Properties

Label 225.4.h.d.46.14
Level $225$
Weight $4$
Character 225.46
Analytic conductor $13.275$
Analytic rank $0$
Dimension $64$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [225,4,Mod(46,225)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(225, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 6]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("225.46");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 225 = 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 225.h (of order \(5\), 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: \(13.2754297513\)
Analytic rank: \(0\)
Dimension: \(64\)
Relative dimension: \(16\) over \(\Q(\zeta_{5})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 46.14
Character \(\chi\) \(=\) 225.46
Dual form 225.4.h.d.181.14

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.31991 - 4.06225i) q^{2} +(-8.28762 - 6.02131i) q^{4} +(4.79821 - 10.0984i) q^{5} +33.6094 q^{7} +(-7.75447 + 5.63395i) q^{8} +O(q^{10})\) \(q+(1.31991 - 4.06225i) q^{2} +(-8.28762 - 6.02131i) q^{4} +(4.79821 - 10.0984i) q^{5} +33.6094 q^{7} +(-7.75447 + 5.63395i) q^{8} +(-34.6890 - 32.8205i) q^{10} +(9.92549 - 30.5475i) q^{11} +(23.5572 + 72.5016i) q^{13} +(44.3613 - 136.530i) q^{14} +(-12.6733 - 39.0045i) q^{16} +(33.4899 - 24.3319i) q^{17} +(-2.91326 + 2.11660i) q^{19} +(-100.571 + 54.8000i) q^{20} +(-110.991 - 80.6398i) q^{22} +(-38.2254 + 117.646i) q^{23} +(-78.9543 - 96.9083i) q^{25} +325.613 q^{26} +(-278.542 - 202.372i) q^{28} +(-153.999 - 111.887i) q^{29} +(-267.535 + 194.376i) q^{31} -251.854 q^{32} +(-54.6386 - 168.160i) q^{34} +(161.265 - 339.400i) q^{35} +(-39.9391 - 122.920i) q^{37} +(4.75296 + 14.6281i) q^{38} +(19.6862 + 105.340i) q^{40} +(129.358 + 398.124i) q^{41} -41.9887 q^{43} +(-266.195 + 193.402i) q^{44} +(427.452 + 310.562i) q^{46} +(375.583 + 272.877i) q^{47} +786.592 q^{49} +(-497.878 + 192.823i) q^{50} +(241.321 - 742.710i) q^{52} +(-200.790 - 145.882i) q^{53} +(-260.856 - 246.805i) q^{55} +(-260.623 + 189.354i) q^{56} +(-657.777 + 477.903i) q^{58} +(-66.6949 - 205.266i) q^{59} +(57.9582 - 178.377i) q^{61} +(436.482 + 1343.35i) q^{62} +(-231.037 + 711.060i) q^{64} +(845.181 + 109.989i) q^{65} +(-223.332 + 162.260i) q^{67} -424.061 q^{68} +(-1165.88 - 1103.08i) q^{70} +(-328.894 - 238.955i) q^{71} +(-161.479 + 496.983i) q^{73} -552.048 q^{74} +36.8887 q^{76} +(333.590 - 1026.68i) q^{77} +(295.531 + 214.716i) q^{79} +(-454.691 - 59.1718i) q^{80} +1788.02 q^{82} +(550.242 - 399.774i) q^{83} +(-85.0205 - 454.944i) q^{85} +(-55.4211 + 170.569i) q^{86} +(95.1364 + 292.800i) q^{88} +(91.6049 - 281.931i) q^{89} +(791.743 + 2436.73i) q^{91} +(1025.18 - 744.835i) q^{92} +(1604.23 - 1165.54i) q^{94} +(7.39584 + 39.5751i) q^{95} +(-185.918 - 135.077i) q^{97} +(1038.23 - 3195.33i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 64 q - 72 q^{4} + 20 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 64 q - 72 q^{4} + 20 q^{7} + 50 q^{10} + 180 q^{13} - 244 q^{16} - 116 q^{19} - 210 q^{22} + 440 q^{25} + 980 q^{28} + 42 q^{31} + 40 q^{34} - 1170 q^{37} - 3040 q^{40} + 1040 q^{43} + 700 q^{46} + 4188 q^{49} + 3280 q^{52} + 2640 q^{55} - 4530 q^{58} + 88 q^{61} - 3018 q^{64} - 2860 q^{67} - 3720 q^{70} - 5280 q^{73} + 9288 q^{76} - 1144 q^{79} + 2840 q^{82} + 470 q^{85} + 7610 q^{88} - 1180 q^{91} + 2170 q^{94} + 2050 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(1\) \(e\left(\frac{3}{5}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.31991 4.06225i 0.466657 1.43622i −0.390229 0.920718i \(-0.627604\pi\)
0.856886 0.515506i \(-0.172396\pi\)
\(3\) 0 0
\(4\) −8.28762 6.02131i −1.03595 0.752663i
\(5\) 4.79821 10.0984i 0.429165 0.903226i
\(6\) 0 0
\(7\) 33.6094 1.81474 0.907368 0.420336i \(-0.138088\pi\)
0.907368 + 0.420336i \(0.138088\pi\)
\(8\) −7.75447 + 5.63395i −0.342702 + 0.248988i
\(9\) 0 0
\(10\) −34.6890 32.8205i −1.09696 1.03787i
\(11\) 9.92549 30.5475i 0.272059 0.837312i −0.717924 0.696122i \(-0.754907\pi\)
0.989983 0.141190i \(-0.0450927\pi\)
\(12\) 0 0
\(13\) 23.5572 + 72.5016i 0.502584 + 1.54679i 0.804795 + 0.593553i \(0.202275\pi\)
−0.302211 + 0.953241i \(0.597725\pi\)
\(14\) 44.3613 136.530i 0.846860 2.60637i
\(15\) 0 0
\(16\) −12.6733 39.0045i −0.198021 0.609445i
\(17\) 33.4899 24.3319i 0.477794 0.347138i −0.322677 0.946509i \(-0.604583\pi\)
0.800471 + 0.599371i \(0.204583\pi\)
\(18\) 0 0
\(19\) −2.91326 + 2.11660i −0.0351761 + 0.0255570i −0.605234 0.796047i \(-0.706921\pi\)
0.570058 + 0.821604i \(0.306921\pi\)
\(20\) −100.571 + 54.8000i −1.12442 + 0.612682i
\(21\) 0 0
\(22\) −110.991 80.6398i −1.07561 0.781475i
\(23\) −38.2254 + 117.646i −0.346545 + 1.06656i 0.614206 + 0.789146i \(0.289476\pi\)
−0.960751 + 0.277411i \(0.910524\pi\)
\(24\) 0 0
\(25\) −78.9543 96.9083i −0.631635 0.775266i
\(26\) 325.613 2.45608
\(27\) 0 0
\(28\) −278.542 202.372i −1.87998 1.36589i
\(29\) −153.999 111.887i −0.986100 0.716444i −0.0270367 0.999634i \(-0.508607\pi\)
