Properties

Label 324.3.f.p.271.1
Level $324$
Weight $3$
Character 324.271
Analytic conductor $8.828$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [324,3,Mod(55,324)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(324, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 4]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("324.55");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 324 = 2^{2} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 324.f (of order \(6\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(8.82836056527\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: 8.0.207360000.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} + 6x^{6} + 32x^{4} + 24x^{2} + 16 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{4}\cdot 3^{2} \)
Twist minimal: no (minimal twist has level 108)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 271.1
Root \(1.14412 - 1.98168i\) of defining polynomial
Character \(\chi\) \(=\) 324.271
Dual form 324.3.f.p.55.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.58114 - 1.22474i) q^{2} +(1.00000 + 3.87298i) q^{4} +(-0.540182 + 0.935622i) q^{5} +(-5.20820 + 3.00696i) q^{7} +(3.16228 - 7.34847i) q^{8} +O(q^{10})\) \(q+(-1.58114 - 1.22474i) q^{2} +(1.00000 + 3.87298i) q^{4} +(-0.540182 + 0.935622i) q^{5} +(-5.20820 + 3.00696i) q^{7} +(3.16228 - 7.34847i) q^{8} +(2.00000 - 0.817763i) q^{10} +(15.3500 - 8.86234i) q^{11} +(-6.20820 + 10.7529i) q^{13} +(11.9176 + 1.62430i) q^{14} +(-14.0000 + 7.74597i) q^{16} -26.3786 q^{17} -5.19615i q^{19} +(-4.16383 - 1.15649i) q^{20} +(-35.1246 - 4.78727i) q^{22} +(-25.8384 - 14.9178i) q^{23} +(11.9164 + 20.6398i) q^{25} +(22.9856 - 9.39840i) q^{26} +(-16.8541 - 17.1643i) q^{28} +(-2.16073 - 3.74249i) q^{29} +(-38.8328 - 22.4201i) q^{31} +(31.6228 + 4.89898i) q^{32} +(41.7082 + 32.3070i) q^{34} -6.49721i q^{35} -20.4164 q^{37} +(-6.36396 + 8.21584i) q^{38} +(5.16718 + 6.92820i) q^{40} +(-29.6197 + 51.3028i) q^{41} +(-16.5836 + 9.57454i) q^{43} +(49.6737 + 50.5880i) q^{44} +(22.5836 + 55.2326i) q^{46} +(-35.5617 + 20.5315i) q^{47} +(-6.41641 + 11.1135i) q^{49} +(6.43702 - 47.2290i) q^{50} +(-47.8541 - 13.2913i) q^{52} -70.0430 q^{53} +19.1491i q^{55} +(5.62675 + 47.7812i) q^{56} +(-1.16718 + 8.56373i) q^{58} +(25.0733 + 14.4761i) q^{59} +(-9.20820 - 15.9491i) q^{61} +(33.9411 + 83.0096i) q^{62} +(-44.0000 - 46.4758i) q^{64} +(-6.70711 - 11.6171i) q^{65} +(82.1656 + 47.4383i) q^{67} +(-26.3786 - 102.164i) q^{68} +(-7.95743 + 10.2730i) q^{70} -83.8931i q^{71} +55.8328 q^{73} +(32.2812 + 25.0049i) q^{74} +(20.1246 - 5.19615i) q^{76} +(-53.2974 + 92.3137i) q^{77} +(35.5426 - 20.5205i) q^{79} +(0.315246 - 17.2829i) q^{80} +(109.666 - 44.8403i) q^{82} +(-30.7000 + 17.7247i) q^{83} +(14.2492 - 24.6804i) q^{85} +(37.9473 + 5.17199i) q^{86} +(-16.5836 - 140.824i) q^{88} -26.3786 q^{89} -74.6712i q^{91} +(31.9380 - 114.990i) q^{92} +(81.3738 + 11.0908i) q^{94} +(4.86163 + 2.80687i) q^{95} +(-38.1656 - 66.1048i) q^{97} +(23.7565 - 9.71359i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 8 q^{4} + 12 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 8 q^{4} + 12 q^{7} + 16 q^{10} + 4 q^{13} - 112 q^{16} - 120 q^{22} - 12 q^{25} - 108 q^{28} - 96 q^{31} + 280 q^{34} - 56 q^{37} + 256 q^{40} - 240 q^{43} + 288 q^{46} + 56 q^{49} - 356 q^{52} - 224 q^{58} - 20 q^{61} - 352 q^{64} + 228 q^{67} + 312 q^{70} + 232 q^{73} + 660 q^{79} + 448 q^{82} - 208 q^{85} - 240 q^{88} + 168 q^{94} + 124 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/324\mathbb{Z}\right)^\times\).

\(n\) \(163\) \(245\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.58114 1.22474i −0.790569 0.612372i
\(3\) 0 0
\(4\) 1.00000 + 3.87298i 0.250000 + 0.968246i
\(5\) −0.540182 + 0.935622i −0.108036 + 0.187124i −0.914975 0.403511i \(-0.867790\pi\)
0.806938 + 0.590636i \(0.201123\pi\)
\(6\) 0 0
\(7\) −5.20820 + 3.00696i −0.744029 + 0.429565i −0.823532 0.567269i \(-0.808000\pi\)
0.0795033 + 0.996835i \(0.474667\pi\)
\(8\) 3.16228 7.34847i 0.395285 0.918559i
\(9\) 0 0
\(10\) 2.00000 0.817763i 0.200000 0.0817763i
\(11\) 15.3500 8.86234i 1.39546 0.805667i 0.401544 0.915840i \(-0.368474\pi\)
0.993912 + 0.110173i \(0.0351404\pi\)
\(12\) 0 0
\(13\) −6.20820 + 10.7529i −0.477554 + 0.827148i −0.999669 0.0257271i \(-0.991810\pi\)
0.522115 + 0.852875i \(0.325143\pi\)
\(14\) 11.9176 + 1.62430i 0.851261 + 0.116022i
\(15\) 0 0
\(16\) −14.0000 + 7.74597i −0.875000 + 0.484123i
\(17\) −26.3786 −1.55168 −0.775841 0.630929i \(-0.782674\pi\)
−0.775841 + 0.630929i \(0.782674\pi\)
\(18\) 0 0
\(19\) 5.19615i 0.273482i −0.990607 0.136741i \(-0.956337\pi\)
0.990607 0.136741i \(-0.0436628\pi\)
\(20\) −4.16383 1.15649i −0.208191 0.0578246i
\(21\) 0 0
\(22\) −35.1246 4.78727i −1.59657 0.217603i
\(23\) −25.8384 14.9178i −1.12341 0.648600i −0.181140 0.983457i \(-0.557979\pi\)
−0.942269 + 0.334857i \(0.891312\pi\)
\(24\) 0 0
\(25\) 11.9164 + 20.6398i 0.476656 + 0.825593i
\(26\) 22.9856 9.39840i 0.884062 0.361477i
\(27\) 0 0
\(28\) −16.8541 17.1643i −0.601932 0.613012i
\(29\) −2.16073 3.74249i −0.0745078 0.129051i 0.826364 0.563136i \(-0.190405\pi\)
−0.900872 + 0.434085i \(0.857072\pi\)
\(30\) 0 0
\(31\) −38.8328 22.4201i −1.25267 0.723230i −0.281032 0.959698i \(-0.590677\pi\)
−0.971639 + 0.236468i \(0.924010\pi\)
\(32\) 31.6228 + 4.89898i 0.988212 + 0.153093i
\(33\) 0 0
\(34\) 41.7082 + 32.3070i 1.22671 + 0.950207i
\(35\) 6.49721i 0.185635i
\(36\) 0 0
\(37\) −20.4164 −0.551795 −0.275897 0.961187i \(-0.588975\pi\)
−0.275897 + 0.961187i \(0.588975\pi\)
\(38\) −6.36396 + 8.21584i −0.167473 + 0.216206i
\(39\) 0 0
\(40\) 5.16718 + 6.92820i 0.129180 + 0.173205i
\(41\) −29.6197 + 51.3028i −0.722431 + 1.25129i 0.237592 + 0.971365i \(0.423642\pi\)
−0.960023 + 0.279922i \(0.909691\pi\)
\(42\) 0 0
\(43\) −16.5836 + 9.57454i −0.385665 + 0.222664i −0.680280 0.732952i \(-0.738142\pi\)
0.294615 + 0.955616i \(0.404809\pi\)
\(44\) 49.6737 + 50.5880i 1.12895 + 1.14973i
\(45\) 0 0
\(46\) 22.5836 + 55.2326i 0.490948 + 1.20071i
\(47\) −35.5617 + 20.5315i −0.756631 + 0.436841i −0.828085 0.560603i \(-0.810570\pi\)
0.0714537 + 0.997444i \(0.477236\pi\)
\(48\) 0 0
\(49\) −6.41641 + 11.1135i −0.130947 + 0.226807i
\(50\) 6.43702 47.2290i 0.128740 0.944580i
\(51\) 0 0
\(52\) −47.8541 13.2913i −0.920271 0.255603i
