Properties

Label 729.2.g.b.55.1
Level $729$
Weight $2$
Character 729.55
Analytic conductor $5.821$
Analytic rank $0$
Dimension $144$
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] = [729,2,Mod(28,729)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(729, base_ring=CyclotomicField(54))
 
chi = DirichletCharacter(H, H._module([44]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("729.28");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 729 = 3^{6} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 729.g (of order \(27\), degree \(18\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(5.82109430735\)
Analytic rank: \(0\)
Dimension: \(144\)
Relative dimension: \(8\) over \(\Q(\zeta_{27})\)
Twist minimal: no (minimal twist has level 81)
Sato-Tate group: $\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label 55.1
Character \(\chi\) \(=\) 729.55
Dual form 729.2.g.b.676.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.03275 + 2.39419i) q^{2} +(-3.29308 - 3.49047i) q^{4} +(0.0188451 + 0.323558i) q^{5} +(-3.75109 - 0.889024i) q^{7} +(6.85740 - 2.49589i) q^{8} +O(q^{10})\) \(q+(-1.03275 + 2.39419i) q^{2} +(-3.29308 - 3.49047i) q^{4} +(0.0188451 + 0.323558i) q^{5} +(-3.75109 - 0.889024i) q^{7} +(6.85740 - 2.49589i) q^{8} +(-0.794122 - 0.289037i) q^{10} +(1.05229 + 0.692099i) q^{11} +(3.90613 + 0.456561i) q^{13} +(6.00244 - 8.06268i) q^{14} +(-0.548323 + 9.41435i) q^{16} +(3.68665 - 3.09347i) q^{17} +(-3.47862 - 2.91891i) q^{19} +(1.06731 - 1.13128i) q^{20} +(-2.74377 + 1.80460i) q^{22} +(0.546542 - 0.129533i) q^{23} +(4.86186 - 0.568270i) q^{25} +(-5.12716 + 8.88050i) q^{26} +(9.24954 + 16.0207i) q^{28} +(1.27398 + 1.71125i) q^{29} +(-1.09026 + 3.64174i) q^{31} +(-8.93090 - 4.48526i) q^{32} +(3.59895 + 12.0213i) q^{34} +(0.216961 - 1.23045i) q^{35} +(-0.248079 - 1.40693i) q^{37} +(10.5810 - 5.31397i) q^{38} +(0.936794 + 2.17173i) q^{40} +(3.74004 + 8.67039i) q^{41} +(-3.23349 + 1.62392i) q^{43} +(-1.04952 - 5.95211i) q^{44} +(-0.254317 + 1.44230i) q^{46} +(1.09079 + 3.64349i) q^{47} +(7.02487 + 3.52802i) q^{49} +(-3.66055 + 12.2271i) q^{50} +(-11.2696 - 15.1377i) q^{52} +(3.57369 + 6.18982i) q^{53} +(-0.204104 + 0.353518i) q^{55} +(-27.9416 + 3.26591i) q^{56} +(-5.41276 + 1.28285i) q^{58} +(4.88395 - 3.21222i) q^{59} +(6.33580 - 6.71556i) q^{61} +(-7.59304 - 6.37131i) q^{62} +(5.51392 - 4.62673i) q^{64} +(-0.0741126 + 1.27246i) q^{65} +(0.128801 - 0.173010i) q^{67} +(-22.9381 - 2.68108i) q^{68} +(2.72186 + 1.79020i) q^{70} +(11.2063 + 4.07874i) q^{71} +(7.37938 - 2.68588i) q^{73} +(3.62465 + 0.859058i) q^{74} +(1.26704 + 21.7542i) q^{76} +(-3.33192 - 3.53163i) q^{77} +(3.30367 - 7.65876i) q^{79} -3.05642 q^{80} -24.6211 q^{82} +(-0.262659 + 0.608912i) q^{83} +(1.07039 + 1.13455i) q^{85} +(-0.548576 - 9.41868i) q^{86} +(8.94335 + 2.11961i) q^{88} +(-1.56940 + 0.571214i) q^{89} +(-14.2463 - 5.18524i) q^{91} +(-2.25194 - 1.48112i) q^{92} +(-9.84973 - 1.15127i) q^{94} +(0.878882 - 1.18054i) q^{95} +(0.937298 - 16.0928i) q^{97} +(-15.7017 + 13.1753i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 144 q - 9 q^{2} + 9 q^{4} - 9 q^{5} + 9 q^{7} + 18 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 144 q - 9 q^{2} + 9 q^{4} - 9 q^{5} + 9 q^{7} + 18 q^{8} - 18 q^{10} - 9 q^{11} + 9 q^{13} - 9 q^{14} + 9 q^{16} + 18 q^{17} - 18 q^{19} + 63 q^{20} + 9 q^{22} - 36 q^{23} + 9 q^{25} - 45 q^{26} - 9 q^{28} + 45 q^{29} + 9 q^{31} - 63 q^{32} + 9 q^{34} - 9 q^{35} - 18 q^{37} + 9 q^{38} + 9 q^{40} + 27 q^{41} + 9 q^{43} - 54 q^{44} - 18 q^{46} - 63 q^{47} + 9 q^{49} + 225 q^{50} + 27 q^{52} - 45 q^{53} - 9 q^{55} - 99 q^{56} + 9 q^{58} + 117 q^{59} + 9 q^{61} - 81 q^{62} - 18 q^{64} - 81 q^{65} + 36 q^{67} + 18 q^{68} + 63 q^{70} + 90 q^{71} - 18 q^{73} - 81 q^{74} + 90 q^{76} - 81 q^{77} + 63 q^{79} + 288 q^{80} - 36 q^{82} - 45 q^{83} + 63 q^{85} - 81 q^{86} + 90 q^{88} + 81 q^{89} - 18 q^{91} + 63 q^{92} + 63 q^{94} - 153 q^{95} + 36 q^{97} - 81 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/729\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{17}{27}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.03275 + 2.39419i −0.730266 + 1.69295i −0.00932059 + 0.999957i \(0.502967\pi\)
−0.720946 + 0.692991i \(0.756292\pi\)
\(3\) 0 0
\(4\) −3.29308 3.49047i −1.64654 1.74523i
\(5\) 0.0188451 + 0.323558i 0.00842779 + 0.144700i 0.999897 + 0.0143579i \(0.00457041\pi\)
−0.991469 + 0.130342i \(0.958393\pi\)
\(6\) 0 0
\(7\) −3.75109 0.889024i −1.41778 0.336020i −0.550913 0.834563i \(-0.685720\pi\)
−0.866865 + 0.498543i \(0.833869\pi\)
\(8\) 6.85740 2.49589i 2.42446 0.882430i
\(9\) 0 0
\(10\) −0.794122 0.289037i −0.251123 0.0914014i
\(11\) 1.05229 + 0.692099i 0.317276 + 0.208676i 0.698151 0.715951i \(-0.254007\pi\)
−0.380874 + 0.924627i \(0.624377\pi\)
\(12\) 0 0
\(13\) 3.90613 + 0.456561i 1.08337 + 0.126627i 0.638991 0.769214i \(-0.279352\pi\)
0.444374 + 0.895841i \(0.353426\pi\)
\(14\) 6.00244 8.06268i 1.60422 2.15484i
\(15\) 0 0
\(16\) −0.548323 + 9.41435i −0.137081 + 2.35359i
\(17\) 3.68665 3.09347i 0.894145 0.750277i −0.0748921 0.997192i \(-0.523861\pi\)
0.969037 + 0.246915i \(0.0794168\pi\)
\(18\) 0 0
\(19\) −3.47862 2.91891i −0.798050 0.669644i 0.149673 0.988735i \(-0.452178\pi\)
