Properties

Label 392.3.g.h.99.1
Level $392$
Weight $3$
Character 392.99
Analytic conductor $10.681$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [392,3,Mod(99,392)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(392, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1, 0]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("392.99");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 392 = 2^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 392.g (of order \(2\), degree \(1\), 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: \(10.6812263629\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\sqrt{2}, \sqrt{-7})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} + 6x^{2} + 16 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2 \)
Twist minimal: no (minimal twist has level 56)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 99.1
Root \(0.707107 + 1.87083i\) of defining polynomial
Character \(\chi\) \(=\) 392.99
Dual form 392.3.g.h.99.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.707107 - 1.87083i) q^{2} -0.585786 q^{3} +(-3.00000 + 2.64575i) q^{4} +9.03316i q^{5} +(0.414214 + 1.09591i) q^{6} +(7.07107 + 3.74166i) q^{8} -8.65685 q^{9} +O(q^{10})\) \(q+(-0.707107 - 1.87083i) q^{2} -0.585786 q^{3} +(-3.00000 + 2.64575i) q^{4} +9.03316i q^{5} +(0.414214 + 1.09591i) q^{6} +(7.07107 + 3.74166i) q^{8} -8.65685 q^{9} +(16.8995 - 6.38741i) q^{10} +12.4853 q^{11} +(1.75736 - 1.54985i) q^{12} -9.03316i q^{13} -5.29150i q^{15} +(2.00000 - 15.8745i) q^{16} -12.3431 q^{17} +(6.12132 + 16.1955i) q^{18} -28.8701 q^{19} +(-23.8995 - 27.0995i) q^{20} +(-8.82843 - 23.3578i) q^{22} +24.6418i q^{23} +(-4.14214 - 2.19181i) q^{24} -56.5980 q^{25} +(-16.8995 + 6.38741i) q^{26} +10.3431 q^{27} -22.4499i q^{29} +(-9.89949 + 3.74166i) q^{30} -16.7824i q^{31} +(-31.1127 + 7.48331i) q^{32} -7.31371 q^{33} +(8.72792 + 23.0919i) q^{34} +(25.9706 - 22.9039i) q^{36} -16.2506i q^{37} +(20.4142 + 54.0109i) q^{38} +5.29150i q^{39} +(-33.7990 + 63.8741i) q^{40} -6.97056 q^{41} -22.8284 q^{43} +(-37.4558 + 33.0329i) q^{44} -78.1987i q^{45} +(46.1005 - 17.4244i) q^{46} -6.19938i q^{47} +(-1.17157 + 9.29907i) q^{48} +(40.0208 + 105.885i) q^{50} +7.23045 q^{51} +(23.8995 + 27.0995i) q^{52} -8.01514i q^{53} +(-7.31371 - 19.3503i) q^{54} +112.782i q^{55} +16.9117 q^{57} +(-42.0000 + 15.8745i) q^{58} -30.4437 q^{59} +(14.0000 + 15.8745i) q^{60} -15.2325i q^{61} +(-31.3970 + 11.8669i) q^{62} +(36.0000 + 52.9150i) q^{64} +81.5980 q^{65} +(5.17157 + 13.6827i) q^{66} -78.6274 q^{67} +(37.0294 - 32.6569i) q^{68} -14.4348i q^{69} +17.5345i q^{71} +(-61.2132 - 32.3910i) q^{72} -46.6863 q^{73} +(-30.4020 + 11.4909i) q^{74} +33.1543 q^{75} +(86.6102 - 76.3830i) q^{76} +(9.89949 - 3.74166i) q^{78} +81.0325i q^{79} +(143.397 + 18.0663i) q^{80} +71.8528 q^{81} +(4.92893 + 13.0407i) q^{82} -40.3848 q^{83} -111.498i q^{85} +(16.1421 + 42.7081i) q^{86} +13.1509i q^{87} +(88.2843 + 46.7156i) q^{88} -111.941 q^{89} +(-146.296 + 55.2949i) q^{90} +(-65.1960 - 73.9253i) q^{92} +9.83089i q^{93} +(-11.5980 + 4.38362i) q^{94} -260.788i q^{95} +(18.2254 - 4.38362i) q^{96} +164.108 q^{97} -108.083 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 8 q^{3} - 12 q^{4} - 4 q^{6} - 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 8 q^{3} - 12 q^{4} - 4 q^{6} - 12 q^{9} + 28 q^{10} + 16 q^{11} + 24 q^{12} + 8 q^{16} - 72 q^{17} + 16 q^{18} - 8 q^{19} - 56 q^{20} - 24 q^{22} + 40 q^{24} - 68 q^{25} - 28 q^{26} + 64 q^{27} + 16 q^{33} - 16 q^{34} + 36 q^{36} + 76 q^{38} - 56 q^{40} + 40 q^{41} - 80 q^{43} - 48 q^{44} + 224 q^{46} - 16 q^{48} + 112 q^{50} + 176 q^{51} + 56 q^{52} + 16 q^{54} - 136 q^{57} - 168 q^{58} - 184 q^{59} + 56 q^{60} + 112 q^{62} + 144 q^{64} + 168 q^{65} + 32 q^{66} - 224 q^{67} + 216 q^{68} - 160 q^{72} - 232 q^{73} - 280 q^{74} - 88 q^{75} + 24 q^{76} + 336 q^{80} - 52 q^{81} + 48 q^{82} - 88 q^{83} + 8 q^{86} + 240 q^{88} - 312 q^{89} - 308 q^{90} + 56 q^{92} + 112 q^{94} - 176 q^{96} + 136 q^{97} - 240 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/392\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(295\) \(297\)
\(\chi(n)\) \(-1\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.707107 1.87083i −0.353553 0.935414i
\(3\) −0.585786 −0.195262 −0.0976311 0.995223i \(-0.531127\pi\)
−0.0976311 + 0.995223i \(0.531127\pi\)
\(4\) −3.00000 + 2.64575i −0.750000 + 0.661438i
\(5\) 9.03316i 1.80663i 0.428976 + 0.903316i \(0.358875\pi\)
−0.428976 + 0.903316i \(0.641125\pi\)
\(6\) 0.414214 + 1.09591i 0.0690356 + 0.182651i
\(7\) 0 0
\(8\) 7.07107 + 3.74166i 0.883883 + 0.467707i
\(9\) −8.65685 −0.961873
\(10\) 16.8995 6.38741i 1.68995 0.638741i
\(11\) 12.4853 1.13503 0.567513 0.823365i \(-0.307906\pi\)
0.567513 + 0.823365i \(0.307906\pi\)
\(12\) 1.75736 1.54985i 0.146447 0.129154i
\(13\) 9.03316i 0.694858i −0.937706 0.347429i \(-0.887055\pi\)
0.937706 0.347429i \(-0.112945\pi\)
\(14\) 0 0
\(15\) 5.29150i 0.352767i
\(16\) 2.00000 15.8745i 0.125000 0.992157i
\(17\) −12.3431 −0.726067 −0.363034 0.931776i \(-0.618259\pi\)
−0.363034 + 0.931776i \(0.618259\pi\)
\(18\) 6.12132 + 16.1955i 0.340073 + 0.899750i
\(19\) −28.8701 −1.51948 −0.759738 0.650229i \(-0.774673\pi\)
−0.759738 + 0.650229i \(0.774673\pi\)
\(20\) −23.8995 27.0995i −1.19497 1.35497i
\(21\) 0 0
\(22\) −8.82843 23.3578i −0.401292 1.06172i
\(23\) 24.6418i 1.07138i 0.844414 + 0.535690i \(0.179949\pi\)
−0.844414 + 0.535690i \(0.820051\pi\)
\(24\) −4.14214 2.19181i −0.172589 0.0913255i
\(25\) −56.5980 −2.26392
\(26\) −16.8995 + 6.38741i −0.649981 + 0.245670i
\(27\) 10.3431 0.383079
\(28\) 0 0
\(29\) 22.4499i 0.774136i −0.922051 0.387068i \(-0.873488\pi\)
0.922051 0.387068i \(-0.126512\pi\)
\(30\) −9.89949 + 3.74166i −0.329983 + 0.124722i
\(31\) 16.7824i 0.541367i −0.962668 0.270684i \(-0.912750\pi\)
0.962668 0.270684i \(-0.0872497\pi\)
\(32\) −31.1127 + 7.48331i −0.972272 + 0.233854i
\(33\) −7.31371 −0.221628
\(34\) 8.72792 + 23.0919i 0.256704 + 0.679174i
\(35\) 0 0
\(36\) 25.9706 22.9039i 0.721405 0.636219i
\(37\) 16.2506i 0.439204i −0.975589 0.219602i \(-0.929524\pi\)
0.975589 0.219602i \(-0.0704759\pi\)
\(38\) 20.4142 + 54.0109i 0.537216 + 1.42134i
\(39\) 5.29150i 0.135680i
\(40\) −33.7990 + 63.8741i −0.844975 + 1.59685i
\(41\) −6.97056 −0.170014 −0.0850069 0.996380i \(-0.527091\pi\)
−0.0850069 + 0.996380i \(0.527091\pi\)
\(42\) 0 0
\(43\) −22.8284 −0.530894 −0.265447 0.964126i \(-0.585519\pi\)
