Properties

Label 441.2.f.c.295.3
Level $441$
Weight $2$
Character 441.295
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(148,441)]
 
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([2, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("441.148");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 441.f (of order \(3\), degree \(2\), 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 295.3
Root \(0.939693 + 0.342020i\) of defining polynomial
Character \(\chi\) \(=\) 441.295
Dual form 441.2.f.c.148.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.439693 - 0.761570i) q^{2} +(0.592396 + 1.62760i) q^{3} +(0.613341 + 1.06234i) q^{4} +(0.673648 + 1.16679i) q^{5} +(1.50000 + 0.264490i) q^{6} +2.83750 q^{8} +(-2.29813 + 1.92836i) q^{9} +O(q^{10})\) \(q+(0.439693 - 0.761570i) q^{2} +(0.592396 + 1.62760i) q^{3} +(0.613341 + 1.06234i) q^{4} +(0.673648 + 1.16679i) q^{5} +(1.50000 + 0.264490i) q^{6} +2.83750 q^{8} +(-2.29813 + 1.92836i) q^{9} +1.18479 q^{10} +(-0.826352 + 1.43128i) q^{11} +(-1.36571 + 1.62760i) q^{12} +(-1.68479 - 2.91815i) q^{13} +(-1.50000 + 1.78763i) q^{15} +(0.0209445 - 0.0362770i) q^{16} -0.467911 q^{17} +(0.458111 + 2.59808i) q^{18} +3.22668 q^{19} +(-0.826352 + 1.43128i) q^{20} +(0.726682 + 1.25865i) q^{22} +(-4.47178 - 7.74535i) q^{23} +(1.68092 + 4.61830i) q^{24} +(1.59240 - 2.75811i) q^{25} -2.96316 q^{26} +(-4.50000 - 2.59808i) q^{27} +(-3.13429 + 5.42874i) q^{29} +(0.701867 + 1.92836i) q^{30} +(4.61721 + 7.99724i) q^{31} +(2.81908 + 4.88279i) q^{32} +(-2.81908 - 0.497079i) q^{33} +(-0.205737 + 0.356347i) q^{34} +(-3.45811 - 1.25865i) q^{36} +9.23442 q^{37} +(1.41875 - 2.45734i) q^{38} +(3.75150 - 4.47086i) q^{39} +(1.91147 + 3.31077i) q^{40} +(1.70574 + 2.95442i) q^{41} +(2.20574 - 3.82045i) q^{43} -2.02734 q^{44} +(-3.79813 - 1.38241i) q^{45} -7.86484 q^{46} +(4.67752 - 8.10170i) q^{47} +(0.0714517 + 0.0125989i) q^{48} +(-1.40033 - 2.42544i) q^{50} +(-0.277189 - 0.761570i) q^{51} +(2.06670 - 3.57964i) q^{52} -0.573978 q^{53} +(-3.95723 + 2.28471i) q^{54} -2.22668 q^{55} +(1.91147 + 5.25173i) q^{57} +(2.75624 + 4.77396i) q^{58} +(-5.19846 - 9.00400i) q^{59} +(-2.81908 - 0.497079i) q^{60} +(3.81908 - 6.61484i) q^{61} +8.12061 q^{62} +5.04189 q^{64} +(2.26991 - 3.93161i) q^{65} +(-1.61809 + 1.92836i) q^{66} +(-0.298133 - 0.516382i) q^{67} +(-0.286989 - 0.497079i) q^{68} +(9.95723 - 11.8666i) q^{69} -0.554378 q^{71} +(-6.52094 + 5.47172i) q^{72} -2.04963 q^{73} +(4.06031 - 7.03266i) q^{74} +(5.43242 + 0.957882i) q^{75} +(1.97906 + 3.42782i) q^{76} +(-1.75537 - 4.82283i) q^{78} +(1.20187 - 2.08169i) q^{79} +0.0564370 q^{80} +(1.56283 - 8.86327i) q^{81} +3.00000 q^{82} +(-7.52481 + 13.0334i) q^{83} +(-0.315207 - 0.545955i) q^{85} +(-1.93969 - 3.35965i) q^{86} +(-10.6925 - 1.88538i) q^{87} +(-2.34477 + 4.06126i) q^{88} -9.08647 q^{89} +(-2.72281 + 2.28471i) q^{90} +(5.48545 - 9.50108i) q^{92} +(-10.2811 + 12.2525i) q^{93} +(-4.11334 - 7.12452i) q^{94} +(2.17365 + 3.76487i) q^{95} +(-6.27719 + 7.48086i) q^{96} +(-0.949493 + 1.64457i) q^{97} +(-0.860967 - 4.88279i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - 3 q^{2} - 3 q^{4} + 3 q^{5} + 9 q^{6} + 12 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - 3 q^{2} - 3 q^{4} + 3 q^{5} + 9 q^{6} + 12 q^{8} - 6 q^{11} - 18 q^{12} - 3 q^{13} - 9 q^{15} - 3 q^{16} - 12 q^{17} + 9 q^{18} + 6 q^{19} - 6 q^{20} - 9 q^{22} - 12 q^{23} + 27 q^{24} + 6 q^{25} + 6 q^{26} - 27 q^{27} - 9 q^{29} + 18 q^{30} - 3 q^{31} + 9 q^{34} - 27 q^{36} - 6 q^{37} + 6 q^{38} - 18 q^{39} - 9 q^{40} + 3 q^{43} + 30 q^{44} - 9 q^{45} + 3 q^{47} + 6 q^{50} + 9 q^{51} - 21 q^{52} + 12 q^{53} + 27 q^{54} - 9 q^{57} + 9 q^{58} - 3 q^{59} + 6 q^{61} + 60 q^{62} + 24 q^{64} - 15 q^{65} - 36 q^{66} + 12 q^{67} + 6 q^{68} + 9 q^{69} + 18 q^{71} - 36 q^{72} + 42 q^{73} + 30 q^{74} + 9 q^{75} + 15 q^{76} + 54 q^{78} + 21 q^{79} + 30 q^{80} + 18 q^{82} - 18 q^{83} - 9 q^{85} - 6 q^{86} - 9 q^{87} - 27 q^{88} - 24 q^{89} - 27 q^{90} - 3 q^{92} - 27 q^{93} - 18 q^{94} + 12 q^{95} - 27 q^{96} - 3 q^{97} + 18 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(199\) \(344\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.439693 0.761570i 0.310910 0.538511i −0.667650 0.744475i \(-0.732700\pi\)
0.978560 + 0.205964i \(0.0660330\pi\)
\(3\) 0.592396 + 1.62760i 0.342020 + 0.939693i
\(4\) 0.613341 + 1.06234i 0.306670 + 0.531169i
\(5\) 0.673648 + 1.16679i 0.301265 + 0.521806i 0.976423 0.215867i \(-0.0692579\pi\)
−0.675158 + 0.737673i \(0.735925\pi\)
\(6\) 1.50000 + 0.264490i 0.612372 + 0.107978i
\(7\) 0 0
\(8\) 2.83750 1.00321
\(9\) −2.29813 + 1.92836i −0.766044 + 0.642788i
\(10\) 1.18479 0.374664
\(11\) −0.826352 + 1.43128i −0.249154 + 0.431548i −0.963291 0.268458i \(-0.913486\pi\)
0.714137 + 0.700006i \(0.246819\pi\)
\(12\) −1.36571 + 1.62760i −0.394248 + 0.469846i
\(13\) −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
\(16\) 0.0209445 0.0362770i 0.00523613 0.00906925i
\(17\) −0.467911 −0.113485 −0.0567426 0.998389i \(-0.518071\pi\)
−0.0567426 + 0.998389i \(0.518071\pi\)
\(18\) 0.458111 + 2.59808i 0.107978 + 0.612372i
\(19\) 3.22668 0.740252 0.370126 0.928982i \(-0.379315\pi\)
0.370126 + 0.928982i \(0.379315\pi\)
\(20\) −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 −0.779152 0.626835i \(-0.784350\pi\)
−0.153279 0.988183i \(-0.548983\pi\)
\(24\) 1.68092 + 4.61830i 0.343117 + 0.942706i
\(25\) 1.59240 2.75811i 0.318479 0.551622i
\(26\) −2.96316 −0.581124
\(27\) −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 \(0.968928\pi\)
\(30\) 0.701867 + 1.92836i 0.128143 + 0.352069i
\(31\) 4.61721 + 7.99724i 0.829276 + 1.43635i 0.898607 + 0.438754i \(0.144580\pi\)
−0.0693317 + 0.997594i \(0.522087\pi\)
\(32\) 2.81908 + 4.88279i 0.498347 + 0.863163i
\(33\) −2.81908 0.497079i −0.490738 0.0865304i
\(34\) −0.205737 + 0.356347i −0.0352836 + 0.0611130i
\(35\) 0 0
\(36\) −3.45811 1.25865i −0.576352 0.209775i
\(37\) 9.23442 1.51813 0.759065 0.651015i \(-0.225657\pi\)
0.759065 + 0.651015i \(0.225657\pi\)
\(38\) 1.41875 2.45734i 0.230151 0.398634i
\(39\) 3.75150 4.47086i 0.600720 0.715910i
