Properties

Label 441.2.h.e.214.1
Level $441$
Weight $2$
Character 441.214
Analytic conductor $3.521$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [441,2,Mod(214,441)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(441, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("441.214");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 441.h (of order \(3\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.52140272914\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\zeta_{18})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - x^{3} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 63)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 214.1
Root \(0.939693 - 0.342020i\) of defining polynomial
Character \(\chi\) \(=\) 441.214
Dual form 441.2.h.e.373.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-0.879385 q^{2} +(-1.70574 - 0.300767i) q^{3} -1.22668 q^{4} +(0.673648 - 1.16679i) q^{5} +(1.50000 + 0.264490i) q^{6} +2.83750 q^{8} +(2.81908 + 1.02606i) q^{9} +O(q^{10})\) \(q-0.879385 q^{2} +(-1.70574 - 0.300767i) q^{3} -1.22668 q^{4} +(0.673648 - 1.16679i) q^{5} +(1.50000 + 0.264490i) q^{6} +2.83750 q^{8} +(2.81908 + 1.02606i) q^{9} +(-0.592396 + 1.02606i) q^{10} +(-0.826352 - 1.43128i) q^{11} +(2.09240 + 0.368946i) q^{12} +(-1.68479 - 2.91815i) q^{13} +(-1.50000 + 1.78763i) q^{15} -0.0418891 q^{16} +(0.233956 - 0.405223i) q^{17} +(-2.47906 - 0.902302i) q^{18} +(-1.61334 - 2.79439i) q^{19} +(-0.826352 + 1.43128i) q^{20} +(0.726682 + 1.25865i) q^{22} +(-4.47178 + 7.74535i) q^{23} +(-4.84002 - 0.853427i) q^{24} +(1.59240 + 2.75811i) q^{25} +(1.48158 + 2.56617i) q^{26} +(-4.50000 - 2.59808i) q^{27} +(-3.13429 + 5.42874i) q^{29} +(1.31908 - 1.57202i) q^{30} -9.23442 q^{31} -5.63816 q^{32} +(0.979055 + 2.68993i) q^{33} +(-0.205737 + 0.356347i) q^{34} +(-3.45811 - 1.25865i) q^{36} +(-4.61721 - 7.99724i) q^{37} +(1.41875 + 2.45734i) q^{38} +(1.99613 + 5.48432i) q^{39} +(1.91147 - 3.31077i) q^{40} +(1.70574 + 2.95442i) q^{41} +(2.20574 - 3.82045i) q^{43} +(1.01367 + 1.75573i) q^{44} +(3.09627 - 2.59808i) q^{45} +(3.93242 - 6.81115i) q^{46} -9.35504 q^{47} +(0.0714517 + 0.0125989i) q^{48} +(-1.40033 - 2.42544i) q^{50} +(-0.520945 + 0.620838i) q^{51} +(2.06670 + 3.57964i) q^{52} +(0.286989 - 0.497079i) q^{53} +(3.95723 + 2.28471i) q^{54} -2.22668 q^{55} +(1.91147 + 5.25173i) q^{57} +(2.75624 - 4.77396i) q^{58} +10.3969 q^{59} +(1.84002 - 2.19285i) q^{60} -7.63816 q^{61} +8.12061 q^{62} +5.04189 q^{64} -4.53983 q^{65} +(-0.860967 - 2.36549i) q^{66} +0.596267 q^{67} +(-0.286989 + 0.497079i) q^{68} +(9.95723 - 11.8666i) q^{69} -0.554378 q^{71} +(7.99912 + 2.91144i) q^{72} +(1.02481 - 1.77503i) q^{73} +(4.06031 + 7.03266i) q^{74} +(-1.88666 - 5.18355i) q^{75} +(1.97906 + 3.42782i) q^{76} +(-1.75537 - 4.82283i) q^{78} -2.40373 q^{79} +(-0.0282185 + 0.0488759i) q^{80} +(6.89440 + 5.78509i) q^{81} +(-1.50000 - 2.59808i) q^{82} +(-7.52481 + 13.0334i) q^{83} +(-0.315207 - 0.545955i) q^{85} +(-1.93969 + 3.35965i) q^{86} +(6.97906 - 8.31731i) q^{87} +(-2.34477 - 4.06126i) q^{88} +(4.54323 + 7.86911i) q^{89} +(-2.72281 + 2.28471i) q^{90} +(5.48545 - 9.50108i) q^{92} +(15.7515 + 2.77741i) q^{93} +8.22668 q^{94} -4.34730 q^{95} +(9.61721 + 1.69577i) q^{96} +(-0.949493 + 1.64457i) q^{97} +(-0.860967 - 4.88279i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + 6 q^{2} + 6 q^{4} + 3 q^{5} + 9 q^{6} + 12 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 6 q + 6 q^{2} + 6 q^{4} + 3 q^{5} + 9 q^{6} + 12 q^{8} - 6 q^{11} + 9 q^{12} - 3 q^{13} - 9 q^{15} + 6 q^{16} + 6 q^{17} - 18 q^{18} - 3 q^{19} - 6 q^{20} - 9 q^{22} - 12 q^{23} - 9 q^{24} + 6 q^{25} - 3 q^{26} - 27 q^{27} - 9 q^{29} - 9 q^{30} + 6 q^{31} + 9 q^{33} + 9 q^{34} - 27 q^{36} + 3 q^{37} + 6 q^{38} + 36 q^{39} - 9 q^{40} + 3 q^{43} - 15 q^{44} - 9 q^{45} - 6 q^{47} + 6 q^{50} - 21 q^{52} - 6 q^{53} - 27 q^{54} - 9 q^{57} + 9 q^{58} + 6 q^{59} - 9 q^{60} - 12 q^{61} + 60 q^{62} + 24 q^{64} + 30 q^{65} + 18 q^{66} - 24 q^{67} + 6 q^{68} + 9 q^{69} + 18 q^{71} - 9 q^{72} - 21 q^{73} + 30 q^{74} - 18 q^{75} + 15 q^{76} + 54 q^{78} - 42 q^{79} - 15 q^{80} - 9 q^{82} - 18 q^{83} - 9 q^{85} - 6 q^{86} + 45 q^{87} - 27 q^{88} + 12 q^{89} - 27 q^{90} - 3 q^{92} + 54 q^{93} + 36 q^{94} - 24 q^{95} + 27 q^{96} - 3 q^{97} + 18 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(344\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.879385 −0.621819 −0.310910 0.950439i \(-0.600634\pi\)
−0.310910 + 0.950439i \(0.600634\pi\)
\(3\) −1.70574 0.300767i −0.984808 0.173648i
\(4\) −1.22668 −0.613341
\(5\) 0.673648 1.16679i 0.301265 0.521806i −0.675158 0.737673i \(-0.735925\pi\)
0.976423 + 0.215867i \(0.0692579\pi\)
\(6\) 1.50000 + 0.264490i 0.612372 + 0.107978i
\(7\) 0 0
\(8\) 2.83750 1.00321
\(9\) 2.81908 + 1.02606i 0.939693 + 0.342020i
\(10\) −0.592396 + 1.02606i −0.187332 + 0.324469i
\(11\) −0.826352 1.43128i −0.249154 0.431548i 0.714137 0.700006i \(-0.246819\pi\)
−0.963291 + 0.268458i \(0.913486\pi\)
\(12\) 2.09240 + 0.368946i 0.604023 + 0.106506i
\(13\) −1.68479 2.91815i −0.467277 0.809348i 0.532024 0.846729i \(-0.321432\pi\)
−0.999301 + 0.0373813i \(0.988098\pi\)
\(14\) 0 0
\(15\) −1.50000 + 1.78763i −0.387298 + 0.461564i
\(16\) −0.0418891 −0.0104723
\(17\) 0.233956 0.405223i 0.0567426 0.0982810i −0.836259 0.548335i \(-0.815262\pi\)
0.893001 + 0.450054i \(0.148595\pi\)
\(18\) −2.47906 0.902302i −0.584319 0.212675i
\(19\) −1.61334 2.79439i −0.370126 0.641077i 0.619459 0.785029i \(-0.287352\pi\)
−0.989585 + 0.143953i \(0.954019\pi\)
\(20\) −0.826352 + 1.43128i −0.184778 + 0.320045i
\(21\) 0 0
\(22\) 0.726682 + 1.25865i 0.154929 + 0.268345i
\(23\) −4.47178 + 7.74535i −0.932431 + 1.61502i −0.153279 + 0.988183i \(0.548983\pi\)
−0.779152 + 0.626835i \(0.784350\pi\)
\(24\) −4.84002 0.853427i −0.987965 0.174205i
\(25\) 1.59240 + 2.75811i 0.318479 + 0.551622i
\(26\) 1.48158 + 2.56617i 0.290562 + 0.503268i
\(27\) −4.50000 2.59808i −0.866025 0.500000i
\(28\) 0 0
\(29\) −3.13429 + 5.42874i −0.582022 + 1.00809i 0.413217 + 0.910632i \(0.364405\pi\)
−0.995239 + 0.0974595i \(0.968928\pi\)
\(30\) 1.31908 1.57202i 0.240830 0.287010i
\(31\) −9.23442 −1.65855 −0.829276 0.558840i \(-0.811247\pi\)
−0.829276 + 0.558840i \(0.811247\pi\)
\(32\) −5.63816 −0.996695
\(33\) 0.979055 + 2.68993i 0.170432 + 0.468257i
\(34\) −0.205737 + 0.356347i −0.0352836 + 0.0611130i
\(35\) 0 0
\(36\) −3.45811 1.25865i −0.576352 0.209775i
\(37\) −4.61721 7.99724i −0.759065 1.31474i −0.943328 0.331862i \(-0.892323\pi\)
0.184263 0.982877i \(-0.441010\pi\)
\(38\) 1.41875 + 2.45734i 0.230151 + 0.398634i
\(39\) 1.99613 + 5.48432i 0.319637 + 0.878194i
\(40\) 1.91147 3.31077i 0.302231 0.523479i
\(41\) 1.70574 + 2.95442i 0.266391 + 0.461403i 0.967927 0.251231i \(-0.0808353\pi\)
−0.701536 + 0.712634i \(0.747502\pi\)
\(42\) 0 0
\(43\) 2.20574 3.82045i 0.336372 0.582613i −0.647376 0.762171i \(-0.724133\pi\)
0.983747 + 0.179558i \(0.0574668\pi\)
\(44\) 1.01367 + 1.75573i 0.152817 + 0.264686i
\(45\) 3.09627 2.59808i 0.461564 0.387298i
\(46\) 3.93242 6.81115i 0.579803 1.00425i
\(47\) −9.35504 −1.36457 −0.682286 0.731085i \(-0.739014\pi\)
−0.682286 + 0.731085i \(0.739014\pi\)
\(48\) 0.0714517 + 0.0125989i 0.0103132 + 0.00181849i
