Properties

Label 414.2.i.d.361.1
Level $414$
Weight $2$
Character 414.361
Analytic conductor $3.306$
Analytic rank $0$
Dimension $10$
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] = [414,2,Mod(55,414)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(414, base_ring=CyclotomicField(22))
 
chi = DirichletCharacter(H, H._module([0, 10]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("414.55");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 414 = 2 \cdot 3^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 414.i (of order \(11\), degree \(10\), 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: \(3.30580664368\)
Analytic rank: \(0\)
Dimension: \(10\)
Coefficient field: \(\Q(\zeta_{22})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 138)
Sato-Tate group: $\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label 361.1
Root \(-0.841254 - 0.540641i\) of defining polynomial
Character \(\chi\) \(=\) 414.361
Dual form 414.2.i.d.289.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.654861 - 0.755750i) q^{2} +(-0.142315 - 0.989821i) q^{4} +(0.614354 + 1.34525i) q^{5} +(3.07385 - 0.902563i) q^{7} +(-0.841254 - 0.540641i) q^{8} +O(q^{10})\) \(q+(0.654861 - 0.755750i) q^{2} +(-0.142315 - 0.989821i) q^{4} +(0.614354 + 1.34525i) q^{5} +(3.07385 - 0.902563i) q^{7} +(-0.841254 - 0.540641i) q^{8} +(1.41899 + 0.416652i) q^{10} +(0.0362090 + 0.0417874i) q^{11} +(0.773100 + 0.227003i) q^{13} +(1.33083 - 2.91411i) q^{14} +(-0.959493 + 0.281733i) q^{16} +(0.293103 - 2.03857i) q^{17} +(0.523231 + 3.63915i) q^{19} +(1.24412 - 0.799549i) q^{20} +0.0552927 q^{22} +(4.62936 + 1.25259i) q^{23} +(1.84204 - 2.12583i) q^{25} +(0.677830 - 0.435615i) q^{26} +(-1.33083 - 2.91411i) q^{28} +(1.04541 - 7.27098i) q^{29} +(-6.69256 - 4.30105i) q^{31} +(-0.415415 + 0.909632i) q^{32} +(-1.34871 - 1.55649i) q^{34} +(3.10260 + 3.58059i) q^{35} +(-1.28287 + 2.80909i) q^{37} +(3.09293 + 1.98771i) q^{38} +(0.210468 - 1.46384i) q^{40} +(0.606395 + 1.32782i) q^{41} +(-10.5428 + 6.77544i) q^{43} +(0.0362090 - 0.0417874i) q^{44} +(3.97823 - 2.67837i) q^{46} +1.27459 q^{47} +(2.74514 - 1.76419i) q^{49} +(-0.400315 - 2.78425i) q^{50} +(0.114669 - 0.797537i) q^{52} +(-10.5975 + 3.11170i) q^{53} +(-0.0339693 + 0.0743823i) q^{55} +(-3.07385 - 0.902563i) q^{56} +(-4.81044 - 5.55155i) q^{58} +(-5.14362 - 1.51030i) q^{59} +(10.2645 + 6.59662i) q^{61} +(-7.63321 + 2.24131i) q^{62} +(0.415415 + 0.909632i) q^{64} +(0.169582 + 1.17947i) q^{65} +(-2.96073 + 3.41687i) q^{67} -2.05954 q^{68} +4.73780 q^{70} +(-9.56286 + 11.0361i) q^{71} +(1.40345 + 9.76122i) q^{73} +(1.28287 + 2.80909i) q^{74} +(3.52765 - 1.03581i) q^{76} +(0.149017 + 0.0957672i) q^{77} +(-3.47320 - 1.01982i) q^{79} +(-0.968468 - 1.11767i) q^{80} +(1.40060 + 0.411254i) q^{82} +(4.16838 - 9.12749i) q^{83} +(2.92245 - 0.858110i) q^{85} +(-1.78352 + 12.4047i) q^{86} +(-0.00786897 - 0.0547299i) q^{88} +(6.94243 - 4.46163i) q^{89} +2.58128 q^{91} +(0.581014 - 4.76051i) q^{92} +(0.834679 - 0.963271i) q^{94} +(-4.57411 + 2.93960i) q^{95} +(2.91463 + 6.38215i) q^{97} +(0.464395 - 3.22994i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q + q^{2} - q^{4} - 8 q^{5} + 8 q^{7} + q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 10 q + q^{2} - q^{4} - 8 q^{5} + 8 q^{7} + q^{8} - 3 q^{10} - 7 q^{11} + 3 q^{13} + 3 q^{14} - q^{16} - 4 q^{17} + 3 q^{20} - 26 q^{22} + 12 q^{23} - 15 q^{25} - 3 q^{26} - 3 q^{28} + 25 q^{29} + 6 q^{31} + q^{32} - 7 q^{34} - 2 q^{35} + 9 q^{37} - 11 q^{38} - 3 q^{40} - 24 q^{41} - 30 q^{43} - 7 q^{44} + 21 q^{46} + 48 q^{47} + 9 q^{49} - 7 q^{50} + 14 q^{52} - 15 q^{53} - 23 q^{55} - 8 q^{56} - 3 q^{58} - 5 q^{59} + 12 q^{61} - 28 q^{62} - q^{64} + 13 q^{65} + 18 q^{67} + 18 q^{68} + 2 q^{70} - 28 q^{71} + 19 q^{73} - 9 q^{74} + 22 q^{76} + 12 q^{77} - 52 q^{79} - 8 q^{80} - 20 q^{82} - 7 q^{83} + 23 q^{85} - 14 q^{86} - 4 q^{88} - 3 q^{89} + 42 q^{91} + 23 q^{92} + 29 q^{94} - 22 q^{95} + 51 q^{97} + 2 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/414\mathbb{Z}\right)^\times\).

\(n\) \(47\) \(235\)
\(\chi(n)\) \(1\) \(e\left(\frac{4}{11}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.654861 0.755750i 0.463056 0.534396i
\(3\) 0 0
\(4\) −0.142315 0.989821i −0.0711574 0.494911i
\(5\) 0.614354 + 1.34525i 0.274747 + 0.601613i 0.995829 0.0912371i \(-0.0290821\pi\)
−0.721082 + 0.692850i \(0.756355\pi\)
\(6\) 0 0
\(7\) 3.07385 0.902563i 1.16180 0.341137i 0.356671 0.934230i \(-0.383912\pi\)
0.805134 + 0.593093i \(0.202093\pi\)
\(8\) −0.841254 0.540641i −0.297428 0.191145i
\(9\) 0 0
\(10\) 1.41899 + 0.416652i 0.448723 + 0.131757i
\(11\) 0.0362090 + 0.0417874i 0.0109174 + 0.0125994i 0.761182 0.648538i \(-0.224619\pi\)
−0.750265 + 0.661138i \(0.770074\pi\)
\(12\) 0 0
\(13\) 0.773100 + 0.227003i 0.214419 + 0.0629592i 0.387178 0.922005i \(-0.373450\pi\)
−0.172759 + 0.984964i \(0.555268\pi\)
\(14\) 1.33083 2.91411i 0.355679 0.778829i
\(15\) 0 0
\(16\) −0.959493 + 0.281733i −0.239873 + 0.0704331i
\(17\) 0.293103 2.03857i 0.0710879 0.494427i −0.922909 0.385018i \(-0.874195\pi\)
0.993997 0.109409i \(-0.0348957\pi\)
\(18\) 0 0
\(19\) 0.523231 + 3.63915i 0.120037 + 0.834879i 0.957510 + 0.288399i \(0.0931231\pi\)
−0.837473 + 0.546479i \(0.815968\pi\)
\(20\) 1.24412 0.799549i 0.278194 0.178785i
\(21\) 0 0
\(22\) 0.0552927 0.0117884
\(23\) 4.62936 + 1.25259i 0.965289 + 0.261183i
\(24\) 0 0
\(25\) 1.84204 2.12583i 0.368409 0.425167i
\(26\) 0.677830 0.435615i 0.132933 0.0854311i
\(27\) 0 0
\(28\) −1.33083 2.91411i −0.251503 0.550715i
\(29\) 1.04541 7.27098i 0.194128 1.35019i −0.626811 0.779171i \(-0.715640\pi\)
0.820939 0.571016i \(-0.193451\pi\)
\(30\) 0 0
\(31\) −6.69256 4.30105i −1.20202 0.772491i −0.222715 0.974884i \(-0.571492\pi\)
−0.979305 + 0.202392i \(0.935128\pi\)
\(32\) −0.415415 + 0.909632i −0.0734357 + 0.160802i
\(33\) 0 0
\(34\) −1.34871 1.55649i −0.231302 0.266937i
\(35\) 3.10260 + 3.58059i 0.524435 + 0.605230i
\(36\) 0 0
\(37\) −1.28287 + 2.80909i −0.210902 + 0.461811i −0.985288 0.170903i \(-0.945332\pi\)
0.774386 + 0.632713i \(0.218059\pi\)
\(38\) 3.09293 + 1.98771i 0.501740 + 0.322448i
\(39\) 0 0
\(40\) 0.210468 1.46384i 0.0332779 0.231453i
\(41\) 0.606395 + 1.32782i 0.0947030 + 0.207371i 0.951055 0.309022i \(-0.100002\pi\)
−0.856352 + 0.516393i \(0.827274\pi\)
\(42\) 0 0
\(43\) −10.5428 + 6.77544i −1.60776 + 1.03324i −0.644526 + 0.764582i \(0.722945\pi\)
−0.963234 + 0.268663i \(0.913418\pi\)
\(44\) 0.0362090 0.0417874i 0.00545871 0.00629969i
\(45\) 0 0
