Properties

Label 322.2.g.a.45.6
Level $322$
Weight $2$
Character 322.45
Analytic conductor $2.571$
Analytic rank $0$
Dimension $16$
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] = [322,2,Mod(45,322)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(322, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([1, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("322.45");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 322 = 2 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 322.g (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.57118294509\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} + 18x^{14} + 226x^{12} + 1434x^{10} + 6585x^{8} + 14406x^{6} + 22423x^{4} + 8085x^{2} + 2401 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 7 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 45.6
Root \(0.306090 + 0.530164i\) of defining polynomial
Character \(\chi\) \(=\) 322.45
Dual form 322.2.g.a.229.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{2} +(1.05590 + 0.609623i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.23610 + 2.14099i) q^{5} -1.21925i q^{6} +(-1.54219 + 2.14980i) q^{7} +1.00000 q^{8} +(-0.756718 - 1.31067i) q^{9} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{2} +(1.05590 + 0.609623i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.23610 + 2.14099i) q^{5} -1.21925i q^{6} +(-1.54219 + 2.14980i) q^{7} +1.00000 q^{8} +(-0.756718 - 1.31067i) q^{9} +(1.23610 - 2.14099i) q^{10} +(1.09791 + 0.633878i) q^{11} +(-1.05590 + 0.609623i) q^{12} +3.39445i q^{13} +(2.63288 + 0.260678i) q^{14} +3.01423i q^{15} +(-0.500000 - 0.866025i) q^{16} +(-2.14715 + 3.71897i) q^{17} +(-0.756718 + 1.31067i) q^{18} +(1.23610 + 2.14099i) q^{19} -2.47221 q^{20} +(-2.93897 + 1.32981i) q^{21} -1.26776i q^{22} +(-1.21471 - 4.63945i) q^{23} +(1.05590 + 0.609623i) q^{24} +(-0.555899 + 0.962845i) q^{25} +(2.93968 - 1.69722i) q^{26} -5.50299i q^{27} +(-1.09069 - 2.41048i) q^{28} +8.99116 q^{29} +(2.61040 - 1.50711i) q^{30} +(3.32605 + 1.92030i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(0.772854 + 1.33862i) q^{33} +4.29430 q^{34} +(-6.50901 - 0.644450i) q^{35} +1.51344 q^{36} +(1.24062 - 0.716272i) q^{37} +(1.23610 - 2.14099i) q^{38} +(-2.06934 + 3.58419i) q^{39} +(1.23610 + 2.14099i) q^{40} +3.39445i q^{41} +(2.62114 + 1.88031i) q^{42} -12.9877i q^{43} +(-1.09791 + 0.633878i) q^{44} +(1.87076 - 3.24026i) q^{45} +(-3.41053 + 3.37169i) q^{46} +(-1.43968 + 0.831199i) q^{47} -1.21925i q^{48} +(-2.24328 - 6.63081i) q^{49} +1.11180 q^{50} +(-4.53435 + 2.61791i) q^{51} +(-2.93968 - 1.69722i) q^{52} +(7.14474 + 4.12502i) q^{53} +(-4.76573 + 2.75150i) q^{54} +3.13415i q^{55} +(-1.54219 + 2.14980i) q^{56} +3.01423i q^{57} +(-4.49558 - 7.78657i) q^{58} +(8.43785 + 4.87160i) q^{59} +(-2.61040 - 1.50711i) q^{60} +(-4.61935 - 8.00096i) q^{61} -3.84060i q^{62} +(3.98469 + 0.394520i) q^{63} +1.00000 q^{64} +(-7.26749 + 4.19589i) q^{65} +(0.772854 - 1.33862i) q^{66} +(-9.87789 - 5.70300i) q^{67} +(-2.14715 - 3.71897i) q^{68} +(1.54571 - 5.63930i) q^{69} +(2.69640 + 5.95920i) q^{70} -10.1030 q^{71} +(-0.756718 - 1.31067i) q^{72} +(3.32605 + 1.92030i) q^{73} +(-1.24062 - 0.716272i) q^{74} +(-1.17395 + 0.677778i) q^{75} -2.47221 q^{76} +(-3.05590 + 1.38272i) q^{77} +4.13867 q^{78} +(6.44145 - 3.71897i) q^{79} +(1.23610 - 2.14099i) q^{80} +(1.08460 - 1.87858i) q^{81} +(2.93968 - 1.69722i) q^{82} -5.21176 q^{83} +(0.317831 - 3.21013i) q^{84} -10.6164 q^{85} +(-11.2477 + 6.49384i) q^{86} +(9.49375 + 5.48122i) q^{87} +(1.09791 + 0.633878i) q^{88} +(-3.43192 - 5.94426i) q^{89} -3.74153 q^{90} +(-7.29739 - 5.23489i) q^{91} +(4.62523 + 1.26776i) q^{92} +(2.34132 + 4.05528i) q^{93} +(1.43968 + 0.831199i) q^{94} +(-3.05590 + 5.29297i) q^{95} +(-1.05590 + 0.609623i) q^{96} -6.49915 q^{97} +(-4.62081 + 5.25815i) q^{98} -1.91867i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 8 q^{2} + 6 q^{3} - 8 q^{4} + 16 q^{8} + 10 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 8 q^{2} + 6 q^{3} - 8 q^{4} + 16 q^{8} + 10 q^{9} - 6 q^{12} - 8 q^{16} + 10 q^{18} - 4 q^{23} + 6 q^{24} + 2 q^{25} - 6 q^{26} + 16 q^{29} - 24 q^{31} - 8 q^{32} + 4 q^{35} - 20 q^{36} + 22 q^{39} - 4 q^{46} + 30 q^{47} - 58 q^{49} - 4 q^{50} + 6 q^{52} + 54 q^{54} - 8 q^{58} + 36 q^{59} + 16 q^{64} - 32 q^{70} - 12 q^{71} + 10 q^{72} - 24 q^{73} - 96 q^{75} - 38 q^{77} - 44 q^{78} - 36 q^{81} - 6 q^{82} + 24 q^{85} + 42 q^{87} + 8 q^{92} - 38 q^{93} - 30 q^{94} - 38 q^{95} - 6 q^{96} + 56 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/322\mathbb{Z}\right)^\times\).

\(n\) \(185\) \(281\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 0.866025i −0.353553 0.612372i
\(3\) 1.05590 + 0.609623i 0.609623 + 0.351966i 0.772818 0.634628i \(-0.218847\pi\)
−0.163195 + 0.986594i \(0.552180\pi\)
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) 1.23610 + 2.14099i 0.552802 + 0.957481i 0.998071 + 0.0620841i \(0.0197747\pi\)
−0.445269 + 0.895397i \(0.646892\pi\)
\(6\) 1.21925i 0.497755i
\(7\) −1.54219 + 2.14980i −0.582894 + 0.812548i
\(8\) 1.00000 0.353553
\(9\) −0.756718 1.31067i −0.252239 0.436892i
\(10\) 1.23610 2.14099i 0.390890 0.677041i
\(11\) 1.09791 + 0.633878i 0.331032 + 0.191121i 0.656299 0.754501i \(-0.272121\pi\)
−0.325267 + 0.945622i \(0.605454\pi\)
\(12\) −1.05590 + 0.609623i −0.304812 + 0.175983i
\(13\) 3.39445i 0.941451i 0.882280 + 0.470725i \(0.156008\pi\)
−0.882280 + 0.470725i \(0.843992\pi\)
\(14\) 2.63288 + 0.260678i 0.703666 + 0.0696692i
\(15\) 3.01423i 0.778270i
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −2.14715 + 3.71897i −0.520760 + 0.901983i 0.478948 + 0.877843i \(0.341018\pi\)
−0.999709 + 0.0241402i \(0.992315\pi\)
\(18\) −0.756718 + 1.31067i −0.178360 + 0.308929i
\(19\) 1.23610 + 2.14099i 0.283581 + 0.491177i 0.972264 0.233885i \(-0.0751441\pi\)
−0.688683 + 0.725063i \(0.741811\pi\)
\(20\) −2.47221 −0.552802
\(21\) −2.93897 + 1.32981i −0.641336 + 0.290189i
\(22\) 1.26776i 0.270287i
\(23\) −1.21471 4.63945i −0.253284 0.967392i
\(24\) 1.05590 + 0.609623i 0.215534 + 0.124439i
\(25\) −0.555899 + 0.962845i −0.111180 + 0.192569i
\(26\) 2.93968 1.69722i 0.576518 0.332853i
\(27\) 5.50299i 1.05905i
\(28\) −1.09069 2.41048i −0.206120 0.455538i
\(29\) 8.99116 1.66962 0.834808 0.550541i \(-0.185579\pi\)
0.834808 + 0.550541i \(0.185579\pi\)
\(30\) 2.61040 1.50711i 0.476591 0.275160i
\(31\) 3.32605 + 1.92030i 0.597377 + 0.344896i 0.768009 0.640439i \(-0.221248\pi\)
−0.170632 + 0.985335i \(0.554581\pi\)
\(32\) −0.500000 + 0.866025i −0.0883883 + 0.153093i
\(33\) 0.772854 + 1.33862i 0.134537 + 0.233024i
\(34\) 4.29430 0.736466
\(35\) −6.50901 0.644450i −1.10022 0.108932i
\(36\) 1.51344 0.252239
\(37\) 1.24062 0.716272i 0.203957 0.117754i −0.394543 0.918877i \(-0.629097\pi\)
0.598500 + 0.801123i \(0.295764\pi\)
\(38\) 1.23610 2.14099i 0.200522 0.347315i
\(39\) −2.06934 + 3.58419i −0.331359 + 0.573930i
\(40\) 1.23610 + 2.14099i 0.195445 + 0.338521i
\(41\) 3.39445i 0.530124i 0.964231 + 0.265062i \(0.0853924\pi\)
−0.964231 + 0.265062i \(0.914608\pi\)
\(42\) 2.62114 + 1.88031i 0.404450 + 0.290139i
\(43\) 12.9877i 1.98060i −0.138933 0.990302i \(-0.544367\pi\)
0.138933 0.990302i \(-0.455633\pi\)
\(44\) −1.09791 + 0.633878i −0.165516 + 0.0955607i
\(45\) 1.87076 3.24026i 0.278877 0.483029i
\(46\) −3.41053 + 3.37169i −0.502855 + 0.497129i
\(47\) −1.43968 + 0.831199i −0.209999 + 0.121243i −0.601311 0.799015i \(-0.705355\pi\)
0.391312 + 0.920258i \(0.372021\pi\)
