Properties

Label 231.2.l.b.32.20
Level $231$
Weight $2$
Character 231.32
Analytic conductor $1.845$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [231,2,Mod(32,231)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(231, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 4, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("231.32");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 231 = 3 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 231.l (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: \(1.84454428669\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(24\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 32.20
Character \(\chi\) \(=\) 231.32
Dual form 231.2.l.b.65.20

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.939478 + 1.62722i) q^{2} +(1.16688 + 1.27999i) q^{3} +(-0.765237 + 1.32543i) q^{4} +(-2.63713 + 1.52255i) q^{5} +(-0.986571 + 3.10131i) q^{6} +(-0.738610 - 2.54056i) q^{7} +0.882219 q^{8} +(-0.276760 + 2.98721i) q^{9} +O(q^{10})\) \(q+(0.939478 + 1.62722i) q^{2} +(1.16688 + 1.27999i) q^{3} +(-0.765237 + 1.32543i) q^{4} +(-2.63713 + 1.52255i) q^{5} +(-0.986571 + 3.10131i) q^{6} +(-0.738610 - 2.54056i) q^{7} +0.882219 q^{8} +(-0.276760 + 2.98721i) q^{9} +(-4.95505 - 2.86080i) q^{10} +(0.988816 + 3.16579i) q^{11} +(-2.58948 + 0.567126i) q^{12} -1.24436i q^{13} +(3.44015 - 3.58868i) q^{14} +(-5.02608 - 1.59887i) q^{15} +(2.35930 + 4.08643i) q^{16} +(2.83407 - 4.90876i) q^{17} +(-5.12086 + 2.35606i) q^{18} +(0.532275 - 0.307309i) q^{19} -4.66044i q^{20} +(2.39003 - 3.90996i) q^{21} +(-4.22248 + 4.58322i) q^{22} +(4.41744 - 2.55041i) q^{23} +(1.02945 + 1.12923i) q^{24} +(2.13630 - 3.70019i) q^{25} +(2.02485 - 1.16905i) q^{26} +(-4.14655 + 3.13147i) q^{27} +(3.93255 + 0.965157i) q^{28} +1.47768 q^{29} +(-2.12017 - 9.68065i) q^{30} +(3.18007 - 5.50805i) q^{31} +(-3.55080 + 6.15016i) q^{32} +(-2.89836 + 4.95979i) q^{33} +10.6502 q^{34} +(5.81594 + 5.57522i) q^{35} +(-3.74754 - 2.65275i) q^{36} +(-3.15832 - 5.47036i) q^{37} +(1.00012 + 0.577420i) q^{38} +(1.59277 - 1.45202i) q^{39} +(-2.32653 + 1.34322i) q^{40} -10.3640 q^{41} +(8.60775 + 0.215789i) q^{42} +2.31140i q^{43} +(-4.95271 - 1.11198i) q^{44} +(-3.81831 - 8.29903i) q^{45} +(8.30018 + 4.79211i) q^{46} +(-9.35776 + 5.40270i) q^{47} +(-2.47756 + 7.78827i) q^{48} +(-5.90891 + 3.75297i) q^{49} +8.02804 q^{50} +(9.59020 - 2.10036i) q^{51} +(1.64931 + 0.952228i) q^{52} +(2.58050 + 1.48985i) q^{53} +(-8.99120 - 3.80541i) q^{54} +(-7.42771 - 6.84309i) q^{55} +(-0.651616 - 2.24133i) q^{56} +(1.01446 + 0.322713i) q^{57} +(1.38825 + 2.40451i) q^{58} +(5.38180 + 3.10718i) q^{59} +(5.96533 - 5.43819i) q^{60} +(8.24852 - 4.76229i) q^{61} +11.9504 q^{62} +(7.79360 - 1.50325i) q^{63} -3.90639 q^{64} +(1.89459 + 3.28153i) q^{65} +(-10.7936 - 0.0566571i) q^{66} +(2.31763 - 4.01426i) q^{67} +(4.33747 + 7.51272i) q^{68} +(8.41916 + 2.67826i) q^{69} +(-3.60819 + 14.7016i) q^{70} -7.90967i q^{71} +(-0.244163 + 2.63537i) q^{72} +(-1.01586 - 0.586510i) q^{73} +(5.93434 - 10.2786i) q^{74} +(7.22903 - 1.58324i) q^{75} +0.940657i q^{76} +(7.31254 - 4.85043i) q^{77} +(3.85913 + 1.22765i) q^{78} +(-3.34216 + 1.92960i) q^{79} +(-12.4436 - 7.18429i) q^{80} +(-8.84681 - 1.65348i) q^{81} +(-9.73679 - 16.8646i) q^{82} -15.6693 q^{83} +(3.35344 + 6.15986i) q^{84} +17.2600i q^{85} +(-3.76117 + 2.17151i) q^{86} +(1.72428 + 1.89142i) q^{87} +(0.872352 + 2.79292i) q^{88} +(1.19552 - 0.690235i) q^{89} +(9.91716 - 14.0100i) q^{90} +(-3.16137 + 0.919095i) q^{91} +7.80668i q^{92} +(10.7610 - 2.35679i) q^{93} +(-17.5828 - 10.1514i) q^{94} +(-0.935785 + 1.62083i) q^{95} +(-12.0155 + 2.63154i) q^{96} +9.19643 q^{97} +(-11.6582 - 6.08929i) q^{98} +(-9.73054 + 2.07763i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q - 6 q^{3} - 36 q^{4} - 10 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 48 q - 6 q^{3} - 36 q^{4} - 10 q^{9} + 14 q^{12} + 4 q^{15} - 28 q^{16} - 24 q^{22} - 36 q^{27} - 4 q^{31} - 26 q^{33} + 56 q^{34} + 12 q^{36} - 28 q^{37} + 96 q^{42} + 30 q^{45} - 72 q^{48} + 24 q^{49} - 80 q^{55} + 16 q^{58} - 32 q^{60} + 256 q^{64} - 42 q^{66} + 16 q^{67} + 36 q^{69} - 76 q^{70} + 34 q^{75} + 104 q^{78} - 26 q^{81} - 4 q^{82} - 16 q^{88} - 36 q^{91} + 52 q^{93} - 144 q^{97} - 36 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/231\mathbb{Z}\right)^\times\).

\(n\) \(155\) \(199\) \(211\)
\(\chi(n)\) \(-1\) \(e\left(\frac{2}{3}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.939478 + 1.62722i 0.664311 + 1.15062i 0.979472 + 0.201582i \(0.0646083\pi\)
−0.315161 + 0.949038i \(0.602058\pi\)
\(3\) 1.16688 + 1.27999i 0.673701 + 0.739004i
\(4\) −0.765237 + 1.32543i −0.382618 + 0.662715i
\(5\) −2.63713 + 1.52255i −1.17936 + 0.680904i −0.955867 0.293801i \(-0.905080\pi\)
−0.223494 + 0.974705i \(0.571746\pi\)
\(6\) −0.986571 + 3.10131i −0.402766 + 1.26610i
\(7\) −0.738610 2.54056i −0.279168 0.960242i
\(8\) 0.882219 0.311911
\(9\) −0.276760 + 2.98721i −0.0922534 + 0.995736i
\(10\) −4.95505 2.86080i −1.56692 0.904664i
\(11\) 0.988816 + 3.16579i 0.298139 + 0.954522i
\(12\) −2.58948 + 0.567126i −0.747519 + 0.163715i
\(13\) 1.24436i 0.345123i −0.984999 0.172561i \(-0.944796\pi\)
0.984999 0.172561i \(-0.0552043\pi\)
\(14\) 3.44015 3.58868i 0.919420 0.959116i
\(15\) −5.02608 1.59887i −1.29773 0.412826i
\(16\) 2.35930 + 4.08643i 0.589825 + 1.02161i
\(17\) 2.83407 4.90876i 0.687363 1.19055i −0.285325 0.958431i \(-0.592101\pi\)
0.972688 0.232117i \(-0.0745653\pi\)
\(18\) −5.12086 + 2.35606i −1.20700 + 0.555330i
\(19\) 0.532275 0.307309i 0.122112 0.0705015i −0.437700 0.899121i \(-0.644207\pi\)
0.559812 + 0.828620i \(0.310873\pi\)
\(20\) 4.66044i 1.04211i
\(21\) 2.39003 3.90996i 0.521547 0.853223i
\(22\) −4.22248 + 4.58322i −0.900236 + 0.977145i
\(23\) 4.41744 2.55041i 0.921101 0.531798i 0.0371147 0.999311i \(-0.488183\pi\)
0.883986 + 0.467513i \(0.154850\pi\)
\(24\) 1.02945 + 1.12923i 0.210135 + 0.230504i
\(25\) 2.13630 3.70019i 0.427261 0.740037i
\(26\) 2.02485 1.16905i 0.397105 0.229269i
\(27\) −4.14655 + 3.13147i −0.798004 + 0.602653i
\(28\) 3.93255 + 0.965157i 0.743181 + 0.182397i
\(29\) 1.47768 0.274398 0.137199 0.990544i \(-0.456190\pi\)
0.137199 + 0.990544i \(0.456190\pi\)
\(30\) −2.12017 9.68065i −0.387089 1.76744i
\(31\) 3.18007 5.50805i 0.571158 0.989275i −0.425289 0.905057i \(-0.639828\pi\)
0.996447 0.0842172i \(-0.0268390\pi\)
\(32\) −3.55080 + 6.15016i −0.627698 + 1.08721i
\(33\) −2.89836 + 4.95979i −0.504539 + 0.863389i
\(34\) 10.6502 1.82649
\(35\) 5.81594 + 5.57522i 0.983073 + 0.942385i
\(36\) −3.74754 2.65275i −0.624591 0.442124i
\(37\) −3.15832 5.47036i −0.519224 0.899322i −0.999750 0.0223421i \(-0.992888\pi\)
0.480526 0.876980i \(-0.340446\pi\)
\(38\) 1.00012 + 0.577420i 0.162241 + 0.0936699i
\(39\) 1.59277 1.45202i 0.255047 0.232510i
\(40\) −2.32653 + 1.34322i −0.367856 + 0.212382i
\(41\) −10.3640 −1.61859 −0.809296 0.587401i \(-0.800151\pi\)
−0.809296 + 0.587401i \(0.800151\pi\)
\(42\) 8.60775 + 0.215789i 1.32820 + 0.0332970i
\(43\) 2.31140i 0.352486i 0.984347 + 0.176243i \(0.0563944\pi\)
−0.984347 + 0.176243i \(0.943606\pi\)
\(44\) −4.95271 1.11198i −0.746649 0.167637i
\(45\) −3.81831 8.29903i −0.569200 1.23715i
\(46\) 8.30018 + 4.79211i 1.22379 + 0.706558i
\(47\) −9.35776 + 5.40270i −1.36497 + 0.788065i −0.990280 0.139086i \(-0.955584\pi\)
−0.374689 + 0.927151i \(0.622250\pi\)
\(48\) −2.47756 + 7.78827i −0.357605 + 1.12414i
\(49\) −5.90891 + 3.75297i −0.844130 + 0.536138i
\(50\) 8.02804 1.13534
\(51\) 9.59020 2.10036i 1.34290 0.294110i
\(52\) 1.64931 + 0.952228i 0.228718 + 0.132050i
\(53\) 2.58050 + 1.48985i 0.354459 + 0.204647i 0.666647 0.745373i \(-0.267729\pi\)
