Properties

Label 189.4.i.a.143.12
Level $189$
Weight $4$
Character 189.143
Analytic conductor $11.151$
Analytic rank $0$
Dimension $44$
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] = [189,4,Mod(143,189)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(189, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([1, 1]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("189.143");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 189 = 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 189.i (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: \(11.1513609911\)
Analytic rank: \(0\)
Dimension: \(44\)
Relative dimension: \(22\) over \(\Q(\zeta_{6})\)
Twist minimal: no (minimal twist has level 63)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 143.12
Character \(\chi\) \(=\) 189.143
Dual form 189.4.i.a.152.11

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+0.257625i q^{2} +7.93363 q^{4} +(-3.19386 + 5.53193i) q^{5} +(-15.2112 + 10.5650i) q^{7} +4.10490i q^{8} +O(q^{10})\) \(q+0.257625i q^{2} +7.93363 q^{4} +(-3.19386 + 5.53193i) q^{5} +(-15.2112 + 10.5650i) q^{7} +4.10490i q^{8} +(-1.42516 - 0.822818i) q^{10} +(-52.8984 + 30.5409i) q^{11} +(-8.78677 + 5.07304i) q^{13} +(-2.72180 - 3.91879i) q^{14} +62.4115 q^{16} +(22.5082 - 38.9853i) q^{17} +(-69.6373 + 40.2051i) q^{19} +(-25.3389 + 43.8883i) q^{20} +(-7.86810 - 13.6279i) q^{22} +(-23.9716 - 13.8400i) q^{23} +(42.0985 + 72.9167i) q^{25} +(-1.30694 - 2.26369i) q^{26} +(-120.680 + 83.8187i) q^{28} +(-48.9383 - 28.2545i) q^{29} +106.409i q^{31} +48.9180i q^{32} +(10.0436 + 5.79867i) q^{34} +(-9.86226 - 117.890i) q^{35} +(95.6403 + 165.654i) q^{37} +(-10.3578 - 17.9403i) q^{38} +(-22.7080 - 13.1105i) q^{40} +(-15.0856 - 26.1289i) q^{41} +(-185.062 + 320.536i) q^{43} +(-419.676 + 242.300i) q^{44} +(3.56553 - 6.17569i) q^{46} -496.082 q^{47} +(119.762 - 321.413i) q^{49} +(-18.7852 + 10.8456i) q^{50} +(-69.7110 + 40.2476i) q^{52} +(601.424 + 347.232i) q^{53} -390.174i q^{55} +(-43.3682 - 62.4405i) q^{56} +(7.27907 - 12.6077i) q^{58} +635.340 q^{59} -747.913i q^{61} -27.4135 q^{62} +486.690 q^{64} -64.8104i q^{65} +164.786 q^{67} +(178.572 - 309.295i) q^{68} +(30.3715 - 2.54076i) q^{70} +278.490i q^{71} +(-313.876 - 181.216i) q^{73} +(-42.6766 + 24.6393i) q^{74} +(-552.477 + 318.973i) q^{76} +(481.985 - 1023.44i) q^{77} +557.480 q^{79} +(-199.334 + 345.256i) q^{80} +(6.73147 - 3.88641i) q^{82} +(514.684 - 891.459i) q^{83} +(143.776 + 249.028i) q^{85} +(-82.5781 - 47.6765i) q^{86} +(-125.367 - 217.143i) q^{88} +(730.130 + 1264.62i) q^{89} +(80.0608 - 169.999i) q^{91} +(-190.182 - 109.802i) q^{92} -127.803i q^{94} -513.638i q^{95} +(-878.164 - 507.008i) q^{97} +(82.8039 + 30.8537i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 44 q - 162 q^{4} + 3 q^{5} + 5 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 44 q - 162 q^{4} + 3 q^{5} + 5 q^{7} - 6 q^{10} - 9 q^{11} - 36 q^{13} - 54 q^{14} + 526 q^{16} + 72 q^{17} - 6 q^{19} - 24 q^{20} + 14 q^{22} + 285 q^{23} - 349 q^{25} + 96 q^{26} - 156 q^{28} + 132 q^{29} + 24 q^{34} - 765 q^{35} + 82 q^{37} + 873 q^{38} + 420 q^{40} - 618 q^{41} + 82 q^{43} - 603 q^{44} + 266 q^{46} + 402 q^{47} - 79 q^{49} + 1845 q^{50} + 189 q^{52} - 564 q^{53} - 66 q^{56} + 269 q^{58} - 1494 q^{59} + 2904 q^{62} - 1144 q^{64} - 590 q^{67} - 3504 q^{68} - 105 q^{70} - 6 q^{73} - 1515 q^{74} - 144 q^{76} + 4443 q^{77} + 1102 q^{79} + 4239 q^{80} + 18 q^{82} - 1830 q^{83} - 237 q^{85} - 1209 q^{86} - 623 q^{88} - 4266 q^{89} - 1140 q^{91} - 7896 q^{92} - 792 q^{97} - 5667 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/189\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(136\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.257625i 0.0910841i 0.998962 + 0.0455421i \(0.0145015\pi\)
−0.998962 + 0.0455421i \(0.985498\pi\)
\(3\) 0 0
\(4\) 7.93363 0.991704
\(5\) −3.19386 + 5.53193i −0.285668 + 0.494791i −0.972771 0.231769i \(-0.925549\pi\)
0.687103 + 0.726560i \(0.258882\pi\)
\(6\) 0 0
\(7\) −15.2112 + 10.5650i −0.821328 + 0.570456i
\(8\) 4.10490i 0.181413i
\(9\) 0 0
\(10\) −1.42516 0.822818i −0.0450676 0.0260198i
\(11\) −52.8984 + 30.5409i −1.44995 + 0.837130i −0.998478 0.0551546i \(-0.982435\pi\)
−0.451474 + 0.892284i \(0.649102\pi\)
\(12\) 0 0
\(13\) −8.78677 + 5.07304i −0.187462 + 0.108231i −0.590794 0.806822i \(-0.701185\pi\)
0.403332 + 0.915054i \(0.367852\pi\)
\(14\) −2.72180 3.91879i −0.0519595 0.0748100i
\(15\) 0 0
\(16\) 62.4115 0.975180
\(17\) 22.5082 38.9853i 0.321120 0.556196i −0.659599 0.751617i \(-0.729274\pi\)
0.980719 + 0.195421i \(0.0626074\pi\)
\(18\) 0 0
\(19\) −69.6373 + 40.2051i −0.840837 + 0.485457i −0.857549 0.514403i \(-0.828014\pi\)
0.0167118 + 0.999860i \(0.494680\pi\)
\(20\) −25.3389 + 43.8883i −0.283298 + 0.490686i
\(21\) 0 0
\(22\) −7.86810 13.6279i −0.0762493 0.132068i
\(23\) −23.9716 13.8400i −0.217323 0.125471i 0.387387 0.921917i \(-0.373378\pi\)
−0.604710 + 0.796446i \(0.706711\pi\)
\(24\) 0 0
\(25\) 42.0985 + 72.9167i 0.336788 + 0.583334i
\(26\) −1.30694 2.26369i −0.00985817 0.0170749i
\(27\) 0 0
\(28\) −120.680 + 83.8187i −0.814514 + 0.565723i
\(29\) −48.9383 28.2545i −0.313366 0.180922i 0.335066 0.942195i \(-0.391241\pi\)
−0.648432 + 0.761273i \(0.724575\pi\)
\(30\) 0 0
\(31\) 106.409i 0.616502i 0.951305 + 0.308251i \(0.0997436\pi\)
−0.951305 + 0.308251i \(0.900256\pi\)
\(32\) 48.9180i 0.270236i
\(33\) 0 0
\(34\) 10.0436 + 5.79867i 0.0506607 + 0.0292489i
\(35\) −9.86226 117.890i −0.0476293 0.569347i
\(36\) 0 0
\(37\) 95.6403 + 165.654i 0.424951 + 0.736036i 0.996416 0.0845902i \(-0.0269581\pi\)
−0.571465 + 0.820626i \(0.693625\pi\)
\(38\) −10.3578 17.9403i −0.0442175 0.0765869i
\(39\) 0 0
\(40\) −22.7080 13.1105i −0.0897613 0.0518237i
\(41\) −15.0856 26.1289i −0.0574626 0.0995282i 0.835863 0.548938i \(-0.184968\pi\)
−0.893326 + 0.449410i \(0.851634\pi\)
\(42\) 0 0
\(43\) −185.062 + 320.536i −0.656317 + 1.13678i 0.325244 + 0.945630i \(0.394553\pi\)
−0.981562 + 0.191145i \(0.938780\pi\)
\(44\) −419.676 + 242.300i −1.43792 + 0.830185i
\(45\) 0 0
\(46\) 3.56553 6.17569i 0.0114285 0.0197947i
