Properties

Label 195.2.v.a.49.1
Level $195$
Weight $2$
Character 195.49
Analytic conductor $1.557$
Analytic rank $0$
Dimension $32$
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] = [195,2,Mod(4,195)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(195, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 3, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("195.4");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 195 = 3 \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 195.v (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: \(1.55708283941\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(16\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 49.1
Character \(\chi\) \(=\) 195.49
Dual form 195.2.v.a.4.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.36408 - 2.36265i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-2.72141 + 4.71362i) q^{4} +(-1.91068 + 1.16160i) q^{5} +(-2.36265 - 1.36408i) q^{6} +(-1.86649 + 3.23285i) q^{7} +9.39252 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(-1.36408 - 2.36265i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-2.72141 + 4.71362i) q^{4} +(-1.91068 + 1.16160i) q^{5} +(-2.36265 - 1.36408i) q^{6} +(-1.86649 + 3.23285i) q^{7} +9.39252 q^{8} +(0.500000 - 0.866025i) q^{9} +(5.35076 + 2.92975i) q^{10} +(-2.02671 + 1.17012i) q^{11} +5.44282i q^{12} +(-1.39527 + 3.32464i) q^{13} +10.1841 q^{14} +(-1.07390 + 1.96131i) q^{15} +(-7.36930 - 12.7640i) q^{16} +(-2.29853 - 1.32706i) q^{17} -2.72815 q^{18} +(-1.93887 - 1.11941i) q^{19} +(-0.275594 - 12.1674i) q^{20} +3.73298i q^{21} +(5.52918 + 3.19227i) q^{22} +(-0.387679 + 0.223827i) q^{23} +(8.13416 - 4.69626i) q^{24} +(2.30138 - 4.43888i) q^{25} +(9.75821 - 1.23852i) q^{26} -1.00000i q^{27} +(-10.1590 - 17.5958i) q^{28} +(0.774666 + 1.34176i) q^{29} +(6.09877 - 0.138139i) q^{30} +3.17845i q^{31} +(-10.7121 + 18.5538i) q^{32} +(-1.17012 + 2.02671i) q^{33} +7.24083i q^{34} +(-0.189018 - 8.34505i) q^{35} +(2.72141 + 4.71362i) q^{36} +(-0.797986 - 1.38215i) q^{37} +6.10781i q^{38} +(0.453977 + 3.57686i) q^{39} +(-17.9461 + 10.9103i) q^{40} +(-0.866750 + 0.500418i) q^{41} +(8.81972 - 5.09207i) q^{42} +(10.1144 + 5.83954i) q^{43} -12.7375i q^{44} +(0.0506345 + 2.23549i) q^{45} +(1.05765 + 0.610634i) q^{46} -8.06550 q^{47} +(-12.7640 - 7.36930i) q^{48} +(-3.46757 - 6.00600i) q^{49} +(-13.6268 + 0.617616i) q^{50} -2.65411 q^{51} +(-11.8740 - 15.6245i) q^{52} +8.33803i q^{53} +(-2.36265 + 1.36408i) q^{54} +(2.51318 - 4.58996i) q^{55} +(-17.5310 + 30.3647i) q^{56} -2.23881 q^{57} +(2.11341 - 3.66053i) q^{58} +(-4.61091 - 2.66211i) q^{59} +(-6.32236 - 10.3995i) q^{60} +(0.317815 - 0.550471i) q^{61} +(7.50957 - 4.33565i) q^{62} +(1.86649 + 3.23285i) q^{63} +28.9710 q^{64} +(-1.19598 - 7.97306i) q^{65} +6.38455 q^{66} +(5.06226 + 8.76809i) q^{67} +(12.5105 - 7.22292i) q^{68} +(-0.223827 + 0.387679i) q^{69} +(-19.4586 + 11.8299i) q^{70} +(3.28689 + 1.89769i) q^{71} +(4.69626 - 8.13416i) q^{72} +0.0493999 q^{73} +(-2.17703 + 3.77072i) q^{74} +(-0.226386 - 4.99487i) q^{75} +(10.5529 - 6.09271i) q^{76} -8.73609i q^{77} +(7.83160 - 5.95169i) q^{78} +1.93513 q^{79} +(28.9070 + 15.8277i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(2.36463 + 1.36522i) q^{82} +7.63279 q^{83} +(-17.5958 - 10.1590i) q^{84} +(5.93326 - 0.134390i) q^{85} -31.8623i q^{86} +(1.34176 + 0.774666i) q^{87} +(-19.0360 + 10.9904i) q^{88} +(-4.56030 + 2.63289i) q^{89} +(5.21262 - 3.16902i) q^{90} +(-8.14381 - 10.7161i) q^{91} -2.43650i q^{92} +(1.58923 + 2.75262i) q^{93} +(11.0020 + 19.0559i) q^{94} +(5.00485 - 0.113361i) q^{95} +21.4241i q^{96} +(6.24133 - 10.8103i) q^{97} +(-9.46005 + 16.3853i) q^{98} +2.34025i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q - 20 q^{4} + 16 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 32 q - 20 q^{4} + 16 q^{9} + 2 q^{10} - 12 q^{11} + 8 q^{14} - 6 q^{15} - 28 q^{16} - 30 q^{20} - 4 q^{25} + 52 q^{26} - 24 q^{29} + 4 q^{30} - 2 q^{35} + 20 q^{36} + 4 q^{40} - 36 q^{41} + 12 q^{45} - 48 q^{46} - 28 q^{49} + 54 q^{50} - 40 q^{51} + 24 q^{55} - 56 q^{56} + 84 q^{59} - 32 q^{61} + 136 q^{64} + 20 q^{65} + 8 q^{66} - 24 q^{69} + 12 q^{71} + 40 q^{74} - 16 q^{75} + 48 q^{76} - 104 q^{79} + 66 q^{80} - 16 q^{81} - 48 q^{84} - 54 q^{85} - 48 q^{89} + 4 q^{90} + 12 q^{91} - 8 q^{94} + 12 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/195\mathbb{Z}\right)^\times\).

\(n\) \(106\) \(131\) \(157\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.36408 2.36265i −0.964547 1.67065i −0.710826 0.703368i \(-0.751679\pi\)
−0.253722 0.967277i \(-0.581655\pi\)
\(3\) 0.866025 0.500000i 0.500000 0.288675i
\(4\) −2.72141 + 4.71362i −1.36070 + 2.35681i
\(5\) −1.91068 + 1.16160i −0.854481 + 0.519482i
\(6\) −2.36265 1.36408i −0.964547 0.556882i
\(7\) −1.86649 + 3.23285i −0.705467 + 1.22190i 0.261056 + 0.965324i \(0.415929\pi\)
−0.966523 + 0.256581i \(0.917404\pi\)
\(8\) 9.39252 3.32076
\(9\) 0.500000 0.866025i 0.166667 0.288675i
\(10\) 5.35076 + 2.92975i 1.69206 + 0.926469i
\(11\) −2.02671 + 1.17012i −0.611077 + 0.352805i −0.773387 0.633934i \(-0.781439\pi\)
0.162310 + 0.986740i \(0.448106\pi\)
\(12\) 5.44282i 1.57121i
\(13\) −1.39527 + 3.32464i −0.386979 + 0.922088i
\(14\) 10.1841 2.72182
\(15\) −1.07390 + 1.96131i −0.277279 + 0.506409i
\(16\) −7.36930 12.7640i −1.84233 3.19100i
\(17\) −2.29853 1.32706i −0.557475 0.321859i 0.194656 0.980872i \(-0.437641\pi\)
−0.752132 + 0.659013i \(0.770974\pi\)
\(18\) −2.72815 −0.643032
\(19\) −1.93887 1.11941i −0.444806 0.256809i 0.260828 0.965385i \(-0.416005\pi\)
−0.705634 + 0.708576i \(0.749338\pi\)
\(20\) −0.275594 12.1674i −0.0616247 2.72071i
\(21\) 3.73298i 0.814603i
\(22\) 5.52918 + 3.19227i 1.17883 + 0.680595i
\(23\) −0.387679 + 0.223827i −0.0808367 + 0.0466711i −0.539874 0.841746i \(-0.681528\pi\)
0.459037 + 0.888417i \(0.348195\pi\)
\(24\) 8.13416 4.69626i 1.66038 0.958620i
\(25\) 2.30138 4.43888i 0.460276 0.887776i
\(26\) 9.75821 1.23852i 1.91374 0.242893i
\(27\) 1.00000i 0.192450i
\(28\) −10.1590 17.5958i −1.91986 3.32530i
\(29\) 0.774666 + 1.34176i 0.143852 + 0.249159i 0.928944 0.370220i \(-0.120718\pi\)
−0.785092 + 0.619379i \(0.787384\pi\)
\(30\) 6.09877 0.138139i 1.11348 0.0252205i
\(31\) 3.17845i 0.570867i 0.958399 + 0.285433i \(0.0921375\pi\)
−0.958399 + 0.285433i \(0.907862\pi\)
\(32\) −10.7121 + 18.5538i −1.89364 + 3.27988i
\(33\) −1.17012 + 2.02671i −0.203692 + 0.352805i
\(34\) 7.24083i 1.24179i
\(35\) −0.189018 8.34505i −0.0319498 1.41057i
\(36\) 2.72141 + 4.71362i 0.453568 + 0.785603i
\(37\) −0.797986 1.38215i −0.131188 0.227224i 0.792947 0.609291i \(-0.208546\pi\)
−0.924135 + 0.382067i \(0.875213\pi\)
\(38\) 6.10781i 0.990818i
\(39\) 0.453977 + 3.57686i 0.0726945 + 0.572755i
\(40\) −17.9461 + 10.9103i −2.83753 + 1.72508i
\(41\) −0.866750 + 0.500418i −0.135364 + 0.0781522i −0.566153 0.824301i \(-0.691569\pi\)
0.430789 + 0.902453i \(0.358235\pi\)
\(42\) 8.81972 5.09207i 1.36091 0.785723i
\(43\) 10.1144 + 5.83954i 1.54243 + 0.890522i 0.998685 + 0.0512703i \(0.0163270\pi\)
0.543744 + 0.839251i \(0.317006\pi\)
\(44\) 12.7375i 1.92026i
\(45\) 0.0506345 + 2.23549i 0.00754814 + 0.333248i
\(46\) 1.05765 + 0.610634i 0.155942 + 0.0900330i
\(47\) −8.06550 −1.17647 −0.588237 0.808689i \(-0.700178\pi\)
−0.588237 + 0.808689i \(0.700178\pi\)
\(48\) −12.7640 7.36930i −1.84233 1.06367i
\(49\) −3.46757 6.00600i −0.495367 0.858000i
\(50\) −13.6268 + 0.617616i −1.92712 + 0.0873441i
\(51\) −2.65411 −0.371650
