Properties

Label 546.2.bg.a.311.1
Level $546$
Weight $2$
Character 546.311
Analytic conductor $4.360$
Analytic rank $0$
Dimension $36$
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(311,546)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(546, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 1, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("546.311");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 546.bg (of order \(6\), degree \(2\), 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: \(36\)
Relative dimension: \(18\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 311.1
Character \(\chi\) \(=\) 546.311
Dual form 546.2.bg.a.467.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{2} +(-1.71076 - 0.270722i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(2.20332 - 1.27209i) q^{5} +(0.620929 + 1.61693i) q^{6} +(2.32714 - 1.25873i) q^{7} +1.00000 q^{8} +(2.85342 + 0.926282i) q^{9} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{2} +(-1.71076 - 0.270722i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(2.20332 - 1.27209i) q^{5} +(0.620929 + 1.61693i) q^{6} +(2.32714 - 1.25873i) q^{7} +1.00000 q^{8} +(2.85342 + 0.926282i) q^{9} +(-2.20332 - 1.27209i) q^{10} +(-2.05512 + 3.55958i) q^{11} +(1.08983 - 1.34620i) q^{12} +(0.691594 + 3.53860i) q^{13} +(-2.25366 - 1.38600i) q^{14} +(-4.11374 + 1.57975i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(2.85089 - 4.93789i) q^{17} +(-0.624526 - 2.93427i) q^{18} +(4.22658 + 7.32066i) q^{19} +2.54418i q^{20} +(-4.32196 + 1.52338i) q^{21} +4.11024 q^{22} +(1.13269 - 0.653959i) q^{23} +(-1.71076 - 0.270722i) q^{24} +(0.736416 - 1.27551i) q^{25} +(2.71872 - 2.36824i) q^{26} +(-4.63076 - 2.35713i) q^{27} +(-0.0734817 + 2.64473i) q^{28} -6.06189i q^{29} +(3.42498 + 2.77273i) q^{30} +(-0.00131550 + 0.00227852i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(4.47948 - 5.53322i) q^{33} -5.70178 q^{34} +(3.52623 - 5.73372i) q^{35} +(-2.22889 + 2.00799i) q^{36} +(6.13142 - 3.53998i) q^{37} +(4.22658 - 7.32066i) q^{38} +(-0.225177 - 6.24094i) q^{39} +(2.20332 - 1.27209i) q^{40} -2.51379i q^{41} +(3.48026 + 2.98124i) q^{42} +3.31665 q^{43} +(-2.05512 - 3.55958i) q^{44} +(7.46531 - 1.58890i) q^{45} +(-1.13269 - 0.653959i) q^{46} +(3.68624 - 2.12825i) q^{47} +(0.620929 + 1.61693i) q^{48} +(3.83121 - 5.85849i) q^{49} -1.47283 q^{50} +(-6.21399 + 7.67576i) q^{51} +(-3.41032 - 1.17036i) q^{52} +(-4.39543 - 2.53770i) q^{53} +(0.274044 + 5.18892i) q^{54} +10.4572i q^{55} +(2.32714 - 1.25873i) q^{56} +(-5.24882 - 13.6681i) q^{57} +(-5.24975 + 3.03094i) q^{58} +(1.68327 + 0.971837i) q^{59} +(0.688764 - 4.35248i) q^{60} +(-3.15576 + 1.82198i) q^{61} +0.00263100 q^{62} +(7.80626 - 1.43609i) q^{63} +1.00000 q^{64} +(6.02522 + 6.91691i) q^{65} +(-7.03165 - 1.11273i) q^{66} +(-2.80901 - 1.62178i) q^{67} +(2.85089 + 4.93789i) q^{68} +(-2.11481 + 0.812125i) q^{69} +(-6.72866 - 0.186950i) q^{70} -6.68865 q^{71} +(2.85342 + 0.926282i) q^{72} +(-1.31969 + 2.28578i) q^{73} +(-6.13142 - 3.53998i) q^{74} +(-1.60514 + 1.98273i) q^{75} -8.45317 q^{76} +(-0.302028 + 10.8705i) q^{77} +(-5.29222 + 3.31548i) q^{78} +(-7.07859 - 12.2605i) q^{79} +(-2.20332 - 1.27209i) q^{80} +(7.28400 + 5.28614i) q^{81} +(-2.17701 + 1.25689i) q^{82} +11.1300i q^{83} +(0.841696 - 4.50461i) q^{84} -14.5063i q^{85} +(-1.65832 - 2.87230i) q^{86} +(-1.64109 + 10.3705i) q^{87} +(-2.05512 + 3.55958i) q^{88} +(3.31853 - 1.91595i) q^{89} +(-5.10869 - 5.67070i) q^{90} +(6.06358 + 7.36431i) q^{91} +1.30792i q^{92} +(0.00286736 - 0.00354187i) q^{93} +(-3.68624 - 2.12825i) q^{94} +(18.6250 + 10.7532i) q^{95} +(1.08983 - 1.34620i) q^{96} +3.91287 q^{97} +(-6.98920 - 0.388679i) q^{98} +(-9.16129 + 8.25334i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36 q - 18 q^{2} - 18 q^{4} + 36 q^{8} + 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 36 q - 18 q^{2} - 18 q^{4} + 36 q^{8} + 4 q^{9} - 14 q^{15} - 18 q^{16} + 4 q^{18} + 23 q^{21} + 14 q^{25} - 6 q^{26} + 7 q^{30} - 18 q^{32} + 24 q^{33} - 8 q^{36} - 10 q^{39} - 16 q^{42} - 16 q^{43} - 9 q^{45} + 72 q^{47} + 12 q^{49} - 28 q^{50} - 3 q^{51} + 6 q^{52} + 9 q^{54} - 8 q^{57} + 24 q^{59} + 7 q^{60} - 36 q^{61} - 39 q^{63} + 36 q^{64} + 18 q^{65} - 24 q^{66} - 72 q^{71} + 4 q^{72} + 54 q^{75} + 20 q^{78} + 20 q^{79} - 20 q^{81} - 24 q^{82} - 7 q^{84} + 8 q^{86} - 24 q^{87} - 72 q^{89} - 2 q^{91} - 14 q^{93} - 72 q^{94} - 12 q^{98} + 72 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(157\) \(365\) \(379\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(-1\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 0.866025i −0.353553 0.612372i
\(3\) −1.71076 0.270722i −0.987709 0.156301i
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) 2.20332 1.27209i 0.985355 0.568895i 0.0814725 0.996676i \(-0.474038\pi\)
0.903883 + 0.427781i \(0.140704\pi\)
\(6\) 0.620929 + 1.61693i 0.253493 + 0.660107i
\(7\) 2.32714 1.25873i 0.879578 0.475755i
\(8\) 1.00000 0.353553
\(9\) 2.85342 + 0.926282i 0.951140 + 0.308761i
\(10\) −2.20332 1.27209i −0.696751 0.402270i
\(11\) −2.05512 + 3.55958i −0.619643 + 1.07325i 0.369908 + 0.929068i \(0.379389\pi\)
−0.989551 + 0.144184i \(0.953944\pi\)
\(12\) 1.08983 1.34620i 0.314608 0.388615i
\(13\) 0.691594 + 3.53860i 0.191814 + 0.981431i
\(14\) −2.25366 1.38600i −0.602317 0.370425i
\(15\) −4.11374 + 1.57975i −1.06216 + 0.407891i
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 2.85089 4.93789i 0.691443 1.19761i −0.279922 0.960023i \(-0.590309\pi\)
0.971365 0.237591i \(-0.0763579\pi\)
\(18\) −0.624526 2.93427i −0.147202 0.691615i
\(19\) 4.22658 + 7.32066i 0.969645 + 1.67947i 0.696581 + 0.717478i \(0.254704\pi\)
0.273064 + 0.961996i \(0.411963\pi\)
\(20\) 2.54418i 0.568895i
\(21\) −4.32196 + 1.52338i −0.943129 + 0.332428i
\(22\) 4.11024 0.876307
\(23\) 1.13269 0.653959i 0.236182 0.136360i −0.377238 0.926116i \(-0.623126\pi\)
0.613421 + 0.789756i \(0.289793\pi\)
\(24\) −1.71076 0.270722i −0.349208 0.0552609i
\(25\) 0.736416 1.27551i 0.147283 0.255102i
\(26\) 2.71872 2.36824i 0.533185 0.464450i
\(27\) −4.63076 2.35713i −0.891190 0.453630i
\(28\) −0.0734817 + 2.64473i −0.0138867 + 0.499807i
\(29\) 6.06189i 1.12566i −0.826571 0.562832i \(-0.809712\pi\)
0.826571 0.562832i \(-0.190288\pi\)
\(30\) 3.42498 + 2.77273i 0.625313 + 0.506229i
\(31\) −0.00131550 + 0.00227852i −0.000236271 + 0.000409234i −0.866144 0.499795i \(-0.833409\pi\)
0.865907 + 0.500205i \(0.166742\pi\)
\(32\) −0.500000 + 0.866025i −0.0883883 + 0.153093i
\(33\) 4.47948 5.53322i 0.779778 0.963211i
\(34\) −5.70178 −0.977848
\(35\) 3.52623 5.73372i 0.596042 0.969175i
\(36\) −2.22889 + 2.00799i −0.371482 + 0.334665i
\(37\) 6.13142 3.53998i 1.00800 0.581969i 0.0973943 0.995246i \(-0.468949\pi\)
0.910605 + 0.413277i \(0.135616\pi\)
\(38\) 4.22658 7.32066i 0.685642 1.18757i
\(39\) −0.225177 6.24094i −0.0360572 0.999350i
\(40\) 2.20332 1.27209i 0.348376 0.201135i
\(41\) 2.51379i 0.392588i −0.980545 0.196294i \(-0.937109\pi\)
0.980545 0.196294i \(-0.0628907\pi\)
\(42\) 3.48026 + 2.98124i 0.537016 + 0.460015i
\(43\) 3.31665 0.505784 0.252892 0.967494i \(-0.418618\pi\)
0.252892 + 0.967494i \(0.418618\pi\)
\(44\) −2.05512 3.55958i −0.309821 0.536626i
\(45\) 7.46531 1.58890i 1.11286 0.236860i
\(46\) −1.13269 0.653959i −0.167006 0.0964211i
\(47\) 3.68624 2.12825i 0.537693 0.310437i −0.206451 0.978457i \(-0.566191\pi\)
0.744143 + 0.668020i \(0.232858\pi\)
\(48\) 0.620929 + 1.61693i 0.0896234 + 0.233383i
\(49\) 3.83121 5.85849i 0.547315 0.836927i
\(50\) −1.47283 −0.208290
\(51\) −6.21399 + 7.67576i −0.870133 + 1.07482i
\(52\) −3.41032 1.17036i −0.472926 0.162300i
\(53\) −4.39543 2.53770i −0.603758 0.348580i 0.166760 0.985997i \(-0.446669\pi\)
