Properties

Label 637.2.f.h.295.4
Level $637$
Weight $2$
Character 637.295
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 295.4
Root \(-1.87694 + 1.08365i\) of defining polynomial
Character \(\chi\) \(=\) 637.295
Dual form 637.2.f.h.393.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.651388 - 1.12824i) q^{2} +(1.44073 - 2.49541i) q^{3} +(0.151388 + 0.262211i) q^{4} -2.88145 q^{5} +(-1.87694 - 3.25096i) q^{6} +3.00000 q^{8} +(-2.65139 - 4.59234i) q^{9} +O(q^{10})\) \(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})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 2 q^{2} - 6 q^{4} + 24 q^{8} - 14 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 2 q^{2} - 6 q^{4} + 24 q^{8} - 14 q^{9} + 2 q^{11} - 26 q^{15} + 6 q^{16} - 12 q^{18} - 38 q^{22} - 12 q^{23} + 12 q^{25} + 2 q^{29} + 14 q^{32} - 8 q^{36} - 20 q^{37} - 52 q^{39} + 14 q^{43} + 72 q^{44} + 20 q^{46} + 10 q^{50} + 52 q^{51} + 48 q^{53} + 52 q^{57} + 14 q^{58} + 52 q^{60} - 16 q^{64} + 26 q^{65} - 4 q^{67} - 16 q^{71} - 42 q^{72} - 36 q^{74} + 78 q^{78} - 24 q^{79} + 16 q^{81} - 26 q^{85} - 144 q^{86} + 6 q^{88} - 16 q^{92} + 26 q^{93} - 26 q^{95} - 92 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(197\) \(248\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

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 −0.538390 0.842696i \(-0.680967\pi\)
0.998991 + 0.0449118i \(0.0143007\pi\)
\(3\) 1.44073 2.49541i 0.831804 1.44073i −0.0648022 0.997898i \(-0.520642\pi\)
0.896606 0.442829i \(-0.146025\pi\)
\(4\) 0.151388 + 0.262211i 0.0756939 + 0.131106i
\(5\) −2.88145 −1.28863 −0.644313 0.764762i \(-0.722856\pi\)
−0.644313 + 0.764762i \(0.722856\pi\)
\(6\) −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 0.0516924 0.998663i \(-0.483538\pi\)
0.839021 0.544098i \(-0.183128\pi\)
\(12\) 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 \(-0.200406\pi\)
−0.914064 + 0.405570i \(0.867073\pi\)
\(18\) −6.90833 −1.62831
\(19\) 1.44073 + 2.49541i 0.330525 + 0.572487i 0.982615 0.185655i \(-0.0594407\pi\)
−0.652090 + 0.758142i \(0.726107\pi\)
\(20\) −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 0.283590 + 0.958946i \(0.408475\pi\)
−0.972266 + 0.233877i \(0.924859\pi\)
\(24\) 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 −0.920146 0.391575i \(-0.871931\pi\)
0.799187 + 0.601083i \(0.205264\pi\)
\(30\) 5.40833 + 9.36750i 0.987421 + 1.71026i
\(31\) −0.872434 −0.156694 −0.0783469 0.996926i \(-0.524964\pi\)
−0.0783469 + 0.996926i \(0.524964\pi\)
\(32\) 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 −0.917629 0.397438i \(-0.869899\pi\)
0.803006 + 0.595971i \(0.203233\pi\)
\(38\) 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 −0.408458 0.912777i \(-0.633934\pi\)
0.994717 0.102653i \(-0.0327331\pi\)
\(42\) 0 0
\(43\) −2.75694 4.77516i −0.420429 0.728205i 0.575552 0.817765i \(-0.304787\pi\)
−0.995981 + 0.0895602i \(0.971454\pi\)
\(44\) 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 \(-0.140442\pi\)
0.904235 + 0.427035i \(0.140442\pi\)
\(48\) −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 \(-0.0245016\pi\)
−0.565115 + 0.825012i \(0.691168\pi\)
\(60\) −2.51388 −0.324540
\(61\) 2.88145 + 4.99082i 0.368932 + 0.639010i 0.989399 0.145223i \(-0.0463901\pi\)
−0.620467 + 0.784233i \(0.713057\pi\)
\(62\) −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 −0.894951 0.446165i \(-0.852789\pi\)
