Properties

Label 841.2.d.j.645.1
Level $841$
Weight $2$
Character 841.645
Analytic conductor $6.715$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $6$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [841,2,Mod(190,841)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(841, base_ring=CyclotomicField(14))
 
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("841.190");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 841 = 29^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 841.d (of order \(7\), 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: \(6.71541880999\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(2\) over \(\Q(\zeta_{7})\)
Coefficient field: 12.0.74049191673856.2
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} + 2x^{10} + 4x^{8} + 8x^{6} + 16x^{4} + 32x^{2} + 64 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 29)
Sato-Tate group: $\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label 645.1
Root \(0.881748 - 1.10568i\) of defining polynomial
Character \(\chi\) \(=\) 841.645
Dual form 841.2.d.j.605.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.0921712 - 0.403828i) q^{2} +(0.373194 + 0.179721i) q^{3} +(1.64736 - 0.793325i) q^{4} +(0.222521 + 0.974928i) q^{5} +(0.0381786 - 0.167271i) q^{6} +(-2.54832 - 1.22721i) q^{7} +(-0.988722 - 1.23982i) q^{8} +(-1.76350 - 2.21135i) q^{9} +O(q^{10})\) \(q+(-0.0921712 - 0.403828i) q^{2} +(0.373194 + 0.179721i) q^{3} +(1.64736 - 0.793325i) q^{4} +(0.222521 + 0.974928i) q^{5} +(0.0381786 - 0.167271i) q^{6} +(-2.54832 - 1.22721i) q^{7} +(-0.988722 - 1.23982i) q^{8} +(-1.76350 - 2.21135i) q^{9} +(0.373194 - 0.179721i) q^{10} +(1.50524 - 1.88751i) q^{11} +0.757359 q^{12} +(1.14001 - 1.42952i) q^{13} +(-0.260699 + 1.14220i) q^{14} +(-0.0921712 + 0.403828i) q^{15} +(1.87047 - 2.34549i) q^{16} -4.82843 q^{17} +(-0.730464 + 0.915973i) q^{18} +(-5.40581 + 2.60330i) q^{19} +(1.14001 + 1.42952i) q^{20} +(-0.730464 - 0.915973i) q^{21} +(-0.900969 - 0.433884i) q^{22} +(1.70381 - 7.46488i) q^{23} +(-0.146164 - 0.640386i) q^{24} +(3.60388 - 1.73553i) q^{25} +(-0.682357 - 0.328606i) q^{26} +(-0.537213 - 2.35368i) q^{27} -5.17157 q^{28} +0.171573 q^{30} +(0.905898 + 3.96900i) q^{31} +(-3.97707 - 1.91526i) q^{32} +(0.900969 - 0.433884i) q^{33} +(0.445042 + 1.94986i) q^{34} +(0.629384 - 2.75751i) q^{35} +(-4.65943 - 2.24386i) q^{36} +(-2.49396 - 3.12733i) q^{37} +(1.54955 + 1.94307i) q^{38} +(0.682357 - 0.328606i) q^{39} +(0.988722 - 1.23982i) q^{40} +12.4853 q^{41} +(-0.302568 + 0.379408i) q^{42} +(-1.42730 + 6.25340i) q^{43} +(0.982255 - 4.30354i) q^{44} +(1.76350 - 2.21135i) q^{45} -3.17157 q^{46} +(3.26873 - 4.09886i) q^{47} +(1.11958 - 0.539162i) q^{48} +(0.623490 + 0.781831i) q^{49} +(-1.03303 - 1.29538i) q^{50} +(-1.80194 - 0.867767i) q^{51} +(0.743920 - 3.25933i) q^{52} +(1.66563 + 7.29761i) q^{53} +(-0.900969 + 0.433884i) q^{54} +(2.17513 + 1.04749i) q^{55} +(0.998069 + 4.37283i) q^{56} -2.48528 q^{57} +7.65685 q^{59} +(0.168528 + 0.738371i) q^{60} +(-0.746387 - 0.359441i) q^{61} +(1.51930 - 0.731654i) q^{62} +(1.78017 + 7.79942i) q^{63} +(0.928262 - 4.06698i) q^{64} +(1.64736 + 0.793325i) q^{65} +(-0.258258 - 0.323845i) q^{66} +(-3.52699 - 4.42271i) q^{67} +(-7.95414 + 3.83051i) q^{68} +(1.97744 - 2.47964i) q^{69} -1.17157 q^{70} +(-1.97744 + 2.47964i) q^{71} +(-0.998069 + 4.37283i) q^{72} +(-0.890084 + 3.89971i) q^{73} +(-1.03303 + 1.29538i) q^{74} +1.65685 q^{75} +(-6.84003 + 8.57713i) q^{76} +(-6.15220 + 2.96274i) q^{77} +(-0.195594 - 0.245267i) q^{78} +(0.258258 + 0.323845i) q^{79} +(2.70291 + 1.30165i) q^{80} +(-1.66563 + 7.29761i) q^{81} +(-1.15078 - 5.04191i) q^{82} +(3.29471 - 1.58665i) q^{83} +(-1.93000 - 0.929438i) q^{84} +(-1.07443 - 4.70737i) q^{85} +2.65685 q^{86} -3.82843 q^{88} +(-0.998069 - 4.37283i) q^{89} +(-1.05555 - 0.508326i) q^{90} +(-4.65943 + 2.24386i) q^{91} +(-3.11529 - 13.6490i) q^{92} +(-0.375235 + 1.64401i) q^{93} +(-1.95652 - 0.942210i) q^{94} +(-3.74094 - 4.69099i) q^{95} +(-1.14001 - 1.42952i) q^{96} +(11.2488 - 5.41716i) q^{97} +(0.258258 - 0.323845i) q^{98} -6.82843 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 2 q^{5} + 6 q^{6} + 6 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 2 q^{5} + 6 q^{6} + 6 q^{8} - 2 q^{10} - 2 q^{11} + 60 q^{12} + 2 q^{13} - 8 q^{14} + 2 q^{15} - 6 q^{16} - 24 q^{17} + 8 q^{18} - 12 q^{19} + 2 q^{20} + 8 q^{21} - 2 q^{22} + 4 q^{23} + 10 q^{24} + 8 q^{25} - 10 q^{26} - 2 q^{27} - 96 q^{28} + 36 q^{30} - 6 q^{31} - 6 q^{32} + 2 q^{33} + 4 q^{34} - 16 q^{36} + 8 q^{37} + 12 q^{38} + 10 q^{39} - 6 q^{40} + 48 q^{41} - 16 q^{42} - 10 q^{43} + 6 q^{44} - 72 q^{46} - 2 q^{47} - 6 q^{48} - 2 q^{49} - 8 q^{50} - 4 q^{51} + 18 q^{52} - 2 q^{53} - 2 q^{54} + 2 q^{55} - 8 q^{56} + 72 q^{57} + 24 q^{59} + 10 q^{60} + 4 q^{61} + 26 q^{62} + 16 q^{63} + 14 q^{64} - 2 q^{65} - 2 q^{66} - 12 q^{68} - 12 q^{69} - 48 q^{70} + 12 q^{71} + 8 q^{72} - 8 q^{73} - 8 q^{74} - 48 q^{75} - 12 q^{76} - 8 q^{77} - 22 q^{78} + 2 q^{79} + 6 q^{80} + 2 q^{81} - 16 q^{82} - 4 q^{83} + 24 q^{84} - 4 q^{85} - 36 q^{86} - 12 q^{88} + 8 q^{89} - 8 q^{90} - 16 q^{91} - 28 q^{92} - 26 q^{93} - 10 q^{94} + 12 q^{95} - 2 q^{96} + 8 q^{97} + 2 q^{98} - 48 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/841\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{3}{7}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.0921712 0.403828i −0.0651749 0.285550i 0.931829 0.362897i \(-0.118212\pi\)
−0.997004 + 0.0773470i \(0.975355\pi\)
\(3\) 0.373194 + 0.179721i 0.215463 + 0.103762i 0.538502 0.842624i \(-0.318990\pi\)
−0.323039 + 0.946386i \(0.604705\pi\)
\(4\) 1.64736 0.793325i 0.823678 0.396662i
\(5\) 0.222521 + 0.974928i 0.0995144 + 0.436001i 0.999999 + 0.00111393i \(0.000354575\pi\)
−0.900485 + 0.434887i \(0.856788\pi\)
\(6\) 0.0381786 0.167271i 0.0155863 0.0682882i
\(7\) −2.54832 1.22721i −0.963176 0.463841i −0.114889 0.993378i \(-0.536651\pi\)
−0.848287 + 0.529537i \(0.822366\pi\)
\(8\) −0.988722 1.23982i −0.349566 0.438342i
\(9\) −1.76350 2.21135i −0.587832 0.737118i
\(10\) 0.373194 0.179721i 0.118014 0.0568326i
\(11\) 1.50524 1.88751i 0.453846 0.569105i −0.501287 0.865281i \(-0.667140\pi\)
0.955133 + 0.296176i \(0.0957114\pi\)
\(12\) 0.757359 0.218631
\(13\) 1.14001 1.42952i 0.316181 0.396478i −0.598191 0.801353i \(-0.704114\pi\)
0.914372 + 0.404875i \(0.132685\pi\)
\(14\) −0.260699 + 1.14220i −0.0696749 + 0.305266i
\(15\) −0.0921712 + 0.403828i −0.0237985 + 0.104268i
\(16\) 1.87047 2.34549i 0.467617 0.586374i
\(17\) −4.82843 −1.17107 −0.585533 0.810649i \(-0.699115\pi\)
−0.585533 + 0.810649i \(0.699115\pi\)
\(18\) −0.730464 + 0.915973i −0.172172 + 0.215897i
\(19\) −5.40581 + 2.60330i −1.24018 + 0.597239i −0.934862 0.355012i \(-0.884477\pi\)
−0.305317 + 0.952251i \(0.598762\pi\)
\(20\) 1.14001 + 1.42952i 0.254913 + 0.319651i
\(21\) −0.730464 0.915973i −0.159400 0.199882i
\(22\) −0.900969 0.433884i −0.192087 0.0925043i
\(23\) 1.70381 7.46488i 0.355269 1.55654i −0.409549 0.912288i \(-0.634314\pi\)
0.764818 0.644247i \(-0.222829\pi\)
\(24\) −0.146164 0.640386i −0.0298356 0.130718i
\(25\) 3.60388 1.73553i 0.720775 0.347107i
\(26\) −0.682357 0.328606i −0.133821 0.0644449i
\(27\) −0.537213 2.35368i −0.103387 0.452967i
\(28\) −5.17157 −0.977335
\(29\) 0 0
\(30\) 0.171573 0.0313248
\(31\) 0.905898 + 3.96900i 0.162704 + 0.712853i 0.988790 + 0.149310i \(0.0477051\pi\)
−0.826086 + 0.563543i \(0.809438\pi\)
\(32\) −3.97707 1.91526i −0.703053 0.338573i
\(33\) 0.900969 0.433884i 0.156839 0.0755295i
\(34\) 0.445042 + 1.94986i 0.0763241 + 0.334398i
\(35\) 0.629384 2.75751i 0.106385 0.466105i
\(36\) −4.65943 2.24386i −0.776571 0.373977i
\(37\) −2.49396 3.12733i −0.410004 0.514129i 0.533360 0.845889i \(-0.320929\pi\)
−0.943364 + 0.331759i \(0.892358\pi\)
\(38\) 1.54955 + 1.94307i 0.251370 + 0.315208i
\(39\) 0.682357 0.328606i 0.109265 0.0526191i
\(40\) 0.988722 1.23982i 0.156331 0.196032i
\(41\) 12.4853 1.94987 0.974937 0.222483i \(-0.0714160\pi\)
0.974937 + 0.222483i \(0.0714160\pi\)
\(42\) −0.302568 + 0.379408i −0.0466873 + 0.0585440i
