Properties

Label 483.2.i.h.415.2
Level $483$
Weight $2$
Character 483.415
Analytic conductor $3.857$
Analytic rank $0$
Dimension $20$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [483,2,Mod(277,483)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(483, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 4, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("483.277");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 483 = 3 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 483.i (of order \(3\), 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: \(3.85677441763\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(10\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{20} - 3 x^{19} + 22 x^{18} - 43 x^{17} + 245 x^{16} - 416 x^{15} + 1707 x^{14} - 2021 x^{13} + 7135 x^{12} - 6640 x^{11} + 20315 x^{10} - 10565 x^{9} + 29358 x^{8} - 9009 x^{7} + \cdots + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 415.2
Root \(1.25760 + 2.17823i\) of defining polynomial
Character \(\chi\) \(=\) 483.415
Dual form 483.2.i.h.277.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.25760 + 2.17823i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-2.16313 - 3.74664i) q^{4} +(-2.15868 + 3.73894i) q^{5} -2.51520 q^{6} +(1.42694 + 2.22797i) q^{7} +5.85100 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(-1.25760 + 2.17823i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-2.16313 - 3.74664i) q^{4} +(-2.15868 + 3.73894i) q^{5} -2.51520 q^{6} +(1.42694 + 2.22797i) q^{7} +5.85100 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-5.42951 - 9.40419i) q^{10} +(-0.864575 - 1.49749i) q^{11} +(2.16313 - 3.74664i) q^{12} -2.88941 q^{13} +(-6.64755 + 0.306300i) q^{14} -4.31735 q^{15} +(-3.03197 + 5.25153i) q^{16} +(2.46562 + 4.27058i) q^{17} +(-1.25760 - 2.17823i) q^{18} +(-1.22078 + 2.11445i) q^{19} +18.6780 q^{20} +(-1.21601 + 2.34975i) q^{21} +4.34917 q^{22} +(-0.500000 + 0.866025i) q^{23} +(2.92550 + 5.06711i) q^{24} +(-6.81978 - 11.8122i) q^{25} +(3.63373 - 6.29380i) q^{26} -1.00000 q^{27} +(5.26076 - 10.1656i) q^{28} +8.05817 q^{29} +(5.42951 - 9.40419i) q^{30} +(-0.457930 - 0.793157i) q^{31} +(-1.77504 - 3.07445i) q^{32} +(0.864575 - 1.49749i) q^{33} -12.4031 q^{34} +(-11.4105 + 0.525765i) q^{35} +4.32625 q^{36} +(4.57790 - 7.92916i) q^{37} +(-3.07051 - 5.31828i) q^{38} +(-1.44471 - 2.50230i) q^{39} +(-12.6304 + 21.8765i) q^{40} -6.60783 q^{41} +(-3.58904 - 5.60380i) q^{42} +10.7440 q^{43} +(-3.74037 + 6.47851i) q^{44} +(-2.15868 - 3.73894i) q^{45} +(-1.25760 - 2.17823i) q^{46} +(0.199824 - 0.346106i) q^{47} -6.06395 q^{48} +(-2.92770 + 6.35835i) q^{49} +34.3063 q^{50} +(-2.46562 + 4.27058i) q^{51} +(6.25016 + 10.8256i) q^{52} +(-3.27256 - 5.66824i) q^{53} +(1.25760 - 2.17823i) q^{54} +7.46536 q^{55} +(8.34901 + 13.0358i) q^{56} -2.44156 q^{57} +(-10.1340 + 17.5526i) q^{58} +(0.917541 + 1.58923i) q^{59} +(9.33898 + 16.1756i) q^{60} +(0.650629 - 1.12692i) q^{61} +2.30357 q^{62} +(-2.64295 + 0.121779i) q^{63} -3.19874 q^{64} +(6.23731 - 10.8033i) q^{65} +(2.17458 + 3.76649i) q^{66} +(5.10699 + 8.84556i) q^{67} +(10.6669 - 18.4756i) q^{68} -1.00000 q^{69} +(13.2047 - 25.5160i) q^{70} -9.00190 q^{71} +(-2.92550 + 5.06711i) q^{72} +(1.30858 + 2.26652i) q^{73} +(11.5144 + 19.9435i) q^{74} +(6.81978 - 11.8122i) q^{75} +10.5628 q^{76} +(2.10266 - 4.06307i) q^{77} +7.26746 q^{78} +(-5.09351 + 8.82221i) q^{79} +(-13.0901 - 22.6727i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(8.31002 - 14.3934i) q^{82} -10.8838 q^{83} +(11.4341 - 0.526849i) q^{84} -21.2899 q^{85} +(-13.5117 + 23.4029i) q^{86} +(4.02908 + 6.97858i) q^{87} +(-5.05863 - 8.76180i) q^{88} +(-7.49312 + 12.9785i) q^{89} +10.8590 q^{90} +(-4.12301 - 6.43752i) q^{91} +4.32625 q^{92} +(0.457930 - 0.793157i) q^{93} +(0.502599 + 0.870527i) q^{94} +(-5.27054 - 9.12884i) q^{95} +(1.77504 - 3.07445i) q^{96} -3.07116 q^{97} +(-10.1681 - 14.3735i) q^{98} +1.72915 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q - 3 q^{2} + 10 q^{3} - 15 q^{4} + 5 q^{5} - 6 q^{6} + 18 q^{8} - 10 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 20 q - 3 q^{2} + 10 q^{3} - 15 q^{4} + 5 q^{5} - 6 q^{6} + 18 q^{8} - 10 q^{9} - 11 q^{10} - 8 q^{11} + 15 q^{12} + 11 q^{14} + 10 q^{15} - 37 q^{16} + 11 q^{17} - 3 q^{18} - q^{19} - 30 q^{20} + 12 q^{22} - 10 q^{23} + 9 q^{24} - 21 q^{25} - q^{26} - 20 q^{27} + 44 q^{28} + 44 q^{29} + 11 q^{30} + 3 q^{31} - 11 q^{32} + 8 q^{33} - 6 q^{34} - 9 q^{35} + 30 q^{36} + 3 q^{37} - 16 q^{38} - 39 q^{40} - 52 q^{41} + 7 q^{42} + 54 q^{43} - 16 q^{44} + 5 q^{45} - 3 q^{46} - 11 q^{47} - 74 q^{48} + 22 q^{49} + 4 q^{50} - 11 q^{51} - 29 q^{52} - 5 q^{53} + 3 q^{54} - 36 q^{55} + 43 q^{56} - 2 q^{57} - 16 q^{58} + 10 q^{59} - 15 q^{60} - 22 q^{61} - 64 q^{62} + 138 q^{64} + 11 q^{65} + 6 q^{66} + 2 q^{67} + 21 q^{68} - 20 q^{69} + 84 q^{70} + 54 q^{71} - 9 q^{72} + 8 q^{73} - 14 q^{74} + 21 q^{75} - 44 q^{76} + 8 q^{77} - 2 q^{78} - 21 q^{79} + 53 q^{80} - 10 q^{81} - 36 q^{82} - 24 q^{83} + 25 q^{84} + 46 q^{85} - 18 q^{86} + 22 q^{87} + 10 q^{88} - 6 q^{89} + 22 q^{90} - 62 q^{91} + 30 q^{92} - 3 q^{93} - 35 q^{94} - 44 q^{95} + 11 q^{96} + 12 q^{97} + 2 q^{98} + 16 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/483\mathbb{Z}\right)^\times\).

\(n\) \(323\) \(346\) \(442\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.25760 + 2.17823i −0.889259 + 1.54024i −0.0485058 + 0.998823i \(0.515446\pi\)
−0.840753 + 0.541419i \(0.817887\pi\)
\(3\) 0.500000 + 0.866025i 0.288675 + 0.500000i
\(4\) −2.16313 3.74664i −1.08156 1.87332i
\(5\) −2.15868 + 3.73894i −0.965390 + 1.67210i −0.256826 + 0.966458i \(0.582677\pi\)
−0.708564 + 0.705647i \(0.750657\pi\)
\(6\) −2.51520 −1.02683
\(7\) 1.42694 + 2.22797i 0.539332 + 0.842093i
\(8\) 5.85100 2.06864
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) −5.42951 9.40419i −1.71696 2.97387i
\(11\) −0.864575 1.49749i −0.260679 0.451510i 0.705743 0.708468i \(-0.250613\pi\)
−0.966423 + 0.256958i \(0.917280\pi\)
\(12\) 2.16313 3.74664i 0.624441 1.08156i
\(13\) −2.88941 −0.801378 −0.400689 0.916214i \(-0.631229\pi\)
−0.400689 + 0.916214i \(0.631229\pi\)
\(14\) −6.64755 + 0.306300i −1.77663 + 0.0818622i
\(15\) −4.31735 −1.11474
\(16\) −3.03197 + 5.25153i −0.757993 + 1.31288i
\(17\) 2.46562 + 4.27058i 0.598001 + 1.03577i 0.993116 + 0.117136i \(0.0373715\pi\)
−0.395115 + 0.918632i \(0.629295\pi\)
\(18\) −1.25760 2.17823i −0.296420 0.513414i
\(19\) −1.22078 + 2.11445i −0.280066 + 0.485089i −0.971401 0.237446i \(-0.923690\pi\)
0.691335 + 0.722535i \(0.257023\pi\)
\(20\) 18.6780 4.17652
\(21\) −1.21601 + 2.34975i −0.265355 + 0.512757i
\(22\) 4.34917 0.927245
\(23\) −0.500000 + 0.866025i −0.104257 + 0.180579i
\(24\) 2.92550 + 5.06711i 0.597165 + 1.03432i
\(25\) −6.81978 11.8122i −1.36396 2.36244i
\(26\) 3.63373 6.29380i 0.712633 1.23432i
\(27\) −1.00000 −0.192450
\(28\) 5.26076 10.1656i 0.994191 1.92112i
\(29\) 8.05817 1.49636 0.748182 0.663493i \(-0.230927\pi\)
0.748182 + 0.663493i \(0.230927\pi\)
\(30\) 5.42951 9.40419i 0.991289 1.71696i
\(31\) −0.457930 0.793157i −0.0822466 0.142455i 0.821968 0.569534i \(-0.192876\pi\)
−0.904215 + 0.427078i \(0.859543\pi\)
\(32\) −1.77504 3.07445i −0.313785 0.543491i
\(33\) 0.864575 1.49749i 0.150503 0.260679i
\(34\) −12.4031 −2.12711
\(35\) −11.4105 + 0.525765i −1.92873 + 0.0888705i
\(36\) 4.32625 0.721042
