Properties

Label 324.3.f.o.271.3
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 271.3
Root \(1.14412 + 1.98168i\) of defining polynomial
Character \(\chi\) \(=\) 324.271
Dual form 324.3.f.o.55.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.270091 + 1.98168i) q^{2} +(-3.85410 + 1.07047i) q^{4} +(0.540182 - 0.935622i) q^{5} +(5.20820 - 3.00696i) q^{7} +(-3.16228 - 7.34847i) q^{8} +O(q^{10})\) \(q+(0.270091 + 1.98168i) q^{2} +(-3.85410 + 1.07047i) q^{4} +(0.540182 - 0.935622i) q^{5} +(5.20820 - 3.00696i) q^{7} +(-3.16228 - 7.34847i) q^{8} +(2.00000 + 0.817763i) q^{10} +(15.3500 - 8.86234i) q^{11} +(-6.20820 + 10.7529i) q^{13} +(7.36551 + 9.50884i) q^{14} +(13.7082 - 8.25137i) q^{16} +26.3786 q^{17} +5.19615i q^{19} +(-1.08036 + 4.18423i) q^{20} +(21.7082 + 28.0252i) q^{22} +(-25.8384 - 14.9178i) q^{23} +(11.9164 + 20.6398i) q^{25} +(-22.9856 - 9.39840i) q^{26} +(-16.8541 + 17.1643i) q^{28} +(2.16073 + 3.74249i) q^{29} +(38.8328 + 22.4201i) q^{31} +(20.0540 + 24.9366i) q^{32} +(7.12461 + 52.2739i) q^{34} -6.49721i q^{35} -20.4164 q^{37} +(-10.2971 + 1.40343i) q^{38} +(-8.58359 - 1.01081i) q^{40} +(29.6197 - 51.3028i) q^{41} +(16.5836 - 9.57454i) q^{43} +(-49.6737 + 50.5880i) q^{44} +(22.5836 - 55.2326i) q^{46} +(-35.5617 + 20.5315i) q^{47} +(-6.41641 + 11.1135i) q^{49} +(-37.6830 + 29.1891i) q^{50} +(12.4164 - 48.0885i) q^{52} +70.0430 q^{53} -19.1491i q^{55} +(-38.5663 - 28.7635i) q^{56} +(-6.83282 + 5.29268i) q^{58} +(25.0733 + 14.4761i) q^{59} +(-9.20820 - 15.9491i) q^{61} +(-33.9411 + 83.0096i) q^{62} +(-44.0000 + 46.4758i) q^{64} +(6.70711 + 11.6171i) q^{65} +(-82.1656 - 47.4383i) q^{67} +(-101.666 + 28.2374i) q^{68} +(12.8754 - 1.75484i) q^{70} -83.8931i q^{71} +55.8328 q^{73} +(-5.51428 - 40.4588i) q^{74} +(-5.56231 - 20.0265i) q^{76} +(53.2974 - 92.3137i) q^{77} +(-35.5426 + 20.5205i) q^{79} +(-0.315246 - 17.2829i) q^{80} +(109.666 + 44.8403i) q^{82} +(-30.7000 + 17.7247i) q^{83} +(14.2492 - 24.6804i) q^{85} +(23.4527 + 30.2774i) q^{86} +(-113.666 - 84.7740i) q^{88} +26.3786 q^{89} +74.6712i q^{91} +(115.553 + 29.8356i) q^{92} +(-50.2918 - 64.9264i) q^{94} +(4.86163 + 2.80687i) q^{95} +(-38.1656 - 66.1048i) q^{97} +(-23.7565 - 9.71359i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 4 q^{4} - 12 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 4 q^{4} - 12 q^{7} + 16 q^{10} + 4 q^{13} + 56 q^{16} + 120 q^{22} - 12 q^{25} - 108 q^{28} + 96 q^{31} - 104 q^{34} - 56 q^{37} - 176 q^{40} + 240 q^{43} + 288 q^{46} + 56 q^{49} - 8 q^{52} + 160 q^{58} - 20 q^{61} - 352 q^{64} - 228 q^{67} + 264 q^{70} + 232 q^{73} + 36 q^{76} - 660 q^{79} + 448 q^{82} - 208 q^{85} - 480 q^{88} - 456 q^{94} + 124 q^{97}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.270091 + 1.98168i 0.135045 + 0.990839i
\(3\) 0 0
\(4\) −3.85410 + 1.07047i −0.963525 + 0.267617i
\(5\) 0.540182 0.935622i 0.108036 0.187124i −0.806938 0.590636i \(-0.798877\pi\)
0.914975 + 0.403511i \(0.132210\pi\)
\(6\) 0 0
\(7\) 5.20820 3.00696i 0.744029 0.429565i −0.0795033 0.996835i \(-0.525333\pi\)
0.823532 + 0.567269i \(0.192000\pi\)
\(8\) −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 \(0.325143\pi\)
\(14\) 7.36551 + 9.50884i 0.526108 + 0.679203i
\(15\) 0 0
\(16\) 13.7082 8.25137i 0.856763 0.515711i
\(17\) 26.3786 1.55168 0.775841 0.630929i \(-0.217326\pi\)
0.775841 + 0.630929i \(0.217326\pi\)
\(18\) 0 0
\(19\) 5.19615i 0.273482i 0.990607 + 0.136741i \(0.0436628\pi\)
−0.990607 + 0.136741i \(0.956337\pi\)
\(20\) −1.08036 + 4.18423i −0.0540182 + 0.209211i
\(21\) 0 0
\(22\) 21.7082 + 28.0252i 0.986737 + 1.27387i
\(23\) −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 0.900872 0.434085i \(-0.142928\pi\)
−0.826364 + 0.563136i \(0.809595\pi\)
\(30\) 0 0
\(31\) 38.8328 + 22.4201i 1.25267 + 0.723230i 0.971639 0.236468i \(-0.0759899\pi\)
0.281032 + 0.959698i \(0.409323\pi\)
\(32\) 20.0540 + 24.9366i 0.626688 + 0.779270i
\(33\) 0 0
\(34\) 7.12461 + 52.2739i 0.209547 + 1.53747i
\(35\) 6.49721i 0.185635i
\(36\) 0 0
\(37\) −20.4164 −0.551795 −0.275897 0.961187i \(-0.588975\pi\)
−0.275897 + 0.961187i \(0.588975\pi\)
