Properties

Label 126.2.l.a.101.4
Level $126$
Weight $2$
Character 126.101
Analytic conductor $1.006$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

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 101.4
Root \(1.58110 - 0.707199i\) of defining polynomial
Character \(\chi\) \(=\) 126.101
Dual form 126.2.l.a.5.8

$q$-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 \(\left(\mathbb{Z}/126\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(73\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{6}\right)\)

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 −0.948949 0.315430i \(-0.897851\pi\)
0.747645 + 0.664099i \(0.231185\pi\)
\(6\) −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 −0.849310 0.527894i \(-0.822982\pi\)
0.0325150 + 0.999471i \(0.489648\pi\)
\(12\) −1.64774 + 0.533822i −0.475660 + 0.154101i
\(13\) −1.99033 + 1.14912i −0.552019 + 0.318708i −0.749936 0.661511i \(-0.769916\pi\)
0.197917 + 0.980219i \(0.436582\pi\)
\(14\) −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 0.363704 + 0.931515i \(0.381512\pi\)
−0.988567 + 0.150780i \(0.951821\pi\)
\(18\) −1.75919 2.43007i −0.414646 0.572773i
\(19\) 2.38111 1.37474i 0.546264 0.315386i −0.201350 0.979519i \(-0.564533\pi\)
0.747614 + 0.664134i \(0.231199\pi\)
\(20\) 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 0.337027 0.941495i \(-0.390579\pi\)
−0.646845 + 0.762621i \(0.723912\pi\)
\(24\) 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 0.317686 0.948196i \(-0.397094\pi\)
−0.662319 + 0.749222i \(0.730428\pi\)
\(30\) 1.52494 + 0.325502i 0.278415 + 0.0594282i
\(31\) 10.0032i 1.79662i 0.439363 + 0.898309i \(0.355204\pi\)
−0.439363 + 0.898309i \(0.644796\pi\)
\(32\) 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 −0.932657 0.360766i \(-0.882515\pi\)
0.153896 0.988087i \(-0.450818\pi\)
\(38\) −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 0.945496 0.325634i \(-0.105578\pi\)
−0.754755 + 0.656007i \(0.772244\pi\)
\(42\) −4.34605 1.45321i −0.670611 0.224235i
\(43\) −0.273155 + 0.473119i −0.0416558 + 0.0721499i −0.886102 0.463491i \(-0.846597\pi\)
0.844446 + 0.535641i \(0.179930\pi\)
\(44\) 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 −0.973454 0.228885i \(-0.926492\pi\)
−0.684947 0.728593i \(-0.740175\pi\)
\(54\) −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 \(-0.846271\pi\)
0.885627 0.464397i \(-0.153729\pi\)
\(62\) 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 \(-0.682816\pi\)
0.543275 0.839555i \(-0.317184\pi\)
\(72\) 1.75919 + 2.43007i 0.207323 + 0.286386i
\(73\) −10.9190 6.30409i −1.27797 0.737838i −0.301498 0.953467i \(-0.597487\pi\)
−0.976475 + 0.215629i \(0.930820\pi\)
\(74\) −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 −0.855726 0.517430i \(-0.826889\pi\)
0.875970 + 0.482365i \(0.160222\pi\)
\(84\) −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 0.986247 + 0.165277i \(0.0528518\pi\)
−0.349990 + 0.936754i \(0.613815\pi\)
\(90\) 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 0.877338 0.479873i \(-0.159317\pi\)
0.0230864 + 0.999733i \(0.492651\pi\)
\(98\) −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 0.790415 0.612571i \(-0.209865\pi\)
−0.925710 + 0.378234i \(0.876531\pi\)
