Properties

Label 60.3.l.a.23.19
Level $60$
Weight $3$
Character 60.23
Analytic conductor $1.635$
Analytic rank $0$
Dimension $40$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [60,3,Mod(23,60)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(60, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 2, 3]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("60.23");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 60 = 2^{2} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 60.l (of order \(4\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(1.63488158616\)
Analytic rank: \(0\)
Dimension: \(40\)
Relative dimension: \(20\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 23.19
Character \(\chi\) \(=\) 60.23
Dual form 60.3.l.a.47.19

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.84549 - 0.770813i) q^{2} +(1.12501 + 2.78107i) q^{3} +(2.81170 - 2.84506i) q^{4} +(-3.86232 - 3.17529i) q^{5} +(4.21989 + 4.26527i) q^{6} +(4.75159 + 4.75159i) q^{7} +(2.99596 - 7.41783i) q^{8} +(-6.46869 + 6.25748i) q^{9} +O(q^{10})\) \(q+(1.84549 - 0.770813i) q^{2} +(1.12501 + 2.78107i) q^{3} +(2.81170 - 2.84506i) q^{4} +(-3.86232 - 3.17529i) q^{5} +(4.21989 + 4.26527i) q^{6} +(4.75159 + 4.75159i) q^{7} +(2.99596 - 7.41783i) q^{8} +(-6.46869 + 6.25748i) q^{9} +(-9.57545 - 2.88285i) q^{10} -11.9496 q^{11} +(11.0755 + 4.61879i) q^{12} +(-4.22368 - 4.22368i) q^{13} +(12.4316 + 5.10644i) q^{14} +(4.48553 - 14.3136i) q^{15} +(-0.188739 - 15.9989i) q^{16} +(-9.35253 - 9.35253i) q^{17} +(-7.11458 + 16.5343i) q^{18} +1.48848 q^{19} +(-19.8936 + 2.06060i) q^{20} +(-7.86889 + 18.5601i) q^{21} +(-22.0529 + 9.21092i) q^{22} +(11.6030 + 11.6030i) q^{23} +(24.0000 - 0.0132009i) q^{24} +(4.83510 + 24.5280i) q^{25} +(-11.0504 - 4.53911i) q^{26} +(-24.6799 - 10.9501i) q^{27} +(26.8786 - 0.158538i) q^{28} +39.3671 q^{29} +(-2.75512 - 29.8732i) q^{30} +43.6522i q^{31} +(-12.6805 - 29.3804i) q^{32} +(-13.4435 - 33.2327i) q^{33} +(-24.4691 - 10.0510i) q^{34} +(-3.26452 - 33.4399i) q^{35} +(-0.385062 + 35.9979i) q^{36} +(49.1693 - 49.1693i) q^{37} +(2.74698 - 1.14734i) q^{38} +(6.99465 - 16.4981i) q^{39} +(-35.1251 + 19.1370i) q^{40} +27.0663i q^{41} +(-0.215630 + 40.3180i) q^{42} +(8.84693 - 8.84693i) q^{43} +(-33.5987 + 33.9974i) q^{44} +(44.8535 - 3.62848i) q^{45} +(30.3570 + 12.4695i) q^{46} +(15.0010 - 15.0010i) q^{47} +(44.2817 - 18.5239i) q^{48} -3.84477i q^{49} +(27.8296 + 41.5393i) q^{50} +(15.4883 - 36.5318i) q^{51} +(-23.8923 + 0.140924i) q^{52} +(-14.6333 + 14.6333i) q^{53} +(-53.9870 - 1.18482i) q^{54} +(46.1533 + 37.9435i) q^{55} +(49.4821 - 21.0109i) q^{56} +(1.67456 + 4.13957i) q^{57} +(72.6517 - 30.3447i) q^{58} +61.7260i q^{59} +(-28.1112 - 53.0072i) q^{60} -84.6009 q^{61} +(33.6477 + 80.5598i) q^{62} +(-60.4695 - 1.00356i) q^{63} +(-46.0485 - 44.4470i) q^{64} +(2.90182 + 29.7246i) q^{65} +(-50.4261 - 50.9683i) q^{66} +(-65.7467 - 65.7467i) q^{67} +(-52.9050 + 0.312049i) q^{68} +(-19.2152 + 45.3223i) q^{69} +(-31.8005 - 59.1967i) q^{70} +14.2794 q^{71} +(27.0370 + 66.7308i) q^{72} +(16.0903 + 16.0903i) q^{73} +(52.8413 - 128.642i) q^{74} +(-62.7745 + 41.0411i) q^{75} +(4.18516 - 4.23482i) q^{76} +(-56.7797 - 56.7797i) q^{77} +(0.191673 - 35.8386i) q^{78} +9.32721 q^{79} +(-50.0721 + 62.3922i) q^{80} +(2.68783 - 80.9554i) q^{81} +(20.8630 + 49.9507i) q^{82} +(12.7500 + 12.7500i) q^{83} +(30.6797 + 74.5728i) q^{84} +(6.42553 + 65.8195i) q^{85} +(9.50762 - 23.1463i) q^{86} +(44.2885 + 109.483i) q^{87} +(-35.8005 + 88.6403i) q^{88} -52.4342 q^{89} +(79.9799 - 41.2700i) q^{90} -40.1384i q^{91} +(65.6353 - 0.387136i) q^{92} +(-121.400 + 49.1093i) q^{93} +(16.1213 - 39.2471i) q^{94} +(-5.74900 - 4.72636i) q^{95} +(67.4431 - 68.3186i) q^{96} +(6.90848 - 6.90848i) q^{97} +(-2.96360 - 7.09551i) q^{98} +(77.2983 - 74.7745i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40 q - 4 q^{6}+O(q^{10}) \) Copy content Toggle raw display \( 40 q - 4 q^{6} - 12 q^{10} - 20 q^{12} - 8 q^{13} - 36 q^{16} - 24 q^{18} - 24 q^{21} - 76 q^{22} - 8 q^{25} - 84 q^{28} + 68 q^{30} - 40 q^{33} + 172 q^{36} - 40 q^{37} + 104 q^{40} + 236 q^{42} - 104 q^{45} + 240 q^{46} + 196 q^{48} + 304 q^{52} - 72 q^{57} + 180 q^{58} - 284 q^{60} + 48 q^{61} - 552 q^{66} - 372 q^{70} - 600 q^{72} + 104 q^{73} - 736 q^{76} - 408 q^{78} + 72 q^{81} - 720 q^{82} + 216 q^{85} - 580 q^{88} + 528 q^{90} + 368 q^{93} + 884 q^{96} + 72 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/60\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(37\) \(41\)
\(\chi(n)\) \(-1\) \(e\left(\frac{3}{4}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.84549 0.770813i 0.922747 0.385406i
\(3\) 1.12501 + 2.78107i 0.375005 + 0.927023i
\(4\) 2.81170 2.84506i 0.702924 0.711265i
\(5\) −3.86232 3.17529i −0.772465 0.635058i
\(6\) 4.21989 + 4.26527i 0.703315 + 0.710878i
\(7\) 4.75159 + 4.75159i 0.678799 + 0.678799i 0.959728 0.280930i \(-0.0906428\pi\)
−0.280930 + 0.959728i \(0.590643\pi\)
\(8\) 2.99596 7.41783i 0.374495 0.927229i
\(9\) −6.46869 + 6.25748i −0.718743 + 0.695276i
\(10\) −9.57545 2.88285i −0.957545 0.288285i
\(11\) −11.9496 −1.08633 −0.543164 0.839626i \(-0.682774\pi\)
−0.543164 + 0.839626i \(0.682774\pi\)
\(12\) 11.0755 + 4.61879i 0.922959 + 0.384899i
\(13\) −4.22368 4.22368i −0.324899 0.324899i 0.525744 0.850643i \(-0.323787\pi\)
−0.850643 + 0.525744i \(0.823787\pi\)
\(14\) 12.4316 + 5.10644i 0.887973 + 0.364746i
\(15\) 4.48553 14.3136i 0.299035 0.954242i
\(16\) −0.188739 15.9989i −0.0117962 0.999930i
\(17\) −9.35253 9.35253i −0.550149 0.550149i 0.376335 0.926484i \(-0.377184\pi\)
−0.926484 + 0.376335i \(0.877184\pi\)
\(18\) −7.11458 + 16.5343i −0.395254 + 0.918572i
\(19\) 1.48848 0.0783411 0.0391706 0.999233i \(-0.487528\pi\)
0.0391706 + 0.999233i \(0.487528\pi\)
\(20\) −19.8936 + 2.06060i −0.994678 + 0.103030i
\(21\) −7.86889 + 18.5601i −0.374709 + 0.883815i
\(22\) −22.0529 + 9.21092i −1.00241 + 0.418678i
\(23\) 11.6030 + 11.6030i 0.504478 + 0.504478i 0.912826 0.408348i \(-0.133895\pi\)
−0.408348 + 0.912826i \(0.633895\pi\)
\(24\) 24.0000 0.0132009i 1.00000 0.000550037i
\(25\) 4.83510 + 24.5280i 0.193404 + 0.981119i
\(26\) −11.0504 4.53911i −0.425017 0.174581i
\(27\) −24.6799 10.9501i −0.914069 0.405560i
\(28\) 26.8786 0.158538i 0.959950 0.00566206i
\(29\) 39.3671 1.35749 0.678743 0.734376i \(-0.262525\pi\)
0.678743 + 0.734376i \(0.262525\pi\)
\(30\) −2.75512 29.8732i −0.0918374 0.995774i
\(31\) 43.6522i 1.40813i 0.710133 + 0.704067i \(0.248635\pi\)
−0.710133 + 0.704067i \(0.751365\pi\)
\(32\) −12.6805 29.3804i −0.396264 0.918136i
\(33\) −13.4435 33.2327i −0.407378 1.00705i
\(34\) −24.4691 10.0510i −0.719679 0.295617i
\(35\) −3.26452 33.4399i −0.0932719 0.955424i
\(36\) −0.385062 + 35.9979i −0.0106962 + 0.999943i
\(37\) 49.1693 49.1693i 1.32890 1.32890i 0.422571 0.906330i \(-0.361128\pi\)
0.906330 0.422571i \(-0.138872\pi\)
\(38\) 2.74698 1.14734i 0.0722890 0.0301932i
\(39\) 6.99465 16.4981i 0.179350 0.423027i
\(40\) −35.1251 + 19.1370i −0.878128 + 0.478426i
\(41\) 27.0663i 0.660153i 0.943954 + 0.330077i \(0.107075\pi\)
−0.943954 + 0.330077i \(0.892925\pi\)
\(42\) −0.215630 + 40.3180i −0.00513405 + 0.959953i
\(43\) 8.84693 8.84693i 0.205742 0.205742i −0.596713 0.802455i \(-0.703527\pi\)
0.802455 + 0.596713i \(0.203527\pi\)
\(44\) −33.5987 + 33.9974i −0.763606 + 0.772668i
\(45\) 44.8535 3.62848i 0.996744 0.0806329i
\(46\) 30.3570 + 12.4695i 0.659935 + 0.271077i
\(47\) 15.0010 15.0010i 0.319170 0.319170i −0.529278 0.848448i \(-0.677537\pi\)
0.848448 + 0.529278i \(0.177537\pi\)
\(48\) 44.2817 18.5239i 0.922535 0.385914i
\(49\) 3.84477i 0.0784648i
\(50\) 27.8296 + 41.5393i 0.556592 + 0.830786i
\(51\) 15.4883 36.5318i 0.303692 0.716309i
\(52\) −23.8923 + 0.140924i −0.459468 + 0.00271008i
\(53\) −14.6333 + 14.6333i −0.276100 + 0.276100i −0.831550 0.555450i \(-0.812546\pi\)
0.555450 + 0.831550i \(0.312546\pi\)
