Properties

Label 891.2.f.b.487.1
Level $891$
Weight $2$
Character 891.487
Analytic conductor $7.115$
Analytic rank $0$
Dimension $4$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [891,2,Mod(82,891)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(891, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("891.82");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 891 = 3^{4} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 891.f (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: \(7.11467082010\)
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: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 99)
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 487.1
Root \(0.809017 + 0.587785i\) of defining polynomial
Character \(\chi\) \(=\) 891.487
Dual form 891.2.f.b.730.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(2.11803 - 1.53884i) q^{2} +(1.50000 - 4.61653i) q^{4} +(-2.61803 - 1.90211i) q^{5} +(-0.309017 + 0.951057i) q^{7} +(-2.30902 - 7.10642i) q^{8} -8.47214 q^{10} +(-0.809017 - 3.21644i) q^{11} +(-2.00000 + 1.45309i) q^{13} +(0.809017 + 2.48990i) q^{14} +(-7.97214 - 5.79210i) q^{16} +(1.50000 + 1.08981i) q^{17} +(0.309017 + 0.951057i) q^{19} +(-12.7082 + 9.23305i) q^{20} +(-6.66312 - 5.56758i) q^{22} +2.38197 q^{23} +(1.69098 + 5.20431i) q^{25} +(-2.00000 + 6.15537i) q^{26} +(3.92705 + 2.85317i) q^{28} +(0.572949 - 1.76336i) q^{29} +(1.30902 - 0.951057i) q^{31} -10.8541 q^{32} +4.85410 q^{34} +(2.61803 - 1.90211i) q^{35} +(1.88197 - 5.79210i) q^{37} +(2.11803 + 1.53884i) q^{38} +(-7.47214 + 22.9969i) q^{40} +(-3.54508 - 10.9106i) q^{41} -4.85410 q^{43} +(-16.0623 - 1.08981i) q^{44} +(5.04508 - 3.66547i) q^{46} +(-1.83688 - 5.65334i) q^{47} +(4.85410 + 3.52671i) q^{49} +(11.5902 + 8.42075i) q^{50} +(3.70820 + 11.4127i) q^{52} +(5.73607 - 4.16750i) q^{53} +(-4.00000 + 9.95959i) q^{55} +7.47214 q^{56} +(-1.50000 - 4.61653i) q^{58} +(-0.190983 + 0.587785i) q^{59} +(-3.35410 - 2.43690i) q^{61} +(1.30902 - 4.02874i) q^{62} +(-7.04508 + 5.11855i) q^{64} +8.00000 q^{65} +6.00000 q^{67} +(7.28115 - 5.29007i) q^{68} +(2.61803 - 8.05748i) q^{70} +(11.3992 + 8.28199i) q^{71} +(-2.11803 + 6.51864i) q^{73} +(-4.92705 - 15.1639i) q^{74} +4.85410 q^{76} +(3.30902 + 0.224514i) q^{77} +(7.73607 - 5.62058i) q^{79} +(9.85410 + 30.3278i) q^{80} +(-24.2984 - 17.6538i) q^{82} +(11.5172 + 8.36775i) q^{83} +(-1.85410 - 5.70634i) q^{85} +(-10.2812 + 7.46969i) q^{86} +(-20.9894 + 13.1760i) q^{88} -11.2361 q^{89} +(-0.763932 - 2.35114i) q^{91} +(3.57295 - 10.9964i) q^{92} +(-12.5902 - 9.14729i) q^{94} +(1.00000 - 3.07768i) q^{95} +(-4.85410 + 3.52671i) q^{97} +15.7082 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 4 q^{2} + 6 q^{4} - 6 q^{5} + q^{7} - 7 q^{8} - 16 q^{10} - q^{11} - 8 q^{13} + q^{14} - 14 q^{16} + 6 q^{17} - q^{19} - 24 q^{20} - 11 q^{22} + 14 q^{23} + 9 q^{25} - 8 q^{26} + 9 q^{28} + 9 q^{29}+ \cdots + 36 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(244\) \(650\)
\(\chi(n)\) \(e\left(\frac{4}{5}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.11803 1.53884i 1.49768 1.08813i 0.526381 0.850249i \(-0.323549\pi\)
0.971295 0.237877i \(-0.0764514\pi\)
\(3\) 0 0
\(4\) 1.50000 4.61653i 0.750000 2.30826i
\(5\) −2.61803 1.90211i −1.17082 0.850651i −0.179714 0.983719i \(-0.557517\pi\)
−0.991107 + 0.133068i \(0.957517\pi\)
\(6\) 0 0
\(7\) −0.309017 + 0.951057i −0.116797 + 0.359466i −0.992318 0.123716i \(-0.960519\pi\)
0.875520 + 0.483181i \(0.160519\pi\)
\(8\) −2.30902 7.10642i −0.816361 2.51250i
\(9\) 0 0
\(10\) −8.47214 −2.67912
\(11\) −0.809017 3.21644i −0.243928 0.969793i
\(12\) 0 0
\(13\) −2.00000 + 1.45309i −0.554700 + 0.403013i −0.829515 0.558484i \(-0.811383\pi\)
0.274815 + 0.961497i \(0.411383\pi\)
\(14\) 0.809017 + 2.48990i 0.216219 + 0.665453i
\(15\) 0 0
\(16\) −7.97214 5.79210i −1.99303 1.44802i
\(17\) 1.50000 + 1.08981i 0.363803 + 0.264319i 0.754637 0.656143i \(-0.227813\pi\)
−0.390833 + 0.920461i \(0.627813\pi\)
\(18\) 0 0
\(19\) 0.309017 + 0.951057i 0.0708934 + 0.218187i 0.980226 0.197884i \(-0.0634068\pi\)
−0.909332 + 0.416071i \(0.863407\pi\)
\(20\) −12.7082 + 9.23305i −2.84164 + 2.06457i
\(21\) 0 0
\(22\) −6.66312 5.56758i −1.42058 1.18701i
\(23\) 2.38197 0.496674 0.248337 0.968674i \(-0.420116\pi\)
0.248337 + 0.968674i \(0.420116\pi\)
\(24\) 0 0
\(25\) 1.69098 + 5.20431i 0.338197 + 1.04086i
\(26\) −2.00000 + 6.15537i −0.392232 + 1.20717i
\(27\) 0 0
\(28\) 3.92705 + 2.85317i 0.742143 + 0.539198i
\(29\) 0.572949 1.76336i 0.106394 0.327447i −0.883661 0.468127i \(-0.844929\pi\)
0.990055 + 0.140680i \(0.0449289\pi\)
\(30\) 0 0
\(31\) 1.30902 0.951057i 0.235106 0.170815i −0.463994 0.885838i \(-0.653584\pi\)
0.699100 + 0.715024i \(0.253584\pi\)
\(32\) −10.8541 −1.91875
\(33\) 0 0
\(34\) 4.85410 0.832472
\(35\) 2.61803 1.90211i 0.442529 0.321516i
\(36\) 0 0
\(37\) 1.88197 5.79210i 0.309393 0.952215i −0.668608 0.743615i \(-0.733109\pi\)
0.978001 0.208599i \(-0.0668905\pi\)
\(38\) 2.11803 + 1.53884i 0.343590 + 0.249633i
\(39\) 0 0
\(40\) −7.47214 + 22.9969i −1.18145 + 3.63612i
\(41\) −3.54508 10.9106i −0.553649 1.70396i −0.699484 0.714648i \(-0.746587\pi\)
0.145835 0.989309i \(-0.453413\pi\)
\(42\) 0 0
\(43\) −4.85410 −0.740244 −0.370122 0.928983i \(-0.620684\pi\)
−0.370122 + 0.928983i \(0.620684\pi\)
\(44\) −16.0623 1.08981i −2.42148 0.164296i
\(45\) 0 0
\(46\) 5.04508 3.66547i 0.743857 0.540444i
\(47\) −1.83688 5.65334i −0.267937 0.824624i −0.991002 0.133845i \(-0.957268\pi\)
0.723066 0.690779i \(-0.242732\pi\)
\(48\) 0 0
\(49\) 4.85410 + 3.52671i 0.693443 + 0.503816i
\(50\) 11.5902 + 8.42075i 1.63910 + 1.19087i
\(51\) 0 0
\(52\) 3.70820 + 11.4127i 0.514235 + 1.58265i
\(53\) 5.73607 4.16750i 0.787910 0.572450i −0.119433 0.992842i \(-0.538108\pi\)
0.907342 + 0.420393i \(0.138108\pi\)
\(54\) 0 0
\(55\) −4.00000 + 9.95959i −0.539360 + 1.34295i
\(56\) 7.47214 0.998506
\(57\) 0 0
\(58\) −1.50000 4.61653i −0.196960 0.606179i
\(59\) −0.190983 + 0.587785i −0.0248639 + 0.0765231i −0.962718 0.270505i \(-0.912809\pi\)
0.937855 + 0.347028i \(0.112809\pi\)
\(60\) 0 0
\(61\) −3.35410 2.43690i −0.429449 0.312013i 0.351980 0.936008i \(-0.385509\pi\)
−0.781428 + 0.623995i \(0.785509\pi\)
