Properties

Label 882.2.f.n.589.2
Level $882$
Weight $2$
Character 882.589
Analytic conductor $7.043$
Analytic rank $0$
Dimension $6$
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] = [882,2,Mod(295,882)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(882, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("882.295");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 882.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: \(7.04280545828\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.309123.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 126)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 589.2
Root \(0.500000 + 1.41036i\) of defining polynomial
Character \(\chi\) \(=\) 882.589
Dual form 882.2.f.n.295.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.619562 + 1.61745i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.59097 - 2.75564i) q^{5} +(-1.71053 + 0.272169i) q^{6} -1.00000 q^{8} +(-2.23229 - 2.00422i) q^{9} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.619562 + 1.61745i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.59097 - 2.75564i) q^{5} +(-1.71053 + 0.272169i) q^{6} -1.00000 q^{8} +(-2.23229 - 2.00422i) q^{9} +3.18194 q^{10} +(-1.59097 - 2.75564i) q^{11} +(-1.09097 - 1.34528i) q^{12} +(2.85185 - 4.93955i) q^{13} +(3.47141 + 4.28061i) q^{15} +(-0.500000 - 0.866025i) q^{16} +1.52175 q^{17} +(0.619562 - 2.93533i) q^{18} +1.28263 q^{19} +(1.59097 + 2.75564i) q^{20} +(1.59097 - 2.75564i) q^{22} +(-1.11956 + 1.93914i) q^{23} +(0.619562 - 1.61745i) q^{24} +(-2.56238 - 4.43818i) q^{25} +5.70370 q^{26} +(4.62476 - 2.36887i) q^{27} +(-3.54063 - 6.13255i) q^{29} +(-1.97141 + 5.14663i) q^{30} +(4.71053 - 8.15888i) q^{31} +(0.500000 - 0.866025i) q^{32} +(5.44282 - 0.866025i) q^{33} +(0.760877 + 1.31788i) q^{34} +(2.85185 - 0.931107i) q^{36} -1.00000 q^{37} +(0.641315 + 1.11079i) q^{38} +(6.22257 + 7.67307i) q^{39} +(-1.59097 + 2.75564i) q^{40} +(-2.80150 + 4.85235i) q^{41} +(3.41423 + 5.91362i) q^{43} +3.18194 q^{44} +(-9.07442 + 2.96273i) q^{45} -2.23912 q^{46} +(2.91423 + 5.04759i) q^{47} +(1.71053 - 0.272169i) q^{48} +(2.56238 - 4.43818i) q^{50} +(-0.942820 + 2.46136i) q^{51} +(2.85185 + 4.93955i) q^{52} -2.05718 q^{53} +(4.36389 + 2.82073i) q^{54} -10.1248 q^{55} +(-0.794668 + 2.07459i) q^{57} +(3.54063 - 6.13255i) q^{58} +(0.562382 - 0.974074i) q^{59} +(-5.44282 + 0.866025i) q^{60} +(-1.56238 - 2.70612i) q^{61} +9.42107 q^{62} +1.00000 q^{64} +(-9.07442 - 15.7174i) q^{65} +(3.47141 + 4.28061i) q^{66} +(-5.48345 + 9.49761i) q^{67} +(-0.760877 + 1.31788i) q^{68} +(-2.44282 - 3.01225i) q^{69} +8.69002 q^{71} +(2.23229 + 2.00422i) q^{72} +4.96690 q^{73} +(-0.500000 - 0.866025i) q^{74} +(8.76608 - 1.39480i) q^{75} +(-0.641315 + 1.11079i) q^{76} +(-3.53379 + 9.22544i) q^{78} +(2.06922 + 3.58399i) q^{79} -3.18194 q^{80} +(0.966208 + 8.94799i) q^{81} -5.60301 q^{82} +(-4.03379 - 6.98673i) q^{83} +(2.42107 - 4.19341i) q^{85} +(-3.41423 + 5.91362i) q^{86} +(12.1127 - 1.92730i) q^{87} +(1.59097 + 2.75564i) q^{88} -0.225450 q^{89} +(-7.10301 - 6.37731i) q^{90} +(-1.11956 - 1.93914i) q^{92} +(10.2781 + 12.6740i) q^{93} +(-2.91423 + 5.04759i) q^{94} +(2.04063 - 3.53447i) q^{95} +(1.09097 + 1.34528i) q^{96} +(7.42107 + 12.8537i) q^{97} +(-1.97141 + 9.34004i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + 3 q^{2} - 4 q^{3} - 3 q^{4} + q^{5} - 2 q^{6} - 6 q^{8} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q + 3 q^{2} - 4 q^{3} - 3 q^{4} + q^{5} - 2 q^{6} - 6 q^{8} - 4 q^{9} + 2 q^{10} - q^{11} + 2 q^{12} + 8 q^{13} + 12 q^{15} - 3 q^{16} + 8 q^{17} + 4 q^{18} + 6 q^{19} + q^{20} + q^{22} - 7 q^{23} + 4 q^{24} + 2 q^{25} + 16 q^{26} - 7 q^{27} - 5 q^{29} - 3 q^{30} + 20 q^{31} + 3 q^{32} + 15 q^{33} + 4 q^{34} + 8 q^{36} - 6 q^{37} + 3 q^{38} + 4 q^{39} - q^{40} - 6 q^{43} + 2 q^{44} - 12 q^{45} - 14 q^{46} - 9 q^{47} + 2 q^{48} - 2 q^{50} + 12 q^{51} + 8 q^{52} - 30 q^{53} - 8 q^{54} - 26 q^{55} + 22 q^{57} + 5 q^{58} - 14 q^{59} - 15 q^{60} + 8 q^{61} + 40 q^{62} + 6 q^{64} - 12 q^{65} + 12 q^{66} + q^{67} - 4 q^{68} + 3 q^{69} + 14 q^{71} + 4 q^{72} - 38 q^{73} - 3 q^{74} + 17 q^{75} - 3 q^{76} + 5 q^{78} + 5 q^{79} - 2 q^{80} + 32 q^{81} + 2 q^{83} - 2 q^{85} + 6 q^{86} + 63 q^{87} + q^{88} + 18 q^{89} - 9 q^{90} - 7 q^{92} + q^{93} + 9 q^{94} - 4 q^{95} - 2 q^{96} + 28 q^{97} - 3 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(785\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 + 0.866025i 0.353553 + 0.612372i
\(3\) −0.619562 + 1.61745i −0.357704 + 0.933835i
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) 1.59097 2.75564i 0.711504 1.23236i −0.252788 0.967522i \(-0.581348\pi\)
0.964292 0.264840i \(-0.0853191\pi\)
\(6\) −1.71053 + 0.272169i −0.698322 + 0.111112i
\(7\) 0 0
\(8\) −1.00000 −0.353553
\(9\) −2.23229 2.00422i −0.744096 0.668073i
\(10\) 3.18194 1.00622
\(11\) −1.59097 2.75564i −0.479696 0.830858i 0.520033 0.854146i \(-0.325920\pi\)
−0.999729 + 0.0232884i \(0.992586\pi\)
\(12\) −1.09097 1.34528i −0.314936 0.388349i
\(13\) 2.85185 4.93955i 0.790960 1.36998i −0.134412 0.990925i \(-0.542915\pi\)
0.925373 0.379058i \(-0.123752\pi\)
\(14\) 0 0
\(15\) 3.47141 + 4.28061i 0.896314 + 1.10525i
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 1.52175 0.369079 0.184540 0.982825i \(-0.440921\pi\)
0.184540 + 0.982825i \(0.440921\pi\)
\(18\) 0.619562 2.93533i 0.146032 0.691863i
\(19\) 1.28263 0.294256 0.147128 0.989117i \(-0.452997\pi\)
0.147128 + 0.989117i \(0.452997\pi\)