−0.770519 + 0.637417i \(0.780003\pi\)
\(54\) 0.274044 + 5.18892i 0.0372927 + 0.706123i
\(55\) 10.4572i 1.41005i
\(56\) 2.32714 1.25873i 0.310978 0.168205i
\(57\) −5.24882 13.6681i −0.695223 1.81039i
\(58\) −5.24975 + 3.03094i −0.689326 + 0.397982i
\(59\) 1.68327 + 0.971837i 0.219143 + 0.126522i 0.605554 0.795805i \(-0.292952\pi\)
−0.386410 + 0.922327i \(0.626285\pi\)
\(60\) 0.688764 4.35248i 0.0889191 0.561903i
\(61\) −3.15576 + 1.82198i −0.404054 + 0.233281i −0.688232 0.725491i \(-0.741613\pi\)
0.284178 + 0.958772i \(0.408279\pi\)
\(62\) 0.00263100 0.000334138
\(63\) 7.80626 1.43609i 0.983496 0.180930i
\(64\) 1.00000 0.125000
\(65\) 6.02522 + 6.91691i 0.747336 + 0.857937i
\(66\) −7.03165 1.11273i −0.865537 0.136968i
\(67\) −2.80901 1.62178i −0.343175 0.198132i 0.318500 0.947923i \(-0.396821\pi\)
−0.661675 + 0.749791i \(0.730154\pi\)
\(68\) 2.85089 + 4.93789i 0.345721 + 0.598807i
\(69\) −2.11481 + 0.812125i −0.254593 + 0.0977684i
\(70\) −6.72866 0.186950i −0.804229 0.0223448i
\(71\) −6.68865 −0.793797 −0.396899 0.917862i \(-0.629914\pi\)
−0.396899 + 0.917862i \(0.629914\pi\)
\(72\) 2.85342 + 0.926282i 0.336279 + 0.109163i
\(73\) −1.31969 + 2.28578i −0.154458 + 0.267530i −0.932862 0.360235i \(-0.882697\pi\)
0.778403 + 0.627765i \(0.216030\pi\)
\(74\) −6.13142 3.53998i −0.712763 0.411514i
\(75\) −1.60514 + 1.98273i −0.185346 + 0.228946i
\(76\) −8.45317 −0.969645
\(77\) −0.302028 + 10.8705i −0.0344192 + 1.23881i
\(78\) −5.29222 + 3.31548i −0.599226 + 0.375404i
\(79\) −7.07859 12.2605i −0.796404 1.37941i −0.921944 0.387323i \(-0.873400\pi\)
0.125540 0.992088i \(-0.459934\pi\)
\(80\) −2.20332 1.27209i −0.246339 0.142224i
\(81\) 7.28400 + 5.28614i 0.809334 + 0.587349i
\(82\) −2.17701 + 1.25689i −0.240410 + 0.138801i
\(83\) 11.1300i 1.22168i 0.791755 + 0.610839i \(0.209168\pi\)
−0.791755 + 0.610839i \(0.790832\pi\)
\(84\) 0.841696 4.50461i 0.0918366 0.491494i
\(85\) 14.5063i 1.57343i
\(86\) −1.65832 2.87230i −0.178822 0.309728i
\(87\) −1.64109 + 10.3705i −0.175943 + 1.11183i
\(88\) −2.05512 + 3.55958i −0.219077 + 0.379452i
\(89\) 3.31853 1.91595i 0.351763 0.203091i −0.313698 0.949523i \(-0.601568\pi\)
0.665462 + 0.746432i \(0.268235\pi\)
\(90\) −5.10869 5.67070i −0.538503 0.597744i
\(91\) 6.06358 + 7.36431i 0.635636 + 0.771989i
\(92\) 1.30792i 0.136360i
\(93\) 0.00286736 0.00354187i 0.000297331 0.000367274i
\(94\) −3.68624 2.12825i −0.380206 0.219512i
\(95\) 18.6250 + 10.7532i 1.91089 + 1.10325i
\(96\) 1.08983 1.34620i 0.111231 0.137396i
\(97\) 3.91287 0.397292 0.198646 0.980071i \(-0.436346\pi\)
0.198646 + 0.980071i \(0.436346\pi\)
\(98\) −6.98920 0.388679i −0.706016 0.0392625i
\(99\) −9.16129 + 8.25334i −0.920745 + 0.829492i
\(100\) 0.736416 + 1.27551i 0.0736416 + 0.127551i
\(101\) −7.74790 + 13.4198i −0.770945 + 1.33532i 0.166100 + 0.986109i \(0.446883\pi\)
−0.937045 + 0.349208i \(0.886451\pi\)
\(102\) 9.75440 + 1.54360i 0.965829 + 0.152839i
\(103\) −11.5111 + 6.64596i −1.13423 + 0.654846i −0.944994 0.327087i \(-0.893933\pi\)
−0.189231 + 0.981933i \(0.560600\pi\)
\(104\) 0.691594 + 3.53860i 0.0678164 + 0.346988i
\(105\) −7.58479 + 8.85440i −0.740200 + 0.864101i
\(106\) 5.07540i 0.492967i
\(107\) 12.3570 7.13432i 1.19460 0.689701i 0.235251 0.971935i \(-0.424409\pi\)
0.959346 + 0.282234i \(0.0910754\pi\)
\(108\) 4.35672 2.83179i 0.419225 0.272489i
\(109\) 9.22052 + 5.32347i 0.883166 + 0.509896i 0.871701 0.490038i \(-0.163017\pi\)
0.0114648 + 0.999934i \(0.496351\pi\)
\(110\) 9.05619 5.22859i 0.863474 0.498527i
\(111\) −11.4478 + 4.39615i −1.08657 + 0.417264i
\(112\) −2.25366 1.38600i −0.212951 0.130965i
\(113\) 0.854272i 0.0803632i −0.999192 0.0401816i \(-0.987206\pi\)
0.999192 0.0401816i \(-0.0127936\pi\)
\(114\) −9.21254 + 11.3797i −0.862834 + 1.06580i
\(115\) 1.66379 2.88177i 0.155149 0.268726i
\(116\) 5.24975 + 3.03094i 0.487427 + 0.281416i
\(117\) −1.30433 + 10.7377i −0.120586 + 0.992703i
\(118\) 1.94367i 0.178930i
\(119\) 0.418977 15.0797i 0.0384075 1.38235i
\(120\) −4.11374 + 1.57975i −0.375532 + 0.144211i
\(121\) −2.94705 5.10444i −0.267914 0.464040i
\(122\) 3.15576 + 1.82198i 0.285709 + 0.164954i
\(123\) −0.680538 + 4.30050i −0.0613620 + 0.387763i
\(124\) −0.00131550 0.00227852i −0.000118136 0.000204617i
\(125\) 8.97374i 0.802635i
\(126\) −5.14682 6.04237i −0.458515 0.538297i
\(127\) −12.0715 −1.07117 −0.535584 0.844482i \(-0.679908\pi\)
−0.535584 + 0.844482i \(0.679908\pi\)
\(128\) −0.500000 0.866025i −0.0441942 0.0765466i
\(129\) −5.67400 0.897889i −0.499568 0.0790547i
\(130\) 2.97761 8.67644i 0.261154 0.760974i
\(131\) −8.61673 14.9246i −0.752847 1.30397i −0.946438 0.322887i \(-0.895347\pi\)
0.193591 0.981082i \(-0.437987\pi\)
\(132\) 2.55217 + 6.64596i 0.222138 + 0.578456i
\(133\) 19.0506 + 11.7161i 1.65190 + 1.01592i
\(134\) 3.24356i 0.280201i
\(135\) −13.2015 + 0.697216i −1.13621 + 0.0600068i
\(136\) 2.85089 4.93789i 0.244462 0.423421i
\(137\) 6.52427 11.3004i 0.557406 0.965456i −0.440306 0.897848i \(-0.645130\pi\)
0.997712 0.0676081i \(-0.0215367\pi\)
\(138\) 1.76072 + 1.42541i 0.149883 + 0.121339i
\(139\) 0.623348i 0.0528717i 0.999651 + 0.0264359i \(0.00841577\pi\)
−0.999651 + 0.0264359i \(0.991584\pi\)
\(140\) 3.20243 + 5.92067i 0.270654 + 0.500388i
\(141\) −6.88244 + 2.64299i −0.579606 + 0.222580i
\(142\) 3.34433 + 5.79254i 0.280650 + 0.486099i
\(143\) −14.0172 4.81047i −1.17218 0.402272i
\(144\) −0.624526 2.93427i −0.0520438 0.244523i
\(145\) −7.71125 13.3563i −0.640385 1.10918i
\(146\) 2.63939 0.218437
\(147\) −8.14031 + 8.98529i −0.671401 + 0.741094i
\(148\) 7.07996i 0.581969i
\(149\) 0.986187 + 1.70813i 0.0807916 + 0.139935i 0.903590 0.428398i \(-0.140922\pi\)
−0.822799 + 0.568333i \(0.807589\pi\)
\(150\) 2.51967 + 0.398728i 0.205730 + 0.0325560i
\(151\) 8.14145 + 4.70047i 0.662542 + 0.382519i 0.793245 0.608903i \(-0.208390\pi\)
−0.130703 + 0.991422i \(0.541723\pi\)
\(152\) 4.22658 + 7.32066i 0.342821 + 0.593784i
\(153\) 12.7087 11.4491i 1.02743 0.925608i
\(154\) 9.56513 5.17368i 0.770780 0.416907i
\(155\) 0.00669374i 0.000537654i
\(156\) 5.51740 + 2.92546i 0.441745 + 0.234224i
\(157\) 6.32327 + 3.65074i 0.504652 + 0.291361i 0.730633 0.682771i \(-0.239225\pi\)
−0.225980 + 0.974132i \(0.572559\pi\)
\(158\) −7.07859 + 12.2605i −0.563142 + 0.975391i
\(159\) 6.83252 + 5.53134i 0.541854 + 0.438664i
\(160\) 2.54418i 0.201135i
\(161\) 1.81278 2.94761i 0.142867 0.232304i
\(162\) 0.935930 8.95120i 0.0735336 0.703273i
\(163\) 13.1037 7.56540i 1.02636 0.592568i 0.110418 0.993885i \(-0.464781\pi\)
0.915939 + 0.401317i \(0.131448\pi\)
\(164\) 2.17701 + 1.25689i 0.169996 + 0.0981470i
\(165\) 2.83099 17.8898i 0.220392 1.39272i
\(166\) 9.63888 5.56501i 0.748122 0.431929i
\(167\) 24.2735i 1.87834i 0.343458 + 0.939168i \(0.388402\pi\)
−0.343458 + 0.939168i \(0.611598\pi\)
\(168\) −4.32196 + 1.52338i −0.333446 + 0.117531i
\(169\) −12.0434 + 4.89455i −0.926415 + 0.376504i
\(170\) −12.5629 + 7.25317i −0.963527 + 0.556293i
\(171\) 5.27922 + 24.8039i 0.403712 + 1.89680i
\(172\) −1.65832 + 2.87230i −0.126446 + 0.219011i
\(173\) −0.204681 0.354517i −0.0155616 0.0269535i 0.858140 0.513416i \(-0.171620\pi\)
−0.873701 + 0.486463i \(0.838287\pi\)
\(174\) 9.80162 3.76400i 0.743059 0.285348i
\(175\) 0.108226 3.89524i 0.00818113 0.294453i
\(176\) 4.11024 0.309821
\(177\) −2.61658 2.11828i −0.196674 0.159220i
\(178\) −3.31853 1.91595i −0.248734 0.143607i
\(179\) −20.4933 11.8318i −1.53174 0.884352i −0.999282 0.0378964i \(-0.987934\pi\)
−0.532460 0.846455i \(-0.678732\pi\)
\(180\) −2.35662 + 7.25960i −0.175652 + 0.541099i
\(181\) 14.2247i 1.05732i −0.848835 0.528658i \(-0.822696\pi\)
0.848835 0.528658i \(-0.177304\pi\)
\(182\) 3.34589 8.93337i 0.248014 0.662185i
\(183\) 5.89201 2.26264i 0.435550 0.167259i