\(40\) 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 \(0.0574668\pi\)
\(44\) −2.02734 −0.305633
\(45\) −3.79813 1.38241i −0.566192 0.206077i
\(46\) −7.86484 −1.15961
\(47\) 4.67752 8.10170i 0.682286 1.18175i −0.291995 0.956420i \(-0.594319\pi\)
0.974281 0.225335i \(-0.0723475\pi\)
\(48\) 0.0714517 + 0.0125989i 0.0103132 + 0.00181849i
\(49\) 0 0
\(50\) −1.40033 2.42544i −0.198037 0.343009i
\(51\) −0.277189 0.761570i −0.0388142 0.106641i
\(52\) 2.06670 3.57964i 0.286600 0.496406i
\(53\) −0.573978 −0.0788419 −0.0394210 0.999223i \(-0.512551\pi\)
−0.0394210 + 0.999223i \(0.512551\pi\)
\(54\) −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
\(59\) −5.19846 9.00400i −0.676782 1.17222i −0.975945 0.218019i \(-0.930041\pi\)
0.299162 0.954202i \(-0.403293\pi\)
\(60\) −2.81908 0.497079i −0.363941 0.0641727i
\(61\) 3.81908 6.61484i 0.488983 0.846943i −0.510937 0.859618i \(-0.670701\pi\)
0.999920 + 0.0126752i \(0.00403474\pi\)
\(62\) 8.12061 1.03132
\(63\) 0 0
\(64\) 5.04189 0.630236
\(65\) 2.26991 3.93161i 0.281548 0.487656i
\(66\) −1.61809 + 1.92836i −0.199173 + 0.237365i
\(67\) −0.298133 0.516382i −0.0364228 0.0630861i 0.847239 0.531211i \(-0.178263\pi\)
−0.883662 + 0.468125i \(0.844930\pi\)
\(68\) −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 \(0.510473\pi\)
\(72\) −6.52094 + 5.47172i −0.768501 + 0.644849i
\(73\) −2.04963 −0.239891 −0.119946 0.992780i \(-0.538272\pi\)
−0.119946 + 0.992780i \(0.538272\pi\)
\(74\) 4.06031 7.03266i 0.472001 0.817530i
\(75\) 5.43242 + 0.957882i 0.627282 + 0.110607i
\(76\) 1.97906 + 3.42782i 0.227013 + 0.393198i
\(77\) 0 0
\(78\) −1.75537 4.82283i −0.198756 0.546078i
\(79\) 1.20187 2.08169i 0.135221 0.234209i −0.790461 0.612512i \(-0.790159\pi\)
0.925682 + 0.378303i \(0.123492\pi\)
\(80\) 0.0564370 0.00630985
\(81\) 1.56283 8.86327i 0.173648 0.984808i
\(82\) 3.00000 0.331295
\(83\) −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
\(87\) −10.6925 1.88538i −1.14636 0.202134i
\(88\) −2.34477 + 4.06126i −0.249953 + 0.432932i
\(89\) −9.08647 −0.963164 −0.481582 0.876401i \(-0.659938\pi\)
−0.481582 + 0.876401i \(0.659938\pi\)
\(90\) −2.72281 + 2.28471i −0.287010 + 0.240830i
\(91\) 0 0
\(92\) 5.48545 9.50108i 0.571898 0.990556i
\(93\) −10.2811 + 12.2525i −1.06610 + 1.27052i
\(94\) −4.11334 7.12452i −0.424259 0.734838i
\(95\) 2.17365 + 3.76487i 0.223012 + 0.386267i
\(96\) −6.27719 + 7.48086i −0.640663 + 0.763512i
\(97\) −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
\(100\) 3.90673 0.390673
\(101\) −0.854570 + 1.48016i −0.0850329 + 0.147281i −0.905405 0.424548i \(-0.860433\pi\)
0.820372 + 0.571830i \(0.193766\pi\)
\(102\) −0.701867 0.123758i −0.0694952 0.0122539i
\(103\) −1.81908 3.15074i −0.179239 0.310451i 0.762381 0.647128i \(-0.224030\pi\)
−0.941620 + 0.336677i \(0.890697\pi\)
\(104\) −4.78059 8.28023i −0.468776 0.811943i
\(105\) 0 0
\(106\) −0.252374 + 0.437124i −0.0245127 + 0.0424573i
\(107\) 7.12836 0.689124 0.344562 0.938764i \(-0.388027\pi\)
0.344562 + 0.938764i \(0.388027\pi\)
\(108\) 6.37402i 0.613341i
\(109\) 0.403733 0.0386706 0.0193353 0.999813i \(-0.493845\pi\)
0.0193353 + 0.999813i \(0.493845\pi\)
\(110\) −0.979055 + 1.69577i −0.0933493 + 0.161686i
\(111\) 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 \(-0.402907\pi\)
\(114\) 4.84002 + 0.853427i 0.453310 + 0.0799307i
\(115\) 6.02481 10.4353i 0.561817 0.973095i
\(116\) −7.68954 −0.713956
\(117\) 9.49912 + 3.45740i 0.878194 + 0.319637i
\(118\) −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
\(122\) −3.35844 5.81699i −0.304059 0.526646i
\(123\) −3.79813 + 4.52644i −0.342466 + 0.408135i
\(124\) −5.66385 + 9.81007i −0.508629 + 0.880971i
\(125\) 11.0273 0.986315
\(126\) 0 0
\(127\) −20.7716 −1.84318 −0.921589 0.388167i \(-0.873108\pi\)
−0.921589 + 0.388167i \(0.873108\pi\)
\(128\) −3.42127 + 5.92582i −0.302401 + 0.523774i
\(129\) 7.52481 + 1.32683i 0.662523 + 0.116821i
\(130\) −1.99613 3.45740i −0.175072 0.303234i
\(131\) −3.58260 6.20524i −0.313013 0.542154i 0.666000 0.745952i \(-0.268005\pi\)
−0.979013 + 0.203797i \(0.934672\pi\)
\(132\) −1.20099 3.29969i −0.104533 0.287201i
\(133\) 0 0
\(134\) −0.524348 −0.0452968
\(135\) 7.00076i 0.602529i
\(136\) −1.32770 −0.113849
\(137\) −1.28446 + 2.22475i −0.109739 + 0.190074i −0.915665 0.401943i \(-0.868335\pi\)
0.805925 + 0.592017i \(0.201668\pi\)
\(138\) −4.65910 12.8008i −0.396609 1.08967i
\(139\) −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
\(142\) −0.243756 + 0.422197i −0.0204555 + 0.0354300i
\(143\) 5.56893 0.465697
\(144\) 0.0218219 + 0.123758i 0.00181849 + 0.0103132i
\(145\) −8.44562 −0.701371
\(146\) −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 0.857062 0.515214i \(-0.172288\pi\)
−0.874719 + 0.484630i \(0.838954\pi\)
\(150\) 3.11809 3.71599i 0.254591 0.303410i
\(151\) 1.23530 2.13960i 0.100527 0.174118i −0.811375 0.584526i \(-0.801280\pi\)
0.911902 + 0.410408i \(0.134614\pi\)
\(152\) 9.15570 0.742625
\(153\) 1.07532 0.902302i 0.0869346 0.0729468i
\(154\) 0 0
\(155\) −6.22075 + 10.7747i −0.499663 + 0.865441i
\(156\) 7.05051 + 1.24319i 0.564492 + 0.0995352i
\(157\) 5.06670 + 8.77579i 0.404367 + 0.700384i 0.994248 0.107106i \(-0.0341585\pi\)
−0.589881 + 0.807491i \(0.700825\pi\)
\(158\) −1.05690 1.83061i −0.0840828 0.145636i
\(159\) −0.340022 0.934204i −0.0269655 0.0740872i
\(160\) −3.79813 + 6.57856i −0.300269 + 0.520081i
\(161\) 0 0
\(162\) −6.06283 5.08732i −0.476341 0.399698i
\(163\) −2.59627 −0.203355 −0.101678 0.994817i \(-0.532421\pi\)
−0.101678 + 0.994817i \(0.532421\pi\)
\(164\) −2.09240 + 3.62414i −0.163389 + 0.282998i
\(165\) −1.31908 3.62414i −0.102690 0.282139i
\(166\) 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
\(170\) −0.554378 −0.0425188
\(171\) −7.41534 + 6.22221i −0.567066 + 0.475825i
\(172\) 5.41147 0.412621
\(173\) −2.37598 + 4.11532i −0.180643 + 0.312882i −0.942100 0.335333i \(-0.891151\pi\)
0.761457 + 0.648215i \(0.224484\pi\)
\(174\) −6.13728 + 7.31412i −0.465266 + 0.554482i
\(175\) 0 0
\(176\) 0.0346151 + 0.0599551i 0.00260921 + 0.00451929i
\(177\) 11.5753 13.7949i 0.870054 1.03689i
