Properties

Label 22.5.d.a.17.3
Level $22$
Weight $5$
Character 22.17
Analytic conductor $2.274$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [22,5,Mod(7,22)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(22, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([7]))
 
N = Newforms(chi, 5, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("22.7");
 
S:= CuspForms(chi, 5);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 22 = 2 \cdot 11 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 22.d (of order \(10\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.27413918784\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(4\) over \(\Q(\zeta_{10})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 4 x^{15} + 138 x^{14} - 428 x^{13} + 7783 x^{12} - 18620 x^{11} + 235604 x^{10} - 425164 x^{9} + 4199998 x^{8} - 5446172 x^{7} + 45313276 x^{6} + \cdots + 1499670491 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{8}\cdot 11^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 17.3
Root \(0.809017 - 3.04259i\) of defining polynomial
Character \(\chi\) \(=\) 22.17
Dual form 22.5.d.a.13.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(2.68999 - 0.874032i) q^{2} +(-13.1019 - 9.51912i) q^{3} +(6.47214 - 4.70228i) q^{4} +(8.38512 - 25.8068i) q^{5} +(-43.5642 - 14.1549i) q^{6} +(26.6976 + 36.7461i) q^{7} +(13.3001 - 18.3060i) q^{8} +(56.0169 + 172.402i) q^{9} +O(q^{10})\) \(q+(2.68999 - 0.874032i) q^{2} +(-13.1019 - 9.51912i) q^{3} +(6.47214 - 4.70228i) q^{4} +(8.38512 - 25.8068i) q^{5} +(-43.5642 - 14.1549i) q^{6} +(26.6976 + 36.7461i) q^{7} +(13.3001 - 18.3060i) q^{8} +(56.0169 + 172.402i) q^{9} -76.7489i q^{10} +(-50.8926 - 109.777i) q^{11} -129.559 q^{12} +(148.981 - 48.4067i) q^{13} +(103.934 + 75.5123i) q^{14} +(-355.519 + 258.300i) q^{15} +(19.7771 - 60.8676i) q^{16} +(310.069 + 100.748i) q^{17} +(301.370 + 414.801i) q^{18} +(-62.7848 + 86.4159i) q^{19} +(-67.0810 - 206.454i) q^{20} -735.583i q^{21} +(-232.849 - 250.817i) q^{22} -467.991 q^{23} +(-348.513 + 113.239i) q^{24} +(-90.0429 - 65.4200i) q^{25} +(358.448 - 260.428i) q^{26} +(501.823 - 1544.45i) q^{27} +(345.581 + 112.286i) q^{28} +(104.073 + 143.244i) q^{29} +(-730.582 + 1005.56i) q^{30} +(84.3454 + 259.588i) q^{31} -181.019i q^{32} +(-378.187 + 1922.74i) q^{33} +922.141 q^{34} +(1172.16 - 380.858i) q^{35} +(1173.23 + 852.404i) q^{36} +(-1730.83 + 1257.52i) q^{37} +(-93.3606 + 287.334i) q^{38} +(-2412.72 - 783.942i) q^{39} +(-360.895 - 496.729i) q^{40} +(764.111 - 1051.71i) q^{41} +(-642.924 - 1978.72i) q^{42} +2337.65i q^{43} +(-845.585 - 471.179i) q^{44} +4918.85 q^{45} +(-1258.89 + 409.039i) q^{46} +(2128.07 + 1546.13i) q^{47} +(-838.524 + 609.224i) q^{48} +(104.435 - 321.418i) q^{49} +(-299.394 - 97.2791i) q^{50} +(-3103.48 - 4271.58i) q^{51} +(736.600 - 1013.84i) q^{52} +(503.892 + 1550.82i) q^{53} -4593.18i q^{54} +(-3259.72 + 392.880i) q^{55} +1027.75 q^{56} +(1645.21 - 534.560i) q^{57} +(405.156 + 294.363i) q^{58} +(3560.56 - 2586.90i) q^{59} +(-1086.37 + 3343.50i) q^{60} +(-4518.12 - 1468.03i) q^{61} +(453.777 + 624.571i) q^{62} +(-4839.60 + 6661.14i) q^{63} +(-158.217 - 486.941i) q^{64} -4250.60i q^{65} +(663.217 + 5502.71i) q^{66} -1184.26 q^{67} +(2480.55 - 805.981i) q^{68} +(6131.59 + 4454.86i) q^{69} +(2820.22 - 2049.01i) q^{70} +(1333.37 - 4103.69i) q^{71} +(3901.02 + 1267.52i) q^{72} +(1111.87 + 1530.35i) q^{73} +(-3556.81 + 4895.53i) q^{74} +(556.996 + 1714.26i) q^{75} +854.528i q^{76} +(2675.16 - 4800.88i) q^{77} -7175.40 q^{78} +(-1208.14 + 392.547i) q^{79} +(-1404.96 - 1020.77i) q^{80} +(-9397.71 + 6827.84i) q^{81} +(1136.23 - 3496.95i) q^{82} +(2203.70 + 716.026i) q^{83} +(-3458.92 - 4760.80i) q^{84} +(5199.94 - 7157.10i) q^{85} +(2043.18 + 6288.27i) q^{86} -2867.46i q^{87} +(-2686.44 - 528.401i) q^{88} -13826.8 q^{89} +(13231.7 - 4299.24i) q^{90} +(5756.19 + 4182.11i) q^{91} +(-3028.90 + 2200.62i) q^{92} +(1365.96 - 4204.01i) q^{93} +(7075.85 + 2299.08i) q^{94} +(1703.66 + 2344.88i) q^{95} +(-1723.14 + 2371.70i) q^{96} +(588.049 + 1809.83i) q^{97} -955.893i q^{98} +(16074.9 - 14923.4i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 2 q^{3} + 32 q^{4} + 30 q^{5} - 80 q^{6} + 150 q^{7} + 110 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 2 q^{3} + 32 q^{4} + 30 q^{5} - 80 q^{6} + 150 q^{7} + 110 q^{9} - 30 q^{11} - 384 q^{12} - 510 q^{13} - 96 q^{14} - 1398 q^{15} - 256 q^{16} + 1770 q^{17} + 1120 q^{18} + 1020 q^{19} - 240 q^{20} + 240 q^{22} - 2424 q^{23} - 640 q^{24} - 858 q^{25} + 480 q^{26} + 2224 q^{27} + 1600 q^{28} + 4890 q^{29} + 3360 q^{30} + 602 q^{31} - 2648 q^{33} - 3904 q^{34} - 8670 q^{35} + 720 q^{36} - 4518 q^{37} - 4800 q^{38} - 1130 q^{39} - 1280 q^{40} + 1290 q^{41} - 3808 q^{42} + 720 q^{44} + 12152 q^{45} + 4480 q^{46} + 642 q^{47} - 128 q^{48} + 9534 q^{49} + 6720 q^{50} - 1500 q^{51} + 4000 q^{52} + 2598 q^{53} + 2582 q^{55} - 3072 q^{56} + 9140 q^{57} - 6496 q^{58} + 6660 q^{59} - 5776 q^{60} - 27410 q^{61} - 19680 q^{62} - 27260 q^{63} + 2048 q^{64} + 2528 q^{66} + 21524 q^{67} + 14160 q^{68} + 11416 q^{69} + 34400 q^{70} - 5562 q^{71} + 10240 q^{72} - 7790 q^{73} + 5760 q^{74} + 3576 q^{75} - 1110 q^{77} - 39424 q^{78} - 2770 q^{79} - 3840 q^{80} - 25464 q^{81} - 17472 q^{82} - 36900 q^{83} - 24480 q^{84} - 24750 q^{85} + 624 q^{86} - 5760 q^{88} + 46596 q^{89} + 55360 q^{90} + 32370 q^{91} + 14112 q^{92} + 20722 q^{93} + 58880 q^{94} + 74250 q^{95} - 3732 q^{97} + 45802 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/22\mathbb{Z}\right)^\times\).

\(n\) \(13\)
\(\chi(n)\) \(e\left(\frac{9}{10}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.68999 0.874032i 0.672499 0.218508i
\(3\) −13.1019 9.51912i −1.45577 1.05768i −0.984439 0.175724i \(-0.943773\pi\)
−0.471332 0.881956i \(-0.656227\pi\)
\(4\) 6.47214 4.70228i 0.404508 0.293893i
\(5\) 8.38512 25.8068i 0.335405 1.03227i −0.631117 0.775687i \(-0.717403\pi\)
0.966522 0.256583i \(-0.0825967\pi\)
\(6\) −43.5642 14.1549i −1.21012 0.393190i
\(7\) 26.6976 + 36.7461i 0.544849 + 0.749921i 0.989302 0.145881i \(-0.0466018\pi\)
−0.444453 + 0.895802i \(0.646602\pi\)
\(8\) 13.3001 18.3060i 0.207813 0.286031i
\(9\) 56.0169 + 172.402i 0.691567 + 2.12842i
\(10\) 76.7489i 0.767489i
\(11\) −50.8926 109.777i −0.420600 0.907246i
\(12\) −129.559 −0.899716
\(13\) 148.981 48.4067i 0.881542 0.286430i 0.166944 0.985966i \(-0.446610\pi\)
0.714597 + 0.699536i \(0.246610\pi\)
\(14\) 103.934 + 75.5123i 0.530274 + 0.385267i
\(15\) −355.519 + 258.300i −1.58008 + 1.14800i
\(16\) 19.7771 60.8676i 0.0772542 0.237764i
\(17\) 310.069 + 100.748i 1.07290 + 0.348608i 0.791618 0.611016i \(-0.209239\pi\)
0.281286 + 0.959624i \(0.409239\pi\)
\(18\) 301.370 + 414.801i 0.930155 + 1.28025i
\(19\) −62.7848 + 86.4159i −0.173919 + 0.239379i −0.887074 0.461627i \(-0.847266\pi\)
0.713155 + 0.701007i \(0.247266\pi\)
\(20\) −67.0810 206.454i −0.167702 0.516135i
\(21\) 735.583i 1.66799i
\(22\) −232.849 250.817i −0.481093 0.518217i
\(23\) −467.991 −0.884671 −0.442335 0.896850i \(-0.645850\pi\)
−0.442335 + 0.896850i \(0.645850\pi\)
\(24\) −348.513 + 113.239i −0.605058 + 0.196595i
\(25\) −90.0429 65.4200i −0.144069 0.104672i
\(26\) 358.448 260.428i 0.530248 0.385248i
\(27\) 501.823 1544.45i 0.688372 2.11859i
\(28\) 345.581 + 112.286i 0.440792 + 0.143222i
\(29\) 104.073 + 143.244i 0.123749 + 0.170326i 0.866397 0.499357i \(-0.166430\pi\)
−0.742648 + 0.669682i \(0.766430\pi\)
\(30\) −730.582 + 1005.56i −0.811758 + 1.11729i
\(31\) 84.3454 + 259.588i 0.0877683 + 0.270123i 0.985302 0.170823i \(-0.0546428\pi\)
−0.897533 + 0.440947i \(0.854643\pi\)
\(32\) 181.019i 0.176777i
\(33\) −378.187 + 1922.74i −0.347279 + 1.76560i
\(34\) 922.141 0.797700
\(35\) 1172.16 380.858i 0.956866 0.310905i
\(36\) 1173.23 + 852.404i 0.905273 + 0.657719i
