Properties

Label 729.2.c.e.244.5
Level $729$
Weight $2$
Character 729.244
Analytic conductor $5.821$
Analytic rank $0$
Dimension $12$
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(244,729)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(729, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("729.244");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 729 = 3^{6} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 729.c (of order \(3\), degree \(2\), 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: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{3})\)
Coefficient field: 12.0.1952986685049.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 6 x^{11} + 27 x^{10} - 80 x^{9} + 186 x^{8} - 330 x^{7} + 463 x^{6} - 504 x^{5} + 420 x^{4} - 258 x^{3} + 108 x^{2} - 27 x + 3 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 3^{3} \)
Twist minimal: no (minimal twist has level 27)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 244.5
Root \(0.500000 + 2.22827i\) of defining polynomial
Character \(\chi\) \(=\) 729.244
Dual form 729.2.c.e.487.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.05831 + 1.83305i) q^{2} +(-1.24005 + 2.14782i) q^{4} +(1.34155 - 2.32363i) q^{5} +(-0.486166 - 0.842065i) q^{7} -1.01617 q^{8} +O(q^{10})\) \(q+(1.05831 + 1.83305i) q^{2} +(-1.24005 + 2.14782i) q^{4} +(1.34155 - 2.32363i) q^{5} +(-0.486166 - 0.842065i) q^{7} -1.01617 q^{8} +5.67911 q^{10} +(0.158451 + 0.274445i) q^{11} +(0.757015 - 1.31119i) q^{13} +(1.02903 - 1.78233i) q^{14} +(1.40466 + 2.43295i) q^{16} +1.17468 q^{17} +6.22080 q^{19} +(3.32716 + 5.76282i) q^{20} +(-0.335381 + 0.580897i) q^{22} +(-1.08137 + 1.87299i) q^{23} +(-1.09951 - 1.90440i) q^{25} +3.20463 q^{26} +2.41147 q^{28} +(2.20246 + 3.81476i) q^{29} +(4.33661 - 7.51124i) q^{31} +(-3.98932 + 6.90970i) q^{32} +(1.24318 + 2.15325i) q^{34} -2.60886 q^{35} -4.46665 q^{37} +(6.58355 + 11.4030i) q^{38} +(-1.36325 + 2.36121i) q^{40} +(-2.92259 + 5.06208i) q^{41} +(-2.79550 - 4.84194i) q^{43} -0.785946 q^{44} -4.57771 q^{46} +(1.23803 + 2.14434i) q^{47} +(3.02728 - 5.24341i) q^{49} +(2.32724 - 4.03090i) q^{50} +(1.87747 + 3.25187i) q^{52} -10.8920 q^{53} +0.850279 q^{55} +(0.494029 + 0.855683i) q^{56} +(-4.66177 + 8.07442i) q^{58} +(0.862105 - 1.49321i) q^{59} +(-0.507389 - 0.878823i) q^{61} +18.3580 q^{62} -11.2691 q^{64} +(-2.03115 - 3.51805i) q^{65} +(-0.428276 + 0.741795i) q^{67} +(-1.45666 + 2.52301i) q^{68} +(-2.76099 - 4.78218i) q^{70} -9.59577 q^{71} -15.2418 q^{73} +(-4.72710 - 8.18758i) q^{74} +(-7.71408 + 13.3612i) q^{76} +(0.154067 - 0.266852i) q^{77} +(5.60688 + 9.71141i) q^{79} +7.53771 q^{80} -12.3721 q^{82} +(-2.34247 - 4.05727i) q^{83} +(1.57590 - 2.72953i) q^{85} +(5.91701 - 10.2486i) q^{86} +(-0.161014 - 0.278884i) q^{88} -15.4995 q^{89} -1.47214 q^{91} +(-2.68190 - 4.64519i) q^{92} +(-2.62045 + 4.53876i) q^{94} +(8.34551 - 14.4549i) q^{95} +(2.77474 + 4.80600i) q^{97} +12.8152 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 3 q^{2} - 3 q^{4} + 6 q^{5} - 12 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 3 q^{2} - 3 q^{4} + 6 q^{5} - 12 q^{8} + 6 q^{10} + 12 q^{11} + 6 q^{14} + 3 q^{16} - 18 q^{17} + 6 q^{19} + 6 q^{20} - 6 q^{22} + 15 q^{23} + 6 q^{25} - 30 q^{26} - 12 q^{28} + 12 q^{29} - 24 q^{35} + 6 q^{37} - 3 q^{38} - 6 q^{40} + 15 q^{41} - 6 q^{44} + 6 q^{46} + 21 q^{47} + 12 q^{49} + 3 q^{50} - 12 q^{52} - 18 q^{53} - 12 q^{55} - 6 q^{56} + 12 q^{58} + 24 q^{59} + 9 q^{61} + 24 q^{62} - 24 q^{64} - 6 q^{65} + 9 q^{67} - 9 q^{68} - 15 q^{70} - 54 q^{71} - 12 q^{73} - 12 q^{74} - 6 q^{76} - 12 q^{77} + 42 q^{80} - 12 q^{82} + 12 q^{83} - 21 q^{86} - 12 q^{88} - 18 q^{89} - 12 q^{91} + 6 q^{92} - 6 q^{94} + 12 q^{95} + 90 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.05831 + 1.83305i 0.748339 + 1.29616i 0.948618 + 0.316423i \(0.102482\pi\)
−0.200279 + 0.979739i \(0.564185\pi\)
\(3\) 0 0
\(4\) −1.24005 + 2.14782i −0.620023 + 1.07391i
\(5\) 1.34155 2.32363i 0.599959 1.03916i −0.392868 0.919595i \(-0.628517\pi\)
0.992826 0.119564i \(-0.0381498\pi\)
\(6\) 0 0
\(7\) −0.486166 0.842065i −0.183754 0.318271i 0.759402 0.650621i \(-0.225492\pi\)
−0.943156 + 0.332351i \(0.892158\pi\)
\(8\) −1.01617 −0.359271
\(9\) 0 0
\(10\) 5.67911 1.79589
\(11\) 0.158451 + 0.274445i 0.0477748 + 0.0827484i 0.888924 0.458055i \(-0.151454\pi\)
−0.841149 + 0.540803i \(0.818120\pi\)
\(12\) 0 0
\(13\) 0.757015 1.31119i 0.209958 0.363658i −0.741743 0.670684i \(-0.766001\pi\)
0.951701 + 0.307026i \(0.0993339\pi\)
\(14\) 1.02903 1.78233i 0.275020 0.476349i
\(15\) 0 0
\(16\) 1.40466 + 2.43295i 0.351166 + 0.608238i
\(17\) 1.17468 0.284903 0.142451 0.989802i \(-0.454502\pi\)
0.142451 + 0.989802i \(0.454502\pi\)
\(18\) 0 0
\(19\) 6.22080 1.42715 0.713575 0.700579i \(-0.247075\pi\)
