Properties

Label 312.4.m.a.181.76
Level $312$
Weight $4$
Character 312.181
Analytic conductor $18.409$
Analytic rank $0$
Dimension $84$
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [312,4,Mod(181,312)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(312, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1, 0, 1]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("312.181");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 312 = 2^{3} \cdot 3 \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 312.m (of order \(2\), degree \(1\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(18.4085959218\)
Analytic rank: \(0\)
Dimension: \(84\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 181.76
Character \(\chi\) \(=\) 312.181
Dual form 312.4.m.a.181.75

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(2.56970 + 1.18180i) q^{2} +3.00000i q^{3} +(5.20671 + 6.07373i) q^{4} +8.43796 q^{5} +(-3.54539 + 7.70910i) q^{6} +8.36709i q^{7} +(6.20176 + 21.7609i) q^{8} -9.00000 q^{9} +O(q^{10})\) \(q+(2.56970 + 1.18180i) q^{2} +3.00000i q^{3} +(5.20671 + 6.07373i) q^{4} +8.43796 q^{5} +(-3.54539 + 7.70910i) q^{6} +8.36709i q^{7} +(6.20176 + 21.7609i) q^{8} -9.00000 q^{9} +(21.6830 + 9.97196i) q^{10} -57.7885 q^{11} +(-18.2212 + 15.6201i) q^{12} +(18.9697 + 42.8620i) q^{13} +(-9.88821 + 21.5009i) q^{14} +25.3139i q^{15} +(-9.78034 + 63.2483i) q^{16} -72.1970 q^{17} +(-23.1273 - 10.6362i) q^{18} +144.199 q^{19} +(43.9340 + 51.2499i) q^{20} -25.1013 q^{21} +(-148.499 - 68.2943i) q^{22} +168.461 q^{23} +(-65.2828 + 18.6053i) q^{24} -53.8009 q^{25} +(-1.90787 + 132.561i) q^{26} -27.0000i q^{27} +(-50.8194 + 43.5650i) q^{28} -96.0104i q^{29} +(-29.9159 + 65.0490i) q^{30} +59.3688i q^{31} +(-99.8792 + 150.971i) q^{32} -173.366i q^{33} +(-185.525 - 85.3222i) q^{34} +70.6012i q^{35} +(-46.8604 - 54.6636i) q^{36} -187.632 q^{37} +(370.547 + 170.413i) q^{38} +(-128.586 + 56.9090i) q^{39} +(52.3302 + 183.618i) q^{40} +211.432i q^{41} +(-64.5027 - 29.6646i) q^{42} -160.852i q^{43} +(-300.888 - 350.992i) q^{44} -75.9416 q^{45} +(432.893 + 199.086i) q^{46} +539.374i q^{47} +(-189.745 - 29.3410i) q^{48} +272.992 q^{49} +(-138.252 - 63.5817i) q^{50} -216.591i q^{51} +(-161.563 + 338.387i) q^{52} -583.906i q^{53} +(31.9085 - 69.3819i) q^{54} -487.617 q^{55} +(-182.076 + 51.8907i) q^{56} +432.596i q^{57} +(113.465 - 246.718i) q^{58} -236.128 q^{59} +(-153.750 + 131.802i) q^{60} -438.613i q^{61} +(-70.1619 + 152.560i) q^{62} -75.3038i q^{63} +(-435.076 + 269.912i) q^{64} +(160.065 + 361.668i) q^{65} +(204.883 - 445.497i) q^{66} +639.558 q^{67} +(-375.909 - 438.505i) q^{68} +505.382i q^{69} +(-83.4363 + 181.424i) q^{70} +79.3300i q^{71} +(-55.8159 - 195.848i) q^{72} -40.6482i q^{73} +(-482.158 - 221.743i) q^{74} -161.403i q^{75} +(750.800 + 875.822i) q^{76} -483.522i q^{77} +(-397.682 - 5.72361i) q^{78} +807.497 q^{79} +(-82.5261 + 533.686i) q^{80} +81.0000 q^{81} +(-249.870 + 543.317i) q^{82} +1390.02 q^{83} +(-130.695 - 152.458i) q^{84} -609.195 q^{85} +(190.094 - 413.340i) q^{86} +288.031 q^{87} +(-358.391 - 1257.53i) q^{88} -1051.90i q^{89} +(-195.147 - 89.7476i) q^{90} +(-358.630 + 158.721i) q^{91} +(877.125 + 1023.18i) q^{92} -178.106 q^{93} +(-637.431 + 1386.03i) q^{94} +1216.74 q^{95} +(-452.912 - 299.638i) q^{96} +1002.06i q^{97} +(701.507 + 322.621i) q^{98} +520.097 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 84 q - 756 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 84 q - 756 q^{9} - 36 q^{10} + 12 q^{12} - 208 q^{14} - 148 q^{16} - 104 q^{17} + 620 q^{22} + 2188 q^{25} + 444 q^{26} - 204 q^{30} - 40 q^{38} - 1924 q^{40} + 192 q^{42} + 624 q^{48} - 3396 q^{49} - 1292 q^{52} - 1616 q^{55} + 608 q^{56} - 2120 q^{62} - 2856 q^{64} + 696 q^{65} - 396 q^{66} - 2536 q^{68} - 3936 q^{74} - 156 q^{78} + 3160 q^{79} + 6804 q^{81} + 4276 q^{82} - 2088 q^{87} + 1780 q^{88} + 324 q^{90} + 4792 q^{92} - 860 q^{94} + 2480 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/312\mathbb{Z}\right)^\times\).

\(n\) \(79\) \(145\) \(157\) \(209\)
\(\chi(n)\) \(1\) \(-1\) \(-1\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.56970 + 1.18180i 0.908526 + 0.417828i
\(3\) 3.00000i 0.577350i
\(4\) 5.20671 + 6.07373i 0.650839 + 0.759216i
\(5\) 8.43796 0.754714 0.377357 0.926068i \(-0.376833\pi\)
0.377357 + 0.926068i \(0.376833\pi\)
\(6\) −3.54539 + 7.70910i −0.241233 + 0.524538i
\(7\) 8.36709i 0.451781i 0.974153 + 0.225890i \(0.0725291\pi\)
−0.974153 + 0.225890i \(0.927471\pi\)
\(8\) 6.20176 + 21.7609i 0.274082 + 0.961706i
\(9\) −9.00000 −0.333333
\(10\) 21.6830 + 9.97196i 0.685677 + 0.315341i
\(11\) −57.7885 −1.58399 −0.791995 0.610527i \(-0.790958\pi\)
−0.791995 + 0.610527i \(0.790958\pi\)
\(12\) −18.2212 + 15.6201i −0.438334 + 0.375762i
\(13\) 18.9697 + 42.8620i 0.404711 + 0.914445i
\(14\) −9.88821 + 21.5009i −0.188767 + 0.410454i
\(15\) 25.3139i 0.435734i
\(16\) −9.78034 + 63.2483i −0.152818 + 0.988254i
\(17\) −72.1970 −1.03002 −0.515010 0.857184i \(-0.672212\pi\)
−0.515010 + 0.857184i \(0.672212\pi\)
\(18\) −23.1273 10.6362i −0.302842 0.139276i
\(19\) 144.199 1.74113 0.870563 0.492056i \(-0.163755\pi\)
0.870563 + 0.492056i \(0.163755\pi\)
\(20\) 43.9340 + 51.2499i 0.491197 + 0.572991i
\(21\) −25.1013 −0.260836
\(22\) −148.499 68.2943i −1.43910 0.661836i
\(23\) 168.461 1.52724 0.763619 0.645668i \(-0.223421\pi\)
0.763619 + 0.645668i \(0.223421\pi\)