\(20\) 1.59097 + 2.75564i 0.355752 + 0.616181i
\(21\) 0 0
\(22\) 1.59097 2.75564i 0.339196 0.587505i
\(23\) −1.11956 + 1.93914i −0.233445 + 0.404338i −0.958820 0.284016i \(-0.908333\pi\)
0.725375 + 0.688354i \(0.241666\pi\)
\(24\) 0.619562 1.61745i 0.126467 0.330161i
\(25\) −2.56238 4.43818i −0.512476 0.887635i
\(26\) 5.70370 1.11859
\(27\) 4.62476 2.36887i 0.890036 0.455890i
\(28\) 0 0
\(29\) −3.54063 6.13255i −0.657478 1.13879i −0.981266 0.192656i \(-0.938290\pi\)
0.323788 0.946130i \(-0.395043\pi\)
\(30\) −1.97141 + 5.14663i −0.359929 + 0.939642i
\(31\) 4.71053 8.15888i 0.846037 1.46538i −0.0386810 0.999252i \(-0.512316\pi\)
0.884718 0.466127i \(-0.154351\pi\)
\(32\) 0.500000 0.866025i 0.0883883 0.153093i
\(33\) 5.44282 0.866025i 0.947473 0.150756i
\(34\) 0.760877 + 1.31788i 0.130489 + 0.226014i
\(35\) 0 0
\(36\) 2.85185 0.931107i 0.475308 0.155185i
\(37\) −1.00000 −0.164399 −0.0821995 0.996616i \(-0.526194\pi\)
−0.0821995 + 0.996616i \(0.526194\pi\)
\(38\) 0.641315 + 1.11079i 0.104035 + 0.180194i
\(39\) 6.22257 + 7.67307i 0.996409 + 1.22868i
\(40\) −1.59097 + 2.75564i −0.251555 + 0.435706i
\(41\) −2.80150 + 4.85235i −0.437522 + 0.757810i −0.997498 0.0706992i \(-0.977477\pi\)
0.559976 + 0.828509i \(0.310810\pi\)
\(42\) 0 0
\(43\) 3.41423 + 5.91362i 0.520665 + 0.901819i 0.999711 + 0.0240288i \(0.00764935\pi\)
−0.479046 + 0.877790i \(0.659017\pi\)
\(44\) 3.18194 0.479696
\(45\) −9.07442 + 2.96273i −1.35273 + 0.441658i
\(46\) −2.23912 −0.330141
\(47\) 2.91423 + 5.04759i 0.425084 + 0.736267i 0.996428 0.0844432i \(-0.0269112\pi\)
−0.571344 + 0.820711i \(0.693578\pi\)
\(48\) 1.71053 0.272169i 0.246894 0.0392842i
\(49\) 0 0
\(50\) 2.56238 4.43818i 0.362375 0.627653i
\(51\) −0.942820 + 2.46136i −0.132021 + 0.344659i
\(52\) 2.85185 + 4.93955i 0.395480 + 0.684992i
\(53\) −2.05718 −0.282575 −0.141288 0.989969i \(-0.545124\pi\)
−0.141288 + 0.989969i \(0.545124\pi\)
\(54\) 4.36389 + 2.82073i 0.593850 + 0.383852i
\(55\) −10.1248 −1.36522
\(56\) 0 0
\(57\) −0.794668 + 2.07459i −0.105256 + 0.274786i
\(58\) 3.54063 6.13255i 0.464907 0.805243i
\(59\) 0.562382 0.974074i 0.0732159 0.126814i −0.827093 0.562065i \(-0.810007\pi\)
0.900309 + 0.435251i \(0.143340\pi\)
\(60\) −5.44282 + 0.866025i −0.702665 + 0.111803i
\(61\) −1.56238 2.70612i −0.200042 0.346484i 0.748499 0.663135i \(-0.230775\pi\)
−0.948542 + 0.316652i \(0.897441\pi\)
\(62\) 9.42107 1.19648
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) −9.07442 15.7174i −1.12554 1.94950i
\(66\) 3.47141 + 4.28061i 0.427301 + 0.526906i
\(67\) −5.48345 + 9.49761i −0.669910 + 1.16032i 0.308019 + 0.951380i \(0.400334\pi\)
−0.977929 + 0.208938i \(0.932999\pi\)
\(68\) −0.760877 + 1.31788i −0.0922699 + 0.159816i
\(69\) −2.44282 3.01225i −0.294081 0.362632i
\(70\) 0 0
\(71\) 8.69002 1.03132 0.515658 0.856794i \(-0.327548\pi\)
0.515658 + 0.856794i \(0.327548\pi\)
\(72\) 2.23229 + 2.00422i 0.263078 + 0.236200i
\(73\) 4.96690 0.581331 0.290666 0.956825i \(-0.406123\pi\)
0.290666 + 0.956825i \(0.406123\pi\)
\(74\) −0.500000 0.866025i −0.0581238 0.100673i
\(75\) 8.76608 1.39480i 1.01222 0.161058i
\(76\) −0.641315 + 1.11079i −0.0735639 + 0.127416i
\(77\) 0 0
\(78\) −3.53379 + 9.22544i −0.400123 + 1.04458i
\(79\) 2.06922 + 3.58399i 0.232805 + 0.403231i 0.958633 0.284646i \(-0.0918762\pi\)
−0.725827 + 0.687877i \(0.758543\pi\)
\(80\) −3.18194 −0.355752
\(81\) 0.966208 + 8.94799i 0.107356 + 0.994221i
\(82\) −5.60301 −0.618749
\(83\) −4.03379 6.98673i −0.442766 0.766893i 0.555127 0.831765i \(-0.312669\pi\)
−0.997894 + 0.0648718i \(0.979336\pi\)
\(84\) 0 0
\(85\) 2.42107 4.19341i 0.262602 0.454839i
\(86\) −3.41423 + 5.91362i −0.368166 + 0.637682i
\(87\) 12.1127 1.92730i 1.29862 0.206628i
\(88\) 1.59097 + 2.75564i 0.169598 + 0.293753i
\(89\) −0.225450 −0.0238977 −0.0119488 0.999929i \(-0.503804\pi\)
−0.0119488 + 0.999929i \(0.503804\pi\)
\(90\) −7.10301 6.37731i −0.748723 0.672228i
\(91\) 0 0
\(92\) −1.11956 1.93914i −0.116722 0.202169i
\(93\) 10.2781 + 12.6740i 1.06579 + 1.31423i
\(94\) −2.91423 + 5.04759i −0.300580 + 0.520620i
\(95\) 2.04063 3.53447i 0.209364 0.362629i
\(96\) 1.09097 + 1.34528i 0.111347 + 0.137302i
\(97\) 7.42107 + 12.8537i 0.753495 + 1.30509i 0.946119 + 0.323819i \(0.104967\pi\)
−0.192624 + 0.981273i \(0.561700\pi\)
\(98\) 0 0
\(99\) −1.97141 + 9.34004i −0.198134 + 0.938710i
\(100\) 5.12476 0.512476
\(101\) −9.29467 16.0988i −0.924854 1.60189i −0.791796 0.610786i \(-0.790854\pi\)
−0.133058 0.991108i \(-0.542480\pi\)
\(102\) −2.60301 + 0.414174i −0.257736 + 0.0410093i
\(103\) 0.141315 0.244765i 0.0139242 0.0241174i −0.858979 0.512010i \(-0.828901\pi\)
0.872904 + 0.487893i \(0.162234\pi\)
\(104\) −2.85185 + 4.93955i −0.279647 + 0.484362i
\(105\) 0 0
\(106\) −1.02859 1.78157i −0.0999055 0.173041i
\(107\) −11.3776 −1.09991 −0.549955 0.835194i \(-0.685355\pi\)
−0.549955 + 0.835194i \(0.685355\pi\)
\(108\) −0.260877 + 5.18960i −0.0251029 + 0.499369i
\(109\) 4.42107 0.423461 0.211731 0.977328i \(-0.432090\pi\)
0.211731 + 0.977328i \(0.432090\pi\)
\(110\) −5.06238 8.76830i −0.482679 0.836025i
\(111\) 0.619562 1.61745i 0.0588062 0.153522i
\(112\) 0 0
\(113\) −1.60752 + 2.78431i −0.151223 + 0.261926i −0.931677 0.363287i \(-0.881655\pi\)
0.780454 + 0.625213i \(0.214988\pi\)
\(114\) −2.19398 + 0.349092i −0.205485 + 0.0326954i
\(115\) 3.56238 + 6.17023i 0.332194 + 0.575377i
\(116\) 7.08126 0.657478
\(117\) −16.2661 + 5.31075i −1.50380 + 0.490979i
\(118\) 1.12476 0.103543
\(119\) 0 0
\(120\) −3.47141 4.28061i −0.316895 0.390764i
\(121\) 0.437618 0.757977i 0.0397835 0.0689070i
