Properties

Label 390.2.bn.c.67.2
Level $390$
Weight $2$
Character 390.67
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(67,390)]
 
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, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("390.67");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 390.bn (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 67.2
Character \(\chi\) \(=\) 390.67
Dual form 390.2.bn.c.163.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{2} +(-0.965926 - 0.258819i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.0142140 - 2.23602i) q^{5} +(0.258819 + 0.965926i) q^{6} +(-3.50522 - 2.02374i) q^{7} +1.00000 q^{8} +(0.866025 + 0.500000i) q^{9} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{2} +(-0.965926 - 0.258819i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.0142140 - 2.23602i) q^{5} +(0.258819 + 0.965926i) q^{6} +(-3.50522 - 2.02374i) q^{7} +1.00000 q^{8} +(0.866025 + 0.500000i) q^{9} +(-1.94356 + 1.10570i) q^{10} +(-1.40394 + 5.23956i) q^{11} +(0.707107 - 0.707107i) q^{12} +(2.49480 - 2.60307i) q^{13} +4.04748i q^{14} +(-0.592455 + 2.15615i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-0.0494978 - 0.184728i) q^{17} -1.00000i q^{18} +(-6.09967 + 1.63440i) q^{19} +(1.92935 + 1.13032i) q^{20} +(2.86200 + 2.86200i) q^{21} +(5.23956 - 1.40394i) q^{22} +(-1.67663 + 6.25726i) q^{23} +(-0.965926 - 0.258819i) q^{24} +(-4.99960 - 0.0635655i) q^{25} +(-3.50172 - 0.859025i) q^{26} +(-0.707107 - 0.707107i) q^{27} +(3.50522 - 2.02374i) q^{28} +(-2.98976 + 1.72614i) q^{29} +(2.16351 - 0.564996i) q^{30} +(3.55470 - 3.55470i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(2.71220 - 4.69766i) q^{33} +(-0.135230 + 0.135230i) q^{34} +(-4.57495 + 7.80898i) q^{35} +(-0.866025 + 0.500000i) q^{36} +(-6.84301 + 3.95081i) q^{37} +(4.46527 + 4.46527i) q^{38} +(-3.08352 + 1.86867i) q^{39} +(0.0142140 - 2.23602i) q^{40} +(-5.73777 - 1.53743i) q^{41} +(1.04756 - 3.90956i) q^{42} +(4.93758 - 1.32302i) q^{43} +(-3.83563 - 3.83563i) q^{44} +(1.13032 - 1.92935i) q^{45} +(6.25726 - 1.67663i) q^{46} -2.11952i q^{47} +(0.258819 + 0.965926i) q^{48} +(4.69103 + 8.12510i) q^{49} +(2.44475 + 4.36156i) q^{50} +0.191245i q^{51} +(1.00692 + 3.46210i) q^{52} +(0.255562 - 0.255562i) q^{53} +(-0.258819 + 0.965926i) q^{54} +(11.6958 + 3.21371i) q^{55} +(-3.50522 - 2.02374i) q^{56} +6.31484 q^{57} +(2.98976 + 1.72614i) q^{58} +(1.13076 + 4.22004i) q^{59} +(-1.57106 - 1.59116i) q^{60} +(4.82504 - 8.35721i) q^{61} +(-4.85581 - 1.30111i) q^{62} +(-2.02374 - 3.50522i) q^{63} +1.00000 q^{64} +(-5.78506 - 5.61543i) q^{65} -5.42439 q^{66} +(-6.54148 - 11.3302i) q^{67} +(0.184728 + 0.0494978i) q^{68} +(3.23899 - 5.61010i) q^{69} +(9.05025 + 0.0575307i) q^{70} +(0.0786499 + 0.293526i) q^{71} +(0.866025 + 0.500000i) q^{72} -13.3512 q^{73} +(6.84301 + 3.95081i) q^{74} +(4.81279 + 1.35539i) q^{75} +(1.63440 - 6.09967i) q^{76} +(15.5246 - 15.5246i) q^{77} +(3.16007 + 1.73607i) q^{78} -2.94298i q^{79} +(-1.94356 + 1.10570i) q^{80} +(0.500000 + 0.866025i) q^{81} +(1.53743 + 5.73777i) q^{82} -10.3846i q^{83} +(-3.90956 + 1.04756i) q^{84} +(-0.413760 + 0.108052i) q^{85} +(-3.61456 - 3.61456i) q^{86} +(3.33464 - 0.893514i) q^{87} +(-1.40394 + 5.23956i) q^{88} +(-6.09359 - 1.63277i) q^{89} +(-2.23602 - 0.0142140i) q^{90} +(-14.0127 + 4.07550i) q^{91} +(-4.58063 - 4.58063i) q^{92} +(-4.35360 + 2.51355i) q^{93} +(-1.83556 + 1.05976i) q^{94} +(3.56786 + 13.6622i) q^{95} +(0.707107 - 0.707107i) q^{96} +(4.47453 - 7.75012i) q^{97} +(4.69103 - 8.12510i) q^{98} +(-3.83563 + 3.83563i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q - 16 q^{2} - 16 q^{4} - 12 q^{7} + 32 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 32 q - 16 q^{2} - 16 q^{4} - 12 q^{7} + 32 q^{8} - 4 q^{11} + 8 q^{13} - 4 q^{15} - 16 q^{16} - 4 q^{17} + 20 q^{19} + 8 q^{21} + 8 q^{22} - 16 q^{23} - 8 q^{25} - 4 q^{26} + 12 q^{28} + 24 q^{29} + 8 q^{30} + 12 q^{31} - 16 q^{32} - 16 q^{34} + 12 q^{35} - 24 q^{37} - 4 q^{38} - 20 q^{39} - 28 q^{41} - 16 q^{42} + 4 q^{43} - 4 q^{44} - 4 q^{46} + 20 q^{49} - 8 q^{50} - 4 q^{52} - 4 q^{53} + 68 q^{55} - 12 q^{56} + 16 q^{57} - 24 q^{58} + 36 q^{59} - 4 q^{60} - 28 q^{61} - 48 q^{62} + 32 q^{64} - 28 q^{65} - 28 q^{67} + 20 q^{68} - 20 q^{69} - 24 q^{70} - 4 q^{71} - 48 q^{73} + 24 q^{74} + 24 q^{75} - 16 q^{76} + 20 q^{77} + 4 q^{78} + 16 q^{81} + 44 q^{82} + 8 q^{84} + 64 q^{85} - 8 q^{86} + 20 q^{87} - 4 q^{88} - 16 q^{89} - 40 q^{91} + 20 q^{92} - 24 q^{93} - 24 q^{94} + 68 q^{95} + 8 q^{97} + 20 q^{98} - 4 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 0.866025i −0.353553 0.612372i
\(3\) −0.965926 0.258819i −0.557678 0.149429i
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) 0.0142140 2.23602i 0.00635668 0.999980i
\(6\) 0.258819 + 0.965926i 0.105662 + 0.394338i
\(7\) −3.50522 2.02374i −1.32485 0.764901i −0.340350 0.940299i \(-0.610545\pi\)
−0.984498 + 0.175398i \(0.943879\pi\)
\(8\) 1.00000 0.353553
\(9\) 0.866025 + 0.500000i 0.288675 + 0.166667i
\(10\) −1.94356 + 1.10570i −0.614607 + 0.349654i
\(11\) −1.40394 + 5.23956i −0.423303 + 1.57979i 0.344299 + 0.938860i \(0.388117\pi\)
−0.767602 + 0.640927i \(0.778550\pi\)
\(12\) 0.707107 0.707107i 0.204124 0.204124i
\(13\) 2.49480 2.60307i 0.691933 0.721962i
\(14\) 4.04748i 1.08173i
\(15\) −0.592455 + 2.15615i −0.152971 + 0.556716i
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −0.0494978 0.184728i −0.0120050 0.0448032i 0.959664 0.281151i \(-0.0907162\pi\)
−0.971669 + 0.236348i \(0.924050\pi\)
\(18\) 1.00000i 0.235702i
\(19\) −6.09967 + 1.63440i −1.39936 + 0.374957i −0.878115 0.478450i \(-0.841199\pi\)
−0.521245 + 0.853407i \(0.674532\pi\)
\(20\) 1.92935 + 1.13032i 0.431415 + 0.252747i
\(21\) 2.86200 + 2.86200i 0.624539 + 0.624539i
\(22\) 5.23956 1.40394i 1.11708 0.299320i
\(23\) −1.67663 + 6.25726i −0.349601 + 1.30473i 0.537543 + 0.843236i \(0.319352\pi\)
−0.887144 + 0.461492i \(0.847314\pi\)
\(24\) −0.965926 0.258819i −0.197169 0.0528312i
\(25\) −4.99960 0.0635655i −0.999919 0.0127131i
\(26\) −3.50172 0.859025i −0.686745 0.168469i
\(27\) −0.707107 0.707107i −0.136083 0.136083i
\(28\) 3.50522 2.02374i 0.662424 0.382450i
\(29\) −2.98976 + 1.72614i −0.555184 + 0.320536i −0.751210 0.660063i \(-0.770530\pi\)
0.196026 + 0.980599i \(0.437196\pi\)
\(30\) 2.16351 0.564996i 0.395001 0.103154i
\(31\) 3.55470 3.55470i 0.638443 0.638443i −0.311728 0.950171i \(-0.600908\pi\)
0.950171 + 0.311728i \(0.100908\pi\)
\(32\) −0.500000 + 0.866025i −0.0883883 + 0.153093i
\(33\) 2.71220 4.69766i 0.472133 0.817758i
\(34\) −0.135230 + 0.135230i −0.0231918 + 0.0231918i
\(35\) −4.57495 + 7.80898i −0.773307 + 1.31996i
\(36\) −0.866025 + 0.500000i −0.144338 + 0.0833333i
\(37\) −6.84301 + 3.95081i −1.12498 + 0.649510i −0.942669 0.333730i \(-0.891693\pi\)
−0.182315 + 0.983240i \(0.558359\pi\)
\(38\) 4.46527 + 4.46527i 0.724362 + 0.724362i
\(39\) −3.08352 + 1.86867i −0.493758 + 0.299227i
\(40\) 0.0142140 2.23602i 0.00224743 0.353546i
\(41\) −5.73777 1.53743i −0.896089 0.240106i −0.218753 0.975780i \(-0.570199\pi\)
−0.677336 + 0.735674i \(0.736866\pi\)
\(42\) 1.04756 3.90956i 0.161643 0.603258i
\(43\) 4.93758 1.32302i 0.752973 0.201759i 0.138137 0.990413i \(-0.455889\pi\)
0.614837 + 0.788655i \(0.289222\pi\)
\(44\) −3.83563 3.83563i −0.578242 0.578242i
\(45\) 1.13032 1.92935i 0.168498 0.287610i
\(46\) 6.25726 1.67663i 0.922582 0.247205i
\(47\) 2.11952i 0.309164i −0.987980 0.154582i \(-0.950597\pi\)
0.987980 0.154582i \(-0.0494031\pi\)
\(48\) 0.258819 + 0.965926i 0.0373573 + 0.139419i
\(49\) 4.69103 + 8.12510i 0.670147 + 1.16073i
\(50\) 2.44475 + 4.36156i 0.345740 + 0.616818i
\(51\) 0.191245i 0.0267796i
\(52\) 1.00692 + 3.46210i 0.139635 + 0.480106i
\(53\) 0.255562 0.255562i 0.0351041 0.0351041i −0.689337 0.724441i \(-0.742098\pi\)
0.724441 + 0.689337i \(0.242098\pi\)