\(102\) 8.72821 + 1.86306i 0.864222 + 0.184470i
\(103\) 1.18861 + 0.686242i 0.117117 + 0.0676174i 0.557414 0.830235i \(-0.311794\pi\)
−0.440297 + 0.897852i \(0.645127\pi\)
\(104\) −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 0.235364 0.971907i \(-0.424372\pi\)
0.959378 + 0.282122i \(0.0910385\pi\)
\(108\) −3.06502 + 4.19591i −0.294931 + 0.403752i
\(109\) −2.64583 + 4.58271i −0.253425 + 0.438944i −0.964466 0.264206i \(-0.914890\pi\)
0.711042 + 0.703150i \(0.248224\pi\)
\(110\) −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 −0.604428 0.796659i \(-0.706598\pi\)
0.387713 + 0.921780i \(0.373265\pi\)
\(114\) −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 −0.985828 0.167761i \(-0.946346\pi\)
0.638199 + 0.769871i \(0.279680\pi\)
\(132\) 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 0.627970 0.778237i \(-0.283886\pi\)
0.987958 0.154719i \(-0.0494473\pi\)
\(138\) −0.620337 + 2.90621i −0.0528066 + 0.247393i
\(139\) −11.7109 + 6.76127i −0.993302 + 0.573483i −0.906260 0.422721i \(-0.861075\pi\)
−0.0870425 + 0.996205i \(0.527742\pi\)
\(140\) −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 0.308273 0.951298i \(-0.400249\pi\)
−0.669711 + 0.742621i \(0.733582\pi\)
\(150\) 4.86016 5.38846i 0.396830 0.439966i
\(151\) 10.5877 + 18.3385i 0.861618 + 1.49237i 0.870366 + 0.492405i \(0.163882\pi\)
−0.00874783 + 0.999962i \(0.502785\pi\)
\(152\) 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 \(-0.995428\pi\)
0.999897 0.0143625i \(-0.00457189\pi\)
\(158\) 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 0.999843 0.0177416i \(-0.00564762\pi\)
−0.515286 + 0.857018i \(0.672314\pi\)
\(164\) −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 −0.996224 0.0868188i \(-0.972330\pi\)
0.422925 0.906165i \(-0.361003\pi\)
\(168\) 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 0.290435 0.956895i \(-0.406200\pi\)
−0.683477 + 0.729972i \(0.739533\pi\)
\(180\) −0.277705 2.68646i −0.0206989 0.200237i
\(181\) 7.12701i 0.529746i 0.964283 + 0.264873i \(0.0853301\pi\)
−0.964283 + 0.264873i \(0.914670\pi\)
\(182\) 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 \(-0.825560\pi\)
0.853558 0.520997i \(-0.174440\pi\)
\(192\) −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 \(0.238236\pi\)
−0.732750 + 0.680498i \(0.761764\pi\)
\(198\) 8.56640 + 3.83161i 0.608787 + 0.272300i
\(199\) 11.6008 + 6.69771i 0.822357 + 0.474788i 0.851229 0.524795i \(-0.175858\pi\)
−0.0288716 + 0.999583i \(0.509191\pi\)
\(200\) −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 −0.984258 0.176740i \(-0.943445\pi\)
0.339067 0.940762i \(-0.389889\pi\)
\(212\) 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 0.572362 0.820001i \(-0.306027\pi\)
−0.423961 + 0.905680i \(0.639361\pi\)
\(224\) −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 0.684049 0.729436i \(-0.260217\pi\)
−0.973735 + 0.227686i \(0.926884\pi\)
\(228\) −3.18958 + 3.53629i −0.211235 + 0.234197i
\(229\) −3.40979 1.96865i −0.225325 0.130092i 0.383088 0.923712i \(-0.374861\pi\)
−0.608414 + 0.793620i \(0.708194\pi\)
\(230\) −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 −0.622921 0.782284i \(-0.714054\pi\)
0.366018 + 0.930608i \(0.380721\pi\)
