Properties

Label 126.2.l.a.5.8
Level $126$
Weight $2$
Character 126.5
Analytic conductor $1.006$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [126,2,Mod(5,126)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(126, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([5, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("126.5");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 126.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: \(1.00611506547\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 8 x^{15} + 23 x^{14} - 8 x^{13} - 131 x^{12} + 380 x^{11} - 289 x^{10} - 880 x^{9} + 2785 x^{8} - 2640 x^{7} - 2601 x^{6} + 10260 x^{5} - 10611 x^{4} - 1944 x^{3} + \cdots + 6561 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 3^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 5.8
Root \(1.58110 + 0.707199i\) of defining polynomial
Character \(\chi\) \(=\) 126.5
Dual form 126.2.l.a.101.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000i q^{2} +(1.64774 + 0.533822i) q^{3} -1.00000 q^{4} +(-0.450129 - 0.779646i) q^{5} +(-0.533822 + 1.64774i) q^{6} +(1.57151 + 2.12847i) q^{7} -1.00000i q^{8} +(2.43007 + 1.75919i) q^{9} +O(q^{10})\) \(q+1.00000i q^{2} +(1.64774 + 0.533822i) q^{3} -1.00000 q^{4} +(-0.450129 - 0.779646i) q^{5} +(-0.533822 + 1.64774i) q^{6} +(1.57151 + 2.12847i) q^{7} -1.00000i q^{8} +(2.43007 + 1.75919i) q^{9} +(0.779646 - 0.450129i) q^{10} +(-2.70900 - 1.56404i) q^{11} +(-1.64774 - 0.533822i) q^{12} +(-1.99033 - 1.14912i) q^{13} +(-2.12847 + 1.57151i) q^{14} +(-0.325502 - 1.52494i) q^{15} +1.00000 q^{16} +(-2.57638 - 4.46242i) q^{17} +(-1.75919 + 2.43007i) q^{18} +(2.38111 + 1.37474i) q^{19} +(0.450129 + 0.779646i) q^{20} +(1.45321 + 4.34605i) q^{21} +(1.56404 - 2.70900i) q^{22} +(-1.48584 + 0.857850i) q^{23} +(0.533822 - 1.64774i) q^{24} +(2.09477 - 3.62824i) q^{25} +(1.14912 - 1.99033i) q^{26} +(3.06502 + 4.19591i) q^{27} +(-1.57151 - 2.12847i) q^{28} +(-1.85590 + 1.07151i) q^{29} +(1.52494 - 0.325502i) q^{30} -10.0032i q^{31} +1.00000i q^{32} +(-3.62880 - 4.02326i) q^{33} +(4.46242 - 2.57638i) q^{34} +(0.952070 - 2.18330i) q^{35} +(-2.43007 - 1.75919i) q^{36} +(-4.73701 + 8.20475i) q^{37} +(-1.37474 + 2.38111i) q^{38} +(-2.66612 - 2.95593i) q^{39} +(-0.779646 + 0.450129i) q^{40} +(1.22134 - 2.11542i) q^{41} +(-4.34605 + 1.45321i) q^{42} +(-0.273155 - 0.473119i) q^{43} +(2.70900 + 1.56404i) q^{44} +(0.277705 - 2.68646i) q^{45} +(-0.857850 - 1.48584i) q^{46} +7.86068 q^{47} +(1.64774 + 0.533822i) q^{48} +(-2.06074 + 6.68980i) q^{49} +(3.62824 + 2.09477i) q^{50} +(-1.86306 - 8.72821i) q^{51} +(1.99033 + 1.14912i) q^{52} +(-12.0733 + 6.97054i) q^{53} +(-4.19591 + 3.06502i) q^{54} +2.81608i q^{55} +(2.12847 - 1.57151i) q^{56} +(3.18958 + 3.53629i) q^{57} +(-1.07151 - 1.85590i) q^{58} +7.98443 q^{59} +(0.325502 + 1.52494i) q^{60} +7.25411i q^{61} +10.0032 q^{62} +(0.0744824 + 7.93690i) q^{63} -1.00000 q^{64} +2.06901i q^{65} +(4.02326 - 3.62880i) q^{66} +3.67050 q^{67} +(2.57638 + 4.46242i) q^{68} +(-2.90621 + 0.620337i) q^{69} +(2.18330 + 0.952070i) q^{70} +14.1484i q^{71} +(1.75919 - 2.43007i) q^{72} +(-10.9190 + 6.30409i) q^{73} +(-8.20475 - 4.73701i) q^{74} +(5.38846 - 4.86016i) q^{75} +(-2.38111 - 1.37474i) q^{76} +(-0.928202 - 8.22392i) q^{77} +(2.95593 - 2.66612i) q^{78} -6.54804 q^{79} +(-0.450129 - 0.779646i) q^{80} +(2.81047 + 8.54993i) q^{81} +(2.11542 + 1.22134i) q^{82} +(0.184437 + 0.319454i) q^{83} +(-1.45321 - 4.34605i) q^{84} +(-2.31940 + 4.01733i) q^{85} +(0.473119 - 0.273155i) q^{86} +(-3.63003 + 0.774838i) q^{87} +(-1.56404 + 2.70900i) q^{88} +(6.00244 - 10.3965i) q^{89} +(2.68646 + 0.277705i) q^{90} +(-0.681960 - 6.04220i) q^{91} +(1.48584 - 0.857850i) q^{92} +(5.33990 - 16.4826i) q^{93} +7.86068i q^{94} -2.47523i q^{95} +(-0.533822 + 1.64774i) q^{96} +(8.86815 - 5.12003i) q^{97} +(-6.68980 - 2.06074i) q^{98} +(-3.83161 - 8.56640i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 16 q^{4} + 2 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 16 q^{4} + 2 q^{7} + 12 q^{11} + 6 q^{13} - 6 q^{14} - 18 q^{15} + 16 q^{16} - 18 q^{17} - 12 q^{18} - 12 q^{21} - 6 q^{23} - 8 q^{25} + 12 q^{26} + 36 q^{27} - 2 q^{28} + 6 q^{29} + 30 q^{35} - 2 q^{37} - 12 q^{39} - 6 q^{41} - 2 q^{43} - 12 q^{44} - 30 q^{45} + 6 q^{46} - 36 q^{47} - 8 q^{49} - 12 q^{50} + 6 q^{51} - 6 q^{52} - 36 q^{53} + 18 q^{54} + 6 q^{56} + 6 q^{57} + 6 q^{58} + 60 q^{59} + 18 q^{60} + 36 q^{62} + 36 q^{63} - 16 q^{64} + 24 q^{66} - 28 q^{67} + 18 q^{68} - 42 q^{69} - 18 q^{70} + 12 q^{72} + 18 q^{74} + 60 q^{75} - 42 q^{77} + 32 q^{79} - 36 q^{81} + 12 q^{84} - 12 q^{85} + 24 q^{86} - 24 q^{87} - 24 q^{89} + 18 q^{90} - 12 q^{91} + 6 q^{92} - 42 q^{93} + 6 q^{97} - 24 q^{98} + 18 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/126\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(73\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{6}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) 1.64774 + 0.533822i 0.951321 + 0.308202i
\(4\) −1.00000 −0.500000
\(5\) −0.450129 0.779646i −0.201304 0.348668i 0.747645 0.664099i \(-0.231185\pi\)
−0.948949 + 0.315430i \(0.897851\pi\)
\(6\) −0.533822 + 1.64774i −0.217932 + 0.672685i
\(7\) 1.57151 + 2.12847i 0.593974 + 0.804485i
\(8\) 1.00000i 0.353553i
\(9\) 2.43007 + 1.75919i 0.810023 + 0.586398i
\(10\) 0.779646 0.450129i 0.246546 0.142343i
\(11\) −2.70900 1.56404i −0.816795 0.471577i 0.0325150 0.999471i \(-0.489648\pi\)
−0.849310 + 0.527894i \(0.822982\pi\)
\(12\) −1.64774 0.533822i −0.475660 0.154101i
\(13\) −1.99033 1.14912i −0.552019 0.318708i 0.197917 0.980219i \(-0.436582\pi\)
−0.749936 + 0.661511i \(0.769916\pi\)
\(14\) −2.12847 + 1.57151i −0.568856 + 0.420003i
\(15\) −0.325502 1.52494i −0.0840442 0.393738i
\(16\) 1.00000 0.250000
\(17\) −2.57638 4.46242i −0.624863 1.08230i −0.988567 0.150780i \(-0.951821\pi\)
0.363704 0.931515i \(-0.381512\pi\)
\(18\) −1.75919 + 2.43007i −0.414646 + 0.572773i
\(19\) 2.38111 + 1.37474i 0.546264 + 0.315386i 0.747614 0.664134i \(-0.231199\pi\)
−0.201350 + 0.979519i \(0.564533\pi\)
\(20\) 0.450129 + 0.779646i 0.100652 + 0.174334i
\(21\) 1.45321 + 4.34605i 0.317116 + 0.948387i
\(22\) 1.56404 2.70900i 0.333455 0.577561i
\(23\) −1.48584 + 0.857850i −0.309819 + 0.178874i −0.646845 0.762621i \(-0.723912\pi\)
0.337027 + 0.941495i \(0.390579\pi\)
\(24\) 0.533822 1.64774i 0.108966 0.336343i
\(25\) 2.09477 3.62824i 0.418954 0.725649i
\(26\) 1.14912 1.99033i 0.225361 0.390336i
\(27\) 3.06502 + 4.19591i 0.589863 + 0.807504i
\(28\) −1.57151 2.12847i −0.296987 0.402242i
\(29\) −1.85590 + 1.07151i −0.344633 + 0.198974i −0.662319 0.749222i \(-0.730428\pi\)
0.317686 + 0.948196i \(0.397094\pi\)
\(30\) 1.52494 0.325502i 0.278415 0.0594282i
\(31\) 10.0032i 1.79662i −0.439363 0.898309i \(-0.644796\pi\)
0.439363 0.898309i \(-0.355204\pi\)
\(32\) 1.00000i 0.176777i
\(33\) −3.62880 4.02326i −0.631693 0.700359i
\(34\) 4.46242 2.57638i 0.765298 0.441845i
\(35\) 0.952070 2.18330i 0.160929 0.369046i
\(36\) −2.43007 1.75919i −0.405011 0.293199i
\(37\) −4.73701 + 8.20475i −0.778760 + 1.34885i 0.153896 + 0.988087i \(0.450818\pi\)
−0.932657 + 0.360766i \(0.882515\pi\)
\(38\) −1.37474 + 2.38111i −0.223012 + 0.386267i
\(39\) −2.66612 2.95593i −0.426921 0.473327i
\(40\) −0.779646 + 0.450129i −0.123273 + 0.0711716i
\(41\) 1.22134 2.11542i 0.190741 0.330373i −0.754755 0.656007i \(-0.772244\pi\)
0.945496 + 0.325634i \(0.105578\pi\)
\(42\) −4.34605 + 1.45321i −0.670611 + 0.224235i
\(43\) −0.273155 0.473119i −0.0416558 0.0721499i 0.844446 0.535641i \(-0.179930\pi\)
−0.886102 + 0.463491i \(0.846597\pi\)
\(44\) 2.70900 + 1.56404i 0.408397 + 0.235788i
\(45\) 0.277705 2.68646i 0.0413979 0.400474i
\(46\) −0.857850 1.48584i −0.126483 0.219075i
\(47\) 7.86068 1.14660 0.573299 0.819346i \(-0.305663\pi\)
0.573299 + 0.819346i \(0.305663\pi\)
\(48\) 1.64774 + 0.533822i 0.237830 + 0.0770505i
\(49\) −2.06074 + 6.68980i −0.294391 + 0.955685i
