Properties

Label 6.5.b.a.5.1
Level $6$
Weight $5$
Character 6.5
Analytic conductor $0.620$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [6,5,Mod(5,6)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 5, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("6.5");
 
S:= CuspForms(chi, 5);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6 = 2 \cdot 3 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 6.b (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: \(0.620219778503\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{-2}) \)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} + 2 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 5.1
Root \(-1.41421i\) of defining polynomial
Character \(\chi\) \(=\) 6.5
Dual form 6.5.b.a.5.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.82843i q^{2} +(-3.00000 + 8.48528i) q^{3} -8.00000 q^{4} -16.9706i q^{5} +(24.0000 + 8.48528i) q^{6} +26.0000 q^{7} +22.6274i q^{8} +(-63.0000 - 50.9117i) q^{9} +O(q^{10})\) \(q-2.82843i q^{2} +(-3.00000 + 8.48528i) q^{3} -8.00000 q^{4} -16.9706i q^{5} +(24.0000 + 8.48528i) q^{6} +26.0000 q^{7} +22.6274i q^{8} +(-63.0000 - 50.9117i) q^{9} -48.0000 q^{10} +118.794i q^{11} +(24.0000 - 67.8823i) q^{12} +50.0000 q^{13} -73.5391i q^{14} +(144.000 + 50.9117i) q^{15} +64.0000 q^{16} -203.647i q^{17} +(-144.000 + 178.191i) q^{18} -358.000 q^{19} +135.765i q^{20} +(-78.0000 + 220.617i) q^{21} +336.000 q^{22} -373.352i q^{23} +(-192.000 - 67.8823i) q^{24} +337.000 q^{25} -141.421i q^{26} +(621.000 - 381.838i) q^{27} -208.000 q^{28} +1442.50i q^{29} +(144.000 - 407.294i) q^{30} -742.000 q^{31} -181.019i q^{32} +(-1008.00 - 356.382i) q^{33} -576.000 q^{34} -441.235i q^{35} +(504.000 + 407.294i) q^{36} +1874.00 q^{37} +1012.58i q^{38} +(-150.000 + 424.264i) q^{39} +384.000 q^{40} -2409.82i q^{41} +(624.000 + 220.617i) q^{42} -262.000 q^{43} -950.352i q^{44} +(-864.000 + 1069.15i) q^{45} -1056.00 q^{46} +1697.06i q^{47} +(-192.000 + 543.058i) q^{48} -1725.00 q^{49} -953.180i q^{50} +(1728.00 + 610.940i) q^{51} -400.000 q^{52} +458.205i q^{53} +(-1080.00 - 1756.45i) q^{54} +2016.00 q^{55} +588.313i q^{56} +(1074.00 - 3037.73i) q^{57} +4080.00 q^{58} +1815.85i q^{59} +(-1152.00 - 407.294i) q^{60} -1486.00 q^{61} +2098.69i q^{62} +(-1638.00 - 1323.70i) q^{63} -512.000 q^{64} -848.528i q^{65} +(-1008.00 + 2851.05i) q^{66} -4486.00 q^{67} +1629.17i q^{68} +(3168.00 + 1120.06i) q^{69} -1248.00 q^{70} -3563.82i q^{71} +(1152.00 - 1425.53i) q^{72} +290.000 q^{73} -5300.47i q^{74} +(-1011.00 + 2859.54i) q^{75} +2864.00 q^{76} +3088.64i q^{77} +(1200.00 + 424.264i) q^{78} +9818.00 q^{79} -1086.12i q^{80} +(1377.00 + 6414.87i) q^{81} -6816.00 q^{82} -7110.67i q^{83} +(624.000 - 1764.94i) q^{84} -3456.00 q^{85} +741.048i q^{86} +(-12240.0 - 4327.49i) q^{87} -2688.00 q^{88} +7840.40i q^{89} +(3024.00 + 2443.76i) q^{90} +1300.00 q^{91} +2986.82i q^{92} +(2226.00 - 6296.08i) q^{93} +4800.00 q^{94} +6075.46i q^{95} +(1536.00 + 543.058i) q^{96} -478.000 q^{97} +4879.04i q^{98} +(6048.00 - 7484.02i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 6 q^{3} - 16 q^{4} + 48 q^{6} + 52 q^{7} - 126 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 6 q^{3} - 16 q^{4} + 48 q^{6} + 52 q^{7} - 126 q^{9} - 96 q^{10} + 48 q^{12} + 100 q^{13} + 288 q^{15} + 128 q^{16} - 288 q^{18} - 716 q^{19} - 156 q^{21} + 672 q^{22} - 384 q^{24} + 674 q^{25} + 1242 q^{27} - 416 q^{28} + 288 q^{30} - 1484 q^{31} - 2016 q^{33} - 1152 q^{34} + 1008 q^{36} + 3748 q^{37} - 300 q^{39} + 768 q^{40} + 1248 q^{42} - 524 q^{43} - 1728 q^{45} - 2112 q^{46} - 384 q^{48} - 3450 q^{49} + 3456 q^{51} - 800 q^{52} - 2160 q^{54} + 4032 q^{55} + 2148 q^{57} + 8160 q^{58} - 2304 q^{60} - 2972 q^{61} - 3276 q^{63} - 1024 q^{64} - 2016 q^{66} - 8972 q^{67} + 6336 q^{69} - 2496 q^{70} + 2304 q^{72} + 580 q^{73} - 2022 q^{75} + 5728 q^{76} + 2400 q^{78} + 19636 q^{79} + 2754 q^{81} - 13632 q^{82} + 1248 q^{84} - 6912 q^{85} - 24480 q^{87} - 5376 q^{88} + 6048 q^{90} + 2600 q^{91} + 4452 q^{93} + 9600 q^{94} + 3072 q^{96} - 956 q^{97} + 12096 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/6\mathbb{Z}\right)^\times\).

\(n\) \(5\)
\(\chi(n)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.82843i 0.707107i
\(3\) −3.00000 + 8.48528i −0.333333 + 0.942809i
\(4\) −8.00000 −0.500000
\(5\) 16.9706i 0.678823i −0.940638 0.339411i \(-0.889772\pi\)
0.940638 0.339411i \(-0.110228\pi\)
\(6\) 24.0000 + 8.48528i 0.666667 + 0.235702i
\(7\) 26.0000 0.530612 0.265306 0.964164i \(-0.414527\pi\)
0.265306 + 0.964164i \(0.414527\pi\)
\(8\) 22.6274i 0.353553i
\(9\) −63.0000 50.9117i −0.777778 0.628539i
\(10\) −48.0000 −0.480000
\(11\) 118.794i 0.981768i 0.871225 + 0.490884i \(0.163326\pi\)
−0.871225 + 0.490884i \(0.836674\pi\)
\(12\) 24.0000 67.8823i 0.166667 0.471405i
\(13\) 50.0000 0.295858 0.147929 0.988998i \(-0.452739\pi\)
0.147929 + 0.988998i \(0.452739\pi\)
\(14\) 73.5391i 0.375200i
\(15\) 144.000 + 50.9117i 0.640000 + 0.226274i
\(16\) 64.0000 0.250000
\(17\) 203.647i 0.704660i −0.935876 0.352330i \(-0.885389\pi\)
0.935876 0.352330i \(-0.114611\pi\)
\(18\) −144.000 + 178.191i −0.444444 + 0.549972i
\(19\) −358.000 −0.991690 −0.495845 0.868411i \(-0.665142\pi\)
−0.495845 + 0.868411i \(0.665142\pi\)
\(20\) 135.765i 0.339411i
\(21\) −78.0000 + 220.617i −0.176871 + 0.500266i
\(22\) 336.000 0.694215
\(23\) 373.352i 0.705770i −0.935667 0.352885i \(-0.885201\pi\)
0.935667 0.352885i \(-0.114799\pi\)
\(24\) −192.000 67.8823i −0.333333 0.117851i
\(25\) 337.000 0.539200
\(26\) 141.421i 0.209203i
\(27\) 621.000 381.838i 0.851852 0.523783i
\(28\) −208.000 −0.265306
\(29\) 1442.50i 1.71522i 0.514303 + 0.857609i \(0.328051\pi\)
−0.514303 + 0.857609i \(0.671949\pi\)
\(30\) 144.000 407.294i 0.160000 0.452548i
\(31\) −742.000 −0.772112 −0.386056 0.922475i \(-0.626163\pi\)
−0.386056 + 0.922475i \(0.626163\pi\)
\(32\) 181.019i 0.176777i
\(33\) −1008.00 356.382i −0.925620 0.327256i
\(34\) −576.000 −0.498270
\(35\) 441.235i 0.360192i
\(36\) 504.000 + 407.294i 0.388889 + 0.314270i
\(37\) 1874.00 1.36888 0.684441 0.729068i \(-0.260046\pi\)
0.684441 + 0.729068i \(0.260046\pi\)
\(38\) 1012.58i 0.701231i
\(39\) −150.000 + 424.264i −0.0986193 + 0.278938i
\(40\) 384.000 0.240000
\(41\) 2409.82i 1.43356i −0.697298 0.716782i \(-0.745614\pi\)
0.697298 0.716782i \(-0.254386\pi\)
\(42\) 624.000 + 220.617i 0.353741 + 0.125067i
\(43\) −262.000 −0.141698 −0.0708491 0.997487i \(-0.522571\pi\)