\(234\) 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 −0.723982 0.689819i \(-0.757690\pi\)
0.235409 + 0.971896i \(0.424357\pi\)
\(240\) −0.325502 + 1.52494i −0.0210110 + 0.0984344i
\(241\) −17.1314 + 9.89079i −1.10353 + 0.637122i −0.937145 0.348939i \(-0.886542\pi\)
−0.166382 + 0.986061i \(0.553209\pi\)
\(242\) 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 −0.999419 0.0340869i \(-0.989148\pi\)
0.529230 + 0.848479i \(0.322481\pi\)
\(258\) 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 −0.689449 0.724334i \(-0.742147\pi\)
0.282567 + 0.959248i \(0.408814\pi\)
\(264\) −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 −0.967257 0.253797i \(-0.918320\pi\)
0.703424 + 0.710771i \(0.251654\pi\)
\(270\) 4.27833 1.89167i 0.260371 0.115124i
\(271\) −15.6611 + 9.04193i −0.951343 + 0.549258i −0.893498 0.449068i \(-0.851756\pi\)
−0.0578449 + 0.998326i \(0.518423\pi\)
\(272\) −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 0.676241 0.736681i \(-0.263608\pi\)
−0.976105 + 0.217301i \(0.930275\pi\)
\(278\) 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 0.0581797 0.998306i \(-0.481470\pi\)
−0.835469 + 0.549538i \(0.814804\pi\)
\(282\) −4.19620 12.9523i −0.249880 0.771300i
\(283\) 4.02933i 0.239519i −0.992803 0.119759i \(-0.961788\pi\)
0.992803 0.119759i \(-0.0382123\pi\)
\(284\) 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 0.991817 0.127665i \(-0.0407483\pi\)
−0.606470 + 0.795106i \(0.707415\pi\)
\(294\) −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 \(-0.693434\pi\)
0.570974 0.820968i \(-0.306566\pi\)
\(308\) 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 \(-0.826283\pi\)
0.854740 0.519056i \(-0.173717\pi\)
\(314\) −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 \(0.163081\pi\)
−0.871603 + 0.490213i \(0.836919\pi\)
\(318\) −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 −0.869626 0.493712i \(-0.835640\pi\)
0.00724616 0.999974i \(-0.497693\pi\)
\(338\) 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 \(0.109140\pi\)
−0.941793 + 0.336195i \(0.890860\pi\)
\(348\) 3.63003 + 0.774838i 0.194590 + 0.0415357i
\(349\) 12.2560 + 7.07599i 0.656047 + 0.378769i 0.790769 0.612115i \(-0.209681\pi\)
−0.134722 + 0.990883i \(0.543014\pi\)
\(350\) 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 0.792362 0.610052i \(-0.208851\pi\)
−0.924501 + 0.381180i \(0.875518\pi\)
\(354\) −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 −0.0488375 0.998807i \(-0.515552\pi\)
0.840573 + 0.541698i \(0.182218\pi\)
\(360\) −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 −0.468673 0.883372i \(-0.655268\pi\)
0.530686 + 0.847569i \(0.321934\pi\)
\(368\) −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 −0.797025 0.603946i \(-0.793594\pi\)
0.921545 + 0.388271i \(0.126928\pi\)
\(374\) −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 −0.112940 0.993602i \(-0.536027\pi\)
0.916955 0.398992i \(-0.130640\pi\)
\(384\) 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 −0.408068 0.912952i \(-0.633797\pi\)
0.586605 + 0.809873i \(0.300464\pi\)
\(390\) −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 −0.592715 0.805412i \(-0.701944\pi\)
0.401150 + 0.916013i \(0.368611\pi\)
\(398\) 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 0.844144 0.536116i \(-0.180109\pi\)
