Properties

Label 11.4.c.a.4.1
Level $11$
Weight $4$
Character 11.4
Analytic conductor $0.649$
Analytic rank $0$
Dimension $8$
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] = [11,4,Mod(3,11)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(11, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([8]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("11.3");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 11 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 11.c (of order \(5\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(0.649021010063\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{5})\)
Coefficient field: 8.0.29283765625.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - x^{7} + 10x^{6} - 19x^{5} + 109x^{4} + 171x^{3} + 810x^{2} + 729x + 6561 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 4.1
Root \(-2.05602 - 1.49379i\) of defining polynomial
Character \(\chi\) \(=\) 11.4
Dual form 11.4.c.a.3.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-4.17405 - 3.03263i) q^{2} +(1.40336 - 4.31911i) q^{3} +(5.75376 + 17.7083i) q^{4} +(6.98613 - 5.07572i) q^{5} +(-18.9560 + 13.7723i) q^{6} +(0.513765 + 1.58121i) q^{7} +(16.9313 - 52.1091i) q^{8} +(5.15818 + 3.74763i) q^{9} +O(q^{10})\) \(q+(-4.17405 - 3.03263i) q^{2} +(1.40336 - 4.31911i) q^{3} +(5.75376 + 17.7083i) q^{4} +(6.98613 - 5.07572i) q^{5} +(-18.9560 + 13.7723i) q^{6} +(0.513765 + 1.58121i) q^{7} +(16.9313 - 52.1091i) q^{8} +(5.15818 + 3.74763i) q^{9} -44.5532 q^{10} +(-26.2401 + 25.3467i) q^{11} +84.5585 q^{12} +(23.1570 + 16.8245i) q^{13} +(2.65073 - 8.15810i) q^{14} +(-12.1185 - 37.2969i) q^{15} +(-108.191 + 78.6055i) q^{16} +(-6.36020 + 4.62095i) q^{17} +(-10.1653 - 31.2857i) q^{18} +(14.8350 - 45.6575i) q^{19} +(130.079 + 94.5077i) q^{20} +7.55040 q^{21} +(186.395 - 26.2219i) q^{22} -153.265 q^{23} +(-201.304 - 146.256i) q^{24} +(-15.5841 + 47.9628i) q^{25} +(-45.6359 - 140.453i) q^{26} +(122.625 - 89.0921i) q^{27} +(-25.0443 + 18.1958i) q^{28} +(74.9153 + 230.566i) q^{29} +(-62.5244 + 192.430i) q^{30} +(-134.251 - 97.5391i) q^{31} +251.651 q^{32} +(72.6507 + 148.905i) q^{33} +40.5614 q^{34} +(11.6150 + 8.43878i) q^{35} +(-36.6852 + 112.905i) q^{36} +(-21.2522 - 65.4077i) q^{37} +(-200.384 + 145.588i) q^{38} +(105.165 - 76.4065i) q^{39} +(-146.207 - 449.979i) q^{40} +(95.0373 - 292.495i) q^{41} +(-31.5158 - 22.8976i) q^{42} -52.9746 q^{43} +(-599.825 - 318.828i) q^{44} +55.0576 q^{45} +(639.737 + 464.796i) q^{46} +(-16.8521 + 51.8654i) q^{47} +(187.674 + 577.602i) q^{48} +(275.257 - 199.986i) q^{49} +(210.502 - 152.939i) q^{50} +(11.0327 + 33.9553i) q^{51} +(-164.693 + 506.874i) q^{52} +(-202.450 - 147.088i) q^{53} -782.025 q^{54} +(-54.6643 + 310.263i) q^{55} +91.0939 q^{56} +(-176.381 - 128.148i) q^{57} +(386.519 - 1189.58i) q^{58} +(117.153 + 360.561i) q^{59} +(590.737 - 429.195i) q^{60} +(-565.131 + 410.592i) q^{61} +(264.571 + 814.267i) q^{62} +(-3.27569 + 10.0815i) q^{63} +(-184.877 - 134.321i) q^{64} +247.174 q^{65} +(148.325 - 841.859i) q^{66} -278.021 q^{67} +(-118.424 - 86.0402i) q^{68} +(-215.087 + 661.969i) q^{69} +(-22.8899 - 70.4479i) q^{70} +(125.156 - 90.9311i) q^{71} +(282.620 - 205.336i) q^{72} +(-293.936 - 904.642i) q^{73} +(-109.649 + 337.465i) q^{74} +(185.287 + 134.619i) q^{75} +893.872 q^{76} +(-53.5596 - 28.4688i) q^{77} -670.675 q^{78} +(-1.79641 - 1.30517i) q^{79} +(-356.858 + 1098.30i) q^{80} +(-159.515 - 490.936i) q^{81} +(-1283.72 + 932.676i) q^{82} +(614.553 - 446.499i) q^{83} +(43.4432 + 133.704i) q^{84} +(-20.9785 + 64.5651i) q^{85} +(221.119 + 160.652i) q^{86} +1100.97 q^{87} +(876.514 + 1796.50i) q^{88} +1157.64 q^{89} +(-229.813 - 166.969i) q^{90} +(-14.7058 + 45.2598i) q^{91} +(-881.852 - 2714.06i) q^{92} +(-609.685 + 442.962i) q^{93} +(227.630 - 165.383i) q^{94} +(-128.105 - 394.267i) q^{95} +(353.159 - 1086.91i) q^{96} +(-598.393 - 434.758i) q^{97} -1755.42 q^{98} +(-230.341 + 32.4042i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 7 q^{2} - 3 q^{3} + 3 q^{4} - 7 q^{5} - 29 q^{6} - 35 q^{7} + 47 q^{8} + 31 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 7 q^{2} - 3 q^{3} + 3 q^{4} - 7 q^{5} - 29 q^{6} - 35 q^{7} + 47 q^{8} + 31 q^{9} + 40 q^{10} + 67 q^{11} + 190 q^{12} - 65 q^{13} - 196 q^{14} - 121 q^{15} - 377 q^{16} - 31 q^{17} - 102 q^{18} + 148 q^{19} + 342 q^{20} + 334 q^{21} + 647 q^{22} - 12 q^{23} - 447 q^{24} - 201 q^{25} - 140 q^{26} + 72 q^{27} - 42 q^{28} - 199 q^{29} - 114 q^{30} - 361 q^{31} + 324 q^{32} - 232 q^{33} - 298 q^{34} + 237 q^{35} + 120 q^{36} + 81 q^{37} - 52 q^{38} + 365 q^{39} + 532 q^{40} - 31 q^{41} + 170 q^{42} - 650 q^{43} - 1208 q^{44} + 452 q^{45} + 1204 q^{46} + 857 q^{47} + 644 q^{48} + 1375 q^{49} - 147 q^{50} - 246 q^{51} - 590 q^{52} - 1493 q^{53} - 3100 q^{54} - 1583 q^{55} - 1560 q^{56} + 102 q^{57} + 1392 q^{58} + 676 q^{59} + 1068 q^{60} - 525 q^{61} + 2456 q^{62} - 68 q^{63} + 471 q^{64} + 1790 q^{65} + 1014 q^{66} + 86 q^{67} + 710 q^{68} - 42 q^{69} - 144 q^{70} + 1143 q^{71} + 919 q^{72} - 2155 q^{73} - 1476 q^{74} - 160 q^{75} - 242 q^{76} - 2015 q^{77} - 1340 q^{78} - 861 q^{79} - 1916 q^{80} - 26 q^{81} - 3497 q^{82} + 52 q^{83} - 84 q^{84} + 2383 q^{85} + 1061 q^{86} + 2310 q^{87} + 4543 q^{88} + 3782 q^{89} - 1682 q^{90} + 135 q^{91} - 2450 q^{92} - 2077 q^{93} + 702 q^{94} - 1317 q^{95} + 1252 q^{96} - 1344 q^{97} + 2740 q^{98} + 2099 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/11\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{1}{5}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −4.17405 3.03263i −1.47575 1.07220i −0.978895 0.204363i \(-0.934488\pi\)
−0.496856 0.867833i \(-0.665512\pi\)
\(3\) 1.40336 4.31911i 0.270078 0.831213i −0.720402 0.693556i \(-0.756043\pi\)
0.990480 0.137657i \(-0.0439571\pi\)
\(4\) 5.75376 + 17.7083i 0.719220 + 2.21353i
\(5\) 6.98613 5.07572i 0.624858 0.453986i −0.229757 0.973248i \(-0.573793\pi\)
0.854615 + 0.519262i \(0.173793\pi\)
\(6\) −18.9560 + 13.7723i −1.28979 + 0.937088i
\(7\) 0.513765 + 1.58121i 0.0277407 + 0.0853771i 0.963968 0.266017i \(-0.0857077\pi\)
−0.936228 + 0.351394i \(0.885708\pi\)
\(8\) 16.9313 52.1091i 0.748264 2.30292i
\(9\) 5.15818 + 3.74763i 0.191044 + 0.138801i
\(10\) −44.5532 −1.40890
\(11\) −26.2401 + 25.3467i −0.719246 + 0.694756i
\(12\) 84.5585 2.03416
\(13\) 23.1570 + 16.8245i 0.494045 + 0.358945i 0.806738 0.590910i \(-0.201231\pi\)
−0.312693 + 0.949854i \(0.601231\pi\)
\(14\) 2.65073 8.15810i 0.0506026 0.155739i
\(15\) −12.1185 37.2969i −0.208599 0.642002i
\(16\) −108.191 + 78.6055i −1.69049 + 1.22821i
\(17\) −6.36020 + 4.62095i −0.0907397 + 0.0659262i −0.632230 0.774781i \(-0.717860\pi\)
0.541490 + 0.840707i \(0.317860\pi\)
\(18\) −10.1653 31.2857i −0.133111 0.409672i
\(19\) 14.8350 45.6575i 0.179126 0.551292i −0.820672 0.571399i \(-0.806401\pi\)
0.999798 + 0.0201074i \(0.00640081\pi\)
\(20\) 130.079 + 94.5077i 1.45432 + 1.05663i
\(21\) 7.55040 0.0784587
\(22\) 186.395 26.2219i 1.80634 0.254115i
\(23\) −153.265 −1.38948 −0.694739 0.719262i \(-0.744480\pi\)
−0.694739 + 0.719262i \(0.744480\pi\)
\(24\) −201.304 146.256i −1.71213 1.24393i
\(25\) −15.5841 + 47.9628i −0.124673 + 0.383703i
\(26\) −45.6359 140.453i −0.344228 1.05943i
\(27\) 122.625 89.0921i 0.874042 0.635029i
\(28\) −25.0443 + 18.1958i −0.169033 + 0.122810i
\(29\) 74.9153 + 230.566i 0.479704 + 1.47638i 0.839507 + 0.543350i \(0.182844\pi\)
−0.359802 + 0.933029i \(0.617156\pi\)
\(30\) −62.5244 + 192.430i −0.380511 + 1.17109i
\(31\) −134.251 97.5391i −0.777813 0.565114i 0.126509 0.991965i \(-0.459623\pi\)
−0.904322 + 0.426851i \(0.859623\pi\)
\(32\) 251.651 1.39019
\(33\) 72.6507 + 148.905i 0.383238 + 0.785484i
\(34\) 40.5614 0.204595
\(35\) 11.6150 + 8.43878i 0.0560940 + 0.0407547i
\(36\) −36.6852 + 112.905i −0.169839 + 0.522710i
\(37\) −21.2522 65.4077i −0.0944283 0.290620i 0.892676 0.450699i \(-0.148825\pi\)