\(37\) −1730.83 + 1257.52i −1.26430 + 0.918571i −0.998961 0.0455830i \(-0.985485\pi\)
−0.265344 + 0.964154i \(0.585485\pi\)
\(38\) −93.3606 + 287.334i −0.0646541 + 0.198985i
\(39\) −2412.72 783.942i −1.58627 0.515412i
\(40\) −360.895 496.729i −0.225559 0.310456i
\(41\) 764.111 1051.71i 0.454557 0.625645i −0.518812 0.854889i \(-0.673625\pi\)
0.973369 + 0.229244i \(0.0736254\pi\)
\(42\) −642.924 1978.72i −0.364469 1.12172i
\(43\) 2337.65i 1.26428i 0.774855 + 0.632139i \(0.217823\pi\)
−0.774855 + 0.632139i \(0.782177\pi\)
\(44\) −845.585 471.179i −0.436769 0.243378i
\(45\) 4918.85 2.42906
\(46\) −1258.89 + 409.039i −0.594940 + 0.193308i
\(47\) 2128.07 + 1546.13i 0.963361 + 0.699923i 0.953929 0.300032i \(-0.0969975\pi\)
0.00943244 + 0.999956i \(0.496998\pi\)
\(48\) −838.524 + 609.224i −0.363943 + 0.264420i
\(49\) 104.435 321.418i 0.0434965 0.133869i
\(50\) −299.394 97.2791i −0.119758 0.0389116i
\(51\) −3103.48 4271.58i −1.19319 1.64228i
\(52\) 736.600 1013.84i 0.272411 0.374942i
\(53\) 503.892 + 1550.82i 0.179385 + 0.552090i 0.999807 0.0196691i \(-0.00626126\pi\)
−0.820422 + 0.571759i \(0.806261\pi\)
\(54\) 4593.18i 1.57517i
\(55\) −3259.72 + 392.880i −1.07759 + 0.129878i
\(56\) 1027.75 0.327727
\(57\) 1645.21 534.560i 0.506373 0.164531i
\(58\) 405.156 + 294.363i 0.120439 + 0.0875038i
\(59\) 3560.56 2586.90i 1.02286 0.743149i 0.0559900 0.998431i \(-0.482169\pi\)
0.966866 + 0.255283i \(0.0821685\pi\)
\(60\) −1086.37 + 3343.50i −0.301769 + 0.928750i
\(61\) −4518.12 1468.03i −1.21422 0.394525i −0.369248 0.929331i \(-0.620385\pi\)
−0.844975 + 0.534806i \(0.820385\pi\)
\(62\) 453.777 + 624.571i 0.118048 + 0.162479i
\(63\) −4839.60 + 6661.14i −1.21935 + 1.67829i
\(64\) −158.217 486.941i −0.0386271 0.118882i
\(65\) 4250.60i 1.00606i
\(66\) 663.217 + 5502.71i 0.152254 + 1.26325i
\(67\) −1184.26 −0.263813 −0.131907 0.991262i \(-0.542110\pi\)
−0.131907 + 0.991262i \(0.542110\pi\)
\(68\) 2480.55 805.981i 0.536452 0.174304i
\(69\) 6131.59 + 4454.86i 1.28788 + 0.935698i
\(70\) 2820.22 2049.01i 0.575556 0.418166i
\(71\) 1333.37 4103.69i 0.264505 0.814062i −0.727302 0.686317i \(-0.759226\pi\)
0.991807 0.127745i \(-0.0407739\pi\)
\(72\) 3901.02 + 1267.52i 0.752511 + 0.244506i
\(73\) 1111.87 + 1530.35i 0.208644 + 0.287174i 0.900495 0.434866i \(-0.143204\pi\)
−0.691851 + 0.722041i \(0.743204\pi\)
\(74\) −3556.81 + 4895.53i −0.649528 + 0.893998i
\(75\) 556.996 + 1714.26i 0.0990216 + 0.304757i
\(76\) 854.528i 0.147945i
\(77\) 2675.16 4800.88i 0.451199 0.809729i
\(78\) −7175.40 −1.17939
\(79\) −1208.14 + 392.547i −0.193580 + 0.0628981i −0.404203 0.914669i \(-0.632451\pi\)
0.210622 + 0.977568i \(0.432451\pi\)
\(80\) −1404.96 1020.77i −0.219525 0.159495i
\(81\) −9397.71 + 6827.84i −1.43236 + 1.04067i
\(82\) 1136.23 3496.95i 0.168981 0.520069i
\(83\) 2203.70 + 716.026i 0.319887 + 0.103938i 0.464559 0.885542i \(-0.346213\pi\)
−0.144672 + 0.989480i \(0.546213\pi\)
\(84\) −3458.92 4760.80i −0.490210 0.674716i
\(85\) 5199.94 7157.10i 0.719715 0.990603i
\(86\) 2043.18 + 6288.27i 0.276255 + 0.850226i
\(87\) 2867.46i 0.378843i
\(88\) −2686.44 528.401i −0.346907 0.0682336i
\(89\) −13826.8 −1.74558 −0.872792 0.488092i \(-0.837693\pi\)
−0.872792 + 0.488092i \(0.837693\pi\)
\(90\) 13231.7 4299.24i 1.63354 0.530770i
\(91\) 5756.19 + 4182.11i 0.695108 + 0.505025i
\(92\) −3028.90 + 2200.62i −0.357857 + 0.259998i
\(93\) 1365.96 4204.01i 0.157933 0.486068i
\(94\) 7075.85 + 2299.08i 0.800798 + 0.260195i
\(95\) 1703.66 + 2344.88i 0.188771 + 0.259821i
\(96\) −1723.14 + 2371.70i −0.186973 + 0.257346i
\(97\) 588.049 + 1809.83i 0.0624986 + 0.192351i 0.977430 0.211257i \(-0.0677558\pi\)
−0.914932 + 0.403608i \(0.867756\pi\)
\(98\) 955.893i 0.0995307i
\(99\) 16074.9 14923.4i 1.64013 1.52264i
\(100\) −890.394 −0.0890394
\(101\) −11404.7 + 3705.62i −1.11800 + 0.363261i −0.809005 0.587802i \(-0.799993\pi\)
−0.308997 + 0.951063i \(0.599993\pi\)
\(102\) −12081.8 8777.97i −1.16127 0.843711i
\(103\) 1974.12 1434.28i 0.186080 0.135195i −0.490846 0.871247i \(-0.663312\pi\)
0.676925 + 0.736052i \(0.263312\pi\)
\(104\) 1095.32 3371.05i 0.101268 0.311672i
\(105\) −18983.0 6167.96i −1.72182 0.559452i
\(106\) 2710.93 + 3731.28i 0.241272 + 0.332083i
\(107\) −7701.96 + 10600.8i −0.672719 + 0.925919i −0.999818 0.0190714i \(-0.993929\pi\)
0.327099 + 0.944990i \(0.393929\pi\)
\(108\) −4014.59 12355.6i −0.344186 1.05930i
\(109\) 934.389i 0.0786457i 0.999227 + 0.0393228i \(0.0125201\pi\)
−0.999227 + 0.0393228i \(0.987480\pi\)
\(110\) −8425.25 + 3905.95i −0.696302 + 0.322806i
\(111\) 34647.8 2.81209
\(112\) 2764.65 898.289i 0.220396 0.0716111i
\(113\) −5601.04 4069.39i −0.438643 0.318693i 0.346452 0.938068i \(-0.387386\pi\)
−0.785096 + 0.619375i \(0.787386\pi\)
\(114\) 3958.37 2875.93i 0.304584 0.221293i
\(115\) −3924.16 + 12077.3i −0.296723 + 0.913219i
\(116\) 1347.15 + 437.715i 0.100115 + 0.0325294i
\(117\) 16690.9 + 22973.0i 1.21929 + 1.67821i
\(118\) 7316.86 10070.8i 0.525486 0.723269i
\(119\) 4576.03 + 14083.6i 0.323143 + 0.994532i
\(120\) 9943.52i 0.690522i
\(121\) −9460.89 + 11173.6i −0.646192 + 0.763175i
\(122\) −13436.8 −0.902770
\(123\) −20022.7 + 6505.76i −1.32346 + 0.430019i
\(124\) 1766.55 + 1283.48i 0.114890 + 0.0834727i
\(125\) 11277.0 8193.25i 0.721730 0.524368i
\(126\) −7196.44 + 22148.4i −0.453291 + 1.39509i
\(127\) 13172.5 + 4280.02i 0.816699 + 0.265362i 0.687433 0.726248i \(-0.258738\pi\)
0.129267 + 0.991610i \(0.458738\pi\)
\(128\) −851.204 1171.58i −0.0519534 0.0715077i
\(129\) 22252.4 30627.8i 1.33720 1.84050i
\(130\) −3715.16 11434.1i −0.219832 0.676574i
\(131\) 23230.6i 1.35368i 0.736128 + 0.676842i \(0.236652\pi\)
−0.736128 + 0.676842i \(0.763348\pi\)
\(132\) 6593.60 + 14222.6i 0.378420 + 0.816264i
\(133\) −4851.66 −0.274275
\(134\) −3185.64 + 1035.08i −0.177414 + 0.0576453i
\(135\) −35649.5 25900.9i −1.95608 1.42117i
\(136\) 5968.22 4336.17i 0.322676 0.234438i
\(137\) 285.958 880.087i 0.0152356 0.0468905i −0.943150 0.332368i \(-0.892152\pi\)
0.958385 + 0.285478i \(0.0921523\pi\)
\(138\) 20387.6 + 6624.34i 1.07055 + 0.347844i
\(139\) −20601.7 28355.8i −1.06629 1.46762i −0.873780 0.486321i \(-0.838339\pi\)
−0.192506 0.981296i \(-0.561661\pi\)
\(140\) 5795.48 7976.80i 0.295688 0.406980i
\(141\) −13164.0 40514.6i −0.662140 2.03786i
\(142\) 12204.3i 0.605252i
\(143\) −12895.9 13891.1i −0.630639 0.679303i
\(144\) 11601.6 0.559489
\(145\) 4569.33 1484.67i 0.217328 0.0706143i
\(146\) 4328.49 + 3144.83i 0.203063 + 0.147534i
\(147\) −4427.92 + 3217.07i −0.204911 + 0.148877i
\(148\) −5288.95 + 16277.7i −0.241461 + 0.743139i
\(149\) 9990.22 + 3246.02i 0.449990 + 0.146210i 0.525240 0.850954i \(-0.323976\pi\)
−0.0752503 + 0.997165i \(0.523976\pi\)
\(150\) 2996.63 + 4124.51i 0.133184 + 0.183312i
\(151\) 13070.9 17990.5i 0.573258 0.789023i −0.419678 0.907673i \(-0.637857\pi\)
0.992936 + 0.118651i \(0.0378569\pi\)
\(152\) 746.885 + 2298.67i 0.0323271 + 0.0994925i
\(153\) 59100.2i 2.52468i
\(154\) 3000.04 15252.5i 0.126499 0.643132i
\(155\) 7406.38 0.308278
\(156\) −19301.8 + 6271.53i −0.793137 + 0.257706i
\(157\) 5926.18 + 4305.62i 0.240423 + 0.174677i 0.701472 0.712697i \(-0.252527\pi\)
−0.461049 + 0.887375i \(0.652527\pi\)
\(158\) −2906.78 + 2111.90i −0.116439 + 0.0845978i
\(159\) 8160.48 25115.4i 0.322791 0.993448i
\(160\) −4671.52 1517.87i −0.182481 0.0592918i
\(161\) −12494.2 17196.8i −0.482012 0.663433i
\(162\) −19312.0 + 26580.7i −0.735865 + 1.01283i
\(163\) 13118.6 + 40375.0i 0.493758 + 1.51963i 0.818884 + 0.573959i \(0.194593\pi\)
−0.325126 + 0.945671i \(0.605407\pi\)
\(164\) 10399.9i 0.386670i
\(165\) 46448.6 + 25882.2i 1.70610 + 0.950678i
\(166\) 6553.77 0.237835
\(167\) −13590.5 + 4415.82i −0.487306 + 0.158335i −0.542357 0.840148i \(-0.682468\pi\)
0.0550508 + 0.998484i \(0.482468\pi\)
\(168\) −13465.6 9783.31i −0.477096 0.346631i