\(53\) −70.0430 −1.32157 −0.660783 0.750577i \(-0.729776\pi\)
−0.660783 + 0.750577i \(0.729776\pi\)
\(54\) 0 0
\(55\) 19.1491i 0.348165i
\(56\) 5.62675 + 47.7812i 0.100478 + 0.853235i
\(57\) 0 0
\(58\) −1.16718 + 8.56373i −0.0201239 + 0.147651i
\(59\) 25.0733 + 14.4761i 0.424971 + 0.245357i 0.697202 0.716875i \(-0.254428\pi\)
−0.272231 + 0.962232i \(0.587761\pi\)
\(60\) 0 0
\(61\) −9.20820 15.9491i −0.150954 0.261460i 0.780624 0.625001i \(-0.214901\pi\)
−0.931578 + 0.363540i \(0.881568\pi\)
\(62\) 33.9411 + 83.0096i 0.547438 + 1.33887i
\(63\) 0 0
\(64\) −44.0000 46.4758i −0.687500 0.726184i
\(65\) −6.70711 11.6171i −0.103186 0.178724i
\(66\) 0 0
\(67\) 82.1656 + 47.4383i 1.22635 + 0.708035i 0.966265 0.257550i \(-0.0829152\pi\)
0.260088 + 0.965585i \(0.416249\pi\)
\(68\) −26.3786 102.164i −0.387920 1.50241i
\(69\) 0 0
\(70\) −7.95743 + 10.2730i −0.113678 + 0.146757i
\(71\) 83.8931i 1.18159i −0.806821 0.590797i \(-0.798814\pi\)
0.806821 0.590797i \(-0.201186\pi\)
\(72\) 0 0
\(73\) 55.8328 0.764833 0.382417 0.923990i \(-0.375092\pi\)
0.382417 + 0.923990i \(0.375092\pi\)
\(74\) 32.2812 + 25.0049i 0.436232 + 0.337904i
\(75\) 0 0
\(76\) 20.1246 5.19615i 0.264798 0.0683704i
\(77\) −53.2974 + 92.3137i −0.692173 + 1.19888i
\(78\) 0 0
\(79\) 35.5426 20.5205i 0.449906 0.259753i −0.257885 0.966176i \(-0.583025\pi\)
0.707790 + 0.706422i \(0.249692\pi\)
\(80\) 0.315246 17.2829i 0.00394057 0.216037i
\(81\) 0 0
\(82\) 109.666 44.8403i 1.33739 0.546833i
\(83\) −30.7000 + 17.7247i −0.369880 + 0.213550i −0.673406 0.739273i \(-0.735169\pi\)
0.303526 + 0.952823i \(0.401836\pi\)
\(84\) 0 0
\(85\) 14.2492 24.6804i 0.167638 0.290357i
\(86\) 37.9473 + 5.17199i 0.441248 + 0.0601394i
\(87\) 0 0
\(88\) −16.5836 140.824i −0.188450 1.60028i
\(89\) −26.3786 −0.296389 −0.148194 0.988958i \(-0.547346\pi\)
−0.148194 + 0.988958i \(0.547346\pi\)
\(90\) 0 0
\(91\) 74.6712i 0.820563i
\(92\) 31.9380 114.990i 0.347152 1.24989i
\(93\) 0 0
\(94\) 81.3738 + 11.0908i 0.865679 + 0.117987i
\(95\) 4.86163 + 2.80687i 0.0511751 + 0.0295460i
\(96\) 0 0
\(97\) −38.1656 66.1048i −0.393460 0.681493i 0.599443 0.800417i \(-0.295389\pi\)
−0.992903 + 0.118924i \(0.962055\pi\)
\(98\) 23.7565 9.71359i 0.242413 0.0991183i
\(99\) 0 0
\(100\) −68.0213 + 66.7919i −0.680213 + 0.667919i
\(101\) −36.1019 62.5302i −0.357444 0.619111i 0.630089 0.776523i \(-0.283018\pi\)
−0.987533 + 0.157412i \(0.949685\pi\)
\(102\) 0 0
\(103\) −50.2082 28.9877i −0.487458 0.281434i 0.236061 0.971738i \(-0.424143\pi\)
−0.723519 + 0.690304i \(0.757477\pi\)
\(104\) 59.3855 + 79.6245i 0.571014 + 0.765620i
\(105\) 0 0
\(106\) 110.748 + 85.7848i 1.04479 + 0.809290i
\(107\) 64.4015i 0.601883i −0.953643 0.300942i \(-0.902699\pi\)
0.953643 0.300942i \(-0.0973009\pi\)
\(108\) 0 0
\(109\) −43.1672 −0.396029 −0.198015 0.980199i \(-0.563449\pi\)
−0.198015 + 0.980199i \(0.563449\pi\)
\(110\) 23.4527 30.2774i 0.213207 0.275249i
\(111\) 0 0
\(112\) 49.6231 82.4400i 0.443063 0.736071i
\(113\) 40.6482 70.4048i 0.359719 0.623051i −0.628195 0.778056i \(-0.716206\pi\)
0.987914 + 0.155005i \(0.0495392\pi\)
\(114\) 0 0
\(115\) 27.9149 16.1166i 0.242738 0.140145i
\(116\) 12.3339 12.1109i 0.106326 0.104405i
\(117\) 0 0
\(118\) −21.9149 53.5971i −0.185719 0.454212i
\(119\) 137.385 79.3193i 1.15450 0.666549i
\(120\) 0 0
\(121\) 96.5820 167.285i 0.798199 1.38252i
\(122\) −4.97410 + 36.4954i −0.0407713 + 0.299143i
\(123\) 0 0
\(124\) 48.0000 172.819i 0.387097 1.39370i
\(125\) −52.7572 −0.422057
\(126\) 0 0
\(127\) 191.968i 1.51156i 0.654826 + 0.755780i \(0.272742\pi\)
−0.654826 + 0.755780i \(0.727258\pi\)
\(128\) 12.6491 + 127.373i 0.0988212 + 0.995105i
\(129\) 0 0
\(130\) −3.62306 + 26.5827i −0.0278697 + 0.204482i
\(131\) −122.800 70.8987i −0.937406 0.541211i −0.0482596 0.998835i \(-0.515367\pi\)
−0.889146 + 0.457623i \(0.848701\pi\)
\(132\) 0 0
\(133\) 15.6246 + 27.0626i 0.117478 + 0.203478i
\(134\) −71.8154 175.639i −0.535936 1.31074i
\(135\) 0 0
\(136\) −83.4164 + 193.842i −0.613356 + 1.42531i
\(137\) 43.8893 + 76.0185i 0.320360 + 0.554880i 0.980562 0.196208i \(-0.0628628\pi\)
−0.660202 + 0.751088i \(0.729529\pi\)
\(138\) 0 0
\(139\) 158.916 + 91.7504i 1.14328 + 0.660075i 0.947242 0.320520i \(-0.103858\pi\)
0.196042 + 0.980596i \(0.437191\pi\)
\(140\) 25.1636 6.49721i 0.179740 0.0464087i
\(141\) 0 0
\(142\) −102.748 + 132.647i −0.723575 + 0.934131i
\(143\) 220.077i 1.53900i
\(144\) 0 0
\(145\) 4.66874 0.0321982
\(146\) −88.2794 68.3810i −0.604654 0.468363i
\(147\) 0 0
\(148\) −20.4164 79.0724i −0.137949 0.534273i
\(149\) 76.9750 133.325i 0.516611 0.894796i −0.483203 0.875508i \(-0.660527\pi\)
0.999814 0.0192880i \(-0.00613996\pi\)
\(150\) 0 0
\(151\) 160.539 92.6875i 1.06318 0.613825i 0.136866 0.990590i \(-0.456297\pi\)
0.926309 + 0.376765i \(0.122964\pi\)
\(152\) −38.1838 16.4317i −0.251209 0.108103i
\(153\) 0 0
\(154\) 197.331 80.6851i 1.28137 0.523930i
\(155\) 41.9535 24.2219i 0.270668 0.156270i
\(156\) 0 0
\(157\) −98.0820 + 169.883i −0.624726 + 1.08206i 0.363867 + 0.931451i \(0.381456\pi\)
−0.988594 + 0.150607i \(0.951877\pi\)
\(158\) −81.3301 11.0848i −0.514748 0.0701570i
\(159\) 0 0
\(160\) −21.6656 + 26.9406i −0.135410 + 0.168379i
\(161\) 179.429 1.11447
\(162\) 0 0
\(163\) 129.325i 0.793403i −0.917948 0.396701i \(-0.870155\pi\)
0.917948 0.396701i \(-0.129845\pi\)
\(164\) −228.314 63.4137i −1.39216 0.386669i
\(165\) 0 0
\(166\) 70.2492 + 9.57454i 0.423188 + 0.0576780i
\(167\) 119.469 + 68.9753i 0.715382 + 0.413026i 0.813051 0.582193i \(-0.197805\pi\)
−0.0976688 + 0.995219i \(0.531139\pi\)
\(168\) 0 0
\(169\) 7.41641 + 12.8456i 0.0438841 + 0.0760094i
\(170\) −52.7572 + 21.5714i −0.310336 + 0.126891i
\(171\) 0 0
\(172\) −53.6656 54.6534i −0.312009 0.317753i
\(173\) 80.2161 + 138.938i 0.463677 + 0.803112i 0.999141 0.0414461i \(-0.0131965\pi\)
−0.535464 + 0.844558i \(0.679863\pi\)
\(174\) 0 0
\(175\) −124.126 71.6643i −0.709292 0.409510i
\(176\) −146.253 + 242.973i −0.830982 + 1.38053i
\(177\) 0 0
\(178\) 41.7082 + 32.3070i 0.234316 + 0.181500i
\(179\) 201.469i 1.12552i 0.826619 + 0.562762i \(0.190261\pi\)
−0.826619 + 0.562762i \(0.809739\pi\)
\(180\) 0 0
\(181\) −48.2523 −0.266587 −0.133294 0.991077i \(-0.542555\pi\)
−0.133294 + 0.991077i \(0.542555\pi\)
\(182\) −91.4532 + 118.066i −0.502490 + 0.648712i
\(183\) 0 0
