Properties

Label 322.2.g.a.45.2
Level $322$
Weight $2$
Character 322.45
Analytic conductor $2.571$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [322,2,Mod(45,322)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(322, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([1, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("322.45");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 322 = 2 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 322.g (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.57118294509\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} + 18x^{14} + 226x^{12} + 1434x^{10} + 6585x^{8} + 14406x^{6} + 22423x^{4} + 8085x^{2} + 2401 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 7 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 45.2
Root \(-1.52769 - 2.64604i\) of defining polynomial
Character \(\chi\) \(=\) 322.45
Dual form 322.2.g.a.229.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{2} +(-1.86037 - 1.07408i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.264227 + 0.457654i) q^{5} +2.14817i q^{6} +(1.26346 + 2.32458i) q^{7} +1.00000 q^{8} +(0.807314 + 1.39831i) q^{9} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{2} +(-1.86037 - 1.07408i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.264227 + 0.457654i) q^{5} +2.14817i q^{6} +(1.26346 + 2.32458i) q^{7} +1.00000 q^{8} +(0.807314 + 1.39831i) q^{9} +(0.264227 - 0.457654i) q^{10} +(1.77580 + 1.02526i) q^{11} +(1.86037 - 1.07408i) q^{12} +3.70082i q^{13} +(1.38141 - 2.25648i) q^{14} -1.13521i q^{15} +(-0.500000 - 0.866025i) q^{16} +(3.44977 - 5.97518i) q^{17} +(0.807314 - 1.39831i) q^{18} +(0.264227 + 0.457654i) q^{19} -0.528453 q^{20} +(0.146281 - 5.68164i) q^{21} -2.05052i q^{22} +(3.94348 + 2.72928i) q^{23} +(-1.86037 - 1.07408i) q^{24} +(2.36037 - 4.08828i) q^{25} +(3.20501 - 1.85041i) q^{26} +2.97601i q^{27} +(-2.64487 - 0.0680958i) q^{28} +3.68928 q^{29} +(-0.983118 + 0.567604i) q^{30} +(-4.28231 - 2.47239i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-2.20243 - 3.81471i) q^{33} -6.89954 q^{34} +(-0.730011 + 1.19245i) q^{35} -1.61463 q^{36} +(7.50830 - 4.33492i) q^{37} +(0.264227 - 0.457654i) q^{38} +(3.97500 - 6.88490i) q^{39} +(0.264227 + 0.457654i) q^{40} +3.70082i q^{41} +(-4.99358 + 2.71414i) q^{42} +8.98453i q^{43} +(-1.77580 + 1.02526i) q^{44} +(-0.426628 + 0.738941i) q^{45} +(0.391884 - 4.77979i) q^{46} +(-1.70501 + 0.984386i) q^{47} +2.14817i q^{48} +(-3.80731 + 5.87404i) q^{49} -4.72074 q^{50} +(-12.8357 + 7.41069i) q^{51} +(-3.20501 - 1.85041i) q^{52} +(11.8526 + 6.84309i) q^{53} +(2.57730 - 1.48801i) q^{54} +1.08360i q^{55} +(1.26346 + 2.32458i) q^{56} -1.13521i q^{57} +(-1.84464 - 3.19501i) q^{58} +(-5.00305 - 2.88851i) q^{59} +(0.983118 + 0.567604i) q^{60} +(2.92132 + 5.05987i) q^{61} +4.94479i q^{62} +(-2.23046 + 3.64338i) q^{63} +1.00000 q^{64} +(-1.69370 + 0.977857i) q^{65} +(-2.20243 + 3.81471i) q^{66} +(-0.710579 - 0.410253i) q^{67} +(3.44977 + 5.97518i) q^{68} +(-4.40485 - 9.31309i) q^{69} +(1.39769 + 0.0359855i) q^{70} +1.03146 q^{71} +(0.807314 + 1.39831i) q^{72} +(-4.28231 - 2.47239i) q^{73} +(-7.50830 - 4.33492i) q^{74} +(-8.78231 + 5.07047i) q^{75} -0.528453 q^{76} +(-0.139632 + 5.42336i) q^{77} -7.94999 q^{78} +(-10.3493 + 5.97518i) q^{79} +(0.264227 - 0.457654i) q^{80} +(5.61843 - 9.73141i) q^{81} +(3.20501 - 1.85041i) q^{82} +16.4544 q^{83} +(4.84730 + 2.96750i) q^{84} +3.64609 q^{85} +(7.78083 - 4.49227i) q^{86} +(-6.86342 - 3.96259i) q^{87} +(1.77580 + 1.02526i) q^{88} +(-3.81582 - 6.60920i) q^{89} +0.853256 q^{90} +(-8.60285 + 4.67586i) q^{91} +(-4.33536 + 2.05052i) q^{92} +(5.31112 + 9.19912i) q^{93} +(1.70501 + 0.984386i) q^{94} +(-0.139632 + 0.241849i) q^{95} +(1.86037 - 1.07408i) q^{96} -11.1402 q^{97} +(6.99073 + 0.360210i) q^{98} +3.31082i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 8 q^{2} + 6 q^{3} - 8 q^{4} + 16 q^{8} + 10 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 8 q^{2} + 6 q^{3} - 8 q^{4} + 16 q^{8} + 10 q^{9} - 6 q^{12} - 8 q^{16} + 10 q^{18} - 4 q^{23} + 6 q^{24} + 2 q^{25} - 6 q^{26} + 16 q^{29} - 24 q^{31} - 8 q^{32} + 4 q^{35} - 20 q^{36} + 22 q^{39} - 4 q^{46} + 30 q^{47} - 58 q^{49} - 4 q^{50} + 6 q^{52} + 54 q^{54} - 8 q^{58} + 36 q^{59} + 16 q^{64} - 32 q^{70} - 12 q^{71} + 10 q^{72} - 24 q^{73} - 96 q^{75} - 38 q^{77} - 44 q^{78} - 36 q^{81} - 6 q^{82} + 24 q^{85} + 42 q^{87} + 8 q^{92} - 38 q^{93} - 30 q^{94} - 38 q^{95} - 6 q^{96} + 56 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/322\mathbb{Z}\right)^\times\).

\(n\) \(185\) \(281\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 0.866025i −0.353553 0.612372i
\(3\) −1.86037 1.07408i −1.07408 0.620123i −0.144790 0.989462i \(-0.546251\pi\)
−0.929294 + 0.369340i \(0.879584\pi\)
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) 0.264227 + 0.457654i 0.118166 + 0.204669i 0.919041 0.394162i \(-0.128965\pi\)
−0.800875 + 0.598832i \(0.795632\pi\)
\(6\) 2.14817i 0.876986i
\(7\) 1.26346 + 2.32458i 0.477545 + 0.878607i
\(8\) 1.00000 0.353553
\(9\) 0.807314 + 1.39831i 0.269105 + 0.466103i
\(10\) 0.264227 0.457654i 0.0835558 0.144723i
\(11\) 1.77580 + 1.02526i 0.535423 + 0.309127i 0.743222 0.669045i \(-0.233297\pi\)
−0.207799 + 0.978172i \(0.566630\pi\)
\(12\) 1.86037 1.07408i 0.537042 0.310061i
\(13\) 3.70082i 1.02642i 0.858262 + 0.513212i \(0.171544\pi\)
−0.858262 + 0.513212i \(0.828456\pi\)
\(14\) 1.38141 2.25648i 0.369197 0.603070i
\(15\) 1.13521i 0.293109i
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 3.44977 5.97518i 0.836692 1.44919i −0.0559526 0.998433i \(-0.517820\pi\)
0.892645 0.450760i \(-0.148847\pi\)
\(18\) 0.807314 1.39831i 0.190286 0.329585i
\(19\) 0.264227 + 0.457654i 0.0606178 + 0.104993i 0.894742 0.446584i \(-0.147360\pi\)
−0.834124 + 0.551577i \(0.814026\pi\)
\(20\) −0.528453 −0.118166
\(21\) 0.146281 5.68164i 0.0319212 1.23983i
\(22\) 2.05052i 0.437171i
\(23\) 3.94348 + 2.72928i 0.822273 + 0.569094i
\(24\) −1.86037 1.07408i −0.379746 0.219247i
\(25\) 2.36037 4.08828i 0.472074 0.817656i
\(26\) 3.20501 1.85041i 0.628554 0.362896i
\(27\) 2.97601i 0.572734i
\(28\) −2.64487 0.0680958i −0.499834 0.0128689i
\(29\) 3.68928 0.685082 0.342541 0.939503i \(-0.388713\pi\)
0.342541 + 0.939503i \(0.388713\pi\)
\(30\) −0.983118 + 0.567604i −0.179492 + 0.103630i
\(31\) −4.28231 2.47239i −0.769126 0.444055i 0.0634370 0.997986i \(-0.479794\pi\)
−0.832563 + 0.553931i \(0.813127\pi\)
\(32\) −0.500000 + 0.866025i −0.0883883 + 0.153093i
\(33\) −2.20243 3.81471i −0.383393 0.664056i
\(34\) −6.89954 −1.18326
\(35\) −0.730011 + 1.19245i −0.123394 + 0.201560i
\(36\) −1.61463 −0.269105
\(37\) 7.50830 4.33492i 1.23436 0.712656i 0.266421 0.963857i \(-0.414159\pi\)
0.967935 + 0.251201i \(0.0808255\pi\)
\(38\) 0.264227 0.457654i 0.0428632 0.0742413i
\(39\) 3.97500 6.88490i 0.636509 1.10247i
\(40\) 0.264227 + 0.457654i 0.0417779 + 0.0723615i
\(41\) 3.70082i 0.577972i 0.957333 + 0.288986i \(0.0933180\pi\)
−0.957333 + 0.288986i \(0.906682\pi\)
\(42\) −4.99358 + 2.71414i −0.770526 + 0.418800i
\(43\) 8.98453i 1.37013i 0.728483 + 0.685064i \(0.240226\pi\)
−0.728483 + 0.685064i \(0.759774\pi\)
\(44\) −1.77580 + 1.02526i −0.267712 + 0.154563i
\(45\) −0.426628 + 0.738941i −0.0635979 + 0.110155i
\(46\) 0.391884 4.77979i 0.0577801 0.704742i
\(47\) −1.70501 + 0.984386i −0.248701 + 0.143588i −0.619169 0.785258i \(-0.712531\pi\)
0.370468 + 0.928845i \(0.379197\pi\)
\(48\) 2.14817i 0.310061i