\(24\) −65.2828 + 18.6053i −0.555241 + 0.158241i
\(25\) −53.8009 −0.430407
\(26\) −1.90787 + 132.561i −0.0143909 + 0.999896i
\(27\) 27.0000i 0.192450i
\(28\) −50.8194 + 43.5650i −0.342999 + 0.294036i
\(29\) 96.0104i 0.614782i −0.951583 0.307391i \(-0.900544\pi\)
0.951583 0.307391i \(-0.0994560\pi\)
\(30\) −29.9159 + 65.0490i −0.182062 + 0.395876i
\(31\) 59.3688i 0.343966i 0.985100 + 0.171983i \(0.0550174\pi\)
−0.985100 + 0.171983i \(0.944983\pi\)
\(32\) −99.8792 + 150.971i −0.551760 + 0.834003i
\(33\) 173.366i 0.914517i
\(34\) −185.525 85.3222i −0.935800 0.430372i
\(35\) 70.6012i 0.340965i
\(36\) −46.8604 54.6636i −0.216946 0.253072i
\(37\) −187.632 −0.833689 −0.416845 0.908978i \(-0.636864\pi\)
−0.416845 + 0.908978i \(0.636864\pi\)
\(38\) 370.547 + 170.413i 1.58186 + 0.727492i
\(39\) −128.586 + 56.9090i −0.527955 + 0.233660i
\(40\) 52.3302 + 183.618i 0.206853 + 0.725813i
\(41\) 211.432i 0.805370i 0.915339 + 0.402685i \(0.131923\pi\)
−0.915339 + 0.402685i \(0.868077\pi\)
\(42\) −64.5027 29.6646i −0.236976 0.108985i
\(43\) 160.852i 0.570456i −0.958460 0.285228i \(-0.907931\pi\)
0.958460 0.285228i \(-0.0920694\pi\)
\(44\) −300.888 350.992i −1.03092 1.20259i
\(45\) −75.9416 −0.251571
\(46\) 432.893 + 199.086i 1.38753 + 0.638123i
\(47\) 539.374i 1.67395i 0.547239 + 0.836976i \(0.315679\pi\)
−0.547239 + 0.836976i \(0.684321\pi\)
\(48\) −189.745 29.3410i −0.570569 0.0882294i
\(49\) 272.992 0.795894
\(50\) −138.252 63.5817i −0.391036 0.179836i
\(51\) 216.591i 0.594682i
\(52\) −161.563 + 338.387i −0.430860 + 0.902419i
\(53\) 583.906i 1.51332i −0.653811 0.756658i \(-0.726831\pi\)
0.653811 0.756658i \(-0.273169\pi\)
\(54\) 31.9085 69.3819i 0.0804111 0.174846i
\(55\) −487.617 −1.19546
\(56\) −182.076 + 51.8907i −0.434480 + 0.123825i
\(57\) 432.596i 1.00524i
\(58\) 113.465 246.718i 0.256874 0.558546i
\(59\) −236.128 −0.521038 −0.260519 0.965469i \(-0.583894\pi\)
−0.260519 + 0.965469i \(0.583894\pi\)
\(60\) −153.750 + 131.802i −0.330816 + 0.283593i
\(61\) 438.613i 0.920634i −0.887755 0.460317i \(-0.847736\pi\)
0.887755 0.460317i \(-0.152264\pi\)
\(62\) −70.1619 + 152.560i −0.143719 + 0.312502i
\(63\) 75.3038i 0.150594i
\(64\) −435.076 + 269.912i −0.849758 + 0.527172i
\(65\) 160.065 + 361.668i 0.305441 + 0.690144i
\(66\) 204.883 445.497i 0.382111 0.830863i
\(67\) 639.558 1.16619 0.583093 0.812405i \(-0.301842\pi\)
0.583093 + 0.812405i \(0.301842\pi\)
\(68\) −375.909 438.505i −0.670377 0.782008i
\(69\) 505.382i 0.881751i
\(70\) −83.4363 + 181.424i −0.142465 + 0.309776i
\(71\) 79.3300i 0.132602i 0.997800 + 0.0663009i \(0.0211197\pi\)
−0.997800 + 0.0663009i \(0.978880\pi\)
\(72\) −55.8159 195.848i −0.0913606 0.320569i
\(73\) 40.6482i 0.0651713i −0.999469 0.0325857i \(-0.989626\pi\)
0.999469 0.0325857i \(-0.0103742\pi\)
\(74\) −482.158 221.743i −0.757429 0.348339i
\(75\) 161.403i 0.248496i
\(76\) 750.800 + 875.822i 1.13319 + 1.32189i
\(77\) 483.522i 0.715616i
\(78\) −397.682 5.72361i −0.577290 0.00830860i
\(79\) 807.497 1.15001 0.575004 0.818151i \(-0.305001\pi\)
0.575004 + 0.818151i \(0.305001\pi\)
\(80\) −82.5261 + 533.686i −0.115334 + 0.745849i
\(81\) 81.0000 0.111111
\(82\) −249.870 + 543.317i −0.336506 + 0.731699i
\(83\) 1390.02 1.83825 0.919124 0.393969i \(-0.128898\pi\)
0.919124 + 0.393969i \(0.128898\pi\)
\(84\) −130.695 152.458i −0.169762 0.198031i
\(85\) −609.195 −0.777370
\(86\) 190.094 413.340i 0.238353 0.518275i
\(87\) 288.031 0.354945
\(88\) −358.391 1257.53i −0.434143 1.52333i
\(89\) 1051.90i 1.25282i −0.779494 0.626409i \(-0.784524\pi\)
0.779494 0.626409i \(-0.215476\pi\)
\(90\) −195.147 89.7476i −0.228559 0.105114i
\(91\) −358.630 + 158.721i −0.413128 + 0.182840i
\(92\) 877.125 + 1023.18i 0.993985 + 1.15950i
\(93\) −178.106 −0.198589
\(94\) −637.431 + 1386.03i −0.699425 + 1.52083i
\(95\) 1216.74 1.31405
\(96\) −452.912 299.638i −0.481512 0.318559i
\(97\) 1002.06i 1.04890i 0.851441 + 0.524450i \(0.175729\pi\)
−0.851441 + 0.524450i \(0.824271\pi\)
\(98\) 701.507 + 322.621i 0.723091 + 0.332547i
\(99\) 520.097 0.527997
\(100\) −280.126 326.772i −0.280126 0.326772i
\(101\) 709.387i 0.698878i −0.936959 0.349439i \(-0.886372\pi\)
0.936959 0.349439i \(-0.113628\pi\)
\(102\) 255.967 556.574i 0.248475 0.540284i
\(103\) 535.679 0.512446 0.256223 0.966618i \(-0.417522\pi\)
0.256223 + 0.966618i \(0.417522\pi\)
\(104\) −815.072 + 678.618i −0.768504 + 0.639846i
\(105\) −211.804 −0.196856
\(106\) 690.059 1500.46i 0.632306 1.37489i
\(107\) 1877.42i 1.69623i −0.529810 0.848116i \(-0.677737\pi\)
0.529810 0.848116i \(-0.322263\pi\)
\(108\) 163.991 140.581i 0.146111 0.125254i
\(109\) 1084.63 0.953110 0.476555 0.879145i \(-0.341885\pi\)
0.476555 + 0.879145i \(0.341885\pi\)
\(110\) −1253.03 576.265i −1.08611 0.499497i
\(111\) 562.896i 0.481331i
\(112\) −529.204 81.8330i −0.446474 0.0690401i
\(113\) 393.209 0.327345 0.163672 0.986515i \(-0.447666\pi\)
0.163672 + 0.986515i \(0.447666\pi\)
\(114\) −511.240 + 1111.64i −0.420018 + 0.913287i
\(115\) 1421.46 1.15263
\(116\) 583.141 499.898i 0.466752 0.400124i
\(117\) −170.727 385.758i −0.134904 0.304815i
\(118\) −606.778 279.055i −0.473377 0.217705i
\(119\) 604.079i 0.465343i
\(120\) −550.853 + 156.991i −0.419048 + 0.119427i
\(121\) 2008.51 1.50903
\(122\) 518.352 1127.10i 0.384667 0.836419i
\(123\) −634.297 −0.464980
\(124\) −360.590 + 309.116i −0.261144 + 0.223866i
\(125\) −1508.71 −1.07955
\(126\) 88.9939 193.508i 0.0629223 0.136818i