\(50\) 3.62824 + 2.09477i 0.513111 + 0.296245i
\(51\) −1.86306 8.72821i −0.260880 1.22219i
\(52\) 1.99033 + 1.14912i 0.276009 + 0.159354i
\(53\) −12.0733 + 6.97054i −1.65840 + 0.957478i −0.684947 + 0.728593i \(0.740175\pi\)
−0.973454 + 0.228885i \(0.926492\pi\)
\(54\) −4.19591 + 3.06502i −0.570991 + 0.417096i
\(55\) 2.81608i 0.379721i
\(56\) 2.12847 1.57151i 0.284428 0.210001i
\(57\) 3.18958 + 3.53629i 0.422470 + 0.468393i
\(58\) −1.07151 1.85590i −0.140696 0.243692i
\(59\) 7.98443 1.03948 0.519742 0.854323i \(-0.326028\pi\)
0.519742 + 0.854323i \(0.326028\pi\)
\(60\) 0.325502 + 1.52494i 0.0420221 + 0.196869i
\(61\) 7.25411i 0.928793i 0.885627 + 0.464397i \(0.153729\pi\)
−0.885627 + 0.464397i \(0.846271\pi\)
\(62\) 10.0032 1.27040
\(63\) 0.0744824 + 7.93690i 0.00938390 + 0.999956i
\(64\) −1.00000 −0.125000
\(65\) 2.06901i 0.256629i
\(66\) 4.02326 3.62880i 0.495228 0.446675i
\(67\) 3.67050 0.448423 0.224212 0.974540i \(-0.428019\pi\)
0.224212 + 0.974540i \(0.428019\pi\)
\(68\) 2.57638 + 4.46242i 0.312432 + 0.541148i
\(69\) −2.90621 + 0.620337i −0.349867 + 0.0746798i
\(70\) 2.18330 + 0.952070i 0.260955 + 0.113794i
\(71\) 14.1484i 1.67911i 0.543275 + 0.839555i \(0.317184\pi\)
−0.543275 + 0.839555i \(0.682816\pi\)
\(72\) 1.75919 2.43007i 0.207323 0.286386i
\(73\) −10.9190 + 6.30409i −1.27797 + 0.737838i −0.976475 0.215629i \(-0.930820\pi\)
−0.301498 + 0.953467i \(0.597487\pi\)
\(74\) −8.20475 4.73701i −0.953783 0.550667i
\(75\) 5.38846 4.86016i 0.622206 0.561203i
\(76\) −2.38111 1.37474i −0.273132 0.157693i
\(77\) −0.928202 8.22392i −0.105778 0.937203i
\(78\) 2.95593 2.66612i 0.334693 0.301878i
\(79\) −6.54804 −0.736712 −0.368356 0.929685i \(-0.620079\pi\)
−0.368356 + 0.929685i \(0.620079\pi\)
\(80\) −0.450129 0.779646i −0.0503259 0.0871671i
\(81\) 2.81047 + 8.54993i 0.312274 + 0.949992i
\(82\) 2.11542 + 1.22134i 0.233609 + 0.134874i
\(83\) 0.184437 + 0.319454i 0.0202446 + 0.0350646i 0.875970 0.482365i \(-0.160222\pi\)
−0.855726 + 0.517430i \(0.826889\pi\)
\(84\) −1.45321 4.34605i −0.158558 0.474193i
\(85\) −2.31940 + 4.01733i −0.251575 + 0.435740i
\(86\) 0.473119 0.273155i 0.0510177 0.0294551i
\(87\) −3.63003 + 0.774838i −0.389180 + 0.0830714i
\(88\) −1.56404 + 2.70900i −0.166728 + 0.288781i
\(89\) 6.00244 10.3965i 0.636258 1.10203i −0.349990 0.936754i \(-0.613815\pi\)
0.986247 0.165277i \(-0.0528518\pi\)
\(90\) 2.68646 + 0.277705i 0.283178 + 0.0292727i
\(91\) −0.681960 6.04220i −0.0714888 0.633395i
\(92\) 1.48584 0.857850i 0.154909 0.0894370i
\(93\) 5.33990 16.4826i 0.553722 1.70916i
\(94\) 7.86068i 0.810767i
\(95\) 2.47523i 0.253953i
\(96\) −0.533822 + 1.64774i −0.0544830 + 0.168171i
\(97\) 8.86815 5.12003i 0.900424 0.519860i 0.0230864 0.999733i \(-0.492651\pi\)
0.877338 + 0.479873i \(0.159317\pi\)
\(98\) −6.68980 2.06074i −0.675771 0.208166i
\(99\) −3.83161 8.56640i −0.385091 0.860955i
\(100\) −2.09477 + 3.62824i −0.209477 + 0.362824i
\(101\) −1.35969 + 2.35506i −0.135294 + 0.234337i −0.925710 0.378234i \(-0.876531\pi\)
0.790415 + 0.612571i \(0.209865\pi\)
\(102\) 8.72821 1.86306i 0.864222 0.184470i
\(103\) 1.18861 0.686242i 0.117117 0.0676174i −0.440297 0.897852i \(-0.645127\pi\)
0.557414 + 0.830235i \(0.311794\pi\)
\(104\) −1.14912 + 1.99033i −0.112680 + 0.195168i
\(105\) 2.73425 3.08927i 0.266836 0.301482i
\(106\) −6.97054 12.0733i −0.677039 1.17267i
\(107\) 12.3585 + 7.13519i 1.19474 + 0.689785i 0.959378 0.282122i \(-0.0910385\pi\)
0.235364 + 0.971907i \(0.424372\pi\)
\(108\) −3.06502 4.19591i −0.294931 0.403752i
\(109\) −2.64583 4.58271i −0.253425 0.438944i 0.711042 0.703150i \(-0.248224\pi\)
−0.964466 + 0.264206i \(0.914890\pi\)
\(110\) −2.81608 −0.268503
\(111\) −12.1852 + 10.9905i −1.15657 + 1.04318i
\(112\) 1.57151 + 2.12847i 0.148493 + 0.201121i
\(113\) −2.30371 1.33005i −0.216715 0.125121i 0.387713 0.921780i \(-0.373265\pi\)
−0.604428 + 0.796659i \(0.706598\pi\)
\(114\) −3.53629 + 3.18958i −0.331204 + 0.298732i
\(115\) 1.33764 + 0.772286i 0.124735 + 0.0720160i
\(116\) 1.85590 1.07151i 0.172316 0.0994869i
\(117\) −2.81512 6.29382i −0.260258 0.581864i
\(118\) 7.98443i 0.735026i
\(119\) 5.44931 12.4964i 0.499537 1.14555i
\(120\) −1.52494 + 0.325502i −0.139207 + 0.0297141i
\(121\) −0.607537 1.05229i −0.0552307 0.0956623i
\(122\) −7.25411 −0.656756
\(123\) 3.14170 2.83368i 0.283277 0.255504i
\(124\) 10.0032i 0.898309i
\(125\) −8.27295 −0.739955
\(126\) −7.93690 + 0.0744824i −0.707076 + 0.00663542i
\(127\) 6.10587 0.541808 0.270904 0.962606i \(-0.412677\pi\)
0.270904 + 0.962606i \(0.412677\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) −0.197527 0.925391i −0.0173913 0.0814761i
\(130\) −2.06901 −0.181464
\(131\) −3.97879 6.89147i −0.347629 0.602111i 0.638199 0.769871i \(-0.279680\pi\)
−0.985828 + 0.167761i \(0.946346\pi\)
\(132\) 3.62880 + 4.02326i 0.315847 + 0.350179i
\(133\) 0.815855 + 7.22852i 0.0707436 + 0.626792i
\(134\) 3.67050i 0.317083i
\(135\) 1.89167 4.27833i 0.162809 0.368220i
\(136\) −4.46242 + 2.57638i −0.382649 + 0.220923i
\(137\) 18.9140 + 10.9200i 1.61593 + 0.932957i 0.987958 + 0.154719i \(0.0494473\pi\)
0.627970 + 0.778237i \(0.283886\pi\)
\(138\) −0.620337 2.90621i −0.0528066 0.247393i
\(139\) −11.7109 6.76127i −0.993302 0.573483i −0.0870425 0.996205i \(-0.527742\pi\)
−0.906260 + 0.422721i \(0.861075\pi\)
\(140\) −0.952070 + 2.18330i −0.0804646 + 0.184523i
\(141\) 12.9523 + 4.19620i 1.09078 + 0.353384i
\(142\) −14.1484 −1.18731
\(143\) 3.59454 + 6.22593i 0.300591 + 0.520639i
\(144\) 2.43007 + 1.75919i 0.202506 + 0.146600i
\(145\) 1.67079 + 0.964632i 0.138752 + 0.0801083i
\(146\) −6.30409 10.9190i −0.521730 0.903663i
\(147\) −6.96671 + 9.92295i −0.574604 + 0.818431i
\(148\) 4.73701 8.20475i 0.389380 0.674426i
\(149\) −4.41192 + 2.54722i −0.361438 + 0.208676i −0.669711 0.742621i \(-0.733582\pi\)
0.308273 + 0.951298i \(0.400249\pi\)
\(150\) 4.86016 + 5.38846i 0.396830 + 0.439966i
\(151\) 10.5877 18.3385i 0.861618 1.49237i −0.00874783 0.999962i \(-0.502785\pi\)
0.870366 0.492405i \(-0.163882\pi\)
\(152\) 1.37474 2.38111i 0.111506 0.193134i
\(153\) 1.58949 15.3763i 0.128502 1.24310i
\(154\) 8.22392 0.928202i 0.662703 0.0747966i
\(155\) −7.79892 + 4.50271i −0.626424 + 0.361666i
\(156\) 2.66612 + 2.95593i 0.213460 + 0.236664i
\(157\) 0.359924i 0.0287250i 0.999897 + 0.0143625i \(0.00457189\pi\)
−0.999897 + 0.0143625i \(0.995428\pi\)
\(158\) 6.54804i 0.520934i
\(159\) −23.6147 + 5.04061i −1.87277 + 0.399746i
\(160\) 0.779646 0.450129i 0.0616364 0.0355858i
\(161\) −4.16091 1.81444i −0.327926 0.142998i
\(162\) −8.54993 + 2.81047i −0.671746 + 0.220811i
\(163\) 6.18640 10.7152i 0.484557 0.839277i −0.515286 0.857018i \(-0.672314\pi\)
0.999843 + 0.0177416i \(0.00564762\pi\)
\(164\) −1.22134 + 2.11542i −0.0953705 + 0.165186i
\(165\) −1.50329 + 4.64016i −0.117031 + 0.361236i
\(166\) −0.319454 + 0.184437i −0.0247944 + 0.0143151i
\(167\) −7.40866 + 12.8322i −0.573299 + 0.992984i 0.422925 + 0.906165i \(0.361003\pi\)
−0.996224 + 0.0868188i \(0.972330\pi\)
\(168\) 4.34605 1.45321i 0.335305 0.112117i
\(169\) −3.85905 6.68407i −0.296850 0.514159i
\(170\) −4.01733 2.31940i −0.308115 0.177890i
\(171\) 3.36784 + 7.52954i 0.257545 + 0.575798i
\(172\) 0.273155 + 0.473119i 0.0208279 + 0.0360750i
\(173\) 4.63544 0.352426 0.176213 0.984352i \(-0.443615\pi\)
0.176213 + 0.984352i \(0.443615\pi\)
\(174\) −0.774838 3.63003i −0.0587403 0.275192i
\(175\) 11.0145 1.24317i 0.832621 0.0939746i
\(176\) −2.70900 1.56404i −0.204199 0.117894i
\(177\) 13.1562 + 4.26226i 0.988883 + 0.320371i
\(178\) 10.3965 + 6.00244i 0.779253 + 0.449902i
\(179\) −5.25855 + 3.03602i −0.393042 + 0.226923i −0.683477 0.729972i \(-0.739533\pi\)
0.290435 + 0.956895i \(0.406200\pi\)
\(180\) −0.277705 + 2.68646i −0.0206989 + 0.200237i
\(181\) 7.12701i 0.529746i −0.964283 0.264873i \(-0.914670\pi\)
0.964283 0.264873i \(-0.0853301\pi\)
\(182\) 6.04220 0.681960i 0.447878 0.0505502i
\(183\) −3.87240 + 11.9529i −0.286256 + 0.883581i
\(184\) 0.857850 + 1.48584i 0.0632415 + 0.109538i
