Properties

Label 99.3.k.c.19.4
Level $99$
Weight $3$
Character 99.19
Analytic conductor $2.698$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [99,3,Mod(19,99)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(99, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 3]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("99.19");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 99 = 3^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 99.k (of order \(10\), degree \(4\), 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: \(2.69755461717\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(4\) over \(\Q(\zeta_{10})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 2 x^{15} + 3 x^{14} - 4 x^{13} + 77 x^{12} + 88 x^{11} - 577 x^{10} + 578 x^{9} + 1520 x^{8} + 1868 x^{7} - 1619 x^{6} - 16804 x^{5} + 32427 x^{4} + 43316 x^{3} + \cdots + 83521 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 33)
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 19.4
Root \(2.24350 + 2.23726i\) of defining polynomial
Character \(\chi\) \(=\) 99.19
Dual form 99.3.k.c.73.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.577539 + 0.794915i) q^{2} +(0.937730 - 2.88604i) q^{4} +(0.321645 + 0.233689i) q^{5} +(6.87311 + 2.23321i) q^{7} +(6.57364 - 2.13591i) q^{8} +O(q^{10})\) \(q+(0.577539 + 0.794915i) q^{2} +(0.937730 - 2.88604i) q^{4} +(0.321645 + 0.233689i) q^{5} +(6.87311 + 2.23321i) q^{7} +(6.57364 - 2.13591i) q^{8} +0.390645i q^{10} +(0.495253 - 10.9888i) q^{11} +(7.14728 + 9.83739i) q^{13} +(2.19428 + 6.75330i) q^{14} +(-4.32564 - 3.14276i) q^{16} +(-12.2903 + 16.9162i) q^{17} +(-10.5689 + 3.43403i) q^{19} +(0.976052 - 0.709143i) q^{20} +(9.02122 - 5.95281i) q^{22} +5.92990 q^{23} +(-7.67658 - 23.6261i) q^{25} +(-3.69205 + 11.3630i) q^{26} +(12.8902 - 17.7419i) q^{28} +(-23.7332 - 7.71140i) q^{29} +(-48.2383 + 35.0472i) q^{31} -32.9013i q^{32} -20.5451 q^{34} +(1.68883 + 2.32447i) q^{35} +(-1.84391 + 5.67498i) q^{37} +(-8.83370 - 6.41806i) q^{38} +(2.61352 + 0.849184i) q^{40} +(49.4926 - 16.0811i) q^{41} +17.6439i q^{43} +(-31.2498 - 11.7339i) q^{44} +(3.42475 + 4.71376i) q^{46} +(17.1074 + 52.6513i) q^{47} +(2.61054 + 1.89667i) q^{49} +(14.3472 - 19.7472i) q^{50} +(35.0933 - 11.4025i) q^{52} +(-76.5751 + 55.6350i) q^{53} +(2.72727 - 3.41878i) q^{55} +49.9513 q^{56} +(-7.57698 - 23.3195i) q^{58} +(7.75795 - 23.8765i) q^{59} +(19.6356 - 27.0261i) q^{61} +(-55.7191 - 18.1042i) q^{62} +(8.85121 - 6.43078i) q^{64} +4.83439i q^{65} +94.6640 q^{67} +(37.2957 + 51.3331i) q^{68} +(-0.872392 + 2.68495i) q^{70} +(66.9252 + 48.6240i) q^{71} +(-44.2990 - 14.3936i) q^{73} +(-5.57606 + 1.81177i) q^{74} +33.7223i q^{76} +(27.9443 - 74.4215i) q^{77} +(35.4547 + 48.7992i) q^{79} +(-0.656893 - 2.02171i) q^{80} +(41.3671 + 30.0549i) q^{82} +(88.5635 - 121.897i) q^{83} +(-7.90625 + 2.56890i) q^{85} +(-14.0254 + 10.1900i) q^{86} +(-20.2155 - 73.2946i) q^{88} -134.190 q^{89} +(27.1551 + 83.5748i) q^{91} +(5.56064 - 17.1139i) q^{92} +(-31.9731 + 44.0072i) q^{94} +(-4.20192 - 1.36529i) q^{95} +(-30.4243 + 22.1046i) q^{97} +3.17056i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 20 q^{4} + 4 q^{5} - 30 q^{7} + 40 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 20 q^{4} + 4 q^{5} - 30 q^{7} + 40 q^{8} + 10 q^{11} + 30 q^{13} + 2 q^{14} + 16 q^{16} + 10 q^{17} - 42 q^{20} + 42 q^{22} - 132 q^{23} - 2 q^{25} - 46 q^{26} - 50 q^{28} - 160 q^{29} + 10 q^{31} - 368 q^{34} + 320 q^{35} - 126 q^{37} + 130 q^{38} + 30 q^{40} + 120 q^{41} + 206 q^{44} + 50 q^{46} + 150 q^{47} + 210 q^{49} - 330 q^{50} + 110 q^{52} - 342 q^{53} + 244 q^{55} - 524 q^{56} + 150 q^{58} - 110 q^{59} - 90 q^{61} - 40 q^{62} - 168 q^{64} + 36 q^{67} - 80 q^{68} + 340 q^{70} + 236 q^{71} - 350 q^{73} + 730 q^{74} + 390 q^{77} + 210 q^{79} + 806 q^{80} + 114 q^{82} + 190 q^{83} + 110 q^{85} - 736 q^{86} + 144 q^{88} - 76 q^{89} + 306 q^{91} + 150 q^{92} - 350 q^{94} - 430 q^{95} - 354 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/99\mathbb{Z}\right)^\times\).

\(n\) \(46\) \(56\)
\(\chi(n)\) \(e\left(\frac{3}{10}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.577539 + 0.794915i 0.288770 + 0.397457i 0.928614 0.371047i \(-0.121001\pi\)
−0.639844 + 0.768505i \(0.721001\pi\)
\(3\) 0 0
\(4\) 0.937730 2.88604i 0.234433 0.721509i
\(5\) 0.321645 + 0.233689i 0.0643291 + 0.0467378i 0.619485 0.785008i \(-0.287341\pi\)
−0.555156 + 0.831746i \(0.687341\pi\)
\(6\) 0 0
\(7\) 6.87311 + 2.23321i 0.981872 + 0.319030i 0.755599 0.655034i \(-0.227346\pi\)
0.226273 + 0.974064i \(0.427346\pi\)
\(8\) 6.57364 2.13591i 0.821705 0.266988i
\(9\) 0 0
\(10\) 0.390645i 0.0390645i
\(11\) 0.495253 10.9888i 0.0450230 0.998986i
\(12\) 0 0
\(13\) 7.14728 + 9.83739i 0.549791 + 0.756722i 0.989984 0.141181i \(-0.0450899\pi\)
−0.440193 + 0.897903i \(0.645090\pi\)
\(14\) 2.19428 + 6.75330i 0.156734 + 0.482379i
\(15\) 0 0
\(16\) −4.32564 3.14276i −0.270352 0.196422i
\(17\) −12.2903 + 16.9162i −0.722960 + 0.995069i 0.276460 + 0.961025i \(0.410839\pi\)
−0.999420 + 0.0340440i \(0.989161\pi\)
\(18\) 0 0
\(19\) −10.5689 + 3.43403i −0.556256 + 0.180739i −0.573636 0.819110i \(-0.694468\pi\)
0.0173798 + 0.999849i \(0.494468\pi\)
\(20\) 0.976052 0.709143i 0.0488026 0.0354572i
\(21\) 0 0
\(22\) 9.02122 5.95281i 0.410056 0.270582i
\(23\) 5.92990 0.257822 0.128911 0.991656i \(-0.458852\pi\)
0.128911 + 0.991656i \(0.458852\pi\)
\(24\) 0 0
\(25\) −7.67658 23.6261i −0.307063 0.945043i
\(26\) −3.69205 + 11.3630i −0.142002 + 0.437037i
\(27\) 0 0
\(28\) 12.8902 17.7419i 0.460366 0.633639i
\(29\) −23.7332 7.71140i −0.818388 0.265910i −0.130242 0.991482i \(-0.541575\pi\)
−0.688146 + 0.725572i \(0.741575\pi\)
\(30\) 0 0
\(31\) −48.2383 + 35.0472i −1.55607 + 1.13055i −0.616937 + 0.787012i \(0.711627\pi\)
−0.939137 + 0.343542i \(0.888373\pi\)
\(32\) 32.9013i 1.02817i
\(33\) 0 0
\(34\) −20.5451 −0.604267
\(35\) 1.68883 + 2.32447i 0.0482522 + 0.0664135i
\(36\) 0 0
\(37\) −1.84391 + 5.67498i −0.0498355 + 0.153378i −0.972877 0.231322i \(-0.925695\pi\)
0.923042 + 0.384700i \(0.125695\pi\)
\(38\) −8.83370 6.41806i −0.232466 0.168896i
\(39\) 0 0
\(40\) 2.61352 + 0.849184i 0.0653380 + 0.0212296i
\(41\) 49.4926 16.0811i 1.20714 0.392223i 0.364755 0.931104i \(-0.381153\pi\)
0.842382 + 0.538881i \(0.181153\pi\)
\(42\) 0 0
\(43\) 17.6439i 0.410323i 0.978728 + 0.205161i \(0.0657719\pi\)
