Properties

Label 588.2.e.b.491.8
Level $588$
Weight $2$
Character 588.491
Analytic conductor $4.695$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [588,2,Mod(491,588)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(588, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("588.491");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 588.e (of order \(2\), degree \(1\), 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: \(4.69520363885\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: 8.0.3317760000.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 8x^{6} + 13x^{4} + 12x^{2} + 36 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 491.8
Root \(-0.578737 - 0.965926i\) of defining polynomial
Character \(\chi\) \(=\) 588.491
Dual form 588.2.e.b.491.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.866025 + 1.11803i) q^{2} +(1.58114 - 0.707107i) q^{3} +(-0.500000 + 1.93649i) q^{4} +2.44949i q^{5} +(2.15988 + 1.15539i) q^{6} +(-2.59808 + 1.11803i) q^{8} +(2.00000 - 2.23607i) q^{9} +O(q^{10})\) \(q+(0.866025 + 1.11803i) q^{2} +(1.58114 - 0.707107i) q^{3} +(-0.500000 + 1.93649i) q^{4} +2.44949i q^{5} +(2.15988 + 1.15539i) q^{6} +(-2.59808 + 1.11803i) q^{8} +(2.00000 - 2.23607i) q^{9} +(-2.73861 + 2.12132i) q^{10} -3.46410 q^{11} +(0.578737 + 3.41542i) q^{12} +5.47723 q^{13} +(1.73205 + 3.87298i) q^{15} +(-3.50000 - 1.93649i) q^{16} +4.89898i q^{17} +(4.23205 + 0.299576i) q^{18} +4.24264i q^{19} +(-4.74342 - 1.22474i) q^{20} +(-3.00000 - 3.87298i) q^{22} +(-3.31735 + 3.60488i) q^{24} -1.00000 q^{25} +(4.74342 + 6.12372i) q^{26} +(1.58114 - 4.94975i) q^{27} -4.47214i q^{29} +(-2.83013 + 5.29059i) q^{30} -8.48528i q^{31} +(-0.866025 - 5.59017i) q^{32} +(-5.47723 + 2.44949i) q^{33} +(-5.47723 + 4.24264i) q^{34} +(3.33013 + 4.99102i) q^{36} -2.00000 q^{37} +(-4.74342 + 3.67423i) q^{38} +(8.66025 - 3.87298i) q^{39} +(-2.73861 - 6.36396i) q^{40} -7.74597i q^{43} +(1.73205 - 6.70820i) q^{44} +(5.47723 + 4.89898i) q^{45} +(-6.90329 - 0.586988i) q^{48} +(-0.866025 - 1.11803i) q^{50} +(3.46410 + 7.74597i) q^{51} +(-2.73861 + 10.6066i) q^{52} +4.47214i q^{53} +(6.90329 - 2.51884i) q^{54} -8.48528i q^{55} +(3.00000 + 6.70820i) q^{57} +(5.00000 - 3.87298i) q^{58} +9.48683 q^{59} +(-8.36603 + 1.41761i) q^{60} -5.47723 q^{61} +(9.48683 - 7.34847i) q^{62} +(5.50000 - 5.80948i) q^{64} +13.4164i q^{65} +(-7.48203 - 4.00240i) q^{66} +7.74597i q^{67} +(-9.48683 - 2.44949i) q^{68} -3.46410 q^{71} +(-2.69615 + 8.04554i) q^{72} +10.9545 q^{73} +(-1.73205 - 2.23607i) q^{74} +(-1.58114 + 0.707107i) q^{75} +(-8.21584 - 2.12132i) q^{76} +(11.8301 + 6.32836i) q^{78} -15.4919i q^{79} +(4.74342 - 8.57321i) q^{80} +(-1.00000 - 8.94427i) q^{81} +9.48683 q^{83} -12.0000 q^{85} +(8.66025 - 6.70820i) q^{86} +(-3.16228 - 7.07107i) q^{87} +(9.00000 - 3.87298i) q^{88} -9.79796i q^{89} +(-0.733809 + 10.3664i) q^{90} +(-6.00000 - 13.4164i) q^{93} -10.3923 q^{95} +(-5.32215 - 8.22646i) q^{96} +(-6.92820 + 7.74597i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 4 q^{4} + 16 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 4 q^{4} + 16 q^{9} - 28 q^{16} + 20 q^{18} - 24 q^{22} - 8 q^{25} + 12 q^{30} - 8 q^{36} - 16 q^{37} + 24 q^{57} + 40 q^{58} - 60 q^{60} + 44 q^{64} + 20 q^{72} + 60 q^{78} - 8 q^{81} - 96 q^{85} + 72 q^{88} - 48 q^{93}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/588\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(295\) \(493\)
\(\chi(n)\) \(-1\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.866025 + 1.11803i 0.612372 + 0.790569i
\(3\) 1.58114 0.707107i 0.912871 0.408248i
\(4\) −0.500000 + 1.93649i −0.250000 + 0.968246i
\(5\) 2.44949i 1.09545i 0.836660 + 0.547723i \(0.184505\pi\)
−0.836660 + 0.547723i \(0.815495\pi\)
\(6\) 2.15988 + 1.15539i 0.881766 + 0.471688i
\(7\) 0 0
\(8\) −2.59808 + 1.11803i −0.918559 + 0.395285i
\(9\) 2.00000 2.23607i 0.666667 0.745356i
\(10\) −2.73861 + 2.12132i −0.866025 + 0.670820i
\(11\) −3.46410 −1.04447 −0.522233 0.852803i \(-0.674901\pi\)
−0.522233 + 0.852803i \(0.674901\pi\)
\(12\) 0.578737 + 3.41542i 0.167067 + 0.985946i
\(13\) 5.47723 1.51911 0.759555 0.650444i \(-0.225417\pi\)
0.759555 + 0.650444i \(0.225417\pi\)
\(14\) 0 0
\(15\) 1.73205 + 3.87298i 0.447214 + 1.00000i
\(16\) −3.50000 1.93649i −0.875000 0.484123i
\(17\) 4.89898i 1.18818i 0.804400 + 0.594089i \(0.202487\pi\)
−0.804400 + 0.594089i \(0.797513\pi\)
\(18\) 4.23205 + 0.299576i 0.997504 + 0.0706108i
\(19\) 4.24264i 0.973329i 0.873589 + 0.486664i \(0.161786\pi\)
−0.873589 + 0.486664i \(0.838214\pi\)
\(20\) −4.74342 1.22474i −1.06066 0.273861i
\(21\) 0 0
\(22\) −3.00000 3.87298i −0.639602 0.825723i
\(23\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(24\) −3.31735 + 3.60488i −0.677151 + 0.735844i
\(25\) −1.00000 −0.200000
\(26\) 4.74342 + 6.12372i 0.930261 + 1.20096i
\(27\) 1.58114 4.94975i 0.304290 0.952579i
\(28\) 0 0
\(29\) 4.47214i 0.830455i −0.909718 0.415227i \(-0.863702\pi\)
0.909718 0.415227i \(-0.136298\pi\)
\(30\) −2.83013 + 5.29059i −0.516708 + 0.965926i
\(31\) 8.48528i 1.52400i −0.647576 0.762001i \(-0.724217\pi\)
0.647576 0.762001i \(-0.275783\pi\)
\(32\) −0.866025 5.59017i −0.153093 0.988212i
\(33\) −5.47723 + 2.44949i −0.953463 + 0.426401i
\(34\) −5.47723 + 4.24264i −0.939336 + 0.727607i
\(35\) 0 0
\(36\) 3.33013 + 4.99102i 0.555021 + 0.831836i
\(37\) −2.00000 −0.328798 −0.164399 0.986394i \(-0.552568\pi\)
−0.164399 + 0.986394i \(0.552568\pi\)
\(38\) −4.74342 + 3.67423i −0.769484 + 0.596040i
\(39\) 8.66025 3.87298i 1.38675 0.620174i
\(40\) −2.73861 6.36396i −0.433013 1.00623i
\(41\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(42\) 0 0
\(43\) 7.74597i 1.18125i −0.806947 0.590624i \(-0.798881\pi\)
0.806947 0.590624i \(-0.201119\pi\)
\(44\) 1.73205 6.70820i 0.261116 1.01130i
\(45\) 5.47723 + 4.89898i 0.816497 + 0.730297i
\(46\) 0 0
\(47\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(48\) −6.90329 0.586988i −0.996404 0.0847245i
\(49\) 0 0
\(50\) −0.866025 1.11803i −0.122474 0.158114i
\(51\) 3.46410 + 7.74597i 0.485071 + 1.08465i
\(52\) −2.73861 + 10.6066i −0.379777 + 1.47087i
\(53\) 4.47214i 0.614295i 0.951662 + 0.307148i \(0.0993745\pi\)
−0.951662 + 0.307148i \(0.900625\pi\)
\(54\) 6.90329 2.51884i 0.939419 0.342771i
\(55\) 8.48528i 1.14416i
\(56\) 0 0
\(57\) 3.00000 + 6.70820i 0.397360 + 0.888523i
\(58\) 5.00000 3.87298i 0.656532 0.508548i