−0.0422180 + 0.999108i \(0.513442\pi\)
\(402\) −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 \(0.210994\pi\)
−0.788238 + 0.615370i \(0.789006\pi\)
\(410\) 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 0.796270 0.604941i \(-0.206803\pi\)
−0.922029 + 0.387120i \(0.873470\pi\)
\(420\) −2.73425 3.08927i −0.133418 0.150741i
\(421\) −13.5022 + 23.3864i −0.658055 + 1.13978i 0.323063 + 0.946377i \(0.395287\pi\)
−0.981119 + 0.193408i \(0.938046\pi\)
\(422\) −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 0.291829 0.956471i \(-0.405736\pi\)
−0.682413 + 0.730966i \(0.739070\pi\)
\(432\) 3.06502 4.19591i 0.147466 0.201876i
\(433\) 21.0373i 1.01099i −0.862830 0.505494i \(-0.831310\pi\)
0.862830 0.505494i \(-0.168690\pi\)
\(434\) 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 \(0.162042\pi\)
−0.873198 + 0.487365i \(0.837958\pi\)
\(440\) 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 \(0.279172\pi\)
−0.639427 + 0.768852i \(0.720828\pi\)
\(444\) 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 \(0.169969\pi\)
−0.860791 + 0.508958i \(0.830031\pi\)
\(450\) 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 −0.215684 0.976463i \(-0.569198\pi\)
0.953484 0.301444i \(-0.0974687\pi\)
\(462\) 14.0464 2.86068i 0.653495 0.133091i
\(463\) 4.40058 + 7.62202i 0.204512 + 0.354225i 0.949977 0.312319i \(-0.101106\pi\)
−0.745465 + 0.666545i \(0.767773\pi\)
\(464\) −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 0.997639 0.0686693i \(-0.0218753\pi\)
−0.558289 + 0.829646i \(0.688542\pi\)
\(468\) 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 0.998167 + 0.0605197i \(0.0192758\pi\)
−0.446672 + 0.894698i \(0.647391\pi\)
\(480\) 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 −0.660716 0.750636i \(-0.729747\pi\)
0.980428 + 0.196879i \(0.0630806\pi\)
\(488\) 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 −0.860645 0.509206i \(-0.829939\pi\)
0.0106626 + 0.999943i \(0.496606\pi\)
\(492\) −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 −0.756204 0.654336i \(-0.772948\pi\)
0.944774 + 0.327724i \(0.106282\pi\)
\(500\) 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 0.319082 + 0.947727i \(0.396625\pi\)
−0.980297 + 0.197530i \(0.936708\pi\)
\(510\) −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 −0.997154 0.0753863i \(-0.975981\pi\)
0.563864 + 0.825868i \(0.309314\pi\)
\(522\) 0.661062 + 6.39496i 0.0289339 + 0.279900i
\(523\) −10.5932 + 6.11597i −0.463207 + 0.267433i −0.713392 0.700766i \(-0.752842\pi\)
0.250185 + 0.968198i \(0.419509\pi\)
\(524\) 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 0.858427 0.512936i \(-0.171442\pi\)
−0.873429 + 0.486951i \(0.838109\pi\)
\(542\) 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 0.0681854 0.997673i \(-0.478279\pi\)
0.829917 0.557887i \(-0.188388\pi\)
\(548\) −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 0.599340 0.800495i \(-0.295430\pi\)
−0.393579 + 0.919291i \(0.628763\pi\)
\(558\) 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 \(0.0591709\pi\)
−0.982772 + 0.184822i \(0.940829\pi\)
\(570\) 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 0.791923 0.610621i \(-0.209080\pi\)
−0.132852 + 0.991136i \(0.542413\pi\)
