Properties

Label 405.2.e.j.136.1
Level $405$
Weight $2$
Character 405.136
Analytic conductor $3.234$
Analytic rank $0$
Dimension $4$
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] = [405,2,Mod(136,405)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(405, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("405.136");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 405 = 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 405.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.23394128186\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{13})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{3} + 4x^{2} + 3x + 9 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 135)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 136.1
Root \(1.15139 - 1.99426i\) of defining polynomial
Character \(\chi\) \(=\) 405.136
Dual form 405.2.e.j.271.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.15139 + 1.99426i) q^{2} +(-1.65139 - 2.86029i) q^{4} +(0.500000 + 0.866025i) q^{5} +(1.30278 - 2.25647i) q^{7} +3.00000 q^{8} +O(q^{10})\) \(q+(-1.15139 + 1.99426i) q^{2} +(-1.65139 - 2.86029i) q^{4} +(0.500000 + 0.866025i) q^{5} +(1.30278 - 2.25647i) q^{7} +3.00000 q^{8} -2.30278 q^{10} +(2.30278 - 3.98852i) q^{11} +(-3.30278 - 5.72058i) q^{13} +(3.00000 + 5.19615i) q^{14} +(-0.151388 + 0.262211i) q^{16} -1.60555 q^{17} +3.60555 q^{19} +(1.65139 - 2.86029i) q^{20} +(5.30278 + 9.18468i) q^{22} +(-1.50000 - 2.59808i) q^{23} +(-0.500000 + 0.866025i) q^{25} +15.2111 q^{26} -8.60555 q^{28} +(0.697224 - 1.20763i) q^{29} +(2.80278 + 4.85455i) q^{31} +(2.65139 + 4.59234i) q^{32} +(1.84861 - 3.20189i) q^{34} +2.60555 q^{35} +2.00000 q^{37} +(-4.15139 + 7.19041i) q^{38} +(1.50000 + 2.59808i) q^{40} +(-2.30278 - 3.98852i) q^{41} +(-0.302776 + 0.524423i) q^{43} -15.2111 q^{44} +6.90833 q^{46} +(-4.60555 + 7.97705i) q^{47} +(0.105551 + 0.182820i) q^{49} +(-1.15139 - 1.99426i) q^{50} +(-10.9083 + 18.8938i) q^{52} -1.60555 q^{53} +4.60555 q^{55} +(3.90833 - 6.76942i) q^{56} +(1.60555 + 2.78090i) q^{58} +(-0.697224 - 1.20763i) q^{59} +(2.10555 - 3.64692i) q^{61} -12.9083 q^{62} -12.8167 q^{64} +(3.30278 - 5.72058i) q^{65} +(0.394449 + 0.683205i) q^{67} +(2.65139 + 4.59234i) q^{68} +(-3.00000 + 5.19615i) q^{70} -7.39445 q^{71} +12.6056 q^{73} +(-2.30278 + 3.98852i) q^{74} +(-5.95416 - 10.3129i) q^{76} +(-6.00000 - 10.3923i) q^{77} +(5.80278 - 10.0507i) q^{79} -0.302776 q^{80} +10.6056 q^{82} +(1.50000 - 2.59808i) q^{83} +(-0.802776 - 1.39045i) q^{85} +(-0.697224 - 1.20763i) q^{86} +(6.90833 - 11.9656i) q^{88} +13.8167 q^{89} -17.2111 q^{91} +(-4.95416 + 8.58086i) q^{92} +(-10.6056 - 18.3694i) q^{94} +(1.80278 + 3.12250i) q^{95} +(-4.00000 + 6.92820i) q^{97} -0.486122 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - q^{2} - 3 q^{4} + 2 q^{5} - 2 q^{7} + 12 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - q^{2} - 3 q^{4} + 2 q^{5} - 2 q^{7} + 12 q^{8} - 2 q^{10} + 2 q^{11} - 6 q^{13} + 12 q^{14} + 3 q^{16} + 8 q^{17} + 3 q^{20} + 14 q^{22} - 6 q^{23} - 2 q^{25} + 32 q^{26} - 20 q^{28} + 10 q^{29} + 4 q^{31} + 7 q^{32} + 11 q^{34} - 4 q^{35} + 8 q^{37} - 13 q^{38} + 6 q^{40} - 2 q^{41} + 6 q^{43} - 32 q^{44} + 6 q^{46} - 4 q^{47} - 14 q^{49} - q^{50} - 22 q^{52} + 8 q^{53} + 4 q^{55} - 6 q^{56} - 8 q^{58} - 10 q^{59} - 6 q^{61} - 30 q^{62} - 8 q^{64} + 6 q^{65} + 16 q^{67} + 7 q^{68} - 12 q^{70} - 44 q^{71} + 36 q^{73} - 2 q^{74} - 13 q^{76} - 24 q^{77} + 16 q^{79} + 6 q^{80} + 28 q^{82} + 6 q^{83} + 4 q^{85} - 10 q^{86} + 6 q^{88} + 12 q^{89} - 40 q^{91} - 9 q^{92} - 28 q^{94} - 16 q^{97} - 38 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/405\mathbb{Z}\right)^\times\).

\(n\) \(82\) \(326\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.15139 + 1.99426i −0.814154 + 1.41016i 0.0957796 + 0.995403i \(0.469466\pi\)
−0.909934 + 0.414754i \(0.863868\pi\)
\(3\) 0 0
\(4\) −1.65139 2.86029i −0.825694 1.43014i
\(5\) 0.500000 + 0.866025i 0.223607 + 0.387298i
\(6\) 0 0
\(7\) 1.30278 2.25647i 0.492403 0.852867i −0.507559 0.861617i \(-0.669452\pi\)
0.999962 + 0.00875026i \(0.00278533\pi\)
\(8\) 3.00000 1.06066
\(9\) 0 0
\(10\) −2.30278 −0.728202
\(11\) 2.30278 3.98852i 0.694313 1.20259i −0.276099 0.961129i \(-0.589042\pi\)
0.970412 0.241456i \(-0.0776250\pi\)
\(12\) 0 0
\(13\) −3.30278 5.72058i −0.916025 1.58660i −0.805393 0.592741i \(-0.798046\pi\)
−0.110632 0.993861i \(-0.535287\pi\)
\(14\) 3.00000 + 5.19615i 0.801784 + 1.38873i
\(15\) 0 0
\(16\) −0.151388 + 0.262211i −0.0378470 + 0.0655528i
\(17\) −1.60555 −0.389403 −0.194702 0.980863i \(-0.562374\pi\)
−0.194702 + 0.980863i \(0.562374\pi\)
\(18\) 0 0
\(19\) 3.60555 0.827170 0.413585 0.910465i \(-0.364276\pi\)
0.413585 + 0.910465i \(0.364276\pi\)
\(20\) 1.65139 2.86029i 0.369262 0.639580i
\(21\) 0 0
\(22\) 5.30278 + 9.18468i 1.13056 + 1.95818i
\(23\) −1.50000 2.59808i −0.312772 0.541736i 0.666190 0.745782i \(-0.267924\pi\)
−0.978961 + 0.204046i \(0.934591\pi\)
\(24\) 0 0
\(25\) −0.500000 + 0.866025i −0.100000 + 0.173205i
\(26\) 15.2111 2.98314
\(27\) 0 0
\(28\) −8.60555 −1.62630
\(29\) 0.697224 1.20763i 0.129471 0.224251i −0.794001 0.607917i \(-0.792005\pi\)
0.923472 + 0.383666i \(0.125339\pi\)
\(30\) 0 0
\(31\) 2.80278 + 4.85455i 0.503393 + 0.871903i 0.999992 + 0.00392276i \(0.00124866\pi\)
−0.496599 + 0.867980i \(0.665418\pi\)
\(32\) 2.65139 + 4.59234i 0.468704 + 0.811818i
\(33\) 0 0
\(34\) 1.84861 3.20189i 0.317034 0.549120i
\(35\) 2.60555 0.440419
\(36\) 0 0
\(37\) 2.00000 0.328798 0.164399 0.986394i \(-0.447432\pi\)
0.164399 + 0.986394i \(0.447432\pi\)
\(38\) −4.15139 + 7.19041i −0.673444 + 1.16644i
\(39\) 0 0
\(40\) 1.50000 + 2.59808i 0.237171 + 0.410792i
\(41\) −2.30278 3.98852i −0.359633 0.622903i 0.628266 0.777998i \(-0.283765\pi\)
−0.987899 + 0.155095i \(0.950431\pi\)
\(42\) 0 0
\(43\) −0.302776 + 0.524423i −0.0461729 + 0.0799737i −0.888188 0.459480i \(-0.848036\pi\)
0.842015 + 0.539454i \(0.181369\pi\)
\(44\) −15.2111 −2.29316
\(45\) 0 0
\(46\) 6.90833 1.01858