0.713575 + 0.700579i \(0.247075\pi\)
\(20\) 3.32716 + 5.76282i 0.743977 + 1.28861i
\(21\) 0 0
\(22\) −0.335381 + 0.580897i −0.0715035 + 0.123848i
\(23\) −1.08137 + 1.87299i −0.225481 + 0.390545i −0.956464 0.291851i \(-0.905729\pi\)
0.730982 + 0.682396i \(0.239062\pi\)
\(24\) 0 0
\(25\) −1.09951 1.90440i −0.219901 0.380880i
\(26\) 3.20463 0.628480
\(27\) 0 0
\(28\) 2.41147 0.455726
\(29\) 2.20246 + 3.81476i 0.408986 + 0.708384i 0.994776 0.102078i \(-0.0325493\pi\)
−0.585791 + 0.810462i \(0.699216\pi\)
\(30\) 0 0
\(31\) 4.33661 7.51124i 0.778879 1.34906i −0.153710 0.988116i \(-0.549122\pi\)
0.932588 0.360942i \(-0.117545\pi\)
\(32\) −3.98932 + 6.90970i −0.705218 + 1.22147i
\(33\) 0 0
\(34\) 1.24318 + 2.15325i 0.213204 + 0.369280i
\(35\) −2.60886 −0.440978
\(36\) 0 0
\(37\) −4.46665 −0.734312 −0.367156 0.930159i \(-0.619668\pi\)
−0.367156 + 0.930159i \(0.619668\pi\)
\(38\) 6.58355 + 11.4030i 1.06799 + 1.84982i
\(39\) 0 0
\(40\) −1.36325 + 2.36121i −0.215548 + 0.373340i
\(41\) −2.92259 + 5.06208i −0.456432 + 0.790564i −0.998769 0.0495972i \(-0.984206\pi\)
0.542337 + 0.840161i \(0.317540\pi\)
\(42\) 0 0
\(43\) −2.79550 4.84194i −0.426309 0.738389i 0.570233 0.821483i \(-0.306853\pi\)
−0.996542 + 0.0830943i \(0.973520\pi\)
\(44\) −0.785946 −0.118486
\(45\) 0 0
\(46\) −4.57771 −0.674946
\(47\) 1.23803 + 2.14434i 0.180586 + 0.312784i 0.942080 0.335388i \(-0.108867\pi\)
−0.761494 + 0.648172i \(0.775534\pi\)
\(48\) 0 0
\(49\) 3.02728 5.24341i 0.432469 0.749059i
\(50\) 2.32724 4.03090i 0.329122 0.570055i
\(51\) 0 0
\(52\) 1.87747 + 3.25187i 0.260358 + 0.450953i
\(53\) −10.8920 −1.49613 −0.748063 0.663628i \(-0.769016\pi\)
−0.748063 + 0.663628i \(0.769016\pi\)
\(54\) 0 0
\(55\) 0.850279 0.114652
\(56\) 0.494029 + 0.855683i 0.0660174 + 0.114345i
\(57\) 0 0
\(58\) −4.66177 + 8.07442i −0.612120 + 1.06022i
\(59\) 0.862105 1.49321i 0.112237 0.194399i −0.804435 0.594040i \(-0.797532\pi\)
0.916672 + 0.399641i \(0.130865\pi\)
\(60\) 0 0
\(61\) −0.507389 0.878823i −0.0649645 0.112522i 0.831714 0.555205i \(-0.187360\pi\)
−0.896678 + 0.442683i \(0.854027\pi\)
\(62\) 18.3580 2.33146
\(63\) 0 0
\(64\) −11.2691 −1.40864
\(65\) −2.03115 3.51805i −0.251933 0.436360i
\(66\) 0 0
\(67\) −0.428276 + 0.741795i −0.0523222 + 0.0906247i −0.891000 0.454003i \(-0.849996\pi\)
0.838678 + 0.544627i \(0.183329\pi\)
\(68\) −1.45666 + 2.52301i −0.176646 + 0.305960i
\(69\) 0 0
\(70\) −2.76099 4.78218i −0.330001 0.571579i
\(71\) −9.59577 −1.13881 −0.569404 0.822058i \(-0.692826\pi\)
−0.569404 + 0.822058i \(0.692826\pi\)
\(72\) 0 0
\(73\) −15.2418 −1.78392 −0.891960 0.452113i \(-0.850670\pi\)
−0.891960 + 0.452113i \(0.850670\pi\)
\(74\) −4.72710 8.18758i −0.549514 0.951787i
\(75\) 0 0
\(76\) −7.71408 + 13.3612i −0.884866 + 1.53263i
\(77\) 0.154067 0.266852i 0.0175576 0.0304106i
\(78\) 0 0
\(79\) 5.60688 + 9.71141i 0.630824 + 1.09262i 0.987384 + 0.158346i \(0.0506162\pi\)
−0.356560 + 0.934272i \(0.616050\pi\)
\(80\) 7.53771 0.842741
\(81\) 0 0
\(82\) −12.3721 −1.36626
\(83\) −2.34247 4.05727i −0.257119 0.445343i 0.708350 0.705861i \(-0.249440\pi\)
−0.965469 + 0.260518i \(0.916107\pi\)
\(84\) 0 0
\(85\) 1.57590 2.72953i 0.170930 0.296059i
\(86\) 5.91701 10.2486i 0.638048 1.10513i
\(87\) 0 0
\(88\) −0.161014 0.278884i −0.0171641 0.0297291i
\(89\) −15.4995 −1.64295 −0.821473 0.570248i \(-0.806847\pi\)
−0.821473 + 0.570248i \(0.806847\pi\)
\(90\) 0 0
\(91\) −1.47214 −0.154322
\(92\) −2.68190 4.64519i −0.279607 0.484294i
\(93\) 0 0
\(94\) −2.62045 + 4.53876i −0.270279 + 0.468137i
\(95\) 8.34551 14.4549i 0.856231 1.48304i
\(96\) 0 0
\(97\) 2.77474 + 4.80600i 0.281732 + 0.487975i 0.971812 0.235759i \(-0.0757576\pi\)
−0.690079 + 0.723734i \(0.742424\pi\)
\(98\) 12.8152 1.29453
\(99\) 0 0
\(100\) 5.45376 0.545376
\(101\) 5.06952 + 8.78067i 0.504436 + 0.873709i 0.999987 + 0.00513025i \(0.00163302\pi\)
−0.495550 + 0.868579i \(0.665034\pi\)
\(102\) 0 0
\(103\) 4.92665 8.53320i 0.485437 0.840801i −0.514423 0.857536i \(-0.671994\pi\)
0.999860 + 0.0167353i \(0.00532726\pi\)
\(104\) −0.769258 + 1.33239i −0.0754320 + 0.130652i
\(105\) 0 0
\(106\) −11.5271 19.9655i −1.11961 1.93922i
\(107\) 5.17080 0.499880 0.249940 0.968261i \(-0.419589\pi\)
0.249940 + 0.968261i \(0.419589\pi\)
\(108\) 0 0
\(109\) −7.31065 −0.700234 −0.350117 0.936706i \(-0.613858\pi\)
−0.350117 + 0.936706i \(0.613858\pi\)
\(110\) 0.899860 + 1.55860i 0.0857983 + 0.148607i
\(111\) 0 0
\(112\) 1.36580 2.36564i 0.129056 0.223532i
\(113\) −5.18782 + 8.98557i −0.488029 + 0.845291i −0.999905 0.0137681i \(-0.995617\pi\)
0.511876 + 0.859059i \(0.328951\pi\)
\(114\) 0 0
\(115\) 2.90142 + 5.02541i 0.270559 + 0.468622i
\(116\) −10.9246 −1.01432
\(117\) 0 0
\(118\) 3.64950 0.335964
\(119\) −0.571092 0.989160i −0.0523519 0.0906762i
\(120\) 0 0