\(37\) 4.57790 7.92916i 0.752603 1.30355i −0.193955 0.981011i \(-0.562131\pi\)
0.946557 0.322536i \(-0.104535\pi\)
\(38\) −3.07051 5.31828i −0.498103 0.862739i
\(39\) −1.44471 2.50230i −0.231338 0.400689i
\(40\) −12.6304 + 21.8765i −1.99704 + 3.45898i
\(41\) −6.60783 −1.03197 −0.515985 0.856598i \(-0.672574\pi\)
−0.515985 + 0.856598i \(0.672574\pi\)
\(42\) −3.58904 5.60380i −0.553801 0.864685i
\(43\) 10.7440 1.63845 0.819223 0.573475i \(-0.194405\pi\)
0.819223 + 0.573475i \(0.194405\pi\)
\(44\) −3.74037 + 6.47851i −0.563882 + 0.976672i
\(45\) −2.15868 3.73894i −0.321797 0.557368i
\(46\) −1.25760 2.17823i −0.185423 0.321163i
\(47\) 0.199824 0.346106i 0.0291474 0.0504847i −0.851084 0.525030i \(-0.824054\pi\)
0.880231 + 0.474545i \(0.157387\pi\)
\(48\) −6.06395 −0.875255
\(49\) −2.92770 + 6.35835i −0.418243 + 0.908335i
\(50\) 34.3063 4.85164
\(51\) −2.46562 + 4.27058i −0.345256 + 0.598001i
\(52\) 6.25016 + 10.8256i 0.866741 + 1.50124i
\(53\) −3.27256 5.66824i −0.449521 0.778593i 0.548834 0.835931i \(-0.315072\pi\)
−0.998355 + 0.0573383i \(0.981739\pi\)
\(54\) 1.25760 2.17823i 0.171138 0.296420i
\(55\) 7.46536 1.00663
\(56\) 8.34901 + 13.0358i 1.11568 + 1.74199i
\(57\) −2.44156 −0.323393
\(58\) −10.1340 + 17.5526i −1.33066 + 2.30476i
\(59\) 0.917541 + 1.58923i 0.119454 + 0.206900i 0.919551 0.392970i \(-0.128552\pi\)
−0.800098 + 0.599870i \(0.795219\pi\)
\(60\) 9.33898 + 16.1756i 1.20566 + 2.08826i
\(61\) 0.650629 1.12692i 0.0833045 0.144288i −0.821363 0.570406i \(-0.806786\pi\)
0.904667 + 0.426118i \(0.140119\pi\)
\(62\) 2.30357 0.292554
\(63\) −2.64295 + 0.121779i −0.332980 + 0.0153428i
\(64\) −3.19874 −0.399843
\(65\) 6.23731 10.8033i 0.773642 1.33999i
\(66\) 2.17458 + 3.76649i 0.267673 + 0.463623i
\(67\) 5.10699 + 8.84556i 0.623918 + 1.08066i 0.988749 + 0.149583i \(0.0477933\pi\)
−0.364831 + 0.931074i \(0.618873\pi\)
\(68\) 10.6669 18.4756i 1.29355 2.24050i
\(69\) −1.00000 −0.120386
\(70\) 13.2047 25.5160i 1.57826 3.04974i
\(71\) −9.00190 −1.06833 −0.534164 0.845381i \(-0.679374\pi\)
−0.534164 + 0.845381i \(0.679374\pi\)
\(72\) −2.92550 + 5.06711i −0.344773 + 0.597165i
\(73\) 1.30858 + 2.26652i 0.153158 + 0.265277i 0.932387 0.361463i \(-0.117722\pi\)
−0.779229 + 0.626739i \(0.784389\pi\)
\(74\) 11.5144 + 19.9435i 1.33852 + 2.31838i
\(75\) 6.81978 11.8122i 0.787480 1.36396i
\(76\) 10.5628 1.21164
\(77\) 2.10266 4.06307i 0.239621 0.463030i
\(78\) 7.26746 0.822877
\(79\) −5.09351 + 8.82221i −0.573064 + 0.992577i 0.423185 + 0.906043i \(0.360912\pi\)
−0.996249 + 0.0865331i \(0.972421\pi\)
\(80\) −13.0901 22.6727i −1.46352 2.53489i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 8.31002 14.3934i 0.917688 1.58948i
\(83\) −10.8838 −1.19465 −0.597327 0.801998i \(-0.703771\pi\)
−0.597327 + 0.801998i \(0.703771\pi\)
\(84\) 11.4341 0.526849i 1.24756 0.0574839i
\(85\) −21.2899 −2.30922
\(86\) −13.5117 + 23.4029i −1.45700 + 2.52360i
\(87\) 4.02908 + 6.97858i 0.431963 + 0.748182i
\(88\) −5.05863 8.76180i −0.539251 0.934011i
\(89\) −7.49312 + 12.9785i −0.794269 + 1.37571i 0.129033 + 0.991640i \(0.458813\pi\)
−0.923302 + 0.384074i \(0.874521\pi\)
\(90\) 10.8590 1.14464
\(91\) −4.12301 6.43752i −0.432209 0.674835i
\(92\) 4.32625 0.451043
\(93\) 0.457930 0.793157i 0.0474851 0.0822466i
\(94\) 0.502599 + 0.870527i 0.0518391 + 0.0897880i
\(95\) −5.27054 9.12884i −0.540746 0.936600i
\(96\) 1.77504 3.07445i 0.181164 0.313785i
\(97\) −3.07116 −0.311829 −0.155914 0.987771i \(-0.549832\pi\)
−0.155914 + 0.987771i \(0.549832\pi\)
\(98\) −10.1681 14.3735i −1.02713 1.45194i
\(99\) 1.72915 0.173786
\(100\) −29.5041 + 51.1025i −2.95041 + 5.11025i
\(101\) −0.544049 0.942320i −0.0541349 0.0937644i 0.837688 0.546149i \(-0.183907\pi\)
−0.891823 + 0.452385i \(0.850573\pi\)
\(102\) −6.20154 10.7414i −0.614044 1.06356i
\(103\) 1.61555 2.79821i 0.159185 0.275716i −0.775390 0.631482i \(-0.782447\pi\)
0.934575 + 0.355766i \(0.115780\pi\)
\(104\) −16.9059 −1.65776
\(105\) −6.16060 9.61894i −0.601213 0.938712i
\(106\) 16.4623 1.59896
\(107\) 0.468449 0.811378i 0.0452867 0.0784389i −0.842494 0.538706i \(-0.818913\pi\)
0.887780 + 0.460268i \(0.152247\pi\)
\(108\) 2.16313 + 3.74664i 0.208147 + 0.360521i
\(109\) 7.48909 + 12.9715i 0.717324 + 1.24244i 0.962056 + 0.272852i \(0.0879668\pi\)
−0.244732 + 0.969591i \(0.578700\pi\)
\(110\) −9.38845 + 16.2613i −0.895153 + 1.55045i
\(111\) 9.15581 0.869031
\(112\) −16.0267 + 0.738464i −1.51438 + 0.0697783i
\(113\) −14.1424 −1.33040 −0.665201 0.746665i \(-0.731654\pi\)
−0.665201 + 0.746665i \(0.731654\pi\)
\(114\) 3.07051 5.31828i 0.287580 0.498103i
\(115\) −2.15868 3.73894i −0.201298 0.348658i
\(116\) −17.4308 30.1911i −1.61841 2.80317i
\(117\) 1.44471 2.50230i 0.133563 0.231338i
\(118\) −4.61560 −0.424901
\(119\) −5.99644 + 11.5872i −0.549693 + 1.06220i
\(120\) −25.2608 −2.30599
\(121\) 4.00502 6.93690i 0.364093 0.630627i
\(122\) 1.63646 + 2.83444i 0.148158 + 0.256618i
\(123\) −3.30392 5.72255i −0.297904 0.515985i
\(124\) −1.98112 + 3.43140i −0.177910 + 0.308149i
\(125\) 37.3000 3.33621
\(126\) 3.05851 5.91010i 0.272474 0.526513i
\(127\) −1.77968 −0.157921 −0.0789604 0.996878i \(-0.525160\pi\)
−0.0789604 + 0.996878i \(0.525160\pi\)
\(128\) 7.57281 13.1165i 0.669349 1.15935i
\(129\) 5.37200 + 9.30458i 0.472979 + 0.819223i
\(130\) 15.6881 + 27.1726i 1.37594 + 2.38319i
\(131\) −4.44632 + 7.70125i −0.388477 + 0.672862i −0.992245 0.124298i \(-0.960332\pi\)
0.603768 + 0.797160i \(0.293665\pi\)
\(132\) −7.48074 −0.651115
\(133\) −6.45291 + 0.297332i −0.559539 + 0.0257819i
\(134\) −25.6902 −2.21930
\(135\) 2.15868 3.73894i 0.185789 0.321797i
\(136\) 14.4263 + 24.9872i 1.23705 + 2.14263i
\(137\) −0.123702 0.214258i −0.0105686 0.0183053i 0.860693 0.509125i \(-0.170031\pi\)
−0.871261 + 0.490819i \(0.836697\pi\)
\(138\) 1.25760 2.17823i 0.107054 0.185423i
\(139\) −8.59949 −0.729399 −0.364699 0.931125i \(-0.618828\pi\)
−0.364699 + 0.931125i \(0.618828\pi\)
\(140\) 26.6523 + 41.6139i 2.25253 + 3.51702i
\(141\) 0.399649 0.0336565
\(142\) 11.3208 19.6082i 0.950021 1.64548i
\(143\) 2.49811 + 4.32686i 0.208903 + 0.361830i
\(144\) −3.03197 5.25153i −0.252664 0.437628i
\(145\) −17.3950 + 30.1290i −1.44458 + 2.50208i
\(146\) −6.58268 −0.544787
\(147\) −6.97034 + 0.643713i −0.574904 + 0.0530926i
\(148\) −39.6103 −3.25595
\(149\) −2.25334 + 3.90291i −0.184601 + 0.319739i −0.943442 0.331537i \(-0.892433\pi\)
0.758841 + 0.651276i \(0.225766\pi\)
\(150\) 17.1531 + 29.7101i 1.40055 + 2.42582i
\(151\) 2.26383 + 3.92107i 0.184228 + 0.319092i 0.943316 0.331896i \(-0.107688\pi\)
−0.759088 + 0.650988i \(0.774355\pi\)
\(152\) −7.14278 + 12.3717i −0.579356 + 1.00347i
\(153\) −4.93124 −0.398667
\(154\) 6.20599 + 9.68981i 0.500093 + 0.780827i
\(155\) 3.95409 0.317600
\(156\) −6.25016 + 10.8256i −0.500413 + 0.866741i
\(157\) 1.63364 + 2.82954i 0.130378 + 0.225822i 0.923822 0.382821i \(-0.125047\pi\)
−0.793444 + 0.608643i \(0.791714\pi\)
\(158\) −12.8112 22.1897i −1.01921 1.76532i
\(159\) 3.27256 5.66824i 0.259531 0.449521i
\(160\) 15.3269 1.21170
\(161\) −2.64295 + 0.121779i −0.208293 + 0.00959757i
\(162\) 2.51520 0.197613
\(163\) −5.32102 + 9.21628i −0.416774 + 0.721875i −0.995613 0.0935677i \(-0.970173\pi\)
0.578838 + 0.815442i \(0.303506\pi\)
\(164\) 14.2936 + 24.7572i 1.11614 + 1.93321i
\(165\) 3.73268 + 6.46519i 0.290589 + 0.503314i
\(166\) 13.6875 23.7075i 1.06236 1.84006i
\(167\) 2.99812 0.232001 0.116001 0.993249i \(-0.462993\pi\)