\(62\) 1.30902 4.02874i 0.166245 0.511650i
\(63\) 0 0
\(64\) −7.04508 + 5.11855i −0.880636 + 0.639819i
\(65\) 8.00000 0.992278
\(66\) 0 0
\(67\) 6.00000 0.733017 0.366508 0.930415i \(-0.380553\pi\)
0.366508 + 0.930415i \(0.380553\pi\)
\(68\) 7.28115 5.29007i 0.882969 0.641515i
\(69\) 0 0
\(70\) 2.61803 8.05748i 0.312915 0.963053i
\(71\) 11.3992 + 8.28199i 1.35283 + 0.982892i 0.998865 + 0.0476350i \(0.0151684\pi\)
0.353970 + 0.935257i \(0.384832\pi\)
\(72\) 0 0
\(73\) −2.11803 + 6.51864i −0.247897 + 0.762949i 0.747249 + 0.664544i \(0.231374\pi\)
−0.995146 + 0.0984051i \(0.968626\pi\)
\(74\) −4.92705 15.1639i −0.572758 1.76277i
\(75\) 0 0
\(76\) 4.85410 0.556804
\(77\) 3.30902 + 0.224514i 0.377097 + 0.0255857i
\(78\) 0 0
\(79\) 7.73607 5.62058i 0.870376 0.632365i −0.0603121 0.998180i \(-0.519210\pi\)
0.930688 + 0.365815i \(0.119210\pi\)
\(80\) 9.85410 + 30.3278i 1.10172 + 3.39075i
\(81\) 0 0
\(82\) −24.2984 17.6538i −2.68331 1.94954i
\(83\) 11.5172 + 8.36775i 1.26418 + 0.918480i 0.998955 0.0457068i \(-0.0145540\pi\)
0.265224 + 0.964187i \(0.414554\pi\)
\(84\) 0 0
\(85\) −1.85410 5.70634i −0.201106 0.618939i
\(86\) −10.2812 + 7.46969i −1.10865 + 0.805478i
\(87\) 0 0
\(88\) −20.9894 + 13.1760i −2.23747 + 1.40457i
\(89\) −11.2361 −1.19102 −0.595510 0.803348i \(-0.703050\pi\)
−0.595510 + 0.803348i \(0.703050\pi\)
\(90\) 0 0
\(91\) −0.763932 2.35114i −0.0800818 0.246467i
\(92\) 3.57295 10.9964i 0.372506 1.14645i
\(93\) 0 0
\(94\) −12.5902 9.14729i −1.29858 0.943471i
\(95\) 1.00000 3.07768i 0.102598 0.315764i
\(96\) 0 0
\(97\) −4.85410 + 3.52671i −0.492859 + 0.358083i −0.806283 0.591530i \(-0.798524\pi\)
0.313423 + 0.949613i \(0.398524\pi\)
\(98\) 15.7082 1.58677
\(99\) 0 0
\(100\) 26.5623 2.65623
\(101\) −0.381966 + 0.277515i −0.0380070 + 0.0276137i −0.606627 0.794987i \(-0.707478\pi\)
0.568620 + 0.822601i \(0.307478\pi\)
\(102\) 0 0
\(103\) −1.78115 + 5.48183i −0.175502 + 0.540140i −0.999656 0.0262257i \(-0.991651\pi\)
0.824154 + 0.566366i \(0.191651\pi\)
\(104\) 14.9443 + 10.8576i 1.46541 + 1.06468i
\(105\) 0 0
\(106\) 5.73607 17.6538i 0.557136 1.71469i
\(107\) −4.64590 14.2986i −0.449136 1.38230i −0.877884 0.478874i \(-0.841045\pi\)
0.428748 0.903424i \(-0.358955\pi\)
\(108\) 0 0
\(109\) 13.8541 1.32698 0.663491 0.748184i \(-0.269074\pi\)
0.663491 + 0.748184i \(0.269074\pi\)
\(110\) 6.85410 + 27.2501i 0.653513 + 2.59820i
\(111\) 0 0
\(112\) 7.97214 5.79210i 0.753296 0.547302i
\(113\) 3.94427 + 12.1392i 0.371046 + 1.14196i 0.946108 + 0.323852i \(0.104978\pi\)
−0.575062 + 0.818110i \(0.695022\pi\)
\(114\) 0 0
\(115\) −6.23607 4.53077i −0.581516 0.422496i
\(116\) −7.28115 5.29007i −0.676038 0.491170i
\(117\) 0 0
\(118\) 0.500000 + 1.53884i 0.0460287 + 0.141662i
\(119\) −1.50000 + 1.08981i −0.137505 + 0.0999031i
\(120\) 0 0
\(121\) −9.69098 + 5.20431i −0.880998 + 0.473119i
\(122\) −10.8541 −0.982684
\(123\) 0 0
\(124\) −2.42705 7.46969i −0.217956 0.670798i
\(125\) 0.472136 1.45309i 0.0422291 0.129968i
\(126\) 0 0
\(127\) −7.73607 5.62058i −0.686465 0.498746i 0.189031 0.981971i \(-0.439465\pi\)
−0.875496 + 0.483225i \(0.839465\pi\)
\(128\) −0.336881 + 1.03681i −0.0297764 + 0.0916422i
\(129\) 0 0
\(130\) 16.9443 12.3107i 1.48611 1.07972i
\(131\) 16.7639 1.46467 0.732336 0.680944i \(-0.238430\pi\)
0.732336 + 0.680944i \(0.238430\pi\)
\(132\) 0 0
\(133\) −1.00000 −0.0867110
\(134\) 12.7082 9.23305i 1.09782 0.797614i
\(135\) 0 0
\(136\) 4.28115 13.1760i 0.367106 1.12984i
\(137\) 5.16312 + 3.75123i 0.441115 + 0.320489i 0.786078 0.618128i \(-0.212108\pi\)
−0.344963 + 0.938616i \(0.612108\pi\)
\(138\) 0 0
\(139\) −1.14590 + 3.52671i −0.0971938 + 0.299132i −0.987819 0.155606i \(-0.950267\pi\)
0.890625 + 0.454738i \(0.150267\pi\)
\(140\) −4.85410 14.9394i −0.410246 1.26261i
\(141\) 0 0
\(142\) 36.8885 3.09562
\(143\) 6.29180 + 5.25731i 0.526146 + 0.439638i
\(144\) 0 0
\(145\) −4.85410 + 3.52671i −0.403111 + 0.292877i
\(146\) 5.54508 + 17.0660i 0.458914 + 1.41239i
\(147\) 0 0
\(148\) −23.9164 17.3763i −1.96592 1.42832i
\(149\) −5.80902 4.22050i −0.475893 0.345757i 0.323840 0.946112i \(-0.395026\pi\)
−0.799734 + 0.600355i \(0.795026\pi\)
\(150\) 0 0
\(151\) −3.50000 10.7719i −0.284826 0.876604i −0.986451 0.164058i \(-0.947542\pi\)
0.701625 0.712547i \(-0.252458\pi\)
\(152\) 6.04508 4.39201i 0.490321 0.356239i
\(153\) 0 0
\(154\) 7.35410 4.61653i 0.592610 0.372010i
\(155\) −5.23607 −0.420571
\(156\) 0 0
\(157\) 4.28115 + 13.1760i 0.341673 + 1.05156i 0.963341 + 0.268281i \(0.0864555\pi\)
−0.621668 + 0.783281i \(0.713545\pi\)
\(158\) 7.73607 23.8092i 0.615449 1.89416i
\(159\) 0 0
\(160\) 28.4164 + 20.6457i 2.24651 + 1.63219i
\(161\) −0.736068 + 2.26538i −0.0580103 + 0.178537i
\(162\) 0 0
\(163\) −5.89919 + 4.28601i −0.462060 + 0.335706i −0.794339 0.607475i \(-0.792182\pi\)
0.332279 + 0.943181i \(0.392182\pi\)
\(164\) −55.6869 −4.34842
\(165\) 0 0
\(166\) 37.2705 2.89275
\(167\) 8.28115 6.01661i 0.640815 0.465579i −0.219315 0.975654i \(-0.570382\pi\)
0.860130 + 0.510075i \(0.170382\pi\)
\(168\) 0 0
\(169\) −2.12868 + 6.55139i −0.163744 + 0.503953i
\(170\) −12.7082 9.23305i −0.974675 0.708143i
\(171\) 0 0
\(172\) −7.28115 + 22.4091i −0.555183 + 1.70868i
\(173\) −3.68034 11.3269i −0.279811 0.861170i −0.987906 0.155053i \(-0.950445\pi\)
0.708095 0.706117i \(-0.249555\pi\)
\(174\) 0 0
\(175\) −5.47214 −0.413655
\(176\) −12.1803 + 30.3278i −0.918128 + 2.28604i
\(177\) 0 0
\(178\) −23.7984 + 17.2905i −1.78376 + 1.29598i
\(179\) −7.09017 21.8213i −0.529944 1.63100i −0.754327 0.656499i \(-0.772036\pi\)
0.224382 0.974501i \(-0.427964\pi\)
\(180\) 0 0
\(181\) 17.0623 + 12.3965i 1.26823 + 0.921424i 0.999131 0.0416882i \(-0.0132736\pi\)
0.269101 + 0.963112i \(0.413274\pi\)
\(182\) −5.23607 3.80423i −0.388123 0.281988i
\(183\) 0 0
\(184\) −5.50000 16.9273i −0.405465 1.24789i
\(185\) −15.9443 + 11.5842i −1.17225 + 0.851687i
\(186\) 0 0
\(187\) 2.29180 5.70634i 0.167593 0.417289i
\(188\) −28.8541 −2.10440
\(189\) 0 0
\(190\) −2.61803 8.05748i −0.189932 0.584551i
\(191\) −3.69098 + 11.3597i −0.267070 + 0.821957i 0.724139 + 0.689654i \(0.242237\pi\)
−0.991209 + 0.132303i \(0.957763\pi\)
\(192\) 0 0
\(193\) 8.89919 + 6.46564i 0.640577 + 0.465407i 0.860049 0.510212i \(-0.170433\pi\)