−0.265447 + 0.964126i \(0.585519\pi\)
\(44\) −37.4558 + 33.0329i −0.851269 + 0.750749i
\(45\) 78.1987i 1.73775i
\(46\) 46.1005 17.4244i 1.00218 0.378790i
\(47\) 6.19938i 0.131902i −0.997823 0.0659509i \(-0.978992\pi\)
0.997823 0.0659509i \(-0.0210081\pi\)
\(48\) −1.17157 + 9.29907i −0.0244078 + 0.193731i
\(49\) 0 0
\(50\) 40.0208 + 105.885i 0.800416 + 2.11770i
\(51\) 7.23045 0.141773
\(52\) 23.8995 + 27.0995i 0.459606 + 0.521144i
\(53\) 8.01514i 0.151229i −0.997137 0.0756145i \(-0.975908\pi\)
0.997137 0.0756145i \(-0.0240918\pi\)
\(54\) −7.31371 19.3503i −0.135439 0.358338i
\(55\) 112.782i 2.05057i
\(56\) 0 0
\(57\) 16.9117 0.296696
\(58\) −42.0000 + 15.8745i −0.724138 + 0.273698i
\(59\) −30.4437 −0.515994 −0.257997 0.966146i \(-0.583062\pi\)
−0.257997 + 0.966146i \(0.583062\pi\)
\(60\) 14.0000 + 15.8745i 0.233333 + 0.264575i
\(61\) 15.2325i 0.249714i −0.992175 0.124857i \(-0.960153\pi\)
0.992175 0.124857i \(-0.0398472\pi\)
\(62\) −31.3970 + 11.8669i −0.506403 + 0.191402i
\(63\) 0 0
\(64\) 36.0000 + 52.9150i 0.562500 + 0.826797i
\(65\) 81.5980 1.25535
\(66\) 5.17157 + 13.6827i 0.0783572 + 0.207314i
\(67\) −78.6274 −1.17354 −0.586772 0.809752i \(-0.699601\pi\)
−0.586772 + 0.809752i \(0.699601\pi\)
\(68\) 37.0294 32.6569i 0.544551 0.480248i
\(69\) 14.4348i 0.209200i
\(70\) 0 0
\(71\) 17.5345i 0.246965i 0.992347 + 0.123482i \(0.0394062\pi\)
−0.992347 + 0.123482i \(0.960594\pi\)
\(72\) −61.2132 32.3910i −0.850183 0.449875i
\(73\) −46.6863 −0.639538 −0.319769 0.947495i \(-0.603605\pi\)
−0.319769 + 0.947495i \(0.603605\pi\)
\(74\) −30.4020 + 11.4909i −0.410838 + 0.155282i
\(75\) 33.1543 0.442058
\(76\) 86.6102 76.3830i 1.13961 1.00504i
\(77\) 0 0
\(78\) 9.89949 3.74166i 0.126917 0.0479700i
\(79\) 81.0325i 1.02573i 0.858470 + 0.512864i \(0.171416\pi\)
−0.858470 + 0.512864i \(0.828584\pi\)
\(80\) 143.397 + 18.0663i 1.79246 + 0.225829i
\(81\) 71.8528 0.887072
\(82\) 4.92893 + 13.0407i 0.0601089 + 0.159033i
\(83\) −40.3848 −0.486564 −0.243282 0.969956i \(-0.578224\pi\)
−0.243282 + 0.969956i \(0.578224\pi\)
\(84\) 0 0
\(85\) 111.498i 1.31174i
\(86\) 16.1421 + 42.7081i 0.187699 + 0.496606i
\(87\) 13.1509i 0.151159i
\(88\) 88.2843 + 46.7156i 1.00323 + 0.530860i
\(89\) −111.941 −1.25777 −0.628883 0.777500i \(-0.716487\pi\)
−0.628883 + 0.777500i \(0.716487\pi\)
\(90\) −146.296 + 55.2949i −1.62552 + 0.614387i
\(91\) 0 0
\(92\) −65.1960 73.9253i −0.708652 0.803536i
\(93\) 9.83089i 0.105709i
\(94\) −11.5980 + 4.38362i −0.123383 + 0.0466343i
\(95\) 260.788i 2.74514i
\(96\) 18.2254 4.38362i 0.189848 0.0456628i
\(97\) 164.108 1.69183 0.845916 0.533317i \(-0.179055\pi\)
0.845916 + 0.533317i \(0.179055\pi\)
\(98\) 0 0
\(99\) −108.083 −1.09175
\(100\) 169.794 149.744i 1.69794 1.49744i
\(101\) 12.1329i 0.120127i 0.998195 + 0.0600636i \(0.0191304\pi\)
−0.998195 + 0.0600636i \(0.980870\pi\)
\(102\) −5.11270 13.5269i −0.0501245 0.132617i
\(103\) 106.582i 1.03478i −0.855750 0.517389i \(-0.826904\pi\)
0.855750 0.517389i \(-0.173096\pi\)
\(104\) 33.7990 63.8741i 0.324990 0.614174i
\(105\) 0 0
\(106\) −14.9949 + 5.66756i −0.141462 + 0.0534675i
\(107\) −63.5980 −0.594374 −0.297187 0.954819i \(-0.596048\pi\)
−0.297187 + 0.954819i \(0.596048\pi\)
\(108\) −31.0294 + 27.3654i −0.287310 + 0.253383i
\(109\) 130.848i 1.20044i 0.799835 + 0.600220i \(0.204920\pi\)
−0.799835 + 0.600220i \(0.795080\pi\)
\(110\) 210.995 79.7486i 1.91814 0.724987i
\(111\) 9.51936i 0.0857600i
\(112\) 0 0
\(113\) −138.225 −1.22323 −0.611617 0.791154i \(-0.709481\pi\)
−0.611617 + 0.791154i \(0.709481\pi\)
\(114\) −11.9584 31.6389i −0.104898 0.277534i
\(115\) −222.593 −1.93559
\(116\) 59.3970 + 67.3498i 0.512043 + 0.580602i
\(117\) 78.1987i 0.668365i
\(118\) 21.5269 + 56.9549i 0.182431 + 0.482668i
\(119\) 0 0
\(120\) 19.7990 37.4166i 0.164992 0.311805i
\(121\) 34.8823 0.288283
\(122\) −28.4975 + 10.7710i −0.233586 + 0.0882872i
\(123\) 4.08326 0.0331972
\(124\) 44.4020 + 50.3472i 0.358081 + 0.406025i
\(125\) 285.430i 2.28344i
\(126\) 0 0
\(127\) 114.442i 0.901114i 0.892748 + 0.450557i \(0.148775\pi\)
−0.892748 + 0.450557i \(0.851225\pi\)
\(128\) 73.5391 104.766i 0.574524 0.818488i
\(129\) 13.3726 0.103663
\(130\) −57.6985 152.656i −0.443834 1.17428i
\(131\) 168.350 1.28512 0.642558 0.766237i \(-0.277873\pi\)
0.642558 + 0.766237i \(0.277873\pi\)
\(132\) 21.9411 19.3503i 0.166221 0.146593i
\(133\) 0 0
\(134\) 55.5980 + 147.098i 0.414910 + 1.09775i
\(135\) 93.4313i 0.692084i
\(136\) −87.2792 46.1838i −0.641759 0.339587i
\(137\) 34.6863 0.253185 0.126592 0.991955i \(-0.459596\pi\)
0.126592 + 0.991955i \(0.459596\pi\)
\(138\) −27.0051 + 10.2069i −0.195689 + 0.0739634i
\(139\) −107.664 −0.774561 −0.387281 0.921962i \(-0.626586\pi\)
−0.387281 + 0.921962i \(0.626586\pi\)
\(140\) 0 0
\(141\) 3.63151i 0.0257554i
\(142\) 32.8040 12.3988i 0.231014 0.0873152i
\(143\) 112.782i 0.788682i
\(144\) −17.3137 + 137.423i −0.120234 + 0.954328i
\(145\) 202.794 1.39858
\(146\) 33.0122 + 87.3421i 0.226111 + 0.598233i
\(147\) 0 0
\(148\) 42.9949 + 48.7517i 0.290506 + 0.329403i
\(149\) 252.176i 1.69246i −0.532819 0.846229i \(-0.678867\pi\)
0.532819 0.846229i \(-0.321133\pi\)
\(150\) −23.4437 62.0261i −0.156291 0.413507i
\(151\) 234.486i 1.55289i 0.630186 + 0.776444i \(0.282979\pi\)
−0.630186 + 0.776444i \(0.717021\pi\)
\(152\) −204.142 108.022i −1.34304 0.710670i
\(153\) 106.853 0.698384
\(154\) 0 0
\(155\) 151.598 0.978051
\(156\) −14.0000 15.8745i −0.0897436 0.101760i
\(157\) 10.0968i 0.0643109i −0.999483 0.0321554i \(-0.989763\pi\)
0.999483 0.0321554i \(-0.0102372\pi\)
\(158\) 151.598 57.2987i 0.959481 0.362650i
\(159\) 4.69516i 0.0295293i
\(160\) −67.5980 281.046i −0.422487 1.75654i
\(161\) 0 0
\(162\) −50.8076 134.424i −0.313627 0.829780i
\(163\) 104.534 0.641313 0.320657 0.947196i \(-0.396096\pi\)
0.320657 + 0.947196i \(0.396096\pi\)
\(164\) 20.9117 18.4424i 0.127510 0.112454i
\(165\) 66.0659i 0.400399i
\(166\) 28.5563 + 75.5530i 0.172026 + 0.455139i
\(167\) 296.765i 1.77703i 0.458843 + 0.888517i \(0.348264\pi\)
−0.458843 + 0.888517i \(0.651736\pi\)
\(168\) 0 0
\(169\) 87.4020 0.517172
\(170\) −208.593 + 78.8407i −1.22702 + 0.463769i
\(171\) 249.924 1.46154
\(172\) 68.4853 60.3983i 0.398170 0.351153i
\(173\) 40.0301i 0.231388i −0.993285 0.115694i \(-0.963091\pi\)
0.993285 0.115694i \(-0.0369091\pi\)
\(174\) 24.6030 9.29907i 0.141397 0.0534429i
\(175\) 0 0
\(176\) 24.9706 198.198i 0.141878 1.12612i
\(177\) 17.8335 0.100754
\(178\) 79.1543 + 209.423i 0.444687 + 1.17653i