−0.312189 + 0.950020i \(0.601062\pi\)
\(54\) −8.99120 3.80541i −1.22355 0.517851i
\(55\) −7.42771 6.84309i −1.00155 0.922722i
\(56\) −0.651616 2.24133i −0.0870758 0.299511i
\(57\) 1.01446 + 0.322713i 0.134368 + 0.0427444i
\(58\) 1.38825 + 2.40451i 0.182286 + 0.315728i
\(59\) 5.38180 + 3.10718i 0.700650 + 0.404521i 0.807590 0.589745i \(-0.200772\pi\)
−0.106939 + 0.994266i \(0.534105\pi\)
\(60\) 5.96533 5.43819i 0.770120 0.702068i
\(61\) 8.24852 4.76229i 1.05612 0.609749i 0.131760 0.991282i \(-0.457937\pi\)
0.924355 + 0.381533i \(0.124604\pi\)
\(62\) 11.9504 1.51771
\(63\) 7.79360 1.50325i 0.981902 0.189392i
\(64\) −3.90639 −0.488299
\(65\) 1.89459 + 3.28153i 0.234995 + 0.407024i
\(66\) −10.7936 0.0566571i −1.32860 0.00697401i
\(67\) 2.31763 4.01426i 0.283144 0.490420i −0.689013 0.724749i \(-0.741956\pi\)
0.972157 + 0.234329i \(0.0752893\pi\)
\(68\) 4.33747 + 7.51272i 0.525996 + 0.911051i
\(69\) 8.41916 + 2.67826i 1.01355 + 0.322424i
\(70\) −3.60819 + 14.7016i −0.431261 + 1.75718i
\(71\) 7.90967i 0.938705i −0.883011 0.469353i \(-0.844487\pi\)
0.883011 0.469353i \(-0.155513\pi\)
\(72\) −0.244163 + 2.63537i −0.0287749 + 0.310581i
\(73\) −1.01586 0.586510i −0.118898 0.0686458i 0.439372 0.898305i \(-0.355201\pi\)
−0.558270 + 0.829660i \(0.688534\pi\)
\(74\) 5.93434 10.2786i 0.689853 1.19486i
\(75\) 7.22903 1.58324i 0.834736 0.182817i
\(76\) 0.940657i 0.107901i
\(77\) 7.31254 4.85043i 0.833342 0.552758i
\(78\) 3.85913 + 1.22765i 0.436961 + 0.139004i
\(79\) −3.34216 + 1.92960i −0.376022 + 0.217097i −0.676086 0.736822i \(-0.736325\pi\)
0.300064 + 0.953919i \(0.402992\pi\)
\(80\) −12.4436 7.18429i −1.39123 0.803228i
\(81\) −8.84681 1.65348i −0.982979 0.183720i
\(82\) −9.73679 16.8646i −1.07525 1.86238i
\(83\) −15.6693 −1.71993 −0.859966 0.510352i \(-0.829515\pi\)
−0.859966 + 0.510352i \(0.829515\pi\)
\(84\) 3.35344 + 6.15986i 0.365890 + 0.672095i
\(85\) 17.2600i 1.87211i
\(86\) −3.76117 + 2.17151i −0.405577 + 0.234160i
\(87\) 1.72428 + 1.89142i 0.184862 + 0.202781i
\(88\) 0.872352 + 2.79292i 0.0929931 + 0.297726i
\(89\) 1.19552 0.690235i 0.126725 0.0731648i −0.435297 0.900287i \(-0.643357\pi\)
0.562022 + 0.827122i \(0.310023\pi\)
\(90\) 9.91716 14.0100i 1.04536 1.47678i
\(91\) −3.16137 + 0.919095i −0.331401 + 0.0963473i
\(92\) 7.80668i 0.813903i
\(93\) 10.7610 2.35679i 1.11587 0.244388i
\(94\) −17.5828 10.1514i −1.81353 1.04704i
\(95\) −0.935785 + 1.62083i −0.0960095 + 0.166293i
\(96\) −12.0155 + 2.63154i −1.22633 + 0.268580i
\(97\) 9.19643 0.933756 0.466878 0.884322i \(-0.345379\pi\)
0.466878 + 0.884322i \(0.345379\pi\)
\(98\) −11.6582 6.08929i −1.17766 0.615111i
\(99\) −9.73054 + 2.07763i −0.977956 + 0.208810i
\(100\) 3.26956 + 5.66304i 0.326956 + 0.566304i
\(101\) −5.50095 + 9.52793i −0.547365 + 0.948064i 0.451089 + 0.892479i \(0.351036\pi\)
−0.998454 + 0.0555851i \(0.982298\pi\)
\(102\) 12.4275 + 13.6322i 1.23051 + 1.34978i
\(103\) −1.24322 2.15333i −0.122499 0.212174i 0.798254 0.602321i \(-0.205757\pi\)
−0.920752 + 0.390148i \(0.872424\pi\)
\(104\) 1.09780i 0.107648i
\(105\) −0.349715 + 13.9500i −0.0341286 + 1.36138i
\(106\) 5.59873i 0.543797i
\(107\) −6.89744 11.9467i −0.666800 1.15493i −0.978794 0.204848i \(-0.934330\pi\)
0.311994 0.950084i \(-0.399003\pi\)
\(108\) −0.977456 7.89228i −0.0940558 0.759435i
\(109\) −2.99294 1.72797i −0.286671 0.165510i 0.349768 0.936836i \(-0.386260\pi\)
−0.636440 + 0.771326i \(0.719594\pi\)
\(110\) 4.15706 18.5155i 0.396361 1.76538i
\(111\) 3.31663 10.4259i 0.314801 0.989583i
\(112\) 8.63922 9.01222i 0.816329 0.851575i
\(113\) 7.98997i 0.751633i 0.926694 + 0.375817i \(0.122638\pi\)
−0.926694 + 0.375817i \(0.877362\pi\)
\(114\) 0.427933 + 1.95393i 0.0400796 + 0.183002i
\(115\) −7.76625 + 13.4515i −0.724207 + 1.25436i
\(116\) −1.13077 + 1.95856i −0.104990 + 0.181847i
\(117\) 3.71715 + 0.344389i 0.343651 + 0.0318387i
\(118\) 11.6765i 1.07491i
\(119\) −14.5643 3.57448i −1.33510 0.327672i
\(120\) −4.43410 1.41055i −0.404776 0.128765i
\(121\) −9.04449 + 6.26077i −0.822226 + 0.569161i
\(122\) 15.4986 + 8.94813i 1.40318 + 0.810125i
\(123\) −12.0936 13.2659i −1.09045 1.19615i
\(124\) 4.86702 + 8.42992i 0.437071 + 0.757029i
\(125\) 2.21498i 0.198114i
\(126\) 9.76805 + 11.2697i 0.870207 + 1.00398i
\(127\) 11.9269i 1.05834i −0.848514 0.529172i \(-0.822502\pi\)
0.848514 0.529172i \(-0.177498\pi\)
\(128\) 3.43163 + 5.94376i 0.303316 + 0.525359i
\(129\) −2.95858 + 2.69714i −0.260488 + 0.237470i
\(130\) −3.55986 + 6.16585i −0.312220 + 0.540781i
\(131\) 1.54608 + 2.67789i 0.135082 + 0.233968i 0.925629 0.378433i \(-0.123537\pi\)
−0.790547 + 0.612401i \(0.790204\pi\)
\(132\) −4.35592 7.63698i −0.379135 0.664714i
\(133\) −1.17388 1.12530i −0.101788 0.0975755i
\(134\) 8.70946 0.752383
\(135\) 6.16717 14.5714i 0.530785 1.25411i
\(136\) 2.50027 4.33060i 0.214396 0.371346i
\(137\) −2.68265 1.54883i −0.229194 0.132325i 0.381006 0.924573i \(-0.375578\pi\)
−0.610200 + 0.792247i \(0.708911\pi\)
\(138\) 3.55149 + 16.2160i 0.302323 + 1.38040i
\(139\) 12.1764i 1.03279i 0.856351 + 0.516394i \(0.172726\pi\)
−0.856351 + 0.516394i \(0.827274\pi\)
\(140\) −11.8401 + 3.44225i −1.00067 + 0.290923i
\(141\) −17.8348 5.67352i −1.50196 0.477797i
\(142\) 12.8708 7.43096i 1.08009 0.623592i
\(143\) 3.93938 1.23044i 0.329427 0.102895i
\(144\) −12.8600 + 5.91675i −1.07166 + 0.493063i
\(145\) −3.89683 + 2.24983i −0.323614 + 0.186839i
\(146\) 2.20405i 0.182409i
\(147\) −11.6988 3.18408i −0.964900 0.262618i
\(148\) 9.66744 0.794659
\(149\) 10.7473 + 18.6148i 0.880452 + 1.52499i 0.850840 + 0.525425i \(0.176094\pi\)
0.0296119 + 0.999561i \(0.490573\pi\)
\(150\) 9.36780 + 10.2758i 0.764877 + 0.839018i
\(151\) −19.8835 11.4797i −1.61810 0.934208i −0.987412 0.158168i \(-0.949441\pi\)
−0.630683 0.776040i \(-0.717225\pi\)
\(152\) 0.469583 0.271114i 0.0380882 0.0219902i
\(153\) 13.8791 + 9.82450i 1.12206 + 0.794264i
\(154\) 14.7627 + 7.34226i 1.18961 + 0.591657i
\(155\) 19.3673i 1.55562i
\(156\) 0.705707 + 3.22224i 0.0565018 + 0.257986i
\(157\) 5.67235 9.82480i 0.452703 0.784105i −0.545850 0.837883i \(-0.683793\pi\)
0.998553 + 0.0537783i \(0.0171264\pi\)
\(158\) −6.27977 3.62563i −0.499592 0.288439i
\(159\) 1.10415 + 5.04150i 0.0875645 + 0.399817i
\(160\) 21.6250i 1.70961i
\(161\) −9.74225 9.33903i −0.767797 0.736019i
\(162\) −5.62080 15.9491i −0.441612 1.25308i
\(163\) 6.79598 + 11.7710i 0.532302 + 0.921975i 0.999289 + 0.0377102i \(0.0120064\pi\)
−0.466986 + 0.884265i \(0.654660\pi\)
\(164\) 7.93095 13.7368i 0.619303 1.07266i
\(165\) 0.0918203 17.4925i 0.00714820 1.36179i
\(166\) −14.7210 25.4975i −1.14257 1.97899i
\(167\) 6.57900 0.509099 0.254549 0.967060i \(-0.418073\pi\)
0.254549 + 0.967060i \(0.418073\pi\)
\(168\) 2.10853 3.44944i 0.162676 0.266130i
\(169\) 11.4516 0.880890
\(170\) −28.0859 + 16.2154i −2.15409 + 1.24367i
\(171\) 0.770683 + 1.67507i 0.0589356 + 0.128095i
\(172\) −3.06360 1.76877i −0.233597 0.134867i
\(173\) 1.14593 + 1.98481i 0.0871234 + 0.150902i 0.906294 0.422648i \(-0.138899\pi\)
−0.819171 + 0.573550i \(0.805566\pi\)
\(174\) −1.45783 + 4.58273i −0.110518 + 0.347416i
\(175\) −10.9784 2.69442i −0.829893 0.203679i
\(176\) −10.6039 + 11.5098i −0.799296 + 0.867582i
\(177\) 2.30277 + 10.5144i 0.173087 + 0.790310i
\(178\) 2.24633 + 1.29692i 0.168370 + 0.0972083i
\(179\) −12.2722 7.08537i −0.917269 0.529585i −0.0345062 0.999404i \(-0.510986\pi\)
−0.882763 + 0.469819i \(0.844319\pi\)
\(180\) 13.9217 + 1.28982i 1.03766 + 0.0961378i
\(181\) 9.13748 0.679184 0.339592 0.940573i \(-0.389711\pi\)
0.339592 + 0.940573i \(0.389711\pi\)
\(182\) −4.46561 4.28078i −0.331013 0.317313i
\(183\) 15.7208 + 5.00101i 1.16211 + 0.369685i
\(184\) 3.89715 2.25002i 0.287302 0.165874i
