Properties

Label 810.4.e.i.271.1
Level $810$
Weight $4$
Character 810.271
Analytic conductor $47.792$
Analytic rank $0$
Dimension $2$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [810,4,Mod(271,810)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(810, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2, 0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("810.271");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 810 = 2 \cdot 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 810.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(47.7915471046\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 30)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 271.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 810.271
Dual form 810.4.e.i.541.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.00000 - 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(2.50000 - 4.33013i) q^{5} +(2.00000 + 3.46410i) q^{7} +8.00000 q^{8} +O(q^{10})\) \(q+(-1.00000 - 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(2.50000 - 4.33013i) q^{5} +(2.00000 + 3.46410i) q^{7} +8.00000 q^{8} -10.0000 q^{10} +(24.0000 + 41.5692i) q^{11} +(-1.00000 + 1.73205i) q^{13} +(4.00000 - 6.92820i) q^{14} +(-8.00000 - 13.8564i) q^{16} -114.000 q^{17} +140.000 q^{19} +(10.0000 + 17.3205i) q^{20} +(48.0000 - 83.1384i) q^{22} +(-36.0000 + 62.3538i) q^{23} +(-12.5000 - 21.6506i) q^{25} +4.00000 q^{26} -16.0000 q^{28} +(-105.000 - 181.865i) q^{29} +(-136.000 + 235.559i) q^{31} +(-16.0000 + 27.7128i) q^{32} +(114.000 + 197.454i) q^{34} +20.0000 q^{35} -334.000 q^{37} +(-140.000 - 242.487i) q^{38} +(20.0000 - 34.6410i) q^{40} +(99.0000 - 171.473i) q^{41} +(134.000 + 232.095i) q^{43} -192.000 q^{44} +144.000 q^{46} +(-108.000 - 187.061i) q^{47} +(163.500 - 283.190i) q^{49} +(-25.0000 + 43.3013i) q^{50} +(-4.00000 - 6.92820i) q^{52} -78.0000 q^{53} +240.000 q^{55} +(16.0000 + 27.7128i) q^{56} +(-210.000 + 363.731i) q^{58} +(-120.000 + 207.846i) q^{59} +(-151.000 - 261.540i) q^{61} +544.000 q^{62} +64.0000 q^{64} +(5.00000 + 8.66025i) q^{65} +(-298.000 + 516.151i) q^{67} +(228.000 - 394.908i) q^{68} +(-20.0000 - 34.6410i) q^{70} -768.000 q^{71} -478.000 q^{73} +(334.000 + 578.505i) q^{74} +(-280.000 + 484.974i) q^{76} +(-96.0000 + 166.277i) q^{77} +(320.000 + 554.256i) q^{79} -80.0000 q^{80} -396.000 q^{82} +(174.000 + 301.377i) q^{83} +(-285.000 + 493.634i) q^{85} +(268.000 - 464.190i) q^{86} +(192.000 + 332.554i) q^{88} +210.000 q^{89} -8.00000 q^{91} +(-144.000 - 249.415i) q^{92} +(-216.000 + 374.123i) q^{94} +(350.000 - 606.218i) q^{95} +(767.000 + 1328.48i) q^{97} -654.000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 2 q^{2} - 4 q^{4} + 5 q^{5} + 4 q^{7} + 16 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 2 q^{2} - 4 q^{4} + 5 q^{5} + 4 q^{7} + 16 q^{8} - 20 q^{10} + 48 q^{11} - 2 q^{13} + 8 q^{14} - 16 q^{16} - 228 q^{17} + 280 q^{19} + 20 q^{20} + 96 q^{22} - 72 q^{23} - 25 q^{25} + 8 q^{26} - 32 q^{28} - 210 q^{29} - 272 q^{31} - 32 q^{32} + 228 q^{34} + 40 q^{35} - 668 q^{37} - 280 q^{38} + 40 q^{40} + 198 q^{41} + 268 q^{43} - 384 q^{44} + 288 q^{46} - 216 q^{47} + 327 q^{49} - 50 q^{50} - 8 q^{52} - 156 q^{53} + 480 q^{55} + 32 q^{56} - 420 q^{58} - 240 q^{59} - 302 q^{61} + 1088 q^{62} + 128 q^{64} + 10 q^{65} - 596 q^{67} + 456 q^{68} - 40 q^{70} - 1536 q^{71} - 956 q^{73} + 668 q^{74} - 560 q^{76} - 192 q^{77} + 640 q^{79} - 160 q^{80} - 792 q^{82} + 348 q^{83} - 570 q^{85} + 536 q^{86} + 384 q^{88} + 420 q^{89} - 16 q^{91} - 288 q^{92} - 432 q^{94} + 700 q^{95} + 1534 q^{97} - 1308 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/810\mathbb{Z}\right)^\times\).

\(n\) \(487\) \(731\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 1.73205i −0.353553 0.612372i
\(3\) 0 0
\(4\) −2.00000 + 3.46410i −0.250000 + 0.433013i
\(5\) 2.50000 4.33013i 0.223607 0.387298i
\(6\) 0 0
\(7\) 2.00000 + 3.46410i 0.107990 + 0.187044i 0.914956 0.403554i \(-0.132225\pi\)
−0.806966 + 0.590598i \(0.798892\pi\)
\(8\) 8.00000 0.353553
\(9\) 0 0
\(10\) −10.0000 −0.316228
\(11\) 24.0000 + 41.5692i 0.657843 + 1.13942i 0.981173 + 0.193131i \(0.0618643\pi\)
−0.323330 + 0.946286i \(0.604802\pi\)
\(12\) 0 0
\(13\) −1.00000 + 1.73205i −0.0213346 + 0.0369527i −0.876496 0.481410i \(-0.840125\pi\)
0.855161 + 0.518363i \(0.173458\pi\)
\(14\) 4.00000 6.92820i 0.0763604 0.132260i
\(15\) 0 0
\(16\) −8.00000 13.8564i −0.125000 0.216506i
\(17\) −114.000 −1.62642 −0.813208 0.581974i \(-0.802281\pi\)
−0.813208 + 0.581974i \(0.802281\pi\)
\(18\) 0 0
\(19\) 140.000 1.69043 0.845216 0.534425i \(-0.179472\pi\)
0.845216 + 0.534425i \(0.179472\pi\)
\(20\) 10.0000 + 17.3205i 0.111803 + 0.193649i
\(21\) 0 0
\(22\) 48.0000 83.1384i 0.465165 0.805690i
