Properties

Label 216.3.p.b.19.6
Level $216$
Weight $3$
Character 216.19
Analytic conductor $5.886$
Analytic rank $0$
Dimension $40$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [216,3,Mod(19,216)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(216, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 3, 4]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("216.19");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 216 = 2^{3} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 216.p (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: \(5.88557371018\)
Analytic rank: \(0\)
Dimension: \(40\)
Relative dimension: \(20\) over \(\Q(\zeta_{6})\)
Twist minimal: no (minimal twist has level 72)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 19.6
Character \(\chi\) \(=\) 216.19
Dual form 216.3.p.b.91.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.35259 - 1.47326i) q^{2} +(-0.340985 + 3.98544i) q^{4} +(-0.0166003 + 0.00958419i) q^{5} +(-4.07208 - 2.35102i) q^{7} +(6.33280 - 4.88832i) q^{8} +O(q^{10})\) \(q+(-1.35259 - 1.47326i) q^{2} +(-0.340985 + 3.98544i) q^{4} +(-0.0166003 + 0.00958419i) q^{5} +(-4.07208 - 2.35102i) q^{7} +(6.33280 - 4.88832i) q^{8} +(0.0365734 + 0.0114930i) q^{10} +(-2.84945 + 4.93540i) q^{11} +(-10.0617 + 5.80910i) q^{13} +(2.04421 + 9.17921i) q^{14} +(-15.7675 - 2.71795i) q^{16} +0.376814 q^{17} -15.0519 q^{19} +(-0.0325368 - 0.0694276i) q^{20} +(11.1253 - 2.47760i) q^{22} +(-39.1821 + 22.6218i) q^{23} +(-12.4998 + 21.6503i) q^{25} +(22.1676 + 6.96608i) q^{26} +(10.7584 - 15.4274i) q^{28} +(32.0010 + 18.4758i) q^{29} +(26.3839 - 15.2328i) q^{31} +(17.3227 + 26.9058i) q^{32} +(-0.509675 - 0.555144i) q^{34} +0.0901304 q^{35} +53.4253i q^{37} +(20.3591 + 22.1754i) q^{38} +(-0.0582758 + 0.141842i) q^{40} +(-29.0192 - 50.2628i) q^{41} +(-23.0516 + 39.9265i) q^{43} +(-18.6981 - 13.0392i) q^{44} +(86.3252 + 27.1273i) q^{46} +(-34.2487 - 19.7735i) q^{47} +(-13.4454 - 23.2882i) q^{49} +(48.8037 - 10.8686i) q^{50} +(-19.7209 - 42.0809i) q^{52} -0.989874i q^{53} -0.109239i q^{55} +(-37.2802 + 5.01711i) q^{56} +(-16.0647 - 72.1360i) q^{58} +(-29.4331 - 50.9797i) q^{59} +(75.1051 + 43.3619i) q^{61} +(-58.1285 - 18.2666i) q^{62} +(16.2087 - 61.9135i) q^{64} +(0.111351 - 0.192866i) q^{65} +(-34.1445 - 59.1400i) q^{67} +(-0.128488 + 1.50177i) q^{68} +(-0.121910 - 0.132785i) q^{70} -42.3565i q^{71} +26.6644 q^{73} +(78.7093 - 72.2627i) q^{74} +(5.13248 - 59.9886i) q^{76} +(23.2064 - 13.3982i) q^{77} +(-121.208 - 69.9797i) q^{79} +(0.287794 - 0.106000i) q^{80} +(-34.7989 + 110.738i) q^{82} +(-40.9931 + 71.0021i) q^{83} +(-0.00625522 + 0.00361145i) q^{85} +(90.0015 - 20.0434i) q^{86} +(6.08078 + 45.1839i) q^{88} +42.6370 q^{89} +54.6292 q^{91} +(-76.7973 - 163.872i) q^{92} +(17.1930 + 77.2026i) q^{94} +(0.249867 - 0.144261i) q^{95} +(55.9278 - 96.8698i) q^{97} +(-16.1233 + 51.3080i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40 q + 5 q^{2} + 7 q^{4} - 46 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 40 q + 5 q^{2} + 7 q^{4} - 46 q^{8} - 12 q^{10} + 16 q^{11} - 6 q^{14} + 31 q^{16} + 4 q^{17} - 76 q^{19} + 12 q^{20} + 35 q^{22} + 118 q^{25} + 72 q^{26} - 36 q^{28} + 5 q^{32} + 5 q^{34} + 108 q^{35} + 169 q^{38} - 6 q^{40} - 20 q^{41} - 16 q^{43} - 362 q^{44} - 96 q^{46} + 166 q^{49} - 73 q^{50} - 24 q^{52} - 186 q^{56} + 36 q^{58} + 64 q^{59} - 384 q^{62} - 518 q^{64} + 102 q^{65} - 64 q^{67} + 295 q^{68} - 6 q^{70} - 292 q^{73} - 318 q^{74} + 197 q^{76} + 720 q^{80} + 386 q^{82} - 554 q^{83} + 295 q^{86} + 59 q^{88} + 688 q^{89} - 204 q^{91} + 378 q^{92} - 66 q^{94} + 92 q^{97} + 614 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/216\mathbb{Z}\right)^\times\).

\(n\) \(55\) \(109\) \(137\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.35259 1.47326i −0.676296 0.736630i
\(3\) 0 0
\(4\) −0.340985 + 3.98544i −0.0852462 + 0.996360i
\(5\) −0.0166003 + 0.00958419i −0.00332006 + 0.00191684i −0.501659 0.865065i \(-0.667277\pi\)
0.498339 + 0.866982i \(0.333943\pi\)
\(6\) 0 0
\(7\) −4.07208 2.35102i −0.581726 0.335860i 0.180093 0.983650i \(-0.442360\pi\)
−0.761819 + 0.647790i \(0.775694\pi\)
\(8\) 6.33280 4.88832i 0.791600 0.611040i
\(9\) 0 0
\(10\) 0.0365734 + 0.0114930i 0.00365734 + 0.00114930i
\(11\) −2.84945 + 4.93540i −0.259041 + 0.448673i −0.965985 0.258597i \(-0.916740\pi\)
0.706944 + 0.707269i \(0.250073\pi\)
\(12\) 0 0
\(13\) −10.0617 + 5.80910i −0.773974 + 0.446854i −0.834290 0.551325i \(-0.814122\pi\)
0.0603167 + 0.998179i \(0.480789\pi\)
\(14\) 2.04421 + 9.17921i 0.146015 + 0.655658i
\(15\) 0 0
\(16\) −15.7675 2.71795i −0.985466 0.169872i
\(17\) 0.376814 0.0221655 0.0110828 0.999939i \(-0.496472\pi\)
0.0110828 + 0.999939i \(0.496472\pi\)
\(18\) 0 0
\(19\) −15.0519 −0.792207 −0.396103 0.918206i \(-0.629638\pi\)
−0.396103 + 0.918206i \(0.629638\pi\)
\(20\) −0.0325368 0.0694276i −0.00162684 0.00347138i
\(21\) 0 0
\(22\) 11.1253 2.47760i 0.505694 0.112618i
\(23\) −39.1821 + 22.6218i −1.70357 + 0.983556i −0.761484 + 0.648184i \(0.775529\pi\)
−0.942086 + 0.335372i \(0.891138\pi\)
\(24\) 0 0
\(25\) −12.4998 + 21.6503i −0.499993 + 0.866013i
\(26\) 22.1676 + 6.96608i 0.852601 + 0.267926i
\(27\) 0 0
\(28\) 10.7584 15.4274i 0.384227 0.550978i
\(29\) 32.0010 + 18.4758i 1.10348 + 0.637096i 0.937134 0.348971i \(-0.113469\pi\)
0.166349 + 0.986067i \(0.446802\pi\)
\(30\) 0 0
\(31\) 26.3839 15.2328i 0.851094 0.491379i −0.00992571 0.999951i \(-0.503160\pi\)
0.861020 + 0.508571i \(0.169826\pi\)
\(32\) 17.3227 + 26.9058i 0.541335 + 0.840807i
\(33\) 0 0
\(34\) −0.509675 0.555144i −0.0149905 0.0163278i
\(35\) 0.0901304 0.00257515
\(36\) 0 0
\(37\) 53.4253i 1.44393i 0.691931 + 0.721964i \(0.256760\pi\)
−0.691931 + 0.721964i \(0.743240\pi\)
\(38\) 20.3591 + 22.1754i 0.535767 + 0.583563i
\(39\) 0 0
\(40\) −0.0582758 + 0.141842i −0.00145689 + 0.00354606i
\(41\) −29.0192 50.2628i −0.707786 1.22592i −0.965677 0.259747i \(-0.916361\pi\)
0.257891 0.966174i \(-0.416973\pi\)
\(42\) 0 0
\(43\) −23.0516 + 39.9265i −0.536083 + 0.928524i 0.463027 + 0.886344i \(0.346763\pi\)
−0.999110 + 0.0421794i \(0.986570\pi\)
\(44\) −18.6981 13.0392i −0.424957 0.296346i
\(45\) 0 0
\(46\) 86.3252 + 27.1273i 1.87663 + 0.589724i
\(47\) −34.2487 19.7735i −0.728695 0.420712i 0.0892497 0.996009i \(-0.471553\pi\)
−0.817944 + 0.575297i \(0.804886\pi\)
\(48\) 0 0
\(49\) −13.4454 23.2882i −0.274396 0.475268i
\(50\) 48.8037 10.8686i 0.976074 0.217372i
\(51\) 0 0
\(52\) −19.7209 42.0809i −0.379249 0.809249i
