Properties

Label 729.2.g.a.55.5
Level $729$
Weight $2$
Character 729.55
Analytic conductor $5.821$
Analytic rank $0$
Dimension $144$
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] = [729,2,Mod(28,729)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(729, base_ring=CyclotomicField(54))
 
chi = DirichletCharacter(H, H._module([44]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("729.28");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 729 = 3^{6} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 729.g (of order \(27\), degree \(18\), 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: \(5.82109430735\)
Analytic rank: \(0\)
Dimension: \(144\)
Relative dimension: \(8\) over \(\Q(\zeta_{27})\)
Twist minimal: no (minimal twist has level 81)
Sato-Tate group: $\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label 55.5
Character \(\chi\) \(=\) 729.55
Dual form 729.2.g.a.676.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.0742143 + 0.172048i) q^{2} +(1.34839 + 1.42921i) q^{4} +(0.0921050 + 1.58138i) q^{5} +(-3.93765 - 0.933240i) q^{7} +(-0.698107 + 0.254090i) q^{8} +O(q^{10})\) \(q+(-0.0742143 + 0.172048i) q^{2} +(1.34839 + 1.42921i) q^{4} +(0.0921050 + 1.58138i) q^{5} +(-3.93765 - 0.933240i) q^{7} +(-0.698107 + 0.254090i) q^{8} +(-0.278909 - 0.101515i) q^{10} +(-3.21202 - 2.11258i) q^{11} +(1.58861 + 0.185682i) q^{13} +(0.452792 - 0.608205i) q^{14} +(-0.220403 + 3.78417i) q^{16} +(-5.79317 + 4.86105i) q^{17} +(1.26984 + 1.06552i) q^{19} +(-2.13593 + 2.26396i) q^{20} +(0.601842 - 0.395838i) q^{22} +(-6.23886 + 1.47864i) q^{23} +(2.47391 - 0.289158i) q^{25} +(-0.149844 + 0.259538i) q^{26} +(-3.97569 - 6.88610i) q^{28} +(0.163549 + 0.219684i) q^{29} +(0.530826 - 1.77308i) q^{31} +(-1.96248 - 0.985594i) q^{32} +(-0.406398 - 1.35746i) q^{34} +(1.11313 - 6.31289i) q^{35} +(-0.295248 - 1.67443i) q^{37} +(-0.277561 + 0.139396i) q^{38} +(-0.466113 - 1.08057i) q^{40} +(-1.18553 - 2.74838i) q^{41} +(-4.35056 + 2.18493i) q^{43} +(-1.31174 - 7.43922i) q^{44} +(0.208616 - 1.18312i) q^{46} +(0.0382623 + 0.127805i) q^{47} +(8.37873 + 4.20796i) q^{49} +(-0.133850 + 0.447090i) q^{50} +(1.87669 + 2.52084i) q^{52} +(4.93888 + 8.55438i) q^{53} +(3.04495 - 5.27400i) q^{55} +(2.98603 - 0.349017i) q^{56} +(-0.0499339 + 0.0118346i) q^{58} +(6.47138 - 4.25629i) q^{59} +(-2.83624 + 3.00624i) q^{61} +(0.265660 + 0.222915i) q^{62} +(-5.49230 + 4.60858i) q^{64} +(-0.147315 + 2.52931i) q^{65} +(-8.03004 + 10.7862i) q^{67} +(-14.7589 - 1.72507i) q^{68} +(1.00351 + 0.660018i) q^{70} +(-2.39924 - 0.873251i) q^{71} +(5.29149 - 1.92595i) q^{73} +(0.309995 + 0.0734701i) q^{74} +(0.189384 + 3.25160i) q^{76} +(10.6763 + 11.3162i) q^{77} +(3.20983 - 7.44121i) q^{79} -6.00452 q^{80} +0.560836 q^{82} +(-2.17210 + 5.03548i) q^{83} +(-8.22075 - 8.71349i) q^{85} +(-0.0530398 - 0.910658i) q^{86} +(2.77911 + 0.658662i) q^{88} +(6.33932 - 2.30732i) q^{89} +(-6.08212 - 2.21371i) q^{91} +(-10.5257 - 6.92286i) q^{92} +(-0.0248282 - 0.00290200i) q^{94} +(-1.56804 + 2.10624i) q^{95} +(-0.108820 + 1.86837i) q^{97} +(-1.34579 + 1.12925i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 144 q - 9 q^{2} + 9 q^{4} - 9 q^{5} + 9 q^{7} + 18 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 144 q - 9 q^{2} + 9 q^{4} - 9 q^{5} + 9 q^{7} + 18 q^{8} - 18 q^{10} - 9 q^{11} + 9 q^{13} - 9 q^{14} + 9 q^{16} + 18 q^{17} - 18 q^{19} - 45 q^{20} + 9 q^{22} + 45 q^{23} + 9 q^{25} - 45 q^{26} - 9 q^{28} - 36 q^{29} + 9 q^{31} + 99 q^{32} + 9 q^{34} - 9 q^{35} - 18 q^{37} - 18 q^{38} + 9 q^{40} - 27 q^{41} + 9 q^{43} - 54 q^{44} - 18 q^{46} + 99 q^{47} + 9 q^{49} - 126 q^{50} - 27 q^{52} - 45 q^{53} - 9 q^{55} + 225 q^{56} + 9 q^{58} - 72 q^{59} + 9 q^{61} - 81 q^{62} - 18 q^{64} + 81 q^{65} - 45 q^{67} - 117 q^{68} - 99 q^{70} + 90 q^{71} - 18 q^{73} - 81 q^{74} - 153 q^{76} - 81 q^{77} - 99 q^{79} + 288 q^{80} - 36 q^{82} - 45 q^{83} - 99 q^{85} - 81 q^{86} - 153 q^{88} + 81 q^{89} - 18 q^{91} - 207 q^{92} - 99 q^{94} + 171 q^{95} - 45 q^{97} - 81 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/729\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{17}{27}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.0742143 + 0.172048i −0.0524774 + 0.121656i −0.942438 0.334382i \(-0.891473\pi\)
0.889960 + 0.456038i \(0.150732\pi\)
\(3\) 0 0
\(4\) 1.34839 + 1.42921i 0.674195 + 0.714605i
\(5\) 0.0921050 + 1.58138i 0.0411906 + 0.707215i 0.954180 + 0.299233i \(0.0967307\pi\)
−0.912990 + 0.407983i \(0.866232\pi\)
\(6\) 0 0
\(7\) −3.93765 0.933240i −1.48829 0.352732i −0.595557 0.803313i \(-0.703069\pi\)
−0.892735 + 0.450582i \(0.851217\pi\)
\(8\) −0.698107 + 0.254090i −0.246818 + 0.0898344i
\(9\) 0 0
\(10\) −0.278909 0.101515i −0.0881988 0.0321017i
\(11\) −3.21202 2.11258i −0.968459 0.636966i −0.0364251 0.999336i \(-0.511597\pi\)
−0.932034 + 0.362371i \(0.881967\pi\)
\(12\) 0 0
\(13\) 1.58861 + 0.185682i 0.440602 + 0.0514990i 0.333502 0.942749i \(-0.391769\pi\)
0.107100 + 0.994248i \(0.465844\pi\)
\(14\) 0.452792 0.608205i 0.121014 0.162550i
\(15\) 0 0
\(16\) −0.220403 + 3.78417i −0.0551007 + 0.946042i
\(17\) −5.79317 + 4.86105i −1.40505 + 1.17898i −0.446246 + 0.894910i \(0.647239\pi\)
−0.958804 + 0.284067i \(0.908316\pi\)
\(18\) 0 0
\(19\) 1.26984 + 1.06552i 0.291321 + 0.244447i 0.776721 0.629845i \(-0.216882\pi\)
−0.485400 + 0.874292i \(0.661326\pi\)
\(20\) −2.13593 + 2.26396i −0.477609 + 0.506236i
\(21\) 0 0
\(22\) 0.601842 0.395838i 0.128313 0.0843929i
\(23\) −6.23886 + 1.47864i −1.30089 + 0.308317i −0.821965 0.569538i \(-0.807122\pi\)
−0.478926 + 0.877855i \(0.658974\pi\)
\(24\) 0 0
\(25\) 2.47391 0.289158i 0.494781 0.0578316i
\(26\) −0.149844 + 0.259538i −0.0293868 + 0.0508995i
\(27\) 0 0
\(28\) −3.97569 6.88610i −0.751336 1.30135i
\(29\) 0.163549 + 0.219684i 0.0303703 + 0.0407944i 0.817049 0.576568i \(-0.195609\pi\)
−0.786679 + 0.617363i \(0.788201\pi\)
\(30\) 0 0
\(31\) 0.530826 1.77308i 0.0953391 0.318455i −0.896995 0.442041i \(-0.854254\pi\)
0.992334 + 0.123586i \(0.0394396\pi\)
\(32\) −1.96248 0.985594i −0.346920 0.174230i
\(33\) 0 0
\(34\) −0.406398 1.35746i −0.0696966 0.232803i
\(35\) 1.11313 6.31289i 0.188154 1.06707i
\(36\) 0 0
\(37\) −0.295248 1.67443i −0.0485385 0.275275i 0.950873 0.309582i \(-0.100189\pi\)
−0.999411 + 0.0343062i \(0.989078\pi\)
\(38\) −0.277561 + 0.139396i −0.0450263 + 0.0226131i
\(39\) 0 0
\(40\) −0.466113 1.08057i −0.0736989 0.170853i
\(41\) −1.18553 2.74838i −0.185149 0.429224i 0.800209 0.599721i \(-0.204722\pi\)
−0.985358 + 0.170497i \(0.945463\pi\)
\(42\) 0 0
\(43\) −4.35056 + 2.18493i −0.663454 + 0.333199i −0.748459 0.663182i \(-0.769206\pi\)
0.0850049 + 0.996381i \(0.472909\pi\)
