Properties

Label 231.2.l.b.32.19
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 32.19
Character \(\chi\) \(=\) 231.32
Dual form 231.2.l.b.65.19

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.939478 + 1.62722i) q^{2} +(-1.69195 - 0.370556i) q^{3} +(-0.765237 + 1.32543i) q^{4} +(2.63713 - 1.52255i) q^{5} +(-0.986571 - 3.10131i) q^{6} +(0.738610 + 2.54056i) q^{7} +0.882219 q^{8} +(2.72538 + 1.25392i) q^{9} +O(q^{10})\) \(q+(0.939478 + 1.62722i) q^{2} +(-1.69195 - 0.370556i) 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} +(2.72538 + 1.25392i) q^{9} +(4.95505 + 2.86080i) q^{10} +(-3.23606 + 0.726556i) q^{11} +(1.78589 - 1.95899i) 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} +(0.520020 + 5.61283i) q^{18} +(-0.532275 + 0.307309i) q^{19} +4.66044i q^{20} +(-0.308270 - 4.57220i) q^{21} +(-4.22248 - 4.58322i) q^{22} +(-4.41744 + 2.55041i) q^{23} +(-1.49267 - 0.326911i) 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} +(-7.32360 - 6.67645i) q^{30} +(3.18007 - 5.50805i) q^{31} +(-3.55080 + 6.15016i) q^{32} +(5.74448 - 0.0301535i) 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} +(0.461104 - 2.10539i) q^{39} +(2.32653 - 1.34322i) q^{40} -10.3640 q^{41} +(7.15037 - 4.79710i) q^{42} -2.31140i q^{43} +(1.51336 - 4.84516i) q^{44} +(9.09633 - 0.842761i) 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} +(-6.61407 + 7.25518i) q^{51} +(-1.64931 - 0.952228i) q^{52} +(-2.58050 - 1.48985i) q^{53} +(1.20002 - 9.68931i) 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} +(1.72695 - 7.88522i) q^{60} +(-8.24852 + 4.76229i) q^{61} +11.9504 q^{62} +(-1.17268 + 7.85015i) q^{63} -3.90639 q^{64} +(1.89459 + 3.28153i) q^{65} +(5.44588 + 9.31923i) 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} +(2.40438 + 1.10623i) q^{72} +(1.01586 + 0.586510i) q^{73} +(5.93434 - 10.2786i) q^{74} +(-4.98564 + 5.46890i) q^{75} -0.940657i q^{76} +(-4.23605 - 7.68478i) q^{77} +(3.85913 - 1.22765i) q^{78} +(3.34216 - 1.92960i) q^{79} +(12.4436 + 7.18429i) q^{80} +(5.85536 + 6.83482i) q^{81} +(-9.73679 - 16.8646i) q^{82} -15.6693 q^{83} +(6.29602 + 3.09022i) q^{84} -17.2600i q^{85} +(3.76117 - 2.17151i) q^{86} +(-2.50015 - 0.547562i) q^{87} +(-2.85492 + 0.640982i) q^{88} +(-1.19552 + 0.690235i) q^{89} +(9.91716 + 14.0100i) q^{90} +(-3.16137 + 0.919095i) q^{91} -7.80668i q^{92} +(-7.42156 + 8.14094i) q^{93} +(17.5828 + 10.1514i) q^{94} +(-0.935785 + 1.62083i) q^{95} +(8.28675 - 9.08999i) 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 \(0.602058\pi\)
\(3\) −1.69195 0.370556i −0.976847 0.213940i
\(4\) −0.765237 + 1.32543i −0.382618 + 0.662715i
\(5\) 2.63713 1.52255i 1.17936 0.680904i 0.223494 0.974705i \(-0.428254\pi\)
0.955867 + 0.293801i \(0.0949204\pi\)
\(6\) −0.986571 3.10131i −0.402766 1.26610i
\(7\) 0.738610 + 2.54056i 0.279168 + 0.960242i
\(8\) 0.882219 0.311911
\(9\) 2.72538 + 1.25392i 0.908459 + 0.417974i
\(10\) 4.95505 + 2.86080i 1.56692 + 0.904664i
\(11\) −3.23606 + 0.726556i −0.975710 + 0.219065i
\(12\) 1.78589 1.95899i 0.515541 0.565513i
\(13\) 1.24436i 0.345123i 0.984999 + 0.172561i \(0.0552043\pi\)
−0.984999 + 0.172561i \(0.944796\pi\)
\(14\) −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 \(-0.0745653\pi\)
\(18\) 0.520020 + 5.61283i 0.122570 + 1.32296i
\(19\) −0.532275 + 0.307309i −0.122112 + 0.0705015i −0.559812 0.828620i \(-0.689127\pi\)
0.437700 + 0.899121i \(0.355793\pi\)
\(20\) 4.66044i 1.04211i
\(21\) −0.308270 4.57220i −0.0672700 0.997735i
\(22\) −4.22248 4.58322i −0.900236 0.977145i
\(23\) −4.41744 + 2.55041i −0.921101 + 0.531798i −0.883986 0.467513i \(-0.845150\pi\)
−0.0371147 + 0.999311i \(0.511817\pi\)
\(24\) −1.49267 0.326911i −0.304690 0.0667305i
\(25\) 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 \(0.456190\pi\)
\(30\) −7.32360 6.67645i −1.33710 1.21895i
\(31\) 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
\(33\) 5.74448 0.0301535i 0.999986 0.00524905i
\(34\) 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
\(39\) 0.461104 2.10539i 0.0738357 0.337132i
\(40\) 2.32653 1.34322i 0.367856 0.212382i
\(41\) −10.3640 −1.61859 −0.809296 0.587401i \(-0.800151\pi\)
−0.809296 + 0.587401i \(0.800151\pi\)
\(42\) 7.15037 4.79710i 1.10333 0.740209i
\(43\) 2.31140i 0.352486i −0.984347 0.176243i \(-0.943606\pi\)
0.984347 0.176243i \(-0.0563944\pi\)
\(44\) 1.51336 4.84516i 0.228147 0.730436i
\(45\) 9.09633 0.842761i 1.35600 0.125631i
\(46\) −8.30018 4.79211i −1.22379 0.706558i
\(47\) 9.35776 5.40270i 1.36497 0.788065i 0.374689 0.927151i \(-0.377750\pi\)
0.990280 + 0.139086i \(0.0444163\pi\)
\(48\) −2.47756 7.78827i −0.357605 1.12414i
\(49\) −5.90891 + 3.75297i −0.844130 + 0.536138i
\(50\) 8.02804 1.13534
\(51\) −6.61407 + 7.25518i −0.926155 + 1.01593i
\(52\) −1.64931 0.952228i −0.228718 0.132050i
\(53\) −2.58050 1.48985i −0.354459 0.204647i 0.312189 0.950020i \(-0.398938\pi\)
−0.666647 + 0.745373i \(0.732271\pi\)
\(54\) 1.20002 9.68931i 0.163302 1.31855i
\(55\) −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 0.106939 0.994266i \(-0.465895\pi\)
−0.807590 + 0.589745i \(0.799228\pi\)
\(60\) 1.72695 7.88522i 0.222949 1.01798i
\(61\) −8.24852 + 4.76229i −1.05612 + 0.609749i −0.924355 0.381533i \(-0.875396\pi\)
−0.131760 + 0.991282i \(0.542063\pi\)
\(62\) 11.9504 1.51771
\(63\) −1.17268 + 7.85015i −0.147743 + 0.989026i
\(64\) −3.90639 −0.488299
\(65\) 1.89459 + 3.28153i 0.234995 + 0.407024i
\(66\) 5.44588 + 9.31923i 0.670342 + 1.14712i