\(46\) 3.97823 2.67837i 0.586559 0.394904i
\(47\) 1.27459 0.185918 0.0929591 0.995670i \(-0.470367\pi\)
0.0929591 + 0.995670i \(0.470367\pi\)
\(48\) 0 0
\(49\) 2.74514 1.76419i 0.392163 0.252028i
\(50\) −0.400315 2.78425i −0.0566130 0.393752i
\(51\) 0 0
\(52\) 0.114669 0.797537i 0.0159017 0.110598i
\(53\) −10.5975 + 3.11170i −1.45567 + 0.427424i −0.911413 0.411492i \(-0.865008\pi\)
−0.544260 + 0.838916i \(0.683190\pi\)
\(54\) 0 0
\(55\) −0.0339693 + 0.0743823i −0.00458041 + 0.0100297i
\(56\) −3.07385 0.902563i −0.410760 0.120610i
\(57\) 0 0
\(58\) −4.81044 5.55155i −0.631642 0.728954i
\(59\) −5.14362 1.51030i −0.669642 0.196625i −0.0707986 0.997491i \(-0.522555\pi\)
−0.598844 + 0.800866i \(0.704373\pi\)
\(60\) 0 0
\(61\) 10.2645 + 6.59662i 1.31424 + 0.844611i 0.994686 0.102957i \(-0.0328303\pi\)
0.319555 + 0.947568i \(0.396467\pi\)
\(62\) −7.63321 + 2.24131i −0.969419 + 0.284647i
\(63\) 0 0
\(64\) 0.415415 + 0.909632i 0.0519269 + 0.113704i
\(65\) 0.169582 + 1.17947i 0.0210341 + 0.146295i
\(66\) 0 0
\(67\) −2.96073 + 3.41687i −0.361711 + 0.417437i −0.907212 0.420673i \(-0.861794\pi\)
0.545501 + 0.838110i \(0.316339\pi\)
\(68\) −2.05954 −0.249756
\(69\) 0 0
\(70\) 4.73780 0.566275
\(71\) −9.56286 + 11.0361i −1.13490 + 1.30975i −0.190228 + 0.981740i \(0.560923\pi\)
−0.944675 + 0.328008i \(0.893623\pi\)
\(72\) 0 0
\(73\) 1.40345 + 9.76122i 0.164262 + 1.14246i 0.890487 + 0.455008i \(0.150364\pi\)
−0.726226 + 0.687456i \(0.758727\pi\)
\(74\) 1.28287 + 2.80909i 0.149130 + 0.326550i
\(75\) 0 0
\(76\) 3.52765 1.03581i 0.404649 0.118816i
\(77\) 0.149017 + 0.0957672i 0.0169820 + 0.0109137i
\(78\) 0 0
\(79\) −3.47320 1.01982i −0.390765 0.114739i 0.0804469 0.996759i \(-0.474365\pi\)
−0.471212 + 0.882020i \(0.656183\pi\)
\(80\) −0.968468 1.11767i −0.108278 0.124959i
\(81\) 0 0
\(82\) 1.40060 + 0.411254i 0.154671 + 0.0454155i
\(83\) 4.16838 9.12749i 0.457540 1.00187i −0.530502 0.847684i \(-0.677996\pi\)
0.988041 0.154188i \(-0.0492763\pi\)
\(84\) 0 0
\(85\) 2.92245 0.858110i 0.316985 0.0930751i
\(86\) −1.78352 + 12.4047i −0.192322 + 1.33763i
\(87\) 0 0
\(88\) −0.00786897 0.0547299i −0.000838835 0.00583422i
\(89\) 6.94243 4.46163i 0.735896 0.472932i −0.118237 0.992985i \(-0.537724\pi\)
0.854134 + 0.520054i \(0.174088\pi\)
\(90\) 0 0
\(91\) 2.58128 0.270591
\(92\) 0.581014 4.76051i 0.0605749 0.496317i
\(93\) 0 0
\(94\) 0.834679 0.963271i 0.0860906 0.0993539i
\(95\) −4.57411 + 2.93960i −0.469294 + 0.301597i
\(96\) 0 0
\(97\) 2.91463 + 6.38215i 0.295936 + 0.648009i 0.997939 0.0641646i \(-0.0204383\pi\)
−0.702004 + 0.712173i \(0.747711\pi\)
\(98\) 0.464395 3.22994i 0.0469110 0.326273i
\(99\) 0 0
\(100\) −2.36635 1.52076i −0.236635 0.152076i
\(101\) −6.37690 + 13.9635i −0.634526 + 1.38942i 0.269943 + 0.962876i \(0.412995\pi\)
−0.904468 + 0.426541i \(0.859732\pi\)
\(102\) 0 0
\(103\) −10.0337 11.5795i −0.988648 1.14096i −0.990015 0.140962i \(-0.954981\pi\)
0.00136697 0.999999i \(-0.499565\pi\)
\(104\) −0.527646 0.608936i −0.0517400 0.0597111i
\(105\) 0 0
\(106\) −4.58820 + 10.0468i −0.445645 + 0.975827i
\(107\) 8.13948 + 5.23093i 0.786873 + 0.505693i 0.871308 0.490736i \(-0.163272\pi\)
−0.0844348 + 0.996429i \(0.526908\pi\)
\(108\) 0 0
\(109\) 1.90704 13.2638i 0.182662 1.27044i −0.667775 0.744363i \(-0.732753\pi\)
0.850437 0.526077i \(-0.176338\pi\)
\(110\) 0.0339693 + 0.0743823i 0.00323884 + 0.00709207i
\(111\) 0 0
\(112\) −2.69505 + 1.73201i −0.254659 + 0.163659i
\(113\) 5.38879 6.21899i 0.506934 0.585033i −0.443377 0.896335i \(-0.646220\pi\)
0.950311 + 0.311302i \(0.100765\pi\)
\(114\) 0 0
\(115\) 1.15902 + 6.99717i 0.108079 + 0.652490i
\(116\) −7.34575 −0.682036
\(117\) 0 0
\(118\) −4.50977 + 2.89825i −0.415158 + 0.266806i
\(119\) −0.938989 6.53081i −0.0860769 0.598678i
\(120\) 0 0
\(121\) 1.56503 10.8850i 0.142275 0.989546i
\(122\) 11.7072 3.43756i 1.05992 0.311222i
\(123\) 0 0
\(124\) −3.30482 + 7.23654i −0.296782 + 0.649861i
\(125\) 11.0864 + 3.25525i 0.991595 + 0.291159i
\(126\) 0 0
\(127\) −12.6731 14.6256i −1.12456 1.29781i −0.949681 0.313219i \(-0.898593\pi\)
−0.174877 0.984590i \(-0.555953\pi\)
\(128\) 0.959493 + 0.281733i 0.0848080 + 0.0249019i
\(129\) 0 0
\(130\) 1.00244 + 0.644227i 0.0879196 + 0.0565025i
\(131\) −20.0561 + 5.88899i −1.75231 + 0.514523i −0.990999 0.133869i \(-0.957260\pi\)
−0.761306 + 0.648392i \(0.775442\pi\)
\(132\) 0 0
\(133\) 4.89289 + 10.7139i 0.424268 + 0.929017i
\(134\) 0.643429 + 4.47515i 0.0555838 + 0.386594i
\(135\) 0 0
\(136\) −1.34871 + 1.55649i −0.115651 + 0.133468i
\(137\) −5.89909 −0.503993 −0.251997 0.967728i \(-0.581087\pi\)
−0.251997 + 0.967728i \(0.581087\pi\)
\(138\) 0 0
\(139\) −4.04356 −0.342971 −0.171485 0.985187i \(-0.554857\pi\)
−0.171485 + 0.985187i \(0.554857\pi\)
\(140\) 3.10260 3.58059i 0.262217 0.302615i
\(141\) 0 0
\(142\) 2.07821 + 14.4543i 0.174399 + 1.21297i
\(143\) 0.0185073 + 0.0405254i 0.00154766 + 0.00338890i
\(144\) 0 0
\(145\) 10.4235 3.06062i 0.865626 0.254171i
\(146\) 8.29611 + 5.33158i 0.686591 + 0.441245i
\(147\) 0 0
\(148\) 2.96306 + 0.870034i 0.243562 + 0.0715164i
\(149\) −5.37873 6.20739i −0.440643 0.508529i 0.491372 0.870950i \(-0.336496\pi\)
−0.932014 + 0.362421i \(0.881950\pi\)
\(150\) 0 0
\(151\) 12.3286 + 3.62000i 1.00328 + 0.294591i 0.741803 0.670617i \(-0.233971\pi\)
0.261482 + 0.965208i \(0.415789\pi\)
\(152\) 1.52730 3.34433i 0.123881 0.271261i
\(153\) 0 0
\(154\) 0.169961 0.0499051i 0.0136959 0.00402147i
\(155\) 1.67437 11.6455i 0.134489 0.935390i
\(156\) 0 0
\(157\) −0.557702 3.87890i −0.0445095 0.309570i −0.999899 0.0142211i \(-0.995473\pi\)
0.955389 0.295349i \(-0.0954360\pi\)
\(158\) −3.04519 + 1.95703i −0.242262 + 0.155693i
\(159\) 0 0
\(160\) −1.47889 −0.116917
\(161\) 15.3605 0.328020i 1.21058 0.0258516i
\(162\) 0 0
\(163\) −10.2975 + 11.8839i −0.806560 + 0.930820i −0.998722 0.0505437i \(-0.983905\pi\)
0.192162 + 0.981363i \(0.438450\pi\)
\(164\) 1.22801 0.789191i 0.0958911 0.0616255i
\(165\) 0 0
\(166\) −4.16838 9.12749i −0.323529 0.708431i
\(167\) −0.572056 + 3.97873i −0.0442670 + 0.307884i 0.955644 + 0.294525i \(0.0951614\pi\)
−0.999911 + 0.0133587i \(0.995748\pi\)
\(168\) 0 0
\(169\) −10.3901 6.67734i −0.799242 0.513641i
\(170\) 1.26528 2.77059i 0.0970429 0.212494i
\(171\) 0 0
\(172\) 8.20687 + 9.47123i 0.625768 + 0.722175i
\(173\) 3.44095 + 3.97106i 0.261610 + 0.301914i 0.871325 0.490707i \(-0.163261\pi\)
−0.609715 + 0.792621i \(0.708716\pi\)
\(174\) 0 0
\(175\) 3.74347 8.19705i 0.282979 0.619638i
\(176\) −0.0465151 0.0298935i −0.00350621 0.00225331i
