Properties

Label 441.2.u.d.190.4
Level $441$
Weight $2$
Character 441.190
Analytic conductor $3.521$
Analytic rank $0$
Dimension $36$
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] = [441,2,Mod(64,441)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(441, base_ring=CyclotomicField(14))
 
chi = DirichletCharacter(H, H._module([0, 10]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("441.64");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 441.u (of order \(7\), degree \(6\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.52140272914\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(6\) over \(\Q(\zeta_{7})\)
Twist minimal: no (minimal twist has level 147)
Sato-Tate group: $\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label 190.4
Character \(\chi\) \(=\) 441.190
Dual form 441.2.u.d.253.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.385632 - 0.483568i) q^{2} +(0.359916 + 1.57690i) q^{4} +(3.63892 + 1.75241i) q^{5} +(-2.64500 - 0.0631583i) q^{7} +(2.01584 + 0.970778i) q^{8} +O(q^{10})\) \(q+(0.385632 - 0.483568i) q^{2} +(0.359916 + 1.57690i) q^{4} +(3.63892 + 1.75241i) q^{5} +(-2.64500 - 0.0631583i) q^{7} +(2.01584 + 0.970778i) q^{8} +(2.25069 - 1.08388i) q^{10} +(-0.0332349 + 0.0416752i) q^{11} +(-0.237234 + 0.297483i) q^{13} +(-1.05054 + 1.25468i) q^{14} +(-1.66773 + 0.803137i) q^{16} +(0.172451 - 0.755556i) q^{17} -4.32244 q^{19} +(-1.45366 + 6.36892i) q^{20} +(0.00733635 + 0.0321427i) q^{22} +(0.445501 + 1.95187i) q^{23} +(7.05333 + 8.84459i) q^{25} +(0.0523677 + 0.229438i) q^{26} +(-0.852384 - 4.19362i) q^{28} +(1.94604 - 8.52617i) q^{29} +5.67978 q^{31} +(-1.25050 + 5.47882i) q^{32} +(-0.298860 - 0.374759i) q^{34} +(-9.51425 - 4.86495i) q^{35} +(2.39948 - 10.5128i) q^{37} +(-1.66687 + 2.09020i) q^{38} +(5.63428 + 7.06516i) q^{40} +(1.87432 + 0.902623i) q^{41} +(-6.37201 + 3.06860i) q^{43} +(-0.0776793 - 0.0374084i) q^{44} +(1.11566 + 0.537273i) q^{46} +(6.67934 - 8.37562i) q^{47} +(6.99202 + 0.334107i) q^{49} +6.99695 q^{50} +(-0.554484 - 0.267025i) q^{52} +(1.51990 + 6.65912i) q^{53} +(-0.193971 + 0.0934116i) q^{55} +(-5.27058 - 2.69502i) q^{56} +(-3.37252 - 4.22901i) q^{58} +(6.38163 - 3.07323i) q^{59} +(1.24542 - 5.45654i) q^{61} +(2.19031 - 2.74656i) q^{62} +(-0.141068 - 0.176894i) q^{64} +(-1.38459 + 0.666783i) q^{65} -10.4126 q^{67} +1.25350 q^{68} +(-6.02153 + 2.72470i) q^{70} +(2.39721 + 10.5029i) q^{71} +(-1.54213 - 1.93377i) q^{73} +(-4.15834 - 5.21440i) q^{74} +(-1.55572 - 6.81605i) q^{76} +(0.0905384 - 0.108132i) q^{77} -10.7607 q^{79} -7.47616 q^{80} +(1.15928 - 0.558278i) q^{82} +(-0.559861 - 0.702043i) q^{83} +(1.95158 - 2.44720i) q^{85} +(-0.973378 + 4.26465i) q^{86} +(-0.107454 + 0.0517470i) q^{88} +(-7.55992 - 9.47984i) q^{89} +(0.646273 - 0.771857i) q^{91} +(-2.91755 + 1.40502i) q^{92} +(-1.47441 - 6.45983i) q^{94} +(-15.7290 - 7.57469i) q^{95} +9.99553 q^{97} +(2.85791 - 3.25227i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36 q + q^{2} - 9 q^{4} + 4 q^{5} - 6 q^{7} + 15 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 36 q + q^{2} - 9 q^{4} + 4 q^{5} - 6 q^{7} + 15 q^{8} + 10 q^{10} + 7 q^{11} - 12 q^{13} + q^{14} - 3 q^{16} + 3 q^{17} + 6 q^{19} - 25 q^{20} - 21 q^{22} + 20 q^{23} - 2 q^{25} - 6 q^{26} - q^{28} + 22 q^{29} + 16 q^{31} - 26 q^{32} + 6 q^{34} + 9 q^{35} + 32 q^{37} - 17 q^{38} - 21 q^{40} + 5 q^{41} - 34 q^{43} - 2 q^{44} - 32 q^{46} + 7 q^{47} + 20 q^{49} - 236 q^{50} + 20 q^{52} + 32 q^{53} - 17 q^{55} + 39 q^{56} - 53 q^{58} + q^{59} + 14 q^{61} + 60 q^{62} - 21 q^{64} + 39 q^{65} - 22 q^{67} + 110 q^{68} - 40 q^{70} - 36 q^{71} - 11 q^{73} + 46 q^{74} - 101 q^{76} + 17 q^{77} - 14 q^{79} + 112 q^{80} + 2 q^{82} - 12 q^{83} - 44 q^{85} - 184 q^{86} + 204 q^{88} - 12 q^{89} - 16 q^{91} + 105 q^{92} - 5 q^{94} - 18 q^{95} + 172 q^{97} - q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(344\)
\(\chi(n)\) \(e\left(\frac{1}{7}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.385632 0.483568i 0.272683 0.341934i −0.626568 0.779367i \(-0.715541\pi\)
0.899251 + 0.437433i \(0.144112\pi\)
\(3\) 0 0
\(4\) 0.359916 + 1.57690i 0.179958 + 0.788448i
\(5\) 3.63892 + 1.75241i 1.62737 + 0.783702i 0.999988 + 0.00499272i \(0.00158924\pi\)
0.627385 + 0.778709i \(0.284125\pi\)
\(6\) 0 0
\(7\) −2.64500 0.0631583i −0.999715 0.0238716i
\(8\) 2.01584 + 0.970778i 0.712708 + 0.343222i
\(9\) 0 0
\(10\) 2.25069 1.08388i 0.711732 0.342752i
\(11\) −0.0332349 + 0.0416752i −0.0100207 + 0.0125656i −0.786817 0.617187i \(-0.788272\pi\)
0.776796 + 0.629752i \(0.216844\pi\)
\(12\) 0 0
\(13\) −0.237234 + 0.297483i −0.0657970 + 0.0825068i −0.813641 0.581368i \(-0.802518\pi\)
0.747844 + 0.663875i \(0.231089\pi\)
\(14\) −1.05054 + 1.25468i −0.280768 + 0.335327i
\(15\) 0 0
\(16\) −1.66773 + 0.803137i −0.416933 + 0.200784i
\(17\) 0.172451 0.755556i 0.0418254 0.183249i −0.949700 0.313161i \(-0.898612\pi\)
0.991526 + 0.129911i \(0.0414693\pi\)
\(18\) 0 0
\(19\) −4.32244 −0.991637 −0.495818 0.868426i \(-0.665132\pi\)
−0.495818 + 0.868426i \(0.665132\pi\)
\(20\) −1.45366 + 6.36892i −0.325049 + 1.42413i
\(21\) 0 0
\(22\) 0.00733635 + 0.0321427i 0.00156412 + 0.00685284i
\(23\) 0.445501 + 1.95187i 0.0928934 + 0.406992i 0.999900 0.0141234i \(-0.00449576\pi\)
−0.907007 + 0.421116i \(0.861639\pi\)
\(24\) 0 0
\(25\) 7.05333 + 8.84459i 1.41067 + 1.76892i
\(26\) 0.0523677 + 0.229438i 0.0102702 + 0.0449965i
\(27\) 0 0