0.116001 + 0.993249i \(0.462993\pi\)
\(168\) −7.11487 + 13.7484i −0.548924 + 1.06071i
\(169\) −4.65131 −0.357793
\(170\) 26.7742 46.3744i 2.05349 3.55675i
\(171\) −1.22078 2.11445i −0.0933554 0.161696i
\(172\) −23.2406 40.2540i −1.77208 3.06934i
\(173\) 6.64982 11.5178i 0.505576 0.875684i −0.494403 0.869233i \(-0.664613\pi\)
0.999979 0.00645084i \(-0.00205338\pi\)
\(174\) −20.2679 −1.53651
\(175\) 16.5858 32.0495i 1.25377 2.42272i
\(176\) 10.4855 0.790373
\(177\) −0.917541 + 1.58923i −0.0689666 + 0.119454i
\(178\) −18.8467 32.6435i −1.41262 2.44673i
\(179\) −9.81485 16.9998i −0.733596 1.27063i −0.955336 0.295520i \(-0.904507\pi\)
0.221740 0.975106i \(-0.428826\pi\)
\(180\) −9.33898 + 16.1756i −0.696086 + 1.20566i
\(181\) 19.2095 1.42783 0.713915 0.700232i \(-0.246920\pi\)
0.713915 + 0.700232i \(0.246920\pi\)
\(182\) 19.2075 0.885027i 1.42375 0.0656026i
\(183\) 1.30126 0.0961917
\(184\) −2.92550 + 5.06711i −0.215671 + 0.373552i
\(185\) 19.7644 + 34.2330i 1.45311 + 2.51686i
\(186\) 1.15179 + 1.99495i 0.0844531 + 0.146277i
\(187\) 4.26343 7.38448i 0.311773 0.540007i
\(188\) −1.72898 −0.126099
\(189\) −1.42694 2.22797i −0.103794 0.162061i
\(190\) 26.5130 1.92345
\(191\) 3.57687 6.19533i 0.258814 0.448278i −0.707111 0.707103i \(-0.750002\pi\)
0.965924 + 0.258825i \(0.0833351\pi\)
\(192\) −1.59937 2.77019i −0.115425 0.199921i
\(193\) 10.9786 + 19.0156i 0.790259 + 1.36877i 0.925806 + 0.377999i \(0.123388\pi\)
−0.135547 + 0.990771i \(0.543279\pi\)
\(194\) 3.86229 6.68969i 0.277296 0.480291i
\(195\) 12.4746 0.893325
\(196\) 30.1554 2.78487i 2.15396 0.198919i
\(197\) 3.21028 0.228723 0.114361 0.993439i \(-0.463518\pi\)
0.114361 + 0.993439i \(0.463518\pi\)
\(198\) −2.17458 + 3.76649i −0.154541 + 0.267673i
\(199\) −6.35849 11.0132i −0.450741 0.780707i 0.547691 0.836681i \(-0.315507\pi\)
−0.998432 + 0.0559738i \(0.982174\pi\)
\(200\) −39.9025 69.1131i −2.82153 4.88704i
\(201\) −5.10699 + 8.84556i −0.360219 + 0.623918i
\(202\) 2.73679 0.192560
\(203\) 11.4985 + 17.9534i 0.807037 + 1.26008i
\(204\) 21.3338 1.49366
\(205\) 14.2642 24.7063i 0.996253 1.72556i
\(206\) 4.06343 + 7.03807i 0.283113 + 0.490366i
\(207\) −0.500000 0.866025i −0.0347524 0.0601929i
\(208\) 8.76062 15.1738i 0.607439 1.05212i
\(209\) 4.22183 0.292030
\(210\) 28.6998 1.32241i 1.98048 0.0912547i
\(211\) −17.0500 −1.17377 −0.586884 0.809671i \(-0.699646\pi\)
−0.586884 + 0.809671i \(0.699646\pi\)
\(212\) −14.1579 + 24.5222i −0.972370 + 1.68419i
\(213\) −4.50095 7.79587i −0.308400 0.534164i
\(214\) 1.17825 + 2.04078i 0.0805432 + 0.139505i
\(215\) −23.1928 + 40.1712i −1.58174 + 2.73965i
\(216\) −5.85100 −0.398110
\(217\) 1.11369 2.15204i 0.0756024 0.146090i
\(218\) −37.6732 −2.55155
\(219\) −1.30858 + 2.26652i −0.0884255 + 0.153158i
\(220\) −16.1485 27.9700i −1.08873 1.88574i
\(221\) −7.12419 12.3395i −0.479225 0.830042i
\(222\) −11.5144 + 19.9435i −0.772793 + 1.33852i
\(223\) 23.3278 1.56215 0.781073 0.624440i \(-0.214673\pi\)
0.781073 + 0.624440i \(0.214673\pi\)
\(224\) 4.31692 8.34177i 0.288436 0.557358i
\(225\) 13.6396 0.909303
\(226\) 17.7855 30.8053i 1.18307 2.04914i
\(227\) 3.83797 + 6.64756i 0.254735 + 0.441214i 0.964824 0.262898i \(-0.0846784\pi\)
−0.710088 + 0.704113i \(0.751345\pi\)
\(228\) 5.28140 + 9.14765i 0.349769 + 0.605818i
\(229\) 11.4368 19.8091i 0.755766 1.30903i −0.189227 0.981933i \(-0.560598\pi\)
0.944993 0.327092i \(-0.106069\pi\)
\(230\) 10.8590 0.716023
\(231\) 4.57005 0.210575i 0.300687 0.0138548i
\(232\) 47.1483 3.09544
\(233\) −11.7779 + 20.4000i −0.771599 + 1.33645i 0.165088 + 0.986279i \(0.447209\pi\)
−0.936686 + 0.350169i \(0.886124\pi\)
\(234\) 3.63373 + 6.29380i 0.237544 + 0.411439i
\(235\) 0.862713 + 1.49426i 0.0562772 + 0.0974749i
\(236\) 3.96951 6.87540i 0.258393 0.447550i
\(237\) −10.1870 −0.661718
\(238\) −17.6984 27.6337i −1.14722 1.79123i
\(239\) 13.1829 0.852732 0.426366 0.904551i \(-0.359794\pi\)
0.426366 + 0.904551i \(0.359794\pi\)
\(240\) 13.0901 22.6727i 0.844963 1.46352i
\(241\) 8.63351 + 14.9537i 0.556134 + 0.963252i 0.997814 + 0.0660793i \(0.0210490\pi\)
−0.441681 + 0.897172i \(0.645618\pi\)
\(242\) 10.0734 + 17.4477i 0.647545 + 1.12158i
\(243\) 0.500000 0.866025i 0.0320750 0.0555556i
\(244\) −5.62957 −0.360396
\(245\) −17.4535 24.6721i −1.11506 1.57624i
\(246\) 16.6200 1.05966
\(247\) 3.52733 6.10952i 0.224439 0.388740i
\(248\) −2.67934 4.64076i −0.170139 0.294689i
\(249\) −5.44191 9.42566i −0.344867 0.597327i
\(250\) −46.9086 + 81.2480i −2.96676 + 5.13858i
\(251\) 4.74956 0.299790 0.149895 0.988702i \(-0.452106\pi\)
0.149895 + 0.988702i \(0.452106\pi\)
\(252\) 6.17329 + 9.63876i 0.388881 + 0.607185i
\(253\) 1.72915 0.108711
\(254\) 2.23812 3.87655i 0.140432 0.243236i
\(255\) −10.6450 18.4376i −0.666613 1.15461i
\(256\) 15.8484 + 27.4503i 0.990527 + 1.71564i
\(257\) −0.714418 + 1.23741i −0.0445641 + 0.0771874i −0.887447 0.460910i \(-0.847523\pi\)
0.842883 + 0.538097i \(0.180857\pi\)
\(258\) −27.0234 −1.68240
\(259\) 24.1983 1.11499i 1.50361 0.0692821i
\(260\) −53.9683 −3.34697
\(261\) −4.02908 + 6.97858i −0.249394 + 0.431963i
\(262\) −11.1834 19.3702i −0.690913 1.19670i
\(263\) −4.40873 7.63614i −0.271854 0.470865i 0.697483 0.716602i \(-0.254303\pi\)
−0.969337 + 0.245737i \(0.920970\pi\)
\(264\) 5.05863 8.76180i 0.311337 0.539251i
\(265\) 28.2576 1.73585
\(266\) 7.46754 14.4299i 0.457864 0.884751i
\(267\) −14.9862 −0.917143
\(268\) 22.0941 38.2681i 1.34961 2.33760i
\(269\) 6.45927 + 11.1878i 0.393829 + 0.682132i 0.992951 0.118526i \(-0.0378169\pi\)
−0.599122 + 0.800658i \(0.704484\pi\)
\(270\) 5.42951 + 9.40419i 0.330430 + 0.572321i
\(271\) −6.67426 + 11.5602i −0.405433 + 0.702230i −0.994372 0.105947i \(-0.966212\pi\)
0.588939 + 0.808177i \(0.299546\pi\)
\(272\) −29.9028 −1.81312
\(273\) 3.51355 6.78939i 0.212650 0.410913i
\(274\) 0.622271 0.0375927
\(275\) −11.7924 + 20.4251i −0.711110 + 1.23168i
\(276\) 2.16313 + 3.74664i 0.130205 + 0.225521i
\(277\) 7.74930 + 13.4222i 0.465610 + 0.806461i 0.999229 0.0392646i \(-0.0125015\pi\)
−0.533619 + 0.845725i \(0.679168\pi\)
\(278\) 10.8147 18.7317i 0.648624 1.12345i
\(279\) 0.915859 0.0548311
\(280\) −66.7630 + 3.07625i −3.98985 + 0.183841i
\(281\) 23.6088 1.40838 0.704192 0.710009i \(-0.251309\pi\)
0.704192 + 0.710009i \(0.251309\pi\)
\(282\) −0.502599 + 0.870527i −0.0299293 + 0.0518391i
\(283\) −11.8407 20.5087i −0.703858 1.21912i −0.967102 0.254388i \(-0.918126\pi\)
0.263244 0.964729i \(-0.415207\pi\)
\(284\) 19.4722 + 33.7269i 1.15546 + 2.00132i
\(285\) 5.27054 9.12884i 0.312200 0.540746i
\(286\) −12.5665 −0.743074
\(287\) −9.42896 14.7220i −0.556574 0.869015i
\(288\) 3.55007 0.209190
\(289\) −3.65858 + 6.33684i −0.215210 + 0.372755i
\(290\) −43.7519 75.7806i −2.56920 4.44999i
\(291\) −1.53558 2.65970i −0.0900172 0.155914i
\(292\) 5.66124 9.80555i 0.331299 0.573827i
\(293\) 21.1268 1.23424 0.617121 0.786868i \(-0.288299\pi\)
0.617121 + 0.786868i \(0.288299\pi\)
\(294\) 7.36376 15.9925i 0.429463 0.932704i
\(295\) −7.92270 −0.461277
\(296\) 26.7853 46.3935i 1.55686 2.69657i
\(297\) 0.864575 + 1.49749i 0.0501678 + 0.0868931i
\(298\) −5.66762 9.81661i −0.328316 0.568661i
\(299\) 1.44471 2.50230i 0.0835495 0.144712i
\(300\) −59.0081 −3.40684
\(301\) 15.3310 + 23.9373i 0.883666 + 1.37972i
\(302\) −11.3880 −0.655305
\(303\) 0.544049 0.942320i 0.0312548 0.0541349i
\(304\) −7.40274 12.8219i −0.424577 0.735388i