−0.987104 + 0.160079i \(0.948825\pi\)
\(38\) −200.384 + 145.588i −0.855438 + 0.621512i
\(39\) 105.165 76.4065i 0.431790 0.313714i
\(40\) −146.207 449.979i −0.577934 1.77870i
\(41\) 95.0373 292.495i 0.362008 1.11415i −0.589825 0.807531i \(-0.700803\pi\)
0.951833 0.306616i \(-0.0991966\pi\)
\(42\) −31.5158 22.8976i −0.115786 0.0841231i
\(43\) −52.9746 −0.187873 −0.0939367 0.995578i \(-0.529945\pi\)
−0.0939367 + 0.995578i \(0.529945\pi\)
\(44\) −599.825 318.828i −2.05516 1.09239i
\(45\) 55.0576 0.182389
\(46\) 639.737 + 464.796i 2.05052 + 1.48979i
\(47\) −16.8521 + 51.8654i −0.0523007 + 0.160965i −0.973795 0.227426i \(-0.926969\pi\)
0.921495 + 0.388391i \(0.126969\pi\)
\(48\) 187.674 + 577.602i 0.564343 + 1.73687i
\(49\) 275.257 199.986i 0.802497 0.583048i
\(50\) 210.502 152.939i 0.595390 0.432576i
\(51\) 11.0327 + 33.9553i 0.0302920 + 0.0932292i
\(52\) −164.693 + 506.874i −0.439209 + 1.35174i
\(53\) −202.450 147.088i −0.524691 0.381210i 0.293677 0.955905i \(-0.405121\pi\)
−0.818368 + 0.574694i \(0.805121\pi\)
\(54\) −782.025 −1.97074
\(55\) −54.6643 + 310.263i −0.134017 + 0.760651i
\(56\) 91.0939 0.217374
\(57\) −176.381 128.148i −0.409863 0.297783i
\(58\) 386.519 1189.58i 0.875042 2.69310i
\(59\) 117.153 + 360.561i 0.258509 + 0.795610i 0.993118 + 0.117119i \(0.0373658\pi\)
−0.734609 + 0.678491i \(0.762634\pi\)
\(60\) 590.737 429.195i 1.27106 0.923481i
\(61\) −565.131 + 410.592i −1.18619 + 0.861818i −0.992856 0.119315i \(-0.961930\pi\)
−0.193334 + 0.981133i \(0.561930\pi\)
\(62\) 264.571 + 814.267i 0.541945 + 1.66794i
\(63\) −3.27569 + 10.0815i −0.00655077 + 0.0201612i
\(64\) −184.877 134.321i −0.361088 0.262346i
\(65\) 247.174 0.471664
\(66\) 148.325 841.859i 0.276629 1.57009i
\(67\) −278.021 −0.506949 −0.253475 0.967342i \(-0.581573\pi\)
−0.253475 + 0.967342i \(0.581573\pi\)
\(68\) −118.424 86.0402i −0.211192 0.153440i
\(69\) −215.087 + 661.969i −0.375267 + 1.15495i
\(70\) −22.8899 70.4479i −0.0390838 0.120288i
\(71\) 125.156 90.9311i 0.209201 0.151993i −0.478251 0.878223i \(-0.658729\pi\)
0.687452 + 0.726230i \(0.258729\pi\)
\(72\) 282.620 205.336i 0.462599 0.336098i
\(73\) −293.936 904.642i −0.471268 1.45042i −0.850925 0.525288i \(-0.823958\pi\)
0.379656 0.925128i \(-0.376042\pi\)
\(74\) −109.649 + 337.465i −0.172249 + 0.530129i
\(75\) 185.287 + 134.619i 0.285268 + 0.207259i
\(76\) 893.872 1.34913
\(77\) −53.5596 28.4688i −0.0792686 0.0421341i
\(78\) −670.675 −0.973577
\(79\) −1.79641 1.30517i −0.00255838 0.00185877i 0.586505 0.809945i \(-0.300503\pi\)
−0.589064 + 0.808087i \(0.700503\pi\)
\(80\) −356.858 + 1098.30i −0.498724 + 1.53492i
\(81\) −159.515 490.936i −0.218813 0.673437i
\(82\) −1283.72 + 932.676i −1.72882 + 1.25606i
\(83\) 614.553 446.499i 0.812722 0.590477i −0.101897 0.994795i \(-0.532491\pi\)
0.914618 + 0.404318i \(0.132491\pi\)
\(84\) 43.4432 + 133.704i 0.0564291 + 0.173671i
\(85\) −20.9785 + 64.5651i −0.0267698 + 0.0823891i
\(86\) 221.119 + 160.652i 0.277254 + 0.201437i
\(87\) 1100.97 1.35674
\(88\) 876.514 + 1796.50i 1.06178 + 2.17622i
\(89\) 1157.64 1.37876 0.689382 0.724398i \(-0.257882\pi\)
0.689382 + 0.724398i \(0.257882\pi\)
\(90\) −229.813 166.969i −0.269161 0.195557i
\(91\) −14.7058 + 45.2598i −0.0169405 + 0.0521375i
\(92\) −881.852 2714.06i −0.999341 3.07566i
\(93\) −609.685 + 442.962i −0.679800 + 0.493904i
\(94\) 227.630 165.383i 0.249769 0.181468i
\(95\) −128.105 394.267i −0.138351 0.425800i
\(96\) 353.159 1086.91i 0.375459 1.15554i
\(97\) −598.393 434.758i −0.626368 0.455083i 0.228772 0.973480i \(-0.426529\pi\)
−0.855140 + 0.518397i \(0.826529\pi\)
\(98\) −1755.42 −1.80943
\(99\) −230.341 + 32.4042i −0.233840 + 0.0328964i
\(100\) −939.006 −0.939006
\(101\) −498.530 362.203i −0.491144 0.356837i 0.314480 0.949264i \(-0.398170\pi\)
−0.805624 + 0.592427i \(0.798170\pi\)
\(102\) 56.9225 175.189i 0.0552565 0.170062i
\(103\) 472.029 + 1452.76i 0.451558 + 1.38975i 0.875129 + 0.483889i \(0.160776\pi\)
−0.423572 + 0.905862i \(0.639224\pi\)
\(104\) 1268.79 921.828i 1.19630 0.869160i
\(105\) 52.7481 38.3237i 0.0490256 0.0356192i
\(106\) 398.972 + 1227.91i 0.365581 + 1.12514i
\(107\) −23.0481 + 70.9348i −0.0208238 + 0.0640890i −0.960928 0.276797i \(-0.910727\pi\)
0.940105 + 0.340886i \(0.110727\pi\)
\(108\) 2283.22 + 1658.86i 2.03429 + 1.47800i
\(109\) 583.022 0.512325 0.256162 0.966634i \(-0.417542\pi\)
0.256162 + 0.966634i \(0.417542\pi\)
\(110\) 1169.08 1129.28i 1.01334 0.978840i
\(111\) −312.328 −0.267070
\(112\) −179.876 130.688i −0.151756 0.110258i
\(113\) −56.3647 + 173.473i −0.0469234 + 0.144415i −0.971773 0.235917i \(-0.924191\pi\)
0.924850 + 0.380333i \(0.124191\pi\)
\(114\) 347.597 + 1069.79i 0.285574 + 0.878907i
\(115\) −1070.73 + 777.931i −0.868227 + 0.630804i
\(116\) −3651.87 + 2653.24i −2.92300 + 2.12368i
\(117\) 56.3955 + 173.568i 0.0445621 + 0.137148i
\(118\) 604.442 1860.28i 0.471554 1.45130i
\(119\) −10.5743 7.68270i −0.00814577 0.00591825i
\(120\) −2148.69 −1.63456
\(121\) 46.0904 1330.20i 0.0346284 0.999400i
\(122\) 3604.06 2.67456
\(123\) −1129.95 820.953i −0.828323 0.601812i
\(124\) 954.799 2938.57i 0.691480 2.12816i
\(125\) 468.131 + 1440.76i 0.334968 + 1.03092i
\(126\) 44.2465 32.1470i 0.0312841 0.0227292i
\(127\) 117.331 85.2459i 0.0819798 0.0595618i −0.546040 0.837759i \(-0.683866\pi\)
0.628020 + 0.778197i \(0.283866\pi\)
\(128\) −257.776 793.352i −0.178003 0.547836i
\(129\) −74.3427 + 228.803i −0.0507404 + 0.156163i
\(130\) −1031.72 749.587i −0.696059 0.505716i
\(131\) −2.12942 −0.00142022 −0.000710109 1.00000i \(-0.500226\pi\)
−0.000710109 1.00000i \(0.500226\pi\)
\(132\) −2218.83 + 2143.28i −1.46306 + 1.41325i
\(133\) 79.8156 0.0520368
\(134\) 1160.47 + 843.133i 0.748131 + 0.543549i
\(135\) 404.466 1244.82i 0.257858 0.793606i
\(136\) 133.108 + 409.663i 0.0839256 + 0.258296i
\(137\) 321.914 233.884i 0.200752 0.145855i −0.482868 0.875693i \(-0.660405\pi\)
0.683619 + 0.729839i \(0.260405\pi\)
\(138\) 2905.29 2110.82i 1.79214 1.30206i
\(139\) 80.7202 + 248.431i 0.0492561 + 0.151595i 0.972659 0.232237i \(-0.0746044\pi\)
−0.923403 + 0.383831i \(0.874604\pi\)
\(140\) −82.6062 + 254.236i −0.0498679 + 0.153478i
\(141\) 200.363 + 145.572i 0.119671 + 0.0869460i
\(142\) −798.168 −0.471695
\(143\) −1034.09 + 145.475i −0.604719 + 0.0850713i
\(144\) −852.654 −0.493434
\(145\) 1693.65 + 1230.51i 0.970002 + 0.704748i
\(146\) −1516.54 + 4667.42i −0.859654 + 2.64574i
\(147\) −477.475 1469.52i −0.267901 0.824515i
\(148\) 1035.98 752.680i 0.575383 0.418040i
\(149\) −766.961 + 557.230i −0.421691 + 0.306376i −0.778318 0.627871i \(-0.783927\pi\)
0.356627 + 0.934247i \(0.383927\pi\)
\(150\) −365.148 1123.81i −0.198762 0.611725i
\(151\) 560.925 1726.35i 0.302301 0.930386i −0.678370 0.734721i \(-0.737313\pi\)
0.980671 0.195666i \(-0.0626868\pi\)
\(152\) −2127.99 1546.08i −1.13555 0.825023i
\(153\) −50.1247 −0.0264859
\(154\) 137.225 + 281.257i 0.0718048 + 0.147171i
\(155\) −1432.98 −0.742577
\(156\) 1958.12 + 1422.66i 1.00497 + 0.730152i
\(157\) −285.706 + 879.314i −0.145235 + 0.446986i −0.997041 0.0768703i \(-0.975507\pi\)
0.851806 + 0.523857i \(0.175507\pi\)
\(158\) 3.54023 + 10.8957i 0.00178257 + 0.00548617i
\(159\) −919.402 + 667.985i −0.458574 + 0.333174i
\(160\) 1758.07 1277.31i 0.868672 0.631127i
\(161\) −78.7423 242.344i −0.0385451 0.118630i
\(162\) −823.002 + 2532.94i −0.399143 + 1.22844i
\(163\) 2372.06 + 1723.40i 1.13984 + 0.828143i 0.987097 0.160123i \(-0.0511891\pi\)
0.152744 + 0.988266i \(0.451189\pi\)
\(164\) 5726.40 2.72656
\(165\) 1263.35 + 671.513i 0.596068 + 0.316832i
\(166\) −3919.24 −1.83248
\(167\) −890.503 646.988i −0.412630 0.299793i 0.362036 0.932164i \(-0.382082\pi\)
−0.774666 + 0.632371i \(0.782082\pi\)
\(168\) 127.838 393.445i 0.0587078 0.180684i
\(169\) −425.730 1310.26i −0.193778 0.596387i
\(170\) 283.367 205.878i 0.127843 0.0928833i