0.833866 + 0.551967i \(0.186123\pi\)
\(68\) 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 0.722599 0.691268i \(-0.242948\pi\)
−0.959955 + 0.280155i \(0.909614\pi\)
\(72\) −7.95416 13.7770i −0.937407 1.62364i
\(73\) 5.76291 0.674497 0.337249 0.941416i \(-0.390504\pi\)
0.337249 + 0.941416i \(0.390504\pi\)
\(74\) 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 \(-0.381356\pi\)
0.364162 + 0.931336i \(0.381356\pi\)
\(84\) 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 \(-0.681846\pi\)
0.998863 + 0.0476677i \(0.0151788\pi\)
\(90\) 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 \(-0.295770\pi\)
−0.993045 + 0.117736i \(0.962436\pi\)
\(98\) 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 \(-0.974846\pi\)
0.566806 + 0.823851i \(0.308179\pi\)
\(102\) −1.63751 + 2.83625i −0.162138 + 0.280831i
\(103\) −4.89047 −0.481873 −0.240936 0.970541i \(-0.577455\pi\)
−0.240936 + 0.970541i \(0.577455\pi\)
\(104\) −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 −0.998364 0.0571755i \(-0.981791\pi\)
0.548698 + 0.836021i \(0.315124\pi\)
\(108\) −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 0.969530 + 0.244972i \(0.0787786\pi\)
−0.272613 + 0.962124i \(0.587888\pi\)
\(114\) 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 −0.794267 0.607569i \(-0.792145\pi\)
0.923303 + 0.384071i \(0.125478\pi\)
\(128\) 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 \(-0.766941\pi\)
−0.743722 + 0.668489i \(0.766941\pi\)
\(132\) 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 0.802648 0.596453i \(-0.203424\pi\)
−0.917868 + 0.396887i \(0.870091\pi\)
\(138\) 24.7965 2.11082
\(139\) 8.51229 + 14.7437i 0.722003 + 1.25055i 0.960196 + 0.279327i \(0.0901115\pi\)
−0.238193 + 0.971218i \(0.576555\pi\)
\(140\) 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 0.855309 0.518118i \(-0.173367\pi\)
−0.876358 + 0.481660i \(0.840034\pi\)
\(150\) −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 \(-0.623994\pi\)
−0.379761 + 0.925084i \(0.623994\pi\)
\(158\) 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 0.976749 + 0.214387i \(0.0687753\pi\)
−0.302710 + 0.953083i \(0.597891\pi\)
\(164\) 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 \(-0.772738\pi\)
0.944990 + 0.327100i \(0.106071\pi\)
\(168\) 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 0.814821 + 0.579713i \(0.196835\pi\)
0.0946356 + 0.995512i \(0.469831\pi\)
\(174\) 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 0.461069 + 0.887364i \(0.347466\pi\)
−0.999014 + 0.0443850i \(0.985867\pi\)
\(180\) −2.31316 + 4.00651i −0.172413 + 0.298628i
\(181\) −9.25264 −0.687744 −0.343872 0.939017i \(-0.611739\pi\)
−0.343872 + 0.939017i \(0.611739\pi\)
\(182\) 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 −0.969038 0.246911i \(-0.920585\pi\)
0.270688 0.962667i \(-0.412749\pi\)
\(192\) 12.7024 22.0012i 0.916716 1.58780i
\(193\) 0.908327 1.57327i 0.0653828 0.113246i −0.831481 0.555553i \(-0.812506\pi\)
0.896864 + 0.442307i \(0.145840\pi\)
\(194\) −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 −0.572130 0.820163i \(-0.693883\pi\)
0.996347 + 0.0853980i \(0.0272162\pi\)
\(198\) −20.4083 + 35.3483i −1.45036 + 2.51209i
\(199\) 0.436217 + 0.755550i 0.0309226 + 0.0535595i 0.881073 0.472981i \(-0.156822\pi\)
−0.850150 + 0.526541i \(0.823489\pi\)