\(127\) −1119.16 −0.781966 −0.390983 0.920398i \(-0.627865\pi\)
−0.390983 + 0.920398i \(0.627865\pi\)
\(128\) −1437.00 + 179.421i −0.992295 + 0.123897i
\(129\) 482.555 0.329353
\(130\) −16.0985 + 1118.54i −0.0108610 + 0.754636i
\(131\) 2927.91i 1.95277i 0.216041 + 0.976384i \(0.430686\pi\)
−0.216041 + 0.976384i \(0.569314\pi\)
\(132\) 1052.98 902.664i 0.694316 0.595203i
\(133\) 1206.52i 0.786607i
\(134\) 1643.47 + 755.828i 1.05951 + 0.487266i
\(135\) 227.825i 0.145245i
\(136\) −447.749 1571.07i −0.282310 0.990577i
\(137\) 366.021i 0.228257i 0.993466 + 0.114129i \(0.0364076\pi\)
−0.993466 + 0.114129i \(0.963592\pi\)
\(138\) −597.259 + 1298.68i −0.368421 + 0.801093i
\(139\) 1679.55i 1.02488i 0.858724 + 0.512439i \(0.171258\pi\)
−0.858724 + 0.512439i \(0.828742\pi\)
\(140\) −428.812 + 367.600i −0.258866 + 0.221913i
\(141\) −1618.12 −0.966457
\(142\) −93.7519 + 203.854i −0.0554048 + 0.120472i
\(143\) −1096.23 2476.93i −0.641058 1.44847i
\(144\) 88.0231 569.235i 0.0509393 0.329418i
\(145\) 810.132i 0.463985i
\(146\) 48.0379 104.454i 0.0272304 0.0592099i
\(147\) 818.975i 0.459510i
\(148\) −976.945 1139.63i −0.542597 0.632950i
\(149\) 693.976 0.381562 0.190781 0.981633i \(-0.438898\pi\)
0.190781 + 0.981633i \(0.438898\pi\)
\(150\) 190.745 414.756i 0.103829 0.225765i
\(151\) 1464.84i 0.789448i 0.918800 + 0.394724i \(0.129160\pi\)
−0.918800 + 0.394724i \(0.870840\pi\)
\(152\) 894.285 + 3137.89i 0.477211 + 1.67445i
\(153\) 649.773 0.343340
\(154\) 571.425 1242.51i 0.299005 0.650156i
\(155\) 500.951i 0.259596i
\(156\) −1015.16 484.688i −0.521012 0.248757i
\(157\) 3120.49i 1.58625i −0.609056 0.793127i \(-0.708451\pi\)
0.609056 0.793127i \(-0.291549\pi\)
\(158\) 2075.03 + 954.298i 1.04481 + 0.480506i
\(159\) 1751.72 0.873713
\(160\) −842.776 + 1273.88i −0.416421 + 0.629434i
\(161\) 1409.53i 0.689976i
\(162\) 208.146 + 95.7256i 0.100947 + 0.0464254i
\(163\) 2488.19 1.19565 0.597824 0.801628i \(-0.296032\pi\)
0.597824 + 0.801628i \(0.296032\pi\)
\(164\) −1284.18 + 1100.87i −0.611450 + 0.524166i
\(165\) 1462.85i 0.690199i
\(166\) 3571.93 + 1642.72i 1.67010 + 0.768072i
\(167\) 2905.66i 1.34639i −0.739466 0.673194i \(-0.764922\pi\)
0.739466 0.673194i \(-0.235078\pi\)
\(168\) −155.672 546.227i −0.0714903 0.250847i
\(169\) −1477.30 + 1626.16i −0.672419 + 0.740171i
\(170\) −1565.45 719.945i −0.706261 0.324808i
\(171\) −1297.79 −0.580376
\(172\) 976.968 837.507i 0.433100 0.371275i
\(173\) 2339.59i 1.02818i −0.857735 0.514092i \(-0.828129\pi\)
0.857735 0.514092i \(-0.171871\pi\)
\(174\) 740.154 + 340.395i 0.322476 + 0.148306i
\(175\) 450.157i 0.194449i
\(176\) 565.192 3655.02i 0.242062 1.56539i
\(177\) 708.384i 0.300822i
\(178\) 1243.13 2703.06i 0.523463 1.13822i
\(179\) 4222.06i 1.76297i −0.472214 0.881484i \(-0.656545\pi\)
0.472214 0.881484i \(-0.343455\pi\)
\(180\) −395.406 461.249i −0.163732 0.190997i
\(181\) 3070.52i 1.26094i 0.776215 + 0.630469i \(0.217137\pi\)
−0.776215 + 0.630469i \(0.782863\pi\)
\(182\) −1109.15 15.9633i −0.451734 0.00650154i
\(183\) 1315.84 0.531528
\(184\) 1044.75 + 3665.86i 0.418588 + 1.46875i
\(185\) −1583.23 −0.629197
\(186\) −457.680 210.486i −0.180423 0.0829761i
\(187\) 4172.16 1.63154
\(188\) −3276.01 + 2808.36i −1.27089 + 1.08947i
\(189\) 225.911 0.0869452
\(190\) 3126.66 + 1437.94i 1.19385 + 0.549049i
\(191\) −623.978 −0.236385 −0.118192 0.992991i \(-0.537710\pi\)
−0.118192 + 0.992991i \(0.537710\pi\)
\(192\) −809.737 1305.23i −0.304363 0.490608i
\(193\) 197.490i 0.0736560i −0.999322 0.0368280i \(-0.988275\pi\)
0.999322 0.0368280i \(-0.0117254\pi\)
\(194\) −1184.23 + 2574.98i −0.438260 + 0.952953i
\(195\) −1085.00 + 480.196i −0.398455 + 0.176346i
\(196\) 1421.39 + 1658.08i 0.517999 + 0.604256i
\(197\) −3571.39 −1.29163 −0.645815 0.763494i \(-0.723482\pi\)
−0.645815 + 0.763494i \(0.723482\pi\)
\(198\) 1336.49 + 614.649i 0.479699 + 0.220612i
\(199\) 2395.86 0.853458 0.426729 0.904379i \(-0.359666\pi\)
0.426729 + 0.904379i \(0.359666\pi\)
\(200\) −333.660 1170.76i −0.117967 0.413925i
\(201\) 1918.67i 0.673298i
\(202\) 838.352 1822.91i 0.292011 0.634949i
\(203\) 803.328 0.277747
\(204\) 1315.51 1127.73i 0.451492 0.387042i
\(205\) 1784.06i 0.607824i
\(206\) 1376.53 + 633.064i 0.465571 + 0.214115i
\(207\) −1516.14 −0.509079
\(208\) −2896.48 + 780.594i −0.965551 + 0.260214i
\(209\) −8333.02 −2.75793
\(210\) −544.271 250.309i −0.178849 0.0822521i
\(211\) 197.614i 0.0644754i 0.999480 + 0.0322377i \(0.0102633\pi\)
−0.999480 + 0.0322377i \(0.989737\pi\)
\(212\) 3546.49 3040.23i 1.14893 0.984924i
\(213\) −237.990 −0.0765577
\(214\) 2218.73 4824.40i 0.708734 1.54107i
\(215\) 1357.26i 0.430531i
\(216\) 587.545 167.448i 0.185080 0.0527471i
\(217\) −496.744 −0.155397
\(218\) 2787.18 + 1281.82i 0.865925 + 0.398236i
\(219\) 121.945 0.0376267
\(220\) −2538.88 2961.65i −0.778051 0.907612i
\(221\) −1369.55 3094.51i −0.416860 0.941897i
\(222\) 665.229 1446.47i 0.201114 0.437302i
\(223\) 2694.89i 0.809252i −0.914482 0.404626i \(-0.867402\pi\)
0.914482 0.404626i \(-0.132598\pi\)
\(224\) −1263.19 835.698i −0.376786 0.249274i
\(225\) 484.208 0.143469
\(226\) 1010.43 + 464.693i 0.297401 + 0.136774i
\(227\) 825.056 0.241237 0.120619 0.992699i \(-0.461512\pi\)
0.120619 + 0.992699i \(0.461512\pi\)
\(228\) −2627.47 + 2252.40i −0.763194 + 0.654249i
\(229\) −838.916 −0.242084 −0.121042 0.992647i \(-0.538624\pi\)
−0.121042 + 0.992647i \(0.538624\pi\)
