Properties

Label 390.2.bd.c.37.3
Level $390$
Weight $2$
Character 390.37
Analytic conductor $3.114$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [390,2,Mod(7,390)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(390, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([0, 3, 11]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("390.7");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 390.bd (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: \(3.11416567883\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(8\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 37.3
Character \(\chi\) \(=\) 390.37
Dual form 390.2.bd.c.253.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.866025 - 0.500000i) q^{2} +(-0.965926 - 0.258819i) q^{3} +(0.500000 - 0.866025i) q^{4} +(1.50593 - 1.65293i) q^{5} +(-0.965926 + 0.258819i) q^{6} +(0.627513 - 1.08688i) q^{7} -1.00000i q^{8} +(0.866025 + 0.500000i) q^{9} +O(q^{10})\) \(q+(0.866025 - 0.500000i) q^{2} +(-0.965926 - 0.258819i) q^{3} +(0.500000 - 0.866025i) q^{4} +(1.50593 - 1.65293i) q^{5} +(-0.965926 + 0.258819i) q^{6} +(0.627513 - 1.08688i) q^{7} -1.00000i q^{8} +(0.866025 + 0.500000i) q^{9} +(0.477706 - 2.18444i) q^{10} +(-1.61087 - 0.431631i) q^{11} +(-0.707107 + 0.707107i) q^{12} +(1.52233 + 3.26841i) q^{13} -1.25503i q^{14} +(-1.88242 + 1.20685i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.24008 - 4.62805i) q^{17} +1.00000 q^{18} +(-1.68516 - 6.28910i) q^{19} +(-0.678517 - 2.13064i) q^{20} +(-0.887437 + 0.887437i) q^{21} +(-1.61087 + 0.431631i) q^{22} +(-1.26866 + 4.73471i) q^{23} +(-0.258819 + 0.965926i) q^{24} +(-0.464364 - 4.97839i) q^{25} +(2.95258 + 2.06936i) q^{26} +(-0.707107 - 0.707107i) q^{27} +(-0.627513 - 1.08688i) q^{28} +(6.16323 - 3.55834i) q^{29} +(-1.02680 + 1.98637i) q^{30} +(4.97092 + 4.97092i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(1.44427 + 0.833847i) q^{33} +(-3.38797 - 3.38797i) q^{34} +(-0.851556 - 2.67400i) q^{35} +(0.866025 - 0.500000i) q^{36} +(5.13448 + 8.89318i) q^{37} +(-4.60394 - 4.60394i) q^{38} +(-0.624535 - 3.55105i) q^{39} +(-1.65293 - 1.50593i) q^{40} +(0.614688 - 2.29405i) q^{41} +(-0.324825 + 1.21226i) q^{42} +(-6.17528 + 1.65466i) q^{43} +(-1.17924 + 1.17924i) q^{44} +(2.13064 - 0.678517i) q^{45} +(1.26866 + 4.73471i) q^{46} -3.93547 q^{47} +(0.258819 + 0.965926i) q^{48} +(2.71245 + 4.69811i) q^{49} +(-2.89135 - 4.07923i) q^{50} +4.79131i q^{51} +(3.59169 + 0.315825i) q^{52} +(-2.76048 + 2.76048i) q^{53} +(-0.965926 - 0.258819i) q^{54} +(-3.13931 + 2.01265i) q^{55} +(-1.08688 - 0.627513i) q^{56} +6.51095i q^{57} +(3.55834 - 6.16323i) q^{58} +(7.25043 - 1.94275i) q^{59} +(0.103947 + 2.23365i) q^{60} +(-4.86857 + 8.43262i) q^{61} +(6.79040 + 1.81948i) q^{62} +(1.08688 - 0.627513i) q^{63} -1.00000 q^{64} +(7.69498 + 2.40567i) q^{65} +1.66769 q^{66} +(-1.61393 + 0.931803i) q^{67} +(-4.62805 - 1.24008i) q^{68} +(2.45087 - 4.24503i) q^{69} +(-2.07447 - 1.88998i) q^{70} +(1.32703 - 0.355575i) q^{71} +(0.500000 - 0.866025i) q^{72} +10.6790i q^{73} +(8.89318 + 5.13448i) q^{74} +(-0.839961 + 4.92894i) q^{75} +(-6.28910 - 1.68516i) q^{76} +(-1.47997 + 1.47997i) q^{77} +(-2.31639 - 2.76303i) q^{78} +8.54874i q^{79} +(-2.18444 - 0.477706i) q^{80} +(0.500000 + 0.866025i) q^{81} +(-0.614688 - 2.29405i) q^{82} -3.67899 q^{83} +(0.324825 + 1.21226i) q^{84} +(-9.51732 - 4.91974i) q^{85} +(-4.52062 + 4.52062i) q^{86} +(-6.87419 + 1.84193i) q^{87} +(-0.431631 + 1.61087i) q^{88} +(-1.32475 + 4.94404i) q^{89} +(1.50593 - 1.65293i) q^{90} +(4.50767 + 0.396369i) q^{91} +(3.46605 + 3.46605i) q^{92} +(-3.51497 - 6.08811i) q^{93} +(-3.40821 + 1.96773i) q^{94} +(-12.9332 - 6.68548i) q^{95} +(0.707107 + 0.707107i) q^{96} +(12.6374 + 7.29623i) q^{97} +(4.69811 + 2.71245i) q^{98} +(-1.17924 - 1.17924i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q + 16 q^{4}+O(q^{10}) \) Copy content Toggle raw display \( 32 q + 16 q^{4} - 4 q^{11} + 20 q^{13} + 4 q^{15} - 16 q^{16} - 20 q^{17} + 32 q^{18} - 20 q^{19} + 8 q^{21} - 4 q^{22} + 4 q^{23} + 8 q^{25} - 4 q^{26} - 24 q^{29} + 4 q^{30} + 12 q^{31} - 12 q^{33} + 16 q^{34} + 12 q^{35} + 20 q^{37} + 4 q^{38} + 20 q^{39} - 28 q^{41} + 8 q^{42} - 4 q^{43} + 4 q^{44} - 4 q^{46} - 16 q^{47} - 20 q^{49} + 28 q^{50} + 16 q^{52} - 4 q^{53} - 40 q^{55} - 12 q^{56} - 36 q^{59} - 4 q^{60} - 28 q^{61} - 36 q^{62} + 12 q^{63} - 32 q^{64} - 32 q^{65} - 36 q^{67} - 4 q^{68} + 20 q^{69} - 24 q^{70} - 4 q^{71} + 16 q^{72} - 24 q^{74} - 16 q^{76} - 20 q^{77} - 16 q^{78} + 16 q^{81} + 28 q^{82} - 40 q^{83} - 8 q^{84} + 88 q^{85} - 8 q^{86} - 16 q^{87} - 8 q^{88} + 16 q^{89} - 40 q^{91} + 20 q^{92} + 24 q^{94} - 8 q^{95} + 72 q^{97} + 72 q^{98} + 4 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/390\mathbb{Z}\right)^\times\).

\(n\) \(131\) \(157\) \(301\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{4}\right)\) \(e\left(\frac{7}{12}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.866025 0.500000i 0.612372 0.353553i
\(3\) −0.965926 0.258819i −0.557678 0.149429i
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) 1.50593 1.65293i 0.673471 0.739213i
\(6\) −0.965926 + 0.258819i −0.394338 + 0.105662i
\(7\) 0.627513 1.08688i 0.237178 0.410804i −0.722726 0.691135i \(-0.757111\pi\)
0.959903 + 0.280331i \(0.0904443\pi\)
\(8\) 1.00000i 0.353553i
\(9\) 0.866025 + 0.500000i 0.288675 + 0.166667i
\(10\) 0.477706 2.18444i 0.151064 0.690782i
\(11\) −1.61087 0.431631i −0.485695 0.130142i 0.00765795 0.999971i \(-0.497562\pi\)
−0.493353 + 0.869829i \(0.664229\pi\)
\(12\) −0.707107 + 0.707107i −0.204124 + 0.204124i
\(13\) 1.52233 + 3.26841i 0.422219 + 0.906494i
\(14\) 1.25503i 0.335420i
\(15\) −1.88242 + 1.20685i −0.486040 + 0.311606i
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −1.24008 4.62805i −0.300764 1.12247i −0.936531 0.350585i \(-0.885983\pi\)
0.635767 0.771881i \(-0.280684\pi\)
\(18\) 1.00000 0.235702
\(19\) −1.68516 6.28910i −0.386602 1.44282i −0.835626 0.549299i \(-0.814895\pi\)
0.449024 0.893520i \(-0.351772\pi\)
\(20\) −0.678517 2.13064i −0.151721 0.476425i
\(21\) −0.887437 + 0.887437i −0.193655 + 0.193655i
\(22\) −1.61087 + 0.431631i −0.343439 + 0.0920241i
\(23\) −1.26866 + 4.73471i −0.264535 + 0.987256i 0.698000 + 0.716098i \(0.254073\pi\)
−0.962535 + 0.271159i \(0.912593\pi\)
\(24\) −0.258819 + 0.965926i −0.0528312 + 0.197169i
\(25\) −0.464364 4.97839i −0.0928729 0.995678i
\(26\) 2.95258 + 2.06936i 0.579049 + 0.405835i
\(27\) −0.707107 0.707107i −0.136083 0.136083i
\(28\) −0.627513 1.08688i −0.118589 0.205402i
\(29\) 6.16323 3.55834i 1.14448 0.660767i 0.196946 0.980414i \(-0.436898\pi\)
0.947537 + 0.319647i \(0.103564\pi\)
\(30\) −1.02680 + 1.98637i −0.187468 + 0.362660i
\(31\) 4.97092 + 4.97092i 0.892803 + 0.892803i 0.994786 0.101983i \(-0.0325186\pi\)
−0.101983 + 0.994786i \(0.532519\pi\)
\(32\) −0.866025 0.500000i −0.153093 0.0883883i
\(33\) 1.44427 + 0.833847i 0.251414 + 0.145154i
\(34\) −3.38797 3.38797i −0.581031 0.581031i
\(35\) −0.851556 2.67400i −0.143939 0.451989i
\(36\) 0.866025 0.500000i 0.144338 0.0833333i
\(37\) 5.13448 + 8.89318i 0.844103 + 1.46203i 0.886397 + 0.462925i \(0.153200\pi\)
−0.0422940 + 0.999105i \(0.513467\pi\)
\(38\) −4.60394 4.60394i −0.746858 0.746858i
\(39\) −0.624535 3.55105i −0.100006 0.568623i
\(40\) −1.65293 1.50593i −0.261351 0.238108i
\(41\) 0.614688 2.29405i 0.0959981 0.358270i −0.901171 0.433464i \(-0.857291\pi\)
0.997169 + 0.0751944i \(0.0239577\pi\)
\(42\) −0.324825 + 1.21226i −0.0501215 + 0.187056i
\(43\) −6.17528 + 1.65466i −0.941721 + 0.252334i −0.696846 0.717221i \(-0.745414\pi\)
−0.244876 + 0.969554i \(0.578747\pi\)
\(44\) −1.17924 + 1.17924i −0.177777 + 0.177777i
\(45\) 2.13064 0.678517i 0.317617 0.101147i
\(46\) 1.26866 + 4.73471i 0.187054 + 0.698096i
\(47\) −3.93547 −0.574047 −0.287023 0.957924i \(-0.592666\pi\)
−0.287023 + 0.957924i \(0.592666\pi\)