\(184\) −191.331 + 142.698i −1.03984 + 0.775535i
\(185\) 11.0286 19.1020i 0.0596139 0.103254i
\(186\) 0 0
\(187\) −404.912 + 233.776i −2.16530 + 1.25014i
\(188\) −115.080 117.198i −0.612128 0.623395i
\(189\) 0 0
\(190\) −4.24922 10.3923i −0.0223643 0.0546963i
\(191\) −127.662 + 73.7056i −0.668386 + 0.385893i −0.795465 0.606000i \(-0.792773\pi\)
0.127079 + 0.991893i \(0.459440\pi\)
\(192\) 0 0
\(193\) −12.5820 + 21.7927i −0.0651919 + 0.112916i −0.896779 0.442479i \(-0.854099\pi\)
0.831587 + 0.555394i \(0.187433\pi\)
\(194\) −20.6164 + 151.264i −0.106270 + 0.779712i
\(195\) 0 0
\(196\) −49.4590 13.7371i −0.252342 0.0700872i
\(197\) 385.506 1.95688 0.978441 0.206528i \(-0.0662165\pi\)
0.978441 + 0.206528i \(0.0662165\pi\)
\(198\) 0 0
\(199\) 121.386i 0.609978i −0.952356 0.304989i \(-0.901347\pi\)
0.952356 0.304989i \(-0.0986528\pi\)
\(200\) 189.354 22.2985i 0.946771 0.111493i
\(201\) 0 0
\(202\) −19.5016 + 143.085i −0.0965423 + 0.708339i
\(203\) 22.5070 + 12.9944i 0.110872 + 0.0640119i
\(204\) 0 0
\(205\) −32.0000 55.4256i −0.156098 0.270369i
\(206\) 43.8836 + 107.326i 0.213027 + 0.520999i
\(207\) 0 0
\(208\) 3.62306 198.629i 0.0174186 0.954949i
\(209\) −46.0501 79.7610i −0.220335 0.381632i
\(210\) 0 0
\(211\) −226.579 130.815i −1.07383 0.619978i −0.144607 0.989489i \(-0.546192\pi\)
−0.929226 + 0.369511i \(0.879525\pi\)
\(212\) −70.0430 271.275i −0.330391 1.27960i
\(213\) 0 0
\(214\) −78.8754 + 101.828i −0.368577 + 0.475830i
\(215\) 20.6880i 0.0962231i
\(216\) 0 0
\(217\) 269.666 1.24270
\(218\) 68.2533 + 52.8688i 0.313089 + 0.242517i
\(219\) 0 0
\(220\) −74.1641 + 19.1491i −0.337109 + 0.0870413i
\(221\) 163.764 283.647i 0.741012 1.28347i
\(222\) 0 0
\(223\) 60.6687 35.0271i 0.272057 0.157072i −0.357765 0.933812i \(-0.616461\pi\)
0.629822 + 0.776739i \(0.283128\pi\)
\(224\) −179.429 + 69.5735i −0.801022 + 0.310596i
\(225\) 0 0
\(226\) −150.498 + 61.5361i −0.665922 + 0.272283i
\(227\) −258.384 + 149.178i −1.13826 + 0.657172i −0.945998 0.324172i \(-0.894914\pi\)
−0.192258 + 0.981344i \(0.561581\pi\)
\(228\) 0 0
\(229\) −129.833 + 224.877i −0.566956 + 0.981996i 0.429909 + 0.902872i \(0.358546\pi\)
−0.996865 + 0.0791237i \(0.974788\pi\)
\(230\) −63.8760 8.70592i −0.277722 0.0378518i
\(231\) 0 0
\(232\) −34.3344 + 4.04324i −0.147993 + 0.0174278i
\(233\) 7.38192 0.0316821 0.0158410 0.999875i \(-0.494957\pi\)
0.0158410 + 0.999875i \(0.494957\pi\)
\(234\) 0 0
\(235\) 44.3630i 0.188779i
\(236\) −30.9923 + 111.584i −0.131323 + 0.472816i
\(237\) 0 0
\(238\) −314.371 42.8468i −1.32089 0.180029i
\(239\) 71.1233 + 41.0631i 0.297587 + 0.171812i 0.641358 0.767241i \(-0.278371\pi\)
−0.343771 + 0.939053i \(0.611704\pi\)
\(240\) 0 0
\(241\) 207.913 + 360.116i 0.862711 + 1.49426i 0.869302 + 0.494281i \(0.164568\pi\)
−0.00659158 + 0.999978i \(0.502098\pi\)
\(242\) −357.591 + 146.212i −1.47765 + 0.604184i
\(243\) 0 0
\(244\) 52.5623 51.6123i 0.215419 0.211526i
\(245\) −6.93205 12.0067i −0.0282941 0.0490068i
\(246\) 0 0
\(247\) 55.8738 + 32.2588i 0.226210 + 0.130602i
\(248\) −287.554 + 214.463i −1.15949 + 0.864770i
\(249\) 0 0
\(250\) 83.4164 + 64.6141i 0.333666 + 0.258456i
\(251\) 140.030i 0.557890i −0.960307 0.278945i \(-0.910015\pi\)
0.960307 0.278945i \(-0.0899847\pi\)
\(252\) 0 0
\(253\) −528.827 −2.09022
\(254\) 235.112 303.528i 0.925637 1.19499i
\(255\) 0 0
\(256\) 136.000 216.887i 0.531250 0.847215i
\(257\) 33.4913 58.0086i 0.130316 0.225714i −0.793482 0.608593i \(-0.791734\pi\)
0.923798 + 0.382879i \(0.125067\pi\)
\(258\) 0 0
\(259\) 106.333 61.3913i 0.410551 0.237032i
\(260\) 38.2856 37.5936i 0.147252 0.144591i
\(261\) 0 0
\(262\) 107.331 + 262.500i 0.409661 + 1.00191i
\(263\) 32.2303 18.6082i 0.122549 0.0707534i −0.437473 0.899232i \(-0.644126\pi\)
0.560021 + 0.828478i \(0.310793\pi\)
\(264\) 0 0
\(265\) 37.8359 65.5337i 0.142777 0.247297i
\(266\) 8.44013 61.9259i 0.0317298 0.232804i
\(267\) 0 0
\(268\) −101.562 + 365.664i −0.378964 + 1.36442i
\(269\) 279.092 1.03752 0.518758 0.854921i \(-0.326395\pi\)
0.518758 + 0.854921i \(0.326395\pi\)
\(270\) 0 0
\(271\) 406.305i 1.49928i 0.661845 + 0.749641i \(0.269774\pi\)
−0.661845 + 0.749641i \(0.730226\pi\)
\(272\) 369.300 204.328i 1.35772 0.751205i
\(273\) 0 0
\(274\) 23.7082 173.949i 0.0865263 0.634851i
\(275\) 365.834 + 211.214i 1.33031 + 0.768053i
\(276\) 0 0
\(277\) −2.41641 4.18534i −0.00872349 0.0151095i 0.861631 0.507536i \(-0.169443\pi\)
−0.870354 + 0.492426i \(0.836110\pi\)
\(278\) −138.898 339.702i −0.499633 1.22195i
\(279\) 0 0
\(280\) −47.7446 20.5460i −0.170516 0.0733785i
\(281\) −2.16073 3.74249i −0.00768942 0.0133185i 0.862155 0.506644i \(-0.169114\pi\)
−0.869845 + 0.493326i \(0.835781\pi\)
\(282\) 0 0
\(283\) 38.4195 + 22.1815i 0.135758 + 0.0783799i 0.566341 0.824171i \(-0.308359\pi\)
−0.430583 + 0.902551i \(0.641692\pi\)
\(284\) 324.917 83.8931i 1.14407 0.295398i
\(285\) 0 0
\(286\) 269.538 347.972i 0.942440 1.21669i
\(287\) 356.260i 1.24133i
\(288\) 0 0
\(289\) 406.830 1.40772
\(290\) −7.38192 5.71801i −0.0254549 0.0197173i
\(291\) 0 0
\(292\) 55.8328 + 216.240i 0.191208 + 0.740546i
\(293\) −194.464 + 336.821i −0.663699 + 1.14956i 0.315938 + 0.948780i \(0.397681\pi\)
−0.979636 + 0.200780i \(0.935652\pi\)
\(294\) 0 0
\(295\) −27.0883 + 15.6394i −0.0918246 + 0.0530149i
\(296\) −64.5624 + 150.029i −0.218116 + 0.506856i
\(297\) 0 0
\(298\) −284.997 + 116.530i −0.956365 + 0.391040i
\(299\) 320.820 185.226i 1.07298 0.619484i
\(300\) 0 0
\(301\) 57.5805 99.7323i 0.191297 0.331337i
\(302\) −367.354 50.0681i −1.21640 0.165788i
\(303\) 0 0
\(304\) 40.2492 + 72.7461i 0.132399 + 0.239296i
\(305\) 19.8964 0.0652341
\(306\) 0 0
\(307\) 96.6999i 0.314983i −0.987520 0.157492i \(-0.949659\pi\)
0.987520 0.157492i \(-0.0503407\pi\)
\(308\) −410.827 114.106i −1.33385 0.370474i
\(309\) 0 0
\(310\) −96.0000 13.0842i −0.309677 0.0422071i
\(311\) −117.939 68.0918i −0.379224 0.218945i 0.298257 0.954486i \(-0.403595\pi\)
−0.677480 + 0.735541i \(0.736928\pi\)
\(312\) 0 0
\(313\) −141.080 244.359i −0.450736 0.780698i 0.547696 0.836678i \(-0.315505\pi\)
−0.998432 + 0.0559794i \(0.982172\pi\)
\(314\) 363.145 148.483i 1.15651 0.472877i
\(315\) 0 0
\(316\) 115.018 + 117.135i 0.363982 + 0.370681i
\(317\) −137.745 238.581i −0.434526 0.752620i 0.562731 0.826640i \(-0.309751\pi\)
−0.997257 + 0.0740196i \(0.976417\pi\)
\(318\) 0 0
