Properties

Label 495.2.u.a.364.6
Level $495$
Weight $2$
Character 495.364
Analytic conductor $3.953$
Analytic rank $0$
Dimension $52$
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] = [495,2,Mod(34,495)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(495, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4, 3, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("495.34");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 495 = 3^{2} \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 495.u (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: \(3.95259490005\)
Analytic rank: \(0\)
Dimension: \(52\)
Relative dimension: \(26\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 364.6
Character \(\chi\) \(=\) 495.364
Dual form 495.2.u.a.34.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.32180 + 0.763144i) q^{2} +(-0.144418 - 1.72602i) q^{3} +(0.164778 - 0.285404i) q^{4} +(2.06762 + 0.851443i) q^{5} +(1.50809 + 2.17125i) q^{6} +(3.72773 - 2.15221i) q^{7} -2.54958i q^{8} +(-2.95829 + 0.498536i) q^{9} +O(q^{10})\) \(q+(-1.32180 + 0.763144i) q^{2} +(-0.144418 - 1.72602i) q^{3} +(0.164778 - 0.285404i) q^{4} +(2.06762 + 0.851443i) q^{5} +(1.50809 + 2.17125i) q^{6} +(3.72773 - 2.15221i) q^{7} -2.54958i q^{8} +(-2.95829 + 0.498536i) q^{9} +(-3.38276 + 0.452450i) q^{10} +(-0.500000 - 0.866025i) q^{11} +(-0.516411 - 0.243193i) q^{12} +(2.08585 + 1.20426i) q^{13} +(-3.28489 + 5.68959i) q^{14} +(1.17101 - 3.69171i) q^{15} +(2.27525 + 3.94085i) q^{16} -0.975056i q^{17} +(3.52982 - 2.91657i) q^{18} -1.61782 q^{19} +(0.583704 - 0.449808i) q^{20} +(-4.25310 - 6.12332i) q^{21} +(1.32180 + 0.763144i) q^{22} +(-5.95108 - 3.43586i) q^{23} +(-4.40062 + 0.368205i) q^{24} +(3.55009 + 3.52092i) q^{25} -3.67611 q^{26} +(1.28771 + 5.03406i) q^{27} -1.41855i q^{28} +(2.29024 + 3.96681i) q^{29} +(1.26947 + 5.77337i) q^{30} +(4.81902 - 8.34679i) q^{31} +(-1.59888 - 0.923114i) q^{32} +(-1.42257 + 0.988079i) q^{33} +(0.744108 + 1.28883i) q^{34} +(9.54000 - 1.27599i) q^{35} +(-0.345177 + 0.926456i) q^{36} -6.88755i q^{37} +(2.13845 - 1.23463i) q^{38} +(1.77735 - 3.77413i) q^{39} +(2.17082 - 5.27156i) q^{40} +(-2.71245 + 4.69810i) q^{41} +(10.2947 + 4.84810i) q^{42} +(5.45113 - 3.14721i) q^{43} -0.329557 q^{44} +(-6.54108 - 1.48803i) q^{45} +10.4882 q^{46} +(4.78238 - 2.76111i) q^{47} +(6.47340 - 4.49626i) q^{48} +(5.76397 - 9.98350i) q^{49} +(-7.37949 - 1.94473i) q^{50} +(-1.68296 + 0.140815i) q^{51} +(0.687405 - 0.396873i) q^{52} -5.92144i q^{53} +(-5.54382 - 5.67134i) q^{54} +(-0.296438 - 2.21633i) q^{55} +(-5.48722 - 9.50414i) q^{56} +(0.233643 + 2.79239i) q^{57} +(-6.05449 - 3.49556i) q^{58} +(1.92108 - 3.32741i) q^{59} +(-0.860675 - 0.942525i) q^{60} +(4.71499 + 8.16660i) q^{61} +14.7104i q^{62} +(-9.95474 + 8.22525i) q^{63} -6.28314 q^{64} +(3.28737 + 4.26594i) q^{65} +(1.12631 - 2.39167i) q^{66} +(10.0414 + 5.79738i) q^{67} +(-0.278285 - 0.160668i) q^{68} +(-5.07092 + 10.7679i) q^{69} +(-11.6362 + 8.96701i) q^{70} -4.77737 q^{71} +(1.27106 + 7.54238i) q^{72} +3.30736i q^{73} +(5.25619 + 9.10399i) q^{74} +(5.56447 - 6.63601i) q^{75} +(-0.266582 + 0.461734i) q^{76} +(-3.72773 - 2.15221i) q^{77} +(0.530896 + 6.34504i) q^{78} +(-1.22749 - 2.12608i) q^{79} +(1.34894 + 10.0854i) q^{80} +(8.50292 - 2.94963i) q^{81} -8.27996i q^{82} +(-11.4287 + 6.59836i) q^{83} +(-2.44844 + 0.204864i) q^{84} +(0.830204 - 2.01604i) q^{85} +(-4.80355 + 8.32000i) q^{86} +(6.51603 - 4.52587i) q^{87} +(-2.20800 + 1.27479i) q^{88} -7.13662 q^{89} +(9.78161 - 3.02491i) q^{90} +10.3673 q^{91} +(-1.96122 + 1.13231i) q^{92} +(-15.1027 - 7.11230i) q^{93} +(-4.21424 + 7.29929i) q^{94} +(-3.34504 - 1.37748i) q^{95} +(-1.36241 + 2.89301i) q^{96} +(-7.15690 + 4.13204i) q^{97} +17.5950i q^{98} +(1.91089 + 2.31268i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 52 q + 20 q^{4} + q^{5} + 4 q^{6} + 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 52 q + 20 q^{4} + q^{5} + 4 q^{6} + 6 q^{9} - 26 q^{11} - 10 q^{14} - 8 q^{16} + 40 q^{19} - 11 q^{20} - 26 q^{21} - 36 q^{24} + q^{25} - 24 q^{26} - 6 q^{29} + 4 q^{30} + 30 q^{31} - 22 q^{34} + 64 q^{36} + 4 q^{39} - 15 q^{40} + 6 q^{41} - 40 q^{44} - 25 q^{45} - 84 q^{46} - 12 q^{49} - 55 q^{50} + 12 q^{51} + 2 q^{54} - 2 q^{55} + 30 q^{56} - 30 q^{59} + 39 q^{60} + 74 q^{61} + 20 q^{64} + 7 q^{65} - 2 q^{66} - 30 q^{69} - 28 q^{70} - 48 q^{71} + 14 q^{74} + 94 q^{75} + 74 q^{76} - 32 q^{79} - 10 q^{80} - 30 q^{81} + 132 q^{84} - 25 q^{85} + 14 q^{86} + 92 q^{89} - 73 q^{90} - 104 q^{91} - 50 q^{94} + 6 q^{95} + 60 q^{96} + 6 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/495\mathbb{Z}\right)^\times\).

\(n\) \(46\) \(56\) \(397\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.32180 + 0.763144i −0.934657 + 0.539624i −0.888281 0.459300i \(-0.848100\pi\)
−0.0463756 + 0.998924i \(0.514767\pi\)
\(3\) −0.144418 1.72602i −0.0833797 0.996518i
\(4\) 0.164778 0.285404i 0.0823892 0.142702i
\(5\) 2.06762 + 0.851443i 0.924667 + 0.380777i
\(6\) 1.50809 + 2.17125i 0.615677 + 0.886409i
\(7\) 3.72773 2.15221i 1.40895 0.813457i 0.413662 0.910431i \(-0.364250\pi\)
0.995287 + 0.0969734i \(0.0309162\pi\)
\(8\) 2.54958i 0.901412i
\(9\) −2.95829 + 0.498536i −0.986096 + 0.166179i
\(10\) −3.38276 + 0.452450i −1.06972 + 0.143077i
\(11\) −0.500000 0.866025i −0.150756 0.261116i
\(12\) −0.516411 0.243193i −0.149075 0.0702038i
\(13\) 2.08585 + 1.20426i 0.578510 + 0.334003i 0.760541 0.649290i \(-0.224934\pi\)
−0.182031 + 0.983293i \(0.558267\pi\)
\(14\) −3.28489 + 5.68959i −0.877923 + 1.52061i
\(15\) 1.17101 3.69171i 0.302352 0.953196i
\(16\) 2.27525 + 3.94085i 0.568813 + 0.985213i
\(17\) 0.975056i 0.236486i −0.992985 0.118243i \(-0.962274\pi\)
0.992985 0.118243i \(-0.0377261\pi\)
\(18\) 3.52982 2.91657i 0.831987 0.687441i
\(19\) −1.61782 −0.371154 −0.185577 0.982630i \(-0.559415\pi\)
−0.185577 + 0.982630i \(0.559415\pi\)
\(20\) 0.583704 0.449808i 0.130520 0.100580i
\(21\) −4.25310 6.12332i −0.928102 1.33622i
\(22\) 1.32180 + 0.763144i 0.281810 + 0.162703i
\(23\) −5.95108 3.43586i −1.24089 0.716426i −0.271612 0.962407i \(-0.587557\pi\)
−0.969275 + 0.245981i \(0.920890\pi\)
\(24\) −4.40062 + 0.368205i −0.898273 + 0.0751595i
\(25\) 3.55009 + 3.52092i 0.710018 + 0.704183i
\(26\) −3.67611 −0.720944
\(27\) 1.28771 + 5.03406i 0.247820 + 0.968806i
\(28\) 1.41855i 0.268080i
\(29\) 2.29024 + 3.96681i 0.425286 + 0.736617i 0.996447 0.0842208i \(-0.0268401\pi\)
−0.571161 + 0.820838i \(0.693507\pi\)
\(30\) 1.26947 + 5.77337i 0.231772 + 1.05407i
\(31\) 4.81902 8.34679i 0.865522 1.49913i −0.00100620 0.999999i \(-0.500320\pi\)
0.866528 0.499128i \(-0.166346\pi\)
\(32\) −1.59888 0.923114i −0.282645 0.163185i
\(33\) −1.42257 + 0.988079i −0.247637 + 0.172003i
\(34\) 0.744108 + 1.28883i 0.127613 + 0.221033i
\(35\) 9.54000 1.27599i 1.61255 0.215682i
\(36\) −0.345177 + 0.926456i −0.0575295 + 0.154409i
\(37\) 6.88755i 1.13231i −0.824300 0.566153i \(-0.808431\pi\)
0.824300 0.566153i \(-0.191569\pi\)
\(38\) 2.13845 1.23463i 0.346902 0.200284i
\(39\) 1.77735 3.77413i 0.284604 0.604344i
\(40\) 2.17082 5.27156i 0.343237 0.833506i
\(41\) −2.71245 + 4.69810i −0.423613 + 0.733720i −0.996290 0.0860618i \(-0.972572\pi\)
0.572677 + 0.819781i \(0.305905\pi\)
\(42\) 10.2947 + 4.84810i 1.58851 + 0.748078i
\(43\) 5.45113 3.14721i 0.831290 0.479945i −0.0230043 0.999735i \(-0.507323\pi\)
0.854294 + 0.519790i \(0.173990\pi\)
\(44\) −0.329557 −0.0496825
\(45\) −6.54108 1.48803i −0.975087 0.221822i
\(46\) 10.4882 1.54640
\(47\) 4.78238 2.76111i 0.697581 0.402749i −0.108865 0.994057i \(-0.534722\pi\)
0.806446 + 0.591308i \(0.201388\pi\)
\(48\) 6.47340 4.49626i 0.934355 0.648979i