\(47\) −496.082 −1.53960 −0.769798 0.638288i \(-0.779643\pi\)
−0.769798 + 0.638288i \(0.779643\pi\)
\(48\) 0 0
\(49\) 119.762 321.413i 0.349161 0.937063i
\(50\) −18.7852 + 10.8456i −0.0531325 + 0.0306760i
\(51\) 0 0
\(52\) −69.7110 + 40.2476i −0.185907 + 0.107334i
\(53\) 601.424 + 347.232i 1.55871 + 0.899924i 0.997380 + 0.0723355i \(0.0230452\pi\)
0.561335 + 0.827589i \(0.310288\pi\)
\(54\) 0 0
\(55\) 390.174i 0.956564i
\(56\) −43.3682 62.4405i −0.103488 0.148999i
\(57\) 0 0
\(58\) 7.27907 12.6077i 0.0164791 0.0285427i
\(59\) 635.340 1.40194 0.700968 0.713193i \(-0.252752\pi\)
0.700968 + 0.713193i \(0.252752\pi\)
\(60\) 0 0
\(61\) 747.913i 1.56984i −0.619595 0.784922i \(-0.712703\pi\)
0.619595 0.784922i \(-0.287297\pi\)
\(62\) −27.4135 −0.0561536
\(63\) 0 0
\(64\) 486.690 0.950566
\(65\) 64.8104i 0.123673i
\(66\) 0 0
\(67\) 164.786 0.300475 0.150237 0.988650i \(-0.451996\pi\)
0.150237 + 0.988650i \(0.451996\pi\)
\(68\) 178.572 309.295i 0.318456 0.551582i
\(69\) 0 0
\(70\) 30.3715 2.54076i 0.0518584 0.00433828i
\(71\) 278.490i 0.465502i 0.972536 + 0.232751i \(0.0747728\pi\)
−0.972536 + 0.232751i \(0.925227\pi\)
\(72\) 0 0
\(73\) −313.876 181.216i −0.503238 0.290545i 0.226812 0.973939i \(-0.427170\pi\)
−0.730050 + 0.683394i \(0.760503\pi\)
\(74\) −42.6766 + 24.6393i −0.0670412 + 0.0387063i
\(75\) 0 0
\(76\) −552.477 + 318.973i −0.833861 + 0.481430i
\(77\) 481.985 1023.44i 0.713341 1.51469i
\(78\) 0 0
\(79\) 557.480 0.793942 0.396971 0.917831i \(-0.370061\pi\)
0.396971 + 0.917831i \(0.370061\pi\)
\(80\) −199.334 + 345.256i −0.278577 + 0.482510i
\(81\) 0 0
\(82\) 6.73147 3.88641i 0.00906544 0.00523393i
\(83\) 514.684 891.459i 0.680650 1.17892i −0.294133 0.955765i \(-0.595031\pi\)
0.974783 0.223156i \(-0.0716358\pi\)
\(84\) 0 0
\(85\) 143.776 + 249.028i 0.183467 + 0.317775i
\(86\) −82.5781 47.6765i −0.103542 0.0597801i
\(87\) 0 0
\(88\) −125.367 217.143i −0.151866 0.263040i
\(89\) 730.130 + 1264.62i 0.869591 + 1.50618i 0.862415 + 0.506201i \(0.168951\pi\)
0.00717569 + 0.999974i \(0.497716\pi\)
\(90\) 0 0
\(91\) 80.0608 169.999i 0.0922269 0.195833i
\(92\) −190.182 109.802i −0.215520 0.124431i
\(93\) 0 0
\(94\) 127.803i 0.140233i
\(95\) 513.638i 0.554718i
\(96\) 0 0
\(97\) −878.164 507.008i −0.919217 0.530710i −0.0358320 0.999358i \(-0.511408\pi\)
−0.883385 + 0.468647i \(0.844741\pi\)
\(98\) 82.8039 + 30.8537i 0.0853516 + 0.0318030i
\(99\) 0 0
\(100\) 333.994 + 578.494i 0.333994 + 0.578494i
\(101\) −71.8520 124.451i −0.0707875 0.122608i 0.828459 0.560050i \(-0.189218\pi\)
−0.899247 + 0.437442i \(0.855885\pi\)
\(102\) 0 0
\(103\) 473.681 + 273.480i 0.453138 + 0.261619i 0.709155 0.705053i \(-0.249077\pi\)
−0.256017 + 0.966672i \(0.582410\pi\)
\(104\) −20.8243 36.0688i −0.0196346 0.0340080i
\(105\) 0 0
\(106\) −89.4556 + 154.942i −0.0819689 + 0.141974i
\(107\) 1153.06 665.722i 1.04178 0.601475i 0.121447 0.992598i \(-0.461247\pi\)
0.920338 + 0.391123i \(0.127913\pi\)
\(108\) 0 0
\(109\) 527.013 912.813i 0.463107 0.802125i −0.536007 0.844214i \(-0.680068\pi\)
0.999114 + 0.0420888i \(0.0134013\pi\)
\(110\) 100.518 0.0871278
\(111\) 0 0
\(112\) −949.355 + 659.377i −0.800943 + 0.556297i
\(113\) −804.987 + 464.760i −0.670149 + 0.386911i −0.796133 0.605122i \(-0.793125\pi\)
0.125984 + 0.992032i \(0.459791\pi\)
\(114\) 0 0
\(115\) 153.124 88.4062i 0.124164 0.0716863i
\(116\) −388.258 224.161i −0.310766 0.179421i
\(117\) 0 0
\(118\) 163.679i 0.127694i
\(119\) 69.5026 + 830.813i 0.0535403 + 0.640004i
\(120\) 0 0
\(121\) 1199.99 2078.45i 0.901573 1.56157i
\(122\) 192.681 0.142988
\(123\) 0 0
\(124\) 844.207i 0.611387i
\(125\) −1336.29 −0.956173
\(126\) 0 0
\(127\) −1387.22 −0.969259 −0.484629 0.874720i \(-0.661046\pi\)
−0.484629 + 0.874720i \(0.661046\pi\)
\(128\) 516.727i 0.356818i
\(129\) 0 0
\(130\) 16.6968 0.0112646
\(131\) −196.378 + 340.137i −0.130974 + 0.226854i −0.924052 0.382266i \(-0.875144\pi\)
0.793078 + 0.609120i \(0.208477\pi\)
\(132\) 0 0
\(133\) 634.502 1347.29i 0.413671 0.878380i
\(134\) 42.4530i 0.0273685i
\(135\) 0 0
\(136\) 160.031 + 92.3939i 0.100901 + 0.0582552i
\(137\) −1802.86 + 1040.88i −1.12430 + 0.649112i −0.942494 0.334223i \(-0.891526\pi\)
−0.181801 + 0.983335i \(0.558193\pi\)
\(138\) 0 0
\(139\) −1088.49 + 628.441i −0.664206 + 0.383479i −0.793878 0.608078i \(-0.791941\pi\)
0.129672 + 0.991557i \(0.458608\pi\)
\(140\) −78.2435 935.299i −0.0472342 0.564623i
\(141\) 0 0
\(142\) −71.7459 −0.0423999
\(143\) 309.871 536.712i 0.181208 0.313861i
\(144\) 0 0
\(145\) 312.604 180.482i 0.179037 0.103367i
\(146\) 46.6858 80.8622i 0.0264640 0.0458370i
\(147\) 0 0
\(148\) 758.775 + 1314.24i 0.421425 + 0.729930i
\(149\) 2604.69 + 1503.82i 1.43211 + 0.826830i 0.997282 0.0736835i \(-0.0234755\pi\)
0.434829 + 0.900513i \(0.356809\pi\)
\(150\) 0 0
\(151\) 1435.11 + 2485.69i 0.773428 + 1.33962i 0.935674 + 0.352867i \(0.114793\pi\)
−0.162245 + 0.986750i \(0.551874\pi\)
\(152\) −165.038 285.854i −0.0880681 0.152538i
\(153\) 0 0
\(154\) 263.662 + 124.171i 0.137964 + 0.0649740i
\(155\) −588.645 339.855i −0.305040 0.176115i
\(156\) 0 0
\(157\) 917.702i 0.466501i −0.972417 0.233250i \(-0.925064\pi\)
0.972417 0.233250i \(-0.0749361\pi\)
\(158\) 143.621i 0.0723155i
\(159\) 0 0
\(160\) −270.611 156.237i −0.133710 0.0771977i
\(161\) 510.857 42.7363i 0.250069 0.0209198i
\(162\) 0 0
\(163\) −806.536 1396.96i −0.387563 0.671279i 0.604558 0.796561i \(-0.293350\pi\)
−0.992121 + 0.125282i \(0.960016\pi\)
\(164\) −119.683 207.297i −0.0569859 0.0987025i
\(165\) 0 0
\(166\) 229.662 + 132.595i 0.107381 + 0.0619964i
\(167\) −922.384 1597.62i −0.427402 0.740282i 0.569239 0.822172i \(-0.307238\pi\)
−0.996641 + 0.0818896i \(0.973905\pi\)
\(168\) 0 0
\(169\) −1047.03 + 1813.51i −0.476572 + 0.825447i
\(170\) −64.1557 + 37.0403i −0.0289442 + 0.0167110i
\(171\) 0 0
\(172\) −1468.21 + 2543.02i −0.650872 + 1.12734i
\(173\) −2005.80 −0.881494 −0.440747 0.897631i \(-0.645286\pi\)
−0.440747 + 0.897631i \(0.645286\pi\)
\(174\) 0 0
\(175\) −1410.73 664.382i −0.609380 0.286986i
\(176\) −3301.47 + 1906.10i −1.41396 + 0.816352i
\(177\) 0 0