\(28\) −0.852384 4.19362i −0.161085 0.792520i
\(29\) 1.94604 8.52617i 0.361371 1.58327i −0.388347 0.921513i \(-0.626954\pi\)
0.749718 0.661757i \(-0.230189\pi\)
\(30\) 0 0
\(31\) 5.67978 1.02012 0.510059 0.860139i \(-0.329623\pi\)
0.510059 + 0.860139i \(0.329623\pi\)
\(32\) −1.25050 + 5.47882i −0.221060 + 0.968527i
\(33\) 0 0
\(34\) −0.298860 0.374759i −0.0512541 0.0642706i
\(35\) −9.51425 4.86495i −1.60820 0.822326i
\(36\) 0 0
\(37\) 2.39948 10.5128i 0.394472 1.72830i −0.254131 0.967170i \(-0.581789\pi\)
0.648603 0.761127i \(-0.275353\pi\)
\(38\) −1.66687 + 2.09020i −0.270403 + 0.339074i
\(39\) 0 0
\(40\) 5.63428 + 7.06516i 0.890858 + 1.11710i
\(41\) 1.87432 + 0.902623i 0.292719 + 0.140966i 0.574480 0.818519i \(-0.305204\pi\)
−0.281761 + 0.959485i \(0.590919\pi\)
\(42\) 0 0
\(43\) −6.37201 + 3.06860i −0.971722 + 0.467956i −0.851250 0.524760i \(-0.824155\pi\)
−0.120472 + 0.992717i \(0.538441\pi\)
\(44\) −0.0776793 0.0374084i −0.0117106 0.00563953i
\(45\) 0 0
\(46\) 1.11566 + 0.537273i 0.164495 + 0.0792166i
\(47\) 6.67934 8.37562i 0.974282 1.22171i −0.000830966 1.00000i \(-0.500265\pi\)
0.975112 0.221711i \(-0.0711641\pi\)
\(48\) 0 0
\(49\) 6.99202 + 0.334107i 0.998860 + 0.0477296i
\(50\) 6.99695 0.989518
\(51\) 0 0
\(52\) −0.554484 0.267025i −0.0768931 0.0370298i
\(53\) 1.51990 + 6.65912i 0.208775 + 0.914701i 0.965384 + 0.260834i \(0.0839974\pi\)
−0.756609 + 0.653867i \(0.773145\pi\)
\(54\) 0 0
\(55\) −0.193971 + 0.0934116i −0.0261551 + 0.0125956i
\(56\) −5.27058 2.69502i −0.704312 0.360138i
\(57\) 0 0
\(58\) −3.37252 4.22901i −0.442834 0.555297i
\(59\) 6.38163 3.07323i 0.830817 0.400101i 0.0303958 0.999538i \(-0.490323\pi\)
0.800422 + 0.599437i \(0.204609\pi\)
\(60\) 0 0
\(61\) 1.24542 5.45654i 0.159460 0.698638i −0.830468 0.557066i \(-0.811927\pi\)
0.989928 0.141572i \(-0.0452158\pi\)
\(62\) 2.19031 2.74656i 0.278169 0.348813i
\(63\) 0 0
\(64\) −0.141068 0.176894i −0.0176336 0.0221118i
\(65\) −1.38459 + 0.666783i −0.171737 + 0.0827042i
\(66\) 0 0
\(67\) −10.4126 −1.27210 −0.636049 0.771649i \(-0.719432\pi\)
−0.636049 + 0.771649i \(0.719432\pi\)
\(68\) 1.25350 0.152009
\(69\) 0 0
\(70\) −6.02153 + 2.72470i −0.719711 + 0.325664i
\(71\) 2.39721 + 10.5029i 0.284496 + 1.24646i 0.891961 + 0.452113i \(0.149329\pi\)
−0.607465 + 0.794347i \(0.707813\pi\)
\(72\) 0 0
\(73\) −1.54213 1.93377i −0.180493 0.226330i 0.683352 0.730089i \(-0.260522\pi\)
−0.863844 + 0.503759i \(0.831950\pi\)
\(74\) −4.15834 5.21440i −0.483397 0.606161i
\(75\) 0 0
\(76\) −1.55572 6.81605i −0.178453 0.781854i
\(77\) 0.0905384 0.108132i 0.0103178 0.0123228i
\(78\) 0 0
\(79\) −10.7607 −1.21067 −0.605337 0.795969i \(-0.706962\pi\)
−0.605337 + 0.795969i \(0.706962\pi\)
\(80\) −7.47616 −0.835861