\(177\) 0 0
\(178\) 1.17445 8.16849i 0.0880288 0.612254i
\(179\) 0.877732 + 1.92196i 0.0656048 + 0.143654i 0.939594 0.342291i \(-0.111203\pi\)
−0.873989 + 0.485945i \(0.838475\pi\)
\(180\) 0 0
\(181\) −0.194228 + 0.124823i −0.0144369 + 0.00927802i −0.547839 0.836584i \(-0.684549\pi\)
0.533402 + 0.845862i \(0.320913\pi\)
\(182\) 1.69038 1.95080i 0.125299 0.144603i
\(183\) 0 0
\(184\) −3.21727 3.55657i −0.237180 0.262194i
\(185\) −4.56705 −0.335776
\(186\) 0 0
\(187\) 0.0957997 0.0615667i 0.00700557 0.00450220i
\(188\) −0.181393 1.26162i −0.0132295 0.0920129i
\(189\) 0 0
\(190\) −0.773802 + 5.38191i −0.0561375 + 0.390445i
\(191\) 4.22482 1.24052i 0.305697 0.0897608i −0.125286 0.992121i \(-0.539985\pi\)
0.430984 + 0.902360i \(0.358167\pi\)
\(192\) 0 0
\(193\) 8.93029 19.5546i 0.642817 1.40757i −0.254886 0.966971i \(-0.582038\pi\)
0.897703 0.440601i \(-0.145235\pi\)
\(194\) 6.73198 + 1.97669i 0.483328 + 0.141918i
\(195\) 0 0
\(196\) −2.13691 2.46613i −0.152636 0.176152i
\(197\) 8.53190 + 2.50519i 0.607873 + 0.178487i 0.571160 0.820838i \(-0.306493\pi\)
0.0367120 + 0.999326i \(0.488312\pi\)
\(198\) 0 0
\(199\) 15.2730 + 9.81535i 1.08267 + 0.695792i 0.955173 0.296047i \(-0.0956685\pi\)
0.127500 + 0.991839i \(0.459305\pi\)
\(200\) −2.69894 + 0.792480i −0.190844 + 0.0560368i
\(201\) 0 0
\(202\) 6.37690 + 13.9635i 0.448677 + 0.982466i
\(203\) −3.34909 23.2934i −0.235060 1.63488i
\(204\) 0 0
\(205\) −1.41370 + 1.63150i −0.0987374 + 0.113949i
\(206\) −15.3219 −1.06752
\(207\) 0 0
\(208\) −0.805738 −0.0558679
\(209\) −0.133125 + 0.153634i −0.00920845 + 0.0106271i
\(210\) 0 0
\(211\) −2.44839 17.0289i −0.168554 1.17232i −0.881876 0.471482i \(-0.843719\pi\)
0.713322 0.700836i \(-0.247190\pi\)
\(212\) 4.58820 + 10.0468i 0.315119 + 0.690014i
\(213\) 0 0
\(214\) 9.28350 2.72588i 0.634607 0.186337i
\(215\) −15.5916 10.0201i −1.06334 0.683368i
\(216\) 0 0
\(217\) −24.4539 7.18031i −1.66004 0.487431i
\(218\) −8.77525 10.1272i −0.594335 0.685899i
\(219\) 0 0
\(220\) 0.0784595 + 0.0230378i 0.00528974 + 0.00155321i
\(221\) 0.689360 1.50949i 0.0463713 0.101539i
\(222\) 0 0
\(223\) 9.25505 2.71753i 0.619764 0.181979i 0.0432473 0.999064i \(-0.486230\pi\)
0.576517 + 0.817085i \(0.304411\pi\)
\(224\) −0.455922 + 3.17101i −0.0304626 + 0.211872i
\(225\) 0 0
\(226\) −1.17109 8.14514i −0.0779001 0.541807i
\(227\) 11.1785 7.18400i 0.741944 0.476819i −0.114263 0.993450i \(-0.536451\pi\)
0.856208 + 0.516632i \(0.172814\pi\)
\(228\) 0 0
\(229\) 10.3343 0.682912 0.341456 0.939898i \(-0.389080\pi\)
0.341456 + 0.939898i \(0.389080\pi\)
\(230\) 6.04711 + 3.70624i 0.398735 + 0.244382i
\(231\) 0 0
\(232\) −4.81044 + 5.55155i −0.315821 + 0.364477i
\(233\) 0.186234 0.119685i 0.0122006 0.00784085i −0.534526 0.845152i \(-0.679510\pi\)
0.546727 + 0.837311i \(0.315874\pi\)
\(234\) 0 0
\(235\) 0.783050 + 1.71464i 0.0510805 + 0.111851i
\(236\) −0.762917 + 5.30620i −0.0496617 + 0.345404i
\(237\) 0 0
\(238\) −5.55056 3.56713i −0.359790 0.231223i
\(239\) −4.19290 + 9.18117i −0.271216 + 0.593881i −0.995409 0.0957174i \(-0.969485\pi\)
0.724192 + 0.689598i \(0.242213\pi\)
\(240\) 0 0
\(241\) 1.63492 + 1.88680i 0.105315 + 0.121540i 0.805960 0.591970i \(-0.201650\pi\)
−0.700645 + 0.713510i \(0.747104\pi\)
\(242\) −7.20147 8.31093i −0.462928 0.534247i
\(243\) 0 0
\(244\) 5.06868 11.0989i 0.324489 0.710532i
\(245\) 4.05976 + 2.60905i 0.259369 + 0.166686i
\(246\) 0 0
\(247\) −0.421587 + 2.93220i −0.0268249 + 0.186572i
\(248\) 3.30482 + 7.23654i 0.209856 + 0.459521i
\(249\) 0 0
\(250\) 9.72018 6.24678i 0.614758 0.395081i
\(251\) 9.41401 10.8643i 0.594207 0.685752i −0.376390 0.926461i \(-0.622835\pi\)
0.970597 + 0.240710i \(0.0773802\pi\)
\(252\) 0 0
\(253\) 0.115282 + 0.238804i 0.00724772 + 0.0150135i
\(254\) −19.3524 −1.21428
\(255\) 0 0
\(256\) 0.841254 0.540641i 0.0525783 0.0337901i
\(257\) −2.43482 16.9346i −0.151880 1.05635i −0.913065 0.407814i \(-0.866291\pi\)
0.761185 0.648535i \(-0.224618\pi\)
\(258\) 0 0
\(259\) −1.40796 + 9.79257i −0.0874863 + 0.608480i
\(260\) 1.14333 0.335712i 0.0709064 0.0208200i
\(261\) 0 0
\(262\) −8.68332 + 19.0138i −0.536457 + 1.17468i
\(263\) −9.43152 2.76934i −0.581573 0.170765i −0.0223034 0.999751i \(-0.507100\pi\)
−0.559269 + 0.828986i \(0.688918\pi\)
\(264\) 0 0
\(265\) −10.6966 12.3445i −0.657086 0.758318i
\(266\) 11.3012 + 3.31834i 0.692922 + 0.203460i
\(267\) 0 0
\(268\) 3.80345 + 2.44433i 0.232332 + 0.149311i
\(269\) 25.9470 7.61874i 1.58202 0.464523i 0.631548 0.775337i \(-0.282420\pi\)
0.950471 + 0.310814i \(0.100602\pi\)
\(270\) 0 0
\(271\) 5.82097 + 12.7462i 0.353599 + 0.774274i 0.999937 + 0.0112226i \(0.00357233\pi\)
−0.646338 + 0.763051i \(0.723700\pi\)
\(272\) 0.293103 + 2.03857i 0.0177720 + 0.123607i
\(273\) 0 0
\(274\) −3.86308 + 4.45824i −0.233377 + 0.269332i
\(275\) 0.155532 0.00937891
\(276\) 0 0
\(277\) −6.65528 −0.399877 −0.199938 0.979808i \(-0.564074\pi\)
−0.199938 + 0.979808i \(0.564074\pi\)
\(278\) −2.64797 + 3.05592i −0.158815 + 0.183282i
\(279\) 0 0
\(280\) −0.674259 4.68958i −0.0402947 0.280256i
\(281\) 6.11673 + 13.3938i 0.364894 + 0.799006i 0.999654 + 0.0262969i \(0.00837151\pi\)
−0.634760 + 0.772709i \(0.718901\pi\)
\(282\) 0 0
\(283\) 13.1361 3.85711i 0.780861 0.229282i 0.133077 0.991106i \(-0.457514\pi\)
0.647784 + 0.761824i \(0.275696\pi\)
\(284\) 12.2847 + 7.89492i 0.728965 + 0.468477i
\(285\) 0 0
\(286\) 0.0427468 + 0.0125516i 0.00252767 + 0.000742191i
\(287\) 3.06241 + 3.53421i 0.180768 + 0.208618i
\(288\) 0 0
\(289\) 12.2415 + 3.59443i 0.720089 + 0.211437i
\(290\) 4.51289 9.88185i 0.265006 0.580282i
\(291\) 0 0
\(292\) 9.46214 2.77833i 0.553730 0.162590i
\(293\) 4.21529 29.3180i 0.246260 1.71278i −0.373203 0.927750i \(-0.621740\pi\)
0.619463 0.785026i \(-0.287350\pi\)
\(294\) 0 0
\(295\) −1.12827 7.84730i −0.0656905 0.456887i
\(296\) 2.59792 1.66958i 0.151001 0.0970425i
\(297\) 0 0
\(298\) −8.21355 −0.475798
\(299\) 3.29462 + 2.01926i 0.190533 + 0.116777i
\(300\) 0 0
\(301\) −26.2917 + 30.3422i −1.51543 + 1.74890i
\(302\) 10.8093 6.94672i 0.622006 0.399739i
\(303\) 0 0
\(304\) −1.52730 3.34433i −0.0875969 0.191810i
\(305\) −2.56803 + 17.8610i −0.147045 + 1.02272i
\(306\) 0 0
\(307\) 7.67787 + 4.93427i 0.438199 + 0.281613i 0.741082 0.671414i \(-0.234313\pi\)
−0.302883 + 0.953028i \(0.597949\pi\)
\(308\) 0.0735851 0.161129i 0.00419290 0.00918118i
\(309\) 0 0
\(310\) −7.70461 8.89160i −0.437593 0.505009i
\(311\) 15.0457 + 17.3636i 0.853162 + 0.984602i 0.999990 0.00456050i \(-0.00145166\pi\)
−0.146827 + 0.989162i \(0.546906\pi\)