\(53\) 0.989874i 0.0186769i −0.999956 0.00933844i \(-0.997027\pi\)
0.999956 0.00933844i \(-0.00297256\pi\)
\(54\) 0 0
\(55\) 0.109239i 0.00198616i
\(56\) −37.2802 + 5.01711i −0.665718 + 0.0895913i
\(57\) 0 0
\(58\) −16.0647 72.1360i −0.276978 1.24372i
\(59\) −29.4331 50.9797i −0.498866 0.864062i 0.501133 0.865370i \(-0.332917\pi\)
−0.999999 + 0.00130851i \(0.999583\pi\)
\(60\) 0 0
\(61\) 75.1051 + 43.3619i 1.23123 + 0.710851i 0.967286 0.253687i \(-0.0816432\pi\)
0.263944 + 0.964538i \(0.414977\pi\)
\(62\) −58.1285 18.2666i −0.937557 0.294623i
\(63\) 0 0
\(64\) 16.2087 61.9135i 0.253261 0.967398i
\(65\) 0.111351 0.192866i 0.00171309 0.00296716i
\(66\) 0 0
\(67\) −34.1445 59.1400i −0.509620 0.882687i −0.999938 0.0111436i \(-0.996453\pi\)
0.490318 0.871543i \(-0.336881\pi\)
\(68\) −0.128488 + 1.50177i −0.00188953 + 0.0220848i
\(69\) 0 0
\(70\) −0.121910 0.132785i −0.00174157 0.00189694i
\(71\) 42.3565i 0.596571i −0.954477 0.298285i \(-0.903585\pi\)
0.954477 0.298285i \(-0.0964147\pi\)
\(72\) 0 0
\(73\) 26.6644 0.365266 0.182633 0.983181i \(-0.441538\pi\)
0.182633 + 0.983181i \(0.441538\pi\)
\(74\) 78.7093 72.2627i 1.06364 0.976523i
\(75\) 0 0
\(76\) 5.13248 59.9886i 0.0675326 0.789323i
\(77\) 23.2064 13.3982i 0.301382 0.174003i
\(78\) 0 0
\(79\) −121.208 69.9797i −1.53428 0.885819i −0.999157 0.0410462i \(-0.986931\pi\)
−0.535126 0.844772i \(-0.679736\pi\)
\(80\) 0.287794 0.106000i 0.00359742 0.00132499i
\(81\) 0 0
\(82\) −34.7989 + 110.738i −0.424377 + 1.35046i
\(83\) −40.9931 + 71.0021i −0.493892 + 0.855447i −0.999975 0.00703820i \(-0.997760\pi\)
0.506083 + 0.862485i \(0.331093\pi\)
\(84\) 0 0
\(85\) −0.00625522 + 0.00361145i −7.35908e−5 + 4.24877e-5i
\(86\) 90.0015 20.0434i 1.04653 0.233062i
\(87\) 0 0
\(88\) 6.08078 + 45.1839i 0.0690998 + 0.513454i
\(89\) 42.6370 0.479068 0.239534 0.970888i \(-0.423005\pi\)
0.239534 + 0.970888i \(0.423005\pi\)
\(90\) 0 0
\(91\) 54.6292 0.600321
\(92\) −76.7973 163.872i −0.834753 1.78121i
\(93\) 0 0
\(94\) 17.1930 + 77.2026i 0.182905 + 0.821304i
\(95\) 0.249867 0.144261i 0.00263017 0.00151853i
\(96\) 0 0
\(97\) 55.9278 96.8698i 0.576576 0.998658i −0.419293 0.907851i \(-0.637722\pi\)
0.995868 0.0908072i \(-0.0289447\pi\)
\(98\) −16.1233 + 51.3080i −0.164523 + 0.523551i
\(99\) 0 0
\(100\) −82.0238 57.1997i −0.820238 0.571997i
\(101\) 92.9636 + 53.6726i 0.920432 + 0.531412i 0.883773 0.467916i \(-0.154995\pi\)
0.0366592 + 0.999328i \(0.488328\pi\)
\(102\) 0 0
\(103\) 44.0704 25.4441i 0.427868 0.247030i −0.270570 0.962700i \(-0.587212\pi\)
0.698438 + 0.715671i \(0.253879\pi\)
\(104\) −35.3217 + 85.9724i −0.339632 + 0.826658i
\(105\) 0 0
\(106\) −1.45834 + 1.33890i −0.0137579 + 0.0126311i
\(107\) 49.7181 0.464656 0.232328 0.972638i \(-0.425366\pi\)
0.232328 + 0.972638i \(0.425366\pi\)
\(108\) 0 0
\(109\) 40.3370i 0.370064i −0.982732 0.185032i \(-0.940761\pi\)
0.982732 0.185032i \(-0.0592389\pi\)
\(110\) −0.160937 + 0.147756i −0.00146306 + 0.00134323i
\(111\) 0 0
\(112\) 57.8165 + 48.1373i 0.516218 + 0.429797i
\(113\) 12.9411 + 22.4146i 0.114523 + 0.198360i 0.917589 0.397530i \(-0.130133\pi\)
−0.803066 + 0.595890i \(0.796799\pi\)
\(114\) 0 0
\(115\) 0.433623 0.751057i 0.00377063 0.00653093i
\(116\) −84.5460 + 121.238i −0.728845 + 1.04516i
\(117\) 0 0
\(118\) −35.2952 + 112.317i −0.299112 + 0.951842i
\(119\) −1.53442 0.885896i −0.0128943 0.00744450i
\(120\) 0 0
\(121\) 44.2612 + 76.6627i 0.365795 + 0.633576i
\(122\) −37.7032 169.300i −0.309043 1.38771i
\(123\) 0 0
\(124\) 51.7127 + 110.346i 0.417038 + 0.889884i
\(125\) 0.958412i 0.00766729i
\(126\) 0 0
\(127\) 38.2335i 0.301051i −0.988606 0.150526i \(-0.951903\pi\)
0.988606 0.150526i \(-0.0480966\pi\)
\(128\) −113.138 + 59.8641i −0.883893 + 0.467689i
\(129\) 0 0
\(130\) −0.434754 + 0.0968198i −0.00334426 + 0.000744767i
\(131\) 61.9020 + 107.217i 0.472534 + 0.818453i 0.999506 0.0314294i \(-0.0100059\pi\)
−0.526972 + 0.849883i \(0.676673\pi\)
\(132\) 0 0
\(133\) 61.2927 + 35.3874i 0.460848 + 0.266070i
\(134\) −40.9450 + 130.296i −0.305559 + 0.972359i
\(135\) 0 0
\(136\) 2.38628 1.84198i 0.0175462 0.0135440i
\(137\) −56.1949 + 97.3324i −0.410182 + 0.710456i −0.994909 0.100774i \(-0.967868\pi\)
0.584728 + 0.811230i \(0.301201\pi\)
\(138\) 0 0
\(139\) 56.1874 + 97.3194i 0.404226 + 0.700140i 0.994231 0.107260i \(-0.0342077\pi\)
−0.590005 + 0.807399i \(0.700874\pi\)
\(140\) −0.0307331 + 0.359209i −0.000219522 + 0.00256578i
\(141\) 0 0
\(142\) −62.4021 + 57.2911i −0.439452 + 0.403459i
\(143\) 66.2111i 0.463014i
\(144\) 0 0
\(145\) −0.708302 −0.00488484
\(146\) −36.0661 39.2836i −0.247028 0.269066i
\(147\) 0 0
\(148\) −212.923 18.2172i −1.43867 0.123089i
\(149\) −0.193825 + 0.111905i −0.00130084 + 0.000751040i −0.500650 0.865650i \(-0.666906\pi\)
0.499349 + 0.866401i \(0.333572\pi\)
\(150\) 0 0
\(151\) −106.870 61.7013i −0.707747 0.408618i 0.102479 0.994735i \(-0.467323\pi\)
−0.810226 + 0.586117i \(0.800656\pi\)
\(152\) −95.3209 + 73.5786i −0.627111 + 0.484070i
\(153\) 0 0
\(154\) −51.1279 16.0667i −0.332000 0.104329i
\(155\) −0.291987 + 0.505737i −0.00188379 + 0.00326282i
\(156\) 0 0
\(157\) −169.459 + 97.8372i −1.07936 + 0.623167i −0.930723 0.365726i \(-0.880821\pi\)
−0.148634 + 0.988892i \(0.547488\pi\)
\(158\) 60.8474 + 273.225i 0.385110 + 1.72927i
\(159\) 0 0
\(160\) −0.545433 0.280621i −0.00340895 0.00175388i
\(161\) 212.737 1.32135
\(162\) 0 0
\(163\) 36.1007 0.221477 0.110738 0.993850i \(-0.464678\pi\)
0.110738 + 0.993850i \(0.464678\pi\)
\(164\) 210.214 98.5155i 1.28179 0.600704i
\(165\) 0 0
\(166\) 160.051 35.6435i 0.964165 0.214720i
\(167\) −89.8711 + 51.8871i −0.538150 + 0.310701i −0.744329 0.667813i \(-0.767230\pi\)
0.206179 + 0.978514i \(0.433897\pi\)
\(168\) 0 0
\(169\) −17.0087 + 29.4600i −0.100643 + 0.174319i
\(170\) 0.0137814 + 0.00433073i 8.10669e−5 + 2.54749e-5i
\(171\) 0 0
\(172\) −151.265 105.485i −0.879445 0.613285i
\(173\) −53.5978 30.9447i −0.309814 0.178871i 0.337029 0.941494i \(-0.390578\pi\)
−0.646843 + 0.762623i \(0.723911\pi\)
\(174\) 0 0
\(175\) 101.801 58.7746i 0.581718 0.335855i
\(176\) 58.3428 70.0740i 0.331493 0.398148i
\(177\) 0 0
\(178\) −57.6705 62.8154i −0.323992 0.352895i
\(179\) 235.967 1.31825 0.659125 0.752033i \(-0.270927\pi\)
0.659125 + 0.752033i \(0.270927\pi\)
\(180\) 0 0
\(181\) 274.398i 1.51601i −0.652250 0.758004i \(-0.726175\pi\)
0.652250 0.758004i \(-0.273825\pi\)
\(182\) −73.8911 80.4830i −0.405995 0.442214i
\(183\) 0 0
\(184\) −137.550 + 334.794i −0.747553 + 1.81953i