\(48\) 1.21925i 0.175983i
\(49\) −2.24328 6.63081i −0.320469 0.947259i
\(50\) 1.11180 0.157232
\(51\) −4.53435 + 2.61791i −0.634935 + 0.366580i
\(52\) −2.93968 1.69722i −0.407660 0.235363i
\(53\) 7.14474 + 4.12502i 0.981406 + 0.566615i 0.902694 0.430282i \(-0.141586\pi\)
0.0787118 + 0.996897i \(0.474919\pi\)
\(54\) −4.76573 + 2.75150i −0.648534 + 0.374431i
\(55\) 3.13415i 0.422609i
\(56\) −1.54219 + 2.14980i −0.206084 + 0.287279i
\(57\) 3.01423i 0.399244i
\(58\) −4.49558 7.78657i −0.590298 1.02243i
\(59\) 8.43785 + 4.87160i 1.09851 + 0.634228i 0.935830 0.352450i \(-0.114651\pi\)
0.162684 + 0.986678i \(0.447985\pi\)
\(60\) −2.61040 1.50711i −0.337001 0.194568i
\(61\) −4.61935 8.00096i −0.591448 1.02442i −0.994038 0.109037i \(-0.965223\pi\)
0.402590 0.915380i \(-0.368110\pi\)
\(62\) 3.84060i 0.487756i
\(63\) 3.98469 + 0.394520i 0.502024 + 0.0497048i
\(64\) 1.00000 0.125000
\(65\) −7.26749 + 4.19589i −0.901421 + 0.520436i
\(66\) 0.772854 1.33862i 0.0951317 0.164773i
\(67\) −9.87789 5.70300i −1.20678 0.696732i −0.244722 0.969593i \(-0.578697\pi\)
−0.962054 + 0.272861i \(0.912030\pi\)
\(68\) −2.14715 3.71897i −0.260380 0.450992i
\(69\) 1.54571 5.63930i 0.186081 0.678892i
\(70\) 2.69640 + 5.95920i 0.322281 + 0.712260i
\(71\) −10.1030 −1.19900 −0.599500 0.800375i \(-0.704634\pi\)
−0.599500 + 0.800375i \(0.704634\pi\)
\(72\) −0.756718 1.31067i −0.0891801 0.154464i
\(73\) 3.32605 + 1.92030i 0.389285 + 0.224754i 0.681850 0.731492i \(-0.261176\pi\)
−0.292565 + 0.956246i \(0.594509\pi\)
\(74\) −1.24062 0.716272i −0.144219 0.0832649i
\(75\) −1.17395 + 0.677778i −0.135556 + 0.0782631i
\(76\) −2.47221 −0.283581
\(77\) −3.05590 + 1.38272i −0.348252 + 0.157576i
\(78\) 4.13867 0.468612
\(79\) 6.44145 3.71897i 0.724720 0.418417i −0.0917676 0.995780i \(-0.529252\pi\)
0.816487 + 0.577363i \(0.195918\pi\)
\(80\) 1.23610 2.14099i 0.138200 0.239370i
\(81\) 1.08460 1.87858i 0.120511 0.208731i
\(82\) 2.93968 1.69722i 0.324633 0.187427i
\(83\) −5.21176 −0.572065 −0.286033 0.958220i \(-0.592337\pi\)
−0.286033 + 0.958220i \(0.592337\pi\)
\(84\) 0.317831 3.21013i 0.0346782 0.350254i
\(85\) −10.6164 −1.15151
\(86\) −11.2477 + 6.49384i −1.21287 + 0.700249i
\(87\) 9.49375 + 5.48122i 1.01784 + 0.587648i
\(88\) 1.09791 + 0.633878i 0.117037 + 0.0675716i
\(89\) −3.43192 5.94426i −0.363783 0.630090i 0.624797 0.780787i \(-0.285182\pi\)
−0.988580 + 0.150697i \(0.951848\pi\)
\(90\) −3.74153 −0.394391
\(91\) −7.29739 5.23489i −0.764974 0.548766i
\(92\) 4.62523 + 1.26776i 0.482214 + 0.132173i
\(93\) 2.34132 + 4.05528i 0.242783 + 0.420513i
\(94\) 1.43968 + 0.831199i 0.148492 + 0.0857316i
\(95\) −3.05590 + 5.29297i −0.313529 + 0.543047i
\(96\) −1.05590 + 0.609623i −0.107767 + 0.0622194i
\(97\) −6.49915 −0.659889 −0.329944 0.944000i \(-0.607030\pi\)
−0.329944 + 0.944000i \(0.607030\pi\)
\(98\) −4.62081 + 5.25815i −0.466773 + 0.531153i
\(99\) 1.91867i 0.192833i
\(100\) −0.555899 0.962845i −0.0555899 0.0962845i
\(101\) 6.16770 + 3.56092i 0.613709 + 0.354325i 0.774416 0.632677i \(-0.218044\pi\)
−0.160707 + 0.987002i \(0.551377\pi\)
\(102\) 4.53435 + 2.61791i 0.448967 + 0.259211i
\(103\) −6.95337 12.0436i −0.685136 1.18669i −0.973394 0.229137i \(-0.926410\pi\)
0.288259 0.957553i \(-0.406924\pi\)
\(104\) 3.39445i 0.332853i
\(105\) −6.47999 4.64852i −0.632382 0.453649i
\(106\) 8.25004i 0.801315i
\(107\) −5.07809 + 2.93183i −0.490917 + 0.283431i −0.724955 0.688796i \(-0.758139\pi\)
0.234038 + 0.972228i \(0.424806\pi\)
\(108\) 4.76573 + 2.75150i 0.458583 + 0.264763i
\(109\) 12.3456 + 7.12772i 1.18249 + 0.682712i 0.956590 0.291438i \(-0.0941338\pi\)
0.225902 + 0.974150i \(0.427467\pi\)
\(110\) 2.71426 1.56708i 0.258794 0.149415i
\(111\) 1.74662 0.165782
\(112\) 2.63288 + 0.260678i 0.248784 + 0.0246318i
\(113\) 15.6954i 1.47650i 0.674528 + 0.738249i \(0.264347\pi\)
−0.674528 + 0.738249i \(0.735653\pi\)
\(114\) 2.61040 1.50711i 0.244486 0.141154i
\(115\) 8.43152 8.33552i 0.786243 0.777291i
\(116\) −4.49558 + 7.78657i −0.417404 + 0.722965i
\(117\) 4.44902 2.56864i 0.411312 0.237471i
\(118\) 9.74319i 0.896934i
\(119\) −4.68373 10.3513i −0.429357 0.948904i
\(120\) 3.01423i 0.275160i
\(121\) −4.69640 8.13440i −0.426945 0.739491i
\(122\) −4.61935 + 8.00096i −0.418217 + 0.724373i
\(123\) −2.06934 + 3.58419i −0.186586 + 0.323176i
\(124\) −3.32605 + 1.92030i −0.298688 + 0.172448i
\(125\) 9.61243 0.859762
\(126\) −1.65068 3.64811i −0.147055 0.324999i
\(127\) 1.99116 0.176686 0.0883432 0.996090i \(-0.471843\pi\)
0.0883432 + 0.996090i \(0.471843\pi\)
\(128\) −0.500000 0.866025i −0.0441942 0.0765466i
\(129\) 7.91760 13.7137i 0.697106 1.20742i
\(130\) 7.26749 + 4.19589i 0.637401 + 0.368004i
\(131\) 9.81980 5.66947i 0.857960 0.495344i −0.00536840 0.999986i \(-0.501709\pi\)
0.863329 + 0.504642i \(0.168375\pi\)
\(132\) −1.54571 −0.134537
\(133\) −6.50901 0.644450i −0.564403 0.0558809i
\(134\) 11.4060i 0.985328i
\(135\) 11.7819 6.80226i 1.01402 0.585446i
\(136\) −2.14715 + 3.71897i −0.184117 + 0.318899i
\(137\) 1.36978 + 0.790842i 0.117028 + 0.0675662i 0.557371 0.830263i \(-0.311810\pi\)
−0.440343 + 0.897829i \(0.645143\pi\)
\(138\) −5.65663 + 1.48103i −0.481525 + 0.126074i
\(139\) 14.1603i 1.20106i −0.799603 0.600528i \(-0.794957\pi\)
0.799603 0.600528i \(-0.205043\pi\)
\(140\) 3.81262 5.31475i 0.322225 0.449178i
\(141\) −2.02687 −0.170694
\(142\) 5.05148 + 8.74941i 0.423910 + 0.734235i
\(143\) −2.15167 + 3.72680i −0.179931 + 0.311650i
\(144\) −0.756718 + 1.31067i −0.0630599 + 0.109223i
\(145\) 11.1140 + 19.2500i 0.922967 + 1.59863i
\(146\) 3.84060i 0.317850i
\(147\) 1.67362 8.36903i 0.138038 0.690266i
\(148\) 1.43254i 0.117754i
\(149\) 2.19582 1.26776i 0.179888 0.103859i −0.407352 0.913271i \(-0.633548\pi\)
0.587240 + 0.809413i \(0.300214\pi\)
\(150\) 1.17395 + 0.677778i 0.0958523 + 0.0553403i
\(151\) −4.01344 + 6.95148i −0.326609 + 0.565703i −0.981837 0.189728i \(-0.939239\pi\)
0.655228 + 0.755431i \(0.272573\pi\)
\(152\) 1.23610 + 2.14099i 0.100261 + 0.173657i
\(153\) 6.49915 0.525425
\(154\) 2.72542 + 1.95512i 0.219621 + 0.157548i
\(155\) 9.49474i 0.762636i
\(156\) −2.06934 3.58419i −0.165679 0.286965i
\(157\) −9.60150 + 16.6303i −0.766283 + 1.32724i 0.173282 + 0.984872i \(0.444563\pi\)
−0.939566 + 0.342369i \(0.888771\pi\)
\(158\) −6.44145 3.71897i −0.512454 0.295866i
\(159\) 5.02942 + 8.71121i 0.398859 + 0.690844i
\(160\) −2.47221 −0.195445
\(161\) 11.8472 + 4.54355i 0.933690 + 0.358082i
\(162\) −2.16920 −0.170428
\(163\) 1.24328 + 2.15343i 0.0973813 + 0.168669i 0.910600 0.413289i \(-0.135620\pi\)
−0.813219 + 0.581958i \(0.802287\pi\)
\(164\) −2.93968 1.69722i −0.229550 0.132531i
\(165\) −1.91065 + 3.30935i −0.148744 + 0.257632i
\(166\) 2.60588 + 4.51352i 0.202256 + 0.350317i
\(167\) 8.20178i 0.634673i 0.948313 + 0.317337i \(0.102788\pi\)
−0.948313 + 0.317337i \(0.897212\pi\)
\(168\) −2.93897 + 1.32981i −0.226746 + 0.102597i
\(169\) 1.47772 0.113671
\(170\) 5.30819 + 9.19406i 0.407120 + 0.705152i
\(171\) 1.87076 3.24026i 0.143061 0.247789i
\(172\) 11.2477 + 6.49384i 0.857627 + 0.495151i
\(173\) 15.2173 8.78574i 1.15695 0.667967i 0.206381 0.978472i \(-0.433831\pi\)
0.950572 + 0.310504i \(0.100498\pi\)
\(174\) 10.9624i 0.831060i
\(175\) −1.21262 2.67996i −0.0916655 0.202586i
\(176\) 1.26776i 0.0955607i
\(177\) 5.93968 + 10.2878i 0.446454 + 0.773280i
\(178\) −3.43192 + 5.94426i −0.257233 + 0.445541i
\(179\) −3.25672 + 5.64080i −0.243419 + 0.421613i −0.961686 0.274154i \(-0.911602\pi\)
0.718267 + 0.695767i \(0.244936\pi\)