\(185\) 8.52907 0.627070
\(186\) 16.4826 + 5.33990i 1.20856 + 0.391540i
\(187\) 16.1183i 1.17868i
\(188\) −7.86068 −0.573299
\(189\) −4.11416 + 13.1177i −0.299261 + 0.954171i
\(190\) 2.47523 0.179572
\(191\) 14.4006i 1.04199i 0.853558 + 0.520997i \(0.174440\pi\)
−0.853558 + 0.520997i \(0.825560\pi\)
\(192\) −1.64774 0.533822i −0.118915 0.0385253i
\(193\) 17.8115 1.28210 0.641048 0.767501i \(-0.278500\pi\)
0.641048 + 0.767501i \(0.278500\pi\)
\(194\) 5.12003 + 8.86815i 0.367597 + 0.636696i
\(195\) −1.10448 + 3.40918i −0.0790935 + 0.244136i
\(196\) 2.06074 6.68980i 0.147195 0.477843i
\(197\) 19.1025i 1.36100i −0.732750 0.680498i \(-0.761764\pi\)
0.732750 0.680498i \(-0.238236\pi\)
\(198\) 8.56640 3.83161i 0.608787 0.272300i
\(199\) 11.6008 6.69771i 0.822357 0.474788i −0.0288716 0.999583i \(-0.509191\pi\)
0.851229 + 0.524795i \(0.175858\pi\)
\(200\) −3.62824 2.09477i −0.256556 0.148122i
\(201\) 6.04802 + 1.95940i 0.426595 + 0.138205i
\(202\) −2.35506 1.35969i −0.165701 0.0956677i
\(203\) −5.19723 2.26635i −0.364774 0.159066i
\(204\) 1.86306 + 8.72821i 0.130440 + 0.611097i
\(205\) −2.19904 −0.153587
\(206\) 0.686242 + 1.18861i 0.0478127 + 0.0828141i
\(207\) −5.11982 0.529247i −0.355852 0.0367852i
\(208\) −1.99033 1.14912i −0.138005 0.0796771i
\(209\) −4.30029 7.44832i −0.297457 0.515211i
\(210\) 3.08927 + 2.73425i 0.213180 + 0.188681i
\(211\) −9.37193 + 16.2327i −0.645190 + 1.11750i 0.339067 + 0.940762i \(0.389889\pi\)
−0.984258 + 0.176740i \(0.943445\pi\)
\(212\) 12.0733 6.97054i 0.829200 0.478739i
\(213\) −7.55274 + 23.3129i −0.517505 + 1.59737i
\(214\) −7.13519 + 12.3585i −0.487752 + 0.844810i
\(215\) −0.245910 + 0.425929i −0.0167709 + 0.0290481i
\(216\) 4.19591 3.06502i 0.285496 0.208548i
\(217\) 21.2914 15.7200i 1.44535 1.06714i
\(218\) 4.58271 2.64583i 0.310380 0.179198i
\(219\) −21.3569 + 4.55868i −1.44317 + 0.308047i
\(220\) 2.81608i 0.189860i
\(221\) 11.8423i 0.796597i
\(222\) −10.9905 12.1852i −0.737637 0.817819i
\(223\) 2.21609 1.27946i 0.148400 0.0856789i −0.423961 0.905680i \(-0.639361\pi\)
0.572362 + 0.820001i \(0.306027\pi\)
\(224\) −2.12847 + 1.57151i −0.142214 + 0.105001i
\(225\) 11.4732 5.13178i 0.764881 0.342119i
\(226\) 1.33005 2.30371i 0.0884736 0.153241i
\(227\) −4.36455 + 7.55962i −0.289685 + 0.501749i −0.973735 0.227686i \(-0.926884\pi\)
0.684049 + 0.729436i \(0.260217\pi\)
\(228\) −3.18958 3.53629i −0.211235 0.234197i
\(229\) −3.40979 + 1.96865i −0.225325 + 0.130092i −0.608414 0.793620i \(-0.708194\pi\)
0.383088 + 0.923712i \(0.374861\pi\)
\(230\) −0.772286 + 1.33764i −0.0509230 + 0.0882013i
\(231\) 2.86068 14.0464i 0.188219 0.924182i
\(232\) 1.07151 + 1.85590i 0.0703478 + 0.121846i
\(233\) −3.92147 2.26406i −0.256904 0.148324i 0.366018 0.930608i \(-0.380721\pi\)
−0.622921 + 0.782284i \(0.714054\pi\)
\(234\) 6.29382 2.81512i 0.411440 0.184030i
\(235\) −3.53832 6.12855i −0.230815 0.399782i
\(236\) −7.98443 −0.519742
\(237\) −10.7894 3.49548i −0.700849 0.227056i
\(238\) 12.4964 + 5.44931i 0.810024 + 0.353226i
\(239\) −7.55315 4.36081i −0.488573 0.282078i 0.235409 0.971896i \(-0.424357\pi\)
−0.723982 + 0.689819i \(0.757690\pi\)
\(240\) −0.325502 1.52494i −0.0210110 0.0984344i
\(241\) −17.1314 9.89079i −1.10353 0.637122i −0.166382 0.986061i \(-0.553209\pi\)
−0.937145 + 0.348939i \(0.886542\pi\)
\(242\) 1.05229 0.607537i 0.0676435 0.0390540i
\(243\) 0.0667715 + 15.5883i 0.00428340 + 0.999991i
\(244\) 7.25411i 0.464397i
\(245\) 6.14327 1.40463i 0.392479 0.0897383i
\(246\) 2.83368 + 3.14170i 0.180669 + 0.200307i
\(247\) −3.15947 5.47236i −0.201032 0.348198i
\(248\) −10.0032 −0.635201
\(249\) 0.133372 + 0.624832i 0.00845209 + 0.0395971i
\(250\) 8.27295i 0.523227i
\(251\) 3.80791 0.240353 0.120176 0.992753i \(-0.461654\pi\)
0.120176 + 0.992753i \(0.461654\pi\)
\(252\) −0.0744824 7.93690i −0.00469195 0.499978i
\(253\) 5.36686 0.337411
\(254\) 6.10587i 0.383116i
\(255\) −5.96630 + 5.38134i −0.373624 + 0.336993i
\(256\) 1.00000 0.0625000
\(257\) −7.53771 13.0557i −0.470189 0.814392i 0.529230 0.848479i \(-0.322481\pi\)
−0.999419 + 0.0340869i \(0.989148\pi\)
\(258\) 0.925391 0.197527i 0.0576123 0.0122975i
\(259\) −24.9078 + 2.81124i −1.54769 + 0.174682i
\(260\) 2.06901i 0.128314i
\(261\) −6.39496 0.661062i −0.395838 0.0409187i
\(262\) 6.89147 3.97879i 0.425756 0.245811i
\(263\) −6.59852 3.80965i −0.406882 0.234913i 0.282567 0.959248i \(-0.408814\pi\)
−0.689449 + 0.724334i \(0.742147\pi\)
\(264\) −4.02326 + 3.62880i −0.247614 + 0.223337i
\(265\) 10.8691 + 6.27529i 0.667684 + 0.385488i
\(266\) −7.22852 + 0.815855i −0.443209 + 0.0500233i
\(267\) 15.4403 13.9265i 0.944933 0.852289i
\(268\) −3.67050 −0.224212
\(269\) −4.32720 7.49493i −0.263834 0.456974i 0.703424 0.710771i \(-0.251654\pi\)
−0.967257 + 0.253797i \(0.918320\pi\)
\(270\) 4.27833 + 1.89167i 0.260371 + 0.115124i
\(271\) −15.6611 9.04193i −0.951343 0.549258i −0.0578449 0.998326i \(-0.518423\pi\)
−0.893498 + 0.449068i \(0.851756\pi\)
\(272\) −2.57638 4.46242i −0.156216 0.270574i
\(273\) 2.10177 10.3200i 0.127205 0.624595i
\(274\) −10.9200 + 18.9140i −0.659700 + 1.14263i
\(275\) −11.3495 + 6.55262i −0.684398 + 0.395138i
\(276\) 2.90621 0.620337i 0.174933 0.0373399i
\(277\) −4.99073 + 8.64419i −0.299864 + 0.519379i −0.976105 0.217301i \(-0.930275\pi\)
0.676241 + 0.736681i \(0.263608\pi\)
\(278\) 6.76127 11.7109i 0.405514 0.702371i
\(279\) 17.5975 24.3083i 1.05353 1.45530i
\(280\) −2.18330 0.952070i −0.130477 0.0568971i
\(281\) −13.0297 + 7.52272i −0.777289 + 0.448768i −0.835469 0.549538i \(-0.814804\pi\)
0.0581797 + 0.998306i \(0.481470\pi\)
\(282\) −4.19620 + 12.9523i −0.249880 + 0.771300i
\(283\) 4.02933i 0.239519i 0.992803 + 0.119759i \(0.0382123\pi\)
−0.992803 + 0.119759i \(0.961788\pi\)
\(284\) 14.1484i 0.839555i
\(285\) 1.32133 4.07853i 0.0782690 0.241591i
\(286\) −6.22593 + 3.59454i −0.368147 + 0.212550i
\(287\) 6.42194 0.724819i 0.379075 0.0427847i
\(288\) −1.75919 + 2.43007i −0.103662 + 0.143193i
\(289\) −4.77544 + 8.27131i −0.280908 + 0.486548i
\(290\) −0.964632 + 1.67079i −0.0566451 + 0.0981123i
\(291\) 17.3456 3.70245i 1.01681 0.217041i
\(292\) 10.9190 6.30409i 0.638987 0.368919i
\(293\) 6.59608 11.4248i 0.385347 0.667441i −0.606470 0.795106i \(-0.707415\pi\)
0.991817 + 0.127665i \(0.0407483\pi\)
\(294\) −9.92295 6.96671i −0.578718 0.406307i
\(295\) −3.59402 6.22503i −0.209252 0.362435i
\(296\) 8.20475 + 4.73701i 0.476891 + 0.275333i
\(297\) −1.74055 16.1606i −0.100997 0.937730i
\(298\) −2.54722 4.41192i −0.147557 0.255575i
\(299\) 3.94309 0.228035
\(300\) −5.38846 + 4.86016i −0.311103 + 0.280601i
\(301\) 0.577752 1.32491i 0.0333011 0.0763666i
\(302\) 18.3385 + 10.5877i 1.05526 + 0.609256i
\(303\) −3.49760 + 3.15468i −0.200932 + 0.181232i
\(304\) 2.38111 + 1.37474i 0.136566 + 0.0788465i
\(305\) 5.65564 3.26528i 0.323841 0.186970i
\(306\) 15.3763 + 1.58949i 0.879006 + 0.0908649i
\(307\) 28.7690i 1.64194i 0.570974 + 0.820968i \(0.306566\pi\)
−0.570974 + 0.820968i \(0.693434\pi\)
\(308\) 0.928202 + 8.22392i 0.0528892 + 0.468602i
\(309\) 2.32484 0.496242i 0.132255 0.0282302i
\(310\) −4.50271 7.79892i −0.255737 0.442949i
\(311\) 30.8457 1.74910 0.874550 0.484936i \(-0.161157\pi\)
0.874550 + 0.484936i \(0.161157\pi\)
\(312\) −2.95593 + 2.66612i −0.167346 + 0.150939i
\(313\) 18.3661i 1.03811i 0.854740 + 0.519056i \(0.173717\pi\)
−0.854740 + 0.519056i \(0.826283\pi\)
\(314\) −0.359924 −0.0203117
\(315\) 6.15445 3.63070i 0.346764 0.204567i
\(316\) 6.54804 0.368356
\(317\) 17.4560i 0.980426i −0.871603 0.490213i \(-0.836919\pi\)
0.871603 0.490213i \(-0.163081\pi\)
\(318\) −5.04061 23.6147i −0.282663 1.32425i
\(319\) 6.70353 0.375326
\(320\) 0.450129 + 0.779646i 0.0251630 + 0.0435835i
\(321\) 16.5546 + 18.3542i 0.923990 + 1.02443i
\(322\) 1.81444 4.16091i 0.101115 0.231878i
\(323\) 14.1673i 0.788292i
\(324\) −2.81047 8.54993i −0.156137 0.474996i
\(325\) −8.33857 + 4.81428i −0.462541 + 0.267048i
\(326\) 10.7152 + 6.18640i 0.593458 + 0.342633i