\(200\) 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 0.483499 + 0.875345i \(0.339366\pi\)
−0.999820 + 0.0189499i \(0.993968\pi\)
\(212\) 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 \(-0.983044\pi\)
0.545402 + 0.838175i \(0.316377\pi\)
\(224\) 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 0.814399 + 0.580306i \(0.197067\pi\)
0.0953602 + 0.995443i \(0.469600\pi\)
\(228\) 1.25694 + 2.17708i 0.0832428 + 0.144181i
\(229\) −20.7785 −1.37308 −0.686540 0.727092i \(-0.740871\pi\)
−0.686540 + 0.727092i \(0.740871\pi\)
\(230\) −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 \(-0.187278\pi\)
−0.896564 + 0.442915i \(0.853944\pi\)
\(242\) −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 −0.964546 0.263915i \(-0.914986\pi\)
0.253716 0.967279i \(-0.418347\pi\)
\(252\) 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 0.253865 + 0.967240i \(0.418298\pi\)
−0.964587 + 0.263767i \(0.915035\pi\)
\(258\) −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 −0.581480 0.813561i \(-0.697526\pi\)
0.995304 + 0.0967960i \(0.0308594\pi\)
\(264\) −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 \(-0.0729699\pi\)
−0.683714 + 0.729750i \(0.739637\pi\)
\(270\) 12.4542 21.5712i 0.757936 1.31278i
\(271\) 14.8435 25.7097i 0.901678 1.56175i 0.0763615 0.997080i \(-0.475670\pi\)
0.825316 0.564671i \(-0.190997\pi\)
\(272\) −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 0.569667 0.821875i \(-0.307072\pi\)
−0.996599 + 0.0824088i \(0.973739\pi\)
\(278\) 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 \(-0.795229\pi\)
0.919539 + 0.392998i \(0.128562\pi\)
\(284\) 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 \(-0.134163\pi\)
−0.810546 + 0.585675i \(0.800830\pi\)
\(294\) 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 \(-0.643616\pi\)
−0.436029 + 0.899932i \(0.643616\pi\)
\(308\) 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 \(-0.339661\pi\)
0.482687 + 0.875793i \(0.339661\pi\)
\(312\) −24.9083 + 18.7350i −1.41016 + 1.06066i
\(313\) −13.2707 −0.750103 −0.375052 0.927004i \(-0.622375\pi\)
−0.375052 + 0.927004i \(0.622375\pi\)
\(314\) −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 0.856286 0.516503i \(-0.172766\pi\)
−0.875447 + 0.483314i \(0.839433\pi\)
\(332\) 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 0.855244 0.518226i \(-0.173407\pi\)
−0.876419 + 0.481550i \(0.840074\pi\)
\(348\) −0.568293 + 0.984312i −0.0304637 + 0.0527647i
\(349\) 11.9620 20.7188i 0.640313 1.10905i −0.345050 0.938584i \(-0.612138\pi\)
0.985363 0.170470i \(-0.0545286\pi\)
\(350\) 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 \(-0.779101\pi\)
0.938262 + 0.345924i \(0.112435\pi\)
\(354\) 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 0.215011 + 0.976612i \(0.431021\pi\)
−0.953276 + 0.302100i \(0.902312\pi\)
\(368\) 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 0.996141 0.0877661i \(-0.0279728\pi\)
−0.574078 + 0.818800i \(0.694639\pi\)
\(374\) −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 −0.983857 0.178954i \(-0.942729\pi\)
0.646908 + 0.762568i \(0.276062\pi\)
\(380\) 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 \(-0.330779\pi\)
−0.999968 + 0.00802473i \(0.997446\pi\)
\(384\) −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 \(-0.120472\pi\)
−0.784614 + 0.619985i \(0.787139\pi\)