\(48\) 0.258819 + 0.965926i 0.0373573 + 0.139419i
\(49\) 2.71245 + 4.69811i 0.387494 + 0.671159i
\(50\) −2.89135 4.07923i −0.408898 0.576890i
\(51\) 4.79131i 0.670917i
\(52\) 3.59169 + 0.315825i 0.498078 + 0.0437971i
\(53\) −2.76048 + 2.76048i −0.379181 + 0.379181i −0.870807 0.491626i \(-0.836403\pi\)
0.491626 + 0.870807i \(0.336403\pi\)
\(54\) −0.965926 0.258819i −0.131446 0.0352208i
\(55\) −3.13931 + 2.01265i −0.423304 + 0.271386i
\(56\) −1.08688 0.627513i −0.145241 0.0838549i
\(57\) 6.51095i 0.862397i
\(58\) 3.55834 6.16323i 0.467233 0.809271i
\(59\) 7.25043 1.94275i 0.943925 0.252924i 0.246143 0.969234i \(-0.420837\pi\)
0.697783 + 0.716310i \(0.254170\pi\)
\(60\) 0.103947 + 2.23365i 0.0134196 + 0.288363i
\(61\) −4.86857 + 8.43262i −0.623357 + 1.07969i 0.365499 + 0.930812i \(0.380898\pi\)
−0.988856 + 0.148874i \(0.952435\pi\)
\(62\) 6.79040 + 1.81948i 0.862382 + 0.231075i
\(63\) 1.08688 0.627513i 0.136935 0.0790592i
\(64\) −1.00000 −0.125000
\(65\) 7.69498 + 2.40567i 0.954445 + 0.298387i
\(66\) 1.66769 0.205279
\(67\) −1.61393 + 0.931803i −0.197173 + 0.113838i −0.595336 0.803477i \(-0.702981\pi\)
0.398163 + 0.917315i \(0.369648\pi\)
\(68\) −4.62805 1.24008i −0.561233 0.150382i
\(69\) 2.45087 4.24503i 0.295050 0.511041i
\(70\) −2.07447 1.88998i −0.247947 0.225896i
\(71\) 1.32703 0.355575i 0.157489 0.0421990i −0.179213 0.983810i \(-0.557355\pi\)
0.336702 + 0.941611i \(0.390688\pi\)
\(72\) 0.500000 0.866025i 0.0589256 0.102062i
\(73\) 10.6790i 1.24988i 0.780672 + 0.624941i \(0.214877\pi\)
−0.780672 + 0.624941i \(0.785123\pi\)
\(74\) 8.89318 + 5.13448i 1.03381 + 0.596871i
\(75\) −0.839961 + 4.92894i −0.0969903 + 0.569145i
\(76\) −6.28910 1.68516i −0.721409 0.193301i
\(77\) −1.47997 + 1.47997i −0.168659 + 0.168659i
\(78\) −2.31639 2.76303i −0.262279 0.312852i
\(79\) 8.54874i 0.961809i 0.876773 + 0.480904i \(0.159692\pi\)
−0.876773 + 0.480904i \(0.840308\pi\)
\(80\) −2.18444 0.477706i −0.244228 0.0534091i
\(81\) 0.500000 + 0.866025i 0.0555556 + 0.0962250i
\(82\) −0.614688 2.29405i −0.0678809 0.253335i
\(83\) −3.67899 −0.403822 −0.201911 0.979404i \(-0.564715\pi\)
−0.201911 + 0.979404i \(0.564715\pi\)
\(84\) 0.324825 + 1.21226i 0.0354413 + 0.132269i
\(85\) −9.51732 4.91974i −1.03230 0.533620i
\(86\) −4.52062 + 4.52062i −0.487471 + 0.487471i
\(87\) −6.87419 + 1.84193i −0.736990 + 0.197476i
\(88\) −0.431631 + 1.61087i −0.0460120 + 0.171719i
\(89\) −1.32475 + 4.94404i −0.140423 + 0.524067i 0.859493 + 0.511147i \(0.170779\pi\)
−0.999917 + 0.0129199i \(0.995887\pi\)
\(90\) 1.50593 1.65293i 0.158739 0.174234i
\(91\) 4.50767 + 0.396369i 0.472532 + 0.0415507i
\(92\) 3.46605 + 3.46605i 0.361361 + 0.361361i
\(93\) −3.51497 6.08811i −0.364485 0.631307i
\(94\) −3.40821 + 1.96773i −0.351530 + 0.202956i
\(95\) −12.9332 6.68548i −1.32692 0.685915i
\(96\) 0.707107 + 0.707107i 0.0721688 + 0.0721688i
\(97\) 12.6374 + 7.29623i 1.28314 + 0.740820i 0.977421 0.211303i \(-0.0677705\pi\)
0.305717 + 0.952122i \(0.401104\pi\)
\(98\) 4.69811 + 2.71245i 0.474581 + 0.273999i
\(99\) −1.17924 1.17924i −0.118518 0.118518i
\(100\) −4.54359 2.08704i −0.454359 0.208704i
\(101\) 15.1633 8.75455i 1.50881 0.871110i 0.508860 0.860849i \(-0.330067\pi\)
0.999947 0.0102612i \(-0.00326631\pi\)
\(102\) 2.39565 + 4.14939i 0.237205 + 0.410851i
\(103\) 6.26904 + 6.26904i 0.617707 + 0.617707i 0.944943 0.327236i \(-0.106117\pi\)
−0.327236 + 0.944943i \(0.606117\pi\)
\(104\) 3.26841 1.52233i 0.320494 0.149277i
\(105\) 0.130457 + 2.80329i 0.0127313 + 0.273573i
\(106\) −1.01041 + 3.77088i −0.0981393 + 0.366261i
\(107\) 0.290076 1.08258i 0.0280427 0.104657i −0.950486 0.310767i \(-0.899414\pi\)
0.978529 + 0.206111i \(0.0660807\pi\)
\(108\) −0.965926 + 0.258819i −0.0929463 + 0.0249049i
\(109\) 13.1086 13.1086i 1.25557 1.25557i 0.302388 0.953185i \(-0.402216\pi\)
0.953185 0.302388i \(-0.0977837\pi\)
\(110\) −1.71240 + 3.31266i −0.163271 + 0.315850i
\(111\) −2.65780 9.91906i −0.252267 0.941475i
\(112\) −1.25503 −0.118589
\(113\) −1.99540 7.44692i −0.187711 0.700548i −0.994034 0.109072i \(-0.965212\pi\)
0.806323 0.591476i \(-0.201454\pi\)
\(114\) 3.25548 + 5.63865i 0.304903 + 0.528108i
\(115\) 5.91564 + 9.22715i 0.551637 + 0.860436i
\(116\) 7.11668i 0.660767i
\(117\) −0.315825 + 3.59169i −0.0291980 + 0.332052i
\(118\) 5.30768 5.30768i 0.488612 0.488612i
\(119\) −5.80832 1.55633i −0.532448 0.142669i
\(120\) 1.20685 + 1.88242i 0.110169 + 0.171841i
\(121\) −7.11768 4.10940i −0.647062 0.373582i
\(122\) 9.73715i 0.881560i
\(123\) −1.18749 + 2.05678i −0.107072 + 0.185454i
\(124\) 6.79040 1.81948i 0.609796 0.163394i
\(125\) −8.92824 6.72953i −0.798566 0.601908i
\(126\) 0.627513 1.08688i 0.0559033 0.0968274i
\(127\) −9.65497 2.58704i −0.856740 0.229563i −0.196395 0.980525i \(-0.562923\pi\)
−0.660345 + 0.750962i \(0.729590\pi\)
\(128\) −0.866025 + 0.500000i −0.0765466 + 0.0441942i
\(129\) 6.39312 0.562883
\(130\) 7.86689 1.76411i 0.689972 0.154723i
\(131\) 7.04662 0.615666 0.307833 0.951440i \(-0.400396\pi\)
0.307833 + 0.951440i \(0.400396\pi\)
\(132\) 1.44427 0.833847i 0.125707 0.0725771i
\(133\) −7.89298 2.11492i −0.684408 0.183387i
\(134\) −0.931803 + 1.61393i −0.0804955 + 0.139422i
\(135\) −2.23365 + 0.103947i −0.192242 + 0.00894637i
\(136\) −4.62805 + 1.24008i −0.396852 + 0.106336i
\(137\) 1.91461 3.31620i 0.163576 0.283322i −0.772573 0.634926i \(-0.781030\pi\)
0.936149 + 0.351604i \(0.114364\pi\)
\(138\) 4.90174i 0.417264i
\(139\) −13.7399 7.93271i −1.16540 0.672844i −0.212807 0.977094i \(-0.568261\pi\)
−0.952592 + 0.304251i \(0.901594\pi\)
\(140\) −2.74153 0.599533i −0.231702 0.0506698i
\(141\) 3.80137 + 1.01857i 0.320133 + 0.0857794i
\(142\) 0.971450 0.971450i 0.0815223 0.0815223i
\(143\) −1.04153 5.92207i −0.0870974 0.495228i
\(144\) 1.00000i 0.0833333i
\(145\) 3.39968 15.5460i 0.282328 1.29102i
\(146\) 5.33950 + 9.24828i 0.441900 + 0.765393i
\(147\) −1.40407 5.24006i −0.115806 0.432193i
\(148\) 10.2690 0.844103
\(149\) −2.04976 7.64982i −0.167923 0.626698i −0.997649 0.0685269i \(-0.978170\pi\)
0.829726 0.558171i \(-0.188497\pi\)
\(150\) 1.73704 + 4.68857i 0.141829 + 0.382820i
\(151\) −11.2421 + 11.2421i −0.914868 + 0.914868i −0.996650 0.0817826i \(-0.973939\pi\)
0.0817826 + 0.996650i \(0.473939\pi\)
\(152\) −6.28910 + 1.68516i −0.510113 + 0.136684i
\(153\) 1.24008 4.62805i 0.100255 0.374156i
\(154\) −0.541708 + 2.02168i −0.0436521 + 0.162912i
\(155\) 15.7024 0.730744i 1.26125 0.0586948i
\(156\) −3.38757 1.23466i −0.271222 0.0988521i
\(157\) 2.01620 + 2.01620i 0.160911 + 0.160911i 0.782970 0.622059i \(-0.213704\pi\)
−0.622059 + 0.782970i \(0.713704\pi\)
\(158\) 4.27437 + 7.40343i 0.340051 + 0.588985i
\(159\) 3.38088 1.95195i 0.268121 0.154800i
\(160\) −2.13064 + 0.678517i −0.168442 + 0.0536415i
\(161\) 4.34998 + 4.34998i 0.342827 + 0.342827i
\(162\) 0.866025 + 0.500000i 0.0680414 + 0.0392837i
\(163\) 3.59412 + 2.07507i 0.281513 + 0.162532i 0.634108 0.773244i \(-0.281367\pi\)
−0.352595 + 0.935776i \(0.614701\pi\)
\(164\) −1.67936 1.67936i −0.131136 0.131136i
\(165\) 3.55325 1.13156i 0.276620 0.0880917i
\(166\) −3.18610 + 1.83950i −0.247289 + 0.142773i
\(167\) −2.69591 4.66946i −0.208616 0.361334i 0.742663 0.669666i \(-0.233563\pi\)
−0.951279 + 0.308332i \(0.900229\pi\)
\(168\) 0.887437 + 0.887437i 0.0684673 + 0.0684673i
\(169\) −8.36500 + 9.95122i −0.643462 + 0.765478i
\(170\) −10.7021 + 0.498044i −0.820814 + 0.0381982i
\(171\) 1.68516 6.28910i 0.128867 0.480939i
\(172\) −1.65466 + 6.17528i −0.126167 + 0.470861i
\(173\) −7.11700 + 1.90699i −0.541096 + 0.144986i −0.519007 0.854770i \(-0.673698\pi\)
−0.0220885 + 0.999756i \(0.507032\pi\)
\(174\) −5.03225 + 5.03225i −0.381494 + 0.381494i
\(175\) −5.70233 2.61929i −0.431056 0.198000i
\(176\) 0.431631 + 1.61087i 0.0325354 + 0.121424i
\(177\) −7.50620 −0.564200
\(178\) 1.32475 + 4.94404i 0.0992943 + 0.370571i
\(179\) −1.48610 2.57401i −0.111077 0.192390i 0.805128 0.593101i \(-0.202097\pi\)