\(23\) −36.0000 + 62.3538i −0.326370 + 0.565290i −0.981789 0.189976i \(-0.939159\pi\)
0.655418 + 0.755266i \(0.272492\pi\)
\(24\) 0 0
\(25\) −12.5000 21.6506i −0.100000 0.173205i
\(26\) 4.00000 0.0301717
\(27\) 0 0
\(28\) −16.0000 −0.107990
\(29\) −105.000 181.865i −0.672345 1.16454i −0.977237 0.212149i \(-0.931954\pi\)
0.304892 0.952387i \(-0.401380\pi\)
\(30\) 0 0
\(31\) −136.000 + 235.559i −0.787946 + 1.36476i 0.139278 + 0.990253i \(0.455522\pi\)
−0.927223 + 0.374509i \(0.877811\pi\)
\(32\) −16.0000 + 27.7128i −0.0883883 + 0.153093i
\(33\) 0 0
\(34\) 114.000 + 197.454i 0.575025 + 0.995972i
\(35\) 20.0000 0.0965891
\(36\) 0 0
\(37\) −334.000 −1.48403 −0.742017 0.670381i \(-0.766131\pi\)
−0.742017 + 0.670381i \(0.766131\pi\)
\(38\) −140.000 242.487i −0.597658 1.03517i
\(39\) 0 0
\(40\) 20.0000 34.6410i 0.0790569 0.136931i
\(41\) 99.0000 171.473i 0.377102 0.653161i −0.613537 0.789666i \(-0.710254\pi\)
0.990639 + 0.136505i \(0.0435871\pi\)
\(42\) 0 0
\(43\) 134.000 + 232.095i 0.475228 + 0.823119i 0.999597 0.0283717i \(-0.00903221\pi\)
−0.524369 + 0.851491i \(0.675699\pi\)
\(44\) −192.000 −0.657843
\(45\) 0 0
\(46\) 144.000 0.461557
\(47\) −108.000 187.061i −0.335179 0.580547i 0.648340 0.761351i \(-0.275464\pi\)
−0.983519 + 0.180804i \(0.942130\pi\)
\(48\) 0 0
\(49\) 163.500 283.190i 0.476676 0.825628i
\(50\) −25.0000 + 43.3013i −0.0707107 + 0.122474i
\(51\) 0 0
\(52\) −4.00000 6.92820i −0.0106673 0.0184763i
\(53\) −78.0000 −0.202153 −0.101077 0.994879i \(-0.532229\pi\)
−0.101077 + 0.994879i \(0.532229\pi\)
\(54\) 0 0
\(55\) 240.000 0.588393
\(56\) 16.0000 + 27.7128i 0.0381802 + 0.0661300i
\(57\) 0 0
\(58\) −210.000 + 363.731i −0.475420 + 0.823451i
\(59\) −120.000 + 207.846i −0.264791 + 0.458631i −0.967509 0.252837i \(-0.918636\pi\)
0.702718 + 0.711469i \(0.251970\pi\)
\(60\) 0 0
\(61\) −151.000 261.540i −0.316944 0.548963i 0.662905 0.748704i \(-0.269323\pi\)
−0.979849 + 0.199741i \(0.935990\pi\)
\(62\) 544.000 1.11432
\(63\) 0 0
\(64\) 64.0000 0.125000
\(65\) 5.00000 + 8.66025i 0.00954113 + 0.0165257i
\(66\) 0 0
\(67\) −298.000 + 516.151i −0.543381 + 0.941163i 0.455326 + 0.890325i \(0.349523\pi\)
−0.998707 + 0.0508381i \(0.983811\pi\)
\(68\) 228.000 394.908i 0.406604 0.704259i
\(69\) 0 0
\(70\) −20.0000 34.6410i −0.0341494 0.0591485i
\(71\) −768.000 −1.28373 −0.641865 0.766818i \(-0.721839\pi\)
−0.641865 + 0.766818i \(0.721839\pi\)
\(72\) 0 0
\(73\) −478.000 −0.766379 −0.383190 0.923670i \(-0.625174\pi\)
−0.383190 + 0.923670i \(0.625174\pi\)
\(74\) 334.000 + 578.505i 0.524685 + 0.908782i
\(75\) 0 0
\(76\) −280.000 + 484.974i −0.422608 + 0.731978i
\(77\) −96.0000 + 166.277i −0.142081 + 0.246091i
\(78\) 0 0
\(79\) 320.000 + 554.256i 0.455732 + 0.789351i 0.998730 0.0503832i \(-0.0160443\pi\)
−0.542998 + 0.839734i \(0.682711\pi\)
\(80\) −80.0000 −0.111803
\(81\) 0 0
\(82\) −396.000 −0.533303
\(83\) 174.000 + 301.377i 0.230108 + 0.398559i 0.957840 0.287303i \(-0.0927587\pi\)
−0.727732 + 0.685862i \(0.759425\pi\)
\(84\) 0 0
\(85\) −285.000 + 493.634i −0.363678 + 0.629908i
\(86\) 268.000 464.190i 0.336037 0.582033i
\(87\) 0 0
\(88\) 192.000 + 332.554i 0.232583 + 0.402845i
\(89\) 210.000 0.250112 0.125056 0.992150i \(-0.460089\pi\)
0.125056 + 0.992150i \(0.460089\pi\)
\(90\) 0 0
\(91\) −8.00000 −0.00921569
\(92\) −144.000 249.415i −0.163185 0.282645i
\(93\) 0 0
\(94\) −216.000 + 374.123i −0.237007 + 0.410509i
\(95\) 350.000 606.218i 0.377992 0.654701i
\(96\) 0 0
\(97\) 767.000 + 1328.48i 0.802856 + 1.39059i 0.917729 + 0.397207i \(0.130021\pi\)
−0.114873 + 0.993380i \(0.536646\pi\)
\(98\) −654.000 −0.674122
\(99\) 0 0
\(100\) 100.000 0.100000
\(101\) −861.000 1491.30i −0.848245 1.46920i −0.882773 0.469799i \(-0.844326\pi\)
0.0345288 0.999404i \(-0.489007\pi\)
\(102\) 0 0
\(103\) −526.000 + 911.059i −0.503188 + 0.871546i 0.496806 + 0.867862i \(0.334506\pi\)
−0.999993 + 0.00368461i \(0.998827\pi\)
\(104\) −8.00000 + 13.8564i −0.00754293 + 0.0130647i
\(105\) 0 0
\(106\) 78.0000 + 135.100i 0.0714720 + 0.123793i
\(107\) −564.000 −0.509570 −0.254785 0.966998i \(-0.582005\pi\)
−0.254785 + 0.966998i \(0.582005\pi\)
\(108\) 0 0
\(109\) −610.000 −0.536031 −0.268016 0.963415i \(-0.586368\pi\)
−0.268016 + 0.963415i \(0.586368\pi\)
\(110\) −240.000 415.692i −0.208028 0.360315i
\(111\) 0 0
\(112\) 32.0000 55.4256i 0.0269975 0.0467610i
\(113\) −651.000 + 1127.57i −0.541955 + 0.938694i 0.456837 + 0.889551i \(0.348982\pi\)
−0.998792 + 0.0491432i \(0.984351\pi\)
\(114\) 0 0
\(115\) 180.000 + 311.769i 0.145957 + 0.252805i
\(116\) 840.000 0.672345
\(117\) 0 0
\(118\) 480.000 0.374471
\(119\) −228.000 394.908i −0.175636 0.304211i
\(120\) 0 0
\(121\) −486.500 + 842.643i −0.365515 + 0.633090i
\(122\) −302.000 + 523.079i −0.224113 + 0.388175i
\(123\) 0 0
