Properties

Label 891.2.n.e.433.1
Level $891$
Weight $2$
Character 891.433
Analytic conductor $7.115$
Analytic rank $0$
Dimension $16$
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [891,2,Mod(136,891)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(891, base_ring=CyclotomicField(30))
 
chi = DirichletCharacter(H, H._module([20, 6]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("891.136");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 891 = 3^{4} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 891.n (of order \(15\), degree \(8\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(7.11467082010\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(2\) over \(\Q(\zeta_{15})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - x^{14} - 15x^{12} + 116x^{10} + 69x^{8} - 814x^{6} + 2420x^{4} - 7986x^{2} + 14641 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 99)
Sato-Tate group: $\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label 433.1
Root \(-0.224628 + 2.13719i\) of defining polynomial
Character \(\chi\) \(=\) 891.433
Dual form 891.2.n.e.784.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.224628 + 2.13719i) q^{2} +(-2.56082 - 0.544320i) q^{4} +(0.224628 + 2.13719i) q^{5} +(-2.83448 + 3.14801i) q^{7} +(0.410415 - 1.26313i) q^{8} -4.61803 q^{10} +(0.935653 + 3.18191i) q^{11} +(0.215659 - 0.0960175i) q^{13} +(-6.09119 - 6.76496i) q^{14} +(-2.17603 - 0.968833i) q^{16} +(4.96199 - 3.60510i) q^{17} +(-0.736068 + 2.26538i) q^{19} +(0.588083 - 5.59523i) q^{20} +(-7.01052 + 1.28492i) q^{22} +(-1.99220 + 3.45059i) q^{23} +(0.373619 - 0.0794152i) q^{25} +(0.156765 + 0.482472i) q^{26} +(8.97214 - 6.51864i) q^{28} +(4.65326 - 5.16797i) q^{29} +(-4.21878 + 1.87832i) q^{31} +(3.88751 - 6.73336i) q^{32} +(6.59017 + 11.4145i) q^{34} +(-7.36460 - 5.35069i) q^{35} +(0.545085 + 1.67760i) q^{37} +(-4.67621 - 2.08198i) q^{38} +(2.79173 + 0.593401i) q^{40} +(-1.98718 - 2.20699i) q^{41} +(-1.35410 - 2.34537i) q^{43} +(-0.664066 - 8.65761i) q^{44} +(-6.92705 - 5.03280i) q^{46} +(-3.40111 + 0.722928i) q^{47} +(-1.14399 - 10.8843i) q^{49} +(0.0858001 + 0.816334i) q^{50} +(-0.604528 + 0.128496i) q^{52} +(1.48490 + 1.07884i) q^{53} +(-6.59017 + 2.71441i) q^{55} +(2.81303 + 4.87231i) q^{56} +(9.99967 + 11.1058i) q^{58} +(7.29843 + 1.55133i) q^{59} +(-10.3470 - 4.60680i) q^{61} +(-3.06668 - 9.43826i) q^{62} +(9.66312 + 7.02067i) q^{64} +(0.253650 + 0.439335i) q^{65} +(1.42705 - 2.47172i) q^{67} +(-14.6691 + 6.53110i) q^{68} +(13.0897 - 14.5376i) q^{70} +(-8.69273 + 6.31564i) q^{71} +(0.763932 + 2.35114i) q^{73} +(-3.70779 + 0.788114i) q^{74} +(3.11803 - 5.40059i) q^{76} +(-12.6688 - 6.07362i) q^{77} +(0.990108 - 9.42025i) q^{79} +(1.58178 - 4.86822i) q^{80} +(5.16312 - 3.75123i) q^{82} +(7.56627 + 3.36872i) q^{83} +(8.81937 + 9.79490i) q^{85} +(5.31667 - 2.36714i) q^{86} +(4.40317 + 0.124055i) q^{88} +8.90937 q^{89} +(-0.309017 + 0.951057i) q^{91} +(6.97989 - 7.75195i) q^{92} +(-0.781051 - 7.43120i) q^{94} +(-5.00690 - 1.06425i) q^{95} +(-1.23327 + 11.7337i) q^{97} +23.5188 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 2 q^{4} + 6 q^{7} - 56 q^{10} + 6 q^{13} - 2 q^{16} + 24 q^{19} - 28 q^{22} - 8 q^{25} + 72 q^{28} - 12 q^{31} + 16 q^{34} - 36 q^{37} + 16 q^{40} + 32 q^{43} - 84 q^{46} + 44 q^{49} - 6 q^{52} - 16 q^{55}+ \cdots + 54 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/891\mathbb{Z}\right)^\times\).

\(n\) \(244\) \(650\)
\(\chi(n)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.224628 + 2.13719i −0.158836 + 1.51122i 0.567209 + 0.823574i \(0.308023\pi\)
−0.726045 + 0.687647i \(0.758644\pi\)
\(3\) 0 0
\(4\) −2.56082 0.544320i −1.28041 0.272160i
\(5\) 0.224628 + 2.13719i 0.100457 + 0.955780i 0.922407 + 0.386220i \(0.126220\pi\)
−0.821950 + 0.569560i \(0.807114\pi\)
\(6\) 0 0
\(7\) −2.83448 + 3.14801i −1.07133 + 1.18984i −0.0903171 + 0.995913i \(0.528788\pi\)
−0.981017 + 0.193924i \(0.937879\pi\)
\(8\) 0.410415 1.26313i 0.145104 0.446583i
\(9\) 0 0
\(10\) −4.61803 −1.46035
\(11\) 0.935653 + 3.18191i 0.282110 + 0.959382i
\(12\) 0 0
\(13\) 0.215659 0.0960175i 0.0598130 0.0266305i −0.376612 0.926371i \(-0.622911\pi\)
0.436425 + 0.899741i \(0.356244\pi\)
\(14\) −6.09119 6.76496i −1.62794 1.80801i
\(15\) 0 0
\(16\) −2.17603 0.968833i −0.544009 0.242208i
\(17\) 4.96199 3.60510i 1.20346 0.874364i 0.208838 0.977950i \(-0.433032\pi\)
0.994620 + 0.103586i \(0.0330318\pi\)
\(18\) 0 0
\(19\) −0.736068 + 2.26538i −0.168866 + 0.519715i −0.999300 0.0374011i \(-0.988092\pi\)
0.830435 + 0.557116i \(0.188092\pi\)
\(20\) 0.588083 5.59523i 0.131499 1.25113i
\(21\) 0 0
\(22\) −7.01052 + 1.28492i −1.49465 + 0.273946i
\(23\) −1.99220 + 3.45059i −0.415402 + 0.719497i −0.995471 0.0950706i \(-0.969692\pi\)
0.580069 + 0.814567i \(0.303026\pi\)
\(24\) 0 0
\(25\) 0.373619 0.0794152i 0.0747238 0.0158830i
\(26\) 0.156765 + 0.482472i 0.0307441 + 0.0946205i
\(27\) 0 0
\(28\) 8.97214 6.51864i 1.69557 1.23191i
\(29\) 4.65326 5.16797i 0.864088 0.959667i −0.135427 0.990787i \(-0.543241\pi\)
0.999516 + 0.0311201i \(0.00990742\pi\)
\(30\) 0 0
\(31\) −4.21878 + 1.87832i −0.757716 + 0.337357i −0.748969 0.662605i \(-0.769451\pi\)
−0.00874681 + 0.999962i \(0.502784\pi\)
\(32\) 3.88751 6.73336i 0.687221 1.19030i
\(33\) 0 0
\(34\) 6.59017 + 11.4145i 1.13020 + 1.95757i
\(35\) −7.36460 5.35069i −1.24484 0.904432i
\(36\) 0 0
\(37\) 0.545085 + 1.67760i 0.0896114 + 0.275796i 0.985812 0.167854i \(-0.0536836\pi\)
−0.896201 + 0.443649i \(0.853684\pi\)
\(38\) −4.67621 2.08198i −0.758582 0.337742i
\(39\) 0 0
\(40\) 2.79173 + 0.593401i 0.441412 + 0.0938250i
\(41\) −1.98718 2.20699i −0.310345 0.344673i 0.567714 0.823226i \(-0.307828\pi\)
−0.878059 + 0.478553i \(0.841161\pi\)
\(42\) 0 0
\(43\) −1.35410 2.34537i −0.206499 0.357666i 0.744111 0.668056i \(-0.232874\pi\)
−0.950609 + 0.310390i \(0.899540\pi\)
\(44\) −0.664066 8.65761i −0.100112 1.30518i
\(45\) 0 0
\(46\) −6.92705 5.03280i −1.02134 0.742045i
\(47\) −3.40111 + 0.722928i −0.496103 + 0.105450i −0.449167 0.893448i \(-0.648279\pi\)
−0.0469361 + 0.998898i \(0.514946\pi\)
\(48\) 0 0
\(49\) −1.14399 10.8843i −0.163427 1.55490i
\(50\) 0.0858001 + 0.816334i 0.0121340 + 0.115447i
\(51\) 0 0
\(52\) −0.604528 + 0.128496i −0.0838330 + 0.0178193i
\(53\) 1.48490 + 1.07884i 0.203966 + 0.148190i 0.685079 0.728468i \(-0.259767\pi\)
−0.481113 + 0.876658i \(0.659767\pi\)
\(54\) 0 0
\(55\) −6.59017 + 2.71441i −0.888618 + 0.366011i
\(56\) 2.81303 + 4.87231i 0.375906 + 0.651089i
\(57\) 0 0