−0.978728 + 0.205161i \(0.934228\pi\)
\(44\) −31.2498 11.7339i −0.710223 0.266679i
\(45\) 0 0
\(46\) 3.42475 + 4.71376i 0.0744511 + 0.102473i
\(47\) 17.1074 + 52.6513i 0.363988 + 1.12024i 0.950612 + 0.310381i \(0.100457\pi\)
−0.586624 + 0.809860i \(0.699543\pi\)
\(48\) 0 0
\(49\) 2.61054 + 1.89667i 0.0532763 + 0.0387075i
\(50\) 14.3472 19.7472i 0.286944 0.394944i
\(51\) 0 0
\(52\) 35.0933 11.4025i 0.674871 0.219279i
\(53\) −76.5751 + 55.6350i −1.44481 + 1.04972i −0.457803 + 0.889054i \(0.651364\pi\)
−0.987009 + 0.160664i \(0.948636\pi\)
\(54\) 0 0
\(55\) 2.72727 3.41878i 0.0495867 0.0621596i
\(56\) 49.9513 0.891987
\(57\) 0 0
\(58\) −7.57698 23.3195i −0.130638 0.402061i
\(59\) 7.75795 23.8765i 0.131491 0.404687i −0.863537 0.504285i \(-0.831756\pi\)
0.995028 + 0.0995988i \(0.0317559\pi\)
\(60\) 0 0
\(61\) 19.6356 27.0261i 0.321896 0.443052i −0.617149 0.786846i \(-0.711712\pi\)
0.939045 + 0.343795i \(0.111712\pi\)
\(62\) −55.7191 18.1042i −0.898694 0.292004i
\(63\) 0 0
\(64\) 8.85121 6.43078i 0.138300 0.100481i
\(65\) 4.83439i 0.0743753i
\(66\) 0 0
\(67\) 94.6640 1.41290 0.706448 0.707765i \(-0.250296\pi\)
0.706448 + 0.707765i \(0.250296\pi\)
\(68\) 37.2957 + 51.3331i 0.548466 + 0.754899i
\(69\) 0 0
\(70\) −0.872392 + 2.68495i −0.0124627 + 0.0383564i
\(71\) 66.9252 + 48.6240i 0.942609 + 0.684845i 0.949047 0.315134i \(-0.102049\pi\)
−0.00643861 + 0.999979i \(0.502049\pi\)
\(72\) 0 0
\(73\) −44.2990 14.3936i −0.606836 0.197173i −0.0105491 0.999944i \(-0.503358\pi\)
−0.596287 + 0.802771i \(0.703358\pi\)
\(74\) −5.57606 + 1.81177i −0.0753522 + 0.0244834i
\(75\) 0 0
\(76\) 33.7223i 0.443715i
\(77\) 27.9443 74.4215i 0.362913 0.966513i
\(78\) 0 0
\(79\) 35.4547 + 48.7992i 0.448794 + 0.617712i 0.972138 0.234410i \(-0.0753158\pi\)
−0.523344 + 0.852121i \(0.675316\pi\)
\(80\) −0.656893 2.02171i −0.00821116 0.0252713i
\(81\) 0 0
\(82\) 41.3671 + 30.0549i 0.504476 + 0.366524i
\(83\) 88.5635 121.897i 1.06703 1.46864i 0.193982 0.981005i \(-0.437860\pi\)
0.873048 0.487635i \(-0.162140\pi\)
\(84\) 0 0
\(85\) −7.90625 + 2.56890i −0.0930147 + 0.0302223i
\(86\) −14.0254 + 10.1900i −0.163086 + 0.118489i
\(87\) 0 0
\(88\) −20.2155 73.2946i −0.229722 0.832893i
\(89\) −134.190 −1.50775 −0.753874 0.657019i \(-0.771817\pi\)
−0.753874 + 0.657019i \(0.771817\pi\)
\(90\) 0 0
\(91\) 27.1551 + 83.5748i 0.298408 + 0.918405i
\(92\) 5.56064 17.1139i 0.0604418 0.186021i
\(93\) 0 0
\(94\) −31.9731 + 44.0072i −0.340139 + 0.468161i
\(95\) −4.20192 1.36529i −0.0442308 0.0143715i
\(96\) 0 0
\(97\) −30.4243 + 22.1046i −0.313653 + 0.227882i −0.733462 0.679730i \(-0.762097\pi\)
0.419809 + 0.907612i \(0.362097\pi\)
\(98\) 3.17056i 0.0323526i
\(99\) 0 0
\(100\) −75.3843 −0.753843
\(101\) 47.4940 + 65.3699i 0.470238 + 0.647227i 0.976592 0.215098i \(-0.0690072\pi\)
−0.506354 + 0.862325i \(0.669007\pi\)
\(102\) 0 0
\(103\) 30.7976 94.7853i 0.299006 0.920246i −0.682840 0.730568i \(-0.739256\pi\)
0.981846 0.189678i \(-0.0607444\pi\)
\(104\) 67.9954 + 49.4016i 0.653802 + 0.475015i
\(105\) 0 0
\(106\) −88.4502 28.7392i −0.834436 0.271125i
\(107\) −102.955 + 33.4522i −0.962199 + 0.312637i −0.747663 0.664079i \(-0.768824\pi\)
−0.214536 + 0.976716i \(0.568824\pi\)
\(108\) 0 0
\(109\) 175.446i 1.60960i −0.593546 0.804800i \(-0.702273\pi\)
0.593546 0.804800i \(-0.297727\pi\)
\(110\) 4.29274 + 0.193468i 0.0390249 + 0.00175880i
\(111\) 0 0
\(112\) −22.7121 31.2606i −0.202787 0.279112i
\(113\) −30.4454 93.7013i −0.269428 0.829215i −0.990640 0.136500i \(-0.956414\pi\)
0.721212 0.692715i \(-0.243586\pi\)
\(114\) 0 0
\(115\) 1.90732 + 1.38575i 0.0165854 + 0.0120500i
\(116\) −44.5108 + 61.2638i −0.383713 + 0.528136i
\(117\) 0 0
\(118\) 23.4603 7.62272i 0.198816 0.0645993i
\(119\) −122.250 + 88.8199i −1.02731 + 0.746385i
\(120\) 0 0
\(121\) −120.509 10.8845i −0.995946 0.0899546i
\(122\) 32.8238 0.269048
\(123\) 0 0
\(124\) 55.9129 + 172.082i 0.450911 + 1.38776i
\(125\) 6.12346 18.8461i 0.0489877 0.150769i
\(126\) 0 0
\(127\) −12.8526 + 17.6901i −0.101202 + 0.139292i −0.856614 0.515957i \(-0.827436\pi\)
0.755413 + 0.655249i \(0.227436\pi\)
\(128\) −114.940 37.3464i −0.897971 0.291768i
\(129\) 0 0
\(130\) −3.84293 + 2.79205i −0.0295610 + 0.0214773i
\(131\) 16.3593i 0.124880i −0.998049 0.0624402i \(-0.980112\pi\)
0.998049 0.0624402i \(-0.0198883\pi\)
\(132\) 0 0
\(133\) −80.3099 −0.603834
\(134\) 54.6722 + 75.2499i 0.408002 + 0.561566i
\(135\) 0 0
\(136\) −44.6608 + 137.452i −0.328388 + 1.01068i
\(137\) 24.7472 + 17.9799i 0.180637 + 0.131240i 0.674429 0.738340i \(-0.264390\pi\)
−0.493793 + 0.869580i \(0.664390\pi\)
\(138\) 0 0
\(139\) −26.3884 8.57411i −0.189845 0.0616843i 0.212552 0.977150i \(-0.431823\pi\)
−0.402396 + 0.915466i \(0.631823\pi\)
\(140\) 8.29217 2.69429i 0.0592298 0.0192449i
\(141\) 0 0
\(142\) 81.2821i 0.572409i
\(143\) 111.641 73.6684i 0.780708 0.515164i
\(144\) 0 0
\(145\) −5.83162 8.02654i −0.0402181 0.0553554i
\(146\) −14.1427 43.5268i −0.0968680 0.298129i
\(147\) 0 0
\(148\) 14.6491 + 10.6432i 0.0989805 + 0.0719135i
\(149\) 116.856 160.838i 0.784265 1.07945i −0.210533 0.977587i \(-0.567520\pi\)
0.994799 0.101862i \(-0.0324800\pi\)
\(150\) 0 0
\(151\) 124.120 40.3290i 0.821986 0.267079i 0.132320 0.991207i \(-0.457757\pi\)
0.689666 + 0.724128i \(0.257757\pi\)
\(152\) −62.1412 + 45.1482i −0.408824 + 0.297028i
\(153\) 0 0
\(154\) 75.2977 20.7680i 0.488946 0.134857i
\(155\) −23.7058 −0.152940
\(156\) 0 0
\(157\) −21.8126 67.1324i −0.138934 0.427595i 0.857247 0.514905i \(-0.172173\pi\)
−0.996181 + 0.0873102i \(0.972173\pi\)
\(158\) −18.3147 + 56.3669i −0.115916 + 0.356753i
\(159\) 0 0
\(160\) 7.68868 10.5826i 0.0480543 0.0661410i
\(161\) 40.7568 + 13.2427i 0.253148 + 0.0822527i
\(162\) 0 0
\(163\) 62.2214 45.2065i 0.381726 0.277340i −0.380330 0.924851i \(-0.624190\pi\)
0.762057 + 0.647510i \(0.224190\pi\)
\(164\) 157.917i 0.962910i
\(165\) 0 0
\(166\) 148.047 0.891848
\(167\) 59.8117 + 82.3237i 0.358154 + 0.492956i 0.949633 0.313364i \(-0.101456\pi\)
−0.591479 + 0.806320i \(0.701456\pi\)
\(168\) 0 0
\(169\) 6.53325 20.1073i 0.0386583 0.118978i
\(170\) −6.60823 4.80116i −0.0388719 0.0282421i
\(171\) 0 0
\(172\) 50.9209 + 16.5452i 0.296052 + 0.0961930i
\(173\) 118.789 38.5969i 0.686643 0.223104i 0.0551414 0.998479i \(-0.482439\pi\)
0.631501 + 0.775375i \(0.282439\pi\)
\(174\) 0 0
\(175\) 179.528i 1.02587i
\(176\) −36.6776 + 45.9773i −0.208395 + 0.261235i