\(81\) 0 0
\(82\) 1.15928 0.558278i 0.128021 0.0616515i
\(83\) −0.559861 0.702043i −0.0614527 0.0770593i 0.750155 0.661262i \(-0.229979\pi\)
−0.811608 + 0.584203i \(0.801407\pi\)
\(84\) 0 0
\(85\) 1.95158 2.44720i 0.211678 0.265436i
\(86\) −0.973378 + 4.26465i −0.104962 + 0.459869i
\(87\) 0 0
\(88\) −0.107454 + 0.0517470i −0.0114546 + 0.00551625i
\(89\) −7.55992 9.47984i −0.801350 1.00486i −0.999694 0.0247285i \(-0.992128\pi\)
0.198344 0.980132i \(-0.436444\pi\)
\(90\) 0 0
\(91\) 0.646273 0.771857i 0.0677478 0.0809126i
\(92\) −2.91755 + 1.40502i −0.304176 + 0.146483i
\(93\) 0 0
\(94\) −1.47441 6.45983i −0.152074 0.666280i
\(95\) −15.7290 7.57469i −1.61376 0.777147i
\(96\) 0 0
\(97\) 9.99553 1.01489 0.507446 0.861684i \(-0.330590\pi\)
0.507446 + 0.861684i \(0.330590\pi\)
\(98\) 2.85791 3.25227i 0.288693 0.328529i
\(99\) 0 0
\(100\) −11.4084 + 14.3057i −1.14084 + 1.43057i
\(101\) 6.36439 + 3.06493i 0.633280 + 0.304972i 0.722846 0.691009i \(-0.242834\pi\)
−0.0895657 + 0.995981i \(0.528548\pi\)
\(102\) 0 0
\(103\) −16.6568 8.02148i −1.64124 0.790380i −0.999729 0.0232665i \(-0.992593\pi\)
−0.641512 0.767113i \(-0.721692\pi\)
\(104\) −0.767017 + 0.369376i −0.0752122 + 0.0362203i
\(105\) 0 0
\(106\) 3.80626 + 1.83300i 0.369697 + 0.178037i
\(107\) −7.11877 8.92665i −0.688197 0.862972i 0.307883 0.951424i \(-0.400379\pi\)
−0.996080 + 0.0884522i \(0.971808\pi\)
\(108\) 0 0
\(109\) −3.11134 + 3.90149i −0.298012 + 0.373695i −0.908182 0.418575i \(-0.862530\pi\)
0.610170 + 0.792270i \(0.291101\pi\)
\(110\) −0.0296307 + 0.129821i −0.00282518 + 0.0123779i
\(111\) 0 0
\(112\) 4.46187 2.01897i 0.421607 0.190774i
\(113\) −7.46766 9.36415i −0.702499 0.880905i 0.294709 0.955587i \(-0.404777\pi\)
−0.997207 + 0.0746818i \(0.976206\pi\)
\(114\) 0 0
\(115\) −1.79933 + 7.88338i −0.167788 + 0.735129i
\(116\) 14.1453 1.31336
\(117\) 0 0
\(118\) 0.974848 4.27109i 0.0897420 0.393186i
\(119\) −0.503851 + 1.98755i −0.0461880 + 0.182199i
\(120\) 0 0
\(121\) 2.44710 + 10.7214i 0.222463 + 0.974676i
\(122\) −2.15833 2.70646i −0.195406 0.245032i
\(123\) 0 0
\(124\) 2.04425 + 8.95643i 0.183579 + 0.804311i
\(125\) 5.67342 + 24.8569i 0.507447 + 2.22327i
\(126\) 0 0
\(127\) 0.318999 1.39762i 0.0283065 0.124019i −0.958801 0.284080i \(-0.908312\pi\)
0.987107 + 0.160061i \(0.0511690\pi\)
\(128\) −11.3794 −1.00580
\(129\) 0 0
\(130\) −0.211508 + 0.926675i −0.0185504 + 0.0812748i
\(131\) 4.69568 2.26132i 0.410263 0.197572i −0.217357 0.976092i \(-0.569743\pi\)
0.627620 + 0.778520i \(0.284029\pi\)
\(132\) 0 0
\(133\) 11.4329 + 0.272998i 0.991354 + 0.0236720i
\(134\) −4.01543 + 5.03518i −0.346880 + 0.434974i
\(135\) 0 0
\(136\) 1.08111 1.35567i 0.0927045 0.116248i