\(54\) −0.258819 + 0.965926i −0.0352208 + 0.131446i
\(55\) 11.6958 + 3.21371i 1.57706 + 0.433336i
\(56\) −3.50522 2.02374i −0.468404 0.270433i
\(57\) 6.31484 0.836421
\(58\) 2.98976 + 1.72614i 0.392574 + 0.226653i
\(59\) 1.13076 + 4.22004i 0.147212 + 0.549403i 0.999647 + 0.0265695i \(0.00845833\pi\)
−0.852435 + 0.522833i \(0.824875\pi\)
\(60\) −1.57106 1.59116i −0.202822 0.205418i
\(61\) 4.82504 8.35721i 0.617783 1.07003i −0.372107 0.928190i \(-0.621364\pi\)
0.989889 0.141841i \(-0.0453022\pi\)
\(62\) −4.85581 1.30111i −0.616689 0.165241i
\(63\) −2.02374 3.50522i −0.254967 0.441616i
\(64\) 1.00000 0.125000
\(65\) −5.78506 5.61543i −0.717549 0.696508i
\(66\) −5.42439 −0.667697
\(67\) −6.54148 11.3302i −0.799169 1.38420i −0.920158 0.391548i \(-0.871940\pi\)
0.120989 0.992654i \(-0.461393\pi\)
\(68\) 0.184728 + 0.0494978i 0.0224016 + 0.00600249i
\(69\) 3.23899 5.61010i 0.389929 0.675377i
\(70\) 9.05025 + 0.0575307i 1.08171 + 0.00687623i
\(71\) 0.0786499 + 0.293526i 0.00933403 + 0.0348351i 0.970436 0.241359i \(-0.0775933\pi\)
−0.961102 + 0.276195i \(0.910927\pi\)
\(72\) 0.866025 + 0.500000i 0.102062 + 0.0589256i
\(73\) −13.3512 −1.56264 −0.781320 0.624131i \(-0.785453\pi\)
−0.781320 + 0.624131i \(0.785453\pi\)
\(74\) 6.84301 + 3.95081i 0.795484 + 0.459273i
\(75\) 4.81279 + 1.35539i 0.555733 + 0.156507i
\(76\) 1.63440 6.09967i 0.187479 0.699680i
\(77\) 15.5246 15.5246i 1.76919 1.76919i
\(78\) 3.16007 + 1.73607i 0.357808 + 0.196571i
\(79\) 2.94298i 0.331111i −0.986200 0.165555i \(-0.947058\pi\)
0.986200 0.165555i \(-0.0529417\pi\)
\(80\) −1.94356 + 1.10570i −0.217297 + 0.123621i
\(81\) 0.500000 + 0.866025i 0.0555556 + 0.0962250i
\(82\) 1.53743 + 5.73777i 0.169781 + 0.633631i
\(83\) 10.3846i 1.13986i −0.821693 0.569930i \(-0.806970\pi\)
0.821693 0.569930i \(-0.193030\pi\)
\(84\) −3.90956 + 1.04756i −0.426568 + 0.114299i
\(85\) −0.413760 + 0.108052i −0.0448786 + 0.0117199i
\(86\) −3.61456 3.61456i −0.389768 0.389768i
\(87\) 3.33464 0.893514i 0.357511 0.0957948i
\(88\) −1.40394 + 5.23956i −0.149660 + 0.558539i
\(89\) −6.09359 1.63277i −0.645919 0.173073i −0.0790358 0.996872i \(-0.525184\pi\)
−0.566883 + 0.823798i \(0.691851\pi\)
\(90\) −2.23602 0.0142140i −0.235697 0.00149828i
\(91\) −14.0127 + 4.07550i −1.46893 + 0.427229i
\(92\) −4.58063 4.58063i −0.477564 0.477564i
\(93\) −4.35360 + 2.51355i −0.451448 + 0.260643i
\(94\) −1.83556 + 1.05976i −0.189324 + 0.109306i
\(95\) 3.56786 + 13.6622i 0.366055 + 1.40172i
\(96\) 0.707107 0.707107i 0.0721688 0.0721688i
\(97\) 4.47453 7.75012i 0.454320 0.786905i −0.544329 0.838872i \(-0.683216\pi\)
0.998649 + 0.0519668i \(0.0165490\pi\)
\(98\) 4.69103 8.12510i 0.473865 0.820759i
\(99\) −3.83563 + 3.83563i −0.385495 + 0.385495i
\(100\) 2.55485 4.29799i 0.255485 0.429799i
\(101\) 7.96916 4.60100i 0.792961 0.457816i −0.0480430 0.998845i \(-0.515298\pi\)
0.841004 + 0.541029i \(0.181965\pi\)
\(102\) 0.165623 0.0956223i 0.0163991 0.00946802i
\(103\) −11.7362 11.7362i −1.15640 1.15640i −0.985243 0.171162i \(-0.945248\pi\)
−0.171162 0.985243i \(-0.554752\pi\)
\(104\) 2.49480 2.60307i 0.244635 0.255252i
\(105\) 6.44017 6.35881i 0.628496 0.620556i
\(106\) −0.349104 0.0935422i −0.0339080 0.00908562i
\(107\) −0.575877 + 2.14920i −0.0556722 + 0.207771i −0.988159 0.153432i \(-0.950967\pi\)
0.932487 + 0.361203i \(0.117634\pi\)
\(108\) 0.965926 0.258819i 0.0929463 0.0249049i
\(109\) 2.61160 + 2.61160i 0.250145 + 0.250145i 0.821030 0.570885i \(-0.193400\pi\)
−0.570885 + 0.821030i \(0.693400\pi\)
\(110\) −3.06476 11.7357i −0.292213 1.11896i
\(111\) 7.63239 2.04509i 0.724434 0.194112i
\(112\) 4.04748i 0.382450i
\(113\) 3.63361 + 13.5608i 0.341821 + 1.27569i 0.896282 + 0.443484i \(0.146258\pi\)
−0.554462 + 0.832209i \(0.687076\pi\)
\(114\) −3.15742 5.46881i −0.295720 0.512201i
\(115\) 13.9675 + 3.83792i 1.30248 + 0.357888i
\(116\) 3.45227i 0.320536i
\(117\) 3.46210 1.00692i 0.320071 0.0930902i
\(118\) 3.08929 3.08929i 0.284392 0.284392i
\(119\) −0.200341 + 0.747683i −0.0183652 + 0.0685400i
\(120\) −0.592455 + 2.15615i −0.0540835 + 0.196829i
\(121\) −15.9557 9.21202i −1.45052 0.837457i
\(122\) −9.65007 −0.873677
\(123\) 5.14435 + 2.97009i 0.463850 + 0.267804i
\(124\) 1.30111 + 4.85581i 0.116843 + 0.436065i
\(125\) −0.213198 + 11.1783i −0.0190690 + 0.999818i
\(126\) −2.02374 + 3.50522i −0.180289 + 0.312269i
\(127\) −11.4986 3.08105i −1.02034 0.273399i −0.290396 0.956907i \(-0.593787\pi\)
−0.729943 + 0.683508i \(0.760454\pi\)
\(128\) −0.500000 0.866025i −0.0441942 0.0765466i
\(129\) −5.11175 −0.450065
\(130\) −1.97057 + 7.81773i −0.172831 + 0.685660i
\(131\) −12.2710 −1.07213 −0.536063 0.844178i \(-0.680089\pi\)
−0.536063 + 0.844178i \(0.680089\pi\)
\(132\) 2.71220 + 4.69766i 0.236066 + 0.408879i
\(133\) 24.6883 + 6.61520i 2.14074 + 0.573611i
\(134\) −6.54148 + 11.3302i −0.565098 + 0.978778i
\(135\) −1.59116 + 1.57106i −0.136945 + 0.135215i
\(136\) −0.0494978 0.184728i −0.00424440 0.0158403i
\(137\) −5.28505 3.05133i −0.451533 0.260692i 0.256945 0.966426i \(-0.417284\pi\)
−0.708477 + 0.705734i \(0.750618\pi\)
\(138\) −6.47799 −0.551443
\(139\) 1.61309 + 0.931321i 0.136821 + 0.0789936i 0.566848 0.823822i \(-0.308163\pi\)
−0.430027 + 0.902816i \(0.641496\pi\)
\(140\) −4.47530 7.86651i −0.378232 0.664841i
\(141\) −0.548573 + 2.04730i −0.0461981 + 0.172414i
\(142\) 0.214876 0.214876i 0.0180320 0.0180320i
\(143\) 10.1364 + 16.7262i 0.847649 + 1.39872i
\(144\) 1.00000i 0.0833333i
\(145\) 3.81718 + 6.70970i 0.317000 + 0.557210i
\(146\) 6.67560 + 11.5625i 0.552477 + 0.956917i
\(147\) −2.42825 9.06237i −0.200279 0.747452i
\(148\) 7.90163i 0.649510i
\(149\) 3.67395 0.984433i 0.300982 0.0806479i −0.105168 0.994455i \(-0.533538\pi\)
0.406149 + 0.913807i \(0.366871\pi\)
\(150\) −1.23259 4.84569i −0.100641 0.395649i
\(151\) 5.59995 + 5.59995i 0.455717 + 0.455717i 0.897247 0.441530i \(-0.145564\pi\)
−0.441530 + 0.897247i \(0.645564\pi\)
\(152\) −6.09967 + 1.63440i −0.494749 + 0.132567i
\(153\) 0.0494978 0.184728i 0.00400166 0.0149344i
\(154\) −21.2070 5.68240i −1.70891 0.457901i
\(155\) −7.89787 7.99892i −0.634372 0.642489i
\(156\) −0.0765584 3.60474i −0.00612958 0.288610i
\(157\) 10.3659 + 10.3659i 0.827291 + 0.827291i 0.987141 0.159850i \(-0.0511012\pi\)
−0.159850 + 0.987141i \(0.551101\pi\)
\(158\) −2.54869 + 1.47149i −0.202763 + 0.117065i
\(159\) −0.312998 + 0.180710i −0.0248224 + 0.0143312i
\(160\) 1.92935 + 1.13032i 0.152528 + 0.0893597i
\(161\) 18.5400 18.5400i 1.46116 1.46116i
\(162\) 0.500000 0.866025i 0.0392837 0.0680414i
\(163\) −3.30721 + 5.72825i −0.259041 + 0.448672i −0.965985 0.258597i \(-0.916740\pi\)
0.706945 + 0.707269i \(0.250073\pi\)
\(164\) 4.20034 4.20034i 0.327991 0.327991i
\(165\) −10.4655 6.13131i −0.814740 0.477322i
\(166\) −8.99334 + 5.19231i −0.698019 + 0.403001i
\(167\) 15.6131 9.01425i 1.20818 0.697543i 0.245819 0.969316i \(-0.420943\pi\)
0.962362 + 0.271772i \(0.0876098\pi\)
\(168\) 2.86200 + 2.86200i 0.220808 + 0.220808i
\(169\) −0.551946 12.9883i −0.0424574 0.999098i
\(170\) 0.300456 + 0.304300i 0.0230439 + 0.0233388i
\(171\) −6.09967 1.63440i −0.466453 0.124986i
\(172\) −1.32302 + 4.93758i −0.100879 + 0.376487i
\(173\) −10.2059 + 2.73466i −0.775939 + 0.207912i −0.624993 0.780630i \(-0.714898\pi\)
−0.150945 + 0.988542i \(0.548232\pi\)
\(174\) −2.44113 2.44113i −0.185061 0.185061i
\(175\) 17.3960 + 10.3407i 1.31502 + 0.781682i
\(176\) 5.23956 1.40394i 0.394947 0.105826i
\(177\) 4.36891i 0.328387i
\(178\) 1.63277 + 6.09359i 0.122381 + 0.456734i
\(179\) 8.52320 + 14.7626i 0.637054 + 1.10341i 0.986076 + 0.166295i \(0.0531805\pi\)
−0.349022 + 0.937115i \(0.613486\pi\)
\(180\) 1.10570 + 1.94356i 0.0824141 + 0.144864i
\(181\) 16.2382i 1.20698i 0.797371 + 0.603489i \(0.206223\pi\)
−0.797371 + 0.603489i \(0.793777\pi\)
\(182\) 10.5359 + 10.0976i 0.780970 + 0.748487i