\(44\) −1.31174 7.43922i −0.197752 1.12151i
\(45\) 0 0
\(46\) 0.208616 1.18312i 0.0307587 0.174441i
\(47\) 0.0382623 + 0.127805i 0.00558113 + 0.0186423i 0.960735 0.277469i \(-0.0894954\pi\)
−0.955154 + 0.296111i \(0.904310\pi\)
\(48\) 0 0
\(49\) 8.37873 + 4.20796i 1.19696 + 0.601136i
\(50\) −0.133850 + 0.447090i −0.0189293 + 0.0632281i
\(51\) 0 0
\(52\) 1.87669 + 2.52084i 0.260250 + 0.349577i
\(53\) 4.93888 + 8.55438i 0.678407 + 1.17504i 0.975461 + 0.220174i \(0.0706626\pi\)
−0.297054 + 0.954861i \(0.596004\pi\)
\(54\) 0 0
\(55\) 3.04495 5.27400i 0.410580 0.711146i
\(56\) 2.98603 0.349017i 0.399025 0.0466393i
\(57\) 0 0
\(58\) −0.0499339 + 0.0118346i −0.00655665 + 0.00155395i
\(59\) 6.47138 4.25629i 0.842501 0.554122i −0.0532989 0.998579i \(-0.516974\pi\)
0.895800 + 0.444457i \(0.146603\pi\)
\(60\) 0 0
\(61\) −2.83624 + 3.00624i −0.363143 + 0.384909i −0.883023 0.469330i \(-0.844495\pi\)
0.519879 + 0.854240i \(0.325977\pi\)
\(62\) 0.265660 + 0.222915i 0.0337389 + 0.0283103i
\(63\) 0 0
\(64\) −5.49230 + 4.60858i −0.686537 + 0.576073i
\(65\) −0.147315 + 2.52931i −0.0182722 + 0.313722i
\(66\) 0 0
\(67\) −8.03004 + 10.7862i −0.981026 + 1.31775i −0.0330332 + 0.999454i \(0.510517\pi\)
−0.947993 + 0.318292i \(0.896891\pi\)
\(68\) −14.7589 1.72507i −1.78978 0.209195i
\(69\) 0 0
\(70\) 1.00351 + 0.660018i 0.119942 + 0.0788873i
\(71\) −2.39924 0.873251i −0.284737 0.103636i 0.195703 0.980663i \(-0.437301\pi\)
−0.480441 + 0.877027i \(0.659523\pi\)
\(72\) 0 0
\(73\) 5.29149 1.92595i 0.619322 0.225415i −0.0132549 0.999912i \(-0.504219\pi\)
0.632577 + 0.774497i \(0.281997\pi\)
\(74\) 0.309995 + 0.0734701i 0.0360362 + 0.00854073i
\(75\) 0 0
\(76\) 0.189384 + 3.25160i 0.0217239 + 0.372985i
\(77\) 10.6763 + 11.3162i 1.21667 + 1.28960i
\(78\) 0 0
\(79\) 3.20983 7.44121i 0.361134 0.837202i −0.636681 0.771127i \(-0.719693\pi\)
0.997815 0.0660746i \(-0.0210475\pi\)
\(80\) −6.00452 −0.671325
\(81\) 0 0
\(82\) 0.560836 0.0619340
\(83\) −2.17210 + 5.03548i −0.238418 + 0.552716i −0.994850 0.101357i \(-0.967682\pi\)
0.756432 + 0.654073i \(0.226941\pi\)
\(84\) 0 0
\(85\) −8.22075 8.71349i −0.891666 0.945111i
\(86\) −0.0530398 0.910658i −0.00571942 0.0981987i
\(87\) 0 0
\(88\) 2.77911 + 0.658662i 0.296255 + 0.0702136i
\(89\) 6.33932 2.30732i 0.671966 0.244576i 0.0165720 0.999863i \(-0.494725\pi\)
0.655394 + 0.755287i \(0.272503\pi\)
\(90\) 0 0
\(91\) −6.08212 2.21371i −0.637580 0.232060i
\(92\) −10.5257 6.92286i −1.09738 0.721758i
\(93\) 0 0
\(94\) −0.0248282 0.00290200i −0.00256083 0.000299319i
\(95\) −1.56804 + 2.10624i −0.160877 + 0.216096i
\(96\) 0 0
\(97\) −0.108820 + 1.86837i −0.0110490 + 0.189704i 0.988267 + 0.152734i \(0.0488078\pi\)
−0.999316 + 0.0369704i \(0.988229\pi\)
\(98\) −1.34579 + 1.12925i −0.135945 + 0.114072i
\(99\) 0 0
\(100\) 3.74906 + 3.14584i 0.374906 + 0.314584i
\(101\) −11.4483 + 12.1345i −1.13915 + 1.20743i −0.163863 + 0.986483i \(0.552395\pi\)
−0.975286 + 0.220944i \(0.929086\pi\)
\(102\) 0 0
\(103\) 4.80896 3.16291i 0.473841 0.311650i −0.290032 0.957017i \(-0.593666\pi\)
0.763873 + 0.645367i \(0.223295\pi\)
\(104\) −1.15620 + 0.274025i −0.113375 + 0.0268704i
\(105\) 0 0
\(106\) −1.83830 + 0.214866i −0.178551 + 0.0208697i
\(107\) −0.810593 + 1.40399i −0.0783630 + 0.135729i −0.902544 0.430598i \(-0.858303\pi\)
0.824181 + 0.566327i \(0.191636\pi\)
\(108\) 0 0
\(109\) 5.75519 + 9.96829i 0.551248 + 0.954789i 0.998185 + 0.0602237i \(0.0191814\pi\)
−0.446937 + 0.894565i \(0.647485\pi\)
\(110\) 0.681403 + 0.915283i 0.0649692 + 0.0872688i
\(111\) 0 0
\(112\) 4.39941 14.6951i 0.415705 1.38855i
\(113\) 7.80192 + 3.91827i 0.733943 + 0.368600i 0.776183 0.630508i \(-0.217153\pi\)
−0.0422404 + 0.999107i \(0.513450\pi\)
\(114\) 0 0
\(115\) −2.91292 9.72982i −0.271631 0.907311i
\(116\) −0.0934474 + 0.529966i −0.00867637 + 0.0492061i
\(117\) 0 0
\(118\) 0.252018 + 1.42926i 0.0232001 + 0.131575i
\(119\) 27.3480 13.7347i 2.50699 1.25906i
\(120\) 0 0
\(121\) 1.49719 + 3.47088i 0.136108 + 0.315534i
\(122\) −0.306728 0.711075i −0.0277698 0.0643777i
\(123\) 0 0
\(124\) 3.24987 1.63214i 0.291847 0.146571i
\(125\) 2.06048 + 11.6855i 0.184295 + 1.04519i
\(126\) 0 0
\(127\) −3.29466 + 18.6850i −0.292354 + 1.65802i 0.385411 + 0.922745i \(0.374060\pi\)
−0.677766 + 0.735278i \(0.737052\pi\)
\(128\) −1.64497 5.49458i −0.145396 0.485657i
\(129\) 0 0
\(130\) −0.424229 0.213056i −0.0372074 0.0186863i
\(131\) 1.73595 5.79846i 0.151670 0.506614i −0.848058 0.529903i \(-0.822228\pi\)
0.999729 + 0.0232885i \(0.00741363\pi\)
\(132\) 0 0
\(133\) −4.00579 5.38071i −0.347346 0.466567i
\(134\) −1.25980 2.18204i −0.108830 0.188500i
\(135\) 0 0
\(136\) 2.80911 4.86552i 0.240879 0.417215i
\(137\) 22.0876 2.58167i 1.88707 0.220567i 0.907271 0.420547i \(-0.138162\pi\)
0.979800 + 0.199980i \(0.0640878\pi\)
\(138\) 0 0
\(139\) −12.3791 + 2.93391i −1.04998 + 0.248851i −0.719162 0.694843i \(-0.755474\pi\)
−0.330822 + 0.943693i \(0.607326\pi\)
\(140\) 10.5234 6.92133i 0.889388 0.584960i
\(141\) 0 0
\(142\) 0.328299 0.347977i 0.0275502 0.0292015i
\(143\) −4.71039 3.95248i −0.393902 0.330523i
\(144\) 0 0
\(145\) −0.332341 + 0.278867i −0.0275994 + 0.0231587i
\(146\) −0.0613491 + 1.05332i −0.00507729 + 0.0871737i
\(147\) 0 0
\(148\) 1.99501 2.67976i 0.163989 0.220275i
\(149\) 9.73145 + 1.13744i 0.797231 + 0.0931830i 0.504949 0.863149i \(-0.331511\pi\)
0.292282 + 0.956332i \(0.405585\pi\)
\(150\) 0 0
\(151\) 7.95586 + 5.23265i 0.647439 + 0.425827i 0.830304 0.557311i \(-0.188167\pi\)
−0.182865 + 0.983138i \(0.558537\pi\)
\(152\) −1.15722 0.421194i −0.0938630 0.0341633i
\(153\) 0 0
\(154\) −2.73925 + 0.997007i −0.220735 + 0.0803411i
\(155\) 2.85281 + 0.676128i 0.229143 + 0.0543079i
\(156\) 0 0
\(157\) −0.431930 7.41595i −0.0344718 0.591857i −0.970675 0.240397i \(-0.922722\pi\)
0.936203 0.351460i \(-0.114315\pi\)
\(158\) 1.04203 + 1.10449i 0.0828995 + 0.0878684i
\(159\) 0 0
\(160\) 1.37785 3.19421i 0.108928 0.252524i
\(161\) 25.9464 2.04486
\(162\) 0 0
\(163\) 4.98806 0.390695 0.195347 0.980734i \(-0.437417\pi\)
0.195347 + 0.980734i \(0.437417\pi\)
\(164\) 2.32945 5.40026i 0.181899 0.421690i
\(165\) 0 0
\(166\) −0.705144 0.747409i −0.0547298 0.0580102i
\(167\) −0.253555 4.35337i −0.0196207 0.336874i −0.993806 0.111126i \(-0.964554\pi\)
0.974186 0.225748i \(-0.0724827\pi\)
\(168\) 0 0
\(169\) −10.1604 2.40805i −0.781567 0.185235i
\(170\) 2.10924 0.767699i 0.161771 0.0588798i
\(171\) 0 0
\(172\) −8.98898 3.27172i −0.685403 0.249466i
\(173\) −13.4039 8.81588i −1.01908 0.670259i −0.0740530 0.997254i \(-0.523593\pi\)
−0.945026 + 0.326996i \(0.893964\pi\)
\(174\) 0 0
\(175\) −10.0112 1.17015i −0.756778 0.0884547i
\(176\) 8.70228 11.6892i 0.655959 0.881106i
\(177\) 0 0