\(58\) 9.99967 + 11.1058i 1.31302 + 1.45826i
\(59\) 7.29843 + 1.55133i 0.950175 + 0.201966i 0.656828 0.754040i \(-0.271898\pi\)
0.293347 + 0.956006i \(0.405231\pi\)
\(60\) 0 0
\(61\) −10.3470 4.60680i −1.32480 0.589840i −0.382299 0.924039i \(-0.624868\pi\)
−0.942503 + 0.334199i \(0.891534\pi\)
\(62\) −3.06668 9.43826i −0.389468 1.19866i
\(63\) 0 0
\(64\) 9.66312 + 7.02067i 1.20789 + 0.877583i
\(65\) 0.253650 + 0.439335i 0.0314615 + 0.0544929i
\(66\) 0 0
\(67\) 1.42705 2.47172i 0.174342 0.301969i −0.765591 0.643327i \(-0.777553\pi\)
0.939933 + 0.341358i \(0.110887\pi\)
\(68\) −14.6691 + 6.53110i −1.77889 + 0.792013i
\(69\) 0 0
\(70\) 13.0897 14.5376i 1.56452 1.73758i
\(71\) −8.69273 + 6.31564i −1.03164 + 0.749528i −0.968636 0.248485i \(-0.920067\pi\)
−0.0630016 + 0.998013i \(0.520067\pi\)
\(72\) 0 0
\(73\) 0.763932 + 2.35114i 0.0894115 + 0.275180i 0.985757 0.168176i \(-0.0537877\pi\)
−0.896346 + 0.443356i \(0.853788\pi\)
\(74\) −3.70779 + 0.788114i −0.431022 + 0.0916164i
\(75\) 0 0
\(76\) 3.11803 5.40059i 0.357663 0.619491i
\(77\) −12.6688 6.07362i −1.44374 0.692154i
\(78\) 0 0
\(79\) 0.990108 9.42025i 0.111396 1.05986i −0.785877 0.618383i \(-0.787788\pi\)
0.897272 0.441477i \(-0.145545\pi\)
\(80\) 1.58178 4.86822i 0.176849 0.544284i
\(81\) 0 0
\(82\) 5.16312 3.75123i 0.570171 0.414254i
\(83\) 7.56627 + 3.36872i 0.830506 + 0.369765i 0.777542 0.628831i \(-0.216466\pi\)
0.0529644 + 0.998596i \(0.483133\pi\)
\(84\) 0 0
\(85\) 8.81937 + 9.79490i 0.956595 + 1.06241i
\(86\) 5.31667 2.36714i 0.573312 0.255255i
\(87\) 0 0
\(88\) 4.40317 + 0.124055i 0.469379 + 0.0132243i
\(89\) 8.90937 0.944392 0.472196 0.881494i \(-0.343462\pi\)
0.472196 + 0.881494i \(0.343462\pi\)
\(90\) 0 0
\(91\) −0.309017 + 0.951057i −0.0323938 + 0.0996978i
\(92\) 6.97989 7.75195i 0.727703 0.808197i
\(93\) 0 0
\(94\) −0.781051 7.43120i −0.0805592 0.766470i
\(95\) −5.00690 1.06425i −0.513697 0.109190i
\(96\) 0 0
\(97\) −1.23327 + 11.7337i −0.125219 + 1.19138i 0.733774 + 0.679394i \(0.237757\pi\)
−0.858993 + 0.511987i \(0.828910\pi\)
\(98\) 23.5188 2.37576
\(99\) 0 0
\(100\) −1.00000 −0.100000
\(101\) 0.0327727 0.311812i 0.00326101 0.0310264i −0.992770 0.120029i \(-0.961701\pi\)
0.996031 + 0.0890025i \(0.0283679\pi\)
\(102\) 0 0
\(103\) 10.7051 + 2.27544i 1.05481 + 0.224206i 0.702504 0.711680i \(-0.252065\pi\)
0.352303 + 0.935886i \(0.385399\pi\)
\(104\) −0.0327727 0.311812i −0.00321363 0.0305756i
\(105\) 0 0
\(106\) −2.63923 + 2.93117i −0.256345 + 0.284700i
\(107\) −3.38021 + 10.4032i −0.326777 + 1.00572i 0.643855 + 0.765147i \(0.277334\pi\)
−0.970632 + 0.240569i \(0.922666\pi\)
\(108\) 0 0
\(109\) −13.7082 −1.31301 −0.656504 0.754323i \(-0.727965\pi\)
−0.656504 + 0.754323i \(0.727965\pi\)
\(110\) −4.32088 14.6942i −0.411980 1.40103i
\(111\) 0 0
\(112\) 9.21783 4.10404i 0.871003 0.387796i
\(113\) 11.9726 + 13.2969i 1.12629 + 1.25087i 0.964512 + 0.264041i \(0.0850554\pi\)
0.161775 + 0.986828i \(0.448278\pi\)
\(114\) 0 0
\(115\) −7.82206 3.48260i −0.729410 0.324754i
\(116\) −14.7292 + 10.7014i −1.36757 + 0.993599i
\(117\) 0 0
\(118\) −4.95492 + 15.2497i −0.456137 + 1.40385i
\(119\) −2.71579 + 25.8390i −0.248956 + 2.36866i
\(120\) 0 0
\(121\) −9.24911 + 5.95433i −0.840828 + 0.541303i
\(122\) 12.1698 21.0788i 1.10180 1.90838i
\(123\) 0 0
\(124\) 11.8260 2.51369i 1.06200 0.225736i
\(125\) 3.57398 + 10.9996i 0.319666 + 0.983832i
\(126\) 0 0
\(127\) 2.23607 1.62460i 0.198419 0.144160i −0.484139 0.874991i \(-0.660867\pi\)
0.682558 + 0.730831i \(0.260867\pi\)
\(128\) −6.77009 + 7.51895i −0.598397 + 0.664588i
\(129\) 0 0
\(130\) −0.995920 + 0.443412i −0.0873479 + 0.0388898i
\(131\) −1.23125 + 2.13258i −0.107574 + 0.186324i −0.914787 0.403936i \(-0.867642\pi\)
0.807213 + 0.590261i \(0.200975\pi\)
\(132\) 0 0
\(133\) −5.04508 8.73834i −0.437464 0.757710i
\(134\) 4.96199 + 3.60510i 0.428650 + 0.311433i
\(135\) 0 0
\(136\) −2.51722 7.74721i −0.215850 0.664318i
\(137\) 0.286423 + 0.127524i 0.0244708 + 0.0108951i 0.418936 0.908016i \(-0.362403\pi\)
−0.394465 + 0.918911i \(0.629070\pi\)
\(138\) 0 0
\(139\) 11.1332 + 2.36644i 0.944309 + 0.200719i 0.654240 0.756287i \(-0.272988\pi\)
0.290069 + 0.957006i \(0.406322\pi\)
\(140\) 15.9470 + 17.7109i 1.34776 + 1.49684i
\(141\) 0 0
\(142\) −11.5451 19.9967i −0.968842 1.67808i
\(143\) 0.507301 + 0.596368i 0.0424226 + 0.0498708i
\(144\) 0 0
\(145\) 12.0902 + 8.78402i 1.00403 + 0.729473i
\(146\) −5.19643 + 1.10454i −0.430060 + 0.0914120i
\(147\) 0 0
\(148\) −0.482716 4.59274i −0.0396790 0.377521i
\(149\) 0.482028 + 4.58619i 0.0394893 + 0.375715i 0.996363 + 0.0852109i \(0.0271564\pi\)
−0.956874 + 0.290504i \(0.906177\pi\)
\(150\) 0 0
\(151\) 12.9468 2.75193i 1.05360 0.223949i 0.351616 0.936144i \(-0.385632\pi\)
0.701982 + 0.712195i \(0.252299\pi\)
\(152\) 2.55938 + 1.85950i 0.207593 + 0.150825i
\(153\) 0 0
\(154\) 15.8262 25.7113i 1.27531 2.07187i
\(155\) −4.96199 8.59441i −0.398556 0.690320i
\(156\) 0 0
\(157\) −13.8192 15.3478i −1.10289 1.22489i −0.972371 0.233441i \(-0.925002\pi\)
−0.130521 0.991445i \(-0.541665\pi\)
\(158\) 19.9104 + 4.23209i 1.58399 + 0.336687i
\(159\) 0 0
\(160\) 15.2637 + 6.79584i 1.20670 + 0.537258i
\(161\) −5.21564 16.0521i −0.411050 1.26508i
\(162\) 0 0
\(163\) −1.11803 0.812299i −0.0875712 0.0636242i 0.543138 0.839643i \(-0.317236\pi\)
−0.630709 + 0.776019i \(0.717236\pi\)
\(164\) 3.88751 + 6.73336i 0.303563 + 0.525787i
\(165\) 0 0
\(166\) −8.89919 + 15.4138i −0.690711 + 1.19635i
\(167\) −9.81587 + 4.37031i −0.759575 + 0.338184i −0.749710 0.661767i \(-0.769807\pi\)
−0.00986504 + 0.999951i \(0.503140\pi\)
\(168\) 0 0
\(169\) −8.66141 + 9.61947i −0.666262 + 0.739959i
\(170\) −22.9146 + 16.6485i −1.75747 + 1.27688i
\(171\) 0 0
\(172\) 2.19098 + 6.74315i 0.167061 + 0.514161i
\(173\) 13.1082 2.78624i 0.996600 0.211834i 0.319390 0.947623i \(-0.396522\pi\)
0.677210 + 0.735790i \(0.263189\pi\)
\(174\) 0 0
\(175\) −0.809017 + 1.40126i −0.0611559 + 0.105925i
\(176\) 1.04673 7.83044i 0.0789000 0.590241i
\(177\) 0 0
\(178\) −2.00129 + 19.0410i −0.150003 + 1.42718i
\(179\) 0.604187 1.85950i 0.0451590 0.138985i −0.925935 0.377684i \(-0.876721\pi\)
0.971094 + 0.238698i \(0.0767207\pi\)
\(180\) 0 0
\(181\) −9.89919 + 7.19218i −0.735801 + 0.534591i −0.891393 0.453231i \(-0.850271\pi\)
0.155592 + 0.987821i \(0.450271\pi\)
\(182\) −1.96317 0.874061i −0.145520 0.0647897i
\(183\) 0 0
\(184\) 3.54090 + 3.93257i 0.261039 + 0.289913i
\(185\) −3.46290 + 1.54178i −0.254598 + 0.113354i
\(186\) 0 0
\(187\) 16.1138 + 12.4155i 1.17836 + 0.907910i