\(47\) −4.60555 + 7.97705i −0.671789 + 1.16357i 0.305608 + 0.952157i \(0.401140\pi\)
−0.977396 + 0.211415i \(0.932193\pi\)
\(48\) 0 0
\(49\) 0.105551 + 0.182820i 0.0150788 + 0.0261172i
\(50\) −1.15139 1.99426i −0.162831 0.282031i
\(51\) 0 0
\(52\) −10.9083 + 18.8938i −1.51271 + 2.62010i
\(53\) −1.60555 −0.220539 −0.110270 0.993902i \(-0.535171\pi\)
−0.110270 + 0.993902i \(0.535171\pi\)
\(54\) 0 0
\(55\) 4.60555 0.621012
\(56\) 3.90833 6.76942i 0.522272 0.904602i
\(57\) 0 0
\(58\) 1.60555 + 2.78090i 0.210819 + 0.365150i
\(59\) −0.697224 1.20763i −0.0907709 0.157220i 0.817065 0.576546i \(-0.195600\pi\)
−0.907836 + 0.419326i \(0.862266\pi\)
\(60\) 0 0
\(61\) 2.10555 3.64692i 0.269588 0.466940i −0.699167 0.714958i \(-0.746446\pi\)
0.968756 + 0.248018i \(0.0797791\pi\)
\(62\) −12.9083 −1.63936
\(63\) 0 0
\(64\) −12.8167 −1.60208
\(65\) 3.30278 5.72058i 0.409659 0.709550i
\(66\) 0 0
\(67\) 0.394449 + 0.683205i 0.0481896 + 0.0834668i 0.889114 0.457686i \(-0.151322\pi\)
−0.840924 + 0.541153i \(0.817988\pi\)
\(68\) 2.65139 + 4.59234i 0.321528 + 0.556903i
\(69\) 0 0
\(70\) −3.00000 + 5.19615i −0.358569 + 0.621059i
\(71\) −7.39445 −0.877560 −0.438780 0.898595i \(-0.644589\pi\)
−0.438780 + 0.898595i \(0.644589\pi\)
\(72\) 0 0
\(73\) 12.6056 1.47537 0.737684 0.675146i \(-0.235919\pi\)
0.737684 + 0.675146i \(0.235919\pi\)
\(74\) −2.30278 + 3.98852i −0.267692 + 0.463657i
\(75\) 0 0
\(76\) −5.95416 10.3129i −0.682989 1.18297i
\(77\) −6.00000 10.3923i −0.683763 1.18431i
\(78\) 0 0
\(79\) 5.80278 10.0507i 0.652863 1.13079i −0.329562 0.944134i \(-0.606901\pi\)
0.982425 0.186658i \(-0.0597657\pi\)
\(80\) −0.302776 −0.0338513
\(81\) 0 0
\(82\) 10.6056 1.17119
\(83\) 1.50000 2.59808i 0.164646 0.285176i −0.771883 0.635764i \(-0.780685\pi\)
0.936530 + 0.350588i \(0.114018\pi\)
\(84\) 0 0
\(85\) −0.802776 1.39045i −0.0870732 0.150815i
\(86\) −0.697224 1.20763i −0.0751836 0.130222i
\(87\) 0 0
\(88\) 6.90833 11.9656i 0.736430 1.27553i
\(89\) 13.8167 1.46456 0.732281 0.681002i \(-0.238456\pi\)
0.732281 + 0.681002i \(0.238456\pi\)
\(90\) 0 0
\(91\) −17.2111 −1.80421
\(92\) −4.95416 + 8.58086i −0.516507 + 0.894617i
\(93\) 0 0
\(94\) −10.6056 18.3694i −1.09388 1.89465i
\(95\) 1.80278 + 3.12250i 0.184961 + 0.320362i
\(96\) 0 0
\(97\) −4.00000 + 6.92820i −0.406138 + 0.703452i −0.994453 0.105180i \(-0.966458\pi\)
0.588315 + 0.808632i \(0.299792\pi\)
\(98\) −0.486122 −0.0491057
\(99\) 0 0
\(100\) 3.30278 0.330278
\(101\) 6.00000 10.3923i 0.597022 1.03407i −0.396236 0.918149i \(-0.629684\pi\)
0.993258 0.115924i \(-0.0369830\pi\)
\(102\) 0 0
\(103\) 2.00000 + 3.46410i 0.197066 + 0.341328i 0.947576 0.319531i \(-0.103525\pi\)
−0.750510 + 0.660859i \(0.770192\pi\)
\(104\) −9.90833 17.1617i −0.971591 1.68285i
\(105\) 0 0
\(106\) 1.84861 3.20189i 0.179553 0.310995i
\(107\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(108\) 0 0
\(109\) −7.00000 −0.670478 −0.335239 0.942133i \(-0.608817\pi\)
−0.335239 + 0.942133i \(0.608817\pi\)
\(110\) −5.30278 + 9.18468i −0.505600 + 0.875725i
\(111\) 0 0
\(112\) 0.394449 + 0.683205i 0.0372719 + 0.0645568i
\(113\) −7.60555 13.1732i −0.715470 1.23923i −0.962778 0.270294i \(-0.912879\pi\)
0.247308 0.968937i \(-0.420454\pi\)
\(114\) 0 0
\(115\) 1.50000 2.59808i 0.139876 0.242272i
\(116\) −4.60555 −0.427615
\(117\) 0 0
\(118\) 3.21110 0.295606
\(119\) −2.09167 + 3.62288i −0.191743 + 0.332109i
\(120\) 0 0
\(121\) −5.10555 8.84307i −0.464141 0.803916i
\(122\) 4.84861 + 8.39804i 0.438973 + 0.760323i
\(123\) 0 0
\(124\) 9.25694 16.0335i 0.831298 1.43985i
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) −19.2111 −1.70471 −0.852355 0.522964i \(-0.824826\pi\)
−0.852355 + 0.522964i \(0.824826\pi\)
\(128\) 9.45416 16.3751i 0.835638 1.44737i
\(129\) 0 0
\(130\) 7.60555 + 13.1732i 0.667051 + 1.15537i
\(131\) 3.00000 + 5.19615i 0.262111 + 0.453990i 0.966803 0.255524i \(-0.0822479\pi\)
−0.704692 + 0.709514i \(0.748915\pi\)
\(132\) 0 0
\(133\) 4.69722 8.13583i 0.407301 0.705466i
\(134\) −1.81665 −0.156935
\(135\) 0 0
\(136\) −4.81665 −0.413025
\(137\) 8.40833 14.5636i 0.718372 1.24426i −0.243273 0.969958i \(-0.578221\pi\)
0.961645 0.274299i \(-0.0884457\pi\)
\(138\) 0 0
\(139\) 2.00000 + 3.46410i 0.169638 + 0.293821i 0.938293 0.345843i \(-0.112407\pi\)
−0.768655 + 0.639664i \(0.779074\pi\)
\(140\) −4.30278 7.45263i −0.363651 0.629862i
\(141\) 0 0
\(142\) 8.51388 14.7465i 0.714469 1.23750i
\(143\) −30.4222 −2.54403
\(144\) 0 0
\(145\) 1.39445 0.115803
\(146\) −14.5139 + 25.1388i −1.20118 + 2.08050i
\(147\) 0 0
\(148\) −3.30278 5.72058i −0.271486 0.470228i
\(149\) 11.5139 + 19.9426i 0.943254 + 1.63376i 0.759211 + 0.650845i \(0.225585\pi\)
0.184043 + 0.982918i \(0.441081\pi\)
\(150\) 0 0
\(151\) −7.21110 + 12.4900i −0.586831 + 1.01642i 0.407813 + 0.913065i \(0.366291\pi\)
−0.994644 + 0.103356i \(0.967042\pi\)
\(152\) 10.8167 0.877346
\(153\) 0 0
\(154\) 27.6333 2.22676
\(155\) −2.80278 + 4.85455i −0.225124 + 0.389927i
\(156\) 0 0
\(157\) 8.90833 + 15.4297i 0.710962 + 1.23142i 0.964496 + 0.264096i \(0.0850735\pi\)
−0.253535 + 0.967326i \(0.581593\pi\)
\(158\) 13.3625 + 23.1445i 1.06306 + 1.84128i
\(159\) 0 0
\(160\) −2.65139 + 4.59234i −0.209611 + 0.363056i
\(161\) −7.81665 −0.616039
\(162\) 0 0
\(163\) 2.00000 0.156652 0.0783260 0.996928i \(-0.475042\pi\)
0.0783260 + 0.996928i \(0.475042\pi\)
\(164\) −7.60555 + 13.1732i −0.593894 + 1.02865i
\(165\) 0 0
\(166\) 3.45416 + 5.98279i 0.268095 + 0.464354i
\(167\) −1.50000 2.59808i −0.116073 0.201045i 0.802135 0.597143i \(-0.203697\pi\)
−0.918208 + 0.396098i \(0.870364\pi\)
\(168\) 0 0
\(169\) −15.3167 + 26.5292i −1.17820 + 2.04071i
\(170\) 3.69722 0.283564
\(171\) 0 0
\(172\) 2.00000 0.152499
\(173\) −5.40833 + 9.36750i −0.411187 + 0.712198i −0.995020 0.0996766i \(-0.968219\pi\)
0.583832 + 0.811874i \(0.301553\pi\)
\(174\) 0 0
\(175\) 1.30278 + 2.25647i 0.0984806 + 0.170573i
\(176\) 0.697224 + 1.20763i 0.0525553 + 0.0910284i
\(177\) 0 0
\(178\) −15.9083 + 27.5540i −1.19238 + 2.06526i
\(179\) 21.2111 1.58539 0.792696 0.609617i \(-0.208677\pi\)