\(171\) 247.629 179.913i 0.110741 0.0804579i
\(172\) −304.803 938.088i −0.135122 0.415864i
\(173\) −1115.66 + 3433.65i −0.490301 + 1.50899i 0.333852 + 0.942626i \(0.391651\pi\)
−0.824153 + 0.566367i \(0.808349\pi\)
\(174\) −4595.52 3338.84i −2.00221 1.45469i
\(175\) −83.8457 −0.0362179
\(176\) 846.563 4804.91i 0.362569 2.05786i
\(177\) 1721.71 0.731139
\(178\) −4832.07 3510.70i −2.03471 1.47831i
\(179\) 1060.08 3262.59i 0.442648 1.36233i −0.442395 0.896821i \(-0.645871\pi\)
0.885043 0.465510i \(-0.154129\pi\)
\(180\) 316.788 + 974.974i 0.131178 + 0.403724i
\(181\) 2997.81 2178.04i 1.23108 0.894433i 0.234111 0.972210i \(-0.424782\pi\)
0.996971 + 0.0777766i \(0.0247821\pi\)
\(182\) 198.639 144.320i 0.0809016 0.0587785i
\(183\) 980.307 + 3017.07i 0.395991 + 1.21873i
\(184\) −2594.98 + 7986.51i −1.03970 + 3.19986i
\(185\) −480.462 349.076i −0.190942 0.138727i
\(186\) 3888.20 1.53278
\(187\) 49.7666 282.464i 0.0194615 0.110459i
\(188\) −1015.41 −0.393917
\(189\) 203.873 + 148.123i 0.0784635 + 0.0570070i
\(190\) −660.948 + 2034.19i −0.252370 + 0.776713i
\(191\) −939.172 2890.48i −0.355791 1.09501i −0.955549 0.294831i \(-0.904736\pi\)
0.599758 0.800181i \(-0.295264\pi\)
\(192\) −839.596 + 610.003i −0.315587 + 0.229287i
\(193\) 565.820 411.092i 0.211029 0.153322i −0.477250 0.878768i \(-0.658366\pi\)
0.688279 + 0.725446i \(0.258366\pi\)
\(194\) 1179.27 + 3629.41i 0.436425 + 1.34318i
\(195\) 346.875 1067.57i 0.127386 0.392053i
\(196\) 5125.16 + 3723.65i 1.86777 + 1.35701i
\(197\) −4239.08 −1.53311 −0.766553 0.642181i \(-0.778030\pi\)
−0.766553 + 0.642181i \(0.778030\pi\)
\(198\) 1059.73 + 563.283i 0.380361 + 0.202176i
\(199\) −2020.32 −0.719680 −0.359840 0.933014i \(-0.617169\pi\)
−0.359840 + 0.933014i \(0.617169\pi\)
\(200\) 2235.44 + 1624.14i 0.790348 + 0.574222i
\(201\) −390.164 + 1200.80i −0.136916 + 0.421383i
\(202\) 982.464 + 3023.71i 0.342207 + 1.05321i
\(203\) −326.083 + 236.913i −0.112742 + 0.0819115i
\(204\) −537.809 + 390.741i −0.184579 + 0.134105i
\(205\) −820.678 2525.79i −0.279603 0.860530i
\(206\) 2435.40 7495.38i 0.823699 2.53509i
\(207\) −790.569 574.382i −0.265451 0.192861i
\(208\) −3827.88 −1.27604
\(209\) 767.993 + 1574.08i 0.254178 + 0.520963i
\(210\) −336.395 −0.110540
\(211\) 4472.00 + 3249.10i 1.45908 + 1.06008i 0.983602 + 0.180350i \(0.0577231\pi\)
0.475473 + 0.879730i \(0.342277\pi\)
\(212\) 1439.83 4431.35i 0.466453 1.43559i
\(213\) −217.102 668.171i −0.0698384 0.214941i
\(214\) 311.323 226.189i 0.0994467 0.0722523i
\(215\) −370.087 + 268.884i −0.117394 + 0.0852919i
\(216\) −2566.32 7898.31i −0.808406 2.48802i
\(217\) 85.2560 262.391i 0.0266707 0.0820841i
\(218\) −2433.57 1768.09i −0.756064 0.549312i
\(219\) −4319.75 −1.33288
\(220\) −5808.74 + 817.168i −1.78011 + 0.250425i
\(221\) −225.028 −0.0684934
\(222\) 1303.67 + 947.173i 0.394130 + 0.286352i
\(223\) −1011.25 + 3112.31i −0.303670 + 0.934600i 0.676500 + 0.736442i \(0.263496\pi\)
−0.980170 + 0.198157i \(0.936504\pi\)
\(224\) 129.290 + 397.913i 0.0385649 + 0.118690i
\(225\) −260.133 + 188.997i −0.0770763 + 0.0559992i
\(226\) 761.347 553.151i 0.224089 0.162810i
\(227\) 1742.88 + 5364.04i 0.509600 + 1.56839i 0.792897 + 0.609355i \(0.208572\pi\)
−0.283298 + 0.959032i \(0.591428\pi\)
\(228\) 1254.43 3860.73i 0.364371 1.12142i
\(229\) −883.468 641.877i −0.254940 0.185225i 0.452973 0.891524i \(-0.350363\pi\)
−0.707913 + 0.706299i \(0.750363\pi\)
\(230\) 6828.46 1.95763
\(231\) −198.124 + 191.378i −0.0564311 + 0.0545097i
\(232\) 13283.0 3.75892
\(233\) 1331.44 + 967.350i 0.374359 + 0.271988i 0.759016 0.651072i \(-0.225680\pi\)
−0.384657 + 0.923060i \(0.625680\pi\)
\(234\) 290.968 895.507i 0.0812871 0.250176i
\(235\) 145.523 + 447.875i 0.0403953 + 0.124324i
\(236\) −5710.83 + 4149.16i −1.57518 + 1.14444i
\(237\) −8.15819 + 5.92727i −0.00223600 + 0.00162455i
\(238\) 20.8391 + 64.1360i 0.00567561 + 0.0174677i
\(239\) 251.820 775.023i 0.0681544 0.209758i −0.911179 0.412011i \(-0.864826\pi\)
0.979333 + 0.202253i \(0.0648265\pi\)
\(240\) 4242.86 + 3082.62i 1.14115 + 0.829092i
\(241\) −6368.48 −1.70220 −0.851100 0.525004i \(-0.824064\pi\)
−0.851100 + 0.525004i \(0.824064\pi\)
\(242\) −4226.39 + 5412.56i −1.12266 + 1.43774i
\(243\) 1748.19 0.461509
\(244\) −10522.5 7645.04i −2.76079 2.00583i
\(245\) 907.907 2794.25i 0.236751 0.728645i
\(246\) 2226.81 + 6853.41i 0.577138 + 1.77625i
\(247\) 1111.70 807.697i 0.286379 0.208067i
\(248\) −7355.72 + 5344.24i −1.88342 + 1.36839i
\(249\) −1066.04 3280.92i −0.271314 0.835020i
\(250\) 2415.28 7433.48i 0.611024 1.88054i
\(251\) 512.385 + 372.269i 0.128850 + 0.0936153i 0.650344 0.759640i \(-0.274625\pi\)
−0.521493 + 0.853255i \(0.674625\pi\)
\(252\) −197.374 −0.0493389
\(253\) 4021.70 3884.77i 0.999376 0.965348i
\(254\) −748.264 −0.184844
\(255\) 249.424 + 181.217i 0.0612530 + 0.0445029i
\(256\) −1894.91 + 5831.92i −0.462623 + 1.42381i
\(257\) 141.266 + 434.772i 0.0342877 + 0.105527i 0.966736 0.255778i \(-0.0823315\pi\)
−0.932448 + 0.361304i \(0.882332\pi\)
\(258\) 1004.19 729.583i 0.242317 0.176054i
\(259\) 92.5044 67.2083i 0.0221928 0.0161240i
\(260\) 1422.18 + 4377.02i 0.339230 + 1.04404i
\(261\) −477.649 + 1470.05i −0.113279 + 0.348636i
\(262\) 8.88832 + 6.45774i 0.00209589 + 0.00152275i
\(263\) 6954.78 1.63061 0.815305 0.579032i \(-0.196570\pi\)
0.815305 + 0.579032i \(0.196570\pi\)
\(264\) 8989.36 1264.62i 2.09567 0.294817i
\(265\) −2160.92 −0.500922
\(266\) −333.155 242.051i −0.0767933 0.0557936i
\(267\) 1624.60 4999.99i 0.372373 1.14605i
\(268\) −1599.66 4923.26i −0.364608 1.12215i
\(269\) 3576.88 2598.76i 0.810730 0.589030i −0.103312 0.994649i \(-0.532944\pi\)
0.914042 + 0.405619i \(0.132944\pi\)
\(270\) −5463.33 + 3969.34i −1.23144 + 0.894690i
\(271\) 1080.12 + 3324.28i 0.242114 + 0.745151i 0.996098 + 0.0882573i \(0.0281298\pi\)
−0.753984 + 0.656893i \(0.771870\pi\)
\(272\) 324.885 999.893i 0.0724230 0.222895i
\(273\) 174.844 + 127.032i 0.0387621 + 0.0281623i
\(274\) −2052.97 −0.452644
\(275\) −806.771 1653.56i −0.176910 0.362594i
\(276\) −12959.9 −2.82643
\(277\) −2219.84 1612.80i −0.481505 0.349834i 0.320403 0.947281i \(-0.396182\pi\)
−0.801908 + 0.597447i \(0.796182\pi\)
\(278\) 416.469 1281.76i 0.0898495 0.276528i
\(279\) −326.950 1006.25i −0.0701576 0.215923i
\(280\) 636.394 462.367i 0.135828 0.0986847i
\(281\) 1415.40 1028.35i 0.300483 0.218313i −0.427319 0.904101i \(-0.640542\pi\)
0.727802 + 0.685787i \(0.240542\pi\)
\(282\) −394.859 1215.25i −0.0833813 0.256621i
\(283\) −640.941 + 1972.61i −0.134629 + 0.414345i −0.995532 0.0944237i \(-0.969899\pi\)
0.860903 + 0.508769i \(0.169899\pi\)
\(284\) 2330.35 + 1693.10i 0.486904 + 0.353756i
\(285\) −1882.66 −0.391296
\(286\) 4757.51 + 2528.78i 0.983627 + 0.522833i
\(287\) 511.321 0.105165
\(288\) 1298.06 + 943.097i 0.265587 + 0.192960i
\(289\) −1499.10 + 4613.76i −0.305130 + 0.939092i
\(290\) −3337.72 10272.4i −0.675854 2.08006i
\(291\) −2717.53 + 1974.40i −0.547438 + 0.397737i
\(292\) 14328.4 10410.2i 2.87160 2.08634i
\(293\) −1088.24 3349.25i −0.216981 0.667799i −0.999007 0.0445534i \(-0.985814\pi\)
0.782026 0.623246i \(-0.214186\pi\)
\(294\) −2463.49 + 7581.84i −0.488686 + 1.50402i
\(295\) 2648.55 + 1924.29i 0.522727 + 0.379784i
\(296\) −3768.16 −0.739932
\(297\) −959.501 + 5445.92i −0.187461 + 1.06399i
\(298\) 4891.21 0.950806
\(299\) −3549.16 2578.61i −0.686465 0.498746i
\(300\) −1317.77 + 4055.67i −0.253604 + 0.780514i
\(301\) −27.2165 83.7638i −0.00521174 0.0160401i
\(302\) −7576.71 + 5504.80i −1.44368 + 1.04889i
\(303\) −2264.01 + 1644.90i −0.429255 + 0.311872i
\(304\) 1983.91 + 6105.85i 0.374293 + 1.15196i
\(305\) −1864.03 + 5736.89i −0.349948 + 1.07703i
\(306\) 209.223 + 152.009i 0.0390866 + 0.0283981i
\(307\) 6944.40 1.29100 0.645501 0.763759i \(-0.276648\pi\)
0.645501 + 0.763759i \(0.276648\pi\)
\(308\) 195.964 1112.25i 0.0362536 0.205767i
\(309\) 6937.05 1.27714
