Properties

Label 722.2.e.m.245.1
Level $722$
Weight $2$
Character 722.245
Analytic conductor $5.765$
Analytic rank $0$
Dimension $6$
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] = [722,2,Mod(99,722)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(722, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("722.99");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 722 = 2 \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 722.e (of order \(9\), degree \(6\), not 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: \(5.76519902594\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: \(\Q(\zeta_{18})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - x^{3} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 38)
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 245.1
Root \(-0.766044 - 0.642788i\) of defining polynomial
Character \(\chi\) \(=\) 722.245
Dual form 722.2.e.m.389.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.173648 - 0.984808i) q^{2} +(1.17365 + 0.984808i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(-1.87939 + 0.684040i) q^{5} +(1.17365 - 0.984808i) q^{6} +(-1.34730 - 2.33359i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-0.113341 - 0.642788i) q^{9} +O(q^{10})\) \(q+(0.173648 - 0.984808i) q^{2} +(1.17365 + 0.984808i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(-1.87939 + 0.684040i) q^{5} +(1.17365 - 0.984808i) q^{6} +(-1.34730 - 2.33359i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-0.113341 - 0.642788i) q^{9} +(0.347296 + 1.96962i) q^{10} +(-1.59240 + 2.75811i) q^{11} +(-0.766044 - 1.32683i) q^{12} +(-4.41147 + 3.70167i) q^{13} +(-2.53209 + 0.921605i) q^{14} +(-2.87939 - 1.04801i) q^{15} +(0.766044 + 0.642788i) q^{16} +(-1.13176 + 6.41852i) q^{17} -0.652704 q^{18} +2.00000 q^{20} +(0.716881 - 4.06564i) q^{21} +(2.43969 + 2.04715i) q^{22} +(0.652704 + 0.237565i) q^{23} +(-1.43969 + 0.524005i) q^{24} +(-0.766044 + 0.642788i) q^{25} +(2.87939 + 4.98724i) q^{26} +(2.79813 - 4.84651i) q^{27} +(0.467911 + 2.65366i) q^{28} +(-0.490200 - 2.78006i) q^{29} +(-1.53209 + 2.65366i) q^{30} +(-1.22668 - 2.12467i) q^{31} +(0.766044 - 0.642788i) q^{32} +(-4.58512 + 1.66885i) q^{33} +(6.12449 + 2.22913i) q^{34} +(4.12836 + 3.46410i) q^{35} +(-0.113341 + 0.642788i) q^{36} -4.36959 q^{37} -8.82295 q^{39} +(0.347296 - 1.96962i) q^{40} +(-0.266044 - 0.223238i) q^{41} +(-3.87939 - 1.41198i) q^{42} +(-5.69846 + 2.07407i) q^{43} +(2.43969 - 2.04715i) q^{44} +(0.652704 + 1.13052i) q^{45} +(0.347296 - 0.601535i) q^{46} +(1.36959 + 7.76730i) q^{47} +(0.266044 + 1.50881i) q^{48} +(-0.130415 + 0.225885i) q^{49} +(0.500000 + 0.866025i) q^{50} +(-7.64930 + 6.41852i) q^{51} +(5.41147 - 1.96962i) q^{52} +(-7.71688 - 2.80872i) q^{53} +(-4.28699 - 3.59721i) q^{54} +(1.10607 - 6.27282i) q^{55} +2.69459 q^{56} -2.82295 q^{58} +(0.0996702 - 0.565258i) q^{59} +(2.34730 + 1.96962i) q^{60} +(-2.75877 - 1.00411i) q^{61} +(-2.30541 + 0.839100i) q^{62} +(-1.34730 + 1.13052i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(5.75877 - 9.97448i) q^{65} +(0.847296 + 4.80526i) q^{66} +(-0.860967 - 4.88279i) q^{67} +(3.25877 - 5.64436i) q^{68} +(0.532089 + 0.921605i) q^{69} +(4.12836 - 3.46410i) q^{70} +(7.94356 - 2.89122i) q^{71} +(0.613341 + 0.223238i) q^{72} +(12.0778 + 10.1345i) q^{73} +(-0.758770 + 4.30320i) q^{74} -1.53209 q^{75} +8.58172 q^{77} +(-1.53209 + 8.68891i) q^{78} +(-6.94356 - 5.82634i) q^{79} +(-1.87939 - 0.684040i) q^{80} +(6.21688 - 2.26276i) q^{81} +(-0.266044 + 0.223238i) q^{82} +(-4.23783 - 7.34013i) q^{83} +(-2.06418 + 3.57526i) q^{84} +(-2.26352 - 12.8370i) q^{85} +(1.05303 + 5.97205i) q^{86} +(2.16250 - 3.74557i) q^{87} +(-1.59240 - 2.75811i) q^{88} +(5.92855 - 4.97464i) q^{89} +(1.22668 - 0.446476i) q^{90} +(14.5817 + 5.30731i) q^{91} +(-0.532089 - 0.446476i) q^{92} +(0.652704 - 3.70167i) q^{93} +7.88713 q^{94} +1.53209 q^{96} +(-0.0603074 + 0.342020i) q^{97} +(0.199807 + 0.167658i) q^{98} +(1.95336 + 0.710966i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + 6 q^{3} + 6 q^{6} - 6 q^{7} - 3 q^{8} + 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q + 6 q^{3} + 6 q^{6} - 6 q^{7} - 3 q^{8} + 6 q^{9} - 6 q^{11} - 6 q^{13} - 6 q^{14} - 6 q^{15} - 12 q^{17} - 6 q^{18} + 12 q^{20} - 12 q^{21} + 9 q^{22} + 6 q^{23} - 3 q^{24} + 6 q^{26} + 3 q^{27} + 12 q^{28} + 6 q^{31} - 6 q^{33} + 24 q^{34} - 12 q^{35} + 6 q^{36} - 12 q^{37} - 12 q^{39} + 3 q^{41} - 12 q^{42} - 6 q^{43} + 9 q^{44} + 6 q^{45} - 6 q^{47} - 3 q^{48} - 15 q^{49} + 3 q^{50} - 6 q^{51} + 12 q^{52} - 30 q^{53} - 18 q^{54} - 18 q^{55} + 12 q^{56} + 24 q^{58} + 15 q^{59} + 12 q^{60} + 6 q^{61} - 18 q^{62} - 6 q^{63} - 3 q^{64} + 12 q^{65} + 3 q^{66} + 18 q^{67} - 3 q^{68} - 6 q^{69} - 12 q^{70} + 18 q^{71} - 3 q^{72} + 33 q^{73} + 18 q^{74} - 12 q^{77} - 12 q^{79} + 21 q^{81} + 3 q^{82} - 6 q^{83} + 6 q^{84} - 24 q^{85} - 6 q^{86} + 18 q^{87} - 6 q^{88} + 36 q^{89} - 6 q^{90} + 24 q^{91} + 6 q^{92} + 6 q^{93} - 12 q^{94} - 6 q^{97} - 36 q^{98} - 15 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/722\mathbb{Z}\right)^\times\).

\(n\) \(363\)
\(\chi(n)\) \(e\left(\frac{5}{9}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.173648 0.984808i 0.122788 0.696364i
\(3\) 1.17365 + 0.984808i 0.677606 + 0.568579i 0.915306 0.402760i \(-0.131949\pi\)
−0.237700 + 0.971339i \(0.576393\pi\)
\(4\) −0.939693 0.342020i −0.469846 0.171010i
\(5\) −1.87939 + 0.684040i −0.840487 + 0.305912i −0.726155 0.687531i \(-0.758695\pi\)
−0.114331 + 0.993443i \(0.536473\pi\)
\(6\) 1.17365 0.984808i 0.479140 0.402046i
\(7\) −1.34730 2.33359i −0.509230 0.882013i −0.999943 0.0106911i \(-0.996597\pi\)
0.490713 0.871321i \(-0.336736\pi\)
\(8\) −0.500000 + 0.866025i −0.176777 + 0.306186i
\(9\) −0.113341 0.642788i −0.0377803 0.214263i
\(10\) 0.347296 + 1.96962i 0.109825 + 0.622847i
\(11\) −1.59240 + 2.75811i −0.480126 + 0.831602i −0.999740 0.0227990i \(-0.992742\pi\)
0.519615 + 0.854401i \(0.326076\pi\)
\(12\) −0.766044 1.32683i −0.221138 0.383022i
\(13\) −4.41147 + 3.70167i −1.22352 + 1.02666i −0.224890 + 0.974384i \(0.572202\pi\)
−0.998633 + 0.0522733i \(0.983353\pi\)
\(14\) −2.53209 + 0.921605i −0.676729 + 0.246309i
\(15\) −2.87939 1.04801i −0.743454 0.270595i
\(16\) 0.766044 + 0.642788i 0.191511 + 0.160697i
\(17\) −1.13176 + 6.41852i −0.274492 + 1.55672i 0.466079 + 0.884743i \(0.345666\pi\)
−0.740571 + 0.671978i \(0.765445\pi\)
\(18\) −0.652704 −0.153844
\(19\) 0 0
\(20\) 2.00000 0.447214
\(21\) 0.716881 4.06564i 0.156436 0.887195i
\(22\) 2.43969 + 2.04715i 0.520144 + 0.436453i
\(23\) 0.652704 + 0.237565i 0.136098 + 0.0495357i 0.409171 0.912458i \(-0.365818\pi\)
−0.273073 + 0.961993i \(0.588040\pi\)
\(24\) −1.43969 + 0.524005i −0.293876 + 0.106962i
\(25\) −0.766044 + 0.642788i −0.153209 + 0.128558i
\(26\) 2.87939 + 4.98724i 0.564694 + 0.978079i
\(27\) 2.79813 4.84651i 0.538501 0.932711i
\(28\) 0.467911 + 2.65366i 0.0884269 + 0.501494i
\(29\) −0.490200 2.78006i −0.0910278 0.516244i −0.995892 0.0905448i \(-0.971139\pi\)
0.904865 0.425700i \(-0.139972\pi\)
\(30\) −1.53209 + 2.65366i −0.279720 + 0.484489i
\(31\) −1.22668 2.12467i −0.220319 0.381603i 0.734586 0.678515i \(-0.237376\pi\)
−0.954905 + 0.296913i \(0.904043\pi\)
\(32\) 0.766044 0.642788i 0.135419 0.113630i
\(33\) −4.58512 + 1.66885i −0.798167 + 0.290509i
\(34\) 6.12449 + 2.22913i 1.05034 + 0.382293i
\(35\) 4.12836 + 3.46410i 0.697819 + 0.585540i
\(36\) −0.113341 + 0.642788i −0.0188901 + 0.107131i
\(37\) −4.36959 −0.718355 −0.359178 0.933269i \(-0.616943\pi\)
−0.359178 + 0.933269i \(0.616943\pi\)
\(38\) 0 0
\(39\) −8.82295 −1.41280
\(40\) 0.347296 1.96962i 0.0549124 0.311424i
\(41\) −0.266044 0.223238i −0.0415492 0.0348639i 0.621777 0.783195i \(-0.286411\pi\)
−0.663326 + 0.748331i \(0.730856\pi\)
\(42\) −3.87939 1.41198i −0.598602 0.217873i
\(43\) −5.69846 + 2.07407i −0.869007 + 0.316293i −0.737765 0.675057i \(-0.764119\pi\)
−0.131242 + 0.991350i \(0.541897\pi\)
\(44\) 2.43969 2.04715i 0.367798 0.308619i