\(188\) 9.10315 0.663915
\(189\) 0 0
\(190\) 3.39919 10.4616i 0.246603 0.758966i
\(191\) −6.64044 + 7.37495i −0.480485 + 0.533633i −0.933837 0.357699i \(-0.883561\pi\)
0.453352 + 0.891332i \(0.350228\pi\)
\(192\) 0 0
\(193\) −0.771626 7.34153i −0.0555428 0.528455i −0.986551 0.163456i \(-0.947736\pi\)
0.931008 0.364999i \(-0.118931\pi\)
\(194\) −24.8002 5.27144i −1.78055 0.378468i
\(195\) 0 0
\(196\) −2.99500 + 28.4955i −0.213929 + 2.03539i
\(197\) −2.46249 −0.175445 −0.0877226 0.996145i \(-0.527959\pi\)
−0.0877226 + 0.996145i \(0.527959\pi\)
\(198\) 0 0
\(199\) 0.416408 0.0295184 0.0147592 0.999891i \(-0.495302\pi\)
0.0147592 + 0.999891i \(0.495302\pi\)
\(200\) 0.0530274 0.504522i 0.00374960 0.0356751i
\(201\) 0 0
\(202\) 0.659039 + 0.140083i 0.0463698 + 0.00985621i
\(203\) 3.07924 + 29.2970i 0.216120 + 2.05625i
\(204\) 0 0
\(205\) 4.27037 4.74273i 0.298255 0.331246i
\(206\) −7.26771 + 22.3677i −0.506366 + 1.55843i
\(207\) 0 0
\(208\) −0.562306 −0.0389889
\(209\) −7.89695 0.222489i −0.546244 0.0153899i
\(210\) 0 0
\(211\) −16.4753 + 7.33527i −1.13421 + 0.504981i −0.885981 0.463722i \(-0.846514\pi\)
−0.248224 + 0.968703i \(0.579847\pi\)
\(212\) −3.21532 3.57098i −0.220829 0.245256i
\(213\) 0 0
\(214\) −21.4743 9.56099i −1.46795 0.653576i
\(215\) 4.70834 3.42081i 0.321106 0.233297i
\(216\) 0 0
\(217\) 6.04508 18.6049i 0.410367 1.26298i
\(218\) 3.07924 29.2970i 0.208553 1.98424i
\(219\) 0 0
\(220\) 18.3538 3.36397i 1.23741 0.226799i
\(221\) 0.723944 1.25391i 0.0486978 0.0843470i
\(222\) 0 0
\(223\) −3.11084 + 0.661230i −0.208317 + 0.0442792i −0.310888 0.950446i \(-0.600626\pi\)
0.102571 + 0.994726i \(0.467293\pi\)
\(224\) 10.1776 + 31.3235i 0.680021 + 2.09289i
\(225\) 0 0
\(226\) −31.1074 + 22.6008i −2.06923 + 1.50339i
\(227\) 7.31934 8.12895i 0.485801 0.539537i −0.449551 0.893255i \(-0.648416\pi\)
0.935352 + 0.353718i \(0.115083\pi\)
\(228\) 0 0
\(229\) −16.8751 + 7.51329i −1.11514 + 0.496492i −0.879763 0.475412i \(-0.842299\pi\)
−0.235377 + 0.971904i \(0.575632\pi\)
\(230\) 9.20003 15.9349i 0.606632 1.05072i
\(231\) 0 0
\(232\) −4.61803 7.99867i −0.303189 0.525138i
\(233\) −18.6167 13.5258i −1.21962 0.886106i −0.223552 0.974692i \(-0.571765\pi\)
−0.996069 + 0.0885854i \(0.971765\pi\)
\(234\) 0 0
\(235\) −2.30902 7.10642i −0.150624 0.463572i
\(236\) −17.8456 7.94537i −1.16165 0.517199i
\(237\) 0 0
\(238\) −54.6127 11.6083i −3.54002 0.752454i
\(239\) 7.65879 + 8.50595i 0.495406 + 0.550204i 0.938053 0.346492i \(-0.112627\pi\)
−0.442647 + 0.896696i \(0.645961\pi\)
\(240\) 0 0
\(241\) −7.00000 12.1244i −0.450910 0.780998i 0.547533 0.836784i \(-0.315567\pi\)
−0.998443 + 0.0557856i \(0.982234\pi\)
\(242\) −10.6479 21.1046i −0.684474 1.35665i
\(243\) 0 0
\(244\) 23.9894 + 17.4293i 1.53576 + 1.11580i
\(245\) 23.0049 4.88984i 1.46973 0.312400i
\(246\) 0 0
\(247\) 0.0587770 + 0.559226i 0.00373989 + 0.0355827i
\(248\) 0.641110 + 6.09976i 0.0407105 + 0.387335i
\(249\) 0 0
\(250\) −24.3110 + 5.16746i −1.53756 + 0.326819i
\(251\) 18.3631 + 13.3415i 1.15907 + 0.842111i 0.989660 0.143436i \(-0.0458150\pi\)
0.169406 + 0.985546i \(0.445815\pi\)
\(252\) 0 0
\(253\) −12.8435 3.11044i −0.807461 0.195552i
\(254\) 2.96979 + 5.14383i 0.186341 + 0.322753i
\(255\) 0 0
\(256\) 1.43589 + 1.59471i 0.0897429 + 0.0996696i
\(257\) 12.1158 + 2.57529i 0.755762 + 0.160642i 0.569651 0.821886i \(-0.307078\pi\)
0.186111 + 0.982529i \(0.440412\pi\)
\(258\) 0 0
\(259\) −6.82614 3.03919i −0.424155 0.188846i
\(260\) −0.410415 1.26313i −0.0254529 0.0783359i
\(261\) 0 0
\(262\) −4.28115 3.11044i −0.264491 0.192164i
\(263\) 3.22344 + 5.58316i 0.198766 + 0.344273i 0.948129 0.317887i \(-0.102973\pi\)
−0.749363 + 0.662160i \(0.769640\pi\)
\(264\) 0 0
\(265\) −1.97214 + 3.41584i −0.121147 + 0.209833i
\(266\) 19.8088 8.81943i 1.21455 0.540754i
\(267\) 0 0
\(268\) −4.99983 + 5.55288i −0.305414 + 0.339196i
\(269\) −16.3709 + 11.8941i −0.998149 + 0.725198i −0.961690 0.274138i \(-0.911608\pi\)
−0.0364584 + 0.999335i \(0.511608\pi\)
\(270\) 0 0
\(271\) −0.298374 0.918300i −0.0181249 0.0557828i 0.941585 0.336775i \(-0.109336\pi\)
−0.959710 + 0.280993i \(0.909336\pi\)
\(272\) −14.2902 + 3.03747i −0.866470 + 0.184174i
\(273\) 0 0
\(274\) −0.336881 + 0.583495i −0.0203517 + 0.0352502i
\(275\) 0.602270 + 1.11452i 0.0363182 + 0.0672079i
\(276\) 0 0
\(277\) −2.02597 + 19.2758i −0.121729 + 1.15817i 0.747674 + 0.664066i \(0.231171\pi\)
−0.869403 + 0.494104i \(0.835496\pi\)
\(278\) −7.55837 + 23.2623i −0.453321 + 1.39518i
\(279\) 0 0
\(280\) −9.78115 + 7.10642i −0.584536 + 0.424690i
\(281\) −15.1325 6.73744i −0.902732 0.401922i −0.0977427 0.995212i \(-0.531162\pi\)
−0.804989 + 0.593290i \(0.797829\pi\)
\(282\) 0 0
\(283\) −7.32315 8.13318i −0.435316 0.483467i 0.485072 0.874474i \(-0.338793\pi\)
−0.920388 + 0.391007i \(0.872127\pi\)
\(284\) 25.6983 11.4416i 1.52491 0.678935i
\(285\) 0 0
\(286\) −1.38850 + 0.950237i −0.0821040 + 0.0561887i
\(287\) 12.5802 0.742588
\(288\) 0 0
\(289\) 6.37132 19.6089i 0.374784 1.15347i
\(290\) −21.4889 + 23.8658i −1.26187 + 1.40145i
\(291\) 0 0
\(292\) −0.676522 6.43668i −0.0395905 0.376678i
\(293\) 4.88975 + 1.03935i 0.285663 + 0.0607194i 0.348514 0.937303i \(-0.386686\pi\)
−0.0628519 + 0.998023i \(0.520020\pi\)
\(294\) 0 0
\(295\) −1.67606 + 15.9466i −0.0975837 + 0.928447i
\(296\) 2.34273 0.136169
\(297\) 0 0
\(298\) −9.90983 −0.574061
\(299\) −0.0983182 + 0.935435i −0.00568589 + 0.0540976i
\(300\) 0 0
\(301\) 11.2214 + 2.38519i 0.646793 + 0.137480i
\(302\) 2.97319 + 28.2880i 0.171088 + 1.62779i
\(303\) 0 0
\(304\) 3.79649 4.21643i 0.217744 0.241829i
\(305\) 7.52136 23.1484i 0.430672 1.32547i
\(306\) 0 0
\(307\) 17.2705 0.985680 0.492840 0.870120i \(-0.335959\pi\)
0.492840 + 0.870120i \(0.335959\pi\)
\(308\) 29.1365 + 22.4493i 1.66021 + 1.27917i
\(309\) 0 0
\(310\) 19.4825 8.67416i 1.10653 0.492659i
\(311\) −19.2424 21.3709i −1.09114 1.21183i −0.975837 0.218499i \(-0.929884\pi\)
−0.115300 0.993331i \(-0.536783\pi\)
\(312\) 0 0
\(313\) 28.9160 + 12.8742i 1.63443 + 0.727694i 0.999010 0.0444751i \(-0.0141615\pi\)
0.635417 + 0.772169i \(0.280828\pi\)
\(314\) 35.9053 26.0867i 2.02625 1.47216i
\(315\) 0 0
\(316\) −7.66312 + 23.5847i −0.431084 + 1.32674i
\(317\) 0.0327727 0.311812i 0.00184070 0.0175131i −0.993563 0.113281i \(-0.963864\pi\)
0.995404 + 0.0957679i \(0.0305306\pi\)
\(318\) 0 0
\(319\) 20.7978 + 9.97082i 1.16446 + 0.558259i
\(320\) −12.8339 + 22.2289i −0.717436 + 1.24264i
\(321\) 0 0
\(322\) 35.4779 7.54106i 1.97711 0.420247i