\(43\) −1.42730 + 6.25340i −0.217661 + 0.953634i 0.741540 + 0.670908i \(0.234096\pi\)
−0.959201 + 0.282725i \(0.908761\pi\)
\(44\) 0.982255 4.30354i 0.148081 0.648783i
\(45\) 1.76350 2.21135i 0.262886 0.329649i
\(46\) −3.17157 −0.467623
\(47\) 3.26873 4.09886i 0.476794 0.597880i −0.484026 0.875053i \(-0.660826\pi\)
0.960820 + 0.277173i \(0.0893975\pi\)
\(48\) 1.11958 0.539162i 0.161598 0.0778213i
\(49\) 0.623490 + 0.781831i 0.0890700 + 0.111690i
\(50\) −1.03303 1.29538i −0.146093 0.183195i
\(51\) −1.80194 0.867767i −0.252322 0.121512i
\(52\) 0.743920 3.25933i 0.103163 0.451987i
\(53\) 1.66563 + 7.29761i 0.228792 + 1.00240i 0.950626 + 0.310338i \(0.100442\pi\)
−0.721834 + 0.692066i \(0.756701\pi\)
\(54\) −0.900969 + 0.433884i −0.122606 + 0.0590441i
\(55\) 2.17513 + 1.04749i 0.293295 + 0.141243i
\(56\) 0.998069 + 4.37283i 0.133373 + 0.584343i
\(57\) −2.48528 −0.329184
\(58\) 0 0
\(59\) 7.65685 0.996838 0.498419 0.866936i \(-0.333914\pi\)
0.498419 + 0.866936i \(0.333914\pi\)
\(60\) 0.168528 + 0.738371i 0.0217569 + 0.0953233i
\(61\) −0.746387 0.359441i −0.0955651 0.0460217i 0.385491 0.922712i \(-0.374032\pi\)
−0.481056 + 0.876690i \(0.659747\pi\)
\(62\) 1.51930 0.731654i 0.192951 0.0929202i
\(63\) 1.78017 + 7.79942i 0.224280 + 0.982635i
\(64\) 0.928262 4.06698i 0.116033 0.508373i
\(65\) 1.64736 + 0.793325i 0.204329 + 0.0983998i
\(66\) −0.258258 0.323845i −0.0317894 0.0398626i
\(67\) −3.52699 4.42271i −0.430891 0.540320i 0.518226 0.855243i \(-0.326592\pi\)
−0.949117 + 0.314924i \(0.898021\pi\)
\(68\) −7.95414 + 3.83051i −0.964581 + 0.464518i
\(69\) 1.97744 2.47964i 0.238056 0.298513i
\(70\) −1.17157 −0.140030
\(71\) −1.97744 + 2.47964i −0.234679 + 0.294279i −0.885201 0.465209i \(-0.845979\pi\)
0.650521 + 0.759488i \(0.274550\pi\)
\(72\) −0.998069 + 4.37283i −0.117624 + 0.515342i
\(73\) −0.890084 + 3.89971i −0.104176 + 0.456427i 0.895753 + 0.444552i \(0.146637\pi\)
−0.999929 + 0.0118748i \(0.996220\pi\)
\(74\) −1.03303 + 1.29538i −0.120087 + 0.150585i
\(75\) 1.65685 0.191317
\(76\) −6.84003 + 8.57713i −0.784606 + 0.983864i
\(77\) −6.15220 + 2.96274i −0.701108 + 0.337636i
\(78\) −0.195594 0.245267i −0.0221467 0.0277710i
\(79\) 0.258258 + 0.323845i 0.0290563 + 0.0364354i 0.796147 0.605103i \(-0.206868\pi\)
−0.767091 + 0.641538i \(0.778297\pi\)
\(80\) 2.70291 + 1.30165i 0.302194 + 0.145529i
\(81\) −1.66563 + 7.29761i −0.185070 + 0.810846i
\(82\) −1.15078 5.04191i −0.127083 0.556786i
\(83\) 3.29471 1.58665i 0.361642 0.174157i −0.244235 0.969716i \(-0.578537\pi\)
0.605877 + 0.795559i \(0.292823\pi\)
\(84\) −1.93000 0.929438i −0.210580 0.101410i
\(85\) −1.07443 4.70737i −0.116538 0.510586i
\(86\) 2.65685 0.286496
\(87\) 0 0
\(88\) −3.82843 −0.408112
\(89\) −0.998069 4.37283i −0.105795 0.463519i −0.999878 0.0156172i \(-0.995029\pi\)
0.894083 0.447901i \(-0.147828\pi\)
\(90\) −1.05555 0.508326i −0.111265 0.0535823i
\(91\) −4.65943 + 2.24386i −0.488441 + 0.235221i
\(92\) −3.11529 13.6490i −0.324792 1.42301i
\(93\) −0.375235 + 1.64401i −0.0389101 + 0.170476i
\(94\) −1.95652 0.942210i −0.201800 0.0971816i
\(95\) −3.74094 4.69099i −0.383812 0.481285i
\(96\) −1.14001 1.42952i −0.116351 0.145900i
\(97\) 11.2488 5.41716i 1.14215 0.550029i 0.235482 0.971879i \(-0.424333\pi\)
0.906666 + 0.421849i \(0.138619\pi\)
\(98\) 0.258258 0.323845i 0.0260880 0.0327133i
\(99\) −6.82843 −0.686283
\(100\) 4.56002 5.71809i 0.456002 0.571809i
\(101\) 3.03894 13.3144i 0.302385 1.32484i −0.564130 0.825686i \(-0.690788\pi\)
0.866515 0.499151i \(-0.166355\pi\)
\(102\) −0.184342 + 0.807657i −0.0182526 + 0.0799699i
\(103\) 0.516516 0.647690i 0.0508938 0.0638188i −0.755733 0.654880i \(-0.772719\pi\)
0.806627 + 0.591061i \(0.201291\pi\)
\(104\) −2.89949 −0.284319
\(105\) 0.730464 0.915973i 0.0712860 0.0893898i
\(106\) 2.79346 1.34526i 0.271325 0.130663i
\(107\) −5.71838 7.17062i −0.552817 0.693210i 0.424395 0.905477i \(-0.360487\pi\)
−0.977212 + 0.212267i \(0.931915\pi\)
\(108\) −2.75222 3.45117i −0.264832 0.332089i
\(109\) −1.21013 0.582769i −0.115910 0.0558192i 0.375030 0.927013i \(-0.377632\pi\)
−0.490940 + 0.871193i \(0.663347\pi\)
\(110\) 0.222521 0.974928i 0.0212165 0.0929557i
\(111\) −0.368685 1.61531i −0.0349940 0.153319i
\(112\) −7.64497 + 3.68163i −0.722382 + 0.347881i
\(113\) −8.39136 4.04107i −0.789393 0.380152i −0.00466273 0.999989i \(-0.501484\pi\)
−0.784730 + 0.619838i \(0.787198\pi\)
\(114\) 0.229071 + 1.00363i 0.0214545 + 0.0939983i
\(115\) 7.65685 0.714005
\(116\) 0 0
\(117\) −5.17157 −0.478112
\(118\) −0.705741 3.09205i −0.0649688 0.284647i
\(119\) 12.3044 + 5.92549i 1.12794 + 0.543189i
\(120\) 0.591805 0.284998i 0.0540242 0.0260167i
\(121\) 1.15078 + 5.04191i 0.104617 + 0.458356i
\(122\) −0.0763571 + 0.334542i −0.00691305 + 0.0302880i
\(123\) 4.65943 + 2.24386i 0.420126 + 0.202322i
\(124\) 4.64104 + 5.81968i 0.416778 + 0.522623i
\(125\) 5.61141 + 7.03648i 0.501900 + 0.629362i
\(126\) 2.98555 1.43776i 0.265974 0.128086i
\(127\) −9.76189 + 12.2410i −0.866228 + 1.08622i 0.129287 + 0.991607i \(0.458731\pi\)
−0.995515 + 0.0946078i \(0.969840\pi\)
\(128\) −10.5563 −0.933058
\(129\) −1.65652 + 2.07721i −0.145849 + 0.182888i
\(130\) 0.168528 0.738371i 0.0147809 0.0647594i
\(131\) 0.292328 1.28077i 0.0255408 0.111901i −0.960551 0.278105i \(-0.910294\pi\)
0.986091 + 0.166203i \(0.0531508\pi\)
\(132\) 1.14001 1.42952i 0.0992248 0.124424i
\(133\) 16.9706 1.47153
\(134\) −1.46093 + 1.83195i −0.126205 + 0.158256i
\(135\) 2.17513 1.04749i 0.187205 0.0901534i
\(136\) 4.77397 + 5.98637i 0.409365 + 0.513327i
\(137\) 7.48188 + 9.38198i 0.639220 + 0.801556i 0.990905 0.134562i \(-0.0429627\pi\)
−0.351685 + 0.936118i \(0.614391\pi\)
\(138\) −1.18361 0.569997i −0.100756 0.0485213i
\(139\) −3.11529 + 13.6490i −0.264236 + 1.15769i 0.652370 + 0.757900i \(0.273775\pi\)
−0.916606 + 0.399792i \(0.869082\pi\)
\(140\) −1.15078 5.04191i −0.0972589 0.426119i
\(141\) 1.95652 0.942210i 0.164769 0.0793484i
\(142\) 1.18361 + 0.569997i 0.0993264 + 0.0478331i
\(143\) −0.982255 4.30354i −0.0821403 0.359880i
\(144\) −8.48528 −0.707107
\(145\) 0 0
\(146\) 1.65685 0.137122
\(147\) 0.0921712 + 0.403828i 0.00760215 + 0.0333072i
\(148\) −6.58942 3.17330i −0.541647 0.260844i
\(149\) 1.95652 0.942210i 0.160284 0.0771889i −0.352022 0.935992i \(-0.614506\pi\)
0.512306 + 0.858803i \(0.328791\pi\)
\(150\) −0.152714 0.669085i −0.0124691 0.0546305i
\(151\) −3.14692 + 13.7876i −0.256093 + 1.12202i 0.669296 + 0.742996i \(0.266596\pi\)
−0.925389 + 0.379020i \(0.876261\pi\)
\(152\) 8.57247 + 4.12828i 0.695319 + 0.334848i
\(153\) 8.51491 + 10.6774i 0.688390 + 0.863213i
\(154\) 1.76350 + 2.21135i 0.142107 + 0.178196i
\(155\) −3.66791 + 1.76637i −0.294613 + 0.141878i
\(156\) 0.863394 1.08266i 0.0691268 0.0866823i
\(157\) −8.48528 −0.677199 −0.338600 0.940931i \(-0.609953\pi\)
−0.338600 + 0.940931i \(0.609953\pi\)
\(158\) 0.106974 0.134141i 0.00851039 0.0106717i
\(159\) −0.689927 + 3.02277i −0.0547148 + 0.239721i
\(160\) 0.982255 4.30354i 0.0776541 0.340225i
\(161\) −13.5028 + 16.9320i −1.06417 + 1.33443i
\(162\) 3.10051 0.243599
\(163\) 11.2671 14.1285i 0.882509 1.10663i −0.111106 0.993809i \(-0.535439\pi\)
0.993615 0.112823i \(-0.0359894\pi\)
\(164\) 20.5677 9.90488i 1.60607 0.773441i
\(165\) 0.623490 + 0.781831i 0.0485386 + 0.0608655i
\(166\) −0.944412 1.18425i −0.0733006 0.0919160i
\(167\) 7.95414 + 3.83051i 0.615510 + 0.296414i 0.715541 0.698570i \(-0.246180\pi\)
−0.100032 + 0.994984i \(0.531894\pi\)
\(168\) −0.413414 + 1.81128i −0.0318956 + 0.139744i
\(169\) 2.14885 + 9.41474i 0.165296 + 0.724211i
\(170\) −1.80194 + 0.867767i −0.138202 + 0.0665547i
\(171\) 15.2899 + 7.36325i 1.16925 + 0.563082i
\(172\) 2.60971 + 11.4339i 0.198988 + 0.871825i
\(173\) 23.6569 1.79860 0.899299 0.437335i \(-0.144078\pi\)
0.899299 + 0.437335i \(0.144078\pi\)
\(174\) 0 0
\(175\) −11.3137 −0.855236
\(176\) −1.61164 7.06105i −0.121482 0.532247i
\(177\) 2.85749 + 1.37609i 0.214782 + 0.103434i
\(178\) −1.67388 + 0.806097i −0.125462 + 0.0604195i
\(179\) −2.33319 10.2224i −0.174391 0.764058i −0.984156 0.177303i \(-0.943263\pi\)
0.809765 0.586754i \(-0.199595\pi\)