\(179\) 294.794 1.64689 0.823447 0.567394i \(-0.192048\pi\)
0.823447 + 0.567394i \(0.192048\pi\)
\(180\) 206.894 + 234.596i 1.14941 + 1.30331i
\(181\) 40.4706i 0.223595i −0.993731 0.111797i \(-0.964339\pi\)
0.993731 0.111797i \(-0.0356608\pi\)
\(182\) 0 0
\(183\) 8.92302i 0.0487596i
\(184\) −92.2010 + 174.244i −0.501092 + 0.946976i
\(185\) 146.794 0.793481
\(186\) 18.3919 6.95149i 0.0988813 0.0373736i
\(187\) −154.108 −0.824105
\(188\) 16.4020 + 18.5981i 0.0872448 + 0.0989263i
\(189\) 0 0
\(190\) −487.889 + 184.405i −2.56784 + 0.970552i
\(191\) 156.929i 0.821619i −0.911721 0.410810i \(-0.865246\pi\)
0.911721 0.410810i \(-0.134754\pi\)
\(192\) −21.0883 30.9969i −0.109835 0.161442i
\(193\) −261.304 −1.35390 −0.676952 0.736027i \(-0.736700\pi\)
−0.676952 + 0.736027i \(0.736700\pi\)
\(194\) −116.042 307.017i −0.598153 1.58256i
\(195\) −47.7990 −0.245123
\(196\) 0 0
\(197\) 145.283i 0.737475i −0.929533 0.368738i \(-0.879790\pi\)
0.929533 0.368738i \(-0.120210\pi\)
\(198\) 76.4264 + 202.205i 0.385992 + 1.02124i
\(199\) 390.508i 1.96235i 0.193122 + 0.981175i \(0.438139\pi\)
−0.193122 + 0.981175i \(0.561861\pi\)
\(200\) −400.208 211.770i −2.00104 1.05885i
\(201\) 46.0589 0.229149
\(202\) 22.6985 8.57922i 0.112369 0.0424714i
\(203\) 0 0
\(204\) −21.6913 + 19.1300i −0.106330 + 0.0937743i
\(205\) 62.9662i 0.307152i
\(206\) −199.397 + 75.3650i −0.967946 + 0.365849i
\(207\) 213.320i 1.03053i
\(208\) −143.397 18.0663i −0.689409 0.0868573i
\(209\) −360.451 −1.72464
\(210\) 0 0
\(211\) −164.049 −0.777482 −0.388741 0.921347i \(-0.627090\pi\)
−0.388741 + 0.921347i \(0.627090\pi\)
\(212\) 21.2061 + 24.0454i 0.100029 + 0.113422i
\(213\) 10.2715i 0.0482229i
\(214\) 44.9706 + 118.981i 0.210143 + 0.555986i
\(215\) 206.213i 0.959129i
\(216\) 73.1371 + 38.7005i 0.338598 + 0.179169i
\(217\) 0 0
\(218\) 244.794 92.5234i 1.12291 0.424419i
\(219\) 27.3482 0.124878
\(220\) −298.392 338.345i −1.35633 1.53793i
\(221\) 111.498i 0.504514i
\(222\) 17.8091 6.73120i 0.0802211 0.0303207i
\(223\) 10.5830i 0.0474574i 0.999718 + 0.0237287i \(0.00755379\pi\)
−0.999718 + 0.0237287i \(0.992446\pi\)
\(224\) 0 0
\(225\) 489.960 2.17760
\(226\) 97.7401 + 258.596i 0.432478 + 1.14423i
\(227\) 213.806 0.941877 0.470939 0.882166i \(-0.343915\pi\)
0.470939 + 0.882166i \(0.343915\pi\)
\(228\) −50.7351 + 44.7441i −0.222522 + 0.196246i
\(229\) 232.028i 1.01322i 0.862174 + 0.506612i \(0.169102\pi\)
−0.862174 + 0.506612i \(0.830898\pi\)
\(230\) 157.397 + 416.433i 0.684335 + 1.81058i
\(231\) 0 0
\(232\) 84.0000 158.745i 0.362069 0.684246i
\(233\) −192.863 −0.827738 −0.413869 0.910336i \(-0.635823\pi\)
−0.413869 + 0.910336i \(0.635823\pi\)
\(234\) 146.296 55.2949i 0.625199 0.236303i
\(235\) 56.0000 0.238298
\(236\) 91.3310 80.5463i 0.386996 0.341298i
\(237\) 47.4678i 0.200286i
\(238\) 0 0
\(239\) 327.917i 1.37204i 0.727583 + 0.686020i \(0.240644\pi\)
−0.727583 + 0.686020i \(0.759356\pi\)
\(240\) −84.0000 10.5830i −0.350000 0.0440959i
\(241\) −71.8721 −0.298225 −0.149112 0.988820i \(-0.547642\pi\)
−0.149112 + 0.988820i \(0.547642\pi\)
\(242\) −24.6655 65.2587i −0.101923 0.269664i
\(243\) −135.179 −0.556291
\(244\) 40.3015 + 45.6976i 0.165170 + 0.187285i
\(245\) 0 0
\(246\) −2.88730 7.63908i −0.0117370 0.0310532i
\(247\) 260.788i 1.05582i
\(248\) 62.7939 118.669i 0.253201 0.478506i
\(249\) 23.6569 0.0950074
\(250\) −533.990 + 201.829i −2.13596 + 0.807317i
\(251\) 256.919 1.02358 0.511790 0.859110i \(-0.328982\pi\)
0.511790 + 0.859110i \(0.328982\pi\)
\(252\) 0 0
\(253\) 307.659i 1.21604i
\(254\) 214.101 80.9224i 0.842915 0.318592i
\(255\) 65.3138i 0.256133i
\(256\) −248.000 63.4980i −0.968750 0.248039i
\(257\) −319.352 −1.24262 −0.621308 0.783566i \(-0.713398\pi\)
−0.621308 + 0.783566i \(0.713398\pi\)
\(258\) −9.45584 25.0178i −0.0366506 0.0969683i
\(259\) 0 0
\(260\) −244.794 + 215.888i −0.941515 + 0.830338i
\(261\) 194.346i 0.744620i
\(262\) −119.042 314.955i −0.454357 1.20212i
\(263\) 377.357i 1.43482i 0.696653 + 0.717408i \(0.254672\pi\)
−0.696653 + 0.717408i \(0.745328\pi\)
\(264\) −51.7157 27.3654i −0.195893 0.103657i
\(265\) 72.4020 0.273215
\(266\) 0 0
\(267\) 65.5736 0.245594
\(268\) 235.882 208.029i 0.880158 0.776226i
\(269\) 28.1631i 0.104696i 0.998629 + 0.0523478i \(0.0166704\pi\)
−0.998629 + 0.0523478i \(0.983330\pi\)
\(270\) 174.794 66.0659i 0.647385 0.244689i
\(271\) 399.715i 1.47496i 0.675367 + 0.737482i \(0.263985\pi\)
−0.675367 + 0.737482i \(0.736015\pi\)
\(272\) −24.6863 + 195.941i −0.0907584 + 0.720373i
\(273\) 0 0
\(274\) −24.5269 64.8921i −0.0895143 0.236833i
\(275\) −706.642 −2.56961
\(276\) 38.1909 + 43.3044i 0.138373 + 0.156900i
\(277\) 102.951i 0.371663i 0.982582 + 0.185831i \(0.0594979\pi\)
−0.982582 + 0.185831i \(0.940502\pi\)
\(278\) 76.1299 + 201.421i 0.273849 + 0.724536i
\(279\) 145.283i 0.520726i
\(280\) 0 0
\(281\) −150.235 −0.534646 −0.267323 0.963607i \(-0.586139\pi\)
−0.267323 + 0.963607i \(0.586139\pi\)
\(282\) 6.79394 2.56787i 0.0240920 0.00910591i
\(283\) 178.561 0.630959 0.315480 0.948932i \(-0.397835\pi\)
0.315480 + 0.948932i \(0.397835\pi\)
\(284\) −46.3919 52.6035i −0.163352 0.185224i
\(285\) 152.766i 0.536021i
\(286\) −210.995 + 79.7486i −0.737745 + 0.278841i
\(287\) 0 0
\(288\) 269.338 64.7820i 0.935202 0.224937i
\(289\) −136.647 −0.472826
\(290\) −143.397 379.393i −0.494472 1.30825i
\(291\) −96.1320 −0.330351
\(292\) 140.059 123.520i 0.479654 0.423015i
\(293\) 219.189i 0.748085i −0.927411 0.374043i \(-0.877971\pi\)
0.927411 0.374043i \(-0.122029\pi\)
\(294\) 0 0
\(295\) 275.002i 0.932211i
\(296\) 60.8040 114.909i 0.205419 0.388206i
\(297\) 129.137 0.434805
\(298\) −471.779 + 178.316i −1.58315 + 0.598375i
\(299\) 222.593 0.744458
\(300\) −99.4630 + 87.7181i −0.331543 + 0.292394i
\(301\) 0 0
\(302\) 438.683 165.807i 1.45259 0.549029i
\(303\) 7.10726i 0.0234563i
\(304\) −57.7401 + 458.298i −0.189935 + 1.50756i
\(305\) 137.598 0.451141
\(306\) −75.5563 199.903i −0.246916 0.653279i
\(307\) −316.669 −1.03150 −0.515748 0.856741i \(-0.672486\pi\)
−0.515748 + 0.856741i \(0.672486\pi\)
\(308\) 0 0
\(309\) 62.4344i 0.202053i
\(310\) −107.196 283.614i −0.345793 0.914883i
\(311\) 72.2653i 0.232364i 0.993228 + 0.116182i \(0.0370656\pi\)
−0.993228 + 0.116182i \(0.962934\pi\)
\(312\) −19.7990 + 37.4166i −0.0634583 + 0.119925i
\(313\) −81.9512 −0.261825 −0.130913 0.991394i \(-0.541791\pi\)
−0.130913 + 0.991394i \(0.541791\pi\)
\(314\) −18.8894 + 7.13952i −0.0601573 + 0.0227373i