\(180\) 1.87076 + 3.24026i 0.139438 + 0.241514i
\(181\) 10.2407 0.761184 0.380592 0.924743i \(-0.375720\pi\)
0.380592 + 0.924743i \(0.375720\pi\)
\(182\) −0.884859 + 8.93717i −0.0655901 + 0.662467i
\(183\) 11.2643i 0.832679i
\(184\) −1.21471 4.63945i −0.0895495 0.342025i
\(185\) 3.06707 + 1.77077i 0.225495 + 0.130190i
\(186\) 2.34132 4.05528i 0.171674 0.297348i
\(187\) −4.71475 + 2.72206i −0.344777 + 0.199057i
\(188\) 1.66240i 0.121243i
\(189\) 11.8303 + 8.48668i 0.860530 + 0.617315i
\(190\) 6.11180 0.443396
\(191\) 8.51452 4.91586i 0.616089 0.355699i −0.159256 0.987237i \(-0.550909\pi\)
0.775345 + 0.631538i \(0.217576\pi\)
\(192\) 1.05590 + 0.609623i 0.0762029 + 0.0439958i
\(193\) 3.94227 6.82822i 0.283771 0.491506i −0.688539 0.725199i \(-0.741748\pi\)
0.972310 + 0.233693i \(0.0750811\pi\)
\(194\) 3.24958 + 5.62843i 0.233306 + 0.404098i
\(195\) −10.2316 −0.732703
\(196\) 6.86409 + 1.37267i 0.490292 + 0.0980477i
\(197\) −5.96063 −0.424677 −0.212339 0.977196i \(-0.568108\pi\)
−0.212339 + 0.977196i \(0.568108\pi\)
\(198\) −1.66162 + 0.959334i −0.118086 + 0.0681769i
\(199\) 11.6259 20.1367i 0.824139 1.42745i −0.0784372 0.996919i \(-0.524993\pi\)
0.902576 0.430531i \(-0.141674\pi\)
\(200\) −0.555899 + 0.962845i −0.0393080 + 0.0680834i
\(201\) −6.95337 12.0436i −0.490453 0.849489i
\(202\) 7.12184i 0.501091i
\(203\) −13.8661 + 19.3292i −0.973209 + 1.35664i
\(204\) 5.23581i 0.366580i
\(205\) −7.26749 + 4.19589i −0.507583 + 0.293053i
\(206\) −6.95337 + 12.0436i −0.484464 + 0.839116i
\(207\) −5.16162 + 5.10284i −0.358757 + 0.354672i
\(208\) 2.93968 1.69722i 0.203830 0.117681i
\(209\) 3.13415i 0.216794i
\(210\) −0.785744 + 7.93610i −0.0542215 + 0.547643i
\(211\) −7.62889 −0.525194 −0.262597 0.964906i \(-0.584579\pi\)
−0.262597 + 0.964906i \(0.584579\pi\)
\(212\) −7.14474 + 4.12502i −0.490703 + 0.283308i
\(213\) −10.6677 6.15900i −0.730939 0.422008i
\(214\) 5.07809 + 2.93183i 0.347131 + 0.200416i
\(215\) 27.8065 16.0541i 1.89639 1.09488i
\(216\) 5.50299i 0.374431i
\(217\) −9.25767 + 4.18888i −0.628452 + 0.284360i
\(218\) 14.2554i 0.965500i
\(219\) 2.34132 + 4.05528i 0.158212 + 0.274031i
\(220\) −2.71426 1.56708i −0.182995 0.105652i
\(221\) −12.6239 7.28839i −0.849173 0.490270i
\(222\) −0.873312 1.51262i −0.0586129 0.101520i
\(223\) 8.38464i 0.561477i −0.959784 0.280738i \(-0.909421\pi\)
0.959784 0.280738i \(-0.0905794\pi\)
\(224\) −1.09069 2.41048i −0.0728745 0.161057i
\(225\) 1.68264 0.112176
\(226\) 13.5926 7.84770i 0.904167 0.522021i
\(227\) 6.49463 11.2490i 0.431064 0.746625i −0.565901 0.824473i \(-0.691472\pi\)
0.996965 + 0.0778483i \(0.0248050\pi\)
\(228\) −2.61040 1.50711i −0.172878 0.0998111i
\(229\) −1.55022 2.68507i −0.102442 0.177434i 0.810248 0.586087i \(-0.199332\pi\)
−0.912690 + 0.408652i \(0.865999\pi\)
\(230\) −11.4345 3.13415i −0.753970 0.206660i
\(231\) −4.06966 0.402932i −0.267764 0.0265110i
\(232\) 8.99116 0.590298
\(233\) 12.4182 + 21.5089i 0.813541 + 1.40909i 0.910371 + 0.413794i \(0.135796\pi\)
−0.0968297 + 0.995301i \(0.530870\pi\)
\(234\) −4.44902 2.56864i −0.290841 0.167917i
\(235\) −3.55918 2.05489i −0.232175 0.134047i
\(236\) −8.43785 + 4.87160i −0.549257 + 0.317114i
\(237\) 9.06869 0.589075
\(238\) −6.62264 + 9.23189i −0.429282 + 0.598414i
\(239\) −24.6701 −1.59578 −0.797889 0.602804i \(-0.794050\pi\)
−0.797889 + 0.602804i \(0.794050\pi\)
\(240\) 2.61040 1.50711i 0.168500 0.0972838i
\(241\) −10.0757 + 17.4516i −0.649032 + 1.12416i 0.334323 + 0.942459i \(0.391492\pi\)
−0.983355 + 0.181697i \(0.941841\pi\)
\(242\) −4.69640 + 8.13440i −0.301896 + 0.522899i
\(243\) −12.0067 + 6.93210i −0.770233 + 0.444694i
\(244\) 9.23871 0.591448
\(245\) 11.4236 12.9992i 0.729827 0.830489i
\(246\) 4.13867 0.263872
\(247\) −7.26749 + 4.19589i −0.462419 + 0.266978i
\(248\) 3.32605 + 1.92030i 0.211205 + 0.121939i
\(249\) −5.50310 3.17721i −0.348744 0.201348i
\(250\) −4.80622 8.32461i −0.303972 0.526495i
\(251\) −29.3772 −1.85427 −0.927137 0.374721i \(-0.877738\pi\)
−0.927137 + 0.374721i \(0.877738\pi\)
\(252\) −2.33401 + 3.25359i −0.147029 + 0.204957i
\(253\) 1.60721 5.86367i 0.101044 0.368646i
\(254\) −0.995578 1.72439i −0.0624681 0.108198i
\(255\) −11.2098 6.47200i −0.701987 0.405292i
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 3.93918 2.27429i 0.245720 0.141866i −0.372083 0.928199i \(-0.621356\pi\)
0.617803 + 0.786333i \(0.288023\pi\)
\(258\) −15.8352 −0.985856
\(259\) −0.373433 + 3.77171i −0.0232040 + 0.234363i
\(260\) 8.39177i 0.520436i
\(261\) −6.80377 11.7845i −0.421143 0.729441i
\(262\) −9.81980 5.66947i −0.606670 0.350261i
\(263\) −4.94893 2.85726i −0.305164 0.176186i 0.339596 0.940571i \(-0.389710\pi\)
−0.644760 + 0.764385i \(0.723043\pi\)
\(264\) 0.772854 + 1.33862i 0.0475659 + 0.0823865i
\(265\) 20.3958i 1.25290i
\(266\) 2.69640 + 5.95920i 0.165327 + 0.365382i
\(267\) 8.36872i 0.512157i
\(268\) 9.87789 5.70300i 0.603388 0.348366i
\(269\) −7.17395 4.14188i −0.437403 0.252535i 0.265092 0.964223i \(-0.414598\pi\)
−0.702496 + 0.711688i \(0.747931\pi\)
\(270\) −11.7819 6.80226i −0.717022 0.413973i
\(271\) 0.343470 0.198302i 0.0208643 0.0120460i −0.489532 0.871986i \(-0.662832\pi\)
0.510396 + 0.859940i \(0.329499\pi\)
\(272\) 4.29430 0.260380
\(273\) −4.51399 9.97618i −0.273199 0.603786i
\(274\) 1.58168i 0.0955531i
\(275\) −1.22065 + 0.704744i −0.0736081 + 0.0424977i
\(276\) 4.11093 + 4.15827i 0.247449 + 0.250299i
\(277\) 8.75948 15.1719i 0.526306 0.911589i −0.473224 0.880942i \(-0.656910\pi\)
0.999530 0.0306472i \(-0.00975682\pi\)
\(278\) −12.2631 + 7.08013i −0.735494 + 0.424638i
\(279\) 5.81250i 0.347985i
\(280\) −6.50901 0.644450i −0.388988 0.0385133i
\(281\) 20.4451i 1.21965i 0.792536 + 0.609826i \(0.208761\pi\)
−0.792536 + 0.609826i \(0.791239\pi\)
\(282\) 1.01344 + 1.75532i 0.0603493 + 0.104528i
\(283\) −7.00655 + 12.1357i −0.416496 + 0.721393i −0.995584 0.0938724i \(-0.970075\pi\)
0.579088 + 0.815265i \(0.303409\pi\)
\(284\) 5.05148 8.74941i 0.299750 0.519182i
\(285\) −6.45344 + 3.72590i −0.382269 + 0.220703i
\(286\) 4.30333 0.254461
\(287\) −7.29739 5.23489i −0.430751 0.309006i
\(288\) 1.51344 0.0891801
\(289\) −0.720506 1.24795i −0.0423827 0.0734090i
\(290\) 11.1140 19.2500i 0.652636 1.13040i
\(291\) −6.86245 3.96204i −0.402284 0.232259i
\(292\) −3.32605 + 1.92030i −0.194643 + 0.112377i
\(293\) 4.28527 0.250348 0.125174 0.992135i \(-0.460051\pi\)
0.125174 + 0.992135i \(0.460051\pi\)
\(294\) −8.08460 + 2.73511i −0.471503 + 0.159515i
\(295\) 24.0872i 1.40241i
\(296\) 1.24062 0.716272i 0.0721095 0.0416325i
\(297\) 3.48823 6.04179i 0.202407 0.350580i
\(298\) −2.19582 1.26776i −0.127200 0.0734391i
\(299\) 15.7484 4.12326i 0.910752 0.238455i
\(300\) 1.35556i 0.0782631i
\(301\) 27.9209 + 20.0295i 1.60934 + 1.15448i
\(302\) 8.02687 0.461895
\(303\) 4.34164 + 7.51995i 0.249421 + 0.432010i
\(304\) 1.23610 2.14099i 0.0708953 0.122794i
\(305\) 11.4200 19.7800i 0.653907 1.13260i
\(306\) −3.24958 5.62843i −0.185766 0.321756i
\(307\) 29.9300i 1.70820i 0.520111 + 0.854098i \(0.325890\pi\)
−0.520111 + 0.854098i \(0.674110\pi\)
\(308\) 0.330476 3.33785i 0.0188306 0.190192i
\(309\) 16.9557i 0.964578i
\(310\) 8.22269 4.74737i 0.467017 0.269633i
\(311\) 4.83673 + 2.79248i 0.274266 + 0.158347i 0.630825 0.775926i \(-0.282717\pi\)
−0.356559 + 0.934273i \(0.616050\pi\)
\(312\) −2.06934 + 3.58419i −0.117153 + 0.202915i
\(313\) −4.42798 7.66948i −0.250284 0.433505i 0.713320 0.700839i \(-0.247191\pi\)
−0.963604 + 0.267334i \(0.913857\pi\)
