Properties

Label 429.2.bn.a.4.13
Level $429$
Weight $2$
Character 429.4
Analytic conductor $3.426$
Analytic rank $0$
Dimension $112$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [429,2,Mod(4,429)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(429, base_ring=CyclotomicField(30))
 
chi = DirichletCharacter(H, H._module([0, 6, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("429.4");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 429 = 3 \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 429.bn (of order \(30\), degree \(8\), 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: \(3.42558224671\)
Analytic rank: \(0\)
Dimension: \(112\)
Relative dimension: \(14\) over \(\Q(\zeta_{30})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label 4.13
Character \(\chi\) \(=\) 429.4
Dual form 429.2.bn.a.322.13

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.896442 + 2.01344i) q^{2} +(-0.669131 - 0.743145i) q^{3} +(-1.91208 + 2.12358i) q^{4} +(0.00844073 + 0.0116177i) q^{5} +(0.896442 - 2.01344i) q^{6} +(1.50438 + 1.35455i) q^{7} +(-1.79754 - 0.584056i) q^{8} +(-0.104528 + 0.994522i) q^{9} +O(q^{10})\) \(q+(0.896442 + 2.01344i) q^{2} +(-0.669131 - 0.743145i) q^{3} +(-1.91208 + 2.12358i) q^{4} +(0.00844073 + 0.0116177i) q^{5} +(0.896442 - 2.01344i) q^{6} +(1.50438 + 1.35455i) q^{7} +(-1.79754 - 0.584056i) q^{8} +(-0.104528 + 0.994522i) q^{9} +(-0.0158249 + 0.0274095i) q^{10} +(-2.17987 + 2.49964i) q^{11} +2.85756 q^{12} +(-3.18964 + 1.68112i) q^{13} +(-1.37872 + 4.24327i) q^{14} +(0.00298566 - 0.0140464i) q^{15} +(0.161965 + 1.54099i) q^{16} +(4.34505 + 1.93454i) q^{17} +(-2.09612 + 0.681069i) q^{18} +(0.768649 + 3.61621i) q^{19} +(-0.0408104 - 0.00428934i) q^{20} -2.02435i q^{21} +(-6.98700 - 2.14826i) q^{22} +(-0.869781 + 1.50651i) q^{23} +(0.768750 + 1.72664i) q^{24} +(1.54502 - 4.75509i) q^{25} +(-6.24418 - 4.91513i) q^{26} +(0.809017 - 0.587785i) q^{27} +(-5.75300 + 0.604664i) q^{28} +(-2.53578 - 0.538996i) q^{29} +(0.0309581 - 0.00658035i) q^{30} +(4.45712 - 6.13469i) q^{31} +(-6.23116 + 3.59756i) q^{32} +(3.31621 - 0.0526264i) q^{33} +10.4827i q^{34} +(-0.00303865 + 0.0289108i) q^{35} +(-1.91208 - 2.12358i) q^{36} +(1.74330 - 8.20157i) q^{37} +(-6.59198 + 4.78935i) q^{38} +(3.38361 + 1.24547i) q^{39} +(-0.00838717 - 0.0258131i) q^{40} +(-6.52336 + 5.87366i) q^{41} +(4.07591 - 1.81471i) q^{42} +(-2.03391 - 3.52284i) q^{43} +(-1.14010 - 9.40862i) q^{44} +(-0.0124363 + 0.00718012i) q^{45} +(-3.81297 - 0.400759i) q^{46} +(7.78071 + 2.52811i) q^{47} +(1.03681 - 1.15149i) q^{48} +(-0.303343 - 2.88612i) q^{49} +(10.9591 - 1.15185i) q^{50} +(-1.46976 - 4.52346i) q^{51} +(2.52885 - 9.98790i) q^{52} +(5.09189 + 3.69948i) q^{53} +(1.90871 + 1.10199i) q^{54} +(-0.0474396 - 0.00422622i) q^{55} +(-1.91305 - 3.31350i) q^{56} +(2.17304 - 2.99094i) q^{57} +(-1.18794 - 5.58882i) q^{58} +(4.63924 + 4.17719i) q^{59} +(0.0241199 + 0.0331982i) q^{60} +(-2.33499 - 1.03961i) q^{61} +(16.3474 + 3.47475i) q^{62} +(-1.50438 + 1.35455i) q^{63} +(-10.3222 - 7.49955i) q^{64} +(-0.0464537 - 0.0228663i) q^{65} +(3.07875 + 6.62981i) q^{66} +(6.17671 + 3.56612i) q^{67} +(-12.4162 + 5.52806i) q^{68} +(1.70155 - 0.361675i) q^{69} +(-0.0609343 + 0.0197987i) q^{70} +(5.86118 - 13.1644i) q^{71} +(0.768750 - 1.72664i) q^{72} +(10.4280 - 3.38828i) q^{73} +(18.0762 - 3.84221i) q^{74} +(-4.56754 + 2.03360i) q^{75} +(-9.14903 - 5.28219i) q^{76} +(-6.66524 + 0.807666i) q^{77} +(0.525516 + 7.92919i) q^{78} +(8.24623 + 5.99124i) q^{79} +(-0.0165357 + 0.0148888i) q^{80} +(-0.978148 - 0.207912i) q^{81} +(-17.6741 - 7.86902i) q^{82} +(-1.73085 - 2.38231i) q^{83} +(4.29886 + 3.87071i) q^{84} +(0.0142005 + 0.0668083i) q^{85} +(5.26974 - 7.25318i) q^{86} +(1.29621 + 2.24511i) q^{87} +(5.37832 - 3.22003i) q^{88} +(9.72766 + 5.61627i) q^{89} +(-0.0256052 - 0.0186033i) q^{90} +(-7.07562 - 1.79148i) q^{91} +(-1.53609 - 4.72760i) q^{92} +(-7.54136 + 0.792629i) q^{93} +(1.88476 + 17.9323i) q^{94} +(-0.0355240 + 0.0394534i) q^{95} +(6.84297 + 2.22342i) q^{96} +(-12.6792 - 1.33264i) q^{97} +(5.53911 - 3.19800i) q^{98} +(-2.25808 - 2.42921i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 112 q - 14 q^{3} - 20 q^{4} + 14 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 112 q - 14 q^{3} - 20 q^{4} + 14 q^{9} + 21 q^{11} + 120 q^{12} - 15 q^{13} + 30 q^{14} - 6 q^{15} - 8 q^{16} - 12 q^{19} - 66 q^{20} - 17 q^{22} + 12 q^{23} + 14 q^{25} + 9 q^{26} + 28 q^{27} + 18 q^{28} - 2 q^{29} + 10 q^{30} - 30 q^{32} - 24 q^{33} + 16 q^{35} - 20 q^{36} + 38 q^{38} - 12 q^{39} - 60 q^{40} - 36 q^{41} + 12 q^{43} - 6 q^{45} + 54 q^{46} - 42 q^{48} - 40 q^{49} - 51 q^{50} - 30 q^{51} - 15 q^{52} - 22 q^{53} + 22 q^{55} - 76 q^{56} + 132 q^{58} + 72 q^{59} + 34 q^{61} + 17 q^{62} - 84 q^{64} + 28 q^{65} - 24 q^{66} - 48 q^{67} - 12 q^{68} - 7 q^{69} + 30 q^{71} + 20 q^{74} + 32 q^{75} - 48 q^{76} - 136 q^{77} - 14 q^{78} - 36 q^{79} + 18 q^{80} + 14 q^{81} - 5 q^{82} - 27 q^{84} - 66 q^{85} + 52 q^{87} + 52 q^{88} - 96 q^{89} - 20 q^{90} - 125 q^{91} - 10 q^{92} - 18 q^{93} + 22 q^{94} + 72 q^{95} - 93 q^{97} + 24 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/429\mathbb{Z}\right)^\times\).

\(n\) \(67\) \(79\) \(287\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{5}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.896442 + 2.01344i 0.633880 + 1.42372i 0.889497 + 0.456940i \(0.151055\pi\)
−0.255617 + 0.966778i \(0.582279\pi\)
\(3\) −0.669131 0.743145i −0.386323 0.429055i
\(4\) −1.91208 + 2.12358i −0.956039 + 1.06179i
\(5\) 0.00844073 + 0.0116177i 0.00377481 + 0.00519558i 0.810900 0.585184i \(-0.198978\pi\)
−0.807125 + 0.590380i \(0.798978\pi\)
\(6\) 0.896442 2.01344i 0.365971 0.821984i
\(7\) 1.50438 + 1.35455i 0.568603 + 0.511973i 0.902530 0.430626i \(-0.141707\pi\)
−0.333927 + 0.942599i \(0.608374\pi\)
\(8\) −1.79754 0.584056i −0.635526 0.206495i
\(9\) −0.104528 + 0.994522i −0.0348428 + 0.331507i
\(10\) −0.0158249 + 0.0274095i −0.00500427 + 0.00866764i
\(11\) −2.17987 + 2.49964i −0.657255 + 0.753669i
\(12\) 2.85756 0.824906
\(13\) −3.18964 + 1.68112i −0.884648 + 0.466260i
\(14\) −1.37872 + 4.24327i −0.368479 + 1.13406i
\(15\) 0.00298566 0.0140464i 0.000770894 0.00362677i
\(16\) 0.161965 + 1.54099i 0.0404913 + 0.385249i
\(17\) 4.34505 + 1.93454i 1.05383 + 0.469195i 0.859178 0.511677i \(-0.170976\pi\)
0.194652 + 0.980872i \(0.437642\pi\)
\(18\) −2.09612 + 0.681069i −0.494059 + 0.160530i
\(19\) 0.768649 + 3.61621i 0.176340 + 0.829616i 0.974007 + 0.226517i \(0.0727340\pi\)
−0.797667 + 0.603098i \(0.793933\pi\)
\(20\) −0.0408104 0.00428934i −0.00912548 0.000959126i
\(21\) 2.02435i 0.441749i
\(22\) −6.98700 2.14826i −1.48963 0.458010i
\(23\) −0.869781 + 1.50651i −0.181362 + 0.314128i −0.942345 0.334644i \(-0.891384\pi\)
0.760983 + 0.648772i \(0.224717\pi\)
\(24\) 0.768750 + 1.72664i 0.156920 + 0.352449i
\(25\) 1.54502 4.75509i 0.309004 0.951017i
\(26\) −6.24418 4.91513i −1.22458 0.963936i
\(27\) 0.809017 0.587785i 0.155695 0.113119i
\(28\) −5.75300 + 0.604664i −1.08721 + 0.114271i
\(29\) −2.53578 0.538996i −0.470882 0.100089i −0.0336420 0.999434i \(-0.510711\pi\)
−0.437240 + 0.899345i \(0.644044\pi\)
\(30\) 0.0309581 0.00658035i 0.00565216 0.00120140i
\(31\) 4.45712 6.13469i 0.800522 1.10182i −0.192196 0.981357i \(-0.561561\pi\)
0.992717 0.120467i \(-0.0384392\pi\)
\(32\) −6.23116 + 3.59756i −1.10152 + 0.635965i
\(33\) 3.31621 0.0526264i 0.577278 0.00916108i
\(34\) 10.4827i 1.79777i
\(35\) −0.00303865 + 0.0289108i −0.000513626 + 0.00488682i
\(36\) −1.91208 2.12358i −0.318680 0.353930i
\(37\) 1.74330 8.20157i 0.286596 1.34833i −0.565415 0.824807i \(-0.691284\pi\)
0.852011 0.523524i \(-0.175383\pi\)
\(38\) −6.59198 + 4.78935i −1.06936 + 0.776936i
\(39\) 3.38361 + 1.24547i 0.541811 + 0.199436i
\(40\) −0.00838717 0.0258131i −0.00132613 0.00408140i
\(41\) −6.52336 + 5.87366i −1.01878 + 0.917312i −0.996596 0.0824418i \(-0.973728\pi\)
−0.0221825 + 0.999754i \(0.507061\pi\)
\(42\) 4.07591 1.81471i 0.628926 0.280016i
\(43\) −2.03391 3.52284i −0.310168 0.537227i 0.668230 0.743954i \(-0.267052\pi\)
−0.978399 + 0.206727i \(0.933719\pi\)
\(44\) −1.14010 9.40862i −0.171876 1.41840i