\(310\) 5981.32 + 4345.68i 1.09586 + 0.796188i
\(311\) 707.667 2177.98i 0.129029 0.397111i −0.865584 0.500763i \(-0.833053\pi\)
0.994614 + 0.103652i \(0.0330527\pi\)
\(312\) −2200.91 6773.69i −0.399365 1.22912i
\(313\) −6406.71 + 4654.75i −1.15696 + 0.840581i −0.989391 0.145279i \(-0.953592\pi\)
−0.167570 + 0.985860i \(0.553592\pi\)
\(314\) 3859.19 2803.86i 0.693587 0.503921i
\(315\) 28.2867 + 87.0574i 0.00505960 + 0.0155718i
\(316\) 12.7762 39.3210i 0.00227441 0.00699993i
\(317\) 1122.42 + 815.485i 0.198869 + 0.144486i 0.682763 0.730640i \(-0.260778\pi\)
−0.483894 + 0.875126i \(0.660778\pi\)
\(318\) 5863.38 1.03397
\(319\) −7809.87 4151.22i −1.37075 0.728601i
\(320\) −1973.35 −0.344730
\(321\) 274.030 + 199.095i 0.0476476 + 0.0346180i
\(322\) −406.264 + 1250.35i −0.0703112 + 0.216396i
\(323\) 116.628 + 358.943i 0.0200908 + 0.0618331i
\(324\) 7775.81 5649.45i 1.33330 0.968699i
\(325\) −1167.83 + 848.479i −0.199322 + 0.144816i
\(326\) −4674.67 14387.1i −0.794190 2.44427i
\(327\) 818.192 2518.14i 0.138367 0.425851i
\(328\) −13632.5 9904.62i −2.29491 1.66735i
\(329\) −90.6680 −0.0151936
\(330\) −3236.82 6634.19i −0.539943 1.10667i
\(331\) −11641.4 −1.93315 −0.966574 0.256389i \(-0.917467\pi\)
−0.966574 + 0.256389i \(0.917467\pi\)
\(332\) 11442.7 + 8313.61i 1.89157 + 1.37430i
\(333\) 135.501 417.030i 0.0222986 0.0686279i
\(334\) 1754.93 + 5401.13i 0.287502 + 0.884840i
\(335\) −1942.29 + 1411.15i −0.316772 + 0.230148i
\(336\) −816.887 + 593.503i −0.132634 + 0.0963639i
\(337\) −2619.63 8062.40i −0.423444 1.30323i −0.904477 0.426523i \(-0.859738\pi\)
0.481033 0.876702i \(-0.340262\pi\)
\(338\) −2196.52 + 6760.19i −0.353476 + 1.08789i
\(339\) 670.147 + 486.890i 0.107367 + 0.0780066i
\(340\) −1264.04 −0.201624
\(341\) 5995.06 843.380i 0.952055 0.133934i
\(342\) −1579.23 −0.249692
\(343\) 918.989 + 667.685i 0.144667 + 0.105107i
\(344\) −896.928 + 2760.46i −0.140579 + 0.432657i
\(345\) 1857.35 + 5716.32i 0.289844 + 0.892048i
\(346\) 15069.8 10948.9i 2.34150 1.70120i
\(347\) 1546.04 1123.27i 0.239181 0.173775i −0.461737 0.887017i \(-0.652774\pi\)
0.700918 + 0.713241i \(0.252774\pi\)
\(348\) 6334.73 + 19496.3i 0.975797 + 3.00319i
\(349\) 2665.62 8203.92i 0.408846 1.25830i −0.508796 0.860887i \(-0.669909\pi\)
0.917641 0.397410i \(-0.130091\pi\)
\(350\) 349.977 + 254.273i 0.0534487 + 0.0388327i
\(351\) 4338.55 0.659756
\(352\) −6603.37 + 6378.53i −0.999889 + 0.965843i
\(353\) 6345.10 0.956702 0.478351 0.878169i \(-0.341235\pi\)
0.478351 + 0.878169i \(0.341235\pi\)
\(354\) −7186.51 5221.30i −1.07898 0.783924i
\(355\) 412.814 1270.51i 0.0617181 0.189949i
\(356\) 6660.81 + 20499.9i 0.991635 + 3.05194i
\(357\) −48.0221 + 34.8901i −0.00711932 + 0.00517249i
\(358\) −14319.0 + 10403.4i −2.11392 + 1.53586i
\(359\) 1412.92 + 4348.52i 0.207719 + 0.639292i 0.999591 + 0.0286053i \(0.00910660\pi\)
−0.791872 + 0.610687i \(0.790893\pi\)
\(360\) 932.195 2869.00i 0.136475 0.420027i
\(361\) 3684.52 + 2676.96i 0.537180 + 0.390284i
\(362\) −19118.2 −2.77578
\(363\) −5680.61 2065.83i −0.821362 0.298699i
\(364\) −886.085 −0.127592
\(365\) −6645.18 4828.01i −0.952944 0.692354i
\(366\) 5057.81 15566.3i 0.722338 2.22313i
\(367\) 440.465 + 1355.61i 0.0626487 + 0.192813i 0.977482 0.211019i \(-0.0676781\pi\)
−0.914833 + 0.403832i \(0.867678\pi\)
\(368\) 16582.0 12047.5i 2.34890 1.70657i
\(369\) 1586.38 1152.57i 0.223804 0.162603i
\(370\) 946.856 + 2914.12i 0.133040 + 0.409454i
\(371\) 128.565 395.684i 0.0179913 0.0553716i
\(372\) −11352.1 8247.77i −1.58220 1.14953i
\(373\) 8121.64 1.12741 0.563703 0.825977i \(-0.309376\pi\)
0.563703 + 0.825977i \(0.309376\pi\)
\(374\) −1064.34 + 1028.10i −0.147154 + 0.142144i
\(375\) 6879.76 0.947385
\(376\) 2417.33 + 1756.30i 0.331554 + 0.240888i
\(377\) −2144.34 + 6599.61i −0.292943 + 0.901585i
\(378\) −401.777 1236.54i −0.0546698 0.168256i
\(379\) −4285.43 + 3113.54i −0.580811 + 0.421984i −0.839017 0.544106i \(-0.816869\pi\)
0.258205 + 0.966090i \(0.416869\pi\)
\(380\) 6244.70 4537.04i 0.843017 0.612488i
\(381\) −203.528 626.396i −0.0273676 0.0842290i
\(382\) −4845.58 + 14913.2i −0.649009 + 1.99744i
\(383\) −8929.36 6487.56i −1.19130 0.865532i −0.197901 0.980222i \(-0.563412\pi\)
−0.993401 + 0.114690i \(0.963412\pi\)
\(384\) −3788.33 −0.503443
\(385\) −518.674 + 72.9666i −0.0686599 + 0.00965902i
\(386\) −3608.45 −0.475817
\(387\) −273.252 198.529i −0.0358920 0.0260771i
\(388\) 4255.80 13098.0i 0.556844 1.71379i
\(389\) 3436.44 + 10576.3i 0.447903 + 1.37851i 0.879268 + 0.476327i \(0.158032\pi\)
−0.431365 + 0.902178i \(0.641968\pi\)
\(390\) −4685.42 + 3404.16i −0.608348 + 0.441990i
\(391\) 974.797 708.232i 0.126081 0.0916031i
\(392\) −5760.63 17729.4i −0.742234 2.28436i
\(393\) −2.98835 + 9.19721i −0.000383569 + 0.00118050i
\(394\) 17694.1 + 12855.6i 2.26248 + 1.64379i
\(395\) −19.1746 −0.00244248
\(396\) −1899.15 3892.50i −0.241000 0.493953i
\(397\) −2320.56 −0.293364 −0.146682 0.989184i \(-0.546859\pi\)
−0.146682 + 0.989184i \(0.546859\pi\)
\(398\) 8432.91 + 6126.86i 1.06207 + 0.771638i
\(399\) 112.010 344.732i 0.0140540 0.0432537i
\(400\) −2084.08 6414.15i −0.260511 0.801769i
\(401\) −394.560 + 286.665i −0.0491357 + 0.0356992i −0.612082 0.790794i \(-0.709668\pi\)
0.562946 + 0.826493i \(0.309668\pi\)
\(402\) 5270.15 3828.99i 0.653859 0.475056i
\(403\) −1467.80 4517.42i −0.181430 0.558384i
\(404\) 3545.57 10912.1i 0.436630 1.34381i
\(405\) −3606.24 2620.09i −0.442458 0.321465i
\(406\) 2079.56 0.254204
\(407\) 2215.53 + 1177.63i 0.269827 + 0.143423i
\(408\) 1956.18 0.237366
\(409\) 8135.14 + 5910.52i 0.983513 + 0.714564i 0.958491 0.285123i \(-0.0920345\pi\)
0.0250218 + 0.999687i \(0.492034\pi\)
\(410\) −4234.22 + 13031.6i −0.510032 + 1.56972i
\(411\) −558.409 1718.61i −0.0670177 0.206259i
\(412\) −23009.8 + 16717.6i −2.75149 + 1.99907i
\(413\) −509.931 + 370.487i −0.0607556 + 0.0441416i
\(414\) 1557.99 + 4795.00i 0.184954 + 0.569231i
\(415\) 2027.04 6238.59i 0.239768 0.737929i
\(416\) 5827.48 + 4233.91i 0.686817 + 0.499002i
\(417\) 1186.28 0.139310
\(418\) 1567.95 8899.32i 0.183471 1.04134i
\(419\) 1237.92 0.144335 0.0721675 0.997393i \(-0.477008\pi\)
0.0721675 + 0.997393i \(0.477008\pi\)
\(420\) 982.146 + 713.571i 0.114104 + 0.0829017i
\(421\) −1224.17 + 3767.59i −0.141715 + 0.436155i −0.996574 0.0827059i \(-0.973644\pi\)
0.854859 + 0.518861i \(0.173644\pi\)
\(422\) −8813.06 27123.8i −1.01662 3.12883i
\(423\) −281.299 + 204.376i −0.0323338 + 0.0234919i
\(424\) −11092.4 + 8059.08i −1.27050 + 0.923075i
\(425\) −122.516 377.066i −0.0139833 0.0430363i
\(426\) −1120.12 + 3447.37i −0.127394 + 0.392079i
\(427\) −939.575 682.641i −0.106485 0.0773661i
\(428\) −1388.74 −0.156840
\(429\) −822.881 + 4670.49i −0.0926085 + 0.525626i
\(430\) 2360.19 0.264694
\(431\) −6886.78 5003.54i −0.769662 0.559192i 0.132197 0.991224i \(-0.457797\pi\)
−0.901859 + 0.432031i \(0.857797\pi\)
\(432\) −6263.79 + 19278.0i −0.697608 + 2.14702i
\(433\) −3339.00 10276.4i −0.370582 1.14053i −0.946411 0.322964i \(-0.895321\pi\)
0.575829 0.817570i \(-0.304679\pi\)
\(434\) −1151.60 + 836.684i −0.127370 + 0.0925395i
\(435\) 7691.53 5588.22i 0.847771 0.615942i
\(436\) 3354.57 + 10324.3i 0.368474 + 1.13405i
\(437\) −2273.69 + 6997.70i −0.248891 + 0.766008i
\(438\) 18030.9 + 13100.2i 1.96700 + 1.42911i
\(439\) 3175.21 0.345204 0.172602 0.984992i \(-0.444783\pi\)
0.172602 + 0.984992i \(0.444783\pi\)
\(440\) 15242.0 + 8101.65i 1.65144 + 0.877798i
\(441\) 2169.29 0.234240
\(442\) 939.280 + 682.427i 0.101079 + 0.0734383i
\(443\) −733.995 + 2259.00i −0.0787204 + 0.242276i −0.982670 0.185362i \(-0.940654\pi\)
0.903950 + 0.427638i \(0.140654\pi\)
\(444\) −1797.06 5530.78i −0.192082 0.591169i
\(445\) 8087.45 5875.87i 0.861532 0.625940i
\(446\) 13659.5 9924.21i 1.45022 1.05364i
\(447\) 1330.41 + 4094.59i 0.140775 + 0.433260i
\(448\) 117.406 361.338i 0.0123815 0.0381063i