\(169\) −3254.34 + 2364.41i −0.113943 + 0.0827847i
\(170\) 7732.27 23797.5i 0.267553 0.823442i
\(171\) −18415.3 5983.50i −0.629777 0.204627i
\(172\) 10992.3 + 15129.6i 0.371562 + 0.511412i
\(173\) 16635.9 22897.3i 0.555845 0.765055i −0.434946 0.900457i \(-0.643233\pi\)
0.990791 + 0.135402i \(0.0432325\pi\)
\(174\) −2506.25 7713.45i −0.0827801 0.254771i
\(175\) 5055.29i 0.165071i
\(176\) −7688.36 + 926.644i −0.248204 + 0.0299149i
\(177\) −71275.3 −2.27506
\(178\) −37193.9 + 12085.0i −1.17390 + 0.381424i
\(179\) −9919.07 7206.63i −0.309574 0.224919i 0.422139 0.906531i \(-0.361279\pi\)
−0.731714 + 0.681612i \(0.761279\pi\)
\(180\) 31835.5 23129.8i 0.982577 0.713884i
\(181\) −8052.11 + 24781.8i −0.245783 + 0.756443i 0.749723 + 0.661752i \(0.230187\pi\)
−0.995507 + 0.0946919i \(0.969813\pi\)
\(182\) 19139.4 + 6218.77i 0.577811 + 0.187742i
\(183\) 45221.8 + 62242.5i 1.35035 + 1.85860i
\(184\) −6224.31 + 8567.02i −0.183846 + 0.253043i
\(185\) 17939.4 + 55211.7i 0.524160 + 1.61320i
\(186\) 12502.6i 0.361390i
\(187\) −4720.47 39165.7i −0.134990 1.12001i
\(188\) 21043.5 0.595390
\(189\) 70150.2 22793.2i 1.96384 0.638089i
\(190\) 6632.33 + 4818.67i 0.183721 + 0.133481i
\(191\) 9625.10 6993.05i 0.263839 0.191690i −0.447999 0.894034i \(-0.647863\pi\)
0.711838 + 0.702344i \(0.247863\pi\)
\(192\) −2562.30 + 7885.96i −0.0695069 + 0.213920i
\(193\) −17700.3 5751.17i −0.475188 0.154398i 0.0616245 0.998099i \(-0.480372\pi\)
−0.536813 + 0.843701i \(0.680372\pi\)
\(194\) 3163.70 + 4354.46i 0.0840604 + 0.115699i
\(195\) −40462.0 + 55691.1i −1.06409 + 1.46459i
\(196\) −835.481 2571.35i −0.0217483 0.0669343i
\(197\) 51063.1i 1.31575i −0.753125 0.657877i \(-0.771455\pi\)
0.753125 0.657877i \(-0.228545\pi\)
\(198\) 30198.0 54193.7i 0.770278 1.38235i
\(199\) −32814.0 −0.828616 −0.414308 0.910137i \(-0.635976\pi\)
−0.414308 + 0.910137i \(0.635976\pi\)
\(200\) −2395.15 + 778.233i −0.0598788 + 0.0194558i
\(201\) 15516.1 + 11273.1i 0.384051 + 0.279030i
\(202\) −27439.9 + 19936.2i −0.672479 + 0.488585i
\(203\) −2485.17 + 7648.56i −0.0603064 + 0.185604i
\(204\) −40172.3 13052.8i −0.965309 0.313648i
\(205\) −20734.0 28537.9i −0.493374 0.679070i
\(206\) 4056.76 5583.65i 0.0955971 0.131578i
\(207\) −26215.4 80682.7i −0.611809 1.88295i
\(208\) 10025.4i 0.231727i
\(209\) 12681.7 + 2494.39i 0.290326 + 0.0571047i
\(210\) −56455.2 −1.28016
\(211\) 61926.5 20121.1i 1.39095 0.451947i 0.484697 0.874682i \(-0.338930\pi\)
0.906254 + 0.422734i \(0.138930\pi\)
\(212\) 10553.7 + 7667.68i 0.234818 + 0.170605i
\(213\) −56533.2 + 41073.8i −1.24608 + 0.905327i
\(214\) −11452.8 + 35248.0i −0.250082 + 0.769674i
\(215\) 60327.2 + 19601.5i 1.30508 + 0.424045i
\(216\) −21598.4 29727.7i −0.462929 0.637168i
\(217\) −7287.05 + 10029.8i −0.154751 + 0.212996i
\(218\) 816.686 + 2513.50i 0.0171847 + 0.0528891i
\(219\) 30634.6i 0.638739i
\(220\) −19249.9 + 17870.9i −0.397726 + 0.369234i
\(221\) 51071.2 1.04566
\(222\) 93202.3 30283.3i 1.89113 0.614465i
\(223\) −15247.4 11077.9i −0.306610 0.222765i 0.423831 0.905741i \(-0.360685\pi\)
−0.730440 + 0.682977i \(0.760685\pi\)
\(224\) 6651.76 4832.79i 0.132569 0.0963167i
\(225\) 6234.64 19188.2i 0.123153 0.379027i
\(226\) −18623.5 6051.15i −0.364624 0.118473i
\(227\) −35440.6 48779.8i −0.687780 0.946648i 0.312214 0.950012i \(-0.398929\pi\)
−0.999994 + 0.00336373i \(0.998929\pi\)
\(228\) 8134.35 11196.0i 0.156478 0.215373i
\(229\) 25553.4 + 78645.3i 0.487279 + 1.49969i 0.828652 + 0.559764i \(0.189108\pi\)
−0.341373 + 0.939928i \(0.610892\pi\)
\(230\) 35917.8i 0.678975i
\(231\) −80750.0 + 37435.7i −1.51328 + 0.701556i
\(232\) 4006.40 0.0744352
\(233\) −38593.9 + 12539.9i −0.710897 + 0.230984i −0.642072 0.766644i \(-0.721925\pi\)
−0.0688249 + 0.997629i \(0.521925\pi\)
\(234\) 64977.5 + 47208.9i 1.18667 + 0.862168i
\(235\) 57744.7 41954.0i 1.04563 0.759692i
\(236\) 10880.1 33485.5i 0.195348 0.601220i
\(237\) 19565.6 + 6357.26i 0.348335 + 0.113181i
\(238\) 24619.0 + 33885.1i 0.434626 + 0.598212i
\(239\) −45431.0 + 62530.4i −0.795347 + 1.09470i 0.198075 + 0.980187i \(0.436531\pi\)
−0.993422 + 0.114514i \(0.963469\pi\)
\(240\) 8690.96 + 26748.0i 0.150885 + 0.464375i
\(241\) 81225.5i 1.39849i −0.714884 0.699243i \(-0.753521\pi\)
0.714884 0.699243i \(-0.246479\pi\)
\(242\) −15683.6 + 38326.2i −0.267803 + 0.654432i
\(243\) 56584.6 0.958265
\(244\) −36145.0 + 11744.2i −0.607111 + 0.197262i
\(245\) −7419.06 5390.26i −0.123600 0.0898003i
\(246\) −48174.6 + 35000.9i −0.796064 + 0.578375i
\(247\) −5170.61 + 15913.5i −0.0847516 + 0.260839i
\(248\) 5873.81 + 1908.52i 0.0955030 + 0.0310308i
\(249\) −22056.8 30358.6i −0.355750 0.489647i
\(250\) 23174.0 31896.3i 0.370784 0.510340i
\(251\) −21528.8 66258.7i −0.341721 1.05171i −0.963316 0.268370i \(-0.913515\pi\)
0.621595 0.783339i \(-0.286485\pi\)
\(252\) 65868.9i 1.03724i
\(253\) 23817.3 + 51374.5i 0.372092 + 0.802614i
\(254\) 39174.9 0.607213
\(255\) −136259. + 44273.1i −2.09548 + 0.680863i
\(256\) −3313.73 2407.57i −0.0505636 0.0367366i
\(257\) 55501.3 40324.1i 0.840305 0.610517i −0.0821509 0.996620i \(-0.526179\pi\)
0.922456 + 0.386103i \(0.126179\pi\)
\(258\) 33089.1 101838.i 0.497102 1.52992i
\(259\) −92418.2 30028.5i −1.37771 0.447645i
\(260\) −19987.5 27510.5i −0.295674 0.406960i
\(261\) −18865.8 + 25966.5i −0.276945 + 0.381182i
\(262\) 20304.3 + 62490.1i 0.295791 + 0.910350i
\(263\) 29173.5i 0.421772i 0.977511 + 0.210886i \(0.0676349\pi\)
−0.977511 + 0.210886i \(0.932365\pi\)
\(264\) 30167.7 + 32495.7i 0.432847 + 0.466249i
\(265\) 44246.9 0.630073
\(266\) −13050.9 + 4240.50i −0.184450 + 0.0599314i
\(267\) 181158. + 131619.i 2.54117 + 1.84627i
\(268\) −7664.67 + 5568.71i −0.106715 + 0.0775327i
\(269\) −2622.05 + 8069.84i −0.0362357 + 0.111522i −0.967538 0.252724i \(-0.918673\pi\)
0.931303 + 0.364246i \(0.118673\pi\)
\(270\) −118535. 38514.4i −1.62600 0.528318i
\(271\) 46946.4 + 64616.2i 0.639240 + 0.879838i 0.998575 0.0533708i \(-0.0169965\pi\)
−0.359335 + 0.933209i \(0.616997\pi\)
\(272\) 12264.5 16880.7i 0.165773 0.228167i
\(273\) −35607.2 109588.i −0.477763 1.47040i
\(274\) 2617.36i 0.0348629i
\(275\) −2599.08 + 13214.0i −0.0343681 + 0.174731i
\(276\) 60632.5 0.795953
\(277\) 46263.9 15032.0i 0.602952 0.195911i 0.00839523 0.999965i \(-0.497328\pi\)
0.594556 + 0.804054i \(0.297328\pi\)
\(278\) −80202.4 58270.4i −1.03776 0.753978i
\(279\) −40028.9 + 29082.7i −0.514239 + 0.373616i
\(280\) 8617.84 26523.0i 0.109921 0.338303i
\(281\) 6074.58 + 1973.75i 0.0769314 + 0.0249965i 0.347230 0.937780i \(-0.387122\pi\)
−0.270298 + 0.962777i \(0.587122\pi\)
\(282\) −70822.1 97478.3i −0.890576 1.22577i
\(283\) 74679.6 102788.i 0.932458 1.28342i −0.0264353 0.999651i \(-0.508416\pi\)
0.958893 0.283768i \(-0.0915844\pi\)
\(284\) −10667.0 32829.5i −0.132252 0.407031i
\(285\) 46939.8i 0.577899i
\(286\) −46831.2 26095.4i −0.572537 0.319031i
\(287\) 59046.2 0.716849
\(288\) 31208.2 10140.1i 0.376256 0.122253i
\(289\) 18423.0 + 13385.1i 0.220579 + 0.160260i
\(290\) 10993.8 7987.48i 0.130723 0.0949760i
\(291\) 9523.39 29310.0i 0.112462 0.346122i
\(292\) 14392.3 + 4676.34i 0.168797 + 0.0548454i
\(293\) −52337.8 72036.8i −0.609649 0.839110i 0.386899 0.922122i \(-0.373546\pi\)
−0.996549 + 0.0830119i \(0.973546\pi\)
\(294\) −9099.26 + 12524.1i −0.105272 + 0.144894i
\(295\) −36903.8 113578.i −0.424059 1.30512i
\(296\) 48409.7i 0.552521i
\(297\) −195084. + 23512.6i −2.21161 + 0.266556i
\(298\) 29710.8 0.334566
\(299\) −69721.5 + 22653.9i −0.779874 + 0.253396i
\(300\) 11665.9 + 8475.76i 0.129621 + 0.0941751i
\(301\) −85899.6 + 62409.7i −0.948109 + 0.688842i
\(302\) 19436.3 59818.7i 0.213108 0.655878i
\(303\) 184699. + 60012.2i 2.01177 + 0.653664i
\(304\) 4018.23 + 5530.62i 0.0434798 + 0.0598448i
\(305\) −75770.0 + 104288.i −0.814512 + 1.12108i
\(306\) 51655.5 + 158979.i 0.551663 + 1.69784i
