Properties

Label 456.2.j.e.419.20
Level $456$
Weight $2$
Character 456.419
Analytic conductor $3.641$
Analytic rank $0$
Dimension $24$
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] = [456,2,Mod(419,456)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(456, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1, 1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("456.419");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 456 = 2^{3} \cdot 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 456.j (of order \(2\), degree \(1\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.64117833217\)
Analytic rank: \(0\)
Dimension: \(24\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 419.20
Character \(\chi\) \(=\) 456.419
Dual form 456.2.j.e.419.19

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.960810 + 1.03771i) q^{2} +(0.153689 + 1.72522i) q^{3} +(-0.153689 + 1.99409i) q^{4} +1.97287 q^{5} +(-1.64261 + 1.81709i) q^{6} -2.35621i q^{7} +(-2.21695 + 1.75645i) q^{8} +(-2.95276 + 0.530294i) q^{9} +O(q^{10})\) \(q+(0.960810 + 1.03771i) q^{2} +(0.153689 + 1.72522i) q^{3} +(-0.153689 + 1.99409i) q^{4} +1.97287 q^{5} +(-1.64261 + 1.81709i) q^{6} -2.35621i q^{7} +(-2.21695 + 1.75645i) q^{8} +(-2.95276 + 0.530294i) q^{9} +(1.89556 + 2.04727i) q^{10} +4.83256i q^{11} +(-3.46386 + 0.0413220i) q^{12} +2.14536i q^{13} +(2.44507 - 2.26387i) q^{14} +(0.303209 + 3.40364i) q^{15} +(-3.95276 - 0.612938i) q^{16} -5.22103i q^{17} +(-3.38733 - 2.55460i) q^{18} +1.00000 q^{19} +(-0.303209 + 3.93408i) q^{20} +(4.06498 - 0.362124i) q^{21} +(-5.01481 + 4.64318i) q^{22} +8.06939 q^{23} +(-3.37099 - 3.55478i) q^{24} -1.10777 q^{25} +(-2.22626 + 2.06128i) q^{26} +(-1.36868 - 5.01266i) q^{27} +(4.69849 + 0.362124i) q^{28} +0.590664 q^{29} +(-3.24067 + 3.58489i) q^{30} +4.48507i q^{31} +(-3.16180 - 4.69074i) q^{32} +(-8.33723 + 0.742712i) q^{33} +(5.41793 - 5.01642i) q^{34} -4.64850i q^{35} +(-0.603646 - 5.96956i) q^{36} -8.77578i q^{37} +(0.960810 + 1.03771i) q^{38} +(-3.70121 + 0.329718i) q^{39} +(-4.37376 + 3.46526i) q^{40} -6.54069i q^{41} +(4.28145 + 3.87034i) q^{42} -1.36072 q^{43} +(-9.63655 - 0.742712i) q^{44} +(-5.82542 + 1.04620i) q^{45} +(7.75315 + 8.37370i) q^{46} -5.54780 q^{47} +(0.449957 - 6.91358i) q^{48} +1.44828 q^{49} +(-1.06436 - 1.14955i) q^{50} +(9.00743 - 0.802416i) q^{51} +(-4.27802 - 0.329718i) q^{52} +13.0520 q^{53} +(3.88665 - 6.23650i) q^{54} +9.53404i q^{55} +(4.13857 + 5.22360i) q^{56} +(0.153689 + 1.72522i) q^{57} +(0.567516 + 0.612938i) q^{58} +14.0204i q^{59} +(-6.83375 + 0.0815230i) q^{60} -10.1557i q^{61} +(-4.65421 + 4.30930i) q^{62} +(1.24948 + 6.95732i) q^{63} +(1.82975 - 7.78794i) q^{64} +4.23251i q^{65} +(-8.78121 - 7.93803i) q^{66} +5.68558 q^{67} +(10.4112 + 0.802416i) q^{68} +(1.24018 + 13.9215i) q^{69} +(4.82380 - 4.46633i) q^{70} +3.57493 q^{71} +(5.61469 - 6.36202i) q^{72} -3.06303 q^{73} +(9.10673 - 8.43186i) q^{74} +(-0.170252 - 1.91115i) q^{75} +(-0.153689 + 1.99409i) q^{76} +11.3865 q^{77} +(-3.89831 - 3.52399i) q^{78} +3.01433i q^{79} +(-7.79829 - 1.20925i) q^{80} +(8.43758 - 3.13166i) q^{81} +(6.78735 - 6.28436i) q^{82} -6.41871i q^{83} +(0.0973633 + 8.16157i) q^{84} -10.3004i q^{85} +(-1.30740 - 1.41204i) q^{86} +(0.0907785 + 1.01902i) q^{87} +(-8.48817 - 10.7136i) q^{88} +6.77889i q^{89} +(-6.68278 - 5.03990i) q^{90} +5.05491 q^{91} +(-1.24018 + 16.0911i) q^{92} +(-7.73773 + 0.689307i) q^{93} +(-5.33038 - 5.75702i) q^{94} +1.97287 q^{95} +(7.60662 - 6.17571i) q^{96} -12.2390 q^{97} +(1.39152 + 1.50289i) q^{98} +(-2.56268 - 14.2694i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q + 6 q^{3} - 6 q^{4} + q^{6} - 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 24 q + 6 q^{3} - 6 q^{4} + q^{6} - 6 q^{9} + 4 q^{10} - 33 q^{12} - 30 q^{16} - 19 q^{18} + 24 q^{19} - 28 q^{22} + 21 q^{24} + 96 q^{25} + 34 q^{28} + 8 q^{30} + 24 q^{33} + 58 q^{34} - 9 q^{36} - 24 q^{40} - 31 q^{42} + 16 q^{43} - 6 q^{46} + 3 q^{48} - 36 q^{49} + 38 q^{51} - 6 q^{52} - 8 q^{54} + 6 q^{57} - 42 q^{58} - 50 q^{60} + 18 q^{64} + 10 q^{66} + 20 q^{67} - 96 q^{70} - 33 q^{72} - 12 q^{73} - 30 q^{75} - 6 q^{76} - 17 q^{78} + 34 q^{81} + 68 q^{82} - 29 q^{84} - 76 q^{88} - 70 q^{90} - 36 q^{91} - 12 q^{94} + 29 q^{96} - 104 q^{97} + 56 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/456\mathbb{Z}\right)^\times\).

\(n\) \(97\) \(229\) \(305\) \(343\)
\(\chi(n)\) \(1\) \(-1\) \(-1\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.960810 + 1.03771i 0.679395 + 0.733773i
\(3\) 0.153689 + 1.72522i 0.0887324 + 0.996056i
\(4\) −0.153689 + 1.99409i −0.0768445 + 0.997043i
\(5\) 1.97287 0.882296 0.441148 0.897434i \(-0.354571\pi\)
0.441148 + 0.897434i \(0.354571\pi\)
\(6\) −1.64261 + 1.81709i −0.670594 + 0.741825i
\(7\) 2.35621i 0.890564i −0.895390 0.445282i \(-0.853104\pi\)
0.895390 0.445282i \(-0.146896\pi\)
\(8\) −2.21695 + 1.75645i −0.783811 + 0.621000i
\(9\) −2.95276 + 0.530294i −0.984253 + 0.176765i
\(10\) 1.89556 + 2.04727i 0.599427 + 0.647404i
\(11\) 4.83256i 1.45707i 0.685007 + 0.728537i \(0.259799\pi\)
−0.685007 + 0.728537i \(0.740201\pi\)
\(12\) −3.46386 + 0.0413220i −0.999929 + 0.0119286i
\(13\) 2.14536i 0.595014i 0.954720 + 0.297507i \(0.0961552\pi\)
−0.954720 + 0.297507i \(0.903845\pi\)
\(14\) 2.44507 2.26387i 0.653471 0.605045i
\(15\) 0.303209 + 3.40364i 0.0782882 + 0.878816i
\(16\) −3.95276 0.612938i −0.988190 0.153235i
\(17\) 5.22103i 1.26629i −0.774035 0.633143i \(-0.781764\pi\)
0.774035 0.633143i \(-0.218236\pi\)
\(18\) −3.38733 2.55460i −0.798402 0.602125i
\(19\) 1.00000 0.229416
\(20\) −0.303209 + 3.93408i −0.0677996 + 0.879687i
\(21\) 4.06498 0.362124i 0.887051 0.0790219i
\(22\) −5.01481 + 4.64318i −1.06916 + 0.989928i
\(23\) 8.06939 1.68258 0.841292 0.540580i \(-0.181795\pi\)
0.841292 + 0.540580i \(0.181795\pi\)
\(24\) −3.37099 3.55478i −0.688100 0.725616i
\(25\) −1.10777 −0.221554
\(26\) −2.22626 + 2.06128i −0.436605 + 0.404250i
\(27\) −1.36868 5.01266i −0.263403 0.964686i
\(28\) 4.69849 + 0.362124i 0.887930 + 0.0684349i
\(29\) 0.590664 0.109684 0.0548418 0.998495i \(-0.482535\pi\)
0.0548418 + 0.998495i \(0.482535\pi\)
\(30\) −3.24067 + 3.58489i −0.591662 + 0.654509i
\(31\) 4.48507i 0.805543i 0.915301 + 0.402771i \(0.131953\pi\)
−0.915301 + 0.402771i \(0.868047\pi\)
\(32\) −3.16180 4.69074i −0.558932 0.829213i
\(33\) −8.33723 + 0.742712i −1.45133 + 0.129290i
\(34\) 5.41793 5.01642i 0.929167 0.860309i
\(35\) 4.64850i 0.785740i
\(36\) −0.603646 5.96956i −0.100608 0.994926i
\(37\) 8.77578i 1.44273i −0.692555 0.721365i \(-0.743515\pi\)
0.692555 0.721365i \(-0.256485\pi\)
\(38\) 0.960810 + 1.03771i 0.155864 + 0.168339i
\(39\) −3.70121 + 0.329718i −0.592667 + 0.0527971i
\(40\) −4.37376 + 3.46526i −0.691553 + 0.547906i
\(41\) 6.54069i 1.02148i −0.859734 0.510742i \(-0.829371\pi\)
0.859734 0.510742i \(-0.170629\pi\)
\(42\) 4.28145 + 3.87034i 0.660642 + 0.597207i
\(43\) −1.36072 −0.207508 −0.103754 0.994603i \(-0.533086\pi\)
−0.103754 + 0.994603i \(0.533086\pi\)
\(44\) −9.63655 0.742712i −1.45276 0.111968i
\(45\) −5.82542 + 1.04620i −0.868402 + 0.155959i
\(46\) 7.75315 + 8.37370i 1.14314 + 1.23463i
\(47\) −5.54780 −0.809230 −0.404615 0.914487i \(-0.632594\pi\)
−0.404615 + 0.914487i \(0.632594\pi\)
\(48\) 0.449957 6.91358i 0.0649457 0.997889i
