Properties

Label 462.2.u.a.13.5
Level $462$
Weight $2$
Character 462.13
Analytic conductor $3.689$
Analytic rank $0$
Dimension $32$
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] = [462,2,Mod(13,462)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(462, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 5, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("462.13");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 462.u (of order \(10\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.68908857338\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(8\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 13.5
Character \(\chi\) \(=\) 462.13
Dual form 462.2.u.a.391.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.951057 + 0.309017i) q^{2} +(-0.587785 - 0.809017i) q^{3} +(0.809017 + 0.587785i) q^{4} +(-3.18685 + 1.03547i) q^{5} +(-0.309017 - 0.951057i) q^{6} +(2.59478 + 0.516820i) q^{7} +(0.587785 + 0.809017i) q^{8} +(-0.309017 + 0.951057i) q^{9} +O(q^{10})\) \(q+(0.951057 + 0.309017i) q^{2} +(-0.587785 - 0.809017i) q^{3} +(0.809017 + 0.587785i) q^{4} +(-3.18685 + 1.03547i) q^{5} +(-0.309017 - 0.951057i) q^{6} +(2.59478 + 0.516820i) q^{7} +(0.587785 + 0.809017i) q^{8} +(-0.309017 + 0.951057i) q^{9} -3.35085 q^{10} +(0.695687 + 3.24284i) q^{11} -1.00000i q^{12} +(-1.25628 + 3.86645i) q^{13} +(2.30808 + 1.29336i) q^{14} +(2.71089 + 1.96958i) q^{15} +(0.309017 + 0.951057i) q^{16} +(1.34308 + 4.13359i) q^{17} +(-0.587785 + 0.809017i) q^{18} +(6.45286 - 4.68828i) q^{19} +(-3.18685 - 1.03547i) q^{20} +(-1.10706 - 2.40300i) q^{21} +(-0.340455 + 3.29910i) q^{22} +1.33151 q^{23} +(0.309017 - 0.951057i) q^{24} +(5.03871 - 3.66084i) q^{25} +(-2.38960 + 3.28900i) q^{26} +(0.951057 - 0.309017i) q^{27} +(1.79544 + 1.94329i) q^{28} +(-5.08234 + 6.99524i) q^{29} +(1.96958 + 2.71089i) q^{30} +(-4.15890 - 1.35131i) q^{31} +1.00000i q^{32} +(2.21460 - 2.46892i) q^{33} +4.34631i q^{34} +(-8.80432 + 1.03979i) q^{35} +(-0.809017 + 0.587785i) q^{36} +(-4.73950 - 3.44345i) q^{37} +(7.58579 - 2.46477i) q^{38} +(3.86645 - 1.25628i) q^{39} +(-2.71089 - 1.96958i) q^{40} +(3.41909 - 2.48412i) q^{41} +(-0.310307 - 2.62749i) q^{42} +7.53044i q^{43} +(-1.34327 + 3.03243i) q^{44} -3.35085i q^{45} +(1.26634 + 0.411458i) q^{46} +(-1.67901 - 2.31096i) q^{47} +(0.587785 - 0.809017i) q^{48} +(6.46579 + 2.68207i) q^{49} +(5.92336 - 1.92462i) q^{50} +(2.55470 - 3.51624i) q^{51} +(-3.28900 + 2.38960i) q^{52} +(4.02534 - 12.3887i) q^{53} +1.00000 q^{54} +(-5.57491 - 9.61407i) q^{55} +(1.10706 + 2.40300i) q^{56} +(-7.58579 - 2.46477i) q^{57} +(-6.99524 + 5.08234i) q^{58} +(-1.54007 + 2.11973i) q^{59} +(1.03547 + 3.18685i) q^{60} +(-2.11173 - 6.49924i) q^{61} +(-3.53777 - 2.57034i) q^{62} +(-1.29336 + 2.30808i) q^{63} +(-0.309017 + 0.951057i) q^{64} -13.6226i q^{65} +(2.86915 - 1.66373i) q^{66} -1.42737 q^{67} +(-1.34308 + 4.13359i) q^{68} +(-0.782639 - 1.07721i) q^{69} +(-8.69472 - 1.73179i) q^{70} +(-3.40310 - 10.4737i) q^{71} +(-0.951057 + 0.309017i) q^{72} +(6.22243 + 4.52086i) q^{73} +(-3.44345 - 4.73950i) q^{74} +(-5.92336 - 1.92462i) q^{75} +7.97617 q^{76} +(0.129193 + 8.77401i) q^{77} +4.06542 q^{78} +(8.00297 + 2.60032i) q^{79} +(-1.96958 - 2.71089i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(4.01938 - 1.30598i) q^{82} +(5.05077 + 15.5447i) q^{83} +(0.516820 - 2.59478i) q^{84} +(-8.56040 - 11.7824i) q^{85} +(-2.32703 + 7.16188i) q^{86} +8.64659 q^{87} +(-2.21460 + 2.46892i) q^{88} -8.96914i q^{89} +(1.03547 - 3.18685i) q^{90} +(-5.25804 + 9.38332i) q^{91} +(1.07721 + 0.782639i) q^{92} +(1.35131 + 4.15890i) q^{93} +(-0.882707 - 2.71669i) q^{94} +(-15.7097 + 21.6226i) q^{95} +(0.809017 - 0.587785i) q^{96} +(-3.40913 - 1.10769i) q^{97} +(5.32053 + 4.54884i) q^{98} +(-3.29910 - 0.340455i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q + 8 q^{4} - 10 q^{5} + 8 q^{6} - 10 q^{7} + 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 32 q + 8 q^{4} - 10 q^{5} + 8 q^{6} - 10 q^{7} + 8 q^{9} - 4 q^{10} + 8 q^{11} - 2 q^{14} + 6 q^{15} - 8 q^{16} + 12 q^{17} + 16 q^{19} - 10 q^{20} + 8 q^{21} - 4 q^{22} + 8 q^{23} - 8 q^{24} + 6 q^{25} + 20 q^{29} + 50 q^{31} + 16 q^{33} + 32 q^{35} - 8 q^{36} - 16 q^{37} - 6 q^{40} - 40 q^{41} - 10 q^{42} + 12 q^{44} - 28 q^{49} + 40 q^{51} + 32 q^{54} + 40 q^{55} - 8 q^{56} + 10 q^{58} - 60 q^{59} + 4 q^{60} + 4 q^{61} - 20 q^{62} - 10 q^{63} + 8 q^{64} - 8 q^{66} - 16 q^{67} - 12 q^{68} - 30 q^{69} - 18 q^{70} - 48 q^{71} + 74 q^{73} - 40 q^{74} + 24 q^{76} - 70 q^{77} - 60 q^{79} - 8 q^{81} - 20 q^{82} - 4 q^{83} + 2 q^{84} - 10 q^{85} - 36 q^{86} - 20 q^{87} - 16 q^{88} + 4 q^{90} - 60 q^{91} - 8 q^{92} - 10 q^{93} - 20 q^{95} + 8 q^{96} - 60 q^{97} + 40 q^{98} - 8 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/462\mathbb{Z}\right)^\times\).

\(n\) \(155\) \(199\) \(211\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{1}{10}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.951057 + 0.309017i 0.672499 + 0.218508i
\(3\) −0.587785 0.809017i −0.339358 0.467086i
\(4\) 0.809017 + 0.587785i 0.404508 + 0.293893i
\(5\) −3.18685 + 1.03547i −1.42520 + 0.463076i −0.917251 0.398310i \(-0.869597\pi\)
−0.507950 + 0.861386i \(0.669597\pi\)
\(6\) −0.309017 0.951057i −0.126156 0.388267i
\(7\) 2.59478 + 0.516820i 0.980736 + 0.195340i
\(8\) 0.587785 + 0.809017i 0.207813 + 0.286031i
\(9\) −0.309017 + 0.951057i −0.103006 + 0.317019i
\(10\) −3.35085 −1.05963
\(11\) 0.695687 + 3.24284i 0.209758 + 0.977753i
\(12\) 1.00000i 0.288675i
\(13\) −1.25628 + 3.86645i −0.348431 + 1.07236i 0.611291 + 0.791406i \(0.290651\pi\)
−0.959721 + 0.280953i \(0.909349\pi\)
\(14\) 2.30808 + 1.29336i 0.616860 + 0.345664i
\(15\) 2.71089 + 1.96958i 0.699950 + 0.508543i
\(16\) 0.309017 + 0.951057i 0.0772542 + 0.237764i
\(17\) 1.34308 + 4.13359i 0.325746 + 1.00254i 0.971103 + 0.238661i \(0.0767085\pi\)
−0.645357 + 0.763881i \(0.723291\pi\)
\(18\) −0.587785 + 0.809017i −0.138542 + 0.190687i
\(19\) 6.45286 4.68828i 1.48039 1.07556i 0.502956 0.864312i \(-0.332246\pi\)
0.977432 0.211253i \(-0.0677542\pi\)
\(20\) −3.18685 1.03547i −0.712600 0.231538i
\(21\) −1.10706 2.40300i −0.241580 0.524378i
\(22\) −0.340455 + 3.29910i −0.0725852 + 0.703371i
\(23\) 1.33151 0.277638 0.138819 0.990318i \(-0.455669\pi\)
0.138819 + 0.990318i \(0.455669\pi\)
\(24\) 0.309017 0.951057i 0.0630778 0.194134i
\(25\) 5.03871 3.66084i 1.00774 0.732167i
\(26\) −2.38960 + 3.28900i −0.468638 + 0.645025i
\(27\) 0.951057 0.309017i 0.183031 0.0594703i
\(28\) 1.79544 + 1.94329i 0.339307 + 0.367248i
\(29\) −5.08234 + 6.99524i −0.943766 + 1.29898i 0.0104750 + 0.999945i \(0.496666\pi\)
−0.954241 + 0.299038i \(0.903334\pi\)
\(30\) 1.96958 + 2.71089i 0.359594 + 0.494939i
\(31\) −4.15890 1.35131i −0.746961 0.242702i −0.0892877 0.996006i \(-0.528459\pi\)
−0.657673 + 0.753304i \(0.728459\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 2.21460 2.46892i 0.385512 0.429783i
\(34\) 4.34631i 0.745386i
\(35\) −8.80432 + 1.03979i −1.48820 + 0.175757i
\(36\) −0.809017 + 0.587785i −0.134836 + 0.0979642i
\(37\) −4.73950 3.44345i −0.779169 0.566099i 0.125561 0.992086i \(-0.459927\pi\)
−0.904729 + 0.425987i \(0.859927\pi\)
\(38\) 7.58579 2.46477i 1.23058 0.399839i
\(39\) 3.86645 1.25628i 0.619127 0.201167i
\(40\) −2.71089 1.96958i −0.428630 0.311418i
\(41\) 3.41909 2.48412i 0.533972 0.387954i −0.287869 0.957670i \(-0.592947\pi\)
0.821842 + 0.569716i \(0.192947\pi\)
\(42\) −0.310307 2.62749i −0.0478814 0.405431i
\(43\) 7.53044i 1.14838i 0.818721 + 0.574191i \(0.194683\pi\)
−0.818721 + 0.574191i \(0.805317\pi\)
\(44\) −1.34327 + 3.03243i −0.202506 + 0.457156i
\(45\) 3.35085i 0.499515i
\(46\) 1.26634 + 0.411458i 0.186711 + 0.0606661i
\(47\) −1.67901 2.31096i −0.244909 0.337088i 0.668811 0.743432i \(-0.266803\pi\)