\(178\) −0.0734975 + 1.26190i −0.00550887 + 0.0945836i
\(179\) 14.7729 12.3960i 1.10418 0.926518i 0.106483 0.994315i \(-0.466041\pi\)
0.997699 + 0.0677961i \(0.0215967\pi\)
\(180\) 0 0
\(181\) 0.116035 + 0.0973645i 0.00862478 + 0.00723705i 0.647090 0.762414i \(-0.275986\pi\)
−0.638465 + 0.769651i \(0.720430\pi\)
\(182\) 0.832245 0.882128i 0.0616901 0.0653877i
\(183\) 0 0
\(184\) 3.97968 2.61748i 0.293386 0.192963i
\(185\) 2.62073 0.621124i 0.192680 0.0456659i
\(186\) 0 0
\(187\) 28.8771 3.37525i 2.11170 0.246823i
\(188\) −0.131068 + 0.227016i −0.00955910 + 0.0165568i
\(189\) 0 0
\(190\) −0.246003 0.426090i −0.0178470 0.0309119i
\(191\) 6.39393 + 8.58854i 0.462649 + 0.621445i 0.970820 0.239811i \(-0.0770855\pi\)
−0.508171 + 0.861256i \(0.669678\pi\)
\(192\) 0 0
\(193\) −4.55179 + 15.2040i −0.327645 + 1.09441i 0.622505 + 0.782616i \(0.286115\pi\)
−0.950150 + 0.311794i \(0.899070\pi\)
\(194\) −0.313374 0.157382i −0.0224989 0.0112994i
\(195\) 0 0
\(196\) 5.28374 + 17.6489i 0.377410 + 1.26064i
\(197\) 0.213838 1.21273i 0.0152353 0.0864037i −0.976242 0.216683i \(-0.930476\pi\)
0.991477 + 0.130279i \(0.0415874\pi\)
\(198\) 0 0
\(199\) 0.406772 + 2.30692i 0.0288353 + 0.163533i 0.995825 0.0912821i \(-0.0290965\pi\)
−0.966990 + 0.254815i \(0.917985\pi\)
\(200\) −1.65358 + 0.830459i −0.116926 + 0.0587223i
\(201\) 0 0
\(202\) −1.23809 2.87021i −0.0871116 0.201947i
\(203\) −0.438980 1.01767i −0.0308104 0.0714265i
\(204\) 0 0
\(205\) 4.23704 2.12792i 0.295928 0.148620i
\(206\) 0.187278 + 1.06211i 0.0130483 + 0.0740004i
\(207\) 0 0
\(208\) −1.05279 + 5.97066i −0.0729978 + 0.413991i
\(209\) −1.82775 6.10510i −0.126428 0.422298i
\(210\) 0 0
\(211\) −10.1780 5.11157i −0.700681 0.351895i 0.0625316 0.998043i \(-0.480083\pi\)
−0.763212 + 0.646148i \(0.776379\pi\)
\(212\) −5.56648 + 18.5933i −0.382308 + 1.27700i
\(213\) 0 0
\(214\) −0.181396 0.243657i −0.0124000 0.0166560i
\(215\) −3.85592 6.67865i −0.262971 0.455480i
\(216\) 0 0
\(217\) −3.74492 + 6.48639i −0.254222 + 0.440325i
\(218\) −2.14214 + 0.250380i −0.145084 + 0.0169579i
\(219\) 0 0
\(220\) 11.6434 2.75954i 0.785000 0.186048i
\(221\) −10.1057 + 6.64664i −0.679785 + 0.447101i
\(222\) 0 0
\(223\) 10.3801 11.0023i 0.695106 0.736770i −0.279635 0.960106i \(-0.590213\pi\)
0.974741 + 0.223337i \(0.0716950\pi\)
\(224\) 6.80776 + 5.71239i 0.454863 + 0.381675i
\(225\) 0 0
\(226\) −1.25314 + 1.05151i −0.0833579 + 0.0699456i
\(227\) −1.23726 + 21.2429i −0.0821198 + 1.40994i 0.665789 + 0.746140i \(0.268095\pi\)
−0.747908 + 0.663802i \(0.768942\pi\)
\(228\) 0 0
\(229\) 2.33003 3.12978i 0.153973 0.206822i −0.718443 0.695586i \(-0.755145\pi\)
0.872416 + 0.488764i \(0.162552\pi\)
\(230\) 1.89018 + 0.220930i 0.124635 + 0.0145677i
\(231\) 0 0
\(232\) −0.169994 0.111807i −0.0111607 0.00734049i
\(233\) −18.1958 6.62273i −1.19205 0.433869i −0.331604 0.943419i \(-0.607590\pi\)
−0.860441 + 0.509549i \(0.829812\pi\)
\(234\) 0 0
\(235\) −0.198584 + 0.0722788i −0.0129542 + 0.00471495i
\(236\) 14.8091 + 3.50982i 0.963989 + 0.228470i
\(237\) 0 0
\(238\) 0.333413 + 5.72448i 0.0216120 + 0.371063i
\(239\) −9.74423 10.3283i −0.630302 0.668081i 0.330983 0.943637i \(-0.392620\pi\)
−0.961285 + 0.275556i \(0.911138\pi\)
\(240\) 0 0
\(241\) −4.42332 + 10.2544i −0.284931 + 0.660544i −0.999227 0.0392991i \(-0.987487\pi\)
0.714297 + 0.699843i \(0.246747\pi\)
\(242\) −0.708270 −0.0455293
\(243\) 0 0
\(244\) −8.12090 −0.519888
\(245\) −5.88266 + 13.6375i −0.375829 + 0.871271i
\(246\) 0 0
\(247\) 1.81943 + 1.92849i 0.115768 + 0.122707i
\(248\) 0.0799494 + 1.37268i 0.00507679 + 0.0871651i
\(249\) 0 0
\(250\) −2.16339 0.512733i −0.136825 0.0324281i
\(251\) 8.61554 3.13580i 0.543808 0.197930i −0.0554853 0.998460i \(-0.517671\pi\)
0.599293 + 0.800530i \(0.295448\pi\)
\(252\) 0 0
\(253\) 23.1630 + 8.43066i 1.45625 + 0.530031i
\(254\) −2.97020 1.95353i −0.186367 0.122575i
\(255\) 0 0
\(256\) −13.1750 1.53994i −0.823437 0.0962460i
\(257\) −10.3133 + 13.8532i −0.643328 + 0.864139i −0.997473 0.0710513i \(-0.977365\pi\)
0.354145 + 0.935191i \(0.384772\pi\)
\(258\) 0 0
\(259\) −0.400066 + 6.86888i −0.0248589 + 0.426811i
\(260\) −3.81355 + 3.19995i −0.236506 + 0.198452i
\(261\) 0 0
\(262\) 0.868782 + 0.728995i 0.0536735 + 0.0450375i
\(263\) −3.22173 + 3.41483i −0.198660 + 0.210568i −0.819044 0.573731i \(-0.805495\pi\)
0.620384 + 0.784299i \(0.286977\pi\)
\(264\) 0 0
\(265\) −13.0729 + 8.59815i −0.803059 + 0.528180i
\(266\) 1.22303 0.289863i 0.0749886 0.0177726i
\(267\) 0 0
\(268\) −26.2434 + 3.06741i −1.60307 + 0.187372i
\(269\) −6.52546 + 11.3024i −0.397864 + 0.689121i −0.993462 0.114162i \(-0.963582\pi\)
0.595598 + 0.803283i \(0.296915\pi\)
\(270\) 0 0
\(271\) −11.8170 20.4676i −0.717832 1.24332i −0.961857 0.273552i \(-0.911801\pi\)
0.244026 0.969769i \(-0.421532\pi\)
\(272\) −17.1182 22.9937i −1.03794 1.39420i
\(273\) 0 0
\(274\) −1.19504 + 3.99172i −0.0721952 + 0.241149i
\(275\) −8.55710 4.29753i −0.516012 0.259151i
\(276\) 0 0
\(277\) −6.82482 22.7965i −0.410064 1.36971i −0.874897 0.484310i \(-0.839071\pi\)
0.464833 0.885398i \(-0.346114\pi\)
\(278\) 0.413935 2.34754i 0.0248262 0.140796i
\(279\) 0 0
\(280\) 0.826957 + 4.68990i 0.0494201 + 0.280275i
\(281\) 12.3376 6.19616i 0.735997 0.369632i −0.0409803 0.999160i \(-0.513048\pi\)
0.776978 + 0.629528i \(0.216752\pi\)
\(282\) 0 0
\(283\) 5.81388 + 13.4781i 0.345599 + 0.801189i 0.999023 + 0.0441964i \(0.0140727\pi\)
−0.653424 + 0.756992i \(0.726668\pi\)
\(284\) −1.98705 4.60650i −0.117910 0.273346i
\(285\) 0 0
\(286\) 1.02959 0.517082i 0.0608812 0.0305757i
\(287\) 2.10332 + 11.9285i 0.124155 + 0.704119i
\(288\) 0 0
\(289\) 6.97903 39.5800i 0.410531 2.32824i
\(290\) −0.0233141 0.0778746i −0.00136905 0.00457295i
\(291\) 0 0
\(292\) 9.88758 + 4.96573i 0.578627 + 0.290597i
\(293\) 1.11671 3.73009i 0.0652392 0.217914i −0.919154 0.393899i \(-0.871126\pi\)
0.984393 + 0.175985i \(0.0563111\pi\)
\(294\) 0 0
\(295\) 7.32687 + 9.84169i 0.426587 + 0.573005i
\(296\) 0.631572 + 1.09391i 0.0367094 + 0.0635825i
\(297\) 0 0
\(298\) −0.917907 + 1.58986i −0.0531729 + 0.0920982i
\(299\) −10.1857 + 1.19054i −0.589054 + 0.0688505i
\(300\) 0 0
\(301\) 19.1700 4.54338i 1.10494 0.261876i
\(302\) −1.49071 + 0.980453i −0.0857805 + 0.0564187i
\(303\) 0 0
\(304\) −4.31199 + 4.57044i −0.247309 + 0.262133i
\(305\) −5.01524 4.20829i −0.287172 0.240966i
\(306\) 0 0
\(307\) −0.636621 + 0.534188i −0.0363339 + 0.0304877i −0.660774 0.750585i \(-0.729772\pi\)
0.624440 + 0.781073i \(0.285327\pi\)
\(308\) −1.77743 + 30.5172i −0.101278 + 1.73888i
\(309\) 0 0
\(310\) −0.328046 + 0.440642i −0.0186317 + 0.0250268i
\(311\) 10.9127 + 1.27552i 0.618805 + 0.0723279i 0.419719 0.907654i \(-0.362129\pi\)
0.199086 + 0.979982i \(0.436203\pi\)
\(312\) 0 0