\(183\) −6.82363 + 6.82363i −0.504417 + 0.504417i
\(184\) −1.67663 + 6.25726i −0.123603 + 0.461291i
\(185\) 8.73684 + 15.3573i 0.642346 + 1.12909i
\(186\) 4.35360 + 2.51355i 0.319222 + 0.184303i
\(187\) 1.03739 0.0758612
\(188\) 1.83556 + 1.05976i 0.133872 + 0.0772910i
\(189\) 1.04756 + 3.90956i 0.0761990 + 0.284379i
\(190\) 10.0479 9.92097i 0.728952 0.719743i
\(191\) 2.66551 4.61680i 0.192869 0.334060i −0.753331 0.657642i \(-0.771554\pi\)
0.946200 + 0.323582i \(0.104887\pi\)
\(192\) −0.965926 0.258819i −0.0697097 0.0186787i
\(193\) −10.6343 18.4192i −0.765476 1.32584i −0.939994 0.341190i \(-0.889170\pi\)
0.174518 0.984654i \(-0.444163\pi\)
\(194\) −8.94906 −0.642505
\(195\) 4.13456 + 6.92137i 0.296082 + 0.495650i
\(196\) −9.38206 −0.670147
\(197\) 1.53503 + 2.65874i 0.109366 + 0.189428i 0.915514 0.402287i \(-0.131785\pi\)
−0.806148 + 0.591715i \(0.798451\pi\)
\(198\) 5.23956 + 1.40394i 0.372359 + 0.0997734i
\(199\) −1.64001 + 2.84058i −0.116257 + 0.201363i −0.918282 0.395928i \(-0.870423\pi\)
0.802024 + 0.597291i \(0.203756\pi\)
\(200\) −4.99960 0.0635655i −0.353525 0.00449476i
\(201\) 3.38612 + 12.6372i 0.238838 + 0.891357i
\(202\) −7.96916 4.60100i −0.560708 0.323725i
\(203\) 13.9730 0.980712
\(204\) −0.165623 0.0956223i −0.0115959 0.00669490i
\(205\) −3.51929 + 12.8079i −0.245798 + 0.894545i
\(206\) −4.29576 + 16.0320i −0.299300 + 1.11700i
\(207\) −4.58063 + 4.58063i −0.318376 + 0.318376i
\(208\) −3.50172 0.859025i −0.242801 0.0595627i
\(209\) 34.2542i 2.36941i
\(210\) −8.72698 2.39795i −0.602219 0.165474i
\(211\) 7.85506 + 13.6054i 0.540765 + 0.936632i 0.998860 + 0.0477292i \(0.0151985\pi\)
−0.458095 + 0.888903i \(0.651468\pi\)
\(212\) 0.0935422 + 0.349104i 0.00642450 + 0.0239766i
\(213\) 0.303880i 0.0208215i
\(214\) 2.14920 0.575877i 0.146917 0.0393662i
\(215\) −2.88812 11.0593i −0.196968 0.754241i
\(216\) −0.707107 0.707107i −0.0481125 0.0481125i
\(217\) −19.6538 + 5.26622i −1.33419 + 0.357494i
\(218\) 0.955910 3.56751i 0.0647424 0.241622i
\(219\) 12.8963 + 3.45554i 0.871449 + 0.233504i
\(220\) −8.63107 + 8.52203i −0.581906 + 0.574555i
\(221\) −0.604347 0.332014i −0.0406528 0.0223337i
\(222\) −5.58729 5.58729i −0.374995 0.374995i
\(223\) −20.5563 + 11.8682i −1.37655 + 0.794752i −0.991743 0.128245i \(-0.959066\pi\)
−0.384808 + 0.922997i \(0.625732\pi\)
\(224\) 3.50522 2.02374i 0.234202 0.135217i
\(225\) −4.29799 2.55485i −0.286533 0.170323i
\(226\) 9.92720 9.92720i 0.660347 0.660347i
\(227\) −12.0786 + 20.9208i −0.801687 + 1.38856i 0.116818 + 0.993153i \(0.462731\pi\)
−0.918505 + 0.395410i \(0.870603\pi\)
\(228\) −3.15742 + 5.46881i −0.209105 + 0.362181i
\(229\) −4.88588 + 4.88588i −0.322868 + 0.322868i −0.849866 0.526998i \(-0.823317\pi\)
0.526998 + 0.849866i \(0.323317\pi\)
\(230\) −3.66004 14.0152i −0.241336 0.924135i
\(231\) −19.0137 + 10.9775i −1.25101 + 0.722270i
\(232\) −2.98976 + 1.72614i −0.196287 + 0.113326i
\(233\) 1.90223 + 1.90223i 0.124619 + 0.124619i 0.766666 0.642047i \(-0.221914\pi\)
−0.642047 + 0.766666i \(0.721914\pi\)
\(234\) −2.60307 2.49480i −0.170168 0.163090i
\(235\) −4.73930 0.0301268i −0.309158 0.00196526i
\(236\) −4.22004 1.13076i −0.274701 0.0736060i
\(237\) −0.761699 + 2.84270i −0.0494776 + 0.184653i
\(238\) 0.747683 0.200341i 0.0484651 0.0129862i
\(239\) −17.1352 17.1352i −1.10838 1.10838i −0.993363 0.115020i \(-0.963307\pi\)
−0.115020 0.993363i \(-0.536693\pi\)
\(240\) 2.16351 0.564996i 0.139654 0.0364703i
\(241\) 7.77282 2.08272i 0.500691 0.134160i 0.000370473 1.00000i \(-0.499882\pi\)
0.500321 + 0.865840i \(0.333215\pi\)
\(242\) 18.4240i 1.18434i
\(243\) −0.258819 0.965926i −0.0166032 0.0619642i
\(244\) 4.82504 + 8.35721i 0.308891 + 0.535016i
\(245\) 18.2346 10.3738i 1.16496 0.662755i
\(246\) 5.94018i 0.378732i
\(247\) −10.9630 + 19.9554i −0.697559 + 1.26973i
\(248\) 3.55470 3.55470i 0.225724 0.225724i
\(249\) −2.68774 + 10.0308i −0.170328 + 0.635674i
\(250\) 9.78730 5.40452i 0.619003 0.341812i
\(251\) −11.2743 6.50919i −0.711625 0.410857i 0.100038 0.994984i \(-0.468104\pi\)
−0.811662 + 0.584127i \(0.801437\pi\)
\(252\) 4.04748 0.254967
\(253\) −30.4314 17.5696i −1.91321 1.10459i
\(254\) 3.08105 + 11.4986i 0.193322 + 0.721489i
\(255\) 0.427627 + 0.00271834i 0.0267791 + 0.000170229i
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −5.40791 1.44905i −0.337336 0.0903890i 0.0861745 0.996280i \(-0.472536\pi\)
−0.423511 + 0.905891i \(0.639202\pi\)
\(258\) 2.55588 + 4.42691i 0.159122 + 0.275607i
\(259\) 31.9816 1.98724
\(260\) 7.75564 2.20230i 0.480984 0.136581i
\(261\) −3.45227 −0.213690
\(262\) 6.13552 + 10.6270i 0.379054 + 0.656540i
\(263\) −27.5672 7.38660i −1.69986 0.455477i −0.726958 0.686681i \(-0.759067\pi\)
−0.972905 + 0.231204i \(0.925733\pi\)
\(264\) 2.71220 4.69766i 0.166924 0.289121i
\(265\) −0.567810 0.575075i −0.0348803 0.0353266i
\(266\) −6.61520 24.6883i −0.405604 1.51373i
\(267\) 5.46336 + 3.15427i 0.334352 + 0.193038i
\(268\) 13.0830 0.799169
\(269\) −2.39259 1.38136i −0.145879 0.0842232i 0.425284 0.905060i \(-0.360174\pi\)
−0.571163 + 0.820837i \(0.693508\pi\)
\(270\) 2.15615 + 0.592455i 0.131219 + 0.0360557i
\(271\) 2.91877 10.8930i 0.177302 0.661701i −0.818846 0.574014i \(-0.805386\pi\)
0.996148 0.0876877i \(-0.0279477\pi\)
\(272\) −0.135230 + 0.135230i −0.00819955 + 0.00819955i
\(273\) 14.5901 0.309868i 0.883032 0.0187541i
\(274\) 6.10265i 0.368675i
\(275\) 7.35217 26.1064i 0.443353 1.57428i
\(276\) 3.23899 + 5.61010i 0.194965 + 0.337689i
\(277\) −0.606728 2.26434i −0.0364548 0.136051i 0.945300 0.326202i \(-0.105769\pi\)
−0.981755 + 0.190151i \(0.939102\pi\)
\(278\) 1.86264i 0.111714i
\(279\) 4.85581 1.30111i 0.290710 0.0778955i
\(280\) −4.57495 + 7.80898i −0.273405 + 0.466676i
\(281\) 16.1274 + 16.1274i 0.962081 + 0.962081i 0.999307 0.0372258i \(-0.0118521\pi\)
−0.0372258 + 0.999307i \(0.511852\pi\)
\(282\) 2.04730 0.548573i 0.121915 0.0326670i
\(283\) 5.83670 21.7829i 0.346956 1.29486i −0.543355 0.839503i \(-0.682846\pi\)
0.890311 0.455353i \(-0.150487\pi\)
\(284\) −0.293526 0.0786499i −0.0174175 0.00466702i
\(285\) 0.0897589 14.1201i 0.00531686 0.836404i
\(286\) 9.41711 17.1415i 0.556846 1.01360i
\(287\) 17.0008 + 17.0008i 1.00352 + 1.00352i
\(288\) −0.866025 + 0.500000i −0.0510310 + 0.0294628i
\(289\) 14.6908 8.48171i 0.864162 0.498924i
\(290\) 3.90218 6.66063i 0.229144 0.391126i
\(291\) −6.32794 + 6.32794i −0.370951 + 0.370951i
\(292\) 6.67560 11.5625i 0.390660 0.676643i
\(293\) 8.52875 14.7722i 0.498255 0.863003i −0.501743 0.865017i \(-0.667308\pi\)
0.999998 + 0.00201373i \(0.000640990\pi\)
\(294\) −6.63412 + 6.63412i −0.386909 + 0.386909i
\(295\) 9.45219 2.46842i 0.550328 0.143717i
\(296\) −6.84301 + 3.95081i −0.397742 + 0.229636i
\(297\) 4.69766 2.71220i 0.272586 0.157378i
\(298\) −2.68952 2.68952i −0.155800 0.155800i
\(299\) 12.1052 + 19.9750i 0.700064 + 1.15518i
\(300\) −3.58020 + 3.49030i −0.206703 + 0.201513i
\(301\) −19.9847 5.35489i −1.15190 0.308651i
\(302\) 2.04972 7.64967i 0.117948 0.440189i
\(303\) −8.88844 + 2.38165i −0.510628 + 0.136822i
\(304\) 4.46527 + 4.46527i 0.256101 + 0.256101i
\(305\) −18.6183 10.9077i −1.06608 0.624572i
\(306\) −0.184728 + 0.0494978i −0.0105602 + 0.00282960i
\(307\) 1.24867i 0.0712656i 0.999365 + 0.0356328i \(0.0113447\pi\)
−0.999365 + 0.0356328i \(0.988655\pi\)
\(308\) 5.68240 + 21.2070i 0.323785 + 1.20838i
\(309\) 8.29877 + 14.3739i 0.472100 + 0.817702i
\(310\) −2.97833 + 10.8392i −0.169158 + 0.615626i
\(311\) 18.1794i 1.03086i −0.856932 0.515429i \(-0.827633\pi\)
0.856932 0.515429i \(-0.172367\pi\)
\(312\) −3.08352 + 1.86867i −0.174570 + 0.105793i
\(313\) −16.4742 + 16.4742i −0.931180 + 0.931180i −0.997780 0.0666002i \(-0.978785\pi\)
0.0666002 + 0.997780i \(0.478785\pi\)
\(314\) 3.79419 14.1601i 0.214119 0.799102i
\(315\) −7.86651 + 4.47530i −0.443228 + 0.252155i
\(316\) 2.54869 + 1.47149i 0.143375 + 0.0827777i