\(319\) −66.3344 38.2982i −0.207945 0.120057i
\(320\) 67.2518 16.0620i 0.210162 0.0501937i
\(321\) 0 0
\(322\) −283.702 219.755i −0.881062 0.682468i
\(323\) 137.067i 0.424356i
\(324\) 0 0
\(325\) −295.918 −0.910517
\(326\) −158.390 + 204.480i −0.485858 + 0.627240i
\(327\) 0 0
\(328\) 283.331 + 379.893i 0.863815 + 1.15821i
\(329\) 123.475 213.865i 0.375304 0.650045i
\(330\) 0 0
\(331\) −48.0836 + 27.7611i −0.145268 + 0.0838703i −0.570872 0.821039i \(-0.693395\pi\)
0.425605 + 0.904909i \(0.360061\pi\)
\(332\) −99.3474 101.176i −0.299239 0.304747i
\(333\) 0 0
\(334\) −104.420 255.378i −0.312633 0.764606i
\(335\) −88.7687 + 51.2506i −0.264981 + 0.152987i
\(336\) 0 0
\(337\) 215.330 372.962i 0.638961 1.10671i −0.346701 0.937976i \(-0.612698\pi\)
0.985661 0.168736i \(-0.0539686\pi\)
\(338\) 4.00621 29.3939i 0.0118527 0.0869641i
\(339\) 0 0
\(340\) 109.836 + 30.5066i 0.323047 + 0.0897254i
\(341\) −794.779 −2.33073
\(342\) 0 0
\(343\) 371.857i 1.08413i
\(344\) 17.9163 + 152.141i 0.0520823 + 0.442271i
\(345\) 0 0
\(346\) 43.3313 317.925i 0.125235 0.918859i
\(347\) −117.668 67.9354i −0.339100 0.195779i 0.320774 0.947156i \(-0.396057\pi\)
−0.659874 + 0.751376i \(0.729390\pi\)
\(348\) 0 0
\(349\) −144.041 249.486i −0.412725 0.714861i 0.582462 0.812858i \(-0.302090\pi\)
−0.995187 + 0.0979975i \(0.968756\pi\)
\(350\) 108.490 + 265.334i 0.309972 + 0.758097i
\(351\) 0 0
\(352\) 528.827 205.052i 1.50235 0.582535i
\(353\) 99.4820 + 172.308i 0.281819 + 0.488124i 0.971833 0.235672i \(-0.0757290\pi\)
−0.690014 + 0.723796i \(0.742396\pi\)
\(354\) 0 0
\(355\) 78.4922 + 45.3175i 0.221105 + 0.127655i
\(356\) −26.3786 102.164i −0.0740971 0.286977i
\(357\) 0 0
\(358\) 246.748 318.550i 0.689239 0.889804i
\(359\) 324.658i 0.904339i 0.891932 + 0.452170i \(0.149350\pi\)
−0.891932 + 0.452170i \(0.850650\pi\)
\(360\) 0 0
\(361\) 334.000 0.925208
\(362\) 76.2936 + 59.0968i 0.210756 + 0.163251i
\(363\) 0 0
\(364\) 289.200 74.6712i 0.794507 0.205141i
\(365\) −30.1599 + 52.2384i −0.0826297 + 0.143119i
\(366\) 0 0
\(367\) 152.543 88.0705i 0.415647 0.239974i −0.277566 0.960707i \(-0.589528\pi\)
0.693213 + 0.720732i \(0.256194\pi\)
\(368\) 477.290 + 8.70592i 1.29699 + 0.0236574i
\(369\) 0 0
\(370\) −40.8328 + 16.6958i −0.110359 + 0.0451238i
\(371\) 364.798 210.616i 0.983283 0.567699i
\(372\) 0 0
\(373\) −298.290 + 516.654i −0.799706 + 1.38513i 0.120102 + 0.992762i \(0.461678\pi\)
−0.919808 + 0.392369i \(0.871655\pi\)
\(374\) 926.538 + 126.281i 2.47737 + 0.337651i
\(375\) 0 0
\(376\) 38.4195 + 326.250i 0.102180 + 0.867687i
\(377\) 53.6569 0.142326
\(378\) 0 0
\(379\) 30.3082i 0.0799689i 0.999200 + 0.0399844i \(0.0127308\pi\)
−0.999200 + 0.0399844i \(0.987269\pi\)
\(380\) −6.00931 + 21.6359i −0.0158140 + 0.0569366i
\(381\) 0 0
\(382\) 292.122 + 39.8144i 0.764716 + 0.104226i
\(383\) −612.470 353.610i −1.59914 0.923264i −0.991653 0.128934i \(-0.958845\pi\)
−0.607486 0.794330i \(-0.707822\pi\)
\(384\) 0 0
\(385\) −57.5805 99.7323i −0.149560 0.259045i
\(386\) 46.5845 19.0475i 0.120685 0.0493460i
\(387\) 0 0
\(388\) 217.857 213.920i 0.561488 0.551339i
\(389\) 288.544 + 499.773i 0.741758 + 1.28476i 0.951694 + 0.307048i \(0.0993411\pi\)
−0.209936 + 0.977715i \(0.567326\pi\)
\(390\) 0 0
\(391\) 681.580 + 393.511i 1.74317 + 1.00642i
\(392\) 61.3771 + 82.2949i 0.156574 + 0.209936i
\(393\) 0 0
\(394\) −609.538 472.146i −1.54705 1.19834i
\(395\) 44.3392i 0.112251i
\(396\) 0 0
\(397\) 26.8266 0.0675733 0.0337867 0.999429i \(-0.489243\pi\)
0.0337867 + 0.999429i \(0.489243\pi\)
\(398\) −148.666 + 191.928i −0.373534 + 0.482230i
\(399\) 0 0
\(400\) −326.705 196.653i −0.816763 0.491634i
\(401\) −252.532 + 437.399i −0.629756 + 1.09077i 0.357844 + 0.933781i \(0.383512\pi\)
−0.987600 + 0.156989i \(0.949821\pi\)
\(402\) 0 0
\(403\) 482.164 278.378i 1.19644 0.690763i
\(404\) 206.077 202.352i 0.510091 0.500872i
\(405\) 0 0
\(406\) −19.6718 48.1113i −0.0484528 0.118501i
\(407\) −313.392 + 180.937i −0.770005 + 0.444563i
\(408\) 0 0
\(409\) 341.664 591.780i 0.835364 1.44689i −0.0583688 0.998295i \(-0.518590\pi\)
0.893733 0.448599i \(-0.148077\pi\)
\(410\) −17.2858 + 126.827i −0.0421605 + 0.309335i
\(411\) 0 0
\(412\) 62.0608 223.443i 0.150633 0.542338i
\(413\) −174.116 −0.421588
\(414\) 0 0
\(415\) 38.2982i 0.0922847i
\(416\) −248.999 + 309.623i −0.598555 + 0.744287i
\(417\) 0 0
\(418\) −24.8754 + 182.513i −0.0595105 + 0.436634i
\(419\) −265.541 153.310i −0.633749 0.365895i 0.148453 0.988919i \(-0.452571\pi\)
−0.782203 + 0.623024i \(0.785904\pi\)
\(420\) 0 0
\(421\) 9.29335 + 16.0966i 0.0220745 + 0.0382341i 0.876852 0.480761i \(-0.159640\pi\)
−0.854777 + 0.518995i \(0.826306\pi\)
\(422\) 198.037 + 484.339i 0.469283 + 1.14772i
\(423\) 0 0
\(424\) −221.495 + 514.709i −0.522395 + 1.21394i
\(425\) −314.338 544.449i −0.739619 1.28106i
\(426\) 0 0
\(427\) 95.9164 + 55.3774i 0.224629 + 0.129689i
\(428\) 249.426 64.4015i 0.582771 0.150471i
\(429\) 0 0
\(430\) −25.3375 + 32.7105i −0.0589244 + 0.0760710i
\(431\) 308.130i 0.714918i 0.933929 + 0.357459i \(0.116357\pi\)
−0.933929 + 0.357459i \(0.883643\pi\)
\(432\) 0 0
\(433\) 174.839 0.403785 0.201893 0.979408i \(-0.435291\pi\)
0.201893 + 0.979408i \(0.435291\pi\)
\(434\) −426.379 330.272i −0.982440 0.760994i
\(435\) 0 0
\(436\) −43.1672 167.186i −0.0990073 0.383454i
\(437\) −77.5152 + 134.260i −0.177380 + 0.307232i
\(438\) 0 0
\(439\) −415.830 + 240.079i −0.947220 + 0.546878i −0.892216 0.451608i \(-0.850850\pi\)
−0.0550040 + 0.998486i \(0.517517\pi\)
\(440\) 140.716 + 60.5547i 0.319810 + 0.137624i
\(441\) 0 0
\(442\) −606.328 + 247.917i −1.37178 + 0.560897i
\(443\) −481.477 + 277.981i −1.08686 + 0.627497i −0.932738 0.360556i \(-0.882587\pi\)
−0.154119 + 0.988052i \(0.549254\pi\)
\(444\) 0 0
\(445\) 14.2492 24.6804i 0.0320207 0.0554615i
\(446\) −138.825 18.9210i −0.311267 0.0424238i
\(447\) 0 0
\(448\) 368.912 + 109.749i 0.823464 + 0.244976i
\(449\) −801.711 −1.78555 −0.892774 0.450504i \(-0.851244\pi\)
−0.892774 + 0.450504i \(0.851244\pi\)
\(450\) 0 0
\(451\) 1050.00i 2.32816i
\(452\) 313.325 + 87.0251i 0.693197 + 0.192533i
\(453\) 0 0
\(454\) 591.246 + 80.5832i 1.30230 + 0.177496i
\(455\) 69.8640 + 40.3360i 0.153547 + 0.0886506i
\(456\) 0 0
\(457\) 68.9149 + 119.364i 0.150798 + 0.261190i 0.931521 0.363687i \(-0.118482\pi\)
−0.780723 + 0.624877i \(0.785149\pi\)