\(313\) −14.4466 9.50167i −0.816570 0.537066i 0.0711419 0.997466i \(-0.477336\pi\)
−0.887712 + 0.460400i \(0.847706\pi\)
\(314\) 1.30795 + 0.476057i 0.0738121 + 0.0268654i
\(315\) 0 0
\(316\) 14.9632 5.44614i 0.841743 0.306370i
\(317\) 17.7179 + 4.19923i 0.995138 + 0.235852i 0.695754 0.718281i \(-0.255071\pi\)
0.299384 + 0.954133i \(0.403219\pi\)
\(318\) 0 0
\(319\) −0.0612219 1.05114i −0.00342777 0.0588525i
\(320\) −7.79380 8.26094i −0.435687 0.461801i
\(321\) 0 0
\(322\) −1.92559 + 4.46402i −0.107309 + 0.248770i
\(323\) −12.5359 −0.697518
\(324\) 0 0
\(325\) 3.98377 0.220980
\(326\) −0.370185 + 0.858185i −0.0205026 + 0.0475305i
\(327\) 0 0
\(328\) 1.52596 + 1.61743i 0.0842573 + 0.0893075i
\(329\) −0.0313908 0.538959i −0.00173063 0.0297138i
\(330\) 0 0
\(331\) 17.5916 + 4.16929i 0.966923 + 0.229165i 0.683598 0.729859i \(-0.260414\pi\)
0.283325 + 0.959024i \(0.408562\pi\)
\(332\) −10.1256 + 3.68542i −0.555714 + 0.202263i
\(333\) 0 0
\(334\) 0.767807 + 0.279459i 0.0420125 + 0.0152913i
\(335\) −17.7967 11.7051i −0.972340 0.639518i
\(336\) 0 0
\(337\) 20.8508 + 2.43711i 1.13582 + 0.132758i 0.663152 0.748485i \(-0.269218\pi\)
0.472664 + 0.881243i \(0.343292\pi\)
\(338\) 1.16834 1.56936i 0.0635496 0.0853619i
\(339\) 0 0
\(340\) 1.36862 23.4984i 0.0742241 1.27438i
\(341\) −5.45079 + 4.57376i −0.295177 + 0.247683i
\(342\) 0 0
\(343\) −7.36564 6.18050i −0.397707 0.333716i
\(344\) 2.48198 2.63075i 0.133820 0.141840i
\(345\) 0 0
\(346\) 2.51151 1.65185i 0.135020 0.0888039i
\(347\) 19.8413 4.70248i 1.06514 0.252443i 0.339562 0.940584i \(-0.389721\pi\)
0.725577 + 0.688141i \(0.241573\pi\)
\(348\) 0 0
\(349\) −17.5899 + 2.05597i −0.941567 + 0.110053i −0.573007 0.819550i \(-0.694223\pi\)
−0.368560 + 0.929604i \(0.620149\pi\)
\(350\) 0.944298 1.63557i 0.0504748 0.0874250i
\(351\) 0 0
\(352\) 4.22137 + 7.31163i 0.225000 + 0.389711i
\(353\) −12.4103 16.6700i −0.660535 0.887252i 0.338012 0.941142i \(-0.390245\pi\)
−0.998547 + 0.0538897i \(0.982838\pi\)
\(354\) 0 0
\(355\) 1.15996 3.87454i 0.0615644 0.205639i
\(356\) 11.8455 + 5.94905i 0.627811 + 0.315299i
\(357\) 0 0
\(358\) 1.03634 + 3.46161i 0.0547722 + 0.182952i
\(359\) −3.40920 + 19.3346i −0.179931 + 1.02044i 0.752366 + 0.658745i \(0.228912\pi\)
−0.932297 + 0.361693i \(0.882199\pi\)
\(360\) 0 0
\(361\) −2.82216 16.0053i −0.148535 0.842383i
\(362\) −0.0253628 + 0.0127377i −0.00133304 + 0.000669477i
\(363\) 0 0
\(364\) −5.03722 11.6776i −0.264022 0.612071i
\(365\) 3.53303 + 8.19048i 0.184927 + 0.428709i
\(366\) 0 0
\(367\) −29.1383 + 14.6338i −1.52101 + 0.763878i −0.996179 0.0873300i \(-0.972167\pi\)
−0.524828 + 0.851209i \(0.675870\pi\)
\(368\) −4.22035 23.9348i −0.220001 1.24769i
\(369\) 0 0
\(370\) −0.0876322 + 0.496987i −0.00455578 + 0.0258371i
\(371\) −11.4643 38.2933i −0.595195 1.98809i
\(372\) 0 0
\(373\) −15.8648 7.96762i −0.821450 0.412548i −0.0121379 0.999926i \(-0.503864\pi\)
−0.809312 + 0.587379i \(0.800160\pi\)
\(374\) −1.56239 + 5.21874i −0.0807891 + 0.269854i
\(375\) 0 0
\(376\) −0.0591852 0.0794995i −0.00305224 0.00409987i
\(377\) 0.219025 + 0.379362i 0.0112803 + 0.0195381i
\(378\) 0 0
\(379\) −13.5735 + 23.5099i −0.697222 + 1.20762i 0.272204 + 0.962240i \(0.412247\pi\)
−0.969426 + 0.245384i \(0.921086\pi\)
\(380\) −5.12458 + 0.598978i −0.262886 + 0.0307269i
\(381\) 0 0
\(382\) −1.95216 + 0.462671i −0.0998814 + 0.0236723i
\(383\) −29.7103 + 19.5408i −1.51813 + 0.998488i −0.529465 + 0.848332i \(0.677607\pi\)
−0.988662 + 0.150156i \(0.952022\pi\)
\(384\) 0 0
\(385\) −16.9118 + 17.9255i −0.861908 + 0.913569i
\(386\) −2.27802 1.91148i −0.115948 0.0972919i
\(387\) 0 0
\(388\) −2.81703 + 2.36377i −0.143013 + 0.120002i
\(389\) −1.18310 + 20.3130i −0.0599855 + 1.02991i 0.825250 + 0.564768i \(0.191034\pi\)
−0.885236 + 0.465143i \(0.846003\pi\)
\(390\) 0 0
\(391\) 28.9550 38.8934i 1.46432 1.96692i
\(392\) −6.91845 0.808650i −0.349434 0.0408430i
\(393\) 0 0
\(394\) 0.192779 + 0.126793i 0.00971205 + 0.00638771i
\(395\) 12.0630 + 4.39059i 0.606957 + 0.220914i
\(396\) 0 0
\(397\) −24.9491 + 9.08072i −1.25216 + 0.455748i −0.881130 0.472874i \(-0.843217\pi\)
−0.371028 + 0.928622i \(0.620995\pi\)
\(398\) −0.427089 0.101222i −0.0214080 0.00507380i
\(399\) 0 0
\(400\) 0.548968 + 9.42541i 0.0274484 + 0.471271i
\(401\) −17.6522 18.7102i −0.881508 0.934344i 0.116761 0.993160i \(-0.462749\pi\)
−0.998269 + 0.0588160i \(0.981267\pi\)
\(402\) 0 0
\(403\) 1.17251 2.71818i 0.0584067 0.135402i
\(404\) −32.7795 −1.63084
\(405\) 0 0
\(406\) 0.207667 0.0103063
\(407\) −2.58903 + 6.00204i −0.128333 + 0.297510i
\(408\) 0 0
\(409\) 19.1127 + 20.2582i 0.945060 + 1.00170i 0.999995 + 0.00321505i \(0.00102338\pi\)
−0.0549349 + 0.998490i \(0.517495\pi\)
\(410\) 0.0516558 + 0.886896i 0.00255110 + 0.0438007i
\(411\) 0 0
\(412\) 11.0048 + 2.60819i 0.542169 + 0.128496i
\(413\) −29.4542 + 10.7204i −1.44934 + 0.527518i
\(414\) 0 0
\(415\) −8.16308 2.97112i −0.400710 0.145846i
\(416\) −2.93461 1.93013i −0.143881 0.0946322i
\(417\) 0 0
\(418\) 1.18601 + 0.138625i 0.0580099 + 0.00678038i
\(419\) −0.643757 + 0.864716i −0.0314496 + 0.0422441i −0.817570 0.575829i \(-0.804679\pi\)
0.786120 + 0.618074i \(0.212087\pi\)
\(420\) 0 0
\(421\) −0.456887 + 7.84445i −0.0222673 + 0.382315i 0.968702 + 0.248226i \(0.0798477\pi\)
−0.990969 + 0.134089i \(0.957189\pi\)
\(422\) 1.63479 1.37175i 0.0795801 0.0667757i
\(423\) 0 0
\(424\) −5.62145 4.71695i −0.273002 0.229076i
\(425\) −12.9262 + 13.7009i −0.627011 + 0.664592i
\(426\) 0 0
\(427\) 13.9737 9.19062i 0.676233 0.444765i
\(428\) −3.09959 + 0.734617i −0.149824 + 0.0355090i
\(429\) 0 0
\(430\) 1.43521 0.167752i 0.0692121 0.00808973i
\(431\) 13.8447 23.9798i 0.666877 1.15507i −0.311895 0.950116i \(-0.600964\pi\)
0.978773 0.204949i \(-0.0657028\pi\)
\(432\) 0 0
\(433\) 9.89513 + 17.1389i 0.475530 + 0.823642i 0.999607 0.0280289i \(-0.00892305\pi\)
−0.524077 + 0.851671i \(0.675590\pi\)
\(434\) −0.838044 1.12569i −0.0402274 0.0540348i
\(435\) 0 0
\(436\) −6.48653 + 21.6665i −0.310649 + 1.03764i
\(437\) −9.49785 4.77000i −0.454344 0.228180i
\(438\) 0 0
\(439\) 9.64837 + 32.2278i 0.460492 + 1.53815i 0.801445 + 0.598069i \(0.204065\pi\)
−0.340953 + 0.940080i \(0.610750\pi\)
\(440\) −0.785626 + 4.45551i −0.0374533 + 0.212408i
\(441\) 0 0
\(442\) −0.393552 2.23195i −0.0187194 0.106163i
\(443\) 14.1788 7.12086i 0.673655 0.338322i −0.0788709 0.996885i \(-0.525132\pi\)
0.752526 + 0.658563i \(0.228835\pi\)
\(444\) 0 0
\(445\) 4.23264 + 9.81236i 0.200646 + 0.465151i
\(446\) 1.12257 + 2.60241i 0.0531553 + 0.123228i
\(447\) 0 0
\(448\) 25.9277 13.0214i 1.22497 0.615202i
\(449\) −0.153072 0.868114i −0.00722391 0.0409688i 0.980983 0.194095i \(-0.0621770\pi\)
−0.988207 + 0.153126i \(0.951066\pi\)