\(327\) −1.91328 8.96350i −0.105805 0.495683i
\(328\) −2.11542 1.22134i −0.116804 0.0674371i
\(329\) 12.3531 + 16.7312i 0.681049 + 0.922420i
\(330\) −4.64016 1.50329i −0.255433 0.0827532i
\(331\) 10.4294 0.573254 0.286627 0.958042i \(-0.407466\pi\)
0.286627 + 0.958042i \(0.407466\pi\)
\(332\) −0.184437 0.319454i −0.0101223 0.0175323i
\(333\) −25.9450 + 11.6048i −1.42178 + 0.635938i
\(334\) −12.8322 7.40866i −0.702145 0.405384i
\(335\) −1.65220 2.86169i −0.0902693 0.156351i
\(336\) 1.45321 + 4.34605i 0.0792789 + 0.237097i
\(337\) −15.8312 + 27.4204i −0.862380 + 1.49369i 0.00724616 + 0.999974i \(0.497693\pi\)
−0.869626 + 0.493712i \(0.835640\pi\)
\(338\) 6.68407 3.85905i 0.363566 0.209905i
\(339\) −3.08590 3.42134i −0.167603 0.185822i
\(340\) 2.31940 4.01733i 0.125787 0.217870i
\(341\) −15.6454 + 27.0986i −0.847244 + 1.46747i
\(342\) −7.52954 + 3.36784i −0.407151 + 0.182112i
\(343\) −17.4775 + 6.12685i −0.943694 + 0.330819i
\(344\) −0.473119 + 0.273155i −0.0255089 + 0.0147275i
\(345\) 1.79181 + 1.98658i 0.0964679 + 0.106954i
\(346\) 4.63544i 0.249203i
\(347\) 12.5252i 0.672389i −0.941793 0.336195i \(-0.890860\pi\)
0.941793 0.336195i \(-0.109140\pi\)
\(348\) 3.63003 0.774838i 0.194590 0.0415357i
\(349\) 12.2560 7.07599i 0.656047 0.378769i −0.134722 0.990883i \(-0.543014\pi\)
0.790769 + 0.612115i \(0.209681\pi\)
\(350\) 1.24317 + 11.0145i 0.0664501 + 0.588752i
\(351\) −1.27880 11.8733i −0.0682572 0.633751i
\(352\) 1.56404 2.70900i 0.0833638 0.144390i
\(353\) −2.48267 + 4.30012i −0.132139 + 0.228872i −0.924501 0.381180i \(-0.875518\pi\)
0.792362 + 0.610052i \(0.208851\pi\)
\(354\) −4.26226 + 13.1562i −0.226537 + 0.699246i
\(355\) 11.0308 6.36862i 0.585452 0.338011i
\(356\) −6.00244 + 10.3965i −0.318129 + 0.551015i
\(357\) 15.6499 17.6819i 0.828280 0.935825i
\(358\) −3.03602 5.25855i −0.160459 0.277923i
\(359\) 15.0013 + 8.66098i 0.791736 + 0.457109i 0.840573 0.541698i \(-0.182218\pi\)
−0.0488375 + 0.998807i \(0.515552\pi\)
\(360\) −2.68646 0.277705i −0.141589 0.0146364i
\(361\) −5.72021 9.90769i −0.301063 0.521457i
\(362\) 7.12701 0.374587
\(363\) −0.439328 2.05821i −0.0230588 0.108028i
\(364\) 0.681960 + 6.04220i 0.0357444 + 0.316698i
\(365\) 9.82992 + 5.67531i 0.514522 + 0.297059i
\(366\) −11.9529 3.87240i −0.624786 0.202414i
\(367\) 1.18799 + 0.685884i 0.0620124 + 0.0358029i 0.530686 0.847569i \(-0.321934\pi\)
−0.468673 + 0.883372i \(0.655268\pi\)
\(368\) −1.48584 + 0.857850i −0.0774547 + 0.0447185i
\(369\) 6.68937 2.99204i 0.348235 0.155760i
\(370\) 8.52907i 0.443405i
\(371\) −33.8099 14.7434i −1.75532 0.765441i
\(372\) −5.33990 + 16.4826i −0.276861 + 0.854581i
\(373\) 2.40488 + 4.16537i 0.124520 + 0.215675i 0.921545 0.388271i \(-0.126928\pi\)
−0.797025 + 0.603946i \(0.793594\pi\)
\(374\) −16.1183 −0.833456
\(375\) −13.6316 4.41628i −0.703935 0.228056i
\(376\) 7.86068i 0.405384i
\(377\) 4.92515 0.253658
\(378\) −13.1177 4.11416i −0.674701 0.211610i
\(379\) 19.5669 1.00508 0.502542 0.864553i \(-0.332398\pi\)
0.502542 + 0.864553i \(0.332398\pi\)
\(380\) 2.47523i 0.126977i
\(381\) 10.0609 + 3.25944i 0.515433 + 0.166986i
\(382\) −14.4006 −0.736801
\(383\) 15.7349 + 27.2536i 0.804014 + 1.39259i 0.916955 + 0.398992i \(0.130640\pi\)
−0.112940 + 0.993602i \(0.536027\pi\)
\(384\) 0.533822 1.64774i 0.0272415 0.0840857i
\(385\) −5.99394 + 4.42549i −0.305479 + 0.225544i
\(386\) 17.8115i 0.906579i
\(387\) 0.168522 1.63024i 0.00856646 0.0828700i
\(388\) −8.86815 + 5.12003i −0.450212 + 0.259930i
\(389\) 3.52130 + 2.03303i 0.178537 + 0.103078i 0.586605 0.809873i \(-0.300464\pi\)
−0.408068 + 0.912952i \(0.633797\pi\)
\(390\) −3.40918 1.10448i −0.172630 0.0559276i
\(391\) 7.65617 + 4.42029i 0.387189 + 0.223544i
\(392\) 6.68980 + 2.06074i 0.337886 + 0.104083i
\(393\) −2.87718 13.4793i −0.145135 0.679940i
\(394\) 19.1025 0.962369
\(395\) 2.94746 + 5.10515i 0.148303 + 0.256868i
\(396\) 3.83161 + 8.56640i 0.192545 + 0.430478i
\(397\) −3.81692 2.20370i −0.191566 0.110601i 0.401150 0.916013i \(-0.368611\pi\)
−0.592715 + 0.805412i \(0.701944\pi\)
\(398\) 6.69771 + 11.6008i 0.335726 + 0.581494i
\(399\) −2.51443 + 12.3462i −0.125879 + 0.618084i
\(400\) 2.09477 3.62824i 0.104738 0.181412i
\(401\) 16.0586 9.27141i 0.801926 0.462992i −0.0422180 0.999108i \(-0.513442\pi\)
0.844144 + 0.536116i \(0.180109\pi\)
\(402\) −1.95940 + 6.04802i −0.0977257 + 0.301648i
\(403\) −11.4948 + 19.9096i −0.572597 + 0.991768i
\(404\) 1.35969 2.35506i 0.0676472 0.117168i
\(405\) 5.40085 6.03974i 0.268370 0.300117i
\(406\) 2.26635 5.19723i 0.112477 0.257934i
\(407\) 25.6652 14.8178i 1.27218 0.734491i
\(408\) −8.72821 + 1.86306i −0.432111 + 0.0922350i
\(409\) 24.8902i 1.23074i −0.788238 0.615370i \(-0.789006\pi\)
0.788238 0.615370i \(-0.210994\pi\)
\(410\) 2.19904i 0.108603i
\(411\) 25.3359 + 28.0899i 1.24973 + 1.38557i
\(412\) −1.18861 + 0.686242i −0.0585584 + 0.0338087i
\(413\) 12.5476 + 16.9946i 0.617426 + 0.836249i
\(414\) 0.529247 5.11982i 0.0260111 0.251625i
\(415\) 0.166041 0.287591i 0.00815062 0.0141173i
\(416\) 1.14912 1.99033i 0.0563402 0.0975841i
\(417\) −15.6871 17.3923i −0.768200 0.851705i
\(418\) 7.44832 4.30029i 0.364309 0.210334i
\(419\) −2.57422 + 4.45869i −0.125759 + 0.217821i −0.922029 0.387120i \(-0.873470\pi\)
0.796270 + 0.604941i \(0.206803\pi\)
\(420\) −2.73425 + 3.08927i −0.133418 + 0.150741i
\(421\) −13.5022 23.3864i −0.658055 1.13978i −0.981119 0.193408i \(-0.938046\pi\)
0.323063 0.946377i \(-0.395287\pi\)
\(422\) −16.2327 9.37193i −0.790193 0.456218i
\(423\) 19.1020 + 13.8285i 0.928771 + 0.672363i
\(424\) 6.97054 + 12.0733i 0.338520 + 0.586333i
\(425\) −21.5877 −1.04715
\(426\) −23.3129 7.55274i −1.12951 0.365931i
\(427\) −15.4401 + 11.3999i −0.747200 + 0.551679i
\(428\) −12.3585 7.13519i −0.597371 0.344892i
\(429\) 2.59932 + 12.1775i 0.125496 + 0.587937i
\(430\) −0.425929 0.245910i −0.0205401 0.0118588i
\(431\) −8.10874 + 4.68159i −0.390584 + 0.225504i −0.682413 0.730966i \(-0.739070\pi\)
0.291829 + 0.956471i \(0.405736\pi\)
\(432\) 3.06502 + 4.19591i 0.147466 + 0.201876i
\(433\) 21.0373i 1.01099i 0.862830 + 0.505494i \(0.168690\pi\)
−0.862830 + 0.505494i \(0.831310\pi\)
\(434\) 15.7200 + 21.2914i 0.754585 + 1.02202i
\(435\) 2.23808 + 2.48136i 0.107308 + 0.118972i
\(436\) 2.64583 + 4.58271i 0.126712 + 0.219472i
\(437\) −4.71727 −0.225657
\(438\) −4.55868 21.3569i −0.217822 1.02047i
\(439\) 20.4229i 0.974730i −0.873198 0.487365i \(-0.837958\pi\)
0.873198 0.487365i \(-0.162042\pi\)
\(440\) 2.81608 0.134252
\(441\) −16.7764 + 12.6314i −0.798875 + 0.601497i
\(442\) −11.8423 −0.563279
\(443\) 32.3649i 1.53770i −0.639427 0.768852i \(-0.720828\pi\)
0.639427 0.768852i \(-0.279172\pi\)
\(444\) 12.1852 10.9905i 0.578285 0.521588i
\(445\) −10.8075 −0.512324
\(446\) 1.27946 + 2.21609i 0.0605841 + 0.104935i
\(447\) −8.62944 + 1.84197i −0.408158 + 0.0871223i
\(448\) −1.57151 2.12847i −0.0742467 0.100561i
\(449\) 21.5693i 1.01792i −0.860791 0.508958i \(-0.830031\pi\)
0.860791 0.508958i \(-0.169969\pi\)
\(450\) 5.13178 + 11.4732i 0.241914 + 0.540853i
\(451\) −6.61721 + 3.82045i −0.311592 + 0.179898i
\(452\) 2.30371 + 1.33005i 0.108358 + 0.0625603i
\(453\) 27.2353 24.5651i 1.27963 1.15417i
\(454\) −7.55962 4.36455i −0.354790 0.204838i
\(455\) −4.40381 + 3.25146i −0.206454 + 0.152431i
\(456\) 3.53629 3.18958i 0.165602 0.149366i
\(457\) 21.0700 0.985611 0.492806 0.870139i \(-0.335971\pi\)
0.492806 + 0.870139i \(0.335971\pi\)
\(458\) −1.96865 3.40979i −0.0919887 0.159329i
\(459\) 10.8273 24.4876i 0.505374 1.14298i
\(460\) −1.33764 0.772286i −0.0623677 0.0360080i
\(461\) 15.8412 + 27.4378i 0.737800 + 1.27791i 0.953484 + 0.301444i \(0.0974687\pi\)
−0.215684 + 0.976463i \(0.569198\pi\)
\(462\) 14.0464 + 2.86068i 0.653495 + 0.133091i
\(463\) 4.40058 7.62202i 0.204512 0.354225i −0.745465 0.666545i \(-0.767773\pi\)
0.949977 + 0.312319i \(0.101106\pi\)
\(464\) −1.85590 + 1.07151i −0.0861582 + 0.0497434i
\(465\) −15.2542 + 3.25604i −0.707397 + 0.150995i
\(466\) 2.26406 3.92147i 0.104881 0.181658i