\(52\) −11.8740 15.6245i −1.64662 2.16672i
\(53\) 8.33803i 1.14532i 0.819794 + 0.572658i \(0.194088\pi\)
−0.819794 + 0.572658i \(0.805912\pi\)
\(54\) −2.36265 + 1.36408i −0.321516 + 0.185627i
\(55\) 2.51318 4.58996i 0.338878 0.618909i
\(56\) −17.5310 + 30.3647i −2.34268 + 4.05765i
\(57\) −2.23881 −0.296538
\(58\) 2.11341 3.66053i 0.277504 0.480651i
\(59\) −4.61091 2.66211i −0.600289 0.346577i 0.168866 0.985639i \(-0.445989\pi\)
−0.769155 + 0.639062i \(0.779323\pi\)
\(60\) −6.32236 10.3995i −0.816214 1.34257i
\(61\) 0.317815 0.550471i 0.0406920 0.0704806i −0.844962 0.534826i \(-0.820377\pi\)
0.885654 + 0.464346i \(0.153710\pi\)
\(62\) 7.50957 4.33565i 0.953716 0.550628i
\(63\) 1.86649 + 3.23285i 0.235156 + 0.407301i
\(64\) 28.9710 3.62138
\(65\) −1.19598 7.97306i −0.148342 0.988936i
\(66\) 6.38455 0.785884
\(67\) 5.06226 + 8.76809i 0.618453 + 1.07119i 0.989768 + 0.142685i \(0.0455737\pi\)
−0.371315 + 0.928507i \(0.621093\pi\)
\(68\) 12.5105 7.22292i 1.51712 0.875908i
\(69\) −0.223827 + 0.387679i −0.0269456 + 0.0466711i
\(70\) −19.4586 + 11.8299i −2.32575 + 1.41394i
\(71\) 3.28689 + 1.89769i 0.390082 + 0.225214i 0.682196 0.731170i \(-0.261025\pi\)
−0.292114 + 0.956384i \(0.594359\pi\)
\(72\) 4.69626 8.13416i 0.553460 0.958620i
\(73\) 0.0493999 0.00578182 0.00289091 0.999996i \(-0.499080\pi\)
0.00289091 + 0.999996i \(0.499080\pi\)
\(74\) −2.17703 + 3.77072i −0.253074 + 0.438338i
\(75\) −0.226386 4.99487i −0.0261408 0.576758i
\(76\) 10.5529 6.09271i 1.21050 0.698882i
\(77\) 8.73609i 0.995570i
\(78\) 7.83160 5.95169i 0.886754 0.673897i
\(79\) 1.93513 0.217720 0.108860 0.994057i \(-0.465280\pi\)
0.108860 + 0.994057i \(0.465280\pi\)
\(80\) 28.9070 + 15.8277i 3.23190 + 1.76959i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 2.36463 + 1.36522i 0.261129 + 0.150763i
\(83\) 7.63279 0.837807 0.418904 0.908031i \(-0.362415\pi\)
0.418904 + 0.908031i \(0.362415\pi\)
\(84\) −17.5958 10.1590i −1.91986 1.10843i
\(85\) 5.93326 0.134390i 0.643552 0.0145766i
\(86\) 31.8623i 3.43580i
\(87\) 1.34176 + 0.774666i 0.143852 + 0.0830529i
\(88\) −19.0360 + 10.9904i −2.02924 + 1.17158i
\(89\) −4.56030 + 2.63289i −0.483391 + 0.279086i −0.721828 0.692072i \(-0.756698\pi\)
0.238438 + 0.971158i \(0.423365\pi\)
\(90\) 5.21262 3.16902i 0.549458 0.334044i
\(91\) −8.14381 10.7161i −0.853703 1.12335i
\(92\) 2.43650i 0.254022i
\(93\) 1.58923 + 2.75262i 0.164795 + 0.285433i
\(94\) 11.0020 + 19.0559i 1.13476 + 1.96547i
\(95\) 5.00485 0.113361i 0.513487 0.0116306i
\(96\) 21.4241i 2.18659i
\(97\) 6.24133 10.8103i 0.633711 1.09762i −0.353075 0.935595i \(-0.614864\pi\)
0.986787 0.162025i \(-0.0518026\pi\)
\(98\) −9.46005 + 16.3853i −0.955609 + 1.65516i
\(99\) 2.34025i 0.235204i
\(100\) 14.6602 + 22.9278i 1.46602 + 2.29278i
\(101\) 0.348954 + 0.604407i 0.0347222 + 0.0601407i 0.882864 0.469628i \(-0.155612\pi\)
−0.848142 + 0.529769i \(0.822279\pi\)
\(102\) 3.62041 + 6.27074i 0.358474 + 0.620896i
\(103\) 3.92434i 0.386676i 0.981132 + 0.193338i \(0.0619315\pi\)
−0.981132 + 0.193338i \(0.938069\pi\)
\(104\) −13.1051 + 31.2267i −1.28506 + 3.06203i
\(105\) −4.33622 7.13252i −0.423172 0.696063i
\(106\) 19.6998 11.3737i 1.91342 1.10471i
\(107\) 1.40633 0.811946i 0.135955 0.0784938i −0.430480 0.902600i \(-0.641656\pi\)
0.566435 + 0.824106i \(0.308322\pi\)
\(108\) 4.71362 + 2.72141i 0.453568 + 0.261868i
\(109\) 17.6077i 1.68651i −0.537512 0.843256i \(-0.680636\pi\)
0.537512 0.843256i \(-0.319364\pi\)
\(110\) −14.2726 + 0.323278i −1.36084 + 0.0308234i
\(111\) −1.38215 0.797986i −0.131188 0.0757415i
\(112\) 55.0189 5.19880
\(113\) −16.2305 9.37069i −1.52684 0.881520i −0.999492 0.0318695i \(-0.989854\pi\)
−0.527346 0.849651i \(-0.676813\pi\)
\(114\) 3.05391 + 5.28952i 0.286025 + 0.495409i
\(115\) 0.480734 0.877989i 0.0448286 0.0818729i
\(116\) −8.43272 −0.782959
\(117\) 2.18158 + 2.87066i 0.201688 + 0.265393i
\(118\) 14.5253i 1.33716i
\(119\) 8.58036 4.95387i 0.786561 0.454121i
\(120\) −10.0866 + 18.4217i −0.920776 + 1.68166i
\(121\) −2.76162 + 4.78327i −0.251057 + 0.434843i
\(122\) −1.73409 −0.156997
\(123\) −0.500418 + 0.866750i −0.0451212 + 0.0781522i
\(124\) −14.9820 8.64986i −1.34542 0.776780i
\(125\) 0.758998 + 11.1545i 0.0678869 + 0.997693i
\(126\) 5.09207 8.81972i 0.453637 0.785723i
\(127\) −10.7726 + 6.21958i −0.955916 + 0.551898i −0.894914 0.446239i \(-0.852763\pi\)
−0.0610024 + 0.998138i \(0.519430\pi\)
\(128\) −18.0946 31.3407i −1.59935 2.77016i
\(129\) 11.6791 1.02829
\(130\) −17.2061 + 13.7015i −1.50908 + 1.20170i
\(131\) −5.54798 −0.484730 −0.242365 0.970185i \(-0.577923\pi\)
−0.242365 + 0.970185i \(0.577923\pi\)
\(132\) −6.36877 11.0310i −0.554330 0.960128i
\(133\) 7.23775 4.17872i 0.627592 0.362341i
\(134\) 13.8106 23.9207i 1.19305 2.06643i
\(135\) 1.16160 + 1.91068i 0.0999744 + 0.164445i
\(136\) −21.5890 12.4644i −1.85124 1.06881i
\(137\) 6.77644 11.7371i 0.578951 1.00277i −0.416650 0.909067i \(-0.636796\pi\)
0.995600 0.0937045i \(-0.0298709\pi\)
\(138\) 1.22127 0.103961
\(139\) −2.70422 + 4.68385i −0.229369 + 0.397279i −0.957621 0.288030i \(-0.907000\pi\)
0.728252 + 0.685309i \(0.240333\pi\)
\(140\) 39.8498 + 21.8193i 3.36792 + 1.84407i
\(141\) −6.98492 + 4.03275i −0.588237 + 0.339619i
\(142\) 10.3544i 0.868918i
\(143\) −1.06242 8.37073i −0.0888439 0.699995i
\(144\) −14.7386 −1.22822
\(145\) −3.03872 1.66382i −0.252352 0.138173i
\(146\) −0.0673852 0.116715i −0.00557684 0.00965937i
\(147\) −6.00600 3.46757i −0.495367 0.286000i
\(148\) 8.68658 0.714033
\(149\) 12.7018 + 7.33339i 1.04057 + 0.600775i 0.919995 0.391929i \(-0.128192\pi\)
0.120577 + 0.992704i \(0.461525\pi\)
\(150\) −11.4923 + 7.34826i −0.938344 + 0.599983i
\(151\) 12.3287i 1.00329i 0.865073 + 0.501646i \(0.167272\pi\)
−0.865073 + 0.501646i \(0.832728\pi\)
\(152\) −18.2108 10.5140i −1.47709 0.852801i
\(153\) −2.29853 + 1.32706i −0.185825 + 0.107286i
\(154\) −20.6403 + 11.9167i −1.66324 + 0.960275i
\(155\) −3.69208 6.07300i −0.296555 0.487795i
\(156\) −18.0954 7.59421i −1.44879 0.608024i
\(157\) 24.7850i 1.97806i −0.147709 0.989031i \(-0.547190\pi\)
0.147709 0.989031i \(-0.452810\pi\)
\(158\) −2.63967 4.57204i −0.210001 0.363732i
\(159\) 4.16902 + 7.22095i 0.330625 + 0.572658i
\(160\) −1.08480 47.8935i −0.0857609 3.78631i
\(161\) 1.67108i 0.131700i
\(162\) −1.36408 + 2.36265i −0.107172 + 0.185627i
\(163\) −7.96570 + 13.7970i −0.623922 + 1.08066i 0.364827 + 0.931075i \(0.381128\pi\)
−0.988748 + 0.149589i \(0.952205\pi\)
\(164\) 5.44737i 0.425368i
\(165\) −0.118497 5.23161i −0.00922500 0.407280i
\(166\) −10.4117 18.0336i −0.808105 1.39968i
\(167\) 12.7158 + 22.0244i 0.983977 + 1.70430i 0.646399 + 0.763000i \(0.276274\pi\)
0.337578 + 0.941298i \(0.390392\pi\)
\(168\) 35.0621i 2.70510i
\(169\) −9.10643 9.27755i −0.700494 0.713658i
\(170\) −8.41093 13.8349i −0.645089 1.06109i
\(171\) −1.93887 + 1.11941i −0.148269 + 0.0856030i
\(172\) −55.0507 + 31.7835i −4.19758 + 2.42347i
\(173\) 11.7189 + 6.76594i 0.890975 + 0.514405i 0.874261 0.485456i \(-0.161346\pi\)
0.0167136 + 0.999860i \(0.494680\pi\)
\(174\) 4.22681i 0.320434i
\(175\) 10.0548 + 15.7251i 0.760068 + 1.18871i
\(176\) 29.8709 + 17.2460i 2.25161 + 1.29997i
\(177\) −5.32422 −0.400193
\(178\) 12.4412 + 7.18293i 0.932507 + 0.538383i
\(179\) 5.88270 + 10.1891i 0.439694 + 0.761572i 0.997666 0.0682881i \(-0.0217537\pi\)
−0.557972 + 0.829860i \(0.688420\pi\)
\(180\) −10.6751 5.84502i −0.795672 0.435662i
\(181\) 13.2944 0.988163 0.494081 0.869416i \(-0.335505\pi\)
0.494081 + 0.869416i \(0.335505\pi\)
\(182\) −14.2096 + 33.8586i −1.05329 + 2.50976i