\(450\) 0 0
\(451\) −1.99820 + 11.3324i −0.0940916 + 0.533620i
\(452\) 4.92000 + 16.4339i 0.231417 + 0.772988i
\(453\) 0 0
\(454\) −3.56298 1.78940i −0.167219 0.0839805i
\(455\) 2.94053 9.82205i 0.137854 0.460465i
\(456\) 0 0
\(457\) −11.0899 14.8963i −0.518763 0.696820i 0.463122 0.886294i \(-0.346729\pi\)
−0.981886 + 0.189474i \(0.939322\pi\)
\(458\) 0.365551 + 0.633152i 0.0170811 + 0.0295853i
\(459\) 0 0
\(460\) 9.97822 17.2828i 0.465237 0.805814i
\(461\) −3.04933 + 0.356416i −0.142022 + 0.0165999i −0.186807 0.982397i \(-0.559814\pi\)
0.0447850 + 0.998997i \(0.485740\pi\)
\(462\) 0 0
\(463\) −27.8853 + 6.60895i −1.29594 + 0.307144i −0.820016 0.572341i \(-0.806035\pi\)
−0.475926 + 0.879485i \(0.657887\pi\)
\(464\) −0.867370 + 0.570478i −0.0402666 + 0.0264838i
\(465\) 0 0
\(466\) 2.48981 2.63905i 0.115338 0.122252i
\(467\) −10.6188 8.91027i −0.491382 0.412318i 0.363139 0.931735i \(-0.381705\pi\)
−0.854521 + 0.519417i \(0.826149\pi\)
\(468\) 0 0
\(469\) 41.6856 34.9784i 1.92486 1.61515i
\(470\) 0.00230237 0.0395302i 0.000106200 0.00182339i
\(471\) 0 0
\(472\) −3.43623 + 4.61566i −0.158165 + 0.212453i
\(473\) 18.5899 + 2.17285i 0.854764 + 0.0999076i
\(474\) 0 0
\(475\) 3.44956 + 2.26881i 0.158277 + 0.104100i
\(476\) 56.5056 + 20.5663i 2.58993 + 0.942657i
\(477\) 0 0
\(478\) 2.50012 0.909969i 0.114353 0.0416210i
\(479\) −24.7530 5.86656i −1.13099 0.268050i −0.377824 0.925878i \(-0.623327\pi\)
−0.753169 + 0.657827i \(0.771476\pi\)
\(480\) 0 0
\(481\) −0.158122 2.71485i −0.00720975 0.123787i
\(482\) −1.43598 1.52205i −0.0654069 0.0693273i
\(483\) 0 0
\(484\) −2.94182 + 6.81990i −0.133719 + 0.309995i
\(485\) −2.96463 −0.134617
\(486\) 0 0
\(487\) −1.98229 −0.0898263 −0.0449132 0.998991i \(-0.514301\pi\)
−0.0449132 + 0.998991i \(0.514301\pi\)
\(488\) 1.21614 2.81934i 0.0550522 0.127625i
\(489\) 0 0
\(490\) −1.90973 2.02420i −0.0862730 0.0914440i
\(491\) −0.0272326 0.467566i −0.00122899 0.0211010i 0.997638 0.0686921i \(-0.0218826\pi\)
−0.998867 + 0.0475911i \(0.984846\pi\)
\(492\) 0 0
\(493\) −2.01536 0.477650i −0.0907674 0.0215123i
\(494\) −0.466820 + 0.169909i −0.0210032 + 0.00764456i
\(495\) 0 0
\(496\) 6.59265 + 2.39953i 0.296019 + 0.107742i
\(497\) 8.63241 + 5.67763i 0.387217 + 0.254676i
\(498\) 0 0
\(499\) 23.5292 + 2.75017i 1.05331 + 0.123115i 0.625085 0.780557i \(-0.285064\pi\)
0.428227 + 0.903671i \(0.359138\pi\)
\(500\) −13.9228 + 18.7015i −0.622645 + 0.836358i
\(501\) 0 0
\(502\) −0.0998878 + 1.71501i −0.00445821 + 0.0765445i
\(503\) 0.513245 0.430663i 0.0228844 0.0192023i −0.631274 0.775560i \(-0.717468\pi\)
0.654158 + 0.756358i \(0.273023\pi\)
\(504\) 0 0
\(505\) −20.2437 16.9865i −0.900834 0.755889i
\(506\) −3.16951 + 3.35948i −0.140902 + 0.149347i
\(507\) 0 0
\(508\) −31.1472 + 20.4859i −1.38194 + 0.908913i
\(509\) 7.12235 1.68803i 0.315693 0.0748206i −0.0697149 0.997567i \(-0.522209\pi\)
0.385408 + 0.922746i \(0.374061\pi\)
\(510\) 0 0
\(511\) −22.6334 + 2.64547i −1.00124 + 0.117029i
\(512\) 6.97825 12.0867i 0.308398 0.534161i
\(513\) 0 0
\(514\) −1.61802 2.80249i −0.0713678 0.123613i
\(515\) 5.44469 + 7.31349i 0.239922 + 0.322271i
\(516\) 0 0
\(517\) 0.147099 0.491344i 0.00646939 0.0216093i
\(518\) −1.15209 0.578599i −0.0506197 0.0254222i
\(519\) 0 0
\(520\) −0.539830 1.80316i −0.0236731 0.0790737i
\(521\) −0.747254 + 4.23789i −0.0327378 + 0.185665i −0.996791 0.0800423i \(-0.974494\pi\)
0.964054 + 0.265708i \(0.0856056\pi\)
\(522\) 0 0
\(523\) −1.42678 8.09165i −0.0623885 0.353823i −0.999981 0.00608816i \(-0.998062\pi\)
0.937593 0.347735i \(-0.113049\pi\)
\(524\) 10.6280 5.33756i 0.464285 0.233172i
\(525\) 0 0
\(526\) −0.348417 0.807721i −0.0151917 0.0352183i
\(527\) 5.54387 + 12.8521i 0.241495 + 0.559848i
\(528\) 0 0
\(529\) 16.1834 8.12761i 0.703627 0.353375i
\(530\) −0.509102 2.88726i −0.0221140 0.125415i
\(531\) 0 0
\(532\) 2.28880 12.9804i 0.0992320 0.562773i
\(533\) −1.37303 4.58624i −0.0594726 0.198652i
\(534\) 0 0
\(535\) −2.29490 1.15254i −0.0992173 0.0498288i
\(536\) 2.86516 9.57029i 0.123756 0.413373i
\(537\) 0 0
\(538\) −1.46028 1.96149i −0.0629570 0.0845660i
\(539\) −18.0230 31.2167i −0.776305 1.34460i
\(540\) 0 0
\(541\) −1.90293 + 3.29597i −0.0818132 + 0.141705i −0.904029 0.427472i \(-0.859404\pi\)
0.822216 + 0.569176i \(0.192738\pi\)
\(542\) 4.39841 0.514100i 0.188928 0.0220825i
\(543\) 0 0
\(544\) 16.1600 3.82999i 0.692854 0.164209i
\(545\) −15.2336 + 10.0193i −0.652535 + 0.429179i
\(546\) 0 0
\(547\) 19.7705 20.9555i 0.845325 0.895992i −0.150375 0.988629i \(-0.548048\pi\)
0.995700 + 0.0926369i \(0.0295296\pi\)
\(548\) 33.4725 + 28.0867i 1.42987 + 1.19981i
\(549\) 0 0
\(550\) 1.37444 1.15329i 0.0586064 0.0491766i
\(551\) −0.0263976 + 0.453228i −0.00112457 + 0.0193082i
\(552\) 0 0
\(553\) −19.5836 + 26.3054i −0.832780 + 1.11862i
\(554\) 4.42859 + 0.517628i 0.188153 + 0.0219919i
\(555\) 0 0
\(556\) −20.8851 13.7363i −0.885724 0.582550i
\(557\) 0.617137 + 0.224620i 0.0261489 + 0.00951744i 0.355062 0.934843i \(-0.384460\pi\)
−0.328913 + 0.944360i \(0.606682\pi\)
\(558\) 0 0
\(559\) −7.31706 + 2.66319i −0.309479 + 0.112641i
\(560\) 23.6437 + 5.60366i 0.999128 + 0.236798i
\(561\) 0 0
\(562\) 0.150413 + 2.58250i 0.00634480 + 0.108936i
\(563\) −6.57618 6.97035i −0.277153 0.293765i 0.573812 0.818987i \(-0.305464\pi\)
−0.850965 + 0.525222i \(0.823982\pi\)
\(564\) 0 0
\(565\) −5.47769 + 12.6987i −0.230448 + 0.534238i
\(566\) −2.75035 −0.115606
\(567\) 0 0
\(568\) 1.89681 0.0795884
\(569\) −10.0440 + 23.2846i −0.421066 + 0.976142i 0.567225 + 0.823563i \(0.308017\pi\)
−0.988291 + 0.152579i \(0.951242\pi\)
\(570\) 0 0
\(571\) −5.55709 5.89017i −0.232557 0.246496i 0.600577 0.799567i \(-0.294937\pi\)
−0.833134 + 0.553071i \(0.813456\pi\)
\(572\) −0.702509 12.0616i −0.0293734 0.504322i
\(573\) 0 0
\(574\) −2.20838 0.523395i −0.0921759 0.0218461i
\(575\) −15.0068 + 5.46202i −0.625826 + 0.227782i
\(576\) 0 0
\(577\) 2.58521 + 0.940940i 0.107624 + 0.0391718i 0.395271 0.918565i \(-0.370651\pi\)
−0.287647 + 0.957736i \(0.592873\pi\)
\(578\) 6.29172 + 4.13813i 0.261701 + 0.172124i
\(579\) 0 0
\(580\) −0.846686 0.0989634i −0.0351567 0.00410923i
\(581\) 13.2523 17.8009i 0.549797 0.738505i
\(582\) 0 0
\(583\) 2.20804 37.9106i 0.0914476 1.57010i
\(584\) −3.20466 + 2.68903i −0.132610 + 0.111273i
\(585\) 0 0
\(586\) 0.558878 + 0.468954i 0.0230870 + 0.0193723i
\(587\) 28.8821 30.6133i 1.19209 1.26354i 0.235580 0.971855i \(-0.424301\pi\)
0.956513 0.291689i \(-0.0942174\pi\)
\(588\) 0 0
\(589\) 2.56332 1.68592i 0.105620 0.0694671i
\(590\) −2.23700 + 0.530179i −0.0920959 + 0.0218271i
\(591\) 0 0
\(592\) 6.40142 0.748219i 0.263097 0.0307516i
\(593\) −3.28564 + 5.69090i −0.134925 + 0.233697i −0.925569 0.378579i \(-0.876413\pi\)