−0.916205 + 0.400711i \(0.868763\pi\)
\(180\) 0.477706 2.18444i 0.0356061 0.162819i
\(181\) 8.57582i 0.637436i −0.947850 0.318718i \(-0.896748\pi\)
0.947850 0.318718i \(-0.103252\pi\)
\(182\) 4.10194 1.91057i 0.304056 0.141621i
\(183\) 6.88520 6.88520i 0.508969 0.508969i
\(184\) 4.73471 + 1.26866i 0.349048 + 0.0935271i
\(185\) 22.4320 + 4.90554i 1.64923 + 0.360663i
\(186\) −6.08811 3.51497i −0.446402 0.257730i
\(187\) 7.99044i 0.584319i
\(188\) −1.96773 + 3.40821i −0.143512 + 0.248570i
\(189\) −1.21226 + 0.324825i −0.0881791 + 0.0236275i
\(190\) −14.5432 + 0.676797i −1.05507 + 0.0491000i
\(191\) −11.4751 + 19.8754i −0.830308 + 1.43814i 0.0674864 + 0.997720i \(0.478502\pi\)
−0.897794 + 0.440415i \(0.854831\pi\)
\(192\) 0.965926 + 0.258819i 0.0697097 + 0.0186787i
\(193\) −7.78132 + 4.49255i −0.560112 + 0.323381i −0.753190 0.657803i \(-0.771486\pi\)
0.193079 + 0.981183i \(0.438153\pi\)
\(194\) 14.5925 1.04768
\(195\) −6.81015 4.31531i −0.487685 0.309026i
\(196\) 5.42491 0.387494
\(197\) −21.9778 + 12.6889i −1.56585 + 0.904047i −0.569210 + 0.822192i \(0.692751\pi\)
−0.996644 + 0.0818546i \(0.973916\pi\)
\(198\) −1.61087 0.431631i −0.114480 0.0306747i
\(199\) 12.6150 21.8497i 0.894250 1.54889i 0.0595206 0.998227i \(-0.481043\pi\)
0.834730 0.550660i \(-0.185624\pi\)
\(200\) −4.97839 + 0.464364i −0.352025 + 0.0328355i
\(201\) 1.80011 0.482337i 0.126970 0.0340214i
\(202\) 8.75455 15.1633i 0.615968 1.06689i
\(203\) 8.93162i 0.626877i
\(204\) 4.14939 + 2.39565i 0.290516 + 0.167729i
\(205\) −2.86622 4.47070i −0.200186 0.312247i
\(206\) 8.56367 + 2.29463i 0.596659 + 0.159874i
\(207\) −3.46605 + 3.46605i −0.240907 + 0.240907i
\(208\) 2.06936 2.95258i 0.143484 0.204725i
\(209\) 10.8583i 0.751083i
\(210\) 1.51462 + 2.36249i 0.104519 + 0.163027i
\(211\) −1.45207 2.51505i −0.0999644 0.173143i 0.811705 0.584067i \(-0.198540\pi\)
−0.911670 + 0.410924i \(0.865206\pi\)
\(212\) 1.01041 + 3.77088i 0.0693949 + 0.258985i
\(213\) −1.37384 −0.0941338
\(214\) −0.290076 1.08258i −0.0198292 0.0740034i
\(215\) −6.56448 + 12.6991i −0.447694 + 0.866072i
\(216\) −0.707107 + 0.707107i −0.0481125 + 0.0481125i
\(217\) 8.52213 2.28350i 0.578520 0.155014i
\(218\) 4.79807 17.9066i 0.324966 1.21279i
\(219\) 2.76393 10.3151i 0.186769 0.697031i
\(220\) 0.173353 + 3.72505i 0.0116874 + 0.251143i
\(221\) 13.2385 11.0985i 0.890520 0.746568i
\(222\) −7.26125 7.26125i −0.487343 0.487343i
\(223\) 2.26260 + 3.91894i 0.151515 + 0.262432i 0.931785 0.363012i \(-0.118251\pi\)
−0.780270 + 0.625443i \(0.784918\pi\)
\(224\) −1.08688 + 0.627513i −0.0726205 + 0.0419275i
\(225\) 2.08704 4.54359i 0.139136 0.302906i
\(226\) −5.45153 5.45153i −0.362630 0.362630i
\(227\) −20.2480 11.6902i −1.34391 0.775907i −0.356531 0.934284i \(-0.616041\pi\)
−0.987379 + 0.158377i \(0.949374\pi\)
\(228\) 5.63865 + 3.25548i 0.373429 + 0.215599i
\(229\) −9.49103 9.49103i −0.627185 0.627185i 0.320174 0.947359i \(-0.396259\pi\)
−0.947359 + 0.320174i \(0.896259\pi\)
\(230\) 9.73667 + 5.03312i 0.642017 + 0.331874i
\(231\) 1.81259 1.04650i 0.119260 0.0688546i
\(232\) −3.55834 6.16323i −0.233616 0.404636i
\(233\) −8.47713 8.47713i −0.555355 0.555355i 0.372626 0.927981i \(-0.378457\pi\)
−0.927981 + 0.372626i \(0.878457\pi\)
\(234\) 1.52233 + 3.26841i 0.0995181 + 0.213663i
\(235\) −5.92653 + 6.50506i −0.386604 + 0.424343i
\(236\) 1.94275 7.25043i 0.126462 0.471963i
\(237\) 2.21258 8.25745i 0.143722 0.536379i
\(238\) −5.80832 + 1.55633i −0.376497 + 0.100882i
\(239\) −14.9221 + 14.9221i −0.965231 + 0.965231i −0.999416 0.0341841i \(-0.989117\pi\)
0.0341841 + 0.999416i \(0.489117\pi\)
\(240\) 1.98637 + 1.02680i 0.128220 + 0.0662799i
\(241\) −1.80748 6.74561i −0.116430 0.434523i 0.882960 0.469448i \(-0.155547\pi\)
−0.999390 + 0.0349257i \(0.988881\pi\)
\(242\) −8.21879 −0.528324
\(243\) −0.258819 0.965926i −0.0166032 0.0619642i
\(244\) 4.86857 + 8.43262i 0.311679 + 0.539843i
\(245\) 11.8504 + 2.59151i 0.757095 + 0.165566i
\(246\) 2.37497i 0.151423i
\(247\) 17.9900 15.0819i 1.14467 0.959638i
\(248\) 4.97092 4.97092i 0.315654 0.315654i
\(249\) 3.55363 + 0.952193i 0.225202 + 0.0603428i
\(250\) −11.0968 1.36383i −0.701826 0.0862560i
\(251\) 3.65199 + 2.10848i 0.230512 + 0.133086i 0.610808 0.791779i \(-0.290845\pi\)
−0.380296 + 0.924865i \(0.624178\pi\)
\(252\) 1.25503i 0.0790592i
\(253\) 4.08730 7.07941i 0.256966 0.445079i
\(254\) −9.65497 + 2.58704i −0.605807 + 0.162325i
\(255\) 7.91970 + 7.21536i 0.495951 + 0.451844i
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −11.7678 3.15318i −0.734057 0.196690i −0.127622 0.991823i \(-0.540734\pi\)
−0.606435 + 0.795133i \(0.707401\pi\)
\(258\) 5.53661 3.19656i 0.344694 0.199009i
\(259\) 12.8878 0.800810
\(260\) 5.93087 5.46121i 0.367817 0.338690i
\(261\) 7.11668 0.440511
\(262\) 6.10255 3.52331i 0.377017 0.217671i
\(263\) 16.2092 + 4.34325i 0.999504 + 0.267816i 0.721238 0.692688i \(-0.243573\pi\)
0.278267 + 0.960504i \(0.410240\pi\)
\(264\) 0.833847 1.44427i 0.0513198 0.0888884i
\(265\) 0.405801 + 8.71996i 0.0249282 + 0.535663i
\(266\) −7.89298 + 2.11492i −0.483950 + 0.129674i
\(267\) 2.55922 4.43270i 0.156622 0.271277i
\(268\) 1.86361i 0.113838i
\(269\) 4.39441 + 2.53712i 0.267932 + 0.154691i 0.627948 0.778256i \(-0.283895\pi\)
−0.360015 + 0.932946i \(0.617229\pi\)
\(270\) −1.88242 + 1.20685i −0.114561 + 0.0734463i
\(271\) 29.9794 + 8.03296i 1.82112 + 0.487968i 0.996927 0.0783409i \(-0.0249623\pi\)
0.824193 + 0.566309i \(0.191629\pi\)
\(272\) −3.38797 + 3.38797i −0.205426 + 0.205426i
\(273\) −4.25148 1.54953i −0.257312 0.0937820i
\(274\) 3.82922i 0.231332i
\(275\) −1.40080 + 8.21997i −0.0844713 + 0.495683i
\(276\) −2.45087 4.24503i −0.147525 0.255521i
\(277\) −7.16219 26.7296i −0.430334 1.60603i −0.751992 0.659172i \(-0.770907\pi\)
0.321658 0.946856i \(-0.395760\pi\)
\(278\) −15.8654 −0.951545
\(279\) 1.81948 + 6.79040i 0.108930 + 0.406531i
\(280\) −2.67400 + 0.851556i −0.159802 + 0.0508902i
\(281\) −6.36885 + 6.36885i −0.379933 + 0.379933i −0.871078 0.491145i \(-0.836579\pi\)
0.491145 + 0.871078i \(0.336579\pi\)
\(282\) 3.80137 1.01857i 0.226368 0.0606552i
\(283\) 5.27508 19.6869i 0.313571 1.17026i −0.611741 0.791058i \(-0.709531\pi\)
0.925312 0.379206i \(-0.123803\pi\)
\(284\) 0.355575 1.32703i 0.0210995 0.0787445i
\(285\) 10.7622 + 9.80503i 0.637495 + 0.580800i
\(286\) −3.86303 4.60789i −0.228426 0.272470i
\(287\) −2.10764 2.10764i −0.124410 0.124410i
\(288\) −0.500000 0.866025i −0.0294628 0.0510310i
\(289\) −5.15859 + 2.97832i −0.303447 + 0.175195i
\(290\) −4.82879 15.1631i −0.283556 0.890406i
\(291\) −10.3184 10.3184i −0.604877 0.604877i
\(292\) 9.24828 + 5.33950i 0.541215 + 0.312470i
\(293\) 20.2491 + 11.6908i 1.18297 + 0.682986i 0.956699 0.291080i \(-0.0940145\pi\)
0.226267 + 0.974065i \(0.427348\pi\)
\(294\) −3.83599 3.83599i −0.223720 0.223720i
\(295\) 7.70739 14.9101i 0.448742 0.868099i
\(296\) 8.89318 5.13448i 0.516906 0.298436i
\(297\) 0.833847 + 1.44427i 0.0483847 + 0.0838048i
\(298\) −5.60006 5.60006i −0.324403 0.324403i
\(299\) −17.4063 + 3.06131i −1.00663 + 0.177040i
\(300\) 3.84861 + 3.19190i 0.222200 + 0.184284i
\(301\) −2.07664 + 7.75014i −0.119696 + 0.446710i
\(302\) −4.11489 + 15.3570i −0.236785 + 0.883694i
\(303\) −16.9125 + 4.53169i −0.971597 + 0.260339i
\(304\) −4.60394 + 4.60394i −0.264054 + 0.264054i
\(305\) 6.60682 + 20.7463i 0.378305 + 1.18793i
\(306\) −1.24008 4.62805i −0.0708908 0.264568i
\(307\) 15.1164 0.862739 0.431370 0.902175i \(-0.358031\pi\)
0.431370 + 0.902175i \(0.358031\pi\)
\(308\) 0.541708 + 2.02168i 0.0308667 + 0.115196i
\(309\) −4.43288 7.67797i −0.252178 0.436785i
\(310\) 13.2333 8.48406i 0.751603 0.481862i
\(311\) 32.3149i 1.83241i −0.400711 0.916205i \(-0.631237\pi\)
0.400711 0.916205i \(-0.368763\pi\)
\(312\) −3.55105 + 0.624535i −0.201039 + 0.0353573i
\(313\) −18.4185 + 18.4185i −1.04107 + 1.04107i −0.0419546 + 0.999120i \(0.513358\pi\)