\(305\) 2.80899 + 4.86532i 0.160843 + 0.278587i
\(306\) 6.20154 10.7414i 0.354518 0.614044i
\(307\) −1.97923 −0.112961 −0.0564804 0.998404i \(-0.517988\pi\)
−0.0564804 + 0.998404i \(0.517988\pi\)
\(308\) −19.7712 + 0.911001i −1.12657 + 0.0519091i
\(309\) 3.23110 0.183811
\(310\) −4.97267 + 8.61292i −0.282429 + 0.489181i
\(311\) 1.94840 + 3.37472i 0.110483 + 0.191363i 0.915965 0.401258i \(-0.131427\pi\)
−0.805482 + 0.592620i \(0.798093\pi\)
\(312\) −8.45296 14.6410i −0.478555 0.828881i
\(313\) −8.82919 + 15.2926i −0.499056 + 0.864390i −0.999999 0.00109025i \(-0.999653\pi\)
0.500944 + 0.865480i \(0.332986\pi\)
\(314\) −8.21786 −0.463761
\(315\) 5.24994 10.1447i 0.295801 0.571589i
\(316\) 44.0716 2.47922
\(317\) 6.16616 10.6801i 0.346326 0.599855i −0.639268 0.768984i \(-0.720762\pi\)
0.985594 + 0.169130i \(0.0540957\pi\)
\(318\) 8.23116 + 14.2568i 0.461581 + 0.799481i
\(319\) −6.96689 12.0670i −0.390071 0.675623i
\(320\) 6.90505 11.9599i 0.386004 0.668579i
\(321\) 0.936899 0.0522926
\(322\) 3.05851 5.91010i 0.170444 0.329357i
\(323\) −12.0399 −0.669919
\(324\) −2.16313 + 3.74664i −0.120174 + 0.208147i
\(325\) 19.7051 + 34.1303i 1.09304 + 1.89321i
\(326\) −13.3835 23.1808i −0.741241 1.28387i
\(327\) −7.48909 + 12.9715i −0.414147 + 0.717324i
\(328\) −38.6624 −2.13477
\(329\) 1.05625 0.0486690i 0.0582330 0.00268321i
\(330\) −18.7769 −1.03363
\(331\) −2.90282 + 5.02784i −0.159554 + 0.276355i −0.934708 0.355417i \(-0.884339\pi\)
0.775154 + 0.631772i \(0.217672\pi\)
\(332\) 23.5431 + 40.7778i 1.29209 + 2.23797i
\(333\) 4.57790 + 7.92916i 0.250868 + 0.434515i
\(334\) −3.77044 + 6.53059i −0.206309 + 0.357338i
\(335\) −44.0973 −2.40930
\(336\) −8.65287 13.5103i −0.472053 0.737047i
\(337\) −22.5441 −1.22805 −0.614027 0.789285i \(-0.710452\pi\)
−0.614027 + 0.789285i \(0.710452\pi\)
\(338\) 5.84949 10.1316i 0.318170 0.551087i
\(339\) −7.07118 12.2476i −0.384054 0.665201i
\(340\) 46.0528 + 79.7657i 2.49756 + 4.32591i
\(341\) −0.791829 + 1.37149i −0.0428800 + 0.0742703i
\(342\) 6.14102 0.332068
\(343\) −18.3438 + 2.55014i −0.990475 + 0.137695i
\(344\) 62.8631 3.38935
\(345\) 2.15868 3.73894i 0.116219 0.201298i
\(346\) 16.7256 + 28.9697i 0.899176 + 1.55742i
\(347\) 3.74865 + 6.49285i 0.201238 + 0.348555i 0.948928 0.315494i \(-0.102170\pi\)
−0.747690 + 0.664048i \(0.768837\pi\)
\(348\) 17.4308 30.1911i 0.934391 1.61841i
\(349\) −7.97347 −0.426810 −0.213405 0.976964i \(-0.568455\pi\)
−0.213405 + 0.976964i \(0.568455\pi\)
\(350\) 48.9529 + 76.4333i 2.61664 + 4.08553i
\(351\) 2.88941 0.154225
\(352\) −3.06930 + 5.31619i −0.163594 + 0.283354i
\(353\) 14.7645 + 25.5728i 0.785833 + 1.36110i 0.928500 + 0.371331i \(0.121099\pi\)
−0.142668 + 0.989771i \(0.545568\pi\)
\(354\) −2.30780 3.99723i −0.122658 0.212450i
\(355\) 19.4322 33.6575i 1.03135 1.78636i
\(356\) 64.8342 3.43621
\(357\) −13.0330 + 0.600524i −0.689780 + 0.0317831i
\(358\) 49.3727 2.60943
\(359\) 6.56032 11.3628i 0.346241 0.599706i −0.639338 0.768926i \(-0.720791\pi\)
0.985578 + 0.169220i \(0.0541247\pi\)
\(360\) −12.6304 21.8765i −0.665681 1.15299i
\(361\) 6.51939 + 11.2919i 0.343126 + 0.594312i
\(362\) −24.1579 + 41.8427i −1.26971 + 2.19920i
\(363\) 8.01004 0.420418
\(364\) −15.2005 + 29.3726i −0.796723 + 1.53954i
\(365\) −11.2992 −0.591427
\(366\) −1.63646 + 2.83444i −0.0855393 + 0.148158i
\(367\) −2.63184 4.55848i −0.137381 0.237951i 0.789124 0.614234i \(-0.210535\pi\)
−0.926504 + 0.376284i \(0.877202\pi\)
\(368\) −3.03197 5.25153i −0.158053 0.273755i
\(369\) 3.30392 5.72255i 0.171995 0.297904i
\(370\) −99.4232 −5.16876
\(371\) 7.95893 15.3794i 0.413207 0.798459i
\(372\) −3.96224 −0.205432
\(373\) 6.32477 10.9548i 0.327484 0.567219i −0.654528 0.756038i \(-0.727133\pi\)
0.982012 + 0.188819i \(0.0604659\pi\)
\(374\) 10.7234 + 18.5735i 0.554494 + 0.960411i
\(375\) 18.6500 + 32.3028i 0.963082 + 1.66811i
\(376\) 1.16917 2.02506i 0.0602954 0.104435i
\(377\) −23.2834 −1.19915
\(378\) 6.64755 0.306300i 0.341913 0.0157544i
\(379\) 12.7987 0.657426 0.328713 0.944430i \(-0.393385\pi\)
0.328713 + 0.944430i \(0.393385\pi\)
\(380\) −22.8017 + 39.4937i −1.16970 + 2.02598i
\(381\) −0.889838 1.54125i −0.0455878 0.0789604i
\(382\) 8.99657 + 15.5825i 0.460305 + 0.797271i
\(383\) 8.31345 14.3993i 0.424797 0.735771i −0.571604 0.820530i \(-0.693679\pi\)
0.996401 + 0.0847589i \(0.0270120\pi\)
\(384\) 15.1456 0.772897
\(385\) 10.6526 + 16.6326i 0.542907 + 0.847675i
\(386\) −55.2270 −2.81098
\(387\) −5.37200 + 9.30458i −0.273074 + 0.472979i
\(388\) 6.64330 + 11.5065i 0.337262 + 0.584155i
\(389\) 14.9352 + 25.8684i 0.757242 + 1.31158i 0.944252 + 0.329224i \(0.106787\pi\)
−0.187010 + 0.982358i \(0.559880\pi\)
\(390\) −15.6881 + 27.1726i −0.794398 + 1.37594i
\(391\) −4.93124 −0.249384
\(392\) −17.1299 + 37.2027i −0.865193 + 1.87902i
\(393\) −8.89264 −0.448574
\(394\) −4.03725 + 6.99272i −0.203394 + 0.352288i
\(395\) −21.9905 38.0886i −1.10646 1.91645i
\(396\) −3.74037 6.47851i −0.187961 0.325557i
\(397\) 2.99218 5.18262i 0.150173 0.260108i −0.781118 0.624384i \(-0.785350\pi\)
0.931291 + 0.364276i \(0.118683\pi\)
\(398\) 31.9858 1.60330
\(399\) −3.48395 5.43972i −0.174416 0.272327i
\(400\) 82.7095 4.13548
\(401\) 7.93175 13.7382i 0.396092 0.686052i −0.597147 0.802131i \(-0.703699\pi\)
0.993240 + 0.116079i \(0.0370326\pi\)
\(402\) −12.8451 22.2484i −0.640656 1.10965i
\(403\) 1.32315 + 2.29176i 0.0659106 + 0.114161i
\(404\) −2.35369 + 4.07671i −0.117101 + 0.202824i
\(405\) 4.31735 0.214531
\(406\) −53.5671 + 2.46822i −2.65849 + 0.122496i
\(407\) −15.8318 −0.784752
\(408\) −14.4263 + 24.9872i −0.714210 + 1.23705i
\(409\) −12.4692 21.5973i −0.616563 1.06792i −0.990108 0.140306i \(-0.955191\pi\)
0.373546 0.927612i \(-0.378142\pi\)
\(410\) 35.8773 + 62.1413i 1.77185 + 3.06894i
\(411\) 0.123702 0.214258i 0.00610176 0.0105686i
\(412\) −13.9785 −0.688673
\(413\) −2.23148 + 4.31198i −0.109804 + 0.212179i
\(414\) 2.51520 0.123616
\(415\) 23.4947 40.6939i 1.15331 1.99759i
\(416\) 5.12881 + 8.88335i 0.251460 + 0.435542i
\(417\) −4.29974 7.44737i −0.210559 0.364699i
\(418\) −5.30938 + 9.19611i −0.259690 + 0.449796i
\(419\) −13.2262 −0.646140 −0.323070 0.946375i \(-0.604715\pi\)
−0.323070 + 0.946375i \(0.604715\pi\)
\(420\) −22.7126 + 43.8885i −1.10826 + 2.14154i
\(421\) −5.82168 −0.283731 −0.141866 0.989886i \(-0.545310\pi\)
−0.141866 + 0.989886i \(0.545310\pi\)
\(422\) 21.4421 37.1388i 1.04378 1.80789i
\(423\) 0.199824 + 0.346106i 0.00971579 + 0.0168282i
\(424\) −19.1477 33.1649i −0.929897 1.61063i
\(425\) 33.6300 58.2488i 1.63129 2.82548i
\(426\) 22.6416 1.09699
\(427\) 3.43915 0.158466i 0.166432 0.00766873i
\(428\) −4.05326 −0.195922
\(429\) −2.49811 + 4.32686i −0.120610 + 0.208903i
\(430\) −58.3347 101.039i −2.81315 4.87252i
\(431\) −3.10956 5.38592i −0.149782 0.259431i 0.781365 0.624075i \(-0.214524\pi\)
−0.931147 + 0.364644i \(0.881191\pi\)
\(432\) 3.03197 5.25153i 0.145876 0.252664i
\(433\) −2.16316 −0.103955 −0.0519774 0.998648i \(-0.516552\pi\)
−0.0519774 + 0.998648i \(0.516552\pi\)
\(434\) 3.28705 + 5.13229i 0.157784 + 0.246358i
\(435\) −34.7900 −1.66805
\(436\) 32.3997 56.1179i 1.55166 2.68756i
\(437\) −1.22078 2.11445i −0.0583978 0.101148i
\(438\) −3.29134 5.70077i −0.157266 0.272393i
\(439\) −5.76278 + 9.98142i −0.275042 + 0.476387i −0.970146 0.242522i \(-0.922025\pi\)
0.695103 + 0.718910i \(0.255359\pi\)
\(440\) 43.6798 2.08235
\(441\) −4.04264 5.71463i −0.192507 0.272125i
\(442\) 35.8376 1.70462