\(49\) 1.44828 0.206896
\(50\) −1.06436 1.14955i −0.150523 0.162570i
\(51\) 9.00743 0.802416i 1.26129 0.112361i
\(52\) −4.27802 0.329718i −0.593255 0.0457236i
\(53\) 13.0520 1.79283 0.896416 0.443214i \(-0.146162\pi\)
0.896416 + 0.443214i \(0.146162\pi\)
\(54\) 3.88665 6.23650i 0.528906 0.848681i
\(55\) 9.53404i 1.28557i
\(56\) 4.13857 + 5.22360i 0.553040 + 0.698033i
\(57\) 0.153689 + 1.72522i 0.0203566 + 0.228511i
\(58\) 0.567516 + 0.612938i 0.0745184 + 0.0804828i
\(59\) 14.0204i 1.82530i 0.408744 + 0.912649i \(0.365967\pi\)
−0.408744 + 0.912649i \(0.634033\pi\)
\(60\) −6.83375 + 0.0815230i −0.882233 + 0.0105246i
\(61\) 10.1557i 1.30031i −0.759804 0.650153i \(-0.774705\pi\)
0.759804 0.650153i \(-0.225295\pi\)
\(62\) −4.65421 + 4.30930i −0.591085 + 0.547282i
\(63\) 1.24948 + 6.95732i 0.157420 + 0.876540i
\(64\) 1.82975 7.78794i 0.228718 0.973493i
\(65\) 4.23251i 0.524979i
\(66\) −8.78121 7.93803i −1.08089 0.977104i
\(67\) 5.68558 0.694604 0.347302 0.937753i \(-0.387098\pi\)
0.347302 + 0.937753i \(0.387098\pi\)
\(68\) 10.4112 + 0.802416i 1.26254 + 0.0973072i
\(69\) 1.24018 + 13.9215i 0.149300 + 1.67595i
\(70\) 4.82380 4.46633i 0.576555 0.533828i
\(71\) 3.57493 0.424266 0.212133 0.977241i \(-0.431959\pi\)
0.212133 + 0.977241i \(0.431959\pi\)
\(72\) 5.61469 6.36202i 0.661697 0.749771i
\(73\) −3.06303 −0.358501 −0.179250 0.983803i \(-0.557367\pi\)
−0.179250 + 0.983803i \(0.557367\pi\)
\(74\) 9.10673 8.43186i 1.05864 0.980184i
\(75\) −0.170252 1.91115i −0.0196590 0.220680i
\(76\) −0.153689 + 1.99409i −0.0176293 + 0.228737i
\(77\) 11.3865 1.29762
\(78\) −3.89831 3.52399i −0.441396 0.399013i
\(79\) 3.01433i 0.339139i 0.985518 + 0.169570i \(0.0542377\pi\)
−0.985518 + 0.169570i \(0.945762\pi\)
\(80\) −7.79829 1.20925i −0.871876 0.135198i
\(81\) 8.43758 3.13166i 0.937508 0.347963i
\(82\) 6.78735 6.28436i 0.749538 0.693992i
\(83\) 6.41871i 0.704545i −0.935898 0.352272i \(-0.885409\pi\)
0.935898 0.352272i \(-0.114591\pi\)
\(84\) 0.0973633 + 8.16157i 0.0106232 + 0.890500i
\(85\) 10.3004i 1.11724i
\(86\) −1.30740 1.41204i −0.140980 0.152264i
\(87\) 0.0907785 + 1.01902i 0.00973248 + 0.109251i
\(88\) −8.48817 10.7136i −0.904842 1.14207i
\(89\) 6.77889i 0.718561i 0.933230 + 0.359280i \(0.116978\pi\)
−0.933230 + 0.359280i \(0.883022\pi\)
\(90\) −6.68278 5.03990i −0.704427 0.531252i
\(91\) 5.05491 0.529898
\(92\) −1.24018 + 16.0911i −0.129297 + 1.67761i
\(93\) −7.73773 + 0.689307i −0.802365 + 0.0714778i
\(94\) −5.33038 5.75702i −0.549787 0.593791i
\(95\) 1.97287 0.202413
\(96\) 7.60662 6.17571i 0.776347 0.630305i
\(97\) −12.2390 −1.24268 −0.621340 0.783541i \(-0.713411\pi\)
−0.621340 + 0.783541i \(0.713411\pi\)
\(98\) 1.39152 + 1.50289i 0.140564 + 0.151815i
\(99\) −2.56268 14.2694i −0.257559 1.43413i
\(100\) 0.170252 2.20899i 0.0170252 0.220899i
\(101\) 1.74580 0.173714 0.0868568 0.996221i \(-0.472318\pi\)
0.0868568 + 0.996221i \(0.472318\pi\)
\(102\) 9.48710 + 8.57614i 0.939363 + 0.849164i
\(103\) 13.1313i 1.29387i −0.762547 0.646933i \(-0.776051\pi\)
0.762547 0.646933i \(-0.223949\pi\)
\(104\) −3.76821 4.75615i −0.369504 0.466379i
\(105\) 8.01969 0.714424i 0.782641 0.0697206i
\(106\) 12.5405 + 13.5442i 1.21804 + 1.31553i
\(107\) 9.99113i 0.965879i 0.875654 + 0.482940i \(0.160431\pi\)
−0.875654 + 0.482940i \(0.839569\pi\)
\(108\) 10.2060 1.95888i 0.982075 0.188493i
\(109\) 4.66192i 0.446531i −0.974758 0.223266i \(-0.928328\pi\)
0.974758 0.223266i \(-0.0716717\pi\)
\(110\) −9.89358 + 9.16040i −0.943316 + 0.873410i
\(111\) 15.1401 1.34874i 1.43704 0.128017i
\(112\) −1.44421 + 9.31353i −0.136465 + 0.880046i
\(113\) 15.4604i 1.45439i 0.686432 + 0.727194i \(0.259176\pi\)
−0.686432 + 0.727194i \(0.740824\pi\)
\(114\) −1.64261 + 1.81709i −0.153845 + 0.170186i
\(115\) 15.9199 1.48454
\(116\) −0.0907785 + 1.17783i −0.00842858 + 0.109359i
\(117\) −1.13767 6.33472i −0.105178 0.585645i
\(118\) −14.5491 + 13.4709i −1.33935 + 1.24010i
\(119\) −12.3019 −1.12771
\(120\) −6.65053 7.01313i −0.607107 0.640208i
\(121\) −12.3537 −1.12306
\(122\) 10.5387 9.75770i 0.954128 0.883421i
\(123\) 11.2841 1.00523i 1.01746 0.0906388i
\(124\) −8.94362 0.689307i −0.803161 0.0619016i
\(125\) −12.0499 −1.07777
\(126\) −6.01917 + 7.98127i −0.536230 + 0.711028i
\(127\) 11.0587i 0.981300i −0.871357 0.490650i \(-0.836759\pi\)
0.871357 0.490650i \(-0.163241\pi\)
\(128\) 9.83967 5.58398i 0.869712 0.493559i
\(129\) −0.209128 2.34754i −0.0184127 0.206690i
\(130\) −4.39213 + 4.06664i −0.385215 + 0.356668i
\(131\) 5.46142i 0.477166i −0.971122 0.238583i \(-0.923317\pi\)
0.971122 0.238583i \(-0.0766829\pi\)
\(132\) −0.199691 16.7393i −0.0173809 1.45697i
\(133\) 2.35621i 0.204309i
\(134\) 5.46276 + 5.89999i 0.471911 + 0.509681i
\(135\) −2.70023 9.88933i −0.232399 0.851138i
\(136\) 9.17050 + 11.5748i 0.786364 + 0.992529i
\(137\) 1.19513i 0.102106i 0.998696 + 0.0510532i \(0.0162578\pi\)
−0.998696 + 0.0510532i \(0.983742\pi\)
\(138\) −13.2549 + 14.6628i −1.12833 + 1.24818i
\(139\) −4.81905 −0.408746 −0.204373 0.978893i \(-0.565516\pi\)
−0.204373 + 0.978893i \(0.565516\pi\)
\(140\) 9.26952 + 0.714424i 0.783417 + 0.0603799i
\(141\) −0.852636 9.57117i −0.0718049 0.806038i
\(142\) 3.43483 + 3.70974i 0.288244 + 0.311315i
\(143\) −10.3676 −0.866980
\(144\) 11.9966 0.286267i 0.999715 0.0238556i
\(145\) 1.16530 0.0967733
\(146\) −2.94299 3.17854i −0.243564 0.263058i
\(147\) 0.222584 + 2.49859i 0.0183584 + 0.206080i
\(148\) 17.4997 + 1.34874i 1.43846 + 0.110866i
\(149\) −23.1362 −1.89539 −0.947697 0.319172i \(-0.896595\pi\)
−0.947697 + 0.319172i \(0.896595\pi\)
\(150\) 1.81964 2.01292i 0.148573 0.164354i
\(151\) 5.63190i 0.458317i 0.973389 + 0.229159i \(0.0735975\pi\)
−0.973389 + 0.229159i \(0.926403\pi\)
\(152\) −2.21695 + 1.75645i −0.179819 + 0.142467i
\(153\) 2.76869 + 15.4165i 0.223835 + 1.24635i
\(154\) 10.9403 + 11.8159i 0.881594 + 0.952155i
\(155\) 8.84848i 0.710727i
\(156\) −0.0886503 7.43120i −0.00709771 0.594972i
\(157\) 4.71242i 0.376092i −0.982160 0.188046i \(-0.939785\pi\)
0.982160 0.188046i \(-0.0602154\pi\)
\(158\) −3.12801 + 2.89620i −0.248851 + 0.230409i
\(159\) 2.00595 + 22.5176i 0.159082 + 1.78576i
\(160\) −6.23782 9.25424i −0.493143 0.731612i
\(161\) 19.0132i 1.49845i
\(162\) 11.3567 + 5.74683i 0.892264 + 0.451514i
\(163\) −21.8296 −1.70983 −0.854913 0.518771i \(-0.826390\pi\)
−0.854913 + 0.518771i \(0.826390\pi\)
\(164\) 13.0427 + 1.00523i 1.01846 + 0.0784955i
\(165\) −16.4483 + 1.46528i −1.28050 + 0.114072i
\(166\) 6.66077 6.16716i 0.516976 0.478664i
\(167\) 0.772221 0.0597562 0.0298781 0.999554i \(-0.490488\pi\)
0.0298781 + 0.999554i \(0.490488\pi\)
\(168\) −8.37580 + 7.94275i −0.646207 + 0.612797i
\(169\) 8.39745 0.645958
\(170\) 10.6889 9.89676i 0.819800 0.759047i
\(171\) −2.95276 + 0.530294i −0.225803 + 0.0405526i
\(172\) 0.209128 2.71340i 0.0159459 0.206895i
\(173\) 2.64330 0.200966 0.100483 0.994939i \(-0.467961\pi\)
0.100483 + 0.994939i \(0.467961\pi\)
\(174\) −0.970232 + 1.07329i −0.0735531 + 0.0813659i
\(175\) 2.61014i 0.197308i
\(176\) 2.96206 19.1020i 0.223274 1.43986i
\(177\) −24.1882 + 2.15478i −1.81810 + 0.161963i
\(178\) −7.03453 + 6.51322i −0.527260 + 0.488187i
\(179\) 13.7988i 1.03137i −0.856778 0.515686i \(-0.827537\pi\)
0.856778 0.515686i \(-0.172463\pi\)
\(180\) −1.19092 11.7772i −0.0887657 0.877819i