\(467\) 9.49444 16.4449i 0.439350 0.760977i −0.558289 0.829646i \(-0.688542\pi\)
0.997639 + 0.0686693i \(0.0218753\pi\)
\(468\) 2.81512 + 6.29382i 0.130129 + 0.290932i
\(469\) 5.76822 + 7.81254i 0.266352 + 0.360750i
\(470\) 6.12855 3.53832i 0.282689 0.163211i
\(471\) −0.192135 + 0.593059i −0.00885312 + 0.0273267i
\(472\) 7.98443i 0.367513i
\(473\) 1.70891i 0.0785756i
\(474\) 3.49548 10.7894i 0.160553 0.495575i
\(475\) 9.97575 5.75950i 0.457719 0.264264i
\(476\) −5.44931 + 12.4964i −0.249769 + 0.572774i
\(477\) −41.6016 4.30045i −1.90481 0.196904i
\(478\) 4.36081 7.55315i 0.199459 0.345473i
\(479\) 12.0701 20.9060i 0.551495 0.955218i −0.446672 0.894698i \(-0.647391\pi\)
0.998167 0.0605197i \(-0.0192758\pi\)
\(480\) 1.52494 0.325502i 0.0696037 0.0148570i
\(481\) 18.8565 10.8868i 0.859781 0.496395i
\(482\) 9.89079 17.1314i 0.450513 0.780312i
\(483\) −5.88749 5.21091i −0.267890 0.237104i
\(484\) 0.607537 + 1.05229i 0.0276153 + 0.0478312i
\(485\) −7.98362 4.60935i −0.362518 0.209300i
\(486\) −15.5883 + 0.0667715i −0.707100 + 0.00302882i
\(487\) 7.05542 + 12.2204i 0.319712 + 0.553757i 0.980428 0.196879i \(-0.0630806\pi\)
−0.660716 + 0.750636i \(0.729747\pi\)
\(488\) 7.25411 0.328378
\(489\) 15.9136 14.3533i 0.719636 0.649080i
\(490\) 1.40463 + 6.14327i 0.0634546 + 0.277525i
\(491\) −18.8344 10.8740i −0.849982 0.490738i 0.0106626 0.999943i \(-0.496606\pi\)
−0.860645 + 0.509206i \(0.829939\pi\)
\(492\) −3.14170 + 2.83368i −0.141639 + 0.127752i
\(493\) 9.56302 + 5.52121i 0.430697 + 0.248663i
\(494\) 5.47236 3.15947i 0.246213 0.142151i
\(495\) −4.95404 + 6.84328i −0.222668 + 0.307582i
\(496\) 10.0032i 0.449155i
\(497\) −30.1144 + 22.2343i −1.35082 + 0.997347i
\(498\) −0.624832 + 0.133372i −0.0279994 + 0.00597653i
\(499\) 4.21233 + 7.29596i 0.188570 + 0.326612i 0.944774 0.327724i \(-0.106282\pi\)
−0.756204 + 0.654336i \(0.772948\pi\)
\(500\) 8.27295 0.369978
\(501\) −19.0576 + 17.1891i −0.851431 + 0.767954i
\(502\) 3.80791i 0.169955i
\(503\) −8.71316 −0.388501 −0.194250 0.980952i \(-0.562227\pi\)
−0.194250 + 0.980952i \(0.562227\pi\)
\(504\) 7.93690 0.0744824i 0.353538 0.00331771i
\(505\) 2.44815 0.108941
\(506\) 5.36686i 0.238586i
\(507\) −2.79059 13.0736i −0.123935 0.580620i
\(508\) −6.10587 −0.270904
\(509\) −14.9177 25.8382i −0.661214 1.14526i −0.980297 0.197530i \(-0.936708\pi\)
0.319082 0.947727i \(-0.396625\pi\)
\(510\) −5.38134 5.96630i −0.238290 0.264192i
\(511\) −30.5773 13.3338i −1.35266 0.589853i
\(512\) 1.00000i 0.0441942i
\(513\) 1.52987 + 14.2045i 0.0675456 + 0.627145i
\(514\) 13.0557 7.53771i 0.575862 0.332474i
\(515\) −1.07005 0.617794i −0.0471521 0.0272233i
\(516\) 0.197527 + 0.925391i 0.00869563 + 0.0407381i
\(517\) −21.2946 12.2944i −0.936536 0.540709i
\(518\) −2.81124 24.9078i −0.123519 1.09439i
\(519\) 7.63798 + 2.47450i 0.335270 + 0.108618i
\(520\) 2.06901 0.0907320
\(521\) −9.89004 17.1301i −0.433291 0.750482i 0.563864 0.825868i \(-0.309314\pi\)
−0.997154 + 0.0753863i \(0.975981\pi\)
\(522\) 0.661062 6.39496i 0.0289339 0.279900i
\(523\) −10.5932 6.11597i −0.463207 0.267433i 0.250185 0.968198i \(-0.419509\pi\)
−0.713392 + 0.700766i \(0.752842\pi\)
\(524\) 3.97879 + 6.89147i 0.173814 + 0.301055i
\(525\) 18.8127 + 3.83139i 0.821053 + 0.167215i
\(526\) 3.80965 6.59852i 0.166109 0.287709i
\(527\) −44.6382 + 25.7719i −1.94447 + 1.12264i
\(528\) −3.62880 4.02326i −0.157923 0.175090i
\(529\) −10.0282 + 17.3693i −0.436008 + 0.755188i
\(530\) −6.27529 + 10.8691i −0.272581 + 0.472124i
\(531\) 19.4027 + 14.0462i 0.842006 + 0.609552i
\(532\) −0.815855 7.22852i −0.0353718 0.313396i
\(533\) −4.86174 + 2.80693i −0.210585 + 0.121581i
\(534\) 13.9265 + 15.4403i 0.602659 + 0.668169i
\(535\) 12.8470i 0.555425i
\(536\) 3.67050i 0.158542i
\(537\) −10.2854 + 2.19544i −0.443848 + 0.0947402i
\(538\) 7.49493 4.32720i 0.323129 0.186559i
\(539\) 16.0457 14.8996i 0.691136 0.641771i
\(540\) −1.89167 + 4.27833i −0.0814047 + 0.184110i
\(541\) −0.348944 + 0.604389i −0.0150023 + 0.0259847i −0.873429 0.486951i \(-0.838109\pi\)
0.858427 + 0.512936i \(0.171442\pi\)
\(542\) 9.04193 15.6611i 0.388384 0.672701i
\(543\) 3.80455 11.7434i 0.163269 0.503959i
\(544\) 4.46242 2.57638i 0.191325 0.110461i
\(545\) −2.38193 + 4.12562i −0.102031 + 0.176722i
\(546\) 10.3200 + 2.10177i 0.441655 + 0.0899474i
\(547\) 21.0049 + 36.3815i 0.898103 + 1.55556i 0.829917 + 0.557887i \(0.188388\pi\)
0.0681854 + 0.997673i \(0.478279\pi\)
\(548\) −18.9140 10.9200i −0.807964 0.466478i
\(549\) −12.7614 + 17.6280i −0.544643 + 0.752344i
\(550\) −6.55262 11.3495i −0.279404 0.483943i
\(551\) −5.89215 −0.251014
\(552\) 0.620337 + 2.90621i 0.0264033 + 0.123697i
\(553\) −10.2903 13.9373i −0.437587 0.592673i
\(554\) −8.64419 4.99073i −0.367257 0.212036i
\(555\) 14.0537 + 4.55300i 0.596544 + 0.193264i
\(556\) 11.7109 + 6.76127i 0.496651 + 0.286742i
\(557\) 4.85612 2.80368i 0.205760 0.118796i −0.393579 0.919291i \(-0.628763\pi\)
0.599340 + 0.800495i \(0.295430\pi\)
\(558\) 24.3083 + 17.5975i 1.02905 + 0.744961i
\(559\) 1.25555i 0.0531042i
\(560\) 0.952070 2.18330i 0.0402323 0.0922614i
\(561\) −8.60428 + 26.5586i −0.363273 + 1.12131i
\(562\) −7.52272 13.0297i −0.317327 0.549626i
\(563\) −35.1896 −1.48306 −0.741532 0.670918i \(-0.765900\pi\)
−0.741532 + 0.670918i \(0.765900\pi\)
\(564\) −12.9523 4.19620i −0.545391 0.176692i
\(565\) 2.39478i 0.100749i
\(566\) −4.02933 −0.169365
\(567\) −13.7816 + 19.4183i −0.578771 + 0.815490i
\(568\) 14.1484 0.593655
\(569\) 8.81739i 0.369644i −0.982772 0.184822i \(-0.940829\pi\)
0.982772 0.184822i \(-0.0591709\pi\)
\(570\) 4.07853 + 1.32133i 0.170831 + 0.0553445i
\(571\) −11.8828 −0.497280 −0.248640 0.968596i \(-0.579984\pi\)
−0.248640 + 0.968596i \(0.579984\pi\)
\(572\) −3.59454 6.22593i −0.150295 0.260319i
\(573\) −7.68738 + 23.7285i −0.321145 + 0.991271i
\(574\) 0.724819 + 6.42194i 0.0302534 + 0.268047i
\(575\) 7.18799i 0.299760i
\(576\) −2.43007 1.75919i −0.101253 0.0732998i
\(577\) 15.8314 9.14028i 0.659071 0.380515i −0.132852 0.991136i \(-0.542413\pi\)
0.791923 + 0.610621i \(0.209080\pi\)
\(578\) −8.27131 4.77544i −0.344041 0.198632i
\(579\) 29.3486 + 9.50814i 1.21969 + 0.395145i
\(580\) −1.67079 0.964632i −0.0693758 0.0400542i
\(581\) −0.390103 + 0.894591i −0.0161842 + 0.0371139i
\(582\) 3.70245 + 17.3456i 0.153471 + 0.718996i
\(583\) 43.6089 1.80610
\(584\) 6.30409 + 10.9190i 0.260865 + 0.451832i
\(585\) −3.63979 + 5.02783i −0.150487 + 0.207875i
\(586\) 11.4248 + 6.59608i 0.471952 + 0.272482i
\(587\) −1.75389 3.03782i −0.0723907 0.125384i 0.827558 0.561380i \(-0.189730\pi\)
−0.899949 + 0.435996i \(0.856396\pi\)
\(588\) 6.96671 9.92295i 0.287302 0.409216i
\(589\) 13.7517 23.8186i 0.566628 0.981429i
\(590\) 6.22503 3.59402i 0.256280 0.147964i
\(591\) 10.1973 31.4759i 0.419462 1.29474i
\(592\) −4.73701 + 8.20475i −0.194690 + 0.337213i
\(593\) −24.2336 + 41.9738i −0.995155 + 1.72366i −0.412428 + 0.910990i \(0.635319\pi\)
−0.582727 + 0.812668i \(0.698014\pi\)
\(594\) 16.1606 1.74055i 0.663076 0.0714155i
\(595\) −12.1957 + 1.37648i −0.499975 + 0.0564302i
\(596\) 4.41192 2.54722i 0.180719 0.104338i
\(597\) 22.6904 4.84331i 0.928656 0.198224i
\(598\) 3.94309i 0.161245i
\(599\) 25.1463i 1.02745i 0.857955 + 0.513724i \(0.171734\pi\)
−0.857955 + 0.513724i \(0.828266\pi\)
\(600\) −4.86016 5.38846i −0.198415 0.219983i
\(601\) 11.2731 6.50854i 0.459840 0.265489i −0.252137 0.967692i \(-0.581133\pi\)
0.711977 + 0.702203i \(0.247800\pi\)
\(602\) 1.32491 + 0.577752i 0.0539993 + 0.0235474i
\(603\) 8.91958 + 6.45713i 0.363233 + 0.262955i
\(604\) −10.5877 + 18.3385i −0.430809 + 0.746183i
\(605\) −0.546940 + 0.947328i −0.0222363 + 0.0385144i
\(606\) −3.15468 3.49760i −0.128150 0.142080i
\(607\) −7.10546 + 4.10234i −0.288402 + 0.166509i −0.637221 0.770681i \(-0.719916\pi\)
0.348819 + 0.937190i \(0.386583\pi\)
\(608\) −1.37474 + 2.38111i −0.0557529 + 0.0965668i
\(609\) −7.35384 6.50874i −0.297993 0.263747i
\(610\) 3.26528 + 5.65564i 0.132207 + 0.228990i