\(45\) −0.0124363 + 0.00718012i −0.00185390 + 0.00107035i
\(46\) −3.81297 0.400759i −0.562192 0.0590887i
\(47\) 7.78071 + 2.52811i 1.13493 + 0.368762i 0.815449 0.578829i \(-0.196490\pi\)
0.319485 + 0.947591i \(0.396490\pi\)
\(48\) 1.03681 1.15149i 0.149650 0.166203i
\(49\) −0.303343 2.88612i −0.0433348 0.412303i
\(50\) 10.9591 1.15185i 1.54985 0.162896i
\(51\) −1.46976 4.52346i −0.205808 0.633411i
\(52\) 2.52885 9.98790i 0.350688 1.38507i
\(53\) 5.09189 + 3.69948i 0.699426 + 0.508162i 0.879745 0.475446i \(-0.157713\pi\)
−0.180320 + 0.983608i \(0.557713\pi\)
\(54\) 1.90871 + 1.10199i 0.259742 + 0.149962i
\(55\) −0.0474396 0.00422622i −0.00639676 0.000569863i
\(56\) −1.91305 3.31350i −0.255642 0.442786i
\(57\) 2.17304 2.99094i 0.287826 0.396159i
\(58\) −1.18794 5.58882i −0.155984 0.733848i
\(59\) 4.63924 + 4.17719i 0.603978 + 0.543824i 0.913380 0.407107i \(-0.133462\pi\)
−0.309403 + 0.950931i \(0.600129\pi\)
\(60\) 0.0241199 + 0.0331982i 0.00311386 + 0.00428586i
\(61\) −2.33499 1.03961i −0.298965 0.133108i 0.251772 0.967787i \(-0.418987\pi\)
−0.550737 + 0.834679i \(0.685653\pi\)
\(62\) 16.3474 + 3.47475i 2.07612 + 0.441293i
\(63\) −1.50438 + 1.35455i −0.189534 + 0.170658i
\(64\) −10.3222 7.49955i −1.29028 0.937444i
\(65\) −0.0464537 0.0228663i −0.00576187 0.00283622i
\(66\) 3.07875 + 6.62981i 0.378968 + 0.816074i
\(67\) 6.17671 + 3.56612i 0.754605 + 0.435671i 0.827355 0.561679i \(-0.189844\pi\)
−0.0727506 + 0.997350i \(0.523178\pi\)
\(68\) −12.4162 + 5.52806i −1.50569 + 0.670376i
\(69\) 1.70155 0.361675i 0.204842 0.0435406i
\(70\) −0.0609343 + 0.0197987i −0.00728304 + 0.00236640i
\(71\) 5.86118 13.1644i 0.695594 1.56233i −0.125855 0.992049i \(-0.540167\pi\)
0.821449 0.570281i \(-0.193166\pi\)
\(72\) 0.768750 1.72664i 0.0905981 0.203487i
\(73\) 10.4280 3.38828i 1.22051 0.396568i 0.373243 0.927734i \(-0.378246\pi\)
0.847268 + 0.531166i \(0.178246\pi\)
\(74\) 18.0762 3.84221i 2.10131 0.446647i
\(75\) −4.56754 + 2.03360i −0.527414 + 0.234820i
\(76\) −9.14903 5.28219i −1.04947 0.605909i
\(77\) −6.66524 + 0.807666i −0.759575 + 0.0920421i
\(78\) 0.525516 + 7.92919i 0.0595030 + 0.897804i
\(79\) 8.24623 + 5.99124i 0.927773 + 0.674067i 0.945447 0.325777i \(-0.105626\pi\)
−0.0176733 + 0.999844i \(0.505626\pi\)
\(80\) −0.0165357 + 0.0148888i −0.00184874 + 0.00166462i
\(81\) −0.978148 0.207912i −0.108683 0.0231013i
\(82\) −17.6741 7.86902i −1.95178 0.868987i
\(83\) −1.73085 2.38231i −0.189985 0.261492i 0.703389 0.710805i \(-0.251669\pi\)
−0.893375 + 0.449312i \(0.851669\pi\)
\(84\) 4.29886 + 3.87071i 0.469044 + 0.422329i
\(85\) 0.0142005 + 0.0668083i 0.00154027 + 0.00724638i
\(86\) 5.26974 7.25318i 0.568251 0.782130i
\(87\) 1.29621 + 2.24511i 0.138969 + 0.240701i
\(88\) 5.37832 3.22003i 0.573331 0.343256i
\(89\) 9.72766 + 5.61627i 1.03113 + 0.595323i 0.917308 0.398178i \(-0.130357\pi\)
0.113822 + 0.993501i \(0.463691\pi\)
\(90\) −0.0256052 0.0186033i −0.00269902 0.00196096i
\(91\) −7.07562 1.79148i −0.741726 0.187799i
\(92\) −1.53609 4.72760i −0.160149 0.492887i
\(93\) −7.54136 + 0.792629i −0.782002 + 0.0821918i
\(94\) 1.88476 + 17.9323i 0.194398 + 1.84958i
\(95\) −0.0355240 + 0.0394534i −0.00364468 + 0.00404783i
\(96\) 6.84297 + 2.22342i 0.698408 + 0.226926i
\(97\) −12.6792 1.33264i −1.28738 0.135309i −0.564009 0.825769i \(-0.690742\pi\)
−0.723371 + 0.690460i \(0.757408\pi\)
\(98\) 5.53911 3.19800i 0.559534 0.323047i
\(99\) −2.25808 2.42921i −0.226946 0.244145i
\(100\) 7.14360 + 12.3731i 0.714360 + 1.23731i
\(101\) −6.51146 + 2.89909i −0.647915 + 0.288470i −0.704261 0.709941i \(-0.748722\pi\)
0.0563464 + 0.998411i \(0.482055\pi\)
\(102\) 7.79017 7.01430i 0.771342 0.694519i
\(103\) −4.19585 12.9135i −0.413429 1.27240i −0.913649 0.406505i \(-0.866747\pi\)
0.500219 0.865899i \(-0.333253\pi\)
\(104\) 6.71538 1.15896i 0.658497 0.113645i
\(105\) 0.0235182 0.0170870i 0.00229514 0.00166752i
\(106\) −2.88410 + 13.5686i −0.280128 + 1.31790i
\(107\) −0.885799 0.983779i −0.0856334 0.0951055i 0.698805 0.715312i \(-0.253715\pi\)
−0.784439 + 0.620207i \(0.787049\pi\)
\(108\) −0.298696 + 2.84190i −0.0287420 + 0.273462i
\(109\) 7.82216i 0.749227i −0.927181 0.374613i \(-0.877775\pi\)
0.927181 0.374613i \(-0.122225\pi\)
\(110\) −0.0340176 0.0993055i −0.00324345 0.00946841i
\(111\) −7.26145 + 4.19240i −0.689226 + 0.397925i
\(112\) −1.84370 + 2.53764i −0.174213 + 0.239784i
\(113\) −15.3197 + 3.25631i −1.44116 + 0.306328i −0.861179 0.508302i \(-0.830273\pi\)
−0.579981 + 0.814630i \(0.696940\pi\)
\(114\) 7.97008 + 1.69409i 0.746466 + 0.158666i
\(115\) −0.0248437 + 0.00261117i −0.00231668 + 0.000243493i
\(116\) 5.99321 4.35432i 0.556455 0.404288i
\(117\) −1.33851 3.34789i −0.123745 0.309513i
\(118\) −4.25172 + 13.0855i −0.391403 + 1.20461i
\(119\) 3.91618 + 8.79589i 0.358996 + 0.806318i
\(120\) −0.0135707 + 0.0235052i −0.00123883 + 0.00214572i
\(121\) −1.49636 10.8977i −0.136033 0.990704i
\(122\) 5.63332i 0.510017i
\(123\) 8.72997 + 0.917556i 0.787154 + 0.0827333i
\(124\) 4.50515 + 21.1951i 0.404574 + 1.90337i
\(125\) 0.136571 0.0443746i 0.0122153 0.00396899i
\(126\) −4.07591 1.81471i −0.363111 0.161667i
\(127\) 0.617933 + 5.87924i 0.0548326 + 0.521698i 0.987120 + 0.159980i \(0.0511430\pi\)
−0.932288 + 0.361718i \(0.882190\pi\)
\(128\) 2.85471 13.4304i 0.252323 1.18709i
\(129\) −1.25703 + 3.86873i −0.110675 + 0.340622i
\(130\) 0.00439694 0.114030i 0.000385637 0.0100011i
\(131\) −6.06289 −0.529717 −0.264859 0.964287i \(-0.585325\pi\)
−0.264859 + 0.964287i \(0.585325\pi\)
\(132\) −6.22909 + 7.14285i −0.542173 + 0.621706i
\(133\) −3.74201 + 6.48134i −0.324473 + 0.562004i
\(134\) −1.64312 + 15.6333i −0.141944 + 1.35051i
\(135\) 0.0136574 + 0.00443756i 0.00117544 + 0.000381924i
\(136\) −6.68052 6.01516i −0.572849 0.515796i
\(137\) 6.51041 14.6226i 0.556222 1.24929i −0.388508 0.921445i \(-0.627009\pi\)
0.944730 0.327850i \(-0.106324\pi\)
\(138\) 2.25355 + 3.10175i 0.191835 + 0.264038i
\(139\) −0.732168 + 0.813154i −0.0621016 + 0.0689709i −0.773395 0.633924i \(-0.781443\pi\)
0.711293 + 0.702895i \(0.248110\pi\)
\(140\) −0.0555843 0.0617326i −0.00469773 0.00521736i
\(141\) −3.32756 7.47383i −0.280231 0.629410i
\(142\) 31.7600 2.66524
\(143\) 2.75080 11.6376i 0.230033 0.973183i
\(144\) −1.54948 −0.129124
\(145\) −0.0151419 0.0340093i −0.00125747 0.00282432i
\(146\) 16.1702 + 17.9589i 1.33826 + 1.48629i
\(147\) −1.94183 + 2.15662i −0.160159 + 0.177875i
\(148\) 14.0834 + 19.3841i 1.15765 + 1.59336i
\(149\) 6.66092 14.9607i 0.545684 1.22563i −0.404673 0.914462i \(-0.632615\pi\)
0.950356 0.311164i \(-0.100719\pi\)
\(150\) −8.18907 7.37347i −0.668635 0.602041i
\(151\) 16.7411 + 5.43950i 1.36237 + 0.442660i 0.896833 0.442369i \(-0.145862\pi\)
0.465535 + 0.885029i \(0.345862\pi\)
\(152\) 0.730392 6.94921i 0.0592426 0.563656i
\(153\) −2.37812 + 4.11903i −0.192260 + 0.333004i
\(154\) −7.60119 12.6961i −0.612522 1.02308i
\(155\) 0.108892 0.00874643
\(156\) −9.11459 + 4.80391i −0.729751 + 0.384621i
\(157\) 1.25199 3.85323i 0.0999196 0.307521i −0.888585 0.458712i \(-0.848311\pi\)
0.988505 + 0.151191i \(0.0483109\pi\)
\(158\) −4.67074 + 21.9741i −0.371584 + 1.74817i
\(159\) −0.657895 6.25945i −0.0521744 0.496407i
\(160\) −0.0943909 0.0420255i −0.00746225 0.00332241i
\(161\) −3.34912 + 1.08820i −0.263948 + 0.0857619i
\(162\) −0.458235 2.15582i −0.0360023 0.169378i
\(163\) −6.47880 0.680949i −0.507459 0.0533361i −0.152660 0.988279i \(-0.548784\pi\)
−0.354799 + 0.934943i \(0.615451\pi\)
\(164\) 25.0838i 1.95871i
\(165\) 0.0286026 + 0.0380824i 0.00222671 + 0.00296471i
\(166\) 3.24503 5.62056i 0.251864 0.436240i
\(167\) 7.77244 + 17.4572i 0.601449 + 1.35088i 0.915825 + 0.401579i \(0.131538\pi\)
−0.314375 + 0.949299i \(0.601795\pi\)
\(168\) −1.18233 + 3.63884i −0.0912189 + 0.280743i
\(169\) 7.34764 10.7244i 0.565203 0.824952i
\(170\) −0.121785 + 0.0884817i −0.00934046 + 0.00678624i
\(171\) −3.67675 + 0.386442i −0.281168 + 0.0295519i
\(172\) 11.3700 + 2.41677i 0.866955 + 0.184277i
\(173\) 0.932953 0.198305i 0.0709311 0.0150769i −0.172309 0.985043i \(-0.555123\pi\)
0.243241 + 0.969966i \(0.421790\pi\)
\(174\) −3.35841 + 4.62246i −0.254601 + 0.350428i
\(175\) 8.76532 5.06066i 0.662596 0.382550i
\(176\) −4.20499 2.95431i −0.316963 0.222689i
\(177\) 6.24272i 0.469231i
