Properties

Label 882.2.h.p.67.3
Level $882$
Weight $2$
Character 882.67
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(67,882)]
 
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([2, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("882.67");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 882.h (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: \(7.04280545828\)
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 67.3
Root \(0.500000 + 1.41036i\) of defining polynomial
Character \(\chi\) \(=\) 882.67
Dual form 882.2.h.p.79.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{2} +(1.09097 + 1.34528i) q^{3} +(-0.500000 - 0.866025i) q^{4} +3.18194 q^{5} +(1.71053 - 0.272169i) q^{6} -1.00000 q^{8} +(-0.619562 + 2.93533i) q^{9} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{2} +(1.09097 + 1.34528i) q^{3} +(-0.500000 - 0.866025i) q^{4} +3.18194 q^{5} +(1.71053 - 0.272169i) q^{6} -1.00000 q^{8} +(-0.619562 + 2.93533i) q^{9} +(1.59097 - 2.75564i) q^{10} +3.18194 q^{11} +(0.619562 - 1.61745i) q^{12} +(-2.85185 + 4.93955i) q^{13} +(3.47141 + 4.28061i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.760877 - 1.31788i) q^{17} +(2.23229 + 2.00422i) q^{18} +(0.641315 + 1.11079i) q^{19} +(-1.59097 - 2.75564i) q^{20} +(1.59097 - 2.75564i) q^{22} +2.23912 q^{23} +(-1.09097 - 1.34528i) q^{24} +5.12476 q^{25} +(2.85185 + 4.93955i) q^{26} +(-4.62476 + 2.36887i) q^{27} +(-3.54063 - 6.13255i) q^{29} +(5.44282 - 0.866025i) q^{30} +(-4.71053 - 8.15888i) q^{31} +(0.500000 + 0.866025i) q^{32} +(3.47141 + 4.28061i) q^{33} +(-0.760877 - 1.31788i) q^{34} +(2.85185 - 0.931107i) q^{36} +(0.500000 + 0.866025i) q^{37} +1.28263 q^{38} +(-9.75636 + 1.55237i) q^{39} -3.18194 q^{40} +(2.80150 - 4.85235i) q^{41} +(3.41423 + 5.91362i) q^{43} +(-1.59097 - 2.75564i) q^{44} +(-1.97141 + 9.34004i) q^{45} +(1.11956 - 1.93914i) q^{46} +(-2.91423 + 5.04759i) q^{47} +(-1.71053 + 0.272169i) q^{48} +(2.56238 - 4.43818i) q^{50} +(2.60301 - 0.414174i) q^{51} +5.70370 q^{52} +(1.02859 - 1.78157i) q^{53} +(-0.260877 + 5.18960i) q^{54} +10.1248 q^{55} +(-0.794668 + 2.07459i) q^{57} -7.08126 q^{58} +(-0.562382 - 0.974074i) q^{59} +(1.97141 - 5.14663i) q^{60} +(1.56238 - 2.70612i) q^{61} -9.42107 q^{62} +1.00000 q^{64} +(-9.07442 + 15.7174i) q^{65} +(5.44282 - 0.866025i) q^{66} +(-5.48345 - 9.49761i) q^{67} -1.52175 q^{68} +(2.44282 + 3.01225i) q^{69} +8.69002 q^{71} +(0.619562 - 2.93533i) q^{72} +(2.48345 - 4.30146i) q^{73} +1.00000 q^{74} +(5.59097 + 6.89425i) q^{75} +(0.641315 - 1.11079i) q^{76} +(-3.53379 + 9.22544i) q^{78} +(2.06922 - 3.58399i) q^{79} +(-1.59097 + 2.75564i) q^{80} +(-8.23229 - 3.63723i) q^{81} +(-2.80150 - 4.85235i) q^{82} +(4.03379 + 6.98673i) q^{83} +(2.42107 - 4.19341i) q^{85} +6.82846 q^{86} +(4.38727 - 11.4536i) q^{87} -3.18194 q^{88} +(-0.112725 - 0.195246i) q^{89} +(7.10301 + 6.37731i) q^{90} +(-1.11956 - 1.93914i) q^{92} +(5.83693 - 15.2381i) q^{93} +(2.91423 + 5.04759i) q^{94} +(2.04063 + 3.53447i) q^{95} +(-0.619562 + 1.61745i) q^{96} +(-7.42107 - 12.8537i) q^{97} +(-1.97141 + 9.34004i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + 3 q^{2} - 2 q^{3} - 3 q^{4} + 2 q^{5} + 2 q^{6} - 6 q^{8} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q + 3 q^{2} - 2 q^{3} - 3 q^{4} + 2 q^{5} + 2 q^{6} - 6 q^{8} - 4 q^{9} + q^{10} + 2 q^{11} + 4 q^{12} - 8 q^{13} + 12 q^{15} - 3 q^{16} + 4 q^{17} + 4 q^{18} + 3 q^{19} - q^{20} + q^{22} + 14 q^{23} + 2 q^{24} - 4 q^{25} + 8 q^{26} + 7 q^{27} - 5 q^{29} + 15 q^{30} - 20 q^{31} + 3 q^{32} + 12 q^{33} - 4 q^{34} + 8 q^{36} + 3 q^{37} + 6 q^{38} + q^{39} - 2 q^{40} - 6 q^{43} - q^{44} - 3 q^{45} + 7 q^{46} + 9 q^{47} - 2 q^{48} - 2 q^{50} - 18 q^{51} + 16 q^{52} + 15 q^{53} - q^{54} + 26 q^{55} + 22 q^{57} - 10 q^{58} + 14 q^{59} + 3 q^{60} - 8 q^{61} - 40 q^{62} + 6 q^{64} - 12 q^{65} + 15 q^{66} + q^{67} - 8 q^{68} - 3 q^{69} + 14 q^{71} + 4 q^{72} - 19 q^{73} + 6 q^{74} + 25 q^{75} + 3 q^{76} + 5 q^{78} + 5 q^{79} - q^{80} - 40 q^{81} - 2 q^{83} - 2 q^{85} - 12 q^{86} + 36 q^{87} - 2 q^{88} + 9 q^{89} + 9 q^{90} - 7 q^{92} + 37 q^{93} - 9 q^{94} - 4 q^{95} - 4 q^{96} - 28 q^{97} - 3 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(199\) \(785\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\)

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
\(3\) 1.09097 + 1.34528i 0.629873 + 0.776698i
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 3.18194 1.42301 0.711504 0.702682i \(-0.248014\pi\)
0.711504 + 0.702682i \(0.248014\pi\)
\(6\) 1.71053 0.272169i 0.698322 0.111112i
\(7\) 0 0
\(8\) −1.00000 −0.353553
\(9\) −0.619562 + 2.93533i −0.206521 + 0.978442i
\(10\) 1.59097 2.75564i 0.503109 0.871411i
\(11\) 3.18194 0.959392 0.479696 0.877435i \(-0.340747\pi\)
0.479696 + 0.877435i \(0.340747\pi\)
\(12\) 0.619562 1.61745i 0.178852 0.466917i
\(13\) −2.85185 + 4.93955i −0.790960 + 1.36998i 0.134412 + 0.990925i \(0.457085\pi\)
−0.925373 + 0.379058i \(0.876248\pi\)
\(14\) 0 0
\(15\) 3.47141 + 4.28061i 0.896314 + 1.10525i