\(185\) −0.512038 0.886876i −0.00276777 0.00479392i
\(186\) 0 0
\(187\) −1.07371 + 1.85973i −0.00574178 + 0.00994506i
\(188\) 90.4842 129.753i 0.481299 0.690178i
\(189\) 0 0
\(190\) −0.550501 0.172992i −0.00289737 0.000910486i
\(191\) 75.3616 + 43.5100i 0.394563 + 0.227801i 0.684135 0.729355i \(-0.260180\pi\)
−0.289572 + 0.957156i \(0.593513\pi\)
\(192\) 0 0
\(193\) 51.8130 + 89.7428i 0.268461 + 0.464989i 0.968465 0.249151i \(-0.0801515\pi\)
−0.700003 + 0.714140i \(0.746818\pi\)
\(194\) −218.362 + 48.6293i −1.12558 + 0.250666i
\(195\) 0 0
\(196\) 97.3982 45.6450i 0.496930 0.232883i
\(197\) 200.158i 1.01603i −0.861349 0.508014i \(-0.830380\pi\)
0.861349 0.508014i \(-0.169620\pi\)
\(198\) 0 0
\(199\) 178.871i 0.898847i 0.893319 + 0.449424i \(0.148371\pi\)
−0.893319 + 0.449424i \(0.851629\pi\)
\(200\) 26.6748 + 198.210i 0.133374 + 0.991051i
\(201\) 0 0
\(202\) −46.6683 209.557i −0.231031 1.03741i
\(203\) −86.8738 150.470i −0.427950 0.741231i
\(204\) 0 0
\(205\) 0.963456 + 0.556251i 0.00469978 + 0.00271342i
\(206\) −97.0951 30.5117i −0.471335 0.148115i
\(207\) 0 0
\(208\) 174.436 64.2477i 0.838633 0.308883i
\(209\) 42.8898 74.2873i 0.205214 0.355442i
\(210\) 0 0
\(211\) −95.3087 165.079i −0.451700 0.782367i 0.546792 0.837269i \(-0.315849\pi\)
−0.998492 + 0.0549013i \(0.982516\pi\)
\(212\) 3.94508 + 0.337532i 0.0186089 + 0.00159213i
\(213\) 0 0
\(214\) −67.2484 73.2477i −0.314245 0.342279i
\(215\) 0.883723i 0.00411034i
\(216\) 0 0
\(217\) −143.250 −0.660139
\(218\) −59.4269 + 54.5596i −0.272600 + 0.250273i
\(219\) 0 0
\(220\) 0.435365 + 0.0372488i 0.00197893 + 0.000169313i
\(221\) −3.79137 + 2.18895i −0.0171555 + 0.00990474i
\(222\) 0 0
\(223\) 188.439 + 108.795i 0.845018 + 0.487871i 0.858967 0.512031i \(-0.171107\pi\)
−0.0139487 + 0.999903i \(0.504440\pi\)
\(224\) −7.28342 150.289i −0.0325153 0.670932i
\(225\) 0 0
\(226\) 15.5185 49.3835i 0.0686661 0.218511i
\(227\) −68.5871 + 118.796i −0.302146 + 0.523332i −0.976622 0.214965i \(-0.931036\pi\)
0.674476 + 0.738297i \(0.264370\pi\)
\(228\) 0 0
\(229\) −222.151 + 128.259i −0.970090 + 0.560082i −0.899264 0.437407i \(-0.855897\pi\)
−0.0708262 + 0.997489i \(0.522564\pi\)
\(230\) −1.69302 + 0.377035i −0.00736094 + 0.00163928i
\(231\) 0 0
\(232\) 292.971 39.4276i 1.26281 0.169947i
\(233\) −305.481 −1.31108 −0.655538 0.755162i \(-0.727558\pi\)
−0.655538 + 0.755162i \(0.727558\pi\)
\(234\) 0 0
\(235\) 0.758051 0.00322575
\(236\) 213.213 99.9206i 0.903443 0.423392i
\(237\) 0 0
\(238\) 0.770287 + 3.45885i 0.00323650 + 0.0145330i
\(239\) 68.4669 39.5294i 0.286472 0.165395i −0.349878 0.936795i \(-0.613777\pi\)
0.636350 + 0.771401i \(0.280443\pi\)
\(240\) 0 0
\(241\) 111.403 192.956i 0.462254 0.800647i −0.536819 0.843697i \(-0.680374\pi\)
0.999073 + 0.0430503i \(0.0137076\pi\)
\(242\) 53.0766 168.902i 0.219325 0.697941i
\(243\) 0 0
\(244\) −198.426 + 284.541i −0.813221 + 1.16615i
\(245\) 0.446396 + 0.257727i 0.00182202 + 0.00105195i
\(246\) 0 0
\(247\) 151.447 87.4382i 0.613147 0.354001i
\(248\) 92.6215 225.439i 0.373474 0.909028i
\(249\) 0 0
\(250\) −1.41199 + 1.29634i −0.00564795 + 0.00518536i
\(251\) −393.373 −1.56722 −0.783611 0.621252i \(-0.786624\pi\)
−0.783611 + 0.621252i \(0.786624\pi\)
\(252\) 0 0
\(253\) 257.839i 1.01913i
\(254\) −56.3279 + 51.7144i −0.221763 + 0.203600i
\(255\) 0 0
\(256\) 241.226 + 85.7103i 0.942287 + 0.334806i
\(257\) −89.6613 155.298i −0.348877 0.604272i 0.637173 0.770720i \(-0.280103\pi\)
−0.986050 + 0.166448i \(0.946770\pi\)
\(258\) 0 0
\(259\) 125.604 217.552i 0.484957 0.839970i
\(260\) 0.730685 + 0.509547i 0.00281033 + 0.00195980i
\(261\) 0 0
\(262\) 74.2308 236.219i 0.283324 0.901600i
\(263\) 241.721 + 139.558i 0.919092 + 0.530638i 0.883345 0.468723i \(-0.155286\pi\)
0.0357465 + 0.999361i \(0.488619\pi\)
\(264\) 0 0
\(265\) 0.00948714 + 0.0164322i 3.58005e−5 + 6.20083e-5i
\(266\) −30.7693 138.165i −0.115674 0.519416i
\(267\) 0 0
\(268\) 247.342 115.915i 0.922917 0.432519i
\(269\) 112.462i 0.418076i 0.977908 + 0.209038i \(0.0670332\pi\)
−0.977908 + 0.209038i \(0.932967\pi\)
\(270\) 0 0
\(271\) 500.279i 1.84605i 0.384740 + 0.923025i \(0.374291\pi\)
−0.384740 + 0.923025i \(0.625709\pi\)
\(272\) −5.94139 1.02416i −0.0218434 0.00376529i
\(273\) 0 0
\(274\) 219.405 48.8615i 0.800747 0.178327i
\(275\) −71.2353 123.383i −0.259037 0.448666i
\(276\) 0 0
\(277\) 222.630 + 128.535i 0.803718 + 0.464027i 0.844770 0.535130i \(-0.179737\pi\)
−0.0410514 + 0.999157i \(0.513071\pi\)
\(278\) 67.3780 214.412i 0.242367 0.771267i
\(279\) 0 0
\(280\) 0.570778 0.440586i 0.00203849 0.00157352i
\(281\) −139.228 + 241.150i −0.495474 + 0.858187i −0.999986 0.00521797i \(-0.998339\pi\)
0.504512 + 0.863405i \(0.331672\pi\)
\(282\) 0 0
\(283\) 93.9509 + 162.728i 0.331982 + 0.575009i 0.982900 0.184138i \(-0.0589494\pi\)
−0.650919 + 0.759148i \(0.725616\pi\)
\(284\) 168.809 + 14.4429i 0.594399 + 0.0508554i
\(285\) 0 0
\(286\) −97.5460 + 89.5566i −0.341070 + 0.313135i
\(287\) 272.899i 0.950868i
\(288\) 0 0
\(289\) −288.858 −0.999509
\(290\) 0.958044 + 1.04351i 0.00330360 + 0.00359832i
\(291\) 0 0
\(292\) −9.09216 + 106.269i −0.0311375 + 0.363936i
\(293\) −442.987 + 255.759i −1.51190 + 0.872897i −0.511999 + 0.858986i \(0.671095\pi\)
−0.999903 + 0.0139109i \(0.995572\pi\)
\(294\) 0 0
\(295\) 0.977197 + 0.564185i 0.00331253 + 0.00191249i
\(296\) 261.160 + 338.332i 0.882297 + 1.14301i
\(297\) 0 0
\(298\) 0.427031 + 0.134193i 0.00143299 + 0.000450311i
\(299\) 262.825 455.225i 0.879012 1.52249i
\(300\) 0 0
\(301\) 187.736 108.389i 0.623708 0.360098i
\(302\) 53.6494 + 240.904i 0.177647 + 0.797695i
\(303\) 0 0
\(304\) 237.331 + 40.9104i 0.780693 + 0.134574i
\(305\) −1.66236 −0.00545035
\(306\) 0 0
\(307\) −195.885 −0.638061 −0.319031 0.947744i \(-0.603357\pi\)
−0.319031 + 0.947744i \(0.603357\pi\)
\(308\) 45.4848 + 97.0564i 0.147678 + 0.315118i
\(309\) 0 0
\(310\) 1.14002 0.253883i 0.00367749 0.000818978i
\(311\) 395.492 228.338i 1.27168 0.734205i 0.296376 0.955071i \(-0.404222\pi\)
0.975304 + 0.220867i \(0.0708886\pi\)
\(312\) 0 0
\(313\) −185.314 + 320.973i −0.592058 + 1.02547i 0.401897 + 0.915685i \(0.368351\pi\)
−0.993955 + 0.109789i \(0.964982\pi\)
\(314\) 373.348 + 117.323i 1.18901 + 0.373640i
\(315\) 0 0
\(316\) 320.230 459.207i 1.01339 1.45319i
\(317\) −435.393 251.374i −1.37348 0.792979i −0.382115 0.924115i \(-0.624804\pi\)
−0.991364 + 0.131136i \(0.958138\pi\)
\(318\) 0 0
\(319\) −182.371 + 105.292i −0.571695 + 0.330068i
\(320\) 0.324321 + 1.18313i 0.00101350 + 0.00369728i
\(321\) 0 0