\(54\) −53.9870 1.18482i −0.999759 0.0219410i
\(55\) 46.1533 + 37.9435i 0.839151 + 0.689881i
\(56\) 49.4821 21.0109i 0.883608 0.375195i
\(57\) 1.67456 + 4.13957i 0.0293783 + 0.0726240i
\(58\) 72.6517 30.3447i 1.25262 0.523184i
\(59\) 61.7260i 1.04620i 0.852270 + 0.523102i \(0.175225\pi\)
−0.852270 + 0.523102i \(0.824775\pi\)
\(60\) −28.1112 53.0072i −0.468520 0.883453i
\(61\) −84.6009 −1.38690 −0.693450 0.720505i \(-0.743910\pi\)
−0.693450 + 0.720505i \(0.743910\pi\)
\(62\) 33.6477 + 80.5598i 0.542704 + 1.29935i
\(63\) −60.4695 1.00356i −0.959834 0.0159295i
\(64\) −46.0485 44.4470i −0.719507 0.694485i
\(65\) 2.90182 + 29.7246i 0.0446434 + 0.457302i
\(66\) −50.4261 50.9683i −0.764031 0.772248i
\(67\) −65.7467 65.7467i −0.981293 0.981293i 0.0185347 0.999828i \(-0.494100\pi\)
−0.999828 + 0.0185347i \(0.994100\pi\)
\(68\) −52.9050 + 0.312049i −0.778014 + 0.00458896i
\(69\) −19.2152 + 45.3223i −0.278481 + 0.656844i
\(70\) −31.8005 59.1967i −0.454293 0.845667i
\(71\) 14.2794 0.201118 0.100559 0.994931i \(-0.467937\pi\)
0.100559 + 0.994931i \(0.467937\pi\)
\(72\) 27.0370 + 66.7308i 0.375514 + 0.926817i
\(73\) 16.0903 + 16.0903i 0.220415 + 0.220415i 0.808673 0.588258i \(-0.200186\pi\)
−0.588258 + 0.808673i \(0.700186\pi\)
\(74\) 52.8413 128.642i 0.714072 1.73841i
\(75\) −62.7745 + 41.0411i −0.836993 + 0.547214i
\(76\) 4.18516 4.23482i 0.0550678 0.0557213i
\(77\) −56.7797 56.7797i −0.737399 0.737399i
\(78\) 0.191673 35.8386i 0.00245735 0.459470i
\(79\) 9.32721 0.118066 0.0590330 0.998256i \(-0.481198\pi\)
0.0590330 + 0.998256i \(0.481198\pi\)
\(80\) −50.0721 + 62.3922i −0.625901 + 0.779902i
\(81\) 2.68783 80.9554i 0.0331831 0.999449i
\(82\) 20.8630 + 49.9507i 0.254427 + 0.609154i
\(83\) 12.7500 + 12.7500i 0.153615 + 0.153615i 0.779730 0.626116i \(-0.215356\pi\)
−0.626116 + 0.779730i \(0.715356\pi\)
\(84\) 30.6797 + 74.5728i 0.365234 + 0.887772i
\(85\) 6.42553 + 65.8195i 0.0755945 + 0.774347i
\(86\) 9.50762 23.1463i 0.110554 0.269143i
\(87\) 44.2885 + 109.483i 0.509063 + 1.25842i
\(88\) −35.8005 + 88.6403i −0.406824 + 1.00728i
\(89\) −52.4342 −0.589148 −0.294574 0.955629i \(-0.595178\pi\)
−0.294574 + 0.955629i \(0.595178\pi\)
\(90\) 79.9799 41.2700i 0.888666 0.458555i
\(91\) 40.1384i 0.441082i
\(92\) 65.6353 0.387136i 0.713427 0.00420800i
\(93\) −121.400 + 49.1093i −1.30537 + 0.528057i
\(94\) 16.1213 39.2471i 0.171503 0.417523i
\(95\) −5.74900 4.72636i −0.0605158 0.0497511i
\(96\) 67.4431 68.3186i 0.702533 0.711652i
\(97\) 6.90848 6.90848i 0.0712214 0.0712214i −0.670599 0.741820i \(-0.733963\pi\)
0.741820 + 0.670599i \(0.233963\pi\)
\(98\) −2.96360 7.09551i −0.0302408 0.0724031i
\(99\) 77.2983 74.7745i 0.780791 0.755298i
\(100\) 83.3784 + 55.2091i 0.833784 + 0.552091i
\(101\) 15.0065i 0.148579i −0.997237 0.0742894i \(-0.976331\pi\)
0.997237 0.0742894i \(-0.0236689\pi\)
\(102\) 0.424424 79.3577i 0.00416102 0.778017i
\(103\) −10.0417 + 10.0417i −0.0974926 + 0.0974926i −0.754171 0.656678i \(-0.771961\pi\)
0.656678 + 0.754171i \(0.271961\pi\)
\(104\) −43.9845 + 18.6766i −0.422928 + 0.179583i
\(105\) 89.3259 46.6991i 0.850723 0.444754i
\(106\) −15.7261 + 38.2852i −0.148360 + 0.361181i
\(107\) −15.4027 + 15.4027i −0.143950 + 0.143950i −0.775409 0.631459i \(-0.782456\pi\)
0.631459 + 0.775409i \(0.282456\pi\)
\(108\) −100.546 + 39.4273i −0.930981 + 0.365068i
\(109\) 15.6958i 0.143998i 0.997405 + 0.0719992i \(0.0229379\pi\)
−0.997405 + 0.0719992i \(0.977062\pi\)
\(110\) 114.423 + 34.4489i 1.04021 + 0.313172i
\(111\) 192.059 + 81.4271i 1.73027 + 0.733577i
\(112\) 75.1234 76.9170i 0.670744 0.686759i
\(113\) 33.3231 33.3231i 0.294895 0.294895i −0.544116 0.839010i \(-0.683135\pi\)
0.839010 + 0.544116i \(0.183135\pi\)
\(114\) 6.28123 + 6.34877i 0.0550985 + 0.0556910i
\(115\) −7.97168 81.6574i −0.0693190 0.710064i
\(116\) 110.688 112.002i 0.954209 0.965532i
\(117\) 53.7513 + 0.892063i 0.459413 + 0.00762447i
\(118\) 47.5792 + 113.915i 0.403214 + 0.965382i
\(119\) 88.8788i 0.746881i
\(120\) −92.7377 76.1559i −0.772814 0.634633i
\(121\) 21.7934 0.180110
\(122\) −156.130 + 65.2114i −1.27976 + 0.534520i
\(123\) −75.2732 + 30.4500i −0.611977 + 0.247561i
\(124\) 124.193 + 122.737i 1.00156 + 0.989812i
\(125\) 59.2087 110.088i 0.473670 0.880703i
\(126\) −112.370 + 44.7586i −0.891823 + 0.355227i
\(127\) 11.9832 + 11.9832i 0.0943557 + 0.0943557i 0.752709 0.658353i \(-0.228747\pi\)
−0.658353 + 0.752709i \(0.728747\pi\)
\(128\) −119.243 46.5320i −0.931582 0.363531i
\(129\) 34.5568 + 14.6510i 0.267882 + 0.113574i
\(130\) 28.2674 + 52.6199i 0.217442 + 0.404768i
\(131\) −228.815 −1.74668 −0.873341 0.487109i \(-0.838051\pi\)
−0.873341 + 0.487109i \(0.838051\pi\)
\(132\) −132.348 55.1927i −1.00264 0.418127i
\(133\) 7.07265 + 7.07265i 0.0531778 + 0.0531778i
\(134\) −172.013 70.6567i −1.28368 0.527289i
\(135\) 60.5518 + 120.659i 0.448532 + 0.893767i
\(136\) −97.3953 + 41.3557i −0.716142 + 0.304086i
\(137\) 155.485 + 155.485i 1.13492 + 1.13492i 0.989347 + 0.145578i \(0.0465042\pi\)
0.145578 + 0.989347i \(0.453496\pi\)
\(138\) −0.526552 + 98.4533i −0.00381559 + 0.713430i
\(139\) −220.188 −1.58409 −0.792043 0.610465i \(-0.790982\pi\)
−0.792043 + 0.610465i \(0.790982\pi\)
\(140\) −104.317 84.7349i −0.745123 0.605249i
\(141\) 58.5950 + 24.8424i 0.415568 + 0.176187i
\(142\) 26.3525 11.0067i 0.185581 0.0775123i
\(143\) 50.4714 + 50.4714i 0.352947 + 0.352947i
\(144\) 101.334 + 102.311i 0.703706 + 0.710491i
\(145\) −152.048 125.002i −1.04861 0.862082i
\(146\) 42.0971 + 17.2919i 0.288337 + 0.118438i
\(147\) 10.6926 4.32542i 0.0727386 0.0294247i
\(148\) −1.64054 278.139i −0.0110848 1.87932i
\(149\) 24.2943 0.163049 0.0815247 0.996671i \(-0.474021\pi\)
0.0815247 + 0.996671i \(0.474021\pi\)
\(150\) −84.2149 + 124.128i −0.561433 + 0.827522i
\(151\) 120.766i 0.799772i −0.916565 0.399886i \(-0.869050\pi\)
0.916565 0.399886i \(-0.130950\pi\)
\(152\) 4.45943 11.0413i 0.0293383 0.0726402i
\(153\) 119.022 + 1.97530i 0.777921 + 0.0129105i
\(154\) −148.553 61.0201i −0.964630 0.396234i
\(155\) 138.608 168.599i 0.894247 1.08773i
\(156\) −27.2711 66.2877i −0.174815 0.424921i
\(157\) −77.1260 + 77.1260i −0.491249 + 0.491249i −0.908700 0.417451i \(-0.862924\pi\)
0.417451 + 0.908700i \(0.362924\pi\)
\(158\) 17.2133 7.18953i 0.108945 0.0455034i
\(159\) −57.1589 24.2336i −0.359490 0.152412i
\(160\) −44.3151 + 153.741i −0.276969 + 0.960879i
\(161\) 110.265i 0.684878i
\(162\) −57.4411 151.474i −0.354575 0.935028i
\(163\) 179.764 179.764i 1.10285 1.10285i 0.108783 0.994065i \(-0.465305\pi\)
0.994065 0.108783i \(-0.0346955\pi\)
\(164\) 77.0052 + 76.1022i 0.469544 + 0.464038i
\(165\) −53.6003 + 171.042i −0.324850 + 1.03662i
\(166\) 33.3580 + 13.7022i 0.200952 + 0.0825434i
\(167\) 56.8272 56.8272i 0.340283 0.340283i −0.516191 0.856474i \(-0.672651\pi\)
0.856474 + 0.516191i \(0.172651\pi\)
\(168\) 114.101 + 113.975i 0.679172 + 0.678425i
\(169\) 133.321i 0.788882i
\(170\) 62.5928 + 116.517i 0.368193 + 0.685392i
\(171\) −9.62852 + 9.31414i −0.0563071 + 0.0544687i
\(172\) −0.295179 50.0449i −0.00171616 0.290959i
\(173\) 130.746 130.746i 0.755756 0.755756i −0.219791 0.975547i \(-0.570538\pi\)
0.975547 + 0.219791i \(0.0705377\pi\)
\(174\) 166.125 + 167.911i 0.954740 + 0.965007i
\(175\) −93.5725 + 139.521i −0.534700 + 0.797265i
\(176\) 2.25536 + 191.181i 0.0128145 + 1.08625i
\(177\) −171.664 + 69.4427i −0.969855 + 0.392331i
\(178\) −96.7670 + 40.4170i −0.543635 + 0.227062i
\(179\) 213.930i 1.19514i 0.801816 + 0.597571i \(0.203867\pi\)
−0.801816 + 0.597571i \(0.796133\pi\)
\(180\) 115.791 137.813i 0.643284 0.765628i
\(181\) 155.404 0.858588 0.429294 0.903165i \(-0.358762\pi\)
0.429294 + 0.903165i \(0.358762\pi\)
\(182\) −30.9392 74.0752i −0.169996 0.407007i
\(183\) −95.1771 235.281i −0.520094 1.28569i
\(184\) 120.831 51.3070i 0.656691 0.278842i
\(185\) −346.035 + 33.7811i −1.87046 + 0.182601i
\(186\) −186.188 + 184.207i −1.00101 + 0.990362i