\(184\) 1.13269 0.653959i 0.0835031 0.0482105i
\(185\) 9.00633 15.5994i 0.662158 1.14689i
\(186\) −0.00450102 0.000712270i −0.000330031 5.22262e-5i
\(187\) 11.7179 + 20.2959i 0.856895 + 1.48419i
\(188\) 4.25650i 0.310437i
\(189\) −13.7434 + 0.343482i −0.999688 + 0.0249846i
\(190\) 21.5063i 1.56023i
\(191\) −13.8603 + 8.00228i −1.00290 + 0.579024i −0.909105 0.416567i \(-0.863233\pi\)
−0.0937947 + 0.995592i \(0.529900\pi\)
\(192\) −1.71076 0.270722i −0.123464 0.0195377i
\(193\) −14.6848 8.47830i −1.05704 0.610281i −0.132427 0.991193i \(-0.542277\pi\)
−0.924611 + 0.380912i \(0.875610\pi\)
\(194\) −1.95644 3.38865i −0.140464 0.243291i
\(195\) −8.43516 13.4643i −0.604054 0.964202i
\(196\) 3.15799 + 6.24716i 0.225571 + 0.446226i
\(197\) −2.56563 −0.182794 −0.0913969 0.995815i \(-0.529133\pi\)
−0.0913969 + 0.995815i \(0.529133\pi\)
\(198\) 11.7282 + 3.80724i 0.833490 + 0.270569i
\(199\) 18.7467 + 10.8234i 1.32892 + 0.767249i 0.985132 0.171800i \(-0.0549582\pi\)
0.343783 + 0.939049i \(0.388292\pi\)
\(200\) 0.736416 1.27551i 0.0520725 0.0901922i
\(201\) 4.36649 + 3.53494i 0.307988 + 0.249335i
\(202\) 15.4958 1.09028
\(203\) −7.63027 14.1069i −0.535540 0.990110i
\(204\) −3.54041 9.21936i −0.247878 0.645484i
\(205\) −3.19776 5.53868i −0.223341 0.386839i
\(206\) 11.5111 + 6.64596i 0.802019 + 0.463046i
\(207\) 3.83779 0.816830i 0.266745 0.0567736i
\(208\) 2.71872 2.36824i 0.188509 0.164208i
\(209\) −34.7446 −2.40333
\(210\) 11.4605 + 2.14142i 0.790852 + 0.147772i
\(211\) −7.00715 −0.482392 −0.241196 0.970476i \(-0.577540\pi\)
−0.241196 + 0.970476i \(0.577540\pi\)
\(212\) 4.39543 2.53770i 0.301879 0.174290i
\(213\) 11.4427 + 1.81076i 0.784041 + 0.124072i
\(214\) −12.3570 7.13432i −0.844707 0.487692i
\(215\) 7.30764 4.21907i 0.498377 0.287738i
\(216\) −4.63076 2.35713i −0.315083 0.160382i
\(217\) −0.000193331 0.00695830i −1.31241e−5 0.000472360i
\(218\) 10.6469i 0.721102i
\(219\) 2.87649 3.55315i 0.194375 0.240100i
\(220\) −9.05619 5.22859i −0.610568 0.352512i
\(221\) 19.4449 + 6.67315i 1.30800 + 0.448885i
\(222\) 9.53106 + 7.71597i 0.639683 + 0.517862i
\(223\) −21.1582 −1.41686 −0.708429 0.705782i \(-0.750596\pi\)
−0.708429 + 0.705782i \(0.750596\pi\)
\(224\) −0.0734817 + 2.64473i −0.00490970 + 0.176709i
\(225\) 3.28279 2.95744i 0.218852 0.197162i
\(226\) −0.739822 + 0.427136i −0.0492122 + 0.0284127i
\(227\) −11.6624 6.73328i −0.774059 0.446903i 0.0602614 0.998183i \(-0.480807\pi\)
−0.834321 + 0.551279i \(0.814140\pi\)
\(228\) 14.4614 + 2.28846i 0.957727 + 0.151557i
\(229\) −1.12680 1.95167i −0.0744607 0.128970i 0.826391 0.563097i \(-0.190390\pi\)
−0.900852 + 0.434127i \(0.857057\pi\)
\(230\) −3.32758 −0.219414
\(231\) 3.45958 18.5151i 0.227623 1.21820i
\(232\) 6.06189i 0.397982i
\(233\) 1.12902 0.651840i 0.0739645 0.0427034i −0.462562 0.886587i \(-0.653070\pi\)
0.536526 + 0.843884i \(0.319736\pi\)
\(234\) 9.95131 4.23928i 0.650537 0.277130i
\(235\) 5.41464 9.37843i 0.353212 0.611782i
\(236\) −1.68327 + 0.971837i −0.109572 + 0.0632612i
\(237\) 8.79061 + 22.8911i 0.571012 + 1.48694i
\(238\) −13.2689 + 7.17700i −0.860093 + 0.465216i
\(239\) −3.50122 −0.226475 −0.113238 0.993568i \(-0.536122\pi\)
−0.113238 + 0.993568i \(0.536122\pi\)
\(240\) 3.42498 + 2.77273i 0.221081 + 0.178979i
\(241\) −6.59729 + 11.4268i −0.424969 + 0.736067i −0.996418 0.0845704i \(-0.973048\pi\)
0.571449 + 0.820638i \(0.306382\pi\)
\(242\) −2.94705 + 5.10444i −0.189444 + 0.328126i
\(243\) −11.0301 11.0153i −0.707583 0.706630i
\(244\) 3.64396i 0.233281i
\(245\) 0.988867 17.7818i 0.0631764 1.13603i
\(246\) 4.06461 1.56089i 0.259150 0.0995184i
\(247\) −22.9818 + 20.0191i −1.46230 + 1.27379i
\(248\) −0.00131550 + 0.00227852i −8.35345e−5 + 0.000144686i
\(249\) 3.01314 19.0408i 0.190950 1.20666i
\(250\) 7.77148 4.48687i 0.491512 0.283774i
\(251\) 28.4357 1.79485 0.897424 0.441169i \(-0.145436\pi\)
0.897424 + 0.441169i \(0.145436\pi\)
\(252\) −2.65944 + 7.47846i −0.167529 + 0.471099i
\(253\) 5.37586i 0.337978i
\(254\) 6.03573 + 10.4542i 0.378715 + 0.655954i
\(255\) −3.92718 + 24.8169i −0.245930 + 1.55410i
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 9.54939 + 16.5400i 0.595675 + 1.03174i 0.993451 + 0.114257i \(0.0364486\pi\)
−0.397776 + 0.917482i \(0.630218\pi\)
\(258\) 2.05940 + 5.36277i 0.128213 + 0.333872i
\(259\) 9.81284 15.9558i 0.609740 0.991448i
\(260\) −9.00282 + 1.75954i −0.558331 + 0.109122i
\(261\) 5.61502 17.2971i 0.347561 1.07066i
\(262\) −8.61673 + 14.9246i −0.532343 + 0.922045i
\(263\) −4.49853 2.59723i −0.277391 0.160152i 0.354851 0.934923i \(-0.384532\pi\)
−0.632242 + 0.774771i \(0.717865\pi\)
\(264\) 4.47948 5.53322i 0.275693 0.340546i
\(265\) −12.9127 −0.793222
\(266\) 0.621153 22.3564i 0.0380853 1.37076i
\(267\) −6.19590 + 2.37934i −0.379183 + 0.145613i
\(268\) 2.80901 1.62178i 0.171587 0.0990660i
\(269\) −3.10207 + 5.37294i −0.189136 + 0.327594i −0.944963 0.327179i \(-0.893902\pi\)
0.755826 + 0.654772i \(0.227235\pi\)
\(270\) 7.20457 + 11.0843i 0.438456 + 0.674566i
\(271\) −12.8489 22.2550i −0.780518 1.35190i −0.931640 0.363382i \(-0.881622\pi\)
0.151123 0.988515i \(-0.451711\pi\)
\(272\) −5.70178 −0.345721
\(273\) −8.37966 14.2401i −0.507160 0.861852i
\(274\) −13.0485 −0.788292
\(275\) 3.02685 + 5.24266i 0.182526 + 0.316144i
\(276\) 0.354082 2.23754i 0.0213132 0.134684i
\(277\) −12.1581 + 21.0584i −0.730507 + 1.26528i 0.226159 + 0.974090i \(0.427383\pi\)
−0.956667 + 0.291186i \(0.905950\pi\)
\(278\) 0.539835 0.311674i 0.0323772 0.0186930i
\(279\) −0.00586423 + 0.00528304i −0.000351082 + 0.000316287i
\(280\) 3.52623 5.73372i 0.210733 0.342655i
\(281\) −22.7215 −1.35545 −0.677724 0.735316i \(-0.737034\pi\)
−0.677724 + 0.735316i \(0.737034\pi\)
\(282\) 5.73011 + 4.63887i 0.341223 + 0.276241i
\(283\) 16.6217 + 9.59655i 0.988059 + 0.570456i 0.904693 0.426063i \(-0.140100\pi\)
0.0833652 + 0.996519i \(0.473433\pi\)
\(284\) 3.34433 5.79254i 0.198449 0.343724i
\(285\) −28.9519 23.4383i −1.71496 1.38837i
\(286\) 2.84262 + 14.5445i 0.168088 + 0.860035i
\(287\) −3.16418 5.84995i −0.186775 0.345312i
\(288\) −2.22889 + 2.00799i −0.131339 + 0.118322i
\(289\) −7.75517 13.4323i −0.456186 0.790138i
\(290\) −7.71125 + 13.3563i −0.452820 + 0.784308i
\(291\) −6.69399 1.05930i −0.392409 0.0620972i
\(292\) −1.31969 2.28578i −0.0772292 0.133765i
\(293\) 11.7362i 0.685634i 0.939402 + 0.342817i \(0.111381\pi\)
−0.939402 + 0.342817i \(0.888619\pi\)
\(294\) 11.8516 + 2.55707i 0.691202 + 0.149131i
\(295\) 4.94505 0.287912
\(296\) 6.13142 3.53998i 0.356382 0.205757i
\(297\) 17.9072 11.6393i 1.03908 0.675383i
\(298\) 0.986187 1.70813i 0.0571283 0.0989491i
\(299\) 3.09746 + 3.55587i 0.179131 + 0.205641i
\(300\) −0.914525 2.38146i −0.0528001 0.137494i
\(301\) 7.71832 4.17476i 0.444877 0.240629i
\(302\) 9.40094i 0.540963i
\(303\) 16.8879 20.8605i 0.970182 1.19840i
\(304\) 4.22658 7.32066i 0.242411 0.419869i
\(305\) −4.63544 + 8.02882i −0.265425 + 0.459729i
\(306\) −16.2696 5.28146i −0.930070 0.301921i
\(307\) 27.2408 1.55471 0.777357 0.629060i \(-0.216560\pi\)
0.777357 + 0.629060i \(0.216560\pi\)
\(308\) −9.26310 5.69681i −0.527814 0.324606i
\(309\) 21.4920 8.25334i 1.22264 0.469516i
\(310\) 0.00579695 0.00334687i 0.000329245 0.000190089i
\(311\) −1.45991 + 2.52863i −0.0827837 + 0.143386i −0.904445 0.426591i \(-0.859714\pi\)
0.821661 + 0.569977i \(0.193048\pi\)
\(312\) −0.225177 6.24094i −0.0127481 0.353323i
\(313\) 5.81374 3.35656i 0.328612 0.189724i −0.326613 0.945158i \(-0.605907\pi\)
0.655225 + 0.755434i \(0.272574\pi\)
\(314\) 7.30149i 0.412047i
\(315\) 15.3729 13.0944i 0.866163 0.737786i
\(316\) 14.1572 0.796404
\(317\) 7.72251 + 13.3758i 0.433740 + 0.751259i 0.997192 0.0748897i \(-0.0238605\pi\)
−0.563452 + 0.826149i \(0.690527\pi\)
\(318\) 1.37402 8.68281i 0.0770514 0.486908i