\(230\) 3652.73 + 1679.88i 1.04719 + 0.481600i
\(231\) 1450.57 0.413161
\(232\) 2089.28 595.434i 0.591240 0.168501i
\(233\) 486.416 0.136765 0.0683824 0.997659i \(-0.478216\pi\)
0.0683824 + 0.997659i \(0.478216\pi\)
\(234\) 17.1708 1193.05i 0.00479697 0.333299i
\(235\) 4551.21i 1.26336i
\(236\) −1229.45 1434.18i −0.339112 0.395581i
\(237\) 2422.49i 0.663957i
\(238\) 713.899 1552.30i 0.194434 0.422776i
\(239\) 690.902i 0.186990i 0.995620 + 0.0934952i \(0.0298040\pi\)
−0.995620 + 0.0934952i \(0.970196\pi\)
\(240\) −1601.06 247.578i −0.430616 0.0665880i
\(241\) 1005.08i 0.268643i 0.990938 + 0.134322i \(0.0428855\pi\)
−0.990938 + 0.134322i \(0.957114\pi\)
\(242\) 5161.28 + 2373.66i 1.37099 + 0.630514i
\(243\) 243.000i 0.0641500i
\(244\) 2664.02 2283.73i 0.698960 0.599184i
\(245\) 2303.49 0.600673
\(246\) −1629.95 749.610i −0.422447 0.194282i
\(247\) 2735.40 + 6180.64i 0.704653 + 1.59216i
\(248\) −1291.92 + 368.191i −0.330794 + 0.0942748i
\(249\) 4170.06i 1.06131i
\(250\) −3876.94 1782.99i −0.980797 0.451066i
\(251\) 2502.31i 0.629262i −0.949214 0.314631i \(-0.898119\pi\)
0.949214 0.314631i \(-0.101881\pi\)
\(252\) 457.375 392.085i 0.114333 0.0980121i
\(253\) −9735.09 −2.41913
\(254\) −2875.91 1322.62i −0.710437 0.326728i
\(255\) 1827.59i 0.448815i
\(256\) −3904.69 1237.18i −0.953293 0.302046i
\(257\) −1805.64 −0.438259 −0.219130 0.975696i \(-0.570322\pi\)
−0.219130 + 0.975696i \(0.570322\pi\)
\(258\) 1240.02 + 570.282i 0.299226 + 0.137613i
\(259\) 1569.93i 0.376645i
\(260\) −1363.26 + 2855.29i −0.325176 + 0.681068i
\(261\) 864.094i 0.204927i
\(262\) −3460.20 + 7523.85i −0.815922 + 1.77414i
\(263\) −7806.91 −1.83040 −0.915199 0.403002i \(-0.867967\pi\)
−0.915199 + 0.403002i \(0.867967\pi\)
\(264\) 3772.60 1075.17i 0.879497 0.250653i
\(265\) 4926.98i 1.14212i
\(266\) −1425.86 + 3100.40i −0.328667 + 0.714653i
\(267\) 3155.69 0.723315
\(268\) 3329.99 + 3884.50i 0.758999 + 0.885387i
\(269\) 5945.63i 1.34763i 0.738902 + 0.673813i \(0.235345\pi\)
−0.738902 + 0.673813i \(0.764655\pi\)
\(270\) 269.243 585.441i 0.0606874 0.131959i
\(271\) 1898.73i 0.425608i −0.977095 0.212804i \(-0.931740\pi\)
0.977095 0.212804i \(-0.0682596\pi\)
\(272\) 706.111 4566.34i 0.157405 1.01792i
\(273\) −476.163 1075.89i −0.105563 0.238520i
\(274\) −432.562 + 940.563i −0.0953724 + 0.207378i
\(275\) 3109.07 0.681761
\(276\) −3069.55 + 2631.38i −0.669439 + 0.573878i
\(277\) 2881.71i 0.625073i −0.949906 0.312536i \(-0.898821\pi\)
0.949906 0.312536i \(-0.101179\pi\)
\(278\) −1984.89 + 4315.95i −0.428223 + 0.931128i
\(279\) 534.319i 0.114655i
\(280\) −1536.35 + 437.852i −0.327908 + 0.0934523i
\(281\) 2630.79i 0.558505i 0.960218 + 0.279252i \(0.0900866\pi\)
−0.960218 + 0.279252i \(0.909913\pi\)
\(282\) −4158.09 1912.29i −0.878051 0.403813i
\(283\) 6320.15i 1.32754i 0.747937 + 0.663770i \(0.231045\pi\)
−0.747937 + 0.663770i \(0.768955\pi\)
\(284\) −481.829 + 413.048i −0.100673 + 0.0863024i
\(285\) 3650.22i 0.758669i
\(286\) 110.253 7660.49i 0.0227951 1.58383i
\(287\) −1769.07 −0.363850
\(288\) 898.913 1358.74i 0.183920 0.278001i
\(289\) 299.405 0.0609414
\(290\) 957.411 2081.79i 0.193866 0.421542i
\(291\) −3006.17 −0.605583
\(292\) 246.886 211.643i 0.0494791 0.0424160i
\(293\) 4914.81 0.979953 0.489976 0.871736i \(-0.337005\pi\)
0.489976 + 0.871736i \(0.337005\pi\)
\(294\) −967.863 + 2104.52i −0.191996 + 0.417477i
\(295\) −1992.44 −0.393235
\(296\) −1163.65 4083.05i −0.228499 0.801764i
\(297\) 1560.29i 0.304839i
\(298\) 1783.31 + 820.139i 0.346659 + 0.159427i
\(299\) 3195.64 + 7220.56i 0.618089 + 1.39657i
\(300\) 980.316 840.377i 0.188662 0.161731i
\(301\) 1345.86 0.257721
\(302\) −1731.14 + 3764.19i −0.329854 + 0.717234i
\(303\) 2128.16 0.403497
\(304\) −1410.31 + 9120.31i −0.266075 + 1.72068i
\(305\) 3701.00i 0.694815i
\(306\) 1669.72 + 767.900i 0.311933 + 0.143457i
\(307\) −34.9320 −0.00649405 −0.00324702 0.999995i \(-0.501034\pi\)
−0.00324702 + 0.999995i \(0.501034\pi\)
\(308\) 2936.78 2517.56i 0.543307 0.465751i
\(309\) 1607.04i 0.295861i
\(310\) −592.023 + 1287.29i −0.108467 + 0.235850i
\(311\) −6754.52 −1.23155 −0.615777 0.787920i \(-0.711158\pi\)
−0.615777 + 0.787920i \(0.711158\pi\)
\(312\) −2035.85 2445.22i −0.369415 0.443696i
\(313\) 3933.85 0.710397 0.355199 0.934791i \(-0.384413\pi\)
0.355199 + 0.934791i \(0.384413\pi\)
\(314\) 3687.78 8018.71i 0.662782 1.44115i
\(315\) 635.411i 0.113655i
\(316\) 4204.40 + 4904.52i 0.748469 + 0.873104i
\(317\) −4978.06 −0.882005 −0.441003 0.897506i \(-0.645377\pi\)
−0.441003 + 0.897506i \(0.645377\pi\)
\(318\) 4501.39 + 2070.18i 0.793791 + 0.365062i
\(319\) 5548.30i 0.973809i
\(320\) −3671.16 + 2277.51i −0.641324 + 0.397864i
\(321\) 5632.25 0.979320
\(322\) −1665.77 + 3622.06i −0.288292 + 0.626861i
\(323\) −10410.7 −1.79340
\(324\) 421.744 + 491.972i 0.0723154 + 0.0843573i
\(325\) −1020.58 2306.01i −0.174190 0.393583i
\(326\) 6393.91 + 2940.54i 1.08628 + 0.499575i
\(327\) 3253.90i 0.550278i
\(328\) −4600.96 + 1311.25i −0.774529 + 0.220737i
\(329\) −4512.99 −0.756259
\(330\) 1728.79 3759.09i 0.288385 0.627064i
\(331\) −9305.29 −1.54521 −0.772606 0.634886i \(-0.781047\pi\)
−0.772606 + 0.634886i \(0.781047\pi\)
\(332\) 7237.43 + 8442.60i 1.19640 + 1.39563i
\(333\) 1688.69 0.277896
\(334\) 3433.90 7466.68i 0.562560 1.22323i
\(335\) 5396.57 0.880137
\(336\) 245.499 1587.61i 0.0398603 0.257772i
\(337\) −9088.98 −1.46916 −0.734582 0.678520i \(-0.762622\pi\)
−0.734582 + 0.678520i \(0.762622\pi\)