\(449\) −6609.71 4802.23i −0.694725 0.504747i 0.183485 0.983022i \(-0.441262\pi\)
−0.878210 + 0.478275i \(0.841262\pi\)
\(450\) 1658.97 0.173788
\(451\) 4919.98 + 10084.0i 0.513687 + 1.05285i
\(452\) −3396.21 −0.353416
\(453\) −6669.11 4845.39i −0.691705 0.502553i
\(454\) 8992.25 27675.3i 0.929576 2.86094i
\(455\) 126.989 + 390.833i 0.0130843 + 0.0402693i
\(456\) −9664.03 + 7021.33i −0.992456 + 0.721061i
\(457\) −7454.30 + 5415.86i −0.763014 + 0.554362i −0.899833 0.436234i \(-0.856312\pi\)
0.136819 + 0.990596i \(0.456312\pi\)
\(458\) 1741.07 + 5358.46i 0.177631 + 0.546691i
\(459\) −368.227 + 1133.29i −0.0374452 + 0.115245i
\(460\) −19936.5 14484.7i −2.02075 1.46816i
\(461\) −4588.84 −0.463609 −0.231804 0.972762i \(-0.574463\pi\)
−0.231804 + 0.972762i \(0.574463\pi\)
\(462\) 1407.36 197.986i 0.141723 0.0199375i
\(463\) −11230.6 −1.12728 −0.563639 0.826021i \(-0.690599\pi\)
−0.563639 + 0.826021i \(0.690599\pi\)
\(464\) −26228.9 19056.4i −2.62424 1.90662i
\(465\) −2010.99 + 6189.18i −0.200553 + 0.617240i
\(466\) −2623.90 8075.54i −0.260837 0.802773i
\(467\) 10566.7 7677.17i 1.04704 0.760722i 0.0753954 0.997154i \(-0.475978\pi\)
0.971648 + 0.236432i \(0.0759781\pi\)
\(468\) −2749.09 + 1997.33i −0.271532 + 0.197279i
\(469\) −142.837 439.608i −0.0140631 0.0432819i
\(470\) 750.816 2310.77i 0.0736863 0.226783i
\(471\) 3396.90 + 2467.99i 0.332316 + 0.241442i
\(472\) 20772.0 2.02566
\(473\) 1390.06 1342.73i 0.135127 0.130526i
\(474\) 52.0280 0.00504161
\(475\) 1958.67 + 1423.06i 0.189200 + 0.137462i
\(476\) 75.2051 231.457i 0.00724164 0.0222875i
\(477\) −493.038 1517.42i −0.0473264 0.145656i
\(478\) −3401.47 + 2471.31i −0.325480 + 0.236475i
\(479\) −12911.7 + 9380.93i −1.23163 + 0.894835i −0.997012 0.0772519i \(-0.975385\pi\)
−0.234623 + 0.972087i \(0.575385\pi\)
\(480\) −3049.64 9385.82i −0.289992 0.892505i
\(481\) 608.315 1872.20i 0.0576648 0.177474i
\(482\) 26582.4 + 19313.2i 2.51202 + 1.82509i
\(483\) −1157.21 −0.109017
\(484\) 23820.8 6837.48i 2.23711 0.642138i
\(485\) −6387.16 −0.597992
\(486\) −7297.06 5301.62i −0.681073 0.494828i
\(487\) −1342.84 + 4132.82i −0.124948 + 0.384550i −0.993892 0.110361i \(-0.964799\pi\)
0.868944 + 0.494911i \(0.164799\pi\)
\(488\) 11827.2 + 36400.3i 1.09711 + 3.37657i
\(489\) 10772.4 7826.63i 0.996208 0.723788i
\(490\) −12263.6 + 8910.01i −1.13064 + 0.821455i
\(491\) 898.493 + 2765.28i 0.0825834 + 0.254165i 0.983819 0.179163i \(-0.0573390\pi\)
−0.901236 + 0.433329i \(0.857339\pi\)
\(492\) 8036.22 24732.9i 0.736383 2.26636i
\(493\) −1541.91 1120.26i −0.140860 0.102341i
\(494\) −7089.74 −0.645713
\(495\) −1444.72 + 1395.53i −0.131182 + 0.126716i
\(496\) 22191.9 2.00896
\(497\) 208.081 + 151.180i 0.0187801 + 0.0136446i
\(498\) −5500.12 + 16927.6i −0.494912 + 1.52318i
\(499\) 4900.21 + 15081.3i 0.439606 + 1.35297i 0.888292 + 0.459279i \(0.151892\pi\)
−0.448686 + 0.893690i \(0.648108\pi\)
\(500\) −22819.8 + 16579.6i −2.04107 + 1.48292i
\(501\) −4044.11 + 2938.22i −0.360634 + 0.262016i
\(502\) −1009.77 3107.75i −0.0897772 0.276306i
\(503\) 592.264 1822.80i 0.0525005 0.161580i −0.921369 0.388690i \(-0.872928\pi\)
0.973869 + 0.227110i \(0.0729277\pi\)
\(504\) 469.879 + 341.387i 0.0415279 + 0.0301718i
\(505\) −5321.24 −0.468895
\(506\) −28567.9 + 4018.90i −2.50987 + 0.353087i
\(507\) −6256.62 −0.548060
\(508\) 2184.65 + 1587.24i 0.190803 + 0.138627i
\(509\) 2745.05 8448.39i 0.239041 0.735694i −0.757518 0.652814i \(-0.773588\pi\)
0.996560 0.0828798i \(-0.0264118\pi\)
\(510\) −491.544 1512.82i −0.0426783 0.131350i
\(511\) 1279.41 929.547i 0.110759 0.0804711i
\(512\) 20196.6 14673.7i 1.74330 1.26658i
\(513\) −2248.58 6920.42i −0.193523 0.595602i
\(514\) 728.850 2243.17i 0.0625451 0.192494i
\(515\) 10671.4 + 7753.26i 0.913087 + 0.663397i
\(516\) −4479.46 −0.382165
\(517\) −872.416 1788.10i −0.0742143 0.152110i
\(518\) −589.936 −0.0500392
\(519\) 13264.6 + 9637.33i 1.12187 + 0.815090i
\(520\) 4184.97 12880.0i 0.352929 1.08620i
\(521\) −4332.81 13335.0i −0.364346 1.12134i −0.950390 0.311061i \(-0.899316\pi\)
0.586044 0.810279i \(-0.300684\pi\)
\(522\) 6451.86 4687.55i 0.540977 0.393043i
\(523\) 12238.5 8891.81i 1.02324 0.743425i 0.0562933 0.998414i \(-0.482072\pi\)
0.966944 + 0.254989i \(0.0820718\pi\)
\(524\) −12.2522 37.7084i −0.00102145 0.00314370i
\(525\) −117.666 + 362.139i −0.00978165 + 0.0301048i
\(526\) −29029.6 21091.3i −2.40637 1.74833i
\(527\) 1304.59 0.107834
\(528\) −19564.9 10399.4i −1.61260 0.857154i
\(529\) 11323.2 0.930650
\(530\) 9019.80 + 6553.27i 0.739236 + 0.537086i
\(531\) −746.952 + 2298.88i −0.0610451 + 0.187878i
\(532\) 459.240 + 1413.40i 0.0374259 + 0.115185i
\(533\) 7121.86 5174.33i 0.578765 0.420498i
\(534\) −21944.3 + 15943.4i −1.77832 + 1.29202i
\(535\) 199.028 + 612.545i 0.0160836 + 0.0495002i
\(536\) −4707.24 + 14487.4i −0.379332 + 1.16746i
\(537\) −12603.8 9157.19i −1.01284 0.735870i
\(538\) −22811.2 −1.82799
\(539\) −2153.80 + 12224.5i −0.172116 + 0.976895i
\(540\) 24370.7 1.94213
\(541\) 9680.26 + 7033.12i 0.769292 + 0.558923i 0.901746 0.432266i \(-0.142286\pi\)
−0.132455 + 0.991189i \(0.542286\pi\)
\(542\) 5572.81 17151.4i 0.441647 1.35925i
\(543\) −5200.17 16004.5i −0.410977 1.26486i
\(544\) −1600.55 + 1162.87i −0.126145 + 0.0916500i
\(545\) 4073.07 2959.26i 0.320130 0.232588i
\(546\) −344.570 1060.48i −0.0270077 0.0831212i
\(547\) 4819.71 14833.5i 0.376738 1.15948i −0.565560 0.824707i \(-0.691340\pi\)
0.942299 0.334774i \(-0.108660\pi\)
\(548\) 5993.90 + 4354.82i 0.467238 + 0.339469i
\(549\) −4453.79 −0.346235
\(550\) −1647.12 + 9348.67i −0.127697 + 0.724780i
\(551\) 11638.4 0.899843
\(552\) 30852.9 + 22416.0i 2.37896 + 1.72842i
\(553\) 1.14081 3.51105i 8.77254e−5 0.000269991i
\(554\) 4374.68 + 13463.9i 0.335491 + 1.03254i
\(555\) −2181.96 + 1585.29i −0.166881 + 0.121246i
\(556\) −3934.84 + 2858.83i −0.300134 + 0.218060i
\(557\) 5765.73 + 17745.1i 0.438603 + 1.34988i 0.889349 + 0.457228i \(0.151158\pi\)
−0.450747 + 0.892652i \(0.648842\pi\)
\(558\) −1686.87 + 5191.65i −0.127976 + 0.393871i
\(559\) −1226.73 891.272i −0.0928179 0.0674361i
\(560\) −1919.97 −0.144882
\(561\) −1150.15 611.348i −0.0865589 0.0460091i
\(562\) −9026.55 −0.677512
\(563\) −12107.4 8796.55i −0.906335 0.658491i 0.0337505 0.999430i \(-0.489255\pi\)
−0.940085 + 0.340940i \(0.889255\pi\)
\(564\) −1424.99 + 4385.67i −0.106388 + 0.327429i
\(565\) 486.727 + 1497.99i 0.0362421 + 0.111542i
\(566\) 8657.52 6290.06i 0.642938 0.467122i
\(567\) 694.318 504.451i 0.0514261 0.0373632i
\(568\) −2619.29 8061.34i −0.193491 0.595504i
\(569\) 4038.36 12428.8i 0.297534 0.915715i −0.684825 0.728708i \(-0.740121\pi\)
0.982359 0.187007i \(-0.0598788\pi\)
\(570\) 7858.33 + 5709.41i 0.577455 + 0.419546i
\(571\) −13852.7 −1.01527 −0.507633 0.861573i \(-0.669480\pi\)
−0.507633 + 0.861573i \(0.669480\pi\)
\(572\) −8526.00 17474.9i −0.623234 1.27738i
\(573\) −13802.3 −1.00628
\(574\) −2134.28 1550.65i −0.155197 0.112757i
\(575\) 2388.50 7351.04i 0.173230 0.533147i
\(576\) −450.242 1385.70i −0.0325696 0.100239i
\(577\) −10358.9 + 7526.18i −0.747395 + 0.543014i −0.895018 0.446030i \(-0.852838\pi\)
0.147624 + 0.989044i \(0.452838\pi\)
\(578\) 20249.2 14711.9i 1.45719 1.05871i
\(579\) −981.501 3020.75i −0.0704487 0.216819i
\(580\) −12045.3 + 37071.7i −0.862337 + 2.65400i
\(581\) 1021.74 + 742.339i 0.0729587 + 0.0530076i
\(582\) 17330.8 1.23434
\(583\) 9040.52 1271.81i 0.642230 0.0903483i
\(584\) −52116.8 −3.69282
\(585\) 1274.97 + 926.318i 0.0901084 + 0.0654676i
\(586\) −5614.67 + 17280.2i −0.395802 + 1.21815i
\(587\) 3729.16 + 11477.2i 0.262213 + 0.807008i 0.992322 + 0.123678i \(0.0394691\pi\)
−0.730109 + 0.683330i \(0.760531\pi\)
\(588\) 23275.3 16910.5i 1.63241 1.18602i
\(589\) −6445.01 + 4682.57i −0.450869 + 0.327576i
\(590\) −5219.56 16064.1i −0.364213 1.12093i
\(591\) −5948.97 + 18309.1i −0.414058 + 1.27434i
\(592\) 7440.71 + 5405.99i 0.516573 + 0.375312i