\(307\) 88760.8i 0.941769i −0.882195 0.470885i \(-0.843935\pi\)
0.882195 0.470885i \(-0.156065\pi\)
\(308\) −5261.10 43651.3i −0.0554594 0.460147i
\(309\) −39517.9 −0.413882
\(310\) 19923.1 6473.42i 0.207317 0.0673612i
\(311\) 104314. + 75788.4i 1.07850 + 0.783577i 0.977421 0.211301i \(-0.0677700\pi\)
0.101081 + 0.994878i \(0.467770\pi\)
\(312\) −46440.2 + 33740.8i −0.477073 + 0.346614i
\(313\) −29030.5 + 89346.6i −0.296323 + 0.911989i 0.686451 + 0.727176i \(0.259168\pi\)
−0.982774 + 0.184813i \(0.940832\pi\)
\(314\) 19704.6 + 6402.43i 0.199852 + 0.0649360i
\(315\) 131322. + 180749.i 1.32347 + 1.82161i
\(316\) −5973.35 + 8221.61i −0.0598197 + 0.0823347i
\(317\) 1162.02 + 3576.32i 0.0115636 + 0.0355892i 0.956672 0.291168i \(-0.0940440\pi\)
−0.945108 + 0.326758i \(0.894044\pi\)
\(318\) 74692.7i 0.738625i
\(319\) 10428.3 18714.9i 0.102479 0.183910i
\(320\) −13893.0 −0.135674
\(321\) 201821. 65575.7i 1.95865 0.636404i
\(322\) −48640.0 35339.1i −0.469118 0.340834i
\(323\) −28173.9 + 20469.5i −0.270048 + 0.196201i
\(324\) −28716.9 + 88381.4i −0.273556 + 0.841920i
\(325\) −16581.4 5387.63i −0.156984 0.0510071i
\(326\) 70578.2 + 97142.5i 0.664102 + 0.914059i
\(327\) 8894.56 12242.3i 0.0831819 0.114490i
\(328\) −9089.82 27975.6i −0.0844904 0.260035i
\(329\) 119476.i 1.10380i
\(330\) 147568. + 29025.4i 1.35508 + 0.266533i
\(331\) −98750.2 −0.901326 −0.450663 0.892694i \(-0.648812\pi\)
−0.450663 + 0.892694i \(0.648812\pi\)
\(332\) 17629.6 5728.21i 0.159943 0.0519688i
\(333\) −313756. 227957.i −2.82946 2.05572i
\(334\) −32698.7 + 23757.0i −0.293115 + 0.212961i
\(335\) −9930.14 + 30561.8i −0.0884842 + 0.272326i
\(336\) −44773.2 14547.7i −0.396588 0.128859i
\(337\) 71066.4 + 97814.5i 0.625755 + 0.861278i 0.997756 0.0669543i \(-0.0213282\pi\)
−0.372001 + 0.928232i \(0.621328\pi\)
\(338\) −6687.57 + 9204.65i −0.0585376 + 0.0805701i
\(339\) 34647.4 + 106634.i 0.301489 + 0.927888i
\(340\) 70773.3i 0.612226i
\(341\) 24204.2 22470.3i 0.208153 0.193241i
\(342\) −54766.9 −0.468237
\(343\) 118317. 38443.4i 1.00567 0.326764i
\(344\) 42793.0 + 31090.9i 0.361623 + 0.262734i
\(345\) 166380. 120882.i 1.39785 1.01560i
\(346\) 24737.4 76134.0i 0.206634 0.635955i
\(347\) −90973.1 29559.0i −0.755534 0.245488i −0.0941733 0.995556i \(-0.530021\pi\)
−0.661361 + 0.750068i \(0.730021\pi\)
\(348\) −13483.6 18558.6i −0.111339 0.153245i
\(349\) −71159.3 + 97942.4i −0.584226 + 0.804118i −0.994151 0.108001i \(-0.965555\pi\)
0.409925 + 0.912119i \(0.365555\pi\)
\(350\) −4418.48 13598.7i −0.0360693 0.111010i
\(351\) 254385.i 2.06480i
\(352\) −19871.7 + 9212.54i −0.160380 + 0.0743522i
\(353\) −170898. −1.37148 −0.685739 0.727848i \(-0.740521\pi\)
−0.685739 + 0.727848i \(0.740521\pi\)
\(354\) −191730. + 62296.9i −1.52997 + 0.497119i
\(355\) −94722.4 68819.9i −0.751616 0.546081i
\(356\) −89488.8 + 65017.4i −0.706104 + 0.513014i
\(357\) 74108.3 228082.i 0.581474 1.78959i
\(358\) −32981.1 10716.2i −0.257335 0.0836132i
\(359\) −86522.0 119087.i −0.671333 0.924010i 0.328457 0.944519i \(-0.393471\pi\)
−0.999790 + 0.0205088i \(0.993471\pi\)
\(360\) 65421.1 90044.4i 0.504792 0.694787i
\(361\) 36745.6 + 113091.i 0.281962 + 0.867791i
\(362\) 73700.8i 0.562413i
\(363\) 230319. 56337.1i 1.74790 0.427545i
\(364\) 56920.3 0.429600
\(365\) 48816.6 15861.5i 0.366422 0.119058i
\(366\) 176048. + 127907.i 1.31423 + 0.954841i
\(367\) 73050.5 53074.3i 0.542364 0.394051i −0.282598 0.959238i \(-0.591196\pi\)
0.824962 + 0.565188i \(0.191196\pi\)
\(368\) −9255.49 + 28485.5i −0.0683446 + 0.210343i
\(369\) 224120. + 72821.0i 1.64599 + 0.534816i
\(370\) 96513.5 + 132839.i 0.704993 + 0.970340i
\(371\) −43533.9 + 59919.3i −0.316286 + 0.435330i
\(372\) −10927.7 33632.0i −0.0789666 0.243034i
\(373\) 225814.i 1.62305i 0.584316 + 0.811526i \(0.301363\pi\)
−0.584316 + 0.811526i \(0.698637\pi\)
\(374\) −46930.1 101230.i −0.335512 0.723710i
\(375\) −225744. −1.60529
\(376\) 56606.8 18392.7i 0.400399 0.130098i
\(377\) 22438.8 + 16302.8i 0.157876 + 0.114704i
\(378\) 168782. 122627.i 1.18125 0.858228i
\(379\) −68671.2 + 211348.i −0.478075 + 1.47137i 0.363689 + 0.931520i \(0.381517\pi\)
−0.841765 + 0.539845i \(0.818483\pi\)
\(380\) 22052.6 + 7165.32i 0.152719 + 0.0496213i
\(381\) −131844. 181468.i −0.908260 1.25011i
\(382\) 19779.3 27223.9i 0.135545 0.186562i
\(383\) −25147.5 77396.0i −0.171434 0.527620i 0.828019 0.560700i \(-0.189468\pi\)
−0.999453 + 0.0330810i \(0.989468\pi\)
\(384\) 23452.7i 0.159049i
\(385\) −101464. 109293.i −0.684525 0.737347i
\(386\) −52640.4 −0.353301
\(387\) −403017. + 130948.i −2.69092 + 0.874333i
\(388\) 12316.3 + 8948.29i 0.0818117 + 0.0594397i
\(389\) −147847. + 107417.i −0.977039 + 0.709860i −0.957045 0.289940i \(-0.906365\pi\)
−0.0199941 + 0.999800i \(0.506365\pi\)
\(390\) −60166.7 + 185174.i −0.395573 + 1.21745i
\(391\) −145110. 47149.0i −0.949167 0.308403i
\(392\) −4494.88 6186.67i −0.0292513 0.0402610i
\(393\) 221135. 304366.i 1.43176 1.97065i
\(394\) −44630.8 137359.i −0.287503 0.884843i
\(395\) 34469.6i 0.220924i
\(396\) 33865.3 172175.i 0.215956 1.09794i
\(397\) 272916. 1.73160 0.865799 0.500391i \(-0.166811\pi\)
0.865799 + 0.500391i \(0.166811\pi\)
\(398\) −88269.6 + 28680.5i −0.557243 + 0.181059i
\(399\) 63566.1 + 46183.5i 0.399282 + 0.290096i
\(400\) −5762.75 + 4186.88i −0.0360172 + 0.0261680i
\(401\) 80904.1 248997.i 0.503132 1.54848i −0.300757 0.953701i \(-0.597239\pi\)
0.803888 0.594780i \(-0.202761\pi\)
\(402\) 51591.1 + 16763.0i 0.319244 + 0.103729i
\(403\) 25131.6 + 34590.7i 0.154743 + 0.212985i
\(404\) −56388.1 + 77611.6i −0.345482 + 0.475515i
\(405\) 97403.4 + 299777.i 0.593833 + 1.82763i
\(406\) 22746.7i 0.137996i
\(407\) 226133. + 126007.i 1.36514 + 0.760685i
\(408\) −119472. −0.717704
\(409\) 204557. 66464.5i 1.22283 0.397322i 0.374720 0.927138i \(-0.377739\pi\)
0.848113 + 0.529816i \(0.177739\pi\)
\(410\) −80717.5 58644.7i −0.480175 0.348868i
\(411\) −12124.3 + 8808.78i −0.0717747 + 0.0521474i
\(412\) 6032.37 18565.7i 0.0355380 0.109375i
\(413\) 190117. + 61772.8i 1.11461 + 0.362157i
\(414\) −141039. 194123.i −0.822881 1.13260i
\(415\) 36956.6 50866.4i 0.214583 0.295349i
\(416\) −8762.55 26968.4i −0.0506342 0.155836i
\(417\) 567627.i 3.26430i
\(418\) 36294.0 4374.36i 0.207722 0.0250358i
\(419\) 6203.42 0.0353348 0.0176674 0.999844i \(-0.494376\pi\)
0.0176674 + 0.999844i \(0.494376\pi\)
\(420\) −151864. + 49343.7i −0.860908 + 0.279726i
\(421\) −194115. 141033.i −1.09521 0.795713i −0.114935 0.993373i \(-0.536666\pi\)
−0.980271 + 0.197660i \(0.936666\pi\)
\(422\) 148995. 108252.i 0.836658 0.607868i
\(423\) −147349. + 453493.i −0.823504 + 2.53448i
\(424\) 35091.1 + 11401.8i 0.195193 + 0.0634221i
\(425\) −21328.6 29356.4i −0.118082 0.162527i
\(426\) −116174. + 159900.i −0.640163 + 0.881109i
\(427\) −66678.8 205216.i −0.365706 1.12553i
\(428\) 104827.i 0.572249i
\(429\) 36731.1 + 304758.i 0.199581 + 1.65592i
\(430\) 179412. 0.970320
\(431\) 161263. 52397.5i 0.868120 0.282069i 0.159104 0.987262i \(-0.449139\pi\)
0.709016 + 0.705193i \(0.249139\pi\)
\(432\) −84082.6 61089.6i −0.450546 0.327341i
\(433\) 166162. 120724.i 0.886249 0.643898i −0.0486480 0.998816i \(-0.515491\pi\)
0.934897 + 0.354918i \(0.115491\pi\)
\(434\) −10835.8 + 33349.1i −0.0575282 + 0.177054i
\(435\) −73999.8 24044.0i −0.391068 0.127066i
\(436\) 4393.76 + 6047.49i 0.0231134 + 0.0318128i
\(437\) 29382.7 40441.9i 0.153861 0.211772i
\(438\) −26775.6 82406.8i −0.139570 0.429551i
\(439\) 155401.i 0.806350i −0.915123 0.403175i \(-0.867907\pi\)
0.915123 0.403175i \(-0.132093\pi\)
\(440\) −36162.5 + 64897.7i −0.186790 + 0.335216i
\(441\) 61263.4 0.315010
\(442\) 137381. 44637.8i 0.703206 0.228485i
\(443\) −118242. 85907.9i −0.602511 0.437750i 0.244259 0.969710i \(-0.421455\pi\)
−0.846769 + 0.531961i \(0.821455\pi\)
\(444\) 224245. 162924.i 1.13752 0.826453i