\(45\) 0.652704 + 1.13052i 0.0972993 + 0.168527i
\(46\) 0.347296 0.601535i 0.0512061 0.0886915i
\(47\) 1.36959 + 7.76730i 0.199775 + 1.13298i 0.905453 + 0.424446i \(0.139531\pi\)
−0.705679 + 0.708532i \(0.749358\pi\)
\(48\) 0.266044 + 1.50881i 0.0384002 + 0.217778i
\(49\) −0.130415 + 0.225885i −0.0186307 + 0.0322693i
\(50\) 0.500000 + 0.866025i 0.0707107 + 0.122474i
\(51\) −7.64930 + 6.41852i −1.07112 + 0.898773i
\(52\) 5.41147 1.96962i 0.750436 0.273137i
\(53\) −7.71688 2.80872i −1.06000 0.385807i −0.247569 0.968870i \(-0.579632\pi\)
−0.812426 + 0.583064i \(0.801854\pi\)
\(54\) −4.28699 3.59721i −0.583385 0.489518i
\(55\) 1.10607 6.27282i 0.149142 0.845826i
\(56\) 2.69459 0.360080
\(57\) 0 0
\(58\) −2.82295 −0.370671
\(59\) 0.0996702 0.565258i 0.0129760 0.0735903i −0.977632 0.210322i \(-0.932549\pi\)
0.990608 + 0.136732i \(0.0436598\pi\)
\(60\) 2.34730 + 1.96962i 0.303035 + 0.254276i
\(61\) −2.75877 1.00411i −0.353224 0.128563i 0.159313 0.987228i \(-0.449072\pi\)
−0.512537 + 0.858665i \(0.671294\pi\)
\(62\) −2.30541 + 0.839100i −0.292787 + 0.106566i
\(63\) −1.34730 + 1.13052i −0.169743 + 0.142432i
\(64\) −0.500000 0.866025i −0.0625000 0.108253i
\(65\) 5.75877 9.97448i 0.714288 1.23718i
\(66\) 0.847296 + 4.80526i 0.104295 + 0.591486i
\(67\) −0.860967 4.88279i −0.105184 0.596527i −0.991147 0.132771i \(-0.957612\pi\)
0.885963 0.463756i \(-0.153499\pi\)
\(68\) 3.25877 5.64436i 0.395184 0.684479i
\(69\) 0.532089 + 0.921605i 0.0640560 + 0.110948i
\(70\) 4.12836 3.46410i 0.493433 0.414039i
\(71\) 7.94356 2.89122i 0.942727 0.343125i 0.175485 0.984482i \(-0.443851\pi\)
0.767242 + 0.641357i \(0.221628\pi\)
\(72\) 0.613341 + 0.223238i 0.0722829 + 0.0263088i
\(73\) 12.0778 + 10.1345i 1.41361 + 1.18616i 0.954663 + 0.297690i \(0.0962161\pi\)
0.458943 + 0.888466i \(0.348228\pi\)
\(74\) −0.758770 + 4.30320i −0.0882053 + 0.500237i
\(75\) −1.53209 −0.176910
\(76\) 0 0
\(77\) 8.58172 0.977978
\(78\) −1.53209 + 8.68891i −0.173475 + 0.983825i
\(79\) −6.94356 5.82634i −0.781212 0.655515i 0.162342 0.986735i \(-0.448095\pi\)
−0.943554 + 0.331220i \(0.892540\pi\)
\(80\) −1.87939 0.684040i −0.210122 0.0764780i
\(81\) 6.21688 2.26276i 0.690765 0.251418i
\(82\) −0.266044 + 0.223238i −0.0293797 + 0.0246525i
\(83\) −4.23783 7.34013i −0.465162 0.805684i 0.534047 0.845455i \(-0.320671\pi\)
−0.999209 + 0.0397709i \(0.987337\pi\)
\(84\) −2.06418 + 3.57526i −0.225220 + 0.390093i
\(85\) −2.26352 12.8370i −0.245513 1.39237i
\(86\) 1.05303 + 5.97205i 0.113552 + 0.643983i
\(87\) 2.16250 3.74557i 0.231845 0.401567i
\(88\) −1.59240 2.75811i −0.169750 0.294016i
\(89\) 5.92855 4.97464i 0.628425 0.527311i −0.272014 0.962293i \(-0.587690\pi\)
0.900439 + 0.434982i \(0.143245\pi\)
\(90\) 1.22668 0.446476i 0.129304 0.0470627i
\(91\) 14.5817 + 5.30731i 1.52858 + 0.556357i
\(92\) −0.532089 0.446476i −0.0554741 0.0465483i
\(93\) 0.652704 3.70167i 0.0676822 0.383845i
\(94\) 7.88713 0.813495
\(95\) 0 0
\(96\) 1.53209 0.156368
\(97\) −0.0603074 + 0.342020i −0.00612329 + 0.0347269i −0.987716 0.156258i \(-0.950057\pi\)
0.981593 + 0.190985i \(0.0611681\pi\)
\(98\) 0.199807 + 0.167658i 0.0201836 + 0.0169360i
\(99\) 1.95336 + 0.710966i 0.196320 + 0.0714548i
\(100\) 0.939693 0.342020i 0.0939693 0.0342020i
\(101\) −0.283119 + 0.237565i −0.0281714 + 0.0236386i −0.656765 0.754096i \(-0.728075\pi\)
0.628593 + 0.777734i \(0.283631\pi\)
\(102\) 4.99273 + 8.64766i 0.494354 + 0.856245i
\(103\) −4.29086 + 7.43199i −0.422791 + 0.732295i −0.996211 0.0869659i \(-0.972283\pi\)
0.573420 + 0.819261i \(0.305616\pi\)
\(104\) −1.00000 5.67128i −0.0980581 0.556115i
\(105\) 1.43376 + 8.13127i 0.139921 + 0.793531i
\(106\) −4.10607 + 7.11192i −0.398816 + 0.690770i
\(107\) 5.72668 + 9.91890i 0.553619 + 0.958897i 0.998010 + 0.0630633i \(0.0200870\pi\)
−0.444390 + 0.895833i \(0.646580\pi\)
\(108\) −4.28699 + 3.59721i −0.412516 + 0.346142i
\(109\) −8.17024 + 2.97373i −0.782568 + 0.284831i −0.702243 0.711937i \(-0.747818\pi\)
−0.0803246 + 0.996769i \(0.525596\pi\)
\(110\) −5.98545 2.17853i −0.570690 0.207714i
\(111\) −5.12836 4.30320i −0.486762 0.408442i
\(112\) 0.467911 2.65366i 0.0442134 0.250747i
\(113\) 2.85978 0.269026 0.134513 0.990912i \(-0.457053\pi\)
0.134513 + 0.990912i \(0.457053\pi\)
\(114\) 0 0
\(115\) −1.38919 −0.129542
\(116\) −0.490200 + 2.78006i −0.0455139 + 0.258122i
\(117\) 2.87939 + 2.41609i 0.266199 + 0.223368i
\(118\) −0.539363 0.196312i −0.0496524 0.0180720i
\(119\) 16.5030 6.00660i 1.51283 0.550624i
\(120\) 2.34730 1.96962i 0.214278 0.179800i
\(121\) 0.428548 + 0.742267i 0.0389589 + 0.0674789i
\(122\) −1.46791 + 2.54250i −0.132898 + 0.230187i
\(123\) −0.0923963 0.524005i −0.00833109 0.0472480i
\(124\) 0.426022 + 2.41609i 0.0382579 + 0.216971i
\(125\) 6.00000 10.3923i 0.536656 0.929516i
\(126\) 0.879385 + 1.52314i 0.0783419 + 0.135692i
\(127\) 7.45336 6.25411i 0.661379 0.554963i −0.249121 0.968472i \(-0.580142\pi\)
0.910500 + 0.413510i \(0.135697\pi\)
\(128\) −0.939693 + 0.342020i −0.0830579 + 0.0302306i
\(129\) −8.73055 3.17766i −0.768682 0.279777i
\(130\) −8.82295 7.40333i −0.773824 0.649315i
\(131\) −1.12314 + 6.36965i −0.0981293 + 0.556519i 0.895614 + 0.444832i \(0.146737\pi\)
−0.993743 + 0.111687i \(0.964375\pi\)
\(132\) 4.87939 0.424696
\(133\) 0 0
\(134\) −4.95811 −0.428316
\(135\) −1.94356 + 11.0225i −0.167275 + 0.948665i
\(136\) −4.99273 4.18939i −0.428123 0.359238i
\(137\) 10.9572 + 3.98811i 0.936140 + 0.340727i 0.764640 0.644457i \(-0.222917\pi\)
0.171499 + 0.985184i \(0.445139\pi\)
\(138\) 1.00000 0.363970i 0.0851257 0.0309832i
\(139\) −6.33022 + 5.31169i −0.536922 + 0.450531i −0.870484 0.492197i \(-0.836194\pi\)
0.333561 + 0.942728i \(0.391750\pi\)
\(140\) −2.69459 4.66717i −0.227735 0.394448i
\(141\) −6.04189 + 10.4649i −0.508819 + 0.881300i
\(142\) −1.46791 8.32494i −0.123184 0.698613i
\(143\) −3.18479 18.0619i −0.266326 1.51041i
\(144\) 0.326352 0.565258i 0.0271960 0.0471048i
\(145\) 2.82295 + 4.88949i 0.234433 + 0.406050i
\(146\) 12.0778 10.1345i 0.999570 0.838739i
\(147\) −0.375515 + 0.136676i −0.0309719 + 0.0112729i
\(148\) 4.10607 + 1.49449i 0.337517 + 0.122846i
\(149\) −12.6040 10.5760i −1.03256 0.866421i −0.0414071 0.999142i \(-0.513184\pi\)
−0.991153 + 0.132721i \(0.957629\pi\)
\(150\) −0.266044 + 1.50881i −0.0217224 + 0.123194i
\(151\) 4.65539 0.378850 0.189425 0.981895i \(-0.439338\pi\)
0.189425 + 0.981895i \(0.439338\pi\)
\(152\) 0 0
\(153\) 4.25402 0.343917
\(154\) 1.49020 8.45134i 0.120084 0.681029i
\(155\) 3.75877 + 3.15398i 0.301912 + 0.253334i
\(156\) 8.29086 + 3.01763i 0.663800 + 0.241603i
\(157\) −7.94356 + 2.89122i −0.633965 + 0.230745i −0.638956 0.769243i \(-0.720634\pi\)
0.00499096 + 0.999988i \(0.498411\pi\)
\(158\) −6.94356 + 5.82634i −0.552400 + 0.463519i
\(159\) −6.29086 10.8961i −0.498898 0.864116i
\(160\) −1.00000 + 1.73205i −0.0790569 + 0.136931i
\(161\) −0.325008 1.84321i −0.0256142 0.145265i
\(162\) −1.14883 6.51536i −0.0902609 0.511895i
\(163\) −8.52481 + 14.7654i −0.667715 + 1.15652i 0.310826 + 0.950467i \(0.399394\pi\)
−0.978542 + 0.206050i \(0.933939\pi\)
\(164\) 0.173648 + 0.300767i 0.0135596 + 0.0234860i
\(165\) 7.47565 6.27282i 0.581979 0.488338i
\(166\) −7.96451 + 2.89884i −0.618166 + 0.224994i
\(167\) 3.00000 + 1.09191i 0.232147 + 0.0844946i 0.455474 0.890249i \(-0.349470\pi\)
−0.223327 + 0.974743i \(0.571692\pi\)
\(168\) 3.16250 + 2.65366i 0.243992 + 0.204734i
\(169\) 3.50134 19.8571i 0.269334 1.52747i
\(170\) −13.0351 −0.999745
\(171\) 0 0
\(172\) 6.06418 0.462389
\(173\) 1.67230 9.48411i 0.127143 0.721063i −0.852869 0.522125i \(-0.825139\pi\)
0.980012 0.198938i \(-0.0637494\pi\)
\(174\) −3.31315 2.78006i −0.251169 0.210756i
\(175\) 2.53209 + 0.921605i 0.191408 + 0.0696668i
\(176\) −2.99273 + 1.08926i −0.225585 + 0.0821063i
\(177\) 0.673648 0.565258i 0.0506345 0.0424874i
\(178\) −3.86959 6.70232i −0.290038 0.502360i
\(179\) −9.40807 + 16.2953i −0.703192 + 1.21796i 0.264148 + 0.964482i \(0.414909\pi\)
−0.967340 + 0.253482i \(0.918424\pi\)