\(49\) −3.80731 + 5.87404i −0.543902 + 0.839149i
\(50\) −4.72074 −0.667613
\(51\) −12.8357 + 7.41069i −1.79736 + 1.03770i
\(52\) −3.20501 1.85041i −0.444455 0.256606i
\(53\) 11.8526 + 6.84309i 1.62808 + 0.939970i 0.984666 + 0.174448i \(0.0558141\pi\)
0.643410 + 0.765522i \(0.277519\pi\)
\(54\) 2.57730 1.48801i 0.350726 0.202492i
\(55\) 1.08360i 0.146113i
\(56\) 1.26346 + 2.32458i 0.168838 + 0.310635i
\(57\) 1.13521i 0.150362i
\(58\) −1.84464 3.19501i −0.242213 0.419525i
\(59\) −5.00305 2.88851i −0.651341 0.376052i 0.137629 0.990484i \(-0.456052\pi\)
−0.788970 + 0.614432i \(0.789385\pi\)
\(60\) 0.983118 + 0.567604i 0.126920 + 0.0732773i
\(61\) 2.92132 + 5.05987i 0.374036 + 0.647850i 0.990182 0.139782i \(-0.0446402\pi\)
−0.616146 + 0.787632i \(0.711307\pi\)
\(62\) 4.94479i 0.627988i
\(63\) −2.23046 + 3.64338i −0.281012 + 0.459022i
\(64\) 1.00000 0.125000
\(65\) −1.69370 + 0.977857i −0.210077 + 0.121288i
\(66\) −2.20243 + 3.81471i −0.271100 + 0.469559i
\(67\) −0.710579 0.410253i −0.0868110 0.0501204i 0.455966 0.889997i \(-0.349294\pi\)
−0.542777 + 0.839877i \(0.682627\pi\)
\(68\) 3.44977 + 5.97518i 0.418346 + 0.724597i
\(69\) −4.40485 9.31309i −0.530282 1.12116i
\(70\) 1.39769 + 0.0359855i 0.167056 + 0.00430109i
\(71\) 1.03146 0.122412 0.0612059 0.998125i \(-0.480505\pi\)
0.0612059 + 0.998125i \(0.480505\pi\)
\(72\) 0.807314 + 1.39831i 0.0951429 + 0.164792i
\(73\) −4.28231 2.47239i −0.501206 0.289372i 0.228005 0.973660i \(-0.426780\pi\)
−0.729212 + 0.684288i \(0.760113\pi\)
\(74\) −7.50830 4.33492i −0.872822 0.503924i
\(75\) −8.78231 + 5.07047i −1.01409 + 0.585487i
\(76\) −0.528453 −0.0606178
\(77\) −0.139632 + 5.42336i −0.0159125 + 0.618049i
\(78\) −7.94999 −0.900159
\(79\) −10.3493 + 5.97518i −1.16439 + 0.672260i −0.952352 0.305002i \(-0.901343\pi\)
−0.212037 + 0.977262i \(0.568010\pi\)
\(80\) 0.264227 0.457654i 0.0295414 0.0511673i
\(81\) 5.61843 9.73141i 0.624270 1.08127i
\(82\) 3.20501 1.85041i 0.353934 0.204344i
\(83\) 16.4544 1.80610 0.903051 0.429533i \(-0.141322\pi\)
0.903051 + 0.429533i \(0.141322\pi\)
\(84\) 4.84730 + 2.96750i 0.528884 + 0.323781i
\(85\) 3.64609 0.395474
\(86\) 7.78083 4.49227i 0.839029 0.484414i
\(87\) −6.86342 3.96259i −0.735835 0.424835i
\(88\) 1.77580 + 1.02526i 0.189301 + 0.109293i
\(89\) −3.81582 6.60920i −0.404476 0.700574i 0.589784 0.807561i \(-0.299213\pi\)
−0.994260 + 0.106987i \(0.965880\pi\)
\(90\) 0.853256 0.0899410
\(91\) −8.60285 + 4.67586i −0.901824 + 0.490163i
\(92\) −4.33536 + 2.05052i −0.451993 + 0.213781i
\(93\) 5.31112 + 9.19912i 0.550737 + 0.953905i
\(94\) 1.70501 + 0.984386i 0.175858 + 0.101532i
\(95\) −0.139632 + 0.241849i −0.0143259 + 0.0248132i
\(96\) 1.86037 1.07408i 0.189873 0.109623i
\(97\) −11.1402 −1.13112 −0.565558 0.824709i \(-0.691339\pi\)
−0.565558 + 0.824709i \(0.691339\pi\)
\(98\) 6.99073 + 0.360210i 0.706170 + 0.0363867i
\(99\) 3.31082i 0.332750i
\(100\) 2.36037 + 4.08828i 0.236037 + 0.408828i
\(101\) −2.58111 1.49020i −0.256830 0.148281i 0.366058 0.930592i \(-0.380707\pi\)
−0.622887 + 0.782311i \(0.714041\pi\)
\(102\) 12.8357 + 7.41069i 1.27092 + 0.733768i
\(103\) 0.881293 + 1.52644i 0.0868363 + 0.150405i 0.906172 0.422909i \(-0.138991\pi\)
−0.819336 + 0.573314i \(0.805658\pi\)
\(104\) 3.70082i 0.362896i
\(105\) 2.63888 1.43429i 0.257528 0.139973i
\(106\) 13.6862i 1.32932i
\(107\) 7.69873 4.44487i 0.744265 0.429701i −0.0793532 0.996847i \(-0.525285\pi\)
0.823618 + 0.567145i \(0.191952\pi\)
\(108\) −2.57730 1.48801i −0.248001 0.143183i
\(109\) −6.00504 3.46701i −0.575178 0.332079i 0.184037 0.982919i \(-0.441083\pi\)
−0.759215 + 0.650840i \(0.774417\pi\)
\(110\) 0.938427 0.541801i 0.0894755 0.0516587i
\(111\) −18.6243 −1.76774
\(112\) 1.38141 2.25648i 0.130531 0.213217i
\(113\) 5.00860i 0.471169i −0.971854 0.235585i \(-0.924299\pi\)
0.971854 0.235585i \(-0.0757005\pi\)
\(114\) −0.983118 + 0.567604i −0.0920775 + 0.0531609i
\(115\) −0.207092 + 2.52590i −0.0193115 + 0.235541i
\(116\) −1.84464 + 3.19501i −0.171270 + 0.296649i
\(117\) −5.17489 + 2.98773i −0.478419 + 0.276215i
\(118\) 5.77702i 0.531818i
\(119\) 18.2484 + 0.469830i 1.67283 + 0.0430692i
\(120\) 1.13521i 0.103630i
\(121\) −3.39769 5.88498i −0.308881 0.534998i
\(122\) 2.92132 5.05987i 0.264484 0.458099i
\(123\) 3.97500 6.88490i 0.358413 0.620790i
\(124\) 4.28231 2.47239i 0.384563 0.222027i
\(125\) 5.13696 0.459463
\(126\) 4.27049 + 0.109949i 0.380445 + 0.00979507i
\(127\) −3.31072 −0.293779 −0.146890 0.989153i \(-0.546926\pi\)
−0.146890 + 0.989153i \(0.546926\pi\)
\(128\) −0.500000 0.866025i −0.0441942 0.0765466i
\(129\) 9.65015 16.7145i 0.849648 1.47163i
\(130\) 1.69370 + 0.977857i 0.148547 + 0.0857637i
\(131\) −14.1457 + 8.16704i −1.23592 + 0.713557i −0.968257 0.249956i \(-0.919584\pi\)
−0.267661 + 0.963513i \(0.586251\pi\)
\(132\) 4.40485 0.383393
\(133\) −0.730011 + 1.19245i −0.0633000 + 0.103398i
\(134\) 0.820506i 0.0708809i
\(135\) −1.36198 + 0.786342i −0.117221 + 0.0676776i
\(136\) 3.44977 5.97518i 0.295815 0.512367i
\(137\) −8.49141 4.90252i −0.725470 0.418851i 0.0912924 0.995824i \(-0.470900\pi\)
−0.816763 + 0.576974i \(0.804234\pi\)
\(138\) −5.86295 + 8.47126i −0.499087 + 0.721122i
\(139\) 18.4468i 1.56464i −0.622879 0.782318i \(-0.714037\pi\)
0.622879 0.782318i \(-0.285963\pi\)
\(140\) −0.667682 1.22843i −0.0564295 0.103821i
\(141\) 4.22926 0.356168
\(142\) −0.515730 0.893270i −0.0432791 0.0749616i
\(143\) −3.79430 + 6.57192i −0.317295 + 0.549571i
\(144\) 0.807314 1.39831i 0.0672762 0.116526i
\(145\) 0.974806 + 1.68841i 0.0809532 + 0.140215i
\(146\) 4.94479i 0.409233i
\(147\) 13.3922 6.83851i 1.10457 0.564030i
\(148\) 8.66983i 0.712656i
\(149\) 3.55160 2.05052i 0.290958 0.167985i −0.347416 0.937711i \(-0.612941\pi\)
0.638374 + 0.769726i \(0.279607\pi\)
\(150\) 8.78231 + 5.07047i 0.717073 + 0.414002i
\(151\) −0.885372 + 1.53351i −0.0720506 + 0.124795i −0.899800 0.436303i \(-0.856288\pi\)
0.827749 + 0.561098i \(0.189621\pi\)
\(152\) 0.264227 + 0.457654i 0.0214316 + 0.0371207i
\(153\) 11.1402 0.900631
\(154\) 4.76658 2.59075i 0.384102 0.208769i
\(155\) 2.61309i 0.209888i
\(156\) 3.97500 + 6.88490i 0.318254 + 0.551233i
\(157\) −3.73372 + 6.46700i −0.297983 + 0.516123i −0.975675 0.219224i \(-0.929647\pi\)
0.677691 + 0.735347i \(0.262981\pi\)
\(158\) 10.3493 + 5.97518i 0.823347 + 0.475360i
\(159\) −14.7001 25.4613i −1.16579 2.01921i
\(160\) −0.528453 −0.0417779
\(161\) −1.36197 + 12.6153i −0.107338 + 0.994223i
\(162\) −11.2369 −0.882851
\(163\) 2.80731 + 4.86241i 0.219886 + 0.380853i 0.954773 0.297336i \(-0.0960982\pi\)
−0.734887 + 0.678189i \(0.762765\pi\)
\(164\) −3.20501 1.85041i −0.250269 0.144493i
\(165\) 1.16388 2.01590i 0.0906079 0.156938i
\(166\) −8.22719 14.2499i −0.638554 1.10601i
\(167\) 4.65513i 0.360225i −0.983646 0.180112i \(-0.942354\pi\)
0.983646 0.180112i \(-0.0576461\pi\)
\(168\) 0.146281 5.68164i 0.0112858 0.438348i
\(169\) −0.696095 −0.0535458
\(170\) −1.82304 3.15760i −0.139821 0.242177i
\(171\) −0.426628 + 0.738941i −0.0326250 + 0.0565082i
\(172\) −7.78083 4.49227i −0.593283 0.342532i
\(173\) −12.8049 + 7.39291i −0.973538 + 0.562072i −0.900313 0.435243i \(-0.856662\pi\)
−0.0732248 + 0.997315i \(0.523329\pi\)
\(174\) 7.92519i 0.600807i
\(175\) 12.4858 + 0.321462i 0.943835 + 0.0243003i
\(176\) 2.05052i 0.154563i
\(177\) 6.20501 + 10.7474i 0.466397 + 0.807823i
\(178\) −3.81582 + 6.60920i −0.286008 + 0.495381i
\(179\) −1.69269 + 2.93182i −0.126517 + 0.219134i −0.922325 0.386415i \(-0.873713\pi\)
0.795808 + 0.605549i \(0.207047\pi\)