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 0.760877 1.31788i 0.184540 0.319632i −0.758882 0.651229i \(-0.774254\pi\)
0.943421 + 0.331596i \(0.107587\pi\)
\(18\) 2.23229 + 2.00422i 0.526155 + 0.472399i
\(19\) 0.641315 + 1.11079i 0.147128 + 0.254833i 0.930165 0.367142i \(-0.119664\pi\)
−0.783037 + 0.621975i \(0.786330\pi\)
\(20\) −1.59097 2.75564i −0.355752 0.616181i
\(21\) 0 0
\(22\) 1.59097 2.75564i 0.339196 0.587505i
\(23\) 2.23912 0.466889 0.233445 0.972370i \(-0.425000\pi\)
0.233445 + 0.972370i \(0.425000\pi\)
\(24\) −1.09097 1.34528i −0.222694 0.274604i
\(25\) 5.12476 1.02495
\(26\) 2.85185 + 4.93955i 0.559293 + 0.968725i
\(27\) −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 \(-0.395043\pi\)
\(30\) 5.44282 0.866025i 0.993718 0.158114i
\(31\) −4.71053 8.15888i −0.846037 1.46538i −0.884718 0.466127i \(-0.845649\pi\)
0.0386810 0.999252i \(-0.487684\pi\)
\(32\) 0.500000 + 0.866025i 0.0883883 + 0.153093i
\(33\) 3.47141 + 4.28061i 0.604295 + 0.745158i
\(34\) −0.760877 1.31788i −0.130489 0.226014i
\(35\) 0 0
\(36\) 2.85185 0.931107i 0.475308 0.155185i
\(37\) 0.500000 + 0.866025i 0.0821995 + 0.142374i 0.904194 0.427121i \(-0.140472\pi\)
−0.821995 + 0.569495i \(0.807139\pi\)
\(38\) 1.28263 0.208070
\(39\) −9.75636 + 1.55237i −1.56227 + 0.248578i
\(40\) −3.18194 −0.503109
\(41\) 2.80150 4.85235i 0.437522 0.757810i −0.559976 0.828509i \(-0.689190\pi\)
0.997498 + 0.0706992i \(0.0225230\pi\)
\(42\) 0 0
\(43\) 3.41423 + 5.91362i 0.520665 + 0.901819i 0.999711 + 0.0240288i \(0.00764935\pi\)
−0.479046 + 0.877790i \(0.659017\pi\)
\(44\) −1.59097 2.75564i −0.239848 0.415429i
\(45\) −1.97141 + 9.34004i −0.293880 + 1.39233i
\(46\) 1.11956 1.93914i 0.165070 0.285910i
\(47\) −2.91423 + 5.04759i −0.425084 + 0.736267i −0.996428 0.0844432i \(-0.973089\pi\)
0.571344 + 0.820711i \(0.306422\pi\)
\(48\) −1.71053 + 0.272169i −0.246894 + 0.0392842i
\(49\) 0 0
\(50\) 2.56238 4.43818i 0.362375 0.627653i
\(51\) 2.60301 0.414174i 0.364494 0.0579959i
\(52\) 5.70370 0.790960
\(53\) 1.02859 1.78157i 0.141288 0.244717i −0.786694 0.617343i \(-0.788209\pi\)
0.927982 + 0.372626i \(0.121542\pi\)
\(54\) −0.260877 + 5.18960i −0.0355008 + 0.706215i
\(55\) 10.1248 1.36522
\(56\) 0 0
\(57\) −0.794668 + 2.07459i −0.105256 + 0.274786i
\(58\) −7.08126 −0.929815
\(59\) −0.562382 0.974074i −0.0732159 0.126814i 0.827093 0.562065i \(-0.189993\pi\)
−0.900309 + 0.435251i \(0.856660\pi\)
\(60\) 1.97141 5.14663i 0.254508 0.664427i
\(61\) 1.56238 2.70612i 0.200042 0.346484i −0.748499 0.663135i \(-0.769225\pi\)
0.948542 + 0.316652i \(0.102559\pi\)
\(62\) −9.42107 −1.19648
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) −9.07442 + 15.7174i −1.12554 + 1.94950i
\(66\) 5.44282 0.866025i 0.669965 0.106600i
\(67\) −5.48345 9.49761i −0.669910 1.16032i −0.977929 0.208938i \(-0.932999\pi\)
0.308019 0.951380i \(-0.400334\pi\)
\(68\) −1.52175 −0.184540
\(69\) 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 \(0.327548\pi\)
\(72\) 0.619562 2.93533i 0.0730160 0.345932i
\(73\) 2.48345 4.30146i 0.290666 0.503448i −0.683302 0.730136i \(-0.739457\pi\)
0.973967 + 0.226689i \(0.0727899\pi\)
\(74\) 1.00000 0.116248
\(75\) 5.59097 + 6.89425i 0.645590 + 0.796079i
\(76\) 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 −0.725827 0.687877i \(-0.758543\pi\)
0.958633 + 0.284646i \(0.0918762\pi\)
\(80\) −1.59097 + 2.75564i −0.177876 + 0.308090i
\(81\) −8.23229 3.63723i −0.914699 0.404137i
\(82\) −2.80150 4.85235i −0.309374 0.535852i
\(83\) 4.03379 + 6.98673i 0.442766 + 0.766893i 0.997894 0.0648718i \(-0.0206639\pi\)
−0.555127 + 0.831765i \(0.687331\pi\)
\(84\) 0 0
\(85\) 2.42107 4.19341i 0.262602 0.454839i
\(86\) 6.82846 0.736332
\(87\) 4.38727 11.4536i 0.470365 1.22795i
\(88\) −3.18194 −0.339196
\(89\) −0.112725 0.195246i −0.0119488 0.0206960i 0.859989 0.510312i \(-0.170470\pi\)
−0.871938 + 0.489616i \(0.837137\pi\)
\(90\) 7.10301 + 6.37731i 0.748723 + 0.672228i
\(91\) 0 0
\(92\) −1.11956 1.93914i −0.116722 0.202169i
\(93\) 5.83693 15.2381i 0.605262 1.58012i
\(94\) 2.91423 + 5.04759i 0.300580 + 0.520620i
\(95\) 2.04063 + 3.53447i 0.209364 + 0.362629i
\(96\) −0.619562 + 1.61745i −0.0632337 + 0.165080i
\(97\) −7.42107 12.8537i −0.753495 1.30509i −0.946119 0.323819i \(-0.895033\pi\)
0.192624 0.981273i \(-0.438300\pi\)
\(98\) 0 0
\(99\) −1.97141 + 9.34004i −0.198134 + 0.938710i
\(100\) −2.56238 4.43818i −0.256238 0.443818i
\(101\) −18.5893 −1.84971 −0.924854 0.380322i \(-0.875813\pi\)
−0.924854 + 0.380322i \(0.875813\pi\)
\(102\) 0.942820 2.46136i 0.0933531 0.243711i
\(103\) 0.282630 0.0278484 0.0139242 0.999903i \(-0.495568\pi\)
0.0139242 + 0.999903i \(0.495568\pi\)
\(104\) 2.85185 4.93955i 0.279647 0.484362i
\(105\) 0 0
\(106\) −1.02859 1.78157i −0.0999055 0.173041i
\(107\) 5.68878 + 9.85326i 0.549955 + 0.952550i 0.998277 + 0.0586780i \(0.0186885\pi\)
−0.448322 + 0.893872i \(0.647978\pi\)
\(108\) 4.36389 + 2.82073i 0.419915 + 0.271424i
\(109\) −2.21053 + 3.82876i −0.211731 + 0.366728i −0.952256 0.305300i \(-0.901243\pi\)