\(315\) 0 0
\(316\) −214.392 243.098i −0.678455 0.769296i
\(317\) 109.150i 0.344322i 0.985069 + 0.172161i \(0.0550749\pi\)
−0.985069 + 0.172161i \(0.944925\pi\)
\(318\) 8.78384 3.31998i 0.0276221 0.0104402i
\(319\) 280.294i 0.878664i
\(320\) −477.990 + 325.194i −1.49372 + 1.01623i
\(321\) 37.2548 0.116059
\(322\) 0 0
\(323\) 356.347 1.10324
\(324\) −215.558 + 190.105i −0.665304 + 0.586743i
\(325\) 511.259i 1.57310i
\(326\) −73.9167 195.565i −0.226738 0.599894i
\(327\) 76.6489i 0.234400i
\(328\) −49.2893 26.0815i −0.150272 0.0795166i
\(329\) 0 0
\(330\) −123.598 + 46.7156i −0.374539 + 0.141563i
\(331\) 321.740 0.972025 0.486012 0.873952i \(-0.338451\pi\)
0.486012 + 0.873952i \(0.338451\pi\)
\(332\) 121.154 106.848i 0.364923 0.321832i
\(333\) 140.679i 0.422459i
\(334\) 555.196 209.844i 1.66226 0.628276i
\(335\) 710.254i 2.12016i
\(336\) 0 0
\(337\) −164.049 −0.486792 −0.243396 0.969927i \(-0.578261\pi\)
−0.243396 + 0.969927i \(0.578261\pi\)
\(338\) −61.8026 163.514i −0.182848 0.483770i
\(339\) 80.9706 0.238851
\(340\) 294.995 + 334.493i 0.867632 + 0.983802i
\(341\) 209.533i 0.614466i
\(342\) −176.723 467.565i −0.516734 1.36715i
\(343\) 0 0
\(344\) −161.421 85.4162i −0.469248 0.248303i
\(345\) 130.392 0.377948
\(346\) −74.8894 + 28.3055i −0.216443 + 0.0818079i
\(347\) −330.309 −0.951898 −0.475949 0.879473i \(-0.657895\pi\)
−0.475949 + 0.879473i \(0.657895\pi\)
\(348\) −34.7939 39.4526i −0.0999826 0.113370i
\(349\) 262.402i 0.751869i 0.926646 + 0.375934i \(0.122678\pi\)
−0.926646 + 0.375934i \(0.877322\pi\)
\(350\) 0 0
\(351\) 93.4313i 0.266186i
\(352\) −388.451 + 93.4313i −1.10355 + 0.265430i
\(353\) 578.098 1.63767 0.818835 0.574029i \(-0.194620\pi\)
0.818835 + 0.574029i \(0.194620\pi\)
\(354\) −12.6102 33.3634i −0.0356220 0.0942468i
\(355\) −158.392 −0.446174
\(356\) 335.823 296.168i 0.943324 0.831934i
\(357\) 0 0
\(358\) −208.451 551.509i −0.582265 1.54053i
\(359\) 365.114i 1.01703i −0.861053 0.508515i \(-0.830195\pi\)
0.861053 0.508515i \(-0.169805\pi\)
\(360\) 292.593 552.949i 0.812758 1.53597i
\(361\) 472.480 1.30881
\(362\) −75.7136 + 28.6171i −0.209154 + 0.0790527i
\(363\) −20.4335 −0.0562908
\(364\) 0 0
\(365\) 421.725i 1.15541i
\(366\) 16.6934 6.30953i 0.0456105 0.0172391i
\(367\) 520.071i 1.41709i −0.705666 0.708544i \(-0.749352\pi\)
0.705666 0.708544i \(-0.250648\pi\)
\(368\) 391.176 + 49.2835i 1.06298 + 0.133923i
\(369\) 60.3431 0.163532
\(370\) −103.799 274.626i −0.280538 0.742233i
\(371\) 0 0
\(372\) −26.0101 29.4927i −0.0699196 0.0792814i
\(373\) 526.711i 1.41210i −0.708164 0.706048i \(-0.750476\pi\)
0.708164 0.706048i \(-0.249524\pi\)
\(374\) 108.971 + 288.309i 0.291365 + 0.770880i
\(375\) 167.201i 0.445869i
\(376\) 23.1960 43.8362i 0.0616914 0.116586i
\(377\) −202.794 −0.537915
\(378\) 0 0
\(379\) 121.976 0.321835 0.160918 0.986968i \(-0.448555\pi\)
0.160918 + 0.986968i \(0.448555\pi\)
\(380\) 689.980 + 782.364i 1.81574 + 2.05885i
\(381\) 67.0383i 0.175954i
\(382\) −293.588 + 110.966i −0.768555 + 0.290486i
\(383\) 316.427i 0.826179i 0.910690 + 0.413089i \(0.135550\pi\)
−0.910690 + 0.413089i \(0.864450\pi\)
\(384\) −43.0782 + 61.3707i −0.112183 + 0.159820i
\(385\) 0 0
\(386\) 184.770 + 488.854i 0.478678 + 1.26646i
\(387\) 197.622 0.510652
\(388\) −492.323 + 434.188i −1.26887 + 1.11904i
\(389\) 92.1474i 0.236883i 0.992961 + 0.118441i \(0.0377898\pi\)
−0.992961 + 0.118441i \(0.962210\pi\)
\(390\) 33.7990 + 89.4237i 0.0866641 + 0.229292i
\(391\) 304.157i 0.777895i
\(392\) 0 0
\(393\) −98.6173 −0.250935
\(394\) −271.799 + 102.730i −0.689845 + 0.260737i
\(395\) −731.980 −1.85311
\(396\) 324.250 285.961i 0.818813 0.722125i
\(397\) 562.267i 1.41629i −0.706068 0.708144i \(-0.749533\pi\)
0.706068 0.708144i \(-0.250467\pi\)
\(398\) 730.573 276.131i 1.83561 0.693795i
\(399\) 0 0
\(400\) −113.196 + 898.465i −0.282990 + 2.24616i
\(401\) 81.2061 0.202509 0.101254 0.994861i \(-0.467714\pi\)
0.101254 + 0.994861i \(0.467714\pi\)
\(402\) −32.5685 86.1683i −0.0810163 0.214349i
\(403\) −151.598 −0.376174
\(404\) −32.1005 36.3986i −0.0794567 0.0900954i
\(405\) 649.058i 1.60261i
\(406\) 0 0
\(407\) 202.893i 0.498508i
\(408\) 51.1270 + 27.0539i 0.125311 + 0.0663085i
\(409\) −450.735 −1.10204 −0.551021 0.834491i \(-0.685762\pi\)
−0.551021 + 0.834491i \(0.685762\pi\)
\(410\) −117.799 + 44.5238i −0.287315 + 0.108595i
\(411\) −20.3188 −0.0494374
\(412\) 281.990 + 319.746i 0.684442 + 0.776084i
\(413\) 0 0
\(414\) −399.085 + 150.840i −0.963974 + 0.364348i
\(415\) 364.802i 0.879041i
\(416\) 67.5980 + 281.046i 0.162495 + 0.675591i
\(417\) 63.0681 0.151242
\(418\) 254.877 + 674.342i 0.609754 + 1.61326i
\(419\) −624.988 −1.49162 −0.745809 0.666160i \(-0.767937\pi\)
−0.745809 + 0.666160i \(0.767937\pi\)
\(420\) 0 0
\(421\) 566.476i 1.34555i 0.739848 + 0.672774i \(0.234897\pi\)
−0.739848 + 0.672774i \(0.765103\pi\)
\(422\) 116.000 + 306.907i 0.274882 + 0.727268i
\(423\) 53.6671i 0.126873i
\(424\) 29.9899 56.6756i 0.0707309 0.133669i
\(425\) 698.597 1.64376
\(426\) −19.2162 + 7.26303i −0.0451084 + 0.0170494i
\(427\) 0 0
\(428\) 190.794 168.264i 0.445780 0.393141i
\(429\) 66.0659i 0.154000i
\(430\) −385.789 + 145.814i −0.897183 + 0.339103i
\(431\) 289.528i 0.671760i 0.941905 + 0.335880i \(0.109034\pi\)
−0.941905 + 0.335880i \(0.890966\pi\)
\(432\) 20.6863 164.192i 0.0478849 0.380075i
\(433\) 597.696 1.38036 0.690180 0.723638i \(-0.257532\pi\)
0.690180 + 0.723638i \(0.257532\pi\)
\(434\) 0 0
\(435\) −118.794 −0.273090
\(436\) −346.191 392.544i −0.794016 0.900329i
\(437\) 711.409i 1.62794i
\(438\) −19.3381 51.1638i −0.0441509 0.116812i
\(439\) 38.3890i 0.0874464i 0.999044 + 0.0437232i \(0.0139220\pi\)
−0.999044 + 0.0437232i \(0.986078\pi\)
\(440\) −421.990 + 797.486i −0.959068 + 1.81247i
\(441\) 0 0
\(442\) 208.593 78.8407i 0.471930 0.178373i
\(443\) 599.058 1.35228 0.676138 0.736775i \(-0.263652\pi\)
0.676138 + 0.736775i \(0.263652\pi\)
\(444\) −25.1859 28.5581i −0.0567249 0.0643200i
\(445\) 1011.18i 2.27232i
\(446\) 19.7990 7.48331i 0.0443924 0.0167787i
\(447\) 147.721i 0.330473i
\(448\) 0 0
\(449\) −460.039 −1.02459 −0.512293 0.858811i \(-0.671204\pi\)
−0.512293 + 0.858811i \(0.671204\pi\)
\(450\) −346.454 916.632i −0.769899 2.03696i
\(451\) −87.0294 −0.192970
\(452\) 414.676 365.710i 0.917425 0.809093i
\(453\) 137.359i 0.303220i
\(454\) −151.184 399.995i −0.333004 0.881045i
\(455\) 0 0
\(456\) 119.584 + 63.2777i 0.262245 + 0.138767i
\(457\) 266.323 0.582764 0.291382 0.956607i \(-0.405885\pi\)