\(178\) −2.58774 + 24.6207i −0.193960 + 1.84540i
\(179\) 1.34427 + 1.49297i 0.100476 + 0.111590i 0.791285 0.611447i \(-0.209412\pi\)
−0.690809 + 0.723037i \(0.742746\pi\)
\(180\) 0.00853169 0.0401385i 0.000635915 0.00299174i
\(181\) −10.1565 + 7.37916i −0.754930 + 0.548489i −0.897351 0.441317i \(-0.854511\pi\)
0.142421 + 0.989806i \(0.454511\pi\)
\(182\) −2.73583 15.8523i −0.202793 1.17505i
\(183\) 0.789837 + 2.43087i 0.0583865 + 0.179695i
\(184\) 2.44335 2.20000i 0.180126 0.162186i
\(185\) 0.109998 0.0489742i 0.00808721 0.00360066i
\(186\) −8.35630 14.4735i −0.612714 1.06125i
\(187\) −14.3073 + 6.64400i −1.04625 + 0.485858i
\(188\) −20.2460 + 11.6890i −1.47659 + 0.852509i
\(189\) 2.01326 + 0.211602i 0.146443 + 0.0153918i
\(190\) −0.111282 0.0361578i −0.00807327 0.00262316i
\(191\) −6.11704 + 6.79367i −0.442614 + 0.491572i −0.922629 0.385687i \(-0.873964\pi\)
0.480016 + 0.877260i \(0.340631\pi\)
\(192\) 1.33368 + 12.6891i 0.0962499 + 0.915757i
\(193\) −20.4112 + 2.14530i −1.46923 + 0.154422i −0.805076 0.593172i \(-0.797875\pi\)
−0.664156 + 0.747594i \(0.731209\pi\)
\(194\) −8.68299 26.7235i −0.623402 1.91864i
\(195\) 0.0140906 + 0.0498223i 0.00100905 + 0.00356785i
\(196\) 6.70892 + 4.87432i 0.479209 + 0.348165i
\(197\) −11.5560 6.67187i −0.823332 0.475351i 0.0282322 0.999601i \(-0.491012\pi\)
−0.851564 + 0.524251i \(0.824346\pi\)
\(198\) 2.86683 6.72417i 0.203737 0.477866i
\(199\) 0.758465 + 1.31370i 0.0537662 + 0.0931258i 0.891656 0.452714i \(-0.149544\pi\)
−0.837890 + 0.545840i \(0.816211\pi\)
\(200\) −5.55447 + 7.64507i −0.392760 + 0.540588i
\(201\) −1.48288 6.97639i −0.104594 0.492077i
\(202\) −11.6743 10.5116i −0.821401 0.739592i
\(203\) −3.08468 4.24570i −0.216502 0.297990i
\(204\) 12.4162 + 5.52806i 0.869310 + 0.387042i
\(205\) −0.123300 0.0262083i −0.00861166 0.00183047i
\(206\) 22.2392 20.0243i 1.54948 1.39516i
\(207\) −1.40734 1.02249i −0.0978166 0.0710679i
\(208\) −3.10721 4.64294i −0.215447 0.321930i
\(209\) −10.7148 5.96151i −0.741156 0.412367i
\(210\) 0.0554863 + 0.0320350i 0.00382892 + 0.00221063i
\(211\) 20.8779 9.29546i 1.43730 0.639926i 0.467534 0.883975i \(-0.345142\pi\)
0.969763 + 0.244049i \(0.0784758\pi\)
\(212\) −17.5922 + 3.73935i −1.20824 + 0.256819i
\(213\) −13.7050 + 4.45302i −0.939049 + 0.305116i
\(214\) 1.18671 2.66541i 0.0811222 0.182203i
\(215\) 0.0237595 0.0533646i 0.00162038 0.00363944i
\(216\) −1.79754 + 0.584056i −0.122307 + 0.0397400i
\(217\) 15.0150 3.19153i 1.01928 0.216655i
\(218\) 15.7495 7.01211i 1.06669 0.474920i
\(219\) −9.49571 5.48235i −0.641660 0.370463i
\(220\) 0.0996830 0.0926609i 0.00672063 0.00624720i
\(221\) −17.1114 + 1.13408i −1.15103 + 0.0762862i
\(222\) −14.9506 10.8623i −1.00342 0.729028i
\(223\) −8.19102 + 7.37523i −0.548511 + 0.493882i −0.896153 0.443746i \(-0.853649\pi\)
0.347641 + 0.937628i \(0.386983\pi\)
\(224\) −14.2471 3.02832i −0.951927 0.202338i
\(225\) 4.56754 + 2.03360i 0.304503 + 0.135573i
\(226\) −20.2897 27.9263i −1.34965 1.85763i
\(227\) 4.97257 + 4.47732i 0.330041 + 0.297170i 0.817445 0.576006i \(-0.195390\pi\)
−0.487404 + 0.873176i \(0.662056\pi\)
\(228\) 2.19646 + 10.3335i 0.145464 + 0.684355i
\(229\) −9.84423 + 13.5494i −0.650525 + 0.895371i −0.999122 0.0419021i \(-0.986658\pi\)
0.348597 + 0.937273i \(0.386658\pi\)
\(230\) −0.0275284 0.0476805i −0.00181517 0.00314396i
\(231\) 5.06013 + 4.41281i 0.332932 + 0.290341i
\(232\) 4.24335 + 2.44990i 0.278590 + 0.160844i
\(233\) −3.96056 2.87751i −0.259465 0.188512i 0.450446 0.892804i \(-0.351265\pi\)
−0.709911 + 0.704291i \(0.751265\pi\)
\(234\) 5.54090 5.69620i 0.362220 0.372372i
\(235\) 0.0363042 + 0.111733i 0.00236823 + 0.00728865i
\(236\) −17.7412 + 1.86467i −1.15485 + 0.121380i
\(237\) −1.06545 10.1371i −0.0692083 0.658473i
\(238\) −14.1994 + 15.7700i −0.920409 + 1.02222i
\(239\) 11.7745 + 3.82575i 0.761627 + 0.247467i 0.663977 0.747753i \(-0.268867\pi\)
0.0976500 + 0.995221i \(0.468867\pi\)
\(240\) 0.0221290 + 0.00232586i 0.00142842 + 0.000150133i
\(241\) −1.02568 + 0.592177i −0.0660699 + 0.0381455i −0.532671 0.846322i \(-0.678812\pi\)
0.466601 + 0.884468i \(0.345478\pi\)
\(242\) 20.6006 12.7820i 1.32426 0.821661i
\(243\) 0.500000 + 0.866025i 0.0320750 + 0.0555556i
\(244\) 6.67237 2.97073i 0.427155 0.190182i
\(245\) 0.0309696 0.0278851i 0.00197857 0.00178151i
\(246\) 5.97846 + 18.3998i 0.381173 + 1.17313i
\(247\) −8.53102 10.2422i −0.542816 0.651697i
\(248\) −11.5948 + 8.42414i −0.736273 + 0.534934i
\(249\) −0.612237 + 2.88035i −0.0387989 + 0.182535i
\(250\) 0.211774 + 0.235199i 0.0133938 + 0.0148753i
\(251\) −1.93348 + 18.3958i −0.122040 + 1.16113i 0.746456 + 0.665435i \(0.231754\pi\)
−0.868495 + 0.495697i \(0.834913\pi\)
\(252\) 5.78469i 0.364401i
\(253\) −1.86971 5.45812i −0.117548 0.343149i
\(254\) −11.2836 + 6.51457i −0.707993 + 0.408760i
\(255\) 0.0401462 0.0552565i 0.00251405 0.00346030i
\(256\) 4.63997 0.986257i 0.289998 0.0616411i
\(257\) 14.0875 + 2.99439i 0.878753 + 0.186785i 0.625132 0.780519i \(-0.285045\pi\)
0.253621 + 0.967304i \(0.418379\pi\)
\(258\) −8.91631 + 0.937142i −0.555105 + 0.0583439i
\(259\) 13.7321 9.97692i 0.853268 0.619936i
\(260\) 0.137381 0.0549259i 0.00852004 0.00340636i
\(261\) 0.801104 2.46555i 0.0495871 0.152613i
\(262\) −5.43503 12.2073i −0.335777 0.754168i
\(263\) −6.52888 + 11.3083i −0.402588 + 0.697302i −0.994037 0.109039i \(-0.965223\pi\)
0.591450 + 0.806342i \(0.298556\pi\)
\(264\) −5.99175 1.84225i −0.368767 0.113383i
\(265\) 0.0903823i 0.00555214i
\(266\) −16.4043 1.72416i −1.00581 0.105715i
\(267\) −2.33538 10.9871i −0.142923 0.672398i
\(268\) −19.3833 + 6.29801i −1.18402 + 0.384712i
\(269\) 0.693792 + 0.308896i 0.0423012 + 0.0188337i 0.427778 0.903884i \(-0.359296\pi\)
−0.385477 + 0.922717i \(0.625963\pi\)
\(270\) 0.00330830 + 0.0314764i 0.000201337 + 0.00191559i
\(271\) 3.30331 15.5409i 0.200662 0.944040i −0.756389 0.654122i \(-0.773038\pi\)
0.957051 0.289919i \(-0.0936282\pi\)
\(272\) −2.27737 + 7.00903i −0.138086 + 0.424985i
\(273\) 3.40318 + 6.45694i 0.205970 + 0.390792i
\(274\) 35.2780 2.13122
\(275\) 8.51805 + 14.2274i 0.513657 + 0.857947i
\(276\) −2.48545 + 4.30492i −0.149606 + 0.259126i
\(277\) −2.93062 + 27.8830i −0.176084 + 1.67532i 0.448051 + 0.894008i \(0.352118\pi\)
−0.624135 + 0.781317i \(0.714548\pi\)
\(278\) −2.29359 0.745231i −0.137560 0.0446960i
\(279\) 5.63519 + 5.07395i 0.337370 + 0.303769i
\(280\) 0.0223476 0.0501936i 0.00133553 0.00299964i
\(281\) −14.6466 20.1593i −0.873743 1.20260i −0.978115 0.208066i \(-0.933283\pi\)
0.104372 0.994538i \(-0.466717\pi\)
\(282\) 12.0652 13.3997i 0.718470 0.797941i
\(283\) 5.74823 + 6.38406i 0.341697 + 0.379493i 0.889361 0.457205i \(-0.151150\pi\)
−0.547664 + 0.836698i \(0.684483\pi\)
\(284\) 16.7487 + 37.6181i 0.993850 + 2.23222i
\(285\) 0.0530898 0.00314477
\(286\) 25.8975 4.89384i 1.53135 0.289379i
\(287\) −17.7698 −1.04892
\(288\) −2.92652 6.57308i −0.172447 0.387322i
\(289\) 3.76179 + 4.17789i 0.221282 + 0.245758i
\(290\) 0.0549020 0.0609748i 0.00322395 0.00358056i
\(291\) 7.49371 + 10.3142i 0.439289 + 0.604629i
\(292\) −12.7440 + 28.6234i −0.745785 + 1.67506i
\(293\) 3.81359 + 3.43377i 0.222792 + 0.200603i 0.772966 0.634447i \(-0.218772\pi\)
−0.550174 + 0.835050i \(0.685439\pi\)
\(294\) −6.08297 1.97648i −0.354766 0.115270i
\(295\) −0.00937065 + 0.0891557i −0.000545580 + 0.00519085i
\(296\) −7.92382 + 13.7245i −0.460563 + 0.797718i
\(297\) −0.294300 + 3.30354i −0.0170770 + 0.191691i
\(298\) 36.0936 2.09084
\(299\) 0.241668 6.26742i 0.0139760 0.362454i
\(300\) 4.41499 13.5879i 0.254899 0.784499i
\(301\) 1.71209 8.05473i 0.0986830 0.464267i
\(302\) 4.05527 + 38.5834i 0.233355 + 2.22022i
\(303\) 6.51146 + 2.89909i 0.374074 + 0.166548i
\(304\) −5.44807 + 1.77018i −0.312468 + 0.101527i
\(305\) −0.00763125 0.0359022i −0.000436964 0.00205575i
\(306\) −10.4253 1.09574i −0.595974 0.0626394i
\(307\) 10.3253i 0.589299i 0.955605 + 0.294649i \(0.0952029\pi\)
−0.955605 + 0.294649i \(0.904797\pi\)
\(308\) 11.0293 15.6985i 0.628454 0.894505i
\(309\) −6.78902 + 11.7589i −0.386214 + 0.668942i
\(310\) 0.0976155 + 0.219248i 0.00554419 + 0.0124525i
\(311\) −7.54042 + 23.2070i −0.427578 + 1.31595i 0.472927 + 0.881102i \(0.343198\pi\)
−0.900504 + 0.434847i \(0.856802\pi\)