\(319\) 21.5777 + 12.4579i 1.20812 + 0.697509i
\(320\) 2.20332 1.27209i 0.123169 0.0711119i
\(321\) −23.0713 + 8.85982i −1.28772 + 0.494507i
\(322\) −3.45909 0.0961081i −0.192768 0.00535589i
\(323\) 48.1981 2.68182
\(324\) −8.21993 + 3.66506i −0.456663 + 0.203615i
\(325\) 5.02282 + 1.72375i 0.278616 + 0.0956163i
\(326\) −13.1037 7.56540i −0.725744 0.419009i
\(327\) −14.3329 11.6034i −0.792614 0.641669i
\(328\) 2.51379i 0.138801i
\(329\) 5.89952 9.59271i 0.325251 0.528863i
\(330\) −16.9085 + 6.49317i −0.930781 + 0.357437i
\(331\) −4.14357 + 2.39229i −0.227751 + 0.131492i −0.609534 0.792760i \(-0.708643\pi\)
0.381783 + 0.924252i \(0.375310\pi\)
\(332\) −9.63888 5.56501i −0.529002 0.305420i
\(333\) 20.7745 4.42162i 1.13844 0.242303i
\(334\) 21.0214 12.1367i 1.15024 0.664092i
\(335\) −8.25219 −0.450865
\(336\) 3.48026 + 2.98124i 0.189864 + 0.162640i
\(337\) 26.6494 1.45169 0.725843 0.687860i \(-0.241450\pi\)
0.725843 + 0.687860i \(0.241450\pi\)
\(338\) 10.2605 + 7.98261i 0.558098 + 0.434197i
\(339\) −0.231270 + 1.46146i −0.0125609 + 0.0793755i
\(340\) 12.5629 + 7.25317i 0.681317 + 0.393358i
\(341\) −0.00540703 0.00936526i −0.000292807 0.000507157i
\(342\) 18.8412 16.9739i 1.01882 0.917843i
\(343\) 1.54153 18.4560i 0.0832347 0.996530i
\(344\) 3.31665 0.178822
\(345\) −3.62650 + 4.47959i −0.195244 + 0.241173i
\(346\) −0.204681 + 0.354517i −0.0110037 + 0.0190590i
\(347\) 5.45892 + 3.15171i 0.293050 + 0.169193i 0.639317 0.768944i \(-0.279217\pi\)
−0.346266 + 0.938136i \(0.612551\pi\)
\(348\) −8.16053 6.60645i −0.437450 0.354143i
\(349\) −9.52826 −0.510036 −0.255018 0.966936i \(-0.582081\pi\)
−0.255018 + 0.966936i \(0.582081\pi\)
\(350\) −3.42749 + 1.85390i −0.183207 + 0.0990949i
\(351\) 5.13834 18.0166i 0.274264 0.961654i
\(352\) −2.05512 3.55958i −0.109538 0.189726i
\(353\) 14.3774 + 8.30082i 0.765234 + 0.441808i 0.831172 0.556016i \(-0.187671\pi\)
−0.0659376 + 0.997824i \(0.521004\pi\)
\(354\) −0.526195 + 3.32517i −0.0279670 + 0.176731i
\(355\) −14.7373 + 8.50856i −0.782172 + 0.451587i
\(356\) 3.83190i 0.203091i
\(357\) −4.79917 + 25.6843i −0.253999 + 1.35936i
\(358\) 23.6636i 1.25066i
\(359\) 8.18866 + 14.1832i 0.432181 + 0.748559i 0.997061 0.0766138i \(-0.0244109\pi\)
−0.564880 + 0.825173i \(0.691078\pi\)
\(360\) 7.46531 1.58890i 0.393456 0.0837426i
\(361\) −26.2280 + 45.4283i −1.38042 + 2.39096i
\(362\) −12.3190 + 7.11236i −0.647471 + 0.373817i
\(363\) 3.65982 + 9.53032i 0.192091 + 0.500212i
\(364\) −9.40947 + 1.56906i −0.493190 + 0.0822410i
\(365\) 6.71506i 0.351482i
\(366\) −4.90551 3.97131i −0.256415 0.207584i
\(367\) −26.9853 15.5800i −1.40862 0.813269i −0.413368 0.910564i \(-0.635648\pi\)
−0.995256 + 0.0972954i \(0.968981\pi\)
\(368\) −1.13269 0.653959i −0.0590456 0.0340900i
\(369\) 2.32848 7.17289i 0.121216 0.373406i
\(370\) −18.0127 −0.936434
\(371\) −13.4231 0.372949i −0.696891 0.0193626i
\(372\) 0.00163367 + 0.00425414i 8.47018e−5 + 0.000220567i
\(373\) −11.8848 20.5851i −0.615372 1.06585i −0.990319 0.138809i \(-0.955673\pi\)
0.374948 0.927046i \(-0.377661\pi\)
\(374\) 11.7179 20.2959i 0.605916 1.04948i
\(375\) 2.42939 15.3519i 0.125453 0.792771i
\(376\) 3.68624 2.12825i 0.190103 0.109756i
\(377\) 21.4506 4.19237i 1.10476 0.215918i
\(378\) 7.16918 + 11.7304i 0.368743 + 0.603348i
\(379\) 5.87885i 0.301976i −0.988536 0.150988i \(-0.951755\pi\)
0.988536 0.150988i \(-0.0482455\pi\)
\(380\) −18.6250 + 10.7532i −0.955445 + 0.551626i
\(381\) 20.6514 + 3.26801i 1.05800 + 0.167425i
\(382\) 13.8603 + 8.00228i 0.709157 + 0.409432i
\(383\) 12.8839 7.43851i 0.658336 0.380090i −0.133307 0.991075i \(-0.542560\pi\)
0.791643 + 0.610985i \(0.209226\pi\)
\(384\) 0.620929 + 1.61693i 0.0316867 + 0.0825134i
\(385\) 13.1628 + 24.3354i 0.670836 + 1.24025i
\(386\) 16.9566i 0.863068i
\(387\) 9.46379 + 3.07215i 0.481071 + 0.156166i
\(388\) −1.95644 + 3.38865i −0.0993229 + 0.172032i
\(389\) −26.8563 15.5055i −1.36167 0.786158i −0.371821 0.928305i \(-0.621266\pi\)
−0.989846 + 0.142146i \(0.954600\pi\)
\(390\) −7.44288 + 14.0372i −0.376885 + 0.710803i
\(391\) 7.45747i 0.377140i
\(392\) 3.83121 5.85849i 0.193505 0.295898i
\(393\) 10.7008 + 27.8652i 0.539782 + 1.40561i
\(394\) 1.28282 + 2.22190i 0.0646273 + 0.111938i
\(395\) −31.1928 18.0092i −1.56948 0.906140i
\(396\) −2.56695 12.0606i −0.128994 0.606067i
\(397\) 7.10552 + 12.3071i 0.356616 + 0.617677i 0.987393 0.158287i \(-0.0505972\pi\)
−0.630777 + 0.775964i \(0.717264\pi\)
\(398\) 21.6468i 1.08505i
\(399\) −29.4192 25.2009i −1.47280 1.26162i
\(400\) −1.47283 −0.0736416
\(401\) −19.1854 33.2301i −0.958073 1.65943i −0.727174 0.686453i \(-0.759167\pi\)
−0.230899 0.972978i \(-0.574167\pi\)
\(402\) 0.878102 5.54896i 0.0437958 0.276757i
\(403\) −0.00897256 0.00307923i −0.000446955 0.000153387i
\(404\) −7.74790 13.4198i −0.385473 0.667658i
\(405\) 22.7734 + 2.38117i 1.13162 + 0.118321i
\(406\) −8.40179 + 13.6615i −0.416974 + 0.678006i
\(407\) 29.1004i 1.44245i
\(408\) −6.21399 + 7.67576i −0.307639 + 0.380007i
\(409\) −2.09152 + 3.62262i −0.103419 + 0.179127i −0.913091 0.407755i \(-0.866312\pi\)
0.809672 + 0.586882i \(0.199645\pi\)
\(410\) −3.19776 + 5.53868i −0.157926 + 0.273536i
\(411\) −14.2207 + 17.5660i −0.701457 + 0.866467i
\(412\) 13.2919i 0.654846i
\(413\) 5.14050 + 0.142824i 0.252947 + 0.00702793i
\(414\) −2.62629 2.91521i −0.129075 0.143275i
\(415\) 14.1584 + 24.5230i 0.695007 + 1.20379i
\(416\) −3.41032 1.17036i −0.167204 0.0573817i
\(417\) 0.168754 1.06640i 0.00826392 0.0522219i
\(418\) 17.3723 + 30.0897i 0.849706 + 1.47173i
\(419\) −24.4059 −1.19231 −0.596154 0.802870i \(-0.703305\pi\)
−0.596154 + 0.802870i \(0.703305\pi\)
\(420\) −3.87574 10.9958i −0.189117 0.536541i
\(421\) 7.06979i 0.344560i −0.985048 0.172280i \(-0.944887\pi\)
0.985048 0.172280i \(-0.0551135\pi\)
\(422\) 3.50357 + 6.06837i 0.170551 + 0.295404i
\(423\) 12.4897 2.65829i 0.607272 0.129251i
\(424\) −4.39543 2.53770i −0.213461 0.123242i
\(425\) −4.19888 7.27268i −0.203676 0.352777i
\(426\) −4.15318 10.8151i −0.201222 0.523991i
\(427\) −5.05054 + 8.21226i −0.244413 + 0.397419i
\(428\) 14.2686i 0.689701i
\(429\) 22.6779 + 12.0244i 1.09490 + 0.580541i
\(430\) −7.30764 4.21907i −0.352406 0.203462i
\(431\) −1.83652 + 3.18094i −0.0884620 + 0.153221i −0.906861 0.421429i \(-0.861529\pi\)
0.818399 + 0.574650i \(0.194862\pi\)
\(432\) 0.274044 + 5.18892i 0.0131849 + 0.249652i
\(433\) 30.9079i 1.48534i −0.669658 0.742669i \(-0.733559\pi\)
0.669658 0.742669i \(-0.266441\pi\)
\(434\) 0.00612273 0.00331172i 0.000293900 0.000158968i
\(435\) 9.57629 + 24.9370i 0.459148 + 1.19564i
\(436\) −9.22052 + 5.32347i −0.441583 + 0.254948i
\(437\) 9.57483 + 5.52803i 0.458026 + 0.264441i
\(438\) −4.51536 0.714539i −0.215752 0.0341420i
\(439\) 31.8737 18.4023i 1.52125 0.878294i 0.521564 0.853212i \(-0.325349\pi\)
0.999685 0.0250815i \(-0.00798452\pi\)
\(440\) 10.4572i 0.498527i
\(441\) 16.3586 13.1679i 0.778983 0.627045i
\(442\) −3.94332 20.1763i −0.187565 0.959690i
\(443\) −31.8442 + 18.3852i −1.51296 + 0.873509i −0.513077 + 0.858342i \(0.671495\pi\)
−0.999885 + 0.0151669i \(0.995172\pi\)
\(444\) 1.91670 12.1121i 0.0909625 0.574816i
\(445\) 4.87452 8.44292i 0.231074 0.400233i
\(446\) 10.5791 + 18.3235i 0.500935 + 0.867645i
\(447\) −1.22470 3.18918i −0.0579265 0.150843i
\(448\) 2.32714 1.25873i 0.109947 0.0594693i
\(449\) 3.94653 0.186248 0.0931240 0.995655i \(-0.470315\pi\)
0.0931240 + 0.995655i \(0.470315\pi\)
\(450\) −4.20261 1.36426i −0.198113 0.0643117i
\(451\) 8.94802 + 5.16614i 0.421346 + 0.243264i
\(452\) 0.739822 + 0.427136i 0.0347983 + 0.0200908i
\(453\) −12.6556 10.2455i −0.594611 0.481374i
\(454\) 13.4666i 0.632017i
\(455\) 22.7281 + 8.51253i 1.06551 + 0.399074i
\(456\) −5.24882 13.6681i −0.245799 0.640069i