\(49\) 0 0
\(50\) −1.40033 2.42544i −0.198037 0.343009i
\(51\) −0.520945 + 0.620838i −0.0729468 + 0.0869346i
\(52\) 2.06670 + 3.57964i 0.286600 + 0.496406i
\(53\) 0.286989 0.497079i 0.0394210 0.0682791i −0.845642 0.533751i \(-0.820782\pi\)
0.885063 + 0.465472i \(0.154115\pi\)
\(54\) 3.95723 + 2.28471i 0.538511 + 0.310910i
\(55\) −2.22668 −0.300246
\(56\) 0 0
\(57\) 1.91147 + 5.25173i 0.253181 + 0.695609i
\(58\) 2.75624 4.77396i 0.361913 0.626851i
\(59\) 10.3969 1.35356 0.676782 0.736183i \(-0.263374\pi\)
0.676782 + 0.736183i \(0.263374\pi\)
\(60\) 1.84002 2.19285i 0.237546 0.283096i
\(61\) −7.63816 −0.977966 −0.488983 0.872293i \(-0.662632\pi\)
−0.488983 + 0.872293i \(0.662632\pi\)
\(62\) 8.12061 1.03132
\(63\) 0 0
\(64\) 5.04189 0.630236
\(65\) −4.53983 −0.563097
\(66\) −0.860967 2.36549i −0.105978 0.291171i
\(67\) 0.596267 0.0728456 0.0364228 0.999336i \(-0.488404\pi\)
0.0364228 + 0.999336i \(0.488404\pi\)
\(68\) −0.286989 + 0.497079i −0.0348025 + 0.0602797i
\(69\) 9.95723 11.8666i 1.19871 1.42857i
\(70\) 0 0
\(71\) −0.554378 −0.0657925 −0.0328963 0.999459i \(-0.510473\pi\)
−0.0328963 + 0.999459i \(0.510473\pi\)
\(72\) 7.99912 + 2.91144i 0.942706 + 0.343117i
\(73\) 1.02481 1.77503i 0.119946 0.207752i −0.799800 0.600266i \(-0.795061\pi\)
0.919746 + 0.392514i \(0.128395\pi\)
\(74\) 4.06031 + 7.03266i 0.472001 + 0.817530i
\(75\) −1.88666 5.18355i −0.217853 0.598545i
\(76\) 1.97906 + 3.42782i 0.227013 + 0.393198i
\(77\) 0 0
\(78\) −1.75537 4.82283i −0.198756 0.546078i
\(79\) −2.40373 −0.270441 −0.135221 0.990816i \(-0.543174\pi\)
−0.135221 + 0.990816i \(0.543174\pi\)
\(80\) −0.0282185 + 0.0488759i −0.00315492 + 0.00546449i
\(81\) 6.89440 + 5.78509i 0.766044 + 0.642788i
\(82\) −1.50000 2.59808i −0.165647 0.286910i
\(83\) −7.52481 + 13.0334i −0.825956 + 1.43060i 0.0752309 + 0.997166i \(0.476031\pi\)
−0.901187 + 0.433431i \(0.857303\pi\)
\(84\) 0 0
\(85\) −0.315207 0.545955i −0.0341891 0.0592172i
\(86\) −1.93969 + 3.35965i −0.209162 + 0.362280i
\(87\) 6.97906 8.31731i 0.748233 0.891710i
\(88\) −2.34477 4.06126i −0.249953 0.432932i
\(89\) 4.54323 + 7.86911i 0.481582 + 0.834124i 0.999777 0.0211385i \(-0.00672911\pi\)
−0.518195 + 0.855263i \(0.673396\pi\)
\(90\) −2.72281 + 2.28471i −0.287010 + 0.240830i
\(91\) 0 0
\(92\) 5.48545 9.50108i 0.571898 0.990556i
\(93\) 15.7515 + 2.77741i 1.63335 + 0.288004i
\(94\) 8.22668 0.848517
\(95\) −4.34730 −0.446023
\(96\) 9.61721 + 1.69577i 0.981553 + 0.173074i
\(97\) −0.949493 + 1.64457i −0.0964064 + 0.166981i −0.910195 0.414181i \(-0.864068\pi\)
0.813788 + 0.581161i \(0.197402\pi\)
\(98\) 0 0
\(99\) −0.860967 4.88279i −0.0865304 0.490738i
\(100\) −1.95336 3.38332i −0.195336 0.338332i
\(101\) −0.854570 1.48016i −0.0850329 0.147281i 0.820372 0.571830i \(-0.193766\pi\)
−0.905405 + 0.424548i \(0.860433\pi\)
\(102\) 0.458111 0.545955i 0.0453597 0.0540576i
\(103\) −1.81908 + 3.15074i −0.179239 + 0.310451i −0.941620 0.336677i \(-0.890697\pi\)
0.762381 + 0.647128i \(0.224030\pi\)
\(104\) −4.78059 8.28023i −0.468776 0.811943i
\(105\) 0 0
\(106\) −0.252374 + 0.437124i −0.0245127 + 0.0424573i
\(107\) −3.56418 6.17334i −0.344562 0.596799i 0.640712 0.767781i \(-0.278639\pi\)
−0.985274 + 0.170982i \(0.945306\pi\)
\(108\) 5.52007 + 3.18701i 0.531169 + 0.306670i
\(109\) −0.201867 + 0.349643i −0.0193353 + 0.0334898i −0.875531 0.483162i \(-0.839488\pi\)
0.856196 + 0.516651i \(0.172822\pi\)
\(110\) 1.95811 0.186699
\(111\) 5.47044 + 15.0299i 0.519231 + 1.42658i
\(112\) 0 0
\(113\) −7.18479 12.4444i −0.675888 1.17067i −0.976208 0.216835i \(-0.930427\pi\)
0.300320 0.953839i \(-0.402907\pi\)
\(114\) −1.68092 4.61830i −0.157433 0.432543i
\(115\) 6.02481 + 10.4353i 0.561817 + 0.973095i
\(116\) 3.84477 6.65934i 0.356978 0.618304i
\(117\) −1.75537 9.95518i −0.162284 0.920357i
\(118\) −9.14290 −0.841672
\(119\) 0 0
\(120\) −4.25624 + 5.07239i −0.388540 + 0.463044i
\(121\) 4.13429 7.16079i 0.375844 0.650981i
\(122\) 6.71688 0.608118
\(123\) −2.02094 5.55250i −0.182222 0.500652i
\(124\) 11.3277 1.01726
\(125\) 11.0273 0.986315
\(126\) 0 0
\(127\) −20.7716 −1.84318 −0.921589 0.388167i \(-0.873108\pi\)
−0.921589 + 0.388167i \(0.873108\pi\)
\(128\) 6.84255 0.604802
\(129\) −4.91147 + 5.85327i −0.432431 + 0.515351i
\(130\) 3.99226 0.350144
\(131\) −3.58260 + 6.20524i −0.313013 + 0.542154i −0.979013 0.203797i \(-0.934672\pi\)
0.666000 + 0.745952i \(0.268005\pi\)
\(132\) −1.20099 3.29969i −0.104533 0.287201i
\(133\) 0 0
\(134\) −0.524348 −0.0452968
\(135\) −6.06283 + 3.50038i −0.521806 + 0.301265i
\(136\) 0.663848 1.14982i 0.0569245 0.0985961i
\(137\) −1.28446 2.22475i −0.109739 0.190074i 0.805925 0.592017i \(-0.201668\pi\)
−0.915665 + 0.401943i \(0.868335\pi\)
\(138\) −8.75624 + 10.4353i −0.745381 + 0.888310i
\(139\) −3.06670 5.31169i −0.260114 0.450531i 0.706158 0.708055i \(-0.250427\pi\)
−0.966272 + 0.257523i \(0.917094\pi\)
\(140\) 0 0
\(141\) 15.9572 + 2.81369i 1.34384 + 0.236956i
\(142\) 0.487511 0.0409111
\(143\) −2.78446 + 4.82283i −0.232848 + 0.403305i
\(144\) −0.118089 0.0429807i −0.00984071 0.00358173i
\(145\) 4.22281 + 7.31412i 0.350685 + 0.607405i
\(146\) −0.901207 + 1.56094i −0.0745844 + 0.129184i
\(147\) 0 0
\(148\) 5.66385 + 9.81007i 0.465565 + 0.806383i
\(149\) −0.215537 + 0.373321i −0.0176575 + 0.0305837i −0.874719 0.484630i \(-0.838954\pi\)
0.857062 + 0.515214i \(0.172288\pi\)
\(150\) 1.65910 + 4.55834i 0.135465 + 0.372187i
\(151\) 1.23530 + 2.13960i 0.100527 + 0.174118i 0.911902 0.410408i \(-0.134614\pi\)
−0.811375 + 0.584526i \(0.801280\pi\)
\(152\) −4.57785 7.92907i −0.371313 0.643132i
\(153\) 1.07532 0.902302i 0.0869346 0.0729468i
\(154\) 0 0
\(155\) −6.22075 + 10.7747i −0.499663 + 0.865441i
\(156\) −2.44862 6.72752i −0.196046 0.538632i
\(157\) −10.1334 −0.808734 −0.404367 0.914597i \(-0.632508\pi\)
−0.404367 + 0.914597i \(0.632508\pi\)
\(158\) 2.11381 0.168166
\(159\) −0.639033 + 0.761570i −0.0506786 + 0.0603964i
\(160\) −3.79813 + 6.57856i −0.300269 + 0.520081i
\(161\) 0 0
\(162\) −6.06283 5.08732i −0.476341 0.399698i
\(163\) 1.29813 + 2.24843i 0.101678 + 0.176111i 0.912376 0.409353i \(-0.134246\pi\)
−0.810698 + 0.585464i \(0.800912\pi\)
\(164\) −2.09240 3.62414i −0.163389 0.282998i
\(165\) 3.79813 + 0.669713i 0.295684 + 0.0521371i
\(166\) 6.61721 11.4613i 0.513595 0.889573i
\(167\) −11.5915 20.0771i −0.896979 1.55361i −0.831337 0.555769i \(-0.812424\pi\)
−0.0656422 0.997843i \(-0.520910\pi\)
\(168\) 0 0
\(169\) 0.822948 1.42539i 0.0633037 0.109645i
\(170\) 0.277189 + 0.480105i 0.0212594 + 0.0368224i
\(171\) −1.68092 9.53298i −0.128543 0.729005i
\(172\) −2.70574 + 4.68647i −0.206311 + 0.357340i
\(173\) 4.75196 0.361285 0.180643 0.983549i \(-0.442182\pi\)
0.180643 + 0.983549i \(0.442182\pi\)
\(174\) −6.13728 + 7.31412i −0.465266 + 0.554482i
\(175\) 0 0
\(176\) 0.0346151 + 0.0599551i 0.00260921 + 0.00451929i
\(177\) −17.7344 3.12706i −1.33300 0.235044i
\(178\) −3.99525 6.91998i −0.299457 0.518674i
\(179\) 4.26604 7.38901i 0.318859 0.552280i −0.661391 0.750041i \(-0.730034\pi\)
0.980250 + 0.197761i \(0.0633670\pi\)
\(180\) −3.79813 + 3.18701i −0.283096 + 0.237546i
\(181\) 17.2344 1.28102 0.640512 0.767948i \(-0.278722\pi\)
0.640512 + 0.767948i \(0.278722\pi\)
\(182\) 0 0