−0.947724 + 0.319092i \(0.896622\pi\)
\(20\) 1.06731 1.13128i 0.238658 0.252962i
\(21\) 0 0
\(22\) −2.74377 + 1.80460i −0.584973 + 0.384743i
\(23\) 0.546542 0.129533i 0.113962 0.0270095i −0.173239 0.984880i \(-0.555423\pi\)
0.287201 + 0.957870i \(0.407275\pi\)
\(24\) 0 0
\(25\) 4.86186 0.568270i 0.972371 0.113654i
\(26\) −5.12716 + 8.88050i −1.00552 + 1.74161i
\(27\) 0 0
\(28\) 9.24954 + 16.0207i 1.74800 + 3.02762i
\(29\) 1.27398 + 1.71125i 0.236572 + 0.317771i 0.904516 0.426441i \(-0.140233\pi\)
−0.667944 + 0.744212i \(0.732825\pi\)
\(30\) 0 0
\(31\) −1.09026 + 3.64174i −0.195817 + 0.654075i 0.802530 + 0.596611i \(0.203487\pi\)
−0.998348 + 0.0574639i \(0.981699\pi\)
\(32\) −8.93090 4.48526i −1.57877 0.792890i
\(33\) 0 0
\(34\) 3.59895 + 12.0213i 0.617215 + 2.06164i
\(35\) 0.216961 1.23045i 0.0366732 0.207984i
\(36\) 0 0
\(37\) −0.248079 1.40693i −0.0407839 0.231297i 0.957602 0.288095i \(-0.0930220\pi\)
−0.998386 + 0.0567981i \(0.981911\pi\)
\(38\) 10.5810 5.31397i 1.71646 0.862039i
\(39\) 0 0
\(40\) 0.936794 + 2.17173i 0.148120 + 0.343381i
\(41\) 3.74004 + 8.67039i 0.584096 + 1.35409i 0.912317 + 0.409486i \(0.134292\pi\)
−0.328221 + 0.944601i \(0.606449\pi\)
\(42\) 0 0
\(43\) −3.23349 + 1.62392i −0.493102 + 0.247645i −0.677931 0.735126i \(-0.737123\pi\)
0.184829 + 0.982771i \(0.440827\pi\)
\(44\) −1.04952 5.95211i −0.158221 0.897314i
\(45\) 0 0
\(46\) −0.254317 + 1.44230i −0.0374969 + 0.212656i
\(47\) 1.09079 + 3.64349i 0.159108 + 0.531458i 0.999952 0.00982012i \(-0.00312589\pi\)
−0.840844 + 0.541278i \(0.817941\pi\)
\(48\) 0 0
\(49\) 7.02487 + 3.52802i 1.00355 + 0.504003i
\(50\) −3.66055 + 12.2271i −0.517680 + 1.72917i
\(51\) 0 0
\(52\) −11.2696 15.1377i −1.56281 2.09922i
\(53\) 3.57369 + 6.18982i 0.490884 + 0.850237i 0.999945 0.0104941i \(-0.00334044\pi\)
−0.509061 + 0.860731i \(0.670007\pi\)
\(54\) 0 0
\(55\) −0.204104 + 0.353518i −0.0275214 + 0.0476684i
\(56\) −27.9416 + 3.26591i −3.73386 + 0.436425i
\(57\) 0 0
\(58\) −5.41276 + 1.28285i −0.710731 + 0.168446i
\(59\) 4.88395 3.21222i 0.635836 0.418196i −0.190254 0.981735i \(-0.560931\pi\)
0.826089 + 0.563539i \(0.190561\pi\)
\(60\) 0 0
\(61\) 6.33580 6.71556i 0.811216 0.859839i −0.181113 0.983462i \(-0.557970\pi\)
0.992329 + 0.123623i \(0.0394514\pi\)
\(62\) −7.59304 6.37131i −0.964317 0.809158i
\(63\) 0 0
\(64\) 5.51392 4.62673i 0.689240 0.578341i
\(65\) −0.0741126 + 1.27246i −0.00919253 + 0.157830i
\(66\) 0 0
\(67\) 0.128801 0.173010i 0.0157355 0.0211365i −0.794186 0.607675i \(-0.792102\pi\)
0.809921 + 0.586539i \(0.199510\pi\)
\(68\) −22.9381 2.68108i −2.78165 0.325129i
\(69\) 0 0
\(70\) 2.72186 + 1.79020i 0.325325 + 0.213969i
\(71\) 11.2063 + 4.07874i 1.32994 + 0.484058i 0.906629 0.421928i \(-0.138646\pi\)
0.423308 + 0.905986i \(0.360869\pi\)
\(72\) 0 0
\(73\) 7.37938 2.68588i 0.863691 0.314358i 0.128082 0.991764i \(-0.459118\pi\)
0.735610 + 0.677406i \(0.236896\pi\)
\(74\) 3.62465 + 0.859058i 0.421357 + 0.0998635i
\(75\) 0 0
\(76\) 1.26704 + 21.7542i 0.145339 + 2.49538i
\(77\) −3.33192 3.53163i −0.379708 0.402467i
\(78\) 0 0
\(79\) 3.30367 7.65876i 0.371691 0.861678i −0.625017 0.780611i \(-0.714908\pi\)
0.996709 0.0810667i \(-0.0258327\pi\)
\(80\) −3.05642 −0.341718
\(81\) 0 0
\(82\) −24.6211 −2.71894
\(83\) −0.262659 + 0.608912i −0.0288306 + 0.0668367i −0.932023 0.362399i \(-0.881958\pi\)
0.903192 + 0.429236i \(0.141217\pi\)
\(84\) 0 0
\(85\) 1.07039 + 1.13455i 0.116100 + 0.123059i
\(86\) −0.548576 9.41868i −0.0591545 1.01564i
\(87\) 0 0
\(88\) 8.94335 + 2.11961i 0.953364 + 0.225951i
\(89\) −1.56940 + 0.571214i −0.166356 + 0.0605486i −0.423856 0.905730i \(-0.639324\pi\)
0.257500 + 0.966278i \(0.417101\pi\)
\(90\) 0 0
\(91\) −14.2463 5.18524i −1.49342 0.543561i
\(92\) −2.25194 1.48112i −0.234781 0.154418i
\(93\) 0 0
\(94\) −9.84973 1.15127i −1.01592 0.118744i
\(95\) 0.878882 1.18054i 0.0901714 0.121121i
\(96\) 0 0
\(97\) 0.937298 16.0928i 0.0951682 1.63397i −0.526133 0.850403i \(-0.676358\pi\)
0.621301 0.783572i \(-0.286605\pi\)
\(98\) −15.7017 + 13.1753i −1.58611 + 1.33091i
\(99\) 0 0
\(100\) −17.9940 15.0988i −1.79940 1.50988i
\(101\) 2.37235 2.51454i 0.236057 0.250206i −0.598506 0.801118i \(-0.704239\pi\)
0.834563 + 0.550912i \(0.185720\pi\)
\(102\) 0 0
\(103\) 5.19032 3.41373i 0.511417 0.336364i −0.267431 0.963577i \(-0.586175\pi\)
0.778848 + 0.627213i \(0.215804\pi\)
\(104\) 27.9254 6.61845i 2.73831 0.648992i
\(105\) 0 0
\(106\) −18.5103 + 2.16355i −1.79788 + 0.210142i
\(107\) 0.773565 1.33985i 0.0747833 0.129529i −0.826209 0.563364i \(-0.809507\pi\)
0.900992 + 0.433836i \(0.142840\pi\)
\(108\) 0 0
\(109\) 6.28071 + 10.8785i 0.601583 + 1.04197i 0.992581 + 0.121581i \(0.0387965\pi\)
−0.390998 + 0.920391i \(0.627870\pi\)
\(110\) −0.635601 0.853760i −0.0606022 0.0814029i
\(111\) 0 0
\(112\) 10.4264 34.8266i 0.985201 3.29080i
\(113\) −17.4823 8.77994i −1.64460 0.825947i −0.998007 0.0631087i \(-0.979899\pi\)
−0.646589 0.762838i \(-0.723805\pi\)
\(114\) 0 0
\(115\) 0.0522110 + 0.174397i 0.00486871 + 0.0162626i
\(116\) 1.77774 10.0821i 0.165059 0.936097i
\(117\) 0 0
\(118\) 2.64676 + 15.0105i 0.243654 + 1.38183i
\(119\) −16.5791 + 8.32636i −1.51981 + 0.763276i
\(120\) 0 0
\(121\) −3.72857 8.64381i −0.338961 0.785800i