\(578\) −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 −0.899949 0.435996i \(-0.856396\pi\)
0.827558 + 0.561380i \(0.189730\pi\)
\(588\) 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 −0.582727 0.812668i \(-0.698014\pi\)
−0.412428 0.910990i \(-0.635319\pi\)
\(594\) 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 \(-0.828266\pi\)
0.857955 0.513724i \(-0.171734\pi\)
\(600\) −4.86016 + 5.38846i −0.198415 + 0.219983i
\(601\) 11.2731 + 6.50854i 0.459840 + 0.265489i 0.711977 0.702203i \(-0.247800\pi\)
−0.252137 + 0.967692i \(0.581133\pi\)
\(602\) 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 0.348819 0.937190i \(-0.386583\pi\)
−0.637221 + 0.770681i \(0.719916\pi\)
\(608\) −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 −0.814646 0.579959i \(-0.803069\pi\)
0.909582 + 0.415525i \(0.136402\pi\)
\(614\) −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 −0.116668 0.993171i \(-0.537221\pi\)
0.801777 + 0.597623i \(0.203888\pi\)
\(618\) 0.496242 2.32484i 0.0199618 0.0935187i
\(619\) 30.0586 17.3544i 1.20816 0.697531i 0.245802 0.969320i \(-0.420949\pi\)
0.962357 + 0.271789i \(0.0876153\pi\)
\(620\) 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 −0.244003 0.969774i \(-0.578461\pi\)
0.717848 + 0.696200i \(0.245127\pi\)
\(642\) −18.3542 16.5546i −0.724381 0.653360i
\(643\) −27.9684 + 16.1476i −1.10297 + 0.636797i −0.936998 0.349334i \(-0.886408\pi\)
−0.165967 + 0.986131i \(0.553075\pi\)
\(644\) 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 −0.986693 0.162595i \(-0.948014\pi\)
0.634158 + 0.773204i \(0.281347\pi\)
\(648\) 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 0.621597 0.783338i \(-0.286484\pi\)
−0.367592 + 0.929987i \(0.619818\pi\)
\(654\) 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 0.307256 0.951627i \(-0.400589\pi\)
−0.670505 + 0.741905i \(0.733923\pi\)
\(660\) 1.50329 + 4.64016i 0.0585154 + 0.180618i
\(661\) 11.6409i 0.452778i −0.974037 0.226389i \(-0.927308\pi\)
0.974037 0.226389i \(-0.0726920\pi\)
\(662\) 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 −0.876449 0.481496i \(-0.840094\pi\)
0.855212 + 0.518279i \(0.173427\pi\)
\(674\) −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 0.997967 0.0637365i \(-0.0203017\pi\)
0.443786 + 0.896133i \(0.353635\pi\)
\(684\) −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 \(0.210024\pi\)
−0.790108 + 0.612967i \(0.789976\pi\)
\(692\) −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 \(-0.864283\pi\)
0.910474 0.413566i \(-0.135717\pi\)
\(702\) 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 0.765966 0.642881i \(-0.222261\pi\)
−0.939734 + 0.341906i \(0.888928\pi\)
\(720\) 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 0.369876 0.929081i \(-0.379400\pi\)
−0.619670 + 0.784863i \(0.712733\pi\)
\(728\) −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 0.950222 0.311572i \(-0.100856\pi\)
0.205282 + 0.978703i \(0.434189\pi\)
\(734\) −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 −0.554005 0.832513i \(-0.686901\pi\)
0.997980 + 0.0635263i \(0.0202347\pi\)
\(740\) −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 −0.293291 0.956023i \(-0.594751\pi\)
0.681295 + 0.732009i \(0.261417\pi\)