\(185\) 16.6578 + 9.61738i 1.22470 + 0.707084i
\(186\) 13.9448 + 15.2965i 1.02248 + 1.12159i
\(187\) 18.3425 + 4.11823i 1.34133 + 0.301154i
\(188\) 16.5374i 1.20611i
\(189\) 11.0184 + 8.22163i 0.801470 + 0.598035i
\(190\) −3.51660 −0.255121
\(191\) 1.37505 0.793888i 0.0994954 0.0574437i −0.449427 0.893317i \(-0.648372\pi\)
0.548922 + 0.835874i \(0.315038\pi\)
\(192\) −4.55831 5.00015i −0.328967 0.360855i
\(193\) 11.2686 + 6.50595i 0.811135 + 0.468309i 0.847350 0.531035i \(-0.178197\pi\)
−0.0362150 + 0.999344i \(0.511530\pi\)
\(194\) 8.63984 + 14.9646i 0.620305 + 1.07440i
\(195\) −1.98956 + 6.25423i −0.142476 + 0.447875i
\(196\) −0.452577 10.7038i −0.0323270 0.764554i
\(197\) 0.114518 0.00815905 0.00407953 0.999992i \(-0.498701\pi\)
0.00407953 + 0.999992i \(0.498701\pi\)
\(198\) −12.5224 13.8819i −0.889928 0.986542i
\(199\) −11.9254 + 20.6554i −0.845370 + 1.46422i 0.0399293 + 0.999203i \(0.487287\pi\)
−0.885299 + 0.465021i \(0.846047\pi\)
\(200\) 1.88469 3.26437i 0.133268 0.230826i
\(201\) 7.84263 1.71762i 0.553176 0.121152i
\(202\) −20.6721 −1.45448
\(203\) −1.09143 3.75413i −0.0766032 0.263488i
\(204\) −4.55490 + 14.3184i −0.318906 + 1.00249i
\(205\) 27.3313 15.7798i 1.90890 1.10211i
\(206\) 2.33596 4.04601i 0.162754 0.281899i
\(207\) 6.39604 + 13.9017i 0.444555 + 0.966233i
\(208\) 5.08497 2.93581i 0.352579 0.203562i
\(209\) 1.49920 + 1.38120i 0.103702 + 0.0955396i
\(210\) −23.0283 + 12.5366i −1.58910 + 0.865111i
\(211\) 5.75491i 0.396184i 0.980183 + 0.198092i \(0.0634746\pi\)
−0.980183 + 0.198092i \(0.936525\pi\)
\(212\) −3.94939 + 2.28018i −0.271245 + 0.156603i
\(213\) 10.1243 9.22968i 0.693707 0.632407i
\(214\) 12.9600 22.4473i 0.885926 1.53447i
\(215\) −3.51922 6.09547i −0.240009 0.415708i
\(216\) −3.65816 + 2.76265i −0.248906 + 0.187974i
\(217\) −16.3424 4.01087i −1.10939 0.272276i
\(218\) 6.49357i 0.439800i
\(219\) −0.434669 1.98469i −0.0293722 0.134113i
\(220\) 14.7540 4.60832i 0.994713 0.310693i
\(221\) −6.10825 3.52660i −0.410885 0.237225i
\(222\) 20.0812 4.39800i 1.34776 0.295175i
\(223\) −10.9109 −0.730650 −0.365325 0.930880i \(-0.619042\pi\)
−0.365325 + 0.930880i \(0.619042\pi\)
\(224\) 18.2475 + 4.47845i 1.21921 + 0.299229i
\(225\) 10.4620 + 7.40564i 0.697465 + 0.493710i
\(226\) −13.0015 + 7.50640i −0.864845 + 0.499318i
\(227\) 4.04895 7.01299i 0.268739 0.465469i −0.699798 0.714341i \(-0.746727\pi\)
0.968536 + 0.248872i \(0.0800599\pi\)
\(228\) −1.20403 + 1.09764i −0.0797391 + 0.0726929i
\(229\) −0.452439 0.783647i −0.0298980 0.0517848i 0.850689 0.525669i \(-0.176185\pi\)
−0.880587 + 0.473884i \(0.842852\pi\)
\(230\) −29.1849 −1.92439
\(231\) 14.7414 + 3.70010i 0.969914 + 0.243449i
\(232\) 1.30363 0.0855878
\(233\) 0.199109 + 0.344867i 0.0130441 + 0.0225930i 0.872474 0.488661i \(-0.162514\pi\)
−0.859430 + 0.511254i \(0.829181\pi\)
\(234\) 2.93179 + 6.37218i 0.191657 + 0.416563i
\(235\) 16.4517 28.4953i 1.07319 1.85883i
\(236\) −8.23670 + 4.75546i −0.536164 + 0.309554i
\(237\) −6.36978 2.02632i −0.413762 0.131624i
\(238\) −7.86633 27.0575i −0.509899 1.75387i
\(239\) −18.8807 −1.22129 −0.610647 0.791903i \(-0.709091\pi\)
−0.610647 + 0.791903i \(0.709091\pi\)
\(240\) −5.32436 24.3109i −0.343686 1.56926i
\(241\) 2.61969 + 1.51248i 0.168749 + 0.0974274i 0.581996 0.813192i \(-0.302272\pi\)
−0.413247 + 0.910619i \(0.635605\pi\)
\(242\) −18.6848 8.83554i −1.20110 0.567970i
\(243\) −8.20676 13.2533i −0.526464 0.850197i
\(244\) 14.5771i 0.933204i
\(245\) 9.86849 18.8937i 0.630475 1.20707i
\(246\) 10.2249 32.1421i 0.651913 2.04930i
\(247\) −0.382402 0.662340i −0.0243317 0.0421437i
\(248\) 2.80552 4.85930i 0.178151 0.308566i
\(249\) −18.2843 20.0566i −1.15872 1.27104i
\(250\) 3.60427 2.08092i 0.227954 0.131609i
\(251\) 7.80267i 0.492500i 0.969206 + 0.246250i \(0.0791985\pi\)
−0.969206 + 0.246250i \(0.920802\pi\)
\(252\) −3.97149 + 11.4802i −0.250181 + 0.723185i
\(253\) 12.4421 + 11.4628i 0.782229 + 0.720661i
\(254\) 19.4078 11.2051i 1.21775 0.703070i
\(255\) −22.0927 + 20.1405i −1.38350 + 1.26125i
\(256\) −10.3543 + 17.9341i −0.647142 + 1.12088i
\(257\) 9.02456 5.21033i 0.562937 0.325012i −0.191387 0.981515i \(-0.561298\pi\)
0.754323 + 0.656503i \(0.227965\pi\)
\(258\) −7.16837 2.28036i −0.446283 0.141969i
\(259\) −11.5650 + 12.0644i −0.718616 + 0.749643i
\(260\) −5.79925 −0.359654
\(261\) −0.408962 + 4.41413i −0.0253141 + 0.273228i
\(262\) −2.90501 + 5.03163i −0.179472 + 0.310855i
\(263\) 15.4549 26.7686i 0.952989 1.65062i 0.214083 0.976815i \(-0.431324\pi\)
0.738905 0.673809i \(-0.235343\pi\)
\(264\) −2.55698 + 4.37562i −0.157371 + 0.269301i
\(265\) −9.07348 −0.557380
\(266\) 0.728272 2.96736i 0.0446532 0.181940i
\(267\) 2.27853 + 0.724834i 0.139444 + 0.0443591i
\(268\) 3.54708 + 6.14372i 0.216672 + 0.375287i
\(269\) 7.00519 + 4.04445i 0.427114 + 0.246594i 0.698116 0.715984i \(-0.254022\pi\)
−0.271002 + 0.962579i \(0.587355\pi\)
\(270\) 29.5049 3.65417i 1.79561 0.222386i
\(271\) −11.9023 + 6.87180i −0.723014 + 0.417432i −0.815861 0.578248i \(-0.803736\pi\)
0.0928473 + 0.995680i \(0.470403\pi\)
\(272\) 26.7457 1.62170
\(273\) −4.86538 2.97405i −0.294466 0.179998i
\(274\) 5.82036i 0.351621i
\(275\) 13.8264 + 3.10429i 0.833765 + 0.187196i
\(276\) −9.99249 + 9.10949i −0.601477 + 0.548327i
\(277\) 23.6582 + 13.6590i 1.42148 + 0.820692i 0.996426 0.0844752i \(-0.0269214\pi\)
0.425055 + 0.905167i \(0.360255\pi\)
\(278\) −19.8137 + 11.4394i −1.18835 + 0.686092i
\(279\) 15.5736 + 11.0239i 0.932365 + 0.659986i
\(280\) 5.13093 + 4.91857i 0.306632 + 0.293941i
\(281\) 0.129664 0.00773512 0.00386756 0.999993i \(-0.498769\pi\)
0.00386756 + 0.999993i \(0.498769\pi\)
\(282\) −7.52335 34.3514i −0.448009 2.04560i
\(283\) 25.0814 + 14.4807i 1.49093 + 0.860790i 0.999946 0.0103778i \(-0.00330341\pi\)
0.490986 + 0.871168i \(0.336637\pi\)
\(284\) 10.4837 + 6.05277i 0.622094 + 0.359166i
\(285\) −3.16660 + 0.693521i −0.187573 + 0.0410806i
\(286\) 5.70316 + 5.25427i 0.337235 + 0.310692i
\(287\) 7.65499 + 26.3305i 0.451859 + 1.55424i
\(288\) −17.3891 12.3091i −1.02466 0.725320i
\(289\) −7.56392 13.1011i −0.444936 0.770653i
\(290\) −7.32197 4.22734i −0.429961 0.248238i
\(291\) 10.7312 + 11.7714i 0.629073 + 0.690049i
\(292\) 1.55475 0.897638i 0.0909851 0.0525303i
\(293\) 4.79018 0.279845 0.139923 0.990162i \(-0.455315\pi\)
0.139923 + 0.990162i \(0.455315\pi\)
\(294\) −5.80955 22.0279i −0.338820 1.28469i
\(295\) −18.9233 −1.10176
\(296\) −2.78633 4.82606i −0.161952 0.280509i
\(297\) −14.0138 10.0307i −0.813162 0.582038i
\(298\) −20.1937 + 34.9764i −1.16979 + 2.02613i
\(299\) −3.17362 5.49688i −0.183535 0.317893i
\(300\) −3.43345 + 10.7931i −0.198230 + 0.623141i
\(301\) 5.87226 1.70722i 0.338471 0.0984028i
\(302\) 43.1398i 2.48242i
\(303\) −18.6146 + 4.07682i −1.06938 + 0.234207i
\(304\) 2.51159 + 1.45007i 0.144050 + 0.0831671i
\(305\) −14.5016 + 25.1175i −0.830360 + 1.43823i
\(306\) −2.94755 + 31.8143i −0.168500 + 1.81870i
\(307\) 14.6773i 0.837677i −0.908061 0.418839i \(-0.862437\pi\)
0.908061 0.418839i \(-0.137563\pi\)
\(308\) 0.833080 + 13.4040i 0.0474691 + 0.763763i
\(309\) 1.30554 4.10400i 0.0742697 0.233468i
\(310\) −31.5148 + 18.1951i −1.78992 + 1.03341i
\(311\) −13.2520 7.65105i −0.751453 0.433852i 0.0747658 0.997201i \(-0.476179\pi\)
−0.826219 + 0.563350i \(0.809512\pi\)
\(312\) 1.40517 1.28100i 0.0795521 0.0725224i
\(313\) 9.92967 + 17.1987i 0.561258 + 0.972127i 0.997387 + 0.0722432i \(0.0230158\pi\)
−0.436129 + 0.899884i \(0.643651\pi\)
\(314\) 21.3162 1.20294
\(315\) −18.2640 + 15.8304i −1.02906 + 0.891942i
\(316\) 5.90639i 0.332261i
\(317\) −15.6174 + 9.01672i −0.877161 + 0.506429i −0.869721 0.493543i \(-0.835702\pi\)
−0.00743978 + 0.999972i \(0.502368\pi\)