\(317\) 24.3400 1.36707 0.683535 0.729917i \(-0.260441\pi\)
0.683535 + 0.729917i \(0.260441\pi\)
\(318\) 0.312998 + 0.180710i 0.0175521 + 0.0101337i
\(319\) −4.84677 18.0884i −0.271367 1.01276i
\(320\) 0.0142140 2.23602i 0.000794585 0.124997i
\(321\) 1.11251 1.92692i 0.0620942 0.107550i
\(322\) −25.3261 6.78611i −1.41137 0.378175i
\(323\) 0.603840 + 1.04588i 0.0335986 + 0.0581944i
\(324\) −1.00000 −0.0555556
\(325\) −12.6385 + 12.8557i −0.701055 + 0.713107i
\(326\) 6.61442 0.366339
\(327\) −1.84668 3.19854i −0.102121 0.176880i
\(328\) −5.73777 1.53743i −0.316815 0.0848904i
\(329\) −4.28936 + 7.42938i −0.236480 + 0.409595i
\(330\) −0.0771021 + 12.1291i −0.00424433 + 0.667683i
\(331\) −1.38659 5.17481i −0.0762137 0.284434i 0.917292 0.398215i \(-0.130370\pi\)
−0.993506 + 0.113782i \(0.963704\pi\)
\(332\) 8.99334 + 5.19231i 0.493574 + 0.284965i
\(333\) −7.90163 −0.433007
\(334\) −15.6131 9.01425i −0.854313 0.493238i
\(335\) −25.4275 + 14.4659i −1.38925 + 0.790354i
\(336\) 1.04756 3.90956i 0.0571493 0.213284i
\(337\) 4.73224 4.73224i 0.257781 0.257781i −0.566370 0.824151i \(-0.691653\pi\)
0.824151 + 0.566370i \(0.191653\pi\)
\(338\) −10.9722 + 6.97214i −0.596809 + 0.379234i
\(339\) 14.0392i 0.762503i
\(340\) 0.113304 0.412353i 0.00614476 0.0223630i
\(341\) 13.6345 + 23.6157i 0.738350 + 1.27886i
\(342\) 1.63440 + 6.09967i 0.0883783 + 0.329832i
\(343\) 9.64131i 0.520582i
\(344\) 4.93758 1.32302i 0.266216 0.0713324i
\(345\) −12.4983 7.32221i −0.672885 0.394214i
\(346\) 7.47122 + 7.47122i 0.401655 + 0.401655i
\(347\) 22.1429 5.93317i 1.18869 0.318509i 0.390324 0.920677i \(-0.372363\pi\)
0.798369 + 0.602168i \(0.205696\pi\)
\(348\) −0.893514 + 3.33464i −0.0478974 + 0.178755i
\(349\) 16.4469 + 4.40694i 0.880383 + 0.235898i 0.670573 0.741844i \(-0.266049\pi\)
0.209811 + 0.977742i \(0.432715\pi\)
\(350\) 0.257280 20.2357i 0.0137522 1.08165i
\(351\) −3.60474 + 0.0765584i −0.192407 + 0.00408639i
\(352\) −3.83563 3.83563i −0.204440 0.204440i
\(353\) 10.0175 5.78360i 0.533177 0.307830i −0.209132 0.977887i \(-0.567064\pi\)
0.742309 + 0.670057i \(0.233731\pi\)
\(354\) −3.78359 + 2.18446i −0.201095 + 0.116102i
\(355\) 0.657448 0.171691i 0.0348937 0.00911241i
\(356\) 4.46081 4.46081i 0.236423 0.236423i
\(357\) 0.387029 0.670354i 0.0204837 0.0354789i
\(358\) 8.52320 14.7626i 0.450465 0.780229i
\(359\) 16.2123 16.2123i 0.855651 0.855651i −0.135171 0.990822i \(-0.543158\pi\)
0.990822 + 0.135171i \(0.0431584\pi\)
\(360\) 1.13032 1.92935i 0.0595732 0.101685i
\(361\) 18.0802 10.4386i 0.951590 0.549401i
\(362\) 14.0627 8.11912i 0.739121 0.426732i
\(363\) 13.0278 + 13.0278i 0.683780 + 0.683780i
\(364\) 3.47688 14.1731i 0.182238 0.742875i
\(365\) −0.189773 + 29.8536i −0.00993320 + 1.56261i
\(366\) 9.32126 + 2.49762i 0.487230 + 0.130553i
\(367\) −0.915524 + 3.41678i −0.0477900 + 0.178355i −0.985695 0.168536i \(-0.946096\pi\)
0.937905 + 0.346891i \(0.112763\pi\)
\(368\) 6.25726 1.67663i 0.326182 0.0874002i
\(369\) −4.20034 4.20034i −0.218661 0.218661i
\(370\) 8.93138 15.2450i 0.464320 0.792548i
\(371\) −1.41299 + 0.378610i −0.0733588 + 0.0196564i
\(372\) 5.02711i 0.260643i
\(373\) 4.97018 + 18.5490i 0.257346 + 0.960429i 0.966770 + 0.255647i \(0.0822886\pi\)
−0.709424 + 0.704782i \(0.751045\pi\)
\(374\) −0.518693 0.898403i −0.0268210 0.0464553i
\(375\) 3.09909 10.7422i 0.160036 0.554727i
\(376\) 2.11952i 0.109306i
\(377\) −2.96559 + 12.0889i −0.152736 + 0.622611i
\(378\) 2.86200 2.86200i 0.147205 0.147205i
\(379\) 6.74069 25.1566i 0.346246 1.29221i −0.544903 0.838499i \(-0.683434\pi\)
0.891150 0.453709i \(-0.149900\pi\)
\(380\) −13.6158 3.74126i −0.698474 0.191923i
\(381\) 10.3094 + 5.95213i 0.528166 + 0.304937i
\(382\) −5.33102 −0.272759
\(383\) −19.1720 11.0690i −0.979644 0.565598i −0.0774812 0.996994i \(-0.524688\pi\)
−0.902163 + 0.431396i \(0.858021\pi\)
\(384\) 0.258819 + 0.965926i 0.0132078 + 0.0492922i
\(385\) −34.4927 34.9340i −1.75791 1.78040i
\(386\) −10.6343 + 18.4192i −0.541274 + 0.937513i
\(387\) 4.93758 + 1.32302i 0.250991 + 0.0672529i
\(388\) 4.47453 + 7.75012i 0.227160 + 0.393452i
\(389\) −17.6059 −0.892653 −0.446327 0.894870i \(-0.647268\pi\)
−0.446327 + 0.894870i \(0.647268\pi\)
\(390\) 3.92680 7.04132i 0.198841 0.356551i
\(391\) 1.23888 0.0626529
\(392\) 4.69103 + 8.12510i 0.236933 + 0.410379i
\(393\) 11.8529 + 3.17598i 0.597900 + 0.160207i
\(394\) 1.53503 2.65874i 0.0773335 0.133946i
\(395\) −6.58057 0.0418314i −0.331104 0.00210477i
\(396\) −1.40394 5.23956i −0.0705505 0.263298i
\(397\) 21.9503 + 12.6730i 1.10165 + 0.636039i 0.936654 0.350255i \(-0.113905\pi\)
0.164997 + 0.986294i \(0.447238\pi\)
\(398\) 3.28002 0.164412
\(399\) −22.1349 12.7796i −1.10813 0.639779i
\(400\) 2.44475 + 4.36156i 0.122237 + 0.218078i
\(401\) −5.34321 + 19.9411i −0.266827 + 0.995813i 0.694295 + 0.719690i \(0.255716\pi\)
−0.961122 + 0.276122i \(0.910950\pi\)
\(402\) 9.25105 9.25105i 0.461400 0.461400i
\(403\) −0.384867 18.1214i −0.0191716 0.902692i
\(404\) 9.20199i 0.457816i
\(405\) 1.94356 1.10570i 0.0965762 0.0549428i
\(406\) −6.98649 12.1010i −0.346734 0.600561i
\(407\) −11.0934 41.4011i −0.549879 2.05217i
\(408\) 0.191245i 0.00946802i
\(409\) 5.68835 1.52419i 0.281271 0.0753662i −0.115426 0.993316i \(-0.536823\pi\)
0.396696 + 0.917950i \(0.370157\pi\)
\(410\) 12.8516 3.35618i 0.634697 0.165750i
\(411\) 4.31523 + 4.31523i 0.212855 + 0.212855i
\(412\) 16.0320 4.29576i 0.789839 0.211637i
\(413\) 4.57671 17.0805i 0.225205 0.840477i
\(414\) 6.25726 + 1.67663i 0.307527 + 0.0824017i
\(415\) −23.2202 0.147607i −1.13984 0.00724572i
\(416\) 1.00692 + 3.46210i 0.0493685 + 0.169743i
\(417\) −1.31709 1.31709i −0.0644980 0.0644980i
\(418\) −29.6650 + 17.1271i −1.45096 + 0.837714i
\(419\) −13.2160 + 7.63025i −0.645643 + 0.372762i −0.786785 0.617227i \(-0.788256\pi\)
0.141142 + 0.989989i \(0.454923\pi\)
\(420\) 2.28681 + 8.75676i 0.111585 + 0.427286i
\(421\) −2.19096 + 2.19096i −0.106781 + 0.106781i −0.758479 0.651698i \(-0.774057\pi\)
0.651698 + 0.758479i \(0.274057\pi\)
\(422\) 7.85506 13.6054i 0.382379 0.662299i
\(423\) 1.05976 1.83556i 0.0515273 0.0892480i
\(424\) 0.255562 0.255562i 0.0124112 0.0124112i
\(425\) 0.235726 + 0.926713i 0.0114344 + 0.0449522i
\(426\) −0.263168 + 0.151940i −0.0127505 + 0.00736152i
\(427\) −33.8256 + 19.5292i −1.63694 + 0.945085i
\(428\) −1.57333 1.57333i −0.0760496 0.0760496i
\(429\) −5.46196 18.7798i −0.263706 0.906696i
\(430\) −8.13361 + 8.03085i −0.392237 + 0.387282i
\(431\) −10.5621 2.83012i −0.508761 0.136322i −0.00469777 0.999989i \(-0.501495\pi\)
−0.504063 + 0.863667i \(0.668162\pi\)
\(432\) −0.258819 + 0.965926i −0.0124524 + 0.0464731i
\(433\) 32.1258 8.60807i 1.54387 0.413677i 0.616353 0.787470i \(-0.288609\pi\)
0.927512 + 0.373793i \(0.121943\pi\)
\(434\) 14.3876 + 14.3876i 0.690625 + 0.690625i
\(435\) −1.95052 7.46903i −0.0935202 0.358113i
\(436\) −3.56751 + 0.955910i −0.170853 + 0.0457798i
\(437\) 40.9075i 1.95687i
\(438\) −3.45554 12.8963i −0.165112 0.616208i
\(439\) 6.66616 + 11.5461i 0.318158 + 0.551067i 0.980104 0.198486i \(-0.0636023\pi\)
−0.661945 + 0.749552i \(0.730269\pi\)
\(440\) 11.6958 + 3.21371i 0.557577 + 0.153208i
\(441\) 9.38206i 0.446765i
\(442\) 0.0146414 + 0.689387i 0.000696420 + 0.0327908i
\(443\) 4.80640 4.80640i 0.228359 0.228359i −0.583648 0.812007i \(-0.698375\pi\)
0.812007 + 0.583648i \(0.198375\pi\)
\(444\) −2.04509 + 7.63239i −0.0970558 + 0.362217i
\(445\) −3.73753 + 13.6022i −0.177176 + 0.644806i
\(446\) 20.5563 + 11.8682i 0.973368 + 0.561975i
\(447\) −3.80356 −0.179902
\(448\) −3.50522 2.02374i −0.165606 0.0956126i
\(449\) −7.48614 27.9387i −0.353293 1.31851i −0.882619 0.470088i \(-0.844222\pi\)
0.529326 0.848418i \(-0.322445\pi\)
\(450\) −0.0635655 + 4.99960i −0.00299651 + 0.235683i
\(451\) 16.1109 27.9050i 0.758634 1.31399i
\(452\) −13.5608 3.63361i −0.637846 0.170910i
\(453\) −3.95976 6.85851i −0.186046 0.322241i