\(181\) 12.3871i 0.920729i 0.887730 + 0.460365i \(0.152281\pi\)
−0.887730 + 0.460365i \(0.847719\pi\)
\(182\) 4.85680 + 5.24553i 0.360010 + 0.388825i
\(183\) 17.5208 1.56082i 1.29518 0.115379i
\(184\) −17.8895 + 14.1735i −1.31883 + 1.04488i
\(185\) 17.3135i 1.27291i
\(186\) −8.14979 7.36724i −0.597572 0.540192i
\(187\) 25.2310 1.84507
\(188\) 0.852636 11.0628i 0.0621849 0.806837i
\(189\) −11.8109 + 3.22490i −0.859114 + 0.234577i
\(190\) 1.89556 + 2.04727i 0.137518 + 0.148525i
\(191\) 0.794407 0.0574813 0.0287406 0.999587i \(-0.490850\pi\)
0.0287406 + 0.999587i \(0.490850\pi\)
\(192\) 13.7171 + 1.95979i 0.989947 + 0.141436i
\(193\) −10.5422 −0.758842 −0.379421 0.925224i \(-0.623877\pi\)
−0.379421 + 0.925224i \(0.623877\pi\)
\(194\) −11.7593 12.7005i −0.844271 0.911845i
\(195\) −7.30201 + 0.650491i −0.522908 + 0.0465826i
\(196\) −0.222584 + 2.88799i −0.0158989 + 0.206285i
\(197\) 10.3447 0.737032 0.368516 0.929621i \(-0.379866\pi\)
0.368516 + 0.929621i \(0.379866\pi\)
\(198\) 12.3453 16.3695i 0.877340 1.16333i
\(199\) 11.1911i 0.793315i −0.917967 0.396657i \(-0.870170\pi\)
0.917967 0.396657i \(-0.129830\pi\)
\(200\) 2.45587 1.94575i 0.173657 0.137585i
\(201\) 0.873811 + 9.80887i 0.0616339 + 0.691864i
\(202\) 1.67738 + 1.81164i 0.118020 + 0.127466i
\(203\) 1.39173i 0.0976801i
\(204\) 0.215743 + 18.0849i 0.0151051 + 1.26620i
\(205\) 12.9040i 0.901252i
\(206\) 13.6265 12.6167i 0.949403 0.879046i
\(207\) −23.8270 + 4.27915i −1.65609 + 0.297422i
\(208\) 1.31497 8.48007i 0.0911768 0.587987i
\(209\) 4.83256i 0.334275i
\(210\) 8.44676 + 7.63569i 0.582882 + 0.526913i
\(211\) −5.93112 −0.408315 −0.204158 0.978938i \(-0.565446\pi\)
−0.204158 + 0.978938i \(0.565446\pi\)
\(212\) −2.00595 + 26.0268i −0.137769 + 1.78753i
\(213\) 0.549427 + 6.16753i 0.0376461 + 0.422592i
\(214\) −10.3679 + 9.59958i −0.708736 + 0.656214i
\(215\) −2.68453 −0.183084
\(216\) 11.8388 + 8.70879i 0.805528 + 0.592558i
\(217\) 10.5678 0.717387
\(218\) 4.83773 4.47922i 0.327652 0.303371i
\(219\) −0.470754 5.28440i −0.0318106 0.357087i
\(220\) −19.0117 1.46528i −1.28177 0.0987890i
\(221\) 11.2010 0.753459
\(222\) 15.9464 + 14.4152i 1.07025 + 0.967486i
\(223\) 3.45829i 0.231584i 0.993273 + 0.115792i \(0.0369406\pi\)
−0.993273 + 0.115792i \(0.963059\pi\)
\(224\) −11.0524 + 7.44986i −0.738467 + 0.497765i
\(225\) 3.27098 0.587445i 0.218065 0.0391630i
\(226\) −16.0434 + 14.8545i −1.06719 + 0.988104i
\(227\) 14.3152i 0.950130i 0.879951 + 0.475065i \(0.157576\pi\)
−0.879951 + 0.475065i \(0.842424\pi\)
\(228\) −3.46386 + 0.0413220i −0.229399 + 0.00273661i
\(229\) 13.4895i 0.891412i −0.895179 0.445706i \(-0.852953\pi\)
0.895179 0.445706i \(-0.147047\pi\)
\(230\) 15.2960 + 16.5202i 1.00859 + 1.08931i
\(231\) 1.74999 + 19.6443i 0.115141 + 1.29250i
\(232\) −1.30947 + 1.03747i −0.0859711 + 0.0681134i
\(233\) 14.0612i 0.921181i −0.887613 0.460591i \(-0.847638\pi\)
0.887613 0.460591i \(-0.152362\pi\)
\(234\) 5.48052 7.26703i 0.358273 0.475061i
\(235\) −10.9451 −0.713980
\(236\) −27.9579 2.15478i −1.81990 0.140264i
\(237\) −5.20039 + 0.463270i −0.337801 + 0.0300926i
\(238\) −11.8197 12.7658i −0.766160 0.827482i
\(239\) −10.9776 −0.710079 −0.355040 0.934851i \(-0.615533\pi\)
−0.355040 + 0.934851i \(0.615533\pi\)
\(240\) 0.887708 13.6396i 0.0573013 0.880433i
\(241\) −12.3554 −0.795878 −0.397939 0.917412i \(-0.630275\pi\)
−0.397939 + 0.917412i \(0.630275\pi\)
\(242\) −11.8695 12.8196i −0.763003 0.824072i
\(243\) 6.69957 + 14.0754i 0.429777 + 0.902935i
\(244\) 20.2514 + 1.56082i 1.29646 + 0.0999213i
\(245\) 2.85726 0.182544
\(246\) 11.8850 + 10.7438i 0.757763 + 0.685001i
\(247\) 2.14536i 0.136506i
\(248\) −7.87782 9.94319i −0.500242 0.631393i
\(249\) 11.0737 0.986485i 0.701766 0.0625160i
\(250\) −11.5776 12.5043i −0.732233 0.790840i
\(251\) 3.35841i 0.211981i 0.994367 + 0.105991i \(0.0338013\pi\)
−0.994367 + 0.105991i \(0.966199\pi\)
\(252\) −14.0655 + 1.42232i −0.886045 + 0.0895975i
\(253\) 38.9959i 2.45165i
\(254\) 11.4757 10.6253i 0.720051 0.666691i
\(255\) 17.7705 1.58306i 1.11283 0.0991354i
\(256\) 15.2486 + 4.84560i 0.953038 + 0.302850i
\(257\) 5.93733i 0.370360i −0.982705 0.185180i \(-0.940713\pi\)
0.982705 0.185180i \(-0.0592868\pi\)
\(258\) 2.23514 2.47256i 0.139154 0.153935i
\(259\) −20.6776 −1.28484
\(260\) −8.44000 0.650491i −0.523426 0.0403417i
\(261\) −1.74409 + 0.313226i −0.107956 + 0.0193882i
\(262\) 5.66737 5.24738i 0.350132 0.324184i
\(263\) −21.0419 −1.29750 −0.648749 0.761002i \(-0.724707\pi\)
−0.648749 + 0.761002i \(0.724707\pi\)
\(264\) 17.1787 16.2905i 1.05728 1.00261i
\(265\) 25.7500 1.58181
\(266\) 2.44507 2.26387i 0.149917 0.138807i
\(267\) −11.6951 + 1.04184i −0.715727 + 0.0637596i
\(268\) −0.873811 + 11.3375i −0.0533765 + 0.692550i
\(269\) −10.4505 −0.637180 −0.318590 0.947893i \(-0.603209\pi\)
−0.318590 + 0.947893i \(0.603209\pi\)
\(270\) 7.66786 12.3038i 0.466651 0.748787i
\(271\) 31.8860i 1.93694i −0.249131 0.968470i \(-0.580145\pi\)
0.249131 0.968470i \(-0.419855\pi\)
\(272\) −3.20017 + 20.6375i −0.194039 + 1.25133i
\(273\) 0.776884 + 8.72082i 0.0470191 + 0.527808i
\(274\) −1.24020 + 1.14829i −0.0749229 + 0.0693706i
\(275\) 5.35337i 0.322821i
\(276\) −27.9512 + 0.333443i −1.68247 + 0.0200709i
\(277\) 19.3036i 1.15984i 0.814674 + 0.579920i \(0.196916\pi\)
−0.814674 + 0.579920i \(0.803084\pi\)
\(278\) −4.63019 5.00078i −0.277700 0.299927i
\(279\) −2.37841 13.2433i −0.142392 0.792858i
\(280\) 8.16488 + 10.3055i 0.487945 + 0.615872i
\(281\) 3.94758i 0.235493i −0.993044 0.117747i \(-0.962433\pi\)
0.993044 0.117747i \(-0.0375670\pi\)
\(282\) 9.11289 10.0809i 0.542665 0.600307i
\(283\) −16.8230 −1.00002 −0.500011 0.866019i \(-0.666671\pi\)
−0.500011 + 0.866019i \(0.666671\pi\)
\(284\) −0.549427 + 7.12872i −0.0326025 + 0.423011i
\(285\) 0.303209 + 3.40364i 0.0179606 + 0.201614i
\(286\) −9.96126 10.7585i −0.589022 0.636166i
\(287\) −15.4112 −0.909697
\(288\) 11.8235 + 12.1739i 0.696706 + 0.717356i
\(289\) −10.2592 −0.603482
\(290\) 1.11964 + 1.20925i 0.0657473 + 0.0710096i
\(291\) −1.88100 21.1149i −0.110266 1.23778i
\(292\) 0.470754 6.10795i 0.0275488 0.357441i
\(293\) −10.1353 −0.592112 −0.296056 0.955171i \(-0.595671\pi\)
−0.296056 + 0.955171i \(0.595671\pi\)
\(294\) −2.37896 + 2.63165i −0.138744 + 0.153481i
\(295\) 27.6604i 1.61045i
\(296\) 15.4142 + 19.4555i 0.895935 + 1.13083i
\(297\) 24.2240 6.61424i 1.40562 0.383797i
\(298\) −22.2295 24.0087i −1.28772 1.39079i
\(299\) 17.3117i 1.00116i
\(300\) 3.83716 0.0457753i 0.221538 0.00264284i
\(301\) 3.20615i 0.184799i
\(302\) −5.84428 + 5.41118i −0.336301 + 0.311379i
\(303\) 0.268310 + 3.01189i 0.0154140 + 0.173028i
\(304\) −3.95276 0.612938i −0.226706 0.0351544i
\(305\) 20.0359i 1.14725i
\(306\) −13.3377 + 17.6854i −0.762463 + 1.01101i
\(307\) 26.0177 1.48491 0.742454 0.669897i \(-0.233662\pi\)
0.742454 + 0.669897i \(0.233662\pi\)
\(308\) −1.74999 + 22.7057i −0.0997147 + 1.29378i
\(309\) 22.6544 2.01814i 1.28876 0.114808i
\(310\) −9.18217 + 8.50171i −0.521512 + 0.482865i
\(311\) −24.6649 −1.39862 −0.699309 0.714819i \(-0.746509\pi\)
−0.699309 + 0.714819i \(0.746509\pi\)
\(312\) 7.62626 7.23196i 0.431752 0.409429i
\(313\) 23.7033 1.33979 0.669894 0.742456i \(-0.266339\pi\)
0.669894 + 0.742456i \(0.266339\pi\)
\(314\) 4.89013 4.52774i 0.275966 0.255515i
