Properties

Label 637.2.f.h.393.3
Level $637$
Weight $2$
Character 637.393
Analytic conductor $5.086$
Analytic rank $0$
Dimension $8$
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [637,2,Mod(295,637)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(637, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("637.295");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 637 = 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 637.f (of order \(3\), degree \(2\), 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: \(5.08647060876\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: 8.0.100088711424.6
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 13x^{6} + 130x^{4} - 507x^{2} + 1521 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 393.3
Root \(1.87694 + 1.08365i\) of defining polynomial
Character \(\chi\) \(=\) 637.393
Dual form 637.2.f.h.295.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.651388 + 1.12824i) q^{2} +(-1.44073 - 2.49541i) q^{3} +(0.151388 - 0.262211i) q^{4} +2.88145 q^{5} +(1.87694 - 3.25096i) q^{6} +3.00000 q^{8} +(-2.65139 + 4.59234i) q^{9} +(1.87694 + 3.25096i) q^{10} +(2.95416 + 5.11676i) q^{11} -0.872434 q^{12} +(3.31767 - 1.41176i) q^{13} +(-4.15139 - 7.19041i) q^{15} +(1.65139 + 2.86029i) q^{16} +(0.436217 - 0.755550i) q^{17} -6.90833 q^{18} +(-1.44073 + 2.49541i) q^{19} +(0.436217 - 0.755550i) q^{20} +(-3.84861 + 6.66599i) q^{22} +(-3.30278 - 5.72058i) q^{23} +(-4.32218 - 7.48624i) q^{24} +3.30278 q^{25} +(3.75389 + 2.82352i) q^{26} +6.63534 q^{27} +(-0.651388 - 1.12824i) q^{29} +(5.40833 - 9.36750i) q^{30} +0.872434 q^{31} +(0.848612 - 1.46984i) q^{32} +(8.51229 - 14.7437i) q^{33} +1.13659 q^{34} +(0.802776 + 1.39045i) q^{36} +(-0.697224 - 1.20763i) q^{37} -3.75389 q^{38} +(-8.30278 - 6.24500i) q^{39} +8.64436 q^{40} +(-3.75389 - 6.50192i) q^{41} +(-2.75694 + 4.77516i) q^{43} +1.78890 q^{44} +(-7.63985 + 13.2326i) q^{45} +(4.30278 - 7.45263i) q^{46} -12.3982 q^{47} +(4.75840 - 8.24179i) q^{48} +(2.15139 + 3.72631i) q^{50} -2.51388 q^{51} +(0.132076 - 1.08365i) q^{52} +9.60555 q^{53} +(4.32218 + 7.48624i) q^{54} +(8.51229 + 14.7437i) q^{55} +8.30278 q^{57} +(0.848612 - 1.46984i) q^{58} +(-3.31767 + 5.74637i) q^{59} -2.51388 q^{60} +(-2.88145 + 4.99082i) q^{61} +(0.568293 + 0.984312i) q^{62} +8.81665 q^{64} +(9.55971 - 4.06792i) q^{65} +22.1792 q^{66} +(-0.500000 - 0.866025i) q^{67} +(-0.132076 - 0.228762i) q^{68} +(-9.51680 + 16.4836i) q^{69} +(-2.00000 + 3.46410i) q^{71} +(-7.95416 + 13.7770i) q^{72} -5.76291 q^{73} +(0.908327 - 1.57327i) q^{74} +(-4.75840 - 8.24179i) q^{75} +(0.436217 + 0.755550i) q^{76} +(1.63751 - 13.4354i) q^{78} +0.605551 q^{79} +(4.75840 + 8.24179i) q^{80} +(-1.60555 - 2.78090i) q^{81} +(4.89047 - 8.47055i) q^{82} -6.63534 q^{83} +(1.25694 - 2.17708i) q^{85} -7.18335 q^{86} +(-1.87694 + 3.25096i) q^{87} +(8.86249 + 15.3503i) q^{88} +(-4.32218 - 7.48624i) q^{89} -19.9060 q^{90} -2.00000 q^{92} +(-1.25694 - 2.17708i) q^{93} +(-8.07607 - 13.9882i) q^{94} +(-4.15139 + 7.19041i) q^{95} -4.89047 q^{96} +(3.88596 - 6.73069i) q^{97} -31.3305 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 2 q^{2} - 6 q^{4} + 24 q^{8} - 14 q^{9} + 2 q^{11} - 26 q^{15} + 6 q^{16} - 12 q^{18} - 38 q^{22} - 12 q^{23} + 12 q^{25} + 2 q^{29} + 14 q^{32} - 8 q^{36} - 20 q^{37} - 52 q^{39} + 14 q^{43} + 72 q^{44}+ \cdots - 92 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(248\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
<
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.651388 + 1.12824i 0.460601 + 0.797784i 0.998991 0.0449118i \(-0.0143007\pi\)
−0.538390 + 0.842696i \(0.680967\pi\)
\(3\) −1.44073 2.49541i −0.831804 1.44073i −0.896606 0.442829i \(-0.853975\pi\)
0.0648022 0.997898i \(-0.479358\pi\)
\(4\) 0.151388 0.262211i 0.0756939 0.131106i
\(5\) 2.88145 1.28863 0.644313 0.764762i \(-0.277144\pi\)
0.644313 + 0.764762i \(0.277144\pi\)
\(6\) 1.87694 3.25096i 0.766259 1.32720i
\(7\) 0 0
\(8\) 3.00000 1.06066
\(9\) −2.65139 + 4.59234i −0.883796 + 1.53078i
\(10\) 1.87694 + 3.25096i 0.593542 + 1.02804i
\(11\) 2.95416 + 5.11676i 0.890714 + 1.54276i 0.839021 + 0.544098i \(0.183128\pi\)
0.0516924 + 0.998663i \(0.483538\pi\)
\(12\) −0.872434 −0.251850
\(13\) 3.31767 1.41176i 0.920156 0.391551i
\(14\) 0 0
\(15\) −4.15139 7.19041i −1.07188 1.85656i
\(16\) 1.65139 + 2.86029i 0.412847 + 0.715072i
\(17\) 0.436217 0.755550i 0.105798 0.183248i −0.808266 0.588818i \(-0.799594\pi\)
0.914064 + 0.405570i \(0.132927\pi\)
\(18\) −6.90833 −1.62831
\(19\) −1.44073 + 2.49541i −0.330525 + 0.572487i −0.982615 0.185655i \(-0.940559\pi\)
0.652090 + 0.758142i \(0.273893\pi\)
\(20\) 0.436217 0.755550i 0.0975411 0.168946i
\(21\) 0 0
\(22\) −3.84861 + 6.66599i −0.820527 + 1.42119i
\(23\) −3.30278 5.72058i −0.688676 1.19282i −0.972266 0.233877i \(-0.924859\pi\)
0.283590 0.958946i \(-0.408475\pi\)
\(24\) −4.32218 7.48624i −0.882261 1.52812i
\(25\) 3.30278 0.660555
\(26\) 3.75389 + 2.82352i 0.736198 + 0.553737i
\(27\) 6.63534 1.27697
\(28\) 0 0
\(29\) −0.651388 1.12824i −0.120960 0.209508i 0.799187 0.601083i \(-0.205264\pi\)
−0.920146 + 0.391575i \(0.871931\pi\)
\(30\) 5.40833 9.36750i 0.987421 1.71026i
\(31\) 0.872434 0.156694 0.0783469 0.996926i \(-0.475036\pi\)