\(458\) 480.701 196.550i 1.04956 0.429148i
\(459\) 0 0
\(460\) 90.3344 + 91.9971i 0.196379 + 0.199994i
\(461\) −94.1705 163.108i −0.204274 0.353814i 0.745627 0.666364i \(-0.232150\pi\)
−0.949901 + 0.312550i \(0.898817\pi\)
\(462\) 0 0
\(463\) −474.950 274.212i −1.02581 0.592251i −0.110028 0.993928i \(-0.535094\pi\)
−0.915781 + 0.401677i \(0.868427\pi\)
\(464\) 59.2393 + 35.6579i 0.127671 + 0.0768489i
\(465\) 0 0
\(466\) −11.6718 9.04097i −0.0250469 0.0194012i
\(467\) 618.597i 1.32462i −0.749231 0.662309i \(-0.769577\pi\)
0.749231 0.662309i \(-0.230423\pi\)
\(468\) 0 0
\(469\) −570.580 −1.21659
\(470\) −54.3334 + 70.1441i −0.115603 + 0.149243i
\(471\) 0 0
\(472\) 185.666 138.473i 0.393359 0.293375i
\(473\) −169.706 + 293.939i −0.358786 + 0.621435i
\(474\) 0 0
\(475\) 107.248 61.9195i 0.225785 0.130357i
\(476\) 444.587 + 452.771i 0.934007 + 0.951199i
\(477\) 0 0
\(478\) −62.1641 152.034i −0.130050 0.318064i
\(479\) 667.208 385.213i 1.39292 0.804202i 0.399281 0.916829i \(-0.369260\pi\)
0.993637 + 0.112627i \(0.0359265\pi\)
\(480\) 0 0
\(481\) 126.749 219.536i 0.263512 0.456416i
\(482\) 112.311 824.035i 0.233010 1.70962i
\(483\) 0 0
\(484\) 744.474 + 206.776i 1.53817 + 0.427222i
\(485\) 82.4655 0.170032
\(486\) 0 0
\(487\) 549.208i 1.12774i −0.825865 0.563868i \(-0.809313\pi\)
0.825865 0.563868i \(-0.190687\pi\)
\(488\) −146.320 + 17.2308i −0.299836 + 0.0353090i
\(489\) 0 0
\(490\) −3.74457 + 27.4742i −0.00764197 + 0.0560698i
\(491\) 19.9407 + 11.5128i 0.0406125 + 0.0234476i 0.520169 0.854063i \(-0.325869\pi\)
−0.479556 + 0.877511i \(0.659202\pi\)
\(492\) 0 0
\(493\) 56.9969 + 98.7215i 0.115612 + 0.200246i
\(494\) −48.8355 119.437i −0.0988573 0.241775i
\(495\) 0 0
\(496\) 717.325 + 13.0842i 1.44622 + 0.0263795i
\(497\) 252.263 + 436.932i 0.507572 + 0.879140i
\(498\) 0 0
\(499\) −542.833 313.405i −1.08784 0.628065i −0.154840 0.987939i \(-0.549486\pi\)
−0.933001 + 0.359874i \(0.882820\pi\)
\(500\) −52.7572 204.328i −0.105514 0.408655i
\(501\) 0 0
\(502\) −171.502 + 221.408i −0.341637 + 0.441051i
\(503\) 732.896i 1.45705i −0.685019 0.728525i \(-0.740206\pi\)
0.685019 0.728525i \(-0.259794\pi\)
\(504\) 0 0
\(505\) 78.0062 0.154468
\(506\) 836.148 + 647.678i 1.65247 + 1.28000i
\(507\) 0 0
\(508\) −743.489 + 191.968i −1.46356 + 0.377890i
\(509\) −218.682 + 378.768i −0.429630 + 0.744140i −0.996840 0.0794323i \(-0.974689\pi\)
0.567211 + 0.823573i \(0.308023\pi\)
\(510\) 0 0
\(511\) −290.789 + 167.887i −0.569058 + 0.328546i
\(512\) −480.666 + 176.363i −0.938801 + 0.344459i
\(513\) 0 0
\(514\) −124.000 + 50.7013i −0.241245 + 0.0986407i
\(515\) 54.2431 31.3173i 0.105326 0.0608102i
\(516\) 0 0
\(517\) −363.915 + 630.319i −0.703897 + 1.21919i
\(518\) −243.316 33.1624i −0.469721 0.0640201i
\(519\) 0 0
\(520\) −106.577 + 12.5506i −0.204957 + 0.0241359i
\(521\) −385.236 −0.739417 −0.369709 0.929148i \(-0.620542\pi\)
−0.369709 + 0.929148i \(0.620542\pi\)
\(522\) 0 0
\(523\) 418.572i 0.800328i −0.916443 0.400164i \(-0.868953\pi\)
0.916443 0.400164i \(-0.131047\pi\)
\(524\) 151.789 546.502i 0.289674 1.04294i
\(525\) 0 0
\(526\) −73.7508 10.0518i −0.140211 0.0191099i
\(527\) 1024.35 + 591.411i 1.94375 + 1.12222i
\(528\) 0 0
\(529\) 180.582 + 312.777i 0.341365 + 0.591261i
\(530\) −140.086 + 57.2786i −0.264313 + 0.108073i
\(531\) 0 0
\(532\) −89.1885 + 87.5765i −0.167648 + 0.164617i
\(533\) −367.770 636.996i −0.690000 1.19511i
\(534\) 0 0
\(535\) 60.2554 + 34.7885i 0.112627 + 0.0650252i
\(536\) 608.430 453.778i 1.13513 0.846601i
\(537\) 0 0
\(538\) −441.282 341.816i −0.820228 0.635346i
\(539\) 227.457i 0.421999i
\(540\) 0 0
\(541\) −23.4257 −0.0433008 −0.0216504 0.999766i \(-0.506892\pi\)
−0.0216504 + 0.999766i \(0.506892\pi\)
\(542\) 497.620 642.425i 0.918119 1.18529i
\(543\) 0 0
\(544\) −834.164 129.228i −1.53339 0.237552i
\(545\) 23.3181 40.3882i 0.0427855 0.0741067i
\(546\) 0 0
\(547\) 625.412 361.082i 1.14335 0.660113i 0.196091 0.980586i \(-0.437175\pi\)
0.947258 + 0.320473i \(0.103842\pi\)
\(548\) −250.529 + 246.001i −0.457170 + 0.448907i
\(549\) 0 0
\(550\) −319.751 782.013i −0.581365 1.42184i
\(551\) −19.4465 + 11.2275i −0.0352932 + 0.0203765i
\(552\) 0 0
\(553\) −123.409 + 213.750i −0.223162 + 0.386528i
\(554\) −1.30530 + 9.57709i −0.00235614 + 0.0172872i
\(555\) 0 0
\(556\) −196.431 + 707.231i −0.353294 + 1.27200i
\(557\) −2.34135 −0.00420349 −0.00210175 0.999998i \(-0.500669\pi\)
−0.00210175 + 0.999998i \(0.500669\pi\)
\(558\) 0 0
\(559\) 237.763i 0.425336i
\(560\) 50.3272 + 90.9610i 0.0898700 + 0.162430i
\(561\) 0 0
\(562\) −1.16718 + 8.56373i −0.00207684 + 0.0152380i
\(563\) −311.591 179.897i −0.553448 0.319533i 0.197064 0.980391i \(-0.436859\pi\)
−0.750511 + 0.660857i \(0.770193\pi\)
\(564\) 0 0
\(565\) 43.9149 + 76.0628i 0.0777254 + 0.134624i
\(566\) −33.5799 82.1262i −0.0593284 0.145099i
\(567\) 0 0
\(568\) −616.486 265.293i −1.08536 0.467066i
\(569\) −9.31771 16.1388i −0.0163756 0.0283634i 0.857721 0.514115i \(-0.171879\pi\)
−0.874097 + 0.485751i \(0.838546\pi\)
\(570\) 0 0
\(571\) 246.409 + 142.264i 0.431539 + 0.249149i 0.700002 0.714141i \(-0.253182\pi\)
−0.268463 + 0.963290i \(0.586516\pi\)
\(572\) −852.354 + 220.077i −1.49013 + 0.384750i
\(573\) 0 0
\(574\) −436.328 + 563.297i −0.760154 + 0.981354i
\(575\) 711.067i 1.23664i
\(576\) 0 0
\(577\) 664.823 1.15221 0.576104 0.817377i \(-0.304572\pi\)
0.576104 + 0.817377i \(0.304572\pi\)
\(578\) −643.254 498.263i −1.11290 0.862046i
\(579\) 0 0
\(580\) 4.66874 + 18.0819i 0.00804955 + 0.0311758i
\(581\) 106.595 184.627i 0.183468 0.317775i
\(582\) 0 0
\(583\) −1075.16 + 620.744i −1.84419 + 1.06474i
\(584\) 176.559 410.286i 0.302327 0.702544i
\(585\) 0 0
\(586\) 719.994 294.392i 1.22866 0.502376i
\(587\) −653.388 + 377.234i −1.11310 + 0.642647i −0.939630 0.342193i \(-0.888830\pi\)
−0.173467 + 0.984840i \(0.555497\pi\)
\(588\) 0 0
\(589\) −116.498 + 201.781i −0.197790 + 0.342583i
\(590\) 61.9846 + 8.44812i 0.105059 + 0.0143188i
\(591\) 0 0
\(592\) 285.830 158.145i 0.482820 0.267137i
\(593\) 550.801 0.928838 0.464419 0.885615i \(-0.346263\pi\)
0.464419 + 0.885615i \(0.346263\pi\)
\(594\) 0 0
\(595\) 171.387i 0.288046i
\(596\) 593.339 + 164.798i 0.995536 + 0.276507i
\(597\) 0 0
\(598\) −734.115 100.055i −1.22762 0.167317i
\(599\) 22.5070 + 12.9944i 0.0375743 + 0.0216935i 0.518669 0.854975i \(-0.326428\pi\)