−0.959064 + 0.283191i \(0.908607\pi\)
\(30\) 0 0
\(31\) −267.535 + 194.376i −1.55002 + 1.12616i −0.606390 + 0.795168i \(0.707383\pi\)
−0.943634 + 0.330990i \(0.892617\pi\)
\(32\) −251.854 −1.39131
\(33\) 0 0
\(34\) −54.6386 168.160i −0.275601 0.848214i
\(35\) 161.265 339.400i 0.778822 1.63912i
\(36\) 0 0
\(37\) −39.9391 122.920i −0.177458 0.546160i 0.822279 0.569084i \(-0.192702\pi\)
−0.999737 + 0.0229247i \(0.992702\pi\)
\(38\) 4.75296 + 14.6281i 0.0202903 + 0.0624471i
\(39\) 0 0
\(40\) 19.6862 + 105.340i 0.0778165 + 0.416395i
\(41\) 129.358 + 398.124i 0.492741 + 1.51650i 0.820448 + 0.571721i \(0.193724\pi\)
−0.327708 + 0.944779i \(0.606276\pi\)
\(42\) 0 0
\(43\) −41.9887 −0.148912 −0.0744559 0.997224i \(-0.523722\pi\)
−0.0744559 + 0.997224i \(0.523722\pi\)
\(44\) −266.195 + 193.402i −0.912054 + 0.662646i
\(45\) 0 0
\(46\) 427.452 + 310.562i 1.37010 + 0.995433i
\(47\) 375.583 + 272.877i 1.16563 + 0.846877i 0.990479 0.137666i \(-0.0439599\pi\)
0.175147 + 0.984542i \(0.443960\pi\)
\(48\) 0 0
\(49\) 786.592 2.29327
\(50\) −497.878 + 192.823i −1.40821 + 0.545385i
\(51\) 0 0
\(52\) 241.321 742.710i 0.643562 1.98068i
\(53\) −200.790 145.882i −0.520388 0.378084i 0.296362 0.955076i \(-0.404226\pi\)
−0.816750 + 0.576992i \(0.804226\pi\)
\(54\) 0 0
\(55\) −260.856 246.805i −0.639523 0.605076i
\(56\) −260.623 + 189.354i −0.621915 + 0.451848i
\(57\) 0 0
\(58\) −657.777 + 477.903i −1.48914 + 1.08193i
\(59\) −66.6949 205.266i −0.147169 0.452938i 0.850115 0.526597i \(-0.176532\pi\)
−0.997283 + 0.0736590i \(0.976532\pi\)
\(60\) 0 0
\(61\) 57.9582 178.377i 0.121652 0.374407i −0.871624 0.490175i \(-0.836933\pi\)
0.993276 + 0.115768i \(0.0369329\pi\)
\(62\) 436.482 + 1343.35i 0.894085 + 2.75171i
\(63\) 0 0
\(64\) −231.037 + 711.060i −0.451245 + 1.38879i
\(65\) 845.181 + 109.989i 1.61280 + 0.209883i
\(66\) 0 0
\(67\) −223.332 + 162.260i −0.407228 + 0.295869i −0.772479 0.635041i \(-0.780983\pi\)
0.365250 + 0.930909i \(0.380983\pi\)
\(68\) −424.061 −0.756250
\(69\) 0 0
\(70\) −1165.88 1103.08i −1.99070 1.88347i
\(71\) −328.894 238.955i −0.549754 0.399419i 0.277941 0.960598i \(-0.410348\pi\)
−0.827695 + 0.561179i \(0.810348\pi\)
\(72\) 0 0
\(73\) −161.479 + 496.983i −0.258901 + 0.796814i 0.734136 + 0.679003i \(0.237588\pi\)
−0.993036 + 0.117811i \(0.962412\pi\)
\(74\) −552.048 −0.867219
\(75\) 0 0
\(76\) 36.8887 0.0556766
\(77\) 333.590 1026.68i 0.493716 1.51950i
\(78\) 0 0
\(79\) 295.531 + 214.716i 0.420884 + 0.305790i 0.777993 0.628273i \(-0.216238\pi\)
−0.357109 + 0.934063i \(0.616238\pi\)
\(80\) −454.691 59.1718i −0.635450 0.0826951i
\(81\) 0 0
\(82\) 1788.02 2.40797
\(83\) 550.242 399.774i 0.727673 0.528686i −0.161153 0.986929i \(-0.551521\pi\)
0.888827 + 0.458244i \(0.151521\pi\)
\(84\) 0 0
\(85\) −85.0205 454.944i −0.108491 0.580536i
\(86\) −55.4211 + 170.569i −0.0694908 + 0.213871i
\(87\) 0 0
\(88\) 95.1364 + 292.800i 0.115245 + 0.354688i
\(89\) 91.6049 281.931i 0.109102 0.335782i −0.881569 0.472055i \(-0.843512\pi\)
0.990671 + 0.136273i \(0.0435124\pi\)
\(90\) 0 0
\(91\) 791.743 + 2436.73i 0.912058 + 2.80702i
\(92\) 1025.18 744.835i 1.16176 0.844070i
\(93\) 0 0
\(94\) 1604.23 1165.54i 1.76025 1.27890i
\(95\) 7.39584 + 39.5751i 0.00798734 + 0.0427402i
\(96\) 0 0
\(97\) −185.918 135.077i −0.194609 0.141392i 0.486214 0.873840i \(-0.338378\pi\)
−0.680823 + 0.732448i \(0.738378\pi\)
\(98\) 1038.23 3195.33i 1.07017 3.29365i
\(99\) 0 0
\(100\) 70.8289 + 1278.55i 0.0708289 + 1.27855i
\(101\) −514.024 −0.506409 −0.253205 0.967413i \(-0.581485\pi\)
−0.253205 + 0.967413i \(0.581485\pi\)
\(102\) 0 0
\(103\) 77.0965 + 56.0139i 0.0737528 + 0.0535846i 0.624051 0.781384i \(-0.285486\pi\)
−0.550298 + 0.834968i \(0.685486\pi\)
\(104\) −591.144 429.491i −0.557370 0.404953i
\(105\) 0 0
\(106\) −857.634 + 623.107i −0.785856 + 0.570958i
\(107\) 780.381 0.705068 0.352534 0.935799i \(-0.385320\pi\)
0.352534 + 0.935799i \(0.385320\pi\)
\(108\) 0 0
\(109\) 190.124 + 585.140i 0.167069 + 0.514186i 0.999183 0.0404192i \(-0.0128693\pi\)
−0.832114 + 0.554605i \(0.812869\pi\)
\(110\) −1346.89 + 733.903i −1.16746 + 0.636136i
\(111\) 0 0
\(112\) −425.943 1310.92i −0.359356 1.10598i
\(113\) 130.179 + 400.650i 0.108374 + 0.333539i 0.990507 0.137459i \(-0.0438936\pi\)
−0.882134 + 0.470999i \(0.843894\pi\)
\(114\) 0 0
\(115\) 1004.62 + 950.503i 0.814617 + 0.770738i
\(116\) 602.580 + 1854.55i 0.482312 + 1.48440i
\(117\) 0 0
\(118\) −921.873 −0.719198
\(119\) 1125.58 817.780i 0.867071 0.629964i
\(120\) 0 0
\(121\) 242.165 + 175.943i 0.181942 + 0.132189i
\(122\) −648.113 470.882i −0.480962 0.349440i
\(123\) 0 0
\(124\) 3387.62 2.45337
\(125\) −1357.46 + 332.324i −0.971316 + 0.237792i
\(126\) 0 0
\(127\) 354.912 1092.31i 0.247979 0.763202i −0.747153 0.664652i \(-0.768580\pi\)
0.995132 0.0985497i \(-0.0314204\pi\)
\(128\) 953.522 + 692.775i 0.658440 + 0.478384i
\(129\) 0 0
\(130\) 1562.36 3288.16i 1.05406 2.21839i