\(177\) 0 0
\(178\) −77.4997 106.669i −0.435392 0.599265i
\(179\) 31.8999 + 98.1779i 0.178212 + 0.548480i 0.999766 0.0216514i \(-0.00689238\pi\)
−0.821554 + 0.570131i \(0.806892\pi\)
\(180\) 0 0
\(181\) 90.9834 + 66.1033i 0.502671 + 0.365212i 0.810036 0.586380i \(-0.199447\pi\)
−0.307365 + 0.951592i \(0.599447\pi\)
\(182\) −50.7517 + 69.8537i −0.278856 + 0.383812i
\(183\) 0 0
\(184\) 38.9810 12.6657i 0.211853 0.0688353i
\(185\) −1.91927 + 1.39443i −0.0103744 + 0.00753746i
\(186\) 0 0
\(187\) 179.802 + 143.434i 0.961511 + 0.767028i
\(188\) 167.996 0.893595
\(189\) 0 0
\(190\) −1.34149 4.12868i −0.00706047 0.0217299i
\(191\) −59.0444 + 181.720i −0.309133 + 0.951414i 0.668969 + 0.743290i \(0.266736\pi\)
−0.978102 + 0.208124i \(0.933264\pi\)
\(192\) 0 0
\(193\) 32.0683 44.1382i 0.166157 0.228695i −0.717817 0.696232i \(-0.754858\pi\)
0.883974 + 0.467537i \(0.154858\pi\)
\(194\) −35.1425 11.4185i −0.181147 0.0588582i
\(195\) 0 0
\(196\) 7.92184 5.75555i 0.0404175 0.0293651i
\(197\) 75.2950i 0.382208i −0.981570 0.191104i \(-0.938793\pi\)
0.981570 0.191104i \(-0.0612068\pi\)
\(198\) 0 0
\(199\) −60.7193 −0.305122 −0.152561 0.988294i \(-0.548752\pi\)
−0.152561 + 0.988294i \(0.548752\pi\)
\(200\) −100.926 138.913i −0.504631 0.694565i
\(201\) 0 0
\(202\) −24.5338 + 75.5074i −0.121455 + 0.373799i
\(203\) −145.900 106.003i −0.718719 0.522180i
\(204\) 0 0
\(205\) 19.6771 + 6.39346i 0.0959856 + 0.0311876i
\(206\) 93.1331 30.2608i 0.452102 0.146897i
\(207\) 0 0
\(208\) 65.0152i 0.312573i
\(209\) 32.5018 + 117.840i 0.155511 + 0.563830i
\(210\) 0 0
\(211\) 240.517 + 331.043i 1.13989 + 1.56893i 0.767751 + 0.640748i \(0.221376\pi\)
0.372140 + 0.928177i \(0.378624\pi\)
\(212\) 88.7580 + 273.169i 0.418670 + 1.28853i
\(213\) 0 0
\(214\) −86.0524 62.5207i −0.402114 0.292153i
\(215\) −4.12318 + 5.67507i −0.0191776 + 0.0263957i
\(216\) 0 0
\(217\) −409.815 + 133.157i −1.88855 + 0.613626i
\(218\) 139.465 101.327i 0.639747 0.464804i
\(219\) 0 0
\(220\) −7.30927 11.0769i −0.0332240 0.0503495i
\(221\) −254.254 −1.15047
\(222\) 0 0
\(223\) −45.5218 140.102i −0.204133 0.628258i −0.999748 0.0224549i \(-0.992852\pi\)
0.795614 0.605803i \(-0.207148\pi\)
\(224\) 73.4755 226.134i 0.328016 1.00953i
\(225\) 0 0
\(226\) 56.9011 78.3177i 0.251775 0.346539i
\(227\) 130.316 + 42.3421i 0.574078 + 0.186529i 0.581646 0.813442i \(-0.302409\pi\)
−0.00756813 + 0.999971i \(0.502409\pi\)
\(228\) 0 0
\(229\) −69.3377 + 50.3768i −0.302785 + 0.219986i −0.728794 0.684733i \(-0.759919\pi\)
0.426010 + 0.904719i \(0.359919\pi\)
\(230\) 2.31649i 0.0100717i
\(231\) 0 0
\(232\) −172.485 −0.743469
\(233\) −127.215 175.096i −0.545986 0.751486i 0.443474 0.896287i \(-0.353746\pi\)
−0.989461 + 0.144801i \(0.953746\pi\)
\(234\) 0 0
\(235\) −6.80150 + 20.9329i −0.0289426 + 0.0890761i
\(236\) −61.6336 44.7794i −0.261159 0.189743i
\(237\) 0 0
\(238\) −141.208 45.8814i −0.593313 0.192779i
\(239\) −157.155 + 51.0629i −0.657554 + 0.213652i −0.618742 0.785594i \(-0.712357\pi\)
−0.0388122 + 0.999247i \(0.512357\pi\)
\(240\) 0 0
\(241\) 233.818i 0.970199i 0.874459 + 0.485100i \(0.161217\pi\)
−0.874459 + 0.485100i \(0.838783\pi\)
\(242\) −60.9467 102.081i −0.251846 0.421822i
\(243\) 0 0
\(244\) −59.5855 82.0124i −0.244203 0.336116i
\(245\) 0.396437 + 1.22011i 0.00161811 + 0.00498004i
\(246\) 0 0
\(247\) −109.321 79.4261i −0.442594 0.321563i
\(248\) −242.244 + 333.420i −0.976790 + 1.34444i
\(249\) 0 0
\(250\) 18.5176 6.01672i 0.0740703 0.0240669i
\(251\) 216.317 157.163i 0.861819 0.626148i −0.0665602 0.997782i \(-0.521202\pi\)
0.928379 + 0.371634i \(0.121202\pi\)
\(252\) 0 0
\(253\) 2.93680 65.1627i 0.0116079 0.257560i
\(254\) −21.4850 −0.0845866
\(255\) 0 0
\(256\) −50.2188 154.558i −0.196167 0.603741i
\(257\) −15.3004 + 47.0899i −0.0595348 + 0.183229i −0.976401 0.215965i \(-0.930710\pi\)
0.916866 + 0.399195i \(0.130710\pi\)
\(258\) 0 0
\(259\) −25.3468 + 34.8869i −0.0978642 + 0.134698i
\(260\) 13.9522 + 4.53336i 0.0536625 + 0.0174360i
\(261\) 0 0
\(262\) 13.0043 9.44816i 0.0496347 0.0360617i
\(263\) 198.763i 0.755752i 0.925856 + 0.377876i \(0.123345\pi\)
−0.925856 + 0.377876i \(0.876655\pi\)
\(264\) 0 0
\(265\) −37.6313 −0.142005
\(266\) −46.3821 63.8395i −0.174369 0.239998i
\(267\) 0 0
\(268\) 88.7693 273.204i 0.331229 1.01942i
\(269\) 8.71548 + 6.33217i 0.0323995 + 0.0235397i 0.603867 0.797085i \(-0.293626\pi\)
−0.571468 + 0.820625i \(0.693626\pi\)
\(270\) 0 0
\(271\) 277.924 + 90.3028i 1.02555 + 0.333221i 0.773029 0.634371i \(-0.218741\pi\)
0.252520 + 0.967592i \(0.418741\pi\)
\(272\) 106.327 34.5477i 0.390908 0.127014i
\(273\) 0 0
\(274\) 30.0560i 0.109693i
\(275\) −263.425 + 72.6559i −0.957910 + 0.264203i
\(276\) 0 0
\(277\) −103.077 141.874i −0.372120 0.512179i 0.581356 0.813650i \(-0.302523\pi\)
−0.953476 + 0.301470i \(0.902523\pi\)
\(278\) −8.42466 25.9284i −0.0303045 0.0932677i
\(279\) 0 0
\(280\) 16.0666 + 11.6731i 0.0573807 + 0.0416895i
\(281\) −133.651 + 183.955i −0.475626 + 0.654644i −0.977657 0.210206i \(-0.932586\pi\)
0.502031 + 0.864850i \(0.332586\pi\)
\(282\) 0 0
\(283\) −225.825 + 73.3749i −0.797967 + 0.259275i −0.679493 0.733682i \(-0.737800\pi\)
−0.118474 + 0.992957i \(0.537800\pi\)
\(284\) 203.088 147.552i 0.715100 0.519551i
\(285\) 0 0
\(286\) 123.037 + 46.1989i 0.430201 + 0.161535i
\(287\) 376.080 1.31038
\(288\) 0 0
\(289\) −45.7992 140.955i −0.158475 0.487735i
\(290\) 3.01242 9.27128i 0.0103877 0.0319699i
\(291\) 0 0
\(292\) −83.0811 + 114.351i −0.284524 + 0.391614i
\(293\) −27.8981 9.06463i −0.0952152 0.0309373i 0.261022 0.965333i \(-0.415940\pi\)
−0.356237 + 0.934396i \(0.615940\pi\)
\(294\) 0 0
\(295\) 8.07499 5.86682i 0.0273728 0.0198875i
\(296\) 41.2437i 0.139337i
\(297\) 0 0
\(298\) 195.341 0.655507
\(299\) 42.3827 + 58.3347i 0.141748 + 0.195099i
\(300\) 0 0
\(301\) −39.4025 + 121.268i −0.130905 + 0.402885i
\(302\) 103.742 + 75.3731i 0.343517 + 0.249580i
\(303\) 0 0
\(304\) 56.5094 + 18.3610i 0.185886 + 0.0603981i
\(305\) 12.6314 4.10420i 0.0414145 0.0134564i
\(306\) 0 0
\(307\) 347.331i 1.13137i 0.824621 + 0.565686i \(0.191389\pi\)
−0.824621 + 0.565686i \(0.808611\pi\)
\(308\) −188.579 150.436i −0.612269 0.488427i
\(309\) 0 0
\(310\) −13.6910 18.8441i −0.0441646 0.0607873i
\(311\) −136.144 419.008i −0.437762 1.34729i −0.890230 0.455512i \(-0.849456\pi\)
0.452467 0.891781i \(-0.350544\pi\)
\(312\) 0 0