0.790644 + 0.612277i \(0.209746\pi\)
\(594\) 0 0
\(595\) 24.2387 + 41.9826i 0.993689 + 1.72112i
\(596\) 11.4961 + 15.4420i 0.470901 + 0.632529i
\(597\) 0 0
\(598\) 0.551094 1.84078i 0.0225359 0.0752752i
\(599\) −13.3200 6.68956i −0.544241 0.273328i 0.155365 0.987857i \(-0.450345\pi\)
−0.699606 + 0.714529i \(0.746641\pi\)
\(600\) 0 0
\(601\) 7.32196 + 24.4570i 0.298669 + 0.997624i 0.967216 + 0.253954i \(0.0817312\pi\)
−0.668547 + 0.743670i \(0.733084\pi\)
\(602\) −0.641010 + 3.63535i −0.0261256 + 0.148166i
\(603\) 0 0
\(604\) 3.24905 + 18.4263i 0.132202 + 0.749754i
\(605\) −5.35088 + 2.68731i −0.217544 + 0.109255i
\(606\) 0 0
\(607\) −11.8994 27.5859i −0.482982 1.11968i −0.969297 0.245894i \(-0.920918\pi\)
0.486315 0.873784i \(-0.338341\pi\)
\(608\) −1.44186 3.34261i −0.0584751 0.135561i
\(609\) 0 0
\(610\) 1.09623 0.550547i 0.0443851 0.0222910i
\(611\) 0.0370529 + 0.210137i 0.00149900 + 0.00850125i
\(612\) 0 0
\(613\) −2.50656 + 14.2154i −0.101239 + 0.574154i 0.891417 + 0.453183i \(0.149712\pi\)
−0.992656 + 0.120970i \(0.961399\pi\)
\(614\) −0.0446597 0.149174i −0.00180232 0.00602016i
\(615\) 0 0
\(616\) −10.3285 5.18716i −0.416147 0.208997i
\(617\) 3.90332 13.0380i 0.157142 0.524890i −0.842769 0.538276i \(-0.819076\pi\)
0.999910 + 0.0133857i \(0.00426094\pi\)
\(618\) 0 0
\(619\) 13.0490 + 17.5278i 0.524482 + 0.704502i 0.982880 0.184245i \(-0.0589840\pi\)
−0.458398 + 0.888747i \(0.651577\pi\)
\(620\) 2.88037 + 4.98895i 0.115679 + 0.200361i
\(621\) 0 0
\(622\) −1.02933 + 1.78285i −0.0412724 + 0.0714859i
\(623\) −27.1153 + 3.16932i −1.08635 + 0.126976i
\(624\) 0 0
\(625\) −6.17147 + 1.46267i −0.246859 + 0.0585066i
\(626\) 2.70689 1.78035i 0.108189 0.0711570i
\(627\) 0 0
\(628\) 10.0165 10.6169i 0.399704 0.423661i
\(629\) 9.84993 + 8.26507i 0.392742 + 0.329550i
\(630\) 0 0
\(631\) −18.5327 + 15.5508i −0.737775 + 0.619066i −0.932239 0.361843i \(-0.882148\pi\)
0.194464 + 0.980910i \(0.437703\pi\)
\(632\) −0.350063 + 6.01035i −0.0139248 + 0.239079i
\(633\) 0 0
\(634\) −2.03739 + 2.73669i −0.0809151 + 0.108688i
\(635\) −29.8515 3.48914i −1.18462 0.138462i
\(636\) 0 0
\(637\) 12.5292 + 8.24060i 0.496426 + 0.326504i
\(638\) 0.185390 + 0.0674764i 0.00733966 + 0.00267142i
\(639\) 0 0
\(640\) 8.53752 3.10740i 0.337475 0.122831i
\(641\) 34.7871 + 8.24470i 1.37401 + 0.325646i 0.850321 0.526264i \(-0.176408\pi\)
0.523688 + 0.851910i \(0.324556\pi\)
\(642\) 0 0
\(643\) −2.63836 45.2988i −0.104047 1.78641i −0.497896 0.867237i \(-0.665894\pi\)
0.393850 0.919175i \(-0.371143\pi\)
\(644\) 34.9858 + 37.0828i 1.37863 + 1.46127i
\(645\) 0 0
\(646\) 0.930345 2.15678i 0.0366039 0.0848575i
\(647\) 18.8974 0.742935 0.371468 0.928446i \(-0.378855\pi\)
0.371468 + 0.928446i \(0.378855\pi\)
\(648\) 0 0
\(649\) −29.7779 −1.16888
\(650\) −0.295653 + 0.685400i −0.0115965 + 0.0268836i
\(651\) 0 0
\(652\) 6.72585 + 7.12898i 0.263405 + 0.279192i
\(653\) 1.26424 + 21.7062i 0.0494737 + 0.849430i 0.928195 + 0.372095i \(0.121360\pi\)
−0.878721 + 0.477336i \(0.841603\pi\)
\(654\) 0 0
\(655\) 9.32948 + 2.21113i 0.364533 + 0.0863959i
\(656\) 10.6616 3.88051i 0.416266 0.151509i
\(657\) 0 0
\(658\) 0.0950565 + 0.0345978i 0.00370569 + 0.00134876i
\(659\) −13.6785 8.99649i −0.532839 0.350453i 0.254403 0.967098i \(-0.418121\pi\)
−0.787241 + 0.616645i \(0.788491\pi\)
\(660\) 0 0
\(661\) −20.5523 2.40222i −0.799392 0.0934355i −0.293418 0.955984i \(-0.594793\pi\)
−0.505974 + 0.862549i \(0.668867\pi\)
\(662\) −2.02287 + 2.71718i −0.0786210 + 0.105606i
\(663\) 0 0
\(664\) 0.236888 4.06721i 0.00919304 0.157838i
\(665\) 8.14001 6.83028i 0.315656 0.264867i
\(666\) 0 0
\(667\) −1.34519 1.12875i −0.0520860 0.0437054i
\(668\) 5.87999 6.23243i 0.227504 0.241140i
\(669\) 0 0
\(670\) 3.33461 2.19321i 0.128827 0.0847310i
\(671\) 15.4610 3.66431i 0.596863 0.141459i
\(672\) 0 0
\(673\) 23.8569 2.78847i 0.919615 0.107488i 0.356904 0.934141i \(-0.383832\pi\)
0.562711 + 0.826654i \(0.309758\pi\)
\(674\) −1.96673 + 3.40647i −0.0757555 + 0.131212i
\(675\) 0 0
\(676\) −10.2585 17.7683i −0.394559 0.683396i
\(677\) −27.0852 36.3818i −1.04097 1.39827i −0.913696 0.406399i \(-0.866784\pi\)
−0.127275 0.991867i \(-0.540623\pi\)
\(678\) 0 0
\(679\) 2.17214 7.25544i 0.0833589 0.278438i
\(680\) 7.95298 + 3.99413i 0.304983 + 0.153168i
\(681\) 0 0
\(682\) −0.382379 1.27724i −0.0146421 0.0489079i
\(683\) 3.38555 19.2004i 0.129544 0.734683i −0.848960 0.528457i \(-0.822771\pi\)
0.978504 0.206226i \(-0.0661181\pi\)
\(684\) 0 0
\(685\) 6.11698 + 34.6911i 0.233718 + 1.32548i
\(686\) 1.60998 0.808562i 0.0614693 0.0308710i
\(687\) 0 0
\(688\) −7.30928 16.9448i −0.278664 0.646015i
\(689\) 6.25757 + 14.5067i 0.238394 + 0.552660i
\(690\) 0 0
\(691\) 18.3456 9.21350i 0.697899 0.350498i −0.0642194 0.997936i \(-0.520456\pi\)
0.762118 + 0.647438i \(0.224159\pi\)
\(692\) −5.47393 31.0442i −0.208088 1.18012i
\(693\) 0 0
\(694\) −0.663458 + 3.76266i −0.0251845 + 0.142828i
\(695\) −5.77980 19.3059i −0.219240 0.732314i
\(696\) 0 0
\(697\) 20.2280 + 10.1589i 0.766190 + 0.384795i
\(698\) 0.951699 3.17889i 0.0360223 0.120323i
\(699\) 0 0
\(700\) −11.8267 15.8860i −0.447006 0.600433i
\(701\) 3.27119 + 5.66587i 0.123551 + 0.213997i 0.921166 0.389171i \(-0.127238\pi\)
−0.797615 + 0.603168i \(0.793905\pi\)
\(702\) 0 0
\(703\) 1.40923 2.44085i 0.0531500 0.0920585i
\(704\) 27.3773 3.19995i 1.03182 0.120603i
\(705\) 0 0
\(706\) 3.78905 0.898022i 0.142603 0.0337975i
\(707\) 56.4038 37.0974i 2.12128 1.39519i
\(708\) 0 0
\(709\) −6.58581 + 6.98055i −0.247335 + 0.262160i −0.839133 0.543927i \(-0.816937\pi\)
0.591798 + 0.806087i \(0.298418\pi\)
\(710\) 0.580522 + 0.487116i 0.0217866 + 0.0182811i
\(711\) 0 0
\(712\) −3.83925 + 3.22152i −0.143882 + 0.120731i
\(713\) −0.690003 + 11.8469i −0.0258408 + 0.443670i
\(714\) 0 0
\(715\) 5.81653 7.81296i 0.217526 0.292188i
\(716\) 37.6362 + 4.39904i 1.40653 + 0.164400i
\(717\) 0 0
\(718\) −3.07346 2.02145i −0.114700 0.0754397i
\(719\) −24.3548 8.86441i −0.908280 0.330587i −0.154714 0.987959i \(-0.549446\pi\)
−0.753566 + 0.657372i \(0.771668\pi\)
\(720\) 0 0
\(721\) −21.8878 + 7.96650i −0.815143 + 0.296688i
\(722\) 2.96312 + 0.702272i 0.110276 + 0.0261359i
\(723\) 0 0
\(724\) 0.0173055 + 0.297123i 0.000643152 + 0.0110425i
\(725\) 0.468129 + 0.496187i 0.0173859 + 0.0184279i
\(726\) 0 0
\(727\) −8.25148 + 19.1291i −0.306030 + 0.709458i −0.999944 0.0106003i \(-0.996626\pi\)
0.693913 + 0.720058i \(0.255885\pi\)
\(728\) 4.80845 0.178213
\(729\) 0 0
\(730\) −1.67136 −0.0618597
\(731\) 14.5825 33.8059i 0.539352 1.25036i
\(732\) 0 0
\(733\) −5.85032 6.20098i −0.216086 0.229038i 0.610259 0.792202i \(-0.291065\pi\)
−0.826345 + 0.563164i \(0.809584\pi\)