\(183\) 0.635629i 0.0469871i
\(184\) −3.64129 + 2.10230i −0.268439 + 0.154984i
\(185\) 3.13020 + 1.71391i 0.230137 + 0.126009i
\(186\) 4.33565 7.50957i 0.317905 0.550628i
\(187\) 6.21128 0.454214
\(188\) 21.9495 38.0177i 1.60083 2.77272i
\(189\) 3.23285 + 1.86649i 0.235156 + 0.135767i
\(190\) −7.09483 11.6701i −0.514713 0.846636i
\(191\) −8.30162 + 14.3788i −0.600684 + 1.04042i 0.392033 + 0.919951i \(0.371772\pi\)
−0.992718 + 0.120465i \(0.961562\pi\)
\(192\) 25.0896 14.4855i 1.81069 1.04540i
\(193\) 6.56697 + 11.3743i 0.472701 + 0.818742i 0.999512 0.0312407i \(-0.00994585\pi\)
−0.526811 + 0.849982i \(0.676613\pi\)
\(194\) −34.0546 −2.44498
\(195\) −5.02227 6.30688i −0.359652 0.451645i
\(196\) 37.7467 2.69619
\(197\) 8.29927 + 14.3748i 0.591298 + 1.02416i 0.994058 + 0.108853i \(0.0347178\pi\)
−0.402759 + 0.915306i \(0.631949\pi\)
\(198\) 5.52918 3.19227i 0.392942 0.226865i
\(199\) −7.70000 + 13.3368i −0.545839 + 0.945420i 0.452715 + 0.891655i \(0.350455\pi\)
−0.998554 + 0.0537648i \(0.982878\pi\)
\(200\) 21.6158 41.6923i 1.52847 2.94809i
\(201\) 8.76809 + 5.06226i 0.618453 + 0.357064i
\(202\) 0.952000 1.64891i 0.0669825 0.116017i
\(203\) −5.78362 −0.405931
\(204\) 7.22292 12.5105i 0.505706 0.875908i
\(205\) 1.07479 1.96295i 0.0750669 0.137099i
\(206\) 9.27183 5.35309i 0.645999 0.372968i
\(207\) 0.447654i 0.0311141i
\(208\) 52.7179 6.69099i 3.65533 0.463936i
\(209\) 5.23937 0.362415
\(210\) −10.9367 + 19.9743i −0.754705 + 1.37836i
\(211\) 2.80652 + 4.86103i 0.193209 + 0.334647i 0.946312 0.323255i \(-0.104777\pi\)
−0.753103 + 0.657902i \(0.771444\pi\)
\(212\) −39.3023 22.6912i −2.69929 1.55844i
\(213\) 3.79537 0.260055
\(214\) −3.83669 2.21511i −0.262271 0.151422i
\(215\) −26.1085 + 0.591364i −1.78059 + 0.0403307i
\(216\) 9.39252i 0.639080i
\(217\) −10.2755 5.93255i −0.697544 0.402727i
\(218\) −41.6008 + 24.0182i −2.81756 + 1.62672i
\(219\) 0.0427816 0.0246999i 0.00289091 0.00166907i
\(220\) 14.7959 + 24.3373i 0.997539 + 1.64082i
\(221\) 7.61906 5.79017i 0.512513 0.389489i
\(222\) 4.35406i 0.292225i
\(223\) −9.04102 15.6595i −0.605431 1.04864i −0.991983 0.126370i \(-0.959667\pi\)
0.386552 0.922268i \(-0.373666\pi\)
\(224\) −39.9879 69.2610i −2.67180 4.62770i
\(225\) −2.69349 4.21249i −0.179566 0.280833i
\(226\) 51.1293i 3.40107i
\(227\) 4.23521 7.33560i 0.281101 0.486881i −0.690555 0.723280i \(-0.742634\pi\)
0.971656 + 0.236399i \(0.0759671\pi\)
\(228\) 6.09271 10.5529i 0.403500 0.698882i
\(229\) 23.6883i 1.56537i −0.622419 0.782684i \(-0.713850\pi\)
0.622419 0.782684i \(-0.286150\pi\)
\(230\) −2.73014 + 0.0618382i −0.180020 + 0.00407749i
\(231\) −4.36805 7.56568i −0.287396 0.497785i
\(232\) 7.27606 + 12.6025i 0.477697 + 0.827396i
\(233\) 4.75242i 0.311341i −0.987809 0.155671i \(-0.950246\pi\)
0.987809 0.155671i \(-0.0497539\pi\)
\(234\) 3.80652 9.07012i 0.248840 0.592932i
\(235\) 15.4106 9.36886i 1.00527 0.611157i
\(236\) 25.0963 14.4894i 1.63363 0.943177i
\(237\) 1.67588 0.967567i 0.108860 0.0628502i
\(238\) −23.4085 13.5149i −1.51735 0.876042i
\(239\) 13.2798i 0.859002i 0.903066 + 0.429501i \(0.141310\pi\)
−0.903066 + 0.429501i \(0.858690\pi\)
\(240\) 32.9481 0.746282i 2.12679 0.0481723i
\(241\) 8.62590 + 4.98016i 0.555643 + 0.320801i 0.751395 0.659853i \(-0.229381\pi\)
−0.195752 + 0.980653i \(0.562715\pi\)
\(242\) 15.0683 0.968624
\(243\) −0.866025 0.500000i −0.0555556 0.0320750i
\(244\) 1.72981 + 2.99611i 0.110739 + 0.191806i
\(245\) 13.6020 + 7.44762i 0.868998 + 0.475811i
\(246\) 2.73043 0.174086
\(247\) 6.42686 4.88415i 0.408932 0.310771i
\(248\) 29.8537i 1.89571i
\(249\) 6.61019 3.81639i 0.418904 0.241854i
\(250\) 25.3190 17.0089i 1.60131 1.07574i
\(251\) −9.95334 + 17.2397i −0.628249 + 1.08816i 0.359654 + 0.933086i \(0.382895\pi\)
−0.987903 + 0.155073i \(0.950439\pi\)
\(252\) −20.3179 −1.27991
\(253\) 0.523810 0.907266i 0.0329317 0.0570393i
\(254\) 29.3894 + 16.9680i 1.84405 + 1.06466i
\(255\) 5.07116 3.08301i 0.317568 0.193066i
\(256\) −20.3937 + 35.3230i −1.27461 + 2.20769i
\(257\) −15.9957 + 9.23510i −0.997782 + 0.576070i −0.907591 0.419855i \(-0.862081\pi\)
−0.0901908 + 0.995925i \(0.528748\pi\)
\(258\) −15.9312 27.5936i −0.991830 1.71790i
\(259\) 5.95773 0.370195
\(260\) 40.8367 + 16.0606i 2.53258 + 0.996034i
\(261\) 1.54933 0.0959012
\(262\) 7.56787 + 13.1079i 0.467545 + 0.809811i
\(263\) 8.70446 5.02552i 0.536740 0.309887i −0.207017 0.978337i \(-0.566375\pi\)
0.743757 + 0.668450i \(0.233042\pi\)
\(264\) −10.9904 + 19.0360i −0.676413 + 1.17158i
\(265\) −9.68544 15.9313i −0.594972 0.978652i
\(266\) −19.7457 11.4002i −1.21069 0.698989i
\(267\) −2.63289 + 4.56030i −0.161130 + 0.279086i
\(268\) −55.1059 −3.36613
\(269\) −11.1969 + 19.3936i −0.682688 + 1.18245i 0.291469 + 0.956580i \(0.405856\pi\)
−0.974157 + 0.225870i \(0.927477\pi\)
\(270\) 2.92975 5.35076i 0.178299 0.325637i
\(271\) 13.0612 7.54088i 0.793410 0.458076i −0.0477516 0.998859i \(-0.515206\pi\)
0.841162 + 0.540784i \(0.181872\pi\)
\(272\) 39.1179i 2.37187i
\(273\) −12.4108 5.20852i −0.751136 0.315234i
\(274\) −36.9743 −2.23370
\(275\) 0.529800 + 11.6892i 0.0319481 + 0.704887i
\(276\) −1.21825 2.11007i −0.0733299 0.127011i
\(277\) 11.0406 + 6.37430i 0.663366 + 0.382994i 0.793558 0.608494i \(-0.208226\pi\)
−0.130192 + 0.991489i \(0.541559\pi\)
\(278\) 14.7551 0.884950
\(279\) 2.75262 + 1.58923i 0.164795 + 0.0951445i
\(280\) −1.77535 78.3811i −0.106098 4.68417i
\(281\) 2.48331i 0.148142i 0.997253 + 0.0740709i \(0.0235991\pi\)
−0.997253 + 0.0740709i \(0.976401\pi\)
\(282\) 19.0559 + 11.0020i 1.13476 + 0.655157i
\(283\) 6.72924 3.88513i 0.400012 0.230947i −0.286477 0.958087i \(-0.592484\pi\)
0.686489 + 0.727140i \(0.259151\pi\)
\(284\) −17.8899 + 10.3288i −1.06157 + 0.612899i
\(285\) 4.27764 2.60060i 0.253386 0.154046i
\(286\) −18.3279 + 13.9284i −1.08375 + 0.823605i
\(287\) 3.73610i 0.220535i
\(288\) 10.7121 + 18.5538i 0.631214 + 1.09329i
\(289\) −4.97784 8.62187i −0.292814 0.507169i
\(290\) 0.214022 + 9.44901i 0.0125678 + 0.554865i
\(291\) 12.4827i 0.731747i
\(292\) −0.134437 + 0.232852i −0.00786734 + 0.0136266i
\(293\) 7.69740 13.3323i 0.449687 0.778881i −0.548678 0.836034i \(-0.684869\pi\)
0.998365 + 0.0571527i \(0.0182022\pi\)
\(294\) 18.9201i 1.10344i
\(295\) 11.9023 0.269589i 0.692976 0.0156961i
\(296\) −7.49510 12.9819i −0.435644 0.754558i
\(297\) 1.17012 + 2.02671i 0.0678974 + 0.117602i
\(298\) 40.0132i 2.31790i
\(299\) −0.203224 1.60119i −0.0117528 0.0925994i
\(300\) 24.1600 + 12.5260i 1.39488 + 0.723188i
\(301\) −37.7568 + 21.7989i −2.17626 + 1.25647i
\(302\) 29.1283 16.8172i 1.67614 0.967722i
\(303\) 0.604407 + 0.348954i 0.0347222 + 0.0200469i
\(304\) 32.9969i 1.89250i
\(305\) 0.0321848 + 1.42095i 0.00184289 + 0.0813631i
\(306\) 6.27074 + 3.62041i 0.358474 + 0.206965i
\(307\) −26.0526 −1.48690 −0.743451 0.668790i \(-0.766812\pi\)
−0.743451 + 0.668790i \(0.766812\pi\)
\(308\) 41.1786 + 23.7745i 2.34637 + 1.35468i
\(309\) 1.96217 + 3.39858i 0.111624 + 0.193338i
\(310\) −9.31208 + 17.0071i −0.528891 + 0.965940i
\(311\) −10.6032 −0.601255 −0.300627 0.953742i \(-0.597196\pi\)
−0.300627 + 0.953742i \(0.597196\pi\)
\(312\) 4.26399 + 33.5957i 0.241401 + 1.90198i
\(313\) 1.86028i 0.105149i −0.998617 0.0525745i \(-0.983257\pi\)
0.998617 0.0525745i \(-0.0167427\pi\)
\(314\) −58.5584 + 33.8087i −3.30464 + 1.90793i
\(315\) −7.32154 4.00883i −0.412522 0.225872i
\(316\) −5.26629 + 9.12148i −0.296252 + 0.513123i
\(317\) −8.78399 −0.493358 −0.246679 0.969097i \(-0.579339\pi\)
−0.246679 + 0.969097i \(0.579339\pi\)