\(744\) −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 −0.569028 0.822318i \(-0.692680\pi\)
0.996662 + 0.0816339i \(0.0260138\pi\)
\(752\) 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 −0.604224 0.796815i \(-0.706517\pi\)
0.992174 + 0.124866i \(0.0398500\pi\)
\(762\) −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 −0.858616 0.512620i \(-0.828675\pi\)
0.0146339 + 0.999893i \(0.495342\pi\)
\(770\) −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 −0.682712 0.730687i \(-0.739200\pi\)
0.974150 + 0.225903i \(0.0725332\pi\)
\(774\) 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 \(-0.761171\pi\)
0.731483 0.681860i \(-0.238829\pi\)
\(788\) 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 0.933204 0.359347i \(-0.117000\pi\)
−0.777805 + 0.628505i \(0.783667\pi\)
\(798\) −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 0.888513 0.458851i \(-0.151739\pi\)
0.0468805 + 0.998901i \(0.485072\pi\)
\(810\) 6.03974 5.40085i 0.212215 0.189766i
\(811\) 8.70634i 0.305721i −0.988248 0.152861i \(-0.951151\pi\)
0.988248 0.152861i \(-0.0488485\pi\)
\(812\) 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 \(0.367803\pi\)
−0.403473 + 0.914992i \(0.632197\pi\)
\(822\) −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 \(-0.847622\pi\)
0.887590 0.460634i \(-0.152378\pi\)
\(828\) 5.11982 0.529247i 0.177926 0.0183926i
\(829\) −5.14134 2.96835i −0.178566 0.103095i 0.408053 0.912958i \(-0.366208\pi\)
−0.586619 + 0.809863i \(0.699541\pi\)
\(830\) 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 −0.924207 0.381891i \(-0.875273\pi\)
0.792831 + 0.609441i \(0.208606\pi\)
\(840\) −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 0.00949029 0.999955i \(-0.496979\pi\)
−0.861241 + 0.508196i \(0.830312\pi\)
\(854\) −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 −0.972714 0.232006i \(-0.925471\pi\)
0.285434 0.958398i \(-0.407862\pi\)
\(858\) −12.1775 2.59932i −0.415734 0.0887394i
\(859\) −13.3256 7.69355i −0.454664 0.262501i 0.255134 0.966906i \(-0.417881\pi\)
−0.709798 + 0.704405i \(0.751214\pi\)
\(860\) 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 −0.189099 0.981958i \(-0.560557\pi\)
0.755851 + 0.654744i \(0.227224\pi\)
\(864\) −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 −0.760549 0.649281i \(-0.775070\pi\)
0.942568 + 0.334014i \(0.108403\pi\)
\(878\) 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 −0.848927 0.528510i \(-0.822751\pi\)
0.882167 + 0.470937i \(0.156084\pi\)
\(888\) 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 −0.997020 0.0771381i \(-0.975422\pi\)
0.431707 0.902014i \(-0.357912\pi\)
\(908\) 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 0.386955 0.922099i \(-0.373527\pi\)
−0.605083 + 0.796162i \(0.706860\pi\)
\(912\) 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 0.790213 0.612832i \(-0.209970\pi\)
−0.925835 + 0.377929i \(0.876636\pi\)
\(920\) 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 \(0.0565157\pi\)
−0.984280 + 0.176618i \(0.943484\pi\)
\(938\) −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 \(-0.864614\pi\)
0.910904 0.412618i \(-0.135386\pi\)
\(948\) 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 \(0.0967674\pi\)
−0.954146 + 0.299343i \(0.903233\pi\)