\(312\) −5.35474 4.21500i −0.303152 0.238628i
\(313\) 20.8180 15.1252i 1.17670 0.854926i 0.184908 0.982756i \(-0.440801\pi\)
0.991796 + 0.127830i \(0.0408011\pi\)
\(314\) 8.88059 0.933387i 0.501160 0.0526741i
\(315\) −0.0284348 0.00604401i −0.00160212 0.000340542i
\(316\) −28.4903 + 6.05580i −1.60270 + 0.340665i
\(317\) −1.24420 + 1.71249i −0.0698812 + 0.0961832i −0.842527 0.538654i \(-0.818933\pi\)
0.772646 + 0.634837i \(0.218933\pi\)
\(318\) 12.0133 6.93587i 0.673671 0.388944i
\(319\) 6.87495 5.16358i 0.384923 0.289105i
\(320\) 0.183222i 0.0102424i
\(321\) −0.138375 + 1.31655i −0.00772336 + 0.0734829i
\(322\) −5.19332 5.76776i −0.289412 0.321425i
\(323\) −3.65589 + 17.1996i −0.203419 + 0.957011i
\(324\) 2.31181 1.67963i 0.128434 0.0933128i
\(325\) 3.06583 + 17.7644i 0.170061 + 0.985392i
\(326\) −4.43682 13.6551i −0.245733 0.756287i
\(327\) −5.81300 + 5.23405i −0.321459 + 0.289443i
\(328\) 15.1565 6.74813i 0.836880 0.372603i
\(329\) 8.28072 + 14.3426i 0.456531 + 0.790735i
\(330\) −0.0510361 + 0.0917284i −0.00280945 + 0.00504948i
\(331\) 28.4948 16.4515i 1.56622 0.904257i 0.569614 0.821912i \(-0.307093\pi\)
0.996604 0.0823445i \(-0.0262408\pi\)
\(332\) 8.36854 + 0.879569i 0.459283 + 0.0482726i
\(333\) 7.97442 + 2.59105i 0.436996 + 0.141988i
\(334\) −28.1815 + 31.2987i −1.54202 + 1.71259i
\(335\) 0.0107059 + 0.101860i 0.000584925 + 0.00556519i
\(336\) 3.11951 0.327873i 0.170183 0.0178870i
\(337\) 0.561712 + 1.72877i 0.0305984 + 0.0941722i 0.965189 0.261552i \(-0.0842343\pi\)
−0.934591 + 0.355724i \(0.884234\pi\)
\(338\) 28.1796 + 5.18027i 1.53277 + 0.281770i
\(339\) 12.6708 + 9.20589i 0.688184 + 0.499995i
\(340\) −0.169025 0.0975868i −0.00916668 0.00529239i
\(341\) 5.61858 + 24.5140i 0.304263 + 1.32751i
\(342\) −4.07407 7.05649i −0.220300 0.381571i
\(343\) 11.7822 16.2168i 0.636181 0.875627i
\(344\) 1.59850 + 7.52035i 0.0861853 + 0.405470i
\(345\) 0.0185641 + 0.0167152i 0.000999460 + 0.000899918i
\(346\) 1.23561 + 1.70068i 0.0664270 + 0.0914289i
\(347\) −3.44014 1.53165i −0.184677 0.0822233i 0.312315 0.949979i \(-0.398895\pi\)
−0.496992 + 0.867755i \(0.665562\pi\)
\(348\) −7.24613 1.54021i −0.388433 0.0825640i
\(349\) 6.33369 5.70288i 0.339035 0.305268i −0.481972 0.876187i \(-0.660079\pi\)
0.821007 + 0.570918i \(0.193413\pi\)
\(350\) 18.0469 + 13.1119i 0.964650 + 0.700859i
\(351\) −1.59233 + 3.23488i −0.0849926 + 0.172665i
\(352\) 4.59050 23.4178i 0.244675 1.24818i
\(353\) −27.1451 15.6722i −1.44479 0.834147i −0.446622 0.894723i \(-0.647373\pi\)
−0.998164 + 0.0605755i \(0.980706\pi\)
\(354\) 12.5693 5.59623i 0.668053 0.297436i
\(355\) 0.202413 0.0430241i 0.0107429 0.00228348i
\(356\) −30.5266 + 9.91871i −1.61791 + 0.525690i
\(357\) 3.91618 8.79589i 0.207266 0.465528i
\(358\) −1.80094 + 4.04498i −0.0951826 + 0.213784i
\(359\) 10.3949 3.37750i 0.548621 0.178258i −0.0215740 0.999767i \(-0.506868\pi\)
0.570195 + 0.821510i \(0.306868\pi\)
\(360\) 0.0265484 0.00564303i 0.00139922 0.000297414i
\(361\) 4.87120 2.16880i 0.256379 0.114147i
\(362\) −23.9623 13.8346i −1.25943 0.727132i
\(363\) −7.09734 + 8.40403i −0.372514 + 0.441097i
\(364\) 17.3335 11.6002i 0.908522 0.608014i
\(365\) 0.127384 + 0.0925501i 0.00666760 + 0.00484429i
\(366\) −4.18637 + 3.76943i −0.218825 + 0.197031i
\(367\) 4.05350 + 0.861599i 0.211591 + 0.0449751i 0.312488 0.949922i \(-0.398838\pi\)
−0.100896 + 0.994897i \(0.532171\pi\)
\(368\) −2.46239 1.09633i −0.128361 0.0571500i
\(369\) −5.15961 7.10159i −0.268599 0.369694i
\(370\) 0.197213 + 0.177572i 0.0102526 + 0.00923152i
\(371\) 2.64902 + 12.4627i 0.137530 + 0.647030i
\(372\) 12.7365 17.5302i 0.660355 0.908900i
\(373\) 0.594382 + 1.02950i 0.0307759 + 0.0533055i 0.881003 0.473110i \(-0.156869\pi\)
−0.850227 + 0.526416i \(0.823536\pi\)
\(374\) −26.2030 22.8509i −1.35492 1.18159i
\(375\) −0.124361 0.0717997i −0.00642196 0.00370772i
\(376\) −12.5096 9.08874i −0.645132 0.468716i
\(377\) 8.99434 2.54375i 0.463232 0.131010i
\(378\) 1.37872 + 4.24327i 0.0709137 + 0.218250i
\(379\) 2.14468 0.225414i 0.110165 0.0115788i −0.0492857 0.998785i \(-0.515694\pi\)
0.159450 + 0.987206i \(0.449028\pi\)
\(380\) −0.0158577 0.150876i −0.000813483 0.00773977i
\(381\) 3.95565 4.39319i 0.202654 0.225070i
\(382\) −19.1622 6.22619i −0.980425 0.318559i
\(383\) −20.5391 2.15875i −1.04950 0.110307i −0.435956 0.899968i \(-0.643590\pi\)
−0.613543 + 0.789661i \(0.710256\pi\)
\(384\) −11.8909 + 6.86520i −0.606804 + 0.350338i
\(385\) −0.0656427 0.0706173i −0.00334546 0.00359899i
\(386\) −22.6169 39.1737i −1.15117 1.99389i
\(387\) 3.71614 1.65453i 0.188902 0.0841046i
\(388\) 27.0736 24.3772i 1.37445 1.23756i
\(389\) −5.93635 18.2702i −0.300985 0.926336i −0.981145 0.193273i \(-0.938090\pi\)
0.680160 0.733064i \(-0.261910\pi\)
\(390\) −0.0876830 + 0.0730335i −0.00444000 + 0.00369819i
\(391\) −6.69364 + 4.86321i −0.338512 + 0.245943i
\(392\) −1.14038 + 5.36508i −0.0575981 + 0.270978i
\(393\) 4.05687 + 4.50561i 0.204642 + 0.227278i
\(394\) 3.07412 29.2483i 0.154872 1.47351i
\(395\) 0.146372i 0.00736479i
\(396\) 9.47625 0.150383i 0.476200 0.00755702i
\(397\) −29.7721 + 17.1889i −1.49422 + 0.862686i −0.999978 0.00663971i \(-0.997886\pi\)
−0.494239 + 0.869326i \(0.664553\pi\)
\(398\) −1.96514 + 2.70478i −0.0985035 + 0.135578i
\(399\) 7.32047 1.55601i 0.366482 0.0778981i
\(400\) 7.57780 + 1.61071i 0.378890 + 0.0805356i
\(401\) 20.7007 2.17573i 1.03375 0.108651i 0.427570 0.903982i \(-0.359370\pi\)
0.606175 + 0.795331i \(0.292703\pi\)
\(402\) 12.7172 9.23962i 0.634278 0.460830i
\(403\) −3.90342 + 27.0604i −0.194443 + 1.34798i
\(404\) 6.29398 19.3709i 0.313137 0.963738i
\(405\) −0.00584083 0.0131187i −0.000290233 0.000651875i
\(406\) 5.78323 10.0169i 0.287017 0.497128i
\(407\) 16.7008 + 22.2360i 0.827828 + 1.10220i
\(408\) 8.98952i 0.445048i
\(409\) −11.0578 1.16223i −0.546775 0.0574684i −0.172886 0.984942i \(-0.555309\pi\)
−0.373889 + 0.927473i \(0.621976\pi\)
\(410\) −0.0577627 0.271752i −0.00285270 0.0134209i
\(411\) −15.2230 + 4.94627i −0.750897 + 0.243981i
\(412\) 35.4456 + 15.7814i 1.74628 + 0.777494i
\(413\) 1.32097 + 12.5682i 0.0650007 + 0.618441i
\(414\) 0.797128 3.75019i 0.0391767 0.184312i
\(415\) 0.0130672 0.0402169i 0.000641446 0.00197417i
\(416\) 13.8272 21.9503i 0.677936 1.07620i
\(417\) 1.09421 0.0535836
\(418\) 2.39800 26.9177i 0.117290 1.31659i
\(419\) −7.61072 + 13.1822i −0.371808 + 0.643990i −0.989844 0.142160i \(-0.954595\pi\)
0.618036 + 0.786150i \(0.287929\pi\)
\(420\) −0.00868312 + 0.0826144i −0.000423693 + 0.00403117i
\(421\) 34.1656 + 11.1011i 1.66513 + 0.541033i 0.981937 0.189206i \(-0.0605913\pi\)
0.683192 + 0.730239i \(0.260591\pi\)
\(422\) 37.4317 + 33.7037i 1.82215 + 1.64067i
\(423\) −3.32756 + 7.47383i −0.161792 + 0.363390i
\(424\) −6.99218 9.62390i −0.339570 0.467378i
\(425\) 15.9121 17.6722i 0.771850 0.857227i
\(426\) −21.2516 23.6023i −1.02964 1.14353i
\(427\) −2.10452 4.72684i −0.101845 0.228748i
\(428\) 3.78285 0.182851
\(429\) −10.4890 + 5.74282i −0.506416 + 0.277266i
\(430\) 0.128745 0.00620866
\(431\) −14.4740 32.5092i −0.697190 1.56592i −0.819279 0.573396i \(-0.805626\pi\)
0.122088 0.992519i \(-0.461041\pi\)
\(432\) 1.03681 + 1.15149i 0.0498834 + 0.0554011i
\(433\) 20.4936 22.7605i 0.984860 1.09380i −0.0107255 0.999942i \(-0.503414\pi\)
0.995586 0.0938557i \(-0.0299192\pi\)
\(434\) 19.8860 + 27.3708i 0.954560 + 1.31384i
\(435\) −0.0151419 + 0.0340093i −0.000726000 + 0.00163062i
\(436\) 16.6110 + 14.9566i 0.795521 + 0.716290i
\(437\) −6.11640 1.98734i −0.292587 0.0950673i
\(438\) 2.52604 24.0337i 0.120699 1.14837i
\(439\) −0.997592 + 1.72788i −0.0476125 + 0.0824672i −0.888849 0.458199i \(-0.848495\pi\)
0.841237 + 0.540667i \(0.181828\pi\)
\(440\) 0.0828062 + 0.0353042i 0.00394763 + 0.00168306i
\(441\) 2.90202 0.138191
\(442\) −17.6227 33.4361i −0.838228 1.59039i
\(443\) 4.60428 14.1705i 0.218756 0.673261i −0.780110 0.625643i \(-0.784837\pi\)
0.998866 0.0476185i \(-0.0151632\pi\)
\(444\) 4.98157 23.4365i 0.236415 1.11225i
\(445\) 0.0168606 + 0.160418i 0.000799271 + 0.00760455i
\(446\) −22.1924 9.88068i −1.05084 0.467864i
\(447\) −15.5750 + 5.06061i −0.736671 + 0.239359i
\(448\) −5.37008 25.2642i −0.253712 1.19362i
\(449\) −20.0032 2.10242i −0.944010 0.0992195i −0.379999 0.924987i \(-0.624076\pi\)