\(59\) 9.48683 1.23508 0.617540 0.786539i \(-0.288129\pi\)
0.617540 + 0.786539i \(0.288129\pi\)
\(60\) −8.36603 + 1.41761i −1.08005 + 0.183013i
\(61\) −5.47723 −0.701287 −0.350643 0.936509i \(-0.614037\pi\)
−0.350643 + 0.936509i \(0.614037\pi\)
\(62\) 9.48683 7.34847i 1.20483 0.933257i
\(63\) 0 0
\(64\) 5.50000 5.80948i 0.687500 0.726184i
\(65\) 13.4164i 1.66410i
\(66\) −7.48203 4.00240i −0.920974 0.492662i
\(67\) 7.74597i 0.946320i 0.880976 + 0.473160i \(0.156887\pi\)
−0.880976 + 0.473160i \(0.843113\pi\)
\(68\) −9.48683 2.44949i −1.15045 0.297044i
\(69\) 0 0
\(70\) 0 0
\(71\) −3.46410 −0.411113 −0.205557 0.978645i \(-0.565900\pi\)
−0.205557 + 0.978645i \(0.565900\pi\)
\(72\) −2.69615 + 8.04554i −0.317745 + 0.948176i
\(73\) 10.9545 1.28212 0.641061 0.767490i \(-0.278495\pi\)
0.641061 + 0.767490i \(0.278495\pi\)
\(74\) −1.73205 2.23607i −0.201347 0.259938i
\(75\) −1.58114 + 0.707107i −0.182574 + 0.0816497i
\(76\) −8.21584 2.12132i −0.942421 0.243332i
\(77\) 0 0
\(78\) 11.8301 + 6.32836i 1.33950 + 0.716545i
\(79\) 15.4919i 1.74298i −0.490414 0.871489i \(-0.663155\pi\)
0.490414 0.871489i \(-0.336845\pi\)
\(80\) 4.74342 8.57321i 0.530330 0.958514i
\(81\) −1.00000 8.94427i −0.111111 0.993808i
\(82\) 0 0
\(83\) 9.48683 1.04132 0.520658 0.853766i \(-0.325687\pi\)
0.520658 + 0.853766i \(0.325687\pi\)
\(84\) 0 0
\(85\) −12.0000 −1.30158
\(86\) 8.66025 6.70820i 0.933859 0.723364i
\(87\) −3.16228 7.07107i −0.339032 0.758098i
\(88\) 9.00000 3.87298i 0.959403 0.412861i
\(89\) 9.79796i 1.03858i −0.854598 0.519291i \(-0.826196\pi\)
0.854598 0.519291i \(-0.173804\pi\)
\(90\) −0.733809 + 10.3664i −0.0773503 + 1.09271i
\(91\) 0 0
\(92\) 0 0
\(93\) −6.00000 13.4164i −0.622171 1.39122i
\(94\) 0 0
\(95\) −10.3923 −1.06623
\(96\) −5.32215 8.22646i −0.543190 0.839610i
\(97\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(98\) 0 0
\(99\) −6.92820 + 7.74597i −0.696311 + 0.778499i
\(100\) 0.500000 1.93649i 0.0500000 0.193649i
\(101\) 7.34847i 0.731200i −0.930772 0.365600i \(-0.880864\pi\)
0.930772 0.365600i \(-0.119136\pi\)
\(102\) −5.66025 + 10.5812i −0.560449 + 1.04769i
\(103\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(104\) −14.2302 + 6.12372i −1.39539 + 0.600481i
\(105\) 0 0
\(106\) −5.00000 + 3.87298i −0.485643 + 0.376177i
\(107\) −17.3205 −1.67444 −0.837218 0.546869i \(-0.815820\pi\)
−0.837218 + 0.546869i \(0.815820\pi\)
\(108\) 8.79458 + 5.53674i 0.846258 + 0.532773i
\(109\) 10.0000 0.957826 0.478913 0.877862i \(-0.341031\pi\)
0.478913 + 0.877862i \(0.341031\pi\)
\(110\) 9.48683 7.34847i 0.904534 0.700649i
\(111\) −3.16228 + 1.41421i −0.300150 + 0.134231i
\(112\) 0 0
\(113\) 4.47214i 0.420703i 0.977626 + 0.210352i \(0.0674609\pi\)
−0.977626 + 0.210352i \(0.932539\pi\)
\(114\) −4.90192 + 9.16358i −0.459107 + 0.858248i
\(115\) 0 0
\(116\) 8.66025 + 2.23607i 0.804084 + 0.207614i
\(117\) 10.9545 12.2474i 1.01274 1.13228i
\(118\) 8.21584 + 10.6066i 0.756329 + 0.976417i
\(119\) 0 0
\(120\) −8.83013 8.12581i −0.806077 0.741782i
\(121\) 1.00000 0.0909091
\(122\) −4.74342 6.12372i −0.429449 0.554416i
\(123\) 0 0
\(124\) 16.4317 + 4.24264i 1.47561 + 0.381000i
\(125\) 9.79796i 0.876356i
\(126\) 0 0
\(127\) 7.74597i 0.687343i −0.939090 0.343672i \(-0.888329\pi\)
0.939090 0.343672i \(-0.111671\pi\)
\(128\) 11.2583 + 1.11803i 0.995105 + 0.0988212i
\(129\) −5.47723 12.2474i −0.482243 1.07833i
\(130\) −15.0000 + 11.6190i −1.31559 + 1.01905i
\(131\) −9.48683 −0.828868 −0.414434 0.910079i \(-0.636021\pi\)
−0.414434 + 0.910079i \(0.636021\pi\)
\(132\) −2.00480 11.8313i −0.174496 1.02979i
\(133\) 0 0
\(134\) −8.66025 + 6.70820i −0.748132 + 0.579501i
\(135\) 12.1244 + 3.87298i 1.04350 + 0.333333i
\(136\) −5.47723 12.7279i −0.469668 1.09141i
\(137\) 8.94427i 0.764161i 0.924129 + 0.382080i \(0.124792\pi\)
−0.924129 + 0.382080i \(0.875208\pi\)
\(138\) 0 0
\(139\) 4.24264i 0.359856i 0.983680 + 0.179928i \(0.0575865\pi\)
−0.983680 + 0.179928i \(0.942414\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −3.00000 3.87298i −0.251754 0.325014i
\(143\) −18.9737 −1.58666
\(144\) −11.3301 + 3.95325i −0.944177 + 0.329438i
\(145\) 10.9545 0.909718
\(146\) 9.48683 + 12.2474i 0.785136 + 1.01361i
\(147\) 0 0
\(148\) 1.00000 3.87298i 0.0821995 0.318357i
\(149\) 4.47214i 0.366372i 0.983078 + 0.183186i \(0.0586410\pi\)
−0.983078 + 0.183186i \(0.941359\pi\)
\(150\) −2.15988 1.15539i −0.176353 0.0943376i
\(151\) 7.74597i 0.630358i −0.949032 0.315179i \(-0.897935\pi\)
0.949032 0.315179i \(-0.102065\pi\)
\(152\) −4.74342 11.0227i −0.384742 0.894059i
\(153\) 10.9545 + 9.79796i 0.885615 + 0.792118i
\(154\) 0 0
\(155\) 20.7846 1.66946
\(156\) 3.16987 + 18.7070i 0.253793 + 1.49776i
\(157\) −5.47723 −0.437130 −0.218565 0.975822i \(-0.570138\pi\)
−0.218565 + 0.975822i \(0.570138\pi\)
\(158\) 17.3205 13.4164i 1.37795 1.06735i
\(159\) 3.16228 + 7.07107i 0.250785 + 0.560772i
\(160\) 13.6931 2.12132i 1.08253 0.167705i
\(161\) 0 0
\(162\) 9.13397 8.86400i 0.717633 0.696422i
\(163\) 7.74597i 0.606711i 0.952877 + 0.303355i \(0.0981070\pi\)
−0.952877 + 0.303355i \(0.901893\pi\)
\(164\) 0 0
\(165\) −6.00000 13.4164i −0.467099 1.04447i
\(166\) 8.21584 + 10.6066i 0.637673 + 0.823232i
\(167\) −18.9737 −1.46823 −0.734113 0.679027i \(-0.762402\pi\)
−0.734113 + 0.679027i \(0.762402\pi\)
\(168\) 0 0
\(169\) 17.0000 1.30769
\(170\) −10.3923 13.4164i −0.797053 1.02899i
\(171\) 9.48683 + 8.48528i 0.725476 + 0.648886i
\(172\) 15.0000 + 3.87298i 1.14374 + 0.295312i
\(173\) 2.44949i 0.186231i 0.995655 + 0.0931156i \(0.0296826\pi\)
−0.995655 + 0.0931156i \(0.970317\pi\)
\(174\) 5.16708 9.65926i 0.391715 0.732266i
\(175\) 0 0
\(176\) 12.1244 + 6.70820i 0.913908 + 0.505650i
\(177\) 15.0000 6.70820i 1.12747 0.504219i
\(178\) 10.9545 8.48528i 0.821071 0.635999i
\(179\) 10.3923 0.776757 0.388379 0.921500i \(-0.373035\pi\)
0.388379 + 0.921500i \(0.373035\pi\)
\(180\) −12.2254 + 8.15711i −0.911231 + 0.607995i
\(181\) −16.4317 −1.22136 −0.610678 0.791879i \(-0.709103\pi\)
−0.610678 + 0.791879i \(0.709103\pi\)
\(182\) 0 0
\(183\) −8.66025 + 3.87298i −0.640184 + 0.286299i
\(184\) 0 0
\(185\) 4.89898i 0.360180i
\(186\) 9.80385 18.3272i 0.718853 1.34381i
\(187\) 16.9706i 1.24101i
\(188\) 0 0
\(189\) 0 0
\(190\) −9.00000 11.6190i −0.652929 0.842927i
\(191\) −3.46410 −0.250654 −0.125327 0.992116i \(-0.539998\pi\)
−0.125327 + 0.992116i \(0.539998\pi\)