\(398\) 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 −0.990700 0.136065i \(-0.956554\pi\)
0.613186 + 0.789939i \(0.289888\pi\)
\(402\) 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 \(-0.297426\pi\)
−0.993644 + 0.112567i \(0.964093\pi\)
\(410\) 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 \(-0.767711\pi\)
0.950037 + 0.312137i \(0.101045\pi\)
\(420\) 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 0.363960 + 0.931415i \(0.381424\pi\)
−0.988609 + 0.150509i \(0.951909\pi\)
\(432\) −10.9575 + 18.9790i −0.527194 + 0.913127i
\(433\) −4.19010 7.25747i −0.201364 0.348772i 0.747604 0.664144i \(-0.231204\pi\)
−0.948968 + 0.315372i \(0.897871\pi\)
\(434\) 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 \(-0.952138\pi\)
0.624087 + 0.781355i \(0.285471\pi\)
\(440\) −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 0.749384 0.662136i \(-0.230350\pi\)
−0.948118 + 0.317918i \(0.897016\pi\)
\(450\) −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 −0.979071 0.203519i \(-0.934762\pi\)
0.665788 + 0.746141i \(0.268095\pi\)
\(458\) −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 \(-0.261944\pi\)
−0.974955 + 0.222400i \(0.928611\pi\)
\(462\) 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 \(-0.393884\pi\)
0.327233 + 0.944944i \(0.393884\pi\)
\(468\) −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 \(-0.841599\pi\)
0.852750 + 0.522319i \(0.174933\pi\)
\(480\) −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 0.988044 + 0.154174i \(0.0492717\pi\)
−0.360503 + 0.932758i \(0.617395\pi\)
\(488\) 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 −0.685990 0.727611i \(-0.740630\pi\)
0.973125 + 0.230279i \(0.0739638\pi\)
\(492\) 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 −0.995692 0.0927268i \(-0.970442\pi\)
0.417542 0.908658i \(-0.362892\pi\)
\(504\) 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 \(-0.851807\pi\)
0.835565 + 0.549392i \(0.185141\pi\)
\(510\) 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 \(-0.282565\pi\)
0.631194 + 0.775625i \(0.282565\pi\)
\(522\) 4.50000 7.79423i 0.196960 0.341144i
\(523\) −4.62632 + 8.01302i −0.202295 + 0.350385i −0.949267 0.314470i \(-0.898173\pi\)
0.746973 + 0.664855i \(0.231507\pi\)
\(524\) −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 −0.987663 0.156597i \(-0.949948\pi\)
0.629448 + 0.777042i \(0.283281\pi\)
\(558\) 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 \(-0.298034\pi\)
−0.993857 + 0.110671i \(0.964700\pi\)
\(564\) 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 −0.421909 0.906638i \(-0.638640\pi\)
0.996126 0.0879356i \(-0.0280270\pi\)
\(570\) −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 \(-0.747521\pi\)
−0.701579 + 0.712592i \(0.747521\pi\)
\(578\) −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 0.405137 + 0.914256i \(0.367224\pi\)
−0.994337 + 0.106269i \(0.966110\pi\)
\(588\) 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 \(-0.345016\pi\)
0.467885 + 0.883789i \(0.345016\pi\)
\(594\) 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 0.392716 + 0.919660i \(0.371536\pi\)
−0.992807 + 0.119728i \(0.961798\pi\)
\(602\) 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 \(-0.0305525\pi\)
−0.580695 + 0.814121i \(0.697219\pi\)
\(608\) −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 −0.996508 0.0834983i \(-0.973391\pi\)