0.792696 + 0.609617i \(0.208677\pi\)
\(180\) 0 0
\(181\) −7.00000 −0.520306 −0.260153 0.965567i \(-0.583773\pi\)
−0.260153 + 0.965567i \(0.583773\pi\)
\(182\) 19.8167 34.3235i 1.46891 2.54422i
\(183\) 0 0
\(184\) −4.50000 7.79423i −0.331744 0.574598i
\(185\) 1.00000 + 1.73205i 0.0735215 + 0.127343i
\(186\) 0 0
\(187\) −3.69722 + 6.40378i −0.270368 + 0.468291i
\(188\) 30.4222 2.21877
\(189\) 0 0
\(190\) −8.30278 −0.602347
\(191\) −6.21110 + 10.7579i −0.449420 + 0.778418i −0.998348 0.0574516i \(-0.981703\pi\)
0.548929 + 0.835869i \(0.315036\pi\)
\(192\) 0 0
\(193\) −0.0916731 0.158782i −0.00659877 0.0114294i 0.862707 0.505704i \(-0.168767\pi\)
−0.869306 + 0.494274i \(0.835434\pi\)
\(194\) −9.21110 15.9541i −0.661319 1.14544i
\(195\) 0 0
\(196\) 0.348612 0.603814i 0.0249009 0.0431296i
\(197\) 22.8167 1.62562 0.812810 0.582529i \(-0.197937\pi\)
0.812810 + 0.582529i \(0.197937\pi\)
\(198\) 0 0
\(199\) −1.21110 −0.0858528 −0.0429264 0.999078i \(-0.513668\pi\)
−0.0429264 + 0.999078i \(0.513668\pi\)
\(200\) −1.50000 + 2.59808i −0.106066 + 0.183712i
\(201\) 0 0
\(202\) 13.8167 + 23.9311i 0.972136 + 1.68379i
\(203\) −1.81665 3.14654i −0.127504 0.220844i
\(204\) 0 0
\(205\) 2.30278 3.98852i 0.160833 0.278571i
\(206\) −9.21110 −0.641768
\(207\) 0 0
\(208\) 2.00000 0.138675
\(209\) 8.30278 14.3808i 0.574315 0.994743i
\(210\) 0 0
\(211\) 4.40833 + 7.63545i 0.303482 + 0.525646i 0.976922 0.213596i \(-0.0685175\pi\)
−0.673440 + 0.739242i \(0.735184\pi\)
\(212\) 2.65139 + 4.59234i 0.182098 + 0.315403i
\(213\) 0 0
\(214\) 0 0
\(215\) −0.605551 −0.0412983
\(216\) 0 0
\(217\) 14.6056 0.991489
\(218\) 8.05971 13.9598i 0.545873 0.945479i
\(219\) 0 0
\(220\) −7.60555 13.1732i −0.512766 0.888137i
\(221\) 5.30278 + 9.18468i 0.356703 + 0.617828i
\(222\) 0 0
\(223\) 5.00000 8.66025i 0.334825 0.579934i −0.648626 0.761107i \(-0.724656\pi\)
0.983451 + 0.181173i \(0.0579895\pi\)
\(224\) 13.8167 0.923164
\(225\) 0 0
\(226\) 35.0278 2.33001
\(227\) −5.89445 + 10.2095i −0.391228 + 0.677627i −0.992612 0.121333i \(-0.961283\pi\)
0.601384 + 0.798960i \(0.294616\pi\)
\(228\) 0 0
\(229\) −4.10555 7.11102i −0.271302 0.469910i 0.697893 0.716202i \(-0.254121\pi\)
−0.969196 + 0.246292i \(0.920788\pi\)
\(230\) 3.45416 + 5.98279i 0.227761 + 0.394493i
\(231\) 0 0
\(232\) 2.09167 3.62288i 0.137325 0.237854i
\(233\) 18.0000 1.17922 0.589610 0.807688i \(-0.299282\pi\)
0.589610 + 0.807688i \(0.299282\pi\)
\(234\) 0 0
\(235\) −9.21110 −0.600866
\(236\) −2.30278 + 3.98852i −0.149898 + 0.259631i
\(237\) 0 0
\(238\) −4.81665 8.34269i −0.312217 0.540776i
\(239\) −7.60555 13.1732i −0.491962 0.852104i 0.507995 0.861360i \(-0.330387\pi\)
−0.999957 + 0.00925650i \(0.997054\pi\)
\(240\) 0 0
\(241\) −6.89445 + 11.9415i −0.444110 + 0.769222i −0.997990 0.0633751i \(-0.979814\pi\)
0.553879 + 0.832597i \(0.313147\pi\)
\(242\) 23.5139 1.51153
\(243\) 0 0
\(244\) −13.9083 −0.890389
\(245\) −0.105551 + 0.182820i −0.00674342 + 0.0116800i
\(246\) 0 0
\(247\) −11.9083 20.6258i −0.757709 1.31239i
\(248\) 8.40833 + 14.5636i 0.533929 + 0.924793i
\(249\) 0 0
\(250\) 1.15139 1.99426i 0.0728202 0.126128i
\(251\) −27.6333 −1.74420 −0.872099 0.489329i \(-0.837242\pi\)
−0.872099 + 0.489329i \(0.837242\pi\)
\(252\) 0 0
\(253\) −13.8167 −0.868646
\(254\) 22.1194 38.3120i 1.38790 2.40391i
\(255\) 0 0
\(256\) 8.95416 + 15.5091i 0.559635 + 0.969317i
\(257\) 0.591673 + 1.02481i 0.0369076 + 0.0639258i 0.883889 0.467696i \(-0.154916\pi\)
−0.846982 + 0.531622i \(0.821583\pi\)
\(258\) 0 0
\(259\) 2.60555 4.51295i 0.161901 0.280421i
\(260\) −21.8167 −1.35301
\(261\) 0 0
\(262\) −13.8167 −0.853596
\(263\) −1.39445 + 2.41526i −0.0859854 + 0.148931i −0.905811 0.423683i \(-0.860737\pi\)
0.819825 + 0.572614i \(0.194071\pi\)
\(264\) 0 0
\(265\) −0.802776 1.39045i −0.0493141 0.0854146i
\(266\) 10.8167 + 18.7350i 0.663212 + 1.14872i
\(267\) 0 0
\(268\) 1.30278 2.25647i 0.0795797 0.137836i
\(269\) 3.21110 0.195784 0.0978922 0.995197i \(-0.468790\pi\)
0.0978922 + 0.995197i \(0.468790\pi\)
\(270\) 0 0
\(271\) 31.2389 1.89763 0.948813 0.315839i \(-0.102286\pi\)
0.948813 + 0.315839i \(0.102286\pi\)
\(272\) 0.243061 0.420994i 0.0147377 0.0255265i
\(273\) 0 0
\(274\) 19.3625 + 33.5368i 1.16973 + 2.02603i
\(275\) 2.30278 + 3.98852i 0.138863 + 0.240517i
\(276\) 0 0
\(277\) −3.51388 + 6.08622i −0.211128 + 0.365685i −0.952068 0.305887i \(-0.901047\pi\)
0.740939 + 0.671572i \(0.234381\pi\)
\(278\) −9.21110 −0.552445
\(279\) 0 0
\(280\) 7.81665 0.467134
\(281\) −9.90833 + 17.1617i −0.591081 + 1.02378i 0.403006 + 0.915197i \(0.367965\pi\)
−0.994087 + 0.108585i \(0.965368\pi\)
\(282\) 0 0
\(283\) −1.69722 2.93968i −0.100890 0.174746i 0.811162 0.584822i \(-0.198836\pi\)
−0.912051 + 0.410076i \(0.865502\pi\)
\(284\) 12.2111 + 21.1503i 0.724596 + 1.25504i
\(285\) 0 0
\(286\) 35.0278 60.6699i 2.07123 3.58748i
\(287\) −12.0000 −0.708338
\(288\) 0 0
\(289\) −14.4222 −0.848365
\(290\) −1.60555 + 2.78090i −0.0942812 + 0.163300i
\(291\) 0 0
\(292\) −20.8167 36.0555i −1.21820 2.10999i
\(293\) −3.59167 6.22096i −0.209828 0.363432i 0.741832 0.670585i \(-0.233957\pi\)
−0.951660 + 0.307153i \(0.900624\pi\)
\(294\) 0 0
\(295\) 0.697224 1.20763i 0.0405940 0.0703108i
\(296\) 6.00000 0.348743
\(297\) 0 0
\(298\) −53.0278 −3.07182
\(299\) −9.90833 + 17.1617i −0.573013 + 0.992488i
\(300\) 0 0
\(301\) 0.788897 + 1.36641i 0.0454713 + 0.0787586i
\(302\) −16.6056 28.7617i −0.955542 1.65505i
\(303\) 0 0
\(304\) −0.545837 + 0.945417i −0.0313059 + 0.0542234i
\(305\) 4.21110 0.241127
\(306\) 0 0
\(307\) 8.42221 0.480681 0.240340 0.970689i \(-0.422741\pi\)
0.240340 + 0.970689i \(0.422741\pi\)
\(308\) −19.8167 + 34.3235i −1.12916 + 1.95576i
\(309\) 0 0
\(310\) −6.45416 11.1789i −0.366572 0.634921i
\(311\) −3.90833 6.76942i −0.221621 0.383859i 0.733679 0.679496i \(-0.237801\pi\)
−0.955300 + 0.295637i \(0.904468\pi\)
\(312\) 0 0
\(313\) 9.81665 17.0029i 0.554870 0.961063i −0.443044 0.896500i \(-0.646101\pi\)
0.997914 0.0645631i \(-0.0205654\pi\)
\(314\) −41.0278 −2.31533
\(315\) 0 0
