Properties

Label 162.3.h.a.65.9
Level $162$
Weight $3$
Character 162.65
Analytic conductor $4.414$
Analytic rank $0$
Dimension $324$
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] = [162,3,Mod(5,162)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(162, base_ring=CyclotomicField(54))
 
chi = DirichletCharacter(H, H._module([23]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("162.5");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 162 = 2 \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 162.h (of order \(54\), degree \(18\), 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: \(4.41418028264\)
Analytic rank: \(0\)
Dimension: \(324\)
Relative dimension: \(18\) over \(\Q(\zeta_{54})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{54}]$

Embedding invariants

Embedding label 65.9
Character \(\chi\) \(=\) 162.65
Dual form 162.3.h.a.5.9

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.326140 + 1.37609i) q^{2} +(2.89210 - 0.797352i) q^{3} +(-1.78727 - 0.897598i) q^{4} +(-7.40578 - 5.51340i) q^{5} +(0.154002 + 4.23984i) q^{6} +(-1.07376 - 0.706223i) q^{7} +(1.81808 - 2.16670i) q^{8} +(7.72846 - 4.61204i) q^{9} +O(q^{10})\) \(q+(-0.326140 + 1.37609i) q^{2} +(2.89210 - 0.797352i) q^{3} +(-1.78727 - 0.897598i) q^{4} +(-7.40578 - 5.51340i) q^{5} +(0.154002 + 4.23984i) q^{6} +(-1.07376 - 0.706223i) q^{7} +(1.81808 - 2.16670i) q^{8} +(7.72846 - 4.61204i) q^{9} +(10.0023 - 8.39290i) q^{10} +(-1.07678 - 9.21247i) q^{11} +(-5.88465 - 1.17086i) q^{12} +(4.35535 - 14.5479i) q^{13} +(1.32203 - 1.24727i) q^{14} +(-25.8144 - 10.0403i) q^{15} +(2.38863 + 3.20849i) q^{16} +(0.471048 - 0.0830584i) q^{17} +(3.82604 + 12.1393i) q^{18} +(-3.61111 + 20.4796i) q^{19} +(8.28728 + 16.5013i) q^{20} +(-3.66853 - 1.18630i) q^{21} +(13.0284 + 1.52280i) q^{22} +(-15.9635 - 24.2713i) q^{23} +(3.53043 - 7.71596i) q^{24} +(17.2779 + 57.7123i) q^{25} +(18.5988 + 10.7380i) q^{26} +(18.6740 - 19.5008i) q^{27} +(1.28519 + 2.22601i) q^{28} +(-7.55899 - 7.13154i) q^{29} +(22.2354 - 32.2484i) q^{30} +(-0.914886 - 15.7080i) q^{31} +(-5.19421 + 2.24057i) q^{32} +(-10.4597 - 25.7848i) q^{33} +(-0.0393314 + 0.675294i) q^{34} +(4.05834 + 11.1502i) q^{35} +(-17.9526 + 1.30589i) q^{36} +(61.2478 + 22.2924i) q^{37} +(-27.0042 - 11.6485i) q^{38} +(0.996308 - 45.5466i) q^{39} +(-25.4102 + 6.02232i) q^{40} +(8.54541 + 36.0559i) q^{41} +(2.82891 - 4.66134i) q^{42} +(-12.7320 + 29.5161i) q^{43} +(-6.34460 + 17.4316i) q^{44} +(-82.6633 - 8.45430i) q^{45} +(38.6059 - 14.0514i) q^{46} +(10.0825 + 0.587238i) q^{47} +(9.46646 + 7.37469i) q^{48} +(-18.7537 - 43.4760i) q^{49} +(-85.0525 + 4.95375i) q^{50} +(1.29609 - 0.615804i) q^{51} +(-20.8423 + 22.0915i) q^{52} +(14.3946 - 8.31072i) q^{53} +(20.7445 + 32.0572i) q^{54} +(-42.8176 + 74.1622i) q^{55} +(-3.48235 + 1.04255i) q^{56} +(5.88580 + 62.1084i) q^{57} +(12.2790 - 8.07600i) q^{58} +(-8.16985 + 69.8975i) q^{59} +(37.1250 + 41.1156i) q^{60} +(67.7959 - 34.0484i) q^{61} +(21.9140 + 3.86403i) q^{62} +(-11.5556 - 0.505789i) q^{63} +(-1.38919 - 7.87846i) q^{64} +(-112.463 + 83.7255i) q^{65} +(38.8936 - 5.98413i) q^{66} +(27.1526 + 28.7800i) q^{67} +(-0.916440 - 0.274364i) q^{68} +(-65.5207 - 57.4665i) q^{69} +(-16.6673 + 1.94813i) q^{70} +(-57.4122 - 68.4212i) q^{71} +(4.05802 - 25.1303i) q^{72} +(-97.8021 - 82.0657i) q^{73} +(-50.6518 + 77.0123i) q^{74} +(95.9865 + 153.133i) q^{75} +(24.8365 - 33.3612i) q^{76} +(-5.34985 + 10.6524i) q^{77} +(62.3514 + 16.2256i) q^{78} +(115.638 + 27.4066i) q^{79} -36.9309i q^{80} +(38.4581 - 71.2880i) q^{81} -52.4033 q^{82} +(9.97925 - 42.1058i) q^{83} +(5.49181 + 5.41310i) q^{84} +(-3.94641 - 1.98196i) q^{85} +(-36.4644 - 27.1468i) q^{86} +(-27.5477 - 14.5979i) q^{87} +(-21.9183 - 14.4159i) q^{88} +(52.4426 - 62.4987i) q^{89} +(38.5937 - 110.995i) q^{90} +(-14.9506 + 12.5451i) q^{91} +(6.74510 + 57.7081i) q^{92} +(-15.1707 - 44.6995i) q^{93} +(-4.09640 + 13.6829i) q^{94} +(139.655 - 131.758i) q^{95} +(-13.2357 + 10.6216i) q^{96} +(-83.7265 - 112.464i) q^{97} +(65.9433 - 11.6276i) q^{98} +(-50.8102 - 66.2320i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 324 q+O(q^{10}) \) Copy content Toggle raw display \( 324 q + 72 q^{18} + 108 q^{20} + 270 q^{21} + 162 q^{23} - 54 q^{27} - 162 q^{29} - 216 q^{30} - 378 q^{33} - 486 q^{35} - 180 q^{36} - 108 q^{38} + 216 q^{41} + 432 q^{45} + 324 q^{47} + 126 q^{51} - 216 q^{57} - 378 q^{59} - 540 q^{63} - 1728 q^{65} - 1008 q^{66} + 702 q^{67} - 216 q^{68} - 1872 q^{69} + 540 q^{70} - 1296 q^{71} - 576 q^{72} - 864 q^{74} - 900 q^{75} + 108 q^{76} - 864 q^{77} - 288 q^{78} + 108 q^{79} + 144 q^{81} + 432 q^{83} + 144 q^{84} - 540 q^{85} + 864 q^{86} + 2016 q^{87} - 216 q^{88} + 1782 q^{89} + 1440 q^{90} + 864 q^{92} + 2124 q^{93} - 756 q^{94} + 2808 q^{95} + 288 q^{96} - 918 q^{97} + 1296 q^{98} + 1800 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/162\mathbb{Z}\right)^\times\).

\(n\) \(83\)
\(\chi(n)\) \(e\left(\frac{31}{54}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.326140 + 1.37609i −0.163070 + 0.688047i
\(3\) 2.89210 0.797352i 0.964033 0.265784i
\(4\) −1.78727 0.897598i −0.446816 0.224400i
\(5\) −7.40578 5.51340i −1.48116 1.10268i −0.969974 0.243207i \(-0.921801\pi\)
−0.511181 0.859473i \(-0.670792\pi\)
\(6\) 0.154002 + 4.23984i 0.0256670 + 0.706641i
\(7\) −1.07376 0.706223i −0.153394 0.100889i 0.470492 0.882404i \(-0.344077\pi\)
−0.623886 + 0.781515i \(0.714447\pi\)
\(8\) 1.81808 2.16670i 0.227260 0.270838i
\(9\) 7.72846 4.61204i 0.858718 0.512449i
\(10\) 10.0023 8.39290i 1.00023 0.839290i
\(11\) −1.07678 9.21247i −0.0978894 0.837497i −0.949596 0.313478i \(-0.898506\pi\)
0.851706 0.524020i \(-0.175568\pi\)
\(12\) −5.88465 1.17086i −0.490387 0.0975718i
\(13\) 4.35535 14.5479i 0.335027 1.11907i −0.610090 0.792332i \(-0.708867\pi\)
0.945116 0.326734i \(-0.105948\pi\)
\(14\) 1.32203 1.24727i 0.0944304 0.0890904i
\(15\) −25.8144 10.0403i −1.72096 0.669351i
\(16\) 2.38863 + 3.20849i 0.149290 + 0.200531i
\(17\) 0.471048 0.0830584i 0.0277087 0.00488579i −0.159777 0.987153i \(-0.551077\pi\)
0.187485 + 0.982267i \(0.439966\pi\)
\(18\) 3.82604 + 12.1393i 0.212558 + 0.674403i
\(19\) −3.61111 + 20.4796i −0.190059 + 1.07788i 0.729223 + 0.684276i \(0.239882\pi\)
−0.919282 + 0.393600i \(0.871230\pi\)
\(20\) 8.28728 + 16.5013i 0.414364 + 0.825066i
\(21\) −3.66853 1.18630i −0.174692 0.0564905i
\(22\) 13.0284 + 1.52280i 0.592200 + 0.0692182i
\(23\) −15.9635 24.2713i −0.694065 1.05527i −0.994828 0.101575i \(-0.967612\pi\)
0.300763 0.953699i \(-0.402759\pi\)
\(24\) 3.53043 7.71596i 0.147101 0.321498i
\(25\) 17.2779 + 57.7123i 0.691117 + 2.30849i
\(26\) 18.5988 + 10.7380i 0.715337 + 0.413000i
\(27\) 18.6740 19.5008i 0.691631 0.722251i
\(28\) 1.28519 + 2.22601i 0.0458996 + 0.0795005i
\(29\) −7.55899 7.13154i −0.260655 0.245915i 0.544809 0.838560i \(-0.316602\pi\)
−0.805464 + 0.592645i \(0.798084\pi\)
\(30\) 22.2354 32.2484i 0.741182 1.07495i
\(31\) −0.914886 15.7080i −0.0295124 0.506709i −0.980381 0.197113i \(-0.936843\pi\)
0.950868 0.309596i \(-0.100194\pi\)
\(32\) −5.19421 + 2.24057i −0.162319 + 0.0700177i
\(33\) −10.4597 25.7848i −0.316962 0.781357i
\(34\) −0.0393314 + 0.675294i −0.00115681 + 0.0198616i
\(35\) 4.05834 + 11.1502i 0.115953 + 0.318577i
\(36\) −17.9526 + 1.30589i −0.498682 + 0.0362748i
\(37\) 61.2478 + 22.2924i 1.65535 + 0.602497i 0.989621 0.143700i \(-0.0459001\pi\)
0.665725 + 0.746197i \(0.268122\pi\)
\(38\) −27.0042 11.6485i −0.710636 0.306538i
\(39\) 0.996308 45.5466i 0.0255464 1.16786i
\(40\) −25.4102 + 6.02232i −0.635254 + 0.150558i
\(41\) 8.54541 + 36.0559i 0.208425 + 0.879413i 0.972241 + 0.233980i \(0.0751750\pi\)
−0.763817 + 0.645433i \(0.776677\pi\)
\(42\) 2.82891 4.66134i 0.0673551 0.110984i
\(43\) −12.7320 + 29.5161i −0.296093 + 0.686420i −0.999708 0.0241609i \(-0.992309\pi\)
0.703615 + 0.710581i \(0.251568\pi\)
\(44\) −6.34460 + 17.4316i −0.144195 + 0.396174i
\(45\) −82.6633 8.45430i −1.83696 0.187873i
\(46\) 38.6059 14.0514i 0.839259 0.305465i
\(47\) 10.0825 + 0.587238i 0.214521 + 0.0124944i 0.165069 0.986282i \(-0.447215\pi\)