\(131\) 241.102 175.171i 0.160803 0.116830i −0.504474 0.863427i \(-0.668314\pi\)
0.665277 + 0.746597i \(0.268314\pi\)
\(132\) 0 0
\(133\) −97.9127 + 71.1378i −0.0638354 + 0.0463792i
\(134\) 364.364 + 1121.40i 0.234898 + 0.722940i
\(135\) 0 0
\(136\) −122.612 + 377.362i −0.0773082 + 0.237930i
\(137\) −674.262 2075.17i −0.420483 1.29411i −0.907254 0.420583i \(-0.861826\pi\)
0.486771 0.873529i \(-0.338174\pi\)
\(138\) 0 0
\(139\) −656.504 + 2020.51i −0.400604 + 1.23293i 0.523907 + 0.851775i \(0.324474\pi\)
−0.924511 + 0.381156i \(0.875526\pi\)
\(140\) −3380.14 + 1841.79i −2.04053 + 1.11186i
\(141\) 0 0
\(142\) −1404.81 + 1020.65i −0.830202 + 0.603177i
\(143\) 2448.56 1.43188
\(144\) 0 0
\(145\) −1868.80 + 1018.28i −1.07031 + 0.583199i
\(146\) 1805.73 + 1311.94i 1.02359 + 0.743678i
\(147\) 0 0
\(148\) −409.138 + 1259.20i −0.227236 + 0.699361i
\(149\) −2893.87 −1.59111 −0.795554 0.605882i \(-0.792820\pi\)
−0.795554 + 0.605882i \(0.792820\pi\)
\(150\) 0 0
\(151\) 2519.50 1.35784 0.678921 0.734212i \(-0.262448\pi\)
0.678921 + 0.734212i \(0.262448\pi\)
\(152\) 10.6659 32.8263i 0.00569157 0.0175169i
\(153\) 0 0
\(154\) −3730.34 2710.25i −1.95195 1.41817i
\(155\) 679.188 + 3634.33i 0.351959 + 1.88333i
\(156\) 0 0
\(157\) 2190.79 1.11366 0.556828 0.830628i \(-0.312018\pi\)
0.556828 + 0.830628i \(0.312018\pi\)
\(158\) 1262.30 917.117i 0.635591 0.461784i
\(159\) 0 0
\(160\) −1208.45 + 2543.32i −0.597102 + 1.25667i
\(161\) −1284.73 + 3954.00i −0.628889 + 1.93552i
\(162\) 0 0
\(163\) −150.794 464.095i −0.0724605 0.223010i 0.908267 0.418391i \(-0.137406\pi\)
−0.980728 + 0.195381i \(0.937406\pi\)
\(164\) 1325.15 4078.40i 0.630958 1.94189i
\(165\) 0 0
\(166\) −897.716 2762.89i −0.419737 1.29182i
\(167\) −2984.57 + 2168.42i −1.38295 + 1.00477i −0.386354 + 0.922351i \(0.626266\pi\)
−0.996597 + 0.0824226i \(0.973734\pi\)
\(168\) 0 0
\(169\) −2924.13 + 2124.50i −1.33096 + 0.967002i
\(170\) −1960.32 255.108i −0.884408 0.115093i
\(171\) 0 0
\(172\) 347.986 + 252.827i 0.154266 + 0.112080i
\(173\) −969.377 + 2983.44i −0.426014 + 1.31114i 0.476007 + 0.879442i \(0.342084\pi\)
−0.902020 + 0.431693i \(0.857916\pi\)
\(174\) 0 0
\(175\) −2653.61 3257.03i −1.14625 1.40690i
\(176\) −1317.28 −0.564169
\(177\) 0 0
\(178\) −1024.37 744.245i −0.431345 0.313391i
\(179\) −771.743 560.704i −0.322250 0.234128i 0.414885 0.909874i \(-0.363822\pi\)
−0.737135 + 0.675745i \(0.763822\pi\)
\(180\) 0 0
\(181\) 125.543 91.2125i 0.0515556 0.0374573i −0.561709 0.827335i \(-0.689856\pi\)
0.613265 + 0.789878i \(0.289856\pi\)
\(182\) 10943.7 4.45713
\(183\) 0 0
\(184\) −366.392 1127.64i −0.146798 0.451797i
\(185\) −1432.93 186.476i −0.569464 0.0741079i
\(186\) 0 0
\(187\) −410.874 1264.54i −0.160674 0.494505i
\(188\) −1469.61 4523.00i −0.570119 1.75465i
\(189\) 0 0
\(190\) 170.526 + 22.1916i 0.0651118 + 0.00847340i
\(191\) −424.396 1306.16i −0.160776 0.494818i 0.837924 0.545787i \(-0.183769\pi\)
−0.998700 + 0.0509689i \(0.983769\pi\)
\(192\) 0 0
\(193\) 2565.08 0.956676 0.478338 0.878176i \(-0.341239\pi\)
0.478338 + 0.878176i \(0.341239\pi\)
\(194\) −794.113 + 576.957i −0.293887 + 0.213521i
\(195\) 0 0
\(196\) −6518.97 4736.31i −2.37572 1.72606i
\(197\) 1114.76 + 809.922i 0.403165 + 0.292917i 0.770829 0.637042i \(-0.219842\pi\)
−0.367664 + 0.929959i \(0.619842\pi\)
\(198\) 0 0
\(199\) −988.966 −0.352291 −0.176146 0.984364i \(-0.556363\pi\)
−0.176146 + 0.984364i \(0.556363\pi\)
\(200\) 1158.23 + 306.647i 0.409495 + 0.108416i
\(201\) 0 0
\(202\) −678.464 + 2088.10i −0.236320 + 0.727317i
\(203\) −5175.82 3760.45i −1.78951 1.30016i
\(204\) 0 0
\(205\) 4641.09 + 603.974i 1.58121 + 0.205773i
\(206\) 329.303 239.252i 0.111377 0.0809199i
\(207\) 0 0
\(208\) 2529.34 1837.67i 0.843164 0.612595i
\(209\) 35.7415 + 110.001i 0.0118292 + 0.0364064i
\(210\) 0 0
\(211\) 606.537 1866.73i 0.197895 0.609057i −0.802036 0.597276i \(-0.796250\pi\)
0.999931 0.0117812i \(-0.00375017\pi\)
\(212\) 785.666 + 2418.03i 0.254527 + 0.783354i
\(213\) 0 0
\(214\) 1030.03 3170.11i 0.329025 1.01264i
\(215\) −201.470 + 424.017i −0.0639078 + 0.134501i
\(216\) 0 0
\(217\) −8991.70 + 6532.85i −2.81289 + 2.04368i
\(218\) 2627.93 0.816450
\(219\) 0 0
\(220\) 675.785 + 3616.12i 0.207097 + 1.10818i
\(221\) 2553.03 + 1854.88i 0.777083 + 0.564584i
\(222\) 0 0
\(223\) 1063.53 3273.20i 0.319368 0.982913i −0.654551 0.756018i \(-0.727142\pi\)
0.973919 0.226895i \(-0.0728576\pi\)
\(224\) −8464.67 −2.52486
\(225\) 0 0
\(226\) 1799.36 0.529610
\(227\) −518.565 + 1595.98i −0.151623 + 0.466647i −0.997803 0.0662496i \(-0.978897\pi\)
0.846180 + 0.532897i \(0.178897\pi\)
\(228\) 0 0
\(229\) 436.125 + 316.863i 0.125851 + 0.0914363i 0.648930 0.760848i \(-0.275217\pi\)
−0.523079 + 0.852284i \(0.675217\pi\)
\(230\) 5187.18 2826.43i 1.48710 0.810301i
\(231\) 0 0
\(232\) 1824.55 0.516325
\(233\) 2488.89 1808.28i 0.699796 0.508431i −0.180070 0.983654i \(-0.557632\pi\)
0.879866 + 0.475223i \(0.157632\pi\)
\(234\) 0 0
\(235\) 4557.74 2483.46i 1.26517 0.689374i