\(316\) −38.3305 −2.15626
\(317\) −3.80278 + 6.58660i −0.213585 + 0.369940i −0.952834 0.303492i \(-0.901847\pi\)
0.739249 + 0.673432i \(0.235181\pi\)
\(318\) 0 0
\(319\) −3.21110 5.56179i −0.179787 0.311401i
\(320\) −6.40833 11.0995i −0.358236 0.620484i
\(321\) 0 0
\(322\) 9.00000 15.5885i 0.501550 0.868711i
\(323\) −5.78890 −0.322103
\(324\) 0 0
\(325\) 6.60555 0.366410
\(326\) −2.30278 + 3.98852i −0.127539 + 0.220904i
\(327\) 0 0
\(328\) −6.90833 11.9656i −0.381449 0.660688i
\(329\) 12.0000 + 20.7846i 0.661581 + 1.14589i
\(330\) 0 0
\(331\) −14.6056 + 25.2976i −0.802794 + 1.39048i 0.114977 + 0.993368i \(0.463321\pi\)
−0.917770 + 0.397111i \(0.870013\pi\)
\(332\) −9.90833 −0.543790
\(333\) 0 0
\(334\) 6.90833 0.378007
\(335\) −0.394449 + 0.683205i −0.0215510 + 0.0373275i
\(336\) 0 0
\(337\) −3.30278 5.72058i −0.179914 0.311620i 0.761937 0.647651i \(-0.224249\pi\)
−0.941851 + 0.336031i \(0.890915\pi\)
\(338\) −35.2708 61.0908i −1.91848 3.32290i
\(339\) 0 0
\(340\) −2.65139 + 4.59234i −0.143792 + 0.249055i
\(341\) 25.8167 1.39805
\(342\) 0 0
\(343\) 18.7889 1.01451
\(344\) −0.908327 + 1.57327i −0.0489737 + 0.0848249i
\(345\) 0 0
\(346\) −12.4542 21.5712i −0.669540 1.15968i
\(347\) 15.2111 + 26.3464i 0.816575 + 1.41435i 0.908192 + 0.418555i \(0.137463\pi\)
−0.0916168 + 0.995794i \(0.529203\pi\)
\(348\) 0 0
\(349\) 15.9222 27.5781i 0.852296 1.47622i −0.0268349 0.999640i \(-0.508543\pi\)
0.879131 0.476580i \(-0.158124\pi\)
\(350\) −6.00000 −0.320713
\(351\) 0 0
\(352\) 24.4222 1.30171
\(353\) 10.8167 18.7350i 0.575712 0.997163i −0.420251 0.907408i \(-0.638058\pi\)
0.995964 0.0897554i \(-0.0286085\pi\)
\(354\) 0 0
\(355\) −3.69722 6.40378i −0.196228 0.339877i
\(356\) −22.8167 39.5196i −1.20928 2.09453i
\(357\) 0 0
\(358\) −24.4222 + 42.3005i −1.29075 + 2.23565i
\(359\) 9.63331 0.508427 0.254213 0.967148i \(-0.418183\pi\)
0.254213 + 0.967148i \(0.418183\pi\)
\(360\) 0 0
\(361\) −6.00000 −0.315789
\(362\) 8.05971 13.9598i 0.423609 0.733713i
\(363\) 0 0
\(364\) 28.4222 + 49.2287i 1.48973 + 2.58029i
\(365\) 6.30278 + 10.9167i 0.329902 + 0.571408i
\(366\) 0 0
\(367\) 1.30278 2.25647i 0.0680043 0.117787i −0.830018 0.557736i \(-0.811670\pi\)
0.898023 + 0.439949i \(0.145003\pi\)
\(368\) 0.908327 0.0473498
\(369\) 0 0
\(370\) −4.60555 −0.239431
\(371\) −2.09167 + 3.62288i −0.108594 + 0.188091i
\(372\) 0 0
\(373\) 12.6056 + 21.8335i 0.652691 + 1.13049i 0.982467 + 0.186434i \(0.0596932\pi\)
−0.329777 + 0.944059i \(0.606973\pi\)
\(374\) −8.51388 14.7465i −0.440242 0.762522i
\(375\) 0 0
\(376\) −13.8167 + 23.9311i −0.712540 + 1.23415i
\(377\) −9.21110 −0.474396
\(378\) 0 0
\(379\) 21.6056 1.10980 0.554901 0.831916i \(-0.312756\pi\)
0.554901 + 0.831916i \(0.312756\pi\)
\(380\) 5.95416 10.3129i 0.305442 0.529041i
\(381\) 0 0
\(382\) −14.3028 24.7731i −0.731794 1.26750i
\(383\) 12.3167 + 21.3331i 0.629352 + 1.09007i 0.987682 + 0.156474i \(0.0500128\pi\)
−0.358330 + 0.933595i \(0.616654\pi\)
\(384\) 0 0
\(385\) 6.00000 10.3923i 0.305788 0.529641i
\(386\) 0.422205 0.0214897
\(387\) 0 0
\(388\) 26.4222 1.34138
\(389\) 12.9083 22.3579i 0.654478 1.13359i −0.327546 0.944835i \(-0.606222\pi\)
0.982024 0.188754i \(-0.0604450\pi\)
\(390\) 0 0
\(391\) 2.40833 + 4.17134i 0.121794 + 0.210954i
\(392\) 0.316654 + 0.548461i 0.0159934 + 0.0277014i
\(393\) 0 0
\(394\) −26.2708 + 45.5024i −1.32350 + 2.29238i
\(395\) 11.6056 0.583939
\(396\) 0 0
\(397\) −5.39445 −0.270740 −0.135370 0.990795i \(-0.543222\pi\)
−0.135370 + 0.990795i \(0.543222\pi\)
\(398\) 1.39445 2.41526i 0.0698974 0.121066i
\(399\) 0 0
\(400\) −0.151388 0.262211i −0.00756939 0.0131106i
\(401\) −15.0000 25.9808i −0.749064 1.29742i −0.948272 0.317460i \(-0.897170\pi\)
0.199207 0.979957i \(-0.436163\pi\)
\(402\) 0 0
\(403\) 18.5139 32.0670i 0.922242 1.59737i
\(404\) −39.6333 −1.97183
\(405\) 0 0
\(406\) 8.36669 0.415232
\(407\) 4.60555 7.97705i 0.228289 0.395408i
\(408\) 0 0
\(409\) −2.50000 4.33013i −0.123617 0.214111i 0.797574 0.603220i \(-0.206116\pi\)
−0.921192 + 0.389109i \(0.872783\pi\)
\(410\) 5.30278 + 9.18468i 0.261885 + 0.453599i
\(411\) 0 0
\(412\) 6.60555 11.4412i 0.325432 0.563665i
\(413\) −3.63331 −0.178783
\(414\) 0 0
\(415\) 3.00000 0.147264
\(416\) 17.5139 30.3349i 0.858689 1.48729i
\(417\) 0 0
\(418\) 19.1194 + 33.1158i 0.935162 + 1.61975i
\(419\) 11.5139 + 19.9426i 0.562490 + 0.974261i 0.997278 + 0.0737283i \(0.0234898\pi\)
−0.434789 + 0.900533i \(0.643177\pi\)
\(420\) 0 0
\(421\) −2.71110 + 4.69577i −0.132131 + 0.228858i −0.924498 0.381187i \(-0.875515\pi\)
0.792367 + 0.610045i \(0.208849\pi\)
\(422\) −20.3028 −0.988324
\(423\) 0 0
\(424\) −4.81665 −0.233917
\(425\) 0.802776 1.39045i 0.0389403 0.0674466i
\(426\) 0 0
\(427\) −5.48612 9.50224i −0.265492 0.459846i
\(428\) 0 0
\(429\) 0 0
\(430\) 0.697224 1.20763i 0.0336231 0.0582370i
\(431\) −4.18335 −0.201505 −0.100752 0.994912i \(-0.532125\pi\)
−0.100752 + 0.994912i \(0.532125\pi\)
\(432\) 0 0
\(433\) 22.2389 1.06873 0.534366 0.845253i \(-0.320551\pi\)
0.534366 + 0.845253i \(0.320551\pi\)
\(434\) −16.8167 + 29.1273i −0.807225 + 1.39816i
\(435\) 0 0
\(436\) 11.5597 + 20.0220i 0.553610 + 0.958881i
\(437\) −5.40833 9.36750i −0.258715 0.448108i
\(438\) 0 0
\(439\) −13.8028 + 23.9071i −0.658771 + 1.14102i 0.322164 + 0.946684i \(0.395590\pi\)
−0.980934 + 0.194340i \(0.937743\pi\)
\(440\) 13.8167 0.658683
\(441\) 0 0
\(442\) −24.4222 −1.16165
\(443\) −12.3167 + 21.3331i −0.585182 + 1.01356i 0.409671 + 0.912233i \(0.365644\pi\)
−0.994853 + 0.101331i \(0.967690\pi\)
\(444\) 0 0
\(445\) 6.90833 + 11.9656i 0.327486 + 0.567223i
\(446\) 11.5139 + 19.9426i 0.545198 + 0.944311i
\(447\) 0 0
\(448\) −16.6972 + 28.9204i −0.788870 + 1.36636i
\(449\) −38.2389 −1.80460 −0.902302 0.431105i \(-0.858124\pi\)
−0.902302 + 0.431105i \(0.858124\pi\)
\(450\) 0 0
\(451\) −21.2111 −0.998792
\(452\) −25.1194 + 43.5081i −1.18152 + 2.04645i
\(453\) 0 0
\(454\) −13.5736 23.5102i −0.637040 1.10339i
\(455\) −8.60555 14.9053i −0.403434 0.698769i
\(456\) 0 0
\(457\) 6.60555 11.4412i 0.308995 0.535194i −0.669148 0.743129i \(-0.733341\pi\)