\(187\) 111.759 + 111.759i 0.597643 + 0.597643i
\(188\) −0.500511 84.8569i −0.00266229 0.451366i
\(189\) −65.2381 169.299i −0.345175 0.895762i
\(190\) −14.2529 4.29106i −0.0750151 0.0225845i
\(191\) −102.576 −0.537047 −0.268524 0.963273i \(-0.586536\pi\)
−0.268524 + 0.963273i \(0.586536\pi\)
\(192\) 71.8050 178.068i 0.373985 0.927435i
\(193\) 138.213 + 138.213i 0.716129 + 0.716129i 0.967810 0.251681i \(-0.0809835\pi\)
−0.251681 + 0.967810i \(0.580983\pi\)
\(194\) 7.42441 18.0747i 0.0382701 0.0931685i
\(195\) −79.4017 + 41.5108i −0.407188 + 0.212876i
\(196\) −10.9386 10.8103i −0.0558093 0.0551548i
\(197\) −94.4283 94.4283i −0.479331 0.479331i 0.425586 0.904918i \(-0.360068\pi\)
−0.904918 + 0.425586i \(0.860068\pi\)
\(198\) 85.0165 197.578i 0.429376 0.997871i
\(199\) 185.280 0.931058 0.465529 0.885033i \(-0.345864\pi\)
0.465529 + 0.885033i \(0.345864\pi\)
\(200\) 196.430 + 37.6189i 0.982151 + 0.188094i
\(201\) 108.880 256.812i 0.541692 1.27767i
\(202\) −11.5672 27.6943i −0.0572632 0.137101i
\(203\) 187.056 + 187.056i 0.921459 + 0.921459i
\(204\) −60.3867 146.781i −0.296013 0.719516i
\(205\) 85.9433 104.539i 0.419235 0.509945i
\(206\) −10.7917 + 26.2723i −0.0523868 + 0.127535i
\(207\) −147.662 2.45061i −0.713342 0.0118387i
\(208\) −66.7771 + 68.3714i −0.321044 + 0.328709i
\(209\) −17.7868 −0.0851042
\(210\) 128.854 155.037i 0.613591 0.738269i
\(211\) 270.850i 1.28365i 0.766850 + 0.641826i \(0.221823\pi\)
−0.766850 + 0.641826i \(0.778177\pi\)
\(212\) 0.488243 + 82.7770i 0.00230303 + 0.390458i
\(213\) 16.0645 + 39.7120i 0.0754203 + 0.186441i
\(214\) −16.5530 + 40.2982i −0.0773504 + 0.188309i
\(215\) −62.2612 + 6.07816i −0.289587 + 0.0282705i
\(216\) −155.166 + 150.265i −0.718360 + 0.695671i
\(217\) −207.417 + 207.417i −0.955840 + 0.955840i
\(218\) 12.0985 + 28.9666i 0.0554979 + 0.132874i
\(219\) −26.6464 + 62.8500i −0.121673 + 0.286986i
\(220\) 237.720 24.6234i 1.08055 0.111925i
\(221\) 79.0043i 0.357485i
\(222\) 417.210 + 2.23134i 1.87932 + 0.0100511i
\(223\) −173.313 + 173.313i −0.777190 + 0.777190i −0.979352 0.202162i \(-0.935203\pi\)
0.202162 + 0.979352i \(0.435203\pi\)
\(224\) 79.3511 199.856i 0.354246 0.892214i
\(225\) −184.760 128.408i −0.821156 0.570704i
\(226\) 35.8117 87.1835i 0.158459 0.385768i
\(227\) 192.265 192.265i 0.846983 0.846983i −0.142773 0.989755i \(-0.545602\pi\)
0.989755 + 0.142773i \(0.0456019\pi\)
\(228\) 16.4857 + 6.87497i 0.0723056 + 0.0301534i
\(229\) 74.6665i 0.326054i 0.986622 + 0.163027i \(0.0521258\pi\)
−0.986622 + 0.163027i \(0.947874\pi\)
\(230\) −77.6542 144.554i −0.337627 0.628494i
\(231\) 94.0303 221.786i 0.407058 0.960113i
\(232\) 117.942 292.018i 0.508371 1.25870i
\(233\) −148.778 + 148.778i −0.638532 + 0.638532i −0.950193 0.311661i \(-0.899115\pi\)
0.311661 + 0.950193i \(0.399115\pi\)
\(234\) 99.8853 39.7859i 0.426860 0.170025i
\(235\) −105.571 + 10.3062i −0.449238 + 0.0438562i
\(236\) 175.614 + 173.555i 0.744128 + 0.735402i
\(237\) 10.4932 + 25.9396i 0.0442753 + 0.109450i
\(238\) −68.5089 164.025i −0.287853 0.689182i
\(239\) 214.211i 0.896278i 0.893964 + 0.448139i \(0.147913\pi\)
−0.893964 + 0.448139i \(0.852087\pi\)
\(240\) −229.849 69.0619i −0.957703 0.287758i
\(241\) 167.934 0.696821 0.348411 0.937342i \(-0.386722\pi\)
0.348411 + 0.937342i \(0.386722\pi\)
\(242\) 40.2195 16.7986i 0.166196 0.0694157i
\(243\) 228.166 83.6009i 0.938956 0.344037i
\(244\) −237.872 + 240.695i −0.974885 + 0.986453i
\(245\) −12.2083 + 14.8498i −0.0498296 + 0.0606113i
\(246\) −115.445 + 114.217i −0.469289 + 0.464296i
\(247\) −6.28687 6.28687i −0.0254529 0.0254529i
\(248\) 323.805 + 130.780i 1.30566 + 0.527339i
\(249\) −21.1147 + 49.8027i −0.0847982 + 0.200011i
\(250\) 24.4122 248.805i 0.0976487 0.995221i
\(251\) −166.809 −0.664578 −0.332289 0.943178i \(-0.607821\pi\)
−0.332289 + 0.943178i \(0.607821\pi\)
\(252\) −172.877 + 169.218i −0.686020 + 0.671499i
\(253\) −138.651 138.651i −0.548029 0.548029i
\(254\) 31.3516 + 12.8781i 0.123432 + 0.0507011i
\(255\) −175.820 + 91.9177i −0.689489 + 0.360461i
\(256\) −255.929 + 6.03922i −0.999722 + 0.0235907i
\(257\) −16.3199 16.3199i −0.0635014 0.0635014i 0.674643 0.738144i \(-0.264298\pi\)
−0.738144 + 0.674643i \(0.764298\pi\)
\(258\) 75.0676 + 0.401479i 0.290960 + 0.00155612i
\(259\) 467.265 1.80411
\(260\) 92.7274 + 75.3208i 0.356644 + 0.289695i
\(261\) −254.653 + 246.339i −0.975683 + 0.943827i
\(262\) −422.277 + 176.374i −1.61175 + 0.673183i
\(263\) −121.290 121.290i −0.461180 0.461180i 0.437862 0.899042i \(-0.355736\pi\)
−0.899042 + 0.437862i \(0.855736\pi\)
\(264\) −286.791 + 0.157746i −1.08633 + 0.000597521i
\(265\) 102.984 10.0536i 0.388617 0.0379382i
\(266\) 18.5042 + 7.60085i 0.0695648 + 0.0285746i
\(267\) −58.9892 145.823i −0.220933 0.546154i
\(268\) −371.913 + 2.19365i −1.38773 + 0.00818526i
\(269\) 174.671 0.649336 0.324668 0.945828i \(-0.394747\pi\)
0.324668 + 0.945828i \(0.394747\pi\)
\(270\) 204.753 + 176.000i 0.758345 + 0.651853i
\(271\) 306.881i 1.13240i −0.824268 0.566200i \(-0.808413\pi\)
0.824268 0.566200i \(-0.191587\pi\)
\(272\) −147.865 + 151.395i −0.543621 + 0.556600i
\(273\) 111.628 45.1563i 0.408893 0.165408i
\(274\) 406.796 + 167.096i 1.48466 + 0.609841i
\(275\) −57.7775 293.100i −0.210100 1.06582i
\(276\) 74.9173 + 182.101i 0.271439 + 0.659786i
\(277\) 28.5949 28.5949i 0.103231 0.103231i −0.653605 0.756836i \(-0.726744\pi\)
0.756836 + 0.653605i \(0.226744\pi\)
\(278\) −406.356 + 169.724i −1.46171 + 0.610517i
\(279\) −273.153 282.372i −0.979042 1.01209i
\(280\) −257.832 75.9687i −0.920827 0.271317i
\(281\) 42.3210i 0.150609i −0.997161 0.0753043i \(-0.976007\pi\)
0.997161 0.0753043i \(-0.0239928\pi\)
\(282\) 127.286 + 0.680754i 0.451368 + 0.00241402i
\(283\) −341.834 + 341.834i −1.20789 + 1.20789i −0.236185 + 0.971708i \(0.575897\pi\)
−0.971708 + 0.236185i \(0.924103\pi\)
\(284\) 40.1493 40.6257i 0.141371 0.143048i
\(285\) 6.67662 21.3056i 0.0234267 0.0747564i
\(286\) 132.049 + 54.2407i 0.461709 + 0.189653i
\(287\) −128.608 + 128.608i −0.448111 + 0.448111i
\(288\) 265.873 + 110.705i 0.923170 + 0.384391i
\(289\) 114.060i 0.394672i
\(290\) −376.957 113.489i −1.29985 0.391342i
\(291\) 26.9851 + 11.4408i 0.0927322 + 0.0393155i
\(292\) 91.0189 0.536856i 0.311708 0.00183855i
\(293\) 252.918 252.918i 0.863203 0.863203i −0.128506 0.991709i \(-0.541018\pi\)
0.991709 + 0.128506i \(0.0410181\pi\)
\(294\) 16.3990 16.2245i 0.0557789 0.0551854i
\(295\) 195.998 238.406i 0.664400 0.808156i
\(296\) −217.421 512.039i −0.734529 1.72986i
\(297\) 294.915 + 130.850i 0.992979 + 0.440571i
\(298\) 44.8351 18.7264i 0.150453 0.0628403i
\(299\) 98.0148i 0.327809i
\(300\) −59.7384 + 293.992i −0.199128 + 0.979974i
\(301\) 84.0739 0.279315
\(302\) −93.0877 222.872i −0.308237 0.737987i
\(303\) 41.7340 16.8825i 0.137736 0.0557177i
\(304\) −0.280934 23.8140i −0.000924125 0.0783357i
\(305\) 326.756 + 268.632i 1.07133 + 0.880761i
\(306\) 221.177 88.0982i 0.722800 0.287903i
\(307\) 281.593 + 281.593i 0.917240 + 0.917240i 0.996828 0.0795878i \(-0.0253604\pi\)
−0.0795878 + 0.996828i \(0.525360\pi\)
\(308\) −321.189 + 1.89447i −1.04282 + 0.00615086i
\(309\) −39.2239 16.6297i −0.126938 0.0538177i
\(310\) 125.842 417.989i 0.405943 1.34835i
\(311\) 318.688 1.02472 0.512360 0.858771i \(-0.328771\pi\)
0.512360 + 0.858771i \(0.328771\pi\)
\(312\) −101.424 101.313i −0.325077 0.324720i
\(313\) −165.571 165.571i −0.528979 0.528979i 0.391289 0.920268i \(-0.372029\pi\)
−0.920268 + 0.391289i \(0.872029\pi\)
\(314\) −82.8859 + 201.785i −0.263968 + 0.642629i
\(315\) 230.366 + 195.884i 0.731322 + 0.621855i
\(316\) 26.2253 26.5365i 0.0829914 0.0839762i
\(317\) −6.74356 6.74356i −0.0212731 0.0212731i 0.696390 0.717663i \(-0.254788\pi\)
−0.717663 + 0.696390i \(0.754788\pi\)
\(318\) −124.166 0.664069i −0.390459 0.00208827i
\(319\) −470.422 −1.47468
\(320\) 36.7221 + 317.886i 0.114756 + 0.993394i