\(121\) 5.44979 9.43931i 0.495435 0.858119i
\(122\) 1.07395 1.86014i 0.0972310 0.168409i
\(123\) 0 0
\(124\) 10.7552 + 18.6286i 0.965845 + 1.67289i
\(125\) 7.51532 0.672191
\(126\) 0 0
\(127\) 5.22743 0.463860 0.231930 0.972733i \(-0.425496\pi\)
0.231930 + 0.972733i \(0.425496\pi\)
\(128\) −3.94758 6.83741i −0.348920 0.604348i
\(129\) 0 0
\(130\) 4.29917 7.44638i 0.377062 0.653091i
\(131\) 3.61715 6.26509i 0.316032 0.547383i −0.663624 0.748066i \(-0.730983\pi\)
0.979656 + 0.200683i \(0.0643160\pi\)
\(132\) 0 0
\(133\) −3.02435 5.23832i −0.262244 0.454220i
\(134\) −1.81300 −0.156619
\(135\) 0 0
\(136\) −1.19368 −0.102357
\(137\) −5.62466 9.74220i −0.480547 0.832332i 0.519204 0.854650i \(-0.326229\pi\)
−0.999751 + 0.0223185i \(0.992895\pi\)
\(138\) 0 0
\(139\) −4.69008 + 8.12346i −0.397808 + 0.689023i −0.993455 0.114223i \(-0.963562\pi\)
0.595648 + 0.803246i \(0.296895\pi\)
\(140\) 3.23511 5.60338i 0.273417 0.473572i
\(141\) 0 0
\(142\) −10.1553 17.5895i −0.852215 1.47608i
\(143\) 0.479799 0.0401228
\(144\) 0 0
\(145\) 11.8188 0.981498
\(146\) −16.1306 27.9390i −1.33498 2.31225i
\(147\) 0 0
\(148\) 5.53885 9.59356i 0.455290 0.788586i
\(149\) −9.52562 + 16.4989i −0.780369 + 1.35164i 0.151357 + 0.988479i \(0.451636\pi\)
−0.931727 + 0.363160i \(0.881698\pi\)
\(150\) 0 0
\(151\) −2.00700 3.47623i −0.163327 0.282891i 0.772733 0.634732i \(-0.218889\pi\)
−0.936060 + 0.351840i \(0.885556\pi\)
\(152\) −6.32141 −0.512734
\(153\) 0 0
\(154\) 0.652204 0.0525561
\(155\) −11.6356 20.1534i −0.934591 1.61876i
\(156\) 0 0
\(157\) −3.63796 + 6.30113i −0.290341 + 0.502885i −0.973890 0.227019i \(-0.927102\pi\)
0.683550 + 0.729904i \(0.260435\pi\)
\(158\) −11.8677 + 20.5554i −0.944140 + 1.63530i
\(159\) 0 0
\(160\) 10.7037 + 18.5394i 0.846204 + 1.46567i
\(161\) 2.10290 0.165732
\(162\) 0 0
\(163\) 12.4492 0.975094 0.487547 0.873097i \(-0.337892\pi\)
0.487547 + 0.873097i \(0.337892\pi\)
\(164\) −7.24830 12.5544i −0.565997 0.980335i
\(165\) 0 0
\(166\) 4.95811 8.58771i 0.384824 0.666535i
\(167\) 1.16594 2.01947i 0.0902234 0.156272i −0.817382 0.576097i \(-0.804575\pi\)
0.907605 + 0.419825i \(0.137909\pi\)
\(168\) 0 0
\(169\) 5.35386 + 9.27315i 0.411835 + 0.713319i
\(170\) 6.67116 0.511654
\(171\) 0 0
\(172\) 13.8662 1.05729
\(173\) 1.79113 + 3.10234i 0.136177 + 0.235866i 0.926047 0.377409i \(-0.123185\pi\)
−0.789869 + 0.613275i \(0.789852\pi\)
\(174\) 0 0
\(175\) −1.06909 + 1.85171i −0.0808154 + 0.139976i
\(176\) −0.445141 + 0.771007i −0.0335538 + 0.0581168i
\(177\) 0 0
\(178\) −16.4033 28.4114i −1.22948 2.12952i
\(179\) −19.9957 −1.49455 −0.747275 0.664515i \(-0.768638\pi\)
−0.747275 + 0.664515i \(0.768638\pi\)
\(180\) 0 0
\(181\) 9.73232 0.723398 0.361699 0.932295i \(-0.382197\pi\)
0.361699 + 0.932295i \(0.382197\pi\)
\(182\) −1.55798 2.69851i −0.115485 0.200027i
\(183\) 0 0
\(184\) 1.09886 1.90328i 0.0810090 0.140312i
\(185\) −5.99222 + 10.3788i −0.440557 + 0.763067i
\(186\) 0 0
\(187\) 0.186130 + 0.322387i 0.0136112 + 0.0235752i
\(188\) −6.14088 −0.447869
\(189\) 0 0
\(190\) 35.3286 2.56301
\(191\) 8.87826 + 15.3776i 0.642409 + 1.11268i 0.984894 + 0.173161i \(0.0553981\pi\)
−0.342485 + 0.939523i \(0.611269\pi\)
\(192\) 0 0
\(193\) −5.29217 + 9.16630i −0.380939 + 0.659805i −0.991197 0.132398i \(-0.957732\pi\)
0.610258 + 0.792203i \(0.291066\pi\)
\(194\) −5.87308 + 10.1725i −0.421663 + 0.730341i
\(195\) 0 0
\(196\) 7.50794 + 13.0041i 0.536282 + 0.928867i
\(197\) 14.1589 1.00878 0.504390 0.863476i \(-0.331718\pi\)
0.504390 + 0.863476i \(0.331718\pi\)
\(198\) 0 0
\(199\) 7.54019 0.534510 0.267255 0.963626i \(-0.413883\pi\)
0.267255 + 0.963626i \(0.413883\pi\)
\(200\) 1.11729 + 1.93520i 0.0790043 + 0.136839i
\(201\) 0 0
\(202\) −10.7303 + 18.5854i −0.754979 + 1.30766i
\(203\) 2.14152 3.70922i 0.150305 0.260336i
\(204\) 0 0
\(205\) 7.84160 + 13.5821i 0.547681 + 0.948612i
\(206\) 20.8557 1.45309
\(207\) 0 0
\(208\) 4.25341 0.294921
\(209\) 0.985693 + 1.70727i 0.0681818 + 0.118094i
\(210\) 0 0
\(211\) −2.60682 + 4.51514i −0.179461 + 0.310835i −0.941696 0.336465i \(-0.890769\pi\)
0.762235 + 0.647300i \(0.224102\pi\)
\(212\) 13.5065 23.3940i 0.927632 1.60671i
\(213\) 0 0
\(214\) 5.47232 + 9.47833i 0.374080 + 0.647925i
\(215\) −15.0012 −1.02307
\(216\) 0 0
\(217\) −8.43326 −0.572487
\(218\) −7.73695 13.4008i −0.524012 0.907616i
\(219\) 0 0
\(220\) −1.05439 + 1.82625i −0.0710866 + 0.123126i
\(221\) 0.889254 1.54023i 0.0598177 0.103607i
\(222\) 0 0
\(223\) −8.84690 15.3233i −0.592432 1.02612i −0.993904 0.110251i \(-0.964834\pi\)
0.401471 0.915872i \(-0.368499\pi\)
\(224\) 7.75789 0.518346
\(225\) 0 0
\(226\) −21.9613 −1.46085
\(227\) 7.88599 + 13.6589i 0.523412 + 0.906576i 0.999629 + 0.0272479i \(0.00867435\pi\)
−0.476217 + 0.879328i \(0.657992\pi\)
\(228\) 0 0