\(180\) −0.226682 1.28558i −0.0168958 0.0958211i
\(181\) 0.482459 + 2.73616i 0.0358609 + 0.203377i 0.997474 0.0710313i \(-0.0226290\pi\)
−0.961613 + 0.274409i \(0.911518\pi\)
\(182\) 7.75877 13.4386i 0.575118 0.996134i
\(183\) −2.24897 3.89533i −0.166249 0.287951i
\(184\) −0.532089 + 0.446476i −0.0392261 + 0.0329146i
\(185\) 8.21213 2.98897i 0.603768 0.219754i
\(186\) −3.53209 1.28558i −0.258985 0.0942629i
\(187\) −15.9008 13.3424i −1.16278 0.975689i
\(188\) 1.36959 7.76730i 0.0998873 0.566489i
\(189\) −15.0797 −1.09688
\(190\) 0 0
\(191\) 9.56212 0.691891 0.345945 0.938255i \(-0.387558\pi\)
0.345945 + 0.938255i \(0.387558\pi\)
\(192\) 0.266044 1.50881i 0.0192001 0.108889i
\(193\) −18.1407 15.2218i −1.30579 1.09569i −0.989113 0.147160i \(-0.952987\pi\)
−0.316682 0.948532i \(-0.602569\pi\)
\(194\) 0.326352 + 0.118782i 0.0234307 + 0.00852808i
\(195\) 16.5817 6.03525i 1.18744 0.432193i
\(196\) 0.199807 0.167658i 0.0142719 0.0119756i
\(197\) 11.4611 + 19.8512i 0.816570 + 1.41434i 0.908195 + 0.418547i \(0.137460\pi\)
−0.0916253 + 0.995794i \(0.529206\pi\)
\(198\) 1.03936 1.80023i 0.0738643 0.127937i
\(199\) 1.75103 + 9.93058i 0.124127 + 0.703960i 0.981822 + 0.189802i \(0.0607846\pi\)
−0.857695 + 0.514158i \(0.828104\pi\)
\(200\) −0.173648 0.984808i −0.0122788 0.0696364i
\(201\) 3.79813 6.57856i 0.267900 0.464016i
\(202\) 0.184793 + 0.320070i 0.0130020 + 0.0225201i
\(203\) −5.82707 + 4.88949i −0.408980 + 0.343175i
\(204\) 9.38326 3.41523i 0.656959 0.239114i
\(205\) 0.652704 + 0.237565i 0.0455868 + 0.0165922i
\(206\) 6.57398 + 5.51622i 0.458031 + 0.384333i
\(207\) 0.0787257 0.446476i 0.00547181 0.0310322i
\(208\) −5.75877 −0.399299
\(209\) 0 0
\(210\) 8.25671 0.569767
\(211\) −3.88279 + 22.0204i −0.267302 + 1.51595i 0.495096 + 0.868838i \(0.335133\pi\)
−0.762398 + 0.647108i \(0.775978\pi\)
\(212\) 6.29086 + 5.27866i 0.432058 + 0.362540i
\(213\) 12.1702 + 4.42961i 0.833891 + 0.303512i
\(214\) 10.7626 3.91728i 0.735719 0.267780i
\(215\) 9.29086 7.79596i 0.633631 0.531680i
\(216\) 2.79813 + 4.84651i 0.190389 + 0.329763i
\(217\) −3.30541 + 5.72513i −0.224386 + 0.388647i
\(218\) 1.50980 + 8.56250i 0.102257 + 0.579926i
\(219\) 4.19459 + 23.7887i 0.283444 + 1.60749i
\(220\) −3.18479 + 5.51622i −0.214719 + 0.371904i
\(221\) −18.7665 32.5046i −1.26237 2.18649i
\(222\) −5.12836 + 4.30320i −0.344193 + 0.288812i
\(223\) 8.71688 3.17269i 0.583726 0.212459i −0.0332420 0.999447i \(-0.510583\pi\)
0.616968 + 0.786989i \(0.288361\pi\)
\(224\) −2.53209 0.921605i −0.169182 0.0615773i
\(225\) 0.500000 + 0.419550i 0.0333333 + 0.0279700i
\(226\) 0.496596 2.81634i 0.0330331 0.187340i
\(227\) 7.73648 0.513488 0.256744 0.966479i \(-0.417350\pi\)
0.256744 + 0.966479i \(0.417350\pi\)
\(228\) 0 0
\(229\) −23.0351 −1.52220 −0.761101 0.648634i \(-0.775341\pi\)
−0.761101 + 0.648634i \(0.775341\pi\)
\(230\) −0.241230 + 1.36808i −0.0159062 + 0.0902086i
\(231\) 10.0719 + 8.45134i 0.662684 + 0.556058i
\(232\) 2.65270 + 0.965505i 0.174159 + 0.0633885i
\(233\) −7.89306 + 2.87284i −0.517091 + 0.188206i −0.587365 0.809322i \(-0.699835\pi\)
0.0702741 + 0.997528i \(0.477613\pi\)
\(234\) 2.87939 2.41609i 0.188231 0.157945i
\(235\) −7.88713 13.6609i −0.514499 0.891139i
\(236\) −0.286989 + 0.497079i −0.0186814 + 0.0323571i
\(237\) −2.41147 13.6761i −0.156642 0.888361i
\(238\) −3.04963 17.2953i −0.197678 1.12109i
\(239\) 7.86484 13.6223i 0.508734 0.881153i −0.491215 0.871038i \(-0.663447\pi\)
0.999949 0.0101147i \(-0.00321967\pi\)
\(240\) −1.53209 2.65366i −0.0988959 0.171293i
\(241\) 13.4081 11.2507i 0.863690 0.724722i −0.0990699 0.995080i \(-0.531587\pi\)
0.962760 + 0.270359i \(0.0871423\pi\)
\(242\) 0.805407 0.293144i 0.0517735 0.0188440i
\(243\) −6.25150 2.27536i −0.401034 0.145964i
\(244\) 2.24897 + 1.88711i 0.143976 + 0.120810i
\(245\) 0.0905853 0.513735i 0.00578728 0.0328213i
\(246\) −0.532089 −0.0339247
\(247\) 0 0
\(248\) 2.45336 0.155789
\(249\) 2.25490 12.7882i 0.142898 0.810418i
\(250\) −9.19253 7.71345i −0.581387 0.487841i
\(251\) −8.05051 2.93014i −0.508144 0.184949i 0.0752096 0.997168i \(-0.476037\pi\)
−0.583353 + 0.812219i \(0.698260\pi\)
\(252\) 1.65270 0.601535i 0.104111 0.0378931i
\(253\) −1.69459 + 1.42193i −0.106538 + 0.0893961i
\(254\) −4.86484 8.42615i −0.305247 0.528703i
\(255\) 9.98545 17.2953i 0.625313 1.08307i
\(256\) 0.173648 + 0.984808i 0.0108530 + 0.0615505i
\(257\) −1.39347 7.90274i −0.0869220 0.492959i −0.996925 0.0783582i \(-0.975032\pi\)
0.910003 0.414601i \(-0.136079\pi\)
\(258\) −4.64543 + 8.04612i −0.289212 + 0.500930i
\(259\) 5.88713 + 10.1968i 0.365808 + 0.633598i
\(260\) −8.82295 + 7.40333i −0.547176 + 0.459135i
\(261\) −1.73143 + 0.630189i −0.107173 + 0.0390077i
\(262\) 6.07785 + 2.21216i 0.375491 + 0.136667i
\(263\) −4.56624 3.83153i −0.281566 0.236262i 0.491056 0.871128i \(-0.336611\pi\)
−0.772622 + 0.634866i \(0.781055\pi\)
\(264\) 0.847296 4.80526i 0.0521475 0.295743i
\(265\) 16.4243 1.00893
\(266\) 0 0
\(267\) 11.8571 0.725643
\(268\) −0.860967 + 4.88279i −0.0525919 + 0.298264i
\(269\) −0.879385 0.737892i −0.0536171 0.0449901i 0.615585 0.788070i \(-0.288920\pi\)
−0.669202 + 0.743080i \(0.733364\pi\)
\(270\) 10.5175 + 3.82807i 0.640077 + 0.232969i
\(271\) −18.8452 + 6.85911i −1.14477 + 0.416661i −0.843633 0.536921i \(-0.819587\pi\)
−0.301134 + 0.953582i \(0.597365\pi\)
\(272\) −4.99273 + 4.18939i −0.302728 + 0.254019i
\(273\) 11.8871 + 20.5891i 0.719442 + 1.24611i
\(274\) 5.83022 10.0982i 0.352217 0.610057i
\(275\) −0.553033 3.13641i −0.0333492 0.189133i
\(276\) −0.184793 1.04801i −0.0111232 0.0630828i
\(277\) −8.68004 + 15.0343i −0.521533 + 0.903322i 0.478153 + 0.878277i \(0.341306\pi\)
−0.999686 + 0.0250457i \(0.992027\pi\)
\(278\) 4.13176 + 7.15642i 0.247806 + 0.429213i
\(279\) −1.22668 + 1.02931i −0.0734395 + 0.0616231i
\(280\) −5.06418 + 1.84321i −0.302643 + 0.110153i
\(281\) −2.74510 0.999135i −0.163759 0.0596034i 0.258840 0.965920i \(-0.416660\pi\)
−0.422599 + 0.906317i \(0.638882\pi\)
\(282\) 9.25671 + 7.76730i 0.551229 + 0.462536i
\(283\) −1.64631 + 9.33667i −0.0978628 + 0.555007i 0.895970 + 0.444115i \(0.146482\pi\)
−0.993832 + 0.110892i \(0.964629\pi\)
\(284\) −8.45336 −0.501615
\(285\) 0 0
\(286\) −18.3405 −1.08450
\(287\) −0.162504 + 0.921605i −0.00959230 + 0.0544006i
\(288\) −0.500000 0.419550i −0.0294628 0.0247222i
\(289\) −23.9418 8.71411i −1.40834 0.512594i
\(290\) 5.30541 1.93101i 0.311544 0.113393i
\(291\) −0.407604 + 0.342020i −0.0238942 + 0.0200496i
\(292\) −7.88326 13.6542i −0.461333 0.799052i
\(293\) 13.6459 23.6354i 0.797202 1.38079i −0.124230 0.992253i \(-0.539646\pi\)
0.921432 0.388541i \(-0.127021\pi\)
\(294\) 0.0693923 + 0.393544i 0.00404704 + 0.0229519i
\(295\) 0.199340 + 1.13052i 0.0116060 + 0.0658212i
\(296\) 2.18479 3.78417i 0.126988 0.219951i
\(297\) 8.91147 + 15.4351i 0.517096 + 0.895637i
\(298\) −12.6040 + 10.5760i −0.730131 + 0.612652i
\(299\) −3.75877 + 1.36808i −0.217375 + 0.0791181i
\(300\) 1.43969 + 0.524005i 0.0831207 + 0.0302535i
\(301\) 12.5175 + 10.5035i 0.721499 + 0.605410i
\(302\) 0.808400 4.58467i 0.0465182 0.263818i
\(303\) −0.566237 −0.0325295
\(304\) 0 0
\(305\) 5.87164 0.336209
\(306\) 0.738703 4.18939i 0.0422289 0.239492i
\(307\) 16.3387 + 13.7098i 0.932498 + 0.782458i 0.976264 0.216583i \(-0.0694913\pi\)
−0.0437665 + 0.999042i \(0.513936\pi\)
\(308\) −8.06418 2.93512i −0.459499 0.167244i
\(309\) −12.3550 + 4.49687i −0.702854 + 0.255818i
\(310\) 3.75877 3.15398i 0.213484 0.179134i
\(311\) 14.6459 + 25.3674i 0.830493 + 1.43846i 0.897648 + 0.440713i \(0.145274\pi\)
−0.0671555 + 0.997743i \(0.521392\pi\)
\(312\) 4.41147 7.64090i 0.249751 0.432581i
\(313\) 0.965690 + 5.47670i 0.0545840 + 0.309561i 0.999860 0.0167094i \(-0.00531902\pi\)
−0.945276 + 0.326271i \(0.894208\pi\)
\(314\) 1.46791 + 8.32494i 0.0828390 + 0.469803i
\(315\) 1.75877 3.04628i 0.0990955 0.171638i
\(316\) 4.53209 + 7.84981i 0.254950 + 0.441586i
\(317\) 2.91353 2.44474i 0.163640 0.137311i −0.557290 0.830318i \(-0.688159\pi\)