−0.564011 + 0.825767i \(0.690742\pi\)
\(450\) 11.0195i 0.519463i
\(451\) −0.461957 29.1098i −0.0217527 1.37073i
\(452\) 22.3775 38.7590i 1.05255 1.82307i
\(453\) −7.15962 16.0808i −0.336388 0.755541i
\(454\) −4.55721 + 14.0256i −0.213880 + 0.658256i
\(455\) −0.0389105 0.0973236i −0.00182415 0.00456260i
\(456\) −5.65300 + 4.10714i −0.264726 + 0.192335i
\(457\) −32.9115 + 3.45913i −1.53953 + 0.161811i −0.835952 0.548803i \(-0.815084\pi\)
−0.703582 + 0.710614i \(0.748417\pi\)
\(458\) −36.1057 7.67451i −1.68711 0.358606i
\(459\) 4.65231 0.988880i 0.217151 0.0461570i
\(460\) 0.0419580 0.0577503i 0.00195630 0.00269262i
\(461\) 2.39488 1.38269i 0.111541 0.0643981i −0.443192 0.896427i \(-0.646154\pi\)
0.554733 + 0.832029i \(0.312821\pi\)
\(462\) −4.34882 + 14.1441i −0.202325 + 0.658043i
\(463\) 23.8474i 1.10828i 0.832422 + 0.554142i \(0.186953\pi\)
−0.832422 + 0.554142i \(0.813047\pi\)
\(464\) 0.419883 3.99492i 0.0194926 0.185459i
\(465\) −0.0728631 0.0809227i −0.00337894 0.00375270i
\(466\) 2.24330 10.5539i 0.103919 0.488899i
\(467\) −32.2189 + 23.4084i −1.49091 + 1.08321i −0.517082 + 0.855936i \(0.672982\pi\)
−0.973831 + 0.227275i \(0.927018\pi\)
\(468\) 9.66885 + 3.55901i 0.446943 + 0.164516i
\(469\) 4.46163 + 13.7315i 0.206019 + 0.634061i
\(470\) −0.192423 + 0.173258i −0.00887581 + 0.00799182i
\(471\) −3.70125 + 1.64790i −0.170545 + 0.0759314i
\(472\) −5.89950 10.2182i −0.271547 0.470333i
\(473\) 13.2395 + 2.59528i 0.608751 + 0.119331i
\(474\) 19.4553 11.2325i 0.893610 0.515926i
\(475\) 18.3830 + 1.93213i 0.843469 + 0.0886521i
\(476\) −26.1668 8.50211i −1.19935 0.389694i
\(477\) −4.21146 + 4.67730i −0.192830 + 0.214159i
\(478\) 2.85219 + 27.1368i 0.130456 + 1.24121i
\(479\) 15.9660 1.67809i 0.729505 0.0766740i 0.267508 0.963556i \(-0.413800\pi\)
0.461997 + 0.886882i \(0.347133\pi\)
\(480\) 0.0319288 + 0.0982667i 0.00145734 + 0.00448524i
\(481\) 8.22737 + 29.0908i 0.375136 + 1.32643i
\(482\) −2.11178 1.53430i −0.0961889 0.0698853i
\(483\) 3.04969 + 1.76074i 0.138766 + 0.0801164i
\(484\) 26.0034 + 17.6597i 1.18197 + 0.802714i
\(485\) −0.0915397 0.158551i −0.00415660 0.00719945i
\(486\) −1.29547 + 1.78306i −0.0587637 + 0.0808814i
\(487\) −0.217985 1.02554i −0.00987783 0.0464716i 0.972933 0.231089i \(-0.0742288\pi\)
−0.982810 + 0.184617i \(0.940895\pi\)
\(488\) 3.59005 + 3.23250i 0.162514 + 0.146328i
\(489\) 3.82912 + 5.27033i 0.173159 + 0.238333i
\(490\) 0.0839075 + 0.0373580i 0.00379055 + 0.00168766i
\(491\) −14.2086 3.02013i −0.641226 0.136297i −0.124187 0.992259i \(-0.539632\pi\)
−0.517039 + 0.855962i \(0.672966\pi\)
\(492\) −18.6409 + 16.7843i −0.840396 + 0.756696i
\(493\) −9.97537 7.24753i −0.449268 0.326412i
\(494\) 12.9746 26.3583i 0.583753 1.18591i
\(495\) 0.00916185 0.0467380i 0.000411795 0.00210072i
\(496\) 10.1754 + 5.87478i 0.456890 + 0.263786i
\(497\) 26.6494 11.8651i 1.19539 0.532221i
\(498\) −6.34824 + 1.34936i −0.284472 + 0.0604663i
\(499\) −32.4312 + 10.5375i −1.45182 + 0.471725i −0.925561 0.378598i \(-0.876406\pi\)
−0.526260 + 0.850323i \(0.676406\pi\)
\(500\) −0.166902 + 0.374867i −0.00746407 + 0.0167646i
\(501\) 7.77244 17.4572i 0.347247 0.779929i
\(502\) −38.7721 + 12.5978i −1.73048 + 0.562268i
\(503\) 15.2891 3.24980i 0.681708 0.144902i 0.145974 0.989288i \(-0.453368\pi\)
0.535734 + 0.844387i \(0.320035\pi\)
\(504\) 3.49532 1.55622i 0.155694 0.0693194i
\(505\) −0.0886422 0.0511776i −0.00394452 0.00227737i
\(506\) 9.31352 8.65743i 0.414036 0.384870i
\(507\) −12.8863 + 1.71564i −0.572300 + 0.0761944i
\(508\) −13.6666 9.92933i −0.606355 0.440543i
\(509\) 23.8359 21.4620i 1.05651 0.951286i 0.0576173 0.998339i \(-0.481650\pi\)
0.998892 + 0.0470532i \(0.0149830\pi\)
\(510\) 0.147245 + 0.0312978i 0.00652010 + 0.00138589i
\(511\) 20.2774 + 9.02807i 0.897019 + 0.399378i
\(512\) −9.99582 13.7581i −0.441757 0.608026i
\(513\) 2.74741 + 2.47378i 0.121301 + 0.109220i
\(514\) 6.59959 + 31.0486i 0.291095 + 1.36950i
\(515\) 0.114609 0.157745i 0.00505026 0.00695109i
\(516\) −5.81201 10.0667i −0.255860 0.443162i
\(517\) −23.2803 + 13.9380i −1.02387 + 0.612993i
\(518\) 32.3979 + 18.7050i 1.42348 + 0.821849i
\(519\) −0.771637 0.560627i −0.0338711 0.0246088i
\(520\) 0.0701471 + 0.0682346i 0.00307615 + 0.00299228i
\(521\) −4.93101 15.1761i −0.216031 0.664876i −0.999079 0.0429141i \(-0.986336\pi\)
0.783047 0.621962i \(-0.213664\pi\)
\(522\) 5.68238 0.597242i 0.248711 0.0261406i
\(523\) −0.389192 3.70291i −0.0170182 0.161917i 0.982712 0.185140i \(-0.0592739\pi\)
−0.999730 + 0.0232230i \(0.992607\pi\)
\(524\) 11.5927 12.8750i 0.506431 0.562448i
\(525\) −9.62595 3.12766i −0.420111 0.136502i
\(526\) −28.6215 3.00824i −1.24795 0.131165i
\(527\) 31.2342 18.0331i 1.36058 0.785533i
\(528\) 0.618207 + 5.10173i 0.0269040 + 0.222024i
\(529\) 9.98696 + 17.2979i 0.434216 + 0.752084i
\(530\) −0.181979 + 0.0810225i −0.00790468 + 0.00351939i
\(531\) −4.63924 + 4.17719i −0.201326 + 0.181275i
\(532\) −6.60863 20.3393i −0.286521 0.881820i
\(533\) 10.9328 29.7015i 0.473554 1.28651i
\(534\) 20.0283 14.5514i 0.866710 0.629702i
\(535\) 0.00395243 0.0185947i 0.000170879 0.000803920i
\(536\) −9.02005 10.0178i −0.389607 0.432702i
\(537\) 0.209996 1.99798i 0.00906200 0.0862192i
\(538\) 1.67382i 0.0721634i
\(539\) 7.87550 + 5.53311i 0.339222 + 0.238328i
\(540\) −0.0355375 + 0.0205176i −0.00152929 + 0.000882936i
\(541\) 16.3994 22.5719i 0.705067 0.970441i −0.294822 0.955552i \(-0.595260\pi\)
0.999889 0.0148892i \(-0.00473955\pi\)
\(542\) 34.2519 7.28046i 1.47124 0.312722i
\(543\) 12.2798 + 2.61016i 0.526979 + 0.112013i
\(544\) −34.0343 + 3.57715i −1.45921 + 0.153369i
\(545\) 0.0908753 0.0660247i 0.00389267 0.00282819i
\(546\) −9.94993 + 12.6404i −0.425818 + 0.540958i
\(547\) 1.73077 5.32677i 0.0740025 0.227756i −0.907213 0.420672i \(-0.861794\pi\)
0.981215 + 0.192916i \(0.0617944\pi\)
\(548\) 18.6039 + 41.7850i 0.794718 + 1.78497i
\(549\) 1.27798 2.21353i 0.0545430 0.0944713i
\(550\) −21.0102 + 29.9047i −0.895878 + 1.27514i
\(551\) 9.58420i 0.408301i
\(552\) −3.26984 0.343674i −0.139174 0.0146277i
\(553\) 4.29004 + 20.1831i 0.182431 + 0.858271i
\(554\) −58.7678 + 19.0948i −2.49681 + 0.811262i
\(555\) −0.109998 0.0489742i −0.00466915 0.00207884i
\(556\) −0.326835 3.10963i −0.0138609 0.131878i
\(557\) −5.80660 + 27.3179i −0.246033 + 1.15750i 0.665541 + 0.746361i \(0.268201\pi\)
−0.911574 + 0.411135i \(0.865132\pi\)
\(558\) −5.16448 + 15.8946i −0.218630 + 0.672874i
\(559\) 12.4098 + 7.81733i 0.524877 + 0.330638i
\(560\) −0.0450436 −0.00190344
\(561\) 14.5109 + 6.18667i 0.612650 + 0.261202i
\(562\) 27.4598 47.5618i 1.15832 2.00627i
\(563\) 1.92630 18.3276i 0.0811840 0.772414i −0.875878 0.482532i \(-0.839717\pi\)
0.957062 0.289882i \(-0.0936162\pi\)
\(564\) 22.2338 + 7.22421i 0.936213 + 0.304194i
\(565\) −0.167141 0.150494i −0.00703166 0.00633133i
\(566\) −7.70098 + 17.2967i −0.323696 + 0.727034i
\(567\) −1.18988 1.63773i −0.0499703 0.0687783i
\(568\) −18.2245 + 20.2403i −0.764681 + 0.849264i
\(569\) −17.1629 19.0614i −0.719507 0.799094i 0.266845 0.963739i \(-0.414019\pi\)
−0.986353 + 0.164645i \(0.947352\pi\)
\(570\) 0.0475919 + 0.106893i 0.00199341 + 0.00447726i
\(571\) −19.7991 −0.828568 −0.414284 0.910148i \(-0.635968\pi\)
−0.414284 + 0.910148i \(0.635968\pi\)
\(572\) 19.4536 + 28.0935i 0.813394 + 1.17465i
\(573\) 9.14178 0.381903
\(574\) −15.9296 35.7785i −0.664890 1.49337i
\(575\) 5.81973 + 6.46347i 0.242700 + 0.269545i
\(576\) 8.53744 9.48178i 0.355726 0.395074i
\(577\) −5.63402 7.75456i −0.234547 0.322827i 0.675477 0.737381i \(-0.263938\pi\)
−0.910025 + 0.414554i \(0.863938\pi\)
\(578\) −5.03972 + 11.3194i −0.209625 + 0.470824i
\(579\) 15.2520 + 13.7330i 0.633853 + 0.570724i
\(580\) 0.101174 + 0.0328735i 0.00420102 + 0.00136500i
\(581\) 0.623103 5.92843i 0.0258507 0.245953i
\(582\) −14.0494 + 24.3342i −0.582365 + 1.00869i
\(583\) −20.3470 + 4.66352i −0.842687 + 0.193143i
\(584\) −20.7238 −0.857555
\(585\) 0.0275968 0.0438090i 0.00114099 0.00181128i
\(586\) −3.49503 + 10.7566i −0.144379 + 0.444351i
\(587\) −4.30019 + 20.2308i −0.177488 + 0.835015i 0.795824 + 0.605528i \(0.207038\pi\)
−0.973312 + 0.229487i \(0.926295\pi\)
\(588\) −0.866821 8.24725i −0.0357471 0.340111i