\(192\) 4.58834 13.0747i 0.331135 0.943583i
\(193\) −16.0000 −1.15171 −0.575853 0.817554i \(-0.695330\pi\)
−0.575853 + 0.817554i \(0.695330\pi\)
\(194\) 0 0
\(195\) 9.48683 + 21.2132i 0.679366 + 1.51911i
\(196\) 0 0
\(197\) 22.3607i 1.59313i −0.604551 0.796566i \(-0.706648\pi\)
0.604551 0.796566i \(-0.293352\pi\)
\(198\) −14.6603 1.03776i −1.04186 0.0737506i
\(199\) 16.9706i 1.20301i 0.798869 + 0.601506i \(0.205432\pi\)
−0.798869 + 0.601506i \(0.794568\pi\)
\(200\) 2.59808 1.11803i 0.183712 0.0790569i
\(201\) 5.47723 + 12.2474i 0.386334 + 0.863868i
\(202\) 8.21584 6.36396i 0.578064 0.447767i
\(203\) 0 0
\(204\) −16.7321 + 2.83522i −1.17148 + 0.198505i
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) −19.1703 10.6066i −1.32922 0.735436i
\(209\) 14.6969i 1.01661i
\(210\) 0 0
\(211\) 7.74597i 0.533254i 0.963800 + 0.266627i \(0.0859092\pi\)
−0.963800 + 0.266627i \(0.914091\pi\)
\(212\) −8.66025 2.23607i −0.594789 0.153574i
\(213\) −5.47723 + 2.44949i −0.375293 + 0.167836i
\(214\) −15.0000 19.3649i −1.02538 1.32376i
\(215\) 18.9737 1.29399
\(216\) 1.42607 + 14.6276i 0.0970316 + 0.995281i
\(217\) 0 0
\(218\) 8.66025 + 11.1803i 0.586546 + 0.757228i
\(219\) 17.3205 7.74597i 1.17041 0.523424i
\(220\) 16.4317 + 4.24264i 1.10782 + 0.286039i
\(221\) 26.8328i 1.80497i
\(222\) −4.31975 2.31079i −0.289923 0.155090i
\(223\) 8.48528i 0.568216i 0.958792 + 0.284108i \(0.0916975\pi\)
−0.958792 + 0.284108i \(0.908302\pi\)
\(224\) 0 0
\(225\) −2.00000 + 2.23607i −0.133333 + 0.149071i
\(226\) −5.00000 + 3.87298i −0.332595 + 0.257627i
\(227\) 9.48683 0.629663 0.314832 0.949148i \(-0.398052\pi\)
0.314832 + 0.949148i \(0.398052\pi\)
\(228\) −14.4904 + 2.45537i −0.959649 + 0.162611i
\(229\) −5.47723 −0.361945 −0.180973 0.983488i \(-0.557925\pi\)
−0.180973 + 0.983488i \(0.557925\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 5.00000 + 11.6190i 0.328266 + 0.762821i
\(233\) 8.94427i 0.585959i 0.956119 + 0.292979i \(0.0946467\pi\)
−0.956119 + 0.292979i \(0.905353\pi\)
\(234\) 23.1799 + 1.64085i 1.51532 + 0.107266i
\(235\) 0 0
\(236\) −4.74342 + 18.3712i −0.308770 + 1.19586i
\(237\) −10.9545 24.4949i −0.711568 1.59111i
\(238\) 0 0
\(239\) 6.92820 0.448148 0.224074 0.974572i \(-0.428064\pi\)
0.224074 + 0.974572i \(0.428064\pi\)
\(240\) 1.43782 16.9095i 0.0928110 1.09151i
\(241\) −21.9089 −1.41128 −0.705638 0.708572i \(-0.749340\pi\)
−0.705638 + 0.708572i \(0.749340\pi\)
\(242\) 0.866025 + 1.11803i 0.0556702 + 0.0718699i
\(243\) −7.90569 13.4350i −0.507151 0.861858i
\(244\) 2.73861 10.6066i 0.175322 0.679018i
\(245\) 0 0
\(246\) 0 0
\(247\) 23.2379i 1.47859i
\(248\) 9.48683 + 22.0454i 0.602414 + 1.39988i
\(249\) 15.0000 6.70820i 0.950586 0.425115i
\(250\) −10.9545 + 8.48528i −0.692820 + 0.536656i
\(251\) 9.48683 0.598804 0.299402 0.954127i \(-0.403213\pi\)
0.299402 + 0.954127i \(0.403213\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 8.66025 6.70820i 0.543393 0.420910i
\(255\) −18.9737 + 8.48528i −1.18818 + 0.531369i
\(256\) 8.50000 + 13.5554i 0.531250 + 0.847215i
\(257\) 4.89898i 0.305590i 0.988258 + 0.152795i \(0.0488274\pi\)
−0.988258 + 0.152795i \(0.951173\pi\)
\(258\) 8.94965 16.7303i 0.557181 1.04158i
\(259\) 0 0
\(260\) −25.9808 6.70820i −1.61126 0.416025i
\(261\) −10.0000 8.94427i −0.618984 0.553637i
\(262\) −8.21584 10.6066i −0.507576 0.655278i
\(263\) −3.46410 −0.213606 −0.106803 0.994280i \(-0.534061\pi\)
−0.106803 + 0.994280i \(0.534061\pi\)
\(264\) 11.4916 12.4877i 0.707261 0.768564i
\(265\) −10.9545 −0.672927
\(266\) 0 0
\(267\) −6.92820 15.4919i −0.423999 0.948091i
\(268\) −15.0000 3.87298i −0.916271 0.236580i
\(269\) 2.44949i 0.149348i 0.997208 + 0.0746740i \(0.0237916\pi\)
−0.997208 + 0.0746740i \(0.976208\pi\)
\(270\) 6.16987 + 16.9095i 0.375487 + 1.02908i
\(271\) 8.48528i 0.515444i 0.966219 + 0.257722i \(0.0829719\pi\)
−0.966219 + 0.257722i \(0.917028\pi\)
\(272\) 9.48683 17.1464i 0.575224 1.03965i
\(273\) 0 0
\(274\) −10.0000 + 7.74597i −0.604122 + 0.467951i
\(275\) 3.46410 0.208893
\(276\) 0 0
\(277\) 2.00000 0.120168 0.0600842 0.998193i \(-0.480863\pi\)
0.0600842 + 0.998193i \(0.480863\pi\)
\(278\) −4.74342 + 3.67423i −0.284491 + 0.220366i
\(279\) −18.9737 16.9706i −1.13592 1.01600i
\(280\) 0 0
\(281\) 8.94427i 0.533571i 0.963756 + 0.266785i \(0.0859614\pi\)
−0.963756 + 0.266785i \(0.914039\pi\)
\(282\) 0 0
\(283\) 29.6985i 1.76539i 0.469945 + 0.882696i \(0.344274\pi\)
−0.469945 + 0.882696i \(0.655726\pi\)
\(284\) 1.73205 6.70820i 0.102778 0.398059i
\(285\) −16.4317 + 7.34847i −0.973329 + 0.435286i
\(286\) −16.4317 21.2132i −0.971625 1.25436i
\(287\) 0 0
\(288\) −14.2321 9.24385i −0.838632 0.544699i
\(289\) −7.00000 −0.411765
\(290\) 9.48683 + 12.2474i 0.557086 + 0.719195i
\(291\) 0 0
\(292\) −5.47723 + 21.2132i −0.320530 + 1.24141i
\(293\) 2.44949i 0.143101i −0.997437 0.0715504i \(-0.977205\pi\)
0.997437 0.0715504i \(-0.0227947\pi\)
\(294\) 0 0
\(295\) 23.2379i 1.35296i
\(296\) 5.19615 2.23607i 0.302020 0.129969i
\(297\) −5.47723 + 17.1464i −0.317821 + 0.994937i
\(298\) −5.00000 + 3.87298i −0.289642 + 0.224356i
\(299\) 0 0
\(300\) −0.578737 3.41542i −0.0334134 0.197189i
\(301\) 0 0
\(302\) 8.66025 6.70820i 0.498342 0.386014i
\(303\) −5.19615 11.6190i −0.298511 0.667491i
\(304\) 8.21584 14.8492i 0.471211 0.851662i
\(305\) 13.4164i 0.768221i
\(306\) −1.46762 + 20.7327i −0.0838981 + 1.18521i
\(307\) 21.2132i 1.21070i 0.795959 + 0.605351i \(0.206967\pi\)
−0.795959 + 0.605351i \(0.793033\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 18.0000 + 23.2379i 1.02233 + 1.31982i
\(311\) −18.9737 −1.07590 −0.537949 0.842977i \(-0.680801\pi\)
−0.537949 + 0.842977i \(0.680801\pi\)
\(312\) −18.1699 + 19.7448i −1.02867 + 1.11783i
\(313\) −10.9545 −0.619182 −0.309591 0.950870i \(-0.600192\pi\)
−0.309591 + 0.950870i \(0.600192\pi\)
\(314\) −4.74342 6.12372i −0.267686 0.345582i
\(315\) 0 0
\(316\) 30.0000 + 7.74597i 1.68763 + 0.435745i
\(317\) 4.47214i 0.251180i 0.992082 + 0.125590i \(0.0400824\pi\)
−0.992082 + 0.125590i \(0.959918\pi\)
\(318\) −5.16708 + 9.65926i −0.289756 + 0.541664i
\(319\) 15.4919i 0.867382i
\(320\) 14.2302 + 13.4722i 0.795495 + 0.753119i
\(321\) −27.3861 + 12.2474i −1.52854 + 0.683586i
\(322\) 0 0
\(323\) −20.7846 −1.15649
\(324\) 17.8205 + 2.53564i 0.990028 + 0.140869i
\(325\) −5.47723 −0.303822
\(326\) −8.66025 + 6.70820i −0.479647 + 0.371533i
\(327\) 15.8114 7.07107i 0.874372 0.391031i