\(313\) 20.6012 + 14.9677i 0.0658186 + 0.0478200i 0.620208 0.784437i \(-0.287048\pi\)
−0.554389 + 0.832257i \(0.687048\pi\)
\(314\) 40.7669 56.1108i 0.129831 0.178697i
\(315\) 0 0
\(316\) 174.083 56.5631i 0.550896 0.178997i
\(317\) 73.9310 53.7140i 0.233221 0.169445i −0.465037 0.885291i \(-0.653959\pi\)
0.698258 + 0.715846i \(0.253959\pi\)
\(318\) 0 0
\(319\) −96.4933 + 256.982i −0.302487 + 0.805586i
\(320\) 4.34975 0.0135930
\(321\) 0 0
\(322\) 13.0119 + 40.0464i 0.0404095 + 0.124368i
\(323\) 71.8041 220.990i 0.222304 0.684180i
\(324\) 0 0
\(325\) 177.552 244.380i 0.546315 0.751938i
\(326\) 71.8706 + 23.3522i 0.220462 + 0.0716324i
\(327\) 0 0
\(328\) 290.999 211.423i 0.887192 0.644583i
\(329\) 400.083i 1.21606i
\(330\) 0 0
\(331\) −318.761 −0.963024 −0.481512 0.876439i \(-0.659912\pi\)
−0.481512 + 0.876439i \(0.659912\pi\)
\(332\) −268.751 369.904i −0.809491 1.11417i
\(333\) 0 0
\(334\) −30.8967 + 95.0904i −0.0925052 + 0.284702i
\(335\) 30.4483 + 22.1220i 0.0908903 + 0.0660357i
\(336\) 0 0
\(337\) 587.526 + 190.899i 1.74340 + 0.566465i 0.995275 0.0970929i \(-0.0309544\pi\)
0.748125 + 0.663558i \(0.230954\pi\)
\(338\) 19.7568 6.41937i 0.0584520 0.0189922i
\(339\) 0 0
\(340\) 25.2267i 0.0741961i
\(341\) 361.238 + 547.441i 1.05935 + 1.60540i
\(342\) 0 0
\(343\) −194.436 267.618i −0.566869 0.780228i
\(344\) 37.6857 + 115.985i 0.109551 + 0.337165i
\(345\) 0 0
\(346\) 99.2867 + 72.1360i 0.286956 + 0.208486i
\(347\) 118.221 162.717i 0.340694 0.468925i −0.603950 0.797022i \(-0.706407\pi\)
0.944644 + 0.328097i \(0.106407\pi\)
\(348\) 0 0
\(349\) 461.013 149.792i 1.32095 0.429204i 0.438131 0.898911i \(-0.355640\pi\)
0.882822 + 0.469707i \(0.155640\pi\)
\(350\) 142.709 103.684i 0.407741 0.296241i
\(351\) 0 0
\(352\) −361.548 16.2945i −1.02712 0.0462911i
\(353\) −108.957 −0.308661 −0.154330 0.988019i \(-0.549322\pi\)
−0.154330 + 0.988019i \(0.549322\pi\)
\(354\) 0 0
\(355\) 10.1633 + 31.2794i 0.0286290 + 0.0881109i
\(356\) −125.834 + 387.276i −0.353465 + 1.08785i
\(357\) 0 0
\(358\) −59.6196 + 82.0593i −0.166535 + 0.229216i
\(359\) 407.539 + 132.418i 1.13521 + 0.368851i 0.815553 0.578683i \(-0.196433\pi\)
0.319655 + 0.947534i \(0.396433\pi\)
\(360\) 0 0
\(361\) −192.147 + 139.603i −0.532262 + 0.386711i
\(362\) 110.501i 0.305252i
\(363\) 0 0
\(364\) 266.664 0.732594
\(365\) −10.8849 14.9818i −0.0298218 0.0410462i
\(366\) 0 0
\(367\) 132.239 406.991i 0.360325 1.10897i −0.592532 0.805547i \(-0.701871\pi\)
0.952857 0.303420i \(-0.0981285\pi\)
\(368\) −25.6506 18.6362i −0.0697027 0.0506419i
\(369\) 0 0
\(370\) −2.21691 0.720316i −0.00599164 0.00194680i
\(371\) −650.553 + 211.377i −1.75351 + 0.569751i
\(372\) 0 0
\(373\) 104.312i 0.279656i −0.990176 0.139828i \(-0.955345\pi\)
0.990176 0.139828i \(-0.0446549\pi\)
\(374\) −10.1750 + 225.767i −0.0272059 + 0.603654i
\(375\) 0 0
\(376\) 224.917 + 309.571i 0.598182 + 0.823327i
\(377\) −93.7682 288.589i −0.248722 0.765488i
\(378\) 0 0
\(379\) −181.753 132.051i −0.479558 0.348420i 0.321596 0.946877i \(-0.395781\pi\)
−0.801155 + 0.598457i \(0.795781\pi\)
\(380\) −7.88054 + 10.8466i −0.0207383 + 0.0285438i
\(381\) 0 0
\(382\) −178.552 + 58.0152i −0.467415 + 0.151872i
\(383\) 47.9484 34.8366i 0.125192 0.0909571i −0.523427 0.852070i \(-0.675347\pi\)
0.648619 + 0.761113i \(0.275347\pi\)
\(384\) 0 0
\(385\) 26.3796 17.4071i 0.0685186 0.0452131i
\(386\) 53.6068 0.138878
\(387\) 0 0
\(388\) 35.2648 + 108.534i 0.0908886 + 0.279726i
\(389\) 127.369 392.001i 0.327426 1.00771i −0.642908 0.765944i \(-0.722272\pi\)
0.970334 0.241770i \(-0.0777279\pi\)
\(390\) 0 0
\(391\) −72.8804 + 100.311i −0.186395 + 0.256550i
\(392\) 21.2119 + 6.89215i 0.0541119 + 0.0175820i
\(393\) 0 0
\(394\) 59.8531 43.4858i 0.151911 0.110370i
\(395\) 23.9814i 0.0607125i
\(396\) 0 0
\(397\) 619.925 1.56152 0.780762 0.624829i \(-0.214831\pi\)
0.780762 + 0.624829i \(0.214831\pi\)
\(398\) −35.0678 48.2666i −0.0881100 0.121273i
\(399\) 0 0
\(400\) −41.0450 + 126.323i −0.102612 + 0.315809i
\(401\) −543.725 395.039i −1.35592 0.985135i −0.998693 0.0511186i \(-0.983721\pi\)
−0.357230 0.934017i \(-0.616279\pi\)
\(402\) 0 0
\(403\) −689.546 224.047i −1.71103 0.555948i
\(404\) 233.197 75.7702i 0.577219 0.187550i
\(405\) 0 0
\(406\) 177.199i 0.436450i
\(407\) 61.4483 + 23.0730i 0.150979 + 0.0566905i
\(408\) 0 0
\(409\) −361.103 497.016i −0.882893 1.21520i −0.975611 0.219505i \(-0.929556\pi\)
0.0927184 0.995692i \(-0.470444\pi\)
\(410\) 6.28202 + 19.3341i 0.0153220 + 0.0471562i
\(411\) 0 0
\(412\) −244.674 177.766i −0.593869 0.431471i
\(413\) 106.642 146.781i 0.258214 0.355401i
\(414\) 0 0
\(415\) 56.9721 18.5113i 0.137282 0.0446056i
\(416\) 323.663 235.155i 0.778037 0.565277i
\(417\) 0 0
\(418\) −74.9020 + 93.8936i −0.179191 + 0.224626i
\(419\) 60.9488 0.145462 0.0727312 0.997352i \(-0.476828\pi\)
0.0727312 + 0.997352i \(0.476828\pi\)
\(420\) 0 0
\(421\) 64.4635 + 198.398i 0.153120 + 0.471255i 0.997966 0.0637555i \(-0.0203078\pi\)
−0.844846 + 0.535010i \(0.820308\pi\)
\(422\) −124.243 + 382.381i −0.294415 + 0.906116i
\(423\) 0 0
\(424\) −384.546 + 529.282i −0.906948 + 1.24831i
\(425\) 494.011 + 160.514i 1.16238 + 0.377680i
\(426\) 0 0
\(427\) 195.313 141.903i 0.457407 0.332326i
\(428\) 328.502i 0.767528i
\(429\) 0 0
\(430\) −6.89250 −0.0160291
\(431\) −159.126 219.018i −0.369202 0.508163i 0.583482 0.812126i \(-0.301690\pi\)
−0.952684 + 0.303963i \(0.901690\pi\)
\(432\) 0 0
\(433\) −193.847 + 596.600i −0.447684 + 1.37783i 0.431830 + 0.901955i \(0.357868\pi\)
−0.879514 + 0.475873i \(0.842132\pi\)
\(434\) −342.532 248.864i −0.789245 0.573420i
\(435\) 0 0
\(436\) −506.345 164.521i −1.16134 0.377343i
\(437\) −62.6723 + 20.3635i −0.143415 + 0.0465983i
\(438\) 0 0
\(439\) 495.244i 1.12812i 0.825734 + 0.564060i \(0.190761\pi\)
−0.825734 + 0.564060i \(0.809239\pi\)
\(440\) 10.6259 28.2990i 0.0241498 0.0643159i
\(441\) 0 0
\(442\) −146.841 202.110i −0.332220 0.457262i
\(443\) −229.292 705.688i −0.517589 1.59298i −0.778521 0.627618i \(-0.784030\pi\)
0.260932 0.965357i \(-0.415970\pi\)
\(444\) 0 0
\(445\) −43.1614 31.3586i −0.0969920 0.0704688i
\(446\) 85.0782 117.100i 0.190758 0.262556i
\(447\) 0 0
\(448\) 75.1966 24.4329i 0.167850 0.0545376i
\(449\) −577.287 + 419.423i −1.28572 + 0.934128i −0.999710 0.0240995i \(-0.992328\pi\)
−0.286007 + 0.958227i \(0.592328\pi\)
\(450\) 0 0
\(451\) −152.202 551.831i −0.337476 1.22357i
\(452\) −298.975 −0.661449
\(453\) 0 0