\(318\) −7.16633 + 6.53307i −0.401868 + 0.366356i
\(319\) 1.46115 + 4.67802i 0.0818088 + 0.261919i
\(320\) 10.3017 5.94767i 0.575880 0.332485i
\(321\) 7.24318 22.7691i 0.404275 1.27085i
\(322\) 6.04406 24.6266i 0.336822 1.37239i
\(323\) 3.48374i 0.193841i
\(324\) 8.96147 10.4605i 0.497860 0.581140i
\(325\) −4.60435 2.65833i −0.255404 0.147457i
\(326\) −12.7693 + 22.1172i −0.707229 + 1.22496i
\(327\) −1.28062 5.84728i −0.0708184 0.323355i
\(328\) −9.14336 −0.504857
\(329\) 20.6376 + 19.7835i 1.13779 + 1.09070i
\(330\) 28.5505 16.2844i 1.57165 0.896427i
\(331\) −8.50642 14.7336i −0.467555 0.809830i 0.531757 0.846897i \(-0.321532\pi\)
−0.999313 + 0.0370671i \(0.988198\pi\)
\(332\) 11.9907 20.7686i 0.658078 1.13982i
\(333\) 17.2152 7.92057i 0.943387 0.434044i
\(334\) 6.18083 + 10.7055i 0.338200 + 0.585779i
\(335\) 14.1148i 0.771175i
\(336\) 21.6165 + 0.541908i 1.17928 + 0.0295635i
\(337\) 23.4102i 1.27523i −0.770354 0.637616i \(-0.779921\pi\)
0.770354 0.637616i \(-0.220079\pi\)
\(338\) 10.7585 + 18.6343i 0.585185 + 1.01357i
\(339\) −10.2271 + 9.32337i −0.555460 + 0.506376i
\(340\) −22.8770 13.2080i −1.24068 0.716305i
\(341\) 20.5818 + 4.62100i 1.11457 + 0.250241i
\(342\) −2.00167 + 2.82776i −0.108238 + 0.152908i
\(343\) 13.8990 + 12.2400i 0.750477 + 0.660897i
\(344\) 2.03916i 0.109944i
\(345\) −26.2802 + 5.75566i −1.41488 + 0.309874i
\(346\) −2.15315 + 3.72937i −0.115754 + 0.200492i
\(347\) −11.4850 + 19.8925i −0.616545 + 1.06789i 0.373567 + 0.927603i \(0.378135\pi\)
−0.990111 + 0.140283i \(0.955199\pi\)
\(348\) −3.82642 + 0.838029i −0.205118 + 0.0449231i
\(349\) 10.0181i 0.536258i 0.963383 + 0.268129i \(0.0864053\pi\)
−0.963383 + 0.268129i \(0.913595\pi\)
\(350\) −5.92959 20.3957i −0.316950 1.09020i
\(351\) 3.89667 + 5.15979i 0.207989 + 0.275409i
\(352\) −22.9812 5.15971i −1.22490 0.275014i
\(353\) 4.58642 + 2.64797i 0.244110 + 0.140937i 0.617064 0.786913i \(-0.288322\pi\)
−0.372954 + 0.927850i \(0.621655\pi\)
\(354\) −14.9459 + 13.6251i −0.794363 + 0.724168i
\(355\) 12.0429 + 20.8588i 0.639168 + 1.10707i
\(356\) 2.11277i 0.111977i
\(357\) −12.4195 22.8132i −0.657311 1.20740i
\(358\) 26.6262i 1.40724i
\(359\) 2.99188 + 5.18209i 0.157905 + 0.273500i 0.934113 0.356977i \(-0.116193\pi\)
−0.776208 + 0.630477i \(0.782859\pi\)
\(360\) −3.36859 7.32156i −0.177540 0.385880i
\(361\) −9.31112 + 16.1273i −0.490059 + 0.848807i
\(362\) 8.58446 + 14.8687i 0.451189 + 0.781483i
\(363\) −18.5676 4.27127i −0.974547 0.224184i
\(364\) 1.20100 4.89349i 0.0629495 0.256489i
\(365\) 3.57196 0.186965
\(366\) 6.63156 + 30.2795i 0.346637 + 1.58274i
\(367\) −9.83094 + 17.0277i −0.513171 + 0.888838i 0.486712 + 0.873562i \(0.338196\pi\)
−0.999883 + 0.0152759i \(0.995137\pi\)
\(368\) 20.8441 + 12.0344i 1.08658 + 0.627335i
\(369\) 2.86835 30.9595i 0.149321 1.61169i
\(370\) 36.1412i 1.87889i
\(371\) 1.87908 7.65634i 0.0975569 0.397497i
\(372\) −5.11099 + 16.0665i −0.264992 + 0.833009i
\(373\) −16.8118 + 9.70627i −0.870480 + 0.502572i −0.867508 0.497424i \(-0.834279\pi\)
−0.00297207 + 0.999996i \(0.500946\pi\)
\(374\) 10.5311 + 33.7163i 0.544549 + 1.74343i
\(375\) 2.83516 2.58463i 0.146407 0.133470i
\(376\) −8.25559 + 4.76637i −0.425749 + 0.245807i
\(377\) 1.83876i 0.0947009i
\(378\) −3.02689 + 25.6534i −0.155686 + 1.31947i
\(379\) 2.78311 0.142959 0.0714795 0.997442i \(-0.477228\pi\)
0.0714795 + 0.997442i \(0.477228\pi\)
\(380\) −1.43219 2.48063i −0.0734700 0.127254i
\(381\) 15.2664 13.9174i 0.782121 0.713008i
\(382\) 2.58366 + 1.49168i 0.132192 + 0.0763210i
\(383\) −7.16366 + 4.13594i −0.366046 + 0.211337i −0.671730 0.740796i \(-0.734448\pi\)
0.305684 + 0.952133i \(0.401115\pi\)
\(384\) −3.60365 + 11.3281i −0.183898 + 0.578087i
\(385\) −11.8991 + 23.9249i −0.606435 + 1.21933i
\(386\) 24.4488i 1.24441i
\(387\) −6.90464 0.639704i −0.350982 0.0325180i
\(388\) −7.03745 + 12.1892i −0.357272 + 0.618814i
\(389\) −16.7647 9.67910i −0.850004 0.490750i 0.0106482 0.999943i \(-0.496610\pi\)
−0.860652 + 0.509193i \(0.829944\pi\)
\(390\) −12.0462 + 2.63825i −0.609982 + 0.133593i
\(391\) 28.9122i 1.46215i
\(392\) −5.21295 + 3.31094i −0.263294 + 0.167228i
\(393\) −1.62358 + 5.10375i −0.0818987 + 0.257450i
\(394\) 0.107587 + 0.186346i 0.00542015 + 0.00938797i
\(395\) 5.87581 10.1772i 0.295644 0.512070i
\(396\) 4.69241 14.4870i 0.235803 0.728000i
\(397\) 7.01674 + 12.1534i 0.352160 + 0.609959i 0.986628 0.162990i \(-0.0521139\pi\)
−0.634467 + 0.772950i \(0.718781\pi\)
\(398\) −44.8146 −2.24635
\(399\) 0.0705859 2.81565i 0.00353372 0.140959i
\(400\) 20.1607 1.00804
\(401\) 11.1606 6.44358i 0.557334 0.321777i −0.194741 0.980855i \(-0.562387\pi\)
0.752075 + 0.659078i \(0.229053\pi\)
\(402\) 10.1629 + 11.1480i 0.506881 + 0.556014i
\(403\) −6.85398 3.95715i −0.341421 0.197120i
\(404\) −8.41906 14.5822i −0.418864 0.725494i
\(405\) 25.8477 9.10925i 1.28438 0.452642i
\(406\) 5.08344 5.30292i 0.252287 0.263179i
\(407\) 14.1950 15.4078i 0.703622 0.763734i
\(408\) 8.46066 1.85298i 0.418865 0.0917362i
\(409\) 6.17168 + 3.56322i 0.305170 + 0.176190i 0.644763 0.764382i \(-0.276956\pi\)
−0.339593 + 0.940572i \(0.610289\pi\)
\(410\) 51.3544 + 29.6495i 2.53621 + 1.46428i
\(411\) −1.14785 5.24107i −0.0566195 0.258523i
\(412\) 3.80544 0.187481
\(413\) 3.91894 15.9678i 0.192838 0.785724i
\(414\) −16.6122 + 23.4681i −0.816444 + 1.15339i
\(415\) 41.3220 23.8573i 2.02842 1.17111i
\(416\) 7.65300 + 4.41846i 0.375219 + 0.216633i
\(417\) −15.5857 + 14.2084i −0.763234 + 0.695790i
\(418\) −0.839056 + 3.73714i −0.0410396 + 0.182789i
\(419\) 27.8186i 1.35903i −0.733663 0.679514i \(-0.762191\pi\)
0.733663 0.679514i \(-0.237809\pi\)
\(420\) −18.2221 11.1386i −0.889148 0.543507i
\(421\) −17.5302 −0.854369 −0.427185 0.904164i \(-0.640495\pi\)
−0.427185 + 0.904164i \(0.640495\pi\)
\(422\) −9.36453 + 5.40661i −0.455858 + 0.263190i
\(423\) −13.5491 29.4488i −0.658781 1.43185i
\(424\) 2.27656 + 1.31438i 0.110560 + 0.0638317i
\(425\) −12.1089 20.9732i −0.587367 1.01735i
\(426\) 24.5303 + 7.80345i 1.18850 + 0.378078i
\(427\) −18.1913 17.4384i −0.880340 0.843904i
\(428\) 21.1127 1.02052
\(429\) 6.17175 + 3.60659i 0.297975 + 0.174128i
\(430\) 6.61246 11.4531i 0.318881 0.552318i
\(431\) 6.45778 11.1852i 0.311060 0.538772i −0.667532 0.744581i \(-0.732649\pi\)
0.978592 + 0.205809i \(0.0659826\pi\)
\(432\) −22.5795 9.55648i −1.08636 0.459786i
\(433\) 6.99731 0.336269 0.168135 0.985764i \(-0.446226\pi\)
0.168135 + 0.985764i \(0.446226\pi\)
\(434\) −8.82671 30.3608i −0.423695 1.45737i
\(435\) −7.42692 2.36261i −0.356094 0.113279i
\(436\) 4.58061 2.64462i 0.219371 0.126654i
\(437\) 1.56753 2.71504i 0.0749851 0.129878i
\(438\) 2.82117 2.57187i 0.134801 0.122889i
\(439\) 10.1810 5.87802i 0.485914 0.280543i −0.236964 0.971519i \(-0.576152\pi\)
0.722878 + 0.690976i \(0.242819\pi\)
\(440\) −6.55286 6.03710i −0.312396 0.287807i
\(441\) −9.57554 18.6898i −0.455978 0.889991i
\(442\) 13.2526i 0.630364i
\(443\) −8.29921 + 4.79155i −0.394307 + 0.227653i −0.684025 0.729459i \(-0.739772\pi\)
0.289717 + 0.957112i \(0.406439\pi\)
\(444\) 11.2808 + 12.3742i 0.535363 + 0.587256i
\(445\) −2.10183 + 3.64048i −0.0996364 + 0.172575i
\(446\) −10.2506 17.7545i −0.485379 0.840701i
\(447\) −11.2860 + 35.4778i −0.533810 + 1.67804i
\(448\) 2.88530 + 9.92443i 0.136318 + 0.468885i
\(449\) 30.0895i 1.42001i −0.704197 0.710005i \(-0.748693\pi\)
0.704197 0.710005i \(-0.251307\pi\)
\(450\) −2.22184 + 23.9814i −0.104739 + 1.13049i
\(451\) −10.2481 32.8104i −0.482566 1.54498i
\(452\) −10.5901 6.11422i −0.498118 0.287589i
\(453\) −8.50777 38.8462i −0.399730 1.82516i
\(454\) 15.2156 0.714104
\(455\) 6.93757 7.23710i 0.325238 0.339281i
\(456\) 0.894973 + 0.284704i 0.0419109 + 0.0133325i