\(315\) 2.46508 + 13.7259i 0.138891 + 0.773368i
\(316\) −6.01084 0.463270i −0.338136 0.0260610i
\(317\) 24.2250 1.36061 0.680306 0.732928i \(-0.261847\pi\)
0.680306 + 0.732928i \(0.261847\pi\)
\(318\) −21.4394 + 23.7167i −1.20226 + 1.32997i
\(319\) 2.85442i 0.159817i
\(320\) 3.60986 15.3646i 0.201797 0.858908i
\(321\) −17.2369 + 1.53553i −0.962069 + 0.0857048i
\(322\) 19.7302 18.2681i 1.09952 1.01804i
\(323\) 5.22103i 0.290506i
\(324\) 4.94804 + 17.3066i 0.274891 + 0.961475i
\(325\) 2.37656i 0.131828i
\(326\) −20.9741 22.6528i −1.16165 1.25462i
\(327\) 8.04283 0.716486i 0.444770 0.0396218i
\(328\) 11.4884 + 14.5004i 0.634342 + 0.800651i
\(329\) 13.0718i 0.720671i
\(330\) −17.3242 15.6607i −0.953667 0.862095i
\(331\) −19.4306 −1.06800 −0.534001 0.845484i \(-0.679312\pi\)
−0.534001 + 0.845484i \(0.679312\pi\)
\(332\) 12.7995 + 0.986485i 0.702462 + 0.0541404i
\(333\) 4.65375 + 25.9128i 0.255024 + 1.42001i
\(334\) 0.741957 + 0.801342i 0.0405981 + 0.0438475i
\(335\) 11.2169 0.612846
\(336\) −16.2898 1.06019i −0.888683 0.0578383i
\(337\) 3.54860 0.193305 0.0966524 0.995318i \(-0.469186\pi\)
0.0966524 + 0.995318i \(0.469186\pi\)
\(338\) 8.06835 + 8.71413i 0.438861 + 0.473986i
\(339\) −26.6725 + 2.37609i −1.44865 + 0.129051i
\(340\) 20.5400 + 1.58306i 1.11394 + 0.0858537i
\(341\) −21.6744 −1.17373
\(342\) −3.38733 2.55460i −0.183166 0.138137i
\(343\) 19.9059i 1.07482i
\(344\) 3.01666 2.39004i 0.162647 0.128863i
\(345\) 2.44671 + 27.4653i 0.131727 + 1.47868i
\(346\) 2.53971 + 2.74298i 0.136535 + 0.147463i
\(347\) 19.3122i 1.03673i 0.855158 + 0.518367i \(0.173460\pi\)
−0.855158 + 0.518367i \(0.826540\pi\)
\(348\) −2.04597 + 0.0244074i −0.109676 + 0.00130837i
\(349\) 13.9086i 0.744510i 0.928130 + 0.372255i \(0.121415\pi\)
−0.928130 + 0.372255i \(0.878585\pi\)
\(350\) −2.70857 + 2.50785i −0.144779 + 0.134050i
\(351\) 10.7539 2.93631i 0.574002 0.156728i
\(352\) 22.6683 15.2796i 1.20822 0.814405i
\(353\) 17.9380i 0.954744i −0.878701 0.477372i \(-0.841589\pi\)
0.878701 0.477372i \(-0.158411\pi\)
\(354\) −25.4763 23.0301i −1.35405 1.22403i
\(355\) 7.05288 0.374328
\(356\) −13.5177 1.04184i −0.716436 0.0552175i
\(357\) −1.89066 21.2234i −0.100064 1.12326i
\(358\) 14.3192 13.2580i 0.756792 0.700709i
\(359\) −32.0012 −1.68896 −0.844479 0.535589i \(-0.820090\pi\)
−0.844479 + 0.535589i \(0.820090\pi\)
\(360\) 11.0771 12.5515i 0.583813 0.661520i
\(361\) 1.00000 0.0526316
\(362\) −12.8543 + 11.9017i −0.675606 + 0.625539i
\(363\) −1.89863 21.3128i −0.0996520 1.11863i
\(364\) −0.776884 + 10.0799i −0.0407198 + 0.528331i
\(365\) −6.04297 −0.316304
\(366\) 18.4539 + 16.6819i 0.964598 + 0.871977i
\(367\) 14.3595i 0.749558i 0.927114 + 0.374779i \(0.122281\pi\)
−0.927114 + 0.374779i \(0.877719\pi\)
\(368\) −31.8964 4.94604i −1.66271 0.257830i
\(369\) 3.46849 + 19.3131i 0.180563 + 1.00540i
\(370\) 17.9664 16.6350i 0.934030 0.864812i
\(371\) 30.7533i 1.59663i
\(372\) −0.185332 15.5356i −0.00960902 0.805486i
\(373\) 22.3799i 1.15879i 0.815048 + 0.579393i \(0.196710\pi\)
−0.815048 + 0.579393i \(0.803290\pi\)
\(374\) 24.2422 + 26.1825i 1.25353 + 1.35386i
\(375\) −1.85193 20.7886i −0.0956333 1.07352i
\(376\) 12.2992 9.74445i 0.634283 0.502532i
\(377\) 1.26718i 0.0652633i
\(378\) −14.6945 9.15776i −0.755804 0.471024i
\(379\) 27.5634 1.41583 0.707917 0.706295i \(-0.249635\pi\)
0.707917 + 0.706295i \(0.249635\pi\)
\(380\) −0.303209 + 3.93408i −0.0155543 + 0.201814i
\(381\) 19.0787 1.69960i 0.977430 0.0870731i
\(382\) 0.763274 + 0.824365i 0.0390525 + 0.0421782i
\(383\) 34.4356 1.75958 0.879788 0.475367i \(-0.157685\pi\)
0.879788 + 0.475367i \(0.157685\pi\)
\(384\) 11.1458 + 16.1174i 0.568784 + 0.822487i
\(385\) 22.4642 1.14488
\(386\) −10.1290 10.9397i −0.515554 0.556817i
\(387\) 4.01789 0.721583i 0.204241 0.0366801i
\(388\) 1.88100 24.4056i 0.0954932 1.23901i
\(389\) 9.55684 0.484551 0.242276 0.970207i \(-0.422106\pi\)
0.242276 + 0.970207i \(0.422106\pi\)
\(390\) −7.69087 6.95238i −0.389442 0.352048i
\(391\) 42.1306i 2.13063i
\(392\) −3.21076 + 2.54383i −0.162168 + 0.128483i
\(393\) 9.42214 0.839360i 0.475284 0.0423401i
\(394\) 9.93932 + 10.7348i 0.500736 + 0.540814i
\(395\) 5.94690i 0.299221i
\(396\) 28.8483 2.91716i 1.44968 0.146593i
\(397\) 17.6792i 0.887295i −0.896201 0.443647i \(-0.853684\pi\)
0.896201 0.443647i \(-0.146316\pi\)
\(398\) 11.6131 10.7525i 0.582113 0.538974i
\(399\) 4.06498 0.362124i 0.203503 0.0181289i
\(400\) 4.37875 + 0.678995i 0.218938 + 0.0339498i
\(401\) 34.3290i 1.71431i 0.515058 + 0.857155i \(0.327770\pi\)
−0.515058 + 0.857155i \(0.672230\pi\)
\(402\) −9.33921 + 10.3312i −0.465797 + 0.515274i
\(403\) −9.62207 −0.479310
\(404\) −0.268310 + 3.48127i −0.0133489 + 0.173200i
\(405\) 16.6463 6.17838i 0.827160 0.307006i
\(406\) 1.44421 1.33719i 0.0716750 0.0663634i
\(407\) 42.4095 2.10216
\(408\) −18.5596 + 17.6000i −0.918838 + 0.871332i
\(409\) −21.2316 −1.04983 −0.524917 0.851154i \(-0.675904\pi\)
−0.524917 + 0.851154i \(0.675904\pi\)
\(410\) 13.3906 12.3983i 0.661314 0.612306i
\(411\) −2.06185 + 0.183678i −0.101704 + 0.00906015i
\(412\) 26.1850 + 2.01814i 1.29004 + 0.0994265i
\(413\) 33.0350 1.62554
\(414\) −27.3337 20.6141i −1.34338 1.01313i
\(415\) 12.6633i 0.621617i
\(416\) 10.0633 6.78318i 0.493394 0.332573i
\(417\) −0.740635 8.31391i −0.0362690 0.407134i
\(418\) −5.01481 + 4.64318i −0.245282 + 0.227105i
\(419\) 16.7076i 0.816219i 0.912933 + 0.408110i \(0.133812\pi\)
−0.912933 + 0.408110i \(0.866188\pi\)
\(420\) 0.192085 + 16.1017i 0.00937281 + 0.785685i
\(421\) 3.19194i 0.155565i 0.996970 + 0.0777827i \(0.0247840\pi\)
−0.996970 + 0.0777827i \(0.975216\pi\)
\(422\) −5.69868 6.15479i −0.277407 0.299611i
\(423\) 16.3813 2.94197i 0.796487 0.143043i
\(424\) −28.9357 + 22.9252i −1.40524 + 1.11335i
\(425\) 5.78371i 0.280551i
\(426\) −5.87222 + 6.49597i −0.284510 + 0.314731i
\(427\) −23.9290 −1.15800
\(428\) −19.9232 1.53553i −0.963023 0.0742225i
\(429\) −1.59338 17.8863i −0.0769292 0.863560i
\(430\) −2.57933 2.78577i −0.124386 0.134342i
\(431\) −17.4859 −0.842267 −0.421133 0.906999i \(-0.638368\pi\)
−0.421133 + 0.906999i \(0.638368\pi\)
\(432\) 2.33762 + 20.6527i 0.112469 + 0.993655i
\(433\) −5.03086 −0.241768 −0.120884 0.992667i \(-0.538573\pi\)
−0.120884 + 0.992667i \(0.538573\pi\)
\(434\) 10.1536 + 10.9663i 0.487389 + 0.526399i
\(435\) 0.179095 + 2.01041i 0.00858693 + 0.0963916i
\(436\) 9.29627 + 0.716486i 0.445211 + 0.0343135i
\(437\) 8.06939 0.386011
\(438\) 5.03137 5.56581i 0.240408 0.265945i
\(439\) 1.24339i 0.0593439i −0.999560 0.0296719i \(-0.990554\pi\)
0.999560 0.0296719i \(-0.00944625\pi\)
\(440\) −16.7461 21.1365i −0.798338 1.00764i
\(441\) −4.27641 + 0.768012i −0.203639 + 0.0365720i
\(442\) 10.7620 + 11.6234i 0.511896 + 0.552868i
\(443\) 7.28527i 0.346134i 0.984910 + 0.173067i \(0.0553677\pi\)
−0.984910 + 0.173067i \(0.944632\pi\)
\(444\) 0.362633 + 30.3980i 0.0172098 + 1.44263i
\(445\) 13.3739i 0.633983i
\(446\) −3.58870 + 3.32276i −0.169930 + 0.157337i
\(447\) −3.55578 39.9151i −0.168183 1.88792i
\(448\) −18.3500 4.31127i −0.866957 0.203688i
\(449\) 35.0658i 1.65486i −0.561571 0.827429i \(-0.689803\pi\)
0.561571 0.827429i \(-0.310197\pi\)
\(450\) 3.75239 + 2.82991i 0.176889 + 0.133403i
\(451\) 31.6083 1.48838
\(452\) −30.8293 2.37609i −1.45009 0.111762i
