Properties

Label 336.2.bq.a.205.1
Level $336$
Weight $2$
Character 336.205
Analytic conductor $2.683$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [336,2,Mod(37,336)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(336, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([0, 3, 0, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("336.37");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 336.bq (of order \(12\), degree \(4\), 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: \(2.68297350792\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{12})\)
Coefficient field: \(\Q(\zeta_{24})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - x^{4} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 205.1
Root \(-0.965926 + 0.258819i\) of defining polynomial
Character \(\chi\) \(=\) 336.205
Dual form 336.2.bq.a.277.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.22474 - 0.707107i) q^{2} +(-0.258819 + 0.965926i) q^{3} +(1.00000 + 1.73205i) q^{4} +(-0.473232 - 1.76612i) q^{5} +(1.00000 - 1.00000i) q^{6} +(2.09077 + 1.62132i) q^{7} -2.82843i q^{8} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})\) \(q+(-1.22474 - 0.707107i) q^{2} +(-0.258819 + 0.965926i) q^{3} +(1.00000 + 1.73205i) q^{4} +(-0.473232 - 1.76612i) q^{5} +(1.00000 - 1.00000i) q^{6} +(2.09077 + 1.62132i) q^{7} -2.82843i q^{8} +(-0.866025 - 0.500000i) q^{9} +(-0.669251 + 2.49768i) q^{10} +(0.400100 + 0.107206i) q^{11} +(-1.93185 + 0.517638i) q^{12} +(0.414214 + 0.414214i) q^{13} +(-1.41421 - 3.46410i) q^{14} +1.82843 q^{15} +(-2.00000 + 3.46410i) q^{16} +(0.585786 + 1.01461i) q^{17} +(0.707107 + 1.22474i) q^{18} +(2.73205 - 0.732051i) q^{19} +(2.58579 - 2.58579i) q^{20} +(-2.10721 + 1.59990i) q^{21} +(-0.414214 - 0.414214i) q^{22} +(7.13834 + 4.12132i) q^{23} +(2.73205 + 0.732051i) q^{24} +(1.43488 - 0.828427i) q^{25} +(-0.214413 - 0.800199i) q^{26} +(0.707107 - 0.707107i) q^{27} +(-0.717439 + 5.24264i) q^{28} +(1.87868 + 1.87868i) q^{29} +(-2.23936 - 1.29289i) q^{30} +(1.20711 + 2.09077i) q^{31} +(4.89898 - 2.82843i) q^{32} +(-0.207107 + 0.358719i) q^{33} -1.65685i q^{34} +(1.87404 - 4.45982i) q^{35} -2.00000i q^{36} +(0.732051 + 2.73205i) q^{37} +(-3.86370 - 1.03528i) q^{38} +(-0.507306 + 0.292893i) q^{39} +(-4.99536 + 1.33850i) q^{40} +0.585786i q^{41} +(3.71209 - 0.469450i) q^{42} +(4.58579 - 4.58579i) q^{43} +(0.214413 + 0.800199i) q^{44} +(-0.473232 + 1.76612i) q^{45} +(-5.82843 - 10.0951i) q^{46} +(3.12132 - 5.40629i) q^{47} +(-2.82843 - 2.82843i) q^{48} +(1.74264 + 6.77962i) q^{49} -2.34315 q^{50} +(-1.13165 + 0.303225i) q^{51} +(-0.303225 + 1.13165i) q^{52} +(-8.36188 - 2.24056i) q^{53} +(-1.36603 + 0.366025i) q^{54} -0.757359i q^{55} +(4.58579 - 5.91359i) q^{56} +2.82843i q^{57} +(-0.972476 - 3.62933i) q^{58} +(-2.00050 - 0.536032i) q^{59} +(1.82843 + 3.16693i) q^{60} +(-5.22973 + 1.40130i) q^{61} -3.41421i q^{62} +(-1.00000 - 2.44949i) q^{63} -8.00000 q^{64} +(0.535534 - 0.927572i) q^{65} +(0.507306 - 0.292893i) q^{66} +(3.44584 - 12.8601i) q^{67} +(-1.17157 + 2.02922i) q^{68} +(-5.82843 + 5.82843i) q^{69} +(-5.44879 + 4.13700i) q^{70} +15.8995i q^{71} +(-1.41421 + 2.44949i) q^{72} +(-3.46410 + 2.00000i) q^{73} +(1.03528 - 3.86370i) q^{74} +(0.428825 + 1.60040i) q^{75} +(4.00000 + 4.00000i) q^{76} +(0.662700 + 0.872833i) q^{77} +0.828427 q^{78} +(-5.62132 + 9.73641i) q^{79} +(7.06450 + 1.89293i) q^{80} +(0.500000 + 0.866025i) q^{81} +(0.414214 - 0.717439i) q^{82} +(-8.77817 - 8.77817i) q^{83} +(-4.87832 - 2.04989i) q^{84} +(1.51472 - 1.51472i) q^{85} +(-8.85906 + 2.37378i) q^{86} +(-2.30090 + 1.32843i) q^{87} +(0.303225 - 1.13165i) q^{88} +(-13.4722 - 7.77817i) q^{89} +(1.82843 - 1.82843i) q^{90} +(0.194453 + 1.53760i) q^{91} +16.4853i q^{92} +(-2.33195 + 0.624844i) q^{93} +(-7.64564 + 4.41421i) q^{94} +(-2.58579 - 4.47871i) q^{95} +(1.46410 + 5.46410i) q^{96} +8.31371 q^{97} +(2.65962 - 9.53553i) q^{98} +(-0.292893 - 0.292893i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 8 q^{4} + 8 q^{5} + 8 q^{6}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 8 q^{4} + 8 q^{5} + 8 q^{6} - 4 q^{10} + 4 q^{11} - 8 q^{13} - 8 q^{15} - 16 q^{16} + 16 q^{17} + 8 q^{19} + 32 q^{20} - 12 q^{21} + 8 q^{22} + 8 q^{24} + 8 q^{26} + 32 q^{29} + 4 q^{31} + 4 q^{33} - 16 q^{35} - 8 q^{37} + 8 q^{40} - 4 q^{42} + 48 q^{43} - 8 q^{44} + 8 q^{45} - 24 q^{46} + 8 q^{47} - 20 q^{49} - 64 q^{50} + 8 q^{51} - 8 q^{52} - 16 q^{53} - 4 q^{54} + 48 q^{56} - 12 q^{58} - 20 q^{59} - 8 q^{60} - 4 q^{61} - 8 q^{63} - 64 q^{64} - 24 q^{65} - 32 q^{67} - 32 q^{68} - 24 q^{69} - 44 q^{70} - 16 q^{75} + 32 q^{76} - 8 q^{77} - 16 q^{78} - 28 q^{79} + 32 q^{80} + 4 q^{81} - 8 q^{82} - 8 q^{83} + 80 q^{85} + 8 q^{86} + 8 q^{88} - 8 q^{90} - 28 q^{91} - 4 q^{93} - 32 q^{95} - 16 q^{96} - 24 q^{97} - 8 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/336\mathbb{Z}\right)^\times\).

\(n\) \(85\) \(113\) \(127\) \(241\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.22474 0.707107i −0.866025 0.500000i
\(3\) −0.258819 + 0.965926i −0.149429 + 0.557678i
\(4\) 1.00000 + 1.73205i 0.500000 + 0.866025i
\(5\) −0.473232 1.76612i −0.211636 0.789835i −0.987324 0.158719i \(-0.949264\pi\)
0.775688 0.631116i \(-0.217403\pi\)
\(6\) 1.00000 1.00000i 0.408248 0.408248i
\(7\) 2.09077 + 1.62132i 0.790237 + 0.612801i
\(8\) 2.82843i 1.00000i
\(9\) −0.866025 0.500000i −0.288675 0.166667i
\(10\) −0.669251 + 2.49768i −0.211636 + 0.789835i
\(11\) 0.400100 + 0.107206i 0.120635 + 0.0323239i 0.318631 0.947879i \(-0.396777\pi\)
−0.197997 + 0.980203i \(0.563444\pi\)
\(12\) −1.93185 + 0.517638i −0.557678 + 0.149429i
\(13\) 0.414214 + 0.414214i 0.114882 + 0.114882i 0.762211 0.647329i \(-0.224114\pi\)
−0.647329 + 0.762211i \(0.724114\pi\)
\(14\) −1.41421 3.46410i −0.377964 0.925820i
\(15\) 1.82843 0.472098
\(16\) −2.00000 + 3.46410i −0.500000 + 0.866025i
\(17\) 0.585786 + 1.01461i 0.142074 + 0.246080i 0.928278 0.371888i \(-0.121290\pi\)
−0.786203 + 0.617968i \(0.787956\pi\)
\(18\) 0.707107 + 1.22474i 0.166667 + 0.288675i
\(19\) 2.73205 0.732051i 0.626775 0.167944i 0.0685694 0.997646i \(-0.478157\pi\)
0.558206 + 0.829702i \(0.311490\pi\)
\(20\) 2.58579 2.58579i 0.578199 0.578199i
\(21\) −2.10721 + 1.59990i −0.459830 + 0.349127i
\(22\) −0.414214 0.414214i −0.0883106 0.0883106i
\(23\) 7.13834 + 4.12132i 1.48845 + 0.859355i 0.999913 0.0131907i \(-0.00419886\pi\)
0.488533 + 0.872545i \(0.337532\pi\)
\(24\) 2.73205 + 0.732051i 0.557678 + 0.149429i
\(25\) 1.43488 0.828427i 0.286976 0.165685i
\(26\) −0.214413 0.800199i −0.0420498 0.156932i
\(27\) 0.707107 0.707107i 0.136083 0.136083i
\(28\) −0.717439 + 5.24264i −0.135583 + 0.990766i
\(29\) 1.87868 + 1.87868i 0.348862 + 0.348862i 0.859686 0.510824i \(-0.170659\pi\)
−0.510824 + 0.859686i \(0.670659\pi\)
\(30\) −2.23936 1.29289i −0.408849 0.236049i
\(31\) 1.20711 + 2.09077i 0.216803 + 0.375513i 0.953829 0.300351i \(-0.0971038\pi\)
−0.737026 + 0.675864i \(0.763770\pi\)
\(32\) 4.89898 2.82843i 0.866025 0.500000i
\(33\) −0.207107 + 0.358719i −0.0360527 + 0.0624450i
\(34\) 1.65685i 0.284148i
\(35\) 1.87404 4.45982i 0.316770 0.753847i
\(36\) 2.00000i 0.333333i
\(37\) 0.732051 + 2.73205i 0.120348 + 0.449146i 0.999631 0.0271536i \(-0.00864431\pi\)
−0.879283 + 0.476300i \(0.841978\pi\)
\(38\) −3.86370 1.03528i −0.626775 0.167944i
\(39\) −0.507306 + 0.292893i −0.0812340 + 0.0469005i
\(40\) −4.99536 + 1.33850i −0.789835 + 0.211636i
\(41\) 0.585786i 0.0914845i 0.998953 + 0.0457422i \(0.0145653\pi\)
−0.998953 + 0.0457422i \(0.985435\pi\)
\(42\) 3.71209 0.469450i 0.572788 0.0724377i
\(43\) 4.58579 4.58579i 0.699326 0.699326i −0.264939 0.964265i \(-0.585352\pi\)
0.964265 + 0.264939i \(0.0853519\pi\)
\(44\) 0.214413 + 0.800199i 0.0323239 + 0.120635i
\(45\) −0.473232 + 1.76612i −0.0705452 + 0.263278i
\(46\) −5.82843 10.0951i −0.859355 1.48845i