\(178\) −3.99525 + 6.91998i −0.299457 + 0.518674i
\(179\) −8.53209 −0.637718 −0.318859 0.947802i \(-0.603300\pi\)
−0.318859 + 0.947802i \(0.603300\pi\)
\(180\) −0.860967 4.88279i −0.0641727 0.363941i
\(181\) 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
\(185\) 6.22075 + 10.7747i 0.457359 + 0.792169i
\(186\) 4.81062 + 13.2171i 0.352732 + 0.969123i
\(187\) 0.386659 0.669713i 0.0282753 0.0489743i
\(188\) 11.4757 0.836948
\(189\) 0 0
\(190\) 3.82295 0.277346
\(191\) −6.45471 + 11.1799i −0.467046 + 0.808948i −0.999291 0.0376425i \(-0.988015\pi\)
0.532245 + 0.846590i \(0.321349\pi\)
\(192\) 2.98680 + 8.20616i 0.215553 + 0.592228i
\(193\) 0.319078 + 0.552659i 0.0229677 + 0.0397813i 0.877281 0.479977i \(-0.159355\pi\)
−0.854313 + 0.519759i \(0.826022\pi\)
\(194\) 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 \(0.366319\pi\)
\(198\) −4.09714 1.49124i −0.291171 0.105978i
\(199\) 3.63816 0.257902 0.128951 0.991651i \(-0.458839\pi\)
0.128951 + 0.991651i \(0.458839\pi\)
\(200\) 4.51842 7.82613i 0.319500 0.553391i
\(201\) 0.663848 0.791143i 0.0468242 0.0558029i
\(202\) 0.751497 + 1.30163i 0.0528751 + 0.0915824i
\(203\) 0 0
\(204\) 0.639033 0.761570i 0.0447413 0.0533206i
\(205\) −2.29813 + 3.98048i −0.160509 + 0.278009i
\(206\) −3.19934 −0.222909
\(207\) 25.2126 + 9.17664i 1.75240 + 0.637820i
\(208\) −0.141149 −0.00978691
\(209\) −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
\(213\) −0.328411 0.902302i −0.0225024 0.0618247i
\(214\) 3.13429 5.42874i 0.214255 0.371101i
\(215\) 5.94356 0.405348
\(216\) −12.7687 7.37203i −0.868802 0.501603i
\(217\) 0 0
\(218\) 0.177519 0.307471i 0.0120231 0.0208246i
\(219\) −1.21419 3.33597i −0.0820476 0.225424i
\(220\) −1.36571 2.36549i −0.0920765 0.159481i
\(221\) 0.788333 + 1.36543i 0.0530290 + 0.0918490i
\(222\) 13.8516 + 2.44242i 0.929661 + 0.163924i
\(223\) 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
\(226\) −12.6364 −0.840561
\(227\) −5.97178 + 10.3434i −0.396361 + 0.686517i −0.993274 0.115789i \(-0.963060\pi\)
0.596913 + 0.802306i \(0.296394\pi\)
\(228\) −4.40673 + 5.25173i −0.291843 + 0.347804i
\(229\) −8.77631 15.2010i −0.579955 1.00451i −0.995484 0.0949315i \(-0.969737\pi\)
0.415529 0.909580i \(-0.363597\pi\)
\(230\) −5.29813 9.17664i −0.349349 0.605089i
\(231\) 0 0
\(232\) −8.89352 + 15.4040i −0.583888 + 1.01132i
\(233\) 16.2540 1.06484 0.532418 0.846481i \(-0.321283\pi\)
0.532418 + 0.846481i \(0.321283\pi\)
\(234\) 6.80974 5.71405i 0.445167 0.373539i
\(235\) 12.6040 0.822195
\(236\) 6.37686 11.0450i 0.415098 0.718971i
\(237\) 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 \(0.670934\pi\)
\(240\) 0.0334331 + 0.0918566i 0.00215809 + 0.00592932i
\(241\) −7.81908 + 13.5430i −0.503671 + 0.872384i 0.496320 + 0.868140i \(0.334684\pi\)
−0.999991 + 0.00424420i \(0.998649\pi\)
\(242\) 7.27126 0.467414
\(243\) 15.3516 2.70691i 0.984808 0.173648i
\(244\) 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
\(248\) 13.1013 + 22.6922i 0.831935 + 1.44095i
\(249\) −25.6707 4.52644i −1.62682 0.286851i
\(250\) 4.84864 8.39809i 0.306655 0.531142i
\(251\) −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
\(254\) −9.13310 + 15.8190i −0.573062 + 0.992572i
\(255\) 0.701867 0.836452i 0.0439526 0.0523807i
\(256\) 8.05051 + 13.9439i 0.503157 + 0.871493i
\(257\) 13.2909 + 23.0204i 0.829061 + 1.43598i 0.898776 + 0.438409i \(0.144458\pi\)
−0.0697146 + 0.997567i \(0.522209\pi\)
\(258\) 4.31908 5.14728i 0.268894 0.320455i
\(259\) 0 0
\(260\) 5.56893 0.345370
\(261\) −3.26558 18.5200i −0.202134 1.14636i
\(262\) −6.30096 −0.389275
\(263\) 0.367059 0.635765i 0.0226338 0.0392029i −0.854487 0.519473i \(-0.826128\pi\)
0.877120 + 0.480270i \(0.159461\pi\)
\(264\) −7.99912 1.41046i −0.492312 0.0868079i
\(265\) −0.386659 0.669713i −0.0237523 0.0411402i
\(266\) 0 0
\(267\) −5.38279 14.7891i −0.329421 0.905078i
\(268\) 0.365715 0.633436i 0.0223396 0.0386933i
\(269\) 20.8503 1.27126 0.635632 0.771992i \(-0.280739\pi\)
0.635632 + 0.771992i \(0.280739\pi\)
\(270\) −5.33157 3.07818i −0.324469 0.187332i
\(271\) −6.95811 −0.422675 −0.211338 0.977413i \(-0.567782\pi\)
−0.211338 + 0.977413i \(0.567782\pi\)
\(272\) −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
\(276\) 18.7135 + 3.29969i 1.12642 + 0.198618i
\(277\) −8.93629 + 15.4781i −0.536930 + 0.929989i 0.462138 + 0.886808i \(0.347083\pi\)
−0.999067 + 0.0431811i \(0.986251\pi\)
\(278\) −5.39363 −0.323488
\(279\) −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 \(0.934900\pi\)
\(282\) 9.15910 10.9154i 0.545416 0.650002i
\(283\) −9.29726 16.1033i −0.552665 0.957243i −0.998081 0.0619196i \(-0.980278\pi\)
0.445417 0.895323i \(-0.353056\pi\)
\(284\) −0.340022 0.588936i −0.0201766 0.0349469i
\(285\) −4.84002 + 5.76811i −0.286698 + 0.341674i
\(286\) 2.44862 4.24113i 0.144790 0.250783i
\(287\) 0 0
\(288\) −15.8944 5.78509i −0.936587 0.340890i
\(289\) −16.7811 −0.987121
\(290\) −3.71348 + 6.43193i −0.218063 + 0.377696i
\(291\) −3.23917 0.571153i −0.189884 0.0334816i
\(292\) −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
\(296\) 26.2026 1.52300
\(297\) 7.43717 4.29385i 0.431548 0.249154i
\(298\) −0.379081 −0.0219595
\(299\) −15.0680 + 26.0986i −0.871408 + 1.50932i
\(300\) 2.31433 + 6.35857i 0.133618 + 0.367112i
\(301\) 0 0
\(302\) −1.08630 1.88153i −0.0625098 0.108270i
\(303\) −2.91534 0.514054i −0.167482 0.0295316i
\(304\) 0.0675813 0.117054i 0.00387606 0.00671353i
\(305\) 10.2909 0.589253
\(306\) −0.214355 1.21567i −0.0122539 0.0694952i
\(307\) −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
\(311\) −4.76217 8.24833i −0.270038 0.467720i 0.698833 0.715285i \(-0.253703\pi\)
−0.968871 + 0.247565i \(0.920370\pi\)
\(312\) 10.6449 12.6860i 0.602646 0.718206i
\(313\) −8.81433 + 15.2669i −0.498215 + 0.862934i −0.999998 0.00205946i \(-0.999344\pi\)
0.501782 + 0.864994i \(0.332678\pi\)
\(314\) 8.91117 0.502886
\(315\) 0 0
\(316\) 2.94862 0.165873
\(317\) −4.03849 + 6.99486i −0.226824 + 0.392871i −0.956865 0.290533i \(-0.906168\pi\)
0.730041 + 0.683403i \(0.239501\pi\)
\(318\) −0.860967 0.151812i −0.0482806 0.00851318i