\(312\) 0 0
\(313\) 8.20118 17.9581i 0.463558 1.01505i −0.523104 0.852269i \(-0.675226\pi\)
0.986662 0.162782i \(-0.0520466\pi\)
\(314\) −3.29670 2.11866i −0.186043 0.119563i
\(315\) 0 0
\(316\) −0.515155 + 3.58298i −0.0289797 + 0.201558i
\(317\) 8.65385 + 18.9493i 0.486049 + 1.06430i 0.980756 + 0.195238i \(0.0625480\pi\)
−0.494707 + 0.869060i \(0.664725\pi\)
\(318\) 0 0
\(319\) 0.341689 0.219590i 0.0191309 0.0122947i
\(320\) −0.968468 + 1.11767i −0.0541390 + 0.0624797i
\(321\) 0 0
\(322\) 9.81109 11.8235i 0.546750 0.658898i
\(323\) 7.57204 0.421320
\(324\) 0 0
\(325\) 1.90665 1.22533i 0.105762 0.0679692i
\(326\) 2.23785 + 15.5646i 0.123943 + 0.862044i
\(327\) 0 0
\(328\) 0.207742 1.44488i 0.0114706 0.0797799i
\(329\) 3.91790 1.15040i 0.216001 0.0634235i
\(330\) 0 0
\(331\) −6.45836 + 14.1418i −0.354983 + 0.777305i 0.644931 + 0.764241i \(0.276886\pi\)
−0.999915 + 0.0130646i \(0.995841\pi\)
\(332\) −9.62781 2.82698i −0.528395 0.155151i
\(333\) 0 0
\(334\) 2.63231 + 3.03785i 0.144034 + 0.166224i
\(335\) −6.41547 1.88375i −0.350514 0.102920i
\(336\) 0 0
\(337\) 5.95413 + 3.82649i 0.324342 + 0.208442i 0.692671 0.721253i \(-0.256434\pi\)
−0.368329 + 0.929695i \(0.620070\pi\)
\(338\) −11.8505 + 3.47962i −0.644582 + 0.189266i
\(339\) 0 0
\(340\) −1.26528 2.77059i −0.0686197 0.150256i
\(341\) −0.0626013 0.435401i −0.00339005 0.0235783i
\(342\) 0 0
\(343\) −7.83961 + 9.04740i −0.423299 + 0.488513i
\(344\) 12.5322 0.675693
\(345\) 0 0
\(346\) 5.25447 0.282482
\(347\) −16.6438 + 19.2080i −0.893486 + 1.03114i 0.105839 + 0.994383i \(0.466247\pi\)
−0.999324 + 0.0367541i \(0.988298\pi\)
\(348\) 0 0
\(349\) 3.29197 + 22.8962i 0.176215 + 1.22560i 0.865423 + 0.501041i \(0.167049\pi\)
−0.689208 + 0.724563i \(0.742041\pi\)
\(350\) −3.74347 8.19705i −0.200097 0.438151i
\(351\) 0 0
\(352\) −0.0530529 + 0.0155777i −0.00282773 + 0.000830297i
\(353\) −20.2471 13.0120i −1.07765 0.692561i −0.123634 0.992328i \(-0.539455\pi\)
−0.954013 + 0.299767i \(0.903091\pi\)
\(354\) 0 0
\(355\) −20.7213 6.08432i −1.09977 0.322922i
\(356\) −5.40423 6.23681i −0.286424 0.330550i
\(357\) 0 0
\(358\) 2.02732 + 0.595274i 0.107147 + 0.0314612i
\(359\) −7.96450 + 17.4398i −0.420350 + 0.920438i 0.574445 + 0.818543i \(0.305218\pi\)
−0.994795 + 0.101895i \(0.967509\pi\)
\(360\) 0 0
\(361\) 5.26072 1.54469i 0.276880 0.0812992i
\(362\) −0.0328576 + 0.228530i −0.00172696 + 0.0120113i
\(363\) 0 0
\(364\) −0.367354 2.55500i −0.0192546 0.133918i
\(365\) −12.2690 + 7.88483i −0.642191 + 0.412711i
\(366\) 0 0
\(367\) −26.2686 −1.37121 −0.685606 0.727973i \(-0.740463\pi\)
−0.685606 + 0.727973i \(0.740463\pi\)
\(368\) −4.79474 + 0.102391i −0.249943 + 0.00533748i
\(369\) 0 0
\(370\) −2.99078 + 3.45154i −0.155483 + 0.179437i
\(371\) −29.7665 + 19.1298i −1.54540 + 0.993167i
\(372\) 0 0
\(373\) 8.47650 + 18.5609i 0.438896 + 0.961049i 0.991800 + 0.127803i \(0.0407927\pi\)
−0.552903 + 0.833246i \(0.686480\pi\)
\(374\) 0.0162064 0.112718i 0.000838015 0.00582852i
\(375\) 0 0
\(376\) −1.07225 0.689096i −0.0552973 0.0355374i
\(377\) 2.45874 5.38389i 0.126631 0.277284i
\(378\) 0 0
\(379\) −2.61309 3.01566i −0.134225 0.154904i 0.684658 0.728865i \(-0.259952\pi\)
−0.818883 + 0.573961i \(0.805406\pi\)
\(380\) 3.56064 + 4.10920i 0.182657 + 0.210798i
\(381\) 0 0
\(382\) 1.82915 4.00527i 0.0935873 0.204928i
\(383\) −5.31857 3.41804i −0.271766 0.174654i 0.397658 0.917534i \(-0.369823\pi\)
−0.669425 + 0.742880i \(0.733459\pi\)
\(384\) 0 0
\(385\) −0.0372816 + 0.259299i −0.00190005 + 0.0132151i
\(386\) −8.93029 19.5546i −0.454540 0.995304i
\(387\) 0 0
\(388\) 5.90239 3.79324i 0.299648 0.192572i
\(389\) −16.6443 + 19.2085i −0.843900 + 0.973912i −0.999904 0.0138443i \(-0.995593\pi\)
0.156005 + 0.987756i \(0.450139\pi\)
\(390\) 0 0
\(391\) 3.91038 9.07017i 0.197756 0.458698i
\(392\) −3.26315 −0.164814
\(393\) 0 0
\(394\) 7.48050 4.80743i 0.376862 0.242195i
\(395\) −0.761858 5.29884i −0.0383333 0.266614i
\(396\) 0 0
\(397\) 0.488864 3.40012i 0.0245354 0.170647i −0.973869 0.227109i \(-0.927073\pi\)
0.998405 + 0.0564614i \(0.0179818\pi\)
\(398\) 17.4196 5.11486i 0.873167 0.256385i
\(399\) 0 0
\(400\) −1.16851 + 2.55869i −0.0584256 + 0.127934i
\(401\) −8.01654 2.35387i −0.400327 0.117547i 0.0753705 0.997156i \(-0.475986\pi\)
−0.475697 + 0.879609i \(0.657804\pi\)
\(402\) 0 0
\(403\) −4.19767 4.84437i −0.209101 0.241315i
\(404\) 14.7289 + 4.32479i 0.732789 + 0.215166i
\(405\) 0 0
\(406\) −19.7972 12.7229i −0.982518 0.631426i
\(407\) −0.163836 + 0.0481065i −0.00812103 + 0.00238455i
\(408\) 0 0
\(409\) −1.73917 3.80824i −0.0859962 0.188305i 0.861748 0.507336i \(-0.169370\pi\)
−0.947744 + 0.319031i \(0.896643\pi\)
\(410\) 0.307227 + 2.13681i 0.0151729 + 0.105530i
\(411\) 0 0
\(412\) −10.0337 + 11.5795i −0.494324 + 0.570480i
\(413\) −17.1738 −0.845070
\(414\) 0 0
\(415\) 14.8396 0.728447
\(416\) −0.527646 + 0.608936i −0.0258700 + 0.0298556i
\(417\) 0 0
\(418\) 0.0289308 + 0.201218i 0.00141505 + 0.00984191i
\(419\) −3.73254 8.17311i −0.182346 0.399283i 0.796280 0.604928i \(-0.206798\pi\)
−0.978627 + 0.205645i \(0.934071\pi\)
\(420\) 0 0
\(421\) 6.48508 1.90419i 0.316063 0.0928046i −0.119853 0.992792i \(-0.538242\pi\)
0.435917 + 0.899987i \(0.356424\pi\)
\(422\) −14.4729 9.30119i −0.704532 0.452775i
\(423\) 0 0
\(424\) 10.5975 + 3.11170i 0.514658 + 0.151117i
\(425\) −3.79376 4.37823i −0.184024 0.212375i
\(426\) 0 0
\(427\) 37.5055 + 11.0126i 1.81502 + 0.532938i
\(428\) 4.01932 8.80107i 0.194281 0.425416i
\(429\) 0 0
\(430\) −17.7831 + 5.22158i −0.857576 + 0.251807i
\(431\) −3.22681 + 22.4430i −0.155430 + 1.08104i 0.751492 + 0.659742i \(0.229334\pi\)
−0.906922 + 0.421298i \(0.861575\pi\)
\(432\) 0 0
\(433\) −4.26292 29.6492i −0.204863 1.42485i −0.789596 0.613627i \(-0.789710\pi\)
0.584734 0.811225i \(-0.301199\pi\)
\(434\) −21.4404 + 13.7789i −1.02917 + 0.661409i
\(435\) 0 0
\(436\) −13.4002 −0.641752
\(437\) −2.13614 + 17.5024i −0.102185 + 0.837251i
\(438\) 0 0
\(439\) 0.983215 1.13469i 0.0469263 0.0541559i −0.731801 0.681518i \(-0.761320\pi\)
0.778727 + 0.627362i \(0.215865\pi\)
\(440\) 0.0687909 0.0442092i 0.00327948 0.00210759i
\(441\) 0 0
\(442\) −0.689360 1.50949i −0.0327895 0.0717990i
\(443\) −0.838999 + 5.83536i −0.0398620 + 0.277246i −0.999997 0.00228902i \(-0.999271\pi\)
0.960135 + 0.279536i \(0.0901805\pi\)
\(444\) 0 0
\(445\) 10.2671 + 6.59827i 0.486707 + 0.312788i
\(446\) 4.00700 8.77411i 0.189737 0.415466i
\(447\) 0 0
\(448\) 2.09792 + 2.42113i 0.0991175 + 0.114388i
\(449\) −24.1373 27.8559i −1.13911 1.31460i −0.942533 0.334114i \(-0.891563\pi\)