\(49\) 5.76397 9.98350i 0.823425 1.42621i
\(50\) −7.37949 1.94473i −1.04362 0.275027i
\(51\) −1.68296 + 0.140815i −0.235662 + 0.0197181i
\(52\) 0.687405 0.396873i 0.0953259 0.0550364i
\(53\) 5.92144i 0.813372i −0.913568 0.406686i \(-0.866684\pi\)
0.913568 0.406686i \(-0.133316\pi\)
\(54\) −5.54382 5.67134i −0.754419 0.771771i
\(55\) −0.296438 2.21633i −0.0399717 0.298850i
\(56\) −5.48722 9.50414i −0.733260 1.27004i
\(57\) 0.233643 + 2.79239i 0.0309467 + 0.369862i
\(58\) −6.05449 3.49556i −0.794993 0.458990i
\(59\) 1.92108 3.32741i 0.250103 0.433192i −0.713451 0.700705i \(-0.752869\pi\)
0.963554 + 0.267514i \(0.0862021\pi\)
\(60\) −0.860675 0.942525i −0.111113 0.121679i
\(61\) 4.71499 + 8.16660i 0.603692 + 1.04563i 0.992257 + 0.124204i \(0.0396378\pi\)
−0.388564 + 0.921422i \(0.627029\pi\)
\(62\) 14.7104i 1.86823i
\(63\) −9.95474 + 8.22525i −1.25418 + 1.03628i
\(64\) −6.28314 −0.785392
\(65\) 3.28737 + 4.26594i 0.407748 + 0.529124i
\(66\) 1.12631 2.39167i 0.138639 0.294395i
\(67\) 10.0414 + 5.79738i 1.22675 + 0.708263i 0.966348 0.257239i \(-0.0828126\pi\)
0.260399 + 0.965501i \(0.416146\pi\)
\(68\) −0.278285 0.160668i −0.0337470 0.0194839i
\(69\) −5.07092 + 10.7679i −0.610467 + 1.29630i
\(70\) −11.6362 + 8.96701i −1.39080 + 1.07176i
\(71\) −4.77737 −0.566969 −0.283485 0.958977i \(-0.591491\pi\)
−0.283485 + 0.958977i \(0.591491\pi\)
\(72\) 1.27106 + 7.54238i 0.149796 + 0.888879i
\(73\) 3.30736i 0.387097i 0.981091 + 0.193549i \(0.0619997\pi\)
−0.981091 + 0.193549i \(0.938000\pi\)
\(74\) 5.25619 + 9.10399i 0.611020 + 1.05832i
\(75\) 5.56447 6.63601i 0.642530 0.766260i
\(76\) −0.266582 + 0.461734i −0.0305791 + 0.0529645i
\(77\) −3.72773 2.15221i −0.424814 0.245267i
\(78\) 0.530896 + 6.34504i 0.0601121 + 0.718434i
\(79\) −1.22749 2.12608i −0.138104 0.239203i 0.788675 0.614810i \(-0.210767\pi\)
−0.926779 + 0.375607i \(0.877434\pi\)
\(80\) 1.34894 + 10.0854i 0.150817 + 1.12759i
\(81\) 8.50292 2.94963i 0.944769 0.327736i
\(82\) 8.27996i 0.914368i
\(83\) −11.4287 + 6.59836i −1.25446 + 0.724264i −0.971992 0.235012i \(-0.924487\pi\)
−0.282470 + 0.959276i \(0.591154\pi\)
\(84\) −2.44844 + 0.204864i −0.267147 + 0.0223525i
\(85\) 0.830204 2.01604i 0.0900482 0.218671i
\(86\) −4.80355 + 8.32000i −0.517981 + 0.897169i
\(87\) 6.51603 4.52587i 0.698592 0.485224i
\(88\) −2.20800 + 1.27479i −0.235374 + 0.135893i
\(89\) −7.13662 −0.756480 −0.378240 0.925708i \(-0.623471\pi\)
−0.378240 + 0.925708i \(0.623471\pi\)
\(90\) 9.78161 3.02491i 1.03107 0.318853i
\(91\) 10.3673 1.08679
\(92\) −1.96122 + 1.13231i −0.204471 + 0.118052i
\(93\) −15.1027 7.11230i −1.56607 0.737511i
\(94\) −4.21424 + 7.29929i −0.434666 + 0.752864i
\(95\) −3.34504 1.37748i −0.343194 0.141327i
\(96\) −1.36241 + 2.89301i −0.139050 + 0.295267i
\(97\) −7.15690 + 4.13204i −0.726673 + 0.419545i −0.817204 0.576349i \(-0.804477\pi\)
0.0905307 + 0.995894i \(0.471144\pi\)
\(98\) 17.5950i 1.77736i
\(99\) 1.91089 + 2.31268i 0.192052 + 0.232433i
\(100\) 1.58986 0.433041i 0.158986 0.0433041i
\(101\) 7.56000 + 13.0943i 0.752248 + 1.30293i 0.946731 + 0.322026i \(0.104364\pi\)
−0.194483 + 0.980906i \(0.562303\pi\)
\(102\) 2.11709 1.47048i 0.209623 0.145599i
\(103\) −9.83884 5.68045i −0.969449 0.559712i −0.0703810 0.997520i \(-0.522422\pi\)
−0.899068 + 0.437808i \(0.855755\pi\)
\(104\) 3.07037 5.31803i 0.301074 0.521476i
\(105\) −3.58013 16.2819i −0.349385 1.58896i
\(106\) 4.51891 + 7.82699i 0.438916 + 0.760224i
\(107\) 11.9110i 1.15148i −0.817633 0.575739i \(-0.804714\pi\)
0.817633 0.575739i \(-0.195286\pi\)
\(108\) 1.64893 + 0.461986i 0.158668 + 0.0444546i
\(109\) −10.5178 −1.00743 −0.503714 0.863871i \(-0.668033\pi\)
−0.503714 + 0.863871i \(0.668033\pi\)
\(110\) 2.08321 + 2.70333i 0.198627 + 0.257753i
\(111\) −11.8880 + 0.994685i −1.12836 + 0.0944113i
\(112\) 16.9631 + 9.79362i 1.60286 + 0.925410i
\(113\) 9.65059 + 5.57177i 0.907851 + 0.524148i 0.879739 0.475457i \(-0.157717\pi\)
0.0281121 + 0.999605i \(0.491050\pi\)
\(114\) −2.43983 3.51270i −0.228511 0.328994i
\(115\) −9.37913 12.1711i −0.874609 1.13496i
\(116\) 1.50953 0.140156
\(117\) −6.77090 2.52269i −0.625970 0.233223i
\(118\) 5.86424i 0.539847i
\(119\) −2.09852 3.63474i −0.192371 0.333196i
\(120\) −9.41231 2.98557i −0.859223 0.272544i
\(121\) −0.500000 + 0.866025i −0.0454545 + 0.0787296i
\(122\) −12.4646 7.19643i −1.12849 0.651534i
\(123\) 8.50073 + 4.00325i 0.766485 + 0.360961i
\(124\) −1.58814 2.75074i −0.142619 0.247024i
\(125\) 4.34238 + 10.3026i 0.388394 + 0.921493i
\(126\) 6.88117 18.4691i 0.613023 1.64536i
\(127\) 18.0905i 1.60528i 0.596466 + 0.802638i \(0.296571\pi\)
−0.596466 + 0.802638i \(0.703429\pi\)
\(128\) 11.5028 6.64117i 1.01672 0.587002i
\(129\) −6.21939 8.95425i −0.547587 0.788377i
\(130\) −7.60079 3.13000i −0.666633 0.274519i
\(131\) −0.161342 + 0.279453i −0.0140965 + 0.0244159i −0.872988 0.487742i \(-0.837821\pi\)
0.858891 + 0.512158i \(0.171154\pi\)
\(132\) 0.0475939 + 0.568821i 0.00414252 + 0.0495095i
\(133\) −6.03081 + 3.48189i −0.522937 + 0.301918i
\(134\) −17.6969 −1.52878
\(135\) −1.62372 + 11.5049i −0.139747 + 0.990187i
\(136\) −2.48598 −0.213171
\(137\) 1.48548 0.857643i 0.126913 0.0732734i −0.435199 0.900334i \(-0.643322\pi\)
0.562113 + 0.827061i \(0.309989\pi\)
\(138\) −1.51469 18.1029i −0.128939 1.54102i
\(139\) 2.54182 4.40255i 0.215594 0.373420i −0.737862 0.674951i \(-0.764165\pi\)
0.953456 + 0.301532i \(0.0974979\pi\)
\(140\) 1.20781 2.93301i 0.102079 0.247885i
\(141\) −5.45638 7.85572i −0.459510 0.661571i
\(142\) 6.31475 3.64582i 0.529922 0.305951i
\(143\) 2.40853i 0.201411i
\(144\) −8.69551 10.5239i −0.724626 0.876990i
\(145\) 1.35783 + 10.1518i 0.112761 + 0.843065i
\(146\) −2.52399 4.37168i −0.208887 0.361803i
\(147\) −18.0641 8.50694i −1.48990 0.701640i
\(148\) −1.96574 1.13492i −0.161583 0.0932897i
\(149\) −3.77090 + 6.53139i −0.308924 + 0.535072i −0.978127 0.208007i \(-0.933302\pi\)
0.669203 + 0.743079i \(0.266636\pi\)
\(150\) −2.29091 + 13.0180i −0.187052 + 1.06292i
\(151\) 4.01226 + 6.94944i 0.326513 + 0.565537i 0.981817 0.189828i \(-0.0607929\pi\)
−0.655304 + 0.755365i \(0.727460\pi\)
\(152\) 4.12477i 0.334563i
\(153\) 0.486100 + 2.88449i 0.0392989 + 0.233198i
\(154\) 6.56977 0.529407
\(155\) 17.0707 13.1549i 1.37115 1.05662i
\(156\) −0.784285 1.12916i −0.0627930 0.0904050i
\(157\) −15.2413 8.79959i −1.21639 0.702284i −0.252248 0.967663i \(-0.581170\pi\)
−0.964144 + 0.265379i \(0.914503\pi\)
\(158\) 3.24502 + 1.87351i 0.258160 + 0.149048i
\(159\) −10.2205 + 0.855162i −0.810540 + 0.0678187i
\(160\) −2.51990 3.27000i −0.199215 0.258516i
\(161\) −29.5787 −2.33113
\(162\) −8.98821 + 10.3878i −0.706181 + 0.816142i
\(163\) 22.7004i 1.77804i 0.457872 + 0.889018i \(0.348612\pi\)
−0.457872 + 0.889018i \(0.651388\pi\)
\(164\) 0.893905 + 1.54829i 0.0698023 + 0.120901i
\(165\) −3.78262 + 0.831736i −0.294477 + 0.0647506i
\(166\) 10.0710 17.4435i 0.781661 1.35388i
\(167\) 1.22950 + 0.709853i 0.0951416 + 0.0549301i 0.546816 0.837253i \(-0.315840\pi\)
−0.451674 + 0.892183i \(0.649173\pi\)
\(168\) −15.6119 + 10.8436i −1.20448 + 0.836603i
\(169\) −3.59950 6.23451i −0.276884 0.479578i
\(170\) 0.441164 + 3.29838i 0.0338357 + 0.252974i
\(171\) 4.78599 0.806544i 0.365994 0.0616779i
\(172\) 2.07437i 0.158169i
\(173\) 16.9464 9.78398i 1.28841 0.743863i 0.310038 0.950724i \(-0.399658\pi\)
0.978370 + 0.206862i \(0.0663250\pi\)
\(174\) −5.15903 + 10.9550i −0.391105 + 0.830496i
\(175\) 20.8115 + 5.48450i 1.57320 + 0.414589i
\(176\) 2.27525 3.94085i 0.171504 0.297053i
\(177\) −6.02061 2.83528i −0.452537 0.213113i
\(178\) 9.43321 5.44627i 0.707049 0.408215i
\(179\) 9.44959 0.706296 0.353148 0.935568i \(-0.385111\pi\)
0.353148 + 0.935568i \(0.385111\pi\)