\(454\) 41.6040 + 128.044i 0.0916388 + 0.282035i
\(455\) −10.7962 + 33.2273i −0.0237279 + 0.0730270i
\(456\) 0 0
\(457\) −166.058 + 228.559i −0.363364 + 0.500128i −0.951082 0.308938i \(-0.900027\pi\)
0.587718 + 0.809066i \(0.300027\pi\)
\(458\) −80.0905 26.0230i −0.174870 0.0568187i
\(459\) 0 0
\(460\) 5.78789 4.20515i 0.0125824 0.00914162i
\(461\) 198.186i 0.429905i 0.976624 + 0.214953i \(0.0689597\pi\)
−0.976624 + 0.214953i \(0.931040\pi\)
\(462\) 0 0
\(463\) −226.915 −0.490097 −0.245049 0.969511i \(-0.578804\pi\)
−0.245049 + 0.969511i \(0.578804\pi\)
\(464\) 78.4263 + 107.945i 0.169022 + 0.232639i
\(465\) 0 0
\(466\) 65.7150 202.250i 0.141019 0.434013i
\(467\) 121.076 + 87.9672i 0.259264 + 0.188367i 0.709823 0.704380i \(-0.248775\pi\)
−0.450558 + 0.892747i \(0.648775\pi\)
\(468\) 0 0
\(469\) 650.636 + 211.404i 1.38728 + 0.450756i
\(470\) −20.5680 + 6.68295i −0.0437617 + 0.0142190i
\(471\) 0 0
\(472\) 173.526i 0.367640i
\(473\) 193.886 + 8.73818i 0.409907 + 0.0184740i
\(474\) 0 0
\(475\) 162.266 + 223.339i 0.341612 + 0.470188i
\(476\) 141.700 + 436.107i 0.297689 + 0.916192i
\(477\) 0 0
\(478\) −131.354 95.4344i −0.274799 0.199653i
\(479\) −191.483 + 263.554i −0.399755 + 0.550216i −0.960683 0.277649i \(-0.910445\pi\)
0.560927 + 0.827865i \(0.310445\pi\)
\(480\) 0 0
\(481\) −69.0060 + 22.4214i −0.143464 + 0.0466142i
\(482\) −185.865 + 135.039i −0.385613 + 0.280164i
\(483\) 0 0
\(484\) −144.418 + 337.588i −0.298385 + 0.697496i
\(485\) −14.9514 −0.0308277
\(486\) 0 0
\(487\) −94.8447 291.902i −0.194753 0.599388i −0.999979 0.00642054i \(-0.997956\pi\)
0.805226 0.592967i \(-0.202044\pi\)
\(488\) 71.3524 219.600i 0.146214 0.450000i
\(489\) 0 0
\(490\) −0.740925 + 1.01980i −0.00151209 + 0.00208121i
\(491\) 583.829 + 189.698i 1.18906 + 0.386349i 0.835726 0.549147i \(-0.185047\pi\)
0.353335 + 0.935497i \(0.385047\pi\)
\(492\) 0 0
\(493\) 422.137 306.700i 0.856261 0.622110i
\(494\) 132.772i 0.268770i
\(495\) 0 0
\(496\) 318.806 0.642754
\(497\) 351.397 + 483.656i 0.707035 + 0.973151i
\(498\) 0 0
\(499\) 126.532 389.425i 0.253571 0.780412i −0.740537 0.672016i \(-0.765429\pi\)
0.994108 0.108396i \(-0.0345714\pi\)
\(500\) −48.6483 35.3451i −0.0972966 0.0706901i
\(501\) 0 0
\(502\) 249.863 + 81.1853i 0.497734 + 0.161724i
\(503\) −673.153 + 218.721i −1.33828 + 0.434832i −0.888732 0.458426i \(-0.848413\pi\)
−0.449543 + 0.893259i \(0.648413\pi\)
\(504\) 0 0
\(505\) 32.1248i 0.0636134i
\(506\) 53.4949 35.2995i 0.105721 0.0697619i
\(507\) 0 0
\(508\) 39.0019 + 53.6816i 0.0767755 + 0.105672i
\(509\) −63.6414 195.868i −0.125032 0.384810i 0.868875 0.495032i \(-0.164844\pi\)
−0.993907 + 0.110222i \(0.964844\pi\)
\(510\) 0 0
\(511\) −272.328 197.858i −0.532932 0.387197i
\(512\) −190.291 + 261.913i −0.371662 + 0.511549i
\(513\) 0 0
\(514\) −46.2691 + 15.0337i −0.0900177 + 0.0292485i
\(515\) 32.0562 23.2902i 0.0622450 0.0452237i
\(516\) 0 0
\(517\) 587.050 161.915i 1.13549 0.313183i
\(518\) −42.3709 −0.0817971
\(519\) 0 0
\(520\) 10.3258 + 31.7796i 0.0198573 + 0.0611146i
\(521\) 102.734 316.183i 0.197186 0.606877i −0.802758 0.596305i \(-0.796635\pi\)
0.999944 0.0105716i \(-0.00336511\pi\)
\(522\) 0 0
\(523\) 183.858 253.058i 0.351544 0.483859i −0.596225 0.802818i \(-0.703333\pi\)
0.947769 + 0.318959i \(0.103333\pi\)
\(524\) −47.2137 15.3406i −0.0901024 0.0292760i
\(525\) 0 0
\(526\) −157.999 + 114.793i −0.300379 + 0.218238i
\(527\) 1246.75i 2.36575i
\(528\) 0 0
\(529\) −493.836 −0.933528
\(530\) −21.7336 29.9137i −0.0410067 0.0564409i
\(531\) 0 0
\(532\) −75.3090 + 231.777i −0.141558 + 0.435671i
\(533\) 511.934 + 371.942i 0.960477 + 0.697827i
\(534\) 0 0
\(535\) −40.9325 13.2998i −0.0765094 0.0248594i
\(536\) 622.288 202.194i 1.16098 0.377227i
\(537\) 0 0
\(538\) 10.5851i 0.0196750i
\(539\) 22.1351 27.7475i 0.0410669 0.0514796i
\(540\) 0 0
\(541\) 35.8960 + 49.4065i 0.0663511 + 0.0913245i 0.840903 0.541186i \(-0.182025\pi\)
−0.774552 + 0.632510i \(0.782025\pi\)
\(542\) 88.7288 + 273.079i 0.163706 + 0.503836i
\(543\) 0 0
\(544\) 556.565 + 404.368i 1.02310 + 0.743324i
\(545\) 40.9999 56.4315i 0.0752292 0.103544i
\(546\) 0 0
\(547\) 543.135 176.475i 0.992933 0.322624i 0.232895 0.972502i \(-0.425180\pi\)
0.760038 + 0.649878i \(0.225180\pi\)
\(548\) 75.0968 54.5610i 0.137038 0.0995639i
\(549\) 0 0
\(550\) −209.894 167.439i −0.381625 0.304435i
\(551\) 277.315 0.503294
\(552\) 0 0
\(553\) 134.705 + 414.580i 0.243590 + 0.749692i
\(554\) 53.2463 163.875i 0.0961125 0.295804i
\(555\) 0 0
\(556\) −49.4904 + 68.1177i −0.0890115 + 0.122514i
\(557\) −669.660 217.586i −1.20226 0.390638i −0.361669 0.932307i \(-0.617793\pi\)
−0.840592 + 0.541668i \(0.817793\pi\)
\(558\) 0 0
\(559\) −173.570 + 126.106i −0.310501 + 0.225592i
\(560\) 15.3624i 0.0274328i
\(561\) 0 0
\(562\) −223.417 −0.397539
\(563\) 296.842 + 408.568i 0.527251 + 0.725699i 0.986708 0.162501i \(-0.0519561\pi\)
−0.459457 + 0.888200i \(0.651956\pi\)
\(564\) 0 0
\(565\) 12.1044 37.2534i 0.0214236 0.0659351i
\(566\) −188.749 137.135i −0.333480 0.242287i
\(567\) 0 0
\(568\) 543.799 + 176.691i 0.957392 + 0.311076i
\(569\) 640.526 208.120i 1.12570 0.365764i 0.313763 0.949501i \(-0.398410\pi\)
0.811942 + 0.583738i \(0.198410\pi\)
\(570\) 0 0
\(571\) 446.598i 0.782134i −0.920362 0.391067i \(-0.872106\pi\)
0.920362 0.391067i \(-0.127894\pi\)
\(572\) −107.920 391.282i −0.188672 0.684059i
\(573\) 0 0
\(574\) 217.201 + 298.952i 0.378399 + 0.520822i
\(575\) −45.5213 140.100i −0.0791675 0.243653i
\(576\) 0 0
\(577\) 466.552 + 338.970i 0.808583 + 0.587470i 0.913419 0.407020i \(-0.133432\pi\)
−0.104837 + 0.994489i \(0.533432\pi\)
\(578\) 85.5967 117.814i 0.148091 0.203830i
\(579\) 0 0
\(580\) −28.6334 + 9.30354i −0.0493679 + 0.0160406i
\(581\) 880.928 640.031i 1.51623 1.10160i
\(582\) 0 0
\(583\) 573.441 + 869.025i 0.983603 + 1.49061i
\(584\) −321.949 −0.551283
\(585\) 0 0
\(586\) −8.90662 27.4118i −0.0151990 0.0467777i
\(587\) −280.070 + 861.968i −0.477122 + 1.46843i 0.365953 + 0.930633i \(0.380743\pi\)
−0.843075 + 0.537796i \(0.819257\pi\)
\(588\) 0 0
\(589\) 389.471 536.061i 0.661241 0.910121i
\(590\) 9.32725 + 3.03061i 0.0158089 + 0.00513662i
\(591\) 0 0
\(592\) 25.8112 18.7529i 0.0436000 0.0316772i
\(593\) 724.877i 1.22239i 0.791480 + 0.611195i \(0.209311\pi\)
−0.791480 + 0.611195i \(0.790689\pi\)
\(594\) 0 0
\(595\) −60.0774 −0.100970
\(596\) −354.605 488.072i −0.594975 0.818912i
\(597\) 0 0