0.740526 + 0.672028i \(0.234577\pi\)
\(110\) 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 \(0.214988\pi\)
\(114\) 1.39931 + 1.72550i 0.131058 + 0.161608i
\(115\) 7.12476 0.664388
\(116\) −3.54063 + 6.13255i −0.328739 + 0.569393i
\(117\) −12.7323 11.4315i −1.17710 1.05684i
\(118\) −1.12476 −0.103543
\(119\) 0 0
\(120\) −3.47141 4.28061i −0.316895 0.390764i
\(121\) −0.875237 −0.0795670
\(122\) −1.56238 2.70612i −0.141451 0.245001i
\(123\) 9.58414 1.52496i 0.864172 0.137501i
\(124\) −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
\(129\) −4.23065 + 11.0447i −0.372488 + 0.972431i
\(130\) 9.07442 + 15.7174i 0.795879 + 1.37850i
\(131\) −6.36389 −0.556015 −0.278008 0.960579i \(-0.589674\pi\)
−0.278008 + 0.960579i \(0.589674\pi\)
\(132\) 1.97141 5.14663i 0.171589 0.447957i
\(133\) 0 0
\(134\) −10.9669 −0.947396
\(135\) −14.7157 + 7.53762i −1.26653 + 0.648735i
\(136\) −0.760877 + 1.31788i −0.0652446 + 0.113007i
\(137\) 2.74145 0.234218 0.117109 0.993119i \(-0.462637\pi\)
0.117109 + 0.993119i \(0.462637\pi\)
\(138\) 3.83009 0.609419i 0.326039 0.0518772i
\(139\) 3.98345 6.89953i 0.337872 0.585211i −0.646161 0.763202i \(-0.723626\pi\)
0.984032 + 0.177991i \(0.0569597\pi\)
\(140\) 0 0
\(141\) −9.96978 + 1.58632i −0.839607 + 0.133593i
\(142\) 4.34501 7.52578i 0.364625 0.631550i
\(143\) −9.07442 + 15.7174i −0.758841 + 1.31435i
\(144\) −2.23229 2.00422i −0.186024 0.167018i
\(145\) −11.2661 19.5134i −0.935597 1.62050i
\(146\) −2.48345 4.30146i −0.205532 0.355991i
\(147\) 0 0
\(148\) 0.500000 0.866025i 0.0410997 0.0711868i
\(149\) −23.2599 −1.90553 −0.952764 0.303712i \(-0.901774\pi\)
−0.952764 + 0.303712i \(0.901774\pi\)
\(150\) 8.76608 1.39480i 0.715747 0.113885i
\(151\) −8.12476 −0.661184 −0.330592 0.943774i \(-0.607248\pi\)
−0.330592 + 0.943774i \(0.607248\pi\)
\(152\) −0.641315 1.11079i −0.0520175 0.0900970i
\(153\) 3.39699 + 3.04993i 0.274630 + 0.246572i
\(154\) 0 0
\(155\) −14.9887 25.9611i −1.20392 2.08525i
\(156\) 6.22257 + 7.67307i 0.498204 + 0.614338i
\(157\) −5.63160 9.75422i −0.449451 0.778471i 0.548900 0.835888i \(-0.315047\pi\)
−0.998350 + 0.0574170i \(0.981714\pi\)
\(158\) −2.06922 3.58399i −0.164618 0.285127i
\(159\) 3.51887 0.559900i 0.279065 0.0444030i
\(160\) 1.59097 + 2.75564i 0.125777 + 0.217853i
\(161\) 0 0
\(162\) −7.26608 + 5.31075i −0.570877 + 0.417252i
\(163\) −1.99028 3.44727i −0.155891 0.270011i 0.777492 0.628893i \(-0.216492\pi\)
−0.933383 + 0.358881i \(0.883158\pi\)
\(164\) −5.60301 −0.437522
\(165\) 11.0458 + 13.6207i 0.859917 + 1.06037i
\(166\) 8.06758 0.626166
\(167\) −2.61956 + 4.53721i −0.202708 + 0.351100i −0.949400 0.314070i \(-0.898307\pi\)
0.746692 + 0.665170i \(0.231641\pi\)
\(168\) 0 0
\(169\) −9.76608 16.9153i −0.751237 1.30118i
\(170\) −2.42107 4.19341i −0.185687 0.321620i
\(171\) −3.65787 + 1.19427i −0.279724 + 0.0913278i
\(172\) 3.41423 5.91362i 0.260333 0.450909i
\(173\) 1.27579 2.20974i 0.0969968 0.168003i −0.813443 0.581644i \(-0.802410\pi\)
0.910440 + 0.413641i \(0.135743\pi\)
\(174\) −7.72545 9.52628i −0.585665 0.722185i
\(175\) 0 0
\(176\) −1.59097 + 2.75564i −0.119924 + 0.207714i
\(177\) 0.696860 1.81925i 0.0523792 0.136743i
\(178\) −0.225450 −0.0168982
\(179\) 3.51887 6.09487i 0.263013 0.455552i −0.704028 0.710172i \(-0.748617\pi\)
0.967041 + 0.254620i \(0.0819504\pi\)
\(180\) 9.07442 2.96273i 0.676367 0.220829i
\(181\) 12.9669 0.963822 0.481911 0.876220i \(-0.339943\pi\)
0.481911 + 0.876220i \(0.339943\pi\)
\(182\) 0 0
\(183\) 5.34501 0.850463i 0.395115 0.0628680i
\(184\) −2.23912 −0.165070
\(185\) 1.59097 + 2.75564i 0.116971 + 0.202599i
\(186\) −10.2781 12.6740i −0.753628 0.929301i
\(187\) 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 −0.899627 0.436660i \(-0.856161\pi\)
0.827972 + 0.560769i \(0.189495\pi\)
\(192\) 1.09097 + 1.34528i 0.0787341 + 0.0970873i
\(193\) 2.27292 + 3.93680i 0.163608 + 0.283377i 0.936160 0.351574i \(-0.114353\pi\)
−0.772552 + 0.634951i \(0.781020\pi\)
\(194\) −14.8421 −1.06560
\(195\) −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 \(0.783320\pi\)
\(198\) 7.10301 + 6.37731i 0.504789 + 0.453216i
\(199\) −6.14132 + 10.6371i −0.435346 + 0.754042i −0.997324 0.0731106i \(-0.976707\pi\)
0.561978 + 0.827152i \(0.310041\pi\)
\(200\) −5.12476 −0.362375
\(201\) 6.79467 17.7384i 0.479259 1.25117i
\(202\) −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
\(206\) 0.141315 0.244765i 0.00984589 0.0170536i
\(207\) −1.38727 + 6.57256i −0.0964223 + 0.456824i
\(208\) −2.85185 4.93955i −0.197740 0.342496i
\(209\) 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 \(0.972308\pi\)
\(212\) −2.05718 −0.141288
\(213\) 9.48057 + 11.6905i 0.649598 + 0.801021i
\(214\) 11.3776 0.777754
\(215\) 10.8639 + 18.8168i 0.740911 + 1.28330i
\(216\) 4.62476 2.36887i 0.314675 0.161181i
\(217\) 0 0
\(218\) 2.21053 + 3.82876i 0.149716 + 0.259316i
\(219\) 8.49604 1.35183i 0.574109 0.0913485i
\(220\) −5.06238 8.76830i −0.341306 0.591159i
\(221\) 4.33981 + 7.51677i 0.291927 + 0.505633i
\(222\) 1.09097 + 1.34528i 0.0732212 + 0.0902893i