−0.219471 + 0.975619i \(0.570433\pi\)
\(194\) −4.85410 + 14.9394i −0.348504 + 1.07259i
\(195\) 0 0
\(196\) 23.5623 17.1190i 1.68302 1.22279i
\(197\) 3.76393 0.268169 0.134085 0.990970i \(-0.457191\pi\)
0.134085 + 0.990970i \(0.457191\pi\)
\(198\) 0 0
\(199\) −13.8541 −0.982091 −0.491046 0.871134i \(-0.663385\pi\)
−0.491046 + 0.871134i \(0.663385\pi\)
\(200\) 33.0795 24.0337i 2.33908 1.69944i
\(201\) 0 0
\(202\) −0.381966 + 1.17557i −0.0268750 + 0.0827129i
\(203\) 1.50000 + 1.08981i 0.105279 + 0.0764899i
\(204\) 0 0
\(205\) −11.4721 + 35.3076i −0.801249 + 2.46599i
\(206\) 4.66312 + 14.3516i 0.324895 + 0.999924i
\(207\) 0 0
\(208\) 24.3607 1.68911
\(209\) 2.80902 1.76336i 0.194304 0.121974i
\(210\) 0 0
\(211\) −9.32624 + 6.77591i −0.642045 + 0.466473i −0.860552 0.509363i \(-0.829881\pi\)
0.218507 + 0.975835i \(0.429881\pi\)
\(212\) −10.6353 32.7319i −0.730432 2.24804i
\(213\) 0 0
\(214\) −31.8435 23.1356i −2.17677 1.58152i
\(215\) 12.7082 + 9.23305i 0.866692 + 0.629689i
\(216\) 0 0
\(217\) 0.500000 + 1.53884i 0.0339422 + 0.104463i
\(218\) 29.3435 21.3193i 1.98739 1.44392i
\(219\) 0 0
\(220\) 39.9787 + 33.4055i 2.69536 + 2.25220i
\(221\) −4.58359 −0.308326
\(222\) 0 0
\(223\) 6.95492 + 21.4050i 0.465736 + 1.43339i 0.858055 + 0.513558i \(0.171673\pi\)
−0.392320 + 0.919829i \(0.628327\pi\)
\(224\) 3.35410 10.3229i 0.224105 0.689725i
\(225\) 0 0
\(226\) 27.0344 + 19.6417i 1.79830 + 1.30654i
\(227\) −4.44427 + 13.6781i −0.294977 + 0.907845i 0.688253 + 0.725471i \(0.258378\pi\)
−0.983229 + 0.182374i \(0.941622\pi\)
\(228\) 0 0
\(229\) 9.85410 7.15942i 0.651177 0.473108i −0.212495 0.977162i \(-0.568159\pi\)
0.863672 + 0.504054i \(0.168159\pi\)
\(230\) −20.1803 −1.33065
\(231\) 0 0
\(232\) −13.8541 −0.909566
\(233\) −23.5623 + 17.1190i −1.54362 + 1.12150i −0.595603 + 0.803279i \(0.703087\pi\)
−0.948015 + 0.318225i \(0.896913\pi\)
\(234\) 0 0
\(235\) −5.94427 + 18.2946i −0.387762 + 1.19341i
\(236\) 2.42705 + 1.76336i 0.157988 + 0.114785i
\(237\) 0 0
\(238\) −1.50000 + 4.61653i −0.0972306 + 0.299245i
\(239\) 0.472136 + 1.45309i 0.0305399 + 0.0939923i 0.965165 0.261643i \(-0.0842644\pi\)
−0.934625 + 0.355636i \(0.884264\pi\)
\(240\) 0 0
\(241\) 26.8328 1.72845 0.864227 0.503102i \(-0.167808\pi\)
0.864227 + 0.503102i \(0.167808\pi\)
\(242\) −12.5172 + 25.9358i −0.804637 + 1.66722i
\(243\) 0 0
\(244\) −16.2812 + 11.8290i −1.04229 + 0.757271i
\(245\) −6.00000 18.4661i −0.383326 1.17976i
\(246\) 0 0
\(247\) −2.00000 1.45309i −0.127257 0.0924576i
\(248\) −9.78115 7.10642i −0.621104 0.451258i
\(249\) 0 0
\(250\) −1.23607 3.80423i −0.0781758 0.240600i
\(251\) −0.354102 + 0.257270i −0.0223507 + 0.0162387i −0.598905 0.800820i \(-0.704397\pi\)
0.576554 + 0.817059i \(0.304397\pi\)
\(252\) 0 0
\(253\) −1.92705 7.66145i −0.121153 0.481671i
\(254\) −25.0344 −1.57080
\(255\) 0 0
\(256\) −4.50000 13.8496i −0.281250 0.865598i
\(257\) −8.06231 + 24.8132i −0.502913 + 1.54781i 0.301339 + 0.953517i \(0.402567\pi\)
−0.804251 + 0.594289i \(0.797433\pi\)
\(258\) 0 0
\(259\) 4.92705 + 3.57971i 0.306152 + 0.222432i
\(260\) 12.0000 36.9322i 0.744208 2.29044i
\(261\) 0 0
\(262\) 35.5066 25.7970i 2.19360 1.59375i
\(263\) 0.708204 0.0436697 0.0218349 0.999762i \(-0.493049\pi\)
0.0218349 + 0.999762i \(0.493049\pi\)
\(264\) 0 0
\(265\) −22.9443 −1.40946
\(266\) −2.11803 + 1.53884i −0.129865 + 0.0943524i
\(267\) 0 0
\(268\) 9.00000 27.6992i 0.549762 1.69199i
\(269\) −9.92705 7.21242i −0.605263 0.439749i 0.242480 0.970156i \(-0.422039\pi\)
−0.847743 + 0.530407i \(0.822039\pi\)
\(270\) 0 0
\(271\) 4.70820 14.4904i 0.286003 0.880227i −0.700093 0.714051i \(-0.746858\pi\)
0.986096 0.166175i \(-0.0531418\pi\)
\(272\) −5.64590 17.3763i −0.342333 1.05359i
\(273\) 0 0
\(274\) 16.7082 1.00938
\(275\) 15.3713 9.64932i 0.926926 0.581876i
\(276\) 0 0
\(277\) 11.9443 8.67802i 0.717662 0.521412i −0.167975 0.985791i \(-0.553723\pi\)
0.885636 + 0.464380i \(0.153723\pi\)
\(278\) 3.00000 + 9.23305i 0.179928 + 0.553762i
\(279\) 0 0
\(280\) −19.5623 14.2128i −1.16907 0.849380i
\(281\) −5.11803 3.71847i −0.305316 0.221825i 0.424568 0.905396i \(-0.360426\pi\)
−0.729884 + 0.683571i \(0.760426\pi\)
\(282\) 0 0
\(283\) −5.25329 16.1680i −0.312276 0.961086i −0.976861 0.213874i \(-0.931392\pi\)
0.664586 0.747212i \(-0.268608\pi\)
\(284\) 55.3328 40.2016i 3.28340 2.38553i
\(285\) 0 0
\(286\) 21.4164 + 1.45309i 1.26638 + 0.0859227i
\(287\) 11.4721 0.677179
\(288\) 0 0
\(289\) −4.19098 12.8985i −0.246528 0.758736i
\(290\) −4.85410 + 14.9394i −0.285043 + 0.877271i
\(291\) 0 0
\(292\) 26.9164 + 19.5559i 1.57516 + 1.14442i
\(293\) −2.10739 + 6.48588i −0.123115 + 0.378909i −0.993553 0.113369i \(-0.963836\pi\)
0.870438 + 0.492278i \(0.163836\pi\)
\(294\) 0 0
\(295\) 1.61803 1.17557i 0.0942056 0.0684444i
\(296\) −45.5066 −2.64502
\(297\) 0 0
\(298\) −18.7984 −1.08896
\(299\) −4.76393 + 3.46120i −0.275505 + 0.200166i
\(300\) 0 0
\(301\) 1.50000 4.61653i 0.0864586 0.266092i
\(302\) −23.9894 17.4293i −1.38043 1.00294i
\(303\) 0 0
\(304\) 3.04508 9.37181i 0.174648 0.537510i
\(305\) 4.14590 + 12.7598i 0.237393 + 0.730622i
\(306\) 0 0
\(307\) 1.14590 0.0653999 0.0326999 0.999465i \(-0.489589\pi\)
0.0326999 + 0.999465i \(0.489589\pi\)
\(308\) 6.00000 14.9394i 0.341882 0.851251i
\(309\) 0 0
\(310\) −11.0902 + 8.05748i −0.629879 + 0.457634i
\(311\) −2.21885 6.82891i −0.125819 0.387232i 0.868230 0.496162i \(-0.165258\pi\)
−0.994049 + 0.108930i \(0.965258\pi\)
\(312\) 0 0
\(313\) 4.42705 + 3.21644i 0.250232 + 0.181804i 0.705829 0.708382i \(-0.250574\pi\)
−0.455598 + 0.890186i \(0.650574\pi\)
\(314\) 29.3435 + 21.3193i 1.65595 + 1.20312i
\(315\) 0 0
\(316\) −14.3435 44.1446i −0.806883 2.48333i
\(317\) −2.47214 + 1.79611i −0.138849 + 0.100880i −0.655042 0.755593i \(-0.727349\pi\)
0.516193 + 0.856473i \(0.327349\pi\)
\(318\) 0 0
\(319\) −6.13525 0.416272i −0.343508 0.0233067i
\(320\) 28.1803 1.57533
\(321\) 0 0
\(322\) 1.92705 + 5.93085i 0.107390 + 0.330514i
\(323\) −0.572949 + 1.76336i −0.0318797 + 0.0981157i
\(324\) 0 0
\(325\) −10.9443 7.95148i −0.607079 0.441069i
\(326\) −5.89919 + 18.1558i −0.326726 + 1.00556i
\(327\) 0 0
\(328\) −69.3500 + 50.3858i −3.82922 + 2.78209i