\(229\) 0.883432 1.53015i 0.0583788 0.101115i −0.835359 0.549705i \(-0.814740\pi\)
0.893738 + 0.448590i \(0.148074\pi\)
\(230\) −6.14122 + 10.6369i −0.404940 + 0.701377i
\(231\) 0 0
\(232\) −2.23807 3.87646i −0.146937 0.254502i
\(233\) −13.8984 −0.910514 −0.455257 0.890360i \(-0.650453\pi\)
−0.455257 + 0.890360i \(0.650453\pi\)
\(234\) 0 0
\(235\) 6.64354 0.433376
\(236\) 2.13810 + 3.70330i 0.139178 + 0.241064i
\(237\) 0 0
\(238\) 1.20879 2.09368i 0.0783540 0.135713i
\(239\) 9.91634 17.1756i 0.641435 1.11100i −0.343678 0.939088i \(-0.611673\pi\)
0.985113 0.171910i \(-0.0549939\pi\)
\(240\) 0 0
\(241\) −9.68735 16.7790i −0.624017 1.08083i −0.988730 0.149709i \(-0.952166\pi\)
0.364713 0.931120i \(-0.381167\pi\)
\(242\) 23.0703 1.48301
\(243\) 0 0
\(244\) 2.51674 0.161118
\(245\) −8.12250 14.0686i −0.518928 0.898809i
\(246\) 0 0
\(247\) 4.70924 8.15665i 0.299642 0.518995i
\(248\) −4.40675 + 7.63271i −0.279829 + 0.484678i
\(249\) 0 0
\(250\) 7.95355 + 13.7759i 0.503026 + 0.871267i
\(251\) −5.47572 −0.345625 −0.172812 0.984955i \(-0.555285\pi\)
−0.172812 + 0.984955i \(0.555285\pi\)
\(252\) 0 0
\(253\) −0.685377 −0.0430893
\(254\) 5.53225 + 9.58214i 0.347124 + 0.601237i
\(255\) 0 0
\(256\) −2.91356 + 5.04643i −0.182097 + 0.315402i
\(257\) 5.78258 10.0157i 0.360708 0.624764i −0.627370 0.778721i \(-0.715869\pi\)
0.988077 + 0.153957i \(0.0492019\pi\)
\(258\) 0 0
\(259\) 2.17153 + 3.76121i 0.134933 + 0.233710i
\(260\) 10.0749 0.624816
\(261\) 0 0
\(262\) 15.3123 0.945996
\(263\) −3.23897 5.61006i −0.199723 0.345931i 0.748715 0.662892i \(-0.230671\pi\)
−0.948439 + 0.316961i \(0.897338\pi\)
\(264\) 0 0
\(265\) −14.6121 + 25.3089i −0.897614 + 1.55471i
\(266\) 6.40140 11.0875i 0.392495 0.679821i
\(267\) 0 0
\(268\) −1.06216 1.83972i −0.0648819 0.112379i
\(269\) −13.8387 −0.843758 −0.421879 0.906652i \(-0.638629\pi\)
−0.421879 + 0.906652i \(0.638629\pi\)
\(270\) 0 0
\(271\) 1.94536 0.118172 0.0590860 0.998253i \(-0.481181\pi\)
0.0590860 + 0.998253i \(0.481181\pi\)
\(272\) 1.65004 + 2.85795i 0.100048 + 0.173289i
\(273\) 0 0
\(274\) 11.9053 20.6206i 0.719224 1.24573i
\(275\) 0.348436 0.603509i 0.0210115 0.0363930i
\(276\) 0 0
\(277\) −6.23634 10.8017i −0.374706 0.649009i 0.615577 0.788076i \(-0.288923\pi\)
−0.990283 + 0.139067i \(0.955590\pi\)
\(278\) −19.8543 −1.19078
\(279\) 0 0
\(280\) 2.65106 0.158431
\(281\) −4.87793 8.44883i −0.290993 0.504015i 0.683052 0.730370i \(-0.260652\pi\)
−0.974045 + 0.226355i \(0.927319\pi\)
\(282\) 0 0
\(283\) −13.2856 + 23.0114i −0.789748 + 1.36788i 0.136373 + 0.990658i \(0.456455\pi\)
−0.926121 + 0.377226i \(0.876878\pi\)
\(284\) 11.8992 20.6100i 0.706087 1.22298i
\(285\) 0 0
\(286\) 0.507777 + 0.879496i 0.0300255 + 0.0520057i
\(287\) 5.68346 0.335484
\(288\) 0 0
\(289\) −15.6201 −0.918830
\(290\) 12.5080 + 21.6645i 0.734494 + 1.27218i
\(291\) 0 0
\(292\) 18.9006 32.7367i 1.10607 1.91577i
\(293\) −6.12873 + 10.6153i −0.358044 + 0.620151i −0.987634 0.156777i \(-0.949890\pi\)
0.629590 + 0.776928i \(0.283223\pi\)
\(294\) 0 0
\(295\) −2.31311 4.00643i −0.134675 0.233263i
\(296\) 4.53888 0.263817
\(297\) 0 0
\(298\) −40.3243 −2.33592
\(299\) 1.63723 + 2.83576i 0.0946834 + 0.163996i
\(300\) 0 0
\(301\) −2.71815 + 4.70798i −0.156672 + 0.271363i
\(302\) 4.24806 7.35786i 0.244449 0.423397i
\(303\) 0 0
\(304\) 8.73814 + 15.1349i 0.501167 + 0.868046i
\(305\) −2.72275 −0.155904
\(306\) 0 0
\(307\) −26.4740 −1.51095 −0.755475 0.655178i \(-0.772594\pi\)
−0.755475 + 0.655178i \(0.772594\pi\)
\(308\) 0.382101 + 0.661818i 0.0217722 + 0.0377106i
\(309\) 0 0
\(310\) 24.6281 42.6571i 1.39878 2.42276i
\(311\) 8.82974 15.2936i 0.500689 0.867218i −0.499311 0.866423i \(-0.666413\pi\)
1.00000 0.000795555i \(-0.000253233\pi\)
\(312\) 0 0
\(313\) −4.82360 8.35473i −0.272646 0.472237i 0.696892 0.717176i \(-0.254566\pi\)
−0.969539 + 0.244939i \(0.921232\pi\)
\(314\) −15.4004 −0.869093
\(315\) 0 0
\(316\) −27.8112 −1.56450
\(317\) 1.85525 + 3.21338i 0.104201 + 0.180481i 0.913411 0.407037i \(-0.133438\pi\)
−0.809211 + 0.587519i \(0.800105\pi\)
\(318\) 0 0
\(319\) −0.697963 + 1.20891i −0.0390784 + 0.0676858i
\(320\) −15.1181 + 26.1852i −0.845125 + 1.46380i
\(321\) 0 0
\(322\) 2.22553 + 3.85473i 0.124024 + 0.214816i
\(323\) 7.30748 0.406599
\(324\) 0 0
\(325\) −3.32937 −0.184680
\(326\) 13.1751 + 22.8199i 0.729701 + 1.26388i
\(327\) 0 0
\(328\) 2.96986 5.14394i 0.163983 0.284027i
\(329\) 1.20378 2.08501i 0.0663666 0.114950i
\(330\) 0 0
\(331\) 0.706398 + 1.22352i 0.0388271 + 0.0672506i 0.884786 0.465998i \(-0.154304\pi\)
−0.845959 + 0.533248i \(0.820971\pi\)
\(332\) 11.6191 0.637678
\(333\) 0 0
\(334\) 4.93573 0.270071
\(335\) 1.14911 + 1.99031i 0.0627823 + 0.108742i
\(336\) 0 0
\(337\) 6.49503 11.2497i 0.353807 0.612812i −0.633106 0.774065i \(-0.718220\pi\)
0.986913 + 0.161253i \(0.0515536\pi\)