\(338\) −5718.01 + 2432.86i −0.920174 + 0.391509i
\(339\) 1179.63i 0.188993i
\(340\) −3171.90 3700.09i −0.505943 0.590192i
\(341\) 3430.83i 0.544839i
\(342\) −3334.92 1533.72i −0.527286 0.242497i
\(343\) 5154.06i 0.811350i
\(344\) 3500.28 997.563i 0.548612 0.156352i
\(345\) 4264.39i 0.665470i
\(346\) 2764.92 6012.05i 0.429605 0.934132i
\(347\) 3.22515i 0.000498948i −1.00000 0.000249474i \(-0.999921\pi\)
1.00000 0.000249474i \(-7.94101e-5\pi\)
\(348\) 1499.69 + 1749.42i 0.231012 + 0.269480i
\(349\) −12260.0 −1.88041 −0.940207 0.340604i \(-0.889368\pi\)
−0.940207 + 0.340604i \(0.889368\pi\)
\(350\) 531.994 1156.77i 0.0812465 0.176662i
\(351\) 1157.27 512.181i 0.175985 0.0778866i
\(352\) 5771.87 8724.37i 0.873982 1.32105i
\(353\) 8026.84i 1.21027i 0.796123 + 0.605135i \(0.206881\pi\)
−0.796123 + 0.605135i \(0.793119\pi\)
\(354\) 837.166 1820.33i 0.125692 0.273304i
\(355\) 669.383i 0.100076i
\(356\) 6388.94 5476.92i 0.951160 0.815383i
\(357\) 1812.24 0.268666
\(358\) 4989.61 10849.4i 0.736618 1.60170i
\(359\) 5963.70i 0.876747i −0.898793 0.438374i \(-0.855555\pi\)
0.898793 0.438374i \(-0.144445\pi\)
\(360\) −470.972 1652.56i −0.0689511 0.241938i
\(361\) 13934.2 2.03152
\(362\) −3628.73 + 7890.30i −0.526855 + 1.14559i
\(363\) 6025.54i 0.871236i
\(364\) −2831.31 1351.81i −0.407695 0.194654i
\(365\) 342.988i 0.0491857i
\(366\) 3381.31 + 1555.06i 0.482907 + 0.222088i
\(367\) −9542.35 −1.35724 −0.678619 0.734490i \(-0.737421\pi\)
−0.678619 + 0.734490i \(0.737421\pi\)
\(368\) −1647.60 + 10654.8i −0.233389 + 1.50930i
\(369\) 1902.89i 0.268457i
\(370\) −4068.43 1871.06i −0.571642 0.262896i
\(371\) 4885.60 0.683686
\(372\) −927.348 1081.77i −0.129249 0.150772i
\(373\) 7120.07i 0.988373i 0.869356 + 0.494186i \(0.164534\pi\)
−0.869356 + 0.494186i \(0.835466\pi\)
\(374\) 10721.2 + 4930.64i 1.48230 + 0.681705i
\(375\) 4526.14i 0.623277i
\(376\) −11737.3 + 3345.07i −1.60985 + 0.458800i
\(377\) 4115.20 1821.29i 0.562184 0.248809i
\(378\) 580.525 + 266.982i 0.0789920 + 0.0363282i
\(379\) 1748.05 0.236917 0.118458 0.992959i \(-0.462205\pi\)
0.118458 + 0.992959i \(0.462205\pi\)
\(380\) 6335.22 + 7390.15i 0.855236 + 0.997650i
\(381\) 3357.49i 0.451468i
\(382\) −1603.44 737.416i −0.214762 0.0987682i
\(383\) 5565.09i 0.742462i −0.928541 0.371231i \(-0.878936\pi\)
0.928541 0.371231i \(-0.121064\pi\)
\(384\) −538.264 4310.99i −0.0715317 0.572902i
\(385\) 4079.94i 0.540085i
\(386\) 233.393 507.489i 0.0307756 0.0669184i
\(387\) 1447.66i 0.190152i
\(388\) −6086.21 + 5217.41i −0.796342 + 0.682665i
\(389\) 561.404i 0.0731731i 0.999330 + 0.0365865i \(0.0116485\pi\)
−0.999330 + 0.0365865i \(0.988352\pi\)
\(390\) −3355.63 48.2956i −0.435689 0.00627062i
\(391\) −12162.3 −1.57308
\(392\) 1693.03 + 5940.56i 0.218140 + 0.765417i
\(393\) −8783.73 −1.12743
\(394\) −9177.40 4220.66i −1.17348 0.539680i
\(395\) 6813.63 0.867926
\(396\) 2707.99 + 3158.93i 0.343641 + 0.400864i
\(397\) 5649.99 0.714269 0.357134 0.934053i \(-0.383754\pi\)
0.357134 + 0.934053i \(0.383754\pi\)
\(398\) 6156.65 + 2831.42i 0.775389 + 0.356599i
\(399\) −3619.57 −0.454148
\(400\) 526.191 3402.81i 0.0657739 0.425352i
\(401\) 5458.35i 0.679743i −0.940472 0.339871i \(-0.889616\pi\)
0.940472 0.339871i \(-0.110384\pi\)
\(402\) −2267.48 + 4930.42i −0.281323 + 0.611709i
\(403\) −2544.66 + 1126.21i −0.314538 + 0.139207i
\(404\) 4308.62 3693.57i 0.530599 0.454857i
\(405\) 683.475 0.0838571
\(406\) 2064.31 + 949.371i 0.252340 + 0.116050i
\(407\) 10843.0 1.32056
\(408\) 4713.22 1343.25i 0.571910 0.162992i
\(409\) 12750.8i 1.54154i −0.637116 0.770768i \(-0.719873\pi\)
0.637116 0.770768i \(-0.280127\pi\)
\(410\) −2108.39 + 4584.49i −0.253966 + 0.552224i
\(411\) −1098.06 −0.131784
\(412\) 2789.12 + 3253.57i 0.333520 + 0.389058i
\(413\) 1975.71i 0.235395i
\(414\) −3896.04 1791.78i −0.462512 0.212708i
\(415\) 11728.9 1.38735
\(416\) −8365.58 1417.16i −0.985953 0.167024i
\(417\) −5038.66 −0.591713
\(418\) −21413.4 9847.94i −2.50565 1.15234i
\(419\) 4624.93i 0.539242i −0.962966 0.269621i \(-0.913102\pi\)
0.962966 0.269621i \(-0.0868985\pi\)
\(420\) −1102.80 1286.44i −0.128122 0.149456i
\(421\) −1108.40 −0.128314 −0.0641568 0.997940i \(-0.520436\pi\)
−0.0641568 + 0.997940i \(0.520436\pi\)
\(422\) −233.540 + 507.808i −0.0269396 + 0.0585775i
\(423\) 4854.37i 0.557984i
\(424\) 12706.3 3621.25i 1.45536 0.414772i
\(425\) 3884.26 0.443328
\(426\) −611.562 281.256i −0.0695547 0.0319880i
\(427\) 3669.92 0.415924
\(428\) 11402.9 9775.17i 1.28781 1.10397i
\(429\) 7430.80 3288.69i 0.836276 0.370115i
\(430\) 1604.00 3487.75i 0.179888 0.391149i
\(431\) 2059.16i 0.230130i 0.993358 + 0.115065i \(0.0367077\pi\)
−0.993358 + 0.115065i \(0.963292\pi\)
\(432\) 1707.70 + 264.069i 0.190190 + 0.0294098i
\(433\) 8396.61 0.931906 0.465953 0.884809i \(-0.345712\pi\)
0.465953 + 0.884809i \(0.345712\pi\)
\(434\) −1276.48 587.051i −0.141182 0.0649293i
\(435\) 2430.40 0.267882
\(436\) 5647.37 + 6587.76i 0.620321 + 0.723616i
\(437\) 24291.8 2.65911
\(438\) 313.361 + 144.114i 0.0341848 + 0.0157215i
\(439\) −827.173 −0.0899290 −0.0449645 0.998989i \(-0.514317\pi\)
−0.0449645 + 0.998989i \(0.514317\pi\)
\(440\) −3024.09 10611.0i −0.327654 1.14968i
\(441\) −2456.93 −0.265298
\(442\) 137.742 9570.49i 0.0148229 1.02991i
\(443\) 14728.4i 1.57961i −0.613358 0.789805i \(-0.710182\pi\)
0.613358 0.789805i \(-0.289818\pi\)
\(444\) 3418.88 2930.84i 0.365434 0.313269i