\(183\) 13.0287 + 2.29731i 0.963108 + 0.169822i
\(184\) −12.6887 + 21.9774i −0.935421 + 1.62020i
\(185\) −12.4415 −0.914718
\(186\) −13.8516 2.44242i −1.01565 0.179087i
\(187\) −0.773318 −0.0565506
\(188\) 11.4757 0.836948
\(189\) 0 0
\(190\) 3.82295 0.277346
\(191\) 12.9094 0.934092 0.467046 0.884233i \(-0.345318\pi\)
0.467046 + 0.884233i \(0.345318\pi\)
\(192\) −8.60014 1.51644i −0.620661 0.109439i
\(193\) −0.638156 −0.0459355 −0.0229677 0.999736i \(-0.507311\pi\)
−0.0229677 + 0.999736i \(0.507311\pi\)
\(194\) 0.834970 1.44621i 0.0599473 0.103832i
\(195\) 7.74376 + 1.36543i 0.554542 + 0.0977807i
\(196\) 0 0
\(197\) 11.4456 0.815467 0.407733 0.913101i \(-0.366319\pi\)
0.407733 + 0.913101i \(0.366319\pi\)
\(198\) 0.757122 + 4.29385i 0.0538063 + 0.305151i
\(199\) −1.81908 + 3.15074i −0.128951 + 0.223350i −0.923270 0.384151i \(-0.874494\pi\)
0.794319 + 0.607500i \(0.207828\pi\)
\(200\) 4.51842 + 7.82613i 0.319500 + 0.553391i
\(201\) −1.01707 0.179338i −0.0717389 0.0126495i
\(202\) 0.751497 + 1.30163i 0.0528751 + 0.0915824i
\(203\) 0 0
\(204\) 0.639033 0.761570i 0.0447413 0.0533206i
\(205\) 4.59627 0.321017
\(206\) 1.59967 2.77071i 0.111454 0.193045i
\(207\) −20.5535 + 17.2464i −1.42857 + 1.19871i
\(208\) 0.0705744 + 0.122238i 0.00489345 + 0.00847571i
\(209\) −2.66637 + 4.61830i −0.184437 + 0.319454i
\(210\) 0 0
\(211\) −2.91147 5.04282i −0.200434 0.347162i 0.748234 0.663435i \(-0.230902\pi\)
−0.948668 + 0.316273i \(0.897569\pi\)
\(212\) −0.352044 + 0.609758i −0.0241785 + 0.0418784i
\(213\) 0.945622 + 0.166739i 0.0647930 + 0.0114248i
\(214\) 3.13429 + 5.42874i 0.214255 + 0.371101i
\(215\) −2.97178 5.14728i −0.202674 0.351041i
\(216\) −12.7687 7.37203i −0.868802 0.501603i
\(217\) 0 0
\(218\) 0.177519 0.307471i 0.0120231 0.0208246i
\(219\) −2.28194 + 2.71951i −0.154199 + 0.183767i
\(220\) 2.73143 0.184153
\(221\) −1.57667 −0.106058
\(222\) −4.81062 13.2171i −0.322868 0.887072i
\(223\) 3.54189 6.13473i 0.237182 0.410812i −0.722722 0.691139i \(-0.757109\pi\)
0.959905 + 0.280327i \(0.0904428\pi\)
\(224\) 0 0
\(225\) 1.65910 + 9.40923i 0.110607 + 0.627282i
\(226\) 6.31820 + 10.9434i 0.420280 + 0.727947i
\(227\) −5.97178 10.3434i −0.396361 0.686517i 0.596913 0.802306i \(-0.296394\pi\)
−0.993274 + 0.115789i \(0.963060\pi\)
\(228\) −2.34477 6.44220i −0.155286 0.426645i
\(229\) −8.77631 + 15.2010i −0.579955 + 1.00451i 0.415529 + 0.909580i \(0.363597\pi\)
−0.995484 + 0.0949315i \(0.969737\pi\)
\(230\) −5.29813 9.17664i −0.349349 0.605089i
\(231\) 0 0
\(232\) −8.89352 + 15.4040i −0.583888 + 1.01132i
\(233\) −8.12701 14.0764i −0.532418 0.922175i −0.999284 0.0378470i \(-0.987950\pi\)
0.466865 0.884328i \(-0.345383\pi\)
\(234\) 1.54364 + 8.75444i 0.100911 + 0.572296i
\(235\) −6.30200 + 10.9154i −0.411097 + 0.712042i
\(236\) −12.7537 −0.830196
\(237\) 4.10014 + 0.722965i 0.266333 + 0.0469616i
\(238\) 0 0
\(239\) 7.54963 + 13.0763i 0.488345 + 0.845838i 0.999910 0.0134062i \(-0.00426745\pi\)
−0.511565 + 0.859244i \(0.670934\pi\)
\(240\) 0.0628336 0.0748822i 0.00405589 0.00483362i
\(241\) −7.81908 13.5430i −0.503671 0.872384i −0.999991 0.00424420i \(-0.998649\pi\)
0.496320 0.868140i \(-0.334684\pi\)
\(242\) −3.63563 + 6.29710i −0.233707 + 0.404793i
\(243\) −10.0201 11.9415i −0.642788 0.766044i
\(244\) 9.36959 0.599826
\(245\) 0 0
\(246\) 1.77719 + 4.88279i 0.113309 + 0.311315i
\(247\) −5.43629 + 9.41593i −0.345903 + 0.599121i
\(248\) −26.2026 −1.66387
\(249\) 16.7554 19.9683i 1.06183 1.26544i
\(250\) −9.69728 −0.613310
\(251\) −19.0651 −1.20338 −0.601690 0.798730i \(-0.705506\pi\)
−0.601690 + 0.798730i \(0.705506\pi\)
\(252\) 0 0
\(253\) 14.7811 0.929277
\(254\) 18.2662 1.14612
\(255\) 0.373455 + 1.02606i 0.0233867 + 0.0642544i
\(256\) −16.1010 −1.00631
\(257\) 13.2909 23.0204i 0.829061 1.43598i −0.0697146 0.997567i \(-0.522209\pi\)
0.898776 0.438409i \(-0.144458\pi\)
\(258\) 4.31908 5.14728i 0.268894 0.320455i
\(259\) 0 0
\(260\) 5.56893 0.345370
\(261\) −14.4060 + 12.0881i −0.891710 + 0.748233i
\(262\) 3.15048 5.45680i 0.194637 0.337122i
\(263\) 0.367059 + 0.635765i 0.0226338 + 0.0392029i 0.877120 0.480270i \(-0.159461\pi\)
−0.854487 + 0.519473i \(0.826128\pi\)
\(264\) 2.77807 + 7.63267i 0.170978 + 0.469759i
\(265\) −0.386659 0.669713i −0.0237523 0.0411402i
\(266\) 0 0
\(267\) −5.38279 14.7891i −0.329421 0.905078i
\(268\) −0.731429 −0.0446792
\(269\) −10.4251 + 18.0569i −0.635632 + 1.10095i 0.350749 + 0.936470i \(0.385927\pi\)
−0.986381 + 0.164478i \(0.947406\pi\)
\(270\) 5.33157 3.07818i 0.324469 0.187332i
\(271\) 3.47906 + 6.02590i 0.211338 + 0.366047i 0.952133 0.305683i \(-0.0988847\pi\)
−0.740796 + 0.671730i \(0.765551\pi\)
\(272\) −0.00980018 + 0.0169744i −0.000594223 + 0.00102922i
\(273\) 0 0
\(274\) 1.12954 + 1.95642i 0.0682379 + 0.118191i
\(275\) 2.63176 4.55834i 0.158701 0.274878i
\(276\) −12.2144 + 14.5565i −0.735218 + 0.876198i
\(277\) −8.93629 15.4781i −0.536930 0.929989i −0.999067 0.0431811i \(-0.986251\pi\)
0.462138 0.886808i \(-0.347083\pi\)
\(278\) 2.69681 + 4.67102i 0.161744 + 0.280149i
\(279\) −26.0326 9.47508i −1.55853 0.567258i
\(280\) 0 0
\(281\) −11.1552 + 19.3214i −0.665465 + 1.15262i 0.313694 + 0.949524i \(0.398433\pi\)
−0.979159 + 0.203095i \(0.934900\pi\)
\(282\) −14.0326 2.47432i −0.835627 0.147344i
\(283\) 18.5945 1.10533 0.552665 0.833404i \(-0.313611\pi\)
0.552665 + 0.833404i \(0.313611\pi\)
\(284\) 0.680045 0.0403532
\(285\) 7.41534 + 1.30753i 0.439247 + 0.0774511i
\(286\) 2.44862 4.24113i 0.144790 0.250783i
\(287\) 0 0
\(288\) −15.8944 5.78509i −0.936587 0.340890i
\(289\) 8.39053 + 14.5328i 0.493561 + 0.854872i
\(290\) −3.71348 6.43193i −0.218063 0.377696i
\(291\) 2.11422 2.51963i 0.123938 0.147703i
\(292\) −1.25712 + 2.17740i −0.0735675 + 0.127423i
\(293\) 6.54576 + 11.3376i 0.382407 + 0.662349i 0.991406 0.130822i \(-0.0417618\pi\)
−0.608998 + 0.793171i \(0.708428\pi\)
\(294\) 0 0
\(295\) 7.00387 12.1311i 0.407781 0.706298i
\(296\) −13.1013 22.6922i −0.761499 1.31895i
\(297\) 8.58770i 0.498309i
\(298\) 0.189540 0.328293i 0.0109798 0.0190175i
\(299\) 30.1361 1.74282
\(300\) 2.31433 + 6.35857i 0.133618 + 0.367112i
\(301\) 0 0
\(302\) −1.08630 1.88153i −0.0625098 0.108270i
\(303\) 1.01249 + 2.78179i 0.0581659 + 0.159810i
\(304\) 0.0675813 + 0.117054i 0.00387606 + 0.00671353i
\(305\) −5.14543 + 8.91215i −0.294626 + 0.510308i
\(306\) −0.945622 + 0.793471i −0.0540576 + 0.0453597i
\(307\) −6.31046 −0.360157 −0.180078 0.983652i \(-0.557635\pi\)
−0.180078 + 0.983652i \(0.557635\pi\)
\(308\) 0 0
\(309\) 4.05051 4.82721i 0.230425 0.274610i
\(310\) 5.47044 9.47508i 0.310700 0.538148i
\(311\) 9.52435 0.540076 0.270038 0.962850i \(-0.412964\pi\)
0.270038 + 0.962850i \(0.412964\pi\)
\(312\) 5.66401 + 15.5617i 0.320661 + 0.881010i
\(313\) 17.6287 0.996431 0.498215 0.867053i \(-0.333989\pi\)
0.498215 + 0.867053i \(0.333989\pi\)
\(314\) 8.91117 0.502886
\(315\) 0 0
\(316\) 2.94862 0.165873
\(317\) 8.07697 0.453648 0.226824 0.973936i \(-0.427166\pi\)
0.226824 + 0.973936i \(0.427166\pi\)
\(318\) 0.561956 0.669713i 0.0315129 0.0375557i
\(319\) 10.3601 0.580054
\(320\) 3.39646 5.88284i 0.189868 0.328861i
\(321\) 4.22281 + 11.6021i 0.235694 + 0.647565i
\(322\) 0 0
\(323\) −1.50980 −0.0840075
\(324\) −8.45723 7.09646i −0.469846 0.394248i