\(457\) 0.843279 0.486868i 0.0394469 0.0227747i −0.480147 0.877188i \(-0.659417\pi\)
0.519594 + 0.854413i \(0.326083\pi\)
\(458\) −1.12680 + 1.95167i −0.0526517 + 0.0911954i
\(459\) −24.8410 + 16.1463i −1.15948 + 0.753642i
\(460\) 1.66379 + 2.88177i 0.0775745 + 0.134363i
\(461\) 10.2088i 0.475471i 0.971330 + 0.237736i \(0.0764052\pi\)
−0.971330 + 0.237736i \(0.923595\pi\)
\(462\) −17.7643 + 6.26145i −0.826470 + 0.291309i
\(463\) 11.4435i 0.531824i −0.963997 0.265912i \(-0.914327\pi\)
0.963997 0.265912i \(-0.0856731\pi\)
\(464\) −5.24975 + 3.03094i −0.243713 + 0.140708i
\(465\) 0.00181214 0.0114514i 8.40360e−5 0.000531046i
\(466\) −1.12902 0.651840i −0.0523008 0.0301959i
\(467\) 12.8601 + 22.2744i 0.595097 + 1.03074i 0.993533 + 0.113542i \(0.0362196\pi\)
−0.398437 + 0.917196i \(0.630447\pi\)
\(468\) −8.64697 6.49845i −0.399707 0.300391i
\(469\) −8.57834 0.238342i −0.396111 0.0110056i
\(470\) −10.8293 −0.499518
\(471\) −9.82929 7.95741i −0.452910 0.366658i
\(472\) 1.68327 + 0.971837i 0.0774789 + 0.0447324i
\(473\) −6.81612 + 11.8059i −0.313405 + 0.542834i
\(474\) 15.4290 19.0584i 0.708676 0.875383i
\(475\) 12.4501 0.571250
\(476\) 12.8499 + 7.90269i 0.588974 + 0.362219i
\(477\) −10.1914 11.3125i −0.466631 0.517965i
\(478\) 1.75061 + 3.03215i 0.0800711 + 0.138687i
\(479\) −27.5828 15.9249i −1.26029 0.727629i −0.287160 0.957883i \(-0.592711\pi\)
−0.973131 + 0.230254i \(0.926044\pi\)
\(480\) 0.688764 4.35248i 0.0314376 0.198663i
\(481\) 16.7670 + 19.2484i 0.764511 + 0.877653i
\(482\) 13.1946 0.600996
\(483\) −3.89922 + 4.55190i −0.177420 + 0.207119i
\(484\) 5.89410 0.267914
\(485\) 8.62131 4.97752i 0.391474 0.226017i
\(486\) −4.02444 + 15.0600i −0.182552 + 0.683136i
\(487\) −17.8940 10.3311i −0.810854 0.468147i 0.0363981 0.999337i \(-0.488412\pi\)
−0.847252 + 0.531190i \(0.821745\pi\)
\(488\) −3.15576 + 1.82198i −0.142855 + 0.0824772i
\(489\) −24.4654 + 9.39516i −1.10636 + 0.424864i
\(490\) −15.8939 + 8.03450i −0.718013 + 0.362962i
\(491\) 9.08674i 0.410079i 0.978754 + 0.205039i \(0.0657322\pi\)
−0.978754 + 0.205039i \(0.934268\pi\)
\(492\) −3.38407 2.73961i −0.152566 0.123511i
\(493\) −29.9329 17.2818i −1.34811 0.778332i
\(494\) 28.8280 + 9.89327i 1.29703 + 0.445119i
\(495\) −9.68630 + 29.8387i −0.435367 + 1.34115i
\(496\) 0.00263100 0.000118136
\(497\) −15.5655 + 8.41920i −0.698207 + 0.377653i
\(498\) −17.9964 + 6.91096i −0.806438 + 0.309687i
\(499\) 14.4611 8.34913i 0.647368 0.373758i −0.140079 0.990140i \(-0.544736\pi\)
0.787447 + 0.616382i \(0.211402\pi\)
\(500\) −7.77148 4.48687i −0.347551 0.200659i
\(501\) 6.57135 41.5261i 0.293586 1.85525i
\(502\) −14.2179 24.6261i −0.634575 1.09912i
\(503\) −29.9262 −1.33434 −0.667171 0.744904i \(-0.732495\pi\)
−0.667171 + 0.744904i \(0.732495\pi\)
\(504\) 7.80626 1.43609i 0.347718 0.0639684i
\(505\) 39.4241i 1.75435i
\(506\) 4.65564 2.68793i 0.206968 0.119493i
\(507\) 21.9285 5.11301i 0.973877 0.227077i
\(508\) 6.03573 10.4542i 0.267792 0.463829i
\(509\) −29.2792 + 16.9043i −1.29778 + 0.749272i −0.980020 0.198900i \(-0.936263\pi\)
−0.317757 + 0.948172i \(0.602930\pi\)
\(510\) 23.4557 9.00741i 1.03863 0.398855i
\(511\) −0.193947 + 6.98046i −0.00857969 + 0.308798i
\(512\) 1.00000 0.0441942
\(513\) −2.31654 43.8628i −0.102278 1.93659i
\(514\) 9.54939 16.5400i 0.421206 0.729550i
\(515\) −16.9085 + 29.2864i −0.745077 + 1.29051i
\(516\) 3.61459 4.46488i 0.159124 0.196556i
\(517\) 17.4952i 0.769440i
\(518\) −18.7246 0.520247i −0.822711 0.0228583i
\(519\) 0.254185 + 0.661907i 0.0111575 + 0.0290545i
\(520\) 6.02522 + 6.91691i 0.264223 + 0.303326i
\(521\) −12.3261 + 21.3495i −0.540017 + 0.935338i 0.458885 + 0.888496i \(0.348249\pi\)
−0.998902 + 0.0468419i \(0.985084\pi\)
\(522\) −17.7872 + 3.78581i −0.778526 + 0.165700i
\(523\) −9.97765 + 5.76060i −0.436292 + 0.251893i −0.702024 0.712154i \(-0.747720\pi\)
0.265732 + 0.964047i \(0.414387\pi\)
\(524\) 17.2335 0.752847
\(525\) −1.23968 + 6.63454i −0.0541039 + 0.289555i
\(526\) 5.19445i 0.226489i
\(527\) 0.00750071 + 0.0129916i 0.000326736 + 0.000565923i
\(528\) −7.03165 1.11273i −0.306013 0.0484255i
\(529\) −10.6447 + 18.4371i −0.462812 + 0.801614i
\(530\) 6.45636 + 11.1827i 0.280446 + 0.485747i
\(531\) 3.90288 + 4.33224i 0.169371 + 0.188003i
\(532\) −19.6717 + 10.6402i −0.852878 + 0.461313i
\(533\) 8.89530 1.73852i 0.385298 0.0753037i
\(534\) 5.15852 + 4.17614i 0.223231 + 0.180719i
\(535\) 18.1510 31.4384i 0.784735 1.35920i
\(536\) −2.80901 1.62178i −0.121331 0.0700502i
\(537\) 31.8561 + 25.7894i 1.37469 + 1.11290i
\(538\) 6.20413 0.267479
\(539\) 12.9801 + 25.6774i 0.559094 + 1.10600i
\(540\) 5.99696 11.7815i 0.258068 0.506994i
\(541\) 15.5915 9.00176i 0.670331 0.387016i −0.125871 0.992047i \(-0.540173\pi\)
0.796202 + 0.605031i \(0.206839\pi\)
\(542\) −12.8489 + 22.2550i −0.551909 + 0.955935i
\(543\) −3.85094 + 24.3351i −0.165260 + 1.04432i
\(544\) 2.85089 + 4.93789i 0.122231 + 0.211710i
\(545\) 27.0877 1.16031
\(546\) −8.14248 + 14.3771i −0.348466 + 0.615282i
\(547\) −31.6765 −1.35439 −0.677194 0.735804i \(-0.736804\pi\)
−0.677194 + 0.735804i \(0.736804\pi\)
\(548\) 6.52427 + 11.3004i 0.278703 + 0.482728i
\(549\) −10.6924 + 2.27575i −0.456340 + 0.0971266i
\(550\) 3.02685 5.24266i 0.129065 0.223548i
\(551\) 44.3770 25.6211i 1.89052 1.09149i
\(552\) −2.11481 + 0.812125i −0.0900121 + 0.0345663i
\(553\) −31.9055 19.6219i −1.35676 0.834407i
\(554\) 24.3161 1.03309
\(555\) −19.6308 + 24.2487i −0.833281 + 1.02930i
\(556\) −0.539835 0.311674i −0.0228941 0.0132179i
\(557\) −14.7789 + 25.5978i −0.626201 + 1.08461i 0.362106 + 0.932137i \(0.382058\pi\)
−0.988307 + 0.152475i \(0.951276\pi\)
\(558\) 0.00750736 + 0.00243705i 0.000317812 + 0.000103169i
\(559\) 2.29377 + 11.7363i 0.0970163 + 0.496392i
\(560\) −6.72866 0.186950i −0.284338 0.00790009i
\(561\) −14.5519 37.8938i −0.614383 1.59988i
\(562\) 11.3607 + 19.6774i 0.479224 + 0.830040i
\(563\) −11.5996 + 20.0912i −0.488866 + 0.846741i −0.999918 0.0128088i \(-0.995923\pi\)
0.511052 + 0.859550i \(0.329256\pi\)
\(564\) 1.15233 7.28186i 0.0485217 0.306622i
\(565\) −1.08671 1.88224i −0.0457182 0.0791863i
\(566\) 19.1931i 0.806747i
\(567\) 23.6047 + 3.13303i 0.991306 + 0.131575i
\(568\) −6.68865 −0.280650
\(569\) 15.1314 8.73610i 0.634340 0.366236i −0.148091 0.988974i \(-0.547313\pi\)
0.782431 + 0.622738i \(0.213980\pi\)
\(570\) −5.82224 + 36.7923i −0.243867 + 1.54106i
\(571\) 4.98953 8.64212i 0.208805 0.361662i −0.742533 0.669809i \(-0.766376\pi\)
0.951339 + 0.308148i \(0.0997091\pi\)
\(572\) 11.1746 9.73404i 0.467234 0.407001i
\(573\) 25.8782 9.93770i 1.08108 0.415153i
\(574\) −3.48412 + 5.66523i −0.145424 + 0.236462i
\(575\) 1.92634i 0.0803341i
\(576\) 2.85342 + 0.926282i 0.118892 + 0.0385951i
\(577\) 8.91246 15.4368i 0.371031 0.642644i −0.618694 0.785632i \(-0.712338\pi\)
0.989724 + 0.142988i \(0.0456712\pi\)
\(578\) −7.75517 + 13.4323i −0.322572 + 0.558712i
\(579\) 22.8270 + 18.4799i 0.948659 + 0.767997i
\(580\) 15.4225 0.640385
\(581\) 14.0097 + 25.9012i 0.581219 + 1.07456i
\(582\) 2.42962 + 6.32682i 0.100711 + 0.262255i
\(583\) 18.0663 10.4306i 0.748229 0.431990i
\(584\) −1.31969 + 2.28578i −0.0546093 + 0.0945860i
\(585\) 10.7855 + 25.3179i 0.445924 + 1.04677i
\(586\) 10.1638 5.86808i 0.419863 0.242408i
\(587\) 47.7903i 1.97252i −0.165206 0.986259i \(-0.552829\pi\)
0.165206 0.986259i \(-0.447171\pi\)
\(588\) −3.71134 11.5424i −0.153053 0.475999i
\(589\) −0.0222403 −0.000916396
\(590\) −2.47253 4.28254i −0.101792 0.176309i
\(591\) 4.38919 + 0.694573i 0.180547 + 0.0285709i
\(592\) −6.13142 3.53998i −0.252000 0.145492i
\(593\) 8.78037 5.06935i 0.360566 0.208173i −0.308763 0.951139i \(-0.599915\pi\)
0.669329 + 0.742966i \(0.266582\pi\)
\(594\) −19.0335 9.68838i −0.780956 0.397519i