\(445\) 8875.86i 0.945520i
\(446\) 3184.81 6925.06i 0.338129 0.735227i
\(447\) 2081.93i 0.220295i
\(448\) −2258.38 3640.32i −0.238166 0.383904i
\(449\) 1124.15i 0.118156i −0.998253 0.0590781i \(-0.981184\pi\)
0.998253 0.0590781i \(-0.0188161\pi\)
\(450\) 1244.27 + 572.236i 0.130345 + 0.0599454i
\(451\) 12218.4i 1.27570i
\(452\) 2047.32 + 2388.24i 0.213049 + 0.248525i
\(453\) −4394.51 −0.455788
\(454\) 2120.15 + 975.049i 0.219170 + 0.100796i
\(455\) −3026.11 + 1339.28i −0.311794 + 0.137992i
\(456\) −9413.68 + 2682.86i −0.966746 + 0.275518i
\(457\) 17029.0i 1.74307i −0.490334 0.871535i \(-0.663125\pi\)
0.490334 0.871535i \(-0.336875\pi\)
\(458\) −2155.76 991.429i −0.219939 0.101149i
\(459\) 1949.32i 0.198227i
\(460\) 7401.15 + 8633.58i 0.750174 + 0.875093i
\(461\) 7086.48 0.715944 0.357972 0.933732i \(-0.383468\pi\)
0.357972 + 0.933732i \(0.383468\pi\)
\(462\) 3727.52 + 1714.27i 0.375368 + 0.172630i
\(463\) 9841.61i 0.987859i 0.869502 + 0.493929i \(0.164440\pi\)
−0.869502 + 0.493929i \(0.835560\pi\)
\(464\) 6072.49 + 939.015i 0.607561 + 0.0939497i
\(465\) −1502.85 −0.149878
\(466\) 1249.94 + 574.845i 0.124254 + 0.0571442i
\(467\) 13523.9i 1.34007i −0.742331 0.670034i \(-0.766280\pi\)
0.742331 0.670034i \(-0.233720\pi\)
\(468\) 1454.06 3045.48i 0.143620 0.300806i
\(469\) 5351.24i 0.526860i
\(470\) −5378.61 + 11695.3i −0.527866 + 1.14779i
\(471\) 9361.46 0.915825
\(472\) −1464.41 5138.37i −0.142807 0.501086i
\(473\) 9295.37i 0.903598i
\(474\) −2862.89 + 6225.08i −0.277420 + 0.603222i
\(475\) −7758.01 −0.749393
\(476\) 3669.01 3145.26i 0.353296 0.302863i
\(477\) 5255.16i 0.504438i
\(478\) −816.506 + 1775.41i −0.0781299 + 0.169886i
\(479\) 8823.16i 0.841630i 0.907147 + 0.420815i \(0.138256\pi\)
−0.907147 + 0.420815i \(0.861744\pi\)
\(480\) −3821.65 2528.33i −0.363404 0.240421i
\(481\) −3559.32 8042.28i −0.337403 0.762363i
\(482\) −1187.80 + 2582.76i −0.112247 + 0.244069i
\(483\) −4228.58 −0.398358
\(484\) 10457.7 + 12199.2i 0.982132 + 1.14568i
\(485\) 8455.30i 0.791619i
\(486\) −287.177 + 624.437i −0.0268037 + 0.0582820i
\(487\) 8482.21i 0.789252i 0.918842 + 0.394626i \(0.129126\pi\)
−0.918842 + 0.394626i \(0.870874\pi\)
\(488\) 9544.63 2720.17i 0.885379 0.252329i
\(489\) 7464.58i 0.690307i
\(490\) 5919.28 + 2722.26i 0.545727 + 0.250978i
\(491\) 6293.37i 0.578444i 0.957262 + 0.289222i \(0.0933965\pi\)
−0.957262 + 0.289222i \(0.906603\pi\)
\(492\) −3302.60 3852.54i −0.302627 0.353021i
\(493\) 6931.66i 0.633238i
\(494\) −275.112 + 19115.1i −0.0250564 + 1.74095i
\(495\) 4388.55 0.398487
\(496\) −3754.97 580.647i −0.339926 0.0525642i
\(497\) −663.761 −0.0599069
\(498\) −4928.17 + 10715.8i −0.443447 + 0.964230i
\(499\) −503.304 −0.0451523 −0.0225761 0.999745i \(-0.507187\pi\)
−0.0225761 + 0.999745i \(0.507187\pi\)
\(500\) −7855.44 9163.52i −0.702612 0.819610i
\(501\) 8716.99 0.777338
\(502\) 2957.23 6430.20i 0.262923 0.571701i
\(503\) 4401.21 0.390139 0.195070 0.980789i \(-0.437507\pi\)
0.195070 + 0.980789i \(0.437507\pi\)
\(504\) 1638.68 467.017i 0.144827 0.0412749i
\(505\) 5985.78i 0.527453i
\(506\) −25016.2 11504.9i −2.19784 1.01078i
\(507\) −4878.47 4431.91i −0.427338 0.388221i
\(508\) −5827.16 6797.49i −0.508934 0.593681i
\(509\) −4188.23 −0.364715 −0.182358 0.983232i \(-0.558373\pi\)
−0.182358 + 0.983232i \(0.558373\pi\)
\(510\) 2159.84 4696.35i 0.187528 0.407760i
\(511\) 340.107 0.0294431
\(512\) −8571.78 7793.73i −0.739888 0.672730i
\(513\) 3893.36i 0.335080i
\(514\) −4639.95 2133.90i −0.398170 0.183117i
\(515\) 4520.03 0.386750
\(516\) 2512.52 + 2930.91i 0.214356 + 0.250050i
\(517\) 31169.6i 2.65153i
\(518\) 1855.34 4034.26i 0.157373 0.342191i
\(519\) 7018.77 0.593622
\(520\) −6877.54 + 5726.15i −0.580000 + 0.482900i
\(521\) 280.072 0.0235512 0.0117756 0.999931i \(-0.496252\pi\)
0.0117756 + 0.999931i \(0.496252\pi\)
\(522\) −1021.18 + 2220.46i −0.0856245 + 0.186182i
\(523\) 10351.8i 0.865493i −0.901516 0.432747i \(-0.857544\pi\)
0.901516 0.432747i \(-0.142456\pi\)
\(524\) −17783.3 + 15244.8i −1.48257 + 1.27094i
\(525\) 1350.47 0.112265
\(526\) −20061.4 9226.19i −1.66296 0.764793i
\(527\) 4286.25i 0.354292i
\(528\) 10965.1 + 1695.57i 0.903776 + 0.139755i
\(529\) 16212.0 1.33245
\(530\) 5822.69 12660.8i 0.477210 1.03765i
\(531\) 2125.15 0.173679
\(532\) −7328.09 + 6282.01i −0.597205 + 0.511954i
\(533\) −9062.41 + 4010.80i −0.736466 + 0.325942i
\(534\) 8109.18 + 3729.39i 0.657151 + 0.302222i
\(535\) 15841.6i 1.28017i
\(536\) 3966.39 + 13917.4i 0.319630 + 1.12153i
\(537\) 12666.2 1.01785
\(538\) −7026.53 + 15278.5i −0.563076 + 1.22435i
\(539\) −15775.8 −1.26069
\(540\) 1383.75 1186.22i 0.110272 0.0945309i
\(541\) 16992.5 1.35040 0.675199 0.737635i \(-0.264058\pi\)
0.675199 + 0.737635i \(0.264058\pi\)
\(542\) 2243.92 4879.17i 0.177831 0.386676i
\(543\) −9211.55 −0.728002
\(544\) 7210.98 10899.6i 0.568324 0.859040i
\(545\) 9152.09 0.719325
\(546\) 47.8900 3327.44i 0.00375366 0.260809i
\(547\) 162.426i 0.0126963i −0.999980 0.00634813i \(-0.997979\pi\)
0.999980 0.00634813i \(-0.00202069\pi\)
\(548\) −2223.11 + 1905.76i −0.173297 + 0.148559i
\(549\) 3947.52i 0.306878i
\(550\) 7989.38 + 3674.29i 0.619397 + 0.284859i
\(551\) 13844.6i 1.07041i
\(552\) −10997.6 + 3134.26i −0.847985 + 0.241672i
\(553\) 6756.41i 0.519551i
\(554\) 3405.60 7405.13i 0.261173 0.567895i
\(555\) 4749.69i 0.363267i
\(556\) −10201.2 + 8744.95i −0.778103 + 0.667030i
\(557\) −135.037 −0.0102723 −0.00513617 0.999987i \(-0.501635\pi\)