\(338\) −11.3321 + 19.6278i −0.616385 + 1.06761i
\(339\) 0 0
\(340\) 3.90837 + 6.76949i 0.211961 + 0.367127i
\(341\) 2.74856 0.148843
\(342\) 0 0
\(343\) −12.6934 −0.685378
\(344\) 2.84071 + 4.92025i 0.153161 + 0.265282i
\(345\) 0 0
\(346\) −3.79116 + 6.56648i −0.203814 + 0.353016i
\(347\) 2.40023 4.15732i 0.128851 0.223177i −0.794381 0.607420i \(-0.792204\pi\)
0.923232 + 0.384244i \(0.125538\pi\)
\(348\) 0 0
\(349\) 11.2888 + 19.5527i 0.604275 + 1.04663i 0.992166 + 0.124929i \(0.0398704\pi\)
−0.387891 + 0.921705i \(0.626796\pi\)
\(350\) −4.52571 −0.241909
\(351\) 0 0
\(352\) −2.52845 −0.134767
\(353\) 14.8533 + 25.7266i 0.790560 + 1.36929i 0.925620 + 0.378453i \(0.123544\pi\)
−0.135060 + 0.990837i \(0.543123\pi\)
\(354\) 0 0
\(355\) −12.8732 + 22.2970i −0.683238 + 1.18340i
\(356\) 19.2201 33.2902i 1.01866 1.76438i
\(357\) 0 0
\(358\) −21.1617 36.6531i −1.11843 1.93718i
\(359\) 13.4198 0.708271 0.354136 0.935194i \(-0.384775\pi\)
0.354136 + 0.935194i \(0.384775\pi\)
\(360\) 0 0
\(361\) 19.6984 1.03676
\(362\) 10.2998 + 17.8398i 0.541347 + 0.937640i
\(363\) 0 0
\(364\) 1.82552 3.16190i 0.0956834 0.165728i
\(365\) −20.4477 + 35.4164i −1.07028 + 1.85378i
\(366\) 0 0
\(367\) 3.97499 + 6.88488i 0.207493 + 0.359388i 0.950924 0.309424i \(-0.100136\pi\)
−0.743431 + 0.668812i \(0.766803\pi\)
\(368\) −6.07585 −0.316726
\(369\) 0 0
\(370\) −25.3666 −1.31874
\(371\) 5.29530 + 9.17174i 0.274918 + 0.476173i
\(372\) 0 0
\(373\) 5.71026 9.89045i 0.295666 0.512108i −0.679474 0.733700i \(-0.737792\pi\)
0.975140 + 0.221592i \(0.0711252\pi\)
\(374\) −0.393967 + 0.682371i −0.0203715 + 0.0352845i
\(375\) 0 0
\(376\) −1.25806 2.17902i −0.0648793 0.112374i
\(377\) 6.66917 0.343480
\(378\) 0 0
\(379\) −24.1705 −1.24155 −0.620777 0.783987i \(-0.713183\pi\)
−0.620777 + 0.783987i \(0.713183\pi\)
\(380\) 20.6976 + 35.8494i 1.06177 + 1.83903i
\(381\) 0 0
\(382\) −18.7919 + 32.5486i −0.961479 + 1.66533i
\(383\) −4.72164 + 8.17812i −0.241265 + 0.417883i −0.961075 0.276288i \(-0.910896\pi\)
0.719810 + 0.694171i \(0.244229\pi\)
\(384\) 0 0
\(385\) −0.413377 0.715990i −0.0210677 0.0364902i
\(386\) −22.4030 −1.14029
\(387\) 0 0
\(388\) −13.7632 −0.698722
\(389\) 1.27385 + 2.20638i 0.0645869 + 0.111868i 0.896511 0.443022i \(-0.146094\pi\)
−0.831924 + 0.554890i \(0.812760\pi\)
\(390\) 0 0
\(391\) −1.27027 + 2.20017i −0.0642403 + 0.111267i
\(392\) −3.07624 + 5.32821i −0.155374 + 0.269115i
\(393\) 0 0
\(394\) 14.9845 + 25.9539i 0.754909 + 1.30754i
\(395\) 30.0876 1.51387
\(396\) 0 0
\(397\) 3.67517 0.184452 0.0922258 0.995738i \(-0.470602\pi\)
0.0922258 + 0.995738i \(0.470602\pi\)
\(398\) 7.97987 + 13.8215i 0.399995 + 0.692811i
\(399\) 0 0
\(400\) 3.08888 5.35009i 0.154444 0.267505i
\(401\) −8.07436 + 13.9852i −0.403214 + 0.698388i −0.994112 0.108359i \(-0.965440\pi\)
0.590897 + 0.806747i \(0.298774\pi\)
\(402\) 0 0
\(403\) −6.56576 11.3722i −0.327064 0.566492i
\(404\) −25.1458 −1.25105
\(405\) 0 0
\(406\) 9.06558 0.449917
\(407\) −0.707745 1.22585i −0.0350816 0.0607631i
\(408\) 0 0
\(409\) −4.59099 + 7.95182i −0.227010 + 0.393192i −0.956920 0.290350i \(-0.906228\pi\)
0.729911 + 0.683542i \(0.239562\pi\)
\(410\) −16.5977 + 28.7481i −0.819703 + 1.41977i
\(411\) 0 0
\(412\) 12.2185 + 21.1631i 0.601964 + 1.04263i
\(413\) −1.67651 −0.0824955
\(414\) 0 0
\(415\) −12.5701 −0.617043
\(416\) 6.03995 + 10.4615i 0.296133 + 0.512917i
\(417\) 0 0
\(418\) −2.08634 + 3.61365i −0.102046 + 0.176749i
\(419\) 3.48944 6.04388i 0.170470 0.295263i −0.768114 0.640313i \(-0.778805\pi\)
0.938584 + 0.345050i \(0.112138\pi\)
\(420\) 0 0
\(421\) −15.4053 26.6828i −0.750809 1.30044i −0.947431 0.319960i \(-0.896331\pi\)
0.196622 0.980479i \(-0.437003\pi\)
\(422\) −11.0353 −0.537190
\(423\) 0 0
\(424\) 11.0681 0.537515
\(425\) −1.29157 2.23707i −0.0626505 0.108514i
\(426\) 0 0
\(427\) −0.493351 + 0.854509i −0.0238749 + 0.0413526i
\(428\) −6.41203 + 11.1060i −0.309937 + 0.536827i
\(429\) 0 0
\(430\) −15.8759 27.4979i −0.765605 1.32607i
\(431\) 27.8971 1.34376 0.671879 0.740661i \(-0.265487\pi\)
0.671879 + 0.740661i \(0.265487\pi\)
\(432\) 0 0
\(433\) 19.1706 0.921278 0.460639 0.887588i \(-0.347620\pi\)
0.460639 + 0.887588i \(0.347620\pi\)
\(434\) −8.92502 15.4586i −0.428415 0.742036i
\(435\) 0 0
\(436\) 9.06554 15.7020i 0.434161 0.751989i
\(437\) −6.72700 + 11.6515i −0.321796 + 0.557367i
\(438\) 0 0
\(439\) 11.8745 + 20.5672i 0.566739 + 0.981620i 0.996886 + 0.0788611i \(0.0251284\pi\)
−0.430147 + 0.902759i \(0.641538\pi\)
\(440\) −0.864030 −0.0411910
\(441\) 0 0
\(442\) 3.76443 0.179056
\(443\) −11.6791 20.2288i −0.554892 0.961102i −0.997912 0.0645896i \(-0.979426\pi\)
0.443020 0.896512i \(-0.353907\pi\)
\(444\) 0 0
\(445\) −20.7934 + 36.0151i −0.985700 + 1.70728i
\(446\) 18.7255 32.4336i 0.886680 1.53578i