−0.0708491 + 0.997487i \(0.522571\pi\)
\(44\) 950.352i 0.490884i
\(45\) −864.000 + 1069.15i −0.426667 + 0.527973i
\(46\) −1056.00 −0.499055
\(47\) 1697.06i 0.768246i 0.923282 + 0.384123i \(0.125496\pi\)
−0.923282 + 0.384123i \(0.874504\pi\)
\(48\) −192.000 + 543.058i −0.0833333 + 0.235702i
\(49\) −1725.00 −0.718451
\(50\) 953.180i 0.381272i
\(51\) 1728.00 + 610.940i 0.664360 + 0.234887i
\(52\) −400.000 −0.147929
\(53\) 458.205i 0.163120i 0.996668 + 0.0815602i \(0.0259903\pi\)
−0.996668 + 0.0815602i \(0.974010\pi\)
\(54\) −1080.00 1756.45i −0.370370 0.602350i
\(55\) 2016.00 0.666446
\(56\) 588.313i 0.187600i
\(57\) 1074.00 3037.73i 0.330563 0.934974i
\(58\) 4080.00 1.21284
\(59\) 1815.85i 0.521646i 0.965387 + 0.260823i \(0.0839939\pi\)
−0.965387 + 0.260823i \(0.916006\pi\)
\(60\) −1152.00 407.294i −0.320000 0.113137i
\(61\) −1486.00 −0.399355 −0.199678 0.979862i \(-0.563989\pi\)
−0.199678 + 0.979862i \(0.563989\pi\)
\(62\) 2098.69i 0.545966i
\(63\) −1638.00 1323.70i −0.412698 0.333511i
\(64\) −512.000 −0.125000
\(65\) 848.528i 0.200835i
\(66\) −1008.00 + 2851.05i −0.231405 + 0.654512i
\(67\) −4486.00 −0.999332 −0.499666 0.866218i \(-0.666544\pi\)
−0.499666 + 0.866218i \(0.666544\pi\)
\(68\) 1629.17i 0.352330i
\(69\) 3168.00 + 1120.06i 0.665406 + 0.235257i
\(70\) −1248.00 −0.254694
\(71\) 3563.82i 0.706967i −0.935441 0.353483i \(-0.884997\pi\)
0.935441 0.353483i \(-0.115003\pi\)
\(72\) 1152.00 1425.53i 0.222222 0.274986i
\(73\) 290.000 0.0544192 0.0272096 0.999630i \(-0.491338\pi\)
0.0272096 + 0.999630i \(0.491338\pi\)
\(74\) 5300.47i 0.967946i
\(75\) −1011.00 + 2859.54i −0.179733 + 0.508363i
\(76\) 2864.00 0.495845
\(77\) 3088.64i 0.520938i
\(78\) 1200.00 + 424.264i 0.197239 + 0.0697344i
\(79\) 9818.00 1.57315 0.786573 0.617498i \(-0.211854\pi\)
0.786573 + 0.617498i \(0.211854\pi\)
\(80\) 1086.12i 0.169706i
\(81\) 1377.00 + 6414.87i 0.209877 + 0.977728i
\(82\) −6816.00 −1.01368
\(83\) 7110.67i 1.03218i −0.856535 0.516088i \(-0.827388\pi\)
0.856535 0.516088i \(-0.172612\pi\)
\(84\) 624.000 1764.94i 0.0884354 0.250133i
\(85\) −3456.00 −0.478339
\(86\) 741.048i 0.100196i
\(87\) −12240.0 4327.49i −1.61712 0.571739i
\(88\) −2688.00 −0.347107
\(89\) 7840.40i 0.989825i 0.868943 + 0.494912i \(0.164800\pi\)
−0.868943 + 0.494912i \(0.835200\pi\)
\(90\) 3024.00 + 2443.76i 0.373333 + 0.301699i
\(91\) 1300.00 0.156986
\(92\) 2986.82i 0.352885i
\(93\) 2226.00 6296.08i 0.257371 0.727955i
\(94\) 4800.00 0.543232
\(95\) 6075.46i 0.673181i
\(96\) 1536.00 + 543.058i 0.166667 + 0.0589256i
\(97\) −478.000 −0.0508024 −0.0254012 0.999677i \(-0.508086\pi\)
−0.0254012 + 0.999677i \(0.508086\pi\)
\(98\) 4879.04i 0.508021i
\(99\) 6048.00 7484.02i 0.617080 0.763597i
\(100\) −2696.00 −0.269600
\(101\) 13729.2i 1.34587i −0.739703 0.672933i \(-0.765034\pi\)
0.739703 0.672933i \(-0.234966\pi\)
\(102\) 1728.00 4887.52i 0.166090 0.469773i
\(103\) 2138.00 0.201527 0.100764 0.994910i \(-0.467871\pi\)
0.100764 + 0.994910i \(0.467871\pi\)
\(104\) 1131.37i 0.104602i
\(105\) 3744.00 + 1323.70i 0.339592 + 0.120064i
\(106\) 1296.00 0.115344
\(107\) 10844.2i 0.947174i 0.880747 + 0.473587i \(0.157041\pi\)
−0.880747 + 0.473587i \(0.842959\pi\)
\(108\) −4968.00 + 3054.70i −0.425926 + 0.261891i
\(109\) −4750.00 −0.399798 −0.199899 0.979817i \(-0.564061\pi\)
−0.199899 + 0.979817i \(0.564061\pi\)
\(110\) 5702.11i 0.471249i
\(111\) −5622.00 + 15901.4i −0.456294 + 1.29059i
\(112\) 1664.00 0.132653
\(113\) 3190.47i 0.249860i 0.992166 + 0.124930i \(0.0398707\pi\)
−0.992166 + 0.124930i \(0.960129\pi\)
\(114\) −8592.00 3037.73i −0.661127 0.233744i
\(115\) −6336.00 −0.479093
\(116\) 11540.0i 0.857609i
\(117\) −3150.00 2545.58i −0.230112 0.185958i
\(118\) 5136.00 0.368860
\(119\) 5294.82i 0.373901i
\(120\) −1152.00 + 3258.35i −0.0800000 + 0.226274i
\(121\) 529.000 0.0361314
\(122\) 4203.04i 0.282387i
\(123\) 20448.0 + 7229.46i 1.35158 + 0.477854i
\(124\) 5936.00 0.386056
\(125\) 16325.7i 1.04484i
\(126\) −3744.00 + 4632.96i −0.235828 + 0.291822i
\(127\) 8282.00 0.513485 0.256743 0.966480i \(-0.417351\pi\)
0.256743 + 0.966480i \(0.417351\pi\)
\(128\) 1448.15i 0.0883883i
\(129\) 786.000 2223.14i 0.0472327 0.133594i
\(130\) −2400.00 −0.142012
\(131\) 5413.61i 0.315460i −0.987482 0.157730i \(-0.949582\pi\)
0.987482 0.157730i \(-0.0504176\pi\)
\(132\) 8064.00 + 2851.05i 0.462810 + 0.163628i
\(133\) −9308.00 −0.526203
\(134\) 12688.3i 0.706634i
\(135\) −6480.00 10538.7i −0.355556 0.578256i
\(136\) 4608.00 0.249135
\(137\) 18090.6i 0.963856i 0.876211 + 0.481928i \(0.160063\pi\)
−0.876211 + 0.481928i \(0.839937\pi\)
\(138\) 3168.00 8960.46i 0.166352 0.470513i
\(139\) −23206.0 −1.20108 −0.600538 0.799596i \(-0.705047\pi\)
−0.600538 + 0.799596i \(0.705047\pi\)
\(140\) 3529.88i 0.180096i
\(141\) −14400.0 5091.17i −0.724310 0.256082i
\(142\) −10080.0 −0.499901
\(143\) 5939.70i 0.290464i
\(144\) −4032.00 3258.35i −0.194444 0.157135i
\(145\) 24480.0 1.16433
\(146\) 820.244i 0.0384802i
\(147\) 5175.00 14637.1i 0.239484 0.677362i
\(148\) −14992.0 −0.684441
\(149\) 11183.6i 0.503743i 0.967761 + 0.251872i \(0.0810460\pi\)
−0.967761 + 0.251872i \(0.918954\pi\)
\(150\) 8088.00 + 2859.54i 0.359467 + 0.127091i
\(151\) 14426.0 0.632692 0.316346 0.948644i \(-0.397544\pi\)
0.316346 + 0.948644i \(0.397544\pi\)
\(152\) 8100.62i 0.350615i
\(153\) −10368.0 + 12829.7i −0.442907 + 0.548069i
\(154\) 8736.00 0.368359
\(155\) 12592.2i 0.524127i
\(156\) 1200.00 3394.11i 0.0493097 0.139469i
\(157\) 49010.0 1.98832 0.994158 0.107935i \(-0.0344238\pi\)
0.994158 + 0.107935i \(0.0344238\pi\)
\(158\) 27769.5i 1.11238i
\(159\) −3888.00 1374.62i −0.153791 0.0543735i
\(160\) −3072.00 −0.120000
\(161\) 9707.16i 0.374490i
\(162\) 18144.0 3894.74i 0.691358 0.148405i
\(163\) −42982.0 −1.61775 −0.808875 0.587981i \(-0.799923\pi\)
−0.808875 + 0.587981i \(0.799923\pi\)
\(164\) 19278.6i 0.716782i
\(165\) −6048.00 + 17106.3i −0.222149 + 0.628332i
\(166\) −20112.0 −0.729859
\(167\) 44157.4i 1.58333i −0.610957 0.791663i \(-0.709215\pi\)
0.610957 0.791663i \(-0.290785\pi\)
\(168\) −4992.00 1764.94i −0.176871 0.0625333i
\(169\) −26061.0 −0.912468
\(170\) 9775.04i 0.338237i
\(171\) 22554.0 + 18226.4i 0.771314 + 0.623316i
\(172\) 2096.00 0.0708491
\(173\) 22418.1i 0.749043i 0.927218 + 0.374522i \(0.122193\pi\)
−0.927218 + 0.374522i \(0.877807\pi\)
\(174\) −12240.0 + 34619.9i −0.404281 + 1.14348i
\(175\) 8762.00 0.286106
\(176\) 7602.81i 0.245442i