0.978143 + 0.207935i \(0.0666741\pi\)
\(458\) 18.9083 0.883528
\(459\) 0 0
\(460\) −9.90833 −0.461978
\(461\) 10.8167 18.7350i 0.503782 0.872576i −0.496209 0.868203i \(-0.665275\pi\)
0.999990 0.00437236i \(-0.00139177\pi\)
\(462\) 0 0
\(463\) 0.394449 + 0.683205i 0.0183316 + 0.0317512i 0.875046 0.484040i \(-0.160831\pi\)
−0.856714 + 0.515792i \(0.827498\pi\)
\(464\) 0.211103 + 0.365640i 0.00980019 + 0.0169744i
\(465\) 0 0
\(466\) −20.7250 + 35.8967i −0.960066 + 1.66288i
\(467\) −12.2111 −0.565062 −0.282531 0.959258i \(-0.591174\pi\)
−0.282531 + 0.959258i \(0.591174\pi\)
\(468\) 0 0
\(469\) 2.05551 0.0949148
\(470\) 10.6056 18.3694i 0.489198 0.847315i
\(471\) 0 0
\(472\) −2.09167 3.62288i −0.0962771 0.166757i
\(473\) 1.39445 + 2.41526i 0.0641168 + 0.111054i
\(474\) 0 0
\(475\) −1.80278 + 3.12250i −0.0827170 + 0.143270i
\(476\) 13.8167 0.633285
\(477\) 0 0
\(478\) 35.0278 1.60213
\(479\) −18.9083 + 32.7502i −0.863944 + 1.49639i 0.00414888 + 0.999991i \(0.498679\pi\)
−0.868092 + 0.496403i \(0.834654\pi\)
\(480\) 0 0
\(481\) −6.60555 11.4412i −0.301187 0.521672i
\(482\) −15.8764 27.4987i −0.723149 1.25253i
\(483\) 0 0
\(484\) −16.8625 + 29.2067i −0.766477 + 1.32758i
\(485\) −8.00000 −0.363261
\(486\) 0 0
\(487\) −29.8167 −1.35112 −0.675561 0.737304i \(-0.736098\pi\)
−0.675561 + 0.737304i \(0.736098\pi\)
\(488\) 6.31665 10.9408i 0.285941 0.495265i
\(489\) 0 0
\(490\) −0.243061 0.420994i −0.0109804 0.0190186i
\(491\) 13.6056 + 23.5655i 0.614010 + 1.06350i 0.990557 + 0.137099i \(0.0437779\pi\)
−0.376547 + 0.926397i \(0.622889\pi\)
\(492\) 0 0
\(493\) −1.11943 + 1.93891i −0.0504166 + 0.0873241i
\(494\) 54.8444 2.46757
\(495\) 0 0
\(496\) −1.69722 −0.0762076
\(497\) −9.63331 + 16.6854i −0.432113 + 0.748442i
\(498\) 0 0
\(499\) 10.1972 + 17.6621i 0.456490 + 0.790665i 0.998773 0.0495318i \(-0.0157729\pi\)
−0.542282 + 0.840196i \(0.682440\pi\)
\(500\) 1.65139 + 2.86029i 0.0738523 + 0.127916i
\(501\) 0 0
\(502\) 31.8167 55.1081i 1.42005 2.45959i
\(503\) −2.57779 −0.114938 −0.0574691 0.998347i \(-0.518303\pi\)
−0.0574691 + 0.998347i \(0.518303\pi\)
\(504\) 0 0
\(505\) 12.0000 0.533993
\(506\) 15.9083 27.5540i 0.707211 1.22493i
\(507\) 0 0
\(508\) 31.7250 + 54.9493i 1.40757 + 2.43798i
\(509\) −12.4222 21.5159i −0.550605 0.953675i −0.998231 0.0594544i \(-0.981064\pi\)
0.447626 0.894221i \(-0.352269\pi\)
\(510\) 0 0
\(511\) 16.4222 28.4441i 0.726476 1.25829i
\(512\) −3.42221 −0.151242
\(513\) 0 0
\(514\) −2.72498 −0.120194
\(515\) −2.00000 + 3.46410i −0.0881305 + 0.152647i
\(516\) 0 0
\(517\) 21.2111 + 36.7387i 0.932863 + 1.61577i
\(518\) 6.00000 + 10.3923i 0.263625 + 0.456612i
\(519\) 0 0
\(520\) 9.90833 17.1617i 0.434509 0.752591i
\(521\) 28.6056 1.25323 0.626616 0.779328i \(-0.284439\pi\)
0.626616 + 0.779328i \(0.284439\pi\)
\(522\) 0 0
\(523\) 30.6056 1.33829 0.669144 0.743133i \(-0.266661\pi\)
0.669144 + 0.743133i \(0.266661\pi\)
\(524\) 9.90833 17.1617i 0.432847 0.749713i
\(525\) 0 0
\(526\) −3.21110 5.56179i −0.140011 0.242506i
\(527\) −4.50000 7.79423i −0.196023 0.339522i
\(528\) 0 0
\(529\) 7.00000 12.1244i 0.304348 0.527146i
\(530\) 3.69722 0.160597
\(531\) 0 0
\(532\) −31.0278 −1.34522
\(533\) −15.2111 + 26.3464i −0.658866 + 1.14119i
\(534\) 0 0
\(535\) 0 0
\(536\) 1.18335 + 2.04962i 0.0511128 + 0.0885299i
\(537\) 0 0
\(538\) −3.69722 + 6.40378i −0.159399 + 0.276087i
\(539\) 0.972244 0.0418775
\(540\) 0 0
\(541\) −40.4222 −1.73789 −0.868943 0.494912i \(-0.835200\pi\)
−0.868943 + 0.494912i \(0.835200\pi\)
\(542\) −35.9680 + 62.2985i −1.54496 + 2.67595i
\(543\) 0 0
\(544\) −4.25694 7.37323i −0.182515 0.316125i
\(545\) −3.50000 6.06218i −0.149924 0.259675i
\(546\) 0 0
\(547\) −0.302776 + 0.524423i −0.0129458 + 0.0224227i −0.872426 0.488747i \(-0.837454\pi\)
0.859480 + 0.511169i \(0.170788\pi\)
\(548\) −55.5416 −2.37262
\(549\) 0 0
\(550\) −10.6056 −0.452222
\(551\) 2.51388 4.35416i 0.107095 0.185494i
\(552\) 0 0
\(553\) −15.1194 26.1876i −0.642944 1.11361i
\(554\) −8.09167 14.0152i −0.343782 0.595448i
\(555\) 0 0
\(556\) 6.60555 11.4412i 0.280138 0.485213i
\(557\) −9.63331 −0.408176 −0.204088 0.978953i \(-0.565423\pi\)
−0.204088 + 0.978953i \(0.565423\pi\)
\(558\) 0 0
\(559\) 4.00000 0.169182
\(560\) −0.394449 + 0.683205i −0.0166685 + 0.0288707i
\(561\) 0 0
\(562\) −22.8167 39.5196i −0.962462 1.66703i
\(563\) 12.0000 + 20.7846i 0.505740 + 0.875967i 0.999978 + 0.00664037i \(0.00211371\pi\)
−0.494238 + 0.869326i \(0.664553\pi\)
\(564\) 0 0
\(565\) 7.60555 13.1732i 0.319968 0.554201i
\(566\) 7.81665 0.328558
\(567\) 0 0
\(568\) −22.1833 −0.930793
\(569\) 8.09167 14.0152i 0.339221 0.587547i −0.645066 0.764127i \(-0.723170\pi\)
0.984286 + 0.176580i \(0.0565034\pi\)
\(570\) 0 0
\(571\) −14.2250 24.6384i −0.595297 1.03108i −0.993505 0.113789i \(-0.963701\pi\)
0.398208 0.917295i \(-0.369632\pi\)
\(572\) 50.2389 + 87.0163i 2.10059 + 3.63833i
\(573\) 0 0
\(574\) 13.8167 23.9311i 0.576696 0.998867i
\(575\) 3.00000 0.125109
\(576\) 0 0
\(577\) 6.18335 0.257416 0.128708 0.991683i \(-0.458917\pi\)
0.128708 + 0.991683i \(0.458917\pi\)
\(578\) 16.6056 28.7617i 0.690700 1.19633i
\(579\) 0 0
\(580\) −2.30278 3.98852i −0.0956176 0.165614i
\(581\) −3.90833 6.76942i −0.162145 0.280843i
\(582\) 0 0
\(583\) −3.69722 + 6.40378i −0.153123 + 0.265217i
\(584\) 37.8167 1.56486
\(585\) 0 0
\(586\) 16.5416 0.683329
\(587\) 10.5000 18.1865i 0.433381 0.750639i −0.563781 0.825925i \(-0.690654\pi\)
0.997162 + 0.0752860i \(0.0239870\pi\)
\(588\) 0 0
\(589\) 10.1056 + 17.5033i 0.416392 + 0.721212i
\(590\) 1.60555 + 2.78090i 0.0660995 + 0.114488i
\(591\) 0 0
\(592\) −0.302776 + 0.524423i −0.0124440 + 0.0215536i
\(593\) 29.2389 1.20070 0.600348 0.799739i \(-0.295029\pi\)
0.600348 + 0.799739i \(0.295029\pi\)
\(594\) 0 0
\(595\) −4.18335 −0.171500
\(596\) 38.0278 65.8660i 1.55768 2.69798i
\(597\) 0 0
\(598\) −22.8167 39.5196i −0.933042 1.61608i
\(599\) −11.3028 19.5770i −0.461819 0.799894i 0.537233 0.843434i \(-0.319470\pi\)
−0.999052 + 0.0435402i \(0.986136\pi\)