\(328\) 0 0
\(329\) 0 0
\(330\) 9.80385 18.3272i 0.539684 1.00888i
\(331\) 23.2379i 1.27727i −0.769510 0.638635i \(-0.779499\pi\)
0.769510 0.638635i \(-0.220501\pi\)
\(332\) −4.74342 + 18.3712i −0.260329 + 1.00825i
\(333\) −4.00000 + 4.47214i −0.219199 + 0.245072i
\(334\) −16.4317 21.2132i −0.899101 1.16073i
\(335\) −18.9737 −1.03664
\(336\) 0 0
\(337\) −8.00000 −0.435788 −0.217894 0.975972i \(-0.569919\pi\)
−0.217894 + 0.975972i \(0.569919\pi\)
\(338\) 14.7224 + 19.0066i 0.800795 + 1.03382i
\(339\) 3.16228 + 7.07107i 0.171751 + 0.384048i
\(340\) 6.00000 23.2379i 0.325396 1.26025i
\(341\) 29.3939i 1.59177i
\(342\) −1.27099 + 17.9551i −0.0687275 + 0.970899i
\(343\) 0 0
\(344\) 8.66025 + 20.1246i 0.466930 + 1.08505i
\(345\) 0 0
\(346\) −2.73861 + 2.12132i −0.147229 + 0.114043i
\(347\) −24.2487 −1.30174 −0.650870 0.759190i \(-0.725596\pi\)
−0.650870 + 0.759190i \(0.725596\pi\)
\(348\) 15.2742 2.58819i 0.818783 0.138742i
\(349\) 16.4317 0.879567 0.439784 0.898104i \(-0.355055\pi\)
0.439784 + 0.898104i \(0.355055\pi\)
\(350\) 0 0
\(351\) 8.66025 27.1109i 0.462250 1.44707i
\(352\) 3.00000 + 19.3649i 0.159901 + 1.03215i
\(353\) 14.6969i 0.782239i 0.920340 + 0.391120i \(0.127912\pi\)
−0.920340 + 0.391120i \(0.872088\pi\)
\(354\) 20.4904 + 10.9610i 1.08905 + 0.582572i
\(355\) 8.48528i 0.450352i
\(356\) 18.9737 + 4.89898i 1.00560 + 0.259645i
\(357\) 0 0
\(358\) 9.00000 + 11.6190i 0.475665 + 0.614081i
\(359\) −27.7128 −1.46263 −0.731313 0.682042i \(-0.761092\pi\)
−0.731313 + 0.682042i \(0.761092\pi\)
\(360\) −19.7075 6.60420i −1.03868 0.348072i
\(361\) 1.00000 0.0526316
\(362\) −14.2302 18.3712i −0.747925 0.965567i
\(363\) 1.58114 0.707107i 0.0829883 0.0371135i
\(364\) 0 0
\(365\) 26.8328i 1.40449i
\(366\) −11.8301 6.32836i −0.618371 0.330788i
\(367\) 25.4558i 1.32878i −0.747384 0.664392i \(-0.768691\pi\)
0.747384 0.664392i \(-0.231309\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 5.47723 4.24264i 0.284747 0.220564i
\(371\) 0 0
\(372\) 28.9808 4.91075i 1.50258 0.254610i
\(373\) 26.0000 1.34623 0.673114 0.739538i \(-0.264956\pi\)
0.673114 + 0.739538i \(0.264956\pi\)
\(374\) 18.9737 14.6969i 0.981105 0.759961i
\(375\) 6.92820 + 15.4919i 0.357771 + 0.800000i
\(376\) 0 0
\(377\) 24.4949i 1.26155i
\(378\) 0 0
\(379\) 7.74597i 0.397884i 0.980011 + 0.198942i \(0.0637505\pi\)
−0.980011 + 0.198942i \(0.936250\pi\)
\(380\) 5.19615 20.1246i 0.266557 1.03237i
\(381\) −5.47723 12.2474i −0.280607 0.627456i
\(382\) −3.00000 3.87298i −0.153493 0.198159i
\(383\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(384\) 18.5916 6.19307i 0.948746 0.316039i
\(385\) 0 0
\(386\) −13.8564 17.8885i −0.705273 0.910503i
\(387\) −17.3205 15.4919i −0.880451 0.787499i
\(388\) 0 0
\(389\) 31.3050i 1.58722i −0.608424 0.793612i \(-0.708198\pi\)
0.608424 0.793612i \(-0.291802\pi\)
\(390\) −15.5012 + 28.9778i −0.784936 + 1.46735i
\(391\) 0 0
\(392\) 0 0
\(393\) −15.0000 + 6.70820i −0.756650 + 0.338384i
\(394\) 25.0000 19.3649i 1.25948 0.975590i
\(395\) 37.9473 1.90934
\(396\) −11.5359 17.2894i −0.579701 0.868825i
\(397\) 38.3406 1.92426 0.962129 0.272594i \(-0.0878815\pi\)
0.962129 + 0.272594i \(0.0878815\pi\)
\(398\) −18.9737 + 14.6969i −0.951064 + 0.736691i
\(399\) 0 0
\(400\) 3.50000 + 1.93649i 0.175000 + 0.0968246i
\(401\) 4.47214i 0.223328i −0.993746 0.111664i \(-0.964382\pi\)
0.993746 0.111664i \(-0.0356180\pi\)
\(402\) −8.94965 + 16.7303i −0.446368 + 0.834433i
\(403\) 46.4758i 2.31512i
\(404\) 14.2302 + 3.67423i 0.707981 + 0.182800i
\(405\) 21.9089 2.44949i 1.08866 0.121716i
\(406\) 0 0
\(407\) 6.92820 0.343418
\(408\) −17.6603 16.2516i −0.874313 0.804575i
\(409\) −10.9545 −0.541663 −0.270831 0.962627i \(-0.587299\pi\)
−0.270831 + 0.962627i \(0.587299\pi\)
\(410\) 0 0
\(411\) 6.32456 + 14.1421i 0.311967 + 0.697580i
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 23.2379i 1.14070i
\(416\) −4.74342 30.6186i −0.232565 1.50120i
\(417\) 3.00000 + 6.70820i 0.146911 + 0.328502i
\(418\) 16.4317 12.7279i 0.803700 0.622543i
\(419\) 28.4605 1.39039 0.695193 0.718823i \(-0.255319\pi\)
0.695193 + 0.718823i \(0.255319\pi\)
\(420\) 0 0
\(421\) −10.0000 −0.487370 −0.243685 0.969854i \(-0.578356\pi\)
−0.243685 + 0.969854i \(0.578356\pi\)
\(422\) −8.66025 + 6.70820i −0.421575 + 0.326550i
\(423\) 0 0
\(424\) −5.00000 11.6190i −0.242821 0.564266i
\(425\) 4.89898i 0.237635i
\(426\) −7.48203 4.00240i −0.362506 0.193917i
\(427\) 0 0
\(428\) 8.66025 33.5410i 0.418609 1.62127i
\(429\) −30.0000 + 13.4164i −1.44841 + 0.647750i
\(430\) 16.4317 + 21.2132i 0.792406 + 1.02299i
\(431\) 20.7846 1.00116 0.500580 0.865690i \(-0.333120\pi\)
0.500580 + 0.865690i \(0.333120\pi\)
\(432\) −15.1191 + 14.2623i −0.727420 + 0.686193i
\(433\) 21.9089 1.05287 0.526437 0.850214i \(-0.323527\pi\)
0.526437 + 0.850214i \(0.323527\pi\)
\(434\) 0 0
\(435\) 17.3205 7.74597i 0.830455 0.371391i
\(436\) −5.00000 + 19.3649i −0.239457 + 0.927411i
\(437\) 0 0
\(438\) 23.6603 + 12.6567i 1.13053 + 0.604761i
\(439\) 16.9706i 0.809961i 0.914325 + 0.404980i \(0.132722\pi\)
−0.914325 + 0.404980i \(0.867278\pi\)
\(440\) 9.48683 + 22.0454i 0.452267 + 1.05097i
\(441\) 0 0
\(442\) −30.0000 + 23.2379i −1.42695 + 1.10531i
\(443\) 31.1769 1.48126 0.740630 0.671913i \(-0.234527\pi\)
0.740630 + 0.671913i \(0.234527\pi\)
\(444\) −1.15747 6.83083i −0.0549313 0.324177i
\(445\) 24.0000 1.13771
\(446\) −9.48683 + 7.34847i −0.449215 + 0.347960i
\(447\) 3.16228 + 7.07107i 0.149571 + 0.334450i
\(448\) 0 0
\(449\) 35.7771i 1.68843i −0.536009 0.844213i \(-0.680069\pi\)
0.536009 0.844213i \(-0.319931\pi\)
\(450\) −4.23205 0.299576i −0.199501 0.0141222i
\(451\) 0 0
\(452\) −8.66025 2.23607i −0.407344 0.105176i
\(453\) −5.47723 12.2474i −0.257343 0.575435i
\(454\) 8.21584 + 10.6066i 0.385588 + 0.497792i
\(455\) 0 0
\(456\) −15.2942 14.0743i −0.716218 0.659091i
\(457\) −28.0000 −1.30978 −0.654892 0.755722i \(-0.727286\pi\)
−0.654892 + 0.755722i \(0.727286\pi\)
\(458\) −4.74342 6.12372i −0.221645 0.286143i
\(459\) 24.2487 + 7.74597i 1.13183 + 0.361551i
\(460\) 0 0
\(461\) 36.7423i 1.71126i 0.517587 + 0.855631i \(0.326831\pi\)
−0.517587 + 0.855631i \(0.673169\pi\)
\(462\) 0 0
\(463\) 15.4919i 0.719971i −0.932958 0.359986i \(-0.882782\pi\)
0.932958 0.359986i \(-0.117218\pi\)
\(464\) −8.66025 + 15.6525i −0.402042 + 0.726648i
\(465\) 32.8634 14.6969i 1.52400 0.681554i
\(466\) −10.0000 + 7.74597i −0.463241 + 0.358825i