\(329\) 5.94427 0.327718
\(330\) 0 0
\(331\) −12.4164 −0.682467 −0.341234 0.939978i \(-0.610845\pi\)
−0.341234 + 0.939978i \(0.610845\pi\)
\(332\) 55.9058 40.6179i 3.06823 2.22920i
\(333\) 0 0
\(334\) 8.28115 25.4868i 0.453125 1.39457i
\(335\) −15.7082 11.4127i −0.858231 0.623541i
\(336\) 0 0
\(337\) −0.781153 + 2.40414i −0.0425521 + 0.130962i −0.970076 0.242803i \(-0.921933\pi\)
0.927524 + 0.373765i \(0.121933\pi\)
\(338\) 5.57295 + 17.1518i 0.303128 + 0.932933i
\(339\) 0 0
\(340\) −29.1246 −1.57950
\(341\) −4.11803 3.44095i −0.223004 0.186338i
\(342\) 0 0
\(343\) −10.5172 + 7.64121i −0.567877 + 0.412586i
\(344\) 11.2082 + 34.4953i 0.604306 + 1.85986i
\(345\) 0 0
\(346\) −25.2254 18.3273i −1.35613 0.985284i
\(347\) −21.7533 15.8047i −1.16778 0.848440i −0.177037 0.984204i \(-0.556651\pi\)
−0.990741 + 0.135764i \(0.956651\pi\)
\(348\) 0 0
\(349\) −3.35410 10.3229i −0.179541 0.552570i 0.820271 0.571975i \(-0.193823\pi\)
−0.999812 + 0.0194052i \(0.993823\pi\)
\(350\) −11.5902 + 8.42075i −0.619521 + 0.450108i
\(351\) 0 0
\(352\) 8.78115 + 34.9116i 0.468037 + 1.86079i
\(353\) 10.4164 0.554409 0.277205 0.960811i \(-0.410592\pi\)
0.277205 + 0.960811i \(0.410592\pi\)
\(354\) 0 0
\(355\) −14.0902 43.3651i −0.747829 2.30158i
\(356\) −16.8541 + 51.8716i −0.893266 + 2.74919i
\(357\) 0 0
\(358\) −48.5967 35.3076i −2.56842 1.86606i
\(359\) −4.98936 + 15.3557i −0.263328 + 0.810441i 0.728746 + 0.684784i \(0.240104\pi\)
−0.992074 + 0.125656i \(0.959896\pi\)
\(360\) 0 0
\(361\) 14.5623 10.5801i 0.766437 0.556849i
\(362\) 55.2148 2.90202
\(363\) 0 0
\(364\) −12.0000 −0.628971
\(365\) 17.9443 13.0373i 0.939246 0.682402i
\(366\) 0 0
\(367\) 0.218847 0.673542i 0.0114237 0.0351586i −0.945182 0.326544i \(-0.894116\pi\)
0.956606 + 0.291385i \(0.0941160\pi\)
\(368\) −18.9894 13.7966i −0.989889 0.719196i
\(369\) 0 0
\(370\) −15.9443 + 49.0714i −0.828903 + 2.55110i
\(371\) 2.19098 + 6.74315i 0.113750 + 0.350087i
\(372\) 0 0
\(373\) 25.6525 1.32823 0.664117 0.747628i \(-0.268807\pi\)
0.664117 + 0.747628i \(0.268807\pi\)
\(374\) −3.92705 15.6129i −0.203063 0.807325i
\(375\) 0 0
\(376\) −35.9336 + 26.1073i −1.85314 + 1.34638i
\(377\) 1.41641 + 4.35926i 0.0729487 + 0.224513i
\(378\) 0 0
\(379\) 7.11803 + 5.17155i 0.365629 + 0.265645i 0.755396 0.655269i \(-0.227445\pi\)
−0.389767 + 0.920913i \(0.627445\pi\)
\(380\) −12.7082 9.23305i −0.651917 0.473646i
\(381\) 0 0
\(382\) 9.66312 + 29.7400i 0.494408 + 1.52163i
\(383\) −10.6353 + 7.72696i −0.543436 + 0.394829i −0.825360 0.564607i \(-0.809028\pi\)
0.281923 + 0.959437i \(0.409028\pi\)
\(384\) 0 0
\(385\) −8.23607 6.88191i −0.419749 0.350735i
\(386\) 28.7984 1.46580
\(387\) 0 0
\(388\) 9.00000 + 27.6992i 0.456906 + 1.40621i
\(389\) 2.67376 8.22899i 0.135565 0.417227i −0.860112 0.510105i \(-0.829607\pi\)
0.995677 + 0.0928781i \(0.0296067\pi\)
\(390\) 0 0
\(391\) 3.57295 + 2.59590i 0.180692 + 0.131280i
\(392\) 13.8541 42.6385i 0.699738 2.15357i
\(393\) 0 0
\(394\) 7.97214 5.79210i 0.401630 0.291802i
\(395\) −30.9443 −1.55698
\(396\) 0 0
\(397\) 38.1246 1.91342 0.956710 0.291044i \(-0.0940026\pi\)
0.956710 + 0.291044i \(0.0940026\pi\)
\(398\) −29.3435 + 21.3193i −1.47085 + 1.06864i
\(399\) 0 0
\(400\) 16.6631 51.2838i 0.833156 2.56419i
\(401\) 4.50000 + 3.26944i 0.224719 + 0.163268i 0.694448 0.719542i \(-0.255648\pi\)
−0.469729 + 0.882811i \(0.655648\pi\)
\(402\) 0 0
\(403\) −1.23607 + 3.80423i −0.0615729 + 0.189502i
\(404\) 0.708204 + 2.17963i 0.0352345 + 0.108441i
\(405\) 0 0
\(406\) 4.85410 0.240905
\(407\) −20.1525 1.36733i −0.998921 0.0677759i
\(408\) 0 0
\(409\) −7.07295 + 5.13880i −0.349735 + 0.254097i −0.748758 0.662844i \(-0.769349\pi\)
0.399023 + 0.916941i \(0.369349\pi\)
\(410\) 30.0344 + 92.4365i 1.48330 + 4.56511i
\(411\) 0 0
\(412\) 22.6353 + 16.4455i 1.11516 + 0.810210i
\(413\) −0.500000 0.363271i −0.0246034 0.0178754i
\(414\) 0 0
\(415\) −14.2361 43.8141i −0.698821 2.15075i
\(416\) 21.7082 15.7719i 1.06433 0.773283i
\(417\) 0 0
\(418\) 3.23607 8.05748i 0.158281 0.394104i
\(419\) −3.09017 −0.150965 −0.0754823 0.997147i \(-0.524050\pi\)
−0.0754823 + 0.997147i \(0.524050\pi\)
\(420\) 0 0
\(421\) 1.78115 + 5.48183i 0.0868081 + 0.267168i 0.985032 0.172370i \(-0.0551424\pi\)
−0.898224 + 0.439537i \(0.855142\pi\)
\(422\) −9.32624 + 28.7032i −0.453994 + 1.39725i
\(423\) 0 0
\(424\) −42.8607 31.1401i −2.08150 1.51230i
\(425\) −3.13525 + 9.64932i −0.152082 + 0.468061i
\(426\) 0 0
\(427\) 3.35410 2.43690i 0.162316 0.117930i
\(428\) −72.9787 −3.52756
\(429\) 0 0
\(430\) 41.1246 1.98320
\(431\) −19.4721 + 14.1473i −0.937940 + 0.681453i −0.947924 0.318497i \(-0.896822\pi\)
0.00998408 + 0.999950i \(0.496822\pi\)
\(432\) 0 0
\(433\) −8.57295 + 26.3848i −0.411990 + 1.26797i 0.502926 + 0.864329i \(0.332257\pi\)
−0.914916 + 0.403644i \(0.867743\pi\)
\(434\) 3.42705 + 2.48990i 0.164504 + 0.119519i
\(435\) 0 0
\(436\) 20.7812 63.9578i 0.995237 3.06302i
\(437\) 0.736068 + 2.26538i 0.0352109 + 0.108368i
\(438\) 0 0
\(439\) 12.7082 0.606529 0.303265 0.952906i \(-0.401923\pi\)
0.303265 + 0.952906i \(0.401923\pi\)
\(440\) 80.0132 + 5.42882i 3.81448 + 0.258809i
\(441\) 0 0
\(442\) −9.70820 + 7.05342i −0.461772 + 0.335497i
\(443\) 1.00000 + 3.07768i 0.0475114 + 0.146225i 0.971998 0.234990i \(-0.0755057\pi\)
−0.924486 + 0.381215i \(0.875506\pi\)
\(444\) 0 0
\(445\) 29.4164 + 21.3723i 1.39447 + 1.01314i
\(446\) 47.6697 + 34.6341i 2.25723 + 1.63997i
\(447\) 0 0
\(448\) −2.69098 8.28199i −0.127137 0.391287i
\(449\) 1.19098 0.865300i 0.0562060 0.0408360i −0.559328 0.828947i \(-0.688941\pi\)
0.615533 + 0.788111i \(0.288941\pi\)
\(450\) 0 0
\(451\) −32.2254 + 20.2295i −1.51744 + 0.952568i
\(452\) 61.9574 2.91423
\(453\) 0 0
\(454\) 11.6353 + 35.8096i 0.546070 + 1.68063i
\(455\) −2.47214 + 7.60845i −0.115896 + 0.356690i
\(456\) 0 0
\(457\) 0.809017 + 0.587785i 0.0378442 + 0.0274954i 0.606547 0.795048i \(-0.292554\pi\)
−0.568702 + 0.822543i \(0.692554\pi\)
\(458\) 9.85410 30.3278i 0.460452 1.41713i
\(459\) 0 0
\(460\) −30.2705 + 21.9928i −1.41137 + 1.02542i
\(461\) −22.8541 −1.06442 −0.532211 0.846612i \(-0.678639\pi\)
−0.532211 + 0.846612i \(0.678639\pi\)
\(462\) 0 0
\(463\) 17.0000 0.790057 0.395029 0.918669i \(-0.370735\pi\)