\(600\) 0 0
\(601\) 5.31665 9.20871i 0.216871 0.375631i −0.736979 0.675916i \(-0.763748\pi\)
0.953850 + 0.300285i \(0.0970816\pi\)
\(602\) −3.63331 −0.148083
\(603\) 0 0
\(604\) 47.6333 1.93817
\(605\) 5.10555 8.84307i 0.207570 0.359522i
\(606\) 0 0
\(607\) −12.3028 21.3090i −0.499354 0.864907i 0.500645 0.865652i \(-0.333096\pi\)
−1.00000 0.000745477i \(0.999763\pi\)
\(608\) 9.55971 + 16.5579i 0.387698 + 0.671512i
\(609\) 0 0
\(610\) −4.84861 + 8.39804i −0.196315 + 0.340027i
\(611\) 60.8444 2.46150
\(612\) 0 0
\(613\) −28.8444 −1.16501 −0.582507 0.812825i \(-0.697928\pi\)
−0.582507 + 0.812825i \(0.697928\pi\)
\(614\) −9.69722 + 16.7961i −0.391348 + 0.677835i
\(615\) 0 0
\(616\) −18.0000 31.1769i −0.725241 1.25615i
\(617\) 19.2250 + 33.2986i 0.773969 + 1.34055i 0.935372 + 0.353664i \(0.115065\pi\)
−0.161404 + 0.986888i \(0.551602\pi\)
\(618\) 0 0
\(619\) −17.8167 + 30.8593i −0.716112 + 1.24034i 0.246417 + 0.969164i \(0.420747\pi\)
−0.962529 + 0.271178i \(0.912587\pi\)
\(620\) 18.5139 0.743535
\(621\) 0 0
\(622\) 18.0000 0.721734
\(623\) 18.0000 31.1769i 0.721155 1.24908i
\(624\) 0 0
\(625\) −0.500000 0.866025i −0.0200000 0.0346410i
\(626\) 22.6056 + 39.1540i 0.903500 + 1.56491i
\(627\) 0 0
\(628\) 29.4222 50.9608i 1.17407 2.03356i
\(629\) −3.21110 −0.128035
\(630\) 0 0
\(631\) −6.02776 −0.239961 −0.119981 0.992776i \(-0.538283\pi\)
−0.119981 + 0.992776i \(0.538283\pi\)
\(632\) 17.4083 30.1521i 0.692466 1.19939i
\(633\) 0 0
\(634\) −8.75694 15.1675i −0.347782 0.602377i
\(635\) −9.60555 16.6373i −0.381185 0.660231i
\(636\) 0 0
\(637\) 0.697224 1.20763i 0.0276250 0.0478480i
\(638\) 14.7889 0.585498
\(639\) 0 0
\(640\) 18.9083 0.747417
\(641\) −12.0000 + 20.7846i −0.473972 + 0.820943i −0.999556 0.0297987i \(-0.990513\pi\)
0.525584 + 0.850741i \(0.323847\pi\)
\(642\) 0 0
\(643\) −6.51388 11.2824i −0.256882 0.444933i 0.708523 0.705688i \(-0.249362\pi\)
−0.965405 + 0.260755i \(0.916029\pi\)
\(644\) 12.9083 + 22.3579i 0.508659 + 0.881024i
\(645\) 0 0
\(646\) 6.66527 11.5446i 0.262241 0.454215i
\(647\) −23.7889 −0.935238 −0.467619 0.883930i \(-0.654888\pi\)
−0.467619 + 0.883930i \(0.654888\pi\)
\(648\) 0 0
\(649\) −6.42221 −0.252094
\(650\) −7.60555 + 13.1732i −0.298314 + 0.516695i
\(651\) 0 0
\(652\) −3.30278 5.72058i −0.129347 0.224035i
\(653\) −11.6194 20.1254i −0.454703 0.787569i 0.543968 0.839106i \(-0.316921\pi\)
−0.998671 + 0.0515368i \(0.983588\pi\)
\(654\) 0 0
\(655\) −3.00000 + 5.19615i −0.117220 + 0.203030i
\(656\) 1.39445 0.0544441
\(657\) 0 0
\(658\) −55.2666 −2.15452
\(659\) −6.69722 + 11.5999i −0.260887 + 0.451869i −0.966478 0.256750i \(-0.917348\pi\)
0.705591 + 0.708619i \(0.250682\pi\)
\(660\) 0 0
\(661\) 17.4222 + 30.1761i 0.677645 + 1.17372i 0.975688 + 0.219164i \(0.0703328\pi\)
−0.298043 + 0.954552i \(0.596334\pi\)
\(662\) −33.6333 58.2546i −1.30720 2.26413i
\(663\) 0 0
\(664\) 4.50000 7.79423i 0.174634 0.302475i
\(665\) 9.39445 0.364301
\(666\) 0 0
\(667\) −4.18335 −0.161980
\(668\) −4.95416 + 8.58086i −0.191682 + 0.332004i
\(669\) 0 0
\(670\) −0.908327 1.57327i −0.0350917 0.0607807i
\(671\) −9.69722 16.7961i −0.374357 0.648406i
\(672\) 0 0
\(673\) −12.5139 + 21.6747i −0.482375 + 0.835497i −0.999795 0.0202339i \(-0.993559\pi\)
0.517421 + 0.855731i \(0.326892\pi\)
\(674\) 15.2111 0.585910
\(675\) 0 0
\(676\) 101.175 3.89134
\(677\) 10.8167 18.7350i 0.415718 0.720044i −0.579786 0.814769i \(-0.696864\pi\)
0.995504 + 0.0947247i \(0.0301971\pi\)
\(678\) 0 0
\(679\) 10.4222 + 18.0518i 0.399968 + 0.692764i
\(680\) −2.40833 4.17134i −0.0923551 0.159964i
\(681\) 0 0
\(682\) −29.7250 + 51.4852i −1.13823 + 1.97147i
\(683\) 9.00000 0.344375 0.172188 0.985064i \(-0.444916\pi\)
0.172188 + 0.985064i \(0.444916\pi\)
\(684\) 0 0
\(685\) 16.8167 0.642531
\(686\) −21.6333 + 37.4700i −0.825964 + 1.43061i
\(687\) 0 0
\(688\) −0.0916731 0.158782i −0.00349500 0.00605352i
\(689\) 5.30278 + 9.18468i 0.202020 + 0.349908i
\(690\) 0 0
\(691\) −4.80278 + 8.31865i −0.182706 + 0.316456i −0.942801 0.333356i \(-0.891819\pi\)
0.760095 + 0.649812i \(0.225152\pi\)
\(692\) 35.7250 1.35806
\(693\) 0 0
\(694\) −70.0555 −2.65927
\(695\) −2.00000 + 3.46410i −0.0758643 + 0.131401i
\(696\) 0 0
\(697\) 3.69722 + 6.40378i 0.140042 + 0.242560i
\(698\) 36.6653 + 63.5061i 1.38780 + 2.40374i
\(699\) 0 0
\(700\) 4.30278 7.45263i 0.162630 0.281683i
\(701\) −11.5778 −0.437287 −0.218644 0.975805i \(-0.570163\pi\)
−0.218644 + 0.975805i \(0.570163\pi\)
\(702\) 0 0
\(703\) 7.21110 0.271972
\(704\) −29.5139 + 51.1195i −1.11235 + 1.92664i
\(705\) 0 0
\(706\) 24.9083 + 43.1425i 0.937437 + 1.62369i
\(707\) −15.6333 27.0777i −0.587951 1.01836i
\(708\) 0 0
\(709\) 11.4222 19.7838i 0.428970 0.742998i −0.567812 0.823158i \(-0.692210\pi\)
0.996782 + 0.0801605i \(0.0255433\pi\)
\(710\) 17.0278 0.639040
\(711\) 0 0
\(712\) 41.4500 1.55340
\(713\) 8.40833 14.5636i 0.314894 0.545413i
\(714\) 0 0
\(715\) −15.2111 26.3464i −0.568863 0.985300i
\(716\) −35.0278 60.6699i −1.30905 2.26734i
\(717\) 0 0
\(718\) −11.0917 + 19.2113i −0.413938 + 0.716961i
\(719\) −37.2666 −1.38981 −0.694905 0.719101i \(-0.744554\pi\)
−0.694905 + 0.719101i \(0.744554\pi\)
\(720\) 0 0
\(721\) 10.4222 0.388143
\(722\) 6.90833 11.9656i 0.257101 0.445313i
\(723\) 0 0
\(724\) 11.5597 + 20.0220i 0.429613 + 0.744112i
\(725\) 0.697224 + 1.20763i 0.0258943 + 0.0448502i
\(726\) 0 0
\(727\) −17.8167 + 30.8593i −0.660783 + 1.14451i 0.319627 + 0.947543i \(0.396442\pi\)
−0.980410 + 0.196967i \(0.936891\pi\)
\(728\) −51.6333 −1.91366
\(729\) 0 0
\(730\) −29.0278 −1.07437
\(731\) 0.486122 0.841988i 0.0179799 0.0311420i
\(732\) 0 0
\(733\) −16.0000 27.7128i −0.590973 1.02360i −0.994102 0.108453i \(-0.965410\pi\)
0.403128 0.915144i \(-0.367923\pi\)
\(734\) 3.00000 + 5.19615i 0.110732 + 0.191793i
\(735\) 0 0
\(736\) 7.95416 13.7770i 0.293194 0.507828i
\(737\) 3.63331 0.133835
\(738\) 0 0
\(739\) −6.02776 −0.221735 −0.110867 0.993835i \(-0.535363\pi\)
−0.110867 + 0.993835i \(0.535363\pi\)
\(740\) 3.30278 5.72058i 0.121412 0.210293i
\(741\) 0 0