\(319\) −5.18004 8.97210i −0.290027 0.502341i
\(320\) 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
\(324\) 10.3743 3.77595i 0.576352 0.209775i
\(325\) −10.7314 −0.595273
\(326\) −1.14156 + 1.97724i −0.0632251 + 0.109509i
\(327\) 0.239170 + 0.657115i 0.0132261 + 0.0363385i
\(328\) 4.84002 + 8.38316i 0.267246 + 0.462883i
\(329\) 0 0
\(330\) −3.34002 0.588936i −0.183862 0.0324199i
\(331\) −11.5248 + 19.9616i −0.633461 + 1.09719i 0.353378 + 0.935481i \(0.385033\pi\)
−0.986839 + 0.161706i \(0.948300\pi\)
\(332\) −18.4611 −1.01318
\(333\) −21.2219 + 17.8073i −1.16295 + 0.975835i
\(334\) −20.3868 −1.11552
\(335\) 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
\(339\) 15.9982 19.0660i 0.868905 1.03552i
\(340\) 0.386659 0.669713i 0.0209695 0.0363203i
\(341\) −15.2618 −0.826471
\(342\) 1.47818 + 8.38316i 0.0799307 + 0.453310i
\(343\) 0 0
\(344\) 6.25877 10.8405i 0.337450 0.584481i
\(345\) 20.5535 + 3.62414i 1.10656 + 0.195117i
\(346\) 2.08940 + 3.61895i 0.112327 + 0.194556i
\(347\) −6.47313 11.2118i −0.347496 0.601880i 0.638308 0.769781i \(-0.279635\pi\)
−0.985804 + 0.167901i \(0.946301\pi\)
\(348\) −4.55525 12.5155i −0.244187 0.670899i
\(349\) 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
\(352\) −9.31820 −0.496662
\(353\) 7.16637 12.4125i 0.381428 0.660652i −0.609839 0.792525i \(-0.708766\pi\)
0.991267 + 0.131873i \(0.0420992\pi\)
\(354\) −5.41622 14.8809i −0.287869 0.790913i
\(355\) −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
\(359\) −20.9368 −1.10500 −0.552500 0.833513i \(-0.686326\pi\)
−0.552500 + 0.833513i \(0.686326\pi\)
\(360\) −10.7772 3.92258i −0.568008 0.206738i
\(361\) −8.58853 −0.452028
\(362\) 7.57785 13.1252i 0.398283 0.689846i
\(363\) −9.20574 + 10.9710i −0.483176 + 0.575827i
\(364\) 0 0
\(365\) −1.38073 2.39149i −0.0722707 0.125176i
\(366\) 7.47818 8.91215i 0.390891 0.465845i
\(367\) −6.02869 + 10.4420i −0.314695 + 0.545067i −0.979373 0.202063i \(-0.935236\pi\)
0.664678 + 0.747130i \(0.268569\pi\)
\(368\) −0.374638 −0.0195293
\(369\) −9.61721 3.50038i −0.500652 0.182222i
\(370\) 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 0.875959 0.482386i \(-0.160230\pi\)
−0.855738 + 0.517410i \(0.826896\pi\)
\(374\) −0.340022 0.588936i −0.0175821 0.0304532i
\(375\) 6.53256 + 17.9480i 0.337340 + 0.926833i
\(376\) 13.2724 22.9885i 0.684474 1.18554i
\(377\) 21.1225 1.08786
\(378\) 0 0
\(379\) −6.92396 −0.355660 −0.177830 0.984061i \(-0.556908\pi\)
−0.177830 + 0.984061i \(0.556908\pi\)
\(380\) −2.66637 + 4.61830i −0.136782 + 0.236914i
\(381\) −12.3050 33.8077i −0.630404 1.73202i
\(382\) 5.67617 + 9.83142i 0.290418 + 0.503019i
\(383\) 3.86618 + 6.69642i 0.197553 + 0.342171i 0.947734 0.319061i \(-0.103367\pi\)
−0.750182 + 0.661232i \(0.770034\pi\)
\(384\) −11.6716 2.05802i −0.595613 0.105023i
\(385\) 0 0
\(386\) 0.561185 0.0285636
\(387\) 2.29813 + 13.0334i 0.116821 + 0.662523i
\(388\) −2.32945 −0.118260
\(389\) −2.69981 + 4.67620i −0.136886 + 0.237093i −0.926316 0.376747i \(-0.877043\pi\)
0.789431 + 0.613840i \(0.210376\pi\)
\(390\) 4.44475 5.29704i 0.225068 0.268226i
\(391\) 2.09240 + 3.62414i 0.105817 + 0.183280i
\(392\) 0 0
\(393\) 7.97730 9.50698i 0.402402 0.479564i
\(394\) 5.03256 8.71664i 0.253536 0.439138i
\(395\) 3.23854 0.162949
\(396\) 4.65910 3.90945i 0.234129 0.196457i
\(397\) 29.2344 1.46723 0.733617 0.679563i \(-0.237831\pi\)
0.733617 + 0.679563i \(0.237831\pi\)
\(398\) 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 0.973721 + 0.227743i \(0.0731346\pi\)
−0.289629 + 0.957139i \(0.593532\pi\)
\(402\) −0.310622 0.853427i −0.0154924 0.0425650i
\(403\) 15.5581 26.9474i 0.775003 1.34235i
\(404\) −2.09657 −0.104308
\(405\) 11.3944 4.14722i 0.566192 0.206077i
\(406\) 0 0
\(407\) −7.63088 + 13.2171i −0.378249 + 0.655146i
\(408\) −0.786522 2.16095i −0.0389386 0.106983i
\(409\) −4.51249 7.81586i −0.223128 0.386469i 0.732628 0.680629i \(-0.238294\pi\)
−0.955756 + 0.294160i \(0.904960\pi\)
\(410\) 2.02094 + 3.50038i 0.0998073 + 0.172871i
\(411\) −4.38191 0.772649i −0.216144 0.0381120i
\(412\) 2.23143 3.86495i 0.109935 0.190412i
\(413\) 0 0
\(414\) 18.0744 15.1663i 0.888310 0.745381i
\(415\) −20.2763 −0.995325
\(416\) 9.49912 16.4530i 0.465733 0.806673i
\(417\) 6.82857 8.13798i 0.334397 0.398518i
\(418\) 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 \(-0.0389724\pi\)
\(422\) −5.12061 −0.249268
\(423\) 4.87346 + 27.6387i 0.236956 + 1.34384i
\(424\) −1.62866 −0.0790947
\(425\) −0.745100 + 1.29055i −0.0361427 + 0.0626009i
\(426\) −0.831566 0.146628i −0.0402895 0.00710413i
\(427\) 0 0
\(428\) 4.37211 + 7.57272i 0.211334 + 0.366041i
\(429\) 3.29901 + 9.06396i 0.159278 + 0.437612i
\(430\) 2.61334 4.52644i 0.126026 0.218284i
\(431\) −29.3191 −1.41225 −0.706126 0.708086i \(-0.749559\pi\)
−0.706126 + 0.708086i \(0.749559\pi\)
\(432\) −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
\(437\) −14.4290 24.9918i −0.690233 1.19552i
\(438\) −3.07444 0.542108i −0.146903 0.0259029i
\(439\) −10.9650 + 18.9919i −0.523330 + 0.906434i 0.476302 + 0.879282i \(0.341977\pi\)
−0.999631 + 0.0271516i \(0.991356\pi\)
\(440\) −6.31820 −0.301208
\(441\) 0 0
\(442\) 1.38650 0.0659489
\(443\) 9.35504 16.2034i 0.444471 0.769847i −0.553544 0.832820i \(-0.686725\pi\)
0.998015 + 0.0629732i \(0.0200583\pi\)
\(444\) −12.6116 + 15.0299i −0.598519 + 0.713288i
\(445\) −6.12108 10.6020i −0.290167 0.502584i
\(446\) −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 \(0.449616\pi\)
\(450\) 7.89528 + 2.87365i 0.372187 + 0.135465i
\(451\) −5.63816 −0.265490
\(452\) 8.81345 15.2653i 0.414550 0.718022i
\(453\) 4.21419 + 0.743076i 0.198000 + 0.0349128i
\(454\) 5.25150 + 9.09586i 0.246465 + 0.426890i
\(455\) 0 0
\(456\) 5.42380 + 14.9018i 0.253993 + 0.697839i
\(457\) 9.71436 16.8258i 0.454418 0.787076i −0.544236 0.838932i \(-0.683180\pi\)
0.998655 + 0.0518563i \(0.0165138\pi\)
\(458\) −15.4355 −0.721254
\(459\) 2.10560 + 1.21567i 0.0982810 + 0.0567426i
\(460\) 14.7811 0.689170
\(461\) −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
\(465\) −21.2219 3.74200i −0.984144 0.173531i