−0.913720 + 0.406344i \(0.866803\pi\)
\(48\) 0.587785 0.809017i 0.0848395 0.116772i
\(49\) 6.46579 + 2.68207i 0.923685 + 0.383153i
\(50\) 5.92336 1.92462i 0.837689 0.272182i
\(51\) 2.55470 3.51624i 0.357729 0.492372i
\(52\) −3.28900 + 2.38960i −0.456102 + 0.331377i
\(53\) 4.02534 12.3887i 0.552923 1.70172i −0.148444 0.988921i \(-0.547427\pi\)
0.701367 0.712800i \(-0.252573\pi\)
\(54\) 1.00000 0.136083
\(55\) −5.57491 9.61407i −0.751721 1.29636i
\(56\) 1.10706 + 2.40300i 0.147937 + 0.321115i
\(57\) −7.58579 2.46477i −1.00476 0.326467i
\(58\) −6.99524 + 5.08234i −0.918520 + 0.667344i
\(59\) −1.54007 + 2.11973i −0.200500 + 0.275965i −0.897413 0.441191i \(-0.854556\pi\)
0.696913 + 0.717156i \(0.254556\pi\)
\(60\) 1.03547 + 3.18685i 0.133678 + 0.411420i
\(61\) −2.11173 6.49924i −0.270380 0.832143i −0.990405 0.138195i \(-0.955870\pi\)
0.720025 0.693948i \(-0.244130\pi\)
\(62\) −3.53777 2.57034i −0.449298 0.326434i
\(63\) −1.29336 + 2.30808i −0.162948 + 0.290791i
\(64\) −0.309017 + 0.951057i −0.0386271 + 0.118882i
\(65\) 13.6226i 1.68968i
\(66\) 2.86915 1.66373i 0.353167 0.204791i
\(67\) −1.42737 −0.174381 −0.0871907 0.996192i \(-0.527789\pi\)
−0.0871907 + 0.996192i \(0.527789\pi\)
\(68\) −1.34308 + 4.13359i −0.162873 + 0.501271i
\(69\) −0.782639 1.07721i −0.0942187 0.129681i
\(70\) −8.69472 1.73179i −1.03922 0.206988i
\(71\) −3.40310 10.4737i −0.403874 1.24300i −0.921832 0.387590i \(-0.873308\pi\)
0.517958 0.855406i \(-0.326692\pi\)
\(72\) −0.951057 + 0.309017i −0.112083 + 0.0364180i
\(73\) 6.22243 + 4.52086i 0.728280 + 0.529127i 0.889019 0.457870i \(-0.151388\pi\)
−0.160739 + 0.986997i \(0.551388\pi\)
\(74\) −3.44345 4.73950i −0.400293 0.550956i
\(75\) −5.92336 1.92462i −0.683970 0.222235i
\(76\) 7.97617 0.914930
\(77\) 0.129193 + 8.77401i 0.0147229 + 0.999892i
\(78\) 4.06542 0.460319
\(79\) 8.00297 + 2.60032i 0.900404 + 0.292559i 0.722404 0.691471i \(-0.243037\pi\)
0.178000 + 0.984030i \(0.443037\pi\)
\(80\) −1.96958 2.71089i −0.220206 0.303087i
\(81\) −0.809017 0.587785i −0.0898908 0.0653095i
\(82\) 4.01938 1.30598i 0.443867 0.144221i
\(83\) 5.05077 + 15.5447i 0.554394 + 1.70625i 0.697537 + 0.716549i \(0.254279\pi\)
−0.143143 + 0.989702i \(0.545721\pi\)
\(84\) 0.516820 2.59478i 0.0563897 0.283114i
\(85\) −8.56040 11.7824i −0.928506 1.27798i
\(86\) −2.32703 + 7.16188i −0.250931 + 0.772285i
\(87\) 8.64659 0.927012
\(88\) −2.21460 + 2.46892i −0.236077 + 0.263187i
\(89\) 8.96914i 0.950727i −0.879789 0.475364i \(-0.842317\pi\)
0.879789 0.475364i \(-0.157683\pi\)
\(90\) 1.03547 3.18685i 0.109148 0.335923i
\(91\) −5.25804 + 9.38332i −0.551193 + 0.983639i
\(92\) 1.07721 + 0.782639i 0.112307 + 0.0815958i
\(93\) 1.35131 + 4.15890i 0.140124 + 0.431258i
\(94\) −0.882707 2.71669i −0.0910443 0.280206i
\(95\) −15.7097 + 21.6226i −1.61178 + 2.21843i
\(96\) 0.809017 0.587785i 0.0825700 0.0599906i
\(97\) −3.40913 1.10769i −0.346145 0.112469i 0.130785 0.991411i \(-0.458250\pi\)
−0.476930 + 0.878941i \(0.658250\pi\)
\(98\) 5.32053 + 4.54884i 0.537455 + 0.459502i
\(99\) −3.29910 0.340455i −0.331572 0.0342170i
\(100\) 6.22819 0.622819
\(101\) −2.93130 + 9.02160i −0.291675 + 0.897683i 0.692643 + 0.721280i \(0.256446\pi\)
−0.984318 + 0.176402i \(0.943554\pi\)
\(102\) 3.51624 2.55470i 0.348160 0.252953i
\(103\) 7.73913 10.6520i 0.762559 1.04957i −0.234438 0.972131i \(-0.575325\pi\)
0.996997 0.0774410i \(-0.0246749\pi\)
\(104\) −3.86645 + 1.25628i −0.379136 + 0.123189i
\(105\) 6.01626 + 6.51167i 0.587127 + 0.635474i
\(106\) 7.65665 10.5385i 0.743679 1.02359i
\(107\) −9.11004 12.5389i −0.880701 1.21218i −0.976226 0.216754i \(-0.930453\pi\)
0.0955251 0.995427i \(-0.469547\pi\)
\(108\) 0.951057 + 0.309017i 0.0915155 + 0.0297352i
\(109\) 9.74058i 0.932979i −0.884527 0.466489i \(-0.845519\pi\)
0.884527 0.466489i \(-0.154481\pi\)
\(110\) −2.33114 10.8663i −0.222266 1.03606i
\(111\) 5.85834i 0.556049i
\(112\) 0.310307 + 2.62749i 0.0293212 + 0.248275i
\(113\) 9.62643 6.99401i 0.905578 0.657941i −0.0343143 0.999411i \(-0.510925\pi\)
0.939893 + 0.341470i \(0.110925\pi\)
\(114\) −6.45286 4.68828i −0.604366 0.439097i
\(115\) −4.24330 + 1.37873i −0.395690 + 0.128567i
\(116\) −8.22339 + 2.67194i −0.763523 + 0.248084i
\(117\) −3.28900 2.38960i −0.304068 0.220918i
\(118\) −2.11973 + 1.54007i −0.195137 + 0.141775i
\(119\) 1.34869 + 11.4199i 0.123634 + 1.04686i
\(120\) 3.35085i 0.305889i
\(121\) −10.0320 + 4.51201i −0.912003 + 0.410183i
\(122\) 6.83371i 0.618695i
\(123\) −4.01938 1.30598i −0.362416 0.117756i
\(124\) −2.57034 3.53777i −0.230824 0.317701i
\(125\) −2.41901 + 3.32948i −0.216363 + 0.297798i
\(126\) −1.94329 + 1.79544i −0.173122 + 0.159951i
\(127\) 10.0435 3.26334i 0.891218 0.289574i 0.172611 0.984990i \(-0.444780\pi\)
0.718608 + 0.695416i \(0.244780\pi\)
\(128\) −0.587785 + 0.809017i −0.0519534 + 0.0715077i
\(129\) 6.09226 4.42628i 0.536393 0.389712i
\(130\) 4.20962 12.9559i 0.369208 1.13631i
\(131\) −1.47125 −0.128544 −0.0642720 0.997932i \(-0.520473\pi\)
−0.0642720 + 0.997932i \(0.520473\pi\)
\(132\) 3.24284 0.695687i 0.282253 0.0605518i
\(133\) 19.1668 8.83009i 1.66197 0.765666i
\(134\) −1.35751 0.441082i −0.117271 0.0381037i
\(135\) −2.71089 + 1.96958i −0.233317 + 0.169514i
\(136\) −2.55470 + 3.51624i −0.219063 + 0.301515i
\(137\) 2.83922 + 8.73822i 0.242571 + 0.746557i 0.996026 + 0.0890578i \(0.0283856\pi\)
−0.753455 + 0.657499i \(0.771614\pi\)
\(138\) −0.411458 1.26634i −0.0350256 0.107798i
\(139\) 0.651883 + 0.473621i 0.0552920 + 0.0401720i 0.615088 0.788459i \(-0.289120\pi\)
−0.559796 + 0.828630i \(0.689120\pi\)
\(140\) −7.73402 4.33384i −0.653644 0.366277i
\(141\) −0.882707 + 2.71669i −0.0743374 + 0.228787i
\(142\) 11.0127i 0.924163i
\(143\) −13.4123 1.38409i −1.12159 0.115744i
\(144\) −1.00000 −0.0833333
\(145\) 8.95328 27.5553i 0.743529 2.28835i
\(146\) 4.52086 + 6.22243i 0.374149 + 0.514972i
\(147\) −1.63066 6.80742i −0.134494 0.561466i
\(148\) −1.81033 5.57162i −0.148808 0.457984i
\(149\) 10.5048 3.41323i 0.860590 0.279623i 0.154715 0.987959i \(-0.450554\pi\)
0.705875 + 0.708336i \(0.250554\pi\)
\(150\) −5.03871 3.66084i −0.411409 0.298906i
\(151\) 7.41822 + 10.2103i 0.603686 + 0.830902i 0.996039 0.0889122i \(-0.0283390\pi\)
−0.392354 + 0.919814i \(0.628339\pi\)
\(152\) 7.58579 + 2.46477i 0.615289 + 0.199919i
\(153\) −4.34631 −0.351378
\(154\) −2.58845 + 8.38451i −0.208583 + 0.675643i
\(155\) 14.6530 1.17696
\(156\) 3.86645 + 1.25628i 0.309564 + 0.100583i
\(157\) 0.0381184 + 0.0524654i 0.00304218 + 0.00418720i 0.810535 0.585690i \(-0.199176\pi\)
−0.807493 + 0.589877i \(0.799176\pi\)
\(158\) 6.80773 + 4.94611i 0.541594 + 0.393491i
\(159\) −12.3887 + 4.02534i −0.982489 + 0.319230i
\(160\) −1.03547 3.18685i −0.0818610 0.251942i
\(161\) 3.45497 + 0.688149i 0.272290 + 0.0542337i
\(162\) −0.587785 0.809017i −0.0461808 0.0635624i
\(163\) −4.04450 + 12.4477i −0.316790 + 0.974978i 0.658222 + 0.752824i \(0.271309\pi\)
−0.975012 + 0.222154i \(0.928691\pi\)
\(164\) 4.22623 0.330013
\(165\) −4.50110 + 10.1612i −0.350410 + 0.791049i
\(166\) 16.3446i 1.26859i
\(167\) 0.490022 1.50813i 0.0379190 0.116703i −0.930305 0.366786i \(-0.880458\pi\)
0.968224 + 0.250083i \(0.0804580\pi\)
\(168\) 1.29336 2.30808i 0.0997847 0.178072i
\(169\) −2.85394 2.07351i −0.219534 0.159501i
\(170\) −4.50047 13.8510i −0.345170 1.06233i
\(171\) 2.46477 + 7.58579i 0.188486 + 0.580100i
\(172\) −4.42628 + 6.09226i −0.337501 + 0.464530i
\(173\) 6.33012 4.59910i 0.481270 0.349663i −0.320547 0.947233i \(-0.603867\pi\)
0.801817 + 0.597569i \(0.203867\pi\)
\(174\) 8.22339 + 2.67194i 0.623414 + 0.202559i
\(175\) 14.9663 6.89497i 1.13135 0.521211i
\(176\) −2.86915 + 1.66373i −0.216270 + 0.125408i
\(177\) 2.62013 0.196941
\(178\) 2.77162 8.53016i 0.207741 0.639363i