\(137\) −3.02721 + 1.45783i −0.258632 + 0.124551i −0.558707 0.829365i \(-0.688702\pi\)
0.300075 + 0.953916i \(0.402988\pi\)
\(138\) 0 0
\(139\) 15.7861 + 7.60220i 1.33896 + 0.644810i 0.959843 0.280538i \(-0.0905129\pi\)
0.379119 + 0.925348i \(0.376227\pi\)
\(140\) 4.24719 16.7540i 0.358953 1.41597i
\(141\) 0 0
\(142\) 6.00328 + 2.89103i 0.503784 + 0.242610i
\(143\) −0.00451320 0.0197736i −0.000377413 0.00165355i
\(144\) 0 0
\(145\) 22.0228 27.6158i 1.82890 2.29336i
\(146\) −1.52980 −0.126607
\(147\) 0 0
\(148\) 17.4412 1.43366
\(149\) −10.1445 + 12.7208i −0.831071 + 1.04213i 0.167347 + 0.985898i \(0.446480\pi\)
−0.998418 + 0.0562321i \(0.982091\pi\)
\(150\) 0 0
\(151\) −1.07032 4.68939i −0.0871017 0.381617i 0.912523 0.409026i \(-0.134132\pi\)
−0.999624 + 0.0274088i \(0.991274\pi\)
\(152\) −8.71337 4.19614i −0.706747 0.340352i
\(153\) 0 0
\(154\) −0.0173746 0.0854806i −0.00140008 0.00688822i
\(155\) 20.6682 + 9.95330i 1.66011 + 0.799469i
\(156\) 0 0
\(157\) −5.04259 + 2.42838i −0.402442 + 0.193806i −0.624145 0.781308i \(-0.714553\pi\)
0.221703 + 0.975114i \(0.428838\pi\)
\(158\) −4.14968 + 5.20353i −0.330131 + 0.413971i
\(159\) 0 0
\(160\) −14.1516 + 17.7456i −1.11878 + 1.40291i
\(161\) −1.05507 5.19082i −0.0831513 0.409094i
\(162\) 0 0
\(163\) 2.40582 1.15858i 0.188438 0.0907472i −0.337286 0.941402i \(-0.609509\pi\)
0.525724 + 0.850655i \(0.323794\pi\)
\(164\) −0.748746 + 3.28047i −0.0584672 + 0.256162i
\(165\) 0 0
\(166\) −0.555386 −0.0431063
\(167\) 3.32240 14.5564i 0.257095 1.12641i −0.667245 0.744839i \(-0.732526\pi\)
0.924340 0.381570i \(-0.124616\pi\)
\(168\) 0 0
\(169\) 2.86056 + 12.5329i 0.220043 + 0.964071i
\(170\) −0.430796 1.88744i −0.0330405 0.144760i
\(171\) 0 0
\(172\) −7.13225 8.94356i −0.543829 0.681940i
\(173\) −0.900408 3.94494i −0.0684567 0.299929i 0.929097 0.369837i \(-0.120586\pi\)
−0.997553 + 0.0699084i \(0.977729\pi\)
\(174\) 0 0
\(175\) −18.0974 23.8394i −1.36804 1.80209i
\(176\) 0.0219560 0.0961953i 0.00165499 0.00725100i
\(177\) 0 0
\(178\) −7.49950 −0.562111
\(179\) −1.10290 + 4.83214i −0.0824350 + 0.361171i −0.999275 0.0380847i \(-0.987874\pi\)
0.916840 + 0.399256i \(0.130731\pi\)
\(180\) 0 0
\(181\) −8.04779 10.0916i −0.598188 0.750104i 0.386906 0.922119i \(-0.373544\pi\)
−0.985094 + 0.172015i \(0.944972\pi\)
\(182\) −0.124022 0.610170i −0.00919309 0.0452288i
\(183\) 0 0
\(184\) −0.996771 + 4.36714i −0.0734829 + 0.321950i
\(185\) 27.1543 34.0504i 1.99642 2.50343i
\(186\) 0 0
\(187\) 0.0257566 + 0.0322977i 0.00188351 + 0.00236185i
\(188\) 15.6115 + 7.51810i 1.13859 + 0.548314i
\(189\) 0 0
\(190\) −9.72850 + 4.68500i −0.705779 + 0.339885i
\(191\) −1.39236 0.670526i −0.100748 0.0485175i 0.382831 0.923818i \(-0.374949\pi\)