\(466\) 7.14677 12.3786i 0.331068 0.573426i
\(467\) 34.2148 1.58327 0.791637 0.610992i \(-0.209229\pi\)
0.791637 + 0.610992i \(0.209229\pi\)
\(468\) 2.15328 + 12.2118i 0.0995352 + 0.564492i
\(469\) 0 0
\(470\) 5.54189 9.59883i 0.255628 0.442761i
\(471\) −11.2819 + 13.4453i −0.519844 + 0.619526i
\(472\) −14.7506 25.5488i −0.678952 1.17598i
\(473\) 3.64543 + 6.31407i 0.167617 + 0.290321i
\(474\) 2.35339 2.80466i 0.108095 0.128822i
\(475\) 5.13816 8.89955i 0.235755 0.408339i
\(476\) 0 0
\(477\) 1.31908 1.10684i 0.0603964 0.0506786i
\(478\) 13.2781 0.607325
\(479\) −10.8965 + 18.8732i −0.497872 + 0.862339i −0.999997 0.00245553i \(-0.999218\pi\)
0.502125 + 0.864795i \(0.332552\pi\)
\(480\) −12.9572 2.28471i −0.591414 0.104282i
\(481\) −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
\(485\) −2.55850 −0.116175
\(486\) 4.68850 12.8816i 0.212675 0.584319i
\(487\) 19.3928 0.878772 0.439386 0.898298i \(-0.355196\pi\)
0.439386 + 0.898298i \(0.355196\pi\)
\(488\) 10.8366 18.7696i 0.490551 0.849659i
\(489\) −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 \(-0.367624\pi\)
\(492\) −7.13816 1.25865i −0.321813 0.0567443i
\(493\) 1.46657 2.54017i 0.0660509 0.114403i
\(494\) −9.56118 −0.430178
\(495\) 5.11721 4.29385i 0.230002 0.192994i
\(496\) 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 0.980510 0.196470i \(-0.0629479\pi\)
−0.660403 + 0.750911i \(0.729615\pi\)
\(500\) 6.76352 + 11.7148i 0.302474 + 0.523900i
\(501\) 25.8106 30.7599i 1.15313 1.37425i
\(502\) −8.38279 + 14.5194i −0.374142 + 0.648033i
\(503\) −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
\(506\) 6.49912 11.2568i 0.288921 0.500426i
\(507\) 2.80747 + 0.495032i 0.124684 + 0.0219851i
\(508\) −12.7400 22.0664i −0.565248 0.979039i
\(509\) −12.8045 22.1781i −0.567551 0.983027i −0.996807 0.0798442i \(-0.974558\pi\)
0.429257 0.903183i \(-0.358776\pi\)
\(510\) −0.328411 0.902302i −0.0145423 0.0399546i
\(511\) 0 0
\(512\) 0.473897 0.0209435
\(513\) −14.5201 8.38316i −0.641077 0.370126i
\(514\) 23.3756 1.03105
\(515\) 2.45084 4.24497i 0.107997 0.187056i
\(516\) 3.20574 + 8.80769i 0.141125 + 0.387737i
\(517\) 7.73055 + 13.3897i 0.339989 + 0.588879i
\(518\) 0 0
\(519\) −8.10560 1.42924i −0.355796 0.0627365i
\(520\) 6.44087 11.1559i 0.282451 0.489220i
\(521\) 21.2121 0.929320 0.464660 0.885489i \(-0.346176\pi\)
0.464660 + 0.885489i \(0.346176\pi\)
\(522\) −15.5401 5.65615i −0.680173 0.247563i
\(523\) −20.8057 −0.909770 −0.454885 0.890550i \(-0.650320\pi\)
−0.454885 + 0.890550i \(0.650320\pi\)
\(524\) 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
\(528\) −0.0770768 + 0.0918566i −0.00335434 + 0.00399754i
\(529\) −28.4937 + 49.3525i −1.23885 + 2.14576i
\(530\) −0.680045 −0.0295393
\(531\) 29.3097 + 10.6679i 1.27193 + 0.462946i
\(532\) 0 0
\(533\) 5.74763 9.95518i 0.248957 0.431207i
\(534\) −13.6297 2.40328i −0.589815 0.104000i
\(535\) 4.80200 + 8.31731i 0.207609 + 0.359589i
\(536\) −0.845952 1.46523i −0.0365396 0.0632884i
\(537\) −5.05438 13.8868i −0.218112 0.599259i
\(538\) 9.16772 15.8790i 0.395248 0.684590i
\(539\) 0 0
\(540\) 7.43717 4.29385i 0.320045 0.184778i
\(541\) 26.7297 1.14920 0.574599 0.818435i \(-0.305158\pi\)
0.574599 + 0.818435i \(0.305158\pi\)
\(542\) −3.05943 + 5.29909i −0.131414 + 0.227615i
\(543\) 10.2096 + 28.0507i 0.438136 + 1.20377i
\(544\) −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 \(0.878855\pi\)
\(548\) −3.15125 −0.134615
\(549\) 3.97906 + 22.5663i 0.169822 + 0.963108i
\(550\) 4.62866 0.197367
\(551\) −10.1133 + 17.5168i −0.430843 + 0.746242i
\(552\) 28.2536 33.6713i 1.20255 1.43315i
\(553\) 0 0
\(554\) 7.85844 + 13.6112i 0.333873 + 0.578285i
\(555\) −13.8516 + 16.5077i −0.587969 + 0.700714i
\(556\) 3.76187 6.51575i 0.159539 0.276329i
\(557\) 32.3387 1.37024 0.685118 0.728432i \(-0.259751\pi\)
0.685118 + 0.728432i \(0.259751\pi\)
\(558\) −18.6623 + 15.6595i −0.790036 + 0.662919i
\(559\) −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
\(563\) −8.87093 15.3649i −0.373865 0.647553i 0.616291 0.787518i \(-0.288634\pi\)
−0.990156 + 0.139965i \(0.955301\pi\)
\(564\) 6.79813 + 18.6777i 0.286253 + 0.786474i
\(565\) 9.68004 16.7663i 0.407243 0.705365i
\(566\) −16.3517 −0.687315
\(567\) 0 0
\(568\) −1.57304 −0.0660035
\(569\) 13.3007 23.0374i 0.557593 0.965779i −0.440104 0.897947i \(-0.645058\pi\)
0.997697 0.0678320i \(-0.0216082\pi\)
\(570\) 2.26470 + 6.22221i 0.0948579 + 0.260620i
\(571\) 5.00862 + 8.67518i 0.209604 + 0.363045i 0.951590 0.307371i \(-0.0994491\pi\)
−0.741986 + 0.670416i \(0.766116\pi\)
\(572\) 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
\(576\) −11.5869 + 9.72259i −0.482789 + 0.405108i
\(577\) 32.9145 1.37025 0.685124 0.728427i \(-0.259748\pi\)
0.685124 + 0.728427i \(0.259748\pi\)
\(578\) −7.37851 + 12.7800i −0.306905 + 0.531576i
\(579\) −0.710485 + 0.846723i −0.0295267 + 0.0351886i
\(580\) −5.18004 8.97210i −0.215090 0.372546i
\(581\) 0 0
\(582\) −1.85921 + 2.21572i −0.0770668 + 0.0918447i
\(583\) 0.474308 0.821525i 0.0196438 0.0340241i
\(584\) −5.81582 −0.240660
\(585\) 2.36500 + 13.4126i 0.0977807 + 0.554542i
\(586\) 11.5125 0.475577
\(587\) −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
\(591\) 6.78034 + 18.6288i 0.278906 + 0.766288i
\(592\) 0.193411 0.334997i 0.00794913 0.0137683i
\(593\) −41.0009 −1.68371 −0.841853 0.539706i \(-0.818535\pi\)
−0.841853 + 0.539706i \(0.818535\pi\)
\(594\) 7.55190i 0.309858i
\(595\) 0 0
\(596\) 0.264396 0.457947i 0.0108301 0.0187582i
\(597\) 2.15523 + 5.92145i 0.0882077 + 0.242349i
\(598\) 13.2506 + 22.9507i 0.541858 + 0.938526i
\(599\) −3.03684 5.25996i −0.124082 0.214916i 0.797292 0.603594i \(-0.206265\pi\)
−0.921374 + 0.388678i \(0.872932\pi\)
\(600\) 15.4145 + 2.71799i 0.629293 + 0.110961i
\(601\) −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
\(604\) 3.03064 0.123315
\(605\) −5.57011 + 9.64771i −0.226457 + 0.392235i
\(606\) −1.67334 + 1.99421i −0.0679749 + 0.0810094i
\(607\) 23.0449 + 39.9149i 0.935363 + 1.62010i 0.773986 + 0.633203i \(0.218260\pi\)
0.161377 + 0.986893i \(0.448406\pi\)
\(608\) 9.09627 + 15.7552i 0.368902 + 0.638958i
\(609\) 0 0