−0.481095 + 0.876668i \(0.659761\pi\)
\(600\) 0 0
\(601\) −93.0851 161.228i −0.154884 0.268267i 0.778133 0.628100i \(-0.216167\pi\)
−0.933017 + 0.359833i \(0.882834\pi\)
\(602\) −213.189 + 87.1693i −0.354135 + 0.144799i
\(603\) 0 0
\(604\) 519.517 + 529.079i 0.860127 + 0.875959i
\(605\) 104.344 + 180.729i 0.172469 + 0.298725i
\(606\) 0 0
\(607\) −86.2082 49.7723i −0.142023 0.0819972i 0.427305 0.904108i \(-0.359463\pi\)
−0.569328 + 0.822110i \(0.692797\pi\)
\(608\) 25.4558 164.317i 0.0418682 0.270258i
\(609\) 0 0
\(610\) −31.4590 24.3680i −0.0515721 0.0399476i
\(611\) 509.856i 0.834461i
\(612\) 0 0
\(613\) −960.234 −1.56645 −0.783225 0.621739i \(-0.786427\pi\)
−0.783225 + 0.621739i \(0.786427\pi\)
\(614\) −118.433 + 152.896i −0.192887 + 0.249016i
\(615\) 0 0
\(616\) 509.823 + 683.576i 0.827636 + 1.10970i
\(617\) −177.312 + 307.114i −0.287378 + 0.497754i −0.973183 0.230032i \(-0.926117\pi\)
0.685805 + 0.727786i \(0.259450\pi\)
\(618\) 0 0
\(619\) −312.330 + 180.324i −0.504571 + 0.291314i −0.730599 0.682806i \(-0.760759\pi\)
0.226028 + 0.974121i \(0.427426\pi\)
\(620\) 135.765 + 138.263i 0.218975 + 0.223006i
\(621\) 0 0
\(622\) 103.082 + 252.107i 0.165727 + 0.405317i
\(623\) 137.385 79.3193i 0.220522 0.127318i
\(624\) 0 0
\(625\) −269.412 + 466.635i −0.431059 + 0.746616i
\(626\) −76.2091 + 559.152i −0.121740 + 0.893215i
\(627\) 0 0
\(628\) −756.036 209.987i −1.20388 0.334374i
\(629\) 538.556 0.856210
\(630\) 0 0
\(631\) 82.7121i 0.131081i −0.997850 0.0655405i \(-0.979123\pi\)
0.997850 0.0655405i \(-0.0208772\pi\)
\(632\) −38.3989 326.075i −0.0607577 0.515942i
\(633\) 0 0
\(634\) −74.4071 + 545.931i −0.117361 + 0.861090i
\(635\) −179.610 103.698i −0.282850 0.163303i
\(636\) 0 0
\(637\) −79.6687 137.990i −0.125069 0.216625i
\(638\) 57.9784 + 141.797i 0.0908752 + 0.222253i
\(639\) 0 0
\(640\) −126.006 56.9700i −0.196885 0.0890156i
\(641\) −380.284 658.672i −0.593267 1.02757i −0.993789 0.111282i \(-0.964504\pi\)
0.400521 0.916287i \(-0.368829\pi\)
\(642\) 0 0
\(643\) −681.580 393.511i −1.06000 0.611992i −0.134568 0.990904i \(-0.542965\pi\)
−0.925432 + 0.378913i \(0.876298\pi\)
\(644\) 179.429 + 694.925i 0.278616 + 1.07908i
\(645\) 0 0
\(646\) 167.872 216.722i 0.259864 0.335483i
\(647\) 978.962i 1.51308i 0.653948 + 0.756539i \(0.273111\pi\)
−0.653948 + 0.756539i \(0.726889\pi\)
\(648\) 0 0
\(649\) 513.167 0.790704
\(650\) 467.887 + 362.424i 0.719827 + 0.557575i
\(651\) 0 0
\(652\) 500.872 129.325i 0.768209 0.198351i
\(653\) 469.774 813.672i 0.719409 1.24605i −0.241826 0.970320i \(-0.577746\pi\)
0.961234 0.275733i \(-0.0889205\pi\)
\(654\) 0 0
\(655\) 132.669 76.5963i 0.202548 0.116941i
\(656\) 17.2858 947.672i 0.0263503 1.44462i
\(657\) 0 0
\(658\) −457.161 + 186.925i −0.694774 + 0.284080i
\(659\) 129.463 74.7455i 0.196454 0.113423i −0.398547 0.917148i \(-0.630485\pi\)
0.595000 + 0.803726i \(0.297152\pi\)
\(660\) 0 0
\(661\) −168.710 + 292.214i −0.255234 + 0.442078i −0.964959 0.262400i \(-0.915486\pi\)
0.709725 + 0.704479i \(0.248819\pi\)
\(662\) 110.027 + 14.9960i 0.166204 + 0.0226526i
\(663\) 0 0
\(664\) 33.1672 + 281.649i 0.0499506 + 0.424170i
\(665\) −33.7605 −0.0507677
\(666\) 0 0
\(667\) 128.933i 0.193303i
\(668\) −147.671 + 531.676i −0.221065 + 0.795922i
\(669\) 0 0
\(670\) 203.125 + 27.6846i 0.303171 + 0.0413204i
\(671\) −282.692 163.212i −0.421300 0.243238i
\(672\) 0 0
\(673\) 160.670 + 278.289i 0.238737 + 0.413505i 0.960352 0.278789i \(-0.0899331\pi\)
−0.721615 + 0.692295i \(0.756600\pi\)
\(674\) −797.249 + 325.981i −1.18286 + 0.483651i
\(675\) 0 0
\(676\) −42.3344 + 41.5692i −0.0626248 + 0.0614929i
\(677\) 370.921 + 642.454i 0.547889 + 0.948971i 0.998419 + 0.0562100i \(0.0179016\pi\)
−0.450530 + 0.892761i \(0.648765\pi\)
\(678\) 0 0
\(679\) 397.549 + 229.525i 0.585492 + 0.338034i
\(680\) −136.303 182.756i −0.200446 0.268759i
\(681\) 0 0
\(682\) 1256.66 + 973.402i 1.84260 + 1.42728i
\(683\) 1259.02i 1.84337i 0.387938 + 0.921686i \(0.373188\pi\)
−0.387938 + 0.921686i \(0.626812\pi\)
\(684\) 0 0
\(685\) −94.8328 −0.138442
\(686\) −455.430 + 587.958i −0.663893 + 0.857082i
\(687\) 0 0
\(688\) 158.006 262.500i 0.229660 0.381540i
\(689\) 434.841 753.167i 0.631119 1.09313i
\(690\) 0 0
\(691\) 192.924 111.385i 0.279196 0.161194i −0.353864 0.935297i \(-0.615132\pi\)
0.633059 + 0.774103i \(0.281799\pi\)
\(692\) −457.890 + 449.614i −0.661691 + 0.649731i
\(693\) 0 0
\(694\) 102.845 + 251.528i 0.148192 + 0.362432i
\(695\) −171.687 + 99.1238i −0.247032 + 0.142624i
\(696\) 0 0
\(697\) 781.325 1353.29i 1.12098 1.94160i
\(698\) −77.8083 + 570.886i −0.111473 + 0.817888i
\(699\) 0 0
\(700\) 153.428 552.403i 0.219183 0.789147i
\(701\) −2.34135 −0.00334001 −0.00167000 0.999999i \(-0.500532\pi\)
−0.00167000 + 0.999999i \(0.500532\pi\)
\(702\) 0 0
\(703\) 106.087i 0.150906i
\(704\) −1087.29 323.462i −1.54444 0.459462i
\(705\) 0 0
\(706\) 53.7384 394.283i 0.0761166 0.558474i
\(707\) 376.052 + 217.113i 0.531898 + 0.307091i
\(708\) 0 0
\(709\) 247.543 + 428.756i 0.349143 + 0.604734i 0.986098 0.166168i \(-0.0531393\pi\)
−0.636954 + 0.770902i \(0.719806\pi\)
\(710\) −68.6047 167.786i −0.0966264 0.236319i
\(711\) 0 0
\(712\) −83.4164 + 193.842i −0.117158 + 0.272250i
\(713\) 668.919 + 1158.60i 0.938175 + 1.62497i
\(714\) 0 0
\(715\) −205.909 118.881i −0.287984 0.166268i
\(716\) −780.285 + 201.469i −1.08978 + 0.281381i
\(717\) 0 0
\(718\) 397.623 513.329i 0.553793 0.714943i
\(719\) 962.433i 1.33857i 0.743005 + 0.669286i \(0.233400\pi\)
−0.743005 + 0.669286i \(0.766600\pi\)
\(720\) 0 0
\(721\) 348.659 0.483578
\(722\) −528.100 409.065i −0.731441 0.566572i
\(723\) 0 0
\(724\) −48.2523 186.880i −0.0666469 0.258122i
\(725\) 51.4962 89.1940i 0.0710292 0.123026i
\(726\) 0 0
\(727\) 471.659 272.313i 0.648775 0.374570i −0.139212 0.990263i \(-0.544457\pi\)
0.787987 + 0.615692i \(0.211124\pi\)
\(728\) −548.719 236.131i −0.753735 0.324356i
\(729\) 0 0
\(730\) 111.666 45.6580i 0.152967 0.0625453i
\(731\) 437.452 252.563i 0.598429 0.345503i
\(732\) 0 0
\(733\) 73.0851 126.587i 0.0997069 0.172697i −0.811856 0.583857i \(-0.801543\pi\)
0.911563 + 0.411160i \(0.134876\pi\)
\(734\) −349.055 47.5741i −0.475552 0.0648148i
\(735\) 0 0
\(736\) −744.000 598.324i −1.01087 0.812941i
\(737\) 1681.66 2.28176
\(738\) 0 0
\(739\) 1172.87i 1.58710i 0.608505 + 0.793550i \(0.291769\pi\)