\(236\) −683.227 + 2102.76i −0.188450 + 0.579990i
\(237\) 0 0
\(238\) −1836.37 5651.77i −0.500144 1.53929i
\(239\) 134.744 414.700i 0.0364681 0.112237i −0.931165 0.364597i \(-0.881207\pi\)
0.967633 + 0.252360i \(0.0812067\pi\)
\(240\) 0 0
\(241\) 1239.98 + 3816.27i 0.331429 + 1.02003i 0.968455 + 0.249190i \(0.0801644\pi\)
−0.637026 + 0.770842i \(0.719836\pi\)
\(242\) 1034.36 751.508i 0.274758 0.199623i
\(243\) 0 0
\(244\) −1554.40 + 1129.34i −0.407828 + 0.296305i
\(245\) 3774.23 7943.30i 0.984191 2.07134i
\(246\) 0 0
\(247\) −222.085 161.354i −0.0572103 0.0415657i
\(248\) 979.490 3014.56i 0.250797 0.771874i
\(249\) 0 0
\(250\) −441.729 + 5952.97i −0.111750 + 1.50599i
\(251\) 4706.56 1.18357 0.591784 0.806097i \(-0.298424\pi\)
0.591784 + 0.806097i \(0.298424\pi\)
\(252\) 0 0
\(253\) 3214.38 + 2335.38i 0.798760 + 0.580333i
\(254\) −3968.78 2883.49i −0.980407 0.712308i
\(255\) 0 0
\(256\) −766.121 + 556.620i −0.187041 + 0.135893i
\(257\) −573.257 −0.139139 −0.0695696 0.997577i \(-0.522163\pi\)
−0.0695696 + 0.997577i \(0.522163\pi\)
\(258\) 0 0
\(259\) −1342.33 4131.26i −0.322040 0.991136i
\(260\) −6342.26 6000.63i −1.51281 1.43132i
\(261\) 0 0
\(262\) −393.357 1210.63i −0.0927544 0.285469i
\(263\) −1428.46 4396.36i −0.334915 1.03076i −0.966764 0.255672i \(-0.917703\pi\)
0.631848 0.775092i \(-0.282297\pi\)
\(264\) 0 0
\(265\) −2436.60 + 1327.67i −0.564828 + 0.307768i
\(266\) 159.744 + 491.642i 0.0368216 + 0.113325i
\(267\) 0 0
\(268\) 2827.90 0.644559
\(269\) 5498.69 3995.03i 1.24632 0.905507i 0.248321 0.968678i \(-0.420121\pi\)
0.998003 + 0.0631703i \(0.0201211\pi\)
\(270\) 0 0
\(271\) −4062.81 2951.81i −0.910695 0.661659i 0.0304957 0.999535i \(-0.490291\pi\)
−0.941190 + 0.337876i \(0.890291\pi\)
\(272\) −1373.48 997.893i −0.306175 0.222449i
\(273\) 0 0
\(274\) −9319.81 −2.05486
\(275\) −3743.97 + 1450.00i −0.820981 + 0.317957i
\(276\) 0 0
\(277\) −1967.28 + 6054.66i −0.426723 + 1.31332i 0.474612 + 0.880195i \(0.342589\pi\)
−0.901335 + 0.433123i \(0.857411\pi\)
\(278\) 7341.30 + 5333.77i 1.58382 + 1.15071i
\(279\) 0 0
\(280\) 661.641 + 3540.43i 0.141216 + 0.755647i
\(281\) −1793.59 + 1303.12i −0.380771 + 0.276646i −0.761663 0.647973i \(-0.775617\pi\)
0.380892 + 0.924619i \(0.375617\pi\)
\(282\) 0 0
\(283\) 5646.82 4102.66i 1.18611 0.861759i 0.193261 0.981147i \(-0.438093\pi\)
0.992848 + 0.119389i \(0.0380935\pi\)
\(284\) 1286.92 + 3960.74i 0.268890 + 0.827559i
\(285\) 0 0
\(286\) 3231.87 9946.68i 0.668198 2.05650i
\(287\) 4347.65 + 13380.7i 0.894195 + 2.75205i
\(288\) 0 0
\(289\) −988.664 + 3042.79i −0.201234 + 0.619335i
\(290\) 1669.89 + 8935.56i 0.338136 + 1.80936i
\(291\) 0 0
\(292\) 4330.76 3146.48i 0.867941 0.630596i
\(293\) −8443.08 −1.68345 −0.841724 0.539908i \(-0.818459\pi\)
−0.841724 + 0.539908i \(0.818459\pi\)
\(294\) 0 0
\(295\) −2392.87 311.399i −0.472265 0.0614588i
\(296\) 1002.23 + 728.164i 0.196802 + 0.142985i
\(297\) 0 0
\(298\) −3819.64 + 11755.6i −0.742503 + 2.28519i
\(299\) −9429.98 −1.82391
\(300\) 0 0
\(301\) −1411.21 −0.270236
\(302\) 3325.50 10234.8i 0.633647 1.95016i
\(303\) 0 0
\(304\) 119.478 + 86.8056i 0.0225412 + 0.0163771i
\(305\) −1523.22 1441.17i −0.285965 0.270562i
\(306\) 0 0
\(307\) −2853.33 −0.530450 −0.265225 0.964187i \(-0.585446\pi\)
−0.265225 + 0.964187i \(0.585446\pi\)
\(308\) −8946.64 + 6500.12i −1.65514 + 1.20253i
\(309\) 0 0
\(310\) 15660.0 + 2037.94i 2.86913 + 0.373377i
\(311\) 2085.97 6419.96i 0.380336 1.17055i −0.559471 0.828850i \(-0.688996\pi\)
0.939807 0.341705i \(-0.111004\pi\)
\(312\) 0 0
\(313\) 1021.84 + 3144.90i 0.184530 + 0.567924i 0.999940 0.0109593i \(-0.00348854\pi\)
−0.815410 + 0.578884i \(0.803489\pi\)
\(314\) 2891.64 8899.54i 0.519696 1.59946i
\(315\) 0 0
\(316\) −1156.38 3558.96i −0.205859 0.633568i
\(317\) −2682.89 + 1949.24i −0.475351 + 0.345363i −0.799523 0.600635i \(-0.794914\pi\)
0.324172 + 0.945998i \(0.394914\pi\)
\(318\) 0 0
\(319\) −4946.39 + 3593.76i −0.868164 + 0.630758i
\(320\) 6071.98 + 5744.92i 1.06073 + 1.00360i
\(321\) 0 0
\(322\) 14366.4 + 10437.8i 2.48636 + 1.80645i
\(323\) −46.0638 + 141.770i −0.00793517 + 0.0244219i
\(324\) 0 0
\(325\) 5166.06 8007.20i 0.881728 1.36665i
\(326\) −2084.30 −0.354107
\(327\) 0 0
\(328\) −3246.12 2358.44i −0.546454 0.397022i
\(329\) 12623.1 + 9171.23i 2.11530 + 1.53686i
\(330\) 0 0
\(331\) 6061.25 4403.76i 1.00651 0.731276i 0.0430396 0.999073i \(-0.486296\pi\)
0.963475 + 0.267798i \(0.0862958\pi\)
\(332\) −6967.36 −1.15176
\(333\) 0 0
\(334\) 4869.31 + 14986.2i 0.797714 + 2.45511i
\(335\) 566.969 + 3033.84i 0.0924682 + 0.494796i
\(336\) 0 0
\(337\) −2497.93 7687.83i −0.403771 1.24268i −0.921917 0.387387i \(-0.873378\pi\)
0.518146 0.855292i \(-0.326622\pi\)
\(338\) 4770.70 + 14682.7i 0.767727 + 2.36282i
\(339\) 0 0
\(340\) −2034.74 + 4282.33i −0.324556 + 0.683065i
\(341\) 3282.28 + 10101.8i 0.521247 + 1.60423i
\(342\) 0 0
\(343\) 14908.8 2.34694
\(344\) 325.600 236.562i 0.0510325 0.0370773i