0.0783469 + 0.996926i \(0.475036\pi\)
\(32\) 0.848612 1.46984i 0.150015 0.259833i
\(33\) 8.51229 14.7437i 1.48180 2.56655i
\(34\) 1.13659 0.194923
\(35\) 0 0
\(36\) 0.802776 + 1.39045i 0.133796 + 0.231741i
\(37\) −0.697224 1.20763i −0.114623 0.198533i 0.803006 0.595971i \(-0.203233\pi\)
−0.917629 + 0.397438i \(0.869899\pi\)
\(38\) −3.75389 −0.608961
\(39\) −8.30278 6.24500i −1.32951 1.00000i
\(40\) 8.64436 1.36679
\(41\) −3.75389 6.50192i −0.586259 1.01543i −0.994717 0.102653i \(-0.967267\pi\)
0.408458 0.912777i \(-0.366066\pi\)
\(42\) 0 0
\(43\) −2.75694 + 4.77516i −0.420429 + 0.728205i −0.995981 0.0895602i \(-0.971454\pi\)
0.575552 + 0.817765i \(0.304787\pi\)
\(44\) 1.78890 0.269686
\(45\) −7.63985 + 13.2326i −1.13888 + 1.97260i
\(46\) 4.30278 7.45263i 0.634410 1.09883i
\(47\) −12.3982 −1.80847 −0.904235 0.427035i \(-0.859558\pi\)
−0.904235 + 0.427035i \(0.859558\pi\)
\(48\) 4.75840 8.24179i 0.686816 1.18960i
\(49\) 0 0
\(50\) 2.15139 + 3.72631i 0.304252 + 0.526980i
\(51\) −2.51388 −0.352013
\(52\) 0.132076 1.08365i 0.0183156 0.150276i
\(53\) 9.60555 1.31942 0.659712 0.751519i \(-0.270678\pi\)
0.659712 + 0.751519i \(0.270678\pi\)
\(54\) 4.32218 + 7.48624i 0.588174 + 1.01875i
\(55\) 8.51229 + 14.7437i 1.14780 + 1.98804i
\(56\) 0 0
\(57\) 8.30278 1.09973
\(58\) 0.848612 1.46984i 0.111428 0.192999i
\(59\) −3.31767 + 5.74637i −0.431924 + 0.748114i −0.997039 0.0768979i \(-0.975498\pi\)
0.565115 + 0.825012i \(0.308832\pi\)
\(60\) −2.51388 −0.324540
\(61\) −2.88145 + 4.99082i −0.368932 + 0.639010i −0.989399 0.145223i \(-0.953610\pi\)
0.620467 + 0.784233i \(0.286943\pi\)
\(62\) 0.568293 + 0.984312i 0.0721733 + 0.125008i
\(63\) 0 0
\(64\) 8.81665 1.10208
\(65\) 9.55971 4.06792i 1.18574 0.504563i
\(66\) 22.1792 2.73007
\(67\) −0.500000 0.866025i −0.0610847 0.105802i 0.833866 0.551967i \(-0.186123\pi\)
−0.894951 + 0.446165i \(0.852789\pi\)
\(68\) −0.132076 0.228762i −0.0160166 0.0277415i
\(69\) −9.51680 + 16.4836i −1.14569 + 1.98439i
\(70\) 0 0
\(71\) −2.00000 + 3.46410i −0.237356 + 0.411113i −0.959955 0.280155i \(-0.909614\pi\)
0.722599 + 0.691268i \(0.242948\pi\)
\(72\) −7.95416 + 13.7770i −0.937407 + 1.62364i
\(73\) −5.76291 −0.674497 −0.337249 0.941416i \(-0.609496\pi\)
−0.337249 + 0.941416i \(0.609496\pi\)
\(74\) 0.908327 1.57327i 0.105591 0.182889i
\(75\) −4.75840 8.24179i −0.549452 0.951680i
\(76\) 0.436217 + 0.755550i 0.0500375 + 0.0866675i
\(77\) 0 0
\(78\) 1.63751 13.4354i 0.185411 1.52126i
\(79\) 0.605551 0.0681298 0.0340649 0.999420i \(-0.489155\pi\)
0.0340649 + 0.999420i \(0.489155\pi\)
\(80\) 4.75840 + 8.24179i 0.532005 + 0.921460i
\(81\) −1.60555 2.78090i −0.178395 0.308988i
\(82\) 4.89047 8.47055i 0.540062 0.935416i
\(83\) −6.63534 −0.728323 −0.364162 0.931336i \(-0.618644\pi\)
−0.364162 + 0.931336i \(0.618644\pi\)
\(84\) 0 0
\(85\) 1.25694 2.17708i 0.136334 0.236138i
\(86\) −7.18335 −0.774600
\(87\) −1.87694 + 3.25096i −0.201230 + 0.348540i
\(88\) 8.86249 + 15.3503i 0.944745 + 1.63635i
\(89\) −4.32218 7.48624i −0.458150 0.793539i 0.540713 0.841207i \(-0.318154\pi\)
−0.998863 + 0.0476677i \(0.984821\pi\)
\(90\) −19.9060 −2.09828
\(91\) 0 0
\(92\) −2.00000 −0.208514
\(93\) −1.25694 2.17708i −0.130339 0.225753i
\(94\) −8.07607 13.9882i −0.832983 1.44277i
\(95\) −4.15139 + 7.19041i −0.425923 + 0.737721i
\(96\) −4.89047 −0.499132
\(97\) 3.88596 6.73069i 0.394560 0.683398i −0.598485 0.801134i \(-0.704230\pi\)
0.993045 + 0.117736i \(0.0375638\pi\)
\(98\) 0 0
\(99\) −31.3305 −3.14884
\(100\) 0.500000 0.866025i 0.0500000 0.0866025i
\(101\) 4.32218 + 7.48624i 0.430073 + 0.744908i 0.996879 0.0789429i \(-0.0251545\pi\)
−0.566806 + 0.823851i \(0.691821\pi\)
\(102\) −1.63751 2.83625i −0.162138 0.280831i
\(103\) 4.89047 0.481873 0.240936 0.970541i \(-0.422545\pi\)
0.240936 + 0.970541i \(0.422545\pi\)
\(104\) 9.95301 4.23527i 0.975973 0.415303i
\(105\) 0 0
\(106\) 6.25694 + 10.8373i 0.607728 + 1.05262i
\(107\) −4.65139 8.05644i −0.449667 0.778845i 0.548698 0.836021i \(-0.315124\pi\)
−0.998364 + 0.0571755i \(0.981791\pi\)
\(108\) 1.00451 1.73986i 0.0966590 0.167418i
\(109\) −6.21110 −0.594916 −0.297458 0.954735i \(-0.596139\pi\)
−0.297458 + 0.954735i \(0.596139\pi\)
\(110\) −11.0896 + 19.2077i −1.05735 + 1.83139i
\(111\) −2.00902 + 3.47972i −0.190688 + 0.330281i
\(112\) 0 0
\(113\) 7.40833 12.8316i 0.696917 1.20710i −0.272613 0.962124i \(-0.587888\pi\)
0.969530 0.244972i \(-0.0787786\pi\)
\(114\) 5.40833 + 9.36750i 0.506536 + 0.877346i
\(115\) −9.51680 16.4836i −0.887446 1.53710i
\(116\) −0.394449 −0.0366236
\(117\) −2.31316 + 18.9790i −0.213852 + 1.75461i
\(118\) −8.64436 −0.795778
\(119\) 0 0
\(120\) −12.4542 21.5712i −1.13690 1.96918i
\(121\) −11.9542 + 20.7052i −1.08674 + 1.88229i
\(122\) −7.50778 −0.679722
\(123\) −10.8167 + 18.7350i −0.975305 + 1.68928i
\(124\) 0.132076 0.228762i 0.0118608 0.0205434i
\(125\) −4.89047 −0.437417
\(126\) 0 0
\(127\) 1.45416 + 2.51868i 0.129036 + 0.223497i 0.923303 0.384071i \(-0.125478\pi\)
−0.794267 + 0.607569i \(0.792145\pi\)
\(128\) 4.04584 + 7.00759i 0.357605 + 0.619390i
\(129\) 15.8880 1.39886
\(130\) 10.8167 + 8.13583i 0.948683 + 0.713560i
\(131\) 17.0246 1.48744 0.743722 0.668489i \(-0.233059\pi\)
0.743722 + 0.668489i \(0.233059\pi\)
\(132\) −2.57731 4.46404i −0.224326 0.388544i
\(133\) 0 0