\(177\) −15408.0 5447.55i −0.491813 0.173882i
\(178\) 22176.0 0.699912
\(179\) 30597.9i 0.954962i −0.878642 0.477481i \(-0.841550\pi\)
0.878642 0.477481i \(-0.158450\pi\)
\(180\) 6912.00 8553.16i 0.213333 0.263987i
\(181\) −13102.0 −0.399927 −0.199963 0.979803i \(-0.564082\pi\)
−0.199963 + 0.979803i \(0.564082\pi\)
\(182\) 3676.96i 0.111006i
\(183\) 4458.00 12609.1i 0.133118 0.376516i
\(184\) 8448.00 0.249527
\(185\) 31802.8i 0.929228i
\(186\) −17808.0 6296.08i −0.514742 0.181989i
\(187\) 24192.0 0.691813
\(188\) 13576.5i 0.384123i
\(189\) 16146.0 9927.78i 0.452003 0.277926i
\(190\) 17184.0 0.476011
\(191\) 70326.0i 1.92774i 0.266367 + 0.963872i \(0.414177\pi\)
−0.266367 + 0.963872i \(0.585823\pi\)
\(192\) 1536.00 4344.46i 0.0416667 0.117851i
\(193\) 18050.0 0.484577 0.242288 0.970204i \(-0.422102\pi\)
0.242288 + 0.970204i \(0.422102\pi\)
\(194\) 1351.99i 0.0359227i
\(195\) 7200.00 + 2545.58i 0.189349 + 0.0669450i
\(196\) 13800.0 0.359225
\(197\) 26321.3i 0.678228i 0.940745 + 0.339114i \(0.110127\pi\)
−0.940745 + 0.339114i \(0.889873\pi\)
\(198\) −21168.0 17106.3i −0.539945 0.436341i
\(199\) −37222.0 −0.939926 −0.469963 0.882686i \(-0.655733\pi\)
−0.469963 + 0.882686i \(0.655733\pi\)
\(200\) 7625.44i 0.190636i
\(201\) 13458.0 38065.0i 0.333111 0.942179i
\(202\) −38832.0 −0.951671
\(203\) 37504.9i 0.910115i
\(204\) −13824.0 4887.52i −0.332180 0.117443i
\(205\) −40896.0 −0.973135
\(206\) 6047.18i 0.142501i
\(207\) −19008.0 + 23521.2i −0.443604 + 0.548932i
\(208\) 3200.00 0.0739645
\(209\) 42528.2i 0.973609i
\(210\) 3744.00 10589.6i 0.0848980 0.240128i
\(211\) 15098.0 0.339121 0.169560 0.985520i \(-0.445765\pi\)
0.169560 + 0.985520i \(0.445765\pi\)
\(212\) 3665.64i 0.0815602i
\(213\) 30240.0 + 10691.5i 0.666534 + 0.235656i
\(214\) 30672.0 0.669753
\(215\) 4446.29i 0.0961879i
\(216\) 8640.00 + 14051.6i 0.185185 + 0.301175i
\(217\) −19292.0 −0.409692
\(218\) 13435.0i 0.282700i
\(219\) −870.000 + 2460.73i −0.0181397 + 0.0513069i
\(220\) −16128.0 −0.333223
\(221\) 10182.3i 0.208479i
\(222\) 44976.0 + 15901.4i 0.912588 + 0.322649i
\(223\) 58778.0 1.18197 0.590983 0.806684i \(-0.298740\pi\)
0.590983 + 0.806684i \(0.298740\pi\)
\(224\) 4706.50i 0.0937999i
\(225\) −21231.0 17157.2i −0.419378 0.338908i
\(226\) 9024.00 0.176678
\(227\) 68001.0i 1.31967i −0.751412 0.659833i \(-0.770627\pi\)
0.751412 0.659833i \(-0.229373\pi\)
\(228\) −8592.00 + 24301.8i −0.165282 + 0.467487i
\(229\) 28562.0 0.544650 0.272325 0.962205i \(-0.412207\pi\)
0.272325 + 0.962205i \(0.412207\pi\)
\(230\) 17920.9i 0.338770i
\(231\) −26208.0 9265.93i −0.491145 0.173646i
\(232\) −32640.0 −0.606421
\(233\) 22503.0i 0.414503i −0.978288 0.207252i \(-0.933548\pi\)
0.978288 0.207252i \(-0.0664519\pi\)
\(234\) −7200.00 + 8909.55i −0.131492 + 0.162714i
\(235\) 28800.0 0.521503
\(236\) 14526.8i 0.260823i
\(237\) −29454.0 + 83308.5i −0.524382 + 1.48318i
\(238\) −14976.0 −0.264388
\(239\) 1289.76i 0.0225795i −0.999936 0.0112897i \(-0.996406\pi\)
0.999936 0.0112897i \(-0.00359371\pi\)
\(240\) 9216.00 + 3258.35i 0.160000 + 0.0565685i
\(241\) −61246.0 −1.05449 −0.527246 0.849712i \(-0.676776\pi\)
−0.527246 + 0.849712i \(0.676776\pi\)
\(242\) 1496.24i 0.0255488i
\(243\) −58563.0 7560.39i −0.991770 0.128036i
\(244\) 11888.0 0.199678
\(245\) 29274.2i 0.487700i
\(246\) 20448.0 57835.7i 0.337894 0.955709i
\(247\) −17900.0 −0.293399
\(248\) 16789.5i 0.272983i
\(249\) 60336.0 + 21332.0i 0.973146 + 0.344059i
\(250\) −46176.0 −0.738816
\(251\) 45260.5i 0.718409i 0.933259 + 0.359205i \(0.116952\pi\)
−0.933259 + 0.359205i \(0.883048\pi\)
\(252\) 13104.0 + 10589.6i 0.206349 + 0.166755i
\(253\) 44352.0 0.692903
\(254\) 23425.0i 0.363089i
\(255\) 10368.0 29325.1i 0.159446 0.450982i
\(256\) 4096.00 0.0625000
\(257\) 85260.1i 1.29086i 0.763819 + 0.645431i \(0.223322\pi\)
−0.763819 + 0.645431i \(0.776678\pi\)
\(258\) −6288.00 2223.14i −0.0944655 0.0333986i
\(259\) 48724.0 0.726346
\(260\) 6788.23i 0.100418i
\(261\) 73440.0 90877.4i 1.07808 1.33406i
\(262\) −15312.0 −0.223064
\(263\) 84751.0i 1.22527i −0.790364 0.612637i \(-0.790109\pi\)
0.790364 0.612637i \(-0.209891\pi\)
\(264\) 8064.00 22808.4i 0.115702 0.327256i
\(265\) 7776.00 0.110730
\(266\) 26327.0i 0.372082i
\(267\) −66528.0 23521.2i −0.933216 0.329942i
\(268\) 35888.0 0.499666
\(269\) 42918.6i 0.593117i 0.955015 + 0.296559i \(0.0958390\pi\)
−0.955015 + 0.296559i \(0.904161\pi\)
\(270\) −29808.0 + 18328.2i −0.408889 + 0.251416i
\(271\) −27430.0 −0.373497 −0.186749 0.982408i \(-0.559795\pi\)
−0.186749 + 0.982408i \(0.559795\pi\)
\(272\) 13033.4i 0.176165i
\(273\) −3900.00 + 11030.9i −0.0523286 + 0.148008i
\(274\) 51168.0 0.681549
\(275\) 40033.6i 0.529369i
\(276\) −25344.0 8960.46i −0.332703 0.117628i
\(277\) −93934.0 −1.22423 −0.612115 0.790768i \(-0.709681\pi\)
−0.612115 + 0.790768i \(0.709681\pi\)
\(278\) 65636.5i 0.849289i
\(279\) 46746.0 + 37776.5i 0.600532 + 0.485303i
\(280\) 9984.00 0.127347
\(281\) 24471.6i 0.309919i −0.987921 0.154960i \(-0.950475\pi\)
0.987921 0.154960i \(-0.0495248\pi\)
\(282\) −14400.0 + 40729.4i −0.181077 + 0.512164i
\(283\) −65830.0 −0.821961 −0.410980 0.911644i \(-0.634813\pi\)
−0.410980 + 0.911644i \(0.634813\pi\)
\(284\) 28510.5i 0.353483i
\(285\) −51552.0 18226.4i −0.634681 0.224394i
\(286\) 16800.0 0.205389
\(287\) 62655.3i 0.760666i
\(288\) −9216.00 + 11404.2i −0.111111 + 0.137493i
\(289\) 42049.0 0.503454
\(290\) 69239.9i 0.823304i
\(291\) 1434.00 4055.96i 0.0169341 0.0478970i
\(292\) −2320.00 −0.0272096
\(293\) 90028.8i 1.04869i −0.851506 0.524344i \(-0.824311\pi\)
0.851506 0.524344i \(-0.175689\pi\)
\(294\) −41400.0 14637.1i −0.478967 0.169340i
\(295\) 30816.0 0.354105
\(296\) 42403.8i 0.483973i
\(297\) 45360.0 + 73771.0i 0.514233 + 0.836321i
\(298\) 31632.0 0.356200
\(299\) 18667.6i 0.208808i
\(300\) 8088.00 22876.3i 0.0898667 0.254181i
\(301\) −6812.00 −0.0751868
\(302\) 40802.9i 0.447380i
\(303\) 116496. + 41187.6i 1.26890 + 0.448622i
\(304\) −22912.0 −0.247922
\(305\) 25218.3i 0.271091i
\(306\) 36288.0 + 29325.1i 0.387543 + 0.313182i
\(307\) 67322.0 0.714299 0.357150 0.934047i \(-0.383749\pi\)
0.357150 + 0.934047i \(0.383749\pi\)
\(308\) 24709.1i 0.260469i
\(309\) −6414.00 + 18141.5i −0.0671757 + 0.190001i
\(310\) 35616.0 0.370614
\(311\) 131997.i 1.36472i 0.731017 + 0.682360i \(0.239046\pi\)
−0.731017 + 0.682360i \(0.760954\pi\)
\(312\) −9600.00 3394.11i −0.0986193 0.0348672i
\(313\) −22078.0 −0.225357 −0.112679 0.993631i \(-0.535943\pi\)
−0.112679 + 0.993631i \(0.535943\pi\)