\(321\) −60.1642 25.5077i −0.187427 0.0794633i
\(322\) 84.9940 + 203.494i 0.263956 + 0.631969i
\(323\) −13.9211 13.9211i −0.0430993 0.0430993i
\(324\) −222.766 235.269i −0.687548 0.726139i
\(325\) 83.1765 124.020i 0.255928 0.381601i
\(326\) 193.189 470.319i 0.592605 1.44270i
\(327\) −43.6512 + 17.6580i −0.133490 + 0.0540001i
\(328\) 200.773 + 81.0894i 0.612113 + 0.247224i
\(329\) 142.557 0.433304
\(330\) 32.9226 + 356.974i 0.0997656 + 1.08174i
\(331\) 278.406i 0.841105i 0.907268 + 0.420553i \(0.138164\pi\)
−0.907268 + 0.420553i \(0.861836\pi\)
\(332\) 72.1238 0.425407i 0.217240 0.00128135i
\(333\) −10.3848 + 625.737i −0.0311856 + 1.87909i
\(334\) 61.0711 148.677i 0.182848 0.445142i
\(335\) 45.1704 + 462.700i 0.134837 + 1.38119i
\(336\) 298.426 + 122.391i 0.888173 + 0.364258i
\(337\) 282.964 282.964i 0.839656 0.839656i −0.149157 0.988813i \(-0.547656\pi\)
0.988813 + 0.149157i \(0.0476560\pi\)
\(338\) −102.766 246.043i −0.304040 0.727938i
\(339\) 130.163 + 55.1849i 0.383961 + 0.162787i
\(340\) 205.327 + 166.783i 0.603903 + 0.490539i
\(341\) 521.627i 1.52970i
\(342\) −10.5899 + 24.6110i −0.0309647 + 0.0719619i
\(343\) 251.097 251.097i 0.732060 0.732060i
\(344\) −39.1200 92.1300i −0.113721 0.267820i
\(345\) 218.127 114.035i 0.632251 0.330538i
\(346\) 140.510 342.071i 0.406098 0.988644i
\(347\) 36.0256 36.0256i 0.103820 0.103820i −0.653289 0.757109i \(-0.726611\pi\)
0.757109 + 0.653289i \(0.226611\pi\)
\(348\) 436.010 + 181.828i 1.25290 + 0.522495i
\(349\) 382.830i 1.09693i 0.836173 + 0.548467i \(0.184788\pi\)
−0.836173 + 0.548467i \(0.815212\pi\)
\(350\) −65.1427 + 329.613i −0.186122 + 0.941750i
\(351\) 57.9901 + 150.490i 0.165214 + 0.428745i
\(352\) 151.527 + 351.084i 0.430474 + 0.997398i
\(353\) −215.726 + 215.726i −0.611121 + 0.611121i −0.943238 0.332117i \(-0.892237\pi\)
0.332117 + 0.943238i \(0.392237\pi\)
\(354\) −263.278 + 260.477i −0.743724 + 0.735811i
\(355\) −55.1517 45.3412i −0.155357 0.127722i
\(356\) −147.429 + 149.178i −0.414126 + 0.419041i
\(357\) 247.178 99.9899i 0.692375 0.280084i
\(358\) 164.900 + 394.807i 0.460615 + 1.10281i
\(359\) 473.986i 1.32030i −0.751136 0.660148i \(-0.770494\pi\)
0.751136 0.660148i \(-0.229506\pi\)
\(360\) 107.464 343.586i 0.298510 0.954406i
\(361\) −358.784 −0.993863
\(362\) 286.798 119.788i 0.792260 0.330905i
\(363\) 24.5178 + 60.6088i 0.0675422 + 0.166966i
\(364\) −114.196 112.857i −0.313726 0.310047i
\(365\) −11.0546 113.237i −0.0302866 0.310239i
\(366\) −357.006 360.846i −0.975427 0.985917i
\(367\) −249.323 249.323i −0.679354 0.679354i 0.280500 0.959854i \(-0.409500\pi\)
−0.959854 + 0.280500i \(0.909500\pi\)
\(368\) 183.445 187.825i 0.498492 0.510394i
\(369\) −169.367 175.083i −0.458989 0.474481i
\(370\) −612.566 + 329.071i −1.65558 + 0.889380i
\(371\) −139.063 −0.374833
\(372\) −201.620 + 483.470i −0.541989 + 1.29965i
\(373\) −108.084 108.084i −0.289769 0.289769i 0.547220 0.836989i \(-0.315686\pi\)
−0.836989 + 0.547220i \(0.815686\pi\)
\(374\) 292.396 + 120.105i 0.781808 + 0.321138i
\(375\) 372.772 + 40.8131i 0.994060 + 0.108835i
\(376\) −66.3324 156.217i −0.176416 0.415471i
\(377\) −166.274 166.274i −0.441045 0.441045i
\(378\) −250.894 262.154i −0.663742 0.693529i
\(379\) −60.0656 −0.158484 −0.0792422 0.996855i \(-0.525250\pi\)
−0.0792422 + 0.996855i \(0.525250\pi\)
\(380\) −29.6112 + 3.06717i −0.0779242 + 0.00807150i
\(381\) −19.8448 + 46.8073i −0.0520861 + 0.122854i
\(382\) −189.303 + 79.0669i −0.495559 + 0.206981i
\(383\) −375.372 375.372i −0.980084 0.980084i 0.0197220 0.999806i \(-0.493722\pi\)
−0.999806 + 0.0197220i \(0.993722\pi\)
\(384\) −4.74093 383.971i −0.0123462 0.999924i
\(385\) 39.0097 + 399.593i 0.101324 + 1.03790i
\(386\) 361.607 + 148.535i 0.936806 + 0.384805i
\(387\) −1.86852 + 112.587i −0.00482821 + 0.290924i
\(388\) −0.230503 39.0796i −0.000594079 0.100721i
\(389\) −464.374 −1.19376 −0.596882 0.802329i \(-0.703594\pi\)
−0.596882 + 0.802329i \(0.703594\pi\)
\(390\) −114.538 + 137.812i −0.293688 + 0.353364i
\(391\) 217.035i 0.555076i
\(392\) −28.5199 11.5188i −0.0727548 0.0293846i
\(393\) −257.421 636.351i −0.655014 1.61921i
\(394\) −247.053 101.480i −0.627039 0.257564i
\(395\) −36.0247 29.6166i −0.0912018 0.0749787i
\(396\) 4.60135 430.162i 0.0116196 1.08627i
\(397\) −125.935 + 125.935i −0.317215 + 0.317215i −0.847697 0.530481i \(-0.822011\pi\)
0.530481 + 0.847697i \(0.322011\pi\)
\(398\) 341.934 142.817i 0.859131 0.358836i
\(399\) −11.7127 + 27.6264i −0.0293551 + 0.0692390i
\(400\) 391.508 81.9855i 0.978770 0.204964i
\(401\) 508.065i 1.26699i 0.773745 + 0.633497i \(0.218381\pi\)
−0.773745 + 0.633497i \(0.781619\pi\)
\(402\) 2.98363 557.871i 0.00742196 1.38774i
\(403\) 184.373 184.373i 0.457501 0.457501i
\(404\) −42.6943 42.1936i −0.105679 0.104440i
\(405\) −267.438 + 304.141i −0.660341 + 0.750966i
\(406\) 489.397 + 201.026i 1.20541 + 0.495138i
\(407\) −587.555 + 587.555i −1.44362 + 1.44362i
\(408\) −224.584 224.337i −0.550451 0.549846i
\(409\) 583.921i 1.42768i 0.700309 + 0.713840i \(0.253046\pi\)
−0.700309 + 0.713840i \(0.746954\pi\)
\(410\) 78.0279 259.172i 0.190312 0.632126i
\(411\) −257.491 + 607.336i −0.626499 + 1.47770i
\(412\) 0.335045 + 56.8037i 0.000813215 + 0.137873i
\(413\) −293.297 + 293.297i −0.710162 + 0.710162i
\(414\) −274.398 + 109.297i −0.662796 + 0.264002i
\(415\) −8.75973 89.7297i −0.0211078 0.216216i
\(416\) −70.5351 + 177.652i −0.169556 + 0.427047i
\(417\) −247.715 612.358i −0.594040 1.46848i
\(418\) −32.8254 + 13.7103i −0.0785297 + 0.0327997i
\(419\) 283.902i 0.677571i 0.940864 + 0.338786i \(0.110016\pi\)
−0.940864 + 0.338786i \(0.889984\pi\)
\(420\) 118.295 385.441i 0.281656 0.917717i
\(421\) −468.185 −1.11208 −0.556039 0.831156i \(-0.687679\pi\)
−0.556039 + 0.831156i \(0.687679\pi\)
\(422\) 208.775 + 499.853i 0.494728 + 1.18449i
\(423\) −3.16828 + 190.905i −0.00749003 + 0.451312i
\(424\) 64.7066 + 152.388i 0.152610 + 0.359406i
\(425\) 184.178 274.619i 0.433361 0.646163i
\(426\) 60.2575 + 60.9055i 0.141449 + 0.142971i
\(427\) −401.989 401.989i −0.941425 0.941425i
\(428\) 0.513914 + 87.1293i 0.00120073 + 0.203573i
\(429\) −83.5834 + 197.145i −0.194833 + 0.459546i
\(430\) −110.218 + 59.2090i −0.256320 + 0.137695i
\(431\) 849.775 1.97164 0.985818 0.167821i \(-0.0536730\pi\)
0.985818 + 0.167821i \(0.0536730\pi\)
\(432\) −170.532 + 396.917i −0.394749 + 0.918789i
\(433\) 153.887 + 153.887i 0.355398 + 0.355398i 0.862113 0.506715i \(-0.169141\pi\)
−0.506715 + 0.862113i \(0.669141\pi\)
\(434\) −222.907 + 542.667i −0.513612 + 1.25039i
\(435\) 176.582 563.486i 0.405936 1.29537i
\(436\) 44.6556 + 44.1319i 0.102421 + 0.101220i
\(437\) 17.2708 + 17.2708i 0.0395214 + 0.0395214i
\(438\) −0.730188 + 136.529i −0.00166710 + 0.311709i
\(439\) 55.5775 0.126600 0.0633001 0.997995i \(-0.479837\pi\)
0.0633001 + 0.997995i \(0.479837\pi\)
\(440\) 419.732 228.680i 0.953936 0.519728i
\(441\) 24.0586 + 24.8706i 0.0545547 + 0.0563960i
\(442\) 60.8975 + 145.802i 0.137777 + 0.329868i
\(443\) 543.074 + 543.074i 1.22590 + 1.22590i 0.965501 + 0.260398i \(0.0838539\pi\)
0.260398 + 0.965501i \(0.416146\pi\)
\(444\) 771.678 317.473i 1.73801 0.715028i
\(445\) 202.518 + 166.494i 0.455096 + 0.374143i
\(446\) −186.257 + 453.441i −0.417616 + 1.01668i
\(447\) 27.3315 + 67.5643i 0.0611443 + 0.151150i
\(448\) −7.60946 429.998i −0.0169854 0.959816i
\(449\) −36.3462 −0.0809493 −0.0404746 0.999181i \(-0.512887\pi\)
−0.0404746 + 0.999181i \(0.512887\pi\)
\(450\) −439.952 94.5613i −0.977672 0.210136i
\(451\) 323.432i 0.717144i
\(452\) −1.11183 188.501i −0.00245981 0.417037i
\(453\) 335.857 135.863i 0.741407 0.299918i
\(454\) 206.624 503.024i 0.455118 1.10798i
\(455\) −127.451 + 155.028i −0.280112 + 0.340720i
\(456\) 35.7235 0.0196493i 0.0783411 4.30905e-5i
\(457\) 465.155 465.155i 1.01784 1.01784i 0.0180061 0.999838i \(-0.494268\pi\)
0.999838 0.0180061i \(-0.00573181\pi\)
\(458\) 57.5539 + 137.797i 0.125663 + 0.300866i