\(180\) −0.426628 0.738941i −0.0317990 0.0550774i
\(181\) 10.2869 0.764622 0.382311 0.924034i \(-0.375128\pi\)
0.382311 + 0.924034i \(0.375128\pi\)
\(182\) 8.35084 + 5.11236i 0.619005 + 0.378953i
\(183\) 12.5510i 0.927794i
\(184\) 3.94348 + 2.72928i 0.290717 + 0.201205i
\(185\) 3.96779 + 2.29080i 0.291717 + 0.168423i
\(186\) 5.31112 9.19912i 0.389430 0.674512i
\(187\) 12.2522 7.07381i 0.895969 0.517288i
\(188\) 1.96877i 0.143588i
\(189\) −6.91797 + 3.76009i −0.503208 + 0.273506i
\(190\) 0.279263 0.0202599
\(191\) 3.36116 1.94057i 0.243205 0.140414i −0.373444 0.927653i \(-0.621823\pi\)
0.616649 + 0.787238i \(0.288490\pi\)
\(192\) −1.86037 1.07408i −0.134261 0.0775154i
\(193\) −6.84769 + 11.8605i −0.492907 + 0.853740i −0.999967 0.00817078i \(-0.997399\pi\)
0.507059 + 0.861911i \(0.330732\pi\)
\(194\) 5.57010 + 9.64769i 0.399910 + 0.692664i
\(195\) 4.20120 0.300854
\(196\) −3.18341 6.23425i −0.227387 0.445304i
\(197\) 20.4976 1.46039 0.730196 0.683238i \(-0.239429\pi\)
0.730196 + 0.683238i \(0.239429\pi\)
\(198\) 2.86725 1.65541i 0.203767 0.117645i
\(199\) 10.4428 18.0875i 0.740272 1.28219i −0.212099 0.977248i \(-0.568030\pi\)
0.952371 0.304941i \(-0.0986368\pi\)
\(200\) 2.36037 4.08828i 0.166903 0.289085i
\(201\) 0.881293 + 1.52644i 0.0621616 + 0.107667i
\(202\) 2.98040i 0.209700i
\(203\) 4.66127 + 8.57601i 0.327157 + 0.601918i
\(204\) 14.8214i 1.03770i
\(205\) −1.69370 + 0.977857i −0.118293 + 0.0682965i
\(206\) 0.881293 1.52644i 0.0614026 0.106352i
\(207\) −0.632747 + 7.71759i −0.0439789 + 0.536409i
\(208\) 3.20501 1.85041i 0.222227 0.128303i
\(209\) 1.08360i 0.0749543i
\(210\) −2.56157 1.56819i −0.176765 0.108215i
\(211\) −26.0807 −1.79547 −0.897736 0.440533i \(-0.854789\pi\)
−0.897736 + 0.440533i \(0.854789\pi\)
\(212\) −11.8526 + 6.84309i −0.814038 + 0.469985i
\(213\) −1.91889 1.10787i −0.131480 0.0759103i
\(214\) −7.69873 4.44487i −0.526275 0.303845i
\(215\) −4.11181 + 2.37395i −0.280423 + 0.161902i
\(216\) 2.97601i 0.202492i
\(217\) 0.336719 13.0783i 0.0228580 0.887816i
\(218\) 6.93402i 0.469631i
\(219\) 5.31112 + 9.19912i 0.358892 + 0.621619i
\(220\) −0.938427 0.541801i −0.0632687 0.0365282i
\(221\) 22.1131 + 12.7670i 1.48749 + 0.858801i
\(222\) 9.31213 + 16.1291i 0.624989 + 1.08251i
\(223\) 3.15541i 0.211302i 0.994403 + 0.105651i \(0.0336926\pi\)
−0.994403 + 0.105651i \(0.966307\pi\)
\(224\) −2.64487 0.0680958i −0.176718 0.00454984i
\(225\) 7.62223 0.508149
\(226\) −4.33757 + 2.50430i −0.288531 + 0.166584i
\(227\) 3.89612 6.74828i 0.258595 0.447899i −0.707271 0.706943i \(-0.750074\pi\)
0.965866 + 0.259043i \(0.0834072\pi\)
\(228\) 0.983118 + 0.567604i 0.0651086 + 0.0375905i
\(229\) −2.83922 4.91767i −0.187621 0.324969i 0.756836 0.653605i \(-0.226744\pi\)
−0.944456 + 0.328636i \(0.893411\pi\)
\(230\) 2.29104 1.08360i 0.151067 0.0714506i
\(231\) 6.08491 9.93947i 0.400358 0.653969i
\(232\) 3.68928 0.242213
\(233\) −14.2518 24.6849i −0.933669 1.61716i −0.776991 0.629512i \(-0.783255\pi\)
−0.156678 0.987650i \(-0.550078\pi\)
\(234\) 5.17489 + 2.98773i 0.338293 + 0.195314i
\(235\) −0.901017 0.520202i −0.0587759 0.0339343i
\(236\) 5.00305 2.88851i 0.325671 0.188026i
\(237\) 25.6714 1.66754
\(238\) −8.71733 16.0385i −0.565060 1.03962i
\(239\) 2.10460 0.136135 0.0680676 0.997681i \(-0.478317\pi\)
0.0680676 + 0.997681i \(0.478317\pi\)
\(240\) −0.983118 + 0.567604i −0.0634600 + 0.0366387i
\(241\) −7.60361 + 13.1698i −0.489792 + 0.848344i −0.999931 0.0117478i \(-0.996260\pi\)
0.510139 + 0.860092i \(0.329594\pi\)
\(242\) −3.39769 + 5.88498i −0.218412 + 0.378301i
\(243\) −13.1728 + 7.60532i −0.845035 + 0.487881i
\(244\) −5.84264 −0.374036
\(245\) −3.69427 0.190354i −0.236018 0.0121613i
\(246\) −7.94999 −0.506873
\(247\) −1.69370 + 0.977857i −0.107767 + 0.0622195i
\(248\) −4.28231 2.47239i −0.271927 0.156997i
\(249\) −30.6112 17.6734i −1.93991 1.12001i
\(250\) −2.56848 4.44874i −0.162445 0.281363i
\(251\) −21.0463 −1.32843 −0.664214 0.747543i \(-0.731234\pi\)
−0.664214 + 0.747543i \(0.731234\pi\)
\(252\) −2.04003 3.75333i −0.128510 0.236437i
\(253\) 4.20461 + 8.88973i 0.264342 + 0.558893i
\(254\) 1.65536 + 2.86717i 0.103867 + 0.179902i
\(255\) −6.78307 3.91620i −0.424772 0.245242i
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 19.3956 11.1981i 1.20987 0.698517i 0.247136 0.968981i \(-0.420511\pi\)
0.962730 + 0.270464i \(0.0871772\pi\)
\(258\) −19.3003 −1.20158
\(259\) 19.5633 + 11.9766i 1.21561 + 0.744189i
\(260\) 1.95571i 0.121288i
\(261\) 2.97840 + 5.15875i 0.184359 + 0.319319i
\(262\) 14.1457 + 8.16704i 0.873926 + 0.504561i
\(263\) −8.30098 4.79257i −0.511860 0.295523i 0.221738 0.975106i \(-0.428827\pi\)
−0.733598 + 0.679584i \(0.762160\pi\)
\(264\) −2.20243 3.81471i −0.135550 0.234779i
\(265\) 7.23251i 0.444289i
\(266\) 1.39769 + 0.0359855i 0.0856981 + 0.00220641i
\(267\) 16.3941i 1.00330i
\(268\) 0.710579 0.410253i 0.0434055 0.0250602i
\(269\) −14.7823 8.53457i −0.901293 0.520362i −0.0236738 0.999720i \(-0.507536\pi\)
−0.877620 + 0.479358i \(0.840870\pi\)
\(270\) 1.36198 + 0.786342i 0.0828877 + 0.0478553i
\(271\) 12.9093 7.45316i 0.784182 0.452747i −0.0537286 0.998556i \(-0.517111\pi\)
0.837910 + 0.545808i \(0.183777\pi\)
\(272\) −6.89954 −0.418346
\(273\) 21.0267 + 0.541361i 1.27260 + 0.0327647i
\(274\) 9.80504i 0.592344i
\(275\) 8.38308 4.83997i 0.505519 0.291861i
\(276\) 10.2678 + 0.841833i 0.618049 + 0.0506724i
\(277\) −14.9407 + 25.8781i −0.897701 + 1.55486i −0.0672747 + 0.997734i \(0.521430\pi\)
−0.830426 + 0.557129i \(0.811903\pi\)
\(278\) −15.9754 + 9.22340i −0.958140 + 0.553183i
\(279\) 7.98399i 0.477989i
\(280\) −0.730011 + 1.19245i −0.0436265 + 0.0712622i
\(281\) 21.7934i 1.30009i 0.759897 + 0.650044i \(0.225249\pi\)
−0.759897 + 0.650044i \(0.774751\pi\)
\(282\) −2.11463 3.66264i −0.125924 0.218107i
\(283\) −13.3641 + 23.1474i −0.794416 + 1.37597i 0.128793 + 0.991671i \(0.458890\pi\)
−0.923209 + 0.384297i \(0.874444\pi\)
\(284\) −0.515730 + 0.893270i −0.0306029 + 0.0530058i
\(285\) 0.519532 0.299952i 0.0307744 0.0177676i
\(286\) 7.58860 0.448723
\(287\) −8.60285 + 4.67586i −0.507810 + 0.276007i
\(288\) −1.61463 −0.0951429
\(289\) −15.3018 26.5036i −0.900108 1.55903i
\(290\) 0.974806 1.68841i 0.0572426 0.0991470i
\(291\) 20.7249 + 11.9655i 1.21491 + 0.701430i
\(292\) 4.28231 2.47239i 0.250603 0.144686i
\(293\) −21.3877 −1.24948 −0.624741 0.780832i \(-0.714795\pi\)
−0.624741 + 0.780832i \(0.714795\pi\)
\(294\) −12.6184 8.17875i −0.735922 0.476994i
\(295\) 3.05289i 0.177746i
\(296\) 7.50830 4.33492i 0.436411 0.251962i
\(297\) −3.05118 + 5.28480i −0.177047 + 0.306655i
\(298\) −3.55160 2.05052i −0.205738 0.118783i
\(299\) −10.1006 + 14.5941i −0.584131 + 0.844000i
\(300\) 10.1409i 0.585487i
\(301\) −20.8852 + 11.3516i −1.20381 + 0.654298i
\(302\) 1.77074 0.101895
\(303\) 3.20120 + 5.54465i 0.183904 + 0.318532i
\(304\) 0.264227 0.457654i 0.0151544 0.0262483i
\(305\) −1.54378 + 2.67391i −0.0883966 + 0.153107i
\(306\) −5.57010 9.64769i −0.318421 0.551522i
\(307\) 2.16565i 0.123600i 0.998089 + 0.0618001i \(0.0196841\pi\)
−0.998089 + 0.0618001i \(0.980316\pi\)
\(308\) −4.62695 2.83260i −0.263645 0.161403i
\(309\) 3.78633i 0.215397i
\(310\) −2.26300 + 1.30654i −0.128530 + 0.0742067i
\(311\) 16.2365 + 9.37413i 0.920686 + 0.531558i 0.883854 0.467763i \(-0.154940\pi\)
0.0368318 + 0.999321i \(0.488273\pi\)
\(312\) 3.97500 6.88490i 0.225040 0.389780i
\(313\) 15.6552 + 27.1156i 0.884883 + 1.53266i 0.845847 + 0.533425i \(0.179095\pi\)
0.0390359 + 0.999238i \(0.487571\pi\)