\(325\) 5.36571 9.29369i 0.297636 0.515521i
\(326\) −1.14156 1.97724i −0.0632251 0.109509i
\(327\) 0.449493 0.535685i 0.0248570 0.0296234i
\(328\) 4.84002 + 8.38316i 0.267246 + 0.462883i
\(329\) 0 0
\(330\) −3.34002 0.588936i −0.183862 0.0324199i
\(331\) 23.0496 1.26692 0.633461 0.773775i \(-0.281634\pi\)
0.633461 + 0.773775i \(0.281634\pi\)
\(332\) 9.23055 15.9878i 0.506592 0.877444i
\(333\) −4.81062 27.2824i −0.263620 1.49507i
\(334\) 10.1934 + 17.6555i 0.557759 + 0.966066i
\(335\) 0.401674 0.695720i 0.0219458 0.0380112i
\(336\) 0 0
\(337\) −14.5116 25.1348i −0.790498 1.36918i −0.925659 0.378359i \(-0.876489\pi\)
0.135161 0.990824i \(-0.456845\pi\)
\(338\) −0.723689 + 1.25347i −0.0393635 + 0.0681795i
\(339\) 8.51249 + 23.3879i 0.462335 + 1.27025i
\(340\) 0.386659 + 0.669713i 0.0209695 + 0.0363203i
\(341\) 7.63088 + 13.2171i 0.413235 + 0.715745i
\(342\) 1.47818 + 8.38316i 0.0799307 + 0.453310i
\(343\) 0 0
\(344\) 6.25877 10.8405i 0.337450 0.584481i
\(345\) −7.13816 19.6119i −0.384305 1.05587i
\(346\) −4.17881 −0.224654
\(347\) 12.9463 0.694991 0.347496 0.937682i \(-0.387032\pi\)
0.347496 + 0.937682i \(0.387032\pi\)
\(348\) −8.56108 + 10.2027i −0.458922 + 0.546922i
\(349\) 0.731429 1.26687i 0.0391525 0.0678141i −0.845785 0.533524i \(-0.820868\pi\)
0.884938 + 0.465710i \(0.154201\pi\)
\(350\) 0 0
\(351\) 17.5089i 0.934555i
\(352\) 4.65910 + 8.06980i 0.248331 + 0.430122i
\(353\) 7.16637 + 12.4125i 0.381428 + 0.660652i 0.991267 0.131873i \(-0.0420992\pi\)
−0.609839 + 0.792525i \(0.708766\pi\)
\(354\) 15.5954 + 2.74989i 0.828886 + 0.146155i
\(355\) −0.373455 + 0.646844i −0.0198210 + 0.0343309i
\(356\) −5.57310 9.65289i −0.295374 0.511602i
\(357\) 0 0
\(358\) −3.75150 + 6.49778i −0.198273 + 0.343418i
\(359\) 10.4684 + 18.1318i 0.552500 + 0.956958i 0.998093 + 0.0617224i \(0.0196594\pi\)
−0.445593 + 0.895235i \(0.647007\pi\)
\(360\) 8.78564 7.37203i 0.463044 0.388540i
\(361\) 4.29426 7.43788i 0.226014 0.391467i
\(362\) −15.1557 −0.796566
\(363\) −9.20574 + 10.9710i −0.483176 + 0.575827i
\(364\) 0 0
\(365\) −1.38073 2.39149i −0.0722707 0.125176i
\(366\) −11.4572 2.02022i −0.598879 0.105599i
\(367\) −6.02869 10.4420i −0.314695 0.545067i 0.664678 0.747130i \(-0.268569\pi\)
−0.979373 + 0.202063i \(0.935236\pi\)
\(368\) 0.187319 0.324446i 0.00976466 0.0169129i
\(369\) 1.77719 + 10.0789i 0.0925168 + 0.524689i
\(370\) 10.9409 0.568789
\(371\) 0 0
\(372\) −19.3221 3.40700i −1.00180 0.176645i
\(373\) 0.390530 0.676417i 0.0202209 0.0350235i −0.855738 0.517410i \(-0.826896\pi\)
0.875959 + 0.482386i \(0.160230\pi\)
\(374\) 0.680045 0.0351643
\(375\) −18.8097 3.31667i −0.971331 0.171272i
\(376\) −26.5449 −1.36895
\(377\) 21.1225 1.08786
\(378\) 0 0
\(379\) −6.92396 −0.355660 −0.177830 0.984061i \(-0.556908\pi\)
−0.177830 + 0.984061i \(0.556908\pi\)
\(380\) 5.33275 0.273564
\(381\) 35.4308 + 6.24741i 1.81518 + 0.320065i
\(382\) −11.3523 −0.580837
\(383\) 3.86618 6.69642i 0.197553 0.342171i −0.750182 0.661232i \(-0.770034\pi\)
0.947734 + 0.319061i \(0.103367\pi\)
\(384\) −11.6716 2.05802i −0.595613 0.105023i
\(385\) 0 0
\(386\) 0.561185 0.0285636
\(387\) 10.1382 8.50692i 0.515351 0.432431i
\(388\) 1.16473 2.01736i 0.0591300 0.102416i
\(389\) −2.69981 4.67620i −0.136886 0.237093i 0.789431 0.613840i \(-0.210376\pi\)
−0.926316 + 0.376747i \(0.877043\pi\)
\(390\) −6.80974 1.20074i −0.344825 0.0608019i
\(391\) 2.09240 + 3.62414i 0.105817 + 0.183280i
\(392\) 0 0
\(393\) 7.97730 9.50698i 0.402402 0.479564i
\(394\) −10.0651 −0.507073
\(395\) −1.61927 + 2.80466i −0.0814743 + 0.141118i
\(396\) 1.05613 + 5.98962i 0.0530726 + 0.300990i
\(397\) −14.6172 25.3178i −0.733617 1.27066i −0.955328 0.295549i \(-0.904497\pi\)
0.221711 0.975112i \(-0.428836\pi\)
\(398\) 1.59967 2.77071i 0.0801842 0.138883i
\(399\) 0 0
\(400\) −0.0667040 0.115535i −0.00333520 0.00577674i
\(401\) 13.6989 23.7272i 0.684092 1.18488i −0.289629 0.957139i \(-0.593532\pi\)
0.973721 0.227743i \(-0.0731346\pi\)
\(402\) 0.894400 + 0.157707i 0.0446086 + 0.00786570i
\(403\) 15.5581 + 26.9474i 0.775003 + 1.34235i
\(404\) 1.04829 + 1.81568i 0.0521542 + 0.0903337i
\(405\) 11.3944 4.14722i 0.566192 0.206077i
\(406\) 0 0
\(407\) −7.63088 + 13.2171i −0.378249 + 0.655146i
\(408\) −1.47818 + 1.76162i −0.0731807 + 0.0872134i
\(409\) 9.02498 0.446256 0.223128 0.974789i \(-0.428373\pi\)
0.223128 + 0.974789i \(0.428373\pi\)
\(410\) −4.04189 −0.199615
\(411\) 1.52182 + 4.18117i 0.0750659 + 0.206242i
\(412\) 2.23143 3.86495i 0.109935 0.190412i
\(413\) 0 0
\(414\) 18.0744 15.1663i 0.888310 0.745381i
\(415\) 10.1382 + 17.5598i 0.497662 + 0.861977i
\(416\) 9.49912 + 16.4530i 0.465733 + 0.806673i
\(417\) 3.63341 + 9.98271i 0.177929 + 0.488855i
\(418\) 2.34477 4.06126i 0.114686 0.198643i
\(419\) 0.0876485 + 0.151812i 0.00428191 + 0.00741649i 0.868158 0.496287i \(-0.165304\pi\)
−0.863877 + 0.503704i \(0.831970\pi\)
\(420\) 0 0
\(421\) 12.3525 21.3952i 0.602025 1.04274i −0.390490 0.920607i \(-0.627694\pi\)
0.992514 0.122130i \(-0.0389724\pi\)
\(422\) 2.56031 + 4.43458i 0.124634 + 0.215872i
\(423\) −26.3726 9.59883i −1.28228 0.466711i
\(424\) 0.814330 1.41046i 0.0395474 0.0684980i
\(425\) 1.49020 0.0722853
\(426\) −0.831566 0.146628i −0.0402895 0.00710413i
\(427\) 0 0
\(428\) 4.37211 + 7.57272i 0.211334 + 0.366041i
\(429\) 6.20011 7.38901i 0.299344 0.356745i
\(430\) 2.61334 + 4.52644i 0.126026 + 0.218284i
\(431\) 14.6596 25.3911i 0.706126 1.22305i −0.260157 0.965566i \(-0.583774\pi\)
0.966283 0.257481i \(-0.0828924\pi\)
\(432\) 0.188501 + 0.108831i 0.00906925 + 0.00523613i
\(433\) −19.6554 −0.944578 −0.472289 0.881444i \(-0.656572\pi\)
−0.472289 + 0.881444i \(0.656572\pi\)
\(434\) 0 0
\(435\) −5.00316 13.7461i −0.239883 0.659073i
\(436\) 0.247626 0.428901i 0.0118591 0.0205406i
\(437\) 28.8580 1.38047
\(438\) 2.00670 2.39149i 0.0958839 0.114270i
\(439\) 21.9299 1.04666 0.523330 0.852130i \(-0.324690\pi\)
0.523330 + 0.852130i \(0.324690\pi\)
\(440\) −6.31820 −0.301208
\(441\) 0 0
\(442\) 1.38650 0.0659489
\(443\) −18.7101 −0.888942 −0.444471 0.895793i \(-0.646608\pi\)
−0.444471 + 0.895793i \(0.646608\pi\)
\(444\) −6.71048 18.4369i −0.318466 0.874977i
\(445\) 12.2422 0.580334
\(446\) −3.11468 + 5.39479i −0.147485 + 0.255451i
\(447\) 0.479933 0.571962i 0.0227000 0.0270529i
\(448\) 0 0
\(449\) 6.68004 0.315251 0.157625 0.987499i \(-0.449616\pi\)
0.157625 + 0.987499i \(0.449616\pi\)
\(450\) −1.45899 8.27433i −0.0687774 0.390056i
\(451\) 2.81908 4.88279i 0.132745 0.229921i
\(452\) 8.81345 + 15.2653i 0.414550 + 0.718022i
\(453\) −1.46357 4.02114i −0.0687647 0.188929i
\(454\) 5.25150 + 9.09586i 0.246465 + 0.426890i
\(455\) 0 0
\(456\) 5.42380 + 14.9018i 0.253993 + 0.697839i
\(457\) −19.4287 −0.908837 −0.454418 0.890788i \(-0.650153\pi\)
−0.454418 + 0.890788i \(0.650153\pi\)
\(458\) 7.71776 13.3676i 0.360627 0.624625i
\(459\) −2.10560 + 1.21567i −0.0982810 + 0.0567426i
\(460\) −7.39053 12.8008i −0.344585 0.596839i
\(461\) −0.482926 + 0.836452i −0.0224921 + 0.0389575i −0.877052 0.480395i \(-0.840493\pi\)
0.854560 + 0.519352i \(0.173827\pi\)
\(462\) 0 0
\(463\) 0.222811 + 0.385920i 0.0103549 + 0.0179352i 0.871156 0.491006i \(-0.163371\pi\)
−0.860802 + 0.508941i \(0.830037\pi\)
\(464\) 0.131292 0.227405i 0.00609509 0.0105570i