\(447\) 0 0
\(448\) 5.47866 + 9.48931i 0.258842 + 0.448328i
\(449\) 4.81906 0.227426 0.113713 0.993514i \(-0.463726\pi\)
0.113713 + 0.993514i \(0.463726\pi\)
\(450\) 0 0
\(451\) −1.85235 −0.0872238
\(452\) −12.8663 22.2850i −0.605178 1.04820i
\(453\) 0 0
\(454\) −16.6917 + 28.9108i −0.783379 + 1.35685i
\(455\) −1.97495 + 3.42071i −0.0925871 + 0.160366i
\(456\) 0 0
\(457\) 2.44680 + 4.23798i 0.114456 + 0.198244i 0.917562 0.397592i \(-0.130154\pi\)
−0.803106 + 0.595836i \(0.796821\pi\)
\(458\) 3.73978 0.174749
\(459\) 0 0
\(460\) −14.3916 −0.671012
\(461\) −13.9952 24.2404i −0.651823 1.12899i −0.982680 0.185309i \(-0.940671\pi\)
0.330857 0.943681i \(-0.392662\pi\)
\(462\) 0 0
\(463\) 13.7377 23.7943i 0.638444 1.10582i −0.347331 0.937743i \(-0.612912\pi\)
0.985774 0.168074i \(-0.0537548\pi\)
\(464\) −6.18742 + 10.7169i −0.287244 + 0.497521i
\(465\) 0 0
\(466\) −14.7088 25.4764i −0.681373 1.18017i
\(467\) −21.2465 −0.983170 −0.491585 0.870830i \(-0.663582\pi\)
−0.491585 + 0.870830i \(0.663582\pi\)
\(468\) 0 0
\(469\) 0.832853 0.0384576
\(470\) 7.03093 + 12.1779i 0.324313 + 0.561726i
\(471\) 0 0
\(472\) −0.876048 + 1.51736i −0.0403234 + 0.0698421i
\(473\) 0.885898 1.53442i 0.0407337 0.0705528i
\(474\) 0 0
\(475\) −6.83982 11.8469i −0.313832 0.543574i
\(476\) 2.83272 0.129838
\(477\) 0 0
\(478\) 41.9783 1.92004
\(479\) 20.8394 + 36.0949i 0.952177 + 1.64922i 0.740699 + 0.671837i \(0.234494\pi\)
0.211478 + 0.977383i \(0.432172\pi\)
\(480\) 0 0
\(481\) −3.38132 + 5.85662i −0.154175 + 0.267039i
\(482\) 20.5045 35.5148i 0.933953 1.61765i
\(483\) 0 0
\(484\) 13.5160 + 23.4103i 0.614362 + 1.06411i
\(485\) 14.8898 0.676112
\(486\) 0 0
\(487\) 4.02801 0.182527 0.0912634 0.995827i \(-0.470909\pi\)
0.0912634 + 0.995827i \(0.470909\pi\)
\(488\) 0.515595 + 0.893036i 0.0233399 + 0.0404258i
\(489\) 0 0
\(490\) 17.1923 29.7779i 0.776668 1.34523i
\(491\) 19.3107 33.4471i 0.871479 1.50945i 0.0110115 0.999939i \(-0.496495\pi\)
0.860467 0.509506i \(-0.170172\pi\)
\(492\) 0 0
\(493\) 2.58719 + 4.48114i 0.116521 + 0.201821i
\(494\) 19.9354 0.896935
\(495\) 0 0
\(496\) 24.3660 1.09406
\(497\) 4.66514 + 8.08026i 0.209260 + 0.362449i
\(498\) 0 0
\(499\) 2.03593 3.52633i 0.0911407 0.157860i −0.816851 0.576849i \(-0.804282\pi\)
0.907991 + 0.418989i \(0.137615\pi\)
\(500\) −9.31934 + 16.1416i −0.416774 + 0.721873i
\(501\) 0 0
\(502\) −5.79502 10.0373i −0.258644 0.447985i
\(503\) −3.42594 −0.152755 −0.0763775 0.997079i \(-0.524335\pi\)
−0.0763775 + 0.997079i \(0.524335\pi\)
\(504\) 0 0
\(505\) 27.2041 1.21056
\(506\) −0.725343 1.25633i −0.0322454 0.0558507i
\(507\) 0 0
\(508\) −6.48225 + 11.2276i −0.287604 + 0.498144i
\(509\) 6.13171 10.6204i 0.271783 0.470742i −0.697535 0.716550i \(-0.745720\pi\)
0.969319 + 0.245808i \(0.0790533\pi\)
\(510\) 0 0
\(511\) 7.41006 + 12.8346i 0.327802 + 0.567770i
\(512\) −28.1241 −1.24292
\(513\) 0 0
\(514\) 24.4791 1.07973
\(515\) −13.2187 22.8954i −0.582484 1.00889i
\(516\) 0 0
\(517\) −0.392336 + 0.679545i −0.0172549 + 0.0298864i
\(518\) −4.59632 + 7.96105i −0.201951 + 0.349789i
\(519\) 0 0
\(520\) 2.06399 + 3.57494i 0.0905121 + 0.156772i
\(521\) 14.0823 0.616959 0.308479 0.951231i \(-0.400180\pi\)
0.308479 + 0.951231i \(0.400180\pi\)
\(522\) 0 0
\(523\) 9.77912 0.427611 0.213806 0.976876i \(-0.431414\pi\)
0.213806 + 0.976876i \(0.431414\pi\)
\(524\) 8.97086 + 15.5380i 0.391894 + 0.678780i
\(525\) 0 0
\(526\) 6.85567 11.8744i 0.298922 0.517747i
\(527\) 5.09415 8.82333i 0.221905 0.384350i
\(528\) 0 0
\(529\) 9.16127 + 15.8678i 0.398316 + 0.689904i
\(530\) −61.8566 −2.68688
\(531\) 0 0
\(532\) 15.0013 0.650389
\(533\) 4.42489 + 7.66414i 0.191663 + 0.331971i
\(534\) 0 0
\(535\) 6.93688 12.0150i 0.299908 0.519455i
\(536\) 0.435202 0.753792i 0.0187979 0.0325588i
\(537\) 0 0
\(538\) −14.6456 25.3669i −0.631417 1.09365i
\(539\) 1.91871 0.0826445
\(540\) 0 0
\(541\) 40.9454 1.76038 0.880189 0.474623i \(-0.157416\pi\)
0.880189 + 0.474623i \(0.157416\pi\)
\(542\) 2.05879 + 3.56594i 0.0884328 + 0.153170i
\(543\) 0 0
\(544\) −4.68619 + 8.11672i −0.200919 + 0.348001i
\(545\) −9.80760 + 16.9873i −0.420111 + 0.727654i
\(546\) 0 0
\(547\) −0.555138 0.961528i −0.0237360 0.0411120i 0.853913 0.520415i \(-0.174223\pi\)
−0.877649 + 0.479303i \(0.840889\pi\)
\(548\) 27.8993 1.19180
\(549\) 0 0
\(550\) 1.47502 0.0628949
\(551\) 13.7010 + 23.7309i 0.583684 + 1.01097i
\(552\) 0 0
\(553\) 5.45176 9.44272i 0.231832 0.401545i
\(554\) 13.2000 22.8630i 0.560814 0.971358i
\(555\) 0 0
\(556\) −11.6318 20.1469i −0.493300 0.854420i
\(557\) 35.0403 1.48470 0.742352 0.670010i \(-0.233710\pi\)
0.742352 + 0.670010i \(0.233710\pi\)
\(558\) 0 0
\(559\) −8.46493 −0.358028
\(560\) −3.66458 6.34724i −0.154857 0.268220i
\(561\) 0 0
\(562\) 10.3247 17.8830i 0.435523 0.754348i