\(122\) 1.56238 2.70612i 0.141451 0.245001i
\(123\) −6.11273 7.53762i −0.551166 0.679645i
\(124\) 4.71053 + 8.15888i 0.423018 + 0.732689i
\(125\) −0.396990 −0.0355079
\(126\) 0 0
\(127\) 20.1053 1.78406 0.892030 0.451976i \(-0.149281\pi\)
0.892030 + 0.451976i \(0.149281\pi\)
\(128\) 0.500000 + 0.866025i 0.0441942 + 0.0765466i
\(129\) −11.6803 + 1.85849i −1.02839 + 0.163631i
\(130\) 9.07442 15.7174i 0.795879 1.37850i
\(131\) −3.18194 + 5.51129i −0.278008 + 0.481523i −0.970890 0.239528i \(-0.923007\pi\)
0.692882 + 0.721051i \(0.256341\pi\)
\(132\) −1.97141 + 5.14663i −0.171589 + 0.447957i
\(133\) 0 0
\(134\) −10.9669 −0.947396
\(135\) 0.830095 16.5130i 0.0714432 1.42121i
\(136\) −1.52175 −0.130489
\(137\) −1.37072 2.37416i −0.117109 0.202838i 0.801512 0.597979i \(-0.204029\pi\)
−0.918621 + 0.395140i \(0.870696\pi\)
\(138\) 1.38727 3.62167i 0.118093 0.308297i
\(139\) −3.98345 + 6.89953i −0.337872 + 0.585211i −0.984032 0.177991i \(-0.943040\pi\)
0.646161 + 0.763202i \(0.276374\pi\)
\(140\) 0 0
\(141\) −9.96978 + 1.58632i −0.839607 + 0.133593i
\(142\) 4.34501 + 7.52578i 0.364625 + 0.631550i
\(143\) −18.1488 −1.51768
\(144\) −0.619562 + 2.93533i −0.0516301 + 0.244611i
\(145\) −22.5322 −1.87119
\(146\) 2.48345 + 4.30146i 0.205532 + 0.355991i
\(147\) 0 0
\(148\) 0.500000 0.866025i 0.0410997 0.0711868i
\(149\) 11.6300 20.1437i 0.952764 1.65024i 0.213360 0.976974i \(-0.431559\pi\)
0.739404 0.673262i \(-0.235107\pi\)
\(150\) 5.59097 + 6.89425i 0.456501 + 0.562913i
\(151\) 4.06238 + 7.03625i 0.330592 + 0.572602i 0.982628 0.185586i \(-0.0594183\pi\)
−0.652036 + 0.758188i \(0.726085\pi\)
\(152\) −1.28263 −0.104035
\(153\) −3.39699 3.04993i −0.274630 0.246572i
\(154\) 0 0
\(155\) −14.9887 25.9611i −1.20392 2.08525i
\(156\) −9.75636 + 1.55237i −0.781134 + 0.124289i
\(157\) 5.63160 9.75422i 0.449451 0.778471i −0.548900 0.835888i \(-0.684953\pi\)
0.998350 + 0.0574170i \(0.0182864\pi\)
\(158\) −2.06922 + 3.58399i −0.164618 + 0.285127i
\(159\) 1.27455 3.32738i 0.101078 0.263879i
\(160\) −1.59097 2.75564i −0.125777 0.217853i
\(161\) 0 0
\(162\) −7.26608 + 5.31075i −0.570877 + 0.417252i
\(163\) 3.98057 0.311782 0.155891 0.987774i \(-0.450175\pi\)
0.155891 + 0.987774i \(0.450175\pi\)
\(164\) −2.80150 4.85235i −0.218761 0.378905i
\(165\) 6.27292 16.3763i 0.488346 1.27489i
\(166\) 4.03379 6.98673i 0.313083 0.542276i
\(167\) 2.61956 4.53721i 0.202708 0.351100i −0.746692 0.665170i \(-0.768359\pi\)
0.949400 + 0.314070i \(0.101693\pi\)
\(168\) 0 0
\(169\) −9.76608 16.9153i −0.751237 1.30118i
\(170\) 4.84213 0.371375
\(171\) −2.86320 2.57067i −0.218954 0.196584i
\(172\) −6.82846 −0.520665
\(173\) −1.27579 2.20974i −0.0969968 0.168003i 0.813443 0.581644i \(-0.197590\pi\)
−0.910440 + 0.413641i \(0.864257\pi\)
\(174\) 7.72545 + 9.52628i 0.585665 + 0.722185i
\(175\) 0 0
\(176\) −1.59097 + 2.75564i −0.119924 + 0.207714i
\(177\) 1.22708 + 1.51312i 0.0922334 + 0.113733i
\(178\) −0.112725 0.195246i −0.00844910 0.0146343i
\(179\) −7.03775 −0.526026 −0.263013 0.964792i \(-0.584716\pi\)
−0.263013 + 0.964792i \(0.584716\pi\)
\(180\) 1.97141 9.34004i 0.146940 0.696166i
\(181\) −12.9669 −0.963822 −0.481911 0.876220i \(-0.660057\pi\)
−0.481911 + 0.876220i \(0.660057\pi\)
\(182\) 0 0
\(183\) 5.34501 0.850463i 0.395115 0.0628680i
\(184\) 1.11956 1.93914i 0.0825352 0.142955i
\(185\) −1.59097 + 2.75564i −0.116971 + 0.202599i
\(186\) −5.83693 + 15.2381i −0.427985 + 1.11731i
\(187\) −2.42107 4.19341i −0.177046 0.306653i
\(188\) −5.82846 −0.425084
\(189\) 0 0
\(190\) 4.08126 0.296085
\(191\) −0.990285 1.71522i −0.0716545 0.124109i 0.827972 0.560769i \(-0.189495\pi\)
−0.899627 + 0.436660i \(0.856161\pi\)
\(192\) −0.619562 + 1.61745i −0.0447130 + 0.116729i
\(193\) 2.27292 3.93680i 0.163608 0.283377i −0.772552 0.634951i \(-0.781020\pi\)
0.936160 + 0.351574i \(0.114353\pi\)
\(194\) −7.42107 + 12.8537i −0.532802 + 0.922839i
\(195\) 31.0442 4.93955i 2.22312 0.353728i
\(196\) 0 0
\(197\) −21.8148 −1.55424 −0.777120 0.629353i \(-0.783320\pi\)
−0.777120 + 0.629353i \(0.783320\pi\)
\(198\) −9.07442 + 2.96273i −0.644891 + 0.210552i
\(199\) −12.2826 −0.870693 −0.435346 0.900263i \(-0.643374\pi\)
−0.435346 + 0.900263i \(0.643374\pi\)
\(200\) 2.56238 + 4.43818i 0.181188 + 0.313826i
\(201\) −11.9646 14.7536i −0.843916 1.04064i
\(202\) 9.29467 16.0988i 0.653971 1.13271i
\(203\) 0 0
\(204\) −1.66019 2.04719i −0.116237 0.143332i
\(205\) 8.91423 + 15.4399i 0.622597 + 1.07837i
\(206\) 0.282630 0.0196918
\(207\) 6.38564 2.08486i 0.443833 0.144908i
\(208\) −5.70370 −0.395480
\(209\) −2.04063 3.53447i −0.141153 0.244485i
\(210\) 0 0
\(211\) −8.32846 + 14.4253i −0.573355 + 0.993080i 0.422863 + 0.906193i \(0.361025\pi\)
−0.996218 + 0.0868863i \(0.972308\pi\)
\(212\) 1.02859 1.78157i 0.0706438 0.122359i
\(213\) −5.38401 + 14.0557i −0.368906 + 0.963079i
\(214\) −5.68878 9.85326i −0.388877 0.673555i
\(215\) 21.7278 1.48182
\(216\) −4.62476 + 2.36887i −0.314675 + 0.161181i
\(217\) 0 0
\(218\) 2.21053 + 3.82876i 0.149716 + 0.259316i
\(219\) −3.07730 + 8.03371i −0.207945 + 0.542867i
\(220\) 5.06238 8.76830i 0.341306 0.591159i
\(221\) 4.33981 7.51677i 0.291927 0.505633i
\(222\) 1.71053 0.272169i 0.114803 0.0182668i
\(223\) −5.32846 9.22916i −0.356820 0.618031i 0.630608 0.776102i \(-0.282806\pi\)
−0.987428 + 0.158071i \(0.949472\pi\)
\(224\) 0 0
\(225\) −3.17511 + 15.0429i −0.211674 + 1.00286i
\(226\) −3.21505 −0.213862
\(227\) 7.25404 + 12.5644i 0.481468 + 0.833926i 0.999774 0.0212688i \(-0.00677059\pi\)
−0.518306 + 0.855195i \(0.673437\pi\)