\(322\) −287.747 313.417i −0.893623 0.973344i
\(323\) −5.67177 −0.0175597
\(324\) 0 0
\(325\) 290.451i 0.893695i
\(326\) −48.8296 53.1858i −0.149784 0.163146i
\(327\) 0 0
\(328\) −429.473 176.449i −1.30937 0.537954i
\(329\) 92.9756 + 161.038i 0.282601 + 0.489479i
\(330\) 0 0
\(331\) −187.810 + 325.297i −0.567402 + 0.982769i 0.429420 + 0.903105i \(0.358718\pi\)
−0.996822 + 0.0796642i \(0.974615\pi\)
\(332\) −268.996 187.586i −0.810230 0.565018i
\(333\) 0 0
\(334\) 198.002 + 62.2213i 0.592821 + 0.186291i
\(335\) 1.13362 + 0.654495i 0.00338394 + 0.00195372i
\(336\) 0 0
\(337\) −161.252 279.296i −0.478492 0.828772i 0.521204 0.853432i \(-0.325483\pi\)
−0.999696 + 0.0246599i \(0.992150\pi\)
\(338\) 66.4080 14.7891i 0.196473 0.0437547i
\(339\) 0 0
\(340\) −0.0122603 0.0261612i −3.60597e−5 7.69448e-5i
\(341\) 173.620i 0.509150i
\(342\) 0 0
\(343\) 356.842i 1.04035i
\(344\) 49.1925 + 365.530i 0.143001 + 1.06259i
\(345\) 0 0
\(346\) 26.9064 + 120.819i 0.0777642 + 0.349188i
\(347\) 42.4458 + 73.5183i 0.122322 + 0.211868i 0.920683 0.390311i \(-0.127633\pi\)
−0.798361 + 0.602179i \(0.794299\pi\)
\(348\) 0 0
\(349\) −35.4597 20.4727i −0.101604 0.0586610i 0.448337 0.893865i \(-0.352016\pi\)
−0.549941 + 0.835204i \(0.685350\pi\)
\(350\) −224.285 70.4806i −0.640814 0.201373i
\(351\) 0 0
\(352\) −182.151 + 8.82757i −0.517475 + 0.0250783i
\(353\) 272.714 472.355i 0.772561 1.33812i −0.163593 0.986528i \(-0.552309\pi\)
0.936155 0.351588i \(-0.114358\pi\)
\(354\) 0 0
\(355\) 0.405953 + 0.703131i 0.00114353 + 0.00198065i
\(356\) −14.5386 + 169.927i −0.0408387 + 0.477324i
\(357\) 0 0
\(358\) −319.167 347.640i −0.891528 0.971062i
\(359\) 24.1503i 0.0672710i −0.999434 0.0336355i \(-0.989291\pi\)
0.999434 0.0336355i \(-0.0107085\pi\)
\(360\) 0 0
\(361\) −134.439 −0.372408
\(362\) −404.259 + 371.148i −1.11674 + 1.02527i
\(363\) 0 0
\(364\) −18.6277 + 217.721i −0.0511751 + 0.598136i
\(365\) −0.442637 + 0.255557i −0.00121270 + 0.000700155i
\(366\) 0 0
\(367\) −227.281 131.221i −0.619295 0.357550i 0.157299 0.987551i \(-0.449721\pi\)
−0.776595 + 0.630001i \(0.783055\pi\)
\(368\) 679.287 250.193i 1.84589 0.679873i
\(369\) 0 0
\(370\) −0.614019 + 1.95395i −0.00165951 + 0.00528094i
\(371\) −2.32721 + 4.03085i −0.00627281 + 0.0108648i
\(372\) 0 0
\(373\) −97.0579 + 56.0364i −0.260209 + 0.150232i −0.624430 0.781081i \(-0.714669\pi\)
0.364221 + 0.931313i \(0.381335\pi\)
\(374\) 4.19215 0.933594i 0.0112090 0.00249624i
\(375\) 0 0
\(376\) −313.549 + 42.1969i −0.833907 + 0.112226i
\(377\) −429.311 −1.13876
\(378\) 0 0
\(379\) 305.554 0.806210 0.403105 0.915154i \(-0.367931\pi\)
0.403105 + 0.915154i \(0.367931\pi\)
\(380\) 0.489741 + 1.04502i 0.00128879 + 0.00275005i
\(381\) 0 0
\(382\) −37.8320 169.878i −0.0990366 0.444708i
\(383\) −50.9660 + 29.4252i −0.133070 + 0.0768283i −0.565057 0.825052i \(-0.691146\pi\)
0.431987 + 0.901880i \(0.357813\pi\)
\(384\) 0 0
\(385\) −0.256823 + 0.444830i −0.000667071 + 0.00115540i
\(386\) 62.1325 197.719i 0.160965 0.512227i
\(387\) 0 0
\(388\) 366.998 + 255.928i 0.945872 + 0.659609i
\(389\) −417.667 241.140i −1.07369 0.619897i −0.144505 0.989504i \(-0.546159\pi\)
−0.929188 + 0.369607i \(0.879492\pi\)
\(390\) 0 0
\(391\) −14.7643 + 8.52420i −0.0377605 + 0.0218010i
\(392\) −198.987 81.7537i −0.507620 0.208555i
\(393\) 0 0
\(394\) −294.884 + 270.732i −0.748436 + 0.687136i
\(395\) 2.68279 0.00679188
\(396\) 0 0
\(397\) 74.8863i 0.188631i 0.995542 + 0.0943153i \(0.0300662\pi\)
−0.995542 + 0.0943153i \(0.969934\pi\)
\(398\) 263.523 241.939i 0.662117 0.607887i
\(399\) 0 0
\(400\) 255.935 307.397i 0.639837 0.768492i
\(401\) 299.864 + 519.380i 0.747791 + 1.29521i 0.948879 + 0.315639i \(0.102219\pi\)
−0.201088 + 0.979573i \(0.564448\pi\)
\(402\) 0 0
\(403\) −176.977 + 306.534i −0.439150 + 0.760629i
\(404\) −245.608 + 352.199i −0.607941 + 0.871781i
\(405\) 0 0
\(406\) −104.176 + 331.512i −0.256592 + 0.816533i
\(407\) −263.675 152.233i −0.647851 0.374037i
\(408\) 0 0
\(409\) 274.176 + 474.886i 0.670356 + 1.16109i 0.977803 + 0.209526i \(0.0671921\pi\)
−0.307447 + 0.951565i \(0.599475\pi\)
\(410\) −0.483661 2.17180i −0.00117966 0.00529708i
\(411\) 0 0
\(412\) 86.3785 + 184.316i 0.209656 + 0.447369i
\(413\) 276.791i 0.670197i
\(414\) 0 0
\(415\) 1.57154i 0.00378685i
\(416\) −330.594 170.088i −0.794697 0.408865i
\(417\) 0 0
\(418\) −167.457 + 37.2927i −0.400614 + 0.0892170i
\(419\) 134.464 + 232.899i 0.320917 + 0.555845i 0.980677 0.195631i \(-0.0626756\pi\)
−0.659761 + 0.751476i \(0.729342\pi\)
\(420\) 0 0
\(421\) −235.498 135.965i −0.559378 0.322957i 0.193518 0.981097i \(-0.438010\pi\)
−0.752896 + 0.658140i \(0.771344\pi\)
\(422\) −114.291 + 363.700i −0.270832 + 0.861848i
\(423\) 0 0
\(424\) −4.83882 6.26867i −0.0114123 0.0147846i
\(425\) −4.71010 + 8.15813i −0.0110826 + 0.0191956i
\(426\) 0 0
\(427\) −203.889 353.147i −0.477493 0.827042i
\(428\) −16.9531 + 198.149i −0.0396101 + 0.462964i
\(429\) 0 0
\(430\) −1.30195 + 1.19532i −0.00302780 + 0.00277981i
\(431\) 140.920i 0.326960i 0.986547 + 0.163480i \(0.0522719\pi\)
−0.986547 + 0.163480i \(0.947728\pi\)
\(432\) 0 0
\(433\) 649.144 1.49918 0.749589 0.661903i \(-0.230251\pi\)
0.749589 + 0.661903i \(0.230251\pi\)
\(434\) 193.759 + 211.044i 0.446449 + 0.486278i
\(435\) 0 0
\(436\) 160.761 + 13.7543i 0.368717 + 0.0315466i
\(437\) 589.766 340.502i 1.34958 0.779180i
\(438\) 0 0
\(439\) −135.712 78.3535i −0.309140 0.178482i 0.337402 0.941361i \(-0.390452\pi\)
−0.646541 + 0.762879i \(0.723785\pi\)
\(440\) −0.533994 0.691787i −0.00121362 0.00157224i
\(441\) 0 0
\(442\) 8.35307 + 2.62491i 0.0188983 + 0.00593872i
\(443\) −6.92104 + 11.9876i −0.0156231 + 0.0270600i −0.873731 0.486409i \(-0.838307\pi\)
0.858108 + 0.513469i \(0.171640\pi\)
\(444\) 0 0
\(445\) −0.707787 + 0.408641i −0.00159053 + 0.000918295i
\(446\) −94.5976 424.775i −0.212102 0.952411i
\(447\) 0 0
\(448\) −211.563 + 214.010i −0.472239 + 0.477701i
\(449\) 682.313 1.51963 0.759814 0.650140i \(-0.225290\pi\)
0.759814 + 0.650140i \(0.225290\pi\)
\(450\) 0 0
\(451\) 330.756 0.733383
\(452\) −93.7449 + 43.9329i −0.207400 + 0.0971967i
\(453\) 0 0
\(454\) 267.788 59.6365i 0.589842 0.131358i
\(455\) −0.906861 + 0.523577i −0.00199310 + 0.00115072i
\(456\) 0 0
\(457\) −140.879 + 244.010i −0.308270 + 0.533938i −0.977984 0.208680i \(-0.933083\pi\)
0.669714 + 0.742619i \(0.266417\pi\)
\(458\) 489.438 + 153.804i 1.06864 + 0.335816i
\(459\) 0 0
\(460\) 2.84543 + 1.98428i 0.00618573 + 0.00431365i