\(465\) 13.8516 16.5077i 0.642354 0.765528i
\(466\) 7.14677 + 12.3786i 0.331068 + 0.573426i
\(467\) −17.1074 29.6309i −0.791637 1.37115i −0.924953 0.380081i \(-0.875896\pi\)
0.133317 0.991074i \(-0.457437\pi\)
\(468\) 2.15328 + 12.2118i 0.0995352 + 0.564492i
\(469\) 0 0
\(470\) 5.54189 9.59883i 0.255628 0.442761i
\(471\) 17.2849 + 3.04780i 0.796448 + 0.140435i
\(472\) 29.5012 1.35790
\(473\) −7.29086 −0.335234
\(474\) −3.60560 0.635765i −0.165611 0.0292016i
\(475\) 5.13816 8.89955i 0.235755 0.408339i
\(476\) 0 0
\(477\) 1.31908 1.10684i 0.0603964 0.0506786i
\(478\) −6.63903 11.4991i −0.303662 0.525959i
\(479\) −10.8965 18.8732i −0.497872 0.862339i 0.502125 0.864795i \(-0.332552\pi\)
−0.999997 + 0.00245553i \(0.999218\pi\)
\(480\) 8.45723 10.0789i 0.386018 0.460038i
\(481\) −15.5581 + 26.9474i −0.709388 + 1.22870i
\(482\) 6.87598 + 11.9095i 0.313192 + 0.542465i
\(483\) 0 0
\(484\) −5.07145 + 8.78401i −0.230521 + 0.399273i
\(485\) 1.27925 + 2.21572i 0.0580877 + 0.100611i
\(486\) 8.81150 + 10.5011i 0.399698 + 0.476341i
\(487\) −9.69640 + 16.7947i −0.439386 + 0.761039i −0.997642 0.0686297i \(-0.978137\pi\)
0.558256 + 0.829669i \(0.311471\pi\)
\(488\) −21.6732 −0.981101
\(489\) −1.53802 4.22567i −0.0695516 0.191091i
\(490\) 0 0
\(491\) −13.0783 22.6523i −0.590216 1.02228i −0.994203 0.107519i \(-0.965709\pi\)
0.403987 0.914765i \(-0.367624\pi\)
\(492\) 2.47906 + 6.81115i 0.111764 + 0.307070i
\(493\) 1.46657 + 2.54017i 0.0660509 + 0.114403i
\(494\) 4.78059 8.28023i 0.215089 0.372545i
\(495\) −6.27719 2.28471i −0.282139 0.102690i
\(496\) 0.386821 0.0173688
\(497\) 0 0
\(498\) −14.7344 + 17.5598i −0.660265 + 0.786873i
\(499\) 7.15064 12.3853i 0.320107 0.554441i −0.660403 0.750911i \(-0.729615\pi\)
0.980510 + 0.196470i \(0.0629479\pi\)
\(500\) −13.5270 −0.604947
\(501\) 13.7335 + 37.7326i 0.613570 + 1.68577i
\(502\) 16.7656 0.748284
\(503\) −18.7033 −0.833937 −0.416969 0.908921i \(-0.636908\pi\)
−0.416969 + 0.908921i \(0.636908\pi\)
\(504\) 0 0
\(505\) −2.30272 −0.102470
\(506\) −12.9982 −0.577842
\(507\) −1.83244 + 2.18382i −0.0813817 + 0.0969869i
\(508\) 25.4801 1.13050
\(509\) −12.8045 + 22.1781i −0.567551 + 0.983027i 0.429257 + 0.903183i \(0.358776\pi\)
−0.996807 + 0.0798442i \(0.974558\pi\)
\(510\) −0.328411 0.902302i −0.0145423 0.0399546i
\(511\) 0 0
\(512\) 0.473897 0.0209435
\(513\) 16.7663i 0.740252i
\(514\) −11.6878 + 20.2438i −0.515526 + 0.892917i
\(515\) 2.45084 + 4.24497i 0.107997 + 0.187056i
\(516\) 6.02481 7.18009i 0.265228 0.316086i
\(517\) 7.73055 + 13.3897i 0.339989 + 0.588879i
\(518\) 0 0
\(519\) −8.10560 1.42924i −0.355796 0.0627365i
\(520\) −12.8817 −0.564902
\(521\) −10.6061 + 18.3702i −0.464660 + 0.804815i −0.999186 0.0403370i \(-0.987157\pi\)
0.534526 + 0.845152i \(0.320490\pi\)
\(522\) 12.6684 10.6301i 0.554482 0.465266i
\(523\) 10.4029 + 18.0183i 0.454885 + 0.787884i 0.998682 0.0513330i \(-0.0163470\pi\)
−0.543796 + 0.839217i \(0.683014\pi\)
\(524\) 4.39470 7.61185i 0.191984 0.332525i
\(525\) 0 0
\(526\) −0.322786 0.559082i −0.0140741 0.0243771i
\(527\) −2.16044 + 3.74200i −0.0941104 + 0.163004i
\(528\) −0.0410117 0.112679i −0.00178481 0.00490371i
\(529\) −28.4937 49.3525i −1.23885 2.14576i
\(530\) 0.340022 + 0.588936i 0.0147696 + 0.0255817i
\(531\) 29.3097 + 10.6679i 1.27193 + 0.462946i
\(532\) 0 0
\(533\) 5.74763 9.95518i 0.248957 0.431207i
\(534\) 4.73355 + 13.0053i 0.204841 + 0.562795i
\(535\) −9.60401 −0.415217
\(536\) 1.69190 0.0730791
\(537\) −9.49912 + 11.3206i −0.409917 + 0.488521i
\(538\) 9.16772 15.8790i 0.395248 0.684590i
\(539\) 0 0
\(540\) 7.43717 4.29385i 0.320045 0.184778i
\(541\) −13.3648 23.1486i −0.574599 0.995235i −0.996085 0.0884001i \(-0.971825\pi\)
0.421486 0.906835i \(-0.361509\pi\)
\(542\) −3.05943 5.29909i −0.131414 0.227615i
\(543\) −29.3974 5.18355i −1.26156 0.222448i
\(544\) −1.31908 + 2.28471i −0.0565550 + 0.0979561i
\(545\) 0.271974 + 0.471073i 0.0116501 + 0.0201786i
\(546\) 0 0
\(547\) −18.3812 + 31.8372i −0.785923 + 1.36126i 0.142523 + 0.989792i \(0.454479\pi\)
−0.928446 + 0.371467i \(0.878855\pi\)
\(548\) 1.57563 + 2.72907i 0.0673074 + 0.116580i
\(549\) −21.5326 7.83721i −0.918987 0.334484i
\(550\) −2.31433 + 4.00854i −0.0986834 + 0.170925i
\(551\) 20.2267 0.861686
\(552\) 28.2536 33.6713i 1.20255 1.43315i
\(553\) 0 0
\(554\) 7.85844 + 13.6112i 0.333873 + 0.578285i
\(555\) 21.2219 + 3.74200i 0.900821 + 0.158839i
\(556\) 3.76187 + 6.51575i 0.159539 + 0.276329i
\(557\) −16.1694 + 28.0062i −0.685118 + 1.18666i 0.288282 + 0.957546i \(0.406916\pi\)
−0.973400 + 0.229114i \(0.926417\pi\)
\(558\) 22.8926 + 8.33224i 0.969123 + 0.352732i
\(559\) −14.8648 −0.628716
\(560\) 0 0
\(561\) 1.31908 + 0.232589i 0.0556915 + 0.00981992i
\(562\) 9.80974 16.9910i 0.413799 0.716721i
\(563\) 17.7419 0.747730 0.373865 0.927483i \(-0.378032\pi\)
0.373865 + 0.927483i \(0.378032\pi\)
\(564\) −19.5744 3.45150i −0.824233 0.145334i
\(565\) −19.3601 −0.814485
\(566\) −16.3517 −0.687315
\(567\) 0 0
\(568\) −1.57304 −0.0660035
\(569\) −26.6013 −1.11519 −0.557593 0.830115i \(-0.688275\pi\)
−0.557593 + 0.830115i \(0.688275\pi\)
\(570\) −6.52094 1.14982i −0.273132 0.0481606i
\(571\) −10.0172 −0.419208 −0.209604 0.977786i \(-0.567218\pi\)
−0.209604 + 0.977786i \(0.567218\pi\)
\(572\) 3.41565 5.91608i 0.142815 0.247364i
\(573\) −22.0201 3.88273i −0.919902 0.162203i
\(574\) 0 0
\(575\) −28.4834 −1.18784
\(576\) 14.2135 + 5.17328i 0.592228 + 0.215553i
\(577\) −16.4572 + 28.5048i −0.685124 + 1.18667i 0.288274 + 0.957548i \(0.406918\pi\)
−0.973398 + 0.229121i \(0.926415\pi\)
\(578\) −7.37851 12.7800i −0.306905 0.531576i
\(579\) 1.08853 + 0.191936i 0.0452376 + 0.00797661i
\(580\) −5.18004 8.97210i −0.215090 0.372546i
\(581\) 0 0
\(582\) −1.85921 + 2.21572i −0.0770668 + 0.0918447i
\(583\) −0.948615 −0.0392876
\(584\) 2.90791 5.03665i 0.120330 0.208418i
\(585\) −12.7981 4.65814i −0.529138 0.192590i
\(586\) −5.75624 9.97011i −0.237788 0.411861i
\(587\) −7.53643 + 13.0535i −0.311062 + 0.538774i −0.978592 0.205808i \(-0.934018\pi\)
0.667531 + 0.744582i \(0.267351\pi\)
\(588\) 0 0
\(589\) 14.8983 + 25.8046i 0.613873 + 1.06326i
\(590\) −6.15910 + 10.6679i −0.253566 + 0.439189i
\(591\) −19.5232 3.44247i −0.803078 0.141604i
\(592\) 0.193411 + 0.334997i 0.00794913 + 0.0137683i
\(593\) 20.5005 + 35.5079i 0.841853 + 1.45813i 0.888326 + 0.459213i \(0.151869\pi\)
−0.0464729 + 0.998920i \(0.514798\pi\)
\(594\) 7.55190i 0.309858i
\(595\) 0 0
\(596\) 0.264396 0.457947i 0.0108301 0.0187582i
\(597\) 4.05051 4.82721i 0.165776 0.197564i
\(598\) −26.5012 −1.08372
\(599\) 6.07367 0.248164 0.124082 0.992272i \(-0.460401\pi\)
0.124082 + 0.992272i \(0.460401\pi\)
\(600\) −5.35339 14.7083i −0.218551 0.600464i
\(601\) −7.06758 + 12.2414i −0.288293 + 0.499338i −0.973402 0.229102i \(-0.926421\pi\)
0.685110 + 0.728440i \(0.259754\pi\)
\(602\) 0 0
\(603\) 1.68092 + 0.611806i 0.0684524 + 0.0249147i
\(604\) −1.51532 2.62461i −0.0616575 0.106794i
\(605\) −5.57011 9.64771i −0.226457 0.392235i
\(606\) −0.890367 2.44626i −0.0361687 0.0993727i
\(607\) 23.0449 39.9149i 0.935363 1.62010i 0.161377 0.986893i \(-0.448406\pi\)
0.773986 0.633203i \(-0.218260\pi\)
\(608\) 9.09627 + 15.7552i 0.368902 + 0.638958i
\(609\) 0 0