0.720931 + 0.693007i \(0.243715\pi\)
\(318\) −11.8229 + 4.30320i −0.662998 + 0.241312i
\(319\) 8.44831 + 3.07493i 0.473015 + 0.172163i
\(320\) 1.53209 + 1.28558i 0.0856464 + 0.0718658i
\(321\) −3.04710 + 17.2810i −0.170073 + 0.964530i
\(322\) −1.87164 −0.104303
\(323\) 0 0
\(324\) −6.61587 −0.367548
\(325\) 1.00000 5.67128i 0.0554700 0.314586i
\(326\) 13.0608 + 10.9593i 0.723369 + 0.606979i
\(327\) −12.5175 4.55601i −0.692222 0.251948i
\(328\) 0.326352 0.118782i 0.0180198 0.00655866i
\(329\) 16.2804 13.6609i 0.897569 0.753150i
\(330\) −4.87939 8.45134i −0.268601 0.465231i
\(331\) −10.2110 + 17.6859i −0.561245 + 0.972104i 0.436144 + 0.899877i \(0.356344\pi\)
−0.997388 + 0.0722272i \(0.976989\pi\)
\(332\) 1.47178 + 8.34689i 0.0807745 + 0.458095i
\(333\) 0.495252 + 2.80872i 0.0271397 + 0.153917i
\(334\) 1.59627 2.76481i 0.0873438 0.151284i
\(335\) 4.95811 + 8.58770i 0.270891 + 0.469196i
\(336\) 3.16250 2.65366i 0.172529 0.144769i
\(337\) −19.0856 + 6.94659i −1.03966 + 0.378405i −0.804751 0.593613i \(-0.797701\pi\)
−0.234908 + 0.972018i \(0.575479\pi\)
\(338\) −18.9474 6.89630i −1.03060 0.375109i
\(339\) 3.35638 + 2.81634i 0.182294 + 0.152963i
\(340\) −2.26352 + 12.8370i −0.122757 + 0.696187i
\(341\) 7.81345 0.423122
\(342\) 0 0
\(343\) −18.1593 −0.980511
\(344\) 1.05303 5.97205i 0.0567758 0.321991i
\(345\) −1.63041 1.36808i −0.0877786 0.0736550i
\(346\) −9.04963 3.29380i −0.486511 0.177076i
\(347\) −4.90033 + 1.78357i −0.263063 + 0.0957473i −0.470185 0.882568i \(-0.655813\pi\)
0.207121 + 0.978315i \(0.433591\pi\)
\(348\) −3.31315 + 2.78006i −0.177603 + 0.149027i
\(349\) −7.17024 12.4192i −0.383814 0.664786i 0.607790 0.794098i \(-0.292056\pi\)
−0.991604 + 0.129312i \(0.958723\pi\)
\(350\) 1.34730 2.33359i 0.0720160 0.124735i
\(351\) 5.59627 + 31.7380i 0.298707 + 1.69405i
\(352\) 0.553033 + 3.13641i 0.0294768 + 0.167171i
\(353\) −13.1250 + 22.7331i −0.698571 + 1.20996i 0.270391 + 0.962750i \(0.412847\pi\)
−0.968962 + 0.247209i \(0.920486\pi\)
\(354\) −0.439693 0.761570i −0.0233694 0.0404770i
\(355\) −12.9513 + 10.8674i −0.687384 + 0.576784i
\(356\) −7.27244 + 2.64695i −0.385439 + 0.140288i
\(357\) 25.2841 + 9.20264i 1.33817 + 0.487055i
\(358\) 14.4140 + 12.0948i 0.761804 + 0.639229i
\(359\) −5.85029 + 33.1786i −0.308766 + 1.75110i 0.296457 + 0.955046i \(0.404195\pi\)
−0.605224 + 0.796055i \(0.706916\pi\)
\(360\) −1.30541 −0.0688010
\(361\) 0 0
\(362\) 2.77837 0.146028
\(363\) −0.228026 + 1.29320i −0.0119682 + 0.0678753i
\(364\) −11.8871 9.97448i −0.623055 0.522805i
\(365\) −29.6313 10.7849i −1.55098 0.564509i
\(366\) −4.22668 + 1.53839i −0.220932 + 0.0804127i
\(367\) −8.01960 + 6.72924i −0.418620 + 0.351264i −0.827638 0.561263i \(-0.810316\pi\)
0.409018 + 0.912526i \(0.365871\pi\)
\(368\) 0.347296 + 0.601535i 0.0181041 + 0.0313572i
\(369\) −0.113341 + 0.196312i −0.00590029 + 0.0102196i
\(370\) −1.51754 8.60640i −0.0788932 0.447426i
\(371\) 3.84255 + 21.7922i 0.199495 + 1.13139i
\(372\) −1.87939 + 3.25519i −0.0974416 + 0.168774i
\(373\) −11.9513 20.7003i −0.618815 1.07182i −0.989702 0.143141i \(-0.954280\pi\)
0.370887 0.928678i \(-0.379054\pi\)
\(374\) −15.9008 + 13.3424i −0.822211 + 0.689917i
\(375\) 17.2763 6.28806i 0.892145 0.324714i
\(376\) −7.41147 2.69756i −0.382218 0.139116i
\(377\) 12.4534 + 10.4496i 0.641381 + 0.538182i
\(378\) −2.61856 + 14.8506i −0.134684 + 0.763831i
\(379\) 17.8135 0.915016 0.457508 0.889206i \(-0.348742\pi\)
0.457508 + 0.889206i \(0.348742\pi\)
\(380\) 0 0
\(381\) 14.9067 0.763695
\(382\) 1.66044 9.41685i 0.0849557 0.481808i
\(383\) 19.2121 + 16.1209i 0.981694 + 0.823739i 0.984344 0.176257i \(-0.0563991\pi\)
−0.00264996 + 0.999996i \(0.500844\pi\)
\(384\) −1.43969 0.524005i −0.0734690 0.0267405i
\(385\) −16.1284 + 5.87024i −0.821977 + 0.299175i
\(386\) −18.1407 + 15.2218i −0.923336 + 0.774771i
\(387\) 1.97906 + 3.42782i 0.100601 + 0.174246i
\(388\) 0.173648 0.300767i 0.00881565 0.0152692i
\(389\) −1.63547 9.27520i −0.0829215 0.470271i −0.997786 0.0665097i \(-0.978814\pi\)
0.914864 0.403761i \(-0.132297\pi\)
\(390\) −3.06418 17.3778i −0.155161 0.879960i
\(391\) −2.26352 + 3.92053i −0.114471 + 0.198270i
\(392\) −0.130415 0.225885i −0.00658695 0.0114089i
\(393\) −7.59105 + 6.36965i −0.382918 + 0.321306i
\(394\) 21.5398 7.83986i 1.08516 0.394966i
\(395\) 17.0351 + 6.20026i 0.857128 + 0.311969i
\(396\) −1.59240 1.33618i −0.0800209 0.0671455i
\(397\) 1.18984 6.74795i 0.0597166 0.338670i −0.940282 0.340397i \(-0.889439\pi\)
0.999999 + 0.00172704i \(0.000549734\pi\)
\(398\) 10.0838 0.505454
\(399\) 0 0
\(400\) −1.00000 −0.0500000
\(401\) 0.824292 4.67479i 0.0411632 0.233448i −0.957284 0.289148i \(-0.906628\pi\)
0.998448 + 0.0557001i \(0.0177391\pi\)
\(402\) −5.81908 4.88279i −0.290229 0.243531i
\(403\) 13.2763 + 4.83218i 0.661340 + 0.240708i
\(404\) 0.347296 0.126406i 0.0172786 0.00628891i
\(405\) −10.1361 + 8.50519i −0.503667 + 0.422627i
\(406\) 3.80335 + 6.58759i 0.188757 + 0.326937i
\(407\) 6.95811 12.0518i 0.344901 0.597386i
\(408\) −1.73396 9.83375i −0.0858436 0.486843i
\(409\) 5.50340 + 31.2114i 0.272126 + 1.54330i 0.747946 + 0.663760i \(0.231040\pi\)
−0.475820 + 0.879543i \(0.657849\pi\)
\(410\) 0.347296 0.601535i 0.0171517 0.0297077i
\(411\) 8.93242 + 15.4714i 0.440604 + 0.763148i
\(412\) 6.57398 5.51622i 0.323877 0.271765i
\(413\) −1.45336 + 0.528981i −0.0715153 + 0.0260295i
\(414\) −0.426022 0.155059i −0.0209378 0.00762075i
\(415\) 12.9855 + 10.8961i 0.637431 + 0.534868i
\(416\) −1.00000 + 5.67128i −0.0490290 + 0.278057i
\(417\) −12.6604 −0.619985
\(418\) 0 0
\(419\) −11.0101 −0.537879 −0.268939 0.963157i \(-0.586673\pi\)
−0.268939 + 0.963157i \(0.586673\pi\)
\(420\) 1.43376 8.13127i 0.0699605 0.396766i
\(421\) −6.63816 5.57007i −0.323524 0.271469i 0.466531 0.884505i \(-0.345504\pi\)
−0.790055 + 0.613036i \(0.789948\pi\)
\(422\) 21.0116 + 7.64760i 1.02283 + 0.372279i
\(423\) 4.83750 1.76070i 0.235207 0.0856084i
\(424\) 6.29086 5.27866i 0.305511 0.256354i
\(425\) −3.25877 5.64436i −0.158074 0.273791i
\(426\) 6.47565 11.2162i 0.313746 0.543425i
\(427\) 1.37370 + 7.79066i 0.0664782 + 0.377017i
\(428\) −1.98886 11.2794i −0.0961350 0.545208i
\(429\) 14.0496 24.3347i 0.678323 1.17489i
\(430\) −6.06418 10.5035i −0.292441 0.506522i
\(431\) −22.8949 + 19.2111i −1.10281 + 0.925365i −0.997611 0.0690866i \(-0.977992\pi\)
−0.105196 + 0.994451i \(0.533547\pi\)
\(432\) 5.25877 1.91404i 0.253013 0.0920891i
\(433\) −8.70233 3.16739i −0.418207 0.152215i 0.124341 0.992240i \(-0.460318\pi\)
−0.542549 + 0.840024i \(0.682541\pi\)
\(434\) 5.06418 + 4.24935i 0.243088 + 0.203975i
\(435\) −1.50206 + 8.51860i −0.0720182 + 0.408436i
\(436\) 8.69459 0.416395
\(437\) 0 0
\(438\) 24.1557 1.15420
\(439\) 3.62267 20.5452i 0.172901 0.980569i −0.767638 0.640883i \(-0.778568\pi\)
0.940539 0.339686i \(-0.110321\pi\)
\(440\) 4.87939 + 4.09429i 0.232616 + 0.195188i
\(441\) 0.159978 + 0.0582271i 0.00761798 + 0.00277272i
\(442\) −35.2695 + 12.8370i −1.67760 + 0.610596i
\(443\) 18.2533 15.3163i 0.867241 0.727701i −0.0962745 0.995355i \(-0.530693\pi\)
0.963515 + 0.267653i \(0.0862482\pi\)
\(444\) 3.34730 + 5.79769i 0.158856 + 0.275146i
\(445\) −7.73917 + 13.4046i −0.366872 + 0.635441i
\(446\) −1.61081 9.13538i −0.0762743 0.432573i
\(447\) −4.37733 24.8250i −0.207040 1.17418i
\(448\) −1.34730 + 2.33359i −0.0636538 + 0.110252i
\(449\) 1.09105 + 1.88976i 0.0514899 + 0.0891832i 0.890622 0.454745i \(-0.150270\pi\)
−0.839132 + 0.543928i \(0.816936\pi\)
\(450\) 0.500000 0.419550i 0.0235702 0.0197778i
\(451\) 1.03936 0.378297i 0.0489417 0.0178133i
\(452\) −2.68732 0.978104i −0.126401 0.0460061i
\(453\) 5.46379 + 4.58467i 0.256711 + 0.215406i
\(454\) 1.34343 7.61895i 0.0630501 0.357575i
\(455\) −31.0351 −1.45495
\(456\) 0 0
\(457\) 1.78106 0.0833144 0.0416572 0.999132i \(-0.486736\pi\)
0.0416572 + 0.999132i \(0.486736\pi\)
\(458\) −4.00000 + 22.6851i −0.186908 + 1.06001i
\(459\) 27.9406 + 23.4450i 1.30416 + 1.09432i
\(460\) 1.30541 + 0.475129i 0.0608649 + 0.0221530i