\(134\) 0.651388 1.12824i 0.0562713 0.0974648i
\(135\) 19.1194 1.64554
\(136\) 1.30865 2.26665i 0.112216 0.194364i
\(137\) −1.34861 + 2.33586i −0.115220 + 0.199566i −0.917868 0.396887i \(-0.870091\pi\)
0.802648 + 0.596453i \(0.203424\pi\)
\(138\) −24.7965 −2.11082
\(139\) −8.51229 + 14.7437i −0.722003 + 1.25055i 0.238193 + 0.971218i \(0.423445\pi\)
−0.960196 + 0.279327i \(0.909889\pi\)
\(140\) 0 0
\(141\) 17.8625 + 30.9387i 1.50429 + 2.60551i
\(142\) −5.21110 −0.437306
\(143\) 17.0246 + 12.8052i 1.42367 + 1.07082i
\(144\) −17.5139 −1.45949
\(145\) −1.87694 3.25096i −0.155872 0.269978i
\(146\) −3.75389 6.50192i −0.310674 0.538103i
\(147\) 0 0
\(148\) −0.422205 −0.0347050
\(149\) −0.256939 + 0.445032i −0.0210493 + 0.0364584i −0.876358 0.481660i \(-0.840034\pi\)
0.855309 + 0.518118i \(0.173367\pi\)
\(150\) 6.19912 10.7372i 0.506156 0.876689i
\(151\) −6.21110 −0.505452 −0.252726 0.967538i \(-0.581327\pi\)
−0.252726 + 0.967538i \(0.581327\pi\)
\(152\) −4.32218 + 7.48624i −0.350575 + 0.607214i
\(153\) 2.31316 + 4.00651i 0.187008 + 0.323907i
\(154\) 0 0
\(155\) 2.51388 0.201920
\(156\) −2.89445 + 1.23167i −0.231741 + 0.0986122i
\(157\) 9.51680 0.759523 0.379761 0.925084i \(-0.376006\pi\)
0.379761 + 0.925084i \(0.376006\pi\)
\(158\) 0.394449 + 0.683205i 0.0313807 + 0.0543529i
\(159\) −13.8390 23.9698i −1.09750 1.90093i
\(160\) 2.44524 4.23527i 0.193313 0.334828i
\(161\) 0 0
\(162\) 2.09167 3.62288i 0.164337 0.284641i
\(163\) 8.60555 14.9053i 0.674039 1.16747i −0.302710 0.953083i \(-0.597891\pi\)
0.976749 0.214387i \(-0.0687753\pi\)
\(164\) −2.27317 −0.177505
\(165\) 24.5278 42.4833i 1.90948 3.30732i
\(166\) −4.32218 7.48624i −0.335466 0.581045i
\(167\) −2.44524 4.23527i −0.189218 0.327735i 0.755772 0.654835i \(-0.227262\pi\)
−0.944990 + 0.327100i \(0.893929\pi\)
\(168\) 0 0
\(169\) 9.01388 9.36750i 0.693375 0.720577i
\(170\) 3.27502 0.251183
\(171\) −7.63985 13.2326i −0.584234 1.01192i
\(172\) 0.834734 + 1.44580i 0.0636479 + 0.110241i
\(173\) −11.9620 + 20.7188i −0.909456 + 1.57522i −0.0946356 + 0.995512i \(0.530169\pi\)
−0.814821 + 0.579713i \(0.803165\pi\)
\(174\) −4.89047 −0.370746
\(175\) 0 0
\(176\) −9.75694 + 16.8995i −0.735457 + 1.27385i
\(177\) 19.1194 1.43710
\(178\) 5.63083 9.75289i 0.422049 0.731010i
\(179\) −7.19722 12.4660i −0.537946 0.931749i −0.999014 0.0443850i \(-0.985867\pi\)
0.461069 0.887364i \(-0.347466\pi\)
\(180\) 2.31316 + 4.00651i 0.172413 + 0.298628i
\(181\) 9.25264 0.687744 0.343872 0.939017i \(-0.388261\pi\)
0.343872 + 0.939017i \(0.388261\pi\)
\(182\) 0 0
\(183\) 16.6056 1.22752
\(184\) −9.90833 17.1617i −0.730452 1.26518i
\(185\) −2.00902 3.47972i −0.147706 0.255834i
\(186\) 1.63751 2.83625i 0.120068 0.207964i
\(187\) 5.15463 0.376944
\(188\) −1.87694 + 3.25096i −0.136890 + 0.237101i
\(189\) 0 0
\(190\) −10.8167 −0.784723
\(191\) −9.65139 + 16.7167i −0.698350 + 1.20958i 0.270688 + 0.962667i \(0.412749\pi\)
−0.969038 + 0.246911i \(0.920585\pi\)
\(192\) −12.7024 22.0012i −0.916716 1.58780i
\(193\) 0.908327 + 1.57327i 0.0653828 + 0.113246i 0.896864 0.442307i \(-0.145840\pi\)
−0.831481 + 0.555553i \(0.812506\pi\)
\(194\) 10.1251 0.726938
\(195\) −23.9241 17.9947i −1.71324 1.28863i
\(196\) 0 0
\(197\) 5.95416 + 10.3129i 0.424217 + 0.734765i 0.996347 0.0853980i \(-0.0272162\pi\)
−0.572130 + 0.820163i \(0.693883\pi\)
\(198\) −20.4083 35.3483i −1.45036 2.51209i
\(199\) −0.436217 + 0.755550i −0.0309226 + 0.0535595i −0.881073 0.472981i \(-0.843178\pi\)
0.850150 + 0.526541i \(0.176511\pi\)
\(200\) 9.90833 0.700625
\(201\) −1.44073 + 2.49541i −0.101621 + 0.176013i
\(202\) −5.63083 + 9.75289i −0.396184 + 0.686211i
\(203\) 0 0
\(204\) −0.380571 + 0.659168i −0.0266453 + 0.0461510i
\(205\) −10.8167 18.7350i −0.755468 1.30851i
\(206\) 3.18559 + 5.51761i 0.221951 + 0.384430i
\(207\) 35.0278 2.43460
\(208\) 9.51680 + 7.15813i 0.659871 + 0.496327i
\(209\) −17.0246 −1.17761
\(210\) 0 0
\(211\) −7.50000 12.9904i −0.516321 0.894295i −0.999820 0.0189499i \(-0.993968\pi\)
0.483499 0.875345i \(-0.339366\pi\)
\(212\) 1.45416 2.51868i 0.0998724 0.172984i
\(213\) 11.5258 0.789736
\(214\) 6.05971 10.4957i 0.414234 0.717474i
\(215\) −7.94399 + 13.7594i −0.541776 + 0.938383i
\(216\) 19.9060 1.35443
\(217\) 0 0
\(218\) −4.04584 7.00759i −0.274019 0.474614i
\(219\) 8.30278 + 14.3808i 0.561050 + 0.971766i
\(220\) 5.15463 0.347525
\(221\) 0.380571 3.12250i 0.0255999 0.210042i
\(222\) −5.23460 −0.351324
\(223\) 6.76742 + 11.7215i 0.453180 + 0.784930i 0.998582 0.0532444i \(-0.0169562\pi\)
−0.545402 + 0.838175i \(0.683623\pi\)
\(224\) 0 0
\(225\) −8.75694 + 15.1675i −0.583796 + 1.01116i
\(226\) 19.3028 1.28400
\(227\) −13.7069 + 23.7410i −0.909759 + 1.57575i −0.0953602 + 0.995443i \(0.530400\pi\)
−0.814399 + 0.580306i \(0.802933\pi\)
\(228\) 1.25694 2.17708i 0.0832428 0.144181i
\(229\) 20.7785 1.37308 0.686540 0.727092i \(-0.259129\pi\)
0.686540 + 0.727092i \(0.259129\pi\)
\(230\) 12.3982 21.4744i 0.817516 1.41598i
\(231\) 0 0
\(232\) −1.95416 3.38471i −0.128297 0.222217i
\(233\) −23.9083 −1.56629 −0.783143 0.621841i \(-0.786385\pi\)
−0.783143 + 0.621841i \(0.786385\pi\)
\(234\) −22.9196 + 9.75289i −1.49830 + 0.637566i
\(235\) −35.7250 −2.33044
\(236\) 1.00451 + 1.73986i 0.0653880 + 0.113255i
\(237\) −0.872434 1.51110i −0.0566707 0.0981565i