\(610\) 4.52481 7.83721i 0.183204 0.317319i
\(611\) −31.5226 −1.27527
\(612\) 1.61809 + 0.588936i 0.0654074 + 0.0238063i
\(613\) −26.4938 −1.07008 −0.535038 0.844828i \(-0.679703\pi\)
−0.535038 + 0.844828i \(0.679703\pi\)
\(614\) −2.77466 + 4.80586i −0.111976 + 0.193949i
\(615\) −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 \(0.818913\pi\)
\(618\) −1.89528 5.20723i −0.0762392 0.209466i
\(619\) 3.09539 5.36137i 0.124414 0.215492i −0.797090 0.603861i \(-0.793628\pi\)
0.921504 + 0.388369i \(0.126962\pi\)
\(620\) −15.2618 −0.612927
\(621\) 46.4721i 1.86486i
\(622\) −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
\(626\) 7.75119 + 13.4255i 0.309800 + 0.536589i
\(627\) −9.09627 1.60392i −0.363270 0.0640543i
\(628\) −6.21523 + 10.7651i −0.248015 + 0.429574i
\(629\) −4.32089 −0.172285
\(630\) 0 0
\(631\) 26.1661 1.04166 0.520829 0.853661i \(-0.325623\pi\)
0.520829 + 0.853661i \(0.325623\pi\)
\(632\) 3.41029 5.90680i 0.135654 0.234960i
\(633\) 6.48293 7.72605i 0.257673 0.307083i
\(634\) 3.55138 + 6.15118i 0.141043 + 0.244295i
\(635\) −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
\(639\) 1.27403 1.06904i 0.0504000 0.0422906i
\(640\) −9.21894 −0.364411
\(641\) −2.44444 + 4.23389i −0.0965496 + 0.167229i −0.910254 0.414050i \(-0.864114\pi\)
0.813705 + 0.581278i \(0.197447\pi\)
\(642\) 10.6925 + 1.88538i 0.422001 + 0.0744101i
\(643\) −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
\(646\) −0.663848 + 1.14982i −0.0261188 + 0.0452390i
\(647\) 2.28075 0.0896657 0.0448329 0.998995i \(-0.485724\pi\)
0.0448329 + 0.998995i \(0.485724\pi\)
\(648\) 4.43453 25.1495i 0.174205 0.987965i
\(649\) 17.1830 0.674493
\(650\) −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 0.539522 0.841971i \(-0.318605\pi\)
−0.998930 + 0.0462542i \(0.985272\pi\)
\(654\) 0.605600 + 0.106784i 0.0236808 + 0.00417557i
\(655\) 4.82682 8.36030i 0.188599 0.326664i
\(656\) 0.142903 0.00557944
\(657\) 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 \(-0.217195\pi\)
\(660\) 3.04101 3.62414i 0.118371 0.141069i
\(661\) 14.6545 + 25.3824i 0.569995 + 0.987260i 0.996566 + 0.0828055i \(0.0263880\pi\)
−0.426571 + 0.904454i \(0.640279\pi\)
\(662\) 10.1348 + 17.5539i 0.393898 + 0.682252i
\(663\) −1.75537 + 2.09196i −0.0681728 + 0.0812452i
\(664\) −21.3516 + 36.9821i −0.828604 + 1.43518i
\(665\) 0 0
\(666\) 4.23039 + 23.9917i 0.163924 + 0.929661i
\(667\) 56.0634 2.17078
\(668\) 14.2191 24.6282i 0.550154 0.952894i
\(669\) 12.0831 + 2.13057i 0.467158 + 0.0823726i
\(670\) −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 \(0.997330\pi\)
\(674\) −25.5226 −0.983094
\(675\) −14.3316 + 8.27433i −0.551622 + 0.318479i
\(676\) 2.01899 0.0776535
\(677\) 17.9454 31.0823i 0.689697 1.19459i −0.282239 0.959344i \(-0.591077\pi\)
0.971936 0.235246i \(-0.0755895\pi\)
\(678\) −7.48576 20.5669i −0.287489 0.789869i
\(679\) 0 0
\(680\) −0.894400 1.54915i −0.0342987 0.0594070i
\(681\) −20.3726 3.59224i −0.780679 0.137655i
\(682\) −6.71048 + 11.6229i −0.256958 + 0.445064i
\(683\) 35.0642 1.34169 0.670847 0.741596i \(-0.265931\pi\)
0.670847 + 0.741596i \(0.265931\pi\)
\(684\) −11.1582 4.06126i −0.426645 0.155286i
\(685\) −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
\(689\) 0.967034 + 1.67495i 0.0368411 + 0.0638106i
\(690\) 11.7973 14.0594i 0.449114 0.535233i
\(691\) 1.03343 1.78996i 0.0393136 0.0680932i −0.845699 0.533660i \(-0.820816\pi\)
0.885013 + 0.465567i \(0.154150\pi\)
\(692\) −5.82915 −0.221591
\(693\) 0 0
\(694\) −11.3847 −0.432159
\(695\) 4.13176 7.15642i 0.156727 0.271458i
\(696\) −30.3400 5.34976i −1.15004 0.202782i
\(697\) −0.798133 1.38241i −0.0302315 0.0523624i
\(698\) −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 \(0.544387\pi\)
\(702\) 13.3342 + 7.69852i 0.503268 + 0.290562i
\(703\) 29.7965 1.12380
\(704\) −4.16637 + 7.21637i −0.157026 + 0.271977i
\(705\) 7.46657 + 20.5142i 0.281207 + 0.772610i
\(706\) −6.30200 10.9154i −0.237179 0.410806i
\(707\) 0 0
\(708\) 21.7545 + 3.83590i 0.817584 + 0.144162i
\(709\) −4.55438 + 7.88841i −0.171043 + 0.296256i −0.938785 0.344504i \(-0.888047\pi\)
0.767742 + 0.640760i \(0.221380\pi\)
\(710\) −0.656822 −0.0246501
\(711\) 1.25221 + 7.10165i 0.0469616 + 0.266333i
\(712\) −25.7828 −0.966252
\(713\) 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
\(717\) −16.8106 + 20.0341i −0.627804 + 0.748188i
\(718\) −9.20574 + 15.9448i −0.343555 + 0.595055i
\(719\) 25.9537 0.967908 0.483954 0.875093i \(-0.339200\pi\)
0.483954 + 0.875093i \(0.339200\pi\)
\(720\) −0.129700 + 0.108831i −0.00483362 + 0.00405589i
\(721\) 0 0
\(722\) −3.77631 + 6.54076i −0.140540 + 0.243422i
\(723\) −26.6746 4.70345i −0.992038 0.174923i
\(724\) 10.5706 + 18.3088i 0.392852 + 0.680440i
\(725\) 9.98205 + 17.2894i 0.370724 + 0.642113i
\(726\) 4.30747 + 11.8347i 0.159865 + 0.439226i
\(727\) −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
\(730\) −2.42839 −0.0898786
\(731\) −1.03209 + 1.78763i −0.0381732 + 0.0661179i
\(732\) 5.55051 + 15.2499i 0.205153 + 0.563652i
\(733\) 20.3307 + 35.2138i 0.750931 + 1.30065i 0.947372 + 0.320135i \(0.103728\pi\)
−0.196441 + 0.980516i \(0.562938\pi\)
\(734\) 5.30154 + 9.18253i 0.195683 + 0.338933i
\(735\) 0 0
\(736\) 25.2126 43.6695i 0.929349 1.60968i
\(737\) 0.985452 0.0362996
\(738\) −6.89440 + 5.78509i −0.253786 + 0.212952i
\(739\) −25.3618 −0.932951 −0.466475 0.884534i \(-0.654476\pi\)
−0.466475 + 0.884534i \(0.654476\pi\)
\(740\) −7.63088 + 13.2171i −0.280517 + 0.485869i
\(741\) 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 \(0.698269\pi\)
\(744\) −29.1725 + 34.7664i −1.06951 + 1.27460i
\(745\) 0.290393 0.502975i 0.0106392 0.0184276i
\(746\) 0.686852 0.0251474
\(747\) −7.84002 44.4630i −0.286851 1.62682i
\(748\) 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 0.555978 0.831197i \(-0.312344\pi\)
−0.997827 + 0.0658924i \(0.979011\pi\)
\(752\) −0.195937 0.339373i −0.00714508 0.0123756i
\(753\) −11.2941 31.0303i −0.411580 1.13081i
\(754\) 9.28740 16.0862i 0.338227 0.585827i
\(755\) 3.32863 0.121141
\(756\) 0 0
\(757\) 9.11793 0.331397 0.165698 0.986176i \(-0.447012\pi\)