\(742\) −4.81665 8.34269i −0.176825 0.306270i
\(743\) −2.78890 4.83051i −0.102315 0.177214i 0.810323 0.585983i \(-0.199292\pi\)
−0.912638 + 0.408769i \(0.865958\pi\)
\(744\) 0 0
\(745\) −11.5139 + 19.9426i −0.421836 + 0.730641i
\(746\) −58.0555 −2.12556
\(747\) 0 0
\(748\) 24.4222 0.892964
\(749\) 0 0
\(750\) 0 0
\(751\) 15.0139 + 26.0048i 0.547864 + 0.948929i 0.998421 + 0.0561807i \(0.0178923\pi\)
−0.450556 + 0.892748i \(0.648774\pi\)
\(752\) −1.39445 2.41526i −0.0508503 0.0880753i
\(753\) 0 0
\(754\) 10.6056 18.3694i 0.386231 0.668972i
\(755\) −14.4222 −0.524878
\(756\) 0 0
\(757\) 16.7889 0.610203 0.305101 0.952320i \(-0.401310\pi\)
0.305101 + 0.952320i \(0.401310\pi\)
\(758\) −24.8764 + 43.0871i −0.903550 + 1.56500i
\(759\) 0 0
\(760\) 5.40833 + 9.36750i 0.196181 + 0.339795i
\(761\) 5.72498 + 9.91596i 0.207530 + 0.359453i 0.950936 0.309388i \(-0.100124\pi\)
−0.743406 + 0.668841i \(0.766791\pi\)
\(762\) 0 0
\(763\) −9.11943 + 15.7953i −0.330146 + 0.571829i
\(764\) 41.0278 1.48433
\(765\) 0 0
\(766\) −56.7250 −2.04956
\(767\) −4.60555 + 7.97705i −0.166297 + 0.288035i
\(768\) 0 0
\(769\) −20.5000 35.5070i −0.739249 1.28042i −0.952834 0.303492i \(-0.901847\pi\)
0.213585 0.976924i \(-0.431486\pi\)
\(770\) 13.8167 + 23.9311i 0.497918 + 0.862419i
\(771\) 0 0
\(772\) −0.302776 + 0.524423i −0.0108971 + 0.0188744i
\(773\) 4.81665 0.173243 0.0866215 0.996241i \(-0.472393\pi\)
0.0866215 + 0.996241i \(0.472393\pi\)
\(774\) 0 0
\(775\) −5.60555 −0.201357
\(776\) −12.0000 + 20.7846i −0.430775 + 0.746124i
\(777\) 0 0
\(778\) 29.7250 + 51.4852i 1.06569 + 1.84583i
\(779\) −8.30278 14.3808i −0.297478 0.515247i
\(780\) 0 0
\(781\) −17.0278 + 29.4929i −0.609301 + 1.05534i
\(782\) −11.0917 −0.396637
\(783\) 0 0
\(784\) −0.0639167 −0.00228274
\(785\) −8.90833 + 15.4297i −0.317952 + 0.550709i
\(786\) 0 0
\(787\) 19.5139 + 33.7990i 0.695595 + 1.20481i 0.969980 + 0.243185i \(0.0781923\pi\)
−0.274385 + 0.961620i \(0.588474\pi\)
\(788\) −37.6791 65.2622i −1.34226 2.32487i
\(789\) 0 0
\(790\) −13.3625 + 23.1445i −0.475416 + 0.823445i
\(791\) −39.6333 −1.40920
\(792\) 0 0
\(793\) −27.8167 −0.987798
\(794\) 6.21110 10.7579i 0.220424 0.381785i
\(795\) 0 0
\(796\) 2.00000 + 3.46410i 0.0708881 + 0.122782i
\(797\) 20.8305 + 36.0795i 0.737855 + 1.27800i 0.953459 + 0.301522i \(0.0974947\pi\)
−0.215604 + 0.976481i \(0.569172\pi\)
\(798\) 0 0
\(799\) 7.39445 12.8076i 0.261597 0.453099i
\(800\) −5.30278 −0.187481
\(801\) 0 0
\(802\) 69.0833 2.43942
\(803\) 29.0278 50.2775i 1.02437 1.77426i
\(804\) 0 0
\(805\) −3.90833 6.76942i −0.137750 0.238591i
\(806\) 42.6333 + 73.8431i 1.50169 + 2.60101i
\(807\) 0 0
\(808\) 18.0000 31.1769i 0.633238 1.09680i
\(809\) −43.3944 −1.52567 −0.762834 0.646595i \(-0.776193\pi\)
−0.762834 + 0.646595i \(0.776193\pi\)
\(810\) 0 0
\(811\) 13.5778 0.476781 0.238390 0.971169i \(-0.423380\pi\)
0.238390 + 0.971169i \(0.423380\pi\)
\(812\) −6.00000 + 10.3923i −0.210559 + 0.364698i
\(813\) 0 0
\(814\) 10.6056 + 18.3694i 0.371724 + 0.643846i
\(815\) 1.00000 + 1.73205i 0.0350285 + 0.0606711i
\(816\) 0 0
\(817\) −1.09167 + 1.89083i −0.0381928 + 0.0661519i
\(818\) 11.5139 0.402573
\(819\) 0 0
\(820\) −15.2111 −0.531195
\(821\) 15.0000 25.9808i 0.523504 0.906735i −0.476122 0.879379i \(-0.657958\pi\)
0.999626 0.0273557i \(-0.00870868\pi\)
\(822\) 0 0
\(823\) 8.90833 + 15.4297i 0.310525 + 0.537845i 0.978476 0.206360i \(-0.0661619\pi\)
−0.667951 + 0.744205i \(0.732829\pi\)
\(824\) 6.00000 + 10.3923i 0.209020 + 0.362033i
\(825\) 0 0
\(826\) 4.18335 7.24577i 0.145557 0.252113i
\(827\) 48.2111 1.67646 0.838232 0.545314i \(-0.183589\pi\)
0.838232 + 0.545314i \(0.183589\pi\)
\(828\) 0 0
\(829\) −12.7889 −0.444177 −0.222088 0.975027i \(-0.571287\pi\)
−0.222088 + 0.975027i \(0.571287\pi\)
\(830\) −3.45416 + 5.98279i −0.119896 + 0.207666i
\(831\) 0 0
\(832\) 42.3305 + 73.3186i 1.46755 + 2.54187i
\(833\) −0.169468 0.293527i −0.00587172 0.0101701i
\(834\) 0 0
\(835\) 1.50000 2.59808i 0.0519096 0.0899101i
\(836\) −54.8444 −1.89683
\(837\) 0 0
\(838\) −53.0278 −1.83181
\(839\) 16.6056 28.7617i 0.573287 0.992963i −0.422938 0.906159i \(-0.639001\pi\)
0.996225 0.0868041i \(-0.0276654\pi\)
\(840\) 0 0
\(841\) 13.5278 + 23.4308i 0.466474 + 0.807957i
\(842\) −6.24306 10.8133i −0.215150 0.372651i
\(843\) 0 0
\(844\) 14.5597 25.2182i 0.501166 0.868045i
\(845\) −30.6333 −1.05382
\(846\) 0 0
\(847\) −26.6056 −0.914178
\(848\) 0.243061 0.420994i 0.00834675 0.0144570i
\(849\) 0 0
\(850\) 1.84861 + 3.20189i 0.0634069 + 0.109824i
\(851\) −3.00000 5.19615i −0.102839 0.178122i
\(852\) 0 0
\(853\) −14.6056 + 25.2976i −0.500085 + 0.866172i 0.499915 + 0.866074i \(0.333364\pi\)
−1.00000 9.76338e-5i \(0.999969\pi\)
\(854\) 25.2666 0.864606
\(855\) 0 0
\(856\) 0 0
\(857\) 2.61943 4.53698i 0.0894780 0.154980i −0.817813 0.575485i \(-0.804813\pi\)
0.907291 + 0.420504i \(0.138147\pi\)
\(858\) 0 0
\(859\) 15.0139 + 26.0048i 0.512267 + 0.887272i 0.999899 + 0.0142230i \(0.00452748\pi\)
−0.487632 + 0.873049i \(0.662139\pi\)
\(860\) 1.00000 + 1.73205i 0.0340997 + 0.0590624i
\(861\) 0 0
\(862\) 4.81665 8.34269i 0.164056 0.284153i
\(863\) −30.2111 −1.02840 −0.514199 0.857671i \(-0.671911\pi\)
−0.514199 + 0.857671i \(0.671911\pi\)
\(864\) 0 0
\(865\) −10.8167 −0.367777
\(866\) −25.6056 + 44.3501i −0.870112 + 1.50708i
\(867\) 0 0
\(868\) −24.1194 41.7761i −0.818667 1.41797i
\(869\) −26.7250 46.2890i −0.906583 1.57025i
\(870\) 0 0
\(871\) 2.60555 4.51295i 0.0882857 0.152915i
\(872\) −21.0000 −0.711150
\(873\) 0 0
\(874\) 24.9083 0.842537
\(875\) −1.30278 + 2.25647i −0.0440419 + 0.0762827i
\(876\) 0 0
\(877\) −11.3305 19.6251i −0.382605 0.662691i 0.608829 0.793302i \(-0.291640\pi\)
−0.991434 + 0.130610i \(0.958306\pi\)
\(878\) −31.7847 55.0527i −1.07268 1.85794i
\(879\) 0 0
\(880\) −0.697224 + 1.20763i −0.0235034 + 0.0407091i
\(881\) 25.3944 0.855561 0.427780 0.903883i \(-0.359296\pi\)
0.427780 + 0.903883i \(0.359296\pi\)
\(882\) 0 0
\(883\) 15.8167 0.532273 0.266136 0.963935i \(-0.414253\pi\)
0.266136 + 0.963935i \(0.414253\pi\)