\(611\) −15.6454 9.03286i −0.632944 0.365430i
\(612\) −1.58949 + 15.3763i −0.0642512 + 0.621551i
\(613\) 2.35051 + 4.07120i 0.0949361 + 0.164434i 0.909582 0.415525i \(-0.136402\pi\)
−0.814646 + 0.579959i \(0.803069\pi\)
\(614\) −28.7690 −1.16102
\(615\) −3.62343 1.17389i −0.146111 0.0473360i
\(616\) −8.22392 + 0.928202i −0.331351 + 0.0373983i
\(617\) 17.0178 + 9.82521i 0.685109 + 0.395548i 0.801777 0.597623i \(-0.203888\pi\)
−0.116668 + 0.993171i \(0.537221\pi\)
\(618\) 0.496242 + 2.32484i 0.0199618 + 0.0935187i
\(619\) 30.0586 + 17.3544i 1.20816 + 0.697531i 0.962357 0.271789i \(-0.0876153\pi\)
0.245802 + 0.969320i \(0.420949\pi\)
\(620\) 7.79892 4.50271i 0.313212 0.180833i
\(621\) −8.15358 3.60513i −0.327192 0.144669i
\(622\) 30.8457i 1.23680i
\(623\) 31.5615 3.56223i 1.26449 0.142718i
\(624\) −2.66612 2.95593i −0.106730 0.118332i
\(625\) −6.74995 11.6912i −0.269998 0.467650i
\(626\) −18.3661 −0.734057
\(627\) −3.10967 14.5685i −0.124188 0.581808i
\(628\) 0.359924i 0.0143625i
\(629\) 48.8174 1.94648
\(630\) 3.63070 + 6.15445i 0.144651 + 0.245199i
\(631\) 22.9139 0.912188 0.456094 0.889932i \(-0.349248\pi\)
0.456094 + 0.889932i \(0.349248\pi\)
\(632\) 6.54804i 0.260467i
\(633\) −24.1078 + 21.7442i −0.958199 + 0.864254i
\(634\) 17.4560 0.693266
\(635\) −2.74843 4.76041i −0.109068 0.188911i
\(636\) 23.6147 5.04061i 0.936384 0.199873i
\(637\) 11.7889 10.9469i 0.467094 0.433732i
\(638\) 6.70353i 0.265395i
\(639\) −24.8898 + 34.3816i −0.984627 + 1.36012i
\(640\) −0.779646 + 0.450129i −0.0308182 + 0.0177929i
\(641\) 11.9968 + 6.92634i 0.473844 + 0.273574i 0.717848 0.696200i \(-0.245127\pi\)
−0.244003 + 0.969774i \(0.578461\pi\)
\(642\) −18.3542 + 16.5546i −0.724381 + 0.653360i
\(643\) −27.9684 16.1476i −1.10297 0.636797i −0.165967 0.986131i \(-0.553075\pi\)
−0.936998 + 0.349334i \(0.886408\pi\)
\(644\) 4.16091 + 1.81444i 0.163963 + 0.0714990i
\(645\) −0.632565 + 0.570546i −0.0249072 + 0.0224652i
\(646\) 14.1673 0.557407
\(647\) −8.96715 15.5316i −0.352535 0.610609i 0.634158 0.773204i \(-0.281347\pi\)
−0.986693 + 0.162595i \(0.948014\pi\)
\(648\) 8.54993 2.81047i 0.335873 0.110406i
\(649\) −21.6298 12.4880i −0.849046 0.490197i
\(650\) −4.81428 8.33857i −0.188831 0.327066i
\(651\) 43.4742 14.5366i 1.70389 0.569736i
\(652\) −6.18640 + 10.7152i −0.242278 + 0.419638i
\(653\) 6.49080 3.74747i 0.254005 0.146650i −0.367592 0.929987i \(-0.619818\pi\)
0.621597 + 0.783338i \(0.286484\pi\)
\(654\) 8.96350 1.91328i 0.350501 0.0748151i
\(655\) −3.58194 + 6.20410i −0.139958 + 0.242414i
\(656\) 1.22134 2.11542i 0.0476852 0.0825932i
\(657\) −37.6241 3.88928i −1.46785 0.151735i
\(658\) −16.7312 + 12.3531i −0.652250 + 0.481574i
\(659\) −9.32497 + 5.38377i −0.363249 + 0.209722i −0.670505 0.741905i \(-0.733923\pi\)
0.307256 + 0.951627i \(0.400589\pi\)
\(660\) 1.50329 4.64016i 0.0585154 0.180618i
\(661\) 11.6409i 0.452778i 0.974037 + 0.226389i \(0.0726920\pi\)
−0.974037 + 0.226389i \(0.927308\pi\)
\(662\) 10.4294i 0.405352i
\(663\) −6.32166 + 19.5129i −0.245513 + 0.757819i
\(664\) 0.319454 0.184437i 0.0123972 0.00715754i
\(665\) 5.26845 3.88984i 0.204302 0.150842i
\(666\) −11.6048 25.9450i −0.449676 1.00535i
\(667\) 1.83838 3.18417i 0.0711825 0.123292i
\(668\) 7.40866 12.8322i 0.286650 0.496492i
\(669\) 4.33453 0.925215i 0.167583 0.0357709i
\(670\) 2.86169 1.65220i 0.110557 0.0638301i
\(671\) 11.3457 19.6514i 0.437997 0.758634i
\(672\) −4.34605 + 1.45321i −0.167653 + 0.0560587i
\(673\) −0.550931 0.954241i −0.0212368 0.0367833i 0.855212 0.518279i \(-0.173427\pi\)
−0.876449 + 0.481496i \(0.840094\pi\)
\(674\) −27.4204 15.8312i −1.05619 0.609794i
\(675\) 21.6443 2.33116i 0.833089 0.0897265i
\(676\) 3.85905 + 6.68407i 0.148425 + 0.257080i
\(677\) −11.2324 −0.431695 −0.215847 0.976427i \(-0.569251\pi\)
−0.215847 + 0.976427i \(0.569251\pi\)
\(678\) 3.42134 3.08590i 0.131396 0.118513i
\(679\) 24.8342 + 10.8294i 0.953048 + 0.415594i
\(680\) 4.01733 + 2.31940i 0.154057 + 0.0889451i
\(681\) −11.2271 + 10.1264i −0.430224 + 0.388043i
\(682\) −27.0986 15.6454i −1.03766 0.599092i
\(683\) 37.6792 21.7541i 1.44175 0.832396i 0.443786 0.896133i \(-0.353635\pi\)
0.997967 + 0.0637365i \(0.0203017\pi\)
\(684\) −3.36784 7.52954i −0.128772 0.287899i
\(685\) 19.6616i 0.751231i
\(686\) −6.12685 17.4775i −0.233924 0.667293i
\(687\) −6.66935 + 1.42359i −0.254451 + 0.0543132i
\(688\) −0.273155 0.473119i −0.0104139 0.0180375i
\(689\) 32.0399 1.22062
\(690\) −1.98658 + 1.79181i −0.0756280 + 0.0682131i
\(691\) 32.2260i 1.22593i −0.790108 0.612967i \(-0.789976\pi\)
0.790108 0.612967i \(-0.210024\pi\)
\(692\) −4.63544 −0.176213
\(693\) 12.2119 21.6176i 0.463891 0.821184i
\(694\) 12.5252 0.475451
\(695\) 12.1738i 0.461777i
\(696\) 0.774838 + 3.63003i 0.0293702 + 0.137596i
\(697\) −12.5865 −0.476748
\(698\) 7.07599 + 12.2560i 0.267830 + 0.463895i
\(699\) −5.25294 5.82394i −0.198684 0.220282i
\(700\) −11.0145 + 1.24317i −0.416310 + 0.0469873i
\(701\) 21.8995i 0.827133i 0.910474 + 0.413566i \(0.135717\pi\)
−0.910474 + 0.413566i \(0.864283\pi\)
\(702\) 11.8733 1.27880i 0.448130 0.0482651i
\(703\) −22.5587 + 13.0243i −0.850818 + 0.491220i
\(704\) 2.70900 + 1.56404i 0.102099 + 0.0589471i
\(705\) −2.55866 11.9871i −0.0963649 0.451459i
\(706\) −4.30012 2.48267i −0.161837 0.0934366i
\(707\) −7.14942 + 0.806927i −0.268882 + 0.0303476i
\(708\) −13.1562 4.26226i −0.494442 0.160186i
\(709\) −18.0470 −0.677770 −0.338885 0.940828i \(-0.610050\pi\)
−0.338885 + 0.940828i \(0.610050\pi\)
\(710\) 6.36862 + 11.0308i 0.239010 + 0.413977i
\(711\) −15.9122 11.5193i −0.596753 0.432006i
\(712\) −10.3965 6.00244i −0.389627 0.224951i
\(713\) 8.58120 + 14.8631i 0.321369 + 0.556627i
\(714\) 17.6819 + 15.6499i 0.661728 + 0.585683i
\(715\) 3.23602 5.60494i 0.121020 0.209613i
\(716\) 5.25855 3.03602i 0.196521 0.113462i
\(717\) −10.1177 11.2175i −0.377852 0.418925i
\(718\) −8.66098 + 15.0013i −0.323225 + 0.559842i
\(719\) −4.65944 + 8.07039i −0.173768 + 0.300975i −0.939734 0.341906i \(-0.888928\pi\)
0.765966 + 0.642881i \(0.222261\pi\)
\(720\) 0.277705 2.68646i 0.0103495 0.100118i
\(721\) 3.32854 + 1.45147i 0.123961 + 0.0540557i
\(722\) 9.90769 5.72021i 0.368726 0.212884i
\(723\) −22.9480 25.4425i −0.853446 0.946217i
\(724\) 7.12701i 0.264873i
\(725\) 8.97823i 0.333443i
\(726\) 2.05821 0.439328i 0.0763872 0.0163050i
\(727\) −6.73516 + 3.88855i −0.249793 + 0.144218i −0.619670 0.784863i \(-0.712733\pi\)
0.369876 + 0.929081i \(0.379400\pi\)
\(728\) −6.04220 + 0.681960i −0.223939 + 0.0252751i
\(729\) −8.21136 + 25.7211i −0.304124 + 0.952632i
\(730\) −5.67531 + 9.82992i −0.210053 + 0.363822i
\(731\) −1.40750 + 2.43787i −0.0520583 + 0.0901677i
\(732\) 3.87240 11.9529i 0.143128 0.441790i
\(733\) 31.2841 18.0619i 1.15550 0.667131i 0.205282 0.978703i \(-0.434189\pi\)
0.950222 + 0.311572i \(0.100856\pi\)
\(734\) −0.685884 + 1.18799i −0.0253164 + 0.0438494i
\(735\) 10.8723 + 0.964957i 0.401031 + 0.0355930i
\(736\) −0.857850 1.48584i −0.0316208 0.0547688i
\(737\) −9.94341 5.74083i −0.366270 0.211466i
\(738\) 2.99204 + 6.68937i 0.110139 + 0.246239i
\(739\) 12.0693 + 20.9046i 0.443975 + 0.768987i 0.997980 0.0635263i \(-0.0202347\pi\)
−0.554005 + 0.832513i \(0.686901\pi\)
\(740\) −8.52907 −0.313535
\(741\) −2.28471 10.7036i −0.0839308 0.393207i
\(742\) 14.7434 33.8099i 0.541248 1.24120i
\(743\) 10.5762 + 6.10618i 0.388003 + 0.224014i 0.681295 0.732009i \(-0.261417\pi\)
−0.293291 + 0.956023i \(0.594751\pi\)
\(744\) −16.4826 5.33990i −0.604280 0.195770i
\(745\) 3.97186 + 2.29316i 0.145518 + 0.0840147i
\(746\) −4.16537 + 2.40488i −0.152505 + 0.0880488i
\(747\) −0.113788 + 1.10076i −0.00416327 + 0.0402745i
\(748\) 16.1183i 0.589342i
\(749\) 4.23447 + 37.5177i 0.154724 + 1.37087i
\(750\) 4.41628 13.6316i 0.161260 0.497757i
\(751\) 11.7190 + 20.2980i 0.427634 + 0.740684i 0.996662 0.0816339i \(-0.0260138\pi\)
−0.569028 + 0.822318i \(0.692680\pi\)
\(752\) 7.86068 0.286650
\(753\) 6.27443 + 2.03274i 0.228653 + 0.0740773i
\(754\) 4.92515i 0.179364i