\(223\) 5.32846 + 9.22916i 0.356820 + 0.618031i 0.987428 0.158071i \(-0.0505276\pi\)
−0.630608 + 0.776102i \(0.717194\pi\)
\(224\) 0 0
\(225\) −3.17511 + 15.0429i −0.211674 + 1.00286i
\(226\) 1.60752 + 2.78431i 0.106931 + 0.185210i
\(227\) 14.5081 0.962935 0.481468 0.876464i \(-0.340104\pi\)
0.481468 + 0.876464i \(0.340104\pi\)
\(228\) 2.19398 0.349092i 0.145300 0.0231192i
\(229\) −10.2495 −0.677308 −0.338654 0.940911i \(-0.609972\pi\)
−0.338654 + 0.940911i \(0.609972\pi\)
\(230\) 3.56238 6.17023i 0.234896 0.406853i
\(231\) 0 0
\(232\) 3.54063 + 6.13255i 0.232454 + 0.402622i
\(233\) 0.540628 + 0.936396i 0.0354177 + 0.0613453i 0.883191 0.469014i \(-0.155390\pi\)
−0.847773 + 0.530359i \(0.822057\pi\)
\(234\) −16.2661 + 5.31075i −1.06335 + 0.347175i
\(235\) −9.27292 + 16.0612i −0.604898 + 1.04771i
\(236\) −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 \(0.297125\pi\)
\(240\) −5.44282 + 0.866025i −0.351333 + 0.0559017i
\(241\) 13.0000 0.837404 0.418702 0.908124i \(-0.362485\pi\)
0.418702 + 0.908124i \(0.362485\pi\)
\(242\) −0.437618 + 0.757977i −0.0281312 + 0.0487246i
\(243\) −4.08809 15.0429i −0.262251 0.965000i
\(244\) −3.12476 −0.200042
\(245\) 0 0
\(246\) 3.47141 9.06259i 0.221329 0.577809i
\(247\) −7.31573 −0.465489
\(248\) 4.71053 + 8.15888i 0.299119 + 0.518090i
\(249\) −4.99837 + 13.0489i −0.316759 + 0.826941i
\(250\) 0.198495 0.343803i 0.0125539 0.0217440i
\(251\) −5.11109 −0.322609 −0.161305 0.986905i \(-0.551570\pi\)
−0.161305 + 0.986905i \(0.551570\pi\)
\(252\) 0 0
\(253\) 7.12476 0.447930
\(254\) 10.0527 17.4117i 0.630760 1.09251i
\(255\) 8.28263 1.31788i 0.518678 0.0825287i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −7.66019 −0.477830 −0.238915 0.971041i \(-0.576792\pi\)
−0.238915 + 0.971041i \(0.576792\pi\)
\(258\) 7.44966 + 9.18620i 0.463795 + 0.571908i
\(259\) 0 0
\(260\) 18.1488 1.12554
\(261\) 20.1947 6.59341i 1.25002 0.408122i
\(262\) −3.18194 + 5.51129i −0.196581 + 0.340488i
\(263\) −3.09493 −0.190842 −0.0954208 0.995437i \(-0.530420\pi\)
−0.0954208 + 0.995437i \(0.530420\pi\)
\(264\) −3.47141 4.28061i −0.213651 0.263453i
\(265\) 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
\(269\) 13.4451 23.2877i 0.819765 1.41987i −0.0860906 0.996287i \(-0.527437\pi\)
0.905855 0.423587i \(-0.139229\pi\)
\(270\) −0.830095 + 16.5130i −0.0505180 + 1.00495i
\(271\) 11.1082 + 19.2400i 0.674776 + 1.16875i 0.976534 + 0.215362i \(0.0690930\pi\)
−0.301759 + 0.953384i \(0.597574\pi\)
\(272\) 0.760877 + 1.31788i 0.0461349 + 0.0799080i
\(273\) 0 0
\(274\) 1.37072 2.37416i 0.0828084 0.143428i
\(275\) 16.3067 0.983331
\(276\) 1.38727 3.62167i 0.0835041 0.217999i
\(277\) −14.6375 −0.879482 −0.439741 0.898125i \(-0.644930\pi\)
−0.439741 + 0.898125i \(0.644930\pi\)
\(278\) −3.98345 6.89953i −0.238911 0.413807i
\(279\) 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 \(0.587445\pi\)
\(282\) −3.61109 + 9.42724i −0.215037 + 0.561384i
\(283\) −13.0624 22.6247i −0.776478 1.34490i −0.933960 0.357377i \(-0.883671\pi\)
0.157482 0.987522i \(-0.449662\pi\)
\(284\) −4.34501 7.52578i −0.257829 0.446573i
\(285\) −2.52859 + 6.60123i −0.149781 + 0.391023i
\(286\) 9.07442 + 15.7174i 0.536582 + 0.929387i
\(287\) 0 0
\(288\) −2.85185 + 0.931107i −0.168047 + 0.0548660i
\(289\) 7.34213 + 12.7169i 0.431890 + 0.748056i
\(290\) −22.5322 −1.32313
\(291\) 9.19562 24.0064i 0.539057 1.40728i
\(292\) −4.96690 −0.290666
\(293\) −12.9315 + 22.3980i −0.755465 + 1.30850i 0.189678 + 0.981846i \(0.439255\pi\)
−0.945143 + 0.326657i \(0.894078\pi\)
\(294\) 0 0
\(295\) −1.78947 3.09945i −0.104187 0.180457i
\(296\) −0.500000 0.866025i −0.0290619 0.0503367i
\(297\) −14.7157 + 7.53762i −0.853894 + 0.437377i
\(298\) −11.6300 + 20.1437i −0.673706 + 1.16689i
\(299\) −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
\(303\) −20.2804 25.0079i −1.16508 1.43667i
\(304\) −1.28263 −0.0735639
\(305\) 4.97141 8.61073i 0.284662 0.493049i
\(306\) 4.33981 1.41692i 0.248090 0.0809997i
\(307\) −3.53216 −0.201591 −0.100795 0.994907i \(-0.532139\pi\)
−0.100795 + 0.994907i \(0.532139\pi\)
\(308\) 0 0
\(309\) 0.308342 + 0.380217i 0.0175409 + 0.0216298i
\(310\) −29.9773 −1.70260
\(311\) 0.851848 + 1.47544i 0.0483039 + 0.0836648i 0.889166 0.457584i \(-0.151285\pi\)
−0.840863 + 0.541249i \(0.817952\pi\)
\(312\) 9.75636 1.55237i 0.552345 0.0878855i
\(313\) −1.42107 + 2.46136i −0.0803234 + 0.139124i −0.903389 0.428822i \(-0.858929\pi\)
0.823065 + 0.567947i \(0.192262\pi\)
\(314\) −11.2632 −0.635619
\(315\) 0 0
\(316\) −4.13844 −0.232805
\(317\) 12.4601 21.5815i 0.699827 1.21214i −0.268700 0.963224i \(-0.586594\pi\)
0.968526 0.248911i \(-0.0800728\pi\)
\(318\) 1.27455 3.32738i 0.0714732 0.186590i
\(319\) −11.2661 19.5134i −0.630779 1.09254i
\(320\) 3.18194 0.177876
\(321\) −7.04910 + 18.4026i −0.393442 + 1.02713i
\(322\) 0 0
\(323\) 1.95185 0.108604
\(324\) 0.966208 + 8.94799i 0.0536782 + 0.497110i
\(325\) −14.6150 + 25.3140i −0.810697 + 1.40417i
\(326\) −3.98057 −0.220463
\(327\) −7.56238 + 1.20328i −0.418201 + 0.0665413i