\(457\) −35.4804 + 20.4846i −1.65970 + 0.958230i −0.686853 + 0.726796i \(0.741008\pi\)
−0.972851 + 0.231434i \(0.925658\pi\)
\(458\) 0.850112 1.47244i 0.0397231 0.0688025i
\(459\) 3.62003 + 29.2292i 0.168969 + 1.36430i
\(460\) −11.8860 20.5872i −0.554190 0.959884i
\(461\) −5.45941 −0.254270 −0.127135 0.991885i \(-0.540578\pi\)
−0.127135 + 0.991885i \(0.540578\pi\)
\(462\) 7.82834 + 27.4637i 0.364207 + 1.27773i
\(463\) 6.44042 0.299312 0.149656 0.988738i \(-0.452183\pi\)
0.149656 + 0.988738i \(0.452183\pi\)
\(464\) 3.48628 + 6.03842i 0.161847 + 0.280327i
\(465\) −24.7899 + 22.5993i −1.14961 + 1.04802i
\(466\) −0.374117 + 0.647990i −0.0173306 + 0.0300176i
\(467\) 2.59974 1.50096i 0.120301 0.0694561i −0.438642 0.898662i \(-0.644540\pi\)
0.558943 + 0.829206i \(0.311207\pi\)
\(468\) −3.30096 + 4.66328i −0.152587 + 0.215560i
\(469\) −11.9103 2.92312i −0.549966 0.134977i
\(470\) 61.8242 2.85174
\(471\) 19.1947 4.20385i 0.884443 0.193703i
\(472\) 4.74792 + 2.74122i 0.218541 + 0.126175i
\(473\) −7.31742 + 2.28555i −0.336455 + 0.105090i
\(474\) −2.68699 12.2687i −0.123418 0.563522i
\(475\) 2.62602i 0.120490i
\(476\) 15.8828 16.5686i 0.727989 0.759420i
\(477\) −5.16467 + 7.29615i −0.236474 + 0.334068i
\(478\) −17.7380 30.7232i −0.811319 1.40525i
\(479\) −10.7538 + 18.6261i −0.491353 + 0.851049i −0.999950 0.00995594i \(-0.996831\pi\)
0.508597 + 0.861005i \(0.330164\pi\)
\(480\) 27.6799 25.2339i 1.26341 1.15177i
\(481\) −6.80709 + 3.93007i −0.310377 + 0.179196i
\(482\) 5.68377i 0.258888i
\(483\) 0.585805 23.3676i 0.0266551 1.06326i
\(484\) −1.37704 16.7788i −0.0625926 0.762673i
\(485\) −24.2522 + 14.0020i −1.10124 + 0.635798i
\(486\) 13.8559 25.8054i 0.628519 1.17056i
\(487\) 16.6319 28.8073i 0.753665 1.30539i −0.192371 0.981322i \(-0.561618\pi\)
0.946035 0.324063i \(-0.105049\pi\)
\(488\) 7.27700 4.20138i 0.329415 0.190188i
\(489\) −7.13664 + 22.4342i −0.322730 + 1.01451i
\(490\) 40.0154 1.69194i 1.80771 0.0764340i
\(491\) 3.76057 0.169712 0.0848562 0.996393i \(-0.472957\pi\)
0.0848562 + 0.996393i \(0.472957\pi\)
\(492\) 26.8375 5.87772i 1.20993 0.264988i
\(493\) 4.18784 7.25356i 0.188611 0.326684i
\(494\) 0.718517 1.24451i 0.0323276 0.0559930i
\(495\) 22.4974 20.2942i 1.01118 0.912157i
\(496\) 30.0110 1.34753
\(497\) −20.0950 + 5.84216i −0.901385 + 0.262057i
\(498\) 15.4589 48.5954i 0.692730 2.17761i
\(499\) −1.01365 1.75570i −0.0453773 0.0785958i 0.842445 0.538783i \(-0.181116\pi\)
−0.887822 + 0.460187i \(0.847782\pi\)
\(500\) 2.93580 + 1.69498i 0.131293 + 0.0758020i
\(501\) 7.67694 + 8.42107i 0.342980 + 0.376226i
\(502\) −12.6967 + 7.33044i −0.566681 + 0.327173i
\(503\) 12.6627 0.564602 0.282301 0.959326i \(-0.408902\pi\)
0.282301 + 0.959326i \(0.408902\pi\)
\(504\) 6.87566 1.32620i 0.306266 0.0590736i
\(505\) 33.5018i 1.49081i
\(506\) −6.96348 + 31.0152i −0.309564 + 1.37879i
\(507\) 13.3627 + 14.6579i 0.593457 + 0.650981i
\(508\) 15.8083 + 9.12693i 0.701381 + 0.404942i
\(509\) −24.5196 + 14.1564i −1.08681 + 0.627471i −0.932726 0.360586i \(-0.882577\pi\)
−0.154086 + 0.988057i \(0.549243\pi\)
\(510\) −53.5287 17.0282i −2.37029 0.754023i
\(511\) −0.739737 + 3.01407i −0.0327240 + 0.133335i
\(512\) −25.1839 −1.11298
\(513\) −1.24477 + 2.94108i −0.0549581 + 0.129852i
\(514\) 16.9568 + 9.78999i 0.747930 + 0.431818i
\(515\) 6.55709 + 3.78574i 0.288940 + 0.166819i
\(516\) −1.31086 5.98534i −0.0577072 0.263490i
\(517\) −26.3569 24.2824i −1.15918 1.06794i
\(518\) −30.4965 7.48469i −1.33994 0.328859i
\(519\) −1.20337 + 3.78282i −0.0528221 + 0.166047i
\(520\) 1.67145 + 2.89503i 0.0732978 + 0.126955i
\(521\) 4.46847 + 2.57987i 0.195767 + 0.113026i 0.594680 0.803963i \(-0.297279\pi\)
−0.398912 + 0.916989i \(0.630612\pi\)
\(522\) −7.56698 + 3.48150i −0.331198 + 0.152381i
\(523\) −1.50137 + 0.866814i −0.0656502 + 0.0379031i −0.532466 0.846452i \(-0.678735\pi\)
0.466816 + 0.884355i \(0.345401\pi\)
\(524\) −4.73247 −0.206739
\(525\) −9.36175 17.1964i −0.408580 0.750513i
\(526\) 58.0781 2.53232
\(527\) −18.0251 31.2204i −0.785186 1.35998i
\(528\) −27.1059 0.142282i −1.17963 0.00619204i
\(529\) 1.50921 2.61402i 0.0656177 0.113653i
\(530\) −8.52433 14.7646i −0.370273 0.641332i
\(531\) −10.7713 + 15.2166i −0.467433 + 0.660344i
\(532\) 2.38980 0.694778i 0.103611 0.0301225i
\(533\) 12.8966i 0.558613i
\(534\) 0.961163 + 4.38865i 0.0415936 + 0.189915i
\(535\) 36.3789 + 21.0034i 1.57280 + 0.908054i
\(536\) 2.04466 3.54145i 0.0883158 0.152968i
\(537\) −5.25105 23.9762i −0.226599 1.03465i
\(538\) 15.1987i 0.655262i
\(539\) −17.7239 14.9954i −0.763424 0.645897i
\(540\) 14.5940 + 19.3247i 0.628028 + 0.831604i
\(541\) 21.1393 12.2048i 0.908850 0.524725i 0.0287892 0.999586i \(-0.490835\pi\)
0.880061 + 0.474861i \(0.157502\pi\)
\(542\) −22.3639 12.9118i −0.960612 0.554610i
\(543\) 10.6624 + 11.6959i 0.457567 + 0.501919i
\(544\) 20.1264 + 34.8600i 0.862914 + 1.49461i
\(545\) 10.5237 0.450785
\(546\) 0.268519 10.7111i 0.0114915 0.458394i
\(547\) 22.7953i 0.974657i 0.873219 + 0.487329i \(0.162029\pi\)
−0.873219 + 0.487329i \(0.837971\pi\)
\(548\) 4.10572 2.37044i 0.175388 0.101260i
\(549\) 11.9431 + 25.9581i 0.509718 + 1.10786i
\(550\) 7.93825 + 25.4151i 0.338488 + 1.08370i
\(551\) 0.786530 0.454104i 0.0335073 0.0193455i
\(552\) 7.42754 + 2.36281i 0.316137 + 0.100568i
\(553\) 7.37081 + 7.06575i 0.313439 + 0.300466i
\(554\) 51.3295i 2.18078i
\(555\) 7.12755 + 32.5442i 0.302547 + 1.38142i
\(556\) −16.1389 9.31782i −0.684443 0.395163i
\(557\) −9.05269 + 15.6797i −0.383575 + 0.664371i −0.991570 0.129569i \(-0.958641\pi\)
0.607995 + 0.793941i \(0.291974\pi\)
\(558\) −3.30740 + 35.6984i −0.140014 + 1.51123i
\(559\) 2.87621 0.121651
\(560\) −9.06120 + 36.9200i −0.382906 + 1.56016i
\(561\) 16.1323 + 28.2837i 0.681105 + 1.19414i
\(562\) 0.121817 + 0.210993i 0.00513853 + 0.00890019i
\(563\) 12.5996 21.8232i 0.531011 0.919737i −0.468335 0.883551i \(-0.655146\pi\)
0.999345 0.0361860i \(-0.0115209\pi\)
\(564\) 21.1677 19.2972i 0.891322 0.812560i
\(565\) −12.1651 21.0706i −0.511790 0.886446i
\(566\) 54.4173i 2.28733i
\(567\) 2.33357 + 23.6971i 0.0980008 + 0.995186i
\(568\) 6.97806i 0.292793i
\(569\) −5.47239 9.47846i −0.229415 0.397358i 0.728220 0.685343i \(-0.240348\pi\)
−0.957635 + 0.287986i \(0.907014\pi\)
\(570\) −4.10346 4.50122i −0.171875 0.188535i
\(571\) −13.1413 7.58714i −0.549946 0.317512i 0.199154 0.979968i \(-0.436181\pi\)
−0.749100 + 0.662456i \(0.769514\pi\)
\(572\) −1.38369 + 6.16294i −0.0578552 + 0.257686i
\(573\) 2.62070 + 0.833683i 0.109481 + 0.0348276i
\(574\) −35.6539 + 37.1933i −1.48817 + 1.55242i
\(575\) 21.7938i 0.908865i
\(576\) 1.08113 11.6692i 0.0450472 0.486216i
\(577\) −0.568986 + 0.985512i −0.0236872 + 0.0410274i −0.877626 0.479346i \(-0.840874\pi\)
0.853939 + 0.520373i \(0.174207\pi\)
\(578\) 14.2123 24.6164i 0.591152 1.02391i
\(579\) 4.82164 + 22.0155i 0.200380 + 0.914932i
\(580\) 6.88663i 0.285952i
\(581\) 11.5735 + 39.8089i 0.480150 + 1.65155i
\(582\) −9.07293 + 28.5209i −0.376085 + 1.18223i
\(583\) −2.16492 + 9.64251i −0.0896619 + 0.399352i
\(584\) −0.896215 0.517430i −0.0370856 0.0214114i
\(585\) −10.3270 + 4.75135i −0.426967 + 0.196444i
\(586\) 4.50027 + 7.79470i 0.185904 + 0.321996i
\(587\) 21.1025i 0.870991i −0.900191 0.435496i \(-0.856573\pi\)
0.900191 0.435496i \(-0.143427\pi\)
\(588\) 13.1726 13.0693i 0.543229 0.538971i
\(589\) 3.90906i 0.161070i
\(590\) −17.7781 30.7925i −0.731911 1.26771i
\(591\) 0.133629 + 0.146582i 0.00549676 + 0.00602957i
\(592\) 14.9028 25.8124i 0.612502 1.06089i
\(593\) 17.5906 + 30.4678i 0.722359 + 1.25116i 0.960052 + 0.279823i \(0.0902757\pi\)
−0.237692 + 0.971341i \(0.576391\pi\)
\(594\) 3.15649 32.2271i 0.129512 1.32229i