0.291382 + 0.956607i \(0.405885\pi\)
\(458\) 434.085 164.069i 0.947785 0.358229i
\(459\) −127.667 −0.278142
\(460\) 667.779 588.926i 1.45169 1.28027i
\(461\) 763.123i 1.65537i 0.561196 + 0.827683i \(0.310341\pi\)
−0.561196 + 0.827683i \(0.689659\pi\)
\(462\) 0 0
\(463\) 123.988i 0.267792i 0.990995 + 0.133896i \(0.0427488\pi\)
−0.990995 + 0.133896i \(0.957251\pi\)
\(464\) −356.382 44.8999i −0.768064 0.0967670i
\(465\) −88.8040 −0.190976
\(466\) 136.375 + 360.813i 0.292650 + 0.774278i
\(467\) 768.718 1.64608 0.823038 0.567986i \(-0.192277\pi\)
0.823038 + 0.567986i \(0.192277\pi\)
\(468\) −206.894 234.596i −0.442082 0.501274i
\(469\) 0 0
\(470\) −39.5980 104.766i −0.0842510 0.222907i
\(471\) 5.91457i 0.0125575i
\(472\) −215.269 113.910i −0.456079 0.241334i
\(473\) −285.019 −0.602578
\(474\) −88.8040 + 33.5648i −0.187350 + 0.0708118i
\(475\) 1633.99 3.43997
\(476\) 0 0
\(477\) 69.3859i 0.145463i
\(478\) 613.477 231.873i 1.28343 0.485089i
\(479\) 118.981i 0.248394i 0.992258 + 0.124197i \(0.0396355\pi\)
−0.992258 + 0.124197i \(0.960364\pi\)
\(480\) 39.5980 + 164.633i 0.0824958 + 0.342985i
\(481\) −146.794 −0.305185
\(482\) 50.8213 + 134.460i 0.105438 + 0.278964i
\(483\) 0 0
\(484\) −104.647 + 92.2898i −0.216212 + 0.190681i
\(485\) 1482.41i 3.05652i
\(486\) 95.5858 + 252.896i 0.196679 + 0.520363i
\(487\) 282.577i 0.580240i −0.956990 0.290120i \(-0.906305\pi\)
0.956990 0.290120i \(-0.0936952\pi\)
\(488\) 56.9949 107.710i 0.116793 0.220718i
\(489\) −61.2346 −0.125224
\(490\) 0 0
\(491\) −388.049 −0.790323 −0.395162 0.918612i \(-0.629311\pi\)
−0.395162 + 0.918612i \(0.629311\pi\)
\(492\) −12.2498 + 10.8033i −0.0248979 + 0.0219579i
\(493\) 277.103i 0.562075i
\(494\) 487.889 184.405i 0.987630 0.373289i
\(495\) 976.333i 1.97239i
\(496\) −266.412 33.5648i −0.537121 0.0676709i
\(497\) 0 0
\(498\) −16.7279 44.2579i −0.0335902 0.0888713i
\(499\) −27.7157 −0.0555425 −0.0277713 0.999614i \(-0.508841\pi\)
−0.0277713 + 0.999614i \(0.508841\pi\)
\(500\) 755.176 + 856.289i 1.51035 + 1.71258i
\(501\) 173.841i 0.346988i
\(502\) −181.669 480.651i −0.361891 0.957472i
\(503\) 727.477i 1.44628i −0.690703 0.723138i \(-0.742699\pi\)
0.690703 0.723138i \(-0.257301\pi\)
\(504\) 0 0
\(505\) −109.598 −0.217026
\(506\) 575.578 217.548i 1.13751 0.429937i
\(507\) −51.1989 −0.100984
\(508\) −302.784 343.325i −0.596031 0.675836i
\(509\) 634.183i 1.24594i 0.782246 + 0.622969i \(0.214074\pi\)
−0.782246 + 0.622969i \(0.785926\pi\)
\(510\) 122.191 46.1838i 0.239590 0.0905565i
\(511\) 0 0
\(512\) 56.5685 + 508.865i 0.110485 + 0.993878i
\(513\) −298.607 −0.582080
\(514\) 225.816 + 597.454i 0.439331 + 1.16236i
\(515\) 962.774 1.86946
\(516\) −40.1177 + 35.3805i −0.0777476 + 0.0685669i
\(517\) 77.4010i 0.149712i
\(518\) 0 0
\(519\) 23.4491i 0.0451813i
\(520\) 576.985 + 305.312i 1.10959 + 0.587138i
\(521\) −833.127 −1.59909 −0.799546 0.600605i \(-0.794927\pi\)
−0.799546 + 0.600605i \(0.794927\pi\)
\(522\) 363.588 137.423i 0.696529 0.263263i
\(523\) −876.434 −1.67578 −0.837891 0.545838i \(-0.816211\pi\)
−0.837891 + 0.545838i \(0.816211\pi\)
\(524\) −505.051 + 445.413i −0.963838 + 0.850025i
\(525\) 0 0
\(526\) 705.970 266.831i 1.34215 0.507284i
\(527\) 207.147i 0.393069i
\(528\) −14.6274 + 116.102i −0.0277034 + 0.219889i
\(529\) −78.2162 −0.147857
\(530\) −51.1960 135.452i −0.0965961 0.255569i
\(531\) 263.546 0.496321
\(532\) 0 0
\(533\) 62.9662i 0.118135i
\(534\) −46.3675 122.677i −0.0868306 0.229732i
\(535\) 574.491i 1.07381i
\(536\) −555.980 294.197i −1.03728 0.548875i
\(537\) −172.686 −0.321576
\(538\) 52.6884 19.9143i 0.0979338 0.0370155i
\(539\) 0 0
\(540\) −247.196 280.294i −0.457770 0.519063i
\(541\) 405.915i 0.750305i 0.926963 + 0.375152i \(0.122410\pi\)
−0.926963 + 0.375152i \(0.877590\pi\)
\(542\) 747.799 282.641i 1.37970 0.521479i
\(543\) 23.7072i 0.0436596i
\(544\) 384.029 92.3676i 0.705935 0.169793i
\(545\) −1181.97 −2.16875
\(546\) 0 0
\(547\) −606.024 −1.10791 −0.553953 0.832548i \(-0.686881\pi\)
−0.553953 + 0.832548i \(0.686881\pi\)
\(548\) −104.059 + 91.7713i −0.189888 + 0.167466i
\(549\) 131.866i 0.240193i
\(550\) 499.671 + 1322.01i 0.908493 + 2.40365i
\(551\) 648.131i 1.17628i
\(552\) 54.0101 102.069i 0.0978444 0.184909i
\(553\) 0 0
\(554\) 192.603 72.7971i 0.347659 0.131403i
\(555\) −85.9899 −0.154937
\(556\) 322.992 284.852i 0.580921 0.512324i
\(557\) 36.4442i 0.0654294i −0.999465 0.0327147i \(-0.989585\pi\)
0.999465 0.0327147i \(-0.0104153\pi\)
\(558\) 271.799 102.730i 0.487095 0.184105i
\(559\) 206.213i 0.368896i
\(560\) 0 0
\(561\) 90.2742 0.160917
\(562\) 106.233 + 281.065i 0.189026 + 0.500115i
\(563\) 186.389 0.331064 0.165532 0.986204i \(-0.447066\pi\)
0.165532 + 0.986204i \(0.447066\pi\)
\(564\) −9.60808 10.8945i −0.0170356 0.0193166i
\(565\) 1248.61i 2.20993i
\(566\) −126.262 334.058i −0.223078 0.590208i
\(567\) 0 0
\(568\) −65.6081 + 123.988i −0.115507 + 0.218288i
\(569\) −670.891 −1.17907 −0.589536 0.807742i \(-0.700689\pi\)
−0.589536 + 0.807742i \(0.700689\pi\)
\(570\) 285.799 108.022i 0.501402 0.189512i
\(571\) −677.082 −1.18578 −0.592892 0.805282i \(-0.702014\pi\)
−0.592892 + 0.805282i \(0.702014\pi\)
\(572\) 298.392 + 338.345i 0.521664 + 0.591512i
\(573\) 91.9271i 0.160431i
\(574\) 0 0
\(575\) 1394.67i 2.42552i
\(576\) −311.647 458.078i −0.541053 0.795274i
\(577\) −927.901 −1.60815 −0.804073 0.594530i \(-0.797338\pi\)
−0.804073 + 0.594530i \(0.797338\pi\)
\(578\) 96.6238 + 255.643i 0.167169 + 0.442288i
\(579\) 153.068 0.264366
\(580\) −608.382 + 536.542i −1.04893 + 0.925073i
\(581\) 0 0
\(582\) 67.9756 + 179.847i 0.116797 + 0.309015i
\(583\) 100.071i 0.171649i
\(584\) −330.122 174.684i −0.565277 0.299117i
\(585\) −706.382 −1.20749
\(586\) −410.065 + 154.990i −0.699770 + 0.264488i
\(587\) 321.120 0.547053 0.273526 0.961865i \(-0.411810\pi\)
0.273526 + 0.961865i \(0.411810\pi\)
\(588\) 0 0
\(589\) 484.508i 0.822595i
\(590\) −514.482 + 194.456i −0.872004 + 0.329587i
\(591\) 85.1046i 0.144001i
\(592\) −257.970 32.5011i −0.435760 0.0549006i
\(593\) 219.255 0.369738 0.184869 0.982763i \(-0.440814\pi\)
0.184869 + 0.982763i \(0.440814\pi\)
\(594\) −91.3137 241.593i −0.153727 0.406723i
\(595\) 0 0
\(596\) 667.196 + 756.529i 1.11946 + 1.26934i
\(597\) 228.754i 0.383173i
\(598\) −157.397 416.433i −0.263206 0.696377i
\(599\) 154.802i 0.258434i −0.991616 0.129217i \(-0.958754\pi\)
0.991616 0.129217i \(-0.0412464\pi\)
\(600\) 234.437 + 124.052i 0.390728 + 0.206754i