\(178\) −325.798 + 188.100i −0.137189 + 0.0792060i
\(179\) 1424.92 + 822.678i 0.594992 + 0.343519i 0.767069 0.641565i \(-0.221714\pi\)
−0.172077 + 0.985083i \(0.555048\pi\)
\(180\) 0 0
\(181\) 3394.40i 1.39394i 0.717099 + 0.696971i \(0.245469\pi\)
−0.717099 + 0.696971i \(0.754531\pi\)
\(182\) 43.7960 + 20.6256i 0.0178372 + 0.00840041i
\(183\) 0 0
\(184\) 56.8119 98.4011i 0.0227621 0.0394251i
\(185\) −1221.85 −0.485579
\(186\) 0 0
\(187\) 2749.68i 1.07528i
\(188\) −3935.73 −1.52682
\(189\) 0 0
\(190\) 132.326 0.0505260
\(191\) 113.285i 0.0429165i −0.999770 0.0214582i \(-0.993169\pi\)
0.999770 0.0214582i \(-0.00683090\pi\)
\(192\) 0 0
\(193\) −875.800 −0.326640 −0.163320 0.986573i \(-0.552220\pi\)
−0.163320 + 0.986573i \(0.552220\pi\)
\(194\) 130.618 226.237i 0.0483393 0.0837261i
\(195\) 0 0
\(196\) 950.148 2549.97i 0.346264 0.929289i
\(197\) 1004.09i 0.363140i −0.983378 0.181570i \(-0.941882\pi\)
0.983378 0.181570i \(-0.0581179\pi\)
\(198\) 0 0
\(199\) 1451.86 + 838.230i 0.517183 + 0.298596i 0.735781 0.677219i \(-0.236815\pi\)
−0.218598 + 0.975815i \(0.570148\pi\)
\(200\) −299.316 + 172.810i −0.105824 + 0.0610976i
\(201\) 0 0
\(202\) 32.0618 18.5109i 0.0111676 0.00644762i
\(203\) 1042.92 87.2466i 0.360584 0.0301651i
\(204\) 0 0
\(205\) 192.725 0.0656608
\(206\) −70.4553 + 122.032i −0.0238294 + 0.0412737i
\(207\) 0 0
\(208\) −548.396 + 316.616i −0.182810 + 0.105545i
\(209\) 2455.80 4253.57i 0.812782 1.40778i
\(210\) 0 0
\(211\) 1528.10 + 2646.75i 0.498572 + 0.863552i 0.999999 0.00164804i \(-0.000524587\pi\)
−0.501427 + 0.865200i \(0.667191\pi\)
\(212\) 4771.47 + 2754.81i 1.54578 + 0.892458i
\(213\) 0 0
\(214\) 171.507 + 297.058i 0.0547848 + 0.0948901i
\(215\) −1182.12 2047.50i −0.374977 0.649480i
\(216\) 0 0
\(217\) −1124.21 1618.60i −0.351687 0.506351i
\(218\) 235.163 + 135.772i 0.0730608 + 0.0421817i
\(219\) 0 0
\(220\) 3095.49i 0.948628i
\(221\) 456.740i 0.139021i
\(222\) 0 0
\(223\) −3580.72 2067.33i −1.07526 0.620801i −0.145645 0.989337i \(-0.546526\pi\)
−0.929613 + 0.368536i \(0.879859\pi\)
\(224\) −516.818 744.101i −0.154158 0.221953i
\(225\) 0 0
\(226\) −119.734 207.385i −0.0352414 0.0610400i
\(227\) 2220.58 + 3846.16i 0.649274 + 1.12458i 0.983297 + 0.182010i \(0.0582605\pi\)
−0.334023 + 0.942565i \(0.608406\pi\)
\(228\) 0 0
\(229\) 1125.72 + 649.933i 0.324845 + 0.187549i 0.653550 0.756883i \(-0.273279\pi\)
−0.328705 + 0.944433i \(0.606612\pi\)
\(230\) 22.7756 + 39.4486i 0.00652948 + 0.0113094i
\(231\) 0 0
\(232\) 115.982 200.887i 0.0328215 0.0568485i
\(233\) 1741.16 1005.26i 0.489559 0.282647i −0.234832 0.972036i \(-0.575454\pi\)
0.724392 + 0.689389i \(0.242121\pi\)
\(234\) 0 0
\(235\) 1584.42 2744.29i 0.439813 0.761778i
\(236\) 5040.55 1.39031
\(237\) 0 0
\(238\) −214.038 + 17.9056i −0.0582943 + 0.00487667i
\(239\) −4499.21 + 2597.62i −1.21770 + 0.703038i −0.964425 0.264356i \(-0.914840\pi\)
−0.253273 + 0.967395i \(0.581507\pi\)
\(240\) 0 0
\(241\) 5836.81 3369.88i 1.56009 0.900719i 0.562845 0.826563i \(-0.309707\pi\)
0.997247 0.0741564i \(-0.0236264\pi\)
\(242\) 535.460 + 309.148i 0.142234 + 0.0821190i
\(243\) 0 0
\(244\) 5933.67i 1.55682i
\(245\) 1395.53 + 1689.06i 0.363906 + 0.440450i
\(246\) 0 0
\(247\) 407.925 706.546i 0.105084 0.182010i
\(248\) −436.797 −0.111841
\(249\) 0 0
\(250\) 344.262i 0.0870922i
\(251\) −1818.28 −0.457246 −0.228623 0.973515i \(-0.573422\pi\)
−0.228623 + 0.973515i \(0.573422\pi\)
\(252\) 0 0
\(253\) 1690.75 0.420144
\(254\) 357.382i 0.0882841i
\(255\) 0 0
\(256\) 3760.40 0.918065
\(257\) 232.027 401.882i 0.0563168 0.0975435i −0.836493 0.547978i \(-0.815398\pi\)
0.892809 + 0.450435i \(0.148731\pi\)
\(258\) 0 0
\(259\) −3204.94 1509.36i −0.768900 0.362112i
\(260\) 514.182i 0.122647i
\(261\) 0 0
\(262\) −87.6278 50.5919i −0.0206628 0.0119297i
\(263\) 326.067 188.255i 0.0764492 0.0441380i −0.461288 0.887250i \(-0.652613\pi\)
0.537737 + 0.843112i \(0.319279\pi\)
\(264\) 0 0
\(265\) −3841.73 + 2218.02i −0.890549 + 0.514159i
\(266\) 347.094 + 163.463i 0.0800065 + 0.0376789i
\(267\) 0 0
\(268\) 1307.35 0.297982
\(269\) 1998.09 3460.80i 0.452885 0.784419i −0.545679 0.837994i \(-0.683728\pi\)
0.998564 + 0.0535750i \(0.0170616\pi\)
\(270\) 0 0
\(271\) −729.622 + 421.248i −0.163548 + 0.0944242i −0.579540 0.814944i \(-0.696768\pi\)
0.415992 + 0.909368i \(0.363434\pi\)
\(272\) 1404.77 2433.13i 0.313150 0.542391i
\(273\) 0 0
\(274\) −268.157 464.461i −0.0591238 0.102405i
\(275\) −4453.89 2571.45i −0.976653 0.563871i
\(276\) 0 0
\(277\) −2083.09 3608.02i −0.451844 0.782616i 0.546657 0.837357i \(-0.315900\pi\)
−0.998501 + 0.0547404i \(0.982567\pi\)
\(278\) −161.902 280.422i −0.0349289 0.0604986i
\(279\) 0 0
\(280\) 483.929 40.4836i 0.103287 0.00864056i
\(281\) 4478.35 + 2585.58i 0.950733 + 0.548906i 0.893309 0.449444i \(-0.148378\pi\)
0.0574244 + 0.998350i \(0.481711\pi\)
\(282\) 0 0
\(283\) 6019.50i 1.26439i 0.774810 + 0.632195i \(0.217846\pi\)
−0.774810 + 0.632195i \(0.782154\pi\)
\(284\) 2209.44i 0.461640i
\(285\) 0 0
\(286\) 138.270 + 79.8304i 0.0285877 + 0.0165051i
\(287\) 505.521 + 238.074i 0.103972 + 0.0489654i
\(288\) 0 0
\(289\) 1443.26 + 2499.80i 0.293764 + 0.508814i
\(290\) 46.4967 + 80.5346i 0.00941510 + 0.0163074i
\(291\) 0 0
\(292\) −2490.17 1437.70i −0.499063 0.288134i
\(293\) −2243.89 3886.53i −0.447404 0.774926i 0.550812 0.834629i \(-0.314318\pi\)
−0.998216 + 0.0597027i \(0.980985\pi\)
\(294\) 0 0
\(295\) −2029.19 + 3514.66i −0.400488 + 0.693665i
\(296\) −679.993 + 392.594i −0.133526 + 0.0770914i
\(297\) 0 0
\(298\) −387.421 + 671.033i −0.0753111 + 0.130443i
\(299\) 280.844 0.0543198
\(300\) 0 0
\(301\) −571.449 6830.92i −0.109428 1.30807i
\(302\) −640.374 + 369.720i −0.122018 + 0.0704471i
\(303\) 0 0
\(304\) −4346.17 + 2509.26i −0.819967 + 0.473408i
\(305\) 4137.40 + 2388.73i 0.776744 + 0.448454i
\(306\) 0 0
\(307\) 263.461i 0.0489789i 0.999700 + 0.0244895i \(0.00779602\pi\)
−0.999700 + 0.0244895i \(0.992204\pi\)
\(308\) 3823.89 8119.55i 0.707423 1.50213i
\(309\) 0 0
\(310\) 87.5550 151.650i 0.0160413 0.0277843i
\(311\) −4852.47 −0.884753 −0.442377 0.896829i \(-0.645865\pi\)
−0.442377 + 0.896829i \(0.645865\pi\)