\(122\) 9.53500 + 22.1046i 0.863259 + 2.00126i
\(123\) 0 0
\(124\) 16.3017 8.18702i 1.46393 0.735216i
\(125\) 0.556893 + 3.15830i 0.0498100 + 0.282487i
\(126\) 0 0
\(127\) 0.0822160 0.466270i 0.00729549 0.0413748i −0.980943 0.194297i \(-0.937757\pi\)
0.988238 + 0.152922i \(0.0488685\pi\)
\(128\) −0.349827 1.16850i −0.0309206 0.103282i
\(129\) 0 0
\(130\) −2.96998 1.49158i −0.260484 0.130820i
\(131\) −2.00931 + 6.71155i −0.175554 + 0.586391i 0.824243 + 0.566236i \(0.191601\pi\)
−0.999797 + 0.0201544i \(0.993584\pi\)
\(132\) 0 0
\(133\) 10.4536 + 14.0417i 0.906445 + 1.21757i
\(134\) 0.281198 + 0.487050i 0.0242918 + 0.0420747i
\(135\) 0 0
\(136\) 17.5599 30.4146i 1.50575 2.60803i
\(137\) 19.7273 2.30579i 1.68541 0.196997i 0.781261 0.624205i \(-0.214577\pi\)
0.904153 + 0.427208i \(0.140503\pi\)
\(138\) 0 0
\(139\) 15.0469 3.56618i 1.27626 0.302479i 0.464032 0.885818i \(-0.346402\pi\)
0.812229 + 0.583339i \(0.198254\pi\)
\(140\) −5.00931 + 3.29468i −0.423364 + 0.278451i
\(141\) 0 0
\(142\) −21.3386 + 22.6176i −1.79069 + 1.89802i
\(143\) 3.79438 + 3.18386i 0.317302 + 0.266248i
\(144\) 0 0
\(145\) −0.529681 + 0.444455i −0.0439876 + 0.0369100i
\(146\) −1.19058 + 20.4415i −0.0985332 + 1.69175i
\(147\) 0 0
\(148\) −4.09388 + 5.49904i −0.336515 + 0.452018i
\(149\) 8.59010 + 1.00404i 0.703728 + 0.0822541i 0.460428 0.887697i \(-0.347696\pi\)
0.243300 + 0.969951i \(0.421770\pi\)
\(150\) 0 0
\(151\) 2.53151 + 1.66500i 0.206011 + 0.135496i 0.648322 0.761366i \(-0.275471\pi\)
−0.442311 + 0.896862i \(0.645841\pi\)
\(152\) −31.1396 11.3339i −2.52575 0.919299i
\(153\) 0 0
\(154\) 11.8965 4.32995i 0.958643 0.348918i
\(155\) −1.19886 0.284135i −0.0962947 0.0228223i
\(156\) 0 0
\(157\) −0.540951 9.28776i −0.0431726 0.741244i −0.948548 0.316633i \(-0.897448\pi\)
0.905376 0.424612i \(-0.139589\pi\)
\(158\) 14.9247 + 15.8192i 1.18734 + 1.25851i
\(159\) 0 0
\(160\) 1.28294 2.97419i 0.101425 0.235130i
\(161\) −2.16529 −0.170648
\(162\) 0 0
\(163\) 2.41567 0.189210 0.0946048 0.995515i \(-0.469841\pi\)
0.0946048 + 0.995515i \(0.469841\pi\)
\(164\) 17.9474 41.6068i 1.40146 3.24894i
\(165\) 0 0
\(166\) −1.18659 1.25771i −0.0920971 0.0976173i
\(167\) 0.0292845 + 0.502796i 0.00226611 + 0.0389075i 0.999252 0.0386800i \(-0.0123153\pi\)
−0.996986 + 0.0775876i \(0.975278\pi\)
\(168\) 0 0
\(169\) 2.39981 + 0.568765i 0.184601 + 0.0437512i
\(170\) −3.82178 + 1.39101i −0.293117 + 0.106686i
\(171\) 0 0
\(172\) 16.3164 + 5.93867i 1.24411 + 0.452820i
\(173\) −4.45986 2.93329i −0.339077 0.223014i 0.368538 0.929613i \(-0.379858\pi\)
−0.707615 + 0.706598i \(0.750229\pi\)
\(174\) 0 0
\(175\) −18.7425 2.19068i −1.41680 0.165600i
\(176\) −7.09265 + 9.52709i −0.534629 + 0.718131i
\(177\) 0 0
\(178\) 0.253205 4.34736i 0.0189785 0.325848i
\(179\) 13.8827 11.6490i 1.03764 0.870683i 0.0458999 0.998946i \(-0.485384\pi\)
0.991740 + 0.128263i \(0.0409400\pi\)
\(180\) 0 0
\(181\) 8.98433 + 7.53875i 0.667800 + 0.560351i 0.912413 0.409270i \(-0.134217\pi\)
−0.244613 + 0.969621i \(0.578661\pi\)
\(182\) 27.1274 28.7534i 2.01082 2.13134i
\(183\) 0 0
\(184\) 3.42456 2.25237i 0.252462 0.166047i
\(185\) 0.450547 0.106782i 0.0331249 0.00785074i
\(186\) 0 0
\(187\) 6.02040 0.703684i 0.440255 0.0514585i
\(188\) 9.12542 15.8057i 0.665539 1.15275i
\(189\) 0 0
\(190\) 1.91878 + 3.32342i 0.139203 + 0.241106i
\(191\) 11.8767 + 15.9532i 0.859367 + 1.15433i 0.986713 + 0.162472i \(0.0519466\pi\)
−0.127346 + 0.991858i \(0.540646\pi\)
\(192\) 0 0
\(193\) −4.57679 + 15.2875i −0.329444 + 1.10042i 0.619505 + 0.784993i \(0.287333\pi\)
−0.948950 + 0.315428i \(0.897852\pi\)
\(194\) 37.5612 + 18.8639i 2.69674 + 1.35435i
\(195\) 0 0
\(196\) −10.8190 36.1381i −0.772789 2.58130i
\(197\) 1.15341 6.54129i 0.0821768 0.466048i −0.915753 0.401741i \(-0.868405\pi\)
0.997930 0.0643070i \(-0.0204837\pi\)
\(198\) 0 0
\(199\) −0.983166 5.57581i −0.0696948 0.395259i −0.999621 0.0275137i \(-0.991241\pi\)
0.929927 0.367745i \(-0.119870\pi\)
\(200\) 31.9214 16.0315i 2.25718 1.13360i
\(201\) 0 0
\(202\) 3.57024 + 8.27674i 0.251201 + 0.582350i
\(203\) −3.25746 7.55165i −0.228629 0.530022i
\(204\) 0 0
\(205\) −2.73489 + 1.37351i −0.191013 + 0.0959304i
\(206\) 2.81279 + 15.9521i 0.195977 + 1.11144i
\(207\) 0 0
\(208\) −6.44004 + 36.5233i −0.446537 + 2.53244i
\(209\) −1.64033 5.47908i −0.113464 0.378996i
\(210\) 0 0
\(211\) 13.6528 + 6.85671i 0.939899 + 0.472035i 0.851678 0.524066i \(-0.175585\pi\)
0.0882216 + 0.996101i \(0.471882\pi\)
\(212\) 9.83687 32.8574i 0.675599 2.25666i
\(213\) 0 0
\(214\) 2.40896 + 3.23580i 0.164673 + 0.221195i
\(215\) −0.586367 1.01562i −0.0399899 0.0692645i
\(216\) 0 0
\(217\) 7.32727 12.6912i 0.497408 0.861535i
\(218\) −32.5317 + 3.80241i −2.20332 + 0.257531i
\(219\) 0 0
\(220\) 1.90607 0.451748i 0.128508 0.0304568i
\(221\) 15.8129 10.4003i 1.06369 0.699601i
\(222\) 0 0
\(223\) −13.9427 + 14.7784i −0.933674 + 0.989637i −0.999967 0.00816311i \(-0.997402\pi\)
0.0662922 + 0.997800i \(0.478883\pi\)
\(224\) 29.5131 + 24.7644i 1.97192 + 1.65464i
\(225\) 0 0
\(226\) 39.0757 32.7884i 2.59928 2.18105i
\(227\) −0.0586242 + 1.00654i −0.00389103 + 0.0668063i −0.999695 0.0247091i \(-0.992134\pi\)
0.995804 + 0.0915154i \(0.0291711\pi\)
\(228\) 0 0