\(459\) 128.408 + 333.230i 0.279756 + 0.725992i
\(460\) −254.734 206.916i −0.553770 0.449817i
\(461\) 69.6948i 0.151182i −0.997139 0.0755909i \(-0.975916\pi\)
0.997139 0.0755909i \(-0.0240843\pi\)
\(462\) 2.57670 481.785i 0.00557727 1.04282i
\(463\) −453.386 + 453.386i −0.979236 + 0.979236i −0.999789 0.0205531i \(-0.993457\pi\)
0.0205531 + 0.999789i \(0.493457\pi\)
\(464\) −7.43010 629.830i −0.0160131 1.35739i
\(465\) 624.821 + 195.803i 1.34370 + 0.421082i
\(466\) −159.889 + 389.249i −0.343109 + 0.835298i
\(467\) 434.371 434.371i 0.930130 0.930130i −0.0675833 0.997714i \(-0.521529\pi\)
0.997714 + 0.0675833i \(0.0215288\pi\)
\(468\) 153.670 150.418i 0.328355 0.321405i
\(469\) 624.802i 1.33220i
\(470\) −186.887 + 100.396i −0.397631 + 0.213608i
\(471\) −301.261 127.725i −0.639619 0.271178i
\(472\) 457.873 + 184.929i 0.970071 + 0.391798i
\(473\) −105.717 + 105.717i −0.223504 + 0.223504i
\(474\) 39.3598 + 39.7831i 0.0830376 + 0.0839305i
\(475\) 7.19695 + 36.5094i 0.0151515 + 0.0768620i
\(476\) −252.866 249.900i −0.531230 0.525000i
\(477\) 3.09063 186.226i 0.00647930 0.390411i
\(478\) 165.116 + 395.324i 0.345431 + 0.827038i
\(479\) 307.039i 0.641000i −0.947248 0.320500i \(-0.896149\pi\)
0.947248 0.320500i \(-0.103851\pi\)
\(480\) −477.418 + 49.7171i −0.994621 + 0.103577i
\(481\) −415.351 −0.863516
\(482\) 309.921 129.446i 0.642990 0.268559i
\(483\) −306.656 + 124.050i −0.634898 + 0.256832i
\(484\) 61.2763 62.0034i 0.126604 0.128106i
\(485\) −48.6192 + 4.74637i −0.100246 + 0.00978634i
\(486\) 356.639 330.158i 0.733825 0.679338i
\(487\) 250.434 + 250.434i 0.514237 + 0.514237i 0.915822 0.401585i \(-0.131540\pi\)
−0.401585 + 0.915822i \(0.631540\pi\)
\(488\) −253.461 + 627.555i −0.519386 + 1.28597i
\(489\) 702.174 + 297.700i 1.43594 + 0.608793i
\(490\) −11.0839 + 36.8154i −0.0226202 + 0.0751335i
\(491\) −291.754 −0.594203 −0.297102 0.954846i \(-0.596020\pi\)
−0.297102 + 0.954846i \(0.596020\pi\)
\(492\) −125.013 + 299.773i −0.254092 + 0.609294i
\(493\) −368.182 368.182i −0.746819 0.746819i
\(494\) −16.4484 6.75638i −0.0332963 0.0136769i
\(495\) −535.982 + 43.3590i −1.08279 + 0.0875939i
\(496\) 698.386 8.23886i 1.40804 0.0166106i
\(497\) 67.8498 + 67.8498i 0.136519 + 0.136519i
\(498\) −0.578605 + 108.186i −0.00116186 + 0.217241i
\(499\) 421.977 0.845646 0.422823 0.906212i \(-0.361039\pi\)
0.422823 + 0.906212i \(0.361039\pi\)
\(500\) −146.730 477.986i −0.293459 0.955972i
\(501\) 221.972 + 94.1089i 0.443057 + 0.187842i
\(502\) −307.845 + 128.579i −0.613238 + 0.256133i
\(503\) −288.062 288.062i −0.572688 0.572688i 0.360191 0.932879i \(-0.382712\pi\)
−0.932879 + 0.360191i \(0.882712\pi\)
\(504\) −188.608 + 445.546i −0.374223 + 0.884021i
\(505\) −47.6498 + 57.9598i −0.0943561 + 0.114772i
\(506\) −362.755 149.006i −0.716906 0.294478i
\(507\) 370.775 149.988i 0.731311 0.295834i
\(508\) 67.7859 0.399821i 0.133437 0.000787049i
\(509\) 808.790 1.58898 0.794489 0.607278i \(-0.207739\pi\)
0.794489 + 0.607278i \(0.207739\pi\)
\(510\) −253.623 + 305.158i −0.497300 + 0.598348i
\(511\) 152.909i 0.299235i
\(512\) −467.660 + 208.418i −0.913398 + 0.407067i
\(513\) −36.7355 16.2990i −0.0716091 0.0317720i
\(514\) −42.6977 17.5386i −0.0830695 0.0341219i
\(515\) 70.6699 6.89904i 0.137223 0.0133962i
\(516\) 138.846 57.1221i 0.269082 0.110702i
\(517\) −179.256 + 179.256i −0.346723 + 0.346723i
\(518\) 862.335 360.174i 1.66474 0.695316i
\(519\) 510.704 + 216.522i 0.984015 + 0.417191i
\(520\) 229.186 + 67.5285i 0.440743 + 0.129863i
\(521\) 105.970i 0.203397i 0.994815 + 0.101699i \(0.0324277\pi\)
−0.994815 + 0.101699i \(0.967572\pi\)
\(522\) −280.080 + 650.907i −0.536552 + 1.24695i
\(523\) 229.588 229.588i 0.438982 0.438982i −0.452687 0.891669i \(-0.649535\pi\)
0.891669 + 0.452687i \(0.149535\pi\)
\(524\) −643.359 + 650.994i −1.22778 + 1.24235i
\(525\) −493.289 103.268i −0.939598 0.196701i
\(526\) −317.332 130.348i −0.603294 0.247810i
\(527\) 408.258 408.258i 0.774684 0.774684i
\(528\) −529.149 + 221.353i −1.00218 + 0.419229i
\(529\) 259.741i 0.491004i
\(530\) 182.306 97.9349i 0.343974 0.184783i
\(531\) −386.250 399.286i −0.727400 0.751952i
\(532\) 40.0083 0.235980i 0.0752035 0.000443572i
\(533\) 114.319 114.319i 0.214483 0.214483i
\(534\) −221.267 223.646i −0.414357 0.418813i
\(535\) 108.398 10.5822i 0.202614 0.0197798i
\(536\) −684.672 + 290.724i −1.27737 + 0.542395i
\(537\) −594.955 + 240.675i −1.10792 + 0.448184i
\(538\) 322.355 134.639i 0.599173 0.250258i
\(539\) 45.9436i 0.0852385i
\(540\) 513.534 + 166.981i 0.950989 + 0.309225i
\(541\) 1053.67 1.94763 0.973816 0.227338i \(-0.0730021\pi\)
0.973816 + 0.227338i \(0.0730021\pi\)
\(542\) −236.547 566.346i −0.436434 1.04492i
\(543\) 174.832 + 432.190i 0.321975 + 0.795931i
\(544\) −156.186 + 393.375i −0.287107 + 0.723116i
\(545\) 49.8388 60.6224i 0.0914473 0.111234i
\(546\) 171.201 169.380i 0.313555 0.310219i
\(547\) −559.528 559.528i −1.02290 1.02290i −0.999732 0.0231709i \(-0.992624\pi\)
−0.0231709 0.999732i \(-0.507376\pi\)
\(548\) 879.539 5.18778i 1.60500 0.00946675i
\(549\) 547.256 529.388i 0.996824 0.964278i
\(550\) −332.553 496.379i −0.604642 0.902507i
\(551\) 58.5972 0.106347
\(552\) 278.625 + 278.319i 0.504756 + 0.504201i
\(553\) 44.3191 + 44.3191i 0.0801430 + 0.0801430i
\(554\) 30.7304 74.8131i 0.0554701 0.135042i
\(555\) −483.241 924.342i −0.870705 1.66548i
\(556\) −619.101 + 626.448i −1.11349 + 1.12671i
\(557\) 616.817 + 616.817i 1.10739 + 1.10739i 0.993492 + 0.113899i \(0.0363340\pi\)
0.113899 + 0.993492i \(0.463666\pi\)
\(558\) −721.758 310.567i −1.29347 0.556571i
\(559\) −74.7332 −0.133691
\(560\) −534.384 + 58.5400i −0.954258 + 0.104536i
\(561\) −185.079 + 436.541i −0.329910 + 0.778147i
\(562\) −32.6216 78.1032i −0.0580455 0.138974i
\(563\) −170.898 170.898i −0.303550 0.303550i 0.538851 0.842401i \(-0.318858\pi\)
−0.842401 + 0.538851i \(0.818858\pi\)
\(564\) 235.430 96.8571i 0.417428 0.171732i
\(565\) −234.515 + 22.8942i −0.415071 + 0.0405207i
\(566\) −367.362 + 894.342i −0.649050 + 1.58011i
\(567\) 397.438 371.895i 0.700949 0.655900i
\(568\) 42.7805 105.922i 0.0753177 0.186483i
\(569\) −609.836 −1.07177 −0.535884 0.844291i \(-0.680022\pi\)
−0.535884 + 0.844291i \(0.680022\pi\)
\(570\) −4.10095 44.4657i −0.00719464 0.0780100i
\(571\) 478.800i 0.838529i 0.907864 + 0.419265i \(0.137712\pi\)
−0.907864 + 0.419265i \(0.862288\pi\)
\(572\) 285.504 1.68399i 0.499134 0.00294404i
\(573\) −115.399 285.271i −0.201395 0.497855i
\(574\) −138.212 + 336.478i −0.240788 + 0.586198i
\(575\) −228.496 + 340.700i −0.397385 + 0.592521i
\(576\) 576.000 0.633642i 0.999999 0.00110007i
\(577\) −162.684 + 162.684i −0.281947 + 0.281947i −0.833885 0.551938i \(-0.813889\pi\)
0.551938 + 0.833885i \(0.313889\pi\)
\(578\) −87.9192 210.498i −0.152109 0.364183i
\(579\) −228.888 + 539.871i −0.395316 + 0.932419i
\(580\) −783.152 + 81.1200i −1.35026 + 0.139862i
\(581\) 121.166i 0.208547i
\(582\) 58.6195 + 0.313511i 0.100721 + 0.000538679i
\(583\) 174.862 174.862i 0.299935 0.299935i
\(584\) 167.561 71.1493i 0.286919 0.121831i
\(585\) −204.772 174.121i −0.350038 0.297643i
\(586\) 271.807 661.712i 0.463834 1.12920i
\(587\) −785.786 + 785.786i −1.33865 + 1.33865i −0.441275 + 0.897372i \(0.645474\pi\)
−0.897372 + 0.441275i \(0.854526\pi\)
\(588\) 17.7582 42.5828i 0.0302010 0.0724197i
\(589\) 64.9754i 0.110315i
\(590\) 177.947 591.054i 0.301604 1.00179i
\(591\) 156.378 368.845i 0.264600 0.624103i
\(592\) −795.935 777.374i −1.34448 1.31313i
\(593\) 646.718 646.718i 1.09059 1.09059i 0.0951217 0.995466i \(-0.469676\pi\)
0.995466 0.0951217i \(-0.0303240\pi\)
\(594\) 645.124 + 14.1581i 1.08607 + 0.0238352i
\(595\) −282.216 + 343.279i −0.474312 + 0.576939i
\(596\) 68.3083 69.1189i 0.114611 0.115971i
\(597\) 208.443 + 515.278i 0.349151 + 0.863112i
\(598\) −75.5510 180.886i −0.126340 0.302484i
\(599\) 300.352i 0.501423i −0.968062 0.250711i \(-0.919336\pi\)
0.968062 0.250711i \(-0.0806645\pi\)