\(318\) 11.3737 19.6998i 0.637806 1.10471i
\(319\) −3.14005 1.81291i −0.175809 0.101503i
\(320\) −55.3543 + 33.6527i −3.09440 + 1.88124i
\(321\) 0.811946 1.40633i 0.0453184 0.0784938i
\(322\) −3.94818 + 2.27948i −0.220023 + 0.127031i
\(323\) 2.97103 + 5.14597i 0.165312 + 0.286329i
\(324\) 5.44282 0.302379
\(325\) 11.5466 + 13.8447i 0.640491 + 0.767966i
\(326\) 43.4633 2.40721
\(327\) −8.80385 15.2487i −0.486854 0.843256i
\(328\) −8.14097 + 4.70019i −0.449510 + 0.259525i
\(329\) 15.0542 26.0746i 0.829963 1.43754i
\(330\) −12.1988 + 7.41628i −0.671523 + 0.408253i
\(331\) 13.6130 + 7.85944i 0.748235 + 0.431994i 0.825056 0.565051i \(-0.191144\pi\)
−0.0768205 + 0.997045i \(0.524477\pi\)
\(332\) −20.7719 + 35.9780i −1.14001 + 1.97455i
\(333\) −1.59597 −0.0874587
\(334\) 34.6906 60.0859i 1.89818 3.28775i
\(335\) −19.8573 10.8727i −1.08492 0.594038i
\(336\) 47.6478 27.5095i 2.59940 1.50076i
\(337\) 23.7835i 1.29557i 0.761824 + 0.647784i \(0.224304\pi\)
−0.761824 + 0.647784i \(0.775696\pi\)
\(338\) −9.49774 + 34.1706i −0.516609 + 1.85863i
\(339\) −18.7414 −1.01789
\(340\) −15.5133 + 28.3328i −0.841329 + 1.53656i
\(341\) −3.71918 6.44181i −0.201405 0.348844i
\(342\) 5.28952 + 3.05391i 0.286025 + 0.165136i
\(343\) −0.242143 −0.0130745
\(344\) 94.9996 + 54.8480i 5.12203 + 2.95721i
\(345\) −0.0226667 1.00073i −0.00122033 0.0538773i
\(346\) 36.9170i 1.98467i
\(347\) 25.4580 + 14.6982i 1.36666 + 0.789039i 0.990499 0.137517i \(-0.0439121\pi\)
0.376157 + 0.926556i \(0.377245\pi\)
\(348\) −7.30295 + 4.21636i −0.391479 + 0.226021i
\(349\) −17.1537 + 9.90370i −0.918217 + 0.530133i −0.883066 0.469249i \(-0.844525\pi\)
−0.0351512 + 0.999382i \(0.511191\pi\)
\(350\) 23.4376 45.2062i 1.25279 2.41637i
\(351\) 3.32464 + 1.39527i 0.177456 + 0.0744742i
\(352\) 50.1377i 2.67235i
\(353\) −0.734126 1.27154i −0.0390736 0.0676775i 0.845827 0.533457i \(-0.179107\pi\)
−0.884901 + 0.465779i \(0.845774\pi\)
\(354\) 7.26264 + 12.5793i 0.386005 + 0.668580i
\(355\) −8.48454 + 0.192177i −0.450312 + 0.0101997i
\(356\) 28.6607i 1.51901i
\(357\) 4.95387 8.58036i 0.262187 0.454121i
\(358\) 16.0489 27.7975i 0.848211 1.46914i
\(359\) 35.9295i 1.89629i −0.317840 0.948144i \(-0.602957\pi\)
0.317840 0.948144i \(-0.397043\pi\)
\(360\) 0.475586 + 20.9969i 0.0250656 + 1.10664i
\(361\) −6.99386 12.1137i −0.368098 0.637565i
\(362\) −18.1345 31.4099i −0.953130 1.65087i
\(363\) 5.52324i 0.289895i
\(364\) 72.6743 9.22386i 3.80917 0.483462i
\(365\) −0.0943873 + 0.0573828i −0.00494046 + 0.00300355i
\(366\) −1.50177 + 0.867047i −0.0784987 + 0.0453213i
\(367\) 19.7705 11.4145i 1.03201 0.595833i 0.114453 0.993429i \(-0.463488\pi\)
0.917561 + 0.397595i \(0.130155\pi\)
\(368\) 5.71385 + 3.29889i 0.297855 + 0.171967i
\(369\) 1.00084i 0.0521015i
\(370\) −0.220465 9.73347i −0.0114614 0.506019i
\(371\) −26.9557 15.5629i −1.39947 0.807983i
\(372\) −17.2997 −0.896949
\(373\) −17.8144 10.2851i −0.922394 0.532545i −0.0379961 0.999278i \(-0.512097\pi\)
−0.884398 + 0.466733i \(0.845431\pi\)
\(374\) −8.47266 14.6751i −0.438111 0.758830i
\(375\) 6.23459 + 9.28062i 0.321953 + 0.479249i
\(376\) −75.7554 −3.90678
\(377\) −5.54174 + 0.703360i −0.285414 + 0.0362249i
\(378\) 10.1841i 0.523815i
\(379\) 22.4067 12.9365i 1.15096 0.664505i 0.201836 0.979419i \(-0.435309\pi\)
0.949120 + 0.314914i \(0.101976\pi\)
\(380\) −13.0859 + 23.8994i −0.671292 + 1.22602i
\(381\) −6.21958 + 10.7726i −0.318639 + 0.551898i
\(382\) 45.2962 2.31755
\(383\) 5.90514 10.2280i 0.301739 0.522627i −0.674791 0.738009i \(-0.735766\pi\)
0.976530 + 0.215382i \(0.0690996\pi\)
\(384\) −31.3407 18.0946i −1.59935 0.923385i
\(385\) 10.1478 + 16.6919i 0.517181 + 0.850696i
\(386\) 17.9157 31.0309i 0.911885 1.57943i
\(387\) 10.1144 5.83954i 0.514143 0.296841i
\(388\) 33.9704 + 58.8385i 1.72459 + 2.98707i
\(389\) 4.31443 0.218750 0.109375 0.994001i \(-0.465115\pi\)
0.109375 + 0.994001i \(0.465115\pi\)
\(390\) −8.05019 + 20.4689i −0.407637 + 1.03649i
\(391\) 1.18812 0.0600860
\(392\) −32.5692 56.4115i −1.64499 2.84921i
\(393\) −4.80470 + 2.77399i −0.242365 + 0.139929i
\(394\) 22.6417 39.2165i 1.14067 1.97570i
\(395\) −3.69742 + 2.24785i −0.186037 + 0.113102i
\(396\) −11.0310 6.36877i −0.554330 0.320043i
\(397\) −8.29714 + 14.3711i −0.416421 + 0.721263i −0.995577 0.0939544i \(-0.970049\pi\)
0.579155 + 0.815217i \(0.303383\pi\)
\(398\) 42.0135 2.10595
\(399\) 4.17872 7.23775i 0.209197 0.362341i
\(400\) −73.6175 + 3.33662i −3.68087 + 0.166831i
\(401\) −1.05626 + 0.609829i −0.0527469 + 0.0304534i −0.526142 0.850397i \(-0.676362\pi\)
0.473395 + 0.880850i \(0.343028\pi\)
\(402\) 27.6212i 1.37762i
\(403\) −10.5672 4.43481i −0.526390 0.220913i
\(404\) −3.79859 −0.188987
\(405\) 1.96131 + 1.07390i 0.0974584 + 0.0533623i
\(406\) 7.88930 + 13.6647i 0.391539 + 0.678166i
\(407\) 3.23458 + 1.86748i 0.160332 + 0.0925678i
\(408\) −24.9288 −1.23416
\(409\) −22.0397 12.7246i −1.08979 0.629191i −0.156270 0.987714i \(-0.549947\pi\)
−0.933521 + 0.358523i \(0.883280\pi\)
\(410\) −6.10387 + 0.138254i −0.301449 + 0.00682789i
\(411\) 13.5529i 0.668514i
\(412\) −18.4978 10.6797i −0.911322 0.526152i
\(413\) 17.2124 9.93759i 0.846968 0.488997i
\(414\) 1.05765 0.610634i 0.0519806 0.0300110i
\(415\) −14.5838 + 8.86623i −0.715891 + 0.435226i
\(416\) −46.7385 61.5014i −2.29154 3.01535i
\(417\) 5.40844i 0.264853i
\(418\) −7.14690 12.3788i −0.349566 0.605466i
\(419\) 16.0653 + 27.8259i 0.784840 + 1.35938i 0.929095 + 0.369842i \(0.120588\pi\)
−0.144255 + 0.989541i \(0.546079\pi\)
\(420\) 45.4206 1.02879i 2.21630 0.0501997i
\(421\) 11.6222i 0.566433i 0.959056 + 0.283217i \(0.0914016\pi\)
−0.959056 + 0.283217i \(0.908598\pi\)
\(422\) 7.65660 13.2616i 0.372718 0.645566i
\(423\) −4.03275 + 6.98492i −0.196079 + 0.339619i
\(424\) 78.3152i 3.80332i
\(425\) −11.1804 + 7.14883i −0.542331 + 0.346769i
\(426\) −5.17718 8.96713i −0.250835 0.434459i
\(427\) 1.18640 + 2.05490i 0.0574137 + 0.0994434i
\(428\) 8.83855i 0.427227i
\(429\) −5.10545 6.71805i −0.246493 0.324351i
\(430\) 37.0112 + 60.8786i 1.78484 + 2.93583i
\(431\) 18.2332 10.5269i 0.878260 0.507064i 0.00817569 0.999967i \(-0.497398\pi\)
0.870084 + 0.492903i \(0.164064\pi\)
\(432\) −12.7640 + 7.36930i −0.614109 + 0.354556i
\(433\) −14.4642 8.35090i −0.695105 0.401319i 0.110417 0.993885i \(-0.464781\pi\)
−0.805522 + 0.592566i \(0.798115\pi\)
\(434\) 32.3698i 1.55380i
\(435\) −3.46352 + 0.0784496i −0.166063 + 0.00376137i
\(436\) 82.9959 + 47.9177i 3.97478 + 2.29484i
\(437\) 1.00221 0.0479423
\(438\) −0.116715 0.0673852i −0.00557684 0.00321979i
\(439\) 8.72877 + 15.1187i 0.416601 + 0.721575i 0.995595 0.0937572i \(-0.0298877\pi\)
−0.578994 + 0.815332i \(0.696554\pi\)
\(440\) 23.6051 43.1113i 1.12533 2.05525i
\(441\) −6.93513 −0.330244
\(442\) −24.0731 10.1029i −1.14504 0.480547i
\(443\) 15.4536i 0.734220i −0.930177 0.367110i \(-0.880347\pi\)
0.930177 0.367110i \(-0.119653\pi\)
\(444\) 7.52280 4.34329i 0.357016 0.206123i
\(445\) 5.65490 10.3278i 0.268068 0.489587i
\(446\) −24.6653 + 42.7215i −1.16793 + 2.02292i
\(447\) 14.6668 0.693715
\(448\) −54.0741 + 93.6591i −2.55476 + 4.42498i
\(449\) −15.5420 8.97319i −0.733473 0.423471i 0.0862182 0.996276i \(-0.472522\pi\)
−0.819691 + 0.572805i \(0.805855\pi\)
\(450\) −6.27851 + 12.1099i −0.295972 + 0.570868i
\(451\) 1.17110 2.02841i 0.0551451 0.0955140i
\(452\) 88.3397 51.0029i 4.15515 2.39898i
\(453\) 6.16433 + 10.6769i 0.289625 + 0.501646i
\(454\) −23.1086 −1.08454
\(455\) 28.0080 + 11.0152i 1.31304 + 0.516401i
\(456\) −21.0281 −0.984730