\(180\) 1.15078 5.04191i 0.0857743 0.375802i
\(181\) 12.8962 + 6.21049i 0.958567 + 0.461622i 0.846682 0.532099i \(-0.178597\pi\)
0.111886 + 0.993721i \(0.464311\pi\)
\(182\) 1.33560 + 1.67479i 0.0990012 + 0.124144i
\(183\) −0.213948 0.268282i −0.0158155 0.0198320i
\(184\) −10.9397 + 5.26828i −0.806484 + 0.388382i
\(185\) 2.49396 3.12733i 0.183360 0.229926i
\(186\) 0.698485 0.0512154
\(187\) −7.26793 + 9.11370i −0.531484 + 0.666459i
\(188\) 2.13304 9.34545i 0.155568 0.681587i
\(189\) −1.51947 + 6.65722i −0.110525 + 0.484242i
\(190\) −1.54955 + 1.94307i −0.112416 + 0.140965i
\(191\) 2.68629 0.194373 0.0971866 0.995266i \(-0.469016\pi\)
0.0971866 + 0.995266i \(0.469016\pi\)
\(192\) 1.07734 1.35094i 0.0777504 0.0974960i
\(193\) 9.75608 4.69828i 0.702258 0.338189i −0.0484485 0.998826i \(-0.515428\pi\)
0.750706 + 0.660636i \(0.229713\pi\)
\(194\) −3.22442 4.04330i −0.231500 0.290292i
\(195\) 0.472206 + 0.592127i 0.0338154 + 0.0424031i
\(196\) 1.64736 + 0.793325i 0.117668 + 0.0566661i
\(197\) −0.445042 + 1.94986i −0.0317079 + 0.138921i −0.988304 0.152495i \(-0.951269\pi\)
0.956596 + 0.291416i \(0.0941264\pi\)
\(198\) 0.629384 + 2.75751i 0.0447284 + 0.195968i
\(199\) −14.8527 + 7.15270i −1.05288 + 0.507041i −0.878552 0.477646i \(-0.841490\pi\)
−0.174330 + 0.984687i \(0.555776\pi\)
\(200\) −5.71498 2.75219i −0.404110 0.194609i
\(201\) −0.521399 2.28440i −0.0367766 0.161129i
\(202\) −5.65685 −0.398015
\(203\) 0 0
\(204\) −3.65685 −0.256031
\(205\) 2.77824 + 12.1722i 0.194040 + 0.850147i
\(206\) −0.309164 0.148885i −0.0215405 0.0103733i
\(207\) −19.5122 + 9.39656i −1.35619 + 0.653106i
\(208\) −1.22059 5.34775i −0.0846327 0.370800i
\(209\) −3.22328 + 14.1221i −0.222959 + 0.976846i
\(210\) −0.437223 0.210556i −0.0301713 0.0145297i
\(211\) 10.8392 + 13.5920i 0.746203 + 0.935709i 0.999498 0.0316797i \(-0.0100856\pi\)
−0.253295 + 0.967389i \(0.581514\pi\)
\(212\) 8.53326 + 10.7004i 0.586067 + 0.734905i
\(213\) −1.18361 + 0.569997i −0.0810997 + 0.0390555i
\(214\) −2.36863 + 2.97017i −0.161916 + 0.203037i
\(215\) −6.41421 −0.437446
\(216\) −2.38699 + 2.99318i −0.162414 + 0.203660i
\(217\) 2.56227 11.2260i 0.173938 0.762072i
\(218\) −0.123799 + 0.542400i −0.00838475 + 0.0367360i
\(219\) −1.03303 + 1.29538i −0.0698058 + 0.0875337i
\(220\) 4.41421 0.297606
\(221\) −5.50443 + 6.90234i −0.370268 + 0.464302i
\(222\) −0.618327 + 0.297771i −0.0414994 + 0.0199851i
\(223\) −5.50443 6.90234i −0.368604 0.462215i 0.562591 0.826735i \(-0.309804\pi\)
−0.931196 + 0.364520i \(0.881233\pi\)
\(224\) 7.78445 + 9.76139i 0.520120 + 0.652210i
\(225\) −10.1933 4.90883i −0.679553 0.327256i
\(226\) −0.858456 + 3.76114i −0.0571036 + 0.250187i
\(227\) −4.48205 19.6371i −0.297484 1.30336i −0.873860 0.486178i \(-0.838391\pi\)
0.576376 0.817185i \(-0.304466\pi\)
\(228\) −4.09414 + 1.97164i −0.271141 + 0.130575i
\(229\) 18.4566 + 8.88823i 1.21965 + 0.587351i 0.929213 0.369544i \(-0.120486\pi\)
0.290433 + 0.956895i \(0.406201\pi\)
\(230\) −0.705741 3.09205i −0.0465352 0.203884i
\(231\) −2.82843 −0.186097
\(232\) 0 0
\(233\) −4.31371 −0.282600 −0.141300 0.989967i \(-0.545128\pi\)
−0.141300 + 0.989967i \(0.545128\pi\)
\(234\) 0.476670 + 2.08843i 0.0311609 + 0.136525i
\(235\) 4.72346 + 2.27470i 0.308124 + 0.148385i
\(236\) 12.6136 6.07437i 0.821073 0.395408i
\(237\) 0.0381786 + 0.167271i 0.00247996 + 0.0108654i
\(238\) 1.25877 5.51503i 0.0815938 0.357486i
\(239\) 7.51691 + 3.61996i 0.486229 + 0.234155i 0.660904 0.750471i \(-0.270173\pi\)
−0.174675 + 0.984626i \(0.555887\pi\)
\(240\) 0.774774 + 0.971536i 0.0500114 + 0.0627124i
\(241\) 2.68955 + 3.37259i 0.173249 + 0.217248i 0.860874 0.508819i \(-0.169918\pi\)
−0.687624 + 0.726067i \(0.741346\pi\)
\(242\) 1.93000 0.929438i 0.124065 0.0597465i
\(243\) −6.44885 + 8.08660i −0.413694 + 0.518755i
\(244\) −1.51472 −0.0969699
\(245\) −0.623490 + 0.781831i −0.0398333 + 0.0499494i
\(246\) 0.476670 2.08843i 0.0303914 0.133153i
\(247\) −2.44118 + 10.6955i −0.155329 + 0.680539i
\(248\) 4.02515 5.04738i 0.255597 0.320509i
\(249\) 1.51472 0.0959914
\(250\) 2.32432 2.91461i 0.147003 0.184336i
\(251\) −5.34178 + 2.57247i −0.337170 + 0.162373i −0.594806 0.803870i \(-0.702771\pi\)
0.257635 + 0.966242i \(0.417057\pi\)
\(252\) 9.12005 + 11.4362i 0.574509 + 0.720411i
\(253\) −11.5254 14.4524i −0.724595 0.908613i
\(254\) 5.84304 + 2.81386i 0.366625 + 0.176557i
\(255\) 0.445042 1.94986i 0.0278696 0.122105i
\(256\) −0.883533 3.87101i −0.0552208 0.241938i
\(257\) 21.4687 10.3388i 1.33918 0.644915i 0.379285 0.925280i \(-0.376170\pi\)
0.959893 + 0.280365i \(0.0904555\pi\)
\(258\) 0.991521 + 0.477491i 0.0617294 + 0.0297273i
\(259\) 2.51754 + 11.0301i 0.156432 + 0.685374i
\(260\) 3.34315 0.207333
\(261\) 0 0
\(262\) −0.544156 −0.0336181
\(263\) −2.50172 10.9608i −0.154263 0.675870i −0.991617 0.129209i \(-0.958756\pi\)
0.837354 0.546660i \(-0.184101\pi\)
\(264\) −1.42874 0.688047i −0.0879331 0.0423464i
\(265\) −6.74401 + 3.24774i −0.414281 + 0.199507i
\(266\) −1.56420 6.85319i −0.0959071 0.420196i
\(267\) 0.413414 1.81128i 0.0253005 0.110849i
\(268\) −9.31885 4.48772i −0.569240 0.274131i
\(269\) −12.1305 15.2112i −0.739611 0.927443i 0.259657 0.965701i \(-0.416390\pi\)
−0.999268 + 0.0382582i \(0.987819\pi\)
\(270\) −0.623490 0.781831i −0.0379444 0.0475807i
\(271\) 13.1148 6.31576i 0.796668 0.383655i 0.00915912 0.999958i \(-0.497085\pi\)
0.787509 + 0.616303i \(0.211370\pi\)
\(272\) −9.03143 + 11.3250i −0.547611 + 0.686682i
\(273\) −2.14214 −0.129648
\(274\) 3.09910 3.88614i 0.187223 0.234770i
\(275\) 2.14885 9.41474i 0.129581 0.567730i
\(276\) 1.29040 5.65360i 0.0776728 0.340307i
\(277\) 3.31304 4.15442i 0.199061 0.249615i −0.672275 0.740302i \(-0.734683\pi\)
0.871336 + 0.490687i \(0.163254\pi\)
\(278\) 5.79899 0.347800
\(279\) 7.17931 9.00257i 0.429814 0.538970i
\(280\) −4.04110 + 1.94609i −0.241502 + 0.116301i
\(281\) −1.22863 1.54065i −0.0732937 0.0919074i 0.743833 0.668366i \(-0.233006\pi\)
−0.817127 + 0.576458i \(0.804434\pi\)
\(282\) −0.560826 0.703253i −0.0333967 0.0418781i
\(283\) −0.309164 0.148885i −0.0183779 0.00885032i 0.424672 0.905347i \(-0.360389\pi\)
−0.443050 + 0.896497i \(0.646104\pi\)
\(284\) −1.29040 + 5.65360i −0.0765710 + 0.335479i
\(285\) −0.553027 2.42297i −0.0327585 0.143524i
\(286\) −1.64736 + 0.793325i −0.0974102 + 0.0469103i
\(287\) −31.8166 15.3220i −1.87807 0.904432i
\(288\) 2.77824 + 12.1722i 0.163709 + 0.717257i
\(289\) 6.31371 0.371395
\(290\) 0 0
\(291\) 5.17157 0.303163
\(292\) 1.62745 + 7.13034i 0.0952395 + 0.417272i
\(293\) 3.29471 + 1.58665i 0.192479 + 0.0926931i 0.527641 0.849468i \(-0.323077\pi\)
−0.335162 + 0.942161i \(0.608791\pi\)
\(294\) 0.154582 0.0744427i 0.00901539 0.00434159i
\(295\) 1.70381 + 7.46488i 0.0991997 + 0.434622i
\(296\) −1.41148 + 6.18411i −0.0820408 + 0.359444i
\(297\) −5.25123 2.52886i −0.304707 0.146739i
\(298\) −0.560826 0.703253i −0.0324878 0.0407384i
\(299\) −8.72886 10.9456i −0.504803 0.633003i
\(300\) 2.72943 1.31442i 0.157584 0.0758883i
\(301\) 11.3114 14.1841i 0.651980 0.817558i
\(302\) 5.85786 0.337082
\(303\) 3.52699 4.42271i 0.202620 0.254078i
\(304\) −4.00538 + 17.5487i −0.229724 + 1.00649i
\(305\) 0.184342 0.807657i 0.0105554 0.0462463i
\(306\) 3.52699 4.42271i 0.201625 0.252829i
\(307\) −16.8995 −0.964505 −0.482253 0.876032i \(-0.660181\pi\)
−0.482253 + 0.876032i \(0.660181\pi\)
\(308\) −7.78445 + 9.76139i −0.443560 + 0.556207i
\(309\) 0.309164 0.148885i 0.0175877 0.00846979i
\(310\) 1.05139 + 1.31840i 0.0597147 + 0.0748798i
\(311\) 15.7828 + 19.7911i 0.894963 + 1.12225i 0.991908 + 0.126958i \(0.0405214\pi\)
−0.0969454 + 0.995290i \(0.530907\pi\)
\(312\) −1.08207 0.521099i −0.0612603 0.0295014i
\(313\) −0.928262 + 4.06698i −0.0524685 + 0.229879i −0.994363 0.106029i \(-0.966186\pi\)
0.941895 + 0.335909i \(0.109043\pi\)
\(314\) 0.782098 + 3.42660i 0.0441364 + 0.193374i
\(315\) −7.20775 + 3.47107i −0.406111 + 0.195573i
\(316\) 0.682357 + 0.328606i 0.0383856 + 0.0184855i
\(317\) −4.32933 18.9680i −0.243160 1.06535i −0.938122 0.346305i \(-0.887436\pi\)
0.694962 0.719046i \(-0.255421\pi\)
\(318\) 1.28427 0.0720184
\(319\) 0 0
\(320\) 4.17157 0.233198