\(453\) −9.71626 + 0.865561i −0.456510 + 0.0406676i
\(454\) −14.8550 + 13.7541i −0.697180 + 0.645514i
\(455\) 9.97269 0.467527
\(456\) −3.37099 3.55478i −0.157861 0.166468i
\(457\) −2.98914 −0.139826 −0.0699130 0.997553i \(-0.522272\pi\)
−0.0699130 + 0.997553i \(0.522272\pi\)
\(458\) 13.9982 12.9609i 0.654094 0.605621i
\(459\) −26.1712 + 7.14593i −1.22157 + 0.333543i
\(460\) −2.44671 + 31.7456i −0.114079 + 1.48015i
\(461\) 21.9864 1.02401 0.512005 0.858983i \(-0.328903\pi\)
0.512005 + 0.858983i \(0.328903\pi\)
\(462\) −18.7037 + 20.6904i −0.870173 + 0.962604i
\(463\) 14.2465i 0.662089i 0.943615 + 0.331045i \(0.107401\pi\)
−0.943615 + 0.331045i \(0.892599\pi\)
\(464\) −2.33475 0.362040i −0.108388 0.0168073i
\(465\) −15.2656 + 1.35991i −0.707924 + 0.0630645i
\(466\) 14.5915 13.5102i 0.675938 0.625846i
\(467\) 7.12691i 0.329794i −0.986311 0.164897i \(-0.947271\pi\)
0.986311 0.164897i \(-0.0527292\pi\)
\(468\) 12.8068 1.29504i 0.591995 0.0598630i
\(469\) 13.3964i 0.618589i
\(470\) −10.5162 11.3579i −0.485075 0.523899i
\(471\) 8.12995 0.724247i 0.374609 0.0333716i
\(472\) −24.6261 31.0825i −1.13351 1.43069i
\(473\) 6.57578i 0.302355i
\(474\) −5.47732 4.95139i −0.251582 0.227425i
\(475\) −1.10777 −0.0508280
\(476\) 1.89066 24.5310i 0.0866583 1.12437i
\(477\) −38.5395 + 6.92141i −1.76460 + 0.316910i
\(478\) −10.5473 11.3915i −0.482424 0.521037i
\(479\) −1.78303 −0.0814687 −0.0407344 0.999170i \(-0.512970\pi\)
−0.0407344 + 0.999170i \(0.512970\pi\)
\(480\) 15.0069 12.1839i 0.684968 0.556116i
\(481\) 18.8272 0.858445
\(482\) −11.8711 12.8213i −0.540716 0.583994i
\(483\) 32.8019 2.92212i 1.49254 0.132961i
\(484\) 1.89863 24.6343i 0.0863011 1.11974i
\(485\) −24.1460 −1.09641
\(486\) −8.16915 + 20.4760i −0.370560 + 0.928808i
\(487\) 14.2210i 0.644417i 0.946669 + 0.322208i \(0.104425\pi\)
−0.946669 + 0.322208i \(0.895575\pi\)
\(488\) 17.8380 + 22.5147i 0.807489 + 1.01919i
\(489\) −3.35497 37.6608i −0.151717 1.70308i
\(490\) 2.74529 + 2.96501i 0.124019 + 0.133946i
\(491\) 6.44379i 0.290804i 0.989373 + 0.145402i \(0.0464476\pi\)
−0.989373 + 0.145402i \(0.953552\pi\)
\(492\) 0.270274 + 22.6560i 0.0121849 + 1.02141i
\(493\) 3.08388i 0.138891i
\(494\) −2.22626 + 2.06128i −0.100164 + 0.0927413i
\(495\) −5.05585 28.1517i −0.227243 1.26533i
\(496\) 2.74907 17.7284i 0.123437 0.796029i
\(497\) 8.42328i 0.377836i
\(498\) 11.6634 + 10.5435i 0.522649 + 0.472463i
\(499\) −36.1251 −1.61718 −0.808592 0.588370i \(-0.799770\pi\)
−0.808592 + 0.588370i \(0.799770\pi\)
\(500\) 1.85193 24.0285i 0.0828209 1.07459i
\(501\) 0.118682 + 1.33225i 0.00530232 + 0.0595205i
\(502\) −3.48506 + 3.22680i −0.155546 + 0.144019i
\(503\) 30.4980 1.35984 0.679919 0.733288i \(-0.262015\pi\)
0.679919 + 0.733288i \(0.262015\pi\)
\(504\) −14.9903 13.2294i −0.667719 0.589283i
\(505\) 3.44424 0.153267
\(506\) −40.4664 + 37.4676i −1.79895 + 1.66564i
\(507\) 1.29060 + 14.4874i 0.0573174 + 0.643410i
\(508\) 22.0520 + 1.69960i 0.978399 + 0.0754076i
\(509\) 10.9622 0.485889 0.242944 0.970040i \(-0.421887\pi\)
0.242944 + 0.970040i \(0.421887\pi\)
\(510\) 18.7168 + 16.9196i 0.828796 + 0.749214i
\(511\) 7.21714i 0.319268i
\(512\) 9.62269 + 20.4794i 0.425267 + 0.905068i
\(513\) −1.36868 5.01266i −0.0604287 0.221314i
\(514\) 6.16123 5.70464i 0.271760 0.251621i
\(515\) 25.9064i 1.14157i
\(516\) 4.71335 0.0562277i 0.207493 0.00247529i
\(517\) 26.8101i 1.17911i
\(518\) −19.8672 21.4574i −0.872916 0.942782i
\(519\) 0.406246 + 4.56026i 0.0178322 + 0.200173i
\(520\) −7.43421 9.38328i −0.326012 0.411484i
\(521\) 8.00895i 0.350879i 0.984490 + 0.175439i \(0.0561346\pi\)
−0.984490 + 0.175439i \(0.943865\pi\)
\(522\) −2.00077 1.50891i −0.0875715 0.0660432i
\(523\) −14.1920 −0.620572 −0.310286 0.950643i \(-0.600425\pi\)
−0.310286 + 0.950643i \(0.600425\pi\)
\(524\) 10.8905 + 0.839360i 0.475755 + 0.0366676i
\(525\) −4.50306 + 0.401150i −0.196530 + 0.0175076i
\(526\) −20.2172 21.8354i −0.881514 0.952069i
\(527\) 23.4167 1.02005
\(528\) 33.4103 + 2.17445i 1.45400 + 0.0946306i
\(529\) 42.1151 1.83109
\(530\) 24.7408 + 26.7210i 1.07467 + 1.16069i
\(531\) −7.43493 41.3988i −0.322649 1.79656i
\(532\) 4.69849 + 0.362124i 0.203705 + 0.0157001i
\(533\) 14.0321 0.607798
\(534\) −12.3179 11.1351i −0.533046 0.481863i
\(535\) 19.7112i 0.852191i
\(536\) −12.6047 + 9.98645i −0.544438 + 0.431349i
\(537\) 23.8060 2.12073i 1.02730 0.0915161i
\(538\) −10.0410 10.8446i −0.432897 0.467546i
\(539\) 6.99888i 0.301463i
\(540\) 20.1352 3.86462i 0.866480 0.166307i
\(541\) 17.1733i 0.738337i −0.929362 0.369168i \(-0.879643\pi\)
0.929362 0.369168i \(-0.120357\pi\)
\(542\) 33.0885 30.6364i 1.42127 1.31595i
\(543\) −21.3705 + 1.90377i −0.917098 + 0.0816985i
\(544\) −24.4905 + 16.5079i −1.05002 + 0.707768i
\(545\) 9.19738i 0.393972i
\(546\) −8.30326 + 9.18523i −0.355347 + 0.393092i
\(547\) 20.0528 0.857394 0.428697 0.903448i \(-0.358973\pi\)
0.428697 + 0.903448i \(0.358973\pi\)
\(548\) −2.38318 0.183678i −0.101805 0.00784632i
\(549\) 5.38551 + 29.9874i 0.229848 + 1.27983i
\(550\) 5.55526 5.14357i 0.236877 0.219323i
\(551\) 0.590664 0.0251631
\(552\) −27.2018 28.6849i −1.15779 1.22091i
\(553\) 7.10241 0.302025
\(554\) −20.0315 + 18.5471i −0.851058 + 0.787989i
\(555\) 29.8696 2.66090i 1.26789 0.112949i
\(556\) 0.740635 9.60960i 0.0314099 0.407538i
\(557\) 20.5897 0.872414 0.436207 0.899846i \(-0.356322\pi\)
0.436207 + 0.899846i \(0.356322\pi\)
\(558\) 11.4576 15.1924i 0.485037 0.643147i
\(559\) 2.91923i 0.123470i
\(560\) −2.84925 + 18.3744i −0.120403 + 0.776461i
\(561\) 3.87773 + 43.5290i 0.163718 + 1.83779i
\(562\) 4.09645 3.79288i 0.172798 0.159993i
\(563\) 3.87489i 0.163307i 0.996661 + 0.0816536i \(0.0260201\pi\)
−0.996661 + 0.0816536i \(0.973980\pi\)
\(564\) 19.2168 0.229246i 0.809173 0.00965301i
\(565\) 30.5013i 1.28320i
\(566\) −16.1637 17.4574i −0.679411 0.733789i
\(567\) −7.37886 19.8807i −0.309883 0.834911i
\(568\) −7.92544 + 6.27919i −0.332544 + 0.263469i
\(569\) 0.630264i 0.0264220i 0.999913 + 0.0132110i \(0.00420532\pi\)
−0.999913 + 0.0132110i \(0.995795\pi\)
\(570\) −3.24067 + 3.58489i −0.135737 + 0.150155i
\(571\) 10.7705 0.450731 0.225365 0.974274i \(-0.427642\pi\)
0.225365 + 0.974274i \(0.427642\pi\)
\(572\) 1.59338 20.6738i 0.0666226 0.864416i
\(573\) 0.122092 + 1.37053i 0.00510045 + 0.0572545i
\(574\) −14.8073 15.9924i −0.618044 0.667511i
\(575\) −8.93904 −0.372784
\(576\) −1.27290 + 23.9662i −0.0530376 + 0.998593i
\(577\) 34.5776 1.43948 0.719742 0.694241i \(-0.244260\pi\)
0.719742 + 0.694241i \(0.244260\pi\)
\(578\) −9.85714 10.6461i −0.410003 0.442819i
\(579\) −1.62022 18.1875i −0.0673339 0.755849i
\(580\) −0.179095 + 2.32372i −0.00743650 + 0.0964871i
\(581\) −15.1238 −0.627442
\(582\) 20.1039 22.2394i 0.833334 0.921851i
\(583\) 63.0747i 2.61229i
\(584\) 6.79059 5.38007i 0.280997 0.222629i
\(585\) −2.24448 12.4976i −0.0927978 0.516712i
\(586\) −9.73812 10.5175i −0.402278 0.434476i
\(587\) 15.2181i 0.628116i 0.949404 + 0.314058i \(0.101689\pi\)
−0.949404 + 0.314058i \(0.898311\pi\)
\(588\) −5.01662 + 0.0598456i −0.206882 + 0.00246799i
\(589\) 4.48507i 0.184804i
\(590\) −28.7035 + 26.5764i −1.18171 + 1.09413i
\(591\) 1.58987 + 17.8469i 0.0653986 + 0.734124i
\(592\) −5.37901 + 34.6886i −0.221076 + 1.42569i
\(593\) 4.83383i 0.198502i 0.995062 + 0.0992509i \(0.0316446\pi\)
