0.647089i \(-0.224014\pi\)
\(734\) 8.72523 + 32.5630i 0.322054 + 1.20192i
\(735\) 0.612640 + 19.7128i 0.0225976 + 0.727119i
\(736\) 1.76535 1.76535i 0.0650718 0.0650718i
\(737\) 62.2391i 2.29261i
\(738\) 5.13351 + 3.89201i 0.188967 + 0.143267i
\(739\) 35.6919 35.6919i 1.31295 1.31295i 0.393714 0.919233i \(-0.371190\pi\)
0.919233 0.393714i \(-0.128810\pi\)
\(740\) 4.46977 + 7.74187i 0.164312 + 0.284597i
\(741\) −7.15072 + 34.2420i −0.262688 + 1.25791i
\(742\) 28.6412 + 10.3216i 1.05145 + 0.378919i
\(743\) 29.5583 + 7.92014i 1.08439 + 0.290562i 0.756393 0.654117i \(-0.226960\pi\)
0.327997 + 0.944679i \(0.393626\pi\)
\(744\) −0.618741 + 9.87882i −0.0226841 + 0.362175i
\(745\) −17.2999 + 9.98812i −0.633821 + 0.365937i
\(746\) 5.22288 + 19.4921i 0.191223 + 0.713655i
\(747\) 1.84097 + 13.3836i 0.0673577 + 0.489679i
\(748\) −1.12117 4.18425i −0.0409939 0.152991i
\(749\) −18.3406 + 26.3710i −0.670152 + 0.963576i
\(750\) 20.6790 + 1.29519i 0.755092 + 0.0472937i
\(751\) −27.0037 15.5906i −0.985378 0.568908i −0.0814883 0.996674i \(-0.525967\pi\)
−0.903889 + 0.427766i \(0.859301\pi\)
\(752\) 5.29454 + 5.29454i 0.193072 + 0.193072i
\(753\) −2.67377 0.167467i −0.0974377 0.00610282i
\(754\) −16.3228 12.8501i −0.594442 0.467975i
\(755\) 0.0921071i 0.00335212i
\(756\) −3.42594 13.3140i −0.124600 0.484226i
\(757\) −5.92020 10.2541i −0.215173 0.372691i 0.738153 0.674633i \(-0.235698\pi\)
−0.953326 + 0.301942i \(0.902365\pi\)
\(758\) −9.46890 −0.343926
\(759\) −14.5196 16.4600i −0.527029 0.597459i
\(760\) 2.35826 8.80115i 0.0855431 0.319251i
\(761\) 14.2380 + 14.2380i 0.516126 + 0.516126i 0.916397 0.400271i \(-0.131084\pi\)
−0.400271 + 0.916397i \(0.631084\pi\)
\(762\) 4.36663 12.9872i 0.158186 0.470478i
\(763\) 3.38803 + 18.8639i 0.122655 + 0.682919i
\(764\) −5.23979 9.07557i −0.189569 0.328343i
\(765\) 3.85692 + 1.57146i 0.139447 + 0.0568162i
\(766\) −19.0262 10.9848i −0.687446 0.396897i
\(767\) −0.425139 + 2.94604i −0.0153509 + 0.106375i
\(768\) 0.958098 1.44293i 0.0345724 0.0520673i
\(769\) −9.69031 + 36.1647i −0.349442 + 1.30413i 0.537895 + 0.843012i \(0.319220\pi\)
−0.887337 + 0.461122i \(0.847447\pi\)
\(770\) 14.0948 + 16.6896i 0.507941 + 0.601451i
\(771\) −11.9100 0.745961i −0.428929 0.0268651i
\(772\) −0.790055 + 2.94853i −0.0284347 + 0.106120i
\(773\) −6.20578 1.66283i −0.223206 0.0598079i 0.145483 0.989361i \(-0.453527\pi\)
−0.368689 + 0.929553i \(0.620193\pi\)
\(774\) 23.9000 + 30.7761i 0.859069 + 1.10622i
\(775\) −12.9937 3.48166i −0.466748 0.125065i
\(776\) −13.3902 7.73081i −0.480679 0.277520i
\(777\) 15.0147 + 20.2187i 0.538648 + 0.725341i
\(778\) −2.11550 0.566847i −0.0758445 0.0203225i