\(229\) −6.05300 + 8.13059i −0.399994 + 0.537285i −0.955796 0.294030i \(-0.905004\pi\)
0.555803 + 0.831314i \(0.312411\pi\)
\(230\) −0.471461 0.0551059i −0.0310872 0.00363357i
\(231\) 0 0
\(232\) 13.0073 + 8.55502i 0.853969 + 0.561664i
\(233\) −18.4171 6.70328i −1.20654 0.439146i −0.341040 0.940049i \(-0.610779\pi\)
−0.865504 + 0.500902i \(0.833002\pi\)
\(234\) 0 0
\(235\) −1.15832 + 0.421596i −0.0755608 + 0.0275019i
\(236\) −27.2954 6.46913i −1.77678 0.421104i
\(237\) 0 0
\(238\) −2.81273 48.2927i −0.182322 3.13035i
\(239\) −19.5911 20.7654i −1.26725 1.34320i −0.912951 0.408068i \(-0.866202\pi\)
−0.354295 0.935134i \(-0.615279\pi\)
\(240\) 0 0
\(241\) −4.81958 + 11.1731i −0.310457 + 0.719719i −0.999990 0.00453476i \(-0.998557\pi\)
0.689533 + 0.724254i \(0.257816\pi\)
\(242\) 24.5456 1.57785
\(243\) 0 0
\(244\) −44.3047 −2.83632
\(245\) −1.00914 + 2.33944i −0.0644713 + 0.149461i
\(246\) 0 0
\(247\) −12.2553 12.9898i −0.779785 0.826524i
\(248\) 1.61299 + 27.6940i 0.102425 + 1.75857i
\(249\) 0 0
\(250\) −8.13670 1.92843i −0.514610 0.121965i
\(251\) −4.11036 + 1.49605i −0.259444 + 0.0944298i −0.468467 0.883481i \(-0.655194\pi\)
0.209024 + 0.977911i \(0.432971\pi\)
\(252\) 0 0
\(253\) 0.664768 + 0.241956i 0.0417936 + 0.0152116i
\(254\) 1.03143 + 0.678382i 0.0647177 + 0.0425655i
\(255\) 0 0
\(256\) 17.4574 + 2.04048i 1.09109 + 0.127530i
\(257\) −15.4931 + 20.8108i −0.966432 + 1.29814i −0.0119333 + 0.999929i \(0.503799\pi\)
−0.954499 + 0.298215i \(0.903609\pi\)
\(258\) 0 0
\(259\) −0.320225 + 5.49805i −0.0198978 + 0.341632i
\(260\) 4.68555 3.93164i 0.290585 0.243830i
\(261\) 0 0
\(262\) −13.9936 11.7420i −0.864528 0.725425i
\(263\) −19.5406 + 20.7118i −1.20492 + 1.27714i −0.254182 + 0.967157i \(0.581806\pi\)
−0.950741 + 0.309987i \(0.899675\pi\)
\(264\) 0 0
\(265\) −1.93542 + 1.27294i −0.118892 + 0.0781964i
\(266\) −44.4144 + 10.5264i −2.72322 + 0.645416i
\(267\) 0 0
\(268\) −1.02804 + 0.120160i −0.0627973 + 0.00733995i
\(269\) −14.0246 + 24.2913i −0.855093 + 1.48106i 0.0214661 + 0.999770i \(0.493167\pi\)
−0.876559 + 0.481295i \(0.840167\pi\)
\(270\) 0 0
\(271\) 5.55847 + 9.62755i 0.337653 + 0.584832i 0.983991 0.178219i \(-0.0570337\pi\)
−0.646338 + 0.763051i \(0.723700\pi\)
\(272\) 27.1015 + 36.4037i 1.64327 + 2.20730i
\(273\) 0 0
\(274\) −14.8529 + 49.6121i −0.897296 + 2.99718i
\(275\) 5.50936 + 2.76691i 0.332227 + 0.166851i
\(276\) 0 0
\(277\) −3.13137 10.4595i −0.188146 0.628450i −0.999063 0.0432889i \(-0.986216\pi\)
0.810917 0.585161i \(-0.198969\pi\)
\(278\) −7.00161 + 39.7081i −0.419929 + 2.38153i
\(279\) 0 0
\(280\) −1.58327 8.97919i −0.0946187 0.536609i
\(281\) 4.19170 2.10515i 0.250056 0.125583i −0.319357 0.947634i \(-0.603467\pi\)
0.569413 + 0.822052i \(0.307171\pi\)
\(282\) 0 0
\(283\) −12.8119 29.7014i −0.761590 1.76556i −0.633414 0.773813i \(-0.718347\pi\)
−0.128177 0.991751i \(-0.540912\pi\)
\(284\) −22.6664 52.5467i −1.34500 3.11807i
\(285\) 0 0
\(286\) −11.5414 + 5.79632i −0.682459 + 0.342744i
\(287\) −6.32103 35.8484i −0.373119 2.11606i
\(288\) 0 0
\(289\) 1.06984 6.06738i 0.0629319 0.356905i
\(290\) −0.517080 1.72717i −0.0303640 0.101423i
\(291\) 0 0
\(292\) −33.6759 16.9127i −1.97073 0.989739i
\(293\) 5.74127 19.1772i 0.335409 1.12034i −0.609439 0.792833i \(-0.708605\pi\)
0.944848 0.327510i \(-0.106209\pi\)
\(294\) 0 0
\(295\) 1.13138 + 1.51971i 0.0658714 + 0.0884807i
\(296\) −5.21271 9.02868i −0.302983 0.524781i
\(297\) 0 0
\(298\) −11.2753 + 19.5294i −0.653161 + 1.13131i
\(299\) 2.19400 0.256442i 0.126882 0.0148304i
\(300\) 0 0
\(301\) 13.5728 3.21681i 0.782323 0.185414i
\(302\) −6.60074 + 4.34137i −0.379830 + 0.249818i
\(303\) 0 0
\(304\) 29.3870 31.1484i 1.68546 1.78649i
\(305\) 2.29227 + 1.92344i 0.131255 + 0.110136i
\(306\) 0 0
\(307\) −4.16550 + 3.49527i −0.237738 + 0.199486i −0.753871 0.657023i \(-0.771816\pi\)
0.516133 + 0.856509i \(0.327371\pi\)
\(308\) −1.35474 + 23.2599i −0.0771933 + 1.32536i
\(309\) 0 0
\(310\) 1.91840 2.57686i 0.108958 0.146356i
\(311\) 10.9151 + 1.27580i 0.618941 + 0.0723438i 0.419784 0.907624i \(-0.362106\pi\)
0.199157 + 0.979968i \(0.436180\pi\)
\(312\) 0 0
\(313\) −20.7180 13.6264i −1.17105 0.770211i −0.193538 0.981093i \(-0.561996\pi\)
−0.977512 + 0.210882i \(0.932367\pi\)
\(314\) 22.7953 + 8.29683i 1.28642 + 0.468217i
\(315\) 0 0
\(316\) −37.6119 + 13.6896i −2.11583 + 0.770100i
\(317\) −22.7525 5.39244i −1.27791 0.302870i −0.465025 0.885298i \(-0.653955\pi\)
−0.812882 + 0.582428i \(0.802103\pi\)
\(318\) 0 0
\(319\) 0.156235 + 2.68244i 0.00874746 + 0.150188i
\(320\) 1.60093 + 1.69688i 0.0894945 + 0.0948586i
\(321\) 0 0
\(322\) 2.23620 5.18410i 0.124619 0.288899i
\(323\) −21.8540 −1.21599
\(324\) 0 0
\(325\) 19.2505 1.06783
\(326\) −2.49479 + 5.78357i −0.138173 + 0.320322i
\(327\) 0 0
\(328\) 47.2873 + 50.1216i 2.61100 + 2.76750i
\(329\) −0.852496 14.6368i −0.0469996 0.806953i
\(330\) 0 0
\(331\) −15.2535 3.61514i −0.838406 0.198706i −0.211086 0.977467i \(-0.567700\pi\)
−0.627320 + 0.778761i \(0.715848\pi\)
\(332\) 2.99034 1.08840i 0.164116 0.0597335i
\(333\) 0 0
\(334\) −1.23403 0.449151i −0.0675233 0.0245765i
\(335\) 0.0584059 + 0.0384142i 0.00319106 + 0.00209879i
\(336\) 0 0
\(337\) 9.56786 + 1.11832i 0.521195 + 0.0609189i 0.372623 0.927983i \(-0.378458\pi\)