\(228\) −1.39931 1.72550i −0.0926718 0.114274i
\(229\) −5.12476 + 8.87635i −0.338654 + 0.586566i −0.984180 0.177173i \(-0.943305\pi\)
0.645526 + 0.763738i \(0.276638\pi\)
\(230\) −3.56238 + 6.17023i −0.234896 + 0.406853i
\(231\) 0 0
\(232\) 3.54063 + 6.13255i 0.232454 + 0.402622i
\(233\) −1.08126 −0.0708355 −0.0354177 0.999373i \(-0.511276\pi\)
−0.0354177 + 0.999373i \(0.511276\pi\)
\(234\) −12.7323 11.4315i −0.832336 0.747298i
\(235\) 18.5458 1.20980
\(236\) 0.562382 + 0.974074i 0.0366079 + 0.0634068i
\(237\) −7.07893 + 1.12635i −0.459826 + 0.0731645i
\(238\) 0 0
\(239\) −6.16019 + 10.6698i −0.398470 + 0.690170i −0.993537 0.113506i \(-0.963792\pi\)
0.595068 + 0.803676i \(0.297125\pi\)
\(240\) 1.97141 5.14663i 0.127254 0.332214i
\(241\) 6.50000 + 11.2583i 0.418702 + 0.725213i 0.995809 0.0914555i \(-0.0291519\pi\)
−0.577107 + 0.816668i \(0.695819\pi\)
\(242\) 0.875237 0.0562623
\(243\) −15.0715 3.98104i −0.966840 0.255384i
\(244\) 3.12476 0.200042
\(245\) 0 0
\(246\) 3.47141 9.06259i 0.221329 0.577809i
\(247\) 3.65787 6.33561i 0.232744 0.403125i
\(248\) −4.71053 + 8.15888i −0.299119 + 0.518090i
\(249\) 13.7999 2.19574i 0.874531 0.139150i
\(250\) −0.198495 0.343803i −0.0125539 0.0217440i
\(251\) 5.11109 0.322609 0.161305 0.986905i \(-0.448430\pi\)
0.161305 + 0.986905i \(0.448430\pi\)
\(252\) 0 0
\(253\) 7.12476 0.447930
\(254\) 10.0527 + 17.4117i 0.630760 + 1.09251i
\(255\) 5.28263 + 6.51403i 0.330811 + 0.407924i
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −3.83009 + 6.63392i −0.238915 + 0.413813i −0.960403 0.278614i \(-0.910125\pi\)
0.721488 + 0.692427i \(0.243458\pi\)
\(258\) −7.44966 9.18620i −0.463795 0.571908i
\(259\) 0 0
\(260\) 18.1488 1.12554
\(261\) −4.38727 + 20.7858i −0.271565 + 1.28661i
\(262\) −6.36389 −0.393162
\(263\) 1.54746 + 2.68029i 0.0954208 + 0.165274i 0.909784 0.415082i \(-0.136247\pi\)
−0.814363 + 0.580355i \(0.802914\pi\)
\(264\) −5.44282 + 0.866025i −0.334982 + 0.0533002i
\(265\) −3.27292 + 5.66886i −0.201054 + 0.348235i
\(266\) 0 0
\(267\) 0.139680 0.364654i 0.00854830 0.0223165i
\(268\) −5.48345 9.49761i −0.334955 0.580159i
\(269\) 26.8903 1.63953 0.819765 0.572700i \(-0.194104\pi\)
0.819765 + 0.572700i \(0.194104\pi\)
\(270\) 14.7157 7.53762i 0.895571 0.458725i
\(271\) 22.2164 1.34955 0.674776 0.738023i \(-0.264240\pi\)
0.674776 + 0.738023i \(0.264240\pi\)
\(272\) −0.760877 1.31788i −0.0461349 0.0799080i
\(273\) 0 0
\(274\) 1.37072 2.37416i 0.0828084 0.143428i
\(275\) −8.15335 + 14.1220i −0.491666 + 0.851590i
\(276\) 3.83009 0.609419i 0.230545 0.0366827i
\(277\) 7.31875 + 12.6764i 0.439741 + 0.761653i 0.997669 0.0682357i \(-0.0217370\pi\)
−0.557928 + 0.829889i \(0.688404\pi\)
\(278\) −7.96690 −0.477823
\(279\) −26.8675 + 8.77202i −1.60851 + 0.525167i
\(280\) 0 0
\(281\) 11.6992 + 20.2636i 0.697915 + 1.20882i 0.969188 + 0.246322i \(0.0792219\pi\)
−0.271273 + 0.962502i \(0.587445\pi\)
\(282\) −6.35868 7.84092i −0.378654 0.466920i
\(283\) 13.0624 22.6247i 0.776478 1.34490i −0.157482 0.987522i \(-0.550338\pi\)
0.933960 0.357377i \(-0.116329\pi\)
\(284\) −4.34501 + 7.52578i −0.257829 + 0.446573i
\(285\) 4.45254 + 5.49044i 0.263745 + 0.325225i
\(286\) −9.07442 15.7174i −0.536582 0.929387i
\(287\) 0 0
\(288\) −2.85185 + 0.931107i −0.168047 + 0.0548660i
\(289\) −14.6843 −0.863780
\(290\) −11.2661 19.5134i −0.661567 1.14587i
\(291\) −25.3880 + 4.03956i −1.48827 + 0.236803i
\(292\) −2.48345 + 4.30146i −0.145333 + 0.251724i
\(293\) 12.9315 22.3980i 0.755465 1.30850i −0.189678 0.981846i \(-0.560745\pi\)
0.945143 0.326657i \(-0.105922\pi\)
\(294\) 0 0
\(295\) −1.78947 3.09945i −0.104187 0.180457i
\(296\) 1.00000 0.0581238
\(297\) −13.8856 8.97539i −0.805727 0.520805i
\(298\) 23.2599 1.34741
\(299\) 6.38564 + 11.0603i 0.369291 + 0.639631i
\(300\) −3.17511 + 8.28905i −0.183315 + 0.478568i
\(301\) 0 0
\(302\) −4.06238 + 7.03625i −0.233764 + 0.404891i
\(303\) 31.7977 5.05944i 1.82673 0.290657i
\(304\) −0.641315 1.11079i −0.0367819 0.0637082i
\(305\) −9.94282 −0.569324
\(306\) 0.942820 4.46684i 0.0538974 0.255352i
\(307\) 3.53216 0.201591 0.100795 0.994907i \(-0.467861\pi\)
0.100795 + 0.994907i \(0.467861\pi\)
\(308\) 0 0
\(309\) 0.308342 + 0.380217i 0.0175409 + 0.0216298i
\(310\) 14.9887 25.9611i 0.851298 1.47449i
\(311\) −0.851848 + 1.47544i −0.0483039 + 0.0836648i −0.889166 0.457584i \(-0.848715\pi\)
0.840863 + 0.541249i \(0.182048\pi\)
\(312\) −6.22257 7.67307i −0.352284 0.434402i
\(313\) 1.42107 + 2.46136i 0.0803234 + 0.139124i 0.903389 0.428822i \(-0.141071\pi\)
−0.823065 + 0.567947i \(0.807738\pi\)
\(314\) 11.2632 0.635619
\(315\) 0 0
\(316\) −4.13844 −0.232805
\(317\) 12.4601 + 21.5815i 0.699827 + 1.21214i 0.968526 + 0.248911i \(0.0800728\pi\)
−0.268700 + 0.963224i \(0.586594\pi\)
\(318\) 3.51887 0.559900i 0.197329 0.0313976i
\(319\) −11.2661 + 19.5134i −0.630779 + 1.09254i
\(320\) 1.59097 2.75564i 0.0889380 0.154045i
\(321\) 7.04910 18.4026i 0.393442 1.02713i
\(322\) 0 0
\(323\) 1.95185 0.108604
\(324\) −8.23229 3.63723i −0.457349 0.202068i
\(325\) −29.2301 −1.62139
\(326\) 1.99028 + 3.44727i 0.110232 + 0.190927i
\(327\) −2.73912 + 7.15085i −0.151474 + 0.395443i
\(328\) 2.80150 4.85235i 0.154687 0.267926i
\(329\) 0 0
\(330\) 17.3187 2.75564i 0.953366 0.151693i
\(331\) 3.58577 + 6.21074i 0.197092 + 0.341373i 0.947584 0.319506i \(-0.103517\pi\)
−0.750492 + 0.660879i \(0.770184\pi\)
\(332\) 8.06758 0.442766
\(333\) 2.23229 + 2.00422i 0.122329 + 0.109831i
\(334\) 5.23912 0.286672
\(335\) 17.4480 + 30.2209i 0.953287 + 1.65114i
\(336\) 0 0