\(779\) 6.01412 + 10.4168i 0.215478 + 0.373219i
\(780\) 7.57350 + 6.77042i 0.271175 + 0.242420i
\(781\) 38.3328 66.3943i 1.37165 2.37578i
\(782\) 0.551459 + 2.05807i 0.0197201 + 0.0735965i
\(783\) −28.2650 + 9.86959i −1.01011 + 0.352710i
\(784\) −4.46536 + 5.39079i −0.159477 + 0.192528i
\(785\) 4.67597 4.67597i 0.166893 0.166893i
\(786\) 4.20836 12.5165i 0.150107 0.446448i
\(787\) −36.2132 9.70329i −1.29086 0.345885i −0.452873 0.891575i \(-0.649601\pi\)
−0.837987 + 0.545690i \(0.816268\pi\)
\(788\) −21.4008 + 5.73433i −0.762372 + 0.204277i
\(789\) 8.18949 4.06816i 0.291554 0.144830i
\(790\) 17.0170 9.82479i 0.605439 0.349550i
\(791\) −16.8434 + 24.2183i −0.598884 + 0.861104i
\(792\) −12.1342 9.19965i −0.431171 0.326895i
\(793\) 20.9584 2.49484i 0.744256 0.0885945i
\(794\) −9.12011 5.26550i −0.323661 0.186866i
\(795\) −10.3321 + 30.7299i −0.366443 + 1.08988i
\(796\) −2.47908 + 4.29390i −0.0878687 + 0.152193i
\(797\) −18.3966 + 31.8639i −0.651642 + 1.12868i 0.331083 + 0.943602i \(0.392586\pi\)
−0.982724 + 0.185075i \(0.940747\pi\)
\(798\) 3.75062 25.3933i 0.132771 0.898912i
\(799\) −6.17245 + 1.65390i −0.218366 + 0.0585109i
\(800\) 1.66449 + 1.66449i 0.0588484 + 0.0588484i
\(801\) −8.03782 + 19.7277i −0.284003 + 0.697045i
\(802\) 12.2662 + 21.2457i 0.433135 + 0.750211i
\(803\) −27.7540 + 48.0713i −0.979416 + 1.69640i
\(804\) 4.20375 + 20.8181i 0.148255 + 0.734199i
\(805\) −6.93270 8.20897i −0.244345 0.289328i
\(806\) −12.3394 16.5013i −0.434636 0.581235i
\(807\) −27.4872 18.2514i −0.967597 0.642478i
\(808\) 1.49947 + 1.49947i 0.0527512 + 0.0527512i
\(809\) 4.84604i 0.170378i 0.996365 + 0.0851888i \(0.0271494\pi\)
−0.996365 + 0.0851888i \(0.972851\pi\)
\(810\) 14.0963 3.95282i 0.495294 0.138888i
\(811\) 8.37484 + 8.37484i 0.294080 + 0.294080i 0.838690 0.544609i \(-0.183322\pi\)
−0.544609 + 0.838690i \(0.683322\pi\)
\(812\) 12.5148 + 8.70388i 0.439185 + 0.305446i
\(813\) −0.333764 + 0.294419i −0.0117056 + 0.0103257i
\(814\) 26.9440 + 7.21963i 0.944388 + 0.253048i
\(815\) 14.3436 8.28127i 0.502434 0.290080i
\(816\) 0.657627 + 1.32385i 0.0230216 + 0.0463440i
\(817\) 18.8304 + 70.2761i 0.658794 + 2.45865i
\(818\) −4.67413 −0.163427
\(819\) 23.3859 + 16.4954i 0.817171 + 0.576396i
\(820\) 3.49306 0.121983
\(821\) −5.92719 22.1206i −0.206860 0.772014i −0.988874 0.148753i \(-0.952474\pi\)
0.782014 0.623261i \(-0.214192\pi\)
\(822\) 5.57647 + 11.2258i 0.194502 + 0.391545i
\(823\) −4.04630 + 2.33613i −0.141045 + 0.0814324i −0.568862 0.822433i \(-0.692616\pi\)
0.427817 + 0.903865i \(0.359283\pi\)
\(824\) −2.71567 0.727662i −0.0946049 0.0253493i
\(825\) 15.5195 13.6900i 0.540319 0.476625i