\(321\) −0.845355 3.70374i −0.0471831 0.206723i
\(322\) 8.08220 + 3.89218i 0.450403 + 0.216903i
\(323\) 26.1016 12.5699i 1.45233 0.699406i
\(324\) 3.04549 + 13.3431i 0.169194 + 0.741286i
\(325\) 1.62745 7.13034i 0.0902749 0.395520i
\(326\) −6.74401 3.24774i −0.373516 0.179876i
\(327\) −0.346878 0.434971i −0.0191824 0.0240540i
\(328\) −12.3445 15.4795i −0.681609 0.854711i
\(329\) −13.3600 + 6.43381i −0.736558 + 0.354708i
\(330\) 0.258258 0.323845i 0.0142166 0.0178271i
\(331\) 0.414214 0.0227672 0.0113836 0.999935i \(-0.496376\pi\)
0.0113836 + 0.999935i \(0.496376\pi\)
\(332\) 4.16883 5.22755i 0.228795 0.286899i
\(333\) −2.51754 + 11.0301i −0.137960 + 0.604443i
\(334\) 0.813727 3.56517i 0.0445251 0.195077i
\(335\) 3.52699 4.42271i 0.192700 0.241638i
\(336\) −3.51472 −0.191744
\(337\) −11.0975 + 13.9158i −0.604519 + 0.758043i −0.986075 0.166303i \(-0.946817\pi\)
0.381556 + 0.924346i \(0.375388\pi\)
\(338\) 3.60388 1.73553i 0.196025 0.0944007i
\(339\) −2.40534 3.01620i −0.130640 0.163817i
\(340\) −5.50443 6.90234i −0.298520 0.374332i
\(341\) 8.85511 + 4.26439i 0.479531 + 0.230930i
\(342\) 1.56420 6.85319i 0.0845821 0.370578i
\(343\) 3.77631 + 16.5451i 0.203901 + 0.893350i
\(344\) 9.16427 4.41328i 0.494104 0.237948i
\(345\) 2.85749 + 1.37609i 0.153842 + 0.0740864i
\(346\) −2.18048 9.55331i −0.117223 0.513589i
\(347\) −14.4853 −0.777611 −0.388805 0.921320i \(-0.627112\pi\)
−0.388805 + 0.921320i \(0.627112\pi\)
\(348\) 0 0
\(349\) 23.1421 1.23877 0.619385 0.785087i \(-0.287382\pi\)
0.619385 + 0.785087i \(0.287382\pi\)
\(350\) 1.04280 + 4.56880i 0.0557399 + 0.244212i
\(351\) −3.97707 1.91526i −0.212280 0.102229i
\(352\) −9.60149 + 4.62384i −0.511761 + 0.246451i
\(353\) 1.55110 + 6.79580i 0.0825565 + 0.361704i 0.999285 0.0378069i \(-0.0120372\pi\)
−0.916729 + 0.399511i \(0.869180\pi\)
\(354\) 0.292328 1.28077i 0.0155370 0.0680722i
\(355\) −2.85749 1.37609i −0.151660 0.0730355i
\(356\) −5.11325 6.41181i −0.271002 0.339825i
\(357\) 3.52699 + 4.42271i 0.186668 + 0.234074i
\(358\) −3.91304 + 1.88442i −0.206811 + 0.0995947i
\(359\) 11.2671 14.1285i 0.594656 0.745675i −0.389878 0.920866i \(-0.627483\pi\)
0.984534 + 0.175191i \(0.0560543\pi\)
\(360\) −4.48528 −0.236395
\(361\) 10.5993 13.2911i 0.557859 0.699533i
\(362\) 1.31931 5.78028i 0.0693415 0.303805i
\(363\) −0.476670 + 2.08843i −0.0250187 + 0.109614i
\(364\) −5.89562 + 7.39288i −0.309015 + 0.387492i
\(365\) −4.00000 −0.209370
\(366\) −0.0886201 + 0.111126i −0.00463225 + 0.00580865i
\(367\) −16.2174 + 7.80991i −0.846543 + 0.407674i −0.806293 0.591516i \(-0.798530\pi\)
−0.0402500 + 0.999190i \(0.512815\pi\)
\(368\) −14.3219 17.9591i −0.746581 0.936183i
\(369\) −22.0177 27.6094i −1.14620 1.43729i
\(370\) −1.49277 0.718882i −0.0776056 0.0373729i
\(371\) 4.71112 20.6408i 0.244589 1.07161i
\(372\) 0.686090 + 3.00596i 0.0355721 + 0.155852i
\(373\) 3.32123 1.59942i 0.171967 0.0828149i −0.345920 0.938264i \(-0.612433\pi\)
0.517887 + 0.855449i \(0.326719\pi\)
\(374\) 4.35026 + 2.09498i 0.224947 + 0.108329i
\(375\) 0.829541 + 3.63446i 0.0428373 + 0.187682i
\(376\) −8.31371 −0.428747
\(377\) 0 0
\(378\) 2.82843 0.145479
\(379\) −6.00151 26.2944i −0.308277 1.35065i −0.857289 0.514836i \(-0.827853\pi\)
0.549012 0.835815i \(-0.315004\pi\)
\(380\) −9.88414 4.75995i −0.507045 0.244180i
\(381\) −5.84304 + 2.81386i −0.299348 + 0.144158i
\(382\) −0.247599 1.08480i −0.0126683 0.0555032i
\(383\) 4.55840 19.9717i 0.232924 1.02050i −0.714277 0.699863i \(-0.753244\pi\)
0.947201 0.320642i \(-0.103899\pi\)
\(384\) −3.93956 1.89719i −0.201040 0.0968157i
\(385\) −4.25745 5.33868i −0.216980 0.272084i
\(386\) −2.79653 3.50673i −0.142339 0.178488i
\(387\) 16.3455 7.87158i 0.830888 0.400135i
\(388\) 14.2333 17.8480i 0.722586 0.906094i
\(389\) 36.9706 1.87448 0.937241 0.348682i \(-0.113371\pi\)
0.937241 + 0.348682i \(0.113371\pi\)
\(390\) 0.195594 0.245267i 0.00990429 0.0124196i
\(391\) −8.22672 + 36.0436i −0.416043 + 1.82280i
\(392\) 0.352871 1.54603i 0.0178227 0.0780862i
\(393\) 0.339276 0.425438i 0.0171142 0.0214605i
\(394\) 0.828427 0.0417356
\(395\) −0.258258 + 0.323845i −0.0129944 + 0.0162944i
\(396\) −11.2488 + 5.41716i −0.565276 + 0.272223i
\(397\) 19.1142 + 23.9685i 0.959316 + 1.20294i 0.979150 + 0.203141i \(0.0651150\pi\)
−0.0198335 + 0.999803i \(0.506314\pi\)
\(398\) 4.25745 + 5.33868i 0.213407 + 0.267604i
\(399\) 6.33330 + 3.04996i 0.317062 + 0.152689i
\(400\) 2.67025 11.6991i 0.133513 0.584957i
\(401\) 1.63400 + 7.15904i 0.0815982 + 0.357505i 0.999200 0.0399961i \(-0.0127345\pi\)
−0.917602 + 0.397501i \(0.869877\pi\)
\(402\) −0.874447 + 0.421111i −0.0436134 + 0.0210031i
\(403\) 6.70650 + 3.22968i 0.334074 + 0.160882i
\(404\) −5.55647 24.3445i −0.276445 1.21118i
\(405\) −7.48528 −0.371947
\(406\) 0 0
\(407\) −9.65685 −0.478672
\(408\) 0.705741 + 3.09205i 0.0349394 + 0.153080i
\(409\) −13.4880 6.49548i −0.666939 0.321181i 0.0696008 0.997575i \(-0.477827\pi\)
−0.736540 + 0.676394i \(0.763542\pi\)
\(410\) 4.65943 2.24386i 0.230113 0.110816i
\(411\) 1.10605 + 4.84594i 0.0545576 + 0.239033i
\(412\) 0.337057 1.47674i 0.0166056 0.0727538i
\(413\) −19.5122 9.39656i −0.960130 0.462374i
\(414\) 5.59305 + 7.01347i 0.274884 + 0.344693i
\(415\) 2.28001 + 2.85904i 0.111921 + 0.140345i
\(416\) −7.27178 + 3.50191i −0.356528 + 0.171695i
\(417\) −3.61561 + 4.53383i −0.177057 + 0.222023i
\(418\) 6.00000 0.293470
\(419\) −16.5133 + 20.7070i −0.806728 + 1.01160i 0.192811 + 0.981236i \(0.438240\pi\)
−0.999539 + 0.0303686i \(0.990332\pi\)
\(420\) 0.476670 2.08843i 0.0232591 0.101905i
\(421\) 5.58810 24.4831i 0.272347 1.19323i −0.634887 0.772605i \(-0.718953\pi\)
0.907234 0.420626i \(-0.138190\pi\)
\(422\) 4.48976 5.62998i 0.218558 0.274063i
\(423\) −14.8284 −0.720983
\(424\) 7.40086 9.28038i 0.359418 0.450695i
\(425\) −17.4011 + 8.37990i −0.844075 + 0.406485i
\(426\) 0.339276 + 0.425438i 0.0164380 + 0.0206125i
\(427\) 1.46093 + 1.83195i 0.0706992 + 0.0886540i
\(428\) −15.1088 7.27604i −0.730314 0.351700i
\(429\) 0.406863 1.78258i 0.0196435 0.0860640i
\(430\) 0.591206 + 2.59024i 0.0285105 + 0.124913i
\(431\) −7.51691 + 3.61996i −0.362077 + 0.174367i −0.606073 0.795409i \(-0.707256\pi\)
0.243996 + 0.969776i \(0.421542\pi\)
\(432\) −6.52539 3.14246i −0.313953 0.151192i
\(433\) 3.25491 + 14.2607i 0.156421 + 0.685324i 0.990935 + 0.134339i \(0.0428910\pi\)
−0.834515 + 0.550986i \(0.814252\pi\)
\(434\) −4.76955 −0.228946
\(435\) 0 0
\(436\) −2.45584 −0.117614
\(437\) 10.2229 + 44.7893i 0.489026 + 2.14256i
\(438\) 0.618327 + 0.297771i 0.0295448 + 0.0142280i
\(439\) 10.5025 5.05772i 0.501255 0.241392i −0.166131 0.986104i \(-0.553127\pi\)
0.667386 + 0.744712i \(0.267413\pi\)
\(440\) −0.851905 3.73244i −0.0406130 0.177937i
\(441\) 0.629384 2.75751i 0.0299707 0.131310i
\(442\) 3.29471 + 1.58665i 0.156713 + 0.0754692i
\(443\) −22.2317 27.8777i −1.05626 1.32451i −0.943678 0.330865i \(-0.892660\pi\)
−0.112581 0.993643i \(-0.535912\pi\)
\(444\) −1.88882 2.36851i −0.0896396 0.112404i
\(445\) 4.04110 1.94609i 0.191566 0.0922535i
\(446\) −2.28001 + 2.85904i −0.107962 + 0.135380i
\(447\) 0.899495 0.0425447
\(448\) −7.35655 + 9.22482i −0.347564 + 0.435832i
\(449\) 0.229071 1.00363i 0.0108105 0.0473641i −0.969235 0.246137i \(-0.920839\pi\)
0.980046 + 0.198773i \(0.0636957\pi\)
\(450\) −1.04280 + 4.56880i −0.0491580 + 0.215375i
\(451\) 18.7933 23.5661i 0.884943 1.10968i
\(452\) −17.0294 −0.800997
\(453\) −3.65232 + 4.57986i −0.171601 + 0.215181i
\(454\) −7.51691 + 3.61996i −0.352786 + 0.169893i
\(455\) −3.22442 4.04330i −0.151163 0.189553i
\(456\) 2.45725 + 3.08130i 0.115071 + 0.144295i
\(457\) −31.5074 15.1732i −1.47385 0.709770i −0.487304 0.873232i \(-0.662020\pi\)
−0.986550 + 0.163462i \(0.947734\pi\)
\(458\) 1.88815 8.27254i 0.0882276 0.386550i
\(459\) 2.59389 + 11.3646i 0.121073 + 0.530454i
\(460\) 12.6136 6.07437i 0.588110 0.283219i
\(461\) −12.6136 6.07437i −0.587472 0.282912i 0.116441 0.993198i \(-0.462851\pi\)
−0.703913 + 0.710286i \(0.748566\pi\)
\(462\) 0.260699 + 1.14220i 0.0121288 + 0.0531399i
\(463\) −26.0000 −1.20832 −0.604161 0.796862i \(-0.706492\pi\)
−0.604161 + 0.796862i \(0.706492\pi\)