−0.483579 + 0.875301i \(0.660663\pi\)
\(192\) 0 0
\(193\) −13.5003 6.50139i −0.971771 0.467980i −0.120504 0.992713i \(-0.538451\pi\)
−0.851267 + 0.524732i \(0.824165\pi\)
\(194\) 3.85460 4.83351i 0.276744 0.347026i
\(195\) 0 0
\(196\) 1.98969 + 11.1459i 0.142121 + 0.796139i
\(197\) 8.90428 0.634403 0.317202 0.948358i \(-0.397257\pi\)
0.317202 + 0.948358i \(0.397257\pi\)
\(198\) 0 0
\(199\) 12.6578 + 6.09570i 0.897291 + 0.432112i 0.824910 0.565265i \(-0.191226\pi\)
0.0723811 + 0.997377i \(0.476940\pi\)
\(200\) 5.63225 + 24.6765i 0.398260 + 1.74489i
\(201\) 0 0
\(202\) 3.93642 1.89568i 0.276965 0.133379i
\(203\) −5.68578 + 22.4288i −0.399063 + 1.57419i
\(204\) 0 0
\(205\) 5.23871 + 6.56914i 0.365888 + 0.458809i
\(206\) −10.3023 + 4.96134i −0.717797 + 0.345673i
\(207\) 0 0
\(208\) 0.156724 0.686653i 0.0108669 0.0476108i
\(209\) 0.143656 0.180139i 0.00993689 0.0124605i
\(210\) 0 0
\(211\) −8.27635 10.3782i −0.569767 0.714466i 0.410562 0.911832i \(-0.365332\pi\)
−0.980330 + 0.197367i \(0.936761\pi\)
\(212\) −9.95371 + 4.79346i −0.683624 + 0.329216i
\(213\) 0 0
\(214\) −7.06187 −0.482739
\(215\) −28.5646 −1.94809
\(216\) 0 0
\(217\) −15.0230 0.358726i −1.01983 0.0243519i
\(218\) 0.686804 + 3.00909i 0.0465163 + 0.203801i
\(219\) 0 0
\(220\) −0.217114 0.272252i −0.0146378 0.0183552i
\(221\) 0.183854 + 0.230545i 0.0123673 + 0.0155081i
\(222\) 0 0
\(223\) 3.51294 + 15.3912i 0.235244 + 1.03067i 0.945217 + 0.326442i \(0.105850\pi\)
−0.709973 + 0.704228i \(0.751293\pi\)
\(224\) 3.65361 14.4125i 0.244117 0.962974i
\(225\) 0 0
\(226\) −7.40798 −0.492771
\(227\) 15.9623 1.05946 0.529729 0.848167i \(-0.322294\pi\)
0.529729 + 0.848167i \(0.322294\pi\)
\(228\) 0 0
\(229\) −7.76409 + 3.73899i −0.513066 + 0.247079i −0.672457 0.740136i \(-0.734761\pi\)
0.159392 + 0.987215i \(0.449047\pi\)
\(230\) 3.11827 + 3.91019i 0.205613 + 0.257830i
\(231\) 0 0
\(232\) 12.1999 15.2982i 0.800965 1.00438i
\(233\) −1.22070 + 5.34823i −0.0799706 + 0.350374i −0.999044 0.0437119i \(-0.986082\pi\)
0.919074 + 0.394086i \(0.128939\pi\)
\(234\) 0 0
\(235\) 38.9831 18.7733i 2.54298 1.22463i
\(236\) 7.14302 + 8.95707i 0.464971 + 0.583055i
\(237\) 0 0
\(238\) 0.766815 + 1.01011i 0.0497052 + 0.0654758i
\(239\) 4.76555 2.29497i 0.308258 0.148449i −0.273359 0.961912i \(-0.588135\pi\)
0.581617 + 0.813463i \(0.302420\pi\)
\(240\) 0 0
\(241\) −0.149391 0.654524i −0.00962310 0.0421616i 0.969888 0.243550i \(-0.0783119\pi\)
−0.979512 + 0.201388i \(0.935455\pi\)
\(242\) 6.12822 + 2.95120i 0.393937 + 0.189710i
\(243\) 0 0
\(244\) 9.05265 0.579536
\(245\) 24.8579 + 13.4687i 1.58811 + 0.860482i
\(246\) 0 0
\(247\) 1.02543 1.28585i 0.0652467 0.0818168i
\(248\) 11.4495 + 5.51381i 0.727047 + 0.350127i