\(314\) 7.46744 0.421412
\(315\) −2.25675 0.0581031i −0.127154 0.00327374i
\(316\) 11.9504i 0.672260i
\(317\) −14.3234 24.8089i −0.804484 1.39341i −0.916639 0.399717i \(-0.869108\pi\)
0.112154 0.993691i \(-0.464225\pi\)
\(318\) −14.7001 + 25.4613i −0.824341 + 1.42780i
\(319\) 6.55141 + 3.78246i 0.366809 + 0.211777i
\(320\) 0.264227 + 0.457654i 0.0147707 + 0.0255836i
\(321\) −19.0966 −1.06587
\(322\) 11.6061 5.12814i 0.646784 0.285780i
\(323\) 3.64609 0.202874
\(324\) 5.61843 + 9.73141i 0.312135 + 0.540634i
\(325\) 15.1300 + 8.73531i 0.839261 + 0.484548i
\(326\) 2.80731 4.86241i 0.155483 0.269304i
\(327\) 7.44772 + 12.8998i 0.411860 + 0.713362i
\(328\) 3.70082i 0.204344i
\(329\) −4.44250 2.71968i −0.244923 0.149941i
\(330\) −2.32776 −0.128139
\(331\) −13.6550 23.6512i −0.750547 1.29998i −0.947558 0.319584i \(-0.896457\pi\)
0.197011 0.980401i \(-0.436876\pi\)
\(332\) −8.22719 + 14.2499i −0.451526 + 0.782065i
\(333\) 12.1231 + 6.99928i 0.664342 + 0.383558i
\(334\) −4.03146 + 2.32756i −0.220592 + 0.127359i
\(335\) 0.433599i 0.0236901i
\(336\) −4.99358 + 2.71414i −0.272422 + 0.148068i
\(337\) 3.09092i 0.168373i −0.996450 0.0841866i \(-0.973171\pi\)
0.996450 0.0841866i \(-0.0268292\pi\)
\(338\) 0.348047 + 0.602836i 0.0189313 + 0.0327899i
\(339\) −5.37966 + 9.31784i −0.292183 + 0.506076i
\(340\) −1.82304 + 3.15760i −0.0988684 + 0.171245i
\(341\) −5.06968 8.78094i −0.274539 0.475515i
\(342\) 0.853256 0.0461388
\(343\) −18.4651 1.42875i −0.997020 0.0771452i
\(344\) 8.98453i 0.484414i
\(345\) 3.09830 4.47667i 0.166807 0.241016i
\(346\) 12.8049 + 7.39291i 0.688395 + 0.397445i
\(347\) 2.72415 4.71836i 0.146240 0.253295i −0.783595 0.621272i \(-0.786616\pi\)
0.929835 + 0.367977i \(0.119950\pi\)
\(348\) 6.86342 3.96259i 0.367918 0.212417i
\(349\) 7.05311i 0.377544i 0.982021 + 0.188772i \(0.0604508\pi\)
−0.982021 + 0.188772i \(0.939549\pi\)
\(350\) −5.96448 10.9737i −0.318815 0.586570i
\(351\) −11.0137 −0.587868
\(352\) −1.77580 + 1.02526i −0.0946504 + 0.0546464i
\(353\) 7.67718 + 4.43242i 0.408615 + 0.235914i 0.690195 0.723624i \(-0.257525\pi\)
−0.281579 + 0.959538i \(0.590858\pi\)
\(354\) 6.20501 10.7474i 0.329792 0.571217i
\(355\) 0.272539 + 0.472052i 0.0144649 + 0.0250539i
\(356\) 7.63165 0.404476
\(357\) −33.4442 20.4744i −1.77005 1.08362i
\(358\) 3.38537 0.178922
\(359\) 8.33391 4.81159i 0.439847 0.253946i −0.263686 0.964609i \(-0.584938\pi\)
0.703533 + 0.710663i \(0.251605\pi\)
\(360\) −0.426628 + 0.738941i −0.0224853 + 0.0389456i
\(361\) 9.36037 16.2126i 0.492651 0.853297i
\(362\) −5.14347 8.90875i −0.270335 0.468233i
\(363\) 14.5976i 0.766177i
\(364\) 0.252011 9.78822i 0.0132089 0.513042i
\(365\) 2.61309i 0.136775i
\(366\) −10.8695 + 6.27548i −0.568155 + 0.328025i
\(367\) 12.1036 20.9640i 0.631802 1.09431i −0.355381 0.934722i \(-0.615649\pi\)
0.987183 0.159592i \(-0.0510178\pi\)
\(368\) 0.391884 4.77979i 0.0204284 0.249164i
\(369\) −5.17489 + 2.98773i −0.269394 + 0.155535i
\(370\) 4.58160i 0.238186i
\(371\) −0.931971 + 36.1982i −0.0483855 + 1.87932i
\(372\) −10.6222 −0.550737
\(373\) 0.0491634 0.0283845i 0.00254558 0.00146969i −0.498727 0.866759i \(-0.666199\pi\)
0.501272 + 0.865290i \(0.332866\pi\)
\(374\) −12.2522 7.07381i −0.633546 0.365778i
\(375\) −9.55663 5.51752i −0.493502 0.284924i
\(376\) −1.70501 + 0.984386i −0.0879290 + 0.0507659i
\(377\) 13.6534i 0.703184i
\(378\) 6.71532 + 4.11109i 0.345399 + 0.211452i
\(379\) 20.4003i 1.04789i −0.851751 0.523946i \(-0.824459\pi\)
0.851751 0.523946i \(-0.175541\pi\)
\(380\) −0.139632 0.241849i −0.00716295 0.0124066i
\(381\) 6.15916 + 3.55599i 0.315544 + 0.182179i
\(382\) −3.36116 1.94057i −0.171972 0.0992880i
\(383\) −6.47291 11.2114i −0.330750 0.572877i 0.651909 0.758297i \(-0.273969\pi\)
−0.982659 + 0.185421i \(0.940635\pi\)
\(384\) 2.14817i 0.109623i
\(385\) −2.51892 + 1.36909i −0.128376 + 0.0697754i
\(386\) 13.6954 0.697076
\(387\) −12.5632 + 7.25334i −0.638621 + 0.368708i
\(388\) 5.57010 9.64769i 0.282779 0.489787i
\(389\) −30.9988 17.8972i −1.57170 0.907422i −0.995961 0.0897885i \(-0.971381\pi\)
−0.575740 0.817633i \(-0.695286\pi\)
\(390\) −2.10060 3.63835i −0.106368 0.184235i
\(391\) 29.9120 14.1476i 1.51272 0.715476i
\(392\) −3.80731 + 5.87404i −0.192298 + 0.296684i
\(393\) 35.0883 1.76997
\(394\) −10.2488 17.7514i −0.516326 0.894304i
\(395\) −5.46913 3.15760i −0.275182 0.158876i
\(396\) −2.86725 1.65541i −0.144085 0.0831875i
\(397\) 18.9349 10.9321i 0.950315 0.548664i 0.0571360 0.998366i \(-0.481803\pi\)
0.893179 + 0.449702i \(0.148470\pi\)
\(398\) −20.8857 −1.04690
\(399\) 2.63888 1.43429i 0.132109 0.0718045i
\(400\) −4.72074 −0.236037
\(401\) 15.0987 8.71723i 0.753993 0.435318i −0.0731420 0.997322i \(-0.523303\pi\)
0.827135 + 0.562004i \(0.189969\pi\)
\(402\) 0.881293 1.52644i 0.0439549 0.0761321i
\(403\) 9.14989 15.8481i 0.455788 0.789449i
\(404\) 2.58111 1.49020i 0.128415 0.0741403i
\(405\) 5.93816 0.295069
\(406\) 5.09641 8.32478i 0.252930 0.413152i
\(407\) 17.7776 0.881204
\(408\) −12.8357 + 7.41069i −0.635461 + 0.366884i
\(409\) 28.6772 + 16.5568i 1.41800 + 0.818680i 0.996123 0.0879749i \(-0.0280395\pi\)
0.421873 + 0.906655i \(0.361373\pi\)
\(410\) 1.69370 + 0.977857i 0.0836457 + 0.0482929i
\(411\) 10.5314 + 18.2410i 0.519478 + 0.899762i
\(412\) −1.76259 −0.0868363
\(413\) 0.393391 15.2795i 0.0193575 0.751855i
\(414\) 7.00000 3.31082i 0.344031 0.162718i
\(415\) 4.34769 + 7.53041i 0.213419 + 0.369653i
\(416\) −3.20501 1.85041i −0.157138 0.0907239i
\(417\) −19.8134 + 34.3178i −0.970267 + 1.68055i
\(418\) 0.938427 0.541801i 0.0459000 0.0265004i
\(419\) 22.9995 1.12360 0.561799 0.827274i \(-0.310110\pi\)
0.561799 + 0.827274i \(0.310110\pi\)
\(420\) −0.0773029 + 3.00248i −0.00377199 + 0.146506i
\(421\) 13.9931i 0.681984i 0.940066 + 0.340992i \(0.110763\pi\)
−0.940066 + 0.340992i \(0.889237\pi\)
\(422\) 13.0404 + 22.5866i 0.634795 + 1.09950i
\(423\) −2.75295 1.58942i −0.133853 0.0772801i
\(424\) 11.8526 + 6.84309i 0.575612 + 0.332330i
\(425\) −16.2855 28.2072i −0.789961 1.36825i
\(426\) 2.21575i 0.107353i
\(427\) −8.07108 + 13.1838i −0.390587 + 0.638009i
\(428\) 8.88973i 0.429701i
\(429\) 14.1176 8.15079i 0.681603 0.393524i
\(430\) 4.11181 + 2.37395i 0.198289 + 0.114482i
\(431\) −13.0194 7.51677i −0.627124 0.362070i 0.152514 0.988301i \(-0.451263\pi\)
−0.779637 + 0.626231i \(0.784597\pi\)
\(432\) 2.57730 1.48801i 0.124001 0.0715917i
\(433\) 8.50153 0.408557 0.204279 0.978913i \(-0.434515\pi\)
0.204279 + 0.978913i \(0.434515\pi\)
\(434\) −11.4945 + 6.24756i −0.551755 + 0.299893i
\(435\) 4.18809i 0.200804i
\(436\) 6.00504 3.46701i 0.287589 0.166040i
\(437\) −0.207092 + 2.52590i −0.00990657 + 0.120830i
\(438\) 5.31112 9.19912i 0.253775 0.439551i
\(439\) 1.54965 0.894688i 0.0739606 0.0427012i −0.462564 0.886586i \(-0.653070\pi\)
0.536524 + 0.843885i \(0.319737\pi\)
\(440\) 1.08360i 0.0516587i
\(441\) −11.2874 0.581605i −0.537496 0.0276955i
\(442\) 25.5340i 1.21453i
\(443\) −7.21146 12.4906i −0.342627 0.593447i 0.642293 0.766459i \(-0.277983\pi\)
−0.984920 + 0.173012i \(0.944650\pi\)
\(444\) 9.31213 16.1291i 0.441934 0.765452i
\(445\) 2.01649 3.49265i 0.0955906 0.165568i
\(446\) 2.73266 1.57770i 0.129395 0.0747065i
\(447\) −8.80970 −0.416685
\(448\) 1.26346 + 2.32458i 0.0596931 + 0.109826i
\(449\) 9.65218 0.455515 0.227757 0.973718i \(-0.426861\pi\)
0.227757 + 0.973718i \(0.426861\pi\)
\(450\) −3.81112 6.60105i −0.179658 0.311176i
\(451\) −3.79430 + 6.57192i −0.178667 + 0.309459i
\(452\) 4.33757 + 2.50430i 0.204022 + 0.117792i