\(337\) −10.9211 + 18.9158i −0.594908 + 1.03041i 0.398651 + 0.917103i \(0.369478\pi\)
−0.993560 + 0.113309i \(0.963855\pi\)
\(338\) 9.76608 16.9153i 0.531205 0.920073i
\(339\) −3.50752 4.32514i −0.190503 0.234909i
\(340\) 2.42107 + 4.19341i 0.131301 + 0.227420i
\(341\) −29.9773 −1.62336
\(342\) 0.794668 3.76494i 0.0429707 0.203585i
\(343\) 0 0
\(344\) −3.41423 5.91362i −0.184083 0.318841i
\(345\) −12.1871 + 1.93914i −0.656134 + 0.104400i
\(346\) 1.27579 2.20974i 0.0685871 0.118796i
\(347\) 1.05555 1.82826i 0.0566646 0.0981460i −0.836302 0.548270i \(-0.815287\pi\)
0.892966 + 0.450124i \(0.148620\pi\)
\(348\) −4.38727 + 11.4536i −0.235183 + 0.613976i
\(349\) 18.1082 + 31.3643i 0.969310 + 1.67889i 0.697559 + 0.716527i \(0.254269\pi\)
0.271751 + 0.962368i \(0.412397\pi\)
\(350\) 0 0
\(351\) 1.48796 29.5999i 0.0794215 1.57993i
\(352\) −3.18194 −0.169598
\(353\) 5.24433 + 9.08344i 0.279127 + 0.483463i 0.971168 0.238396i \(-0.0766215\pi\)
−0.692041 + 0.721858i \(0.743288\pi\)
\(354\) −0.696860 + 1.81925i −0.0370377 + 0.0966919i
\(355\) 13.8256 23.9466i 0.733786 1.27095i
\(356\) 0.112725 0.195246i 0.00597442 0.0103480i
\(357\) 0 0
\(358\) −3.51887 6.09487i −0.185978 0.322124i
\(359\) −32.4419 −1.71222 −0.856108 0.516796i \(-0.827124\pi\)
−0.856108 + 0.516796i \(0.827124\pi\)
\(360\) 9.07442 2.96273i 0.478264 0.156150i
\(361\) −17.3549 −0.913414
\(362\) −6.48345 11.2297i −0.340762 0.590218i
\(363\) 0.954858 + 1.17744i 0.0501171 + 0.0617995i
\(364\) 0 0
\(365\) 7.90219 13.6870i 0.413620 0.716410i
\(366\) 3.40903 + 4.20368i 0.178193 + 0.219730i
\(367\) 9.05555 + 15.6847i 0.472696 + 0.818733i 0.999512 0.0312465i \(-0.00994768\pi\)
−0.526816 + 0.849979i \(0.676614\pi\)
\(368\) 2.23912 0.116722
\(369\) 15.9789 5.21700i 0.831830 0.271586i
\(370\) −3.18194 −0.165421
\(371\) 0 0
\(372\) −16.1150 + 2.56412i −0.835526 + 0.132943i
\(373\) 5.83530 10.1070i 0.302140 0.523322i −0.674480 0.738293i \(-0.735632\pi\)
0.976621 + 0.214971i \(0.0689656\pi\)
\(374\) 2.42107 4.19341i 0.125190 0.216836i
\(375\) 0.245960 0.642111i 0.0127013 0.0331585i
\(376\) −2.91423 5.04759i −0.150290 0.260310i
\(377\) −40.3893 −2.08016
\(378\) 0 0
\(379\) 14.2690 0.732947 0.366474 0.930428i \(-0.380565\pi\)
0.366474 + 0.930428i \(0.380565\pi\)
\(380\) 2.04063 + 3.53447i 0.104682 + 0.181315i
\(381\) −12.4565 + 32.5194i −0.638165 + 1.66602i
\(382\) 0.990285 1.71522i 0.0506674 0.0877585i
\(383\) 0.824893 1.42876i 0.0421501 0.0730061i −0.844181 0.536059i \(-0.819913\pi\)
0.886331 + 0.463053i \(0.153246\pi\)
\(384\) −1.71053 + 0.272169i −0.0872903 + 0.0138891i
\(385\) 0 0
\(386\) 4.54583 0.231377
\(387\) 4.23065 20.0438i 0.215056 1.01888i
\(388\) −14.8421 −0.753495
\(389\) 16.0338 + 27.7713i 0.812946 + 1.40806i 0.910794 + 0.412862i \(0.135471\pi\)
−0.0978483 + 0.995201i \(0.531196\pi\)
\(390\) 19.7999 + 24.4153i 1.00261 + 1.23632i
\(391\) −1.70370 + 2.95089i −0.0861596 + 0.149233i
\(392\) 0 0
\(393\) −6.94282 8.56122i −0.350219 0.431856i
\(394\) −10.9074 18.8922i −0.549507 0.951773i
\(395\) 13.1683 0.662568
\(396\) −7.10301 6.37731i −0.356940 0.320472i
\(397\) 37.9338 1.90384 0.951921 0.306343i \(-0.0991054\pi\)
0.951921 + 0.306343i \(0.0991054\pi\)
\(398\) −6.14132 10.6371i −0.307836 0.533188i
\(399\) 0 0
\(400\) −2.56238 + 4.43818i −0.128119 + 0.221909i
\(401\) −5.30959 + 9.19647i −0.265148 + 0.459250i −0.967602 0.252479i \(-0.918754\pi\)
0.702454 + 0.711729i \(0.252087\pi\)
\(402\) 6.79467 17.7384i 0.338887 0.884711i
\(403\) −26.8675 46.5358i −1.33836 2.31811i
\(404\) 18.5893 0.924854
\(405\) 26.1947 + 11.5735i 1.30162 + 0.575090i
\(406\) 0 0
\(407\) 1.59097 + 2.75564i 0.0788615 + 0.136592i
\(408\) 0.942820 2.46136i 0.0466765 0.121855i
\(409\) −2.77292 + 4.80283i −0.137112 + 0.237485i −0.926402 0.376535i \(-0.877115\pi\)
0.789290 + 0.614020i \(0.210449\pi\)
\(410\) −8.91423 + 15.4399i −0.440242 + 0.762522i
\(411\) 4.68934 0.746136i 0.231308 0.0368042i
\(412\) 0.141315 + 0.244765i 0.00696209 + 0.0120587i
\(413\) 0 0
\(414\) 4.99837 + 4.48769i 0.245656 + 0.220558i
\(415\) −25.6706 −1.26012
\(416\) −2.85185 4.93955i −0.139823 0.242181i
\(417\) −8.69166 10.7177i −0.425632 0.524849i
\(418\) 2.04063 3.53447i 0.0998104 0.172877i
\(419\) 2.77455 4.80566i 0.135546 0.234772i −0.790260 0.612772i \(-0.790055\pi\)
0.925806 + 0.378000i \(0.123388\pi\)
\(420\) 0 0
\(421\) −3.42107 5.92546i −0.166733 0.288789i 0.770537 0.637396i \(-0.219988\pi\)
−0.937269 + 0.348606i \(0.886655\pi\)
\(422\) −16.6569 −0.810846
\(423\) 3.61109 17.1084i 0.175577 0.831841i
\(424\) 2.05718 0.0999055
\(425\) −3.89931 6.75381i −0.189144 0.327608i
\(426\) −14.8646 + 2.36515i −0.720191 + 0.114592i
\(427\) 0 0
\(428\) 5.68878 9.85326i 0.274978 0.476275i
\(429\) 11.2443 29.3548i 0.542881 1.41726i
\(430\) 10.8639 + 18.8168i 0.523903 + 0.907427i
\(431\) −33.1078 −1.59475 −0.797374 0.603486i \(-0.793778\pi\)
−0.797374 + 0.603486i \(0.793778\pi\)
\(432\) −4.36389 2.82073i −0.209958 0.135712i
\(433\) −12.1111 −0.582022 −0.291011 0.956720i \(-0.593992\pi\)
−0.291011 + 0.956720i \(0.593992\pi\)
\(434\) 0 0
\(435\) 13.9601 36.4446i 0.669334 1.74739i
\(436\) −2.21053 + 3.82876i −0.105865 + 0.183364i
\(437\) −1.43598 + 2.48720i −0.0686924 + 0.118979i
\(438\) −8.49604 + 1.35183i −0.405957 + 0.0645931i
\(439\) 4.41711 + 7.65066i 0.210817 + 0.365146i 0.951970 0.306190i \(-0.0990542\pi\)
−0.741153 + 0.671336i \(0.765721\pi\)
\(440\) 10.1248 0.482679
\(441\) 0 0
\(442\) 8.67962 0.412847
\(443\) −8.75924 15.1715i −0.416164 0.720817i 0.579386 0.815053i \(-0.303292\pi\)
−0.995550 + 0.0942360i \(0.969959\pi\)