\(464\) 0 0
\(465\) −1.68629 −0.0781999
\(466\) 0.397600 + 1.74200i 0.0184184 + 0.0806965i
\(467\) −29.1512 14.0385i −1.34895 0.649622i −0.386809 0.922160i \(-0.626423\pi\)
−0.962145 + 0.272537i \(0.912137\pi\)
\(468\) −8.51942 + 4.10274i −0.393810 + 0.189649i
\(469\) 3.56033 + 15.5988i 0.164401 + 0.720288i
\(470\) 0.483220 2.11713i 0.0222893 0.0976558i
\(471\) −3.16665 1.52498i −0.145912 0.0702673i
\(472\) −7.57050 9.49310i −0.348460 0.436956i
\(473\) 9.65492 + 12.1069i 0.443933 + 0.556675i
\(474\) 0.0640299 0.0308352i 0.00294099 0.00141631i
\(475\) −14.9638 + 18.7640i −0.686584 + 0.860949i
\(476\) 24.9706 1.14452
\(477\) 13.2003 16.5526i 0.604398 0.757892i
\(478\) 0.768998 3.36920i 0.0351731 0.154104i
\(479\) 2.87041 12.5761i 0.131152 0.574616i −0.866056 0.499947i \(-0.833353\pi\)
0.997208 0.0746688i \(-0.0237900\pi\)
\(480\) 1.14001 1.42952i 0.0520339 0.0652484i
\(481\) −7.31371 −0.333476
\(482\) 1.11405 1.39697i 0.0507436 0.0636304i
\(483\) −8.08220 + 3.89218i −0.367753 + 0.177100i
\(484\) 5.89562 + 7.39288i 0.267983 + 0.336040i
\(485\) 7.78445 + 9.76139i 0.353473 + 0.443242i
\(486\) 3.86000 + 1.85888i 0.175093 + 0.0843203i
\(487\) 6.33857 27.7711i 0.287228 1.25843i −0.601083 0.799187i \(-0.705264\pi\)
0.888311 0.459242i \(-0.151879\pi\)
\(488\) 0.292328 + 1.28077i 0.0132331 + 0.0579778i
\(489\) 6.74401 3.24774i 0.304974 0.146868i
\(490\) 0.373194 + 0.179721i 0.0168592 + 0.00811895i
\(491\) 2.83878 + 12.4375i 0.128112 + 0.561297i 0.997716 + 0.0675466i \(0.0215171\pi\)
−0.869604 + 0.493750i \(0.835626\pi\)
\(492\) 9.45584 0.426302
\(493\) 0 0
\(494\) 4.54416 0.204451
\(495\) −1.51947 6.65722i −0.0682950 0.299220i
\(496\) 11.0037 + 5.29911i 0.494081 + 0.237937i
\(497\) 8.08220 3.89218i 0.362536 0.174588i
\(498\) −0.139613 0.611686i −0.00625623 0.0274103i
\(499\) 3.33126 14.5952i 0.149128 0.653372i −0.844001 0.536342i \(-0.819806\pi\)
0.993128 0.117030i \(-0.0373372\pi\)
\(500\) 14.8262 + 7.13992i 0.663048 + 0.319307i
\(501\) 2.28001 + 2.85904i 0.101863 + 0.127733i
\(502\) 1.53119 + 1.92006i 0.0683405 + 0.0856963i
\(503\) −23.1801 + 11.1629i −1.03355 + 0.497730i −0.872191 0.489166i \(-0.837301\pi\)
−0.161357 + 0.986896i \(0.551587\pi\)
\(504\) 7.90977 9.91854i 0.352329 0.441807i
\(505\) 13.6569 0.607722
\(506\) −4.77397 + 5.98637i −0.212229 + 0.266127i
\(507\) −0.890084 + 3.89971i −0.0395300 + 0.173192i
\(508\) −6.37020 + 27.9097i −0.282632 + 1.23829i
\(509\) −17.1368 + 21.4889i −0.759575 + 0.952477i −0.999834 0.0182320i \(-0.994196\pi\)
0.240259 + 0.970709i \(0.422768\pi\)
\(510\) −0.828427 −0.0366834
\(511\) 7.05398 8.84541i 0.312050 0.391298i
\(512\) −20.5037 + 9.87405i −0.906143 + 0.436375i
\(513\) 9.03143 + 11.3250i 0.398747 + 0.500013i
\(514\) −6.15388 7.71672i −0.271436 0.340370i
\(515\) 0.746387 + 0.359441i 0.0328897 + 0.0158389i
\(516\) −1.08098 + 4.73607i −0.0475873 + 0.208494i
\(517\) −2.81642 12.3395i −0.123866 0.542691i
\(518\) 4.22220 2.03331i 0.185513 0.0893383i
\(519\) 8.82858 + 4.25162i 0.387532 + 0.186626i
\(520\) −0.645198 2.82680i −0.0282938 0.123963i
\(521\) −0.857864 −0.0375837 −0.0187919 0.999823i \(-0.505982\pi\)
−0.0187919 + 0.999823i \(0.505982\pi\)
\(522\) 0 0
\(523\) 27.3137 1.19435 0.597173 0.802113i \(-0.296291\pi\)
0.597173 + 0.802113i \(0.296291\pi\)
\(524\) −0.534500 2.34180i −0.0233497 0.102302i
\(525\) −4.22220 2.03331i −0.184272 0.0887407i
\(526\) −4.19568 + 2.02053i −0.182940 + 0.0880994i
\(527\) −4.37406 19.1640i −0.190537 0.834798i
\(528\) 0.667563 2.92478i 0.0290519 0.127285i
\(529\) −32.0992 15.4582i −1.39562 0.672094i
\(530\) 1.93313 + 2.42407i 0.0839699 + 0.105295i
\(531\) −13.5028 16.9320i −0.585973 0.734787i
\(532\) 27.9566 13.4632i 1.21207 0.583702i
\(533\) 14.2333 17.8480i 0.616512 0.773082i
\(534\) −0.769553 −0.0333018
\(535\) 5.71838 7.17062i 0.247227 0.310013i
\(536\) −1.99614 + 8.74565i −0.0862200 + 0.377755i
\(537\) 0.966441 4.23425i 0.0417050 0.182722i
\(538\) −5.02463 + 6.30068i −0.216627 + 0.271642i
\(539\) 2.41421 0.103988
\(540\) 2.75222 3.45117i 0.118437 0.148515i
\(541\) 19.5122 9.39656i 0.838893 0.403990i 0.0354501 0.999371i \(-0.488714\pi\)
0.803443 + 0.595382i \(0.202999\pi\)
\(542\) −3.75929 4.71400i −0.161475 0.202484i
\(543\) 3.69663 + 4.63543i 0.158638 + 0.198925i
\(544\) 19.2030 + 9.24767i 0.823321 + 0.396491i
\(545\) 0.298878 1.30947i 0.0128025 0.0560915i
\(546\) 0.197443 + 0.865055i 0.00844979 + 0.0370209i
\(547\) 3.42277 1.64832i 0.146347 0.0704771i −0.359277 0.933231i \(-0.616977\pi\)
0.505624 + 0.862754i \(0.331262\pi\)
\(548\) 19.7683 + 9.51990i 0.844459 + 0.406670i
\(549\) 0.521399 + 2.28440i 0.0222528 + 0.0974957i
\(550\) −4.00000 −0.170561
\(551\) 0 0
\(552\) −5.02944 −0.214067
\(553\) −0.260699 1.14220i −0.0110861 0.0485712i
\(554\) −1.98304 0.954983i −0.0842514 0.0405733i
\(555\) 1.49277 0.718882i 0.0633647 0.0305148i
\(556\) 5.69609 + 24.9562i 0.241568 + 1.05838i
\(557\) −1.18241 + 5.18048i −0.0501004 + 0.219504i −0.993781 0.111354i \(-0.964481\pi\)
0.943680 + 0.330858i \(0.107338\pi\)
\(558\) −4.29722 2.06943i −0.181916 0.0876060i
\(559\) 7.31224 + 9.16926i 0.309275 + 0.387818i
\(560\) −5.29049 6.63406i −0.223564 0.280340i
\(561\) −4.35026 + 2.09498i −0.183668 + 0.0884500i
\(562\) −0.508913 + 0.638157i −0.0214672 + 0.0269190i
\(563\) −9.24264 −0.389531 −0.194765 0.980850i \(-0.562395\pi\)
−0.194765 + 0.980850i \(0.562395\pi\)
\(564\) 2.47561 3.10431i 0.104242 0.130715i
\(565\) 2.07250 9.08019i 0.0871905 0.382007i
\(566\) −0.0316282 + 0.138572i −0.00132943 + 0.00582462i
\(567\) 13.2003 16.5526i 0.554359 0.695144i
\(568\) 5.02944 0.211030
\(569\) −17.6717 + 22.1596i −0.740835 + 0.928977i −0.999314 0.0370396i \(-0.988207\pi\)
0.258479 + 0.966017i \(0.416779\pi\)
\(570\) −0.927491 + 0.446656i −0.0388483 + 0.0187084i
\(571\) −19.0959 23.9455i −0.799138 1.00209i −0.999749 0.0224161i \(-0.992864\pi\)
0.200611 0.979671i \(-0.435707\pi\)
\(572\) −5.03223 6.31021i −0.210408 0.263843i
\(573\) 1.00251 + 0.482782i 0.0418803 + 0.0201685i
\(574\) −3.25491 + 14.2607i −0.135857 + 0.595229i
\(575\) −6.81524 29.8595i −0.284215 1.24523i
\(576\) −10.6305 + 5.11939i −0.442938 + 0.213308i
\(577\) −8.82858 4.25162i −0.367539 0.176997i 0.240993 0.970527i \(-0.422527\pi\)
−0.608532 + 0.793530i \(0.708241\pi\)
\(578\) −0.581942 2.54965i −0.0242056 0.106052i
\(579\) 4.48528 0.186402
\(580\) 0 0
\(581\) −10.3431 −0.429106
\(582\) −0.476670 2.08843i −0.0197586 0.0865681i
\(583\) 16.2815 + 7.84074i 0.674310 + 0.324730i
\(584\) 5.71498 2.75219i 0.236487 0.113886i
\(585\) −1.15078 5.04191i −0.0475790 0.208457i
\(586\) 0.337057 1.47674i 0.0139237 0.0610036i
\(587\) 3.29471 + 1.58665i 0.135987 + 0.0654880i 0.500640 0.865656i \(-0.333098\pi\)
−0.364653 + 0.931144i \(0.618812\pi\)
\(588\) 0.472206 + 0.592127i 0.0194734 + 0.0244189i
\(589\) −15.2296 19.0973i −0.627525 0.786892i
\(590\) 2.85749 1.37609i 0.117641 0.0566529i
\(591\) −0.516516 + 0.647690i −0.0212466 + 0.0266424i
\(592\) −12.0000 −0.493197
\(593\) −1.56790 + 1.96609i −0.0643860 + 0.0807375i −0.812982 0.582289i \(-0.802157\pi\)
0.748596 + 0.663027i \(0.230728\pi\)
\(594\) −0.537213 + 2.35368i −0.0220421 + 0.0965728i
\(595\) −3.03894 + 13.3144i −0.124584 + 0.545839i
\(596\) 2.47561 3.10431i 0.101405 0.127158i
\(597\) −6.82843 −0.279469
\(598\) −3.61561 + 4.53383i −0.147853 + 0.185402i
\(599\) 39.5256 19.0345i 1.61497 0.777729i 0.615029 0.788505i \(-0.289144\pi\)
0.999942 + 0.0107761i \(0.00343020\pi\)
\(600\) −1.63817 2.05420i −0.0668779 0.0838623i
\(601\) −14.2333 17.8480i −0.580588 0.728034i 0.401625 0.915804i \(-0.368446\pi\)
−0.982213 + 0.187770i \(0.939874\pi\)
\(602\) −6.77053 3.26051i −0.275946 0.132889i
\(603\) −3.56033 + 15.5988i −0.144988 + 0.635234i
\(604\) 5.75392 + 25.2096i 0.234124 + 1.02576i
\(605\) −4.65943 + 2.24386i −0.189433 + 0.0912259i
\(606\) −2.11110 1.01665i −0.0857576 0.0412987i
\(607\) −3.94483 17.2834i −0.160116 0.701513i −0.989703 0.143136i \(-0.954281\pi\)
0.829587 0.558377i \(-0.188576\pi\)
\(608\) 26.4853 1.07412
\(609\) 0 0
\(610\) −0.343146 −0.0138936
\(611\) −2.13304 9.34545i −0.0862935 0.378076i