\(826\) 0.183452 2.17648i 0.00638313 0.0757293i
\(827\) −37.4338 37.4338i −1.30170 1.30170i −0.927245 0.374455i \(-0.877830\pi\)
−0.374455 0.927245i \(-0.622170\pi\)
\(828\) 5.96836 + 4.52496i 0.207415 + 0.157253i
\(829\) 5.98479i 0.207860i 0.994585 + 0.103930i \(0.0331419\pi\)
−0.994585 + 0.103930i \(0.966858\pi\)
\(830\) 5.17972 + 5.17972i 0.179791 + 0.179791i
\(831\) −2.02765 1.34635i −0.0703385 0.0467043i
\(832\) 0.426188 + 3.58027i 0.0147754 + 0.124124i
\(833\) −2.07887 5.60067i −0.0720284 0.194052i
\(834\) −1.52872 7.57063i −0.0529352 0.262150i
\(835\) −9.11039 + 15.7797i −0.315278 + 0.546078i
\(836\) −14.2157 24.6224i −0.491661 0.851582i
\(837\) −29.6130 + 2.19970i −1.02357 + 0.0760327i
\(838\) −14.3302 14.3302i −0.495028 0.495028i
\(839\) −7.35666 + 1.97121i −0.253980 + 0.0680538i −0.383563 0.923515i \(-0.625303\pi\)
0.129583 + 0.991569i \(0.458636\pi\)
\(840\) −5.84177 4.63045i −0.201560 0.159766i
\(841\) 2.09849 3.63470i 0.0723618 0.125334i
\(842\) 4.81563 8.34091i 0.165958 0.287447i
\(843\) −14.2872 + 42.4930i −0.492077 + 1.46354i
\(844\) 4.61226 + 2.66289i 0.158760 + 0.0916604i
\(845\) −21.1402 0.525208i −0.727245 0.0180677i
\(846\) −13.5710 + 17.9000i −0.466580 + 0.615413i
\(847\) 38.9229 + 3.28076i 1.33741 + 0.112728i
\(848\) −9.96523 + 5.75343i −0.342208 + 0.197574i
\(849\) 37.2729 18.5154i 1.27920 0.635448i
\(850\) −1.94048 + 0.519950i −0.0665579 + 0.0178341i
\(851\) −13.2527 3.55106i −0.454298 0.121729i
\(852\) −8.33740 + 24.7971i −0.285634 + 0.849534i
\(853\) 19.9037 19.9037i 0.681490 0.681490i −0.278846 0.960336i \(-0.589952\pi\)
0.960336 + 0.278846i \(0.0899518\pi\)
\(854\) −15.2440 + 2.73788i −0.521637 + 0.0936882i
\(855\) 27.1212 + 3.41075i 0.927526 + 0.116645i
\(856\) −3.14229 11.7272i −0.107401 0.400827i
\(857\) 24.4329 42.3191i 0.834613 1.44559i −0.0597321 0.998214i \(-0.519025\pi\)
0.894345 0.447378i \(-0.147642\pi\)
\(858\) 31.6487 1.77193i 1.08047 0.0604926i
\(859\) 13.8247 + 23.9452i 0.471694 + 0.816999i 0.999476 0.0323818i \(-0.0103092\pi\)
−0.527781 + 0.849380i \(0.676976\pi\)
\(860\) 20.4086 + 5.46846i 0.695926 + 0.186473i
\(861\) 9.77530 1.13071i 0.333141 0.0385344i
\(862\) 4.93248 + 2.84777i 0.168001 + 0.0969955i
\(863\) −26.5462 7.11305i −0.903645 0.242131i −0.223064 0.974804i \(-0.571606\pi\)
−0.680581 + 0.732673i \(0.738273\pi\)
\(864\) 4.68010 + 2.25759i 0.159220 + 0.0768047i
\(865\) 18.7654 + 5.02819i 0.638044 + 0.170963i
\(866\) −8.70376 + 32.4829i −0.295766 + 1.10381i
\(867\) 28.1282 + 1.76175i 0.955284 + 0.0598323i
\(868\) 9.75551 + 11.5514i 0.331124 + 0.392082i
\(869\) 15.8691 59.2244i 0.538323 2.00905i
\(870\) −8.97964 + 13.5237i −0.304438 + 0.458496i