\(67\) 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 \(0.155513\pi\)
−0.883011 + 0.469353i \(0.844487\pi\)
\(72\) 2.40438 + 1.10623i 0.283359 + 0.130371i
\(73\) 1.01586 + 0.586510i 0.118898 + 0.0686458i 0.558270 0.829660i \(-0.311466\pi\)
−0.439372 + 0.898305i \(0.644799\pi\)
\(74\) 5.93434 10.2786i 0.689853 1.19486i
\(75\) −4.98564 + 5.46890i −0.575692 + 0.631495i
\(76\) 0.940657i 0.107901i
\(77\) −4.23605 7.68478i −0.482743 0.875762i
\(78\) 3.85913 1.22765i 0.436961 0.139004i
\(79\) 3.34216 1.92960i 0.376022 0.217097i −0.300064 0.953919i \(-0.597008\pi\)
0.676086 + 0.736822i \(0.263675\pi\)
\(80\) 12.4436 + 7.18429i 1.39123 + 0.803228i
\(81\) 5.85536 + 6.83482i 0.650595 + 0.759424i
\(82\) −9.73679 16.8646i −1.07525 1.86238i
\(83\) −15.6693 −1.71993 −0.859966 0.510352i \(-0.829515\pi\)
−0.859966 + 0.510352i \(0.829515\pi\)
\(84\) 6.29602 + 3.09022i 0.686952 + 0.337171i
\(85\) 17.2600i 1.87211i
\(86\) 3.76117 2.17151i 0.405577 0.234160i
\(87\) −2.50015 0.547562i −0.268045 0.0587048i
\(88\) −2.85492 + 0.640982i −0.304335 + 0.0683289i
\(89\) −1.19552 + 0.690235i −0.126725 + 0.0731648i −0.562022 0.827122i \(-0.689977\pi\)
0.435297 + 0.900287i \(0.356643\pi\)
\(90\) 9.91716 + 14.0100i 1.04536 + 1.47678i
\(91\) −3.16137 + 0.919095i −0.331401 + 0.0963473i
\(92\) 7.80668i 0.813903i
\(93\) −7.42156 + 8.14094i −0.769580 + 0.844176i
\(94\) 17.5828 + 10.1514i 1.81353 + 1.04704i
\(95\) −0.935785 + 1.62083i −0.0960095 + 0.166293i
\(96\) 8.28675 9.08999i 0.845762 0.927743i
\(97\) 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 \(0.982298\pi\)
\(102\) −18.0196 3.94649i −1.78420 0.390761i
\(103\) −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
\(105\) −7.77433 11.5881i −0.758697 1.13088i
\(106\) 5.59873i 0.543797i
\(107\) −6.89744 11.9467i −0.666800 1.15493i −0.978794 0.204848i \(-0.934330\pi\)
0.311994 0.950084i \(-0.399003\pi\)
\(108\) 7.32364 3.09964i 0.704718 0.298263i
\(109\) 2.99294 + 1.72797i 0.286671 + 0.165510i 0.636440 0.771326i \(-0.280406\pi\)
−0.349768 + 0.936836i \(0.613740\pi\)
\(110\) −18.1134 5.65761i −1.72704 0.539432i
\(111\) 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 \(-0.877362\pi\)
0.926694 0.375817i \(-0.122638\pi\)
\(114\) 1.47819 + 1.34757i 0.138445 + 0.126211i
\(115\) −7.76625 + 13.4515i −0.724207 + 1.25436i
\(116\) −1.13077 + 1.95856i −0.104990 + 0.181847i
\(117\) −1.56033 + 3.39134i −0.144252 + 0.313530i
\(118\) 11.6765i 1.07491i
\(119\) 14.5643 + 3.57448i 1.33510 + 0.327672i
\(120\) −4.43410 + 1.41055i −0.404776 + 0.128765i
\(121\) 9.94423 4.70237i 0.904021 0.427488i
\(122\) −15.4986 8.94813i −1.40318 0.810125i
\(123\) 17.5354 + 3.84046i 1.58112 + 0.346282i
\(124\) 4.86702 + 8.42992i 0.437071 + 0.757029i
\(125\) 2.21498i 0.198114i
\(126\) −13.8756 + 5.46683i −1.23614 + 0.487024i
\(127\) 11.9269i 1.05834i 0.848514 + 0.529172i \(0.177498\pi\)
−0.848514 + 0.529172i \(0.822502\pi\)
\(128\) 3.43163 + 5.94376i 0.303316 + 0.525359i
\(129\) −0.856503 + 3.91077i −0.0754109 + 0.344324i
\(130\) −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
\(135\) −15.7028 1.94479i −1.35148 0.167381i
\(136\) 2.50027 4.33060i 0.214396 0.371346i
\(137\) 2.68265 + 1.54883i 0.229194 + 0.132325i 0.610200 0.792247i \(-0.291089\pi\)
−0.381006 + 0.924573i \(0.624422\pi\)
\(138\) 12.2677 + 11.1837i 1.04430 + 0.952018i
\(139\) 12.1764i 1.03279i −0.856351 0.516394i \(-0.827274\pi\)
0.856351 0.516394i \(-0.172726\pi\)
\(140\) −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
\(143\) −0.904096 4.02682i −0.0756043 0.336740i
\(144\) 1.30592 + 14.0954i 0.108827 + 1.17462i
\(145\) 3.89683 2.24983i 0.323614 0.186839i
\(146\) 2.20405i 0.182409i
\(147\) 11.3883 4.16025i 0.939287 0.343131i
\(148\) 9.66744 0.794659
\(149\) 10.7473 + 18.6148i 0.880452 + 1.52499i 0.850840 + 0.525425i \(0.176094\pi\)
0.0296119 + 0.999561i \(0.490573\pi\)
\(150\) −13.5830 2.97484i −1.10905 0.242894i
\(151\) 19.8835 + 11.4797i 1.61810 + 0.934208i 0.987412 + 0.158168i \(0.0505587\pi\)
0.630683 + 0.776040i \(0.282775\pi\)
\(152\) −0.469583 + 0.271114i −0.0380882 + 0.0219902i
\(153\) 13.8791 9.82450i 1.12206 0.794264i
\(154\) 8.52518 14.1127i 0.686979 1.13723i
\(155\) 19.3673i 1.55562i
\(156\) 2.43769 + 2.22228i 0.195171 + 0.177925i
\(157\) 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
\(159\) 3.81400 + 3.47697i 0.302470 + 0.275742i
\(160\) 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
\(165\) 15.1030 8.82577i 1.17577 0.687085i
\(166\) −14.7210 25.4975i −1.14257 1.97899i
\(167\) 6.57900 0.509099 0.254549 0.967060i \(-0.418073\pi\)
0.254549 + 0.967060i \(0.418073\pi\)
\(168\) −0.271962 4.03368i −0.0209823 0.311205i
\(169\) 11.4516 0.880890
\(170\) 28.0859 16.2154i 2.15409 1.24367i
\(171\) −1.83599 + 0.170102i −0.140402 + 0.0130080i
\(172\) 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
\(177\) 7.95434 + 7.25145i 0.597885 + 0.545052i
\(178\) −2.24633 1.29692i −0.168370 0.0972083i
\(179\) 12.2722 + 7.08537i 0.917269 + 0.529585i 0.882763 0.469819i \(-0.155681\pi\)
0.0345062 + 0.999404i \(0.489014\pi\)
\(180\) −5.84383 + 12.7015i −0.435573 + 0.946710i
\(181\) 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
\(186\) −20.2195 4.42830i −1.48257 0.324699i
\(187\) −5.60475 + 17.9442i −0.409860 + 1.31221i
\(188\) 16.5374i 1.20611i
\(189\) 4.89302 12.8475i 0.355915 0.934518i
\(190\) −3.51660 −0.255121
\(191\) −1.37505 + 0.793888i −0.0994954 + 0.0574437i −0.548922 0.835874i \(-0.684962\pi\)
