Properties

Label 990.2.n.e.91.1
Level $990$
Weight $2$
Character 990.91
Analytic conductor $7.905$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [990,2,Mod(91,990)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(990, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 0, 8]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("990.91");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 990 = 2 \cdot 3^{2} \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 990.n (of order \(5\), degree \(4\), 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: \(7.90518980011\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{10})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{3} + x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 330)
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 91.1
Root \(0.809017 + 0.587785i\) of defining polynomial
Character \(\chi\) \(=\) 990.91
Dual form 990.2.n.e.631.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.809017 - 0.587785i) q^{2} +(0.309017 - 0.951057i) q^{4} +(-0.809017 - 0.587785i) q^{5} +(-1.00000 + 3.07768i) q^{7} +(-0.309017 - 0.951057i) q^{8} +O(q^{10})\) \(q+(0.809017 - 0.587785i) q^{2} +(0.309017 - 0.951057i) q^{4} +(-0.809017 - 0.587785i) q^{5} +(-1.00000 + 3.07768i) q^{7} +(-0.309017 - 0.951057i) q^{8} -1.00000 q^{10} +(-3.04508 + 1.31433i) q^{11} +(-2.73607 + 1.98787i) q^{13} +(1.00000 + 3.07768i) q^{14} +(-0.809017 - 0.587785i) q^{16} +(-4.92705 - 3.57971i) q^{17} +(0.381966 + 1.17557i) q^{19} +(-0.809017 + 0.587785i) q^{20} +(-1.69098 + 2.85317i) q^{22} -6.85410 q^{23} +(0.309017 + 0.951057i) q^{25} +(-1.04508 + 3.21644i) q^{26} +(2.61803 + 1.90211i) q^{28} +(0.809017 - 2.48990i) q^{29} +(1.11803 - 0.812299i) q^{31} -1.00000 q^{32} -6.09017 q^{34} +(2.61803 - 1.90211i) q^{35} +(-1.97214 + 6.06961i) q^{37} +(1.00000 + 0.726543i) q^{38} +(-0.309017 + 0.951057i) q^{40} +(-0.381966 - 1.17557i) q^{41} -0.0901699 q^{43} +(0.309017 + 3.30220i) q^{44} +(-5.54508 + 4.02874i) q^{46} +(1.33688 + 4.11450i) q^{47} +(-2.80902 - 2.04087i) q^{49} +(0.809017 + 0.587785i) q^{50} +(1.04508 + 3.21644i) q^{52} +(6.85410 - 4.97980i) q^{53} +(3.23607 + 0.726543i) q^{55} +3.23607 q^{56} +(-0.809017 - 2.48990i) q^{58} +(-4.35410 + 13.4005i) q^{59} +(0.427051 - 1.31433i) q^{62} +(-0.809017 + 0.587785i) q^{64} +3.38197 q^{65} -5.09017 q^{67} +(-4.92705 + 3.57971i) q^{68} +(1.00000 - 3.07768i) q^{70} +(8.47214 + 6.15537i) q^{71} +(4.14590 - 12.7598i) q^{73} +(1.97214 + 6.06961i) q^{74} +1.23607 q^{76} +(-1.00000 - 10.6861i) q^{77} +(3.30902 - 2.40414i) q^{79} +(0.309017 + 0.951057i) q^{80} +(-1.00000 - 0.726543i) q^{82} +(3.23607 + 2.35114i) q^{83} +(1.88197 + 5.79210i) q^{85} +(-0.0729490 + 0.0530006i) q^{86} +(2.19098 + 2.48990i) q^{88} -17.2361 q^{89} +(-3.38197 - 10.4086i) q^{91} +(-2.11803 + 6.51864i) q^{92} +(3.50000 + 2.54290i) q^{94} +(0.381966 - 1.17557i) q^{95} +(-15.0902 + 10.9637i) q^{97} -3.47214 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + q^{2} - q^{4} - q^{5} - 4 q^{7} + q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + q^{2} - q^{4} - q^{5} - 4 q^{7} + q^{8} - 4 q^{10} - q^{11} - 2 q^{13} + 4 q^{14} - q^{16} - 13 q^{17} + 6 q^{19} - q^{20} - 9 q^{22} - 14 q^{23} - q^{25} + 7 q^{26} + 6 q^{28} + q^{29} - 4 q^{32} - 2 q^{34} + 6 q^{35} + 10 q^{37} + 4 q^{38} + q^{40} - 6 q^{41} + 22 q^{43} - q^{44} - 11 q^{46} + 21 q^{47} - 9 q^{49} + q^{50} - 7 q^{52} + 14 q^{53} + 4 q^{55} + 4 q^{56} - q^{58} - 4 q^{59} - 5 q^{62} - q^{64} + 18 q^{65} + 2 q^{67} - 13 q^{68} + 4 q^{70} + 16 q^{71} + 30 q^{73} - 10 q^{74} - 4 q^{76} - 4 q^{77} + 11 q^{79} - q^{80} - 4 q^{82} + 4 q^{83} + 12 q^{85} - 7 q^{86} + 11 q^{88} - 60 q^{89} - 18 q^{91} - 4 q^{92} + 14 q^{94} + 6 q^{95} - 38 q^{97} + 4 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/990\mathbb{Z}\right)^\times\).

\(n\) \(397\) \(541\) \(551\)
\(\chi(n)\) \(1\) \(e\left(\frac{4}{5}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.809017 0.587785i 0.572061 0.415627i
\(3\) 0 0
\(4\) 0.309017 0.951057i 0.154508 0.475528i
\(5\) −0.809017 0.587785i −0.361803 0.262866i
\(6\) 0 0
\(7\) −1.00000 + 3.07768i −0.377964 + 1.16326i 0.563492 + 0.826121i \(0.309457\pi\)
−0.941457 + 0.337134i \(0.890543\pi\)
\(8\) −0.309017 0.951057i −0.109254 0.336249i
\(9\) 0 0
\(10\) −1.00000 −0.316228
\(11\) −3.04508 + 1.31433i −0.918128 + 0.396285i
\(12\) 0 0
\(13\) −2.73607 + 1.98787i −0.758849 + 0.551336i −0.898557 0.438857i \(-0.855384\pi\)
0.139708 + 0.990193i \(0.455384\pi\)
\(14\) 1.00000 + 3.07768i 0.267261 + 0.822546i
\(15\) 0 0
\(16\) −0.809017 0.587785i −0.202254 0.146946i
\(17\) −4.92705 3.57971i −1.19499 0.868208i −0.201203 0.979550i \(-0.564485\pi\)
−0.993782 + 0.111342i \(0.964485\pi\)
\(18\) 0 0
\(19\) 0.381966 + 1.17557i 0.0876290 + 0.269694i 0.985263 0.171048i \(-0.0547153\pi\)
−0.897634 + 0.440742i \(0.854715\pi\)
\(20\) −0.809017 + 0.587785i −0.180902 + 0.131433i
\(21\) 0 0
\(22\) −1.69098 + 2.85317i −0.360519 + 0.608298i
\(23\) −6.85410 −1.42918 −0.714590 0.699544i \(-0.753386\pi\)
−0.714590 + 0.699544i \(0.753386\pi\)
\(24\) 0 0
\(25\) 0.309017 + 0.951057i 0.0618034 + 0.190211i
\(26\) −1.04508 + 3.21644i −0.204958 + 0.630796i
\(27\) 0 0
\(28\) 2.61803 + 1.90211i 0.494762 + 0.359466i
\(29\) 0.809017 2.48990i 0.150231 0.462363i −0.847416 0.530930i \(-0.821843\pi\)
0.997646 + 0.0685673i \(0.0218428\pi\)
\(30\) 0 0
\(31\) 1.11803 0.812299i 0.200805 0.145893i −0.482839 0.875709i \(-0.660394\pi\)
0.683644 + 0.729816i \(0.260394\pi\)
\(32\) −1.00000 −0.176777
\(33\) 0 0
\(34\) −6.09017 −1.04446
\(35\) 2.61803 1.90211i 0.442529 0.321516i
\(36\) 0 0
\(37\) −1.97214 + 6.06961i −0.324217 + 0.997838i 0.647576 + 0.762001i \(0.275783\pi\)
−0.971793 + 0.235837i \(0.924217\pi\)
\(38\) 1.00000 + 0.726543i 0.162221 + 0.117861i
\(39\) 0 0
\(40\) −0.309017 + 0.951057i −0.0488599 + 0.150375i
\(41\) −0.381966 1.17557i −0.0596531 0.183593i 0.916789 0.399371i \(-0.130771\pi\)
−0.976443 + 0.215778i \(0.930771\pi\)
\(42\) 0 0
\(43\) −0.0901699 −0.0137508 −0.00687539 0.999976i \(-0.502189\pi\)
−0.00687539 + 0.999976i \(0.502189\pi\)
\(44\) 0.309017 + 3.30220i 0.0465861 + 0.497825i
\(45\) 0 0
\(46\) −5.54508 + 4.02874i −0.817578 + 0.594005i