0.0494523 + 0.998776i \(0.484252\pi\)
\(48\) 9.46646 + 7.37469i 0.197218 + 0.153639i
\(49\) −18.7537 43.4760i −0.382729 0.887265i
\(50\) −85.0525 + 4.95375i −1.70105 + 0.0990749i
\(51\) 1.29609 0.615804i 0.0254135 0.0120746i
\(52\) −20.8423 + 22.0915i −0.400813 + 0.424837i
\(53\) 14.3946 8.31072i 0.271596 0.156806i −0.358017 0.933715i \(-0.616547\pi\)
0.629613 + 0.776909i \(0.283214\pi\)
\(54\) 20.7445 + 32.0572i 0.384158 + 0.593652i
\(55\) −42.8176 + 74.1622i −0.778502 + 1.34840i
\(56\) −3.48235 + 1.04255i −0.0621849 + 0.0186169i
\(57\) 5.88580 + 62.1084i 0.103260 + 1.08962i
\(58\) 12.2790 8.07600i 0.211706 0.139241i
\(59\) −8.16985 + 69.8975i −0.138472 + 1.18470i 0.728036 + 0.685539i \(0.240434\pi\)
−0.866507 + 0.499164i \(0.833640\pi\)
\(60\) 37.1250 + 41.1156i 0.618750 + 0.685259i
\(61\) 67.7959 34.0484i 1.11141 0.558170i 0.204233 0.978922i \(-0.434530\pi\)
0.907176 + 0.420752i \(0.138234\pi\)
\(62\) 21.9140 + 3.86403i 0.353452 + 0.0623231i
\(63\) −11.5556 0.505789i −0.183423 0.00802840i
\(64\) −1.38919 7.87846i −0.0217060 0.123101i
\(65\) −112.463 + 83.7255i −1.73020 + 1.28809i
\(66\) 38.8936 5.98413i 0.589297 0.0906687i
\(67\) 27.1526 + 28.7800i 0.405262 + 0.429553i 0.897572 0.440867i \(-0.145329\pi\)
−0.492310 + 0.870420i \(0.663847\pi\)
\(68\) −0.916440 0.274364i −0.0134771 0.00403477i
\(69\) −65.5207 57.4665i −0.949576 0.832847i
\(70\) −16.6673 + 1.94813i −0.238104 + 0.0278304i
\(71\) −57.4122 68.4212i −0.808623 0.963679i 0.191217 0.981548i \(-0.438756\pi\)
−0.999840 + 0.0178683i \(0.994312\pi\)
\(72\) 4.05802 25.1303i 0.0563614 0.349032i
\(73\) −97.8021 82.0657i −1.33975 1.12419i −0.981689 0.190491i \(-0.938992\pi\)
−0.358066 0.933696i \(-0.616564\pi\)
\(74\) −50.6518 + 77.0123i −0.684483 + 1.04071i
\(75\) 95.9865 + 153.133i 1.27982 + 2.04177i
\(76\) 24.8365 33.3612i 0.326796 0.438963i
\(77\) −5.34985 + 10.6524i −0.0694786 + 0.138343i
\(78\) 62.3514 + 16.2256i 0.799377 + 0.208020i
\(79\) 115.638 + 27.4066i 1.46377 + 0.346919i 0.883856 0.467760i \(-0.154939\pi\)
0.579912 + 0.814679i \(0.303087\pi\)
\(80\) 36.9309i 0.461636i
\(81\) 38.4581 71.2880i 0.474792 0.880098i
\(82\) −52.4033 −0.639065
\(83\) 9.97925 42.1058i 0.120232 0.507298i −0.879287 0.476292i \(-0.841981\pi\)
0.999519 0.0310065i \(-0.00987125\pi\)
\(84\) 5.49181 + 5.41310i 0.0653787 + 0.0644417i
\(85\) −3.94641 1.98196i −0.0464283 0.0233172i
\(86\) −36.4644 27.1468i −0.424005 0.315660i
\(87\) −27.5477 14.5979i −0.316640 0.167792i
\(88\) −21.9183 14.4159i −0.249072 0.163817i
\(89\) 52.4426 62.4987i 0.589243 0.702233i −0.386217 0.922408i \(-0.626219\pi\)
0.975460 + 0.220175i \(0.0706629\pi\)
\(90\) 38.5937 110.995i 0.428819 1.23328i
\(91\) −14.9506 + 12.5451i −0.164293 + 0.137858i
\(92\) 6.74510 + 57.7081i 0.0733164 + 0.627261i
\(93\) −15.1707 44.6995i −0.163126 0.480640i
\(94\) −4.09640 + 13.6829i −0.0435787 + 0.145563i
\(95\) 139.655 131.758i 1.47006 1.38693i
\(96\) −13.2357 + 10.6216i −0.137871 + 0.110641i
\(97\) −83.7265 112.464i −0.863160 1.15942i −0.985958 0.166993i \(-0.946594\pi\)
0.122799 0.992432i \(-0.460813\pi\)
\(98\) 65.9433 11.6276i 0.672891 0.118649i
\(99\) −50.8102 66.2320i −0.513234 0.669010i
\(100\) 20.9222 118.656i 0.209222 1.18656i
\(101\) 70.2092 + 139.798i 0.695141 + 1.38414i 0.912919 + 0.408141i \(0.133823\pi\)
−0.217778 + 0.975998i \(0.569881\pi\)
\(102\) 0.424697 + 1.98438i 0.00416370 + 0.0194547i
\(103\) 128.865 + 15.0622i 1.25112 + 0.146235i 0.715733 0.698374i \(-0.246093\pi\)
0.535384 + 0.844609i \(0.320167\pi\)
\(104\) −23.6025 35.8859i −0.226947 0.345057i
\(105\) 20.6278 + 29.0115i 0.196455 + 0.276300i
\(106\) 6.74167 + 22.5188i 0.0636007 + 0.212441i
\(107\) 153.633 + 88.7002i 1.43583 + 0.828974i 0.997556 0.0698694i \(-0.0222583\pi\)
0.438269 + 0.898844i \(0.355592\pi\)
\(108\) −50.8793 + 18.0913i −0.471105 + 0.167512i
\(109\) −16.4515 28.4948i −0.150931 0.261420i 0.780639 0.624982i \(-0.214894\pi\)
−0.931570 + 0.363562i \(0.881560\pi\)
\(110\) −88.0896 83.1083i −0.800815 0.755530i
\(111\) 194.910 + 15.6357i 1.75594 + 0.140862i
\(112\) −0.298908 5.13206i −0.00266883 0.0458220i
\(113\) 25.9180 11.1799i 0.229362 0.0989373i −0.278297 0.960495i \(-0.589770\pi\)
0.507660 + 0.861558i \(0.330511\pi\)
\(114\) −87.3866 12.1566i −0.766549 0.106637i
\(115\) −15.5953 + 267.761i −0.135611 + 2.32836i
\(116\) 7.10867 + 19.5309i 0.0612816 + 0.168370i
\(117\) −33.4353 132.520i −0.285772 1.13265i
\(118\) −93.5210 34.0389i −0.792551 0.288465i
\(119\) −0.564450 0.243480i −0.00474328 0.00204605i
\(120\) −68.6868 + 37.6780i −0.572390 + 0.313983i
\(121\) 34.0283 8.06486i 0.281226 0.0666517i
\(122\) 24.7428 + 104.398i 0.202810 + 0.855722i
\(123\) 53.4635 + 97.4636i 0.434662 + 0.792387i
\(124\) −12.4643 + 28.8955i −0.100519 + 0.233028i
\(125\) 111.290 305.767i 0.890320 2.44613i
\(126\) 4.46477 15.7367i 0.0354347 0.124894i
\(127\) −227.754 + 82.8957i −1.79334 + 0.652722i −0.794366 + 0.607440i \(0.792197\pi\)
−0.998974 + 0.0452829i \(0.985581\pi\)
\(128\) 11.2946 + 0.657834i 0.0882388 + 0.00513933i
\(129\) −13.2874 + 95.5152i −0.103003 + 0.740428i
\(130\) −78.5355 182.066i −0.604119 1.40051i
\(131\) 136.773 7.96613i 1.04407 0.0608101i 0.472473 0.881345i \(-0.343361\pi\)
0.571597 + 0.820535i \(0.306324\pi\)
\(132\) −4.45004 + 55.4729i −0.0337124 + 0.420249i
\(133\) 18.3407 19.4400i 0.137900 0.146165i
\(134\) −48.4595 + 27.9781i −0.361638 + 0.208792i
\(135\) −245.811 + 41.4611i −1.82082 + 0.307119i
\(136\) 0.676439 1.17163i 0.00497381 0.00861490i
\(137\) 69.5450 20.8204i 0.507628 0.151974i −0.0227399 0.999741i \(-0.507239\pi\)
0.530368 + 0.847768i \(0.322054\pi\)
\(138\) 100.448 71.4205i 0.727885 0.517540i
\(139\) 66.1114 43.4822i 0.475622 0.312821i −0.288968 0.957339i \(-0.593312\pi\)
0.764590 + 0.644517i \(0.222942\pi\)
\(140\) 2.75507 23.5711i 0.0196791 0.168365i
\(141\) 29.6278 6.34095i 0.210126 0.0449713i
\(142\) 112.878 56.6897i 0.794919 0.399223i
\(143\) −138.712 24.4586i −0.970011 0.171039i
\(144\) 33.2582 + 13.7802i 0.230959 + 0.0956960i
\(145\) 16.6612 + 94.4904i 0.114905 + 0.651658i
\(146\) 144.827 107.820i 0.991967 0.738492i
\(147\) −88.9032 110.783i −0.604784 0.753629i
\(148\) −89.4565 94.8183i −0.604436 0.640664i
\(149\) −269.084 80.5586i −1.80593 0.540661i −0.807169 0.590321i \(-0.799001\pi\)
−0.998766 + 0.0496594i \(0.984186\pi\)
\(150\) −242.030 + 82.1435i −1.61354 + 0.547624i
\(151\) −132.995 + 15.5449i −0.880764 + 0.102947i −0.544440 0.838800i \(-0.683258\pi\)
−0.336324 + 0.941746i \(0.609184\pi\)
\(152\) 37.8080 + 45.0578i 0.248737 + 0.296433i
\(153\) 3.25740 2.81440i 0.0212902 0.0183948i
\(154\) −12.9139 10.8361i −0.0838567 0.0703641i
\(155\) −79.8289 + 121.374i −0.515025 + 0.783058i
\(156\) −42.6632 + 80.5096i −0.273482 + 0.516087i
\(157\) 33.7863 45.3829i 0.215199 0.289063i −0.681395 0.731916i \(-0.738626\pi\)
0.896594 + 0.442853i \(0.146034\pi\)
\(158\) −75.4282 + 150.190i −0.477393 + 0.950568i
\(159\) 35.0040 35.5130i 0.220151 0.223352i
\(160\) 50.8203 + 12.0446i 0.317627 + 0.0752790i
\(161\) 37.3353i 0.231897i
\(162\) 85.5561 + 76.1718i 0.528124 + 0.470197i
\(163\) 76.9281 0.471951 0.235976 0.971759i \(-0.424171\pi\)
0.235976 + 0.971759i \(0.424171\pi\)
\(164\) 17.0908 72.1119i 0.104212 0.439706i
\(165\) −64.6992 + 248.625i −0.392116 + 1.50682i
\(166\) 54.6868 + 27.4648i 0.329439 + 0.165450i
\(167\) 78.1853 + 58.2068i 0.468175 + 0.348544i 0.805251 0.592934i \(-0.202030\pi\)
−0.337076 + 0.941478i \(0.609438\pi\)
\(168\) −9.24003 + 5.79181i −0.0550002 + 0.0344751i
\(169\) −51.4740 33.8550i −0.304580 0.200325i
\(170\) 4.01445 4.78423i 0.0236144 0.0281425i
\(171\) 66.5446 + 174.931i 0.389150 + 1.02299i
\(172\) 49.2490 41.3248i 0.286331 0.240261i
\(173\) 4.06737 + 34.7986i 0.0235108 + 0.201148i 0.999889 0.0149224i \(-0.00475011\pi\)
−0.976378 + 0.216070i \(0.930676\pi\)
\(174\) 29.0725 33.1472i 0.167084 0.190501i
\(175\) 22.2054 74.1712i 0.126888 0.423836i
\(176\) 26.9861 25.4601i 0.153330 0.144659i
\(177\) 32.1050 + 208.665i 0.181384 + 1.17890i
\(178\) 68.9004 + 92.5493i 0.387081 + 0.519940i
\(179\) 111.920 19.7345i 0.625251 0.110249i 0.147959 0.988994i \(-0.452730\pi\)