\(47\) 3.12132 5.40629i 0.455291 0.788588i −0.543414 0.839465i \(-0.682868\pi\)
0.998705 + 0.0508774i \(0.0162018\pi\)
\(48\) −2.82843 2.82843i −0.408248 0.408248i
\(49\) 1.74264 + 6.77962i 0.248949 + 0.968517i
\(50\) −2.34315 −0.331371
\(51\) −1.13165 + 0.303225i −0.158463 + 0.0424600i
\(52\) −0.303225 + 1.13165i −0.0420498 + 0.156932i
\(53\) −8.36188 2.24056i −1.14859 0.307764i −0.366192 0.930540i \(-0.619338\pi\)
−0.782401 + 0.622775i \(0.786005\pi\)
\(54\) −1.36603 + 0.366025i −0.185893 + 0.0498097i
\(55\) 0.757359i 0.102122i
\(56\) 4.58579 5.91359i 0.612801 0.790237i
\(57\) 2.82843i 0.374634i
\(58\) −0.972476 3.62933i −0.127692 0.476554i
\(59\) −2.00050 0.536032i −0.260443 0.0697854i 0.126235 0.992000i \(-0.459711\pi\)
−0.386678 + 0.922215i \(0.626377\pi\)
\(60\) 1.82843 + 3.16693i 0.236049 + 0.408849i
\(61\) −5.22973 + 1.40130i −0.669598 + 0.179418i −0.577574 0.816338i \(-0.696000\pi\)
−0.0920243 + 0.995757i \(0.529334\pi\)
\(62\) 3.41421i 0.433606i
\(63\) −1.00000 2.44949i −0.125988 0.308607i
\(64\) −8.00000 −1.00000
\(65\) 0.535534 0.927572i 0.0664248 0.115051i
\(66\) 0.507306 0.292893i 0.0624450 0.0360527i
\(67\) 3.44584 12.8601i 0.420977 1.57111i −0.351579 0.936158i \(-0.614355\pi\)
0.772555 0.634947i \(-0.218978\pi\)
\(68\) −1.17157 + 2.02922i −0.142074 + 0.246080i
\(69\) −5.82843 + 5.82843i −0.701660 + 0.701660i
\(70\) −5.44879 + 4.13700i −0.651254 + 0.494466i
\(71\) 15.8995i 1.88692i 0.331482 + 0.943461i \(0.392451\pi\)
−0.331482 + 0.943461i \(0.607549\pi\)
\(72\) −1.41421 + 2.44949i −0.166667 + 0.288675i
\(73\) −3.46410 + 2.00000i −0.405442 + 0.234082i −0.688830 0.724923i \(-0.741875\pi\)
0.283387 + 0.959006i \(0.408542\pi\)
\(74\) 1.03528 3.86370i 0.120348 0.449146i
\(75\) 0.428825 + 1.60040i 0.0495165 + 0.184798i
\(76\) 4.00000 + 4.00000i 0.458831 + 0.458831i
\(77\) 0.662700 + 0.872833i 0.0755217 + 0.0994686i
\(78\) 0.828427 0.0938009
\(79\) −5.62132 + 9.73641i −0.632448 + 1.09543i 0.354602 + 0.935017i \(0.384616\pi\)
−0.987050 + 0.160415i \(0.948717\pi\)
\(80\) 7.06450 + 1.89293i 0.789835 + 0.211636i
\(81\) 0.500000 + 0.866025i 0.0555556 + 0.0962250i
\(82\) 0.414214 0.717439i 0.0457422 0.0792279i
\(83\) −8.77817 8.77817i −0.963530 0.963530i 0.0358281 0.999358i \(-0.488593\pi\)
−0.999358 + 0.0358281i \(0.988593\pi\)
\(84\) −4.87832 2.04989i −0.532268 0.223661i
\(85\) 1.51472 1.51472i 0.164294 0.164294i
\(86\) −8.85906 + 2.37378i −0.955297 + 0.255971i
\(87\) −2.30090 + 1.32843i −0.246683 + 0.142422i
\(88\) 0.303225 1.13165i 0.0323239 0.120635i
\(89\) −13.4722 7.77817i −1.42805 0.824485i −0.431083 0.902312i \(-0.641868\pi\)
−0.996967 + 0.0778275i \(0.975202\pi\)
\(90\) 1.82843 1.82843i 0.192733 0.192733i
\(91\) 0.194453 + 1.53760i 0.0203842 + 0.161184i
\(92\) 16.4853i 1.71871i
\(93\) −2.33195 + 0.624844i −0.241812 + 0.0647934i
\(94\) −7.64564 + 4.41421i −0.788588 + 0.455291i
\(95\) −2.58579 4.47871i −0.265296 0.459506i
\(96\) 1.46410 + 5.46410i 0.149429 + 0.557678i
\(97\) 8.31371 0.844129 0.422065 0.906566i \(-0.361306\pi\)
0.422065 + 0.906566i \(0.361306\pi\)
\(98\) 2.65962 9.53553i 0.268662 0.963234i
\(99\) −0.292893 0.292893i −0.0294369 0.0294369i
\(100\) 2.86976 + 1.65685i 0.286976 + 0.165685i
\(101\) −7.39595 1.98174i −0.735925 0.197190i −0.128659 0.991689i \(-0.541067\pi\)
−0.607266 + 0.794498i \(0.707734\pi\)
\(102\) 1.60040 + 0.428825i 0.158463 + 0.0424600i
\(103\) −15.2913 8.82843i −1.50670 0.869891i −0.999970 0.00778320i \(-0.997523\pi\)
−0.506725 0.862108i \(-0.669144\pi\)
\(104\) 1.17157 1.17157i 0.114882 0.114882i
\(105\) 3.82282 + 2.96447i 0.373069 + 0.289302i
\(106\) 8.65685 + 8.65685i 0.840828 + 0.840828i
\(107\) 4.15950 + 15.5235i 0.402114 + 1.50071i 0.809317 + 0.587372i \(0.199837\pi\)
−0.407203 + 0.913338i \(0.633496\pi\)
\(108\) 1.93185 + 0.517638i 0.185893 + 0.0498097i
\(109\) 0.392038 1.46311i 0.0375504 0.140140i −0.944606 0.328207i \(-0.893556\pi\)
0.982156 + 0.188067i \(0.0602222\pi\)
\(110\) −0.535534 + 0.927572i −0.0510612 + 0.0884405i
\(111\) −2.82843 −0.268462
\(112\) −9.79796 + 4.00000i −0.925820 + 0.377964i
\(113\) 3.89949 0.366834 0.183417 0.983035i \(-0.441284\pi\)
0.183417 + 0.983035i \(0.441284\pi\)
\(114\) 2.00000 3.46410i 0.187317 0.324443i
\(115\) 3.90068 14.5575i 0.363740 1.35750i
\(116\) −1.37529 + 5.13265i −0.127692 + 0.476554i
\(117\) −0.151613 0.565826i −0.0140166 0.0523107i
\(118\) 2.07107 + 2.07107i 0.190657 + 0.190657i
\(119\) −0.420266 + 3.07107i −0.0385257 + 0.281524i
\(120\) 5.17157i 0.472098i
\(121\) −9.37769 5.41421i −0.852518 0.492201i
\(122\) 7.39595 + 1.98174i 0.669598 + 0.179418i
\(123\) −0.565826 0.151613i −0.0510188 0.0136705i
\(124\) −2.41421 + 4.18154i −0.216803 + 0.375513i
\(125\) −8.60660 8.60660i −0.769798 0.769798i
\(126\) −0.507306 + 3.70711i −0.0451944 + 0.330255i
\(127\) 11.2426 0.997623 0.498812 0.866710i \(-0.333770\pi\)
0.498812 + 0.866710i \(0.333770\pi\)
\(128\) 9.79796 + 5.65685i 0.866025 + 0.500000i
\(129\) 3.24264 + 5.61642i 0.285499 + 0.494498i
\(130\) −1.31178 + 0.757359i −0.115051 + 0.0664248i
\(131\) 5.53275 1.48250i 0.483398 0.129526i −0.00888618 0.999961i \(-0.502829\pi\)
0.492285 + 0.870434i \(0.336162\pi\)
\(132\) −0.828427 −0.0721053
\(133\) 6.89898 + 2.89898i 0.598217 + 0.251373i
\(134\) −13.3137 + 13.3137i −1.15013 + 1.15013i
\(135\) −1.58346 0.914214i −0.136283 0.0786830i
\(136\) 2.86976 1.65685i 0.246080 0.142074i
\(137\) 11.1097 6.41421i 0.949169 0.548003i 0.0563466 0.998411i \(-0.482055\pi\)
0.892823 + 0.450408i \(0.148721\pi\)
\(138\) 11.2597 3.01702i 0.958486 0.256825i
\(139\) 12.8995 12.8995i 1.09412 1.09412i 0.0990371 0.995084i \(-0.468424\pi\)
0.995084 0.0990371i \(-0.0315763\pi\)
\(140\) 9.59867 1.21390i 0.811236 0.102593i
\(141\) 4.41421 + 4.41421i 0.371744 + 0.371744i
\(142\) 11.2426 19.4728i 0.943461 1.63412i
\(143\) 0.121320 + 0.210133i 0.0101453 + 0.0175722i
\(144\) 3.46410 2.00000i 0.288675 0.166667i
\(145\) 2.42893 4.20703i 0.201712 0.349375i
\(146\) 5.65685 0.468165
\(147\) −6.99964 0.0714323i −0.577320 0.00589164i
\(148\) −4.00000 + 4.00000i −0.328798 + 0.328798i
\(149\) −3.83788 14.3232i −0.314411 1.17340i −0.924536 0.381094i \(-0.875547\pi\)
0.610125 0.792305i \(-0.291119\pi\)
\(150\) 0.606451 2.26330i 0.0495165 0.184798i
\(151\) 8.30153 4.79289i 0.675569 0.390040i −0.122614 0.992454i \(-0.539128\pi\)
0.798184 + 0.602414i \(0.205794\pi\)
\(152\) −2.07055 7.72741i −0.167944 0.626775i
\(153\) 1.17157i 0.0947161i
\(154\) −0.194453 1.53760i −0.0156694 0.123903i
\(155\) 3.12132 3.12132i 0.250710 0.250710i
\(156\) −1.01461 0.585786i −0.0812340 0.0469005i
\(157\) 5.42758 20.2560i 0.433168 1.61661i −0.312244 0.950002i \(-0.601081\pi\)
0.745412 0.666604i \(-0.232253\pi\)
\(158\) 13.7694 7.94975i 1.09543 0.632448i
\(159\) 4.32843 7.49706i 0.343267 0.594555i
\(160\) −7.31371 7.31371i −0.578199 0.578199i
\(161\) 8.24264 + 20.1903i 0.649611 + 1.59122i
\(162\) 1.41421i 0.111111i
\(163\) −7.49303 + 2.00775i −0.586900 + 0.157259i −0.540036 0.841642i \(-0.681589\pi\)
−0.0468638 + 0.998901i \(0.514923\pi\)
\(164\) −1.01461 + 0.585786i −0.0792279 + 0.0457422i
\(165\) 0.731553 + 0.196019i 0.0569513 + 0.0152601i
\(166\) 4.54392 + 16.9581i 0.352676 + 1.31621i
\(167\) 6.00000i 0.464294i 0.972681 + 0.232147i \(0.0745750\pi\)
−0.972681 + 0.232147i \(0.925425\pi\)
\(168\) 4.52520 + 5.96008i 0.349127 + 0.459830i
\(169\) 12.6569i 0.973604i
\(170\) −2.92621 + 0.784076i −0.224430 + 0.0601359i
\(171\) −2.73205 0.732051i −0.208925 0.0559813i
\(172\) 12.5286 + 3.35703i 0.955297 + 0.255971i
\(173\) −16.3923 + 4.39230i −1.24628 + 0.333941i −0.820900 0.571072i \(-0.806528\pi\)
−0.425384 + 0.905013i \(0.639861\pi\)
\(174\) 3.75736 0.284845
\(175\) 4.34315 + 0.594346i 0.328311 + 0.0449283i
\(176\) −1.17157 + 1.17157i −0.0883106 + 0.0883106i
\(177\) 1.03553 1.79360i 0.0778355 0.134815i
\(178\) 11.0000 + 19.0526i 0.824485 + 1.42805i