\(444\) 1.09097 + 1.34528i 0.0517752 + 0.0638442i
\(445\) −0.358685 + 0.621261i −0.0170033 + 0.0294506i
\(446\) 5.32846 9.22916i 0.252310 0.437014i
\(447\) 25.3759 + 31.2911i 1.20024 + 1.48002i
\(448\) 0 0
\(449\) 31.2301 1.47384 0.736920 0.675980i \(-0.236280\pi\)
0.736920 + 0.675980i \(0.236280\pi\)
\(450\) −14.6150 + 4.77170i −0.688960 + 0.224940i
\(451\) 17.8285 0.839509
\(452\) −1.60752 2.78431i −0.0756115 0.130963i
\(453\) −13.8977 + 2.21131i −0.652970 + 0.103896i
\(454\) −7.25404 + 12.5644i −0.340449 + 0.589675i
\(455\) 0 0
\(456\) 0.794668 2.07459i 0.0372138 0.0971516i
\(457\) 16.0624 + 27.8209i 0.751367 + 1.30140i 0.947161 + 0.320760i \(0.103938\pi\)
−0.195794 + 0.980645i \(0.562728\pi\)
\(458\) −10.2495 −0.478929
\(459\) 7.03775 3.60484i 0.328494 0.168260i
\(460\) −7.12476 −0.332194
\(461\) 1.23229 + 2.13438i 0.0573933 + 0.0994081i 0.893295 0.449472i \(-0.148388\pi\)
−0.835901 + 0.548880i \(0.815054\pi\)
\(462\) 0 0
\(463\) 15.1735 26.2812i 0.705171 1.22139i −0.261459 0.965215i \(-0.584204\pi\)
0.966630 0.256177i \(-0.0824631\pi\)
\(464\) −3.54063 + 6.13255i −0.164370 + 0.284696i
\(465\) 51.2772 8.15888i 2.37792 0.378359i
\(466\) −0.540628 0.936396i −0.0250441 0.0433777i
\(467\) 15.9636 0.738709 0.369354 0.929289i \(-0.379579\pi\)
0.369354 + 0.929289i \(0.379579\pi\)
\(468\) 3.53379 16.7422i 0.163350 0.773909i
\(469\) 0 0
\(470\) 9.27292 + 16.0612i 0.427728 + 0.740846i
\(471\) 12.2878 + 15.1522i 0.566193 + 0.698175i
\(472\) −0.562382 + 0.974074i −0.0258857 + 0.0448354i
\(473\) 10.8639 18.8168i 0.499522 0.865198i
\(474\) −4.51492 5.56736i −0.207377 0.255717i
\(475\) −3.28659 5.69254i −0.150799 0.261192i
\(476\) 0 0
\(477\) 4.59222 + 4.12304i 0.210263 + 0.188781i
\(478\) −12.3204 −0.563521
\(479\) 11.5865 + 20.0683i 0.529399 + 0.916946i 0.999412 + 0.0342863i \(0.0109158\pi\)
−0.470013 + 0.882659i \(0.655751\pi\)
\(480\) 5.44282 0.866025i 0.248430 0.0395285i
\(481\) −2.85185 + 4.93955i −0.130033 + 0.225224i
\(482\) −6.50000 + 11.2583i −0.296067 + 0.512803i
\(483\) 0 0
\(484\) 0.437618 + 0.757977i 0.0198917 + 0.0344535i
\(485\) 47.2268 2.14446
\(486\) −4.08809 15.0429i −0.185440 0.682358i
\(487\) −3.41315 −0.154665 −0.0773323 0.997005i \(-0.524640\pi\)
−0.0773323 + 0.997005i \(0.524640\pi\)
\(488\) 1.56238 + 2.70612i 0.0707257 + 0.122500i
\(489\) −2.46621 + 6.43837i −0.111526 + 0.291153i
\(490\) 0 0
\(491\) −9.58414 + 16.6002i −0.432526 + 0.749157i −0.997090 0.0762323i \(-0.975711\pi\)
0.564564 + 0.825389i \(0.309044\pi\)
\(492\) 9.58414 1.52496i 0.432086 0.0687507i
\(493\) −5.38796 9.33223i −0.242662 0.420302i
\(494\) 7.31573 0.329150
\(495\) 22.6014 + 20.2922i 1.01586 + 0.912069i
\(496\) −9.42107 −0.423018
\(497\) 0 0
\(498\) 8.80150 + 10.8532i 0.394405 + 0.486342i
\(499\) −20.5848 + 35.6540i −0.921503 + 1.59609i −0.124413 + 0.992231i \(0.539705\pi\)
−0.797090 + 0.603860i \(0.793629\pi\)
\(500\) 0.198495 0.343803i 0.00887697 0.0153754i
\(501\) 5.71574 + 7.04809i 0.255360 + 0.314886i
\(502\) 2.55555 + 4.42633i 0.114060 + 0.197557i
\(503\) −26.4542 −1.17953 −0.589767 0.807574i \(-0.700780\pi\)
−0.589767 + 0.807574i \(0.700780\pi\)
\(504\) 0 0
\(505\) −59.1502 −2.63215
\(506\) 3.56238 + 6.17023i 0.158367 + 0.274300i
\(507\) 33.4104 5.31604i 1.48381 0.236094i
\(508\) −10.0527 + 17.4117i −0.446015 + 0.772521i
\(509\) −6.38564 + 11.0603i −0.283039 + 0.490237i −0.972132 0.234436i \(-0.924676\pi\)
0.689093 + 0.724673i \(0.258009\pi\)
\(510\) −3.00000 + 7.83191i −0.132842 + 0.346803i
\(511\) 0 0
\(512\) −1.00000 −0.0441942
\(513\) 5.93186 3.03839i 0.261898 0.134148i
\(514\) −7.66019 −0.337876
\(515\) −0.449657 0.778828i −0.0198142 0.0343193i
\(516\) 4.23065 11.0447i 0.186244 0.486215i
\(517\) 9.27292 16.0612i 0.407822 0.706369i
\(518\) 0 0
\(519\) 4.36458 0.694462i 0.191584 0.0304835i
\(520\) 9.07442 + 15.7174i 0.397940 + 0.689252i
\(521\) 6.81230 0.298452 0.149226 0.988803i \(-0.452322\pi\)
0.149226 + 0.988803i \(0.452322\pi\)
\(522\) −20.1947 + 6.59341i −0.883897 + 0.288586i
\(523\) −29.5070 −1.29025 −0.645125 0.764077i \(-0.723195\pi\)
−0.645125 + 0.764077i \(0.723195\pi\)
\(524\) −3.18194 5.51129i −0.139004 0.240762i
\(525\) 0 0
\(526\) −1.54746 + 2.68029i −0.0674727 + 0.116866i
\(527\) 7.16827 12.4158i 0.312255 0.540841i
\(528\) −3.47141 4.28061i −0.151074 0.186290i
\(529\) 8.99316 + 15.5766i 0.391007 + 0.677244i
\(530\) −6.54583 −0.284333
\(531\) −3.20765 + 1.04728i −0.139200 + 0.0454479i
\(532\) 0 0
\(533\) 15.9789 + 27.6763i 0.692125 + 1.19879i
\(534\) 0.385640 0.0613605i 0.0166883 0.00265533i
\(535\) −18.1014 + 31.3525i −0.782591 + 1.35549i
\(536\) 5.48345 9.49761i 0.236849 0.410234i
\(537\) 4.36032 11.3832i 0.188162 0.491222i
\(538\) 13.4451 + 23.2877i 0.579661 + 1.00400i
\(539\) 0 0
\(540\) 13.8856 + 8.97539i 0.597543 + 0.386239i
\(541\) −29.4016 −1.26408 −0.632038 0.774938i \(-0.717781\pi\)
−0.632038 + 0.774938i \(0.717781\pi\)
\(542\) 11.1082 + 19.2400i 0.477139 + 0.826428i
\(543\) 8.03379 20.9733i 0.344763 0.900051i
\(544\) 0.760877 1.31788i 0.0326223 0.0565035i
\(545\) 7.03379 12.1829i 0.301295 0.521857i
\(546\) 0 0
\(547\) 17.6150 + 30.5102i 0.753165 + 1.30452i 0.946281 + 0.323344i \(0.104807\pi\)
−0.193116 + 0.981176i \(0.561859\pi\)
\(548\) 2.74145 0.117109
\(549\) −1.93598 + 9.17220i −0.0826258 + 0.391460i
\(550\) −16.3067 −0.695320
\(551\) −4.54132 7.86579i −0.193467 0.335094i
\(552\) 2.44282 + 3.01225i 0.103973 + 0.128210i
\(553\) 0 0
\(554\) −7.31875 + 12.6764i −0.310944 + 0.538570i
\(555\) −3.47141 4.28061i −0.147353 0.181702i