\(445\) −115939. + 356824.i −0.585478 + 1.80192i
\(446\) −50697.8 16472.7i −0.254870 0.0828124i
\(447\) −99992.0 137627.i −0.500438 0.688794i
\(448\) 13669.2 18814.0i 0.0681062 0.0937401i
\(449\) −1879.14 5783.41i −0.00932110 0.0286874i 0.946288 0.323326i \(-0.104801\pi\)
−0.955609 + 0.294638i \(0.904801\pi\)
\(450\) 57065.5i 0.281805i
\(451\) −154341. 30357.5i −0.758800 0.149250i
\(452\) −55386.1 −0.271096
\(453\) −342507. + 111287.i −1.66907 + 0.542313i
\(454\) −137970. 100241.i −0.669381 0.486334i
\(455\) 156193. 113481.i 0.754465 0.548151i
\(456\) 12095.7 37226.8i 0.0581704 0.179030i
\(457\) −325507. 105763.i −1.55857 0.506411i −0.602147 0.798385i \(-0.705688\pi\)
−0.956426 + 0.291974i \(0.905688\pi\)
\(458\) 137477. + 189221.i 0.655389 + 0.902066i
\(459\) 311200. 428330.i 1.47712 2.03307i
\(460\) 31393.3 + 96618.6i 0.148361 + 0.456610i
\(461\) 394901.i 1.85818i −0.369860 0.929088i \(-0.620594\pi\)
0.369860 0.929088i \(-0.379406\pi\)
\(462\) −184497. + 171280.i −0.864381 + 0.802459i
\(463\) 87290.1 0.407196 0.203598 0.979055i \(-0.434736\pi\)
0.203598 + 0.979055i \(0.434736\pi\)
\(464\) 10777.2 3501.72i 0.0500575 0.0162647i
\(465\) −97038.0 70502.2i −0.448782 0.326060i
\(466\) −92857.0 + 67464.6i −0.427605 + 0.310673i
\(467\) 32278.7 99343.5i 0.148007 0.455518i −0.849379 0.527784i \(-0.823023\pi\)
0.997385 + 0.0722660i \(0.0230230\pi\)
\(468\) 216051. + 70199.2i 0.986426 + 0.320509i
\(469\) −31616.8 43516.8i −0.143738 0.197839i
\(470\) 118664. 163327.i 0.537183 0.739369i
\(471\) −36658.8 112824.i −0.165248 0.508581i
\(472\) 99585.5i 0.447005i
\(473\) 256620. 118969.i 1.14701 0.531755i
\(474\) 58187.9 0.258986
\(475\) 11306.7 3673.76i 0.0501126 0.0162826i
\(476\) 95841.6 + 69633.0i 0.423000 + 0.307327i
\(477\) −239139. + 173744.i −1.05102 + 0.763614i
\(478\) −67555.6 + 207915.i −0.295669 + 0.909975i
\(479\) −26588.0 8638.97i −0.115882 0.0376522i 0.250502 0.968116i \(-0.419404\pi\)
−0.366384 + 0.930464i \(0.619404\pi\)
\(480\) 46757.2 + 64355.8i 0.202939 + 0.279322i
\(481\) −196988. + 271130.i −0.851431 + 1.17189i
\(482\) −70993.6 218496.i −0.305580 0.940480i
\(483\) 344246.i 1.47562i
\(484\) −8690.55 + 116805.i −0.0370985 + 0.498622i
\(485\) 51636.7 0.219520
\(486\) 152212. 49456.7i 0.644432 0.209389i
\(487\) 227490. + 165281.i 0.959188 + 0.696891i 0.952962 0.303089i \(-0.0980181\pi\)
0.00622636 + 0.999981i \(0.498018\pi\)
\(488\) −86964.9 + 63183.7i −0.365178 + 0.265317i
\(489\) 212455. 653869.i 0.888483 2.73447i
\(490\) −24668.5 8015.28i −0.102743 0.0333831i
\(491\) 216203. + 297578.i 0.896808 + 1.23435i 0.971475 + 0.237141i \(0.0762104\pi\)
−0.0746676 + 0.997208i \(0.523790\pi\)
\(492\) −98997.6 + 136258.i −0.408973 + 0.562903i
\(493\) 17838.3 + 54900.7i 0.0733939 + 0.225883i
\(494\) 47326.5i 0.193932i
\(495\) −250333. 539976.i −1.02166 2.20376i
\(496\) 17468.6 0.0710061
\(497\) 186392. 60562.6i 0.754598 0.245184i
\(498\) −85867.2 62386.1i −0.346233 0.251553i
\(499\) −119340. + 86705.4i −0.479274 + 0.348213i −0.801045 0.598605i \(-0.795722\pi\)
0.321770 + 0.946818i \(0.395722\pi\)
\(500\) 34459.6 106056.i 0.137838 0.424223i
\(501\) 220096. + 71513.6i 0.876874 + 0.284914i
\(502\) −115825. 159419.i −0.459614 0.632604i
\(503\) −199460. + 274533.i −0.788352 + 1.08507i 0.205959 + 0.978561i \(0.433968\pi\)
−0.994311 + 0.106513i \(0.966032\pi\)
\(504\) 57571.6 + 177187.i 0.226645 + 0.697543i
\(505\) 325392.i 1.27592i
\(506\) 108971. + 117380.i 0.425609 + 0.458452i
\(507\) 65145.2 0.253435
\(508\) 105380. 34240.1i 0.408350 0.132681i
\(509\) −57307.6 41636.4i −0.221196 0.160708i 0.471669 0.881776i \(-0.343652\pi\)
−0.692865 + 0.721068i \(0.743652\pi\)
\(510\) −327839. + 238189.i −1.26043 + 0.915759i
\(511\) −26550.3 + 81713.5i −0.101678 + 0.312934i
\(512\) −11018.2 3580.04i −0.0420312 0.0136568i
\(513\) 101958. + 140334.i 0.387426 + 0.533246i
\(514\) 114054. 156981.i 0.431701 0.594185i
\(515\) −20460.9 62972.2i −0.0771455 0.237429i
\(516\) 302864.i 1.13749i
\(517\) 61426.5 312299.i 0.229813 1.16839i
\(518\) −274850. −1.02432
\(519\) −435925. + 141641.i −1.61837 + 0.525839i
\(520\) −77811.4 56533.3i −0.287764 0.209073i
\(521\) −252967. + 183791.i −0.931942 + 0.677095i −0.946468 0.322799i \(-0.895376\pi\)
0.0145256 + 0.999894i \(0.495376\pi\)
\(522\) −28053.3 + 86339.0i −0.102954 + 0.316859i
\(523\) −243282. 79047.2i −0.889421 0.288990i −0.171557 0.985174i \(-0.554880\pi\)
−0.717863 + 0.696184i \(0.754880\pi\)
\(524\) 109237. + 150351.i 0.397838 + 0.547577i
\(525\) −48121.9 + 66234.1i −0.174592 + 0.240305i
\(526\) 25498.6 + 78476.7i 0.0921605 + 0.283641i
\(527\) 88988.0i 0.320413i
\(528\) 109553. + 61045.6i 0.392968 + 0.218971i
\(529\) −60825.6 −0.217358
\(530\) 119024. 38673.2i 0.423723 0.137676i
\(531\) 645439. + 468939.i 2.28911 + 1.66313i
\(532\) −31400.6 + 22813.9i −0.110947 + 0.0806075i
\(533\) 62927.9 193672.i 0.221508 0.681731i
\(534\) 602352. + 195716.i 2.11236 + 0.686347i
\(535\) 208992. + 287652.i 0.730165 + 1.00499i
\(536\) −15750.7 + 21679.0i −0.0548239 + 0.0754586i
\(537\) 61358.4 + 188842.i 0.212777 + 0.654861i
\(538\) 23999.6i 0.0829161i
\(539\) −40599.2 + 4893.25i −0.139746 + 0.0168430i
\(540\) −352522. −1.20892
\(541\) −182923. + 59435.3i −0.624991 + 0.203072i −0.604355 0.796715i \(-0.706569\pi\)
−0.0206361 + 0.999787i \(0.506569\pi\)
\(542\) 182762. + 132784.i 0.622139 + 0.452011i
\(543\) 341400. 248041.i 1.15788 0.841249i
\(544\) 18237.3 56128.5i 0.0616257 0.189664i
\(545\) 24113.6 + 7834.97i 0.0811836 + 0.0263781i
\(546\) −191566. 263668.i −0.642590 0.884449i
\(547\) −65954.5 + 90778.6i −0.220429 + 0.303395i −0.904882 0.425662i \(-0.860041\pi\)
0.684453 + 0.729057i \(0.260041\pi\)
\(548\) −2287.66 7040.69i −0.00761782 0.0234452i
\(549\) 861169.i 2.85722i
\(550\) 4557.95 + 37817.3i 0.0150676 + 0.125016i
\(551\) −18912.8 −0.0622948
\(552\) 163101. 52994.7i 0.535277 0.173922i
\(553\) −46678.9 33914.2i −0.152641 0.110900i
\(554\) 111311. 80872.2i 0.362676 0.263500i
\(555\) 290526. 894147.i 0.943190 2.90284i
\(556\) −266674. 86647.7i −0.862644 0.280290i
\(557\) 17182.2 + 23649.2i 0.0553819 + 0.0762267i 0.835810 0.549019i \(-0.184999\pi\)
−0.780428 + 0.625246i \(0.784999\pi\)
\(558\) −82258.2 + 113219.i −0.264187 + 0.363622i
\(559\) 113158. + 348265.i 0.362128 + 1.11451i
\(560\) 78878.9i 0.251527i
\(561\) −310976. + 558082.i −0.988100 + 1.77326i
\(562\) 18065.7 0.0571982
\(563\) −254276. + 82619.2i −0.802210 + 0.260654i −0.681295 0.732009i \(-0.738583\pi\)
−0.120915 + 0.992663i \(0.538583\pi\)
\(564\) −275710. 200315.i −0.866752 0.629732i
\(565\) −151983. + 110422.i −0.476100 + 0.345907i
\(566\) 111048. 341771.i 0.346639 1.06685i
\(567\) −501793. 163042.i −1.56084 0.507148i
\(568\) −57388.1 78987.9i −0.177879 0.244830i
\(569\) 184215. 253550.i 0.568984 0.783139i −0.423450 0.905919i \(-0.639181\pi\)
0.992434 + 0.122781i \(0.0391812\pi\)
\(570\) −41026.9 126268.i −0.126275 0.388636i
\(571\) 467241.i 1.43308i −0.697549 0.716538i \(-0.745726\pi\)
0.697549 0.716538i \(-0.254274\pi\)
\(572\) −148784. 29264.5i −0.454741 0.0894437i
\(573\) −192675. −0.586836
\(574\) 158834. 51608.2i 0.482080 0.156637i
\(575\) 42139.3 + 30616.0i 0.127453 + 0.0926003i
\(576\) 75086.9 54553.8i 0.226318 0.164430i
\(577\) −55363.0 + 170390.i −0.166291 + 0.511790i −0.999129 0.0417260i \(-0.986714\pi\)
0.832838 + 0.553516i \(0.186714\pi\)
\(578\) 61256.7 + 19903.5i 0.183357 + 0.0595764i
\(579\) 177162. + 243843.i 0.528462 + 0.727365i
\(580\) 22592.0 31095.2i 0.0671582 0.0924353i
\(581\) 32522.4 + 100094.i 0.0963453 + 0.296520i
\(582\) 87167.5i 0.257341i
\(583\) 144600. 134241.i 0.425432 0.394955i
\(584\) 42802.5 0.125500
\(585\) 732814. 238106.i 2.14132 0.695757i
\(586\) −203751. 148034.i −0.593340 0.431087i
\(587\) −220845. + 160454.i −0.640932 + 0.465665i −0.860170 0.510007i \(-0.829643\pi\)