\(589\) 25.6103 + 11.4024i 1.05525 + 0.469829i
\(590\) −0.187910 + 0.0610557i −0.00773614 + 0.00251362i
\(591\) 2.77432 + 13.0521i 0.114120 + 0.536893i
\(592\) 12.9209 + 1.35804i 0.531047 + 0.0558153i
\(593\) 18.1407i 0.744950i 0.928042 + 0.372475i \(0.121491\pi\)
−0.928042 + 0.372475i \(0.878509\pi\)
\(594\) −6.91531 + 2.36888i −0.283739 + 0.0971962i
\(595\) −0.0691323 + 0.119741i −0.00283415 + 0.00490889i
\(596\) 19.0339 + 42.7509i 0.779661 + 1.75115i
\(597\) 0.468757 1.44269i 0.0191850 0.0590452i
\(598\) 12.8357 5.13180i 0.524892 0.209855i
\(599\) 28.8557 20.9649i 1.17901 0.856603i 0.186953 0.982369i \(-0.440139\pi\)
0.992060 + 0.125766i \(0.0401389\pi\)
\(600\) 9.39806 0.987776i 0.383674 0.0403258i
\(601\) 7.42090 + 1.57736i 0.302705 + 0.0643419i 0.356760 0.934196i \(-0.383881\pi\)
−0.0540552 + 0.998538i \(0.517215\pi\)
\(602\) 17.7525 3.77341i 0.723539 0.153793i
\(603\) −4.19223 + 5.77011i −0.170721 + 0.234977i
\(604\) −43.5614 + 25.1502i −1.77249 + 1.02335i
\(605\) 0.113976 0.109369i 0.00463379 0.00444649i
\(606\) 15.7093i 0.638147i
\(607\) −2.91714 + 27.7548i −0.118403 + 1.12653i 0.760436 + 0.649413i \(0.224985\pi\)
−0.878839 + 0.477118i \(0.841681\pi\)
\(608\) −17.7991 19.7679i −0.721850 0.801696i
\(609\) −1.09112 + 5.13329i −0.0442142 + 0.208012i
\(610\) 0.0654460 0.0475493i 0.00264983 0.00192522i
\(611\) −29.0678 + 5.01659i −1.17596 + 0.202950i
\(612\) −4.19993 12.9261i −0.169772 0.522505i
\(613\) −20.5475 + 18.5010i −0.829905 + 0.747250i −0.970056 0.242880i \(-0.921908\pi\)
0.140151 + 0.990130i \(0.455241\pi\)
\(614\) −20.7895 + 9.25608i −0.838995 + 0.373545i
\(615\) 0.0630274 + 0.109167i 0.00254151 + 0.00440203i
\(616\) 12.4528 + 2.44106i 0.501736 + 0.0983532i
\(617\) −9.86205 + 5.69386i −0.397031 + 0.229226i −0.685202 0.728353i \(-0.740286\pi\)
0.288171 + 0.957579i \(0.406953\pi\)
\(618\) −29.7619 3.12810i −1.19720 0.125831i
\(619\) −22.0243 7.15614i −0.885233 0.287630i −0.169105 0.985598i \(-0.554088\pi\)
−0.716128 + 0.697968i \(0.754088\pi\)
\(620\) −0.208210 + 0.231241i −0.00836193 + 0.00928687i
\(621\) 0.181834 + 1.73003i 0.00729674 + 0.0694238i
\(622\) −53.4855 + 5.62155i −2.14457 + 0.225404i
\(623\) 7.02660 + 21.6256i 0.281515 + 0.866413i
\(624\) −1.37124 + 5.41584i −0.0548937 + 0.216807i
\(625\) −20.2229 14.6928i −0.808917 0.587713i
\(626\) 49.1158 + 28.3570i 1.96306 + 1.13338i
\(627\) 2.73931 + 11.9517i 0.109397 + 0.477303i
\(628\) 5.78873 + 10.0264i 0.230995 + 0.400096i
\(629\) 23.4410 32.2638i 0.934654 1.28644i
\(630\) −0.0133209 0.0626700i −0.000530718 0.00249683i
\(631\) 6.23244 + 5.61172i 0.248110 + 0.223399i 0.783796 0.621018i \(-0.213281\pi\)
−0.535687 + 0.844417i \(0.679947\pi\)
\(632\) −11.3237 15.5857i −0.450433 0.619967i
\(633\) −20.8779 9.29546i −0.829824 0.369461i
\(634\) −4.56336 0.969971i −0.181234 0.0385225i
\(635\) −0.0630872 + 0.0568040i −0.00250354 + 0.00225420i
\(636\) 14.5504 + 10.5715i 0.576960 + 0.419186i
\(637\) 5.81949 + 8.69574i 0.230576 + 0.344538i
\(638\) 16.5596 + 9.21346i 0.655599 + 0.364764i
\(639\) 12.4797 + 7.20513i 0.493687 + 0.285031i
\(640\) 0.180125 0.0801970i 0.00712008 0.00317006i
\(641\) −2.99067 + 0.635688i −0.118125 + 0.0251081i −0.266595 0.963809i \(-0.585898\pi\)
0.148470 + 0.988917i \(0.452565\pi\)
\(642\) −2.77485 + 0.901603i −0.109515 + 0.0355834i
\(643\) 19.3318 43.4200i 0.762373 1.71232i 0.0625055 0.998045i \(-0.480091\pi\)
0.699867 0.714273i \(-0.253242\pi\)
\(644\) 4.09292 9.19285i 0.161284 0.362249i
\(645\) −0.0555558 + 0.0180512i −0.00218751 + 0.000710764i
\(646\) −37.9077 + 8.05753i −1.49146 + 0.317019i
\(647\) −24.7115 + 11.0023i −0.971511 + 0.432545i −0.830228 0.557425i \(-0.811790\pi\)
−0.141284 + 0.989969i \(0.545123\pi\)
\(648\) 1.63683 + 0.945022i 0.0643006 + 0.0371240i
\(649\) −20.5544 + 2.49069i −0.806830 + 0.0977683i
\(650\) −33.0193 + 22.0976i −1.29512 + 0.866740i
\(651\) −12.4188 9.02275i −0.486729 0.353629i
\(652\) 13.8340 12.4562i 0.541782 0.487823i
\(653\) −0.234297 0.0498014i −0.00916876 0.00194888i 0.203325 0.979111i \(-0.434825\pi\)
−0.212494 + 0.977162i \(0.568159\pi\)
\(654\) −15.7495 7.01211i −0.615853 0.274195i
\(655\) −0.0511752 0.0704367i −0.00199958 0.00275219i
\(656\) −10.1078 9.10114i −0.394645 0.355340i
\(657\) 2.27969 + 10.7251i 0.0889391 + 0.418426i
\(658\) −21.4549 + 29.5301i −0.836398 + 1.15120i
\(659\) −21.2343 36.7790i −0.827173 1.43270i −0.900248 0.435378i \(-0.856615\pi\)
0.0730750 0.997326i \(-0.476719\pi\)
\(660\) −0.135561 0.0120766i −0.00527672 0.000470083i
\(661\) 36.0369 + 20.8059i 1.40167 + 0.809257i 0.994564 0.104123i \(-0.0332035\pi\)
0.407109 + 0.913380i \(0.366537\pi\)
\(662\) 58.6681 + 42.6249i 2.28020 + 1.65666i
\(663\) 12.2925 + 11.9574i 0.477402 + 0.464386i
\(664\) 1.71987 + 5.29320i 0.0667437 + 0.205416i
\(665\) −0.106883 + 0.0112339i −0.00414476 + 0.000435632i
\(666\) 1.93169 + 18.3788i 0.0748513 + 0.712162i
\(667\) 3.01757 3.35135i 0.116841 0.129765i
\(668\) −51.9332 16.8741i −2.00936 0.652879i
\(669\) 10.9617 + 1.15212i 0.423805 + 0.0445437i
\(670\) −0.195491 + 0.112867i −0.00755248 + 0.00436043i
\(671\) 7.68861 3.57043i 0.296815 0.137835i
\(672\) 7.28272 + 12.6140i 0.280937 + 0.486597i
\(673\) −40.5926 + 18.0730i −1.56473 + 0.696663i −0.992365 0.123335i \(-0.960641\pi\)
−0.572366 + 0.819998i \(0.693974\pi\)
\(674\) −2.97724 + 2.68072i −0.114679 + 0.103257i
\(675\) −1.54502 4.75509i −0.0594679 0.183023i
\(676\) 8.72478 + 36.1091i 0.335568 + 1.38881i
\(677\) −19.2788 + 14.0068i −0.740943 + 0.538327i −0.893006 0.450044i \(-0.851408\pi\)
0.152063 + 0.988371i \(0.451408\pi\)
\(678\) −7.17687 + 33.7645i −0.275626 + 1.29672i
\(679\) −17.2693 19.1795i −0.662734 0.736040i
\(680\) 0.0134937 0.128384i 0.000517461 0.00492332i
\(681\) 6.69126i 0.256409i
\(682\) −44.3207 + 33.2881i −1.69713 + 1.27467i
\(683\) 18.7216 10.8089i 0.716363 0.413592i −0.0970499 0.995280i \(-0.530941\pi\)
0.813412 + 0.581687i \(0.197607\pi\)
\(684\) 6.20959 8.54677i 0.237430 0.326794i
\(685\) 0.224833 0.0477898i 0.00859044 0.00182596i
\(686\) 43.2138 + 9.18537i 1.64991 + 0.350699i
\(687\) 16.6563 1.75064i 0.635476 0.0667912i
\(688\) 5.09925 3.70482i 0.194407 0.141245i
\(689\) −22.4606 3.23990i −0.855681 0.123431i
\(690\) −0.0170135 + 0.0523621i −0.000647691 + 0.00199339i
\(691\) −10.2427 23.0054i −0.389650 0.875168i −0.996751 0.0805437i \(-0.974334\pi\)
0.607101 0.794625i \(-0.292332\pi\)
\(692\) −1.36276 + 2.36037i −0.0518044 + 0.0897279i
\(693\) −0.106534 6.71316i −0.00404690 0.255012i
\(694\) 8.29957i 0.315047i
\(695\) −0.0156270 0.00164246i −0.000592766 6.23022e-5i
\(696\) −1.01873 4.79273i −0.0386147 0.181668i
\(697\) −39.7072 + 12.9016i −1.50402 + 0.488685i
\(698\) 17.1602 + 7.64022i 0.649524 + 0.289187i
\(699\) 0.511721 + 4.86870i 0.0193551 + 0.184151i
\(700\) −6.01327 + 28.2902i −0.227280 + 1.06927i
\(701\) 1.09826 3.38009i 0.0414806 0.127664i −0.928172 0.372152i \(-0.878620\pi\)
0.969652 + 0.244488i \(0.0786199\pi\)
\(702\) −7.94069 0.306189i −0.299702 0.0115563i
\(703\) 30.9986 1.16913
\(704\) 41.2473 9.45384i 1.55456 0.356305i
\(705\) 0.0587414 0.101743i 0.00221233 0.00383187i
\(706\) 7.22110 68.7042i 0.271770 2.58572i
\(707\) −13.7227 4.45878i −0.516095 0.167690i
\(708\) 13.2569 + 11.9366i 0.498225 + 0.448604i
\(709\) 7.49697 16.8385i 0.281555 0.632382i −0.716304 0.697788i \(-0.754168\pi\)
0.997859 + 0.0654061i \(0.0208343\pi\)
\(710\) 0.268078 + 0.368977i 0.0100608 + 0.0138475i
\(711\) −6.82038 + 7.57480i −0.255784 + 0.284077i
\(712\) −14.2056 15.7770i −0.532379 0.591266i
\(713\) 5.36523 + 12.0505i 0.200930 + 0.451295i
\(714\) 21.2206 0.794163
\(715\) 0.158420 0.0662718i 0.00592458 0.00247842i
\(716\) −5.74079 −0.214543
\(717\) −5.03556 11.3101i −0.188057 0.422382i
\(718\) 16.1188 + 17.9018i 0.601549 + 0.668087i
\(719\) 20.8072 23.1088i 0.775979 0.861812i −0.217472 0.976067i \(-0.569781\pi\)
0.993452 + 0.114254i \(0.0364478\pi\)
\(720\) −0.0130788 0.0180014i −0.000487417 0.000670872i
\(721\) 11.1798 25.1103i 0.416359 0.935157i
\(722\) 8.73350 + 7.86368i 0.325027 + 0.292656i
\(723\) 1.12639 + 0.365986i 0.0418908 + 0.0136112i
\(724\) 3.74989 35.6778i 0.139363 1.32595i
\(725\) −6.48080 + 11.2251i −0.240691 + 0.416889i
\(726\) −23.2834 6.75636i −0.864127 0.250752i