\(314\) 138621.i 1.40595i
\(315\) −22464.0 + 27797.8i −0.226395 + 0.280149i
\(316\) −78544.0 −0.786573
\(317\) 117894.i 1.17321i −0.809874 0.586604i \(-0.800465\pi\)
0.809874 0.586604i \(-0.199535\pi\)
\(318\) −3888.00 + 10996.9i −0.0384478 + 0.108747i
\(319\) −171360. −1.68395
\(320\) 8688.93i 0.0848528i
\(321\) −92016.0 32532.6i −0.893004 0.315725i
\(322\) −27456.0 −0.264805
\(323\) 72905.5i 0.698804i
\(324\) −11016.0 51319.0i −0.104938 0.488864i
\(325\) 16850.0 0.159527
\(326\) 121571.i 1.14392i
\(327\) 14250.0 40305.1i 0.133266 0.376933i
\(328\) 54528.0 0.506841
\(329\) 44123.5i 0.407641i
\(330\) 48384.0 + 17106.3i 0.444298 + 0.157083i
\(331\) 167642. 1.53012 0.765062 0.643956i \(-0.222708\pi\)
0.765062 + 0.643956i \(0.222708\pi\)
\(332\) 56885.3i 0.516088i
\(333\) −118062. 95408.5i −1.06469 0.860396i
\(334\) −124896. −1.11958
\(335\) 76129.9i 0.678369i
\(336\) −4992.00 + 14119.5i −0.0442177 + 0.125067i
\(337\) 162914. 1.43449 0.717247 0.696819i \(-0.245402\pi\)
0.717247 + 0.696819i \(0.245402\pi\)
\(338\) 73711.6i 0.645212i
\(339\) −27072.0 9571.40i −0.235571 0.0832868i
\(340\) 27648.0 0.239170
\(341\) 88145.1i 0.758035i
\(342\) 51552.0 63792.3i 0.440751 0.545402i
\(343\) −107276. −0.911831
\(344\) 5928.38i 0.0500979i
\(345\) 19008.0 53762.7i 0.159698 0.451693i
\(346\) 63408.0 0.529654
\(347\) 132184.i 1.09779i −0.835892 0.548895i \(-0.815049\pi\)
0.835892 0.548895i \(-0.184951\pi\)
\(348\) 97920.0 + 34619.9i 0.808561 + 0.285870i
\(349\) 53234.0 0.437057 0.218529 0.975831i \(-0.429874\pi\)
0.218529 + 0.975831i \(0.429874\pi\)
\(350\) 24782.7i 0.202308i
\(351\) 31050.0 19091.9i 0.252027 0.154965i
\(352\) 21504.0 0.173554
\(353\) 144861.i 1.16252i 0.813717 + 0.581261i \(0.197440\pi\)
−0.813717 + 0.581261i \(0.802560\pi\)
\(354\) −15408.0 + 43580.4i −0.122953 + 0.347764i
\(355\) −60480.0 −0.479905
\(356\) 62723.2i 0.494912i
\(357\) 44928.0 + 15884.4i 0.352517 + 0.124634i
\(358\) −86544.0 −0.675260
\(359\) 12931.6i 0.100337i −0.998741 0.0501686i \(-0.984024\pi\)
0.998741 0.0501686i \(-0.0159759\pi\)
\(360\) −24192.0 19550.1i −0.186667 0.150849i
\(361\) −2157.00 −0.0165514
\(362\) 37058.1i 0.282791i
\(363\) −1587.00 + 4488.71i −0.0120438 + 0.0340650i
\(364\) −10400.0 −0.0784929
\(365\) 4921.46i 0.0369410i
\(366\) −35664.0 12609.1i −0.266237 0.0941289i
\(367\) −44326.0 −0.329099 −0.164549 0.986369i \(-0.552617\pi\)
−0.164549 + 0.986369i \(0.552617\pi\)
\(368\) 23894.6i 0.176443i
\(369\) −122688. + 151819.i −0.901051 + 1.11499i
\(370\) −89952.0 −0.657064
\(371\) 11913.3i 0.0865537i
\(372\) −17808.0 + 50368.6i −0.128685 + 0.363977i
\(373\) −60718.0 −0.436415 −0.218208 0.975902i \(-0.570021\pi\)
−0.218208 + 0.975902i \(0.570021\pi\)
\(374\) 68425.3i 0.489185i
\(375\) 138528. + 48977.0i 0.985088 + 0.348281i
\(376\) −38400.0 −0.271616
\(377\) 72124.9i 0.507461i
\(378\) −28080.0 45667.8i −0.196523 0.319614i
\(379\) 30458.0 0.212043 0.106021 0.994364i \(-0.466189\pi\)
0.106021 + 0.994364i \(0.466189\pi\)
\(380\) 48603.7i 0.336591i
\(381\) −24846.0 + 70275.1i −0.171162 + 0.484118i
\(382\) 198912. 1.36312
\(383\) 235687.i 1.60671i −0.595498 0.803357i \(-0.703045\pi\)
0.595498 0.803357i \(-0.296955\pi\)
\(384\) −12288.0 4344.46i −0.0833333 0.0294628i
\(385\) 52416.0 0.353625
\(386\) 51053.1i 0.342648i
\(387\) 16506.0 + 13338.9i 0.110210 + 0.0890629i
\(388\) 3824.00 0.0254012
\(389\) 150410.i 0.993980i 0.867756 + 0.496990i \(0.165561\pi\)
−0.867756 + 0.496990i \(0.834439\pi\)
\(390\) 7200.00 20364.7i 0.0473373 0.133890i
\(391\) −76032.0 −0.497328
\(392\) 39032.3i 0.254011i
\(393\) 45936.0 + 16240.8i 0.297419 + 0.105153i
\(394\) 74448.0 0.479579
\(395\) 166617.i 1.06789i
\(396\) −48384.0 + 59872.1i −0.308540 + 0.381799i
\(397\) 172658. 1.09548 0.547742 0.836648i \(-0.315488\pi\)
0.547742 + 0.836648i \(0.315488\pi\)
\(398\) 105280.i 0.664628i
\(399\) 27924.0 78981.0i 0.175401 0.496109i
\(400\) 21568.0 0.134800
\(401\) 167466.i 1.04145i −0.853726 0.520723i \(-0.825662\pi\)
0.853726 0.520723i \(-0.174338\pi\)
\(402\) −107664. 38065.0i −0.666221 0.235545i
\(403\) −37100.0 −0.228436
\(404\) 109833.i 0.672933i
\(405\) 108864. 23368.5i 0.663704 0.142469i
\(406\) 106080. 0.643549
\(407\) 222620.i 1.34393i
\(408\) −13824.0 + 39100.2i −0.0830450 + 0.234887i
\(409\) −150430. −0.899265 −0.449633 0.893214i \(-0.648445\pi\)
−0.449633 + 0.893214i \(0.648445\pi\)
\(410\) 115671.i 0.688110i
\(411\) −153504. 54271.9i −0.908732 0.321285i
\(412\) −17104.0 −0.100764
\(413\) 47212.1i 0.276792i
\(414\) 66528.0 + 53762.7i 0.388154 + 0.313676i
\(415\) −120672. −0.700665
\(416\) 9050.97i 0.0523008i
\(417\) 69618.0 196909.i 0.400359 1.13239i
\(418\) −120288. −0.688446
\(419\) 178276.i 1.01546i 0.861515 + 0.507732i \(0.169516\pi\)
−0.861515 + 0.507732i \(0.830484\pi\)
\(420\) −29952.0 10589.6i −0.169796 0.0600319i
\(421\) −216046. −1.21894 −0.609470 0.792809i \(-0.708618\pi\)
−0.609470 + 0.792809i \(0.708618\pi\)
\(422\) 42703.6i 0.239795i
\(423\) 86400.0 106915.i 0.482873 0.597525i
\(424\) −10368.0 −0.0576718
\(425\) 68629.0i 0.379953i
\(426\) 30240.0 85531.6i 0.166634 0.471311i
\(427\) −38636.0 −0.211903
\(428\) 86753.5i 0.473587i
\(429\) −50400.0 17819.1i −0.273852 0.0968213i
\(430\) 12576.0 0.0680151
\(431\) 5498.46i 0.0295997i 0.999890 + 0.0147998i \(0.00471110\pi\)
−0.999890 + 0.0147998i \(0.995289\pi\)
\(432\) 39744.0 24437.6i 0.212963 0.130946i
\(433\) 108002. 0.576044 0.288022 0.957624i \(-0.407002\pi\)
0.288022 + 0.957624i \(0.407002\pi\)
\(434\) 54566.0i 0.289696i
\(435\) −73440.0 + 207720.i −0.388109 + 1.09774i
\(436\) 38000.0 0.199899
\(437\) 133660.i 0.699905i
\(438\) 6960.00 + 2460.73i 0.0362795 + 0.0128267i
\(439\) 357722. 1.85617 0.928083 0.372374i \(-0.121456\pi\)
0.928083 + 0.372374i \(0.121456\pi\)
\(440\) 45616.9i 0.235624i
\(441\) 108675. + 87822.7i 0.558795 + 0.451575i
\(442\) −28800.0 −0.147417
\(443\) 86261.4i 0.439551i 0.975551 + 0.219775i \(0.0705324\pi\)
−0.975551 + 0.219775i \(0.929468\pi\)
\(444\) 44976.0 127211.i 0.228147 0.645297i
\(445\) 133056. 0.671915
\(446\) 166249.i 0.835776i
\(447\) −94896.0 33550.8i −0.474934 0.167914i
\(448\) −13312.0 −0.0663265
\(449\) 301397.i 1.49502i −0.664251 0.747509i \(-0.731250\pi\)
0.664251 0.747509i \(-0.268750\pi\)
\(450\) −48528.0 + 60050.3i −0.239644 + 0.296545i
\(451\) 286272. 1.40743
\(452\) 25523.7i 0.124930i
\(453\) −43278.0 + 122409.i −0.210897 + 0.596507i
\(454\) −192336. −0.933144
\(455\) 22061.7i 0.106566i