\(954\) 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 0.668222 0.743962i \(-0.267056\pi\)
−0.978401 + 0.206717i \(0.933722\pi\)
\(968\) −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 0.849949 0.526865i \(-0.176633\pi\)
−0.881253 + 0.472645i \(0.843299\pi\)
\(972\) −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 \(0.0862188\pi\)
−0.963540 + 0.267564i \(0.913781\pi\)
\(978\) 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 −0.999849 0.0173733i \(-0.994470\pi\)
0.484879 0.874581i \(-0.338864\pi\)
\(984\) −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 −0.790568 0.612375i \(-0.790214\pi\)
0.925616 + 0.378464i \(0.123548\pi\)
\(992\) 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 −0.337003 0.941503i \(-0.609413\pi\)
0.646864 + 0.762605i \(0.276080\pi\)
\(998\) −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.101.4 yes 16
3.2 odd 2 378.2.l.a.143.7 16
4.3 odd 2 1008.2.ca.c.353.1 16
7.2 even 3 882.2.t.a.803.2 16
7.3 odd 6 882.2.m.a.587.8 16
7.4 even 3 882.2.m.b.587.5 16
7.5 odd 6 126.2.t.a.47.3 yes 16
7.6 odd 2 882.2.l.b.227.1 16
9.2 odd 6 1134.2.k.b.647.7 16
9.4 even 3 378.2.t.a.17.7 16
9.5 odd 6 126.2.t.a.59.3 yes 16
9.7 even 3 1134.2.k.a.647.2 16
12.11 even 2 3024.2.ca.c.2033.6 16
21.2 odd 6 2646.2.t.b.1979.6 16
21.5 even 6 378.2.t.a.89.7 16
21.11 odd 6 2646.2.m.b.1763.3 16
21.17 even 6 2646.2.m.a.1763.2 16
21.20 even 2 2646.2.l.a.521.6 16
28.19 even 6 1008.2.df.c.929.4 16
36.23 even 6 1008.2.df.c.689.4 16
36.31 odd 6 3024.2.df.c.17.6 16
63.4 even 3 2646.2.m.a.881.2 16
63.5 even 6 inner 126.2.l.a.5.8 16
63.13 odd 6 2646.2.t.b.2285.6 16
63.23 odd 6 882.2.l.b.509.5 16
63.31 odd 6 2646.2.m.b.881.3 16
63.32 odd 6 882.2.m.a.293.8 16
63.40 odd 6 378.2.l.a.341.3 16
63.41 even 6 882.2.t.a.815.2 16
63.47 even 6 1134.2.k.a.971.2 16
63.58 even 3 2646.2.l.a.1097.2 16
63.59 even 6 882.2.m.b.293.5 16
63.61 odd 6 1134.2.k.b.971.7 16
84.47 odd 6 3024.2.df.c.1601.6 16
252.103 even 6 3024.2.ca.c.2609.6 16
252.131 odd 6 1008.2.ca.c.257.1 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
126.2.l.a.5.8 16 63.5 even 6 inner
126.2.l.a.101.4 yes 16 1.1 even 1 trivial
126.2.t.a.47.3 yes 16 7.5 odd 6
126.2.t.a.59.3 yes 16 9.5 odd 6
378.2.l.a.143.7 16 3.2 odd 2
378.2.l.a.341.3 16 63.40 odd 6
378.2.t.a.17.7 16 9.4 even 3
378.2.t.a.89.7 16 21.5 even 6
882.2.l.b.227.1 16 7.6 odd 2
882.2.l.b.509.5 16 63.23 odd 6
882.2.m.a.293.8 16 63.32 odd 6
882.2.m.a.587.8 16 7.3 odd 6
882.2.m.b.293.5 16 63.59 even 6
882.2.m.b.587.5 16 7.4 even 3
882.2.t.a.803.2 16 7.2 even 3
882.2.t.a.815.2 16 63.41 even 6
1008.2.ca.c.257.1 16 252.131 odd 6
1008.2.ca.c.353.1 16 4.3 odd 2
1008.2.df.c.689.4 16 36.23 even 6
1008.2.df.c.929.4 16 28.19 even 6
1134.2.k.a.647.2 16 9.7 even 3
1134.2.k.a.971.2 16 63.47 even 6
1134.2.k.b.647.7 16 9.2 odd 6
1134.2.k.b.971.7 16 63.61 odd 6
2646.2.l.a.521.6 16 21.20 even 2
2646.2.l.a.1097.2 16 63.58 even 3
2646.2.m.a.881.2 16 63.4 even 3
2646.2.m.a.1763.2 16 21.17 even 6
2646.2.m.b.881.3 16 63.31 odd 6
2646.2.m.b.1763.3 16 21.11 odd 6
2646.2.t.b.1979.6 16 21.2 odd 6
2646.2.t.b.2285.6 16 63.13 odd 6
3024.2.ca.c.2033.6 16 12.11 even 2
3024.2.ca.c.2609.6 16 252.103 even 6
3024.2.df.c.17.6 16 36.31 odd 6
3024.2.df.c.1601.6 16 84.47 odd 6