\(598\) −21.8935 + 67.3812i −0.0366112 + 0.112678i
\(599\) 322.233 + 234.116i 0.537951 + 0.390844i 0.823323 0.567572i \(-0.192117\pi\)
−0.285373 + 0.958417i \(0.592117\pi\)
\(600\) 0 0
\(601\) −937.236 304.526i −1.55946 0.506700i −0.602797 0.797894i \(-0.705947\pi\)
−0.956664 + 0.291195i \(0.905947\pi\)
\(602\) −119.154 + 38.7156i −0.197931 + 0.0643117i
\(603\) 0 0
\(604\) 396.032i 0.655682i
\(605\) −36.2177 31.6627i −0.0598640 0.0523350i
\(606\) 0 0
\(607\) −105.195 144.789i −0.173304 0.238532i 0.713526 0.700629i \(-0.247097\pi\)
−0.886829 + 0.462097i \(0.847097\pi\)
\(608\) 112.984 + 347.730i 0.185829 + 0.571924i
\(609\) 0 0
\(610\) 10.5576 + 7.67057i 0.0173076 + 0.0125747i
\(611\) −395.680 + 544.607i −0.647594 + 0.891336i
\(612\) 0 0
\(613\) −1008.97 + 327.833i −1.64595 + 0.534800i −0.977856 0.209280i \(-0.932888\pi\)
−0.668090 + 0.744080i \(0.732888\pi\)
\(614\) −276.099 + 200.597i −0.449672 + 0.326706i
\(615\) 0 0
\(616\) 24.7385 548.907i 0.0401599 0.891082i
\(617\) −55.3570 −0.0897196 −0.0448598 0.998993i \(-0.514284\pi\)
−0.0448598 + 0.998993i \(0.514284\pi\)
\(618\) 0 0
\(619\) −232.546 715.704i −0.375681 1.15623i −0.943018 0.332741i \(-0.892027\pi\)
0.567338 0.823485i \(-0.307973\pi\)
\(620\) −22.2296 + 68.4157i −0.0358542 + 0.110348i
\(621\) 0 0
\(622\) 254.447 350.217i 0.409079 0.563049i
\(623\) −922.299 299.673i −1.48042 0.481016i
\(624\) 0 0
\(625\) −496.065 + 360.412i −0.793704 + 0.576660i
\(626\) 25.0206i 0.0399690i
\(627\) 0 0
\(628\) −214.201 −0.341084
\(629\) −73.3367 100.939i −0.116593 0.160476i
\(630\) 0 0
\(631\) −103.743 + 319.289i −0.164411 + 0.506005i −0.998992 0.0448799i \(-0.985709\pi\)
0.834582 + 0.550884i \(0.185709\pi\)
\(632\) 337.297 + 245.061i 0.533698 + 0.387754i
\(633\) 0 0
\(634\) 85.3961 + 27.7469i 0.134694 + 0.0437648i
\(635\) −8.26796 + 2.68642i −0.0130204 + 0.00423059i
\(636\) 0 0
\(637\) 39.2369i 0.0615964i
\(638\) −260.007 + 71.7132i −0.407535 + 0.112403i
\(639\) 0 0
\(640\) −28.2426 38.8726i −0.0441290 0.0607384i
\(641\) 170.606 + 525.071i 0.266156 + 0.819144i 0.991425 + 0.130678i \(0.0417154\pi\)
−0.725269 + 0.688466i \(0.758285\pi\)
\(642\) 0 0
\(643\) 111.934 + 81.3249i 0.174081 + 0.126477i 0.671414 0.741082i \(-0.265687\pi\)
−0.497333 + 0.867560i \(0.665687\pi\)
\(644\) 76.4378 105.208i 0.118692 0.163366i
\(645\) 0 0
\(646\) 217.138 70.5525i 0.336127 0.109214i
\(647\) −819.415 + 595.340i −1.26648 + 0.920154i −0.999057 0.0434241i \(-0.986173\pi\)
−0.267427 + 0.963578i \(0.586173\pi\)
\(648\) 0 0
\(649\) −258.533 97.0758i −0.398356 0.149578i
\(650\) 296.805 0.456623
\(651\) 0 0
\(652\) −72.1207 221.965i −0.110615 0.340437i
\(653\) 2.38169 7.33010i 0.00364731 0.0112253i −0.949216 0.314624i \(-0.898121\pi\)
0.952864 + 0.303399i \(0.0981215\pi\)
\(654\) 0 0
\(655\) 3.82300 5.26191i 0.00583664 0.00803345i
\(656\) −264.626 85.9822i −0.403393 0.131070i
\(657\) 0 0
\(658\) −318.032 + 231.063i −0.483331 + 0.351160i
\(659\) 736.073i 1.11695i −0.829520 0.558477i \(-0.811386\pi\)
0.829520 0.558477i \(-0.188614\pi\)
\(660\) 0 0
\(661\) −471.170 −0.712813 −0.356407 0.934331i \(-0.615998\pi\)
−0.356407 + 0.934331i \(0.615998\pi\)
\(662\) −184.097 253.388i −0.278092 0.382761i
\(663\) 0 0
\(664\) 321.824 990.472i 0.484674 1.49167i
\(665\) −25.8313 18.7675i −0.0388441 0.0282219i
\(666\) 0 0
\(667\) −140.736 45.7278i −0.210998 0.0685574i
\(668\) 293.677 95.4213i 0.439635 0.142846i
\(669\) 0 0
\(670\) 36.9801i 0.0551941i
\(671\) −287.262 229.158i −0.428110 0.341517i
\(672\) 0 0
\(673\) 676.225 + 930.745i 1.00479 + 1.38298i 0.922338 + 0.386384i \(0.126276\pi\)
0.0824545 + 0.996595i \(0.473724\pi\)
\(674\) 187.571 + 577.285i 0.278295 + 0.856505i
\(675\) 0 0
\(676\) −51.9039 37.7104i −0.0767809 0.0557846i
\(677\) 689.120 948.493i 1.01790 1.40102i 0.104239 0.994552i \(-0.466759\pi\)
0.913664 0.406471i \(-0.133241\pi\)
\(678\) 0 0
\(679\) −258.474 + 83.9832i −0.380668 + 0.123687i
\(680\) −46.4860 + 33.7740i −0.0683617 + 0.0496677i
\(681\) 0 0
\(682\) −226.539 + 603.322i −0.332169 + 0.884636i
\(683\) 329.083 0.481820 0.240910 0.970547i \(-0.422554\pi\)
0.240910 + 0.970547i \(0.422554\pi\)
\(684\) 0 0
\(685\) 3.75812 + 11.5663i 0.00548631 + 0.0168851i
\(686\) 100.439 309.120i 0.146413 0.450612i
\(687\) 0 0
\(688\) 55.4505 76.3210i 0.0805966 0.110932i
\(689\) −1094.61 355.659i −1.58869 0.516197i
\(690\) 0 0
\(691\) −581.750 + 422.666i −0.841896 + 0.611674i −0.922900 0.385040i \(-0.874188\pi\)
0.0810034 + 0.996714i \(0.474188\pi\)
\(692\) 379.023i 0.547722i
\(693\) 0 0
\(694\) 197.623 0.284760
\(695\) −6.48403 8.92451i −0.00932955 0.0128410i
\(696\) 0 0
\(697\) −336.249 + 1034.87i −0.482423 + 1.48475i
\(698\) 385.325 + 279.955i 0.552042 + 0.401082i
\(699\) 0 0
\(700\) −518.124 168.349i −0.740178 0.240498i
\(701\) −95.7601 + 31.1144i −0.136605 + 0.0443857i −0.376522 0.926408i \(-0.622880\pi\)
0.239917 + 0.970794i \(0.422880\pi\)
\(702\) 0 0
\(703\) 66.3102i 0.0943246i
\(704\) −66.2833 100.449i −0.0941524 0.142684i
\(705\) 0 0
\(706\) −62.9271 86.6118i −0.0891319 0.122680i
\(707\) 180.447 + 555.358i 0.255229 + 0.785514i
\(708\) 0 0
\(709\) −222.948 161.981i −0.314454 0.228464i 0.419351 0.907824i \(-0.362258\pi\)
−0.733805 + 0.679360i \(0.762258\pi\)
\(710\) −18.9947 + 26.1440i −0.0267532 + 0.0368226i
\(711\) 0 0
\(712\) −882.114 + 286.616i −1.23892 + 0.402551i
\(713\) −286.048 + 207.826i −0.401190 + 0.291481i
\(714\) 0 0
\(715\) 53.1244 + 2.39425i 0.0742999 + 0.00334860i
\(716\) 313.258 0.437512
\(717\) 0 0
\(718\) 130.109 + 400.435i 0.181211 + 0.557710i
\(719\) −28.6486 + 88.1712i −0.0398450 + 0.122630i −0.969000 0.247059i \(-0.920536\pi\)
0.929155 + 0.369689i \(0.120536\pi\)
\(720\) 0 0
\(721\) 423.350 582.692i 0.587171 0.808172i
\(722\) −221.945 72.1142i −0.307403 0.0998811i
\(723\) 0 0
\(724\) 276.095 200.594i 0.381346 0.277064i
\(725\) 619.921i 0.855063i
\(726\) 0 0
\(727\) 40.4150 0.0555915 0.0277958 0.999614i \(-0.491151\pi\)
0.0277958 + 0.999614i \(0.491151\pi\)
\(728\) 357.016 + 491.390i 0.490406 + 0.674987i
\(729\) 0 0
\(730\) 5.62280 17.3052i 0.00770247 0.0237058i
\(731\) −298.467 216.849i −0.408300 0.296647i
\(732\) 0 0
\(733\) 679.400 + 220.751i 0.926876 + 0.301160i 0.733285 0.679922i \(-0.237986\pi\)
0.193592 + 0.981082i \(0.437986\pi\)
\(734\) 399.897 129.934i 0.544818 0.177022i
\(735\) 0 0
\(736\) 195.102i 0.265084i
\(737\) 46.8826 1040.25i 0.0636128 1.41146i
\(738\) 0 0