\(179\) −8.31217 + 6.03915i −0.621281 + 0.451387i −0.853369 0.521308i \(-0.825444\pi\)
0.232088 + 0.972695i \(0.425444\pi\)
\(180\) 1.96958 2.71089i 0.146804 0.202058i
\(181\) −3.21311 + 1.04400i −0.238829 + 0.0776002i −0.425986 0.904730i \(-0.640073\pi\)
0.187157 + 0.982330i \(0.440073\pi\)
\(182\) −7.90030 + 7.29924i −0.585609 + 0.541056i
\(183\) −4.01675 + 5.52859i −0.296927 + 0.408685i
\(184\) 0.782639 + 1.07721i 0.0576969 + 0.0794130i
\(185\) 18.6696 + 6.06613i 1.37262 + 0.445991i
\(186\) 4.37293i 0.320639i
\(187\) −12.4702 + 7.23109i −0.911911 + 0.528790i
\(188\) 2.85650i 0.208332i
\(189\) 2.62749 0.310307i 0.191122 0.0225715i
\(190\) −21.6226 + 15.7097i −1.56867 + 1.13970i
\(191\) 3.94217 + 2.86415i 0.285245 + 0.207243i 0.721202 0.692725i \(-0.243590\pi\)
−0.435957 + 0.899968i \(0.643590\pi\)
\(192\) 0.951057 0.309017i 0.0686366 0.0223014i
\(193\) 23.3253 7.57885i 1.67899 0.545537i 0.694276 0.719709i \(-0.255725\pi\)
0.984715 + 0.174172i \(0.0557248\pi\)
\(194\) −2.89998 2.10696i −0.208207 0.151271i
\(195\) −11.0209 + 8.00717i −0.789225 + 0.573406i
\(196\) 3.65446 + 5.97034i 0.261033 + 0.426453i
\(197\) 3.63422i 0.258928i 0.991584 + 0.129464i \(0.0413256\pi\)
−0.991584 + 0.129464i \(0.958674\pi\)
\(198\) −3.03243 1.34327i −0.215505 0.0954621i
\(199\) 9.89059i 0.701125i 0.936539 + 0.350563i \(0.114010\pi\)
−0.936539 + 0.350563i \(0.885990\pi\)
\(200\) 5.92336 + 1.92462i 0.418845 + 0.136091i
\(201\) 0.838989 + 1.15477i 0.0591777 + 0.0814511i
\(202\) −5.57565 + 7.67423i −0.392302 + 0.539957i
\(203\) −16.8028 + 15.5245i −1.17933 + 1.08960i
\(204\) 4.13359 1.34308i 0.289409 0.0940347i
\(205\) −8.32390 + 11.4569i −0.581366 + 0.800182i
\(206\) 10.6520 7.73913i 0.742159 0.539210i
\(207\) −0.411458 + 1.26634i −0.0285983 + 0.0880165i
\(208\) −4.06542 −0.281886
\(209\) 19.6925 + 17.6640i 1.36216 + 1.22185i
\(210\) 3.70959 + 8.05210i 0.255986 + 0.555647i
\(211\) 6.08793 + 1.97809i 0.419111 + 0.136177i 0.510978 0.859594i \(-0.329283\pi\)
−0.0918671 + 0.995771i \(0.529283\pi\)
\(212\) 10.5385 7.65665i 0.723785 0.525861i
\(213\) −6.47308 + 8.90944i −0.443528 + 0.610465i
\(214\) −4.78943 14.7404i −0.327399 1.00763i
\(215\) −7.79754 23.9984i −0.531788 1.63667i
\(216\) 0.809017 + 0.587785i 0.0550466 + 0.0399937i
\(217\) −10.0931 5.65576i −0.685162 0.383938i
\(218\) 3.01001 9.26385i 0.203863 0.627427i
\(219\) 7.69135i 0.519733i
\(220\) 1.14081 11.0548i 0.0769136 0.745314i
\(221\) −17.6696 −1.18859
\(222\) −1.81033 + 5.57162i −0.121501 + 0.373942i
\(223\) 4.91386 + 6.76334i 0.329056 + 0.452907i 0.941205 0.337835i \(-0.109695\pi\)
−0.612149 + 0.790742i \(0.709695\pi\)
\(224\) −0.516820 + 2.59478i −0.0345315 + 0.173371i
\(225\) 1.92462 + 5.92336i 0.128308 + 0.394890i
\(226\) 11.3165 3.67697i 0.752766 0.244588i
\(227\) −12.3732 8.98966i −0.821239 0.596665i 0.0958282 0.995398i \(-0.469450\pi\)
−0.917067 + 0.398733i \(0.869450\pi\)
\(228\) −4.68828 6.45286i −0.310489 0.427351i
\(229\) −0.824290 0.267828i −0.0544706 0.0176986i 0.281655 0.959516i \(-0.409117\pi\)
−0.336126 + 0.941817i \(0.609117\pi\)
\(230\) −4.46167 −0.294194
\(231\) 7.02239 5.26175i 0.462039 0.346198i
\(232\) −8.64659 −0.567676
\(233\) 14.5931 + 4.74160i 0.956028 + 0.310632i 0.745163 0.666883i \(-0.232372\pi\)
0.210865 + 0.977515i \(0.432372\pi\)
\(234\) −2.38960 3.28900i −0.156213 0.215008i
\(235\) 7.74367 + 5.62610i 0.505141 + 0.367007i
\(236\) −2.49189 + 0.809664i −0.162208 + 0.0527046i
\(237\) −2.60032 8.00297i −0.168909 0.519849i
\(238\) −2.24626 + 11.2777i −0.145603 + 0.731027i
\(239\) −10.3144 14.1965i −0.667182 0.918297i 0.332510 0.943100i \(-0.392104\pi\)
−0.999692 + 0.0248024i \(0.992104\pi\)
\(240\) −1.03547 + 3.18685i −0.0668392 + 0.205710i
\(241\) −20.8041 −1.34011 −0.670055 0.742312i \(-0.733729\pi\)
−0.670055 + 0.742312i \(0.733729\pi\)
\(242\) −10.9353 + 1.19110i −0.702949 + 0.0765671i
\(243\) 1.00000i 0.0641500i
\(244\) 2.11173 6.49924i 0.135190 0.416072i
\(245\) −23.3827 1.85222i −1.49387 0.118334i
\(246\) −3.41909 2.48412i −0.217993 0.158381i
\(247\) 10.0203 + 30.8395i 0.637579 + 1.96227i
\(248\) −1.35131 4.15890i −0.0858082 0.264090i
\(249\) 9.60714 13.2231i 0.608828 0.837980i
\(250\) −3.32948 + 2.41901i −0.210575 + 0.152992i
\(251\) −5.86531 1.90575i −0.370215 0.120290i 0.118000 0.993014i \(-0.462352\pi\)
−0.488215 + 0.872724i \(0.662352\pi\)
\(252\) −2.40300 + 1.10706i −0.151375 + 0.0697382i
\(253\) 0.926312 + 4.31786i 0.0582367 + 0.271462i
\(254\) 10.5604 0.662617
\(255\) −4.50047 + 13.8510i −0.281830 + 0.867385i
\(256\) −0.809017 + 0.587785i −0.0505636 + 0.0367366i
\(257\) 7.70597 10.6064i 0.480685 0.661606i −0.497951 0.867205i \(-0.665914\pi\)
0.978636 + 0.205599i \(0.0659142\pi\)
\(258\) 7.16188 2.32703i 0.445879 0.144875i
\(259\) −10.5183 11.3845i −0.653577 0.707396i
\(260\) 8.00717 11.0209i 0.496584 0.683489i
\(261\) −5.08234 6.99524i −0.314589 0.432994i
\(262\) −1.39924 0.454642i −0.0864456 0.0280879i
\(263\) 3.63307i 0.224024i −0.993707 0.112012i \(-0.964270\pi\)
0.993707 0.112012i \(-0.0357296\pi\)
\(264\) 3.29910 + 0.340455i 0.203046 + 0.0209536i
\(265\) 43.6490i 2.68134i
\(266\) 20.9573 2.47506i 1.28498 0.151756i
\(267\) −7.25619 + 5.27193i −0.444071 + 0.322637i
\(268\) −1.15477 0.838989i −0.0705387 0.0512494i
\(269\) −3.02434 + 0.982667i −0.184397 + 0.0599142i −0.399760 0.916620i \(-0.630907\pi\)
0.215363 + 0.976534i \(0.430907\pi\)
\(270\) −3.18685 + 1.03547i −0.193945 + 0.0630166i
\(271\) −24.4388 17.7558i −1.48455 1.07859i −0.976054 0.217526i \(-0.930201\pi\)
−0.508497 0.861064i \(-0.669799\pi\)
\(272\) −3.51624 + 2.55470i −0.213203 + 0.154901i
\(273\) 10.6819 1.26153i 0.646496 0.0763512i
\(274\) 9.18791i 0.555062i
\(275\) 15.3769 + 13.7929i 0.927260 + 0.831745i
\(276\) 1.33151i 0.0801472i
\(277\) −21.8573 7.10188i −1.31328 0.426710i −0.433098 0.901347i \(-0.642579\pi\)
−0.880182 + 0.474637i \(0.842579\pi\)
\(278\) 0.473621 + 0.651883i 0.0284059 + 0.0390973i
\(279\) 2.57034 3.53777i 0.153882 0.211801i
\(280\) −6.01626 6.51167i −0.359540 0.389147i
\(281\) 16.2054 5.26544i 0.966731 0.314110i 0.217236 0.976119i \(-0.430296\pi\)
0.749496 + 0.662009i \(0.230296\pi\)
\(282\) −1.67901 + 2.31096i −0.0999835 + 0.137616i
\(283\) 14.0633 10.2176i 0.835974 0.607371i −0.0852690 0.996358i \(-0.527175\pi\)
0.921243 + 0.388987i \(0.127175\pi\)
\(284\) 3.40310 10.4737i 0.201937 0.621498i
\(285\) 26.7269 1.58317
\(286\) −12.3281 5.46097i −0.728976 0.322914i
\(287\) 10.1556 4.67869i 0.599469 0.276174i
\(288\) −0.951057 0.309017i −0.0560415 0.0182090i
\(289\) −1.52938 + 1.11116i −0.0899635 + 0.0653623i
\(290\) 17.0301 23.4400i 1.00004 1.37644i
\(291\) 1.10769 + 3.40913i 0.0649342 + 0.199847i
\(292\) 2.37676 + 7.31490i 0.139089 + 0.428072i
\(293\) −2.17095 1.57729i −0.126828 0.0921461i 0.522563 0.852601i \(-0.324976\pi\)
−0.649391 + 0.760455i \(0.724976\pi\)
\(294\) 0.552761 6.97814i 0.0322377 0.406973i
\(295\) 2.71306 8.34994i 0.157961 0.486153i
\(296\) 5.85834i 0.340509i
\(297\) 1.66373 + 2.86915i 0.0965395 + 0.166485i
\(298\) 11.0454 0.639845
\(299\) −1.67275 + 5.14820i −0.0967376 + 0.297728i
\(300\) −3.66084 5.03871i −0.211358 0.290910i
\(301\) −3.89188 + 19.5399i −0.224324 + 1.12626i
\(302\) 3.89999 + 12.0029i 0.224419 + 0.690691i
\(303\) 9.02160 2.93130i 0.518277 0.168398i
\(304\) 6.45286 + 4.68828i 0.370097 + 0.268891i
\(305\) 13.4595 + 18.5255i 0.770691 + 1.06076i
\(306\) −4.13359 1.34308i −0.236301 0.0767790i
\(307\) 27.8314 1.58842 0.794212 0.607641i \(-0.207884\pi\)
0.794212 + 0.607641i \(0.207884\pi\)
\(308\) −5.05272 + 7.17426i −0.287905 + 0.408792i
\(309\) −13.1666 −0.749021
\(310\) 13.9358 + 4.52803i 0.791503 + 0.257175i
\(311\) 0.364789 + 0.502088i 0.0206853 + 0.0284708i 0.819234 0.573459i \(-0.194399\pi\)
−0.798549 + 0.601930i \(0.794399\pi\)
\(312\) 3.28900 + 2.38960i 0.186203 + 0.135284i