−0.00513617 + 0.999987i \(0.501635\pi\)
\(558\) 631.457 1373.04i 0.0479063 0.104167i
\(559\) 6894.42 3051.30i 0.521651 0.230870i
\(560\) −4465.40 690.504i −0.336960 0.0521056i
\(561\) 12516.5i 0.941971i
\(562\) −3109.06 + 6760.34i −0.233359 + 0.507416i
\(563\) 15659.2i 1.17221i −0.810234 0.586106i \(-0.800660\pi\)
0.810234 0.586106i \(-0.199340\pi\)
\(564\) −8425.09 9828.03i −0.629008 0.733750i
\(565\) 3317.88 0.247052
\(566\) −7469.14 + 16240.9i −0.554684 + 1.20610i
\(567\) 677.734i 0.0501978i
\(568\) −1726.29 + 491.986i −0.127524 + 0.0363438i
\(569\) −13692.7 −1.00884 −0.504418 0.863460i \(-0.668293\pi\)
−0.504418 + 0.863460i \(0.668293\pi\)
\(570\) −4313.82 + 9379.97i −0.316993 + 0.689270i
\(571\) 23805.8i 1.74473i 0.488856 + 0.872365i \(0.337414\pi\)
−0.488856 + 0.872365i \(0.662586\pi\)
\(572\) 9336.47 19554.9i 0.682478 1.42942i
\(573\) 1871.93i 0.136477i
\(574\) −4545.98 2090.69i −0.330567 0.152027i
\(575\) −9063.32 −0.657333
\(576\) 3915.69 2429.21i 0.283253 0.175724i
\(577\) 10653.4i 0.768642i 0.923200 + 0.384321i \(0.125564\pi\)
−0.923200 + 0.384321i \(0.874436\pi\)
\(578\) 769.381 + 353.836i 0.0553669 + 0.0254631i
\(579\) 592.469 0.0425253
\(580\) 4920.52 4218.12i 0.352265 0.301979i
\(581\) 11630.4i 0.830484i
\(582\) −7724.94 3552.68i −0.550188 0.253030i
\(583\) 33743.1i 2.39708i
\(584\) 884.542 252.090i 0.0626757 0.0178623i
\(585\) −1440.59 3255.01i −0.101814 0.230048i
\(586\) 12629.6 + 5808.31i 0.890313 + 0.409452i
\(587\) −15680.9 −1.10259 −0.551294 0.834311i \(-0.685866\pi\)
−0.551294 + 0.834311i \(0.685866\pi\)
\(588\) −4974.23 + 4264.17i −0.348867 + 0.299067i
\(589\) 8560.89i 0.598888i
\(590\) −5119.97 2354.66i −0.357264 0.164305i
\(591\) 10714.2i 0.745723i
\(592\) 1835.11 11867.4i 0.127403 0.823897i
\(593\) 7750.92i 0.536749i −0.963315 0.268375i \(-0.913514\pi\)
0.963315 0.268375i \(-0.0864865\pi\)
\(594\) −1843.95 + 4009.48i −0.127370 + 0.276954i
\(595\) 5097.19i 0.351201i
\(596\) 3613.33 + 4215.02i 0.248335 + 0.289688i
\(597\) 7187.59i 0.492744i
\(598\) −321.401 + 22331.3i −0.0219783 + 1.52708i
\(599\) 5641.89 0.384844 0.192422 0.981312i \(-0.438366\pi\)
0.192422 + 0.981312i \(0.438366\pi\)
\(600\) 3512.27 1000.98i 0.238980 0.0681081i
\(601\) 10995.2 0.746264 0.373132 0.927778i \(-0.378284\pi\)
0.373132 + 0.927778i \(0.378284\pi\)
\(602\) 3458.45 + 1590.53i 0.234146 + 0.107683i
\(603\) −5756.02 −0.388729
\(604\) −8897.01 + 7626.97i −0.599361 + 0.513803i
\(605\) 16947.8 1.13888
\(606\) 5468.73 + 2515.06i 0.366588 + 0.168593i
\(607\) −1343.46 −0.0898344 −0.0449172 0.998991i \(-0.514302\pi\)
−0.0449172 + 0.998991i \(0.514302\pi\)
\(608\) −14402.4 + 21769.7i −0.960684 + 1.45210i
\(609\) 2409.98i 0.160357i
\(610\) 4373.83 9510.45i 0.290313 0.631257i
\(611\) −23118.7 + 10231.7i −1.53074 + 0.677467i
\(612\) 3383.18 + 3946.54i 0.223459 + 0.260669i
\(613\) −9486.08 −0.625023 −0.312511 0.949914i \(-0.601170\pi\)
−0.312511 + 0.949914i \(0.601170\pi\)
\(614\) −89.7647 41.2825i −0.00590001 0.00271340i
\(615\) −5352.17 −0.350927
\(616\) 10521.9 2998.69i 0.688213 0.196137i
\(617\) 23208.1i 1.51430i 0.653242 + 0.757149i \(0.273408\pi\)
−0.653242 + 0.757149i \(0.726592\pi\)
\(618\) −1899.19 + 4129.60i −0.123619 + 0.268797i
\(619\) 15457.5 1.00370 0.501849 0.864955i \(-0.332653\pi\)
0.501849 + 0.864955i \(0.332653\pi\)
\(620\) −3042.64 + 2608.31i −0.197089 + 0.168955i
\(621\) 4548.43i 0.293917i
\(622\) −17357.1 7982.47i −1.11890 0.514579i
\(623\) 8801.32 0.565999
\(624\) −2341.78 8689.43i −0.150234 0.557461i
\(625\) −6005.36 −0.384343
\(626\) 10108.8 + 4649.01i 0.645415 + 0.296824i
\(627\) 24999.1i 1.59229i
\(628\) 18953.0 16247.5i 1.20431 1.03240i
\(629\) 13546.5 0.858717
\(630\) 750.927 1632.81i 0.0474883 0.103259i
\(631\) 16138.7i 1.01818i 0.860713 + 0.509091i \(0.170018\pi\)
−0.860713 + 0.509091i \(0.829982\pi\)
\(632\) 5007.91 + 17571.9i 0.315196 + 1.10597i
\(633\) −592.842 −0.0372249
\(634\) −12792.1 5883.06i −0.801325 0.368527i
\(635\) −9443.45 −0.590161
\(636\) 9120.69 + 10639.5i 0.568646 + 0.663337i
\(637\) 5178.56 + 11701.0i 0.322107 + 0.727801i
\(638\) −6556.97 + 14257.5i −0.406885 + 0.884731i
\(639\) 713.970i 0.0442006i
\(640\) −12125.3 + 1513.95i −0.748899 + 0.0935065i
\(641\) −4067.71 −0.250647 −0.125324 0.992116i \(-0.539997\pi\)
−0.125324 + 0.992116i \(0.539997\pi\)
\(642\) 14473.2 + 6656.18i 0.889738 + 0.409188i
\(643\) −14570.0 −0.893603 −0.446801 0.894633i \(-0.647437\pi\)
−0.446801 + 0.894633i \(0.647437\pi\)
\(644\) −8561.07 + 7338.99i −0.523841 + 0.449063i
\(645\) 4071.78 0.248567
\(646\) −26752.4 12303.3i −1.62935 0.749332i
\(647\) 19304.6 1.17302 0.586509 0.809943i \(-0.300502\pi\)
0.586509 + 0.809943i \(0.300502\pi\)
\(648\) 502.343 + 1762.64i 0.0304535 + 0.106856i
\(649\) 13645.5 0.825319
\(650\) 102.645 7131.89i 0.00619395 0.430362i
\(651\) 1490.23i 0.0897186i
\(652\) 12955.3 + 15112.6i 0.778173 + 0.907754i
\(653\) 1649.08i 0.0988260i −0.998778 0.0494130i \(-0.984265\pi\)
0.998778 0.0494130i \(-0.0157351\pi\)
\(654\) −3845.45 + 8361.54i −0.229922 + 0.499942i
\(655\) 24705.6i 1.47378i
\(656\) −13372.7 2067.88i −0.795910 0.123075i
\(657\) 365.834i 0.0217238i
\(658\) −11597.0 5333.44i −0.687081 0.315987i
\(659\) 16643.2i 0.983803i 0.870651 + 0.491902i \(0.163698\pi\)
−0.870651 + 0.491902i \(0.836302\pi\)
\(660\) 8884.96 7616.64i 0.524010 0.449208i
\(661\) 5394.04 0.317403 0.158702 0.987327i \(-0.449269\pi\)