0.477292 + 0.878745i \(0.341619\pi\)
\(180\) 140.153 + 89.3085i 0.778626 + 0.496158i
\(181\) 29.1494 165.315i 0.161047 0.913340i −0.792001 0.610520i \(-0.790961\pi\)
0.953048 0.302821i \(-0.0979283\pi\)
\(182\) −12.3872 24.6649i −0.0680615 0.135522i
\(183\) 168.924 152.528i 0.923081 0.833489i
\(184\) −81.6115 9.53902i −0.443541 0.0518425i
\(185\) −330.681 502.776i −1.78747 2.71771i
\(186\) 66.4585 6.29804i 0.357304 0.0338604i
\(187\) −1.27239 4.25008i −0.00680422 0.0227277i
\(188\) −17.4930 10.0996i −0.0930478 0.0537212i
\(189\) −33.8233 + 7.75113i −0.178959 + 0.0410112i
\(190\) 135.764 + 235.151i 0.714549 + 1.23763i
\(191\) 65.3364 + 61.6418i 0.342076 + 0.322732i 0.838038 0.545613i \(-0.183703\pi\)
−0.495962 + 0.868344i \(0.665184\pi\)
\(192\) −10.2996 21.6776i −0.0536436 0.112904i
\(193\) 16.5515 + 284.178i 0.0857591 + 1.47243i 0.717126 + 0.696943i \(0.245457\pi\)
−0.631367 + 0.775484i \(0.717506\pi\)
\(194\) 182.068 78.5364i 0.938494 0.404827i
\(195\) −258.495 + 331.815i −1.32562 + 1.70162i
\(196\) −5.50612 + 94.5364i −0.0280924 + 0.482328i
\(197\) 95.3202 + 261.890i 0.483859 + 1.32939i 0.906160 + 0.422936i \(0.139000\pi\)
−0.422301 + 0.906456i \(0.638777\pi\)
\(198\) 107.713 48.3186i 0.544003 0.244033i
\(199\) −218.760 79.6221i −1.09930 0.400111i −0.272240 0.962229i \(-0.587764\pi\)
−0.827057 + 0.562118i \(0.809987\pi\)
\(200\) 156.458 + 67.4893i 0.782289 + 0.337447i
\(201\) 101.476 + 61.5845i 0.504854 + 0.306391i
\(202\) −215.273 + 51.0207i −1.06571 + 0.252578i
\(203\) 3.08009 + 12.9959i 0.0151728 + 0.0640192i
\(204\) −2.86920 0.0627622i −0.0140647 0.000307658i
\(205\) 135.505 314.137i 0.661001 1.53237i
\(206\) −62.7550 + 172.418i −0.304636 + 0.836980i
\(207\) −235.313 113.955i −1.13678 0.550510i
\(208\) 57.0801 20.7754i 0.274423 0.0998819i
\(209\) 192.556 + 11.2151i 0.921322 + 0.0536609i
\(210\) −46.6501 + 18.9239i −0.222143 + 0.0901138i
\(211\) −53.3102 123.587i −0.252655 0.585720i 0.743933 0.668254i \(-0.232958\pi\)
−0.996588 + 0.0825340i \(0.973699\pi\)
\(212\) −33.1866 + 1.93290i −0.156541 + 0.00911746i
\(213\) −220.598 152.103i −1.03567 0.714099i
\(214\) −172.166 + 182.485i −0.804513 + 0.852734i
\(215\) 257.024 148.393i 1.19546 0.690200i
\(216\) −8.30151 75.9150i −0.0384329 0.351458i
\(217\) −10.1110 + 17.5127i −0.0465943 + 0.0807037i
\(218\) 44.5769 13.3455i 0.204481 0.0612177i
\(219\) −348.288 159.359i −1.59036 0.727668i
\(220\) 143.094 94.1146i 0.650429 0.427794i
\(221\) 0.843252 7.21449i 0.00381562 0.0326447i
\(222\) −85.0839 + 263.114i −0.383261 + 1.18520i
\(223\) −166.127 + 83.4320i −0.744963 + 0.374135i −0.780436 0.625236i \(-0.785003\pi\)
0.0354724 + 0.999371i \(0.488706\pi\)
\(224\) 7.15968 + 1.26244i 0.0319629 + 0.00563591i
\(225\) 399.703 + 366.341i 1.77646 + 1.62818i
\(226\) 6.93172 + 39.3117i 0.0306713 + 0.173946i
\(227\) 79.2204 58.9774i 0.348989 0.259812i −0.408363 0.912820i \(-0.633900\pi\)
0.757352 + 0.653007i \(0.226493\pi\)
\(228\) 45.2289 116.287i 0.198373 0.510032i
\(229\) −173.425 183.820i −0.757314 0.802706i 0.227963 0.973670i \(-0.426793\pi\)
−0.985277 + 0.170964i \(0.945312\pi\)
\(230\) −363.378 108.788i −1.57990 0.472992i
\(231\) −6.97855 + 35.0736i −0.0302102 + 0.151834i
\(232\) −29.1948 + 3.41238i −0.125839 + 0.0147085i
\(233\) 53.6571 + 63.9461i 0.230288 + 0.274447i 0.868798 0.495167i \(-0.164893\pi\)
−0.638510 + 0.769614i \(0.720449\pi\)
\(234\) 193.264 2.79009i 0.825914 0.0119235i
\(235\) −71.4310 59.9378i −0.303962 0.255054i
\(236\) 77.3416 117.592i 0.327719 0.498272i
\(237\) 356.288 12.9413i 1.50333 0.0546047i
\(238\) 0.519141 0.697327i 0.00218126 0.00292995i
\(239\) −53.7072 + 106.940i −0.224716 + 0.447447i −0.977533 0.210783i \(-0.932399\pi\)
0.752816 + 0.658231i \(0.228695\pi\)
\(240\) −29.4469 106.808i −0.122696 0.445032i
\(241\) −27.5511 6.52973i −0.114320 0.0270943i 0.173058 0.984912i \(-0.444635\pi\)
−0.287378 + 0.957817i \(0.592783\pi\)
\(242\) 49.4564i 0.204365i
\(243\) 54.3831 236.836i 0.223799 0.974635i
\(244\) −151.731 −0.621849
\(245\) −100.815 + 425.370i −0.411488 + 1.73620i
\(246\) −151.556 + 41.7839i −0.616079 + 0.169853i
\(247\) 282.207 + 141.730i 1.14254 + 0.573805i
\(248\) −35.6978 26.5760i −0.143943 0.107161i
\(249\) −4.71217 129.731i −0.0189244 0.521008i
\(250\) 384.467 + 252.868i 1.53787 + 1.01147i
\(251\) −273.161 + 325.540i −1.08829 + 1.29697i −0.136358 + 0.990660i \(0.543540\pi\)
−0.951931 + 0.306313i \(0.900905\pi\)
\(252\) 20.1990 + 11.2763i 0.0801548 + 0.0447472i
\(253\) −206.409 + 173.198i −0.815847 + 0.684577i
\(254\) −39.7925 340.447i −0.156663 1.34034i
\(255\) −12.9937 2.58535i −0.0509558 0.0101386i
\(256\) −4.58885 + 15.3278i −0.0179252 + 0.0598743i
\(257\) 42.8142 40.3931i 0.166592 0.157172i −0.598431 0.801174i \(-0.704209\pi\)
0.765023 + 0.644003i \(0.222727\pi\)
\(258\) −127.104 49.4361i −0.492652 0.191613i
\(259\) −50.0221 67.1913i −0.193135 0.259426i
\(260\) 276.153 48.6932i 1.06213 0.187282i
\(261\) −91.3104 20.2534i −0.349848 0.0775994i
\(262\) −33.6451 + 190.811i −0.128416 + 0.728285i
\(263\) 117.631 + 234.223i 0.447267 + 0.890581i 0.998421 + 0.0561776i \(0.0178913\pi\)
−0.551154 + 0.834403i \(0.685812\pi\)
\(264\) −74.8845 24.2156i −0.283654 0.0917258i
\(265\) −152.423 17.8157i −0.575183 0.0672292i
\(266\) 20.7696 + 31.5786i 0.0780811 + 0.118717i
\(267\) 101.836 222.568i 0.381407 0.833586i
\(268\) −22.6959 75.8096i −0.0846863 0.282872i
\(269\) −363.749 210.011i −1.35223 0.780709i −0.363666 0.931529i \(-0.618475\pi\)
−0.988561 + 0.150821i \(0.951808\pi\)
\(270\) 23.1146 351.781i 0.0856096 1.30289i
\(271\) −10.8189 18.7390i −0.0399223 0.0691475i 0.845374 0.534175i \(-0.179378\pi\)
−0.885296 + 0.465028i \(0.846044\pi\)
\(272\) 1.39165 + 1.31296i 0.00511637 + 0.00482705i
\(273\) −33.2359 + 48.2025i −0.121743 + 0.176566i
\(274\) 5.96941 + 102.491i 0.0217862 + 0.374054i
\(275\) 513.068 221.316i 1.86570 0.804785i
\(276\) 65.5212 + 161.519i 0.237396 + 0.585214i
\(277\) 0.735914 12.6352i 0.00265673 0.0456143i −0.996719 0.0809368i \(-0.974209\pi\)
0.999376 + 0.0353225i \(0.0112458\pi\)
\(278\) 38.2739 + 105.157i 0.137676 + 0.378262i
\(279\) −79.5165 117.179i −0.285005 0.419996i
\(280\) 31.5375 + 11.4787i 0.112634 + 0.0409954i
\(281\) −231.321 99.7821i −0.823206 0.355096i −0.0575468 0.998343i \(-0.518328\pi\)
−0.765659 + 0.643246i \(0.777587\pi\)
\(282\) −0.937073 + 42.8386i −0.00332295 + 0.151910i
\(283\) 412.784 97.8317i 1.45860 0.345695i 0.576633 0.817003i \(-0.304366\pi\)
0.881969 + 0.471308i \(0.156218\pi\)
\(284\) 41.1961 + 173.820i 0.145057 + 0.612042i
\(285\) 298.840 492.412i 1.04856 1.72776i
\(286\) 78.8967 182.903i 0.275863 0.639521i
\(287\) 16.2878 44.7504i 0.0567519 0.155925i
\(288\) −29.8097 + 41.2721i −0.103506 + 0.143306i
\(289\) −271.356 + 98.7656i −0.938949 + 0.341749i
\(290\) −135.461 7.88973i −0.467109 0.0272060i
\(291\) −331.819 258.498i −1.14027 0.888309i
\(292\) 101.136 + 234.460i 0.346357 + 0.802946i
\(293\) −105.493 + 6.14426i −0.360044 + 0.0209702i −0.237214 0.971458i \(-0.576234\pi\)
−0.122830 + 0.992428i \(0.539197\pi\)
\(294\) 181.443 86.2082i 0.617154 0.293225i
\(295\) 445.877 472.602i 1.51145 1.60204i
\(296\) 159.654 92.1764i 0.539372 0.311407i
\(297\) −199.758 151.036i −0.672587 0.508538i
\(298\) 198.615 344.012i 0.666494 1.15440i
\(299\) −422.622 + 126.525i −1.41345 + 0.423160i
\(300\) −34.1014 359.847i −0.113671 1.19949i
\(301\) 34.5160 22.7015i 0.114671 0.0754204i
\(302\) 21.9839 188.084i 0.0727942 0.622794i
\(303\) 314.520 + 348.328i 1.03802 + 1.14960i
\(304\) −74.3344 + 37.3321i −0.244521 + 0.122803i
\(305\) −689.804 121.631i −2.26165 0.398790i
\(306\) 2.81051 + 5.40038i 0.00918469 + 0.0176483i
\(307\) −41.8453 237.317i −0.136304 0.773018i −0.973943 0.226794i \(-0.927176\pi\)
0.837639 0.546224i \(-0.183935\pi\)
\(308\) 19.1232 14.2367i 0.0620883 0.0462231i
\(309\) 384.700 59.1896i 1.24498 0.191552i
\(310\) −140.986 149.437i −0.454795 0.482055i
\(311\) −199.675 59.7789i −0.642043 0.192215i −0.0508004 0.998709i \(-0.516177\pi\)
−0.591243 + 0.806494i \(0.701362\pi\)
\(312\) −96.8745 84.9660i −0.310495 0.272327i
\(313\) −11.5518 + 1.35021i −0.0369067 + 0.00431377i −0.134526 0.990910i \(-0.542951\pi\)