\(314\) 19.2030 1.08369
\(315\) 4.08083 + 9.01887i 0.229929 + 0.508156i
\(316\) 7.43795i 0.418417i
\(317\) −9.52428 16.4965i −0.534937 0.926538i −0.999166 0.0408228i \(-0.987002\pi\)
0.464230 0.885715i \(-0.346331\pi\)
\(318\) 5.02942 8.71121i 0.282036 0.488500i
\(319\) 9.87147 + 5.69930i 0.552696 + 0.319099i
\(320\) 1.23610 + 2.14099i 0.0691002 + 0.119685i
\(321\) −7.14926 −0.399033
\(322\) −1.98878 12.5318i −0.110830 0.698367i
\(323\) −10.6164 −0.590712
\(324\) 1.08460 + 1.87858i 0.0602555 + 0.104366i
\(325\) −3.26833 1.88697i −0.181294 0.104670i
\(326\) 1.24328 2.15343i 0.0688590 0.119267i
\(327\) 8.69045 + 15.0523i 0.480583 + 0.832394i
\(328\) 3.39445i 0.187427i
\(329\) 0.433351 4.37689i 0.0238914 0.241306i
\(330\) 3.82131 0.210356
\(331\) −1.30101 2.25341i −0.0715098 0.123859i 0.828053 0.560649i \(-0.189448\pi\)
−0.899563 + 0.436791i \(0.856115\pi\)
\(332\) 2.60588 4.51352i 0.143016 0.247712i
\(333\) −1.87760 1.08403i −0.102892 0.0594046i
\(334\) 7.10295 4.10089i 0.388656 0.224391i
\(335\) 28.1980i 1.54062i
\(336\) 2.62114 + 1.88031i 0.142995 + 0.102580i
\(337\) 5.37754i 0.292934i −0.989216 0.146467i \(-0.953210\pi\)
0.989216 0.146467i \(-0.0467901\pi\)
\(338\) −0.738859 1.27974i −0.0401886 0.0696088i
\(339\) −9.56828 + 16.5728i −0.519678 + 0.900108i
\(340\) 5.30819 9.19406i 0.287877 0.498618i
\(341\) 2.43447 + 4.21663i 0.131834 + 0.228343i
\(342\) −3.74153 −0.202319
\(343\) 17.7145 + 5.40339i 0.956493 + 0.291755i
\(344\) 12.9877i 0.700249i
\(345\) 13.9844 3.66141i 0.752893 0.197124i
\(346\) −15.2173 8.78574i −0.818090 0.472324i
\(347\) −6.84623 + 11.8580i −0.367525 + 0.636572i −0.989178 0.146721i \(-0.953128\pi\)
0.621653 + 0.783293i \(0.286461\pi\)
\(348\) −9.49375 + 5.48122i −0.508918 + 0.293824i
\(349\) 23.2774i 1.24601i 0.782217 + 0.623006i \(0.214089\pi\)
−0.782217 + 0.623006i \(0.785911\pi\)
\(350\) −1.71461 + 2.39014i −0.0916496 + 0.127759i
\(351\) 18.6796 0.997045
\(352\) −1.09791 + 0.633878i −0.0585187 + 0.0337858i
\(353\) −27.4228 15.8325i −1.45957 0.842681i −0.460576 0.887620i \(-0.652357\pi\)
−0.998990 + 0.0449392i \(0.985691\pi\)
\(354\) 5.93968 10.2878i 0.315690 0.546792i
\(355\) −12.4883 21.6303i −0.662809 1.14802i
\(356\) 6.86384 0.363783
\(357\) 1.36486 13.7853i 0.0722362 0.729593i
\(358\) 6.51344 0.344246
\(359\) 30.4661 17.5896i 1.60794 0.928345i 0.618110 0.786092i \(-0.287899\pi\)
0.989830 0.142253i \(-0.0454346\pi\)
\(360\) 1.87076 3.24026i 0.0985979 0.170777i
\(361\) 6.44410 11.1615i 0.339163 0.587448i
\(362\) −5.12034 8.86869i −0.269119 0.466128i
\(363\) 11.4521i 0.601081i
\(364\) 8.18225 3.70227i 0.428866 0.194052i
\(365\) 9.49474i 0.496977i
\(366\) −9.75514 + 5.63213i −0.509910 + 0.294396i
\(367\) −6.62379 + 11.4727i −0.345759 + 0.598873i −0.985491 0.169725i \(-0.945712\pi\)
0.639732 + 0.768598i \(0.279045\pi\)
\(368\) −3.41053 + 3.37169i −0.177786 + 0.175762i
\(369\) 4.44902 2.56864i 0.231607 0.133718i
\(370\) 3.54154i 0.184116i
\(371\) −19.8865 + 8.99820i −1.03246 + 0.467163i
\(372\) −4.68264 −0.242783
\(373\) −31.6868 + 18.2944i −1.64068 + 0.947246i −0.660086 + 0.751190i \(0.729480\pi\)
−0.980593 + 0.196056i \(0.937186\pi\)
\(374\) 4.71475 + 2.72206i 0.243794 + 0.140755i
\(375\) 10.1498 + 5.85997i 0.524131 + 0.302607i
\(376\) −1.43968 + 0.831199i −0.0742458 + 0.0428658i
\(377\) 30.5200i 1.57186i
\(378\) 1.43451 14.4887i 0.0737833 0.745219i
\(379\) 1.29081i 0.0663045i −0.999450 0.0331523i \(-0.989445\pi\)
0.999450 0.0331523i \(-0.0105546\pi\)
\(380\) −3.05590 5.29297i −0.156764 0.271524i
\(381\) 2.10246 + 1.21386i 0.107712 + 0.0621877i
\(382\) −8.51452 4.91586i −0.435641 0.251517i
\(383\) 2.42354 + 4.19769i 0.123837 + 0.214492i 0.921278 0.388905i \(-0.127147\pi\)
−0.797441 + 0.603397i \(0.793813\pi\)
\(384\) 1.21925i 0.0622194i
\(385\) −6.73780 4.83347i −0.343390 0.246336i
\(386\) −7.88455 −0.401313
\(387\) −17.0226 + 9.82802i −0.865309 + 0.499586i
\(388\) 3.24958 5.62843i 0.164972 0.285740i
\(389\) −12.3624 7.13745i −0.626800 0.361883i 0.152712 0.988271i \(-0.451199\pi\)
−0.779512 + 0.626388i \(0.784533\pi\)
\(390\) 5.11582 + 8.86086i 0.259050 + 0.448687i
\(391\) 19.8621 + 5.44413i 1.00447 + 0.275321i
\(392\) −2.24328 6.63081i −0.113303 0.334907i
\(393\) 13.8250 0.697377
\(394\) 2.98031 + 5.16206i 0.150146 + 0.260061i
\(395\) 15.9246 + 9.19406i 0.801253 + 0.462604i
\(396\) 1.66162 + 0.959334i 0.0834993 + 0.0482084i
\(397\) −27.4857 + 15.8689i −1.37947 + 0.796435i −0.992095 0.125488i \(-0.959950\pi\)
−0.387371 + 0.921924i \(0.626617\pi\)
\(398\) −23.2518 −1.16551
\(399\) −6.47999 4.64852i −0.324405 0.232717i
\(400\) 1.11180 0.0555899
\(401\) −3.68834 + 2.12946i −0.184187 + 0.106340i −0.589258 0.807945i \(-0.700580\pi\)
0.405071 + 0.914285i \(0.367247\pi\)
\(402\) −6.95337 + 12.0436i −0.346802 + 0.600679i
\(403\) −6.51835 + 11.2901i −0.324702 + 0.562401i
\(404\) −6.16770 + 3.56092i −0.306854 + 0.177162i
\(405\) 5.36270 0.266475
\(406\) 23.6726 + 2.34380i 1.17485 + 0.116321i
\(407\) 1.81612 0.0900215
\(408\) −4.53435 + 2.61791i −0.224484 + 0.129606i
\(409\) −6.42276 3.70818i −0.317585 0.183358i 0.332731 0.943022i \(-0.392030\pi\)
−0.650316 + 0.759664i \(0.725363\pi\)
\(410\) 7.26749 + 4.19589i 0.358916 + 0.207220i
\(411\) 0.964232 + 1.67010i 0.0475621 + 0.0823799i
\(412\) 13.9067 0.685136
\(413\) −23.4858 + 10.6268i −1.15566 + 0.522908i
\(414\) 7.00000 + 1.91867i 0.344031 + 0.0942974i
\(415\) −6.44227 11.1583i −0.316239 0.547742i
\(416\) −2.93968 1.69722i −0.144130 0.0832133i
\(417\) 8.63242 14.9518i 0.422732 0.732192i
\(418\) 2.71426 1.56708i 0.132759 0.0766482i
\(419\) 33.1406 1.61903 0.809513 0.587102i \(-0.199731\pi\)
0.809513 + 0.587102i \(0.199731\pi\)
\(420\) 7.26573 3.28757i 0.354531 0.160417i
\(421\) 28.6831i 1.39793i −0.715157 0.698964i \(-0.753645\pi\)
0.715157 0.698964i \(-0.246355\pi\)
\(422\) 3.81444 + 6.60681i 0.185684 + 0.321615i
\(423\) 2.17886 + 1.25797i 0.105940 + 0.0611644i
\(424\) 7.14474 + 4.12502i 0.346979 + 0.200329i
\(425\) −2.38720 4.13475i −0.115796 0.200565i
\(426\) 12.3180i 0.596809i
\(427\) 24.3244 + 2.40833i 1.17714 + 0.116547i
\(428\) 5.86367i 0.283431i
\(429\) −4.54388 + 2.62341i −0.219381 + 0.126660i
\(430\) −27.8065 16.0541i −1.34095 0.774198i
\(431\) 21.2811 + 12.2866i 1.02507 + 0.591827i 0.915570 0.402159i \(-0.131740\pi\)
0.109505 + 0.993986i \(0.465074\pi\)
\(432\) −4.76573 + 2.75150i −0.229291 + 0.132381i
\(433\) −24.3265 −1.16906 −0.584528 0.811374i \(-0.698720\pi\)
−0.584528 + 0.811374i \(0.698720\pi\)
\(434\) 8.25651 + 5.92294i 0.396325 + 0.284310i
\(435\) 27.1014i 1.29941i
\(436\) −12.3456 + 7.12772i −0.591246 + 0.341356i
\(437\) 8.43152 8.33552i 0.403334 0.398742i
\(438\) 2.34132 4.05528i 0.111872 0.193769i
\(439\) 3.93526 2.27202i 0.187820 0.108438i −0.403142 0.915138i \(-0.632082\pi\)
0.590961 + 0.806700i \(0.298749\pi\)
\(440\) 3.13415i 0.149415i
\(441\) −6.99331 + 7.95787i −0.333015 + 0.378946i
\(442\) 14.5768i 0.693347i
\(443\) 10.2326 + 17.7234i 0.486166 + 0.842064i 0.999874 0.0159012i \(-0.00506171\pi\)
−0.513708 + 0.857965i \(0.671728\pi\)
\(444\) −0.873312 + 1.51262i −0.0414456 + 0.0717858i
\(445\) 8.48441 14.6954i 0.402200 0.696630i
\(446\) −7.26131 + 4.19232i −0.343833 + 0.198512i
\(447\) 3.09142 0.146219
\(448\) −1.54219 + 2.14980i −0.0728618 + 0.101569i
\(449\) −31.4921 −1.48620 −0.743102 0.669178i \(-0.766646\pi\)
−0.743102 + 0.669178i \(0.766646\pi\)
\(450\) −0.841318 1.45721i −0.0396601 0.0686933i
\(451\) −2.15167 + 3.72680i −0.101318 + 0.175488i