\(179\) −4.82113 + 17.9927i −0.360348 + 1.34484i 0.513271 + 0.858227i \(0.328434\pi\)
−0.873619 + 0.486611i \(0.838233\pi\)
\(180\) −3.53225 + 0.946464i −0.263278 + 0.0705452i
\(181\) −15.7279 + 15.7279i −1.16905 + 1.16905i −0.186614 + 0.982433i \(0.559751\pi\)
−0.982433 + 0.186614i \(0.940249\pi\)
\(182\) 0.849091 2.02066i 0.0629388 0.149782i
\(183\) 5.41421i 0.400230i
\(184\) 11.6569 20.1903i 0.859355 1.48845i
\(185\) 4.47871 2.58579i 0.329282 0.190111i
\(186\) 3.29788 + 0.883663i 0.241812 + 0.0647934i
\(187\) 0.125600 + 0.468746i 0.00918479 + 0.0342781i
\(188\) 12.4853 0.910583
\(189\) 2.62484 0.331951i 0.190929 0.0241459i
\(190\) 7.31371i 0.530592i
\(191\) −9.65685 + 16.7262i −0.698745 + 1.21026i 0.270156 + 0.962817i \(0.412925\pi\)
−0.968902 + 0.247446i \(0.920409\pi\)
\(192\) 2.07055 7.72741i 0.149429 0.557678i
\(193\) 3.50000 + 6.06218i 0.251936 + 0.436365i 0.964059 0.265689i \(-0.0855996\pi\)
−0.712123 + 0.702055i \(0.752266\pi\)
\(194\) −10.1822 5.87868i −0.731037 0.422065i
\(195\) 0.757359 + 0.757359i 0.0542356 + 0.0542356i
\(196\) −10.0000 + 9.79796i −0.714286 + 0.699854i
\(197\) 3.17157 3.17157i 0.225965 0.225965i −0.585040 0.811005i \(-0.698921\pi\)
0.811005 + 0.585040i \(0.198921\pi\)
\(198\) 0.151613 + 0.565826i 0.0107746 + 0.0402115i
\(199\) −16.3059 + 9.41421i −1.15589 + 0.667356i −0.950317 0.311285i \(-0.899241\pi\)
−0.205578 + 0.978641i \(0.565907\pi\)
\(200\) −2.34315 4.05845i −0.165685 0.286976i
\(201\) 11.5300 + 6.65685i 0.813264 + 0.469538i
\(202\) 7.65685 + 7.65685i 0.538734 + 0.538734i
\(203\) 0.881946 + 6.97383i 0.0619005 + 0.489467i
\(204\) −1.65685 1.65685i −0.116003 0.116003i
\(205\) 1.03457 0.277213i 0.0722576 0.0193614i
\(206\) 12.4853 + 21.6251i 0.869891 + 1.50670i
\(207\) −4.12132 7.13834i −0.286452 0.496149i
\(208\) −2.26330 + 0.606451i −0.156932 + 0.0420498i
\(209\) 1.17157 0.0810394
\(210\) −2.58579 6.33386i −0.178436 0.437078i
\(211\) −8.41421 8.41421i −0.579258 0.579258i 0.355441 0.934699i \(-0.384331\pi\)
−0.934699 + 0.355441i \(0.884331\pi\)
\(212\) −4.48112 16.7238i −0.307764 1.14859i
\(213\) −15.3577 4.11509i −1.05229 0.281961i
\(214\) 5.88242 21.9535i 0.402114 1.50071i
\(215\) −10.2692 5.92893i −0.700354 0.404350i
\(216\) −2.00000 2.00000i −0.136083 0.136083i
\(217\) −0.866025 + 6.32843i −0.0587896 + 0.429602i
\(218\) −1.51472 + 1.51472i −0.102590 + 0.102590i
\(219\) −1.03528 3.86370i −0.0699575 0.261085i
\(220\) 1.31178 0.757359i 0.0884405 0.0510612i
\(221\) −0.177625 + 0.662907i −0.0119484 + 0.0445919i
\(222\) 3.46410 + 2.00000i 0.232495 + 0.134231i
\(223\) 20.5563 1.37655 0.688277 0.725448i \(-0.258367\pi\)
0.688277 + 0.725448i \(0.258367\pi\)
\(224\) 14.8284 + 2.02922i 0.990766 + 0.135583i
\(225\) −1.65685 −0.110457
\(226\) −4.77589 2.75736i −0.317687 0.183417i
\(227\) −2.78421 + 10.3908i −0.184794 + 0.689662i 0.809880 + 0.586596i \(0.199532\pi\)
−0.994674 + 0.103067i \(0.967134\pi\)
\(228\) −4.89898 + 2.82843i −0.324443 + 0.187317i
\(229\) 6.31124 + 23.5539i 0.417059 + 1.55648i 0.780676 + 0.624936i \(0.214875\pi\)
−0.363617 + 0.931548i \(0.618458\pi\)
\(230\) −15.0711 + 15.0711i −0.993757 + 0.993757i
\(231\) −1.01461 + 0.414214i −0.0667566 + 0.0272533i
\(232\) 5.31371 5.31371i 0.348862 0.348862i
\(233\) 4.47871 + 2.58579i 0.293410 + 0.169401i 0.639479 0.768809i \(-0.279150\pi\)
−0.346069 + 0.938209i \(0.612484\pi\)
\(234\) −0.214413 + 0.800199i −0.0140166 + 0.0523107i
\(235\) −11.0253 2.95422i −0.719210 0.192712i
\(236\) −1.07206 4.00100i −0.0697854 0.260443i
\(237\) −7.94975 7.94975i −0.516392 0.516392i
\(238\) 2.68629 3.46410i 0.174126 0.224544i
\(239\) 11.0711 0.716128 0.358064 0.933697i \(-0.383437\pi\)
0.358064 + 0.933697i \(0.383437\pi\)
\(240\) −3.65685 + 6.33386i −0.236049 + 0.408849i
\(241\) −11.5711 20.0417i −0.745358 1.29100i −0.950027 0.312167i \(-0.898945\pi\)
0.204669 0.978831i \(-0.434388\pi\)
\(242\) 7.65685 + 13.2621i 0.492201 + 0.852518i
\(243\) −0.965926 + 0.258819i −0.0619642 + 0.0166032i
\(244\) −7.65685 7.65685i −0.490180 0.490180i
\(245\) 11.1490 6.28605i 0.712282 0.401601i
\(246\) 0.585786 + 0.585786i 0.0373484 + 0.0373484i
\(247\) 1.43488 + 0.828427i 0.0912991 + 0.0527116i
\(248\) 5.91359 3.41421i 0.375513 0.216803i
\(249\) 10.7510 6.20711i 0.681318 0.393359i
\(250\) 4.45510 + 16.6267i 0.281766 + 1.05156i
\(251\) −4.05025 + 4.05025i −0.255650 + 0.255650i −0.823282 0.567632i \(-0.807859\pi\)
0.567632 + 0.823282i \(0.307859\pi\)
\(252\) 3.24264 4.18154i 0.204267 0.263412i
\(253\) 2.41421 + 2.41421i 0.151780 + 0.151780i
\(254\) −13.7694 7.94975i −0.863967 0.498812i
\(255\) 1.07107 + 1.85514i 0.0670729 + 0.116174i
\(256\) −8.00000 13.8564i −0.500000 0.866025i
\(257\) 10.1213 17.5306i 0.631351 1.09353i −0.355925 0.934514i \(-0.615834\pi\)
0.987276 0.159017i \(-0.0508324\pi\)
\(258\) 9.17157i 0.570997i
\(259\) −2.89898 + 6.89898i −0.180134 + 0.428682i
\(260\) 2.14214 0.132850
\(261\) −0.687644 2.56632i −0.0425641 0.158851i
\(262\) −7.82449 2.09656i −0.483398 0.129526i
\(263\) −1.31178 + 0.757359i −0.0808881 + 0.0467008i −0.539899 0.841730i \(-0.681537\pi\)
0.459010 + 0.888431i \(0.348204\pi\)
\(264\) 1.01461 + 0.585786i 0.0624450 + 0.0360527i
\(265\) 15.8284i 0.972333i
\(266\) −6.39960 8.42883i −0.392385 0.516804i
\(267\) 11.0000 11.0000i 0.673189 0.673189i
\(268\) 25.7201 6.89168i 1.57111 0.420977i
\(269\) −0.222032 + 0.828633i −0.0135375 + 0.0505227i −0.972364 0.233469i \(-0.924992\pi\)
0.958827 + 0.283992i \(0.0916589\pi\)
\(270\) 1.29289 + 2.23936i 0.0786830 + 0.136283i
\(271\) −12.8640 + 22.2810i −0.781430 + 1.35348i 0.149679 + 0.988735i \(0.452176\pi\)
−0.931109 + 0.364742i \(0.881157\pi\)
\(272\) −4.68629 −0.284148
\(273\) −1.53553 0.210133i −0.0929347 0.0127178i
\(274\) −18.1421 −1.09601
\(275\) 0.662907 0.177625i 0.0399748 0.0107112i
\(276\) −15.9236 4.26670i −0.958486 0.256825i
\(277\) 9.99071 + 2.67700i 0.600284 + 0.160846i 0.546149 0.837688i \(-0.316093\pi\)
0.0541348 + 0.998534i \(0.482760\pi\)
\(278\) −24.9199 + 6.67727i −1.49460 + 0.400476i
\(279\) 2.41421i 0.144535i
\(280\) −12.6143 5.30057i −0.753847 0.316770i
\(281\) 4.82843i 0.288040i −0.989575 0.144020i \(-0.953997\pi\)
0.989575 0.144020i \(-0.0460029\pi\)
\(282\) −2.28497 8.52761i −0.136068 0.507812i
\(283\) −22.6566 6.07082i −1.34680 0.360873i −0.487844 0.872931i \(-0.662217\pi\)
−0.858951 + 0.512058i \(0.828883\pi\)
\(284\) −27.5387 + 15.8995i −1.63412 + 0.943461i
\(285\) 4.99536 1.33850i 0.295899 0.0792860i
\(286\) 0.343146i 0.0202906i
\(287\) −0.949747 + 1.22474i −0.0560618 + 0.0722944i
\(288\) −5.65685 −0.333333
\(289\) 7.81371 13.5337i 0.459630 0.796102i
\(290\) −5.94964 + 3.43503i −0.349375 + 0.201712i
\(291\) −2.15175 + 8.03043i −0.126138 + 0.470752i
\(292\) −6.92820 4.00000i −0.405442 0.234082i
\(293\) −10.9497 + 10.9497i −0.639691 + 0.639691i −0.950479 0.310788i \(-0.899407\pi\)
0.310788 + 0.950479i \(0.399407\pi\)
\(294\) 8.52226 + 5.03698i 0.497028 + 0.293762i
\(295\) 3.78680i 0.220476i
\(296\) 7.72741 2.07055i 0.449146 0.120348i
\(297\) 0.358719 0.207107i 0.0208150 0.0120176i
\(298\) −5.42758 + 20.2560i −0.314411 + 1.17340i
\(299\) 1.24969 + 4.66390i 0.0722714 + 0.269720i
\(300\) −2.34315 + 2.34315i −0.135282 + 0.135282i
\(301\) 17.0229 2.15280i 0.981181 0.124085i
\(302\) −13.5563 −0.780080
\(303\) 3.82843 6.63103i 0.219937 0.380943i
\(304\) −2.92820 + 10.9282i −0.167944 + 0.626775i
\(305\) 4.94975 + 8.57321i 0.283422 + 0.490901i
\(306\) −0.828427 + 1.43488i −0.0473580 + 0.0820265i
\(307\) 6.31371 + 6.31371i 0.360342 + 0.360342i 0.863939 0.503597i \(-0.167990\pi\)
−0.503597 + 0.863939i \(0.667990\pi\)
\(308\) −0.849091 + 2.02066i −0.0483815 + 0.115138i
\(309\) 12.4853 12.4853i 0.710263 0.710263i
\(310\) −6.02993 + 1.61571i −0.342477 + 0.0917664i
\(311\) 10.0081 5.77817i 0.567507 0.327650i −0.188646 0.982045i \(-0.560410\pi\)
0.756153 + 0.654395i \(0.227077\pi\)
\(312\) 0.828427 + 1.43488i 0.0469005 + 0.0812340i