−0.995062 + 0.0992509i \(0.968355\pi\)
\(594\) 30.1383 + 18.7825i 1.23659 + 0.770654i
\(595\) −24.2700 −0.994973
\(596\) 3.55578 46.1356i 0.145651 1.88979i
\(597\) 19.3071 1.71995i 0.790185 0.0703927i
\(598\) −17.9646 + 16.6333i −0.734625 + 0.680185i
\(599\) 42.3775 1.73150 0.865748 0.500480i \(-0.166843\pi\)
0.865748 + 0.500480i \(0.166843\pi\)
\(600\) 3.73428 + 3.93788i 0.152451 + 0.160763i
\(601\) −6.13637 −0.250308 −0.125154 0.992137i \(-0.539942\pi\)
−0.125154 + 0.992137i \(0.539942\pi\)
\(602\) −3.32706 + 3.08050i −0.135601 + 0.125552i
\(603\) −16.7881 + 3.01503i −0.683666 + 0.122782i
\(604\) −11.2305 0.865561i −0.456962 0.0352192i
\(605\) −24.3722 −0.990873
\(606\) −2.86767 + 3.17228i −0.116491 + 0.128865i
\(607\) 40.2074i 1.63197i −0.578074 0.815985i \(-0.696195\pi\)
0.578074 0.815985i \(-0.303805\pi\)
\(608\) −3.16180 4.69074i −0.128228 0.190235i
\(609\) 2.40103 0.213893i 0.0972948 0.00866739i
\(610\) 20.7915 19.2507i 0.841823 0.779439i
\(611\) 11.9020i 0.481504i
\(612\) −31.1673 + 3.15166i −1.25986 + 0.127398i
\(613\) 41.5016i 1.67623i 0.545491 + 0.838117i \(0.316343\pi\)
−0.545491 + 0.838117i \(0.683657\pi\)
\(614\) 24.9981 + 26.9989i 1.00884 + 1.08959i
\(615\) 22.2622 1.98320i 0.897697 0.0799702i
\(616\) −25.2434 + 19.9999i −1.01709 + 0.805819i
\(617\) 43.6944i 1.75907i 0.475834 + 0.879535i \(0.342146\pi\)
−0.475834 + 0.879535i \(0.657854\pi\)
\(618\) 23.8608 + 21.5697i 0.959822 + 0.867659i
\(619\) −7.56093 −0.303900 −0.151950 0.988388i \(-0.548555\pi\)
−0.151950 + 0.988388i \(0.548555\pi\)
\(620\) −17.6446 1.35991i −0.708626 0.0546155i
\(621\) −11.0444 40.4491i −0.443197 1.62317i
\(622\) −23.6983 25.5951i −0.950215 1.02627i
\(623\) 15.9725 0.639924
\(624\) 14.8321 + 0.965318i 0.593758 + 0.0386436i
\(625\) −18.2340 −0.729360
\(626\) 22.7743 + 24.5972i 0.910246 + 0.983100i
\(627\) −8.33723 + 0.742712i −0.332957 + 0.0296611i
\(628\) 9.39697 + 0.724247i 0.374980 + 0.0289006i
\(629\) −45.8187 −1.82691
\(630\) −11.8751 + 15.7460i −0.473114 + 0.627337i
\(631\) 36.6940i 1.46077i 0.683038 + 0.730383i \(0.260658\pi\)
−0.683038 + 0.730383i \(0.739342\pi\)
\(632\) −5.29454 6.68263i −0.210605 0.265821i
\(633\) −0.911549 10.2325i −0.0362308 0.406705i
\(634\) 23.2756 + 25.1386i 0.924393 + 0.998380i
\(635\) 21.8174i 0.865797i
\(636\) −45.2103 + 0.539335i −1.79270 + 0.0213860i
\(637\) 3.10707i 0.123106i
\(638\) −2.96206 + 2.74256i −0.117269 + 0.108579i
\(639\) −10.5559 + 1.89576i −0.417585 + 0.0749953i
\(640\) 19.4124 11.0165i 0.767344 0.435465i
\(641\) 17.5329i 0.692508i 0.938141 + 0.346254i \(0.112546\pi\)
−0.938141 + 0.346254i \(0.887454\pi\)
\(642\) −18.1548 16.4116i −0.716513 0.647713i
\(643\) −42.2395 −1.66576 −0.832882 0.553451i \(-0.813311\pi\)
−0.832882 + 0.553451i \(0.813311\pi\)
\(644\) 37.9139 + 2.92212i 1.49402 + 0.115148i
\(645\) −0.412583 4.63141i −0.0162455 0.182361i
\(646\) 5.41793 5.01642i 0.213165 0.197368i
\(647\) −46.4035 −1.82431 −0.912156 0.409844i \(-0.865583\pi\)
−0.912156 + 0.409844i \(0.865583\pi\)
\(648\) −13.2051 + 21.7629i −0.518744 + 0.854929i
\(649\) −67.7544 −2.65959
\(650\) 2.46619 2.28342i 0.0967317 0.0895633i
\(651\) 1.62415 + 18.2317i 0.0636555 + 0.714557i
\(652\) 3.35497 43.5301i 0.131391 1.70477i
\(653\) −21.8338 −0.854422 −0.427211 0.904152i \(-0.640504\pi\)
−0.427211 + 0.904152i \(0.640504\pi\)
\(654\) 8.47114 + 7.65773i 0.331248 + 0.299441i
\(655\) 10.7747i 0.421002i
\(656\) −4.00904 + 25.8538i −0.156527 + 1.00942i
\(657\) 9.04440 1.62431i 0.352855 0.0633703i
\(658\) −13.5647 + 12.5595i −0.528809 + 0.489620i
\(659\) 6.39325i 0.249046i 0.992217 + 0.124523i \(0.0397400\pi\)
−0.992217 + 0.124523i \(0.960260\pi\)
\(660\) −0.393965 33.0245i −0.0153351 1.28548i
\(661\) 12.6013i 0.490136i −0.969506 0.245068i \(-0.921190\pi\)
0.969506 0.245068i \(-0.0788102\pi\)
\(662\) −18.6691 20.1633i −0.725595 0.783671i
\(663\) 1.72147 + 19.3241i 0.0668562 + 0.750487i
\(664\) 11.2742 + 14.2300i 0.437522 + 0.552230i
\(665\) 4.64850i 0.180261i
\(666\) −22.4186 + 29.7265i −0.868704 + 1.15188i
\(667\) 4.76630 0.184552
\(668\) −0.118682 + 1.53987i −0.00459194 + 0.0595795i
\(669\) −5.96630 + 0.531501i −0.230671 + 0.0205490i
\(670\) 10.7773 + 11.6399i 0.416365 + 0.449690i
\(671\) 49.0781 1.89464
\(672\) −14.5513 17.9228i −0.561327 0.691387i
\(673\) 18.0854 0.697141 0.348571 0.937282i \(-0.386667\pi\)
0.348571 + 0.937282i \(0.386667\pi\)
\(674\) 3.40953 + 3.68242i 0.131330 + 0.141842i
\(675\) 1.51618 + 5.55287i 0.0583580 + 0.213730i
\(676\) −1.29060 + 16.7452i −0.0496383 + 0.644048i
\(677\) 49.8380 1.91543 0.957715 0.287717i \(-0.0928964\pi\)
0.957715 + 0.287717i \(0.0928964\pi\)
\(678\) −28.0929 25.3954i −1.07890 0.975304i
\(679\) 28.8376i 1.10669i
\(680\) 18.0922 + 22.8356i 0.693806 + 0.875704i
\(681\) −24.6968 + 2.20008i −0.946382 + 0.0843073i
\(682\) −20.8250 22.4918i −0.797430 0.861254i
\(683\) 13.6776i 0.523359i 0.965155 + 0.261680i \(0.0842764\pi\)
−0.965155 + 0.261680i \(0.915724\pi\)
\(684\) −0.603646 5.96956i −0.0230810 0.228252i
\(685\) 2.35783i 0.0900881i
\(686\) 20.6566 19.1258i 0.788672 0.730226i
\(687\) 23.2724 2.07319i 0.887896 0.0790971i
\(688\) 5.37861 + 0.834039i 0.205058 + 0.0317974i
\(689\) 28.0012i 1.06676i
\(690\) −26.1502 + 28.9279i −0.995522 + 1.10127i
\(691\) 14.8089 0.563357 0.281679 0.959509i \(-0.409109\pi\)
0.281679 + 0.959509i \(0.409109\pi\)
\(692\) −0.406246 + 5.27096i −0.0154431 + 0.200372i
\(693\) −33.6217 + 6.03822i −1.27718 + 0.229373i
\(694\) −20.0405 + 18.5554i −0.760727 + 0.704352i
\(695\) −9.50737 −0.360635
\(696\) −1.99112 2.09968i −0.0754732 0.0795881i
\(697\) −34.1492 −1.29349
\(698\) −14.4331 + 13.3635i −0.546301 + 0.505817i
\(699\) 24.2587 2.16106i 0.917548 0.0817386i
\(700\) −5.20485 0.401150i −0.196725 0.0151620i
\(701\) −35.9252 −1.35688 −0.678438 0.734658i \(-0.737343\pi\)
−0.678438 + 0.734658i \(0.737343\pi\)
\(702\) 13.3795 + 8.33824i 0.504977 + 0.314707i
\(703\) 8.77578i 0.330985i
\(704\) 37.6357 + 8.84237i 1.41845 + 0.333260i
\(705\) −1.68214 18.8827i −0.0633532 0.711164i
\(706\) 18.6145 17.2350i 0.700565 0.648649i
\(707\) 4.11347i 0.154703i
\(708\) −0.579350 48.5646i −0.0217733 1.82517i
\(709\) 31.3446i 1.17717i 0.808435 + 0.588585i \(0.200315\pi\)
−0.808435 + 0.588585i \(0.799685\pi\)
\(710\) 6.77648 + 7.31885i 0.254317 + 0.274672i
\(711\) −1.59848 8.90061i −0.0599479 0.333799i
\(712\) −11.9068 15.0285i −0.446226 0.563216i
\(713\) 36.1918i 1.35539i
\(714\) 20.2072 22.3536i 0.756235 0.836562i
\(715\) −20.4539 −0.764932
\(716\) 27.5160 + 2.12073i 1.02832 + 0.0792552i
\(717\) −1.68713 18.9387i −0.0630070 0.707278i
\(718\) −30.7470 33.2080i −1.14747 1.23931i
\(719\) −33.9669 −1.26675 −0.633377 0.773844i \(-0.718332\pi\)
−0.633377 + 0.773844i \(0.718332\pi\)
\(720\) 23.6677 0.564768i 0.882045 0.0210477i
\(721\) −30.9401 −1.15227
\(722\) 0.960810 + 1.03771i 0.0357576 + 0.0386196i
\(723\) −1.89888 21.3157i −0.0706202 0.792739i
\(724\) −24.7010 1.90377i −0.918007 0.0707530i
\(725\) −0.654320 −0.0243008
\(726\) 20.2923 22.4478i 0.753118 0.833115i
\(727\) 4.72559i 0.175263i 0.996153 + 0.0876313i \(0.0279297\pi\)
−0.996153 + 0.0876313i \(0.972070\pi\)
\(728\) −11.2065 + 8.87870i −0.415340 + 0.329067i
\(729\) −23.2534 + 13.7214i −0.861238 + 0.508202i
\(730\) −5.80615 6.27086i −0.214895 0.232095i