0.395029 + 0.918669i \(0.370735\pi\)
\(464\) −14.7812 + 10.7391i −0.686198 + 0.498552i
\(465\) 0 0
\(466\) −23.5623 + 72.5173i −1.09150 + 3.35930i
\(467\) 4.23607 + 3.07768i 0.196022 + 0.142418i 0.681467 0.731849i \(-0.261342\pi\)
−0.485445 + 0.874267i \(0.661342\pi\)
\(468\) 0 0
\(469\) −1.85410 + 5.70634i −0.0856145 + 0.263494i
\(470\) 15.5623 + 47.8959i 0.717836 + 2.20927i
\(471\) 0 0
\(472\) 4.61803 0.212562
\(473\) 3.92705 + 15.6129i 0.180566 + 0.717883i
\(474\) 0 0
\(475\) −4.42705 + 3.21644i −0.203127 + 0.147580i
\(476\) 2.78115 + 8.55951i 0.127474 + 0.392324i
\(477\) 0 0
\(478\) 3.23607 + 2.35114i 0.148014 + 0.107539i
\(479\) 13.1353 + 9.54332i 0.600165 + 0.436045i 0.845937 0.533282i \(-0.179042\pi\)
−0.245772 + 0.969328i \(0.579042\pi\)
\(480\) 0 0
\(481\) 4.65248 + 14.3188i 0.212135 + 0.652883i
\(482\) 56.8328 41.2915i 2.58866 1.88077i
\(483\) 0 0
\(484\) 9.48936 + 52.5451i 0.431334 + 2.38842i
\(485\) 19.4164 0.881654
\(486\) 0 0
\(487\) 10.5000 + 32.3157i 0.475800 + 1.46436i 0.844875 + 0.534963i \(0.179675\pi\)
−0.369075 + 0.929400i \(0.620325\pi\)
\(488\) −9.57295 + 29.4625i −0.433347 + 1.33371i
\(489\) 0 0
\(490\) −41.1246 29.8788i −1.85782 1.34979i
\(491\) −2.57295 + 7.91872i −0.116116 + 0.357367i −0.992178 0.124831i \(-0.960161\pi\)
0.876063 + 0.482198i \(0.160161\pi\)
\(492\) 0 0
\(493\) 2.78115 2.02063i 0.125257 0.0910044i
\(494\) −6.47214 −0.291195
\(495\) 0 0
\(496\) −15.9443 −0.715919
\(497\) −11.3992 + 8.28199i −0.511323 + 0.371498i
\(498\) 0 0
\(499\) 3.57953 11.0167i 0.160242 0.493173i −0.838413 0.545036i \(-0.816516\pi\)
0.998654 + 0.0518631i \(0.0165159\pi\)
\(500\) −6.00000 4.35926i −0.268328 0.194952i
\(501\) 0 0
\(502\) −0.354102 + 1.08981i −0.0158043 + 0.0486408i
\(503\) −5.70820 17.5680i −0.254516 0.783320i −0.993925 0.110063i \(-0.964895\pi\)
0.739408 0.673257i \(-0.235105\pi\)
\(504\) 0 0
\(505\) 1.52786 0.0679891
\(506\) −15.8713 13.2618i −0.705566 0.589559i
\(507\) 0 0
\(508\) −37.5517 + 27.2829i −1.66609 + 1.21048i
\(509\) −1.48936 4.58377i −0.0660146 0.203172i 0.912608 0.408835i \(-0.134065\pi\)
−0.978623 + 0.205663i \(0.934065\pi\)
\(510\) 0 0
\(511\) −5.54508 4.02874i −0.245300 0.178221i
\(512\) −32.6074 23.6907i −1.44106 1.04699i
\(513\) 0 0
\(514\) 21.1074 + 64.9619i 0.931007 + 2.86535i
\(515\) 15.0902 10.9637i 0.664952 0.483116i
\(516\) 0 0
\(517\) −16.6976 + 10.4819i −0.734358 + 0.460992i
\(518\) 15.9443 0.700551
\(519\) 0 0
\(520\) −18.4721 56.8514i −0.810057 2.49310i
\(521\) 1.34752 4.14725i 0.0590361 0.181694i −0.917190 0.398451i \(-0.869548\pi\)
0.976226 + 0.216757i \(0.0695478\pi\)
\(522\) 0 0
\(523\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(524\) 25.1459 77.3911i 1.09850 3.38085i
\(525\) 0 0
\(526\) 1.50000 1.08981i 0.0654031 0.0475181i
\(527\) 3.00000 0.130682
\(528\) 0 0
\(529\) −17.3262 −0.753315
\(530\) −48.5967 + 35.3076i −2.11091 + 1.53366i
\(531\) 0 0
\(532\) −1.50000 + 4.61653i −0.0650332 + 0.200152i
\(533\) 22.9443 + 16.6700i 0.993827 + 0.722057i
\(534\) 0 0
\(535\) −15.0344 + 46.2713i −0.649996 + 2.00048i
\(536\) −13.8541 42.6385i −0.598406 1.84170i
\(537\) 0 0
\(538\) −32.1246 −1.38499
\(539\) 7.41641 18.4661i 0.319447 0.795391i
\(540\) 0 0
\(541\) 18.6803 13.5721i 0.803131 0.583508i −0.108700 0.994075i \(-0.534669\pi\)
0.911831 + 0.410566i \(0.134669\pi\)
\(542\) −12.3262 37.9363i −0.529457 1.62950i
\(543\) 0 0
\(544\) −16.2812 11.8290i −0.698049 0.507162i
\(545\) −36.2705 26.3521i −1.55366 1.12880i
\(546\) 0 0
\(547\) −5.15248 15.8577i −0.220304 0.678026i −0.998734 0.0502950i \(-0.983984\pi\)
0.778430 0.627731i \(-0.216016\pi\)
\(548\) 25.0623 18.2088i 1.07061 0.777843i
\(549\) 0 0
\(550\) 17.7082 44.0916i 0.755080 1.88007i
\(551\) 1.85410 0.0789874
\(552\) 0 0
\(553\) 2.95492 + 9.09429i 0.125656 + 0.386729i
\(554\) 11.9443 36.7607i 0.507463 1.56181i
\(555\) 0 0
\(556\) 14.5623 + 10.5801i 0.617579 + 0.448698i
\(557\) 9.47214 29.1522i 0.401347 1.23522i −0.522560 0.852603i \(-0.675023\pi\)
0.923907 0.382617i \(-0.124977\pi\)
\(558\) 0 0
\(559\) 9.70820 7.05342i 0.410613 0.298328i
\(560\) −31.8885 −1.34754
\(561\) 0 0
\(562\) −16.5623 −0.698639
\(563\) −34.2254 + 24.8662i −1.44243 + 1.04799i −0.454902 + 0.890542i \(0.650326\pi\)
−0.987528 + 0.157445i \(0.949674\pi\)
\(564\) 0 0
\(565\) 12.7639 39.2833i 0.536983 1.65266i
\(566\) −36.0066 26.1603i −1.51347 1.09960i
\(567\) 0 0
\(568\) 32.5344 100.131i 1.36511 4.20139i
\(569\) 4.38854 + 13.5065i 0.183977 + 0.566224i 0.999929 0.0118958i \(-0.00378663\pi\)
−0.815952 + 0.578120i \(0.803787\pi\)
\(570\) 0 0
\(571\) −27.4721 −1.14967 −0.574837 0.818268i \(-0.694934\pi\)
−0.574837 + 0.818268i \(0.694934\pi\)
\(572\) 33.7082 21.1603i 1.40941 0.884755i
\(573\) 0 0
\(574\) 24.2984 17.6538i 1.01419 0.736855i
\(575\) 4.02786 + 12.3965i 0.167974 + 0.516969i
\(576\) 0 0
\(577\) −6.94427 5.04531i −0.289094 0.210039i 0.433780 0.901019i \(-0.357179\pi\)
−0.722874 + 0.690980i \(0.757179\pi\)
\(578\) −28.7254 20.8702i −1.19482 0.868088i
\(579\) 0 0
\(580\) 9.00000 + 27.6992i 0.373705 + 1.15014i
\(581\) −11.5172 + 8.36775i −0.477815 + 0.347153i
\(582\) 0 0
\(583\) −18.0451 15.0781i −0.747351 0.624473i
\(584\) 51.2148 2.11928
\(585\) 0 0
\(586\) 5.51722 + 16.9803i 0.227914 + 0.701448i
\(587\) −4.14590 + 12.7598i −0.171120 + 0.526652i −0.999435 0.0336102i \(-0.989300\pi\)
0.828315 + 0.560262i \(0.189300\pi\)
\(588\) 0 0
\(589\) 1.30902 + 0.951057i 0.0539371 + 0.0391876i
\(590\) 1.61803 4.97980i 0.0666134 0.205015i
\(591\) 0 0
\(592\) −48.5517 + 35.2748i −1.99546 + 1.44979i
\(593\) 6.94427 0.285167 0.142584 0.989783i \(-0.454459\pi\)
0.142584 + 0.989783i \(0.454459\pi\)
\(594\) 0 0
\(595\) 6.00000 0.245976
\(596\) −28.1976 + 20.4867i −1.15502 + 0.839169i
\(597\) 0 0
\(598\) −4.76393 + 14.6619i −0.194812 + 0.599569i
\(599\) −25.3713 18.4333i −1.03664 0.753166i −0.0670165 0.997752i \(-0.521348\pi\)
−0.969628 + 0.244586i \(0.921348\pi\)
\(600\) 0 0
\(601\) −2.63525 + 8.11048i −0.107494 + 0.330833i −0.990308 0.138890i \(-0.955646\pi\)
0.882813 + 0.469724i \(0.155646\pi\)
\(602\) −3.92705 12.0862i −0.160055 0.492598i
\(603\) 0 0
\(604\) −54.9787 −2.23705
\(605\) 35.2705 + 4.80828i 1.43395 + 0.195485i
\(606\) 0 0