\(238\) 0 0
\(239\) 11.6056 0.750701 0.375350 0.926883i \(-0.377522\pi\)
0.375350 + 0.926883i \(0.377522\pi\)
\(240\) 13.7111 23.7483i 0.885048 1.53295i
\(241\) 1.00451 1.73986i 0.0647062 0.112074i −0.831857 0.554989i \(-0.812722\pi\)
0.896564 + 0.442915i \(0.146056\pi\)
\(242\) −31.1472 −2.00222
\(243\) 5.32669 9.22610i 0.341707 0.591854i
\(244\) 0.872434 + 1.51110i 0.0558519 + 0.0967383i
\(245\) 0 0
\(246\) −28.1833 −1.79690
\(247\) −1.25694 + 10.3129i −0.0799771 + 0.656195i
\(248\) 2.61730 0.166199
\(249\) 9.55971 + 16.5579i 0.605822 + 1.04932i
\(250\) −3.18559 5.51761i −0.201475 0.348964i
\(251\) 11.2617 19.5058i 0.710830 1.23119i −0.253716 0.967279i \(-0.581653\pi\)
0.964546 0.263915i \(-0.0850138\pi\)
\(252\) 0 0
\(253\) 19.5139 33.7990i 1.22683 2.12493i
\(254\) −1.89445 + 3.28128i −0.118868 + 0.205886i
\(255\) −7.24362 −0.453613
\(256\) 3.54584 6.14157i 0.221615 0.383848i
\(257\) 11.3937 + 19.7345i 0.710722 + 1.23101i 0.964587 + 0.263767i \(0.0849649\pi\)
−0.253865 + 0.967240i \(0.581702\pi\)
\(258\) 10.3492 + 17.9254i 0.644316 + 1.11599i
\(259\) 0 0
\(260\) 0.380571 3.12250i 0.0236020 0.193649i
\(261\) 6.90833 0.427615
\(262\) 11.0896 + 19.2077i 0.685118 + 1.18666i
\(263\) 6.71110 + 11.6240i 0.413824 + 0.716765i 0.995304 0.0967960i \(-0.0308594\pi\)
−0.581480 + 0.813561i \(0.697526\pi\)
\(264\) 25.5369 44.2311i 1.57168 2.72224i
\(265\) 27.6780 1.70024
\(266\) 0 0
\(267\) −12.4542 + 21.5712i −0.762182 + 1.32014i
\(268\) −0.302776 −0.0184950
\(269\) −4.75840 + 8.24179i −0.290125 + 0.502511i −0.973839 0.227239i \(-0.927030\pi\)
0.683714 + 0.729750i \(0.260363\pi\)
\(270\) 12.4542 + 21.5712i 0.757936 + 1.31278i
\(271\) −14.8435 25.7097i −0.901678 1.56175i −0.825316 0.564671i \(-0.809003\pi\)
−0.0763615 0.997080i \(-0.524330\pi\)
\(272\) 2.88145 0.174714
\(273\) 0 0
\(274\) −3.51388 −0.212281
\(275\) 9.75694 + 16.8995i 0.588366 + 1.01908i
\(276\) 2.88145 + 4.99082i 0.173443 + 0.300412i
\(277\) −7.10555 + 12.3072i −0.426931 + 0.739467i −0.996599 0.0824088i \(-0.973739\pi\)
0.569667 + 0.821875i \(0.307072\pi\)
\(278\) −22.1792 −1.33022
\(279\) −2.31316 + 4.00651i −0.138485 + 0.239864i
\(280\) 0 0
\(281\) 2.18335 0.130248 0.0651238 0.997877i \(-0.479256\pi\)
0.0651238 + 0.997877i \(0.479256\pi\)
\(282\) −23.2708 + 40.3062i −1.38576 + 2.40020i
\(283\) −2.00902 3.47972i −0.119424 0.206848i 0.800116 0.599846i \(-0.204771\pi\)
−0.919539 + 0.392998i \(0.871438\pi\)
\(284\) 0.605551 + 1.04885i 0.0359329 + 0.0622375i
\(285\) 23.9241 1.41714
\(286\) −3.35766 + 27.5489i −0.198543 + 1.62900i
\(287\) 0 0
\(288\) 4.50000 + 7.79423i 0.265165 + 0.459279i
\(289\) 8.11943 + 14.0633i 0.477613 + 0.827251i
\(290\) 2.44524 4.23527i 0.143589 0.248704i
\(291\) −22.3944 −1.31279
\(292\) −0.872434 + 1.51110i −0.0510553 + 0.0884304i
\(293\) −1.74487 + 3.02220i −0.101936 + 0.176559i −0.912482 0.409116i \(-0.865837\pi\)
0.810546 + 0.585675i \(0.199170\pi\)
\(294\) 0 0
\(295\) −9.55971 + 16.5579i −0.556588 + 0.964039i
\(296\) −2.09167 3.62288i −0.121576 0.210576i
\(297\) 19.6019 + 33.9515i 1.13742 + 1.97006i
\(298\) −0.669468 −0.0387812
\(299\) −19.0336 14.3163i −1.10074 0.827931i
\(300\) −2.88145 −0.166361
\(301\) 0 0
\(302\) −4.04584 7.00759i −0.232812 0.403242i
\(303\) 12.4542 21.5712i 0.715473 1.23924i
\(304\) −9.51680 −0.545826
\(305\) −8.30278 + 14.3808i −0.475416 + 0.823444i
\(306\) −3.01353 + 5.21959i −0.172272 + 0.298384i
\(307\) 15.2797 0.872059 0.436029 0.899932i \(-0.356384\pi\)
0.436029 + 0.899932i \(0.356384\pi\)
\(308\) 0 0
\(309\) −7.04584 12.2037i −0.400824 0.694247i
\(310\) 1.63751 + 2.83625i 0.0930043 + 0.161088i
\(311\) −17.0246 −0.965375 −0.482687 0.875793i \(-0.660339\pi\)
−0.482687 + 0.875793i \(0.660339\pi\)
\(312\) −24.9083 18.7350i −1.41016 1.06066i
\(313\) 13.2707 0.750103 0.375052 0.927004i \(-0.377625\pi\)
0.375052 + 0.927004i \(0.377625\pi\)
\(314\) 6.19912 + 10.7372i 0.349837 + 0.605935i
\(315\) 0 0
\(316\) 0.0916731 0.158782i 0.00515701 0.00893221i
\(317\) 8.21110 0.461181 0.230591 0.973051i \(-0.425934\pi\)
0.230591 + 0.973051i \(0.425934\pi\)
\(318\) 18.0291 31.2273i 1.01102 1.75114i
\(319\) 3.84861 6.66599i 0.215481 0.373224i
\(320\) 25.4048 1.42017
\(321\) −13.4028 + 23.2143i −0.748069 + 1.29569i
\(322\) 0 0
\(323\) 1.25694 + 2.17708i 0.0699380 + 0.121136i
\(324\) −0.972244 −0.0540135
\(325\) 10.9575 4.66272i 0.607814 0.258641i
\(326\) 22.4222 1.24185
\(327\) 8.94850 + 15.4993i 0.494853 + 0.857111i
\(328\) −11.2617 19.5058i −0.621821 1.07703i
\(329\) 0 0
\(330\) 63.9083 3.51804
\(331\) −0.348612 + 0.603814i −0.0191615 + 0.0331886i −0.875447 0.483314i \(-0.839433\pi\)
0.856286 + 0.516503i \(0.172766\pi\)
\(332\) −1.00451 + 1.73986i −0.0551296 + 0.0954873i
\(333\) 7.39445 0.405213
\(334\) 3.18559 5.51761i 0.174308 0.301910i
\(335\) −1.44073 2.49541i −0.0787153 0.136339i
\(336\) 0 0
\(337\) −7.11943 −0.387820 −0.193910 0.981019i \(-0.562117\pi\)
−0.193910 + 0.981019i \(0.562117\pi\)
\(338\) 16.4403 + 4.06792i 0.894234 + 0.221265i
\(339\) −42.6935 −2.31879
\(340\) −0.380571 0.659168i −0.0206393 0.0357484i
\(341\) 2.57731 + 4.46404i 0.139569 + 0.241741i
\(342\) 9.95301 17.2391i 0.538197 0.932185i
\(343\) 0 0
\(344\) −8.27082 + 14.3255i −0.445933 + 0.772378i
\(345\) −27.4222 + 47.4967i −1.47636 + 2.55713i