\(457\) 11.5720 + 20.0433i 0.541315 + 0.937586i 0.998829 + 0.0483830i \(0.0154068\pi\)
−0.457514 + 0.889203i \(0.651260\pi\)
\(458\) −55.9672 + 32.3127i −2.61518 + 1.50987i
\(459\) −1.32706 + 2.29853i −0.0619417 + 0.107286i
\(460\) 2.83023 + 4.65536i 0.131960 + 0.217057i
\(461\) −12.0519 6.95814i −0.561311 0.324073i 0.192361 0.981324i \(-0.438386\pi\)
−0.753671 + 0.657251i \(0.771719\pi\)
\(462\) −11.9167 + 20.6403i −0.554415 + 0.960275i
\(463\) −7.46187 −0.346783 −0.173391 0.984853i \(-0.555473\pi\)
−0.173391 + 0.984853i \(0.555473\pi\)
\(464\) 11.4175 19.7757i 0.530044 0.918063i
\(465\) −6.23394 3.41333i −0.289092 0.158289i
\(466\) −11.2283 + 6.48266i −0.520141 + 0.300304i
\(467\) 6.50590i 0.301057i −0.988606 0.150529i \(-0.951902\pi\)
0.988606 0.150529i \(-0.0480975\pi\)
\(468\) −19.4682 + 2.47091i −0.899916 + 0.114218i
\(469\) −37.7946 −1.74519
\(470\) −43.1565 23.6299i −1.99066 1.08997i
\(471\) −12.3925 21.4645i −0.571017 0.989031i
\(472\) −43.3081 25.0039i −1.99341 1.15090i
\(473\) −27.3319 −1.25672
\(474\) −4.57204 2.63967i −0.210001 0.121244i
\(475\) −9.43097 + 6.03022i −0.432723 + 0.276685i
\(476\) 53.9260i 2.47170i
\(477\) 7.22095 + 4.16902i 0.330625 + 0.190886i
\(478\) 31.3756 18.1147i 1.43509 0.828548i
\(479\) −2.56069 + 1.47842i −0.117001 + 0.0675506i −0.557358 0.830272i \(-0.688185\pi\)
0.440357 + 0.897823i \(0.354852\pi\)
\(480\) −24.8862 40.9346i −1.13589 1.86840i
\(481\) 5.70856 0.724534i 0.260288 0.0330359i
\(482\) 27.1733i 1.23771i
\(483\) −0.835541 1.44720i −0.0380184 0.0658498i
\(484\) −15.0310 26.0345i −0.683227 1.18338i
\(485\) 0.632053 + 27.9049i 0.0287001 + 1.26710i
\(486\) 2.72815i 0.123752i
\(487\) −7.61819 + 13.1951i −0.345213 + 0.597927i −0.985392 0.170299i \(-0.945527\pi\)
0.640179 + 0.768226i \(0.278860\pi\)
\(488\) 2.98508 5.17031i 0.135128 0.234049i
\(489\) 15.9314i 0.720443i
\(490\) −0.958010 42.2958i −0.0432785 1.91073i
\(491\) 8.42838 + 14.5984i 0.380367 + 0.658816i 0.991115 0.133010i \(-0.0424642\pi\)
−0.610747 + 0.791826i \(0.709131\pi\)
\(492\) −2.72368 4.71756i −0.122793 0.212684i
\(493\) 4.11210i 0.185200i
\(494\) −20.3063 8.52207i −0.913622 0.383426i
\(495\) −2.71843 4.47146i −0.122184 0.200977i
\(496\) 40.5698 23.4230i 1.82164 1.05172i
\(497\) −12.2699 + 7.08402i −0.550380 + 0.317762i
\(498\) −18.0336 10.4117i −0.808105 0.466560i
\(499\) 5.35532i 0.239737i −0.992790 0.119869i \(-0.961753\pi\)
0.992790 0.119869i \(-0.0382473\pi\)
\(500\) −54.6438 26.7784i −2.44374 1.19757i
\(501\) 22.0244 + 12.7158i 0.983977 + 0.568099i
\(502\) 54.3084 2.42390
\(503\) −35.1282 20.2812i −1.56629 0.904296i −0.996596 0.0824369i \(-0.973730\pi\)
−0.569691 0.821859i \(-0.692937\pi\)
\(504\) 17.5310 + 30.3647i 0.780895 + 1.35255i
\(505\) −1.36882 0.749482i −0.0609115 0.0333515i
\(506\) −2.85807 −0.127057
\(507\) −12.5252 3.48138i −0.556262 0.154614i
\(508\) 67.7040i 3.00388i
\(509\) 29.6048 17.0923i 1.31221 0.757605i 0.329748 0.944069i \(-0.393036\pi\)
0.982462 + 0.186464i \(0.0597027\pi\)
\(510\) −14.2015 7.77590i −0.628854 0.344323i
\(511\) −0.0922044 + 0.159703i −0.00407888 + 0.00706483i
\(512\) 38.8961 1.71898
\(513\) −1.11941 + 1.93887i −0.0494229 + 0.0856030i
\(514\) 43.6386 + 25.1948i 1.92482 + 1.11129i
\(515\) −4.55850 7.49814i −0.200872 0.330408i
\(516\) −31.7835 + 55.0507i −1.39919 + 2.42347i
\(517\) 16.3464 9.43763i 0.718916 0.415066i
\(518\) −8.12680 14.0760i −0.357071 0.618465i
\(519\) 13.5319 0.593983
\(520\) −11.2332 74.8871i −0.492610 3.28402i
\(521\) 41.1861 1.80440 0.902198 0.431321i \(-0.141952\pi\)
0.902198 + 0.431321i \(0.141952\pi\)
\(522\) −2.11341 3.66053i −0.0925013 0.160217i
\(523\) −3.27850 + 1.89284i −0.143359 + 0.0827682i −0.569964 0.821670i \(-0.693043\pi\)
0.426605 + 0.904438i \(0.359709\pi\)
\(524\) 15.0983 26.1511i 0.659573 1.14241i
\(525\) 16.5702 + 8.59100i 0.723185 + 0.374942i
\(526\) −23.7471 13.7104i −1.03542 0.597802i
\(527\) 4.21798 7.30576i 0.183738 0.318244i
\(528\) 34.4920 1.50107
\(529\) −11.3998 + 19.7450i −0.495644 + 0.858480i
\(530\) −24.4284 + 44.6148i −1.06110 + 1.93794i
\(531\) −4.61091 + 2.66211i −0.200096 + 0.115526i
\(532\) 45.4880i 1.97215i
\(533\) −0.454357 3.57985i −0.0196804 0.155060i
\(534\) 14.3659 0.621671
\(535\) −1.74389 + 3.18496i −0.0753950 + 0.137698i
\(536\) 47.5474 + 82.3545i 2.05373 + 3.55717i
\(537\) 10.1891 + 5.88270i 0.439694 + 0.253857i
\(538\) 61.0938 2.63394
\(539\) 14.0555 + 8.11496i 0.605414 + 0.349536i
\(540\) −12.1674 + 0.275594i −0.523601 + 0.0118597i
\(541\) 3.22373i 0.138599i 0.997596 + 0.0692995i \(0.0220764\pi\)
−0.997596 + 0.0692995i \(0.977924\pi\)
\(542\) −35.6329 20.5727i −1.53056 0.883671i
\(543\) 11.5133 6.64718i 0.494081 0.285258i
\(544\) 49.2440 28.4310i 2.11132 1.21897i
\(545\) 20.4531 + 33.6426i 0.876113 + 1.44109i
\(546\) 4.62336 + 36.4272i 0.197862 + 1.55894i
\(547\) 3.95250i 0.168997i 0.996424 + 0.0844983i \(0.0269288\pi\)
−0.996424 + 0.0844983i \(0.973071\pi\)
\(548\) 36.8829 + 63.8831i 1.57556 + 2.72895i
\(549\) −0.317815 0.550471i −0.0135640 0.0234935i
\(550\) 26.8949 17.1967i 1.14680 0.733271i
\(551\) 3.46866i 0.147770i
\(552\) −2.10230 + 3.64129i −0.0894798 + 0.154984i
\(553\) −3.61191 + 6.25601i −0.153594 + 0.266033i
\(554\) 34.7801i 1.47767i
\(555\) 3.56779 0.0808112i 0.151444 0.00343025i
\(556\) −14.7186 25.4933i −0.624207 1.08116i
\(557\) −10.9335 18.9374i −0.463268 0.802404i 0.535853 0.844311i \(-0.319990\pi\)
−0.999122 + 0.0419069i \(0.986657\pi\)
\(558\) 8.67130i 0.367085i
\(559\) −33.5267 + 25.4789i −1.41803 + 1.07764i
\(560\) −105.123 + 63.9099i −4.44227 + 2.70068i
\(561\) 5.37913 3.10564i 0.227107 0.131120i
\(562\) 5.86719 3.38742i 0.247492 0.142890i
\(563\) −18.0807 10.4389i −0.762013 0.439948i 0.0680053 0.997685i \(-0.478337\pi\)
−0.830018 + 0.557737i \(0.811670\pi\)
\(564\) 43.8990i 1.84848i
\(565\) 41.8962 0.948960i 1.76259 0.0399231i
\(566\) −18.3584 10.5992i −0.771661 0.445519i
\(567\) 3.73298 0.156770
\(568\) 30.8722 + 17.8241i 1.29537 + 0.747881i
\(569\) −8.19610 14.1961i −0.343599 0.595130i 0.641500 0.767123i \(-0.278313\pi\)
−0.985098 + 0.171993i \(0.944979\pi\)
\(570\) −11.9793 6.55916i −0.501759 0.274733i
\(571\) 43.2862 1.81147 0.905735 0.423843i \(-0.139319\pi\)
0.905735 + 0.423843i \(0.139319\pi\)
\(572\) 42.3477 + 17.7723i 1.77065 + 0.743099i
\(573\) 16.6032i 0.693610i
\(574\) −8.82710 + 5.09633i −0.368436 + 0.212717i
\(575\) 0.101343 + 2.23597i 0.00422628 + 0.0932465i
\(576\) 14.4855 25.0896i 0.603563 1.04540i
\(577\) −20.6414 −0.859311 −0.429656 0.902993i \(-0.641365\pi\)
−0.429656 + 0.902993i \(0.641365\pi\)
\(578\) −13.5803 + 23.5218i −0.564866 + 0.978377i
\(579\) 11.3743 + 6.56697i 0.472701 + 0.272914i
\(580\) 16.1122 9.79543i 0.669023 0.406733i
\(581\) −14.2465 + 24.6757i −0.591045 + 1.02372i
\(582\) −29.4922 + 17.0273i −1.22249 + 0.705805i
\(583\) −9.75653 16.8988i −0.404074 0.699877i
\(584\) 0.463990 0.0192000
\(585\) −7.50286 2.95078i −0.310205 0.122000i
\(586\) −41.9994 −1.73498
\(587\) −4.86133 8.42007i −0.200649 0.347534i 0.748089 0.663598i \(-0.230972\pi\)
−0.948738 + 0.316065i \(0.897638\pi\)
\(588\) 32.6896 18.8733i 1.34809 0.778323i
\(589\) 3.55797 6.16259i 0.146604 0.253925i
\(590\) −16.8725 27.7531i −0.694631 1.14258i
\(591\) 14.3748 + 8.29927i 0.591298 + 0.341386i
\(592\) −11.7612 + 20.3710i −0.483382 + 0.837243i
\(593\) 6.32051 0.259552 0.129776 0.991543i \(-0.458574\pi\)
0.129776 + 0.991543i \(0.458574\pi\)
\(594\) 3.19227 5.52918i 0.130981 0.226865i
\(595\) −10.6399 + 19.4322i −0.436193 + 0.796642i