−0.999120 + 0.0419546i \(0.986642\pi\)
\(314\) 2.75418 + 0.737982i 0.155428 + 0.0416467i
\(315\) 0.599533 2.74153i 0.0337799 0.154468i
\(316\) 7.40343 + 4.27437i 0.416475 + 0.240452i
\(317\) 14.4575i 0.812015i 0.913870 + 0.406008i \(0.133079\pi\)
−0.913870 + 0.406008i \(0.866921\pi\)
\(318\) 1.95195 3.38088i 0.109460 0.189590i
\(319\) −11.4640 + 3.07178i −0.641863 + 0.171987i
\(320\) −1.50593 + 1.65293i −0.0841839 + 0.0924017i
\(321\) −0.560383 + 0.970612i −0.0312775 + 0.0541743i
\(322\) 5.94219 + 1.59220i 0.331145 + 0.0887301i
\(323\) −27.0165 + 15.5980i −1.50324 + 0.867896i
\(324\) 1.00000 0.0555556
\(325\) 15.5645 9.09650i 0.863363 0.504583i
\(326\) 4.15014 0.229855
\(327\) −16.0546 + 9.26915i −0.887824 + 0.512585i
\(328\) −2.29405 0.614688i −0.126667 0.0339404i
\(329\) −2.46956 + 4.27740i −0.136151 + 0.235821i
\(330\) 2.51143 2.75658i 0.138250 0.151745i
\(331\) −4.05566 + 1.08671i −0.222919 + 0.0597310i −0.368550 0.929608i \(-0.620146\pi\)
0.145631 + 0.989339i \(0.453479\pi\)
\(332\) −1.83950 + 3.18610i −0.100955 + 0.174860i
\(333\) 10.2690i 0.562736i
\(334\) −4.66946 2.69591i −0.255501 0.147514i
\(335\) −0.890256 + 4.07094i −0.0486399 + 0.222419i
\(336\) 1.21226 + 0.324825i 0.0661343 + 0.0177206i
\(337\) 4.57923 4.57923i 0.249447 0.249447i −0.571297 0.820744i \(-0.693559\pi\)
0.820744 + 0.571297i \(0.193559\pi\)
\(338\) −2.26869 + 12.8005i −0.123401 + 0.696256i
\(339\) 7.70962i 0.418729i
\(340\) −9.01928 + 5.78237i −0.489139 + 0.313593i
\(341\) −5.86190 10.1531i −0.317440 0.549821i
\(342\) −1.68516 6.28910i −0.0911230 0.340076i
\(343\) 15.5936 0.841974
\(344\) 1.65466 + 6.17528i 0.0892134 + 0.332949i
\(345\) −3.32591 10.4438i −0.179061 0.562277i
\(346\) −5.21001 + 5.21001i −0.280092 + 0.280092i
\(347\) −0.100412 + 0.0269053i −0.00539040 + 0.00144435i −0.261513 0.965200i \(-0.584222\pi\)
0.256123 + 0.966644i \(0.417555\pi\)
\(348\) −1.84193 + 6.87419i −0.0987379 + 0.368495i
\(349\) −4.45057 + 16.6097i −0.238233 + 0.889099i 0.738431 + 0.674329i \(0.235567\pi\)
−0.976665 + 0.214770i \(0.931100\pi\)
\(350\) −6.24801 + 0.582789i −0.333970 + 0.0311514i
\(351\) 1.23466 3.38757i 0.0659014 0.180815i
\(352\) 1.17924 + 1.17924i 0.0628536 + 0.0628536i
\(353\) 14.8918 + 25.7934i 0.792612 + 1.37284i 0.924345 + 0.381559i \(0.124613\pi\)
−0.131733 + 0.991285i \(0.542054\pi\)
\(354\) −6.50056 + 3.75310i −0.345501 + 0.199475i
\(355\) 1.41066 2.72895i 0.0748702 0.144838i
\(356\) 3.61929 + 3.61929i 0.191822 + 0.191822i
\(357\) 5.20760 + 3.00661i 0.275615 + 0.159127i
\(358\) −2.57401 1.48610i −0.136041 0.0785430i
\(359\) 1.63445 + 1.63445i 0.0862629 + 0.0862629i 0.748922 0.662659i \(-0.230572\pi\)
−0.662659 + 0.748922i \(0.730572\pi\)
\(360\) −0.678517 2.13064i −0.0357610 0.112294i
\(361\) −20.2585 + 11.6963i −1.06624 + 0.615593i
\(362\) −4.28791 7.42688i −0.225368 0.390348i
\(363\) 5.81157 + 5.81157i 0.305028 + 0.305028i
\(364\) 2.59710 3.70557i 0.136125 0.194225i
\(365\) 17.6516 + 16.0818i 0.923929 + 0.841759i
\(366\) 2.52016 9.40536i 0.131731 0.491626i
\(367\) 1.69791 6.33667i 0.0886300 0.330772i −0.907347 0.420383i \(-0.861896\pi\)
0.995977 + 0.0896112i \(0.0285625\pi\)
\(368\) 4.73471 1.26866i 0.246814 0.0661336i
\(369\) 1.67936 1.67936i 0.0874239 0.0874239i
\(370\) 21.8794 6.96766i 1.13746 0.362232i
\(371\) 1.26809 + 4.73256i 0.0658357 + 0.245702i
\(372\) −7.02994 −0.364485
\(373\) 0.688437 + 2.56928i 0.0356459 + 0.133032i 0.981456 0.191689i \(-0.0613963\pi\)
−0.945810 + 0.324721i \(0.894730\pi\)
\(374\) 3.99522 + 6.91992i 0.206588 + 0.357821i
\(375\) 6.88228 + 8.81103i 0.355400 + 0.454999i
\(376\) 3.93547i 0.202956i
\(377\) 21.0126 + 14.7270i 1.08220 + 0.758477i
\(378\) −0.887437 + 0.887437i −0.0456449 + 0.0456449i
\(379\) −11.2762 3.02144i −0.579219 0.155201i −0.0426975 0.999088i \(-0.513595\pi\)
−0.536521 + 0.843887i \(0.680262\pi\)
\(380\) −12.2564 + 7.85772i −0.628739 + 0.403093i
\(381\) 8.65641 + 4.99778i 0.443481 + 0.256044i
\(382\) 22.9502i 1.17423i
\(383\) −6.18679 + 10.7158i −0.316130 + 0.547553i −0.979677 0.200581i \(-0.935717\pi\)
0.663547 + 0.748135i \(0.269050\pi\)
\(384\) 0.965926 0.258819i 0.0492922 0.0132078i
\(385\) 0.217562 + 4.67503i 0.0110880 + 0.238262i
\(386\) −4.49255 + 7.78132i −0.228665 + 0.396059i
\(387\) −6.17528 1.65466i −0.313907 0.0841112i
\(388\) 12.6374 7.29623i 0.641569 0.370410i
\(389\) −2.84284 −0.144138 −0.0720689 0.997400i \(-0.522960\pi\)
−0.0720689 + 0.997400i \(0.522960\pi\)
\(390\) −8.05542 0.332096i −0.407902 0.0168163i
\(391\) 23.4857 1.18772
\(392\) 4.69811 2.71245i 0.237290 0.137000i
\(393\) −6.80651 1.82380i −0.343343 0.0919985i
\(394\) −12.6889 + 21.9778i −0.639257 + 1.10723i
\(395\) 14.1305 + 12.8738i 0.710982 + 0.647750i
\(396\) −1.61087 + 0.431631i −0.0809492 + 0.0216903i
\(397\) 11.2077 19.4123i 0.562499 0.974277i −0.434778 0.900537i \(-0.643173\pi\)
0.997278 0.0737396i \(-0.0234934\pi\)
\(398\) 25.2299i 1.26466i
\(399\) 7.07665 + 4.08571i 0.354276 + 0.204541i
\(400\) −4.07923 + 2.89135i −0.203961 + 0.144567i
\(401\) −33.8471 9.06930i −1.69024 0.452899i −0.719791 0.694191i \(-0.755762\pi\)
−0.970453 + 0.241292i \(0.922429\pi\)
\(402\) 1.31777 1.31777i 0.0657243 0.0657243i
\(403\) −8.67960 + 23.8144i −0.432362 + 1.18628i
\(404\) 17.5091i 0.871110i
\(405\) 2.18444 + 0.477706i 0.108546 + 0.0237374i
\(406\) −4.46581 7.73501i −0.221634 0.383882i
\(407\) −4.43240 16.5420i −0.219706 0.819954i
\(408\) 4.79131 0.237205
\(409\) −4.62665 17.2669i −0.228773 0.853793i −0.980858 0.194727i \(-0.937618\pi\)
0.752084 0.659067i \(-0.229049\pi\)
\(410\) −4.71757 2.43863i −0.232984 0.120435i
\(411\) −2.70767 + 2.70767i −0.133559 + 0.133559i
\(412\) 8.56367 2.29463i 0.421902 0.113048i
\(413\) 2.43820 9.09947i 0.119976 0.447756i
\(414\) −1.26866 + 4.73471i −0.0623514 + 0.232699i
\(415\) −5.54030 + 6.08112i −0.271962 + 0.298511i
\(416\) 0.315825 3.59169i 0.0154846 0.176097i
\(417\) 11.2185 + 11.2185i 0.549374 + 0.549374i
\(418\) 5.42914 + 9.40355i 0.265548 + 0.459943i
\(419\) −5.50409 + 3.17779i −0.268893 + 0.155245i −0.628384 0.777903i \(-0.716283\pi\)
0.359492 + 0.933148i \(0.382950\pi\)
\(420\) 2.49295 + 1.28867i 0.121643 + 0.0628805i
\(421\) −10.3731 10.3731i −0.505556 0.505556i 0.407603 0.913159i \(-0.366365\pi\)
−0.913159 + 0.407603i \(0.866365\pi\)
\(422\) −2.51505 1.45207i −0.122431 0.0706855i
\(423\) −3.40821 1.96773i −0.165713 0.0956745i
\(424\) 2.76048 + 2.76048i 0.134061 + 0.134061i
\(425\) −22.4644 + 8.32271i −1.08968 + 0.403711i
\(426\) −1.18978 + 0.686919i −0.0576450 + 0.0332813i
\(427\) 6.11019 + 10.5832i 0.295693 + 0.512155i
\(428\) −0.792501 0.792501i −0.0383070 0.0383070i
\(429\) −0.526700 + 5.98985i −0.0254293 + 0.289193i
\(430\) 0.664548 + 14.2800i 0.0320474 + 0.688643i
\(431\) −5.58701 + 20.8510i −0.269117 + 1.00436i 0.690565 + 0.723270i \(0.257362\pi\)
−0.959682 + 0.281088i \(0.909305\pi\)
\(432\) −0.258819 + 0.965926i −0.0124524 + 0.0464731i
\(433\) 6.65778 1.78395i 0.319952 0.0857310i −0.0952684 0.995452i \(-0.530371\pi\)
0.415221 + 0.909721i \(0.363704\pi\)
\(434\) 6.23863 6.23863i 0.299464 0.299464i
\(435\) −7.30744 + 14.1364i −0.350365 + 0.677787i
\(436\) −4.79807 17.9066i −0.229786 0.857572i
\(437\) 31.9150 1.52670
\(438\) −2.76393 10.3151i −0.132066 0.492875i
\(439\) 7.70318 + 13.3423i 0.367653 + 0.636793i 0.989198 0.146585i \(-0.0468281\pi\)
−0.621545 + 0.783378i \(0.713495\pi\)
\(440\) 2.01265 + 3.13931i 0.0959494 + 0.149661i
\(441\) 5.42491i 0.258329i
\(442\) 5.91565 16.2309i 0.281379 0.772024i
\(443\) 18.8974 18.8974i 0.897842 0.897842i −0.0974031 0.995245i \(-0.531054\pi\)
0.995245 + 0.0974031i \(0.0310536\pi\)
\(444\) −9.91906 2.65780i −0.470738 0.126134i
\(445\) 6.17718 + 9.63509i 0.292826 + 0.456747i
\(446\) 3.91894 + 2.26260i 0.185567 + 0.107137i
\(447\) 7.91968i 0.374588i
\(448\) −0.627513 + 1.08688i −0.0296472 + 0.0513505i
\(449\) −15.8997 + 4.26032i −0.750354 + 0.201057i −0.613675 0.789559i \(-0.710310\pi\)