\(47\) 1.33688 + 4.11450i 0.195004 + 0.600161i 0.999977 + 0.00684879i \(0.00218005\pi\)
−0.804972 + 0.593312i \(0.797820\pi\)
\(48\) 0 0
\(49\) −2.80902 2.04087i −0.401288 0.291553i
\(50\) 0.809017 + 0.587785i 0.114412 + 0.0831254i
\(51\) 0 0
\(52\) 1.04508 + 3.21644i 0.144927 + 0.446040i
\(53\) 6.85410 4.97980i 0.941483 0.684028i −0.00729395 0.999973i \(-0.502322\pi\)
0.948777 + 0.315946i \(0.102322\pi\)
\(54\) 0 0
\(55\) 3.23607 + 0.726543i 0.436351 + 0.0979670i
\(56\) 3.23607 0.432438
\(57\) 0 0
\(58\) −0.809017 2.48990i −0.106229 0.326940i
\(59\) −4.35410 + 13.4005i −0.566856 + 1.74460i 0.0955164 + 0.995428i \(0.469550\pi\)
−0.662372 + 0.749175i \(0.730450\pi\)
\(60\) 0 0
\(61\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(62\) 0.427051 1.31433i 0.0542355 0.166920i
\(63\) 0 0
\(64\) −0.809017 + 0.587785i −0.101127 + 0.0734732i
\(65\) 3.38197 0.419481
\(66\) 0 0
\(67\) −5.09017 −0.621863 −0.310932 0.950432i \(-0.600641\pi\)
−0.310932 + 0.950432i \(0.600641\pi\)
\(68\) −4.92705 + 3.57971i −0.597493 + 0.434104i
\(69\) 0 0
\(70\) 1.00000 3.07768i 0.119523 0.367854i
\(71\) 8.47214 + 6.15537i 1.00546 + 0.730508i 0.963251 0.268601i \(-0.0865614\pi\)
0.0422061 + 0.999109i \(0.486561\pi\)
\(72\) 0 0
\(73\) 4.14590 12.7598i 0.485241 1.49342i −0.346391 0.938090i \(-0.612593\pi\)
0.831632 0.555327i \(-0.187407\pi\)
\(74\) 1.97214 + 6.06961i 0.229256 + 0.705578i
\(75\) 0 0
\(76\) 1.23607 0.141787
\(77\) −1.00000 10.6861i −0.113961 1.21780i
\(78\) 0 0
\(79\) 3.30902 2.40414i 0.372293 0.270487i −0.385868 0.922554i \(-0.626098\pi\)
0.758161 + 0.652067i \(0.226098\pi\)
\(80\) 0.309017 + 0.951057i 0.0345492 + 0.106331i
\(81\) 0 0
\(82\) −1.00000 0.726543i −0.110432 0.0802332i
\(83\) 3.23607 + 2.35114i 0.355205 + 0.258071i 0.751049 0.660246i \(-0.229548\pi\)
−0.395845 + 0.918318i \(0.629548\pi\)
\(84\) 0 0
\(85\) 1.88197 + 5.79210i 0.204128 + 0.628241i
\(86\) −0.0729490 + 0.0530006i −0.00786629 + 0.00571520i
\(87\) 0 0
\(88\) 2.19098 + 2.48990i 0.233560 + 0.265424i
\(89\) −17.2361 −1.82702 −0.913510 0.406817i \(-0.866639\pi\)
−0.913510 + 0.406817i \(0.866639\pi\)
\(90\) 0 0
\(91\) −3.38197 10.4086i −0.354526 1.09112i
\(92\) −2.11803 + 6.51864i −0.220820 + 0.679615i
\(93\) 0 0
\(94\) 3.50000 + 2.54290i 0.360997 + 0.262280i
\(95\) 0.381966 1.17557i 0.0391889 0.120611i
\(96\) 0 0
\(97\) −15.0902 + 10.9637i −1.53217 + 1.11319i −0.577160 + 0.816631i \(0.695839\pi\)
−0.955015 + 0.296559i \(0.904161\pi\)
\(98\) −3.47214 −0.350739
\(99\) 0 0
\(100\) 1.00000 0.100000
\(101\) 12.6353 9.18005i 1.25725 0.913449i 0.258635 0.965975i \(-0.416727\pi\)
0.998620 + 0.0525259i \(0.0167272\pi\)
\(102\) 0 0
\(103\) 2.09017 6.43288i 0.205951 0.633851i −0.793722 0.608280i \(-0.791860\pi\)
0.999673 0.0255706i \(-0.00814025\pi\)
\(104\) 2.73607 + 1.98787i 0.268294 + 0.194927i
\(105\) 0 0
\(106\) 2.61803 8.05748i 0.254286 0.782612i
\(107\) −1.94427 5.98385i −0.187960 0.578481i 0.812027 0.583620i \(-0.198364\pi\)
−0.999987 + 0.00513899i \(0.998364\pi\)
\(108\) 0 0
\(109\) −2.47214 −0.236788 −0.118394 0.992967i \(-0.537775\pi\)
−0.118394 + 0.992967i \(0.537775\pi\)
\(110\) 3.04508 1.31433i 0.290337 0.125316i
\(111\) 0 0
\(112\) 2.61803 1.90211i 0.247381 0.179733i
\(113\) 6.04508 + 18.6049i 0.568674 + 1.75020i 0.656775 + 0.754086i \(0.271920\pi\)
−0.0881015 + 0.996112i \(0.528080\pi\)
\(114\) 0 0
\(115\) 5.54508 + 4.02874i 0.517082 + 0.375682i
\(116\) −2.11803 1.53884i −0.196655 0.142878i
\(117\) 0 0
\(118\) 4.35410 + 13.4005i 0.400828 + 1.23362i
\(119\) 15.9443 11.5842i 1.46161 1.06192i
\(120\) 0 0
\(121\) 7.54508 8.00448i 0.685917 0.727680i
\(122\) 0 0
\(123\) 0 0
\(124\) −0.427051 1.31433i −0.0383503 0.118030i
\(125\) 0.309017 0.951057i 0.0276393 0.0850651i
\(126\) 0 0
\(127\) −11.8541 8.61251i −1.05188 0.764237i −0.0793121 0.996850i \(-0.525272\pi\)
−0.972569 + 0.232613i \(0.925272\pi\)
\(128\) −0.309017 + 0.951057i −0.0273135 + 0.0840623i
\(129\) 0 0
\(130\) 2.73607 1.98787i 0.239969 0.174348i
\(131\) 3.38197 0.295484 0.147742 0.989026i \(-0.452800\pi\)
0.147742 + 0.989026i \(0.452800\pi\)
\(132\) 0 0
\(133\) −4.00000 −0.346844
\(134\) −4.11803 + 2.99193i −0.355744 + 0.258463i
\(135\) 0 0
\(136\) −1.88197 + 5.79210i −0.161377 + 0.496668i
\(137\) −10.3541 7.52270i −0.884611 0.642707i 0.0498566 0.998756i \(-0.484124\pi\)
−0.934467 + 0.356049i \(0.884124\pi\)
\(138\) 0 0
\(139\) 2.70820 8.33499i 0.229707 0.706965i −0.768073 0.640363i \(-0.778784\pi\)
0.997780 0.0666024i \(-0.0212159\pi\)
\(140\) −1.00000 3.07768i −0.0845154 0.260112i
\(141\) 0 0
\(142\) 10.4721 0.878802
\(143\) 5.71885 9.64932i 0.478234 0.806917i
\(144\) 0 0
\(145\) −2.11803 + 1.53884i −0.175893 + 0.127794i
\(146\) −4.14590 12.7598i −0.343117 1.05601i
\(147\) 0 0
\(148\) 5.16312 + 3.75123i 0.424406 + 0.308349i
\(149\) −6.16312 4.47777i −0.504902 0.366833i 0.305984 0.952037i \(-0.401015\pi\)
−0.810886 + 0.585204i \(0.801015\pi\)
\(150\) 0 0
\(151\) 6.47214 + 19.9192i 0.526695 + 1.62100i 0.760940 + 0.648823i \(0.224738\pi\)
−0.234245 + 0.972178i \(0.575262\pi\)
\(152\) 1.00000 0.726543i 0.0811107 0.0589304i
\(153\) 0 0
\(154\) −7.09017 8.05748i −0.571342 0.649290i
\(155\) −1.38197 −0.111002
\(156\) 0 0
\(157\) −2.86475 8.81678i −0.228632 0.703656i −0.997903 0.0647330i \(-0.979380\pi\)
0.769271 0.638923i \(-0.220620\pi\)
\(158\) 1.26393 3.88998i 0.100553 0.309470i
\(159\) 0 0
\(160\) 0.809017 + 0.587785i 0.0639584 + 0.0464685i
\(161\) 6.85410 21.0948i 0.540179 1.66250i
\(162\) 0 0
\(163\) −0.690983 + 0.502029i −0.0541220 + 0.0393219i −0.614517 0.788903i \(-0.710649\pi\)
0.560395 + 0.828225i \(0.310649\pi\)
\(164\) −1.23607 −0.0965207
\(165\) 0 0
\(166\) 4.00000 0.310460
\(167\) −10.7361 + 7.80021i −0.830782 + 0.603598i −0.919780 0.392433i \(-0.871633\pi\)
0.0889985 + 0.996032i \(0.471633\pi\)
\(168\) 0 0
\(169\) −0.482779 + 1.48584i −0.0371369 + 0.114295i
\(170\) 4.92705 + 3.57971i 0.377888 + 0.274551i
\(171\) 0 0
\(172\) −0.0278640 + 0.0857567i −0.00212461 + 0.00653889i
\(173\) 2.94427 + 9.06154i 0.223849 + 0.688936i 0.998406 + 0.0564325i \(0.0179726\pi\)
−0.774558 + 0.632503i \(0.782027\pi\)
\(174\) 0 0
\(175\) −3.23607 −0.244624
\(176\) 3.23607 + 0.726543i 0.243928 + 0.0547652i
\(177\) 0 0