\(596\) −69.1336 + 39.9143i −2.83182 + 1.63495i
\(597\) 15.4000i 0.630280i
\(598\) −3.50584 + 2.66430i −0.143365 + 0.108951i
\(599\) −7.45206 −0.304483 −0.152241 0.988343i \(-0.548649\pi\)
−0.152241 + 0.988343i \(0.548649\pi\)
\(600\) −2.12634 46.9145i −0.0868074 1.91527i
\(601\) 3.05867 + 5.29776i 0.124766 + 0.216100i 0.921641 0.388043i \(-0.126849\pi\)
−0.796876 + 0.604143i \(0.793515\pi\)
\(602\) 103.006 + 59.4707i 4.19822 + 2.42384i
\(603\) 10.1245 0.412302
\(604\) −58.1125 33.5513i −2.36457 1.36518i
\(605\) −0.279667 12.3472i −0.0113701 0.501984i
\(606\) 1.90400i 0.0773447i
\(607\) −35.6944 20.6082i −1.44879 0.836460i −0.450382 0.892836i \(-0.648712\pi\)
−0.998410 + 0.0563759i \(0.982045\pi\)
\(608\) 41.5385 23.9823i 1.68461 0.972609i
\(609\) −5.00876 + 2.89181i −0.202965 + 0.117182i
\(610\) 3.31329 2.01432i 0.134151 0.0815574i
\(611\) 11.2536 26.8148i 0.455271 1.08481i
\(612\) 14.4458i 0.583939i
\(613\) 12.7973 + 22.1655i 0.516877 + 0.895257i 0.999808 + 0.0195987i \(0.00623886\pi\)
−0.482931 + 0.875658i \(0.660428\pi\)
\(614\) 35.5378 + 61.5532i 1.43419 + 2.48409i
\(615\) −0.0506768 2.23736i −0.00204349 0.0902193i
\(616\) 82.0540i 3.30605i
\(617\) −16.0897 + 27.8683i −0.647749 + 1.12193i 0.335910 + 0.941894i \(0.390956\pi\)
−0.983659 + 0.180040i \(0.942377\pi\)
\(618\) 5.35309 9.27183i 0.215333 0.372968i
\(619\) 19.8298i 0.797028i 0.917162 + 0.398514i \(0.130474\pi\)
−0.917162 + 0.398514i \(0.869526\pi\)
\(620\) 38.6734 0.875963i 1.55316 0.0351795i
\(621\) 0.223827 + 0.387679i 0.00898186 + 0.0155570i
\(622\) 14.4636 + 25.0517i 0.579939 + 1.00448i
\(623\) 19.6570i 0.787543i
\(624\) 42.3095 32.1535i 1.69374 1.28717i
\(625\) −14.4073 20.4311i −0.576292 0.817244i
\(626\) −4.39518 + 2.53756i −0.175667 + 0.101421i
\(627\) 4.53743 2.61968i 0.181207 0.104620i
\(628\) 116.827 + 67.4502i 4.66191 + 2.69156i
\(629\) 4.23589i 0.168896i
\(630\) 0.515669 + 22.7666i 0.0205447 + 0.907042i
\(631\) −19.0859 11.0192i −0.759797 0.438669i 0.0694258 0.997587i \(-0.477883\pi\)
−0.829223 + 0.558918i \(0.811217\pi\)
\(632\) 18.1758 0.722994
\(633\) 4.86103 + 2.80652i 0.193209 + 0.111549i
\(634\) 11.9820 + 20.7535i 0.475867 + 0.824227i
\(635\) 13.3584 24.3971i 0.530111 0.968168i
\(636\) −45.3824 −1.79953
\(637\) 24.8060 3.14839i 0.982849 0.124744i
\(638\) 9.89178i 0.391619i
\(639\) 3.28689 1.89769i 0.130027 0.0750713i
\(640\) 70.9783 + 38.8634i 2.80566 + 1.53621i
\(641\) 22.1778 38.4131i 0.875970 1.51723i 0.0202450 0.999795i \(-0.493555\pi\)
0.855725 0.517430i \(-0.173111\pi\)
\(642\) −4.43023 −0.174847
\(643\) −23.6894 + 41.0312i −0.934218 + 1.61811i −0.158197 + 0.987408i \(0.550568\pi\)
−0.776022 + 0.630706i \(0.782765\pi\)
\(644\) 7.87684 + 4.54769i 0.310391 + 0.179204i
\(645\) −22.3150 + 13.5664i −0.878651 + 0.534176i
\(646\) 8.10542 14.0390i 0.318903 0.552357i
\(647\) −22.5781 + 13.0355i −0.887637 + 0.512478i −0.873169 0.487418i \(-0.837939\pi\)
−0.0144683 + 0.999895i \(0.504606\pi\)
\(648\) −4.69626 8.13416i −0.184487 0.319540i
\(649\) 12.4600 0.489097
\(650\) 16.9597 46.1658i 0.665215 1.81077i
\(651\) −11.8651 −0.465030
\(652\) −43.3558 75.0945i −1.69795 2.94093i
\(653\) 20.0320 11.5655i 0.783913 0.452592i −0.0539022 0.998546i \(-0.517166\pi\)
0.837815 + 0.545954i \(0.183833\pi\)
\(654\) −24.0182 + 41.6008i −0.939188 + 1.62672i
\(655\) 10.6004 6.44453i 0.414192 0.251809i
\(656\) 12.7747 + 7.37547i 0.498768 + 0.287964i
\(657\) 0.0246999 0.0427816i 0.000963637 0.00166907i
\(658\) −82.1401 −3.20215
\(659\) −23.7412 + 41.1210i −0.924828 + 1.60185i −0.132990 + 0.991117i \(0.542458\pi\)
−0.791838 + 0.610731i \(0.790876\pi\)
\(660\) 24.9823 + 13.6788i 0.972434 + 0.532446i
\(661\) −6.14537 + 3.54803i −0.239027 + 0.138002i −0.614729 0.788738i \(-0.710735\pi\)
0.375702 + 0.926740i \(0.377401\pi\)
\(662\) 42.8835i 1.66671i
\(663\) 3.70321 8.82396i 0.143821 0.342694i
\(664\) 71.6911 2.78216
\(665\) −8.97502 + 16.3915i −0.348036 + 0.635636i
\(666\) 2.17703 + 3.77072i 0.0843581 + 0.146113i
\(667\) −0.600644 0.346782i −0.0232570 0.0134274i
\(668\) −138.419 −5.35560
\(669\) −15.6595 9.04102i −0.605431 0.349546i
\(670\) 1.39859 + 61.7471i 0.0540321 + 2.38550i
\(671\) 1.48753i 0.0574254i
\(672\) −69.2610 39.9879i −2.67180 1.54257i
\(673\) 20.3750 11.7635i 0.785398 0.453450i −0.0529421 0.998598i \(-0.516860\pi\)
0.838340 + 0.545148i \(0.183527\pi\)
\(674\) 56.1920 32.4424i 2.16443 1.24964i
\(675\) −4.43888 2.30138i −0.170853 0.0885802i
\(676\) 68.5131 17.6762i 2.63512 0.679854i
\(677\) 39.9097i 1.53385i 0.641735 + 0.766927i \(0.278215\pi\)
−0.641735 + 0.766927i \(0.721785\pi\)
\(678\) 25.5647 + 44.2793i 0.981805 + 1.70054i
\(679\) 23.2988 + 40.3546i 0.894125 + 1.54867i
\(680\) 55.7282 1.26226i 2.13708 0.0484054i
\(681\) 8.47042i 0.324587i
\(682\) −10.1465 + 17.5742i −0.388529 + 0.672952i
\(683\) 17.6681 30.6020i 0.676051 1.17095i −0.300110 0.953905i \(-0.597023\pi\)
0.976161 0.217050i \(-0.0696434\pi\)
\(684\) 12.1854i 0.465922i
\(685\) 0.686243 + 30.2974i 0.0262200 + 1.15760i
\(686\) 0.330302 + 0.572099i 0.0126110 + 0.0218429i
\(687\) −11.8442 20.5147i −0.451883 0.782684i
\(688\) 172.133i 6.56252i
\(689\) −27.7209 11.6338i −1.05608 0.443214i
\(690\) −2.33345 + 1.41862i −0.0888329 + 0.0540060i
\(691\) 8.44945 4.87829i 0.321432 0.185579i −0.330599 0.943771i \(-0.607251\pi\)
0.652031 + 0.758192i \(0.273917\pi\)
\(692\) −63.7841 + 36.8257i −2.42471 + 1.39990i
\(693\) −7.56568 4.36805i −0.287396 0.165928i
\(694\) 80.1977i 3.04426i
\(695\) −0.273854 12.0905i −0.0103879 0.458621i
\(696\) 12.6025 + 7.27606i 0.477697 + 0.275799i
\(697\) 2.65633 0.100616
\(698\) 46.7979 + 27.0188i 1.77133 + 1.02268i
\(699\) −2.37621 4.11572i −0.0898765 0.155671i
\(700\) −101.485 + 4.59970i −3.83579 + 0.173852i
\(701\) −26.4004 −0.997128 −0.498564 0.866853i \(-0.666139\pi\)
−0.498564 + 0.866853i \(0.666139\pi\)
\(702\) −1.23852 9.75821i −0.0467449 0.368300i
\(703\) 3.57308i 0.134761i
\(704\) −58.7160 + 33.8997i −2.21294 + 1.27764i
\(705\) 8.66151 15.8190i 0.326211 0.595776i
\(706\) −2.00281 + 3.46897i −0.0753767 + 0.130556i
\(707\) −2.60528 −0.0979816
\(708\) 14.4894 25.0963i 0.544544 0.943177i
\(709\) 7.54818 + 4.35794i 0.283478 + 0.163666i 0.634997 0.772515i \(-0.281001\pi\)
−0.351519 + 0.936181i \(0.614335\pi\)
\(710\) 12.0276 + 19.7838i 0.451388 + 0.742474i
\(711\) 0.967567 1.67588i 0.0362866 0.0628502i
\(712\) −42.8327 + 24.7295i −1.60522 + 0.926777i
\(713\) −0.711423 1.23222i −0.0266430 0.0461470i
\(714\) −27.0299 −1.01157
\(715\) 11.7534 + 14.7597i 0.439551 + 0.551980i
\(716\) −64.0369 −2.39317
\(717\) 6.63992 + 11.5007i 0.247972 + 0.429501i
\(718\) −84.8889 + 49.0106i −3.16803 + 1.82906i
\(719\) 3.21941 5.57618i 0.120064 0.207956i −0.799729 0.600361i \(-0.795023\pi\)
0.919793 + 0.392405i \(0.128357\pi\)
\(720\) 28.1607 17.1203i 1.04949 0.638037i
\(721\) −12.6868 7.32473i −0.472482 0.272787i
\(722\) −19.0803 + 33.0481i −0.710096 + 1.22992i
\(723\) 9.96033 0.370429
\(724\) −36.1794 + 62.6645i −1.34460 + 2.32891i
\(725\) 7.73871 0.350747i 0.287409 0.0130264i
\(726\) 13.0495 7.53413i 0.484312 0.279618i
\(727\) 14.6296i 0.542580i −0.962498 0.271290i \(-0.912550\pi\)
0.962498 0.271290i \(-0.0874502\pi\)
\(728\) −76.4909 100.651i −2.83494 3.73039i
\(729\) −1.00000 −0.0370370
\(730\) 0.264327 + 0.144729i 0.00978318 + 0.00535668i
\(731\) −15.4988 26.8447i −0.573244 0.992888i
\(732\) 2.99611 + 1.72981i 0.110739 + 0.0639355i
\(733\) −3.51568 −0.129854 −0.0649272 0.997890i \(-0.520682\pi\)
−0.0649272 + 0.997890i \(0.520682\pi\)
\(734\) −53.9370 31.1406i −1.99085 1.14942i