\(556\) −3.98345 6.89953i −0.168936 0.292605i
\(557\) 6.73818 0.285506 0.142753 0.989758i \(-0.454405\pi\)
0.142753 + 0.989758i \(0.454405\pi\)
\(558\) −21.0305 18.8819i −0.890293 0.799334i
\(559\) 38.9475 1.64730
\(560\) 0 0
\(561\) 8.28263 1.31788i 0.349693 0.0556408i
\(562\) −11.6992 + 20.2636i −0.493500 + 0.854768i
\(563\) 0.729964 1.26433i 0.0307643 0.0532853i −0.850233 0.526406i \(-0.823539\pi\)
0.880998 + 0.473121i \(0.156873\pi\)
\(564\) 3.61109 9.42724i 0.152054 0.396958i
\(565\) 5.11505 + 8.85952i 0.215192 + 0.372723i
\(566\) 26.1248 1.09811
\(567\) 0 0
\(568\) −8.69002 −0.364625
\(569\) −9.78263 16.9440i −0.410109 0.710330i 0.584792 0.811183i \(-0.301176\pi\)
−0.994901 + 0.100853i \(0.967843\pi\)
\(570\) −2.52859 + 6.60123i −0.105911 + 0.276495i
\(571\) 10.9629 18.9884i 0.458785 0.794638i −0.540112 0.841593i \(-0.681618\pi\)
0.998897 + 0.0469545i \(0.0149516\pi\)
\(572\) 9.07442 15.7174i 0.379421 0.657176i
\(573\) 3.38783 0.539049i 0.141529 0.0225191i
\(574\) 0 0
\(575\) 11.4750 0.478540
\(576\) −2.23229 2.00422i −0.0930119 0.0835091i
\(577\) −24.7310 −1.02957 −0.514783 0.857320i \(-0.672128\pi\)
−0.514783 + 0.857320i \(0.672128\pi\)
\(578\) −7.34213 12.7169i −0.305392 0.528955i
\(579\) 4.95937 + 6.11542i 0.206104 + 0.254148i
\(580\) 11.2661 19.5134i 0.467798 0.810251i
\(581\) 0 0
\(582\) −16.1923 19.9668i −0.671194 0.827652i
\(583\) 3.27292 + 5.66886i 0.135550 + 0.234780i
\(584\) −4.96690 −0.205532
\(585\) −11.2443 + 53.2728i −0.464896 + 2.20256i
\(586\) 25.8629 1.06839
\(587\) −18.0796 31.3148i −0.746226 1.29250i −0.949620 0.313404i \(-0.898531\pi\)
0.203394 0.979097i \(-0.434803\pi\)
\(588\) 0 0
\(589\) 6.04187 10.4648i 0.248951 0.431196i
\(590\) 1.78947 3.09945i 0.0736712 0.127602i
\(591\) 13.5156 35.2843i 0.555958 1.45140i
\(592\) 0.500000 + 0.866025i 0.0205499 + 0.0355934i
\(593\) 15.1078 0.620404 0.310202 0.950671i \(-0.399603\pi\)
0.310202 + 0.950671i \(0.399603\pi\)
\(594\) 0.830095 16.5130i 0.0340592 0.677537i
\(595\) 0 0
\(596\) 11.6300 + 20.1437i 0.476382 + 0.825118i
\(597\) 7.60985 19.8665i 0.311450 0.813083i
\(598\) −6.38564 + 11.0603i −0.261128 + 0.452287i
\(599\) 2.72708 4.72345i 0.111426 0.192995i −0.804920 0.593384i \(-0.797792\pi\)
0.916345 + 0.400389i \(0.131125\pi\)
\(600\) −8.76608 + 1.39480i −0.357874 + 0.0569425i
\(601\) −3.36840 5.83424i −0.137400 0.237984i 0.789112 0.614250i \(-0.210541\pi\)
−0.926512 + 0.376266i \(0.877208\pi\)
\(602\) 0 0
\(603\) 31.2759 10.2114i 1.27365 0.415839i
\(604\) −8.12476 −0.330592
\(605\) −1.39248 2.41184i −0.0566122 0.0980553i
\(606\) 20.2804 + 25.0079i 0.823837 + 1.01588i
\(607\) −3.33530 + 5.77690i −0.135376 + 0.234477i −0.925741 0.378159i \(-0.876557\pi\)
0.790365 + 0.612636i \(0.209891\pi\)
\(608\) 0.641315 1.11079i 0.0260088 0.0450485i
\(609\) 0 0
\(610\) −4.97141 8.61073i −0.201287 0.348638i
\(611\) 33.2438 1.34490
\(612\) 4.33981 1.41692i 0.175426 0.0572754i
\(613\) −1.30998 −0.0529094 −0.0264547 0.999650i \(-0.508422\pi\)
−0.0264547 + 0.999650i \(0.508422\pi\)
\(614\) 1.76608 + 3.05894i 0.0712731 + 0.123449i
\(615\) −30.4962 + 4.85235i −1.22972 + 0.195666i
\(616\) 0 0
\(617\) 17.2483 29.8749i 0.694390 1.20272i −0.275996 0.961159i \(-0.589008\pi\)
0.970386 0.241560i \(-0.0776589\pi\)
\(618\) −0.175107 + 0.457140i −0.00704383 + 0.0183889i
\(619\) 8.22421 + 14.2447i 0.330559 + 0.572545i 0.982622 0.185620i \(-0.0594295\pi\)
−0.652063 + 0.758165i \(0.726096\pi\)
\(620\) 29.9773 1.20392
\(621\) −0.584135 + 11.6202i −0.0234405 + 0.466301i
\(622\) −1.70370 −0.0683120
\(623\) 0 0
\(624\) 3.53379 9.22544i 0.141465 0.369313i
\(625\) 12.1803 21.0969i 0.487212 0.843877i
\(626\) −1.42107 + 2.46136i −0.0567972 + 0.0983757i
\(627\) 6.98113 1.11079i 0.278799 0.0443607i
\(628\) 5.63160 + 9.75422i 0.224725 + 0.389236i
\(629\) −1.52175 −0.0606763
\(630\) 0 0
\(631\) −30.0118 −1.19475 −0.597375 0.801962i \(-0.703790\pi\)
−0.597375 + 0.801962i \(0.703790\pi\)
\(632\) −2.06922 3.58399i −0.0823091 0.142564i
\(633\) −18.1722 22.4082i −0.722281 0.890647i
\(634\) −12.4601 + 21.5815i −0.494852 + 0.857109i
\(635\) 31.9870 55.4031i 1.26937 2.19861i
\(636\) 2.24433 + 2.76748i 0.0889933 + 0.109738i
\(637\) 0 0
\(638\) −22.5322 −0.892057
\(639\) −19.3986 17.4167i −0.767398 0.688995i
\(640\) 3.18194 0.125777
\(641\) −13.9497 24.1615i −0.550978 0.954322i −0.998204 0.0599014i \(-0.980921\pi\)
0.447226 0.894421i \(-0.352412\pi\)
\(642\) 19.4617 3.09662i 0.768092 0.122214i
\(643\) 14.2524 24.6859i 0.562060 0.973516i −0.435257 0.900306i \(-0.643342\pi\)
0.997317 0.0732100i \(-0.0233243\pi\)
\(644\) 0 0
\(645\) −13.4617 + 35.1436i −0.530054 + 1.38378i
\(646\) 0.975923 + 1.69035i 0.0383972 + 0.0665059i
\(647\) −16.7141 −0.657099 −0.328550 0.944487i \(-0.606560\pi\)
−0.328550 + 0.944487i \(0.606560\pi\)
\(648\) −0.966208 8.94799i −0.0379562 0.351510i
\(649\) −3.57893 −0.140485
\(650\) −14.6150 25.3140i −0.573249 0.992897i
\(651\) 0 0
\(652\) −1.99028 + 3.44727i −0.0779456 + 0.135006i
\(653\) −19.0825 + 33.0519i −0.746756 + 1.29342i 0.202614 + 0.979259i \(0.435056\pi\)
−0.949370 + 0.314161i \(0.898277\pi\)
\(654\) −7.56238 + 1.20328i −0.295713 + 0.0470518i
\(655\) 10.1248 + 17.5366i 0.395607 + 0.685212i
\(656\) 5.60301 0.218761
\(657\) −11.0875 9.95475i −0.432566 0.388372i
\(658\) 0 0
\(659\) 4.37072 + 7.57031i 0.170259 + 0.294898i 0.938510 0.345251i \(-0.112206\pi\)
−0.768251 + 0.640148i \(0.778873\pi\)
\(660\) 11.0458 + 13.6207i 0.429958 + 0.530183i
\(661\) 10.0419 17.3930i 0.390584 0.676511i −0.601943 0.798539i \(-0.705607\pi\)