0.219238 + 0.975671i \(0.429643\pi\)
\(588\) −13530.5 + 41642.7i −0.0391345 + 0.120444i
\(589\) −27728.2 9009.43i −0.0799265 0.0259697i
\(590\) −198542. 273269.i −0.570358 0.785031i
\(591\) −486076. + 669026.i −1.39165 + 1.91544i
\(592\) 42311.6 + 130222.i 0.120730 + 0.371570i
\(593\) 11945.3i 0.0339694i 0.999856 + 0.0169847i \(0.00540665\pi\)
−0.999856 + 0.0169847i \(0.994593\pi\)
\(594\) −504225. + 233759.i −1.42906 + 0.662514i
\(595\) 401822. 1.13501
\(596\) 79921.8 25968.2i 0.224995 0.0731052i
\(597\) 429928. + 312361.i 1.20628 + 0.876411i
\(598\) −167750. + 121878.i −0.469095 + 0.340818i
\(599\) −88096.2 + 271132.i −0.245529 + 0.755662i 0.750019 + 0.661416i \(0.230044\pi\)
−0.995549 + 0.0942462i \(0.969956\pi\)
\(600\) 38789.2 + 12603.4i 0.107748 + 0.0350094i
\(601\) −258160. 355327.i −0.714728 0.983738i −0.999682 0.0251973i \(-0.991979\pi\)
0.284955 0.958541i \(-0.408021\pi\)
\(602\) −176521. + 242961.i −0.487085 + 0.670414i
\(603\) −66338.4 204169.i −0.182444 0.561506i
\(604\) 177900.i 0.487643i
\(605\) 209025. + 337847.i 0.571067 + 0.923017i
\(606\) 549291. 1.49574
\(607\) 386802. 125680.i 1.04981 0.341105i 0.267218 0.963636i \(-0.413896\pi\)
0.782595 + 0.622532i \(0.213896\pi\)
\(608\) 15643.0 + 11365.3i 0.0423167 + 0.0307449i
\(609\) 105368. 76554.3i 0.284102 0.206412i
\(610\) −112669. + 346761.i −0.302793 + 0.931902i
\(611\) 391883. + 127331.i 1.04972 + 0.341076i
\(612\) 277906. + 382505.i 0.741985 + 1.02125i
\(613\) 329984. 454184.i 0.878156 1.20868i −0.0987722 0.995110i \(-0.531492\pi\)
0.976928 0.213568i \(-0.0685085\pi\)
\(614\) −77579.8 238766.i −0.205784 0.633338i
\(615\) 571272.i 1.51040i
\(616\) −52305.0 112823.i −0.137842 0.297330i
\(617\) −361868. −0.950559 −0.475280 0.879835i \(-0.657653\pi\)
−0.475280 + 0.879835i \(0.657653\pi\)
\(618\) −106303. + 34539.9i −0.278335 + 0.0904365i
\(619\) 80076.6 + 58179.1i 0.208989 + 0.151840i 0.687356 0.726320i \(-0.258771\pi\)
−0.478367 + 0.878160i \(0.658771\pi\)
\(620\) 47935.1 34826.9i 0.124701 0.0906007i
\(621\) −234849. + 722790.i −0.608983 + 1.87426i
\(622\) 346845. + 112697.i 0.896509 + 0.291293i
\(623\) −369142. 508080.i −0.951081 1.30905i
\(624\) −95433.3 + 131353.i −0.245093 + 0.337342i
\(625\) −138378. 425883.i −0.354247 1.09026i
\(626\) 265716.i 0.678060i
\(627\) −142411. 153400.i −0.362250 0.390204i
\(628\) 58601.3 0.148589
\(629\) −663371. + 215542.i −1.67670 + 0.544792i
\(630\) 511235. + 371434.i 1.28807 + 0.935837i
\(631\) −3482.93 + 2530.50i −0.00874755 + 0.00635547i −0.592150 0.805827i \(-0.701721\pi\)
0.583403 + 0.812183i \(0.301721\pi\)
\(632\) −8882.33 + 27337.0i −0.0222378 + 0.0684410i
\(633\) −1.00289e6 325860.i −2.50292 0.813249i
\(634\) 6251.64 + 8604.65i 0.0155531 + 0.0214069i
\(635\) 220907. 304052.i 0.547850 0.754051i
\(636\) −65283.8 200923.i −0.161395 0.496724i
\(637\) 52940.4i 0.130469i
\(638\) 11694.8 59457.6i 0.0287310 0.146072i
\(639\) 782176. 1.91559
\(640\) −37372.2 + 12143.0i −0.0912407 + 0.0296459i
\(641\) 306286. + 222530.i 0.745438 + 0.541592i 0.894409 0.447249i \(-0.147596\pi\)
−0.148972 + 0.988841i \(0.547596\pi\)
\(642\) 485583. 352797.i 1.17813 0.855962i
\(643\) −75113.6 + 231176.i −0.181676 + 0.559140i −0.999875 0.0157940i \(-0.994972\pi\)
0.818200 + 0.574934i \(0.194972\pi\)
\(644\) −161729. 52548.9i −0.389956 0.126704i
\(645\) −603815. 831080.i −1.45139 1.99767i
\(646\) −57896.5 + 79687.7i −0.138735 + 0.190953i
\(647\) 65343.8 + 201107.i 0.156097 + 0.480418i 0.998270 0.0587889i \(-0.0187239\pi\)
−0.842173 + 0.539207i \(0.818724\pi\)
\(648\) 262845.i 0.625964i
\(649\) −465188. 259213.i −1.10443 0.615415i
\(650\) −49312.9 −0.116717
\(651\) 190949. 62043.1i 0.450563 0.146397i
\(652\) 274760. + 199625.i 0.646337 + 0.469591i
\(653\) −194030. + 140971.i −0.455032 + 0.330600i −0.791579 0.611066i \(-0.790741\pi\)
0.336547 + 0.941667i \(0.390741\pi\)
\(654\) 13226.1 40705.9i 0.0309227 0.0951703i
\(655\) 599506. + 194791.i 1.39737 + 0.454032i
\(656\) −48903.1 67309.3i −0.113639 0.156411i
\(657\) −201553. + 277414.i −0.466937 + 0.642684i
\(658\) 104426. + 321390.i 0.241189 + 0.742302i
\(659\) 474194.i 1.09191i −0.837816 0.545953i \(-0.816168\pi\)
0.837816 0.545953i \(-0.183832\pi\)
\(660\) 422327. 50901.2i 0.969529 0.116853i
\(661\) 808699. 1.85090 0.925452 0.378865i \(-0.123686\pi\)
0.925452 + 0.378865i \(0.123686\pi\)
\(662\) −265637. + 86310.8i −0.606140 + 0.196947i
\(663\) −669131. 486152.i −1.52224 1.10598i
\(664\) 42416.9 30817.7i 0.0962062 0.0698979i
\(665\) −40681.7 + 125206.i −0.0919933 + 0.283126i
\(666\) −1.04324e6 338970.i −2.35200 0.764211i
\(667\) −48705.2 67036.9i −0.109477 0.150682i
\(668\) −67195.0 + 92486.0i −0.150586 + 0.207264i
\(669\) 94318.8 + 290283.i 0.210739 + 0.648589i
\(670\) 90890.4i 0.202474i
\(671\) 68783.5 + 570697.i 0.152770 + 1.26754i
\(672\) −133155. −0.294862
\(673\) 648968. 210863.i 1.43283 0.465553i 0.513173 0.858285i \(-0.328470\pi\)
0.919653 + 0.392732i \(0.128470\pi\)
\(674\) 276661. + 201006.i 0.609016 + 0.442476i
\(675\) −146224. + 106238.i −0.320930 + 0.233170i
\(676\) −9944.37 + 30605.6i −0.0217612 + 0.0669742i
\(677\) −775084. 251840.i −1.69111 0.549474i −0.704093 0.710107i \(-0.748646\pi\)
−0.987014 + 0.160633i \(0.948646\pi\)
\(678\) 186403. + 256561.i 0.405502 + 0.558126i
\(679\) −50804.7 + 69926.7i −0.110196 + 0.151671i
\(680\) −61858.2 190380.i −0.133776 0.411721i
\(681\) 976474.i 2.10555i
\(682\) 45469.5 81600.2i 0.0977578 0.175438i
\(683\) 303153. 0.649861 0.324930 0.945738i \(-0.394659\pi\)
0.324930 + 0.945738i \(0.394659\pi\)
\(684\) −147323. + 47868.0i −0.314889 + 0.102314i
\(685\) −20314.4 14759.3i −0.0432935 0.0314546i
\(686\) 284670. 206825.i 0.604914 0.439496i
\(687\) 413835. 1.27365e6i 0.876826 2.69859i
\(688\) 142287. + 46231.9i 0.300600 + 0.0976709i
\(689\) 150140. + 206650.i 0.316271 + 0.435309i
\(690\) 341906. 470593.i 0.718138 0.988432i
\(691\) −37702.7 116037.i −0.0789617 0.243019i 0.903782 0.427994i \(-0.140780\pi\)
−0.982743 + 0.184975i \(0.940780\pi\)
\(692\) 226421.i 0.472830i
\(693\) 977538. + 192273.i 2.03548 + 0.400362i
\(694\) −270553. −0.561737
\(695\) −904520. + 293896.i −1.87262 + 0.608450i
\(696\) −52491.6 38137.4i −0.108361 0.0787286i
\(697\) 342884. 249120.i 0.705801 0.512794i
\(698\) −105813. + 325660.i −0.217185 + 0.668426i
\(699\) 625024. + 203083.i 1.27921 + 0.415641i
\(700\) −23771.4 32718.5i −0.0485130 0.0667725i
\(701\) 298000. 410162.i 0.606429 0.834679i −0.389848 0.920879i \(-0.627473\pi\)
0.996278 + 0.0862005i \(0.0274726\pi\)
\(702\) −222341. 684295.i −0.451175 1.38857i
\(703\) 228525.i 0.462405i
\(704\) −45402.8 + 42150.2i −0.0916088 + 0.0850461i
\(705\) −1.15593e6 −2.32570
\(706\) −459716. + 149371.i −0.922317 + 0.299679i
\(707\) −440647. 320149.i −0.881560 0.640491i
\(708\) −461304. + 335157.i −0.920281 + 0.668623i
\(709\) 197648. 608297.i 0.393187 1.21010i −0.537178 0.843469i \(-0.680510\pi\)
0.930365 0.366636i \(-0.119490\pi\)
\(710\) −314954. 102335.i −0.624784 0.203005i
\(711\) −135352. 186296.i −0.267748 0.368523i
\(712\) −183897. + 253112.i −0.362756 + 0.499291i
\(713\) −39472.9 121485.i −0.0776461 0.238970i
\(714\) 678312.i 1.33056i
\(715\) −466618. + 216324.i −0.912744 + 0.423148i
\(716\) −98085.2 −0.191328
\(717\) 1.19047e6 386807.i 2.31569 0.752412i
\(718\) −336830. 244721.i −0.653374 0.474704i
\(719\) −44104.7 + 32043.9i −0.0853153 + 0.0619852i −0.629625 0.776899i \(-0.716792\pi\)
0.544310 + 0.838884i \(0.316792\pi\)
\(720\) 97280.6 299399.i 0.187655 0.577544i
\(721\) 105409. + 34249.3i 0.202771 + 0.0658842i
\(722\) 197691. + 272098.i 0.379239 + 0.521977i
\(723\) −773195. + 1.06421e6i −1.47915 + 2.03588i
\(724\) 64416.9 + 198255.i 0.122892 + 0.378222i
\(725\) 19706.6i 0.0374917i
\(726\) 570317. 352853.i 1.08204 0.669454i
\(727\) −671062. −1.26968 −0.634839 0.772644i \(-0.718934\pi\)