\(727\) −39.5391 −1.46642 −0.733212 0.680000i \(-0.761980\pi\)
−0.733212 + 0.680000i \(0.761980\pi\)
\(728\) 11.6724 + 7.35281i 0.432607 + 0.272513i
\(729\) 0.309017 0.951057i 0.0114451 0.0352243i
\(730\) −0.0721516 + 0.339447i −0.00267045 + 0.0125635i
\(731\) −2.02237 19.2416i −0.0748001 0.711675i
\(732\) −6.67237 2.97073i −0.246618 0.109801i
\(733\) −9.18029 + 2.98286i −0.339082 + 0.110174i −0.473608 0.880736i \(-0.657049\pi\)
0.134526 + 0.990910i \(0.457049\pi\)
\(734\) 1.89895 + 8.93387i 0.0700916 + 0.329755i
\(735\) −0.0414454 0.00435608i −0.00152874 0.000160677i
\(736\) 12.5164i 0.461360i
\(737\) −22.3784 + 7.66584i −0.824319 + 0.282375i
\(738\) 9.67336 16.7547i 0.356081 0.616751i
\(739\) 9.59189 + 21.5437i 0.352843 + 0.792499i 0.999557 + 0.0297660i \(0.00947622\pi\)
−0.646714 + 0.762733i \(0.723857\pi\)
\(740\) −0.106324 + 0.327232i −0.00390855 + 0.0120293i
\(741\) −1.90309 + 13.1932i −0.0699118 + 0.484663i
\(742\) −22.7182 + 16.5057i −0.834010 + 0.605944i
\(743\) 29.5273 3.10344i 1.08325 0.113854i 0.453958 0.891023i \(-0.350012\pi\)
0.629292 + 0.777169i \(0.283345\pi\)
\(744\) 14.0188 + 2.97979i 0.513955 + 0.109244i
\(745\) 0.230031 0.0488946i 0.00842769 0.00179136i
\(746\) −1.54001 + 2.11964i −0.0563837 + 0.0776055i
\(747\) 2.55018 1.47235i 0.0933062 0.0538704i
\(748\) 13.2476 43.0865i 0.484380 1.57540i
\(749\) 2.67984i 0.0979193i
\(750\) 0.0330823 0.314757i 0.00120800 0.0114933i
\(751\) −25.6154 28.4488i −0.934719 1.03811i −0.999192 0.0401906i \(-0.987203\pi\)
0.0644735 0.997919i \(-0.479463\pi\)
\(752\) −2.63560 + 12.3995i −0.0961103 + 0.452163i
\(753\) 14.9645 10.8723i 0.545336 0.396210i
\(754\) 13.1846 + 15.8293i 0.480155 + 0.576468i
\(755\) 0.0781125 + 0.240406i 0.00284280 + 0.00874925i
\(756\) −4.29886 + 3.87071i −0.156348 + 0.140776i
\(757\) 1.40129 0.623896i 0.0509309 0.0226759i −0.381113 0.924528i \(-0.624459\pi\)
0.432044 + 0.901853i \(0.357792\pi\)
\(758\) 2.37644 + 4.11611i 0.0863161 + 0.149504i
\(759\) −2.80509 + 5.04166i −0.101818 + 0.183001i
\(760\) 0.0868987 0.0501710i 0.00315215 0.00181989i
\(761\) 46.9713 + 4.93688i 1.70271 + 0.178962i 0.905385 0.424592i \(-0.139583\pi\)
0.797322 + 0.603554i \(0.206249\pi\)
\(762\) 12.3914 + 4.02622i 0.448894 + 0.145855i
\(763\) 10.5955 11.7675i 0.383584 0.426013i
\(764\) −2.73061 25.9800i −0.0987901 0.939925i
\(765\) −0.0679267 + 0.00713938i −0.00245589 + 0.000258125i
\(766\) −14.0656 43.2895i −0.508211 1.56411i
\(767\) −21.8199 5.52461i −0.787871 0.199482i
\(768\) −3.83768 2.78824i −0.138480 0.100612i
\(769\) −22.1896 12.8112i −0.800177 0.461982i 0.0433563 0.999060i \(-0.486195\pi\)
−0.843533 + 0.537078i \(0.819528\pi\)
\(770\) 0.0833389 0.195472i 0.00300333 0.00704433i
\(771\) −7.20110 12.4727i −0.259341 0.449192i
\(772\) 34.4721 47.4468i 1.24068 1.70765i
\(773\) −6.18850 29.1146i −0.222585 1.04718i −0.937504 0.347973i \(-0.886870\pi\)
0.714919 0.699207i \(-0.246463\pi\)
\(774\) 6.66261 + 5.99904i 0.239482 + 0.215631i
\(775\) −22.2847 30.6722i −0.800489 1.10178i
\(776\) 22.0130 + 9.80084i 0.790222 + 0.351830i
\(777\) −16.6028 3.52904i −0.595623 0.126604i
\(778\) 31.4644 28.3307i 1.12805 1.01570i
\(779\) −26.2546 19.0751i −0.940668 0.683435i
\(780\) −0.132744 0.0653417i −0.00475300 0.00233961i
\(781\) 20.1297 + 43.3475i 0.720297 + 1.55110i
\(782\) −15.7923 9.11766i −0.564730 0.326047i
\(783\) −2.36830 + 1.05444i −0.0846362 + 0.0376824i
\(784\) 4.39836 0.934901i 0.157084 0.0333893i
\(785\) 0.0553332 0.0179789i 0.00197493 0.000641693i
\(786\) −5.43503 + 12.2073i −0.193861 + 0.435419i
\(787\) 9.64667 21.6668i 0.343867 0.772337i −0.655979 0.754779i \(-0.727744\pi\)
0.999846 0.0175583i \(-0.00558927\pi\)
\(788\) 36.2642 11.7830i 1.29186 0.419751i
\(789\) 12.7724 2.71486i 0.454710 0.0966516i
\(790\) −0.294712 + 0.131214i −0.0104854 + 0.00466840i
\(791\) −27.4576 15.8527i −0.976280 0.563656i
\(792\) 2.64020 + 5.68544i 0.0938155 + 0.202023i
\(793\) 9.19550 0.609443i 0.326542 0.0216419i
\(794\) −61.2978 44.5355i −2.17538 1.58050i
\(795\) 0.0671671 0.0604775i 0.00238217 0.00214492i
\(796\) −4.23999 0.901238i −0.150283 0.0319435i
\(797\) −19.6469 8.74735i −0.695928 0.309847i 0.0281123 0.999605i \(-0.491050\pi\)
−0.724040 + 0.689758i \(0.757717\pi\)
\(798\) 9.69532 + 13.3445i 0.343211 + 0.472389i
\(799\) 28.9169 + 26.0369i 1.02301 + 0.921118i
\(800\) 7.47945 + 35.1880i 0.264438 + 1.24408i
\(801\) −6.60232 + 9.08731i −0.233281 + 0.321084i
\(802\) 22.9377 + 39.7293i 0.809959 + 1.40289i
\(803\) −14.2623 + 33.4523i −0.503305 + 1.18051i
\(804\) 17.6503 + 10.1904i 0.622478 + 0.359388i
\(805\) −0.0409114 0.0297239i −0.00144194 0.00104763i
\(806\) −57.9838 + 16.3988i −2.04239 + 0.577623i
\(807\) −0.234683 0.722279i −0.00826123 0.0254254i
\(808\) 13.3978 1.40817i 0.471334 0.0495392i
\(809\) 1.62684 + 15.4783i 0.0571966 + 0.544190i 0.985175 + 0.171555i \(0.0548790\pi\)
−0.927978 + 0.372635i \(0.878454\pi\)
\(810\) 0.0211778 0.0235204i 0.000744113 0.000826421i
\(811\) −13.1099 4.25967i −0.460352 0.149577i 0.0696543 0.997571i \(-0.477810\pi\)
−0.530006 + 0.847994i \(0.677810\pi\)
\(812\) 14.9142 + 1.56755i 0.523387 + 0.0550102i
\(813\) −13.7595 + 7.94403i −0.482565 + 0.278609i
\(814\) −29.7995 + 53.5593i −1.04447 + 1.87725i
\(815\) −0.0467748 0.0810163i −0.00163845 0.00283788i
\(816\) 6.73258 2.99754i 0.235687 0.104935i
\(817\) 11.1760 10.0629i 0.390997 0.352055i
\(818\) −7.57264 23.3062i −0.264771 0.814882i
\(819\) 2.52127 6.84959i 0.0881004 0.239344i
\(820\) 0.291415 0.211725i 0.0101767 0.00739378i
\(821\) 9.43783 44.4015i 0.329383 1.54962i −0.432334 0.901713i \(-0.642310\pi\)
0.761717 0.647910i \(-0.224357\pi\)
\(822\) −23.6056 26.2167i −0.823340 0.914411i
\(823\) −0.642039 + 6.10859i −0.0223801 + 0.212932i 0.977617 + 0.210394i \(0.0674746\pi\)
−0.999997 + 0.00253824i \(0.999192\pi\)
\(824\) 25.6631i 0.894016i
\(825\) 4.87337 15.8502i 0.169669 0.551832i
\(826\) −24.1212 + 13.9264i −0.839282 + 0.484560i
\(827\) 7.89693 10.8692i 0.274603 0.377959i −0.649334 0.760503i \(-0.724952\pi\)
0.923937 + 0.382545i \(0.124952\pi\)
\(828\) 4.86227 1.03351i 0.168976 0.0359169i
\(829\) 50.4803 + 10.7299i 1.75325 + 0.372666i 0.968863 0.247599i \(-0.0796416\pi\)
0.784392 + 0.620265i \(0.212975\pi\)
\(830\) 0.0926883 0.00974194i 0.00321726 0.000338148i
\(831\) 22.6820 16.4795i 0.786831 0.571666i
\(832\) 45.5320 + 6.56791i 1.57854 + 0.227701i
\(833\) 4.26528 13.1272i 0.147783 0.454829i
\(834\) 0.980893 + 2.20312i 0.0339656 + 0.0762879i
\(835\) −0.137207 + 0.237649i −0.00474823 + 0.00822418i
\(836\) 33.1472 11.3548i 1.14642 0.392713i
\(837\) 7.58290i 0.262103i
\(838\) −33.3641 3.50670i −1.15254 0.121137i
\(839\) −5.11964 24.0860i −0.176750 0.831541i −0.973760 0.227576i \(-0.926920\pi\)
0.797011 0.603965i \(-0.206413\pi\)
\(840\) −0.0522546 + 0.0169786i −0.00180296 + 0.000585816i
\(841\) −20.3532 9.06182i −0.701833 0.312476i
\(842\) 8.27611 + 78.7419i 0.285214 + 2.71363i
\(843\) −5.18080 + 24.3738i −0.178436 + 0.839477i
\(844\) −20.1806 + 62.1096i −0.694646 + 2.13790i
\(845\) 0.186612 0.00515908i 0.00641964 0.000177478i
\(846\) −18.0311 −0.619922
\(847\) 12.5105 18.4213i 0.429865 0.632963i
\(848\) −4.87617 + 8.44577i −0.167448 + 0.290029i
\(849\) 0.897962 8.54354i 0.0308180 0.293214i
\(850\) 49.8462 + 16.1960i 1.70971 + 0.555519i
\(851\) 10.8394 + 9.75986i 0.371571 + 0.334564i
\(852\) 16.7487 37.6181i 0.573800 1.28877i
\(853\) −19.3182 26.5893i −0.661443 0.910399i 0.338085 0.941116i \(-0.390221\pi\)
−0.999528 + 0.0307170i \(0.990221\pi\)
\(854\) 7.63063 8.47467i 0.261115 0.289997i
\(855\) −0.0355240 0.0394534i −0.00121489 0.00134928i
\(856\) 1.01768 + 2.28574i 0.0347834 + 0.0781249i
\(857\) 32.9054 1.12403 0.562014 0.827128i \(-0.310027\pi\)
0.562014 + 0.827128i \(0.310027\pi\)
\(858\) −20.9656 15.9710i −0.715755 0.545240i
\(859\) −42.0869 −1.43599 −0.717994 0.696049i \(-0.754939\pi\)
−0.717994 + 0.696049i \(0.754939\pi\)
\(860\) 0.0678940 + 0.152492i 0.00231517 + 0.00519995i
\(861\) 11.8903 + 13.2056i 0.405222 + 0.450044i
\(862\) 52.4803 58.2853i 1.78749 1.98521i
\(863\) 30.8800 + 42.5027i 1.05117 + 1.44681i 0.887793 + 0.460243i \(0.152238\pi\)
0.163374 + 0.986564i \(0.447762\pi\)
\(864\) −2.92652 + 6.57308i −0.0995623 + 0.223621i