\(453\) 3.29424 1.90193i 0.154777 0.0893604i
\(454\) −7.79225 −0.365708
\(455\) −4.41303 2.70164i −0.206886 0.126655i
\(456\) 1.13521i 0.0531609i
\(457\) 31.2955 18.0685i 1.46394 0.845208i 0.464753 0.885440i \(-0.346143\pi\)
0.999190 + 0.0402319i \(0.0128097\pi\)
\(458\) −2.83922 + 4.91767i −0.132668 + 0.229787i
\(459\) 17.7822 + 10.2666i 0.830002 + 0.479202i
\(460\) −2.08395 1.44230i −0.0971645 0.0672474i
\(461\) 27.5367i 1.28251i −0.767326 0.641257i \(-0.778413\pi\)
0.767326 0.641257i \(-0.221587\pi\)
\(462\) −11.6503 0.299952i −0.542020 0.0139550i
\(463\) −0.186065 −0.00864718 −0.00432359 0.999991i \(-0.501376\pi\)
−0.00432359 + 0.999991i \(0.501376\pi\)
\(464\) −1.84464 3.19501i −0.0856352 0.148325i
\(465\) −2.80668 + 4.86131i −0.130157 + 0.225438i
\(466\) −14.2518 + 24.6849i −0.660203 + 1.14351i
\(467\) 8.66213 + 15.0032i 0.400835 + 0.694267i 0.993827 0.110941i \(-0.0353866\pi\)
−0.592992 + 0.805209i \(0.702053\pi\)
\(468\) 5.97545i 0.276215i
\(469\) 0.0558730 2.17014i 0.00257998 0.100208i
\(470\) 1.04040i 0.0479903i
\(471\) 13.8922 8.02066i 0.640119 0.369573i
\(472\) −5.00305 2.88851i −0.230284 0.132954i
\(473\) −9.21146 + 15.9547i −0.423544 + 0.733599i
\(474\) −12.8357 22.2321i −0.589563 1.02115i
\(475\) 2.49469 0.114464
\(476\) −9.53110 + 15.5687i −0.436857 + 0.713590i
\(477\) 22.0981i 1.01180i
\(478\) −1.05230 1.82264i −0.0481310 0.0833654i
\(479\) 16.1836 28.0309i 0.739449 1.28076i −0.213294 0.976988i \(-0.568419\pi\)
0.952744 0.303776i \(-0.0982473\pi\)
\(480\) 0.983118 + 0.567604i 0.0448730 + 0.0259074i
\(481\) 16.0428 + 27.7869i 0.731487 + 1.26697i
\(482\) 15.2072 0.692670
\(483\) 16.0836 22.0062i 0.731830 1.00132i
\(484\) 6.79539 0.308881
\(485\) −2.94354 5.09836i −0.133659 0.231504i
\(486\) 13.1728 + 7.60532i 0.597530 + 0.344984i
\(487\) −15.0010 + 25.9825i −0.679759 + 1.17738i 0.295294 + 0.955407i \(0.404583\pi\)
−0.975053 + 0.221971i \(0.928751\pi\)
\(488\) 2.92132 + 5.05987i 0.132242 + 0.229050i
\(489\) 12.0612i 0.545425i
\(490\) 1.68229 + 3.29451i 0.0759979 + 0.148831i
\(491\) −11.9761 −0.540476 −0.270238 0.962794i \(-0.587102\pi\)
−0.270238 + 0.962794i \(0.587102\pi\)
\(492\) 3.97500 + 6.88490i 0.179207 + 0.310395i
\(493\) 12.7272 22.0441i 0.573203 0.992816i
\(494\) 1.69370 + 0.977857i 0.0762030 + 0.0439958i
\(495\) −1.51521 + 0.874807i −0.0681036 + 0.0393196i
\(496\) 4.94479i 0.222027i
\(497\) 1.30321 + 2.39771i 0.0584571 + 0.107552i
\(498\) 35.3468i 1.58393i
\(499\) 20.1372 + 34.8787i 0.901465 + 1.56138i 0.825593 + 0.564266i \(0.190841\pi\)
0.0758721 + 0.997118i \(0.475826\pi\)
\(500\) −2.56848 + 4.44874i −0.114866 + 0.198953i
\(501\) −5.00000 + 8.66025i −0.223384 + 0.386912i
\(502\) 10.5231 + 18.2266i 0.469670 + 0.813493i
\(503\) 19.6812 0.877540 0.438770 0.898599i \(-0.355414\pi\)
0.438770 + 0.898599i \(0.355414\pi\)
\(504\) −2.23046 + 3.64338i −0.0993527 + 0.162289i
\(505\) 1.57500i 0.0700868i
\(506\) 5.59643 8.08617i 0.248792 0.359474i
\(507\) 1.29499 + 0.747664i 0.0575126 + 0.0332049i
\(508\) 1.65536 2.86717i 0.0734448 0.127210i
\(509\) 25.0722 14.4755i 1.11131 0.641613i 0.172139 0.985073i \(-0.444932\pi\)
0.939168 + 0.343459i \(0.111599\pi\)
\(510\) 7.83241i 0.346825i
\(511\) 0.336719 13.0783i 0.0148956 0.578552i
\(512\) 1.00000 0.0441942
\(513\) −1.36198 + 0.786342i −0.0601331 + 0.0347179i
\(514\) −19.3956 11.1981i −0.855505 0.493926i
\(515\) −0.465722 + 0.806654i −0.0205222 + 0.0355454i
\(516\) 9.65015 + 16.7145i 0.424824 + 0.735817i
\(517\) −4.03700 −0.177547
\(518\) 0.590379 22.9306i 0.0259398 1.00751i
\(519\) 31.7624 1.39422
\(520\) −1.69370 + 0.977857i −0.0742735 + 0.0428818i
\(521\) −14.5786 + 25.2508i −0.638698 + 1.10626i 0.347021 + 0.937857i \(0.387193\pi\)
−0.985719 + 0.168400i \(0.946140\pi\)
\(522\) 2.97840 5.15875i 0.130361 0.225792i
\(523\) −8.36986 14.4970i −0.365989 0.633911i 0.622946 0.782265i \(-0.285936\pi\)
−0.988934 + 0.148354i \(0.952602\pi\)
\(524\) 16.3341i 0.713557i
\(525\) −22.8828 14.0088i −0.998689 0.611394i
\(526\) 9.58514i 0.417932i
\(527\) −29.5460 + 17.0584i −1.28704 + 0.743075i
\(528\) −2.20243 + 3.81471i −0.0958483 + 0.166014i
\(529\) 8.10208 + 21.5257i 0.352264 + 0.935901i
\(530\) 6.26353 3.61625i 0.272071 0.157080i
\(531\) 9.32774i 0.404789i
\(532\) −0.667682 1.22843i −0.0289477 0.0532592i
\(533\) −13.6961 −0.593244
\(534\) 14.1977 8.19703i 0.614394 0.354720i
\(535\) 4.06842 + 2.34890i 0.175893 + 0.101552i
\(536\) −0.710579 0.410253i −0.0306923 0.0177202i
\(537\) 6.29804 3.63617i 0.271780 0.156913i
\(538\) 17.0691i 0.735903i
\(539\) −12.7834 + 6.52764i −0.550621 + 0.281165i
\(540\) 1.57268i 0.0676776i
\(541\) 13.9445 + 24.1526i 0.599522 + 1.03840i 0.992892 + 0.119022i \(0.0379759\pi\)
−0.393370 + 0.919380i \(0.628691\pi\)
\(542\) −12.9093 7.45316i −0.554500 0.320141i
\(543\) −19.1375 11.0490i −0.821268 0.474160i
\(544\) 3.44977 + 5.97518i 0.147908 + 0.256184i
\(545\) 3.66431i 0.156962i
\(546\) −10.0445 18.4804i −0.429866 0.790887i
\(547\) −29.2861 −1.25219 −0.626093 0.779749i \(-0.715347\pi\)
−0.626093 + 0.779749i \(0.715347\pi\)
\(548\) 8.49141 4.90252i 0.362735 0.209425i
\(549\) −4.71684 + 8.16981i −0.201310 + 0.348679i
\(550\) −8.38308 4.83997i −0.357456 0.206377i
\(551\) 0.974806 + 1.68841i 0.0415281 + 0.0719288i
\(552\) −4.40485 9.31309i −0.187483 0.396392i
\(553\) −26.9658 16.5083i −1.14670 0.702006i
\(554\) 29.8814 1.26954
\(555\) −4.92103 8.52347i −0.208886 0.361801i
\(556\) 15.9754 + 9.22340i 0.677507 + 0.391159i
\(557\) −22.9683 13.2608i −0.973199 0.561877i −0.0729893 0.997333i \(-0.523254\pi\)
−0.900210 + 0.435456i \(0.856587\pi\)
\(558\) −6.91434 + 3.99199i −0.292707 + 0.168995i
\(559\) −33.2502 −1.40633
\(560\) 1.39769 + 0.0359855i 0.0590633 + 0.00152066i
\(561\) −30.3915 −1.28313
\(562\) 18.8737 10.8967i 0.796138 0.459650i
\(563\) 11.2503 19.4861i 0.474145 0.821243i −0.525417 0.850845i \(-0.676091\pi\)
0.999562 + 0.0296019i \(0.00942395\pi\)
\(564\) −2.11463 + 3.66264i −0.0890419 + 0.154225i
\(565\) 2.29221 1.32341i 0.0964339 0.0556761i
\(566\) 26.7283 1.12347
\(567\) 29.7201 + 0.765183i 1.24813 + 0.0321347i
\(568\) 1.03146 0.0432791
\(569\) −39.9445 + 23.0619i −1.67456 + 0.966807i −0.709525 + 0.704680i \(0.751091\pi\)
−0.965033 + 0.262127i \(0.915576\pi\)
\(570\) −0.519532 0.299952i −0.0217608 0.0125636i
\(571\) 8.35014 + 4.82096i 0.349442 + 0.201751i 0.664440 0.747342i \(-0.268670\pi\)
−0.314997 + 0.949093i \(0.602004\pi\)
\(572\) −3.79430 6.57192i −0.158648 0.274786i
\(573\) −8.33733 −0.348297
\(574\) 8.35084 + 5.11236i 0.348557 + 0.213386i
\(575\) 20.4661 9.67994i 0.853496 0.403682i
\(576\) 0.807314 + 1.39831i 0.0336381 + 0.0582629i
\(577\) −5.57577 3.21917i −0.232122 0.134016i 0.379428 0.925221i \(-0.376121\pi\)
−0.611551 + 0.791205i \(0.709454\pi\)
\(578\) −15.3018 + 26.5036i −0.636473 + 1.10240i
\(579\) 25.4784 14.7100i 1.05885 0.611326i
\(580\) −1.94961 −0.0809532
\(581\) 20.7895 + 38.2495i 0.862495 + 1.58685i
\(582\) 23.9310i 0.991972i
\(583\) 14.0319 + 24.3039i 0.581140 + 1.00656i
\(584\) −4.28231 2.47239i −0.177203 0.102308i
\(585\) −2.73469 1.57887i −0.113066 0.0652784i
\(586\) 10.6938 + 18.5223i 0.441758 + 0.765148i
\(587\) 23.4844i 0.969303i −0.874707 0.484652i \(-0.838946\pi\)
0.874707 0.484652i \(-0.161054\pi\)
\(588\) −0.773792 + 15.0173i −0.0319106 + 0.619301i
\(589\) 2.61309i 0.107670i
\(590\) −2.64388 + 1.52644i −0.108847 + 0.0628427i
\(591\) −38.1330 22.0161i −1.56858 0.905622i
\(592\) −7.50830 4.33492i −0.308589 0.178164i