\(345\) 0 0
\(346\) 10840.0 + 7875.71i 1.68428 + 1.22370i
\(347\) −8214.67 5968.31i −1.27086 0.923330i −0.271619 0.962405i \(-0.587559\pi\)
−0.999236 + 0.0390745i \(0.987559\pi\)
\(348\) 0 0
\(349\) 915.035 0.140346 0.0701729 0.997535i \(-0.477645\pi\)
0.0701729 + 0.997535i \(0.477645\pi\)
\(350\) −16733.4 + 6480.65i −2.55554 + 0.989730i
\(351\) 0 0
\(352\) −2499.78 + 7693.52i −0.378519 + 1.16496i
\(353\) 64.3813 + 46.7758i 0.00970728 + 0.00705275i 0.592628 0.805476i \(-0.298090\pi\)
−0.582921 + 0.812529i \(0.698090\pi\)
\(354\) 0 0
\(355\) −3991.16 + 2174.73i −0.596701 + 0.325135i
\(356\) −2456.78 + 1784.95i −0.365756 + 0.265737i
\(357\) 0 0
\(358\) −3296.35 + 2394.94i −0.486641 + 0.353565i
\(359\) 1932.90 + 5948.86i 0.284163 + 0.874565i 0.986648 + 0.162866i \(0.0520739\pi\)
−0.702485 + 0.711699i \(0.747926\pi\)
\(360\) 0 0
\(361\) −2115.54 + 6510.96i −0.308433 + 0.949259i
\(362\) −204.823 630.380i −0.0297383 0.0915250i
\(363\) 0 0
\(364\) 8110.66 24962.1i 1.16790 3.59441i
\(365\) 4243.90 + 4015.31i 0.608592 + 0.575810i
\(366\) 0 0
\(367\) 2077.48 1509.38i 0.295487 0.214684i −0.430157 0.902754i \(-0.641542\pi\)
0.725644 + 0.688070i \(0.241542\pi\)
\(368\) 5073.15 0.718631
\(369\) 0 0
\(370\) −2648.84 + 5574.78i −0.372180 + 0.783295i
\(371\) −6748.41 4903.01i −0.944367 0.686123i
\(372\) 0 0
\(373\) 2876.24 8852.16i 0.399266 1.22881i −0.526323 0.850285i \(-0.676430\pi\)
0.925589 0.378530i \(-0.123570\pi\)
\(374\) −5679.20 −0.785199
\(375\) 0 0
\(376\) −4449.82 −0.610325
\(377\) 4484.19 13800.9i 0.612593 1.88537i
\(378\) 0 0
\(379\) 1786.14 + 1297.71i 0.242079 + 0.175880i 0.702209 0.711971i \(-0.252197\pi\)
−0.460130 + 0.887851i \(0.652197\pi\)
\(380\) 177.000 372.515i 0.0238944 0.0502885i
\(381\) 0 0
\(382\) −5866.10 −0.785696
\(383\) 10414.5 7566.60i 1.38945 1.00949i 0.393520 0.919316i \(-0.371257\pi\)
0.995926 0.0901754i \(-0.0287428\pi\)
\(384\) 0 0
\(385\) −8767.21 8294.96i −1.16057 1.09805i
\(386\) 3385.66 10420.0i 0.446440 1.37400i
\(387\) 0 0
\(388\) 727.475 + 2238.94i 0.0951855 + 0.292951i
\(389\) 3872.47 11918.2i 0.504735 1.55341i −0.296481 0.955039i \(-0.595813\pi\)
0.801216 0.598376i \(-0.204187\pi\)
\(390\) 0 0
\(391\) 1582.37 + 4870.04i 0.204665 + 0.629894i
\(392\) −6099.60 + 4431.62i −0.785909 + 0.570996i
\(393\) 0 0
\(394\) 4761.49 3459.43i 0.608834 0.442344i
\(395\) 3586.30 1954.13i 0.456826 0.248919i
\(396\) 0 0
\(397\) −10322.4 7499.67i −1.30496 0.948105i −0.304964 0.952364i \(-0.598645\pi\)
−0.999991 + 0.00425835i \(0.998645\pi\)
\(398\) −1305.34 + 4017.43i −0.164399 + 0.505969i
\(399\) 0 0
\(400\) −2779.24 + 4307.72i −0.347405 + 0.538466i
\(401\) 4960.15 0.617700 0.308850 0.951111i \(-0.400056\pi\)
0.308850 + 0.951111i \(0.400056\pi\)
\(402\) 0 0
\(403\) −20394.9 14817.8i −2.52095 1.83158i
\(404\) 4260.04 + 3095.10i 0.524616 + 0.381156i
\(405\) 0 0
\(406\) −22107.5 + 16062.0i −2.70241 + 1.96341i
\(407\) −4151.31 −0.505585
\(408\) 0 0
\(409\) 3499.05 + 10769.0i 0.423025 + 1.30194i 0.904873 + 0.425682i \(0.139966\pi\)
−0.481848 + 0.876255i \(0.660034\pi\)
\(410\) 8579.30 18056.1i 1.03342 2.17494i
\(411\) 0 0
\(412\) −301.669 928.443i −0.0360733 0.111022i
\(413\) −2241.58 6898.86i −0.267072 0.821963i
\(414\) 0 0
\(415\) −1396.89 7474.75i −0.165231 0.884147i
\(416\) −5932.98 18259.8i −0.699251 2.15207i
\(417\) 0 0
\(418\) 494.028 0.0578079
\(419\) 9318.52 6770.30i 1.08649 0.789382i 0.107688 0.994185i \(-0.465655\pi\)
0.978803 + 0.204803i \(0.0656554\pi\)
\(420\) 0 0
\(421\) 1968.58 + 1430.26i 0.227892 + 0.165574i 0.695872 0.718166i \(-0.255018\pi\)
−0.467980 + 0.883739i \(0.655018\pi\)
\(422\) −6782.56 4927.82i −0.782393 0.568442i
\(423\) 0 0
\(424\) 2378.91 0.272477
\(425\) −5002.14 1324.35i −0.570916 0.151153i
\(426\) 0 0
\(427\) 1947.94 5995.14i 0.220767 0.679450i
\(428\) −6467.50 4698.91i −0.730417 0.530679i
\(429\) 0 0
\(430\) 1456.54 + 1378.09i 0.163351 + 0.154552i
\(431\) −7111.10 + 5166.51i −0.794732 + 0.577407i −0.909364 0.416001i \(-0.863431\pi\)
0.114632 + 0.993408i \(0.463431\pi\)
\(432\) 0 0
\(433\) −6196.51 + 4502.03i −0.687726 + 0.499662i −0.875912 0.482471i \(-0.839739\pi\)
0.188186 + 0.982133i \(0.439739\pi\)
\(434\) 14669.9 + 45149.3i 1.62253 + 4.99363i
\(435\) 0 0
\(436\) 1947.64 5994.21i 0.213933 0.658419i
\(437\) −137.649 423.640i −0.0150678 0.0463740i
\(438\) 0 0
\(439\) 1589.15 4890.90i 0.172770 0.531731i −0.826755 0.562563i \(-0.809815\pi\)
0.999525 + 0.0308313i \(0.00981546\pi\)
\(440\) 3413.29 + 444.192i 0.369823 + 0.0481273i
\(441\) 0 0
\(442\) 10904.8 7922.78i 1.17350 0.852598i
\(443\) 3847.00 0.412588 0.206294 0.978490i \(-0.433860\pi\)
0.206294 + 0.978490i \(0.433860\pi\)
\(444\) 0 0
\(445\) −2407.50 2277.83i −0.256464 0.242650i
\(446\) −11892.8 8640.63i −1.26265 0.917367i
\(447\) 0 0
\(448\) −7765.02 + 23898.3i −0.818890 + 2.52029i
\(449\) −1690.99 −0.177735 −0.0888674 0.996043i \(-0.528325\pi\)
−0.0888674 + 0.996043i \(0.528325\pi\)
\(450\) 0 0