\(461\) 14.5544 5.29736i 0.677865 0.246723i 0.0199344 0.999801i \(-0.493654\pi\)
0.657931 + 0.753079i \(0.271432\pi\)
\(462\) 10.0719 8.45134i 0.468588 0.393192i
\(463\) 1.35504 + 2.34699i 0.0629739 + 0.109074i 0.895793 0.444471i \(-0.146608\pi\)
−0.832820 + 0.553545i \(0.813275\pi\)
\(464\) 1.41147 2.44474i 0.0655260 0.113494i
\(465\) 1.30541 + 7.40333i 0.0605368 + 0.343321i
\(466\) 1.45858 + 8.27201i 0.0675673 + 0.383193i
\(467\) −6.45677 + 11.1834i −0.298784 + 0.517508i −0.975858 0.218406i \(-0.929914\pi\)
0.677074 + 0.735915i \(0.263248\pi\)
\(468\) −1.87939 3.25519i −0.0868746 0.150471i
\(469\) −10.2344 + 8.58770i −0.472582 + 0.396543i
\(470\) −14.8229 + 5.39511i −0.683732 + 0.248858i
\(471\) −12.1702 4.42961i −0.560775 0.204106i
\(472\) 0.439693 + 0.368946i 0.0202385 + 0.0169821i
\(473\) 3.35369 19.0197i 0.154203 0.874528i
\(474\) −13.8871 −0.637857
\(475\) 0 0
\(476\) −17.5621 −0.804958
\(477\) −0.930770 + 5.27866i −0.0426170 + 0.241693i
\(478\) −12.0496 10.1108i −0.551137 0.462459i
\(479\) 17.4338 + 6.34537i 0.796569 + 0.289927i 0.708064 0.706148i \(-0.249569\pi\)
0.0885050 + 0.996076i \(0.471791\pi\)
\(480\) −2.87939 + 1.04801i −0.131425 + 0.0478349i
\(481\) 19.2763 16.1747i 0.878924 0.737505i
\(482\) −8.75150 15.1580i −0.398620 0.690430i
\(483\) 1.43376 2.48335i 0.0652385 0.112996i
\(484\) −0.148833 0.844075i −0.00676515 0.0383671i
\(485\) −0.120615 0.684040i −0.00547683 0.0310607i
\(486\) −3.32635 + 5.76141i −0.150886 + 0.261343i
\(487\) −20.5868 35.6573i −0.932876 1.61579i −0.778379 0.627795i \(-0.783958\pi\)
−0.154497 0.987993i \(-0.549376\pi\)
\(488\) 2.24897 1.88711i 0.101806 0.0854255i
\(489\) −24.5462 + 8.93410i −1.11002 + 0.404014i
\(490\) −0.490200 0.178418i −0.0221450 0.00806011i
\(491\) −17.2954 14.5126i −0.780533 0.654945i 0.162850 0.986651i \(-0.447931\pi\)
−0.943383 + 0.331706i \(0.892376\pi\)
\(492\) −0.0923963 + 0.524005i −0.00416555 + 0.0236240i
\(493\) 18.3987 0.828635
\(494\) 0 0
\(495\) −4.15745 −0.186864
\(496\) 0.426022 2.41609i 0.0191290 0.108486i
\(497\) −17.4492 14.6417i −0.782706 0.656768i
\(498\) −12.2023 4.44129i −0.546800 0.199019i
\(499\) 27.5599 10.0310i 1.23375 0.449048i 0.358870 0.933388i \(-0.383162\pi\)
0.874880 + 0.484339i \(0.160940\pi\)
\(500\) −9.19253 + 7.71345i −0.411103 + 0.344956i
\(501\) 2.44562 + 4.23594i 0.109262 + 0.189248i
\(502\) −4.28359 + 7.41939i −0.191186 + 0.331143i
\(503\) 5.83750 + 33.1061i 0.260281 + 1.47613i 0.782144 + 0.623098i \(0.214126\pi\)
−0.521863 + 0.853029i \(0.674763\pi\)
\(504\) −0.305407 1.73205i −0.0136039 0.0771517i
\(505\) 0.369585 0.640140i 0.0164463 0.0284859i
\(506\) 1.10607 + 1.91576i 0.0491707 + 0.0851661i
\(507\) 23.6648 19.8571i 1.05099 0.881885i
\(508\) −9.14290 + 3.32774i −0.405651 + 0.147645i
\(509\) −3.78611 1.37803i −0.167816 0.0610802i 0.256746 0.966479i \(-0.417350\pi\)
−0.424562 + 0.905399i \(0.639572\pi\)
\(510\) −15.2986 12.8370i −0.677433 0.568434i
\(511\) 7.37733 41.8389i 0.326354 1.85084i
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) −8.02465 −0.353952
\(515\) 2.98040 16.9027i 0.131332 0.744821i
\(516\) 7.11721 + 5.97205i 0.313318 + 0.262905i
\(517\) −23.6040 8.59116i −1.03810 0.377839i
\(518\) 11.0642 4.02703i 0.486132 0.176938i
\(519\) 11.3027 9.48411i 0.496134 0.416306i
\(520\) 5.75877 + 9.97448i 0.252539 + 0.437410i
\(521\) −2.49479 + 4.32110i −0.109299 + 0.189311i −0.915486 0.402349i \(-0.868194\pi\)
0.806188 + 0.591660i \(0.201527\pi\)
\(522\) 0.319955 + 1.81456i 0.0140041 + 0.0794210i
\(523\) −4.61081 26.1492i −0.201617 1.14343i −0.902675 0.430322i \(-0.858400\pi\)
0.701059 0.713104i \(-0.252711\pi\)
\(524\) 3.23396 5.60138i 0.141276 0.244697i
\(525\) 2.06418 + 3.57526i 0.0900881 + 0.156037i
\(526\) −4.56624 + 3.83153i −0.199097 + 0.167063i
\(527\) 15.0256 5.46887i 0.654525 0.238228i
\(528\) −4.58512 1.66885i −0.199542 0.0726273i
\(529\) −17.2494 14.4740i −0.749976 0.629304i
\(530\) 2.85204 16.1747i 0.123885 0.702586i
\(531\) −0.374638 −0.0162579
\(532\) 0 0
\(533\) 2.00000 0.0866296
\(534\) 2.05896 11.6770i 0.0891001 0.505312i
\(535\) −17.5476 14.7242i −0.758648 0.636581i
\(536\) 4.65910 + 1.69577i 0.201242 + 0.0732463i
\(537\) −27.0895 + 9.85976i −1.16900 + 0.425480i
\(538\) −0.879385 + 0.737892i −0.0379130 + 0.0318128i
\(539\) −0.415345 0.719398i −0.0178902 0.0309867i
\(540\) 5.59627 9.69302i 0.240825 0.417121i
\(541\) −2.07873 11.7890i −0.0893714 0.506850i −0.996327 0.0856251i \(-0.972711\pi\)
0.906956 0.421225i \(-0.138400\pi\)
\(542\) 3.48246 + 19.7500i 0.149584 + 0.848335i
\(543\) −2.12836 + 3.68642i −0.0913365 + 0.158199i
\(544\) 3.25877 + 5.64436i 0.139719 + 0.242000i
\(545\) 13.3209 11.1776i 0.570604 0.478794i
\(546\) 22.3405 8.13127i 0.956085 0.347986i
\(547\) −3.00387 1.09332i −0.128436 0.0467470i 0.277002 0.960869i \(-0.410659\pi\)
−0.405439 + 0.914122i \(0.632881\pi\)
\(548\) −8.93242 7.49519i −0.381574 0.320179i
\(549\) −0.332748 + 1.88711i −0.0142014 + 0.0805399i
\(550\) −3.18479 −0.135800
\(551\) 0 0
\(552\) −1.06418 −0.0452944
\(553\) −4.24123 + 24.0532i −0.180355 + 1.02285i
\(554\) 13.2986 + 11.1589i 0.565003 + 0.474094i
\(555\) 12.5817 + 4.57937i 0.534064 + 0.194383i
\(556\) 7.76517 2.82629i 0.329316 0.119861i
\(557\) −18.3669 + 15.4117i −0.778230 + 0.653013i −0.942802 0.333352i \(-0.891820\pi\)
0.164572 + 0.986365i \(0.447376\pi\)
\(558\) 0.800660 + 1.38678i 0.0338946 + 0.0587072i
\(559\) 17.4611 30.2435i 0.738526 1.27916i
\(560\) 0.935822 + 5.30731i 0.0395457 + 0.224275i
\(561\) −5.52229 31.3185i −0.233151 1.32227i
\(562\) −1.46064 + 2.52990i −0.0616133 + 0.106717i
\(563\) 4.37851 + 7.58380i 0.184532 + 0.319619i 0.943419 0.331604i \(-0.107590\pi\)
−0.758887 + 0.651223i \(0.774256\pi\)
\(564\) 9.25671 7.76730i 0.389778 0.327062i
\(565\) −5.37464 + 1.95621i −0.226113 + 0.0822983i
\(566\) 8.90895 + 3.24259i 0.374471 + 0.136296i
\(567\) −13.6563 11.4590i −0.573512 0.481234i
\(568\) −1.46791 + 8.32494i −0.0615922 + 0.349307i
\(569\) −36.4201 −1.52681 −0.763406 0.645919i \(-0.776474\pi\)
−0.763406 + 0.645919i \(0.776474\pi\)
\(570\) 0 0
\(571\) 34.2131 1.43177 0.715886 0.698217i \(-0.246023\pi\)
0.715886 + 0.698217i \(0.246023\pi\)
\(572\) −3.18479 + 18.0619i −0.133163 + 0.755204i
\(573\) 11.2226 + 9.41685i 0.468829 + 0.393394i
\(574\) 0.879385 + 0.320070i 0.0367048 + 0.0133595i
\(575\) −0.652704 + 0.237565i −0.0272196 + 0.00990713i
\(576\) −0.500000 + 0.419550i −0.0208333 + 0.0174812i
\(577\) −7.75490 13.4319i −0.322841 0.559177i 0.658232 0.752815i \(-0.271304\pi\)
−0.981073 + 0.193638i \(0.937971\pi\)
\(578\) −12.7392 + 22.0649i −0.529880 + 0.917778i
\(579\) −6.30019 35.7302i −0.261827 1.48490i
\(580\) −0.980400 5.56012i −0.0407089 0.230872i
\(581\) −11.4192 + 19.7787i −0.473749 + 0.820557i
\(582\) 0.266044 + 0.460802i 0.0110279 + 0.0191009i
\(583\) 20.0351 16.8114i 0.829768 0.696258i
\(584\) −14.8157 + 5.39246i −0.613077 + 0.223142i
\(585\) −7.06418 2.57115i −0.292068 0.106304i
\(586\) −20.9067 17.5428i −0.863649 0.724687i
\(587\) −2.01114 + 11.4058i −0.0830088 + 0.470766i 0.914760 + 0.403998i \(0.132380\pi\)
−0.997769 + 0.0667680i \(0.978731\pi\)
\(588\) 0.399615 0.0164798
\(589\) 0 0
\(590\) 1.14796 0.0472606
\(591\) −6.09833 + 34.5853i −0.250852 + 1.42265i
\(592\) −3.34730 2.80872i −0.137573 0.115437i
\(593\) 43.5950 + 15.8673i 1.79023 + 0.651591i 0.999207 + 0.0398054i \(0.0126738\pi\)
0.791024 + 0.611785i \(0.209548\pi\)
\(594\) 16.7481 6.09581i 0.687183 0.250114i
\(595\) −26.9067 + 22.5774i −1.10307 + 0.925584i
\(596\) 8.22668 + 14.2490i 0.336978 + 0.583663i
\(597\) −7.72462 + 13.3794i −0.316148 + 0.547584i
\(598\) 0.694593 + 3.93923i 0.0284040 + 0.161087i
\(599\) 4.45100 + 25.2429i 0.181863 + 1.03140i 0.929920 + 0.367762i \(0.119876\pi\)
−0.748057 + 0.663634i \(0.769013\pi\)
\(600\) 0.766044 1.32683i 0.0312736 0.0541675i
\(601\) −3.99613 6.92150i −0.163006 0.282334i 0.772940 0.634480i \(-0.218786\pi\)
−0.935945 + 0.352146i \(0.885452\pi\)
\(602\) 12.5175 10.5035i 0.510177 0.428089i