\(443\) −4.56520 + 7.90716i −0.216899 + 0.375681i −0.953858 0.300257i \(-0.902928\pi\)
0.736959 + 0.675937i \(0.236261\pi\)
\(444\) −19.8052 34.3035i −0.939911 1.62797i
\(445\) −32.3504 56.0326i −1.53356 2.65620i
\(446\) −29.3371 + 50.8134i −1.38915 + 2.40608i
\(447\) −4.50669 −0.213159
\(448\) −4.56441 7.12670i −0.215648 0.336705i
\(449\) −20.6827 −0.976079 −0.488039 0.872822i \(-0.662288\pi\)
−0.488039 + 0.872822i \(0.662288\pi\)
\(450\) −17.1531 + 29.7101i −0.808606 + 1.40055i
\(451\) 5.71297 + 9.89515i 0.269013 + 0.465944i
\(452\) 30.5917 + 52.9864i 1.43891 + 2.49227i
\(453\) −2.26383 + 3.92107i −0.106364 + 0.184228i
\(454\) −19.3066 −0.906102
\(455\) 32.9697 1.51915i 1.54565 0.0712189i
\(456\) −14.2856 −0.668983
\(457\) −12.2979 + 21.3006i −0.575271 + 0.996398i 0.420742 + 0.907181i \(0.361770\pi\)
−0.996012 + 0.0892174i \(0.971563\pi\)
\(458\) 28.7659 + 49.8240i 1.34414 + 2.32812i
\(459\) −2.46562 4.27058i −0.115085 0.199334i
\(460\) −9.33898 + 16.1756i −0.435432 + 0.754191i
\(461\) −3.35047 −0.156047 −0.0780235 0.996952i \(-0.524861\pi\)
−0.0780235 + 0.996952i \(0.524861\pi\)
\(462\) −5.28863 + 10.2195i −0.246049 + 0.475452i
\(463\) −30.2309 −1.40495 −0.702476 0.711708i \(-0.747922\pi\)
−0.702476 + 0.711708i \(0.747922\pi\)
\(464\) −24.4322 + 42.3177i −1.13423 + 1.96455i
\(465\) 1.97704 + 3.42434i 0.0916832 + 0.158800i
\(466\) −29.6239 51.3101i −1.37230 2.37690i
\(467\) 15.0708 26.1034i 0.697394 1.20792i −0.271973 0.962305i \(-0.587676\pi\)
0.969367 0.245617i \(-0.0789904\pi\)
\(468\) −12.5003 −0.577827
\(469\) −12.4203 + 24.0003i −0.573516 + 1.10823i
\(470\) −4.33980 −0.200180
\(471\) −1.63364 + 2.82954i −0.0752740 + 0.130378i
\(472\) 5.36853 + 9.29856i 0.247106 + 0.428001i
\(473\) −9.28900 16.0890i −0.427109 0.739774i
\(474\) 12.8112 22.1897i 0.588438 1.01921i
\(475\) 33.3018 1.52799
\(476\) 56.3841 2.59802i 2.58436 0.119080i
\(477\) 6.54512 0.299681
\(478\) −16.5789 + 28.7154i −0.758300 + 1.31341i
\(479\) −14.5172 25.1445i −0.663308 1.14888i −0.979741 0.200268i \(-0.935819\pi\)
0.316433 0.948615i \(-0.397515\pi\)
\(480\) 7.66346 + 13.2735i 0.349787 + 0.605849i
\(481\) −13.2274 + 22.9106i −0.603120 + 1.04463i
\(482\) −43.4301 −1.97819
\(483\) −1.42694 2.22797i −0.0649279 0.101376i
\(484\) −34.6534 −1.57516
\(485\) 6.62963 11.4829i 0.301036 0.521410i
\(486\) 1.25760 + 2.17823i 0.0570460 + 0.0988065i
\(487\) 8.65283 + 14.9871i 0.392097 + 0.679132i 0.992726 0.120396i \(-0.0384163\pi\)
−0.600629 + 0.799528i \(0.705083\pi\)
\(488\) 3.80683 6.59362i 0.172327 0.298479i
\(489\) −10.6420 −0.481250
\(490\) 75.6911 6.99010i 3.41938 0.315781i
\(491\) 14.2287 0.642133 0.321067 0.947057i \(-0.395959\pi\)
0.321067 + 0.947057i \(0.395959\pi\)
\(492\) −14.2936 + 24.7572i −0.644404 + 1.11614i
\(493\) 19.8684 + 34.4131i 0.894827 + 1.54989i
\(494\) 8.87197 + 15.3667i 0.399169 + 0.691380i
\(495\) −3.73268 + 6.46519i −0.167771 + 0.290589i
\(496\) 5.55372 0.249369
\(497\) −12.8451 20.0560i −0.576184 0.899633i
\(498\) 27.3750 1.22670
\(499\) −5.55858 + 9.62774i −0.248836 + 0.430997i −0.963203 0.268774i \(-0.913381\pi\)
0.714367 + 0.699771i \(0.246715\pi\)
\(500\) −80.6846 139.750i −3.60832 6.24980i
\(501\) 1.49906 + 2.59644i 0.0669730 + 0.116001i
\(502\) −5.97306 + 10.3456i −0.266591 + 0.461749i
\(503\) 25.5401 1.13878 0.569389 0.822068i \(-0.307180\pi\)
0.569389 + 0.822068i \(0.307180\pi\)
\(504\) −15.4639 + 0.712531i −0.688816 + 0.0317387i
\(505\) 4.69770 0.209045
\(506\) −2.17458 + 3.76649i −0.0966720 + 0.167441i
\(507\) −2.32565 4.02815i −0.103286 0.178896i
\(508\) 3.84966 + 6.66781i 0.170801 + 0.295836i
\(509\) −15.1797 + 26.2920i −0.672829 + 1.16537i 0.304269 + 0.952586i \(0.401588\pi\)
−0.977098 + 0.212788i \(0.931746\pi\)
\(510\) 53.5485 2.37117
\(511\) −3.18249 + 6.14966i −0.140785 + 0.272045i
\(512\) −49.4328 −2.18464
\(513\) 1.22078 2.11445i 0.0538988 0.0933554i
\(514\) −1.79691 3.11233i −0.0792581 0.137279i
\(515\) 6.97489 + 12.0809i 0.307351 + 0.532347i
\(516\) 23.2406 40.2540i 1.02311 1.77208i
\(517\) −0.691053 −0.0303925
\(518\) −28.0031 + 54.1117i −1.23039 + 2.37753i
\(519\) 13.2996 0.583789
\(520\) 36.4944 63.2102i 1.60039 2.77195i
\(521\) 12.3504 + 21.3914i 0.541079 + 0.937176i 0.998842 + 0.0481022i \(0.0153173\pi\)
−0.457763 + 0.889074i \(0.651349\pi\)
\(522\) −10.1340 17.5526i −0.443552 0.768254i
\(523\) 14.2677 24.7123i 0.623881 1.08059i −0.364875 0.931056i \(-0.618888\pi\)
0.988756 0.149537i \(-0.0477783\pi\)
\(524\) 38.4718 1.68065
\(525\) 36.0486 1.66102i 1.57329 0.0724927i
\(526\) 22.1777 0.966994
\(527\) 2.25816 3.91125i 0.0983671 0.170377i
\(528\) 5.24274 + 9.08069i 0.228161 + 0.395186i
\(529\) −0.500000 0.866025i −0.0217391 0.0376533i
\(530\) −35.5368 + 61.5516i −1.54362 + 2.67363i
\(531\) −1.83508 −0.0796357
\(532\) 15.0725 + 23.5336i 0.653474 + 1.02031i
\(533\) 19.0927 0.826998
\(534\) 18.8467 32.6435i 0.815577 1.41262i
\(535\) 2.02246 + 3.50301i 0.0874387 + 0.151448i
\(536\) 29.8810 + 51.7553i 1.29066 + 2.23549i
\(537\) 9.81485 16.9998i 0.423542 0.733596i
\(538\) −32.4928 −1.40086
\(539\) 12.0528 1.11308i 0.519149 0.0479436i
\(540\) −18.6780 −0.803771
\(541\) 3.87196 6.70643i 0.166469 0.288332i −0.770707 0.637189i \(-0.780097\pi\)
0.937176 + 0.348857i \(0.113430\pi\)
\(542\) −16.7871 29.0762i −0.721069 1.24893i
\(543\) 9.60475 + 16.6359i 0.412179 + 0.713915i
\(544\) 8.75313 15.1609i 0.375287 0.650017i
\(545\) −64.6661 −2.76999
\(546\) 10.3702 + 16.1917i 0.443804 + 0.692940i
\(547\) 36.8996 1.57771 0.788856 0.614578i \(-0.210674\pi\)
0.788856 + 0.614578i \(0.210674\pi\)
\(548\) −0.535165 + 0.926933i −0.0228611 + 0.0395966i
\(549\) 0.650629 + 1.12692i 0.0277682 + 0.0480959i
\(550\) −29.6603 51.3732i −1.26472 2.19056i
\(551\) −9.83725 + 17.0386i −0.419081 + 0.725870i
\(552\) −5.85100 −0.249035
\(553\) −26.9237 + 1.24057i −1.14491 + 0.0527544i
\(554\) −38.9821 −1.65619
\(555\) −19.7644 + 34.2330i −0.838954 + 1.45311i
\(556\) 18.6018 + 32.2192i 0.788891 + 1.36640i
\(557\) −14.1322 24.4778i −0.598802 1.03716i −0.992998 0.118130i \(-0.962310\pi\)
0.394196 0.919026i \(-0.371023\pi\)
\(558\) −1.15179 + 1.99495i −0.0487590 + 0.0844531i
\(559\) −31.0438 −1.31301
\(560\) 31.8354 61.5169i 1.34529 2.59956i
\(561\) 8.52686 0.360004
\(562\) −29.6905 + 51.4255i −1.25242 + 2.16925i
\(563\) 4.81106 + 8.33300i 0.202762 + 0.351194i 0.949417 0.314017i \(-0.101675\pi\)
−0.746655 + 0.665211i \(0.768342\pi\)
\(564\) −0.864490 1.49734i −0.0364016 0.0630494i
\(565\) 30.5288 52.8774i 1.28436 2.22457i
\(566\) 59.5637 2.50365
\(567\) 1.21601 2.34975i 0.0510676 0.0986802i
\(568\) −52.6701 −2.20999
\(569\) 7.85731 13.6093i 0.329396 0.570530i −0.652996 0.757361i \(-0.726488\pi\)
0.982392 + 0.186831i \(0.0598217\pi\)
\(570\) 13.2565 + 22.9609i 0.555253 + 0.961726i
\(571\) −5.67209 9.82434i −0.237369 0.411136i 0.722589 0.691278i \(-0.242952\pi\)
−0.959959 + 0.280142i \(0.909619\pi\)
\(572\) 10.8075 18.7191i 0.451883 0.782684i
\(573\) 7.15375 0.298852
\(574\) 43.9259 2.02398i 1.83343 0.0844793i
\(575\) 13.6396 0.568809
\(576\) 1.59937 2.77019i 0.0666405 0.115425i
\(577\) 3.97526 + 6.88535i 0.165492 + 0.286641i 0.936830 0.349785i \(-0.113745\pi\)
−0.771338 + 0.636426i \(0.780412\pi\)
\(578\) −9.20207 15.9384i −0.382755 0.662952i
\(579\) −10.9786 + 19.0156i −0.456257 + 0.790259i
\(580\) 150.510 6.24959
\(581\) −15.5305 24.2488i −0.644315 1.00601i
\(582\) 7.72458 0.320194