\(180\) −1.50252 + 1.62166i −0.111991 + 0.120871i
\(181\) −15.5981 −1.15939 −0.579697 0.814832i \(-0.696829\pi\)
−0.579697 + 0.814832i \(0.696829\pi\)
\(182\) −13.7035 + 7.91174i −1.01577 + 0.586457i
\(183\) 13.4148 9.31757i 0.991649 0.688774i
\(184\) −8.75999 + 15.1728i −0.645795 + 1.11855i
\(185\) 5.86435 14.2408i 0.431156 1.04701i
\(186\) 25.3905 2.12445i 1.86172 0.155772i
\(187\) −0.844423 + 0.487528i −0.0617503 + 0.0356516i
\(188\) 1.81988i 0.132729i
\(189\) 15.6346 + 15.9942i 1.13725 + 1.16341i
\(190\) 5.47271 0.731985i 0.397032 0.0531038i
\(191\) 10.1233 + 17.5340i 0.732494 + 1.26872i 0.955814 + 0.293972i \(0.0949772\pi\)
−0.223320 + 0.974745i \(0.571689\pi\)
\(192\) 0.907397 + 10.8448i 0.0654858 + 0.782657i
\(193\) −4.24223 2.44925i −0.305362 0.176301i 0.339487 0.940611i \(-0.389747\pi\)
−0.644849 + 0.764310i \(0.723080\pi\)
\(194\) 6.30668 10.9235i 0.452793 0.784261i
\(195\) 6.88834 6.29015i 0.493284 0.450447i
\(196\) −1.89956 3.29013i −0.135683 0.235009i
\(197\) 17.7849i 1.26712i −0.773692 0.633562i \(-0.781592\pi\)
0.773692 0.633562i \(-0.218408\pi\)
\(198\) −4.29073 1.59863i −0.304929 0.113610i
\(199\) −5.26851 −0.373475 −0.186737 0.982410i \(-0.559791\pi\)
−0.186737 + 0.982410i \(0.559791\pi\)
\(200\) 8.97685 9.05124i 0.634759 0.640019i
\(201\) 8.55624 18.1688i 0.603510 1.28153i
\(202\) −19.9857 11.5387i −1.40619 0.811863i
\(203\) 17.0748 + 9.85812i 1.19841 + 0.691904i
\(204\) −0.237127 + 0.503529i −0.0166022 + 0.0352541i
\(205\) −9.60847 + 7.40438i −0.671084 + 0.517144i
\(206\) 17.3400 1.20814
\(207\) 19.3179 + 7.19743i 1.34269 + 0.500256i
\(208\) 10.9600i 0.759941i
\(209\) 0.808912 + 1.40108i 0.0559536 + 0.0969145i
\(210\) 17.1577 + 18.7894i 1.18399 + 1.29659i
\(211\) −8.69214 + 15.0552i −0.598392 + 1.03644i 0.394667 + 0.918824i \(0.370860\pi\)
−0.993059 + 0.117620i \(0.962473\pi\)
\(212\) −1.69001 0.975725i −0.116070 0.0670131i
\(213\) 0.689938 + 8.24583i 0.0472737 + 0.564995i
\(214\) 9.08980 + 15.7440i 0.621366 + 1.07624i
\(215\) 13.9505 1.86591i 0.951418 0.127254i
\(216\) 12.8347 3.28313i 0.873293 0.223388i
\(217\) 41.4861i 2.81626i
\(218\) 13.9025 8.02664i 0.941599 0.543632i
\(219\) 5.70857 0.477642i 0.385749 0.0322761i
\(220\) −0.681397 0.280599i −0.0459398 0.0189180i
\(221\) 1.17422 2.03382i 0.0789869 0.136809i
\(222\) 14.9546 10.3871i 1.00369 0.697134i
\(223\) −3.87590 + 2.23775i −0.259550 + 0.149851i −0.624129 0.781321i \(-0.714546\pi\)
0.364579 + 0.931172i \(0.381213\pi\)
\(224\) −7.94692 −0.530976
\(225\) −12.2575 8.64603i −0.817166 0.576402i
\(226\) −17.0083 −1.13137
\(227\) −4.21272 + 2.43222i −0.279608 + 0.161432i −0.633246 0.773951i \(-0.718278\pi\)
0.353638 + 0.935382i \(0.384945\pi\)
\(228\) 0.835461 + 0.393444i 0.0553298 + 0.0260564i
\(229\) −8.49335 + 14.7109i −0.561256 + 0.972124i 0.436131 + 0.899883i \(0.356348\pi\)
−0.997387 + 0.0722412i \(0.976985\pi\)
\(230\) 21.6856 + 8.93012i 1.42991 + 0.588835i
\(231\) −3.17640 + 6.74495i −0.208992 + 0.443785i
\(232\) 10.1137 5.83914i 0.663996 0.383358i
\(233\) 10.7511i 0.704329i 0.935938 + 0.352165i \(0.114554\pi\)
−0.935938 + 0.352165i \(0.885446\pi\)
\(234\) 10.8750 1.83267i 0.710920 0.119806i
\(235\) 12.2391 1.63699i 0.798388 0.106786i
\(236\) −0.633105 1.09657i −0.0412116 0.0713806i
\(237\) −3.49239 + 2.42572i −0.226855 + 0.157568i
\(238\) 5.54767 + 3.20295i 0.359602 + 0.207616i
\(239\) −6.03693 + 10.4563i −0.390497 + 0.676360i −0.992515 0.122122i \(-0.961030\pi\)
0.602018 + 0.798482i \(0.294363\pi\)
\(240\) 17.2128 3.78482i 1.11108 0.244309i
\(241\) 10.1570 + 17.5925i 0.654272 + 1.13323i 0.982076 + 0.188486i \(0.0603580\pi\)
−0.327804 + 0.944746i \(0.606309\pi\)
\(242\) 1.52629i 0.0981135i
\(243\) −6.31909 14.2502i −0.405370 0.914153i
\(244\) 3.10771 0.198951
\(245\) 20.4181 15.7344i 1.30446 1.00523i
\(246\) −14.2914 + 1.19577i −0.911184 + 0.0762398i
\(247\) −3.37453 1.94829i −0.214716 0.123967i
\(248\) −21.2808 12.2865i −1.35133 0.780192i
\(249\) 13.0394 + 18.7732i 0.826339 + 1.18970i
\(250\) −13.6021 10.3042i −0.860275 0.651694i
\(251\) 22.2945 1.40722 0.703609 0.710587i \(-0.251571\pi\)
0.703609 + 0.710587i \(0.251571\pi\)
\(252\) 0.707197 + 4.19647i 0.0445492 + 0.264353i
\(253\) 6.87172i 0.432021i
\(254\) −13.8057 23.9122i −0.866246 1.50038i
\(255\) −3.59963 1.14180i −0.225417 0.0715020i
\(256\) −3.85320 + 6.67394i −0.240825 + 0.417121i
\(257\) −24.4639 14.1242i −1.52602 0.881045i −0.999524 0.0308651i \(-0.990174\pi\)
−0.526492 0.850180i \(-0.676493\pi\)
\(258\) 15.0542 + 7.08947i 0.937234 + 0.441371i
\(259\) −14.8234 25.6749i −0.921082 1.59536i
\(260\) 1.75921 0.235297i 0.109101 0.0145925i
\(261\) −8.75277 10.5932i −0.541783 0.655702i
\(262\) 0.492510i 0.0304274i
\(263\) −18.5662 + 10.7192i −1.14484 + 0.660974i −0.947625 0.319385i \(-0.896524\pi\)
−0.197217 + 0.980360i \(0.563190\pi\)
\(264\) 2.51919 + 3.62695i 0.155045 + 0.223223i
\(265\) 5.04177 12.2433i 0.309713 0.752098i
\(266\) 5.31437 9.20475i 0.325845 0.564380i
\(267\) 1.03066 + 12.3179i 0.0630751 + 0.753846i
\(268\) 3.30920 1.91056i 0.202141 0.116706i
\(269\) 7.02339 0.428224 0.214112 0.976809i \(-0.431314\pi\)
0.214112 + 0.976809i \(0.431314\pi\)
\(270\) −6.63369 16.4464i −0.403713 1.00090i
\(271\) −6.81758 −0.414139 −0.207069 0.978326i \(-0.566393\pi\)
−0.207069 + 0.978326i \(0.566393\pi\)
\(272\) 3.84255 2.21850i 0.232989 0.134516i
\(273\) −1.49722 17.8942i −0.0906160 1.08300i
\(274\) −1.30901 + 2.26727i −0.0790802 + 0.136971i
\(275\) 1.27416 4.83493i 0.0768346 0.291557i
\(276\) 2.23763 + 3.22158i 0.134689 + 0.193916i
\(277\) −5.65468 + 3.26473i −0.339757 + 0.196159i −0.660164 0.751121i \(-0.729513\pi\)
0.320408 + 0.947280i \(0.396180\pi\)
\(278\) 7.75909i 0.465359i
\(279\) −10.0949 + 27.0947i −0.604364 + 1.62211i
\(280\) −3.25324 24.3230i −0.194418 1.45358i
\(281\) 8.27137 + 14.3264i 0.493429 + 0.854644i 0.999971 0.00757128i \(-0.00241004\pi\)
−0.506543 + 0.862215i \(0.669077\pi\)
\(282\) 13.2073 + 6.21972i 0.786485 + 0.370379i
\(283\) 12.7013 + 7.33310i 0.755014 + 0.435908i 0.827503 0.561462i \(-0.189761\pi\)
−0.0724887 + 0.997369i \(0.523094\pi\)
\(284\) −0.787207 + 1.36348i −0.0467121 + 0.0809078i
\(285\) −1.89448 + 5.97254i −0.112219 + 0.353783i
\(286\) 1.83805 + 3.18360i 0.108686 + 0.188250i
\(287\) 23.3510i 1.37836i
\(288\) 5.19015 + 1.93374i 0.305833 + 0.113946i
\(289\) 16.0493 0.944075
\(290\) −9.54210 12.3825i −0.560332 0.727128i
\(291\) 8.16556 + 11.7562i 0.478674 + 0.689161i
\(292\) 0.943935 + 0.544981i 0.0552396 + 0.0318926i
\(293\) 10.1627 + 5.86744i 0.593712 + 0.342780i 0.766564 0.642168i \(-0.221965\pi\)
−0.172852 + 0.984948i \(0.555298\pi\)
\(294\) 30.3693 2.54103i 1.77117 0.148196i
\(295\) 6.80516 5.24412i 0.396211 0.305324i
\(296\) −17.5603 −1.02067
\(297\) 3.71577 3.63222i 0.215611 0.210763i
\(298\) 11.5110i 0.666812i
\(299\) −8.27536 14.3334i −0.478577 0.828919i
\(300\) −0.977042 2.68160i −0.0564095 0.154822i
\(301\) 13.5469 23.4639i 0.780830 1.35244i
\(302\) −10.6068 6.12387i −0.610356 0.352389i
\(303\) 21.5092 14.9398i 1.23567 0.858266i
\(304\) −3.68096 6.37561i −0.211117 0.365666i
\(305\) 2.79541 + 20.9000i 0.160064 + 1.19673i
\(306\) −2.84381 3.44177i −0.162570 0.196753i
\(307\) 21.0883i 1.20357i −0.798656 0.601787i \(-0.794456\pi\)
0.798656 0.601787i \(-0.205544\pi\)
\(308\) −1.22850 + 0.709274i −0.0700002 + 0.0404146i
\(309\) −8.38367 + 17.8024i −0.476930 + 1.01274i
\(310\) −12.5251 + 30.4156i −0.711377 + 1.72749i
\(311\) −5.88327 + 10.1901i −0.333609 + 0.577828i −0.983217 0.182441i \(-0.941600\pi\)
0.649607 + 0.760270i \(0.274933\pi\)
\(312\) −9.62244 4.53149i −0.544763 0.256545i
\(313\) −4.32389 + 2.49640i −0.244401 + 0.141105i −0.617198 0.786808i \(-0.711732\pi\)