\(739\) −30.3170 41.7277i −0.0410243 0.0564651i 0.788012 0.615660i \(-0.211110\pi\)
−0.829036 + 0.559195i \(0.811110\pi\)
\(740\) 2.22462 + 6.84667i 0.00300624 + 0.00925226i
\(741\) 0 0
\(742\) −543.747 395.055i −0.732813 0.532420i
\(743\) 528.170 726.964i 0.710862 0.978418i −0.288916 0.957354i \(-0.593295\pi\)
0.999778 0.0210631i \(-0.00670509\pi\)
\(744\) 0 0
\(745\) 75.1721 24.4249i 0.100902 0.0327851i
\(746\) 82.9189 60.2441i 0.111151 0.0807562i
\(747\) 0 0
\(748\) 582.563 384.414i 0.778827 0.513922i
\(749\) −782.328 −1.04450
\(750\) 0 0
\(751\) 105.701 + 325.316i 0.140748 + 0.433177i 0.996440 0.0843087i \(-0.0268682\pi\)
−0.855692 + 0.517485i \(0.826868\pi\)
\(752\) 91.4698 281.515i 0.121635 0.374355i
\(753\) 0 0
\(754\) 175.249 241.209i 0.232425 0.319906i
\(755\) 49.3470 + 16.0338i 0.0653603 + 0.0212369i
\(756\) 0 0
\(757\) 653.654 474.907i 0.863479 0.627354i −0.0653503 0.997862i \(-0.520816\pi\)
0.928829 + 0.370508i \(0.120816\pi\)
\(758\) 220.743i 0.291217i
\(759\) 0 0
\(760\) −30.5381 −0.0401817
\(761\) 459.858 + 632.941i 0.604282 + 0.831722i 0.996092 0.0883239i \(-0.0281510\pi\)
−0.391810 + 0.920046i \(0.628151\pi\)
\(762\) 0 0
\(763\) 391.808 1205.86i 0.513510 1.58042i
\(764\) 469.083 + 340.809i 0.613983 + 0.446085i
\(765\) 0 0
\(766\) 55.3842 + 17.9954i 0.0723032 + 0.0234927i
\(767\) 290.331 94.3342i 0.378528 0.122991i
\(768\) 0 0
\(769\) 652.678i 0.848736i 0.905490 + 0.424368i \(0.139504\pi\)
−0.905490 + 0.424368i \(0.860496\pi\)
\(770\) 29.0724 + 10.9163i 0.0377564 + 0.0141770i
\(771\) 0 0
\(772\) −97.3130 133.940i −0.126053 0.173497i
\(773\) 267.215 + 822.403i 0.345686 + 1.06391i 0.961216 + 0.275797i \(0.0889419\pi\)
−0.615530 + 0.788113i \(0.711058\pi\)
\(774\) 0 0
\(775\) 1198.33 + 870.640i 1.54624 + 1.12341i
\(776\) −152.785 + 210.291i −0.196888 + 0.270994i
\(777\) 0 0
\(778\) 385.167 125.148i 0.495074 0.160859i
\(779\) −467.858 + 339.919i −0.600588 + 0.436352i
\(780\) 0 0
\(781\) 567.467 711.350i 0.726590 0.910819i
\(782\) −121.830 −0.155793
\(783\) 0 0
\(784\) −5.33147 16.4086i −0.00680035 0.0209293i
\(785\) 8.67218 26.6902i 0.0110474 0.0340003i
\(786\) 0 0
\(787\) −256.642 + 353.238i −0.326102 + 0.448841i −0.940318 0.340297i \(-0.889472\pi\)
0.614216 + 0.789138i \(0.289472\pi\)
\(788\) −217.304 70.6063i −0.275766 0.0896020i
\(789\) 0 0
\(790\) −19.0632 + 13.8502i −0.0241306 + 0.0175319i
\(791\) 712.010i 0.900139i
\(792\) 0 0
\(793\) 406.208 0.512243
\(794\) 358.031 + 492.787i 0.450921 + 0.620639i
\(795\) 0 0
\(796\) −56.9383 + 175.238i −0.0715305 + 0.220148i
\(797\) 366.573 + 266.331i 0.459941 + 0.334167i 0.793508 0.608560i \(-0.208252\pi\)
−0.333567 + 0.942726i \(0.608252\pi\)
\(798\) 0 0
\(799\) −1100.92 357.709i −1.37787 0.447696i
\(800\) −777.330 + 252.570i −0.971662 + 0.315712i
\(801\) 0 0
\(802\) 660.366i 0.823399i
\(803\) −180.109 + 479.667i −0.224295 + 0.597343i
\(804\) 0 0
\(805\) 10.0146 + 13.7839i 0.0124405 + 0.0171228i
\(806\) −220.142 677.526i −0.273129 0.840603i
\(807\) 0 0
\(808\) 451.833 + 328.276i 0.559199 + 0.406282i
\(809\) −67.7382 + 93.2336i −0.0837307 + 0.115245i −0.848828 0.528670i \(-0.822691\pi\)
0.765097 + 0.643915i \(0.222691\pi\)
\(810\) 0 0
\(811\) 31.6398 10.2804i 0.0390134 0.0126762i −0.289445 0.957195i \(-0.593471\pi\)
0.328459 + 0.944518i \(0.393471\pi\)
\(812\) −442.742 + 321.671i −0.545249 + 0.396146i
\(813\) 0 0
\(814\) 17.1477 + 62.1717i 0.0210660 + 0.0763781i
\(815\) 30.5775 0.0375184
\(816\) 0 0
\(817\) −60.5897 186.476i −0.0741612 0.228245i
\(818\) 186.534 574.093i 0.228037 0.701825i
\(819\) 0 0
\(820\) 36.9035 50.7934i 0.0450043 0.0619431i
\(821\) 680.061 + 220.965i 0.828332 + 0.269141i 0.692343 0.721569i \(-0.256579\pi\)
0.135990 + 0.990710i \(0.456579\pi\)
\(822\) 0 0
\(823\) 127.047 92.3053i 0.154371 0.112157i −0.507918 0.861405i \(-0.669585\pi\)
0.662290 + 0.749248i \(0.269585\pi\)
\(824\) 688.866i 0.836002i
\(825\) 0 0
\(826\) 178.268 0.215821
\(827\) 502.151 + 691.151i 0.607195 + 0.835733i 0.996343 0.0854425i \(-0.0272304\pi\)
−0.389148 + 0.921175i \(0.627230\pi\)
\(828\) 0 0
\(829\) −424.643 + 1306.92i −0.512235 + 1.57650i 0.276023 + 0.961151i \(0.410983\pi\)
−0.788258 + 0.615345i \(0.789017\pi\)
\(830\) 47.6186 + 34.5969i 0.0573718 + 0.0416830i
\(831\) 0 0
\(832\) 126.524 + 41.1102i 0.152072 + 0.0494113i
\(833\) −64.1688 + 20.8497i −0.0770333 + 0.0250296i
\(834\) 0 0
\(835\) 40.4564i 0.0484508i
\(836\) 370.570 + 16.7011i 0.443265 + 0.0199774i
\(837\) 0 0
\(838\) 35.2003 + 48.4491i 0.0420052 + 0.0578151i
\(839\) −201.645 620.599i −0.240339 0.739689i −0.996368 0.0851502i \(-0.972863\pi\)
0.756029 0.654538i \(-0.227137\pi\)
\(840\) 0 0
\(841\) −176.582 128.294i −0.209967 0.152550i
\(842\) −120.479 + 165.826i −0.143087 + 0.196943i
\(843\) 0 0
\(844\) 1180.94 383.712i 1.39922 0.454635i
\(845\) 6.80024 4.94066i 0.00804762 0.00584694i
\(846\) 0 0
\(847\) −803.967 343.933i −0.949193 0.406060i
\(848\) 506.083 0.596796
\(849\) 0 0
\(850\) 157.716 + 485.400i 0.185548 + 0.571058i
\(851\) −10.9342 + 33.6521i −0.0128487 + 0.0395441i
\(852\) 0 0
\(853\) −778.060 + 1070.91i −0.912145 + 1.25546i 0.0542838 + 0.998526i \(0.482712\pi\)
−0.966429 + 0.256934i \(0.917288\pi\)
\(854\) 225.602 + 73.3025i 0.264171 + 0.0858343i
\(855\) 0 0
\(856\) −605.340 + 439.806i −0.707173 + 0.513792i
\(857\) 38.8452i 0.0453269i −0.999743 0.0226634i \(-0.992785\pi\)
0.999743 0.0226634i \(-0.00721462\pi\)
\(858\) 0 0
\(859\) 227.261 0.264564 0.132282 0.991212i \(-0.457770\pi\)
0.132282 + 0.991212i \(0.457770\pi\)
\(860\) 12.5120 + 17.2213i 0.0145489 + 0.0200248i
\(861\) 0 0
\(862\) 82.1993 252.983i 0.0953588 0.293484i
\(863\) 774.412 + 562.643i 0.897348 + 0.651962i 0.937784 0.347220i \(-0.112874\pi\)
−0.0404352 + 0.999182i \(0.512874\pi\)
\(864\) 0 0
\(865\) 47.2277 + 15.3452i 0.0545985 + 0.0177401i
\(866\) −586.200 + 190.468i −0.676906 + 0.219940i
\(867\) 0 0
\(868\) 1307.61i 1.50646i
\(869\) 553.806 365.438i 0.637291 0.420527i
\(870\) 0 0
\(871\) 676.591 + 931.247i 0.776798 + 1.06917i
\(872\) −374.737 1153.32i −0.429744 1.32262i
\(873\) 0 0
\(874\) −52.3829 38.0584i −0.0599347 0.0435451i
\(875\) 84.1744 115.856i 0.0961993 0.132407i
\(876\) 0 0
\(877\) 1145.02 372.039i 1.30561 0.424218i 0.428079 0.903741i \(-0.359190\pi\)
0.877529 + 0.479523i \(0.159190\pi\)
\(878\) −393.677 + 286.023i −0.448379 + 0.325767i
\(879\) 0 0
\(880\) −22.5416 + 6.21724i −0.0256154 + 0.00706504i