\(328\) −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 −0.750492 0.660879i \(-0.770184\pi\)
0.947584 + 0.319506i \(0.103517\pi\)
\(332\) 4.03379 6.98673i 0.221383 0.383447i
\(333\) −2.85185 + 0.931107i −0.156280 + 0.0510244i
\(334\) 2.61956 + 4.53721i 0.143336 + 0.248265i
\(335\) −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 \(0.963855\pi\)
\(338\) −19.5322 −1.06241
\(339\) −5.49944 + 0.875035i −0.298689 + 0.0475254i
\(340\) −4.84213 −0.262602
\(341\) −14.9887 25.9611i −0.811681 1.40587i
\(342\) −0.794668 + 3.76494i −0.0429707 + 0.203585i
\(343\) 0 0
\(344\) −3.41423 5.91362i −0.184083 0.318841i
\(345\) 7.77292 + 9.58481i 0.418480 + 0.516029i
\(346\) −1.27579 2.20974i −0.0685871 0.118796i
\(347\) 1.05555 + 1.82826i 0.0566646 + 0.0981460i 0.892966 0.450124i \(-0.148620\pi\)
−0.836302 + 0.548270i \(0.815287\pi\)
\(348\) −12.1127 + 1.92730i −0.649310 + 0.103314i
\(349\) −18.1082 31.3643i −0.969310 1.67889i −0.697559 0.716527i \(-0.745731\pi\)
−0.271751 0.962368i \(-0.587603\pi\)
\(350\) 0 0
\(351\) 1.48796 29.5999i 0.0794215 1.57993i
\(352\) 1.59097 + 2.75564i 0.0847991 + 0.146876i
\(353\) 10.4887 0.558255 0.279127 0.960254i \(-0.409955\pi\)
0.279127 + 0.960254i \(0.409955\pi\)
\(354\) −1.22708 1.51312i −0.0652188 0.0804216i
\(355\) 27.6512 1.46757
\(356\) −0.112725 + 0.195246i −0.00597442 + 0.0103480i
\(357\) 0 0
\(358\) −3.51887 6.09487i −0.185978 0.322124i
\(359\) 16.2209 + 28.0955i 0.856108 + 1.48282i 0.875613 + 0.483013i \(0.160458\pi\)
−0.0195047 + 0.999810i \(0.506209\pi\)
\(360\) 1.97141 9.34004i 0.103902 0.492264i
\(361\) 8.67743 15.0297i 0.456707 0.791039i
\(362\) 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
\(366\) 1.93598 5.05415i 0.101195 0.264185i
\(367\) 18.1111 0.945391 0.472696 0.881226i \(-0.343281\pi\)
0.472696 + 0.881226i \(0.343281\pi\)
\(368\) −1.11956 + 1.93914i −0.0583612 + 0.101085i
\(369\) 12.5075 + 11.2297i 0.651116 + 0.584593i
\(370\) 3.18194 0.165421
\(371\) 0 0
\(372\) −16.1150 + 2.56412i −0.835526 + 0.132943i
\(373\) −11.6706 −0.604280 −0.302140 0.953263i \(-0.597701\pi\)
−0.302140 + 0.953263i \(0.597701\pi\)
\(374\) −2.42107 4.19341i −0.125190 0.216836i
\(375\) 0.433105 + 0.534063i 0.0223654 + 0.0275789i
\(376\) 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
\(381\) 21.9343 + 27.0473i 1.12373 + 1.38568i
\(382\) 0.990285 + 1.71522i 0.0506674 + 0.0877585i
\(383\) 1.64979 0.0843001 0.0421501 0.999111i \(-0.486579\pi\)
0.0421501 + 0.999111i \(0.486579\pi\)
\(384\) 1.71053 0.272169i 0.0872903 0.0138891i
\(385\) 0 0
\(386\) 4.54583 0.231377
\(387\) −19.4737 + 6.35803i −0.989905 + 0.323197i
\(388\) −7.42107 + 12.8537i −0.376748 + 0.652546i
\(389\) −32.0676 −1.62589 −0.812946 0.582340i \(-0.802137\pi\)
−0.812946 + 0.582340i \(0.802137\pi\)
\(390\) −11.2443 + 29.3548i −0.569379 + 1.48644i
\(391\) 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
\(395\) 6.58414 11.4041i 0.331284 0.573800i
\(396\) 9.07442 2.96273i 0.456007 0.148883i
\(397\) 18.9669 + 32.8516i 0.951921 + 1.64878i 0.741261 + 0.671217i \(0.234228\pi\)
0.210660 + 0.977559i \(0.432439\pi\)
\(398\) 6.14132 + 10.6371i 0.307836 + 0.533188i
\(399\) 0 0
\(400\) −2.56238 + 4.43818i −0.128119 + 0.221909i
\(401\) 10.6192 0.530296 0.265148 0.964208i \(-0.414579\pi\)
0.265148 + 0.964208i \(0.414579\pi\)
\(402\) −11.9646 14.7536i −0.596739 0.735841i
\(403\) 53.7349 2.67673
\(404\) 9.29467 + 16.0988i 0.462427 + 0.800947i
\(405\) −26.1947 11.5735i −1.30162 0.575090i
\(406\) 0 0
\(407\) 1.59097 + 2.75564i 0.0788615 + 0.136592i
\(408\) −2.60301 + 0.414174i −0.128868 + 0.0205047i
\(409\) 2.77292 + 4.80283i 0.137112 + 0.237485i 0.926402 0.376535i \(-0.122885\pi\)
−0.789290 + 0.614020i \(0.789551\pi\)
\(410\) −8.91423 15.4399i −0.440242 0.762522i
\(411\) 2.99084 + 3.68802i 0.147527 + 0.181916i
\(412\) −0.141315 0.244765i −0.00696209 0.0120587i
\(413\) 0 0
\(414\) 4.99837 + 4.48769i 0.245656 + 0.220558i
\(415\) 12.8353 + 22.2314i 0.630060 + 1.09130i
\(416\) −5.70370 −0.279647
\(417\) 13.6276 2.16834i 0.667349 0.106184i
\(418\) 4.08126 0.199621
\(419\) −2.77455 + 4.80566i −0.135546 + 0.234772i −0.925806 0.378000i \(-0.876612\pi\)
0.790260 + 0.612772i \(0.209945\pi\)
\(420\) 0 0
\(421\) −3.42107 5.92546i −0.166733 0.288789i 0.770537 0.637396i \(-0.219988\pi\)
−0.937269 + 0.348606i \(0.886655\pi\)
\(422\) 8.32846 + 14.4253i 0.405423 + 0.702213i
\(423\) −13.0108 11.6815i −0.632606 0.567975i
\(424\) −1.02859 + 1.78157i −0.0499527 + 0.0865207i
\(425\) 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
\(429\) −31.0442 + 4.93955i −1.49883 + 0.238484i
\(430\) 21.7278 1.04781
\(431\) 16.5539 28.6722i 0.797374 1.38109i −0.123947 0.992289i \(-0.539555\pi\)
0.921321 0.388803i \(-0.127111\pi\)
\(432\) 0.260877 5.18960i 0.0125514 0.249685i
\(433\) 12.1111 0.582022 0.291011 0.956720i \(-0.406008\pi\)
0.291011 + 0.956720i \(0.406008\pi\)
\(434\) 0 0
\(435\) 13.9601 36.4446i 0.669334 1.74739i
\(436\) 4.42107 0.211731
\(437\) 1.43598 + 2.48720i 0.0686924 + 0.118979i
\(438\) 3.07730 8.03371i 0.147039 0.383865i