\(313\) 8.51167 + 4.91421i 0.481108 + 0.277768i 0.720878 0.693062i \(-0.243739\pi\)
−0.239770 + 0.970830i \(0.577072\pi\)
\(314\) −20.9706 + 20.9706i −1.18344 + 1.18344i
\(315\) −3.85287 + 2.92530i −0.217085 + 0.164822i
\(316\) −22.4853 −1.26490
\(317\) 10.9566 2.93582i 0.615386 0.164892i 0.0623567 0.998054i \(-0.480138\pi\)
0.553029 + 0.833162i \(0.313472\pi\)
\(318\) −10.6024 + 6.12132i −0.594555 + 0.343267i
\(319\) 0.550253 + 0.953065i 0.0308082 + 0.0533614i
\(320\) 3.78585 + 14.1290i 0.211636 + 0.789835i
\(321\) −16.0711 −0.897000
\(322\) 4.18154 30.5563i 0.233028 1.70284i
\(323\) 2.34315 + 2.34315i 0.130376 + 0.130376i
\(324\) −1.00000 + 1.73205i −0.0555556 + 0.0962250i
\(325\) 0.937492 + 0.251200i 0.0520027 + 0.0139341i
\(326\) 10.5967 + 2.83939i 0.586900 + 0.157259i
\(327\) 1.31178 + 0.757359i 0.0725419 + 0.0418821i
\(328\) 1.65685 0.0914845
\(329\) 15.2913 6.24264i 0.843036 0.344168i
\(330\) −0.757359 0.757359i −0.0416913 0.0416913i
\(331\) 2.07055 + 7.72741i 0.113808 + 0.424737i 0.999195 0.0401178i \(-0.0127733\pi\)
−0.885387 + 0.464854i \(0.846107\pi\)
\(332\) 6.42607 23.9824i 0.352676 1.31621i
\(333\) 0.732051 2.73205i 0.0401161 0.149715i
\(334\) 4.24264 7.34847i 0.232147 0.402090i
\(335\) −24.3431 −1.33001
\(336\) −1.32780 10.4994i −0.0724377 0.572788i
\(337\) −18.6569 −1.01630 −0.508152 0.861268i \(-0.669671\pi\)
−0.508152 + 0.861268i \(0.669671\pi\)
\(338\) −8.94975 + 15.5014i −0.486802 + 0.843166i
\(339\) −1.00926 + 3.76662i −0.0548157 + 0.204575i
\(340\) 4.13829 + 1.10885i 0.224430 + 0.0601359i
\(341\) 0.258819 + 0.965926i 0.0140158 + 0.0523078i
\(342\) 2.82843 + 2.82843i 0.152944 + 0.152944i
\(343\) −7.34847 + 17.0000i −0.396780 + 0.917914i
\(344\) −12.9706 12.9706i −0.699326 0.699326i
\(345\) 13.0519 + 7.53553i 0.702692 + 0.405700i
\(346\) 23.1822 + 6.21166i 1.24628 + 0.333941i
\(347\) −23.6510 6.33726i −1.26965 0.340202i −0.439753 0.898119i \(-0.644934\pi\)
−0.829897 + 0.557917i \(0.811601\pi\)
\(348\) −4.60181 2.65685i −0.246683 0.142422i
\(349\) −3.41421 3.41421i −0.182759 0.182759i 0.609798 0.792557i \(-0.291251\pi\)
−0.792557 + 0.609798i \(0.791251\pi\)
\(350\) −4.89898 3.79899i −0.261861 0.203065i
\(351\) 0.585786 0.0312670
\(352\) 2.26330 0.606451i 0.120635 0.0323239i
\(353\) −9.65685 16.7262i −0.513982 0.890244i −0.999868 0.0162216i \(-0.994836\pi\)
0.485886 0.874022i \(-0.338497\pi\)
\(354\) −2.53653 + 1.46447i −0.134815 + 0.0778355i
\(355\) 28.0805 7.52415i 1.49036 0.399340i
\(356\) 31.1127i 1.64897i
\(357\) −2.85765 1.20080i −0.151243 0.0635529i
\(358\) 18.6274 18.6274i 0.984490 0.984490i
\(359\) 3.16693 + 1.82843i 0.167144 + 0.0965007i 0.581239 0.813733i \(-0.302568\pi\)
−0.414094 + 0.910234i \(0.635902\pi\)
\(360\) 4.99536 + 1.33850i 0.263278 + 0.0705452i
\(361\) −9.52628 + 5.50000i −0.501383 + 0.289474i
\(362\) 30.3840 8.14137i 1.59695 0.427901i
\(363\) 7.65685 7.65685i 0.401881 0.401881i
\(364\) −2.46875 + 1.87440i −0.129397 + 0.0982453i
\(365\) 5.17157 + 5.17157i 0.270692 + 0.270692i
\(366\) −3.82843 + 6.63103i −0.200115 + 0.346610i
\(367\) −5.69239 9.85951i −0.297140 0.514662i 0.678340 0.734748i \(-0.262700\pi\)
−0.975480 + 0.220086i \(0.929366\pi\)
\(368\) −28.5533 + 16.4853i −1.48845 + 0.859355i
\(369\) 0.292893 0.507306i 0.0152474 0.0264093i
\(370\) −7.31371 −0.380222
\(371\) −13.8501 18.2418i −0.719062 0.947066i
\(372\) −3.41421 3.41421i −0.177019 0.177019i
\(373\) 5.15037 + 19.2214i 0.266676 + 0.995248i 0.961217 + 0.275795i \(0.0889410\pi\)
−0.694541 + 0.719454i \(0.744392\pi\)
\(374\) 0.177625 0.662907i 0.00918479 0.0342781i
\(375\) 10.5409 6.08579i 0.544329 0.314269i
\(376\) −15.2913 8.82843i −0.788588 0.455291i
\(377\) 1.55635i 0.0801561i
\(378\) −3.44949 1.44949i −0.177423 0.0745537i
\(379\) −4.65685 + 4.65685i −0.239207 + 0.239207i −0.816522 0.577315i \(-0.804100\pi\)
0.577315 + 0.816522i \(0.304100\pi\)
\(380\) 5.17157 8.95743i 0.265296 0.459506i
\(381\) −2.90981 + 10.8596i −0.149074 + 0.556352i
\(382\) 23.6544 13.6569i 1.21026 0.698745i
\(383\) 14.5355 25.1763i 0.742731 1.28645i −0.208516 0.978019i \(-0.566863\pi\)
0.951247 0.308429i \(-0.0998032\pi\)
\(384\) −8.00000 + 8.00000i −0.408248 + 0.408248i
\(385\) 1.22792 1.58346i 0.0625807 0.0807008i
\(386\) 9.89949i 0.503871i
\(387\) −6.26430 + 1.67851i −0.318432 + 0.0853237i
\(388\) 8.31371 + 14.3998i 0.422065 + 0.731037i
\(389\) −3.66954 0.983251i −0.186053 0.0498528i 0.164589 0.986362i \(-0.447370\pi\)
−0.350643 + 0.936509i \(0.614037\pi\)
\(390\) −0.392038 1.46311i −0.0198516 0.0740872i
\(391\) 9.65685i 0.488368i
\(392\) 19.1757 4.92893i 0.968517 0.248949i
\(393\) 5.72792i 0.288935i
\(394\) −6.12701 + 1.64173i −0.308674 + 0.0827090i
\(395\) 19.8559 + 5.32037i 0.999059 + 0.267697i
\(396\) 0.214413 0.800199i 0.0107746 0.0402115i
\(397\) 31.8471 8.53341i 1.59836 0.428280i 0.653814 0.756655i \(-0.273168\pi\)
0.944547 + 0.328376i \(0.106501\pi\)
\(398\) 26.6274 1.33471
\(399\) −4.58579 + 5.91359i −0.229576 + 0.296050i
\(400\) 6.62742i 0.331371i
\(401\) 12.0000 20.7846i 0.599251 1.03793i −0.393680 0.919247i \(-0.628798\pi\)
0.992932 0.118686i \(-0.0378683\pi\)
\(402\) −9.41421 16.3059i −0.469538 0.813264i
\(403\) −0.366025 + 1.36603i −0.0182330 + 0.0680466i
\(404\) −3.96348 14.7919i −0.197190 0.735925i
\(405\) 1.29289 1.29289i 0.0642444 0.0642444i
\(406\) 3.85108 9.16479i 0.191126 0.454841i
\(407\) 1.17157i 0.0580727i
\(408\) 0.857651 + 3.20080i 0.0424600 + 0.158463i
\(409\) −18.4837 + 10.6716i −0.913960 + 0.527675i −0.881703 0.471804i \(-0.843603\pi\)
−0.0322572 + 0.999480i \(0.510270\pi\)
\(410\) −1.46311 0.392038i −0.0722576 0.0193614i
\(411\) 3.32024 + 12.3913i 0.163775 + 0.611218i
\(412\) 35.3137i 1.73978i
\(413\) −3.31350 4.36417i −0.163047 0.214747i
\(414\) 11.6569i 0.572903i
\(415\) −11.3492 + 19.6575i −0.557112 + 0.964947i
\(416\) 3.20080 + 0.857651i 0.156932 + 0.0420498i
\(417\) 9.12132 + 15.7986i 0.446673 + 0.773660i
\(418\) −1.43488 0.828427i −0.0701822 0.0405197i
\(419\) 25.7990 + 25.7990i 1.26036 + 1.26036i 0.950917 + 0.309446i \(0.100144\pi\)
0.309446 + 0.950917i \(0.399856\pi\)
\(420\) −1.31178 + 9.58579i −0.0640085 + 0.467738i
\(421\) 15.4853 15.4853i 0.754706 0.754706i −0.220647 0.975354i \(-0.570817\pi\)
0.975354 + 0.220647i \(0.0708170\pi\)
\(422\) 4.35552 + 16.2550i 0.212023 + 0.791282i
\(423\) −5.40629 + 3.12132i −0.262863 + 0.151764i
\(424\) −6.33726 + 23.6510i −0.307764 + 1.14859i
\(425\) 1.68106 + 0.970563i 0.0815436 + 0.0470792i
\(426\) 15.8995 + 15.8995i 0.770333 + 0.770333i
\(427\) −13.2061 5.54927i −0.639089 0.268548i
\(428\) −22.7279 + 22.7279i −1.09860 + 1.09860i
\(429\) −0.234373 + 0.0628000i −0.0113156 + 0.00303201i
\(430\) 8.38478 + 14.5229i 0.404350 + 0.700354i
\(431\) −7.19239 12.4576i −0.346445 0.600061i 0.639170 0.769065i \(-0.279278\pi\)
−0.985615 + 0.169005i \(0.945945\pi\)
\(432\) 1.03528 + 3.86370i 0.0498097 + 0.185893i
\(433\) −16.9706 −0.815553 −0.407777 0.913082i \(-0.633696\pi\)
−0.407777 + 0.913082i \(0.633696\pi\)
\(434\) 5.53553 7.13834i 0.265714 0.342651i
\(435\) 3.43503 + 3.43503i 0.164697 + 0.164697i
\(436\) 2.92621 0.784076i 0.140140 0.0375504i
\(437\) 22.5193 + 6.03403i 1.07724 + 0.288647i
\(438\) −1.46410 + 5.46410i −0.0699575 + 0.261085i
\(439\) −22.9985 13.2782i −1.09766 0.633733i −0.162053 0.986782i \(-0.551811\pi\)
−0.935605 + 0.353049i \(0.885145\pi\)
\(440\) −2.14214 −0.102122
\(441\) 1.88064 6.74264i 0.0895542 0.321078i
\(442\) 0.686292 0.686292i 0.0326436 0.0326436i
\(443\) 2.48098 + 9.25916i 0.117875 + 0.439916i 0.999486 0.0320612i \(-0.0102072\pi\)
−0.881611 + 0.471977i \(0.843540\pi\)
\(444\) −2.82843 4.89898i −0.134231 0.232495i
\(445\) −7.36176 + 27.4745i −0.348981 + 1.30241i
\(446\) −25.1763 14.5355i −1.19213 0.688277i
\(447\) 14.8284 0.701361
\(448\) −16.7262 12.9706i −0.790237 0.612801i
\(449\) −10.2426 −0.483380 −0.241690 0.970354i \(-0.577702\pi\)