\(871\) −34.7381 27.3475i −1.17705 0.926636i
\(872\) −6.27346 3.62198i −0.212446 0.122656i
\(873\) 17.5020 42.9562i 0.592353 1.45385i
\(874\) 6.99217 + 12.1108i 0.236514 + 0.409654i
\(875\) 24.1803 20.4209i 0.817443 0.690353i
\(876\) 6.03650 17.9538i 0.203954 0.606601i
\(877\) 23.5780 + 23.5780i 0.796173 + 0.796173i 0.982490 0.186317i \(-0.0596550\pi\)
−0.186317 + 0.982490i \(0.559655\pi\)
\(878\) −0.362720 + 1.35369i −0.0122412 + 0.0456847i
\(879\) −14.5849 16.5340i −0.491937 0.557677i
\(880\) −8.25665 −0.278331
\(881\) 9.75282 + 16.8924i 0.328581 + 0.569118i 0.982230 0.187679i \(-0.0600964\pi\)
−0.653650 + 0.756797i \(0.726763\pi\)
\(882\) −17.8470 11.0673i −0.600940 0.372654i
\(883\) 4.92582i 0.165767i −0.996559 0.0828835i \(-0.973587\pi\)
0.996559 0.0828835i \(-0.0264129\pi\)
\(884\) −2.82803 1.21277i −0.0951169 0.0407899i
\(885\) 2.32142 + 0.145397i 0.0780335 + 0.00488748i
\(886\) 13.1984 + 13.1984i 0.443409 + 0.443409i
\(887\) −30.9567 17.8729i −1.03942 0.600112i −0.119754 0.992804i \(-0.538211\pi\)
−0.919670 + 0.392691i \(0.871544\pi\)
\(888\) −9.50005 0.595017i −0.318801 0.0199675i
\(889\) −8.90546 18.9405i −0.298680 0.635244i
\(890\) 2.98953 + 11.1571i 0.100209 + 0.373986i
\(891\) 22.3808 39.8240i 0.749787 1.33416i
\(892\) 2.72617 + 10.1742i 0.0912789 + 0.340658i
\(893\) −36.3220 + 20.9705i −1.21547 + 0.701752i
\(894\) 1.32962 21.2287i 0.0444692 0.709995i
\(895\) 26.8650 + 7.19847i 0.897999 + 0.240618i
\(896\) −0.467704 2.60408i −0.0156249 0.0869963i
\(897\) −15.5668 + 0.871543i −0.519761 + 0.0291000i
\(898\) −7.08641 12.2740i −0.236477 0.409590i
\(899\) 23.2825 23.2825i 0.776514 0.776514i
\(900\) −4.26641 + 5.62734i −0.142214 + 0.187578i
\(901\) 9.82035i 0.327163i
\(902\) 7.70717 7.70717i 0.256621 0.256621i
\(903\) 58.8833 + 8.69715i 1.95951 + 0.289423i
\(904\) −2.88578 10.7699i −0.0959797 0.358201i
\(905\) 4.36822 16.3024i 0.145204 0.541910i
\(906\) 0.0817031 + 0.0542504i 0.00271440 + 0.00180235i
\(907\) 36.6638i 1.21740i 0.793399 + 0.608701i \(0.208309\pi\)
−0.793399 + 0.608701i \(0.791691\pi\)
\(908\) −3.90354 + 1.04595i −0.129543 + 0.0347111i
\(909\) −3.84345 + 5.06946i −0.127479 + 0.168143i
\(910\) 15.5083 0.533545i 0.514095 0.0176869i
\(911\) 30.8260i 1.02131i 0.859786 + 0.510655i \(0.170597\pi\)
−0.859786 + 0.510655i \(0.829403\pi\)
\(912\) 6.41801 + 7.27569i 0.212522 + 0.240922i
\(913\) 22.8573 0.756466
\(914\) −0.992063 1.71830i −0.0328145 0.0568364i
\(915\) −3.26452 16.1668i −0.107922 0.534459i
\(916\) 5.91603 1.58519i 0.195471 0.0523763i
\(917\) −8.58267 18.2540i −0.283425 0.602799i
\(918\) −3.66565 + 2.49569i −0.120985 + 0.0823699i