\(124\) −544.000 942.236i −0.393973 0.682381i
\(125\) −125.000 −0.0894427
\(126\) 0 0
\(127\) −124.000 −0.0866395 −0.0433198 0.999061i \(-0.513793\pi\)
−0.0433198 + 0.999061i \(0.513793\pi\)
\(128\) −64.0000 110.851i −0.0441942 0.0765466i
\(129\) 0 0
\(130\) 10.0000 17.3205i 0.00674660 0.0116855i
\(131\) −96.0000 + 166.277i −0.0640272 + 0.110898i −0.896262 0.443525i \(-0.853728\pi\)
0.832235 + 0.554423i \(0.187061\pi\)
\(132\) 0 0
\(133\) 280.000 + 484.974i 0.182549 + 0.316185i
\(134\) 1192.00 0.768456
\(135\) 0 0
\(136\) −912.000 −0.575025
\(137\) 1257.00 + 2177.19i 0.783889 + 1.35774i 0.929661 + 0.368417i \(0.120100\pi\)
−0.145772 + 0.989318i \(0.546567\pi\)
\(138\) 0 0
\(139\) −670.000 + 1160.47i −0.408839 + 0.708130i −0.994760 0.102238i \(-0.967400\pi\)
0.585921 + 0.810368i \(0.300733\pi\)
\(140\) −40.0000 + 69.2820i −0.0241473 + 0.0418243i
\(141\) 0 0
\(142\) 768.000 + 1330.22i 0.453867 + 0.786121i
\(143\) −96.0000 −0.0561393
\(144\) 0 0
\(145\) −1050.00 −0.601364
\(146\) 478.000 + 827.920i 0.270956 + 0.469309i
\(147\) 0 0
\(148\) 668.000 1157.01i 0.371009 0.642606i
\(149\) −705.000 + 1221.10i −0.387623 + 0.671383i −0.992129 0.125217i \(-0.960037\pi\)
0.604506 + 0.796600i \(0.293370\pi\)
\(150\) 0 0
\(151\) 1064.00 + 1842.90i 0.573424 + 0.993200i 0.996211 + 0.0869709i \(0.0277187\pi\)
−0.422786 + 0.906229i \(0.638948\pi\)
\(152\) 1120.00 0.597658
\(153\) 0 0
\(154\) 384.000 0.200932
\(155\) 680.000 + 1177.79i 0.352380 + 0.610340i
\(156\) 0 0
\(157\) −1513.00 + 2620.59i −0.769112 + 1.33214i 0.168933 + 0.985627i \(0.445968\pi\)
−0.938045 + 0.346513i \(0.887366\pi\)
\(158\) 640.000 1108.51i 0.322251 0.558155i
\(159\) 0 0
\(160\) 80.0000 + 138.564i 0.0395285 + 0.0684653i
\(161\) −288.000 −0.140979
\(162\) 0 0
\(163\) 2612.00 1.25514 0.627569 0.778561i \(-0.284050\pi\)
0.627569 + 0.778561i \(0.284050\pi\)
\(164\) 396.000 + 685.892i 0.188551 + 0.326580i
\(165\) 0 0
\(166\) 348.000 602.754i 0.162711 0.281824i
\(167\) 12.0000 20.7846i 0.00556041 0.00963091i −0.863232 0.504808i \(-0.831563\pi\)
0.868792 + 0.495177i \(0.164897\pi\)
\(168\) 0 0
\(169\) 1096.50 + 1899.19i 0.499090 + 0.864449i
\(170\) 1140.00 0.514318
\(171\) 0 0
\(172\) −1072.00 −0.475228
\(173\) −981.000 1699.14i −0.431122 0.746725i 0.565849 0.824509i \(-0.308549\pi\)
−0.996970 + 0.0777846i \(0.975215\pi\)
\(174\) 0 0
\(175\) 50.0000 86.6025i 0.0215980 0.0374088i
\(176\) 384.000 665.108i 0.164461 0.284854i
\(177\) 0 0
\(178\) −210.000 363.731i −0.0884279 0.153162i
\(179\) −120.000 −0.0501074 −0.0250537 0.999686i \(-0.507976\pi\)
−0.0250537 + 0.999686i \(0.507976\pi\)
\(180\) 0 0
\(181\) 902.000 0.370415 0.185208 0.982699i \(-0.440704\pi\)
0.185208 + 0.982699i \(0.440704\pi\)
\(182\) 8.00000 + 13.8564i 0.00325824 + 0.00564344i
\(183\) 0 0
\(184\) −288.000 + 498.831i −0.115389 + 0.199860i
\(185\) −835.000 + 1446.26i −0.331840 + 0.574764i
\(186\) 0 0
\(187\) −2736.00 4738.89i −1.06993 1.85317i
\(188\) 864.000 0.335179
\(189\) 0 0
\(190\) −1400.00 −0.534561
\(191\) 84.0000 + 145.492i 0.0318221 + 0.0551175i 0.881498 0.472188i \(-0.156536\pi\)
−0.849676 + 0.527306i \(0.823202\pi\)
\(192\) 0 0
\(193\) 659.000 1141.42i 0.245782 0.425706i −0.716569 0.697516i \(-0.754289\pi\)
0.962351 + 0.271809i \(0.0876220\pi\)
\(194\) 1534.00 2656.97i 0.567705 0.983294i
\(195\) 0 0
\(196\) 654.000 + 1132.76i 0.238338 + 0.412814i
\(197\) −4014.00 −1.45170 −0.725852 0.687851i \(-0.758554\pi\)
−0.725852 + 0.687851i \(0.758554\pi\)
\(198\) 0 0
\(199\) 2000.00 0.712443 0.356222 0.934401i \(-0.384065\pi\)
0.356222 + 0.934401i \(0.384065\pi\)
\(200\) −100.000 173.205i −0.0353553 0.0612372i
\(201\) 0 0
\(202\) −1722.00 + 2982.59i −0.599799 + 1.03888i
\(203\) 420.000 727.461i 0.145213 0.251516i
\(204\) 0 0
\(205\) −495.000 857.365i −0.168645 0.292102i
\(206\) 2104.00 0.711615
\(207\) 0 0
\(208\) 32.0000 0.0106673
\(209\) 3360.00 + 5819.69i 1.11204 + 1.92611i
\(210\) 0 0
\(211\) 1934.00 3349.79i 0.631005 1.09293i −0.356342 0.934356i \(-0.615976\pi\)
0.987347 0.158577i \(-0.0506906\pi\)
\(212\) 156.000 270.200i 0.0505383 0.0875349i
\(213\) 0 0
\(214\) 564.000 + 976.877i 0.180160 + 0.312046i
\(215\) 1340.00 0.425057
\(216\) 0 0
\(217\) −1088.00 −0.340361
\(218\) 610.000 + 1056.55i 0.189516 + 0.328251i
\(219\) 0 0
\(220\) −480.000 + 831.384i −0.147098 + 0.254781i
\(221\) 114.000 197.454i 0.0346990 0.0601004i
\(222\) 0 0
\(223\) 1574.00 + 2726.25i 0.472658 + 0.818668i 0.999510 0.0312886i \(-0.00996110\pi\)
−0.526852 + 0.849957i \(0.676628\pi\)
\(224\) −128.000 −0.0381802
\(225\) 0 0
\(226\) 2604.00 0.766440
\(227\) −1278.00 2213.56i −0.373673 0.647221i 0.616454 0.787391i \(-0.288569\pi\)
−0.990128 + 0.140170i \(0.955235\pi\)
\(228\) 0 0
\(229\) 305.000 528.275i 0.0880130 0.152443i −0.818658 0.574281i \(-0.805282\pi\)