−0.196577 0.980488i \(-0.562983\pi\)
\(450\) 0 0
\(451\) −0.0335292 + 0.0734187i −0.00157883 + 0.00345715i
\(452\) −6.92259 4.44888i −0.325611 0.209258i
\(453\) 0 0
\(454\) 1.89107 13.1527i 0.0887523 0.617286i
\(455\) 1.58582 + 3.47245i 0.0743442 + 0.162791i
\(456\) 0 0
\(457\) −4.87731 + 3.13445i −0.228151 + 0.146624i −0.649723 0.760171i \(-0.725115\pi\)
0.421572 + 0.906795i \(0.361479\pi\)
\(458\) 6.76755 7.81017i 0.316227 0.364945i
\(459\) 0 0
\(460\) 6.76101 2.14303i 0.315233 0.0999192i
\(461\) 19.1277 0.890864 0.445432 0.895316i \(-0.353050\pi\)
0.445432 + 0.895316i \(0.353050\pi\)
\(462\) 0 0
\(463\) −17.1083 + 10.9948i −0.795091 + 0.510974i −0.874010 0.485907i \(-0.838489\pi\)
0.0789197 + 0.996881i \(0.474853\pi\)
\(464\) 1.04541 + 7.27098i 0.0485319 + 0.337547i
\(465\) 0 0
\(466\) 0.0315052 0.219124i 0.00145945 0.0101507i
\(467\) 26.0471 7.64812i 1.20532 0.353913i 0.383433 0.923569i \(-0.374742\pi\)
0.821883 + 0.569656i \(0.192924\pi\)
\(468\) 0 0
\(469\) −6.01690 + 13.1752i −0.277835 + 0.608373i
\(470\) 1.80863 + 0.531061i 0.0834257 + 0.0244960i
\(471\) 0 0
\(472\) 3.51056 + 4.05140i 0.161586 + 0.186481i
\(473\) −0.664872 0.195224i −0.0305708 0.00897641i
\(474\) 0 0
\(475\) 8.70004 + 5.59118i 0.399185 + 0.256541i
\(476\) −6.33070 + 1.85886i −0.290167 + 0.0852008i
\(477\) 0 0
\(478\) 4.19290 + 9.18117i 0.191779 + 0.419937i
\(479\) −0.531346 3.69559i −0.0242778 0.168856i 0.974075 0.226224i \(-0.0726382\pi\)
−0.998353 + 0.0573682i \(0.981729\pi\)
\(480\) 0 0
\(481\) −1.62945 + 1.88049i −0.0742967 + 0.0857430i
\(482\) 2.49660 0.113717
\(483\) 0 0
\(484\) −10.9969 −0.499861
\(485\) −6.79495 + 7.84179i −0.308543 + 0.356077i
\(486\) 0 0
\(487\) −3.28140 22.8226i −0.148694 1.03419i −0.918360 0.395745i \(-0.870486\pi\)
0.769666 0.638446i \(-0.220423\pi\)
\(488\) −5.06868 11.0989i −0.229448 0.502422i
\(489\) 0 0
\(490\) 4.63037 1.35960i 0.209179 0.0614204i
\(491\) 0.944131 + 0.606756i 0.0426080 + 0.0273825i 0.561771 0.827292i \(-0.310120\pi\)
−0.519163 + 0.854675i \(0.673756\pi\)
\(492\) 0 0
\(493\) −14.5160 4.26229i −0.653769 0.191964i
\(494\) 1.93993 + 2.23880i 0.0872816 + 0.100728i
\(495\) 0 0
\(496\) 7.63321 + 2.24131i 0.342741 + 0.100638i
\(497\) −19.4340 + 42.5545i −0.871733 + 1.90883i
\(498\) 0 0
\(499\) −38.0512 + 11.1728i −1.70340 + 0.500165i −0.981441 0.191766i \(-0.938579\pi\)
−0.721964 + 0.691931i \(0.756760\pi\)
\(500\) 1.64436 11.4368i 0.0735381 0.511469i
\(501\) 0 0
\(502\) −2.04586 14.2293i −0.0913112 0.635083i
\(503\) 28.6350 18.4026i 1.27677 0.820530i 0.286284 0.958145i \(-0.407580\pi\)
0.990486 + 0.137614i \(0.0439434\pi\)
\(504\) 0 0
\(505\) −22.7020 −1.01023
\(506\) 0.255970 + 0.0692591i 0.0113792 + 0.00307894i
\(507\) 0 0
\(508\) −12.6731 + 14.6256i −0.562279 + 0.648905i
\(509\) −0.791310 + 0.508544i −0.0350742 + 0.0225408i −0.558060 0.829800i \(-0.688454\pi\)
0.522986 + 0.852341i \(0.324818\pi\)
\(510\) 0 0
\(511\) 13.1241 + 28.7378i 0.580577 + 1.27129i
\(512\) 0.142315 0.989821i 0.00628949 0.0437443i
\(513\) 0 0
\(514\) −14.3928 9.24967i −0.634838 0.407985i
\(515\) 9.41304 20.6117i 0.414788 0.908259i
\(516\) 0 0
\(517\) 0.0461516 + 0.0532618i 0.00202975 + 0.00234245i
\(518\) 6.47871 + 7.47683i 0.284658 + 0.328513i
\(519\) 0 0
\(520\) 0.495008 1.08392i 0.0217075 0.0475329i
\(521\) 33.9920 + 21.8454i 1.48922 + 0.957062i 0.996205 + 0.0870408i \(0.0277410\pi\)
0.493014 + 0.870022i \(0.335895\pi\)
\(522\) 0 0
\(523\) 2.00533 13.9473i 0.0876868 0.609875i −0.897836 0.440330i \(-0.854861\pi\)
0.985523 0.169544i \(-0.0542296\pi\)
\(524\) 8.68332 + 19.0138i 0.379333 + 0.830623i
\(525\) 0 0
\(526\) −8.26927 + 5.31433i −0.360557 + 0.231716i
\(527\) −10.7296 + 12.3826i −0.467389 + 0.539396i
\(528\) 0 0
\(529\) 19.8620 + 11.5974i 0.863567 + 0.504235i
\(530\) −16.3341 −0.709510
\(531\) 0 0
\(532\) 9.90856 6.36784i 0.429591 0.276081i
\(533\) 0.167385 + 1.16419i 0.00725027 + 0.0504267i
\(534\) 0 0
\(535\) −2.03637 + 14.1633i −0.0880399 + 0.612331i
\(536\) 4.33803 1.27376i 0.187374 0.0550180i
\(537\) 0 0
\(538\) 11.2338 24.5987i 0.484325 1.06052i
\(539\) 0.173120 + 0.0508326i 0.00745680 + 0.00218951i
\(540\) 0 0
\(541\) 20.9730 + 24.2042i 0.901701 + 1.04062i 0.998971 + 0.0453605i \(0.0144437\pi\)
−0.0972695 + 0.995258i \(0.531011\pi\)
\(542\) 13.4448 + 3.94776i 0.577505 + 0.169571i
\(543\) 0 0
\(544\) 1.73259 + 1.11347i 0.0742843 + 0.0477396i
\(545\) 19.0147 5.58321i 0.814499 0.239158i
\(546\) 0 0
\(547\) −14.2184 31.1339i −0.607934 1.33119i −0.923978 0.382445i \(-0.875082\pi\)
0.316045 0.948744i \(-0.397645\pi\)
\(548\) 0.839528 + 5.83905i 0.0358629 + 0.249432i
\(549\) 0 0
\(550\) 0.101852 0.117543i 0.00434297 0.00501205i
\(551\) 27.0072 1.15054
\(552\) 0 0
\(553\) −11.5965 −0.493135
\(554\) −4.35828 + 5.02972i −0.185166 + 0.213692i
\(555\) 0 0
\(556\) 0.575459 + 4.00241i 0.0244049 + 0.169740i
\(557\) 4.69734 + 10.2857i 0.199033 + 0.435820i 0.982661 0.185409i \(-0.0593609\pi\)
−0.783629 + 0.621229i \(0.786634\pi\)
\(558\) 0 0
\(559\) −9.68868 + 2.84485i −0.409787 + 0.120324i
\(560\) −3.98569 2.56145i −0.168426 0.108241i
\(561\) 0 0
\(562\) 14.1280 + 4.14834i 0.595952 + 0.174987i
\(563\) 11.3275 + 13.0726i 0.477397 + 0.550946i 0.942454 0.334335i \(-0.108512\pi\)
−0.465057 + 0.885281i \(0.653966\pi\)
\(564\) 0 0
\(565\) 11.6767 + 3.42859i 0.491242 + 0.144242i
\(566\) 5.68732 12.4535i 0.239056 0.523459i
\(567\) 0 0
\(568\) 14.0114 4.11411i 0.587904 0.172624i
\(569\) 4.13566 28.7642i 0.173376 1.20586i −0.698311 0.715794i \(-0.746065\pi\)
0.871687 0.490063i \(-0.163026\pi\)
\(570\) 0 0
\(571\) −0.447773 3.11433i −0.0187387 0.130331i 0.978305 0.207171i \(-0.0664258\pi\)
−0.997043 + 0.0768408i \(0.975517\pi\)
\(572\) 0.0374790 0.0240863i 0.00156708 0.00100710i
\(573\) 0 0
\(574\) 4.67642 0.195190
\(575\) 11.1903 7.53393i 0.466668 0.314186i
\(576\) 0 0
\(577\) −7.10693 + 8.20184i −0.295866 + 0.341447i −0.884147 0.467209i \(-0.845259\pi\)
0.588281 + 0.808656i \(0.299805\pi\)
\(578\) 10.7330 6.89766i 0.446433 0.286905i
\(579\) 0 0
\(580\) −4.51289 9.88185i −0.187387 0.410321i
\(581\) 4.57484 31.8187i 0.189796 1.32006i
\(582\) 0 0
\(583\) −0.513753 0.330169i −0.0212775 0.0136742i
\(584\) 4.09666 8.97043i 0.169521 0.371199i
\(585\) 0 0
\(586\) −19.3966 22.3849i −0.801268 0.924712i
\(587\) −21.1402 24.3971i −0.872549 1.00698i −0.999886 0.0151162i \(-0.995188\pi\)
0.127336 0.991860i \(-0.459357\pi\)
\(588\) 0 0
\(589\) 12.1504 26.6057i 0.500649 1.09627i
\(590\) −6.66945 4.28620i −0.274577 0.176460i