\(600\) 116.366 + 588.608i 0.193943 + 0.981013i
\(601\) 7.74118 0.0128805 0.00644025 0.999979i \(-0.497950\pi\)
0.00644025 + 0.999979i \(0.497950\pi\)
\(602\) 155.158 64.8053i 0.257737 0.107650i
\(603\) 836.703 + 13.8860i 1.38757 + 0.0230282i
\(604\) −343.585 339.556i −0.568850 0.562179i
\(605\) −84.1730 69.2002i −0.139129 0.114380i
\(606\) 64.0066 63.3256i 0.105621 0.104498i
\(607\) 424.929 + 424.929i 0.700047 + 0.700047i 0.964421 0.264373i \(-0.0851650\pi\)
−0.264373 + 0.964421i \(0.585165\pi\)
\(608\) −18.8746 43.7321i −0.0310438 0.0719278i
\(609\) −309.775 + 730.657i −0.508662 + 1.19977i
\(610\) 810.091 + 243.891i 1.32802 + 0.399822i
\(611\) −126.719 −0.207396
\(612\) 340.273 333.071i 0.556002 0.544233i
\(613\) 714.397 + 714.397i 1.16541 + 1.16541i 0.983273 + 0.182138i \(0.0583017\pi\)
0.182138 + 0.983273i \(0.441698\pi\)
\(614\) 736.733 + 302.622i 1.19989 + 0.492870i
\(615\) 387.417 + 121.407i 0.629946 + 0.197409i
\(616\) −591.292 + 251.073i −0.959889 + 0.407586i
\(617\) −464.917 464.917i −0.753513 0.753513i 0.221620 0.975133i \(-0.428865\pi\)
−0.975133 + 0.221620i \(0.928865\pi\)
\(618\) −85.2058 0.455701i −0.137873 0.000737380i
\(619\) −667.181 −1.07784 −0.538918 0.842358i \(-0.681167\pi\)
−0.538918 + 0.842358i \(0.681167\pi\)
\(620\) −89.9499 868.397i −0.145080 1.40064i
\(621\) −159.306 413.414i −0.256532 0.665724i
\(622\) 588.137 245.649i 0.945558 0.394934i
\(623\) −249.146 249.146i −0.399913 0.399913i
\(624\) −265.271 108.793i −0.425113 0.174347i
\(625\) −578.244 + 237.190i −0.925190 + 0.379504i
\(626\) −433.183 177.936i −0.691986 0.284242i
\(627\) −20.0104 49.4663i −0.0319145 0.0788936i
\(628\) 2.57333 + 436.283i 0.00409765 + 0.694718i
\(629\) −919.715 −1.46219
\(630\) 576.130 + 183.934i 0.914492 + 0.291959i
\(631\) 736.830i 1.16772i 0.811855 + 0.583859i \(0.198458\pi\)
−0.811855 + 0.583859i \(0.801542\pi\)
\(632\) 27.9439 69.1877i 0.0442151 0.109474i
\(633\) −753.254 + 304.711i −1.18997 + 0.481375i
\(634\) −17.6432 7.24718i −0.0278284 0.0114309i
\(635\) −8.23287 84.3329i −0.0129652 0.132808i
\(636\) −229.659 + 94.4831i −0.361100 + 0.148558i
\(637\) −16.2391 + 16.2391i −0.0254931 + 0.0254931i
\(638\) −868.160 + 362.607i −1.36075 + 0.568350i
\(639\) −92.3689 + 89.3531i −0.144552 + 0.139833i
\(640\) 312.801 + 558.351i 0.488751 + 0.872423i
\(641\) 367.670i 0.573588i −0.957992 0.286794i \(-0.907410\pi\)
0.957992 0.286794i \(-0.0925895\pi\)
\(642\) −130.694 0.698985i −0.203574 0.00108876i
\(643\) 376.586 376.586i 0.585670 0.585670i −0.350786 0.936456i \(-0.614086\pi\)
0.936456 + 0.350786i \(0.114086\pi\)
\(644\) 313.712 + 310.033i 0.487130 + 0.481417i
\(645\) −86.9485 166.315i −0.134804 0.257852i
\(646\) −36.4218 14.9607i −0.0563805 0.0231590i
\(647\) −311.254 + 311.254i −0.481073 + 0.481073i −0.905474 0.424402i \(-0.860485\pi\)
0.424402 + 0.905474i \(0.360485\pi\)
\(648\) −592.461 262.477i −0.914292 0.405057i
\(649\) 737.603i 1.13652i
\(650\) 57.9053 292.992i 0.0890850 0.450757i
\(651\) −810.189 343.494i −1.24453 0.527641i
\(652\) −5.99787 1016.88i −0.00919919 1.55964i
\(653\) −47.7734 + 47.7734i −0.0731598 + 0.0731598i −0.742740 0.669580i \(-0.766474\pi\)
0.669580 + 0.742740i \(0.266474\pi\)
\(654\) −66.9470 + 66.2347i −0.102365 + 0.101276i
\(655\) 883.759 + 726.555i 1.34925 + 1.10924i
\(656\) 433.030 5.10846i 0.660107 0.00778728i
\(657\) −204.768 3.39835i −0.311671 0.00517253i
\(658\) 263.088 109.885i 0.399830 0.166998i
\(659\) 471.784i 0.715909i −0.933739 0.357954i \(-0.883474\pi\)
0.933739 0.357954i \(-0.116526\pi\)
\(660\) 335.918 + 633.415i 0.508967 + 0.959720i
\(661\) 86.9863 0.131598 0.0657990 0.997833i \(-0.479040\pi\)
0.0657990 + 0.997833i \(0.479040\pi\)
\(662\) 214.599 + 513.796i 0.324167 + 0.776127i
\(663\) −219.716 + 88.8809i −0.331397 + 0.134059i
\(664\) 132.776 56.3790i 0.199964 0.0849082i
\(665\) −4.85917 49.7746i −0.00730702 0.0748490i
\(666\) 463.161 + 1162.80i 0.695437 + 1.74594i
\(667\) 456.776 + 456.776i 0.684822 + 0.684822i
\(668\) −1.89605 321.458i −0.00283840 0.481224i
\(669\) −676.976 287.016i −1.01192 0.429023i
\(670\) 440.016 + 819.091i 0.656741 + 1.22252i
\(671\) 1010.95 1.50663
\(672\) 645.084 4.15973i 0.959946 0.00619007i
\(673\) 561.901 + 561.901i 0.834920 + 0.834920i 0.988185 0.153265i \(-0.0489789\pi\)
−0.153265 + 0.988185i \(0.548979\pi\)
\(674\) 304.096 740.321i 0.451181 1.09840i
\(675\) 149.255 658.292i 0.221118 0.975247i
\(676\) −379.306 374.858i −0.561104 0.554524i
\(677\) −429.992 429.992i −0.635143 0.635143i 0.314210 0.949353i \(-0.398260\pi\)
−0.949353 + 0.314210i \(0.898260\pi\)
\(678\) 282.752 + 1.51222i 0.417038 + 0.00223042i
\(679\) 65.6525 0.0966900
\(680\) 507.489 + 149.529i 0.746307 + 0.219895i
\(681\) 751.003 + 318.401i 1.10279 + 0.467550i
\(682\) −402.077 962.659i −0.589555 1.41152i
\(683\) −371.280 371.280i −0.543602 0.543602i 0.380981 0.924583i \(-0.375586\pi\)
−0.924583 + 0.380981i \(0.875586\pi\)
\(684\) −0.573158 + 53.5823i −0.000837950 + 0.0783366i
\(685\) −106.824 1094.24i −0.155947 1.59743i
\(686\) 269.849 656.946i 0.393366 0.957647i
\(687\) −207.653 + 84.0008i −0.302260 + 0.122272i
\(688\) −143.211 139.871i −0.208155 0.203301i
\(689\) 123.613 0.179409
\(690\) 314.651 378.587i 0.456016 0.548676i
\(691\) 112.536i 0.162860i −0.996679 0.0814301i \(-0.974051\pi\)
0.996679 0.0814301i \(-0.0259487\pi\)
\(692\) −4.36236 739.597i −0.00630398 1.06878i
\(693\) 722.588 + 11.9922i 1.04270 + 0.0173047i
\(694\) 38.7160 94.2540i 0.0557868 0.135813i
\(695\) 850.437 + 699.160i 1.22365 + 1.00599i
\(696\) 944.810 0.519680i 1.35749 0.000746667i
\(697\) 253.138 253.138i 0.363183 0.363183i
\(698\) 295.090 + 706.510i 0.422765 + 1.01219i
\(699\) −581.139 246.384i −0.831386 0.352481i
\(700\) 133.849 + 658.511i 0.191213 + 0.940730i
\(701\) 525.802i 0.750074i −0.927010 0.375037i \(-0.877630\pi\)
0.927010 0.375037i \(-0.122370\pi\)
\(702\) 223.020 + 233.028i 0.317692 + 0.331949i
\(703\) 73.1876 73.1876i 0.104108 0.104108i
\(704\) 550.262 + 531.125i 0.781622 + 0.754439i
\(705\) −147.431 282.006i −0.209122 0.400008i
\(706\) −231.836 + 564.405i −0.328380 + 0.799440i
\(707\) 71.3046 71.3046i 0.100855 0.100855i
\(708\) −285.099 + 683.647i −0.402683 + 0.965603i
\(709\) 638.797i 0.900984i 0.892781 + 0.450492i \(0.148751\pi\)
−0.892781 + 0.450492i \(0.851249\pi\)
\(710\) −136.732 41.1653i −0.192580 0.0579793i
\(711\) −60.3348 + 58.3649i −0.0848591 + 0.0820884i
\(712\) −157.091 + 388.948i −0.220633 + 0.546275i
\(713\) −506.496 + 506.496i −0.710373 + 0.710373i
\(714\) 379.092 375.059i 0.530941 0.525292i
\(715\) −34.6757 355.198i −0.0484975 0.496781i
\(716\) 608.645 + 601.507i 0.850063 + 0.840094i
\(717\) −595.734 + 240.990i −0.830871 + 0.336109i
\(718\) −365.355 874.739i −0.508850 1.21830i
\(719\) 313.578i 0.436131i 0.975934 + 0.218065i \(0.0699746\pi\)
−0.975934 + 0.218065i \(0.930025\pi\)
\(720\) −66.5172 716.921i −0.0923851 0.995723i
\(721\) −95.4285 −0.132356
\(722\) −662.134 + 276.556i −0.917084 + 0.383041i
\(723\) 188.928 + 467.036i 0.261311 + 0.645969i
\(724\) 436.950 442.135i 0.603522 0.610684i
\(725\) 190.344 + 965.595i 0.262543 + 1.33186i
\(726\) 91.9656 + 92.9546i 0.126674 + 0.128037i
\(727\) 318.387 + 318.387i 0.437946 + 0.437946i 0.891320 0.453374i \(-0.149780\pi\)
−0.453374 + 0.891320i \(0.649780\pi\)
\(728\) −297.740 120.253i −0.408984 0.165183i
\(729\) 489.190 + 540.494i 0.671043 + 0.741419i
\(730\) −107.686 200.458i −0.147515 0.274599i
\(731\) −165.482 −0.226378
\(732\) −936.997 390.753i −1.28005 0.533816i
\(733\) −120.156 120.156i −0.163924 0.163924i 0.620379 0.784303i \(-0.286979\pi\)
−0.784303 + 0.620379i \(0.786979\pi\)
\(734\) −652.305 267.942i −0.888699 0.365044i
\(735\) −55.0327 17.2458i −0.0748744 0.0234637i
\(736\) 193.769 488.032i 0.263273 0.663086i
\(737\) 785.647 + 785.647i 1.06601 + 1.06601i
\(738\) −447.522 192.565i −0.606398 0.260928i
\(739\) −376.922 −0.510043 −0.255022 0.966935i \(-0.582083\pi\)