0.372797 + 0.927913i \(0.378399\pi\)
\(314\) 26.8614 1.51588
\(315\) −27.5859 + 8.53079i −1.55429 + 0.480655i
\(316\) −0.809058 −0.0455131
\(317\) −10.4646 + 6.04177i −0.587753 + 0.339339i −0.764209 0.644969i \(-0.776870\pi\)
0.176455 + 0.984309i \(0.443537\pi\)
\(318\) 12.8569 8.93009i 0.720980 0.500774i
\(319\) 2.29024 3.96681i 0.128229 0.222098i
\(320\) −12.9911 5.34973i −0.726226 0.299059i
\(321\) −20.5586 + 1.72016i −1.14747 + 0.0960100i
\(322\) 39.0973 22.5728i 2.17881 1.25793i
\(323\) 1.57747i 0.0877727i
\(324\) 0.559261 2.91281i 0.0310701 0.161823i
\(325\) 3.16483 + 11.6193i 0.175553 + 0.644525i
\(326\) −17.3237 30.0056i −0.959472 1.66185i
\(327\) 1.51897 + 18.1540i 0.0839990 + 1.00392i
\(328\) 11.9782 + 6.91560i 0.661384 + 0.381850i
\(329\) 11.8849 20.5853i 0.655238 1.13490i
\(330\) 4.36515 3.98608i 0.240294 0.219426i
\(331\) 8.52685 + 14.7689i 0.468678 + 0.811774i 0.999359 0.0357973i \(-0.0113971\pi\)
−0.530681 + 0.847572i \(0.678064\pi\)
\(332\) 4.34907i 0.238686i
\(333\) 3.43369 + 20.3753i 0.188165 + 1.11656i
\(334\) −2.16688 −0.118566
\(335\) 15.8256 + 20.5364i 0.864642 + 1.12202i
\(336\) 14.4542 30.6929i 0.788542 1.67444i
\(337\) 31.6436 + 18.2694i 1.72374 + 0.995200i 0.910801 + 0.412846i \(0.135465\pi\)
0.812935 + 0.582354i \(0.197868\pi\)
\(338\) 9.51566 + 5.49387i 0.517584 + 0.298827i
\(339\) 8.22327 17.4618i 0.446627 0.948393i
\(340\) −0.438588 0.569144i −0.0237858 0.0308662i
\(341\) −9.63804 −0.521929
\(342\) −5.71063 + 4.71849i −0.308795 + 0.255147i
\(343\) 19.4901i 1.05237i
\(344\) −8.02406 13.8981i −0.432629 0.749335i
\(345\) −19.6530 + 17.9463i −1.05808 + 0.966195i
\(346\) −14.9332 + 25.8650i −0.802813 + 1.39051i
\(347\) −17.1346 9.89265i −0.919832 0.531065i −0.0362503 0.999343i \(-0.511541\pi\)
−0.883581 + 0.468278i \(0.844875\pi\)
\(348\) −0.218002 2.60547i −0.0116862 0.139668i
\(349\) −7.73754 13.4018i −0.414181 0.717382i 0.581161 0.813788i \(-0.302599\pi\)
−0.995342 + 0.0964061i \(0.969265\pi\)
\(350\) −31.6942 + 8.63275i −1.69413 + 0.461440i
\(351\) −3.37637 + 12.0510i −0.180217 + 0.643236i
\(352\) 1.84623i 0.0984043i
\(353\) −26.2624 + 15.1626i −1.39781 + 0.807025i −0.994163 0.107891i \(-0.965590\pi\)
−0.403645 + 0.914916i \(0.632257\pi\)
\(354\) 10.1218 0.846902i 0.537968 0.0450123i
\(355\) −9.87777 4.06765i −0.524258 0.215889i
\(356\) −1.17596 + 2.03682i −0.0623258 + 0.107951i
\(357\) −5.97057 + 4.14701i −0.315996 + 0.219483i
\(358\) −12.4905 + 7.21140i −0.660144 + 0.381134i
\(359\) 9.35774 0.493883 0.246941 0.969030i \(-0.420575\pi\)
0.246941 + 0.969030i \(0.420575\pi\)
\(360\) −3.79385 + 16.6770i −0.199953 + 0.878955i
\(361\) −16.3826 −0.862245
\(362\) 20.6176 11.9036i 1.08364 0.625637i
\(363\) 1.56699 + 0.737940i 0.0822454 + 0.0387318i
\(364\) 1.70831 2.95887i 0.0895395 0.155087i
\(365\) −2.81603 + 6.83836i −0.147398 + 0.357936i
\(366\) −10.6211 + 22.5534i −0.555172 + 1.17889i
\(367\) 21.1866 12.2321i 1.10593 0.638509i 0.168157 0.985760i \(-0.446218\pi\)
0.937772 + 0.347252i \(0.112885\pi\)
\(368\) 31.2698i 1.63005i
\(369\) 5.68203 15.2506i 0.295795 0.793913i
\(370\) 3.11627 + 23.2989i 0.162007 + 1.21125i
\(371\) −12.7442 22.0735i −0.661643 1.14600i
\(372\) −4.51848 + 3.13842i −0.234272 + 0.162719i
\(373\) −19.6727 11.3580i −1.01861 0.588097i −0.104912 0.994482i \(-0.533456\pi\)
−0.913702 + 0.406385i \(0.866789\pi\)
\(374\) 0.744108 1.28883i 0.0384769 0.0666440i
\(375\) 17.1554 8.98291i 0.885901 0.463875i
\(376\) −7.03966 12.1930i −0.363043 0.628808i
\(377\) 11.0322i 0.568187i
\(378\) −32.8717 9.20977i −1.69074 0.473699i
\(379\) −26.0805 −1.33966 −0.669832 0.742513i \(-0.733634\pi\)
−0.669832 + 0.742513i \(0.733634\pi\)
\(380\) −0.944330 + 0.727710i −0.0484431 + 0.0373307i
\(381\) 31.2246 2.61260i 1.59969 0.133847i
\(382\) −26.7620 15.4510i −1.36926 0.790544i
\(383\) −5.69981 3.29079i −0.291247 0.168151i 0.347257 0.937770i \(-0.387113\pi\)
−0.638504 + 0.769618i \(0.720446\pi\)
\(384\) −13.1240 18.8950i −0.669731 0.964232i
\(385\) −5.87504 7.62389i −0.299420 0.388549i
\(386\) 7.47653 0.380546
\(387\) −14.5570 + 12.0279i −0.739974 + 0.611415i
\(388\) 2.72348i 0.138264i
\(389\) −10.5238 18.2277i −0.533577 0.924182i −0.999231 0.0392152i \(-0.987514\pi\)
0.465654 0.884967i \(-0.345819\pi\)
\(390\) −4.30474 + 13.5711i −0.217979 + 0.687201i
\(391\) −3.35015 + 5.80264i −0.169425 + 0.293452i
\(392\) −25.4537 14.6957i −1.28561 0.742245i
\(393\) 0.505642 + 0.238122i 0.0255063 + 0.0120117i
\(394\) 13.5725 + 23.5082i 0.683771 + 1.18433i
\(395\) −0.727753 5.44107i −0.0366172 0.273770i
\(396\) 0.974923 0.164296i 0.0489917 0.00825618i
\(397\) 16.1200i 0.809040i 0.914529 + 0.404520i \(0.132561\pi\)
−0.914529 + 0.404520i \(0.867439\pi\)
\(398\) 6.96394 4.02063i 0.349071 0.201536i
\(399\) 6.88076 + 9.90644i 0.344469 + 0.495943i
\(400\) −5.79806 + 22.0014i −0.289903 + 1.10007i
\(401\) −1.23111 + 2.13235i −0.0614788 + 0.106484i −0.895127 0.445812i \(-0.852915\pi\)
0.833648 + 0.552296i \(0.186248\pi\)
\(402\) 2.55576 + 30.5453i 0.127470 + 1.52346i
\(403\) 20.1035 11.6067i 1.00143 0.578173i
\(404\) 4.98289 0.247908
\(405\) 20.0922 + 1.14105i 0.998391 + 0.0566992i
\(406\) −30.0927 −1.49347
\(407\) −5.96479 + 3.44377i −0.295664 + 0.170701i
\(408\) 0.359020 + 4.29085i 0.0177741 + 0.212429i
\(409\) 4.49094 7.77854i 0.222063 0.384624i −0.733371 0.679828i \(-0.762054\pi\)
0.955434 + 0.295204i \(0.0953877\pi\)
\(410\) 7.04991 17.1198i 0.348170 0.845486i
\(411\) −1.69484 2.44011i −0.0836002 0.120362i
\(412\) −3.24245 + 1.87203i −0.159744 + 0.0922284i
\(413\) 16.5382i 0.813793i
\(414\) −31.0272 + 5.22876i −1.52490 + 0.256980i
\(415\) −29.2483 + 3.91201i −1.43574 + 0.192033i
\(416\) −2.22335 3.85095i −0.109008 0.188808i
\(417\) −7.96598 3.75142i −0.390096 0.183708i
\(418\) −2.13845 1.23463i −0.104595 0.0603879i
\(419\) −1.58938 + 2.75289i −0.0776464 + 0.134487i −0.902234 0.431247i \(-0.858074\pi\)
0.824588 + 0.565734i \(0.191407\pi\)
\(420\) −5.23687 1.66113i −0.255533 0.0810547i
\(421\) −4.14547 7.18016i −0.202038 0.349940i 0.747147 0.664659i \(-0.231423\pi\)
−0.949185 + 0.314719i \(0.898090\pi\)
\(422\) 26.5334i 1.29163i
\(423\) −12.7711 + 10.5523i −0.620954 + 0.513072i
\(424\) −15.0972 −0.733184
\(425\) 3.43309 3.46154i 0.166529 0.167909i
\(426\) −7.20472 10.3729i −0.349070 0.502567i
\(427\) 35.1524 + 20.2952i 1.70114 + 0.982156i
\(428\) −3.39945 1.96267i −0.164319 0.0948694i
\(429\) −4.15717 + 0.347835i −0.200710 + 0.0167936i
\(430\) −17.0159 + 13.1126i −0.820580 + 0.632347i
\(431\) 9.25057 0.445584 0.222792 0.974866i \(-0.428483\pi\)
0.222792 + 0.974866i \(0.428483\pi\)
\(432\) −16.9086 + 16.5285i −0.813517 + 0.795226i
\(433\) 17.9047i 0.860447i −0.902722 0.430224i \(-0.858435\pi\)
0.902722 0.430224i \(-0.141565\pi\)
\(434\) 31.6599 + 54.8365i 1.51972 + 2.63224i
\(435\) 17.3262 3.80974i 0.830727 0.182663i
\(436\) −1.73311 + 3.00184i −0.0830011 + 0.143762i
\(437\) 9.62780 + 5.55861i 0.460560 + 0.265905i
\(438\) −7.18110 + 4.98781i −0.343126 + 0.238327i
\(439\) −7.23456 12.5306i −0.345287 0.598054i 0.640119 0.768276i \(-0.278885\pi\)
−0.985406 + 0.170222i \(0.945552\pi\)
\(440\) −5.65071 + 0.755793i −0.269387 + 0.0360310i
\(441\) −12.0744 + 32.4076i −0.574969 + 1.54322i
\(442\) 3.58441i 0.170493i
\(443\) 3.42396 1.97682i 0.162677 0.0939217i −0.416451 0.909158i \(-0.636726\pi\)
0.579128 + 0.815236i \(0.303393\pi\)
\(444\) −1.67500 + 3.55680i −0.0794922 + 0.168798i
\(445\) −14.7558 6.07642i −0.699492 0.288050i
\(446\) 3.41546 5.91575i 0.161727 0.280119i
\(447\) 11.8179 + 5.56540i 0.558967 + 0.263234i
\(448\) −23.4218 + 13.5226i −1.10658 + 0.638883i
\(449\) 31.1358 1.46939 0.734696 0.678397i \(-0.237325\pi\)
0.734696 + 0.678397i \(0.237325\pi\)