0.906671 + 0.421838i \(0.138615\pi\)
\(230\) 360.000 623.538i 0.103207 0.178760i
\(231\) 0 0
\(232\) −840.000 1454.92i −0.237710 0.411726i
\(233\) −2058.00 −0.578644 −0.289322 0.957232i \(-0.593430\pi\)
−0.289322 + 0.957232i \(0.593430\pi\)
\(234\) 0 0
\(235\) −1080.00 −0.299793
\(236\) −480.000 831.384i −0.132396 0.229316i
\(237\) 0 0
\(238\) −456.000 + 789.815i −0.124194 + 0.215110i
\(239\) −2460.00 + 4260.84i −0.665792 + 1.15318i 0.313279 + 0.949661i \(0.398573\pi\)
−0.979070 + 0.203523i \(0.934761\pi\)
\(240\) 0 0
\(241\) 719.000 + 1245.34i 0.192178 + 0.332862i 0.945972 0.324249i \(-0.105112\pi\)
−0.753794 + 0.657111i \(0.771778\pi\)
\(242\) 1946.00 0.516916
\(243\) 0 0
\(244\) 1208.00 0.316944
\(245\) −817.500 1415.95i −0.213176 0.369232i
\(246\) 0 0
\(247\) −140.000 + 242.487i −0.0360647 + 0.0624659i
\(248\) −1088.00 + 1884.47i −0.278581 + 0.482516i
\(249\) 0 0
\(250\) 125.000 + 216.506i 0.0316228 + 0.0547723i
\(251\) 792.000 0.199166 0.0995829 0.995029i \(-0.468249\pi\)
0.0995829 + 0.995029i \(0.468249\pi\)
\(252\) 0 0
\(253\) −3456.00 −0.858802
\(254\) 124.000 + 214.774i 0.0306317 + 0.0530557i
\(255\) 0 0
\(256\) −128.000 + 221.703i −0.0312500 + 0.0541266i
\(257\) −1083.00 + 1875.81i −0.262863 + 0.455291i −0.967001 0.254771i \(-0.918000\pi\)
0.704139 + 0.710062i \(0.251333\pi\)
\(258\) 0 0
\(259\) −668.000 1157.01i −0.160261 0.277580i
\(260\) −40.0000 −0.00954113
\(261\) 0 0
\(262\) 384.000 0.0905481
\(263\) −1596.00 2764.35i −0.374196 0.648127i 0.616010 0.787738i \(-0.288748\pi\)
−0.990206 + 0.139611i \(0.955415\pi\)
\(264\) 0 0
\(265\) −195.000 + 337.750i −0.0452028 + 0.0782936i
\(266\) 560.000 969.948i 0.129082 0.223577i
\(267\) 0 0
\(268\) −1192.00 2064.60i −0.271690 0.470581i
\(269\) 5490.00 1.24435 0.622177 0.782877i \(-0.286248\pi\)
0.622177 + 0.782877i \(0.286248\pi\)
\(270\) 0 0
\(271\) −6328.00 −1.41845 −0.709223 0.704985i \(-0.750954\pi\)
−0.709223 + 0.704985i \(0.750954\pi\)
\(272\) 912.000 + 1579.63i 0.203302 + 0.352129i
\(273\) 0 0
\(274\) 2514.00 4354.38i 0.554293 0.960064i
\(275\) 600.000 1039.23i 0.131569 0.227883i
\(276\) 0 0
\(277\) 287.000 + 497.099i 0.0622533 + 0.107826i 0.895472 0.445117i \(-0.146838\pi\)
−0.833219 + 0.552943i \(0.813505\pi\)
\(278\) 2680.00 0.578186
\(279\) 0 0
\(280\) 160.000 0.0341494
\(281\) −2121.00 3673.68i −0.450278 0.779905i 0.548125 0.836397i \(-0.315342\pi\)
−0.998403 + 0.0564915i \(0.982009\pi\)
\(282\) 0 0
\(283\) 314.000 543.864i 0.0659553 0.114238i −0.831162 0.556030i \(-0.812324\pi\)
0.897117 + 0.441792i \(0.145657\pi\)
\(284\) 1536.00 2660.43i 0.320933 0.555871i
\(285\) 0 0
\(286\) 96.0000 + 166.277i 0.0198482 + 0.0343782i
\(287\) 792.000 0.162893
\(288\) 0 0
\(289\) 8083.00 1.64523
\(290\) 1050.00 + 1818.65i 0.212614 + 0.368259i
\(291\) 0 0
\(292\) 956.000 1655.84i 0.191595 0.331852i
\(293\) 279.000 483.242i 0.0556292 0.0963526i −0.836870 0.547402i \(-0.815617\pi\)
0.892499 + 0.451049i \(0.148950\pi\)
\(294\) 0 0
\(295\) 600.000 + 1039.23i 0.118418 + 0.205106i
\(296\) −2672.00 −0.524685
\(297\) 0 0
\(298\) 2820.00 0.548182
\(299\) −72.0000 124.708i −0.0139260 0.0241205i
\(300\) 0 0
\(301\) −536.000 + 928.379i −0.102640 + 0.177777i
\(302\) 2128.00 3685.80i 0.405472 0.702299i
\(303\) 0 0
\(304\) −1120.00 1939.90i −0.211304 0.365989i
\(305\) −1510.00 −0.283483
\(306\) 0 0
\(307\) −6964.00 −1.29465 −0.647323 0.762216i \(-0.724112\pi\)
−0.647323 + 0.762216i \(0.724112\pi\)
\(308\) −384.000 665.108i −0.0710404 0.123046i
\(309\) 0 0
\(310\) 1360.00 2355.59i 0.249170 0.431576i
\(311\) −1416.00 + 2452.58i −0.258180 + 0.447181i −0.965754 0.259458i \(-0.916456\pi\)
0.707574 + 0.706639i \(0.249789\pi\)
\(312\) 0 0
\(313\) −4321.00 7484.19i −0.780311 1.35154i −0.931761 0.363073i \(-0.881727\pi\)
0.151449 0.988465i \(-0.451606\pi\)
\(314\) 6052.00 1.08769
\(315\) 0 0
\(316\) −2560.00 −0.455732
\(317\) 1107.00 + 1917.38i 0.196137 + 0.339719i 0.947273 0.320429i \(-0.103827\pi\)
−0.751136 + 0.660148i \(0.770494\pi\)
\(318\) 0 0
\(319\) 5040.00 8729.54i 0.884595 1.53216i
\(320\) 160.000 277.128i 0.0279508 0.0484123i
\(321\) 0 0
\(322\) 288.000 + 498.831i 0.0498435 + 0.0863315i
\(323\) −15960.0 −2.74934
\(324\) 0 0
\(325\) 50.0000 0.00853385
\(326\) −2612.00 4524.12i −0.443759 0.768612i
\(327\) 0 0
\(328\) 792.000 1371.78i 0.133326 0.230927i
\(329\) 432.000 748.246i 0.0723919 0.125386i
\(330\) 0 0
\(331\) −5386.00 9328.83i −0.894385 1.54912i −0.834564 0.550911i \(-0.814281\pi\)
−0.0598204 0.998209i \(-0.519053\pi\)
\(332\) −1392.00 −0.230108
\(333\) 0 0
\(334\) −48.0000 −0.00786360
\(335\) 1490.00 + 2580.76i 0.243007 + 0.420901i
\(336\) 0 0
\(337\) 827.000 1432.41i 0.133678 0.231537i −0.791414 0.611281i \(-0.790654\pi\)
0.925092 + 0.379744i \(0.123988\pi\)