\(313\) −10.5475 + 3.42710i −0.596182 + 0.193711i −0.591537 0.806278i \(-0.701479\pi\)
−0.00464514 + 0.999989i \(0.501479\pi\)
\(314\) 0.0200400 + 0.0616768i 0.00113092 + 0.00348062i
\(315\) 1.73179 8.69472i 0.0975751 0.489892i
\(316\) 4.94611 + 6.80773i 0.278240 + 0.382965i
\(317\) −4.05992 + 12.4952i −0.228028 + 0.701798i 0.769942 + 0.638114i \(0.220285\pi\)
−0.997970 + 0.0636843i \(0.979715\pi\)
\(318\) −13.0263 −0.730477
\(319\) −26.2202 11.6147i −1.46805 0.650299i
\(320\) 3.35085i 0.187318i
\(321\) −4.78943 + 14.7404i −0.267320 + 0.822727i
\(322\) 3.07322 + 1.72211i 0.171264 + 0.0959695i
\(323\) 28.0461 + 20.3767i 1.56053 + 1.13379i
\(324\) −0.309017 0.951057i −0.0171676 0.0528365i
\(325\) 7.82438 + 24.0810i 0.434018 + 1.33577i
\(326\) −7.69310 + 10.5886i −0.426081 + 0.586450i
\(327\) −7.88030 + 5.72537i −0.435781 + 0.316614i
\(328\) 4.01938 + 1.30598i 0.221933 + 0.0721105i
\(329\) −3.16231 6.86418i −0.174344 0.378434i
\(330\) −7.42079 + 8.27297i −0.408501 + 0.455412i
\(331\) −16.3939 −0.901092 −0.450546 0.892753i \(-0.648771\pi\)
−0.450546 + 0.892753i \(0.648771\pi\)
\(332\) −5.05077 + 15.5447i −0.277197 + 0.853125i
\(333\) 4.73950 3.44345i 0.259723 0.188700i
\(334\) 0.932077 1.28289i 0.0510010 0.0701969i
\(335\) 4.54882 1.47800i 0.248528 0.0807518i
\(336\) 1.94329 1.79544i 0.106015 0.0979495i
\(337\) −20.1910 + 27.7905i −1.09987 + 1.51384i −0.264318 + 0.964436i \(0.585147\pi\)
−0.835554 + 0.549408i \(0.814853\pi\)
\(338\) −2.07351 2.85394i −0.112784 0.155234i
\(339\) −11.3165 3.67697i −0.614631 0.199706i
\(340\) 14.5638i 0.789835i
\(341\) 1.48878 14.4267i 0.0806222 0.781252i
\(342\) 7.97617i 0.431302i
\(343\) 15.3912 + 10.3010i 0.831046 + 0.556204i
\(344\) −6.09226 + 4.42628i −0.328472 + 0.238649i
\(345\) 3.60957 + 2.62251i 0.194333 + 0.141191i
\(346\) 7.44150 2.41789i 0.400057 0.129987i
\(347\) 22.5095 7.31378i 1.20837 0.392625i 0.365539 0.930796i \(-0.380885\pi\)
0.842835 + 0.538172i \(0.180885\pi\)
\(348\) 6.99524 + 5.08234i 0.374984 + 0.272442i
\(349\) 0.432192 0.314006i 0.0231347 0.0168084i −0.576158 0.817338i \(-0.695449\pi\)
0.599293 + 0.800530i \(0.295449\pi\)
\(350\) 16.3645 1.93265i 0.874719 0.103304i
\(351\) 4.06542i 0.216996i
\(352\) −3.24284 + 0.695687i −0.172844 + 0.0370803i
\(353\) 20.1854i 1.07436i −0.843467 0.537180i \(-0.819489\pi\)
0.843467 0.537180i \(-0.180511\pi\)
\(354\) 2.49189 + 0.809664i 0.132442 + 0.0430332i
\(355\) 21.6903 + 29.8542i 1.15120 + 1.58449i
\(356\) 5.27193 7.25619i 0.279412 0.384577i
\(357\) 8.44615 7.80356i 0.447018 0.413008i
\(358\) −9.77154 + 3.17497i −0.516442 + 0.167802i
\(359\) −3.36003 + 4.62468i −0.177336 + 0.244081i −0.888427 0.459018i \(-0.848201\pi\)
0.711091 + 0.703100i \(0.248201\pi\)
\(360\) 2.71089 1.96958i 0.142877 0.103806i
\(361\) 13.7881 42.4355i 0.725691 2.23345i
\(362\) −3.37847 −0.177568
\(363\) 9.54698 + 5.46400i 0.501086 + 0.286785i
\(364\) −9.76922 + 4.50066i −0.512046 + 0.235899i
\(365\) −24.5111 7.96415i −1.28297 0.416863i
\(366\) −5.52859 + 4.01675i −0.288984 + 0.209959i
\(367\) 8.70219 11.9775i 0.454250 0.625222i −0.519054 0.854742i \(-0.673716\pi\)
0.973304 + 0.229520i \(0.0737155\pi\)
\(368\) 0.411458 + 1.26634i 0.0214487 + 0.0660124i
\(369\) 1.30598 + 4.01938i 0.0679864 + 0.209241i
\(370\) 15.8813 + 11.5385i 0.825632 + 0.599857i
\(371\) 16.8476 30.0657i 0.874684 1.56093i
\(372\) −1.35131 + 4.15890i −0.0700621 + 0.215629i
\(373\) 6.75795i 0.349913i 0.984576 + 0.174957i \(0.0559785\pi\)
−0.984576 + 0.174957i \(0.944021\pi\)
\(374\) −14.0944 + 3.02367i −0.728804 + 0.156350i
\(375\) 4.11546 0.212522
\(376\) 0.882707 2.71669i 0.0455221 0.140103i
\(377\) −20.6619 28.4386i −1.06414 1.46466i
\(378\) 2.59478 + 0.516820i 0.133461 + 0.0265824i
\(379\) 7.28121 + 22.4093i 0.374011 + 1.15109i 0.944144 + 0.329534i \(0.106892\pi\)
−0.570133 + 0.821553i \(0.693108\pi\)
\(380\) −25.4188 + 8.25908i −1.30396 + 0.423682i
\(381\) −8.54353 6.20724i −0.437698 0.318006i
\(382\) 2.86415 + 3.94217i 0.146543 + 0.201699i
\(383\) 12.7244 + 4.13441i 0.650187 + 0.211259i 0.615497 0.788139i \(-0.288955\pi\)
0.0346906 + 0.999398i \(0.488955\pi\)
\(384\) 1.00000 0.0510310
\(385\) −9.49694 27.8277i −0.484009 1.41823i
\(386\) 24.5257 1.24832
\(387\) −7.16188 2.32703i −0.364059 0.118290i
\(388\) −2.10696 2.89998i −0.106965 0.147224i
\(389\) −13.9570 10.1404i −0.707649 0.514137i 0.174765 0.984610i \(-0.444083\pi\)
−0.882414 + 0.470473i \(0.844083\pi\)
\(390\) −12.9559 + 4.20962i −0.656047 + 0.213162i
\(391\) 1.78832 + 5.50389i 0.0904394 + 0.278344i
\(392\) 1.63066 + 6.80742i 0.0823606 + 0.343827i
\(393\) 0.864781 + 1.19027i 0.0436224 + 0.0600411i
\(394\) −1.12304 + 3.45635i −0.0565777 + 0.174128i
\(395\) −28.1968 −1.41873
\(396\) −2.46892 2.21460i −0.124068 0.111288i
\(397\) 16.3142i 0.818786i 0.912358 + 0.409393i \(0.134260\pi\)
−0.912358 + 0.409393i \(0.865740\pi\)
\(398\) −3.05636 + 9.40651i −0.153201 + 0.471506i
\(399\) −18.4096 10.3160i −0.921635 0.516448i
\(400\) 5.03871 + 3.66084i 0.251935 + 0.183042i
\(401\) −4.41908 13.6005i −0.220679 0.679179i −0.998702 0.0509430i \(-0.983777\pi\)
0.778023 0.628236i \(-0.216223\pi\)
\(402\) 0.441082 + 1.35751i 0.0219992 + 0.0677066i
\(403\) 10.4495 14.3825i 0.520528 0.716445i
\(404\) −7.67423 + 5.57565i −0.381807 + 0.277399i
\(405\) 3.18685 + 1.03547i 0.158356 + 0.0514529i
\(406\) −20.7778 + 9.57228i −1.03118 + 0.475064i
\(407\) 7.86934 17.7650i 0.390069 0.880579i
\(408\) 4.34631 0.215174
\(409\) 5.52485 17.0038i 0.273186 0.840782i −0.716507 0.697580i \(-0.754260\pi\)
0.989694 0.143202i \(-0.0457398\pi\)
\(410\) −11.4569 + 8.32390i −0.565814 + 0.411088i
\(411\) 5.40052 7.43318i 0.266388 0.366652i
\(412\) 12.5222 4.06870i 0.616923 0.200450i
\(413\) −5.09167 + 4.70429i −0.250545 + 0.231483i
\(414\) −0.782639 + 1.07721i −0.0384646 + 0.0529420i
\(415\) −32.1921 44.3086i −1.58025 2.17502i
\(416\) −3.86645 1.25628i −0.189568 0.0615944i
\(417\) 0.805771i 0.0394588i
\(418\) 13.2702 + 22.8848i 0.649067 + 1.11933i
\(419\) 18.6363i 0.910444i −0.890378 0.455222i \(-0.849560\pi\)
0.890378 0.455222i \(-0.150440\pi\)
\(420\) 1.03979 + 8.80432i 0.0507366 + 0.429607i
\(421\) 10.9174 7.93199i 0.532084 0.386582i −0.289053 0.957313i \(-0.593340\pi\)
0.821137 + 0.570732i \(0.193340\pi\)
\(422\) 5.17870 + 3.76255i 0.252095 + 0.183158i
\(423\) 2.71669 0.882707i 0.132090 0.0429187i
\(424\) 12.3887 4.02534i 0.601649 0.195488i
\(425\) 21.8998 + 15.9111i 1.06230 + 0.771803i
\(426\) −8.90944 + 6.47308i −0.431664 + 0.313622i
\(427\) −2.12055 17.9555i −0.102621 0.868928i
\(428\) 15.4989i 0.749169i
\(429\) 6.76377 + 11.6643i 0.326558 + 0.563157i
\(430\) 25.2334i 1.21686i
\(431\) −29.9821 9.74178i −1.44419 0.469245i −0.520987 0.853564i \(-0.674436\pi\)
−0.923200 + 0.384319i \(0.874436\pi\)
\(432\) 0.587785 + 0.809017i 0.0282798 + 0.0389238i
\(433\) −21.5925 + 29.7196i −1.03767 + 1.42823i −0.138643 + 0.990342i \(0.544274\pi\)
−0.899029 + 0.437890i \(0.855726\pi\)
\(434\) −7.85135 8.49787i −0.376877 0.407911i
\(435\) −27.5553 + 8.95328i −1.32118 + 0.429277i
\(436\) 5.72537 7.88030i 0.274196 0.377398i
\(437\) 8.59202 6.24247i 0.411012 0.298618i
\(438\) 2.37676 7.31490i 0.113566 0.349520i
\(439\) −16.8116 −0.802374 −0.401187 0.915996i \(-0.631402\pi\)
−0.401187 + 0.915996i \(0.631402\pi\)
\(440\) 4.50110 10.1612i 0.214581 0.484417i
\(441\) −4.54884 + 5.32053i −0.216611 + 0.253359i
\(442\) −16.8048 5.46021i −0.799322 0.259715i
\(443\) 6.82698 4.96009i 0.324360 0.235661i −0.413674 0.910425i \(-0.635755\pi\)
0.738034 + 0.674764i \(0.235755\pi\)
\(444\) −3.44345 + 4.73950i −0.163419 + 0.224927i
\(445\) 9.28727 + 28.5833i 0.440259 + 1.35498i
\(446\) 2.58337 + 7.95079i 0.122326 + 0.376481i
\(447\) −8.93595 6.49235i −0.422656 0.307078i
\(448\) −1.29336 + 2.30808i −0.0611054 + 0.109046i