\(178\) −13.9443 + 10.1311i −1.04517 + 0.759359i
\(179\) −5.60739 17.2578i −0.419116 1.28991i −0.908517 0.417848i \(-0.862785\pi\)
0.489401 0.872059i \(-0.337215\pi\)
\(180\) 0 0
\(181\) −17.7082 12.8658i −1.31624 0.956305i −0.999971 0.00763529i \(-0.997570\pi\)
−0.316270 0.948669i \(-0.602430\pi\)
\(182\) −8.85410 6.43288i −0.656310 0.476837i
\(183\) 0 0
\(184\) 2.11803 + 6.51864i 0.156144 + 0.480560i
\(185\) 5.16312 3.75123i 0.379600 0.275796i
\(186\) 0 0
\(187\) 19.7082 + 4.42477i 1.44121 + 0.323571i
\(188\) 4.32624 0.315523
\(189\) 0 0
\(190\) −0.381966 1.17557i −0.0277107 0.0852848i
\(191\) −2.85410 + 8.78402i −0.206516 + 0.635590i 0.793132 + 0.609050i \(0.208449\pi\)
−0.999648 + 0.0265400i \(0.991551\pi\)
\(192\) 0 0
\(193\) 16.9443 + 12.3107i 1.21968 + 0.886146i 0.996073 0.0885344i \(-0.0282183\pi\)
0.223602 + 0.974680i \(0.428218\pi\)
\(194\) −5.76393 + 17.7396i −0.413826 + 1.27363i
\(195\) 0 0
\(196\) −2.80902 + 2.04087i −0.200644 + 0.145776i
\(197\) −10.9443 −0.779747 −0.389874 0.920868i \(-0.627481\pi\)
−0.389874 + 0.920868i \(0.627481\pi\)
\(198\) 0 0
\(199\) 25.9787 1.84158 0.920791 0.390056i \(-0.127544\pi\)
0.920791 + 0.390056i \(0.127544\pi\)
\(200\) 0.809017 0.587785i 0.0572061 0.0415627i
\(201\) 0 0
\(202\) 4.82624 14.8536i 0.339573 1.04510i
\(203\) 6.85410 + 4.97980i 0.481064 + 0.349513i
\(204\) 0 0
\(205\) −0.381966 + 1.17557i −0.0266777 + 0.0821054i
\(206\) −2.09017 6.43288i −0.145629 0.448200i
\(207\) 0 0
\(208\) 3.38197 0.234497
\(209\) −2.70820 3.07768i −0.187330 0.212888i
\(210\) 0 0
\(211\) 20.4164 14.8334i 1.40552 1.02117i 0.411569 0.911379i \(-0.364981\pi\)
0.993954 0.109794i \(-0.0350191\pi\)
\(212\) −2.61803 8.05748i −0.179807 0.553390i
\(213\) 0 0
\(214\) −5.09017 3.69822i −0.347957 0.252805i
\(215\) 0.0729490 + 0.0530006i 0.00497508 + 0.00361461i
\(216\) 0 0
\(217\) 1.38197 + 4.25325i 0.0938140 + 0.288730i
\(218\) −2.00000 + 1.45309i −0.135457 + 0.0984153i
\(219\) 0 0
\(220\) 1.69098 2.85317i 0.114006 0.192361i
\(221\) 20.5967 1.38549
\(222\) 0 0
\(223\) 2.23607 + 6.88191i 0.149738 + 0.460847i 0.997590 0.0693868i \(-0.0221043\pi\)
−0.847852 + 0.530234i \(0.822104\pi\)
\(224\) 1.00000 3.07768i 0.0668153 0.205636i
\(225\) 0 0
\(226\) 15.8262 + 11.4984i 1.05275 + 0.764865i
\(227\) −6.29180 + 19.3642i −0.417601 + 1.28524i 0.492302 + 0.870424i \(0.336155\pi\)
−0.909904 + 0.414820i \(0.863845\pi\)
\(228\) 0 0
\(229\) −0.618034 + 0.449028i −0.0408408 + 0.0296726i −0.608018 0.793923i \(-0.708035\pi\)
0.567178 + 0.823596i \(0.308035\pi\)
\(230\) 6.85410 0.451946
\(231\) 0 0
\(232\) −2.61803 −0.171882
\(233\) −3.59017 + 2.60841i −0.235200 + 0.170883i −0.699142 0.714983i \(-0.746435\pi\)
0.463942 + 0.885865i \(0.346435\pi\)
\(234\) 0 0
\(235\) 1.33688 4.11450i 0.0872085 0.268400i
\(236\) 11.3992 + 8.28199i 0.742024 + 0.539112i
\(237\) 0 0
\(238\) 6.09017 18.7436i 0.394767 1.21497i
\(239\) 1.00000 + 3.07768i 0.0646846 + 0.199079i 0.978175 0.207780i \(-0.0666240\pi\)
−0.913491 + 0.406859i \(0.866624\pi\)
\(240\) 0 0
\(241\) −23.8885 −1.53880 −0.769398 0.638769i \(-0.779444\pi\)
−0.769398 + 0.638769i \(0.779444\pi\)
\(242\) 1.39919 10.9106i 0.0899431 0.701363i
\(243\) 0 0
\(244\) 0 0
\(245\) 1.07295 + 3.30220i 0.0685482 + 0.210970i
\(246\) 0 0
\(247\) −3.38197 2.45714i −0.215189 0.156344i
\(248\) −1.11803 0.812299i −0.0709952 0.0515811i
\(249\) 0 0
\(250\) −0.309017 0.951057i −0.0195440 0.0601501i
\(251\) 6.78115 4.92680i 0.428023 0.310977i −0.352835 0.935685i \(-0.614782\pi\)
0.780858 + 0.624709i \(0.214782\pi\)
\(252\) 0 0
\(253\) 20.8713 9.00854i 1.31217 0.566362i
\(254\) −14.6525 −0.919378
\(255\) 0 0
\(256\) 0.309017 + 0.951057i 0.0193136 + 0.0594410i
\(257\) −9.38197 + 28.8747i −0.585231 + 1.80116i 0.0131100 + 0.999914i \(0.495827\pi\)
−0.598341 + 0.801242i \(0.704173\pi\)
\(258\) 0 0
\(259\) −16.7082 12.1392i −1.03820 0.754294i
\(260\) 1.04508 3.21644i 0.0648134 0.199475i
\(261\) 0 0
\(262\) 2.73607 1.98787i 0.169035 0.122811i
\(263\) −6.85410 −0.422642 −0.211321 0.977417i \(-0.567777\pi\)
−0.211321 + 0.977417i \(0.567777\pi\)
\(264\) 0 0
\(265\) −8.47214 −0.520439
\(266\) −3.23607 + 2.35114i −0.198416 + 0.144158i
\(267\) 0 0
\(268\) −1.57295 + 4.84104i −0.0960832 + 0.295714i
\(269\) 2.59017 + 1.88187i 0.157925 + 0.114740i 0.663942 0.747784i \(-0.268882\pi\)
−0.506016 + 0.862524i \(0.668882\pi\)
\(270\) 0 0
\(271\) −1.97214 + 6.06961i −0.119799 + 0.368703i −0.992918 0.118805i \(-0.962094\pi\)
0.873119 + 0.487507i \(0.162094\pi\)
\(272\) 1.88197 + 5.79210i 0.114111 + 0.351197i
\(273\) 0 0
\(274\) −12.7984 −0.773178
\(275\) −2.19098 2.48990i −0.132121 0.150147i
\(276\) 0 0
\(277\) 19.0172 13.8168i 1.14263 0.830172i 0.155150 0.987891i \(-0.450414\pi\)
0.987484 + 0.157719i \(0.0504139\pi\)
\(278\) −2.70820 8.33499i −0.162427 0.499900i
\(279\) 0 0
\(280\) −2.61803 1.90211i −0.156457 0.113673i
\(281\) −6.09017 4.42477i −0.363309 0.263959i 0.391122 0.920339i \(-0.372087\pi\)
−0.754431 + 0.656379i \(0.772087\pi\)
\(282\) 0 0
\(283\) −6.89919 21.2335i −0.410114 1.26220i −0.916549 0.399923i \(-0.869037\pi\)
0.506435 0.862278i \(-0.330963\pi\)
\(284\) 8.47214 6.15537i 0.502729 0.365254i
\(285\) 0 0
\(286\) −1.04508 11.1679i −0.0617972 0.660373i
\(287\) 4.00000 0.236113
\(288\) 0 0
\(289\) 6.20820 + 19.1069i 0.365188 + 1.12393i
\(290\) −0.809017 + 2.48990i −0.0475071 + 0.146212i
\(291\) 0 0
\(292\) −10.8541 7.88597i −0.635188 0.461491i
\(293\) 6.18034 19.0211i 0.361059 1.11123i −0.591353 0.806413i \(-0.701406\pi\)
0.952412 0.304813i \(-0.0985941\pi\)
\(294\) 0 0
\(295\) 11.3992 8.28199i 0.663686 0.482196i
\(296\) 6.38197 0.370944
\(297\) 0 0
\(298\) −7.61803 −0.441301
\(299\) 18.7533 13.6251i 1.08453 0.787958i
\(300\) 0 0
\(301\) 0.0901699 0.277515i 0.00519731 0.0159957i
\(302\) 16.9443 + 12.3107i 0.975033 + 0.708403i
\(303\) 0 0
\(304\) 0.381966 1.17557i 0.0219073 0.0674236i
\(305\) 0 0
\(306\) 0 0
\(307\) −33.4508 −1.90914 −0.954570 0.297985i \(-0.903685\pi\)
−0.954570 + 0.297985i \(0.903685\pi\)
\(308\) −10.4721 2.35114i −0.596705 0.133969i
\(309\) 0 0
\(310\) −1.11803 + 0.812299i −0.0635001 + 0.0461355i
\(311\) −2.85410 8.78402i −0.161841 0.498096i 0.836948 0.547282i \(-0.184337\pi\)
−0.998790 + 0.0491856i \(0.984337\pi\)
\(312\) 0 0