0.165698 + 0.986176i \(0.447012\pi\)
\(758\) −3.04442 + 5.27308i −0.110578 + 0.191527i
\(759\) 8.75624 + 24.0576i 0.317832 + 0.873235i
\(760\) 6.16772 + 10.6828i 0.223727 + 0.387506i
\(761\) −9.13610 15.8242i −0.331183 0.573626i 0.651561 0.758596i \(-0.274114\pi\)
−0.982744 + 0.184970i \(0.940781\pi\)
\(762\) −31.1573 5.49388i −1.12871 0.199022i
\(763\) 0 0
\(764\) −15.8357 −0.572917
\(765\) 1.77719 + 0.646844i 0.0642544 + 0.0233867i
\(766\) 6.79973 0.245684
\(767\) −17.5167 + 30.3398i −0.632490 + 1.09550i
\(768\) −17.9259 + 21.3633i −0.646846 + 0.770881i
\(769\) 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
\(772\) −0.391407 + 0.677937i −0.0140870 + 0.0243995i
\(773\) 2.96080 0.106493 0.0532463 0.998581i \(-0.483043\pi\)
0.0532463 + 0.998581i \(0.483043\pi\)
\(774\) 10.9363 + 3.98048i 0.393097 + 0.143076i
\(775\) 29.4097 1.05643
\(776\) −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
\(780\) 3.29901 + 9.06396i 0.118124 + 0.324542i
\(781\) 0.458111 0.793471i 0.0163925 0.0283926i
\(782\) 3.68004 0.131598
\(783\) 28.2086 16.2862i 1.00809 0.582022i
\(784\) 0 0
\(785\) −6.82635 + 11.8236i −0.243643 + 0.422002i
\(786\) −3.73267 10.2554i −0.133140 0.365799i
\(787\) −16.7010 28.9270i −0.595326 1.03113i −0.993501 0.113825i \(-0.963690\pi\)
0.398175 0.917310i \(-0.369644\pi\)
\(788\) 7.02007 + 12.1591i 0.250080 + 0.433150i
\(789\) 1.25221 + 0.220799i 0.0445799 + 0.00786064i
\(790\) 1.42396 2.46638i 0.0506623 0.0877497i
\(791\) 0 0
\(792\) −2.44299 13.8549i −0.0868079 0.492312i
\(793\) −25.7374 −0.913962
\(794\) 12.8542 22.2641i 0.456177 0.790122i
\(795\) 0.860967 1.02606i 0.0305354 0.0363906i
\(796\) 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
\(800\) 17.9564 0.634853
\(801\) 20.8819 17.5220i 0.737826 0.619110i
\(802\) 24.0933 0.850763
\(803\) 1.69372 2.93360i 0.0597699 0.103525i
\(804\) 1.24763 + 0.219990i 0.0440004 + 0.00775845i
\(805\) 0 0
\(806\) −13.6816 23.6971i −0.481912 0.834696i
\(807\) 12.3516 + 33.9358i 0.434798 + 1.19460i
\(808\) −2.42484 + 4.19995i −0.0853056 + 0.147754i
\(809\) 19.8280 0.697115 0.348558 0.937287i \(-0.386672\pi\)
0.348558 + 0.937287i \(0.386672\pi\)
\(810\) 1.85163 10.5011i 0.0650598 0.368972i
\(811\) 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
\(815\) −1.74897 3.02931i −0.0612638 0.106112i
\(816\) −0.0334331 0.00589515i −0.00117039 0.000206372i
\(817\) 7.11721 12.3274i 0.249000 0.431280i
\(818\) −7.93643 −0.277491
\(819\) 0 0
\(820\) −5.63816 −0.196893
\(821\) 25.4714 44.1177i 0.888957 1.53972i 0.0478469 0.998855i \(-0.484764\pi\)
0.841110 0.540864i \(-0.181903\pi\)
\(822\) −2.51512 + 2.99740i −0.0877249 + 0.104546i
\(823\) −6.80747 11.7909i −0.237293 0.411004i 0.722643 0.691221i \(-0.242927\pi\)
−0.959937 + 0.280217i \(0.909594\pi\)
\(824\) −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 \(0.283189\pi\)
\(828\) 5.71523 + 32.4127i 0.198618 + 1.12642i
\(829\) −25.3259 −0.879606 −0.439803 0.898094i \(-0.644952\pi\)
−0.439803 + 0.898094i \(0.644952\pi\)
\(830\) −8.91534 + 15.4418i −0.309456 + 0.535994i
\(831\) −30.4859 5.37549i −1.05754 0.186474i
\(832\) −8.49454 14.7130i −0.294495 0.510080i
\(833\) 0 0
\(834\) −3.19517 8.77864i −0.110640 0.303980i
\(835\) 15.6172 27.0498i 0.540456 0.936097i
\(836\) −6.54158 −0.226245
\(837\) 47.9835i 1.65855i
\(838\) 0.154154 0.00532515
\(839\) 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
\(843\) −38.0558 6.71026i −1.31071 0.231114i
\(844\) 3.57145 6.18594i 0.122934 0.212929i
\(845\) 2.21751 0.0762847
\(846\) 23.1917 + 8.44107i 0.797346 + 0.290210i
\(847\) 0 0
\(848\) −0.0120217 + 0.0208222i −0.000412827 + 0.000715037i
\(849\) 20.7020 24.6717i 0.710492 0.846731i
\(850\) 0.655230 + 1.13489i 0.0224742 + 0.0389265i
\(851\) −41.2943 71.5239i −1.41555 2.45181i
\(852\) 0.757122 0.902302i 0.0259386 0.0309124i
\(853\) −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
\(856\) 20.2267 0.691334
\(857\) 3.25015 5.62943i 0.111023 0.192298i −0.805160 0.593058i \(-0.797921\pi\)
0.916183 + 0.400760i \(0.131254\pi\)
\(858\) 8.35339 + 1.47293i 0.285180 + 0.0502849i
\(859\) −26.7763 46.3779i −0.913596 1.58239i −0.808944 0.587886i \(-0.799960\pi\)
−0.104652 0.994509i \(-0.533373\pi\)
\(860\) 3.64543 + 6.31407i 0.124308 + 0.215308i
\(861\) 0 0
\(862\) −12.8914 + 22.3286i −0.439083 + 0.760514i
\(863\) 3.69965 0.125937 0.0629687 0.998016i \(-0.479943\pi\)
0.0629687 + 0.998016i \(0.479943\pi\)
\(864\) 29.2967i 0.996695i
\(865\) −6.40230 −0.217685
\(866\) −8.64233 + 14.9690i −0.293678 + 0.508666i
\(867\) −9.94104 27.3128i −0.337615 0.927590i
\(868\) 0 0
\(869\) 1.98633 + 3.44042i 0.0673816 + 0.116708i
\(870\) −12.6684 2.23379i −0.429500 0.0757325i
\(871\) −1.00459 + 1.73999i −0.0340391 + 0.0589574i
\(872\) 1.14559 0.0387946
\(873\) −0.989266 5.61041i −0.0334816 0.189884i
\(874\) −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 0.948217 0.317622i \(-0.102884\pi\)
−0.749178 + 0.662369i \(0.769551\pi\)
\(878\) 9.64244 + 16.7012i 0.325416 + 0.563638i
\(879\) −14.5753 + 17.3702i −0.491613 + 0.585882i
\(880\) −0.0466368 + 0.0807773i −0.00157213 + 0.00272300i
\(881\) −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 \(0.618031\pi\)
\(884\) −0.967034 + 1.67495i −0.0325249 + 0.0563347i
\(885\) 23.8935 + 4.21307i 0.803172 + 0.141621i
\(886\) −8.22668 14.2490i −0.276381 0.478706i
\(887\) 5.94238 + 10.2925i 0.199526 + 0.345589i 0.948375 0.317152i \(-0.102727\pi\)
−0.748849 + 0.662741i \(0.769393\pi\)
\(888\) 15.5223 + 42.6473i 0.520896 + 1.43115i
\(889\) 0 0
\(890\) −10.7656 −0.360863
\(891\) 11.3944 + 9.56104i 0.381727 + 0.320307i
\(892\) 8.68954 0.290947
\(893\) 15.0929 26.1416i 0.505063 0.874795i
\(894\) −0.224566 0.616990i −0.00751061 0.0206352i
\(895\) −5.74763 9.95518i −0.192122 0.332765i
\(896\) 0 0
\(897\) −51.4043 9.06396i −1.71634 0.302637i
\(898\) 2.93717 5.08732i 0.0980145 0.169766i
\(899\) −57.8866 −1.93063
\(900\) −8.97818 + 7.53359i −0.299273 + 0.251120i
\(901\) 0.268571 0.00894739
\(902\) −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
\(906\) 2.41885 2.88268i 0.0803610 0.0957706i