\(583\) −5.65875 + 9.80125i −0.234362 + 0.405926i
\(584\) 7.65649 + 13.2614i 0.316828 + 0.548762i
\(585\) 6.23731 + 10.8033i 0.257881 + 0.446663i
\(586\) −26.5691 + 46.0191i −1.09756 + 1.90103i
\(587\) 21.2897 0.878718 0.439359 0.898311i \(-0.355206\pi\)
0.439359 + 0.898311i \(0.355206\pi\)
\(588\) 17.4895 + 24.7229i 0.721254 + 1.01956i
\(589\) 2.23613 0.0921379
\(590\) 9.96360 17.2575i 0.410195 0.710478i
\(591\) 1.60514 + 2.78018i 0.0660266 + 0.114361i
\(592\) 27.7602 + 48.0820i 1.14094 + 1.97616i
\(593\) 4.83858 8.38066i 0.198696 0.344152i −0.749410 0.662107i \(-0.769663\pi\)
0.948106 + 0.317954i \(0.102996\pi\)
\(594\) −4.34917 −0.178448
\(595\) −30.3794 47.4333i −1.24543 1.94458i
\(596\) 19.4971 0.798631
\(597\) 6.35849 11.0132i 0.260236 0.450741i
\(598\) 3.63373 + 6.29380i 0.148594 + 0.257373i
\(599\) −12.9896 22.4986i −0.530740 0.919268i −0.999357 0.0358668i \(-0.988581\pi\)
0.468617 0.883402i \(-0.344753\pi\)
\(600\) 39.9025 69.1131i 1.62901 2.82153i
\(601\) 31.2857 1.27617 0.638084 0.769967i \(-0.279727\pi\)
0.638084 + 0.769967i \(0.279727\pi\)
\(602\) −71.4213 + 3.29089i −2.91092 + 0.134127i
\(603\) −10.2140 −0.415945
\(604\) 9.79389 16.9635i 0.398508 0.690236i
\(605\) 17.2911 + 29.9490i 0.702983 + 1.21760i
\(606\) 1.36839 + 2.37013i 0.0555872 + 0.0962798i
\(607\) −14.4582 + 25.0423i −0.586838 + 1.01643i 0.407805 + 0.913069i \(0.366294\pi\)
−0.994644 + 0.103365i \(0.967039\pi\)
\(608\) 8.66771 0.351522
\(609\) −9.79881 + 18.9347i −0.397068 + 0.767272i
\(610\) −14.1304 −0.572123
\(611\) −0.577375 + 1.00004i −0.0233581 + 0.0404574i
\(612\) 10.6669 + 18.4756i 0.431184 + 0.746832i
\(613\) 23.9924 + 41.5560i 0.969043 + 1.67843i 0.698336 + 0.715770i \(0.253924\pi\)
0.270707 + 0.962662i \(0.412742\pi\)
\(614\) 2.48909 4.31123i 0.100451 0.173987i
\(615\) 28.5283 1.15037
\(616\) 12.3027 23.7730i 0.495689 0.957842i
\(617\) 41.9964 1.69071 0.845355 0.534205i \(-0.179389\pi\)
0.845355 + 0.534205i \(0.179389\pi\)
\(618\) −4.06343 + 7.03807i −0.163455 + 0.283113i
\(619\) 4.71191 + 8.16126i 0.189388 + 0.328029i 0.945046 0.326937i \(-0.106016\pi\)
−0.755659 + 0.654966i \(0.772683\pi\)
\(620\) −8.55319 14.8146i −0.343504 0.594967i
\(621\) 0.500000 0.866025i 0.0200643 0.0347524i
\(622\) −9.80123 −0.392994
\(623\) −39.6078 + 1.82502i −1.58685 + 0.0731177i
\(624\) 17.5212 0.701411
\(625\) −46.4198 + 80.4015i −1.85679 + 3.21606i
\(626\) −22.2072 38.4640i −0.887579 1.53733i
\(627\) 2.11091 + 3.65621i 0.0843017 + 0.146015i
\(628\) 7.06752 12.2413i 0.282025 0.488481i
\(629\) 45.1495 1.80023
\(630\) 15.4952 + 24.1936i 0.617342 + 0.963895i
\(631\) 6.84273 0.272405 0.136202 0.990681i \(-0.456510\pi\)
0.136202 + 0.990681i \(0.456510\pi\)
\(632\) −29.8021 + 51.6187i −1.18546 + 2.05328i
\(633\) −8.52498 14.7657i −0.338838 0.586884i
\(634\) 15.5092 + 26.8626i 0.615947 + 1.06685i
\(635\) 3.84175 6.65410i 0.152455 0.264060i
\(636\) −28.3159 −1.12280
\(637\) 8.45932 18.3719i 0.335170 0.727920i
\(638\) 35.0463 1.38750
\(639\) 4.50095 7.79587i 0.178055 0.308400i
\(640\) 32.6945 + 56.6286i 1.29236 + 2.23844i
\(641\) −3.51011 6.07968i −0.138641 0.240133i 0.788342 0.615238i \(-0.210940\pi\)
−0.926982 + 0.375105i \(0.877607\pi\)
\(642\) −1.17825 + 2.04078i −0.0465017 + 0.0805432i
\(643\) −47.1743 −1.86037 −0.930185 0.367090i \(-0.880354\pi\)
−0.930185 + 0.367090i \(0.880354\pi\)
\(644\) 6.17329 + 9.63876i 0.243262 + 0.379820i
\(645\) −46.3857 −1.82643
\(646\) 15.1414 26.2257i 0.595732 1.03184i
\(647\) −11.9835 20.7560i −0.471119 0.816003i 0.528335 0.849036i \(-0.322817\pi\)
−0.999454 + 0.0330335i \(0.989483\pi\)
\(648\) −2.92550 5.06711i −0.114924 0.199055i
\(649\) 1.58657 2.74801i 0.0622782 0.107869i
\(650\) −99.1249 −3.88800
\(651\) 2.42057 0.111533i 0.0948695 0.00437132i
\(652\) 46.0401 1.80307
\(653\) 9.16565 15.8754i 0.358679 0.621251i −0.629061 0.777356i \(-0.716560\pi\)
0.987740 + 0.156105i \(0.0498938\pi\)
\(654\) −18.8366 32.6259i −0.736569 1.27577i
\(655\) −19.1963 33.2490i −0.750063 1.29915i
\(656\) 20.0348 34.7012i 0.782226 1.35486i
\(657\) −2.61716 −0.102105
\(658\) −1.22233 + 2.36196i −0.0476514 + 0.0920789i
\(659\) 16.4341 0.640183 0.320092 0.947387i \(-0.396286\pi\)
0.320092 + 0.947387i \(0.396286\pi\)
\(660\) 16.1485 27.9700i 0.628580 1.08873i
\(661\) 15.0175 + 26.0111i 0.584113 + 1.01171i 0.994985 + 0.100021i \(0.0318910\pi\)
−0.410872 + 0.911693i \(0.634776\pi\)
\(662\) −7.30119 12.6460i −0.283769 0.491502i
\(663\) 7.12419 12.3395i 0.276681 0.479225i
\(664\) −63.6812 −2.47131
\(665\) 12.8181 24.7689i 0.497063 0.960497i
\(666\) −23.0287 −0.892345
\(667\) −4.02908 + 6.97858i −0.156007 + 0.270212i
\(668\) −6.48530 11.2329i −0.250924 0.434613i
\(669\) 11.6639 + 20.2025i 0.450953 + 0.781073i
\(670\) 55.4569 96.0542i 2.14249 3.71090i
\(671\) −2.25007 −0.0868630
\(672\) 9.38265 0.432326i 0.361944 0.0166773i
\(673\) 17.0642 0.657776 0.328888 0.944369i \(-0.393326\pi\)
0.328888 + 0.944369i \(0.393326\pi\)
\(674\) 28.3515 49.1062i 1.09206 1.89150i
\(675\) 6.81978 + 11.8122i 0.262493 + 0.454652i
\(676\) 10.0614 + 17.4268i 0.386975 + 0.670261i
\(677\) 18.8278 32.6106i 0.723610 1.25333i −0.235934 0.971769i \(-0.575815\pi\)
0.959544 0.281560i \(-0.0908518\pi\)
\(678\) 35.5709 1.36609
\(679\) −4.38235 6.84244i −0.168179 0.262589i
\(680\) −124.567 −4.77694
\(681\) −3.83797 + 6.64756i −0.147071 + 0.254735i
\(682\) −1.99161 3.44957i −0.0762628 0.132091i
\(683\) 20.3875 + 35.3121i 0.780104 + 1.35118i 0.931880 + 0.362766i \(0.118167\pi\)
−0.151776 + 0.988415i \(0.548499\pi\)
\(684\) −5.28140 + 9.14765i −0.201939 + 0.349769i
\(685\) 1.06813 0.0408111
\(686\) 17.5145 43.1642i 0.668705 1.64802i
\(687\) 22.8736 0.872683
\(688\) −32.5755 + 56.4225i −1.24193 + 2.15109i
\(689\) 9.45578 + 16.3779i 0.360236 + 0.623948i
\(690\) 5.42951 + 9.40419i 0.206698 + 0.358012i
\(691\) −1.99453 + 3.45463i −0.0758756 + 0.131420i −0.901467 0.432848i \(-0.857509\pi\)
0.825591 + 0.564269i \(0.190842\pi\)
\(692\) −57.5376 −2.18725
\(693\) 2.46739 + 3.85250i 0.0937284 + 0.146344i
\(694\) −18.8572 −0.715811
\(695\) 18.5635 32.1529i 0.704154 1.21963i
\(696\) 23.5742 + 40.8316i 0.893576 + 1.54772i
\(697\) −16.2924 28.2193i −0.617119 1.06888i
\(698\) 10.0275 17.3681i 0.379545 0.657391i
\(699\) −23.5559 −0.890965
\(700\) −155.955 + 7.18598i −5.89456 + 0.271604i
\(701\) 3.27653 0.123753 0.0618763 0.998084i \(-0.480292\pi\)
0.0618763 + 0.998084i \(0.480292\pi\)
\(702\) −3.63373 + 6.29380i −0.137146 + 0.237544i
\(703\) 11.1772 + 19.3595i 0.421557 + 0.730158i
\(704\) 2.76555 + 4.79008i 0.104231 + 0.180533i
\(705\) −0.862713 + 1.49426i −0.0324916 + 0.0562772i
\(706\) −74.2712 −2.79523
\(707\) 1.32314 2.55676i 0.0497617 0.0961567i
\(708\) 7.93902 0.298367
\(709\) 3.58140 6.20316i 0.134502 0.232965i −0.790905 0.611939i \(-0.790390\pi\)
0.925407 + 0.378974i \(0.123723\pi\)
\(710\) 48.8759 + 84.6556i 1.83428 + 3.17707i
\(711\) −5.09351 8.82221i −0.191021 0.330859i
\(712\) −43.8422 + 75.9369i −1.64306 + 2.84586i
\(713\) 0.915859 0.0342992
\(714\) 15.0823 29.1441i 0.564440 1.09069i
\(715\) −21.5705 −0.806690
\(716\) −42.4615 + 73.5455i −1.58686 + 2.74852i
\(717\) 6.59146 + 11.4167i 0.246163 + 0.426366i
\(718\) 16.5006 + 28.5798i 0.615795 + 1.06659i
\(719\) −24.6871 + 42.7593i −0.920673 + 1.59465i −0.122296 + 0.992494i \(0.539026\pi\)
−0.798377 + 0.602158i \(0.794308\pi\)
\(720\) 26.1802 0.975679
\(721\) 8.53962 0.393481i 0.318032 0.0146540i
\(722\) −32.7952 −1.22051