\(461\) 556.528 + 321.312i 1.20722 + 0.696989i 0.962151 0.272517i \(-0.0878561\pi\)
0.245069 + 0.969506i \(0.421189\pi\)
\(462\) 0 0
\(463\) 528.367 305.053i 1.14118 0.658861i 0.194458 0.980911i \(-0.437705\pi\)
0.946723 + 0.322050i \(0.104372\pi\)
\(464\) −454.358 378.293i −0.979220 0.815287i
\(465\) 0 0
\(466\) 413.191 + 450.052i 0.886676 + 0.965777i
\(467\) −289.260 −0.619400 −0.309700 0.950834i \(-0.600229\pi\)
−0.309700 + 0.950834i \(0.600229\pi\)
\(468\) 0 0
\(469\) 321.098i 0.684643i
\(470\) −1.02533 1.11680i −0.00218156 0.00237618i
\(471\) 0 0
\(472\) −435.599 178.965i −0.922879 0.379164i
\(473\) −131.369 227.538i −0.277736 0.481052i
\(474\) 0 0
\(475\) 188.146 325.879i 0.396098 0.686061i
\(476\) 4.05390 5.81325i 0.00851659 0.0122127i
\(477\) 0 0
\(478\) −150.845 47.4023i −0.315575 0.0991680i
\(479\) −115.068 66.4346i −0.240226 0.138694i 0.375055 0.927003i \(-0.377624\pi\)
−0.615281 + 0.788308i \(0.710957\pi\)
\(480\) 0 0
\(481\) −310.353 537.547i −0.645224 1.11756i
\(482\) −434.957 + 96.8651i −0.902401 + 0.200965i
\(483\) 0 0
\(484\) −320.627 + 150.260i −0.662452 + 0.310454i
\(485\) 2.14409i 0.00442081i
\(486\) 0 0
\(487\) 800.882i 1.64452i −0.569111 0.822261i \(-0.692713\pi\)
0.569111 0.822261i \(-0.307287\pi\)
\(488\) 687.592 92.5351i 1.40900 0.189621i
\(489\) 0 0
\(490\) −0.224094 1.00626i −0.000457334 0.00205358i
\(491\) 416.975 + 722.222i 0.849236 + 1.47092i 0.881891 + 0.471454i \(0.156270\pi\)
−0.0326547 + 0.999467i \(0.510396\pi\)
\(492\) 0 0
\(493\) 12.0584 + 6.96193i 0.0244593 + 0.0141216i
\(494\) −333.666 104.853i −0.675437 0.212253i
\(495\) 0 0
\(496\) −457.409 + 168.472i −0.922196 + 0.339661i
\(497\) −99.5810 + 172.479i −0.200364 + 0.347041i
\(498\) 0 0
\(499\) −62.9732 109.073i −0.126199 0.218583i 0.796002 0.605294i \(-0.206944\pi\)
−0.922201 + 0.386711i \(0.873611\pi\)
\(500\) 3.81969 + 0.326804i 0.00763938 + 0.000653608i
\(501\) 0 0
\(502\) 532.073 + 579.540i 1.05991 + 1.15446i
\(503\) 321.537i 0.639239i 0.947546 + 0.319619i \(0.103555\pi\)
−0.947546 + 0.319619i \(0.896445\pi\)
\(504\) 0 0
\(505\) −2.05763 −0.00407452
\(506\) −379.864 + 348.751i −0.750719 + 0.689232i
\(507\) 0 0
\(508\) 152.377 + 13.0370i 0.299955 + 0.0256635i
\(509\) 473.601 273.434i 0.930455 0.537198i 0.0434992 0.999053i \(-0.486149\pi\)
0.886955 + 0.461855i \(0.152816\pi\)
\(510\) 0 0
\(511\) −108.580 62.6885i −0.212485 0.122678i
\(512\) −200.006 471.319i −0.390638 0.920545i
\(513\) 0 0
\(514\) −107.519 + 342.149i −0.209181 + 0.665660i
\(515\) −0.487722 + 0.844758i −0.000947032 + 0.00164031i
\(516\) 0 0
\(517\) 195.180 112.687i 0.377524 0.217964i
\(518\) −490.402 + 109.213i −0.946722 + 0.210835i
\(519\) 0 0
\(520\) −0.237625 1.76570i −0.000456971 0.00339557i
\(521\) −774.144 −1.48588 −0.742940 0.669358i \(-0.766569\pi\)
−0.742940 + 0.669358i \(0.766569\pi\)
\(522\) 0 0
\(523\) 126.448 0.241774 0.120887 0.992666i \(-0.461426\pi\)
0.120887 + 0.992666i \(0.461426\pi\)
\(524\) −448.416 + 210.147i −0.855756 + 0.401044i
\(525\) 0 0
\(526\) −121.346 544.883i −0.230695 1.03590i
\(527\) 9.94182 5.73991i 0.0188649 0.0108917i
\(528\) 0 0
\(529\) 758.991 1314.61i 1.43477 2.48509i
\(530\) 0.0113767 0.0362031i 2.14654e−5 6.83077e-5i
\(531\) 0 0
\(532\) −161.934 + 232.212i −0.304387 + 0.436489i
\(533\) 583.963 + 337.151i 1.09562 + 0.632554i
\(534\) 0 0
\(535\) −0.825336 + 0.476508i −0.00154268 + 0.000890669i
\(536\) −505.326 207.613i −0.942772 0.387337i
\(537\) 0 0
\(538\) 165.686 152.116i 0.307967 0.282743i
\(539\) 153.248 0.284320
\(540\) 0 0
\(541\) 323.091i 0.597210i 0.954377 + 0.298605i \(0.0965213\pi\)
−0.954377 + 0.298605i \(0.903479\pi\)
\(542\) 737.041 676.674i 1.35985 1.24848i
\(543\) 0 0
\(544\) 6.52743 + 10.1385i 0.0119990 + 0.0186369i
\(545\) 0.386598 + 0.669607i 0.000709353 + 0.00122864i
\(546\) 0 0
\(547\) 42.9079 74.3187i 0.0784423 0.135866i −0.824136 0.566392i \(-0.808339\pi\)
0.902578 + 0.430526i \(0.141672\pi\)
\(548\) −368.751 257.150i −0.672903 0.469252i
\(549\) 0 0
\(550\) −85.4230 + 271.835i −0.155315 + 0.494246i
\(551\) −481.677 278.096i −0.874187 0.504712i
\(552\) 0 0
\(553\) 329.047 + 569.926i 0.595022 + 1.03061i
\(554\) −111.762 501.848i −0.201736 0.905863i
\(555\) 0 0
\(556\) −407.020 + 190.747i −0.732050 + 0.343070i
\(557\) 666.623i 1.19681i −0.801194 0.598405i \(-0.795801\pi\)
0.801194 0.598405i \(-0.204199\pi\)
\(558\) 0 0
\(559\) 535.636i 0.958204i
\(560\) −1.42113 0.244970i −0.00253773 0.000437446i
\(561\) 0 0
\(562\) 543.596 121.059i 0.967253 0.215408i
\(563\) −234.690 406.495i −0.416856 0.722016i 0.578765 0.815494i \(-0.303535\pi\)
−0.995621 + 0.0934780i \(0.970202\pi\)
\(564\) 0 0
\(565\) −0.429652 0.248060i −0.000760446 0.000439044i
\(566\) 112.663 358.518i 0.199051 0.633424i
\(567\) 0 0
\(568\) −207.052 268.235i −0.364528 0.472245i
\(569\) 129.732 224.702i 0.228000 0.394907i −0.729215 0.684284i \(-0.760115\pi\)
0.957215 + 0.289377i \(0.0934481\pi\)
\(570\) 0 0
\(571\) 38.3743 + 66.4663i 0.0672055 + 0.116403i 0.897670 0.440668i \(-0.145258\pi\)
−0.830465 + 0.557071i \(0.811925\pi\)
\(572\) 263.880 + 22.5770i 0.461329 + 0.0394702i
\(573\) 0 0
\(574\) 402.051 369.121i 0.700437 0.643068i
\(575\) 1131.07i 1.96708i
\(576\) 0 0
\(577\) 289.811 0.502272 0.251136 0.967952i \(-0.419196\pi\)
0.251136 + 0.967952i \(0.419196\pi\)
\(578\) 390.707 + 425.563i 0.675964 + 0.736268i
\(579\) 0 0
\(580\) 0.241520 2.82289i 0.000416414 0.00486706i
\(581\) 333.854 192.751i 0.574620 0.331757i
\(582\) 0 0
\(583\) 4.88542 + 2.82060i 0.00837980 + 0.00483808i
\(584\) 168.860 130.344i 0.289144 0.223192i
\(585\) 0 0
\(586\) 975.981 + 306.697i 1.66550 + 0.523375i
\(587\) −136.875 + 237.074i −0.233177 + 0.403874i −0.958741 0.284280i \(-0.908245\pi\)
0.725565 + 0.688154i \(0.241579\pi\)
\(588\) 0 0
\(589\) −397.129 + 229.282i −0.674243 + 0.389274i
\(590\) −0.490559 2.20278i −0.000831456 0.00373352i
\(591\) 0 0
\(592\) 145.207 842.381i 0.245282 1.42294i
\(593\) 461.865 0.778861 0.389431 0.921056i \(-0.372672\pi\)
0.389431 + 0.921056i \(0.372672\pi\)
\(594\) 0 0
\(595\) 0.0339624 5.70796e−5
\(596\) −0.379899 0.810636i −0.000637414 0.00136013i
\(597\) 0 0
\(598\) −1026.16 + 228.526i −1.71599 + 0.382151i
\(599\) −551.557 + 318.442i −0.920797 + 0.531622i −0.883889 0.467696i \(-0.845084\pi\)
−0.0369077 + 0.999319i \(0.511751\pi\)
\(600\) 0 0
\(601\) −456.737 + 791.092i −0.759962 + 1.31629i 0.182908 + 0.983130i \(0.441449\pi\)
−0.942869 + 0.333162i \(0.891884\pi\)
\(602\) −413.616 129.977i −0.687070 0.215909i
\(603\) 0 0
\(604\) 282.348 404.884i 0.467464 0.670338i