0.570566 + 0.821252i \(0.306724\pi\)
\(614\) −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 0.887949 + 0.459943i \(0.152130\pi\)
−0.0456524 + 0.998957i \(0.514537\pi\)
\(618\) 9.17914 + 15.8987i 0.369239 + 0.639541i
\(619\) −22.5233 −0.905289 −0.452644 0.891691i \(-0.649519\pi\)
−0.452644 + 0.891691i \(0.649519\pi\)
\(620\) 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 0.720227 0.693738i \(-0.244037\pi\)
−0.960908 + 0.276866i \(0.910704\pi\)
\(632\) 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 0.829240 0.558892i \(-0.188774\pi\)
−0.898635 + 0.438697i \(0.855440\pi\)
\(642\) 34.9216 1.37824
\(643\) −4.19010 7.25747i −0.165242 0.286207i 0.771499 0.636230i \(-0.219507\pi\)
−0.936741 + 0.350023i \(0.886174\pi\)
\(644\) 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 \(-0.847561\pi\)
0.842819 + 0.538198i \(0.180895\pi\)
\(648\) −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 −0.996479 0.0838475i \(-0.973279\pi\)
0.570853 + 0.821052i \(0.306612\pi\)
\(654\) 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 0.538665 0.842520i \(-0.318929\pi\)
−0.998976 + 0.0452373i \(0.985596\pi\)
\(660\) −7.42641 + 12.8629i −0.289073 + 0.500688i
\(661\) −4.89047 + 8.47055i −0.190217 + 0.329466i −0.945322 0.326138i \(-0.894253\pi\)
0.755105 + 0.655604i \(0.227586\pi\)
\(662\) −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 −0.959375 0.282135i \(-0.908958\pi\)
0.724023 + 0.689776i \(0.242291\pi\)
\(674\) −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 \(-0.539069\pi\)
−0.122432 + 0.992477i \(0.539069\pi\)
\(678\) 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 0.829472 0.558549i \(-0.188642\pi\)
−0.898453 + 0.439069i \(0.855308\pi\)
\(684\) 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 −0.362315 0.932056i \(-0.618014\pi\)
0.988341 0.152254i \(-0.0486531\pi\)
\(692\) −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 0.863432 0.504466i \(-0.168311\pi\)
−0.868596 + 0.495521i \(0.834977\pi\)
\(710\) 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 \(-0.0343833\pi\)
−0.590451 + 0.807074i \(0.701050\pi\)
\(720\) 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 \(-0.357155\pi\)
0.433850 + 0.900985i \(0.357155\pi\)
\(728\) 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 \(-0.234767\pi\)
0.740124 + 0.672470i \(0.234767\pi\)
\(734\) 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 −0.639879 0.768476i \(-0.721015\pi\)
0.985459 + 0.169913i \(0.0543487\pi\)
\(740\) 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 −0.279862 0.960040i \(-0.590289\pi\)
0.971350 0.237653i \(-0.0763781\pi\)
\(744\) −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 −0.823148 0.567826i \(-0.807785\pi\)
0.903326 + 0.428954i \(0.141118\pi\)
\(752\) 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 −0.113057 0.993588i \(-0.536064\pi\)
0.917001 0.398884i \(-0.130602\pi\)
\(758\) 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 \(-0.191397\pi\)
−0.902220 + 0.431275i \(0.858064\pi\)
\(762\) −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 0.440523 + 0.897741i \(0.354793\pi\)
−0.997728 + 0.0673662i \(0.978540\pi\)
\(770\) 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 −0.987948 0.154784i \(-0.950532\pi\)
0.359927 0.932980i \(-0.382801\pi\)
\(774\) 19.0458 + 32.9884i 0.684588 + 1.18574i
\(775\) −2.88145 −0.103505
\(776\) −11