\(338\) 2193.00 3798.39i 0.352910 0.611258i
\(339\) 0 0
\(340\) −1140.00 1974.54i −0.181839 0.314954i
\(341\) −13056.0 −2.07338
\(342\) 0 0
\(343\) 2680.00 0.421885
\(344\) 1072.00 + 1856.76i 0.168019 + 0.291017i
\(345\) 0 0
\(346\) −1962.00 + 3398.28i −0.304849 + 0.528014i
\(347\) −1098.00 + 1901.79i −0.169867 + 0.294218i −0.938373 0.345625i \(-0.887667\pi\)
0.768506 + 0.639842i \(0.221000\pi\)
\(348\) 0 0
\(349\) −4135.00 7162.03i −0.634216 1.09849i −0.986681 0.162670i \(-0.947990\pi\)
0.352464 0.935825i \(-0.385344\pi\)
\(350\) −200.000 −0.0305441
\(351\) 0 0
\(352\) −1536.00 −0.232583
\(353\) −5151.00 8921.79i −0.776657 1.34521i −0.933858 0.357643i \(-0.883580\pi\)
0.157201 0.987567i \(-0.449753\pi\)
\(354\) 0 0
\(355\) −1920.00 + 3325.54i −0.287051 + 0.497186i
\(356\) −420.000 + 727.461i −0.0625280 + 0.108302i
\(357\) 0 0
\(358\) 120.000 + 207.846i 0.0177156 + 0.0306844i
\(359\) −2280.00 −0.335192 −0.167596 0.985856i \(-0.553600\pi\)
−0.167596 + 0.985856i \(0.553600\pi\)
\(360\) 0 0
\(361\) 12741.0 1.85756
\(362\) −902.000 1562.31i −0.130962 0.226832i
\(363\) 0 0
\(364\) 16.0000 27.7128i 0.00230392 0.00399051i
\(365\) −1195.00 + 2069.80i −0.171368 + 0.296817i
\(366\) 0 0
\(367\) 4382.00 + 7589.85i 0.623266 + 1.07953i 0.988873 + 0.148759i \(0.0475278\pi\)
−0.365608 + 0.930769i \(0.619139\pi\)
\(368\) 1152.00 0.163185
\(369\) 0 0
\(370\) 3340.00 0.469293
\(371\) −156.000 270.200i −0.0218305 0.0378115i
\(372\) 0 0
\(373\) 659.000 1141.42i 0.0914792 0.158447i −0.816655 0.577127i \(-0.804174\pi\)
0.908134 + 0.418680i \(0.137507\pi\)
\(374\) −5472.00 + 9477.78i −0.756552 + 1.31039i
\(375\) 0 0
\(376\) −864.000 1496.49i −0.118504 0.205254i
\(377\) 420.000 0.0573769
\(378\) 0 0
\(379\) 1100.00 0.149085 0.0745425 0.997218i \(-0.476250\pi\)
0.0745425 + 0.997218i \(0.476250\pi\)
\(380\) 1400.00 + 2424.87i 0.188996 + 0.327351i
\(381\) 0 0
\(382\) 168.000 290.985i 0.0225016 0.0389740i
\(383\) 1764.00 3055.34i 0.235343 0.407625i −0.724030 0.689769i \(-0.757712\pi\)
0.959372 + 0.282144i \(0.0910455\pi\)
\(384\) 0 0
\(385\) 480.000 + 831.384i 0.0635404 + 0.110055i
\(386\) −2636.00 −0.347588
\(387\) 0 0
\(388\) −6136.00 −0.802856
\(389\) 4815.00 + 8339.82i 0.627584 + 1.08701i 0.988035 + 0.154229i \(0.0492895\pi\)
−0.360451 + 0.932778i \(0.617377\pi\)
\(390\) 0 0
\(391\) 4104.00 7108.34i 0.530814 0.919396i
\(392\) 1308.00 2265.52i 0.168531 0.291903i
\(393\) 0 0
\(394\) 4014.00 + 6952.45i 0.513255 + 0.888983i
\(395\) 3200.00 0.407619
\(396\) 0 0
\(397\) −3094.00 −0.391142 −0.195571 0.980690i \(-0.562656\pi\)
−0.195571 + 0.980690i \(0.562656\pi\)
\(398\) −2000.00 3464.10i −0.251887 0.436281i
\(399\) 0 0
\(400\) −200.000 + 346.410i −0.0250000 + 0.0433013i
\(401\) 819.000 1418.55i 0.101992 0.176656i −0.810513 0.585721i \(-0.800812\pi\)
0.912505 + 0.409065i \(0.134145\pi\)
\(402\) 0 0
\(403\) −272.000 471.118i −0.0336211 0.0582334i
\(404\) 6888.00 0.848245
\(405\) 0 0
\(406\) −1680.00 −0.205362
\(407\) −8016.00 13884.1i −0.976261 1.69093i
\(408\) 0 0
\(409\) 6875.00 11907.8i 0.831166 1.43962i −0.0659483 0.997823i \(-0.521007\pi\)
0.897114 0.441799i \(-0.145659\pi\)
\(410\) −990.000 + 1714.73i −0.119250 + 0.206548i
\(411\) 0 0
\(412\) −2104.00 3644.23i −0.251594 0.435773i
\(413\) −960.000 −0.114379
\(414\) 0 0
\(415\) 1740.00 0.205815
\(416\) −32.0000 55.4256i −0.00377146 0.00653237i
\(417\) 0 0
\(418\) 6720.00 11639.4i 0.786330 1.36196i
\(419\) 6240.00 10808.0i 0.727551 1.26016i −0.230364 0.973105i \(-0.573992\pi\)
0.957915 0.287051i \(-0.0926750\pi\)
\(420\) 0 0
\(421\) −3631.00 6289.08i −0.420342 0.728054i 0.575631 0.817710i \(-0.304757\pi\)
−0.995973 + 0.0896557i \(0.971423\pi\)
\(422\) −7736.00 −0.892376
\(423\) 0 0
\(424\) −624.000 −0.0714720
\(425\) 1425.00 + 2468.17i 0.162642 + 0.281703i
\(426\) 0 0
\(427\) 604.000 1046.16i 0.0684534 0.118565i
\(428\) 1128.00 1953.75i 0.127392 0.220650i
\(429\) 0 0
\(430\) −1340.00 2320.95i −0.150280 0.260293i
\(431\) 9792.00 1.09435 0.547174 0.837019i \(-0.315704\pi\)
0.547174 + 0.837019i \(0.315704\pi\)
\(432\) 0 0
\(433\) 1802.00 0.199997 0.0999984 0.994988i \(-0.468116\pi\)
0.0999984 + 0.994988i \(0.468116\pi\)
\(434\) 1088.00 + 1884.47i 0.120336 + 0.208427i
\(435\) 0 0
\(436\) 1220.00 2113.10i 0.134008 0.232108i
\(437\) −5040.00 + 8729.54i −0.551707 + 0.955584i
\(438\) 0 0
\(439\) 1160.00 + 2009.18i 0.126113 + 0.218435i 0.922168 0.386791i \(-0.126416\pi\)
−0.796054 + 0.605225i \(0.793083\pi\)
\(440\) 1920.00 0.208028
\(441\) 0 0
\(442\) −456.000 −0.0490717
\(443\) −5586.00 9675.24i −0.599095 1.03766i −0.992955 0.118492i \(-0.962194\pi\)
0.393861 0.919170i \(-0.371139\pi\)
\(444\) 0 0
\(445\) 525.000 909.327i 0.0559267 0.0968679i
\(446\) 3148.00 5452.50i 0.334220 0.578886i
\(447\) 0 0