\(452\) −13.5926 7.84770i −0.639343 0.369125i
\(453\) −8.47557 + 4.89337i −0.398217 + 0.229911i
\(454\) −12.9893 −0.609617
\(455\) 2.18755 22.0945i 0.102554 1.03581i
\(456\) 3.01423i 0.141154i
\(457\) 9.36053 5.40430i 0.437867 0.252803i −0.264825 0.964296i \(-0.585314\pi\)
0.702692 + 0.711494i \(0.251981\pi\)
\(458\) −1.55022 + 2.68507i −0.0724372 + 0.125465i
\(459\) 20.4655 + 11.8158i 0.955247 + 0.551512i
\(460\) 3.00301 + 11.4697i 0.140016 + 0.534776i
\(461\) 36.3796i 1.69437i 0.531299 + 0.847185i \(0.321704\pi\)
−0.531299 + 0.847185i \(0.678296\pi\)
\(462\) 1.68588 + 3.72590i 0.0784343 + 0.173344i
\(463\) 25.6344 1.19133 0.595666 0.803232i \(-0.296888\pi\)
0.595666 + 0.803232i \(0.296888\pi\)
\(464\) −4.49558 7.78657i −0.208702 0.361482i
\(465\) −5.78822 + 10.0255i −0.268422 + 0.464921i
\(466\) 12.4182 21.5089i 0.575260 0.996380i
\(467\) −18.2010 31.5251i −0.842243 1.45881i −0.887994 0.459855i \(-0.847901\pi\)
0.0457505 0.998953i \(-0.485432\pi\)
\(468\) 5.13728i 0.237471i
\(469\) 27.4939 12.4404i 1.26955 0.574442i
\(470\) 4.10979i 0.189570i
\(471\) −20.2764 + 11.7066i −0.934288 + 0.539412i
\(472\) 8.43785 + 4.87160i 0.388384 + 0.224233i
\(473\) 8.23261 14.2593i 0.378536 0.655643i
\(474\) −4.53435 7.85372i −0.208269 0.360733i
\(475\) −2.74859 −0.126114
\(476\) 11.3064 + 1.11943i 0.518227 + 0.0513090i
\(477\) 12.4859i 0.571691i
\(478\) 12.3351 + 21.3650i 0.564193 + 0.977211i
\(479\) −1.95577 + 3.38750i −0.0893615 + 0.154779i −0.907241 0.420610i \(-0.861816\pi\)
0.817880 + 0.575389i \(0.195149\pi\)
\(480\) −2.61040 1.50711i −0.119148 0.0687900i
\(481\) 2.43135 + 4.21122i 0.110860 + 0.192015i
\(482\) 20.1514 0.917869
\(483\) 9.73960 + 12.0199i 0.443167 + 0.546922i
\(484\) 9.39279 0.426945
\(485\) −8.03362 13.9146i −0.364788 0.631831i
\(486\) 12.0067 + 6.93210i 0.544637 + 0.314446i
\(487\) 15.1951 26.3186i 0.688554 1.19261i −0.283752 0.958898i \(-0.591579\pi\)
0.972306 0.233713i \(-0.0750876\pi\)
\(488\) −4.61935 8.00096i −0.209108 0.362186i
\(489\) 3.03173i 0.137100i
\(490\) −16.9694 3.39352i −0.766601 0.153303i
\(491\) −20.2990 −0.916082 −0.458041 0.888931i \(-0.651449\pi\)
−0.458041 + 0.888931i \(0.651449\pi\)
\(492\) −2.06934 3.58419i −0.0932929 0.161588i
\(493\) −19.3054 + 33.4379i −0.869470 + 1.50597i
\(494\) 7.26749 + 4.19589i 0.326980 + 0.188782i
\(495\) 4.10786 2.37167i 0.184634 0.106599i
\(496\) 3.84060i 0.172448i
\(497\) 15.5807 21.7193i 0.698890 0.974245i
\(498\) 6.35443i 0.284749i
\(499\) −3.40473 5.89716i −0.152417 0.263993i 0.779699 0.626155i \(-0.215372\pi\)
−0.932115 + 0.362162i \(0.882039\pi\)
\(500\) −4.80622 + 8.32461i −0.214941 + 0.372288i
\(501\) −5.00000 + 8.66025i −0.223384 + 0.386912i
\(502\) 14.6886 + 25.4414i 0.655585 + 1.13551i
\(503\) 3.19779 0.142582 0.0712911 0.997456i \(-0.477288\pi\)
0.0712911 + 0.997456i \(0.477288\pi\)
\(504\) 3.98469 + 0.394520i 0.177492 + 0.0175733i
\(505\) 17.6067i 0.783486i
\(506\) −5.88169 + 1.53995i −0.261473 + 0.0684593i
\(507\) 1.56032 + 0.900852i 0.0692963 + 0.0400082i
\(508\) −0.995578 + 1.72439i −0.0441716 + 0.0765075i
\(509\) 7.04396 4.06683i 0.312218 0.180259i −0.335700 0.941969i \(-0.608973\pi\)
0.647919 + 0.761710i \(0.275640\pi\)
\(510\) 12.9440i 0.573170i
\(511\) −9.25767 + 4.18888i −0.409535 + 0.185305i
\(512\) 1.00000 0.0441942
\(513\) 11.7819 6.80226i 0.520182 0.300327i
\(514\) −3.93918 2.27429i −0.173750 0.100315i
\(515\) 17.1901 29.7742i 0.757488 1.31201i
\(516\) 7.91760 + 13.7137i 0.348553 + 0.603711i
\(517\) −2.10752 −0.0926884
\(518\) 3.45312 1.56245i 0.151721 0.0686503i
\(519\) 21.4240 0.940408
\(520\) −7.26749 + 4.19589i −0.318700 + 0.184002i
\(521\) 19.8849 34.4417i 0.871175 1.50892i 0.0103923 0.999946i \(-0.496692\pi\)
0.860782 0.508973i \(-0.169975\pi\)
\(522\) −6.80377 + 11.7845i −0.297793 + 0.515793i
\(523\) 16.2253 + 28.1030i 0.709483 + 1.22886i 0.965049 + 0.262068i \(0.0844046\pi\)
−0.255567 + 0.966791i \(0.582262\pi\)
\(524\) 11.3389i 0.495344i
\(525\) 0.353364 3.56901i 0.0154221 0.155765i
\(526\) 5.71453i 0.249165i
\(527\) −14.2831 + 8.24634i −0.622180 + 0.359216i
\(528\) 0.772854 1.33862i 0.0336342 0.0582561i
\(529\) −20.0490 + 11.2712i −0.871694 + 0.490050i
\(530\) 17.6633 10.1979i 0.767244 0.442968i
\(531\) 14.7457i 0.639909i
\(532\) 3.81262 5.31475i 0.165298 0.230423i
\(533\) −11.5223 −0.499085
\(534\) −7.24752 + 4.18436i −0.313631 + 0.181075i
\(535\) −12.5541 7.24810i −0.542760 0.313363i
\(536\) −9.87789 5.70300i −0.426660 0.246332i
\(537\) −6.87753 + 3.97074i −0.296787 + 0.171350i
\(538\) 8.28376i 0.357138i
\(539\) 1.74021 8.70200i 0.0749561 0.374822i
\(540\) 13.6045i 0.585446i
\(541\) −11.1614 19.3322i −0.479868 0.831156i 0.519865 0.854248i \(-0.325982\pi\)
−0.999733 + 0.0230924i \(0.992649\pi\)
\(542\) −0.343470 0.198302i −0.0147533 0.00851781i
\(543\) 10.8131 + 6.24296i 0.464035 + 0.267911i
\(544\) −2.14715 3.71897i −0.0920583 0.159450i
\(545\) 35.2424i 1.50962i
\(546\) −6.38263 + 8.89732i −0.273151 + 0.380770i
\(547\) −12.9010 −0.551609 −0.275804 0.961214i \(-0.588944\pi\)
−0.275804 + 0.961214i \(0.588944\pi\)
\(548\) −1.36978 + 0.790842i −0.0585141 + 0.0337831i
\(549\) −6.99110 + 12.1089i −0.298373 + 0.516797i
\(550\) 1.22065 + 0.704744i 0.0520488 + 0.0300504i
\(551\) 11.1140 + 19.2500i 0.473472 + 0.820077i
\(552\) 1.54571 5.63930i 0.0657897 0.240025i
\(553\) −1.93891 + 19.5832i −0.0824509 + 0.832763i
\(554\) −17.5190 −0.744310
\(555\) 2.15901 + 3.73951i 0.0916447 + 0.158733i
\(556\) 12.2631 + 7.08013i 0.520073 + 0.300264i
\(557\) 1.60885 + 0.928870i 0.0681692 + 0.0393575i 0.533697 0.845676i \(-0.320802\pi\)
−0.465528 + 0.885033i \(0.654136\pi\)
\(558\) −5.03377 + 2.90625i −0.213097 + 0.123031i
\(559\) 44.0860 1.86464
\(560\) 2.69640 + 5.95920i 0.113944 + 0.251822i
\(561\) −6.63773 −0.280245
\(562\) 17.7060 10.2225i 0.746881 0.431212i
\(563\) −2.88227 + 4.99224i −0.121473 + 0.210398i −0.920349 0.391099i \(-0.872095\pi\)
0.798876 + 0.601496i \(0.205428\pi\)
\(564\) 1.01344 1.75532i 0.0426734 0.0739125i
\(565\) −33.6037 + 19.4011i −1.41372 + 0.816211i
\(566\) 14.0131 0.589015
\(567\) 2.36591 + 5.22881i 0.0993590 + 0.219589i
\(568\) −10.1030 −0.423910
\(569\) 23.8451 13.7670i 0.999641 0.577143i 0.0914986 0.995805i \(-0.470834\pi\)
0.908142 + 0.418662i \(0.137501\pi\)
\(570\) 6.45344 + 3.72590i 0.270305 + 0.156061i
\(571\) −26.7378 15.4371i −1.11894 0.646023i −0.177813 0.984064i \(-0.556902\pi\)
−0.941131 + 0.338042i \(0.890235\pi\)
\(572\) −2.15167 3.72680i −0.0899657 0.155825i
\(573\) 11.9873 0.500777
\(574\) −0.884859 + 8.93717i −0.0369333 + 0.373030i
\(575\) 5.14233 + 1.40949i 0.214450 + 0.0587797i
\(576\) −0.756718 1.31067i −0.0315299 0.0546114i
\(577\) −35.7439 20.6367i −1.48804 0.859119i −0.488131 0.872770i \(-0.662321\pi\)
−0.999907 + 0.0136513i \(0.995655\pi\)
\(578\) −0.720506 + 1.24795i −0.0299691 + 0.0519080i
\(579\) 8.32529 4.80661i 0.345987 0.199756i
\(580\) −22.2280 −0.922967
\(581\) 8.03755 11.2043i 0.333454 0.464831i
\(582\) 7.92407i 0.328463i
\(583\) 5.22952 + 9.05779i 0.216585 + 0.375136i
\(584\) 3.32605 + 1.92030i 0.137633 + 0.0794625i
\(585\) 10.9989 + 6.35021i 0.454748 + 0.262549i
\(586\) −2.14263 3.71115i −0.0885114 0.153306i
\(587\) 13.5868i 0.560787i 0.959885 + 0.280393i \(0.0904649\pi\)
−0.959885 + 0.280393i \(0.909535\pi\)
\(588\) 6.41098 + 5.63391i 0.264384 + 0.232339i
\(589\) 9.49474i 0.391224i
\(590\) 20.8601 12.0436i 0.858797 0.495827i
\(591\) −6.29382 3.63374i −0.258893 0.149472i
\(592\) −1.24062 0.716272i −0.0509891 0.0294386i