\(449\) 10.1726 31.3081i 0.480076 1.47752i −0.358912 0.933372i \(-0.616852\pi\)
0.838988 0.544151i \(-0.183148\pi\)
\(450\) 6.22819i 0.293599i
\(451\) 10.4342 + 9.35940i 0.491328 + 0.440717i
\(452\) 11.8989 0.559678
\(453\) 3.89999 12.0029i 0.183237 0.563947i
\(454\) −8.98966 12.3732i −0.421906 0.580704i
\(455\) 7.04044 35.3477i 0.330061 1.65713i
\(456\) −2.46477 7.58579i −0.115424 0.355237i
\(457\) −11.5893 + 3.76560i −0.542126 + 0.176147i −0.567263 0.823537i \(-0.691998\pi\)
0.0251371 + 0.999684i \(0.491998\pi\)
\(458\) −0.701183 0.509439i −0.0327641 0.0238045i
\(459\) 2.55470 + 3.51624i 0.119243 + 0.164124i
\(460\) −4.24330 1.37873i −0.197845 0.0642837i
\(461\) 17.6247 0.820865 0.410433 0.911891i \(-0.365378\pi\)
0.410433 + 0.911891i \(0.365378\pi\)
\(462\) 8.30466 2.83419i 0.386368 0.131858i
\(463\) −9.39398 −0.436575 −0.218288 0.975884i \(-0.570047\pi\)
−0.218288 + 0.975884i \(0.570047\pi\)
\(464\) −8.22339 2.67194i −0.381761 0.124042i
\(465\) −8.61283 11.8545i −0.399410 0.549741i
\(466\) 12.4137 + 9.01905i 0.575052 + 0.417800i
\(467\) 24.4180 7.93389i 1.12993 0.367137i 0.316381 0.948632i \(-0.397532\pi\)
0.813550 + 0.581495i \(0.197532\pi\)
\(468\) −1.25628 3.86645i −0.0580718 0.178727i
\(469\) −3.70372 0.737695i −0.171022 0.0340636i
\(470\) 5.62610 + 7.74367i 0.259513 + 0.357189i
\(471\) 0.0200400 0.0616768i 0.000923395 0.00284192i
\(472\) −2.62013 −0.120601
\(473\) −24.4200 + 5.23883i −1.12283 + 0.240882i
\(474\) 8.41482i 0.386505i
\(475\) 15.3511 47.2457i 0.704355 2.16778i
\(476\) −5.62133 + 10.0316i −0.257653 + 0.459799i
\(477\) 10.5385 + 7.65665i 0.482523 + 0.350574i
\(478\) −5.42259 16.6890i −0.248024 0.763338i
\(479\) 4.17403 + 12.8463i 0.190716 + 0.586964i 1.00000 0.000453914i \(-0.000144485\pi\)
−0.809284 + 0.587418i \(0.800144\pi\)
\(480\) −1.96958 + 2.71089i −0.0898986 + 0.123735i
\(481\) 19.2681 13.9991i 0.878548 0.638303i
\(482\) −19.7859 6.42882i −0.901221 0.292825i
\(483\) −1.47405 3.19961i −0.0670718 0.145587i
\(484\) −10.7682 2.24639i −0.489463 0.102109i
\(485\) 12.0114 0.545408
\(486\) −0.309017 + 0.951057i −0.0140173 + 0.0431408i
\(487\) −12.8400 + 9.32882i −0.581837 + 0.422729i −0.839386 0.543536i \(-0.817085\pi\)
0.257549 + 0.966265i \(0.417085\pi\)
\(488\) 4.01675 5.52859i 0.181830 0.250267i
\(489\) 12.4477 4.04450i 0.562904 0.182899i
\(490\) −21.6659 8.98721i −0.978765 0.406001i
\(491\) 16.8799 23.2333i 0.761781 1.04850i −0.235282 0.971927i \(-0.575601\pi\)
0.997064 0.0765752i \(-0.0243985\pi\)
\(492\) −2.48412 3.41909i −0.111993 0.154145i
\(493\) −35.7414 11.6131i −1.60971 0.523027i
\(494\) 32.4265i 1.45894i
\(495\) 10.8663 2.33114i 0.488402 0.104777i
\(496\) 4.37293i 0.196350i
\(497\) −3.41731 28.9357i −0.153287 1.29794i
\(498\) 13.2231 9.60714i 0.592541 0.430506i
\(499\) −31.1600 22.6391i −1.39491 1.01346i −0.995306 0.0967776i \(-0.969146\pi\)
−0.399607 0.916686i \(-0.630854\pi\)
\(500\) −3.91404 + 1.27175i −0.175041 + 0.0568743i
\(501\) −1.50813 + 0.490022i −0.0673784 + 0.0218926i
\(502\) −4.98933 3.62496i −0.222685 0.161790i
\(503\) −8.90773 + 6.47185i −0.397176 + 0.288565i −0.768390 0.639982i \(-0.778942\pi\)
0.371214 + 0.928547i \(0.378942\pi\)
\(504\) −2.62749 + 0.310307i −0.117038 + 0.0138222i
\(505\) 31.7857i 1.41445i
\(506\) −0.453318 + 4.39278i −0.0201524 + 0.195283i
\(507\) 3.52767i 0.156669i
\(508\) 10.0435 + 3.26334i 0.445609 + 0.144787i
\(509\) −12.2189 16.8179i −0.541595 0.745442i 0.447247 0.894411i \(-0.352405\pi\)
−0.988842 + 0.148969i \(0.952405\pi\)
\(510\) −8.56040 + 11.7824i −0.379061 + 0.521733i
\(511\) 13.8094 + 14.9465i 0.610891 + 0.661195i
\(512\) −0.951057 + 0.309017i −0.0420312 + 0.0136568i
\(513\) 4.68828 6.45286i 0.206992 0.284901i
\(514\) 10.6064 7.70597i 0.467826 0.339896i
\(515\) −13.6336 + 41.9599i −0.600768 + 1.84897i
\(516\) 7.53044 0.331509
\(517\) 6.32600 7.05246i 0.278217 0.310167i
\(518\) −6.48553 14.0776i −0.284958 0.618535i
\(519\) −7.44150 2.41789i −0.326646 0.106134i
\(520\) 11.0209 8.00717i 0.483300 0.351138i
\(521\) −21.4609 + 29.5384i −0.940218 + 1.29410i 0.0155198 + 0.999880i \(0.495060\pi\)
−0.955738 + 0.294220i \(0.904940\pi\)
\(522\) −2.67194 8.22339i −0.116948 0.359928i
\(523\) 5.06088 + 15.5758i 0.221297 + 0.681081i 0.998646 + 0.0520126i \(0.0165636\pi\)
−0.777350 + 0.629069i \(0.783436\pi\)
\(524\) −1.19027 0.864781i −0.0519971 0.0377781i
\(525\) −14.3751 8.05527i −0.627383 0.351561i
\(526\) 1.12268 3.45525i 0.0489511 0.150656i
\(527\) 19.0061i 0.827919i
\(528\) 3.03243 + 1.34327i 0.131970 + 0.0584584i
\(529\) −21.2271 −0.922917
\(530\) −13.4883 + 41.5127i −0.585894 + 1.80320i
\(531\) −1.54007 2.11973i −0.0668334 0.0919883i
\(532\) 20.6964 + 4.12225i 0.897304 + 0.178722i
\(533\) 5.30935 + 16.3405i 0.229973 + 0.707785i
\(534\) −8.53016 + 2.77162i −0.369136 + 0.119940i
\(535\) 42.0160 + 30.5264i 1.81651 + 1.31977i
\(536\) −0.838989 1.15477i −0.0362388 0.0498784i
\(537\) 9.77154 + 3.17497i 0.421673 + 0.137010i
\(538\) −3.17998 −0.137099
\(539\) −4.19936 + 22.8334i −0.180879 + 0.983505i
\(540\) −3.35085 −0.144198
\(541\) −9.80091 3.18451i −0.421374 0.136913i 0.0906520 0.995883i \(-0.471105\pi\)
−0.512026 + 0.858970i \(0.671105\pi\)
\(542\) −17.7558 24.4388i −0.762678 1.04974i
\(543\) 2.73324 + 1.98581i 0.117294 + 0.0852194i
\(544\) −4.13359 + 1.34308i −0.177226 + 0.0575842i
\(545\) 10.0861 + 31.0417i 0.432040 + 1.32968i
\(546\) 10.5489 + 2.10109i 0.451451 + 0.0899184i
\(547\) −1.55026 2.13375i −0.0662844 0.0912326i 0.774588 0.632466i \(-0.217957\pi\)
−0.840872 + 0.541234i \(0.817957\pi\)
\(548\) −2.83922 + 8.73822i −0.121285 + 0.373278i
\(549\) 6.83371 0.291656
\(550\) 10.3620 + 17.8696i 0.441838 + 0.761961i
\(551\) 68.9667i 2.93808i
\(552\) 0.411458 1.26634i 0.0175128 0.0538989i
\(553\) 19.4221 + 10.8834i 0.825910 + 0.462808i
\(554\) −18.5930 13.5086i −0.789939 0.573924i
\(555\) −6.06613 18.6696i −0.257493 0.792482i
\(556\) 0.248997 + 0.766334i 0.0105598 + 0.0324998i
\(557\) 12.2515 16.8628i 0.519114 0.714499i −0.466309 0.884622i \(-0.654417\pi\)
0.985423 + 0.170123i \(0.0544166\pi\)
\(558\) 3.53777 2.57034i 0.149766 0.108811i
\(559\) −29.1161 9.46038i −1.23148 0.400132i
\(560\) −3.70959 8.05210i −0.156759 0.340263i
\(561\) 13.1799 + 5.83827i 0.556455 + 0.246492i
\(562\) 17.0393 0.718761
\(563\) −11.3867 + 35.0447i −0.479893 + 1.47696i 0.359351 + 0.933202i \(0.382998\pi\)
−0.839244 + 0.543755i \(0.817002\pi\)
\(564\) −2.31096 + 1.67901i −0.0973089 + 0.0706990i
\(565\) −23.4359 + 32.2567i −0.985955 + 1.35705i
\(566\) 16.5324 5.37169i 0.694907 0.225789i
\(567\) −1.79544 1.94329i −0.0754016 0.0816106i
\(568\) 6.47308 8.90944i 0.271605 0.373832i
\(569\) 2.28389 + 3.14351i 0.0957457 + 0.131783i 0.854202 0.519941i \(-0.174046\pi\)
−0.758456 + 0.651724i \(0.774046\pi\)
\(570\) 25.4188 + 8.25908i 1.06468 + 0.345935i
\(571\) 2.92993i 0.122614i 0.998119 + 0.0613069i \(0.0195268\pi\)
−0.998119 + 0.0613069i \(0.980473\pi\)
\(572\) −10.0372 9.00328i −0.419676 0.376446i
\(573\) 4.87279i 0.203564i
\(574\) 11.1044 1.31143i 0.463488 0.0547380i
\(575\) 6.70907 4.87442i 0.279787 0.203277i
\(576\) −0.809017 0.587785i −0.0337090 0.0244911i
\(577\) 17.5272 5.69493i 0.729666 0.237083i 0.0794571 0.996838i \(-0.474681\pi\)
0.650209 + 0.759755i \(0.274681\pi\)
\(578\) −1.79789 + 0.584171i −0.0747825 + 0.0242983i
\(579\) −19.8417 14.4158i −0.824592 0.599101i
\(580\) 23.4400 17.0301i 0.973292 0.707138i
\(581\) 5.07186 + 42.9454i 0.210416 + 1.78168i
\(582\) 3.58458i 0.148585i
\(583\) 42.9750 + 4.43486i 1.77984 + 0.183673i
\(584\) 7.69135i 0.318270i
\(585\) 12.9559 + 4.20962i 0.535660 + 0.174046i
\(586\) −1.57729 2.17095i −0.0651572 0.0896811i
\(587\) −12.1267 + 16.6910i −0.500523 + 0.688910i −0.982285 0.187392i \(-0.939997\pi\)
0.481763 + 0.876302i \(0.339997\pi\)
\(588\) 2.68207 6.46579i 0.110607 0.266645i