\(451\) 13445.6 1.40384
\(452\) 1333.56 4104.28i 0.138773 0.427100i
\(453\) 0 0
\(454\) 5798.82 + 4213.09i 0.599454 + 0.435529i
\(455\) 28406.0 + 3696.65i 2.92680 + 0.380883i
\(456\) 0 0
\(457\) −369.186 −0.0377895 −0.0188947 0.999821i \(-0.506015\pi\)
−0.0188947 + 0.999821i \(0.506015\pi\)
\(458\) 1862.82 1353.42i 0.190052 0.138081i
\(459\) 0 0
\(460\) −2602.60 13926.5i −0.263798 1.41158i
\(461\) −812.481 + 2500.56i −0.0820846 + 0.252630i −0.983673 0.179964i \(-0.942402\pi\)
0.901589 + 0.432595i \(0.142402\pi\)
\(462\) 0 0
\(463\) 587.970 + 1809.58i 0.0590178 + 0.181638i 0.976219 0.216786i \(-0.0695573\pi\)
−0.917201 + 0.398424i \(0.869557\pi\)
\(464\) −2412.41 + 7424.64i −0.241365 + 0.742845i
\(465\) 0 0
\(466\) −4060.60 12497.2i −0.403656 1.24233i
\(467\) −8903.30 + 6468.62i −0.882217 + 0.640968i −0.933837 0.357698i \(-0.883562\pi\)
0.0516199 + 0.998667i \(0.483562\pi\)
\(468\) 0 0
\(469\) −7506.04 + 5453.46i −0.739012 + 0.536924i
\(470\) −4072.64 21792.6i −0.399695 2.13876i
\(471\) 0 0
\(472\) 1673.64 + 1215.97i 0.163211 + 0.118580i
\(473\) −416.758 + 1282.65i −0.0405128 + 0.124686i
\(474\) 0 0
\(475\) 435.131 + 115.203i 0.0420319 + 0.0111282i
\(476\) −14252.5 −1.37239
\(477\) 0 0
\(478\) −1506.77 1094.73i −0.144180 0.104753i
\(479\) −11054.3 8031.41i −1.05445 0.766106i −0.0813995 0.996682i \(-0.525939\pi\)
−0.973054 + 0.230576i \(0.925939\pi\)
\(480\) 0 0
\(481\) 7971.03 5791.30i 0.755609 0.548982i
\(482\) 17139.3 1.61966
\(483\) 0 0
\(484\) −947.564 2916.30i −0.0889899 0.273883i
\(485\) −2256.14 + 1229.34i −0.211229 + 0.115096i
\(486\) 0 0
\(487\) −1524.98 4693.40i −0.141896 0.436711i 0.854703 0.519118i \(-0.173739\pi\)
−0.996599 + 0.0824064i \(0.973739\pi\)
\(488\) 555.532 + 1709.75i 0.0515323 + 0.158600i
\(489\) 0 0
\(490\) −27286.0 25816.3i −2.51563 2.38013i
\(491\) −134.582 414.201i −0.0123699 0.0380705i 0.944681 0.327990i \(-0.106371\pi\)
−0.957051 + 0.289920i \(0.906371\pi\)
\(492\) 0 0
\(493\) −7879.84 −0.719858
\(494\) −948.594 + 689.194i −0.0863953 + 0.0627698i
\(495\) 0 0
\(496\) 10972.1 + 7971.69i 0.993269 + 0.721652i
\(497\) −11053.9 8031.14i −0.997658 0.724841i
\(498\) 0 0
\(499\) 3428.76 0.307600 0.153800 0.988102i \(-0.450849\pi\)
0.153800 + 0.988102i \(0.450849\pi\)
\(500\) 13251.1 + 5419.48i 1.18521 + 0.484733i
\(501\) 0 0
\(502\) 6212.22 19119.2i 0.552320 1.69987i
\(503\) 3567.05 + 2591.62i 0.316197 + 0.229731i 0.734551 0.678553i \(-0.237393\pi\)
−0.418354 + 0.908284i \(0.637393\pi\)
\(504\) 0 0
\(505\) −2466.40 + 5190.81i −0.217333 + 0.457402i
\(506\) 13729.6 9975.13i 1.20623 0.876381i
\(507\) 0 0
\(508\) −9518.50 + 6915.59i −0.831329 + 0.603996i
\(509\) 1764.24 + 5429.77i 0.153632 + 0.472830i 0.998020 0.0629024i \(-0.0200357\pi\)
−0.844388 + 0.535732i \(0.820036\pi\)
\(510\) 0 0
\(511\) −5427.23 + 16703.3i −0.469836 + 1.44601i
\(512\) 4163.63 + 12814.3i 0.359391 + 1.10609i
\(513\) 0 0
\(514\) −756.645 + 2328.72i −0.0649303 + 0.199835i
\(515\) 935.574 509.783i 0.0800511 0.0436189i
\(516\) 0 0
\(517\) 12063.6 8764.69i 1.02622 0.745592i
\(518\) −18554.0 −1.57377
\(519\) 0 0
\(520\) −7173.60 + 3908.81i −0.604968 + 0.329639i
\(521\) 1640.89 + 1192.18i 0.137982 + 0.100250i 0.654635 0.755945i \(-0.272822\pi\)
−0.516653 + 0.856195i \(0.672822\pi\)
\(522\) 0 0
\(523\) −1067.09 + 3284.16i −0.0892171 + 0.274582i −0.985703 0.168489i \(-0.946111\pi\)
0.896486 + 0.443071i \(0.146111\pi\)
\(524\) −3052.92 −0.254518
\(525\) 0 0
\(526\) −19744.5 −1.63670
\(527\) −4230.21 + 13019.3i −0.349660 + 1.07614i
\(528\) 0 0
\(529\) −2536.00 1842.51i −0.208433 0.151435i
\(530\) 2177.26 + 11650.5i 0.178442 + 0.954841i
\(531\) 0 0
\(532\) 1239.81 0.101038
\(533\) −25817.3 + 18757.4i −2.09807 + 1.52434i
\(534\) 0 0
\(535\) 3744.43 7880.58i 0.302591 0.636836i
\(536\) 817.654 2516.48i 0.0658904 0.202790i
\(537\) 0 0
\(538\) −8971.08 27610.2i −0.718905 2.21256i
\(539\) 7807.31 24028.4i 0.623905 1.92018i
\(540\) 0 0
\(541\) 6762.35 + 20812.4i 0.537405 + 1.65396i 0.738394 + 0.674370i \(0.235585\pi\)
−0.200988 + 0.979594i \(0.564415\pi\)
\(542\) −17353.5 + 12608.1i −1.37527 + 0.999194i
\(543\) 0 0
\(544\) −8434.58 + 6128.08i −0.664761 + 0.482977i
\(545\) 6821.22 + 887.687i 0.536126 + 0.0697694i
\(546\) 0 0
\(547\) −6842.63 4971.46i −0.534862 0.388600i 0.287311 0.957837i \(-0.407239\pi\)
−0.822173 + 0.569237i \(0.807239\pi\)
\(548\) −6907.18 + 21258.1i −0.538431 + 1.65712i
\(549\) 0 0
\(550\) 948.569 + 17122.8i 0.0735402 + 1.32749i
\(551\) 685.459 0.0529973
\(552\) 0 0
\(553\) 9932.62 + 7216.47i 0.763793 + 0.554928i
\(554\) 21998.9 + 15983.2i 1.68709 + 1.22574i
\(555\) 0 0
\(556\) 17607.0 12792.2i 1.34299 0.975738i
\(557\) 16513.1 1.25616 0.628080 0.778149i \(-0.283841\pi\)
0.628080 + 0.778149i \(0.283841\pi\)
\(558\) 0 0
\(559\) −989.135 3044.24i −0.0748407 0.230336i
\(560\) −15281.9 1988.73i −1.15318 0.150070i
\(561\) 0 0
\(562\) 2926.23 + 9006.01i 0.219636 + 0.675971i
\(563\) 5502.05 + 16933.6i 0.411872 + 1.26761i 0.915019 + 0.403410i \(0.132175\pi\)