0.148572 + 0.988902i \(0.452532\pi\)
\(338\) −3.84014 + 5.15821i −0.208876 + 0.280569i
\(339\) 0 0
\(340\) 0.435214 7.47234i 0.0236028 0.405244i
\(341\) −3.66771 + 3.07758i −0.198618 + 0.166660i
\(342\) 0 0
\(343\) −2.54270 2.13358i −0.137293 0.115203i
\(344\) −18.1202 + 19.2063i −0.976975 + 1.03553i
\(345\) 0 0
\(346\) 11.6288 7.64838i 0.625168 0.411179i
\(347\) −20.8248 + 4.93558i −1.11794 + 0.264956i −0.747736 0.663996i \(-0.768859\pi\)
−0.370200 + 0.928952i \(0.620711\pi\)
\(348\) 0 0
\(349\) 30.6431 3.58167i 1.64029 0.191722i 0.754661 0.656115i \(-0.227802\pi\)
0.885629 + 0.464393i \(0.153728\pi\)
\(350\) 24.6012 42.6106i 1.31499 2.27763i
\(351\) 0 0
\(352\) −6.29361 10.9008i −0.335450 0.581017i
\(353\) −12.0041 16.1243i −0.638915 0.858211i 0.358237 0.933631i \(-0.383378\pi\)
−0.997152 + 0.0754191i \(0.975971\pi\)
\(354\) 0 0
\(355\) −1.10853 + 3.70274i −0.0588345 + 0.196521i
\(356\) 7.16196 + 3.59687i 0.379583 + 0.190634i
\(357\) 0 0
\(358\) 13.5524 + 45.2683i 0.716268 + 2.39250i
\(359\) 2.90565 16.4788i 0.153354 0.869715i −0.806921 0.590660i \(-0.798868\pi\)
0.960275 0.279056i \(-0.0900214\pi\)
\(360\) 0 0
\(361\) 0.281455 + 1.59621i 0.0148134 + 0.0840111i
\(362\) −27.3278 + 13.7245i −1.43632 + 0.721345i
\(363\) 0 0
\(364\) 28.8155 + 66.8018i 1.51034 + 3.50137i
\(365\) 1.00810 + 2.33704i 0.0527665 + 0.122326i
\(366\) 0 0
\(367\) 21.8093 10.9531i 1.13844 0.571745i 0.223246 0.974762i \(-0.428335\pi\)
0.915193 + 0.403017i \(0.132038\pi\)
\(368\) 0.919785 + 5.21636i 0.0479471 + 0.271922i
\(369\) 0 0
\(370\) −0.209648 + 1.18897i −0.0108991 + 0.0618118i
\(371\) −7.90234 26.3956i −0.410269 1.37039i
\(372\) 0 0
\(373\) 11.5800 + 5.81569i 0.599589 + 0.301125i 0.722585 0.691282i \(-0.242954\pi\)
−0.122996 + 0.992407i \(0.539250\pi\)
\(374\) −4.53283 + 15.1407i −0.234387 + 0.782908i
\(375\) 0 0
\(376\) 16.5737 + 22.2624i 0.854725 + 1.14809i
\(377\) 4.19503 + 7.26601i 0.216055 + 0.374219i
\(378\) 0 0
\(379\) 5.56867 9.64522i 0.286043 0.495442i −0.686818 0.726829i \(-0.740993\pi\)
0.972862 + 0.231387i \(0.0743265\pi\)
\(380\) −7.01488 + 0.819921i −0.359856 + 0.0420611i
\(381\) 0 0
\(382\) −50.4606 + 11.9594i −2.58179 + 0.611895i
\(383\) −26.5219 + 17.4437i −1.35521 + 0.891333i −0.999071 0.0431010i \(-0.986276\pi\)
−0.356136 + 0.934434i \(0.615906\pi\)
\(384\) 0 0
\(385\) 1.07990 1.14462i 0.0550367 0.0583355i
\(386\) −31.8746 26.7459i −1.62237 1.36133i
\(387\) 0 0
\(388\) −59.2579 + 49.7233i −3.00836 + 2.52432i
\(389\) 0.398874 6.84840i 0.0202237 0.347228i −0.972984 0.230873i \(-0.925842\pi\)
0.993208 0.116355i \(-0.0371210\pi\)
\(390\) 0 0
\(391\) 1.61421 2.16825i 0.0816339 0.109653i
\(392\) 56.9779 + 6.65976i 2.87782 + 0.336369i
\(393\) 0 0
\(394\) 14.4699 + 9.51701i 0.728984 + 0.479460i
\(395\) 2.54031 + 0.924598i 0.127817 + 0.0465216i
\(396\) 0 0
\(397\) 3.49386 1.27166i 0.175352 0.0638229i −0.252852 0.967505i \(-0.581369\pi\)
0.428204 + 0.903682i \(0.359146\pi\)
\(398\) 14.3649 + 3.40455i 0.720048 + 0.170655i
\(399\) 0 0
\(400\) 2.68402 + 46.0828i 0.134201 + 2.30414i
\(401\) 22.7501 + 24.1137i 1.13609 + 1.20418i 0.976160 + 0.217052i \(0.0696442\pi\)
0.159926 + 0.987129i \(0.448874\pi\)
\(402\) 0 0
\(403\) −5.92139 + 13.7273i −0.294965 + 0.683807i
\(404\) −16.5892 −0.825346
\(405\) 0 0
\(406\) 21.4442 1.06426
\(407\) 0.712682 1.65218i 0.0353263 0.0818957i
\(408\) 0 0
\(409\) −16.6863 17.6865i −0.825087 0.874541i 0.168720 0.985664i \(-0.446037\pi\)
−0.993807 + 0.111123i \(0.964555\pi\)
\(410\) −0.463987 7.96635i −0.0229147 0.393430i
\(411\) 0 0
\(412\) −29.0076 6.87494i −1.42910 0.338704i
\(413\) −21.1759 + 7.70738i −1.04200 + 0.379255i
\(414\) 0 0
\(415\) −0.201968 0.0735104i −0.00991423 0.00360848i
\(416\) −32.8374 21.5975i −1.60999 1.05891i
\(417\) 0 0
\(418\) 14.8120 + 1.73128i 0.724479 + 0.0846794i
\(419\) −3.36853 + 4.52473i −0.164564 + 0.221047i −0.876754 0.480939i \(-0.840296\pi\)
0.712190 + 0.701986i \(0.247703\pi\)
\(420\) 0 0
\(421\) −1.89250 + 32.4930i −0.0922348 + 1.58361i 0.561882 + 0.827218i \(0.310078\pi\)
−0.654117 + 0.756394i \(0.726959\pi\)
\(422\) −30.5163 + 25.6062i −1.48551 + 1.24649i
\(423\) 0 0
\(424\) 39.9553 + 33.5265i 1.94040 + 1.62819i
\(425\) 16.1661 17.1350i 0.784169 0.831171i
\(426\) 0 0
\(427\) −29.7364 + 19.5580i −1.43905 + 0.946476i
\(428\) −7.22413 + 1.71215i −0.349191 + 0.0827599i
\(429\) 0 0
\(430\) 3.03715 0.354992i 0.146465 0.0171193i
\(431\) 0.705902 1.22266i 0.0340021 0.0588934i −0.848524 0.529158i \(-0.822508\pi\)
0.882526 + 0.470264i \(0.155841\pi\)
\(432\) 0 0
\(433\) −3.07047 5.31820i −0.147557 0.255576i 0.782767 0.622315i \(-0.213808\pi\)
−0.930324 + 0.366739i \(0.880474\pi\)
\(434\) 22.8179 + 30.6498i 1.09529 + 1.47124i
\(435\) 0 0
\(436\) 17.2882 57.7465i 0.827953 2.76555i
\(437\) −2.27931 1.14471i −0.109034 0.0547590i
\(438\) 0 0
\(439\) 3.81709 + 12.7500i 0.182180 + 0.608523i 0.999478 + 0.0323082i \(0.0102858\pi\)
−0.817298 + 0.576215i \(0.804529\pi\)
\(440\) −0.517279 + 2.93364i −0.0246603 + 0.139856i
\(441\) 0 0
\(442\) 8.56950 + 48.6000i 0.407610 + 2.31167i
\(443\) 3.90497 1.96115i 0.185531 0.0931770i −0.353609 0.935393i \(-0.615046\pi\)
0.539140 + 0.842216i \(0.318749\pi\)
\(444\) 0 0
\(445\) −0.214396 0.497027i −0.0101634 0.0235613i