\(884\) 17.5139 30.3349i 0.589055 1.02027i
\(885\) 0 0
\(886\) −28.3625 49.1253i −0.952856 1.65040i
\(887\) −15.3167 26.5292i −0.514283 0.890764i −0.999863 0.0165718i \(-0.994725\pi\)
0.485580 0.874192i \(-0.338609\pi\)
\(888\) 0 0
\(889\) −25.0278 + 43.3493i −0.839404 + 1.45389i
\(890\) −31.8167 −1.06650
\(891\) 0 0
\(892\) −33.0278 −1.10585
\(893\) −16.6056 + 28.7617i −0.555684 + 0.962472i
\(894\) 0 0
\(895\) 10.6056 + 18.3694i 0.354504 + 0.614020i
\(896\) −24.6333 42.6661i −0.822941 1.42538i
\(897\) 0 0
\(898\) 44.0278 76.2583i 1.46923 2.54477i
\(899\) 7.81665 0.260700
\(900\) 0 0
\(901\) 2.57779 0.0858788
\(902\) 24.4222 42.3005i 0.813170 1.40845i
\(903\) 0 0
\(904\) −22.8167 39.5196i −0.758871 1.31440i
\(905\) −3.50000 6.06218i −0.116344 0.201514i
\(906\) 0 0
\(907\) −0.788897 + 1.36641i −0.0261949 + 0.0453709i −0.878826 0.477143i \(-0.841672\pi\)
0.852631 + 0.522514i \(0.175006\pi\)
\(908\) 38.9361 1.29214
\(909\) 0 0
\(910\) 39.6333 1.31383
\(911\) −2.51388 + 4.35416i −0.0832885 + 0.144260i −0.904661 0.426133i \(-0.859876\pi\)
0.821372 + 0.570393i \(0.193209\pi\)
\(912\) 0 0
\(913\) −6.90833 11.9656i −0.228632 0.396003i
\(914\) 15.2111 + 26.3464i 0.503139 + 0.871462i
\(915\) 0 0
\(916\) −13.5597 + 23.4861i −0.448026 + 0.776003i
\(917\) 15.6333 0.516257
\(918\) 0 0
\(919\) 26.4222 0.871588 0.435794 0.900046i \(-0.356468\pi\)
0.435794 + 0.900046i \(0.356468\pi\)
\(920\) 4.50000 7.79423i 0.148361 0.256968i
\(921\) 0 0
\(922\) 24.9083 + 43.1425i 0.820312 + 1.42082i
\(923\) 24.4222 + 42.3005i 0.803867 + 1.39234i
\(924\) 0 0
\(925\) −1.00000 + 1.73205i −0.0328798 + 0.0569495i
\(926\) −1.81665 −0.0596989
\(927\) 0 0
\(928\) 7.39445 0.242735
\(929\) 9.69722 16.7961i 0.318156 0.551062i −0.661948 0.749550i \(-0.730270\pi\)
0.980103 + 0.198488i \(0.0636032\pi\)
\(930\) 0 0
\(931\) 0.380571 + 0.659168i 0.0124727 + 0.0216033i
\(932\) −29.7250 51.4852i −0.973674 1.68645i
\(933\) 0 0
\(934\) 14.0597 24.3521i 0.460048 0.796826i
\(935\) −7.39445 −0.241824
\(936\) 0 0
\(937\) 41.2111 1.34631 0.673154 0.739502i \(-0.264939\pi\)
0.673154 + 0.739502i \(0.264939\pi\)
\(938\) −2.36669 + 4.09923i −0.0772752 + 0.133845i
\(939\) 0 0
\(940\) 15.2111 + 26.3464i 0.496131 + 0.859325i
\(941\) −0.211103 0.365640i −0.00688175 0.0119195i 0.862564 0.505948i \(-0.168857\pi\)
−0.869446 + 0.494028i \(0.835524\pi\)
\(942\) 0 0
\(943\) −6.90833 + 11.9656i −0.224966 + 0.389653i
\(944\) 0.422205 0.0137416
\(945\) 0 0
\(946\) −6.42221 −0.208804
\(947\) 19.5000 33.7750i 0.633665 1.09754i −0.353131 0.935574i \(-0.614883\pi\)
0.986796 0.161966i \(-0.0517835\pi\)
\(948\) 0 0
\(949\) −41.6333 72.1110i −1.35147 2.34082i
\(950\) −4.15139 7.19041i −0.134689 0.233288i
\(951\) 0 0
\(952\) −6.27502 + 10.8687i −0.203375 + 0.352255i
\(953\) 30.8444 0.999148 0.499574 0.866271i \(-0.333490\pi\)
0.499574 + 0.866271i \(0.333490\pi\)
\(954\) 0 0
\(955\) −12.4222 −0.401973
\(956\) −25.1194 + 43.5081i −0.812420 + 1.40715i
\(957\) 0 0
\(958\) −43.5416 75.4163i −1.40677 2.43659i
\(959\) −21.9083 37.9463i −0.707457 1.22535i
\(960\) 0 0
\(961\) −0.211103 + 0.365640i −0.00680976 + 0.0117948i
\(962\) 30.4222 0.980851
\(963\) 0 0
\(964\) 45.5416 1.46680
\(965\) 0.0916731 0.158782i 0.00295106 0.00511139i
\(966\) 0 0
\(967\) −25.0000 43.3013i −0.803946 1.39247i −0.917000 0.398886i \(-0.869397\pi\)
0.113055 0.993589i \(-0.463936\pi\)
\(968\) −15.3167 26.5292i −0.492296 0.852682i
\(969\) 0 0
\(970\) 9.21110 15.9541i 0.295751 0.512255i
\(971\) 18.0000 0.577647 0.288824 0.957382i \(-0.406736\pi\)
0.288824 + 0.957382i \(0.406736\pi\)
\(972\) 0 0
\(973\) 10.4222 0.334121
\(974\) 34.3305 59.4622i 1.10002 1.90529i
\(975\) 0 0
\(976\) 0.637510 + 1.10420i 0.0204062 + 0.0353446i
\(977\) −7.60555 13.1732i −0.243323 0.421448i 0.718336 0.695697i \(-0.244904\pi\)
−0.961659 + 0.274249i \(0.911571\pi\)
\(978\) 0 0
\(979\) 31.8167 55.1081i 1.01686 1.76126i
\(980\) 0.697224 0.0222720
\(981\) 0 0
\(982\) −62.6611 −1.99959
\(983\) −21.3167 + 36.9215i −0.679896 + 1.17761i 0.295116 + 0.955461i \(0.404642\pi\)
−0.975012 + 0.222152i \(0.928692\pi\)
\(984\) 0 0
\(985\) 11.4083 + 19.7598i 0.363500 + 0.629600i
\(986\) −2.57779 4.46487i −0.0820937 0.142190i
\(987\) 0 0
\(988\) −39.3305 + 68.1225i −1.25127 + 2.16726i
\(989\) 1.81665 0.0577662
\(990\) 0 0
\(991\) −29.1833 −0.927040 −0.463520 0.886087i \(-0.653414\pi\)
−0.463520 + 0.886087i \(0.653414\pi\)
\(992\) −14.8625 + 25.7426i −0.471885 + 0.817328i
\(993\) 0 0
\(994\) −22.1833 38.4227i −0.703613 1.21869i
\(995\) −0.605551 1.04885i −0.0191973 0.0332506i
\(996\) 0 0
\(997\) 19.9361 34.5303i 0.631382 1.09359i −0.355887 0.934529i \(-0.615821\pi\)
0.987269 0.159057i \(-0.0508454\pi\)
\(998\) −46.9638 −1.48661
\(999\) 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 405.2.e.j.136.1 4
3.2 odd 2 405.2.e.k.136.2 4
9.2 odd 6 135.2.a.c.1.1 2
9.4 even 3 inner 405.2.e.j.271.1 4
9.5 odd 6 405.2.e.k.271.2 4
9.7 even 3 135.2.a.d.1.2 yes 2
36.7 odd 6 2160.2.a.y.1.2 2
36.11 even 6 2160.2.a.ba.1.2 2
45.2 even 12 675.2.b.i.649.1 4
45.7 odd 12 675.2.b.h.649.4 4
45.29 odd 6 675.2.a.p.1.2 2
45.34 even 6 675.2.a.k.1.1 2
45.38 even 12 675.2.b.i.649.4 4
45.43 odd 12 675.2.b.h.649.1 4
63.20 even 6 6615.2.a.p.1.1 2
63.34 odd 6 6615.2.a.v.1.2 2
72.11 even 6 8640.2.a.ck.1.2 2
72.29 odd 6 8640.2.a.cr.1.1 2
72.43 odd 6 8640.2.a.cy.1.2 2
72.61 even 6 8640.2.a.df.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
135.2.a.c.1.1 2 9.2 odd 6
135.2.a.d.1.2 yes 2 9.7 even 3
405.2.e.j.136.1 4 1.1 even 1 trivial
405.2.e.j.271.1 4 9.4 even 3 inner
405.2.e.k.136.2 4 3.2 odd 2
405.2.e.k.271.2 4 9.5 odd 6
675.2.a.k.1.1 2 45.34 even 6
675.2.a.p.1.2 2 45.29 odd 6
675.2.b.h.649.1 4 45.43 odd 12
675.2.b.h.649.4 4 45.7 odd 12
675.2.b.i.649.1 4 45.2 even 12
675.2.b.i.649.4 4 45.38 even 12
2160.2.a.y.1.2 2 36.7 odd 6
2160.2.a.ba.1.2 2 36.11 even 6
6615.2.a.p.1.1 2 63.20 even 6
6615.2.a.v.1.2 2 63.34 odd 6
8640.2.a.ck.1.2 2 72.11 even 6
8640.2.a.cr.1.1 2 72.29 odd 6
8640.2.a.cy.1.2 2 72.43 odd 6
8640.2.a.df.1.1 2 72.61 even 6