0.158702 + 0.987327i \(0.449269\pi\)
\(662\) −23911.8 10997.0i −1.40387 0.645634i
\(663\) 9283.52 4108.66i 0.543804 0.240674i
\(664\) 8620.58 + 30248.1i 0.503830 + 1.76785i
\(665\) 10180.6i 0.593663i
\(666\) 4339.42 + 1995.69i 0.252476 + 0.116113i
\(667\) 16174.0i 0.938918i
\(668\) 17648.2 15128.9i 1.02220 0.876282i
\(669\) 8084.67 0.467222
\(670\) 13867.6 + 6377.65i 0.799627 + 0.367746i
\(671\) 25346.8i 1.45827i
\(672\) 2507.10 3789.56i 0.143919 0.217538i
\(673\) −29896.5 −1.71237 −0.856186 0.516668i \(-0.827172\pi\)
−0.856186 + 0.516668i \(0.827172\pi\)
\(674\) −23356.0 10741.3i −1.33477 0.613859i
\(675\) 1452.62i 0.0828319i
\(676\) −17568.7 505.817i −0.999586 0.0287789i
\(677\) 5527.06i 0.313770i −0.987617 0.156885i \(-0.949855\pi\)
0.987617 0.156885i \(-0.0501452\pi\)
\(678\) −1394.08 + 3031.28i −0.0789665 + 0.171705i
\(679\) −8384.29 −0.473873
\(680\) −3778.08 13256.7i −0.213063 0.747602i
\(681\) 2475.17i 0.139278i
\(682\) 4054.55 8816.21i 0.227649 0.495000i
\(683\) 1482.94 0.0830790 0.0415395 0.999137i \(-0.486774\pi\)
0.0415395 + 0.999137i \(0.486774\pi\)
\(684\) −6757.20 7882.40i −0.377731 0.440630i
\(685\) 3088.47i 0.172269i
\(686\) −6091.05 + 13244.4i −0.339005 + 0.737133i
\(687\) 2516.75i 0.139767i
\(688\) 10173.6 + 1573.18i 0.563756 + 0.0871759i
\(689\) 25027.4 11076.5i 1.38384 0.612455i
\(690\) −5039.64 + 10958.2i −0.278052 + 0.604596i
\(691\) 18752.3 1.03237 0.516187 0.856476i \(-0.327351\pi\)
0.516187 + 0.856476i \(0.327351\pi\)
\(692\) 14210.0 12181.6i 0.780614 0.669182i
\(693\) 4351.70i 0.238539i
\(694\) 3.81147 8.28766i 0.000208475 0.000453307i
\(695\) 14172.0i 0.773489i
\(696\) 1786.30 + 6267.83i 0.0972839 + 0.341353i
\(697\) 15264.8i 0.829547i
\(698\) −31504.6 14488.9i −1.70840 0.785690i
\(699\) 1459.25i 0.0789612i
\(700\) 2734.13 2343.84i 0.147629 0.126555i
\(701\) 30930.9i 1.66654i −0.552867 0.833269i \(-0.686466\pi\)
0.552867 0.833269i \(-0.313534\pi\)
\(702\) 3579.14 + 51.5125i 0.192430 + 0.00276953i
\(703\) −27056.3 −1.45156
\(704\) 25142.4 15597.8i 1.34601 0.835036i
\(705\) −13653.6 −0.729399
\(706\) −9486.10 + 20626.6i −0.505686 + 1.09956i
\(707\) 5935.51 0.315739
\(708\) 4302.53 3688.35i 0.228389 0.195786i
\(709\) −15172.9 −0.803711 −0.401855 0.915703i \(-0.631635\pi\)
−0.401855 + 0.915703i \(0.631635\pi\)
\(710\) −791.075 + 1720.11i −0.0418148 + 0.0909221i
\(711\) −7267.48 −0.383336
\(712\) 22890.3 6523.62i 1.20484 0.343375i
\(713\) 10001.3i 0.525318i
\(714\) 4656.90 + 2141.70i 0.244090 + 0.112256i
\(715\) −9249.93 20900.2i −0.483815 1.09318i
\(716\) 25643.6 21983.0i 1.33847 1.14741i
\(717\) −2072.71 −0.107959
\(718\) 7047.89 15324.9i 0.366330 0.796547i
\(719\) −7513.99 −0.389742 −0.194871 0.980829i \(-0.562429\pi\)
−0.194871 + 0.980829i \(0.562429\pi\)
\(720\) 742.735 4803.18i 0.0384446 0.248616i
\(721\) 4482.07i 0.231513i
\(722\) 35806.7 + 16467.4i 1.84569 + 0.848828i
\(723\) −3015.25 −0.155101
\(724\) −18649.5 + 15987.3i −0.957324 + 0.820667i
\(725\) 5165.44i 0.264607i
\(726\) −7120.97 + 15483.8i −0.364027 + 0.791541i
\(727\) 9581.83 0.488818 0.244409 0.969672i \(-0.421406\pi\)
0.244409 + 0.969672i \(0.421406\pi\)
\(728\) −5678.06 6819.78i −0.289070 0.347195i
\(729\) −729.000 −0.0370370
\(730\) 405.342 881.375i 0.0205512 0.0446865i
\(731\) 11613.0i 0.587582i
\(732\) 6851.19 + 7992.05i 0.345939 + 0.403545i
\(733\) −1242.65 −0.0626170 −0.0313085 0.999510i \(-0.509967\pi\)
−0.0313085 + 0.999510i \(0.509967\pi\)
\(734\) −24521.0 11277.1i −1.23309 0.567093i
\(735\) 6910.48i 0.346798i
\(736\) −16825.7 + 25432.6i −0.842668 + 1.27372i
\(737\) −36959.1 −1.84723
\(738\) 2248.83 4889.85i 0.112169 0.243900i
\(739\) 7607.91 0.378703 0.189351 0.981909i \(-0.439361\pi\)
0.189351 + 0.981909i \(0.439361\pi\)
\(740\) −8243.42 9616.11i −0.409506 0.477696i
\(741\) −18541.9 + 8206.19i −0.919236 + 0.406831i
\(742\) 12554.5 + 5773.79i 0.621147 + 0.285664i
\(743\) 23962.7i 1.18318i −0.806238 0.591591i \(-0.798500\pi\)
0.806238 0.591591i \(-0.201500\pi\)
\(744\) −1104.57 3875.76i −0.0544296 0.190984i
\(745\) 5855.74 0.287970
\(746\) −8414.48 + 18296.4i −0.412970 + 0.897962i
\(747\) −12510.2 −0.612749
\(748\) 21723.2 + 25340.5i 1.06187 + 1.23869i
\(749\) 15708.5 0.766325
\(750\) 5348.98 11630.8i 0.260423 0.566264i
\(751\) −14661.3 −0.712383 −0.356192 0.934413i \(-0.615925\pi\)
−0.356192 + 0.934413i \(0.615925\pi\)
\(752\) −34114.5 5275.26i −1.65429 0.255810i
\(753\) 7506.94 0.363304
\(754\) 12727.2 + 183.175i 0.614719 + 0.00884728i
\(755\) 12360.2i 0.595807i
\(756\) 1176.26 + 1372.12i 0.0565873 + 0.0660102i
\(757\) 6391.51i 0.306874i −0.988158 0.153437i \(-0.950966\pi\)
0.988158 0.153437i \(-0.0490342\pi\)
\(758\) 4491.97 + 2065.84i 0.215245 + 0.0989906i
\(759\) 29205.3i 1.39668i
\(760\) 7545.94 + 26477.4i 0.360158 + 1.26373i
\(761\) 3654.75i 0.174093i 0.996204 + 0.0870464i \(0.0277428\pi\)
−0.996204 + 0.0870464i \(0.972257\pi\)
\(762\) 3967.87 8627.74i 0.188636 0.410171i
\(763\) 9075.22i 0.430597i
\(764\) −3248.87 3789.87i −0.153848 0.179467i
\(765\) 5482.76 0.259123
\(766\) 6576.81 14300.6i 0.310222 0.674546i
\(767\) −4479.27 10120.9i −0.210870 0.476461i
\(768\) 3711.54 11714.1i 0.174386 0.550384i
\(769\) 13844.0i 0.649188i −0.945853 0.324594i \(-0.894772\pi\)
0.945853 0.324594i \(-0.105228\pi\)
\(770\) 4821.66 10484.2i 0.225663 0.490682i
\(771\) 5416.91i 0.253029i
\(772\) 1199.50 1028.27i 0.0559208 0.0479382i
\(773\) −9330.55 −0.434148