\(601\) −205.862 −0.342533 −0.171266 0.985225i \(-0.554786\pi\)
−0.171266 + 0.985225i \(0.554786\pi\)
\(602\) 0 0
\(603\) 680.666 1.12880
\(604\) −620.392 703.458i −1.02714 1.16467i
\(605\) 315.097i 0.520821i
\(606\) −13.2965 + 5.02559i −0.0219414 + 0.00829305i
\(607\) 790.663i 1.30258i 0.758831 + 0.651288i \(0.225771\pi\)
−0.758831 + 0.651288i \(0.774229\pi\)
\(608\) 898.225 216.044i 1.47734 0.355335i
\(609\) 0 0
\(610\) −97.2965 257.422i −0.159502 0.422004i
\(611\) −56.0000 −0.0916530
\(612\) −320.558 + 282.706i −0.523788 + 0.461938i
\(613\) 741.471i 1.20958i −0.796386 0.604789i \(-0.793257\pi\)
0.796386 0.604789i \(-0.206743\pi\)
\(614\) 223.919 + 592.434i 0.364689 + 0.964875i
\(615\) 36.8848i 0.0599752i
\(616\) 0 0
\(617\) 171.578 0.278084 0.139042 0.990286i \(-0.455598\pi\)
0.139042 + 0.990286i \(0.455598\pi\)
\(618\) 116.804 44.1478i 0.189003 0.0714365i
\(619\) 540.198 0.872695 0.436347 0.899778i \(-0.356272\pi\)
0.436347 + 0.899778i \(0.356272\pi\)
\(620\) −454.794 + 401.091i −0.733539 + 0.646920i
\(621\) 254.873i 0.410424i
\(622\) 135.196 51.0993i 0.217357 0.0821532i
\(623\) 0 0
\(624\) 84.0000 + 10.5830i 0.134615 + 0.0169599i
\(625\) 1163.38 1.86141
\(626\) 57.9483 + 153.317i 0.0925691 + 0.244915i
\(627\) 211.147 0.336758
\(628\) 26.7136 + 30.2904i 0.0425376 + 0.0482331i
\(629\) 200.583i 0.318892i
\(630\) 0 0
\(631\) 269.399i 0.426940i −0.976950 0.213470i \(-0.931523\pi\)
0.976950 0.213470i \(-0.0684766\pi\)
\(632\) −303.196 + 572.987i −0.479740 + 0.906624i
\(633\) 96.0975 0.151813
\(634\) 204.201 77.1807i 0.322084 0.121736i
\(635\) −1033.77 −1.62798
\(636\) −12.4222 14.0855i −0.0195318 0.0221470i
\(637\) 0 0
\(638\) −524.382 + 198.198i −0.821915 + 0.310655i
\(639\) 151.794i 0.237549i
\(640\) 946.372 + 664.291i 1.47871 + 1.03795i
\(641\) 36.1867 0.0564535 0.0282268 0.999602i \(-0.491014\pi\)
0.0282268 + 0.999602i \(0.491014\pi\)
\(642\) −26.3431 69.6974i −0.0410329 0.108563i
\(643\) −266.297 −0.414148 −0.207074 0.978325i \(-0.566394\pi\)
−0.207074 + 0.978325i \(0.566394\pi\)
\(644\) 0 0
\(645\) 120.797i 0.187282i
\(646\) −251.976 666.665i −0.390055 1.03199i
\(647\) 1086.24i 1.67888i −0.543452 0.839440i \(-0.682883\pi\)
0.543452 0.839440i \(-0.317117\pi\)
\(648\) 508.076 + 268.849i 0.784068 + 0.414890i
\(649\) −380.098 −0.585666
\(650\) 956.477 361.514i 1.47150 0.556176i
\(651\) 0 0
\(652\) −313.602 + 276.571i −0.480985 + 0.424189i
\(653\) 1195.35i 1.83055i −0.402832 0.915274i \(-0.631974\pi\)
0.402832 0.915274i \(-0.368026\pi\)
\(654\) −143.397 + 54.1990i −0.219261 + 0.0828730i
\(655\) 1520.74i 2.32173i
\(656\) −13.9411 + 110.654i −0.0212517 + 0.168680i
\(657\) 404.156 0.615154
\(658\) 0 0
\(659\) −685.220 −1.03979 −0.519894 0.854231i \(-0.674029\pi\)
−0.519894 + 0.854231i \(0.674029\pi\)
\(660\) 174.794 + 198.198i 0.264839 + 0.300300i
\(661\) 993.382i 1.50285i −0.659820 0.751423i \(-0.729368\pi\)
0.659820 0.751423i \(-0.270632\pi\)
\(662\) −227.505 601.921i −0.343663 0.909246i
\(663\) 65.3138i 0.0985125i
\(664\) −285.563 151.106i −0.430065 0.227569i
\(665\) 0 0
\(666\) 263.186 99.4749i 0.395174 0.149362i
\(667\) 553.206 0.829394
\(668\) −785.166 890.294i −1.17540 1.33278i
\(669\) 6.19938i 0.00926664i
\(670\) −1328.76 + 502.225i −1.98323 + 0.749590i
\(671\) 190.183i 0.283432i
\(672\) 0 0
\(673\) 106.569 0.158349 0.0791743 0.996861i \(-0.474772\pi\)
0.0791743 + 0.996861i \(0.474772\pi\)
\(674\) 116.000 + 306.907i 0.172107 + 0.455352i
\(675\) −585.401 −0.867261
\(676\) −262.206 + 231.244i −0.387879 + 0.342077i
\(677\) 1004.18i 1.48329i 0.670795 + 0.741643i \(0.265953\pi\)
−0.670795 + 0.741643i \(0.734047\pi\)
\(678\) −57.2548 151.482i −0.0844467 0.223425i
\(679\) 0 0
\(680\) 417.186 788.407i 0.613509 1.15942i
\(681\) −125.245 −0.183913
\(682\) −392.000 + 148.162i −0.574780 + 0.217246i
\(683\) −678.225 −0.993009 −0.496505 0.868034i \(-0.665383\pi\)
−0.496505 + 0.868034i \(0.665383\pi\)
\(684\) −749.772 + 661.236i −1.09616 + 0.966720i
\(685\) 313.327i 0.457411i
\(686\) 0 0
\(687\) 135.919i 0.197844i
\(688\) −45.6569 + 362.390i −0.0663617 + 0.526730i
\(689\) −72.4020 −0.105083
\(690\) −92.2010 243.941i −0.133625 0.353538i
\(691\) 365.175 0.528473 0.264236 0.964458i \(-0.414880\pi\)
0.264236 + 0.964458i \(0.414880\pi\)
\(692\) 105.910 + 120.090i 0.153049 + 0.173541i
\(693\) 0 0
\(694\) 233.563 + 617.951i 0.336547 + 0.890419i
\(695\) 972.546i 1.39935i
\(696\) −49.2061 + 92.9907i −0.0706984 + 0.133607i
\(697\) 86.0387 0.123441
\(698\) 490.910 185.546i 0.703309 0.265826i
\(699\) 112.976 0.161626
\(700\) 0 0
\(701\) 940.292i 1.34136i −0.741748 0.670679i \(-0.766003\pi\)
0.741748 0.670679i \(-0.233997\pi\)
\(702\) −174.794 + 66.0659i −0.248994 + 0.0941110i
\(703\) 469.155i 0.667361i
\(704\) 449.470 + 660.659i 0.638452 + 0.938436i
\(705\) −32.8040 −0.0465306
\(706\) −408.777 1081.52i −0.579004 1.53190i
\(707\) 0 0
\(708\) −53.5004 + 47.1829i −0.0755656 + 0.0666426i
\(709\) 1057.46i 1.49148i 0.666239 + 0.745738i \(0.267903\pi\)
−0.666239 + 0.745738i \(0.732097\pi\)
\(710\) 112.000 + 296.324i 0.157746 + 0.417358i
\(711\) 701.487i 0.986620i
\(712\) −791.543 418.845i −1.11172 0.588266i
\(713\) 413.547 0.580010
\(714\) 0 0
\(715\) 1018.77 1.42486
\(716\) −884.382 + 779.951i −1.23517 + 1.08932i
\(717\) 192.090i 0.267907i
\(718\) −683.065 + 258.174i −0.951344 + 0.359574i
\(719\) 1034.82i 1.43926i −0.694360 0.719628i \(-0.744312\pi\)
0.694360 0.719628i \(-0.255688\pi\)
\(720\) −1241.37 156.397i −1.72412 0.217219i
\(721\) 0 0
\(722\) −334.094 883.930i −0.462734 1.22428i
\(723\) 42.1017 0.0582320
\(724\) 107.075 + 121.412i 0.147894 + 0.167696i
\(725\) 1270.62i 1.75258i
\(726\) 14.4487 + 38.2277i 0.0199018 + 0.0526552i
\(727\) 495.145i 0.681080i −0.940230 0.340540i \(-0.889390\pi\)
0.940230 0.340540i \(-0.110610\pi\)
\(728\) 0 0
\(729\) −567.489 −0.778449
\(730\) −788.975 + 298.204i −1.08079 + 0.408499i
\(731\) 281.775 0.385465
\(732\) −23.6081 26.7690i −0.0322515 0.0365697i
\(733\) 567.494i 0.774207i −0.922036 0.387103i \(-0.873476\pi\)
0.922036 0.387103i \(-0.126524\pi\)
\(734\) −972.965 + 367.746i −1.32556 + 0.501016i
\(735\) 0 0
\(736\) −184.402 766.672i −0.250546 1.04167i
\(737\) −981.685 −1.33200
\(738\) −42.6690 112.892i −0.0578171 0.152970i
\(739\) −544.701 −0.737078 −0.368539 0.929612i \(-0.620142\pi\)
−0.368539 + 0.929612i \(0.620142\pi\)
\(740\) −440.382 + 388.380i −0.595111 + 0.524838i
\(741\) 152.766i 0.206162i
\(742\) 0 0
\(743\) 731.264i 0.984205i 0.870537 + 0.492102i \(0.163771\pi\)