\(456\) 68736.0 + 24301.8i 0.330563 + 0.116872i
\(457\) −399070. −1.91081 −0.955403 0.295305i \(-0.904579\pi\)
−0.955403 + 0.295305i \(0.904579\pi\)
\(458\) 80785.5i 0.385126i
\(459\) −77760.0 126465.i −0.369089 0.600266i
\(460\) 50688.0 0.239546
\(461\) 38268.6i 0.180070i −0.995939 0.0900349i \(-0.971302\pi\)
0.995939 0.0900349i \(-0.0286979\pi\)
\(462\) −26208.0 + 74127.4i −0.122786 + 0.347292i
\(463\) 144410. 0.673652 0.336826 0.941567i \(-0.390647\pi\)
0.336826 + 0.941567i \(0.390647\pi\)
\(464\) 92319.9i 0.428804i
\(465\) −106848. 37776.5i −0.494152 0.174709i
\(466\) −63648.0 −0.293098
\(467\) 148204.i 0.679557i 0.940505 + 0.339779i \(0.110352\pi\)
−0.940505 + 0.339779i \(0.889648\pi\)
\(468\) 25200.0 + 20364.7i 0.115056 + 0.0929792i
\(469\) −116636. −0.530258
\(470\) 81458.7i 0.368758i
\(471\) −147030. + 415864.i −0.662772 + 1.87460i
\(472\) −41088.0 −0.184430
\(473\) 31124.0i 0.139115i
\(474\) 235632. + 83308.5i 1.04876 + 0.370794i
\(475\) −120646. −0.534719
\(476\) 42358.5i 0.186951i
\(477\) 23328.0 28866.9i 0.102528 0.126871i
\(478\) −3648.00 −0.0159661
\(479\) 305606.i 1.33196i −0.745970 0.665979i \(-0.768014\pi\)
0.745970 0.665979i \(-0.231986\pi\)
\(480\) 9216.00 26066.8i 0.0400000 0.113137i
\(481\) 93700.0 0.404995
\(482\) 173230.i 0.745639i
\(483\) 82368.0 + 29121.5i 0.353073 + 0.124830i
\(484\) −4232.00 −0.0180657
\(485\) 8111.93i 0.0344858i
\(486\) −21384.0 + 165641.i −0.0905350 + 0.701287i
\(487\) −196774. −0.829678 −0.414839 0.909895i \(-0.636162\pi\)
−0.414839 + 0.909895i \(0.636162\pi\)
\(488\) 33624.3i 0.141193i
\(489\) 128946. 364714.i 0.539250 1.52523i
\(490\) 82800.0 0.344856
\(491\) 166193.i 0.689365i −0.938719 0.344682i \(-0.887987\pi\)
0.938719 0.344682i \(-0.112013\pi\)
\(492\) −163584. 57835.7i −0.675788 0.238927i
\(493\) 293760. 1.20865
\(494\) 50628.8i 0.207465i
\(495\) −127008. 102638.i −0.518347 0.418888i
\(496\) −47488.0 −0.193028
\(497\) 92659.3i 0.375125i
\(498\) 60336.0 170656.i 0.243286 0.688118i
\(499\) 189050. 0.759234 0.379617 0.925144i \(-0.376056\pi\)
0.379617 + 0.925144i \(0.376056\pi\)
\(500\) 130605.i 0.522422i
\(501\) 374688. + 132472.i 1.49277 + 0.527776i
\(502\) 128016. 0.507992
\(503\) 344061.i 1.35988i 0.733269 + 0.679939i \(0.237994\pi\)
−0.733269 + 0.679939i \(0.762006\pi\)
\(504\) 29952.0 37063.7i 0.117914 0.145911i
\(505\) −232992. −0.913605
\(506\) 125446.i 0.489956i
\(507\) 78183.0 221135.i 0.304156 0.860283i
\(508\) −66256.0 −0.256743
\(509\) 353208.i 1.36331i 0.731673 + 0.681656i \(0.238740\pi\)
−0.731673 + 0.681656i \(0.761260\pi\)
\(510\) −82944.0 29325.1i −0.318893 0.112746i
\(511\) 7540.00 0.0288755
\(512\) 11585.2i 0.0441942i
\(513\) −222318. + 136698.i −0.844773 + 0.519430i
\(514\) 241152. 0.912777
\(515\) 36283.1i 0.136801i
\(516\) −6288.00 + 17785.1i −0.0236164 + 0.0667972i
\(517\) −201600. −0.754240
\(518\) 137812.i 0.513604i
\(519\) −190224. 67254.3i −0.706205 0.249681i
\(520\) 19200.0 0.0710059
\(521\) 276043.i 1.01695i 0.861075 + 0.508477i \(0.169791\pi\)
−0.861075 + 0.508477i \(0.830209\pi\)
\(522\) −257040. 207720.i −0.943321 0.762319i
\(523\) −146950. −0.537237 −0.268619 0.963247i \(-0.586567\pi\)
−0.268619 + 0.963247i \(0.586567\pi\)
\(524\) 43308.9i 0.157730i
\(525\) −26286.0 + 74348.0i −0.0953687 + 0.269743i
\(526\) −239712. −0.866400
\(527\) 151106.i 0.544077i
\(528\) −64512.0 22808.4i −0.231405 0.0818140i
\(529\) 140449. 0.501889
\(530\) 21993.8i 0.0782978i
\(531\) 92448.0 114399.i 0.327875 0.405725i
\(532\) 74464.0 0.263101
\(533\) 120491.i 0.424131i
\(534\) −66528.0 + 188170.i −0.233304 + 0.659883i
\(535\) 184032. 0.642963
\(536\) 101507.i 0.353317i
\(537\) 259632. + 91793.8i 0.900346 + 0.318321i
\(538\) 121392. 0.419397
\(539\) 204920.i 0.705352i
\(540\) 51840.0 + 84309.8i 0.177778 + 0.289128i
\(541\) −244942. −0.836891 −0.418445 0.908242i \(-0.637425\pi\)
−0.418445 + 0.908242i \(0.637425\pi\)
\(542\) 77583.8i 0.264102i
\(543\) 39306.0 111174.i 0.133309 0.377055i
\(544\) −36864.0 −0.124567
\(545\) 80610.2i 0.271392i
\(546\) 31200.0 + 11030.9i 0.104657 + 0.0370019i
\(547\) −283366. −0.947050 −0.473525 0.880780i \(-0.657019\pi\)
−0.473525 + 0.880780i \(0.657019\pi\)
\(548\) 144725.i 0.481928i
\(549\) 93618.0 + 75654.8i 0.310609 + 0.251010i
\(550\) 113232. 0.374321
\(551\) 516414.i 1.70096i
\(552\) −25344.0 + 71683.7i −0.0831758 + 0.235257i
\(553\) 255268. 0.834730
\(554\) 265685.i 0.865662i
\(555\) 269856. + 95408.5i 0.876085 + 0.309743i
\(556\) 185648. 0.600538
\(557\) 47093.3i 0.151792i −0.997116 0.0758960i \(-0.975818\pi\)
0.997116 0.0758960i \(-0.0241817\pi\)
\(558\) 106848. 132218.i 0.343161 0.424640i
\(559\) −13100.0 −0.0419225
\(560\) 28239.0i 0.0900479i
\(561\) −72576.0 + 205276.i −0.230604 + 0.652247i
\(562\) −69216.0 −0.219146
\(563\) 84.8528i 0.000267701i 1.00000 0.000133850i \(4.26059e-5\pi\)
−1.00000 0.000133850i \(0.999957\pi\)
\(564\) 115200. + 40729.4i 0.362155 + 0.128041i
\(565\) 54144.0 0.169611
\(566\) 186195.i 0.581214i
\(567\) 35802.0 + 166787.i 0.111363 + 0.518794i
\(568\) 80640.0 0.249950
\(569\) 239115.i 0.738555i −0.929319 0.369277i \(-0.879605\pi\)
0.929319 0.369277i \(-0.120395\pi\)
\(570\) −51552.0 + 145811.i −0.158670 + 0.448788i
\(571\) −140710. −0.431571 −0.215786 0.976441i \(-0.569231\pi\)
−0.215786 + 0.976441i \(0.569231\pi\)
\(572\) 47517.6i 0.145232i
\(573\) −596736. 210978.i −1.81749 0.642581i
\(574\) −177216. −0.537872
\(575\) 125820.i 0.380551i
\(576\) 32256.0 + 26066.8i 0.0972222 + 0.0785674i
\(577\) 36002.0 0.108137 0.0540686 0.998537i \(-0.482781\pi\)
0.0540686 + 0.998537i \(0.482781\pi\)
\(578\) 118933.i 0.355996i
\(579\) −54150.0 + 153159.i −0.161526 + 0.456863i
\(580\) −195840. −0.582164
\(581\) 184877.i 0.547686i
\(582\) −11472.0 4055.96i −0.0338683 0.0119742i
\(583\) −54432.0 −0.160146
\(584\) 6561.95i 0.0192401i
\(585\) −43200.0 + 53457.3i −0.126233 + 0.156205i
\(586\) −254640. −0.741535
\(587\) 316179.i 0.917606i 0.888538 + 0.458803i \(0.151722\pi\)
−0.888538 + 0.458803i \(0.848278\pi\)
\(588\) −41400.0 + 117097.i −0.119742 + 0.338681i
\(589\) 265636. 0.765696
\(590\) 87160.8i 0.250390i
\(591\) −223344. 78964.0i −0.639439 0.226076i
\(592\) 119936. 0.342221
\(593\) 262093.i 0.745327i 0.927967 + 0.372663i \(0.121555\pi\)
−0.927967 + 0.372663i \(0.878445\pi\)
\(594\) 208656. 128297.i 0.591368 0.363618i
\(595\) −89856.0 −0.253813
\(596\) 89468.8i 0.251872i
\(597\) 111666. 315839.i 0.313309 0.886171i
\(598\) −52800.0 −0.147649