−0.241690 + 0.970354i \(0.577702\pi\)
\(450\) 2.02922 + 1.17157i 0.0956585 + 0.0552285i
\(451\) −0.0628000 + 0.234373i −0.00295714 + 0.0110362i
\(452\) 3.89949 + 6.75412i 0.183417 + 0.317687i
\(453\) 2.48098 + 9.25916i 0.116567 + 0.435033i
\(454\) 10.7574 10.7574i 0.504868 0.504868i
\(455\) 2.62357 1.07107i 0.122995 0.0502124i
\(456\) 8.00000 0.374634
\(457\) −18.7299 10.8137i −0.876147 0.505844i −0.00676121 0.999977i \(-0.502152\pi\)
−0.869386 + 0.494133i \(0.835486\pi\)
\(458\) 8.92545 33.3102i 0.417059 1.55648i
\(459\) 1.13165 + 0.303225i 0.0528210 + 0.0141533i
\(460\) 29.1151 7.80136i 1.35750 0.363740i
\(461\) 8.00000 + 8.00000i 0.372597 + 0.372597i 0.868422 0.495825i \(-0.165134\pi\)
−0.495825 + 0.868422i \(0.665134\pi\)
\(462\) 1.53553 + 0.210133i 0.0714395 + 0.00977627i
\(463\) −3.79899 −0.176554 −0.0882770 0.996096i \(-0.528136\pi\)
−0.0882770 + 0.996096i \(0.528136\pi\)
\(464\) −10.2653 + 2.75058i −0.476554 + 0.127692i
\(465\) 2.20711 + 3.82282i 0.102352 + 0.177279i
\(466\) −3.65685 6.33386i −0.169401 0.293410i
\(467\) 9.79655 2.62498i 0.453330 0.121469i −0.0249270 0.999689i \(-0.507935\pi\)
0.478257 + 0.878220i \(0.341269\pi\)
\(468\) 0.828427 0.828427i 0.0382941 0.0382941i
\(469\) 28.0547 21.3006i 1.29545 0.983571i
\(470\) 11.4142 + 11.4142i 0.526498 + 0.526498i
\(471\) 18.1610 + 10.4853i 0.836817 + 0.483136i
\(472\) −1.51613 + 5.65826i −0.0697854 + 0.260443i
\(473\) 2.32640 1.34315i 0.106968 0.0617579i
\(474\) 4.11509 + 15.3577i 0.189012 + 0.705404i
\(475\) 3.31371 3.31371i 0.152043 0.152043i
\(476\) −5.73951 + 2.34315i −0.263070 + 0.107398i
\(477\) 6.12132 + 6.12132i 0.280276 + 0.280276i
\(478\) −13.5592 7.82843i −0.620185 0.358064i
\(479\) 7.58579 + 13.1390i 0.346603 + 0.600335i 0.985644 0.168839i \(-0.0540016\pi\)
−0.639040 + 0.769173i \(0.720668\pi\)
\(480\) 8.95743 5.17157i 0.408849 0.236049i
\(481\) −0.828427 + 1.43488i −0.0377730 + 0.0654248i
\(482\) 32.7279i 1.49072i
\(483\) −21.6356 + 2.73615i −0.984456 + 0.124499i
\(484\) 21.6569i 0.984402i
\(485\) −3.93431 14.6830i −0.178648 0.666723i
\(486\) 1.36603 + 0.366025i 0.0619642 + 0.0166032i
\(487\) −0.481813 + 0.278175i −0.0218330 + 0.0126053i −0.510877 0.859654i \(-0.670679\pi\)
0.489044 + 0.872259i \(0.337346\pi\)
\(488\) 3.96348 + 14.7919i 0.179418 + 0.669598i
\(489\) 7.75736i 0.350800i
\(490\) −18.0996 0.184709i −0.817655 0.00834429i
\(491\) 15.9497 15.9497i 0.719802 0.719802i −0.248762 0.968565i \(-0.580024\pi\)
0.968565 + 0.248762i \(0.0800239\pi\)
\(492\) −0.303225 1.13165i −0.0136705 0.0510188i
\(493\) −0.805626 + 3.00664i −0.0362836 + 0.135412i
\(494\) −1.17157 2.02922i −0.0527116 0.0912991i
\(495\) −0.378680 + 0.655892i −0.0170204 + 0.0294802i
\(496\) −9.65685 −0.433606
\(497\) −25.7782 + 33.2422i −1.15631 + 1.49112i
\(498\) −17.5563 −0.786719
\(499\) −3.96078 + 1.06129i −0.177309 + 0.0475098i −0.346381 0.938094i \(-0.612590\pi\)
0.169072 + 0.985604i \(0.445923\pi\)
\(500\) 6.30047 23.5137i 0.281766 1.05156i
\(501\) −5.79555 1.55291i −0.258926 0.0693791i
\(502\) 7.82449 2.09656i 0.349224 0.0935743i
\(503\) 40.4853i 1.80515i −0.430533 0.902575i \(-0.641674\pi\)
0.430533 0.902575i \(-0.358326\pi\)
\(504\) −6.92820 + 2.82843i −0.308607 + 0.125988i
\(505\) 14.0000i 0.622992i
\(506\) −1.24969 4.66390i −0.0555554 0.207336i
\(507\) 12.2256 + 3.27583i 0.542957 + 0.145485i
\(508\) 11.2426 + 19.4728i 0.498812 + 0.863967i
\(509\) 2.42903 0.650857i 0.107665 0.0288487i −0.204584 0.978849i \(-0.565584\pi\)
0.312249 + 0.950000i \(0.398918\pi\)
\(510\) 3.02944i 0.134146i
\(511\) −10.4853 1.43488i −0.463842 0.0634753i
\(512\) 22.6274i 1.00000i
\(513\) 1.41421 2.44949i 0.0624391 0.108148i
\(514\) −24.7921 + 14.3137i −1.09353 + 0.631351i
\(515\) −8.35578 + 31.1842i −0.368200 + 1.37414i
\(516\) −6.48528 + 11.2328i −0.285499 + 0.494498i
\(517\) 1.82843 1.82843i 0.0804141 0.0804141i
\(518\) 8.42883 6.39960i 0.370341 0.281182i
\(519\) 16.9706i 0.744925i
\(520\) −2.62357 1.51472i −0.115051 0.0664248i
\(521\) 0.297173 0.171573i 0.0130194 0.00751674i −0.493476 0.869759i \(-0.664274\pi\)
0.506496 + 0.862243i \(0.330941\pi\)
\(522\) −0.972476 + 3.62933i −0.0425641 + 0.158851i
\(523\) −0.920451 3.43517i −0.0402485 0.150209i 0.942877 0.333140i \(-0.108108\pi\)
−0.983126 + 0.182931i \(0.941442\pi\)
\(524\) 8.10051 + 8.10051i 0.353872 + 0.353872i
\(525\) −1.69818 + 4.04133i −0.0741148 + 0.176378i
\(526\) 2.14214 0.0934016
\(527\) −1.41421 + 2.44949i −0.0616041 + 0.106701i
\(528\) −0.828427 1.43488i −0.0360527 0.0624450i
\(529\) 22.4706 + 38.9202i 0.976981 + 1.69218i
\(530\) 11.1924 19.3858i 0.486166 0.842065i
\(531\) 1.46447 + 1.46447i 0.0635524 + 0.0635524i
\(532\) 1.87780 + 14.8484i 0.0814129 + 0.643758i
\(533\) −0.242641 + 0.242641i −0.0105099 + 0.0105099i
\(534\) −21.2504 + 5.69402i −0.919593 + 0.246404i
\(535\) 25.4480 14.6924i 1.10021 0.635207i
\(536\) −36.3737 9.74631i −1.57111 0.420977i
\(537\) −16.1318 9.31371i −0.696139 0.401916i
\(538\) 0.857864 0.857864i 0.0369852 0.0369852i
\(539\) −0.0295882 + 2.89934i −0.00127446 + 0.124884i
\(540\) 3.65685i 0.157366i
\(541\) −15.1234 + 4.05229i −0.650204 + 0.174222i −0.568821 0.822461i \(-0.692600\pi\)
−0.0813829 + 0.996683i \(0.525934\pi\)
\(542\) 31.5101 18.1924i 1.35348 0.781430i
\(543\) −11.1213 19.2627i −0.477262 0.826641i
\(544\) 5.73951 + 3.31371i 0.246080 + 0.142074i
\(545\) −2.76955 −0.118635
\(546\) 1.73205 + 1.34315i 0.0741249 + 0.0574813i
\(547\) −8.82843 8.82843i −0.377476 0.377476i 0.492715 0.870191i \(-0.336005\pi\)
−0.870191 + 0.492715i \(0.836005\pi\)
\(548\) 22.2195 + 12.8284i 0.949169 + 0.548003i
\(549\) 5.22973 + 1.40130i 0.223199 + 0.0598061i
\(550\) −0.937492 0.251200i −0.0399748 0.0107112i
\(551\) 6.50794 + 3.75736i 0.277247 + 0.160069i
\(552\) 16.4853 + 16.4853i 0.701660 + 0.701660i
\(553\) −27.5387 + 11.2426i −1.17107 + 0.478086i
\(554\) −10.3431 10.3431i −0.439438 0.439438i
\(555\) 1.33850 + 4.99536i 0.0568162 + 0.212041i
\(556\) 35.2421 + 9.44309i 1.49460 + 0.400476i
\(557\) 6.20404 23.1538i 0.262874 0.981057i −0.700666 0.713490i \(-0.747113\pi\)
0.963539 0.267568i \(-0.0862198\pi\)
\(558\) −1.70711 + 2.95680i −0.0722676 + 0.125171i
\(559\) 3.79899 0.160680
\(560\) 11.7012 + 15.4115i 0.494466 + 0.651254i
\(561\) −0.485281 −0.0204886
\(562\) −3.41421 + 5.91359i −0.144020 + 0.249450i
\(563\) −1.53452 + 5.72691i −0.0646723 + 0.241360i −0.990694 0.136111i \(-0.956540\pi\)
0.926021 + 0.377471i \(0.123206\pi\)
\(564\) −3.23143 + 12.0599i −0.136068 + 0.507812i
\(565\) −1.84536 6.88700i −0.0776351 0.289738i
\(566\) 23.4558 + 23.4558i 0.985923 + 0.985923i
\(567\) −0.358719 + 2.62132i −0.0150648 + 0.110085i
\(568\) 44.9706 1.88692
\(569\) 1.01461 + 0.585786i 0.0425347 + 0.0245574i 0.521117 0.853486i \(-0.325516\pi\)
−0.478582 + 0.878043i \(0.658849\pi\)
\(570\) −7.06450 1.89293i −0.295899 0.0792860i
\(571\) −40.6091 10.8812i −1.69944 0.455363i −0.726640 0.687019i \(-0.758919\pi\)
−0.972798 + 0.231656i \(0.925586\pi\)
\(572\) −0.242641 + 0.420266i −0.0101453 + 0.0175722i
\(573\) −13.6569 13.6569i −0.570523 0.570523i
\(574\) 2.02922 0.828427i 0.0846982 0.0345779i
\(575\) 13.6569 0.569530
\(576\) 6.92820 + 4.00000i 0.288675 + 0.166667i
\(577\) −18.7426 32.4632i −0.780266 1.35146i −0.931786 0.363007i \(-0.881750\pi\)
0.151520 0.988454i \(-0.451583\pi\)
\(578\) −19.1396 + 11.0503i −0.796102 + 0.459630i
\(579\) −6.76148 + 1.81173i −0.280998 + 0.0752931i
\(580\) 9.71573 0.403424
\(581\) −4.12091 32.5854i −0.170964 1.35187i
\(582\) 8.31371 8.31371i 0.344614 0.344614i
\(583\) −3.10538 1.79289i −0.128612 0.0742541i
\(584\) 5.65685 + 9.79796i 0.234082 + 0.405442i
\(585\) −0.927572 + 0.535534i −0.0383504 + 0.0221416i
\(586\) 21.1533 5.66801i 0.873834 0.234143i
\(587\) 7.12132 7.12132i 0.293928 0.293928i −0.544702 0.838630i \(-0.683357\pi\)
0.838630 + 0.544702i \(0.183357\pi\)
\(588\) −6.87591 12.1952i −0.283558 0.502920i