\(439\) −4.41711 + 7.65066i −0.210817 + 0.365146i −0.951970 0.306190i \(-0.900946\pi\)
0.741153 + 0.671336i \(0.234279\pi\)
\(440\) −10.1248 −0.482679
\(441\) 0 0
\(442\) 8.67962 0.412847
\(443\) −8.75924 + 15.1715i −0.416164 + 0.720817i −0.995550 0.0942360i \(-0.969959\pi\)
0.579386 + 0.815053i \(0.303292\pi\)
\(444\) 1.71053 0.272169i 0.0811783 0.0129166i
\(445\) −0.358685 0.621261i −0.0170033 0.0294506i
\(446\) 10.6569 0.504620
\(447\) −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 \(0.236280\pi\)
\(450\) 11.4399 + 10.2712i 0.539284 + 0.484187i
\(451\) 8.91423 15.4399i 0.419755 0.727036i
\(452\) 3.21505 0.151223
\(453\) −8.86389 10.9301i −0.416462 0.513540i
\(454\) 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 −0.195794 0.980645i \(-0.562728\pi\)
0.947161 0.320760i \(-0.103938\pi\)
\(458\) −5.12476 + 8.87635i −0.239464 + 0.414765i
\(459\) −0.396990 + 7.89729i −0.0185299 + 0.368614i
\(460\) −3.56238 6.17023i −0.166097 0.287688i
\(461\) −1.23229 2.13438i −0.0573933 0.0994081i 0.835901 0.548880i \(-0.184946\pi\)
−0.893295 + 0.449472i \(0.851612\pi\)
\(462\) 0 0
\(463\) 15.1735 26.2812i 0.705171 1.22139i −0.261459 0.965215i \(-0.584204\pi\)
0.966630 0.256177i \(-0.0824631\pi\)
\(464\) 7.08126 0.328739
\(465\) 18.5728 48.4868i 0.861292 2.24852i
\(466\) 1.08126 0.0500882
\(467\) 7.98181 + 13.8249i 0.369354 + 0.639740i 0.989465 0.144774i \(-0.0462456\pi\)
−0.620110 + 0.784515i \(0.712912\pi\)
\(468\) −3.53379 + 16.7422i −0.163350 + 0.773909i
\(469\) 0 0
\(470\) 9.27292 + 16.0612i 0.427728 + 0.740846i
\(471\) 6.97825 18.2177i 0.321541 0.839425i
\(472\) 0.562382 + 0.974074i 0.0258857 + 0.0448354i
\(473\) 10.8639 + 18.8168i 0.499522 + 0.865198i
\(474\) 2.56402 6.69371i 0.117769 0.307452i
\(475\) 3.28659 + 5.69254i 0.150799 + 0.261192i
\(476\) 0 0
\(477\) 4.59222 + 4.12304i 0.210263 + 0.188781i
\(478\) 6.16019 + 10.6698i 0.281761 + 0.488024i
\(479\) 23.1729 1.05880 0.529399 0.848373i \(-0.322418\pi\)
0.529399 + 0.848373i \(0.322418\pi\)
\(480\) −1.97141 + 5.14663i −0.0899821 + 0.234911i
\(481\) −5.70370 −0.260066
\(482\) 6.50000 11.2583i 0.296067 0.512803i
\(483\) 0 0
\(484\) 0.437618 + 0.757977i 0.0198917 + 0.0344535i
\(485\) −23.6134 40.8996i −1.07223 1.85716i
\(486\) −15.0715 3.98104i −0.683659 0.180583i
\(487\) 1.70658 2.95588i 0.0773323 0.133943i −0.824766 0.565474i \(-0.808693\pi\)
0.902098 + 0.431531i \(0.142026\pi\)
\(488\) −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 \(0.309044\pi\)
\(492\) −6.11273 7.53762i −0.275583 0.339822i
\(493\) −10.7759 −0.485323
\(494\) −3.65787 + 6.33561i −0.164575 + 0.285053i
\(495\) −6.27292 + 29.7195i −0.281947 + 1.33579i
\(496\) 9.42107 0.423018
\(497\) 0 0
\(498\) 8.80150 + 10.8532i 0.394405 + 0.486342i
\(499\) 41.1696 1.84301 0.921503 0.388371i \(-0.126962\pi\)
0.921503 + 0.388371i \(0.126962\pi\)
\(500\) −0.198495 0.343803i −0.00887697 0.0153754i
\(501\) −8.96169 + 1.42593i −0.400379 + 0.0637056i
\(502\) −2.55555 + 4.42633i −0.114060 + 0.197557i
\(503\) 26.4542 1.17953 0.589767 0.807574i \(-0.299220\pi\)
0.589767 + 0.807574i \(0.299220\pi\)
\(504\) 0 0
\(505\) −59.1502 −2.63215
\(506\) 3.56238 6.17023i 0.158367 0.274300i
\(507\) 12.1014 31.5923i 0.537441 1.40306i
\(508\) −10.0527 17.4117i −0.446015 0.772521i
\(509\) −12.7713 −0.566077 −0.283039 0.959109i \(-0.591342\pi\)
−0.283039 + 0.959109i \(0.591342\pi\)
\(510\) 3.00000 7.83191i 0.132842 0.346803i
\(511\) 0 0
\(512\) −1.00000 −0.0441942
\(513\) −5.59725 3.61795i −0.247125 0.159736i
\(514\) −3.83009 + 6.63392i −0.168938 + 0.292610i
\(515\) 0.899313 0.0396285
\(516\) 11.6803 1.85849i 0.514197 0.0818156i
\(517\) −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
\(521\) 3.40615 5.89962i 0.149226 0.258467i −0.781716 0.623635i \(-0.785655\pi\)
0.930942 + 0.365168i \(0.118988\pi\)
\(522\) 4.38727 20.7858i 0.192026 0.909770i
\(523\) −14.7535 25.5538i −0.645125 1.11739i −0.984273 0.176656i \(-0.943472\pi\)
0.339148 0.940733i \(-0.389861\pi\)
\(524\) 3.18194 + 5.51129i 0.139004 + 0.240762i
\(525\) 0 0
\(526\) −1.54746 + 2.68029i −0.0674727 + 0.116866i
\(527\) −14.3365 −0.624510
\(528\) −5.44282 + 0.866025i −0.236868 + 0.0376889i
\(529\) −17.9863 −0.782014
\(530\) −3.27292 5.66886i −0.142166 0.246239i
\(531\) 3.20765 1.04728i 0.139200 0.0454479i
\(532\) 0 0
\(533\) 15.9789 + 27.6763i 0.692125 + 1.19879i
\(534\) −0.245960 0.303294i −0.0106437 0.0131248i
\(535\) 18.1014 + 31.3525i 0.782591 + 1.35549i
\(536\) 5.48345 + 9.49761i 0.236849 + 0.410234i
\(537\) 12.0383 1.91546i 0.519491 0.0826580i
\(538\) −13.4451 23.2877i −0.579661 1.00400i
\(539\) 0 0
\(540\) 13.8856 + 8.97539i 0.597543 + 0.386239i
\(541\) 14.7008 + 25.4626i 0.632038 + 1.09472i 0.987135 + 0.159892i \(0.0511145\pi\)
−0.355097 + 0.934829i \(0.615552\pi\)
\(542\) 22.2164 0.954277
\(543\) 14.1465 + 17.4441i 0.607085 + 0.748599i
\(544\) 1.52175 0.0652446
\(545\) −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 \(0.561859\pi\)
\(548\) −1.37072 2.37416i −0.0585544 0.101419i
\(549\) 6.97537 + 6.26271i 0.297701 + 0.267286i