\(38\) −10.2971 + 1.40343i −0.270976 + 0.0369324i
\(39\) 0 0
\(40\) −8.58359 1.01081i −0.214590 0.0252703i
\(41\) 29.6197 51.3028i 0.722431 1.25129i −0.237592 0.971365i \(-0.576358\pi\)
0.960023 0.279922i \(-0.0903087\pi\)
\(42\) 0 0
\(43\) 16.5836 9.57454i 0.385665 0.222664i −0.294615 0.955616i \(-0.595191\pi\)
0.680280 + 0.732952i \(0.261858\pi\)
\(44\) −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
\(50\) −37.6830 + 29.1891i −0.753660 + 0.583782i
\(51\) 0 0
\(52\) 12.4164 48.0885i 0.238777 0.924780i
\(53\) 70.0430 1.32157 0.660783 0.750577i \(-0.270224\pi\)
0.660783 + 0.750577i \(0.270224\pi\)
\(54\) 0 0
\(55\) 19.1491i 0.348165i
\(56\) −38.5663 28.7635i −0.688684 0.513634i
\(57\) 0 0
\(58\) −6.83282 + 5.29268i −0.117807 + 0.0912530i
\(59\) 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 −0.260088 0.965585i \(-0.583751\pi\)
−0.966265 + 0.257550i \(0.917085\pi\)
\(68\) −101.666 + 28.2374i −1.49508 + 0.415256i
\(69\) 0 0
\(70\) 12.8754 1.75484i 0.183934 0.0250691i
\(71\) 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 \(0.375092\pi\)
\(74\) −5.51428 40.4588i −0.0745173 0.546740i
\(75\) 0 0
\(76\) −5.56231 20.0265i −0.0731882 0.263507i
\(77\) 53.2974 92.3137i 0.692173 1.19888i
\(78\) 0 0
\(79\) −35.5426 + 20.5205i −0.449906 + 0.259753i −0.707790 0.706422i \(-0.750308\pi\)
0.257885 + 0.966176i \(0.416975\pi\)
\(80\) −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
\(86\) 23.4527 + 30.2774i 0.272706 + 0.352062i
\(87\) 0 0
\(88\) −113.666 84.7740i −1.29165 0.963341i
\(89\) 26.3786 0.296389 0.148194 0.988958i \(-0.452654\pi\)
0.148194 + 0.988958i \(0.452654\pi\)
\(90\) 0 0
\(91\) 74.6712i 0.820563i
\(92\) 115.553 + 29.8356i 1.25601 + 0.324300i
\(93\) 0 0
\(94\) −50.2918 64.9264i −0.535019 0.690707i
\(95\) 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 0.987533 0.157412i \(-0.0503149\pi\)
−0.630089 + 0.776523i \(0.716982\pi\)
\(102\) 0 0
\(103\) 50.2082 + 28.9877i 0.487458 + 0.281434i 0.723519 0.690304i \(-0.242523\pi\)
−0.236061 + 0.971738i \(0.575857\pi\)
\(104\) 98.6496 + 11.6171i 0.948554 + 0.111703i
\(105\) 0 0
\(106\) 18.9180 + 138.803i 0.178471 + 1.30946i
\(107\) 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 \(0.563449\pi\)
\(110\) 37.9473 5.17199i 0.344976 0.0470181i
\(111\) 0 0
\(112\) 46.5836 84.1948i 0.415925 0.751739i
\(113\) −40.6482 + 70.4048i −0.359719 + 0.623051i −0.987914 0.155005i \(-0.950461\pi\)
0.628195 + 0.778056i \(0.283794\pi\)
\(114\) 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
\(122\) 29.1189 22.5554i 0.238679 0.184880i
\(123\) 0 0
\(124\) −173.666 44.8403i −1.40053 0.361615i
\(125\) 52.7572 0.422057
\(126\) 0 0
\(127\) 191.968i 1.51156i −0.654826 0.755780i \(-0.727258\pi\)
0.654826 0.755780i \(-0.272742\pi\)
\(128\) −103.984 74.6412i −0.812376 0.583134i
\(129\) 0 0
\(130\) −21.2098 + 16.4290i −0.163152 + 0.126377i
\(131\) −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 0.660202 0.751088i \(-0.270471\pi\)
−0.980562 + 0.196208i \(0.937137\pi\)
\(138\) 0 0
\(139\) −158.916 91.7504i −1.14328 0.660075i −0.196042 0.980596i \(-0.562809\pi\)
−0.947242 + 0.320520i \(0.896142\pi\)
\(140\) 6.95505 + 25.0409i 0.0496789 + 0.178864i
\(141\) 0 0
\(142\) 166.249 22.6588i 1.17077 0.159569i
\(143\) 220.077i 1.53900i
\(144\) 0 0
\(145\) 4.66874 0.0321982
\(146\) 15.0799 + 110.643i 0.103287 + 0.757827i
\(147\) 0 0
\(148\) 78.6869 21.8551i 0.531668 0.147669i
\(149\) −76.9750 + 133.325i −0.516611 + 0.894796i 0.483203 + 0.875508i \(0.339473\pi\)
−0.999814 + 0.0192880i \(0.993860\pi\)
\(150\) 0 0
\(151\) −160.539 + 92.6875i −1.06318 + 0.613825i −0.926309 0.376765i \(-0.877036\pi\)
−0.136866 + 0.990590i \(0.543703\pi\)
\(152\) 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 \(0.951877\pi\)
\(158\) −50.2648 64.8916i −0.318132 0.410706i
\(159\) 0 0
\(160\) 34.1641 5.29268i 0.213525 0.0330792i
\(161\) −179.429 −1.11447
\(162\) 0 0
\(163\) 129.325i 0.793403i 0.917948 + 0.396701i \(0.129845\pi\)
−0.917948 + 0.396701i \(0.870155\pi\)
\(164\) −59.2393 + 229.433i −0.361216 + 1.39898i
\(165\) 0 0
\(166\) −43.4164 56.0503i −0.261545 0.337653i