\(323\) 4.51457 + 13.8944i 0.251197 + 0.773105i
\(324\) 0 0
\(325\) 0.0729490 0.0530006i 0.00404648 0.00293994i
\(326\) 1.98718 2.20699i 0.110060 0.122234i
\(327\) 0 0
\(328\) −3.60327 + 1.60428i −0.198957 + 0.0885815i
\(329\) 7.36460 12.7559i 0.406024 0.703253i
\(330\) 0 0
\(331\) −3.64590 6.31488i −0.200397 0.347097i 0.748260 0.663406i \(-0.230890\pi\)
−0.948656 + 0.316309i \(0.897556\pi\)
\(332\) −17.5422 12.7452i −0.962755 0.699482i
\(333\) 0 0
\(334\) −7.13525 21.9601i −0.390424 1.20160i
\(335\) 5.60310 + 2.49466i 0.306130 + 0.136298i
\(336\) 0 0
\(337\) 26.0701 + 5.54136i 1.42013 + 0.301857i 0.853059 0.521814i \(-0.174745\pi\)
0.567067 + 0.823671i \(0.308078\pi\)
\(338\) −18.6130 20.6719i −1.01242 1.12440i
\(339\) 0 0
\(340\) −17.2533 29.8836i −0.935691 1.62066i
\(341\) −9.92398 11.6663i −0.537413 0.631767i
\(342\) 0 0
\(343\) 13.5172 + 9.82084i 0.729861 + 0.530275i
\(344\) −3.51825 + 0.747827i −0.189691 + 0.0403201i
\(345\) 0 0
\(346\) 3.01025 + 28.6406i 0.161832 + 1.53973i
\(347\) −2.62999 25.0226i −0.141185 1.34329i −0.804057 0.594553i \(-0.797329\pi\)
0.662872 0.748733i \(-0.269338\pi\)
\(348\) 0 0
\(349\) −8.97973 + 1.90870i −0.480674 + 0.102170i −0.441875 0.897077i \(-0.645686\pi\)
−0.0387989 + 0.999247i \(0.512353\pi\)
\(350\) −2.81303 2.04378i −0.150363 0.109245i
\(351\) 0 0
\(352\) 25.0623 + 6.06961i 1.33583 + 0.323511i
\(353\) 16.8782 + 29.2338i 0.898334 + 1.55596i 0.829624 + 0.558323i \(0.188555\pi\)
0.0687102 + 0.997637i \(0.478112\pi\)
\(354\) 0 0
\(355\) −15.4503 17.1593i −0.820019 0.910723i
\(356\) −22.8153 4.84955i −1.20921 0.257026i
\(357\) 0 0
\(358\) 3.83838 + 1.70896i 0.202864 + 0.0903211i
\(359\) 0.627058 + 1.92989i 0.0330949 + 0.101856i 0.966239 0.257646i \(-0.0829468\pi\)
−0.933145 + 0.359501i \(0.882947\pi\)
\(360\) 0 0
\(361\) 10.7812 + 7.83297i 0.567429 + 0.412261i
\(362\) −13.1474 22.7720i −0.691013 1.19687i
\(363\) 0 0
\(364\) 1.30902 2.26728i 0.0686111 0.118838i
\(365\) −4.85323 + 2.16080i −0.254030 + 0.113101i
\(366\) 0 0
\(367\) 15.4131 17.1179i 0.804555 0.893548i −0.191572 0.981479i \(-0.561359\pi\)
0.996127 + 0.0879301i \(0.0280252\pi\)
\(368\) 7.67813 5.57849i 0.400250 0.290799i
\(369\) 0 0
\(370\) −2.51722 7.74721i −0.130864 0.402758i
\(371\) −7.60511 + 1.61652i −0.394838 + 0.0839253i
\(372\) 0 0
\(373\) 7.20820 12.4850i 0.373227 0.646448i −0.616833 0.787094i \(-0.711585\pi\)
0.990060 + 0.140646i \(0.0449180\pi\)
\(374\) −30.1538 + 31.6494i −1.55922 + 1.63655i
\(375\) 0 0
\(376\) −0.482716 + 4.59274i −0.0248942 + 0.236852i
\(377\) 0.507301 1.56131i 0.0261273 0.0804116i
\(378\) 0 0
\(379\) −5.04508 + 3.66547i −0.259149 + 0.188282i −0.709772 0.704432i \(-0.751202\pi\)
0.450623 + 0.892714i \(0.351202\pi\)
\(380\) 12.2425 + 5.45071i 0.628026 + 0.279615i
\(381\) 0 0
\(382\) −14.2700 15.8485i −0.730119 0.810879i
\(383\) −31.1244 + 13.8575i −1.59038 + 0.708083i −0.995413 0.0956673i \(-0.969502\pi\)
−0.594967 + 0.803750i \(0.702835\pi\)
\(384\) 0 0
\(385\) 10.1347 28.4399i 0.516513 1.44943i
\(386\) 15.8636 0.807434
\(387\) 0 0
\(388\) 9.54508 29.3768i 0.484578 1.49138i
\(389\) 14.9286 16.5799i 0.756910 0.840634i −0.234405 0.972139i \(-0.575314\pi\)
0.991315 + 0.131505i \(0.0419810\pi\)
\(390\) 0 0
\(391\) 2.55443 + 24.3038i 0.129183 + 1.22910i
\(392\) −14.2178 3.02209i −0.718107 0.152638i
\(393\) 0 0
\(394\) 0.553143 5.26281i 0.0278670 0.265136i
\(395\) 20.3553 1.02418
\(396\) 0 0
\(397\) 24.4164 1.22542 0.612712 0.790306i \(-0.290078\pi\)
0.612712 + 0.790306i \(0.290078\pi\)
\(398\) −0.0935367 + 0.889942i −0.00468857 + 0.0446088i
\(399\) 0 0
\(400\) −0.889948 0.189164i −0.0444974 0.00945822i
\(401\) 1.98888 + 18.9229i 0.0993197 + 0.944964i 0.924780 + 0.380503i \(0.124249\pi\)
−0.825460 + 0.564461i \(0.809084\pi\)
\(402\) 0 0
\(403\) −0.729466 + 0.810154i −0.0363373 + 0.0403567i
\(404\) −0.253650 + 0.780656i −0.0126196 + 0.0388391i
\(405\) 0 0
\(406\) −63.3050 −3.14177
\(407\) −4.82796 + 3.30406i −0.239313 + 0.163776i
\(408\) 0 0
\(409\) −4.61864 + 2.05635i −0.228377 + 0.101680i −0.517735 0.855541i \(-0.673225\pi\)
0.289358 + 0.957221i \(0.406558\pi\)
\(410\) 9.17686 + 10.1919i 0.453213 + 0.503344i
\(411\) 0 0
\(412\) −26.1753 11.6540i −1.28957 0.574152i
\(413\) −25.5709 + 18.5783i −1.25826 + 0.914180i
\(414\) 0 0
\(415\) −5.50000 + 16.9273i −0.269984 + 0.830926i
\(416\) 0.191855 1.82538i 0.00940646 0.0894965i
\(417\) 0 0
\(418\) 2.24937 16.8273i 0.110020 0.823050i
\(419\) 17.6391 30.5518i 0.861727 1.49255i −0.00853378 0.999964i \(-0.502716\pi\)
0.870261 0.492591i \(-0.163950\pi\)
\(420\) 0 0
\(421\) 28.5764 6.07409i 1.39273 0.296033i 0.550355 0.834930i \(-0.314492\pi\)
0.842372 + 0.538897i \(0.181159\pi\)
\(422\) −11.9761 36.8585i −0.582985 1.79424i
\(423\) 0 0
\(424\) 1.97214 1.43284i 0.0957754 0.0695849i
\(425\) 1.56759 1.74099i 0.0760395 0.0844504i
\(426\) 0 0
\(427\) 43.8307 19.5147i 2.12112 0.944383i
\(428\) 14.3188 24.8009i 0.692125 1.19879i
\(429\) 0 0
\(430\) 6.25329 + 10.8310i 0.301560 + 0.522318i
\(431\) 28.7943 + 20.9203i 1.38697 + 1.00770i 0.996190 + 0.0872135i \(0.0277962\pi\)
0.390785 + 0.920482i \(0.372204\pi\)
\(432\) 0 0
\(433\) −0.819660 2.52265i −0.0393904 0.121231i 0.929428 0.369004i \(-0.120301\pi\)
−0.968818 + 0.247773i \(0.920301\pi\)
\(434\) 38.4042 + 17.0987i 1.84346 + 0.820762i
\(435\) 0 0
\(436\) 35.1043 + 7.46165i 1.68119 + 0.357348i
\(437\) −6.35051 7.05296i −0.303786 0.337389i
\(438\) 0 0
\(439\) 12.5000 + 21.6506i 0.596592 + 1.03333i 0.993320 + 0.115392i \(0.0368124\pi\)
−0.396728 + 0.917936i \(0.629854\pi\)
\(440\) 0.723944 + 9.43826i 0.0345127 + 0.449951i
\(441\) 0 0
\(442\) 2.51722 + 1.82887i 0.119732 + 0.0869904i
\(443\) −21.3991 + 4.54852i −1.01670 + 0.216107i −0.685979 0.727622i \(-0.740626\pi\)
−0.330722 + 0.943728i \(0.607292\pi\)
\(444\) 0 0
\(445\) 2.00129 + 19.0410i 0.0948703 + 0.902631i
\(446\) −0.714392 6.79699i −0.0338274 0.321847i
\(447\) 0 0
\(448\) −49.4911 + 10.5197i −2.33823 + 0.497007i
\(449\) −23.8323 17.3152i −1.12472 0.817155i −0.139800 0.990180i \(-0.544646\pi\)
−0.984918 + 0.173024i \(0.944646\pi\)
\(450\) 0 0
\(451\) 5.16312 8.38800i 0.243122 0.394975i
\(452\) −23.4219 40.5680i −1.10167 1.90816i
\(453\) 0 0
\(454\) 15.7290 + 17.4688i 0.738197 + 0.819851i
\(455\) −2.10200 0.446794i −0.0985433 0.0209460i
\(456\) 0 0
\(457\) 32.0565 + 14.2725i 1.49954 + 0.667637i 0.982148 0.188112i \(-0.0602368\pi\)
0.517391 + 0.855749i \(0.326903\pi\)
\(458\) −12.2667 37.7530i −0.573186 1.76408i
\(459\) 0 0
\(460\) 18.1353 + 13.1760i 0.845561 + 0.614336i