\(312\) 0 0
\(313\) 2738.54i 0.494542i −0.968946 0.247271i \(-0.920466\pi\)
0.968946 0.247271i \(-0.0795337\pi\)
\(314\) 236.423 0.0424908
\(315\) 0 0
\(316\) 4422.84 0.787355
\(317\) 7417.18i 1.31417i 0.753819 + 0.657083i \(0.228210\pi\)
−0.753819 + 0.657083i \(0.771790\pi\)
\(318\) 0 0
\(319\) 3451.67 0.605820
\(320\) −1554.42 + 2692.33i −0.271546 + 0.470331i
\(321\) 0 0
\(322\) 11.0099 + 131.609i 0.00190547 + 0.0227774i
\(323\) 3619.78i 0.623560i
\(324\) 0 0
\(325\) −739.820 427.135i −0.126270 0.0729021i
\(326\) 359.892 207.784i 0.0611429 0.0353009i
\(327\) 0 0
\(328\) 107.257 61.9247i 0.0180557 0.0104244i
\(329\) 7546.01 5241.10i 1.26451 0.878271i
\(330\) 0 0
\(331\) 4172.12 0.692811 0.346406 0.938085i \(-0.387402\pi\)
0.346406 + 0.938085i \(0.387402\pi\)
\(332\) 4083.31 7072.51i 0.675003 1.16914i
\(333\) 0 0
\(334\) 411.585 237.629i 0.0674280 0.0389296i
\(335\) −526.303 + 911.584i −0.0858359 + 0.148672i
\(336\) 0 0
\(337\) −528.671 915.685i −0.0854556 0.148013i 0.820130 0.572178i \(-0.193901\pi\)
−0.905585 + 0.424164i \(0.860568\pi\)
\(338\) −467.204 269.741i −0.0751851 0.0434081i
\(339\) 0 0
\(340\) 1140.67 + 1975.69i 0.181945 + 0.315138i
\(341\) −3249.82 5628.85i −0.516092 0.893898i
\(342\) 0 0
\(343\) 1573.99 + 6154.36i 0.247777 + 0.968817i
\(344\) −1315.77 759.660i −0.206225 0.119064i
\(345\) 0 0
\(346\) 516.745i 0.0802901i
\(347\) 4780.66i 0.739594i −0.929113 0.369797i \(-0.879427\pi\)
0.929113 0.369797i \(-0.120573\pi\)
\(348\) 0 0
\(349\) 2180.04 + 1258.65i 0.334370 + 0.193048i 0.657780 0.753211i \(-0.271496\pi\)
−0.323410 + 0.946259i \(0.604829\pi\)
\(350\) 171.161 363.440i 0.0261399 0.0555048i
\(351\) 0 0
\(352\) −1494.00 2587.68i −0.226223 0.391829i
\(353\) 3002.91 + 5201.18i 0.452772 + 0.784224i 0.998557 0.0537011i \(-0.0171018\pi\)
−0.545785 + 0.837925i \(0.683768\pi\)
\(354\) 0 0
\(355\) −1540.59 889.458i −0.230326 0.132979i
\(356\) 5792.58 + 10033.0i 0.862377 + 1.49368i
\(357\) 0 0
\(358\) −211.942 + 367.095i −0.0312891 + 0.0541943i
\(359\) −5772.63 + 3332.83i −0.848656 + 0.489972i −0.860197 0.509961i \(-0.829660\pi\)
0.0115408 + 0.999933i \(0.496326\pi\)
\(360\) 0 0
\(361\) −196.595 + 340.513i −0.0286624 + 0.0496447i
\(362\) −874.481 −0.126966
\(363\) 0 0
\(364\) 635.173 1348.71i 0.0914618 0.194208i
\(365\) 2004.95 1157.56i 0.287518 0.165998i
\(366\) 0 0
\(367\) −1394.22 + 804.953i −0.198304 + 0.114491i −0.595864 0.803085i \(-0.703190\pi\)
0.397560 + 0.917576i \(0.369857\pi\)
\(368\) −1496.10 863.777i −0.211929 0.122357i
\(369\) 0 0
\(370\) 314.778i 0.0442285i
\(371\) −12816.9 + 1072.21i −1.79358 + 0.150044i
\(372\) 0 0
\(373\) −2605.53 + 4512.91i −0.361687 + 0.626460i −0.988239 0.152920i \(-0.951132\pi\)
0.626552 + 0.779380i \(0.284466\pi\)
\(374\) −708.387 −0.0979407
\(375\) 0 0
\(376\) 2036.37i 0.279302i
\(377\) 573.346 0.0783257
\(378\) 0 0
\(379\) −9946.69 −1.34809 −0.674046 0.738689i \(-0.735445\pi\)
−0.674046 + 0.738689i \(0.735445\pi\)
\(380\) 4075.02i 0.550116i
\(381\) 0 0
\(382\) 29.1852 0.00390901
\(383\) −7224.48 + 12513.2i −0.963848 + 1.66943i −0.251170 + 0.967943i \(0.580815\pi\)
−0.712678 + 0.701491i \(0.752518\pi\)
\(384\) 0 0
\(385\) 4122.18 + 5935.01i 0.545677 + 0.785653i
\(386\) 225.628i 0.0297517i
\(387\) 0 0
\(388\) −6967.03 4022.42i −0.911591 0.526307i
\(389\) −7862.92 + 4539.66i −1.02485 + 0.591696i −0.915505 0.402308i \(-0.868208\pi\)
−0.109344 + 0.994004i \(0.534875\pi\)
\(390\) 0 0
\(391\) −1079.12 + 623.028i −0.139574 + 0.0805828i
\(392\) 1319.37 + 491.611i 0.169995 + 0.0633421i
\(393\) 0 0
\(394\) 258.679 0.0330763
\(395\) −1780.51 + 3083.94i −0.226803 + 0.392835i
\(396\) 0 0
\(397\) 1879.14 1084.92i 0.237559 0.137155i −0.376495 0.926419i \(-0.622871\pi\)
0.614055 + 0.789264i \(0.289537\pi\)
\(398\) −215.949 + 374.035i −0.0271973 + 0.0471072i
\(399\) 0 0
\(400\) 2627.43 + 4550.84i 0.328429 + 0.568855i
\(401\) 260.757 + 150.548i 0.0324728 + 0.0187482i 0.516149 0.856499i \(-0.327365\pi\)
−0.483676 + 0.875247i \(0.660699\pi\)
\(402\) 0 0
\(403\) −539.816 934.988i −0.0667249 0.115571i
\(404\) −570.047 987.351i −0.0702003 0.121590i
\(405\) 0 0
\(406\) 22.4769 + 268.682i 0.00274756 + 0.0328435i
\(407\) −10118.4 5841.88i −1.23232 0.711478i
\(408\) 0 0
\(409\) 4548.11i 0.549853i −0.961465 0.274926i \(-0.911347\pi\)
0.961465 0.274926i \(-0.0886535\pi\)
\(410\) 49.6507i 0.00598066i
\(411\) 0 0
\(412\) 3758.01 + 2169.69i 0.449379 + 0.259449i
\(413\) −9664.29 + 6712.36i −1.15145 + 0.799743i
\(414\) 0 0
\(415\) 3287.66 + 5694.40i 0.388879 + 0.673559i
\(416\) −248.163 429.831i −0.0292480 0.0506591i
\(417\) 0 0
\(418\) 1095.83 + 632.676i 0.128226 + 0.0740315i
\(419\) 687.732 + 1191.19i 0.0801859 + 0.138886i 0.903330 0.428947i \(-0.141115\pi\)
−0.823144 + 0.567833i \(0.807782\pi\)
\(420\) 0 0
\(421\) −1505.07 + 2606.85i −0.174234 + 0.301782i −0.939896 0.341461i \(-0.889078\pi\)
0.765662 + 0.643243i \(0.222412\pi\)
\(422\) −681.868 + 393.676i −0.0786559 + 0.0454120i
\(423\) 0 0
\(424\) −1425.35 + 2468.78i −0.163258 + 0.282771i
\(425\) 3790.25 0.432597
\(426\) 0 0
\(427\) 7901.69 + 11376.7i 0.895526 + 1.28936i
\(428\) 9147.99 5281.59i 1.03314 0.596485i
\(429\) 0 0
\(430\) 527.486 304.544i 0.0591573 0.0341545i
\(431\) 2888.94 + 1667.93i 0.322867 + 0.186407i 0.652670 0.757643i \(-0.273649\pi\)
−0.329803 + 0.944050i \(0.606982\pi\)
\(432\) 0 0
\(433\) 3574.98i 0.396772i 0.980124 + 0.198386i \(0.0635700\pi\)
−0.980124 + 0.198386i \(0.936430\pi\)
\(434\) 416.993 289.623i 0.0461205 0.0320331i
\(435\) 0 0
\(436\) 4181.12 7241.92i 0.459265 0.795470i
\(437\) 2225.76 0.243644
\(438\) 0 0
\(439\) 6057.88i 0.658603i 0.944225 + 0.329301i \(0.106813\pi\)
−0.944225 + 0.329301i \(0.893187\pi\)
\(440\) 1601.62 0.173533
\(441\) 0 0
\(442\) −117.668 −0.0126626
\(443\) 15905.0i 1.70580i −0.522071 0.852902i \(-0.674841\pi\)
0.522071 0.852902i \(-0.325159\pi\)
\(444\) 0 0
\(445\) −9327.73 −0.993656
\(446\) 532.595 922.482i 0.0565451 0.0979390i
\(447\) 0 0
\(448\) −7403.14 + 5141.87i −0.780727 + 0.542256i
\(449\) 3388.65i 0.356169i −0.984015 0.178085i \(-0.943010\pi\)
0.984015 0.178085i \(-0.0569901\pi\)