\(593\) 10537.6 0.729729 0.364864 0.931061i \(-0.381115\pi\)
0.364864 + 0.931061i \(0.381115\pi\)
\(594\) 20520.5 19821.8i 1.41745 1.36919i
\(595\) −112.869 −0.00777676
\(596\) −14280.5 10375.4i −0.981462 0.713074i
\(597\) −2835.24 + 8725.96i −0.194369 + 0.598208i
\(598\) 6994.40 + 21526.5i 0.478298 + 1.47205i
\(599\) −4430.23 + 3218.75i −0.302194 + 0.219557i −0.728540 0.685003i \(-0.759801\pi\)
0.426346 + 0.904560i \(0.359801\pi\)
\(600\) 10152.0 7375.86i 0.690756 0.501864i
\(601\) 5285.43 + 16266.9i 0.358731 + 1.10406i 0.953814 + 0.300396i \(0.0971190\pi\)
−0.595083 + 0.803664i \(0.702881\pi\)
\(602\) −140.421 + 432.172i −0.00950688 + 0.0292592i
\(603\) −1434.08 1041.92i −0.0968494 0.0703652i
\(604\) 33798.1 2.27686
\(605\) −6429.74 9526.90i −0.432076 0.640204i
\(606\) 14438.5 0.967861
\(607\) −1317.77 957.418i −0.0881165 0.0640204i 0.542855 0.839827i \(-0.317343\pi\)
−0.630971 + 0.775806i \(0.717343\pi\)
\(608\) 3733.25 11489.8i 0.249019 0.766401i
\(609\) 565.641 + 1740.86i 0.0376370 + 0.115835i
\(610\) 25178.4 18293.2i 1.67122 1.21421i
\(611\) −1262.85 + 917.517i −0.0836164 + 0.0607509i
\(612\) −288.405 887.621i −0.0190492 0.0586273i
\(613\) −4887.80 + 15043.1i −0.322049 + 0.991166i 0.650706 + 0.759330i \(0.274473\pi\)
−0.972755 + 0.231836i \(0.925527\pi\)
\(614\) −28986.3 21059.8i −1.90520 1.38421i
\(615\) −12060.9 −0.790799
\(616\) −2390.32 + 2308.93i −0.156345 + 0.151022i
\(617\) −9377.02 −0.611839 −0.305919 0.952057i \(-0.598964\pi\)
−0.305919 + 0.952057i \(0.598964\pi\)
\(618\) −28955.6 21037.5i −1.88473 1.36934i
\(619\) 1974.65 6077.36i 0.128220 0.394620i −0.866254 0.499604i \(-0.833479\pi\)
0.994474 + 0.104984i \(0.0334790\pi\)
\(620\) −8245.00 25375.5i −0.534076 1.64372i
\(621\) −18794.1 + 13654.7i −1.21446 + 0.882359i
\(622\) −9558.83 + 6944.90i −0.616197 + 0.447693i
\(623\) 594.757 + 1830.47i 0.0382479 + 0.117715i
\(624\) −5371.91 + 16533.0i −0.344629 + 1.06066i
\(625\) 5483.36 + 3983.90i 0.350935 + 0.254969i
\(626\) 40858.1 2.60865
\(627\) 7876.39 1108.04i 0.501679 0.0705757i
\(628\) −17215.0 −1.09387
\(629\) 437.414 + 317.800i 0.0277279 + 0.0201455i
\(630\) 145.943 449.165i 0.00922936 0.0284050i
\(631\) −5471.23 16838.7i −0.345176 1.06234i −0.961489 0.274842i \(-0.911374\pi\)
0.616313 0.787501i \(-0.288626\pi\)
\(632\) −98.4268 + 71.5112i −0.00619495 + 0.00450089i
\(633\) 20309.0 14755.4i 1.27522 0.926499i
\(634\) −2211.97 6807.76i −0.138563 0.426452i
\(635\) 387.004 1191.08i 0.0241855 0.0744353i
\(636\) −17118.9 12437.6i −1.06731 0.775444i
\(637\) 9738.77 0.605752
\(638\) 20009.7 + 41011.8i 1.24168 + 2.54494i
\(639\) 986.352 0.0610634
\(640\) −5827.68 4234.06i −0.359937 0.261509i
\(641\) 5615.05 17281.3i 0.345992 1.06485i −0.615058 0.788482i \(-0.710868\pi\)
0.961051 0.276373i \(-0.0891324\pi\)
\(642\) −540.037 1662.06i −0.0331987 0.102175i
\(643\) −4417.63 + 3209.60i −0.270940 + 0.196849i −0.714956 0.699169i \(-0.753553\pi\)
0.444016 + 0.896019i \(0.353553\pi\)
\(644\) 3838.42 2788.78i 0.234868 0.170642i
\(645\) 641.973 + 1975.79i 0.0391902 + 0.120615i
\(646\) 601.730 1851.93i 0.0366482 0.112792i
\(647\) 9107.65 + 6617.09i 0.553414 + 0.402079i 0.829043 0.559186i \(-0.188886\pi\)
−0.275629 + 0.961264i \(0.588886\pi\)
\(648\) −28283.0 −1.71460
\(649\) −12213.1 6491.72i −0.738686 0.392638i
\(650\) 7447.71 0.449421
\(651\) −1013.65 736.460i −0.0610262 0.0443381i
\(652\) −16870.2 + 51921.1i −1.01332 + 3.11869i
\(653\) 710.830 + 2187.71i 0.0425986 + 0.131105i 0.970094 0.242730i \(-0.0780427\pi\)
−0.927495 + 0.373835i \(0.878043\pi\)
\(654\) −11051.8 + 8029.57i −0.660791 + 0.480093i
\(655\) −14.8764 + 10.8083i −0.000887434 + 0.000644759i
\(656\) 12709.5 + 39115.8i 0.756437 + 2.32807i
\(657\) 1874.09 5767.87i 0.111287 0.342505i
\(658\) 378.453 + 274.962i 0.0224219 + 0.0162905i
\(659\) −8719.26 −0.515408 −0.257704 0.966224i \(-0.582966\pi\)
−0.257704 + 0.966224i \(0.582966\pi\)
\(660\) −4622.34 + 26235.4i −0.272612 + 1.54729i
\(661\) 22031.4 1.29640 0.648201 0.761469i \(-0.275522\pi\)
0.648201 + 0.761469i \(0.275522\pi\)
\(662\) 48592.0 + 35304.2i 2.85284 + 2.07271i
\(663\) −315.796 + 971.921i −0.0184985 + 0.0569326i
\(664\) −12861.5 39583.6i −0.751690 2.31346i
\(665\) 557.602 405.122i 0.0325156 0.0236240i
\(666\) −1830.29 + 1329.78i −0.106490 + 0.0773693i
\(667\) −11481.9 35337.7i −0.666539 2.05140i
\(668\) 6333.29 19491.9i 0.366830 1.12899i
\(669\) 12023.3 + 8735.41i 0.694837 + 0.504829i
\(670\) 12386.7 0.714240
\(671\) 4421.98 25098.2i 0.254409 1.44397i
\(672\) 1900.07 0.109073
\(673\) 7198.75 + 5230.20i 0.412320 + 0.299568i 0.774540 0.632525i \(-0.217981\pi\)
−0.362220 + 0.932092i \(0.617981\pi\)
\(674\) −13515.8 + 41597.3i −0.772416 + 2.37725i
\(675\) 2362.12 + 7269.85i 0.134693 + 0.414543i
\(676\) 20752.9 15077.9i 1.18075 0.857867i
\(677\) −14765.0 + 10727.4i −0.838207 + 0.608993i −0.921869 0.387501i \(-0.873338\pi\)
0.0836624 + 0.996494i \(0.473338\pi\)
\(678\) −1320.67 4064.61i −0.0748085 0.230237i
\(679\) 380.009 1169.55i 0.0214778 0.0661018i
\(680\) 3009.24 + 2186.34i 0.169704 + 0.123298i
\(681\) 25613.8 1.44130
\(682\) −27581.4 14660.5i −1.54860 0.823136i
\(683\) −17118.2 −0.959018 −0.479509 0.877537i \(-0.659185\pi\)
−0.479509 + 0.877537i \(0.659185\pi\)
\(684\) 4610.75 + 3349.90i 0.257743 + 0.187261i
\(685\) 1061.80 3267.89i 0.0592253 0.182277i
\(686\) −1811.07 5573.91i −0.100797 0.310223i
\(687\) −4012.17 + 2915.01i −0.222815 + 0.161884i
\(688\) 5731.39 4164.10i 0.317598 0.230748i
\(689\) −2213.43 6812.24i −0.122388 0.376670i
\(690\) 9582.82 29492.9i 0.528712 1.62721i
\(691\) 3859.56 + 2804.13i 0.212481 + 0.154377i 0.688936 0.724823i \(-0.258078\pi\)
−0.476454 + 0.879199i \(0.658078\pi\)
\(692\) −67223.2 −3.69284
\(693\) −169.579 347.569i −0.00929550 0.0190520i
\(694\) −9859.71 −0.539293
\(695\) 1824.89 + 1325.86i 0.0995999 + 0.0723636i
\(696\) 18640.9 57370.7i 1.01520 3.12447i
\(697\) 747.149 + 2299.49i 0.0406030 + 0.124963i
\(698\) −36005.9 + 26159.8i −1.95250 + 1.41857i
\(699\) 6046.59 4393.10i 0.327186 0.237715i
\(700\) −482.428 1484.76i −0.0260487 0.0801696i
\(701\) −3565.64 + 10973.9i −0.192114 + 0.591267i 0.807884 + 0.589342i \(0.200613\pi\)
−0.999998 + 0.00192549i \(0.999387\pi\)
\(702\) −18109.3 13157.2i −0.973636 0.707388i
\(703\) −3301.63 −0.177131
\(704\) 8255.79 1161.42i 0.441977 0.0621769i
\(705\) 2138.64 0.114250
\(706\) −26484.8 19242.3i −1.41185 1.02577i
\(707\) 316.591 974.366i 0.0168410 0.0518314i
\(708\) 9906.31 + 30488.5i 0.525850 + 1.61840i
\(709\) −4649.09 + 3377.76i −0.246263 + 0.178920i −0.704069 0.710132i \(-0.748635\pi\)
0.457806 + 0.889052i \(0.348635\pi\)
\(710\) −5576.10 + 4051.27i −0.294743 + 0.214143i
\(711\) −4.37491 13.4646i −0.000230762 0.000710213i
\(712\) 19600.4 60323.8i 1.03168 3.17518i
\(713\) 20576.0 + 14949.4i 1.08075 + 0.785214i
\(714\) 306.255 0.0160523
\(715\) −6485.88 + 6265.04i −0.339242 + 0.327691i
\(716\) 63874.2 3.33392
\(717\) −2994.01 2175.28i −0.155946 0.113302i
\(718\) 7289.83 22435.8i 0.378906 1.16615i
\(719\) 5927.94 + 18244.3i 0.307475 + 0.946312i 0.978742 + 0.205096i \(0.0657506\pi\)
−0.671267 + 0.741216i \(0.734249\pi\)
\(720\) −5956.75 + 4327.83i −0.308326 + 0.224012i
\(721\) −2054.60 + 1492.75i −0.106126 + 0.0771054i
\(722\) −7261.16 22347.6i −0.374283 1.15193i
\(723\) −8937.30 + 27506.2i −0.459726 + 1.41489i
\(724\) 55818.0 + 40554.2i 2.86528 + 2.08174i
\(725\) −12226.1 −0.626296
\(726\) 17446.3 + 25850.0i 0.891862 + 1.32147i
\(727\) 35335.6 1.80265 0.901323 0.433148i \(-0.142597\pi\)
0.901323 + 0.433148i \(0.142597\pi\)
\(728\) 2109.46 + 1532.61i 0.107392 + 0.0780252i
\(729\) 6760.25 20805.9i 0.343456 1.05705i
\(730\) 13095.8 + 40304.7i 0.663969 + 2.04349i
\(731\) 336.929 244.793i 0.0170476 0.0123858i
\(732\) −47786.7 + 34719.0i −2.41290 + 1.75308i
\(733\) 4628.65 + 14245.5i 0.233238 + 0.717831i 0.997350 + 0.0727486i \(0.0231771\pi\)