\(461\) −0.760951 1.31801i −0.0354410 0.0613857i 0.847761 0.530379i \(-0.177950\pi\)
−0.883202 + 0.468993i \(0.844617\pi\)
\(462\) 0 0
\(463\) 10.7812 18.6735i 0.501043 0.867831i −0.498957 0.866627i \(-0.666283\pi\)
0.999999 0.00120439i \(-0.000383369\pi\)
\(464\) −15.1325 + 6.73744i −0.702511 + 0.312778i
\(465\) 0 0
\(466\) 33.0891 36.7491i 1.53282 1.70237i
\(467\) −17.1318 + 12.4470i −0.792766 + 0.575978i −0.908783 0.417269i \(-0.862987\pi\)
0.116017 + 0.993247i \(0.462987\pi\)
\(468\) 0 0
\(469\) 3.73607 + 11.4984i 0.172516 + 0.530948i
\(470\) 15.7064 3.33851i 0.724484 0.153994i
\(471\) 0 0
\(472\) 4.95492 8.58216i 0.228068 0.395026i
\(473\) 6.19580 6.50309i 0.284883 0.299012i
\(474\) 0 0
\(475\) −0.0951031 + 0.904846i −0.00436363 + 0.0415172i
\(476\) 21.0193 64.6908i 0.963419 2.96510i
\(477\) 0 0
\(478\) −19.8992 + 14.4576i −0.910168 + 0.661275i
\(479\) −33.6604 14.9866i −1.53798 0.684754i −0.549417 0.835548i \(-0.685150\pi\)
−0.988565 + 0.150795i \(0.951817\pi\)
\(480\) 0 0
\(481\) 0.278631 + 0.309451i 0.0127045 + 0.0141098i
\(482\) 27.4844 12.2369i 1.25188 0.557374i
\(483\) 0 0
\(484\) 26.9264 10.2135i 1.22393 0.464251i
\(485\) −25.3542 −1.15128
\(486\) 0 0
\(487\) 5.83688 17.9641i 0.264494 0.814030i −0.727315 0.686304i \(-0.759232\pi\)
0.991809 0.127726i \(-0.0407679\pi\)
\(488\) −10.0655 + 11.1789i −0.455646 + 0.506046i
\(489\) 0 0
\(490\) 5.28298 + 50.2642i 0.238660 + 2.27070i
\(491\) 18.9904 + 4.03654i 0.857025 + 0.182166i 0.615411 0.788206i \(-0.288990\pi\)
0.241614 + 0.970372i \(0.422323\pi\)
\(492\) 0 0
\(493\) 4.45840 42.4188i 0.200796 1.91045i
\(494\) −1.20837 −0.0543673
\(495\) 0 0
\(496\) 11.0000 0.493915
\(497\) 4.75769 45.2664i 0.213412 2.03047i
\(498\) 0 0
\(499\) −32.0271 6.80758i −1.43373 0.304749i −0.575412 0.817864i \(-0.695158\pi\)
−0.858320 + 0.513115i \(0.828492\pi\)
\(500\) −3.16504 30.1134i −0.141545 1.34671i
\(501\) 0 0
\(502\) −32.6382 + 36.2484i −1.45672 + 1.61785i
\(503\) 1.83543 5.64888i 0.0818379 0.251871i −0.901763 0.432231i \(-0.857726\pi\)
0.983601 + 0.180360i \(0.0577264\pi\)
\(504\) 0 0
\(505\) 0.673762 0.0299820
\(506\) 9.53259 26.7502i 0.423775 1.18919i
\(507\) 0 0
\(508\) −6.61048 + 2.94317i −0.293292 + 0.130582i
\(509\) 10.9542 + 12.1659i 0.485538 + 0.539245i 0.935278 0.353915i \(-0.115150\pi\)
−0.449739 + 0.893160i \(0.648483\pi\)
\(510\) 0 0
\(511\) −9.56677 4.25940i −0.423209 0.188425i
\(512\) −20.1016 + 14.6047i −0.888374 + 0.645441i
\(513\) 0 0
\(514\) −8.22542 + 25.3153i −0.362808 + 1.11661i
\(515\) −2.45839 + 23.3900i −0.108329 + 1.03069i
\(516\) 0 0
\(517\) −5.48255 10.1456i −0.241122 0.446204i
\(518\) 8.02866 13.9061i 0.352759 0.610997i
\(519\) 0 0
\(520\) 0.659039 0.140083i 0.0289008 0.00614305i
\(521\) −8.28232 25.4903i −0.362855 1.11675i −0.951313 0.308225i \(-0.900265\pi\)
0.588459 0.808527i \(-0.299735\pi\)
\(522\) 0 0
\(523\) 30.2984 22.0131i 1.32486 0.962564i 0.324997 0.945715i \(-0.394637\pi\)
0.999858 0.0168489i \(-0.00536341\pi\)
\(524\) 4.31381 4.79097i 0.188450 0.209294i
\(525\) 0 0
\(526\) −12.6564 + 5.63497i −0.551843 + 0.245696i
\(527\) −14.1620 + 24.5293i −0.616907 + 1.06851i
\(528\) 0 0
\(529\) 3.56231 + 6.17009i 0.154883 + 0.268265i
\(530\) −6.85730 4.98212i −0.297862 0.216409i
\(531\) 0 0
\(532\) 8.16312 + 25.1235i 0.353916 + 1.08924i
\(533\) −0.640462 0.285152i −0.0277415 0.0123513i
\(534\) 0 0
\(535\) −22.9929 4.88729i −0.994070 0.211296i
\(536\) −2.53642 2.81698i −0.109557 0.121675i
\(537\) 0 0
\(538\) −21.7426 37.6594i −0.937392 1.62361i
\(539\) 33.5625 13.8240i 1.44564 0.595442i
\(540\) 0 0
\(541\) −31.2533 22.7068i −1.34368 0.976243i −0.999300 0.0374146i \(-0.988088\pi\)
−0.344384 0.938829i \(-0.611912\pi\)
\(542\) 2.02960 0.431406i 0.0871790 0.0185305i
\(543\) 0 0
\(544\) −4.98464 47.4257i −0.213715 2.03336i
\(545\) −3.07924 29.2970i −0.131900 1.25495i
\(546\) 0 0
\(547\) −19.5966 + 4.16539i −0.837892 + 0.178099i −0.606822 0.794838i \(-0.707556\pi\)
−0.231070 + 0.972937i \(0.574223\pi\)
\(548\) −0.664066 0.482472i −0.0283675 0.0206102i
\(549\) 0 0
\(550\) −2.51722 + 1.03681i −0.107335 + 0.0442099i
\(551\) 8.28232 + 14.3454i 0.352838 + 0.611134i
\(552\) 0 0
\(553\) 26.8486 + 29.8184i 1.14172 + 1.26801i
\(554\) −40.7409 8.65975i −1.73092 0.367917i
\(555\) 0 0
\(556\) −27.2222 12.1201i −1.15448 0.514006i
\(557\) 1.67867 + 5.16641i 0.0711274 + 0.218908i 0.980301 0.197510i \(-0.0632855\pi\)
−0.909173 + 0.416418i \(0.863285\pi\)
\(558\) 0 0
\(559\) −0.517221 0.375783i −0.0218761 0.0158939i
\(560\) 10.8417 + 18.7784i 0.458145 + 0.793531i
\(561\) 0 0
\(562\) 17.7984 30.8277i 0.750779 1.30039i
\(563\) 14.2733 6.35487i 0.601547 0.267826i −0.0832865 0.996526i \(-0.526542\pi\)
0.684833 + 0.728700i \(0.259875\pi\)
\(564\) 0 0
\(565\) −25.7286 + 28.5746i −1.08241 + 1.20214i
\(566\) 19.0271 13.8240i 0.799770 0.581067i
\(567\) 0 0
\(568\) 4.40983 + 13.5721i 0.185032 + 0.569471i
\(569\) −31.0338 + 6.59644i −1.30100 + 0.276537i −0.805773 0.592224i \(-0.798250\pi\)
−0.495231 + 0.868761i \(0.664917\pi\)
\(570\) 0 0
\(571\) −5.98936 + 10.3739i −0.250647 + 0.434133i −0.963704 0.266973i \(-0.913977\pi\)
0.713057 + 0.701106i \(0.247310\pi\)
\(572\) −0.974493 1.80333i −0.0407456 0.0754009i
\(573\) 0 0
\(574\) −2.82587 + 26.8863i −0.117949 + 1.12221i
\(575\) −0.470294 + 1.44742i −0.0196126 + 0.0603614i
\(576\) 0 0
\(577\) 1.09017 0.792055i 0.0453844 0.0329737i −0.564862 0.825186i \(-0.691071\pi\)
0.610246 + 0.792212i \(0.291071\pi\)
\(578\) 40.4768 + 18.0214i 1.68361 + 0.749592i
\(579\) 0 0
\(580\) −26.1795 29.0753i −1.08704 1.20728i
\(581\) −32.0512 + 14.2701i −1.32971 + 0.592025i
\(582\) 0 0
\(583\) −2.04342 + 5.73422i −0.0846300 + 0.237487i
\(584\) 3.28332 0.135865
\(585\) 0 0
\(586\) −3.31966 + 10.2169i −0.137134 + 0.422055i
\(587\) 24.5746 27.2928i 1.01430 1.12650i 0.0223656 0.999750i \(-0.492880\pi\)
0.991935 0.126745i \(-0.0404531\pi\)
\(588\) 0 0
\(589\) −1.14981 10.9397i −0.0473772 0.450764i
\(590\) −33.7044 7.16409i −1.38759 0.294941i
\(591\) 0 0
\(592\) 0.439190 4.17861i 0.0180506 0.171740i
\(593\) 27.3094 1.12146 0.560732 0.827997i \(-0.310520\pi\)
0.560732 + 0.827997i \(0.310520\pi\)
\(594\) 0 0
\(595\) −55.8328 −2.28892
\(596\) 1.26197 12.0068i 0.0516921 0.491818i
\(597\) 0 0
\(598\) −1.97712 0.420249i −0.0808503 0.0171853i
\(599\) −1.79702 17.0975i −0.0734243 0.698585i −0.967877 0.251423i \(-0.919101\pi\)
0.894453 0.447162i \(-0.147565\pi\)
\(600\) 0 0
\(601\) −6.26352 + 6.95634i −0.255494 + 0.283755i −0.857223 0.514945i \(-0.827812\pi\)