\(593\) 12.3664 7.13972i 0.507826 0.293193i −0.224114 0.974563i \(-0.571949\pi\)
0.731939 + 0.681370i \(0.238615\pi\)
\(594\) −6.97645 −0.286247
\(595\) 16.3725 22.8231i 0.671208 0.935657i
\(596\) 2.53551i 0.103859i
\(597\) 24.5516 14.1749i 1.00483 0.580138i
\(598\) −11.4450 11.5769i −0.468022 0.473413i
\(599\) −11.6674 + 20.2085i −0.476716 + 0.825696i −0.999644 0.0266806i \(-0.991506\pi\)
0.522928 + 0.852377i \(0.324840\pi\)
\(600\) −1.17395 + 0.677778i −0.0479261 + 0.0276702i
\(601\) 41.8019i 1.70513i −0.522618 0.852567i \(-0.675045\pi\)
0.522618 0.852567i \(-0.324955\pi\)
\(602\) 3.38561 34.1950i 0.137987 1.39368i
\(603\) 17.2623i 0.702974i
\(604\) −4.01344 6.95148i −0.163304 0.282852i
\(605\) 11.6105 20.1099i 0.472032 0.817584i
\(606\) 4.34164 7.51995i 0.176367 0.305477i
\(607\) −6.12191 + 3.53448i −0.248480 + 0.143460i −0.619068 0.785337i \(-0.712490\pi\)
0.370588 + 0.928797i \(0.379156\pi\)
\(608\) −2.47221 −0.100261
\(609\) −26.4247 + 11.9566i −1.07078 + 0.484505i
\(610\) −22.8400 −0.924764
\(611\) −2.82146 4.88692i −0.114144 0.197703i
\(612\) −3.24958 + 5.62843i −0.131356 + 0.227516i
\(613\) −36.2475 20.9275i −1.46402 0.845254i −0.464829 0.885401i \(-0.653884\pi\)
−0.999194 + 0.0401467i \(0.987217\pi\)
\(614\) 25.9202 14.9650i 1.04605 0.603939i
\(615\) −10.2316 −0.412580
\(616\) −3.05590 + 1.38272i −0.123126 + 0.0557115i
\(617\) 44.8424i 1.80529i −0.430390 0.902643i \(-0.641624\pi\)
0.430390 0.902643i \(-0.358376\pi\)
\(618\) −14.6841 + 8.47787i −0.590681 + 0.341030i
\(619\) 2.13812 3.70333i 0.0859382 0.148849i −0.819852 0.572575i \(-0.805945\pi\)
0.905791 + 0.423726i \(0.139278\pi\)
\(620\) −8.22269 4.74737i −0.330231 0.190659i
\(621\) −25.5309 + 6.68453i −1.02452 + 0.268241i
\(622\) 5.58497i 0.223937i
\(623\) 18.0717 + 1.78925i 0.724026 + 0.0716849i
\(624\) 4.13867 0.165679
\(625\) 14.6614 + 25.3944i 0.586458 + 1.01577i
\(626\) −4.42798 + 7.66948i −0.176978 + 0.306534i
\(627\) −1.91065 + 3.30935i −0.0763041 + 0.132163i
\(628\) −9.60150 16.6303i −0.383142 0.663621i
\(629\) 6.15177i 0.245287i
\(630\) 5.77016 8.04353i 0.229888 0.320462i
\(631\) 34.7236i 1.38232i −0.722700 0.691162i \(-0.757099\pi\)
0.722700 0.691162i \(-0.242901\pi\)
\(632\) 6.44145 3.71897i 0.256227 0.147933i
\(633\) −8.05533 4.65075i −0.320171 0.184851i
\(634\) −9.52428 + 16.4965i −0.378257 + 0.655161i
\(635\) 2.46127 + 4.26305i 0.0976726 + 0.169174i
\(636\) −10.0588 −0.398859
\(637\) 22.5080 7.61470i 0.891798 0.301706i
\(638\) 11.3986i 0.451275i
\(639\) 7.64509 + 13.2417i 0.302435 + 0.523833i
\(640\) 1.23610 2.14099i 0.0488612 0.0846302i
\(641\) 6.73329 + 3.88746i 0.265949 + 0.153546i 0.627045 0.778983i \(-0.284264\pi\)
−0.361096 + 0.932529i \(0.617597\pi\)
\(642\) 3.57463 + 6.19144i 0.141079 + 0.244357i
\(643\) −29.0738 −1.14656 −0.573278 0.819361i \(-0.694329\pi\)
−0.573278 + 0.819361i \(0.694329\pi\)
\(644\) −9.85843 + 7.98821i −0.388476 + 0.314779i
\(645\) 39.1479 1.54145
\(646\) 5.30819 + 9.19406i 0.208848 + 0.361736i
\(647\) 0.980757 + 0.566241i 0.0385576 + 0.0222612i 0.519155 0.854680i \(-0.326247\pi\)
−0.480597 + 0.876941i \(0.659580\pi\)
\(648\) 1.08460 1.87858i 0.0426071 0.0737976i
\(649\) 6.17600 + 10.6971i 0.242429 + 0.419899i
\(650\) 3.77394i 0.148026i
\(651\) −12.3288 1.22066i −0.483204 0.0478415i
\(652\) −2.48656 −0.0973813
\(653\) 11.5471 + 20.0001i 0.451871 + 0.782664i 0.998502 0.0547097i \(-0.0174233\pi\)
−0.546631 + 0.837374i \(0.684090\pi\)
\(654\) 8.69045 15.0523i 0.339824 0.588592i
\(655\) 24.2766 + 14.0161i 0.948564 + 0.547654i
\(656\) 2.93968 1.69722i 0.114775 0.0662655i
\(657\) 5.81250i 0.226767i
\(658\) −4.00717 + 1.81315i −0.156216 + 0.0706840i
\(659\) 4.27458i 0.166514i −0.996528 0.0832569i \(-0.973468\pi\)
0.996528 0.0832569i \(-0.0265322\pi\)
\(660\) −1.91065 3.30935i −0.0743721 0.128816i
\(661\) 18.4774 32.0038i 0.718688 1.24480i −0.242831 0.970069i \(-0.578076\pi\)
0.961520 0.274736i \(-0.0885905\pi\)
\(662\) −1.30101 + 2.25341i −0.0505651 + 0.0875813i
\(663\) −8.88635 15.3916i −0.345117 0.597760i
\(664\) −5.21176 −0.202256
\(665\) −6.66605 14.7324i −0.258498 0.571296i
\(666\) 2.16806i 0.0840108i
\(667\) −10.9216 41.7140i −0.422887 1.61517i
\(668\) −7.10295 4.10089i −0.274822 0.158668i
\(669\) 5.11147 8.85333i 0.197621 0.342290i
\(670\) −24.4202 + 14.0990i −0.943433 + 0.544691i
\(671\) 11.7124i 0.452153i
\(672\) 0.317831 3.21013i 0.0122606 0.123833i
\(673\) 16.0507 0.618711 0.309355 0.950947i \(-0.399887\pi\)
0.309355 + 0.950947i \(0.399887\pi\)
\(674\) −4.65709 + 2.68877i −0.179384 + 0.103568i
\(675\) 5.29853 + 3.05911i 0.203941 + 0.117745i
\(676\) −0.738859 + 1.27974i −0.0284177 + 0.0492208i
\(677\) −2.01347 3.48744i −0.0773841 0.134033i 0.824736 0.565517i \(-0.191323\pi\)
−0.902121 + 0.431484i \(0.857990\pi\)
\(678\) 19.1366 0.734935
\(679\) 10.0229 13.9719i 0.384645 0.536191i
\(680\) −10.6164 −0.407120
\(681\) 13.7154 7.91856i 0.525574 0.303440i
\(682\) 2.43447 4.21663i 0.0932207 0.161463i
\(683\) 11.6692 20.2116i 0.446509 0.773377i −0.551647 0.834078i \(-0.686000\pi\)
0.998156 + 0.0607009i \(0.0193336\pi\)
\(684\) 1.87076 + 3.24026i 0.0715304 + 0.123894i
\(685\) 3.91025i 0.149403i
\(686\) −4.17778 18.0429i −0.159508 0.688881i
\(687\) 3.78021i 0.144224i
\(688\) −11.2477 + 6.49384i −0.428813 + 0.247575i
\(689\) −14.0022 + 24.2525i −0.533440 + 0.923946i
\(690\) −10.1631 10.2801i −0.386901 0.391357i
\(691\) −32.7506 + 18.9086i −1.24589 + 0.719317i −0.970288 0.241954i \(-0.922212\pi\)
−0.275605 + 0.961271i \(0.588878\pi\)
\(692\) 17.5715i 0.667967i
\(693\) 4.12475 + 2.95896i 0.156686 + 0.112402i
\(694\) 13.6925 0.519759
\(695\) 30.3170 17.5035i 1.14999 0.663946i
\(696\) 9.49375 + 5.48122i 0.359860 + 0.207765i
\(697\) −12.6239 7.28839i −0.478163 0.276067i
\(698\) 20.1589 11.6387i 0.763024 0.440532i
\(699\) 30.2816i 1.14536i
\(700\) 2.92723 + 0.289821i 0.110639 + 0.0109542i
\(701\) 26.4771i 1.00003i −0.866017 0.500014i \(-0.833328\pi\)
0.866017 0.500014i \(-0.166672\pi\)
\(702\) −9.33982 16.1770i −0.352509 0.610563i
\(703\) 3.06707 + 1.77077i 0.115677 + 0.0667859i
\(704\) 1.09791 + 0.633878i 0.0413790 + 0.0238902i
\(705\) −2.50542 4.33952i −0.0943597 0.163436i
\(706\) 31.6651i 1.19173i
\(707\) −17.1670 + 7.76769i −0.645633 + 0.292134i
\(708\) −11.8794 −0.446454
\(709\) −14.1532 + 8.17135i −0.531534 + 0.306882i −0.741641 0.670797i \(-0.765952\pi\)
0.210107 + 0.977678i \(0.432619\pi\)
\(710\) −12.4883 + 21.6303i −0.468677 + 0.811772i
\(711\) −9.74873 5.62843i −0.365606 0.211083i
\(712\) −3.43192 5.94426i −0.128617 0.222771i
\(713\) 4.86894 17.7637i 0.182343 0.665254i
\(714\) −12.6208 + 5.71062i −0.472322 + 0.213715i
\(715\) −10.6387 −0.397866
\(716\) −3.25672 5.64080i −0.121709 0.210807i
\(717\) −26.0492 15.0395i −0.972824 0.561660i
\(718\) −30.4661 17.5896i −1.13699 0.656439i
\(719\) −37.3661 + 21.5733i −1.39352 + 0.804549i −0.993703 0.112046i \(-0.964260\pi\)
−0.399817 + 0.916595i \(0.630926\pi\)
\(720\) −3.74153 −0.139438
\(721\) 36.6147 + 3.62518i 1.36360 + 0.135009i
\(722\) −12.8882 −0.479649
\(723\) −21.2778 + 12.2847i −0.791330 + 0.456875i
\(724\) −5.12034 + 8.86869i −0.190296 + 0.329602i
\(725\) −4.99817 + 8.65709i −0.185627 + 0.321516i
\(726\) −9.91784 + 5.72607i −0.368086 + 0.212514i
\(727\) −13.4385 −0.498405 −0.249203 0.968451i \(-0.580168\pi\)
−0.249203 + 0.968451i \(0.580168\pi\)
\(728\) −7.29739 5.23489i −0.270459 0.194018i
\(729\) −23.4115 −0.867092
\(730\) 8.22269 4.74737i 0.304335 0.175708i
\(731\) 48.3009 + 27.8865i 1.78647 + 1.03142i