\(612\) 22.4977 + 10.8343i 0.909416 + 0.437951i
\(613\) 8.10872 3.90495i 0.327508 0.157720i −0.262903 0.964822i \(-0.584680\pi\)
0.590411 + 0.807103i \(0.298966\pi\)
\(614\) 1.55765 + 6.82450i 0.0628615 + 0.275414i
\(615\) −1.15078 + 5.04191i −0.0464041 + 0.203309i
\(616\) 9.75608 + 4.69828i 0.393083 + 0.189299i
\(617\) 14.5359 + 18.2274i 0.585192 + 0.733807i 0.982989 0.183666i \(-0.0587966\pi\)
−0.397797 + 0.917473i \(0.630225\pi\)
\(618\) −0.0886201 0.111126i −0.00356482 0.00447015i
\(619\) −32.8081 + 15.7995i −1.31867 + 0.635037i −0.955032 0.296504i \(-0.904179\pi\)
−0.363636 + 0.931541i \(0.618465\pi\)
\(620\) −4.64104 + 5.81968i −0.186389 + 0.233724i
\(621\) −18.4853 −0.741789
\(622\) 6.53747 8.19772i 0.262129 0.328699i
\(623\) −2.82297 + 12.3682i −0.113100 + 0.495522i
\(624\) 0.505585 2.21511i 0.0202396 0.0886755i
\(625\) 6.85839 8.60015i 0.274336 0.344006i
\(626\) 1.72792 0.0690617
\(627\) −3.74094 + 4.69099i −0.149399 + 0.187340i
\(628\) −13.9783 + 6.73158i −0.557794 + 0.268619i
\(629\) 12.0419 + 15.1001i 0.480142 + 0.602079i
\(630\) 2.06606 + 2.59076i 0.0823139 + 0.103218i
\(631\) 28.0846 + 13.5248i 1.11803 + 0.538415i 0.899284 0.437366i \(-0.144089\pi\)
0.218747 + 0.975782i \(0.429803\pi\)
\(632\) 0.146164 0.640386i 0.00581408 0.0254732i
\(633\) 1.60238 + 7.02047i 0.0636887 + 0.279038i
\(634\) −7.26080 + 3.49661i −0.288363 + 0.138868i
\(635\) −14.1063 6.79325i −0.559793 0.269582i
\(636\) 1.26148 + 5.52691i 0.0500210 + 0.219156i
\(637\) 1.82843 0.0724449
\(638\) 0 0
\(639\) 8.97056 0.354870
\(640\) −2.34901 10.2917i −0.0928527 0.406814i
\(641\) 19.6402 + 9.45823i 0.775742 + 0.373578i 0.779489 0.626415i \(-0.215479\pi\)
−0.00374766 + 0.999993i \(0.501193\pi\)
\(642\) −1.41776 + 0.682756i −0.0559545 + 0.0269462i
\(643\) −3.45235 15.1257i −0.136147 0.596501i −0.996261 0.0863977i \(-0.972464\pi\)
0.860113 0.510103i \(-0.170393\pi\)
\(644\) −8.81138 + 38.6052i −0.347217 + 1.52126i
\(645\) −2.39374 1.15277i −0.0942535 0.0453901i
\(646\) −7.48188 9.38198i −0.294371 0.369129i
\(647\) 17.6717 + 22.1596i 0.694745 + 0.871182i 0.996619 0.0821655i \(-0.0261836\pi\)
−0.301874 + 0.953348i \(0.597612\pi\)
\(648\) 10.6946 5.15023i 0.420122 0.202320i
\(649\) 11.5254 14.4524i 0.452411 0.567305i
\(650\) −3.02944 −0.118824
\(651\) 2.97377 3.72899i 0.116551 0.146150i
\(652\) 7.35245 32.2132i 0.287944 1.26157i
\(653\) 0.413414 1.81128i 0.0161781 0.0708810i −0.966194 0.257814i \(-0.916998\pi\)
0.982373 + 0.186933i \(0.0598548\pi\)
\(654\) −0.143682 + 0.180171i −0.00561839 + 0.00704524i
\(655\) 1.31371 0.0513308
\(656\) 23.3533 29.2842i 0.911795 1.14335i
\(657\) 10.1933 4.90883i 0.397678 0.191512i
\(658\) 3.82956 + 4.80212i 0.149292 + 0.187206i
\(659\) 7.22362 + 9.05813i 0.281392 + 0.352855i 0.902361 0.430980i \(-0.141832\pi\)
−0.620969 + 0.783835i \(0.713261\pi\)
\(660\) 1.64736 + 0.793325i 0.0641232 + 0.0308801i
\(661\) −2.37792 + 10.4184i −0.0924905 + 0.405227i −0.999887 0.0150488i \(-0.995210\pi\)
0.907396 + 0.420276i \(0.138067\pi\)
\(662\) −0.0381786 0.167271i −0.00148385 0.00650118i
\(663\) −3.29471 + 1.58665i −0.127956 + 0.0616204i
\(664\) −5.22471 2.51609i −0.202758 0.0976431i
\(665\) 3.77631 + 16.5451i 0.146439 + 0.641591i
\(666\) 4.68629 0.181590
\(667\) 0 0
\(668\) 16.1421 0.624558
\(669\) −0.813727 3.56517i −0.0314605 0.137837i
\(670\) −2.11110 1.01665i −0.0815590 0.0392767i
\(671\) −1.80194 + 0.867767i −0.0695630 + 0.0334998i
\(672\) 1.15078 + 5.04191i 0.0443924 + 0.194496i
\(673\) −5.25759 + 23.0350i −0.202665 + 0.887935i 0.766640 + 0.642077i \(0.221927\pi\)
−0.969306 + 0.245858i \(0.920930\pi\)
\(674\) 6.64247 + 3.19884i 0.255858 + 0.123215i
\(675\) −6.02095 7.55003i −0.231746 0.290601i
\(676\) 11.0089 + 13.8047i 0.423418 + 0.530949i
\(677\) 19.8213 9.54544i 0.761795 0.366861i −0.0123051 0.999924i \(-0.503917\pi\)
0.774100 + 0.633063i \(0.218203\pi\)
\(678\) −0.996324 + 1.24935i −0.0382636 + 0.0479810i
\(679\) −35.3137 −1.35522
\(680\) −4.77397 + 5.98637i −0.183073 + 0.229567i
\(681\) 1.85652 8.13397i 0.0711422 0.311694i
\(682\) 0.905898 3.96900i 0.0346886 0.151981i
\(683\) −8.08701 + 10.1408i −0.309441 + 0.388027i −0.912097 0.409974i \(-0.865538\pi\)
0.602656 + 0.798001i \(0.294109\pi\)
\(684\) 31.0294 1.18644
\(685\) −7.48188 + 9.38198i −0.285868 + 0.358467i
\(686\) 6.33330 3.04996i 0.241807 0.116448i
\(687\) 5.29049 + 6.63406i 0.201845 + 0.253105i
\(688\) 11.9976 + 15.0445i 0.457404 + 0.573566i
\(689\) 12.3309 + 5.93826i 0.469771 + 0.226230i
\(690\) 0.292328 1.28077i 0.0111287 0.0487581i
\(691\) −10.6810 46.7965i −0.406325 1.78022i −0.600887 0.799334i \(-0.705186\pi\)
0.194562 0.980890i \(-0.437671\pi\)
\(692\) 38.9713 18.7676i 1.48146 0.713436i
\(693\) 17.4011 + 8.37990i 0.661011 + 0.318326i
\(694\) 1.33513 + 5.84957i 0.0506807 + 0.222047i
\(695\) −14.0000 −0.531050
\(696\) 0 0
\(697\) −60.2843 −2.28343
\(698\) −2.13304 9.34545i −0.0807367 0.353731i
\(699\) −1.60985 0.775262i −0.0608900 0.0293231i
\(700\) −18.6377 + 8.97545i −0.704439 + 0.339240i
\(701\) −4.92054 21.5583i −0.185846 0.814245i −0.978776 0.204932i \(-0.934303\pi\)
0.792930 0.609313i \(-0.208555\pi\)
\(702\) −0.406863 + 1.78258i −0.0153561 + 0.0672793i
\(703\) 21.6233 + 10.4132i 0.815536 + 0.392742i
\(704\) −6.27921 7.87388i −0.236657 0.296758i
\(705\) 1.35395 + 1.69780i 0.0509928 + 0.0639430i
\(706\) 2.60137 1.25275i 0.0979038 0.0471480i
\(707\) −24.0838 + 30.2001i −0.905765 + 1.13579i
\(708\) 5.79899 0.217939
\(709\) 0.534870 0.670705i 0.0200875 0.0251889i −0.771686 0.636003i \(-0.780586\pi\)
0.791774 + 0.610814i \(0.209158\pi\)
\(710\) −0.292328 + 1.28077i −0.0109709 + 0.0480665i
\(711\) 0.260699 1.14220i 0.00977699 0.0428358i
\(712\) −4.43469 + 5.56093i −0.166197 + 0.208405i
\(713\) 31.1716 1.16738
\(714\) 1.46093 1.83195i 0.0546738 0.0685588i
\(715\) 3.97707 1.91526i 0.148734 0.0716265i
\(716\) −11.9533 14.9889i −0.446715 0.560163i
\(717\) 2.15468 + 2.70189i 0.0804681 + 0.100904i
\(718\) −6.74401 3.24774i −0.251684 0.121205i
\(719\) −1.81180 + 7.93800i −0.0675686 + 0.296037i −0.997410 0.0719227i \(-0.977087\pi\)
0.929842 + 0.367960i \(0.119944\pi\)
\(720\) −1.88815 8.27254i −0.0703673 0.308299i
\(721\) −2.11110 + 1.01665i −0.0786215 + 0.0378621i
\(722\) −6.34429 3.05525i −0.236110 0.113705i
\(723\) 0.397600 + 1.74200i 0.0147869 + 0.0647856i
\(724\) 26.1716 0.972659
\(725\) 0 0
\(726\) 0.887302 0.0329309
\(727\) 4.74275 + 20.7793i 0.175899 + 0.770663i 0.983496 + 0.180929i \(0.0579103\pi\)
−0.807598 + 0.589734i \(0.799233\pi\)
\(728\) 7.38885 + 3.55828i 0.273849 + 0.131879i
\(729\) 16.3720 7.88435i 0.606371 0.292013i
\(730\) 0.368685 + 1.61531i 0.0136456 + 0.0597854i
\(731\) 6.89160 30.1941i 0.254895 1.11677i
\(732\) −0.565283 0.272226i −0.0208935 0.0100618i
\(733\) 30.7099 + 38.5090i 1.13430 + 1.42236i 0.891928 + 0.452177i \(0.149352\pi\)
0.242367 + 0.970185i \(0.422076\pi\)
\(734\) 4.64864 + 5.82921i 0.171585 + 0.215160i
\(735\) −0.373194 + 0.179721i −0.0137655 + 0.00662909i
\(736\) −21.0733 + 26.4251i −0.776773 + 0.974043i
\(737\) −13.6569 −0.503057
\(738\) −9.12005 + 11.4362i −0.335714 + 0.420971i
\(739\) 2.24102 9.81857i 0.0824374 0.361182i −0.916837 0.399261i \(-0.869267\pi\)
0.999275 + 0.0380792i \(0.0121239\pi\)
\(740\) 1.62745 7.13034i 0.0598264 0.262116i
\(741\) −2.83323 + 3.55276i −0.104081 + 0.130514i
\(742\) −8.76955 −0.321940
\(743\) 7.69583 9.65026i 0.282332 0.354034i −0.620362 0.784315i \(-0.713014\pi\)
0.902695 + 0.430282i \(0.141586\pi\)
\(744\) 2.40928 1.16025i 0.0883285 0.0425367i
\(745\) 1.35395 + 1.69780i 0.0496050 + 0.0622027i
\(746\) −0.952014 1.19379i −0.0348557 0.0437077i
\(747\) −9.31885 4.48772i −0.340959 0.164197i
\(748\) −4.74275 + 20.7793i −0.173412 + 0.759768i
\(749\) 5.77244 + 25.2907i 0.210920 + 0.924103i
\(750\) 1.39124 0.669984i 0.0508008 0.0244644i
\(751\) −2.42027 1.16554i −0.0883167 0.0425311i 0.389204 0.921152i \(-0.372750\pi\)
−0.477521 + 0.878621i \(0.658464\pi\)
\(752\) −3.49979 15.3336i −0.127624 0.559159i
\(753\) −2.45584 −0.0894959
\(754\) 0 0
\(755\) −14.1421 −0.514685
\(756\) 2.77824 + 12.1722i 0.101043 + 0.442700i
\(757\) −38.2779 18.4337i −1.39123 0.669983i −0.419872 0.907584i \(-0.637925\pi\)