0.0976195 + 0.995224i \(0.468877\pi\)
\(314\) 51.4320 + 61.2943i 0.163796 + 0.195205i
\(315\) 82.7899 + 67.4566i 0.262825 + 0.214148i
\(316\) −182.075 152.779i −0.576187 0.483478i
\(317\) −251.024 + 381.663i −0.791873 + 1.20398i 0.183413 + 0.983036i \(0.441286\pi\)
−0.975286 + 0.220948i \(0.929085\pi\)
\(318\) 37.4530 + 59.7510i 0.117777 + 0.187896i
\(319\) −57.5597 + 77.3161i −0.180438 + 0.242370i
\(320\) −33.1491 + 66.0053i −0.103591 + 0.206267i
\(321\) 515.048 + 134.030i 1.60451 + 0.417539i
\(322\) −51.3769 12.1766i −0.159556 0.0378154i
\(323\) 9.94682i 0.0307951i
\(324\) −132.723 + 92.8905i −0.409638 + 0.286699i
\(325\) 914.842 2.81490
\(326\) −25.0893 + 105.860i −0.0769611 + 0.324725i
\(327\) −70.2996 69.2920i −0.214983 0.211902i
\(328\) 93.6586 + 47.0371i 0.285545 + 0.143406i
\(329\) −10.4115 7.75104i −0.0316458 0.0235594i
\(330\) −321.030 170.119i −0.972819 0.515511i
\(331\) −26.1929 17.2273i −0.0791326 0.0520464i 0.509326 0.860574i \(-0.329895\pi\)
−0.588459 + 0.808527i \(0.700265\pi\)
\(332\) −55.6296 + 66.2968i −0.167559 + 0.199689i
\(333\) 576.165 110.192i 1.73022 0.330906i
\(334\) −105.597 + 88.6067i −0.316160 + 0.265290i
\(335\) −42.4101 362.841i −0.126597 1.08311i
\(336\) −4.95653 14.6041i −0.0147516 0.0434645i
\(337\) 51.5282 172.116i 0.152903 0.510731i −0.846876 0.531791i \(-0.821519\pi\)
0.999778 + 0.0210607i \(0.00670431\pi\)
\(338\) 63.3753 59.7915i 0.187501 0.176898i
\(339\) 66.0429 52.9991i 0.194817 0.156340i
\(340\) 5.27427 + 7.08458i 0.0155126 + 0.0208370i
\(341\) −143.724 + 25.3424i −0.421478 + 0.0743180i
\(342\) −262.424 + 34.5197i −0.767321 + 0.100935i
\(343\) −21.5021 + 121.945i −0.0626884 + 0.355524i
\(344\) 40.8047 + 81.2489i 0.118618 + 0.236189i
\(345\) 168.397 + 786.826i 0.488106 + 2.28065i
\(346\) −49.2126 5.75213i −0.142233 0.0166246i
\(347\) 236.896 + 360.183i 0.682699 + 1.03799i 0.996088 + 0.0883681i \(0.0281652\pi\)
−0.313389 + 0.949625i \(0.601464\pi\)
\(348\) 36.1320 + 50.8172i 0.103827 + 0.146026i
\(349\) −71.6709 239.397i −0.205361 0.685952i −0.997170 0.0751836i \(-0.976046\pi\)
0.791809 0.610769i \(-0.209139\pi\)
\(350\) 94.8244 + 54.7469i 0.270927 + 0.156420i
\(351\) −202.363 356.600i −0.576532 1.01595i
\(352\) 26.2342 + 45.4389i 0.0745289 + 0.129088i
\(353\) −146.063 137.803i −0.413776 0.390378i 0.451009 0.892519i \(-0.351064\pi\)
−0.864786 + 0.502141i \(0.832546\pi\)
\(354\) −297.613 23.8745i −0.840714 0.0674421i
\(355\) 47.9488 + 823.249i 0.135067 + 2.31901i
\(356\) −149.828 + 64.6293i −0.420864 + 0.181543i
\(357\) −1.82658 0.254102i −0.00511648 0.000711771i
\(358\) −9.34505 + 160.448i −0.0261035 + 0.448180i
\(359\) 47.7911 + 131.305i 0.133123 + 0.365752i 0.988287 0.152605i \(-0.0487661\pi\)
−0.855164 + 0.518357i \(0.826544\pi\)
\(360\) −168.606 + 163.736i −0.468351 + 0.454822i
\(361\) −67.1462 24.4392i −0.186001 0.0676987i
\(362\) 217.982 + 94.0281i 0.602159 + 0.259746i
\(363\) 91.9827 50.4569i 0.253396 0.139000i
\(364\) 37.9812 9.00171i 0.104344 0.0247300i
\(365\) 271.840 + 1146.98i 0.744767 + 3.14242i
\(366\) 154.801 + 282.201i 0.422952 + 0.771040i
\(367\) 147.218 341.290i 0.401140 0.929946i −0.591213 0.806515i \(-0.701351\pi\)
0.992353 0.123431i \(-0.0393898\pi\)
\(368\) 39.7434 109.194i 0.107998 0.296723i
\(369\) 232.334 + 239.245i 0.629632 + 0.648360i
\(370\) 799.715 291.073i 2.16139 0.786682i
\(371\) −21.3256 1.24207i −0.0574813 0.00334790i
\(372\) −13.0081 + 93.5071i −0.0349680 + 0.251363i
\(373\) 144.432 + 334.831i 0.387217 + 0.897670i 0.994650 + 0.103299i \(0.0329399\pi\)
−0.607433 + 0.794371i \(0.707801\pi\)
\(374\) 6.26348 0.364806i 0.0167473 0.000975417i
\(375\) 78.0576 973.044i 0.208154 2.59478i
\(376\) 19.6031 20.7781i 0.0521360 0.0552609i
\(377\) −136.671 + 78.9069i −0.362522 + 0.209302i
\(378\) 0.364873 49.0720i 0.000965272 0.129820i
\(379\) −323.872 + 560.962i −0.854543 + 1.48011i 0.0225260 + 0.999746i \(0.492829\pi\)
−0.877069 + 0.480365i \(0.840504\pi\)
\(380\) −367.867 + 110.132i −0.968072 + 0.289822i
\(381\) −592.590 + 421.343i −1.55536 + 1.10589i
\(382\) −106.134 + 69.8052i −0.277837 + 0.182736i
\(383\) −40.5347 + 346.797i −0.105835 + 0.905475i 0.831136 + 0.556069i \(0.187691\pi\)
−0.936971 + 0.349406i \(0.886383\pi\)
\(384\) 33.1895 7.10323i 0.0864310 0.0184980i
\(385\) 98.3509 49.3937i 0.255457 0.128295i
\(386\) −396.454 69.9056i −1.02708 0.181102i
\(387\) 37.7307 + 286.834i 0.0974954 + 0.741174i
\(388\) 48.6938 + 276.156i 0.125499 + 0.711742i
\(389\) 362.665 269.994i 0.932300 0.694072i −0.0198177 0.999804i \(-0.506309\pi\)
0.952118 + 0.305732i \(0.0989012\pi\)
\(390\) −372.303 463.931i −0.954623 1.18957i
\(391\) −9.53550 10.1070i −0.0243875 0.0258492i
\(392\) −128.295 38.4090i −0.327283 0.0979822i
\(393\) 389.210 132.095i 0.990355 0.336120i
\(394\) −391.473 + 45.7566i −0.993586 + 0.116134i
\(395\) −705.283 840.524i −1.78553 2.12791i
\(396\) 31.3615 + 163.981i 0.0791957 + 0.414094i
\(397\) 2.65467 + 2.22753i 0.00668683 + 0.00561091i 0.646125 0.763232i \(-0.276389\pi\)
−0.639438 + 0.768843i \(0.720833\pi\)
\(398\) 180.914 275.066i 0.454557 0.691121i
\(399\) 37.5425 70.8462i 0.0940914 0.177559i
\(400\) −143.899 + 193.290i −0.359747 + 0.483224i
\(401\) 74.6610 148.662i 0.186187 0.370729i −0.781103 0.624402i \(-0.785343\pi\)
0.967290 + 0.253674i \(0.0816389\pi\)
\(402\) −117.841 + 119.555i −0.293138 + 0.297400i
\(403\) −232.502 55.1040i −0.576929 0.136735i
\(404\) 312.876i 0.774445i
\(405\) −677.851 + 315.908i −1.67371 + 0.780019i
\(406\) −18.8881 −0.0465224
\(407\) 139.417 588.248i 0.342549 1.44533i
\(408\) 1.02213 3.92782i 0.00250521 0.00962700i
\(409\) −63.8997 32.0917i −0.156234 0.0784637i 0.368964 0.929444i \(-0.379713\pi\)
−0.525198 + 0.850980i \(0.676009\pi\)
\(410\) 388.087 + 288.920i 0.946555 + 0.704684i
\(411\) 184.530 115.667i 0.448978 0.281427i
\(412\) −216.796 142.589i −0.526204 0.346090i
\(413\) 58.1357 69.2834i 0.140764 0.167756i
\(414\) 233.558 286.648i 0.564151 0.692386i
\(415\) −306.050 + 256.806i −0.737470 + 0.618811i
\(416\) 9.97285 + 85.3232i 0.0239732 + 0.205104i
\(417\) 156.530 178.469i 0.375372 0.427983i
\(418\) −78.2334 + 261.318i −0.187161 + 0.625162i
\(419\) −75.3841 + 71.1212i −0.179914 + 0.169740i −0.770930 0.636919i \(-0.780208\pi\)
0.591016 + 0.806660i \(0.298727\pi\)
\(420\) −10.8266 70.3668i −0.0257775 0.167540i
\(421\) 313.478 + 421.074i 0.744604 + 1.00018i 0.999449 + 0.0331946i \(0.0105681\pi\)
−0.254845 + 0.966982i \(0.582024\pi\)
\(422\) 187.454 33.0531i 0.444203 0.0783250i
\(423\) 80.6305 41.9624i 0.190616 0.0992020i
\(424\) 8.16364 46.2983i 0.0192539 0.109194i
\(425\) 12.9322 + 25.7502i 0.0304287 + 0.0605886i
\(426\) 281.254 253.956i 0.660220 0.596141i
\(427\) −96.8423 11.3192i −0.226797 0.0265088i
\(428\) −194.966 296.432i −0.455529 0.692598i
\(429\) −420.669 + 39.8654i −0.980581 + 0.0929262i
\(430\) 120.377 + 402.086i 0.279946 + 0.935084i
\(431\) 153.358 + 88.5410i 0.355818 + 0.205432i 0.667245 0.744839i \(-0.267474\pi\)
−0.311427 + 0.950270i \(0.600807\pi\)
\(432\) 107.174 + 13.3353i 0.248087 + 0.0308687i
\(433\) 209.442 + 362.764i 0.483699 + 0.837791i 0.999825 0.0187215i \(-0.00595958\pi\)
−0.516126 + 0.856513i \(0.672626\pi\)
\(434\) −20.8015 19.6252i −0.0479298 0.0452194i
\(435\) 123.528 + 259.991i 0.283972 + 0.597679i
\(436\) 3.82627 + 65.6945i 0.00877585 + 0.150675i
\(437\) 554.713 239.280i 1.26937 0.547551i
\(438\) 332.884 427.304i 0.760009 0.975580i
\(439\) −14.7253 + 252.824i −0.0335429 + 0.575909i 0.939106 + 0.343628i \(0.111656\pi\)
−0.972649 + 0.232281i \(0.925381\pi\)
\(440\) 82.8417 + 227.606i 0.188277 + 0.517286i
\(441\) −345.450 249.509i −0.783334 0.565781i
\(442\) 9.65279 + 3.51333i 0.0218389 + 0.00794870i
\(443\) 147.773 + 63.7430i 0.333573 + 0.143889i 0.556278 0.830997i \(-0.312229\pi\)
−0.222704 + 0.974886i \(0.571488\pi\)
\(444\) −334.321 202.896i −0.752974 0.456972i
\(445\) −732.959 + 173.714i −1.64710 + 0.390369i
\(446\) −60.6296 255.817i −0.135941 0.573580i
\(447\) −842.452 18.4282i −1.88468 0.0412264i
\(448\) −4.07230 + 9.44065i −0.00908996 + 0.0210729i
\(449\) −200.378 + 550.534i −0.446276 + 1.22613i 0.489022 + 0.872272i \(0.337354\pi\)