−0.255022 + 0.966935i \(0.582083\pi\)
\(740\) −876.835 + 1079.47i −1.18491 + 1.45875i
\(741\) 10.4114 24.5570i 0.0140505 0.0331404i
\(742\) −256.640 + 107.191i −0.345876 + 0.144463i
\(743\) 139.469 + 139.469i 0.187710 + 0.187710i 0.794705 0.606995i \(-0.207625\pi\)
−0.606995 + 0.794705i \(0.707625\pi\)
\(744\) 0.576247 + 1047.65i 0.000774526 + 1.40813i
\(745\) −93.8327 77.1416i −0.125950 0.103546i
\(746\) −282.780 116.156i −0.379062 0.155705i
\(747\) −162.259 2.69287i −0.217214 0.00360491i
\(748\) 632.194 3.72887i 0.845180 0.00498512i
\(749\) −146.375 −0.195427
\(750\) 719.409 212.017i 0.959211 0.282690i
\(751\) 387.240i 0.515633i −0.966194 0.257816i \(-0.916997\pi\)
0.966194 0.257816i \(-0.0830029\pi\)
\(752\) −242.830 237.168i −0.322912 0.315382i
\(753\) −187.663 463.908i −0.249220 0.616079i
\(754\) −435.024 178.692i −0.576955 0.236992i
\(755\) −383.466 + 466.436i −0.507901 + 0.617796i
\(756\) −665.096 290.411i −0.879756 0.384141i
\(757\) −765.761 + 765.761i −1.01157 + 1.01157i −0.0116408 + 0.999932i \(0.503705\pi\)
−0.999932 + 0.0116408i \(0.996295\pi\)
\(758\) −110.851 + 46.2993i −0.146241 + 0.0610809i
\(759\) 229.614 541.584i 0.302522 0.713549i
\(760\) −52.2831 + 28.4851i −0.0687935 + 0.0374804i
\(761\) 1139.50i 1.49737i −0.662925 0.748686i \(-0.730685\pi\)
0.662925 0.748686i \(-0.269315\pi\)
\(762\) −0.543804 + 101.679i −0.000713654 + 0.133437i
\(763\) −74.5802 + 74.5802i −0.0977460 + 0.0977460i
\(764\) −288.412 + 291.835i −0.377503 + 0.381983i
\(765\) −453.429 385.558i −0.592718 0.503997i
\(766\) −982.088 403.405i −1.28210 0.526639i
\(767\) 260.711 260.711i 0.339910 0.339910i
\(768\) −304.719 704.961i −0.396769 0.917918i
\(769\) 1312.74i 1.70708i −0.521031 0.853538i \(-0.674452\pi\)
0.521031 0.853538i \(-0.325548\pi\)
\(770\) 380.004 + 707.378i 0.493512 + 0.918673i
\(771\) 27.0266 63.7467i 0.0350539 0.0826805i
\(772\) 781.836 4.61150i 1.01274 0.00597345i
\(773\) −335.897 + 335.897i −0.434537 + 0.434537i −0.890168 0.455632i \(-0.849413\pi\)
0.455632 + 0.890168i \(0.349413\pi\)
\(774\) 83.3355 + 209.220i 0.107669 + 0.270310i
\(775\) −1070.70 + 211.062i −1.38155 + 0.272339i
\(776\) −30.5484 71.9434i −0.0393665 0.0927106i
\(777\) 525.680 + 1299.50i 0.676550 + 1.67245i
\(778\) −857.000 + 357.946i −1.10154 + 0.460084i
\(779\) 40.2877i 0.0517171i
\(780\) −105.153 + 342.618i −0.134811 + 0.439254i
\(781\) −170.633 −0.218481
\(782\) −167.293 400.536i −0.213930 0.512195i
\(783\) −971.574 431.074i −1.24084 0.550541i
\(784\) −61.5121 + 0.725658i −0.0784593 + 0.000925584i
\(785\) 542.783 52.9884i 0.691443 0.0675011i
\(786\) −965.576 975.960i −1.22847 1.24168i
\(787\) −168.467 168.467i −0.214063 0.214063i 0.591928 0.805991i \(-0.298367\pi\)
−0.805991 + 0.591928i \(0.798367\pi\)
\(788\) −534.158 + 3.15062i −0.677865 + 0.00399825i
\(789\) 200.863 473.770i 0.254580 0.600468i
\(790\) −89.3122 26.8889i −0.113053 0.0340366i
\(791\) 316.676 0.400348
\(792\) −323.082 797.407i −0.407932 1.00683i
\(793\) 357.327 + 357.327i 0.450602 + 0.450602i
\(794\) −135.339 + 329.483i −0.170453 + 0.414966i
\(795\) 143.818 + 275.094i 0.180903 + 0.346030i
\(796\) 520.952 527.134i 0.654463 0.662229i
\(797\) 639.400 + 639.400i 0.802258 + 0.802258i 0.983448 0.181190i \(-0.0579949\pi\)
−0.181190 + 0.983448i \(0.557995\pi\)
\(798\) −0.320962 + 60.0126i −0.000402208 + 0.0752037i
\(799\) −280.594 −0.351182
\(800\) 659.330 453.083i 0.824162 0.566354i
\(801\) 339.180 328.106i 0.423446 0.409621i
\(802\) 391.623 + 937.631i 0.488308 + 1.16912i
\(803\) −192.273 192.273i −0.239443 0.239443i
\(804\) −424.508 1031.85i −0.527995 1.28339i
\(805\) 350.124 425.881i 0.434937 0.529044i
\(806\) 198.142 482.376i 0.245834 0.598482i
\(807\) 196.508 + 485.773i 0.243504 + 0.601949i
\(808\) −111.315 44.9587i −0.137767 0.0556420i
\(809\) 857.503 1.05995 0.529977 0.848012i \(-0.322200\pi\)
0.529977 + 0.848012i \(0.322200\pi\)
\(810\) −259.119 + 767.436i −0.319900 + 0.947451i
\(811\) 1573.57i 1.94028i −0.242547 0.970140i \(-0.577983\pi\)
0.242547 0.970140i \(-0.422017\pi\)
\(812\) 1058.13 6.24117i 1.30312 0.00768617i
\(813\) 853.456 345.245i 1.04976 0.424656i
\(814\) −631.434 + 1537.22i −0.775717 + 1.88848i
\(815\) −1265.11 + 123.505i −1.55228 + 0.151539i
\(816\) −587.391 240.901i −0.719842 0.295221i
\(817\) 13.1685 13.1685i 0.0161181 0.0161181i
\(818\) 450.094 + 1077.62i 0.550237 + 1.31739i
\(819\) 251.165 + 259.643i 0.306673 + 0.317024i
\(820\) −55.7729 538.445i −0.0680157 0.656640i
\(821\) 1040.55i 1.26742i 0.773571 + 0.633710i \(0.218469\pi\)
−0.773571 + 0.633710i \(0.781531\pi\)
\(822\) −7.05600 + 1319.31i −0.00858394 + 1.60500i
\(823\) 309.894 309.894i 0.376542 0.376542i −0.493311 0.869853i \(-0.664214\pi\)
0.869853 + 0.493311i \(0.164214\pi\)
\(824\) 44.4033 + 104.573i 0.0538875 + 0.126908i
\(825\) 750.131 490.425i 0.909249 0.594454i
\(826\) −315.201 + 767.355i −0.381599 + 0.929001i
\(827\) 527.373 527.373i 0.637694 0.637694i −0.312292 0.949986i \(-0.601097\pi\)
0.949986 + 0.312292i \(0.101097\pi\)
\(828\) −422.152 + 413.216i −0.509845 + 0.499053i
\(829\) 1067.23i 1.28737i 0.765292 + 0.643683i \(0.222594\pi\)
−0.765292 + 0.643683i \(0.777406\pi\)
\(830\) −85.3309 158.844i −0.102808 0.191378i
\(831\) 111.694 + 47.3548i 0.134409 + 0.0569853i
\(832\) 6.76404 + 382.224i 0.00812986 + 0.459404i
\(833\) −35.9584 + 35.9584i −0.0431673 + 0.0431673i
\(834\) −929.169 939.161i −1.11411 1.12609i
\(835\) −399.928 + 39.0423i −0.478955 + 0.0467573i
\(836\) −50.0110 + 50.6045i −0.0598218 + 0.0605317i
\(837\) 477.996 1077.33i 0.571083 1.28713i
\(838\) 218.836 + 523.940i 0.261140 + 0.625227i
\(839\) 1290.47i 1.53811i −0.639182 0.769055i \(-0.720727\pi\)
0.639182 0.769055i \(-0.279273\pi\)
\(840\) −78.7898 802.513i −0.0937974 0.955373i
\(841\) 708.767 0.842767
\(842\) −864.032 + 360.883i −1.02617 + 0.428602i
\(843\) 117.698 47.6117i 0.139618 0.0564789i
\(844\) 770.586 + 761.549i 0.913017 + 0.902309i
\(845\) −423.333 + 514.929i −0.500985 + 0.609383i
\(846\) 141.305 + 354.756i 0.167027 + 0.419333i
\(847\) 103.553 + 103.553i 0.122259 + 0.122259i
\(848\) 236.878 + 231.355i 0.279338 + 0.272824i
\(849\) −1335.23 566.095i −1.57271 0.666779i
\(850\) 128.220 648.775i 0.150847 0.763265i
\(851\) 1141.02 1.34080
\(852\) 158.152 + 65.9535i 0.185624 + 0.0774102i
\(853\) −547.033 547.033i −0.641305 0.641305i 0.309572 0.950876i \(-0.399814\pi\)
−0.950876 + 0.309572i \(0.899814\pi\)
\(854\) −1051.73 432.010i −1.23153 0.505866i
\(855\) 66.7635 5.40093i 0.0780860 0.00631687i
\(856\) 68.1088 + 160.400i 0.0795664 + 0.187384i
\(857\) −29.4871 29.4871i −0.0344074 0.0344074i 0.689694 0.724101i \(-0.257745\pi\)
−0.724101 + 0.689694i \(0.757745\pi\)
\(858\) −2.29043 + 428.258i −0.00266949 + 0.499135i
\(859\) 1301.37 1.51499 0.757493 0.652843i \(-0.226424\pi\)
0.757493 + 0.652843i \(0.226424\pi\)
\(860\) −157.767 + 194.227i −0.183450 + 0.225845i
\(861\) −502.353 212.982i −0.583453 0.247366i
\(862\) 1568.25 655.017i 1.81932 0.759881i
\(863\) 7.00094 + 7.00094i 0.00811233 + 0.00811233i 0.711151 0.703039i \(-0.248174\pi\)
−0.703039 + 0.711151i \(0.748174\pi\)
\(864\) −8.76628 + 863.956i −0.0101462 + 0.999949i
\(865\) −920.138 + 89.8271i −1.06374 + 0.103846i
\(866\) 402.616 + 165.380i 0.464915 + 0.190970i
\(867\) 317.210 128.319i 0.365870 0.148004i
\(868\) 6.92052 + 1173.31i 0.00797295 + 1.35174i
\(869\) −111.457 −0.128258
\(870\) −108.461 1176.02i −0.124668 1.35175i
\(871\) 555.386i 0.637642i
\(872\) 116.429 + 47.0240i 0.133520 + 0.0539267i
\(873\) −1.45911 + 87.9184i −0.00167137 + 0.100708i
\(874\) 45.1858 + 18.5606i 0.0517000 + 0.0212364i
\(875\) 804.428 241.757i 0.919346 0.276294i
\(876\) 103.891 + 252.526i 0.118596 + 0.288271i
\(877\) −43.0680 + 43.0680i −0.0491084 + 0.0491084i −0.731235 0.682126i \(-0.761055\pi\)
0.682126 + 0.731235i \(0.261055\pi\)
\(878\) 102.568 42.8398i 0.116820 0.0487925i
\(879\) 987.920 + 418.847i 1.12391 + 0.476504i