0.992527 + 0.122028i \(0.0389399\pi\)
\(662\) −3.58577 + 6.21074i −0.139365 + 0.241387i
\(663\) 9.46922 + 11.6765i 0.367754 + 0.453479i
\(664\) 4.03379 + 6.98673i 0.156541 + 0.271138i
\(665\) 0 0
\(666\) −0.619562 + 2.93533i −0.0240075 + 0.113742i
\(667\) 15.8558 0.613939
\(668\) 2.61956 + 4.53721i 0.101354 + 0.175550i
\(669\) 18.2290 2.90048i 0.704775 0.112139i
\(670\) −17.4480 + 30.2209i −0.674076 + 1.16753i
\(671\) −4.97141 + 8.61073i −0.191919 + 0.332414i
\(672\) 0 0
\(673\) −17.0264 29.4906i −0.656319 1.13678i −0.981561 0.191148i \(-0.938779\pi\)
0.325242 0.945631i \(-0.394554\pi\)
\(674\) −21.8421 −0.841328
\(675\) −22.3639 14.4556i −0.860786 0.556394i
\(676\) 19.5322 0.751237
\(677\) 0.358685 + 0.621261i 0.0137854 + 0.0238770i 0.872836 0.488014i \(-0.162279\pi\)
−0.859050 + 0.511891i \(0.828945\pi\)
\(678\) 1.99192 5.20018i 0.0764992 0.199712i
\(679\) 0 0
\(680\) −2.42107 + 4.19341i −0.0928437 + 0.160810i
\(681\) −24.8166 + 3.94865i −0.950972 + 0.151312i
\(682\) −14.9887 25.9611i −0.573945 0.994102i
\(683\) 21.0539 0.805605 0.402803 0.915287i \(-0.368036\pi\)
0.402803 + 0.915287i \(0.368036\pi\)
\(684\) 3.65787 1.19427i 0.139862 0.0456639i
\(685\) −8.72313 −0.333294
\(686\) 0 0
\(687\) −11.1819 13.7885i −0.426618 0.526064i
\(688\) 3.41423 5.91362i 0.130166 0.225455i
\(689\) −5.86677 + 10.1615i −0.223506 + 0.387124i
\(690\) −7.77292 9.58481i −0.295910 0.364887i
\(691\) −2.92395 5.06442i −0.111232 0.192660i 0.805035 0.593227i \(-0.202146\pi\)
−0.916267 + 0.400567i \(0.868813\pi\)
\(692\) 2.55159 0.0969968
\(693\) 0 0
\(694\) 2.11109 0.0801359
\(695\) 12.6751 + 21.9539i 0.480794 + 0.832760i
\(696\) −12.1127 + 1.92730i −0.459132 + 0.0730540i
\(697\) −4.26320 + 7.38408i −0.161480 + 0.279692i
\(698\) −18.1082 + 31.3643i −0.685406 + 1.18716i
\(699\) 0.669905 1.74888i 0.0253381 0.0661486i
\(700\) 0 0
\(701\) 10.2711 0.387935 0.193967 0.981008i \(-0.437864\pi\)
0.193967 + 0.981008i \(0.437864\pi\)
\(702\) 26.3782 13.5113i 0.995583 0.509953i
\(703\) −1.28263 −0.0483753
\(704\) −1.59097 2.75564i −0.0599620 0.103857i
\(705\) −11.4903 + 29.9969i −0.432749 + 1.12975i
\(706\) −5.24433 + 9.08344i −0.197373 + 0.341860i
\(707\) 0 0
\(708\) −1.92395 + 0.306125i −0.0723063 + 0.0115049i
\(709\) −21.7427 37.6594i −0.816564 1.41433i −0.908200 0.418538i \(-0.862543\pi\)
0.0916356 0.995793i \(-0.470790\pi\)
\(710\) 27.6512 1.03773
\(711\) 2.56402 12.1477i 0.0961581 0.455573i
\(712\) 0.225450 0.00844910
\(713\) 10.5475 + 18.2687i 0.395006 + 0.684170i
\(714\) 0 0
\(715\) −28.8743 + 50.0117i −1.07984 + 1.87033i
\(716\) 3.51887 6.09487i 0.131507 0.227776i
\(717\) −13.4412 16.5744i −0.501970 0.618981i
\(718\) −16.2209 28.0955i −0.605360 1.04851i
\(719\) −50.8824 −1.89759 −0.948796 0.315889i \(-0.897697\pi\)
−0.948796 + 0.315889i \(0.897697\pi\)
\(720\) 7.10301 + 6.37731i 0.264714 + 0.237668i
\(721\) 0 0
\(722\) −8.67743 15.0297i −0.322941 0.559349i
\(723\) −22.2369 + 3.53819i −0.827000 + 0.131587i
\(724\) 6.48345 11.2297i 0.240955 0.417347i
\(725\) −18.1449 + 31.4279i −0.673884 + 1.16720i
\(726\) −0.542263 + 1.41565i −0.0201253 + 0.0525397i
\(727\) 6.07210 + 10.5172i 0.225202 + 0.390061i 0.956380 0.292126i \(-0.0943626\pi\)
−0.731178 + 0.682186i \(0.761029\pi\)
\(728\) 0 0
\(729\) 15.7769 21.9110i 0.584329 0.811517i
\(730\) 15.8044 0.584946
\(731\) 5.19562 + 8.99907i 0.192167 + 0.332843i
\(732\) −1.93598 + 5.05415i −0.0715560 + 0.186807i
\(733\) 23.0848 39.9841i 0.852657 1.47685i −0.0261440 0.999658i \(-0.508323\pi\)
0.878801 0.477188i \(-0.158344\pi\)
\(734\) −9.05555 + 15.6847i −0.334246 + 0.578932i
\(735\) 0 0
\(736\) 1.11956 + 1.93914i 0.0412676 + 0.0714776i
\(737\) 34.8960 1.28541
\(738\) 12.5075 + 11.2297i 0.460408 + 0.413370i
\(739\) 4.99208 0.183637 0.0918184 0.995776i \(-0.470732\pi\)
0.0918184 + 0.995776i \(0.470732\pi\)
\(740\) −1.59097 2.75564i −0.0584853 0.101299i
\(741\) 7.98126 + 9.84172i 0.293199 + 0.361545i
\(742\) 0 0
\(743\) −15.7060 + 27.2036i −0.576198 + 0.998004i 0.419712 + 0.907657i \(0.362131\pi\)
−0.995910 + 0.0903470i \(0.971202\pi\)
\(744\) −10.2781 12.6740i −0.376814 0.464651i
\(745\) −37.0059 64.0961i −1.35579 2.34830i
\(746\) 11.6706 0.427291
\(747\) −4.99837 + 23.6810i −0.182881 + 0.866442i
\(748\) 4.84213 0.177046
\(749\) 0 0
\(750\) 0.679065 0.108048i 0.0247959 0.00394536i
\(751\) −1.64815 + 2.85468i −0.0601419 + 0.104169i −0.894529 0.447010i \(-0.852489\pi\)
0.834387 + 0.551179i \(0.185822\pi\)
\(752\) 2.91423 5.04759i 0.106271 0.184067i
\(753\) −3.16664 + 8.26693i −0.115399 + 0.301264i
\(754\) −20.1947 34.9782i −0.735447 1.27383i
\(755\) 25.8525 0.940870
\(756\) 0 0
\(757\) −10.1384 −0.368488 −0.184244 0.982881i \(-0.558984\pi\)
−0.184244 + 0.982881i \(0.558984\pi\)
\(758\) 7.13448 + 12.3573i 0.259136 + 0.448837i
\(759\) −4.41423 + 11.5239i −0.160226 + 0.418293i
\(760\) −2.04063 + 3.53447i −0.0740214 + 0.128209i
\(761\) −7.03379 + 12.1829i −0.254975 + 0.441629i −0.964889 0.262659i \(-0.915400\pi\)
0.709914 + 0.704288i \(0.248734\pi\)
\(762\) −34.3908 + 5.47204i −1.24585 + 0.198231i
\(763\) 0 0
\(764\) 1.98057 0.0716545
\(765\) −13.8090 + 4.50855i −0.499267 + 0.163007i
\(766\) 1.64979 0.0596092
\(767\) −3.20765 5.55582i −0.115822 0.200609i
\(768\) −1.09097 1.34528i −0.0393670 0.0485436i
\(769\) 11.3461 19.6520i 0.409151 0.708669i −0.585644 0.810568i \(-0.699158\pi\)
0.994795 + 0.101899i \(0.0324918\pi\)
\(770\) 0 0
\(771\) −8.35705 10.3051i −0.300972 0.371129i
\(772\) 2.27292 + 3.93680i 0.0818040 + 0.141689i
\(773\) −0.655544 −0.0235783 −0.0117891 0.999931i \(-0.503753\pi\)