\(734\) −0.355239 6.09922i −0.0131121 0.225126i
\(735\) 0 0
\(736\) 13.7010 + 3.24719i 0.505024 + 0.119693i
\(737\) 48.5793 17.6814i 1.78944 0.651304i
\(738\) 0 0
\(739\) 34.6163 + 12.5993i 1.27338 + 0.463473i 0.888238 0.459384i \(-0.151930\pi\)
0.385143 + 0.922857i \(0.374152\pi\)
\(740\) 4.42148 + 2.90805i 0.162537 + 0.106902i
\(741\) 0 0
\(742\) 7.43910 + 0.869507i 0.273098 + 0.0319206i
\(743\) 17.8874 24.0269i 0.656223 0.881461i −0.342081 0.939670i \(-0.611132\pi\)
0.998304 + 0.0582096i \(0.0185392\pi\)
\(744\) 0 0
\(745\) −0.902417 + 15.4939i −0.0330620 + 0.567653i
\(746\) 2.54821 2.13820i 0.0932966 0.0782852i
\(747\) 0 0
\(748\) 43.7615 + 36.7203i 1.60008 + 1.34263i
\(749\) 4.50209 4.77194i 0.164503 0.174363i
\(750\) 0 0
\(751\) −5.85565 + 3.85132i −0.213676 + 0.140537i −0.651835 0.758360i \(-0.726001\pi\)
0.438160 + 0.898897i \(0.355630\pi\)
\(752\) −0.492069 + 0.116622i −0.0179439 + 0.00425278i
\(753\) 0 0
\(754\) −0.0815232 + 0.00952870i −0.00296890 + 0.000347015i
\(755\) −7.54205 + 13.0632i −0.274483 + 0.475419i
\(756\) 0 0
\(757\) −11.1739 19.3538i −0.406123 0.703426i 0.588328 0.808622i \(-0.299786\pi\)
−0.994452 + 0.105196i \(0.966453\pi\)
\(758\) −3.03749 4.08006i −0.110327 0.148194i
\(759\) 0 0
\(760\) 0.559483 1.86880i 0.0202946 0.0677886i
\(761\) −2.87464 1.44370i −0.104206 0.0523340i 0.395933 0.918279i \(-0.370421\pi\)
−0.500139 + 0.865945i \(0.666718\pi\)
\(762\) 0 0
\(763\) −13.3591 44.6226i −0.483633 1.61545i
\(764\) −3.65332 + 20.7190i −0.132172 + 0.749587i
\(765\) 0 0
\(766\) −1.15702 6.56181i −0.0418050 0.237088i
\(767\) 11.0708 5.55998i 0.399745 0.200759i
\(768\) 0 0
\(769\) −2.22533 5.15891i −0.0802476 0.186035i 0.873369 0.487060i \(-0.161931\pi\)
−0.953616 + 0.301025i \(0.902671\pi\)
\(770\) −1.82895 4.23998i −0.0659107 0.152798i
\(771\) 0 0
\(772\) −27.8673 + 13.9955i −1.00297 + 0.503709i
\(773\) 9.17966 + 52.0604i 0.330169 + 1.87248i 0.470531 + 0.882383i \(0.344062\pi\)
−0.140362 + 0.990100i \(0.544827\pi\)
\(774\) 0 0
\(775\) 0.800512 4.53993i 0.0287552 0.163079i
\(776\) −0.398767 1.33197i −0.0143149 0.0478150i
\(777\) 0 0
\(778\) −3.40701 1.71106i −0.122147 0.0613447i
\(779\) 1.42302 4.75320i 0.0509848 0.170301i
\(780\) 0 0
\(781\) 5.86158 + 7.87347i 0.209744 + 0.281735i
\(782\) 4.54265 + 7.86810i 0.162445 + 0.281363i
\(783\) 0 0
\(784\) −17.7703 + 30.7791i −0.634654 + 1.09925i
\(785\) 11.6877 1.36609i 0.417151 0.0487579i
\(786\) 0 0
\(787\) −14.9797 + 3.55026i −0.533969 + 0.126553i −0.488750 0.872424i \(-0.662547\pi\)
−0.0452195 + 0.998977i \(0.514399\pi\)
\(788\) 2.02159 1.32962i 0.0720161 0.0473657i
\(789\) 0 0
\(790\) −1.65064 + 1.74958i −0.0587272 + 0.0622472i
\(791\) −27.0645 22.7098i −0.962304 0.807469i
\(792\) 0 0
\(793\) −5.06389 + 4.24911i −0.179824 + 0.150890i
\(794\) 0.289257 4.96636i 0.0102654 0.176249i
\(795\) 0 0
\(796\) −2.74858 + 3.69199i −0.0974210 + 0.130859i
\(797\) 21.4001 + 2.50131i 0.758030 + 0.0886010i 0.486323 0.873779i \(-0.338338\pi\)
0.271707 + 0.962380i \(0.412412\pi\)
\(798\) 0 0
\(799\) −0.842926 0.554401i −0.0298206 0.0196133i
\(800\) −5.13998 1.87080i −0.181726 0.0661428i
\(801\) 0 0
\(802\) 4.52910 1.64846i 0.159928 0.0582091i
\(803\) −21.0651 4.99251i −0.743370 0.176182i
\(804\) 0 0
\(805\) 2.38979 + 41.0311i 0.0842290 + 1.44616i
\(806\) 0.380640 + 0.403455i 0.0134075 + 0.0142111i
\(807\) 0 0
\(808\) 4.90889 11.3801i 0.172694 0.400350i
\(809\) 19.2040 0.675177 0.337588 0.941294i \(-0.390389\pi\)
0.337588 + 0.941294i \(0.390389\pi\)
\(810\) 0 0
\(811\) −4.66474 −0.163801 −0.0819006 0.996641i \(-0.526099\pi\)
−0.0819006 + 0.996641i \(0.526099\pi\)
\(812\) 0.862549 1.99961i 0.0302695 0.0701727i
\(813\) 0 0
\(814\) −0.840497 0.890875i −0.0294594 0.0312251i
\(815\) 0.459425 + 7.88802i 0.0160930 + 0.276305i
\(816\) 0 0
\(817\) −7.85259 1.86110i −0.274727 0.0651116i
\(818\) −4.90382 + 1.78484i −0.171458 + 0.0624056i
\(819\) 0 0
\(820\) 8.75443 + 3.18635i 0.305718 + 0.111272i
\(821\) 35.2261 + 23.1686i 1.22940 + 0.808589i 0.986864 0.161553i \(-0.0516502\pi\)
0.242537 + 0.970142i \(0.422021\pi\)
\(822\) 0 0
\(823\) 8.45091 + 0.987770i 0.294580 + 0.0344315i 0.262099 0.965041i \(-0.415585\pi\)
0.0324808 + 0.999472i \(0.489659\pi\)
\(824\) −2.55351 + 3.42996i −0.0889557 + 0.119488i
\(825\) 0 0
\(826\) 0.341489 5.86314i 0.0118819 0.204005i
\(827\) 28.1921 23.6560i 0.980336 0.822600i −0.00380365 0.999993i \(-0.501211\pi\)
0.984140 + 0.177393i \(0.0567663\pi\)
\(828\) 0 0
\(829\) −16.2832 13.6632i −0.565537 0.474542i 0.314624 0.949216i \(-0.398121\pi\)
−0.880162 + 0.474674i \(0.842566\pi\)
\(830\) 1.11699 1.18394i 0.0387714 0.0410952i
\(831\) 0 0
\(832\) −9.58087 + 6.30144i −0.332157 + 0.218463i
\(833\) −68.9945 + 16.3520i −2.39052 + 0.566563i
\(834\) 0 0
\(835\) 6.86099 0.801935i 0.237434 0.0277521i
\(836\) 6.26095 10.8443i 0.216540 0.375058i
\(837\) 0 0
\(838\) −0.100997 0.174931i −0.00348887 0.00604290i
\(839\) 24.7813 + 33.2871i 0.855545 + 1.14920i 0.987450 + 0.157934i \(0.0504835\pi\)
−0.131904 + 0.991262i \(0.542109\pi\)
\(840\) 0 0
\(841\) 8.29578 27.7098i 0.286061 0.955512i
\(842\) −1.31571 0.660776i −0.0453425 0.0227719i
\(843\) 0 0
\(844\) −6.41837 21.4389i −0.220929 0.737956i
\(845\) 2.87223 16.2892i 0.0988076 0.560366i
\(846\) 0 0
\(847\) −2.65625 15.0643i −0.0912698 0.517617i
\(848\) −33.4598 + 16.8041i −1.14901 + 0.577056i
\(849\) 0 0
\(850\) −1.39791 3.24072i −0.0479480 0.111156i
\(851\) 4.31789 + 10.0100i 0.148015 + 0.343138i
\(852\) 0 0
\(853\) −20.4252 + 10.2579i −0.699346 + 0.351225i −0.762687 0.646767i \(-0.776120\pi\)
0.0633417 + 0.997992i \(0.479824\pi\)
\(854\) 0.544183 + 3.08622i 0.0186216 + 0.105608i
\(855\) 0 0
\(856\) 0.209141 1.18610i 0.00714829 0.0405400i
\(857\) 14.7869 + 49.3915i 0.505109 + 1.68718i 0.706534 + 0.707679i \(0.250258\pi\)
−0.201425 + 0.979504i \(0.564557\pi\)
\(858\) 0 0
\(859\) −23.7183 11.9118i −0.809257 0.406424i −0.00447138 0.999990i \(-0.501423\pi\)
−0.804785 + 0.593566i \(0.797720\pi\)
\(860\) 4.34591 14.5163i 0.148194 0.495003i
\(861\) 0 0
\(862\) 3.09820 + 4.16160i 0.105525 + 0.141745i
\(863\) −1.22953 2.12962i −0.0418538 0.0724930i 0.844340 0.535808i \(-0.179993\pi\)
−0.886193 + 0.463315i \(0.846660\pi\)
\(864\) 0 0
\(865\) 12.7067 22.0087i 0.432041 0.748317i
\(866\) −3.68307 + 0.430489i −0.125156 + 0.0146286i
\(867\) 0 0
\(868\) −14.3200 + 3.39391i −0.486053 + 0.115197i
\(869\) −26.0301 + 17.1203i −0.883012 + 0.580766i
\(870\) 0 0
\(871\) −14.7594 + 15.6441i −0.500105 + 0.530080i
\(872\) −6.55058 5.49659i −0.221831 0.186138i
\(873\) 0 0
\(874\) 1.52555 1.28008i 0.0516023 0.0432995i
\(875\) 2.79198 47.9365i 0.0943862 1.62055i
\(876\) 0 0
\(877\) 1.51036 2.02876i 0.0510011 0.0685064i −0.775891 0.630867i \(-0.782699\pi\)