−0.136679 + 0.990615i \(0.543643\pi\)
\(450\) −0.464364 4.97839i −0.0218903 0.234684i
\(451\) −1.98036 + 3.43009i −0.0932516 + 0.161517i
\(452\) −7.44692 1.99540i −0.350274 0.0938556i
\(453\) 13.7687 7.94935i 0.646909 0.373493i
\(454\) −23.3804 −1.09730
\(455\) 7.44339 6.85396i 0.348952 0.321319i
\(456\) 6.51095 0.304903
\(457\) −15.1270 + 8.73356i −0.707610 + 0.408539i −0.810176 0.586187i \(-0.800628\pi\)
0.102565 + 0.994726i \(0.467295\pi\)
\(458\) −12.9650 3.47396i −0.605814 0.162327i
\(459\) −2.39565 + 4.14939i −0.111820 + 0.193677i
\(460\) 10.9488 0.509523i 0.510489 0.0237566i
\(461\) −10.3366 + 2.76968i −0.481423 + 0.128997i −0.491365 0.870954i \(-0.663502\pi\)
0.00994207 + 0.999951i \(0.496835\pi\)
\(462\) 1.04650 1.81259i 0.0486876 0.0843294i
\(463\) 26.0675i 1.21146i 0.795671 + 0.605729i \(0.207118\pi\)
−0.795671 + 0.605729i \(0.792882\pi\)
\(464\) −6.16323 3.55834i −0.286121 0.165192i
\(465\) −15.3565 3.35824i −0.712141 0.155735i
\(466\) −11.5800 3.10284i −0.536432 0.143737i
\(467\) 11.2734 11.2734i 0.521672 0.521672i −0.396404 0.918076i \(-0.629742\pi\)
0.918076 + 0.396404i \(0.129742\pi\)
\(468\) 2.95258 + 2.06936i 0.136483 + 0.0956561i
\(469\) 2.33887i 0.107999i
\(470\) −1.88000 + 8.59681i −0.0867177 + 0.396541i
\(471\) −1.42567 2.46933i −0.0656915 0.113781i
\(472\) −1.94275 7.25043i −0.0894221 0.333728i
\(473\) 10.6618 0.490229
\(474\) −2.21258 8.25745i −0.101627 0.379277i
\(475\) −30.5271 + 11.3098i −1.40068 + 0.518930i
\(476\) −4.25199 + 4.25199i −0.194889 + 0.194889i
\(477\) −3.77088 + 1.01041i −0.172657 + 0.0462633i
\(478\) −5.46187 + 20.3840i −0.249820 + 0.932342i
\(479\) −5.77188 + 21.5410i −0.263724 + 0.984232i 0.699303 + 0.714826i \(0.253494\pi\)
−0.963027 + 0.269406i \(0.913173\pi\)
\(480\) 2.23365 0.103947i 0.101952 0.00474453i
\(481\) −21.2502 + 30.3200i −0.968924 + 1.38247i
\(482\) −4.93813 4.93813i −0.224925 0.224925i
\(483\) −3.07590 5.32762i −0.139958 0.242415i
\(484\) −7.11768 + 4.10940i −0.323531 + 0.186791i
\(485\) 31.0912 9.90123i 1.41178 0.449592i
\(486\) −0.707107 0.707107i −0.0320750 0.0320750i
\(487\) −21.0987 12.1814i −0.956075 0.551990i −0.0611119 0.998131i \(-0.519465\pi\)
−0.894963 + 0.446141i \(0.852798\pi\)
\(488\) 8.43262 + 4.86857i 0.381727 + 0.220390i
\(489\) −2.93459 2.93459i −0.132707 0.132707i
\(490\) 11.5585 3.68089i 0.522160 0.166286i
\(491\) 33.1654 19.1480i 1.49673 0.864139i 0.496740 0.867899i \(-0.334530\pi\)
0.999993 + 0.00376002i \(0.00119685\pi\)
\(492\) 1.18749 + 2.05678i 0.0535360 + 0.0927270i
\(493\) −24.1111 24.1111i −1.08591 1.08591i
\(494\) 8.03883 22.0563i 0.361684 0.992360i
\(495\) −3.72505 + 0.173353i −0.167428 + 0.00779162i
\(496\) 1.81948 6.79040i 0.0816972 0.304898i
\(497\) 0.446256 1.66545i 0.0200173 0.0747057i
\(498\) 3.55363 0.952193i 0.159242 0.0426688i
\(499\) −9.21088 + 9.21088i −0.412335 + 0.412335i −0.882551 0.470216i \(-0.844176\pi\)
0.470216 + 0.882551i \(0.344176\pi\)
\(500\) −10.2921 + 4.36731i −0.460275 + 0.195312i
\(501\) 1.39551 + 5.20810i 0.0623467 + 0.232681i
\(502\) 4.21696 0.188212
\(503\) −6.03151 22.5099i −0.268932 1.00367i −0.959800 0.280686i \(-0.909438\pi\)
0.690868 0.722981i \(-0.257229\pi\)
\(504\) −0.627513 1.08688i −0.0279516 0.0484137i
\(505\) 8.36420 38.2477i 0.372202 1.70200i
\(506\) 8.17460i 0.363405i
\(507\) 10.6555 7.44712i 0.473229 0.330738i
\(508\) −7.06793 + 7.06793i −0.313589 + 0.313589i
\(509\) 6.05234 + 1.62172i 0.268265 + 0.0718815i 0.390444 0.920627i \(-0.372321\pi\)
−0.122179 + 0.992508i \(0.538988\pi\)
\(510\) 10.4663 + 2.28884i 0.463458 + 0.101351i
\(511\) 11.6068 + 6.70121i 0.513456 + 0.296444i
\(512\) 1.00000i 0.0441942i
\(513\) −3.25548 + 5.63865i −0.143733 + 0.248953i
\(514\) −11.7678 + 3.15318i −0.519057 + 0.139081i
\(515\) 19.8030 0.921573i 0.872625 0.0406093i
\(516\) 3.19656 5.53661i 0.140721 0.243735i
\(517\) 6.33952 + 1.69867i 0.278812 + 0.0747074i
\(518\) 11.1612 6.44391i 0.490394 0.283129i
\(519\) 7.36806 0.323422
\(520\) 2.40567 7.69498i 0.105496 0.337447i
\(521\) −27.8634 −1.22072 −0.610358 0.792126i \(-0.708974\pi\)
−0.610358 + 0.792126i \(0.708974\pi\)
\(522\) 6.16323 3.55834i 0.269757 0.155744i
\(523\) 32.8088 + 8.79109i 1.43463 + 0.384408i 0.890649 0.454691i \(-0.150250\pi\)
0.543979 + 0.839099i \(0.316917\pi\)
\(524\) 3.52331 6.10255i 0.153916 0.266591i
\(525\) 4.83010 + 4.00591i 0.210803 + 0.174832i
\(526\) 16.2092 4.34325i 0.706756 0.189375i
\(527\) 16.8413 29.1700i 0.733619 1.27067i
\(528\) 1.66769i 0.0725771i
\(529\) −0.889431 0.513513i −0.0386709 0.0223267i
\(530\) 4.71142 + 7.34881i 0.204651 + 0.319212i
\(531\) 7.25043 + 1.94275i 0.314642 + 0.0843080i
\(532\) −5.77806 + 5.77806i −0.250511 + 0.250511i
\(533\) 8.43364 1.48325i 0.365301 0.0642468i
\(534\) 5.11845i 0.221497i
\(535\) −1.35259 2.10976i −0.0584777 0.0912128i
\(536\) 0.931803 + 1.61393i 0.0402478 + 0.0697112i
\(537\) 0.769264 + 2.87093i 0.0331962 + 0.123890i
\(538\) 5.07423 0.218766
\(539\) −2.34156 8.73882i −0.100858 0.376408i
\(540\) −1.02680 + 1.98637i −0.0441866 + 0.0854798i
\(541\) −14.8357 + 14.8357i −0.637838 + 0.637838i −0.950022 0.312184i \(-0.898939\pi\)
0.312184 + 0.950022i \(0.398939\pi\)
\(542\) 29.9794 8.03296i 1.28773 0.345045i
\(543\) −2.21959 + 8.28361i −0.0952515 + 0.355484i
\(544\) −1.24008 + 4.62805i −0.0531681 + 0.198426i
\(545\) −1.92701 41.4081i −0.0825440 1.77373i
\(546\) −4.45666 + 0.783807i −0.190727 + 0.0335439i
\(547\) −9.75842 9.75842i −0.417240 0.417240i 0.467011 0.884251i \(-0.345331\pi\)
−0.884251 + 0.467011i \(0.845331\pi\)
\(548\) −1.91461 3.31620i −0.0817881 0.141661i
\(549\) −8.43262 + 4.86857i −0.359895 + 0.207786i
\(550\) 2.89686 + 7.81910i 0.123522 + 0.333408i
\(551\) −32.7648 32.7648i −1.39583 1.39583i
\(552\) −4.24503 2.45087i −0.180680 0.104316i
\(553\) 9.29149 + 5.36445i 0.395114 + 0.228119i
\(554\) −19.5675 19.5675i −0.831341 0.831341i
\(555\) −20.3980 10.5442i −0.865846 0.447577i
\(556\) −13.7399 + 7.93271i −0.582700 + 0.336422i
\(557\) −11.3638 19.6827i −0.481499 0.833982i 0.518275 0.855214i \(-0.326574\pi\)
−0.999775 + 0.0212324i \(0.993241\pi\)
\(558\) 4.97092 + 4.97092i 0.210436 + 0.210436i
\(559\) −14.8089 17.6644i −0.626352 0.747124i
\(560\) −1.88998 + 2.07447i −0.0798662 + 0.0876624i
\(561\) 2.06808 7.71817i 0.0873143 0.325861i
\(562\) −2.33116 + 8.70000i −0.0983340 + 0.366988i
\(563\) 32.8109 8.79167i 1.38282 0.370525i 0.510673 0.859775i \(-0.329396\pi\)
0.872143 + 0.489250i \(0.162730\pi\)
\(564\) 2.78280 2.78280i 0.117177 0.117177i
\(565\) −15.3142 7.91627i −0.644272 0.333040i
\(566\) −5.27508 19.6869i −0.221728 0.827501i
\(567\) 1.25503 0.0527061
\(568\) −0.355575 1.32703i −0.0149196 0.0556808i
\(569\) 3.96963 + 6.87559i 0.166415 + 0.288240i 0.937157 0.348908i \(-0.113447\pi\)
−0.770742 + 0.637148i \(0.780114\pi\)
\(570\) 14.2228 + 3.11032i 0.595728 + 0.130277i
\(571\) 4.89604i 0.204893i −0.994739 0.102446i \(-0.967333\pi\)
0.994739 0.102446i \(-0.0326670\pi\)
\(572\) −5.64943 2.05904i −0.236214 0.0860928i
\(573\) 16.2282 16.2282i 0.677944 0.677944i
\(574\) −2.87909 0.771449i −0.120171 0.0321997i
\(575\) 24.1604 + 4.11727i 1.00756 + 0.171702i
\(576\) −0.866025 0.500000i −0.0360844 0.0208333i
\(577\) 5.23478i 0.217927i 0.994046 + 0.108963i \(0.0347531\pi\)
−0.994046 + 0.108963i \(0.965247\pi\)
\(578\) −2.97832 + 5.15859i −0.123882 + 0.214569i
\(579\) 8.67893 2.32551i 0.360684 0.0966450i
\(580\) −11.7634 10.7172i −0.488448 0.445008i
\(581\) −2.30862 + 3.99864i −0.0957775 + 0.165892i
\(582\) −14.0952 3.77681i −0.584266 0.156554i
\(583\) 5.63828 3.25526i 0.233514 0.134819i
\(584\) 10.6790 0.441900
\(585\) 5.46121 + 5.93087i 0.225793 + 0.245211i
\(586\) 23.3817 0.965887
\(587\) 4.85069 2.80055i 0.200210 0.115591i −0.396544 0.918016i \(-0.629790\pi\)
0.596753 + 0.802425i \(0.296457\pi\)
\(588\) −5.24006 1.40407i −0.216096 0.0579029i
\(589\) 22.8858 39.6394i 0.942994 1.63331i