\(346\) −31.1677 −1.67559
\(347\) −0.394449 + 0.683205i −0.0211751 + 0.0366764i −0.876419 0.481550i \(-0.840074\pi\)
0.855244 + 0.518226i \(0.173407\pi\)
\(348\) 0.568293 + 0.984312i 0.0304637 + 0.0527647i
\(349\) −11.9620 20.7188i −0.640313 1.10905i −0.985363 0.170470i \(-0.945471\pi\)
0.345050 0.938584i \(-0.387862\pi\)
\(350\) 0 0
\(351\) 22.0139 9.36750i 1.17501 0.500000i
\(352\) 10.0278 0.534481
\(353\) −3.18559 5.51761i −0.169552 0.293673i 0.768710 0.639597i \(-0.220899\pi\)
−0.938262 + 0.345924i \(0.887565\pi\)
\(354\) 12.4542 + 21.5712i 0.661931 + 1.14650i
\(355\) −5.76291 + 9.98165i −0.305863 + 0.529771i
\(356\) −2.61730 −0.138717
\(357\) 0 0
\(358\) 9.37637 16.2403i 0.495556 0.858329i
\(359\) −22.9083 −1.20906 −0.604528 0.796584i \(-0.706638\pi\)
−0.604528 + 0.796584i \(0.706638\pi\)
\(360\) −22.9196 + 39.6978i −1.20797 + 2.09226i
\(361\) 5.34861 + 9.26407i 0.281506 + 0.487583i
\(362\) 6.02706 + 10.4392i 0.316775 + 0.548671i
\(363\) 68.8907 3.61583
\(364\) 0 0
\(365\) −16.6056 −0.869174
\(366\) 10.8167 + 18.7350i 0.565396 + 0.979294i
\(367\) 14.1431 + 24.4966i 0.738265 + 1.27871i 0.953276 + 0.302100i \(0.0976878\pi\)
−0.215011 + 0.976612i \(0.568979\pi\)
\(368\) 10.9083 18.8938i 0.568636 0.984906i
\(369\) 39.8120 2.07253
\(370\) 2.61730 4.53330i 0.136067 0.235675i
\(371\) 0 0
\(372\) −0.761141 −0.0394633
\(373\) 8.15139 14.1186i 0.422063 0.731034i −0.574078 0.818800i \(-0.694639\pi\)
0.996141 + 0.0877661i \(0.0279728\pi\)
\(374\) 3.35766 + 5.81564i 0.173620 + 0.300719i
\(375\) 7.04584 + 12.2037i 0.363845 + 0.630199i
\(376\) −37.1947 −1.91817
\(377\) −3.75389 2.82352i −0.193335 0.145418i
\(378\) 0 0
\(379\) −6.55971 11.3618i −0.336950 0.583614i 0.646908 0.762568i \(-0.276062\pi\)
−0.983857 + 0.178954i \(0.942729\pi\)
\(380\) 1.25694 + 2.17708i 0.0644796 + 0.111682i
\(381\) 4.19010 7.25747i 0.214666 0.371812i
\(382\) −25.1472 −1.28664
\(383\) 9.64887 16.7123i 0.493034 0.853960i −0.506934 0.861985i \(-0.669221\pi\)
0.999968 + 0.00802473i \(0.00255438\pi\)
\(384\) 11.6579 20.1921i 0.594914 1.03042i
\(385\) 0 0
\(386\) −1.18335 + 2.04962i −0.0602307 + 0.104323i
\(387\) −14.6194 25.3216i −0.743147 1.28717i
\(388\) −1.17658 2.03789i −0.0597316 0.103458i
\(389\) −7.02776 −0.356321 −0.178161 0.984001i \(-0.557015\pi\)
−0.178161 + 0.984001i \(0.557015\pi\)
\(390\) 4.71841 38.7135i 0.238926 1.96034i
\(391\) −5.76291 −0.291443
\(392\) 0 0
\(393\) −24.5278 42.4833i −1.23726 2.14300i
\(394\) −7.75694 + 13.4354i −0.390789 + 0.676866i
\(395\) 1.74487 0.0877938
\(396\) −4.74306 + 8.21522i −0.238348 + 0.412830i
\(397\) −2.88145 + 4.99082i −0.144616 + 0.250482i −0.929230 0.369503i \(-0.879528\pi\)
0.784614 + 0.619985i \(0.212861\pi\)
\(398\) −1.13659 −0.0569719
\(399\) 0 0
\(400\) 5.45416 + 9.44689i 0.272708 + 0.472344i
\(401\) −7.55971 13.0938i −0.377514 0.653874i 0.613186 0.789939i \(-0.289888\pi\)
−0.990700 + 0.136065i \(0.956554\pi\)
\(402\) −3.75389 −0.187227
\(403\) 2.89445 1.23167i 0.144183 0.0613536i
\(404\) 2.61730 0.130216
\(405\) −4.62632 8.01302i −0.229884 0.398170i
\(406\) 0 0
\(407\) 4.11943 7.13506i 0.204193 0.353672i
\(408\) −7.54163 −0.373367
\(409\) 8.07607 13.9882i 0.399336 0.691670i −0.594308 0.804237i \(-0.702574\pi\)
0.993644 + 0.112567i \(0.0359074\pi\)
\(410\) 14.0917 24.4075i 0.695938 1.20540i
\(411\) 7.77193 0.383361
\(412\) 0.740358 1.28234i 0.0364748 0.0631763i
\(413\) 0 0
\(414\) 22.8167 + 39.5196i 1.12138 + 1.94228i
\(415\) −19.1194 −0.938536
\(416\) 0.740358 6.07448i 0.0362990 0.297826i
\(417\) 49.0555 2.40226
\(418\) −11.0896 19.2077i −0.542410 0.939482i
\(419\) −4.19010 7.25747i −0.204700 0.354551i 0.745337 0.666688i \(-0.232289\pi\)
−0.950037 + 0.312137i \(0.898955\pi\)
\(420\) 0 0
\(421\) −31.0278 −1.51220 −0.756100 0.654456i \(-0.772898\pi\)
−0.756100 + 0.654456i \(0.772898\pi\)
\(422\) 9.77082 16.9236i 0.475636 0.823826i
\(423\) 32.8726 56.9370i 1.59832 2.76837i
\(424\) 28.8167 1.39946
\(425\) 1.44073 2.49541i 0.0698855 0.121045i
\(426\) 7.50778 + 13.0038i 0.363753 + 0.630039i
\(427\) 0 0
\(428\) −2.81665 −0.136148
\(429\) 7.42641 60.9321i 0.358550 2.94183i
\(430\) −20.6985 −0.998169
\(431\) −12.9680 22.4613i −0.624649 1.08192i −0.988609 0.150509i \(-0.951909\pi\)
0.363960 0.931415i \(-0.381424\pi\)
\(432\) 10.9575 + 18.9790i 0.527194 + 0.913127i
\(433\) 4.19010 7.25747i 0.201364 0.348772i −0.747604 0.664144i \(-0.768796\pi\)
0.948968 + 0.315372i \(0.102129\pi\)
\(434\) 0 0
\(435\) −5.40833 + 9.36750i −0.259309 + 0.449137i
\(436\) −0.940285 + 1.62862i −0.0450315 + 0.0779968i
\(437\) 19.0336 0.910500
\(438\) −10.8167 + 18.7350i −0.516840 + 0.895193i
\(439\) 7.63985 + 13.2326i 0.364630 + 0.631558i 0.988717 0.149797i \(-0.0478621\pi\)
−0.624087 + 0.781355i \(0.714529\pi\)
\(440\) 25.5369 + 44.2311i 1.21742 + 2.10864i
\(441\) 0 0
\(442\) 3.77082 1.60458i 0.179359 0.0763223i
\(443\) 30.2389 1.43669 0.718346 0.695686i \(-0.244900\pi\)
0.718346 + 0.695686i \(0.244900\pi\)
\(444\) 0.608282 + 1.05358i 0.0288678 + 0.0500005i
\(445\) −12.4542 21.5712i −0.590384 1.02258i
\(446\) −8.81643 + 15.2705i −0.417470 + 0.723079i
\(447\) 1.48072 0.0700355
\(448\) 0 0
\(449\) −4.21110 + 7.29384i −0.198734 + 0.344218i −0.948118 0.317918i \(-0.897016\pi\)
0.749384 + 0.662136i \(0.230350\pi\)
\(450\) −22.8167 −1.07559