\(446\) −20.9830 48.6440i −0.993573 2.30336i
\(447\) 0 0
\(448\) −24.7965 + 12.4533i −1.17152 + 0.588361i
\(449\) 5.92614 + 33.6088i 0.279672 + 1.58610i 0.723719 + 0.690095i \(0.242431\pi\)
−0.444047 + 0.896003i \(0.646458\pi\)
\(450\) 0 0
\(451\) −2.06518 + 11.7122i −0.0972454 + 0.551506i
\(452\) 26.9246 + 89.9344i 1.26643 + 4.23016i
\(453\) 0 0
\(454\) −2.34930 1.17986i −0.110258 0.0553737i
\(455\) 1.40925 4.70724i 0.0660668 0.220679i
\(456\) 0 0
\(457\) 1.56049 + 2.09610i 0.0729966 + 0.0980515i 0.837122 0.547016i \(-0.184236\pi\)
−0.764125 + 0.645068i \(0.776829\pi\)
\(458\) −13.2149 22.8889i −0.617493 1.06953i
\(459\) 0 0
\(460\) 0.436791 0.756545i 0.0203655 0.0352741i
\(461\) 5.83610 0.682142i 0.271814 0.0317705i 0.0209061 0.999781i \(-0.493345\pi\)
0.250908 + 0.968011i \(0.419271\pi\)
\(462\) 0 0
\(463\) 24.7970 5.87700i 1.15241 0.273127i 0.390374 0.920657i \(-0.372346\pi\)
0.762040 + 0.647529i \(0.224198\pi\)
\(464\) −16.8089 + 11.0554i −0.780331 + 0.513232i
\(465\) 0 0
\(466\) 35.0692 37.1712i 1.62455 1.72192i
\(467\) 20.6922 + 17.3628i 0.957522 + 0.803456i 0.980548 0.196279i \(-0.0628857\pi\)
−0.0230263 + 0.999735i \(0.507330\pi\)
\(468\) 0 0
\(469\) −0.636953 + 0.534467i −0.0294118 + 0.0246794i
\(470\) 0.186883 3.20865i 0.00862026 0.148004i
\(471\) 0 0
\(472\) 25.4738 34.2173i 1.17253 1.57498i
\(473\) −4.52646 0.529068i −0.208127 0.0243266i
\(474\) 0 0
\(475\) −18.5713 12.2145i −0.852109 0.560441i
\(476\) 83.6593 + 30.4495i 3.83452 + 1.39565i
\(477\) 0 0
\(478\) 69.9491 25.4594i 3.19940 1.16449i
\(479\) 25.3313 + 6.00363i 1.15742 + 0.274313i 0.764105 0.645092i \(-0.223181\pi\)
0.393312 + 0.919405i \(0.371329\pi\)
\(480\) 0 0
\(481\) −0.326681 5.60890i −0.0148954 0.255744i
\(482\) −21.7730 23.0780i −0.991731 1.05117i
\(483\) 0 0
\(484\) −17.8924 + 41.4792i −0.813291 + 1.88542i
\(485\) 5.22461 0.237238
\(486\) 0 0
\(487\) −7.41759 −0.336123 −0.168061 0.985777i \(-0.553751\pi\)
−0.168061 + 0.985777i \(0.553751\pi\)
\(488\) 26.6858 61.8647i 1.20801 2.80048i
\(489\) 0 0
\(490\) −4.55888 4.83213i −0.205949 0.218293i
\(491\) −0.974800 16.7367i −0.0439921 0.755315i −0.946114 0.323834i \(-0.895028\pi\)
0.902122 0.431481i \(-0.142009\pi\)
\(492\) 0 0
\(493\) 9.99042 + 2.36777i 0.449946 + 0.106639i
\(494\) 43.7568 15.9262i 1.96871 0.716553i
\(495\) 0 0
\(496\) −33.6868 12.2610i −1.51258 0.550534i
\(497\) −38.4095 25.2624i −1.72290 1.13317i
\(498\) 0 0
\(499\) −18.1347 2.11964i −0.811821 0.0948882i −0.299955 0.953953i \(-0.596972\pi\)
−0.511866 + 0.859065i \(0.671046\pi\)
\(500\) 9.19003 12.3444i 0.410991 0.552056i
\(501\) 0 0
\(502\) 0.663161 11.3860i 0.0295983 0.508184i
\(503\) 20.5047 17.2055i 0.914261 0.767156i −0.0586635 0.998278i \(-0.518684\pi\)
0.972925 + 0.231121i \(0.0742395\pi\)
\(504\) 0 0
\(505\) 0.858307 + 0.720205i 0.0381942 + 0.0320487i
\(506\) −1.26583 + 1.34170i −0.0562730 + 0.0596459i
\(507\) 0 0
\(508\) −1.89824 + 1.24849i −0.0842209 + 0.0553930i
\(509\) 28.5748 6.77235i 1.26656 0.300179i 0.458187 0.888856i \(-0.348499\pi\)
0.808369 + 0.588677i \(0.200351\pi\)
\(510\) 0 0
\(511\) −30.0685 + 3.51451i −1.33015 + 0.155473i
\(512\) −21.6947 + 37.5763i −0.958780 + 1.66066i
\(513\) 0 0
\(514\) −33.8245 58.5858i −1.49194 2.58411i
\(515\) 1.20235 + 1.61504i 0.0529819 + 0.0711670i
\(516\) 0 0
\(517\) −1.37383 + 4.58893i −0.0604212 + 0.201821i
\(518\) −12.8327 6.44481i −0.563835 0.283169i
\(519\) 0 0
\(520\) 2.66771 + 8.91077i 0.116987 + 0.390763i
\(521\) 1.78086 10.0998i 0.0780209 0.442479i −0.920625 0.390449i \(-0.872320\pi\)
0.998646 0.0520298i \(-0.0165691\pi\)
\(522\) 0 0
\(523\) −5.81644 32.9867i −0.254335 1.44241i −0.797774 0.602957i \(-0.793989\pi\)
0.543439 0.839449i \(-0.317122\pi\)
\(524\) 30.0432 15.0883i 1.31244 0.659134i
\(525\) 0 0
\(526\) −29.4074 68.1740i −1.28222 2.97253i
\(527\) 7.24618 + 16.7985i 0.315648 + 0.731755i
\(528\) 0 0
\(529\) −20.2716 + 10.1808i −0.881375 + 0.442643i
\(530\) −1.04886 5.94840i −0.0455597 0.258382i
\(531\) 0 0
\(532\) 14.5873 82.7284i 0.632438 3.58673i
\(533\) 10.6505 + 35.5752i 0.461325 + 1.54093i
\(534\) 0 0
\(535\) 0.448098 + 0.225043i 0.0193730 + 0.00972948i
\(536\) 0.451426 1.50787i 0.0194986 0.0651300i
\(537\) 0 0
\(538\) −43.6740 58.6643i −1.88292 2.52920i
\(539\) 4.95043 + 8.57440i 0.213230 + 0.369325i
\(540\) 0 0
\(541\) −19.3141 + 33.4530i −0.830377 + 1.43826i 0.0673627 + 0.997729i \(0.478542\pi\)
−0.897740 + 0.440526i \(0.854792\pi\)
\(542\) −28.7907 + 3.36515i −1.23667 + 0.144546i
\(543\) 0 0
\(544\) −46.8002 + 11.0918i −2.00654 + 0.475559i
\(545\) −3.40147 + 2.23718i −0.145703 + 0.0958304i
\(546\) 0 0
\(547\) 7.78178 8.24821i 0.332725 0.352668i −0.539314 0.842105i \(-0.681316\pi\)
0.872039 + 0.489437i \(0.162798\pi\)
\(548\) −73.0118 61.2642i −3.11891 2.61708i
\(549\) 0 0
\(550\) −12.3143 + 10.3329i −0.525084 + 0.440598i
\(551\) 0.563296 9.67142i 0.0239972 0.412016i
\(552\) 0 0
\(553\) −19.2012 + 25.7916i −0.816517 + 1.09677i
\(554\) 28.2759 + 3.30498i 1.20133 + 0.140415i
\(555\) 0 0
\(556\) −61.9983 40.7769i −2.62931 1.72933i
\(557\) −11.1013 4.04055i −0.470377 0.171203i 0.0959459 0.995387i \(-0.469412\pi\)
−0.566323 + 0.824183i \(0.691635\pi\)
\(558\) 0 0
\(559\) −13.3718 + 4.86695i −0.565568 + 0.205850i
\(560\) 11.4649 + 2.71723i 0.484481 + 0.114824i