\(563\) 19.3856 33.5768i 0.817005 1.41509i −0.0908735 0.995862i \(-0.528966\pi\)
0.907879 0.419232i \(-0.137701\pi\)
\(564\) 0 0
\(565\) 13.9194 + 24.1092i 0.585595 + 1.01428i
\(566\) −56.2413 −2.36400
\(567\) 0 0
\(568\) 9.75095 0.409141
\(569\) 16.9842 + 29.4174i 0.712013 + 1.23324i 0.964100 + 0.265539i \(0.0855498\pi\)
−0.252087 + 0.967705i \(0.581117\pi\)
\(570\) 0 0
\(571\) −5.04443 + 8.73721i −0.211103 + 0.365641i −0.952060 0.305911i \(-0.901039\pi\)
0.740957 + 0.671552i \(0.234372\pi\)
\(572\) −0.594973 + 1.03052i −0.0248771 + 0.0430884i
\(573\) 0 0
\(574\) 6.01487 + 10.4181i 0.251056 + 0.434842i
\(575\) 4.75590 0.198335
\(576\) 0 0
\(577\) −12.1323 −0.505074 −0.252537 0.967587i \(-0.581265\pi\)
−0.252537 + 0.967587i \(0.581265\pi\)
\(578\) −16.5309 28.6324i −0.687597 1.19095i
\(579\) 0 0
\(580\) −14.6559 + 25.3847i −0.608551 + 1.05404i
\(581\) −2.27766 + 3.94501i −0.0944931 + 0.163667i
\(582\) 0 0
\(583\) −1.72584 2.98925i −0.0714771 0.123802i
\(584\) 15.4883 0.640911
\(585\) 0 0
\(586\) −25.9444 −1.07175
\(587\) −15.8746 27.4956i −0.655215 1.13487i −0.981840 0.189711i \(-0.939245\pi\)
0.326625 0.945154i \(-0.394089\pi\)
\(588\) 0 0
\(589\) 26.9772 46.7259i 1.11158 1.92531i
\(590\) 4.89599 8.48010i 0.201565 0.349120i
\(591\) 0 0
\(592\) −6.27414 10.8671i −0.257866 0.446636i
\(593\) 13.4906 0.553993 0.276996 0.960871i \(-0.410661\pi\)
0.276996 + 0.960871i \(0.410661\pi\)
\(594\) 0 0
\(595\) −3.06459 −0.125636
\(596\) −23.6244 40.9187i −0.967694 1.67609i
\(597\) 0 0
\(598\) −3.46539 + 6.00224i −0.141711 + 0.245450i
\(599\) 21.2152 36.7458i 0.866829 1.50139i 0.00160947 0.999999i \(-0.499488\pi\)
0.865220 0.501393i \(-0.167179\pi\)
\(600\) 0 0
\(601\) 9.90237 + 17.1514i 0.403926 + 0.699620i 0.994196 0.107586i \(-0.0343120\pi\)
−0.590270 + 0.807206i \(0.700979\pi\)
\(602\) −11.5066 −0.468974
\(603\) 0 0
\(604\) 9.95509 0.405067
\(605\) −14.6223 25.3266i −0.594481 1.02967i
\(606\) 0 0
\(607\) 17.9995 31.1761i 0.730578 1.26540i −0.226059 0.974114i \(-0.572584\pi\)
0.956637 0.291284i \(-0.0940825\pi\)
\(608\) −24.8168 + 42.9839i −1.00645 + 1.74323i
\(609\) 0 0
\(610\) −2.88152 4.99093i −0.116669 0.202077i
\(611\) 3.74884 0.151662
\(612\) 0 0
\(613\) 26.4628 1.06882 0.534411 0.845225i \(-0.320533\pi\)
0.534411 + 0.845225i \(0.320533\pi\)
\(614\) −28.0177 48.5281i −1.13070 1.95843i
\(615\) 0 0
\(616\) −0.156559 + 0.271168i −0.00630793 + 0.0109257i
\(617\) −24.5584 + 42.5363i −0.988683 + 1.71245i −0.364419 + 0.931235i \(0.618732\pi\)
−0.624264 + 0.781214i \(0.714601\pi\)
\(618\) 0 0
\(619\) 12.1031 + 20.9632i 0.486465 + 0.842582i 0.999879 0.0155592i \(-0.00495283\pi\)
−0.513414 + 0.858141i \(0.671619\pi\)
\(620\) 57.7145 2.31787
\(621\) 0 0
\(622\) 37.3785 1.49874
\(623\) 7.53534 + 13.0516i 0.301897 + 0.522901i
\(624\) 0 0
\(625\) 15.5797 26.9848i 0.623188 1.07939i
\(626\) 10.2097 17.6838i 0.408064 0.706787i
\(627\) 0 0
\(628\) −9.02247 15.6274i −0.360036 0.623600i
\(629\) −5.24690 −0.209208
\(630\) 0 0
\(631\) 17.6968 0.704500 0.352250 0.935906i \(-0.385417\pi\)
0.352250 + 0.935906i \(0.385417\pi\)
\(632\) −5.69756 9.86846i −0.226637 0.392546i
\(633\) 0 0
\(634\) −3.92685 + 6.80151i −0.155955 + 0.270123i
\(635\) 7.01286 12.1466i 0.278297 0.482024i
\(636\) 0 0
\(637\) −4.58340 7.93868i −0.181601 0.314542i
\(638\) −2.95465 −0.116976
\(639\) 0 0
\(640\) −21.1835 −0.837351
\(641\) −19.0252 32.9526i −0.751450 1.30155i −0.947120 0.320880i \(-0.896021\pi\)
0.195669 0.980670i \(-0.437312\pi\)
\(642\) 0 0
\(643\) −23.4712 + 40.6534i −0.925616 + 1.60321i −0.135048 + 0.990839i \(0.543119\pi\)
−0.790568 + 0.612374i \(0.790215\pi\)
\(644\) −2.60770 + 4.51667i −0.102758 + 0.177982i
\(645\) 0 0
\(646\) 7.73359 + 13.3950i 0.304274 + 0.527018i
\(647\) −28.2333 −1.10997 −0.554983 0.831862i \(-0.687275\pi\)
−0.554983 + 0.831862i \(0.687275\pi\)
\(648\) 0 0
\(649\) 0.546406 0.0214483
\(650\) −3.52351 6.10291i −0.138204 0.239376i
\(651\) 0 0
\(652\) −15.4375 + 26.7386i −0.604580 + 1.04716i
\(653\) −17.6536 + 30.5769i −0.690839 + 1.19657i 0.280725 + 0.959788i \(0.409425\pi\)
−0.971563 + 0.236780i \(0.923908\pi\)
\(654\) 0 0
\(655\) −9.70517 16.8098i −0.379212 0.656815i
\(656\) −16.4210 −0.641134
\(657\) 0 0
\(658\) 5.09590 0.198659
\(659\) −20.8469 36.1078i −0.812078 1.40656i −0.911407 0.411506i \(-0.865003\pi\)
0.0993285 0.995055i \(-0.468331\pi\)
\(660\) 0 0
\(661\) −0.636957 + 1.10324i −0.0247747 + 0.0429111i −0.878147 0.478391i \(-0.841220\pi\)
0.853372 + 0.521302i \(0.174554\pi\)
\(662\) −1.49518 + 2.58972i −0.0581117 + 0.100652i
\(663\) 0 0
\(664\) 2.38035 + 4.12288i 0.0923754 + 0.159999i
\(665\) −16.2292 −0.629343
\(666\) 0 0
\(667\) −9.52668 −0.368875
\(668\) 2.89165 + 5.00848i 0.111881 + 0.193784i
\(669\) 0 0
\(670\) −2.43222 + 4.21273i −0.0939649 + 0.162752i
\(671\) 0.160793 0.278501i 0.00620733 0.0107514i