0.826892 + 0.562361i \(0.190107\pi\)
\(878\) −6.26078 0.731780i −0.211291 0.0246964i
\(879\) 0 0
\(880\) 19.2866 + 12.6850i 0.650151 + 0.427611i
\(881\) −46.6808 16.9904i −1.57272 0.572421i −0.599111 0.800666i \(-0.704479\pi\)
−0.973604 + 0.228244i \(0.926702\pi\)
\(882\) 0 0
\(883\) 29.8038 10.8477i 1.00298 0.365054i 0.212245 0.977216i \(-0.431922\pi\)
0.790732 + 0.612162i \(0.209700\pi\)
\(884\) −23.1259 5.48094i −0.777809 0.184344i
\(885\) 0 0
\(886\) 0.172861 + 2.96790i 0.00580737 + 0.0997087i
\(887\) 1.98208 + 2.10088i 0.0665516 + 0.0705406i 0.759794 0.650164i \(-0.225300\pi\)
−0.693242 + 0.720705i \(0.743818\pi\)
\(888\) 0 0
\(889\) 30.4108 70.5002i 1.01995 2.36450i
\(890\) −2.00232 −0.0671179
\(891\) 0 0
\(892\) 29.7211 0.995137
\(893\) −0.0875919 + 0.203061i −0.00293115 + 0.00679518i
\(894\) 0 0
\(895\) 20.9634 + 22.2199i 0.700730 + 0.742731i
\(896\) 1.34955 + 23.1709i 0.0450853 + 0.774085i
\(897\) 0 0
\(898\) 0.160717 + 0.0380907i 0.00536321 + 0.00127110i
\(899\) 0.476334 0.173372i 0.0158866 0.00578227i
\(900\) 0 0
\(901\) −70.1950 25.5489i −2.33854 0.851157i
\(902\) −1.80141 1.18481i −0.0599805 0.0394498i
\(903\) 0 0
\(904\) −6.44217 0.752981i −0.214263 0.0250438i
\(905\) −0.143283 + 0.192463i −0.00476289 + 0.00639768i
\(906\) 0 0
\(907\) −1.79688 + 30.8512i −0.0596644 + 1.02440i 0.827064 + 0.562107i \(0.190009\pi\)
−0.886729 + 0.462290i \(0.847028\pi\)
\(908\) −32.0289 + 26.8755i −1.06292 + 0.891893i
\(909\) 0 0
\(910\) 1.47163 + 1.23485i 0.0487842 + 0.0409348i
\(911\) −29.3161 + 31.0733i −0.971287 + 1.02950i 0.0282657 + 0.999600i \(0.491002\pi\)
−0.999553 + 0.0299037i \(0.990480\pi\)
\(912\) 0 0
\(913\) 17.6146 11.5853i 0.582960 0.383419i
\(914\) 3.38591 0.802475i 0.111996 0.0265435i
\(915\) 0 0
\(916\) 7.61491 0.890055i 0.251604 0.0294083i
\(917\) −12.2469 + 21.2123i −0.404429 + 0.700491i
\(918\) 0 0
\(919\) −10.3318 17.8951i −0.340813 0.590306i 0.643771 0.765218i \(-0.277369\pi\)
−0.984584 + 0.174913i \(0.944036\pi\)
\(920\) 4.50578 + 6.05231i 0.148551 + 0.199539i
\(921\) 0 0
\(922\) 0.164983 0.551083i 0.00543344 0.0181489i
\(923\) −3.64932 1.83276i −0.120119 0.0603259i
\(924\) 0 0
\(925\) −1.21459 4.05702i −0.0399356 0.133394i
\(926\) 0.932434 5.28810i 0.0306417 0.173778i
\(927\) 0 0
\(928\) −0.104442 0.592319i −0.00342847 0.0194438i
\(929\) −37.6341 + 18.9005i −1.23473 + 0.620106i −0.941847 0.336041i \(-0.890912\pi\)
−0.292886 + 0.956147i \(0.594616\pi\)
\(930\) 0 0
\(931\) 6.15596 + 14.2711i 0.201754 + 0.467717i
\(932\) −15.0698 34.9356i −0.493626 1.14435i
\(933\) 0 0
\(934\) 2.32106 1.16568i 0.0759476 0.0381423i
\(935\) 7.99728 + 45.3548i 0.261539 + 1.48326i
\(936\) 0 0
\(937\) 5.62432 31.8971i 0.183738 1.04203i −0.743827 0.668372i \(-0.766991\pi\)
0.927566 0.373660i \(-0.121897\pi\)
\(938\) 2.92430 + 9.76783i 0.0954816 + 0.318931i
\(939\) 0 0
\(940\) −0.371071 0.186359i −0.0121030 0.00607835i
\(941\) 1.43114 4.78033i 0.0466538 0.155834i −0.931489 0.363770i \(-0.881489\pi\)
0.978142 + 0.207936i \(0.0666745\pi\)
\(942\) 0 0
\(943\) 11.4602 + 15.3938i 0.373196 + 0.501289i
\(944\) 14.6802 + 25.4269i 0.477800 + 0.827575i
\(945\) 0 0
\(946\) −1.75347 + 3.03710i −0.0570102 + 0.0987445i
\(947\) 1.36483 0.159526i 0.0443512 0.00518391i −0.0938884 0.995583i \(-0.529930\pi\)
0.138240 + 0.990399i \(0.455856\pi\)
\(948\) 0 0
\(949\) 8.76375 2.07705i 0.284483 0.0674238i
\(950\) −0.646352 + 0.425112i −0.0209704 + 0.0137925i
\(951\) 0 0
\(952\) −15.6020 + 16.5371i −0.505663 + 0.535972i
\(953\) −23.8952 20.0504i −0.774041 0.649497i 0.167699 0.985838i \(-0.446366\pi\)
−0.941740 + 0.336341i \(0.890811\pi\)
\(954\) 0 0
\(955\) −12.9929 + 10.9023i −0.420439 + 0.352790i
\(956\) 1.62226 27.8531i 0.0524676 0.900834i
\(957\) 0 0
\(958\) 2.84635 3.82332i 0.0919616 0.123526i
\(959\) −89.3826 10.4473i −2.88631 0.337362i
\(960\) 0 0
\(961\) 23.0381 + 15.1524i 0.743164 + 0.488787i
\(962\) 0.478820 + 0.174276i 0.0154378 + 0.00561889i
\(963\) 0 0
\(964\) −20.6201 + 7.50509i −0.664127 + 0.241723i
\(965\) −24.4626 5.79775i −0.787480 0.186636i
\(966\) 0 0
\(967\) −1.30389 22.3869i −0.0419303 0.719915i −0.952120 0.305724i \(-0.901102\pi\)
0.910190 0.414191i \(-0.135935\pi\)
\(968\) −1.92711 2.04262i −0.0619398 0.0656523i
\(969\) 0 0
\(970\) 0.220018 0.510059i 0.00706435 0.0163770i
\(971\) 25.8564 0.829773 0.414886 0.909873i \(-0.363821\pi\)
0.414886 + 0.909873i \(0.363821\pi\)
\(972\) 0 0
\(973\) 51.4827 1.65046
\(974\) 0.147114 0.341050i 0.00471385 0.0109279i
\(975\) 0 0
\(976\) −10.7510 11.3954i −0.344131 0.364758i
\(977\) 1.54843 + 26.5856i 0.0495388 + 0.850548i 0.927964 + 0.372669i \(0.121557\pi\)
−0.878426 + 0.477879i \(0.841406\pi\)
\(978\) 0 0
\(979\) −25.2364 5.98113i −0.806558 0.191158i
\(980\) −27.4230 + 9.98117i −0.875997 + 0.318837i
\(981\) 0 0
\(982\) 0.0824649 + 0.0300148i 0.00263156 + 0.000957810i
\(983\) −5.96401 3.92259i −0.190222 0.125111i 0.450826 0.892612i \(-0.351130\pi\)
−0.641048 + 0.767501i \(0.721500\pi\)
\(984\) 0 0
\(985\) 1.93749 + 0.226460i 0.0617336 + 0.00721562i
\(986\) 0.231748 0.311291i 0.00738034 0.00991352i
\(987\) 0 0
\(988\) −0.302907 + 5.20071i −0.00963675 + 0.165457i
\(989\) 23.9118 20.0644i 0.760350 0.638010i
\(990\) 0 0
\(991\) 33.2529 + 27.9025i 1.05631 + 0.886353i 0.993743 0.111688i \(-0.0356256\pi\)
0.0625710 + 0.998041i \(0.480070\pi\)
\(992\) −2.78927 + 2.95646i −0.0885595 + 0.0938676i
\(993\) 0 0
\(994\) −1.61747 + 1.06383i −0.0513031 + 0.0337426i
\(995\) −3.61065 + 0.855741i −0.114465 + 0.0271288i
\(996\) 0 0
\(997\) 2.80791 0.328198i 0.0889276 0.0103941i −0.0715128 0.997440i \(-0.522783\pi\)
0.160440 + 0.987046i \(0.448709\pi\)
\(998\) −2.21936 + 3.84405i −0.0702528 + 0.121681i
\(999\) 0 0
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 729.2.g.a.55.5 144
3.2 odd 2 729.2.g.d.55.4 144
9.2 odd 6 81.2.g.a.61.5 yes 144
9.4 even 3 729.2.g.b.541.5 144
9.5 odd 6 729.2.g.c.541.4 144
9.7 even 3 243.2.g.a.19.4 144
81.4 even 27 729.2.g.b.190.5 144
81.23 odd 54 81.2.g.a.4.5 144
81.29 odd 54 6561.2.a.c.1.40 72
81.31 even 27 inner 729.2.g.a.676.5 144
81.50 odd 54 729.2.g.d.676.4 144
81.52 even 27 6561.2.a.d.1.33 72
81.58 even 27 243.2.g.a.64.4 144
81.77 odd 54 729.2.g.c.190.4 144
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
81.2.g.a.4.5 144 81.23 odd 54
81.2.g.a.61.5 yes 144 9.2 odd 6
243.2.g.a.19.4 144 9.7 even 3
243.2.g.a.64.4 144 81.58 even 27
729.2.g.a.55.5 144 1.1 even 1 trivial
729.2.g.a.676.5 144 81.31 even 27 inner
729.2.g.b.190.5 144 81.4 even 27
729.2.g.b.541.5 144 9.4 even 3
729.2.g.c.190.4 144 81.77 odd 54
729.2.g.c.541.4 144 9.5 odd 6
729.2.g.d.55.4 144 3.2 odd 2
729.2.g.d.676.4 144 81.50 odd 54
6561.2.a.c.1.40 72 81.29 odd 54
6561.2.a.d.1.33 72 81.52 even 27