\(589\) 4.82843 + 4.82843i 0.198952 + 0.198952i
\(590\) 2.67767 4.63786i 0.110238 0.190938i
\(591\) 2.24264 + 3.88437i 0.0922499 + 0.159782i
\(592\) −10.9282 2.92820i −0.449146 0.120348i
\(593\) −9.70711 + 16.8132i −0.398623 + 0.690435i −0.993556 0.113340i \(-0.963845\pi\)
0.594933 + 0.803775i \(0.297178\pi\)
\(594\) −0.585786 −0.0240351
\(595\) 5.62277 0.711085i 0.230511 0.0291516i
\(596\) 20.9706 20.9706i 0.858988 0.858988i
\(597\) −4.87316 18.1869i −0.199445 0.744339i
\(598\) 1.76733 6.59575i 0.0722714 0.269720i
\(599\) 35.7787 20.6569i 1.46188 0.844016i 0.462781 0.886473i \(-0.346852\pi\)
0.999098 + 0.0424567i \(0.0135184\pi\)
\(600\) 4.52661 1.21290i 0.184798 0.0495165i
\(601\) 14.6569i 0.597866i −0.954274 0.298933i \(-0.903369\pi\)
0.954274 0.298933i \(-0.0966306\pi\)
\(602\) −22.3709 9.40035i −0.911770 0.383130i
\(603\) −9.41421 + 9.41421i −0.383376 + 0.383376i
\(604\) 16.6031 + 9.58579i 0.675569 + 0.390040i
\(605\) −5.12436 + 19.1244i −0.208335 + 0.777516i
\(606\) −9.37769 + 5.41421i −0.380943 + 0.219937i
\(607\) −15.0355 + 26.0423i −0.610273 + 1.05702i 0.380921 + 0.924608i \(0.375607\pi\)
−0.991194 + 0.132417i \(0.957726\pi\)
\(608\) 11.3137 11.3137i 0.458831 0.458831i
\(609\) −6.96447 0.953065i −0.282214 0.0386202i
\(610\) 14.0000i 0.566843i
\(611\) 3.53225 0.946464i 0.142900 0.0382898i
\(612\) 2.02922 1.17157i 0.0820265 0.0473580i
\(613\) −19.8843 5.32799i −0.803121 0.215196i −0.166167 0.986098i \(-0.553139\pi\)
−0.636954 + 0.770902i \(0.719806\pi\)
\(614\) −3.26822 12.1971i −0.131894 0.492237i
\(615\) 1.07107i 0.0431896i
\(616\) 2.46875 1.87440i 0.0994686 0.0755217i
\(617\) 23.7574i 0.956435i 0.878241 + 0.478218i \(0.158717\pi\)
−0.878241 + 0.478218i \(0.841283\pi\)
\(618\) −24.1197 + 6.46286i −0.970237 + 0.259974i
\(619\) 27.8863 + 7.47212i 1.12085 + 0.300330i 0.771226 0.636562i \(-0.219644\pi\)
0.349620 + 0.936891i \(0.386311\pi\)
\(620\) 8.52761 + 2.28497i 0.342477 + 0.0917664i
\(621\) 7.96178 2.13335i 0.319495 0.0856085i
\(622\) −16.3431 −0.655300
\(623\) −15.5563 38.1051i −0.623252 1.52665i
\(624\) 2.34315i 0.0938009i
\(625\) −6.98528 + 12.0989i −0.279411 + 0.483954i
\(626\) −6.94975 12.0373i −0.277768 0.481108i
\(627\) −0.303225 + 1.13165i −0.0121097 + 0.0451938i
\(628\) 40.5120 10.8552i 1.61661 0.433168i
\(629\) −2.34315 + 2.34315i −0.0934273 + 0.0934273i
\(630\) 6.78729 0.858355i 0.270412 0.0341977i
\(631\) 17.2426i 0.686419i −0.939259 0.343209i \(-0.888486\pi\)
0.939259 0.343209i \(-0.111514\pi\)
\(632\) 27.5387 + 15.8995i 1.09543 + 0.632448i
\(633\) 10.3053 5.94975i 0.409598 0.236481i
\(634\) −15.4950 4.15188i −0.615386 0.164892i
\(635\) −5.32037 19.8559i −0.211133 0.787958i
\(636\) 17.3137 0.686533
\(637\) −2.08638 + 3.53003i −0.0826655 + 0.139865i
\(638\) 1.55635i 0.0616165i
\(639\) 7.94975 13.7694i 0.314487 0.544708i
\(640\) 5.35401 19.9814i 0.211636 0.789835i
\(641\) −12.2635 21.2409i −0.484377 0.838966i 0.515462 0.856913i \(-0.327620\pi\)
−0.999839 + 0.0179465i \(0.994287\pi\)
\(642\) 19.6830 + 11.3640i 0.776824 + 0.448500i
\(643\) 31.0711 + 31.0711i 1.22532 + 1.22532i 0.965714 + 0.259610i \(0.0835939\pi\)
0.259610 + 0.965714i \(0.416406\pi\)
\(644\) −26.7279 + 34.4669i −1.05323 + 1.35819i
\(645\) 8.38478 8.38478i 0.330150 0.330150i
\(646\) −1.21290 4.52661i −0.0477210 0.178097i
\(647\) 7.43551 4.29289i 0.292320 0.168771i −0.346668 0.937988i \(-0.612687\pi\)
0.638988 + 0.769217i \(0.279353\pi\)
\(648\) 2.44949 1.41421i 0.0962250 0.0555556i
\(649\) −0.742932 0.428932i −0.0291626 0.0168371i
\(650\) −0.970563 0.970563i −0.0380686 0.0380686i
\(651\) −5.88865 2.47443i −0.230794 0.0969807i
\(652\) −10.9706 10.9706i −0.429640 0.429640i
\(653\) −0.497180 + 0.133219i −0.0194562 + 0.00521326i −0.268534 0.963270i \(-0.586539\pi\)
0.249078 + 0.968483i \(0.419872\pi\)
\(654\) −1.07107 1.85514i −0.0418821 0.0725419i
\(655\) −5.23654 9.06996i −0.204609 0.354393i
\(656\) −2.02922 1.17157i −0.0792279 0.0457422i
\(657\) 4.00000 0.156055
\(658\) −23.1421 3.16693i −0.902174 0.123460i
\(659\) −18.5858 18.5858i −0.723999 0.723999i 0.245418 0.969417i \(-0.421075\pi\)
−0.969417 + 0.245418i \(0.921075\pi\)
\(660\) 0.392038 + 1.46311i 0.0152601 + 0.0569513i
\(661\) 11.2597 + 3.01702i 0.437950 + 0.117348i 0.471056 0.882104i \(-0.343873\pi\)
−0.0331057 + 0.999452i \(0.510540\pi\)
\(662\) 2.92820 10.9282i 0.113808 0.424737i
\(663\) −0.594346 0.343146i −0.0230825 0.0133267i
\(664\) −24.8284 + 24.8284i −0.963530 + 0.963530i
\(665\) 1.85514 13.5563i 0.0719394 0.525693i
\(666\) −2.82843 + 2.82843i −0.109599 + 0.109599i
\(667\) 5.66801 + 21.1533i 0.219466 + 0.819059i
\(668\) −10.3923 + 6.00000i −0.402090 + 0.232147i
\(669\) −5.32037 + 19.8559i −0.205698 + 0.767674i
\(670\) 29.8141 + 17.2132i 1.15182 + 0.665004i
\(671\) −2.24264 −0.0865762
\(672\) −5.79796 + 13.7980i −0.223661 + 0.532268i
\(673\) −30.9411 −1.19269 −0.596346 0.802727i \(-0.703382\pi\)
−0.596346 + 0.802727i \(0.703382\pi\)
\(674\) 22.8499 + 13.1924i 0.880145 + 0.508152i
\(675\) 0.428825 1.60040i 0.0165055 0.0615994i
\(676\) 21.9223 12.6569i 0.843166 0.486802i
\(677\) 11.0404 + 41.2034i 0.424317 + 1.58357i 0.765409 + 0.643544i \(0.222537\pi\)
−0.341092 + 0.940030i \(0.610797\pi\)
\(678\) 3.89949 3.89949i 0.149759 0.149759i
\(679\) 17.3821 + 13.4792i 0.667062 + 0.517284i
\(680\) −4.28427 4.28427i −0.164294 0.164294i
\(681\) −9.31615 5.37868i −0.356996 0.206111i
\(682\) 0.366025 1.36603i 0.0140158 0.0523078i
\(683\) −15.8549 4.24831i −0.606671 0.162557i −0.0576100 0.998339i \(-0.518348\pi\)
−0.549061 + 0.835782i \(0.685015\pi\)
\(684\) −1.46410 5.46410i −0.0559813 0.208925i
\(685\) −16.5858 16.5858i −0.633710 0.633710i
\(686\) 21.0208 15.6245i 0.802578 0.596547i
\(687\) −24.3848 −0.930337
\(688\) 6.71406 + 25.0572i 0.255971 + 0.955297i
\(689\) −2.53553 4.39167i −0.0965961 0.167309i
\(690\) −10.6569 18.4582i −0.405700 0.702692i
\(691\) 39.3402 10.5412i 1.49657 0.401005i 0.584620 0.811307i \(-0.301243\pi\)
0.911950 + 0.410302i \(0.134577\pi\)
\(692\) −24.0000 24.0000i −0.912343 0.912343i
\(693\) −0.137499 1.08725i −0.00522314 0.0413011i
\(694\) 24.4853 + 24.4853i 0.929449 + 0.929449i
\(695\) −28.8866 16.6777i −1.09573 0.632620i
\(696\) 3.75736 + 6.50794i 0.142422 + 0.246683i
\(697\) −0.594346 + 0.343146i −0.0225125 + 0.0129976i
\(698\) 1.76733 + 6.59575i 0.0668943 + 0.249653i
\(699\) −3.65685 + 3.65685i −0.138315 + 0.138315i
\(700\) 3.31371 + 8.11689i 0.125246 + 0.306790i
\(701\) −15.8787 15.8787i −0.599729 0.599729i 0.340511 0.940241i \(-0.389400\pi\)
−0.940241 + 0.340511i \(0.889400\pi\)
\(702\) −0.717439 0.414214i −0.0270780 0.0156335i
\(703\) 4.00000 + 6.92820i 0.150863 + 0.261302i
\(704\) −3.20080 0.857651i −0.120635 0.0323239i
\(705\) 5.70711 9.88500i 0.214942 0.372291i
\(706\) 27.3137i 1.02796i
\(707\) −12.2502 16.1346i −0.460716 0.606803i
\(708\) 4.14214 0.155671
\(709\) 1.52690 + 5.69847i 0.0573440 + 0.214011i 0.988652 0.150221i \(-0.0479984\pi\)
−0.931309 + 0.364231i \(0.881332\pi\)
\(710\) −39.7118 10.6407i −1.49036 0.399340i
\(711\) 9.73641 5.62132i 0.365144 0.210816i
\(712\) −22.0000 + 38.1051i −0.824485 + 1.42805i
\(713\) 19.8995i 0.745242i
\(714\) 2.65080 + 3.49133i 0.0992038 + 0.130660i
\(715\) 0.313708 0.313708i 0.0117320 0.0117320i
\(716\) −35.9854 + 9.64226i −1.34484 + 0.360348i
\(717\) −2.86540 + 10.6938i −0.107010 + 0.399368i
\(718\) −2.58579 4.47871i −0.0965007 0.167144i
\(719\) 10.4350 18.0740i 0.389161 0.674046i −0.603176 0.797608i \(-0.706098\pi\)
0.992337 + 0.123562i \(0.0394317\pi\)
\(720\) −5.17157 5.17157i −0.192733 0.192733i
\(721\) −17.6569 43.2503i −0.657576 1.61072i
\(722\) 15.5563 0.578947
\(723\) 22.3536 5.98963i 0.831339 0.222757i
\(724\) −42.9695 11.5136i −1.59695 0.427901i
\(725\) 4.25203 + 1.13933i 0.157916 + 0.0423135i
\(726\) −14.7919 + 3.96348i −0.548979 + 0.147099i
\(727\) 16.5563i 0.614041i −0.951703 0.307021i \(-0.900668\pi\)