\(732\) 9.75514 + 5.63213i 0.360560 + 0.208170i
\(733\) 15.4206 + 26.7093i 0.569573 + 0.986530i 0.996608 + 0.0822949i \(0.0262249\pi\)
−0.427035 + 0.904235i \(0.640442\pi\)
\(734\) 13.2476 0.488977
\(735\) 19.9868 6.76176i 0.737224 0.249411i
\(736\) 4.62523 + 1.26776i 0.170488 + 0.0467301i
\(737\) −7.23001 12.5228i −0.266321 0.461282i
\(738\) −4.44902 2.56864i −0.163771 0.0945530i
\(739\) −0.993256 + 1.72037i −0.0365375 + 0.0632848i −0.883716 0.468024i \(-0.844966\pi\)
0.847178 + 0.531309i \(0.178300\pi\)
\(740\) −3.06707 + 1.77077i −0.112748 + 0.0650948i
\(741\) −10.2316 −0.375869
\(742\) 17.7359 + 12.7232i 0.651107 + 0.467082i
\(743\) 1.57808i 0.0578941i −0.999581 0.0289471i \(-0.990785\pi\)
0.999581 0.0289471i \(-0.00921543\pi\)
\(744\) 2.34132 + 4.05528i 0.0858369 + 0.148674i
\(745\) 5.42851 + 3.13415i 0.198885 + 0.114826i
\(746\) 31.6868 + 18.2944i 1.16014 + 0.669804i
\(747\) 3.94384 + 6.83093i 0.144297 + 0.249931i
\(748\) 5.44413i 0.199057i
\(749\) 1.52853 15.4383i 0.0558513 0.564104i
\(750\) 11.7199i 0.427951i
\(751\) −14.9992 + 8.65979i −0.547329 + 0.316000i −0.748044 0.663649i \(-0.769007\pi\)
0.200715 + 0.979650i \(0.435673\pi\)
\(752\) 1.43968 + 0.831199i 0.0524997 + 0.0303107i
\(753\) −31.0194 17.9091i −1.13041 0.652642i
\(754\) 26.4311 15.2600i 0.962564 0.555737i
\(755\) −19.8441 −0.722200
\(756\) −13.2648 + 6.00203i −0.482438 + 0.218292i
\(757\) 29.1470i 1.05937i 0.848196 + 0.529683i \(0.177689\pi\)
−0.848196 + 0.529683i \(0.822311\pi\)
\(758\) −1.11788 + 0.645406i −0.0406031 + 0.0234422i
\(759\) 5.27168 5.21165i 0.191350 0.189171i
\(760\) −3.05590 + 5.29297i −0.110849 + 0.191996i
\(761\) −16.6464 + 9.61082i −0.603432 + 0.348392i −0.770391 0.637572i \(-0.779939\pi\)
0.166958 + 0.985964i \(0.446605\pi\)
\(762\) 2.42771i 0.0879467i
\(763\) −34.3624 + 15.5482i −1.24400 + 0.562883i
\(764\) 9.83173i 0.355699i
\(765\) 8.03362 + 13.9146i 0.290456 + 0.503085i
\(766\) 2.42354 4.19769i 0.0875659 0.151669i
\(767\) −16.5364 + 28.6419i −0.597094 + 1.03420i
\(768\) −1.05590 + 0.609623i −0.0381015 + 0.0219979i
\(769\) −32.3533 −1.16669 −0.583344 0.812225i \(-0.698256\pi\)
−0.583344 + 0.812225i \(0.698256\pi\)
\(770\) −0.817005 + 8.25184i −0.0294428 + 0.297376i
\(771\) 5.54584 0.199729
\(772\) 3.94227 + 6.82822i 0.141886 + 0.245753i
\(773\) 18.0142 31.2015i 0.647925 1.12224i −0.335693 0.941971i \(-0.608970\pi\)
0.983618 0.180267i \(-0.0576962\pi\)
\(774\) 17.0226 + 9.82802i 0.611866 + 0.353261i
\(775\) −3.69790 + 2.13498i −0.132832 + 0.0766909i
\(776\) −6.49915 −0.233306
\(777\) −2.69363 + 3.75489i −0.0966335 + 0.134706i
\(778\) 14.2749i 0.511780i
\(779\) −7.26749 + 4.19589i −0.260385 + 0.150333i
\(780\) 5.11582 8.86086i 0.183176 0.317270i
\(781\) −11.0921 6.40404i −0.396907 0.229155i
\(782\) −5.21632 19.9232i −0.186535 0.712452i
\(783\) 49.4783i 1.76821i
\(784\) −4.62081 + 5.25815i −0.165029 + 0.187791i
\(785\) −47.4738 −1.69441
\(786\) −6.91248 11.9728i −0.246560 0.427054i
\(787\) 14.6732 25.4147i 0.523042 0.905935i −0.476598 0.879121i \(-0.658130\pi\)
0.999640 0.0268143i \(-0.00853627\pi\)
\(788\) 2.98031 5.16206i 0.106169 0.183891i
\(789\) −3.48371 6.03396i −0.124023 0.214815i
\(790\) 18.3881i 0.654220i
\(791\) −33.7420 24.2053i −1.19973 0.860642i
\(792\) 1.91867i 0.0681769i
\(793\) 27.1588 15.6802i 0.964439 0.556819i
\(794\) 27.4857 + 15.8689i 0.975430 + 0.563165i
\(795\) −12.4338 + 21.5359i −0.440980 + 0.763799i
\(796\) 11.6259 + 20.1367i 0.412069 + 0.713725i
\(797\) −23.8046 −0.843202 −0.421601 0.906782i \(-0.638532\pi\)
−0.421601 + 0.906782i \(0.638532\pi\)
\(798\) −0.785744 + 7.93610i −0.0278150 + 0.280935i
\(799\) 7.13883i 0.252554i
\(800\) −0.555899 0.962845i −0.0196540 0.0340417i
\(801\) −5.19399 + 8.99626i −0.183521 + 0.317867i
\(802\) 3.68834 + 2.12946i 0.130240 + 0.0751940i
\(803\) 2.43447 + 4.21663i 0.0859106 + 0.148801i
\(804\) 13.9067 0.490453
\(805\) 4.91666 + 30.9811i 0.173290 + 1.09194i
\(806\) 13.0367 0.459198
\(807\) −5.04997 8.74681i −0.177768 0.307902i
\(808\) 6.16770 + 3.56092i 0.216979 + 0.125273i
\(809\) 25.5237 44.2084i 0.897366 1.55428i 0.0665172 0.997785i \(-0.478811\pi\)
0.830849 0.556498i \(-0.187855\pi\)
\(810\) −2.68135 4.64424i −0.0942131 0.163182i
\(811\) 48.7844i 1.71305i −0.516104 0.856526i \(-0.672618\pi\)
0.516104 0.856526i \(-0.327382\pi\)
\(812\) −9.80652 21.6730i −0.344141 0.760573i
\(813\) 0.483559 0.0169591
\(814\) −0.908058 1.57280i −0.0318274 0.0551267i
\(815\) −3.07365 + 5.32371i −0.107665 + 0.186482i
\(816\) 4.53435 + 2.61791i 0.158734 + 0.0916450i
\(817\) 27.8065 16.0541i 0.972828 0.561662i
\(818\) 7.41636i 0.259307i
\(819\) −1.33918 + 13.5258i −0.0467947 + 0.472631i
\(820\) 8.39177i 0.293053i
\(821\) −0.368516 0.638289i −0.0128613 0.0222764i 0.859523 0.511097i \(-0.170761\pi\)
−0.872384 + 0.488820i \(0.837427\pi\)
\(822\) 0.964232 1.67010i 0.0336315 0.0582514i
\(823\) −25.2931 + 43.8089i −0.881662 + 1.52708i −0.0321698 + 0.999482i \(0.510242\pi\)
−0.849492 + 0.527601i \(0.823092\pi\)
\(824\) −6.95337 12.0436i −0.242232 0.419558i
\(825\) −1.71851 −0.0598310
\(826\) 20.9459 + 15.0259i 0.728802 + 0.522817i
\(827\) 18.2125i 0.633310i 0.948541 + 0.316655i \(0.102560\pi\)
−0.948541 + 0.316655i \(0.897440\pi\)
\(828\) −1.83838 7.02151i −0.0638883 0.244014i
\(829\) 21.2080 + 12.2444i 0.736585 + 0.425267i 0.820826 0.571178i \(-0.193513\pi\)
−0.0842416 + 0.996445i \(0.526847\pi\)
\(830\) −6.44227 + 11.1583i −0.223615 + 0.387312i
\(831\) 18.4983 10.6800i 0.641697 0.370484i
\(832\) 3.39445i 0.117681i
\(833\) 29.4765 + 5.89465i 1.02130 + 0.204237i
\(834\) −17.2648 −0.597833
\(835\) −17.5600 + 10.1382i −0.607687 + 0.350848i
\(836\) −2.71426 1.56708i −0.0938745 0.0541985i
\(837\) 10.5674 18.3033i 0.365262 0.632653i
\(838\) −16.5703 28.7006i −0.572412 0.991447i
\(839\) 20.0986 0.693881 0.346940 0.937887i \(-0.387221\pi\)
0.346940 + 0.937887i \(0.387221\pi\)
\(840\) −6.47999 4.64852i −0.223581 0.160389i
\(841\) 51.8409 1.78762
\(842\) −24.8403 + 14.3415i −0.856052 + 0.494242i
\(843\) −12.4638 + 21.5879i −0.429276 + 0.743528i
\(844\) 3.81444 6.60681i 0.131299 0.227416i
\(845\) 1.82661 + 3.16378i 0.0628373 + 0.108837i
\(846\) 2.51593i 0.0864996i
\(847\) 24.7301 + 2.44850i 0.849736 + 0.0841313i
\(848\) 8.25004i 0.283308i
\(849\) −14.7964 + 8.54272i −0.507812 + 0.293185i
\(850\) −2.38720 + 4.13475i −0.0818802 + 0.141821i
\(851\) −4.83010 4.88573i −0.165574 0.167481i
\(852\) 10.6677 6.15900i 0.365469 0.211004i
\(853\) 28.1854i 0.965050i −0.875882 0.482525i \(-0.839720\pi\)
0.875882 0.482525i \(-0.160280\pi\)
\(854\) −10.0765 22.2697i −0.344812 0.762054i
\(855\) 9.24982 0.316337
\(856\) −5.07809 + 2.93183i −0.173565 + 0.100208i
\(857\) −45.4805 26.2582i −1.55358 0.896962i −0.997846 0.0656045i \(-0.979102\pi\)
−0.555738 0.831357i \(-0.687564\pi\)
\(858\) 4.54388 + 2.62341i 0.155126 + 0.0895618i
\(859\) −8.57908 + 4.95314i −0.292715 + 0.168999i −0.639165 0.769069i \(-0.720720\pi\)
0.346451 + 0.938068i \(0.387387\pi\)
\(860\) 32.1082i 1.09488i
\(861\) −4.51399 9.97618i −0.153836 0.339987i
\(862\) 24.5733i 0.836970i
\(863\) −3.48933 6.04369i −0.118778 0.205730i 0.800506 0.599325i \(-0.204564\pi\)
−0.919284 + 0.393596i \(0.871231\pi\)
\(864\) 4.76573 + 2.75150i 0.162134 + 0.0936078i
\(865\) 37.6204 + 21.7201i 1.27913 + 0.738507i
\(866\) 12.1632 + 21.0673i 0.413323 + 0.715897i
\(867\) 1.75695i 0.0596691i
\(868\) 1.00116 10.1118i 0.0339816 0.343218i
\(869\) 9.42950 0.319874
\(870\) 23.4705 13.5507i 0.795724 0.459412i
\(871\) 19.3585 33.5300i 0.655939 1.13612i