\(448\) 128.000 + 221.703i 0.0134987 + 0.0233805i
\(449\) 6810.00 0.715777 0.357888 0.933764i \(-0.383497\pi\)
0.357888 + 0.933764i \(0.383497\pi\)
\(450\) 0 0
\(451\) 9504.00 0.992297
\(452\) −2604.00 4510.26i −0.270978 0.469347i
\(453\) 0 0
\(454\) −2556.00 + 4427.12i −0.264227 + 0.457654i
\(455\) −20.0000 + 34.6410i −0.00206069 + 0.00356922i
\(456\) 0 0
\(457\) −8533.00 14779.6i −0.873429 1.51282i −0.858427 0.512935i \(-0.828558\pi\)
−0.0150014 0.999887i \(-0.504775\pi\)
\(458\) −1220.00 −0.124469
\(459\) 0 0
\(460\) −1440.00 −0.145957
\(461\) 9459.00 + 16383.5i 0.955639 + 1.65522i 0.732899 + 0.680337i \(0.238167\pi\)
0.222740 + 0.974878i \(0.428500\pi\)
\(462\) 0 0
\(463\) −526.000 + 911.059i −0.0527976 + 0.0914481i −0.891216 0.453579i \(-0.850147\pi\)
0.838419 + 0.545027i \(0.183480\pi\)
\(464\) −1680.00 + 2909.85i −0.168086 + 0.291134i
\(465\) 0 0
\(466\) 2058.00 + 3564.56i 0.204582 + 0.354346i
\(467\) 11076.0 1.09751 0.548754 0.835984i \(-0.315102\pi\)
0.548754 + 0.835984i \(0.315102\pi\)
\(468\) 0 0
\(469\) −2384.00 −0.234718
\(470\) 1080.00 + 1870.61i 0.105993 + 0.183585i
\(471\) 0 0
\(472\) −960.000 + 1662.77i −0.0936178 + 0.162151i
\(473\) −6432.00 + 11140.6i −0.625251 + 1.08297i
\(474\) 0 0
\(475\) −1750.00 3031.09i −0.169043 0.292791i
\(476\) 1824.00 0.175636
\(477\) 0 0
\(478\) 9840.00 0.941571
\(479\) 4500.00 + 7794.23i 0.429249 + 0.743481i 0.996807 0.0798526i \(-0.0254450\pi\)
−0.567558 + 0.823334i \(0.692112\pi\)
\(480\) 0 0
\(481\) 334.000 578.505i 0.0316613 0.0548390i
\(482\) 1438.00 2490.69i 0.135890 0.235369i
\(483\) 0 0
\(484\) −1946.00 3370.57i −0.182757 0.316545i
\(485\) 7670.00 0.718096
\(486\) 0 0
\(487\) −8764.00 −0.815472 −0.407736 0.913100i \(-0.633682\pi\)
−0.407736 + 0.913100i \(0.633682\pi\)
\(488\) −1208.00 2092.32i −0.112057 0.194088i
\(489\) 0 0
\(490\) −1635.00 + 2831.90i −0.150738 + 0.261086i
\(491\) −2796.00 + 4842.81i −0.256989 + 0.445118i −0.965434 0.260648i \(-0.916064\pi\)
0.708445 + 0.705766i \(0.249397\pi\)
\(492\) 0 0
\(493\) 11970.0 + 20732.6i 1.09351 + 1.89402i
\(494\) 560.000 0.0510032
\(495\) 0 0
\(496\) 4352.00 0.393973
\(497\) −1536.00 2660.43i −0.138630 0.240114i
\(498\) 0 0
\(499\) −2350.00 + 4070.32i −0.210823 + 0.365155i −0.951972 0.306184i \(-0.900948\pi\)
0.741150 + 0.671340i \(0.234281\pi\)
\(500\) 250.000 433.013i 0.0223607 0.0387298i
\(501\) 0 0
\(502\) −792.000 1371.78i −0.0704157 0.121964i
\(503\) −11808.0 −1.04671 −0.523353 0.852116i \(-0.675319\pi\)
−0.523353 + 0.852116i \(0.675319\pi\)
\(504\) 0 0
\(505\) −8610.00 −0.758693
\(506\) 3456.00 + 5985.97i 0.303632 + 0.525907i
\(507\) 0 0
\(508\) 248.000 429.549i 0.0216599 0.0375160i
\(509\) −585.000 + 1013.25i −0.0509424 + 0.0882348i −0.890372 0.455233i \(-0.849556\pi\)
0.839430 + 0.543468i \(0.182889\pi\)
\(510\) 0 0
\(511\) −956.000 1655.84i −0.0827612 0.143347i
\(512\) 512.000 0.0441942
\(513\) 0 0
\(514\) 4332.00 0.371744
\(515\) 2630.00 + 4555.29i 0.225032 + 0.389767i
\(516\) 0 0
\(517\) 5184.00 8978.95i 0.440990 0.763818i
\(518\) −1336.00 + 2314.02i −0.113321 + 0.196278i
\(519\) 0 0
\(520\) 40.0000 + 69.2820i 0.00337330 + 0.00584273i
\(521\) −16638.0 −1.39909 −0.699543 0.714590i \(-0.746613\pi\)
−0.699543 + 0.714590i \(0.746613\pi\)
\(522\) 0 0
\(523\) 15692.0 1.31198 0.655988 0.754771i \(-0.272252\pi\)
0.655988 + 0.754771i \(0.272252\pi\)
\(524\) −384.000 665.108i −0.0320136 0.0554492i
\(525\) 0 0
\(526\) −3192.00 + 5528.71i −0.264597 + 0.458295i
\(527\) 15504.0 26853.7i 1.28153 2.21967i
\(528\) 0 0
\(529\) 3491.50 + 6047.46i 0.286965 + 0.497038i
\(530\) 780.000 0.0639265
\(531\) 0 0
\(532\) −2240.00 −0.182549
\(533\) 198.000 + 342.946i 0.0160907 + 0.0278699i
\(534\) 0 0
\(535\) −1410.00 + 2442.19i −0.113943 + 0.197355i
\(536\) −2384.00 + 4129.21i −0.192114 + 0.332751i
\(537\) 0 0
\(538\) −5490.00 9508.96i −0.439946 0.762008i
\(539\) 15696.0 1.25431
\(540\) 0 0
\(541\) −22018.0 −1.74977 −0.874887 0.484327i \(-0.839064\pi\)
−0.874887 + 0.484327i \(0.839064\pi\)
\(542\) 6328.00 + 10960.4i 0.501496 + 0.868617i
\(543\) 0 0
\(544\) 1824.00 3159.26i 0.143756 0.248993i
\(545\) −1525.00 + 2641.38i −0.119860 + 0.207604i
\(546\) 0 0
\(547\) 2282.00 + 3952.54i 0.178375 + 0.308955i 0.941324 0.337504i \(-0.109583\pi\)
−0.762949 + 0.646459i \(0.776249\pi\)
\(548\) −10056.0 −0.783889
\(549\) 0 0
\(550\) −2400.00 −0.186066
\(551\) −14700.0 25461.1i −1.13655 1.96857i
\(552\) 0 0
\(553\) −1280.00 + 2217.03i −0.0984288 + 0.170484i
\(554\) 574.000 994.197i 0.0440197 0.0762444i
\(555\) 0 0
\(556\) −2680.00 4641.90i −0.204420 0.354065i
\(557\) −7734.00 −0.588331 −0.294165 0.955755i \(-0.595042\pi\)
−0.294165 + 0.955755i \(0.595042\pi\)
\(558\) 0 0
\(559\) −536.000 −0.0405552
\(560\) −160.000 277.128i −0.0120736 0.0209121i
\(561\) 0 0