\(454\) 24.1573 1.13376
\(455\) 8.91374 + 31.3907i 0.417883 + 1.47162i
\(456\) 6.31484 0.295720
\(457\) −4.52778 7.84234i −0.211801 0.366849i 0.740478 0.672081i \(-0.234599\pi\)
−0.952278 + 0.305232i \(0.901266\pi\)
\(458\) 6.67424 + 1.78836i 0.311867 + 0.0835645i
\(459\) −0.0956223 + 0.165623i −0.00446327 + 0.00773061i
\(460\) −10.3075 + 10.1773i −0.480590 + 0.474518i
\(461\) 5.56197 + 20.7576i 0.259047 + 0.966776i 0.965794 + 0.259310i \(0.0834951\pi\)
−0.706747 + 0.707466i \(0.749838\pi\)
\(462\) 19.0137 + 10.9775i 0.884596 + 0.510722i
\(463\) 29.8973 1.38945 0.694723 0.719277i \(-0.255527\pi\)
0.694723 + 0.719277i \(0.255527\pi\)
\(464\) 2.98976 + 1.72614i 0.138796 + 0.0801339i
\(465\) 5.55848 + 9.77048i 0.257768 + 0.453095i
\(466\) 0.696264 2.59849i 0.0322538 0.120373i
\(467\) −25.6198 + 25.6198i −1.18554 + 1.18554i −0.207257 + 0.978287i \(0.566454\pi\)
−0.978287 + 0.207257i \(0.933546\pi\)
\(468\) −0.859025 + 3.50172i −0.0397085 + 0.161867i
\(469\) 52.9530i 2.44514i
\(470\) 2.34356 + 4.11942i 0.108100 + 0.190015i
\(471\) −7.32981 12.6956i −0.337740 0.584983i
\(472\) 1.13076 + 4.22004i 0.0520473 + 0.194243i
\(473\) 27.7282i 1.27494i
\(474\) 2.84270 0.761699i 0.130569 0.0349860i
\(475\) 30.5998 7.78362i 1.40401 0.357137i
\(476\) −0.547342 0.547342i −0.0250874 0.0250874i
\(477\) 0.349104 0.0935422i 0.0159844 0.00428300i
\(478\) −6.27192 + 23.4071i −0.286871 + 1.07062i
\(479\) 13.0654 + 3.50087i 0.596974 + 0.159959i 0.544638 0.838671i \(-0.316667\pi\)
0.0523353 + 0.998630i \(0.483334\pi\)
\(480\) −1.57106 1.59116i −0.0717086 0.0726261i
\(481\) −6.78770 + 27.6693i −0.309492 + 1.26161i
\(482\) −5.69010 5.69010i −0.259177 0.259177i
\(483\) −22.7068 + 13.1098i −1.03319 + 0.596514i
\(484\) 15.9557 9.21202i 0.725259 0.418728i
\(485\) −17.2658 10.1153i −0.784001 0.459313i
\(486\) −0.707107 + 0.707107i −0.0320750 + 0.0320750i
\(487\) −11.3404 + 19.6421i −0.513882 + 0.890069i 0.485989 + 0.873965i \(0.338460\pi\)
−0.999870 + 0.0161039i \(0.994874\pi\)
\(488\) 4.82504 8.35721i 0.218419 0.378313i
\(489\) 4.67710 4.67710i 0.211506 0.211506i
\(490\) −18.1012 10.6047i −0.817730 0.479073i
\(491\) 31.8367 18.3809i 1.43677 0.829520i 0.439146 0.898416i \(-0.355281\pi\)
0.997624 + 0.0688962i \(0.0219477\pi\)
\(492\) −5.14435 + 2.97009i −0.231925 + 0.133902i
\(493\) 0.466852 + 0.466852i 0.0210260 + 0.0210260i
\(494\) 22.7634 0.483454i 1.02417 0.0217516i
\(495\) 8.52203 + 8.63107i 0.383037 + 0.387938i
\(496\) −4.85581 1.30111i −0.218032 0.0584216i
\(497\) 0.318334 1.18804i 0.0142792 0.0532908i
\(498\) 10.0308 2.68774i 0.449490 0.120440i
\(499\) 20.9091 + 20.9091i 0.936020 + 0.936020i 0.998073 0.0620524i \(-0.0197646\pi\)
−0.0620524 + 0.998073i \(0.519765\pi\)
\(500\) −9.57410 5.77379i −0.428167 0.258212i
\(501\) −17.4142 + 4.66612i −0.778008 + 0.208467i
\(502\) 13.0184i 0.581039i
\(503\) 2.23473 + 8.34011i 0.0996415 + 0.371867i 0.997682 0.0680452i \(-0.0216762\pi\)
−0.898041 + 0.439912i \(0.855010\pi\)
\(504\) −2.02374 3.50522i −0.0901444 0.156135i
\(505\) −10.1747 17.8846i −0.452766 0.795855i
\(506\) 35.1392i 1.56213i
\(507\) −2.82847 + 12.6886i −0.125617 + 0.563519i
\(508\) 8.41759 8.41759i 0.373470 0.373470i
\(509\) 1.27084 4.74284i 0.0563290 0.210223i −0.932025 0.362393i \(-0.881960\pi\)
0.988354 + 0.152171i \(0.0486264\pi\)
\(510\) −0.211460 0.371695i −0.00936359 0.0164589i
\(511\) 46.7988 + 27.0193i 2.07026 + 1.19526i
\(512\) 1.00000 0.0441942
\(513\) 5.46881 + 3.15742i 0.241454 + 0.139404i
\(514\) 1.44905 + 5.40791i 0.0639147 + 0.238533i
\(515\) −26.4093 + 26.0757i −1.16373 + 1.14903i
\(516\) 2.55588 4.42691i 0.112516 0.194884i
\(517\) 11.1054 + 2.97567i 0.488413 + 0.130870i
\(518\) −15.9908 27.6969i −0.702596 1.21693i
\(519\) 10.5659 0.463792
\(520\) −5.78506 5.61543i −0.253692 0.246253i
\(521\) −28.5387 −1.25030 −0.625151 0.780503i \(-0.714963\pi\)
−0.625151 + 0.780503i \(0.714963\pi\)
\(522\) 1.72614 + 2.98976i 0.0755509 + 0.130858i
\(523\) −10.1391 2.71677i −0.443354 0.118796i 0.0302342 0.999543i \(-0.490375\pi\)
−0.473588 + 0.880747i \(0.657041\pi\)
\(524\) 6.13552 10.6270i 0.268031 0.464244i
\(525\) −14.1269 14.4908i −0.616549 0.632428i
\(526\) 7.38660 + 27.5672i 0.322071 + 1.20199i
\(527\) −0.832603 0.480704i −0.0362688 0.0209398i
\(528\) −5.42439 −0.236066
\(529\) −16.4236 9.48217i −0.714070 0.412268i
\(530\) −0.214125 + 0.779275i −0.00930098 + 0.0338496i
\(531\) −1.13076 + 4.22004i −0.0490707 + 0.183134i
\(532\) −18.0731 + 18.0731i −0.783567 + 0.783567i
\(533\) −18.3166 + 11.1002i −0.793382 + 0.480805i
\(534\) 6.30854i 0.272997i
\(535\) 4.79748 + 1.31822i 0.207413 + 0.0569918i
\(536\) −6.54148 11.3302i −0.282549 0.489389i
\(537\) −4.41193 16.4656i −0.190389 0.710541i
\(538\) 2.76273i 0.119110i
\(539\) −49.1579 + 13.1718i −2.11738 + 0.567350i
\(540\) −0.564996 2.16351i −0.0243135 0.0931027i
\(541\) 0.105018 + 0.105018i 0.00451507 + 0.00451507i 0.709361 0.704846i \(-0.248984\pi\)
−0.704846 + 0.709361i \(0.748984\pi\)
\(542\) −10.8930 + 2.91877i −0.467894 + 0.125372i
\(543\) 4.20277 15.6849i 0.180358 0.673105i
\(544\) 0.184728 + 0.0494978i 0.00792016 + 0.00212220i
\(545\) 5.87671 5.80247i 0.251731 0.248550i
\(546\) −7.56340 12.4805i −0.323684 0.534114i
\(547\) 8.37204 + 8.37204i 0.357962 + 0.357962i 0.863061 0.505099i \(-0.168544\pi\)
−0.505099 + 0.863061i \(0.668544\pi\)
\(548\) 5.28505 3.05133i 0.225766 0.130346i
\(549\) 8.35721 4.82504i 0.356677 0.205928i
\(550\) −26.2849 + 6.68606i −1.12079 + 0.285095i
\(551\) 15.4153 15.4153i 0.656715 0.656715i
\(552\) 3.23899 5.61010i 0.137861 0.238782i
\(553\) −5.95581 + 10.3158i −0.253267 + 0.438671i
\(554\) −1.65761 + 1.65761i −0.0704252 + 0.0704252i
\(555\) −4.46439 17.0953i −0.189503 0.725653i
\(556\) −1.61309 + 0.931321i −0.0684105 + 0.0394968i
\(557\) −22.5857 + 13.0399i −0.956987 + 0.552517i −0.895244 0.445575i \(-0.852999\pi\)
−0.0617426 + 0.998092i \(0.519666\pi\)
\(558\) −3.55470 3.55470i −0.150483 0.150483i
\(559\) 8.87435 16.1535i 0.375345 0.683221i
\(560\) 9.05025 + 0.0575307i 0.382443 + 0.00243111i
\(561\) −1.00204 0.268495i −0.0423061 0.0113359i
\(562\) 5.90304 22.0305i 0.249005 0.929299i
\(563\) −6.40965 + 1.71746i −0.270135 + 0.0723824i −0.391344 0.920245i \(-0.627990\pi\)
0.121209 + 0.992627i \(0.461323\pi\)
\(564\) −1.49873 1.49873i −0.0631078 0.0631078i
\(565\) 30.3739 7.93207i 1.27784 0.333705i
\(566\) −21.7829 + 5.83670i −0.915602 + 0.245335i
\(567\) 4.04748i 0.169978i
\(568\) 0.0786499 + 0.293526i 0.00330008 + 0.0123161i
\(569\) −16.3447 28.3099i −0.685207 1.18681i −0.973372 0.229232i \(-0.926379\pi\)
0.288165 0.957581i \(-0.406955\pi\)
\(570\) −12.2733 + 6.98233i −0.514071 + 0.292458i
\(571\) 43.9760i 1.84034i −0.391522 0.920169i \(-0.628051\pi\)
0.391522 0.920169i \(-0.371949\pi\)
\(572\) −19.5535 + 0.415283i −0.817574 + 0.0173639i
\(573\) −3.76960 + 3.76960i −0.157477 + 0.157477i
\(574\) 6.22272 23.2235i 0.259731 0.969330i
\(575\) 8.78020 31.1772i 0.366160 1.30018i
\(576\) 0.866025 + 0.500000i 0.0360844 + 0.0208333i
\(577\) −28.7300 −1.19605 −0.598023 0.801479i \(-0.704047\pi\)
−0.598023 + 0.801479i \(0.704047\pi\)
\(578\) −14.6908 8.48171i −0.611055 0.352793i
\(579\) 5.50474 + 20.5440i 0.228769 + 0.853778i
\(580\) −7.71936 0.0490705i −0.320529 0.00203754i
\(581\) −21.0157 + 36.4003i −0.871880 + 1.51014i
\(582\) 8.64413 + 2.31619i 0.358311 + 0.0960091i
\(583\) 0.980240 + 1.69783i 0.0405974 + 0.0703168i
\(584\) −13.3512 −0.552477
\(585\) −2.20230 7.75564i −0.0910538 0.320656i
\(586\) −17.0575 −0.704639
\(587\) 10.4009 + 18.0149i 0.429291 + 0.743553i 0.996810 0.0798064i \(-0.0254302\pi\)
−0.567520 + 0.823360i \(0.692097\pi\)
\(588\) 9.06237 + 2.42825i 0.373726 + 0.100140i
\(589\) −15.8727 + 27.4923i −0.654023 + 1.13280i
\(590\) −6.86380 6.95163i −0.282578 0.286194i
\(591\) −0.794588 2.96544i −0.0326850 0.121982i