\(603\) −3.04101 + 1.10684i −0.123840 + 0.0450739i
\(604\) −4.37464 1.59224i −0.178001 0.0647872i
\(605\) −1.31315 1.10186i −0.0533871 0.0447971i
\(606\) −0.0983261 + 0.557635i −0.00399422 + 0.0226524i
\(607\) −26.9905 −1.09551 −0.547755 0.836639i \(-0.684518\pi\)
−0.547755 + 0.836639i \(0.684518\pi\)
\(608\) 0 0
\(609\) −11.6541 −0.472249
\(610\) 1.01960 5.78244i 0.0412824 0.234124i
\(611\) −34.7939 29.1955i −1.40761 1.18112i
\(612\) −3.99747 1.45496i −0.161588 0.0588133i
\(613\) 13.3919 4.87424i 0.540893 0.196869i −0.0571028 0.998368i \(-0.518186\pi\)
0.597995 + 0.801499i \(0.295964\pi\)
\(614\) 16.3387 13.7098i 0.659375 0.553282i
\(615\) 0.532089 + 0.921605i 0.0214559 + 0.0371627i
\(616\) −4.29086 + 7.43199i −0.172884 + 0.299443i
\(617\) −5.30675 30.0961i −0.213642 1.21162i −0.883248 0.468906i \(-0.844648\pi\)
0.669606 0.742716i \(-0.266463\pi\)
\(618\) 2.28312 + 12.9482i 0.0918405 + 0.520853i
\(619\) 14.3375 24.8333i 0.576273 0.998133i −0.419629 0.907695i \(-0.637840\pi\)
0.995902 0.0904380i \(-0.0288267\pi\)
\(620\) −2.45336 4.24935i −0.0985294 0.170658i
\(621\) 2.97771 2.49860i 0.119491 0.100265i
\(622\) 27.5253 10.0184i 1.10366 0.401701i
\(623\) −19.5963 7.13246i −0.785108 0.285756i
\(624\) −6.75877 5.67128i −0.270567 0.227033i
\(625\) −3.29932 + 18.7113i −0.131973 + 0.748454i
\(626\) 5.56118 0.222270
\(627\) 0 0
\(628\) 8.45336 0.337326
\(629\) 4.94532 28.0463i 0.197183 1.11828i
\(630\) −2.69459 2.26103i −0.107355 0.0900817i
\(631\) 4.22668 + 1.53839i 0.168262 + 0.0612422i 0.424777 0.905298i \(-0.360352\pi\)
−0.256516 + 0.966540i \(0.582575\pi\)
\(632\) 8.51754 3.10013i 0.338810 0.123317i
\(633\) −26.2429 + 22.0204i −1.04306 + 0.875232i
\(634\) −1.90167 3.29380i −0.0755251 0.130813i
\(635\) −9.72967 + 16.8523i −0.386110 + 0.668763i
\(636\) 2.18479 + 12.3906i 0.0866327 + 0.491318i
\(637\) −0.260830 1.47924i −0.0103345 0.0586096i
\(638\) 4.49525 7.78601i 0.177969 0.308251i
\(639\) −2.75877 4.77833i −0.109135 0.189028i
\(640\) 1.53209 1.28558i 0.0605611 0.0508168i
\(641\) 10.9081 3.97021i 0.430843 0.156814i −0.117490 0.993074i \(-0.537485\pi\)
0.548333 + 0.836260i \(0.315263\pi\)
\(642\) 16.4893 + 6.00162i 0.650782 + 0.236865i
\(643\) 19.9520 + 16.7417i 0.786831 + 0.660229i 0.944959 0.327189i \(-0.106101\pi\)
−0.158128 + 0.987419i \(0.550546\pi\)
\(644\) −0.325008 + 1.84321i −0.0128071 + 0.0726326i
\(645\) 18.5817 0.731654
\(646\) 0 0
\(647\) −2.31490 −0.0910082 −0.0455041 0.998964i \(-0.514489\pi\)
−0.0455041 + 0.998964i \(0.514489\pi\)
\(648\) −1.14883 + 6.51536i −0.0451304 + 0.255947i
\(649\) 1.40033 + 1.17502i 0.0549678 + 0.0461234i
\(650\) −5.41147 1.96962i −0.212255 0.0772547i
\(651\) −9.51754 + 3.46410i −0.373022 + 0.135769i
\(652\) 13.0608 10.9593i 0.511499 0.429199i
\(653\) −1.65270 2.86257i −0.0646753 0.112021i 0.831875 0.554964i \(-0.187268\pi\)
−0.896550 + 0.442943i \(0.853934\pi\)
\(654\) −6.66044 + 11.5362i −0.260444 + 0.451102i
\(655\) −2.24628 12.7393i −0.0877695 0.497766i
\(656\) −0.0603074 0.342020i −0.00235461 0.0133536i
\(657\) 5.14543 8.91215i 0.200742 0.347696i
\(658\) −10.6263 18.4053i −0.414256 0.717513i
\(659\) −10.5326 + 8.83786i −0.410290 + 0.344274i −0.824455 0.565928i \(-0.808518\pi\)
0.414165 + 0.910202i \(0.364074\pi\)
\(660\) −9.17024 + 3.33770i −0.356951 + 0.129920i
\(661\) 3.13341 + 1.14047i 0.121875 + 0.0443590i 0.402238 0.915535i \(-0.368232\pi\)
−0.280363 + 0.959894i \(0.590455\pi\)
\(662\) 15.6441 + 13.1269i 0.608025 + 0.510193i
\(663\) 9.98545 56.6303i 0.387803 2.19934i
\(664\) 8.47565 0.328919
\(665\) 0 0
\(666\) 2.85204 0.110514
\(667\) 0.340489 1.93101i 0.0131838 0.0747690i
\(668\) −2.44562 2.05212i −0.0946240 0.0793989i
\(669\) 13.3550 + 4.86084i 0.516336 + 0.187931i
\(670\) 9.31820 3.39155i 0.359993 0.131027i
\(671\) 7.16250 6.01005i 0.276505 0.232016i
\(672\) −2.06418 3.57526i −0.0796274 0.137919i
\(673\) −19.4905 + 33.7585i −0.751304 + 1.30130i 0.195887 + 0.980626i \(0.437241\pi\)
−0.947191 + 0.320670i \(0.896092\pi\)
\(674\) 3.52687 + 20.0019i 0.135850 + 0.770444i
\(675\) 0.971782 + 5.51125i 0.0374039 + 0.212128i
\(676\) −10.0817 + 17.4620i −0.387758 + 0.671617i
\(677\) 21.7939 + 37.7481i 0.837606 + 1.45078i 0.891891 + 0.452250i \(0.149379\pi\)
−0.0542853 + 0.998525i \(0.517288\pi\)
\(678\) 3.35638 2.81634i 0.128901 0.108161i
\(679\) 0.879385 0.320070i 0.0337477 0.0122832i
\(680\) 12.2490 + 4.45826i 0.469727 + 0.170966i
\(681\) 9.07991 + 7.61895i 0.347943 + 0.291959i
\(682\) 1.35679 7.69475i 0.0519542 0.294647i
\(683\) 32.9317 1.26010 0.630048 0.776556i \(-0.283035\pi\)
0.630048 + 0.776556i \(0.283035\pi\)
\(684\) 0 0
\(685\) −23.3209 −0.891045
\(686\) −3.15333 + 17.8834i −0.120395 + 0.682793i
\(687\) −27.0351 22.6851i −1.03145 0.865492i
\(688\) −5.69846 2.07407i −0.217252 0.0790732i
\(689\) 44.4397 16.1747i 1.69302 0.616209i
\(690\) −1.63041 + 1.36808i −0.0620688 + 0.0520819i
\(691\) −17.1604 29.7228i −0.652814 1.13071i −0.982437 0.186594i \(-0.940255\pi\)
0.329623 0.944113i \(-0.393078\pi\)
\(692\) −4.81521 + 8.34018i −0.183047 + 0.317046i
\(693\) −0.972659 5.51622i −0.0369483 0.209544i
\(694\) 0.905544 + 5.13560i 0.0343740 + 0.194945i
\(695\) 8.26352 14.3128i 0.313453 0.542917i
\(696\) 2.16250 + 3.74557i 0.0819695 + 0.141975i
\(697\) 1.73396 1.45496i 0.0656783 0.0551106i
\(698\) −13.4757 + 4.90474i −0.510061 + 0.185647i
\(699\) −12.0929 4.40144i −0.457394 0.166478i
\(700\) −2.06418 1.73205i −0.0780186 0.0654654i
\(701\) 1.12061 6.35532i 0.0423250 0.240037i −0.956305 0.292372i \(-0.905555\pi\)
0.998630 + 0.0523352i \(0.0166664\pi\)
\(702\) 32.2276 1.21635
\(703\) 0 0
\(704\) 3.18479 0.120031
\(705\) 4.19665 23.8004i 0.158055 0.896375i
\(706\) 20.1086 + 16.8731i 0.756797 + 0.635028i
\(707\) 0.935822 + 0.340611i 0.0351952 + 0.0128100i
\(708\) −0.826352 + 0.300767i −0.0310562 + 0.0113035i
\(709\) −2.58853 + 2.17203i −0.0972141 + 0.0815723i −0.690099 0.723715i \(-0.742433\pi\)
0.592885 + 0.805287i \(0.297989\pi\)
\(710\) 8.45336 + 14.6417i 0.317249 + 0.549492i
\(711\) −2.95811 + 5.12360i −0.110938 + 0.192150i
\(712\) 1.34389 + 7.62159i 0.0503645 + 0.285631i
\(713\) −0.295912 1.67820i −0.0110820 0.0628491i
\(714\) 13.4534 23.3019i 0.503479 0.872052i
\(715\) 18.3405 + 31.7667i 0.685895 + 1.18801i
\(716\) 14.4140 12.0948i 0.538676 0.452003i
\(717\) 22.6459 8.24243i 0.845727 0.307819i
\(718\) 31.6587 + 11.5228i 1.18149 + 0.430028i
\(719\) −23.9026 20.0567i −0.891417 0.747988i 0.0770770 0.997025i \(-0.475441\pi\)
−0.968494 + 0.249038i \(0.919886\pi\)
\(720\) −0.226682 + 1.28558i −0.00844792 + 0.0479106i
\(721\) 23.1242 0.861192
\(722\) 0 0
\(723\) 26.8161 0.997303
\(724\) 0.482459 2.73616i 0.0179304 0.101689i
\(725\) 2.16250 + 1.81456i 0.0803134 + 0.0673909i
\(726\) 1.23396 + 0.449123i 0.0457964 + 0.0166685i
\(727\) 24.1138 8.77671i 0.894332 0.325510i 0.146353 0.989232i \(-0.453247\pi\)
0.747979 + 0.663722i \(0.231024\pi\)
\(728\) −11.8871 + 9.97448i −0.440566 + 0.369679i
\(729\) −15.0201 26.0155i −0.556299 0.963538i
\(730\) −15.7665 + 27.3084i −0.583545 + 1.01073i
\(731\) −6.86319 38.9231i −0.253844 1.43962i
\(732\) 0.781059 + 4.42961i 0.0288688 + 0.163723i
\(733\) 11.9368 20.6751i 0.440894 0.763651i −0.556862 0.830605i \(-0.687995\pi\)
0.997756 + 0.0669540i \(0.0213281\pi\)
\(734\) 5.23442 + 9.06629i 0.193206 + 0.334643i
\(735\) 0.612245 0.513735i 0.0225830 0.0189494i
\(736\) 0.652704 0.237565i 0.0240590 0.00875675i
\(737\) 14.8383 + 5.40069i 0.546575 + 0.198937i
\(738\) 0.173648 + 0.145708i 0.00639208 + 0.00536359i
\(739\) −7.97746 + 45.2424i −0.293456 + 1.66427i 0.379958 + 0.925004i \(0.375939\pi\)
−0.673413 + 0.739266i \(0.735173\pi\)
\(740\) −8.73917 −0.321258
\(741\) 0 0
\(742\) 22.1284 0.812357
\(743\) −8.85803 + 50.2364i −0.324970 + 1.84299i 0.184919 + 0.982754i \(0.440798\pi\)
−0.509889 + 0.860240i \(0.670313\pi\)
\(744\) 2.87939 + 2.41609i 0.105563 + 0.0885782i
\(745\) 30.9222 + 11.2548i 1.13290 + 0.412343i
\(746\) −22.4611 + 8.17517i −0.822359 + 0.299314i