\(881\) −1170.77 −1.32892 −0.664458 0.747326i \(-0.731337\pi\)
−0.664458 + 0.747326i \(0.731337\pi\)
\(882\) 0 0
\(883\) 112.550 + 346.392i 0.127463 + 0.392290i 0.994342 0.106229i \(-0.0338775\pi\)
−0.866879 + 0.498519i \(0.833878\pi\)
\(884\) −238.421 + 733.785i −0.269707 + 0.830074i
\(885\) 0 0
\(886\) 428.537 589.830i 0.483676 0.665723i
\(887\) 270.792 + 87.9858i 0.305290 + 0.0991948i 0.457656 0.889129i \(-0.348689\pi\)
−0.152366 + 0.988324i \(0.548689\pi\)
\(888\) 0 0
\(889\) −127.843 + 92.8833i −0.143805 + 0.104481i
\(890\) 52.4205i 0.0588995i
\(891\) 0 0
\(892\) −447.025 −0.501150
\(893\) −361.613 497.717i −0.404941 0.557354i
\(894\) 0 0
\(895\) −12.6826 + 39.0331i −0.0141705 + 0.0436124i
\(896\) −706.594 513.371i −0.788610 0.572959i
\(897\) 0 0
\(898\) −666.812 216.660i −0.742552 0.241270i
\(899\) 1415.11 459.799i 1.57410 0.511456i
\(900\) 0 0
\(901\) 1979.13i 2.19659i
\(902\) 350.756 439.691i 0.388865 0.487463i
\(903\) 0 0
\(904\) −400.274 550.931i −0.442781 0.609436i
\(905\) 13.8168 + 42.5237i 0.0152672 + 0.0469875i
\(906\) 0 0
\(907\) −612.207 444.795i −0.674981 0.490402i 0.196708 0.980462i \(-0.436975\pi\)
−0.871689 + 0.490060i \(0.836975\pi\)
\(908\) 244.402 336.390i 0.269165 0.370474i
\(909\) 0 0
\(910\) −32.6481 + 10.6080i −0.0358770 + 0.0116572i
\(911\) −533.420 + 387.552i −0.585532 + 0.425414i −0.840714 0.541479i \(-0.817865\pi\)
0.255182 + 0.966893i \(0.417865\pi\)
\(912\) 0 0
\(913\) −1295.65 1033.58i −1.41911 1.13207i
\(914\) −277.589 −0.303708
\(915\) 0 0
\(916\) 80.3692 + 247.351i 0.0877393 + 0.270034i
\(917\) 36.5338 112.439i 0.0398406 0.122617i
\(918\) 0 0
\(919\) −439.038 + 604.284i −0.477735 + 0.657545i −0.978068 0.208288i \(-0.933211\pi\)
0.500333 + 0.865833i \(0.333211\pi\)
\(920\) 15.4979 + 5.03557i 0.0168456 + 0.00547345i
\(921\) 0 0
\(922\) −157.541 + 114.460i −0.170869 + 0.124144i
\(923\) 1005.90i 1.08981i
\(924\) 0 0
\(925\) 148.233 0.160251
\(926\) −131.052 180.378i −0.141525 0.194793i
\(927\) 0 0
\(928\) −253.715 + 780.855i −0.273400 + 0.841439i
\(929\) −981.029 712.759i −1.05601 0.767233i −0.0826603 0.996578i \(-0.526342\pi\)
−0.973345 + 0.229345i \(0.926342\pi\)
\(930\) 0 0
\(931\) −34.1037 11.0810i −0.0366312 0.0119022i
\(932\) −624.627 + 202.954i −0.670201 + 0.217761i
\(933\) 0 0
\(934\) 147.050i 0.157441i
\(935\) 24.3136 + 88.1528i 0.0260039 + 0.0942811i
\(936\) 0 0
\(937\) −935.658 1287.82i −0.998568 1.37441i −0.926200 0.377033i \(-0.876944\pi\)
−0.0723682 0.997378i \(-0.523056\pi\)
\(938\) 207.719 + 639.295i 0.221449 + 0.681551i
\(939\) 0 0
\(940\) 54.0351 + 39.2588i 0.0574841 + 0.0417647i
\(941\) −350.794 + 482.827i −0.372789 + 0.513100i −0.953656 0.300898i \(-0.902713\pi\)
0.580867 + 0.813998i \(0.302713\pi\)
\(942\) 0 0
\(943\) 293.486 95.3594i 0.311226 0.101123i
\(944\) −108.596 + 78.8997i −0.115038 + 0.0835802i
\(945\) 0 0
\(946\) 105.031 + 159.169i 0.111026 + 0.168255i
\(947\) 883.411 0.932852 0.466426 0.884560i \(-0.345541\pi\)
0.466426 + 0.884560i \(0.345541\pi\)
\(948\) 0 0
\(949\) −175.022 538.662i −0.184428 0.567610i
\(950\) −83.8210 + 257.975i −0.0882326 + 0.271552i
\(951\) 0 0
\(952\) −613.917 + 844.985i −0.644871 + 0.887589i
\(953\) 269.023 + 87.4107i 0.282290 + 0.0917216i 0.446740 0.894664i \(-0.352585\pi\)
−0.164450 + 0.986385i \(0.552585\pi\)
\(954\) 0 0
\(955\) −61.4573 + 44.6514i −0.0643532 + 0.0467554i
\(956\) 501.440i 0.524518i
\(957\) 0 0
\(958\) −320.091 −0.334125
\(959\) 129.937 + 178.843i 0.135493 + 0.186489i
\(960\) 0 0
\(961\) 801.664 2467.27i 0.834198 2.56740i
\(962\) −57.6768 41.9046i −0.0599551 0.0435599i
\(963\) 0 0
\(964\) 674.808 + 219.258i 0.700008 + 0.227446i
\(965\) 20.6292 6.70284i 0.0213774 0.00694595i
\(966\) 0 0
\(967\) 335.731i 0.347188i −0.984817 0.173594i \(-0.944462\pi\)
0.984817 0.173594i \(-0.0555381\pi\)
\(968\) −815.434 + 185.846i −0.842391 + 0.191990i
\(969\) 0 0
\(970\) −8.63505 11.8851i −0.00890211 0.0122527i
\(971\) −431.183 1327.04i −0.444061 1.36668i −0.883511 0.468411i \(-0.844827\pi\)
0.439450 0.898267i \(-0.355173\pi\)
\(972\) 0 0
\(973\) −162.223 117.862i −0.166724 0.121132i
\(974\) 177.261 243.978i 0.181992 0.250491i
\(975\) 0 0
\(976\) −169.873 + 55.1952i −0.174051 + 0.0565524i
\(977\) −941.558 + 684.082i −0.963724 + 0.700187i −0.954013 0.299766i \(-0.903091\pi\)
−0.00971140 + 0.999953i \(0.503091\pi\)
\(978\) 0 0
\(979\) −66.4577 + 1474.59i −0.0678833 + 1.50622i
\(980\) 3.89303 0.00397248
\(981\) 0 0
\(982\) 186.391 + 573.652i 0.189807 + 0.584167i
\(983\) 126.632 389.732i 0.128821 0.396472i −0.865756 0.500466i \(-0.833162\pi\)
0.994578 + 0.103994i \(0.0331622\pi\)
\(984\) 0 0
\(985\) 17.5956 24.2183i 0.0178636 0.0245871i
\(986\) 487.601 + 158.431i 0.494525 + 0.160681i
\(987\) 0 0
\(988\) −331.740 + 241.023i −0.335769 + 0.243951i
\(989\) 104.626i 0.105790i
\(990\) 0 0
\(991\) 1604.17 1.61874 0.809372 0.587297i \(-0.199808\pi\)
0.809372 + 0.587297i \(0.199808\pi\)
\(992\) 1153.10 + 1587.10i 1.16240 + 1.59990i
\(993\) 0 0
\(994\) −181.520 + 558.661i −0.182616 + 0.562033i
\(995\) −19.5301 14.1894i −0.0196282 0.0142607i
\(996\) 0 0
\(997\) 68.8415 + 22.3680i 0.0690487 + 0.0224353i 0.343338 0.939212i \(-0.388442\pi\)
−0.274289 + 0.961647i \(0.588442\pi\)
\(998\) 382.637 124.326i 0.383404 0.124576i
\(999\) 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 99.3.k.c.19.4 16
3.2 odd 2 33.3.g.a.19.1 yes 16
11.2 odd 10 1089.3.c.m.604.10 16
11.7 odd 10 inner 99.3.k.c.73.4 16
11.9 even 5 1089.3.c.m.604.7 16
12.11 even 2 528.3.bf.b.481.3 16
33.2 even 10 363.3.c.e.241.7 16
33.5 odd 10 363.3.g.a.112.4 16
33.8 even 10 363.3.g.a.94.4 16
33.14 odd 10 363.3.g.g.94.1 16
33.17 even 10 363.3.g.g.112.1 16
33.20 odd 10 363.3.c.e.241.10 16
33.26 odd 10 363.3.g.f.40.4 16
33.29 even 10 33.3.g.a.7.1 16
33.32 even 2 363.3.g.f.118.4 16
132.95 odd 10 528.3.bf.b.337.3 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
33.3.g.a.7.1 16 33.29 even 10
33.3.g.a.19.1 yes 16 3.2 odd 2
99.3.k.c.19.4 16 1.1 even 1 trivial
99.3.k.c.73.4 16 11.7 odd 10 inner
363.3.c.e.241.7 16 33.2 even 10
363.3.c.e.241.10 16 33.20 odd 10
363.3.g.a.94.4 16 33.8 even 10
363.3.g.a.112.4 16 33.5 odd 10
363.3.g.f.40.4 16 33.26 odd 10
363.3.g.f.118.4 16 33.32 even 2
363.3.g.g.94.1 16 33.14 odd 10
363.3.g.g.112.1 16 33.17 even 10
528.3.bf.b.337.3 16 132.95 odd 10
528.3.bf.b.481.3 16 12.11 even 2
1089.3.c.m.604.7 16 11.9 even 5
1089.3.c.m.604.10 16 11.2 odd 10