0.449427 + 0.893317i \(0.351628\pi\)
\(192\) 6.60941 + 1.44753i 0.476993 + 0.104467i
\(193\) −11.2686 6.50595i −0.811135 0.468309i 0.0362150 0.999344i \(-0.488470\pi\)
−0.847350 + 0.531035i \(0.821803\pi\)
\(194\) 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 \(0.498701\pi\)
\(198\) −5.76086 17.7857i −0.409406 1.26397i
\(199\) −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
\(201\) −5.40882 + 5.93310i −0.381509 + 0.418489i
\(202\) −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
\(207\) −15.2372 + 1.41171i −1.05906 + 0.0981203i
\(208\) −5.08497 + 2.93581i −0.352579 + 0.203562i
\(209\) 1.49920 1.38120i 0.103702 0.0955396i
\(210\) 11.5526 23.5374i 0.797208 1.62423i
\(211\) 5.75491i 0.396184i −0.980183 0.198092i \(-0.936525\pi\)
0.980183 0.198092i \(-0.0634746\pi\)
\(212\) 3.94939 2.28018i 0.271245 0.156603i
\(213\) 2.93097 13.3828i 0.200827 0.916971i
\(214\) 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
\(219\) −1.50146 1.36878i −0.101459 0.0924935i
\(220\) −3.38607 15.0815i −0.228289 1.01679i
\(221\) 6.10825 + 3.52660i 0.410885 + 0.237225i
\(222\) −13.8494 + 15.1918i −0.929509 + 1.01961i
\(223\) −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 \(0.0800599\pi\)
\(228\) −0.348566 + 1.59154i −0.0230843 + 0.105402i
\(229\) −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
\(231\) 4.31954 + 14.5719i 0.284205 + 0.958764i
\(232\) 1.30363 0.0855878
\(233\) 0.199109 + 0.344867i 0.0130441 + 0.0225930i 0.872474 0.488661i \(-0.162514\pi\)
−0.859430 + 0.511254i \(0.829181\pi\)
\(234\) −6.98436 + 0.647091i −0.456582 + 0.0423016i
\(235\) 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 \(0.709091\pi\)
\(240\) −18.3917 16.7665i −1.18718 1.08227i
\(241\) −2.61969 1.51248i −0.168749 0.0974274i 0.413247 0.910619i \(-0.364395\pi\)
−0.581996 + 0.813192i \(0.697728\pi\)
\(242\) 16.9942 + 11.7637i 1.09243 + 0.756200i
\(243\) −7.37428 13.7339i −0.473060 0.881030i
\(244\) 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
\(249\) 26.5117 + 5.80636i 1.68011 + 0.367963i
\(250\) −3.60427 + 2.08092i −0.227954 + 0.131609i
\(251\) 7.80267i 0.492500i −0.969206 0.246250i \(-0.920802\pi\)
0.969206 0.246250i \(-0.0791985\pi\)
\(252\) −9.50744 7.56152i −0.598912 0.476331i
\(253\) 12.4421 11.4628i 0.782229 0.720661i
\(254\) −19.4078 + 11.2051i −1.21775 + 0.703070i
\(255\) −6.39580 + 29.2031i −0.400521 + 1.82877i
\(256\) −10.3543 + 17.9341i −0.647142 + 1.12088i
\(257\) −9.02456 + 5.21033i −0.562937 + 0.325012i −0.754323 0.656503i \(-0.772035\pi\)
0.191387 + 0.981515i \(0.438702\pi\)
\(258\) −7.16837 + 2.28036i −0.446283 + 0.141969i
\(259\) 11.5650 12.0644i 0.718616 0.749643i
\(260\) −5.79925 −0.359654
\(261\) 4.02723 + 1.85289i 0.249279 + 0.114691i
\(262\) −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 \(-0.235343\pi\)
\(264\) 5.06789 0.0266020i 0.311907 0.00163724i
\(265\) −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 0.271002 0.962579i \(-0.412645\pi\)
−0.698116 + 0.715984i \(0.745978\pi\)
\(270\) −11.5878 27.3791i −0.705213 1.66624i
\(271\) 11.9023 6.87180i 0.723014 0.417432i −0.0928473 0.995680i \(-0.529597\pi\)
0.815861 + 0.578248i \(0.196264\pi\)
\(272\) 26.7457 1.62170
\(273\) 5.68944 0.383598i 0.344341 0.0232164i
\(274\) 5.82036i 0.351621i
\(275\) −4.22482 + 13.5262i −0.254766 + 0.815660i
\(276\) −2.89281 + 13.2085i −0.174127 + 0.795058i
\(277\) −23.6582 13.6590i −1.42148 0.820692i −0.425055 0.905167i \(-0.639745\pi\)
−0.996426 + 0.0844752i \(0.973079\pi\)
\(278\) 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 \(0.498769\pi\)
\(282\) −25.9875 23.6911i −1.54753 1.41079i
\(283\) −25.0814 14.4807i −1.49093 0.860790i −0.490986 0.871168i \(-0.663363\pi\)
−0.999946 + 0.0103778i \(0.996697\pi\)
\(284\) −10.4837 6.05277i −0.622094 0.359166i
\(285\) 2.18391 2.39560i 0.129363 0.141903i
\(286\) 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
\(291\) −15.5599 3.40779i −0.912137 0.199768i
\(292\) −1.55475 + 0.897638i −0.0909851 + 0.0525303i
\(293\) 4.79018 0.279845 0.139923 0.990162i \(-0.455315\pi\)
0.139923 + 0.990162i \(0.455315\pi\)
\(294\) 17.4687 + 14.6228i 1.01879 + 0.852817i
\(295\) −18.9233 −1.10176
\(296\) −2.78633 4.82606i −0.161952 0.280509i
\(297\) 15.6937 + 7.12095i 0.910640 + 0.413200i
\(298\) −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
\(303\) 12.8380 14.0823i 0.737521 0.809010i
\(304\) −2.51159 1.45007i −0.144050 0.0831671i
\(305\) −14.5016 + 25.1175i −0.830360 + 1.43823i
\(306\) 29.0258 + 13.3545i 1.65929 + 0.763426i
\(307\) 14.6773i 0.837677i 0.908061 + 0.418839i \(0.137563\pi\)
−0.908061 + 0.418839i \(0.862437\pi\)
\(308\) 13.4272 + 0.266093i 0.765087 + 0.0151620i
\(309\) 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 0.826219 0.563350i \(-0.190488\pi\)
−0.0747658 + 0.997201i \(0.523821\pi\)
\(312\) 0.406794 1.85741i 0.0230302 0.105155i
\(313\) 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
\(315\) 8.85973 + 22.4873i 0.499189 + 1.26702i
\(316\) 5.90639i 0.332261i
\(317\) 15.6174 9.01672i 0.877161 0.506429i 0.00743978 0.999972i \(-0.497632\pi\)
0.869721 + 0.493543i \(0.164298\pi\)
\(318\) −2.07464 + 9.47276i −0.116340 + 0.531206i
\(319\) −4.78186 + 1.07362i −0.267733 + 0.0601110i
\(320\) −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
\(324\) −13.5398 + 2.53061i −0.752212 + 0.140589i
\(325\) 4.60435 + 2.65833i 0.255404 + 0.147457i
\(326\) −12.7693 + 22.1172i −0.707229 + 1.22496i
\(327\) −4.42358 4.03269i −0.244625 0.223008i