\(593\) −4.62619 + 2.67093i −0.189975 + 0.109682i −0.591971 0.805959i \(-0.701650\pi\)
0.401996 + 0.915641i \(0.368317\pi\)
\(594\) 6.10236 0.250383
\(595\) 4.60670 + 8.47561i 0.188856 + 0.347466i
\(596\) 4.10103i 0.167985i
\(597\) −38.8550 + 22.4330i −1.59023 + 0.918120i
\(598\) 17.6892 + 1.45029i 0.723364 + 0.0593069i
\(599\) −7.02881 + 12.1742i −0.287189 + 0.497426i −0.973138 0.230224i \(-0.926054\pi\)
0.685948 + 0.727650i \(0.259388\pi\)
\(600\) −8.78231 + 5.07047i −0.358536 + 0.207001i
\(601\) 13.0270i 0.531383i −0.964058 0.265691i \(-0.914400\pi\)
0.964058 0.265691i \(-0.0856002\pi\)
\(602\) 20.2734 + 12.4113i 0.826283 + 0.505848i
\(603\) 1.32481i 0.0539505i
\(604\) −0.885372 1.53351i −0.0360253 0.0623976i
\(605\) 1.79552 3.10994i 0.0729984 0.126437i
\(606\) 3.20120 5.54465i 0.130040 0.225236i
\(607\) 34.3614 19.8386i 1.39469 0.805222i 0.400856 0.916141i \(-0.368713\pi\)
0.993829 + 0.110919i \(0.0353794\pi\)
\(608\) −0.528453 −0.0214316
\(609\) 0.539672 20.9611i 0.0218686 0.849388i
\(610\) 3.08756 0.125012
\(611\) −3.64304 6.30993i −0.147382 0.255272i
\(612\) −5.57010 + 9.64769i −0.225158 + 0.389985i
\(613\) −22.8371 13.1850i −0.922380 0.532537i −0.0379867 0.999278i \(-0.512094\pi\)
−0.884394 + 0.466742i \(0.845428\pi\)
\(614\) 1.87551 1.08283i 0.0756893 0.0436993i
\(615\) 4.20120 0.169409
\(616\) −0.139632 + 5.42336i −0.00562592 + 0.218513i
\(617\) 10.7491i 0.432744i 0.976311 + 0.216372i \(0.0694224\pi\)
−0.976311 + 0.216372i \(0.930578\pi\)
\(618\) −3.27906 + 1.89316i −0.131903 + 0.0761543i
\(619\) −17.9379 + 31.0694i −0.720985 + 1.24878i 0.239620 + 0.970867i \(0.422977\pi\)
−0.960605 + 0.277917i \(0.910356\pi\)
\(620\) 2.26300 + 1.30654i 0.0908843 + 0.0524721i
\(621\) −8.12237 + 11.7358i −0.325939 + 0.470943i
\(622\) 18.7483i 0.751737i
\(623\) 10.5424 17.2207i 0.422374 0.689931i
\(624\) −7.94999 −0.318254
\(625\) −10.4445 18.0904i −0.417781 0.723618i
\(626\) 15.6552 27.1156i 0.625707 1.08376i
\(627\) 1.16388 2.01590i 0.0464809 0.0805073i
\(628\) −3.73372 6.46700i −0.148992 0.258061i
\(629\) 59.8179i 2.38510i
\(630\) 1.07806 + 1.98346i 0.0429509 + 0.0790229i
\(631\) 33.2092i 1.32204i −0.750370 0.661018i \(-0.770124\pi\)
0.750370 0.661018i \(-0.229876\pi\)
\(632\) −10.3493 + 5.97518i −0.411674 + 0.237680i
\(633\) 48.5198 + 28.0129i 1.92849 + 1.11341i
\(634\) −14.3234 + 24.8089i −0.568856 + 0.985288i
\(635\) −0.874781 1.51517i −0.0347146 0.0601275i
\(636\) 29.4002 1.16579
\(637\) −21.7388 14.0902i −0.861322 0.558274i
\(638\) 7.56492i 0.299498i
\(639\) 0.832712 + 1.44230i 0.0329416 + 0.0570565i
\(640\) 0.264227 0.457654i 0.0104445 0.0180904i
\(641\) −4.72515 2.72807i −0.186632 0.107752i 0.403773 0.914859i \(-0.367699\pi\)
−0.590405 + 0.807107i \(0.701032\pi\)
\(642\) 9.54832 + 16.5382i 0.376842 + 0.652710i
\(643\) 19.3950 0.764865 0.382432 0.923983i \(-0.375086\pi\)
0.382432 + 0.923983i \(0.375086\pi\)
\(644\) −10.2442 7.48713i −0.403676 0.295034i
\(645\) 10.1993 0.401597
\(646\) −1.82304 3.15760i −0.0717267 0.124234i
\(647\) −32.8996 18.9946i −1.29342 0.746755i −0.314159 0.949370i \(-0.601723\pi\)
−0.979258 + 0.202615i \(0.935056\pi\)
\(648\) 5.61843 9.73141i 0.220713 0.382286i
\(649\) −5.92294 10.2588i −0.232496 0.402694i
\(650\) 17.4706i 0.685254i
\(651\) −14.6737 + 23.9689i −0.575106 + 0.939414i
\(652\) −5.61463 −0.219886
\(653\) 3.32891 + 5.76584i 0.130270 + 0.225635i 0.923781 0.382922i \(-0.125082\pi\)
−0.793510 + 0.608557i \(0.791749\pi\)
\(654\) 7.44772 12.8998i 0.291229 0.504423i
\(655\) −7.47536 4.31590i −0.292086 0.168636i
\(656\) 3.20501 1.85041i 0.125135 0.0722464i
\(657\) 7.98399i 0.311485i
\(658\) −0.134065 + 5.20716i −0.00522641 + 0.202996i
\(659\) 7.65972i 0.298380i −0.988809 0.149190i \(-0.952333\pi\)
0.988809 0.149190i \(-0.0476667\pi\)
\(660\) 1.16388 + 2.01590i 0.0453040 + 0.0784688i
\(661\) −11.6853 + 20.2395i −0.454504 + 0.787225i −0.998660 0.0517599i \(-0.983517\pi\)
0.544155 + 0.838985i \(0.316850\pi\)
\(662\) −13.6550 + 23.6512i −0.530717 + 0.919228i
\(663\) −27.4257 47.5026i −1.06512 1.84485i
\(664\) 16.4544 0.638554
\(665\) −0.738616 0.0190167i −0.0286423 0.000737434i
\(666\) 13.9986i 0.542433i
\(667\) 14.5486 + 10.0691i 0.563324 + 0.389876i
\(668\) 4.03146 + 2.32756i 0.155982 + 0.0900562i
\(669\) 3.38917 5.87022i 0.131033 0.226956i
\(670\) −0.375508 + 0.216800i −0.0145071 + 0.00837570i
\(671\) 11.9804i 0.462499i
\(672\) 4.84730 + 2.96750i 0.186989 + 0.114474i
\(673\) −32.0944 −1.23715 −0.618575 0.785726i \(-0.712290\pi\)
−0.618575 + 0.785726i \(0.712290\pi\)
\(674\) −2.67682 + 1.54546i −0.103107 + 0.0595289i
\(675\) 12.1668 + 7.02449i 0.468299 + 0.270373i
\(676\) 0.348047 0.602836i 0.0133864 0.0231860i
\(677\) −5.30587 9.19004i −0.203921 0.353202i 0.745867 0.666095i \(-0.232035\pi\)
−0.949788 + 0.312893i \(0.898702\pi\)
\(678\) 10.7593 0.413209
\(679\) −14.0752 25.8962i −0.540158 0.993806i
\(680\) 3.64609 0.139821
\(681\) −14.4965 + 8.36953i −0.555505 + 0.320721i
\(682\) −5.06968 + 8.78094i −0.194128 + 0.336240i
\(683\) 20.7369 35.9173i 0.793474 1.37434i −0.130330 0.991471i \(-0.541604\pi\)
0.923804 0.382866i \(-0.125063\pi\)
\(684\) −0.426628 0.738941i −0.0163125 0.0282541i
\(685\) 5.18151i 0.197975i
\(686\) 7.99520 + 16.7056i 0.305258 + 0.637822i
\(687\) 12.1982i 0.465392i
\(688\) 7.78083 4.49227i 0.296642 0.171266i
\(689\) −25.3251 + 43.8643i −0.964808 + 1.67110i
\(690\) −5.42606 0.444869i −0.206566 0.0169359i
\(691\) −3.74856 + 2.16423i −0.142602 + 0.0823313i −0.569603 0.821920i \(-0.692903\pi\)
0.427002 + 0.904251i \(0.359570\pi\)
\(692\) 14.7858i 0.562072i
\(693\) −7.69625 + 4.18310i −0.292356 + 0.158903i
\(694\) −5.44829 −0.206814
\(695\) 8.44225 4.87414i 0.320233 0.184887i
\(696\) −6.86342 3.96259i −0.260157 0.150202i
\(697\) 22.1131 + 12.7670i 0.837593 + 0.483584i
\(698\) 6.10817 3.52655i 0.231198 0.133482i
\(699\) 61.2307i 2.31596i
\(700\) −6.52127 + 10.6523i −0.246481 + 0.402617i
\(701\) 4.85553i 0.183391i 0.995787 + 0.0916954i \(0.0292286\pi\)
−0.995787 + 0.0916954i \(0.970771\pi\)
\(702\) 5.50685 + 9.53814i 0.207843 + 0.359994i
\(703\) 3.96779 + 2.29080i 0.149648 + 0.0863992i
\(704\) 1.77580 + 1.02526i 0.0669279 + 0.0386409i
\(705\) 1.11748 + 1.93554i 0.0420868 + 0.0728965i
\(706\) 8.86485i 0.333633i
\(707\) 0.202953 7.88279i 0.00763284 0.296463i
\(708\) −12.4100 −0.466397
\(709\) −12.1318 + 7.00431i −0.455620 + 0.263052i −0.710201 0.703999i \(-0.751396\pi\)
0.254581 + 0.967051i \(0.418062\pi\)
\(710\) 0.272539 0.472052i 0.0102282 0.0177158i
\(711\) −16.7103 9.64769i −0.626685 0.361817i
\(712\) −3.81582 6.60920i −0.143004 0.247690i
\(713\) −10.1394 21.4374i −0.379722 0.802839i
\(714\) −1.00927 + 39.2007i −0.0377711 + 1.46705i
\(715\) −4.01022 −0.149974
\(716\) −1.69269 2.93182i −0.0632587 0.109567i
\(717\) −3.91533 2.26052i −0.146221 0.0844205i
\(718\) −8.33391 4.81159i −0.311019 0.179567i
\(719\) −29.9439 + 17.2881i −1.11672 + 0.644739i −0.940562 0.339623i \(-0.889700\pi\)
−0.176159 + 0.984362i \(0.556367\pi\)
\(720\) 0.853256 0.0317990
\(721\) −2.43485 + 3.97724i −0.0906787 + 0.148120i
\(722\) −18.7207 −0.696714
\(723\) 28.2910 16.3338i 1.05215 0.607462i
\(724\) −5.14347 + 8.90875i −0.191155 + 0.331091i
\(725\) 8.70805 15.0828i 0.323409 0.560161i
\(726\) 12.6419 7.29882i 0.469186 0.270885i
\(727\) −29.9681 −1.11146 −0.555728 0.831364i \(-0.687560\pi\)
−0.555728 + 0.831364i \(0.687560\pi\)
\(728\) −8.60285 + 4.67586i −0.318843 + 0.173299i
\(729\) −1.03559 −0.0383550
\(730\) −2.26300 + 1.30654i −0.0837574 + 0.0483574i
\(731\) 53.6842 + 30.9946i 1.98558 + 1.14638i