\(595\) −18.2595 33.7584i −0.748568 1.38396i
\(596\) −1.97237 −0.0807916
\(597\) −29.1410 23.5914i −1.19266 0.965531i
\(598\) 1.53074 4.46042i 0.0625966 0.182400i
\(599\) −10.0365 5.79458i −0.410081 0.236760i 0.280744 0.959783i \(-0.409419\pi\)
−0.690824 + 0.723023i \(0.742752\pi\)
\(600\) −1.60514 + 1.98273i −0.0655296 + 0.0809447i
\(601\) 4.44714i 0.181403i 0.995878 + 0.0907013i \(0.0289109\pi\)
−0.995878 + 0.0907013i \(0.971089\pi\)
\(602\) −7.47461 4.59688i −0.304642 0.187355i
\(603\) −6.51304 7.22955i −0.265232 0.294410i
\(604\) −8.14145 + 4.70047i −0.331271 + 0.191259i
\(605\) −12.9866 7.49782i −0.527981 0.304830i
\(606\) −26.5097 4.19505i −1.07688 0.170412i
\(607\) 5.35667 3.09268i 0.217421 0.125528i −0.387335 0.921939i \(-0.626604\pi\)
0.604755 + 0.796411i \(0.293271\pi\)
\(608\) −8.45317 −0.342821
\(609\) 9.23454 + 26.1992i 0.374202 + 1.06165i
\(610\) 9.27088 0.375367
\(611\) 10.0804 + 11.5722i 0.407810 + 0.468162i
\(612\) 3.56091 + 16.7306i 0.143941 + 0.676294i
\(613\) −19.9940 11.5435i −0.807549 0.466239i 0.0385548 0.999256i \(-0.487725\pi\)
−0.846104 + 0.533018i \(0.821058\pi\)
\(614\) −13.6204 23.5912i −0.549674 0.952064i
\(615\) 3.97117 + 10.3411i 0.160133 + 0.416993i
\(616\) −0.302028 + 10.8705i −0.0121690 + 0.437984i
\(617\) 14.5000 0.583749 0.291874 0.956457i \(-0.405721\pi\)
0.291874 + 0.956457i \(0.405721\pi\)
\(618\) −17.8936 14.4860i −0.719787 0.582711i
\(619\) −11.4323 + 19.8013i −0.459503 + 0.795882i −0.998935 0.0461472i \(-0.985306\pi\)
0.539432 + 0.842029i \(0.318639\pi\)
\(620\) −0.00579695 0.00334687i −0.000232811 0.000134414i
\(621\) −6.78669 + 0.358427i −0.272340 + 0.0143832i
\(622\) 2.91981 0.117074
\(623\) 5.31103 8.63582i 0.212782 0.345987i
\(624\) −5.29222 + 3.31548i −0.211858 + 0.132725i
\(625\) 15.0975 + 26.1496i 0.603899 + 1.04598i
\(626\) −5.81374 3.35656i −0.232364 0.134155i
\(627\) 59.4397 + 9.40612i 2.37379 + 0.375644i
\(628\) −6.32327 + 3.65074i −0.252326 + 0.145681i
\(629\) 40.3684i 1.60959i
\(630\) −19.0265 6.76608i −0.758035 0.269567i
\(631\) 10.1877i 0.405568i −0.979224 0.202784i \(-0.935001\pi\)
0.979224 0.202784i \(-0.0649989\pi\)
\(632\) −7.07859 12.2605i −0.281571 0.487696i
\(633\) 11.9876 + 1.89699i 0.476463 + 0.0753985i
\(634\) 7.72251 13.3758i 0.306700 0.531220i
\(635\) −26.5973 + 15.3559i −1.05548 + 0.609382i
\(636\) −8.20655 + 3.15147i −0.325411 + 0.124964i
\(637\) 23.3805 + 9.50541i 0.926369 + 0.376618i
\(638\) 24.9158i 0.986427i
\(639\) −19.0855 6.19558i −0.755012 0.245093i
\(640\) −2.20332 1.27209i −0.0870939 0.0502837i
\(641\) −24.5592 14.1793i −0.970030 0.560047i −0.0707844 0.997492i \(-0.522550\pi\)
−0.899245 + 0.437445i \(0.855884\pi\)
\(642\) 19.2085 + 15.5504i 0.758099 + 0.613727i
\(643\) 7.46124 0.294243 0.147121 0.989118i \(-0.452999\pi\)
0.147121 + 0.989118i \(0.452999\pi\)
\(644\) 1.64631 + 3.04372i 0.0648739 + 0.119939i
\(645\) −13.6438 + 5.23949i −0.537226 + 0.206305i
\(646\) −24.0991 41.7408i −0.948165 1.64227i
\(647\) 12.5324 21.7068i 0.492701 0.853382i −0.507264 0.861791i \(-0.669343\pi\)
0.999965 + 0.00840826i \(0.00267646\pi\)
\(648\) 7.28400 + 5.28614i 0.286143 + 0.207659i
\(649\) −6.91866 + 3.99449i −0.271581 + 0.156797i
\(650\) −1.01860 5.21177i −0.0399529 0.204422i
\(651\) 0.00221451 0.0118517i 8.67933e−5 0.000464503i
\(652\) 15.1308i 0.592568i
\(653\) 9.06026 5.23094i 0.354555 0.204703i −0.312134 0.950038i \(-0.601044\pi\)
0.666690 + 0.745335i \(0.267711\pi\)
\(654\) −2.88236 + 18.2144i −0.112709 + 0.712239i
\(655\) −37.9708 21.9225i −1.48364 0.856582i
\(656\) −2.17701 + 1.25689i −0.0849978 + 0.0490735i
\(657\) −5.88291 + 5.29987i −0.229514 + 0.206768i
\(658\) −11.2573 0.312775i −0.438855 0.0121932i
\(659\) 24.8852i 0.969389i −0.874684 0.484694i \(-0.838931\pi\)
0.874684 0.484694i \(-0.161069\pi\)
\(660\) 14.0775 + 11.3966i 0.547966 + 0.443612i
\(661\) −24.9458 + 43.2074i −0.970280 + 1.68057i −0.275574 + 0.961280i \(0.588868\pi\)
−0.694706 + 0.719294i \(0.744465\pi\)
\(662\) 4.14357 + 2.39229i 0.161044 + 0.0929790i
\(663\) −31.4590 16.6803i −1.22177 0.647811i
\(664\) 11.1300i 0.431929i
\(665\) 56.8785 + 1.58032i 2.20565 + 0.0612823i
\(666\) −14.2165 15.7805i −0.550878 0.611481i
\(667\) −3.96423 6.86624i −0.153496 0.265862i
\(668\) −21.0214 12.1367i −0.813343 0.469584i
\(669\) 36.1967 + 5.72799i 1.39944 + 0.221457i
\(670\) 4.12609 + 7.14660i 0.159405 + 0.276097i
\(671\) 14.9776i 0.578203i
\(672\) 0.841696 4.50461i 0.0324691 0.173769i
\(673\) 14.9301 0.575513 0.287756 0.957704i \(-0.407091\pi\)
0.287756 + 0.957704i \(0.407091\pi\)
\(674\) −13.3247 23.0791i −0.513249 0.888973i
\(675\) −6.41671 + 4.17075i −0.246979 + 0.160532i
\(676\) 1.78289 12.8772i 0.0685728 0.495275i
\(677\) −17.9807 31.1435i −0.691056 1.19694i −0.971492 0.237071i \(-0.923813\pi\)
0.280437 0.959873i \(-0.409521\pi\)
\(678\) 1.38129 0.530443i 0.0530483 0.0203715i
\(679\) 9.10582 4.92524i 0.349449 0.189013i
\(680\) 14.5063i 0.556293i
\(681\) 18.1287 + 14.6763i 0.694694 + 0.562397i
\(682\) −0.00540703 + 0.00936526i −0.000207046 + 0.000358614i
\(683\) −13.5825 + 23.5256i −0.519721 + 0.900184i 0.480016 + 0.877260i \(0.340631\pi\)
−0.999737 + 0.0229240i \(0.992702\pi\)
\(684\) −24.1204 7.83001i −0.922268 0.299388i
\(685\) 33.1978i 1.26842i
\(686\) −16.7541 + 7.89299i −0.639675 + 0.301356i
\(687\) 1.39932 + 3.64389i 0.0533874 + 0.139023i
\(688\) −1.65832 2.87230i −0.0632230 0.109505i
\(689\) 5.94006 17.3087i 0.226298 0.659410i
\(690\) 5.69269 + 0.900847i 0.216717 + 0.0342947i
\(691\) −15.9012 27.5418i −0.604912 1.04774i −0.992065 0.125723i \(-0.959875\pi\)
0.387153 0.922015i \(-0.373458\pi\)
\(692\) 0.409361 0.0155616
\(693\) −10.9309 + 30.7383i −0.415232 + 1.16765i
\(694\) 6.30342i 0.239275i
\(695\) 0.792954 + 1.37344i 0.0300785 + 0.0520974i
\(696\) −1.64109 + 10.3705i −0.0622052 + 0.393091i
\(697\) −12.4128 7.16654i −0.470169 0.271452i
\(698\) 4.76413 + 8.25172i 0.180325 + 0.312332i
\(699\) −2.10795 + 0.809493i −0.0797301 + 0.0306178i
\(700\) 3.31927 + 2.04135i 0.125457 + 0.0771557i
\(701\) 24.3611i 0.920107i 0.887891 + 0.460053i \(0.152170\pi\)
−0.887891 + 0.460053i \(0.847830\pi\)
\(702\) −18.1720 + 4.55836i −0.685858 + 0.172044i
\(703\) 51.8299 + 29.9240i 1.95480 + 1.12861i
\(704\) −2.05512 + 3.55958i −0.0774553 + 0.134157i
\(705\) −11.8021 + 14.5784i −0.444493 + 0.549055i
\(706\) 16.6016i 0.624811i
\(707\) −1.13866 + 40.9822i −0.0428236 + 1.54130i
\(708\) 3.14278 1.20688i 0.118113 0.0453575i
\(709\) −37.1207 + 21.4317i −1.39410 + 0.804883i −0.993766 0.111487i \(-0.964439\pi\)
−0.400332 + 0.916370i \(0.631105\pi\)
\(710\) 14.7373 + 8.50856i 0.553079 + 0.319320i
\(711\) −8.84153 41.5411i −0.331583 1.55791i
\(712\) 3.31853 1.91595i 0.124367 0.0718034i
\(713\) 0.00344114i 0.000128872i
\(714\) 24.6429 8.68596i 0.922236 0.325064i
\(715\) −37.0038 + 7.23213i −1.38386 + 0.270466i
\(716\) 20.4933 11.8318i 0.765871 0.442176i
\(717\) 5.98976 + 0.947857i 0.223692 + 0.0353984i
\(718\) 8.18866 14.1832i 0.305598 0.529311i
\(719\) −14.3834 24.9128i −0.536410 0.929090i −0.999094 0.0425664i \(-0.986447\pi\)
0.462683 0.886524i \(-0.346887\pi\)
\(720\) −5.10869 5.67070i −0.190390 0.211334i
\(721\) −18.4226 + 29.9555i −0.686094 + 1.11560i
\(722\) 52.4560 1.95221
\(723\) 14.3799 17.7626i 0.534794 0.660597i
\(724\) 12.3190 + 7.11236i 0.457831 + 0.264329i
\(725\) −7.73200 4.46407i −0.287159 0.165791i
\(726\) 6.42359 7.93466i 0.238402 0.294483i
\(727\) 9.23311i 0.342437i 0.985233 + 0.171219i \(0.0547704\pi\)
−0.985233 + 0.171219i \(0.945230\pi\)
\(728\) 6.06358 + 7.36431i 0.224731 + 0.272939i
\(729\) 15.8879 + 21.8306i 0.588439 + 0.808541i
\(730\) 5.81541 3.35753i 0.215238 0.124268i
\(731\) 9.45541 16.3772i 0.349721 0.605734i
\(732\) −0.986500 + 6.23395i −0.0364621 + 0.230414i