\(561\) 0 0
\(562\) 0.711141 + 12.2098i 0.0299977 + 0.515040i
\(563\) 14.0789 + 14.9227i 0.593354 + 0.628918i 0.952564 0.304338i \(-0.0984354\pi\)
−0.359210 + 0.933257i \(0.616954\pi\)
\(564\) 0 0
\(565\) 2.51136 5.82200i 0.105654 0.244933i
\(566\) 84.3423 3.54517
\(567\) 0 0
\(568\) 87.0259 3.65152
\(569\) 6.45233 14.9582i 0.270496 0.627080i −0.727778 0.685813i \(-0.759447\pi\)
0.998274 + 0.0587332i \(0.0187061\pi\)
\(570\) 0 0
\(571\) −13.8809 14.7129i −0.580898 0.615716i 0.368562 0.929603i \(-0.379850\pi\)
−0.949460 + 0.313887i \(0.898369\pi\)
\(572\) −1.38205 23.7289i −0.0577864 0.992154i
\(573\) 0 0
\(574\) 92.3559 + 21.8887i 3.85486 + 0.913618i
\(575\) 2.58360 0.940353i 0.107744 0.0392154i
\(576\) 0 0
\(577\) 3.36027 + 1.22304i 0.139890 + 0.0509157i 0.411016 0.911628i \(-0.365174\pi\)
−0.271126 + 0.962544i \(0.587396\pi\)
\(578\) 13.4216 + 8.82751i 0.558264 + 0.367176i
\(579\) 0 0
\(580\) 3.29564 + 0.385205i 0.136844 + 0.0159948i
\(581\) 1.52659 2.05057i 0.0633338 0.0850720i
\(582\) 0 0
\(583\) −0.523422 + 8.98680i −0.0216779 + 0.372195i
\(584\) 43.8997 36.8362i 1.81658 1.52429i
\(585\) 0 0
\(586\) 39.9845 + 33.5510i 1.65174 + 1.38598i
\(587\) −5.44859 + 5.77516i −0.224887 + 0.238367i −0.829986 0.557784i \(-0.811652\pi\)
0.605099 + 0.796150i \(0.293133\pi\)
\(588\) 0 0
\(589\) 14.4225 9.48584i 0.594269 0.390857i
\(590\) −4.80690 + 1.13926i −0.197897 + 0.0469024i
\(591\) 0 0
\(592\) 13.3813 1.56405i 0.549969 0.0642821i
\(593\) 13.0180 22.5478i 0.534584 0.925926i −0.464599 0.885521i \(-0.653802\pi\)
0.999183 0.0404055i \(-0.0128650\pi\)
\(594\) 0 0
\(595\) −3.00650 5.20740i −0.123254 0.213483i
\(596\) −24.7834 33.2898i −1.01517 1.36360i
\(597\) 0 0
\(598\) −1.65189 + 5.51770i −0.0675509 + 0.225636i
\(599\) −16.8175 8.44609i −0.687146 0.345098i 0.0707306 0.997495i \(-0.477467\pi\)
−0.757877 + 0.652398i \(0.773763\pi\)
\(600\) 0 0
\(601\) −2.30500 7.69924i −0.0940230 0.314059i 0.898021 0.439953i \(-0.145005\pi\)
−0.992044 + 0.125895i \(0.959820\pi\)
\(602\) −6.31568 + 35.8180i −0.257408 + 1.45983i
\(603\) 0 0
\(604\) −2.52485 14.3191i −0.102734 0.582636i
\(605\) 2.72651 1.36930i 0.110848 0.0556701i
\(606\) 0 0
\(607\) 7.68029 + 17.8049i 0.311734 + 0.722680i 0.999996 0.00278207i \(-0.000885561\pi\)
−0.688263 + 0.725462i \(0.741626\pi\)
\(608\) 17.9751 + 41.6710i 0.728987 + 1.68998i
\(609\) 0 0
\(610\) −6.97244 + 3.50169i −0.282306 + 0.141779i
\(611\) 2.59729 + 14.7300i 0.105075 + 0.595910i
\(612\) 0 0
\(613\) −2.54229 + 14.4180i −0.102682 + 0.582339i 0.889439 + 0.457054i \(0.151095\pi\)
−0.992121 + 0.125284i \(0.960016\pi\)
\(614\) −4.06641 13.5828i −0.164107 0.548156i
\(615\) 0 0
\(616\) −31.6629 15.9017i −1.27573 0.640698i
\(617\) −5.94031 + 19.8420i −0.239148 + 0.798809i 0.751184 + 0.660092i \(0.229483\pi\)
−0.990332 + 0.138717i \(0.955702\pi\)
\(618\) 0 0
\(619\) −15.4730 20.7838i −0.621912 0.835373i 0.373836 0.927495i \(-0.378042\pi\)
−0.995748 + 0.0921222i \(0.970635\pi\)
\(620\) 2.95618 + 5.12026i 0.118723 + 0.205635i
\(621\) 0 0
\(622\) −14.3271 + 24.8154i −0.574466 + 0.995005i
\(623\) 6.39477 0.747442i 0.256201 0.0299456i
\(624\) 0 0
\(625\) 22.8037 5.40457i 0.912146 0.216183i
\(626\) 54.0208 35.5300i 2.15911 1.42007i
\(627\) 0 0
\(628\) −30.6372 + 32.4736i −1.22256 + 1.29584i
\(629\) −5.26686 4.41942i −0.210004 0.176214i
\(630\) 0 0
\(631\) −13.6194 + 11.4280i −0.542180 + 0.454943i −0.872283 0.489002i \(-0.837361\pi\)
0.330102 + 0.943945i \(0.392917\pi\)
\(632\) 3.53914 60.7648i 0.140780 2.41709i
\(633\) 0 0
\(634\) 36.4082 48.9047i 1.44596 1.94225i
\(635\) 0.152415 + 0.0178147i 0.00604840 + 0.000706956i
\(636\) 0 0
\(637\) 25.8293 + 16.9882i 1.02339 + 0.673097i
\(638\) −6.58363 2.39625i −0.260648 0.0948683i
\(639\) 0 0
\(640\) 0.371486 0.135210i 0.0146843 0.00534464i
\(641\) 4.60209 + 1.09071i 0.181771 + 0.0430806i 0.320493 0.947251i \(-0.396151\pi\)
−0.138722 + 0.990331i \(0.544299\pi\)
\(642\) 0 0
\(643\) 0.490195 + 8.41632i 0.0193314 + 0.331907i 0.994084 + 0.108618i \(0.0346425\pi\)
−0.974752 + 0.223289i \(0.928321\pi\)
\(644\) 7.13047 + 7.55785i 0.280980 + 0.297821i
\(645\) 0 0
\(646\) 22.5698 52.3227i 0.887997 2.05861i
\(647\) −23.1964 −0.911943 −0.455971 0.889994i \(-0.650708\pi\)
−0.455971 + 0.889994i \(0.650708\pi\)
\(648\) 0 0
\(649\) 7.36248 0.289003
\(650\) −19.8810 + 46.0893i −0.779797 + 1.80777i
\(651\) 0 0
\(652\) −7.95500 8.43180i −0.311542 0.330215i
\(653\) 2.10012 + 36.0577i 0.0821841 + 1.41105i 0.747390 + 0.664386i \(0.231307\pi\)
−0.665206 + 0.746660i \(0.731656\pi\)
\(654\) 0 0
\(655\) −2.20944 0.523647i −0.0863300 0.0204606i
\(656\) −83.6768 + 30.4559i −3.26703 + 1.18910i
\(657\) 0 0
\(658\) 35.9237 + 13.0752i 1.40045 + 0.509722i
\(659\) 25.3331 + 16.6619i 0.986839 + 0.649054i 0.936863 0.349696i \(-0.113715\pi\)
0.0499756 + 0.998750i \(0.484086\pi\)
\(660\) 0 0
\(661\) 12.8043 + 1.49661i 0.498030 + 0.0582114i 0.361400 0.932411i \(-0.382299\pi\)
0.136630 + 0.990622i \(0.456373\pi\)
\(662\) 24.4084 32.7862i 0.948659 1.27427i
\(663\) 0 0
\(664\) −0.281381 + 4.83112i −0.0109197 + 0.187484i
\(665\) −4.34629 + 3.64697i −0.168542 + 0.141424i
\(666\) 0 0
\(667\) 0.917946 + 0.770248i 0.0355430 + 0.0298241i
\(668\) 1.65856 1.75797i 0.0641715 0.0680178i