−0.971363 + 0.237600i \(0.923639\pi\)
\(758\) −10.0652 + 4.84716i −0.365586 + 0.176057i
\(759\) −1.70381 7.46488i −0.0618444 0.270958i
\(760\) −2.11722 + 9.27616i −0.0767998 + 0.336482i
\(761\) 30.2707 + 14.5776i 1.09731 + 0.528438i 0.892813 0.450428i \(-0.148729\pi\)
0.204501 + 0.978866i \(0.434443\pi\)
\(762\) 1.67488 + 2.10023i 0.0606743 + 0.0760832i
\(763\) 2.36863 + 2.97017i 0.0857502 + 0.107527i
\(764\) 4.42528 2.13110i 0.160101 0.0771006i
\(765\) −8.51491 + 10.6774i −0.307857 + 0.386041i
\(766\) −8.48528 −0.306586
\(767\) 8.72886 10.9456i 0.315181 0.395224i
\(768\) 0.365971 1.60343i 0.0132059 0.0578586i
\(769\) −2.91785 + 12.7839i −0.105220 + 0.461001i 0.894678 + 0.446713i \(0.147405\pi\)
−0.999898 + 0.0142880i \(0.995452\pi\)
\(770\) −1.76350 + 2.21135i −0.0635520 + 0.0796916i
\(771\) 9.87006 0.355461
\(772\) 12.3445 15.4795i 0.444287 0.557118i
\(773\) 32.8721 15.8304i 1.18233 0.569379i 0.263739 0.964594i \(-0.415044\pi\)
0.918589 + 0.395215i \(0.129330\pi\)
\(774\) −4.68535 5.87524i −0.168411 0.211181i
\(775\) 10.1531 + 12.7316i 0.364709 + 0.457331i
\(776\) −17.8383 8.59046i −0.640357 0.308380i
\(777\) −1.04280 + 4.56880i −0.0374102 + 0.163905i
\(778\) −3.40762 14.9298i −0.122169 0.535258i
\(779\) −67.4931 + 32.5030i −2.41819 + 1.16454i
\(780\) 1.24764 + 0.600832i 0.0446727 + 0.0215132i
\(781\) 1.70381 + 7.46488i 0.0609671 + 0.267114i
\(782\) 15.3137 0.547617
\(783\) 0 0
\(784\) 3.00000 0.107143
\(785\) −1.88815 8.27254i −0.0673911 0.295260i
\(786\) −0.203075 0.0977960i −0.00724346 0.00348827i
\(787\) −37.9157 + 18.2592i −1.35155 + 0.650872i −0.962735 0.270445i \(-0.912829\pi\)
−0.388814 + 0.921316i \(0.627115\pi\)
\(788\) 0.813727 + 3.56517i 0.0289878 + 0.127004i
\(789\) 1.03625 4.54010i 0.0368914 0.161632i
\(790\) 0.154582 + 0.0744427i 0.00549977 + 0.00264855i
\(791\) 16.4247 + 20.5959i 0.583994 + 0.732306i
\(792\) 6.75141 + 8.46601i 0.239901 + 0.300826i
\(793\) −1.36471 + 0.657212i −0.0484624 + 0.0233383i
\(794\) 7.91738 9.92808i 0.280977 0.352334i
\(795\) −3.10051 −0.109964
\(796\) −18.7933 + 23.5661i −0.666111 + 0.835277i
\(797\) 12.4033 54.3426i 0.439349 1.92491i 0.0642348 0.997935i \(-0.479539\pi\)
0.375114 0.926979i \(-0.377604\pi\)
\(798\) 0.647912 2.83869i 0.0229358 0.100488i
\(799\) −15.7828 + 19.7911i −0.558357 + 0.700157i
\(800\) −17.6569 −0.624264
\(801\) −7.90977 + 9.91854i −0.279478 + 0.350454i
\(802\) 2.74041 1.31971i 0.0967674 0.0466007i
\(803\) 6.02095 + 7.55003i 0.212475 + 0.266435i
\(804\) −2.67120 3.34958i −0.0942059 0.118131i
\(805\) −19.5122 9.39656i −0.687713 0.331185i
\(806\) 0.686090 3.00596i 0.0241665 0.105880i
\(807\) −1.79327 7.85682i −0.0631260 0.276573i
\(808\) −19.5122 + 9.39656i −0.686435 + 0.330570i
\(809\) 18.2755 + 8.80102i 0.642532 + 0.309427i 0.726629 0.687030i \(-0.241086\pi\)
−0.0840964 + 0.996458i \(0.526800\pi\)
\(810\) 0.689927 + 3.02277i 0.0242416 + 0.106209i
\(811\) 5.17157 0.181598 0.0907992 0.995869i \(-0.471058\pi\)
0.0907992 + 0.995869i \(0.471058\pi\)
\(812\) 0 0
\(813\) 6.02944 0.211462
\(814\) 0.890084 + 3.89971i 0.0311974 + 0.136685i
\(815\) 16.2815 + 7.84074i 0.570315 + 0.274649i
\(816\) −5.40581 + 2.60330i −0.189241 + 0.0911338i
\(817\) −8.56378 37.5204i −0.299609 1.31267i
\(818\) −1.37985 + 6.04554i −0.0482455 + 0.211377i
\(819\) 13.1788 + 6.34660i 0.460506 + 0.221768i
\(820\) 14.2333 + 17.8480i 0.497048 + 0.623279i
\(821\) 9.65492 + 12.1069i 0.336959 + 0.422533i 0.921226 0.389029i \(-0.127189\pi\)
−0.584267 + 0.811562i \(0.698618\pi\)
\(822\) 1.85498 0.893312i 0.0646999 0.0311578i
\(823\) 1.42422 1.78592i 0.0496452 0.0622531i −0.756389 0.654122i \(-0.773038\pi\)
0.806034 + 0.591869i \(0.201610\pi\)
\(824\) −1.31371 −0.0457652
\(825\) 2.49396 3.12733i 0.0868285 0.108880i
\(826\) −1.99614 + 8.74565i −0.0694545 + 0.304300i
\(827\) −2.91514 + 12.7720i −0.101369 + 0.444128i 0.898616 + 0.438736i \(0.144574\pi\)
−0.999985 + 0.00539209i \(0.998284\pi\)
\(828\) −24.6889 + 30.9589i −0.858000 + 1.07590i
\(829\) 9.79899 0.340333 0.170166 0.985415i \(-0.445569\pi\)
0.170166 + 0.985415i \(0.445569\pi\)
\(830\) 0.944412 1.18425i 0.0327810 0.0411061i
\(831\) 1.98304 0.954983i 0.0687910 0.0331280i
\(832\) −4.75562 5.96335i −0.164871 0.206742i
\(833\) −3.01048 3.77502i −0.104307 0.130797i
\(834\) 2.16415 + 1.04220i 0.0749382 + 0.0360883i
\(835\) −1.96451 + 8.60708i −0.0679847 + 0.297860i
\(836\) 5.89353 + 25.8212i 0.203832 + 0.893046i
\(837\) 8.85511 4.26439i 0.306077 0.147399i
\(838\) 9.88414 + 4.75995i 0.341442 + 0.164430i
\(839\) 4.91127 + 21.5177i 0.169556 + 0.742874i 0.986176 + 0.165698i \(0.0529878\pi\)
−0.816620 + 0.577175i \(0.804155\pi\)
\(840\) −1.85786 −0.0641024
\(841\) 0 0
\(842\) −10.4020 −0.358477
\(843\) −0.181629 0.795769i −0.00625564 0.0274077i
\(844\) 28.6389 + 13.7918i 0.985792 + 0.474732i
\(845\) −8.70053 + 4.18995i −0.299307 + 0.144139i
\(846\) 1.36675 + 5.98814i 0.0469900 + 0.205876i
\(847\) 3.25491 14.2607i 0.111840 0.490003i
\(848\) 20.2320 + 9.74323i 0.694770 + 0.334584i
\(849\) −0.0886201 0.111126i −0.00304143 0.00381384i
\(850\) 4.98792 + 6.25465i 0.171084 + 0.214533i
\(851\) −27.5943 + 13.2887i −0.945922 + 0.455532i
\(852\) −1.49764 + 1.87798i −0.0513081 + 0.0643384i
\(853\) 10.9706 0.375625 0.187812 0.982205i \(-0.439860\pi\)
0.187812 + 0.982205i \(0.439860\pi\)
\(854\) 0.605136 0.758817i 0.0207073 0.0259662i
\(855\) −3.77631 + 16.5451i −0.129147 + 0.565830i
\(856\) −3.23638 + 14.1795i −0.110617 + 0.484645i
\(857\) −7.37490 + 9.24784i −0.251922 + 0.315900i −0.891671 0.452684i \(-0.850467\pi\)
0.639749 + 0.768584i \(0.279038\pi\)
\(858\) −0.757359 −0.0258558
\(859\) −3.57130 + 4.47827i −0.121851 + 0.152797i −0.839015 0.544108i \(-0.816868\pi\)
0.717164 + 0.696904i \(0.245440\pi\)
\(860\) −10.5665 + 5.08855i −0.360314 + 0.173518i
\(861\) −9.12005 11.4362i −0.310810 0.389744i
\(862\) 2.15468 + 2.70189i 0.0733888 + 0.0920267i
\(863\) 40.6451 + 19.5737i 1.38358 + 0.666295i 0.969759 0.244064i \(-0.0784809\pi\)
0.413818 + 0.910360i \(0.364195\pi\)
\(864\) −2.37137 + 10.3897i −0.0806758 + 0.353464i
\(865\) 5.26415 + 23.0637i 0.178986 + 0.784190i
\(866\) 5.45886 2.62885i 0.185500 0.0893319i
\(867\) 2.35624 + 1.13470i 0.0800219 + 0.0385365i
\(868\) −4.68492 20.5260i −0.159016 0.696696i
\(869\) 1.00000 0.0339227
\(870\) 0 0
\(871\) −10.3431 −0.350464
\(872\) 0.473957 + 2.07654i 0.0160502 + 0.0703205i
\(873\) −31.8166 15.3220i −1.07683 0.518573i
\(874\) 17.1449 8.25656i 0.579936 0.279282i
\(875\) −5.66446 24.8176i −0.191494 0.838988i
\(876\) −0.674113 + 2.95348i −0.0227762 + 0.0997889i
\(877\) 7.98066 + 3.84328i 0.269488 + 0.129778i 0.563748 0.825947i \(-0.309359\pi\)
−0.294260 + 0.955725i \(0.595073\pi\)
\(878\) −3.01048 3.77502i −0.101599 0.127401i
\(879\) 0.944412 + 1.18425i 0.0318542 + 0.0399439i
\(880\) 6.52539 3.14246i 0.219971 0.105932i
\(881\) 8.72886 10.9456i 0.294083 0.368768i −0.612737 0.790287i \(-0.709931\pi\)
0.906820 + 0.421519i \(0.138503\pi\)
\(882\) −1.17157 −0.0394489
\(883\) −28.9464 + 36.2976i −0.974124 + 1.22151i 0.00103381 + 0.999999i \(0.499671\pi\)
−0.975157 + 0.221513i \(0.928901\pi\)
\(884\) −3.59196 + 15.7374i −0.120811 + 0.529307i
\(885\) −0.705741 + 3.09205i −0.0237232 + 0.103938i
\(886\) −9.20867 + 11.5473i −0.309371 + 0.387939i
\(887\) 36.8995 1.23896 0.619482 0.785011i \(-0.287343\pi\)
0.619482 + 0.785011i \(0.287343\pi\)
\(888\) −1.63817 + 2.05420i −0.0549733 + 0.0689343i
\(889\) 39.8987 19.2142i 1.33816 0.644424i
\(890\) −1.15836 1.45254i −0.0388283 0.0486891i
\(891\) 11.2671 + 14.1285i 0.377463 + 0.473324i
\(892\) −14.5436 7.00381i −0.486954 0.234505i
\(893\) −6.99958 + 30.6672i −0.234232 + 1.02624i
\(894\) −0.0829075 0.363242i −0.00277284 0.0121486i
\(895\) 9.44691 4.54939i 0.315775 0.152069i
\(896\) 26.9010 + 12.9548i 0.898700 + 0.432791i
\(897\) −1.29040 5.65360i −0.0430851 0.188768i
\(898\) −0.426407 −0.0142294
\(899\) 0 0
\(900\) −20.6863 −0.689543
\(901\) −8.04238 35.2360i −0.267931 1.17388i
\(902\) −11.2488 5.41716i −0.374546 0.180372i
\(903\) 6.77053 3.26051i 0.225309 0.108503i
\(904\) 3.28653 + 14.3992i 0.109309 + 0.478912i