\(865\) 0.0101786 + 0.00916489i 0.000346084 + 0.000311616i
\(866\) 64.1982 + 20.8593i 2.18154 + 0.708827i
\(867\) 0.587650 5.59111i 0.0199576 0.189884i
\(868\) −21.9323 + 37.9879i −0.744432 + 1.28939i
\(869\) −32.9516 + 7.55248i −1.11781 + 0.256200i
\(870\) −0.0820497 −0.00278175
\(871\) −25.6966 0.990846i −0.870695 0.0335735i
\(872\) −4.56858 + 14.0606i −0.154712 + 0.476153i
\(873\) 2.65068 12.4705i 0.0897118 0.422061i
\(874\) −1.48161 14.0965i −0.0501161 0.476823i
\(875\) 0.265563 + 0.118236i 0.00897767 + 0.00399712i
\(876\) 29.7987 9.68220i 1.00681 0.327131i
\(877\) −2.02165 9.51110i −0.0682661 0.321167i 0.930743 0.365674i \(-0.119162\pi\)
−0.999009 + 0.0445073i \(0.985828\pi\)
\(878\) −4.37327 0.459649i −0.147591 0.0155124i
\(879\) 5.13169i 0.173088i
\(880\) −0.00117099 0.0737887i −3.94739e−5 0.00248742i
\(881\) 17.8482 30.9141i 0.601323 1.04152i −0.391298 0.920264i \(-0.627974\pi\)
0.992621 0.121258i \(-0.0386927\pi\)
\(882\) 2.60149 + 5.84304i 0.0875968 + 0.196746i
\(883\) −9.87443 + 30.3904i −0.332301 + 1.02272i 0.635735 + 0.771907i \(0.280697\pi\)
−0.968036 + 0.250810i \(0.919303\pi\)
\(884\) 30.3100 38.5058i 1.01943 1.29509i
\(885\) 0.0725258 0.0526931i 0.00243793 0.00177126i
\(886\) 32.6590 3.43260i 1.09720 0.115320i
\(887\) −7.89055 1.67719i −0.264939 0.0563145i 0.0735269 0.997293i \(-0.476575\pi\)
−0.338466 + 0.940979i \(0.609908\pi\)
\(888\) 15.5013 3.29491i 0.520191 0.110570i
\(889\) −7.03413 + 9.68164i −0.235917 + 0.324712i
\(890\) −0.307878 + 0.177754i −0.0103201 + 0.00595831i
\(891\) 2.65194 1.99179i 0.0888432 0.0667276i
\(892\) 31.4963i 1.05457i
\(893\) −3.16153 + 30.0799i −0.105797 + 1.00659i
\(894\) −24.1513 26.8227i −0.807740 0.897087i
\(895\) −0.00599815 + 0.0282191i −0.000200496 + 0.000943259i
\(896\) 22.4867 16.3376i 0.751228 0.545799i
\(897\) −4.81931 + 4.01413i −0.160912 + 0.134028i
\(898\) −13.6986 42.1600i −0.457129 1.40690i
\(899\) −14.6088 + 13.1538i −0.487232 + 0.438705i
\(900\) −13.0520 + 5.81113i −0.435067 + 0.193704i
\(901\) 14.9677 + 25.9249i 0.498648 + 0.863684i
\(902\) 58.1969 27.0254i 1.93774 0.899848i
\(903\) −7.13144 + 4.11734i −0.237320 + 0.137016i
\(904\) 29.4397 + 3.09424i 0.979149 + 0.102913i
\(905\) −0.171457 0.0557099i −0.00569944 0.00185186i
\(906\) 25.9595 28.8310i 0.862447 0.957845i
\(907\) −4.39931 41.8566i −0.146077 1.38983i −0.784494 0.620136i \(-0.787077\pi\)
0.638417 0.769690i \(-0.279589\pi\)
\(908\) −19.0159 + 1.99865i −0.631065 + 0.0663276i
\(909\) −2.20257 6.77883i −0.0730548 0.224840i
\(910\) 0.161074 0.165589i 0.00533957 0.00548922i
\(911\) −4.23328 3.07566i −0.140255 0.101901i 0.515445 0.856922i \(-0.327626\pi\)
−0.655700 + 0.755021i \(0.727626\pi\)
\(912\) 4.96097 + 2.86422i 0.164274 + 0.0948437i
\(913\) 9.72792 + 0.866624i 0.321947 + 0.0286811i
\(914\) −36.4680 63.1644i −1.20625 2.08929i
\(915\) −0.0215742 + 0.0296944i −0.000713222 + 0.000981666i
\(916\) −9.95031 46.8125i −0.328768 1.54673i
\(917\) −9.12091 8.21251i −0.301199 0.271201i
\(918\) 6.16158 + 8.48069i 0.203363 + 0.279904i
\(919\) 38.7989 + 17.2744i 1.27986 + 0.569829i 0.930202 0.367049i \(-0.119632\pi\)
0.349656 + 0.936878i \(0.386298\pi\)
\(920\) 0.0461825 + 0.00981640i 0.00152259 + 0.000323637i
\(921\) 7.67323 6.90901i 0.252841 0.227659i
\(922\) 4.93083 + 3.58246i 0.162388 + 0.117982i
\(923\) 3.43597 + 51.8432i 0.113096 + 1.70644i
\(924\) −19.0463 + 2.30795i −0.626578 + 0.0759261i
\(925\) −36.3058 20.9611i −1.19373 0.689198i
\(926\) −48.0154 + 21.3778i −1.57788 + 0.702519i
\(927\) 13.2813 2.82303i 0.436216 0.0927206i
\(928\) 17.7399 5.76405i 0.582341 0.189214i
\(929\) 1.73917 3.90623i 0.0570602 0.128159i −0.882765 0.469814i \(-0.844321\pi\)
0.939825 + 0.341655i \(0.110987\pi\)
\(930\) 0.0976155 0.219248i 0.00320094 0.00718943i
\(931\) 10.2037 3.31537i 0.334411 0.108657i
\(932\) 13.6835 2.90852i 0.448219 0.0952718i
\(933\) 22.2917 9.92490i 0.729797 0.324927i
\(934\) −76.0138 43.8866i −2.48725 1.43601i
\(935\) −0.197952 0.110137i −0.00647371 0.00360187i
\(936\) 0.450660 + 6.79973i 0.0147303 + 0.222256i
\(937\) 23.7614 + 17.2637i 0.776252 + 0.563980i 0.903852 0.427846i \(-0.140727\pi\)
−0.127600 + 0.991826i \(0.540727\pi\)
\(938\) −23.6480 + 21.2927i −0.772133 + 0.695232i
\(939\) −25.1702 5.35009i −0.821398 0.174593i
\(940\) −0.306690 0.136547i −0.0100031 0.00445368i
\(941\) −26.7019 36.7521i −0.870458 1.19808i −0.978973 0.203988i \(-0.934610\pi\)
0.108515 0.994095i \(-0.465390\pi\)
\(942\) −6.63591 5.97500i −0.216210 0.194676i
\(943\) −3.17481 14.9363i −0.103386 0.486392i
\(944\) −5.68564 + 7.82561i −0.185052 + 0.254702i
\(945\) 0.0145350 + 0.0251754i 0.000472825 + 0.000818957i
\(946\) 6.64297 + 28.9834i 0.215982 + 0.942331i
\(947\) −29.3591 16.9505i −0.954042 0.550816i −0.0597078 0.998216i \(-0.519017\pi\)
−0.894334 + 0.447400i \(0.852350\pi\)
\(948\) 23.5641 + 17.1203i 0.765325 + 0.556041i
\(949\) −27.5656 + 28.3382i −0.894818 + 0.919898i
\(950\) 12.5890 + 38.7451i 0.408443 + 1.25706i
\(951\) 2.10516 0.221261i 0.0682645 0.00717489i
\(952\) −1.90220 18.0982i −0.0616506 0.586567i
\(953\) −10.0697 + 11.1835i −0.326188 + 0.362269i −0.883826 0.467816i \(-0.845041\pi\)
0.557638 + 0.830084i \(0.311708\pi\)
\(954\) −13.1928 4.28660i −0.427133 0.138784i
\(955\) −0.130559 0.0137223i −0.00422479 0.000444043i
\(956\) −30.6380 + 17.6889i −0.990903 + 0.572098i
\(957\) −8.43753 1.65397i −0.272747 0.0534654i
\(958\) 17.6913 + 30.6423i 0.571581 + 0.990007i
\(959\) 29.6013 13.1793i 0.955875 0.425583i
\(960\) −0.136161 + 0.122600i −0.00439456 + 0.00395688i
\(961\) −8.18906 25.2033i −0.264163 0.813011i
\(962\) −51.1973 + 42.6435i −1.65067 + 1.37488i
\(963\) 1.07098 0.778113i 0.0345119 0.0250744i
\(964\) 0.703648 3.31040i 0.0226630 0.106621i
\(965\) −0.197209 0.219023i −0.00634838 0.00705059i
\(966\) −0.811276 + 7.71877i −0.0261024 + 0.248347i
\(967\) 3.68617i 0.118539i −0.998242 0.0592696i \(-0.981123\pi\)
0.998242 0.0592696i \(-0.0188772\pi\)
\(968\) −3.67512 + 20.4631i −0.118123 + 0.657708i
\(969\) 15.2281 8.79193i 0.489196 0.282437i
\(970\) 0.237174 0.326442i 0.00761520 0.0104814i
\(971\) 0.0104265 0.00221622i 0.000334602 7.11219e-5i −0.207744 0.978183i \(-0.566612\pi\)
0.208079 + 0.978112i \(0.433279\pi\)
\(972\) −2.79511 0.594119i −0.0896533 0.0190564i
\(973\) −2.20292 + 0.231536i −0.0706224 + 0.00742271i
\(974\) 1.86945 1.35824i 0.0599010 0.0435207i
\(975\) 11.1501 14.1651i 0.357088 0.453645i
\(976\) 1.22384 3.76659i 0.0391741 0.120566i
\(977\) −12.3877 27.8231i −0.396316 0.890141i −0.995954 0.0898688i \(-0.971355\pi\)
0.599637 0.800272i \(-0.295311\pi\)
\(978\) −7.17892 + 12.4343i −0.229557 + 0.397604i
\(979\) −35.2436 + 12.0729i −1.12639 + 0.385852i
\(980\) 0.119085i 0.00380403i
\(981\) 7.77931 + 0.817638i 0.248374 + 0.0261052i
\(982\) −6.65633 31.3156i −0.212412 0.999320i
\(983\) 36.9126 11.9936i 1.17733 0.382538i 0.345956 0.938251i \(-0.387555\pi\)
0.831374 + 0.555713i \(0.187555\pi\)
\(984\) −15.1565 6.74813i −0.483173 0.215122i
\(985\) −0.0200297 0.190569i −0.000638198 0.00607205i
\(986\) 5.65014 26.5818i 0.179937 0.846537i
\(987\) 5.11777 15.7509i 0.162900 0.501356i
\(988\) 38.0621 + 1.46766i 1.21092 + 0.0466924i
\(989\) 7.07623 0.225011
\(990\) 0.102317 0.0234510i 0.00325186 0.000745323i
\(991\) 4.78280 8.28405i 0.151931 0.263152i −0.780007 0.625771i \(-0.784784\pi\)
0.931937 + 0.362620i \(0.118118\pi\)
\(992\) −5.70306 + 54.2610i −0.181072 + 1.72279i
\(993\) −31.2926 10.1676i −0.993041 0.322659i
\(994\) 47.7792 + 43.0206i 1.51547 + 1.36453i
\(995\) −0.00886014 + 0.0199002i −0.000280885 + 0.000630879i
\(996\) −4.94600 6.80758i −0.156720 0.215706i
\(997\) 6.69030 7.43033i 0.211884 0.235321i −0.627829 0.778351i \(-0.716056\pi\)
0.839713 + 0.543030i \(0.182723\pi\)
\(998\) −50.2895 55.8521i −1.59189 1.76797i
\(999\) −3.41041 7.65990i −0.107900 0.242348i
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 429.2.bn.a.4.13 112
11.3 even 5 inner 429.2.bn.a.355.13 yes 112
13.10 even 6 inner 429.2.bn.a.400.13 yes 112
143.36 even 30 inner 429.2.bn.a.322.13 yes 112
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
429.2.bn.a.4.13 112 1.1 even 1 trivial
429.2.bn.a.322.13 yes 112 143.36 even 30 inner
429.2.bn.a.355.13 yes 112 11.3 even 5 inner
429.2.bn.a.400.13 yes 112 13.10 even 6 inner