\(313\) −6.85410 4.97980i −0.387417 0.281475i 0.376979 0.926222i \(-0.376963\pi\)
−0.764396 + 0.644747i \(0.776963\pi\)
\(314\) −7.50000 5.44907i −0.423249 0.307509i
\(315\) 0 0
\(316\) −1.26393 3.88998i −0.0711017 0.218829i
\(317\) −22.1803 + 16.1150i −1.24577 + 0.905106i −0.997969 0.0637041i \(-0.979709\pi\)
−0.247803 + 0.968810i \(0.579709\pi\)
\(318\) 0 0
\(319\) 0.809017 + 8.64527i 0.0452963 + 0.484042i
\(320\) 1.00000 0.0559017
\(321\) 0 0
\(322\) −6.85410 21.0948i −0.381964 1.17556i
\(323\) 2.32624 7.15942i 0.129435 0.398361i
\(324\) 0 0
\(325\) −2.73607 1.98787i −0.151770 0.110267i
\(326\) −0.263932 + 0.812299i −0.0146178 + 0.0449891i
\(327\) 0 0
\(328\) −1.00000 + 0.726543i −0.0552158 + 0.0401166i
\(329\) −14.0000 −0.771845
\(330\) 0 0
\(331\) 9.23607 0.507660 0.253830 0.967249i \(-0.418310\pi\)
0.253830 + 0.967249i \(0.418310\pi\)
\(332\) 3.23607 2.35114i 0.177602 0.129036i
\(333\) 0 0
\(334\) −4.10081 + 12.6210i −0.224387 + 0.690591i
\(335\) 4.11803 + 2.99193i 0.224992 + 0.163466i
\(336\) 0 0
\(337\) −4.70820 + 14.4904i −0.256472 + 0.789340i 0.737064 + 0.675823i \(0.236212\pi\)
−0.993536 + 0.113517i \(0.963788\pi\)
\(338\) 0.482779 + 1.48584i 0.0262597 + 0.0808191i
\(339\) 0 0
\(340\) 6.09017 0.330286
\(341\) −2.33688 + 3.94298i −0.126549 + 0.213525i
\(342\) 0 0
\(343\) −9.23607 + 6.71040i −0.498701 + 0.362327i
\(344\) 0.0278640 + 0.0857567i 0.00150233 + 0.00462369i
\(345\) 0 0
\(346\) 7.70820 + 5.60034i 0.414396 + 0.301076i
\(347\) 29.0344 + 21.0948i 1.55865 + 1.13243i 0.937105 + 0.349048i \(0.113495\pi\)
0.621546 + 0.783378i \(0.286505\pi\)
\(348\) 0 0
\(349\) −3.52786 10.8576i −0.188842 0.581197i 0.811151 0.584837i \(-0.198841\pi\)
−0.999993 + 0.00363995i \(0.998841\pi\)
\(350\) −2.61803 + 1.90211i −0.139940 + 0.101672i
\(351\) 0 0
\(352\) 3.04508 1.31433i 0.162304 0.0700539i
\(353\) −23.6180 −1.25706 −0.628531 0.777785i \(-0.716343\pi\)
−0.628531 + 0.777785i \(0.716343\pi\)
\(354\) 0 0
\(355\) −3.23607 9.95959i −0.171753 0.528600i
\(356\) −5.32624 + 16.3925i −0.282290 + 0.868799i
\(357\) 0 0
\(358\) −14.6803 10.6659i −0.775880 0.563710i
\(359\) 3.76393 11.5842i 0.198653 0.611390i −0.801262 0.598314i \(-0.795838\pi\)
0.999915 0.0130763i \(-0.00416243\pi\)
\(360\) 0 0
\(361\) 14.1353 10.2699i 0.743961 0.540519i
\(362\) −21.8885 −1.15044
\(363\) 0 0
\(364\) −10.9443 −0.573636
\(365\) −10.8541 + 7.88597i −0.568130 + 0.412770i
\(366\) 0 0
\(367\) −8.27051 + 25.4540i −0.431717 + 1.32869i 0.464696 + 0.885470i \(0.346163\pi\)
−0.896414 + 0.443219i \(0.853837\pi\)
\(368\) 5.54508 + 4.02874i 0.289058 + 0.210013i
\(369\) 0 0
\(370\) 1.97214 6.06961i 0.102526 0.315544i
\(371\) 8.47214 + 26.0746i 0.439851 + 1.35372i
\(372\) 0 0
\(373\) −11.5279 −0.596890 −0.298445 0.954427i \(-0.596468\pi\)
−0.298445 + 0.954427i \(0.596468\pi\)
\(374\) 18.5451 8.00448i 0.958944 0.413902i
\(375\) 0 0
\(376\) 3.50000 2.54290i 0.180499 0.131140i
\(377\) 2.73607 + 8.42075i 0.140915 + 0.433691i
\(378\) 0 0
\(379\) 10.0000 + 7.26543i 0.513665 + 0.373200i 0.814212 0.580567i \(-0.197169\pi\)
−0.300547 + 0.953767i \(0.597169\pi\)
\(380\) −1.00000 0.726543i −0.0512989 0.0372708i
\(381\) 0 0
\(382\) 2.85410 + 8.78402i 0.146029 + 0.449430i
\(383\) −0.263932 + 0.191758i −0.0134863 + 0.00979837i −0.594508 0.804090i \(-0.702653\pi\)
0.581022 + 0.813888i \(0.302653\pi\)
\(384\) 0 0
\(385\) −5.47214 + 9.23305i −0.278886 + 0.470560i
\(386\) 20.9443 1.06604
\(387\) 0 0
\(388\) 5.76393 + 17.7396i 0.292619 + 0.900590i
\(389\) −2.11803 + 6.51864i −0.107389 + 0.330508i −0.990284 0.139062i \(-0.955591\pi\)
0.882895 + 0.469570i \(0.155591\pi\)
\(390\) 0 0
\(391\) 33.7705 + 24.5357i 1.70785 + 1.24082i
\(392\) −1.07295 + 3.30220i −0.0541921 + 0.166786i
\(393\) 0 0
\(394\) −8.85410 + 6.43288i −0.446063 + 0.324084i
\(395\) −4.09017 −0.205799
\(396\) 0 0
\(397\) 2.20163 0.110496 0.0552482 0.998473i \(-0.482405\pi\)
0.0552482 + 0.998473i \(0.482405\pi\)
\(398\) 21.0172 15.2699i 1.05350 0.765411i
\(399\) 0 0
\(400\) 0.309017 0.951057i 0.0154508 0.0475528i
\(401\) 17.8541 + 12.9718i 0.891591 + 0.647779i 0.936292 0.351221i \(-0.114234\pi\)
−0.0447011 + 0.999000i \(0.514234\pi\)
\(402\) 0 0
\(403\) −1.44427 + 4.44501i −0.0719443 + 0.221422i
\(404\) −4.82624 14.8536i −0.240114 0.738996i
\(405\) 0 0
\(406\) 8.47214 0.420465
\(407\) −1.97214 21.0745i −0.0977551 1.04462i
\(408\) 0 0
\(409\) −10.5000 + 7.62870i −0.519192 + 0.377215i −0.816299 0.577629i \(-0.803978\pi\)
0.297108 + 0.954844i \(0.403978\pi\)
\(410\) 0.381966 + 1.17557i 0.0188640 + 0.0580573i
\(411\) 0 0
\(412\) −5.47214 3.97574i −0.269593 0.195871i
\(413\) −36.8885 26.8011i −1.81517 1.31880i
\(414\) 0 0
\(415\) −1.23607 3.80423i −0.0606762 0.186742i
\(416\) 2.73607 1.98787i 0.134147 0.0974633i
\(417\) 0 0
\(418\) −4.00000 0.898056i −0.195646 0.0439254i
\(419\) −22.8541 −1.11650 −0.558248 0.829674i \(-0.688526\pi\)
−0.558248 + 0.829674i \(0.688526\pi\)
\(420\) 0 0
\(421\) −0.763932 2.35114i −0.0372318 0.114588i 0.930713 0.365750i \(-0.119187\pi\)
−0.967945 + 0.251162i \(0.919187\pi\)
\(422\) 7.79837 24.0009i 0.379619 1.16835i
\(423\) 0 0
\(424\) −6.85410 4.97980i −0.332865 0.241840i
\(425\) 1.88197 5.79210i 0.0912888 0.280958i
\(426\) 0 0
\(427\) 0 0
\(428\) −6.29180 −0.304125
\(429\) 0 0
\(430\) 0.0901699 0.00434838
\(431\) 18.0902 13.1433i 0.871373 0.633089i −0.0595822 0.998223i \(-0.518977\pi\)
0.930955 + 0.365134i \(0.118977\pi\)
\(432\) 0 0
\(433\) −7.05573 + 21.7153i −0.339077 + 1.04357i 0.625602 + 0.780142i \(0.284853\pi\)
−0.964679 + 0.263428i \(0.915147\pi\)
\(434\) 3.61803 + 2.62866i 0.173671 + 0.126180i
\(435\) 0 0
\(436\) −0.763932 + 2.35114i −0.0365857 + 0.112599i
\(437\) −2.61803 8.05748i −0.125238 0.385442i
\(438\) 0 0
\(439\) 1.67376 0.0798843 0.0399422 0.999202i \(-0.487283\pi\)
0.0399422 + 0.999202i \(0.487283\pi\)
\(440\) −0.309017 3.30220i −0.0147318 0.157426i
\(441\) 0 0
\(442\) 16.6631 12.1065i 0.792584 0.575846i
\(443\) 5.76393 + 17.7396i 0.273853 + 0.842832i 0.989521 + 0.144391i \(0.0461224\pi\)
−0.715668 + 0.698441i \(0.753878\pi\)
\(444\) 0 0
\(445\) 13.9443 + 10.1311i 0.661022 + 0.480261i
\(446\) 5.85410 + 4.25325i 0.277200 + 0.201397i
\(447\) 0 0
\(448\) −1.00000 3.07768i −0.0472456 0.145407i