\(919\) 24.8070 0.818309 0.409154 0.912465i \(-0.365824\pi\)
0.409154 + 0.912465i \(0.365824\pi\)
\(920\) 4.06113 0.133891
\(921\) 15.5781 + 5.23773i 0.513314 + 0.172589i
\(922\) 11.6521 6.72737i 0.383743 0.221554i
\(923\) −20.2140 50.5683i −0.665353 1.66448i
\(924\) −23.1061 + 2.67268i −0.760136 + 0.0879249i
\(925\) 3.34816 12.4955i 0.110087 0.410850i
\(926\) 31.4085 + 18.1337i 1.03215 + 0.595911i
\(927\) 1.05242 8.36849i 0.0345659 0.274857i
\(928\) −5.56536 + 1.49123i −0.182692 + 0.0489521i
\(929\) 8.20806 8.20806i 0.269298 0.269298i −0.559519 0.828817i \(-0.689014\pi\)
0.828817 + 0.559519i \(0.189014\pi\)
\(930\) −12.0746 + 10.6512i −0.395943 + 0.349268i
\(931\) −22.6934 31.9752i −0.743745 1.04794i
\(932\) 10.8939 + 6.28957i 0.356840 + 0.206022i
\(933\) 23.0294 + 1.44240i 0.753950 + 0.0472222i
\(934\) −8.04119 + 8.04119i −0.263116 + 0.263116i
\(935\) 3.52325 6.10245i 0.115223 0.199572i
\(936\) −10.4664 + 2.73030i −0.342105 + 0.0892428i
\(937\) 32.6123 1.06540 0.532698 0.846305i \(-0.321178\pi\)
0.532698 + 0.846305i \(0.321178\pi\)
\(938\) 26.6340 + 18.5235i 0.869630 + 0.604814i
\(939\) −24.8556 + 37.4335i −0.811132 + 1.22159i
\(940\) 12.1799i 0.397264i
\(941\) −0.962648 3.59265i −0.0313814 0.117117i 0.948458 0.316902i \(-0.102642\pi\)
−0.979840 + 0.199784i \(0.935976\pi\)
\(942\) 1.39368 + 6.90191i 0.0454087 + 0.224876i
\(943\) −3.79087 + 3.79087i −0.123448 + 0.123448i
\(944\) 0.583751 + 0.583751i 0.0189995 + 0.0189995i
\(945\) 11.3736 19.2548i 0.369982 0.626359i
\(946\) 57.0956 32.9642i 1.85634 1.07176i
\(947\) 24.2322 6.49299i 0.787440 0.210994i 0.157378 0.987538i \(-0.449696\pi\)
0.630062 + 0.776545i \(0.283029\pi\)
\(948\) −1.30788 + 20.8816i −0.0424779 + 0.678203i
\(949\) 14.6355 + 36.6128i 0.475089 + 1.18850i
\(950\) −11.4188 + 6.59266i −0.370475 + 0.213894i
\(951\) 1.87761 + 9.29842i 0.0608855 + 0.301522i
\(952\) 2.12424 + 0.765529i 0.0688472 + 0.0248109i
\(953\) −7.75491 + 13.4319i −0.251206 + 0.435102i −0.963858 0.266416i \(-0.914161\pi\)
0.712652 + 0.701518i \(0.247494\pi\)
\(954\) −21.1732 27.2647i −0.685508 0.882728i
\(955\) 4.41204 16.4660i 0.142770 0.532826i
\(956\) 5.22824 19.5121i 0.169093 0.631065i
\(957\) 10.0261 + 49.6518i 0.324097 + 1.60502i
\(958\) −2.30496 + 3.99230i −0.0744697 + 0.128985i
\(959\) 18.0129 + 6.49144i 0.581667 + 0.209619i
\(960\) 2.76174 0.557670i 0.0891347 0.0179987i
\(961\) 1.43588 0.829003i 0.0463186 0.0267420i
\(962\) 15.8686 11.8663i 0.511625 0.382583i
\(963\) 33.5688 14.1332i 1.08174 0.455436i
\(964\) −22.8441 + 6.12107i −0.735760 + 0.197146i
\(965\) −4.30023 + 2.48274i −0.138429 + 0.0799222i
\(966\) 11.3650 1.31459i 0.365664 0.0422963i