0.601729 + 0.798701i \(0.294479\pi\)
\(602\) −7.61825 + 23.4466i −0.310497 + 0.955611i
\(603\) 0 0
\(604\) −34.6525 −1.40999
\(605\) −14.8031 18.4296i −0.601833 0.749269i
\(606\) 0 0
\(607\) −26.1439 + 11.6400i −1.06115 + 0.472453i −0.861680 0.507451i \(-0.830588\pi\)
−0.199467 + 0.979905i \(0.563921\pi\)
\(608\) 12.3922 + 13.7629i 0.502569 + 0.558160i
\(609\) 0 0
\(610\) 47.7830 + 21.2743i 1.93468 + 0.861373i
\(611\) −0.664066 + 0.482472i −0.0268652 + 0.0195187i
\(612\) 0 0
\(613\) 7.74265 23.8294i 0.312723 0.962461i −0.663959 0.747769i \(-0.731125\pi\)
0.976682 0.214692i \(-0.0688748\pi\)
\(614\) −3.87943 + 36.9103i −0.156561 + 1.48958i
\(615\) 0 0
\(616\) −12.8712 + 13.5096i −0.518596 + 0.544317i
\(617\) −8.43908 + 14.6169i −0.339745 + 0.588455i −0.984385 0.176031i \(-0.943674\pi\)
0.644640 + 0.764486i \(0.277007\pi\)
\(618\) 0 0
\(619\) −6.73801 + 1.43221i −0.270824 + 0.0575653i −0.341322 0.939947i \(-0.610875\pi\)
0.0704980 + 0.997512i \(0.477541\pi\)
\(620\) 8.02866 + 24.7097i 0.322439 + 0.992365i
\(621\) 0 0
\(622\) 49.9959 36.3242i 2.00465 1.45647i
\(623\) −25.2535 + 28.0468i −1.01176 + 1.12367i
\(624\) 0 0
\(625\) −20.9606 + 9.33228i −0.838425 + 0.373291i
\(626\) −34.0100 + 58.9070i −1.35931 + 2.35440i
\(627\) 0 0
\(628\) 27.0344 + 46.8250i 1.07879 + 1.86852i
\(629\) 8.75261 + 6.35914i 0.348989 + 0.253556i
\(630\) 0 0
\(631\) −5.37132 16.5312i −0.213829 0.658098i −0.999235 0.0391166i \(-0.987546\pi\)
0.785406 0.618981i \(-0.212454\pi\)
\(632\) −11.4926 5.11684i −0.457152 0.203537i
\(633\) 0 0
\(634\) 0.659039 + 0.140083i 0.0261738 + 0.00556341i
\(635\) 3.97436 + 4.41397i 0.157718 + 0.175163i
\(636\) 0 0
\(637\) −1.29180 2.23746i −0.0511828 0.0886513i
\(638\) −25.9813 + 42.2092i −1.02861 + 1.67108i
\(639\) 0 0
\(640\) −17.5902 12.7800i −0.695313 0.505174i
\(641\) 20.9029 4.44304i 0.825614 0.175490i 0.224318 0.974516i \(-0.427985\pi\)
0.601296 + 0.799026i \(0.294651\pi\)
\(642\) 0 0
\(643\) 4.30229 + 40.9336i 0.169666 + 1.61426i 0.665877 + 0.746061i \(0.268057\pi\)
−0.496212 + 0.868202i \(0.665276\pi\)
\(644\) 4.61886 + 43.9455i 0.182009 + 1.73170i
\(645\) 0 0
\(646\) −30.7091 + 6.52741i −1.20823 + 0.256818i
\(647\) 9.45368 + 6.86850i 0.371663 + 0.270029i 0.757900 0.652371i \(-0.226225\pi\)
−0.386237 + 0.922399i \(0.626225\pi\)
\(648\) 0 0
\(649\) 1.89261 + 24.6745i 0.0742914 + 0.968558i
\(650\) 0.0968859 + 0.167811i 0.00380018 + 0.00658210i
\(651\) 0 0
\(652\) 2.42094 + 2.68872i 0.0948112 + 0.105299i
\(653\) 33.4425 + 7.10842i 1.30871 + 0.278174i 0.808891 0.587959i \(-0.200068\pi\)
0.499814 + 0.866133i \(0.333402\pi\)
\(654\) 0 0
\(655\) −4.83430 2.15237i −0.188892 0.0841000i
\(656\) 2.18597 + 6.72772i 0.0853477 + 0.262673i
\(657\) 0 0
\(658\) 25.6074 + 18.6049i 0.998280 + 0.725293i
\(659\) 16.8782 + 29.2338i 0.657480 + 1.13879i 0.981266 + 0.192658i \(0.0617108\pi\)
−0.323786 + 0.946130i \(0.604956\pi\)
\(660\) 0 0
\(661\) −1.21885 + 2.11111i −0.0474077 + 0.0821125i −0.888755 0.458382i \(-0.848429\pi\)
0.841348 + 0.540494i \(0.181763\pi\)
\(662\) 14.3151 6.37348i 0.556371 0.247712i
\(663\) 0 0
\(664\) 7.36044 8.17459i 0.285640 0.317236i
\(665\) 17.5422 12.7452i 0.680258 0.494237i
\(666\) 0 0
\(667\) 8.56231 + 26.3521i 0.331534 + 1.02036i
\(668\) 27.5156 5.84861i 1.06461 0.226290i
\(669\) 0 0
\(670\) −6.59017 + 11.4145i −0.254600 + 0.440981i
\(671\) 4.97718 37.2337i 0.192142 1.43739i
\(672\) 0 0
\(673\) −1.90619 + 18.1362i −0.0734782 + 0.699098i 0.894330 + 0.447408i \(0.147653\pi\)
−0.967808 + 0.251690i \(0.919014\pi\)
\(674\) −17.6990 + 54.4719i −0.681740 + 2.09818i
\(675\) 0 0
\(676\) 27.4164 19.9192i 1.05448 0.766123i
\(677\) −7.85269 3.49624i −0.301804 0.134372i 0.250248 0.968182i \(-0.419488\pi\)
−0.552051 + 0.833810i \(0.686155\pi\)
\(678\) 0 0
\(679\) −33.4423 37.1414i −1.28340 1.42536i
\(680\) 15.9918 7.12001i 0.613258 0.273040i
\(681\) 0 0
\(682\) 27.1624 18.5888i 1.04010 0.711803i
\(683\) −0.940588 −0.0359906 −0.0179953 0.999838i \(-0.505728\pi\)
−0.0179953 + 0.999838i \(0.505728\pi\)
\(684\) 0 0
\(685\) −0.208204 + 0.640786i −0.00795506 + 0.0244832i
\(686\) −24.0253 + 26.6828i −0.917291 + 1.01875i
\(687\) 0 0
\(688\) 0.674297 + 6.41551i 0.0257073 + 0.244589i
\(689\) 0.423818 + 0.0900854i 0.0161462 + 0.00343198i
\(690\) 0 0
\(691\) −3.38261 + 32.1834i −0.128681 + 1.22431i 0.719456 + 0.694538i \(0.244391\pi\)
−0.848137 + 0.529777i \(0.822276\pi\)
\(692\) −35.0845 −1.33371
\(693\) 0 0
\(694\) 54.0689 2.05243
\(695\) −2.55670 + 24.3254i −0.0969813 + 0.922715i
\(696\) 0 0
\(697\) −17.8167 3.78707i −0.674857 0.143445i
\(698\) −2.06216 19.6201i −0.0780538 0.742633i
\(699\) 0 0
\(700\) 2.83448 3.14801i 0.107133 0.118984i
\(701\) 7.23071 22.2538i 0.273100 0.840515i −0.716616 0.697468i \(-0.754310\pi\)
0.989716 0.143047i \(-0.0456901\pi\)
\(702\) 0 0
\(703\) −4.20163 −0.158467
\(704\) −13.2978 + 37.3161i −0.501180 + 1.40640i
\(705\) 0 0
\(706\) −66.2695 + 29.5051i −2.49409 + 1.11044i
\(707\) 0.888693 + 0.986994i 0.0334227 + 0.0371197i
\(708\) 0 0
\(709\) −13.8874 6.18306i −0.521551 0.232210i 0.129038 0.991640i \(-0.458811\pi\)
−0.650589 + 0.759430i \(0.725478\pi\)
\(710\) 40.1433 29.1658i 1.50655 1.09457i
\(711\) 0 0
\(712\) 3.65654 11.2537i 0.137035 0.421749i
\(713\) 1.92333 18.2993i 0.0720293 0.685313i
\(714\) 0 0
\(715\) −1.16060 + 1.21816i −0.0434039 + 0.0455565i
\(716\) −2.55938 + 4.43297i −0.0956484 + 0.165668i
\(717\) 0 0
\(718\) −4.26539 + 0.906636i −0.159183 + 0.0338354i
\(719\) −4.00726 12.3331i −0.149446 0.459947i 0.848110 0.529820i \(-0.177741\pi\)
−0.997556 + 0.0698732i \(0.977741\pi\)
\(720\) 0 0
\(721\) −37.5066 + 27.2501i −1.39682 + 1.01485i
\(722\) −19.1623 + 21.2819i −0.713146 + 0.792029i
\(723\) 0 0
\(724\) 29.2649 13.0296i 1.08762 0.484241i
\(725\) 1.32813 2.30039i 0.0493255 0.0854344i
\(726\) 0 0
\(727\) −9.78115 16.9415i −0.362763 0.628324i 0.625652 0.780103i \(-0.284833\pi\)
−0.988414 + 0.151779i \(0.951500\pi\)
\(728\) 1.07448 + 0.780656i 0.0398229 + 0.0289330i
\(729\) 0 0
\(730\) −3.52786 10.8576i −0.130572 0.401860i
\(731\) −15.1743 6.75605i −0.561243 0.249881i
\(732\) 0 0
\(733\) 14.3323 + 3.04642i 0.529375 + 0.112522i 0.464842 0.885393i \(-0.346111\pi\)
0.0645326 + 0.997916i \(0.479444\pi\)
\(734\) 33.1220 + 36.7858i 1.22256 + 1.35779i
\(735\) 0 0
\(736\) 15.4894 + 26.8284i 0.570945 + 0.988906i
\(737\) 9.20003 + 2.22807i 0.338888 + 0.0820721i
\(738\) 0 0
\(739\) −14.7533 10.7189i −0.542709 0.394301i 0.282381 0.959302i \(-0.408876\pi\)
−0.825090 + 0.565001i \(0.808876\pi\)