\(723\) −8.63351 + 14.9537i −0.321084 + 0.556134i
\(724\) −41.5526 71.9711i −1.54429 2.67479i
\(725\) −54.9549 95.1847i −2.04097 3.53507i
\(726\) −10.0734 + 17.4477i −0.373860 + 0.647545i
\(727\) −15.4034 −0.571281 −0.285640 0.958337i \(-0.592206\pi\)
−0.285640 + 0.958337i \(0.592206\pi\)
\(728\) −24.1237 37.6659i −0.894084 1.39599i
\(729\) 1.00000 0.0370370
\(730\) 14.2099 24.6122i 0.525932 0.910940i
\(731\) 26.4907 + 45.8832i 0.979792 + 1.69705i
\(732\) −2.81478 4.87535i −0.104037 0.180198i
\(733\) −6.10551 + 10.5751i −0.225512 + 0.390599i −0.956473 0.291821i \(-0.905739\pi\)
0.730961 + 0.682420i \(0.239072\pi\)
\(734\) 13.2392 0.488669
\(735\) 12.6399 27.4512i 0.466230 1.01255i
\(736\) 3.55007 0.130857
\(737\) 8.83075 15.2953i 0.325285 0.563410i
\(738\) 8.31002 + 14.3934i 0.305896 + 0.529828i
\(739\) −16.2402 28.1288i −0.597404 1.03473i −0.993203 0.116397i \(-0.962865\pi\)
0.395798 0.918337i \(-0.370468\pi\)
\(740\) 85.5059 148.101i 3.14326 5.44429i
\(741\) 7.05467 0.259160
\(742\) 23.4907 + 36.6776i 0.862371 + 1.34648i
\(743\) −40.1671 −1.47359 −0.736795 0.676117i \(-0.763662\pi\)
−0.736795 + 0.676117i \(0.763662\pi\)
\(744\) 2.67934 4.64076i 0.0982295 0.170139i
\(745\) −9.72849 16.8502i −0.356424 0.617345i
\(746\) 15.9081 + 27.5536i 0.582436 + 1.00881i
\(747\) 5.44191 9.42566i 0.199109 0.344867i
\(748\) −36.8893 −1.34881
\(749\) 2.47617 0.114095i 0.0904774 0.00416894i
\(750\) −93.8171 −3.42572
\(751\) −22.1518 + 38.3680i −0.808330 + 1.40007i 0.105689 + 0.994399i \(0.466295\pi\)
−0.914020 + 0.405670i \(0.867038\pi\)
\(752\) 1.21172 + 2.09877i 0.0441870 + 0.0765342i
\(753\) 2.37478 + 4.11324i 0.0865418 + 0.149895i
\(754\) 29.2812 50.7165i 1.06636 1.84699i
\(755\) −19.5475 −0.711406
\(756\) −5.26076 + 10.1656i −0.191332 + 0.369719i
\(757\) 41.4696 1.50724 0.753620 0.657311i \(-0.228306\pi\)
0.753620 + 0.657311i \(0.228306\pi\)
\(758\) −16.0957 + 27.8786i −0.584622 + 1.01259i
\(759\) 0.864575 + 1.49749i 0.0313821 + 0.0543554i
\(760\) −30.8379 53.4128i −1.11861 1.93749i
\(761\) 1.58650 2.74790i 0.0575107 0.0996114i −0.835837 0.548978i \(-0.815017\pi\)
0.893347 + 0.449367i \(0.148350\pi\)
\(762\) 4.47625 0.162157
\(763\) −18.2136 + 35.1950i −0.659377 + 1.27414i
\(764\) −30.9489 −1.11969
\(765\) 10.6450 18.4376i 0.384869 0.666613i
\(766\) 20.9100 + 36.2172i 0.755510 + 1.30858i
\(767\) −2.65115 4.59193i −0.0957275 0.165805i
\(768\) −15.8484 + 27.4503i −0.571881 + 0.990527i
\(769\) −13.6487 −0.492184 −0.246092 0.969246i \(-0.579147\pi\)
−0.246092 + 0.969246i \(0.579147\pi\)
\(770\) −49.6263 + 2.28664i −1.78841 + 0.0824048i
\(771\) −1.42884 −0.0514582
\(772\) 47.4963 82.2661i 1.70943 2.96082i
\(773\) 14.2374 + 24.6599i 0.512083 + 0.886954i 0.999902 + 0.0140088i \(0.00445929\pi\)
−0.487819 + 0.872945i \(0.662207\pi\)
\(774\) −13.5117 23.4029i −0.485667 0.841201i
\(775\) −6.24595 + 10.8183i −0.224361 + 0.388605i
\(776\) −17.9693 −0.645061
\(777\) 13.0648 + 20.3989i 0.468696 + 0.731805i
\(778\) −75.1299 −2.69354
\(779\) 8.06671 13.9719i 0.289020 0.500597i
\(780\) −26.9841 46.7379i −0.966187 1.67349i
\(781\) 7.78282 + 13.4802i 0.278491 + 0.482361i
\(782\) 6.20154 10.7414i 0.221767 0.384111i
\(783\) −8.05817 −0.287975
\(784\) −24.5144 34.6532i −0.875513 1.23762i
\(785\) −14.1060 −0.503464
\(786\) 11.1834 19.3702i 0.398899 0.690913i
\(787\) −24.0339 41.6280i −0.856717 1.48388i −0.875043 0.484046i \(-0.839167\pi\)
0.0183253 0.999832i \(-0.494167\pi\)
\(788\) −6.94423 12.0278i −0.247378 0.428471i
\(789\) 4.40873 7.63614i 0.156955 0.271854i
\(790\) 110.621 3.93572
\(791\) −20.1803 31.5088i −0.717528 1.12032i
\(792\) 10.1173 0.359501
\(793\) −1.87993 + 3.25614i −0.0667584 + 0.115629i
\(794\) 7.52595 + 13.0353i 0.267086 + 0.462607i
\(795\) 14.1288 + 24.4718i 0.501097 + 0.867926i
\(796\) −27.5084 + 47.6460i −0.975010 + 1.68877i
\(797\) −28.0705 −0.994308 −0.497154 0.867662i \(-0.665622\pi\)
−0.497154 + 0.867662i \(0.665622\pi\)
\(798\) 16.2304 0.747850i 0.574550 0.0264736i
\(799\) 1.97077 0.0697207
\(800\) −24.2107 + 41.9341i −0.855977 + 1.48260i
\(801\) −7.49312 12.9785i −0.264756 0.458571i
\(802\) 19.9500 + 34.5543i 0.704458 + 1.22016i
\(803\) 2.26273 3.91916i 0.0798500 0.138304i
\(804\) 44.1882 1.55840
\(805\) 5.24994 10.1447i 0.185036 0.357554i
\(806\) −6.65597 −0.234446
\(807\) −6.45927 + 11.1878i −0.227377 + 0.393829i
\(808\) −3.18323 5.51351i −0.111986 0.193965i
\(809\) −21.3800 37.0312i −0.751681 1.30195i −0.947008 0.321211i \(-0.895910\pi\)
0.195327 0.980738i \(-0.437423\pi\)
\(810\) −5.42951 + 9.40419i −0.190774 + 0.330430i
\(811\) 50.7214 1.78107 0.890534 0.454916i \(-0.150331\pi\)
0.890534 + 0.454916i \(0.150331\pi\)
\(812\) 42.3921 81.9162i 1.48767 2.87469i
\(813\) −13.3485 −0.468153
\(814\) 19.9101 34.4852i 0.697847 1.20871i
\(815\) −22.9727 39.7899i −0.804700 1.39378i
\(816\) −14.9514 25.8966i −0.523404 0.906562i
\(817\) −13.1161 + 22.7177i −0.458873 + 0.794792i
\(818\) 62.7252 2.19314
\(819\) 7.63656 0.351871i 0.266843 0.0122954i
\(820\) −123.421 −4.31004
\(821\) −21.1418 + 36.6188i −0.737856 + 1.27800i 0.215604 + 0.976481i \(0.430828\pi\)
−0.953459 + 0.301522i \(0.902505\pi\)
\(822\) 0.311135 + 0.538902i 0.0108521 + 0.0187964i
\(823\) 8.24278 + 14.2769i 0.287325 + 0.497662i 0.973170 0.230086i \(-0.0739006\pi\)
−0.685845 + 0.727747i \(0.740567\pi\)
\(824\) 9.45256 16.3723i 0.329296 0.570357i
\(825\) −23.5848 −0.821119
\(826\) −6.58618 10.2834i −0.229162 0.357806i
\(827\) 21.3447 0.742229 0.371115 0.928587i \(-0.378976\pi\)
0.371115 + 0.928587i \(0.378976\pi\)
\(828\) −2.16313 + 3.74664i −0.0751738 + 0.130205i
\(829\) −4.41319 7.64387i −0.153276 0.265483i 0.779154 0.626833i \(-0.215649\pi\)
−0.932430 + 0.361350i \(0.882316\pi\)
\(830\) 59.0938 + 102.354i 2.05118 + 3.55274i
\(831\) −7.74930 + 13.4222i −0.268820 + 0.465610i
\(832\) 9.24248 0.320425
\(833\) −34.3724 + 3.17431i −1.19093 + 0.109983i
\(834\) 21.6295 0.748967
\(835\) −6.47196 + 11.2098i −0.223972 + 0.387930i
\(836\) −9.13234 15.8177i −0.315849 0.547066i
\(837\) 0.457930 + 0.793157i 0.0158284 + 0.0274155i
\(838\) 16.6332 28.8096i 0.574586 0.995212i
\(839\) −32.7270 −1.12986 −0.564932 0.825138i \(-0.691097\pi\)
−0.564932 + 0.825138i \(0.691097\pi\)
\(840\) −36.0456 56.2804i −1.24369 1.94186i
\(841\) 35.9341 1.23911
\(842\) 7.32135 12.6810i 0.252310 0.437014i
\(843\) 11.8044 + 20.4458i 0.406566 + 0.704192i
\(844\) 36.8812 + 63.8802i 1.26950 + 2.19885i
\(845\) 10.0407 17.3910i 0.345410 0.598267i
\(846\) −1.00520 −0.0345594
\(847\) 21.1701 0.975458i 0.727413 0.0335171i
\(848\) 39.6893 1.36294
\(849\) 11.8407 20.5087i 0.406373 0.703858i
\(850\) 84.5862 + 146.508i 2.90128 + 5.02517i
\(851\) 4.57790 + 7.92916i 0.156929 + 0.271808i
\(852\) −19.4722 + 33.7269i −0.667108 + 1.15546i
\(853\) 8.42097 0.288329 0.144164 0.989554i \(-0.453951\pi\)
0.144164 + 0.989554i \(0.453951\pi\)
\(854\) −3.97991 + 7.69056i −0.136190 + 0.263165i
\(855\) 10.5411 0.360497
\(856\) 2.74090 4.74737i 0.0936819 0.162262i
\(857\) 2.80361 + 4.85600i 0.0957697 + 0.165878i 0.909930 0.414763i \(-0.136135\pi\)
−0.814160 + 0.580641i \(0.802802\pi\)
\(858\) −6.28326 10.8829i −0.214507 0.371537i
\(859\) −3.10337 + 5.37519i −0.105886 + 0.183399i −0.914100 0.405490i \(-0.867101\pi\)
0.808214 + 0.588889i \(0.200434\pi\)
\(860\) 200.676 6.84300
\(861\) 8.03518 15.5267i 0.273838 0.529150i
\(862\) 15.6424 0.532781
\(863\) 3.65496 6.33058i 0.124416 0.215495i −0.797088 0.603863i \(-0.793628\pi\)