−0.503147 + 0.864201i \(0.667825\pi\)
\(564\) 0 0
\(565\) 4670.54 + 607.806i 0.347772 + 0.0452577i
\(566\) −9212.76 28354.0i −0.684172 2.10566i
\(567\) 0 0
\(568\) 3896.66 0.287853
\(569\) −3984.70 + 2895.05i −0.293580 + 0.213299i −0.724819 0.688939i \(-0.758077\pi\)
0.431239 + 0.902238i \(0.358077\pi\)
\(570\) 0 0
\(571\) −10205.8 7414.97i −0.747987 0.543444i 0.147215 0.989104i \(-0.452969\pi\)
−0.895202 + 0.445660i \(0.852969\pi\)
\(572\) −20292.7 14743.5i −1.48336 1.07772i
\(573\) 0 0
\(574\) 60094.3 4.36984
\(575\) 14418.9 5584.28i 1.04576 0.405009i
\(576\) 0 0
\(577\) 3968.83 12214.8i 0.286351 0.881297i −0.699640 0.714496i \(-0.746656\pi\)
0.985991 0.166801i \(-0.0533439\pi\)
\(578\) 11055.7 + 8032.41i 0.795597 + 0.578035i
\(579\) 0 0
\(580\) 21619.3 + 2813.45i 1.54774 + 0.201417i
\(581\) 18493.3 13436.2i 1.32054 0.959425i
\(582\) 0 0
\(583\) −6449.27 + 4685.67i −0.458150 + 0.332866i
\(584\) −1547.79 4763.61i −0.109671 0.337533i
\(585\) 0 0
\(586\) −11144.1 + 34297.9i −0.785593 + 2.41781i
\(587\) −2104.99 6478.50i −0.148011 0.455530i 0.849375 0.527790i \(-0.176979\pi\)
−0.997386 + 0.0722593i \(0.976979\pi\)
\(588\) 0 0
\(589\) 367.982 1132.53i 0.0257427 0.0792278i
\(590\) −4423.34 + 9309.42i −0.308655 + 0.649598i
\(591\) 0 0
\(592\) −4288.27 + 3115.61i −0.297714 + 0.216302i
\(593\) −20641.3 −1.42941 −0.714703 0.699428i \(-0.753438\pi\)
−0.714703 + 0.699428i \(0.753438\pi\)
\(594\) 0 0
\(595\) −2857.49 15290.4i −0.196883 1.05352i
\(596\) 23983.3 + 17424.9i 1.64831 + 1.19757i
\(597\) 0 0
\(598\) −12446.7 + 38307.0i −0.851142 + 2.61955i
\(599\) −15650.0 −1.06751 −0.533757 0.845638i \(-0.679220\pi\)
−0.533757 + 0.845638i \(0.679220\pi\)
\(600\) 0 0
\(601\) −17812.8 −1.20898 −0.604491 0.796612i \(-0.706623\pi\)
−0.604491 + 0.796612i \(0.706623\pi\)
\(602\) −1862.67 + 5732.71i −0.126108 + 0.388119i
\(603\) 0 0
\(604\) −20880.6 15170.7i −1.40666 1.02200i
\(605\) 2938.70 1601.26i 0.197480 0.107604i
\(606\) 0 0
\(607\) −22919.5 −1.53258 −0.766290 0.642495i \(-0.777899\pi\)
−0.766290 + 0.642495i \(0.777899\pi\)
\(608\) 733.716 533.076i 0.0489409 0.0355577i
\(609\) 0 0
\(610\) −7864.93 + 4285.50i −0.522035 + 0.284450i
\(611\) −10936.3 + 33658.6i −0.724119 + 2.22861i
\(612\) 0 0
\(613\) −2407.59 7409.79i −0.158632 0.488220i 0.839879 0.542774i \(-0.182626\pi\)
−0.998511 + 0.0545546i \(0.982626\pi\)
\(614\) −3766.13 + 11591.0i −0.247538 + 0.761845i
\(615\) 0 0
\(616\) 3197.48 + 9840.82i 0.209140 + 0.643666i
\(617\) −24594.0 + 17868.6i −1.60473 + 1.16590i −0.727134 + 0.686496i \(0.759148\pi\)
−0.877593 + 0.479406i \(0.840852\pi\)
\(618\) 0 0
\(619\) 16760.8 12177.5i 1.08833 0.790716i 0.109212 0.994019i \(-0.465167\pi\)
0.979116 + 0.203302i \(0.0651674\pi\)
\(620\) 16254.5 34209.5i 1.05290 2.21595i
\(621\) 0 0
\(622\) −23326.2 16947.5i −1.50369 1.09250i
\(623\) 3078.79 9475.53i 0.197992 0.609356i
\(624\) 0 0
\(625\) −3157.43 + 15302.7i −0.202075 + 0.979370i
\(626\) 14124.1 0.901778
\(627\) 0 0
\(628\) −18156.4 13191.4i −1.15369 0.838208i
\(629\) −4328.43 3144.79i −0.274381 0.199350i
\(630\) 0 0
\(631\) 18557.5 13482.8i 1.17078 0.850624i 0.179681 0.983725i \(-0.442493\pi\)
0.991102 + 0.133101i \(0.0424935\pi\)
\(632\) −3501.38 −0.220376
\(633\) 0 0
\(634\) 4377.12 + 13471.4i 0.274192 + 0.843876i
\(635\) −9327.59 8825.16i −0.582920 0.551521i
\(636\) 0 0
\(637\) 18529.9 + 57029.1i 1.15256 + 3.54722i
\(638\) 8070.00 + 24836.9i 0.500775 + 1.54123i
\(639\) 0 0
\(640\) 11571.1 6304.95i 0.714669 0.389414i
\(641\) 5387.35 + 16580.5i 0.331962 + 1.02167i 0.968199 + 0.250180i \(0.0804897\pi\)
−0.636238 + 0.771493i \(0.719510\pi\)
\(642\) 0 0
\(643\) 29188.0 1.79014 0.895072 0.445921i \(-0.147124\pi\)
0.895072 + 0.445921i \(0.147124\pi\)
\(644\) 34455.6 25033.5i 2.10829 1.53176i
\(645\) 0 0
\(646\) 515.105 + 374.246i 0.0313724 + 0.0227934i
\(647\) 1185.75 + 861.499i 0.0720506 + 0.0523478i 0.623227 0.782041i \(-0.285821\pi\)
−0.551177 + 0.834388i \(0.685821\pi\)
\(648\) 0 0
\(649\) −6932.35 −0.419289
\(650\) −25708.6 31554.6i −1.55134 1.90411i
\(651\) 0 0
\(652\) −1544.74 + 4754.21i −0.0927862 + 0.285567i
\(653\) −5424.96 3941.46i −0.325107 0.236204i 0.413244 0.910620i \(-0.364395\pi\)
−0.738352 + 0.674416i \(0.764395\pi\)
\(654\) 0 0
\(655\) −612.083 3275.25i −0.0365131 0.195381i
\(656\) 13889.2 10091.1i 0.826651 0.600597i
\(657\) 0 0
\(658\) 53917.2 39173.1i 3.19439 2.32086i
\(659\) −360.964 1110.93i −0.0213371 0.0656689i 0.939821 0.341667i \(-0.110992\pi\)
−0.961158 + 0.275998i \(0.910992\pi\)
\(660\) 0 0
\(661\) 811.577 2497.78i 0.0477559 0.146978i −0.924335 0.381582i \(-0.875379\pi\)
0.972091 + 0.234604i \(0.0753794\pi\)
\(662\) −9888.89 30434.9i −0.580578 1.78684i
\(663\) 0 0
\(664\) −2014.53 + 6200.07i −0.117739 + 0.362364i
\(665\) 248.570 + 1330.09i 0.0144949 + 0.0775621i
\(666\) 0 0
\(667\) 19049.7 13840.4i 1.10586 0.803452i
\(668\) 37791.7 2.18893
\(669\) 0 0
\(670\) 13072.6 + 1701.22i 0.753788 + 0.0980951i