\(599\) 606494.i 1.69034i 0.534501 + 0.845168i \(0.320499\pi\)
−0.534501 + 0.845168i \(0.679501\pi\)
\(600\) −64704.0 22876.3i −0.179733 0.0635453i
\(601\) 306530. 0.848641 0.424321 0.905512i \(-0.360513\pi\)
0.424321 + 0.905512i \(0.360513\pi\)
\(602\) 19267.2i 0.0531651i
\(603\) 282618. + 228390.i 0.777258 + 0.628119i
\(604\) −115408. −0.316346
\(605\) 8977.43i 0.0245268i
\(606\) 116496. 329500.i 0.317224 0.897244i
\(607\) 563162. 1.52847 0.764233 0.644940i \(-0.223118\pi\)
0.764233 + 0.644940i \(0.223118\pi\)
\(608\) 64804.9i 0.175308i
\(609\) −318240. 112515.i −0.858065 0.303372i
\(610\) 71328.0 0.191690
\(611\) 84852.8i 0.227292i
\(612\) 82944.0 102638.i 0.221453 0.274034i
\(613\) 111314. 0.296230 0.148115 0.988970i \(-0.452679\pi\)
0.148115 + 0.988970i \(0.452679\pi\)
\(614\) 190415.i 0.505086i
\(615\) 122688. 347014.i 0.324378 0.917481i
\(616\) −69888.0 −0.184179
\(617\) 121340.i 0.318737i −0.987219 0.159368i \(-0.949054\pi\)
0.987219 0.159368i \(-0.0509457\pi\)
\(618\) 51312.0 + 18141.5i 0.134351 + 0.0475004i
\(619\) −581158. −1.51675 −0.758373 0.651821i \(-0.774005\pi\)
−0.758373 + 0.651821i \(0.774005\pi\)
\(620\) 100737.i 0.262064i
\(621\) −142560. 231852.i −0.369670 0.601212i
\(622\) 373344. 0.965002
\(623\) 203850.i 0.525213i
\(624\) −9600.00 + 27152.9i −0.0246548 + 0.0697344i
\(625\) −66431.0 −0.170063
\(626\) 62446.0i 0.159351i
\(627\) 360864. + 127585.i 0.917928 + 0.324536i
\(628\) −392080. −0.994158
\(629\) 381634.i 0.964597i
\(630\) 78624.0 + 63537.8i 0.198095 + 0.160085i
\(631\) 232346. 0.583548 0.291774 0.956487i \(-0.405755\pi\)
0.291774 + 0.956487i \(0.405755\pi\)
\(632\) 222156.i 0.556191i
\(633\) −45294.0 + 128111.i −0.113040 + 0.319726i
\(634\) −333456. −0.829583
\(635\) 140550.i 0.348565i
\(636\) 31104.0 + 10996.9i 0.0768957 + 0.0271867i
\(637\) −86250.0 −0.212559
\(638\) 484679.i 1.19073i
\(639\) −181440. + 224521.i −0.444356 + 0.549863i
\(640\) 24576.0 0.0600000
\(641\) 653570.i 1.59066i 0.606179 + 0.795328i \(0.292701\pi\)
−0.606179 + 0.795328i \(0.707299\pi\)
\(642\) −92016.0 + 260261.i −0.223251 + 0.631449i
\(643\) −424678. −1.02716 −0.513580 0.858042i \(-0.671681\pi\)
−0.513580 + 0.858042i \(0.671681\pi\)
\(644\) 77657.3i 0.187245i
\(645\) −37728.0 13338.9i −0.0906869 0.0320626i
\(646\) 206208. 0.494129
\(647\) 427964.i 1.02235i −0.859478 0.511173i \(-0.829211\pi\)
0.859478 0.511173i \(-0.170789\pi\)
\(648\) −145152. + 31158.0i −0.345679 + 0.0742026i
\(649\) −215712. −0.512136
\(650\) 47659.0i 0.112802i
\(651\) 57876.0 163698.i 0.136564 0.386262i
\(652\) 343856. 0.808875
\(653\) 720621.i 1.68998i −0.534785 0.844988i \(-0.679607\pi\)
0.534785 0.844988i \(-0.320393\pi\)
\(654\) −114000. 40305.1i −0.266532 0.0942333i
\(655\) −91872.0 −0.214141
\(656\) 154228.i 0.358391i
\(657\) −18270.0 14764.4i −0.0423261 0.0342046i
\(658\) 124800. 0.288246
\(659\) 40135.4i 0.0924180i 0.998932 + 0.0462090i \(0.0147140\pi\)
−0.998932 + 0.0462090i \(0.985286\pi\)
\(660\) 48384.0 136851.i 0.111074 0.314166i
\(661\) −358510. −0.820537 −0.410269 0.911965i \(-0.634565\pi\)
−0.410269 + 0.911965i \(0.634565\pi\)
\(662\) 474163.i 1.08196i
\(663\) 86400.0 + 30547.0i 0.196556 + 0.0694931i
\(664\) 160896. 0.364930
\(665\) 157962.i 0.357198i
\(666\) −269856. + 333930.i −0.608392 + 0.752847i
\(667\) 538560. 1.21055
\(668\) 353259.i 0.791663i
\(669\) −176334. + 498748.i −0.393989 + 1.11437i
\(670\) 215328. 0.479679
\(671\) 176528.i 0.392074i
\(672\) 39936.0 + 14119.5i 0.0884354 + 0.0312666i
\(673\) 582434. 1.28593 0.642964 0.765896i \(-0.277705\pi\)
0.642964 + 0.765896i \(0.277705\pi\)
\(674\) 460790.i 1.01434i
\(675\) 209277. 128679.i 0.459319 0.282424i
\(676\) 208488. 0.456234
\(677\) 37352.2i 0.0814965i −0.999169 0.0407482i \(-0.987026\pi\)
0.999169 0.0407482i \(-0.0129742\pi\)
\(678\) −27072.0 + 76571.2i −0.0588926 + 0.166574i
\(679\) −12428.0 −0.0269564
\(680\) 78200.4i 0.169118i
\(681\) 577008. + 204003.i 1.24419 + 0.439889i
\(682\) −249312. −0.536012
\(683\) 161848.i 0.346950i −0.984838 0.173475i \(-0.944500\pi\)
0.984838 0.173475i \(-0.0554995\pi\)
\(684\) −180432. 145811.i −0.385657 0.311658i
\(685\) 307008. 0.654287
\(686\) 303422.i 0.644762i
\(687\) −85686.0 + 242357.i −0.181550 + 0.513501i
\(688\) −16768.0 −0.0354246
\(689\) 22910.3i 0.0482605i
\(690\) −152064. 53762.7i −0.319395 0.112923i
\(691\) −630118. −1.31967 −0.659836 0.751410i \(-0.729374\pi\)
−0.659836 + 0.751410i \(0.729374\pi\)
\(692\) 179345.i 0.374522i
\(693\) 157248. 194584.i 0.327430 0.405174i
\(694\) −373872. −0.776254
\(695\) 393819.i 0.815318i
\(696\) 97920.0 276960.i 0.202140 0.571739i
\(697\) −490752. −1.01017
\(698\) 150568.i 0.309046i
\(699\) 190944. + 67508.9i 0.390797 + 0.138168i
\(700\) −70096.0 −0.143053
\(701\) 457747.i 0.931514i 0.884913 + 0.465757i \(0.154218\pi\)
−0.884913 + 0.465757i \(0.845782\pi\)
\(702\) −54000.0 87822.7i −0.109577 0.178210i
\(703\) −670892. −1.35751
\(704\) 60822.5i 0.122721i
\(705\) −86400.0 + 244376.i −0.173834 + 0.491678i
\(706\) 409728. 0.822027
\(707\) 356959.i 0.714133i
\(708\) 123264. + 43580.4i 0.245906 + 0.0869410i
\(709\) 274130. 0.545336 0.272668 0.962108i \(-0.412094\pi\)
0.272668 + 0.962108i \(0.412094\pi\)
\(710\) 171063.i 0.339344i
\(711\) −618534. 499851.i −1.22356 0.988784i
\(712\) −177408. −0.349956
\(713\) 277027.i 0.544934i
\(714\) 44928.0 127076.i 0.0881294 0.249267i
\(715\) 100800. 0.197173
\(716\) 244783.i 0.477481i
\(717\) 10944.0 + 3869.29i 0.0212881 + 0.00752650i
\(718\) −36576.0 −0.0709492
\(719\) 304045.i 0.588138i 0.955784 + 0.294069i \(0.0950096\pi\)
−0.955784 + 0.294069i \(0.904990\pi\)
\(720\) −55296.0 + 68425.3i −0.106667 + 0.131993i
\(721\) 55588.0 0.106933
\(722\) 6100.92i 0.0117036i
\(723\) 183738. 519690.i 0.351498 0.994185i
\(724\) 104816. 0.199963
\(725\) 486122.i 0.924845i
\(726\) 12696.0 + 4488.71i 0.0240876 + 0.00851626i
\(727\) 364058. 0.688814 0.344407 0.938821i \(-0.388080\pi\)
0.344407 + 0.938821i \(0.388080\pi\)
\(728\) 29415.6i 0.0555029i
\(729\) 239841. 474242.i 0.451303 0.892371i
\(730\) −13920.0 −0.0261212
\(731\) 53355.4i 0.0998491i
\(732\) −35664.0 + 100873.i −0.0665592 + 0.188258i
\(733\) −301198. −0.560588 −0.280294 0.959914i \(-0.590432\pi\)
−0.280294 + 0.959914i \(0.590432\pi\)
\(734\) 125373.i 0.232708i
\(735\) −248400. 87822.7i −0.459808 0.162567i
\(736\) −67584.0 −0.124764
\(737\) 532910.i 0.981112i
\(738\) 429408. + 347014.i 0.788420 + 0.637139i
\(739\) 872570. 1.59776 0.798880 0.601491i \(-0.205426\pi\)