\(328\) −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
\(333\) −1.74819 18.8691i −0.0958004 1.03402i
\(334\) 6.18083 + 10.7055i 0.338200 + 0.585779i
\(335\) 14.1148i 0.771175i
\(336\) 17.9566 12.0469i 0.979615 0.657212i
\(337\) 23.4102i 1.27523i 0.770354 + 0.637616i \(0.220079\pi\)
−0.770354 + 0.637616i \(0.779921\pi\)
\(338\) 10.7585 + 18.6343i 0.585185 + 1.01357i
\(339\) −2.96073 + 13.5186i −0.160805 + 0.734230i
\(340\) 22.8770 + 13.2080i 1.24068 + 0.716305i
\(341\) −6.28901 + 20.1349i −0.340569 + 1.09037i
\(342\) −2.00167 2.82776i −0.108238 0.152908i
\(343\) −13.8990 12.2400i −0.750477 0.660897i
\(344\) 2.03916i 0.109944i
\(345\) 18.1246 19.8815i 0.975798 1.07038i
\(346\) −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 \(0.955199\pi\)
\(348\) 2.63896 2.89476i 0.141463 0.155176i
\(349\) 10.0181i 0.536258i −0.963383 0.268129i \(-0.913595\pi\)
0.963383 0.268129i \(-0.0864053\pi\)
\(350\) 5.92959 + 20.3957i 0.316950 + 1.09020i
\(351\) 3.89667 5.15979i 0.207989 0.275409i
\(352\) 7.02217 22.4822i 0.374283 1.19830i
\(353\) −4.58642 2.64797i −0.244110 0.140937i 0.372954 0.927850i \(-0.378345\pi\)
−0.617064 + 0.786913i \(0.711678\pi\)
\(354\) −4.32680 + 19.7561i −0.229967 + 1.05002i
\(355\) 12.0429 + 20.8588i 0.639168 + 1.10707i
\(356\) 2.11277i 0.111977i
\(357\) −23.3174 11.4447i −1.23409 0.605718i
\(358\) 26.6262i 1.40724i
\(359\) 2.99188 + 5.18209i 0.157905 + 0.273500i 0.934113 0.356977i \(-0.116193\pi\)
−0.776208 + 0.630477i \(0.782859\pi\)
\(360\) 8.02495 0.743500i 0.422952 0.0391859i
\(361\) −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
\(366\) 22.9071 + 20.8829i 1.19737 + 1.09156i
\(367\) −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
\(369\) −28.2459 12.9957i −1.47042 0.676529i
\(370\) 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 0.00297207 0.999996i \(-0.499054\pi\)
0.867508 + 0.497424i \(0.165721\pi\)
\(374\) −34.4647 + 7.73796i −1.78213 + 0.400120i
\(375\) 0.820774 3.74763i 0.0423846 0.193527i
\(376\) 8.25559 4.76637i 0.425749 0.245807i
\(377\) 1.83876i 0.0947009i
\(378\) 25.5026 4.10790i 1.31171 0.211288i
\(379\) 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
\(381\) 4.41960 20.1798i 0.226423 1.03384i
\(382\) −2.58366 1.49168i −0.132192 0.0763210i
\(383\) 7.16366 4.13594i 0.366046 0.211337i −0.305684 0.952133i \(-0.598885\pi\)
0.671730 + 0.740796i \(0.265552\pi\)
\(384\) −3.60365 11.3281i −0.183898 0.578087i
\(385\) −22.8715 13.8162i −1.16564 0.704138i
\(386\) 24.4488i 1.24441i
\(387\) 2.89832 6.29944i 0.147330 0.320219i
\(388\) −7.03745 + 12.1892i −0.357272 + 0.618814i
\(389\) 16.7647 + 9.67910i 0.850004 + 0.490750i 0.860652 0.509193i \(-0.170056\pi\)
−0.0106482 + 0.999943i \(0.503390\pi\)
\(390\) 8.30789 9.11318i 0.420686 0.461464i
\(391\) 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
\(396\) 10.1999 11.3073i 0.512565 0.568211i
\(397\) 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
\(399\) 1.56916 + 2.33893i 0.0785563 + 0.117093i
\(400\) 20.1607 1.00804
\(401\) −11.1606 + 6.44358i −0.557334 + 0.321777i −0.752075 0.659078i \(-0.770947\pi\)
0.194741 + 0.980855i \(0.437613\pi\)
\(402\) −14.7360 3.22734i −0.734962 0.160965i
\(403\) 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
\(408\) −5.83506 + 6.40066i −0.288878 + 0.316880i
\(409\) −6.17168 3.56322i −0.305170 0.176190i 0.339593 0.940572i \(-0.389711\pi\)
−0.644763 + 0.764382i \(0.723044\pi\)
\(410\) −51.3544 29.6495i −2.53621 1.46428i
\(411\) −3.96497 3.61461i −0.195578 0.178295i
\(412\) 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
\(417\) −4.51203 + 20.6018i −0.220955 + 1.00887i
\(418\) 3.65598 + 1.14192i 0.178820 + 0.0558533i
\(419\) 27.8186i 1.35903i 0.733663 + 0.679514i \(0.237809\pi\)
−0.733663 + 0.679514i \(0.762191\pi\)
\(420\) 21.3084 1.43667i 1.03975 0.0701025i
\(421\) −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
\(423\) 32.2780 2.99051i 1.56941 0.145403i
\(424\) −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
\(429\) 0.0375217 + 7.14819i 0.00181157 + 0.345118i
\(430\) 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 \(0.0659826\pi\)
\(432\) 3.01359 24.3326i 0.144991 1.17070i
\(433\) 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
\(438\) 0.816724 3.72914i 0.0390246 0.178185i
\(439\) −10.1810 + 5.87802i −0.485914 + 0.280543i −0.722878 0.690976i \(-0.757181\pi\)
0.236964 + 0.971519i \(0.423848\pi\)
\(440\) −6.55286 + 6.03710i −0.312396 + 0.287807i
\(441\) −20.8099 + 2.81894i −0.990949 + 0.134235i
\(442\) 13.2526i 0.630364i
\(443\) 8.29921 4.79155i 0.394307 0.227653i −0.289717 0.957112i \(-0.593561\pi\)
0.684025 + 0.729459i \(0.260228\pi\)
\(444\) −16.3568 3.58233i −0.776260 0.170010i
\(445\) −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 \(0.251307\pi\)
−0.704197 + 0.710005i \(0.748693\pi\)
\(450\) 21.8794 + 10.0665i 1.03141 + 0.474541i
\(451\) 33.5387 7.53006i 1.57928 0.354577i
\(452\) 10.5901 + 6.11422i 0.498118 + 0.287589i
\(453\) −29.3880 26.7911i −1.38077 1.25875i
\(454\) 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 \(-0.258992\pi\)
0.972851 0.231434i \(-0.0743418\pi\)
\(458\) 0.850112 1.47244i 0.0397231 0.0688025i
\(459\) −27.1233 + 11.4796i −1.26601 + 0.535820i
\(460\) −11.8860 20.5872i −0.554190 0.959884i
\(461\) −5.45941 −0.254270 −0.127135 0.991885i \(-0.540578\pi\)
−0.127135 + 0.991885i \(0.540578\pi\)
\(462\) −19.6537 + 20.7189i −0.914373 + 0.963929i
\(463\) 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