\(167\) 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 0.535464 0.844558i \(-0.320137\pi\)
−0.999141 + 0.0414461i \(0.986804\pi\)
\(174\) 0 0
\(175\) 124.126 + 71.6643i 0.709292 + 0.409510i
\(176\) 137.295 248.145i 0.780084 1.40992i
\(177\) 0 0
\(178\) 7.12461 + 52.2739i 0.0400259 + 0.293673i
\(179\) 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 \(0.542555\pi\)
\(182\) −147.974 + 20.1680i −0.813046 + 0.110813i
\(183\) 0 0
\(184\) −27.9149 + 237.047i −0.151711 + 1.28830i
\(185\) −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 \(0.187433\pi\)
\(194\) 120.690 93.4863i 0.622115 0.481888i
\(195\) 0 0
\(196\) 12.8328 49.7013i 0.0654735 0.253578i
\(197\) −385.506 −1.95688 −0.978441 0.206528i \(-0.933784\pi\)
−0.978441 + 0.206528i \(0.933784\pi\)
\(198\) 0 0
\(199\) 121.386i 0.609978i 0.952356 + 0.304989i \(0.0986528\pi\)
−0.952356 + 0.304989i \(0.901347\pi\)
\(200\) 113.988 152.836i 0.569941 0.764181i
\(201\) 0 0
\(202\) −114.164 + 88.4311i −0.565169 + 0.437778i
\(203\) 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 0.929226 0.369511i \(-0.120475\pi\)
0.144607 + 0.989489i \(0.453808\pi\)
\(212\) −269.953 + 74.9786i −1.27336 + 0.353673i
\(213\) 0 0
\(214\) 127.623 17.3942i 0.596369 0.0812815i
\(215\) 20.6880i 0.0962231i
\(216\) 0 0
\(217\) 269.666 1.24270
\(218\) −11.6591 85.5435i −0.0534819 0.392401i
\(219\) 0 0
\(220\) 20.4984 + 73.8025i 0.0931748 + 0.335466i
\(221\) −163.764 + 283.647i −0.741012 + 1.28347i
\(222\) 0 0
\(223\) −60.6687 + 35.0271i −0.272057 + 0.157072i −0.629822 0.776739i \(-0.716872\pi\)
0.357765 + 0.933812i \(0.383539\pi\)
\(224\) 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 \(0.974788\pi\)
\(230\) −39.4776 50.9653i −0.171642 0.221588i
\(231\) 0 0
\(232\) 20.6687 27.7128i 0.0890894 0.119452i
\(233\) −7.38192 −0.0316821 −0.0158410 0.999875i \(-0.505043\pi\)
−0.0158410 + 0.999875i \(0.505043\pi\)
\(234\) 0 0
\(235\) 44.3630i 0.188779i
\(236\) −112.131 28.9521i −0.475132 0.122679i
\(237\) 0 0
\(238\) 194.292 + 250.830i 0.816352 + 1.05391i
\(239\) 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
\(248\) 41.9535 356.260i 0.169167 1.43653i
\(249\) 0 0
\(250\) 14.2492 + 104.548i 0.0569969 + 0.418191i
\(251\) 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
\(254\) 380.419 51.8488i 1.49771 0.204129i
\(255\) 0 0
\(256\) 119.830 226.223i 0.468085 0.883684i
\(257\) −33.4913 + 58.0086i −0.130316 + 0.225714i −0.923798 0.382879i \(-0.874933\pi\)
0.793482 + 0.608593i \(0.208266\pi\)
\(258\) 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
\(266\) −49.4094 + 38.2723i −0.185749 + 0.143881i
\(267\) 0 0
\(268\) 367.456 + 94.8767i 1.37110 + 0.354018i
\(269\) −279.092 −1.03752 −0.518758 0.854921i \(-0.673605\pi\)
−0.518758 + 0.854921i \(0.673605\pi\)
\(270\) 0 0
\(271\) 406.305i 1.49928i −0.661845 0.749641i \(-0.730226\pi\)
0.661845 0.749641i \(-0.269774\pi\)
\(272\) 361.603 217.660i 1.32942 0.800219i
\(273\) 0 0
\(274\) 138.790 107.506i 0.506534 0.392359i
\(275\) 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 0.869845 0.493326i \(-0.164219\pi\)
−0.862155 + 0.506644i \(0.830886\pi\)
\(282\) 0 0
\(283\) −38.4195 22.1815i −0.135758 0.0783799i 0.430583 0.902551i \(-0.358308\pi\)
−0.566341 + 0.824171i \(0.691641\pi\)
\(284\) 89.8048 + 323.333i 0.316214 + 1.13850i
\(285\) 0 0
\(286\) −436.122 + 59.4407i −1.52490 + 0.207835i
\(287\) 356.260i 1.24133i
\(288\) 0 0
\(289\) 406.830 1.40772
\(290\) 1.26098 + 9.25194i 0.00434822 + 0.0319032i
\(291\) 0 0
\(292\) −215.185 + 59.7671i −0.736936 + 0.204682i
\(293\) 194.464 336.821i 0.663699 1.14956i −0.315938 0.948780i \(-0.602319\pi\)
0.979636 0.200780i \(-0.0643475\pi\)
\(294\) 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
\(302\) −227.037 293.104i −0.751778 0.970542i
\(303\) 0 0
\(304\) 42.8754 + 71.2299i 0.141037 + 0.234309i
\(305\) −19.8964 −0.0652341
\(306\) 0 0
\(307\) 96.6999i 0.314983i 0.987520 + 0.157492i \(0.0503407\pi\)
−0.987520 + 0.157492i \(0.949659\pi\)
\(308\) −106.595 + 412.839i −0.346087 + 1.34039i
\(309\) 0 0
\(310\) 59.3313 + 76.5963i 0.191391 + 0.247085i