\(733\) −19.7916 34.2800i −0.731018 1.26616i −0.956449 0.291901i \(-0.905712\pi\)
0.225431 0.974259i \(-0.427621\pi\)
\(734\) 31.1600i 1.15014i
\(735\) −6.50563 + 30.1527i −0.239964 + 1.11220i
\(736\) 1.30792i 0.0482105i
\(737\) 11.5457 6.66591i 0.425291 0.245542i
\(738\) −7.37615 + 1.56993i −0.271520 + 0.0577898i
\(739\) 25.0159 + 14.4429i 0.920224 + 0.531291i 0.883706 0.468042i \(-0.155040\pi\)
0.0365171 + 0.999333i \(0.488374\pi\)
\(740\) 9.00633 + 15.5994i 0.331079 + 0.573446i
\(741\) 44.7360 28.0263i 1.64342 1.02957i
\(742\) 6.38855 + 11.8112i 0.234531 + 0.433603i
\(743\) 14.2072 0.521211 0.260605 0.965445i \(-0.416078\pi\)
0.260605 + 0.965445i \(0.416078\pi\)
\(744\) 0.00286736 0.00354187i 0.000105122 0.000129851i
\(745\) 4.34577 + 2.50903i 0.159217 + 0.0919238i
\(746\) −11.8848 + 20.5851i −0.435133 + 0.753673i
\(747\) −10.3095 + 31.7586i −0.377206 + 1.16199i
\(748\) −23.4357 −0.856895
\(749\) 19.7764 32.1567i 0.722613 1.17498i
\(750\) −14.5099 + 5.57206i −0.529825 + 0.203463i
\(751\) −8.05134 13.9453i −0.293798 0.508873i 0.680907 0.732370i \(-0.261586\pi\)
−0.974704 + 0.223498i \(0.928253\pi\)
\(752\) −3.68624 2.12825i −0.134423 0.0776093i
\(753\) −48.6468 7.69818i −1.77279 0.280537i
\(754\) −14.3560 16.4806i −0.522815 0.600187i
\(755\) 23.9176 0.870452
\(756\) 6.57425 12.0739i 0.239103 0.439124i
\(757\) 24.7260 0.898684 0.449342 0.893360i \(-0.351659\pi\)
0.449342 + 0.893360i \(0.351659\pi\)
\(758\) −5.09123 + 2.93942i −0.184922 + 0.106765i
\(759\) 1.45536 9.19683i 0.0528264 0.333824i
\(760\) 18.6250 + 10.7532i 0.675601 + 0.390059i
\(761\) −2.32242 + 1.34085i −0.0841876 + 0.0486057i −0.541503 0.840699i \(-0.682144\pi\)
0.457315 + 0.889305i \(0.348811\pi\)
\(762\) −7.49552 19.5186i −0.271534 0.707085i
\(763\) 28.1583 + 0.782355i 1.01940 + 0.0283232i
\(764\) 16.0046i 0.579024i
\(765\) 13.4370 41.3927i 0.485814 1.49656i
\(766\) −12.8839 7.43851i −0.465514 0.268764i
\(767\) −2.27480 + 6.62854i −0.0821384 + 0.239343i
\(768\) 1.08983 1.34620i 0.0393260 0.0485769i
\(769\) 39.1298 1.41106 0.705528 0.708682i \(-0.250710\pi\)
0.705528 + 0.708682i \(0.250710\pi\)
\(770\) 14.4937 23.5670i 0.522316 0.849295i
\(771\) −11.8590 30.8813i −0.427091 1.11216i
\(772\) 14.6848 8.47830i 0.528519 0.305141i
\(773\) −24.0664 13.8947i −0.865607 0.499758i 0.000279226 1.00000i \(-0.499911\pi\)
−0.865886 + 0.500242i \(0.833244\pi\)
\(774\) −2.07133 9.73196i −0.0744526 0.349808i
\(775\) 0.00193751 + 0.00335587i 6.95976e−5 + 0.000120547i
\(776\) 3.91287 0.140464
\(777\) −21.1070 + 24.6401i −0.757211 + 0.883959i
\(778\) 31.0109i 1.11180i
\(779\) 18.4026 10.6247i 0.659341 0.380671i
\(780\) 15.8780 0.572890i 0.568525 0.0205128i
\(781\) 13.7460 23.8088i 0.491870 0.851945i
\(782\) −6.45836 + 3.72873i −0.230950 + 0.133339i
\(783\) −14.2887 + 28.0711i −0.510635 + 1.00318i
\(784\) −6.98920 0.388679i −0.249614 0.0138814i
\(785\) 18.5763 0.663016
\(786\) 18.7816 23.1997i 0.669917 0.827507i
\(787\) 22.3703 38.7465i 0.797415 1.38116i −0.123879 0.992297i \(-0.539534\pi\)
0.921294 0.388866i \(-0.127133\pi\)
\(788\) 1.28282 2.22190i 0.0456984 0.0791520i
\(789\) 6.99279 + 5.66109i 0.248950 + 0.201540i
\(790\) 36.0184i 1.28148i
\(791\) −1.07530 1.98802i −0.0382332 0.0706857i
\(792\) −9.16129 + 8.25334i −0.325532 + 0.293270i
\(793\) −8.62977 9.90692i −0.306452 0.351805i
\(794\) 7.10552 12.3071i 0.252166 0.436763i
\(795\) 22.0906 + 3.49576i 0.783473 + 0.123982i
\(796\) −18.7467 + 10.8234i −0.664458 + 0.383625i
\(797\) 16.6004 0.588016 0.294008 0.955803i \(-0.405011\pi\)
0.294008 + 0.955803i \(0.405011\pi\)
\(798\) −7.11500 + 38.0783i −0.251868 + 1.34796i
\(799\) 24.2696i 0.858598i
\(800\) 0.736416 + 1.27551i 0.0260362 + 0.0450961i
\(801\) 11.2439 2.39312i 0.397282 0.0845569i
\(802\) −19.1854 + 33.2301i −0.677460 + 1.17339i
\(803\) −5.42426 9.39509i −0.191418 0.331546i
\(804\) −5.24459 + 2.01402i −0.184963 + 0.0710291i
\(805\) 0.244516 8.80054i 0.00861805 0.310178i
\(806\) 0.00181959 + 0.00931008i 6.40922e−5 + 0.000327933i
\(807\) 6.76147 8.35202i 0.238015 0.294005i
\(808\) −7.74790 + 13.4198i −0.272570 + 0.472106i
\(809\) −11.8831 6.86068i −0.417786 0.241209i 0.276344 0.961059i \(-0.410877\pi\)
−0.694130 + 0.719850i \(0.744211\pi\)
\(810\) −9.32456 20.9130i −0.327632 0.734807i
\(811\) 27.2852 0.958114 0.479057 0.877784i \(-0.340979\pi\)
0.479057 + 0.877784i \(0.340979\pi\)
\(812\) 16.0321 + 0.445438i 0.562615 + 0.0156318i
\(813\) 15.9566 + 41.5516i 0.559622 + 1.45728i
\(814\) 25.2016 14.5502i 0.883317 0.509983i
\(815\) 19.2477 33.3380i 0.674218 1.16778i
\(816\) 9.75440 + 1.54360i 0.341472 + 0.0540367i
\(817\) 14.0181 + 24.2800i 0.490431 + 0.849451i
\(818\) 4.18304 0.146257
\(819\) 10.4805 + 26.6300i 0.366218 + 0.930529i
\(820\) 6.39552 0.223341
\(821\) 25.2745 + 43.7767i 0.882085 + 1.52782i 0.849018 + 0.528364i \(0.177194\pi\)
0.0330672 + 0.999453i \(0.489472\pi\)
\(822\) 22.3230 + 3.53253i 0.778603 + 0.123211i
\(823\) 22.1516 38.3677i 0.772156 1.33741i −0.164224 0.986423i \(-0.552512\pi\)
0.936379 0.350990i \(-0.114155\pi\)
\(824\) −11.5111 + 6.64596i −0.401009 + 0.231523i
\(825\) −3.75892 9.78838i −0.130869 0.340788i
\(826\) −2.44656 4.52321i −0.0851266 0.157383i
\(827\) −19.9119 −0.692405 −0.346203 0.938160i \(-0.612529\pi\)
−0.346203 + 0.938160i \(0.612529\pi\)
\(828\) −1.21150 + 3.73204i −0.0421026 + 0.129697i
\(829\) 7.87052 + 4.54405i 0.273354 + 0.157821i 0.630411 0.776261i \(-0.282886\pi\)
−0.357057 + 0.934083i \(0.616220\pi\)
\(830\) 14.1584 24.5230i 0.491444 0.851206i
\(831\) 26.5005 32.7345i 0.919293 1.13555i
\(832\) 0.691594 + 3.53860i 0.0239767 + 0.122679i
\(833\) −18.0062 35.6200i −0.623878 1.23416i
\(834\) −1.00791 + 0.387055i −0.0349010 + 0.0134026i
\(835\) 30.8780 + 53.4822i 1.06858 + 1.85083i
\(836\) 17.3723 30.0897i 0.600833 1.04067i
\(837\) 0.0114625 0.00745045i 0.000396203 0.000257525i
\(838\) 12.2030 + 21.1362i 0.421544 + 0.730136i
\(839\) 27.0968i 0.935486i 0.883865 + 0.467743i \(0.154933\pi\)
−0.883865 + 0.467743i \(0.845067\pi\)
\(840\) −7.58479 + 8.85440i −0.261700 + 0.305506i
\(841\) −7.74648 −0.267120
\(842\) −6.12262 + 3.53489i −0.210999 + 0.121821i
\(843\) 38.8710 + 6.15120i 1.33879 + 0.211858i
\(844\) 3.50357 6.06837i 0.120598 0.208882i
\(845\) −20.3092 + 26.1045i −0.698657 + 0.898023i
\(846\) −8.54702 9.48728i −0.293853 0.326179i
\(847\) −13.2833 8.16924i −0.456420 0.280698i
\(848\) 5.07540i 0.174290i
\(849\) −25.8378 20.9173i −0.886752 0.717880i
\(850\) −4.19888 + 7.27268i −0.144021 + 0.249451i
\(851\) 4.63000 8.01940i 0.158715 0.274902i
\(852\) −7.28952 + 9.00429i −0.249735 + 0.308482i
\(853\) −22.7608 −0.779314 −0.389657 0.920960i \(-0.627406\pi\)
−0.389657 + 0.920960i \(0.627406\pi\)
\(854\) 9.63730 + 0.267764i 0.329782 + 0.00916271i
\(855\) 43.1846 + 47.9353i 1.47688 + 1.63935i
\(856\) 12.3570 7.13432i 0.422354 0.243846i
\(857\) 12.6132 21.8466i 0.430857 0.746267i −0.566090 0.824343i \(-0.691545\pi\)
0.996947 + 0.0780766i \(0.0248779\pi\)
\(858\) −0.925532 25.6518i −0.0315972 0.875737i
\(859\) −30.6299 + 17.6842i −1.04508 + 0.603377i −0.921268 0.388928i \(-0.872845\pi\)
−0.123812 + 0.992306i \(0.539512\pi\)
\(860\) 8.43814i 0.287738i
\(861\) 3.82945 + 10.8645i 0.130507 + 0.370261i
\(862\) 3.67304 0.125104
\(863\) 4.16054 + 7.20627i 0.141627 + 0.245304i 0.928109 0.372308i \(-0.121433\pi\)
−0.786483 + 0.617612i \(0.788100\pi\)
\(864\) 4.35672 2.83179i 0.148218 0.0963394i
\(865\) −0.901955 0.520744i −0.0306674 0.0177058i
\(866\) −26.7670 + 15.4540i −0.909581 + 0.525147i
\(867\) 9.63082 + 25.0790i 0.327080 + 0.851729i
\(868\) −0.00592940 0.00364658i −0.000201257 0.000123773i
\(869\) 58.1895 1.97394
\(870\) 16.8080 20.7618i 0.569843 0.703892i
\(871\) 3.79614 11.0616i 0.128627 0.374807i
\(872\) 9.22052 + 5.32347i 0.312246 + 0.180275i