\(731\) 7.10438i 0.262765i
\(732\) 0.419654 + 35.1779i 0.0155109 + 1.30021i
\(733\) 32.6808i 1.20709i 0.797328 + 0.603546i \(0.206246\pi\)
−0.797328 + 0.603546i \(0.793754\pi\)
\(734\) −14.9010 + 13.7967i −0.550005 + 0.509246i
\(735\) 0.439130 + 4.92941i 0.0161976 + 0.181824i
\(736\) −25.5138 37.8514i −0.940451 1.39522i
\(737\) 27.4759i 1.01209i
\(738\) −16.7089 + 22.1555i −0.615061 + 0.815555i
\(739\) 36.5392 1.34412 0.672059 0.740498i \(-0.265410\pi\)
0.672059 + 0.740498i \(0.265410\pi\)
\(740\) 34.5246 + 2.66090i 1.26915 + 0.0978165i
\(741\) −3.70121 + 0.329718i −0.135967 + 0.0121125i
\(742\) 31.9130 29.5481i 1.17156 1.08474i
\(743\) −20.4413 −0.749917 −0.374958 0.927042i \(-0.622343\pi\)
−0.374958 + 0.927042i \(0.622343\pi\)
\(744\) 15.9434 15.1191i 0.584515 0.554294i
\(745\) −45.6448 −1.67230
\(746\) −23.2239 + 21.5028i −0.850286 + 0.787274i
\(747\) 3.40381 + 18.9529i 0.124539 + 0.693450i
\(748\) −3.87773 + 50.3128i −0.141784 + 1.83962i
\(749\) 23.5412 0.860177
\(750\) 19.7933 21.8957i 0.722747 0.799518i
\(751\) 16.0510i 0.585709i 0.956157 + 0.292855i \(0.0946052\pi\)
−0.956157 + 0.292855i \(0.905395\pi\)
\(752\) 21.9291 + 3.40046i 0.799673 + 0.124002i
\(753\) −5.79400 + 0.516151i −0.211145 + 0.0188096i
\(754\) −1.31497 + 1.21752i −0.0478884 + 0.0443395i
\(755\) 11.1110i 0.404371i
\(756\) −4.61553 24.0475i −0.167865 0.874600i
\(757\) 11.7433i 0.426817i 0.976963 + 0.213408i \(0.0684565\pi\)
−0.976963 + 0.213408i \(0.931543\pi\)
\(758\) 26.4832 + 28.6028i 0.961911 + 1.03890i
\(759\) −67.2764 + 5.99324i −2.44198 + 0.217541i
\(760\) −4.37376 + 3.46526i −0.158653 + 0.125698i
\(761\) 35.7369i 1.29546i −0.761870 0.647730i \(-0.775718\pi\)
0.761870 0.647730i \(-0.224282\pi\)
\(762\) 20.0947 + 18.1652i 0.727953 + 0.658054i
\(763\) −10.9845 −0.397664
\(764\) −0.122092 + 1.58412i −0.00441712 + 0.0573113i
\(765\) 5.46227 + 30.4147i 0.197489 + 1.09965i
\(766\) 33.0860 + 35.7342i 1.19545 + 1.29113i
\(767\) −30.0787 −1.08608
\(768\) −6.01617 + 27.0519i −0.217090 + 0.976152i
\(769\) 40.1108 1.44643 0.723216 0.690622i \(-0.242663\pi\)
0.723216 + 0.690622i \(0.242663\pi\)
\(770\) 21.5838 + 23.3113i 0.777827 + 0.840083i
\(771\) 10.2432 0.912502i 0.368899 0.0328630i
\(772\) 1.62022 21.0220i 0.0583128 0.756598i
\(773\) 23.0364 0.828561 0.414280 0.910149i \(-0.364033\pi\)
0.414280 + 0.910149i \(0.364033\pi\)
\(774\) 4.60922 + 3.47610i 0.165675 + 0.124946i
\(775\) 4.96843i 0.178471i
\(776\) 27.1332 21.4972i 0.974026 0.771704i
\(777\) −3.17792 35.6734i −0.114007 1.27977i
\(778\) 9.18231 + 9.91724i 0.329202 + 0.355550i
\(779\) 6.54069i 0.234345i
\(780\) −0.174896 14.6608i −0.00626228 0.524941i
\(781\) 17.2761i 0.618187i
\(782\) 43.7194 40.4795i 1.56340 1.44754i
\(783\) −0.808430 2.96079i −0.0288909 0.105810i
\(784\) −5.72468 0.887704i −0.204453 0.0317037i
\(785\) 9.29701i 0.331824i
\(786\) 9.92390 + 8.97099i 0.353974 + 0.319985i
\(787\) 28.5826 1.01886 0.509430 0.860512i \(-0.329856\pi\)
0.509430 + 0.860512i \(0.329856\pi\)
\(788\) −1.58987 + 20.6283i −0.0566368 + 0.734852i
\(789\) −3.23391 36.3018i −0.115130 1.29238i
\(790\) −6.17117 + 5.71384i −0.219560 + 0.203289i
\(791\) 36.4278 1.29522
\(792\) 30.7449 + 27.1333i 1.09247 + 0.964141i
\(793\) 21.7876 0.773700
\(794\) 18.3459 16.9864i 0.651073 0.602824i
\(795\) 3.95749 + 44.4243i 0.140358 + 1.57557i
\(796\) 22.3160 + 1.71995i 0.790969 + 0.0609619i
\(797\) 4.29989 0.152310 0.0761549 0.997096i \(-0.475736\pi\)
0.0761549 + 0.997096i \(0.475736\pi\)
\(798\) 4.28145 + 3.87034i 0.151562 + 0.137009i
\(799\) 28.9653i 1.02472i
\(800\) 3.50255 + 5.19627i 0.123834 + 0.183716i
\(801\) −3.59481 20.0164i −0.127016 0.707246i
\(802\) −35.6236 + 32.9837i −1.25791 + 1.16469i
\(803\) 14.8023i 0.522362i
\(804\) −19.6940 + 0.234939i −0.694555 + 0.00828567i
\(805\) 37.5106i 1.32208i
\(806\) −9.24498 9.98493i −0.325641 0.351704i
\(807\) −1.60613 18.0295i −0.0565386 0.634667i
\(808\) −3.87035 + 3.06641i −0.136159 + 0.107876i
\(809\) 15.9007i 0.559038i −0.960140 0.279519i \(-0.909825\pi\)
0.960140 0.279519i \(-0.0901750\pi\)
\(810\) 22.4053 + 11.3378i 0.787241 + 0.398369i
\(811\) 31.8029 1.11675 0.558376 0.829588i \(-0.311425\pi\)
0.558376 + 0.829588i \(0.311425\pi\)
\(812\) 2.77523 + 0.213893i 0.0973913 + 0.00750618i
\(813\) 55.0104 4.90054i 1.92930 0.171869i
\(814\) 40.7475 + 44.0089i 1.42820 + 1.54251i
\(815\) −43.0670 −1.50857
\(816\) −36.0960 2.34924i −1.26361 0.0822399i
\(817\) −1.36072 −0.0476056
\(818\) −20.3995 22.0322i −0.713252 0.770339i
\(819\) −14.9259 + 2.68059i −0.521554 + 0.0936674i
\(820\) 25.7316 + 1.98320i 0.898587 + 0.0692562i
\(821\) 12.9857 0.453204 0.226602 0.973987i \(-0.427238\pi\)
0.226602 + 0.973987i \(0.427238\pi\)
\(822\) −2.17165 1.96313i −0.0757451 0.0684720i
\(823\) 27.8018i 0.969108i −0.874761 0.484554i \(-0.838982\pi\)
0.874761 0.484554i \(-0.161018\pi\)
\(824\) 23.0645 + 29.1115i 0.803491 + 1.01415i
\(825\) 9.23574 0.822755i 0.321547 0.0286447i
\(826\) 31.7403 + 34.2808i 1.10439 + 1.19278i
\(827\) 10.5836i 0.368028i 0.982924 + 0.184014i \(0.0589092\pi\)
−0.982924 + 0.184014i \(0.941091\pi\)
\(828\) −4.87106 48.1707i −0.169281 1.67405i
\(829\) 4.56921i 0.158695i −0.996847 0.0793477i \(-0.974716\pi\)
0.996847 0.0793477i \(-0.0252837\pi\)
\(830\) 13.1408 12.1670i 0.456125 0.422323i
\(831\) −33.3029 + 2.96675i −1.15526 + 0.102915i
\(832\) 16.7079 + 3.92546i 0.579242 + 0.136091i
\(833\) 7.56150i 0.261990i
\(834\) 7.91583 8.75665i 0.274103 0.303218i
\(835\) 1.52349 0.0527227
\(836\) −9.63655 0.742712i −0.333287 0.0256872i
\(837\) 22.4821 6.13863i 0.777096 0.212182i
\(838\) −17.3377 + 16.0528i −0.598919 + 0.554535i
\(839\) −32.2093 −1.11199 −0.555994 0.831187i \(-0.687662\pi\)
−0.555994 + 0.831187i \(0.687662\pi\)
\(840\) −16.5244 + 15.6700i −0.570146 + 0.540668i
\(841\) −28.6511 −0.987970
\(842\) −3.31231 + 3.06684i −0.114150 + 0.105690i
\(843\) 6.81044 0.606700i 0.234564 0.0208959i
\(844\) 0.911549 11.8272i 0.0313768 0.407108i
\(845\) 16.5671 0.569926
\(846\) 18.7923 + 14.1724i 0.646091 + 0.487258i
\(847\) 29.1079i 1.00016i
\(848\) −51.5915 8.00008i −1.77166 0.274724i
\(849\) −2.58551 29.0233i −0.0887344 0.996078i
\(850\) −6.00182 + 5.55705i −0.205861 + 0.190605i
\(851\) 70.8152i 2.42752i
\(852\) −12.3830 + 0.147723i −0.424236 + 0.00506091i
\(853\) 32.0084i 1.09595i −0.836496 0.547974i \(-0.815399\pi\)
0.836496 0.547974i \(-0.184601\pi\)
\(854\) −22.9912 24.8314i −0.786742 0.849712i
\(855\) −5.82542 + 1.04620i −0.199225 + 0.0357794i
\(856\) −17.5489 22.1499i −0.599811 0.757066i
\(857\) 23.9200i 0.817092i −0.912738 0.408546i \(-0.866036\pi\)
0.912738 0.408546i \(-0.133964\pi\)
\(858\) 17.0299 18.8388i 0.581391 0.643147i
\(859\) 42.0614 1.43512 0.717559 0.696498i \(-0.245259\pi\)
0.717559 + 0.696498i \(0.245259\pi\)
\(860\) 0.412583 5.35319i 0.0140690 0.182542i
\(861\) −2.36854 26.5878i −0.0807196 0.906109i
\(862\) −16.8006 18.1453i −0.572232 0.618032i
\(863\) −29.7612 −1.01308 −0.506542 0.862215i \(-0.669076\pi\)
−0.506542 + 0.862215i \(0.669076\pi\)
\(864\) −19.1856 + 22.2691i −0.652706 + 0.757611i
\(865\) 5.21489 0.177312
\(866\) −4.83370 5.22058i −0.164256 0.177403i
\(867\) −1.57673 17.6994i −0.0535484 0.601102i
\(868\) −1.62415 + 21.0731i −0.0551273 + 0.715266i
\(869\) −14.5670 −0.494151
\(870\) −1.91414 + 2.11747i −0.0648956 + 0.0717888i