\(450\) 22.8002 + 2.07413i 1.07481 + 0.0977755i
\(451\) 5.42490 0.255448
\(452\) 3.18042 1.83621i 0.149594 0.0863683i
\(453\) 11.4154 7.92886i 0.536343 0.372531i
\(454\) 3.71227 6.42983i 0.174225 0.301767i
\(455\) 21.4356 + 8.82716i 1.00492 + 0.413823i
\(456\) 7.11943 0.595690i 0.333398 0.0278958i
\(457\) −0.963332 + 0.556180i −0.0450628 + 0.0260170i −0.522362 0.852724i \(-0.674949\pi\)
0.477299 + 0.878741i \(0.341616\pi\)
\(458\) 25.9266i 1.21147i
\(459\) 4.90849 1.25559i 0.229109 0.0586060i
\(460\) −5.01915 + 0.671320i −0.234019 + 0.0313005i
\(461\) 8.34560 + 14.4550i 0.388694 + 0.673237i 0.992274 0.124065i \(-0.0395932\pi\)
−0.603581 + 0.797302i \(0.706260\pi\)
\(462\) −0.948793 11.3396i −0.0441418 0.527564i
\(463\) −15.4022 8.89247i −0.715801 0.413268i 0.0974040 0.995245i \(-0.468946\pi\)
−0.813205 + 0.581977i \(0.802279\pi\)
\(464\) −10.4217 + 18.0510i −0.483817 + 0.837995i
\(465\) −25.1709 27.5646i −1.16727 1.27828i
\(466\) −8.20465 14.2109i −0.380073 0.658306i
\(467\) 29.7965i 1.37882i 0.724372 + 0.689410i \(0.242130\pi\)
−0.724372 + 0.689410i \(0.757870\pi\)
\(468\) −1.83568 + 1.51676i −0.0848545 + 0.0701123i
\(469\) 49.9086 2.30456
\(470\) −14.9284 + 11.5039i −0.688594 + 0.530638i
\(471\) −12.9871 + 27.5777i −0.598416 + 1.27071i
\(472\) −8.48349 4.89794i −0.390484 0.225446i
\(473\) −5.45113 3.14721i −0.250643 0.144709i
\(474\) 2.76508 5.87153i 0.127004 0.269688i
\(475\) −5.74342 5.69622i −0.263526 0.261361i
\(476\) −1.38316 −0.0633971
\(477\) 2.95205 + 17.5173i 0.135165 + 0.802063i
\(478\) 18.4282i 0.842886i
\(479\) −4.20132 7.27690i −0.191963 0.332490i 0.753937 0.656946i \(-0.228152\pi\)
−0.945901 + 0.324456i \(0.894819\pi\)
\(480\) −5.28017 + 4.82164i −0.241006 + 0.220077i
\(481\) 8.29442 14.3664i 0.378193 0.655050i
\(482\) −26.8512 15.5026i −1.22304 0.706122i
\(483\) 4.27169 + 51.0534i 0.194369 + 2.32301i
\(484\) 0.164778 + 0.285404i 0.00748992 + 0.0129729i
\(485\) −18.3159 + 2.44979i −0.831684 + 0.111239i
\(486\) 19.2276 + 14.0136i 0.872181 + 0.635672i
\(487\) 4.39317i 0.199074i −0.995034 0.0995368i \(-0.968264\pi\)
0.995034 0.0995368i \(-0.0317361\pi\)
\(488\) 20.8214 12.0212i 0.942540 0.544176i
\(489\) 39.1814 3.27835i 1.77184 0.148252i
\(490\) −14.9811 + 36.3797i −0.676778 + 1.64347i
\(491\) 12.6918 21.9829i 0.572774 0.992074i −0.423505 0.905894i \(-0.639200\pi\)
0.996280 0.0861805i \(-0.0274662\pi\)
\(492\) 2.54328 1.76650i 0.114660 0.0796399i
\(493\) 3.86786 2.23311i 0.174199 0.100574i
\(494\) 5.94730 0.267581
\(495\) 1.98187 + 6.40876i 0.0890785 + 0.288052i
\(496\) 43.8580 1.96928
\(497\) −17.8087 + 10.2819i −0.798831 + 0.461205i
\(498\) −31.5622 14.8636i −1.41434 0.666053i
\(499\) −5.63521 + 9.76047i −0.252267 + 0.436938i −0.964149 0.265360i \(-0.914509\pi\)
0.711883 + 0.702298i \(0.247843\pi\)
\(500\) 3.65594 + 0.458314i 0.163499 + 0.0204964i
\(501\) 1.04766 2.22466i 0.0468059 0.0993904i
\(502\) −29.4690 + 17.0139i −1.31527 + 0.759370i
\(503\) 18.6918i 0.833424i 0.909038 + 0.416712i \(0.136818\pi\)
−0.909038 + 0.416712i \(0.863182\pi\)
\(504\) 20.9709 + 25.3804i 0.934119 + 1.13053i
\(505\) 4.48214 + 33.5109i 0.199453 + 1.49122i
\(506\) −5.24411 9.08307i −0.233129 0.403792i
\(507\) −10.2411 + 7.11318i −0.454821 + 0.315907i
\(508\) 5.16312 + 2.98093i 0.229077 + 0.132257i
\(509\) 5.30802 9.19375i 0.235274 0.407506i −0.724079 0.689718i \(-0.757735\pi\)
0.959352 + 0.282212i \(0.0910680\pi\)
\(510\) 5.62936 1.23780i 0.249272 0.0548108i
\(511\) 7.11812 + 12.3289i 0.314887 + 0.545400i
\(512\) 14.8025i 0.654183i
\(513\) −2.08329 8.14423i −0.0919796 0.359576i
\(514\) 43.1153 1.90173
\(515\) −15.5064 20.1222i −0.683293 0.886691i
\(516\) −3.58040 + 0.299576i −0.157618 + 0.0131881i
\(517\) −4.78238 2.76111i −0.210329 0.121433i
\(518\) 39.1873 + 22.6248i 1.72179 + 0.994077i
\(519\) −19.3347 27.8368i −0.848699 1.22190i
\(520\) 10.8763 8.38142i 0.476959 0.367549i
\(521\) −13.8643 −0.607405 −0.303703 0.952767i \(-0.598223\pi\)
−0.303703 + 0.952767i \(0.598223\pi\)
\(522\) 19.6536 + 7.32249i 0.860214 + 0.320497i
\(523\) 10.3793i 0.453855i 0.973912 + 0.226928i \(0.0728681\pi\)
−0.973912 + 0.226928i \(0.927132\pi\)
\(524\) 0.0531714 + 0.0920956i 0.00232280 + 0.00402322i
\(525\) 6.46079 36.7131i 0.281972 1.60229i
\(526\) 16.3606 28.3374i 0.713356 1.23557i
\(527\) −8.13858 4.69881i −0.354522 0.204684i
\(528\) −7.13058 3.35800i −0.310319 0.146138i
\(529\) 12.1103 + 20.9756i 0.526533 + 0.911982i
\(530\) 2.67916 + 20.0308i 0.116375 + 0.870083i
\(531\) −4.02427 + 10.8012i −0.174639 + 0.468730i
\(532\) 2.29496i 0.0994991i
\(533\) −11.3155 + 6.53301i −0.490129 + 0.282976i
\(534\) −10.7627 15.4954i −0.465747 0.670550i
\(535\) 10.1415 24.6274i 0.438456 1.06473i
\(536\) 14.7809 25.6012i 0.638436 1.10580i
\(537\) −1.36469 16.3102i −0.0588907 0.703836i
\(538\) −9.28355 + 5.35986i −0.400242 + 0.231080i
\(539\) −11.5279 −0.496544
\(540\) 3.01601 + 2.35918i 0.129788 + 0.101523i
\(541\) 7.07060 0.303989 0.151994 0.988381i \(-0.451430\pi\)
0.151994 + 0.988381i \(0.451430\pi\)
\(542\) 9.01151 5.20280i 0.387078 0.223479i
\(543\) 2.25264 + 26.9225i 0.0966700 + 1.15536i
\(544\) −0.900087 + 1.55900i −0.0385909 + 0.0668414i
\(545\) −21.7469 8.95534i −0.931535 0.383605i
\(546\) 15.6349 + 22.5100i 0.669110 + 0.963338i
\(547\) 3.43787 1.98485i 0.146993 0.0848662i −0.424700 0.905334i \(-0.639620\pi\)
0.571692 + 0.820468i \(0.306287\pi\)
\(548\) 0.565284i 0.0241477i
\(549\) −18.0196 21.8086i −0.769059 0.930766i
\(550\) 2.00556 + 7.36320i 0.0855173 + 0.313968i
\(551\) −3.70520 6.41759i −0.157847 0.273399i
\(552\) 27.4536 + 12.9287i 1.16850 + 0.550282i
\(553\) −9.15153 5.28364i −0.389163 0.224683i
\(554\) 4.98292 8.63067i 0.211704 0.366682i
\(555\) −25.4268 8.06535i −1.07931 0.342355i
\(556\) −0.837672 1.45089i −0.0355252 0.0615315i
\(557\) 33.8162i 1.43284i −0.697670 0.716419i \(-0.745780\pi\)
0.697670 0.716419i \(-0.254220\pi\)
\(558\) −7.33369 43.5177i −0.310460 1.84225i
\(559\) 15.1603 0.641212
\(560\) 26.7344 + 34.6925i 1.12973 + 1.46603i
\(561\) 0.963432 + 1.38708i 0.0406761 + 0.0585627i
\(562\) −21.8663 12.6245i −0.922373 0.532532i
\(563\) 38.2056 + 22.0580i 1.61017 + 0.929635i 0.989328 + 0.145702i \(0.0465442\pi\)
0.620846 + 0.783932i \(0.286789\pi\)
\(564\) −3.14115 + 0.262824i −0.132266 + 0.0110669i
\(565\) 15.2097 + 19.7372i 0.639877 + 0.830351i
\(566\) −22.3849 −0.940906
\(567\) 25.3484 29.2954i 1.06453 1.23029i
\(568\) 12.1803i 0.511073i
\(569\) 9.07396 + 15.7166i 0.380400 + 0.658872i 0.991119 0.132975i \(-0.0424530\pi\)
−0.610719 + 0.791847i \(0.709120\pi\)
\(570\) −2.05378 9.34029i −0.0860233 0.391222i
\(571\) −5.53080 + 9.57962i −0.231457 + 0.400895i −0.958237 0.285975i \(-0.907682\pi\)
0.726780 + 0.686870i \(0.241016\pi\)
\(572\) −0.687405 0.396873i −0.0287418 0.0165941i
\(573\) 28.8021 20.0052i 1.20322 0.835729i
\(574\) −17.8202 30.8654i −0.743799 1.28830i
\(575\) −9.02951 33.1509i −0.376557 1.38249i
\(576\) 18.5873 3.13237i 0.774472 0.130515i
\(577\) 44.3187i 1.84501i 0.385984 + 0.922505i \(0.373862\pi\)
−0.385984 + 0.922505i \(0.626138\pi\)
\(578\) −21.2140 + 12.2479i −0.882386 + 0.509446i
\(579\) −3.61480 + 7.67589i −0.150226 + 0.318999i
\(580\) 3.12112 + 1.28527i 0.129598 + 0.0533681i
\(581\) −28.4020 + 49.1938i −1.17832 + 2.04090i
\(582\) −19.7650 9.30791i −0.819284 0.385825i
\(583\) −5.12812 + 2.96072i −0.212385 + 0.122620i
\(584\) 8.43238 0.348934
\(585\) −11.8517 10.9810i −0.490008 0.454008i
\(586\) −17.9108 −0.739889
\(587\) −4.91737 + 2.83905i −0.202962 + 0.117180i −0.598036 0.801469i \(-0.704052\pi\)
0.395074 + 0.918649i \(0.370719\pi\)
\(588\) −5.40449 + 3.75382i −0.222878 + 0.154805i
\(589\) −7.79633 + 13.5036i −0.321242 + 0.556408i