\(873\) 11.1651 + 3.62442i 0.377880 + 0.122668i
\(874\) 11.0561i 0.373977i
\(875\) 11.2955 + 20.8832i 0.381857 + 0.705980i
\(876\) 1.63887 + 4.26769i 0.0553724 + 0.144192i
\(877\) 6.00709 3.46819i 0.202845 0.117113i −0.395137 0.918622i \(-0.629303\pi\)
0.597982 + 0.801510i \(0.295969\pi\)
\(878\) −31.8737 18.4023i −1.07569 0.621047i
\(879\) 3.17724 20.0778i 0.107166 0.677207i
\(880\) 9.05619 5.22859i 0.305284 0.176256i
\(881\) 10.2056 0.343835 0.171917 0.985111i \(-0.445004\pi\)
0.171917 + 0.985111i \(0.445004\pi\)
\(882\) −19.5831 7.58303i −0.659397 0.255334i
\(883\) −16.1358 −0.543013 −0.271506 0.962437i \(-0.587522\pi\)
−0.271506 + 0.962437i \(0.587522\pi\)
\(884\) −15.5016 + 13.5032i −0.521374 + 0.454161i
\(885\) −8.45981 1.33873i −0.284373 0.0450010i
\(886\) 31.8442 + 18.3852i 1.06983 + 0.617664i
\(887\) −12.1918 21.1167i −0.409359 0.709031i 0.585459 0.810702i \(-0.300914\pi\)
−0.994818 + 0.101671i \(0.967581\pi\)
\(888\) −11.4478 + 4.39615i −0.384162 + 0.147525i
\(889\) −28.0920 + 15.1947i −0.942176 + 0.509613i
\(890\) −9.74904 −0.326789
\(891\) −33.7859 + 15.0643i −1.13187 + 0.504673i
\(892\) 10.5791 18.3235i 0.354214 0.613517i
\(893\) 31.1604 + 17.9904i 1.04274 + 0.602027i
\(894\) −2.14956 + 2.65522i −0.0718920 + 0.0888037i
\(895\) −60.2045 −2.01241
\(896\) −2.25366 1.38600i −0.0752896 0.0463031i
\(897\) −4.33638 6.92180i −0.144787 0.231112i
\(898\) −1.97326 3.41779i −0.0658486 0.114053i
\(899\) 0.0138121 + 0.00797443i 0.000460660 + 0.000265962i
\(900\) 0.919822 + 4.32169i 0.0306607 + 0.144056i
\(901\) −25.0618 + 14.4694i −0.834929 + 0.482046i
\(902\) 10.3323i 0.344027i
\(903\) −14.3344 + 5.05251i −0.477020 + 0.168137i
\(904\) 0.854272i 0.0284127i
\(905\) −18.0951 31.3416i −0.601501 1.04183i
\(906\) −2.54504 + 16.0828i −0.0845533 + 0.534315i
\(907\) −9.19556 + 15.9272i −0.305334 + 0.528853i −0.977336 0.211696i \(-0.932101\pi\)
0.672002 + 0.740549i \(0.265435\pi\)
\(908\) 11.6624 6.73328i 0.387030 0.223452i
\(909\) −34.5385 + 31.1155i −1.14557 + 1.03204i
\(910\) −3.99196 23.9393i −0.132332 0.793581i
\(911\) 29.8085i 0.987598i −0.869576 0.493799i \(-0.835608\pi\)
0.869576 0.493799i \(-0.164392\pi\)
\(912\) −9.21254 + 11.3797i −0.305058 + 0.376819i
\(913\) −39.6182 22.8736i −1.31117 0.757004i
\(914\) −0.843279 0.486868i −0.0278932 0.0161041i
\(915\) 10.1037 12.4805i 0.334019 0.412592i
\(916\) 2.25359 0.0744607
\(917\) −38.8384 23.8856i −1.28256 0.788772i
\(918\) 26.4036 + 13.4399i 0.871448 + 0.443581i
\(919\) 5.75307 + 9.96461i 0.189776 + 0.328702i 0.945176 0.326563i \(-0.105890\pi\)
−0.755399 + 0.655265i \(0.772557\pi\)
\(920\) 1.66379 2.88177i 0.0548535 0.0950090i
\(921\) −46.6025 7.37468i −1.53561 0.243004i
\(922\) 8.84108 5.10440i 0.291166 0.168105i
\(923\) −4.62583 23.6685i −0.152261 0.779057i
\(924\) 14.3047 + 12.2536i 0.470591 + 0.403114i
\(925\) 10.4276i 0.342857i
\(926\) −9.91036 + 5.72175i −0.325675 + 0.188028i
\(927\) −39.0021 + 8.30115i −1.28100 + 0.272645i
\(928\) 5.24975 + 3.03094i 0.172331 + 0.0994956i
\(929\) −26.9309 + 15.5486i −0.883576 + 0.510133i −0.871836 0.489798i \(-0.837070\pi\)
−0.0117399 + 0.999931i \(0.503737\pi\)
\(930\) −0.0108233 + 0.00415634i −0.000354909 + 0.000136292i
\(931\) 59.0809 + 3.28556i 1.93630 + 0.107680i
\(932\) 1.30368i 0.0427034i
\(933\) 3.18211 3.93066i 0.104178 0.128684i
\(934\) 12.8601 22.2744i 0.420797 0.728842i
\(935\) 51.6364 + 29.8123i 1.68869 + 0.974966i
\(936\) −1.30433 + 10.7377i −0.0426335 + 0.350973i
\(937\) 39.5487i 1.29200i −0.763338 0.645999i \(-0.776441\pi\)
0.763338 0.645999i \(-0.223559\pi\)
\(938\) 4.08276 + 7.54823i 0.133307 + 0.246459i
\(939\) −10.8546 + 4.16838i −0.354227 + 0.136030i
\(940\) 5.41464 + 9.37843i 0.176606 + 0.305891i
\(941\) −2.74724 1.58612i −0.0895573 0.0517059i 0.454553 0.890720i \(-0.349799\pi\)
−0.544110 + 0.839014i \(0.683133\pi\)
\(942\) −1.97667 + 12.4911i −0.0644035 + 0.406983i
\(943\) −1.64392 2.84735i −0.0535333 0.0927223i
\(944\) 1.94367i 0.0632612i
\(945\) −29.8443 + 18.2397i −0.970834 + 0.593336i
\(946\) 13.6322 0.443222
\(947\) −4.60358 7.97363i −0.149596 0.259108i 0.781482 0.623928i \(-0.214464\pi\)
−0.931078 + 0.364819i \(0.881131\pi\)
\(948\) −24.2196 3.83266i −0.786615 0.124479i
\(949\) −9.00114 3.08904i −0.292189 0.100274i
\(950\) −6.22505 10.7821i −0.201967 0.349817i
\(951\) −9.59027 24.9734i −0.310986 0.809820i
\(952\) 0.418977 15.0797i 0.0135791 0.488735i
\(953\) 31.9720i 1.03567i −0.855479 0.517837i \(-0.826737\pi\)
0.855479 0.517837i \(-0.173263\pi\)
\(954\) −4.70125 + 14.4823i −0.152209 + 0.468880i
\(955\) −20.3592 + 35.2632i −0.658808 + 1.14109i
\(956\) 1.75061 3.03215i 0.0566188 0.0980666i
\(957\) −33.5418 27.1541i −1.08425 0.877768i
\(958\) 31.8499i 1.02902i
\(959\) 0.958829 34.5099i 0.0309622 1.11438i
\(960\) −4.11374 + 1.57975i −0.132770 + 0.0509863i
\(961\) 15.5000 + 26.8468i 0.500000 + 0.866025i
\(962\) 8.28612 24.1449i 0.267155 0.778462i
\(963\) 41.8681 8.91114i 1.34918 0.287157i
\(964\) −6.59729 11.4268i −0.212484 0.368034i
\(965\) −43.1406 −1.38874
\(966\) 5.89167 + 1.10087i 0.189561 + 0.0354199i
\(967\) 8.89193i 0.285945i −0.989727 0.142973i \(-0.954334\pi\)
0.989727 0.142973i \(-0.0456661\pi\)
\(968\) −2.94705 5.10444i −0.0947218 0.164063i
\(969\) −82.4556 13.0483i −2.64885 0.419171i
\(970\) −8.62131 4.97752i −0.276814 0.159818i
\(971\) 10.8088 + 18.7213i 0.346870 + 0.600796i 0.985692 0.168559i \(-0.0539113\pi\)
−0.638822 + 0.769355i \(0.720578\pi\)
\(972\) 15.0546 4.04474i 0.482876 0.129735i
\(973\) 0.784626 + 1.45062i 0.0251540 + 0.0465048i
\(974\) 20.6622i 0.662060i
\(975\) −8.12620 4.30871i −0.260247 0.137989i
\(976\) 3.15576 + 1.82198i 0.101014 + 0.0583202i
\(977\) −22.6382 + 39.2106i −0.724261 + 1.25446i 0.235016 + 0.971991i \(0.424486\pi\)
−0.959277 + 0.282466i \(0.908848\pi\)
\(978\) 20.3691 + 16.4900i 0.651333 + 0.527294i
\(979\) 15.7501i 0.503374i
\(980\) 14.9050 + 9.74726i 0.476123 + 0.311365i
\(981\) 21.3790 + 23.7309i 0.682578 + 0.757669i
\(982\) 7.86934 4.54337i 0.251121 0.144985i
\(983\) 26.7378 + 15.4371i 0.852802 + 0.492365i 0.861595 0.507596i \(-0.169466\pi\)
−0.00879326 + 0.999961i \(0.502799\pi\)
\(984\) −0.680538 + 4.30050i −0.0216947 + 0.137095i
\(985\) −5.65291 + 3.26371i −0.180117 + 0.103990i
\(986\) 34.5636i 1.10073i
\(987\) −12.6896 + 14.8137i −0.403915 + 0.471526i
\(988\) −5.84616 29.9124i −0.185991 0.951640i
\(989\) 3.75674 2.16895i 0.119457 0.0689687i
\(990\) 30.6842 6.53079i 0.975209 0.207562i
\(991\) 8.78463 15.2154i 0.279053 0.483334i −0.692097 0.721805i \(-0.743313\pi\)
0.971150 + 0.238471i \(0.0766462\pi\)
\(992\) −0.00131550 0.00227852i −4.17672e−5 7.23430e-5i
\(993\) 7.73631 2.97089i 0.245504 0.0942782i
\(994\) 15.0740 + 9.27049i 0.478117 + 0.294042i
\(995\) 55.0732 1.74594
\(996\) 14.9833 + 12.1299i 0.474763 + 0.384350i
\(997\) −25.9590 14.9874i −0.822129 0.474656i 0.0290211 0.999579i \(-0.490761\pi\)
−0.851150 + 0.524922i \(0.824094\pi\)
\(998\) −14.4611 8.34913i −0.457759 0.264287i
\(999\) −36.7373 + 1.94022i −1.16232 + 0.0613858i
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.bg.a.311.1 36
3.2 odd 2 546.2.bg.b.311.6 yes 36
7.5 odd 6 inner 546.2.bg.a.467.6 yes 36
13.12 even 2 546.2.bg.b.311.1 yes 36
21.5 even 6 546.2.bg.b.467.1 yes 36
39.38 odd 2 inner 546.2.bg.a.311.6 yes 36
91.12 odd 6 546.2.bg.b.467.6 yes 36
273.194 even 6 inner 546.2.bg.a.467.1 yes 36
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
546.2.bg.a.311.1 36 1.1 even 1 trivial
546.2.bg.a.311.6 yes 36 39.38 odd 2 inner
546.2.bg.a.467.1 yes 36 273.194 even 6 inner
546.2.bg.a.467.6 yes 36 7.5 odd 6 inner
546.2.bg.b.311.1 yes 36 13.12 even 2
546.2.bg.b.311.6 yes 36 3.2 odd 2
546.2.bg.b.467.1 yes 36 21.5 even 6
546.2.bg.b.467.6 yes 36 91.12 odd 6