\(607\) 24.6074 17.8783i 0.998783 0.725658i 0.0369562 0.999317i \(-0.488234\pi\)
0.961827 + 0.273658i \(0.0882338\pi\)
\(608\) −3.35410 10.3229i −0.136027 0.418647i
\(609\) 0 0
\(610\) 28.4164 + 20.6457i 1.15055 + 0.835921i
\(611\) 11.8885 + 8.63753i 0.480959 + 0.349437i
\(612\) 0 0
\(613\) 4.06231 + 12.5025i 0.164075 + 0.504971i 0.998967 0.0454430i \(-0.0144699\pi\)
−0.834892 + 0.550414i \(0.814470\pi\)
\(614\) 2.42705 1.76336i 0.0979478 0.0711632i
\(615\) 0 0
\(616\) −6.04508 24.0337i −0.243563 0.968345i
\(617\) 42.1591 1.69726 0.848630 0.528987i \(-0.177428\pi\)
0.848630 + 0.528987i \(0.177428\pi\)
\(618\) 0 0
\(619\) 2.29837 + 7.07367i 0.0923794 + 0.284315i 0.986562 0.163388i \(-0.0522423\pi\)
−0.894182 + 0.447703i \(0.852242\pi\)
\(620\) −7.85410 + 24.1724i −0.315428 + 0.970789i
\(621\) 0 0
\(622\) −15.2082 11.0494i −0.609793 0.443041i
\(623\) 3.47214 10.6861i 0.139108 0.428131i
\(624\) 0 0
\(625\) 18.1353 13.1760i 0.725410 0.527041i
\(626\) 14.3262 0.572592
\(627\) 0 0
\(628\) 67.2492 2.68354
\(629\) 9.13525 6.63715i 0.364246 0.264641i
\(630\) 0 0
\(631\) 7.69098 23.6704i 0.306173 0.942304i −0.673064 0.739585i \(-0.735022\pi\)
0.979237 0.202720i \(-0.0649780\pi\)
\(632\) −57.8050 41.9978i −2.29936 1.67058i
\(633\) 0 0
\(634\) −2.47214 + 7.60845i −0.0981811 + 0.302170i
\(635\) 9.56231 + 29.4298i 0.379469 + 1.16788i
\(636\) 0 0
\(637\) −14.8328 −0.587698
\(638\) −13.6353 + 8.55951i −0.539825 + 0.338874i
\(639\) 0 0
\(640\) 2.85410 2.07363i 0.112818 0.0819673i
\(641\) 10.9549 + 33.7158i 0.432693 + 1.33169i 0.895432 + 0.445198i \(0.146867\pi\)
−0.462739 + 0.886495i \(0.653133\pi\)
\(642\) 0 0
\(643\) 0.118034 + 0.0857567i 0.00465481 + 0.00338191i 0.590110 0.807323i \(-0.299084\pi\)
−0.585455 + 0.810705i \(0.699084\pi\)
\(644\) 9.35410 + 6.79615i 0.368603 + 0.267806i
\(645\) 0 0
\(646\) 1.50000 + 4.61653i 0.0590167 + 0.181635i
\(647\) −14.7082 + 10.6861i −0.578239 + 0.420115i −0.838089 0.545534i \(-0.816327\pi\)
0.259850 + 0.965649i \(0.416327\pi\)
\(648\) 0 0
\(649\) 2.04508 + 0.138757i 0.0802766 + 0.00544670i
\(650\) −35.4164 −1.38915
\(651\) 0 0
\(652\) 10.9377 + 33.6628i 0.428353 + 1.31834i
\(653\) 13.3992 41.2385i 0.524351 1.61379i −0.241246 0.970464i \(-0.577556\pi\)
0.765596 0.643321i \(-0.222444\pi\)
\(654\) 0 0
\(655\) −43.8885 31.8869i −1.71487 1.24592i
\(656\) −34.9336 + 107.515i −1.36393 + 4.19774i
\(657\) 0 0
\(658\) 12.5902 9.14729i 0.490816 0.356599i
\(659\) −36.9787 −1.44049 −0.720243 0.693722i \(-0.755970\pi\)
−0.720243 + 0.693722i \(0.755970\pi\)
\(660\) 0 0
\(661\) −17.7082 −0.688769 −0.344385 0.938829i \(-0.611912\pi\)
−0.344385 + 0.938829i \(0.611912\pi\)
\(662\) −26.2984 + 19.1069i −1.02212 + 0.742610i
\(663\) 0 0
\(664\) 32.8713 101.168i 1.27565 3.92606i
\(665\) 2.61803 + 1.90211i 0.101523 + 0.0737608i
\(666\) 0 0
\(667\) 1.36475 4.20025i 0.0528431 0.162634i
\(668\) −15.3541 47.2551i −0.594068 1.82835i
\(669\) 0 0
\(670\) −50.8328 −1.96384
\(671\) −5.12461 + 12.7598i −0.197833 + 0.492585i
\(672\) 0 0
\(673\) 7.63525 5.54734i 0.294317 0.213834i −0.430821 0.902438i \(-0.641776\pi\)
0.725138 + 0.688603i \(0.241776\pi\)
\(674\) 2.04508 + 6.29412i 0.0787737 + 0.242441i
\(675\) 0 0
\(676\) 27.0517 + 19.6542i 1.04045 + 0.755930i
\(677\) −19.3713 14.0741i −0.744500 0.540911i 0.149617 0.988744i \(-0.452196\pi\)
−0.894117 + 0.447833i \(0.852196\pi\)
\(678\) 0 0
\(679\) −1.85410 5.70634i −0.0711539 0.218989i
\(680\) −36.2705 + 26.3521i −1.39091 + 1.01056i
\(681\) 0 0
\(682\) −14.0172 0.951057i −0.536747 0.0364178i
\(683\) −14.4721 −0.553761 −0.276880 0.960904i \(-0.589301\pi\)
−0.276880 + 0.960904i \(0.589301\pi\)
\(684\) 0 0
\(685\) −6.38197 19.6417i −0.243842 0.750470i
\(686\) −10.5172 + 32.3687i −0.401549 + 1.23584i
\(687\) 0 0
\(688\) 38.6976 + 28.1154i 1.47533 + 1.07189i
\(689\) −5.41641 + 16.6700i −0.206349 + 0.635076i
\(690\) 0 0
\(691\) 27.9894 20.3355i 1.06477 0.773597i 0.0898012 0.995960i \(-0.471377\pi\)
0.974964 + 0.222362i \(0.0713768\pi\)
\(692\) −57.8115 −2.19766
\(693\) 0 0
\(694\) −70.3951 −2.67216
\(695\) 9.70820 7.05342i 0.368253 0.267552i
\(696\) 0 0
\(697\) 6.57295 20.2295i 0.248968 0.766245i
\(698\) −22.9894 16.7027i −0.870160 0.632208i
\(699\) 0 0
\(700\) −8.20820 + 25.2623i −0.310241 + 0.954823i
\(701\) 12.8926 + 39.6794i 0.486947 + 1.49867i 0.829141 + 0.559040i \(0.188830\pi\)
−0.342194 + 0.939629i \(0.611170\pi\)
\(702\) 0 0
\(703\) 6.09017 0.229695
\(704\) 22.1631 + 18.5191i 0.835304 + 0.697965i
\(705\) 0 0
\(706\) 22.0623 16.0292i 0.830326 0.603267i
\(707\) −0.145898 0.449028i −0.00548706 0.0168874i
\(708\) 0 0
\(709\) 24.4615 + 17.7723i 0.918671 + 0.667453i 0.943193 0.332246i \(-0.107806\pi\)
−0.0245221 + 0.999699i \(0.507806\pi\)
\(710\) −96.5755 70.1662i −3.62441 2.63329i
\(711\) 0 0
\(712\) 25.9443 + 79.8483i 0.972303 + 2.99244i
\(713\) 3.11803 2.26538i 0.116771 0.0848393i
\(714\) 0 0
\(715\) −6.47214 25.7315i −0.242044 0.962305i
\(716\) −111.374 −4.16224
\(717\) 0 0
\(718\) 13.0623 + 40.2016i 0.487481 + 1.50031i
\(719\) 9.14590 28.1482i 0.341084 1.04975i −0.622562 0.782570i \(-0.713908\pi\)
0.963647 0.267180i \(-0.0860917\pi\)
\(720\) 0 0
\(721\) −4.66312 3.38795i −0.173664 0.126174i
\(722\) 14.5623 44.8182i 0.541953 1.66796i
\(723\) 0 0
\(724\) 82.8222 60.1738i 3.07806 2.23634i
\(725\) 10.1459 0.376809
\(726\) 0 0
\(727\) −34.8328 −1.29188 −0.645939 0.763389i \(-0.723534\pi\)
−0.645939 + 0.763389i \(0.723534\pi\)
\(728\) −14.9443 + 10.8576i −0.553872 + 0.402411i
\(729\) 0 0
\(730\) 17.9443 55.2268i 0.664147 2.04404i
\(731\) −7.28115 5.29007i −0.269303 0.195660i
\(732\) 0 0
\(733\) 12.2148 37.5932i 0.451163 1.38854i −0.424418 0.905466i \(-0.639521\pi\)
0.875581 0.483071i \(-0.160479\pi\)
\(734\) −0.572949 1.76336i −0.0211479 0.0650866i
\(735\) 0 0
\(736\) −25.8541 −0.952995
\(737\) −4.85410 19.2986i −0.178803 0.710875i
\(738\) 0 0
\(739\) 19.8541 14.4248i 0.730345 0.530627i −0.159328 0.987226i \(-0.550933\pi\)
0.889673 + 0.456599i \(0.150933\pi\)
\(740\) 29.5623 + 90.9834i 1.08673 + 3.34462i
\(741\) 0 0
\(742\) 15.0172 + 10.9106i 0.551300 + 0.400543i
\(743\) −1.90983 1.38757i −0.0700649 0.0509051i 0.552201 0.833711i \(-0.313788\pi\)
−0.622266 + 0.782806i \(0.713788\pi\)
\(744\) 0 0