\(467\) −28.4605 −1.31699 −0.658497 0.752583i \(-0.728808\pi\)
−0.658497 + 0.752583i \(0.728808\pi\)
\(468\) 18.2399 + 27.3369i 0.843138 + 1.26365i
\(469\) 0 0
\(470\) 0 0
\(471\) −8.66025 + 3.87298i −0.399043 + 0.178458i
\(472\) −24.6475 + 10.6066i −1.13449 + 0.488208i
\(473\) 26.8328i 1.23377i
\(474\) 17.8993 33.4607i 0.822142 1.53690i
\(475\) 4.24264i 0.194666i
\(476\) 0 0
\(477\) 10.0000 + 8.94427i 0.457869 + 0.409530i
\(478\) 6.00000 + 7.74597i 0.274434 + 0.354292i
\(479\) −37.9473 −1.73386 −0.866929 0.498432i \(-0.833909\pi\)
−0.866929 + 0.498432i \(0.833909\pi\)
\(480\) 20.1506 13.0366i 0.919746 0.595035i
\(481\) −10.9545 −0.499480
\(482\) −18.9737 24.4949i −0.864227 1.11571i
\(483\) 0 0
\(484\) −0.500000 + 1.93649i −0.0227273 + 0.0880223i
\(485\) 0 0
\(486\) 8.17429 20.4739i 0.370793 0.928715i
\(487\) 7.74597i 0.351003i 0.984479 + 0.175502i \(0.0561547\pi\)
−0.984479 + 0.175502i \(0.943845\pi\)
\(488\) 14.2302 6.12372i 0.644173 0.277208i
\(489\) 5.47723 + 12.2474i 0.247689 + 0.553849i
\(490\) 0 0
\(491\) −31.1769 −1.40699 −0.703497 0.710698i \(-0.748379\pi\)
−0.703497 + 0.710698i \(0.748379\pi\)
\(492\) 0 0
\(493\) 21.9089 0.986727
\(494\) −25.9808 + 20.1246i −1.16893 + 0.905449i
\(495\) −18.9737 16.9706i −0.852803 0.762770i
\(496\) −16.4317 + 29.6985i −0.737804 + 1.33350i
\(497\) 0 0
\(498\) 20.4904 + 10.9610i 0.918196 + 0.491176i
\(499\) 23.2379i 1.04027i 0.854084 + 0.520136i \(0.174119\pi\)
−0.854084 + 0.520136i \(0.825881\pi\)
\(500\) −18.9737 4.89898i −0.848528 0.219089i
\(501\) −30.0000 + 13.4164i −1.34030 + 0.599401i
\(502\) 8.21584 + 10.6066i 0.366691 + 0.473396i
\(503\) −18.9737 −0.845994 −0.422997 0.906131i \(-0.639022\pi\)
−0.422997 + 0.906131i \(0.639022\pi\)
\(504\) 0 0
\(505\) 18.0000 0.800989
\(506\) 0 0
\(507\) 26.8794 12.0208i 1.19375 0.533863i
\(508\) 15.0000 + 3.87298i 0.665517 + 0.171836i
\(509\) 36.7423i 1.62858i −0.580461 0.814288i \(-0.697128\pi\)
0.580461 0.814288i \(-0.302872\pi\)
\(510\) −25.9185 13.8647i −1.14769 0.613941i
\(511\) 0 0
\(512\) −7.79423 + 21.2426i −0.344459 + 0.938801i
\(513\) 21.0000 + 6.70820i 0.927173 + 0.296174i
\(514\) −5.47723 + 4.24264i −0.241590 + 0.187135i
\(515\) 0 0
\(516\) 26.4557 4.48288i 1.16465 0.197348i
\(517\) 0 0
\(518\) 0 0
\(519\) 1.73205 + 3.87298i 0.0760286 + 0.170005i
\(520\) −15.0000 34.8569i −0.657794 1.52857i
\(521\) 29.3939i 1.28777i −0.765123 0.643885i \(-0.777322\pi\)
0.765123 0.643885i \(-0.222678\pi\)
\(522\) 1.33975 18.9263i 0.0586391 0.828382i
\(523\) 21.2132i 0.927589i 0.885943 + 0.463794i \(0.153512\pi\)
−0.885943 + 0.463794i \(0.846488\pi\)
\(524\) 4.74342 18.3712i 0.207217 0.802548i
\(525\) 0 0
\(526\) −3.00000 3.87298i −0.130806 0.168870i
\(527\) 41.5692 1.81078
\(528\) 23.9137 + 2.03339i 1.04071 + 0.0884918i
\(529\) −23.0000 −1.00000
\(530\) −9.48683 12.2474i −0.412082 0.531995i
\(531\) 18.9737 21.2132i 0.823387 0.920575i
\(532\) 0 0
\(533\) 0 0
\(534\) 11.3205 21.1624i 0.489886 0.915786i
\(535\) 42.4264i 1.83425i
\(536\) −8.66025 20.1246i −0.374066 0.869251i
\(537\) 16.4317 7.34847i 0.709079 0.317110i
\(538\) −2.73861 + 2.12132i −0.118070 + 0.0914566i
\(539\) 0 0
\(540\) −13.5622 + 21.5422i −0.583623 + 0.927030i
\(541\) 38.0000 1.63375 0.816874 0.576816i \(-0.195705\pi\)
0.816874 + 0.576816i \(0.195705\pi\)
\(542\) −9.48683 + 7.34847i −0.407494 + 0.315644i
\(543\) −25.9808 + 11.6190i −1.11494 + 0.498617i
\(544\) 27.3861 4.24264i 1.17417 0.181902i
\(545\) 24.4949i 1.04925i
\(546\) 0 0
\(547\) 38.7298i 1.65597i 0.560752 + 0.827984i \(0.310512\pi\)
−0.560752 + 0.827984i \(0.689488\pi\)
\(548\) −17.3205 4.47214i −0.739895 0.191040i
\(549\) −10.9545 + 12.2474i −0.467525 + 0.522708i
\(550\) 3.00000 + 3.87298i 0.127920 + 0.165145i
\(551\) 18.9737 0.808305
\(552\) 0 0
\(553\) 0 0
\(554\) 1.73205 + 2.23607i 0.0735878 + 0.0950014i
\(555\) −3.46410 7.74597i −0.147043 0.328798i
\(556\) −8.21584 2.12132i −0.348429 0.0899640i
\(557\) 22.3607i 0.947452i −0.880672 0.473726i \(-0.842909\pi\)
0.880672 0.473726i \(-0.157091\pi\)
\(558\) 2.54199 35.9101i 0.107611 1.52020i
\(559\) 42.4264i 1.79445i
\(560\) 0 0
\(561\) −12.0000 26.8328i −0.506640 1.13288i
\(562\) −10.0000 + 7.74597i −0.421825 + 0.326744i
\(563\) 9.48683 0.399822 0.199911 0.979814i \(-0.435935\pi\)
0.199911 + 0.979814i \(0.435935\pi\)
\(564\) 0 0
\(565\) −10.9545 −0.460857
\(566\) −33.2039 + 25.7196i −1.39566 + 1.08108i
\(567\) 0 0
\(568\) 9.00000 3.87298i 0.377632 0.162507i
\(569\) 31.3050i 1.31237i −0.754599 0.656186i \(-0.772169\pi\)
0.754599 0.656186i \(-0.227831\pi\)
\(570\) −22.4461 12.0072i −0.940163 0.502927i
\(571\) 23.2379i 0.972476i 0.873826 + 0.486238i \(0.161631\pi\)
−0.873826 + 0.486238i \(0.838369\pi\)
\(572\) 9.48683 36.7423i 0.396664 1.53627i
\(573\) −5.47723 + 2.44949i −0.228814 + 0.102329i
\(574\) 0 0
\(575\) 0 0
\(576\) −1.99038 23.9173i −0.0829325 0.996555i
\(577\) 43.8178 1.82416 0.912080 0.410013i \(-0.134476\pi\)
0.912080 + 0.410013i \(0.134476\pi\)
\(578\) −6.06218 7.82624i −0.252153 0.325529i
\(579\) −25.2982 + 11.3137i −1.05136 + 0.470182i
\(580\) −5.47723 + 21.2132i −0.227429 + 0.880830i
\(581\) 0 0
\(582\) 0 0
\(583\) 15.4919i 0.641610i
\(584\) −28.4605 + 12.2474i −1.17770 + 0.506803i
\(585\) 30.0000 + 26.8328i 1.24035 + 1.10940i
\(586\) 2.73861 2.12132i 0.113131 0.0876309i
\(587\) 9.48683 0.391564 0.195782 0.980647i \(-0.437276\pi\)
0.195782 + 0.980647i \(0.437276\pi\)
\(588\) 0 0
\(589\) 36.0000 1.48335
\(590\) −25.9808 + 20.1246i −1.06961 + 0.828517i
\(591\) −15.8114 35.3553i −0.650394 1.45432i
\(592\) 7.00000 + 3.87298i 0.287698 + 0.159179i
\(593\) 34.2929i 1.40824i −0.710082 0.704119i \(-0.751342\pi\)
0.710082 0.704119i \(-0.248658\pi\)
\(594\) −23.9137 + 8.72552i −0.981191 + 0.358012i
\(595\) 0 0
\(596\) −8.66025 2.23607i −0.354738 0.0915929i
\(597\) 12.0000 + 26.8328i 0.491127 + 1.09819i
\(598\) 0 0
\(599\) −24.2487 −0.990775 −0.495388 0.868672i \(-0.664974\pi\)
−0.495388 + 0.868672i \(0.664974\pi\)
\(600\) 3.31735 3.60488i 0.135430 0.147169i
\(601\) −10.9545 −0.446841 −0.223421 0.974722i \(-0.571722\pi\)
−0.223421 + 0.974722i \(0.571722\pi\)
\(602\) 0 0
\(603\) 17.3205 + 15.4919i 0.705346 + 0.630880i
\(604\) 15.0000 + 3.87298i 0.610341 + 0.157589i
\(605\) 2.44949i 0.0995859i
\(606\) 8.49038 15.8718i 0.344898 0.644747i
\(607\) 25.4558i 1.03322i −0.856221 0.516610i \(-0.827194\pi\)
0.856221 0.516610i \(-0.172806\pi\)