\(591\) 0 0
\(592\) 0.439490 3.05672i 0.0180629 0.125631i
\(593\) −14.5904 31.9486i −0.599157 1.31197i −0.929748 0.368196i \(-0.879975\pi\)
0.330591 0.943774i \(-0.392752\pi\)
\(594\) 0 0
\(595\) 8.20868 5.27540i 0.336523 0.216270i
\(596\) −5.37873 + 6.20739i −0.220321 + 0.254264i
\(597\) 0 0
\(598\) 3.68357 1.16758i 0.150632 0.0477458i
\(599\) 33.0831 1.35174 0.675870 0.737021i \(-0.263768\pi\)
0.675870 + 0.737021i \(0.263768\pi\)
\(600\) 0 0
\(601\) −34.4280 + 22.1256i −1.40435 + 0.902521i −0.999927 0.0120520i \(-0.996164\pi\)
−0.404422 + 0.914573i \(0.632527\pi\)
\(602\) 5.71372 + 39.7398i 0.232874 + 1.61967i
\(603\) 0 0
\(604\) 1.82861 12.7183i 0.0744051 0.517499i
\(605\) 15.6045 4.58190i 0.634413 0.186281i
\(606\) 0 0
\(607\) 0.360269 0.788879i 0.0146229 0.0320196i −0.902180 0.431360i \(-0.858034\pi\)
0.916803 + 0.399341i \(0.130761\pi\)
\(608\) −3.52765 1.03581i −0.143065 0.0420077i
\(609\) 0 0
\(610\) 11.8168 + 13.6373i 0.478446 + 0.552157i
\(611\) 0.985386 + 0.289336i 0.0398645 + 0.0117053i
\(612\) 0 0
\(613\) 11.4396 + 7.35175i 0.462039 + 0.296935i 0.750875 0.660444i \(-0.229632\pi\)
−0.288836 + 0.957379i \(0.593268\pi\)
\(614\) 8.75700 2.57129i 0.353404 0.103769i
\(615\) 0 0
\(616\) −0.0735851 0.161129i −0.00296483 0.00649207i
\(617\) −6.07169 42.2295i −0.244437 1.70010i −0.629332 0.777137i \(-0.716671\pi\)
0.384895 0.922960i \(-0.374238\pi\)
\(618\) 0 0
\(619\) 20.6446 23.8251i 0.829775 0.957612i −0.169837 0.985472i \(-0.554324\pi\)
0.999612 + 0.0278606i \(0.00886945\pi\)
\(620\) −11.7653 −0.472505
\(621\) 0 0
\(622\) 22.9754 0.921229
\(623\) 17.3131 19.9803i 0.693633 0.800496i
\(624\) 0 0
\(625\) 0.430261 + 2.99253i 0.0172104 + 0.119701i
\(626\) −8.20118 17.9581i −0.327785 0.717749i
\(627\) 0 0
\(628\) −3.76005 + 1.10405i −0.150042 + 0.0440564i
\(629\) 5.35052 + 3.43857i 0.213339 + 0.137105i
\(630\) 0 0
\(631\) 46.7584 + 13.7295i 1.86142 + 0.546563i 0.999198 + 0.0400350i \(0.0127469\pi\)
0.862224 + 0.506528i \(0.169071\pi\)
\(632\) 2.37048 + 2.73568i 0.0942927 + 0.108820i
\(633\) 0 0
\(634\) 19.9880 + 5.86900i 0.793824 + 0.233088i
\(635\) 11.8892 26.0338i 0.471809 1.03312i
\(636\) 0 0
\(637\) 2.52274 0.740745i 0.0999548 0.0293494i
\(638\) 0.0578035 0.402032i 0.00228846 0.0159166i
\(639\) 0 0
\(640\) 0.210468 + 1.46384i 0.00831949 + 0.0578633i
\(641\) −25.3919 + 16.3184i −1.00292 + 0.644537i −0.935551 0.353191i \(-0.885097\pi\)
−0.0673684 + 0.997728i \(0.521460\pi\)
\(642\) 0 0
\(643\) 34.4723 1.35946 0.679728 0.733464i \(-0.262098\pi\)
0.679728 + 0.733464i \(0.262098\pi\)
\(644\) −2.51071 15.1575i −0.0989358 0.597288i
\(645\) 0 0
\(646\) 4.95863 5.72257i 0.195095 0.225151i
\(647\) −11.7496 + 7.55102i −0.461925 + 0.296861i −0.750829 0.660497i \(-0.770346\pi\)
0.288903 + 0.957358i \(0.406709\pi\)
\(648\) 0 0
\(649\) −0.123134 0.269625i −0.00483342 0.0105837i
\(650\) 0.322549 2.24338i 0.0126514 0.0879924i
\(651\) 0 0
\(652\) 13.2284 + 8.50140i 0.518065 + 0.332940i
\(653\) −15.3401 + 33.5902i −0.600306 + 1.31449i 0.328705 + 0.944433i \(0.393388\pi\)
−0.929011 + 0.370053i \(0.879339\pi\)
\(654\) 0 0
\(655\) −20.2437 23.3624i −0.790985 0.912845i
\(656\) −0.955922 1.10319i −0.0373225 0.0430724i
\(657\) 0 0
\(658\) 1.69626 3.71430i 0.0661272 0.144798i
\(659\) 9.28343 + 5.96610i 0.361631 + 0.232406i 0.708821 0.705389i \(-0.249228\pi\)
−0.347189 + 0.937795i \(0.612864\pi\)
\(660\) 0 0
\(661\) −4.83516 + 33.6292i −0.188066 + 1.30803i 0.648943 + 0.760837i \(0.275211\pi\)
−0.837009 + 0.547189i \(0.815698\pi\)
\(662\) 6.45836 + 14.1418i 0.251011 + 0.549638i
\(663\) 0 0
\(664\) −8.44136 + 5.42493i −0.327588 + 0.210528i
\(665\) −11.4069 + 13.1643i −0.442342 + 0.510490i
\(666\) 0 0
\(667\) 13.9471 32.3505i 0.540036 1.25262i
\(668\) 4.01965 0.155525
\(669\) 0 0
\(670\) −5.62488 + 3.61489i −0.217308 + 0.139655i
\(671\) 0.0960131 + 0.667786i 0.00370655 + 0.0257796i
\(672\) 0 0
\(673\) 4.46767 31.0733i 0.172216 1.19779i −0.701974 0.712203i \(-0.747698\pi\)
0.874190 0.485585i \(-0.161393\pi\)
\(674\) 6.79099 1.99402i 0.261579 0.0768066i
\(675\) 0 0
\(676\) −5.13070 + 11.2347i −0.197335 + 0.432103i
\(677\) −37.7447 11.0828i −1.45065 0.425948i −0.540891 0.841093i \(-0.681913\pi\)
−0.909756 + 0.415144i \(0.863731\pi\)
\(678\) 0 0
\(679\) 14.7194 + 16.9871i 0.564879 + 0.651905i
\(680\) −2.92245 0.858110i −0.112071 0.0329070i
\(681\) 0 0
\(682\) −0.370050 0.237816i −0.0141699 0.00910646i
\(683\) 30.3414 8.90905i 1.16098 0.340895i 0.356168 0.934422i \(-0.384083\pi\)
0.804814 + 0.593527i \(0.202265\pi\)
\(684\) 0 0
\(685\) −3.62413 7.93574i −0.138471 0.303209i
\(686\) 1.70371 + 11.8496i 0.0650480 + 0.452419i
\(687\) 0 0
\(688\) 8.20687 9.47123i 0.312884 0.361087i
\(689\) −8.89927 −0.339035
\(690\) 0 0
\(691\) 22.2620 0.846886 0.423443 0.905923i \(-0.360821\pi\)
0.423443 + 0.905923i \(0.360821\pi\)
\(692\) 3.44095 3.97106i 0.130805 0.150957i
\(693\) 0 0
\(694\) 3.61704 + 25.1571i 0.137301 + 0.954950i
\(695\) −2.48418 5.43959i −0.0942303 0.206336i
\(696\) 0 0
\(697\) 2.88460 0.846994i 0.109262 0.0320822i
\(698\) 19.4596 + 12.5059i 0.736555 + 0.473355i
\(699\) 0 0
\(700\) −8.64636 2.53880i −0.326802 0.0959577i
\(701\) 9.06733 + 10.4643i 0.342468 + 0.395230i 0.900690 0.434462i \(-0.143062\pi\)
−0.558222 + 0.829692i \(0.688516\pi\)
\(702\) 0 0
\(703\) −10.8939 3.19874i −0.410872 0.120643i
\(704\) −0.0229694 + 0.0502960i −0.000865692 + 0.00189560i
\(705\) 0 0
\(706\) −23.0929 + 6.78069i −0.869113 + 0.255195i
\(707\) −6.99871 + 48.6771i −0.263214 + 1.83069i
\(708\) 0 0
\(709\) −6.98803 48.6028i −0.262441 1.82532i −0.514367 0.857570i \(-0.671973\pi\)
0.251926 0.967746i \(-0.418936\pi\)
\(710\) −18.1678 + 11.6757i −0.681825 + 0.438182i
\(711\) 0 0
\(712\) −8.25248 −0.309275
\(713\) −25.5949 28.2942i −0.958535 1.05962i
\(714\) 0 0
\(715\) −0.0431466 + 0.0497938i −0.00161359 + 0.00186218i
\(716\) 1.77749 1.14232i 0.0664278 0.0426906i
\(717\) 0 0
\(718\) 7.96450 + 17.4398i 0.297232 + 0.650848i
\(719\) 5.20770 36.2204i 0.194214 1.35079i −0.626486 0.779433i \(-0.715507\pi\)
0.820701 0.571359i \(-0.193583\pi\)
\(720\) 0 0
\(721\) −41.2932 26.5375i −1.53784 0.988310i
\(722\) 2.27764 4.98734i 0.0847650 0.185609i
\(723\) 0 0
\(724\) 0.151194 + 0.174487i 0.00561908 + 0.00648477i
\(725\) −13.5312 15.6158i −0.502536 0.579958i
\(726\) 0 0
\(727\) 7.73116 16.9289i 0.286733 0.627857i −0.710378 0.703821i \(-0.751476\pi\)
0.997111 + 0.0759632i \(0.0242032\pi\)
\(728\) −2.17151 1.39554i −0.0804814 0.0517223i
\(729\) 0 0
\(730\) −2.07555 + 14.4358i −0.0768197 + 0.534293i