\(311\) −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 0.997257 0.0740196i \(-0.0235827\pi\)
−0.562731 + 0.826640i \(0.690249\pi\)
\(318\) 0 0
\(319\) 66.3344 + 38.2982i 0.207945 + 0.120057i
\(320\) 19.7158 + 66.2727i 0.0616118 + 0.207102i
\(321\) 0 0
\(322\) −48.4621 355.570i −0.150503 1.10426i
\(323\) 137.067i 0.424356i
\(324\) 0 0
\(325\) −295.918 −0.910517
\(326\) −256.280 + 34.9294i −0.786135 + 0.107145i
\(327\) 0 0
\(328\) −470.663 55.4256i −1.43495 0.168981i
\(329\) −123.475 + 213.865i −0.375304 + 0.650045i
\(330\) 0 0
\(331\) 48.0836 27.7611i 0.145268 0.0838703i −0.425605 0.904909i \(-0.639939\pi\)
0.570872 + 0.821039i \(0.306605\pi\)
\(332\) 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 \(-0.0539686\pi\)
\(338\) −23.4527 + 18.1664i −0.0693868 + 0.0537468i
\(339\) 0 0
\(340\) −28.4984 + 110.374i −0.0838190 + 0.324629i
\(341\) 794.779 2.33073
\(342\) 0 0
\(343\) 371.857i 1.08413i
\(344\) −122.800 91.5867i −0.356977 0.266240i
\(345\) 0 0
\(346\) 253.666 196.489i 0.733138 0.567886i
\(347\) −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 0.690014 0.723796i \(-0.257604\pi\)
−0.971833 + 0.235672i \(0.924271\pi\)
\(354\) 0 0
\(355\) −78.4922 45.3175i −0.221105 0.127655i
\(356\) −101.666 + 28.2374i −0.285578 + 0.0793185i
\(357\) 0 0
\(358\) −399.246 + 54.4148i −1.11521 + 0.151997i
\(359\) 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
\(362\) −13.0325 95.6206i −0.0360014 0.264145i
\(363\) 0 0
\(364\) −79.9330 287.791i −0.219596 0.790633i
\(365\) 30.1599 52.2384i 0.0826297 0.143119i
\(366\) 0 0
\(367\) −152.543 + 88.0705i −0.415647 + 0.239974i −0.693213 0.720732i \(-0.743806\pi\)
0.277566 + 0.960707i \(0.410472\pi\)
\(368\) −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 \(0.871655\pi\)
\(374\) 572.632 + 739.264i 1.53110 + 1.97664i
\(375\) 0 0
\(376\) 263.331 + 196.397i 0.700349 + 0.522334i
\(377\) −53.6569 −0.142326
\(378\) 0 0
\(379\) 30.3082i 0.0799689i −0.999200 0.0399844i \(-0.987269\pi\)
0.999200 0.0399844i \(-0.0127308\pi\)
\(380\) −21.7419 5.61373i −0.0572155 0.0147730i
\(381\) 0 0
\(382\) −180.541 233.077i −0.472620 0.610150i
\(383\) −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 \(-0.900659\pi\)
0.209936 0.977715i \(-0.432674\pi\)
\(390\) 0 0
\(391\) −681.580 393.511i −1.74317 1.00642i
\(392\) 101.958 + 12.0067i 0.260097 + 0.0306292i
\(393\) 0 0
\(394\) −104.122 763.948i −0.264268 1.93896i
\(395\) 44.3392i 0.112251i
\(396\) 0 0
\(397\) 26.8266 0.0675733 0.0337867 0.999429i \(-0.489243\pi\)
0.0337867 + 0.999429i \(0.489243\pi\)
\(398\) −240.547 + 32.7851i −0.604390 + 0.0823747i
\(399\) 0 0
\(400\) 333.659 + 184.608i 0.834149 + 0.461520i
\(401\) 252.532 437.399i 0.629756 1.09077i −0.357844 0.933781i \(-0.616488\pi\)
0.987600 0.156989i \(-0.0501787\pi\)
\(402\) 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 \(-0.148077\pi\)
\(410\) 101.193 78.3837i 0.246812 0.191180i
\(411\) 0 0
\(412\) −224.538 57.9754i −0.544995 0.140717i
\(413\) 174.116 0.421588
\(414\) 0 0
\(415\) 38.2982i 0.0922847i
\(416\) −392.641 + 60.8277i −0.943849 + 0.146220i
\(417\) 0 0
\(418\) −145.623 + 112.799i −0.348381 + 0.269854i
\(419\) −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
\(428\) 68.9396 + 248.210i 0.161074 + 0.579930i
\(429\) 0 0
\(430\) 40.9969 5.58763i 0.0953416 0.0129945i
\(431\) 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 \(0.435291\pi\)
\(434\) 72.8342 + 534.391i 0.167821 + 1.23131i
\(435\) 0 0
\(436\) 166.371 46.2090i 0.381584 0.105984i
\(437\) 77.5152 134.260i 0.177380 0.307232i
\(438\) 0 0
\(439\) 415.830 240.079i 0.947220 0.546878i 0.0550040 0.998486i \(-0.482483\pi\)
0.892216 + 0.451608i \(0.149150\pi\)
\(440\) −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
\(446\) −85.7986 110.765i −0.192373 0.248353i
\(447\) 0 0
\(448\) −89.4102 + 374.362i −0.199576 + 0.835629i
\(449\) 801.711 1.78555 0.892774 0.450504i \(-0.148756\pi\)
0.892774 + 0.450504i \(0.148756\pi\)
\(450\) 0 0
\(451\) 1050.00i 2.32816i
\(452\) 81.2965 314.860i 0.179859 0.696593i
\(453\) 0 0
\(454\) −365.410 471.743i −0.804868 1.03908i