−0.764113 + 0.645083i \(0.776823\pi\)
\(734\) 2272.54 6994.16i 0.114279 0.351716i
\(735\) −10794.5 7842.70i −0.541718 0.393581i
\(736\) −38569.4 −1.93164
\(737\) 7295.30 7046.90i 0.364621 0.352206i
\(738\) −10117.0 −0.504622
\(739\) −17366.5 12617.5i −0.864463 0.628069i 0.0646324 0.997909i \(-0.479413\pi\)
−0.929095 + 0.369840i \(0.879413\pi\)
\(740\) 3417.06 10516.6i 0.169748 0.522432i
\(741\) −1928.41 5935.04i −0.0956032 0.294236i
\(742\) −1736.60 + 1261.71i −0.0859200 + 0.0624245i
\(743\) −20729.2 + 15060.6i −1.02353 + 0.743636i −0.967003 0.254766i \(-0.918002\pi\)
−0.0565237 + 0.998401i \(0.518002\pi\)
\(744\) 12759.6 + 39270.1i 0.628750 + 1.93509i
\(745\) −2529.75 + 7785.76i −0.124406 + 0.382883i
\(746\) −33900.2 24629.9i −1.66377 1.20880i
\(747\) 4843.28 0.237224
\(748\) 5288.30 743.953i 0.258502 0.0363658i
\(749\) −124.004 −0.00604940
\(750\) −28716.5 20863.8i −1.39810 1.01578i
\(751\) −313.521 + 964.918i −0.0152337 + 0.0468846i −0.958384 0.285481i \(-0.907847\pi\)
0.943151 + 0.332365i \(0.107847\pi\)
\(752\) −2253.66 6936.05i −0.109285 0.336346i
\(753\) 2326.94 1690.62i 0.112614 0.0818188i
\(754\) 28964.8 21044.1i 1.39899 1.01642i
\(755\) −4843.77 14907.6i −0.233487 0.718600i
\(756\) −1449.95 + 4462.50i −0.0697544 + 0.214682i
\(757\) 3918.89 + 2847.24i 0.188156 + 0.136704i 0.677876 0.735177i \(-0.262901\pi\)
−0.489719 + 0.871880i \(0.662901\pi\)
\(758\) 27329.8 1.30958
\(759\) −11134.8 22821.9i −0.532501 1.09141i
\(760\) −22713.9 −1.08410
\(761\) −16023.6 11641.9i −0.763280 0.554556i 0.136634 0.990622i \(-0.456371\pi\)
−0.899915 + 0.436066i \(0.856371\pi\)
\(762\) −1050.09 + 3231.84i −0.0499221 + 0.153644i
\(763\) 299.536 + 921.878i 0.0142122 + 0.0437408i
\(764\) 45781.5 33262.2i 2.16795 1.57511i
\(765\) −350.177 + 254.419i −0.0165499 + 0.0120242i
\(766\) 17597.3 + 54158.8i 0.830046 + 2.55462i
\(767\) −3353.34 + 10320.5i −0.157865 + 0.485858i
\(768\) 22529.5 + 16368.6i 1.05854 + 0.769077i
\(769\) −30538.7 −1.43206 −0.716030 0.698069i \(-0.754043\pi\)
−0.716030 + 0.698069i \(0.754043\pi\)
\(770\) 2386.25 + 1268.38i 0.111681 + 0.0593626i
\(771\) 2076.08 0.0969754
\(772\) 10535.3 + 7654.36i 0.491159 + 0.356848i
\(773\) 728.385 2241.74i 0.0338916 0.104308i −0.932680 0.360706i \(-0.882536\pi\)
0.966571 + 0.256398i \(0.0825359\pi\)
\(774\) 538.504 + 1657.35i 0.0250079 + 0.0769665i
\(775\) 6770.43 4919.01i 0.313808 0.227995i
\(776\) −32786.4 + 23820.7i −1.51671 + 1.10195i
\(777\) −160.463 493.854i −0.00740872 0.0228017i
\(778\) 17730.0 54567.4i 0.817034 2.51457i
\(779\) −11944.7 8678.33i −0.549375 0.399144i
\(780\) 20900.7 0.959441
\(781\) −979.307 + 5558.33i −0.0448686 + 0.254664i
\(782\) −6216.66 −0.284280
\(783\) 29728.0 + 21598.7i 1.35682 + 0.985791i
\(784\) −14060.4 + 43273.4i −0.640505 + 1.97127i
\(785\) 2467.17 + 7593.16i 0.112175 + 0.345238i
\(786\) 40.3653 29.3271i 0.00183178 0.00133087i
\(787\) 21210.6 15410.4i 0.960705 0.697993i 0.00739057 0.999973i \(-0.497647\pi\)
0.953314 + 0.301980i \(0.0976475\pi\)
\(788\) −24390.7 75066.7i −1.10264 3.39358i
\(789\) 9760.09 30038.5i 0.440391 1.35538i
\(790\) 80.0360 + 58.1495i 0.00360450 + 0.00261882i
\(791\) −303.254 −0.0136314
\(792\) −2211.42 + 12551.5i −0.0992163 + 0.563130i
\(793\) −19994.7 −0.895376
\(794\) 9686.15 + 7037.40i 0.432933 + 0.314544i
\(795\) −3032.56 + 9333.25i −0.135288 + 0.416373i
\(796\) −11624.4 35776.3i −0.517609 1.59304i
\(797\) −14698.5 + 10679.1i −0.653260 + 0.474621i −0.864380 0.502839i \(-0.832289\pi\)
0.211120 + 0.977460i \(0.432289\pi\)
\(798\) −1512.98 + 1099.25i −0.0671165 + 0.0487630i
\(799\) −132.485 407.747i −0.00586606 0.0180539i
\(800\) −3921.75 + 12069.9i −0.173319 + 0.533420i
\(801\) 5971.33 + 4338.43i 0.263404 + 0.191374i
\(802\) 2516.27 0.110789
\(803\) 30642.6 + 16287.6i 1.34664 + 0.715788i
\(804\) −23509.0 −1.03122
\(805\) −1780.17 1293.37i −0.0779414 0.0566278i
\(806\) −7572.98 + 23307.2i −0.330951 + 1.01856i
\(807\) −6204.65 19096.0i −0.270650 0.832974i
\(808\) −27314.8 + 19845.4i −1.18927 + 0.864057i
\(809\) 2514.96 1827.23i 0.109297 0.0794091i −0.531794 0.846874i \(-0.678482\pi\)
0.641091 + 0.767465i \(0.278482\pi\)
\(810\) 7106.90 + 21872.8i 0.308285 + 0.948804i
\(811\) −6414.12 + 19740.6i −0.277719 + 0.854731i 0.710768 + 0.703426i \(0.248348\pi\)
−0.988487 + 0.151305i \(0.951652\pi\)
\(812\) −6071.52 4411.22i −0.262400 0.190645i
\(813\) 15873.8 0.684769
\(814\) −5676.42 11634.4i −0.244421 0.500964i
\(815\) 25319.0 1.08820
\(816\) −3862.72 2806.43i −0.165713 0.120398i
\(817\) −785.879 + 2418.69i −0.0336529 + 0.103573i
\(818\) −16032.1 49341.7i −0.685268 2.10904i
\(819\) −245.472 + 178.346i −0.0104731 + 0.00760917i
\(820\) 40005.3 29065.6i 1.70372 1.23782i
\(821\) −2446.51 7529.59i −0.104000 0.320079i 0.885495 0.464650i \(-0.153820\pi\)
−0.989494 + 0.144571i \(0.953820\pi\)
\(822\) −2881.06 + 8867.00i −0.122249 + 0.376244i
\(823\) −23678.5 17203.4i −1.00289 0.728643i −0.0401845 0.999192i \(-0.512795\pi\)
−0.962706 + 0.270550i \(0.912795\pi\)
\(824\) 83693.9 3.53837
\(825\) −8274.09 + 1163.99i −0.349172 + 0.0491212i
\(826\) 3252.03 0.136989
\(827\) 11248.1 + 8172.24i 0.472957 + 0.343624i 0.798593 0.601872i \(-0.205578\pi\)
−0.325635 + 0.945495i \(0.605578\pi\)
\(828\) 5622.56 17304.5i 0.235987 0.726294i
\(829\) −2924.52 9000.74i −0.122524 0.377091i 0.870918 0.491429i \(-0.163525\pi\)
−0.993442 + 0.114338i \(0.963525\pi\)
\(830\) −27380.3 + 19893.0i −1.14504 + 0.831921i
\(831\) −10081.1 + 7324.36i −0.420830 + 0.305751i
\(832\) −2021.30 6220.93i −0.0842260 0.259221i
\(833\) −826.562 + 2543.90i −0.0343802 + 0.105811i
\(834\) −4951.60 3597.55i −0.205588 0.149368i
\(835\) −9505.10 −0.393937
\(836\) −23455.3 + 22656.7i −0.970358 + 0.937318i
\(837\) −25152.5 −1.03871
\(838\) −5167.15 3754.15i −0.213003 0.154755i
\(839\) −11790.8 + 36288.4i −0.485178 + 1.49323i 0.346544 + 0.938034i \(0.387355\pi\)
−0.831723 + 0.555191i \(0.812645\pi\)
\(840\) −1103.92 3397.52i −0.0453440 0.139554i
\(841\) −27817.1 + 20210.3i −1.14056 + 0.828665i
\(842\) 16535.4 12013.7i 0.676780 0.491710i
\(843\) −2455.23 7556.41i −0.100311 0.308727i
\(844\) −31805.0 + 97885.8i −1.29713 + 3.99214i
\(845\) −9624.72 6992.77i −0.391835 0.284685i
\(846\) 1793.95 0.0729046
\(847\) 2127.00 610.533i 0.0862865 0.0247676i
\(848\) 33465.3 1.35519
\(849\) 7620.46 + 5536.59i 0.308049 + 0.223811i
\(850\) −632.113 + 1945.44i −0.0255074 + 0.0785037i
\(851\) 3257.23 + 10024.7i 0.131206 + 0.403811i
\(852\) 10583.0 7689.00i 0.425549 0.309179i
\(853\) 33219.9 24135.6i 1.33344 0.968802i 0.333784 0.942650i \(-0.391674\pi\)
0.999658 0.0261527i \(-0.00832562\pi\)
\(854\) 1851.64 + 5698.76i 0.0741942 + 0.228346i
\(855\) 816.780 2513.79i 0.0326705 0.100550i
\(856\) 3306.11 + 2402.03i 0.132010 + 0.0959110i
\(857\) 2923.27 0.116519 0.0582596 0.998301i \(-0.481445\pi\)
0.0582596 + 0.998301i \(0.481445\pi\)
\(858\) 17598.6 16999.4i 0.700241 0.676399i
\(859\) 18049.4 0.716924 0.358462 0.933544i \(-0.383301\pi\)
0.358462 + 0.933544i \(0.383301\pi\)
\(860\) −6890.87 5006.51i −0.273229 0.198512i
\(861\) 717.570 2208.45i 0.0284027 0.0874145i
\(862\) 13571.9 + 41770.1i 0.536266 + 1.65046i
\(863\) 28309.1 20567.8i 1.11663 0.811280i 0.132937 0.991125i \(-0.457559\pi\)
0.983695 + 0.179844i \(0.0575594\pi\)
\(864\) 30858.7 22420.1i 1.21509 0.882811i
\(865\) 9634.10 + 29650.7i 0.378693 + 1.16550i
\(866\) −17227.3 + 53020.1i −0.675989 + 2.08048i
\(867\) 17823.6 + 12949.6i 0.698177 + 0.507255i
\(868\) 5137.03 0.200878
\(869\) 80.2199 11.2853i 0.00313150 0.000440536i
\(870\) −49051.9 −1.91151
\(871\) −6438.11 4677.56i −0.250456 0.181967i
\(872\) 9871.30 30380.8i 0.383354 1.17984i
\(873\) −1457.30 4485.12i −0.0564974 0.173881i
\(874\) 30711.9 22313.5i 1.18861 0.863577i
\(875\) −2037.63 + 1480.42i −0.0787251 + 0.0571971i
\(876\) −24854.8 76495.2i −0.958637 2.95038i
\(877\) 9368.87 28834.4i 0.360734 1.11023i −0.591875 0.806030i \(-0.701612\pi\)