0.951703 0.307021i \(-0.0993320\pi\)
\(728\) 4.34898 0.549995i 0.161184 0.0203842i
\(729\) 1.00000i 0.0370370i
\(730\) −2.67700 9.99071i −0.0990803 0.369773i
\(731\) 7.33908 + 1.96650i 0.271446 + 0.0727337i
\(732\) 9.37769 5.41421i 0.346610 0.200115i
\(733\) −40.5689 + 10.8704i −1.49845 + 0.401507i −0.912579 0.408900i \(-0.865912\pi\)
−0.585867 + 0.810407i \(0.699246\pi\)
\(734\) 16.1005i 0.594280i
\(735\) 3.18629 + 12.3960i 0.117528 + 0.457235i
\(736\) 46.6274 1.71871
\(737\) 2.75736 4.77589i 0.101569 0.175922i
\(738\) −0.717439 + 0.414214i −0.0264093 + 0.0152474i
\(739\) −10.0235 + 37.4083i −0.368721 + 1.37609i 0.493584 + 0.869698i \(0.335686\pi\)
−0.862305 + 0.506389i \(0.830980\pi\)
\(740\) 8.95743 + 5.17157i 0.329282 + 0.190111i
\(741\) −1.17157 + 1.17157i −0.0430388 + 0.0430388i
\(742\) 4.06396 + 32.1350i 0.149193 + 1.17971i
\(743\) 17.3137i 0.635178i 0.948228 + 0.317589i \(0.102873\pi\)
−0.948228 + 0.317589i \(0.897127\pi\)
\(744\) 1.76733 + 6.59575i 0.0647934 + 0.241812i
\(745\) −23.4803 + 13.5563i −0.860251 + 0.496666i
\(746\) 7.28372 27.1832i 0.266676 0.995248i
\(747\) 3.21303 + 11.9912i 0.117559 + 0.438735i
\(748\) −0.686292 + 0.686292i −0.0250933 + 0.0250933i
\(749\) −16.4719 + 39.1999i −0.601872 + 1.43233i
\(750\) −17.2132 −0.628537
\(751\) −7.96447 + 13.7949i −0.290627 + 0.503382i −0.973958 0.226727i \(-0.927197\pi\)
0.683331 + 0.730109i \(0.260531\pi\)
\(752\) 12.4853 + 21.6251i 0.455291 + 0.788588i
\(753\) −2.86396 4.96053i −0.104369 0.180772i
\(754\) 1.10051 1.90613i 0.0400780 0.0694172i
\(755\) −12.3934 12.3934i −0.451042 0.451042i
\(756\) 3.19980 + 4.21441i 0.116376 + 0.153277i
\(757\) −10.3137 + 10.3137i −0.374858 + 0.374858i −0.869243 0.494385i \(-0.835393\pi\)
0.494385 + 0.869243i \(0.335393\pi\)
\(758\) 8.99635 2.41057i 0.326762 0.0875557i
\(759\) −2.95680 + 1.70711i −0.107325 + 0.0619641i
\(760\) −12.6677 + 7.31371i −0.459506 + 0.265296i
\(761\) −20.5235 11.8492i −0.743976 0.429535i 0.0795372 0.996832i \(-0.474656\pi\)
−0.823513 + 0.567297i \(0.807989\pi\)
\(762\) 11.2426 11.2426i 0.407278 0.407278i
\(763\) 3.19182 2.42340i 0.115552 0.0877329i
\(764\) −38.6274 −1.39749
\(765\) −2.06914 + 0.554425i −0.0748101 + 0.0200453i
\(766\) −35.6046 + 20.5563i −1.28645 + 0.742731i
\(767\) −0.606602 1.05066i −0.0219031 0.0379373i
\(768\) 15.4548 4.14110i 0.557678 0.149429i
\(769\) 19.8284 0.715031 0.357516 0.933907i \(-0.383624\pi\)
0.357516 + 0.933907i \(0.383624\pi\)
\(770\) −2.62357 + 1.07107i −0.0945469 + 0.0385986i
\(771\) 14.3137 + 14.3137i 0.515496 + 0.515496i
\(772\) −7.00000 + 12.1244i −0.251936 + 0.436365i
\(773\) −2.06914 0.554425i −0.0744219 0.0199413i 0.221416 0.975179i \(-0.428932\pi\)
−0.295838 + 0.955238i \(0.595599\pi\)
\(774\) 8.85906 + 2.37378i 0.318432 + 0.0853237i
\(775\) 3.46410 + 2.00000i 0.124434 + 0.0718421i
\(776\) 23.5147i 0.844129i
\(777\) −5.91359 4.58579i −0.212149 0.164514i
\(778\) 3.79899 + 3.79899i 0.136200 + 0.136200i
\(779\) 0.428825 + 1.60040i 0.0153643 + 0.0573402i
\(780\) −0.554425 + 2.06914i −0.0198516 + 0.0740872i
\(781\) −1.70453 + 6.36138i −0.0609928 + 0.227628i
\(782\) 6.82843 11.8272i 0.244184 0.422939i
\(783\) 2.65685 0.0949482
\(784\) −26.9706 7.52255i −0.963234 0.268662i
\(785\) −38.3431 −1.36853
\(786\) 4.05025 7.01524i 0.144468 0.250225i
\(787\) 12.2933 45.8790i 0.438207 1.63541i −0.295066 0.955477i \(-0.595342\pi\)
0.733273 0.679934i \(-0.237992\pi\)
\(788\) 8.66490 + 2.32175i 0.308674 + 0.0827090i
\(789\) −0.392038 1.46311i −0.0139569 0.0520879i
\(790\) −20.5563 20.5563i −0.731362 0.731362i
\(791\) 8.15295 + 6.32233i 0.289885 + 0.224796i
\(792\) −0.828427 + 0.828427i −0.0294369 + 0.0294369i
\(793\) −2.74666 1.58579i −0.0975369 0.0563129i
\(794\) −45.0386 12.0681i −1.59836 0.428280i
\(795\) −15.2891 4.09670i −0.542248 0.145295i
\(796\) −32.6118 18.8284i −1.15589 0.667356i
\(797\) 30.2635 + 30.2635i 1.07199 + 1.07199i 0.997200 + 0.0747871i \(0.0238277\pi\)
0.0747871 + 0.997200i \(0.476172\pi\)
\(798\) 9.79796 4.00000i 0.346844 0.141598i
\(799\) 7.31371 0.258740
\(800\) 4.68629 8.11689i 0.165685 0.286976i
\(801\) 7.77817 + 13.4722i 0.274828 + 0.476017i
\(802\) −29.3939 + 16.9706i −1.03793 + 0.599251i
\(803\) −1.60040 + 0.428825i −0.0564768 + 0.0151329i
\(804\) 26.6274i 0.939077i
\(805\) 31.7578 24.1122i 1.11932 0.849844i
\(806\) 1.41421 1.41421i 0.0498135 0.0498135i
\(807\) −0.742932 0.428932i −0.0261525 0.0150991i
\(808\) −5.60521 + 20.9189i −0.197190 + 0.735925i
\(809\) −5.49333 + 3.17157i −0.193135 + 0.111507i −0.593449 0.804871i \(-0.702234\pi\)
0.400314 + 0.916378i \(0.368901\pi\)
\(810\) −2.49768 + 0.669251i −0.0877595 + 0.0235151i
\(811\) −15.5563 + 15.5563i −0.546257 + 0.546257i −0.925356 0.379099i \(-0.876234\pi\)
0.379099 + 0.925356i \(0.376234\pi\)
\(812\) −11.1971 + 8.50140i −0.392940 + 0.298341i
\(813\) −18.1924 18.1924i −0.638035 0.638035i
\(814\) 0.828427 1.43488i 0.0290364 0.0502924i
\(815\) 7.09188 + 12.2835i 0.248418 + 0.430272i
\(816\) 1.21290 4.52661i 0.0424600 0.158463i
\(817\) 9.17157 15.8856i 0.320873 0.555768i
\(818\) 30.1838 1.05535
\(819\) 0.600398 1.42883i 0.0209796 0.0499272i
\(820\) 1.51472 + 1.51472i 0.0528963 + 0.0528963i
\(821\) −1.29410 4.82963i −0.0451642 0.168555i 0.939660 0.342110i \(-0.111141\pi\)
−0.984824 + 0.173554i \(0.944475\pi\)
\(822\) 4.69553 17.5240i 0.163775 0.611218i
\(823\) 25.6836 14.8284i 0.895274 0.516886i 0.0196098 0.999808i \(-0.493758\pi\)
0.875664 + 0.482921i \(0.160424\pi\)
\(824\) −24.9706 + 43.2503i −0.869891 + 1.50670i
\(825\) 0.686292i 0.0238936i
\(826\) 0.972263 + 7.68799i 0.0338293 + 0.267499i
\(827\) −20.0503 + 20.0503i −0.697216 + 0.697216i −0.963809 0.266593i \(-0.914102\pi\)
0.266593 + 0.963809i \(0.414102\pi\)
\(828\) 8.24264 14.2767i 0.286452 0.496149i
\(829\) 3.58668 13.3857i 0.124571 0.464904i −0.875253 0.483664i \(-0.839305\pi\)
0.999824 + 0.0187610i \(0.00597216\pi\)
\(830\) 27.7999 16.0503i 0.964947 0.557112i
\(831\) −5.17157 + 8.95743i −0.179400 + 0.310730i
\(832\) −3.31371 3.31371i −0.114882 0.114882i
\(833\) −5.85786 + 5.73951i −0.202963 + 0.198862i
\(834\) 25.7990i 0.893346i
\(835\) 10.5967 2.83939i 0.366716 0.0982612i
\(836\) 1.17157 + 2.02922i 0.0405197 + 0.0701822i
\(837\) 2.33195 + 0.624844i 0.0806040 + 0.0215978i
\(838\) −13.3545 49.8398i −0.461325 1.72169i
\(839\) 19.7990i 0.683537i −0.939784 0.341769i \(-0.888974\pi\)
0.939784 0.341769i \(-0.111026\pi\)
\(840\) 8.38478 10.8126i 0.289302 0.373069i
\(841\) 21.9411i 0.756591i
\(842\) −29.9153 + 8.01577i −1.03095 + 0.276242i
\(843\) 4.66390 + 1.24969i 0.160633 + 0.0430416i
\(844\) 6.15963 22.9881i 0.212023 0.791282i
\(845\) −22.3536 + 5.98963i −0.768987 + 0.206049i
\(846\) 8.82843 0.303528
\(847\) −10.8284 26.5241i −0.372069 0.911380i
\(848\) 24.4853 24.4853i 0.840828 0.840828i
\(849\) 11.7279 20.3134i 0.402501 0.697153i
\(850\) −1.37258 2.37738i −0.0470792 0.0815436i
\(851\) −6.03403 + 22.5193i −0.206844 + 0.771952i
\(852\) −8.23018 30.7155i −0.281961 1.05229i
\(853\) −9.07107 + 9.07107i −0.310587 + 0.310587i −0.845137 0.534550i \(-0.820481\pi\)
0.534550 + 0.845137i \(0.320481\pi\)
\(854\) 12.2502 + 16.1346i 0.419193 + 0.552114i
\(855\) 5.17157i 0.176864i
\(856\) 43.9070 11.7648i 1.50071 0.402114i
\(857\) −14.0665 + 8.12132i −0.480504 + 0.277419i −0.720626 0.693324i \(-0.756146\pi\)
0.240123 + 0.970743i \(0.422812\pi\)
\(858\) 0.331453 + 0.0888127i 0.0113156 + 0.00303201i
\(859\) 1.92971 + 7.20179i 0.0658410 + 0.245722i 0.991001 0.133856i \(-0.0427359\pi\)
−0.925160 + 0.379578i \(0.876069\pi\)
\(860\) 23.7157i 0.808700i
\(861\) −0.937200 1.23437i −0.0319397 0.0420673i
\(862\) 20.3431i 0.692890i
\(863\) −0.192388 + 0.333226i −0.00654897 + 0.0113431i −0.869281 0.494318i \(-0.835418\pi\)
0.862732 + 0.505661i \(0.168751\pi\)
\(864\) 1.46410 5.46410i 0.0498097 0.185893i
\(865\) 15.5147 + 26.8723i 0.527516 + 0.913685i