\(450\) 0 0
\(451\) 1596.00 + 921.453i 0.166636 + 0.0962073i
\(452\) −6386.47 + 3687.23i −0.664589 + 0.383701i
\(453\) 0 0
\(454\) −990.867 + 572.077i −0.102431 + 0.0591386i
\(455\) 684.721 + 985.845i 0.0705499 + 0.101576i
\(456\) 0 0
\(457\) 2281.48 0.233530 0.116765 0.993160i \(-0.462748\pi\)
0.116765 + 0.993160i \(0.462748\pi\)
\(458\) −167.439 + 290.013i −0.0170828 + 0.0295882i
\(459\) 0 0
\(460\) 1214.83 701.382i 0.123134 0.0710915i
\(461\) −2730.79 + 4729.87i −0.275891 + 0.477856i −0.970359 0.241666i \(-0.922306\pi\)
0.694469 + 0.719523i \(0.255639\pi\)
\(462\) 0 0
\(463\) −5628.16 9748.26i −0.564931 0.978488i −0.997056 0.0766749i \(-0.975570\pi\)
0.432126 0.901813i \(-0.357764\pi\)
\(464\) −3054.31 1763.41i −0.305588 0.176431i
\(465\) 0 0
\(466\) 258.980 + 448.567i 0.0257447 + 0.0445911i
\(467\) 8118.96 + 14062.5i 0.804498 + 1.39343i 0.916629 + 0.399738i \(0.130899\pi\)
−0.112131 + 0.993693i \(0.535768\pi\)
\(468\) 0 0
\(469\) −2506.59 + 1740.96i −0.246788 + 0.171407i
\(470\) 706.998 + 408.185i 0.0693859 + 0.0400600i
\(471\) 0 0
\(472\) 2608.01i 0.254329i
\(473\) 22607.8i 2.19769i
\(474\) 0 0
\(475\) −5863.25 3385.15i −0.566367 0.326992i
\(476\) 551.408 + 6591.37i 0.0530961 + 0.634695i
\(477\) 0 0
\(478\) −669.212 1159.11i −0.0640356 0.110913i
\(479\) 3133.26 + 5426.96i 0.298877 + 0.517670i 0.975879 0.218311i \(-0.0700546\pi\)
−0.677002 + 0.735981i \(0.736721\pi\)
\(480\) 0 0
\(481\) −1680.74 970.375i −0.159325 0.0919861i
\(482\) 868.166 + 1503.71i 0.0820412 + 0.142100i
\(483\) 0 0
\(484\) 9520.30 16489.6i 0.894093 1.54861i
\(485\) 5609.47 3238.63i 0.525181 0.303214i
\(486\) 0 0
\(487\) 262.826 455.227i 0.0244554 0.0423580i −0.853539 0.521029i \(-0.825548\pi\)
0.877994 + 0.478671i \(0.158882\pi\)
\(488\) 3070.11 0.284790
\(489\) 0 0
\(490\) −435.145 + 359.523i −0.0401180 + 0.0331461i
\(491\) 13426.5 7751.78i 1.23407 0.712491i 0.266194 0.963919i \(-0.414234\pi\)
0.967876 + 0.251429i \(0.0809004\pi\)
\(492\) 0 0
\(493\) −2203.02 + 1271.92i −0.201256 + 0.116195i
\(494\) 182.024 + 105.092i 0.0165782 + 0.00957144i
\(495\) 0 0
\(496\) 6641.13i 0.601200i
\(497\) −2942.24 4236.17i −0.265548 0.382330i
\(498\) 0 0
\(499\) −4660.34 + 8071.95i −0.418087 + 0.724148i −0.995747 0.0921292i \(-0.970633\pi\)
0.577660 + 0.816278i \(0.303966\pi\)
\(500\) −10601.6 −0.948240
\(501\) 0 0
\(502\) 468.434i 0.0416479i
\(503\) 1065.29 0.0944311 0.0472155 0.998885i \(-0.484965\pi\)
0.0472155 + 0.998885i \(0.484965\pi\)
\(504\) 0 0
\(505\) 917.941 0.0808868
\(506\) 435.578i 0.0382684i
\(507\) 0 0
\(508\) −11005.7 −0.961218
\(509\) 4693.68 8129.69i 0.408730 0.707941i −0.586018 0.810298i \(-0.699305\pi\)
0.994748 + 0.102357i \(0.0326384\pi\)
\(510\) 0 0
\(511\) 6688.98 559.574i 0.579066 0.0484425i
\(512\) 5102.59i 0.440439i
\(513\) 0 0
\(514\) 103.535 + 59.7758i 0.00888467 + 0.00512957i
\(515\) −3025.74 + 1746.91i −0.258894 + 0.149472i
\(516\) 0 0
\(517\) 26241.9 15150.8i 2.23234 1.28884i
\(518\) 388.848 825.672i 0.0329827 0.0700346i
\(519\) 0 0
\(520\) 266.040 0.0224358
\(521\) 10087.0 17471.2i 0.848216 1.46915i −0.0345837 0.999402i \(-0.511011\pi\)
0.882799 0.469751i \(-0.155656\pi\)
\(522\) 0 0
\(523\) 13914.0 8033.23i 1.16332 0.671642i 0.211221 0.977438i \(-0.432256\pi\)
0.952097 + 0.305797i \(0.0989227\pi\)
\(524\) −1557.99 + 2698.52i −0.129888 + 0.224972i
\(525\) 0 0
\(526\) 48.4991 + 84.0029i 0.00402027 + 0.00696331i
\(527\) 4148.38 + 2395.07i 0.342896 + 0.197971i
\(528\) 0 0
\(529\) −5700.41 9873.40i −0.468514 0.811490i
\(530\) −571.418 989.725i −0.0468317 0.0811149i
\(531\) 0 0
\(532\) 5033.90 10688.9i 0.410239 0.871093i
\(533\) 265.106 + 153.059i 0.0215442 + 0.0124385i
\(534\) 0 0
\(535\) 8504.90i 0.687288i
\(536\) 676.430i 0.0545099i
\(537\) 0 0
\(538\) 891.588 + 514.759i 0.0714482 + 0.0412506i
\(539\) 3481.01 + 20659.9i 0.278177 + 1.65099i
\(540\) 0 0
\(541\) −12174.8 21087.4i −0.967535 1.67582i −0.702645 0.711541i \(-0.747998\pi\)
−0.264890 0.964279i \(-0.585336\pi\)
\(542\) −108.524 187.969i −0.00860055 0.0148966i
\(543\) 0 0
\(544\) 1907.08 + 1101.06i 0.150304 + 0.0867782i
\(545\) 3366.41 + 5830.79i 0.264589 + 0.458282i
\(546\) 0 0
\(547\) 5442.16 9426.10i 0.425393 0.736802i −0.571064 0.820906i \(-0.693469\pi\)
0.996457 + 0.0841031i \(0.0268025\pi\)
\(548\) −14303.2 + 8257.96i −1.11497 + 0.643727i
\(549\) 0 0
\(550\) 662.470 1147.43i 0.0513597 0.0889576i
\(551\) 4543.91 0.351319
\(552\) 0 0
\(553\) −8479.95 + 5889.77i −0.652087 + 0.452908i
\(554\) 929.515 536.656i 0.0712839 0.0411558i
\(555\) 0 0
\(556\) −8635.69 + 4985.82i −0.658695 + 0.380298i
\(557\) 21701.2 + 12529.2i 1.65082 + 0.953104i 0.976734 + 0.214455i \(0.0687975\pi\)
0.674090 + 0.738649i \(0.264536\pi\)
\(558\) 0 0
\(559\) 3755.31i 0.284137i
\(560\) −615.519 7357.72i −0.0464472 0.555215i
\(561\) 0 0
\(562\) −666.109 + 1153.73i −0.0499966 + 0.0865967i
\(563\) −17896.2 −1.33967 −0.669836 0.742509i \(-0.733635\pi\)
−0.669836 + 0.742509i \(0.733635\pi\)
\(564\) 0 0
\(565\) 5937.51i 0.442112i
\(566\) −1550.77 −0.115166
\(567\) 0 0
\(568\) −1143.17 −0.0844480
\(569\) 883.312i 0.0650797i −0.999470 0.0325399i \(-0.989640\pi\)
0.999470 0.0325399i \(-0.0103596\pi\)
\(570\) 0 0
\(571\) 10459.5 0.766579 0.383290 0.923628i \(-0.374791\pi\)
0.383290 + 0.923628i \(0.374791\pi\)
\(572\) 2458.40 4258.07i 0.179704 0.311257i
\(573\) 0 0
\(574\) −61.3339 + 130.235i −0.00445998 + 0.00947021i
\(575\) 2330.58i 0.169029i
\(576\) 0 0
\(577\) 17098.4 + 9871.79i 1.23365 + 0.712249i 0.967789 0.251762i \(-0.0810099\pi\)
0.265863 + 0.964011i \(0.414343\pi\)
\(578\) −644.011 + 371.820i −0.0463449 + 0.0267572i
\(579\) 0 0
\(580\) 2480.08 1431.88i 0.177552 0.102509i
\(581\) 1589.28 + 18997.8i 0.113485 + 1.35656i
\(582\) 0 0
\(583\) −42419.1 −3.01341
\(584\) 743.874 1288.43i 0.0527084 0.0912937i
\(585\) 0 0
\(586\) 1001.27 578.082i 0.0705835 0.0407514i
\(587\) 4130.99 7155.09i 0.290467 0.503104i −0.683453 0.729995i \(-0.739523\pi\)
0.973920 + 0.226890i \(0.0728559\pi\)
\(588\) 0 0
\(589\) −4278.17 7410.01i −0.299285 0.518377i
\(590\) −905.463 522.769i −0.0631819 0.0364781i
\(591\) 0 0
\(592\) 5969.06 + 10338.7i 0.414403 + 0.717768i