−0.935298 + 0.353862i \(0.884868\pi\)
\(450\) −634.478 + 430.551i −1.40995 + 0.956779i
\(451\) 322.963 117.549i 0.716103 0.260640i
\(452\) −56.3573 3.28244i −0.124684 0.00726204i
\(453\) −372.241 + 151.002i −0.821724 + 0.333337i
\(454\) 55.3215 + 128.250i 0.121853 + 0.282488i
\(455\) 179.887 10.4772i 0.395356 0.0230269i
\(456\) 145.271 + 100.165i 0.318577 + 0.219661i
\(457\) 419.468 444.610i 0.917873 0.972889i −0.0818445 0.996645i \(-0.526081\pi\)
0.999718 + 0.0237563i \(0.00756257\pi\)
\(458\) 309.514 178.698i 0.675794 0.390170i
\(459\) 7.17665 10.7368i 0.0156354 0.0233918i
\(460\) 268.215 464.562i 0.583076 1.00992i
\(461\) 199.763 59.8051i 0.433325 0.129729i −0.0627094 0.998032i \(-0.519974\pi\)
0.496034 + 0.868303i \(0.334789\pi\)
\(462\) −45.9885 21.0420i −0.0995423 0.0455455i
\(463\) 192.773 126.789i 0.416355 0.273841i −0.324000 0.946057i \(-0.605028\pi\)
0.740355 + 0.672216i \(0.234657\pi\)
\(464\) 4.82583 41.2876i 0.0104005 0.0889820i
\(465\) −134.095 + 414.677i −0.288377 + 0.891779i
\(466\) −105.495 + 52.9818i −0.226385 + 0.113695i
\(467\) 282.995 + 49.8997i 0.605986 + 0.106852i 0.468218 0.883613i \(-0.344896\pi\)
0.137768 + 0.990465i \(0.456007\pi\)
\(468\) −59.1917 + 266.859i −0.126478 + 0.570212i
\(469\) −8.83021 50.0786i −0.0188277 0.106777i
\(470\) 105.776 78.7477i 0.225056 0.167548i
\(471\) 61.5271 158.191i 0.130631 0.335863i
\(472\) 136.594 + 144.781i 0.289393 + 0.306739i
\(473\) 285.625 + 85.5106i 0.603859 + 0.180784i
\(474\) −98.3914 + 494.506i −0.207577 + 1.04326i
\(475\) −1244.32 + 145.440i −2.61962 + 0.306190i
\(476\) 0.790274 + 0.941812i 0.00166024 + 0.00197860i
\(477\) 72.9186 130.618i 0.152869 0.273831i
\(478\) −129.643 108.784i −0.271220 0.227581i
\(479\) 93.8272 142.657i 0.195882 0.297823i −0.724169 0.689622i \(-0.757777\pi\)
0.920051 + 0.391799i \(0.128147\pi\)
\(480\) 156.581 5.68744i 0.326211 0.0118488i
\(481\) 591.062 793.934i 1.22882 1.65059i
\(482\) 17.9710 35.7833i 0.0372843 0.0742392i
\(483\) 29.7694 + 107.977i 0.0616344 + 0.223556i
\(484\) −68.0566 16.1297i −0.140613 0.0333259i
\(485\) 1294.50i 2.66908i
\(486\) 308.172 + 152.078i 0.634100 + 0.312918i
\(487\) 319.557 0.656174 0.328087 0.944647i \(-0.393596\pi\)
0.328087 + 0.944647i \(0.393596\pi\)
\(488\) 49.4856 208.796i 0.101405 0.427861i
\(489\) 222.483 61.3388i 0.454976 0.125437i
\(490\) −552.469 277.460i −1.12749 0.566246i
\(491\) 147.406 + 109.740i 0.300217 + 0.223503i 0.736717 0.676201i \(-0.236375\pi\)
−0.436501 + 0.899704i \(0.643782\pi\)
\(492\) −8.07023 222.182i −0.0164029 0.451589i
\(493\) −4.15298 2.73146i −0.00842390 0.00554048i
\(494\) −287.073 + 342.120i −0.581119 + 0.692550i
\(495\) 11.1254 + 770.636i 0.0224756 + 1.55684i
\(496\) 48.2136 40.4560i 0.0972049 0.0815646i
\(497\) 13.3263 + 114.014i 0.0268135 + 0.229404i
\(498\) 180.059 + 35.8261i 0.361564 + 0.0719399i
\(499\) −202.950 + 677.900i −0.406713 + 1.35852i 0.472182 + 0.881501i \(0.343467\pi\)
−0.878895 + 0.477015i \(0.841719\pi\)
\(500\) −473.360 + 446.592i −0.946721 + 0.893185i
\(501\) 272.531 + 105.999i 0.543974 + 0.211574i
\(502\) −358.885 482.066i −0.714910 0.960291i
\(503\) 299.434 52.7983i 0.595296 0.104967i 0.132121 0.991234i \(-0.457821\pi\)
0.463175 + 0.886267i \(0.346710\pi\)
\(504\) −22.1049 + 24.1181i −0.0438590 + 0.0478533i
\(505\) 250.808 1422.40i 0.496650 2.81664i
\(506\) −171.018 340.525i −0.337981 0.672975i
\(507\) −175.862 56.8690i −0.346868 0.112168i
\(508\) 481.464 + 56.2751i 0.947764 + 0.110778i
\(509\) −364.645 554.416i −0.716395 1.08923i −0.991788 0.127894i \(-0.959178\pi\)
0.275393 0.961332i \(-0.411192\pi\)
\(510\) 7.79545 17.0374i 0.0152852 0.0334066i
\(511\) 47.0593 + 157.189i 0.0920925 + 0.307610i
\(512\) −19.5959 11.3137i −0.0382733 0.0220971i
\(513\) 331.935 + 452.857i 0.647046 + 0.882762i
\(514\) 41.6212 + 72.0901i 0.0809752 + 0.140253i
\(515\) −871.302 822.031i −1.69185 1.59618i
\(516\) 109.483 158.784i 0.212175 0.307721i
\(517\) −5.44674 93.5170i −0.0105353 0.180884i
\(518\) 108.776 46.9212i 0.209992 0.0905816i
\(519\) 39.5099 + 97.3977i 0.0761270 + 0.187664i
\(520\) −23.0581 + 395.893i −0.0443426 + 0.761333i
\(521\) −168.127 461.925i −0.322700 0.886612i −0.989904 0.141737i \(-0.954731\pi\)
0.667204 0.744875i \(-0.267491\pi\)
\(522\) 57.6506 119.046i 0.110442 0.228058i
\(523\) 592.196 + 215.542i 1.13231 + 0.412126i 0.839129 0.543933i \(-0.183065\pi\)
0.293177 + 0.956058i \(0.405288\pi\)
\(524\) −251.600 108.530i −0.480153 0.207118i
\(525\) 5.07960 232.216i 0.00967543 0.442316i
\(526\) −360.677 + 85.4819i −0.685697 + 0.162513i
\(527\) −1.73563 7.32322i −0.00329342 0.0138960i
\(528\) 57.7458 95.1504i 0.109367 0.180209i
\(529\) −124.737 + 289.173i −0.235798 + 0.546641i
\(530\) 74.2275 203.938i 0.140052 0.384790i
\(531\) 259.230 + 577.880i 0.488192 + 1.08829i
\(532\) −50.2289 + 18.2818i −0.0944152 + 0.0343643i
\(533\) 561.755 + 32.7185i 1.05395 + 0.0613856i
\(534\) 273.061 + 212.724i 0.511350 + 0.398359i
\(535\) −648.735 1503.94i −1.21259 2.81110i
\(536\) 111.723 6.50713i 0.208439 0.0121402i
\(537\) 307.948 146.314i 0.573460 0.272465i
\(538\) 407.627 432.060i 0.757672 0.803085i
\(539\) −380.327 + 219.582i −0.705616 + 0.407388i
\(540\) 476.546 + 146.538i 0.882492 + 0.271366i
\(541\) 253.875 439.724i 0.469270 0.812799i −0.530113 0.847927i \(-0.677850\pi\)
0.999383 + 0.0351278i \(0.0111838\pi\)
\(542\) 29.3151 8.77635i 0.0540868 0.0161925i
\(543\) −47.5110 501.348i −0.0874973 0.923294i
\(544\) −2.26062 + 1.48684i −0.00415556 + 0.00273315i
\(545\) −35.2671 + 301.729i −0.0647103 + 0.553632i
\(546\) −55.4916 61.4564i −0.101633 0.112558i
\(547\) −379.035 + 190.359i −0.692934 + 0.348005i −0.760162 0.649733i \(-0.774881\pi\)
0.0672283 + 0.997738i \(0.478584\pi\)
\(548\) −142.984 25.2119i −0.260919 0.0460071i
\(549\) 366.925 575.819i 0.668352 1.04885i
\(550\) 137.219 + 778.210i 0.249490 + 1.41493i
\(551\) 173.348 129.053i 0.314606 0.234215i
\(552\) −243.634 + 37.4854i −0.441367 + 0.0679083i
\(553\) −104.812 111.094i −0.189533 0.200894i
\(554\) 17.1471 + 5.13352i 0.0309515 + 0.00926627i
\(555\) −1357.25 1190.41i −2.44550 2.14488i
\(556\) −157.188 + 18.3727i −0.282713 + 0.0330444i
\(557\) −123.616 147.319i −0.221931 0.264487i 0.643578 0.765381i \(-0.277449\pi\)
−0.865509 + 0.500893i \(0.833005\pi\)
\(558\) 187.183 71.2054i 0.335453 0.127608i
\(559\) 373.944 + 313.776i 0.668951 + 0.561317i
\(560\) −26.0814 + 39.6549i −0.0465740 + 0.0708123i
\(561\) −7.06868 11.2771i −0.0126001 0.0201018i
\(562\) 212.752 285.776i 0.378563 0.508499i
\(563\) 256.994 511.718i 0.456473 0.908913i −0.541210 0.840887i \(-0.682034\pi\)
0.997684 0.0680255i \(-0.0216699\pi\)
\(564\) −58.6443 15.2609i −0.103979 0.0270583i
\(565\) −253.582 60.1000i −0.448818 0.106372i
\(566\) 599.937i 1.05996i
\(567\) −91.6400 + 49.3861i −0.161623 + 0.0871008i
\(568\) −252.628 −0.444768
\(569\) 226.892 957.333i 0.398756 1.68248i −0.289630 0.957139i \(-0.593532\pi\)
0.688386 0.725344i \(-0.258320\pi\)
\(570\) 580.141 + 571.827i 1.01779 + 1.00320i
\(571\) −17.2215 8.64899i −0.0301603 0.0151471i 0.433655 0.901079i \(-0.357224\pi\)
−0.463815 + 0.885932i \(0.653520\pi\)
\(572\) 225.960 + 168.221i 0.395036 + 0.294093i
\(573\) 238.110 + 126.178i 0.415549 + 0.220206i
\(574\) 56.2686 + 37.0084i 0.0980289 + 0.0644746i
\(575\) 1124.94 1340.65i 1.95641 2.33156i
\(576\) −47.0721 54.4814i −0.0817223 0.0945857i
\(577\) 284.913 239.070i 0.493783 0.414333i −0.361597 0.932335i \(-0.617768\pi\)
0.855380 + 0.518001i \(0.173324\pi\)
\(578\) −47.4105 405.623i −0.0820251 0.701770i
\(579\) 274.459 + 808.674i 0.474022 + 1.39667i
\(580\) 55.0364 183.834i 0.0948904 0.316956i
\(581\) −40.4514 + 38.1639i −0.0696237 + 0.0656866i
\(582\) 463.937 372.307i 0.797142 0.639703i
\(583\) −92.0621 123.661i −0.157911 0.212111i
\(584\) −355.624 + 62.7060i −0.608945 + 0.107373i
\(585\) −483.019 + 1165.75i −0.825674 + 1.99274i
\(586\) 25.9504 147.172i 0.0442839 0.251147i
\(587\) 395.573 + 787.652i 0.673890 + 1.34183i 0.927246 + 0.374452i \(0.122169\pi\)
−0.253356 + 0.967373i \(0.581534\pi\)
\(588\) 59.4546 + 277.799i 0.101113 + 0.472447i
\(589\) 324.997 + 37.9867i 0.551778 + 0.0644936i