−0.608505 + 0.793550i \(0.708231\pi\)
\(740\) 85.0104 + 23.6114i 0.114879 + 0.0319073i
\(741\) 0 0
\(742\) −834.748 113.771i −1.12500 0.153330i
\(743\) −428.541 247.418i −0.576771 0.332999i 0.183078 0.983098i \(-0.441394\pi\)
−0.759849 + 0.650099i \(0.774727\pi\)
\(744\) 0 0
\(745\) 83.1610 + 144.039i 0.111625 + 0.193341i
\(746\) 1104.41 451.572i 1.48044 0.605324i
\(747\) 0 0
\(748\) −1310.32 1334.44i −1.75177 1.78401i
\(749\) 193.653 + 335.416i 0.258548 + 0.447819i
\(750\) 0 0
\(751\) 803.022 + 463.625i 1.06927 + 0.617344i 0.927982 0.372625i \(-0.121542\pi\)
0.141289 + 0.989968i \(0.454875\pi\)
\(752\) 338.827 562.901i 0.450567 0.748539i
\(753\) 0 0
\(754\) −84.8390 65.7160i −0.112519 0.0871565i
\(755\) 200.272i 0.265261i
\(756\) 0 0
\(757\) −757.748 −1.00099 −0.500494 0.865740i \(-0.666848\pi\)
−0.500494 + 0.865740i \(0.666848\pi\)
\(758\) 37.1198 47.9215i 0.0489707 0.0632209i
\(759\) 0 0
\(760\) 36.0000 26.8495i 0.0473684 0.0353283i
\(761\) 476.570 825.443i 0.626241 1.08468i −0.362058 0.932156i \(-0.617926\pi\)
0.988299 0.152526i \(-0.0487409\pi\)
\(762\) 0 0
\(763\) 224.823 129.802i 0.294657 0.170120i
\(764\) −413.122 420.726i −0.540736 0.550689i
\(765\) 0 0
\(766\) 535.319 + 1309.23i 0.698850 + 1.70917i
\(767\) −311.320 + 179.741i −0.405893 + 0.234343i
\(768\) 0 0
\(769\) −72.8375 + 126.158i −0.0947171 + 0.164055i −0.909491 0.415725i \(-0.863528\pi\)
0.814773 + 0.579780i \(0.196861\pi\)
\(770\) −31.1039 + 228.212i −0.0403947 + 0.296379i
\(771\) 0 0
\(772\) −96.9849 26.9373i −0.125628 0.0348929i
\(773\) −60.1391 −0.0777996 −0.0388998 0.999243i \(-0.512385\pi\)
−0.0388998 + 0.999243i \(0.512385\pi\)
\(774\) 0 0
\(775\) 1068.67i 1.37893i
\(776\) −606.460 + 71.4172i −0.781520 + 0.0920325i
\(777\) 0 0
\(778\) 155.866 1143.60i 0.200342 1.46993i
\(779\) 266.577 + 153.908i 0.342204 + 0.197572i
\(780\) 0 0
\(781\) −743.489 1287.76i −0.951971 1.64886i
\(782\) −595.723 1456.96i −0.761794 1.86312i
\(783\) 0 0
\(784\) 3.74457 205.291i 0.00477623 0.261851i
\(785\) −105.964 183.535i −0.134986 0.233803i
\(786\) 0 0
\(787\) −284.327 164.156i −0.361279 0.208585i 0.308363 0.951269i \(-0.400219\pi\)
−0.669642 + 0.742684i \(0.733552\pi\)
\(788\) 385.506 + 1493.06i 0.489220 + 1.89474i
\(789\) 0 0
\(790\) 54.3042 70.1064i 0.0687395 0.0887423i
\(791\) 488.910i 0.618091i
\(792\) 0 0
\(793\) 228.666 0.288355
\(794\) −42.4166 32.8557i −0.0534214 0.0413800i
\(795\) 0 0
\(796\) 470.125 121.386i 0.590609 0.152495i
\(797\) −223.363 + 386.875i −0.280254 + 0.485414i −0.971447 0.237256i \(-0.923752\pi\)
0.691193 + 0.722670i \(0.257085\pi\)
\(798\) 0 0
\(799\) 938.067 541.593i 1.17405 0.677838i
\(800\) 275.716 + 711.067i 0.344645 + 0.888833i
\(801\) 0 0
\(802\) 934.991 382.301i 1.16582 0.476684i
\(803\) 857.035 494.809i 1.06729 0.616201i
\(804\) 0 0
\(805\) −96.9242 + 167.878i −0.120403 + 0.208544i
\(806\) −1103.31 150.374i −1.36887 0.186569i
\(807\) 0 0
\(808\) −573.666 + 67.5554i −0.709982 + 0.0836081i
\(809\) 793.341 0.980644 0.490322 0.871541i \(-0.336879\pi\)
0.490322 + 0.871541i \(0.336879\pi\)
\(810\) 0 0
\(811\) 788.930i 0.972787i −0.873740 0.486394i \(-0.838312\pi\)
0.873740 0.486394i \(-0.161688\pi\)
\(812\) −27.8202 + 100.164i −0.0342613 + 0.123354i
\(813\) 0 0
\(814\) 717.118 + 97.7389i 0.880981 + 0.120072i
\(815\) 120.999 + 69.8588i 0.148465 + 0.0857163i
\(816\) 0 0
\(817\) 49.7508 + 86.1709i 0.0608945 + 0.105472i
\(818\) −1265.00 + 517.234i −1.54645 + 0.632316i
\(819\) 0 0
\(820\) 182.663 179.361i 0.222759 0.218733i
\(821\) −724.377 1254.66i −0.882310 1.52821i −0.848766 0.528769i \(-0.822654\pi\)
−0.0335444 0.999437i \(-0.510680\pi\)
\(822\) 0 0
\(823\) 112.530 + 64.9693i 0.136732 + 0.0789421i 0.566805 0.823852i \(-0.308179\pi\)
−0.430074 + 0.902794i \(0.641512\pi\)
\(824\) −371.788 + 277.286i −0.451199 + 0.336512i
\(825\) 0 0
\(826\) 275.301 + 213.247i 0.333294 + 0.258169i
\(827\) 350.389i 0.423687i −0.977304 0.211843i \(-0.932053\pi\)
0.977304 0.211843i \(-0.0679467\pi\)
\(828\) 0 0
\(829\) 167.748 0.202349 0.101175 0.994869i \(-0.467740\pi\)
0.101175 + 0.994869i \(0.467740\pi\)
\(830\) −46.9055 + 60.5547i −0.0565126 + 0.0729575i
\(831\) 0 0
\(832\) 772.912 184.597i 0.928980 0.221872i
\(833\) 169.256 293.160i 0.203188 0.351932i
\(834\) 0 0
\(835\) −129.070 + 74.5184i −0.154574 + 0.0892436i
\(836\) 262.863 258.112i 0.314430 0.308747i
\(837\) 0 0
\(838\) 232.091 + 567.625i 0.276959 + 0.677356i
\(839\) −573.036 + 330.842i −0.682998 + 0.394329i −0.800984 0.598686i \(-0.795690\pi\)
0.117985 + 0.993015i \(0.462356\pi\)
\(840\) 0 0
\(841\) 411.163 712.154i 0.488897 0.846795i
\(842\) 5.02010 36.8329i 0.00596211 0.0437445i
\(843\) 0 0
\(844\) 280.067 1008.35i 0.331833 1.19473i
\(845\) −16.0248 −0.0189643
\(846\) 0 0
\(847\) 1161.67i 1.37151i
\(848\) 980.602 542.551i 1.15637 0.639800i
\(849\) 0 0
\(850\) −169.800 + 1245.83i −0.199764 + 1.46569i
\(851\) 527.527 + 304.568i 0.619891 + 0.357894i
\(852\) 0 0
\(853\) −8.53947 14.7908i −0.0100111 0.0173397i 0.860976 0.508645i \(-0.169853\pi\)
−0.870988 + 0.491305i \(0.836520\pi\)
\(854\) −83.8340 205.032i −0.0981663 0.240085i
\(855\) 0 0
\(856\) −473.252 203.655i −0.552865 0.237915i
\(857\) 211.209 + 365.825i 0.246452 + 0.426867i 0.962539 0.271144i \(-0.0874019\pi\)
−0.716087 + 0.698011i \(0.754069\pi\)
\(858\) 0 0
\(859\) 1145.91 + 661.590i 1.33400 + 0.770186i 0.985910 0.167275i \(-0.0534967\pi\)
0.348091 + 0.937461i \(0.386830\pi\)
\(860\) 80.1241 20.6880i 0.0931676 0.0240558i
\(861\) 0 0
\(862\) 377.380 487.196i 0.437796 0.565192i
\(863\) 1455.50i 1.68656i −0.537473 0.843281i \(-0.680621\pi\)
0.537473 0.843281i \(-0.319379\pi\)
\(864\) 0 0
\(865\) −173.325 −0.200376
\(866\) −276.445 214.133i −0.319220 0.247267i
\(867\) 0 0
\(868\) 269.666 + 1044.41i 0.310675 + 1.20324i
\(869\) 363.719 629.981i 0.418549 0.724949i
\(870\) 0 0
\(871\) −1020.20 + 589.014i −1.17130 + 0.676250i
\(872\) −136.507 + 317.213i −0.156544 + 0.363776i
\(873\) 0 0
\(874\) 286.997 117.348i 0.328372 0.134265i
\(875\) 274.770 158.639i 0.314023 0.181301i
\(876\) 0 0
\(877\) 376.543 652.191i 0.429353 0.743661i −0.567463 0.823399i \(-0.692075\pi\)
0.996816 + 0.0797378i \(0.0254083\pi\)
\(878\) 951.521 + 129.686i 1.08374 + 0.147707i
\(879\) 0 0
\(880\) −148.328 268.087i −0.168555 0.304644i
\(881\) −996.177 −1.13073 −0.565367 0.824839i \(-0.691265\pi\)