\(455\) 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 0.949901 0.312550i \(-0.101183\pi\)
−0.745627 + 0.666364i \(0.767850\pi\)
\(462\) 0 0
\(463\) 474.950 + 274.212i 1.02581 + 0.592251i 0.915781 0.401677i \(-0.131573\pi\)
0.110028 + 0.993928i \(0.464906\pi\)
\(464\) 60.5003 + 33.4738i 0.130389 + 0.0721419i
\(465\) 0 0
\(466\) −1.99379 14.6286i −0.00427852 0.0313918i
\(467\) 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
\(470\) −87.9133 + 11.9820i −0.187050 + 0.0254937i
\(471\) 0 0
\(472\) 27.0883 230.028i 0.0573904 0.487347i
\(473\) 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
\(482\) −657.480 + 509.282i −1.36407 + 1.05660i
\(483\) 0 0
\(484\) −193.164 + 748.121i −0.399099 + 1.54571i
\(485\) −82.4655 −0.170032
\(486\) 0 0
\(487\) 549.208i 1.12774i 0.825865 + 0.563868i \(0.190687\pi\)
−0.825865 + 0.563868i \(0.809313\pi\)
\(488\) −88.0824 + 118.102i −0.180497 + 0.242012i
\(489\) 0 0
\(490\) −21.9211 + 16.9800i −0.0447369 + 0.0346530i
\(491\) 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 0.933001 0.359874i \(-0.117180\pi\)
0.154840 + 0.987939i \(0.450514\pi\)
\(500\) −203.332 + 56.4748i −0.406663 + 0.112950i
\(501\) 0 0
\(502\) 277.495 37.8209i 0.552780 0.0753405i
\(503\) 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
\(506\) −142.831 1047.96i −0.282275 2.07108i
\(507\) 0 0
\(508\) 205.495 + 739.865i 0.404518 + 1.45643i
\(509\) 218.682 378.768i 0.429630 0.744140i −0.567211 0.823573i \(-0.691977\pi\)
0.996840 + 0.0794323i \(0.0253108\pi\)
\(510\) 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
\(518\) −150.377 194.136i −0.290304 0.374780i
\(519\) 0 0
\(520\) 64.1579 86.0234i 0.123381 0.165430i
\(521\) 385.236 0.739417 0.369709 0.929148i \(-0.379458\pi\)
0.369709 + 0.929148i \(0.379458\pi\)
\(522\) 0 0
\(523\) 418.572i 0.800328i 0.916443 + 0.400164i \(0.131047\pi\)
−0.916443 + 0.400164i \(0.868953\pi\)
\(524\) 549.179 + 141.797i 1.04805 + 0.270606i
\(525\) 0 0
\(526\) 45.5805 + 58.8442i 0.0866549 + 0.111871i
\(527\) 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
\(536\) −88.7687 + 753.805i −0.165613 + 1.40635i
\(537\) 0 0
\(538\) −75.3800 553.070i −0.140112 1.02801i
\(539\) 227.457i 0.421999i
\(540\) 0 0
\(541\) −23.4257 −0.0433008 −0.0216504 0.999766i \(-0.506892\pi\)
−0.0216504 + 0.999766i \(0.506892\pi\)
\(542\) 805.167 109.739i 1.48555 0.202471i
\(543\) 0 0
\(544\) 528.997 + 657.793i 0.972421 + 1.20918i
\(545\) −23.3181 + 40.3882i −0.0427855 + 0.0741067i
\(546\) 0 0
\(547\) −625.412 + 361.082i −1.14335 + 0.660113i −0.947258 0.320473i \(-0.896158\pi\)
−0.196091 + 0.980586i \(0.562825\pi\)
\(548\) 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
\(554\) 7.64135 5.91897i 0.0137931 0.0106841i
\(555\) 0 0
\(556\) 710.696 + 183.501i 1.27823 + 0.330038i
\(557\) 2.34135 0.00420349 0.00210175 0.999998i \(-0.499331\pi\)
0.00210175 + 0.999998i \(0.499331\pi\)
\(558\) 0 0
\(559\) 237.763i 0.425336i
\(560\) −53.6109 89.0651i −0.0957338 0.159045i
\(561\) 0 0
\(562\) −6.83282 + 5.29268i −0.0121580 + 0.00941757i
\(563\) −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 0.874097 0.485751i \(-0.161454\pi\)
−0.857721 + 0.514115i \(0.828121\pi\)
\(570\) 0 0
\(571\) −246.409 142.264i −0.431539 0.249149i 0.268463 0.963290i \(-0.413484\pi\)
−0.700002 + 0.714141i \(0.746818\pi\)
\(572\) −235.585 848.198i −0.411861 1.48286i
\(573\) 0 0
\(574\) 705.994 96.2227i 1.22995 0.167635i
\(575\) 711.067i 1.23664i
\(576\) 0 0
\(577\) 664.823 1.15221 0.576104 0.817377i \(-0.304572\pi\)
0.576104 + 0.817377i \(0.304572\pi\)
\(578\) 109.881 + 806.206i 0.190105 + 1.39482i
\(579\) 0 0
\(580\) −17.9938 + 4.99773i −0.0310238 + 0.00861677i
\(581\) −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
\(590\) 38.3086 + 49.4562i 0.0649298 + 0.0838240i
\(591\) 0 0
\(592\) −279.872 + 168.463i −0.472757 + 0.284567i
\(593\) −550.801 −0.928838 −0.464419 0.885615i \(-0.653737\pi\)
−0.464419 + 0.885615i \(0.653737\pi\)
\(594\) 0 0
\(595\) 171.387i 0.288046i
\(596\) 153.950 596.246i 0.258305 1.00041i
\(597\) 0 0
\(598\) 453.708 + 585.735i 0.758709 + 0.979490i