\(590\) 504.926 + 767.703i 0.855807 + 1.30119i
\(591\) 484.494 + 681.408i 0.819787 + 1.15297i
\(592\) 74.7737 + 249.762i 0.126307 + 0.421894i
\(593\) 226.200 + 130.597i 0.381450 + 0.220230i 0.678449 0.734648i \(-0.262652\pi\)
−0.296999 + 0.954878i \(0.595986\pi\)
\(594\) 272.989 225.627i 0.459577 0.379844i
\(595\) 2.83779 + 4.91520i 0.00476939 + 0.00826083i
\(596\) 408.616 + 385.509i 0.685597 + 0.646827i
\(597\) −696.162 55.8462i −1.16610 0.0935447i
\(598\) −36.2759 622.832i −0.0606620 1.04153i
\(599\) −910.950 + 392.945i −1.52078 + 0.656002i −0.982416 0.186707i \(-0.940218\pi\)
−0.538368 + 0.842710i \(0.680959\pi\)
\(600\) 506.304 + 70.4337i 0.843840 + 0.117390i
\(601\) 28.7286 493.251i 0.0478014 0.820718i −0.886168 0.463364i \(-0.846642\pi\)
0.933969 0.357353i \(-0.116321\pi\)
\(602\) 19.9824 + 54.9012i 0.0331933 + 0.0911979i
\(603\) 342.582 + 97.1965i 0.568130 + 0.161188i
\(604\) 251.651 + 91.5935i 0.416641 + 0.151645i
\(605\) −296.471 127.885i −0.490035 0.211380i
\(606\) −581.910 + 319.205i −0.960247 + 0.526741i
\(607\) −785.689 + 186.212i −1.29438 + 0.306774i −0.819400 0.573222i \(-0.805693\pi\)
−0.474981 + 0.879996i \(0.657545\pi\)
\(608\) −27.1291 114.467i −0.0446202 0.188267i
\(609\) 19.2702 + 35.1295i 0.0316424 + 0.0576839i
\(610\) 392.348 909.566i 0.643194 1.49109i
\(611\) 52.4558 144.121i 0.0858524 0.235877i
\(612\) −8.34805 + 2.10625i −0.0136406 + 0.00344158i
\(613\) −781.441 + 284.421i −1.27478 + 0.463982i −0.888703 0.458484i \(-0.848393\pi\)
−0.386078 + 0.922466i \(0.626170\pi\)
\(614\) 340.217 + 19.8154i 0.554100 + 0.0322726i
\(615\) 141.417 1016.56i 0.229946 1.65294i
\(616\) 13.3542 + 30.9585i 0.0216789 + 0.0502573i
\(617\) −428.414 + 24.9523i −0.694351 + 0.0404413i −0.401691 0.915775i \(-0.631577\pi\)
−0.292660 + 0.956217i \(0.594540\pi\)
\(618\) −44.0157 + 548.687i −0.0712228 + 0.887843i
\(619\) 249.491 264.445i 0.403055 0.427214i −0.493774 0.869590i \(-0.664383\pi\)
0.896829 + 0.442376i \(0.145864\pi\)
\(620\) 251.620 145.273i 0.405840 0.234312i
\(621\) −771.412 141.943i −1.24221 0.228571i
\(622\) 147.383 255.276i 0.236951 0.410411i
\(623\) −100.449 + 30.0724i −0.161234 + 0.0482703i
\(624\) 148.516 105.598i 0.238006 0.169227i
\(625\) −1251.69 + 823.251i −2.00271 + 1.31720i
\(626\) 1.90949 16.3367i 0.00305030 0.0260970i
\(627\) 565.834 121.100i 0.902447 0.193142i
\(628\) −101.121 + 50.7847i −0.161020 + 0.0808674i
\(629\) 30.7022 + 5.41363i 0.0488111 + 0.00860672i
\(630\) −119.828 + 91.9263i −0.190203 + 0.145915i
\(631\) 26.3829 + 149.625i 0.0418112 + 0.237123i 0.998550 0.0538237i \(-0.0171409\pi\)
−0.956739 + 0.290947i \(0.906030\pi\)
\(632\) 269.620 200.725i 0.426614 0.317603i
\(633\) −252.721 314.918i −0.399243 0.497501i
\(634\) −443.335 469.908i −0.699267 0.741179i
\(635\) 2143.73 + 641.792i 3.37596 + 1.01070i
\(636\) −94.4378 + 32.0516i −0.148487 + 0.0503956i
\(637\) −714.161 + 83.4735i −1.12113 + 0.131042i
\(638\) −87.6217 104.423i −0.137338 0.163673i
\(639\) −759.270 264.003i −1.18822 0.413150i
\(640\) −80.0182 67.1432i −0.125028 0.104911i
\(641\) 59.5235 90.5010i 0.0928603 0.141187i −0.786070 0.618138i \(-0.787887\pi\)
0.878930 + 0.476950i \(0.158258\pi\)
\(642\) −352.415 + 665.042i −0.548934 + 1.03589i
\(643\) −248.096 + 333.251i −0.385842 + 0.518275i −0.952032 0.305999i \(-0.901009\pi\)
0.566190 + 0.824275i \(0.308417\pi\)
\(644\) 33.5121 66.7282i 0.0520375 0.103615i
\(645\) 625.017 634.106i 0.969019 0.983110i
\(646\) −13.6877 3.24406i −0.0211885 0.00502176i
\(647\) 299.044i 0.462201i −0.972930 0.231100i \(-0.925767\pi\)
0.972930 0.231100i \(-0.0742326\pi\)
\(648\) −84.5398 212.934i −0.130463 0.328602i
\(649\) 652.726 1.00574
\(650\) −298.367 + 1258.91i −0.459026 + 1.93678i
\(651\) −15.2781 + 58.7105i −0.0234687 + 0.0901851i
\(652\) −137.491 69.0505i −0.210876 0.105906i
\(653\) −246.801 183.736i −0.377949 0.281373i 0.391375 0.920231i \(-0.372000\pi\)
−0.769324 + 0.638858i \(0.779407\pi\)
\(654\) 118.280 74.1399i 0.180856 0.113364i
\(655\) −1056.83 695.090i −1.61348 1.06121i
\(656\) −95.2733 + 113.542i −0.145234 + 0.173083i
\(657\) −1134.35 183.174i −1.72656 0.278804i
\(658\) 14.0617 11.7992i 0.0213704 0.0179319i
\(659\) −14.9611 128.001i −0.0227028 0.194234i 0.977128 0.212654i \(-0.0682107\pi\)
−0.999830 + 0.0184194i \(0.994137\pi\)
\(660\) 338.800 386.285i 0.513334 0.585281i
\(661\) −268.576 + 897.105i −0.406317 + 1.35719i 0.473044 + 0.881039i \(0.343155\pi\)
−0.879361 + 0.476155i \(0.842030\pi\)
\(662\) 32.2490 30.4253i 0.0487145 0.0459597i
\(663\) −3.31372 21.5374i −0.00499807 0.0324847i
\(664\) −73.0875 98.1736i −0.110072 0.147852i
\(665\) −243.007 + 42.8487i −0.365424 + 0.0644342i
\(666\) −36.2762 + 828.794i −0.0544688 + 1.24444i
\(667\) −52.4239 + 297.311i −0.0785966 + 0.445744i
\(668\) −87.4916 174.210i −0.130975 0.260793i
\(669\) −413.930 + 373.755i −0.618730 + 0.558677i
\(670\) 513.135 + 59.9769i 0.765874 + 0.0895178i
\(671\) −386.671 587.905i −0.576261 0.876162i
\(672\) 21.7131 2.05767i 0.0323112 0.00306202i
\(673\) 136.270 + 455.174i 0.202482 + 0.676336i 0.997559 + 0.0698280i \(0.0222450\pi\)
−0.795077 + 0.606508i \(0.792570\pi\)
\(674\) 220.043 + 127.042i 0.326473 + 0.188489i
\(675\) 1448.08 + 740.788i 2.14531 + 1.09746i
\(676\) 61.6095 + 106.711i 0.0911383 + 0.157856i
\(677\) 461.324 + 435.237i 0.681424 + 0.642890i 0.947013 0.321196i \(-0.104085\pi\)
−0.265589 + 0.964086i \(0.585566\pi\)
\(678\) 51.3925 + 108.166i 0.0758002 + 0.159537i
\(679\) 10.4773 + 179.889i 0.0154306 + 0.264932i
\(680\) −11.4692 + 4.94733i −0.0168665 + 0.00727548i
\(681\) 182.087 233.735i 0.267382 0.343223i
\(682\) 12.0006 206.043i 0.0175962 0.302116i
\(683\) 333.383 + 915.962i 0.488116 + 1.34109i 0.902384 + 0.430932i \(0.141815\pi\)
−0.414268 + 0.910155i \(0.635963\pi\)
\(684\) 38.0846 372.378i 0.0556792 0.544412i
\(685\) −629.827 229.238i −0.919455 0.334654i
\(686\) −160.794 69.3600i −0.234394 0.101108i
\(687\) −648.131 393.344i −0.943422 0.572553i
\(688\) −125.114 + 29.6526i −0.181852 + 0.0430997i
\(689\) −58.2098 245.607i −0.0844845 0.356468i
\(690\) −1137.67 24.8859i −1.64879 0.0360665i
\(691\) 230.766 534.975i 0.333959 0.774204i −0.665651 0.746264i \(-0.731846\pi\)
0.999610 0.0279405i \(-0.00889488\pi\)
\(692\) 23.9657 65.8451i 0.0346325 0.0951519i
\(693\) 7.78335 + 107.001i 0.0112314 + 0.154402i
\(694\) −572.908 + 208.521i −0.825515 + 0.300463i
\(695\) −729.341 42.4793i −1.04941 0.0611213i
\(696\) −81.7132 + 33.1474i −0.117404 + 0.0476256i
\(697\) 7.02004 + 16.2743i 0.0100718 + 0.0233491i
\(698\) 352.808 20.5487i 0.505455 0.0294394i
\(699\) 206.169 + 142.155i 0.294949 + 0.203369i
\(700\) −106.263 + 112.632i −0.151804 + 0.160903i
\(701\) 20.0883 11.5980i 0.0286567 0.0165449i −0.485603 0.874179i \(-0.661400\pi\)
0.514260 + 0.857634i \(0.328067\pi\)
\(702\) 556.714 162.169i 0.793039 0.231010i
\(703\) −677.713 + 1173.83i −0.964029 + 1.66975i
\(704\) −71.0842 + 21.2812i −0.100972 + 0.0302290i
\(705\) −254.377 116.390i −0.360818 0.165092i
\(706\) 237.267 156.053i 0.336073 0.221039i
\(707\) 23.3408 199.693i 0.0330138 0.282451i
\(708\) 129.917 401.756i 0.183499 0.567453i
\(709\) 446.038 224.009i 0.629108 0.315950i −0.105523 0.994417i \(-0.533652\pi\)
0.734631 + 0.678467i \(0.237355\pi\)
\(710\) −1148.51 202.513i −1.61761 0.285229i
\(711\) 1020.10 321.515i 1.43474 0.452201i
\(712\) −40.0712 227.255i −0.0562798 0.319178i
\(713\) −366.648 + 272.960i −0.514233 + 0.382832i
\(714\) 0.945390 2.43068i 0.00132408 0.00340431i
\(715\) 892.417 + 945.907i 1.24814 + 1.32295i
\(716\) −217.744 65.1883i −0.304112 0.0910451i
\(717\) −70.0578 + 352.104i −0.0977096 + 0.491080i
\(718\) −196.275 + 22.9412i −0.273363 + 0.0319515i
\(719\) −644.746 768.379i −0.896726 1.06868i −0.997277 0.0737450i \(-0.976505\pi\)
0.100551 0.994932i \(-0.467940\pi\)
\(720\) −170.327 285.419i −0.236565 0.396415i
\(721\) −127.733 107.181i −0.177161 0.148655i
\(722\) 55.5297 84.4289i 0.0769110 0.116937i
\(723\) −84.8870 + 3.08332i −0.117409 + 0.00426462i
\(724\) −200.484 + 269.297i −0.276911 + 0.371957i
\(725\) 280.974 559.465i 0.387550 0.771676i
\(726\) 39.4342 + 143.033i 0.0543171 + 0.197015i