\(562\) −4242.00 + 7347.36i −0.318395 + 0.551476i
\(563\) 10074.0 17448.7i 0.754118 1.30617i −0.191693 0.981455i \(-0.561398\pi\)
0.945812 0.324716i \(-0.105269\pi\)
\(564\) 0 0
\(565\) 3255.00 + 5637.83i 0.242370 + 0.419797i
\(566\) −1256.00 −0.0932749
\(567\) 0 0
\(568\) −6144.00 −0.453867
\(569\) 12015.0 + 20810.6i 0.885228 + 1.53326i 0.845452 + 0.534052i \(0.179331\pi\)
0.0397769 + 0.999209i \(0.487335\pi\)
\(570\) 0 0
\(571\) −1186.00 + 2054.21i −0.0869222 + 0.150554i −0.906209 0.422831i \(-0.861036\pi\)
0.819287 + 0.573384i \(0.194370\pi\)
\(572\) 192.000 332.554i 0.0140348 0.0243090i
\(573\) 0 0
\(574\) −792.000 1371.78i −0.0575914 0.0997512i
\(575\) 1800.00 0.130548
\(576\) 0 0
\(577\) 8546.00 0.616594 0.308297 0.951290i \(-0.400241\pi\)
0.308297 + 0.951290i \(0.400241\pi\)
\(578\) −8083.00 14000.2i −0.581676 1.00749i
\(579\) 0 0
\(580\) 2100.00 3637.31i 0.150341 0.260398i
\(581\) −696.000 + 1205.51i −0.0496987 + 0.0860807i
\(582\) 0 0
\(583\) −1872.00 3242.40i −0.132985 0.230337i
\(584\) −3824.00 −0.270956
\(585\) 0 0
\(586\) −1116.00 −0.0786716
\(587\) 7722.00 + 13374.9i 0.542966 + 0.940445i 0.998732 + 0.0503450i \(0.0160321\pi\)
−0.455766 + 0.890100i \(0.650635\pi\)
\(588\) 0 0
\(589\) −19040.0 + 32978.2i −1.33197 + 2.30704i
\(590\) 1200.00 2078.46i 0.0837343 0.145032i
\(591\) 0 0
\(592\) 2672.00 + 4628.04i 0.185504 + 0.321303i
\(593\) 18342.0 1.27018 0.635089 0.772439i \(-0.280963\pi\)
0.635089 + 0.772439i \(0.280963\pi\)
\(594\) 0 0
\(595\) −2280.00 −0.157094
\(596\) −2820.00 4884.38i −0.193812 0.335692i
\(597\) 0 0
\(598\) −144.000 + 249.415i −0.00984715 + 0.0170558i
\(599\) −12300.0 + 21304.2i −0.839006 + 1.45320i 0.0517213 + 0.998662i \(0.483529\pi\)
−0.890727 + 0.454539i \(0.849804\pi\)
\(600\) 0 0
\(601\) 4499.00 + 7792.50i 0.305354 + 0.528889i 0.977340 0.211675i \(-0.0678917\pi\)
−0.671986 + 0.740564i \(0.734558\pi\)
\(602\) 2144.00 0.145154
\(603\) 0 0
\(604\) −8512.00 −0.573424
\(605\) 2432.50 + 4213.21i 0.163463 + 0.283126i
\(606\) 0 0
\(607\) −2038.00 + 3529.92i −0.136277 + 0.236038i −0.926084 0.377316i \(-0.876847\pi\)
0.789808 + 0.613354i \(0.210180\pi\)
\(608\) −2240.00 + 3879.79i −0.149414 + 0.258793i
\(609\) 0 0
\(610\) 1510.00 + 2615.40i 0.100226 + 0.173597i
\(611\) 432.000 0.0286037
\(612\) 0 0
\(613\) −4078.00 −0.268693 −0.134347 0.990934i \(-0.542894\pi\)
−0.134347 + 0.990934i \(0.542894\pi\)
\(614\) 6964.00 + 12062.0i 0.457727 + 0.792806i
\(615\) 0 0
\(616\) −768.000 + 1330.22i −0.0502331 + 0.0870063i
\(617\) −5043.00 + 8734.73i −0.329049 + 0.569930i −0.982324 0.187191i \(-0.940062\pi\)
0.653274 + 0.757122i \(0.273395\pi\)
\(618\) 0 0
\(619\) −4390.00 7603.70i −0.285055 0.493730i 0.687568 0.726120i \(-0.258679\pi\)
−0.972622 + 0.232391i \(0.925345\pi\)
\(620\) −5440.00 −0.352380
\(621\) 0 0
\(622\) 5664.00 0.365122
\(623\) 420.000 + 727.461i 0.0270095 + 0.0467819i
\(624\) 0 0
\(625\) −312.500 + 541.266i −0.0200000 + 0.0346410i
\(626\) −8642.00 + 14968.4i −0.551763 + 0.955682i
\(627\) 0 0
\(628\) −6052.00 10482.4i −0.384556 0.666070i
\(629\) 38076.0 2.41366
\(630\) 0 0
\(631\) 2792.00 0.176145 0.0880727 0.996114i \(-0.471929\pi\)
0.0880727 + 0.996114i \(0.471929\pi\)
\(632\) 2560.00 + 4434.05i 0.161126 + 0.279078i
\(633\) 0 0
\(634\) 2214.00 3834.76i 0.138690 0.240217i
\(635\) −310.000 + 536.936i −0.0193732 + 0.0335553i
\(636\) 0 0
\(637\) 327.000 + 566.381i 0.0203394 + 0.0352289i
\(638\) −20160.0 −1.25101
\(639\) 0 0
\(640\) −640.000 −0.0395285
\(641\) −3801.00 6583.53i −0.234213 0.405669i 0.724831 0.688927i \(-0.241918\pi\)
−0.959044 + 0.283258i \(0.908585\pi\)
\(642\) 0 0
\(643\) −12106.0 + 20968.2i −0.742479 + 1.28601i 0.208884 + 0.977940i \(0.433017\pi\)
−0.951363 + 0.308071i \(0.900317\pi\)
\(644\) 576.000 997.661i 0.0352447 0.0610456i
\(645\) 0 0
\(646\) 15960.0 + 27643.5i 0.972040 + 1.68362i
\(647\) 9456.00 0.574581 0.287290 0.957844i \(-0.407246\pi\)
0.287290 + 0.957844i \(0.407246\pi\)
\(648\) 0 0
\(649\) −11520.0 −0.696764
\(650\) −50.0000 86.6025i −0.00301717 0.00522589i
\(651\) 0 0
\(652\) −5224.00 + 9048.23i −0.313785 + 0.543491i
\(653\) 4779.00 8277.47i 0.286396 0.496053i −0.686551 0.727082i \(-0.740876\pi\)
0.972947 + 0.231029i \(0.0742093\pi\)
\(654\) 0 0
\(655\) 480.000 + 831.384i 0.0286338 + 0.0495952i
\(656\) −3168.00 −0.188551
\(657\) 0 0
\(658\) −1728.00 −0.102378
\(659\) 14640.0 + 25357.2i 0.865392 + 1.49890i 0.866657 + 0.498904i \(0.166264\pi\)
−0.00126511 + 0.999999i \(0.500403\pi\)
\(660\) 0 0
\(661\) 14549.0 25199.6i 0.856113 1.48283i −0.0194961 0.999810i \(-0.506206\pi\)
0.875609 0.483021i \(-0.160460\pi\)
\(662\) −10772.0 + 18657.7i −0.632425 + 1.09539i
\(663\) 0 0
\(664\) 1392.00 + 2411.01i 0.0813555 + 0.140912i
\(665\) 2800.00 0.163277
\(666\) 0 0