\(589\) −33.1721 + 10.7783i −1.36683 + 0.444111i
\(590\) 5.16055 7.10289i 0.212456 0.292421i
\(591\) 2.94015 2.13614i 0.120941 0.0878691i
\(592\) 1.81033 5.57162i 0.0744040 0.228992i
\(593\) −11.9095 −0.489063 −0.244532 0.969641i \(-0.578634\pi\)
−0.244532 + 0.969641i \(0.578634\pi\)
\(594\) 0.695687 + 3.24284i 0.0285444 + 0.133055i
\(595\) −16.1230 34.9969i −0.660979 1.43473i
\(596\) 10.5048 + 3.41323i 0.430295 + 0.139811i
\(597\) 8.00165 5.81354i 0.327486 0.237932i
\(598\) −3.18176 + 4.37932i −0.130112 + 0.179084i
\(599\) 1.11447 + 3.42999i 0.0455361 + 0.140146i 0.971240 0.238104i \(-0.0765260\pi\)
−0.925703 + 0.378250i \(0.876526\pi\)
\(600\) −1.92462 5.92336i −0.0785721 0.241820i
\(601\) −38.8729 28.2428i −1.58566 1.15205i −0.909822 0.414998i \(-0.863782\pi\)
−0.675837 0.737051i \(-0.736218\pi\)
\(602\) −9.73955 + 17.3809i −0.396954 + 0.708391i
\(603\) 0.441082 1.35751i 0.0179623 0.0552822i
\(604\) 12.6206i 0.513526i
\(605\) 27.2985 24.7669i 1.10984 1.00692i
\(606\) 9.48587 0.385337
\(607\) 3.41023 10.4956i 0.138417 0.426004i −0.857689 0.514169i \(-0.828100\pi\)
0.996106 + 0.0881655i \(0.0281004\pi\)
\(608\) 4.68828 + 6.45286i 0.190135 + 0.261698i
\(609\) 22.4360 + 4.46873i 0.909153 + 0.181082i
\(610\) 7.07610 + 21.7780i 0.286503 + 0.881765i
\(611\) 11.0445 3.58858i 0.446813 0.145178i
\(612\) −3.51624 2.55470i −0.142136 0.103268i
\(613\) 6.75980 + 9.30406i 0.273026 + 0.375788i 0.923408 0.383819i \(-0.125391\pi\)
−0.650383 + 0.759607i \(0.725391\pi\)
\(614\) 26.4693 + 8.60038i 1.06821 + 0.347083i
\(615\) 14.1615 0.571045
\(616\) −7.02239 + 5.26175i −0.282940 + 0.212002i
\(617\) −2.23443 −0.0899547 −0.0449773 0.998988i \(-0.514322\pi\)
−0.0449773 + 0.998988i \(0.514322\pi\)
\(618\) −12.5222 4.06870i −0.503715 0.163667i
\(619\) 14.3148 + 19.7026i 0.575359 + 0.791913i 0.993177 0.116617i \(-0.0372051\pi\)
−0.417818 + 0.908531i \(0.637205\pi\)
\(620\) 11.8545 + 8.61283i 0.476090 + 0.345899i
\(621\) 1.26634 0.411458i 0.0508163 0.0165112i
\(622\) 0.191781 + 0.590240i 0.00768970 + 0.0236665i
\(623\) 4.63543 23.2730i 0.185715 0.932412i
\(624\) 2.38960 + 3.28900i 0.0956604 + 0.131665i
\(625\) −5.36164 + 16.5014i −0.214466 + 0.660057i
\(626\) −11.0903 −0.443259
\(627\) 2.71553 26.3142i 0.108448 1.05089i
\(628\) 0.0648508i 0.00258783i
\(629\) 7.86825 24.2160i 0.313728 0.965554i
\(630\) 4.33384 7.73402i 0.172664 0.308131i
\(631\) 23.8486 + 17.3270i 0.949396 + 0.689776i 0.950664 0.310223i \(-0.100404\pi\)
−0.00126809 + 0.999999i \(0.500404\pi\)
\(632\) 2.60032 + 8.00297i 0.103435 + 0.318341i
\(633\) −1.97809 6.08793i −0.0786220 0.241974i
\(634\) −7.72243 + 10.6290i −0.306697 + 0.422132i
\(635\) −28.6281 + 20.7995i −1.13607 + 0.825403i
\(636\) −12.3887 4.02534i −0.491245 0.159615i
\(637\) −18.4930 + 21.6302i −0.732718 + 0.857020i
\(638\) −21.3477 19.1487i −0.845164 0.758105i
\(639\) 11.0127 0.435654
\(640\) 1.03547 3.18685i 0.0409305 0.125971i
\(641\) 26.4650 19.2279i 1.04530 0.759458i 0.0739901 0.997259i \(-0.476427\pi\)
0.971314 + 0.237801i \(0.0764267\pi\)
\(642\) −9.11004 + 12.5389i −0.359545 + 0.494871i
\(643\) 33.1283 10.7640i 1.30645 0.424492i 0.428630 0.903480i \(-0.358996\pi\)
0.877821 + 0.478988i \(0.158996\pi\)
\(644\) 2.39064 + 2.58750i 0.0942046 + 0.101962i
\(645\) −14.8318 + 20.4142i −0.584002 + 0.803809i
\(646\) 20.3767 + 28.0461i 0.801711 + 1.10346i
\(647\) 10.4783 + 3.40462i 0.411946 + 0.133849i 0.507656 0.861560i \(-0.330512\pi\)
−0.0957099 + 0.995409i \(0.530512\pi\)
\(648\) 1.00000i 0.0392837i
\(649\) −7.94535 3.51954i −0.311882 0.138154i
\(650\) 25.3202i 0.993140i
\(651\) 1.35695 + 11.4898i 0.0531830 + 0.450322i
\(652\) −10.5886 + 7.69310i −0.414683 + 0.301285i
\(653\) −1.53109 1.11240i −0.0599163 0.0435317i 0.557424 0.830228i \(-0.311790\pi\)
−0.617340 + 0.786696i \(0.711790\pi\)
\(654\) −9.26385 + 3.01001i −0.362245 + 0.117701i
\(655\) 4.68866 1.52344i 0.183201 0.0595256i
\(656\) 3.41909 + 2.48412i 0.133493 + 0.0969884i
\(657\) −6.22243 + 4.52086i −0.242760 + 0.176376i
\(658\) −0.886392 7.50543i −0.0345552 0.292592i
\(659\) 18.1765i 0.708055i −0.935235 0.354028i \(-0.884812\pi\)
0.935235 0.354028i \(-0.115188\pi\)
\(660\) −9.61407 + 5.57491i −0.374227 + 0.217003i
\(661\) 33.3978i 1.29902i −0.760351 0.649512i \(-0.774973\pi\)
0.760351 0.649512i \(-0.225027\pi\)
\(662\) −15.5915 5.06600i −0.605983 0.196896i
\(663\) 10.3859 + 14.2950i 0.403356 + 0.555172i
\(664\) −9.60714 + 13.2231i −0.372829 + 0.513156i
\(665\) −51.9382 + 47.9867i −2.01408 + 1.86085i
\(666\) 5.57162 1.81033i 0.215896 0.0701488i
\(667\) −6.76716 + 9.31420i −0.262025 + 0.360647i
\(668\) 1.28289 0.932077i 0.0496367 0.0360632i
\(669\) 2.58337 7.95079i 0.0998787 0.307395i
\(670\) 4.78291 0.184780
\(671\) 19.6069 11.3695i 0.756916 0.438913i
\(672\) 2.40300 1.10706i 0.0926978 0.0427057i
\(673\) 18.2164 + 5.91888i 0.702192 + 0.228156i 0.638285 0.769800i \(-0.279644\pi\)
0.0639066 + 0.997956i \(0.479644\pi\)
\(674\) −27.7905 + 20.1910i −1.07045 + 0.777727i
\(675\) 3.66084 5.03871i 0.140906 0.193940i
\(676\) −1.09011 3.35501i −0.0419273 0.129039i
\(677\) −14.6937 45.2227i −0.564727 1.73805i −0.668762 0.743476i \(-0.733176\pi\)
0.104036 0.994574i \(-0.466824\pi\)
\(678\) −9.62643 6.99401i −0.369701 0.268603i
\(679\) −8.27348 4.63614i −0.317507 0.177919i
\(680\) 4.50047 13.8510i 0.172585 0.531163i
\(681\) 15.2941i 0.586072i
\(682\) 5.87403 13.2606i 0.224928 0.507774i
\(683\) 28.8662 1.10453 0.552267 0.833667i \(-0.313763\pi\)
0.552267 + 0.833667i \(0.313763\pi\)
\(684\) −2.46477 + 7.58579i −0.0942430 + 0.290050i
\(685\) −18.0963 24.9074i −0.691425 0.951665i
\(686\) 11.4547 + 14.5530i 0.437342 + 0.555637i
\(687\) 0.267828 + 0.824290i 0.0102183 + 0.0314486i
\(688\) −7.16188 + 2.32703i −0.273044 + 0.0887174i
\(689\) 42.8434 + 31.1275i 1.63220 + 1.18586i
\(690\) 2.62251 + 3.60957i 0.0998371 + 0.137414i
\(691\) −10.2129 3.31838i −0.388518 0.126237i 0.108243 0.994124i \(-0.465478\pi\)
−0.496761 + 0.867887i \(0.665478\pi\)
\(692\) 7.82445 0.297441
\(693\) −8.38451 2.58845i −0.318501 0.0983271i
\(694\) 23.6679 0.898421
\(695\) −2.56787 0.834351i −0.0974049 0.0316488i
\(696\) 5.08234 + 6.99524i 0.192645 + 0.265154i
\(697\) 14.8604 + 10.7967i 0.562879 + 0.408956i
\(698\) 0.508073 0.165083i 0.0192308 0.00624848i
\(699\) −4.74160 14.5931i −0.179344 0.551963i
\(700\) 16.1608 + 3.21885i 0.610820 + 0.121661i
\(701\) 11.7169 + 16.1270i 0.442542 + 0.609107i 0.970775 0.239993i \(-0.0771450\pi\)
−0.528232 + 0.849100i \(0.677145\pi\)
\(702\) −1.25628 + 3.86645i −0.0474154 + 0.145930i
\(703\) −46.7272 −1.76235
\(704\) −3.29910 0.340455i −0.124340 0.0128314i
\(705\) 9.57170i 0.360491i
\(706\) 6.23763 19.1975i 0.234756 0.722506i
\(707\) −12.2686 + 21.8941i −0.461409 + 0.823414i
\(708\) 2.11973 + 1.54007i 0.0796642 + 0.0578795i
\(709\) −5.38972 16.5879i −0.202415 0.622970i −0.999810 0.0195117i \(-0.993789\pi\)
0.797394 0.603459i \(-0.206211\pi\)
\(710\) 11.4033 + 35.0957i 0.427957 + 1.31712i
\(711\) −4.94611 + 6.80773i −0.185493 + 0.255310i
\(712\) 7.25619 5.27193i 0.271937 0.197574i
\(713\) −5.53760 1.79927i −0.207385 0.0673834i
\(714\) 10.4442 4.81162i 0.390864 0.180070i
\(715\) 44.1760 9.47709i 1.65209 0.354423i
\(716\) −10.2744 −0.383973
\(717\) −5.42259 + 16.6890i −0.202510 + 0.623263i
\(718\) −4.62468 + 3.36003i −0.172592 + 0.125395i
\(719\) −15.8269 + 21.7838i −0.590243 + 0.812400i −0.994772 0.102125i \(-0.967436\pi\)
0.404528 + 0.914526i \(0.367436\pi\)
\(720\) 3.18685 1.03547i 0.118767 0.0385897i
\(721\) 25.5865 23.6399i 0.952891 0.880395i
\(722\) 26.2266 36.0978i 0.976053 1.34342i
\(723\) 12.2283 + 16.8309i 0.454777 + 0.625947i
\(724\) −3.21311 1.04400i −0.119414 0.0388001i
\(725\) 53.8526i 2.00003i
\(726\) 7.39124 + 8.14675i 0.274315 + 0.302354i