\(608\) 23.7171 3.67423i 0.961855 0.149010i
\(609\) 0 0
\(610\) 15.0000 11.6190i 0.607332 0.470438i
\(611\) 0 0
\(612\) −24.4509 + 16.3142i −0.988369 + 0.659463i
\(613\) −14.0000 −0.565455 −0.282727 0.959200i \(-0.591239\pi\)
−0.282727 + 0.959200i \(0.591239\pi\)
\(614\) −23.7171 + 18.3712i −0.957144 + 0.741400i
\(615\) 0 0
\(616\) 0 0
\(617\) 22.3607i 0.900207i 0.892976 + 0.450104i \(0.148613\pi\)
−0.892976 + 0.450104i \(0.851387\pi\)
\(618\) 0 0
\(619\) 4.24264i 0.170526i 0.996358 + 0.0852631i \(0.0271731\pi\)
−0.996358 + 0.0852631i \(0.972827\pi\)
\(620\) −10.3923 + 40.2492i −0.417365 + 1.61645i
\(621\) 0 0
\(622\) −16.4317 21.2132i −0.658850 0.850572i
\(623\) 0 0
\(624\) −37.8109 3.21507i −1.51365 0.128706i
\(625\) −29.0000 −1.16000
\(626\) −9.48683 12.2474i −0.379170 0.489506i
\(627\) −10.3923 23.2379i −0.415029 0.928032i
\(628\) 2.73861 10.6066i 0.109283 0.423249i
\(629\) 9.79796i 0.390670i
\(630\) 0 0
\(631\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(632\) 17.3205 + 40.2492i 0.688973 + 1.60103i
\(633\) 5.47723 + 12.2474i 0.217700 + 0.486792i
\(634\) −5.00000 + 3.87298i −0.198575 + 0.153816i
\(635\) 18.9737 0.752947
\(636\) −15.2742 + 2.58819i −0.605662 + 0.102628i
\(637\) 0 0
\(638\) −17.3205 + 13.4164i −0.685725 + 0.531161i
\(639\) −6.92820 + 7.74597i −0.274075 + 0.306426i
\(640\) −2.73861 + 27.5772i −0.108253 + 1.09008i
\(641\) 31.3050i 1.23647i −0.785993 0.618236i \(-0.787848\pi\)
0.785993 0.618236i \(-0.212152\pi\)
\(642\) −37.4101 20.0120i −1.47646 0.789811i
\(643\) 21.2132i 0.836567i −0.908317 0.418284i \(-0.862632\pi\)
0.908317 0.418284i \(-0.137368\pi\)
\(644\) 0 0
\(645\) 30.0000 13.4164i 1.18125 0.528271i
\(646\) −18.0000 23.2379i −0.708201 0.914283i
\(647\) 18.9737 0.745932 0.372966 0.927845i \(-0.378341\pi\)
0.372966 + 0.927845i \(0.378341\pi\)
\(648\) 12.5981 + 22.1199i 0.494899 + 0.868950i
\(649\) −32.8634 −1.29000
\(650\) −4.74342 6.12372i −0.186052 0.240192i
\(651\) 0 0
\(652\) −15.0000 3.87298i −0.587445 0.151678i
\(653\) 31.3050i 1.22506i −0.790448 0.612529i \(-0.790152\pi\)
0.790448 0.612529i \(-0.209848\pi\)
\(654\) 21.5988 + 11.5539i 0.844578 + 0.451795i
\(655\) 23.2379i 0.907980i
\(656\) 0 0
\(657\) 21.9089 24.4949i 0.854748 0.955637i
\(658\) 0 0
\(659\) 24.2487 0.944596 0.472298 0.881439i \(-0.343425\pi\)
0.472298 + 0.881439i \(0.343425\pi\)
\(660\) 28.9808 4.91075i 1.12807 0.191151i
\(661\) 38.3406 1.49128 0.745638 0.666351i \(-0.232145\pi\)
0.745638 + 0.666351i \(0.232145\pi\)
\(662\) 25.9808 20.1246i 1.00977 0.782165i
\(663\) 18.9737 + 42.4264i 0.736876 + 1.64771i
\(664\) −24.6475 + 10.6066i −0.956509 + 0.411616i
\(665\) 0 0
\(666\) −8.46410 0.599153i −0.327977 0.0232167i
\(667\) 0 0
\(668\) 9.48683 36.7423i 0.367057 1.42160i
\(669\) 6.00000 + 13.4164i 0.231973 + 0.518708i
\(670\) −16.4317 21.2132i −0.634811 0.819538i
\(671\) 18.9737 0.732470
\(672\) 0 0
\(673\) −26.0000 −1.00223 −0.501113 0.865382i \(-0.667076\pi\)
−0.501113 + 0.865382i \(0.667076\pi\)
\(674\) −6.92820 8.94427i −0.266864 0.344520i
\(675\) −1.58114 + 4.94975i −0.0608581 + 0.190516i
\(676\) −8.50000 + 32.9204i −0.326923 + 1.26617i
\(677\) 7.34847i 0.282425i −0.989979 0.141212i \(-0.954900\pi\)
0.989979 0.141212i \(-0.0451000\pi\)
\(678\) −5.16708 + 9.65926i −0.198441 + 0.370962i
\(679\) 0 0
\(680\) 31.1769 13.4164i 1.19558 0.514496i
\(681\) 15.0000 6.70820i 0.574801 0.257059i
\(682\) −32.8634 + 25.4558i −1.25840 + 0.974755i
\(683\) 38.1051 1.45805 0.729026 0.684486i \(-0.239973\pi\)
0.729026 + 0.684486i \(0.239973\pi\)
\(684\) −21.1751 + 14.1285i −0.809650 + 0.540218i
\(685\) −21.9089 −0.837096
\(686\) 0 0
\(687\) −8.66025 + 3.87298i −0.330409 + 0.147764i
\(688\) −15.0000 + 27.1109i −0.571870 + 1.03359i
\(689\) 24.4949i 0.933181i
\(690\) 0 0
\(691\) 12.7279i 0.484193i −0.970252 0.242096i \(-0.922165\pi\)
0.970252 0.242096i \(-0.0778351\pi\)
\(692\) −4.74342 1.22474i −0.180318 0.0465578i
\(693\) 0 0
\(694\) −21.0000 27.1109i −0.797149 1.02912i
\(695\) −10.3923 −0.394203
\(696\) 16.1215 + 14.8356i 0.611085 + 0.562343i
\(697\) 0 0
\(698\) 14.2302 + 18.3712i 0.538623 + 0.695359i
\(699\) 6.32456 + 14.1421i 0.239217 + 0.534905i
\(700\) 0 0
\(701\) 22.3607i 0.844551i 0.906467 + 0.422276i \(0.138769\pi\)
−0.906467 + 0.422276i \(0.861231\pi\)
\(702\) 37.8109 13.7963i 1.42708 0.520706i
\(703\) 8.48528i 0.320028i
\(704\) −19.0526 + 20.1246i −0.718070 + 0.758475i
\(705\) 0 0
\(706\) −16.4317 + 12.7279i −0.618414 + 0.479022i
\(707\) 0 0
\(708\) 5.49038 + 32.4015i 0.206341 + 1.21772i
\(709\) 10.0000 0.375558 0.187779 0.982211i \(-0.439871\pi\)
0.187779 + 0.982211i \(0.439871\pi\)
\(710\) 9.48683 7.34847i 0.356034 0.275783i
\(711\) −34.6410 30.9839i −1.29914 1.16199i
\(712\) 10.9545 + 25.4558i 0.410535 + 0.953998i
\(713\) 0 0
\(714\) 0 0
\(715\) 46.4758i 1.73810i
\(716\) −5.19615 + 20.1246i −0.194189 + 0.752092i
\(717\) 10.9545 4.89898i 0.409101 0.182956i
\(718\) −24.0000 30.9839i −0.895672 1.15631i
\(719\) −37.9473 −1.41520 −0.707598 0.706615i \(-0.750221\pi\)
−0.707598 + 0.706615i \(0.750221\pi\)
\(720\) −9.68346 27.7530i −0.360881 1.03429i
\(721\) 0 0
\(722\) 0.866025 + 1.11803i 0.0322301 + 0.0416089i
\(723\) −34.6410 + 15.4919i −1.28831 + 0.576151i
\(724\) 8.21584 31.8198i 0.305339 1.18257i
\(725\) 4.47214i 0.166091i
\(726\) 2.15988 + 1.15539i 0.0801605 + 0.0428807i
\(727\) 16.9706i 0.629403i −0.949191 0.314702i \(-0.898096\pi\)
0.949191 0.314702i \(-0.101904\pi\)
\(728\) 0 0
\(729\) −22.0000 15.6525i −0.814815 0.579721i
\(730\) −30.0000 + 23.2379i −1.11035 + 0.860073i
\(731\) 37.9473 1.40353
\(732\) −3.16987 18.7070i −0.117162 0.691431i
\(733\) −16.4317 −0.606918 −0.303459 0.952845i \(-0.598142\pi\)
−0.303459 + 0.952845i \(0.598142\pi\)
\(734\) 28.4605 22.0454i 1.05050 0.813711i
\(735\) 0 0
\(736\) 0 0
\(737\) 26.8328i 0.988399i
\(738\) 0 0
\(739\) 38.7298i 1.42470i 0.701824 + 0.712350i \(0.252369\pi\)
−0.701824 + 0.712350i \(0.747631\pi\)
\(740\) 9.48683 + 2.44949i 0.348743 + 0.0900450i
\(741\) 16.4317 + 36.7423i 0.603633 + 1.34976i
\(742\) 0 0
\(743\) −13.8564 −0.508342 −0.254171 0.967159i \(-0.581803\pi\)
−0.254171 + 0.967159i \(0.581803\pi\)
\(744\) 30.5885 + 28.1486i 1.12143 + 1.03198i
\(745\) −10.9545 −0.401340
\(746\) 22.5167 + 29.0689i 0.824394 + 1.06429i
\(747\) 18.9737 21.2132i 0.694210 0.776151i
\(748\) 32.8634 + 8.48528i 1.20160 + 0.310253i
\(749\) 0 0