\(451\) 22.1792 38.4155i 1.04438 1.80891i
\(452\) −2.24306 3.88510i −0.105505 0.182740i
\(453\) 8.94850 + 15.4993i 0.420437 + 0.728219i
\(454\) −35.7140 −1.67614
\(455\) 0 0
\(456\) 24.9083 1.16644
\(457\) −6.69722 11.5999i −0.313283 0.542622i 0.665788 0.746141i \(-0.268095\pi\)
−0.979071 + 0.203519i \(0.934762\pi\)
\(458\) 13.5348 + 23.4430i 0.632441 + 1.09542i
\(459\) 2.89445 5.01333i 0.135101 0.234002i
\(460\) −5.76291 −0.268697
\(461\) 6.33120 10.9660i 0.294873 0.510736i −0.680082 0.733136i \(-0.738056\pi\)
0.974955 + 0.222400i \(0.0713892\pi\)
\(462\) 0 0
\(463\) −28.2111 −1.31108 −0.655541 0.755160i \(-0.727559\pi\)
−0.655541 + 0.755160i \(0.727559\pi\)
\(464\) 2.15139 3.72631i 0.0998757 0.172990i
\(465\) −3.62181 6.27316i −0.167958 0.290911i
\(466\) −15.5736 26.9743i −0.721433 1.24956i
\(467\) −14.1431 −0.654465 −0.327233 0.944944i \(-0.606116\pi\)
−0.327233 + 0.944944i \(0.606116\pi\)
\(468\) 4.62632 + 3.47972i 0.213852 + 0.160850i
\(469\) 0 0
\(470\) −23.2708 40.3062i −1.07340 1.85919i
\(471\) −13.7111 23.7483i −0.631774 1.09427i
\(472\) −9.95301 + 17.2391i −0.458125 + 0.793495i
\(473\) −32.5778 −1.49793
\(474\) 1.13659 1.96862i 0.0522051 0.0904219i
\(475\) −4.75840 + 8.24179i −0.218330 + 0.378159i
\(476\) 0 0
\(477\) −25.4680 + 44.1119i −1.16610 + 2.01975i
\(478\) 7.55971 + 13.0938i 0.345773 + 0.598897i
\(479\) 0.568293 + 0.984312i 0.0259660 + 0.0449744i 0.878716 0.477344i \(-0.158401\pi\)
−0.852750 + 0.522319i \(0.825067\pi\)
\(480\) −14.0917 −0.643194
\(481\) −4.01804 3.02220i −0.183207 0.137800i
\(482\) 2.61730 0.119215
\(483\) 0 0
\(484\) 3.61943 + 6.26904i 0.164520 + 0.284956i
\(485\) 11.1972 19.3942i 0.508440 0.880644i
\(486\) 13.8790 0.629563
\(487\) 13.8486 23.9865i 0.627541 1.08693i −0.360503 0.932758i \(-0.617395\pi\)
0.988044 0.154174i \(-0.0492717\pi\)
\(488\) −8.64436 + 14.9725i −0.391312 + 0.677772i
\(489\) −49.5930 −2.24267
\(490\) 0 0
\(491\) 6.36249 + 11.0202i 0.287135 + 0.497333i 0.973125 0.230279i \(-0.0739638\pi\)
−0.685990 + 0.727611i \(0.740630\pi\)
\(492\) 3.27502 + 5.67250i 0.147649 + 0.255736i
\(493\) −1.13659 −0.0511892
\(494\) −12.4542 + 5.29958i −0.560339 + 0.238439i
\(495\) −90.2775 −4.05767
\(496\) 1.44073 + 2.49541i 0.0646905 + 0.112047i
\(497\) 0 0
\(498\) −12.4542 + 21.5712i −0.558084 + 0.966631i
\(499\) 31.3305 1.40255 0.701274 0.712892i \(-0.252615\pi\)
0.701274 + 0.712892i \(0.252615\pi\)
\(500\) −0.740358 + 1.28234i −0.0331098 + 0.0573479i
\(501\) −7.04584 + 12.2037i −0.314785 + 0.545223i
\(502\) 29.3428 1.30964
\(503\) 12.9665 22.4587i 0.578150 1.00138i −0.417542 0.908658i \(-0.637108\pi\)
0.995692 0.0927268i \(-0.0295583\pi\)
\(504\) 0 0
\(505\) 12.4542 + 21.5712i 0.554203 + 0.959908i
\(506\) 50.8444 2.26031
\(507\) −36.3623 8.99734i −1.61491 0.399586i
\(508\) 0.880571 0.0390690
\(509\) 1.30865 + 2.26665i 0.0580049 + 0.100467i 0.893570 0.448924i \(-0.148193\pi\)
−0.835565 + 0.549392i \(0.814859\pi\)
\(510\) −4.71841 8.17252i −0.208935 0.361885i
\(511\) 0 0
\(512\) 25.4222 1.12351
\(513\) −9.55971 + 16.5579i −0.422072 + 0.731050i
\(514\) −14.8435 + 25.7097i −0.654718 + 1.13400i
\(515\) 14.0917 0.620953
\(516\) 2.40525 4.16601i 0.105885 0.183398i
\(517\) −36.6265 63.4389i −1.61083 2.79004i
\(518\) 0 0
\(519\) 68.9361 3.02596
\(520\) 28.6791 12.2037i 1.25766 0.535170i
\(521\) −28.8145 −1.26239 −0.631194 0.775625i \(-0.717435\pi\)
−0.631194 + 0.775625i \(0.717435\pi\)
\(522\) 4.50000 + 7.79423i 0.196960 + 0.341144i
\(523\) 4.62632 + 8.01302i 0.202295 + 0.350385i 0.949267 0.314470i \(-0.101827\pi\)
−0.746973 + 0.664855i \(0.768493\pi\)
\(524\) 2.57731 4.46404i 0.112590 0.195012i
\(525\) 0 0
\(526\) −8.74306 + 15.1434i −0.381216 + 0.660285i
\(527\) 0.380571 0.659168i 0.0165779 0.0287138i
\(528\) 56.2283 2.44702
\(529\) −10.3167 + 17.8690i −0.448550 + 0.776912i
\(530\) 18.0291 + 31.2273i 0.783133 + 1.35643i
\(531\) −17.5929 30.4717i −0.763465 1.32236i
\(532\) 0 0
\(533\) −21.6333 16.2717i −0.937043 0.704804i
\(534\) −32.4500 −1.40425
\(535\) −13.4028 23.2143i −0.579452 1.00364i
\(536\) −1.50000 2.59808i −0.0647901 0.112220i
\(537\) −20.7385 + 35.9201i −0.894931 + 1.55007i
\(538\) −12.3982 −0.534526
\(539\) 0 0
\(540\) 2.89445 5.01333i 0.124557 0.215739i
\(541\) −18.9361 −0.814126 −0.407063 0.913400i \(-0.633447\pi\)
−0.407063 + 0.913400i \(0.633447\pi\)
\(542\) 19.3377 33.4939i 0.830627 1.43869i
\(543\) −13.3305 23.0892i −0.572068 0.990851i
\(544\) −0.740358 1.28234i −0.0317426 0.0549798i
\(545\) −17.8970 −0.766623
\(546\) 0 0
\(547\) 29.0000 1.23995 0.619975 0.784621i \(-0.287143\pi\)
0.619975 + 0.784621i \(0.287143\pi\)
\(548\) 0.408327 + 0.707243i 0.0174429 + 0.0302119i
\(549\) −15.2797 26.4652i −0.652122 1.12951i
\(550\) −12.7111 + 22.0163i −0.542003 + 0.938777i
\(551\) 3.75389 0.159921
\(552\) −28.5504 + 49.4507i −1.21519 + 2.10476i
\(553\) 0 0
\(554\) −18.5139 −0.786579
\(555\) −5.78890 + 10.0267i −0.245725 + 0.425608i
\(556\) 2.57731 + 4.46404i 0.109302 + 0.189317i
\(557\) −8.45416 14.6430i −0.358214 0.620446i 0.629448 0.777042i \(-0.283281\pi\)
−0.987663 + 0.156597i \(0.949948\pi\)
\(558\) −6.02706 −0.255146
\(559\) −2.40525 + 19.7345i −0.101731 + 0.834682i
\(560\) 0 0
\(561\) −7.42641 12.8629i −0.313543 0.543073i
\(562\) 1.42221 + 2.46333i 0.0599921 + 0.103909i