\(610\) 4.52481 7.83721i 0.183204 0.317319i
\(611\) 15.7613 + 27.2994i 0.637634 + 1.10441i
\(612\) −1.31908 + 1.10684i −0.0533206 + 0.0447413i
\(613\) 13.2469 22.9443i 0.535038 0.926712i −0.464124 0.885770i \(-0.653631\pi\)
0.999162 0.0409421i \(-0.0130359\pi\)
\(614\) 5.54933 0.223953
\(615\) −7.84002 1.38241i −0.316140 0.0557440i
\(616\) 0 0
\(617\) 1.12495 + 1.94847i 0.0452889 + 0.0784426i 0.887781 0.460266i \(-0.152246\pi\)
−0.842492 + 0.538708i \(0.818913\pi\)
\(618\) −3.56196 + 4.24497i −0.143283 + 0.170758i
\(619\) 3.09539 + 5.36137i 0.124414 + 0.215492i 0.921504 0.388369i \(-0.126962\pi\)
−0.797090 + 0.603861i \(0.793628\pi\)
\(620\) 7.63088 13.2171i 0.306464 0.530811i
\(621\) 40.2460 23.2361i 1.61502 0.932431i
\(622\) −8.37557 −0.335830
\(623\) 0 0
\(624\) −0.0836160 0.229733i −0.00334732 0.00919668i
\(625\) −0.533433 + 0.923933i −0.0213373 + 0.0369573i
\(626\) −15.5024 −0.619600
\(627\) 5.93717 7.07564i 0.237108 0.282574i
\(628\) 12.4305 0.496030
\(629\) −4.32089 −0.172285
\(630\) 0 0
\(631\) 26.1661 1.04166 0.520829 0.853661i \(-0.325623\pi\)
0.520829 + 0.853661i \(0.325623\pi\)
\(632\) −6.82058 −0.271308
\(633\) 3.44949 + 9.47740i 0.137105 + 0.376693i
\(634\) −7.10277 −0.282087
\(635\) −13.9927 + 24.2361i −0.555284 + 0.961781i
\(636\) 0.783890 0.934204i 0.0310833 0.0370436i
\(637\) 0 0
\(638\) −9.11051 −0.360689
\(639\) −1.56283 0.568825i −0.0618247 0.0225024i
\(640\) 4.60947 7.98384i 0.182205 0.315589i
\(641\) −2.44444 4.23389i −0.0965496 0.167229i 0.813705 0.581278i \(-0.197447\pi\)
−0.910254 + 0.414050i \(0.864114\pi\)
\(642\) −3.71348 10.2027i −0.146559 0.402668i
\(643\) −20.1839 34.9596i −0.795976 1.37867i −0.922218 0.386671i \(-0.873625\pi\)
0.126242 0.992000i \(-0.459709\pi\)
\(644\) 0 0
\(645\) 3.52094 + 9.67372i 0.138637 + 0.380902i
\(646\) 1.32770 0.0522375
\(647\) −1.14038 + 1.97519i −0.0448329 + 0.0776528i −0.887571 0.460671i \(-0.847609\pi\)
0.842738 + 0.538324i \(0.180942\pi\)
\(648\) 19.5628 + 16.4152i 0.768501 + 0.644849i
\(649\) −8.59152 14.8809i −0.337247 0.584128i
\(650\) −4.71853 + 8.17273i −0.185076 + 0.320561i
\(651\) 0 0
\(652\) −1.59240 2.75811i −0.0623631 0.108016i
\(653\) −11.7396 + 20.3336i −0.459407 + 0.795717i −0.998930 0.0462542i \(-0.985272\pi\)
0.539522 + 0.841971i \(0.318605\pi\)
\(654\) −0.395277 + 0.471073i −0.0154566 + 0.0184204i
\(655\) 4.82682 + 8.36030i 0.188599 + 0.326664i
\(656\) −0.0714517 0.123758i −0.00278972 0.00483194i
\(657\) 4.71032 3.95243i 0.183767 0.154199i
\(658\) 0 0
\(659\) 23.9812 41.5366i 0.934174 1.61804i 0.158073 0.987427i \(-0.449472\pi\)
0.776101 0.630609i \(-0.217195\pi\)
\(660\) −4.65910 0.821525i −0.181355 0.0319778i
\(661\) −29.3090 −1.13999 −0.569995 0.821648i \(-0.693055\pi\)
−0.569995 + 0.821648i \(0.693055\pi\)
\(662\) −20.2695 −0.787797
\(663\) 2.68938 + 0.474210i 0.104447 + 0.0184168i
\(664\) −21.3516 + 36.9821i −0.828604 + 1.43518i
\(665\) 0 0
\(666\) 4.23039 + 23.9917i 0.163924 + 0.929661i
\(667\) −28.0317 48.5523i −1.08539 1.87995i
\(668\) 14.2191 + 24.6282i 0.550154 + 0.952894i
\(669\) −7.88666 + 9.39895i −0.304916 + 0.363385i
\(670\) −0.353226 + 0.611806i −0.0136463 + 0.0236361i
\(671\) 6.31180 + 10.9324i 0.243664 + 0.422039i
\(672\) 0 0
\(673\) −13.1591 + 22.7922i −0.507246 + 0.878576i 0.492719 + 0.870189i \(0.336003\pi\)
−0.999965 + 0.00838731i \(0.997330\pi\)
\(674\) 12.7613 + 22.1032i 0.491547 + 0.851384i
\(675\) 16.5487i 0.636959i
\(676\) −1.00950 + 1.74850i −0.0388267 + 0.0672499i
\(677\) −35.8907 −1.37939 −0.689697 0.724098i \(-0.742256\pi\)
−0.689697 + 0.724098i \(0.742256\pi\)
\(678\) −7.48576 20.5669i −0.287489 0.789869i
\(679\) 0 0
\(680\) −0.894400 1.54915i −0.0342987 0.0594070i
\(681\) 7.07532 + 19.4393i 0.271127 + 0.744915i
\(682\) −6.71048 11.6229i −0.256958 0.445064i
\(683\) −17.5321 + 30.3665i −0.670847 + 1.16194i 0.306818 + 0.951768i \(0.400736\pi\)
−0.977664 + 0.210172i \(0.932597\pi\)
\(684\) 2.06196 + 11.6939i 0.0788409 + 0.447129i
\(685\) −3.46110 −0.132242
\(686\) 0 0
\(687\) 19.5421 23.2893i 0.745576 0.888543i
\(688\) −0.0923963 + 0.160035i −0.00352257 + 0.00610128i
\(689\) −1.93407 −0.0736821
\(690\) 6.27719 + 17.2464i 0.238968 + 0.656561i
\(691\) −2.06687 −0.0786273 −0.0393136 0.999227i \(-0.512517\pi\)
−0.0393136 + 0.999227i \(0.512517\pi\)
\(692\) −5.82915 −0.221591
\(693\) 0 0
\(694\) −11.3847 −0.432159
\(695\) −8.26352 −0.313453
\(696\) 19.8030 23.6003i 0.750632 0.894569i
\(697\) 1.59627 0.0604629
\(698\) −0.643208 + 1.11407i −0.0243458 + 0.0421681i
\(699\) 9.62882 + 26.4550i 0.364196 + 1.00062i
\(700\) 0 0
\(701\) −7.36009 −0.277987 −0.138993 0.990293i \(-0.544387\pi\)
−0.138993 + 0.990293i \(0.544387\pi\)
\(702\) 15.3970i 0.581124i
\(703\) −14.8983 + 25.8046i −0.561899 + 0.973237i
\(704\) −4.16637 7.21637i −0.157026 0.271977i
\(705\) 14.0326 16.7233i 0.528497 0.629838i
\(706\) −6.30200 10.9154i −0.237179 0.410806i
\(707\) 0 0
\(708\) 21.7545 + 3.83590i 0.817584 + 0.144162i
\(709\) 9.10876 0.342086 0.171043 0.985264i \(-0.445286\pi\)
0.171043 + 0.985264i \(0.445286\pi\)
\(710\) 0.328411 0.568825i 0.0123251 0.0213476i
\(711\) −6.77631 2.46638i −0.254132 0.0924963i
\(712\) 12.8914 + 22.3286i 0.483126 + 0.836799i
\(713\) 41.2943 71.5239i 1.54648 2.67859i
\(714\) 0 0
\(715\) 3.75150 + 6.49778i 0.140298 + 0.243003i
\(716\) −5.23308 + 9.06396i −0.195569 + 0.338736i
\(717\) −8.94475 24.5755i −0.334048 0.917788i
\(718\) −9.20574 15.9448i −0.343555 0.595055i
\(719\) −12.9768 22.4765i −0.483954 0.838233i 0.515876 0.856663i \(-0.327467\pi\)
−0.999830 + 0.0184300i \(0.994133\pi\)
\(720\) −0.129700 + 0.108831i −0.00483362 + 0.00405589i
\(721\) 0 0
\(722\) −3.77631 + 6.54076i −0.140540 + 0.243422i
\(723\) 9.26399 + 25.4526i 0.344531 + 0.946592i
\(724\) −21.1411 −0.785705
\(725\) −19.9641 −0.741448
\(726\) 8.09539 9.64771i 0.300448 0.358060i
\(727\) −5.08007 + 8.79894i −0.188409 + 0.326335i −0.944720 0.327878i \(-0.893667\pi\)
0.756311 + 0.654213i \(0.227000\pi\)
\(728\) 0 0
\(729\) 13.5000 + 23.3827i 0.500000 + 0.866025i
\(730\) 1.21419 + 2.10304i 0.0449393 + 0.0778372i
\(731\) −1.03209 1.78763i −0.0381732 0.0661179i
\(732\) −15.9820 2.81807i −0.590714 0.104159i
\(733\) 20.3307 35.2138i 0.750931 1.30065i −0.196441 0.980516i \(-0.562938\pi\)
0.947372 0.320135i \(-0.103728\pi\)
\(734\) 5.30154 + 9.18253i 0.195683 + 0.338933i
\(735\) 0 0
\(736\) 25.2126 43.6695i 0.929349 1.60968i
\(737\) −0.492726 0.853427i −0.0181498 0.0314364i
\(738\) −1.56283 8.86327i −0.0575287 0.326261i
\(739\) 12.6809 21.9640i 0.466475 0.807959i −0.532791 0.846247i \(-0.678857\pi\)
0.999267 + 0.0382877i \(0.0121903\pi\)
\(740\) 15.2618 0.561034
\(741\) 12.1049 14.4260i 0.444684 0.529954i
\(742\) 0 0
\(743\) 11.2221 + 19.4372i 0.411699 + 0.713083i 0.995076 0.0991184i \(-0.0316023\pi\)
−0.583377 + 0.812202i \(0.698269\pi\)
\(744\) 44.6948 + 7.88090i 1.63859 + 0.288928i
\(745\) 0.290393 + 0.502975i 0.0106392 + 0.0184276i
\(746\) −0.343426 + 0.594831i −0.0125737 + 0.0217783i
\(747\) −34.5861 + 29.0211i −1.26544 + 1.06183i
\(748\) 0.948615 0.0346848
\(749\) 0 0
\(750\) 16.5410 + 2.91663i 0.603992 + 0.106500i
\(751\) −12.1086 + 20.9727i −0.441849 + 0.765305i −0.997827 0.0658924i \(-0.979011\pi\)
0.555978 + 0.831197i \(0.312344\pi\)
\(752\) 0.391874 0.0142902