\(669\) 0 0
\(670\) −0.152290 + 0.100163i −0.00588346 + 0.00386962i
\(671\) 11.3149 2.68168i 0.436807 0.103525i
\(672\) 0 0
\(673\) −6.41242 + 0.749505i −0.247181 + 0.0288913i −0.238781 0.971073i \(-0.576748\pi\)
−0.00839975 + 0.999965i \(0.502674\pi\)
\(674\) −12.5587 + 21.7523i −0.483744 + 0.837869i
\(675\) 0 0
\(676\) −5.91752 10.2494i −0.227597 0.394209i
\(677\) −10.4833 14.0815i −0.402905 0.541196i 0.553649 0.832750i \(-0.313235\pi\)
−0.956554 + 0.291554i \(0.905828\pi\)
\(678\) 0 0
\(679\) −17.8228 + 59.5322i −0.683975 + 2.28464i
\(680\) 10.1718 + 5.10848i 0.390072 + 0.195901i
\(681\) 0 0
\(682\) −3.58046 11.9596i −0.137103 0.457956i
\(683\) −3.16828 + 17.9682i −0.121231 + 0.687535i 0.862244 + 0.506492i \(0.169058\pi\)
−0.983475 + 0.181042i \(0.942053\pi\)
\(684\) 0 0
\(685\) 1.11782 + 6.33946i 0.0427097 + 0.242218i
\(686\) 7.73418 3.88425i 0.295292 0.148301i
\(687\) 0 0
\(688\) −13.5151 31.3316i −0.515259 1.19451i
\(689\) 11.1333 + 25.8098i 0.424144 + 0.983276i
\(690\) 0 0
\(691\) −36.4273 + 18.2945i −1.38576 + 0.695954i −0.976309 0.216379i \(-0.930575\pi\)
−0.409449 + 0.912333i \(0.634279\pi\)
\(692\) 4.44812 + 25.2266i 0.169092 + 0.958970i
\(693\) 0 0
\(694\) 9.69020 54.9559i 0.367835 2.08610i
\(695\) 1.43743 + 4.80134i 0.0545247 + 0.182125i
\(696\) 0 0
\(697\) 40.6098 + 20.3950i 1.53821 + 0.772516i
\(698\) −23.0716 + 77.0645i −0.873273 + 2.91693i
\(699\) 0 0
\(700\) 54.0740 + 72.6340i 2.04381 + 2.74531i
\(701\) −21.5739 37.3671i −0.814834 1.41133i −0.909447 0.415820i \(-0.863495\pi\)
0.0946129 0.995514i \(-0.469839\pi\)
\(702\) 0 0
\(703\) −3.24372 + 5.61828i −0.122339 + 0.211897i
\(704\) 9.00438 1.05246i 0.339365 0.0396661i
\(705\) 0 0
\(706\) 51.0020 12.0877i 1.91949 0.454926i
\(707\) −11.1344 + 7.32319i −0.418751 + 0.275417i
\(708\) 0 0
\(709\) 6.46423 6.85169i 0.242769 0.257321i −0.594520 0.804081i \(-0.702658\pi\)
0.837289 + 0.546761i \(0.184139\pi\)
\(710\) −7.72023 6.47804i −0.289735 0.243116i
\(711\) 0 0
\(712\) −9.33630 + 7.83409i −0.349893 + 0.293595i
\(713\) −0.124151 + 2.13159i −0.00464949 + 0.0798286i
\(714\) 0 0
\(715\) −0.958659 + 1.28770i −0.0358518 + 0.0481573i
\(716\) −86.3771 10.0960i −3.22806 0.377306i
\(717\) 0 0
\(718\) 36.4525 + 23.9752i 1.36039 + 0.894745i
\(719\) −20.4128 7.42965i −0.761268 0.277079i −0.0679289 0.997690i \(-0.521639\pi\)
−0.693339 + 0.720611i \(0.743861\pi\)
\(720\) 0 0
\(721\) −22.5042 + 8.19087i −0.838101 + 0.305044i
\(722\) −4.11231 0.974635i −0.153044 0.0362721i
\(723\) 0 0
\(724\) −3.27242 56.1852i −0.121618 2.08811i
\(725\) 7.16635 + 7.59589i 0.266152 + 0.282104i
\(726\) 0 0
\(727\) 8.91954 20.6778i 0.330807 0.766898i −0.668915 0.743339i \(-0.733241\pi\)
0.999722 0.0235590i \(-0.00749975\pi\)
\(728\) −110.635 −4.10039
\(729\) 0 0
\(730\) −6.63645 −0.245626
\(731\) −6.89720 + 15.9895i −0.255102 + 0.591394i
\(732\) 0 0
\(733\) −18.7053 19.8264i −0.690895 0.732306i 0.283046 0.959106i \(-0.408655\pi\)
−0.973941 + 0.226801i \(0.927173\pi\)
\(734\) 3.70006 + 63.5275i 0.136572 + 2.34484i
\(735\) 0 0
\(736\) −5.46210 1.29454i −0.201336 0.0477174i
\(737\) 0.255275 0.0929125i 0.00940318 0.00342248i
\(738\) 0 0
\(739\) −29.4451 10.7172i −1.08316 0.394237i −0.262075 0.965048i \(-0.584407\pi\)
−0.821082 + 0.570811i \(0.806629\pi\)
\(740\) −1.85641 1.22098i −0.0682429 0.0448841i
\(741\) 0 0
\(742\) 71.3573 + 8.34048i 2.61961 + 0.306189i
\(743\) 25.9930 34.9147i 0.953592 1.28090i −0.00614072 0.999981i \(-0.501955\pi\)
0.959733 0.280915i \(-0.0906379\pi\)
\(744\) 0 0
\(745\) −0.162983 + 2.79832i −0.00597125 + 0.102522i
\(746\) −25.8831 + 21.7185i −0.947648 + 0.795171i
\(747\) 0 0
\(748\) −22.2819 18.6967i −0.814706 0.683620i
\(749\) −4.09287 + 4.33819i −0.149550 + 0.158514i
\(750\) 0 0
\(751\) −42.8341 + 28.1724i −1.56304 + 1.02803i −0.587224 + 0.809425i \(0.699779\pi\)
−0.975814 + 0.218601i \(0.929851\pi\)
\(752\) −34.8992 + 8.27126i −1.27264 + 0.301622i
\(753\) 0 0
\(754\) −21.7286 + 2.53971i −0.791311 + 0.0924909i
\(755\) −0.491017 + 0.850466i −0.0178699 + 0.0309516i
\(756\) 0 0
\(757\) −6.51051 11.2765i −0.236629 0.409853i 0.723116 0.690727i \(-0.242709\pi\)
−0.959745 + 0.280874i \(0.909376\pi\)
\(758\) 17.3414 + 23.2936i 0.629869 + 0.846061i
\(759\) 0 0
\(760\) 3.08034 10.2890i 0.111736 0.373223i
\(761\) 21.1840 + 10.6390i 0.767918 + 0.385663i 0.789220 0.614110i \(-0.210485\pi\)
−0.0213023 + 0.999773i \(0.506781\pi\)
\(762\) 0 0
\(763\) −13.8882 46.3900i −0.502788 1.67943i
\(764\) 16.5730 93.9902i 0.599591 3.40045i
\(765\) 0 0
\(766\) −14.3730 81.5136i −0.519319 2.94520i
\(767\) 20.5439 10.3175i 0.741797 0.372545i
\(768\) 0 0
\(769\) 15.9106 + 36.8849i 0.573750 + 1.33010i 0.919985 + 0.391954i \(0.128201\pi\)
−0.346235 + 0.938148i \(0.612540\pi\)
\(770\) 1.62518 + 3.76760i 0.0585675 + 0.135775i
\(771\) 0 0
\(772\) 68.4323 34.3680i 2.46293 1.23693i
\(773\) 0.721794 + 4.09350i 0.0259611 + 0.147233i 0.995033 0.0995459i \(-0.0317390\pi\)
−0.969072 + 0.246779i \(0.920628\pi\)
\(774\) 0 0
\(775\) −3.23122 + 18.3252i −0.116069 + 0.658259i
\(776\) −33.7384 112.694i −1.21114 4.04548i
\(777\) 0 0
\(778\) 15.9844 + 8.02768i 0.573069 + 0.287806i
\(779\) 12.2979 41.0778i 0.440618 1.47177i
\(780\) 0 0
\(781\) 8.96929 + 12.0478i 0.320946 + 0.431106i
\(782\) 3.52414