\(590\) −4.99307 + 12.1250i −0.205561 + 0.499179i
\(591\) −30.6971 + 2.56846i −1.26271 + 0.105652i
\(592\) 27.1428 15.6709i 1.11556 0.644070i
\(593\) 19.1445i 0.786170i 0.919502 + 0.393085i \(0.128592\pi\)
−0.919502 + 0.393085i \(0.871408\pi\)
\(594\) −2.13961 + 7.63676i −0.0877893 + 0.313340i
\(595\) −1.24416 9.30203i −0.0510057 0.381346i
\(596\) 1.24272 + 2.15246i 0.0509040 + 0.0881683i
\(597\) 0.760867 + 9.09354i 0.0311402 + 0.372174i
\(598\) 21.8768 + 12.6306i 0.894610 + 0.516503i
\(599\) 9.64728 16.7096i 0.394177 0.682735i −0.598818 0.800885i \(-0.704363\pi\)
0.992996 + 0.118150i \(0.0376962\pi\)
\(600\) −16.9190 14.1871i −0.690716 0.579184i
\(601\) 7.33407 + 12.7030i 0.299163 + 0.518165i 0.975945 0.218018i \(-0.0699593\pi\)
−0.676782 + 0.736184i \(0.736626\pi\)
\(602\) 41.3529i 1.68542i
\(603\) −32.5954 12.1443i −1.32739 0.494555i
\(604\) 2.64453 0.107605
\(605\) −1.77118 + 1.36489i −0.0720087 + 0.0554906i
\(606\) −17.0298 + 36.1621i −0.691788 + 1.46898i
\(607\) 1.32045 + 0.762361i 0.0535953 + 0.0309433i 0.526558 0.850139i \(-0.323482\pi\)
−0.472963 + 0.881082i \(0.656816\pi\)
\(608\) 2.58671 + 1.49344i 0.104905 + 0.0605668i
\(609\) 14.5494 30.8951i 0.589571 1.25193i
\(610\) −19.6447 25.4924i −0.795389 1.03216i
\(611\) 13.3004 0.538077
\(612\) 0.903346 + 0.336567i 0.0365156 + 0.0136049i
\(613\) 46.0403i 1.85955i −0.368127 0.929776i \(-0.620001\pi\)
0.368127 0.929776i \(-0.379999\pi\)
\(614\) 16.0934 + 27.8747i 0.649478 + 1.12493i
\(615\) 14.1677 + 15.5151i 0.571298 + 0.625628i
\(616\) −5.48722 + 9.50414i −0.221086 + 0.382933i
\(617\) 19.8228 + 11.4447i 0.798036 + 0.460746i 0.842784 0.538252i \(-0.180915\pi\)
−0.0447479 + 0.998998i \(0.514248\pi\)
\(618\) −2.50421 29.9292i −0.100734 1.20393i
\(619\) −15.9645 27.6513i −0.641668 1.11140i −0.985060 0.172209i \(-0.944909\pi\)
0.343393 0.939192i \(-0.388424\pi\)
\(620\) −0.941571 7.03969i −0.0378144 0.282721i
\(621\) 9.63305 34.3825i 0.386561 1.37972i
\(622\) 17.9591i 0.720095i
\(623\) −26.6034 + 15.3595i −1.06584 + 0.615364i
\(624\) 18.9172 1.58282i 0.757295 0.0633636i
\(625\) 0.206294 + 24.9991i 0.00825174 + 0.999966i
\(626\) 3.81023 6.59951i 0.152287 0.263769i
\(627\) 2.30146 1.59854i 0.0919116 0.0638395i
\(628\) −5.02289 + 2.89997i −0.200435 + 0.115721i
\(629\) −6.71574 −0.267774
\(630\) 29.9530 32.3281i 1.19336 1.28798i
\(631\) 7.18053 0.285853 0.142926 0.989733i \(-0.454349\pi\)
0.142926 + 0.989733i \(0.454349\pi\)
\(632\) −5.42061 + 3.12959i −0.215620 + 0.124489i
\(633\) 27.2409 + 12.8286i 1.08273 + 0.509889i
\(634\) 9.22148 15.9721i 0.366232 0.634332i
\(635\) −15.4031 + 37.4043i −0.611252 + 1.48435i
\(636\) −1.44005 + 3.05789i −0.0571018 + 0.121253i
\(637\) 24.0455 13.8827i 0.952719 0.550052i
\(638\) 6.99112i 0.276781i
\(639\) 14.1328 2.38169i 0.559086 0.0942182i
\(640\) 29.4380 3.93739i 1.16364 0.155639i
\(641\) −10.1399 17.5628i −0.400502 0.693689i 0.593285 0.804993i \(-0.297831\pi\)
−0.993786 + 0.111304i \(0.964497\pi\)
\(642\) 25.8617 17.9629i 1.02068 0.708939i
\(643\) −14.9857 8.65200i −0.590978 0.341202i 0.174506 0.984656i \(-0.444167\pi\)
−0.765484 + 0.643455i \(0.777501\pi\)
\(644\) −4.87393 + 8.44189i −0.192060 + 0.332657i
\(645\) −5.23530 23.8094i −0.206140 0.937495i
\(646\) −1.20384 2.08510i −0.0473643 0.0820373i
\(647\) 1.86158i 0.0731863i −0.999330 0.0365932i \(-0.988349\pi\)
0.999330 0.0365932i \(-0.0116506\pi\)
\(648\) −7.52030 21.6789i −0.295425 0.851626i
\(649\) −3.84216 −0.150818
\(650\) −13.0505 12.9433i −0.511884 0.507677i
\(651\) −71.6058 + 5.99133i −2.80645 + 0.234819i
\(652\) 6.47881 + 3.74054i 0.253730 + 0.146491i
\(653\) −4.52608 2.61313i −0.177119 0.102260i 0.408819 0.912615i \(-0.365941\pi\)
−0.585938 + 0.810356i \(0.699274\pi\)
\(654\) −15.8619 22.8369i −0.620250 0.892992i
\(655\) −0.571532 + 0.440428i −0.0223316 + 0.0172090i
\(656\) −24.6860 −0.963827
\(657\) −1.64884 9.78412i −0.0643273 0.381715i
\(658\) 36.2797i 1.41433i
\(659\) 22.3130 + 38.6472i 0.869191 + 1.50548i 0.862825 + 0.505503i \(0.168693\pi\)
0.00636568 + 0.999980i \(0.497974\pi\)
\(660\) −0.385913 + 1.21663i −0.0150216 + 0.0473572i
\(661\) 14.0359 24.3110i 0.545935 0.945587i −0.452613 0.891707i \(-0.649508\pi\)
0.998547 0.0538796i \(-0.0171587\pi\)
\(662\) −22.5417 13.0144i −0.876107 0.505820i
\(663\) −3.67999 1.73301i −0.142919 0.0673047i
\(664\) 16.8230 + 29.1383i 0.652860 + 1.13079i
\(665\) −15.4340 + 2.06433i −0.598506 + 0.0800513i
\(666\) −20.0880 24.3118i −0.778394 0.942064i
\(667\) 31.4757i 1.21874i
\(668\) 0.405190 0.233937i 0.0156773 0.00905128i
\(669\) 4.42216 + 6.36671i 0.170970 + 0.246151i
\(670\) −36.5905 15.0679i −1.41362 0.582125i
\(671\) 4.71499 8.16660i 0.182020 0.315268i
\(672\) 1.14768 + 13.7165i 0.0442726 + 0.529127i
\(673\) −18.3660 + 10.6036i −0.707957 + 0.408739i −0.810304 0.586009i \(-0.800698\pi\)
0.102347 + 0.994749i \(0.467365\pi\)
\(674\) −55.7689 −2.14814
\(675\) −13.1530 + 22.4053i −0.506260 + 0.862381i
\(676\) −2.37248 −0.0912491
\(677\) 22.4937 12.9867i 0.864503 0.499121i −0.00101455 0.999999i \(-0.500323\pi\)
0.865518 + 0.500878i \(0.166990\pi\)
\(678\) 2.45630 + 29.3566i 0.0943335 + 1.12743i
\(679\) −17.7860 + 30.8062i −0.682564 + 1.18223i
\(680\) −5.14006 2.11667i −0.197112 0.0811706i
\(681\) 4.80645 + 6.91999i 0.184183 + 0.265175i
\(682\) 12.7396 7.35522i 0.487825 0.281646i
\(683\) 47.7242i 1.82612i −0.407830 0.913058i \(-0.633714\pi\)
0.407830 0.913058i \(-0.366286\pi\)
\(684\) 0.558436 1.49884i 0.0213523 0.0573097i
\(685\) 3.80164 0.508476i 0.145253 0.0194279i
\(686\) 14.8738 + 25.7622i 0.567884 + 0.983604i
\(687\) 26.6179 + 12.5352i 1.01554 + 0.478246i
\(688\) 24.8054 + 14.3214i 0.945697 + 0.545999i
\(689\) 7.13098 12.3512i 0.271669 0.470544i
\(690\) 12.2818 38.7195i 0.467559 1.47403i
\(691\) −20.6744 35.8090i −0.786490 1.36224i −0.928105 0.372318i \(-0.878563\pi\)
0.141616 0.989922i \(-0.454770\pi\)
\(692\) 6.44876i 0.245145i
\(693\) 12.1006 + 4.50843i 0.459665 + 0.171261i
\(694\) 30.1981 1.14630
\(695\) 9.00403 6.93859i 0.341542 0.263196i
\(696\) −11.5391 16.6131i −0.437387 0.629719i
\(697\) 4.58091 + 2.64479i 0.173514 + 0.100178i
\(698\) 20.4550 + 11.8097i 0.774234 + 0.447004i
\(699\) 18.5566 1.55265i 0.701877 0.0587268i
\(700\) 4.99459 5.03597i 0.188778 0.190342i
\(701\) 8.63388 0.326097 0.163049 0.986618i \(-0.447867\pi\)
0.163049 + 0.986618i \(0.447867\pi\)
\(702\) −4.73377 18.5058i −0.178665 0.698455i
\(703\) 11.1428i 0.420260i
\(704\) 3.14157 + 5.44135i 0.118402 + 0.205079i
\(705\) −4.59302 20.8884i −0.172983 0.786704i
\(706\) 23.1425 40.0840i 0.870981 1.50858i
\(707\) 56.3632 + 32.5413i 2.11976 + 1.22384i
\(708\) −1.80127 + 1.25112i −0.0676958 + 0.0470198i
\(709\) 10.0436 + 17.3960i 0.377194 + 0.653319i 0.990653 0.136408i \(-0.0435557\pi\)
−0.613459 + 0.789727i \(0.710222\pi\)
\(710\) 16.1607 2.16152i 0.606500 0.0811205i
\(711\) 4.69121 + 5.67761i 0.175934 + 0.212927i
\(712\) 18.1954i 0.681900i
\(713\) −57.3568 + 33.1150i −2.14803 + 1.24017i
\(714\) 4.72717 10.0379i 0.176910 0.375661i
\(715\) 2.05072 4.97992i 0.0766927 0.186238i
\(716\) 1.55709 2.69696i 0.0581911 0.100790i
\(717\) 18.9196 + 8.90979i 0.706564 + 0.332742i
\(718\) −12.3691 + 7.14131i −0.461611 + 0.266511i
\(719\) 28.4383 1.06057 0.530285 0.847820i \(-0.322085\pi\)
0.530285 + 0.847820i \(0.322085\pi\)
\(720\) −9.01851 29.1631i −0.336100 1.08684i
\(721\) −48.9020 −1.82121
\(722\) 21.6547 12.5023i 0.805903 0.465288i
\(723\) 28.8981 20.0719i 1.07473 0.746482i
\(724\) −2.57022 + 4.45175i −0.0955215 + 0.165448i
\(725\) −5.83624 + 22.1463i −0.216753 + 0.822491i
\(726\) −2.63440 + 0.220423i −0.0977719 + 0.00818068i
\(727\) −10.0695 + 5.81361i −0.373456 + 0.215615i −0.674967 0.737848i \(-0.735842\pi\)