\(745\) 7.18034 + 22.0988i 0.263067 + 0.809638i
\(746\) 54.3328 39.4751i 1.98927 1.44529i
\(747\) 0 0
\(748\) −22.9058 19.1396i −0.837518 0.699815i
\(749\) 15.0344 0.549347
\(750\) 0 0
\(751\) 15.2188 + 46.8388i 0.555344 + 1.70917i 0.695034 + 0.718977i \(0.255389\pi\)
−0.139691 + 0.990195i \(0.544611\pi\)
\(752\) −18.1008 + 55.7086i −0.660069 + 2.03148i
\(753\) 0 0
\(754\) 9.70820 + 7.05342i 0.353552 + 0.256871i
\(755\) −11.3262 + 34.8586i −0.412204 + 1.26863i
\(756\) 0 0
\(757\) −8.89919 + 6.46564i −0.323446 + 0.234998i −0.737645 0.675189i \(-0.764062\pi\)
0.414198 + 0.910187i \(0.364062\pi\)
\(758\) 23.0344 0.836649
\(759\) 0 0
\(760\) −24.1803 −0.877113
\(761\) 32.3435 23.4989i 1.17245 0.851834i 0.181149 0.983456i \(-0.442018\pi\)
0.991300 + 0.131621i \(0.0420182\pi\)
\(762\) 0 0
\(763\) −4.28115 + 13.1760i −0.154988 + 0.477004i
\(764\) 46.9058 + 34.0790i 1.69699 + 1.23294i
\(765\) 0 0
\(766\) −10.6353 + 32.7319i −0.384267 + 1.18265i
\(767\) −0.472136 1.45309i −0.0170478 0.0524679i
\(768\) 0 0
\(769\) 8.79837 0.317277 0.158639 0.987337i \(-0.449289\pi\)
0.158639 + 0.987337i \(0.449289\pi\)
\(770\) −28.0344 1.90211i −1.01029 0.0685474i
\(771\) 0 0
\(772\) 43.1976 31.3849i 1.55471 1.12957i
\(773\) −2.36475 7.27794i −0.0850540 0.261769i 0.899480 0.436961i \(-0.143945\pi\)
−0.984534 + 0.175192i \(0.943945\pi\)
\(774\) 0 0
\(775\) 7.16312 + 5.20431i 0.257307 + 0.186944i
\(776\) 36.2705 + 26.3521i 1.30204 + 0.945984i
\(777\) 0 0
\(778\) −7.00000 21.5438i −0.250962 0.772382i
\(779\) 9.28115 6.74315i 0.332532 0.241599i
\(780\) 0 0
\(781\) 17.4164 43.3651i 0.623208 1.55172i
\(782\) 11.5623 0.413467
\(783\) 0 0
\(784\) −18.2705 56.2308i −0.652518 2.00824i
\(785\) 13.8541 42.6385i 0.494474 1.52183i
\(786\) 0 0
\(787\) −29.1246 21.1603i −1.03818 0.754282i −0.0682508 0.997668i \(-0.521742\pi\)
−0.969929 + 0.243386i \(0.921742\pi\)
\(788\) 5.64590 17.3763i 0.201127 0.619005i
\(789\) 0 0
\(790\) −65.5410 + 47.6183i −2.33184 + 1.69418i
\(791\) −12.7639 −0.453833
\(792\) 0 0
\(793\) 10.2492 0.363961
\(794\) 80.7492 58.6677i 2.86568 2.08204i
\(795\) 0 0
\(796\) −20.7812 + 63.9578i −0.736568 + 2.26692i
\(797\) 7.50000 + 5.44907i 0.265664 + 0.193016i 0.712640 0.701530i \(-0.247499\pi\)
−0.446977 + 0.894546i \(0.647499\pi\)
\(798\) 0 0
\(799\) 3.40576 10.4819i 0.120487 0.370822i
\(800\) −18.3541 56.4881i −0.648915 1.99716i
\(801\) 0 0
\(802\) 14.5623 0.514213
\(803\) 22.6803 + 1.53884i 0.800372 + 0.0543045i
\(804\) 0 0
\(805\) 6.23607 4.53077i 0.219793 0.159689i
\(806\) 3.23607 + 9.95959i 0.113986 + 0.350812i
\(807\) 0 0
\(808\) 2.85410 + 2.07363i 0.100407 + 0.0729499i
\(809\) 5.59017 + 4.06150i 0.196540 + 0.142795i 0.681703 0.731629i \(-0.261240\pi\)
−0.485163 + 0.874424i \(0.661240\pi\)
\(810\) 0 0
\(811\) −15.9721 49.1572i −0.560858 1.72614i −0.679950 0.733259i \(-0.737998\pi\)
0.119092 0.992883i \(-0.462002\pi\)
\(812\) 7.28115 5.29007i 0.255518 0.185645i
\(813\) 0 0
\(814\) −44.7877 + 28.1154i −1.56981 + 0.985445i
\(815\) 23.5967 0.826558
\(816\) 0 0
\(817\) −1.50000 4.61653i −0.0524784 0.161512i
\(818\) −7.07295 + 21.7683i −0.247300 + 0.761111i
\(819\) 0 0
\(820\) 145.790 + 105.923i 5.09122 + 3.69899i
\(821\) −4.08359 + 12.5680i −0.142518 + 0.438626i −0.996684 0.0813754i \(-0.974069\pi\)
0.854165 + 0.520002i \(0.174069\pi\)
\(822\) 0 0
\(823\) 45.0689 32.7445i 1.57100 1.14140i 0.644814 0.764340i \(-0.276935\pi\)
0.926189 0.377061i \(-0.123065\pi\)
\(824\) 43.0689 1.50038
\(825\) 0 0
\(826\) −1.61803 −0.0562986
\(827\) 22.6246 16.4377i 0.786735 0.571596i −0.120258 0.992743i \(-0.538372\pi\)
0.906993 + 0.421146i \(0.138372\pi\)
\(828\) 0 0
\(829\) −7.27458 + 22.3888i −0.252656 + 0.777597i 0.741626 + 0.670814i \(0.234055\pi\)
−0.994282 + 0.106783i \(0.965945\pi\)
\(830\) −97.5755 70.8927i −3.38689 2.46072i
\(831\) 0 0
\(832\) 6.65248 20.4742i 0.230633 0.709816i
\(833\) 3.43769 + 10.5801i 0.119109 + 0.366580i
\(834\) 0 0
\(835\) −33.1246 −1.14632
\(836\) −3.92705 15.6129i −0.135820 0.539985i
\(837\) 0 0
\(838\) −6.54508 + 4.75528i −0.226096 + 0.164269i
\(839\) −9.48936 29.2052i −0.327609 1.00828i −0.970249 0.242109i \(-0.922161\pi\)
0.642640 0.766168i \(-0.277839\pi\)
\(840\) 0 0
\(841\) 20.6803 + 15.0251i 0.713115 + 0.518108i
\(842\) 12.2082 + 8.86978i 0.420722 + 0.305673i
\(843\) 0 0
\(844\) 17.2918 + 53.2187i 0.595208 + 1.83186i
\(845\) 18.0344 13.1028i 0.620404 0.450750i
\(846\) 0 0
\(847\) −1.95492 10.8249i −0.0671717 0.371948i
\(848\) −69.8673 −2.39925
\(849\) 0 0
\(850\) 8.20820 + 25.2623i 0.281539 + 0.866488i
\(851\) 4.48278 13.7966i 0.153668 0.472941i
\(852\) 0 0
\(853\) 44.9508 + 32.6587i 1.53909 + 1.11821i 0.950904 + 0.309485i \(0.100157\pi\)
0.588184 + 0.808727i \(0.299843\pi\)
\(854\) 3.35410 10.3229i 0.114775 0.353241i
\(855\) 0 0
\(856\) −90.8845 + 66.0314i −3.10637 + 2.25691i
\(857\) −19.3607 −0.661348 −0.330674 0.943745i \(-0.607276\pi\)
−0.330674 + 0.943745i \(0.607276\pi\)
\(858\) 0 0
\(859\) −12.4377 −0.424369 −0.212184 0.977230i \(-0.568058\pi\)
−0.212184 + 0.977230i \(0.568058\pi\)
\(860\) 61.6869 44.8182i 2.10351 1.52829i
\(861\) 0 0
\(862\) −19.4721 + 59.9291i −0.663224 + 2.04119i
\(863\) 33.5344 + 24.3642i 1.14153 + 0.829367i 0.987331 0.158674i \(-0.0507217\pi\)
0.154195 + 0.988041i \(0.450722\pi\)
\(864\) 0 0
\(865\) −11.9098 + 36.6547i −0.404946 + 1.24630i
\(866\) 22.4443 + 69.0764i 0.762687 + 2.34731i
\(867\) 0 0
\(868\) 7.85410 0.266586
\(869\) −24.3369 20.3355i −0.825572 0.689833i
\(870\) 0 0
\(871\) −12.0000 + 8.71851i −0.406604 + 0.295415i
\(872\) −31.9894 98.4531i −1.08330 3.33404i
\(873\) 0 0
\(874\) 5.04508 + 3.66547i 0.170653 + 0.123986i
\(875\) 1.23607 + 0.898056i 0.0417867 + 0.0303598i
\(876\) 0 0
\(877\) −11.6180 35.7566i −0.392313 1.20742i −0.931034 0.364932i \(-0.881092\pi\)
0.538721 0.842484i \(-0.318908\pi\)
\(878\) 26.9164 19.5559i 0.908385 0.659980i
\(879\) 0 0
\(880\) 89.5755 56.2308i 3.01959 1.89554i
\(881\) 24.1803 0.814656 0.407328 0.913282i \(-0.366461\pi\)
0.407328 + 0.913282i \(0.366461\pi\)
\(882\) 0 0
\(883\) −1.34346 4.13474i −0.0452110 0.139145i 0.925903 0.377762i \(-0.123306\pi\)
−0.971114 + 0.238616i \(0.923306\pi\)
\(884\) −6.87539 + 21.1603i −0.231244 + 0.711697i
\(885\) 0 0