\(465\) −7.17665 + 32.7684i −0.332809 + 1.51960i
\(466\) −0.374117 + 0.647990i −0.0173306 + 0.0300176i
\(467\) −2.59974 + 1.50096i −0.120301 + 0.0694561i −0.558943 0.829206i \(-0.688793\pi\)
0.438642 + 0.898662i \(0.355460\pi\)
\(468\) −3.30096 4.66328i −0.152587 0.215560i
\(469\) 11.9103 + 2.92312i 0.549966 + 0.134977i
\(470\) 61.8242 2.85174
\(471\) −13.2380 + 14.5211i −0.609973 + 0.669099i
\(472\) −4.74792 2.74122i −0.218541 0.126175i
\(473\) 1.67936 + 7.47985i 0.0772172 + 0.343924i
\(474\) −9.28155 8.46138i −0.426316 0.388644i
\(475\) 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 \(0.330164\pi\)
\(480\) 8.01328 36.5884i 0.365755 1.67003i
\(481\) 6.80709 3.93007i 0.310377 0.179196i
\(482\) 5.68377i 0.258888i
\(483\) 13.0227 + 19.4112i 0.592556 + 0.883240i
\(484\) −1.37704 + 16.7788i −0.0625926 + 0.762673i
\(485\) 24.2522 14.0020i 1.10124 0.635798i
\(486\) 15.4201 24.9023i 0.699472 1.12959i
\(487\) 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 \(0.472957\pi\)
\(492\) −18.5090 + 20.3031i −0.834450 + 0.915335i
\(493\) 4.18784 7.25356i 0.188611 0.326684i
\(494\) 0.718517 1.24451i 0.0323276 0.0559930i
\(495\) −28.8240 + 9.33623i −1.29554 + 0.419632i
\(496\) 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
\(501\) −11.1313 2.43789i −0.497311 0.108917i
\(502\) 12.6967 7.33044i 0.566681 0.327173i
\(503\) 12.6627 0.564602 0.282301 0.959326i \(-0.408902\pi\)
0.282301 + 0.959326i \(0.408902\pi\)
\(504\) −1.03456 + 6.92555i −0.0460828 + 0.308488i
\(505\) 33.5018i 1.49081i
\(506\) 30.3417 + 9.47703i 1.34885 + 0.421306i
\(507\) −19.3755 4.24345i −0.860495 0.188458i
\(508\) −15.8083 9.12693i −0.701381 0.404942i
\(509\) 24.5196 14.1564i 1.08681 0.627471i 0.154086 0.988057i \(-0.450757\pi\)
0.932726 + 0.360586i \(0.117423\pi\)
\(510\) −53.5287 + 17.0282i −2.37029 + 0.754023i
\(511\) −0.739737 + 3.01407i −0.0327240 + 0.133335i
\(512\) −25.1839 −1.11298
\(513\) 3.16943 + 0.392534i 0.139934 + 0.0173308i
\(514\) −16.9568 9.78999i −0.747930 0.431818i
\(515\) −6.55709 3.78574i −0.288940 0.166819i
\(516\) −4.52802 4.12790i −0.199335 0.181721i
\(517\) −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 0.398912 0.916989i \(-0.369388\pi\)
−0.594680 + 0.803963i \(0.702721\pi\)
\(522\) 0.768422 + 8.29395i 0.0336329 + 0.363016i
\(523\) 1.50137 0.866814i 0.0656502 0.0379031i −0.466816 0.884355i \(-0.654599\pi\)
0.532466 + 0.846452i \(0.321265\pi\)
\(524\) −4.73247 −0.206739
\(525\) −17.5765 8.62694i −0.767103 0.376511i
\(526\) 58.0781 2.53232
\(527\) −18.0251 31.2204i −0.785186 1.35998i
\(528\) 13.6762 + 23.4033i 0.595179 + 1.01850i
\(529\) 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
\(534\) 3.32010 + 3.02671i 0.143675 + 0.130979i
\(535\) −36.3789 21.0034i −1.57280 0.908054i
\(536\) 2.04466 3.54145i 0.0883158 0.152968i
\(537\) −18.1384 16.5356i −0.782731 0.713565i
\(538\) 15.1987i 0.655262i
\(539\) 16.3949 16.4380i 0.706177 0.708035i
\(540\) 14.5940 19.3247i 0.628028 0.831604i
\(541\) −21.1393 + 12.2048i −0.908850 + 0.524725i −0.880061 0.474861i \(-0.842498\pi\)
−0.0287892 + 0.999586i \(0.509165\pi\)
\(542\) 22.3639 + 12.9118i 0.960612 + 0.554610i
\(543\) −15.4601 3.38595i −0.663458 0.145305i
\(544\) 20.1264 + 34.8600i 0.862914 + 1.49461i
\(545\) 10.5237 0.450785
\(546\) 5.96931 + 8.89761i 0.255463 + 0.380783i
\(547\) 22.7953i 0.974657i −0.873219 0.487329i \(-0.837971\pi\)
0.873219 0.487329i \(-0.162029\pi\)
\(548\) −4.10572 + 2.37044i −0.175388 + 0.101260i
\(549\) −28.4519 + 2.63602i −1.21430 + 0.112503i
\(550\) −25.9793 + 5.83282i −1.10776 + 0.248712i
\(551\) −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
\(555\) 24.6203 + 22.4447i 1.04507 + 0.952726i
\(556\) 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 \(0.291974\pi\)
\(558\) 32.5694 + 14.9849i 1.37877 + 0.634362i
\(559\) 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 \(-0.0115209\pi\)
\(564\) 6.12802 27.9804i 0.258036 1.17819i
\(565\) −12.1651 21.0706i −0.511790 0.886446i
\(566\) 54.4173i 2.28733i
\(567\) −13.0395 + 19.9242i −0.547606 + 0.836736i
\(568\) 6.97806i 0.292793i
\(569\) −5.47239 9.47846i −0.229415 0.397358i 0.728220 0.685343i \(-0.240348\pi\)
−0.957635 + 0.287986i \(0.907014\pi\)
\(570\) 5.94990 + 1.30310i 0.249214 + 0.0545807i
\(571\) 13.1413 + 7.58714i 0.549946 + 0.317512i 0.749100 0.662456i \(-0.230486\pi\)
−0.199154 + 0.979968i \(0.563819\pi\)
\(572\) 6.02911 + 1.88316i 0.252090 + 0.0787388i
\(573\) 2.62070 0.833683i 0.109481 0.0348276i
\(574\) 35.6539 37.1933i 1.48817 1.55242i
\(575\) 21.7938i 0.908865i
\(576\) −10.6464 4.89831i −0.443599 0.204096i
\(577\) −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
\(579\) 16.6551 + 15.1834i 0.692164 + 0.631001i
\(580\) 6.88663i 0.285952i
\(581\) −11.5735 39.8089i −0.480150 1.65155i
\(582\) −9.07293 28.5209i −0.376085 1.18223i
\(583\) 9.43312 + 2.94638i 0.390680 + 0.122027i
\(584\) 0.896215 + 0.517430i 0.0370856 + 0.0214114i
\(585\) 1.04870 + 11.3191i 0.0433582 + 0.467987i
\(586\) 4.50027 + 7.79470i 0.185904 + 0.321996i
\(587\) 21.1025i 0.870991i 0.900191 + 0.435496i \(0.143427\pi\)
−0.900191 + 0.435496i \(0.856573\pi\)
\(588\) −3.20060 + 18.2779i −0.131990 + 0.753768i
\(589\) 3.90906i 0.161070i
\(590\) −17.7781 30.7925i −0.731911 1.26771i
\(591\) −0.193758 0.0424352i −0.00797014 0.00174555i
\(592\) 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
\(597\) 27.8312 30.5289i 1.13905 1.24946i
\(598\) 5.96310 10.3284i 0.243849 0.422359i