\(967\) −36.0785 36.0785i −1.16021 1.16021i −0.984430 0.175775i \(-0.943757\pi\)
−0.175775 0.984430i \(-0.556243\pi\)
\(968\) −10.4395 + 10.4395i −0.335537 + 0.335537i
\(969\) −8.11611 + 1.63886i −0.260727 + 0.0526479i
\(970\) −6.50956 24.2940i −0.209009 0.780033i
\(971\) 57.4257i 1.84288i 0.388524 + 0.921439i \(0.372985\pi\)
−0.388524 + 0.921439i \(0.627015\pi\)
\(972\) −4.79630 + 14.8322i −0.153841 + 0.475745i
\(973\) −9.68559 6.73617i −0.310506 0.215952i
\(974\) −9.27311 −0.297130
\(975\) −0.821745 14.6774i −0.0263169 0.470051i
\(976\) 2.92693 5.06959i 0.0936888 0.162274i
\(977\) 5.81297 5.81297i 0.185973 0.185973i −0.607979 0.793953i \(-0.708020\pi\)
0.793953 + 0.607979i \(0.208020\pi\)
\(978\) −1.10240 + 17.6010i −0.0352510 + 0.562818i
\(979\) 31.2133 + 18.0210i 0.997583 + 0.575955i
\(980\) −11.3368 + 1.06446i −0.362142 + 0.0340030i
\(981\) 8.19990 20.1255i 0.261803 0.642558i
\(982\) −19.7531 + 19.7531i −0.630347 + 0.630347i
\(983\) 46.3345 12.4153i 1.47784 0.395986i 0.572228 0.820094i \(-0.306079\pi\)
0.905611 + 0.424108i \(0.139412\pi\)
\(984\) −2.05739 + 3.09850i −0.0655871 + 0.0987767i
\(985\) −31.2117 18.0201i −0.994487 0.574167i
\(986\) 1.27267 4.74967i 0.0405301 0.151260i
\(987\) 3.94264 + 34.0853i 0.125496 + 1.08495i
\(988\) −19.9890 2.88459i −0.635935 0.0917709i
\(989\) −28.0832 + 16.2138i −0.892993 + 0.515570i
\(990\) −3.37543 24.5389i −0.107278 0.779897i
\(991\) 2.87423 0.0913029 0.0456515 0.998957i \(-0.485464\pi\)
0.0456515 + 0.998957i \(0.485464\pi\)
\(992\) −5.71472 −0.181442
\(993\) 1.33770 3.97858i 0.0424506 0.126257i
\(994\) 17.0036 + 36.1639i 0.539321 + 1.14705i
\(995\) −7.79049 + 2.08746i −0.246975 + 0.0661768i
\(996\) −7.64546 + 1.54383i −0.242256 + 0.0489180i
\(997\) −7.68699 13.3143i −0.243449 0.421667i 0.718245 0.695790i \(-0.244946\pi\)
−0.961695 + 0.274123i \(0.911612\pi\)
\(998\) −5.06133 −0.160214
\(999\) −2.11536 28.4775i −0.0669269 0.900989i
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.bw.a.11.13 152
3.2 odd 2 inner 546.2.bw.a.11.32 yes 152
7.2 even 3 546.2.ch.a.401.1 yes 152
13.6 odd 12 546.2.ch.a.305.33 yes 152
21.2 odd 6 546.2.ch.a.401.33 yes 152
39.32 even 12 546.2.ch.a.305.1 yes 152
91.58 odd 12 inner 546.2.bw.a.149.32 yes 152
273.149 even 12 inner 546.2.bw.a.149.13 yes 152
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
546.2.bw.a.11.13 152 1.1 even 1 trivial
546.2.bw.a.11.32 yes 152 3.2 odd 2 inner
546.2.bw.a.149.13 yes 152 273.149 even 12 inner
546.2.bw.a.149.32 yes 152 91.58 odd 12 inner
546.2.ch.a.305.1 yes 152 39.32 even 12
546.2.ch.a.305.33 yes 152 13.6 odd 12
546.2.ch.a.401.1 yes 152 7.2 even 3
546.2.ch.a.401.33 yes 152 21.2 odd 6