\(886\) 6.85410 + 4.97980i 0.230268 + 0.167300i
\(887\) 7.73607 23.8092i 0.259752 0.799434i −0.733104 0.680116i \(-0.761929\pi\)
0.992856 0.119318i \(-0.0380707\pi\)
\(888\) 0 0
\(889\) 7.73607 5.62058i 0.259459 0.188508i
\(890\) 95.1935 3.19089
\(891\) 0 0
\(892\) 109.249 3.65793
\(893\) 4.80902 3.49396i 0.160928 0.116921i
\(894\) 0 0
\(895\) −22.9443 + 70.6152i −0.766942 + 2.36041i
\(896\) −0.881966 0.640786i −0.0294644 0.0214072i
\(897\) 0 0
\(898\) 1.19098 3.66547i 0.0397436 0.122318i
\(899\) −0.927051 2.85317i −0.0309189 0.0951585i
\(900\) 0 0
\(901\) 13.1459 0.437953
\(902\) −37.1246 + 92.4365i −1.23611 + 3.07780i
\(903\) 0 0
\(904\) 77.1591 56.0593i 2.56627 1.86451i
\(905\) −21.0902 64.9089i −0.701061 2.15764i
\(906\) 0 0
\(907\) 33.5066 + 24.3440i 1.11257 + 0.808328i 0.983066 0.183251i \(-0.0586623\pi\)
0.129502 + 0.991579i \(0.458662\pi\)
\(908\) 56.4787 + 41.0342i 1.87431 + 1.36177i
\(909\) 0 0
\(910\) 6.47214 + 19.9192i 0.214549 + 0.660315i
\(911\) −2.57295 + 1.86936i −0.0852456 + 0.0619346i −0.629592 0.776926i \(-0.716778\pi\)
0.544346 + 0.838861i \(0.316778\pi\)
\(912\) 0 0
\(913\) 17.5967 43.8141i 0.582367 1.45004i
\(914\) 2.61803 0.0865969
\(915\) 0 0
\(916\) −18.2705 56.2308i −0.603675 1.85792i
\(917\) −5.18034 + 15.9434i −0.171070 + 0.526499i
\(918\) 0 0
\(919\) −45.1976 32.8380i −1.49093 1.08322i −0.973824 0.227303i \(-0.927009\pi\)
−0.517106 0.855922i \(-0.672991\pi\)
\(920\) −17.7984 + 54.7778i −0.586795 + 1.80597i
\(921\) 0 0
\(922\) −48.4058 + 35.1688i −1.59416 + 1.15822i
\(923\) −34.8328 −1.14654
\(924\) 0 0
\(925\) 33.3262 1.09576
\(926\) 36.0066 26.1603i 1.18325 0.859681i
\(927\) 0 0
\(928\) −6.21885 + 19.1396i −0.204144 + 0.628290i
\(929\) 11.9164 + 8.65778i 0.390965 + 0.284052i 0.765851 0.643018i \(-0.222318\pi\)
−0.374886 + 0.927071i \(0.622318\pi\)
\(930\) 0 0
\(931\) −1.85410 + 5.70634i −0.0607657 + 0.187018i
\(932\) 43.6869 + 134.455i 1.43101 + 4.40420i
\(933\) 0 0
\(934\) 13.7082 0.448546
\(935\) −16.8541 + 10.5801i −0.551188 + 0.346007i
\(936\) 0 0
\(937\) −4.88197 + 3.54696i −0.159487 + 0.115874i −0.664666 0.747140i \(-0.731426\pi\)
0.505179 + 0.863014i \(0.331426\pi\)
\(938\) 4.85410 + 14.9394i 0.158492 + 0.487788i
\(939\) 0 0
\(940\) 75.5410 + 54.8838i 2.46388 + 1.79011i
\(941\) 34.1074 + 24.7805i 1.11187 + 0.807820i 0.982957 0.183836i \(-0.0588515\pi\)
0.128912 + 0.991656i \(0.458851\pi\)
\(942\) 0 0
\(943\) −8.44427 25.9888i −0.274983 0.846312i
\(944\) 4.92705 3.57971i 0.160362 0.116510i
\(945\) 0 0
\(946\) 32.3435 + 27.0256i 1.05158 + 0.878678i
\(947\) 23.2918 0.756882 0.378441 0.925625i \(-0.376460\pi\)
0.378441 + 0.925625i \(0.376460\pi\)
\(948\) 0 0
\(949\) −5.23607 16.1150i −0.169970 0.523114i
\(950\) −4.42705 + 13.6251i −0.143633 + 0.442055i
\(951\) 0 0
\(952\) 11.2082 + 8.14324i 0.363260 + 0.263924i
\(953\) −14.6803 + 45.1814i −0.475543 + 1.46357i 0.369681 + 0.929159i \(0.379467\pi\)
−0.845224 + 0.534412i \(0.820533\pi\)
\(954\) 0 0
\(955\) 31.2705 22.7194i 1.01189 0.735181i
\(956\) 7.41641 0.239864
\(957\) 0 0
\(958\) 42.5066 1.37333
\(959\) −5.16312 + 3.75123i −0.166726 + 0.121133i
\(960\) 0 0
\(961\) −8.77051 + 26.9929i −0.282920 + 0.870737i
\(962\) 31.8885 + 23.1684i 1.02813 + 0.746979i
\(963\) 0 0
\(964\) 40.2492 123.874i 1.29634 3.98972i
\(965\) −11.0000 33.8545i −0.354103 1.08982i
\(966\) 0 0
\(967\) −32.4853 −1.04466 −0.522328 0.852744i \(-0.674936\pi\)
−0.522328 + 0.852744i \(0.674936\pi\)
\(968\) 59.3607 + 56.8514i 1.90792 + 1.82727i
\(969\) 0 0
\(970\) 41.1246 29.8788i 1.32043 0.959350i
\(971\) −7.50000 23.0826i −0.240686 0.740757i −0.996316 0.0857575i \(-0.972669\pi\)
0.755630 0.654999i \(-0.227331\pi\)
\(972\) 0 0
\(973\) −3.00000 2.17963i −0.0961756 0.0698757i
\(974\) 71.9681 + 52.2879i 2.30601 + 1.67541i
\(975\) 0 0
\(976\) 12.6246 + 38.8546i 0.404104 + 1.24370i
\(977\) −16.3713 + 11.8945i −0.523765 + 0.380538i −0.818020 0.575189i \(-0.804928\pi\)
0.294255 + 0.955727i \(0.404928\pi\)
\(978\) 0 0
\(979\) 9.09017 + 36.1401i 0.290523 + 1.15504i
\(980\) −94.2492 −3.01068
\(981\) 0 0
\(982\) 6.73607 + 20.7315i 0.214957 + 0.661568i
\(983\) 15.9894 49.2102i 0.509981 1.56956i −0.282251 0.959341i \(-0.591081\pi\)
0.792232 0.610220i \(-0.208919\pi\)
\(984\) 0 0
\(985\) −9.85410 7.15942i −0.313978 0.228118i
\(986\) 2.78115 8.55951i 0.0885700 0.272590i
\(987\) 0 0
\(988\) −9.70820 + 7.05342i −0.308859 + 0.224399i
\(989\) −11.5623 −0.367660
\(990\) 0 0
\(991\) −28.5967 −0.908406 −0.454203 0.890898i \(-0.650076\pi\)
−0.454203 + 0.890898i \(0.650076\pi\)
\(992\) −14.2082 + 10.3229i −0.451111 + 0.327751i
\(993\) 0 0
\(994\) −11.3992 + 35.0831i −0.361560 + 1.11277i
\(995\) 36.2705 + 26.3521i 1.14985 + 0.835417i
\(996\) 0 0
\(997\) 2.97214 9.14729i 0.0941285 0.289698i −0.892897 0.450261i \(-0.851331\pi\)
0.987026 + 0.160563i \(0.0513310\pi\)
\(998\) −9.37132 28.8420i −0.296644 0.912976i
\(999\) 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.f.b.487.1 4
3.2 odd 2 891.2.f.a.487.1 4
9.2 odd 6 297.2.n.a.91.1 8
9.4 even 3 99.2.m.a.25.1 yes 8
9.5 odd 6 297.2.n.a.289.1 8
9.7 even 3 99.2.m.a.58.1 yes 8
11.2 odd 10 9801.2.a.bc.1.2 2
11.4 even 5 inner 891.2.f.b.730.1 4
11.9 even 5 9801.2.a.n.1.1 2
33.2 even 10 9801.2.a.m.1.1 2
33.20 odd 10 9801.2.a.bb.1.2 2
33.26 odd 10 891.2.f.a.730.1 4
99.4 even 15 99.2.m.a.70.1 yes 8
99.13 odd 30 1089.2.e.d.727.1 4
99.31 even 15 1089.2.e.g.727.2 4
99.59 odd 30 297.2.n.a.235.1 8
99.70 even 15 99.2.m.a.4.1 8
99.79 odd 30 1089.2.e.d.364.1 4
99.92 odd 30 297.2.n.a.37.1 8
99.97 even 15 1089.2.e.g.364.2 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
99.2.m.a.4.1 8 99.70 even 15
99.2.m.a.25.1 yes 8 9.4 even 3
99.2.m.a.58.1 yes 8 9.7 even 3
99.2.m.a.70.1 yes 8 99.4 even 15
297.2.n.a.37.1 8 99.92 odd 30
297.2.n.a.91.1 8 9.2 odd 6
297.2.n.a.235.1 8 99.59 odd 30
297.2.n.a.289.1 8 9.5 odd 6
891.2.f.a.487.1 4 3.2 odd 2
891.2.f.a.730.1 4 33.26 odd 10
891.2.f.b.487.1 4 1.1 even 1 trivial
891.2.f.b.730.1 4 11.4 even 5 inner
1089.2.e.d.364.1 4 99.79 odd 30
1089.2.e.d.727.1 4 99.13 odd 30
1089.2.e.g.364.2 4 99.97 even 15
1089.2.e.g.727.2 4 99.31 even 15
9801.2.a.m.1.1 2 33.2 even 10
9801.2.a.n.1.1 2 11.9 even 5
9801.2.a.bb.1.2 2 33.20 odd 10
9801.2.a.bc.1.2 2 11.2 odd 10