\(905\) −3.18510 + 13.9548i −0.105876 + 0.463874i
\(906\) 2.18612 + 1.05278i 0.0726289 + 0.0349762i
\(907\) −21.3759 26.8045i −0.709775 0.890030i 0.287936 0.957650i \(-0.407031\pi\)
−0.997711 + 0.0676200i \(0.978459\pi\)
\(908\) −22.9621 28.7936i −0.762026 0.955550i
\(909\) −34.8021 + 16.7598i −1.15431 + 0.555888i
\(910\) −1.33560 + 1.67479i −0.0442747 + 0.0555187i
\(911\) −46.5563 −1.54248 −0.771240 0.636544i \(-0.780363\pi\)
−0.771240 + 0.636544i \(0.780363\pi\)
\(912\) −4.64864 + 5.82921i −0.153932 + 0.193025i
\(913\) 1.96451 8.60708i 0.0650158 0.284853i
\(914\) −3.22328 + 14.1221i −0.106617 + 0.467118i
\(915\) 0.213948 0.268282i 0.00707290 0.00886913i
\(916\) 37.4558 1.23758
\(917\) −2.31672 + 2.90507i −0.0765048 + 0.0959340i
\(918\) 4.35026 2.09498i 0.143580 0.0691445i
\(919\) −12.5584 15.7478i −0.414264 0.519471i 0.530295 0.847813i \(-0.322081\pi\)
−0.944559 + 0.328343i \(0.893510\pi\)
\(920\) −7.57050 9.49310i −0.249592 0.312978i
\(921\) −6.30678 3.03719i −0.207816 0.100079i
\(922\) −1.29040 + 5.65360i −0.0424970 + 0.186191i
\(923\) 1.29040 + 5.65360i 0.0424739 + 0.186090i
\(924\) −4.65943 + 2.24386i −0.153284 + 0.0738176i
\(925\) −14.4155 6.94214i −0.473979 0.228256i
\(926\) 2.39645 + 10.4995i 0.0787523 + 0.345036i
\(927\) −2.34315 −0.0769590
\(928\) 0 0
\(929\) 41.3137 1.35546 0.677729 0.735311i \(-0.262964\pi\)
0.677729 + 0.735311i \(0.262964\pi\)
\(930\) 0.155427 + 0.680972i 0.00509667 + 0.0223300i
\(931\) −5.40581 2.60330i −0.177168 0.0853198i
\(932\) −7.10621 + 3.42217i −0.232772 + 0.112097i
\(933\) 2.33319 + 10.2224i 0.0763854 + 0.334666i
\(934\) −2.98223 + 13.0660i −0.0975815 + 0.427533i
\(935\) −10.5025 5.05772i −0.343467 0.165405i
\(936\) 5.11325 + 6.41181i 0.167132 + 0.209576i
\(937\) 17.8489 + 22.3818i 0.583098 + 0.731182i 0.982638 0.185534i \(-0.0594014\pi\)
−0.399540 + 0.916716i \(0.630830\pi\)
\(938\) 5.97110 2.87553i 0.194963 0.0938893i
\(939\) −1.07734 + 1.35094i −0.0351577 + 0.0440864i
\(940\) 9.58579 0.312654
\(941\) 14.0896 17.6678i 0.459308 0.575954i −0.497209 0.867631i \(-0.665642\pi\)
0.956517 + 0.291677i \(0.0942131\pi\)
\(942\) −0.323956 + 1.41934i −0.0105551 + 0.0462447i
\(943\) 21.2726 93.2011i 0.692730 3.03505i
\(944\) 14.3219 17.9591i 0.466139 0.584519i
\(945\) −6.82843 −0.222129
\(946\) 3.99920 5.01483i 0.130025 0.163046i
\(947\) −35.4845 + 17.0884i −1.15309 + 0.555299i −0.909960 0.414695i \(-0.863888\pi\)
−0.243129 + 0.969994i \(0.578174\pi\)
\(948\) 0.195594 + 0.245267i 0.00635260 + 0.00796591i
\(949\) 4.56002 + 5.71809i 0.148025 + 0.185617i
\(950\) 8.95664 + 4.31329i 0.290592 + 0.139942i
\(951\) 1.79327 7.85682i 0.0581507 0.254775i
\(952\) −4.81910 21.1139i −0.156188 0.684305i
\(953\) −8.67400 + 4.17718i −0.280979 + 0.135312i −0.569066 0.822292i \(-0.692695\pi\)
0.288087 + 0.957604i \(0.406981\pi\)
\(954\) −7.90109 3.80497i −0.255807 0.123190i
\(955\) 0.597756 + 2.61894i 0.0193429 + 0.0847469i
\(956\) 15.2548 0.493377
\(957\) 0 0
\(958\) −5.34315 −0.172629
\(959\) −7.55261 33.0902i −0.243887 1.06854i
\(960\) 1.55680 + 0.749717i 0.0502456 + 0.0241970i
\(961\) 12.9977 6.25938i 0.419282 0.201916i
\(962\) 0.674113 + 2.95348i 0.0217343 + 0.0952241i
\(963\) −5.77244 + 25.2907i −0.186014 + 0.814982i
\(964\) 7.10621 + 3.42217i 0.228876 + 0.110221i
\(965\) 6.75141 + 8.46601i 0.217336 + 0.272530i
\(966\) 2.31672 + 2.90507i 0.0745392 + 0.0934692i
\(967\) 24.1075 11.6096i 0.775246 0.373339i −0.00405213 0.999992i \(-0.501290\pi\)
0.779299 + 0.626653i \(0.215576\pi\)
\(968\) 5.11325 6.41181i 0.164346 0.206083i
\(969\) 12.0000 0.385496
\(970\) 3.22442 4.04330i 0.103530 0.129822i
\(971\) 0.966441 4.23425i 0.0310146 0.135884i −0.957050 0.289922i \(-0.906371\pi\)
0.988065 + 0.154038i \(0.0492279\pi\)
\(972\) −4.20825 + 18.4375i −0.134980 + 0.591384i
\(973\) 24.6889 30.9589i 0.791491 0.992498i
\(974\) −11.7990 −0.378064
\(975\) 1.88882 2.36851i 0.0604908 0.0758530i
\(976\) −2.23916 + 1.07832i −0.0716738 + 0.0345163i
\(977\) 26.0796 + 32.7028i 0.834360 + 1.04625i 0.998212 + 0.0597697i \(0.0190366\pi\)
−0.163852 + 0.986485i \(0.552392\pi\)
\(978\) −1.93313 2.42407i −0.0618148 0.0775133i
\(979\) −9.75608 4.69828i −0.311806 0.150158i
\(980\) −0.406863 + 1.78258i −0.0129968 + 0.0569426i
\(981\) 0.845355 + 3.70374i 0.0269901 + 0.118251i
\(982\) 4.76096 2.29276i 0.151928 0.0731649i
\(983\) −28.7139 13.8279i −0.915832 0.441042i −0.0842508 0.996445i \(-0.526850\pi\)
−0.831581 + 0.555403i \(0.812564\pi\)
\(984\) −1.82490 7.99539i −0.0581756 0.254884i
\(985\) −2.00000 −0.0637253
\(986\) 0 0
\(987\) −6.14214 −0.195506
\(988\) 4.46352 + 19.5560i 0.142003 + 0.622158i
\(989\) 44.2490 + 21.3092i 1.40704 + 0.677593i
\(990\) −2.54832 + 1.22721i −0.0809911 + 0.0390032i
\(991\) 1.59583 + 6.99177i 0.0506931 + 0.222101i 0.993929 0.110022i \(-0.0350922\pi\)
−0.943236 + 0.332123i \(0.892235\pi\)
\(992\) 3.99883 17.5200i 0.126963 0.556261i
\(993\) 0.154582 + 0.0744427i 0.00490551 + 0.00236237i
\(994\) −2.31672 2.90507i −0.0734819 0.0921433i
\(995\) −10.2784 12.8887i −0.325847 0.408600i
\(996\) 2.49528 1.20166i 0.0790660 0.0380762i
\(997\) −17.6350 + 22.1135i −0.558505 + 0.700343i −0.978281 0.207285i \(-0.933537\pi\)
0.419776 + 0.907628i \(0.362109\pi\)
\(998\) −6.20101 −0.196290
\(999\) −6.02095 + 7.55003i −0.190494 + 0.238872i
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 841.2.d.j.645.1 12
29.2 odd 28 841.2.b.a.840.2 4
29.3 odd 28 841.2.e.k.63.3 24
29.4 even 14 841.2.d.f.605.2 12
29.5 even 14 841.2.a.d.1.1 2
29.6 even 14 841.2.d.f.571.2 12
29.7 even 7 inner 841.2.d.j.778.2 12
29.8 odd 28 841.2.e.k.651.3 24
29.9 even 14 841.2.d.f.190.2 12
29.10 odd 28 841.2.e.k.236.2 24
29.11 odd 28 841.2.e.k.267.2 24
29.12 odd 4 841.2.e.k.196.3 24
29.13 even 14 841.2.d.f.574.1 12
29.14 odd 28 841.2.e.k.270.3 24
29.15 odd 28 841.2.e.k.270.2 24
29.16 even 7 inner 841.2.d.j.574.2 12
29.17 odd 4 841.2.e.k.196.2 24
29.18 odd 28 841.2.e.k.267.3 24
29.19 odd 28 841.2.e.k.236.3 24
29.20 even 7 inner 841.2.d.j.190.1 12
29.21 odd 28 841.2.e.k.651.2 24
29.22 even 14 841.2.d.f.778.1 12
29.23 even 7 inner 841.2.d.j.571.1 12
29.24 even 7 29.2.a.a.1.2 2
29.25 even 7 inner 841.2.d.j.605.1 12
29.26 odd 28 841.2.e.k.63.2 24
29.27 odd 28 841.2.b.a.840.3 4
29.28 even 2 841.2.d.f.645.2 12
87.5 odd 14 7569.2.a.c.1.2 2
87.53 odd 14 261.2.a.d.1.1 2
116.111 odd 14 464.2.a.h.1.2 2
145.24 even 14 725.2.a.b.1.1 2
145.53 odd 28 725.2.b.b.349.2 4
145.82 odd 28 725.2.b.b.349.3 4
203.111 odd 14 1421.2.a.j.1.2 2
232.53 even 14 1856.2.a.r.1.2 2
232.227 odd 14 1856.2.a.w.1.1 2
319.285 odd 14 3509.2.a.j.1.1 2
348.227 even 14 4176.2.a.bq.1.1 2
377.285 even 14 4901.2.a.g.1.1 2
435.314 odd 14 6525.2.a.o.1.2 2
493.169 even 14 8381.2.a.e.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
29.2.a.a.1.2 2 29.24 even 7
261.2.a.d.1.1 2 87.53 odd 14
464.2.a.h.1.2 2 116.111 odd 14
725.2.a.b.1.1 2 145.24 even 14
725.2.b.b.349.2 4 145.53 odd 28
725.2.b.b.349.3 4 145.82 odd 28
841.2.a.d.1.1 2 29.5 even 14
841.2.b.a.840.2 4 29.2 odd 28
841.2.b.a.840.3 4 29.27 odd 28
841.2.d.f.190.2 12 29.9 even 14
841.2.d.f.571.2 12 29.6 even 14
841.2.d.f.574.1 12 29.13 even 14
841.2.d.f.605.2 12 29.4 even 14
841.2.d.f.645.2 12 29.28 even 2
841.2.d.f.778.1 12 29.22 even 14
841.2.d.j.190.1 12 29.20 even 7 inner
841.2.d.j.571.1 12 29.23 even 7 inner
841.2.d.j.574.2 12 29.16 even 7 inner
841.2.d.j.605.1 12 29.25 even 7 inner
841.2.d.j.645.1 12 1.1 even 1 trivial
841.2.d.j.778.2 12 29.7 even 7 inner
841.2.e.k.63.2 24 29.26 odd 28
841.2.e.k.63.3 24 29.3 odd 28
841.2.e.k.196.2 24 29.17 odd 4
841.2.e.k.196.3 24 29.12 odd 4
841.2.e.k.236.2 24 29.10 odd 28
841.2.e.k.236.3 24 29.19 odd 28
841.2.e.k.267.2 24 29.11 odd 28
841.2.e.k.267.3 24 29.18 odd 28
841.2.e.k.270.2 24 29.15 odd 28
841.2.e.k.270.3 24 29.14 odd 28
841.2.e.k.651.2 24 29.21 odd 28
841.2.e.k.651.3 24 29.8 odd 28
1421.2.a.j.1.2 2 203.111 odd 14
1856.2.a.r.1.2 2 232.53 even 14
1856.2.a.w.1.1 2 232.227 odd 14
3509.2.a.j.1.1 2 319.285 odd 14
4176.2.a.bq.1.1 2 348.227 even 14
4901.2.a.g.1.1 2 377.285 even 14
6525.2.a.o.1.2 2 435.314 odd 14
7569.2.a.c.1.2 2 87.5 odd 14
8381.2.a.e.1.2 2 493.169 even 14