\(599\) 5.52855 + 3.19191i 0.225890 + 0.130418i 0.608675 0.793420i \(-0.291701\pi\)
−0.382784 + 0.923838i \(0.625035\pi\)
\(600\) −4.39843 + 4.82477i −0.179565 + 0.196970i
\(601\) 10.8370i 0.442050i 0.975268 + 0.221025i \(0.0709402\pi\)
−0.975268 + 0.221025i \(0.929060\pi\)
\(602\) 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
\(605\) 19.0647 27.5413i 0.775088 1.11971i
\(606\) 34.9761 + 7.66016i 1.42081 + 0.311173i
\(607\) 19.0804 11.0161i 0.774450 0.447129i −0.0600101 0.998198i \(-0.519113\pi\)
0.834460 + 0.551069i \(0.185780\pi\)
\(608\) 4.36477i 0.177015i
\(609\) −0.455524 6.75623i −0.0184587 0.273776i
\(610\) −54.4958 −2.20647
\(611\) 6.72289 + 11.6444i 0.271979 + 0.471082i
\(612\) 2.40088 + 25.9138i 0.0970498 + 1.04751i
\(613\) 2.01225 + 1.16177i 0.0812739 + 0.0469235i 0.540086 0.841610i \(-0.318392\pi\)
−0.458812 + 0.888533i \(0.651725\pi\)
\(614\) −23.8832 + 13.7890i −0.963849 + 0.556478i
\(615\) 52.0905 16.5707i 2.10049 0.668197i
\(616\) −3.73712 6.77966i −0.150573 0.273160i
\(617\) 6.99701i 0.281689i 0.990032 + 0.140845i \(0.0449818\pi\)
−0.990032 + 0.140845i \(0.955018\pi\)
\(618\) −5.45160 + 5.98003i −0.219295 + 0.240552i
\(619\) 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
\(621\) 26.3037 + 3.25771i 1.05553 + 0.130727i
\(622\) 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
\(627\) −3.04838 + 1.78138i −0.121740 + 0.0711415i
\(628\) 8.68139 + 15.0366i 0.346425 + 0.600026i
\(629\) −35.8036 −1.42758
\(630\) −28.2684 + 35.5431i −1.12624 + 1.41607i
\(631\) −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
\(633\) −2.13252 + 9.73701i −0.0847599 + 0.387011i
\(634\) 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
\(639\) −9.91811 + 21.5568i −0.392354 + 0.852775i
\(640\) 18.0993 + 10.4496i 0.715438 + 0.413058i
\(641\) −42.8336 24.7300i −1.69183 0.976776i −0.953045 0.302830i \(-0.902069\pi\)
−0.738781 0.673946i \(-0.764598\pi\)
\(642\) −30.2456 + 33.1773i −1.19370 + 1.30940i
\(643\) −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 0.925237 0.379390i \(-0.123866\pi\)
0.134058 + 0.990974i \(0.457199\pi\)
\(648\) 5.16571 + 6.02981i 0.202928 + 0.236873i
\(649\) 19.6734 + 6.14486i 0.772248 + 0.241207i
\(650\) 9.98975i 0.391830i
\(651\) −26.1642 12.8419i −1.02546 0.503316i
\(652\) −20.8021 −0.814675
\(653\) −40.2088 + 23.2146i −1.57349 + 0.908456i −0.577756 + 0.816210i \(0.696071\pi\)
−0.995736 + 0.0922467i \(0.970595\pi\)
\(654\) 2.40623 10.9868i 0.0940909 0.429617i
\(655\) 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 \(0.496929\pi\)
\(660\) 0.140529 + 26.7718i 0.00547007 + 1.04209i
\(661\) 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
\(663\) −9.02803 8.23027i −0.350620 0.319637i
\(664\) −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
\(669\) 18.4607 + 4.04311i 0.713733 + 0.156316i
\(670\) 22.9680 13.2606i 0.887330 0.512300i
\(671\) 23.2327 21.4041i 0.896888 0.826296i
\(672\) 29.2144 + 14.3390i 1.12697 + 0.553140i
\(673\) 16.3937i 0.631930i −0.948771 0.315965i \(-0.897672\pi\)
0.948771 0.315965i \(-0.102328\pi\)
\(674\) −38.0936 + 21.9933i −1.46731 + 0.847151i
\(675\) −20.4453 + 8.65322i −0.786941 + 0.333063i
\(676\) −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
\(681\) −9.44933 + 10.3653i −0.362099 + 0.397198i
\(682\) −38.6724 + 8.68266i −1.48084 + 0.332476i
\(683\) 25.9035 + 14.9554i 0.991171 + 0.572253i 0.905624 0.424081i \(-0.139403\pi\)
0.0855471 + 0.996334i \(0.472736\pi\)
\(684\) 1.17951 2.56364i 0.0450997 0.0980234i
\(685\) 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
\(690\) 49.3793 + 10.8146i 1.87984 + 0.411706i
\(691\) −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
\(693\) −1.90872 26.2556i −0.0725062 0.997368i
\(694\) −43.1594 −1.63831
\(695\) −18.5391 32.1107i −0.703229 1.21803i
\(696\) −2.20568 0.483069i −0.0836062 0.0183107i
\(697\) −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 \(0.664035\pi\)
\(702\) 12.0570 + 1.49325i 0.455061 + 0.0563592i
\(703\) 3.36218 + 1.94116i 0.126807 + 0.0732122i
\(704\) 12.6413 2.83821i 0.476438 0.106969i
\(705\) −38.3946 + 42.1162i −1.44602 + 1.58619i
\(706\) 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
\(711\) 11.5282 1.06807i 0.432342 0.0400558i
\(712\) −1.05471 + 0.608938i −0.0395270 + 0.0228209i
\(713\) 32.4420i 1.21496i
\(714\) −3.28313 48.6947i −0.122868 1.82235i
\(715\) −8.51525 9.24272i −0.318452 0.345658i
\(716\) −18.7823 + 10.8440i −0.701928 + 0.405258i
\(717\) 31.9452 + 6.99637i 1.19302 + 0.261284i
\(718\) −5.62161 + 9.73692i −0.209797 + 0.363378i
\(719\) 15.2790 8.82134i 0.569811 0.328980i −0.187263 0.982310i \(-0.559962\pi\)
0.757074 + 0.653329i \(0.226628\pi\)
\(720\) 24.9048 + 35.1831i 0.928149 + 1.31120i
\(721\) 4.55240 4.74896i 0.169540 0.176860i
\(722\) −34.9904 −1.30221
\(723\) 3.87193 + 3.52978i 0.143998 + 0.131274i
\(724\) −6.99234 + 12.1111i −0.259868 + 0.450105i
\(725\) 3.15677 5.46768i 0.117239 0.203065i
\(726\) −24.3942 26.2009i −0.905353 0.972406i
\(727\) −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
\(732\) −5.40163 + 24.6637i −0.199650 + 0.911597i
\(733\) 6.55078 3.78209i 0.241958 0.139695i −0.374118 0.927381i \(-0.622055\pi\)
0.616077 + 0.787686i \(0.288721\pi\)
\(734\) −36.9438 −1.36362
\(735\) 23.6981 28.3103i 0.874119 1.04424i
\(736\) 36.2240i 1.33523i
\(737\) −4.58343 + 14.6743i −0.168833 + 0.540534i
\(738\) −5.38951 58.1716i −0.198391 2.14133i
\(739\) 10.4826 + 6.05211i 0.385607 + 0.222631i 0.680255 0.732975i \(-0.261869\pi\)