−0.565367 + 0.824839i \(0.691265\pi\)
\(882\) 0 0
\(883\) 950.011i 1.07589i −0.842980 0.537945i \(-0.819201\pi\)
0.842980 0.537945i \(-0.180799\pi\)
\(884\) 1262.32 + 350.607i 1.42797 + 0.396614i
\(885\) 0 0
\(886\) 1101.74 + 150.160i 1.24350 + 0.169481i
\(887\) −375.063 216.543i −0.422845 0.244129i 0.273449 0.961887i \(-0.411836\pi\)
−0.696294 + 0.717757i \(0.745169\pi\)
\(888\) 0 0
\(889\) −577.240 999.809i −0.649314 1.12464i
\(890\) −52.7572 + 21.5714i −0.0592777 + 0.0242376i
\(891\) 0 0
\(892\) 196.328 + 199.942i 0.220099 + 0.224150i
\(893\) 106.685 + 184.784i 0.119468 + 0.206925i
\(894\) 0 0
\(895\) −188.498 108.830i −0.210613 0.121597i
\(896\) −448.886 625.352i −0.500989 0.697937i
\(897\) 0 0
\(898\) 1267.62 + 981.892i 1.41160 + 1.09342i
\(899\) 193.775i 0.215545i
\(900\) 0 0
\(901\) 1847.63 2.05065
\(902\) 1285.98 1660.19i 1.42570 1.84057i
\(903\) 0 0
\(904\) −388.827 521.342i −0.430118 0.576706i
\(905\) 26.0650 45.1459i 0.0288011 0.0498850i
\(906\) 0 0
\(907\) −593.837 + 342.852i −0.654727 + 0.378007i −0.790265 0.612765i \(-0.790057\pi\)
0.135538 + 0.990772i \(0.456724\pi\)
\(908\) −836.148 851.539i −0.920868 0.937818i
\(909\) 0 0
\(910\) −61.0634 149.342i −0.0671026 0.164113i
\(911\) −31.2419 + 18.0375i −0.0342941 + 0.0197997i −0.517049 0.855956i \(-0.672970\pi\)
0.482755 + 0.875755i \(0.339636\pi\)
\(912\) 0 0
\(913\) −314.164 + 544.148i −0.344101 + 0.596000i
\(914\) 37.2265 273.134i 0.0407292 0.298834i
\(915\) 0 0
\(916\) −1000.78 277.963i −1.09255 0.303453i
\(917\) 852.758 0.929943
\(918\) 0 0
\(919\) 953.775i 1.03784i 0.854823 + 0.518920i \(0.173666\pi\)
−0.854823 + 0.518920i \(0.826334\pi\)
\(920\) −30.1582 256.097i −0.0327806 0.278366i
\(921\) 0 0
\(922\) −50.8692 + 373.231i −0.0551726 + 0.404806i
\(923\) 902.096 + 520.826i 0.977353 + 0.564275i
\(924\) 0 0
\(925\) −243.290 421.391i −0.263016 0.455558i
\(926\) 415.121 + 1015.26i 0.448295 + 1.09639i
\(927\) 0 0
\(928\) −49.9938 128.933i −0.0538726 0.138937i
\(929\) −74.8143 129.582i −0.0805321 0.139486i 0.822947 0.568119i \(-0.192329\pi\)
−0.903479 + 0.428633i \(0.858995\pi\)
\(930\) 0 0
\(931\) 57.7477 + 33.3406i 0.0620276 + 0.0358116i
\(932\) 7.38192 + 28.5901i 0.00792052 + 0.0306760i
\(933\) 0 0
\(934\) −757.623 + 978.087i −0.811160 + 1.04720i
\(935\) 505.126i 0.540241i
\(936\) 0 0
\(937\) −661.158 −0.705611 −0.352806 0.935697i \(-0.614772\pi\)
−0.352806 + 0.935697i \(0.614772\pi\)
\(938\) 902.167 + 698.816i 0.961798 + 0.745006i
\(939\) 0 0
\(940\) 171.817 44.3630i 0.182784 0.0471947i
\(941\) −233.357 + 404.186i −0.247988 + 0.429528i −0.962967 0.269618i \(-0.913103\pi\)
0.714979 + 0.699145i \(0.246436\pi\)
\(942\) 0 0
\(943\) 1530.65 883.721i 1.62317 0.937138i
\(944\) −463.157 8.44812i −0.490633 0.00894928i
\(945\) 0 0
\(946\) 628.328 256.912i 0.664195 0.271577i
\(947\) −1128.20 + 651.368i −1.19134 + 0.687823i −0.958611 0.284718i \(-0.908100\pi\)
−0.232732 + 0.972541i \(0.574767\pi\)
\(948\) 0 0
\(949\) −346.622 + 600.366i −0.365249 + 0.632630i
\(950\) −245.409 33.4478i −0.258325 0.0352082i
\(951\) 0 0
\(952\) −148.426 1260.40i −0.155909 1.32395i
\(953\) 21.6959 0.0227659 0.0113829 0.999935i \(-0.496377\pi\)
0.0113829 + 0.999935i \(0.496377\pi\)
\(954\) 0 0
\(955\) 159.258i 0.166762i
\(956\) −87.9133 + 316.523i −0.0919595 + 0.331091i
\(957\) 0 0
\(958\) −1526.74 208.085i −1.59367 0.217207i
\(959\) −457.169 263.947i −0.476714 0.275231i
\(960\) 0 0
\(961\) 524.825 + 909.024i 0.546124 + 0.945914i
\(962\) −469.284 + 191.882i −0.487821 + 0.199461i
\(963\) 0 0
\(964\) −1186.81 + 1165.36i −1.23113 + 1.20888i
\(965\) −13.5932 23.5441i −0.0140862 0.0243980i
\(966\) 0 0
\(967\) 555.035 + 320.449i 0.573976 + 0.331385i 0.758736 0.651399i \(-0.225817\pi\)
−0.184760 + 0.982784i \(0.559151\pi\)
\(968\) −923.869 1238.73i −0.954411 1.27968i
\(969\) 0 0
\(970\) −130.389 100.999i −0.134422 0.104123i
\(971\) 1396.09i 1.43779i −0.695121 0.718893i \(-0.744649\pi\)
0.695121 0.718893i \(-0.255351\pi\)
\(972\) 0 0
\(973\) −1103.56 −1.13418
\(974\) −672.639 + 868.373i −0.690595 + 0.891554i
\(975\) 0 0
\(976\) 252.456 + 151.961i 0.258664 + 0.155697i
\(977\) −504.976 + 874.644i −0.516864 + 0.895235i 0.482944 + 0.875651i \(0.339567\pi\)
−0.999808 + 0.0195835i \(0.993766\pi\)
\(978\) 0 0
\(979\) −404.912 + 233.776i −0.413597 + 0.238791i
\(980\) 39.5696 38.8544i 0.0403771 0.0396473i
\(981\) 0 0
\(982\) −17.4288 42.6256i −0.0177483 0.0434069i
\(983\) 420.348 242.688i 0.427618 0.246885i −0.270714 0.962660i \(-0.587260\pi\)
0.698331 + 0.715775i \(0.253926\pi\)
\(984\) 0 0
\(985\) −208.243 + 360.687i −0.211414 + 0.366180i
\(986\) 30.7887 225.899i 0.0312258 0.229107i
\(987\) 0 0
\(988\) −69.0639 + 248.657i −0.0699027 + 0.251677i
\(989\) 571.325 0.577679
\(990\) 0 0
\(991\) 265.720i 0.268133i −0.990972 0.134066i \(-0.957196\pi\)
0.990972 0.134066i \(-0.0428035\pi\)
\(992\) −1118.17 899.228i −1.12718 0.906480i
\(993\) 0 0
\(994\) 136.268 999.809i 0.137090 1.00584i
\(995\) 113.571 + 65.5703i 0.114142 + 0.0658998i
\(996\) 0 0
\(997\) 857.906 + 1485.94i 0.860487 + 1.49041i 0.871460 + 0.490467i \(0.163174\pi\)
−0.0109725 + 0.999940i \(0.503493\pi\)
\(998\) 474.453 + 1160.37i 0.475404 + 1.16269i
\(999\) 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 324.3.f.p.271.1 8
3.2 odd 2 inner 324.3.f.p.271.4 8
4.3 odd 2 324.3.f.o.271.2 8
9.2 odd 6 324.3.f.o.55.3 8
9.4 even 3 108.3.d.d.55.7 yes 8
9.5 odd 6 108.3.d.d.55.2 yes 8
9.7 even 3 324.3.f.o.55.2 8
12.11 even 2 324.3.f.o.271.3 8
36.7 odd 6 inner 324.3.f.p.55.2 8
36.11 even 6 inner 324.3.f.p.55.3 8
36.23 even 6 108.3.d.d.55.1 8
36.31 odd 6 108.3.d.d.55.8 yes 8
72.5 odd 6 1728.3.g.l.703.5 8
72.13 even 6 1728.3.g.l.703.3 8
72.59 even 6 1728.3.g.l.703.6 8
72.67 odd 6 1728.3.g.l.703.4 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
108.3.d.d.55.1 8 36.23 even 6
108.3.d.d.55.2 yes 8 9.5 odd 6
108.3.d.d.55.7 yes 8 9.4 even 3
108.3.d.d.55.8 yes 8 36.31 odd 6
324.3.f.o.55.2 8 9.7 even 3
324.3.f.o.55.3 8 9.2 odd 6
324.3.f.o.271.2 8 4.3 odd 2
324.3.f.o.271.3 8 12.11 even 2
324.3.f.p.55.2 8 36.7 odd 6 inner
324.3.f.p.55.3 8 36.11 even 6 inner
324.3.f.p.271.1 8 1.1 even 1 trivial
324.3.f.p.271.4 8 3.2 odd 2 inner
1728.3.g.l.703.3 8 72.13 even 6
1728.3.g.l.703.4 8 72.67 odd 6
1728.3.g.l.703.5 8 72.5 odd 6
1728.3.g.l.703.6 8 72.59 even 6