\(753\) 32.5201 + 5.73417i 1.18510 + 0.208965i
\(754\) −18.5748 −0.676454
\(755\) 3.32863 0.121141
\(756\) 0 0
\(757\) 9.11793 0.331397 0.165698 0.986176i \(-0.447012\pi\)
0.165698 + 0.986176i \(0.447012\pi\)
\(758\) 6.08883 0.221156
\(759\) −25.2126 4.44566i −0.915159 0.161367i
\(760\) −12.3354 −0.447453
\(761\) −9.13610 + 15.8242i −0.331183 + 0.573626i −0.982744 0.184970i \(-0.940781\pi\)
0.651561 + 0.758596i \(0.274114\pi\)
\(762\) −31.1573 5.49388i −1.12871 0.199022i
\(763\) 0 0
\(764\) −15.8357 −0.572917
\(765\) −0.328411 1.86251i −0.0118737 0.0673393i
\(766\) −3.39986 + 5.88874i −0.122842 + 0.212769i
\(767\) −17.5167 30.3398i −0.632490 1.09550i
\(768\) 27.4641 + 4.84266i 0.991025 + 0.174744i
\(769\) 9.26470 + 16.0469i 0.334094 + 0.578667i 0.983310 0.181936i \(-0.0582365\pi\)
−0.649217 + 0.760604i \(0.724903\pi\)
\(770\) 0 0
\(771\) −29.5945 + 35.2694i −1.06582 + 1.27020i
\(772\) 0.782814 0.0281741
\(773\) −1.48040 + 2.56413i −0.0532463 + 0.0922253i −0.891420 0.453178i \(-0.850290\pi\)
0.838174 + 0.545403i \(0.183624\pi\)
\(774\) −8.91534 + 7.48086i −0.320455 + 0.268894i
\(775\) −14.7049 25.4696i −0.528214 0.914894i
\(776\) −2.69418 + 4.66646i −0.0967155 + 0.167516i
\(777\) 0 0
\(778\) 2.37417 + 4.11218i 0.0851181 + 0.147429i
\(779\) 5.50387 9.53298i 0.197197 0.341555i
\(780\) −9.49912 1.67495i −0.340123 0.0599729i
\(781\) 0.458111 + 0.793471i 0.0163925 + 0.0283926i
\(782\) −1.84002 3.18701i −0.0657991 0.113967i
\(783\) 28.2086 16.2862i 1.00809 0.582022i
\(784\) 0 0
\(785\) −6.82635 + 11.8236i −0.243643 + 0.422002i
\(786\) −7.01512 + 8.36030i −0.250221 + 0.298202i
\(787\) 33.4020 1.19065 0.595326 0.803484i \(-0.297023\pi\)
0.595326 + 0.803484i \(0.297023\pi\)
\(788\) −14.0401 −0.500159
\(789\) −0.434889 1.19485i −0.0154824 0.0425377i
\(790\) 1.42396 2.46638i 0.0506623 0.0877497i
\(791\) 0 0
\(792\) −2.44299 13.8549i −0.0868079 0.492312i
\(793\) 12.8687 + 22.2893i 0.456981 + 0.791515i
\(794\) 12.8542 + 22.2641i 0.456177 + 0.790122i
\(795\) 0.458111 + 1.25865i 0.0162475 + 0.0446397i
\(796\) 2.23143 3.86495i 0.0790909 0.136989i
\(797\) 24.6755 + 42.7391i 0.874050 + 1.51390i 0.857772 + 0.514031i \(0.171848\pi\)
0.0162779 + 0.999868i \(0.494818\pi\)
\(798\) 0 0
\(799\) −2.18866 + 3.79088i −0.0774293 + 0.134112i
\(800\) −8.97818 15.5507i −0.317427 0.549799i
\(801\) 4.73355 + 26.8453i 0.167252 + 0.948531i
\(802\) −12.0466 + 20.8654i −0.425382 + 0.736782i
\(803\) −3.38743 −0.119540
\(804\) 1.24763 + 0.219990i 0.0440004 + 0.00775845i
\(805\) 0 0
\(806\) −13.6816 23.6971i −0.481912 0.834696i
\(807\) 23.2135 27.6647i 0.817153 0.973845i
\(808\) −2.42484 4.19995i −0.0853056 0.147754i
\(809\) −9.91400 + 17.1716i −0.348558 + 0.603720i −0.985993 0.166784i \(-0.946662\pi\)
0.637436 + 0.770503i \(0.279995\pi\)
\(810\) −10.0201 + 3.64701i −0.352069 + 0.128143i
\(811\) 23.8557 0.837686 0.418843 0.908059i \(-0.362436\pi\)
0.418843 + 0.908059i \(0.362436\pi\)
\(812\) 0 0
\(813\) −4.12196 11.3250i −0.144563 0.397185i
\(814\) 6.71048 11.6229i 0.235202 0.407382i
\(815\) 3.49794 0.122528
\(816\) 0.0218219 0.0260063i 0.000763919 0.000910403i
\(817\) −14.2344 −0.497999
\(818\) −7.93643 −0.277491
\(819\) 0 0
\(820\) −5.63816 −0.196893
\(821\) −50.9427 −1.77791 −0.888957 0.457991i \(-0.848569\pi\)
−0.888957 + 0.457991i \(0.848569\pi\)
\(822\) −1.33827 3.67686i −0.0466774 0.128245i
\(823\) 13.6149 0.474587 0.237293 0.971438i \(-0.423740\pi\)
0.237293 + 0.971438i \(0.423740\pi\)
\(824\) −5.16163 + 8.94020i −0.179814 + 0.311447i
\(825\) −5.86009 + 6.98378i −0.204022 + 0.243144i
\(826\) 0 0
\(827\) 36.2158 1.25935 0.629673 0.776861i \(-0.283189\pi\)
0.629673 + 0.776861i \(0.283189\pi\)
\(828\) 25.2126 21.1559i 0.876198 0.735218i
\(829\) 12.6630 21.9329i 0.439803 0.761761i −0.557871 0.829928i \(-0.688382\pi\)
0.997674 + 0.0681664i \(0.0217149\pi\)
\(830\) −8.91534 15.4418i −0.309456 0.535994i
\(831\) 10.5876 + 29.0893i 0.367281 + 1.00910i
\(832\) −8.49454 14.7130i −0.294495 0.510080i
\(833\) 0 0
\(834\) −3.19517 8.77864i −0.110640 0.303980i
\(835\) −31.2344 −1.08091
\(836\) 3.27079 5.66518i 0.113123 0.195934i
\(837\) 41.5549 + 23.9917i 1.43635 + 0.829276i
\(838\) −0.0770768 0.133501i −0.00266257 0.00461171i
\(839\) 4.35710 7.54671i 0.150424 0.260541i −0.780960 0.624582i \(-0.785270\pi\)
0.931383 + 0.364040i \(0.118603\pi\)
\(840\) 0 0
\(841\) −5.14749 8.91571i −0.177500 0.307438i
\(842\) −10.8626 + 18.8146i −0.374350 + 0.648394i
\(843\) 24.8391 29.6021i 0.855506 1.01955i
\(844\) 3.57145 + 6.18594i 0.122934 + 0.212929i
\(845\) −1.10876 1.92042i −0.0381423 0.0660645i
\(846\) 23.1917 + 8.44107i 0.797346 + 0.290210i
\(847\) 0 0
\(848\) −0.0120217 + 0.0208222i −0.000412827 + 0.000715037i
\(849\) −31.7173 5.59262i −1.08854 0.191938i
\(850\) −1.31046 −0.0449484
\(851\) 82.5886 2.83110
\(852\) −1.15998 0.204535i −0.0397402 0.00700727i
\(853\) −5.99067 + 10.3761i −0.205117 + 0.355272i −0.950170 0.311733i \(-0.899091\pi\)
0.745053 + 0.667005i \(0.232424\pi\)
\(854\) 0 0
\(855\) −12.2554 4.46059i −0.419125 0.152549i
\(856\) −10.1133 17.5168i −0.345667 0.598713i
\(857\) 3.25015 + 5.62943i 0.111023 + 0.192298i 0.916183 0.400760i \(-0.131254\pi\)
−0.805160 + 0.593058i \(0.797921\pi\)
\(858\) −5.45229 + 6.49778i −0.186138 + 0.221831i
\(859\) −26.7763 + 46.3779i −0.913596 + 1.58239i −0.104652 + 0.994509i \(0.533373\pi\)
−0.808944 + 0.587886i \(0.799960\pi\)
\(860\) 3.64543 + 6.31407i 0.124308 + 0.215308i
\(861\) 0 0
\(862\) −12.8914 + 22.3286i −0.439083 + 0.760514i
\(863\) −1.84982 3.20399i −0.0629687 0.109065i 0.832822 0.553540i \(-0.186723\pi\)
−0.895791 + 0.444475i \(0.853390\pi\)
\(864\) 25.3717 + 14.6484i 0.863163 + 0.498347i
\(865\) 3.20115 5.54456i 0.108842 0.188521i
\(866\) 17.2847 0.587357
\(867\) −9.94104 27.3128i −0.337615 0.927590i
\(868\) 0 0
\(869\) 1.98633 + 3.44042i 0.0673816 + 0.116708i
\(870\) 4.39970 + 12.0881i 0.149164 + 0.409824i
\(871\) −1.00459 1.73999i −0.0340391 0.0589574i
\(872\) −0.572796 + 0.992112i −0.0193973 + 0.0335971i
\(873\) −4.36412 + 3.66193i −0.147703 + 0.123938i
\(874\) −25.3773 −0.858401
\(875\) 0 0
\(876\) 2.79921 3.33597i 0.0945765 0.112712i
\(877\) 5.89440 10.2094i 0.199040 0.344747i −0.749178 0.662369i \(-0.769551\pi\)
0.948217 + 0.317622i \(0.102884\pi\)
\(878\) −19.2849 −0.650833
\(879\) −7.75537 21.3077i −0.261582 0.718691i
\(880\) 0.0932736 0.00314425
\(881\) −49.4858 −1.66722 −0.833609 0.552355i \(-0.813729\pi\)
−0.833609 + 0.552355i \(0.813729\pi\)
\(882\) 0 0
\(883\) −21.5357 −0.724734 −0.362367 0.932035i \(-0.618031\pi\)
−0.362367 + 0.932035i \(0.618031\pi\)
\(884\) 1.93407 0.0650497
\(885\) −15.5954 + 18.5859i −0.524233 + 0.624757i
\(886\) 16.4534 0.552762
\(887\) 5.94238 10.2925i 0.199526 0.345589i −0.748849 0.662741i \(-0.769393\pi\)
0.948375 + 0.317152i \(0.102727\pi\)
\(888\) 15.5223 + 42.6473i 0.520896 + 1.43115i
\(889\) 0 0
\(890\) −10.7656 −0.360863
\(891\) 2.58290 14.6484i 0.0865304 0.490738i
\(892\) −4.34477 + 7.52536i −0.145474 + 0.251968i
\(893\) 15.0929 + 26.1416i 0.505063 + 0.874795i
\(894\) −0.422046 + 0.502975i −0.0141153 + 0.0168220i
\(895\) −5.74763 9.95518i −0.192122 0.332765i
\(896\) 0 0
\(897\) −51.4043 9.06396i −1.71634 0.302637i
\(898\) −5.87433 −0.196029
\(899\) 28.9433 50.1313i 0.965314 1.67197i