\(563\) 9.51680 16.4836i 0.401085 0.694700i −0.592772 0.805370i \(-0.701966\pi\)
0.993857 + 0.110671i \(0.0352998\pi\)
\(564\) 10.8167 0.455463
\(565\) 21.3468 36.9737i 0.898065 1.55549i
\(566\) 2.61730 4.53330i 0.110013 0.190549i
\(567\) 0 0
\(568\) −6.00000 + 10.3923i −0.251754 + 0.436051i
\(569\) 13.6972 + 23.7243i 0.574218 + 0.994574i 0.996126 + 0.0879356i \(0.0280270\pi\)
−0.421909 + 0.906638i \(0.638640\pi\)
\(570\) 15.5838 + 26.9920i 0.652735 + 1.13057i
\(571\) 21.7250 0.909162 0.454581 0.890705i \(-0.349789\pi\)
0.454581 + 0.890705i \(0.349789\pi\)
\(572\) 5.93497 2.52549i 0.248154 0.105596i
\(573\) 55.6201 2.32356
\(574\) 0 0
\(575\) −10.9083 18.8938i −0.454909 0.787925i
\(576\) −23.3764 + 40.4891i −0.974015 + 1.68704i
\(577\) 33.7050 1.40316 0.701579 0.712592i \(-0.252479\pi\)
0.701579 + 0.712592i \(0.252479\pi\)
\(578\) −10.5778 + 18.3213i −0.439978 + 0.762065i
\(579\) 2.61730 4.53330i 0.108771 0.188398i
\(580\) −1.13659 −0.0471942
\(581\) 0 0
\(582\) −14.5875 25.2662i −0.604670 1.04732i
\(583\) 28.3764 + 49.1493i 1.17523 + 2.03556i
\(584\) −17.2887 −0.715412
\(585\) −6.66527 + 54.6871i −0.275575 + 2.26103i
\(586\) −4.54634 −0.187808
\(587\) 14.2752 + 24.7254i 0.589200 + 1.02052i 0.994337 + 0.106269i \(0.0338904\pi\)
−0.405137 + 0.914256i \(0.632776\pi\)
\(588\) 0 0
\(589\) −1.25694 + 2.17708i −0.0517913 + 0.0897051i
\(590\) −24.9083 −1.02546
\(591\) 17.1566 29.7162i 0.705730 1.22236i
\(592\) 2.30278 3.98852i 0.0946435 0.163927i
\(593\) −22.7875 −0.935770 −0.467885 0.883789i \(-0.654984\pi\)
−0.467885 + 0.883789i \(0.654984\pi\)
\(594\) −25.5369 + 44.2311i −1.04779 + 1.81483i
\(595\) 0 0
\(596\) 0.0777949 + 0.134745i 0.00318660 + 0.00551936i
\(597\) 2.51388 0.102886
\(598\) 3.75389 30.7998i 0.153508 1.25950i
\(599\) 7.51388 0.307009 0.153504 0.988148i \(-0.450944\pi\)
0.153504 + 0.988148i \(0.450944\pi\)
\(600\) −14.2752 24.7254i −0.582782 1.00941i
\(601\) 14.7114 + 25.4809i 0.600091 + 1.03939i 0.992807 + 0.119728i \(0.0382023\pi\)
−0.392716 + 0.919660i \(0.628464\pi\)
\(602\) 0 0
\(603\) 5.30278 0.215946
\(604\) −0.940285 + 1.62862i −0.0382597 + 0.0662677i
\(605\) −34.4454 + 59.6611i −1.40040 + 2.42557i
\(606\) 32.4500 1.31819
\(607\) −10.2172 + 17.6966i −0.414702 + 0.718285i −0.995397 0.0958363i \(-0.969447\pi\)
0.580695 + 0.814121i \(0.302781\pi\)
\(608\) 2.44524 + 4.23527i 0.0991674 + 0.171763i
\(609\) 0 0
\(610\) −21.6333 −0.875907
\(611\) −41.1333 + 17.5033i −1.66408 + 0.708109i
\(612\) 1.40074 0.0566215
\(613\) −10.5458 18.2659i −0.425942 0.737754i 0.570566 0.821252i \(-0.306724\pi\)
−0.996508 + 0.0834983i \(0.973391\pi\)
\(614\) 9.95301 + 17.2391i 0.401671 + 0.695714i
\(615\) −31.1677 + 53.9840i −1.25680 + 2.17685i
\(616\) 0 0
\(617\) 20.9222 36.2383i 0.842296 1.45890i −0.0456524 0.998957i \(-0.514537\pi\)
0.887949 0.459943i \(-0.152130\pi\)
\(618\) 9.17914 15.8987i 0.369239 0.639541i
\(619\) 22.5233 0.905289 0.452644 0.891691i \(-0.350481\pi\)
0.452644 + 0.891691i \(0.350481\pi\)
\(620\) 0.380571 0.659168i 0.0152841 0.0264728i
\(621\) −21.9150 37.9580i −0.879420 1.52320i
\(622\) −11.0896 19.2077i −0.444652 0.770160i
\(623\) 0 0
\(624\) 4.15139 34.0612i 0.166189 1.36354i
\(625\) −30.6056 −1.22422
\(626\) 8.64436 + 14.9725i 0.345498 + 0.598420i
\(627\) 24.5278 + 42.4833i 0.979544 + 1.69662i
\(628\) 1.44073 2.49541i 0.0574913 0.0995778i
\(629\) −1.21656 −0.0485076
\(630\) 0 0
\(631\) −6.04584 + 10.4717i −0.240681 + 0.416872i −0.960908 0.276866i \(-0.910704\pi\)
0.720227 + 0.693738i \(0.244037\pi\)
\(632\) 1.81665 0.0722626
\(633\) −21.6109 + 37.4312i −0.858956 + 1.48776i
\(634\) 5.34861 + 9.26407i 0.212421 + 0.367923i
\(635\) 4.19010 + 7.25747i 0.166279 + 0.288004i
\(636\) −8.38021 −0.332297
\(637\) 0 0
\(638\) 10.0278 0.397003
\(639\) −10.6056 18.3694i −0.419549 0.726680i
\(640\) 11.6579 + 20.1921i 0.460819 + 0.798161i
\(641\) −1.75694 + 3.04311i −0.0693949 + 0.120196i −0.898635 0.438697i \(-0.855440\pi\)
0.829240 + 0.558892i \(0.188774\pi\)
\(642\) −34.9216 −1.37824
\(643\) 4.19010 7.25747i 0.165242 0.286207i −0.771499 0.636230i \(-0.780493\pi\)
0.936741 + 0.350023i \(0.113826\pi\)
\(644\) 0 0
\(645\) 45.7805 1.80261
\(646\) −1.63751 + 2.83625i −0.0644270 + 0.111591i
\(647\) 1.13659 + 1.96862i 0.0446838 + 0.0773946i 0.887502 0.460803i \(-0.152439\pi\)
−0.842819 + 0.538198i \(0.819105\pi\)
\(648\) −4.81665 8.34269i −0.189216 0.327732i
\(649\) −39.2038 −1.53888
\(650\) 12.3982 + 9.32544i 0.486299 + 0.365774i
\(651\) 0 0
\(652\) −2.60555 4.51295i −0.102041 0.176741i
\(653\) −10.8764 18.8384i −0.425625 0.737204i 0.570853 0.821052i \(-0.306612\pi\)
−0.996479 + 0.0838475i \(0.973279\pi\)
\(654\) −11.6579 + 20.1921i −0.455860 + 0.789572i
\(655\) 49.0555 1.91676
\(656\) 12.3982 21.4744i 0.484070 0.838434i
\(657\) 15.2797 26.4652i 0.596118 1.03251i
\(658\) 0 0
\(659\) −11.8167 + 20.4670i −0.460311 + 0.797283i −0.998976 0.0452373i \(-0.985596\pi\)
0.538665 + 0.842520i \(0.318929\pi\)
\(660\) −7.42641 12.8629i −0.289073 0.500688i
\(661\) 4.89047 + 8.47055i 0.190217 + 0.329466i 0.945322 0.326138i \(-0.105747\pi\)
−0.755105 + 0.655604i \(0.772414\pi\)
\(662\) −0.908327 −0.0353031
\(663\) −8.34022 + 3.54899i −0.323907 + 0.137831i
\(664\) −19.9060 −0.772504
\(665\) 0 0
\(666\) 4.81665 + 8.34269i 0.186642 + 0.323273i