\(731\) 10.7221 + 23.4782i 0.396572 + 0.868371i
\(732\) 0 0
\(733\) −19.0255 + 12.2269i −0.702722 + 0.451612i −0.842588 0.538558i \(-0.818969\pi\)
0.139866 + 0.990170i \(0.455333\pi\)
\(734\) −17.2023 + 19.8525i −0.634948 + 0.732769i
\(735\) 0 0
\(736\) −3.06250 + 3.69067i −0.112885 + 0.136040i
\(737\) −0.249987 −0.00920840
\(738\) 0 0
\(739\) −15.0475 + 9.67041i −0.553530 + 0.355732i −0.787310 0.616558i \(-0.788527\pi\)
0.233780 + 0.972289i \(0.424890\pi\)
\(740\) 0.649959 + 4.52056i 0.0238930 + 0.166179i
\(741\) 0 0
\(742\) −5.03559 + 35.0233i −0.184862 + 1.28575i
\(743\) −21.5290 + 6.32150i −0.789824 + 0.231913i −0.651675 0.758498i \(-0.725933\pi\)
−0.138149 + 0.990411i \(0.544115\pi\)
\(744\) 0 0
\(745\) 5.04602 11.0493i 0.184872 0.404813i
\(746\) 19.5783 + 5.74872i 0.716814 + 0.210476i
\(747\) 0 0
\(748\) −0.0745738 0.0860627i −0.00272669 0.00314677i
\(749\) 29.7408 + 8.73267i 1.08670 + 0.319085i
\(750\) 0 0
\(751\) 39.5260 + 25.4018i 1.44232 + 0.926924i 0.999541 + 0.0302948i \(0.00964461\pi\)
0.442781 + 0.896630i \(0.353992\pi\)
\(752\) −1.22296 + 0.359094i −0.0445968 + 0.0130948i
\(753\) 0 0
\(754\) −2.45874 5.38389i −0.0895420 0.196070i
\(755\) 2.70432 + 18.8089i 0.0984201 + 0.684527i
\(756\) 0 0
\(757\) −18.8145 + 21.7131i −0.683825 + 0.789176i −0.986473 0.163926i \(-0.947584\pi\)
0.302647 + 0.953103i \(0.402130\pi\)
\(758\) −3.99029 −0.144934
\(759\) 0 0
\(760\) 5.43725 0.197230
\(761\) 10.2728 11.8554i 0.372387 0.429758i −0.538364 0.842712i \(-0.680958\pi\)
0.910752 + 0.412954i \(0.135503\pi\)
\(762\) 0 0
\(763\) −6.10944 42.4921i −0.221176 1.53832i
\(764\) −1.82915 4.00527i −0.0661762 0.144906i
\(765\) 0 0
\(766\) −6.06611 + 1.78117i −0.219177 + 0.0643563i
\(767\) −3.63369 2.33523i −0.131205 0.0843203i
\(768\) 0 0
\(769\) 19.0114 + 5.58224i 0.685567 + 0.201301i 0.605924 0.795523i \(-0.292804\pi\)
0.0796432 + 0.996823i \(0.474622\pi\)
\(770\) 0.171551 + 0.197980i 0.00618227 + 0.00713472i
\(771\) 0 0
\(772\) −20.6265 6.05648i −0.742364 0.217978i
\(773\) −8.10693 + 17.7517i −0.291586 + 0.638484i −0.997565 0.0697490i \(-0.977780\pi\)
0.705979 + 0.708233i \(0.250507\pi\)
\(774\) 0 0
\(775\) −21.4713 + 6.30455i −0.771272 + 0.226466i
\(776\) 0.998507 6.94477i 0.0358443 0.249303i
\(777\) 0 0
\(778\) 3.61715 + 25.1578i 0.129681 + 0.901952i
\(779\) −4.51485 + 2.90152i −0.161761 + 0.103958i
\(780\) 0 0
\(781\) −0.807433 −0.0288922
\(782\) −4.29402 8.89496i −0.153554 0.318083i
\(783\) 0 0
\(784\) −2.13691 + 2.46613i −0.0763182 + 0.0880759i
\(785\) 4.87546 3.13327i 0.174013 0.111831i
\(786\) 0 0
\(787\) 8.31294 + 18.2028i 0.296324 + 0.648860i 0.997971 0.0636650i \(-0.0202789\pi\)
−0.701647 + 0.712525i \(0.747552\pi\)
\(788\) 1.26548 8.80158i 0.0450807 0.313543i
\(789\) 0 0
\(790\) −4.50351 2.89423i −0.160228 0.102972i
\(791\) 10.9513 23.9799i 0.389382 0.852628i
\(792\) 0 0
\(793\) 6.43807 + 7.42993i 0.228623 + 0.263845i
\(794\) −2.24950 2.59607i −0.0798319 0.0921310i
\(795\) 0 0
\(796\) 7.54187 16.5144i 0.267315 0.585337i
\(797\) 16.5992 + 10.6677i 0.587975 + 0.377868i 0.800541 0.599278i \(-0.204546\pi\)
−0.212566 + 0.977147i \(0.568182\pi\)
\(798\) 0 0
\(799\) 0.373586 2.59835i 0.0132165 0.0919229i
\(800\) 1.16851 + 2.55869i 0.0413132 + 0.0904632i
\(801\) 0 0
\(802\) −7.02865 + 4.51704i −0.248190 + 0.159502i
\(803\) −0.357079 + 0.412091i −0.0126010 + 0.0145424i
\(804\) 0 0
\(805\) 9.87805 + 20.4621i 0.348155 + 0.721196i
\(806\) −6.41002 −0.225783
\(807\) 0 0
\(808\) 12.9138 8.29920i 0.454306 0.291965i
\(809\) 3.95074 + 27.4780i 0.138901 + 0.966075i 0.933407 + 0.358819i \(0.116820\pi\)
−0.794507 + 0.607256i \(0.792270\pi\)
\(810\) 0 0
\(811\) −2.63257 + 18.3099i −0.0924421 + 0.642949i 0.889942 + 0.456074i \(0.150745\pi\)
−0.982384 + 0.186875i \(0.940164\pi\)
\(812\) −22.5797 + 6.63000i −0.792392 + 0.232667i
\(813\) 0 0
\(814\) −0.0709331 + 0.155322i −0.00248620 + 0.00544403i
\(815\) −22.3131 6.55171i −0.781593 0.229496i
\(816\) 0 0
\(817\) −30.1732 34.8217i −1.05563 1.21826i
\(818\) −4.01699 1.17949i −0.140451 0.0412401i
\(819\) 0 0
\(820\) 1.81609 + 1.16713i 0.0634205 + 0.0407579i
\(821\) −3.74080 + 1.09840i −0.130555 + 0.0383343i −0.346357 0.938103i \(-0.612581\pi\)
0.215802 + 0.976437i \(0.430763\pi\)
\(822\) 0 0
\(823\) −5.67680 12.4305i −0.197881 0.433299i 0.784515 0.620110i \(-0.212912\pi\)
−0.982396 + 0.186811i \(0.940185\pi\)
\(824\) 2.18053 + 15.1659i 0.0759623 + 0.528329i
\(825\) 0 0
\(826\) −11.2465 + 12.9791i −0.391315 + 0.451602i
\(827\) −1.97288 −0.0686037 −0.0343019 0.999412i \(-0.510921\pi\)
−0.0343019 + 0.999412i \(0.510921\pi\)
\(828\) 0 0
\(829\) 6.37133 0.221285 0.110643 0.993860i \(-0.464709\pi\)
0.110643 + 0.993860i \(0.464709\pi\)
\(830\) 9.71787 11.2150i 0.337312 0.389279i
\(831\) 0 0
\(832\) 0.114669 + 0.797537i 0.00397542 + 0.0276496i
\(833\) −2.79183 6.11326i −0.0967313 0.211812i
\(834\) 0 0
\(835\) −5.70382 + 1.67479i −0.197389 + 0.0579586i
\(836\) 0.171016 + 0.109906i 0.00591472 + 0.00380116i
\(837\) 0 0
\(838\) −8.62112 2.53139i −0.297812 0.0874454i
\(839\) −0.227540 0.262595i −0.00785555 0.00906578i 0.751808 0.659382i \(-0.229182\pi\)
−0.759664 + 0.650316i \(0.774636\pi\)
\(840\) 0 0
\(841\) −23.9490 7.03205i −0.825827 0.242485i
\(842\) 2.80773 6.14807i 0.0967608 0.211877i
\(843\) 0 0
\(844\) −16.5071 + 4.84693i −0.568199 + 0.166838i
\(845\) 2.59945 18.0796i 0.0894237 0.621956i
\(846\) 0 0
\(847\) −5.01375 34.8714i −0.172274 1.19820i
\(848\) 9.29153 5.97130i 0.319072 0.205055i
\(849\) 0 0
\(850\) −5.79323 −0.198706
\(851\) −9.45749 + 11.3974i −0.324199 + 0.390697i
\(852\) 0 0
\(853\) 14.4584 16.6859i 0.495047 0.571315i −0.452160 0.891937i \(-0.649346\pi\)
0.947207 + 0.320622i \(0.103892\pi\)
\(854\) 32.8837 21.1330i 1.12526 0.723158i
\(855\) 0 0
\(856\) −4.01932 8.80107i −0.137377 0.300814i
\(857\) −2.75575 + 19.1667i −0.0941348 + 0.654722i 0.887053 + 0.461667i \(0.152749\pi\)
−0.981188 + 0.193055i \(0.938161\pi\)
\(858\) 0 0
\(859\) −8.55235 5.49626i −0.291802 0.187530i 0.386547 0.922270i \(-0.373668\pi\)
−0.678349 + 0.734740i \(0.737304\pi\)
\(860\) −7.69923 + 16.8590i −0.262541 + 0.574886i
\(861\) 0 0
\(862\) 14.8481 + 17.1357i 0.505730 + 0.583643i
\(863\) −7.67639 8.85902i −0.261307 0.301565i 0.609902 0.792477i \(-0.291209\pi\)
−0.871209 + 0.490912i \(0.836663\pi\)
\(864\) 0 0
\(865\) −3.22810 + 7.06856i −0.109759 + 0.240338i
\(866\) −25.1990 16.1944i −0.856298 0.550309i
\(867\) 0 0
\(868\) −3.62707 + 25.2268i −0.123111 + 0.856255i
\(869\) −0.0831453 0.182063i −0.00282051 0.00617605i
\(870\) 0 0