0.921505 + 0.388367i \(0.126961\pi\)
\(864\) 1.77504 + 3.07445i 0.0603879 + 0.104595i
\(865\) 28.7096 + 49.7265i 0.976156 + 1.69075i
\(866\) 2.72039 4.71186i 0.0924428 0.160116i
\(867\) −7.31715 −0.248504
\(868\) −10.4720 + 0.482519i −0.355442 + 0.0163778i
\(869\) 17.6149 0.597544
\(870\) 43.7519 75.7806i 1.48333 2.56920i
\(871\) −14.7562 25.5585i −0.499994 0.866015i
\(872\) 43.8186 + 75.8961i 1.48389 + 2.57017i
\(873\) 1.53558 2.65970i 0.0519714 0.0900172i
\(874\) 6.14102 0.207723
\(875\) 53.2248 + 83.1033i 1.79933 + 2.80940i
\(876\) 11.3225 0.382551
\(877\) 16.3936 28.3946i 0.553573 0.958816i −0.444440 0.895808i \(-0.646597\pi\)
0.998013 0.0630076i \(-0.0200692\pi\)
\(878\) −14.4946 25.1053i −0.489168 0.847263i
\(879\) 10.5634 + 18.2964i 0.356295 + 0.617121i
\(880\) −22.6348 + 39.2046i −0.763018 + 1.32159i
\(881\) 17.0828 0.575533 0.287767 0.957701i \(-0.407087\pi\)
0.287767 + 0.957701i \(0.407087\pi\)
\(882\) 17.5318 1.61907i 0.590327 0.0545169i
\(883\) 26.9824 0.908030 0.454015 0.890994i \(-0.349991\pi\)
0.454015 + 0.890994i \(0.349991\pi\)
\(884\) −30.8210 + 53.3836i −1.03662 + 1.79549i
\(885\) −3.96135 6.86126i −0.133159 0.230639i
\(886\) −11.4824 19.8881i −0.385759 0.668155i
\(887\) −3.40233 + 5.89301i −0.114239 + 0.197868i −0.917475 0.397793i \(-0.869776\pi\)
0.803236 + 0.595661i \(0.203110\pi\)
\(888\) 53.5706 1.79771
\(889\) −2.53949 3.96507i −0.0851717 0.132984i
\(890\) 162.736 5.45492
\(891\) −0.864575 + 1.49749i −0.0289644 + 0.0501678i
\(892\) −50.4610 87.4010i −1.68956 2.92640i
\(893\) 0.487883 + 0.845039i 0.0163264 + 0.0282781i
\(894\) 5.66762 9.81661i 0.189554 0.328316i
\(895\) 84.7484 2.83283
\(896\) 40.0291 1.84443i 1.33728 0.0616180i
\(897\) 2.88941 0.0964746
\(898\) 26.0107 45.0518i 0.867987 1.50340i
\(899\) −3.69007 6.39140i −0.123071 0.213165i
\(900\) −29.5041 51.1025i −0.983469 1.70342i
\(901\) 16.1378 27.9515i 0.537628 0.931199i
\(902\) −28.7386 −0.956889
\(903\) −13.0648 + 25.2457i −0.434770 + 0.840125i
\(904\) −82.7469 −2.75212
\(905\) −41.4671 + 71.8231i −1.37841 + 2.38748i
\(906\) −5.69399 9.86228i −0.189170 0.327652i
\(907\) 2.71457 + 4.70177i 0.0901357 + 0.156120i 0.907568 0.419905i \(-0.137937\pi\)
−0.817432 + 0.576025i \(0.804603\pi\)
\(908\) 16.6040 28.7590i 0.551024 0.954402i
\(909\) 1.08810 0.0360899
\(910\) −38.1537 + 73.7262i −1.26478 + 2.44400i
\(911\) −15.8106 −0.523829 −0.261914 0.965091i \(-0.584354\pi\)
−0.261914 + 0.965091i \(0.584354\pi\)
\(912\) 7.40274 12.8219i 0.245129 0.424577i
\(913\) 9.40988 + 16.2984i 0.311422 + 0.539398i
\(914\) −30.9317 53.5752i −1.02313 1.77211i
\(915\) −2.80899 + 4.86532i −0.0928625 + 0.160843i
\(916\) −98.9571 −3.26963
\(917\) −23.5028 + 1.08294i −0.776130 + 0.0357619i
\(918\) 12.4031 0.409363
\(919\) −18.6790 + 32.3530i −0.616165 + 1.06723i 0.374014 + 0.927423i \(0.377981\pi\)
−0.990179 + 0.139805i \(0.955352\pi\)
\(920\) −12.6304 21.8765i −0.416412 0.721247i
\(921\) −0.989617 1.71407i −0.0326090 0.0564804i
\(922\) 4.21356 7.29810i 0.138766 0.240350i
\(923\) 26.0102 0.856135
\(924\) −10.6746 16.6669i −0.351167 0.548300i
\(925\) −124.881 −4.10607
\(926\) 38.0185 65.8500i 1.24937 2.16396i
\(927\) 1.61555 + 2.79821i 0.0530616 + 0.0919053i
\(928\) −14.3035 24.7744i −0.469536 0.813261i
\(929\) −16.3535 + 28.3250i −0.536539 + 0.929314i 0.462548 + 0.886594i \(0.346935\pi\)
−0.999087 + 0.0427192i \(0.986398\pi\)
\(930\) −9.94534 −0.326121
\(931\) −9.87035 13.9526i −0.323488 0.457279i
\(932\) 101.909 3.33813
\(933\) −1.94840 + 3.37472i −0.0637876 + 0.110483i
\(934\) 37.9062 + 65.6554i 1.24033 + 2.14831i
\(935\) 18.4067 + 31.8814i 0.601965 + 1.04263i
\(936\) 8.45296 14.6410i 0.276294 0.478555i
\(937\) 49.2657 1.60944 0.804721 0.593654i \(-0.202315\pi\)
0.804721 + 0.593654i \(0.202315\pi\)
\(938\) −36.6583 57.2370i −1.19694 1.86886i
\(939\) −17.6584 −0.576260
\(940\) 3.73231 6.46455i 0.121735 0.210851i
\(941\) 5.43419 + 9.41229i 0.177149 + 0.306832i 0.940903 0.338676i \(-0.109979\pi\)
−0.763754 + 0.645508i \(0.776646\pi\)
\(942\) −4.10893 7.11688i −0.133876 0.231880i
\(943\) 3.30392 5.72255i 0.107590 0.186352i
\(944\) −11.1278 −0.362180
\(945\) 11.4105 0.525765i 0.371185 0.0171031i
\(946\) 46.7275 1.51924
\(947\) −15.7953 + 27.3583i −0.513279 + 0.889026i 0.486602 + 0.873624i \(0.338236\pi\)
−0.999881 + 0.0154021i \(0.995097\pi\)
\(948\) 22.0358 + 38.1671i 0.715689 + 1.23961i
\(949\) −3.78102 6.54892i −0.122737 0.212587i
\(950\) −41.8804 + 72.5390i −1.35878 + 2.35347i
\(951\) 12.3323 0.399903
\(952\) −35.0851 + 67.7966i −1.13712 + 2.19730i
\(953\) −7.60480 −0.246344 −0.123172 0.992385i \(-0.539307\pi\)
−0.123172 + 0.992385i \(0.539307\pi\)
\(954\) −8.23116 + 14.2568i −0.266494 + 0.461581i
\(955\) 15.4426 + 26.7474i 0.499712 + 0.865527i
\(956\) −28.5163 49.3917i −0.922283 1.59744i
\(957\) 6.96689 12.0670i 0.225208 0.390071i
\(958\) 73.0274 2.35941
\(959\) 0.300845 0.581337i 0.00971480 0.0187723i
\(960\) 13.8101 0.445719
\(961\) 15.0806 26.1204i 0.486471 0.842592i
\(962\) −33.2697 57.6248i −1.07266 1.85790i
\(963\) 0.468449 + 0.811378i 0.0150956 + 0.0261463i
\(964\) 37.3508 64.6934i 1.20299 2.08363i
\(965\) −94.7973 −3.05163
\(966\) 6.64755 0.306300i 0.213881 0.00985505i
\(967\) 10.3379 0.332446 0.166223 0.986088i \(-0.446843\pi\)
0.166223 + 0.986088i \(0.446843\pi\)
\(968\) 23.4333 40.5878i 0.753176 1.30454i
\(969\) −6.01996 10.4269i −0.193389 0.334960i
\(970\) 16.6749 + 28.8817i 0.535398 + 0.927337i
\(971\) −9.87947 + 17.1117i −0.317047 + 0.549142i −0.979871 0.199634i \(-0.936025\pi\)
0.662823 + 0.748776i \(0.269358\pi\)
\(972\) −4.32625 −0.138765
\(973\) −12.2709 19.1594i −0.393388 0.614222i
\(974\) −43.5273 −1.39470
\(975\) −19.7051 + 34.1303i −0.631069 + 1.09304i
\(976\) 3.94538 + 6.83359i 0.126288 + 0.218738i
\(977\) 9.80885 + 16.9894i 0.313813 + 0.543540i 0.979184 0.202972i \(-0.0650601\pi\)
−0.665371 + 0.746512i \(0.731727\pi\)
\(978\) 13.3835 23.1808i 0.427956 0.741241i
\(979\) 25.9135 0.828198
\(980\) −54.6834 + 118.761i −1.74680 + 3.79368i
\(981\) −14.9782 −0.478216
\(982\) −17.8941 + 30.9934i −0.571023 + 0.989040i
\(983\) 7.55281 + 13.0818i 0.240897 + 0.417246i 0.960970 0.276652i \(-0.0892250\pi\)
−0.720073 + 0.693898i \(0.755892\pi\)
\(984\) −19.3312 33.4826i −0.616256 1.06739i
\(985\) −6.92995 + 12.0030i −0.220807 + 0.382448i
\(986\) −99.9461 −3.18293
\(987\) 0.570274 + 0.890405i 0.0181520 + 0.0283419i
\(988\) −30.5203 −0.970979
\(989\) −5.37200 + 9.30458i −0.170820 + 0.295869i
\(990\) −9.38845 16.2613i −0.298384 0.516817i
\(991\) −20.6412 35.7517i −0.655690 1.13569i −0.981720 0.190330i \(-0.939044\pi\)
0.326030 0.945360i \(-0.394289\pi\)
\(992\) −1.62568 + 2.81576i −0.0516155 + 0.0894006i
\(993\) −5.80565 −0.184237
\(994\) 59.8406 2.75728i 1.89803 0.0874557i
\(995\) 54.9037 1.74056
\(996\) −23.5431 + 40.7778i −0.745991 + 1.29209i
\(997\) −9.26904 16.0545i −0.293554 0.508450i 0.681094 0.732196i \(-0.261505\pi\)
−0.974647 + 0.223746i \(0.928171\pi\)
\(998\) −13.9810 24.2157i −0.442559 0.766535i
\(999\) −4.57790 + 7.92916i −0.144838 + 0.250868i
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 483.2.i.h.415.2 yes 20
7.2 even 3 3381.2.a.bi.1.9 10
7.4 even 3 inner 483.2.i.h.277.2 20
7.5 odd 6 3381.2.a.bj.1.9 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
483.2.i.h.277.2 20 7.4 even 3 inner
483.2.i.h.415.2 yes 20 1.1 even 1 trivial
3381.2.a.bi.1.9 10 7.2 even 3
3381.2.a.bj.1.9 10 7.5 odd 6