\(449\) −9.00000 + 6.53888i −0.424736 + 0.308589i −0.779541 0.626352i \(-0.784547\pi\)
0.354804 + 0.934941i \(0.384547\pi\)
\(450\) 0 0
\(451\) 2.70820 + 3.07768i 0.127524 + 0.144922i
\(452\) 19.5623 0.920133
\(453\) 0 0
\(454\) 6.29180 + 19.3642i 0.295289 + 0.908805i
\(455\) −3.38197 + 10.4086i −0.158549 + 0.487964i
\(456\) 0 0
\(457\) −3.76393 2.73466i −0.176069 0.127922i 0.496260 0.868174i \(-0.334706\pi\)
−0.672330 + 0.740252i \(0.734706\pi\)
\(458\) −0.236068 + 0.726543i −0.0110307 + 0.0339491i
\(459\) 0 0
\(460\) 5.54508 4.02874i 0.258541 0.187841i
\(461\) −23.2148 −1.08122 −0.540610 0.841273i \(-0.681807\pi\)
−0.540610 + 0.841273i \(0.681807\pi\)
\(462\) 0 0
\(463\) 11.8885 0.552507 0.276254 0.961085i \(-0.410907\pi\)
0.276254 + 0.961085i \(0.410907\pi\)
\(464\) −2.11803 + 1.53884i −0.0983273 + 0.0714389i
\(465\) 0 0
\(466\) −1.37132 + 4.22050i −0.0635253 + 0.195511i
\(467\) 23.0902 + 16.7760i 1.06849 + 0.776300i 0.975639 0.219380i \(-0.0704035\pi\)
0.0928462 + 0.995680i \(0.470404\pi\)
\(468\) 0 0
\(469\) 5.09017 15.6659i 0.235042 0.723386i
\(470\) −1.33688 4.11450i −0.0616657 0.189788i
\(471\) 0 0
\(472\) 14.0902 0.648553
\(473\) 0.274575 0.118513i 0.0126250 0.00544923i
\(474\) 0 0
\(475\) −1.00000 + 0.726543i −0.0458831 + 0.0333361i
\(476\) −6.09017 18.7436i −0.279142 0.859112i
\(477\) 0 0
\(478\) 2.61803 + 1.90211i 0.119746 + 0.0870006i
\(479\) 10.3262 + 7.50245i 0.471818 + 0.342796i 0.798149 0.602460i \(-0.205813\pi\)
−0.326331 + 0.945255i \(0.605813\pi\)
\(480\) 0 0
\(481\) −6.66970 20.5272i −0.304112 0.935960i
\(482\) −19.3262 + 14.0413i −0.880286 + 0.639565i
\(483\) 0 0
\(484\) −5.28115 9.64932i −0.240052 0.438606i
\(485\) 18.6525 0.846965
\(486\) 0 0
\(487\) 3.52786 + 10.8576i 0.159863 + 0.492007i 0.998621 0.0524969i \(-0.0167180\pi\)
−0.838758 + 0.544504i \(0.816718\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 2.80902 + 2.04087i 0.126898 + 0.0921971i
\(491\) −8.66312 + 26.6623i −0.390961 + 1.20325i 0.541102 + 0.840957i \(0.318007\pi\)
−0.932063 + 0.362297i \(0.881993\pi\)
\(492\) 0 0
\(493\) −12.8992 + 9.37181i −0.580950 + 0.422085i
\(494\) −4.18034 −0.188082
\(495\) 0 0
\(496\) −1.38197 −0.0620521
\(497\) −27.4164 + 19.9192i −1.22979 + 0.893498i
\(498\) 0 0
\(499\) −10.0344 + 30.8828i −0.449203 + 1.38251i 0.428604 + 0.903492i \(0.359005\pi\)
−0.877808 + 0.479013i \(0.840995\pi\)
\(500\) −0.809017 0.587785i −0.0361803 0.0262866i
\(501\) 0 0
\(502\) 2.59017 7.97172i 0.115605 0.355795i
\(503\) 7.51722 + 23.1356i 0.335176 + 1.03157i 0.966635 + 0.256157i \(0.0824565\pi\)
−0.631459 + 0.775409i \(0.717544\pi\)
\(504\) 0 0
\(505\) −15.6180 −0.694993
\(506\) 11.5902 19.5559i 0.515246 0.869366i
\(507\) 0 0
\(508\) −11.8541 + 8.61251i −0.525941 + 0.382118i
\(509\) −2.71885 8.36775i −0.120511 0.370894i 0.872546 0.488532i \(-0.162468\pi\)
−0.993056 + 0.117638i \(0.962468\pi\)
\(510\) 0 0
\(511\) 35.1246 + 25.5195i 1.55382 + 1.12892i
\(512\) 0.809017 + 0.587785i 0.0357538 + 0.0259767i
\(513\) 0 0
\(514\) 9.38197 + 28.8747i 0.413821 + 1.27361i
\(515\) −5.47214 + 3.97574i −0.241131 + 0.175192i
\(516\) 0 0
\(517\) −9.47871 10.7719i −0.416873 0.473747i
\(518\) −20.6525 −0.907418
\(519\) 0 0
\(520\) −1.04508 3.21644i −0.0458300 0.141050i
\(521\) 0.729490 2.24514i 0.0319595 0.0983614i −0.933804 0.357784i \(-0.883532\pi\)
0.965764 + 0.259423i \(0.0835323\pi\)
\(522\) 0 0
\(523\) −31.4164 22.8254i −1.37374 0.998083i −0.997434 0.0715891i \(-0.977193\pi\)
−0.376309 0.926494i \(-0.622807\pi\)
\(524\) 1.04508 3.21644i 0.0456547 0.140511i
\(525\) 0 0
\(526\) −5.54508 + 4.02874i −0.241777 + 0.175661i
\(527\) −8.41641 −0.366624
\(528\) 0 0
\(529\) 23.9787 1.04255
\(530\) −6.85410 + 4.97980i −0.297723 + 0.216309i
\(531\) 0 0
\(532\) −1.23607 + 3.80423i −0.0535903 + 0.164934i
\(533\) 3.38197 + 2.45714i 0.146489 + 0.106431i
\(534\) 0 0
\(535\) −1.94427 + 5.98385i −0.0840582 + 0.258705i
\(536\) 1.57295 + 4.84104i 0.0679410 + 0.209101i
\(537\) 0 0
\(538\) 3.20163 0.138032
\(539\) 11.2361 + 2.52265i 0.483972 + 0.108658i
\(540\) 0 0
\(541\) −21.0902 + 15.3229i −0.906737 + 0.658783i −0.940188 0.340657i \(-0.889350\pi\)
0.0334503 + 0.999440i \(0.489350\pi\)
\(542\) 1.97214 + 6.06961i 0.0847105 + 0.260712i
\(543\) 0 0
\(544\) 4.92705 + 3.57971i 0.211246 + 0.153479i
\(545\) 2.00000 + 1.45309i 0.0856706 + 0.0622433i
\(546\) 0 0
\(547\) 10.6074 + 32.6462i 0.453539 + 1.39585i 0.872842 + 0.488004i \(0.162275\pi\)
−0.419302 + 0.907847i \(0.637725\pi\)
\(548\) −10.3541 + 7.52270i −0.442305 + 0.321354i
\(549\) 0 0
\(550\) −3.23607 0.726543i −0.137986 0.0309799i
\(551\) 3.23607 0.137861
\(552\) 0 0
\(553\) 4.09017 + 12.5882i 0.173932 + 0.535307i
\(554\) 7.26393 22.3561i 0.308615 0.949819i
\(555\) 0 0
\(556\) −7.09017 5.15131i −0.300690 0.218464i
\(557\) 10.8541 33.4055i 0.459903 1.41544i −0.405378 0.914149i \(-0.632860\pi\)
0.865281 0.501287i \(-0.167140\pi\)
\(558\) 0 0
\(559\) 0.246711 0.179246i 0.0104348 0.00758130i
\(560\) −3.23607 −0.136749
\(561\) 0 0
\(562\) −7.52786 −0.317544
\(563\) 13.7984 10.0251i 0.581532 0.422508i −0.257744 0.966213i \(-0.582979\pi\)
0.839276 + 0.543705i \(0.182979\pi\)
\(564\) 0 0
\(565\) 6.04508 18.6049i 0.254319 0.782712i
\(566\) −18.0623 13.1230i −0.759215 0.551602i
\(567\) 0 0
\(568\) 3.23607 9.95959i 0.135782 0.417895i
\(569\) 7.85410 + 24.1724i 0.329261 + 1.01336i 0.969480 + 0.245169i \(0.0788435\pi\)
−0.640219 + 0.768192i \(0.721156\pi\)
\(570\) 0 0
\(571\) −28.3607 −1.18686 −0.593429 0.804887i \(-0.702226\pi\)
−0.593429 + 0.804887i \(0.702226\pi\)
\(572\) −7.40983 8.42075i −0.309821 0.352089i
\(573\) 0 0
\(574\) 3.23607 2.35114i 0.135071 0.0981347i
\(575\) −2.11803 6.51864i −0.0883281 0.271846i
\(576\) 0 0
\(577\) −13.7984 10.0251i −0.574434 0.417351i 0.262279 0.964992i \(-0.415526\pi\)
−0.836713 + 0.547641i \(0.815526\pi\)
\(578\) 16.2533 + 11.8087i 0.676048 + 0.491177i
\(579\) 0 0
\(580\) 0.809017 + 2.48990i 0.0335926 + 0.103387i
\(581\) −10.4721 + 7.60845i −0.434457 + 0.315652i
\(582\) 0 0
\(583\) −14.3262 + 24.1724i −0.593332 + 1.00112i
\(584\) −13.4164 −0.555175
\(585\) 0 0
\(586\) −6.18034 19.0211i −0.255307 0.785756i
\(587\) 8.12461 25.0050i 0.335339 1.03207i −0.631216 0.775607i \(-0.717444\pi\)
0.966555 0.256459i \(-0.0825560\pi\)