\(667\) 15120.0 0.877734
\(668\) 48.0000 + 83.1384i 0.00278020 + 0.00481545i
\(669\) 0 0
\(670\) 2980.00 5161.51i 0.171832 0.297622i
\(671\) 7248.00 12553.9i 0.416998 0.722262i
\(672\) 0 0
\(673\) 5819.00 + 10078.8i 0.333293 + 0.577280i 0.983155 0.182772i \(-0.0585069\pi\)
−0.649863 + 0.760052i \(0.725174\pi\)
\(674\) −3308.00 −0.189050
\(675\) 0 0
\(676\) −8772.00 −0.499090
\(677\) −1713.00 2967.00i −0.0972466 0.168436i 0.813297 0.581848i \(-0.197670\pi\)
−0.910544 + 0.413412i \(0.864337\pi\)
\(678\) 0 0
\(679\) −3068.00 + 5313.93i −0.173401 + 0.300339i
\(680\) −2280.00 + 3949.08i −0.128579 + 0.222706i
\(681\) 0 0
\(682\) 13056.0 + 22613.7i 0.733050 + 1.26968i
\(683\) −20148.0 −1.12876 −0.564379 0.825516i \(-0.690884\pi\)
−0.564379 + 0.825516i \(0.690884\pi\)
\(684\) 0 0
\(685\) 12570.0 0.701131
\(686\) −2680.00 4641.90i −0.149159 0.258350i
\(687\) 0 0
\(688\) 2144.00 3713.52i 0.118807 0.205780i
\(689\) 78.0000 135.100i 0.00431286 0.00747010i
\(690\) 0 0
\(691\) 14714.0 + 25485.4i 0.810053 + 1.40305i 0.912826 + 0.408349i \(0.133895\pi\)
−0.102772 + 0.994705i \(0.532771\pi\)
\(692\) 7848.00 0.431122
\(693\) 0 0
\(694\) 4392.00 0.240228
\(695\) 3350.00 + 5802.37i 0.182838 + 0.316686i
\(696\) 0 0
\(697\) −11286.0 + 19547.9i −0.613325 + 1.06231i
\(698\) −8270.00 + 14324.1i −0.448459 + 0.776753i
\(699\) 0 0
\(700\) 200.000 + 346.410i 0.0107990 + 0.0187044i
\(701\) 16242.0 0.875110 0.437555 0.899192i \(-0.355845\pi\)
0.437555 + 0.899192i \(0.355845\pi\)
\(702\) 0 0
\(703\) −46760.0 −2.50866
\(704\) 1536.00 + 2660.43i 0.0822304 + 0.142427i
\(705\) 0 0
\(706\) −10302.0 + 17843.6i −0.549180 + 0.951207i
\(707\) 3444.00 5965.18i 0.183204 0.317318i
\(708\) 0 0
\(709\) −1015.00 1758.03i −0.0537646 0.0931231i 0.837890 0.545838i \(-0.183789\pi\)
−0.891655 + 0.452715i \(0.850455\pi\)
\(710\) 7680.00 0.405951
\(711\) 0 0
\(712\) 1680.00 0.0884279
\(713\) −9792.00 16960.2i −0.514324 0.890836i
\(714\) 0 0
\(715\) −240.000 + 415.692i −0.0125531 + 0.0217427i
\(716\) 240.000 415.692i 0.0125268 0.0216971i
\(717\) 0 0
\(718\) 2280.00 + 3949.08i 0.118508 + 0.205262i
\(719\) 6960.00 0.361007 0.180504 0.983574i \(-0.442227\pi\)
0.180504 + 0.983574i \(0.442227\pi\)
\(720\) 0 0
\(721\) −4208.00 −0.217357
\(722\) −12741.0 22068.1i −0.656746 1.13752i
\(723\) 0 0
\(724\) −1804.00 + 3124.62i −0.0926038 + 0.160394i
\(725\) −2625.00 + 4546.63i −0.134469 + 0.232907i
\(726\) 0 0
\(727\) −9298.00 16104.6i −0.474338 0.821578i 0.525230 0.850960i \(-0.323979\pi\)
−0.999568 + 0.0293826i \(0.990646\pi\)
\(728\) −64.0000 −0.00325824
\(729\) 0 0
\(730\) 4780.00 0.242350
\(731\) −15276.0 26458.8i −0.772918 1.33873i
\(732\) 0 0
\(733\) −10621.0 + 18396.1i −0.535192 + 0.926979i 0.463962 + 0.885855i \(0.346427\pi\)
−0.999154 + 0.0411244i \(0.986906\pi\)
\(734\) 8764.00 15179.7i 0.440715 0.763342i
\(735\) 0 0
\(736\) −1152.00 1995.32i −0.0576947 0.0999301i
\(737\) −28608.0 −1.42984
\(738\) 0 0
\(739\) −340.000 −0.0169244 −0.00846218 0.999964i \(-0.502694\pi\)
−0.00846218 + 0.999964i \(0.502694\pi\)
\(740\) −3340.00 5785.05i −0.165920 0.287382i
\(741\) 0 0
\(742\) −312.000 + 540.400i −0.0154365 + 0.0267368i
\(743\) 10944.0 18955.6i 0.540372 0.935952i −0.458510 0.888689i \(-0.651617\pi\)
0.998882 0.0472628i \(-0.0150498\pi\)
\(744\) 0 0
\(745\) 3525.00 + 6105.48i 0.173350 + 0.300252i
\(746\) −2636.00 −0.129371
\(747\) 0 0
\(748\) 21888.0 1.06993
\(749\) −1128.00 1953.75i −0.0550283 0.0953119i
\(750\) 0 0
\(751\) −8896.00 + 15408.3i −0.432250 + 0.748679i −0.997067 0.0765376i \(-0.975613\pi\)
0.564817 + 0.825216i \(0.308947\pi\)
\(752\) −1728.00 + 2992.98i −0.0837948 + 0.145137i
\(753\) 0 0
\(754\) −420.000 727.461i −0.0202858 0.0351360i
\(755\) 10640.0 0.512886
\(756\) 0 0
\(757\) 37346.0 1.79308 0.896541 0.442960i \(-0.146072\pi\)
0.896541 + 0.442960i \(0.146072\pi\)
\(758\) −1100.00 1905.26i −0.0527095 0.0912955i
\(759\) 0 0
\(760\) 2800.00 4849.74i 0.133640 0.231472i
\(761\) 5679.00 9836.32i 0.270517 0.468550i −0.698477 0.715632i \(-0.746139\pi\)
0.968994 + 0.247083i \(0.0794720\pi\)
\(762\) 0 0
\(763\) −1220.00 2113.10i −0.0578859 0.100261i
\(764\) −672.000 −0.0318221
\(765\) 0 0
\(766\) −7056.00 −0.332825
\(767\) −240.000 415.692i −0.0112984 0.0195695i
\(768\) 0 0
\(769\) 17135.0 29678.7i 0.803516 1.39173i −0.113772 0.993507i \(-0.536293\pi\)
0.917288 0.398224i \(-0.130373\pi\)
\(770\) 960.000 1662.77i 0.0449299 0.0778208i
\(771\) 0 0
\(772\) 2636.00 + 4565.69i 0.122891 + 0.212853i
\(773\) −13278.0 −0.617822 −0.308911 0.951091i \(-0.599965\pi\)
−0.308911 + 0.951091i \(0.599965\pi\)
\(774\) 0 0
\(775\) 6800.00 0.315178
\(776\) 6136.00 + 10627.9i 0.283853 + 0.491647i
\(777\) 0 0
\(778\) 9630.00 16679.6i 0.443769 0.768630i
\(779\) 13860.0 24006.2i 0.637466 1.10412i
\(780\) 0