\(907\) 13.0107 22.5353i 0.432014 0.748271i −0.565032 0.825069i \(-0.691136\pi\)
0.997047 + 0.0767980i \(0.0244697\pi\)
\(908\) −14.6509 −0.486209
\(909\) −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 \(0.145386\pi\)
\(912\) 0.230552 + 0.0406525i 0.00763434 + 0.00134614i
\(913\) −12.4363 21.5403i −0.411581 0.712879i
\(914\) −8.54266 14.7963i −0.282566 0.489419i
\(915\) 6.09627 + 16.7494i 0.201536 + 0.553717i
\(916\) 10.7657 18.6468i 0.355710 0.616108i
\(917\) 0 0
\(918\) 1.85163 1.06904i 0.0611130 0.0352836i
\(919\) 27.4270 0.904732 0.452366 0.891832i \(-0.350580\pi\)
0.452366 + 0.891832i \(0.350580\pi\)
\(920\) 17.0954 29.6101i 0.563618 0.976216i
\(921\) −3.73829 10.2709i −0.123181 0.338437i
\(922\) 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
\(926\) 0.391874 0.0128778
\(927\) 10.2562 + 3.73297i 0.336859 + 0.122607i
\(928\) −35.3432 −1.16020
\(929\) 3.83837 6.64826i 0.125933 0.218122i −0.796164 0.605081i \(-0.793141\pi\)
0.922097 + 0.386958i \(0.126474\pi\)
\(930\) −12.1809 + 14.5167i −0.399428 + 0.476020i
\(931\) 0 0
\(932\) 9.96926 + 17.2673i 0.326554 + 0.565608i
\(933\) 10.6038 12.6372i 0.347154 0.413722i
\(934\) 15.0440 26.0570i 0.492255 0.852610i
\(935\) 1.04189 0.0340734
\(936\) 26.9537 + 9.81035i 0.881010 + 0.320661i
\(937\) 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
\(941\) −3.06964 5.31677i −0.100067 0.173322i 0.811645 0.584151i \(-0.198573\pi\)
−0.911712 + 0.410829i \(0.865239\pi\)
\(942\) 5.27894 + 14.5038i 0.171997 + 0.472559i
\(943\) 15.2554 26.4231i 0.496783 0.860454i
\(944\) −0.435518 −0.0141749
\(945\) 0 0
\(946\) 6.41147 0.208455
\(947\) −2.78224 + 4.81898i −0.0904107 + 0.156596i −0.907684 0.419654i \(-0.862151\pi\)
0.817273 + 0.576250i \(0.195485\pi\)
\(948\) 1.74675 + 4.79915i 0.0567318 + 0.155869i
\(949\) 3.45320 + 5.98112i 0.112096 + 0.194155i
\(950\) −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 \(0.545108\pi\)
\(954\) −0.262946 1.49124i −0.00851318 0.0482806i
\(955\) −17.3928 −0.562818
\(956\) −9.26099 + 16.0405i −0.299522 + 0.518787i
\(957\) 11.5343 13.7461i 0.372851 0.444347i
\(958\) 9.58219 + 16.5968i 0.309586 + 0.536219i
\(959\) 0 0
\(960\) −7.56283 + 9.01303i −0.244089 + 0.290894i
\(961\) −27.1373 + 47.0031i −0.875396 + 1.51623i
\(962\) −27.3631 −0.882222
\(963\) −16.3819 + 13.7461i −0.527900 + 0.442960i
\(964\) −19.1830 −0.617844
\(965\) −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
\(969\) −0.894400 2.45734i −0.0287323 0.0789413i
\(970\) −1.12495 + 1.94847i −0.0361200 + 0.0625617i
\(971\) 30.7192 0.985828 0.492914 0.870078i \(-0.335932\pi\)
0.492914 + 0.870078i \(0.335932\pi\)
\(972\) 12.2914 + 14.6484i 0.394248 + 0.469846i
\(973\) 0 0
\(974\) 8.52687 14.7690i 0.273219 0.473229i
\(975\) −6.35726 17.4664i −0.203595 0.559373i
\(976\) −0.159978 0.277089i −0.00512076 0.00886941i
\(977\) −5.15002 8.92009i −0.164764 0.285379i 0.771808 0.635856i \(-0.219353\pi\)
−0.936571 + 0.350477i \(0.886019\pi\)
\(978\) −3.89440 0.686688i −0.124529 0.0219579i
\(979\) 7.50862 13.0053i 0.239976 0.415651i
\(980\) 0 0
\(981\) −0.927833 + 0.778544i −0.0296234 + 0.0248570i
\(982\) −23.0018 −0.734015
\(983\) 6.84817 11.8614i 0.218423 0.378319i −0.735903 0.677087i \(-0.763242\pi\)
0.954326 + 0.298767i \(0.0965755\pi\)
\(984\) −10.7772 + 12.8438i −0.343564 + 0.409444i
\(985\) 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
\(989\) −39.4543 −1.25457
\(990\) −1.02007 5.78509i −0.0324199 0.183862i
\(991\) 57.9813 1.84184 0.920919 0.389754i \(-0.127440\pi\)
0.920919 + 0.389754i \(0.127440\pi\)
\(992\) −26.0326 + 45.0897i −0.826534 + 1.43160i
\(993\) −39.3166 6.93258i −1.24767 0.219999i
\(994\) 0 0
\(995\) 2.45084 + 4.24497i 0.0776968 + 0.134575i
\(996\) −10.9363 30.0472i −0.346530 0.952082i
\(997\) 8.10876 14.0448i 0.256807 0.444803i −0.708578 0.705633i \(-0.750663\pi\)
0.965385 + 0.260830i \(0.0839962\pi\)
\(998\) 12.5763 0.398097
\(999\) −41.5549 23.9917i −1.31474 0.759065i
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.f.c.295.3 6
3.2 odd 2 1323.2.f.d.883.1 6
7.2 even 3 441.2.h.e.214.1 6
7.3 odd 6 441.2.g.c.79.3 6
7.4 even 3 441.2.g.b.79.3 6
7.5 odd 6 441.2.h.d.214.1 6
7.6 odd 2 63.2.f.a.43.3 yes 6
9.2 odd 6 3969.2.a.l.1.3 3
9.4 even 3 inner 441.2.f.c.148.3 6
9.5 odd 6 1323.2.f.d.442.1 6
9.7 even 3 3969.2.a.q.1.1 3
21.2 odd 6 1323.2.h.b.802.3 6
21.5 even 6 1323.2.h.c.802.3 6
21.11 odd 6 1323.2.g.e.667.1 6
21.17 even 6 1323.2.g.d.667.1 6
21.20 even 2 189.2.f.b.127.1 6
28.27 even 2 1008.2.r.h.673.2 6
63.4 even 3 441.2.h.e.373.1 6
63.5 even 6 1323.2.g.d.361.1 6
63.13 odd 6 63.2.f.a.22.3 6
63.20 even 6 567.2.a.c.1.3 3
63.23 odd 6 1323.2.g.e.361.1 6
63.31 odd 6 441.2.h.d.373.1 6
63.32 odd 6 1323.2.h.b.226.3 6
63.34 odd 6 567.2.a.h.1.1 3
63.40 odd 6 441.2.g.c.67.3 6
63.41 even 6 189.2.f.b.64.1 6
63.58 even 3 441.2.g.b.67.3 6
63.59 even 6 1323.2.h.c.226.3 6
84.83 odd 2 3024.2.r.k.2017.2 6
252.83 odd 6 9072.2.a.bs.1.2 3
252.139 even 6 1008.2.r.h.337.2 6
252.167 odd 6 3024.2.r.k.1009.2 6
252.223 even 6 9072.2.a.ca.1.2 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
63.2.f.a.22.3 6 63.13 odd 6
63.2.f.a.43.3 yes 6 7.6 odd 2
189.2.f.b.64.1 6 63.41 even 6
189.2.f.b.127.1 6 21.20 even 2
441.2.f.c.148.3 6 9.4 even 3 inner
441.2.f.c.295.3 6 1.1 even 1 trivial
441.2.g.b.67.3 6 63.58 even 3
441.2.g.b.79.3 6 7.4 even 3
441.2.g.c.67.3 6 63.40 odd 6
441.2.g.c.79.3 6 7.3 odd 6
441.2.h.d.214.1 6 7.5 odd 6
441.2.h.d.373.1 6 63.31 odd 6
441.2.h.e.214.1 6 7.2 even 3
441.2.h.e.373.1 6 63.4 even 3
567.2.a.c.1.3 3 63.20 even 6
567.2.a.h.1.1 3 63.34 odd 6
1008.2.r.h.337.2 6 252.139 even 6
1008.2.r.h.673.2 6 28.27 even 2
1323.2.f.d.442.1 6 9.5 odd 6
1323.2.f.d.883.1 6 3.2 odd 2
1323.2.g.d.361.1 6 63.5 even 6
1323.2.g.d.667.1 6 21.17 even 6
1323.2.g.e.361.1 6 63.23 odd 6
1323.2.g.e.667.1 6 21.11 odd 6
1323.2.h.b.226.3 6 63.32 odd 6
1323.2.h.b.802.3 6 21.2 odd 6
1323.2.h.c.226.3 6 63.59 even 6
1323.2.h.c.802.3 6 21.5 even 6
3024.2.r.k.1009.2 6 252.167 odd 6
3024.2.r.k.2017.2 6 84.83 odd 2
3969.2.a.l.1.3 3 9.2 odd 6
3969.2.a.q.1.1 3 9.7 even 3
9072.2.a.bs.1.2 3 252.83 odd 6
9072.2.a.ca.1.2 3 252.223 even 6