\(592\) 6.84301 + 3.95081i 0.281246 + 0.162377i
\(593\) 19.4278 0.797802 0.398901 0.916994i \(-0.369392\pi\)
0.398901 + 0.916994i \(0.369392\pi\)
\(594\) −4.69766 2.71220i −0.192747 0.111283i
\(595\) 1.66899 + 0.458595i 0.0684218 + 0.0188005i
\(596\) −0.984433 + 3.67395i −0.0403239 + 0.150491i
\(597\) 2.31932 2.31932i 0.0949235 0.0949235i
\(598\) 11.2462 20.4709i 0.459892 0.837119i
\(599\) 22.2731i 0.910054i −0.890478 0.455027i \(-0.849630\pi\)
0.890478 0.455027i \(-0.150370\pi\)
\(600\) 4.81279 + 1.35539i 0.196481 + 0.0553336i
\(601\) −6.36361 11.0221i −0.259577 0.449601i 0.706552 0.707662i \(-0.250250\pi\)
−0.966129 + 0.258061i \(0.916917\pi\)
\(602\) 5.35489 + 19.9847i 0.218249 + 0.814516i
\(603\) 13.0830i 0.532779i
\(604\) −7.64967 + 2.04972i −0.311261 + 0.0834020i
\(605\) −20.8251 + 35.5463i −0.846660 + 1.44516i
\(606\) 6.50679 + 6.50679i 0.264320 + 0.264320i
\(607\) 2.87328 0.769893i 0.116623 0.0312490i −0.200036 0.979789i \(-0.564106\pi\)
0.316658 + 0.948540i \(0.397439\pi\)
\(608\) 1.63440 6.09967i 0.0662837 0.247374i
\(609\) −13.4969 3.61648i −0.546921 0.146547i
\(610\) −0.137166 + 21.5778i −0.00555368 + 0.873659i
\(611\) −5.51726 5.28778i −0.223205 0.213921i
\(612\) 0.135230 + 0.135230i 0.00546637 + 0.00546637i
\(613\) −25.6459 + 14.8067i −1.03583 + 0.598036i −0.918649 0.395075i \(-0.870719\pi\)
−0.117180 + 0.993111i \(0.537385\pi\)
\(614\) 1.08138 0.624337i 0.0436411 0.0251962i
\(615\) 6.71431 11.4607i 0.270747 0.462138i
\(616\) 15.5246 15.5246i 0.625504 0.625504i
\(617\) −2.95213 + 5.11323i −0.118848 + 0.205851i −0.919311 0.393531i \(-0.871254\pi\)
0.800463 + 0.599382i \(0.204587\pi\)
\(618\) 8.29877 14.3739i 0.333825 0.578202i
\(619\) 17.1516 17.1516i 0.689381 0.689381i −0.272714 0.962095i \(-0.587921\pi\)
0.962095 + 0.272714i \(0.0879213\pi\)
\(620\) 10.8762 2.84029i 0.436799 0.114069i
\(621\) 5.61010 3.23899i 0.225126 0.129976i
\(622\) −15.7438 + 9.08969i −0.631269 + 0.364463i
\(623\) 18.0550 + 18.0550i 0.723360 + 0.723360i
\(624\) 3.16007 + 1.73607i 0.126504 + 0.0694983i
\(625\) 24.9919 + 0.635604i 0.999677 + 0.0254241i
\(626\) 22.5042 + 6.02999i 0.899450 + 0.241007i
\(627\) −8.86564 + 33.0870i −0.354059 + 1.32137i
\(628\) −14.1601 + 3.79419i −0.565050 + 0.151405i
\(629\) 1.06854 + 1.06854i 0.0426055 + 0.0426055i
\(630\) 7.80898 + 4.57495i 0.311117 + 0.182270i
\(631\) −22.1142 + 5.92547i −0.880351 + 0.235889i −0.670559 0.741857i \(-0.733946\pi\)
−0.209793 + 0.977746i \(0.567279\pi\)
\(632\) 2.94298i 0.117065i
\(633\) −4.06608 15.1748i −0.161612 0.603145i
\(634\) −12.1700 21.0791i −0.483333 0.837156i
\(635\) −7.05274 + 25.6674i −0.279879 + 1.01858i
\(636\) 0.361419i 0.0143312i
\(637\) 32.8534 + 8.05942i 1.30170 + 0.319326i
\(638\) −13.2416 + 13.2416i −0.524241 + 0.524241i
\(639\) −0.0786499 + 0.293526i −0.00311134 + 0.0116117i
\(640\) −1.94356 + 1.10570i −0.0768259 + 0.0437067i
\(641\) −27.4399 15.8424i −1.08381 0.625738i −0.151889 0.988398i \(-0.548536\pi\)
−0.931922 + 0.362659i \(0.881869\pi\)
\(642\) −2.22502 −0.0878145
\(643\) 11.9009 + 6.87099i 0.469326 + 0.270965i 0.715957 0.698144i \(-0.245990\pi\)
−0.246632 + 0.969109i \(0.579324\pi\)
\(644\) 6.78611 + 25.3261i 0.267410 + 0.997988i
\(645\) −0.0726583 + 11.4300i −0.00286092 + 0.450056i
\(646\) 0.603840 1.04588i 0.0237578 0.0411497i
\(647\) −8.86339 2.37494i −0.348456 0.0933685i 0.0803460 0.996767i \(-0.474397\pi\)
−0.428802 + 0.903399i \(0.641064\pi\)
\(648\) 0.500000 + 0.866025i 0.0196419 + 0.0340207i
\(649\) −23.6987 −0.930255
\(650\) 17.4526 + 4.51737i 0.684547 + 0.177186i
\(651\) 20.3471 0.797466
\(652\) −3.30721 5.72825i −0.129520 0.224336i
\(653\) −15.1390 4.05649i −0.592435 0.158743i −0.0498693 0.998756i \(-0.515880\pi\)
−0.542566 + 0.840013i \(0.682547\pi\)
\(654\) −1.84668 + 3.19854i −0.0722108 + 0.125073i
\(655\) −0.174420 + 27.4383i −0.00681516 + 1.07210i
\(656\) 1.53743 + 5.73777i 0.0600266 + 0.224022i
\(657\) −11.5625 6.67560i −0.451095 0.260440i
\(658\) 8.57871 0.334433
\(659\) 12.4891 + 7.21057i 0.486505 + 0.280884i 0.723124 0.690719i \(-0.242706\pi\)
−0.236618 + 0.971603i \(0.576039\pi\)
\(660\) 10.5426 5.99776i 0.410371 0.233463i
\(661\) 8.43403 31.4762i 0.328046 1.22428i −0.583169 0.812351i \(-0.698187\pi\)
0.911214 0.411932i \(-0.135146\pi\)
\(662\) −3.78823 + 3.78823i −0.147234 + 0.147234i
\(663\) 0.497823 + 0.477117i 0.0193339 + 0.0185297i
\(664\) 10.3846i 0.403001i
\(665\) 15.1427 55.1095i 0.587207 2.13705i
\(666\) 3.95081 + 6.84301i 0.153091 + 0.265161i
\(667\) −5.78817 21.6018i −0.224119 0.836424i
\(668\) 18.0285i 0.697543i
\(669\) 22.9276 6.14342i 0.886431 0.237518i
\(670\) 25.2416 + 14.7879i 0.975166 + 0.571308i
\(671\) 37.0141 + 37.0141i 1.42891 + 1.42891i
\(672\) −3.90956 + 1.04756i −0.150815 + 0.0404106i
\(673\) −7.76610 + 28.9835i −0.299361 + 1.11723i 0.638330 + 0.769762i \(0.279625\pi\)
−0.937692 + 0.347469i \(0.887041\pi\)
\(674\) −6.46436 1.73212i −0.248998 0.0667187i
\(675\) 3.49030 + 3.58020i 0.134342 + 0.137802i
\(676\) 11.5242 + 6.01614i 0.443237 + 0.231390i
\(677\) 2.95656 + 2.95656i 0.113630 + 0.113630i 0.761635 0.648006i \(-0.224397\pi\)
−0.648006 + 0.761635i \(0.724397\pi\)
\(678\) −12.1583 + 7.01959i −0.466936 + 0.269586i
\(679\) −31.3684 + 18.1106i −1.20381 + 0.695019i
\(680\) −0.413760 + 0.108052i −0.0158670 + 0.00414362i
\(681\) 17.0818 17.0818i 0.654575 0.654575i
\(682\) 13.6345 23.6157i 0.522092 0.904290i
\(683\) −19.6927 + 34.1087i −0.753519 + 1.30513i 0.192588 + 0.981280i \(0.438312\pi\)
−0.946107 + 0.323854i \(0.895021\pi\)
\(684\) 4.46527 4.46527i 0.170734 0.170734i
\(685\) −6.89796 + 11.7741i −0.263557 + 0.449866i
\(686\) −8.34962 + 4.82066i −0.318790 + 0.184054i
\(687\) 5.98396 3.45484i 0.228302 0.131810i
\(688\) −3.61456 3.61456i −0.137804 0.137804i
\(689\) −0.0276697 1.30282i −0.00105413 0.0496336i
\(690\) −0.0920779 + 14.4849i −0.00350535 + 0.551432i
\(691\) −11.6332 3.11712i −0.442550 0.118581i 0.0306616 0.999530i \(-0.490239\pi\)
−0.473211 + 0.880949i \(0.656905\pi\)
\(692\) 2.73466 10.2059i 0.103956 0.387969i
\(693\) 21.2070 5.68240i 0.805587 0.215856i
\(694\) −16.2097 16.2097i −0.615313 0.615313i
\(695\) 2.10538 3.59368i 0.0798617 0.136316i
\(696\) 3.33464 0.893514i 0.126399 0.0338686i
\(697\) 1.13603i 0.0430301i
\(698\) −4.40694 16.4469i −0.166805 0.622525i
\(699\) −1.34508 2.32974i −0.0508755 0.0881190i
\(700\) −17.6533 + 9.89506i −0.667232 + 0.373998i
\(701\) 20.1190i 0.759884i 0.925010 + 0.379942i \(0.124056\pi\)
−0.925010 + 0.379942i \(0.875944\pi\)
\(702\) 1.86867 + 3.08352i 0.0705284 + 0.116380i
\(703\) 35.2829 35.2829i 1.33072 1.33072i
\(704\) −1.40394 + 5.23956i −0.0529128 + 0.197473i
\(705\) 4.57001 + 1.25572i 0.172117 + 0.0472932i
\(706\) −10.0175 5.78360i −0.377013 0.217669i
\(707\) −37.2448 −1.40074
\(708\) 3.78359 + 2.18446i 0.142196 + 0.0820969i
\(709\) −1.99950 7.46225i −0.0750930 0.280251i 0.918161 0.396207i \(-0.129674\pi\)
−0.993254 + 0.115956i \(0.963007\pi\)
\(710\) −0.477413 0.483521i −0.0179170 0.0181462i
\(711\) 1.47149 2.54869i 0.0551851 0.0955835i
\(712\) −6.09359 1.63277i −0.228367 0.0611907i
\(713\) 16.2828 + 28.2026i 0.609795 + 1.05620i
\(714\) −0.774058 −0.0289684
\(715\) 37.5443 22.4275i 1.40408 0.838740i
\(716\) −17.0464 −0.637054
\(717\) 12.1164 + 20.9862i 0.452496 + 0.783745i
\(718\) −22.1464 5.93410i −0.826496 0.221459i
\(719\) −23.2534 + 40.2761i −0.867207 + 1.50205i −0.00236843 + 0.999997i \(0.500754\pi\)
−0.864839 + 0.502050i \(0.832579\pi\)
\(720\) −2.23602 0.0142140i −0.0833316 0.000529723i
\(721\) 17.3870 + 64.8891i 0.647525 + 2.41660i
\(722\) −18.0802 10.4386i −0.672876 0.388485i
\(723\) −8.04701 −0.299272
\(724\) −14.0627 8.11912i −0.522637 0.301745i
\(725\) 15.0573 8.43994i 0.559214 0.313451i
\(726\) 4.76849 17.7963i 0.176975 0.660481i
\(727\) 35.6693 35.6693i 1.32290 1.32290i 0.411483 0.911417i \(-0.365011\pi\)
0.911417 0.411483i \(-0.134989\pi\)