\(595\) 43.8502 12.7484i 1.79768 0.522635i
\(596\) −32.8969 −1.34751
\(597\) −40.3544 + 8.83806i −1.65159 + 0.361718i
\(598\) 5.96310 10.3284i 0.243849 0.422359i
\(599\) −5.52855 3.19191i −0.225890 0.130418i 0.382784 0.923838i \(-0.374965\pi\)
−0.608675 + 0.793420i \(0.708299\pi\)
\(600\) 6.37759 1.39676i 0.260364 0.0570226i
\(601\) 10.8370i 0.442050i −0.975268 0.221025i \(-0.929060\pi\)
0.975268 0.221025i \(-0.0709402\pi\)
\(602\) 8.29489 + 7.95158i 0.338075 + 0.324082i
\(603\) 11.3500 + 8.03424i 0.462207 + 0.327179i
\(604\) 30.4312 17.5694i 1.23823 0.714890i
\(605\) 14.3192 30.2811i 0.582157 1.23110i
\(606\) −24.1219 26.4601i −0.979887 1.07487i
\(607\) −19.0804 + 11.0161i −0.774450 + 0.447129i −0.834460 0.551069i \(-0.814220\pi\)
0.0600101 + 0.998198i \(0.480887\pi\)
\(608\) 4.36477i 0.177015i
\(609\) 3.53169 5.77766i 0.143111 0.234122i
\(610\) −54.4958 −2.20647
\(611\) 6.72289 + 11.6444i 0.271979 + 0.471082i
\(612\) −23.6425 + 10.8777i −0.955691 + 0.439705i
\(613\) −2.01225 1.16177i −0.0812739 0.0469235i 0.458812 0.888533i \(-0.348275\pi\)
−0.540086 + 0.841610i \(0.681608\pi\)
\(614\) 23.8832 13.7890i 0.963849 0.556478i
\(615\) 52.0905 + 16.5707i 2.10049 + 0.668197i
\(616\) 6.45126 4.27914i 0.259929 0.172412i
\(617\) 6.99701i 0.281689i −0.990032 0.140845i \(-0.955018\pi\)
0.990032 0.140845i \(-0.0449818\pi\)
\(618\) 7.90466 1.73121i 0.317972 0.0696394i
\(619\) 6.40585 11.0953i 0.257473 0.445956i −0.708091 0.706121i \(-0.750444\pi\)
0.965564 + 0.260165i \(0.0837768\pi\)
\(620\) −25.6699 14.8205i −1.03093 0.595207i
\(621\) −10.3306 + 24.4085i −0.414552 + 0.979480i
\(622\) 28.7520i 1.15285i
\(623\) −2.63661 2.52748i −0.105634 0.101262i
\(624\) 9.69139 + 3.08297i 0.387966 + 0.123418i
\(625\) 14.0539 + 24.3421i 0.562157 + 0.973685i
\(626\) −18.6574 + 32.3156i −0.745700 + 1.29159i
\(627\) −0.0185329 + 3.53066i −0.000740132 + 0.141001i
\(628\) 8.68139 + 15.0366i 0.346425 + 0.600026i
\(629\) −35.8036 −1.42758
\(630\) −42.9182 14.8472i −1.70990 0.591528i
\(631\) −40.1391 −1.59791 −0.798957 0.601388i \(-0.794615\pi\)
−0.798957 + 0.601388i \(0.794615\pi\)
\(632\) −2.94852 + 1.70233i −0.117286 + 0.0677149i
\(633\) −7.36624 + 6.71532i −0.292782 + 0.266910i
\(634\) −29.3444 16.9420i −1.16542 0.672853i
\(635\) 18.1593 + 31.4529i 0.720631 + 1.24817i
\(636\) −7.52709 2.39448i −0.298468 0.0949472i
\(637\) 4.67003 + 7.35280i 0.185033 + 0.291328i
\(638\) −6.23946 + 6.77251i −0.247023 + 0.268126i
\(639\) 23.6278 + 2.18908i 0.934702 + 0.0865988i
\(640\) −18.0993 10.4496i −0.715438 0.413058i
\(641\) 42.8336 + 24.7300i 1.69183 + 0.976776i 0.953045 + 0.302830i \(0.0979314\pi\)
0.738781 + 0.673946i \(0.235402\pi\)
\(642\) 43.8552 9.60479i 1.73083 0.379071i
\(643\) −9.38943 −0.370283 −0.185141 0.982712i \(-0.559274\pi\)
−0.185141 + 0.982712i \(0.559274\pi\)
\(644\) 19.8334 5.76609i 0.781544 0.227216i
\(645\) 3.69563 11.6173i 0.145515 0.457430i
\(646\) 5.66883 3.27290i 0.223037 0.128770i
\(647\) −26.9444 15.5564i −1.05929 0.611584i −0.134058 0.990974i \(-0.542801\pi\)
−0.925237 + 0.379390i \(0.876134\pi\)
\(648\) −7.80482 1.45873i −0.306602 0.0573044i
\(649\) −4.51509 + 20.1101i −0.177233 + 0.789390i
\(650\) 9.98975i 0.391830i
\(651\) −13.9358 25.5983i −0.546186 1.00328i
\(652\) −20.8021 −0.814675
\(653\) 40.2088 23.2146i 1.57349 0.908456i 0.577756 0.816210i \(-0.303929\pi\)
0.995736 0.0922467i \(-0.0294048\pi\)
\(654\) 8.31171 7.57724i 0.325014 0.296294i
\(655\) −8.15442 4.70796i −0.318620 0.183955i
\(656\) −24.4519 42.3519i −0.954685 1.65356i
\(657\) 2.03318 2.87227i 0.0793218 0.112058i
\(658\) −12.8035 + 52.1682i −0.499133 + 2.03373i
\(659\) 0.495294 0.0192939 0.00964695 0.999953i \(-0.496929\pi\)
0.00964695 + 0.999953i \(0.496929\pi\)
\(660\) 23.1148 + 13.5076i 0.899743 + 0.525783i
\(661\) 20.7038 35.8600i 0.805283 1.39479i −0.110816 0.993841i \(-0.535346\pi\)
0.916100 0.400951i \(-0.131320\pi\)
\(662\) 15.9832 27.6837i 0.621204 1.07596i
\(663\) −2.61360 11.9336i −0.101504 0.463464i
\(664\) −13.8238 −0.536466
\(665\) 4.80899 + 1.18026i 0.186485 + 0.0457686i
\(666\) 29.0618 + 20.5718i 1.12612 + 0.797141i
\(667\) 6.52756 3.76869i 0.252748 0.145924i
\(668\) −5.03450 + 8.72000i −0.194791 + 0.337387i
\(669\) −12.7318 13.9659i −0.492240 0.539953i
\(670\) −22.9680 + 13.2606i −0.887330 + 0.512300i
\(671\) 23.2327 + 21.4041i 0.896888 + 0.826296i
\(672\) 15.5604 + 28.5825i 0.600255 + 1.10260i
\(673\) 16.3937i 0.631930i 0.948771 + 0.315965i \(0.102328\pi\)
−0.948771 + 0.315965i \(0.897672\pi\)
\(674\) 38.0936 21.9933i 1.46731 0.847151i
\(675\) 2.72875 + 22.0328i 0.105030 + 0.848042i
\(676\) −8.76317 + 15.1783i −0.337045 + 0.583779i
\(677\) 3.90912 + 6.77079i 0.150239 + 0.260222i 0.931315 0.364214i \(-0.118662\pi\)
−0.781076 + 0.624436i \(0.785329\pi\)
\(678\) −24.7793 7.88267i −0.951645 0.302732i
\(679\) −6.79258 23.3641i −0.260675 0.896632i
\(680\) 15.2271i 0.583934i
\(681\) 13.7012 3.00073i 0.525033 0.114988i
\(682\) 11.8168 + 37.8326i 0.452488 + 1.44868i
\(683\) −25.9035 14.9554i −0.991171 0.572253i −0.0855471 0.996334i \(-0.527264\pi\)
−0.905624 + 0.424081i \(0.860597\pi\)
\(684\) −2.80994 0.260336i −0.107441 0.00995421i
\(685\) 9.43266 0.360403
\(686\) −6.85934 + 34.1160i −0.261891 + 1.30256i
\(687\) 0.475118 1.49354i 0.0181269 0.0569822i
\(688\) −9.44537 + 5.45329i −0.360101 + 0.207905i
\(689\) 1.85391 3.21106i 0.0706283 0.122332i
\(690\) −34.0554 37.3564i −1.29647 1.42213i
\(691\) −8.58042 14.8617i −0.326415 0.565367i 0.655383 0.755297i \(-0.272507\pi\)
−0.981798 + 0.189930i \(0.939174\pi\)
\(692\) −3.50763 −0.133340
\(693\) 12.4654 + 23.1865i 0.473523 + 0.880782i
\(694\) −43.1594 −1.63831
\(695\) −18.5391 32.1107i −0.703229 1.21803i
\(696\) 1.52119 + 1.66864i 0.0576606 + 0.0632497i
\(697\) −29.3724 + 50.8746i −1.11256 + 1.92701i
\(698\) −16.3017 + 9.41180i −0.617029 + 0.356242i
\(699\) −0.209090 + 0.657278i −0.00790851 + 0.0248606i
\(700\) 11.9724 12.4893i 0.452513 0.472051i
\(701\) −26.0963 −0.985644 −0.492822 0.870130i \(-0.664035\pi\)
−0.492822 + 0.870130i \(0.664035\pi\)
\(702\) −4.73529 + 11.1883i −0.178722 + 0.422274i
\(703\) −3.36218 1.94116i −0.126807 0.0732122i
\(704\) −3.86270 12.3668i −0.145581 0.466092i
\(705\) 55.6710 12.1926i 2.09669 0.459199i
\(706\) 9.95083i 0.374505i
\(707\) 28.2693 + 6.93809i 1.06318 + 0.260934i
\(708\) −15.6982 4.99384i −0.589976 0.187680i
\(709\) −17.8611 30.9363i −0.670786 1.16184i −0.977681 0.210093i \(-0.932623\pi\)
0.306895 0.951743i \(-0.400710\pi\)
\(710\) −22.6280 + 39.1928i −0.849213 + 1.47088i
\(711\) −4.83913 10.5178i −0.181481 0.394447i
\(712\) 1.05471 0.608938i 0.0395270 0.0228209i
\(713\) 32.4420i 1.21496i
\(714\) 25.4542 41.6418i 0.952601 1.55840i
\(715\) −8.51525 + 9.24272i −0.318452 + 0.345658i
\(716\) 18.7823 10.8440i 0.701928 0.405258i
\(717\) −22.0317 24.1672i −0.822787 0.902541i
\(718\) −5.62161 + 9.73692i −0.209797 + 0.363378i
\(719\) −15.2790 + 8.82134i −0.569811 + 0.328980i −0.757074 0.653329i \(-0.773372\pi\)
0.187263 + 0.982310i \(0.440038\pi\)
\(720\) 24.9048 35.1831i 0.928149 1.31120i
\(721\) −4.55240 + 4.74896i −0.169540 + 0.176860i
\(722\) −34.9904 −1.30221
\(723\) 1.12092 + 5.11808i 0.0416873 + 0.190343i
\(724\) −6.99234 + 12.1111i −0.259868 + 0.450105i
\(725\) 3.15677 5.46768i 0.117239 0.203065i
\(726\) −10.4935 34.2264i −0.389452 1.27026i
\(727\) −9.23458 −0.342492 −0.171246 0.985228i \(-0.554779\pi\)
−0.171246 + 0.985228i \(0.554779\pi\)
\(728\) −2.78902 + 0.810843i −0.103368 + 0.0300518i
\(729\) 7.38773 25.9696i 0.273620 0.961838i
\(730\) 3.35577 + 5.81237i 0.124203 + 0.215125i
\(731\) 11.3461 + 6.55068i 0.419651 + 0.242286i
\(732\) −18.6586 + 17.0098i −0.689641 + 0.628701i