\(755\) −19.0634 −0.693788
\(756\) 4.11416 13.1177i 0.149631 0.477086i
\(757\) 3.52341 0.128060 0.0640302 0.997948i \(-0.479605\pi\)
0.0640302 + 0.997948i \(0.479605\pi\)
\(758\) 19.5669i 0.710702i
\(759\) 8.84316 + 2.86495i 0.320987 + 0.103991i
\(760\) −2.47523 −0.0897861
\(761\) 10.7021 + 18.5365i 0.387950 + 0.671949i 0.992174 0.124866i \(-0.0398500\pi\)
−0.604224 + 0.796815i \(0.706517\pi\)
\(762\) −3.25944 + 10.0609i −0.118077 + 0.364466i
\(763\) 5.59621 12.8333i 0.202596 0.464597i
\(764\) 14.4006i 0.520997i
\(765\) −12.7036 + 5.68209i −0.459299 + 0.205437i
\(766\) −27.2536 + 15.7349i −0.984712 + 0.568524i
\(767\) −15.8917 9.17506i −0.573815 0.331292i
\(768\) 1.64774 + 0.533822i 0.0594576 + 0.0192626i
\(769\) −23.4043 13.5125i −0.843982 0.487273i 0.0146339 0.999893i \(-0.495342\pi\)
−0.858616 + 0.512620i \(0.828675\pi\)
\(770\) −4.42549 5.99394i −0.159484 0.216007i
\(771\) −5.45074 25.5361i −0.196304 0.919661i
\(772\) −17.8115 −0.641048
\(773\) 8.10280 + 14.0345i 0.291437 + 0.504784i 0.974150 0.225903i \(-0.0725332\pi\)
−0.682712 + 0.730687i \(0.739200\pi\)
\(774\) 1.63024 + 0.168522i 0.0585979 + 0.00605740i
\(775\) −36.2939 20.9543i −1.30371 0.752700i
\(776\) −5.12003 8.86815i −0.183798 0.318348i
\(777\) −42.5422 8.66413i −1.52619 0.310824i
\(778\) −2.03303 + 3.52130i −0.0728875 + 0.126245i
\(779\) 5.81628 3.35803i 0.208390 0.120314i
\(780\) 1.10448 3.40918i 0.0395468 0.122068i
\(781\) 22.1288 38.3281i 0.791829 1.37149i
\(782\) −4.42029 + 7.65617i −0.158069 + 0.273784i
\(783\) −10.1843 4.50302i −0.363958 0.160925i
\(784\) −2.06074 + 6.68980i −0.0735977 + 0.238921i
\(785\) 0.280613 0.162012i 0.0100155 0.00578246i
\(786\) 13.4793 2.87718i 0.480790 0.102626i
\(787\) 38.2571i 1.36372i 0.731483 + 0.681860i \(0.238829\pi\)
−0.731483 + 0.681860i \(0.761171\pi\)
\(788\) 19.1025i 0.680498i
\(789\) −8.83894 9.79974i −0.314674 0.348880i
\(790\) −5.10515 + 2.94746i −0.181633 + 0.104866i
\(791\) −0.789335 6.99356i −0.0280655 0.248662i
\(792\) −8.56640 + 3.83161i −0.304394 + 0.136150i
\(793\) 8.33583 14.4381i 0.296014 0.512712i
\(794\) 2.20370 3.81692i 0.0782064 0.135457i
\(795\) 14.5595 + 16.1422i 0.516374 + 0.572504i
\(796\) −11.6008 + 6.69771i −0.411179 + 0.237394i
\(797\) 4.38709 7.59866i 0.155399 0.269158i −0.777805 0.628505i \(-0.783667\pi\)
0.933204 + 0.359347i \(0.117000\pi\)
\(798\) −12.3462 2.51443i −0.437051 0.0890098i
\(799\) −20.2521 35.0776i −0.716467 1.24096i
\(800\) 3.62824 + 2.09477i 0.128278 + 0.0740612i
\(801\) 32.8759 14.7048i 1.16161 0.519570i
\(802\) 9.27141 + 16.0586i 0.327385 + 0.567047i
\(803\) 39.4395 1.39179
\(804\) −6.04802 1.95940i −0.213297 0.0691025i
\(805\) 0.458323 + 4.06077i 0.0161538 + 0.143123i
\(806\) −19.9096 11.4948i −0.701286 0.404887i
\(807\) −3.12913 14.6596i −0.110150 0.516043i
\(808\) 2.35506 + 1.35969i 0.0828506 + 0.0478338i
\(809\) 26.6053 15.3606i 0.935394 0.540050i 0.0468805 0.998901i \(-0.485072\pi\)
0.888513 + 0.458851i \(0.151739\pi\)
\(810\) 6.03974 + 5.40085i 0.212215 + 0.189766i
\(811\) 8.70634i 0.305721i 0.988248 + 0.152861i \(0.0488485\pi\)
−0.988248 + 0.152861i \(0.951151\pi\)
\(812\) 5.19723 + 2.26635i 0.182387 + 0.0795332i
\(813\) −20.9785 23.2589i −0.735750 0.815726i
\(814\) 14.8178 + 25.6652i 0.519363 + 0.899564i
\(815\) −11.1387 −0.390172
\(816\) −1.86306 8.72821i −0.0652200 0.305549i
\(817\) 1.50206i 0.0525506i
\(818\) 24.8902 0.870265
\(819\) 8.97220 15.8827i 0.313514 0.554985i
\(820\) 2.19904 0.0767937
\(821\) 52.4347i 1.82998i −0.403473 0.914992i \(-0.632197\pi\)
0.403473 0.914992i \(-0.367803\pi\)
\(822\) −28.0899 + 25.3359i −0.979749 + 0.883691i
\(823\) 8.36398 0.291550 0.145775 0.989318i \(-0.453432\pi\)
0.145775 + 0.989318i \(0.453432\pi\)
\(824\) −0.686242 1.18861i −0.0239064 0.0414070i
\(825\) −22.1988 + 4.73839i −0.772865 + 0.164970i
\(826\) −16.9946 + 12.5476i −0.591317 + 0.436586i
\(827\) 26.4934i 0.921267i 0.887590 + 0.460634i \(0.152378\pi\)
−0.887590 + 0.460634i \(0.847622\pi\)
\(828\) 5.11982 + 0.529247i 0.177926 + 0.0183926i
\(829\) −5.14134 + 2.96835i −0.178566 + 0.103095i −0.586619 0.809863i \(-0.699541\pi\)
0.408053 + 0.912958i \(0.366208\pi\)
\(830\) 0.287591 + 0.166041i 0.00998243 + 0.00576336i
\(831\) −12.8379 + 11.5792i −0.445340 + 0.401678i
\(832\) 1.99033 + 1.14912i 0.0690024 + 0.0398385i
\(833\) 35.1619 8.03958i 1.21829 0.278555i
\(834\) 17.3923 15.6871i 0.602246 0.543200i
\(835\) 13.3394 0.461629
\(836\) 4.30029 + 7.44832i 0.148729 + 0.257606i
\(837\) 41.9723 30.6598i 1.45078 1.05976i
\(838\) −4.45869 2.57422i −0.154023 0.0889251i
\(839\) −3.80537 6.59110i −0.131376 0.227550i 0.792831 0.609441i \(-0.208606\pi\)
−0.924207 + 0.381891i \(0.875273\pi\)
\(840\) −3.08927 2.73425i −0.106590 0.0943407i
\(841\) −12.2037 + 21.1375i −0.420819 + 0.728880i
\(842\) 23.3864 13.5022i 0.805950 0.465315i
\(843\) −25.4854 + 5.43990i −0.877763 + 0.187360i
\(844\) 9.37193 16.2327i 0.322595 0.558751i
\(845\) −3.47414 + 6.01739i −0.119514 + 0.207004i
\(846\) −13.8285 + 19.1020i −0.475433 + 0.656740i
\(847\) 1.28500 2.94680i 0.0441533 0.101253i
\(848\) −12.0733 + 6.97054i −0.414600 + 0.239369i
\(849\) −2.15094 + 6.63927i −0.0738202 + 0.227859i
\(850\) 21.5877i 0.740450i
\(851\) 16.2546i 0.557200i
\(852\) 7.55274 23.3129i 0.258753 0.798686i
\(853\) −24.8764 + 14.3624i −0.851751 + 0.491759i −0.861241 0.508196i \(-0.830312\pi\)
0.00949029 + 0.999955i \(0.496979\pi\)
\(854\) −11.3999 15.4401i −0.390096 0.528350i
\(855\) 4.35442 6.01498i 0.148918 0.205708i
\(856\) 7.13519 12.3585i 0.243876 0.422405i
\(857\) −20.1198 + 34.8486i −0.687280 + 1.19040i 0.285434 + 0.958398i \(0.407862\pi\)
−0.972714 + 0.232006i \(0.925471\pi\)
\(858\) −12.1775 + 2.59932i −0.415734 + 0.0887394i
\(859\) −13.3256 + 7.69355i −0.454664 + 0.262501i −0.709798 0.704405i \(-0.751214\pi\)
0.255134 + 0.966906i \(0.417881\pi\)
\(860\) 0.245910 0.425929i 0.00838547 0.0145241i
\(861\) 10.9686 + 2.23386i 0.373808 + 0.0761297i
\(862\) −4.68159 8.10874i −0.159455 0.276185i
\(863\) 16.6494 + 9.61252i 0.566751 + 0.327214i 0.755851 0.654744i \(-0.227224\pi\)
−0.189099 + 0.981958i \(0.560557\pi\)
\(864\) −4.19591 + 3.06502i −0.142748 + 0.104274i
\(865\) −2.08655 3.61400i −0.0709447 0.122880i
\(866\) −21.0373 −0.714876
\(867\) −12.2841 + 11.0797i −0.417189 + 0.376286i
\(868\) −21.2914 + 15.7200i −0.722676 + 0.533572i
\(869\) 17.7386 + 10.2414i 0.601742 + 0.347416i
\(870\) −2.48136 + 2.23808i −0.0841261 + 0.0758781i
\(871\) −7.30552 4.21785i −0.247538 0.142916i
\(872\) −4.58271 + 2.64583i −0.155190 + 0.0895991i
\(873\) 30.5573 + 3.15878i 1.03421 + 0.106909i
\(874\) 4.71727i 0.159564i
\(875\) −13.0010 17.6087i −0.439514 0.595283i
\(876\) 21.3569 4.55868i 0.721583 0.154023i
\(877\) 5.39035 + 9.33636i 0.182019 + 0.315267i 0.942568 0.334014i \(-0.108403\pi\)
−0.760549 + 0.649281i \(0.775070\pi\)
\(878\) 20.4229 0.689238
\(879\) 16.9674 15.3038i 0.572296 0.516186i
\(880\) 2.81608i 0.0949302i
\(881\) −44.2875 −1.49208 −0.746041 0.665900i \(-0.768048\pi\)
−0.746041 + 0.665900i \(0.768048\pi\)
\(882\) −12.6314 16.7764i −0.425322 0.564890i
\(883\) −47.6098 −1.60220 −0.801098 0.598533i \(-0.795751\pi\)
−0.801098 + 0.598533i \(0.795751\pi\)
\(884\) 11.8423i 0.398298i
\(885\) −2.59895 12.1758i −0.0873626 0.409284i
\(886\) 32.3649 1.08732
\(887\) 0.989965 + 1.71467i 0.0332398 + 0.0575730i 0.882167 0.470937i \(-0.156084\pi\)
−0.848927 + 0.528510i \(0.822751\pi\)
\(888\) 10.9905 + 12.1852i 0.368818 + 0.408909i
\(889\) 9.59541 + 12.9961i 0.321820 + 0.435876i
\(890\) 10.8075i 0.362268i
\(891\) 5.75889 27.5575i 0.192930 0.923210i
\(892\) −2.21609 + 1.27946i −0.0742001 + 0.0428395i
\(893\) 18.7172 + 10.8064i 0.626346 + 0.361621i
\(894\) −1.84197 8.62944i −0.0616047 0.288612i
\(895\) 4.73405 + 2.73320i 0.158242 + 0.0913609i
\(896\) 2.12847 1.57151i 0.0711071 0.0525003i
\(897\) 6.49717 + 2.10491i 0.216934 + 0.0702807i
\(898\) 21.5693 0.719776
\(899\) 10.7184 + 18.5649i 0.357480 + 0.619173i
\(900\) −11.4732 + 5.13178i −0.382441 + 0.171059i