\(550\) 8.15335 14.1220i 0.347660 0.602165i
\(551\) 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
\(555\) −1.97141 + 5.14663i −0.0836817 + 0.218462i
\(556\) −7.96690 −0.337872
\(557\) −3.36909 + 5.83543i −0.142753 + 0.247255i −0.928532 0.371252i \(-0.878929\pi\)
0.785779 + 0.618507i \(0.212262\pi\)
\(558\) 5.83693 27.6539i 0.247097 1.17068i
\(559\) −38.9475 −1.64730
\(560\) 0 0
\(561\) 8.28263 1.31788i 0.349693 0.0556408i
\(562\) 23.3984 0.987001
\(563\) −0.729964 1.26433i −0.0307643 0.0532853i 0.850233 0.526406i \(-0.176461\pi\)
−0.880998 + 0.473121i \(0.843127\pi\)
\(564\) 6.35868 + 7.84092i 0.267749 + 0.330162i
\(565\) −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 −0.994901 0.100853i \(-0.967843\pi\)
0.584792 + 0.811183i \(0.301176\pi\)
\(570\) 4.45254 + 5.49044i 0.186496 + 0.229969i
\(571\) 10.9629 + 18.9884i 0.458785 + 0.794638i 0.998897 0.0469545i \(-0.0149516\pi\)
−0.540112 + 0.841593i \(0.681618\pi\)
\(572\) 18.1488 0.758841
\(573\) −3.38783 + 0.539049i −0.141529 + 0.0225191i
\(574\) 0 0
\(575\) 11.4750 0.478540
\(576\) −0.619562 + 2.93533i −0.0258151 + 0.122305i
\(577\) −12.3655 + 21.4177i −0.514783 + 0.891631i 0.485069 + 0.874476i \(0.338794\pi\)
−0.999853 + 0.0171554i \(0.994539\pi\)
\(578\) 14.6843 0.610785
\(579\) −2.81642 + 7.35265i −0.117046 + 0.305566i
\(580\) −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
\(584\) −2.48345 + 4.30146i −0.102766 + 0.177996i
\(585\) −40.5134 36.3743i −1.67502 1.50389i
\(586\) 12.9315 + 22.3980i 0.534194 + 0.925251i
\(587\) 18.0796 + 31.3148i 0.746226 + 1.29250i 0.949620 + 0.313404i \(0.101469\pi\)
−0.203394 + 0.979097i \(0.565197\pi\)
\(588\) 0 0
\(589\) 6.04187 10.4648i 0.248951 0.431196i
\(590\) −3.57893 −0.147342
\(591\) −23.7993 29.3470i −0.978973 1.20717i
\(592\) −1.00000 −0.0410997
\(593\) 7.55391 + 13.0838i 0.310202 + 0.537285i 0.978406 0.206693i \(-0.0662700\pi\)
−0.668204 + 0.743978i \(0.732937\pi\)
\(594\) −0.830095 + 16.5130i −0.0340592 + 0.677537i
\(595\) 0 0
\(596\) 11.6300 + 20.1437i 0.476382 + 0.825118i
\(597\) −21.0098 + 3.34295i −0.859876 + 0.136818i
\(598\) 6.38564 + 11.0603i 0.261128 + 0.452287i
\(599\) 2.72708 + 4.72345i 0.111426 + 0.192995i 0.916345 0.400389i \(-0.131125\pi\)
−0.804920 + 0.593384i \(0.797792\pi\)
\(600\) −5.59097 6.89425i −0.228250 0.281456i
\(601\) 3.36840 + 5.83424i 0.137400 + 0.237984i 0.926512 0.376266i \(-0.122792\pi\)
−0.789112 + 0.614250i \(0.789459\pi\)
\(602\) 0 0
\(603\) 31.2759 10.2114i 1.27365 0.415839i
\(604\) 4.06238 + 7.03625i 0.165296 + 0.286301i
\(605\) −2.78495 −0.113224
\(606\) −31.7977 + 5.05944i −1.29169 + 0.205526i
\(607\) −6.67059 −0.270751 −0.135376 0.990794i \(-0.543224\pi\)
−0.135376 + 0.990794i \(0.543224\pi\)
\(608\) −0.641315 + 1.11079i −0.0260088 + 0.0450485i
\(609\) 0 0
\(610\) −4.97141 8.61073i −0.201287 0.348638i
\(611\) −16.6219 28.7899i −0.672449 1.16472i
\(612\) 0.942820 4.46684i 0.0381112 0.180561i
\(613\) 0.654988 1.13447i 0.0264547 0.0458209i −0.852495 0.522735i \(-0.824912\pi\)
0.878950 + 0.476915i \(0.158245\pi\)
\(614\) −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 \(-0.0776589\pi\)
\(618\) 0.483448 0.0769231i 0.0194471 0.00309430i
\(619\) 16.4484 0.661118 0.330559 0.943785i \(-0.392763\pi\)
0.330559 + 0.943785i \(0.392763\pi\)
\(620\) −14.9887 + 25.9611i −0.601959 + 1.04262i
\(621\) −10.3554 + 5.30420i −0.415549 + 0.212850i
\(622\) 1.70370 0.0683120
\(623\) 0 0
\(624\) 3.53379 9.22544i 0.141465 0.369313i
\(625\) −24.3606 −0.974425
\(626\) 1.42107 + 2.46136i 0.0567972 + 0.0983757i
\(627\) −2.52859 + 6.60123i −0.100982 + 0.263628i
\(628\) −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
\(633\) −28.4922 + 4.53349i −1.13246 + 0.180190i
\(634\) −12.4601 21.5815i −0.494852 0.857109i
\(635\) 63.9740 2.53873
\(636\) −2.24433 2.76748i −0.0889933 0.109738i
\(637\) 0 0
\(638\) −22.5322 −0.892057
\(639\) −5.38401 + 25.5081i −0.212988 + 1.00908i
\(640\) 1.59097 2.75564i 0.0628887 0.108926i
\(641\) 27.8993 1.10196 0.550978 0.834520i \(-0.314255\pi\)
0.550978 + 0.834520i \(0.314255\pi\)
\(642\) 12.4126 + 15.3060i 0.489886 + 0.604080i
\(643\) −14.2524 + 24.6859i −0.562060 + 0.973516i 0.435257 + 0.900306i \(0.356658\pi\)
−0.997317 + 0.0732100i \(0.976676\pi\)
\(644\) 0 0
\(645\) −13.4617 + 35.1436i −0.530054 + 1.38378i
\(646\) 0.975923 1.69035i 0.0383972 0.0665059i
\(647\) −8.35705 + 14.4748i −0.328550 + 0.569065i −0.982224 0.187711i \(-0.939893\pi\)
0.653675 + 0.756776i \(0.273226\pi\)
\(648\) 8.23229 + 3.63723i 0.323395 + 0.142884i
\(649\) −1.78947 3.09945i −0.0702427 0.121664i
\(650\) 14.6150 + 25.3140i 0.573249 + 0.992897i
\(651\) 0 0
\(652\) −1.99028 + 3.44727i −0.0779456 + 0.135006i
\(653\) 38.1650 1.49351 0.746756 0.665098i \(-0.231610\pi\)
0.746756 + 0.665098i \(0.231610\pi\)
\(654\) −2.73912 + 7.15085i −0.107108 + 0.279620i
\(655\) −20.2495 −0.791214
\(656\) 2.80150 + 4.85235i 0.109380 + 0.189452i
\(657\) 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 \(0.778873\pi\)
\(660\) 6.27292 16.3763i 0.244173 0.637446i