\(605\) −1.46950 0.848416i −0.00242892 0.00140234i
\(606\) 0 0
\(607\) −108.688 + 62.7511i −0.179058 + 0.103379i −0.586850 0.809696i \(-0.699632\pi\)
0.407792 + 0.913075i \(0.366299\pi\)
\(608\) −260.740 404.985i −0.428849 0.666093i
\(609\) 0 0
\(610\) 2.24849 + 2.44908i 0.00368605 + 0.00401489i
\(611\) 459.464 0.751987
\(612\) 0 0
\(613\) 929.305i 1.51600i 0.652257 + 0.757998i \(0.273822\pi\)
−0.652257 + 0.757998i \(0.726178\pi\)
\(614\) 264.952 + 288.589i 0.431519 + 0.470015i
\(615\) 0 0
\(616\) 81.4668 198.289i 0.132251 0.321897i
\(617\) −9.42520 16.3249i −0.0152759 0.0264585i 0.858286 0.513171i \(-0.171529\pi\)
−0.873562 + 0.486712i \(0.838196\pi\)
\(618\) 0 0
\(619\) 158.239 274.079i 0.255637 0.442777i −0.709431 0.704775i \(-0.751048\pi\)
0.965068 + 0.261998i \(0.0843814\pi\)
\(620\) −1.91602 1.33615i −0.00309036 0.00215507i
\(621\) 0 0
\(622\) −871.341 273.815i −1.40087 0.440217i
\(623\) −173.622 100.240i −0.278686 0.160900i
\(624\) 0 0
\(625\) −312.486 541.242i −0.499978 0.865987i
\(626\) 723.532 161.131i 1.15580 0.257397i
\(627\) 0 0
\(628\) −332.141 708.729i −0.528887 1.12855i
\(629\) 20.1314i 0.0320054i
\(630\) 0 0
\(631\) 254.226i 0.402893i −0.979499 0.201447i \(-0.935436\pi\)
0.979499 0.201447i \(-0.0645643\pi\)
\(632\) −1109.67 + 149.338i −1.75581 + 0.236294i
\(633\) 0 0
\(634\) 218.570 + 981.454i 0.344748 + 1.54803i
\(635\) 0.366437 + 0.634688i 0.000577066 + 0.000999508i
\(636\) 0 0
\(637\) 270.566 + 156.212i 0.424751 + 0.245230i
\(638\) 401.796 + 126.262i 0.629774 + 0.197904i
\(639\) 0 0
\(640\) 1.30438 2.07810i 0.00203810 0.00324703i
\(641\) 509.350 882.221i 0.794618 1.37632i −0.128463 0.991714i \(-0.541004\pi\)
0.923081 0.384605i \(-0.125662\pi\)
\(642\) 0 0
\(643\) 302.348 + 523.683i 0.470215 + 0.814436i 0.999420 0.0340578i \(-0.0108430\pi\)
−0.529205 + 0.848494i \(0.677510\pi\)
\(644\) −72.5401 + 847.851i −0.112640 + 1.31654i
\(645\) 0 0
\(646\) 7.67160 + 8.35599i 0.0118755 + 0.0129350i
\(647\) 86.7767i 0.134122i 0.997749 + 0.0670608i \(0.0213622\pi\)
−0.997749 + 0.0670608i \(0.978638\pi\)
\(648\) 0 0
\(649\) 335.473 0.516908
\(650\) −427.909 + 392.862i −0.658322 + 0.604402i
\(651\) 0 0
\(652\) −12.3098 + 143.877i −0.0188801 + 0.220671i
\(653\) −346.903 + 200.285i −0.531245 + 0.306714i −0.741523 0.670927i \(-0.765896\pi\)
0.210278 + 0.977642i \(0.432563\pi\)
\(654\) 0 0
\(655\) −2.05518 1.18656i −0.00313768 0.00181154i
\(656\) 320.948 + 871.389i 0.489250 + 1.32834i
\(657\) 0 0
\(658\) 111.493 354.797i 0.169443 0.539205i
\(659\) −28.0360 + 48.5597i −0.0425432 + 0.0736870i −0.886513 0.462704i \(-0.846879\pi\)
0.843970 + 0.536391i \(0.180213\pi\)
\(660\) 0 0
\(661\) 675.562 390.036i 1.02203 0.590069i 0.107339 0.994222i \(-0.465767\pi\)
0.914691 + 0.404153i \(0.132434\pi\)
\(662\) 733.277 163.301i 1.10767 0.246678i
\(663\) 0 0
\(664\) 87.4799 + 650.029i 0.131747 + 0.978959i
\(665\) −1.35664 −0.00204006
\(666\) 0 0
\(667\) −1671.82 −2.50648
\(668\) −176.148 375.868i −0.263695 0.562677i
\(669\) 0 0
\(670\) −0.569084 2.55538i −0.000849379 0.00381400i
\(671\) −428.017 + 247.116i −0.637879 + 0.368280i
\(672\) 0 0
\(673\) −353.998 + 613.143i −0.526001 + 0.911060i 0.473541 + 0.880772i \(0.342976\pi\)
−0.999541 + 0.0302878i \(0.990358\pi\)
\(674\) −193.368 + 615.340i −0.286896 + 0.912967i
\(675\) 0 0
\(676\) −111.611 77.8326i −0.165105 0.115137i
\(677\) 503.417 + 290.648i 0.743600 + 0.429318i 0.823377 0.567495i \(-0.192087\pi\)
−0.0797769 + 0.996813i \(0.525421\pi\)
\(678\) 0 0
\(679\) −455.486 + 262.975i −0.670818 + 0.387297i
\(680\) −0.0219591 + 0.0534481i −3.22928e−5 + 7.86001e-5i
\(681\) 0 0
\(682\) 255.788 234.838i 0.375055 0.344337i
\(683\) −558.887 −0.818282 −0.409141 0.912471i \(-0.634172\pi\)
−0.409141 + 0.912471i \(0.634172\pi\)
\(684\) 0 0
\(685\) 2.15433i 0.00314501i
\(686\) 525.720 482.661i 0.766356 0.703588i
\(687\) 0 0
\(688\) 471.983 566.887i 0.686022 0.823963i
\(689\) 5.75028 + 9.95977i 0.00834583 + 0.0144554i
\(690\) 0 0
\(691\) −158.856 + 275.147i −0.229893 + 0.398187i −0.957776 0.287515i \(-0.907171\pi\)
0.727883 + 0.685701i \(0.240504\pi\)
\(692\) 141.604 203.059i 0.204630 0.293438i
\(693\) 0 0
\(694\) 50.8996 161.974i 0.0733423 0.233392i
\(695\) −1.86545 1.07702i −0.00268411 0.00154967i
\(696\) 0 0
\(697\) −10.9348 18.9397i −0.0156884 0.0271732i
\(698\) 17.8010 + 79.9326i 0.0255029 + 0.114517i
\(699\) 0 0
\(700\) 199.530 + 425.761i 0.285043 + 0.608231i
\(701\) 731.568i 1.04361i 0.853066 + 0.521803i \(0.174741\pi\)
−0.853066 + 0.521803i \(0.825259\pi\)
\(702\) 0 0
\(703\) 804.154i 1.14389i
\(704\) 259.382 + 256.416i 0.368440 + 0.364227i
\(705\) 0 0
\(706\) −1064.77 + 237.125i −1.50818 + 0.335871i
\(707\) −252.371 437.119i −0.356960 0.618272i
\(708\) 0 0
\(709\) 112.277 + 64.8230i 0.158359 + 0.0914288i 0.577085 0.816684i \(-0.304190\pi\)
−0.418726 + 0.908113i \(0.637523\pi\)
\(710\) 0.486805 1.54912i 0.000685641 0.00218186i
\(711\) 0 0
\(712\) 270.012 208.423i 0.379230 0.292729i
\(713\) −689.185 + 1193.70i −0.966599 + 1.67420i
\(714\) 0 0
\(715\) 0.634579 + 1.09912i 0.000887523 + 0.00153724i
\(716\) −80.4611 + 940.431i −0.112376 + 1.31345i
\(717\) 0 0
\(718\) −35.5796 + 32.6655i −0.0495538 + 0.0454951i
\(719\) 726.317i 1.01018i 0.863068 + 0.505088i \(0.168540\pi\)
−0.863068 + 0.505088i \(0.831460\pi\)
\(720\) 0 0
\(721\) −239.278 −0.331870
\(722\) 181.842 + 198.064i 0.251858 + 0.274327i
\(723\) 0 0
\(724\) 1093.59 + 93.5654i 1.51049 + 0.129234i
\(725\) −800.013 + 461.888i −1.10347 + 0.637087i
\(726\) 0 0
\(727\) 498.049 + 287.549i 0.685075 + 0.395528i 0.801764 0.597640i \(-0.203895\pi\)
−0.116690 + 0.993168i \(0.537228\pi\)
\(728\) 345.956 267.045i 0.475214 0.366820i
\(729\) 0 0
\(730\) 0.975209 + 0.306455i 0.00133590 + 0.000419801i
\(731\) −8.68615 + 15.0449i −0.0118826 + 0.0205812i
\(732\) 0 0
\(733\) 113.103 65.3000i 0.154301 0.0890859i −0.420861 0.907125i \(-0.638272\pi\)
0.575163 + 0.818039i \(0.304939\pi\)
\(734\) 114.097 + 512.333i 0.155445 + 0.698001i
\(735\) 0 0
\(736\) −1287.40 662.356i −1.74918 0.899940i
\(737\) 389.173 0.528050
\(738\) 0 0
\(739\) −61.7030 −0.0834953 −0.0417477 0.999128i \(-0.513293\pi\)
−0.0417477 + 0.999128i \(0.513293\pi\)
\(740\) 3.70919 1.73829i 0.00501242 0.00234903i
\(741\) 0 0
\(742\) 9.08626 2.02351i 0.0122456 0.00272711i
\(743\) 368.246 212.607i 0.495620 0.286147i −0.231283 0.972887i \(-0.574292\pi\)
0.726903 + 0.686740i \(0.240959\pi\)
\(744\) 0 0
\(745\) 0.00214503 0.00371531i 2.87924e−6 4.98699e-6i
\(746\) 213.836 + 67.1970i 0.286644 + 0.0900764i