\(733\) −6.55078 + 3.78209i −0.241958 + 0.139695i −0.616077 0.787686i \(-0.711279\pi\)
0.374118 + 0.927381i \(0.377945\pi\)
\(734\) −36.9438 −1.36362
\(735\) 35.6991 9.41514i 1.31678 0.347282i
\(736\) 36.2240i 1.33523i
\(737\) 15.0000 + 3.36778i 0.552533 + 0.124054i
\(738\) 53.0728 24.4183i 1.95364 0.898852i
\(739\) −10.4826 6.05211i −0.385607 0.222631i 0.294648 0.955606i \(-0.404798\pi\)
−0.680255 + 0.732975i \(0.738131\pi\)
\(740\) −25.4943 + 14.7191i −0.937189 + 0.541086i
\(741\) 0.401571 1.26235i 0.0147521 0.0463735i
\(742\) 14.2239 4.13528i 0.522177 0.151811i
\(743\) −42.7206 −1.56727 −0.783633 0.621224i \(-0.786636\pi\)
−0.783633 + 0.621224i \(0.786636\pi\)
\(744\) 9.49359 2.07920i 0.348052 0.0762273i
\(745\) −56.6840 32.7265i −2.07674 1.19901i
\(746\) −31.5885 18.2377i −1.15654 0.667728i
\(747\) 4.33664 46.8075i 0.158670 1.71260i
\(748\) −19.4948 + 21.1602i −0.712799 + 0.773695i
\(749\) −25.2568 + 26.3473i −0.922865 + 0.962710i
\(750\) 6.86933 + 2.18524i 0.250833 + 0.0797935i
\(751\) 22.0949 + 38.2695i 0.806255 + 1.39647i 0.915441 + 0.402453i \(0.131842\pi\)
−0.109186 + 0.994021i \(0.534824\pi\)
\(752\) −44.1555 25.4932i −1.61018 0.929641i
\(753\) −9.98736 + 9.10482i −0.363960 + 0.331798i
\(754\) 2.99207 1.72747i 0.108965 0.0629109i
\(755\) 69.9138 2.54442
\(756\) −19.3289 + 8.31260i −0.702984 + 0.302326i
\(757\) 41.7862 1.51875 0.759373 0.650656i \(-0.225506\pi\)
0.759373 + 0.650656i \(0.225506\pi\)
\(758\) 2.61467 + 4.52875i 0.0949692 + 0.164491i
\(759\) −0.153808 + 29.3016i −0.00558287 + 1.06358i
\(760\) −0.825567 + 1.42992i −0.0299465 + 0.0518688i
\(761\) 19.0611 + 33.0148i 0.690965 + 1.19679i 0.971522 + 0.236950i \(0.0761477\pi\)
−0.280556 + 0.959838i \(0.590519\pi\)
\(762\) 36.9891 + 11.7668i 1.33997 + 0.426265i
\(763\) −2.17941 + 8.88004i −0.0788999 + 0.321479i
\(764\) 2.43005i 0.0879161i
\(765\) −51.5593 4.77689i −1.86413 0.172709i
\(766\) −13.4602 7.77125i −0.486337 0.280787i
\(767\) 3.86645 6.69688i 0.139609 0.241810i
\(768\) −35.0378 + 7.67367i −1.26432 + 0.276900i
\(769\) 36.9953i 1.33408i −0.745020 0.667042i \(-0.767560\pi\)
0.745020 0.667042i \(-0.232440\pi\)
\(770\) −50.1101 + 3.11443i −1.80584 + 0.112236i
\(771\) 17.1998 + 5.47151i 0.619436 + 0.197052i
\(772\) −17.2464 + 9.95719i −0.620710 + 0.358367i
\(773\) 36.9288 + 21.3208i 1.32824 + 0.766857i 0.985027 0.172402i \(-0.0551527\pi\)
0.343209 + 0.939259i \(0.388486\pi\)
\(774\) −5.44581 11.8364i −0.195746 0.425450i
\(775\) −13.5872 23.5337i −0.488067 0.845356i
\(776\) 8.11327 0.291249
\(777\) −28.9374 0.725435i −1.03812 0.0260248i
\(778\) 36.3732i 1.30404i
\(779\) −5.51652 + 3.18496i −0.197650 + 0.114113i
\(780\) −6.76706 7.42300i −0.242300 0.265786i
\(781\) 25.0404 7.82121i 0.896015 0.279865i
\(782\) 47.0466 27.1624i 1.68238 0.971324i
\(783\) −6.12726 + 4.62731i −0.218970 + 0.165367i
\(784\) −29.2771 15.2919i −1.04561 0.546141i
\(785\) 34.5457i 1.23299i
\(786\) −9.83026 + 2.15294i −0.350634 + 0.0767928i
\(787\) 40.3211 + 23.2794i 1.43729 + 0.829820i 0.997661 0.0683592i \(-0.0217764\pi\)
0.439630 + 0.898179i \(0.355110\pi\)
\(788\) −0.0876332 + 0.151785i −0.00312180 + 0.00540712i
\(789\) 52.2977 11.4538i 1.86185 0.407766i
\(790\) 22.0808 0.785598
\(791\) 20.2990 5.90147i 0.721750 0.209832i
\(792\) −8.58447 + 1.83293i −0.305036 + 0.0651302i
\(793\) −5.92599 10.2641i −0.210438 0.364489i
\(794\) −13.1841 + 22.8356i −0.467888 + 0.810406i
\(795\) −10.5877 11.6140i −0.375507 0.411906i
\(796\) −18.2515 31.6126i −0.646908 1.12048i
\(797\) 43.3952i 1.53714i −0.639768 0.768568i \(-0.720970\pi\)
0.639768 0.768568i \(-0.279030\pi\)
\(798\) 4.64800 2.53038i 0.164538 0.0895745i
\(799\) 61.2466i 2.16675i
\(800\) 15.1712 + 26.2772i 0.536382 + 0.929040i
\(801\) 1.73100 + 3.76230i 0.0611620 + 0.132934i
\(802\) 20.9703 + 12.1072i 0.740487 + 0.427520i
\(803\) 0.852265 3.79597i 0.0300758 0.133957i
\(804\) −3.72488 + 11.7092i −0.131366 + 0.412953i
\(805\) 39.9107 + 9.79520i 1.40667 + 0.345235i
\(806\) 14.8706i 0.523795i
\(807\) 2.99739 + 13.6860i 0.105513 + 0.481770i
\(808\) −4.85304 + 8.40572i −0.170729 + 0.295712i
\(809\) 21.0777 36.5077i 0.741053 1.28354i −0.210963 0.977494i \(-0.567660\pi\)
0.952016 0.306048i \(-0.0990067\pi\)
\(810\) 39.1061 + 33.5020i 1.37405 + 1.17714i
\(811\) 37.2022i 1.30635i 0.757209 + 0.653173i \(0.226563\pi\)
−0.757209 + 0.653173i \(0.773437\pi\)
\(812\) 5.81104 + 1.42619i 0.203927 + 0.0500495i
\(813\) −22.6845 7.21626i −0.795579 0.253085i
\(814\) 38.4078 + 8.62326i 1.34619 + 0.302245i
\(815\) −35.8438 20.6944i −1.25555 0.724894i
\(816\) 31.2091 + 34.2343i 1.09254 + 1.19844i
\(817\) 0.710315 + 1.23030i 0.0248508 + 0.0430428i
\(818\) 13.3903i 0.468180i
\(819\) −1.87059 9.69803i −0.0653635 0.338876i
\(820\) 48.3010i 1.68674i
\(821\) −10.8482 18.7896i −0.378604 0.655761i 0.612256 0.790660i \(-0.290262\pi\)
−0.990859 + 0.134899i \(0.956929\pi\)
\(822\) 7.45001 6.79169i 0.259849 0.236887i
\(823\) 9.74375 16.8767i 0.339646 0.588284i −0.644720 0.764419i \(-0.723026\pi\)
0.984366 + 0.176135i \(0.0563595\pi\)
\(824\) −1.09680 1.89971i −0.0382087 0.0661794i
\(825\) 12.1604 + 21.3201i 0.423370 + 0.742270i
\(826\) 29.6649 8.62439i 1.03217 0.300081i
\(827\) 38.2080 1.32862 0.664311 0.747457i \(-0.268725\pi\)
0.664311 + 0.747457i \(0.268725\pi\)
\(828\) −23.3202 2.16058i −0.810432 0.0750853i
\(829\) −7.92313 + 13.7233i −0.275182 + 0.476629i −0.970181 0.242382i \(-0.922071\pi\)
0.694999 + 0.719010i \(0.255405\pi\)
\(830\) 77.6423 + 44.8268i 2.69500 + 1.55596i
\(831\) 10.1229 + 46.2208i 0.351159 + 1.60338i
\(832\) 4.86094i 0.168523i
\(833\) 1.67613 + 39.6416i 0.0580745 + 1.37350i
\(834\) −37.7627 12.0129i −1.30761 0.415971i
\(835\) −17.3497 + 10.0168i −0.600411 + 0.346647i
\(836\) −2.97792 + 0.930137i −0.102994 + 0.0321694i
\(837\) 4.06199 + 32.7977i 0.140403 + 1.13365i
\(838\) 45.2671 26.1350i 1.56372 0.902817i
\(839\) 20.1527i 0.695748i 0.937541 + 0.347874i \(0.113096\pi\)
−0.937541 + 0.347874i \(0.886904\pi\)
\(840\) −0.308525 + 12.3070i −0.0106451 + 0.424630i
\(841\) −26.8165 −0.924706
\(842\) −16.4692 28.5255i −0.567567 0.983055i
\(843\) 0.151303 + 0.165969i 0.00521116 + 0.00571628i
\(844\) −7.62773 4.40387i −0.262557 0.151587i
\(845\) −30.1993 + 17.4356i −1.03889 + 0.599802i
\(846\) 35.1907 49.7140i 1.20988 1.70920i
\(847\) 22.5862 + 18.3538i 0.776072 + 0.630644i
\(848\) 14.0600i 0.482823i
\(849\) 10.7318 + 49.0013i 0.368316 + 1.68172i
\(850\) 22.7520 39.4077i 0.780388 1.35167i
\(851\) −27.9034 16.1100i −0.956515 0.552244i
\(852\) 4.48578 + 20.4820i 0.153680 + 0.701700i
\(853\) 20.6654i 0.707570i 0.935327 + 0.353785i \(0.115106\pi\)
−0.935327 + 0.353785i \(0.884894\pi\)
\(854\) 11.2858 45.9844i 0.386194 1.57355i
\(855\) −4.58276 3.24396i −0.156727 0.110941i
\(856\) −6.08505 10.5396i −0.207983 0.360237i
\(857\) 2.12306 3.67725i 0.0725224 0.125612i −0.827484 0.561490i \(-0.810228\pi\)
0.900006 + 0.435877i \(0.143562\pi\)
\(858\) −0.0705017 + 13.4311i −0.00240689 + 0.458531i
\(859\) 11.1034 + 19.2317i 0.378844 + 0.656177i 0.990894 0.134642i \(-0.0429884\pi\)
−0.612050 + 0.790819i \(0.709655\pi\)
\(860\) 10.7721 0.367327
\(861\) −24.7703 + 40.5230i −0.844171 + 1.38102i
\(862\) 24.2677 0.826563
\(863\) 15.9992 9.23715i 0.544619 0.314436i −0.202330 0.979317i \(-0.564851\pi\)
0.746949 + 0.664881i \(0.231518\pi\)
\(864\) −4.53552 36.6212i −0.154302 1.24588i
\(865\) −6.04393 3.48946i −0.205500 0.118645i
\(866\) 6.57381 + 11.3862i 0.223387 + 0.386918i
\(867\) 7.94308 24.9692i 0.269761 0.847999i
\(868\) 17.8219 18.5914i 0.604915 0.631033i
\(869\) −9.41349 8.67257i −0.319331 0.294197i
\(870\) −3.13293 14.3049i −0.106216 0.484981i
\(871\) −4.99517 2.88396i −0.169255 0.0977194i
\(872\) −2.64042 1.52445i −0.0894160 0.0516244i