\(728\) −14.0127 + 4.07550i −0.519347 + 0.151048i
\(729\) 1.00000i 0.0370370i
\(730\) 25.9489 14.7624i 0.960410 0.546383i
\(731\) −0.488798 0.846623i −0.0180788 0.0313135i
\(732\) −2.49762 9.32126i −0.0923148 0.344524i
\(733\) 31.4760i 1.16259i 0.813692 + 0.581296i \(0.197454\pi\)
−0.813692 + 0.581296i \(0.802546\pi\)
\(734\) 3.41678 0.915524i 0.126116 0.0337926i
\(735\) −20.2982 + 5.30082i −0.748710 + 0.195524i
\(736\) −4.58063 4.58063i −0.168844 0.168844i
\(737\) 68.5490 18.3676i 2.52503 0.676581i
\(738\) −1.53743 + 5.73777i −0.0565936 + 0.211210i
\(739\) 4.10767 + 1.10065i 0.151103 + 0.0404880i 0.333578 0.942723i \(-0.391744\pi\)
−0.182475 + 0.983211i \(0.558411\pi\)
\(740\) −17.6682 0.112313i −0.649497 0.00412872i
\(741\) 15.7543 16.4380i 0.578748 0.603864i
\(742\) 1.03438 + 1.03438i 0.0379733 + 0.0379733i
\(743\) −18.5342 + 10.7007i −0.679954 + 0.392572i −0.799838 0.600216i \(-0.795081\pi\)
0.119884 + 0.992788i \(0.461748\pi\)
\(744\) −4.35360 + 2.51355i −0.159611 + 0.0921514i
\(745\) −2.14899 8.22903i −0.0787330 0.301488i
\(746\) 13.5788 13.5788i 0.497155 0.497155i
\(747\) 5.19231 8.99334i 0.189977 0.329049i
\(748\) −0.518693 + 0.898403i −0.0189653 + 0.0328489i
\(749\) 6.36800 6.36800i 0.232682 0.232682i
\(750\) −10.8526 + 2.68723i −0.396281 + 0.0981236i
\(751\) 34.7913 20.0868i 1.26955 0.732977i 0.294650 0.955605i \(-0.404797\pi\)
0.974903 + 0.222628i \(0.0714636\pi\)
\(752\) −1.83556 + 1.05976i −0.0669360 + 0.0386455i
\(753\) 9.20539 + 9.20539i 0.335463 + 0.335463i
\(754\) 11.9521 3.47618i 0.435270 0.126595i
\(755\) 12.6012 12.4420i 0.458605 0.452811i
\(756\) −3.90956 1.04756i −0.142189 0.0380995i
\(757\) 4.51154 16.8373i 0.163975 0.611962i −0.834194 0.551471i \(-0.814067\pi\)
0.998169 0.0604911i \(-0.0192667\pi\)
\(758\) −25.1566 + 6.74069i −0.913729 + 0.244833i
\(759\) 24.8471 + 24.8471i 0.901894 + 0.901894i
\(760\) 3.56786 + 13.6622i 0.129420 + 0.495581i
\(761\) −33.8433 + 9.06830i −1.22682 + 0.328725i −0.813341 0.581788i \(-0.802353\pi\)
−0.413480 + 0.910513i \(0.635687\pi\)
\(762\) 11.9043i 0.431246i
\(763\) −3.86902 14.4394i −0.140068 0.522741i
\(764\) 2.66551 + 4.61680i 0.0964347 + 0.167030i
\(765\) −0.412353 0.113304i −0.0149086 0.00409651i
\(766\) 22.1379i 0.799876i
\(767\) 13.8061 + 7.58472i 0.498509 + 0.273869i
\(768\) 0.707107 0.707107i 0.0255155 0.0255155i
\(769\) 2.18355 8.14911i 0.0787407 0.293864i −0.915315 0.402739i \(-0.868058\pi\)
0.994055 + 0.108875i \(0.0347248\pi\)
\(770\) −13.0074 + 47.3386i −0.468754 + 1.70596i
\(771\) 4.84860 + 2.79934i 0.174618 + 0.100816i
\(772\) 21.2687 0.765476
\(773\) 13.3370 + 7.70010i 0.479697 + 0.276953i 0.720290 0.693673i \(-0.244009\pi\)
−0.240593 + 0.970626i \(0.577342\pi\)
\(774\) −1.32302 4.93758i −0.0475550 0.177477i
\(775\) −17.9980 + 17.5461i −0.646508 + 0.630275i
\(776\) 4.47453 7.75012i 0.160626 0.278213i
\(777\) −30.8919 8.27746i −1.10824 0.296952i
\(778\) 8.80294 + 15.2471i 0.315601 + 0.546636i
\(779\) 37.5113 1.34398
\(780\) −8.06137 + 0.119949i −0.288643 + 0.00429485i
\(781\) −1.64836 −0.0589831
\(782\) −0.619441 1.07290i −0.0221511 0.0383669i
\(783\) 3.33464 + 0.893514i 0.119170 + 0.0319316i
\(784\) 4.69103 8.12510i 0.167537 0.290182i
\(785\) 23.3258 23.0311i 0.832533 0.822015i
\(786\) −3.17598 11.8529i −0.113283 0.422779i
\(787\) −25.4232 14.6781i −0.906238 0.523217i −0.0270193 0.999635i \(-0.508602\pi\)
−0.879219 + 0.476418i \(0.841935\pi\)
\(788\) −3.07005 −0.109366
\(789\) 24.7160 + 14.2698i 0.879914 + 0.508019i
\(790\) 3.25406 + 5.71985i 0.115774 + 0.203503i
\(791\) 14.7069 54.8870i 0.522918 1.95156i
\(792\) −3.83563 + 3.83563i −0.136293 + 0.136293i
\(793\) −9.71690 33.4095i −0.345057 1.18641i
\(794\) 25.3460i 0.899495i
\(795\) 0.399622 + 0.702440i 0.0141731 + 0.0249130i
\(796\) −1.64001 2.84058i −0.0581285 0.100682i
\(797\) −3.28150 12.2467i −0.116237 0.433801i 0.883140 0.469110i \(-0.155425\pi\)
−0.999376 + 0.0353089i \(0.988758\pi\)
\(798\) 25.5592i 0.904785i
\(799\) −0.391535 + 0.104912i −0.0138515 + 0.00371151i
\(800\) 2.55485 4.29799i 0.0903275 0.151957i
\(801\) −4.46081 4.46081i −0.157615 0.157615i
\(802\) 19.9411 5.34321i 0.704146 0.188675i
\(803\) 18.7442 69.9544i 0.661470 2.46864i
\(804\) −12.6372 3.38612i −0.445679 0.119419i
\(805\) −41.1923 41.7194i −1.45184 1.47041i
\(806\) −15.5012 + 9.39401i −0.546005 + 0.330890i
\(807\) 1.95354 + 1.95354i 0.0687679 + 0.0687679i
\(808\) 7.96916 4.60100i 0.280354 0.161862i
\(809\) 6.66118 3.84584i 0.234195 0.135212i −0.378311 0.925679i \(-0.623495\pi\)
0.612506 + 0.790466i \(0.290162\pi\)
\(810\) −1.92935 1.13032i −0.0677903 0.0397154i
\(811\) −9.30453 + 9.30453i −0.326726 + 0.326726i −0.851340 0.524614i \(-0.824210\pi\)
0.524614 + 0.851340i \(0.324210\pi\)
\(812\) −6.98649 + 12.1010i −0.245178 + 0.424661i
\(813\) −5.63862 + 9.76638i −0.197755 + 0.342522i
\(814\) −30.3077 + 30.3077i −1.06228 + 1.06228i
\(815\) 12.7615 + 7.47642i 0.447016 + 0.261887i
\(816\) 0.165623 0.0956223i 0.00579796 0.00334745i
\(817\) −27.9552 + 16.1400i −0.978030 + 0.564666i
\(818\) −4.16416 4.16416i −0.145596 0.145596i
\(819\) −14.1731 3.47688i −0.495250 0.121492i
\(820\) −9.33235 9.45176i −0.325900 0.330070i
\(821\) 23.3227 + 6.24931i 0.813969 + 0.218102i 0.641708 0.766949i \(-0.278226\pi\)
0.172261 + 0.985051i \(0.444893\pi\)
\(822\) 1.57948 5.89471i 0.0550908 0.205602i
\(823\) 15.7789 4.22794i 0.550017 0.147377i 0.0269010 0.999638i \(-0.491436\pi\)
0.523116 + 0.852262i \(0.324769\pi\)
\(824\) −11.7362 11.7362i −0.408851 0.408851i
\(825\) −13.8585 + 23.3140i −0.482491 + 0.811690i
\(826\) −17.0805 + 4.57671i −0.594307 + 0.159244i
\(827\) 19.2456i 0.669235i −0.942354 0.334617i \(-0.891393\pi\)
0.942354 0.334617i \(-0.108607\pi\)
\(828\) −1.67663 6.25726i −0.0582668 0.217455i
\(829\) 1.64125 + 2.84273i 0.0570030 + 0.0987322i 0.893119 0.449821i \(-0.148512\pi\)
−0.836116 + 0.548553i \(0.815179\pi\)
\(830\) 11.4823 + 20.1831i 0.398556 + 0.700566i
\(831\) 2.34422i 0.0813200i
\(832\) 2.49480 2.60307i 0.0864916 0.0902452i
\(833\) 1.26874 1.26874i 0.0439592 0.0439592i
\(834\) −0.482087 + 1.79917i −0.0166933 + 0.0623003i
\(835\) −19.9341 35.0394i −0.689849 1.21259i
\(836\) 29.6650 + 17.1271i 1.02599 + 0.592353i
\(837\) −5.02711 −0.173762
\(838\) 13.2160 + 7.63025i 0.456538 + 0.263583i
\(839\) −0.270259 1.00862i −0.00933039 0.0348215i 0.961104 0.276188i \(-0.0890712\pi\)
−0.970434 + 0.241366i \(0.922404\pi\)
\(840\) 6.44017 6.35881i 0.222207 0.219400i
\(841\) −8.54091 + 14.7933i −0.294514 + 0.510113i
\(842\) 2.99291 + 0.801948i 0.103142 + 0.0276369i
\(843\) −11.4038 19.7520i −0.392768 0.680294i
\(844\) −15.7101 −0.540765
\(845\) −29.0499 + 1.04955i −0.999348 + 0.0361056i
\(846\) −2.11952 −0.0728707
\(847\) 37.2854 + 64.5803i 1.28114 + 2.21900i
\(848\) −0.349104 0.0935422i −0.0119883 0.00321225i
\(849\) −11.2756 + 19.5300i −0.386979 + 0.670267i
\(850\) 0.684693 0.667501i 0.0234848 0.0228951i
\(851\) −13.2481 49.4425i −0.454138 1.69487i
\(852\) 0.263168 + 0.151940i 0.00901598 + 0.00520538i
\(853\) 16.2227 0.555456 0.277728 0.960660i \(-0.410419\pi\)
0.277728 + 0.960660i \(0.410419\pi\)
\(854\) 33.8256 + 19.5292i 1.15749 + 0.668276i
\(855\) −3.74126 + 13.6158i −0.127948 + 0.465649i
\(856\) −0.575877 + 2.14920i −0.0196831 + 0.0734583i
\(857\) 21.1256 21.1256i 0.721638 0.721638i −0.247301 0.968939i \(-0.579544\pi\)
0.968939 + 0.247301i \(0.0795436\pi\)
\(858\) −13.5328 + 14.1201i −0.462001 + 0.482051i
\(859\) 8.87764i 0.302901i −0.988465 0.151451i \(-0.951606\pi\)
0.988465 0.151451i \(-0.0483945\pi\)
\(860\) 11.0217 + 3.02848i 0.375838 + 0.103270i
\(861\) −12.0214 20.8216i −0.409687 0.709599i
\(862\) 2.83012 + 10.5621i 0.0963942 + 0.359748i
\(863\) 5.12570i 0.174481i 0.996187 + 0.0872404i \(0.0278048\pi\)
−0.996187 + 0.0872404i \(0.972195\pi\)
\(864\) 0.965926 0.258819i 0.0328615 0.00880520i
\(865\) 5.96969 + 22.8594i 0.202976 + 0.777245i