\(901\) 62.2109 + 35.9175i 2.07255 + 1.19659i
\(902\) −3.82045 6.61721i −0.127207 0.220329i
\(903\) 1.65925 1.87469i 0.0552164 0.0623857i
\(904\) −1.33005 + 2.30371i −0.0442368 + 0.0766204i
\(905\) −5.55654 + 3.20807i −0.184706 + 0.106640i
\(906\) 24.5651 + 27.2353i 0.816119 + 0.904832i
\(907\) −17.0252 + 29.4886i −0.565314 + 0.979152i 0.431707 + 0.902014i \(0.357912\pi\)
−0.997020 + 0.0771381i \(0.975422\pi\)
\(908\) 4.36455 7.55962i 0.144843 0.250875i
\(909\) −7.44715 + 3.33099i −0.247006 + 0.110482i
\(910\) −3.25146 4.40381i −0.107785 0.145985i
\(911\) −6.58371 + 3.80111i −0.218128 + 0.125936i −0.605083 0.796162i \(-0.706860\pi\)
0.386955 + 0.922099i \(0.373527\pi\)
\(912\) 3.18958 + 3.53629i 0.105618 + 0.117098i
\(913\) 1.15387i 0.0381875i
\(914\) 21.0700i 0.696932i
\(915\) 11.0621 2.36122i 0.365701 0.0780597i
\(916\) 3.40979 1.96865i 0.112663 0.0650459i
\(917\) 8.41556 19.2987i 0.277906 0.637300i
\(918\) 24.4876 + 10.8273i 0.808212 + 0.357353i
\(919\) −4.11136 + 7.12109i −0.135621 + 0.234903i −0.925835 0.377929i \(-0.876636\pi\)
0.790213 + 0.612832i \(0.209970\pi\)
\(920\) 0.772286 1.33764i 0.0254615 0.0441006i
\(921\) −15.3575 + 47.4038i −0.506048 + 1.56201i
\(922\) −27.4378 + 15.8412i −0.903617 + 0.521704i
\(923\) 16.2582 28.1601i 0.535146 0.926900i
\(924\) −2.86068 + 14.0464i −0.0941094 + 0.462091i
\(925\) 19.8459 + 34.3741i 0.652529 + 1.13021i
\(926\) 7.62202 + 4.40058i 0.250475 + 0.144612i
\(927\) 4.09563 + 0.423374i 0.134518 + 0.0139054i
\(928\) −1.07151 1.85590i −0.0351739 0.0609230i
\(929\) 5.07963 0.166657 0.0833287 0.996522i \(-0.473445\pi\)
0.0833287 + 0.996522i \(0.473445\pi\)
\(930\) −3.25604 15.2542i −0.106770 0.500205i
\(931\) −14.1035 + 13.0962i −0.462225 + 0.429210i
\(932\) 3.92147 + 2.26406i 0.128452 + 0.0741618i
\(933\) 50.8256 + 16.4661i 1.66395 + 0.539076i
\(934\) 16.4449 + 9.49444i 0.538092 + 0.310668i
\(935\) 12.5665 7.25530i 0.410970 0.237274i
\(936\) −6.29382 + 2.81512i −0.205720 + 0.0920151i
\(937\) 10.8127i 0.353236i −0.984280 0.176618i \(-0.943484\pi\)
0.984280 0.176618i \(-0.0565157\pi\)
\(938\) −7.81254 + 5.76822i −0.255089 + 0.188339i
\(939\) −9.80422 + 30.2625i −0.319949 + 0.987578i
\(940\) 3.53832 + 6.12855i 0.115407 + 0.199891i
\(941\) −19.1639 −0.624724 −0.312362 0.949963i \(-0.601120\pi\)
−0.312362 + 0.949963i \(0.601120\pi\)
\(942\) −0.593059 0.192135i −0.0193229 0.00626010i
\(943\) 4.19090i 0.136474i
\(944\) 7.98443 0.259871
\(945\) 12.0791 2.69706i 0.392932 0.0877352i
\(946\) −1.70891 −0.0555613
\(947\) 25.3953i 0.825237i 0.910904 + 0.412618i \(0.135386\pi\)
−0.910904 + 0.412618i \(0.864614\pi\)
\(948\) 10.7894 + 3.49548i 0.350425 + 0.113528i
\(949\) 28.9766 0.940620
\(950\) 5.75950 + 9.97575i 0.186863 + 0.323656i
\(951\) 9.31839 28.7629i 0.302170 0.932700i
\(952\) −12.4964 5.44931i −0.405012 0.176613i
\(953\) 18.4818i 0.598686i −0.954146 0.299343i \(-0.903233\pi\)
0.954146 0.299343i \(-0.0967674\pi\)
\(954\) 4.30045 41.6016i 0.139232 1.34690i
\(955\) 11.2274 6.48215i 0.363310 0.209757i
\(956\) 7.55315 + 4.36081i 0.244286 + 0.141039i
\(957\) 11.0456 + 3.57849i 0.357055 + 0.115676i
\(958\) 20.9060 + 12.0701i 0.675441 + 0.389966i
\(959\) 6.48060 + 57.4185i 0.209270 + 1.85414i
\(960\) 0.325502 + 1.52494i 0.0105055 + 0.0492172i
\(961\) −69.0630 −2.22784
\(962\) 10.8868 + 18.8565i 0.351004 + 0.607957i
\(963\) 17.4798 + 39.0800i 0.563280 + 1.25934i
\(964\) 17.1314 + 9.89079i 0.551764 + 0.318561i
\(965\) −8.01745 13.8866i −0.258091 0.447026i
\(966\) 5.21091 5.88749i 0.167658 0.189427i
\(967\) −9.64551 + 16.7065i −0.310179 + 0.537245i −0.978401 0.206717i \(-0.933722\pi\)
0.668222 + 0.743962i \(0.267056\pi\)
\(968\) −1.05229 + 0.607537i −0.0338217 + 0.0195270i
\(969\) 7.56284 23.3441i 0.242953 0.749919i
\(970\) 4.60935 7.98362i 0.147997 0.256339i
\(971\) −0.975444 + 1.68952i −0.0313035 + 0.0542192i −0.881253 0.472645i \(-0.843299\pi\)
0.849949 + 0.526865i \(0.176633\pi\)
\(972\) −0.0667715 15.5883i −0.00214170 0.499995i
\(973\) −4.01256 35.5515i −0.128637 1.13973i
\(974\) −12.2204 + 7.05542i −0.391565 + 0.226070i
\(975\) −16.3097 + 3.48135i −0.522329 + 0.111492i
\(976\) 7.25411i 0.232198i
\(977\) 16.7265i 0.535129i −0.963540 0.267564i \(-0.913781\pi\)
0.963540 0.267564i \(-0.0862188\pi\)
\(978\) 14.3533 + 15.9136i 0.458969 + 0.508859i
\(979\) −32.5213 + 18.7762i −1.03938 + 0.600089i
\(980\) −6.14327 + 1.40463i −0.196240 + 0.0448691i
\(981\) 1.63233 15.7908i 0.0521164 0.504162i
\(982\) 10.8740 18.8344i 0.347004 0.601028i
\(983\) −16.1458 + 27.9653i −0.514970 + 0.891955i 0.484879 + 0.874581i \(0.338864\pi\)
−0.999849 + 0.0173733i \(0.994470\pi\)
\(984\) −2.83368 3.14170i −0.0903343 0.100154i
\(985\) −14.8932 + 8.59858i −0.474536 + 0.273974i
\(986\) −5.52121 + 9.56302i −0.175831 + 0.304549i
\(987\) 11.4232 + 34.1629i 0.363604 + 1.08742i
\(988\) 3.15947 + 5.47236i 0.100516 + 0.174099i
\(989\) 0.811730 + 0.468652i 0.0258115 + 0.0149023i
\(990\) −6.84328 4.95404i −0.217494 0.157450i
\(991\) 4.25134 + 7.36353i 0.135048 + 0.233910i 0.925616 0.378464i \(-0.123548\pi\)
−0.790568 + 0.612375i \(0.790214\pi\)
\(992\) 10.0032 0.317600
\(993\) 17.1850 + 5.56746i 0.545348 + 0.176678i
\(994\) −22.2343 30.1144i −0.705231 0.955172i
\(995\) −10.4437 6.02967i −0.331087 0.191153i
\(996\) −0.133372 0.624832i −0.00422605 0.0197986i
\(997\) 9.78395 + 5.64877i 0.309861 + 0.178898i 0.646864 0.762605i \(-0.276080\pi\)
−0.337003 + 0.941503i \(0.609413\pi\)
\(998\) −7.29596 + 4.21233i −0.230950 + 0.133339i
\(999\) −48.9454 + 5.27159i −1.54857 + 0.166786i
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 126.2.l.a.5.8 16
3.2 odd 2 378.2.l.a.341.3 16
4.3 odd 2 1008.2.ca.c.257.1 16
7.2 even 3 882.2.m.b.293.5 16
7.3 odd 6 126.2.t.a.59.3 yes 16
7.4 even 3 882.2.t.a.815.2 16
7.5 odd 6 882.2.m.a.293.8 16
7.6 odd 2 882.2.l.b.509.5 16
9.2 odd 6 126.2.t.a.47.3 yes 16
9.4 even 3 1134.2.k.a.971.2 16
9.5 odd 6 1134.2.k.b.971.7 16
9.7 even 3 378.2.t.a.89.7 16
12.11 even 2 3024.2.ca.c.2609.6 16
21.2 odd 6 2646.2.m.b.881.3 16
21.5 even 6 2646.2.m.a.881.2 16
21.11 odd 6 2646.2.t.b.2285.6 16
21.17 even 6 378.2.t.a.17.7 16
21.20 even 2 2646.2.l.a.1097.2 16
28.3 even 6 1008.2.df.c.689.4 16
36.7 odd 6 3024.2.df.c.1601.6 16
36.11 even 6 1008.2.df.c.929.4 16
63.2 odd 6 882.2.m.a.587.8 16
63.11 odd 6 882.2.l.b.227.1 16
63.16 even 3 2646.2.m.a.1763.2 16
63.20 even 6 882.2.t.a.803.2 16
63.25 even 3 2646.2.l.a.521.6 16
63.31 odd 6 1134.2.k.b.647.7 16
63.34 odd 6 2646.2.t.b.1979.6 16
63.38 even 6 inner 126.2.l.a.101.4 yes 16
63.47 even 6 882.2.m.b.587.5 16
63.52 odd 6 378.2.l.a.143.7 16
63.59 even 6 1134.2.k.a.647.2 16
63.61 odd 6 2646.2.m.b.1763.3 16
84.59 odd 6 3024.2.df.c.17.6 16
252.115 even 6 3024.2.ca.c.2033.6 16
252.227 odd 6 1008.2.ca.c.353.1 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
126.2.l.a.5.8 16 1.1 even 1 trivial
126.2.l.a.101.4 yes 16 63.38 even 6 inner
126.2.t.a.47.3 yes 16 9.2 odd 6
126.2.t.a.59.3 yes 16 7.3 odd 6
378.2.l.a.143.7 16 63.52 odd 6
378.2.l.a.341.3 16 3.2 odd 2
378.2.t.a.17.7 16 21.17 even 6
378.2.t.a.89.7 16 9.7 even 3
882.2.l.b.227.1 16 63.11 odd 6
882.2.l.b.509.5 16 7.6 odd 2
882.2.m.a.293.8 16 7.5 odd 6
882.2.m.a.587.8 16 63.2 odd 6
882.2.m.b.293.5 16 7.2 even 3
882.2.m.b.587.5 16 63.47 even 6
882.2.t.a.803.2 16 63.20 even 6
882.2.t.a.815.2 16 7.4 even 3
1008.2.ca.c.257.1 16 4.3 odd 2
1008.2.ca.c.353.1 16 252.227 odd 6
1008.2.df.c.689.4 16 28.3 even 6
1008.2.df.c.929.4 16 36.11 even 6
1134.2.k.a.647.2 16 63.59 even 6
1134.2.k.a.971.2 16 9.4 even 3
1134.2.k.b.647.7 16 63.31 odd 6
1134.2.k.b.971.7 16 9.5 odd 6
2646.2.l.a.521.6 16 63.25 even 3
2646.2.l.a.1097.2 16 21.20 even 2
2646.2.m.a.881.2 16 21.5 even 6
2646.2.m.a.1763.2 16 63.16 even 3
2646.2.m.b.881.3 16 21.2 odd 6
2646.2.m.b.1763.3 16 63.61 odd 6
2646.2.t.b.1979.6 16 63.34 odd 6
2646.2.t.b.2285.6 16 21.11 odd 6
3024.2.ca.c.2033.6 16 252.115 even 6
3024.2.ca.c.2609.6 16 12.11 even 2
3024.2.df.c.17.6 16 84.59 odd 6
3024.2.df.c.1601.6 16 36.7 odd 6