\(873\) −2.54521 + 27.4716i −0.0861422 + 0.929774i
\(874\) 5.89064 0.199254
\(875\) −5.62730 + 1.63601i −0.190237 + 0.0553071i
\(876\) 2.96319 + 0.942633i 0.100117 + 0.0318486i
\(877\) −13.8416 + 7.99143i −0.467396 + 0.269851i −0.715149 0.698972i \(-0.753641\pi\)
0.247753 + 0.968823i \(0.420308\pi\)
\(878\) 19.1297 + 11.0445i 0.645596 + 0.372735i
\(879\) 5.58959 + 6.13140i 0.188532 + 0.206807i
\(880\) 10.4396 46.4977i 0.351918 1.56744i
\(881\) 12.5797i 0.423819i 0.977289 + 0.211910i \(0.0679683\pi\)
−0.977289 + 0.211910i \(0.932032\pi\)
\(882\) 21.4165 33.1402i 0.721131 1.11589i
\(883\) 4.39614 0.147942 0.0739710 0.997260i \(-0.476433\pi\)
0.0739710 + 0.997260i \(0.476433\pi\)
\(884\) 9.34851 5.39736i 0.314424 0.181533i
\(885\) −22.0814 24.2217i −0.742257 0.814204i
\(886\) −15.5938 9.00311i −0.523885 0.302465i
\(887\) −4.55516 7.88976i −0.152947 0.264912i 0.779362 0.626573i \(-0.215543\pi\)
−0.932310 + 0.361661i \(0.882210\pi\)
\(888\) 2.92600 9.19793i 0.0981900 0.308662i
\(889\) −30.3011 + 8.80936i −1.01627 + 0.295456i
\(890\) −7.89850 −0.264758
\(891\) −3.51329 29.6421i −0.117700 0.993049i
\(892\) 8.34944 14.4617i 0.279560 0.484212i
\(893\) −3.32060 + 5.75145i −0.111120 + 0.192465i
\(894\) −68.3333 + 14.9658i −2.28541 + 0.500530i
\(895\) 43.1513 1.44239
\(896\) 12.5659 13.1084i 0.419796 0.437921i
\(897\) 3.33271 10.4764i 0.111276 0.349798i
\(898\) 48.9623 28.2684i 1.63389 0.943328i
\(899\) 4.69912 8.13912i 0.156724 0.271455i
\(900\) −17.8215 + 8.19954i −0.594052 + 0.273318i
\(901\) 14.6266 8.44469i 0.487284 0.281333i
\(902\) 43.7620 47.5007i 1.45711 1.58160i
\(903\) 9.03749 + 5.52431i 0.300749 + 0.183838i
\(904\) 7.04890i 0.234443i
\(905\) −24.0967 + 13.9123i −0.801003 + 0.462459i
\(906\) 55.2187 50.3392i 1.83452 1.67241i
\(907\) 15.1268 26.2004i 0.502278 0.869970i −0.497719 0.867338i \(-0.665829\pi\)
0.999997 0.00263193i \(-0.000837770\pi\)
\(908\) 6.19682 + 10.7332i 0.205649 + 0.356194i
\(909\) −26.9394 19.0694i −0.893525 0.632493i
\(910\) 18.2941 + 4.48988i 0.606443 + 0.148838i
\(911\) 19.0232i 0.630267i 0.949047 + 0.315134i \(0.102049\pi\)
−0.949047 + 0.315134i \(0.897951\pi\)
\(912\) 1.07466 + 4.90688i 0.0355856 + 0.162483i
\(913\) −15.4941 49.6058i −0.512779 1.64171i
\(914\) −66.6661 38.4897i −2.20512 1.27313i
\(915\) −49.0720 + 10.7473i −1.62227 + 0.355295i
\(916\) 1.38489 0.0457581
\(917\) 5.66139 5.90582i 0.186956 0.195027i
\(918\) −44.1615 + 33.3508i −1.45755 + 1.10074i
\(919\) 23.5991 13.6250i 0.778463 0.449446i −0.0574223 0.998350i \(-0.518288\pi\)
0.835885 + 0.548904i \(0.184955\pi\)
\(920\) −6.85153 + 11.8672i −0.225888 + 0.391250i
\(921\) 18.7868 17.1267i 0.619047 0.564344i
\(922\) −5.12899 8.88368i −0.168914 0.292568i
\(923\) −9.84246 −0.323968
\(924\) −16.1849 + 16.7072i −0.532444 + 0.549628i
\(925\) −26.9885 −0.887376
\(926\) 6.05063 + 10.4800i 0.198836 + 0.344394i
\(927\) 6.77651 3.11781i 0.222570 0.102402i
\(928\) −5.24693 + 9.08796i −0.172239 + 0.298327i
\(929\) 16.4471 9.49571i 0.539610 0.311544i −0.205311 0.978697i \(-0.565820\pi\)
0.744921 + 0.667153i \(0.232487\pi\)
\(930\) −60.0638 19.1072i −1.96957 0.626549i
\(931\) −1.99184 + 3.81347i −0.0652800 + 0.124982i
\(932\) −0.609463 −0.0199636
\(933\) −5.67028 25.8904i −0.185637 0.847613i
\(934\) 4.88479 + 2.82023i 0.159835 + 0.0922809i
\(935\) −54.6417 + 17.0670i −1.78697 + 0.558151i
\(936\) 3.27934 + 0.303826i 0.107189 + 0.00993087i
\(937\) 33.4823i 1.09382i −0.837192 0.546909i \(-0.815804\pi\)
0.837192 0.546909i \(-0.184196\pi\)
\(938\) −6.43289 22.1269i −0.210041 0.722469i
\(939\) −10.4274 + 32.7788i −0.340286 + 1.06970i
\(940\) 25.1790 + 43.6112i 0.821247 + 1.42244i
\(941\) 10.3259 17.8849i 0.336613 0.583031i −0.647180 0.762337i \(-0.724052\pi\)
0.983793 + 0.179306i \(0.0573852\pi\)
\(942\) 24.8735 + 27.2846i 0.810424 + 0.888979i
\(943\) −45.7826 + 26.4326i −1.49089 + 0.860763i
\(944\) 29.3231i 0.954385i
\(945\) −41.5747 4.90547i −1.35243 0.159575i
\(946\) −10.5937 9.75985i −0.344429 0.317320i
\(947\) −34.0101 + 19.6358i −1.10518 + 0.638077i −0.937577 0.347778i \(-0.886936\pi\)
−0.167604 + 0.985854i \(0.553603\pi\)
\(948\) 7.56014 6.89208i 0.245542 0.223844i
\(949\) −0.729828 + 1.26410i −0.0236912 + 0.0410344i
\(950\) 4.27312 2.46709i 0.138638 0.0800429i
\(951\) −29.7650 9.46870i −0.965198 0.307043i
\(952\) −12.8489 3.15347i −0.416434 0.102205i
\(953\) 7.71381 0.249875 0.124937 0.992165i \(-0.460127\pi\)
0.124937 + 0.992165i \(0.460127\pi\)
\(954\) −16.7246 1.54951i −0.541478 0.0501671i
\(955\) −2.41746 + 4.18717i −0.0782273 + 0.135494i
\(956\) 14.4482 25.0251i 0.467290 0.809369i
\(957\) −4.28283 + 7.32897i −0.138444 + 0.236912i
\(958\) −40.4118 −1.30565
\(959\) −1.95346 + 7.95941i −0.0630806 + 0.257023i
\(960\) 19.6338 + 6.24580i 0.633679 + 0.201582i
\(961\) −4.72573 8.18520i −0.152443 0.264039i
\(962\) −12.7902 7.38443i −0.412373 0.238084i
\(963\) 37.5962 17.2977i 1.21152 0.557410i
\(964\) −4.00937 + 2.31481i −0.129133 + 0.0745551i
\(965\) −39.6225 −1.27549
\(966\) 38.5746 21.0001i 1.24112 0.675667i
\(967\) 15.1529i 0.487283i 0.969865 + 0.243642i \(0.0783421\pi\)
−0.969865 + 0.243642i \(0.921658\pi\)
\(968\) −7.97922 + 5.52337i −0.256462 + 0.177528i
\(969\) 4.45916 4.06513i 0.143249 0.130591i
\(970\) −45.5688 26.3091i −1.46313 0.844736i
\(971\) 24.0452 13.8825i 0.771648 0.445511i −0.0618141 0.998088i \(-0.519689\pi\)
0.833462 + 0.552576i \(0.186355\pi\)
\(972\) 23.8464 0.735596i 0.764873 0.0235943i
\(973\) 30.9349 8.99360i 0.991726 0.288321i
\(974\) 62.5013 2.00267
\(975\) −1.97011 8.99550i −0.0630942 0.288086i
\(976\) 38.9215 + 22.4713i 1.24585 + 0.719289i
\(977\) 44.2071 + 25.5230i 1.41431 + 0.816553i 0.995791 0.0916549i \(-0.0292157\pi\)
0.418520 + 0.908208i \(0.362549\pi\)
\(978\) −43.2101 + 9.46351i −1.38171 + 0.302610i
\(979\) 3.36729 + 3.10226i 0.107619 + 0.0991487i
\(980\) 17.4905 + 27.5381i 0.558713 + 0.879673i
\(981\) 5.99014 8.46228i 0.191250 0.270180i
\(982\) 3.53298 + 6.11929i 0.112742 + 0.195275i
\(983\) 9.49000 + 5.47905i 0.302684 + 0.174755i 0.643648 0.765322i \(-0.277420\pi\)
−0.340964 + 0.940076i \(0.610753\pi\)
\(984\) −10.6692 11.7034i −0.340123 0.373092i
\(985\) −0.301998 + 0.174359i −0.00962246 + 0.00555553i
\(986\) 15.7375 0.501185
\(987\) −1.24095 + 49.5010i −0.0394998 + 1.57564i
\(988\) 1.17051 0.0372390
\(989\) 5.89503 + 10.2105i 0.187451 + 0.324675i
\(990\) 54.1590 + 17.5424i 1.72129 + 0.557533i
\(991\) 9.46591 16.3954i 0.300695 0.520818i −0.675599 0.737269i \(-0.736115\pi\)
0.976293 + 0.216451i \(0.0694482\pi\)
\(992\) 22.5836 + 39.1159i 0.717030 + 1.24193i
\(993\) 8.93282 28.0805i 0.283475 0.891108i
\(994\) −28.3853 27.2105i −0.900328 0.863064i
\(995\) 72.6280i 2.30246i
\(996\) 40.5754 8.88648i 1.28568 0.281579i
\(997\) −24.8780 14.3633i −0.787895 0.454891i 0.0513262 0.998682i \(-0.483655\pi\)
−0.839221 + 0.543791i \(0.816989\pi\)
\(998\) 1.90461 3.29888i 0.0602893 0.104424i
\(999\) 30.2264 + 12.7929i 0.956322 + 0.404751i
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 231.2.l.b.32.20 yes 48
3.2 odd 2 inner 231.2.l.b.32.5 48
7.2 even 3 inner 231.2.l.b.65.19 yes 48
11.10 odd 2 inner 231.2.l.b.32.6 yes 48
21.2 odd 6 inner 231.2.l.b.65.6 yes 48
33.32 even 2 inner 231.2.l.b.32.19 yes 48
77.65 odd 6 inner 231.2.l.b.65.5 yes 48
231.65 even 6 inner 231.2.l.b.65.20 yes 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
231.2.l.b.32.5 48 3.2 odd 2 inner
231.2.l.b.32.6 yes 48 11.10 odd 2 inner
231.2.l.b.32.19 yes 48 33.32 even 2 inner
231.2.l.b.32.20 yes 48 1.1 even 1 trivial
231.2.l.b.65.5 yes 48 77.65 odd 6 inner
231.2.l.b.65.6 yes 48 21.2 odd 6 inner
231.2.l.b.65.19 yes 48 7.2 even 3 inner
231.2.l.b.65.20 yes 48 231.65 even 6 inner