\(727\) 32.3887i 1.20123i 0.799538 + 0.600616i \(0.205078\pi\)
−0.799538 + 0.600616i \(0.794922\pi\)
\(728\) −10.6819 + 1.26153i −0.395896 + 0.0467554i
\(729\) 0.809017 0.587785i 0.0299636 0.0217698i
\(730\) −20.8504 15.1487i −0.771709 0.560679i
\(731\) −31.1277 + 10.1140i −1.15130 + 0.374080i
\(732\) −6.49924 + 2.11173i −0.240219 + 0.0780519i
\(733\) 23.8571 + 17.3332i 0.881183 + 0.640217i 0.933564 0.358410i \(-0.116681\pi\)
−0.0523810 + 0.998627i \(0.516681\pi\)
\(734\) 11.9775 8.70219i 0.442099 0.321204i
\(735\) 12.2455 + 20.0057i 0.451683 + 0.737921i
\(736\) 1.33151i 0.0490799i
\(737\) −0.993005 4.62874i −0.0365778 0.170502i
\(738\) 4.22623i 0.155570i
\(739\) 21.9304 + 7.12561i 0.806721 + 0.262120i 0.683209 0.730223i \(-0.260584\pi\)
0.123513 + 0.992343i \(0.460584\pi\)
\(740\) 11.5385 + 15.8813i 0.424163 + 0.583810i
\(741\) 19.0598 26.2336i 0.700180 0.963716i
\(742\) 25.3138 23.3879i 0.929300 0.858598i
\(743\) −16.2910 + 5.29326i −0.597658 + 0.194191i −0.592196 0.805794i \(-0.701739\pi\)
−0.00546257 + 0.999985i \(0.501739\pi\)
\(744\) −2.57034 + 3.53777i −0.0942333 + 0.129701i
\(745\) −29.9430 + 21.7549i −1.09703 + 0.797037i
\(746\) −2.08832 + 6.42719i −0.0764589 + 0.235316i
\(747\) −16.3446 −0.598019
\(748\) −14.3389 1.47972i −0.524283 0.0541040i
\(749\) −17.1582 37.2440i −0.626948 1.36087i
\(750\) 3.91404 + 1.27175i 0.142921 + 0.0464377i
\(751\) −4.96767 + 3.60922i −0.181273 + 0.131702i −0.674721 0.738073i \(-0.735736\pi\)
0.493448 + 0.869775i \(0.335736\pi\)
\(752\) 1.67901 2.31096i 0.0612272 0.0842719i
\(753\) 1.90575 + 5.86531i 0.0694495 + 0.213744i
\(754\) −10.8626 33.4316i −0.395592 1.21751i
\(755\) −34.2132 24.8573i −1.24514 0.904650i
\(756\) 2.30808 + 1.29336i 0.0839440 + 0.0470389i
\(757\) −3.87785 + 11.9348i −0.140943 + 0.433777i −0.996467 0.0839857i \(-0.973235\pi\)
0.855524 + 0.517763i \(0.173235\pi\)
\(758\) 23.5625i 0.855829i
\(759\) 2.94875 3.28738i 0.107033 0.119324i
\(760\) −26.7269 −0.969488
\(761\) −5.19652 + 15.9933i −0.188374 + 0.579755i −0.999990 0.00443571i \(-0.998588\pi\)
0.811616 + 0.584191i \(0.198588\pi\)
\(762\) −6.20724 8.54353i −0.224864 0.309499i
\(763\) 5.03413 25.2747i 0.182248 0.915005i
\(764\) 1.50577 + 4.63429i 0.0544770 + 0.167663i
\(765\) 13.8510 4.50047i 0.500785 0.162715i
\(766\) 10.8240 + 7.86412i 0.391088 + 0.284142i
\(767\) −6.26105 8.61759i −0.226073 0.311163i
\(768\) 0.951057 + 0.309017i 0.0343183 + 0.0111507i
\(769\) −1.89877 −0.0684712 −0.0342356 0.999414i \(-0.510900\pi\)
−0.0342356 + 0.999414i \(0.510900\pi\)
\(770\) −0.432905 29.4004i −0.0156008 1.05952i
\(771\) −13.1102 −0.472151
\(772\) 23.3253 + 7.57885i 0.839496 + 0.272769i
\(773\) 21.9537 + 30.2167i 0.789620 + 1.08682i 0.994155 + 0.107960i \(0.0344318\pi\)
−0.204535 + 0.978859i \(0.565568\pi\)
\(774\) −6.09226 4.42628i −0.218982 0.159099i
\(775\) −25.9024 + 8.41620i −0.930442 + 0.302319i
\(776\) −1.10769 3.40913i −0.0397639 0.122381i
\(777\) −3.02771 + 15.2011i −0.108618 + 0.545337i
\(778\) −10.1404 13.9570i −0.363550 0.500383i
\(779\) 10.4167 32.0593i 0.373217 1.14864i
\(780\) −13.6226 −0.487768
\(781\) 31.5970 18.3221i 1.13063 0.655617i
\(782\) 5.78714i 0.206948i
\(783\) −2.67194 + 8.22339i −0.0954874 + 0.293880i
\(784\) −0.552761 + 6.97814i −0.0197415 + 0.249219i
\(785\) −0.175804 0.127729i −0.00627470 0.00455884i
\(786\) 0.454642 + 1.39924i 0.0162165 + 0.0499094i
\(787\) 13.7204 + 42.2270i 0.489078 + 1.50523i 0.825986 + 0.563691i \(0.190619\pi\)
−0.336907 + 0.941538i \(0.609381\pi\)
\(788\) −2.13614 + 2.94015i −0.0760969 + 0.104738i
\(789\) −2.93921 + 2.13546i −0.104639 + 0.0760245i
\(790\) −26.8167 8.71328i −0.954097 0.310005i
\(791\) 28.5931 13.1728i 1.01666 0.468371i
\(792\) −1.66373 2.86915i −0.0591181 0.101951i
\(793\) 27.7819 0.986565
\(794\) −5.04137 + 15.5157i −0.178911 + 0.550633i
\(795\) 35.3128 25.6563i 1.25242 0.909934i
\(796\) −5.81354 + 8.00165i −0.206055 + 0.283611i
\(797\) −43.7952 + 14.2299i −1.55131 + 0.504050i −0.954468 0.298312i \(-0.903576\pi\)
−0.596838 + 0.802362i \(0.703576\pi\)
\(798\) −14.3208 15.5000i −0.506950 0.548695i
\(799\) 7.29749 10.0441i 0.258167 0.355336i
\(800\) 3.66084 + 5.03871i 0.129430 + 0.178145i
\(801\) 8.53016 + 2.77162i 0.301398 + 0.0979303i
\(802\) 14.3005i 0.504967i
\(803\) −10.3316 + 23.3235i −0.364593 + 0.823067i
\(804\) 1.42737i 0.0503396i
\(805\) −11.7230 + 1.38449i −0.413182 + 0.0487968i
\(806\) 14.3825 10.4495i 0.506603 0.368069i
\(807\) 2.57265 + 1.86914i 0.0905617 + 0.0657970i
\(808\) −9.02160 + 2.93130i −0.317379 + 0.103123i
\(809\) −48.7918 + 15.8534i −1.71543 + 0.557377i −0.991222 0.132206i \(-0.957794\pi\)
−0.724207 + 0.689583i \(0.757794\pi\)
\(810\) 2.71089 + 1.96958i 0.0952511 + 0.0692040i
\(811\) 10.5956 7.69812i 0.372060 0.270318i −0.386004 0.922497i \(-0.626145\pi\)
0.758065 + 0.652179i \(0.226145\pi\)
\(812\) −22.7188 + 2.68310i −0.797275 + 0.0941582i
\(813\) 30.2080i 1.05944i
\(814\) 12.9739 14.4638i 0.454734 0.506955i
\(815\) 43.8568i 1.53624i
\(816\) 4.13359 + 1.34308i 0.144704 + 0.0470173i
\(817\) 35.3048 + 48.5929i 1.23516 + 1.70005i
\(818\) 10.5089 14.4643i 0.367435 0.505731i
\(819\) −7.29924 7.90030i −0.255056 0.276059i
\(820\) −13.4683 + 4.37613i −0.470335 + 0.152821i
\(821\) −17.0606 + 23.4820i −0.595421 + 0.819526i −0.995279 0.0970505i \(-0.969059\pi\)
0.399859 + 0.916577i \(0.369059\pi\)
\(822\) 7.43318 5.40052i 0.259262 0.188365i
\(823\) −10.8010 + 33.2420i −0.376498 + 1.15874i 0.565964 + 0.824430i \(0.308504\pi\)
−0.942462 + 0.334312i \(0.891496\pi\)
\(824\) 13.1666 0.458680
\(825\) 2.12042 20.5474i 0.0738234 0.715370i
\(826\) −6.29617 + 2.90064i −0.219072 + 0.100926i
\(827\) −5.30991 1.72530i −0.184644 0.0599944i 0.215236 0.976562i \(-0.430948\pi\)
−0.399879 + 0.916568i \(0.630948\pi\)
\(828\) −1.07721 + 0.782639i −0.0374357 + 0.0271986i
\(829\) 3.11236 4.28379i 0.108097 0.148782i −0.751541 0.659686i \(-0.770689\pi\)
0.859638 + 0.510904i \(0.170689\pi\)
\(830\) −16.9244 52.0879i −0.587454 1.80800i
\(831\) 7.10188 + 21.8573i 0.246361 + 0.758222i
\(832\) −3.28900 2.38960i −0.114025 0.0828443i
\(833\) −2.40247 + 30.3292i −0.0832407 + 1.05084i
\(834\) 0.248997 0.766334i 0.00862206 0.0265360i
\(835\) 5.31359i 0.183884i
\(836\) 5.54892 + 25.8655i 0.191914 + 0.894576i
\(837\) −4.37293 −0.151150
\(838\) 5.75894 17.7242i 0.198939 0.612272i
\(839\) 8.33019 + 11.4655i 0.287590 + 0.395834i 0.928230 0.372008i \(-0.121331\pi\)
−0.640639 + 0.767842i \(0.721331\pi\)
\(840\) −1.73179 + 8.69472i −0.0597523 + 0.299996i
\(841\) −14.1417 43.5237i −0.487645 1.50082i
\(842\) 12.8342 4.17009i 0.442297 0.143711i
\(843\) −13.7851 10.0155i −0.474785 0.344951i
\(844\) 3.76255 + 5.17870i 0.129512 + 0.178258i
\(845\) 11.2421 + 3.65279i 0.386741 + 0.125660i
\(846\) 2.85650 0.0982085
\(847\) −28.3629 + 6.52292i −0.974559 + 0.224130i
\(848\) 13.0263 0.447324
\(849\) −16.5324 5.37169i −0.567389 0.184356i
\(850\) 15.9111 + 21.8998i 0.545747 + 0.751157i
\(851\) −6.31067 4.58497i −0.216327 0.157171i
\(852\) −10.4737 + 3.40310i −0.358822 + 0.116588i
\(853\) −7.08231 21.7971i −0.242494 0.746319i −0.996039 0.0889222i \(-0.971658\pi\)
0.753545 0.657396i \(-0.228342\pi\)
\(854\) 3.53180 17.7320i 0.120856 0.606776i
\(855\) −15.7097 21.6226i −0.537261 0.739476i
\(856\) 4.78943 14.7404i 0.163699 0.503815i
\(857\) 1.97573 0.0674897 0.0337448 0.999430i \(-0.489257\pi\)
0.0337448 + 0.999430i \(0.489257\pi\)
\(858\) 2.82826 + 13.1835i 0.0965554 + 0.450078i
\(859\) 16.0866i 0.548867i −0.961606 0.274433i \(-0.911510\pi\)
0.961606 0.274433i \(-0.0884902\pi\)
\(860\) 7.79754 23.9984i 0.265894 0.818337i
\(861\) −9.75447 5.46602i −0.332432 0.186282i
\(862\) −25.5043 18.5300i −0.868680 0.631133i
\(863\) 2.70910 + 8.33775i 0.0922188 + 0.283820i 0.986519 0.163647i \(-0.0523259\pi\)
−0.894300 + 0.447468i \(0.852326\pi\)