\(599\) 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 0.569328 0.822110i \(-0.307203\pi\)
−0.427305 + 0.904108i \(0.640537\pi\)
\(608\) −129.575 + 104.204i −0.213116 + 0.171388i
\(609\) 0 0
\(610\) −5.37384 39.4283i −0.00880957 0.0646365i
\(611\) 509.856i 0.834461i
\(612\) 0 0
\(613\) −960.234 −1.56645 −0.783225 0.621739i \(-0.786427\pi\)
−0.783225 + 0.621739i \(0.786427\pi\)
\(614\) −191.628 + 26.1177i −0.312098 + 0.0425370i
\(615\) 0 0
\(616\) −846.906 99.7323i −1.37485 0.161903i
\(617\) 177.312 307.114i 0.287378 0.497754i −0.685805 0.727786i \(-0.740550\pi\)
0.973183 + 0.230032i \(0.0738829\pi\)
\(618\) 0 0
\(619\) 312.330 180.324i 0.504571 0.291314i −0.226028 0.974121i \(-0.572574\pi\)
0.730599 + 0.682806i \(0.239241\pi\)
\(620\) −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
\(626\) 446.136 345.575i 0.712677 0.552037i
\(627\) 0 0
\(628\) 196.164 759.740i 0.312363 1.20978i
\(629\) −538.556 −0.856210
\(630\) 0 0
\(631\) 82.7121i 0.131081i 0.997850 + 0.0655405i \(0.0208772\pi\)
−0.997850 + 0.0655405i \(0.979123\pi\)
\(632\) 263.190 + 196.292i 0.416440 + 0.310589i
\(633\) 0 0
\(634\) −435.587 + 337.404i −0.687045 + 0.532183i
\(635\) −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 \(0.0354957\pi\)
−0.400521 + 0.916287i \(0.631171\pi\)
\(642\) 0 0
\(643\) 681.580 + 393.511i 1.06000 + 0.611992i 0.925432 0.378913i \(-0.123702\pi\)
0.134568 + 0.990904i \(0.457035\pi\)
\(644\) 691.537 192.073i 1.07382 0.298249i
\(645\) 0 0
\(646\) −271.623 + 37.0206i −0.420469 + 0.0573074i
\(647\) 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
\(650\) −79.9247 586.414i −0.122961 0.902176i
\(651\) 0 0
\(652\) −138.438 498.430i −0.212328 0.764464i
\(653\) −469.774 + 813.672i −0.719409 + 1.24605i 0.241826 + 0.970320i \(0.422254\pi\)
−0.961234 + 0.275733i \(0.911079\pi\)
\(654\) 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 \(0.248819\pi\)
\(662\) 68.0005 + 87.7882i 0.102720 + 0.132611i
\(663\) 0 0
\(664\) 227.331 + 169.548i 0.342366 + 0.255343i
\(665\) 33.7605 0.0507677
\(666\) 0 0
\(667\) 128.933i 0.193303i
\(668\) −534.280 137.951i −0.799821 0.206513i
\(669\) 0 0
\(670\) −125.538 162.069i −0.187370 0.241894i
\(671\) −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 \(-0.982098\pi\)
0.450530 0.892761i \(-0.351235\pi\)
\(678\) 0 0
\(679\) −397.549 229.525i −0.585492 0.338034i
\(680\) −226.423 26.6638i −0.332975 0.0392114i
\(681\) 0 0
\(682\) 214.663 + 1575.00i 0.314754 + 2.30938i
\(683\) 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
\(686\) −736.902 + 100.435i −1.07420 + 0.146407i
\(687\) 0 0
\(688\) 148.328 268.087i 0.215593 0.389662i
\(689\) −434.841 + 753.167i −0.631119 + 1.09313i
\(690\) 0 0
\(691\) −192.924 + 111.385i −0.279196 + 0.161194i −0.633059 0.774103i \(-0.718201\pi\)
0.353864 + 0.935297i \(0.384868\pi\)
\(692\) 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
\(698\) 455.498 352.827i 0.652575 0.505483i
\(699\) 0 0
\(700\) −555.109 143.329i −0.793013 0.204755i
\(701\) 2.34135 0.00334001 0.00167000 0.999999i \(-0.499468\pi\)
0.00167000 + 0.999999i \(0.499468\pi\)
\(702\) 0 0
\(703\) 106.087i 0.150906i
\(704\) −263.517 + 1103.35i −0.374313 + 1.56725i
\(705\) 0 0
\(706\) 314.590 243.680i 0.445595 0.345156i
\(707\) 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
\(716\) −215.665 776.481i −0.301209 1.08447i
\(717\) 0 0
\(718\) −643.368 + 87.6871i −0.896055 + 0.122127i
\(719\) 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
\(722\) 90.2103 + 661.881i 0.124945 + 0.916732i
\(723\) 0 0
\(724\) 185.969 51.6525i 0.256864 0.0713432i
\(725\) −51.4962 + 89.1940i −0.0710292 + 0.123026i
\(726\) 0 0
\(727\) −471.659 + 272.313i −0.648775 + 0.374570i −0.787987 0.615692i \(-0.788876\pi\)
0.139212 + 0.990263i \(0.455543\pi\)
\(728\) 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 \(0.134876\pi\)
\(734\) −215.728 278.503i −0.293907 0.379432i
\(735\) 0 0
\(736\) −146.164 943.485i −0.198592 1.28191i
\(737\) −1681.66 −2.28176
\(738\) 0 0
\(739\) 1172.87i 1.58710i −0.608505 0.793550i \(-0.708231\pi\)
0.608505 0.793550i \(-0.291769\pi\)
\(740\) 22.0571 85.4269i 0.0298069 0.115442i