\(747\) −4.23783 + 3.55596i −0.155054 + 0.130106i
\(748\) 10.3785 + 17.9761i 0.379476 + 0.657271i
\(749\) 15.4311 26.7274i 0.563839 0.976598i
\(750\) −3.19253 18.1058i −0.116575 0.661129i
\(751\) −6.31551 35.8170i −0.230456 1.30698i −0.851975 0.523583i \(-0.824595\pi\)
0.621518 0.783400i \(-0.286516\pi\)
\(752\) −3.94356 + 6.83045i −0.143807 + 0.249081i
\(753\) −6.56283 11.3672i −0.239163 0.414242i
\(754\) 12.4534 10.4496i 0.453525 0.380552i
\(755\) −8.74928 + 3.18448i −0.318419 + 0.115895i
\(756\) 14.1702 + 5.15755i 0.515367 + 0.187578i
\(757\) −4.44562 3.73032i −0.161579 0.135581i 0.558413 0.829563i \(-0.311410\pi\)
−0.719992 + 0.693982i \(0.755855\pi\)
\(758\) 3.09327 17.5428i 0.112353 0.637184i
\(759\) −3.38919 −0.123020
\(760\) 0 0
\(761\) 22.6355 0.820535 0.410268 0.911965i \(-0.365435\pi\)
0.410268 + 0.911965i \(0.365435\pi\)
\(762\) 2.58853 14.6803i 0.0937724 0.531810i
\(763\) 17.9472 + 15.0595i 0.649732 + 0.545190i
\(764\) −8.98545 3.27044i −0.325082 0.118320i
\(765\) −7.99495 + 2.90992i −0.289058 + 0.105208i
\(766\) 19.2121 16.1209i 0.694163 0.582472i
\(767\) 1.65270 + 2.86257i 0.0596757 + 0.103361i
\(768\) −0.766044 + 1.32683i −0.0276422 + 0.0478778i
\(769\) 1.89322 + 10.7370i 0.0682712 + 0.387185i 0.999728 + 0.0233326i \(0.00742768\pi\)
−0.931457 + 0.363853i \(0.881461\pi\)
\(770\) 2.98040 + 16.9027i 0.107406 + 0.609131i
\(771\) 6.14724 10.6473i 0.221387 0.383454i
\(772\) 11.8405 + 20.5083i 0.426149 + 0.738111i
\(773\) −4.02229 + 3.37510i −0.144672 + 0.121394i −0.712251 0.701925i \(-0.752324\pi\)
0.567580 + 0.823319i \(0.307880\pi\)
\(774\) 3.71941 1.35375i 0.133691 0.0486597i
\(775\) 2.30541 + 0.839100i 0.0828127 + 0.0301413i
\(776\) −0.266044 0.223238i −0.00955044 0.00801377i
\(777\) −3.13247 + 17.7651i −0.112377 + 0.637321i
\(778\) −9.41828 −0.337662
\(779\) 0 0
\(780\) −17.6459 −0.631824
\(781\) −4.67499 + 26.5132i −0.167284 + 0.948717i
\(782\) 3.46791 + 2.90992i 0.124012 + 0.104059i
\(783\) −14.8452 5.40322i −0.530525 0.193095i
\(784\) −0.245100 + 0.0892091i −0.00875357 + 0.00318604i
\(785\) 12.9513 10.8674i 0.462252 0.387875i
\(786\) 4.95471 + 8.58180i 0.176729 + 0.306103i
\(787\) 1.19372 2.06758i 0.0425514 0.0737011i −0.843965 0.536398i \(-0.819785\pi\)
0.886517 + 0.462697i \(0.153118\pi\)
\(788\) −3.98040 22.5740i −0.141796 0.804164i
\(789\) −1.58584 8.99373i −0.0564573 0.320185i
\(790\) 9.06418 15.6996i 0.322489 0.558567i
\(791\) −3.85298 6.67355i −0.136996 0.237284i
\(792\) −1.59240 + 1.33618i −0.0565833 + 0.0474791i
\(793\) 15.8871 5.78244i 0.564168 0.205341i
\(794\) −6.43882 2.34354i −0.228505 0.0831690i
\(795\) 19.2763 + 16.1747i 0.683660 + 0.573659i
\(796\) 1.75103 9.93058i 0.0620636 0.351980i
\(797\) 31.0951 1.10145 0.550723 0.834688i \(-0.314352\pi\)
0.550723 + 0.834688i \(0.314352\pi\)
\(798\) 0 0
\(799\) −51.4047 −1.81857
\(800\) −0.173648 + 0.984808i −0.00613939 + 0.0348182i
\(801\) −3.86959 3.24697i −0.136725 0.114726i
\(802\) −4.46064 1.62354i −0.157511 0.0573292i
\(803\) −47.1848 + 17.1739i −1.66512 + 0.606053i
\(804\) −5.81908 + 4.88279i −0.205223 + 0.172203i
\(805\) 1.87164 + 3.24178i 0.0659668 + 0.114258i
\(806\) 7.06418 12.2355i 0.248825 0.430978i
\(807\) −0.305407 1.73205i −0.0107508 0.0609711i
\(808\) −0.0641778 0.363970i −0.00225777 0.0128044i
\(809\) −11.1518 + 19.3155i −0.392077 + 0.679098i −0.992723 0.120417i \(-0.961577\pi\)
0.600646 + 0.799515i \(0.294910\pi\)
\(810\) 6.61587 + 11.4590i 0.232458 + 0.402629i
\(811\) 2.54252 2.13343i 0.0892799 0.0749147i −0.597055 0.802200i \(-0.703663\pi\)
0.686335 + 0.727285i \(0.259218\pi\)
\(812\) 7.14796 2.60164i 0.250844 0.0912998i
\(813\) −28.8726 10.5088i −1.01261 0.368558i
\(814\) −10.6604 8.94517i −0.373648 0.313528i
\(815\) 5.92127 33.5812i 0.207413 1.17630i
\(816\) −9.98545 −0.349561
\(817\) 0 0
\(818\) 31.6928 1.10811
\(819\) 1.75877 9.97448i 0.0614564 0.348537i
\(820\) −0.532089 0.446476i −0.0185813 0.0155916i
\(821\) 1.72193 + 0.626733i 0.0600959 + 0.0218731i 0.371893 0.928276i \(-0.378709\pi\)
−0.311797 + 0.950149i \(0.600931\pi\)
\(822\) 16.7875 6.11013i 0.585530 0.213115i
\(823\) −26.2276 + 22.0076i −0.914237 + 0.767136i −0.972920 0.231141i \(-0.925754\pi\)
0.0586832 + 0.998277i \(0.481310\pi\)
\(824\) −4.29086 7.43199i −0.149479 0.258906i
\(825\) 2.43969 4.22567i 0.0849392 0.147119i
\(826\) 0.268571 + 1.52314i 0.00934477 + 0.0529968i
\(827\) −3.44965 19.5640i −0.119956 0.680306i −0.984176 0.177192i \(-0.943299\pi\)
0.864220 0.503114i \(-0.167812\pi\)
\(828\) −0.226682 + 0.392624i −0.00787773 + 0.0136446i
\(829\) 17.8675 + 30.9475i 0.620565 + 1.07485i 0.989381 + 0.145347i \(0.0464300\pi\)
−0.368816 + 0.929502i \(0.620237\pi\)
\(830\) 12.9855 10.8961i 0.450732 0.378209i
\(831\) −24.9932 + 9.09678i −0.867004 + 0.315564i
\(832\) 5.41147 + 1.96962i 0.187609 + 0.0682841i
\(833\) −1.30225 1.09272i −0.0451204 0.0378605i
\(834\) −2.19846 + 12.4681i −0.0761266 + 0.431735i
\(835\) −6.38507 −0.220964
\(836\) 0 0
\(837\) −13.7297 −0.474567
\(838\) −1.91188 + 10.8428i −0.0660450 + 0.374560i
\(839\) −41.6691 34.9645i −1.43858 1.20711i −0.940416 0.340026i \(-0.889564\pi\)
−0.498162 0.867084i \(-0.665991\pi\)
\(840\) −7.75877 2.82396i −0.267703 0.0974359i
\(841\) 19.7626 7.19301i 0.681470 0.248035i
\(842\) −6.63816 + 5.57007i −0.228766 + 0.191957i
\(843\) −2.23783 3.87603i −0.0770748 0.133498i
\(844\) 11.1800 19.3644i 0.384833 0.666550i
\(845\) 7.00269 + 39.7142i 0.240900 + 1.36621i
\(846\) −0.893933 5.06975i −0.0307341 0.174301i
\(847\) 1.15476 2.00011i 0.0396781 0.0687245i
\(848\) −4.10607 7.11192i −0.141003 0.244224i
\(849\) −11.1270 + 9.33667i −0.381878 + 0.320434i
\(850\) −6.12449 + 2.22913i −0.210068 + 0.0764585i
\(851\) −2.85204 1.03806i −0.0977668 0.0355842i
\(852\) −9.92127 8.32494i −0.339897 0.285208i
\(853\) 2.77425 15.7336i 0.0949886 0.538707i −0.899762 0.436380i \(-0.856260\pi\)
0.994751 0.102327i \(-0.0326287\pi\)
\(854\) 7.91085 0.270704
\(855\) 0 0
\(856\) −11.4534 −0.391468
\(857\) −4.51738 + 25.6193i −0.154311 + 0.875140i 0.805103 + 0.593136i \(0.202110\pi\)
−0.959413 + 0.282004i \(0.909001\pi\)
\(858\) −21.5253 18.0619i −0.734861 0.616622i
\(859\) −50.0578 18.2196i −1.70795 0.621643i −0.711260 0.702929i \(-0.751875\pi\)
−0.996691 + 0.0812851i \(0.974098\pi\)
\(860\) −11.3969 + 4.14814i −0.388632 + 0.141450i
\(861\) −1.09833 + 0.921605i −0.0374309 + 0.0314082i
\(862\) 14.9436 + 25.8830i 0.508980 + 0.881579i
\(863\) −1.61587 + 2.79876i −0.0550048 + 0.0952710i −0.892217 0.451608i \(-0.850851\pi\)
0.837212 + 0.546879i \(0.184184\pi\)
\(864\) −0.971782 5.51125i −0.0330607 0.187496i
\(865\) 3.34461 + 18.9682i 0.113720 + 0.644939i
\(866\) −4.63041 + 8.02011i −0.157348 + 0.272535i
\(867\) −19.5175 33.8054i −0.662850 1.14809i
\(868\) 5.06418 4.24935i 0.171889 0.144232i
\(869\) 27.1266 9.87328i 0.920207 0.334928i
\(870\) 8.12836 + 2.95848i 0.275577 + 0.100302i
\(871\) 21.8726 + 18.3533i 0.741124 + 0.621877i
\(872\) 1.50980 8.56250i 0.0511283 0.289963i
\(873\) 0.226682 0.00767201
\(874\) 0 0
\(875\) −32.3351 −1.09313
\(876\) 4.19459 23.7887i 0.141722 0.803746i
\(877\) 8.98133 + 7.53623i 0.303278 + 0.254481i 0.781707 0.623646i \(-0.214349\pi\)
−0.478429 + 0.878126i \(0.658794\pi\)
\(878\) −19.6040 7.13528i −0.661603 0.240804i
\(879\) 39.2918 14.3010i 1.32528 0.482362i
\(880\) 4.87939 4.09429i 0.164484 0.138018i
\(881\) −13.5236 23.4236i −0.455623 0.789162i 0.543101 0.839667i \(-0.317250\pi\)
−0.998724 + 0.0505056i \(0.983917\pi\)
\(882\) 0.0851223 0.147436i 0.00286622 0.00496443i
\(883\) 2.51460 + 14.2610i 0.0846232 + 0.479922i 0.997437 + 0.0715465i \(0.0227934\pi\)
−0.912814 + 0.408375i \(0.866095\pi\)
\(884\) 6.51754 + 36.9628i 0.219209 + 1.24319i
\(885\) −0.879385 + 1.52314i −0.0295602 + 0.0511998i
\(886\) −11.9140 20.6357i −0.400259 0.693268i
\(887\) −8.87939 + 7.45069i −0.298141 + 0.250170i −0.779570 0.626315i \(-0.784562\pi\)
0.481429 + 0.876485i \(0.340118\pi\)
\(888\) 6.29086 2.28969i 0.211107 0.0768368i
\(889\) −24.6364 8.96692i −0.826278 0.300741i