\(864\) 0.309017 + 0.951057i 0.0105130 + 0.0323556i
\(865\) −15.4109 + 21.2113i −0.523986 + 0.721205i
\(866\) −29.7196 + 21.5925i −1.00991 + 0.733745i
\(867\) 1.79789 + 0.584171i 0.0610597 + 0.0198395i
\(868\) −4.84109 10.5082i −0.164317 0.356670i
\(869\) −2.86487 + 27.7614i −0.0971839 + 0.941740i
\(870\) −28.9734 −0.982291
\(871\) 1.79319 5.51886i 0.0607598 0.187000i
\(872\) 7.88030 5.72537i 0.266861 0.193886i
\(873\) 2.10696 2.89998i 0.0713098 0.0981495i
\(874\) 10.1005 3.28186i 0.341655 0.111011i
\(875\) −7.99755 + 7.38909i −0.270366 + 0.249797i
\(876\) 4.52086 6.22243i 0.152746 0.210236i
\(877\) 28.2777 + 38.9209i 0.954870 + 1.31427i 0.949330 + 0.314281i \(0.101763\pi\)
0.00553948 + 0.999985i \(0.498237\pi\)
\(878\) −15.9888 5.19507i −0.539595 0.175325i
\(879\) 2.68344i 0.0905103i
\(880\) 7.42079 8.27297i 0.250155 0.278882i
\(881\) 27.7281i 0.934182i −0.884209 0.467091i \(-0.845302\pi\)
0.884209 0.467091i \(-0.154698\pi\)
\(882\) −5.97034 + 3.65446i −0.201032 + 0.123052i
\(883\) −32.0456 + 23.2825i −1.07842 + 0.783518i −0.977407 0.211367i \(-0.932208\pi\)
−0.101013 + 0.994885i \(0.532208\pi\)
\(884\) −14.2950 10.3859i −0.480793 0.349317i
\(885\) −8.34994 + 2.71306i −0.280680 + 0.0911986i
\(886\) 8.02560 2.60768i 0.269625 0.0876066i
\(887\) 34.8003 + 25.2839i 1.16848 + 0.848950i 0.990826 0.135144i \(-0.0431496\pi\)
0.177653 + 0.984093i \(0.443150\pi\)
\(888\) −4.73950 + 3.44345i −0.159047 + 0.115555i
\(889\) 27.7473 3.27696i 0.930615 0.109906i
\(890\) 30.0542i 1.00742i
\(891\) 1.34327 3.03243i 0.0450013 0.101590i
\(892\) 8.35995i 0.279912i
\(893\) −21.6688 7.04063i −0.725119 0.235606i
\(894\) −6.49235 8.93595i −0.217137 0.298863i
\(895\) 20.2363 27.8528i 0.676424 0.931017i
\(896\) −1.94329 + 1.79544i −0.0649208 + 0.0599816i
\(897\) 5.14820 1.67275i 0.171893 0.0558515i
\(898\) 19.3495 26.6323i 0.645701 0.888731i
\(899\) 30.5897 22.2247i 1.02022 0.741235i
\(900\) −1.92462 + 5.92336i −0.0641538 + 0.197445i
\(901\) 56.6162 1.88616
\(902\) 7.03131 + 12.1257i 0.234117 + 0.403741i
\(903\) 18.0957 8.33664i 0.602186 0.277426i
\(904\) 11.3165 + 3.67697i 0.376383 + 0.122294i
\(905\) 9.15866 6.65416i 0.304444 0.221192i
\(906\) 7.41822 10.2103i 0.246454 0.339214i
\(907\) −15.6556 48.1830i −0.519835 1.59989i −0.774308 0.632809i \(-0.781902\pi\)
0.254473 0.967080i \(-0.418098\pi\)
\(908\) −4.72615 14.5456i −0.156843 0.482712i
\(909\) −7.67423 5.57565i −0.254538 0.184933i
\(910\) 17.6189 31.4421i 0.584061 1.04229i
\(911\) −18.2798 + 56.2593i −0.605635 + 1.86395i −0.113271 + 0.993564i \(0.536133\pi\)
−0.492364 + 0.870390i \(0.663867\pi\)
\(912\) 7.97617i 0.264117i
\(913\) −46.8952 + 27.1931i −1.55200 + 0.899960i
\(914\) −12.1857 −0.403069
\(915\) 7.07610 21.7780i 0.233929 0.719958i
\(916\) −0.509439 0.701183i −0.0168323 0.0231677i
\(917\) −3.81758 0.760373i −0.126068 0.0251097i
\(918\) 1.34308 + 4.13359i 0.0443284 + 0.136429i
\(919\) 1.38918 0.451373i 0.0458249 0.0148894i −0.286015 0.958225i \(-0.592331\pi\)
0.331840 + 0.943336i \(0.392331\pi\)
\(920\) −3.60957 2.62251i −0.119004 0.0864614i
\(921\) −16.3589 22.5161i −0.539044 0.741931i
\(922\) 16.7621 + 5.44634i 0.552031 + 0.179366i
\(923\) 44.7712 1.47366
\(924\) 8.77401 0.129193i 0.288644 0.00425013i
\(925\) −36.4868 −1.19968
\(926\) −8.93421 2.90290i −0.293596 0.0953952i
\(927\) 7.73913 + 10.6520i 0.254186 + 0.349857i
\(928\) −6.99524 5.08234i −0.229630 0.166836i
\(929\) 15.5035 5.03739i 0.508653 0.165271i −0.0434367 0.999056i \(-0.513831\pi\)
0.552089 + 0.833785i \(0.313831\pi\)
\(930\) −4.52803 13.9358i −0.148480 0.456974i
\(931\) 54.2972 13.0064i 1.77952 0.426268i
\(932\) 9.01905 + 12.4137i 0.295429 + 0.406623i
\(933\) 0.191781 0.590240i 0.00627862 0.0193236i
\(934\) 25.6746 0.840099
\(935\) 32.2530 35.9569i 1.05479 1.17592i
\(936\) 4.06542i 0.132883i
\(937\) −3.92764 + 12.0880i −0.128310 + 0.394899i −0.994490 0.104835i \(-0.966569\pi\)
0.866179 + 0.499733i \(0.166569\pi\)
\(938\) −3.29449 1.84610i −0.107569 0.0602774i
\(939\) 8.97227 + 6.51874i 0.292799 + 0.212731i
\(940\) 2.95782 + 9.10323i 0.0964734 + 0.296915i
\(941\) −0.949834 2.92329i −0.0309637 0.0952965i 0.934380 0.356277i \(-0.115954\pi\)
−0.965344 + 0.260981i \(0.915954\pi\)
\(942\) 0.0381184 0.0524654i 0.00124196 0.00170942i
\(943\) 4.55254 3.30761i 0.148251 0.107711i
\(944\) −2.49189 0.809664i −0.0811041 0.0263523i
\(945\) −8.05210 + 3.70959i −0.261935 + 0.120673i
\(946\) −24.8437 2.56378i −0.807739 0.0833556i
\(947\) −28.0790 −0.912444 −0.456222 0.889866i \(-0.650798\pi\)
−0.456222 + 0.889866i \(0.650798\pi\)
\(948\) 2.60032 8.00297i 0.0844545 0.259924i
\(949\) −25.2968 + 18.3792i −0.821169 + 0.596614i
\(950\) 29.1995 40.1896i 0.947356 1.30392i
\(951\) 12.4952 4.05992i 0.405183 0.131652i
\(952\) −8.44615 + 7.80356i −0.273741 + 0.252915i
\(953\) 10.4437 14.3745i 0.338304 0.465635i −0.605641 0.795738i \(-0.707083\pi\)
0.943945 + 0.330103i \(0.107083\pi\)
\(954\) 7.65665 + 10.5385i 0.247893 + 0.341196i
\(955\) −15.5288 5.04562i −0.502501 0.163272i
\(956\) 17.5479i 0.567539i
\(957\) 6.01532 + 28.0395i 0.194448 + 0.906389i
\(958\) 13.5074i 0.436405i
\(959\) 2.85107 + 24.1412i 0.0920659 + 0.779559i
\(960\) −2.71089 + 1.96958i −0.0874937 + 0.0635679i
\(961\) −9.60911 6.98143i −0.309971 0.225207i
\(962\) 22.6510 7.35975i 0.730297 0.237288i
\(963\) 14.7404 4.78943i 0.475001 0.154337i
\(964\) −16.8309 12.2283i −0.542086 0.393848i
\(965\) −66.4865 + 48.3052i −2.14027 + 1.55500i
\(966\) −0.413175 3.49852i −0.0132937 0.112563i
\(967\) 1.58866i 0.0510879i −0.999674 0.0255440i \(-0.991868\pi\)
0.999674 0.0255440i \(-0.00813178\pi\)
\(968\) −9.54698 5.46400i −0.306851 0.175620i
\(969\) 34.6669i 1.11366i
\(970\) 11.4235 + 3.71172i 0.366786 + 0.119176i
\(971\) −16.1386 22.2129i −0.517912 0.712845i 0.467316 0.884090i \(-0.345221\pi\)
−0.985228 + 0.171245i \(0.945221\pi\)
\(972\) −0.587785 + 0.809017i −0.0188532 + 0.0259492i
\(973\) 1.44672 + 1.56585i 0.0463796 + 0.0501988i
\(974\) −15.0943 + 4.90445i −0.483654 + 0.157149i
\(975\) 14.8828 20.4845i 0.476633 0.656028i
\(976\) 5.52859 4.01675i 0.176966 0.128573i
\(977\) 3.71451 11.4321i 0.118838 0.365745i −0.873890 0.486123i \(-0.838411\pi\)
0.992728 + 0.120378i \(0.0384107\pi\)
\(978\) 13.0883 0.418517
\(979\) 29.0855 6.23972i 0.929577 0.199422i
\(980\) −17.8283 15.2425i −0.569504 0.486903i
\(981\) 9.26385 + 3.01001i 0.295772 + 0.0961021i
\(982\) 23.2333 16.8799i 0.741403 0.538661i
\(983\) 7.93650 10.9236i 0.253135 0.348410i −0.663471 0.748202i \(-0.730917\pi\)
0.916606 + 0.399792i \(0.130917\pi\)
\(984\) −1.30598 4.01938i −0.0416330 0.128133i
\(985\) −3.76312 11.5817i −0.119903 0.369024i
\(986\) −30.4035 22.0894i −0.968244 0.703470i
\(987\) −3.69447 + 6.59303i −0.117596 + 0.209858i
\(988\) −10.0203 + 30.8395i −0.318790 + 0.981134i
\(989\) 10.0268i 0.318834i
\(990\) 11.0548 + 1.14081i 0.351345 + 0.0362574i
\(991\) −43.4002 −1.37865 −0.689327 0.724450i \(-0.742094\pi\)
−0.689327 + 0.724450i \(0.742094\pi\)
\(992\) 1.35131 4.15890i 0.0429041 0.132045i
\(993\) 9.63611 + 13.2630i 0.305793 + 0.420887i
\(994\) 5.69157 28.5755i 0.180526 0.906359i
\(995\) −10.2414 31.5198i −0.324674 0.999244i
\(996\) 15.5447 5.05077i 0.492552 0.160040i
\(997\) −15.7084 11.4128i −0.497489 0.361447i 0.310568 0.950551i \(-0.399481\pi\)
−0.808057 + 0.589104i \(0.799481\pi\)
\(998\) −22.6391 31.1600i −0.716627 0.986353i
\(999\) −5.57162 1.81033i −0.176278 0.0572762i
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 462.2.u.a.13.5 32
7.6 odd 2 462.2.u.b.13.8 yes 32
11.6 odd 10 462.2.u.b.391.8 yes 32
77.6 even 10 inner 462.2.u.a.391.5 yes 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
462.2.u.a.13.5 32 1.1 even 1 trivial
462.2.u.a.391.5 yes 32 77.6 even 10 inner
462.2.u.b.13.8 yes 32 7.6 odd 2
462.2.u.b.391.8 yes 32 11.6 odd 10