\(740\) 9.70711 2.06331i 0.356841 0.0758488i
\(741\) 0 0
\(742\) −1.74648 16.6167i −0.0641154 0.610017i
\(743\) −1.89534 18.0329i −0.0695332 0.661565i −0.972667 0.232205i \(-0.925406\pi\)
0.903134 0.429360i \(-0.141261\pi\)
\(744\) 0 0
\(745\) −9.69328 + 2.06037i −0.355134 + 0.0754861i
\(746\) 25.0636 + 18.2098i 0.917643 + 0.666707i
\(747\) 0 0
\(748\) −34.5066 40.5649i −1.26169 1.48320i
\(749\) −23.1683 40.1286i −0.846550 1.46627i
\(750\) 0 0
\(751\) −1.00810 1.11961i −0.0367860 0.0408550i 0.724471 0.689305i \(-0.242084\pi\)
−0.761257 + 0.648450i \(0.775417\pi\)
\(752\) 8.10133 + 1.72199i 0.295425 + 0.0627945i
\(753\) 0 0
\(754\) 3.22286 + 1.43491i 0.117370 + 0.0522564i
\(755\) 8.78962 + 27.0517i 0.319887 + 0.984511i
\(756\) 0 0
\(757\) 33.0795 + 24.0337i 1.20230 + 0.873519i 0.994509 0.104655i \(-0.0333738\pi\)
0.207787 + 0.978174i \(0.433374\pi\)
\(758\) −6.70053 11.6057i −0.243374 0.421537i
\(759\) 0 0
\(760\) −3.39919 + 5.88756i −0.123301 + 0.213564i
\(761\) 30.5515 13.6024i 1.10749 0.493087i 0.230248 0.973132i \(-0.426046\pi\)
0.877244 + 0.480045i \(0.159380\pi\)
\(762\) 0 0
\(763\) 38.8557 43.1536i 1.40667 1.56226i
\(764\) 21.0193 15.2714i 0.760452 0.552501i
\(765\) 0 0
\(766\) −22.6246 69.6314i −0.817460 2.51588i
\(767\) 1.72293 0.366219i 0.0622113 0.0132234i
\(768\) 0 0
\(769\) 11.1353 19.2868i 0.401548 0.695501i −0.592365 0.805669i \(-0.701806\pi\)
0.993913 + 0.110169i \(0.0351391\pi\)
\(770\) 58.5049 + 28.0482i 2.10837 + 1.01079i
\(771\) 0 0
\(772\) −2.02014 + 19.2204i −0.0727065 + 0.691756i
\(773\) −10.4084 + 32.0338i −0.374364 + 1.15217i 0.569542 + 0.821962i \(0.307121\pi\)
−0.943907 + 0.330213i \(0.892879\pi\)
\(774\) 0 0
\(775\) −1.42705 + 1.03681i −0.0512612 + 0.0372434i
\(776\) 14.3151 + 6.37348i 0.513881 + 0.228794i
\(777\) 0 0
\(778\) 32.0810 + 35.6295i 1.15016 + 1.27738i
\(779\) 6.46237 2.87723i 0.231538 0.103088i
\(780\) 0 0
\(781\) −28.2292 21.7502i −1.01012 0.778285i
\(782\) −52.5157 −1.87796
\(783\) 0 0
\(784\) −8.05573 + 24.7930i −0.287705 + 0.885464i
\(785\) 29.6969 32.9818i 1.05993 1.17717i
\(786\) 0 0
\(787\) −2.90350 27.6249i −0.103498 0.984722i −0.915841 0.401541i \(-0.868475\pi\)
0.812342 0.583181i \(-0.198192\pi\)
\(788\) 6.30600 + 1.34038i 0.224642 + 0.0477491i
\(789\) 0 0
\(790\) −4.57235 + 43.5030i −0.162677 + 1.54777i
\(791\) −75.7950 −2.69496
\(792\) 0 0
\(793\) −2.67376 −0.0949481
\(794\) −5.48460 + 52.1825i −0.194641 + 1.85189i
\(795\) 0 0
\(796\) −1.06635 0.226659i −0.0377957 0.00803372i
\(797\) −0.449255 4.27438i −0.0159134 0.151406i 0.983680 0.179928i \(-0.0575866\pi\)
−0.999593 + 0.0285221i \(0.990920\pi\)
\(798\) 0 0
\(799\) −14.2700 + 15.8485i −0.504838 + 0.560679i
\(800\) 0.917716 2.82444i 0.0324462 0.0998590i
\(801\) 0 0
\(802\) −40.8885 −1.44382
\(803\) −6.76634 + 4.63062i −0.238779 + 0.163411i
\(804\) 0 0
\(805\) 33.1348 14.7525i 1.16785 0.519959i
\(806\) −1.56759 1.74099i −0.0552162 0.0613237i
\(807\) 0 0
\(808\) −0.380408 0.169368i −0.0133827 0.00595836i
\(809\) 5.72294 4.15796i 0.201208 0.146186i −0.482619 0.875830i \(-0.660314\pi\)
0.683827 + 0.729644i \(0.260314\pi\)
\(810\) 0 0
\(811\) −13.6631 + 42.0508i −0.479777 + 1.47660i 0.359628 + 0.933096i \(0.382904\pi\)
−0.839405 + 0.543506i \(0.817096\pi\)
\(812\) 8.06156 76.7006i 0.282905 2.69166i
\(813\) 0 0
\(814\) −5.97691 11.0604i −0.209491 0.387668i
\(815\) 1.48490 2.57191i 0.0520136 0.0900902i
\(816\) 0 0
\(817\) 6.30988 1.34121i 0.220755 0.0469229i
\(818\) −3.35733 10.3328i −0.117386 0.361278i
\(819\) 0 0
\(820\) −13.5172 + 9.82084i −0.472042 + 0.342958i
\(821\) 26.6113 29.5548i 0.928740 1.03147i −0.0706831 0.997499i \(-0.522518\pi\)
0.999423 0.0339711i \(-0.0108154\pi\)
\(822\) 0 0
\(823\) 17.4592 7.77333i 0.608589 0.270961i −0.0792153 0.996858i \(-0.525241\pi\)
0.687804 + 0.725896i \(0.258575\pi\)
\(824\) 7.26771 12.5880i 0.253183 0.438525i
\(825\) 0 0
\(826\) −33.9615 58.8230i −1.18167 2.04672i
\(827\) −9.41667 6.84161i −0.327450 0.237906i 0.411898 0.911230i \(-0.364866\pi\)
−0.739348 + 0.673324i \(0.764866\pi\)
\(828\) 0 0
\(829\) 6.19098 + 19.0539i 0.215022 + 0.661769i 0.999152 + 0.0411726i \(0.0131094\pi\)
−0.784130 + 0.620596i \(0.786891\pi\)
\(830\) −34.9413 15.5569i −1.21283 0.539987i
\(831\) 0 0
\(832\) 2.75804 + 0.586240i 0.0956180 + 0.0203242i
\(833\) −44.9155 49.8837i −1.55623 1.72837i
\(834\) 0 0
\(835\) −11.5451 19.9967i −0.399534 0.692013i
\(836\) 20.1016 + 4.86822i 0.695228 + 0.168371i
\(837\) 0 0
\(838\) 61.3328 + 44.5609i 2.11871 + 1.53933i
\(839\) 13.6768 2.90710i 0.472177 0.100364i 0.0343236 0.999411i \(-0.489072\pi\)
0.437853 + 0.899047i \(0.355739\pi\)
\(840\) 0 0
\(841\) −2.02374 19.2546i −0.0697842 0.663952i
\(842\) 6.56245 + 62.4375i 0.226157 + 2.15174i
\(843\) 0 0
\(844\) 46.1830 9.81651i 1.58969 0.337898i
\(845\) −22.5042 16.3503i −0.774168 0.562466i
\(846\) 0 0
\(847\) 7.47214 45.9937i 0.256746 1.58036i
\(848\) −2.18597 3.78621i −0.0750665 0.130019i
\(849\) 0 0
\(850\) 3.36870 + 3.74132i 0.115545 + 0.128326i
\(851\) −6.87462 1.46124i −0.235659 0.0500908i
\(852\) 0 0
\(853\) −1.07829 0.480087i −0.0369201 0.0164379i 0.388194 0.921578i \(-0.373099\pi\)
−0.425114 + 0.905140i \(0.639766\pi\)
\(854\) 31.8610 + 98.0581i 1.09026 + 3.35548i
\(855\) 0 0
\(856\) 11.7533 + 8.53926i 0.401719 + 0.291866i
\(857\) −6.91718 11.9809i −0.236286 0.409260i 0.723359 0.690472i \(-0.242597\pi\)
−0.959646 + 0.281212i \(0.909264\pi\)
\(858\) 0 0
\(859\) −21.2082 + 36.7337i −0.723615 + 1.25334i 0.235927 + 0.971771i \(0.424187\pi\)
−0.959542 + 0.281566i \(0.909146\pi\)
\(860\) −13.9192 + 6.19724i −0.474642 + 0.211324i
\(861\) 0 0
\(862\) −51.1786 + 56.8396i −1.74315 + 1.93597i
\(863\) 27.8167 20.2100i 0.946893 0.687958i −0.00317717 0.999995i \(-0.501011\pi\)
0.950070 + 0.312037i \(0.101011\pi\)
\(864\) 0 0
\(865\) 8.89919 + 27.3889i 0.302581 + 0.931250i
\(866\) 5.57551 1.18511i 0.189463 0.0402717i
\(867\) 0 0
\(868\) −25.6074 + 44.3533i −0.869171 + 1.50545i
\(869\) 30.9008 5.66365i 1.04824 0.192126i
\(870\) 0 0
\(871\) 0.0704273 0.670071i 0.00238634 0.0227045i
\(872\) −5.62605 + 17.3152i −0.190522 + 0.586367i
\(873\) 0 0
\(874\) 16.5000 11.9880i 0.558121 0.405499i
\(875\) −44.7572 19.9272i −1.51307 0.673661i
\(876\) 0 0
\(877\) 7.67636 + 8.52546i 0.259212 + 0.287884i 0.858677 0.512517i \(-0.171287\pi\)
−0.599465 + 0.800401i \(0.704620\pi\)
\(878\) −49.0793 + 21.8515i −1.65635 + 0.737453i
\(879\) 0 0
\(880\) 16.9702 + 0.478119i 0.572067 + 0.0161174i
\(881\) 34.3376 1.15686 0.578432 0.815730i \(-0.303665\pi\)
0.578432 + 0.815730i \(0.303665\pi\)