\(727\) 1086.94 + 257.610i 1.49510 + 0.354346i 0.895178 0.445710i \(-0.147049\pi\)
0.599926 + 0.800056i \(0.295197\pi\)
\(728\) 55.2015i 0.0758262i
\(729\) −31.5609 728.316i −0.0432935 0.999062i
\(730\) −1667.01 −2.28358
\(731\) −3.54582 + 14.9610i −0.00485064 + 0.0204664i
\(732\) −438.821 + 120.983i −0.599482 + 0.165277i
\(733\) 718.190 + 360.689i 0.979795 + 0.492072i 0.865247 0.501346i \(-0.167162\pi\)
0.114548 + 0.993418i \(0.463458\pi\)
\(734\) 421.634 + 313.895i 0.574433 + 0.427649i
\(735\) 47.6043 + 1310.60i 0.0647677 + 1.78312i
\(736\) 137.299 + 90.3031i 0.186548 + 0.122694i
\(737\) 235.898 281.132i 0.320078 0.381454i
\(738\) −404.997 + 241.686i −0.548776 + 0.327488i
\(739\) −112.239 + 94.1800i −0.151880 + 0.127443i −0.715561 0.698550i \(-0.753829\pi\)
0.563681 + 0.825992i \(0.309385\pi\)
\(740\) 139.724 + 1195.41i 0.188816 + 1.61542i
\(741\) 929.180 + 184.878i 1.25395 + 0.249498i
\(742\) 8.66433 28.9409i 0.0116770 0.0390039i
\(743\) −864.334 + 815.457i −1.16330 + 1.09752i −0.169595 + 0.985514i \(0.554246\pi\)
−0.993708 + 0.112006i \(0.964272\pi\)
\(744\) −124.432 48.3968i −0.167247 0.0650494i
\(745\) 1548.63 + 2080.17i 2.07869 + 2.79217i
\(746\) −507.864 + 89.5500i −0.680782 + 0.120040i
\(747\) −117.069 371.437i −0.156719 0.497239i
\(748\) −1.54076 + 8.73811i −0.00205984 + 0.0116820i
\(749\) −102.323 203.742i −0.136613 0.272019i
\(750\) 1313.54 + 424.763i 1.75139 + 0.566351i
\(751\) 485.615 + 56.7603i 0.646625 + 0.0755796i 0.433082 0.901354i \(-0.357426\pi\)
0.213542 + 0.976934i \(0.431500\pi\)
\(752\) 22.1992 + 33.7523i 0.0295203 + 0.0448834i
\(753\) −530.437 + 1159.30i −0.704431 + 1.53957i
\(754\) −64.0094 213.806i −0.0848932 0.283563i
\(755\) 1070.64 + 618.134i 1.41807 + 0.818721i
\(756\) 67.4087 + 16.5064i 0.0891649 + 0.0218339i
\(757\) −294.470 510.038i −0.388997 0.673762i 0.603318 0.797501i \(-0.293845\pi\)
−0.992315 + 0.123739i \(0.960512\pi\)
\(758\) −666.309 628.630i −0.879035 0.829327i
\(759\) −458.856 + 665.487i −0.604554 + 0.876794i
\(760\) −31.5760 542.138i −0.0415473 0.713340i
\(761\) 105.288 45.4169i 0.138355 0.0596805i −0.325777 0.945447i \(-0.605626\pi\)
0.464132 + 0.885766i \(0.346366\pi\)
\(762\) −386.540 952.876i −0.507270 1.25049i
\(763\) −2.45874 + 42.2149i −0.00322246 + 0.0553276i
\(764\) −61.4440 168.816i −0.0804241 0.220963i
\(765\) −39.6405 + 2.88350i −0.0518177 + 0.00376928i
\(766\) −464.005 168.884i −0.605751 0.220475i
\(767\) 981.277 + 423.282i 1.27937 + 0.551867i
\(768\) −1.04972 + 47.9885i −0.00136683 + 0.0624851i
\(769\) 714.917 169.439i 0.929672 0.220336i 0.262236 0.965004i \(-0.415540\pi\)
0.667436 + 0.744668i \(0.267392\pi\)
\(770\) 35.8941 + 151.449i 0.0466158 + 0.196687i
\(771\) 91.6153 150.959i 0.118827 0.195796i
\(772\) 225.496 522.759i 0.292093 0.677149i
\(773\) −21.3546 + 58.6714i −0.0276256 + 0.0759008i −0.952739 0.303791i \(-0.901748\pi\)
0.925113 + 0.379692i \(0.123970\pi\)
\(774\) −407.016 41.6272i −0.525861 0.0537819i
\(775\) 890.736 324.201i 1.14934 0.418324i
\(776\) −395.897 23.0584i −0.510177 0.0297144i
\(777\) −198.244 154.439i −0.255140 0.198763i
\(778\) 253.257 + 587.116i 0.325523 + 0.754648i
\(779\) −769.271 + 44.8049i −0.987511 + 0.0575159i
\(780\) 759.836 361.017i 0.974148 0.462842i
\(781\) −568.508 + 602.583i −0.727923 + 0.771553i
\(782\) 17.0181 9.82542i 0.0217623 0.0125645i
\(783\) −280.228 + 14.2316i −0.357890 + 0.0181758i
\(784\) 94.6966 164.019i 0.120786 0.209208i
\(785\) −500.428 + 149.818i −0.637488 + 0.190851i
\(786\) 54.8385 + 578.670i 0.0697691 + 0.736222i
\(787\) 971.970 639.274i 1.23503 0.812293i 0.247373 0.968920i \(-0.420433\pi\)
0.987658 + 0.156627i \(0.0500622\pi\)
\(788\) 64.7096 553.626i 0.0821188 0.702572i
\(789\) 526.959 + 583.602i 0.667882 + 0.739673i
\(790\) 1386.66 696.407i 1.75527 0.881528i
\(791\) −35.7252 6.29931i −0.0451646 0.00796373i
\(792\) −235.882 10.3245i −0.297831 0.0130360i
\(793\) −200.057 1134.58i −0.252278 1.43074i
\(794\) −3.93109 + 2.92659i −0.00495099 + 0.00368588i
\(795\) −455.029 + 70.0103i −0.572364 + 0.0880633i
\(796\) 319.513 + 338.664i 0.401399 + 0.425458i
\(797\) 827.952 + 247.873i 1.03884 + 0.311007i 0.760405 0.649449i \(-0.225000\pi\)
0.278431 + 0.960456i \(0.410186\pi\)
\(798\) 85.2469 + 74.7677i 0.106826 + 0.0936939i
\(799\) 4.79811 0.560818i 0.00600514 0.000701900i
\(800\) −219.053 261.058i −0.273817 0.326322i
\(801\) 117.054 724.886i 0.146135 0.904976i
\(802\) 180.223 + 151.225i 0.224717 + 0.188560i
\(803\) −650.716 + 989.366i −0.810356 + 1.23209i
\(804\) −126.086 201.152i −0.156823 0.250189i
\(805\) 205.845 276.497i 0.255708 0.343475i
\(806\) 151.657 301.973i 0.188160 0.374656i
\(807\) −1219.45 317.335i −1.51109 0.393228i
\(808\) 430.546 + 102.041i 0.532854 + 0.126289i
\(809\) 257.116i 0.317819i 0.987293 + 0.158910i \(0.0507978\pi\)
−0.987293 + 0.158910i \(0.949202\pi\)
\(810\) −213.644 1035.82i −0.263758 1.27879i
\(811\) 103.802 0.127993 0.0639965 0.997950i \(-0.479615\pi\)
0.0639965 + 0.997950i \(0.479615\pi\)
\(812\) 6.16017 25.9918i 0.00758642 0.0320096i
\(813\) −46.2310 45.5684i −0.0568647 0.0560497i
\(814\) 764.014 + 383.702i 0.938592 + 0.471379i
\(815\) −569.712 424.135i −0.699034 0.520411i
\(816\) 5.07168 + 2.68756i 0.00621530 + 0.00329358i
\(817\) −558.502 367.332i −0.683600 0.449611i
\(818\) 65.0014 77.4656i 0.0794638 0.0947013i
\(819\) −57.6870 + 165.907i −0.0704358 + 0.202573i
\(820\) −524.152 + 439.816i −0.639210 + 0.536361i
\(821\) −76.6523 655.803i −0.0933646 0.798785i −0.956082 0.293099i \(-0.905313\pi\)
0.862717 0.505686i \(-0.168761\pi\)
\(822\) 98.9854 + 291.654i 0.120420 + 0.354810i
\(823\) 73.9051 246.860i 0.0897997 0.299952i −0.901277 0.433243i \(-0.857369\pi\)
0.991077 + 0.133291i \(0.0425545\pi\)
\(824\) 266.922 251.828i 0.323934 0.305616i
\(825\) 1307.38 1049.16i 1.58470 1.27171i
\(826\) 76.3801 + 102.596i 0.0924698 + 0.124209i
\(827\) −256.359 + 45.2031i −0.309987 + 0.0546591i −0.326478 0.945205i \(-0.605862\pi\)
0.0164904 + 0.999864i \(0.494751\pi\)
\(828\) 318.281 + 414.886i 0.384398 + 0.501070i
\(829\) −142.228 + 806.614i −0.171566 + 0.972996i 0.770468 + 0.637478i \(0.220022\pi\)
−0.942034 + 0.335518i \(0.891089\pi\)
\(830\) −253.574 504.908i −0.305511 0.608323i
\(831\) −7.94634 37.1289i −0.00956238 0.0446798i
\(832\) −120.665 14.1037i −0.145030 0.0169516i
\(833\) −12.4449 18.9216i −0.0149399 0.0227150i
\(834\) 194.539 + 273.606i 0.233260 + 0.328064i
\(835\) −258.106 862.134i −0.309109 1.03250i
\(836\) −334.083 192.883i −0.399620 0.230721i
\(837\) −323.402 275.490i −0.386383 0.329140i
\(838\) −73.2836 126.931i −0.0874506 0.151469i
\(839\) 348.504 + 328.797i 0.415380 + 0.391891i 0.865363 0.501146i \(-0.167088\pi\)
−0.449982 + 0.893038i \(0.648570\pi\)
\(840\) 100.362 + 8.05106i 0.119479 + 0.00958460i
\(841\) −42.6203 731.763i −0.0506781 0.870110i
\(842\) −681.675 + 294.046i −0.809591 + 0.349223i
\(843\) −748.564 104.135i −0.887976 0.123529i
\(844\) −15.6520 + 268.734i −0.0185450 + 0.318405i
\(845\) 194.549 + 534.519i 0.230235 + 0.632567i
\(846\) 31.4474 + 124.641i 0.0371718 + 0.147329i
\(847\) −42.2338 15.3719i −0.0498629 0.0181486i
\(848\) 61.0483 + 26.3337i 0.0719909 + 0.0310539i
\(849\) 1115.81 612.073i 1.31426 0.720934i
\(850\) −39.6523 + 9.39778i −0.0466498 + 0.0110562i
\(851\) −436.664 1842.43i −0.513118 2.16502i
\(852\) 257.739 + 469.857i 0.302511 + 0.551475i
\(853\) 172.697 400.357i 0.202458 0.469351i −0.786492 0.617601i \(-0.788105\pi\)
0.988950 + 0.148250i \(0.0473639\pi\)
\(854\) 47.1605 129.572i 0.0552230 0.151724i
\(855\) 471.647 1662.38i 0.551634 1.94431i
\(856\) 471.504 171.614i 0.550823 0.200483i
\(857\) 757.568 + 44.1233i 0.883977 + 0.0514858i 0.494124 0.869391i \(-0.335489\pi\)
0.389853 + 0.920877i \(0.372526\pi\)
\(858\) 82.3387 591.882i 0.0959659 0.689839i
\(859\) 296.953 + 688.414i 0.345696 + 0.801414i 0.999017 + 0.0443323i \(0.0141160\pi\)
−0.653321 + 0.757081i \(0.726625\pi\)
\(860\) −592.568 + 34.5131i −0.689032 + 0.0401315i
\(861\) 11.4241 142.410i 0.0132684 0.165400i
\(862\) −171.857 + 182.157i −0.199370 + 0.211320i
\(863\) 1042.82 602.074i 1.20837 0.697653i 0.245967 0.969278i \(-0.420894\pi\)