−0.634839 + 0.772644i \(0.718934\pi\)
\(728\) 153115. 49750.2i 0.288905 0.0938711i
\(729\) 19846.8 + 14419.6i 0.0373453 + 0.0271330i
\(730\) 117453. 85334.5i 0.220403 0.160132i
\(731\) −235513. + 724834.i −0.440737 + 1.35645i
\(732\) 585364. + 190196.i 1.09246 + 0.354960i
\(733\) 518514. + 713673.i 0.965056 + 1.32829i 0.944505 + 0.328497i \(0.106542\pi\)
0.0205511 + 0.999789i \(0.493458\pi\)
\(734\) 150117. 206618.i 0.278636 0.383509i
\(735\) 45893.6 + 141246.i 0.0849527 + 0.261457i
\(736\) 84715.4i 0.156389i
\(737\) 60269.9 + 130004.i 0.110960 + 0.239343i
\(738\) 666530. 1.22379
\(739\) −83308.5 + 27068.6i −0.152546 + 0.0495652i −0.384295 0.923211i \(-0.625555\pi\)
0.231749 + 0.972776i \(0.425555\pi\)
\(740\) 375727. + 272982.i 0.686134 + 0.498505i
\(741\) 219228. 159278.i 0.399263 0.290081i
\(742\) −64734.6 + 199233.i −0.117579 + 0.361870i
\(743\) 981482. + 318903.i 1.77789 + 0.577671i 0.998788 0.0492263i \(-0.0156756\pi\)
0.779102 + 0.626898i \(0.215676\pi\)
\(744\) −58791.0 80918.8i −0.106210 0.146185i
\(745\) 167538. 230597.i 0.301858 0.415471i
\(746\) 197368. + 607437.i 0.354650 + 1.09150i
\(747\) 420033.i 0.752735i
\(748\) −214720. 231289.i −0.383768 0.413382i
\(749\) −595164. −1.06090
\(750\) −607249. + 197307.i −1.07955 + 0.350768i
\(751\) −523567. 380394.i −0.928309 0.674456i 0.0172688 0.999851i \(-0.494503\pi\)
−0.945578 + 0.325395i \(0.894503\pi\)
\(752\) 136196. 98952.3i 0.240840 0.174981i
\(753\) −348656. + 1.07305e6i −0.614904 + 1.89248i
\(754\) 74609.4 + 24242.1i 0.131235 + 0.0426410i
\(755\) −354676. 488169.i −0.622211 0.856400i
\(756\) 346842. 477386.i 0.606859 0.835269i
\(757\) 333021. + 1.02493e6i 0.581140 + 1.78856i 0.614249 + 0.789112i \(0.289459\pi\)
−0.0331096 + 0.999452i \(0.510541\pi\)
\(758\) 628547.i 1.09395i
\(759\) 176988. 899825.i 0.307228 1.56198i
\(760\) 65584.1 0.113546
\(761\) 129907. 42209.4i 0.224318 0.0728854i −0.194702 0.980863i \(-0.562374\pi\)
0.419020 + 0.907977i \(0.362374\pi\)
\(762\) −513268. 372911.i −0.883963 0.642237i
\(763\) −34335.2 + 24946.0i −0.0589780 + 0.0428500i
\(764\) 29411.7 90519.9i 0.0503887 0.155081i
\(765\) 1.52519e6 + 495563.i 2.60615 + 0.846790i
\(766\) −135293. 186215.i −0.230578 0.317364i
\(767\) 405231. 557753.i 0.688830 0.948094i
\(768\) 20498.4 + 63087.6i 0.0347534 + 0.106960i
\(769\) 24012.2i 0.0406050i 0.999794 + 0.0203025i \(0.00646292\pi\)
−0.999794 + 0.0203025i \(0.993537\pi\)
\(770\) −368463. 205316.i −0.621458 0.346291i
\(771\) −1.11102e6 −1.86902
\(772\) −141602. + 46009.4i −0.237594 + 0.0771990i
\(773\) 61225.6 + 44483.0i 0.102465 + 0.0744449i 0.637838 0.770171i \(-0.279829\pi\)
−0.535373 + 0.844616i \(0.679829\pi\)
\(774\) −969659. + 704499.i −1.61859 + 1.17598i
\(775\) 9387.57 28892.0i 0.0156297 0.0481032i
\(776\) 40951.8 + 13306.0i 0.0680063 + 0.0220966i
\(777\) 925013. + 1.27317e6i 1.53217 + 2.10885i
\(778\) −303821. + 418173.i −0.501947 + 0.690871i
\(779\) 42909.8 + 132063.i 0.0707101 + 0.217623i
\(780\) 550704.i 0.905168i
\(781\) −518348. + 62474.2i −0.849806 + 0.102423i
\(782\) −431554. −0.705702
\(783\) 273460. 88852.6i 0.446037 0.144926i
\(784\) −17498.5 12713.4i −0.0284688 0.0206838i
\(785\) 160806. 116832.i 0.260953 0.189594i
\(786\) 328825. 1.01202e6i 0.532256 1.63811i
\(787\) −469650. 152599.i −0.758272 0.246378i −0.0957352 0.995407i \(-0.530520\pi\)
−0.662537 + 0.749029i \(0.730520\pi\)
\(788\) −240113. 330487.i −0.386691 0.532234i
\(789\) 277706. 382230.i 0.446100 0.614004i
\(790\) 30127.6 + 92723.1i 0.0482736 + 0.148571i
\(791\) 314459.i 0.502587i
\(792\) −59388.8 492749.i −0.0946791 0.785552i
\(793\) −744175. −1.18339
\(794\) 734141. 238537.i 1.16450 0.378368i
\(795\) −579720. 421191.i −0.917242 0.666415i
\(796\) −212377. + 154301.i −0.335182 + 0.243524i
\(797\) 46535.4 143221.i 0.0732599 0.225471i −0.907721 0.419574i \(-0.862180\pi\)
0.980981 + 0.194103i \(0.0621796\pi\)
\(798\) 211358. + 68674.5i 0.331905 + 0.107842i
\(799\) 504079. + 693805.i 0.789596 + 1.08679i
\(800\) −11842.3 + 16299.5i −0.0185036 + 0.0254680i
\(801\) −774533. 2.38377e6i −1.20719 3.71534i
\(802\) 740514.i 1.15129i
\(803\) 111411. 199941.i 0.172782 0.310077i
\(804\) 153431. 0.237357
\(805\) −548561. + 178238.i −0.846512 + 0.275048i
\(806\) 97837.4 + 71083.0i 0.150603 + 0.109420i
\(807\) 111172. 80770.9i 0.170705 0.124025i
\(808\) −83848.7 + 258060.i −0.128432 + 0.395273i
\(809\) −423444. 137585.i −0.646992 0.210220i −0.0329044 0.999459i \(-0.510476\pi\)
−0.614087 + 0.789238i \(0.710476\pi\)
\(810\) 524029. + 721264.i 0.798703 + 1.09932i
\(811\) 398266. 548166.i 0.605524 0.833432i −0.390676 0.920528i \(-0.627759\pi\)
0.996200 + 0.0870964i \(0.0277588\pi\)
\(812\) 19881.3 + 61188.4i 0.0301532 + 0.0928020i
\(813\) 1.29349e6i 1.95695i
\(814\) 718431. + 141309.i 1.08427 + 0.213266i
\(815\) 1.15195e6 1.73428
\(816\) −321378. + 104422.i −0.482655 + 0.156824i
\(817\) −202010. 146769.i −0.302642 0.219882i
\(818\) 492164. 357578.i 0.735535 0.534398i
\(819\) −398562. + 1.22665e6i −0.594194 + 1.82874i
\(820\) −268387. 87204.2i −0.399148 0.129691i
\(821\) 513481. + 706746.i 0.761795 + 1.04852i 0.997063 + 0.0765900i \(0.0244033\pi\)
−0.235268 + 0.971931i \(0.575597\pi\)
\(822\) −24915.0 + 34292.6i −0.0368737 + 0.0507524i
\(823\) −38380.5 118123.i −0.0566645 0.174395i 0.918718 0.394913i \(-0.129225\pi\)
−0.975383 + 0.220518i \(0.929225\pi\)
\(824\) 55214.2i 0.0813198i
\(825\) 159839. 148388.i 0.234841 0.218018i
\(826\) 565405. 0.828705
\(827\) −69119.1 + 22458.1i −0.101062 + 0.0328370i −0.359111 0.933295i \(-0.616920\pi\)
0.258050 + 0.966132i \(0.416920\pi\)
\(828\) −549062. 398917.i −0.800868 0.581865i
\(829\) 295399. 214620.i 0.429834 0.312292i −0.351749 0.936094i \(-0.614413\pi\)
0.781582 + 0.623802i \(0.214413\pi\)
\(830\) 54954.2 169132.i 0.0797709 0.245510i
\(831\) −749238. 243442.i −1.08497 0.352528i
\(832\) −47142.4 64886.0i −0.0681029 0.0937355i
\(833\) 64764.3 89140.4i 0.0933352 0.128465i
\(834\) 496124. + 1.52691e6i 0.713277 + 2.19524i
\(835\) 387753.i 0.556138i
\(836\) 93807.3 43489.1i 0.134222 0.0622254i
\(837\) 443249. 0.632698
\(838\) 16687.2 5421.98i 0.0237626 0.00772094i
\(839\) 43362.3 + 31504.6i 0.0616011 + 0.0447558i 0.618160 0.786053i \(-0.287879\pi\)
−0.556559 + 0.830808i \(0.687879\pi\)
\(840\) −365386. + 265468.i −0.517837 + 0.376231i
\(841\) 208874. 642849.i 0.295320 0.908901i
\(842\) −645437. 209715.i −0.910394 0.295805i
\(843\) −60800.5 83684.7i −0.0855562 0.117758i
\(844\) 306182. 421423.i 0.429828 0.591607i
\(845\) 33729.8 + 103810.i 0.0472390 + 0.145387i
\(846\) 1.34868e6i 1.88438i
\(847\) −663172. 49341.4i −0.924398 0.0687772i
\(848\) 104360. 0.145125
\(849\) −1.95690e6 + 635834.i −2.71489 + 0.882121i
\(850\) −83032.3 60326.5i −0.114924 0.0834969i
\(851\) 810014. 588509.i 1.11849 0.812633i
\(852\) −172750. + 531670.i −0.237979 + 0.732425i
\(853\) 290734. + 94465.3i 0.399575 + 0.129830i 0.501909 0.864920i \(-0.332631\pi\)
−0.102334 + 0.994750i \(0.532631\pi\)
\(854\) −358731. 493751.i −0.491874 0.677006i
\(855\) −308829. + 425067.i −0.422461 + 0.581468i
\(856\) 91622.1 + 281984.i 0.125041 + 0.384837i
\(857\) 344594.i 0.469187i 0.972094 + 0.234594i \(0.0753759\pi\)
−0.972094 + 0.234594i \(0.924624\pi\)
\(858\) 365175. + 787693.i 0.496051 + 1.07000i
\(859\) −267027. −0.361884 −0.180942 0.983494i \(-0.557915\pi\)
−0.180942 + 0.983494i \(0.557915\pi\)
\(860\) 482618. 156812.i 0.652539 0.212023i
\(861\) −773619. 562067.i −1.04357 0.758197i
\(862\) 387999. 281898.i 0.522175 0.379382i
\(863\) 395026. 1.21577e6i 0.530401 1.63241i −0.222981 0.974823i \(-0.571579\pi\)
0.753382 0.657583i \(-0.228421\pi\)
\(864\) −279576. 90839.7i −0.374518 0.121688i
\(865\) −451412. 621315.i −0.603310 0.830385i
\(866\) 341458. 469977.i 0.455305 0.626673i
\(867\) −113963. 350741.i −0.151609 0.466604i
\(868\) 99179.7i 0.131639i