\(732\) 10.8695 + 6.27548i 0.401747 + 0.231949i
\(733\) 23.8350 + 41.2834i 0.880366 + 1.52484i 0.850934 + 0.525272i \(0.176036\pi\)
0.0294318 + 0.999567i \(0.490630\pi\)
\(734\) −24.2072 −0.893503
\(735\) 6.66825 + 4.32209i 0.245962 + 0.159423i
\(736\) −4.33536 + 2.05052i −0.159804 + 0.0755830i
\(737\) −0.841230 1.45705i −0.0309871 0.0536712i
\(738\) 5.17489 + 2.98773i 0.190490 + 0.109980i
\(739\) 0.172792 0.299285i 0.00635626 0.0110094i −0.862830 0.505495i \(-0.831310\pi\)
0.869186 + 0.494485i \(0.164643\pi\)
\(740\) −3.96779 + 2.29080i −0.145859 + 0.0842115i
\(741\) 4.20120 0.154335
\(742\) 31.8146 17.2920i 1.16795 0.634809i
\(743\) 14.5735i 0.534650i −0.963606 0.267325i \(-0.913860\pi\)
0.963606 0.267325i \(-0.0861397\pi\)
\(744\) 5.31112 + 9.19912i 0.194715 + 0.337256i
\(745\) 1.87685 + 1.08360i 0.0687626 + 0.0397001i
\(746\) −0.0491634 0.0283845i −0.00180000 0.00103923i
\(747\) 13.2838 + 23.0083i 0.486030 + 0.841829i
\(748\) 14.1476i 0.517288i
\(749\) 20.0595 + 12.2804i 0.732959 + 0.448715i
\(750\) 11.0350i 0.402943i
\(751\) −40.0662 + 23.1322i −1.46204 + 0.844107i −0.999105 0.0422873i \(-0.986536\pi\)
−0.462931 + 0.886394i \(0.653202\pi\)
\(752\) 1.70501 + 0.984386i 0.0621752 + 0.0358969i
\(753\) 39.1538 + 22.6054i 1.42684 + 0.823788i
\(754\) 11.8242 6.82668i 0.430611 0.248613i
\(755\) −0.935756 −0.0340557
\(756\) 0.202654 7.87118i 0.00737046 0.286272i
\(757\) 5.74054i 0.208644i −0.994544 0.104322i \(-0.966733\pi\)
0.994544 0.104322i \(-0.0332672\pi\)
\(758\) −17.6672 + 10.2001i −0.641701 + 0.370486i
\(759\) 1.72619 21.0543i 0.0626568 0.764222i
\(760\) −0.139632 + 0.241849i −0.00506497 + 0.00877278i
\(761\) −38.7314 + 22.3616i −1.40401 + 0.810607i −0.994801 0.101834i \(-0.967529\pi\)
−0.409210 + 0.912440i \(0.634196\pi\)
\(762\) 7.11199i 0.257640i
\(763\) 0.472178 18.3396i 0.0170940 0.663939i
\(764\) 3.88113i 0.140414i
\(765\) 2.94354 + 5.09836i 0.106424 + 0.184331i
\(766\) −6.47291 + 11.2114i −0.233876 + 0.405085i
\(767\) 10.6899 18.5154i 0.385989 0.668552i
\(768\) 1.86037 1.07408i 0.0671303 0.0387577i
\(769\) 30.7425 1.10860 0.554301 0.832316i \(-0.312986\pi\)
0.554301 + 0.832316i \(0.312986\pi\)
\(770\) 2.44513 + 1.49690i 0.0881163 + 0.0539445i
\(771\) −48.1107 −1.73266
\(772\) −6.84769 11.8605i −0.246454 0.426870i
\(773\) −14.1519 + 24.5119i −0.509009 + 0.881630i 0.490936 + 0.871196i \(0.336655\pi\)
−0.999946 + 0.0104345i \(0.996679\pi\)
\(774\) 12.5632 + 7.25334i 0.451573 + 0.260716i
\(775\) −20.2157 + 11.6715i −0.726168 + 0.419253i
\(776\) −11.1402 −0.399910
\(777\) −23.5311 43.2935i −0.844173 1.55315i
\(778\) 35.7943i 1.28329i
\(779\) −1.69370 + 0.977857i −0.0606830 + 0.0350353i
\(780\) −2.10060 + 3.63835i −0.0752136 + 0.130274i
\(781\) 1.83166 + 1.05751i 0.0655421 + 0.0378407i
\(782\) −27.2082 18.8308i −0.972964 0.673387i
\(783\) 10.9793i 0.392370i
\(784\) 6.99073 + 0.360210i 0.249669 + 0.0128646i
\(785\) −3.94620 −0.140846
\(786\) −17.5442 30.3874i −0.625780 1.08388i
\(787\) 1.87582 3.24902i 0.0668659 0.115815i −0.830654 0.556789i \(-0.812033\pi\)
0.897520 + 0.440973i \(0.145367\pi\)
\(788\) −10.2488 + 17.7514i −0.365098 + 0.632368i
\(789\) 10.2952 + 17.8319i 0.366521 + 0.634832i
\(790\) 6.31521i 0.224685i
\(791\) 11.6429 6.32819i 0.413973 0.225005i
\(792\) 3.31082i 0.117645i
\(793\) −18.7257 + 10.8113i −0.664969 + 0.383920i
\(794\) −18.9349 10.9321i −0.671974 0.387964i
\(795\) 7.76832 13.4551i 0.275514 0.477204i
\(796\) 10.4428 + 18.0875i 0.370136 + 0.641095i
\(797\) −14.8394 −0.525637 −0.262819 0.964845i \(-0.584652\pi\)
−0.262819 + 0.964845i \(0.584652\pi\)
\(798\) −2.56157 1.56819i −0.0906787 0.0555132i
\(799\) 13.5836i 0.480554i
\(800\) 2.36037 + 4.08828i 0.0834516 + 0.144542i
\(801\) 6.16113 10.6714i 0.217693 0.377055i
\(802\) −15.0987 8.71723i −0.533153 0.307816i
\(803\) −5.06968 8.78094i −0.178905 0.309873i
\(804\) −1.76259 −0.0621616
\(805\) −6.13330 + 2.70998i −0.216170 + 0.0955143i
\(806\) −18.2998 −0.644582
\(807\) 18.3337 + 31.7549i 0.645377 + 1.11783i
\(808\) −2.58111 1.49020i −0.0908030 0.0524251i
\(809\) −23.3360 + 40.4191i −0.820450 + 1.42106i 0.0848982 + 0.996390i \(0.472943\pi\)
−0.905348 + 0.424671i \(0.860390\pi\)
\(810\) −2.96908 5.14260i −0.104323 0.180692i
\(811\) 10.5200i 0.369409i −0.982794 0.184704i \(-0.940867\pi\)
0.982794 0.184704i \(-0.0591328\pi\)
\(812\) −9.75768 0.251224i −0.342427 0.00881625i
\(813\) −32.0213 −1.12304
\(814\) −8.88881 15.3959i −0.311553 0.539625i
\(815\) −1.48353 + 2.56956i −0.0519660 + 0.0900077i
\(816\) 12.8357 + 7.41069i 0.449339 + 0.259426i
\(817\) −4.11181 + 2.37395i −0.143854 + 0.0830541i
\(818\) 33.1136i 1.15779i
\(819\) −13.4835 8.25455i −0.471151 0.288437i
\(820\) 1.95571i 0.0682965i
\(821\) 7.02805 + 12.1729i 0.245281 + 0.424839i 0.962210 0.272307i \(-0.0877866\pi\)
−0.716930 + 0.697145i \(0.754453\pi\)
\(822\) 10.5314 18.2410i 0.367326 0.636228i
\(823\) 3.49718 6.05730i 0.121904 0.211144i −0.798614 0.601843i \(-0.794433\pi\)
0.920519 + 0.390699i \(0.127767\pi\)
\(824\) 0.881293 + 1.52644i 0.0307013 + 0.0531762i
\(825\) −20.7941 −0.723959
\(826\) −13.4291 + 7.29906i −0.467259 + 0.253967i
\(827\) 36.9598i 1.28522i 0.766194 + 0.642609i \(0.222148\pi\)
−0.766194 + 0.642609i \(0.777852\pi\)
\(828\) −6.36725 4.40677i −0.221277 0.153146i
\(829\) 3.07501 + 1.77536i 0.106800 + 0.0616608i 0.552448 0.833547i \(-0.313694\pi\)
−0.445649 + 0.895208i \(0.647027\pi\)
\(830\) 4.34769 7.53041i 0.150910 0.261384i
\(831\) 55.5905 32.0952i 1.92841 1.11337i
\(832\) 3.70082i 0.128303i
\(833\) 21.9641 + 43.0135i 0.761010 + 1.49033i
\(834\) 39.6268 1.37216
\(835\) 2.13044 1.23001i 0.0737269 0.0425662i
\(836\) −0.938427 0.541801i −0.0324562 0.0187386i
\(837\) 7.35787 12.7442i 0.254325 0.440504i
\(838\) −11.4997 19.9181i −0.397252 0.688060i
\(839\) −4.89386 −0.168955 −0.0844774 0.996425i \(-0.526922\pi\)
−0.0844774 + 0.996425i \(0.526922\pi\)
\(840\) 2.63888 1.43429i 0.0910499 0.0494878i
\(841\) −15.3892 −0.530663
\(842\) 12.1184 6.99657i 0.417628 0.241118i
\(843\) 23.4080 40.5438i 0.806214 1.39640i
\(844\) 13.0404 22.5866i 0.448868 0.777462i
\(845\) −0.183927 0.318571i −0.00632728 0.0109592i
\(846\) 3.17884i 0.109291i
\(847\) 9.38722 15.3337i 0.322549 0.526871i
\(848\) 13.6862i 0.469985i
\(849\) 49.7245 28.7084i 1.70654 0.985271i
\(850\) −16.2855 + 28.2072i −0.558587 + 0.967501i
\(851\) 41.4400 + 3.39757i 1.42055 + 0.116467i
\(852\) 1.91889 1.10787i 0.0657402 0.0379551i
\(853\) 15.0374i 0.514871i 0.966296 + 0.257435i \(0.0828774\pi\)
−0.966296 + 0.257435i \(0.917123\pi\)
\(854\) 15.4530 + 0.397859i 0.528792 + 0.0136145i
\(855\) −0.450906 −0.0154207
\(856\) 7.69873 4.44487i 0.263137 0.151922i
\(857\) −21.1705 12.2228i −0.723171 0.417523i 0.0927480 0.995690i \(-0.470435\pi\)
−0.815919 + 0.578167i \(0.803768\pi\)
\(858\) −14.1176 8.15079i −0.481966 0.278263i
\(859\) −39.3337 + 22.7093i −1.34205 + 0.774833i −0.987108 0.160056i \(-0.948833\pi\)
−0.354942 + 0.934889i \(0.615499\pi\)
\(860\) 4.74791i 0.161902i
\(861\) 21.0267 + 0.541361i 0.716589 + 0.0184495i
\(862\) 15.0335i 0.512044i
\(863\) 15.5188 + 26.8793i 0.528265 + 0.914982i 0.999457 + 0.0329515i \(0.0104907\pi\)
−0.471192 + 0.882031i \(0.656176\pi\)
\(864\) −2.57730 1.48801i −0.0876816 0.0506230i
\(865\) −6.76679 3.90681i −0.230078 0.132835i
\(866\) −4.25076 7.36254i −0.144447 0.250189i
\(867\) 65.7419i 2.23271i
\(868\) 11.1578 + 6.83078i 0.378721 + 0.231852i
\(869\) −24.5044 −0.831255
\(870\) −3.62700 + 2.09405i −0.122967 + 0.0709948i