0.798880 + 0.601491i \(0.205426\pi\)
\(740\) 254423.i 0.464614i
\(741\) 53700.0 151887.i 0.0977998 0.276620i
\(742\) 33696.0 0.0612027
\(743\) 874222.i 1.58359i −0.610784 0.791797i \(-0.709146\pi\)
0.610784 0.791797i \(-0.290854\pi\)
\(744\) 142464. + 50368.6i 0.257371 + 0.0909943i
\(745\) 189792. 0.341952
\(746\) 171736.i 0.308592i
\(747\) −362016. + 447972.i −0.648764 + 0.802804i
\(748\) −193536. −0.345906
\(749\) 281949.i 0.502582i
\(750\) 138528. 391816.i 0.246272 0.696562i
\(751\) 916250. 1.62455 0.812277 0.583272i \(-0.198228\pi\)
0.812277 + 0.583272i \(0.198228\pi\)
\(752\) 108612.i 0.192062i
\(753\) −384048. 135781.i −0.677323 0.239470i
\(754\) 204000. 0.358829
\(755\) 244817.i 0.429485i
\(756\) −129168. + 79422.2i −0.226002 + 0.138963i
\(757\) −691630. −1.20693 −0.603465 0.797390i \(-0.706214\pi\)
−0.603465 + 0.797390i \(0.706214\pi\)
\(758\) 86148.2i 0.149937i
\(759\) −133056. + 376339.i −0.230968 + 0.653275i
\(760\) −137472. −0.238006
\(761\) 90249.5i 0.155839i 0.996960 + 0.0779193i \(0.0248277\pi\)
−0.996960 + 0.0779193i \(0.975172\pi\)
\(762\) 198768. + 70275.1i 0.342323 + 0.121030i
\(763\) −123500. −0.212138
\(764\) 562608.i 0.963872i
\(765\) 217728. + 175951.i 0.372042 + 0.300655i
\(766\) −666624. −1.13612
\(767\) 90792.5i 0.154333i
\(768\) −12288.0 + 34755.7i −0.0208333 + 0.0589256i
\(769\) −515326. −0.871424 −0.435712 0.900086i \(-0.643503\pi\)
−0.435712 + 0.900086i \(0.643503\pi\)
\(770\) 148255.i 0.250050i
\(771\) −723456. 255780.i −1.21704 0.430287i
\(772\) −144400. −0.242288
\(773\) 100449.i 0.168107i 0.996461 + 0.0840535i \(0.0267867\pi\)
−0.996461 + 0.0840535i \(0.973213\pi\)
\(774\) 37728.0 46686.0i 0.0629770 0.0779300i
\(775\) −250054. −0.416323
\(776\) 10815.9i 0.0179614i
\(777\) −146172. + 413437.i −0.242115 + 0.684805i
\(778\) 425424. 0.702850
\(779\) 862716.i 1.42165i
\(780\) −57600.0 20364.7i −0.0946746 0.0334725i
\(781\) 423360. 0.694077
\(782\) 215051.i 0.351664i
\(783\) 550800. + 895791.i 0.898401 + 1.46111i
\(784\) −110400. −0.179613
\(785\) 831727.i 1.34971i
\(786\) 45936.0 129927.i 0.0743546 0.210307i
\(787\) −107878. −0.174174 −0.0870870 0.996201i \(-0.527756\pi\)
−0.0870870 + 0.996201i \(0.527756\pi\)
\(788\) 210571.i 0.339114i
\(789\) 719136. + 254253.i 1.15520 + 0.408425i
\(790\) −471264. −0.755110
\(791\) 82952.1i 0.132579i
\(792\) 169344. + 136851.i 0.269972 + 0.218171i
\(793\) −74300.0 −0.118152
\(794\) 488351.i 0.774624i
\(795\) −23328.0 + 65981.5i −0.0369099 + 0.104397i
\(796\) 297776. 0.469963
\(797\) 489482.i 0.770584i −0.922795 0.385292i \(-0.874101\pi\)
0.922795 0.385292i \(-0.125899\pi\)
\(798\) −223392. 78981.0i −0.350802 0.124027i
\(799\) 345600. 0.541353
\(800\) 61003.5i 0.0953180i
\(801\) 399168. 493945.i 0.622144 0.769864i
\(802\) −473664. −0.736413
\(803\) 34450.2i 0.0534270i
\(804\) −107664. + 304520.i −0.166555 + 0.471089i
\(805\) −164736. −0.254212
\(806\) 104935.i 0.161528i
\(807\) −364176. 128756.i −0.559196 0.197706i
\(808\) 310656. 0.475836
\(809\) 1.04074e6i 1.59017i −0.606497 0.795086i \(-0.707426\pi\)
0.606497 0.795086i \(-0.292574\pi\)
\(810\) −66096.0 307914.i −0.100741 0.469309i
\(811\) 611066. 0.929066 0.464533 0.885556i \(-0.346222\pi\)
0.464533 + 0.885556i \(0.346222\pi\)
\(812\) 300040.i 0.455058i
\(813\) 82290.0 232751.i 0.124499 0.352136i
\(814\) 629664. 0.950299
\(815\) 729429.i 1.09817i
\(816\) 110592. + 39100.2i 0.166090 + 0.0587217i
\(817\) 93796.0 0.140521
\(818\) 425480.i 0.635877i
\(819\) −81900.0 66185.2i −0.122100 0.0986718i
\(820\) 327168. 0.486568
\(821\) 345300.i 0.512283i 0.966639 + 0.256142i \(0.0824514\pi\)
−0.966639 + 0.256142i \(0.917549\pi\)
\(822\) −153504. + 434175.i −0.227183 + 0.642571i
\(823\) −178150. −0.263018 −0.131509 0.991315i \(-0.541982\pi\)
−0.131509 + 0.991315i \(0.541982\pi\)
\(824\) 48377.4i 0.0712506i
\(825\) −339696. 120101.i −0.499094 0.176456i
\(826\) 133536. 0.195721
\(827\) 1.13844e6i 1.66455i 0.554361 + 0.832277i \(0.312963\pi\)
−0.554361 + 0.832277i \(0.687037\pi\)
\(828\) 152064. 188170.i 0.221802 0.274466i
\(829\) 100082. 0.145629 0.0728143 0.997346i \(-0.476802\pi\)
0.0728143 + 0.997346i \(0.476802\pi\)
\(830\) 341312.i 0.495445i
\(831\) 281802. 797056.i 0.408077 1.15422i
\(832\) −25600.0 −0.0369822
\(833\) 351291.i 0.506263i
\(834\) −556944. 196909.i −0.800718 0.283096i
\(835\) −749376. −1.07480
\(836\) 340226.i 0.486805i
\(837\) −460782. + 283324.i −0.657725 + 0.404419i
\(838\) 504240. 0.718041
\(839\) 1.13964e6i 1.61899i −0.587127 0.809495i \(-0.699741\pi\)
0.587127 0.809495i \(-0.300259\pi\)
\(840\) −29952.0 + 84717.0i −0.0424490 + 0.120064i
\(841\) −1.37352e6 −1.94197
\(842\) 611070.i 0.861920i
\(843\) 207648. + 73414.7i 0.292195 + 0.103306i
\(844\) −120784. −0.169560
\(845\) 442270.i 0.619404i
\(846\) −302400. 244376.i −0.422514 0.341443i
\(847\) 13754.0 0.0191718
\(848\) 29325.1i 0.0407801i
\(849\) 197490. 558586.i 0.273987 0.774952i
\(850\) −194112. −0.268667
\(851\) 699662.i 0.966116i
\(852\) −241920. 85531.6i −0.333267 0.117828i
\(853\) 172754. 0.237427 0.118713 0.992929i \(-0.462123\pi\)
0.118713 + 0.992929i \(0.462123\pi\)
\(854\) 109279.i 0.149838i
\(855\) 309312. 382754.i 0.423121 0.523585i
\(856\) −245376. −0.334876
\(857\) 299802.i 0.408200i −0.978950 0.204100i \(-0.934573\pi\)
0.978950 0.204100i \(-0.0654267\pi\)
\(858\) −50400.0 + 142553.i −0.0684630 + 0.193643i
\(859\) 8186.00 0.0110939 0.00554696 0.999985i \(-0.498234\pi\)
0.00554696 + 0.999985i \(0.498234\pi\)
\(860\) 35570.3i 0.0480940i
\(861\) 531648. + 187966.i 0.717163 + 0.253555i
\(862\) 15552.0 0.0209301
\(863\) 387336.i 0.520076i 0.965598 + 0.260038i \(0.0837350\pi\)
−0.965598 + 0.260038i \(0.916265\pi\)
\(864\) −69120.0 112413.i −0.0925926 0.150588i
\(865\) 380448. 0.508467
\(866\) 305476.i 0.407325i
\(867\) −126147. + 356798.i −0.167818 + 0.474661i
\(868\) 154336. 0.204846
\(869\) 1.16632e6i 1.54446i
\(870\) 587520. + 207720.i 0.776219 + 0.274435i
\(871\) −224300. −0.295660
\(872\) 107480.i 0.141350i
\(873\) 30114.0 + 24335.8i 0.0395130 + 0.0319313i
\(874\) 378048. 0.494908
\(875\) 424468.i 0.554407i
\(876\) 6960.00 19685.9i 0.00906987 0.0256535i
\(877\) 245426. 0.319096 0.159548 0.987190i \(-0.448996\pi\)
0.159548 + 0.987190i \(0.448996\pi\)
\(878\) 1.01179e6i 1.31251i
\(879\) 763920. + 270087.i 0.988713 + 0.349563i
\(880\) 129024. 0.166612
\(881\) 607071.i 0.782146i 0.920360 + 0.391073i \(0.127896\pi\)
−0.920360 + 0.391073i \(0.872104\pi\)
\(882\) 248400. 307379.i 0.319311 0.395128i