0.301511 + 0.953463i \(0.402509\pi\)
\(728\) 26.4322i 0.979644i
\(729\) −23.6836 + 12.9649i −0.877170 + 0.480180i
\(730\) −1.49642 11.1880i −0.0553849 0.414087i
\(731\) −3.06871 5.31516i −0.113500 0.196588i
\(732\) −0.448809 5.36397i −0.0165885 0.198258i
\(733\) 27.4088 + 15.8245i 1.01237 + 0.584490i 0.911883 0.410449i \(-0.134628\pi\)
0.100482 + 0.994939i \(0.467961\pi\)
\(734\) −18.6697 + 32.3368i −0.689110 + 1.19357i
\(735\) −30.1066 32.9697i −1.11050 1.21610i
\(736\) 6.34338 + 10.9871i 0.233820 + 0.404988i
\(737\) 11.5948i 0.427098i
\(738\) 4.12786 + 24.4945i 0.151949 + 0.901654i
\(739\) −31.4124 −1.15552 −0.577762 0.816205i \(-0.696074\pi\)
−0.577762 + 0.816205i \(0.696074\pi\)
\(740\) −3.09807 4.02029i −0.113887 0.147789i
\(741\) −2.87544 + 6.10588i −0.105632 + 0.224305i
\(742\) 33.6906 + 19.4513i 1.23682 + 0.714078i
\(743\) 11.8649 + 6.85022i 0.435282 + 0.251310i 0.701594 0.712577i \(-0.252472\pi\)
−0.266312 + 0.963887i \(0.585805\pi\)
\(744\) −18.1334 + 38.5055i −0.664801 + 1.41168i
\(745\) −13.3579 + 10.2937i −0.489395 + 0.377132i
\(746\) 34.6713 1.26941
\(747\) 30.5198 25.2175i 1.11666 0.922658i
\(748\) 0.321336i 0.0117492i
\(749\) −25.6349 44.4009i −0.936678 1.62237i
\(750\) −15.8208 + 24.9657i −0.577695 + 0.911618i
\(751\) 19.6923 34.1081i 0.718584 1.24462i −0.242977 0.970032i \(-0.578124\pi\)
0.961561 0.274591i \(-0.0885426\pi\)
\(752\) 21.7622 + 12.5644i 0.793587 + 0.458178i
\(753\) −3.21973 38.4808i −0.117333 1.40232i
\(754\) −8.41916 14.5824i −0.306608 0.531060i
\(755\) 2.37878 + 17.7850i 0.0865725 + 0.647262i
\(756\) 7.14106 1.82668i 0.259718 0.0664358i
\(757\) 19.0646i 0.692915i −0.938066 0.346457i \(-0.887385\pi\)
0.938066 0.346457i \(-0.112615\pi\)
\(758\) 34.4733 19.9032i 1.25213 0.722915i
\(759\) 11.8607 0.992399i 0.430517 0.0360218i
\(760\) −3.51200 + 8.52845i −0.127394 + 0.309359i
\(761\) 7.60898 13.1791i 0.275825 0.477744i −0.694518 0.719476i \(-0.744382\pi\)
0.970343 + 0.241732i \(0.0777155\pi\)
\(762\) −39.2791 + 27.2822i −1.42293 + 0.988332i
\(763\) −39.2077 + 22.6366i −1.41941 + 0.819499i
\(764\) 6.67238 0.241398
\(765\) −1.45091 + 6.37792i −0.0524578 + 0.230594i
\(766\) 10.0454 0.362955
\(767\) 8.01415 4.62697i 0.289374 0.167070i
\(768\) 12.0758 + 5.68686i 0.435749 + 0.205207i
\(769\) −8.42141 + 14.5863i −0.303684 + 0.525996i −0.976967 0.213388i \(-0.931550\pi\)
0.673284 + 0.739384i \(0.264883\pi\)
\(770\) 13.5838 + 5.59378i 0.489525 + 0.201586i
\(771\) −20.8457 + 44.2649i −0.750739 + 1.59416i
\(772\) −1.39806 + 0.807168i −0.0503171 + 0.0290506i
\(773\) 47.5641i 1.71076i −0.517999 0.855381i \(-0.673323\pi\)
0.517999 0.855381i \(-0.326677\pi\)
\(774\) 10.0625 27.0077i 0.361688 0.970771i
\(775\) 46.4963 12.6645i 1.67020 0.454922i
\(776\) 10.5350 + 18.2471i 0.378183 + 0.655032i
\(777\) −42.1746 + 29.2934i −1.51301 + 1.05090i
\(778\) 27.8208 + 16.0623i 0.997423 + 0.575862i
\(779\) 4.38826 7.60069i 0.157226 0.272323i
\(780\) −0.660188 3.00244i −0.0236385 0.107505i
\(781\) 2.38868 + 4.13732i 0.0854738 + 0.148045i
\(782\) 10.2266i 0.365703i
\(783\) −17.0200 + 16.6373i −0.608245 + 0.594569i
\(784\) 52.4580 1.87350
\(785\) −24.0209 31.1713i −0.857344 1.11255i
\(786\) −0.850081 + 0.0711272i −0.0303214 + 0.00253702i
\(787\) −0.572845 0.330732i −0.0204197 0.0117893i 0.489755 0.871860i \(-0.337086\pi\)
−0.510175 + 0.860071i \(0.670419\pi\)
\(788\) −5.07590 2.93057i −0.180821 0.104397i
\(789\) 21.1828 + 30.4976i 0.754129 + 1.08574i
\(790\) 5.11427 + 6.63665i 0.181957 + 0.236121i
\(791\) 47.9664 1.70549
\(792\) 5.89637 4.87196i 0.209518 0.173118i
\(793\) 22.7124i 0.806540i
\(794\) −12.3019 21.3075i −0.436578 0.756175i
\(795\) −21.8603 6.93404i −0.775303 0.245925i
\(796\) −0.868136 + 1.50366i −0.0307703 + 0.0532956i
\(797\) −11.0504 6.37993i −0.391424 0.225989i 0.291353 0.956616i \(-0.405895\pi\)
−0.682777 + 0.730627i \(0.739228\pi\)
\(798\) −16.6551 7.84337i −0.589583 0.277652i
\(799\) −2.69223 4.66308i −0.0952443 0.164968i
\(800\) −2.42596 8.90666i −0.0857708 0.314898i
\(801\) 21.1122 3.55786i 0.745962 0.125711i
\(802\) 3.75806i 0.132702i
\(803\) 2.86426 1.65368i 0.101077 0.0583571i
\(804\) −3.77558 5.43582i −0.133154 0.191706i
\(805\) −61.1575 25.1846i −2.15552 0.887639i
\(806\) −17.7152 + 30.6837i −0.623993 + 1.08079i
\(807\) −1.01430 12.1225i −0.0357052 0.426732i
\(808\) 33.3849 19.2748i 1.17448 0.678085i
\(809\) −41.2002 −1.44852 −0.724261 0.689526i \(-0.757819\pi\)
−0.724261 + 0.689526i \(0.757819\pi\)
\(810\) −27.4288 + 13.8250i −0.963750 + 0.485762i
\(811\) −34.6437 −1.21651 −0.608253 0.793744i \(-0.708129\pi\)
−0.608253 + 0.793744i \(0.708129\pi\)
\(812\) 5.62710 3.24881i 0.197473 0.114011i
\(813\) 0.984581 + 11.7673i 0.0345308 + 0.412697i
\(814\) 5.25619 9.10399i 0.184229 0.319095i
\(815\) −19.3281 + 46.9359i −0.677035 + 1.64409i
\(816\) −4.38410 6.31193i −0.153474 0.220962i
\(817\) −8.81897 + 5.09163i −0.308537 + 0.178134i
\(818\) 13.7089i 0.479322i
\(819\) −30.6694 + 5.16847i −1.07168 + 0.180601i
\(820\) 0.529975 + 3.96238i 0.0185075 + 0.138372i
\(821\) 21.3776 + 37.0271i 0.746083 + 1.29225i 0.949687 + 0.313201i \(0.101401\pi\)
−0.203604 + 0.979053i \(0.565265\pi\)
\(822\) 4.10240 + 1.93194i 0.143088 + 0.0673843i
\(823\) −21.4054 12.3584i −0.746147 0.430788i 0.0781530 0.996941i \(-0.475098\pi\)
−0.824300 + 0.566153i \(0.808431\pi\)
\(824\) −14.4828 + 25.0849i −0.504531 + 0.873873i
\(825\) −8.52919 1.50097i −0.296948 0.0522571i
\(826\) 12.6211 + 21.8603i 0.439143 + 0.760617i
\(827\) 54.2179i 1.88534i −0.333726 0.942670i \(-0.608306\pi\)
0.333726 0.942670i \(-0.391694\pi\)
\(828\) 5.23735 4.32744i 0.182011 0.150389i
\(829\) 15.8577 0.550762 0.275381 0.961335i \(-0.411196\pi\)
0.275381 + 0.961335i \(0.411196\pi\)
\(830\) 35.6751 27.4916i 1.23830 0.954247i
\(831\) 6.45163 + 9.28860i 0.223804 + 0.322218i
\(832\) −13.1057 7.56655i −0.454357 0.262323i
\(833\) −9.73446 5.62019i −0.337279 0.194728i
\(834\) 13.3923 1.12055i 0.463739 0.0388015i
\(835\) 1.93774 + 2.51455i 0.0670583 + 0.0870197i
\(836\) 0.533165 0.0184399
\(837\) 48.2238 + 13.5110i 1.66686 + 0.467008i
\(838\) 4.85171i 0.167600i
\(839\) −1.95661 3.38895i −0.0675497 0.117000i 0.830272 0.557358i \(-0.188185\pi\)
−0.897822 + 0.440358i \(0.854851\pi\)
\(840\) −41.5121 + 9.12783i −1.43230 + 0.314940i
\(841\) 4.00964 6.94489i 0.138263 0.239479i
\(842\) 10.9590 + 6.32718i 0.377672 + 0.218049i
\(843\) 23.5332 16.3455i 0.810526 0.562970i
\(844\) 2.86455 + 4.96155i 0.0986020 + 0.170784i
\(845\) −2.13406 15.9554i −0.0734138 0.548881i
\(846\) 8.82799 23.6943i 0.303512 0.814628i
\(847\) 4.30441i 0.147901i
\(848\) 23.3355 13.4728i 0.801345 0.462657i
\(849\) 10.8228 22.9817i 0.371437 0.788731i
\(850\) −1.89622 + 7.19542i −0.0650399 + 0.246801i
\(851\) −23.6646 + 40.9884i −0.811213 + 1.40506i
\(852\) 2.46708 + 1.16182i 0.0845209 + 0.0398034i
\(853\) 5.35626 3.09244i 0.183395 0.105883i −0.405492 0.914099i \(-0.632900\pi\)
0.588887 + 0.808216i \(0.299566\pi\)
\(854\) −61.9528 −2.11998
\(855\) 10.5823 + 2.40737i 0.361908 + 0.0823302i
\(856\) −30.3680 −1.03796
\(857\) −28.1285 + 16.2400i −0.960850 + 0.554747i −0.896434 0.443176i \(-0.853852\pi\)
−0.0644153 + 0.997923i \(0.520518\pi\)
\(858\) 5.22951 3.63229i 0.178533 0.124004i
\(859\) 23.0399 39.9062i 0.786110 1.36158i −0.142224 0.989835i \(-0.545425\pi\)
0.928334 0.371748i \(-0.121241\pi\)
\(860\) 1.76621 4.28900i 0.0602271 0.146254i
\(861\) 40.3042 3.37230i 1.37356 0.114928i
\(862\) −12.2275 + 7.05952i −0.416469 + 0.240448i
\(863\) 6.33982i 0.215810i 0.994161 + 0.107905i \(0.0344142\pi\)
−0.994161 + 0.107905i \(0.965586\pi\)
\(864\) 2.58812 9.23757i 0.0880495 0.314269i
\(865\) 43.3691 5.80070i 1.47459 0.197230i