\(672\) 0 0
\(673\) −17.8164 30.8589i −0.686771 1.18952i −0.972877 0.231324i \(-0.925694\pi\)
0.286106 0.958198i \(-0.407639\pi\)
\(674\) 27.4951 1.05907
\(675\) 0 0
\(676\) −26.5561 −1.02139
\(677\) −9.00094 15.5901i −0.345934 0.599176i 0.639589 0.768717i \(-0.279105\pi\)
−0.985523 + 0.169541i \(0.945771\pi\)
\(678\) 0 0
\(679\) 2.69797 4.67303i 0.103539 0.179334i
\(680\) −1.60138 + 2.77368i −0.0614102 + 0.106366i
\(681\) 0 0
\(682\) 2.90884 + 5.03825i 0.111385 + 0.192925i
\(683\) 39.7614 1.52143 0.760715 0.649087i \(-0.224849\pi\)
0.760715 + 0.649087i \(0.224849\pi\)
\(684\) 0 0
\(685\) −30.1830 −1.15323
\(686\) −13.4336 23.2676i −0.512895 0.888361i
\(687\) 0 0
\(688\) 7.85347 13.6026i 0.299411 0.518594i
\(689\) −8.24538 + 14.2814i −0.314124 + 0.544079i
\(690\) 0 0
\(691\) 8.42035 + 14.5845i 0.320325 + 0.554820i 0.980555 0.196244i \(-0.0628744\pi\)
−0.660230 + 0.751064i \(0.729541\pi\)
\(692\) −8.88436 −0.337733
\(693\) 0 0
\(694\) 10.1608 0.385697
\(695\) 12.5839 + 21.7960i 0.477336 + 0.826771i
\(696\) 0 0
\(697\) −3.43312 + 5.94634i −0.130039 + 0.225234i
\(698\) −23.8941 + 41.3858i −0.904405 + 1.56648i
\(699\) 0 0
\(700\) −2.65143 4.59242i −0.100215 0.173577i
\(701\) −8.96921 −0.338762 −0.169381 0.985551i \(-0.554177\pi\)
−0.169381 + 0.985551i \(0.554177\pi\)
\(702\) 0 0
\(703\) −27.7861 −1.04797
\(704\) −1.78560 3.09275i −0.0672974 0.116562i
\(705\) 0 0
\(706\) −31.4388 + 54.4536i −1.18321 + 2.04939i
\(707\) 4.92926 8.53773i 0.185384 0.321095i
\(708\) 0 0
\(709\) −9.07082 15.7111i −0.340662 0.590043i 0.643894 0.765115i \(-0.277318\pi\)
−0.984556 + 0.175071i \(0.943984\pi\)
\(710\) −54.4954 −2.04518
\(711\) 0 0
\(712\) 15.7502 0.590263
\(713\) 9.37898 + 16.2449i 0.351245 + 0.608375i
\(714\) 0 0
\(715\) 0.643674 1.11488i 0.0240721 0.0416940i
\(716\) 24.7956 42.9472i 0.926655 1.60501i
\(717\) 0 0
\(718\) 14.2024 + 24.5992i 0.530027 + 0.918034i
\(719\) 31.5720 1.17744 0.588718 0.808339i \(-0.299633\pi\)
0.588718 + 0.808339i \(0.299633\pi\)
\(720\) 0 0
\(721\) −9.58068 −0.356803
\(722\) 20.8470 + 36.1081i 0.775846 + 1.34381i
\(723\) 0 0
\(724\) −12.0685 + 20.9033i −0.448523 + 0.776865i
\(725\) 4.84323 8.38872i 0.179873 0.311549i
\(726\) 0 0
\(727\) −19.2046 33.2634i −0.712260 1.23367i −0.964007 0.265878i \(-0.914338\pi\)
0.251746 0.967793i \(-0.418995\pi\)
\(728\) 1.49595 0.0554436
\(729\) 0 0
\(730\) −86.5599 −3.20373
\(731\) −3.28382 5.68775i −0.121457 0.210369i
\(732\) 0 0
\(733\) 15.1651 26.2668i 0.560138 0.970187i −0.437346 0.899293i \(-0.644082\pi\)
0.997484 0.0708936i \(-0.0225851\pi\)
\(734\) −8.41355 + 14.5727i −0.310550 + 0.537888i
\(735\) 0 0
\(736\) −8.62786 14.9439i −0.318027 0.550839i
\(737\) −0.271443 −0.00999872
\(738\) 0 0
\(739\) 10.0025 0.367949 0.183975 0.982931i \(-0.441104\pi\)
0.183975 + 0.982931i \(0.441104\pi\)
\(740\) −14.8613 25.7405i −0.546311 0.946238i
\(741\) 0 0
\(742\) −11.2082 + 19.4131i −0.411465 + 0.712677i
\(743\) −18.1369 + 31.4140i −0.665378 + 1.15247i 0.313804 + 0.949488i \(0.398396\pi\)
−0.979183 + 0.202981i \(0.934937\pi\)
\(744\) 0 0
\(745\) 25.5582 + 44.2681i 0.936379 + 1.62186i
\(746\) 24.1729 0.885033
\(747\) 0 0
\(748\) −0.923239 −0.0337569
\(749\) −2.51387 4.35415i −0.0918548 0.159097i
\(750\) 0 0
\(751\) 7.27718 12.6044i 0.265548 0.459943i −0.702159 0.712020i \(-0.747780\pi\)
0.967707 + 0.252077i \(0.0811138\pi\)
\(752\) −3.47805 + 6.02415i −0.126831 + 0.219678i
\(753\) 0 0
\(754\) 7.05806 + 12.2249i 0.257039 + 0.445205i
\(755\) −10.7700 −0.391959
\(756\) 0 0
\(757\) −45.5754 −1.65646 −0.828232 0.560385i \(-0.810653\pi\)
−0.828232 + 0.560385i \(0.810653\pi\)
\(758\) −25.5799 44.3057i −0.929104 1.60925i
\(759\) 0 0
\(760\) −8.48048 + 14.6886i −0.307619 + 0.532812i
\(761\) −11.1228 + 19.2652i −0.403200 + 0.698364i −0.994110 0.108374i \(-0.965436\pi\)
0.590910 + 0.806738i \(0.298769\pi\)
\(762\) 0 0
\(763\) 3.55419 + 6.15604i 0.128670 + 0.222864i
\(764\) −44.0378 −1.59323
\(765\) 0 0
\(766\) −19.9879 −0.722191
\(767\) −1.30525 2.26077i −0.0471300 0.0816315i
\(768\) 0 0
\(769\) −6.83247 + 11.8342i −0.246385 + 0.426752i −0.962520 0.271210i \(-0.912576\pi\)
0.716135 + 0.697962i \(0.245909\pi\)
\(770\) 0.874964 1.51548i 0.0315315 0.0546142i
\(771\) 0 0
\(772\) −13.1251 22.7333i −0.472381 0.818188i
\(773\) −20.6540 −0.742871 −0.371436 0.928459i \(-0.621134\pi\)
−0.371436 + 0.928459i \(0.621134\pi\)
\(774\) 0 0
\(775\) −19.0726 −0.685106
\(776\) −2.81962 4.88372i −0.101218 0.175315i
\(777\) 0 0
\(778\) −2.69627 + 4.67007i −0.0966659 + 0.167430i
\(779\) −18.1809 + 31.4902i −0.651397 + 1.12825i
\(780\) 0 0
\(781\) −1.52046 2.63351i −0.0544063 0.0942345i
\(782\) −5.37736 −0.192294
\(783\) 0 0
\(784\) 17.0093 0.607474
\(785\) 9.76100 + 16.9065i 0.348385 + 0.603421i
\(786\) 0 0
\(787\) 12.3517