\(588\) 0 0
\(589\) 1.38197 + 1.00406i 0.0569429 + 0.0413715i
\(590\) 4.35410 13.4005i 0.179256 0.551692i
\(591\) 0 0
\(592\) 5.16312 3.75123i 0.212203 0.154174i
\(593\) 17.6738 0.725774 0.362887 0.931833i \(-0.381791\pi\)
0.362887 + 0.931833i \(0.381791\pi\)
\(594\) 0 0
\(595\) −19.7082 −0.807958
\(596\) −6.16312 + 4.47777i −0.252451 + 0.183417i
\(597\) 0 0
\(598\) 7.16312 22.0458i 0.292922 0.901520i
\(599\) 14.7082 + 10.6861i 0.600961 + 0.436624i 0.846220 0.532834i \(-0.178873\pi\)
−0.245259 + 0.969458i \(0.578873\pi\)
\(600\) 0 0
\(601\) −5.85410 + 18.0171i −0.238794 + 0.734932i 0.757802 + 0.652485i \(0.226273\pi\)
−0.996595 + 0.0824468i \(0.973727\pi\)
\(602\) −0.0901699 0.277515i −0.00367505 0.0113106i
\(603\) 0 0
\(604\) 20.9443 0.852210
\(605\) −10.8090 + 2.04087i −0.439449 + 0.0829732i
\(606\) 0 0
\(607\) 3.61803 2.62866i 0.146851 0.106694i −0.511934 0.859025i \(-0.671071\pi\)
0.658785 + 0.752331i \(0.271071\pi\)
\(608\) −0.381966 1.17557i −0.0154908 0.0476757i
\(609\) 0 0
\(610\) 0 0
\(611\) −11.8369 8.60000i −0.478869 0.347919i
\(612\) 0 0
\(613\) 1.85410 + 5.70634i 0.0748865 + 0.230477i 0.981492 0.191502i \(-0.0613357\pi\)
−0.906606 + 0.421979i \(0.861336\pi\)
\(614\) −27.0623 + 19.6619i −1.09215 + 0.793490i
\(615\) 0 0
\(616\) −9.85410 + 4.25325i −0.397033 + 0.171368i
\(617\) −26.3607 −1.06124 −0.530621 0.847610i \(-0.678041\pi\)
−0.530621 + 0.847610i \(0.678041\pi\)
\(618\) 0 0
\(619\) 2.94427 + 9.06154i 0.118340 + 0.364214i 0.992629 0.121192i \(-0.0386717\pi\)
−0.874289 + 0.485406i \(0.838672\pi\)
\(620\) −0.427051 + 1.31433i −0.0171508 + 0.0527847i
\(621\) 0 0
\(622\) −7.47214 5.42882i −0.299605 0.217676i
\(623\) 17.2361 53.0472i 0.690548 2.12529i
\(624\) 0 0
\(625\) −0.809017 + 0.587785i −0.0323607 + 0.0235114i
\(626\) −8.47214 −0.338615
\(627\) 0 0
\(628\) −9.27051 −0.369934
\(629\) 31.4443 22.8456i 1.25377 0.910914i
\(630\) 0 0
\(631\) −1.75329 + 5.39607i −0.0697973 + 0.214814i −0.979871 0.199633i \(-0.936025\pi\)
0.910073 + 0.414447i \(0.136025\pi\)
\(632\) −3.30902 2.40414i −0.131626 0.0956316i
\(633\) 0 0
\(634\) −8.47214 + 26.0746i −0.336472 + 1.03555i
\(635\) 4.52786 + 13.9353i 0.179683 + 0.553007i
\(636\) 0 0
\(637\) 11.7426 0.465261
\(638\) 5.73607 + 6.51864i 0.227093 + 0.258075i
\(639\) 0 0
\(640\) 0.809017 0.587785i 0.0319792 0.0232343i
\(641\) −3.76393 11.5842i −0.148666 0.457548i 0.848798 0.528717i \(-0.177327\pi\)
−0.997464 + 0.0711694i \(0.977327\pi\)
\(642\) 0 0
\(643\) 3.88197 + 2.82041i 0.153090 + 0.111226i 0.661693 0.749775i \(-0.269838\pi\)
−0.508604 + 0.861001i \(0.669838\pi\)
\(644\) −17.9443 13.0373i −0.707103 0.513741i
\(645\) 0 0
\(646\) −2.32624 7.15942i −0.0915246 0.281684i
\(647\) −10.0172 + 7.27794i −0.393818 + 0.286125i −0.767018 0.641625i \(-0.778260\pi\)
0.373200 + 0.927751i \(0.378260\pi\)
\(648\) 0 0
\(649\) −4.35410 46.5285i −0.170913 1.82640i
\(650\) −3.38197 −0.132652
\(651\) 0 0
\(652\) 0.263932 + 0.812299i 0.0103364 + 0.0318121i
\(653\) −7.58359 + 23.3399i −0.296769 + 0.913361i 0.685853 + 0.727740i \(0.259429\pi\)
−0.982622 + 0.185620i \(0.940571\pi\)
\(654\) 0 0
\(655\) −2.73607 1.98787i −0.106907 0.0776725i
\(656\) −0.381966 + 1.17557i −0.0149133 + 0.0458983i
\(657\) 0 0
\(658\) −11.3262 + 8.22899i −0.441543 + 0.320800i
\(659\) 15.4164 0.600538 0.300269 0.953855i \(-0.402924\pi\)
0.300269 + 0.953855i \(0.402924\pi\)
\(660\) 0 0
\(661\) 8.36068 0.325193 0.162596 0.986693i \(-0.448013\pi\)
0.162596 + 0.986693i \(0.448013\pi\)
\(662\) 7.47214 5.42882i 0.290413 0.210997i
\(663\) 0 0
\(664\) 1.23607 3.80423i 0.0479687 0.147633i
\(665\) 3.23607 + 2.35114i 0.125489 + 0.0911733i
\(666\) 0 0
\(667\) −5.54508 + 17.0660i −0.214707 + 0.660799i
\(668\) 4.10081 + 12.6210i 0.158665 + 0.488321i
\(669\) 0 0
\(670\) 5.09017 0.196650
\(671\) 0 0
\(672\) 0 0
\(673\) 12.7082 9.23305i 0.489865 0.355908i −0.315267 0.949003i \(-0.602094\pi\)
0.805132 + 0.593095i \(0.202094\pi\)
\(674\) 4.70820 + 14.4904i 0.181353 + 0.558148i
\(675\) 0 0
\(676\) 1.26393 + 0.918300i 0.0486128 + 0.0353192i
\(677\) 22.0344 + 16.0090i 0.846852 + 0.615274i 0.924276 0.381724i \(-0.124670\pi\)
−0.0774240 + 0.996998i \(0.524670\pi\)
\(678\) 0 0
\(679\) −18.6525 57.4064i −0.715816 2.20306i
\(680\) 4.92705 3.57971i 0.188944 0.137276i
\(681\) 0 0
\(682\) 0.427051 + 4.56352i 0.0163526 + 0.174746i
\(683\) −21.1246 −0.808311 −0.404155 0.914690i \(-0.632435\pi\)
−0.404155 + 0.914690i \(0.632435\pi\)
\(684\) 0 0
\(685\) 3.95492 + 12.1720i 0.151110 + 0.465067i
\(686\) −3.52786 + 10.8576i −0.134694 + 0.414547i
\(687\) 0 0
\(688\) 0.0729490 + 0.0530006i 0.00278116 + 0.00202063i
\(689\) −8.85410 + 27.2501i −0.337314 + 1.03815i
\(690\) 0 0
\(691\) 16.7082 12.1392i 0.635610 0.461798i −0.222729 0.974880i \(-0.571497\pi\)
0.858339 + 0.513083i \(0.171497\pi\)
\(692\) 9.52786 0.362195
\(693\) 0 0
\(694\) 35.8885 1.36231
\(695\) −7.09017 + 5.15131i −0.268945 + 0.195400i
\(696\) 0 0
\(697\) −2.32624 + 7.15942i −0.0881125 + 0.271183i
\(698\) −9.23607 6.71040i −0.349590 0.253992i
\(699\) 0 0
\(700\) −1.00000 + 3.07768i −0.0377964 + 0.116326i
\(701\) 1.09017 + 3.35520i 0.0411752 + 0.126724i 0.969531 0.244968i \(-0.0787776\pi\)
−0.928356 + 0.371692i \(0.878778\pi\)
\(702\) 0 0
\(703\) −7.88854 −0.297522
\(704\) 1.69098 2.85317i 0.0637313 0.107533i
\(705\) 0 0
\(706\) −19.1074 + 13.8823i −0.719116 + 0.522468i
\(707\) 15.6180 + 48.0674i 0.587377 + 1.80776i
\(708\) 0 0
\(709\) 8.56231 + 6.22088i 0.321564 + 0.233630i 0.736843 0.676064i \(-0.236316\pi\)
−0.415278 + 0.909694i \(0.636316\pi\)
\(710\) −8.47214 6.15537i −0.317954 0.231007i
\(711\) 0 0
\(712\) 5.32624 + 16.3925i 0.199609 + 0.614334i
\(713\) −7.66312 + 5.56758i −0.286986 + 0.208508i
\(714\) 0 0
\(715\) −10.2984 + 4.44501i −0.385137 + 0.166234i
\(716\) −18.1459 −0.678144
\(717\) 0 0
\(718\) −3.76393 11.5842i −0.140469 0.432318i
\(719\) −12.5623 + 38.6628i −0.468495 + 1.44188i 0.386038 + 0.922483i \(0.373843\pi\)
−0.854533 + 0.519397i \(0.826157\pi\)
\(720\) 0 0
\(721\) 17.7082 + 12.8658i 0.659488 + 0.479146i
\(722\) 5.39919 16.6170i 0.200937 0.618420i
\(723\) 0 0
\(724\) −17.7082 + 12.8658i −0.658120 + 0.478152i
\(725\) 2.61803 0.0972313
\(726\) 0 0
\(727\) −50.1803 −1.86109 −0.930543 0.366183i \(-0.880664\pi\)