0.962403 + 0.271625i \(0.0875611\pi\)
\(864\) −53.3042 + 143.132i −0.0616946 + 0.165662i
\(865\) 161.736 280.135i 0.186978 0.323856i
\(866\) −567.504 + 169.900i −0.655316 + 0.196189i
\(867\) −706.038 + 502.006i −0.814346 + 0.579015i
\(868\) 33.7904 22.2243i 0.0389290 0.0256040i
\(869\) 127.966 1094.82i 0.147257 1.25986i
\(870\) −398.059 + 85.1927i −0.457539 + 0.0979226i
\(871\) 536.947 269.665i 0.616472 0.309604i
\(872\) −91.6497 16.1603i −0.105103 0.0185325i
\(873\) −1165.77 483.025i −1.33536 0.553293i
\(874\) 148.357 + 841.376i 0.169745 + 0.962673i
\(875\) −335.438 + 249.724i −0.383358 + 0.285399i
\(876\) 479.443 + 597.440i 0.547310 + 0.682010i
\(877\) 29.0930 + 30.8367i 0.0331733 + 0.0351616i 0.743748 0.668460i \(-0.233046\pi\)
−0.710575 + 0.703622i \(0.751565\pi\)
\(878\) −343.107 102.719i −0.390782 0.116993i
\(879\) −300.196 + 101.885i −0.341520 + 0.115910i
\(880\) −340.225 + 39.7666i −0.386619 + 0.0451893i
\(881\) 486.770 + 580.110i 0.552520 + 0.658468i 0.967946 0.251159i \(-0.0808117\pi\)
−0.415425 + 0.909627i \(0.636367\pi\)
\(882\) 456.013 393.997i 0.517022 0.446708i
\(883\) 564.136 + 473.366i 0.638886 + 0.536089i 0.903676 0.428217i \(-0.140858\pi\)
−0.264790 + 0.964306i \(0.585303\pi\)
\(884\) −7.98283 + 12.1373i −0.00903035 + 0.0137300i
\(885\) 912.689 1722.33i 1.03129 1.94614i
\(886\) −135.911 + 182.560i −0.153398 + 0.206050i
\(887\) −398.300 + 793.080i −0.449042 + 0.894115i 0.549248 + 0.835659i \(0.314914\pi\)
−0.998290 + 0.0584563i \(0.981382\pi\)
\(888\) 388.239 393.884i 0.437206 0.443563i
\(889\) 303.096 + 71.8351i 0.340941 + 0.0808044i
\(890\) 1065.27i 1.19694i
\(891\) −698.149 277.533i −0.783557 0.311484i
\(892\) 371.801 0.416817
\(893\) −48.4354 + 204.365i −0.0542390 + 0.228852i
\(894\) 300.116 1153.28i 0.335700 1.29002i
\(895\) −937.658 470.909i −1.04766 0.526156i
\(896\) −11.6631 8.68284i −0.0130168 0.00969067i
\(897\) −1121.38 + 702.901i −1.25014 + 0.783613i
\(898\) −692.235 455.290i −0.770863 0.507004i
\(899\) −105.107 + 125.261i −0.116915 + 0.139334i
\(900\) −385.549 1013.52i −0.428388 1.12613i
\(901\) 6.09026 5.11034i 0.00675945 0.00567185i
\(902\) 56.4270 + 482.764i 0.0625577 + 0.535215i
\(903\) 81.7226 93.1765i 0.0905012 0.103186i
\(904\) 22.8973 76.4824i 0.0253289 0.0846044i
\(905\) −1127.32 + 1063.57i −1.24566 + 1.17522i
\(906\) −86.3897 561.486i −0.0953529 0.619742i
\(907\) 815.519 + 1095.43i 0.899139 + 1.20775i 0.977523 + 0.210829i \(0.0676165\pi\)
−0.0783843 + 0.996923i \(0.524976\pi\)
\(908\) −194.526 + 34.3002i −0.214236 + 0.0377755i
\(909\) 1187.36 + 756.615i 1.30623 + 0.832360i
\(910\) −44.2507 + 250.958i −0.0486272 + 0.275779i
\(911\) 125.680 + 250.249i 0.137958 + 0.274697i 0.951994 0.306118i \(-0.0990302\pi\)
−0.814036 + 0.580815i \(0.802734\pi\)
\(912\) −185.215 + 167.239i −0.203087 + 0.183376i
\(913\) −398.643 46.5947i −0.436630 0.0510348i
\(914\) 475.020 + 722.232i 0.519715 + 0.790189i
\(915\) −2091.96 + 198.248i −2.28630 + 0.216664i
\(916\) 144.960 + 484.200i 0.158253 + 0.528603i
\(917\) −152.487 88.0386i −0.166289 0.0960072i
\(918\) 12.4343 + 13.3775i 0.0135450 + 0.0145724i
\(919\) −90.9919 157.603i −0.0990119 0.171494i 0.812264 0.583290i \(-0.198235\pi\)
−0.911276 + 0.411796i \(0.864902\pi\)
\(920\) 551.804 + 520.601i 0.599787 + 0.565870i
\(921\) −310.246 652.977i −0.336857 0.708987i
\(922\) 17.1467 + 294.397i 0.0185973 + 0.319303i
\(923\) −1245.43 + 537.227i −1.34933 + 0.582045i
\(924\) 43.9545 56.4219i 0.0475698 0.0610626i
\(925\) −228.309 + 3919.92i −0.246821 + 4.23775i
\(926\) 111.602 + 306.624i 0.120520 + 0.331127i
\(927\) 1065.40 477.924i 1.14929 0.515559i
\(928\) 55.2417 + 20.1063i 0.0595277 + 0.0216663i
\(929\) −58.8759 25.3966i −0.0633755 0.0273375i 0.364156 0.931338i \(-0.381357\pi\)
−0.427532 + 0.904000i \(0.640617\pi\)
\(930\) −526.901 319.770i −0.566560 0.343839i
\(931\) 958.093 227.072i 1.02910 0.243902i
\(932\) −38.5016 162.451i −0.0413108 0.174304i
\(933\) −625.145 13.6747i −0.670038 0.0146567i
\(934\) −160.963 + 373.154i −0.172337 + 0.399522i
\(935\) −14.0093 + 38.4903i −0.0149832 + 0.0411661i
\(936\) −347.918 168.487i −0.371708 0.180007i
\(937\) −428.141 + 155.831i −0.456928 + 0.166308i −0.560222 0.828343i \(-0.689284\pi\)
0.103294 + 0.994651i \(0.467062\pi\)
\(938\) 71.7927 + 4.18145i 0.0765381 + 0.00445784i
\(939\) −32.3323 + 13.1158i −0.0344327 + 0.0139678i
\(940\) 73.8662 + 171.241i 0.0785810 + 0.182171i
\(941\) 15.3409 0.893504i 0.0163027 0.000949527i −0.0499915 0.998750i \(-0.515919\pi\)
0.0662943 + 0.997800i \(0.478882\pi\)
\(942\) 197.620 + 136.260i 0.209787 + 0.144649i
\(943\) 738.710 782.987i 0.783361 0.830315i
\(944\) −243.780 + 140.747i −0.258242 + 0.149096i
\(945\) 293.223 + 129.078i 0.310289 + 0.136591i
\(946\) −210.825 + 365.159i −0.222859 + 0.386003i
\(947\) 1247.83 373.576i 1.31767 0.394484i 0.450623 0.892714i \(-0.351202\pi\)
0.867044 + 0.498231i \(0.166017\pi\)
\(948\) −648.398 296.674i −0.683964 0.312947i
\(949\) −1619.84 + 1065.39i −1.70689 + 1.12264i
\(950\) 205.683 1759.73i 0.216509 1.85235i
\(951\) −421.665 + 1303.96i −0.443391 + 1.37115i
\(952\) −1.55376 + 0.780329i −0.00163210 + 0.000819673i
\(953\) −769.614 135.704i −0.807570 0.142396i −0.245404 0.969421i \(-0.578921\pi\)
−0.562166 + 0.827025i \(0.690032\pi\)
\(954\) 155.960 + 142.942i 0.163480 + 0.149835i
\(955\) −144.012 816.731i −0.150798 0.855216i
\(956\) 191.978 142.922i 0.200814 0.149500i
\(957\) −104.820 + 269.501i −0.109530 + 0.281610i
\(958\) 165.709 + 175.641i 0.172974 + 0.183342i
\(959\) −89.3786 26.7582i −0.0931997 0.0279022i
\(960\) −43.2410 + 217.325i −0.0450427 + 0.226380i
\(961\) 708.598 82.8233i 0.737355 0.0861845i
\(962\) 899.758 + 1072.29i 0.935300 + 1.11465i
\(963\) 1596.44 23.0473i 1.65778 0.0239328i
\(964\) 43.3801 + 36.4002i 0.0450001 + 0.0377595i
\(965\) 1444.21 2195.82i 1.49659 2.27546i
\(966\) −158.296 + 5.74973i −0.163868 + 0.00595210i
\(967\) 290.812 390.629i 0.300737 0.403959i −0.625909 0.779896i \(-0.715272\pi\)
0.926645 + 0.375937i \(0.122679\pi\)
\(968\) 44.3920 88.3917i 0.0458595 0.0913138i
\(969\) 7.93112 + 28.7672i 0.00818485 + 0.0296875i
\(970\) −1781.36 422.189i −1.83645 0.435247i
\(971\) 504.774i 0.519850i 0.965629 + 0.259925i \(0.0836979\pi\)
−0.965629 + 0.259925i \(0.916302\pi\)
\(972\) −309.781 + 374.475i −0.318705 + 0.385263i
\(973\) −101.696 −0.104518
\(974\) −104.220 + 439.740i −0.107002 + 0.451478i
\(975\) 2645.81 729.452i 2.71365 0.748155i
\(976\) 271.184 + 136.194i 0.277852 + 0.139543i
\(977\) −1122.68 835.807i −1.14911 0.855483i −0.157860 0.987461i \(-0.550460\pi\)
−0.991253 + 0.131979i \(0.957867\pi\)
\(978\) 11.8471 + 326.163i 0.0121136 + 0.333500i
\(979\) −632.237 415.829i −0.645798 0.424748i
\(980\) 561.994 669.758i 0.573463 0.683427i
\(981\) −258.563 144.346i −0.263571 0.147141i
\(982\) −199.088 + 167.054i −0.202737 + 0.170116i
\(983\) −3.24176 27.7350i −0.00329782 0.0282147i 0.991489 0.130189i \(-0.0415583\pi\)
−0.994787 + 0.101974i \(0.967484\pi\)
\(984\) 308.375 + 61.3571i 0.313389 + 0.0623547i
\(985\) 737.984 2465.04i 0.749223 2.50258i
\(986\) 5.11319 4.82405i 0.00518580 0.00489255i
\(987\) −36.2913 14.1152i −0.0367693 0.0143011i
\(988\) −377.163 506.618i −0.381744 0.512771i
\(989\) 919.640 162.157i 0.929869 0.163961i
\(990\) −1064.10 236.026i −1.07484 0.238410i
\(991\) −273.407 + 1550.57i −0.275890 + 1.56465i 0.460231 + 0.887799i \(0.347767\pi\)
−0.736121 + 0.676850i \(0.763345\pi\)
\(992\) 39.9469 + 79.5408i 0.0402690 + 0.0801822i
\(993\) −89.4887 28.9382i −0.0901195 0.0291422i
\(994\) −161.240 18.8462i −0.162213 0.0189600i
\(995\) 1181.10 + 1795.77i 1.18703 + 1.80480i
\(996\) −108.024 + 236.093i −0.108458 + 0.237041i
\(997\) −50.8072 169.708i −0.0509601 0.170219i 0.928721 0.370778i \(-0.120909\pi\)
−0.979681 + 0.200560i \(0.935724\pi\)
\(998\) −866.663 500.368i −0.868400 0.501371i
\(999\) 1578.46 778.092i 1.58004 0.778870i
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 162.3.h.a.65.9 yes 324
81.5 odd 54 inner 162.3.h.a.5.9 324
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
162.3.h.a.5.9 324 81.5 odd 54 inner
162.3.h.a.65.9 yes 324 1.1 even 1 trivial