\(871\) 12.1976i 0.413299i
\(872\) 8.18844 + 10.3353i 0.277296 + 0.349996i
\(873\) 36.1388 6.49026i 1.22311 0.219662i
\(874\) 7.75315 + 8.37370i 0.262254 + 0.283245i
\(875\) 28.3920i 0.959825i
\(876\) 10.6099 0.126571i 0.358475 0.00427642i
\(877\) 48.6451i 1.64263i −0.570476 0.821314i \(-0.693241\pi\)
0.570476 0.821314i \(-0.306759\pi\)
\(878\) 1.29028 1.19466i 0.0435449 0.0403179i
\(879\) −1.55769 17.4857i −0.0525395 0.589776i
\(880\) 5.84378 37.6858i 0.196994 1.27039i
\(881\) 26.7539i 0.901362i −0.892685 0.450681i \(-0.851181\pi\)
0.892685 0.450681i \(-0.148819\pi\)
\(882\) −4.90579 3.69976i −0.165187 0.124578i
\(883\) 17.6253 0.593139 0.296569 0.955011i \(-0.404157\pi\)
0.296569 + 0.955011i \(0.404157\pi\)
\(884\) −1.72147 + 22.3357i −0.0578992 + 0.751231i
\(885\) −47.7203 + 4.25111i −1.60410 + 0.142899i
\(886\) −7.56001 + 6.99976i −0.253983 + 0.235162i
\(887\) −25.2876 −0.849075 −0.424538 0.905410i \(-0.639563\pi\)
−0.424538 + 0.905410i \(0.639563\pi\)
\(888\) −31.1960 + 29.5830i −1.04687 + 0.992742i
\(889\) −26.0566 −0.873910
\(890\) −13.8782 + 12.8498i −0.465200 + 0.430725i
\(891\) 15.1340 + 40.7751i 0.507007 + 1.36602i
\(892\) −6.89612 0.531501i −0.230899 0.0177960i
\(893\) −5.54780 −0.185650
\(894\) 38.0039 42.0407i 1.27104 1.40605i
\(895\) 27.2233i 0.909975i
\(896\) −13.1570 23.1843i −0.439545 0.774534i
\(897\) −29.8665 + 2.66062i −0.997213 + 0.0888355i
\(898\) 36.3882 33.6916i 1.21429 1.12430i
\(899\) 2.64917i 0.0883548i
\(900\) 0.668701 + 6.61290i 0.0222900 + 0.220430i
\(901\) 68.1450i 2.27024i
\(902\) 30.3696 + 32.8003i 1.01120 + 1.09213i
\(903\) −5.53131 + 0.492750i −0.184070 + 0.0163977i
\(904\) −27.1554 34.2749i −0.903175 1.13996i
\(905\) 24.4383i 0.812356i
\(906\) −10.2337 9.25103i −0.339991 0.307345i
\(907\) −51.6403 −1.71469 −0.857344 0.514744i \(-0.827887\pi\)
−0.857344 + 0.514744i \(0.827887\pi\)
\(908\) −28.5457 2.20008i −0.947321 0.0730123i
\(909\) −5.15493 + 0.925788i −0.170978 + 0.0307064i
\(910\) 9.58186 + 10.3488i 0.317636 + 0.343058i
\(911\) 37.8190 1.25300 0.626500 0.779421i \(-0.284487\pi\)
0.626500 + 0.779421i \(0.284487\pi\)
\(912\) 0.449957 6.91358i 0.0148996 0.228931i
\(913\) 31.0188 1.02657
\(914\) −2.87199 3.10186i −0.0949970 0.102600i
\(915\) 34.5663 3.07930i 1.14273 0.101799i
\(916\) 26.8993 + 2.07319i 0.888776 + 0.0685001i
\(917\) −12.8682 −0.424947
\(918\) −32.5610 20.2923i −1.07467 0.669746i
\(919\) 20.0850i 0.662543i −0.943535 0.331272i \(-0.892522\pi\)
0.943535 0.331272i \(-0.107478\pi\)
\(920\) −35.2936 + 27.9625i −1.16360 + 0.921897i
\(921\) 3.99864 + 44.8862i 0.131760 + 1.47905i
\(922\) 21.1248 + 22.8155i 0.695707 + 0.751390i
\(923\) 7.66949i 0.252444i
\(924\) −39.4413 + 0.470514i −1.29752 + 0.0154788i
\(925\) 9.72156i 0.319643i
\(926\) −14.7837 + 13.6881i −0.485823 + 0.449820i
\(927\) 6.96346 + 38.7736i 0.228710 + 1.27349i
\(928\) −1.86756 2.77065i −0.0613056 0.0909510i
\(929\) 18.8526i 0.618533i 0.950975 + 0.309267i \(0.100084\pi\)
−0.950975 + 0.309267i \(0.899916\pi\)
\(930\) −16.0785 14.5346i −0.527235 0.476609i
\(931\) 1.44828 0.0474653
\(932\) 28.0393 + 2.16106i 0.918457 + 0.0707877i
\(933\) −3.79073 42.5524i −0.124103 1.39310i
\(934\) 7.39568 6.84761i 0.241994 0.224061i
\(935\) 49.7775 1.62790
\(936\) 13.6488 + 12.0455i 0.446125 + 0.393719i
\(937\) 23.1082 0.754911 0.377456 0.926028i \(-0.376799\pi\)
0.377456 + 0.926028i \(0.376799\pi\)
\(938\) 13.9016 12.8714i 0.453904 0.420266i
\(939\) 3.64294 + 40.8934i 0.118883 + 1.33450i
\(940\) 1.68214 21.8255i 0.0548655 0.711869i
\(941\) −49.7606 −1.62215 −0.811075 0.584942i \(-0.801117\pi\)
−0.811075 + 0.584942i \(0.801117\pi\)
\(942\) 8.56290 + 7.74068i 0.278994 + 0.252205i
\(943\) 52.7794i 1.71873i
\(944\) 8.59363 55.4192i 0.279699 1.80374i
\(945\) −23.3013 + 6.36232i −0.757993 + 0.206966i
\(946\) 6.82376 6.31807i 0.221860 0.205418i
\(947\) 35.0676i 1.13954i −0.821803 0.569772i \(-0.807031\pi\)
0.821803 0.569772i \(-0.192969\pi\)
\(948\) −0.124558 10.4412i −0.00404546 0.339115i
\(949\) 6.57129i 0.213313i
\(950\) −1.06436 1.14955i −0.0345323 0.0372962i
\(951\) 3.72312 + 41.7934i 0.120730 + 1.35525i
\(952\) 27.2726 21.6076i 0.883910 0.700307i
\(953\) 23.3921i 0.757745i −0.925449 0.378872i \(-0.876312\pi\)
0.925449 0.378872i \(-0.123688\pi\)
\(954\) −44.2115 33.3427i −1.43140 1.07951i
\(955\) 1.56726 0.0507155
\(956\) 1.68713 21.8902i 0.0545657 0.707979i
\(957\) −4.92450 + 0.438693i −0.159186 + 0.0141809i
\(958\) −1.71315 1.85027i −0.0553494 0.0597795i
\(959\) 2.81597 0.0909323
\(960\) 27.0621 + 3.86643i 0.873426 + 0.124788i
\(961\) 10.8841 0.351101
\(962\) 18.0893 + 19.5372i 0.583223 + 0.629904i
\(963\) −5.29824 29.5014i −0.170733 0.950669i
\(964\) 1.89888 24.6376i 0.0611589 0.793525i
\(965\) −20.7984 −0.669523
\(966\) 34.5487 + 31.2313i 1.11159 + 1.00485i
\(967\) 17.4787i 0.562076i −0.959697 0.281038i \(-0.909321\pi\)
0.959697 0.281038i \(-0.0906786\pi\)
\(968\) 27.3875 21.6987i 0.880268 0.697421i
\(969\) 9.00743 0.802416i 0.289360 0.0257773i
\(970\) −23.1997 25.0565i −0.744897 0.804517i
\(971\) 13.4578i 0.431882i 0.976406 + 0.215941i \(0.0692819\pi\)
−0.976406 + 0.215941i \(0.930718\pi\)
\(972\) −29.0971 + 11.1963i −0.933291 + 0.359121i
\(973\) 11.3547i 0.364015i
\(974\) −14.7573 + 13.6637i −0.472855 + 0.437814i
\(975\) 4.10009 0.365252i 0.131308 0.0116974i
\(976\) −6.22482 + 40.1431i −0.199252 + 1.28495i
\(977\) 16.8194i 0.538101i 0.963126 + 0.269051i \(0.0867099\pi\)
−0.963126 + 0.269051i \(0.913290\pi\)
\(978\) 35.8576 39.6664i 1.14660 1.26839i
\(979\) −32.7594 −1.04700
\(980\) −0.439130 + 5.69763i −0.0140275 + 0.182004i
\(981\) 2.47219 + 13.7655i 0.0789310 + 0.439500i
\(982\) −6.68679 + 6.19126i −0.213384 + 0.197571i
\(983\) −21.2785 −0.678678 −0.339339 0.940664i \(-0.610203\pi\)
−0.339339 + 0.940664i \(0.610203\pi\)
\(984\) −23.2507 + 22.0486i −0.741206 + 0.702883i
\(985\) 20.4088 0.650280
\(986\) 3.20017 2.96302i 0.101914 0.0943617i
\(987\) −22.5517 + 2.00899i −0.717828 + 0.0639469i
\(988\) −4.27802 0.329718i −0.136102 0.0104897i
\(989\) −10.9802 −0.349150
\(990\) 24.3556 32.2950i 0.774073 1.02640i
\(991\) 25.4403i 0.808139i 0.914728 + 0.404069i \(0.132405\pi\)
−0.914728 + 0.404069i \(0.867595\pi\)
\(992\) 21.0383 14.1809i 0.667967 0.450244i
\(993\) −2.98627 33.5220i −0.0947664 1.06379i
\(994\) 8.74093 8.09317i 0.277246 0.256700i
\(995\) 22.0786i 0.699938i
\(996\) 0.265234 + 22.2335i 0.00840425 + 0.704495i
\(997\) 44.9174i 1.42255i 0.702915 + 0.711274i \(0.251881\pi\)
−0.702915 + 0.711274i \(0.748119\pi\)
\(998\) −34.7094 37.4875i −1.09871 1.18664i
\(999\) −43.9900 + 12.0112i −1.39178 + 0.380019i
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 456.2.j.e.419.20 yes 24
3.2 odd 2 inner 456.2.j.e.419.5 24
4.3 odd 2 1824.2.j.d.1103.14 24
8.3 odd 2 inner 456.2.j.e.419.6 yes 24
8.5 even 2 1824.2.j.d.1103.13 24
12.11 even 2 1824.2.j.d.1103.15 24
24.5 odd 2 1824.2.j.d.1103.16 24
24.11 even 2 inner 456.2.j.e.419.19 yes 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
456.2.j.e.419.5 24 3.2 odd 2 inner
456.2.j.e.419.6 yes 24 8.3 odd 2 inner
456.2.j.e.419.19 yes 24 24.11 even 2 inner
456.2.j.e.419.20 yes 24 1.1 even 1 trivial
1824.2.j.d.1103.13 24 8.5 even 2
1824.2.j.d.1103.14 24 4.3 odd 2
1824.2.j.d.1103.15 24 12.11 even 2
1824.2.j.d.1103.16 24 24.5 odd 2