0.952609 0.304197i \(-0.0983880\pi\)
\(878\) −13253.5 9629.24i −0.509435 0.370126i
\(879\) −15993.0 −0.613685
\(880\) −18474.2 37864.6i −0.707686 1.45047i
\(881\) −33005.5 −1.26218 −0.631092 0.775708i \(-0.717393\pi\)
−0.631092 + 0.775708i \(0.717393\pi\)
\(882\) −9054.75 6578.66i −0.345680 0.251151i
\(883\) −4268.92 + 13138.4i −0.162696 + 0.500727i −0.998859 0.0477542i \(-0.984794\pi\)
0.836163 + 0.548481i \(0.184794\pi\)
\(884\) −1294.76 3984.86i −0.0492618 0.151612i
\(885\) 12028.1 8738.91i 0.456858 0.331927i
\(886\) 9914.45 7203.27i 0.375940 0.273136i
\(887\) 6507.03 + 20026.6i 0.246319 + 0.758091i 0.995417 + 0.0956319i \(0.0304872\pi\)
−0.749098 + 0.662459i \(0.769513\pi\)
\(888\) −5288.10 + 16275.1i −0.199839 + 0.615041i
\(889\) 195.072 + 141.728i 0.00735939 + 0.00534691i
\(890\) −51576.8 −1.94254
\(891\) 16629.3 + 8839.05i 0.625255 + 0.332345i
\(892\) −60932.1 −2.28717
\(893\) 2118.04 + 1538.85i 0.0793703 + 0.0576659i
\(894\) 6864.15 21125.7i 0.256791 0.790323i
\(895\) −9154.13 28173.5i −0.341887 1.05222i
\(896\) 1122.02 815.193i 0.0418348 0.0303947i
\(897\) −16118.1 + 11710.5i −0.599963 + 0.435899i
\(898\) 13025.9 + 40089.6i 0.484053 + 1.48976i
\(899\) 12431.7 38260.9i 0.461202 1.41943i
\(900\) −4843.56 3519.05i −0.179391 0.130335i
\(901\) 1967.31 0.0727421
\(902\) 10044.7 57011.6i 0.370790 2.10452i
\(903\) −399.980 −0.0147403
\(904\) 8085.17 + 5874.22i 0.297466 + 0.216121i
\(905\) 9888.00 30432.1i 0.363191 1.11779i
\(906\) 13143.0 + 40449.9i 0.481949 + 1.48329i
\(907\) 30830.3 22399.5i 1.12867 0.820026i 0.143169 0.989698i \(-0.454271\pi\)
0.985501 + 0.169672i \(0.0542708\pi\)
\(908\) −84959.7 + 61726.8i −3.10516 + 2.25603i
\(909\) −1214.10 3736.62i −0.0443005 0.136343i
\(910\) 655.191 2016.47i 0.0238674 0.0734564i
\(911\) 507.339 + 368.603i 0.0184510 + 0.0134055i 0.596973 0.802262i \(-0.296370\pi\)
−0.578522 + 0.815667i \(0.696370\pi\)
\(912\) 29156.0 1.05861
\(913\) −4808.69 + 27293.1i −0.174309 + 0.989341i
\(914\) 47538.9 1.72040
\(915\) 22162.4 + 16101.9i 0.800727 + 0.581762i
\(916\) 6283.26 19337.9i 0.226643 0.697535i
\(917\) −1.09402 3.36706i −3.93978e−5 0.000121254i
\(918\) 4973.84 3613.70i 0.178825 0.129924i
\(919\) −39549.3 + 28734.2i −1.41960 + 1.03140i −0.427760 + 0.903892i \(0.640697\pi\)
−0.991838 + 0.127506i \(0.959303\pi\)
\(920\) 22408.5 + 68966.1i 0.803027 + 2.47146i
\(921\) 9745.52 29993.6i 0.348671 1.07310i
\(922\) 19154.1 + 13916.3i 0.684171 + 0.497080i
\(923\) 4428.10 0.157912
\(924\) −4528.92 2407.28i −0.161245 0.0857076i
\(925\) 3468.33 0.123284
\(926\) 46877.1 + 34058.2i 1.66358 + 1.20866i
\(927\) −3009.59 + 9262.57i −0.106632 + 0.328180i
\(928\) 18852.5 + 58022.2i 0.666880 + 2.05245i
\(929\) 26061.9 18935.1i 0.920412 0.668719i −0.0232142 0.999731i \(-0.507390\pi\)
0.943627 + 0.331012i \(0.107390\pi\)
\(930\) 27163.5 19735.4i 0.957769 0.695860i
\(931\) −5047.40 15534.3i −0.177682 0.546849i
\(932\) −9469.28 + 29143.4i −0.332807 + 1.02428i
\(933\) −8413.80 6112.99i −0.295236 0.214502i
\(934\) −67388.0 −2.36082
\(935\) −1086.03 2225.93i −0.0379862 0.0778565i
\(936\) 9999.30 0.349185
\(937\) −36759.1 26707.0i −1.28161 0.931143i −0.282008 0.959412i \(-0.591000\pi\)
−0.999600 + 0.0282695i \(0.991000\pi\)
\(938\) −736.957 + 2268.12i −0.0256530 + 0.0789517i
\(939\) 11113.4 + 34203.6i 0.386233 + 1.18870i
\(940\) −7093.78 + 5153.93i −0.246142 + 0.178833i
\(941\) 33853.3 24595.9i 1.17278 0.852076i 0.181442 0.983402i \(-0.441923\pi\)
0.991339 + 0.131326i \(0.0419234\pi\)
\(942\) −6694.35 20603.1i −0.231543 0.712617i
\(943\) −14565.9 + 44829.3i −0.503003 + 1.54808i
\(944\) −41017.0 29800.6i −1.41418 1.02746i
\(945\) 2176.11 0.0749089
\(946\) −9874.20 + 1389.09i −0.339364 + 0.0477414i
\(947\) −24265.2 −0.832644 −0.416322 0.909217i \(-0.636681\pi\)
−0.416322 + 0.909217i \(0.636681\pi\)
\(948\) −151.902 110.363i −0.00520416 0.00378105i
\(949\) 8413.50 25894.1i 0.287791 0.885730i
\(950\) −3860.00 11879.9i −0.131826 0.405719i
\(951\) 5097.33 3703.43i 0.173809 0.126280i
\(952\) −579.375 + 420.941i −0.0197244 + 0.0143306i
\(953\) 14016.6 + 43138.8i 0.476436 + 1.46632i 0.844011 + 0.536326i \(0.180188\pi\)
−0.367575 + 0.929994i \(0.619812\pi\)
\(954\) −2543.79 + 7828.98i −0.0863294 + 0.265694i
\(955\) −21232.4 15426.3i −0.719440 0.522703i
\(956\) 15173.2 0.513323
\(957\) −28889.7 + 27906.0i −0.975831 + 0.942605i
\(958\) 82343.2 2.77702
\(959\) 535.207 + 388.851i 0.0180216 + 0.0130935i
\(960\) −2769.33 + 8523.11i −0.0931038 + 0.286544i
\(961\) −696.452 2143.46i −0.0233779 0.0719499i
\(962\) −8216.83 + 5969.88i −0.275386 + 0.200080i
\(963\) −384.724 + 279.518i −0.0128739 + 0.00935343i
\(964\) −36642.7 112775.i −1.22426 3.76787i
\(965\) 1866.30 5743.88i 0.0622574 0.191608i
\(966\) 4830.28 + 3509.40i 0.160882 + 0.116887i
\(967\) 22874.2 0.760687 0.380343 0.924845i \(-0.375806\pi\)
0.380343 + 0.924845i \(0.375806\pi\)
\(968\) −68535.2 24923.7i −2.27563 0.827561i
\(969\) 1713.98 0.0568226
\(970\) 26660.4 + 19369.9i 0.882487 + 0.641165i
\(971\) 28.7466 88.4729i 0.000950074 0.00292403i −0.950580 0.310479i \(-0.899511\pi\)
0.951530 + 0.307555i \(0.0995107\pi\)
\(972\) 10058.7 + 30957.5i 0.331927 + 1.02157i
\(973\) −351.350 + 255.271i −0.0115763 + 0.00841069i
\(974\) 18138.4 13178.3i 0.596705 0.433532i
\(975\) 2025.78 + 6234.72i 0.0665405 + 0.204791i
\(976\) 28867.4 88844.9i 0.946746 2.91379i
\(977\) 4207.13 + 3056.66i 0.137767 + 0.100093i 0.654534 0.756032i \(-0.272865\pi\)
−0.516767 + 0.856126i \(0.672865\pi\)
\(978\) −68699.9 −2.24620
\(979\) −30376.7 + 29342.4i −0.991670 + 0.957904i
\(980\) 54705.2 1.78316
\(981\) 3007.33 + 2184.95i 0.0978763 + 0.0711113i
\(982\) 4635.70 14267.2i 0.150643 0.463631i
\(983\) −14199.5 43701.7i −0.460727 1.41797i −0.864278 0.503015i \(-0.832224\pi\)
0.403551 0.914957i \(-0.367776\pi\)
\(984\) −61910.5 + 44980.6i −2.00573 + 1.45725i
\(985\) −29614.7 + 21516.4i −0.957974 + 0.696009i
\(986\) 3038.67 + 9352.08i 0.0981451 + 0.302060i
\(987\) −127.240 + 391.605i −0.00410344 + 0.0126291i
\(988\) 20699.4 + 15039.0i 0.666532 + 0.484264i
\(989\) 8119.17 0.261046
\(990\) 10262.5 1443.71i 0.329457 0.0463477i
\(991\) 22935.6 0.735191 0.367595 0.929986i \(-0.380181\pi\)
0.367595 + 0.929986i \(0.380181\pi\)
\(992\) −33784.5 24545.9i −1.08131 0.785617i
\(993\) −16337.2 + 50280.7i −0.522100 + 1.60686i
\(994\) −410.071 1262.07i −0.0130852 0.0402720i
\(995\) −14114.2 + 10254.6i −0.449698 + 0.326725i
\(996\) 51965.7 37755.3i 1.65321 1.20113i
\(997\) −1240.92 3819.17i −0.0394187 0.121318i 0.929411 0.369047i \(-0.120316\pi\)
−0.968829 + 0.247729i \(0.920316\pi\)
\(998\) 25282.2 77810.7i 0.801899 2.46799i
\(999\) −8433.35 6127.19i −0.267087 0.194050i
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 11.4.c.a.4.1 yes 8
3.2 odd 2 99.4.f.c.37.2 8
4.3 odd 2 176.4.m.c.81.1 8
11.2 odd 10 121.4.c.b.27.1 8
11.3 even 5 inner 11.4.c.a.3.1 8
11.4 even 5 121.4.c.h.9.2 8
11.5 even 5 121.4.a.g.1.4 4
11.6 odd 10 121.4.a.f.1.1 4
11.7 odd 10 121.4.c.b.9.1 8
11.8 odd 10 121.4.c.i.3.2 8
11.9 even 5 121.4.c.h.27.2 8
11.10 odd 2 121.4.c.i.81.2 8
33.5 odd 10 1089.4.a.y.1.1 4
33.14 odd 10 99.4.f.c.91.2 8
33.17 even 10 1089.4.a.bh.1.4 4
44.3 odd 10 176.4.m.c.113.1 8
44.27 odd 10 1936.4.a.bk.1.1 4
44.39 even 10 1936.4.a.bl.1.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
11.4.c.a.3.1 8 11.3 even 5 inner
11.4.c.a.4.1 yes 8 1.1 even 1 trivial
99.4.f.c.37.2 8 3.2 odd 2
99.4.f.c.91.2 8 33.14 odd 10
121.4.a.f.1.1 4 11.6 odd 10
121.4.a.g.1.4 4 11.5 even 5
121.4.c.b.9.1 8 11.7 odd 10
121.4.c.b.27.1 8 11.2 odd 10
121.4.c.h.9.2 8 11.4 even 5
121.4.c.h.27.2 8 11.9 even 5
121.4.c.i.3.2 8 11.8 odd 10
121.4.c.i.81.2 8 11.10 odd 2
176.4.m.c.81.1 8 4.3 odd 2
176.4.m.c.113.1 8 44.3 odd 10
1089.4.a.y.1.1 4 33.5 odd 10
1089.4.a.bh.1.4 4 33.17 even 10
1936.4.a.bk.1.1 4 44.27 odd 10
1936.4.a.bl.1.1 4 44.39 even 10