\(880\) 598.342 745.563i 0.679935 0.847230i
\(881\) 648.829i 0.736469i −0.929733 0.368235i \(-0.879962\pi\)
0.929733 0.368235i \(-0.120038\pi\)
\(882\) 63.5706 + 27.3539i 0.0720755 + 0.0310135i
\(883\) −799.685 + 799.685i −0.905645 + 0.905645i −0.995917 0.0902718i \(-0.971226\pi\)
0.0902718 + 0.995917i \(0.471226\pi\)
\(884\) 224.772 + 222.136i 0.254267 + 0.251285i
\(885\) 883.524 + 276.874i 0.998332 + 0.312852i
\(886\) 1420.85 + 583.631i 1.60366 + 0.658726i
\(887\) 103.964 103.964i 0.117209 0.117209i −0.646070 0.763278i \(-0.723588\pi\)
0.763278 + 0.646070i \(0.223588\pi\)
\(888\) 1179.41 1180.71i 1.32817 1.32963i
\(889\) 113.878i 0.128097i
\(890\) 502.081 + 151.160i 0.564136 + 0.169842i
\(891\) −32.1186 + 967.386i −0.0360478 + 1.08573i
\(892\) 5.78263 + 980.391i 0.00648277 + 1.09909i
\(893\) 22.3287 22.3287i 0.0250041 0.0250041i
\(894\) 102.519 + 103.622i 0.114675 + 0.115908i
\(895\) 679.290 826.268i 0.758984 0.923205i
\(896\) −345.491 787.692i −0.385592 0.879121i
\(897\) 272.586 110.268i 0.303886 0.122930i
\(898\) −67.0767 + 28.0161i −0.0746957 + 0.0311984i
\(899\) 1718.46i 1.91152i
\(900\) −884.819 + 164.609i −0.983132 + 0.182899i
\(901\) 273.717 0.303792
\(902\) −249.305 596.891i −0.276392 0.661742i
\(903\) 94.5843 + 233.815i 0.104745 + 0.258932i
\(904\) −147.351 347.020i −0.162998 0.383872i
\(905\) −600.222 493.454i −0.663229 0.545253i
\(906\) 515.098 509.618i 0.568541 0.562492i
\(907\) −695.991 695.991i −0.767355 0.767355i 0.210285 0.977640i \(-0.432561\pi\)
−0.977640 + 0.210285i \(0.932561\pi\)
\(908\) −6.41496 1087.60i −0.00706494 1.19779i
\(909\) 93.9027 + 97.0721i 0.103303 + 0.106790i
\(910\) −115.713 + 384.343i −0.127157 + 0.422355i
\(911\) −1074.43 −1.17939 −0.589696 0.807625i \(-0.700753\pi\)
−0.589696 + 0.807625i \(0.700753\pi\)
\(912\) 65.9124 27.5724i 0.0722724 0.0302329i
\(913\) −152.358 152.358i −0.166876 0.166876i
\(914\) 499.893 1216.99i 0.546929 1.33150i
\(915\) −379.479 + 1210.95i −0.414731 + 1.32344i
\(916\) 212.431 + 209.939i 0.231911 + 0.229191i
\(917\) −1087.24 1087.24i −1.18565 1.18565i
\(918\) 493.834 + 515.996i 0.537946 + 0.562087i
\(919\) −1186.92 −1.29153 −0.645766 0.763535i \(-0.723462\pi\)
−0.645766 + 0.763535i \(0.723462\pi\)
\(920\) −629.604 185.509i −0.684352 0.201641i
\(921\) −466.333 + 1099.92i −0.506333 + 1.19427i
\(922\) −53.7217 128.621i −0.0582665 0.139503i
\(923\) −60.3116 60.3116i −0.0653431 0.0653431i
\(924\) −366.611 891.117i −0.396765 0.964412i
\(925\) 1443.76 + 968.286i 1.56082 + 1.04680i
\(926\) −487.245 + 1186.20i −0.526183 + 1.28099i
\(927\) 2.12087 127.793i 0.00228788 0.137856i
\(928\) −499.193 1156.62i −0.537923 1.24636i
\(929\) 1085.41 1.16836 0.584182 0.811623i \(-0.301415\pi\)
0.584182 + 0.811623i \(0.301415\pi\)
\(930\) 1304.03 120.267i 1.40218 0.129319i
\(931\) 5.72287i 0.00614702i
\(932\) 4.96401 + 841.600i 0.00532619 + 0.903005i
\(933\) 358.528 + 886.293i 0.384275 + 0.949939i
\(934\) 466.810 1136.45i 0.499797 1.21675i
\(935\) −76.7826 786.518i −0.0821204 0.841195i
\(936\) 167.654 396.046i 0.179117 0.423126i
\(937\) −302.640 + 302.640i −0.322988 + 0.322988i −0.849912 0.526924i \(-0.823345\pi\)
0.526924 + 0.849912i \(0.323345\pi\)
\(938\) −481.606 1153.07i −0.513439 1.22928i
\(939\) 274.194 646.732i 0.292006 0.688746i
\(940\) −267.512 + 329.334i −0.284587 + 0.350355i
\(941\) 193.039i 0.205142i 0.994726 + 0.102571i \(0.0327069\pi\)
−0.994726 + 0.102571i \(0.967293\pi\)
\(942\) −654.427 3.50003i −0.694721 0.00371553i
\(943\) −314.050 + 314.050i −0.333033 + 0.333033i
\(944\) 987.548 11.6501i 1.04613 0.0123412i
\(945\) −285.602 + 861.037i −0.302225 + 0.911151i
\(946\) −113.612 + 276.589i −0.120098 + 0.292377i
\(947\) −508.522 + 508.522i −0.536982 + 0.536982i −0.922641 0.385659i \(-0.873974\pi\)
0.385659 + 0.922641i \(0.373974\pi\)
\(948\) 103.304 + 43.0804i 0.108970 + 0.0454434i
\(949\) 135.921i 0.143225i
\(950\) 41.4239 + 61.8304i 0.0436041 + 0.0650847i
\(951\) 11.1677 26.3409i 0.0117431 0.0276981i
\(952\) −659.288 266.277i −0.692529 0.279703i
\(953\) 182.398 182.398i 0.191393 0.191393i −0.604905 0.796298i \(-0.706789\pi\)
0.796298 + 0.604905i \(0.206789\pi\)
\(954\) −137.842 346.061i −0.144488 0.362747i
\(955\) 396.182 + 325.708i 0.414850 + 0.341056i
\(956\) 609.442 + 602.295i 0.637492 + 0.630015i
\(957\) −529.231 1308.27i −0.553010 1.36706i
\(958\) −236.670 566.639i −0.247046 0.591481i
\(959\) 1477.60i 1.54077i
\(960\) −842.750 + 459.753i −0.877865 + 0.478909i
\(961\) −944.513 −0.982844
\(962\) −766.528 + 320.158i −0.796807 + 0.332805i
\(963\) 3.25313 196.017i 0.00337812 0.203549i
\(964\) 472.179 477.782i 0.489812 0.495625i
\(965\) −94.9573 972.688i −0.0984013 1.00797i
\(966\) −470.312 + 465.308i −0.486865 + 0.481685i
\(967\) −754.876 754.876i −0.780637 0.780637i 0.199301 0.979938i \(-0.436133\pi\)
−0.979938 + 0.199301i \(0.936133\pi\)
\(968\) 65.2920 161.659i 0.0674504 0.167004i
\(969\) 23.0540 54.3768i 0.0237916 0.0561164i
\(970\) −86.0678 + 46.2357i −0.0887297 + 0.0476657i
\(971\) −670.107 −0.690121 −0.345060 0.938580i \(-0.612142\pi\)
−0.345060 + 0.938580i \(0.612142\pi\)
\(972\) 403.685 884.207i 0.415313 0.909678i
\(973\) −1046.24 1046.24i −1.07528 1.07528i
\(974\) 655.211 + 269.136i 0.672701 + 0.276321i
\(975\) 438.484 + 91.7950i 0.449727 + 0.0941487i
\(976\) 15.9675 + 1353.52i 0.0163601 + 1.38680i
\(977\) −1030.12 1030.12i −1.05437 1.05437i −0.998435 0.0559325i \(-0.982187\pi\)
−0.0559325 0.998435i \(-0.517813\pi\)
\(978\) 1525.33 + 8.15782i 1.55964 + 0.00834133i
\(979\) 626.569 0.640009
\(980\) 7.92256 + 76.4863i 0.00808424 + 0.0780472i
\(981\) −98.2164 101.531i −0.100119 0.103498i
\(982\) −538.430 + 224.888i −0.548299 + 0.229010i
\(983\) 1099.04 + 1099.04i 1.11804 + 1.11804i 0.992028 + 0.126017i \(0.0402193\pi\)
0.126017 + 0.992028i \(0.459781\pi\)
\(984\) 0.357299 + 649.591i 0.000363109 + 0.660153i
\(985\) 64.8756 + 664.549i 0.0658636 + 0.674669i
\(986\) −963.277 395.678i −0.976954 0.401296i
\(987\) 160.379 + 396.461i 0.162491 + 0.401683i
\(988\) −35.5633 + 0.209763i −0.0359952 + 0.000212310i
\(989\) 205.302 0.207585
\(990\) −955.730 + 493.160i −0.965383 + 0.498142i
\(991\) 893.875i 0.901993i −0.892526 0.450996i \(-0.851069\pi\)
0.892526 0.450996i \(-0.148931\pi\)
\(992\) 1282.52 553.530i 1.29286 0.557994i
\(993\) −774.266 + 313.210i −0.779724 + 0.315418i
\(994\) 177.516 + 72.9169i 0.178588 + 0.0733571i
\(995\) −715.613 588.319i −0.719209 0.591275i
\(996\) 82.3233 + 200.103i 0.0826540 + 0.200906i
\(997\) 465.597 465.597i 0.466998 0.466998i −0.433943 0.900940i \(-0.642878\pi\)
0.900940 + 0.433943i \(0.142878\pi\)
\(998\) 778.757 325.266i 0.780317 0.325917i
\(999\) −1751.90 + 675.082i −1.75365 + 0.675758i
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 60.3.l.a.23.19 yes 40
3.2 odd 2 inner 60.3.l.a.23.2 40
4.3 odd 2 inner 60.3.l.a.23.9 yes 40
5.2 odd 4 inner 60.3.l.a.47.12 yes 40
5.3 odd 4 300.3.l.g.107.9 40
5.4 even 2 300.3.l.g.143.2 40
12.11 even 2 inner 60.3.l.a.23.12 yes 40
15.2 even 4 inner 60.3.l.a.47.9 yes 40
15.8 even 4 300.3.l.g.107.12 40
15.14 odd 2 300.3.l.g.143.19 40
20.3 even 4 300.3.l.g.107.19 40
20.7 even 4 inner 60.3.l.a.47.2 yes 40
20.19 odd 2 300.3.l.g.143.12 40
60.23 odd 4 300.3.l.g.107.2 40
60.47 odd 4 inner 60.3.l.a.47.19 yes 40
60.59 even 2 300.3.l.g.143.9 40
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
60.3.l.a.23.2 40 3.2 odd 2 inner
60.3.l.a.23.9 yes 40 4.3 odd 2 inner
60.3.l.a.23.12 yes 40 12.11 even 2 inner
60.3.l.a.23.19 yes 40 1.1 even 1 trivial
60.3.l.a.47.2 yes 40 20.7 even 4 inner
60.3.l.a.47.9 yes 40 15.2 even 4 inner
60.3.l.a.47.12 yes 40 5.2 odd 4 inner
60.3.l.a.47.19 yes 40 60.47 odd 4 inner
300.3.l.g.107.2 40 60.23 odd 4
300.3.l.g.107.9 40 5.3 odd 4
300.3.l.g.107.12 40 15.8 even 4
300.3.l.g.107.19 40 20.3 even 4
300.3.l.g.143.2 40 5.4 even 2
300.3.l.g.143.9 40 60.59 even 2
300.3.l.g.143.12 40 20.19 odd 2
300.3.l.g.143.19 40 15.14 odd 2