\(872\) 12.3456 + 7.12772i 0.418074 + 0.241375i
\(873\) 4.91803 + 8.51827i 0.166450 + 0.288300i
\(874\) −11.4345 3.13415i −0.386779 0.106014i
\(875\) −14.8242 + 20.6648i −0.501150 + 0.698598i
\(876\) −4.68264 −0.158212
\(877\) 19.5669 + 33.8909i 0.660728 + 1.14441i 0.980425 + 0.196894i \(0.0630855\pi\)
−0.319697 + 0.947520i \(0.603581\pi\)
\(878\) −3.93526 2.27202i −0.132808 0.0766770i
\(879\) 4.52481 + 2.61240i 0.152618 + 0.0881140i
\(880\) 2.71426 1.56708i 0.0914976 0.0528261i
\(881\) 16.1961 0.545660 0.272830 0.962062i \(-0.412040\pi\)
0.272830 + 0.962062i \(0.412040\pi\)
\(882\) 10.3884 + 2.07745i 0.349795 + 0.0699512i
\(883\) 3.29018 0.110723 0.0553617 0.998466i \(-0.482369\pi\)
0.0553617 + 0.998466i \(0.482369\pi\)
\(884\) 12.6239 7.28839i 0.424586 0.245135i
\(885\) −14.6841 + 25.4336i −0.493601 + 0.854942i
\(886\) 10.2326 17.7234i 0.343771 0.595429i
\(887\) −11.9436 + 6.89564i −0.401027 + 0.231533i −0.686927 0.726726i \(-0.741041\pi\)
0.285900 + 0.958259i \(0.407707\pi\)
\(888\) 1.74662 0.0586129
\(889\) −3.07075 + 4.28059i −0.102990 + 0.143566i
\(890\) −16.9688 −0.568796
\(891\) 2.38158 1.37501i 0.0797860 0.0460645i
\(892\) 7.26131 + 4.19232i 0.243127 + 0.140369i
\(893\) −3.55918 2.05489i −0.119103 0.0687644i
\(894\) −1.54571 2.67724i −0.0516962 0.0895405i
\(895\) −16.1026 −0.538249
\(896\) 2.63288 + 0.260678i 0.0879583 + 0.00870865i
\(897\) 19.1423 + 5.24683i 0.639144 + 0.175186i
\(898\) 15.7460 + 27.2730i 0.525452 + 0.910110i
\(899\) 29.9051 + 17.2657i 0.997390 + 0.575843i
\(900\) −0.841318 + 1.45721i −0.0280439 + 0.0485735i
\(901\) −30.6817 + 17.7141i −1.02215 + 0.590141i
\(902\) 4.30333 0.143285
\(903\) 17.2712 + 38.1704i 0.574750 + 1.27023i
\(904\) 15.6954i 0.522021i
\(905\) 12.6585 + 21.9252i 0.420784 + 0.728819i
\(906\) 8.47557 + 4.89337i 0.281582 + 0.162571i
\(907\) −10.0175 5.78359i −0.332625 0.192041i 0.324381 0.945926i \(-0.394844\pi\)
−0.657006 + 0.753885i \(0.728177\pi\)
\(908\) 6.49463 + 11.2490i 0.215532 + 0.373312i
\(909\) 10.7785i 0.357499i
\(910\) −20.2282 + 9.15278i −0.670558 + 0.303412i
\(911\) 52.9276i 1.75357i 0.480882 + 0.876785i \(0.340317\pi\)
−0.480882 + 0.876785i \(0.659683\pi\)
\(912\) 2.61040 1.50711i 0.0864389 0.0499055i
\(913\) −5.72204 3.30362i −0.189372 0.109334i
\(914\) −9.36053 5.40430i −0.309619 0.178758i
\(915\) 24.1167 13.9238i 0.797274 0.460306i
\(916\) 3.10045 0.102442
\(917\) −2.95581 + 29.8540i −0.0976095 + 0.985867i
\(918\) 23.6315i 0.779956i
\(919\) −1.20381 + 0.695019i −0.0397100 + 0.0229266i −0.519724 0.854334i \(-0.673965\pi\)
0.480014 + 0.877261i \(0.340632\pi\)
\(920\) 8.43152 8.33552i 0.277979 0.274814i
\(921\) −18.2460 + 31.6031i −0.601228 + 1.04136i
\(922\) 31.5057 18.1898i 1.03758 0.599050i
\(923\) 34.2940i 1.12880i
\(924\) 2.38378 3.32296i 0.0784206 0.109317i
\(925\) 1.59270i 0.0523676i
\(926\) −12.8172 22.2001i −0.421200 0.729539i
\(927\) −10.5235 + 18.2272i −0.345636 + 0.598660i
\(928\) −4.49558 + 7.78657i −0.147575 + 0.255607i
\(929\) 14.2728 8.24038i 0.468274 0.270358i −0.247243 0.968953i \(-0.579525\pi\)
0.715517 + 0.698596i \(0.246191\pi\)
\(930\) 11.5764 0.379606
\(931\) 11.4236 12.9992i 0.374393 0.426032i
\(932\) −24.8363 −0.813541
\(933\) 3.40473 + 5.89716i 0.111466 + 0.193064i
\(934\) −18.2010 + 31.5251i −0.595556 + 1.03153i
\(935\) −11.6558 6.72950i −0.381186 0.220078i
\(936\) 4.44902 2.56864i 0.145421 0.0839587i
\(937\) 41.9928 1.37184 0.685922 0.727675i \(-0.259399\pi\)
0.685922 + 0.727675i \(0.259399\pi\)
\(938\) −24.5206 17.5903i −0.800627 0.574342i
\(939\) 10.7976i 0.352366i
\(940\) 3.55918 2.05489i 0.116088 0.0670233i
\(941\) −16.7249 + 28.9683i −0.545216 + 0.944341i 0.453378 + 0.891319i \(0.350219\pi\)
−0.998593 + 0.0530227i \(0.983114\pi\)
\(942\) 20.2764 + 11.7066i 0.660642 + 0.381422i
\(943\) 15.7484 4.12326i 0.512837 0.134272i
\(944\) 9.74319i 0.317114i
\(945\) −3.54640 + 35.8191i −0.115365 + 1.16519i
\(946\) −16.4652 −0.535330
\(947\) 5.02687 + 8.70680i 0.163351 + 0.282933i 0.936069 0.351817i \(-0.114436\pi\)
−0.772717 + 0.634750i \(0.781103\pi\)
\(948\) −4.53435 + 7.85372i −0.147269 + 0.255077i
\(949\) −6.51835 + 11.2901i −0.211595 + 0.366493i
\(950\) 1.37430 + 2.38035i 0.0445880 + 0.0772288i
\(951\) 23.2249i 0.753119i
\(952\) −4.68373 10.3513i −0.151801 0.335488i
\(953\) 19.7821i 0.640806i 0.947281 + 0.320403i \(0.103818\pi\)
−0.947281 + 0.320403i \(0.896182\pi\)
\(954\) −10.8131 + 6.24296i −0.350088 + 0.202123i
\(955\) 21.0496 + 12.1530i 0.681151 + 0.393263i
\(956\) 12.3351 21.3650i 0.398945 0.690992i
\(957\) 6.94885 + 12.0358i 0.224624 + 0.389061i
\(958\) 3.91154 0.126376
\(959\) −3.81262 + 1.72512i −0.123116 + 0.0557070i
\(960\) 3.01423i 0.0972838i
\(961\) −8.12491 14.0728i −0.262094 0.453960i
\(962\) 2.43135 4.21122i 0.0783898 0.135775i
\(963\) 7.68536 + 4.43715i 0.247657 + 0.142985i
\(964\) −10.0757 17.4516i −0.324516 0.562078i
\(965\) 19.4922 0.627477
\(966\) 5.53970 14.4447i 0.178237 0.464749i
\(967\) 39.6200 1.27409 0.637047 0.770825i \(-0.280156\pi\)
0.637047 + 0.770825i \(0.280156\pi\)
\(968\) −4.69640 8.13440i −0.150948 0.261449i
\(969\) −11.2098 6.47200i −0.360112 0.207911i
\(970\) −8.03362 + 13.9146i −0.257944 + 0.446772i
\(971\) −23.8065 41.2340i −0.763987 1.32326i −0.940781 0.339016i \(-0.889906\pi\)
0.176794 0.984248i \(-0.443427\pi\)
\(972\) 13.8642i 0.444694i
\(973\) 30.4417 + 21.8378i 0.975916 + 0.700089i
\(974\) −30.3901 −0.973763
\(975\) −2.30068 3.98490i −0.0736808 0.127619i
\(976\) −4.61935 + 8.00096i −0.147862 + 0.256104i
\(977\) 0.251904 + 0.145437i 0.00805912 + 0.00465293i 0.504024 0.863690i \(-0.331852\pi\)
−0.495965 + 0.868342i \(0.665186\pi\)
\(978\) 2.62556 1.51587i 0.0839561 0.0484721i
\(979\) 8.70168i 0.278107i
\(980\) 5.54585 + 16.3927i 0.177156 + 0.523647i
\(981\) 21.5747i 0.688828i
\(982\) 10.1495 + 17.5795i 0.323884 + 0.560983i
\(983\) −15.7179 + 27.2242i −0.501323 + 0.868317i 0.498676 + 0.866789i \(0.333820\pi\)
−0.999999 + 0.00152833i \(0.999514\pi\)
\(984\) −2.06934 + 3.58419i −0.0659680 + 0.114260i
\(985\) −7.36795 12.7617i −0.234762 0.406620i
\(986\) 38.6107 1.22962
\(987\) 3.12583 4.35737i 0.0994963 0.138697i
\(988\) 8.39177i 0.266978i
\(989\) −60.2557 + 15.7762i −1.91602 + 0.501656i
\(990\) −4.10786 2.37167i −0.130556 0.0753767i
\(991\) 6.83645 11.8411i 0.217167 0.376144i −0.736774 0.676139i \(-0.763652\pi\)
0.953941 + 0.299995i \(0.0969850\pi\)
\(992\) −3.32605 + 1.92030i −0.105602 + 0.0609695i
\(993\) 3.17250i 0.100676i
\(994\) −26.5998 2.63362i −0.843696 0.0835333i
\(995\) 57.4832 1.82234
\(996\) 5.50310 3.17721i 0.174372 0.100674i
\(997\) −8.61882 4.97608i −0.272961 0.157594i 0.357272 0.934001i \(-0.383707\pi\)
−0.630232 + 0.776407i \(0.717040\pi\)
\(998\) −3.40473 + 5.89716i −0.107775 + 0.186671i
\(999\) −3.94164 6.82712i −0.124708 0.216001i
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 322.2.g.a.45.6 yes 16
7.3 odd 6 2254.2.c.c.2253.12 16
7.4 even 3 2254.2.c.c.2253.5 16
7.5 odd 6 inner 322.2.g.a.229.5 yes 16
23.22 odd 2 inner 322.2.g.a.45.5 16
161.45 even 6 2254.2.c.c.2253.11 16
161.68 even 6 inner 322.2.g.a.229.6 yes 16
161.137 odd 6 2254.2.c.c.2253.6 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
322.2.g.a.45.5 16 23.22 odd 2 inner
322.2.g.a.45.6 yes 16 1.1 even 1 trivial
322.2.g.a.229.5 yes 16 7.5 odd 6 inner
322.2.g.a.229.6 yes 16 161.68 even 6 inner
2254.2.c.c.2253.5 16 7.4 even 3
2254.2.c.c.2253.6 16 161.137 odd 6
2254.2.c.c.2253.11 16 161.45 even 6
2254.2.c.c.2253.12 16 7.3 odd 6