\(871\) −3.06458 + 1.96949i −0.103839 + 0.0667335i
\(872\) −8.77525 + 10.1272i −0.297167 + 0.342950i
\(873\) 0 0
\(874\) 11.8285 + 13.0760i 0.400106 + 0.442302i
\(875\) 37.0159 1.25136
\(876\) 0 0
\(877\) −25.5664 + 16.4306i −0.863318 + 0.554820i −0.895702 0.444655i \(-0.853326\pi\)
0.0323844 + 0.999475i \(0.489690\pi\)
\(878\) −0.213673 1.48613i −0.00721112 0.0501544i
\(879\) 0 0
\(880\) 0.0116373 0.0809395i 0.000392295 0.00272847i
\(881\) −31.9898 + 9.39305i −1.07776 + 0.316460i −0.771984 0.635642i \(-0.780735\pi\)
−0.305780 + 0.952102i \(0.598917\pi\)
\(882\) 0 0
\(883\) −2.14478 + 4.69641i −0.0721775 + 0.158047i −0.942282 0.334821i \(-0.891324\pi\)
0.870104 + 0.492868i \(0.164051\pi\)
\(884\) −1.59223 0.467521i −0.0535524 0.0157244i
\(885\) 0 0
\(886\) 3.86065 + 4.45542i 0.129701 + 0.149683i
\(887\) −13.0751 3.83921i −0.439020 0.128908i 0.0547505 0.998500i \(-0.482564\pi\)
−0.493771 + 0.869592i \(0.664382\pi\)
\(888\) 0 0
\(889\) −52.1557 33.5185i −1.74925 1.12417i
\(890\) 11.7102 3.43841i 0.392525 0.115256i
\(891\) 0 0
\(892\) −4.00700 8.77411i −0.134164 0.293779i
\(893\) 0.666905 + 4.63843i 0.0223171 + 0.155219i
\(894\) 0 0
\(895\) −2.04628 + 2.36153i −0.0683996 + 0.0789373i
\(896\) 3.20362 0.107025
\(897\) 0 0
\(898\) −36.8587 −1.22999
\(899\) −38.2693 + 44.1651i −1.27635 + 1.47299i
\(900\) 0 0
\(901\) 3.23728 + 22.5158i 0.107849 + 0.750109i
\(902\) 0.0335292 + 0.0734187i 0.00111640 + 0.00244458i
\(903\) 0 0
\(904\) −7.89557 + 2.31835i −0.262603 + 0.0771072i
\(905\) −0.287243 0.184600i −0.00954827 0.00613630i
\(906\) 0 0
\(907\) 21.3147 + 6.25857i 0.707744 + 0.207812i 0.615744 0.787947i \(-0.288856\pi\)
0.0920004 + 0.995759i \(0.470674\pi\)
\(908\) −8.70174 10.0423i −0.288777 0.333267i
\(909\) 0 0
\(910\) 3.66279 + 1.07549i 0.121420 + 0.0356523i
\(911\) 7.55315 16.5391i 0.250247 0.547965i −0.742266 0.670106i \(-0.766249\pi\)
0.992513 + 0.122141i \(0.0389761\pi\)
\(912\) 0 0
\(913\) 0.532347 0.156311i 0.0176181 0.00517315i
\(914\) −0.825094 + 5.73865i −0.0272917 + 0.189818i
\(915\) 0 0
\(916\) −1.47073 10.2291i −0.0485942 0.337980i
\(917\) −56.3341 + 36.2037i −1.86031 + 1.19555i
\(918\) 0 0
\(919\) −30.2025 −0.996289 −0.498145 0.867094i \(-0.665985\pi\)
−0.498145 + 0.867094i \(0.665985\pi\)
\(920\) 2.80792 6.51301i 0.0925745 0.214728i
\(921\) 0 0
\(922\) 12.5260 14.4557i 0.412520 0.476074i
\(923\) −9.89828 + 6.36124i −0.325806 + 0.209383i
\(924\) 0 0
\(925\) 3.60855 + 7.90162i 0.118648 + 0.259804i
\(926\) −2.89421 + 20.1297i −0.0951097 + 0.661503i
\(927\) 0 0
\(928\) 6.17964 + 3.97141i 0.202857 + 0.130368i
\(929\) 10.7210 23.4758i 0.351745 0.770215i −0.648216 0.761456i \(-0.724485\pi\)
0.999962 0.00875875i \(-0.00278803\pi\)
\(930\) 0 0
\(931\) 7.85651 + 9.06690i 0.257487 + 0.297155i
\(932\) −0.144971 0.167306i −0.00474869 0.00548028i
\(933\) 0 0
\(934\) 11.2772 24.6935i 0.369000 0.807997i
\(935\) 0.141677 + 0.0910505i 0.00463334 + 0.00297767i
\(936\) 0 0
\(937\) 2.15628 14.9972i 0.0704424 0.489938i −0.923808 0.382857i \(-0.874940\pi\)
0.994250 0.107081i \(-0.0341506\pi\)
\(938\) 6.01690 + 13.1752i 0.196459 + 0.430185i
\(939\) 0 0
\(940\) 1.58575 1.01910i 0.0517214 0.0332393i
\(941\) 16.5004 19.0424i 0.537897 0.620766i −0.420124 0.907467i \(-0.638013\pi\)
0.958020 + 0.286701i \(0.0925587\pi\)
\(942\) 0 0
\(943\) 1.14401 + 6.90653i 0.0372541 + 0.224908i
\(944\) 5.36077 0.174478
\(945\) 0 0
\(946\) −0.582939 + 0.374632i −0.0189530 + 0.0121803i
\(947\) −0.0871759 0.606322i −0.00283284 0.0197028i 0.988356 0.152159i \(-0.0486226\pi\)
−0.991189 + 0.132456i \(0.957714\pi\)
\(948\) 0 0
\(949\) −1.13081 + 7.86499i −0.0367078 + 0.255308i
\(950\) 9.92285 2.91361i 0.321940 0.0945300i
\(951\) 0 0
\(952\) −2.74089 + 6.00172i −0.0888329 + 0.194517i
\(953\) 32.8894 + 9.65720i 1.06539 + 0.312827i 0.767021 0.641622i \(-0.221738\pi\)
0.298372 + 0.954450i \(0.403556\pi\)
\(954\) 0 0
\(955\) 4.26434 + 4.92131i 0.137991 + 0.159250i
\(956\) 9.68443 + 2.84361i 0.313217 + 0.0919688i
\(957\) 0 0
\(958\) −3.14090 2.01853i −0.101478 0.0652159i
\(959\) −18.1329 + 5.32430i −0.585542 + 0.171931i
\(960\) 0 0
\(961\) 13.4135 + 29.3715i 0.432694 + 0.947467i
\(962\) 0.354114 + 2.46292i 0.0114171 + 0.0794077i
\(963\) 0 0
\(964\) 1.63492 1.88680i 0.0526573 0.0607698i
\(965\) 31.7921 1.02343
\(966\) 0 0
\(967\) 32.9004 1.05801 0.529003 0.848620i \(-0.322566\pi\)
0.529003 + 0.848620i \(0.322566\pi\)
\(968\) −7.20147 + 8.31093i −0.231464 + 0.267124i
\(969\) 0 0
\(970\) 1.47668 + 10.2706i 0.0474135 + 0.329768i
\(971\) 6.37511 + 13.9596i 0.204587 + 0.447983i 0.983916 0.178632i \(-0.0571671\pi\)
−0.779329 + 0.626615i \(0.784440\pi\)
\(972\) 0 0
\(973\) −12.4293 + 3.64957i −0.398465 + 0.117000i
\(974\) −19.3970 12.4657i −0.621521 0.399427i
\(975\) 0 0
\(976\) −11.7072 3.43756i −0.374740 0.110034i
\(977\) −4.97290 5.73903i −0.159097 0.183608i 0.670604 0.741815i \(-0.266035\pi\)
−0.829701 + 0.558207i \(0.811489\pi\)
\(978\) 0 0
\(979\) 0.437818 + 0.128555i 0.0139927 + 0.00410864i
\(980\) 2.00473 4.38975i 0.0640388 0.140225i
\(981\) 0 0
\(982\) 1.07683 0.316186i 0.0343630 0.0100899i
\(983\) 0.398420 2.77108i 0.0127076 0.0883836i −0.982481 0.186365i \(-0.940329\pi\)
0.995188 + 0.0979811i \(0.0312385\pi\)
\(984\) 0 0
\(985\) 1.87150 + 13.0166i 0.0596310 + 0.414743i
\(986\) −12.7272 + 8.17927i −0.405316 + 0.260481i
\(987\) 0 0
\(988\) 2.96236 0.0942451
\(989\) −57.2933 + 18.1602i −1.82182 + 0.577460i
\(990\) 0 0
\(991\) −0.331888 + 0.383020i −0.0105428 + 0.0121670i −0.760996 0.648756i \(-0.775290\pi\)
0.750454 + 0.660923i \(0.229835\pi\)
\(992\) 6.69256 4.30105i 0.212489 0.136558i
\(993\) 0 0
\(994\) 19.4340 + 42.5545i 0.616408 + 1.34975i
\(995\) −3.82106 + 26.5760i −0.121136 + 0.842517i
\(996\) 0 0
\(997\) 10.1906 + 6.54908i 0.322739 + 0.207412i 0.691970 0.721926i \(-0.256743\pi\)
−0.369232 + 0.929337i \(0.620379\pi\)
\(998\) −16.4744 + 36.0738i −0.521487 + 1.14190i
\(999\) 0 0
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 414.2.i.d.361.1 10
3.2 odd 2 138.2.e.a.85.1 yes 10
23.6 even 11 9522.2.a.bt.1.3 5
23.13 even 11 inner 414.2.i.d.289.1 10
23.17 odd 22 9522.2.a.bq.1.3 5
69.17 even 22 3174.2.a.bd.1.3 5
69.29 odd 22 3174.2.a.bc.1.3 5
69.59 odd 22 138.2.e.a.13.1 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
138.2.e.a.13.1 10 69.59 odd 22
138.2.e.a.85.1 yes 10 3.2 odd 2
414.2.i.d.289.1 10 23.13 even 11 inner
414.2.i.d.361.1 10 1.1 even 1 trivial
3174.2.a.bc.1.3 5 69.29 odd 22
3174.2.a.bd.1.3 5 69.17 even 22
9522.2.a.bq.1.3 5 23.17 odd 22
9522.2.a.bt.1.3 5 23.6 even 11