\(671\) −4873.71 3540.96i −0.280399 0.203722i
\(672\) 0 0
\(673\) −6129.43 + 18864.4i −0.351073 + 1.08049i 0.607179 + 0.794565i \(0.292301\pi\)
−0.958252 + 0.285926i \(0.907699\pi\)
\(674\) −34527.0 −1.97319
\(675\) 0 0
\(676\) 37026.4 2.10664
\(677\) −1227.06 + 3776.51i −0.0696600 + 0.214392i −0.979826 0.199852i \(-0.935954\pi\)
0.910166 + 0.414244i \(0.135954\pi\)
\(678\) 0 0
\(679\) −6248.59 4539.87i −0.353165 0.256589i
\(680\) 3222.42 + 3048.85i 0.181727 + 0.171938i
\(681\) 0 0
\(682\) 45368.4 2.54728
\(683\) −9447.69 + 6864.15i −0.529291 + 0.384552i −0.820092 0.572231i \(-0.806078\pi\)
0.290802 + 0.956783i \(0.406078\pi\)
\(684\) 0 0
\(685\) −24191.1 3148.13i −1.34933 0.175597i
\(686\) 19678.3 60563.5i 1.09522 3.37074i
\(687\) 0 0
\(688\) 532.136 + 1637.75i 0.0294876 + 0.0907536i
\(689\) 5846.65 17994.1i 0.323279 0.994952i
\(690\) 0 0
\(691\) −10114.6 31129.6i −0.556844 1.71379i −0.691024 0.722831i \(-0.742840\pi\)
0.134181 0.990957i \(-0.457160\pi\)
\(692\) 25998.0 18888.7i 1.42817 1.03763i
\(693\) 0 0
\(694\) −35087.4 + 25492.5i −1.91916 + 1.39435i
\(695\) 17253.8 + 16324.5i 0.941691 + 0.890967i
\(696\) 0 0
\(697\) 14019.3 + 10185.6i 0.761863 + 0.553526i
\(698\) 1207.76 3717.10i 0.0654934 0.201568i
\(699\) 0 0
\(700\) 2380.52 + 42971.2i 0.128536 + 2.32023i
\(701\) −25681.6 −1.38371 −0.691855 0.722036i \(-0.743206\pi\)
−0.691855 + 0.722036i \(0.743206\pi\)
\(702\) 0 0
\(703\) 376.525 + 273.562i 0.0202005 + 0.0146765i
\(704\) 19428.0 + 14115.2i 1.04008 + 0.755665i
\(705\) 0 0
\(706\) 274.992 199.794i 0.0146593 0.0106506i
\(707\) −17276.0 −0.918999
\(708\) 0 0
\(709\) 8535.60 + 26269.9i 0.452132 + 1.39152i 0.874470 + 0.485080i \(0.161209\pi\)
−0.422338 + 0.906438i \(0.638791\pi\)
\(710\) 3566.36 + 19083.6i 0.188512 + 1.00872i
\(711\) 0 0
\(712\) 878.038 + 2702.32i 0.0462161 + 0.142239i
\(713\) −12640.8 38904.4i −0.663958 2.04345i
\(714\) 0 0
\(715\) 11748.7 24726.5i 0.614513 1.29331i
\(716\) 3019.74 + 9293.80i 0.157616 + 0.485092i
\(717\) 0 0
\(718\) 26717.0 1.38868
\(719\) −4433.43 + 3221.08i −0.229957 + 0.167074i −0.696797 0.717268i \(-0.745392\pi\)
0.466840 + 0.884342i \(0.345392\pi\)
\(720\) 0 0
\(721\) 2591.17 + 1882.59i 0.133842 + 0.0972419i
\(722\) 23656.9 + 17187.7i 1.21942 + 0.885957i
\(723\) 0 0
\(724\) −1589.67 −0.0816018
\(725\) 1316.13 + 23757.7i 0.0674205 + 1.21702i
\(726\) 0 0
\(727\) −7275.89 + 22392.9i −0.371180 + 1.14237i 0.574840 + 0.818266i \(0.305064\pi\)
−0.946020 + 0.324109i \(0.894936\pi\)
\(728\) −19868.0 14434.9i −1.01148 0.734883i
\(729\) 0 0
\(730\) 21912.8 11940.0i 1.11100 0.605368i
\(731\) −1406.20 + 1021.66i −0.0711493 + 0.0516930i
\(732\) 0 0
\(733\) −6158.96 + 4474.74i −0.310350 + 0.225482i −0.732046 0.681255i \(-0.761435\pi\)
0.421697 + 0.906737i \(0.361435\pi\)
\(734\) −3389.40 10431.5i −0.170443 0.524570i
\(735\) 0 0
\(736\) 9627.22 29629.5i 0.482152 1.48391i
\(737\) 2739.96 + 8432.74i 0.136944 + 0.421471i
\(738\) 0 0
\(739\) −3949.52 + 12155.4i −0.196597 + 0.605064i 0.803357 + 0.595498i \(0.203045\pi\)
−0.999954 + 0.00956656i \(0.996955\pi\)
\(740\) 10752.7 + 10173.5i 0.534159 + 0.505387i
\(741\) 0 0
\(742\) −28824.5 + 20942.3i −1.42612 + 1.03614i
\(743\) −8636.53 −0.426438 −0.213219 0.977004i \(-0.568395\pi\)
−0.213219 + 0.977004i \(0.568395\pi\)
\(744\) 0 0
\(745\) −13885.4 + 29223.4i −0.682848 + 1.43713i
\(746\) −32163.4 23368.1i −1.57853 1.14687i
\(747\) 0 0
\(748\) −4209.02 + 12954.0i −0.205745 + 0.633217i
\(749\) 26228.1 1.27951
\(750\) 0 0
\(751\) −13862.3 −0.673558 −0.336779 0.941584i \(-0.609338\pi\)
−0.336779 + 0.941584i \(0.609338\pi\)
\(752\) 5883.54 18107.7i 0.285307 0.878084i
\(753\) 0 0
\(754\) −50144.1 36431.8i −2.42194 1.75964i
\(755\) 12089.1 25442.9i 0.582738 1.22644i
\(756\) 0 0
\(757\) −34297.7 −1.64673 −0.823364 0.567514i \(-0.807905\pi\)
−0.823364 + 0.567514i \(0.807905\pi\)
\(758\) 7629.15 5542.90i 0.365571 0.265603i
\(759\) 0 0
\(760\) −280.315 265.216i −0.0133791 0.0126584i
\(761\) −9289.71 + 28590.8i −0.442512 + 1.36191i 0.442678 + 0.896681i \(0.354029\pi\)
−0.885189 + 0.465231i \(0.845971\pi\)
\(762\) 0 0
\(763\) 6389.94 + 19666.2i 0.303186 + 0.933112i
\(764\) −4347.54 + 13380.3i −0.205875 + 0.633618i
\(765\) 0 0
\(766\) −16991.2 52293.7i −0.801460 2.46664i
\(767\) 13311.0 9670.98i 0.626638 0.455279i
\(768\) 0 0
\(769\) 6704.47 4871.08i 0.314395 0.228421i −0.419385 0.907808i \(-0.637754\pi\)
0.733780 + 0.679387i \(0.237754\pi\)
\(770\) −45268.1 + 24666.0i −2.11864 + 1.15442i
\(771\) 0 0
\(772\) −21258.4 15445.1i −0.991070 0.720055i
\(773\) 1109.96 3416.11i 0.0516463 0.158951i −0.921907 0.387412i \(-0.873369\pi\)
0.973553 + 0.228461i \(0.0733692\pi\)
\(774\) 0 0
\(775\) 39959.7 + 10579.6i 1.85212 + 0.490360i
\(776\) 2202.72 0.101898
\(777\) 0 0
\(778\) −43303.6 31461.9i −1.99551 1.44982i
\(779\) −1219.52 886.036i −0.0560898 0.0407516i
\(780\) 0 0
\(781\) −10563.9 + 7675.14i −0.484004 + 0.351649i
\(782\) 21871.9 1.00018