\(882\) 0 0
\(883\) −4.36068 + 13.4208i −0.146749 + 0.451646i −0.997232 0.0743567i \(-0.976310\pi\)
0.850483 + 0.526002i \(0.176310\pi\)
\(884\) −2.53642 + 2.81698i −0.0853091 + 0.0947453i
\(885\) 0 0
\(886\) −4.91421 46.7556i −0.165096 1.57079i
\(887\) 55.3378 + 11.7624i 1.85806 + 0.394943i 0.994086 0.108592i \(-0.0346343\pi\)
0.863975 + 0.503535i \(0.167968\pi\)
\(888\) 0 0
\(889\) −1.22384 + 11.6441i −0.0410463 + 0.390529i
\(890\) −41.1438 −1.37914
\(891\) 0 0
\(892\) 8.32624 0.278783
\(893\) 0.865738 8.23694i 0.0289708 0.275639i
\(894\) 0 0
\(895\) 4.10981 + 0.873567i 0.137376 + 0.0292001i
\(896\) −4.48003 42.6247i −0.149667 1.42399i
\(897\) 0 0
\(898\) 42.3593 47.0447i 1.41355 1.56990i
\(899\) −9.92398 + 30.5429i −0.330983 + 1.01866i
\(900\) 0 0
\(901\) 11.2574 0.375037
\(902\) 16.7670 + 12.9187i 0.558278 + 0.430147i
\(903\) 0 0
\(904\) 21.7094 9.66566i 0.722045 0.321475i
\(905\) −17.5947 19.5409i −0.584867 0.649561i
\(906\) 0 0
\(907\) −32.7664 14.5885i −1.08799 0.484404i −0.217234 0.976120i \(-0.569703\pi\)
−0.870756 + 0.491716i \(0.836370\pi\)
\(908\) −23.1683 + 16.8327i −0.768866 + 0.558614i
\(909\) 0 0
\(910\) 1.42705 4.39201i 0.0473063 0.145594i
\(911\) −0.996829 + 9.48419i −0.0330264 + 0.314225i 0.965520 + 0.260328i \(0.0838309\pi\)
−0.998547 + 0.0538968i \(0.982836\pi\)
\(912\) 0 0
\(913\) −3.63956 + 27.2272i −0.120452 + 0.901087i
\(914\) −37.7037 + 65.3047i −1.24713 + 2.16009i
\(915\) 0 0
\(916\) 47.3039 10.0548i 1.56296 0.332218i
\(917\) −3.22344 9.92073i −0.106447 0.327611i
\(918\) 0 0
\(919\) 20.3713 14.8006i 0.671988 0.488228i −0.198702 0.980060i \(-0.563673\pi\)
0.870690 + 0.491832i \(0.163673\pi\)
\(920\) −7.60926 + 8.45094i −0.250870 + 0.278619i
\(921\) 0 0
\(922\) 2.98776 1.33024i 0.0983966 0.0438090i
\(923\) −1.26825 + 2.19668i −0.0417450 + 0.0723045i
\(924\) 0 0
\(925\) 0.336881 + 0.583495i 0.0110766 + 0.0191852i
\(926\) 37.4871 + 27.2359i 1.23190 + 0.895029i
\(927\) 0 0
\(928\) −16.7082 51.4226i −0.548474 1.68803i
\(929\) 38.4042 + 17.0987i 1.26000 + 0.560989i 0.924547 0.381068i \(-0.124444\pi\)
0.335454 + 0.942057i \(0.391110\pi\)
\(930\) 0 0
\(931\) 25.4992 + 5.42003i 0.835703 + 0.177634i
\(932\) 40.3117 + 44.7707i 1.32045 + 1.46651i
\(933\) 0 0
\(934\) −22.7533 39.4099i −0.744510 1.28953i
\(935\) −22.9146 + 37.2271i −0.749388 + 1.21746i
\(936\) 0 0
\(937\) −8.75329 6.35964i −0.285957 0.207760i 0.435554 0.900162i \(-0.356552\pi\)
−0.721512 + 0.692402i \(0.756552\pi\)
\(938\) −25.4136 + 5.40182i −0.829782 + 0.176376i
\(939\) 0 0
\(940\) 2.04482 + 19.4551i 0.0666946 + 0.634557i
\(941\) 0.959274 + 9.12689i 0.0312715 + 0.297528i 0.998968 + 0.0454116i \(0.0144599\pi\)
−0.967697 + 0.252116i \(0.918873\pi\)
\(942\) 0 0
\(943\) 11.5742 2.46018i 0.376909 0.0801145i
\(944\) −14.3787 10.4467i −0.467986 0.340011i
\(945\) 0 0
\(946\) 12.5066 + 14.7024i 0.406624 + 0.478015i
\(947\) 11.1922 + 19.3855i 0.363699 + 0.629944i 0.988566 0.150786i \(-0.0481805\pi\)
−0.624868 + 0.780731i \(0.714847\pi\)
\(948\) 0 0
\(949\) 0.390499 + 0.433693i 0.0126761 + 0.0140783i
\(950\) −1.91246 0.406507i −0.0620485 0.0131888i
\(951\) 0 0
\(952\) 31.5233 + 14.0351i 1.02168 + 0.454880i
\(953\) 5.19277 + 15.9817i 0.168210 + 0.517698i 0.999259 0.0385025i \(-0.0122587\pi\)
−0.831048 + 0.556200i \(0.812259\pi\)
\(954\) 0 0
\(955\) −17.2533 12.5352i −0.558303 0.405631i
\(956\) −14.9828 25.9511i −0.484580 0.839317i
\(957\) 0 0
\(958\) 39.5902 68.5722i 1.27910 2.21547i
\(959\) −1.21331 + 0.540200i −0.0391798 + 0.0174440i
\(960\) 0 0
\(961\) −6.47301 + 7.18901i −0.208807 + 0.231903i
\(962\) −0.723944 + 0.525976i −0.0233409 + 0.0169582i
\(963\) 0 0
\(964\) 11.3262 + 34.8586i 0.364794 + 1.12272i
\(965\) 15.5169 3.29822i 0.499507 0.106173i
\(966\) 0 0
\(967\) 8.84346 15.3173i 0.284386 0.492572i −0.688074 0.725641i \(-0.741543\pi\)
0.972460 + 0.233069i \(0.0748768\pi\)
\(968\) 3.72510 + 14.1265i 0.119729 + 0.454044i
\(969\) 0 0
\(970\) 5.69526 54.1868i 0.182864 1.73983i
\(971\) 0.313529 0.964944i 0.0100616 0.0309665i −0.945900 0.324459i \(-0.894818\pi\)
0.955961 + 0.293493i \(0.0948177\pi\)
\(972\) 0 0
\(973\) −39.0066 + 28.3399i −1.25049 + 0.908537i
\(974\) 37.0815 + 16.5097i 1.18817 + 0.529006i
\(975\) 0 0
\(976\) 18.0523 + 20.0491i 0.577840 + 0.641756i
\(977\) −3.06708 + 1.36555i −0.0981245 + 0.0436878i −0.455212 0.890383i \(-0.650436\pi\)
0.357087 + 0.934071i \(0.383770\pi\)
\(978\) 0 0
\(979\) 8.33608 + 28.3488i 0.266422 + 0.906032i
\(980\) −61.5731 −1.96688
\(981\) 0 0
\(982\) −12.8926 + 39.6794i −0.411420 + 1.26622i
\(983\) −33.9306 + 37.6838i −1.08222 + 1.20193i −0.103950 + 0.994583i \(0.533148\pi\)
−0.978268 + 0.207343i \(0.933519\pi\)
\(984\) 0 0
\(985\) −0.553143 5.26281i −0.0176246 0.167687i
\(986\) 89.6556 + 19.0569i 2.85521 + 0.606895i
\(987\) 0 0
\(988\) 0.153880 1.46407i 0.00489558 0.0465783i
\(989\) 10.7905 0.343119
\(990\) 0 0
\(991\) −58.2705 −1.85102 −0.925512 0.378719i \(-0.876365\pi\)
−0.925512 + 0.378719i \(0.876365\pi\)
\(992\) −3.75312 + 35.7086i −0.119162 + 1.13375i
\(993\) 0 0
\(994\) 95.6741 + 20.3362i 3.03460 + 0.645024i
\(995\) 0.0935367 + 0.889942i 0.00296531 + 0.0282131i
\(996\) 0 0
\(997\) 25.9239 28.7914i 0.821018 0.911833i −0.176351 0.984327i \(-0.556429\pi\)
0.997369 + 0.0724947i \(0.0230960\pi\)
\(998\) 21.7433 66.9189i 0.688271 2.11828i
\(999\) 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 891.2.n.e.433.1 16
3.2 odd 2 inner 891.2.n.e.433.2 16
9.2 odd 6 inner 891.2.n.e.136.1 16
9.4 even 3 99.2.f.c.37.1 8
9.5 odd 6 99.2.f.c.37.2 yes 8
9.7 even 3 inner 891.2.n.e.136.2 16
11.3 even 5 inner 891.2.n.e.190.2 16
33.14 odd 10 inner 891.2.n.e.190.1 16
99.5 odd 30 1089.2.a.v.1.1 4
99.14 odd 30 99.2.f.c.91.2 yes 8
99.25 even 15 inner 891.2.n.e.784.1 16
99.47 odd 30 inner 891.2.n.e.784.2 16
99.49 even 15 1089.2.a.v.1.4 4
99.50 even 30 1089.2.a.w.1.4 4
99.58 even 15 99.2.f.c.91.1 yes 8
99.94 odd 30 1089.2.a.w.1.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
99.2.f.c.37.1 8 9.4 even 3
99.2.f.c.37.2 yes 8 9.5 odd 6
99.2.f.c.91.1 yes 8 99.58 even 15
99.2.f.c.91.2 yes 8 99.14 odd 30
891.2.n.e.136.1 16 9.2 odd 6 inner
891.2.n.e.136.2 16 9.7 even 3 inner
891.2.n.e.190.1 16 33.14 odd 10 inner
891.2.n.e.190.2 16 11.3 even 5 inner
891.2.n.e.433.1 16 1.1 even 1 trivial
891.2.n.e.433.2 16 3.2 odd 2 inner
891.2.n.e.784.1 16 99.25 even 15 inner
891.2.n.e.784.2 16 99.47 odd 30 inner
1089.2.a.v.1.1 4 99.5 odd 30
1089.2.a.v.1.4 4 99.49 even 15
1089.2.a.w.1.1 4 99.94 odd 30
1089.2.a.w.1.4 4 99.50 even 30