\(741\) 0 0
\(742\) 515.902 + 666.027i 0.695286 + 0.897611i
\(743\) −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 −0.141289 0.989968i \(-0.545125\pi\)
−0.927982 + 0.372625i \(0.878458\pi\)
\(752\) −318.073 + 574.883i −0.422970 + 0.764472i
\(753\) 0 0
\(754\) −14.4922 106.331i −0.0192205 0.141022i
\(755\) 200.272i 0.265261i
\(756\) 0 0
\(757\) −757.748 −1.00099 −0.500494 0.865740i \(-0.666848\pi\)
−0.500494 + 0.865740i \(0.666848\pi\)
\(758\) 60.0611 8.18596i 0.0792363 0.0107994i
\(759\) 0 0
\(760\) 5.25233 44.6017i 0.00691096 0.0586864i
\(761\) −476.570 + 825.443i −0.626241 + 1.08468i 0.362058 + 0.932156i \(0.382074\pi\)
−0.988299 + 0.152526i \(0.951259\pi\)
\(762\) 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 \(0.196861\pi\)
\(770\) 182.085 141.043i 0.236475 0.183172i
\(771\) 0 0
\(772\) 25.1641 97.4601i 0.0325960 0.126244i
\(773\) 60.1391 0.0777996 0.0388998 0.999243i \(-0.487615\pi\)
0.0388998 + 0.999243i \(0.487615\pi\)
\(774\) 0 0
\(775\) 1068.67i 1.37893i
\(776\) −365.079 + 489.501i −0.470462 + 0.630800i
\(777\) 0 0
\(778\) 912.456 706.785i 1.17282 0.908464i
\(779\) 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 0.669642 0.742684i \(-0.266448\pi\)
−0.308363 + 0.951269i \(0.599781\pi\)
\(788\) 1485.78 412.671i 1.88551 0.523694i
\(789\) 0 0
\(790\) −87.8661 + 11.9756i −0.111223 + 0.0151590i
\(791\) 488.910i 0.618091i
\(792\) 0 0
\(793\) 228.666 0.288355
\(794\) 7.24562 + 53.1617i 0.00912546 + 0.0669543i
\(795\) 0 0
\(796\) −129.939 467.833i −0.163240 0.587730i
\(797\) 223.363 386.875i 0.280254 0.485414i −0.691193 0.722670i \(-0.742915\pi\)
0.971447 + 0.237256i \(0.0762479\pi\)
\(798\) 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
\(806\) −681.883 880.307i −0.846009 1.09219i
\(807\) 0 0
\(808\) 345.337 463.031i 0.427398 0.573059i
\(809\) −793.341 −0.980644 −0.490322 0.871541i \(-0.663121\pi\)
−0.490322 + 0.871541i \(0.663121\pi\)
\(810\) 0 0
\(811\) 788.930i 0.972787i 0.873740 + 0.486394i \(0.161688\pi\)
−0.873740 + 0.486394i \(0.838312\pi\)
\(812\) −100.654 25.9888i −0.123959 0.0320060i
\(813\) 0 0
\(814\) −443.204 572.173i −0.544476 0.702916i
\(815\) 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 \(0.177346\pi\)
0.0335444 + 0.999437i \(0.489320\pi\)
\(822\) 0 0
\(823\) −112.530 64.9693i −0.136732 0.0789421i 0.430074 0.902794i \(-0.358488\pi\)
−0.566805 + 0.823852i \(0.691821\pi\)
\(824\) 54.2431 460.621i 0.0658290 0.559006i
\(825\) 0 0
\(826\) 47.0270 + 345.041i 0.0569335 + 0.417726i
\(827\) 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 \(0.467740\pi\)
\(830\) −75.8947 + 10.3440i −0.0914394 + 0.0124626i
\(831\) 0 0
\(832\) −226.590 761.660i −0.272344 0.915457i
\(833\) −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
\(842\) −29.3881 + 22.7640i −0.0349028 + 0.0270356i
\(843\) 0 0
\(844\) −1013.29 261.631i −1.20058 0.309989i
\(845\) 16.0248 0.0189643
\(846\) 0 0
\(847\) 1161.67i 1.37151i
\(848\) 960.163 577.951i 1.13227 0.681546i
\(849\) 0 0
\(850\) −994.024 + 769.968i −1.16944 + 0.905844i
\(851\) 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 0.716087 0.698011i \(-0.245931\pi\)
−0.962539 + 0.271144i \(0.912598\pi\)
\(858\) 0 0
\(859\) −1145.91 661.590i −1.33400 0.770186i −0.348091 0.937461i \(-0.613170\pi\)
−0.985910 + 0.167275i \(0.946503\pi\)
\(860\) 22.1458 + 79.7335i 0.0257509 + 0.0927134i
\(861\) 0 0
\(862\) −610.614 + 83.2229i −0.708369 + 0.0965463i
\(863\) 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
\(866\) 47.2224 + 346.475i 0.0545293 + 0.400086i
\(867\) 0 0
\(868\) −1039.32 + 288.668i −1.19737 + 0.332567i
\(869\) −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 \(0.0254083\pi\)
\(878\) 588.072 + 759.198i 0.669786 + 0.864690i
\(879\) 0 0
\(880\) −158.006 262.500i −0.179553 0.298295i
\(881\) 996.177 1.13073 0.565367 0.824839i \(-0.308735\pi\)
0.565367 + 0.824839i \(0.308735\pi\)
\(882\) 0 0
\(883\) 950.011i 1.07589i 0.842980 + 0.537945i \(0.180799\pi\)
−0.842980 + 0.537945i \(0.819201\pi\)
\(884\) 327.527 1268.51i 0.370506 1.43496i
\(885\) 0 0
\(886\) −680.912 879.053i −0.768523 0.992159i