\(866\) 20.7846 + 12.0000i 0.706290 + 0.407777i
\(867\) 11.0503 + 11.0503i 0.375286 + 0.375286i
\(868\) −11.8272 + 4.82843i −0.401441 + 0.163887i
\(869\) −3.29289 + 3.29289i −0.111704 + 0.111704i
\(870\) −1.77810 6.63597i −0.0602833 0.224980i
\(871\) 6.75412 3.89949i 0.228855 0.132129i
\(872\) −4.13829 1.10885i −0.140140 0.0375504i
\(873\) −7.19988 4.15685i −0.243679 0.140688i
\(874\) −23.3137 23.3137i −0.788598 0.788598i
\(875\) −4.04037 31.9485i −0.136589 1.08006i
\(876\) 5.65685 5.65685i 0.191127 0.191127i
\(877\) −11.8657 + 3.17940i −0.400676 + 0.107361i −0.453529 0.891241i \(-0.649835\pi\)
0.0528530 + 0.998602i \(0.483169\pi\)
\(878\) 18.7782 + 32.5248i 0.633733 + 1.09766i
\(879\) −7.74264 13.4106i −0.261153 0.452330i
\(880\) 2.62357 + 1.51472i 0.0884405 + 0.0510612i
\(881\) 50.4853 1.70089 0.850446 0.526062i \(-0.176332\pi\)
0.850446 + 0.526062i \(0.176332\pi\)
\(882\) −7.07107 + 6.92820i −0.238095 + 0.233285i
\(883\) −19.0000 19.0000i −0.639401 0.639401i 0.311007 0.950408i \(-0.399334\pi\)
−0.950408 + 0.311007i \(0.899334\pi\)
\(884\) −1.32581 + 0.355251i −0.0445919 + 0.0119484i
\(885\) −3.65776 0.980095i −0.122954 0.0329455i
\(886\) 3.50864 13.0944i 0.117875 0.439916i
\(887\) −5.10911 2.94975i −0.171547 0.0990428i 0.411768 0.911289i \(-0.364911\pi\)
−0.583315 + 0.812246i \(0.698245\pi\)
\(888\) 8.00000i 0.268462i
\(889\) 23.5058 + 18.2279i 0.788359 + 0.611345i
\(890\) 28.4437 28.4437i 0.953433 0.953433i
\(891\) 0.107206 + 0.400100i 0.00359155 + 0.0134038i
\(892\) 20.5563 + 35.6046i 0.688277 + 1.19213i
\(893\) 4.56993 17.0552i 0.152927 0.570731i
\(894\) −18.1610 10.4853i −0.607396 0.350680i
\(895\) 34.0589 1.13846
\(896\) 11.3137 + 27.7128i 0.377964 + 0.925820i
\(897\) −4.82843 −0.161216
\(898\) 12.5446 + 7.24264i 0.418619 + 0.241690i
\(899\) −1.66012 + 6.19565i −0.0553681 + 0.206637i
\(900\) −1.65685 2.86976i −0.0552285 0.0956585i
\(901\) −2.62498 9.79655i −0.0874507 0.326370i
\(902\) 0.242641 0.242641i 0.00807905 0.00807905i
\(903\) −2.32640 + 17.0000i −0.0774176 + 0.565725i
\(904\) 11.0294i 0.366834i
\(905\) 35.2204 + 20.3345i 1.17077 + 0.675942i
\(906\) 3.50864 13.0944i 0.116567 0.435033i
\(907\) 19.0841 + 5.11358i 0.633679 + 0.169794i 0.561338 0.827586i \(-0.310287\pi\)
0.0723402 + 0.997380i \(0.476953\pi\)
\(908\) −20.7816 + 5.56842i −0.689662 + 0.184794i
\(909\) 5.41421 + 5.41421i 0.179578 + 0.179578i
\(910\) −3.97056 0.543359i −0.131623 0.0180122i
\(911\) −13.2721 −0.439724 −0.219862 0.975531i \(-0.570561\pi\)
−0.219862 + 0.975531i \(0.570561\pi\)
\(912\) −9.79796 5.65685i −0.324443 0.187317i
\(913\) −2.57107 4.45322i −0.0850899 0.147380i
\(914\) 15.2929 + 26.4881i 0.505844 + 0.876147i
\(915\) −9.56218 + 2.56218i −0.316116 + 0.0847030i
\(916\) −34.4853 + 34.4853i −1.13943 + 1.13943i
\(917\) 13.9713 + 5.87080i 0.461373 + 0.193871i
\(918\) −1.17157 1.17157i −0.0386677 0.0386677i
\(919\) −8.11689 4.68629i −0.267752 0.154586i 0.360114 0.932908i \(-0.382738\pi\)
−0.627865 + 0.778322i \(0.716071\pi\)
\(920\) −41.1749 11.0328i −1.35750 0.363740i
\(921\) −7.73268 + 4.46447i −0.254801 + 0.147109i
\(922\) −4.14110 15.4548i −0.136380 0.508977i
\(923\) −6.58579 + 6.58579i −0.216774 + 0.216774i
\(924\) −1.73205 1.34315i −0.0569803 0.0441863i
\(925\) 3.31371 + 3.31371i 0.108954 + 0.108954i
\(926\) 4.65279 + 2.68629i 0.152900 + 0.0882770i
\(927\) 8.82843 + 15.2913i 0.289964 + 0.502232i
\(928\) 14.5173 + 3.88990i 0.476554 + 0.127692i
\(929\) −6.17157 + 10.6895i −0.202483 + 0.350710i −0.949328 0.314288i \(-0.898234\pi\)
0.746845 + 0.664998i \(0.231568\pi\)
\(930\) 6.24264i 0.204704i
\(931\) 9.72401 + 17.2466i 0.318691 + 0.565233i
\(932\) 10.3431i 0.338801i
\(933\) 2.99100 + 11.1626i 0.0979211 + 0.365446i
\(934\) −13.8544 3.71228i −0.453330 0.121469i
\(935\) 0.768426 0.443651i 0.0251302 0.0145089i
\(936\) −1.60040 + 0.428825i −0.0523107 + 0.0140166i
\(937\) 27.0000i 0.882052i −0.897494 0.441026i \(-0.854615\pi\)
0.897494 0.441026i \(-0.145385\pi\)
\(938\) −49.4217 + 6.25012i −1.61368 + 0.204074i
\(939\) −6.94975 + 6.94975i −0.226796 + 0.226796i
\(940\) −5.90843 22.0506i −0.192712 0.719210i
\(941\) −9.18427 + 34.2761i −0.299399 + 1.11737i 0.638262 + 0.769819i \(0.279654\pi\)
−0.937661 + 0.347552i \(0.887013\pi\)
\(942\) −14.8284 25.6836i −0.483136 0.836817i
\(943\) −2.41421 + 4.18154i −0.0786176 + 0.136170i
\(944\) 5.85786 5.85786i 0.190657 0.190657i
\(945\) −1.82843 4.47871i −0.0594787 0.145693i
\(946\) −3.79899 −0.123516
\(947\) −5.26994 + 1.41208i −0.171250 + 0.0458863i −0.343425 0.939180i \(-0.611587\pi\)
0.172175 + 0.985066i \(0.444921\pi\)
\(948\) 5.81962 21.7191i 0.189012 0.705404i
\(949\) −2.26330 0.606451i −0.0734700 0.0196862i
\(950\) −6.40159 + 1.71530i −0.207695 + 0.0556517i
\(951\) 11.3431i 0.367827i
\(952\) 8.68629 + 1.18869i 0.281524 + 0.0385257i
\(953\) 55.2548i 1.78988i 0.446187 + 0.894940i \(0.352782\pi\)
−0.446187 + 0.894940i \(0.647218\pi\)
\(954\) −3.16863 11.8255i −0.102588 0.382864i
\(955\) 34.1104 + 9.13986i 1.10379 + 0.295759i
\(956\) 11.0711 + 19.1757i 0.358064 + 0.620185i
\(957\) −1.06301 + 0.284832i −0.0343621 + 0.00920730i
\(958\) 21.4558i 0.693207i
\(959\) 33.6274 + 4.60181i 1.08589 + 0.148600i
\(960\) −14.6274 −0.472098
\(961\) 12.5858 21.7992i 0.405993 0.703201i
\(962\) 2.02922 1.17157i 0.0654248 0.0377730i
\(963\) 4.15950 15.5235i 0.134038 0.500236i
\(964\) 23.1421 40.0834i 0.745358 1.29100i
\(965\) 9.05025 9.05025i 0.291338 0.291338i
\(966\) 28.4329 + 11.9476i 0.914814 + 0.384408i
\(967\) 35.1838i 1.13143i 0.824600 + 0.565717i \(0.191400\pi\)
−0.824600 + 0.565717i \(0.808600\pi\)
\(968\) −15.3137 + 26.5241i −0.492201 + 0.852518i
\(969\) −2.86976 + 1.65685i −0.0921898 + 0.0532258i
\(970\) −5.56396 + 20.7650i −0.178648 + 0.666723i
\(971\) −3.73067 13.9231i −0.119723 0.446812i 0.879874 0.475207i \(-0.157627\pi\)
−0.999597 + 0.0283952i \(0.990960\pi\)
\(972\) −1.41421 1.41421i −0.0453609 0.0453609i
\(973\) 47.8841 6.05567i 1.53509 0.194136i
\(974\) 0.786797 0.0252106
\(975\) −0.485281 + 0.840532i −0.0155414 + 0.0269186i
\(976\) 5.60521 20.9189i 0.179418 0.669598i
\(977\) 16.6569 + 28.8505i 0.532900 + 0.923010i 0.999262 + 0.0384158i \(0.0122311\pi\)
−0.466362 + 0.884594i \(0.654436\pi\)
\(978\) −5.48528 + 9.50079i −0.175400 + 0.303802i
\(979\) −4.55635 4.55635i −0.145622 0.145622i
\(980\) 22.0367 + 13.0245i 0.703938 + 0.416054i
\(981\) −1.07107 + 1.07107i −0.0341966 + 0.0341966i
\(982\) −30.8125 + 8.25620i −0.983268 + 0.263466i
\(983\) −26.4881 + 15.2929i −0.844838 + 0.487768i −0.858906 0.512134i \(-0.828855\pi\)
0.0140677 + 0.999901i \(0.495522\pi\)
\(984\) −0.428825 + 1.60040i −0.0136705 + 0.0510188i
\(985\) −7.10228 4.10051i −0.226298 0.130653i
\(986\) 3.11270 3.11270i 0.0991285 0.0991285i
\(987\) 2.07225 + 16.3860i 0.0659605 + 0.521571i
\(988\) 3.31371i 0.105423i
\(989\) 51.6344 13.8354i 1.64188 0.439940i
\(990\) 0.927572 0.535534i 0.0294802 0.0170204i
\(991\) 15.2782 + 26.4626i 0.485327 + 0.840611i 0.999858 0.0168606i \(-0.00536715\pi\)
−0.514531 + 0.857472i \(0.672034\pi\)
\(992\) 11.8272 + 6.82843i 0.375513 + 0.216803i
\(993\) −8.00000 −0.253872
\(994\) 55.0775 22.4853i 1.74695 0.713190i
\(995\) 24.3431 + 24.3431i 0.771730 + 0.771730i
\(996\) 21.5020 + 12.4142i 0.681318 + 0.393359i
\(997\) 28.7836 + 7.71255i 0.911586 + 0.244259i 0.683985 0.729496i \(-0.260245\pi\)
0.227601 + 0.973755i \(0.426912\pi\)
\(998\) 5.60139 + 1.50089i 0.177309 + 0.0475098i
\(999\) 2.44949 + 1.41421i 0.0774984 + 0.0447437i
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 336.2.bq.a.205.1 yes 8
7.4 even 3 inner 336.2.bq.a.109.2 yes 8
16.5 even 4 inner 336.2.bq.a.37.2 8
112.53 even 12 inner 336.2.bq.a.277.1 yes 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
336.2.bq.a.37.2 8 16.5 even 4 inner
336.2.bq.a.109.2 yes 8 7.4 even 3 inner
336.2.bq.a.205.1 yes 8 1.1 even 1 trivial
336.2.bq.a.277.1 yes 8 112.53 even 12 inner