\(593\) −13435.3 23270.7i −0.930392 1.61149i −0.782652 0.622460i \(-0.786133\pi\)
−0.147741 0.989026i \(-0.547200\pi\)
\(594\) 0 0
\(595\) −4817.98 2269.02i −0.331963 0.156337i
\(596\) 20664.6 + 11930.7i 1.42023 + 0.819970i
\(597\) 0 0
\(598\) 72.3524i 0.00494768i
\(599\) 16691.0i 1.13852i −0.822156 0.569262i \(-0.807229\pi\)
0.822156 0.569262i \(-0.192771\pi\)
\(600\) 0 0
\(601\) 16426.9 + 9484.10i 1.11492 + 0.643702i 0.940100 0.340898i \(-0.110731\pi\)
0.174824 + 0.984600i \(0.444064\pi\)
\(602\) 1759.82 147.219i 0.119144 0.00996713i
\(603\) 0 0
\(604\) 11385.6 + 19720.5i 0.767012 + 1.32850i
\(605\) 7665.23 + 13276.6i 0.515100 + 0.892180i
\(606\) 0 0
\(607\) −4464.29 2577.46i −0.298517 0.172349i 0.343260 0.939241i \(-0.388469\pi\)
−0.641776 + 0.766892i \(0.721802\pi\)
\(608\) −1966.75 3406.52i −0.131188 0.227224i
\(609\) 0 0
\(610\) −615.397 + 1065.90i −0.0408470 + 0.0707491i
\(611\) 4358.96 2516.65i 0.288616 0.166633i
\(612\) 0 0
\(613\) 4050.42 7015.53i 0.266876 0.462242i −0.701178 0.712987i \(-0.747342\pi\)
0.968053 + 0.250744i \(0.0806754\pi\)
\(614\) −67.8742 −0.00446120
\(615\) 0 0
\(616\) 4201.10 + 1978.50i 0.274784 + 0.129409i
\(617\) 6750.27 3897.27i 0.440447 0.254292i −0.263340 0.964703i \(-0.584824\pi\)
0.703787 + 0.710411i \(0.251491\pi\)
\(618\) 0 0
\(619\) 15171.1 8759.06i 0.985104 0.568750i 0.0812970 0.996690i \(-0.474094\pi\)
0.903807 + 0.427940i \(0.140760\pi\)
\(620\) −4670.09 2696.28i −0.302509 0.174654i
\(621\) 0 0
\(622\) 1250.12i 0.0805870i
\(623\) −24466.9 11522.6i −1.57343 0.741002i
\(624\) 0 0
\(625\) −994.380 + 1722.32i −0.0636403 + 0.110228i
\(626\) 705.516 0.0450449
\(627\) 0 0
\(628\) 7280.71i 0.462630i
\(629\) 8610.77 0.545841
\(630\) 0 0
\(631\) 8636.00 0.544839 0.272420 0.962179i \(-0.412176\pi\)
0.272420 + 0.962179i \(0.412176\pi\)
\(632\) 2288.40i 0.144031i
\(633\) 0 0
\(634\) −1910.85 −0.119700
\(635\) 4430.59 7674.00i 0.276886 0.479580i
\(636\) 0 0
\(637\) 578.218 + 3431.74i 0.0359652 + 0.213454i
\(638\) 889.237i 0.0551806i
\(639\) 0 0
\(640\) −2858.50 1650.35i −0.176550 0.101931i
\(641\) 13306.7 7682.65i 0.819945 0.473396i −0.0304525 0.999536i \(-0.509695\pi\)
0.850398 + 0.526141i \(0.176361\pi\)
\(642\) 0 0
\(643\) −6869.74 + 3966.25i −0.421332 + 0.243256i −0.695647 0.718384i \(-0.744882\pi\)
0.274315 + 0.961640i \(0.411549\pi\)
\(644\) 4052.95 339.054i 0.247995 0.0207463i
\(645\) 0 0
\(646\) −932.546 −0.0567965
\(647\) −9673.35 + 16754.7i −0.587788 + 1.01808i 0.406734 + 0.913547i \(0.366668\pi\)
−0.994522 + 0.104531i \(0.966666\pi\)
\(648\) 0 0
\(649\) −33608.5 + 19403.9i −2.03274 + 1.17360i
\(650\) 110.041 190.596i 0.00664023 0.0115012i
\(651\) 0 0
\(652\) −6398.76 11083.0i −0.384348 0.665710i
\(653\) −16717.4 9651.81i −1.00184 0.578414i −0.0930501 0.995661i \(-0.529662\pi\)
−0.908793 + 0.417247i \(0.862995\pi\)
\(654\) 0 0
\(655\) −1254.41 2172.70i −0.0748303 0.129610i
\(656\) −941.512 1630.75i −0.0560364 0.0970579i
\(657\) 0 0
\(658\) 1350.24 + 1944.04i 0.0799966 + 0.115177i
\(659\) −6426.97 3710.61i −0.379908 0.219340i 0.297870 0.954606i \(-0.403724\pi\)
−0.677778 + 0.735266i \(0.737057\pi\)
\(660\) 0 0
\(661\) 14146.3i 0.832415i −0.909270 0.416208i \(-0.863359\pi\)
0.909270 0.416208i \(-0.136641\pi\)
\(662\) 1074.84i 0.0631041i
\(663\) 0 0
\(664\) 3659.35 + 2112.73i 0.213871 + 0.123478i
\(665\) 5426.58 + 7813.06i 0.316442 + 0.455605i
\(666\) 0 0
\(667\) 782.086 + 1354.61i 0.0454011 + 0.0786369i
\(668\) −7317.85 12674.9i −0.423856 0.734141i
\(669\) 0 0
\(670\) −234.847 135.589i −0.0135417 0.00781829i
\(671\) 22841.9 + 39563.4i 1.31416 + 2.27620i
\(672\) 0 0
\(673\) 4164.46 7213.05i 0.238526 0.413139i −0.721766 0.692138i \(-0.756669\pi\)
0.960292 + 0.278998i \(0.0900024\pi\)
\(674\) 235.903 136.199i 0.0134817 0.00778365i
\(675\) 0 0
\(676\) −8306.74 + 14387.7i −0.472618 + 0.818599i
\(677\) 4479.59 0.254305 0.127153 0.991883i \(-0.459416\pi\)
0.127153 + 0.991883i \(0.459416\pi\)
\(678\) 0 0
\(679\) 18714.5 1565.58i 1.05773 0.0884853i
\(680\) −1022.23 + 590.187i −0.0576483 + 0.0332833i
\(681\) 0 0
\(682\) 1450.13 837.234i 0.0814199 0.0470078i
\(683\) −2140.00 1235.53i −0.119890 0.0692184i 0.438856 0.898557i \(-0.355384\pi\)
−0.558746 + 0.829339i \(0.688717\pi\)
\(684\) 0 0
\(685\) 13297.7i 0.741721i
\(686\) −1585.52 + 405.500i −0.0882439 + 0.0225686i
\(687\) 0 0
\(688\) −11550.0 + 20005.2i −0.640028 + 1.10856i
\(689\) −7046.09 −0.389601
\(690\) 0 0
\(691\) 23174.9i 1.27585i 0.770097 + 0.637926i \(0.220208\pi\)
−0.770097 + 0.637926i \(0.779792\pi\)
\(692\) −15913.3 −0.874181
\(693\) 0 0
\(694\) 1231.62 0.0673653
\(695\) 8028.61i 0.438191i
\(696\) 0 0
\(697\) −1358.19 −0.0738096
\(698\) −324.259 + 561.633i −0.0175837 + 0.0304558i
\(699\) 0 0
\(700\) −11192.2 5270.96i −0.604324 0.284605i
\(701\) 21807.9i 1.17500i −0.809225 0.587498i \(-0.800113\pi\)
0.809225 0.587498i \(-0.199887\pi\)
\(702\) 0 0
\(703\) −13320.3 7690.46i −0.714628 0.412591i
\(704\) −25745.1 + 14863.9i −1.37827 + 0.795747i
\(705\) 0 0
\(706\) −1339.95 + 773.623i −0.0714304 + 0.0412404i
\(707\) 2407.78 + 1133.94i 0.128082 + 0.0603200i
\(708\) 0 0
\(709\) 12974.7 0.687270 0.343635 0.939103i \(-0.388342\pi\)
0.343635 + 0.939103i \(0.388342\pi\)
\(710\) 229.147 396.893i 0.0121123 0.0209791i
\(711\) 0 0
\(712\) −5191.14 + 2997.11i −0.273239 + 0.157755i
\(713\) 1472.70 2550.79i 0.0773534 0.133980i
\(714\) 0 0
\(715\) 1979.37 + 3428.37i 0.103530 + 0.179320i
\(716\) 11304.8 + 6526.82i 0.590056 + 0.340669i
\(717\) 0 0
\(718\) −858.620 1487.17i −0.0446287 0.0772992i
\(719\) −8416.91 14578.5i −0.436575 0.756171i 0.560847 0.827919i \(-0.310475\pi\)
−0.997423 + 0.0717486i \(0.977142\pi\)
\(720\) 0 0
\(721\) −10094.6 + 844.474i −0.521417 + 0.0436197i
\(722\) −87.7246 50.6478i −0.00452184 0.00261069i
\(723\) 0 0
\(724\) 26929.9i 1.38238i
\(725\) 4757.89i 0.243729i
\(726\) 0 0
\(727\) 28354.9 + 16370.7i 1.44653 + 0.835152i 0.998272 0.0587547i \(-0.0187130\pi\)
0.448253 + 0.893907i \(0.352046\pi\)
\(728\) 697.830 + 328.641i 0.0355265 + 0.0167311i
\(729\) 0 0
\(730\) 298.216 + 516.525i 0.0151198 + 0.0261883i