\(750\) −11.3205 + 21.1624i −0.413367 + 0.772741i
\(751\) 7.74597i 0.282654i −0.989963 0.141327i \(-0.954863\pi\)
0.989963 0.141327i \(-0.0451370\pi\)
\(752\) 0 0
\(753\) 15.0000 6.70820i 0.546630 0.244461i
\(754\) 27.3861 21.2132i 0.997344 0.772539i
\(755\) 18.9737 0.690522
\(756\) 0 0
\(757\) −38.0000 −1.38113 −0.690567 0.723269i \(-0.742639\pi\)
−0.690567 + 0.723269i \(0.742639\pi\)
\(758\) −8.66025 + 6.70820i −0.314555 + 0.243653i
\(759\) 0 0
\(760\) 27.0000 11.6190i 0.979393 0.421464i
\(761\) 48.9898i 1.77588i 0.459961 + 0.887939i \(0.347864\pi\)
−0.459961 + 0.887939i \(0.652136\pi\)
\(762\) 8.94965 16.7303i 0.324212 0.606076i
\(763\) 0 0
\(764\) 1.73205 6.70820i 0.0626634 0.242694i
\(765\) −24.0000 + 26.8328i −0.867722 + 0.970143i
\(766\) 0 0
\(767\) 51.9615 1.87622
\(768\) 23.0248 + 15.4226i 0.830837 + 0.556516i
\(769\) 21.9089 0.790055 0.395028 0.918669i \(-0.370735\pi\)
0.395028 + 0.918669i \(0.370735\pi\)
\(770\) 0 0
\(771\) 3.46410 + 7.74597i 0.124757 + 0.278964i
\(772\) 8.00000 30.9839i 0.287926 1.11513i
\(773\) 2.44949i 0.0881020i 0.999029 + 0.0440510i \(0.0140264\pi\)
−0.999029 + 0.0440510i \(0.985974\pi\)
\(774\) 2.32051 32.7813i 0.0834089 1.17830i
\(775\) 8.48528i 0.304800i
\(776\) 0 0
\(777\) 0 0
\(778\) 35.0000 27.1109i 1.25481 0.971972i
\(779\) 0 0
\(780\) −45.8226 + 7.76457i −1.64071 + 0.278016i
\(781\) 12.0000 0.429394
\(782\) 0 0
\(783\) −22.1359 7.07107i −0.791074 0.252699i
\(784\) 0 0
\(785\) 13.4164i 0.478852i
\(786\) −20.4904 10.9610i −0.730868 0.390967i
\(787\) 21.2132i 0.756169i −0.925771 0.378085i \(-0.876583\pi\)
0.925771 0.378085i \(-0.123417\pi\)
\(788\) 43.3013 + 11.1803i 1.54254 + 0.398283i
\(789\) −5.47723 + 2.44949i −0.194994 + 0.0872041i
\(790\) 32.8634 + 42.4264i 1.16923 + 1.50946i
\(791\) 0 0
\(792\) 9.33975 27.8706i 0.331873 0.990338i
\(793\) −30.0000 −1.06533
\(794\) 33.2039 + 42.8661i 1.17836 + 1.52126i
\(795\) −17.3205 + 7.74597i −0.614295 + 0.274721i
\(796\) −32.8634 8.48528i −1.16481 0.300753i
\(797\) 41.6413i 1.47501i −0.675341 0.737506i \(-0.736003\pi\)
0.675341 0.737506i \(-0.263997\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0.866025 + 5.59017i 0.0306186 + 0.197642i
\(801\) −21.9089 19.5959i −0.774113 0.692388i
\(802\) 5.00000 3.87298i 0.176556 0.136760i
\(803\) −37.9473 −1.33913
\(804\) −26.4557 + 4.48288i −0.933020 + 0.158099i
\(805\) 0 0
\(806\) 51.9615 40.2492i 1.83027 1.41772i
\(807\) 1.73205 + 3.87298i 0.0609711 + 0.136335i
\(808\) 8.21584 + 19.0919i 0.289032 + 0.671650i
\(809\) 22.3607i 0.786160i −0.919504 0.393080i \(-0.871410\pi\)
0.919504 0.393080i \(-0.128590\pi\)
\(810\) 21.7123 + 22.3736i 0.762892 + 0.786127i
\(811\) 12.7279i 0.446938i 0.974711 + 0.223469i \(0.0717381\pi\)
−0.974711 + 0.223469i \(0.928262\pi\)
\(812\) 0 0
\(813\) 6.00000 + 13.4164i 0.210429 + 0.470534i
\(814\) 6.00000 + 7.74597i 0.210300 + 0.271496i
\(815\) −18.9737 −0.664619
\(816\) 2.87564 33.8191i 0.100668 1.18390i
\(817\) 32.8634 1.14974
\(818\) −9.48683 12.2474i −0.331699 0.428222i
\(819\) 0 0
\(820\) 0 0
\(821\) 31.3050i 1.09255i 0.837606 + 0.546275i \(0.183955\pi\)
−0.837606 + 0.546275i \(0.816045\pi\)
\(822\) −10.3342 + 19.3185i −0.360445 + 0.673811i
\(823\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(824\) 0 0
\(825\) 5.47723 2.44949i 0.190693 0.0852803i
\(826\) 0 0
\(827\) 17.3205 0.602293 0.301147 0.953578i \(-0.402631\pi\)
0.301147 + 0.953578i \(0.402631\pi\)
\(828\) 0 0
\(829\) −49.2950 −1.71209 −0.856044 0.516904i \(-0.827085\pi\)
−0.856044 + 0.516904i \(0.827085\pi\)
\(830\) −25.9808 + 20.1246i −0.901805 + 0.698535i
\(831\) 3.16228 1.41421i 0.109698 0.0490585i
\(832\) 30.1247 31.8198i 1.04439 1.10315i
\(833\) 0 0
\(834\) −4.90192 + 9.16358i −0.169740 + 0.317309i
\(835\) 46.4758i 1.60836i
\(836\) 28.4605 + 7.34847i 0.984327 + 0.254152i
\(837\) −42.0000 13.4164i −1.45173 0.463739i
\(838\) 24.6475 + 31.8198i 0.851434 + 1.09920i
\(839\) −18.9737 −0.655044 −0.327522 0.944844i \(-0.606214\pi\)
−0.327522 + 0.944844i \(0.606214\pi\)
\(840\) 0 0
\(841\) 9.00000 0.310345
\(842\) −8.66025 11.1803i −0.298452 0.385300i
\(843\) 6.32456 + 14.1421i 0.217829 + 0.487081i
\(844\) −15.0000 3.87298i −0.516321 0.133314i
\(845\) 41.6413i 1.43251i
\(846\) 0 0
\(847\) 0 0
\(848\) 8.66025 15.6525i 0.297394 0.537508i
\(849\) 21.0000 + 46.9574i 0.720718 + 1.61157i
\(850\) 5.47723 4.24264i 0.187867 0.145521i
\(851\) 0 0
\(852\) −2.00480 11.8313i −0.0686834 0.405335i
\(853\) 16.4317 0.562610 0.281305 0.959618i \(-0.409233\pi\)
0.281305 + 0.959618i \(0.409233\pi\)
\(854\) 0 0
\(855\) −20.7846 + 23.2379i −0.710819 + 0.794719i
\(856\) 45.0000 19.3649i 1.53807 0.661879i
\(857\) 19.5959i 0.669384i 0.942328 + 0.334692i \(0.108632\pi\)
−0.942328 + 0.334692i \(0.891368\pi\)
\(858\) −40.9808 21.9221i −1.39906 0.748407i
\(859\) 46.6690i 1.59233i 0.605081 + 0.796164i \(0.293141\pi\)
−0.605081 + 0.796164i \(0.706859\pi\)
\(860\) −9.48683 + 36.7423i −0.323498 + 1.25290i
\(861\) 0 0
\(862\) 18.0000 + 23.2379i 0.613082 + 0.791486i
\(863\) 17.3205 0.589597 0.294798 0.955559i \(-0.404747\pi\)
0.294798 + 0.955559i \(0.404747\pi\)
\(864\) −29.0392 4.55223i −0.987935 0.154870i
\(865\) −6.00000 −0.204006
\(866\) 18.9737 + 24.4949i 0.644751 + 0.832370i
\(867\) −11.0680 + 4.94975i −0.375888 + 0.168102i
\(868\) 0 0
\(869\) 53.6656i 1.82048i
\(870\) 23.6603 + 12.6567i 0.802158 + 0.429103i
\(871\) 42.4264i 1.43756i
\(872\) −25.9808 + 11.1803i −0.879820 + 0.378614i
\(873\) 0 0
\(874\) 0 0
\(875\) 0 0
\(876\) 6.33975 + 37.4140i 0.214200 + 1.26410i
\(877\) 22.0000 0.742887 0.371444 0.928456i \(-0.378863\pi\)
0.371444 + 0.928456i \(0.378863\pi\)
\(878\) −18.9737 + 14.6969i −0.640330 + 0.495998i
\(879\) −1.73205 3.87298i −0.0584206 0.130632i
\(880\) −16.4317 + 29.6985i −0.553912 + 1.00114i
\(881\) 44.0908i 1.48546i 0.669593 + 0.742729i \(0.266469\pi\)
−0.669593 + 0.742729i \(0.733531\pi\)
\(882\) 0 0
\(883\) 54.2218i 1.82471i −0.409403 0.912354i \(-0.634263\pi\)
0.409403 0.912354i \(-0.365737\pi\)
\(884\) −51.9615 13.4164i −1.74766 0.451243i
\(885\) 16.4317 + 36.7423i 0.552345 + 1.23508i
\(886\) 27.0000 + 34.8569i 0.907083 + 1.17104i
\(887\) 56.9210 1.91122 0.955610 0.294634i \(-0.0951979\pi\)
0.955610 + 0.294634i \(0.0951979\pi\)
\(888\) 6.63470 7.20977i 0.222646 0.241944i
\(889\) 0 0
\(890\) 20.7846 + 26.8328i 0.696702 + 0.899438i
\(891\) 3.46410 + 30.9839i 0.116052 + 1.03800i
\(892\) −16.4317 4.24264i −0.550173 0.142054i