\(869\) 104578. + 112648.i 0.138484 + 0.149170i
\(870\) −220074. −0.290757
\(871\) −176431. + 57326.0i −0.232562 + 0.0755640i
\(872\) 17104.9 + 12427.4i 0.0224951 + 0.0163436i
\(873\) −279078. + 202762.i −0.366182 + 0.266047i
\(874\) 43691.9 134470.i 0.0571976 0.176036i
\(875\) 602140. + 195647.i 0.786469 + 0.255539i
\(876\) −144052. 198271.i −0.187721 0.258375i
\(877\) −72068.5 + 99193.8i −0.0937014 + 0.128969i −0.853294 0.521431i \(-0.825399\pi\)
0.759592 + 0.650400i \(0.225399\pi\)
\(878\) −135825. 418026.i −0.176194 0.542269i
\(879\) 1.44203e6i 1.86637i
\(880\) −40554.2 + 206182.i −0.0523685 + 0.266247i
\(881\) 870902. 1.12206 0.561032 0.827794i \(-0.310405\pi\)
0.561032 + 0.827794i \(0.310405\pi\)
\(882\) 164798. 53546.2i 0.211843 0.0688321i
\(883\) 625562. + 454497.i 0.802322 + 0.582921i 0.911594 0.411091i \(-0.134852\pi\)
−0.109272 + 0.994012i \(0.534852\pi\)
\(884\) 330540. 240151.i 0.422979 0.307312i
\(885\) −597652. + 1.83938e6i −0.763066 + 2.34848i
\(886\) −393157. 127744.i −0.500839 0.162733i
\(887\) −213314. 293601.i −0.271127 0.373174i 0.651643 0.758526i \(-0.274080\pi\)
−0.922770 + 0.385352i \(0.874080\pi\)
\(888\) 460818. 634261.i 0.584391 0.804345i
\(889\) 194401. + 598306.i 0.245978 + 0.757042i
\(890\) 1.06119e6i 1.33972i
\(891\) 1.22781e6 + 684165.i 1.54659 + 0.861798i
\(892\) −150774. −0.189495
\(893\) −267221. + 86825.2i −0.335094 + 0.108879i
\(894\) −389269. 282820.i −0.487051 0.353863i
\(895\) −269152. + 195551.i −0.336010 + 0.244126i
\(896\) 20326.0 62556.9i 0.0253183 0.0779218i
\(897\) 1.12913e6 + 366877.i 1.40333 + 0.455970i
\(898\) −10109.8 13914.9i −0.0125369 0.0172555i
\(899\) −28406.4 + 39098.1i −0.0351477 + 0.0483767i
\(900\) −49877.1 153506.i −0.0615767 0.189513i
\(901\) 531628.i 0.654875i
\(902\) −441709. + 53237.3i −0.542904 + 0.0654339i
\(903\) 1.71954e6 2.10880
\(904\) −148988. + 48409.2i −0.182312 + 0.0592367i
\(905\) 572021. + 415598.i 0.698417 + 0.507430i
\(906\) −824074. + 598725.i −1.00395 + 0.729409i
\(907\) −333162. + 1.02537e6i −0.404986 + 1.24642i 0.515920 + 0.856637i \(0.327450\pi\)
−0.920907 + 0.389783i \(0.872550\pi\)
\(908\) −458753. 149058.i −0.556426 0.180794i
\(909\) −1.27772e6 1.75863e6i −1.54635 2.12836i
\(910\) 320973. 441781.i 0.387601 0.533487i
\(911\) −173639. 534405.i −0.209223 0.643922i −0.999513 0.0311899i \(-0.990070\pi\)
0.790290 0.612732i \(-0.209930\pi\)
\(912\) 110712.i 0.133108i
\(913\) −33549.0 278356.i −0.0402474 0.333932i
\(914\) −968051. −1.15879
\(915\) 1.98547e6 645118.i 2.37149 0.770543i
\(916\) 535198. + 388844.i 0.637857 + 0.463430i
\(917\) −853633. + 620201.i −1.01516 + 0.737554i
\(918\) 462752. 1.42420e6i 0.549115 1.69000i
\(919\) 293285. + 95294.1i 0.347263 + 0.112833i 0.477455 0.878656i \(-0.341559\pi\)
−0.130192 + 0.991489i \(0.541559\pi\)
\(920\) 168896. + 232465.i 0.199546 + 0.274651i
\(921\) −844924. + 1.16294e6i −0.996090 + 1.37100i
\(922\) −345156. 1.06228e6i −0.406026 1.24962i
\(923\) 675914.i 0.793392i
\(924\) −346592. + 621998.i −0.405951 + 0.728526i
\(925\) 238116. 0.278295
\(926\) 234810. 76294.4i 0.273838 0.0889755i
\(927\) 357857. + 259999.i 0.416438 + 0.302560i
\(928\) 25930.0 18839.2i 0.0301097 0.0218759i
\(929\) −126116. + 388145.i −0.146130 + 0.449742i −0.997155 0.0753841i \(-0.975982\pi\)
0.851025 + 0.525126i \(0.175982\pi\)
\(930\) −322653. 104836.i −0.373052 0.121212i
\(931\) 21218.7 + 29205.1i 0.0244805 + 0.0336945i
\(932\) −190819. + 262639.i −0.219679 + 0.302363i
\(933\) −645274. 1.98595e6i −0.741278 2.28142i
\(934\) 295446.i 0.338676i
\(935\) −1.05032e6 206589.i −1.20143 0.236311i
\(936\) 642532. 0.733404
\(937\) −1.04830e6 + 340614.i −1.19401 + 0.387957i −0.837553 0.546356i \(-0.816015\pi\)
−0.356455 + 0.934313i \(0.616015\pi\)
\(938\) −123084. 89425.9i −0.139893 0.101638i
\(939\) 1.23086e6 894270.i 1.39597 1.01423i
\(940\) 176452. 543064.i 0.199697 0.614604i
\(941\) 1.46503e6 + 476017.i 1.65450 + 0.537580i 0.979709 0.200426i \(-0.0642327\pi\)
0.674793 + 0.738007i \(0.264233\pi\)
\(942\) −197224. 271455.i −0.222258 0.305912i
\(943\) −357597. + 492190.i −0.402134 + 0.553489i
\(944\) −87040.9 267884.i −0.0976741 0.300610i
\(945\) 2.00147e6i 2.24123i
\(946\) 586323. 544320.i 0.655171 0.608236i
\(947\) −1.56708e6 −1.74739 −0.873697 0.486470i \(-0.838284\pi\)
−0.873697 + 0.486470i \(0.838284\pi\)
\(948\) 156525. 50858.1i 0.174168 0.0565905i
\(949\) 239726. + 174171.i 0.266184 + 0.193394i
\(950\) 27203.9 19764.8i 0.0301428 0.0219000i
\(951\) 18818.8 57918.2i 0.0208080 0.0640404i
\(952\) 318675. + 103544.i 0.351620 + 0.114248i
\(953\) 25772.9 + 35473.3i 0.0283777 + 0.0390585i 0.822970 0.568085i \(-0.192315\pi\)
−0.794592 + 0.607143i \(0.792315\pi\)
\(954\) −491423. + 676386.i −0.539957 + 0.743187i
\(955\) −99760.2 307030.i −0.109383 0.336647i
\(956\) 618335.i 0.676563i
\(957\) −314780. + 145932.i −0.343703 + 0.159341i
\(958\) −79072.3 −0.0861576
\(959\) 39974.2 12988.4i 0.0434653 0.0141227i
\(960\) 182026. + 132249.i 0.197511 + 0.143500i
\(961\) 686872. 499042.i 0.743754 0.540369i
\(962\) −292919. + 901513.i −0.316518 + 0.974141i
\(963\) −2.25905e6 734010.i −2.43598 0.791497i
\(964\) −381945. 525702.i −0.411005 0.565699i
\(965\) −296838. + 408563.i −0.318761 + 0.438737i
\(966\) 300882. + 926020.i 0.322435 + 0.992353i
\(967\) 1.00897e6i 1.07901i 0.841982 + 0.539506i \(0.181389\pi\)
−0.841982 + 0.539506i \(0.818611\pi\)
\(968\) 78713.9 + 321801.i 0.0840042 + 0.343429i
\(969\) 563984. 0.600647
\(970\) 138902. 45132.1i 0.147627 0.0479670i
\(971\) −265599. 192969.i −0.281700 0.204667i 0.437958 0.898995i \(-0.355702\pi\)
−0.719659 + 0.694328i \(0.755702\pi\)
\(972\) 366223. 266077.i 0.387626 0.281627i
\(973\) 491950. 1.51407e6i 0.519631 1.59926i
\(974\) 756407. + 245772.i 0.797329 + 0.259068i
\(975\) 165963. + 228429.i 0.174583 + 0.240293i
\(976\) −178711. + 245974.i −0.187608 + 0.258220i
\(977\) 312850. + 962853.i 0.327753 + 1.00872i 0.970182 + 0.242376i \(0.0779266\pi\)
−0.642429 + 0.766345i \(0.722073\pi\)
\(978\) 1.94460e6i 2.03307i
\(979\) 703680. + 1.51786e6i 0.734192 + 1.58368i
\(980\) −73363.7 −0.0763887
\(981\) −161091. + 52341.6i −0.167391 + 0.0543887i
\(982\) 841678. + 611515.i 0.872817 + 0.634139i
\(983\) −842719. + 612271.i −0.872119 + 0.633632i −0.931155 0.364624i \(-0.881198\pi\)
0.0590354 + 0.998256i \(0.481198\pi\)
\(984\) −147209. + 453061.i −0.152035 + 0.467915i
\(985\) −1.31777e6 428171.i −1.35821 0.441311i
\(986\) 95970.0 + 132091.i 0.0987146 + 0.135869i
\(987\) 1.13731e6 1.56537e6i 1.16746 1.60688i
\(988\) 41364.9 + 127308.i 0.0423758 + 0.130419i
\(989\) 1.09400e6i 1.11847i
\(990\) −1.14535e6 1.23373e6i −1.16861 1.25878i
\(991\) −1.89936e6 −1.93401 −0.967006 0.254755i \(-0.918005\pi\)
−0.967006 + 0.254755i \(0.918005\pi\)
\(992\) 46990.5 15268.1i 0.0477515 0.0155154i
\(993\) 1.29382e6 + 940014.i 1.31212 + 0.953314i
\(994\) 448461. 325826.i 0.453891 0.329771i
\(995\) −275150. + 846824.i −0.277922 + 0.855356i
\(996\) −285510. 92767.7i −0.287807 0.0935143i
\(997\) 353820. + 486992.i 0.355953 + 0.489927i 0.949016 0.315229i \(-0.102081\pi\)
−0.593063 + 0.805156i \(0.702081\pi\)
\(998\) −245240. + 337544.i −0.246224 + 0.338898i
\(999\) 1.07361e6 + 3.30425e6i 1.07576 + 3.31086i
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 22.5.d.a.17.3 yes 16
3.2 odd 2 198.5.j.a.127.1 16
4.3 odd 2 176.5.n.c.17.4 16
11.2 odd 10 inner 22.5.d.a.13.3 16
11.3 even 5 242.5.b.e.241.8 16
11.8 odd 10 242.5.b.e.241.16 16
33.2 even 10 198.5.j.a.145.1 16
44.35 even 10 176.5.n.c.145.4 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
22.5.d.a.13.3 16 11.2 odd 10 inner
22.5.d.a.17.3 yes 16 1.1 even 1 trivial
176.5.n.c.17.4 16 4.3 odd 2
176.5.n.c.145.4 16 44.35 even 10
198.5.j.a.127.1 16 3.2 odd 2
198.5.j.a.145.1 16 33.2 even 10
242.5.b.e.241.8 16 11.3 even 5
242.5.b.e.241.16 16 11.8 odd 10