−0.870537 + 0.492102i \(0.836229\pi\)
\(744\) −36.7838 + 69.5149i −0.0494406 + 0.0934340i
\(745\) 2277.95 3.05765
\(746\) −985.387 + 372.441i −1.32089 + 0.499251i
\(747\) 349.605 0.468012
\(748\) 462.323 407.731i 0.618079 0.545094i
\(749\) 0 0
\(750\) 312.804 118.229i 0.417072 0.157638i
\(751\) 666.262i 0.887166i 0.896233 + 0.443583i \(0.146293\pi\)
−0.896233 + 0.443583i \(0.853707\pi\)
\(752\) −98.4121 12.3988i −0.130867 0.0164877i
\(753\) −150.500 −0.199867
\(754\) 143.397 + 379.393i 0.190182 + 0.503173i
\(755\) −2118.15 −2.80550
\(756\) 0 0
\(757\) 238.623i 0.315222i −0.987501 0.157611i \(-0.949621\pi\)
0.987501 0.157611i \(-0.0503791\pi\)
\(758\) −86.2498 228.195i −0.113786 0.301049i
\(759\) 180.223i 0.237447i
\(760\) 975.779 1844.05i 1.28392 2.42638i
\(761\) −614.930 −0.808055 −0.404028 0.914747i \(-0.632390\pi\)
−0.404028 + 0.914747i \(0.632390\pi\)
\(762\) −125.417 + 47.4032i −0.164589 + 0.0622090i
\(763\) 0 0
\(764\) 415.196 + 470.788i 0.543450 + 0.616215i
\(765\) 965.219i 1.26172i
\(766\) 591.980 223.747i 0.772820 0.292098i
\(767\) 275.002i 0.358543i
\(768\) 145.275 + 37.1963i 0.189160 + 0.0484327i
\(769\) −178.950 −0.232705 −0.116353 0.993208i \(-0.537120\pi\)
−0.116353 + 0.993208i \(0.537120\pi\)
\(770\) 0 0
\(771\) 187.072 0.242636
\(772\) 783.911 691.344i 1.01543 0.895524i
\(773\) 631.615i 0.817095i 0.912737 + 0.408548i \(0.133965\pi\)
−0.912737 + 0.408548i \(0.866035\pi\)
\(774\) −139.740 369.718i −0.180543 0.477671i
\(775\) 949.849i 1.22561i
\(776\) 1160.42 + 614.035i 1.49538 + 0.791282i
\(777\) 0 0
\(778\) 172.392 65.1580i 0.221583 0.0837507i
\(779\) 201.241 0.258332
\(780\) 143.397 126.464i 0.183842 0.162134i
\(781\) 218.923i 0.280311i
\(782\) −569.025 + 215.071i −0.727654 + 0.275027i
\(783\) 232.203i 0.296556i
\(784\) 0 0
\(785\) 91.2061 0.116186
\(786\) 69.7330 + 184.496i 0.0887188 + 0.234728i
\(787\) −456.655 −0.580247 −0.290124 0.956989i \(-0.593696\pi\)
−0.290124 + 0.956989i \(0.593696\pi\)
\(788\) 384.382 + 435.848i 0.487794 + 0.553107i
\(789\) 221.050i 0.280165i
\(790\) 517.588 + 1369.41i 0.655175 + 1.73343i
\(791\) 0 0
\(792\) −764.264 404.411i −0.964980 0.510619i
\(793\) −137.598 −0.173516
\(794\) −1051.90 + 397.583i −1.32482 + 0.500734i
\(795\) −42.4121 −0.0533486
\(796\) −1033.19 1171.52i −1.29797 1.47176i
\(797\) 218.566i 0.274236i −0.990555 0.137118i \(-0.956216\pi\)
0.990555 0.137118i \(-0.0437839\pi\)
\(798\) 0 0
\(799\) 76.5199i 0.0957695i
\(800\) 1760.92 423.540i 2.20114 0.529426i
\(801\) 969.058 1.20981
\(802\) −57.4214 151.923i −0.0715977 0.189430i
\(803\) −582.891 −0.725892
\(804\) −138.177 + 121.860i −0.171861 + 0.151568i
\(805\) 0 0
\(806\) 107.196 + 283.614i 0.132997 + 0.351878i
\(807\) 16.4976i 0.0204431i
\(808\) −45.3970 + 85.7922i −0.0561844 + 0.106178i
\(809\) 1347.46 1.66559 0.832794 0.553584i \(-0.186740\pi\)
0.832794 + 0.553584i \(0.186740\pi\)
\(810\) 1214.28 458.953i 1.49911 0.566609i
\(811\) 672.620 0.829371 0.414686 0.909965i \(-0.363892\pi\)
0.414686 + 0.909965i \(0.363892\pi\)
\(812\) 0 0
\(813\) 234.148i 0.288005i
\(814\) −379.578 + 143.467i −0.466312 + 0.176249i
\(815\) 944.273i 1.15862i
\(816\) 14.4609 114.780i 0.0177217 0.140662i
\(817\) 659.058 0.806681
\(818\) 318.718 + 843.248i 0.389631 + 1.03087i
\(819\) 0 0
\(820\) 166.593 + 188.899i 0.203162 + 0.230364i
\(821\) 1162.57i 1.41604i −0.706190 0.708022i \(-0.749588\pi\)
0.706190 0.708022i \(-0.250412\pi\)
\(822\) 14.3675 + 38.0129i 0.0174787 + 0.0462444i
\(823\) 1041.65i 1.26567i −0.774286 0.632835i \(-0.781891\pi\)
0.774286 0.632835i \(-0.218109\pi\)
\(824\) 398.794 753.650i 0.483973 0.914623i
\(825\) 413.941 0.501747
\(826\) 0 0
\(827\) 278.432 0.336678 0.168339 0.985729i \(-0.446160\pi\)
0.168339 + 0.985729i \(0.446160\pi\)
\(828\) 564.392 + 639.960i 0.681633 + 0.772899i
\(829\) 1065.74i 1.28557i 0.766046 + 0.642785i \(0.222221\pi\)
−0.766046 + 0.642785i \(0.777779\pi\)
\(830\) −682.482 + 257.954i −0.822268 + 0.310788i
\(831\) 60.3071i 0.0725717i
\(832\) 477.990 325.194i 0.574507 0.390858i
\(833\) 0 0
\(834\) −44.5959 117.990i −0.0534723 0.141474i
\(835\) −2680.72 −3.21045
\(836\) 1081.35 953.663i 1.29348 1.14075i
\(837\) 173.583i 0.207387i
\(838\) 441.933 + 1169.25i 0.527366 + 1.39528i
\(839\) 305.844i 0.364533i −0.983249 0.182267i \(-0.941657\pi\)
0.983249 0.182267i \(-0.0583434\pi\)
\(840\) 0 0
\(841\) 337.000 0.400713
\(842\) 1059.78 400.559i 1.25864 0.475723i
\(843\) 88.0059 0.104396
\(844\) 492.146 434.032i 0.583112 0.514256i
\(845\) 789.516i 0.934339i
\(846\) 100.402 37.9484i 0.118679 0.0448563i
\(847\) 0 0
\(848\) −127.236 16.0303i −0.150043 0.0189036i
\(849\) −104.599 −0.123202
\(850\) −493.983 1306.96i −0.581156 1.53759i
\(851\) 400.442 0.470555
\(852\) 27.1758 + 30.8144i 0.0318964 + 0.0361672i
\(853\) 164.018i 0.192283i 0.995368 + 0.0961417i \(0.0306502\pi\)
−0.995368 + 0.0961417i \(0.969350\pi\)
\(854\) 0 0
\(855\) 2257.60i 2.64047i
\(856\) −449.706 237.962i −0.525357 0.277993i
\(857\) −851.068 −0.993078 −0.496539 0.868014i \(-0.665396\pi\)
−0.496539 + 0.868014i \(0.665396\pi\)
\(858\) 123.598 46.7156i 0.144054 0.0544471i
\(859\) 1179.69 1.37333 0.686666 0.726973i \(-0.259073\pi\)
0.686666 + 0.726973i \(0.259073\pi\)
\(860\) 545.588 + 618.639i 0.634405 + 0.719347i
\(861\) 0 0
\(862\) 541.658 204.728i 0.628374 0.237503i
\(863\) 279.048i 0.323346i 0.986844 + 0.161673i \(0.0516890\pi\)
−0.986844 + 0.161673i \(0.948311\pi\)
\(864\) −321.803 + 77.4010i −0.372457 + 0.0895845i
\(865\) 361.598 0.418032
\(866\) −422.635 1118.19i −0.488031 1.29121i
\(867\) 80.0458 0.0923250
\(868\) 0 0
\(869\) 1011.71i 1.16423i
\(870\) 84.0000 + 222.243i 0.0965517 + 0.255452i
\(871\) 710.254i 0.815447i
\(872\) −489.588 + 925.234i −0.561454 + 1.06105i
\(873\) −1420.66 −1.62733
\(874\) −1330.92 + 503.042i −1.52280 + 0.575563i
\(875\) 0 0
\(876\) −82.0446 + 72.3565i −0.0936582 + 0.0825988i
\(877\) 674.159i 0.768711i −0.923185 0.384355i \(-0.874424\pi\)
0.923185 0.384355i \(-0.125576\pi\)
\(878\) 71.8192 27.1451i 0.0817986 0.0309170i
\(879\) 128.398i 0.146073i
\(880\) 1790.35 + 225.563i 2.03449 + 0.256322i
\(881\) 1001.29 1.13654 0.568271 0.822841i \(-0.307613\pi\)
0.568271 + 0.822841i \(0.307613\pi\)
\(882\) 0 0
\(883\) 882.010 0.998879 0.499439 0.866349i \(-0.333539\pi\)
0.499439 + 0.866349i \(0.333539\pi\)
\(884\) −294.995 334.493i −0.333705 0.378386i
\(885\) 161.093i 0.182026i
\(886\) −423.598 1120.73i −0.478102 1.26494i
\(887\) 7.08053i 0.00798256i −0.999992 0.00399128i \(-0.998730\pi\)