\(735\) 15.5035 0.351157i 0.571854 0.0129526i
\(736\) 9.59058i 0.353514i
\(737\) −20.5195 11.8469i −0.755845 0.436387i
\(738\) 2.36463 1.36522i 0.0870431 0.0502543i
\(739\) 14.3874 8.30656i 0.529249 0.305562i −0.211462 0.977386i \(-0.567822\pi\)
0.740710 + 0.671824i \(0.234489\pi\)
\(740\) −16.5973 + 10.0903i −0.610127 + 0.370927i
\(741\) 3.12375 7.44323i 0.114754 0.273434i
\(742\) 84.9157i 3.11735i
\(743\) −7.04435 12.2012i −0.258432 0.447618i 0.707390 0.706824i \(-0.249873\pi\)
−0.965822 + 0.259206i \(0.916539\pi\)
\(744\) 14.9268 + 25.8540i 0.547244 + 0.947855i
\(745\) −32.7875 + 0.742645i −1.20124 + 0.0272084i
\(746\) 56.1189i 2.05466i
\(747\) 3.81639 6.61019i 0.139635 0.241854i
\(748\) −16.9034 + 29.2776i −0.618050 + 1.07049i
\(749\) 6.06196i 0.221499i
\(750\) 13.4224 27.3896i 0.490117 1.00013i
\(751\) 3.79642 + 6.57560i 0.138533 + 0.239947i 0.926942 0.375205i \(-0.122428\pi\)
−0.788408 + 0.615152i \(0.789095\pi\)
\(752\) 59.4371 + 102.948i 2.16745 + 3.75413i
\(753\) 19.9067i 0.725439i
\(754\) 9.22114 + 12.1337i 0.335814 + 0.441885i
\(755\) −14.3209 23.5561i −0.521192 0.857294i
\(756\) −17.5958 + 10.1590i −0.639954 + 0.369478i
\(757\) 40.9906 23.6659i 1.48983 0.860152i 0.489895 0.871782i \(-0.337035\pi\)
0.999932 + 0.0116295i \(0.00370185\pi\)
\(758\) −61.1290 35.2928i −2.22030 1.28189i
\(759\) 1.04762i 0.0380262i
\(760\) 47.0082 1.06475i 1.70516 0.0386224i
\(761\) 9.59232 + 5.53813i 0.347721 + 0.200757i 0.663681 0.748016i \(-0.268993\pi\)
−0.315960 + 0.948773i \(0.602327\pi\)
\(762\) 33.9359 1.22937
\(763\) 56.9231 + 32.8646i 2.06076 + 1.18978i
\(764\) −45.1842 78.2613i −1.63471 2.83139i
\(765\) 2.85024 5.20555i 0.103051 0.188207i
\(766\) −32.2203 −1.16417
\(767\) 15.2840 11.6152i 0.551874 0.419401i
\(768\) 40.7875i 1.47179i
\(769\) 36.9061 21.3078i 1.33087 0.768378i 0.345436 0.938442i \(-0.387731\pi\)
0.985433 + 0.170065i \(0.0543976\pi\)
\(770\) 25.5946 46.7447i 0.922365 1.68456i
\(771\) −9.23510 + 15.9957i −0.332594 + 0.576070i
\(772\) −71.4856 −2.57282
\(773\) −3.03622 + 5.25888i −0.109205 + 0.189149i −0.915448 0.402435i \(-0.868164\pi\)
0.806243 + 0.591584i \(0.201497\pi\)
\(774\) −27.5936 15.9312i −0.991830 0.572634i
\(775\) 14.1088 + 7.31482i 0.506802 + 0.262756i
\(776\) 58.6219 101.536i 2.10440 3.64493i
\(777\) 5.15955 2.97887i 0.185098 0.106866i
\(778\) −5.88520 10.1935i −0.210995 0.365454i
\(779\) 2.24068 0.0802808
\(780\) 43.3959 6.50947i 1.55382 0.233076i
\(781\) −8.88211 −0.317827
\(782\) −1.62069 2.80712i −0.0579558 0.100382i
\(783\) 1.34176 0.774666i 0.0479506 0.0276843i
\(784\) −51.1071 + 88.5201i −1.82525 + 3.16143i
\(785\) 28.7903 + 47.3562i 1.02757 + 1.69022i
\(786\) 13.1079 + 7.56787i 0.467545 + 0.269937i
\(787\) 14.8576 25.7341i 0.529616 0.917323i −0.469787 0.882780i \(-0.655669\pi\)
0.999403 0.0345427i \(-0.0109975\pi\)
\(788\) −90.3428 −3.21833
\(789\) 5.02552 8.70446i 0.178913 0.309887i
\(790\) 10.3544 + 5.66947i 0.368394 + 0.201711i
\(791\) 60.5882 34.9806i 2.15427 1.24377i
\(792\) 21.9808i 0.781055i
\(793\) 1.38668 + 1.82468i 0.0492424 + 0.0647961i
\(794\) 45.2717 1.60663
\(795\) −16.3535 8.95418i −0.579998 0.317572i
\(796\) −41.9097 72.5897i −1.48545 2.57287i
\(797\) −4.57027 2.63865i −0.161887 0.0934656i 0.416868 0.908967i \(-0.363128\pi\)
−0.578755 + 0.815502i \(0.696461\pi\)
\(798\) −22.8003 −0.807123
\(799\) 18.5388 + 10.7034i 0.655855 + 0.378658i
\(800\) 57.7057 + 90.2489i 2.04020 + 3.19078i
\(801\) 5.26578i 0.186057i
\(802\) 2.88163 + 1.66371i 0.101754 + 0.0587476i
\(803\) −0.100119 + 0.0578040i −0.00353314 + 0.00203986i
\(804\) −47.7231 + 27.5529i −1.68306 + 0.971717i
\(805\) 1.94113 + 3.19290i 0.0684157 + 0.112535i
\(806\) 3.93657 + 31.0160i 0.138660 + 1.09249i
\(807\) 22.3938i 0.788300i
\(808\) 3.27756 + 5.67690i 0.115304 + 0.199713i
\(809\) −3.85539 6.67773i −0.135548 0.234777i 0.790258 0.612774i \(-0.209946\pi\)
−0.925807 + 0.377997i \(0.876613\pi\)
\(810\) −0.138139 6.09877i −0.00485370 0.214289i
\(811\) 19.8702i 0.697739i −0.937171 0.348869i \(-0.886566\pi\)
0.937171 0.348869i \(-0.113434\pi\)
\(812\) 15.7396 27.2618i 0.552351 0.956701i
\(813\) 7.54088 13.0612i 0.264470 0.458076i
\(814\) 10.1896i 0.357144i
\(815\) −0.806678 35.6146i −0.0282567 1.24752i
\(816\) 19.5590 + 33.8771i 0.684701 + 1.18594i
\(817\) −13.0736 22.6442i −0.457388 0.792219i
\(818\) 69.4293i 2.42754i
\(819\) −13.3523 + 1.69469i −0.466568 + 0.0592171i
\(820\) 6.32765 + 10.4082i 0.220971 + 0.363469i
\(821\) −9.92947 + 5.73278i −0.346541 + 0.200076i −0.663161 0.748477i \(-0.730785\pi\)
0.316620 + 0.948553i \(0.397452\pi\)
\(822\) −32.0207 + 18.4872i −1.11685 + 0.644814i
\(823\) 16.7495 + 9.67033i 0.583851 + 0.337087i 0.762662 0.646797i \(-0.223892\pi\)
−0.178811 + 0.983883i \(0.557225\pi\)
\(824\) 36.8594i 1.28406i
\(825\) 6.30344 + 9.85827i 0.219458 + 0.343221i
\(826\) −46.9581 27.1113i −1.63388 0.943322i
\(827\) 23.2829 0.809624 0.404812 0.914400i \(-0.367337\pi\)
0.404812 + 0.914400i \(0.367337\pi\)
\(828\) −2.11007 1.21825i −0.0733299 0.0423370i
\(829\) −10.2008 17.6683i −0.354289 0.613647i 0.632707 0.774391i \(-0.281944\pi\)
−0.986996 + 0.160745i \(0.948610\pi\)
\(830\) 40.8412 + 22.3622i 1.41762 + 0.776203i
\(831\) 12.7486 0.442244
\(832\) −40.4225 + 96.3182i −1.40140 + 3.33923i
\(833\) 18.4066i 0.637752i
\(834\) 12.7783 7.37753i 0.442475 0.255463i
\(835\) −49.8792 27.3109i −1.72614 0.945131i
\(836\) −14.2585 + 24.6964i −0.493139 + 0.854142i
\(837\) 3.17845 0.109863
\(838\) 43.8285 75.9132i 1.51403 2.62238i
\(839\) 0.271188 + 0.156570i 0.00936244 + 0.00540541i 0.504674 0.863310i \(-0.331613\pi\)
−0.495311 + 0.868715i \(0.664946\pi\)
\(840\) −40.7281 66.9924i −1.40525 2.31146i
\(841\) 13.2998 23.0359i 0.458613 0.794342i
\(842\) 27.4593 15.8536i 0.946309 0.546352i
\(843\) 1.24165 + 2.15061i 0.0427649 + 0.0740709i
\(844\) −30.5507 −1.05160
\(845\) 28.1762 + 7.14841i 0.969292 + 0.245913i
\(846\) 22.0039 0.756510
\(847\) −10.3091 17.8558i −0.354224 0.613534i
\(848\) 106.427 61.4455i 3.65471 2.11005i
\(849\) 3.88513 6.72924i 0.133337 0.230947i
\(850\) 32.1412 + 16.6639i 1.10243 + 0.571567i
\(851\) 0.618726 + 0.357221i 0.0212096 + 0.0122454i
\(852\) −10.3288 + 17.8899i −0.353857 + 0.612899i
\(853\) 24.8887 0.852173 0.426087 0.904682i \(-0.359892\pi\)
0.426087 + 0.904682i \(0.359892\pi\)
\(854\) 3.23667 5.60607i 0.110756 0.191836i
\(855\) 2.40425 4.39101i 0.0822236 0.150169i
\(856\) 13.2090 7.62622i 0.451475 0.260659i
\(857\) 21.1571i 0.722714i −0.932428 0.361357i \(-0.882314\pi\)
0.932428 0.361357i \(-0.117686\pi\)
\(858\) −8.90819 + 21.2263i −0.304121 + 0.724654i
\(859\) 22.8178 0.778535 0.389267 0.921125i \(-0.372728\pi\)
0.389267 + 0.921125i \(0.372728\pi\)
\(860\) 68.2645 124.675i 2.32780 4.25138i
\(861\) −1.86805 3.23556i −0.0636630 0.110268i
\(862\) −49.7428 28.7190i −1.69425 0.978174i
\(863\) 41.2937 1.40565 0.702826 0.711362i \(-0.251921\pi\)
0.702826 + 0.711362i \(0.251921\pi\)
\(864\) 18.5538 + 10.7121i 0.631214 + 0.364432i
\(865\) −30.2504 + 0.685179i −1.02855 + 0.0232968i
\(866\) 45.5651i 1.54836i
\(867\) −8.62187 4.97784i −0.292814 0.169056i
\(868\) 55.9275 32.2898i 1.89830 1.09599i
\(869\) −3.92196 + 2.26435i −0.133043 + 0.0768127i
\(870\) 4.90986 + 8.07607i 0.166460 + 0.273805i
\(871\) −36.2139 + 4.59630i −1.22706 + 0.155740i
\(872\) 165.381i 5.60050i
\(873\) −6.24133 10.8103i −0.211237 0.365873i
\(874\) −1.36709 2.36787i −0.0462426 0.0800945i
\(875\) −37.4777 18.3661i −1.26698 0.620888i
\(876\) 0.268874i 0.00908443i