\(731\) 8330.81 + 14429.4i 0.421513 + 0.730083i
\(732\) 0 0
\(733\) 6413.52 + 3702.85i 0.323177 + 0.186586i 0.652808 0.757524i \(-0.273591\pi\)
−0.329631 + 0.944110i \(0.606924\pi\)
\(734\) −207.376 359.186i −0.0104283 0.0180624i
\(735\) 0 0
\(736\) 677.025 1172.64i 0.0339069 0.0587285i
\(737\) −8716.91 + 5032.71i −0.435674 + 0.251536i
\(738\) 0 0
\(739\) 6333.95 10970.7i 0.315288 0.546095i −0.664210 0.747546i \(-0.731232\pi\)
0.979499 + 0.201450i \(0.0645655\pi\)
\(740\) −9693.69 −0.481550
\(741\) 0 0
\(742\) −276.228 3301.95i −0.0136667 0.163367i
\(743\) −16940.8 + 9780.78i −0.836471 + 0.482937i −0.856063 0.516871i \(-0.827097\pi\)
0.0195919 + 0.999808i \(0.493763\pi\)
\(744\) 0 0
\(745\) −16638.0 + 9605.97i −0.818215 + 0.472397i
\(746\) −1162.64 671.249i −0.0570605 0.0329439i
\(747\) 0 0
\(748\) 21815.0i 1.06636i
\(749\) −10506.2 + 22308.6i −0.512533 + 1.08830i
\(750\) 0 0
\(751\) 1163.24 2014.80i 0.0565211 0.0978975i −0.836380 0.548149i \(-0.815333\pi\)
0.892902 + 0.450252i \(0.148666\pi\)
\(752\) −30961.2 −1.50138
\(753\) 0 0
\(754\) 147.708i 0.00713423i
\(755\) −18334.2 −0.883774
\(756\) 0 0
\(757\) 5811.77 0.279039 0.139519 0.990219i \(-0.455444\pi\)
0.139519 + 0.990219i \(0.455444\pi\)
\(758\) 2562.52i 0.122790i
\(759\) 0 0
\(760\) 2108.43 0.100633
\(761\) −13299.7 + 23035.7i −0.633526 + 1.09730i 0.353299 + 0.935510i \(0.385060\pi\)
−0.986825 + 0.161789i \(0.948274\pi\)
\(762\) 0 0
\(763\) 1627.35 + 19452.9i 0.0772138 + 0.922990i
\(764\) 898.765i 0.0425604i
\(765\) 0 0
\(766\) −3223.70 1861.21i −0.152059 0.0877913i
\(767\) −5582.59 + 3223.11i −0.262810 + 0.151734i
\(768\) 0 0
\(769\) 5505.13 3178.39i 0.258153 0.149045i −0.365339 0.930875i \(-0.619047\pi\)
0.623492 + 0.781830i \(0.285713\pi\)
\(770\) −1529.01 + 1061.98i −0.0715605 + 0.0497025i
\(771\) 0 0
\(772\) −6948.27 −0.323930
\(773\) 3466.39 6003.96i 0.161290 0.279363i −0.774041 0.633135i \(-0.781768\pi\)
0.935332 + 0.353772i \(0.115101\pi\)
\(774\) 0 0
\(775\) −7758.97 + 4479.64i −0.359626 + 0.207630i
\(776\) 2081.22 3604.78i 0.0962776 0.166758i
\(777\) 0 0
\(778\) −1169.53 2025.68i −0.0538942 0.0933474i
\(779\) 2101.03 + 1213.03i 0.0966334 + 0.0557913i
\(780\) 0 0
\(781\) −8505.33 14731.7i −0.389686 0.674956i
\(782\) −160.507 278.007i −0.00733982 0.0127129i
\(783\) 0 0
\(784\) 7474.53 20059.8i 0.340494 0.913805i
\(785\) 5076.66 + 2931.01i 0.230820 + 0.133264i
\(786\) 0 0
\(787\) 33309.9i 1.50873i −0.656455 0.754365i \(-0.727945\pi\)
0.656455 0.754365i \(-0.272055\pi\)
\(788\) 7966.09i 0.360127i
\(789\) 0 0
\(790\) −794.500 458.705i −0.0357810 0.0206582i
\(791\) 7334.66 15574.2i 0.329697 0.700071i
\(792\) 0 0
\(793\) 3794.20 + 6571.74i 0.169907 + 0.294287i
\(794\) 279.502 + 484.112i 0.0124926 + 0.0216379i
\(795\) 0 0
\(796\) 11518.5 + 6650.21i 0.512892 + 0.296119i
\(797\) 17597.8 + 30480.4i 0.782117 + 1.35467i 0.930706 + 0.365768i \(0.119194\pi\)
−0.148589 + 0.988899i \(0.547473\pi\)
\(798\) 0 0
\(799\) −11165.9 + 19339.9i −0.494395 + 0.856318i
\(800\) −3566.94 + 2059.37i −0.157638 + 0.0910123i
\(801\) 0 0
\(802\) −38.7850 + 67.1775i −0.00170766 + 0.00295776i
\(803\) 22138.0 0.972894
\(804\) 0 0
\(805\) −1395.19 + 2962.52i −0.0610858 + 0.129708i
\(806\) 240.876 139.070i 0.0105267 0.00607758i
\(807\) 0 0
\(808\) 510.860 294.945i 0.0222426 0.0128418i
\(809\) 17121.2 + 9884.94i 0.744067 + 0.429587i 0.823546 0.567249i \(-0.191992\pi\)
−0.0794792 + 0.996837i \(0.525326\pi\)
\(810\) 0 0
\(811\) 20597.9i 0.891848i −0.895071 0.445924i \(-0.852875\pi\)
0.895071 0.445924i \(-0.147125\pi\)
\(812\) 8274.13 692.182i 0.357593 0.0299148i
\(813\) 0 0
\(814\) 1505.01 2606.76i 0.0648044 0.112244i
\(815\) 10303.9 0.442857
\(816\) 0 0
\(817\) 29761.7i 1.27446i
\(818\) 1171.71 0.0500829
\(819\) 0 0
\(820\) 1529.01 0.0651161
\(821\) 4298.25i 0.182716i 0.995818 + 0.0913581i \(0.0291208\pi\)
−0.995818 + 0.0913581i \(0.970879\pi\)
\(822\) 0 0
\(823\) −9618.81 −0.407401 −0.203700 0.979033i \(-0.565297\pi\)
−0.203700 + 0.979033i \(0.565297\pi\)
\(824\) −1122.61 + 1944.41i −0.0474610 + 0.0822049i
\(825\) 0 0
\(826\) −1729.27 2489.76i −0.0728439 0.104879i
\(827\) 28304.7i 1.19015i −0.803672 0.595073i \(-0.797123\pi\)
0.803672 0.595073i \(-0.202877\pi\)
\(828\) 0 0
\(829\) 24753.6 + 14291.5i 1.03707 + 0.598750i 0.919001 0.394256i \(-0.128998\pi\)
0.118065 + 0.993006i \(0.462331\pi\)
\(830\) −1467.02 + 846.983i −0.0613505 + 0.0354207i
\(831\) 0 0
\(832\) −4276.43 + 2469.00i −0.178195 + 0.102881i
\(833\) −9834.75 11903.4i −0.409068 0.495111i
\(834\) 0 0
\(835\) 11783.9 0.488380
\(836\) 19483.4 33746.3i 0.806039 1.39610i
\(837\) 0 0
\(838\) −306.879 + 177.177i −0.0126503 + 0.00730366i
\(839\) 16920.3 29306.9i 0.696251 1.20594i −0.273506 0.961870i \(-0.588183\pi\)
0.969757 0.244072i \(-0.0784835\pi\)
\(840\) 0 0
\(841\) −10597.9 18356.0i −0.434535 0.752636i
\(842\) −671.590 387.743i −0.0274876 0.0158700i
\(843\) 0 0
\(844\) 12123.4 + 20998.3i 0.494436 + 0.856388i
\(845\) −6688.13 11584.2i −0.272282 0.471607i
\(846\) 0 0
\(847\) 3705.44 + 44293.7i 0.150319 + 1.79687i
\(848\) 37535.8 + 21671.3i 1.52003 + 0.877588i
\(849\) 0 0
\(850\) 976.462i 0.0394028i
\(851\) 5294.66i 0.213277i
\(852\) 0 0
\(853\) −20134.3 11624.6i −0.808191 0.466609i 0.0381363 0.999273i \(-0.487858\pi\)
−0.846327 + 0.532663i \(0.821191\pi\)
\(854\) −2930.91 + 2035.67i −0.117440 + 0.0815683i
\(855\) 0 0
\(856\) 2732.72 + 4733.22i 0.109115 + 0.188993i
\(857\) 10798.5 + 18703.5i 0.430418 + 0.745506i 0.996909 0.0785619i \(-0.0250328\pi\)
−0.566491 + 0.824068i \(0.691699\pi\)
\(858\) 0 0
\(859\) −11823.9 6826.55i −0.469648 0.271151i 0.246445 0.969157i \(-0.420738\pi\)
−0.716092 + 0.698006i \(0.754071\pi\)
\(860\) −9378.53 16244.1i −0.371866 0.644092i
\(861\) 0 0
\(862\) −429.701 + 744.264i −0.0169787 + 0.0294080i
\(863\) −9232.02 + 5330.11i −0.364150 + 0.210242i −0.670900 0.741548i \(-0.734092\pi\)
0.306750 + 0.951790i \(0.400759\pi\)
\(864\) 0 0
\(865\) 6406.26 11096.0i 0.251814 0.436155i
\(866\) −921.003 −0.0361397
\(867\) 0 0
\(868\) −8919.03 12841.4i −0.348769 0.502150i
\(869\) −29489.8 + 17025.9i −1.15118 + 0.664632i
\(870\) 0 0