\(887\) −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
\(896\) −766.013 76.0707i −0.854926 0.0849003i
\(897\) 0 0
\(898\) 216.535 + 1588.73i 0.241130 + 1.76919i
\(899\) 193.775i 0.215545i
\(900\) 0 0
\(901\) 1847.63 2.05065
\(902\) 2080.76 283.595i 2.30683 0.314407i
\(903\) 0 0
\(904\) 645.909 + 76.0628i 0.714501 + 0.0841402i
\(905\) −26.0650 + 45.1459i −0.0288011 + 0.0498850i
\(906\) 0 0
\(907\) 593.837 342.852i 0.654727 0.378007i −0.135538 0.990772i \(-0.543276\pi\)
0.790265 + 0.612765i \(0.209943\pi\)
\(908\) 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
\(914\) −217.928 + 168.806i −0.238433 + 0.184690i
\(915\) 0 0
\(916\) 259.666 1005.68i 0.283478 1.09790i
\(917\) −852.758 −0.929943
\(918\) 0 0
\(919\) 953.775i 1.03784i −0.854823 0.518920i \(-0.826334\pi\)
0.854823 0.518920i \(-0.173666\pi\)
\(920\) 206.707 + 154.166i 0.224682 + 0.167572i
\(921\) 0 0
\(922\) −297.793 + 230.670i −0.322986 + 0.250184i
\(923\) 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 0.903479 0.428633i \(-0.141005\pi\)
−0.822947 + 0.568119i \(0.807671\pi\)
\(930\) 0 0
\(931\) −57.7477 33.3406i −0.0620276 0.0358116i
\(932\) 28.4507 7.90210i 0.0305265 0.00847865i
\(933\) 0 0
\(934\) 1225.86 167.077i 1.31248 0.178884i
\(935\) 505.126i 0.540241i
\(936\) 0 0
\(937\) −661.158 −0.705611 −0.352806 0.935697i \(-0.614772\pi\)
−0.352806 + 0.935697i \(0.614772\pi\)
\(938\) −154.109 1130.71i −0.164295 1.20544i
\(939\) 0 0
\(940\) −47.4891 170.980i −0.0505204 0.181893i
\(941\) 233.357 404.186i 0.247988 0.429528i −0.714979 0.699145i \(-0.753564\pi\)
0.962967 + 0.269618i \(0.0868973\pi\)
\(942\) 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
\(950\) −151.671 195.807i −0.159654 0.206112i
\(951\) 0 0
\(952\) −1017.33 758.740i −1.06862 0.796996i
\(953\) −21.6959 −0.0227659 −0.0113829 0.999935i \(-0.503623\pi\)
−0.0113829 + 0.999935i \(0.503623\pi\)
\(954\) 0 0
\(955\) 159.258i 0.166762i
\(956\) −318.073 82.1262i −0.332713 0.0859060i
\(957\) 0 0
\(958\) 943.574 + 1218.15i 0.984942 + 1.27155i
\(959\) −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 0.184760 0.982784i \(-0.440849\pi\)
−0.758736 + 0.651399i \(0.774183\pi\)
\(968\) −1534.71 180.729i −1.58544 0.186703i
\(969\) 0 0
\(970\) −22.2732 163.420i −0.0229620 0.168474i
\(971\) 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
\(974\) −1088.35 + 148.336i −1.11741 + 0.152296i
\(975\) 0 0
\(976\) −257.830 142.653i −0.264170 0.146161i
\(977\) 504.976 874.644i 0.516864 0.895235i −0.482944 0.875651i \(-0.660433\pi\)
0.999808 0.0195835i \(-0.00623402\pi\)
\(978\) 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
\(986\) −180.240 + 139.613i −0.182799 + 0.141596i
\(987\) 0 0
\(988\) 249.875 + 64.5175i 0.252910 + 0.0653012i
\(989\) −571.325 −0.577679
\(990\) 0 0
\(991\) 265.720i 0.268133i 0.990972 + 0.134066i \(0.0428035\pi\)
−0.990972 + 0.134066i \(0.957196\pi\)
\(992\) 219.672 + 1417.97i 0.221443 + 1.42941i
\(993\) 0 0
\(994\) 797.726 617.916i 0.802541 0.621646i
\(995\) 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.o.271.3 8
3.2 odd 2 inner 324.3.f.o.271.2 8
4.3 odd 2 324.3.f.p.271.4 8
9.2 odd 6 324.3.f.p.55.2 8
9.4 even 3 108.3.d.d.55.1 8
9.5 odd 6 108.3.d.d.55.8 yes 8
9.7 even 3 324.3.f.p.55.3 8
12.11 even 2 324.3.f.p.271.1 8
36.7 odd 6 inner 324.3.f.o.55.3 8
36.11 even 6 inner 324.3.f.o.55.2 8
36.23 even 6 108.3.d.d.55.7 yes 8
36.31 odd 6 108.3.d.d.55.2 yes 8
72.5 odd 6 1728.3.g.l.703.4 8
72.13 even 6 1728.3.g.l.703.6 8
72.59 even 6 1728.3.g.l.703.3 8
72.67 odd 6 1728.3.g.l.703.5 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
108.3.d.d.55.1 8 9.4 even 3
108.3.d.d.55.2 yes 8 36.31 odd 6
108.3.d.d.55.7 yes 8 36.23 even 6
108.3.d.d.55.8 yes 8 9.5 odd 6
324.3.f.o.55.2 8 36.11 even 6 inner
324.3.f.o.55.3 8 36.7 odd 6 inner
324.3.f.o.271.2 8 3.2 odd 2 inner
324.3.f.o.271.3 8 1.1 even 1 trivial
324.3.f.p.55.2 8 9.2 odd 6
324.3.f.p.55.3 8 9.7 even 3
324.3.f.p.271.1 8 12.11 even 2
324.3.f.p.271.4 8 4.3 odd 2
1728.3.g.l.703.3 8 72.59 even 6
1728.3.g.l.703.4 8 72.5 odd 6
1728.3.g.l.703.5 8 72.67 odd 6
1728.3.g.l.703.6 8 72.13 even 6