\(590\) −0.780250 16.7662i −0.0321224 0.690254i
\(591\) 24.5131 6.56826i 1.00833 0.270182i
\(592\) 5.13448 8.89318i 0.211026 0.365508i
\(593\) 3.71798i 0.152679i −0.997082 0.0763396i \(-0.975677\pi\)
0.997082 0.0763396i \(-0.0243233\pi\)
\(594\) 1.44427 + 0.833847i 0.0592590 + 0.0342132i
\(595\) −11.3194 + 7.25703i −0.464051 + 0.297509i
\(596\) −7.64982 2.04976i −0.313349 0.0839616i
\(597\) −17.8402 + 17.8402i −0.730152 + 0.730152i
\(598\) −13.5437 + 11.3543i −0.553841 + 0.464313i
\(599\) 25.7525i 1.05222i 0.850416 + 0.526110i \(0.176350\pi\)
−0.850416 + 0.526110i \(0.823650\pi\)
\(600\) 4.92894 + 0.839961i 0.201223 + 0.0342912i
\(601\) −21.0389 36.4405i −0.858195 1.48644i −0.873649 0.486557i \(-0.838253\pi\)
0.0154540 0.999881i \(-0.495081\pi\)
\(602\) 2.07664 + 7.75014i 0.0846377 + 0.315872i
\(603\) −1.86361 −0.0758919
\(604\) 4.11489 + 15.3570i 0.167432 + 0.624866i
\(605\) −17.5113 + 5.57659i −0.711934 + 0.226721i
\(606\) −12.3808 + 12.3808i −0.502936 + 0.502936i
\(607\) 34.4515 9.23125i 1.39834 0.374685i 0.520593 0.853805i \(-0.325711\pi\)
0.877750 + 0.479120i \(0.159044\pi\)
\(608\) −1.68516 + 6.28910i −0.0683422 + 0.255057i
\(609\) −2.31167 + 8.62728i −0.0936737 + 0.349595i
\(610\) 16.0948 + 14.6634i 0.651661 + 0.593705i
\(611\) −5.99109 12.8627i −0.242374 0.520370i
\(612\) −3.38797 3.38797i −0.136950 0.136950i
\(613\) −12.4662 21.5921i −0.503505 0.872096i −0.999992 0.00405171i \(-0.998710\pi\)
0.496487 0.868044i \(-0.334623\pi\)
\(614\) 13.0912 7.55821i 0.528318 0.305024i
\(615\) 1.61146 + 5.06020i 0.0649802 + 0.204047i
\(616\) 1.47997 + 1.47997i 0.0596299 + 0.0596299i
\(617\) 31.0469 + 17.9249i 1.24990 + 0.721631i 0.971090 0.238715i \(-0.0767262\pi\)
0.278811 + 0.960346i \(0.410060\pi\)
\(618\) −7.67797 4.43288i −0.308853 0.178317i
\(619\) 11.9813 + 11.9813i 0.481570 + 0.481570i 0.905633 0.424063i \(-0.139396\pi\)
−0.424063 + 0.905633i \(0.639396\pi\)
\(620\) 7.21837 13.9641i 0.289897 0.560811i
\(621\) 4.24503 2.45087i 0.170347 0.0983500i
\(622\) −16.1574 27.9855i −0.647855 1.12212i
\(623\) 4.54230 + 4.54230i 0.181983 + 0.181983i
\(624\) −2.76303 + 2.31639i −0.110610 + 0.0927297i
\(625\) −24.5687 + 4.62357i −0.982749 + 0.184943i
\(626\) −6.74163 + 25.1601i −0.269450 + 1.00560i
\(627\) 2.81033 10.4883i 0.112234 0.418862i
\(628\) 2.75418 0.737982i 0.109904 0.0294487i
\(629\) 34.7909 34.7909i 1.38720 1.38720i
\(630\) −0.851556 2.67400i −0.0339268 0.106535i
\(631\) 0.678114 + 2.53076i 0.0269953 + 0.100748i 0.978109 0.208093i \(-0.0667257\pi\)
−0.951114 + 0.308841i \(0.900059\pi\)
\(632\) 8.54874 0.340051
\(633\) 0.751645 + 2.80518i 0.0298752 + 0.111496i
\(634\) 7.22876 + 12.5206i 0.287091 + 0.497256i
\(635\) −18.8159 + 12.0631i −0.746686 + 0.478710i
\(636\) 3.90391i 0.154800i
\(637\) −11.2261 + 16.0175i −0.444794 + 0.634637i
\(638\) −8.39226 + 8.39226i −0.332253 + 0.332253i
\(639\) 1.32703 + 0.355575i 0.0524963 + 0.0140663i
\(640\) −0.477706 + 2.18444i −0.0188830 + 0.0863477i
\(641\) −10.5572 6.09522i −0.416986 0.240747i 0.276801 0.960927i \(-0.410726\pi\)
−0.693787 + 0.720180i \(0.744059\pi\)
\(642\) 1.12077i 0.0442331i
\(643\) 17.3974 30.1333i 0.686088 1.18834i −0.287005 0.957929i \(-0.592660\pi\)
0.973093 0.230411i \(-0.0740070\pi\)
\(644\) 5.94219 1.59220i 0.234155 0.0627417i
\(645\) 9.62758 10.5674i 0.379085 0.416091i
\(646\) −15.5980 + 27.0165i −0.613695 + 1.06295i
\(647\) −25.0137 6.70240i −0.983389 0.263498i −0.268918 0.963163i \(-0.586666\pi\)
−0.714471 + 0.699665i \(0.753333\pi\)
\(648\) 0.866025 0.500000i 0.0340207 0.0196419i
\(649\) −12.5180 −0.491376
\(650\) 8.93100 15.6601i 0.350303 0.614238i
\(651\) −8.82276 −0.345791
\(652\) 3.59412 2.07507i 0.140757 0.0812659i
\(653\) −11.7499 3.14838i −0.459810 0.123206i 0.0214759 0.999769i \(-0.493163\pi\)
−0.481286 + 0.876564i \(0.659830\pi\)
\(654\) −9.26915 + 16.0546i −0.362453 + 0.627786i
\(655\) 10.6117 11.6476i 0.414633 0.455109i
\(656\) −2.29405 + 0.614688i −0.0895674 + 0.0239995i
\(657\) −5.33950 + 9.24828i −0.208314 + 0.360810i
\(658\) 4.93911i 0.192547i
\(659\) −4.99063 2.88134i −0.194407 0.112241i 0.399637 0.916674i \(-0.369136\pi\)
−0.594044 + 0.804432i \(0.702470\pi\)
\(660\) 0.796667 3.64299i 0.0310102 0.141803i
\(661\) 21.4446 + 5.74606i 0.834098 + 0.223496i 0.650501 0.759506i \(-0.274559\pi\)
0.183597 + 0.983002i \(0.441226\pi\)
\(662\) −2.96895 + 2.96895i −0.115392 + 0.115392i
\(663\) −15.6600 + 7.29397i −0.608182 + 0.283274i
\(664\) 3.67899i 0.142773i
\(665\) −15.3821 + 9.86164i −0.596491 + 0.382418i
\(666\) 5.13448 + 8.89318i 0.198957 + 0.344604i
\(667\) 9.02867 + 33.6955i 0.349591 + 1.30469i
\(668\) −5.39183 −0.208616
\(669\) −1.17121 4.37101i −0.0452816 0.168993i
\(670\) 1.26449 + 3.97067i 0.0488514 + 0.153400i
\(671\) 11.4824 11.4824i 0.443274 0.443274i
\(672\) 1.21226 0.324825i 0.0467640 0.0125304i
\(673\) −10.8866 + 40.6294i −0.419649 + 1.56615i 0.355690 + 0.934604i \(0.384246\pi\)
−0.775338 + 0.631546i \(0.782421\pi\)
\(674\) 1.67612 6.25535i 0.0645615 0.240947i
\(675\) −3.19190 + 3.84861i −0.122856 + 0.148133i
\(676\) 4.43551 + 12.2199i 0.170596 + 0.469997i
\(677\) −30.1855 30.1855i −1.16012 1.16012i −0.984448 0.175676i \(-0.943789\pi\)
−0.175676 0.984448i \(-0.556211\pi\)
\(678\) 3.85481 + 6.67673i 0.148043 + 0.256418i
\(679\) 15.8603 9.15696i 0.608663 0.351412i
\(680\) −4.91974 + 9.51732i −0.188663 + 0.364973i
\(681\) 16.5325 + 16.5325i 0.633525 + 0.633525i
\(682\) −10.1531 5.86190i −0.388783 0.224464i
\(683\) 16.9261 + 9.77230i 0.647660 + 0.373927i 0.787559 0.616239i \(-0.211345\pi\)
−0.139899 + 0.990166i \(0.544678\pi\)
\(684\) −4.60394 4.60394i −0.176036 0.176036i
\(685\) −2.59819 8.15868i −0.0992717 0.311727i
\(686\) 13.5044 7.79679i 0.515602 0.297683i
\(687\) 6.71117 + 11.6241i 0.256047 + 0.443487i
\(688\) 4.52062 + 4.52062i 0.172347 + 0.172347i
\(689\) −13.2247 4.82001i −0.503823 0.183628i
\(690\) −8.10224 7.38166i −0.308447 0.281015i
\(691\) −3.95977 + 14.7781i −0.150637 + 0.562184i 0.848803 + 0.528709i \(0.177324\pi\)
−0.999440 + 0.0334744i \(0.989343\pi\)
\(692\) −1.90699 + 7.11700i −0.0724931 + 0.270548i
\(693\) −2.02168 + 0.541708i −0.0767974 + 0.0205778i
\(694\) −0.0735068 + 0.0735068i −0.00279028 + 0.00279028i
\(695\) −33.8034 + 10.7650i −1.28224 + 0.408338i
\(696\) 1.84193 + 6.87419i 0.0698183 + 0.260565i
\(697\) −11.3792 −0.431019
\(698\) 4.45057 + 16.6097i 0.168456 + 0.628688i
\(699\) 5.99424 + 10.3823i 0.226723 + 0.392695i
\(700\) −5.11954 + 3.62871i −0.193500 + 0.137153i
\(701\) 25.6806i 0.969944i −0.874530 0.484972i \(-0.838830\pi\)
0.874530 0.484972i \(-0.161170\pi\)
\(702\) −0.624535 3.55105i −0.0235715 0.134026i
\(703\) 47.2777 47.2777i 1.78311 1.78311i
\(704\) 1.61087 + 0.431631i 0.0607119 + 0.0162677i
\(705\) 7.40822 4.74950i 0.279010 0.178877i
\(706\) 25.7934 + 14.8918i 0.970747 + 0.560461i
\(707\) 21.9744i 0.826432i
\(708\) −3.75310 + 6.50056i −0.141050 + 0.244306i
\(709\) −2.34589 + 0.628580i −0.0881018 + 0.0236068i −0.302601 0.953117i \(-0.597855\pi\)
0.214499 + 0.976724i \(0.431188\pi\)
\(710\) −0.142807 3.06867i −0.00535945 0.115165i
\(711\) −4.27437 + 7.40343i −0.160301 + 0.277650i
\(712\) 4.94404 + 1.32475i 0.185286 + 0.0496472i
\(713\) −29.8423 + 17.2295i −1.11760 + 0.645248i
\(714\) 6.01322 0.225039
\(715\) −11.3572 7.19662i −0.424737 0.269138i
\(716\) −2.97221 −0.111077
\(717\) 18.2758 10.5515i 0.682522 0.394054i
\(718\) 2.23270 + 0.598250i 0.0833236 + 0.0223265i
\(719\) −22.0098 + 38.1221i −0.820827 + 1.42171i 0.0842403 + 0.996445i \(0.473154\pi\)
−0.905067 + 0.425268i \(0.860180\pi\)
\(720\) −1.65293 1.50593i −0.0616011 0.0561226i
\(721\) 10.7476 2.87982i 0.400262 0.107250i
\(722\) −11.6963 + 20.2585i −0.435290 + 0.753944i
\(723\) 6.98356i 0.259722i
\(724\) −7.42688 4.28791i −0.276018 0.159359i
\(725\) −20.5768 29.0306i −0.764203 1.07817i
\(726\) 7.93875 + 2.12718i 0.294634 + 0.0789471i