\(866\) 13.6639 + 23.6666i 0.464318 + 0.804223i
\(867\) −2.31780 27.7013i −0.0787167 0.940787i
\(868\) −11.8403 6.83601i −0.401887 0.232029i
\(869\) −1.22749 + 2.12608i −0.0416399 + 0.0721224i
\(870\) −19.9945 + 18.2581i −0.677875 + 0.619008i
\(871\) 13.9631 + 24.1849i 0.473123 + 0.819474i
\(872\) 26.8161i 0.908107i
\(873\) 19.1122 15.7917i 0.646850 0.534469i
\(874\) −16.9681 −0.573955
\(875\) 38.3605 + 29.0597i 1.29682 + 0.982396i
\(876\) 0.804327 1.70796i 0.0271757 0.0577065i
\(877\) 9.44831 + 5.45498i 0.319047 + 0.184202i 0.650968 0.759106i \(-0.274363\pi\)
−0.331921 + 0.943307i \(0.607697\pi\)
\(878\) 19.1254 + 11.0420i 0.645449 + 0.372650i
\(879\) 8.65964 18.3884i 0.292083 0.620225i
\(880\) 8.05977 6.21093i 0.271695 0.209371i
\(881\) −8.87958 −0.299161 −0.149580 0.988750i \(-0.547792\pi\)
−0.149580 + 0.988750i \(0.547792\pi\)
\(882\) −8.77173 52.0510i −0.295360 1.75265i
\(883\) 4.32773i 0.145640i 0.997345 + 0.0728198i \(0.0231998\pi\)
−0.997345 + 0.0728198i \(0.976800\pi\)
\(884\) −0.386973 0.670258i −0.0130153 0.0225432i
\(885\) −10.0342 10.9885i −0.337297 0.369374i
\(886\) −3.01720 + 5.22595i −0.101365 + 0.175569i
\(887\) 35.8918 + 20.7222i 1.20513 + 0.695782i 0.961692 0.274134i \(-0.0883912\pi\)
0.243439 + 0.969916i \(0.421724\pi\)
\(888\) 2.53603 + 30.3095i 0.0851035 + 1.01712i
\(889\) 38.9346 + 67.4367i 1.30582 + 2.26175i
\(890\) 24.1415 3.22896i 0.809224 0.108235i
\(891\) −6.80591 5.88893i −0.228007 0.197287i
\(892\) 1.47493i 0.0493844i
\(893\) −7.73704 + 4.46698i −0.258910 + 0.149482i
\(894\) −19.8681 + 1.66239i −0.664490 + 0.0555986i
\(895\) 19.5381 + 8.04578i 0.653088 + 0.268941i
\(896\) 28.5863 49.5129i 0.955001 1.65411i
\(897\) −23.5445 + 16.3534i −0.786129 + 0.546025i
\(898\) −41.1555 + 23.7611i −1.37338 + 0.792920i
\(899\) 44.1468 1.47238
\(900\) −4.48739 + 2.07366i −0.149580 + 0.0691221i
\(901\) −5.77373 −0.192351
\(902\) −7.17065 + 4.13998i −0.238757 + 0.137846i
\(903\) −42.4556 19.9936i −1.41283 0.665345i
\(904\) 14.2057 24.6049i 0.472473 0.818348i
\(905\) −32.2508 13.2808i −1.07205 0.441470i
\(906\) −9.03810 + 19.1920i −0.300271 + 0.637612i
\(907\) 2.58456 1.49220i 0.0858189 0.0495476i −0.456476 0.889736i \(-0.650889\pi\)
0.542295 + 0.840188i \(0.317555\pi\)
\(908\) 1.60311i 0.0532010i
\(909\) −28.8926 34.9678i −0.958308 1.15981i
\(910\) −35.0701 + 4.69069i −1.16256 + 0.155495i
\(911\) −1.59280 2.75881i −0.0527717 0.0914033i 0.838433 0.545005i \(-0.183472\pi\)
−0.891205 + 0.453602i \(0.850139\pi\)
\(912\) −10.4728 + 7.27416i −0.346790 + 0.240871i
\(913\) 11.4287 + 6.59836i 0.378235 + 0.218374i
\(914\) 0.848891 1.47032i 0.0280788 0.0486340i
\(915\) 35.6700 7.84325i 1.17921 0.259290i
\(916\) 2.79904 + 4.84808i 0.0924829 + 0.160185i
\(917\) 1.38897i 0.0458677i
\(918\) −5.52987 + 5.40553i −0.182513 + 0.178409i
\(919\) 21.3228 0.703374 0.351687 0.936118i \(-0.385608\pi\)
0.351687 + 0.936118i \(0.385608\pi\)
\(920\) −31.0311 + 23.9128i −1.02306 + 0.788383i
\(921\) −36.3989 + 3.04553i −1.19938 + 0.100354i
\(922\) −22.0625 12.7378i −0.726590 0.419497i
\(923\) −9.96486 5.75321i −0.327997 0.189369i
\(924\) 1.40164 + 2.01798i 0.0461105 + 0.0663867i
\(925\) 24.2505 24.4514i 0.797351 0.803958i
\(926\) 27.1450 0.892038
\(927\) 31.9380 + 11.8994i 1.04898 + 0.390828i
\(928\) 8.45660i 0.277601i
\(929\) 21.0811 + 36.5136i 0.691649 + 1.19797i 0.971297 + 0.237869i \(0.0764489\pi\)
−0.279648 + 0.960103i \(0.590218\pi\)
\(930\) 54.3067 + 17.2260i 1.78079 + 0.564863i
\(931\) −9.32509 + 16.1515i −0.305618 + 0.529345i
\(932\) 3.06842 + 1.77155i 0.100509 + 0.0580291i
\(933\) 18.4380 + 8.68300i 0.603633 + 0.284269i
\(934\) −22.7391 39.3852i −0.744045 1.28872i
\(935\) −2.16105 + 0.289044i −0.0706738 + 0.00945274i
\(936\) −6.43179 + 17.2629i −0.210230 + 0.564257i
\(937\) 31.4363i 1.02698i 0.858096 + 0.513489i \(0.171647\pi\)
−0.858096 + 0.513489i \(0.828353\pi\)
\(938\) −65.9694 + 38.0875i −2.15398 + 1.24360i
\(939\) 4.93329 + 7.10260i 0.160992 + 0.231785i
\(940\) 1.54952 3.76282i 0.0505399 0.122730i
\(941\) −6.63306 + 11.4888i −0.216232 + 0.374524i −0.953653 0.300909i \(-0.902710\pi\)
0.737421 + 0.675433i \(0.236043\pi\)
\(942\) −3.87927 46.3634i −0.126394 1.51060i
\(943\) 32.2840 18.6392i 1.05131 0.606975i
\(944\) 17.4838 0.569048
\(945\) 18.7082 + 46.3819i 0.608578 + 1.50880i
\(946\) 9.60711 0.312354
\(947\) 7.39605 4.27011i 0.240339 0.138760i −0.374993 0.927027i \(-0.622355\pi\)
0.615333 + 0.788268i \(0.289022\pi\)
\(948\) 0.116842 + 1.39645i 0.00379487 + 0.0453546i
\(949\) −3.98294 + 6.89865i −0.129292 + 0.223940i
\(950\) 11.9387 + 3.14623i 0.387343 + 0.102077i
\(951\) 11.9395 + 17.1896i 0.387165 + 0.557413i
\(952\) −9.26706 + 5.35034i −0.300347 + 0.173406i
\(953\) 5.24954i 0.170049i 0.996379 + 0.0850247i \(0.0270969\pi\)
−0.996379 + 0.0850247i \(0.972903\pi\)
\(954\) −17.2703 20.9016i −0.559146 0.676715i
\(955\) 6.00185 + 44.8730i 0.194215 + 1.45206i
\(956\) 1.98951 + 3.44593i 0.0643454 + 0.111449i
\(957\) −7.17754 3.38011i −0.232017 0.109264i
\(958\) 11.1067 + 6.41243i 0.358840 + 0.207176i
\(959\) 3.69165 6.39412i 0.119210 0.206477i
\(960\) −7.35759 + 23.1955i −0.237465 + 0.748633i
\(961\) −30.9459 53.5999i −0.998256 1.72903i
\(962\) 25.3194i 0.816329i
\(963\) 5.93806 + 35.2361i 0.191351 + 1.13547i
\(964\) 6.69463 0.215620
\(965\) −6.68592 8.67614i −0.215227 0.279295i
\(966\) −44.6075 64.2227i −1.43522 2.06633i
\(967\) −45.3955 26.2091i −1.45982 0.842828i −0.460820 0.887494i \(-0.652445\pi\)
−0.999002 + 0.0446653i \(0.985778\pi\)
\(968\) 2.20800 + 1.27479i 0.0709678 + 0.0409733i
\(969\) 2.72274 0.227815i 0.0874670 0.00731846i
\(970\) 22.3405 17.2158i 0.717312 0.552767i
\(971\) 48.9045 1.56942 0.784711 0.619862i \(-0.212812\pi\)
0.784711 + 0.619862i \(0.212812\pi\)
\(972\) −5.10833 0.544634i −0.163850 0.0174691i
\(973\) 21.8820i 0.701506i
\(974\) 3.35262 + 5.80691i 0.107425 + 0.186065i
\(975\) 19.5981 7.14060i 0.627643 0.228682i
\(976\) −21.4556 + 37.1622i −0.686776 + 1.18953i
\(977\) −19.7507 11.4031i −0.631881 0.364817i 0.149599 0.988747i \(-0.452202\pi\)
−0.781480 + 0.623930i \(0.785535\pi\)
\(978\) −49.2883 + 34.2344i −1.57607 + 1.09470i
\(979\) 3.56831 + 6.18049i 0.114044 + 0.197529i
\(980\) −1.12620 8.42009i −0.0359752 0.268970i
\(981\) 31.1148 5.24353i 0.993419 0.167413i
\(982\) 38.7428i 1.23633i
\(983\) 6.88744 3.97646i 0.219675 0.126829i −0.386125 0.922447i \(-0.626187\pi\)
0.605800 + 0.795617i \(0.292853\pi\)
\(984\) 10.2066 21.6733i 0.325374 0.690919i
\(985\) 15.1428 36.7724i 0.482491 1.17167i
\(986\) −3.40837 + 5.90346i −0.108544 + 0.188005i
\(987\) −37.2470 17.5407i −1.18559 0.558328i
\(988\) −1.11210 + 0.642071i −0.0353806 + 0.0204270i
\(989\) −43.2535 −1.37538
\(990\) −7.51045 6.95867i −0.238698 0.221161i
\(991\) 32.9817 1.04770 0.523850 0.851811i \(-0.324495\pi\)
0.523850 + 0.851811i \(0.324495\pi\)
\(992\) −15.4101 + 8.89701i −0.489270 + 0.282480i
\(993\) 24.2601 16.8504i 0.769869 0.534732i
\(994\) 15.6931 27.1813i 0.497755 0.862137i
\(995\) −10.8933 4.48583i −0.345340 0.142210i
\(996\) 7.50657 0.628083i 0.237855 0.0199016i
\(997\) −17.4914 + 10.0987i −0.553958 + 0.319828i −0.750717 0.660624i \(-0.770292\pi\)
0.196759 + 0.980452i \(0.436958\pi\)
\(998\) 17.2019i 0.544517i
\(999\) 34.6723 8.86918i 1.09698 0.280608i
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 495.2.u.a.364.6 yes 52
5.4 even 2 inner 495.2.u.a.364.21 yes 52
9.7 even 3 inner 495.2.u.a.34.21 yes 52
45.34 even 6 inner 495.2.u.a.34.6 52
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
495.2.u.a.34.6 52 45.34 even 6 inner
495.2.u.a.34.21 yes 52 9.7 even 3 inner
495.2.u.a.364.6 yes 52 1.1 even 1 trivial
495.2.u.a.364.21 yes 52 5.4 even 2 inner