\(893\) 0 0
\(894\) −5.16708 + 9.65926i −0.172813 + 0.323054i
\(895\) 25.4558i 0.850895i
\(896\) 0 0
\(897\) 0 0
\(898\) 40.0000 30.9839i 1.33482 1.03395i
\(899\) −37.9473 −1.26561
\(900\) −3.33013 4.99102i −0.111004 0.166367i
\(901\) −21.9089 −0.729891
\(902\) 0 0
\(903\) 0 0
\(904\) −5.00000 11.6190i −0.166298 0.386441i
\(905\) 40.2492i 1.33793i
\(906\) 8.94965 16.7303i 0.297332 0.555828i
\(907\) 7.74597i 0.257201i −0.991697 0.128600i \(-0.958952\pi\)
0.991697 0.128600i \(-0.0410484\pi\)
\(908\) −4.74342 + 18.3712i −0.157416 + 0.609669i
\(909\) −16.4317 14.6969i −0.545004 0.487467i
\(910\) 0 0
\(911\) −20.7846 −0.688625 −0.344312 0.938855i \(-0.611888\pi\)
−0.344312 + 0.938855i \(0.611888\pi\)
\(912\) 2.49038 29.2882i 0.0824648 0.969829i
\(913\) −32.8634 −1.08762
\(914\) −24.2487 31.3050i −0.802076 1.03548i
\(915\) −9.48683 21.2132i −0.313625 0.701287i
\(916\) 2.73861 10.6066i 0.0904863 0.350452i
\(917\) 0 0
\(918\) 12.3397 + 33.8191i 0.407272 + 1.11620i
\(919\) 30.9839i 1.02206i −0.859562 0.511032i \(-0.829263\pi\)
0.859562 0.511032i \(-0.170737\pi\)
\(920\) 0 0
\(921\) 15.0000 + 33.5410i 0.494267 + 1.10521i
\(922\) −41.0792 + 31.8198i −1.35287 + 1.04793i
\(923\) −18.9737 −0.624526
\(924\) 0 0
\(925\) 2.00000 0.0657596
\(926\) 17.3205 13.4164i 0.569187 0.440891i
\(927\) 0 0
\(928\) −25.0000 + 3.87298i −0.820665 + 0.127137i
\(929\) 24.4949i 0.803652i 0.915716 + 0.401826i \(0.131624\pi\)
−0.915716 + 0.401826i \(0.868376\pi\)
\(930\) 44.8922 + 24.0144i 1.47207 + 0.787464i
\(931\) 0 0
\(932\) −17.3205 4.47214i −0.567352 0.146490i
\(933\) −30.0000 + 13.4164i −0.982156 + 0.439233i
\(934\) −24.6475 31.8198i −0.806491 1.04118i
\(935\) 41.5692 1.35946
\(936\) −14.7674 + 44.0673i −0.482689 + 1.44038i
\(937\) 10.9545 0.357866 0.178933 0.983861i \(-0.442735\pi\)
0.178933 + 0.983861i \(0.442735\pi\)
\(938\) 0 0
\(939\) −17.3205 + 7.74597i −0.565233 + 0.252780i
\(940\) 0 0
\(941\) 12.2474i 0.399255i 0.979872 + 0.199628i \(0.0639733\pi\)
−0.979872 + 0.199628i \(0.936027\pi\)
\(942\) −11.8301 6.32836i −0.385446 0.206189i
\(943\) 0 0
\(944\) −33.2039 18.3712i −1.08070 0.597931i
\(945\) 0 0
\(946\) −30.0000 + 23.2379i −0.975384 + 0.755529i
\(947\) 10.3923 0.337705 0.168852 0.985641i \(-0.445994\pi\)
0.168852 + 0.985641i \(0.445994\pi\)
\(948\) 52.9114 8.96575i 1.71848 0.291194i
\(949\) 60.0000 1.94768
\(950\) 4.74342 3.67423i 0.153897 0.119208i
\(951\) 3.16228 + 7.07107i 0.102544 + 0.229295i
\(952\) 0 0
\(953\) 8.94427i 0.289733i −0.989451 0.144867i \(-0.953725\pi\)
0.989451 0.144867i \(-0.0462753\pi\)
\(954\) −1.33975 + 18.9263i −0.0433759 + 0.612762i
\(955\) 8.48528i 0.274577i
\(956\) −3.46410 + 13.4164i −0.112037 + 0.433918i
\(957\) 10.9545 + 24.4949i 0.354107 + 0.791808i
\(958\) −32.8634 42.4264i −1.06177 1.37073i
\(959\) 0 0
\(960\) 32.0263 + 11.2391i 1.03364 + 0.362740i
\(961\) −41.0000 −1.32258
\(962\) −9.48683 12.2474i −0.305868 0.394874i
\(963\) −34.6410 + 38.7298i −1.11629 + 1.24805i
\(964\) 10.9545 42.4264i 0.352819 1.36646i
\(965\) 39.1918i 1.26163i
\(966\) 0 0
\(967\) 23.2379i 0.747280i −0.927574 0.373640i \(-0.878109\pi\)
0.927574 0.373640i \(-0.121891\pi\)
\(968\) −2.59808 + 1.11803i −0.0835053 + 0.0359350i
\(969\) −32.8634 + 14.6969i −1.05572 + 0.472134i
\(970\) 0 0
\(971\) 47.4342 1.52223 0.761117 0.648614i \(-0.224651\pi\)
0.761117 + 0.648614i \(0.224651\pi\)
\(972\) 29.9697 8.59180i 0.961278 0.275582i
\(973\) 0 0
\(974\) −8.66025 + 6.70820i −0.277492 + 0.214945i
\(975\) −8.66025 + 3.87298i −0.277350 + 0.124035i
\(976\) 19.1703 + 10.6066i 0.613626 + 0.339509i
\(977\) 35.7771i 1.14461i 0.820041 + 0.572305i \(0.193951\pi\)
−0.820041 + 0.572305i \(0.806049\pi\)
\(978\) −8.94965 + 16.7303i −0.286178 + 0.534977i
\(979\) 33.9411i 1.08476i
\(980\) 0 0
\(981\) 20.0000 22.3607i 0.638551 0.713922i
\(982\) −27.0000 34.8569i −0.861605 1.11233i
\(983\) 18.9737 0.605166 0.302583 0.953123i \(-0.402151\pi\)
0.302583 + 0.953123i \(0.402151\pi\)
\(984\) 0 0
\(985\) 54.7723 1.74519
\(986\) 18.9737 + 24.4949i 0.604245 + 0.780076i
\(987\) 0 0
\(988\) −45.0000 11.6190i −1.43164 0.369648i
\(989\) 0 0
\(990\) 2.54199 35.9101i 0.0807897 1.14130i
\(991\) 15.4919i 0.492117i 0.969255 + 0.246059i \(0.0791356\pi\)
−0.969255 + 0.246059i \(0.920864\pi\)
\(992\) −47.4342 + 7.34847i −1.50604 + 0.233314i
\(993\) −16.4317 36.7423i −0.521443 1.16598i
\(994\) 0 0
\(995\) −41.5692 −1.31783
\(996\) 5.49038 + 32.4015i 0.173969 + 1.02668i
\(997\) −5.47723 −0.173465 −0.0867327 0.996232i \(-0.527643\pi\)
−0.0867327 + 0.996232i \(0.527643\pi\)
\(998\) −25.9808 + 20.1246i −0.822407 + 0.637033i
\(999\) −3.16228 + 9.89949i −0.100050 + 0.313206i
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 588.2.e.b.491.8 yes 8
3.2 odd 2 inner 588.2.e.b.491.1 8
4.3 odd 2 inner 588.2.e.b.491.3 yes 8
7.2 even 3 588.2.n.c.263.5 16
7.3 odd 6 588.2.n.c.275.2 16
7.4 even 3 588.2.n.c.275.1 16
7.5 odd 6 588.2.n.c.263.6 16
7.6 odd 2 inner 588.2.e.b.491.7 yes 8
12.11 even 2 inner 588.2.e.b.491.6 yes 8
21.2 odd 6 588.2.n.c.263.4 16
21.5 even 6 588.2.n.c.263.3 16
21.11 odd 6 588.2.n.c.275.8 16
21.17 even 6 588.2.n.c.275.7 16
21.20 even 2 inner 588.2.e.b.491.2 yes 8
28.3 even 6 588.2.n.c.275.3 16
28.11 odd 6 588.2.n.c.275.4 16
28.19 even 6 588.2.n.c.263.7 16
28.23 odd 6 588.2.n.c.263.8 16
28.27 even 2 inner 588.2.e.b.491.4 yes 8
84.11 even 6 588.2.n.c.275.5 16
84.23 even 6 588.2.n.c.263.1 16
84.47 odd 6 588.2.n.c.263.2 16
84.59 odd 6 588.2.n.c.275.6 16
84.83 odd 2 inner 588.2.e.b.491.5 yes 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
588.2.e.b.491.1 8 3.2 odd 2 inner
588.2.e.b.491.2 yes 8 21.20 even 2 inner
588.2.e.b.491.3 yes 8 4.3 odd 2 inner
588.2.e.b.491.4 yes 8 28.27 even 2 inner
588.2.e.b.491.5 yes 8 84.83 odd 2 inner
588.2.e.b.491.6 yes 8 12.11 even 2 inner
588.2.e.b.491.7 yes 8 7.6 odd 2 inner
588.2.e.b.491.8 yes 8 1.1 even 1 trivial
588.2.n.c.263.1 16 84.23 even 6
588.2.n.c.263.2 16 84.47 odd 6
588.2.n.c.263.3 16 21.5 even 6
588.2.n.c.263.4 16 21.2 odd 6
588.2.n.c.263.5 16 7.2 even 3
588.2.n.c.263.6 16 7.5 odd 6
588.2.n.c.263.7 16 28.19 even 6
588.2.n.c.263.8 16 28.23 odd 6
588.2.n.c.275.1 16 7.4 even 3
588.2.n.c.275.2 16 7.3 odd 6
588.2.n.c.275.3 16 28.3 even 6
588.2.n.c.275.4 16 28.11 odd 6
588.2.n.c.275.5 16 84.11 even 6
588.2.n.c.275.6 16 84.59 odd 6
588.2.n.c.275.7 16 21.17 even 6
588.2.n.c.275.8 16 21.11 odd 6