\(727\) −26.8208 + 26.8208i −0.994730 + 0.994730i −0.999986 0.00525659i \(-0.998327\pi\)
0.00525659 + 0.999986i \(0.498327\pi\)
\(728\) 0.396369 4.50767i 0.0146904 0.167065i
\(729\) 1.00000i 0.0370370i
\(730\) 23.3277 + 5.10142i 0.863396 + 0.188812i
\(731\) 15.3157 + 26.5276i 0.566472 + 0.981158i
\(732\) −2.52016 9.40536i −0.0931478 0.347632i
\(733\) −12.0371 −0.444602 −0.222301 0.974978i \(-0.571357\pi\)
−0.222301 + 0.974978i \(0.571357\pi\)
\(734\) −1.69791 6.33667i −0.0626709 0.233891i
\(735\) −10.7759 5.57032i −0.397475 0.205464i
\(736\) 3.46605 3.46605i 0.127760 0.127760i
\(737\) 3.00203 0.804391i 0.110581 0.0296301i
\(738\) 0.614688 2.29405i 0.0226270 0.0844450i
\(739\) −3.43048 + 12.8027i −0.126192 + 0.470956i −0.999879 0.0155321i \(-0.995056\pi\)
0.873687 + 0.486488i \(0.161722\pi\)
\(740\) 15.4643 16.9739i 0.568479 0.623973i
\(741\) −21.2805 + 9.91184i −0.781757 + 0.364121i
\(742\) 3.46447 + 3.46447i 0.127185 + 0.127185i
\(743\) −16.4135 28.4291i −0.602154 1.04296i −0.992494 0.122291i \(-0.960976\pi\)
0.390340 0.920671i \(-0.372357\pi\)
\(744\) −6.08811 + 3.51497i −0.223201 + 0.128865i
\(745\) −15.7314 8.13196i −0.576355 0.297932i
\(746\) 1.88084 + 1.88084i 0.0688626 + 0.0688626i
\(747\) −3.18610 1.83950i −0.116573 0.0673037i
\(748\) 6.91992 + 3.99522i 0.253017 + 0.146080i
\(749\) −0.994610 0.994610i −0.0363422 0.0363422i
\(750\) 10.3657 + 4.18943i 0.378503 + 0.152976i
\(751\) 35.6504 20.5828i 1.30090 0.751076i 0.320344 0.947301i \(-0.396202\pi\)
0.980559 + 0.196225i \(0.0628683\pi\)
\(752\) 1.96773 + 3.40821i 0.0717559 + 0.124285i
\(753\) −2.98184 2.98184i −0.108664 0.108664i
\(754\) 25.5609 + 2.24763i 0.930874 + 0.0818537i
\(755\) 1.65263 + 35.5121i 0.0601453 + 1.29242i
\(756\) −0.324825 + 1.21226i −0.0118138 + 0.0440895i
\(757\) −3.34498 + 12.4836i −0.121575 + 0.453725i −0.999694 0.0247168i \(-0.992132\pi\)
0.878119 + 0.478442i \(0.158798\pi\)
\(758\) −11.2762 + 3.02144i −0.409569 + 0.109744i
\(759\) −5.78032 + 5.78032i −0.209812 + 0.209812i
\(760\) −6.68548 + 12.9332i −0.242508 + 0.469136i
\(761\) 6.49514 + 24.2402i 0.235449 + 0.878707i 0.977946 + 0.208858i \(0.0669745\pi\)
−0.742497 + 0.669849i \(0.766359\pi\)
\(762\) 9.99556 0.362101
\(763\) −6.02170 22.4733i −0.218000 0.813588i
\(764\) 11.4751 + 19.8754i 0.415154 + 0.719068i
\(765\) −5.78237 9.01928i −0.209062 0.326093i
\(766\) 12.3736i 0.447075i
\(767\) 17.3873 + 20.7399i 0.627818 + 0.748873i
\(768\) 0.707107 0.707107i 0.0255155 0.0255155i
\(769\) 1.47911 + 0.396327i 0.0533382 + 0.0142919i 0.285389 0.958412i \(-0.407877\pi\)
−0.232051 + 0.972704i \(0.574544\pi\)
\(770\) 2.52593 + 3.93991i 0.0910282 + 0.141985i
\(771\) 10.5507 + 6.09148i 0.379976 + 0.219379i
\(772\) 8.98509i 0.323381i
\(773\) 11.4479 19.8283i 0.411752 0.713176i −0.583329 0.812236i \(-0.698250\pi\)
0.995081 + 0.0990599i \(0.0315835\pi\)
\(774\) −6.17528 + 1.65466i −0.221966 + 0.0594756i
\(775\) 22.4389 27.0555i 0.806028 0.971862i
\(776\) 7.29623 12.6374i 0.261919 0.453658i
\(777\) −12.4487 3.33561i −0.446594 0.119664i
\(778\) −2.46197 + 1.42142i −0.0882660 + 0.0509604i
\(779\) −15.4633 −0.554031
\(780\) −7.14224 + 3.74010i −0.255733 + 0.133917i
\(781\) −2.29114 −0.0819835
\(782\) 20.3392 11.7429i 0.727330 0.419924i
\(783\) −6.87419 1.84193i −0.245663 0.0658253i
\(784\) 2.71245 4.69811i 0.0968734 0.167790i
\(785\) 6.36890 0.296390i 0.227316 0.0105786i
\(786\) −6.80651 + 1.82380i −0.242780 + 0.0650528i
\(787\) −1.29280 + 2.23919i −0.0460832 + 0.0798184i −0.888147 0.459560i \(-0.848007\pi\)
0.842064 + 0.539378i \(0.181341\pi\)
\(788\) 25.3778i 0.904047i
\(789\) −14.5328 8.39052i −0.517382 0.298710i
\(790\) 18.6743 + 4.08378i 0.664400 + 0.145294i
\(791\) −9.34608 2.50427i −0.332308 0.0890418i
\(792\) −1.17924 + 1.17924i −0.0419024 + 0.0419024i
\(793\) −34.9728 3.07524i −1.24192 0.109205i
\(794\) 22.4154i 0.795494i
\(795\) 1.86492 8.52787i 0.0661419 0.302452i
\(796\) −12.6150 21.8497i −0.447125 0.774443i
\(797\) 12.1417 + 45.3134i 0.430080 + 1.60508i 0.752572 + 0.658510i \(0.228813\pi\)
−0.322492 + 0.946572i \(0.604520\pi\)
\(798\) 8.17142 0.289265
\(799\) 4.88030 + 18.2135i 0.172653 + 0.644348i
\(800\) −2.08704 + 4.54359i −0.0737881 + 0.160640i
\(801\) −3.61929 + 3.61929i −0.127881 + 0.127881i
\(802\) −33.8471 + 9.06930i −1.19518 + 0.320248i
\(803\) 4.60939 17.2025i 0.162662 0.607062i
\(804\) 0.482337 1.80011i 0.0170107 0.0634848i
\(805\) 13.7410 0.639464i 0.484306 0.0225382i
\(806\) 4.39044 + 24.9637i 0.154647 + 0.879308i
\(807\) −3.58802 3.58802i −0.126304 0.126304i
\(808\) −8.75455 15.1633i −0.307984 0.533444i
\(809\) 16.8126 9.70675i 0.591099 0.341271i −0.174433 0.984669i \(-0.555809\pi\)
0.765532 + 0.643398i \(0.222476\pi\)
\(810\) 2.13064 0.678517i 0.0748630 0.0238407i
\(811\) −3.18239 3.18239i −0.111749 0.111749i 0.649021 0.760770i \(-0.275179\pi\)
−0.760770 + 0.649021i \(0.775179\pi\)
\(812\) −7.73501 4.46581i −0.271446 0.156719i
\(813\) −26.8788 15.5185i −0.942681 0.544257i
\(814\) −12.1096 12.1096i −0.424440 0.424440i
\(815\) 8.84243 2.81594i 0.309737 0.0986380i
\(816\) 4.14939 2.39565i 0.145258 0.0838647i
\(817\) 20.8127 + 36.0486i 0.728143 + 1.26118i
\(818\) −12.6403 12.6403i −0.441956 0.441956i
\(819\) 3.70557 + 2.59710i 0.129483 + 0.0907500i
\(820\) −5.30485 + 0.246872i −0.185254 + 0.00862115i
\(821\) 2.04795 7.64305i 0.0714739 0.266744i −0.920937 0.389712i \(-0.872575\pi\)
0.992411 + 0.122968i \(0.0392412\pi\)
\(822\) −0.991075 + 3.69874i −0.0345677 + 0.129008i
\(823\) −28.9161 + 7.74804i −1.00795 + 0.270080i −0.724773 0.688988i \(-0.758055\pi\)
−0.283178 + 0.959067i \(0.591389\pi\)
\(824\) 6.26904 6.26904i 0.218392 0.218392i
\(825\) 3.48055 7.57733i 0.121177 0.263809i
\(826\) −2.43820 9.09947i −0.0848357 0.316611i
\(827\) 52.9999 1.84299 0.921493 0.388394i \(-0.126970\pi\)
0.921493 + 0.388394i \(0.126970\pi\)
\(828\) 1.26866 + 4.73471i 0.0440891 + 0.164543i
\(829\) −6.62400 11.4731i −0.230061 0.398478i 0.727765 0.685827i \(-0.240559\pi\)
−0.957826 + 0.287349i \(0.907226\pi\)
\(830\) −1.75748 + 8.03656i −0.0610029 + 0.278953i
\(831\) 27.6726i 0.959950i
\(832\) −1.52233 3.26841i −0.0527774 0.113312i
\(833\) 18.3794 18.3794i 0.636809 0.636809i
\(834\) 15.3248 + 4.10627i 0.530655 + 0.142189i
\(835\) −11.7781 2.57571i −0.407600 0.0891360i
\(836\) 9.40355 + 5.42914i 0.325229 + 0.187771i
\(837\) 7.02994i 0.242990i
\(838\) −3.17779 + 5.50409i −0.109775 + 0.190136i
\(839\) 20.7102 5.54929i 0.714997 0.191583i 0.117059 0.993125i \(-0.462653\pi\)
0.597938 + 0.801542i \(0.295987\pi\)
\(840\) 2.80329 0.130457i 0.0967227 0.00450118i
\(841\) 10.8236 18.7470i 0.373227 0.646447i
\(842\) −14.1700 3.79683i −0.488330 0.130848i
\(843\) 7.80021 4.50345i 0.268654 0.155107i
\(844\) −2.90413 −0.0999644
\(845\) 3.85160 + 28.8126i 0.132499 + 0.991183i
\(846\) −3.93547 −0.135304
\(847\) −8.93288 + 5.15740i −0.306937 + 0.177210i
\(848\) 3.77088 + 1.01041i 0.129493 + 0.0346975i
\(849\) −10.1907 + 17.6508i −0.349743 + 0.605773i
\(850\) −15.2934 + 18.4399i −0.524558 + 0.632482i
\(851\) −48.6206 + 13.0279i −1.66669 + 0.446589i
\(852\) −0.686919 + 1.18978i −0.0235335 + 0.0407611i
\(853\) 21.3327i 0.730419i 0.930925 + 0.365210i \(0.119003\pi\)
−0.930925 + 0.365210i \(0.880997\pi\)
\(854\) 10.5832 + 6.11019i 0.362148 + 0.209086i
\(855\) −7.85772 12.2564i −0.268728 0.419159i
\(856\) −1.08258 0.290076i −0.0370017 0.00991458i
\(857\) −24.2701 + 24.2701i −0.829051 + 0.829051i −0.987386 0.158334i \(-0.949388\pi\)
0.158334 + 0.987386i \(0.449388\pi\)
\(858\) 2.53879 + 5.45071i 0.0866728 + 0.186084i
\(859\) 22.1224i 0.754807i 0.926049 + 0.377403i \(0.123183\pi\)
−0.926049 + 0.377403i \(0.876817\pi\)
\(860\) 7.71551 + 12.0346i 0.263097 + 0.410375i
\(861\) 1.49032 + 2.58132i 0.0507901 + 0.0879711i
\(862\) 5.58701 + 20.8510i 0.190294 + 0.710188i
\(863\) −35.7630 −1.21739 −0.608693 0.793406i \(-0.708306\pi\)
−0.608693 + 0.793406i \(0.708306\pi\)
\(864\) 0.258819 + 0.965926i 0.00880520 + 0.0328615i