\(877\) −23.1812 + 40.1510i −0.782773 + 1.35580i 0.147547 + 0.989055i \(0.452862\pi\)
−0.930320 + 0.366748i \(0.880471\pi\)
\(878\) 23.8134 41.2460i 0.803664 1.39199i
\(879\) 15.3948i 0.519254i
\(880\) −77.1066 + 1.74648i −2.59926 + 0.0588739i
\(881\) 15.4598 + 26.7772i 0.520855 + 0.902147i 0.999706 + 0.0242508i \(0.00772003\pi\)
−0.478851 + 0.877896i \(0.658947\pi\)
\(882\) 9.46005 + 16.3853i 0.318536 + 0.551721i
\(883\) 22.2922i 0.750193i −0.926986 0.375097i \(-0.877610\pi\)
0.926986 0.375097i \(-0.122390\pi\)
\(884\) 6.55808 + 51.6707i 0.220572 + 1.73787i
\(885\) 10.1729 6.18460i 0.341957 0.207893i
\(886\) −36.5113 + 21.0798i −1.22662 + 0.708190i
\(887\) −21.2844 + 12.2886i −0.714662 + 0.412610i −0.812785 0.582564i \(-0.802049\pi\)
0.0981229 + 0.995174i \(0.468716\pi\)
\(888\) −12.9819 7.49510i −0.435644 0.251519i
\(889\) 46.4351i 1.55738i
\(890\) −32.1148 + 0.727408i −1.07649 + 0.0243828i
\(891\) 2.02671 + 1.17012i 0.0678974 + 0.0392006i
\(892\) 98.4172 3.29525
\(893\) 15.6379 + 9.02856i 0.523303 + 0.302129i
\(894\) −20.0066 34.6525i −0.669121 1.15895i
\(895\) −23.0756 12.6348i −0.771333 0.422335i
\(896\) 135.093 4.51315
\(897\) −0.976594 1.28506i −0.0326075 0.0429070i
\(898\) 48.9605i 1.63383i
\(899\) −4.26472 + 2.46224i −0.142236 + 0.0821202i
\(900\) 27.1862 1.23218i 0.906206 0.0410726i
\(901\) 11.0650 19.1652i 0.368630 0.638486i
\(902\) −6.38989 −0.212760
\(903\) −21.7989 + 37.7568i −0.725421 + 1.25647i
\(904\) −152.445 88.0144i −5.07026 2.92732i
\(905\) −25.4013 + 15.4427i −0.844366 + 0.513333i
\(906\) 16.8172 29.1283i 0.558715 0.967722i
\(907\) 6.54797 3.78047i 0.217422 0.125529i −0.387334 0.921939i \(-0.626604\pi\)
0.604756 + 0.796411i \(0.293271\pi\)
\(908\) 23.0515 + 39.9263i 0.764990 + 1.32500i
\(909\) 0.697909 0.0231482
\(910\) −12.1800 81.1987i −0.403762 2.69171i
\(911\) −30.4986 −1.01046 −0.505232 0.862984i \(-0.668593\pi\)
−0.505232 + 0.862984i \(0.668593\pi\)
\(912\) 16.4985 + 28.5762i 0.546319 + 0.946252i
\(913\) −15.4695 + 8.93130i −0.511965 + 0.295583i
\(914\) 31.5702 54.6812i 1.04425 1.80869i
\(915\) 0.738346 + 1.21448i 0.0244090 + 0.0401496i
\(916\) 111.658 + 64.4656i 3.68927 + 2.13000i
\(917\) 10.3553 17.9358i 0.341961 0.592293i
\(918\) 7.24083 0.238983
\(919\) 6.09823 10.5624i 0.201162 0.348423i −0.747741 0.663990i \(-0.768862\pi\)
0.948903 + 0.315568i \(0.102195\pi\)
\(920\) 4.51530 8.24653i 0.148865 0.271880i
\(921\) −22.5622 + 13.0263i −0.743451 + 0.429232i
\(922\) 37.9657i 1.25033i
\(923\) −10.8952 + 8.27992i −0.358621 + 0.272537i
\(924\) 47.5489 1.56425
\(925\) −7.97168 + 0.361306i −0.262107 + 0.0118797i
\(926\) 10.1786 + 17.6298i 0.334488 + 0.579351i
\(927\) 3.39858 + 1.96217i 0.111624 + 0.0644461i
\(928\) −33.1930 −1.08962
\(929\) −43.7395 25.2530i −1.43505 0.828524i −0.437547 0.899196i \(-0.644153\pi\)
−0.997500 + 0.0706712i \(0.977486\pi\)
\(930\) 0.439067 + 19.3846i 0.0143976 + 0.635647i
\(931\) 15.5264i 0.508859i
\(932\) 22.4011 + 12.9333i 0.733772 + 0.423643i
\(933\) −9.18268 + 5.30162i −0.300627 + 0.173567i
\(934\) −15.3712 + 8.87454i −0.502960 + 0.290384i
\(935\) −11.8678 + 7.21501i −0.388117 + 0.235956i
\(936\) 20.4906 + 26.9627i 0.669756 + 0.881305i
\(937\) 9.97732i 0.325945i −0.986631 0.162972i \(-0.947892\pi\)
0.986631 0.162972i \(-0.0521082\pi\)
\(938\) 51.5547 + 89.2954i 1.68332 + 2.91560i
\(939\) −0.930138 1.61105i −0.0303539 0.0525745i
\(940\) 2.22280 + 98.1360i 0.0724999 + 3.20084i
\(941\) 51.3470i 1.67387i 0.547305 + 0.836933i \(0.315654\pi\)
−0.547305 + 0.836933i \(0.684346\pi\)
\(942\) −33.8087 + 58.5584i −1.10155 + 1.90793i
\(943\) 0.224014 0.388004i 0.00729490 0.0126351i
\(944\) 78.4715i 2.55403i
\(945\) −8.34505 + 0.189018i −0.271465 + 0.00614874i
\(946\) 37.2828 + 64.5758i 1.21217 + 2.09954i
\(947\) 25.2810 + 43.7880i 0.821522 + 1.42292i 0.904548 + 0.426371i \(0.140208\pi\)
−0.0830260 + 0.996547i \(0.526458\pi\)
\(948\) 10.5326i 0.342082i
\(949\) −0.0689263 + 0.164237i −0.00223744 + 0.00533135i
\(950\) 27.1119 + 14.0564i 0.879625 + 0.456050i
\(951\) −7.60716 + 4.39200i −0.246679 + 0.142420i
\(952\) 80.5913 46.5294i 2.61198 1.50803i
\(953\) 30.8855 + 17.8318i 1.00048 + 0.577627i 0.908390 0.418123i \(-0.137312\pi\)
0.0920897 + 0.995751i \(0.470645\pi\)
\(954\) 22.7474i 0.736475i
\(955\) −0.840697 37.1165i −0.0272043 1.20106i
\(956\) −62.5961 36.1399i −2.02450 1.16885i
\(957\) −3.62582 −0.117206
\(958\) 6.98596 + 4.03334i 0.225706 + 0.130311i
\(959\) 25.2963 + 43.8145i 0.816861 + 1.41484i
\(960\) −31.1119 + 56.8212i −1.00413 + 1.83390i
\(961\) 20.8974 0.674111
\(962\) −9.49874 12.4990i −0.306252 0.402984i
\(963\) 1.62389i 0.0523292i
\(964\) −46.9492 + 27.1061i −1.51213 + 0.873029i
\(965\) −25.7598 14.1045i −0.829236 0.454040i
\(966\) −2.27948 + 3.94818i −0.0733412 + 0.127031i
\(967\) −7.79539 −0.250683 −0.125341 0.992114i \(-0.540003\pi\)
−0.125341 + 0.992114i \(0.540003\pi\)
\(968\) −25.9386 + 44.9270i −0.833698 + 1.44401i
\(969\) 5.14597 + 2.97103i 0.165312 + 0.0954432i
\(970\) 65.0674 39.5578i 2.08919 1.27012i
\(971\) 5.58454 9.67270i 0.179216 0.310412i −0.762396 0.647111i \(-0.775977\pi\)
0.941612 + 0.336699i \(0.109310\pi\)
\(972\) 4.71362 2.72141i 0.151189 0.0872892i
\(973\) −10.0948 17.4847i −0.323625 0.560534i
\(974\) 41.5672 1.33190
\(975\) 16.9220 + 6.21656i 0.541938 + 0.199089i
\(976\) −9.36829 −0.299872
\(977\) −17.4149 30.1634i −0.557151 0.965014i −0.997733 0.0673013i \(-0.978561\pi\)
0.440582 0.897712i \(-0.354772\pi\)
\(978\) 37.6403 21.7316i 1.20360 0.694901i
\(979\) 6.16161 10.6722i 0.196926 0.341086i
\(980\) −72.1217 + 43.8464i −2.30384 + 1.40062i
\(981\) −15.2487 8.80385i −0.486854 0.281085i
\(982\) 22.9939 39.8266i 0.733765 1.27092i
\(983\) 20.6364 0.658199 0.329099 0.944295i \(-0.393255\pi\)
0.329099 + 0.944295i \(0.393255\pi\)
\(984\) −4.70019 + 8.14097i −0.149837 + 0.259525i
\(985\) −32.5549 17.8251i −1.03729 0.567955i
\(986\) −9.71545 + 5.60922i −0.309403 + 0.178634i
\(987\) 30.1083i 0.958359i
\(988\) 5.53190 + 43.5855i 0.175993 + 1.38664i
\(989\) −5.22818 −0.166247
\(990\) −6.85635 + 12.5221i −0.217909 + 0.397978i
\(991\) −20.5680 35.6249i −0.653365 1.13166i −0.982301 0.187310i \(-0.940023\pi\)
0.328936 0.944352i \(-0.393310\pi\)
\(992\) −58.9724 34.0477i −1.87238 1.08102i
\(993\) 15.7189 0.498824
\(994\) 33.4741 + 19.3263i 1.06173 + 0.612993i
\(995\) −0.779771 34.4266i −0.0247204 1.09140i
\(996\) 41.5439i 1.31637i
\(997\) 44.2553 + 25.5508i 1.40158 + 0.809202i 0.994555 0.104216i \(-0.0332333\pi\)
0.407024 + 0.913418i \(0.366567\pi\)
\(998\) −12.6527 + 7.30507i −0.400516 + 0.231238i
\(999\) −1.38215 + 0.797986i −0.0437294 + 0.0252472i
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 195.2.v.a.49.1 yes 32
3.2 odd 2 585.2.bf.c.244.16 32
5.2 odd 4 975.2.bc.m.751.8 16
5.3 odd 4 975.2.bc.n.751.1 16
5.4 even 2 inner 195.2.v.a.49.16 yes 32
13.4 even 6 inner 195.2.v.a.4.16 yes 32
15.14 odd 2 585.2.bf.c.244.1 32
39.17 odd 6 585.2.bf.c.199.1 32
65.4 even 6 inner 195.2.v.a.4.1 32
65.17 odd 12 975.2.bc.m.901.8 16
65.43 odd 12 975.2.bc.n.901.1 16
195.134 odd 6 585.2.bf.c.199.16 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
195.2.v.a.4.1 32 65.4 even 6 inner
195.2.v.a.4.16 yes 32 13.4 even 6 inner
195.2.v.a.49.1 yes 32 1.1 even 1 trivial
195.2.v.a.49.16 yes 32 5.4 even 2 inner
585.2.bf.c.199.1 32 39.17 odd 6
585.2.bf.c.199.16 32 195.134 odd 6
585.2.bf.c.244.1 32 15.14 odd 2
585.2.bf.c.244.16 32 3.2 odd 2
975.2.bc.m.751.8 16 5.2 odd 4
975.2.bc.m.901.8 16 65.17 odd 12
975.2.bc.n.751.1 16 5.3 odd 4
975.2.bc.n.901.1 16 65.43 odd 12