−0.930543 + 0.366183i \(0.880664\pi\)
\(728\) −8.85410 + 6.43288i −0.328155 + 0.238418i
\(729\) 0 0
\(730\) −4.14590 + 12.7598i −0.153447 + 0.472260i
\(731\) 0.444272 + 0.322782i 0.0164320 + 0.0119385i
\(732\) 0 0
\(733\) 15.8607 48.8142i 0.585828 1.80299i −0.0100937 0.999949i \(-0.503213\pi\)
0.595921 0.803043i \(-0.296787\pi\)
\(734\) 8.27051 + 25.4540i 0.305270 + 0.939525i
\(735\) 0 0
\(736\) 6.85410 0.252646
\(737\) 15.5000 6.69015i 0.570950 0.246435i
\(738\) 0 0
\(739\) −21.8541 + 15.8779i −0.803916 + 0.584079i −0.912060 0.410056i \(-0.865509\pi\)
0.108144 + 0.994135i \(0.465509\pi\)
\(740\) −1.97214 6.06961i −0.0724972 0.223123i
\(741\) 0 0
\(742\) 22.1803 + 16.1150i 0.814266 + 0.591599i
\(743\) 8.73607 + 6.34712i 0.320495 + 0.232853i 0.736387 0.676561i \(-0.236530\pi\)
−0.415892 + 0.909414i \(0.636530\pi\)
\(744\) 0 0
\(745\) 2.35410 + 7.24518i 0.0862476 + 0.265443i
\(746\) −9.32624 + 6.77591i −0.341458 + 0.248084i
\(747\) 0 0
\(748\) 10.2984 17.3763i 0.376546 0.635340i
\(749\) 20.3607 0.743963
\(750\) 0 0
\(751\) −8.97214 27.6134i −0.327398 1.00763i −0.970347 0.241718i \(-0.922289\pi\)
0.642949 0.765909i \(-0.277711\pi\)
\(752\) 1.33688 4.11450i 0.0487510 0.150040i
\(753\) 0 0
\(754\) 7.16312 + 5.20431i 0.260865 + 0.189530i
\(755\) 6.47214 19.9192i 0.235545 0.724933i
\(756\) 0 0
\(757\) 43.5689 31.6546i 1.58354 1.15051i 0.671044 0.741417i \(-0.265846\pi\)
0.912494 0.409090i \(-0.134154\pi\)
\(758\) 12.3607 0.448960
\(759\) 0 0
\(760\) −1.23607 −0.0448369
\(761\) −8.09017 + 5.87785i −0.293268 + 0.213072i −0.724684 0.689081i \(-0.758014\pi\)
0.431416 + 0.902153i \(0.358014\pi\)
\(762\) 0 0
\(763\) 2.47214 7.60845i 0.0894973 0.275444i
\(764\) 7.47214 + 5.42882i 0.270332 + 0.196408i
\(765\) 0 0
\(766\) −0.100813 + 0.310271i −0.00364252 + 0.0112105i
\(767\) −14.7254 45.3202i −0.531704 1.63642i
\(768\) 0 0
\(769\) −24.4508 −0.881720 −0.440860 0.897576i \(-0.645327\pi\)
−0.440860 + 0.897576i \(0.645327\pi\)
\(770\) 1.00000 + 10.6861i 0.0360375 + 0.385102i
\(771\) 0 0
\(772\) 16.9443 12.3107i 0.609838 0.443073i
\(773\) −6.05573 18.6376i −0.217809 0.670348i −0.998942 0.0459835i \(-0.985358\pi\)
0.781133 0.624365i \(-0.214642\pi\)
\(774\) 0 0
\(775\) 1.11803 + 0.812299i 0.0401610 + 0.0291787i
\(776\) 15.0902 + 10.9637i 0.541706 + 0.393572i
\(777\) 0 0
\(778\) 2.11803 + 6.51864i 0.0759352 + 0.233705i
\(779\) 1.23607 0.898056i 0.0442867 0.0321762i
\(780\) 0 0
\(781\) −33.8885 7.60845i −1.21263 0.272252i
\(782\) 41.7426 1.49271
\(783\) 0 0
\(784\) 1.07295 + 3.30220i 0.0383196 + 0.117936i
\(785\) −2.86475 + 8.81678i −0.102247 + 0.314684i
\(786\) 0 0
\(787\) −17.0172 12.3637i −0.606598 0.440720i 0.241616 0.970372i \(-0.422322\pi\)
−0.848215 + 0.529652i \(0.822322\pi\)
\(788\) −3.38197 + 10.4086i −0.120478 + 0.370792i
\(789\) 0 0
\(790\) −3.30902 + 2.40414i −0.117730 + 0.0855355i
\(791\) −63.3050 −2.25086
\(792\) 0 0
\(793\) 0 0
\(794\) 1.78115 1.29408i 0.0632108 0.0459253i
\(795\) 0 0
\(796\) 8.02786 24.7072i 0.284540 0.875724i
\(797\) −17.5623 12.7598i −0.622089 0.451974i 0.231562 0.972820i \(-0.425616\pi\)
−0.853651 + 0.520846i \(0.825616\pi\)
\(798\) 0 0
\(799\) 8.14183 25.0580i 0.288037 0.886488i
\(800\) −0.309017 0.951057i −0.0109254 0.0336249i
\(801\) 0 0
\(802\) 22.0689 0.779279
\(803\) 4.14590 + 44.3036i 0.146306 + 1.56344i
\(804\) 0 0
\(805\) −17.9443 + 13.0373i −0.632452 + 0.459504i
\(806\) 1.44427 + 4.44501i 0.0508723 + 0.156569i
\(807\) 0 0
\(808\) −12.6353 9.18005i −0.444507 0.322953i
\(809\) −2.14590 1.55909i −0.0754458 0.0548146i 0.549423 0.835544i \(-0.314848\pi\)
−0.624869 + 0.780730i \(0.714848\pi\)
\(810\) 0 0
\(811\) −1.41641 4.35926i −0.0497368 0.153074i 0.923103 0.384552i \(-0.125644\pi\)
−0.972840 + 0.231478i \(0.925644\pi\)
\(812\) 6.85410 4.97980i 0.240532 0.174757i
\(813\) 0 0
\(814\) −13.9828 15.8904i −0.490096 0.556960i
\(815\) 0.854102 0.0299179
\(816\) 0 0
\(817\) −0.0344419 0.106001i −0.00120497 0.00370851i
\(818\) −4.01064 + 12.3435i −0.140229 + 0.431580i
\(819\) 0 0
\(820\) 1.00000 + 0.726543i 0.0349215 + 0.0253720i
\(821\) 13.3820 41.1855i 0.467034 1.43738i −0.389373 0.921080i \(-0.627308\pi\)
0.856407 0.516302i \(-0.172692\pi\)
\(822\) 0 0
\(823\) 10.3262 7.50245i 0.359950 0.261519i −0.393081 0.919504i \(-0.628591\pi\)
0.753031 + 0.657985i \(0.228591\pi\)
\(824\) −6.76393 −0.235633
\(825\) 0 0
\(826\) −45.5967 −1.58651
\(827\) 24.5066 17.8051i 0.852177 0.619143i −0.0735683 0.997290i \(-0.523439\pi\)
0.925745 + 0.378147i \(0.123439\pi\)
\(828\) 0 0
\(829\) 11.0000 33.8545i 0.382046 1.17582i −0.556555 0.830811i \(-0.687877\pi\)
0.938601 0.345005i \(-0.112123\pi\)
\(830\) −3.23607 2.35114i −0.112326 0.0816093i
\(831\) 0 0
\(832\) 1.04508 3.21644i 0.0362318 0.111510i
\(833\) 6.53444 + 20.1109i 0.226405 + 0.696803i
\(834\) 0 0
\(835\) 13.2705 0.459245
\(836\) −3.76393 + 1.62460i −0.130178 + 0.0561879i
\(837\) 0 0
\(838\) −18.4894 + 13.4333i −0.638704 + 0.464046i
\(839\) 7.21478 + 22.2048i 0.249082 + 0.766595i 0.994938 + 0.100488i \(0.0320405\pi\)
−0.745856 + 0.666107i \(0.767959\pi\)
\(840\) 0 0
\(841\) 17.9164 + 13.0170i 0.617807 + 0.448863i
\(842\) −2.00000 1.45309i −0.0689246 0.0500766i
\(843\) 0 0
\(844\) −7.79837 24.0009i −0.268431 0.826146i
\(845\) 1.26393 0.918300i 0.0434806 0.0315905i
\(846\) 0 0
\(847\) 17.0902 + 31.2259i 0.587225 + 1.07293i
\(848\) −8.47214 −0.290934
\(849\) 0 0
\(850\) −1.88197 5.79210i −0.0645509 0.198667i
\(851\) 13.5172 41.6017i 0.463364 1.42609i
\(852\) 0 0
\(853\) 22.2705 + 16.1805i 0.762528 + 0.554009i 0.899685 0.436541i \(-0.143796\pi\)
−0.137157 + 0.990549i \(0.543796\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) −5.09017 + 3.69822i −0.173978 + 0.126403i
\(857\) −24.1591 −0.825258 −0.412629 0.910899i \(-0.635389\pi\)
−0.412629 + 0.910899i \(0.635389\pi\)
\(858\) 0 0
\(859\) −19.1246 −0.652523 −0.326262 0.945279i \(-0.605789\pi\)
−0.326262 + 0.945279i \(0.605789\pi\)
\(860\) 0.0729490 0.0530006i 0.00248754 0.00180730i
\(861\) 0 0
\(862\) 6.90983 21.2663i 0.235350 0.724332i
\(863\) −35.8713 26.0620i −1.22107 0.887162i −0.224885 0.974385i \(-0.572201\pi\)
−0.996189 + 0.0872230i \(0.972201\pi\)
\(864\) 0 0
\(865\) 2.94427 9.06154i 0.100108 0.308102i
\(866\) 7.05573 + 21.7153i 0.239763 + 0.737916i