\(661\) −10.0419 17.3930i −0.390584 0.676511i 0.601943 0.798539i \(-0.294393\pi\)
−0.992527 + 0.122028i \(0.961060\pi\)
\(662\) −3.58577 6.21074i −0.139365 0.241387i
\(663\) −5.37756 + 14.0388i −0.208847 + 0.545224i
\(664\) −4.03379 6.98673i −0.156541 0.271138i
\(665\) 0 0
\(666\) −0.619562 + 2.93533i −0.0240075 + 0.113742i
\(667\) −7.92790 13.7315i −0.306970 0.531687i
\(668\) 5.23912 0.202708
\(669\) −6.60262 + 17.2370i −0.255272 + 0.666422i
\(670\) −34.8960 −1.34815
\(671\) 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 \(-0.394554\pi\)
\(674\) 10.9211 + 18.9158i 0.420664 + 0.728611i
\(675\) −23.7008 + 12.1399i −0.912245 + 0.467266i
\(676\) −9.76608 + 16.9153i −0.375618 + 0.650590i
\(677\) −0.358685 + 0.621261i −0.0137854 + 0.0238770i −0.872836 0.488014i \(-0.837721\pi\)
0.859050 + 0.511891i \(0.171055\pi\)
\(678\) −1.99192 + 5.20018i −0.0764992 + 0.199712i
\(679\) 0 0
\(680\) −2.42107 + 4.19341i −0.0928437 + 0.160810i
\(681\) 15.8279 + 19.5174i 0.606527 + 0.747910i
\(682\) −29.9773 −1.14789
\(683\) −10.5270 + 18.2332i −0.402803 + 0.697675i −0.994063 0.108806i \(-0.965297\pi\)
0.591260 + 0.806481i \(0.298631\pi\)
\(684\) 2.86320 + 2.57067i 0.109477 + 0.0982921i
\(685\) 8.72313 0.333294
\(686\) 0 0
\(687\) −11.1819 13.7885i −0.426618 0.526064i
\(688\) −6.82846 −0.260333
\(689\) 5.86677 + 10.1615i 0.223506 + 0.387124i
\(690\) 12.1871 1.93914i 0.463957 0.0738217i
\(691\) 2.92395 5.06442i 0.111232 0.192660i −0.805035 0.593227i \(-0.797854\pi\)
0.916267 + 0.400567i \(0.131187\pi\)
\(692\) −2.55159 −0.0969968
\(693\) 0 0
\(694\) 2.11109 0.0801359
\(695\) 12.6751 21.9539i 0.480794 0.832760i
\(696\) −4.38727 + 11.4536i −0.166299 + 0.434147i
\(697\) −4.26320 7.38408i −0.161480 0.279692i
\(698\) −36.2164 −1.37081
\(699\) −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 \(0.437864\pi\)
\(702\) −24.8903 16.0886i −0.939423 0.607224i
\(703\) −0.641315 + 1.11079i −0.0241877 + 0.0418942i
\(704\) 3.18194 0.119924
\(705\) −31.7233 + 5.04759i −1.19477 + 0.190103i
\(706\) 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 0.0916356 + 0.995793i \(0.470790\pi\)
−0.908200 + 0.418538i \(0.862543\pi\)
\(710\) 13.8256 23.9466i 0.518865 0.898700i
\(711\) 9.23818 + 8.29434i 0.346459 + 0.311062i
\(712\) 0.112725 + 0.195246i 0.00422455 + 0.00731714i
\(713\) −10.5475 18.2687i −0.395006 0.684170i
\(714\) 0 0
\(715\) −28.8743 + 50.0117i −1.07984 + 1.87033i
\(716\) −7.03775 −0.263013
\(717\) −21.0744 + 3.35322i −0.787039 + 0.125228i
\(718\) 32.4419 1.21072
\(719\) −25.4412 44.0654i −0.948796 1.64336i −0.747966 0.663737i \(-0.768969\pi\)
−0.200830 0.979626i \(-0.564364\pi\)
\(720\) −7.10301 6.37731i −0.264714 0.237668i
\(721\) 0 0
\(722\) −8.67743 15.0297i −0.322941 0.559349i
\(723\) 14.1826 + 17.4887i 0.527458 + 0.650410i
\(724\) −6.48345 11.2297i −0.240955 0.417347i
\(725\) −18.1449 31.4279i −0.673884 1.16720i
\(726\) −1.49712 + 0.238212i −0.0555634 + 0.00884088i
\(727\) −6.07210 10.5172i −0.225202 0.390061i 0.731178 0.682186i \(-0.238971\pi\)
−0.956380 + 0.292126i \(0.905637\pi\)
\(728\) 0 0
\(729\) 15.7769 21.9110i 0.584329 0.811517i
\(730\) −7.90219 13.6870i −0.292473 0.506579i
\(731\) 10.3912 0.384334
\(732\) −3.40903 4.20368i −0.126001 0.155373i
\(733\) 46.1696 1.70531 0.852657 0.522470i \(-0.174989\pi\)
0.852657 + 0.522470i \(0.174989\pi\)
\(734\) 9.05555 15.6847i 0.334246 0.578932i
\(735\) 0 0
\(736\) 1.11956 + 1.93914i 0.0412676 + 0.0714776i
\(737\) −17.4480 30.2209i −0.642706 1.11320i
\(738\) 15.9789 5.21700i 0.588193 0.192041i
\(739\) −2.49604 + 4.32327i −0.0918184 + 0.159034i −0.908276 0.418371i \(-0.862601\pi\)
0.816458 + 0.577405i \(0.195935\pi\)
\(740\) 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 \(0.971202\pi\)
\(744\) −5.83693 + 15.2381i −0.213992 + 0.558656i
\(745\) −74.0118 −2.71158
\(746\) −5.83530 + 10.1070i −0.213645 + 0.370045i
\(747\) −23.0075 + 7.51179i −0.841801 + 0.274842i
\(748\) −4.84213 −0.177046
\(749\) 0 0
\(750\) 0.679065 0.108048i 0.0247959 0.00394536i
\(751\) 3.29630 0.120284 0.0601419 0.998190i \(-0.480845\pi\)
0.0601419 + 0.998190i \(0.480845\pi\)
\(752\) −2.91423 5.04759i −0.106271 0.184067i
\(753\) −5.57605 6.87585i −0.203203 0.250570i
\(754\) 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
\(759\) 7.77292 + 9.58481i 0.282139 + 0.347907i
\(760\) −2.04063 3.53447i −0.0740214 0.128209i
\(761\) −14.0676 −0.509950 −0.254975 0.966948i \(-0.582067\pi\)
−0.254975 + 0.966948i \(0.582067\pi\)
\(762\) 34.3908 5.47204i 1.24585 0.198231i
\(763\) 0 0
\(764\) 1.98057 0.0716545
\(765\) 10.8090 + 9.70470i 0.390801 + 0.350874i
\(766\) 0.824893 1.42876i 0.0298046 0.0516231i
\(767\) 6.41531 0.231643
\(768\) 0.619562 1.61745i 0.0223565 0.0583647i
\(769\) −11.3461 + 19.6520i −0.409151 + 0.708669i −0.994795 0.101899i \(-0.967508\pi\)
0.585644 + 0.810568i \(0.300842\pi\)
\(770\) 0 0
\(771\) −8.35705 10.3051i −0.300972 0.371129i
\(772\) 2.27292 3.93680i 0.0818040 0.141689i
\(773\) −0.327772 + 0.567717i −0.0117891 + 0.0204194i −0.871860 0.489756i \(-0.837086\pi\)
0.860071 + 0.510175i \(0.170419\pi\)