\(883\) 759962. 0.974699 0.487349 0.873207i \(-0.337964\pi\)
0.487349 + 0.873207i \(0.337964\pi\)
\(884\) 81458.7i 0.104240i
\(885\) −92448.0 + 261482.i −0.118035 + 0.333854i
\(886\) 243984. 0.310809
\(887\) 5736.05i 0.00729064i 0.999993 + 0.00364532i \(0.00116034\pi\)
−0.999993 + 0.00364532i \(0.998840\pi\)
\(888\) −359808. 127211.i −0.456294 0.161324i
\(889\) 215332. 0.272461
\(890\) 376339.i 0.475116i
\(891\) −762048. + 163579.i −0.959902 + 0.206050i
\(892\) −470224. −0.590983
\(893\) 607546.i 0.761862i
\(894\) −94896.0 + 268406.i −0.118733 + 0.335829i
\(895\) −519264. −0.648249
\(896\) 37652.0i 0.0468999i
\(897\) 158400. + 56002.9i 0.196866 + 0.0696026i
\(898\) −852480. −1.05714
\(899\) 1.07033e6i 1.32434i
\(900\) 169848. + 137258.i 0.209689 + 0.169454i
\(901\) 93312.0 0.114944
\(902\) 809699.i 0.995201i
\(903\) 20436.0 57801.7i 0.0250623 0.0708868i
\(904\) −72192.0 −0.0883389
\(905\) 222348.i 0.271479i
\(906\) 346224. + 122409.i 0.421794 + 0.149127i
\(907\) −138502. −0.168361 −0.0841805 0.996451i \(-0.526827\pi\)
−0.0841805 + 0.996451i \(0.526827\pi\)
\(908\) 544008.i 0.659833i
\(909\) −698976. + 864939.i −0.845930 + 1.04679i
\(910\) −62400.0 −0.0753532
\(911\) 266845.i 0.321531i 0.986993 + 0.160765i \(0.0513962\pi\)
−0.986993 + 0.160765i \(0.948604\pi\)
\(912\) 68736.0 194415.i 0.0826408 0.233744i
\(913\) 844704. 1.01336
\(914\) 1.12874e6i 1.35114i
\(915\) −213984. 75654.8i −0.255587 0.0903637i
\(916\) −228496. −0.272325
\(917\) 140754.i 0.167387i
\(918\) −357696. + 219938.i −0.424452 + 0.260985i
\(919\) −1.44266e6 −1.70818 −0.854090 0.520125i \(-0.825885\pi\)
−0.854090 + 0.520125i \(0.825885\pi\)
\(920\) 143367.i 0.169385i
\(921\) −201966. + 571246.i −0.238100 + 0.673448i
\(922\) −108240. −0.127329
\(923\) 178191.i 0.209162i
\(924\) 209664. + 74127.4i 0.245573 + 0.0868230i
\(925\) 631538. 0.738101
\(926\) 408453.i 0.476344i
\(927\) −134694. 108849.i −0.156743 0.126668i
\(928\) 261120. 0.303210
\(929\) 511696.i 0.592899i −0.955048 0.296450i \(-0.904197\pi\)
0.955048 0.296450i \(-0.0958027\pi\)
\(930\) −106848. + 302212.i −0.123538 + 0.349418i
\(931\) 617550. 0.712480
\(932\) 180024.i 0.207252i
\(933\) −1.12003e6 395991.i −1.28667 0.454907i
\(934\) 419184. 0.480519
\(935\) 410552.i 0.469618i
\(936\) 57600.0 71276.4i 0.0657462 0.0813568i
\(937\) 868610. 0.989340 0.494670 0.869081i \(-0.335289\pi\)
0.494670 + 0.869081i \(0.335289\pi\)
\(938\) 329896.i 0.374949i
\(939\) 66234.0 187338.i 0.0751190 0.212469i
\(940\) −230400. −0.260751
\(941\) 101942.i 0.115126i −0.998342 0.0575632i \(-0.981667\pi\)
0.998342 0.0575632i \(-0.0183331\pi\)
\(942\) 1.17624e6 + 415864.i 1.32554 + 0.468651i
\(943\) −899712. −1.01177
\(944\) 116214.i 0.130412i
\(945\) −168480. 274007.i −0.188662 0.306830i
\(946\) −88032.0 −0.0983690
\(947\) 233159.i 0.259987i −0.991515 0.129993i \(-0.958504\pi\)
0.991515 0.129993i \(-0.0414956\pi\)
\(948\) 235632. 666468.i 0.262191 0.741588i
\(949\) 14500.0 0.0161004
\(950\) 341238.i 0.378104i
\(951\) 1.00037e6 + 353683.i 1.10611 + 0.391069i
\(952\) 119808. 0.132194
\(953\) 927916.i 1.02170i 0.859670 + 0.510850i \(0.170669\pi\)
−0.859670 + 0.510850i \(0.829331\pi\)
\(954\) −81648.0 65981.5i −0.0897116 0.0724980i
\(955\) 1.19347e6 1.30860
\(956\) 10318.1i 0.0112897i
\(957\) 514080. 1.45404e6i 0.561315 1.58764i
\(958\) −864384. −0.941837
\(959\) 470356.i 0.511434i
\(960\) −73728.0 26066.8i −0.0800000 0.0282843i
\(961\) −372957. −0.403842
\(962\) 265024.i 0.286375i
\(963\) 552096. 683184.i 0.595336 0.736691i
\(964\) 489968. 0.527246
\(965\) 306319.i 0.328942i
\(966\) 82368.0 232972.i 0.0882682 0.249660i
\(967\) 150746. 0.161210 0.0806052 0.996746i \(-0.474315\pi\)
0.0806052 + 0.996746i \(0.474315\pi\)
\(968\) 11969.9i 0.0127744i
\(969\) −618624. 218717.i −0.658839 0.232935i
\(970\) 22944.0 0.0243852
\(971\) 508150.i 0.538956i 0.963007 + 0.269478i \(0.0868511\pi\)
−0.963007 + 0.269478i \(0.913149\pi\)
\(972\) 468504. + 60483.1i 0.495885 + 0.0640179i
\(973\) −603356. −0.637306
\(974\) 556561.i 0.586671i
\(975\) −50550.0 + 142977.i −0.0531755 + 0.150403i
\(976\) −95104.0 −0.0998388
\(977\) 214576.i 0.224798i 0.993663 + 0.112399i \(0.0358534\pi\)
−0.993663 + 0.112399i \(0.964147\pi\)
\(978\) −1.03157e6 364714.i −1.07850 0.381307i
\(979\) −931392. −0.971778
\(980\) 234194.i 0.243850i
\(981\) 299250. + 241831.i 0.310954 + 0.251289i
\(982\) −470064. −0.487454
\(983\) 1.34831e6i 1.39535i 0.716414 + 0.697675i \(0.245782\pi\)
−0.716414 + 0.697675i \(0.754218\pi\)
\(984\) −163584. + 462685.i −0.168947 + 0.477854i
\(985\) 446688. 0.460396
\(986\) 830879.i 0.854641i
\(987\) −374400. 132370.i −0.384328 0.135880i
\(988\) 143200. 0.146700
\(989\) 97818.3i 0.100006i
\(990\) −290304. + 359233.i −0.296198 + 0.366527i
\(991\) −879910. −0.895965 −0.447982 0.894042i \(-0.647857\pi\)
−0.447982 + 0.894042i \(0.647857\pi\)
\(992\) 134316.i 0.136491i
\(993\) −502926. + 1.42249e6i −0.510042 + 1.44262i
\(994\) −262080. −0.265253
\(995\) 631678.i 0.638043i
\(996\) −482688. 170656.i −0.486573 0.172029i
\(997\) 935378. 0.941016 0.470508 0.882396i \(-0.344071\pi\)
0.470508 + 0.882396i \(0.344071\pi\)
\(998\) 534714.i 0.536859i
\(999\) 1.16375e6 715564.i 1.16609 0.716997i
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 6.5.b.a.5.1 2
3.2 odd 2 inner 6.5.b.a.5.2 yes 2
4.3 odd 2 48.5.e.b.17.1 2
5.2 odd 4 150.5.b.a.149.4 4
5.3 odd 4 150.5.b.a.149.1 4
5.4 even 2 150.5.d.a.101.2 2
7.6 odd 2 294.5.b.a.197.1 2
8.3 odd 2 192.5.e.c.65.2 2
8.5 even 2 192.5.e.d.65.1 2
9.2 odd 6 162.5.d.a.53.2 4
9.4 even 3 162.5.d.a.107.2 4
9.5 odd 6 162.5.d.a.107.1 4
9.7 even 3 162.5.d.a.53.1 4
12.11 even 2 48.5.e.b.17.2 2
15.2 even 4 150.5.b.a.149.2 4
15.8 even 4 150.5.b.a.149.3 4
15.14 odd 2 150.5.d.a.101.1 2
21.20 even 2 294.5.b.a.197.2 2
24.5 odd 2 192.5.e.d.65.2 2
24.11 even 2 192.5.e.c.65.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6.5.b.a.5.1 2 1.1 even 1 trivial
6.5.b.a.5.2 yes 2 3.2 odd 2 inner
48.5.e.b.17.1 2 4.3 odd 2
48.5.e.b.17.2 2 12.11 even 2
150.5.b.a.149.1 4 5.3 odd 4
150.5.b.a.149.2 4 15.2 even 4
150.5.b.a.149.3 4 15.8 even 4
150.5.b.a.149.4 4 5.2 odd 4
150.5.d.a.101.1 2 15.14 odd 2
150.5.d.a.101.2 2 5.4 even 2
162.5.d.a.53.1 4 9.7 even 3
162.5.d.a.53.2 4 9.2 odd 6
162.5.d.a.107.1 4 9.5 odd 6
162.5.d.a.107.2 4 9.4 even 3
192.5.e.c.65.1 2 24.11 even 2
192.5.e.c.65.2 2 8.3 odd 2
192.5.e.d.65.1 2 8.5 even 2
192.5.e.d.65.2 2 24.5 odd 2
294.5.b.a.197.1 2 7.6 odd 2
294.5.b.a.197.2 2 21.20 even 2