\(747\) 0 0
\(748\) −7.04570 4.91336i −0.00941939 0.00656866i
\(749\) −202.456 116.888i −0.270302 0.156059i
\(750\) 0 0
\(751\) −1180.47 + 681.543i −1.57186 + 0.907514i −0.575920 + 0.817506i \(0.695356\pi\)
−0.995941 + 0.0900084i \(0.971311\pi\)
\(752\) 486.271 + 404.863i 0.646637 + 0.538382i
\(753\) 0 0
\(754\) 580.683 + 632.486i 0.770136 + 0.838841i
\(755\) 2.36543 0.00313302
\(756\) 0 0
\(757\) 105.684i 0.139610i −0.997561 0.0698048i \(-0.977762\pi\)
0.997561 0.0698048i \(-0.0222376\pi\)
\(758\) −413.290 450.159i −0.545237 0.593878i
\(759\) 0 0
\(760\) 0.877163 2.13500i 0.00115416 0.00280921i
\(761\) −452.651 784.015i −0.594811 1.03024i −0.993574 0.113189i \(-0.963894\pi\)
0.398763 0.917054i \(-0.369440\pi\)
\(762\) 0 0
\(763\) −94.8331 + 164.256i −0.124290 + 0.215276i
\(764\) −199.104 + 285.513i −0.260607 + 0.373708i
\(765\) 0 0
\(766\) 112.287 + 35.2858i 0.146589 + 0.0460650i
\(767\) 592.292 + 341.960i 0.772219 + 0.445841i
\(768\) 0 0
\(769\) −16.2383 28.1255i −0.0211161 0.0365741i 0.855274 0.518176i \(-0.173389\pi\)
−0.876390 + 0.481601i \(0.840055\pi\)
\(770\) 1.00273 0.223307i 0.00130224 0.000290010i
\(771\) 0 0
\(772\) −375.332 + 175.897i −0.486181 + 0.227846i
\(773\) 367.930i 0.475976i 0.971268 + 0.237988i \(0.0764880\pi\)
−0.971268 + 0.237988i \(0.923512\pi\)
\(774\) 0 0
\(775\) 761.627i 0.982744i
\(776\) −119.351 886.850i −0.153803 1.14285i
\(777\) 0 0
\(778\) 209.671 + 941.496i 0.269501 + 1.21015i
\(779\) 436.795 + 756.552i 0.560713 + 0.971183i
\(780\) 0 0
\(781\) 209.046 + 120.693i 0.267665 + 0.154536i
\(782\) 32.5285 + 10.2219i 0.0415966 + 0.0130715i
\(783\) 0 0
\(784\) 148.704 + 403.739i 0.189674 + 0.514973i
\(785\) 1.87538 3.24825i 0.00238902 0.00413790i
\(786\) 0 0
\(787\) 563.311 + 975.684i 0.715770 + 1.23975i 0.962662 + 0.270707i \(0.0872576\pi\)
−0.246891 + 0.969043i \(0.579409\pi\)
\(788\) 797.716 + 68.2507i 1.01233 + 0.0866125i
\(789\) 0 0
\(790\) −3.62873 3.95245i −0.00459333 0.00500310i
\(791\) 121.699i 0.153855i
\(792\) 0 0
\(793\) −1007.58 −1.27059
\(794\) 110.327 101.291i 0.138951 0.127570i
\(795\) 0 0
\(796\) −712.878 60.9921i −0.895575 0.0766233i
\(797\) −297.816 + 171.944i −0.373672 + 0.215739i −0.675061 0.737762i \(-0.735883\pi\)
0.301390 + 0.953501i \(0.402550\pi\)
\(798\) 0 0
\(799\) −12.9054 7.45091i −0.0161519 0.00932530i
\(800\) −799.050 + 38.7242i −0.998813 + 0.0484053i
\(801\) 0 0
\(802\) 359.587 1144.29i 0.448363 1.42679i
\(803\) −75.9790 + 131.600i −0.0946189 + 0.163885i
\(804\) 0 0
\(805\) −3.53150 + 2.03891i −0.00438696 + 0.00253281i
\(806\) 690.982 153.882i 0.857297 0.190920i
\(807\) 0 0
\(808\) 851.089 114.538i 1.05333 0.141755i
\(809\) −273.136 −0.337622 −0.168811 0.985648i \(-0.553993\pi\)
−0.168811 + 0.985648i \(0.553993\pi\)
\(810\) 0 0
\(811\) 615.310 0.758705 0.379352 0.925252i \(-0.376147\pi\)
0.379352 + 0.925252i \(0.376147\pi\)
\(812\) 629.311 294.923i 0.775014 0.363205i
\(813\) 0 0
\(814\) 132.367 + 594.371i 0.162613 + 0.730186i
\(815\) −0.599283 + 0.345996i −0.000735317 + 0.000424535i
\(816\) 0 0
\(817\) 346.971 600.971i 0.424689 0.735583i
\(818\) 328.782 1046.26i 0.401935 1.27905i
\(819\) 0 0
\(820\) −2.54543 + 3.65012i −0.00310418 + 0.00445137i
\(821\) −1110.25 641.002i −1.35231 0.780757i −0.363739 0.931501i \(-0.618500\pi\)
−0.988573 + 0.150744i \(0.951833\pi\)
\(822\) 0 0
\(823\) −241.117 + 139.209i −0.292973 + 0.169148i −0.639282 0.768972i \(-0.720768\pi\)
0.346309 + 0.938121i \(0.387435\pi\)
\(824\) 154.710 376.562i 0.187755 0.456993i
\(825\) 0 0
\(826\) 407.785 374.386i 0.493687 0.453252i
\(827\) −88.6450 −0.107189 −0.0535943 0.998563i \(-0.517068\pi\)
−0.0535943 + 0.998563i \(0.517068\pi\)
\(828\) 0 0
\(829\) 673.447i 0.812361i 0.913793 + 0.406180i \(0.133140\pi\)
−0.913793 + 0.406180i \(0.866860\pi\)
\(830\) −2.31529 + 2.12566i −0.00278950 + 0.00256103i
\(831\) 0 0
\(832\) 196.575 + 717.110i 0.236268 + 0.861911i
\(833\) −5.06642 8.77529i −0.00608213 0.0105346i
\(834\) 0 0
\(835\) 0.994591 1.72268i 0.00119113 0.00206309i
\(836\) 281.443 + 196.265i 0.336654 + 0.234767i
\(837\) 0 0
\(838\) 161.245 513.118i 0.192416 0.612313i
\(839\) −29.6126 17.0968i −0.0352951 0.0203776i 0.482249 0.876034i \(-0.339820\pi\)
−0.517544 + 0.855657i \(0.673154\pi\)
\(840\) 0 0
\(841\) 262.209 + 454.160i 0.311783 + 0.540024i
\(842\) 118.222 + 530.855i 0.140406 + 0.630469i
\(843\) 0 0
\(844\) 690.413 323.557i 0.818025 0.383362i
\(845\) 0.652059i 0.000771667i
\(846\) 0 0
\(847\) 416.236i 0.491424i
\(848\) −2.69043 + 15.6078i −0.00317267 + 0.0184054i
\(849\) 0 0
\(850\) 18.3899 4.09544i 0.0216352 0.00481816i
\(851\) −1208.58 2093.32i −1.42018 2.45983i
\(852\) 0 0
\(853\) −1052.33 607.564i −1.23368 0.712267i −0.265887 0.964004i \(-0.585665\pi\)
−0.967796 + 0.251737i \(0.918998\pi\)
\(854\) −244.497 + 778.046i −0.286297 + 0.911061i
\(855\) 0 0
\(856\) 314.855 243.038i 0.367821 0.283923i
\(857\) −462.160 + 800.484i −0.539276 + 0.934054i 0.459667 + 0.888091i \(0.347969\pi\)
−0.998943 + 0.0459627i \(0.985364\pi\)
\(858\) 0 0
\(859\) −625.687 1083.72i −0.728390 1.26161i −0.957563 0.288223i \(-0.906936\pi\)
0.229174 0.973386i \(-0.426398\pi\)
\(860\) 3.52202 + 0.301336i 0.00409538 + 0.000350391i
\(861\) 0 0
\(862\) 207.611 190.607i 0.240848 0.221122i
\(863\) 291.210i 0.337439i −0.985664 0.168719i \(-0.946037\pi\)
0.985664 0.168719i \(-0.0539632\pi\)
\(864\) 0 0
\(865\) 1.18632 0.00137147
\(866\) −878.028 956.358i −1.01389 1.10434i
\(867\) 0 0
\(868\) 48.8461 570.914i 0.0562743 0.657736i
\(869\) 690.755 398.808i 0.794885 0.458927i
\(870\) 0 0
\(871\) 687.101 + 396.698i 0.788864 + 0.455451i
\(872\) −197.180 255.446i −0.226124 0.292943i
\(873\) 0 0
\(874\) −1299.36 408.318i −1.48668 0.467183i
\(875\) −2.25324 + 3.90273i −0.00257514 + 0.00446027i
\(876\) 0 0
\(877\) 623.417 359.930i 0.710851 0.410410i −0.100525 0.994935i \(-0.532052\pi\)
0.811376 + 0.584524i \(0.198719\pi\)
\(878\) 68.1284 + 305.920i 0.0775950 + 0.348428i
\(879\) 0 0
\(880\) −0.296905 + 1.72242i −0.000337393 + 0.00195729i
\(881\) −136.645 −0.155102 −0.0775512 0.996988i \(-0.524710\pi\)
−0.0775512 + 0.996988i \(0.524710\pi\)
\(882\) 0 0
\(883\) −795.629 −0.901052 −0.450526 0.892763i \(-0.648764\pi\)
−0.450526 + 0.892763i \(0.648764\pi\)
\(884\) −7.43112 15.8567i −0.00840625 0.0179374i
\(885\) 0 0
\(886\) 27.0222 6.01785i 0.0304991 0.00679215i
\(887\) −92.9513 + 53.6654i −0.104793 + 0.0605022i −0.551480 0.834188i \(-0.685937\pi\)
0.446688 + 0.894690i \(0.352604\pi\)
\(888\) 0 0
\(889\) −89.8877 + 155.690i −0.101111 + 0.175129i