\(867\) 0 0
\(868\) 4.47214 0.151794
\(869\) −6.91641 + 11.6699i −0.234623 + 0.395876i
\(870\) 0 0
\(871\) 13.9271 10.1186i 0.471900 0.342856i
\(872\) 0.763932 + 2.35114i 0.0258700 + 0.0796197i
\(873\) 0 0
\(874\) −6.85410 4.97980i −0.231843 0.168444i
\(875\) 2.61803 + 1.90211i 0.0885057 + 0.0643032i
\(876\) 0 0
\(877\) 5.86068 + 18.0373i 0.197901 + 0.609077i 0.999930 + 0.0117923i \(0.00375371\pi\)
−0.802029 + 0.597285i \(0.796246\pi\)
\(878\) 1.35410 0.983813i 0.0456987 0.0332021i
\(879\) 0 0
\(880\) −2.19098 2.48990i −0.0738580 0.0839345i
\(881\) −8.00000 −0.269527 −0.134763 0.990878i \(-0.543027\pi\)
−0.134763 + 0.990878i \(0.543027\pi\)
\(882\) 0 0
\(883\) −1.44427 4.44501i −0.0486036 0.149587i 0.923809 0.382853i \(-0.125058\pi\)
−0.972413 + 0.233267i \(0.925058\pi\)
\(884\) 6.36475 19.5887i 0.214070 0.658838i
\(885\) 0 0
\(886\) 15.0902 + 10.9637i 0.506964 + 0.368331i
\(887\) 13.1180 40.3732i 0.440460 1.35560i −0.446926 0.894571i \(-0.647481\pi\)
0.887386 0.461027i \(-0.152519\pi\)
\(888\) 0 0
\(889\) 38.3607 27.8707i 1.28658 0.934752i
\(890\) 17.2361 0.577754
\(891\) 0 0
\(892\) 7.23607 0.242281
\(893\) −4.32624 + 3.14320i −0.144772 + 0.105183i
\(894\) 0 0
\(895\) −5.60739 + 17.2578i −0.187434 + 0.576864i
\(896\) −2.61803 1.90211i −0.0874624 0.0635451i
\(897\) 0 0
\(898\) −3.43769 + 10.5801i −0.114717 + 0.353064i
\(899\) −1.11803 3.44095i −0.0372885 0.114762i
\(900\) 0 0
\(901\) −51.5967 −1.71894
\(902\) 4.00000 + 0.898056i 0.133185 + 0.0299020i
\(903\) 0 0
\(904\) 15.8262 11.4984i 0.526373 0.382432i
\(905\) 6.76393 + 20.8172i 0.224841 + 0.691989i
\(906\) 0 0
\(907\) 19.0172 + 13.8168i 0.631456 + 0.458780i 0.856904 0.515475i \(-0.172385\pi\)
−0.225448 + 0.974255i \(0.572385\pi\)
\(908\) 16.4721 + 11.9677i 0.546647 + 0.397162i
\(909\) 0 0
\(910\) 3.38197 + 10.4086i 0.112111 + 0.345042i
\(911\) 2.85410 2.07363i 0.0945606 0.0687023i −0.539500 0.841985i \(-0.681387\pi\)
0.634061 + 0.773283i \(0.281387\pi\)
\(912\) 0 0
\(913\) −12.9443 2.90617i −0.428393 0.0961802i
\(914\) −4.65248 −0.153890
\(915\) 0 0
\(916\) 0.236068 + 0.726543i 0.00779991 + 0.0240056i
\(917\) −3.38197 + 10.4086i −0.111682 + 0.343723i
\(918\) 0 0
\(919\) −37.4894 27.2376i −1.23666 0.898486i −0.239289 0.970948i \(-0.576914\pi\)
−0.997371 + 0.0724626i \(0.976914\pi\)
\(920\) 2.11803 6.51864i 0.0698295 0.214913i
\(921\) 0 0
\(922\) −18.7812 + 13.6453i −0.618524 + 0.449384i
\(923\) −35.4164 −1.16575
\(924\) 0 0
\(925\) −6.38197 −0.209838
\(926\) 9.61803 6.98791i 0.316068 0.229637i
\(927\) 0 0
\(928\) −0.809017 + 2.48990i −0.0265573 + 0.0817349i
\(929\) −24.6525 17.9111i −0.808821 0.587643i 0.104667 0.994507i \(-0.466622\pi\)
−0.913489 + 0.406864i \(0.866622\pi\)
\(930\) 0 0
\(931\) 1.32624 4.08174i 0.0434657 0.133774i
\(932\) 1.37132 + 4.22050i 0.0449192 + 0.138247i
\(933\) 0 0
\(934\) 28.5410 0.933891
\(935\) −13.3435 15.1639i −0.436378 0.495913i
\(936\) 0 0
\(937\) 34.5066 25.0705i 1.12728 0.819017i 0.141984 0.989869i \(-0.454652\pi\)
0.985297 + 0.170852i \(0.0546519\pi\)
\(938\) −5.09017 15.6659i −0.166200 0.511511i
\(939\) 0 0
\(940\) −3.50000 2.54290i −0.114157 0.0829402i
\(941\) 0.826238 + 0.600297i 0.0269346 + 0.0195691i 0.601171 0.799120i \(-0.294701\pi\)
−0.574237 + 0.818689i \(0.694701\pi\)
\(942\) 0 0
\(943\) 2.61803 + 8.05748i 0.0852549 + 0.262388i
\(944\) 11.3992 8.28199i 0.371012 0.269556i
\(945\) 0 0
\(946\) 0.152476 0.257270i 0.00495742 0.00836457i
\(947\) 12.0000 0.389948 0.194974 0.980808i \(-0.437538\pi\)
0.194974 + 0.980808i \(0.437538\pi\)
\(948\) 0 0
\(949\) 14.0213 + 43.1531i 0.455150 + 1.40081i
\(950\) −0.381966 + 1.17557i −0.0123926 + 0.0381405i
\(951\) 0 0
\(952\) −15.9443 11.5842i −0.516757 0.375446i
\(953\) 18.2984 56.3166i 0.592742 1.82427i 0.0270855 0.999633i \(-0.491377\pi\)
0.565657 0.824641i \(-0.308623\pi\)
\(954\) 0 0
\(955\) 7.47214 5.42882i 0.241793 0.175673i
\(956\) 3.23607 0.104662
\(957\) 0 0
\(958\) 12.7639 0.412384
\(959\) 33.5066 24.3440i 1.08198 0.786107i
\(960\) 0 0
\(961\) −8.98936 + 27.6664i −0.289979 + 0.892464i
\(962\) −17.4615 12.6865i −0.562981 0.409030i
\(963\) 0 0
\(964\) −7.38197 + 22.7194i −0.237757 + 0.731741i
\(965\) −6.47214 19.9192i −0.208345 0.641221i
\(966\) 0 0
\(967\) 53.3050 1.71417 0.857086 0.515174i \(-0.172273\pi\)
0.857086 + 0.515174i \(0.172273\pi\)
\(968\) −9.94427 4.70228i −0.319621 0.151137i
\(969\) 0 0
\(970\) 15.0902 10.9637i 0.484516 0.352022i
\(971\) −2.58359 7.95148i −0.0829114 0.255175i 0.901004 0.433811i \(-0.142832\pi\)
−0.983915 + 0.178636i \(0.942832\pi\)
\(972\) 0 0
\(973\) 22.9443 + 16.6700i 0.735560 + 0.534415i
\(974\) 9.23607 + 6.71040i 0.295943 + 0.215015i
\(975\) 0 0
\(976\) 0 0
\(977\) 23.3262 16.9475i 0.746272 0.542199i −0.148397 0.988928i \(-0.547411\pi\)
0.894669 + 0.446729i \(0.147411\pi\)
\(978\) 0 0
\(979\) 52.4853 22.6538i 1.67744 0.724020i
\(980\) 3.47214 0.110913
\(981\) 0 0
\(982\) 8.66312 + 26.6623i 0.276451 + 0.850829i
\(983\) 15.8197 48.6879i 0.504569 1.55290i −0.296925 0.954901i \(-0.595961\pi\)
0.801494 0.598002i \(-0.204039\pi\)
\(984\) 0 0
\(985\) 8.85410 + 6.43288i 0.282115 + 0.204969i
\(986\) −4.92705 + 15.1639i −0.156909 + 0.482917i
\(987\) 0 0
\(988\) −3.38197 + 2.45714i −0.107595 + 0.0781721i
\(989\) 0.618034 0.0196523
\(990\) 0 0
\(991\) 54.5197 1.73188 0.865938 0.500151i \(-0.166722\pi\)
0.865938 + 0.500151i \(0.166722\pi\)
\(992\) −1.11803 + 0.812299i −0.0354976 + 0.0257905i
\(993\) 0 0
\(994\) −10.4721 + 32.2299i −0.332156 + 1.02227i
\(995\) −21.0172 15.2699i −0.666291 0.484089i
\(996\) 0 0
\(997\) −7.73607 + 23.8092i −0.245004 + 0.754044i 0.750632 + 0.660720i \(0.229749\pi\)
−0.995636 + 0.0933236i \(0.970251\pi\)
\(998\) 10.0344 + 30.8828i 0.317635 + 0.977579i
\(999\) 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 990.2.n.e.91.1 4
3.2 odd 2 330.2.m.b.91.1 4
11.4 even 5 inner 990.2.n.e.631.1 4
33.2 even 10 3630.2.a.bb.1.2 2
33.20 odd 10 3630.2.a.bj.1.1 2
33.26 odd 10 330.2.m.b.301.1 yes 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
330.2.m.b.91.1 4 3.2 odd 2
330.2.m.b.301.1 yes 4 33.26 odd 10
990.2.n.e.91.1 4 1.1 even 1 trivial
990.2.n.e.631.1 4 11.4 even 5 inner
3630.2.a.bb.1.2 2 33.2 even 10
3630.2.a.bj.1.1 2 33.20 odd 10