\(667\) −4.30278 + 7.45263i −0.166604 + 0.288567i
\(668\) −1.48072 −0.0572906
\(669\) 19.5000 33.7750i 0.753914 1.30582i
\(670\) 1.87694 3.25096i 0.0725127 0.125596i
\(671\) −34.0491 −1.31445
\(672\) 0 0
\(673\) −6.10555 10.5751i −0.235352 0.407641i 0.724023 0.689776i \(-0.242291\pi\)
−0.959375 + 0.282135i \(0.908958\pi\)
\(674\) −4.63751 8.03240i −0.178630 0.309397i
\(675\) 21.9150 0.843510
\(676\) −1.09167 3.78167i −0.0419874 0.145449i
\(677\) 6.37119 0.244865 0.122432 0.992477i \(-0.460931\pi\)
0.122432 + 0.992477i \(0.460931\pi\)
\(678\) −27.8100 48.1684i −1.06804 1.84990i
\(679\) 0 0
\(680\) 3.77082 6.53125i 0.144604 0.250462i
\(681\) 78.9916 3.02696
\(682\) −3.35766 + 5.81564i −0.128571 + 0.222692i
\(683\) −1.80278 + 3.12250i −0.0689813 + 0.119479i −0.898453 0.439069i \(-0.855308\pi\)
0.829472 + 0.558549i \(0.188642\pi\)
\(684\) −4.62632 −0.176892
\(685\) −3.88596 + 6.73069i −0.148475 + 0.257166i
\(686\) 0 0
\(687\) −29.9361 51.8508i −1.14213 1.97823i
\(688\) −18.2111 −0.694292
\(689\) 31.8681 13.5607i 1.21408 0.516622i
\(690\) −71.4500 −2.72005
\(691\) −16.4563 28.5031i −0.626026 1.08431i −0.988341 0.152254i \(-0.951347\pi\)
0.362315 0.932056i \(-0.381986\pi\)
\(692\) 3.62181 + 6.27316i 0.137681 + 0.238470i
\(693\) 0 0
\(694\) −1.02776 −0.0390131
\(695\) −24.5278 + 42.4833i −0.930391 + 1.61148i
\(696\) −5.63083 + 9.75289i −0.213436 + 0.369682i
\(697\) −6.55004 −0.248100
\(698\) 15.5838 26.9920i 0.589857 1.02166i
\(699\) 34.4454 + 59.6611i 1.30284 + 2.25659i
\(700\) 0 0
\(701\) −27.0278 −1.02082 −0.510412 0.859930i \(-0.670507\pi\)
−0.510412 + 0.859930i \(0.670507\pi\)
\(702\) 24.9083 + 18.7350i 0.940104 + 0.707107i
\(703\) 4.01804 0.151543
\(704\) 26.0458 + 45.1127i 0.981639 + 1.70025i
\(705\) 51.4699 + 89.1486i 1.93847 + 3.35753i
\(706\) 4.15012 7.18821i 0.156192 0.270532i
\(707\) 0 0
\(708\) 2.89445 5.01333i 0.108780 0.188413i
\(709\) −0.137510 + 0.238174i −0.00516428 + 0.00894480i −0.868596 0.495521i \(-0.834977\pi\)
0.863432 + 0.504466i \(0.168311\pi\)
\(710\) −15.0156 −0.563524
\(711\) −1.60555 + 2.78090i −0.0602129 + 0.104292i
\(712\) −12.9665 22.4587i −0.485942 0.841676i
\(713\) −2.88145 4.99082i −0.107911 0.186908i
\(714\) 0 0
\(715\) 49.0555 + 36.8975i 1.83457 + 1.37989i
\(716\) −4.35829 −0.162877
\(717\) −16.7204 28.9606i −0.624436 1.08155i
\(718\) −14.9222 25.8460i −0.556892 0.964565i
\(719\) −10.8254 + 18.7502i −0.403721 + 0.699265i −0.994172 0.107808i \(-0.965617\pi\)
0.590451 + 0.807074i \(0.298950\pi\)
\(720\) −50.4654 −1.88074
\(721\) 0 0
\(722\) −6.96804 + 12.0690i −0.259324 + 0.449162i
\(723\) −5.78890 −0.215291
\(724\) 1.40074 2.42615i 0.0520580 0.0901671i
\(725\) −2.15139 3.72631i −0.0799005 0.138392i
\(726\) 44.8746 + 77.7251i 1.66545 + 2.88465i
\(727\) −23.3958 −0.867701 −0.433850 0.900985i \(-0.642845\pi\)
−0.433850 + 0.900985i \(0.642845\pi\)
\(728\) 0 0
\(729\) −40.3305 −1.49372
\(730\) −10.8167 18.7350i −0.400342 0.693413i
\(731\) 2.40525 + 4.16601i 0.0889613 + 0.154085i
\(732\) 2.51388 4.35416i 0.0929156 0.160935i
\(733\) −40.0762 −1.48025 −0.740124 0.672470i \(-0.765233\pi\)
−0.740124 + 0.672470i \(0.765233\pi\)
\(734\) −18.4253 + 31.9136i −0.680091 + 1.17795i
\(735\) 0 0
\(736\) −11.2111 −0.413247
\(737\) 2.95416 5.11676i 0.108818 0.188478i
\(738\) 25.9331 + 44.9174i 0.954610 + 1.65343i
\(739\) 9.39445 + 16.2717i 0.345580 + 0.598563i 0.985459 0.169913i \(-0.0543487\pi\)
−0.639879 + 0.768476i \(0.721015\pi\)
\(740\) −1.21656 −0.0447218
\(741\) 27.5459 11.7215i 1.01192 0.430600i
\(742\) 0 0
\(743\) 18.8486 + 32.6468i 0.691489 + 1.19769i 0.971350 + 0.237653i \(0.0763781\pi\)
−0.279862 + 0.960040i \(0.590289\pi\)
\(744\) −3.77082 6.53125i −0.138245 0.239447i
\(745\) −0.740358 + 1.28234i −0.0271246 + 0.0469812i
\(746\) 21.2389 0.777610
\(747\) 17.5929 30.4717i 0.643689 1.11490i
\(748\) 0.780347 1.35160i 0.0285323 0.0494194i
\(749\) 0 0
\(750\) −9.17914 + 15.8987i −0.335175 + 0.580540i
\(751\) 2.19722 + 3.80570i 0.0801779 + 0.138872i 0.903326 0.428954i \(-0.141118\pi\)
−0.823148 + 0.567826i \(0.807785\pi\)
\(752\) −20.4743 35.4626i −0.746622 1.29319i
\(753\) −64.8999 −2.36508
\(754\) 0.740358 6.07448i 0.0269623 0.221219i
\(755\) −17.8970 −0.651339
\(756\) 0 0
\(757\) 22.1194 + 38.3120i 0.803944 + 1.39247i 0.917001 + 0.398884i \(0.130602\pi\)
−0.113057 + 0.993588i \(0.536064\pi\)
\(758\) 8.54584 14.8018i 0.310399 0.537626i
\(759\) −112.457 −4.08192
\(760\) −12.4542 + 21.5712i −0.451760 + 0.782471i
\(761\) 2.14110 3.70849i 0.0776147 0.134433i −0.824606 0.565708i \(-0.808603\pi\)
0.902220 + 0.431275i \(0.141936\pi\)
\(762\) 10.9175 0.395500
\(763\) 0 0
\(764\) 2.92221 + 5.06141i 0.105722 + 0.183115i
\(765\) 6.66527 + 11.5446i 0.240983 + 0.417395i
\(766\) 25.1406 0.908368
\(767\) −2.89445 + 23.7483i −0.104512 + 0.857502i
\(768\) −20.4343 −0.737360
\(769\) 15.4518 + 26.7632i 0.557205 + 0.965107i 0.997728 + 0.0673662i \(0.0214596\pi\)
−0.440523 + 0.897741i \(0.645207\pi\)
\(770\) 0 0
\(771\) 32.8305 56.8641i 1.18236 2.04791i
\(772\) 0.550039 0.0197963
\(773\) 17.4608 30.2430i 0.628021 1.08776i −0.359927 0.932980i \(-0.617199\pi\)
0.987948 0.154784i \(-0.0494681\pi\)
\(774\) 19.0458 32.9884i 0.684588 1.18574i
\(775\) 2.88145 0.103505
\(776\) 11.6579 20.1921i 0.418494 0.724853i
\(777\) 0 0