0.999992 0.00399128i \(-0.00127047\pi\)
\(888\) −35.6182 + 67.3120i −0.0401106 + 0.0758018i
\(889\) 0 0
\(890\) −1891.75 + 715.014i −2.12556 + 0.803386i
\(891\) 897.103 1.00685
\(892\) −28.0000 31.7490i −0.0313901 0.0355931i
\(893\) 178.976i 0.200422i
\(894\) 276.362 104.455i 0.309129 0.116840i
\(895\) 2662.92i 2.97533i
\(896\) 0 0
\(897\) −130.392 −0.145364
\(898\) 325.296 + 860.654i 0.362246 + 0.958412i
\(899\) −376.764 −0.419092
\(900\) −1469.88 + 1296.31i −1.63320 + 1.44035i
\(901\) 98.9320i 0.109802i
\(902\) 61.5391 + 162.817i 0.0682252 + 0.180507i
\(903\) 0 0
\(904\) −977.401 517.192i −1.08120 0.572115i
\(905\) 365.578 0.403953
\(906\) −256.975 + 97.1273i −0.283637 + 0.107205i
\(907\) 450.372 0.496551 0.248275 0.968689i \(-0.420136\pi\)
0.248275 + 0.968689i \(0.420136\pi\)
\(908\) −641.418 + 565.678i −0.706408 + 0.622993i
\(909\) 105.032i 0.115547i
\(910\) 0 0
\(911\) 202.426i 0.222201i 0.993809 + 0.111101i \(0.0354376\pi\)
−0.993809 + 0.111101i \(0.964562\pi\)
\(912\) 33.8234 268.465i 0.0370870 0.294369i
\(913\) −504.215 −0.552262
\(914\) −188.319 498.245i −0.206038 0.545125i
\(915\) −80.6030 −0.0880907
\(916\) −613.889 696.085i −0.670185 0.759918i
\(917\) 0 0
\(918\) 90.2742 + 238.843i 0.0983379 + 0.260178i
\(919\) 1593.73i 1.73420i 0.498138 + 0.867098i \(0.334017\pi\)
−0.498138 + 0.867098i \(0.665983\pi\)
\(920\) −1573.97 832.866i −1.71084 0.905290i
\(921\) 185.500 0.201412
\(922\) 1427.67 539.610i 1.54845 0.585260i
\(923\) 158.392 0.171606
\(924\) 0 0
\(925\) 919.749i 0.994323i
\(926\) 231.960 87.6725i 0.250496 0.0946787i
\(927\) 922.666i 0.995325i
\(928\) 168.000 + 698.478i 0.181034 + 0.752671i
\(929\) 1039.40 1.11884 0.559419 0.828885i \(-0.311024\pi\)
0.559419 + 0.828885i \(0.311024\pi\)
\(930\) 62.7939 + 166.137i 0.0675204 + 0.178642i
\(931\) 0 0
\(932\) 578.589 510.267i 0.620803 0.547497i
\(933\) 42.3320i 0.0453719i
\(934\) −543.566 1438.14i −0.581976 1.53976i
\(935\) 1392.08i 1.48885i
\(936\) −292.593 + 552.949i −0.312599 + 0.590757i
\(937\) −881.765 −0.941051 −0.470525 0.882386i \(-0.655936\pi\)
−0.470525 + 0.882386i \(0.655936\pi\)
\(938\) 0 0
\(939\) 48.0059 0.0511245
\(940\) −168.000 + 148.162i −0.178723 + 0.157619i
\(941\) 953.344i 1.01312i −0.862205 0.506559i \(-0.830917\pi\)
0.862205 0.506559i \(-0.169083\pi\)
\(942\) 11.0652 4.18223i 0.0117464 0.00443974i
\(943\) 171.767i 0.182149i
\(944\) −60.8873 + 483.278i −0.0644993 + 0.511947i
\(945\) 0 0
\(946\) 201.539 + 533.222i 0.213043 + 0.563660i
\(947\) 16.8957 0.0178413 0.00892063 0.999960i \(-0.497160\pi\)
0.00892063 + 0.999960i \(0.497160\pi\)
\(948\) 125.588 + 142.403i 0.132477 + 0.150214i
\(949\) 421.725i 0.444389i
\(950\) −1155.40 3056.91i −1.21621 3.21780i
\(951\) 63.9386i 0.0672330i
\(952\) 0 0
\(953\) 1526.31 1.60159 0.800794 0.598940i \(-0.204411\pi\)
0.800794 + 0.598940i \(0.204411\pi\)
\(954\) 129.809 49.0632i 0.136068 0.0514290i
\(955\) 1417.57 1.48436
\(956\) −867.588 983.752i −0.907519 1.02903i
\(957\) 164.192i 0.171570i
\(958\) 222.593 84.1322i 0.232352 0.0878207i
\(959\) 0 0
\(960\) 280.000 190.494i 0.291667 0.198431i
\(961\) 679.352 0.706921
\(962\) 103.799 + 274.626i 0.107899 + 0.285474i
\(963\) 550.558 0.571712
\(964\) 215.616 190.156i 0.223669 0.197257i
\(965\) 2360.40i 2.44601i
\(966\) 0 0
\(967\) 1410.39i 1.45852i −0.684235 0.729262i \(-0.739864\pi\)
0.684235 0.729262i \(-0.260136\pi\)
\(968\) 246.655 + 130.517i 0.254809 + 0.134832i
\(969\) −208.743 −0.215421
\(970\) 2773.34 1048.22i 2.85911 1.08064i
\(971\) 596.497 0.614312 0.307156 0.951659i \(-0.400623\pi\)
0.307156 + 0.951659i \(0.400623\pi\)
\(972\) 405.536 357.649i 0.417218 0.367952i
\(973\) 0 0
\(974\) −528.653 + 199.812i −0.542765 + 0.205146i
\(975\) 299.488i 0.307168i
\(976\) −241.809 30.4651i −0.247755 0.0312142i
\(977\) 146.686 0.150140 0.0750698 0.997178i \(-0.476082\pi\)
0.0750698 + 0.997178i \(0.476082\pi\)
\(978\) 43.2994 + 114.560i 0.0442734 + 0.117137i
\(979\) −1397.62 −1.42760
\(980\) 0 0
\(981\) 1132.73i 1.15467i
\(982\) 274.392 + 725.973i 0.279422 + 0.739280i
\(983\) 169.457i 0.172388i 0.996278 + 0.0861939i \(0.0274704\pi\)
−0.996278 + 0.0861939i \(0.972530\pi\)
\(984\) 28.8730 + 15.2782i 0.0293425 + 0.0155266i
\(985\) 1312.36 1.33235
\(986\) 518.412 195.941i 0.525773 0.198723i
\(987\) 0 0
\(988\) −689.980 782.364i −0.698360 0.791866i
\(989\) 562.533i 0.568789i
\(990\) −1826.55 + 690.372i −1.84500 + 0.697345i
\(991\) 1686.90i 1.70222i 0.524988 + 0.851109i \(0.324070\pi\)
−0.524988 + 0.851109i \(0.675930\pi\)
\(992\) 125.588 + 522.145i 0.126601 + 0.526356i
\(993\) −188.471 −0.189800
\(994\) 0 0
\(995\) −3527.52 −3.54524
\(996\) −70.9706 + 62.5902i −0.0712556 + 0.0628415i
\(997\) 1736.14i 1.74136i 0.491849 + 0.870680i \(0.336321\pi\)
−0.491849 + 0.870680i \(0.663679\pi\)
\(998\) 19.5980 + 51.8514i 0.0196373 + 0.0519553i
\(999\) 168.082i 0.168250i
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 392.3.g.h.99.1 4
4.3 odd 2 1568.3.g.h.687.2 4
7.2 even 3 392.3.k.j.67.2 8
7.3 odd 6 392.3.k.i.275.4 8
7.4 even 3 392.3.k.j.275.4 8
7.5 odd 6 392.3.k.i.67.2 8
7.6 odd 2 56.3.g.a.43.1 4
8.3 odd 2 inner 392.3.g.h.99.2 4
8.5 even 2 1568.3.g.h.687.1 4
21.20 even 2 504.3.g.a.379.4 4
28.27 even 2 224.3.g.a.15.3 4
56.3 even 6 392.3.k.i.275.2 8
56.11 odd 6 392.3.k.j.275.2 8
56.13 odd 2 224.3.g.a.15.4 4
56.19 even 6 392.3.k.i.67.4 8
56.27 even 2 56.3.g.a.43.2 yes 4
56.51 odd 6 392.3.k.j.67.4 8
84.83 odd 2 2016.3.g.a.1135.4 4
112.13 odd 4 1792.3.d.g.1023.5 8
112.27 even 4 1792.3.d.g.1023.6 8
112.69 odd 4 1792.3.d.g.1023.4 8
112.83 even 4 1792.3.d.g.1023.3 8
168.83 odd 2 504.3.g.a.379.3 4
168.125 even 2 2016.3.g.a.1135.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
56.3.g.a.43.1 4 7.6 odd 2
56.3.g.a.43.2 yes 4 56.27 even 2
224.3.g.a.15.3 4 28.27 even 2
224.3.g.a.15.4 4 56.13 odd 2
392.3.g.h.99.1 4 1.1 even 1 trivial
392.3.g.h.99.2 4 8.3 odd 2 inner
392.3.k.i.67.2 8 7.5 odd 6
392.3.k.i.67.4 8 56.19 even 6
392.3.k.i.275.2 8 56.3 even 6
392.3.k.i.275.4 8 7.3 odd 6
392.3.k.j.67.2 8 7.2 even 3
392.3.k.j.67.4 8 56.51 odd 6
392.3.k.j.275.2 8 56.11 odd 6
392.3.k.j.275.4 8 7.4 even 3
504.3.g.a.379.3 4 168.83 odd 2
504.3.g.a.379.4 4 21.20 even 2
1568.3.g.h.687.1 4 8.5 even 2
1568.3.g.h.687.2 4 4.3 odd 2
1792.3.d.g.1023.3 8 112.83 even 4
1792.3.d.g.1023.4 8 112.69 odd 4
1792.3.d.g.1023.5 8 112.13 odd 4
1792.3.d.g.1023.6 8 112.27 even 4
2016.3.g.a.1135.1 4 168.125 even 2
2016.3.g.a.1135.4 4 84.83 odd 2