−0.294648 + 0.955606i \(0.595202\pi\)
\(740\) 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 \(0.786636\pi\)
\(744\) −6.54744 + 7.18209i −0.240041 + 0.263308i
\(745\) 56.6840 + 32.7265i 2.07674 + 1.19901i
\(746\) 31.5885 + 18.2377i 1.15654 + 0.667728i
\(747\) −42.7048 19.6481i −1.56249 0.718887i
\(748\) −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
\(753\) −2.89132 + 13.2017i −0.105366 + 0.481097i
\(754\) −2.99207 + 1.72747i −0.108965 + 0.0629109i
\(755\) 69.9138 2.54442
\(756\) 13.2841 + 16.3167i 0.483139 + 0.593434i
\(757\) 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
\(759\) −25.2990 + 14.7840i −0.918297 + 0.536625i
\(760\) −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
\(765\) 21.6427 47.0401i 0.782495 1.70074i
\(766\) 13.4602 + 7.77125i 0.486337 + 0.280787i
\(767\) 3.86645 6.69688i 0.139609 0.241810i
\(768\) 24.1645 26.5068i 0.871961 0.956481i
\(769\) 36.9953i 1.33408i 0.745020 + 0.667042i \(0.232440\pi\)
−0.745020 + 0.667042i \(0.767560\pi\)
\(770\) 0.994774 50.1970i 0.0358492 1.80897i
\(771\) 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 −0.343209 0.939259i \(-0.611514\pi\)
−0.985027 + 0.172402i \(0.944847\pi\)
\(774\) 12.9735 1.20198i 0.466323 0.0432041i
\(775\) −13.5872 23.5337i −0.488067 0.845356i
\(776\) 8.11327 0.291249
\(777\) −24.0380 + 16.1268i −0.862357 + 0.578545i
\(778\) 36.3732i 1.30404i
\(779\) 5.51652 3.18496i 0.197650 0.114113i
\(780\) 9.81203 + 2.14895i 0.351327 + 0.0769446i
\(781\) −5.74682 25.5962i −0.205638 0.915905i
\(782\) −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
\(786\) 6.77963 7.43679i 0.241821 0.265261i
\(787\) −40.3211 23.2794i −1.43729 0.829820i −0.439630 0.898179i \(-0.644890\pi\)
−0.997661 + 0.0683592i \(0.978224\pi\)
\(788\) −0.0876332 + 0.151785i −0.00312180 + 0.00540712i
\(789\) −36.0681 + 39.5642i −1.28406 + 1.40852i
\(790\) 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
\(795\) 15.3519 + 3.36223i 0.544474 + 0.119246i
\(796\) −18.2515 31.6126i −0.646908 1.12048i
\(797\) 43.3952i 1.53714i 0.639768 + 0.768568i \(0.279030\pi\)
−0.639768 + 0.768568i \(0.720970\pi\)
\(798\) −2.33177 + 4.75075i −0.0825438 + 0.168175i
\(799\) 61.2466i 2.16675i
\(800\) 15.1712 + 26.2772i 0.536382 + 0.929040i
\(801\) −4.12375 + 0.382059i −0.145706 + 0.0134994i
\(802\) −20.9703 12.1072i −0.740487 0.427520i
\(803\) −3.71354 1.15990i −0.131048 0.0409320i
\(804\) −3.72488 11.7092i −0.131366 0.412953i
\(805\) −39.9107 9.79520i −1.40667 0.345235i
\(806\) 14.8706i 0.523795i
\(807\) 10.3537 + 9.43881i 0.364468 + 0.332262i
\(808\) −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 \(-0.0990067\pi\)
\(810\) 9.46055 + 50.6179i 0.332410 + 1.77853i
\(811\) 37.2022i 1.30635i −0.757209 0.653173i \(-0.773437\pi\)
0.757209 0.653173i \(-0.226563\pi\)
\(812\) −5.81104 1.42619i −0.203927 0.0500495i
\(813\) −22.6845 + 7.21626i −0.795579 + 0.253085i
\(814\) −11.7359 + 37.5738i −0.411344 + 1.31696i
\(815\) 35.8438 + 20.6944i 1.25555 + 0.724894i
\(816\) −45.2523 9.91077i −1.58415 0.346946i
\(817\) 0.710315 + 1.23030i 0.0248508 + 0.0430428i
\(818\) 13.3903i 0.468180i
\(819\) −9.76839 1.45923i −0.341335 0.0509896i
\(820\) 48.3010i 1.68674i
\(821\) −10.8482 18.7896i −0.378604 0.655761i 0.612256 0.790660i \(-0.290262\pi\)
−0.990859 + 0.134899i \(0.956929\pi\)
\(822\) 2.15677 9.84774i 0.0752259 0.343479i
\(823\) 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 \(0.268725\pi\)
\(828\) 9.78897 21.2761i 0.340190 0.739397i
\(829\) −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
\(831\) 34.9669 + 31.8771i 1.21299 + 1.10580i
\(832\) 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
\(836\) 0.683440 + 3.04403i 0.0236373 + 0.105280i
\(837\) −30.4346 + 12.8811i −1.05198 + 0.445235i
\(838\) −45.2671 + 26.1350i −1.56372 + 0.902817i
\(839\) 20.1527i 0.695748i −0.937541 0.347874i \(-0.886904\pi\)
0.937541 0.347874i \(-0.113096\pi\)
\(840\) −6.85866 10.2233i −0.236646 0.352736i
\(841\) −26.8165 −0.924706
\(842\) −16.4692 28.5255i −0.567567 0.983055i
\(843\) −0.219385 0.0480478i −0.00755603 0.00165485i
\(844\) 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
\(847\) 19.2916 + 21.7907i 0.662866 + 0.748738i
\(848\) 14.0600i 0.482823i
\(849\) 37.0704 + 33.7947i 1.27225 + 1.15983i
\(850\) 22.7520 39.4077i 0.780388 1.35167i
\(851\) 27.9034 + 16.1100i 0.956515 + 0.552244i
\(852\) 15.4950 + 14.1258i 0.530850 + 0.483941i
\(853\) 20.6654i 0.707570i −0.935327 0.353785i \(-0.884894\pi\)
0.935327 0.353785i \(-0.115106\pi\)
\(854\) 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 \(0.143562\pi\)
\(858\) −11.5965 + 6.77662i −0.395896 + 0.231350i
\(859\) 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
\(861\) 3.19492 + 47.3864i 0.108883 + 1.61493i
\(862\) 24.2677 0.826563
\(863\) −15.9992 + 9.23715i −0.544619 + 0.314436i −0.746949 0.664881i \(-0.768482\pi\)
0.202330 + 0.979317i \(0.435149\pi\)
\(864\) 33.9826 14.3827i 1.15611 0.489310i
\(865\) 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
\(870\) −10.8219 9.86563i −0.366897 0.334476i
\(871\) 4.99517 + 2.88396i 0.169255 + 0.0977194i
\(872\) 2.64042 + 1.52445i 0.0894160 + 0.0516244i
\(873\) 25.0637 + 11.5316i 0.848279 + 0.390286i
\(874\) 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 −0.247753 0.968823i \(-0.579692\pi\)
0.715149 + 0.698972i \(0.246359\pi\)
\(878\) −19.1297 11.0445i −0.645596 0.372735i
\(879\) −8.10474 1.77503i −0.273366 0.0598702i