\(871\) −1447.94 + 835.966i −0.0563277 + 0.0325208i
\(872\) 3747.00 + 2163.33i 0.145516 + 0.0840134i
\(873\) 0 0
\(874\) 573.411i 0.0221921i
\(875\) 20326.6 14117.9i 0.785332 0.545454i
\(876\) 0 0
\(877\) 764.513 1324.17i 0.0294364 0.0509854i −0.850932 0.525276i \(-0.823962\pi\)
0.880368 + 0.474291i \(0.157295\pi\)
\(878\) −1560.66 −0.0599883
\(879\) 0 0
\(880\) 24351.3i 0.932822i
\(881\) −22496.2 −0.860292 −0.430146 0.902759i \(-0.641538\pi\)
−0.430146 + 0.902759i \(0.641538\pi\)
\(882\) 0 0
\(883\) −1745.87 −0.0665381 −0.0332691 0.999446i \(-0.510592\pi\)
−0.0332691 + 0.999446i \(0.510592\pi\)
\(884\) 3623.61i 0.137868i
\(885\) 0 0
\(886\) 4097.53 0.155372
\(887\) −4586.51 + 7944.07i −0.173619 + 0.300717i −0.939682 0.342048i \(-0.888879\pi\)
0.766064 + 0.642765i \(0.222213\pi\)
\(888\) 0 0
\(889\) 21101.3 14656.0i 0.796080 0.552919i
\(890\) 2403.06i 0.0905063i
\(891\) 0 0
\(892\) −28408.1 16401.4i −1.06634 0.615650i
\(893\) 34545.8 19945.0i 1.29455 0.747408i
\(894\) 0 0
\(895\) −9101.99 + 5255.04i −0.339940 + 0.196264i
\(896\) −5459.21 7860.04i −0.203549 0.293064i
\(897\) 0 0
\(898\) 872.999 0.0324414
\(899\) 3006.53 5207.46i 0.111539 0.193191i
\(900\) 0 0
\(901\) 27073.9 15631.1i 1.00107 0.577968i
\(902\) −237.389 + 411.170i −0.00876296 + 0.0151779i
\(903\) 0 0
\(904\) −1907.79 3304.39i −0.0701905 0.121574i
\(905\) −18777.6 10841.2i −0.689710 0.398204i
\(906\) 0 0
\(907\) −7220.71 12506.6i −0.264344 0.457857i 0.703048 0.711143i \(-0.251822\pi\)
−0.967391 + 0.253286i \(0.918489\pi\)
\(908\) 17617.3 + 30514.0i 0.643887 + 1.11525i
\(909\) 0 0
\(910\) −253.978 + 176.401i −0.00925197 + 0.00642598i
\(911\) 6737.06 + 3889.65i 0.245015 + 0.141460i 0.617480 0.786587i \(-0.288154\pi\)
−0.372464 + 0.928046i \(0.621487\pi\)
\(912\) 0 0
\(913\) 62875.7i 2.27917i
\(914\) 587.766i 0.0212709i
\(915\) 0 0
\(916\) 8931.03 + 5156.33i 0.322150 + 0.185993i
\(917\) −606.392 7248.63i −0.0218373 0.261037i
\(918\) 0 0
\(919\) −18628.7 32265.9i −0.668667 1.15817i −0.978277 0.207302i \(-0.933532\pi\)
0.309610 0.950864i \(-0.399801\pi\)
\(920\) 362.899 + 628.559i 0.0130048 + 0.0225250i
\(921\) 0 0
\(922\) −1218.53 703.519i −0.0435252 0.0251293i
\(923\) −1412.79 2447.03i −0.0503820 0.0872642i
\(924\) 0 0
\(925\) −8052.63 + 13947.6i −0.286237 + 0.495776i
\(926\) 2511.39 1449.95i 0.0891248 0.0514562i
\(927\) 0 0
\(928\) 1382.15 2393.96i 0.0488916 0.0846827i
\(929\) 5028.76 0.177598 0.0887989 0.996050i \(-0.471697\pi\)
0.0887989 + 0.996050i \(0.471697\pi\)
\(930\) 0 0
\(931\) 4582.52 + 27197.4i 0.161317 + 0.957419i
\(932\) 13813.7 7975.37i 0.485498 0.280302i
\(933\) 0 0
\(934\) −3622.84 + 2091.65i −0.126920 + 0.0732770i
\(935\) −15211.1 8782.11i −0.532037 0.307172i
\(936\) 0 0
\(937\) 4765.66i 0.166155i −0.996543 0.0830776i \(-0.973525\pi\)
0.996543 0.0830776i \(-0.0264749\pi\)
\(938\) −448.515 645.761i −0.0156125 0.0224785i
\(939\) 0 0
\(940\) 12570.2 21772.2i 0.436164 0.755458i
\(941\) 20633.4 0.714804 0.357402 0.933951i \(-0.383663\pi\)
0.357402 + 0.933951i \(0.383663\pi\)
\(942\) 0 0
\(943\) 835.137i 0.0288397i
\(944\) 39652.5 1.36714
\(945\) 0 0
\(946\) 5824.33 0.200175
\(947\) 19798.6i 0.679374i −0.940539 0.339687i \(-0.889679\pi\)
0.940539 0.339687i \(-0.110321\pi\)
\(948\) 0 0
\(949\) 3677.27 0.125784
\(950\) 872.099 1510.52i 0.0297838 0.0515871i
\(951\) 0 0
\(952\) −3410.41 + 285.301i −0.116105 + 0.00971289i
\(953\) 14437.1i 0.490726i 0.969431 + 0.245363i \(0.0789072\pi\)
−0.969431 + 0.245363i \(0.921093\pi\)
\(954\) 0 0
\(955\) 626.687 + 361.818i 0.0212347 + 0.0122599i
\(956\) −35695.1 + 20608.6i −1.20760 + 0.697206i
\(957\) 0 0
\(958\) −1398.12 + 807.205i −0.0471516 + 0.0272230i
\(959\) 16426.8 34880.2i 0.553126 1.17450i
\(960\) 0 0
\(961\) 18468.2 0.619925
\(962\) 249.993 433.000i 0.00837847 0.0145119i
\(963\) 0 0
\(964\) 46307.1 26735.4i 1.54715 0.893246i
\(965\) 2797.18 4844.87i 0.0933104 0.161618i
\(966\) 0 0
\(967\) 24854.3 + 43049.0i 0.826537 + 1.43160i 0.900739 + 0.434362i \(0.143026\pi\)
−0.0742011 + 0.997243i \(0.523641\pi\)
\(968\) 8531.83 + 4925.85i 0.283289 + 0.163557i
\(969\) 0 0
\(970\) 834.351 + 1445.14i 0.0276179 + 0.0478357i
\(971\) 25649.0 + 44425.3i 0.847698 + 1.46826i 0.883258 + 0.468888i \(0.155345\pi\)
−0.0355601 + 0.999368i \(0.511322\pi\)
\(972\) 0 0
\(973\) 9917.81 21059.2i 0.326773 0.693863i
\(974\) 117.278 + 67.7104i 0.00385814 + 0.00222750i
\(975\) 0 0
\(976\) 46678.4i 1.53088i
\(977\) 10042.8i 0.328862i 0.986389 + 0.164431i \(0.0525788\pi\)
−0.986389 + 0.164431i \(0.947421\pi\)
\(978\) 0 0
\(979\) −77245.4 44597.6i −2.52173 1.45592i
\(980\) 11071.6 + 13400.4i 0.360887 + 0.436796i
\(981\) 0 0
\(982\) 1997.05 + 3458.99i 0.0648966 + 0.112404i
\(983\) −3538.32 6128.55i −0.114807 0.198851i 0.802896 0.596119i \(-0.203291\pi\)
−0.917702 + 0.397269i \(0.869958\pi\)
\(984\) 0 0
\(985\) 5554.57 + 3206.93i 0.179678 + 0.103737i
\(986\) −327.677 567.554i −0.0105835 0.0183312i
\(987\) 0 0
\(988\) 3236.32 5605.48i 0.104212 0.180500i
\(989\) 8872.46 5122.52i 0.285266 0.164698i
\(990\) 0 0
\(991\) −13272.9 + 22989.4i −0.425457 + 0.736913i −0.996463 0.0840327i \(-0.973220\pi\)
0.571006 + 0.820946i \(0.306553\pi\)
\(992\) −5205.29 −0.166601
\(993\) 0 0
\(994\) 1091.34 757.995i 0.0348242 0.0241873i
\(995\) −9274.06 + 5354.38i −0.295485 + 0.170598i
\(996\) 0 0
\(997\) 23812.9 13748.4i 0.756431 0.436726i −0.0715818 0.997435i \(-0.522805\pi\)
0.828013 + 0.560709i \(0.189471\pi\)
\(998\) −2079.54 1200.62i −0.0659584 0.0380811i
\(999\) 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 189.4.i.a.143.12 44
3.2 odd 2 63.4.i.a.38.11 yes 44
7.5 odd 6 189.4.s.a.89.12 44
9.4 even 3 63.4.s.a.59.11 yes 44
9.5 odd 6 189.4.s.a.17.12 44
21.5 even 6 63.4.s.a.47.11 yes 44
63.5 even 6 inner 189.4.i.a.152.11 44
63.40 odd 6 63.4.i.a.5.12 44
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
63.4.i.a.5.12 44 63.40 odd 6
63.4.i.a.38.11 yes 44 3.2 odd 2
63.4.s.a.47.11 yes 44 21.5 even 6
63.4.s.a.59.11 yes 44 9.4 even 3
189.4.i.a.143.12 44 1.1 even 1 trivial
189.4.i.a.152.11 44 63.5 even 6 inner
189.4.s.a.17.12 44 9.5 odd 6
189.4.s.a.89.12 44 7.5 odd 6