\(871\) 1.51827 2.62973i 0.0514447 0.0891049i
\(872\) −6.00504 3.46701i −0.203356 0.117408i
\(873\) −8.99363 15.5774i −0.304388 0.527216i
\(874\) 2.29104 1.08360i 0.0774955 0.0366534i
\(875\) 6.49036 + 11.9413i 0.219414 + 0.403688i
\(876\) −10.6222 −0.358892
\(877\) 13.4970 + 23.3775i 0.455761 + 0.789401i 0.998732 0.0503507i \(-0.0160339\pi\)
−0.542971 + 0.839752i \(0.682701\pi\)
\(878\) −1.54965 0.894688i −0.0522980 0.0301943i
\(879\) 39.7890 + 22.9722i 1.34205 + 0.774832i
\(880\) 0.938427 0.541801i 0.0316344 0.0182641i
\(881\) 41.9616 1.41372 0.706860 0.707353i \(-0.250111\pi\)
0.706860 + 0.707353i \(0.250111\pi\)
\(882\) 5.14003 + 10.0660i 0.173074 + 0.338940i
\(883\) −10.3346 −0.347786 −0.173893 0.984765i \(-0.555635\pi\)
−0.173893 + 0.984765i \(0.555635\pi\)
\(884\) −22.1131 + 12.7670i −0.743743 + 0.429400i
\(885\) −3.27906 + 5.67949i −0.110224 + 0.190914i
\(886\) −7.21146 + 12.4906i −0.242274 + 0.419631i
\(887\) −30.0510 + 17.3499i −1.00901 + 0.582554i −0.910903 0.412621i \(-0.864613\pi\)
−0.0981109 + 0.995175i \(0.531280\pi\)
\(888\) −18.6243 −0.624989
\(889\) −4.18298 7.69603i −0.140293 0.258117i
\(890\) −4.03297 −0.135185
\(891\) 19.9544 11.5207i 0.668498 0.385957i
\(892\) −2.73266 1.57770i −0.0914964 0.0528254i
\(893\) −0.901017 0.520202i −0.0301514 0.0174079i
\(894\) 4.40485 + 7.62943i 0.147320 + 0.255166i
\(895\) −1.78901 −0.0598001
\(896\) 1.38141 2.25648i 0.0461497 0.0753837i
\(897\) 34.4661 16.3016i 1.15079 0.544294i
\(898\) −4.82609 8.35903i −0.161049 0.278945i
\(899\) −15.7986 9.12134i −0.526914 0.304214i
\(900\) −3.81112 + 6.60105i −0.127037 + 0.220035i
\(901\) 81.7773 47.2142i 2.72440 1.57293i
\(902\) 7.58860 0.252673
\(903\) 51.0469 + 1.31427i 1.69873 + 0.0437361i
\(904\) 5.00860i 0.166584i
\(905\) 2.71808 + 4.70786i 0.0903522 + 0.156495i
\(906\) −3.29424 1.90193i −0.109444 0.0631874i
\(907\) −27.5555 15.9092i −0.914966 0.528256i −0.0329403 0.999457i \(-0.510487\pi\)
−0.882026 + 0.471201i \(0.843820\pi\)
\(908\) 3.89612 + 6.74828i 0.129297 + 0.223950i
\(909\) 4.81224i 0.159612i
\(910\) −0.133176 + 5.17262i −0.00441474 + 0.171471i
\(911\) 3.68229i 0.122000i −0.998138 0.0609998i \(-0.980571\pi\)
0.998138 0.0609998i \(-0.0194289\pi\)
\(912\) −0.983118 + 0.567604i −0.0325543 + 0.0187952i
\(913\) 29.2197 + 16.8700i 0.967029 + 0.558315i
\(914\) −31.2955 18.0685i −1.03516 0.597653i
\(915\) 5.74400 3.31630i 0.189891 0.109634i
\(916\) 5.67843 0.187621
\(917\) −36.8575 22.5641i −1.21714 0.745131i
\(918\) 20.5331i 0.677694i
\(919\) 45.3869 26.2041i 1.49718 0.864395i 0.497181 0.867647i \(-0.334369\pi\)
0.999995 + 0.00325243i \(0.00103528\pi\)
\(920\) −0.207092 + 2.52590i −0.00682763 + 0.0832764i
\(921\) 2.32609 4.02891i 0.0766473 0.132757i
\(922\) −23.8475 + 13.7684i −0.785376 + 0.453437i
\(923\) 3.81725i 0.125646i
\(924\) 5.56538 + 10.2394i 0.183087 + 0.336852i
\(925\) 40.9280i 1.34570i
\(926\) 0.0930326 + 0.161137i 0.00305724 + 0.00529530i
\(927\) −1.42296 + 2.46464i −0.0467361 + 0.0809493i
\(928\) −1.84464 + 3.19501i −0.0605532 + 0.104881i
\(929\) −1.47463 + 0.851381i −0.0483812 + 0.0279329i −0.523995 0.851721i \(-0.675559\pi\)
0.475614 + 0.879654i \(0.342226\pi\)
\(930\) 5.61336 0.184069
\(931\) −3.69427 0.190354i −0.121075 0.00623861i
\(932\) 28.5037 0.933669
\(933\) −20.1372 34.8787i −0.659263 1.14188i
\(934\) 8.66213 15.0032i 0.283433 0.490921i
\(935\) 6.47472 + 3.73818i 0.211746 + 0.122252i
\(936\) −5.17489 + 2.98773i −0.169147 + 0.0976569i
\(937\) 17.8589 0.583425 0.291713 0.956506i \(-0.405775\pi\)
0.291713 + 0.956506i \(0.405775\pi\)
\(938\) −1.90733 + 1.03668i −0.0622765 + 0.0338488i
\(939\) 67.2599i 2.19495i
\(940\) 0.901017 0.520202i 0.0293879 0.0169671i
\(941\) 28.6616 49.6433i 0.934341 1.61833i 0.158536 0.987353i \(-0.449323\pi\)
0.775805 0.630973i \(-0.217344\pi\)
\(942\) −13.8922 8.02066i −0.452632 0.261327i
\(943\) −10.1006 + 14.5941i −0.328920 + 0.475250i
\(944\) 5.77702i 0.188026i
\(945\) −3.54873 2.17252i −0.115440 0.0706722i
\(946\) 18.4229 0.598981
\(947\) −1.22926 2.12913i −0.0399454 0.0691875i 0.845361 0.534195i \(-0.179385\pi\)
−0.885307 + 0.465007i \(0.846052\pi\)
\(948\) −12.8357 + 22.2321i −0.416884 + 0.722064i
\(949\) 9.14989 15.8481i 0.297018 0.514450i
\(950\) −1.24734 2.16046i −0.0404692 0.0700947i
\(951\) 61.5383i 1.99552i
\(952\) 18.2484 + 0.469830i 0.591435 + 0.0152273i
\(953\) 22.3180i 0.722950i −0.932382 0.361475i \(-0.882273\pi\)
0.932382 0.361475i \(-0.117727\pi\)
\(954\) 19.1375 11.0490i 0.619599 0.357726i
\(955\) 1.77622 + 1.02550i 0.0574770 + 0.0331844i
\(956\) −1.05230 + 1.82264i −0.0340338 + 0.0589482i
\(957\) −8.12536 14.0735i −0.262656 0.454933i
\(958\) −32.3673 −1.04574
\(959\) 0.667682 25.9331i 0.0215606 0.837424i
\(960\) 1.13521i 0.0366387i
\(961\) −3.27455 5.67168i −0.105631 0.182957i
\(962\) 16.0428 27.7869i 0.517239 0.895885i
\(963\) 12.4306 + 7.17680i 0.400570 + 0.231269i
\(964\) −7.60361 13.1698i −0.244896 0.424172i
\(965\) −7.23737 −0.232979
\(966\) −27.0997 2.92574i −0.871919 0.0941340i
\(967\) 52.7700 1.69697 0.848485 0.529220i \(-0.177515\pi\)
0.848485 + 0.529220i \(0.177515\pi\)
\(968\) −3.39769 5.88498i −0.109206 0.189150i
\(969\) −6.78307 3.91620i −0.217903 0.125807i
\(970\) −2.94354 + 5.09836i −0.0945113 + 0.163698i
\(971\) −1.75446 3.03882i −0.0563034 0.0975204i 0.836500 0.547967i \(-0.184598\pi\)
−0.892803 + 0.450447i \(0.851265\pi\)
\(972\) 15.2106i 0.487881i
\(973\) 42.8810 23.3069i 1.37470 0.747184i
\(974\) 30.0020 0.961325
\(975\) −18.7649 32.5018i −0.600958 1.04089i
\(976\) 2.92132 5.05987i 0.0935091 0.161963i
\(977\) −26.1586 15.1027i −0.836887 0.483177i 0.0193177 0.999813i \(-0.493851\pi\)
−0.856205 + 0.516636i \(0.827184\pi\)
\(978\) −10.4453 + 6.03058i −0.334003 + 0.192837i
\(979\) 15.6488i 0.500138i
\(980\) 2.01199 3.10416i 0.0642706 0.0991587i
\(981\) 11.1959i 0.357456i
\(982\) 5.98807 + 10.3716i 0.191087 + 0.330973i
\(983\) 10.5938 18.3490i 0.337890 0.585243i −0.646145 0.763214i \(-0.723620\pi\)
0.984036 + 0.177971i \(0.0569534\pi\)
\(984\) 3.97500 6.88490i 0.126718 0.219482i
\(985\) 5.41601 + 9.38080i 0.172568 + 0.298897i
\(986\) −25.4543 −0.810631
\(987\) 5.34352 + 9.83123i 0.170086 + 0.312931i
\(988\) 1.95571i 0.0622195i
\(989\) −24.5213 + 35.4303i −0.779732 + 1.12662i
\(990\) 1.51521 + 0.874807i 0.0481565 + 0.0278032i
\(991\) 27.8066 48.1624i 0.883305 1.52993i 0.0356618 0.999364i \(-0.488646\pi\)
0.847644 0.530566i \(-0.178021\pi\)
\(992\) 4.28231 2.47239i 0.135963 0.0784986i
\(993\) 58.6665i 1.86172i
\(994\) 1.42487 2.32747i 0.0451941 0.0738228i
\(995\) 11.0371 0.349899
\(996\) 30.6112 17.6734i 0.969953 0.560003i
\(997\) 5.61807 + 3.24359i 0.177926 + 0.102726i 0.586318 0.810081i \(-0.300577\pi\)
−0.408392 + 0.912807i \(0.633910\pi\)
\(998\) 20.1372 34.8787i 0.637432 1.10406i
\(999\) 12.9008 + 22.3448i 0.408162 + 0.706958i
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 322.2.g.a.45.2 yes 16
7.3 odd 6 2254.2.c.c.2253.4 16
7.4 even 3 2254.2.c.c.2253.13 16
7.5 odd 6 inner 322.2.g.a.229.1 yes 16
23.22 odd 2 inner 322.2.g.a.45.1 16
161.45 even 6 2254.2.c.c.2253.3 16
161.68 even 6 inner 322.2.g.a.229.2 yes 16
161.137 odd 6 2254.2.c.c.2253.14 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
322.2.g.a.45.1 16 23.22 odd 2 inner
322.2.g.a.45.2 yes 16 1.1 even 1 trivial
322.2.g.a.229.1 yes 16 7.5 odd 6 inner
322.2.g.a.229.2 yes 16 161.68 even 6 inner
2254.2.c.c.2253.3 16 161.45 even 6
2254.2.c.c.2253.4 16 7.3 odd 6
2254.2.c.c.2253.13 16 7.4 even 3
2254.2.c.c.2253.14 16 161.137 odd 6