\(900\) −2.03519 11.5421i −0.0678396 0.384737i
\(901\) −0.134285 0.232589i −0.00447369 0.00774866i
\(902\) −2.47906 + 4.29385i −0.0825435 + 0.142970i
\(903\) 0 0
\(904\) −20.3868 35.3110i −0.678056 1.17443i
\(905\) 11.6099 20.1090i 0.385927 0.668446i
\(906\) 1.28705 + 3.53613i 0.0427592 + 0.117480i
\(907\) 13.0107 + 22.5353i 0.432014 + 0.748271i 0.997047 0.0767980i \(-0.0244697\pi\)
−0.565032 + 0.825069i \(0.691136\pi\)
\(908\) 7.32547 + 12.6881i 0.243104 + 0.421069i
\(909\) −0.890367 5.04952i −0.0295316 0.167482i
\(910\) 0 0
\(911\) 2.01636 3.49244i 0.0668050 0.115710i −0.830688 0.556738i \(-0.812053\pi\)
0.897493 + 0.441028i \(0.145386\pi\)
\(912\) −0.0800699 0.219990i −0.00265138 0.00728460i
\(913\) 24.8726 0.823162
\(914\) 17.0853 0.565132
\(915\) 11.4572 13.6542i 0.378764 0.451394i
\(916\) 10.7657 18.6468i 0.355710 0.616108i
\(917\) 0 0
\(918\) 1.85163 1.06904i 0.0611130 0.0352836i
\(919\) −13.7135 23.7524i −0.452366 0.783521i 0.546167 0.837677i \(-0.316087\pi\)
−0.998532 + 0.0541559i \(0.982753\pi\)
\(920\) 17.0954 + 29.6101i 0.563618 + 0.976216i
\(921\) 10.7640 + 1.89798i 0.354685 + 0.0625406i
\(922\) 0.424678 0.735564i 0.0139860 0.0242245i
\(923\) 0.934011 + 1.61775i 0.0307434 + 0.0532491i
\(924\) 0 0
\(925\) 14.7049 25.4696i 0.483493 0.837434i
\(926\) −0.195937 0.339373i −0.00643889 0.0111525i
\(927\) −8.36097 + 7.01568i −0.274610 + 0.230425i
\(928\) 17.6716 30.6081i 0.580098 1.00476i
\(929\) −7.67675 −0.251866 −0.125933 0.992039i \(-0.540192\pi\)
−0.125933 + 0.992039i \(0.540192\pi\)
\(930\) −12.1809 + 14.5167i −0.399428 + 0.476020i
\(931\) 0 0
\(932\) 9.96926 + 17.2673i 0.326554 + 0.565608i
\(933\) −16.2460 2.86461i −0.531871 0.0937833i
\(934\) 15.0440 + 26.0570i 0.492255 + 0.852610i
\(935\) −0.520945 + 0.902302i −0.0170367 + 0.0295084i
\(936\) −4.98085 28.2478i −0.162804 0.923308i
\(937\) 2.02465 0.0661425 0.0330713 0.999453i \(-0.489471\pi\)
0.0330713 + 0.999453i \(0.489471\pi\)
\(938\) 0 0
\(939\) −30.0699 5.30213i −0.981293 0.173028i
\(940\) 7.73055 13.3897i 0.252143 0.436724i
\(941\) 6.13928 0.200135 0.100067 0.994981i \(-0.468094\pi\)
0.100067 + 0.994981i \(0.468094\pi\)
\(942\) −15.2001 2.68019i −0.495246 0.0873253i
\(943\) −30.5107 −0.993566
\(944\) −0.435518 −0.0141749
\(945\) 0 0
\(946\) 6.41147 0.208455
\(947\) 5.56448 0.180821 0.0904107 0.995905i \(-0.471182\pi\)
0.0904107 + 0.995905i \(0.471182\pi\)
\(948\) −5.02956 0.886848i −0.163353 0.0288035i
\(949\) −6.90640 −0.224191
\(950\) −4.51842 + 7.82613i −0.146597 + 0.253913i
\(951\) −13.7772 2.42929i −0.446756 0.0787751i
\(952\) 0 0
\(953\) −8.72018 −0.282474 −0.141237 0.989976i \(-0.545108\pi\)
−0.141237 + 0.989976i \(0.545108\pi\)
\(954\) −1.15998 + 0.973337i −0.0375557 + 0.0315129i
\(955\) 8.69640 15.0626i 0.281409 0.487415i
\(956\) −9.26099 16.0405i −0.299522 0.518787i
\(957\) −17.6716 3.11598i −0.571241 0.100725i
\(958\) 9.58219 + 16.5968i 0.309586 + 0.536219i
\(959\) 0 0
\(960\) −7.56283 + 9.01303i −0.244089 + 0.290894i
\(961\) 54.2746 1.75079
\(962\) 13.6816 23.6971i 0.441111 0.764027i
\(963\) −3.71348 21.0602i −0.119665 0.678655i
\(964\) 9.59152 + 16.6130i 0.308922 + 0.535069i
\(965\) −0.429892 + 0.744596i −0.0138387 + 0.0239694i
\(966\) 0 0
\(967\) 28.8849 + 50.0301i 0.928876 + 1.60886i 0.785206 + 0.619235i \(0.212557\pi\)
0.143670 + 0.989626i \(0.454110\pi\)
\(968\) 11.7310 20.3187i 0.377049 0.653068i
\(969\) 2.57532 + 0.454099i 0.0827313 + 0.0145878i
\(970\) −1.12495 1.94847i −0.0361200 0.0625617i
\(971\) −15.3596 26.6036i −0.492914 0.853752i 0.507053 0.861915i \(-0.330735\pi\)
−0.999967 + 0.00816326i \(0.997402\pi\)
\(972\) 12.2914 + 14.6484i 0.394248 + 0.469846i
\(973\) 0 0
\(974\) 8.52687 14.7690i 0.273219 0.473229i
\(975\) −11.9477 + 14.2388i −0.382634 + 0.456005i
\(976\) 0.319955 0.0102415
\(977\) 10.3000 0.329527 0.164764 0.986333i \(-0.447314\pi\)
0.164764 + 0.986333i \(0.447314\pi\)
\(978\) 1.35251 + 3.71599i 0.0432485 + 0.118824i
\(979\) 7.50862 13.0053i 0.239976 0.415651i
\(980\) 0 0
\(981\) −0.927833 + 0.778544i −0.0296234 + 0.0248570i
\(982\) 11.5009 + 19.9201i 0.367008 + 0.635676i
\(983\) 6.84817 + 11.8614i 0.218423 + 0.378319i 0.954326 0.298767i \(-0.0965755\pi\)
−0.735903 + 0.677087i \(0.763242\pi\)
\(984\) −5.73442 15.7552i −0.182807 0.502257i
\(985\) 7.71032 13.3547i 0.245671 0.425515i
\(986\) −1.28968 2.23379i −0.0410717 0.0711383i
\(987\) 0 0
\(988\) 6.66860 11.5503i 0.212156 0.367465i
\(989\) 19.7271 + 34.1684i 0.627287 + 1.08649i
\(990\) 5.52007 + 2.00914i 0.175439 + 0.0638547i
\(991\) −28.9907 + 50.2133i −0.920919 + 1.59508i −0.122922 + 0.992416i \(0.539227\pi\)
−0.797997 + 0.602662i \(0.794107\pi\)
\(992\) 52.0651 1.65307
\(993\) −39.3166 6.93258i −1.24767 0.219999i
\(994\) 0 0
\(995\) 2.45084 + 4.24497i 0.0776968 + 0.134575i
\(996\) −20.5535 + 24.4947i −0.651263 + 0.776145i
\(997\) 8.10876 + 14.0448i 0.256807 + 0.444803i 0.965385 0.260830i \(-0.0839962\pi\)
−0.708578 + 0.705633i \(0.750663\pi\)
\(998\) −6.28817 + 10.8914i −0.199049 + 0.344762i
\(999\) 47.9835i 1.51813i
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 441.2.h.e.214.1 6
3.2 odd 2 1323.2.h.b.802.3 6
7.2 even 3 441.2.g.b.79.3 6
7.3 odd 6 63.2.f.a.43.3 yes 6
7.4 even 3 441.2.f.c.295.3 6
7.5 odd 6 441.2.g.c.79.3 6
7.6 odd 2 441.2.h.d.214.1 6
9.4 even 3 441.2.g.b.67.3 6
9.5 odd 6 1323.2.g.e.361.1 6
21.2 odd 6 1323.2.g.e.667.1 6
21.5 even 6 1323.2.g.d.667.1 6
21.11 odd 6 1323.2.f.d.883.1 6
21.17 even 6 189.2.f.b.127.1 6
21.20 even 2 1323.2.h.c.802.3 6
28.3 even 6 1008.2.r.h.673.2 6
63.4 even 3 441.2.f.c.148.3 6
63.5 even 6 1323.2.h.c.226.3 6
63.11 odd 6 3969.2.a.l.1.3 3
63.13 odd 6 441.2.g.c.67.3 6
63.23 odd 6 1323.2.h.b.226.3 6
63.25 even 3 3969.2.a.q.1.1 3
63.31 odd 6 63.2.f.a.22.3 6
63.32 odd 6 1323.2.f.d.442.1 6
63.38 even 6 567.2.a.c.1.3 3
63.40 odd 6 441.2.h.d.373.1 6
63.41 even 6 1323.2.g.d.361.1 6
63.52 odd 6 567.2.a.h.1.1 3
63.58 even 3 inner 441.2.h.e.373.1 6
63.59 even 6 189.2.f.b.64.1 6
84.59 odd 6 3024.2.r.k.2017.2 6
252.31 even 6 1008.2.r.h.337.2 6
252.59 odd 6 3024.2.r.k.1009.2 6
252.115 even 6 9072.2.a.ca.1.2 3
252.227 odd 6 9072.2.a.bs.1.2 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
63.2.f.a.22.3 6 63.31 odd 6
63.2.f.a.43.3 yes 6 7.3 odd 6
189.2.f.b.64.1 6 63.59 even 6
189.2.f.b.127.1 6 21.17 even 6
441.2.f.c.148.3 6 63.4 even 3
441.2.f.c.295.3 6 7.4 even 3
441.2.g.b.67.3 6 9.4 even 3
441.2.g.b.79.3 6 7.2 even 3
441.2.g.c.67.3 6 63.13 odd 6
441.2.g.c.79.3 6 7.5 odd 6
441.2.h.d.214.1 6 7.6 odd 2
441.2.h.d.373.1 6 63.40 odd 6
441.2.h.e.214.1 6 1.1 even 1 trivial
441.2.h.e.373.1 6 63.58 even 3 inner
567.2.a.c.1.3 3 63.38 even 6
567.2.a.h.1.1 3 63.52 odd 6
1008.2.r.h.337.2 6 252.31 even 6
1008.2.r.h.673.2 6 28.3 even 6
1323.2.f.d.442.1 6 63.32 odd 6
1323.2.f.d.883.1 6 21.11 odd 6
1323.2.g.d.361.1 6 63.41 even 6
1323.2.g.d.667.1 6 21.5 even 6
1323.2.g.e.361.1 6 9.5 odd 6
1323.2.g.e.667.1 6 21.2 odd 6
1323.2.h.b.226.3 6 63.23 odd 6
1323.2.h.b.802.3 6 3.2 odd 2
1323.2.h.c.226.3 6 63.5 even 6
1323.2.h.c.802.3 6 21.20 even 2
3024.2.r.k.1009.2 6 252.59 odd 6
3024.2.r.k.2017.2 6 84.59 odd 6
3969.2.a.l.1.3 3 63.11 odd 6
3969.2.a.q.1.1 3 63.25 even 3
9072.2.a.bs.1.2 3 252.227 odd 6
9072.2.a.ca.1.2 3 252.115 even 6