\(880\) −45.4879 14.2079i −1.53340 0.478948i
\(881\) 12.5797i 0.423819i −0.977289 0.211910i \(-0.932032\pi\)
0.977289 0.211910i \(-0.0679683\pi\)
\(882\) −24.1375 31.2141i −0.812753 1.05103i
\(883\) 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
\(885\) 32.0173 + 7.01215i 1.07625 + 0.235711i
\(886\) 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
\(891\) −23.9142 17.8637i −0.801156 0.598456i
\(892\) 8.34944 14.4617i 0.279560 0.484212i
\(893\) −3.32060 + 5.75145i −0.111120 + 0.192465i
\(894\) 47.1274 51.6955i 1.57617 1.72895i
\(895\) 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
\(900\) 1.80977 + 19.5337i 0.0603255 + 0.651123i
\(901\) −14.6266 + 8.44469i −0.487284 + 0.281333i
\(902\) 43.7620 + 47.5007i 1.45711 + 1.58160i
\(903\) −10.5682 + 0.712536i −0.351687 + 0.0237117i
\(904\) 7.04890i 0.234443i
\(905\) 24.0967 13.9123i 0.801003 0.462459i
\(906\) 15.9857 72.9904i 0.531090 2.42494i
\(907\) 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 \(-0.897951\pi\)
0.949047 0.315134i \(-0.102049\pi\)
\(912\) 3.71215 + 3.38412i 0.122922 + 0.112060i
\(913\) 50.7069 11.3846i 1.67815 0.376777i
\(914\) 66.6661 + 38.4897i 2.20512 + 1.27313i
\(915\) 33.8434 37.1239i 1.11883 1.22728i
\(916\) 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 −0.835885 0.548904i \(-0.815045\pi\)
0.0574223 + 0.998350i \(0.481712\pi\)
\(920\) −6.85153 + 11.8672i −0.225888 + 0.391250i
\(921\) 5.43875 24.8332i 0.179213 0.818282i
\(922\) −5.12899 8.88368i −0.168914 0.292568i
\(923\) −9.84246 −0.323968
\(924\) −22.6196 5.42575i −0.744129 0.178494i
\(925\) −26.9885 −0.887376
\(926\) 6.05063 + 10.4800i 0.198836 + 0.344394i
\(927\) −0.688150 7.42753i −0.0226018 0.243952i
\(928\) −5.24693 + 9.08796i −0.172239 + 0.298327i
\(929\) −16.4471 + 9.49571i −0.539610 + 0.311544i −0.744921 0.667153i \(-0.767513\pi\)
0.205311 + 0.978697i \(0.434180\pi\)
\(930\) −60.0638 + 19.1072i −1.96957 + 0.626549i
\(931\) 1.99184 3.81347i 0.0652800 0.124982i
\(932\) −0.609463 −0.0199636
\(933\) −19.5866 17.8558i −0.641236 0.584573i
\(934\) −4.88479 2.82023i −0.159835 0.0922809i
\(935\) 12.5404 + 55.8546i 0.410115 + 1.82664i
\(936\) −1.37655 + 2.99191i −0.0449939 + 0.0977935i
\(937\) 33.4823i 1.09382i 0.837192 + 0.546909i \(0.184196\pi\)
−0.837192 + 0.546909i \(0.815804\pi\)
\(938\) 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 \(0.0573852\pi\)
\(942\) −36.0659 7.89884i −1.17509 0.257358i
\(943\) 45.7826 26.4326i 1.49089 0.860763i
\(944\) 29.3231i 0.954385i
\(945\) −6.65739 41.3304i −0.216565 1.34448i
\(946\) −10.5937 + 9.75985i −0.344429 + 0.317320i
\(947\) 34.0101 19.6358i 1.10518 0.638077i 0.167604 0.985854i \(-0.446397\pi\)
0.937577 + 0.347778i \(0.113064\pi\)
\(948\) 2.18865 9.99331i 0.0710840 0.324568i
\(949\) −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 \(0.460127\pi\)
\(954\) 7.02037 15.2586i 0.227293 0.494017i
\(955\) −2.41746 + 4.18717i −0.0782273 + 0.135494i
\(956\) 14.4482 25.0251i 0.467290 0.809369i
\(957\) 8.48849 0.0445572i 0.274394 0.00144033i
\(958\) −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
\(963\) −3.81787 41.2081i −0.123029 1.32791i
\(964\) 4.00937 2.31481i 0.129133 0.0745551i
\(965\) −39.6225 −1.27549
\(966\) −19.3518 + 39.4273i −0.622633 + 1.26855i
\(967\) 15.1529i 0.487283i −0.969865 0.243642i \(-0.921658\pi\)
0.969865 0.243642i \(-0.0783421\pi\)
\(968\) 8.77299 4.14852i 0.281975 0.133338i
\(969\) 1.29092 5.89431i 0.0414703 0.189353i
\(970\) 45.5688 + 26.3091i 1.46313 + 0.844736i
\(971\) −24.0452 + 13.8825i −0.771648 + 0.445511i −0.833462 0.552576i \(-0.813645\pi\)
0.0618141 + 0.998088i \(0.480311\pi\)
\(972\) 23.8464 + 0.735596i 0.764873 + 0.0235943i
\(973\) 30.9349 8.99360i 0.991726 0.288321i
\(974\) 62.5013 2.00267
\(975\) −6.80527 6.20392i −0.217943 0.198684i
\(976\) −38.9215 22.4713i −1.24585 0.719289i
\(977\) −44.2071 25.5230i −1.41431 0.816553i −0.418520 0.908208i \(-0.637451\pi\)
−0.995791 + 0.0916549i \(0.970784\pi\)
\(978\) 29.8007 32.6893i 0.952922 1.04529i
\(979\) 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 0.340964 0.940076i \(-0.389247\pi\)
−0.643648 + 0.765322i \(0.722580\pi\)
\(984\) 15.4701 + 3.38812i 0.493168 + 0.108009i
\(985\) 0.301998 0.174359i 0.00962246 0.00555553i
\(986\) 15.7375 0.501185
\(987\) −27.5869 41.1200i −0.878102 1.30886i
\(988\) 1.17051 0.0372390
\(989\) 5.89503 + 10.2105i 0.187451 + 0.324675i
\(990\) −42.2716 38.1319i −1.34348 1.21191i
\(991\) 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
\(996\) −27.9836 + 30.6961i −0.886695 + 0.972644i
\(997\) 24.8780 + 14.3633i 0.787895 + 0.454891i 0.839221 0.543791i \(-0.183011\pi\)
−0.0513262 + 0.998682i \(0.516345\pi\)
\(998\) 1.90461 3.29888i 0.0602893 0.104424i
\(999\) −4.03420 + 32.5733i −0.127636 + 1.03057i
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.32.19 yes 48
3.2 odd 2 inner 231.2.l.b.32.6 yes 48
7.2 even 3 inner 231.2.l.b.65.20 yes 48
11.10 odd 2 inner 231.2.l.b.32.5 48
21.2 odd 6 inner 231.2.l.b.65.5 yes 48
33.32 even 2 inner 231.2.l.b.32.20 yes 48
77.65 odd 6 inner 231.2.l.b.65.6 yes 48
231.65 even 6 inner 231.2.l.b.65.19 yes 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
231.2.l.b.32.5 48 11.10 odd 2 inner
231.2.l.b.32.6 yes 48 3.2 odd 2 inner
231.2.l.b.32.19 yes 48 1.1 even 1 trivial
231.2.l.b.32.20 yes 48 33.32 even 2 inner
231.2.l.b.65.5 yes 48 21.2 odd 6 inner
231.2.l.b.65.6 yes 48 77.65 odd 6 inner
231.2.l.b.65.19 yes 48 231.65 even 6 inner
231.2.l.b.65.20 yes 48 7.2 even 3 inner