\(890\) 11.8571 + 9.94929i 0.397451 + 0.333501i
\(891\) −3.65880 + 20.7501i −0.122574 + 0.695153i
\(892\) −9.27631 −0.310594
\(893\) 0 0
\(894\) −25.2080 −0.843082
\(895\) 6.53478 37.0606i 0.218434 1.23880i
\(896\) 2.06418 + 1.73205i 0.0689593 + 0.0578638i
\(897\) −5.75877 2.09602i −0.192280 0.0699841i
\(898\) 2.05051 0.746324i 0.0684263 0.0249051i
\(899\) −5.30541 + 4.45177i −0.176945 + 0.148475i
\(900\) −0.326352 0.565258i −0.0108784 0.0188419i
\(901\) 26.7615 46.3522i 0.891553 1.54422i
\(902\) −0.192066 1.08926i −0.00639511 0.0362685i
\(903\) 4.34730 + 24.6547i 0.144669 + 0.820458i
\(904\) −1.42989 + 2.47665i −0.0475575 + 0.0823720i
\(905\) −2.77837 4.81228i −0.0923562 0.159966i
\(906\) 5.46379 4.58467i 0.181522 0.152315i
\(907\) −39.4470 + 14.3575i −1.30982 + 0.476734i −0.900181 0.435515i \(-0.856566\pi\)
−0.409635 + 0.912249i \(0.634344\pi\)
\(908\) −7.26991 2.64603i −0.241261 0.0878117i
\(909\) 0.184793 + 0.155059i 0.00612918 + 0.00514299i
\(910\) −5.38919 + 30.5636i −0.178650 + 1.01317i
\(911\) −44.8675 −1.48653 −0.743264 0.668999i \(-0.766723\pi\)
−0.743264 + 0.668999i \(0.766723\pi\)
\(912\) 0 0
\(913\) 26.9932 0.893344
\(914\) 0.309278 1.75400i 0.0102300 0.0580172i
\(915\) 6.89124 + 5.78244i 0.227818 + 0.191162i
\(916\) 21.6459 + 7.87846i 0.715201 + 0.260312i
\(917\) 16.3773 5.96086i 0.540827 0.196845i
\(918\) 27.9406 23.4450i 0.922178 0.773799i
\(919\) 16.2635 + 28.1692i 0.536484 + 0.929217i 0.999090 + 0.0426535i \(0.0135811\pi\)
−0.462606 + 0.886564i \(0.653086\pi\)
\(920\) 0.694593 1.20307i 0.0229000 0.0396640i
\(921\) 5.67436 + 32.1809i 0.186977 + 1.06040i
\(922\) −2.68954 15.2531i −0.0885753 0.502335i
\(923\) −24.3405 + 42.1590i −0.801177 + 1.38768i
\(924\) −6.57398 11.3865i −0.216268 0.374587i
\(925\) 3.34730 2.80872i 0.110058 0.0923500i
\(926\) 2.54664 0.926900i 0.0836877 0.0304598i
\(927\) 5.26352 + 1.91576i 0.172877 + 0.0629219i
\(928\) −2.16250 1.81456i −0.0709877 0.0595657i
\(929\) 2.05603 11.6603i 0.0674560 0.382562i −0.932325 0.361622i \(-0.882223\pi\)
0.999781 0.0209399i \(-0.00666588\pi\)
\(930\) 7.51754 0.246510
\(931\) 0 0
\(932\) 8.39961 0.275139
\(933\) −7.79292 + 44.1958i −0.255129 + 1.44691i
\(934\) 9.89234 + 8.30066i 0.323687 + 0.271606i
\(935\) 39.0104 + 14.1986i 1.27578 + 0.464345i
\(936\) −3.53209 + 1.28558i −0.115450 + 0.0420203i
\(937\) −0.585122 + 0.490976i −0.0191151 + 0.0160395i −0.652295 0.757965i \(-0.726194\pi\)
0.633180 + 0.774005i \(0.281749\pi\)
\(938\) 6.68004 + 11.5702i 0.218111 + 0.377780i
\(939\) −4.26011 + 7.37874i −0.139024 + 0.240796i
\(940\) 2.73917 + 15.5346i 0.0893419 + 0.506683i
\(941\) −3.73236 21.1673i −0.121672 0.690034i −0.983229 0.182374i \(-0.941622\pi\)
0.861558 0.507660i \(-0.169489\pi\)
\(942\) −6.47565 + 11.2162i −0.210988 + 0.365442i
\(943\) −0.120615 0.208911i −0.00392776 0.00680307i
\(944\) 0.439693 0.368946i 0.0143108 0.0120082i
\(945\) 28.3405 10.3151i 0.921916 0.335550i
\(946\) −18.1484 6.60549i −0.590056 0.214763i
\(947\) 24.2722 + 20.3668i 0.788740 + 0.661832i 0.945433 0.325816i \(-0.105639\pi\)
−0.156693 + 0.987647i \(0.550083\pi\)
\(948\) −2.41147 + 13.6761i −0.0783210 + 0.444181i
\(949\) −90.7957 −2.94735
\(950\) 0 0
\(951\) 5.82707 0.188956
\(952\) −3.04963 + 17.2953i −0.0988391 + 0.560544i
\(953\) 42.7998 + 35.9133i 1.38642 + 1.16335i 0.966766 + 0.255661i \(0.0822932\pi\)
0.419655 + 0.907684i \(0.362151\pi\)
\(954\) 5.03684 + 1.83326i 0.163074 + 0.0593539i
\(955\) −17.9709 + 6.54087i −0.581525 + 0.211658i
\(956\) −12.0496 + 10.1108i −0.389713 + 0.327008i
\(957\) 6.88713 + 11.9289i 0.222629 + 0.385605i
\(958\) 9.27631 16.0670i 0.299704 0.519103i
\(959\) −5.45605 30.9428i −0.176185 0.999195i
\(960\) 0.532089 + 3.01763i 0.0171731 + 0.0973935i
\(961\) 12.4905 21.6342i 0.402920 0.697877i
\(962\) −12.5817 21.7922i −0.405651 0.702608i
\(963\) 5.72668 4.80526i 0.184540 0.154847i
\(964\) −16.4474 + 5.98638i −0.529736 + 0.192808i
\(965\) 44.5057 + 16.1987i 1.43269 + 0.521456i
\(966\) −2.19665 1.84321i −0.0706761 0.0593043i
\(967\) 3.74329 21.2292i 0.120376 0.682687i −0.863571 0.504227i \(-0.831778\pi\)
0.983947 0.178460i \(-0.0571114\pi\)
\(968\) −0.857097 −0.0275481
\(969\) 0 0
\(970\) −0.694593 −0.0223020
\(971\) 8.44908 47.9171i 0.271144 1.53773i −0.479806 0.877375i \(-0.659293\pi\)
0.750950 0.660359i \(-0.229596\pi\)
\(972\) 5.09627 + 4.27628i 0.163463 + 0.137162i
\(973\) 20.9240 + 7.61570i 0.670791 + 0.244148i
\(974\) −38.6905 + 14.0822i −1.23972 + 0.451222i
\(975\) 6.75877 5.67128i 0.216454 0.181626i
\(976\) −1.46791 2.54250i −0.0469867 0.0813833i
\(977\) 25.2741 43.7760i 0.808590 1.40052i −0.105251 0.994446i \(-0.533565\pi\)
0.913841 0.406073i \(-0.133102\pi\)
\(978\) 4.53596 + 25.7247i 0.145044 + 0.822585i
\(979\) 4.28002 + 24.2732i 0.136790 + 0.775775i
\(980\) −0.260830 + 0.451771i −0.00833190 + 0.0144313i
\(981\) 2.83750 + 4.91469i 0.0905943 + 0.156914i
\(982\) −17.2954 + 14.5126i −0.551920 + 0.463116i
\(983\) 28.2472 10.2811i 0.900946 0.327918i 0.150314 0.988638i \(-0.451971\pi\)
0.750632 + 0.660721i \(0.229749\pi\)
\(984\) 0.500000 + 0.181985i 0.0159394 + 0.00580147i
\(985\) −35.1189 29.4682i −1.11898 0.938936i
\(986\) 3.19490 18.1192i 0.101746 0.577032i
\(987\) 32.5609 1.03642
\(988\) 0 0
\(989\) −4.21213 −0.133938
\(990\) −0.721934 + 4.09429i −0.0229446 + 0.130125i
\(991\) 2.10876 + 1.76946i 0.0669868 + 0.0562086i 0.675666 0.737208i \(-0.263856\pi\)
−0.608680 + 0.793416i \(0.708300\pi\)
\(992\) −2.30541 0.839100i −0.0731968 0.0266414i
\(993\) −29.4013 + 10.7012i −0.933021 + 0.339592i
\(994\) −17.4492 + 14.6417i −0.553456 + 0.464405i
\(995\) −10.0838 17.4656i −0.319677 0.553697i
\(996\) −6.49273 + 11.2457i −0.205730 + 0.356335i
\(997\) 1.51155 + 8.57245i 0.0478714 + 0.271492i 0.999343 0.0362444i \(-0.0115395\pi\)
−0.951472 + 0.307737i \(0.900428\pi\)
\(998\) −5.09286 28.8831i −0.161212 0.914277i
\(999\) −12.2267 + 21.1772i −0.386835 + 0.670018i
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 722.2.e.m.245.1 6
19.2 odd 18 722.2.c.l.429.3 6
19.3 odd 18 722.2.a.k.1.1 3
19.4 even 9 38.2.e.a.25.1 6
19.5 even 9 722.2.c.k.653.1 6
19.6 even 9 722.2.e.b.99.1 6
19.7 even 3 38.2.e.a.35.1 yes 6
19.8 odd 6 722.2.e.l.423.1 6
19.9 even 9 inner 722.2.e.m.389.1 6
19.10 odd 18 722.2.e.a.389.1 6
19.11 even 3 722.2.e.b.423.1 6
19.12 odd 6 722.2.e.k.415.1 6
19.13 odd 18 722.2.e.l.99.1 6
19.14 odd 18 722.2.c.l.653.3 6
19.15 odd 18 722.2.e.k.595.1 6
19.16 even 9 722.2.a.l.1.3 3
19.17 even 9 722.2.c.k.429.1 6
19.18 odd 2 722.2.e.a.245.1 6
57.23 odd 18 342.2.u.c.253.1 6
57.26 odd 6 342.2.u.c.73.1 6
57.35 odd 18 6498.2.a.bl.1.2 3
57.41 even 18 6498.2.a.bq.1.2 3
76.3 even 18 5776.2.a.bo.1.3 3
76.7 odd 6 304.2.u.c.225.1 6
76.23 odd 18 304.2.u.c.177.1 6
76.35 odd 18 5776.2.a.bn.1.1 3
95.4 even 18 950.2.l.d.101.1 6
95.7 odd 12 950.2.u.b.149.1 12
95.23 odd 36 950.2.u.b.899.1 12
95.42 odd 36 950.2.u.b.899.2 12
95.64 even 6 950.2.l.d.301.1 6
95.83 odd 12 950.2.u.b.149.2 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
38.2.e.a.25.1 6 19.4 even 9
38.2.e.a.35.1 yes 6 19.7 even 3
304.2.u.c.177.1 6 76.23 odd 18
304.2.u.c.225.1 6 76.7 odd 6
342.2.u.c.73.1 6 57.26 odd 6
342.2.u.c.253.1 6 57.23 odd 18
722.2.a.k.1.1 3 19.3 odd 18
722.2.a.l.1.3 3 19.16 even 9
722.2.c.k.429.1 6 19.17 even 9
722.2.c.k.653.1 6 19.5 even 9
722.2.c.l.429.3 6 19.2 odd 18
722.2.c.l.653.3 6 19.14 odd 18
722.2.e.a.245.1 6 19.18 odd 2
722.2.e.a.389.1 6 19.10 odd 18
722.2.e.b.99.1 6 19.6 even 9
722.2.e.b.423.1 6 19.11 even 3
722.2.e.k.415.1 6 19.12 odd 6
722.2.e.k.595.1 6 19.15 odd 18
722.2.e.l.99.1 6 19.13 odd 18
722.2.e.l.423.1 6 19.8 odd 6
722.2.e.m.245.1 6 1.1 even 1 trivial
722.2.e.m.389.1 6 19.9 even 9 inner
950.2.l.d.101.1 6 95.4 even 18
950.2.l.d.301.1 6 95.64 even 6
950.2.u.b.149.1 12 95.7 odd 12
950.2.u.b.149.2 12 95.83 odd 12
950.2.u.b.899.1 12 95.23 odd 36
950.2.u.b.899.2 12 95.42 odd 36
5776.2.a.bn.1.1 3 76.35 odd 18
5776.2.a.bo.1.3 3 76.3 even 18
6498.2.a.bl.1.2 3 57.35 odd 18
6498.2.a.bq.1.2 3 57.41 even 18