\(865\) −7.56556 + 14.6357i −0.257237 + 0.497629i
\(866\) 4.87383 4.87383i 0.165620 0.165620i
\(867\) 5.75366 1.54169i 0.195405 0.0523585i
\(868\) 2.28350 8.52213i 0.0775070 0.289260i
\(869\) 3.68990 13.7709i 0.125171 0.467146i
\(870\) 0.739761 + 15.8962i 0.0250802 + 0.538931i
\(871\) −5.50245 3.85647i −0.186444 0.130672i
\(872\) −13.1086 13.1086i −0.443912 0.443912i
\(873\) 7.29623 + 12.6374i 0.246940 + 0.427713i
\(874\) 27.6392 15.9575i 0.934909 0.539770i
\(875\) −12.9168 + 5.48109i −0.436668 + 0.185295i
\(876\) −7.55119 7.55119i −0.255131 0.255131i
\(877\) −8.43716 4.87120i −0.284903 0.164489i 0.350738 0.936474i \(-0.385931\pi\)
−0.635641 + 0.771985i \(0.719264\pi\)
\(878\) 13.3423 + 7.70318i 0.450281 + 0.259970i
\(879\) −16.5333 16.5333i −0.557655 0.557655i
\(880\) 3.31266 + 1.71240i 0.111670 + 0.0577249i
\(881\) 3.83408 2.21361i 0.129174 0.0745784i −0.434021 0.900903i \(-0.642906\pi\)
0.563194 + 0.826324i \(0.309572\pi\)
\(882\) 2.71245 + 4.69811i 0.0913331 + 0.158194i
\(883\) 8.13776 + 8.13776i 0.273858 + 0.273858i 0.830651 0.556793i \(-0.187969\pi\)
−0.556793 + 0.830651i \(0.687969\pi\)
\(884\) −2.99234 17.0142i −0.100643 0.572249i
\(885\) −11.3038 + 12.4072i −0.379973 + 0.417064i
\(886\) 6.91692 25.8143i 0.232379 0.867249i
\(887\) −8.61028 + 32.1340i −0.289105 + 1.07895i 0.656682 + 0.754167i \(0.271959\pi\)
−0.945787 + 0.324787i \(0.894707\pi\)
\(888\) −9.91906 + 2.65780i −0.332862 + 0.0891900i
\(889\) −8.87043 + 8.87043i −0.297505 + 0.297505i
\(890\) 10.1671 + 5.25564i 0.340803 + 0.176170i
\(891\) −0.431631 1.61087i −0.0144602 0.0539662i
\(892\) 4.52521 0.151515
\(893\) 6.63189 + 24.7505i 0.221928 + 0.828245i
\(894\) 3.95984 + 6.85864i 0.132437 + 0.229387i
\(895\) −6.49262 1.41984i −0.217024 0.0474600i
\(896\) 1.25503i 0.0419275i
\(897\) 17.6055 + 1.54809i 0.587832 + 0.0516893i
\(898\) −11.6394 + 11.6394i −0.388412 + 0.388412i
\(899\) 48.3251 + 12.9487i 1.61173 + 0.431863i
\(900\) −2.89135 4.07923i −0.0963782 0.135974i
\(901\) 16.1988 + 9.35241i 0.539662 + 0.311574i
\(902\) 3.96073i 0.131878i
\(903\) 4.01177 6.94858i 0.133503 0.231234i
\(904\) −7.44692 + 1.99540i −0.247681 + 0.0663659i
\(905\) −14.1752 12.9146i −0.471201 0.429295i
\(906\) 7.94935 13.7687i 0.264100 0.457434i
\(907\) −26.7398 7.16492i −0.887882 0.237907i −0.214077 0.976817i \(-0.568674\pi\)
−0.673805 + 0.738910i \(0.735341\pi\)
\(908\) −20.2480 + 11.6902i −0.671955 + 0.387953i
\(909\) 17.5091 0.580740
\(910\) 3.01918 9.65740i 0.100085 0.320140i
\(911\) 54.7622 1.81435 0.907177 0.420749i \(-0.138233\pi\)
0.907177 + 0.420749i \(0.138233\pi\)
\(912\) 5.63865 3.25548i 0.186714 0.107800i
\(913\) 5.92638 + 1.58797i 0.196134 + 0.0525541i
\(914\) −8.73356 + 15.1270i −0.288881 + 0.500356i
\(915\) −1.01215 21.7494i −0.0334607 0.719013i
\(916\) −12.9650 + 3.47396i −0.428375 + 0.114783i
\(917\) 4.42184 7.65886i 0.146022 0.252918i
\(918\) 4.79131i 0.158137i
\(919\) 15.8534 + 9.15294i 0.522954 + 0.301928i 0.738142 0.674645i \(-0.235703\pi\)
−0.215188 + 0.976573i \(0.569037\pi\)
\(920\) 9.22715 5.91564i 0.304210 0.195033i
\(921\) −14.6013 3.91241i −0.481130 0.128918i
\(922\) −7.56691 + 7.56691i −0.249203 + 0.249203i
\(923\) 3.18234 + 3.79596i 0.104748 + 0.124945i
\(924\) 2.09300i 0.0688546i
\(925\) 41.8895 29.6911i 1.37732 0.976238i
\(926\) 13.0337 + 22.5751i 0.428315 + 0.741863i
\(927\) 2.29463 + 8.56367i 0.0753654 + 0.281268i
\(928\) −7.11668 −0.233616
\(929\) 8.75599 + 32.6778i 0.287275 + 1.07212i 0.947161 + 0.320758i \(0.103938\pi\)
−0.659886 + 0.751365i \(0.729396\pi\)
\(930\) −14.9783 + 4.76993i −0.491156 + 0.156412i
\(931\) 24.9760 24.9760i 0.818554 0.818554i
\(932\) −11.5800 + 3.10284i −0.379315 + 0.101637i
\(933\) −8.36371 + 31.2138i −0.273816 + 1.02189i
\(934\) 4.12636 15.3998i 0.135019 0.503897i
\(935\) 13.2076 + 12.0330i 0.431936 + 0.393522i
\(936\) 3.59169 + 0.315825i 0.117398 + 0.0103231i
\(937\) −24.2014 24.2014i −0.790626 0.790626i 0.190970 0.981596i \(-0.438837\pi\)
−0.981596 + 0.190970i \(0.938837\pi\)
\(938\) 1.16944 + 2.02552i 0.0381835 + 0.0661357i
\(939\) 22.5579 13.0238i 0.736151 0.425017i
\(940\) 2.67028 + 8.38505i 0.0870949 + 0.273490i
\(941\) −18.5270 18.5270i −0.603962 0.603962i 0.337399 0.941362i \(-0.390453\pi\)
−0.941362 + 0.337399i \(0.890453\pi\)
\(942\) −2.46933 1.42567i −0.0804553 0.0464509i
\(943\) 10.0818 + 5.82074i 0.328309 + 0.189549i
\(944\) −5.30768 5.30768i −0.172750 0.172750i
\(945\) −1.28867 + 2.49295i −0.0419203 + 0.0810956i
\(946\) 9.23337 5.33089i 0.300203 0.173322i
\(947\) −24.4277 42.3100i −0.793793 1.37489i −0.923603 0.383351i \(-0.874770\pi\)
0.129809 0.991539i \(-0.458564\pi\)
\(948\) −6.04487 6.04487i −0.196328 0.196328i
\(949\) −34.9033 + 16.2570i −1.13301 + 0.527724i
\(950\) −20.7823 + 25.0581i −0.674267 + 0.812993i
\(951\) 3.74188 13.9649i 0.121339 0.452843i
\(952\) −1.55633 + 5.80832i −0.0504411 + 0.188249i
\(953\) −2.40429 + 0.644227i −0.0778825 + 0.0208686i −0.297550 0.954706i \(-0.596169\pi\)
0.219667 + 0.975575i \(0.429503\pi\)
\(954\) −2.76048 + 2.76048i −0.0893738 + 0.0893738i
\(955\) 15.5721 + 48.8985i 0.503900 + 1.58232i
\(956\) 5.46187 + 20.3840i 0.176650 + 0.659265i
\(957\) 11.8685 0.383653
\(958\) 5.77188 + 21.5410i 0.186481 + 0.695957i
\(959\) −2.40288 4.16192i −0.0775932 0.134395i
\(960\) 1.88242 1.20685i 0.0607550 0.0389508i
\(961\) 18.4201i 0.594196i
\(962\) −3.24320 + 36.8830i −0.104565 + 1.18915i
\(963\) 0.792501 0.792501i 0.0255380 0.0255380i
\(964\) −6.74561 1.80748i −0.217261 0.0582150i
\(965\) −4.29223 + 19.6274i −0.138172 + 0.631830i
\(966\) −5.32762 3.07590i −0.171413 0.0989656i
\(967\) 39.1521i 1.25905i −0.776982 0.629523i \(-0.783251\pi\)
0.776982 0.629523i \(-0.216749\pi\)
\(968\) −4.10940 + 7.11768i −0.132081 + 0.228771i
\(969\) 30.1330 8.07412i 0.968012 0.259378i
\(970\) 21.9752 24.1203i 0.705581 0.774457i
\(971\) −14.5620 + 25.2222i −0.467318 + 0.809418i −0.999303 0.0373354i \(-0.988113\pi\)
0.531985 + 0.846754i \(0.321446\pi\)
\(972\) −0.965926 0.258819i −0.0309821 0.00830162i
\(973\) −17.2439 + 9.95576i −0.552813 + 0.319167i
\(974\) −24.3627 −0.780632
\(975\) −17.3885 + 4.75816i −0.556878 + 0.152383i
\(976\) 9.73715 0.311679
\(977\) −47.8066 + 27.6011i −1.52947 + 0.883039i −0.530084 + 0.847945i \(0.677839\pi\)
−0.999384 + 0.0350931i \(0.988827\pi\)
\(978\) −4.00872 1.07413i −0.128185 0.0343470i
\(979\) 4.26800 7.39240i 0.136406 0.236262i
\(980\) 8.16952 8.96700i 0.260966 0.286440i
\(981\) 17.9066 4.79807i 0.571715 0.153190i
\(982\) 19.1480 33.1654i 0.611039 1.05835i
\(983\) 45.1532i 1.44016i −0.693890 0.720081i \(-0.744105\pi\)
0.693890 0.720081i \(-0.255895\pi\)
\(984\) 2.05678 + 1.18749i 0.0655679 + 0.0378556i
\(985\) −12.1231 + 55.4364i −0.386275 + 1.76635i
\(986\) −32.9363 8.82527i −1.04891 0.281054i
\(987\) 3.49248 3.49248i 0.111167 0.111167i
\(988\) −4.06632 23.1207i −0.129367 0.735568i
\(989\) 31.3374i 0.996471i
\(990\) −3.13931 + 2.01265i −0.0997738 + 0.0639663i
\(991\) −30.2300 52.3598i −0.960286 1.66326i −0.721778 0.692125i \(-0.756675\pi\)
−0.238508 0.971140i \(-0.576658\pi\)
\(992\) −1.81948 6.79040i −0.0577686 0.215595i
\(993\) 4.19873 0.133243
\(994\) −0.446256 1.66545i −0.0141544 0.0528249i
\(995\) −17.1189 53.7558i −0.542706 1.70417i
\(996\) 2.60144 2.60144i 0.0824298 0.0824298i
\(997\) 20.5623 5.50966i 0.651216 0.174493i 0.0819371 0.996638i \(-0.473889\pi\)
0.569278 + 0.822145i \(0.307223\pi\)
\(998\) −3.37141 + 12.5823i −0.106720 + 0.398285i
\(999\) 2.65780 9.91906i 0.0840892 0.313825i
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 390.2.bd.c.37.3 32
5.3 odd 4 390.2.bn.c.193.5 yes 32
13.6 odd 12 390.2.bn.c.97.5 yes 32
65.58 even 12 inner 390.2.bd.c.253.3 yes 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
390.2.bd.c.37.3 32 1.1 even 1 trivial
390.2.bd.c.253.3 yes 32 65.58 even 12 inner
390.2.bn.c.97.5 yes 32 13.6 odd 12
390.2.bn.c.193.5 yes 32 5.3 odd 4