\(890\) 1.55938 + 0.490029i 0.00175212 + 0.000550594i
\(891\) 0 0
\(892\) −497.852 + 713.915i −0.558130 + 0.800353i
\(893\) 515.508 + 297.629i 0.577277 + 0.333291i
\(894\) 0 0
\(895\) −3.91712 + 2.26155i −0.00437667 + 0.00252687i
\(896\) 601.451 + 22.2186i 0.671262 + 0.0247975i
\(897\) 0 0
\(898\) −922.892 1005.22i −1.02772 1.11940i
\(899\) 1125.75 1.25222
\(900\) 0 0
\(901\) 0.372998i 0.000413982i
\(902\) −447.378 487.289i −0.495984 0.540232i
\(903\) 0 0
\(904\) 191.523 + 78.6872i 0.211862 + 0.0870434i
\(905\) 2.62988 + 4.55508i 0.00290594 + 0.00503324i
\(906\) 0 0
\(907\) 686.970 1189.87i 0.757409 1.31187i −0.186759 0.982406i \(-0.559798\pi\)
0.944168 0.329465i \(-0.106868\pi\)
\(908\) −450.068 313.857i −0.495670 0.345658i
\(909\) 0 0
\(910\) 1.99798 + 0.627856i 0.00219558 + 0.000689951i
\(911\) −166.832 96.3207i −0.183131 0.105731i 0.405632 0.914037i \(-0.367051\pi\)
−0.588763 + 0.808306i \(0.700385\pi\)
\(912\) 0 0
\(913\) −233.616 404.634i −0.255877 0.443192i
\(914\) 550.042 122.495i 0.601796 0.134020i
\(915\) 0 0
\(916\) −435.417 929.102i −0.475346 1.01430i
\(917\) 582.131i 0.634821i
\(918\) 0 0
\(919\) 818.741i 0.890905i −0.895306 0.445452i \(-0.853043\pi\)
0.895306 0.445452i \(-0.146957\pi\)
\(920\) −0.925359 6.87598i −0.00100582 0.00747389i
\(921\) 0 0
\(922\) −279.381 1254.51i −0.303016 1.36064i
\(923\) 246.053 + 426.177i 0.266580 + 0.461730i
\(924\) 0 0
\(925\) −1156.67 667.807i −1.25046 0.721953i
\(926\) −1164.09 365.809i −1.25711 0.395042i
\(927\) 0 0
\(928\) 57.2377 + 1181.06i 0.0616786 + 1.27270i
\(929\) 657.748 1139.25i 0.708017 1.22632i −0.257575 0.966258i \(-0.582923\pi\)
0.965592 0.260063i \(-0.0837434\pi\)
\(930\) 0 0
\(931\) 202.380 + 350.532i 0.217379 + 0.376511i
\(932\) 104.164 1217.47i 0.111764 1.30630i
\(933\) 0 0
\(934\) 391.251 + 426.155i 0.418898 + 0.456268i
\(935\) 0.0411627i 4.40242e-5i
\(936\) 0 0
\(937\) −521.572 −0.556640 −0.278320 0.960488i \(-0.589778\pi\)
−0.278320 + 0.960488i \(0.589778\pi\)
\(938\) 473.060 434.314i 0.504328 0.463022i
\(939\) 0 0
\(940\) −0.258484 + 3.02116i −0.000274983 + 0.00321401i
\(941\) −340.545 + 196.614i −0.361896 + 0.208941i −0.669912 0.742440i \(-0.733668\pi\)
0.308016 + 0.951381i \(0.400335\pi\)
\(942\) 0 0
\(943\) 2274.07 + 1312.93i 2.41153 + 1.39229i
\(944\) 325.525 + 883.817i 0.344836 + 0.936247i
\(945\) 0 0
\(946\) −157.533 + 501.306i −0.166526 + 0.529922i
\(947\) −437.860 + 758.396i −0.462366 + 0.800841i −0.999078 0.0429244i \(-0.986333\pi\)
0.536713 + 0.843765i \(0.319666\pi\)
\(948\) 0 0
\(949\) −268.288 + 154.896i −0.282706 + 0.163220i
\(950\) −734.590 + 163.593i −0.773252 + 0.172204i
\(951\) 0 0
\(952\) −14.0477 + 1.89052i −0.0147560 + 0.00198584i
\(953\) −71.0166 −0.0745190 −0.0372595 0.999306i \(-0.511863\pi\)
−0.0372595 + 0.999306i \(0.511863\pi\)
\(954\) 0 0
\(955\) −1.66803 −0.00174663
\(956\) 134.196 + 286.349i 0.140372 + 0.299529i
\(957\) 0 0
\(958\) 57.7650 + 259.384i 0.0602974 + 0.270756i
\(959\) 457.661 264.231i 0.477227 0.275527i
\(960\) 0 0
\(961\) −16.4259 + 28.4504i −0.0170925 + 0.0296050i
\(962\) −372.165 + 1184.31i −0.386866 + 1.23109i
\(963\) 0 0
\(964\) 731.028 + 509.786i 0.758327 + 0.528823i
\(965\) −1.72022 0.993171i −0.00178261 0.00102919i
\(966\) 0 0
\(967\) 194.113 112.071i 0.200737 0.115896i −0.396262 0.918137i \(-0.629693\pi\)
0.596999 + 0.802242i \(0.296359\pi\)
\(968\) 655.049 + 269.126i 0.676704 + 0.278023i
\(969\) 0 0
\(970\) 3.15880 2.90008i 0.00325650 0.00298978i
\(971\) −91.8845 −0.0946287 −0.0473144 0.998880i \(-0.515066\pi\)
−0.0473144 + 0.998880i \(0.515066\pi\)
\(972\) 0 0
\(973\) 528.390i 0.543053i
\(974\) −1179.91 + 1083.27i −1.21140 + 1.11218i
\(975\) 0 0
\(976\) −1066.36 887.839i −1.09258 0.909671i
\(977\) −368.517 638.289i −0.377192 0.653316i 0.613461 0.789725i \(-0.289777\pi\)
−0.990653 + 0.136410i \(0.956444\pi\)
\(978\) 0 0
\(979\) −121.492 + 210.431i −0.124098 + 0.214945i
\(980\) −1.17937 + 1.69120i −0.00120344 + 0.00172572i
\(981\) 0 0
\(982\) 500.022 1591.18i 0.509188 1.62035i
\(983\) 1534.66 + 886.034i 1.56120 + 0.901357i 0.997136 + 0.0756241i \(0.0240949\pi\)
0.564061 + 0.825733i \(0.309238\pi\)
\(984\) 0 0
\(985\) 1.91835 + 3.32267i 0.00194756 + 0.00337327i
\(986\) −6.05340 27.1818i −0.00613935 0.0275678i
\(987\) 0 0
\(988\) 296.838 + 633.399i 0.300444 + 0.641093i
\(989\) 2085.87i 2.10907i
\(990\) 0 0
\(991\) 1115.19i 1.12532i 0.826689 + 0.562659i \(0.190221\pi\)
−0.826689 + 0.562659i \(0.809779\pi\)
\(992\) 866.891 + 446.009i 0.873882 + 0.449605i
\(993\) 0 0
\(994\) 388.799 86.5857i 0.391146 0.0871084i
\(995\) −1.71433 2.96930i −0.00172294 0.00298423i
\(996\) 0 0
\(997\) 193.012 + 111.435i 0.193593 + 0.111771i 0.593663 0.804714i \(-0.297681\pi\)
−0.400071 + 0.916484i \(0.631014\pi\)
\(998\) −75.5153 + 240.307i −0.0756666 + 0.240788i
\(999\) 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 216.3.p.b.19.6 40
3.2 odd 2 72.3.p.b.43.15 yes 40
4.3 odd 2 864.3.t.b.559.10 40
8.3 odd 2 inner 216.3.p.b.19.19 40
8.5 even 2 864.3.t.b.559.11 40
9.2 odd 6 648.3.b.f.163.11 20
9.4 even 3 inner 216.3.p.b.91.19 40
9.5 odd 6 72.3.p.b.67.2 yes 40
9.7 even 3 648.3.b.e.163.10 20
12.11 even 2 288.3.t.b.79.2 40
24.5 odd 2 288.3.t.b.79.1 40
24.11 even 2 72.3.p.b.43.2 40
36.7 odd 6 2592.3.b.f.1135.10 20
36.11 even 6 2592.3.b.e.1135.11 20
36.23 even 6 288.3.t.b.175.1 40
36.31 odd 6 864.3.t.b.847.11 40
72.5 odd 6 288.3.t.b.175.2 40
72.11 even 6 648.3.b.f.163.12 20
72.13 even 6 864.3.t.b.847.10 40
72.29 odd 6 2592.3.b.e.1135.10 20
72.43 odd 6 648.3.b.e.163.9 20
72.59 even 6 72.3.p.b.67.15 yes 40
72.61 even 6 2592.3.b.f.1135.11 20
72.67 odd 6 inner 216.3.p.b.91.6 40
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
72.3.p.b.43.2 40 24.11 even 2
72.3.p.b.43.15 yes 40 3.2 odd 2
72.3.p.b.67.2 yes 40 9.5 odd 6
72.3.p.b.67.15 yes 40 72.59 even 6
216.3.p.b.19.6 40 1.1 even 1 trivial
216.3.p.b.19.19 40 8.3 odd 2 inner
216.3.p.b.91.6 40 72.67 odd 6 inner
216.3.p.b.91.19 40 9.4 even 3 inner
288.3.t.b.79.1 40 24.5 odd 2
288.3.t.b.79.2 40 12.11 even 2
288.3.t.b.175.1 40 36.23 even 6
288.3.t.b.175.2 40 72.5 odd 6
648.3.b.e.163.9 20 72.43 odd 6
648.3.b.e.163.10 20 9.7 even 3
648.3.b.f.163.11 20 9.2 odd 6
648.3.b.f.163.12 20 72.11 even 6
864.3.t.b.559.10 40 4.3 odd 2
864.3.t.b.559.11 40 8.5 even 2
864.3.t.b.847.10 40 72.13 even 6
864.3.t.b.847.11 40 36.31 odd 6
2592.3.b.e.1135.10 20 72.29 odd 6
2592.3.b.e.1135.11 20 36.11 even 6
2592.3.b.f.1135.10 20 36.7 odd 6
2592.3.b.f.1135.11 20 72.61 even 6