\(866\) −23.5177 23.5177i −0.799163 0.799163i
\(867\) −16.3854 + 4.39046i −0.556478 + 0.149108i
\(868\) 5.26622 19.6538i 0.178747 0.667093i
\(869\) 15.4199 + 4.13175i 0.523085 + 0.140160i
\(870\) −5.49311 + 5.42371i −0.186234 + 0.183881i
\(871\) −45.8129 11.2386i −1.55231 0.380805i
\(872\) 2.61160 + 2.61160i 0.0884398 + 0.0884398i
\(873\) 7.75012 4.47453i 0.262302 0.151440i
\(874\) −35.4269 + 20.4537i −1.19833 + 0.691858i
\(875\) 23.3693 38.7509i 0.790025 1.31002i
\(876\) −9.44072 + 9.44072i −0.318972 + 0.318972i
\(877\) 7.32133 12.6809i 0.247224 0.428204i −0.715531 0.698581i \(-0.753815\pi\)
0.962754 + 0.270377i \(0.0871484\pi\)
\(878\) 6.66616 11.5461i 0.224972 0.389663i
\(879\) −12.0615 + 12.0615i −0.406824 + 0.406824i
\(880\) −3.06476 11.7357i −0.103313 0.395612i
\(881\) −9.96403 + 5.75274i −0.335697 + 0.193815i −0.658367 0.752697i \(-0.728753\pi\)
0.322671 + 0.946511i \(0.395419\pi\)
\(882\) 8.12510 4.69103i 0.273586 0.157955i
\(883\) 11.3276 + 11.3276i 0.381204 + 0.381204i 0.871536 0.490332i \(-0.163124\pi\)
−0.490332 + 0.871536i \(0.663124\pi\)
\(884\) 0.589706 0.357373i 0.0198340 0.0120198i
\(885\) −9.76898 0.0620995i −0.328381 0.00208745i
\(886\) −6.56567 1.75927i −0.220578 0.0591037i
\(887\) 1.52231 5.68132i 0.0511140 0.190760i −0.935648 0.352934i \(-0.885184\pi\)
0.986762 + 0.162174i \(0.0518506\pi\)
\(888\) 7.63239 2.04509i 0.256126 0.0686288i
\(889\) 34.0700 + 34.0700i 1.14267 + 1.14267i
\(890\) 13.6486 3.56430i 0.457502 0.119476i
\(891\) −5.23956 + 1.40394i −0.175532 + 0.0470336i
\(892\) 23.7364i 0.794752i
\(893\) 3.46415 + 12.9284i 0.115923 + 0.432632i
\(894\) 1.90178 + 3.29398i 0.0636050 + 0.110167i
\(895\) 33.1307 18.8482i 1.10744 0.630027i
\(896\) 4.04748i 0.135217i
\(897\) −6.52285 22.4274i −0.217792 0.748830i
\(898\) −20.4525 + 20.4525i −0.682509 + 0.682509i
\(899\) −4.49179 + 16.7636i −0.149810 + 0.559097i
\(900\) 4.36156 2.44475i 0.145385 0.0814916i
\(901\) −0.0598593 0.0345598i −0.00199420 0.00115135i
\(902\) −32.2219 −1.07287
\(903\) 17.9178 + 10.3449i 0.596267 + 0.344255i
\(904\) 3.63361 + 13.5608i 0.120852 + 0.451026i
\(905\) 36.3091 + 0.230810i 1.20695 + 0.00767238i
\(906\) −3.95976 + 6.85851i −0.131554 + 0.227859i
\(907\) 10.3697 + 2.77855i 0.344320 + 0.0922604i 0.426835 0.904329i \(-0.359628\pi\)
−0.0825147 + 0.996590i \(0.526295\pi\)
\(908\) −12.0786 20.9208i −0.400844 0.694281i
\(909\) 9.20199 0.305211
\(910\) 22.7283 23.4149i 0.753436 0.776196i
\(911\) −16.8449 −0.558097 −0.279048 0.960277i \(-0.590019\pi\)
−0.279048 + 0.960277i \(0.590019\pi\)
\(912\) −3.15742 5.46881i −0.104553 0.181091i
\(913\) 54.4108 + 14.5793i 1.80074 + 0.482506i
\(914\) −4.52778 + 7.84234i −0.149766 + 0.259402i
\(915\) 15.1608 + 15.3548i 0.501201 + 0.507614i
\(916\) −1.78836 6.67424i −0.0590890 0.220523i
\(917\) 43.0127 + 24.8334i 1.42040 + 0.820070i
\(918\) 0.191245 0.00631201
\(919\) −34.0429 19.6547i −1.12297 0.648348i −0.180814 0.983517i \(-0.557873\pi\)
−0.942158 + 0.335170i \(0.891206\pi\)
\(920\) 13.9675 + 3.83792i 0.460496 + 0.126532i
\(921\) 0.323181 1.20613i 0.0106492 0.0397432i
\(922\) 15.1956 15.1956i 0.500440 0.500440i
\(923\) 0.960283 + 0.527556i 0.0316081 + 0.0173647i
\(924\) 21.9551i 0.722270i
\(925\) 34.4634 19.3175i 1.13315 0.635155i
\(926\) −14.9487 25.8918i −0.491243 0.850859i
\(927\) −4.29576 16.0320i −0.141091 0.526559i
\(928\) 3.45227i 0.113326i
\(929\) −43.8009 + 11.7364i −1.43706 + 0.385059i −0.891503 0.453015i \(-0.850348\pi\)
−0.545557 + 0.838074i \(0.683682\pi\)
\(930\) 5.68225 9.69903i 0.186328 0.318044i
\(931\) −41.8934 41.8934i −1.37300 1.37300i
\(932\) −2.59849 + 0.696264i −0.0851164 + 0.0228069i
\(933\) −4.70517 + 17.5599i −0.154040 + 0.574886i
\(934\) 34.9973 + 9.37750i 1.14515 + 0.306841i
\(935\) 0.0147454 2.31962i 0.000482225 0.0758597i
\(936\) 3.46210 1.00692i 0.113162 0.0329124i
\(937\) −10.6838 10.6838i −0.349026 0.349026i 0.510721 0.859747i \(-0.329379\pi\)
−0.859747 + 0.510721i \(0.829379\pi\)
\(938\) 45.8586 26.4765i 1.49734 0.864488i
\(939\) 20.1767 11.6491i 0.658443 0.380152i
\(940\) 2.39574 4.08929i 0.0781404 0.133378i
\(941\) −20.2840 + 20.2840i −0.661240 + 0.661240i −0.955672 0.294433i \(-0.904869\pi\)
0.294433 + 0.955672i \(0.404869\pi\)
\(942\) −7.32981 + 12.6956i −0.238818 + 0.413645i
\(943\) 19.2402 33.3250i 0.626547 1.08521i
\(944\) 3.08929 3.08929i 0.100548 0.100548i
\(945\) 8.75676 2.28681i 0.284857 0.0743898i
\(946\) 24.0133 13.8641i 0.780740 0.450760i
\(947\) −10.0834 + 5.82164i −0.327666 + 0.189178i −0.654804 0.755798i \(-0.727249\pi\)
0.327139 + 0.944976i \(0.393916\pi\)
\(948\) −2.08100 2.08100i −0.0675877 0.0675877i
\(949\) −33.3086 + 34.7541i −1.08124 + 1.12817i
\(950\) −22.0407 22.6084i −0.715095 0.733512i
\(951\) −23.5106 6.29966i −0.762385 0.204280i
\(952\) −0.200341 + 0.747683i −0.00649309 + 0.0242325i
\(953\) −20.2141 + 5.41636i −0.654800 + 0.175453i −0.570898 0.821021i \(-0.693405\pi\)
−0.0839019 + 0.996474i \(0.526738\pi\)
\(954\) −0.255562 0.255562i −0.00827413 0.00827413i
\(955\) −10.2854 6.02576i −0.332827 0.194989i
\(956\) 23.4071 6.27192i 0.757040 0.202848i
\(957\) 18.7265i 0.605341i
\(958\) −3.50087 13.0654i −0.113108 0.422124i
\(959\) 12.3502 + 21.3911i 0.398808 + 0.690755i
\(960\) −0.592455 + 2.15615i −0.0191214 + 0.0695895i
\(961\) 5.72818i 0.184780i
\(962\) 27.3562 7.95634i 0.881999 0.256523i
\(963\) −1.57333 + 1.57333i −0.0506997 + 0.0506997i
\(964\) −2.08272 + 7.77282i −0.0670799 + 0.250346i
\(965\) −41.3369 + 23.5168i −1.33068 + 0.757033i
\(966\) 22.7068 + 13.1098i 0.730578 + 0.421799i
\(967\) −10.0253 −0.322393 −0.161197 0.986922i \(-0.551535\pi\)
−0.161197 + 0.986922i \(0.551535\pi\)
\(968\) −15.9557 9.21202i −0.512835 0.296086i
\(969\) −0.312571 1.16653i −0.0100412 0.0374743i
\(970\) −0.127202 + 20.0103i −0.00408420 + 0.642492i
\(971\) −1.61154 + 2.79127i −0.0517167 + 0.0895760i −0.890725 0.454543i \(-0.849803\pi\)
0.839008 + 0.544119i \(0.183136\pi\)
\(972\) 0.965926 + 0.258819i 0.0309821 + 0.00830162i
\(973\) −3.76950 6.52896i −0.120845 0.209309i
\(974\) 22.6808 0.726738
\(975\) 15.5351 9.14659i 0.497522 0.292925i
\(976\) −9.65007 −0.308891
\(977\) 17.7725 + 30.7828i 0.568592 + 0.984829i 0.996706 + 0.0811048i \(0.0258448\pi\)
−0.428114 + 0.903725i \(0.640822\pi\)
\(978\) −6.38904 1.71194i −0.204299 0.0547417i
\(979\) 17.1100 29.6354i 0.546838 0.947152i
\(980\) −0.133356 + 20.9785i −0.00425991 + 0.670133i
\(981\) 0.955910 + 3.56751i 0.0305199 + 0.113902i
\(982\) −31.8367 18.3809i −1.01595 0.586559i
\(983\) −33.0159 −1.05304 −0.526522 0.850161i \(-0.676504\pi\)
−0.526522 + 0.850161i \(0.676504\pi\)
\(984\) 5.14435 + 2.97009i 0.163996 + 0.0946830i
\(985\) 5.96683 3.39456i 0.190119 0.108160i
\(986\) 0.170880 0.637732i 0.00544192 0.0203095i
\(987\) 6.06607 6.06607i 0.193085 0.193085i
\(988\) −11.8004 19.4719i −0.375420 0.619484i
\(989\) 33.1139i 1.05296i
\(990\) 3.21371 11.6958i 0.102138 0.371718i
\(991\) −10.4655 18.1268i −0.332447 0.575815i 0.650544 0.759469i \(-0.274541\pi\)
−0.982991 + 0.183653i \(0.941208\pi\)
\(992\) 1.30111 + 4.85581i 0.0413103 + 0.154172i
\(993\) 5.35736i 0.170011i
\(994\) −1.18804 + 0.318334i −0.0376823 + 0.0100969i
\(995\) 6.32828 + 3.70747i 0.200620 + 0.117535i
\(996\) −7.34303 7.34303i −0.232673 0.232673i
\(997\) −1.01046 + 0.270753i −0.0320017 + 0.00857484i −0.274784 0.961506i \(-0.588606\pi\)
0.242783 + 0.970081i \(0.421940\pi\)
\(998\) 7.65327 28.5624i 0.242260 0.904126i
\(999\) 7.63239 + 2.04509i 0.241478 + 0.0647038i
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.bn.c.67.2 yes 32
5.3 odd 4 390.2.bd.c.223.8 yes 32
13.7 odd 12 390.2.bd.c.7.8 32
65.33 even 12 inner 390.2.bn.c.163.2 yes 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
390.2.bd.c.7.8 32 13.7 odd 12
390.2.bd.c.223.8 yes 32 5.3 odd 4
390.2.bn.c.67.2 yes 32 1.1 even 1 trivial
390.2.bn.c.163.2 yes 32 65.33 even 12 inner