\(249\) 0 0
\(250\) 14.2079 + 6.84214i 0.898584 + 0.432735i
\(251\) 9.37828 4.51634i 0.591952 0.285069i −0.113828 0.993501i \(-0.536311\pi\)
0.705780 + 0.708431i \(0.250597\pi\)
\(252\) 0 0
\(253\) −0.0961507 0.0463037i −0.00604494 0.00291109i
\(254\) −0.552830 0.693227i −0.0346876 0.0434969i
\(255\) 0 0
\(256\) −4.10612 + 5.14891i −0.256632 + 0.321807i
\(257\) −0.883387 + 3.87037i −0.0551041 + 0.241427i −0.994978 0.100095i \(-0.968085\pi\)
0.939874 + 0.341522i \(0.110942\pi\)
\(258\) 0 0
\(259\) −7.01060 + 27.6548i −0.435617 + 1.71839i
\(260\) −1.54978 1.94337i −0.0961135 0.120522i
\(261\) 0 0
\(262\) 0.717305 3.14272i 0.0443152 0.194158i
\(263\) −6.59671 −0.406771 −0.203385 0.979099i \(-0.565194\pi\)
−0.203385 + 0.979099i \(0.565194\pi\)
\(264\) 0 0
\(265\) −6.13872 + 26.8955i −0.377098 + 1.65218i
\(266\) 4.54089 5.42328i 0.278420 0.332523i
\(267\) 0 0
\(268\) −3.74766 16.4196i −0.228924 1.00298i
\(269\) 13.9706 + 17.5186i 0.851804 + 1.06813i 0.996898 + 0.0787100i \(0.0250801\pi\)
−0.145094 + 0.989418i \(0.546348\pi\)
\(270\) 0 0
\(271\) 0.933332 + 4.08919i 0.0566959 + 0.248401i 0.995332 0.0965074i \(-0.0307672\pi\)
−0.938636 + 0.344908i \(0.887910\pi\)
\(272\) 0.319214 + 1.39857i 0.0193552 + 0.0848006i
\(273\) 0 0
\(274\) −0.462432 + 2.02605i −0.0279365 + 0.122398i
\(275\) −0.603017 −0.0363633
\(276\) 0 0
\(277\) −4.48945 + 19.6696i −0.269745 + 1.18183i 0.640566 + 0.767904i \(0.278700\pi\)
−0.910310 + 0.413926i \(0.864157\pi\)
\(278\) 9.76382 4.70201i 0.585595 0.282008i
\(279\) 0 0
\(280\) −14.4564 19.0432i −0.863937 1.13805i
\(281\) −10.7077 + 13.4270i −0.638767 + 0.800988i −0.990848 0.134981i \(-0.956903\pi\)
0.352081 + 0.935969i \(0.385474\pi\)
\(282\) 0 0
\(283\) 6.91185 8.66719i 0.410867 0.515211i −0.532740 0.846279i \(-0.678838\pi\)
0.943607 + 0.331068i \(0.107409\pi\)
\(284\) −15.6991 + 7.56030i −0.931572 + 0.448621i
\(285\) 0 0
\(286\) −0.0113023 0.00544291i −0.000668320 0.000321846i
\(287\) −4.90055 2.50581i −0.289270 0.147913i
\(288\) 0 0
\(289\) 14.7753 + 7.11543i 0.869138 + 0.418555i
\(290\) −4.86137 21.2991i −0.285470 1.25072i
\(291\) 0 0
\(292\) 2.49432 3.12777i 0.145969 0.183039i
\(293\) −32.7132 −1.91112 −0.955562 0.294791i \(-0.904750\pi\)
−0.955562 + 0.294791i \(0.904750\pi\)
\(294\) 0 0
\(295\) 28.6078 1.66561
\(296\) 15.0426 18.8628i 0.874333 1.09638i
\(297\) 0 0
\(298\) 2.23932 + 9.81112i 0.129721 + 0.568343i
\(299\) −0.686335 0.330521i −0.0396918 0.0191145i
\(300\) 0 0
\(301\) 17.0477 7.71398i 0.982616 0.444627i
\(302\) −2.68039 1.29081i −0.154239 0.0742777i
\(303\) 0 0
\(304\) 7.20868 3.47152i 0.413446 0.199105i
\(305\) 14.0941 17.6734i 0.807024 1.01198i
\(306\) 0 0
\(307\) −3.38992 + 4.25082i −0.193473 + 0.242607i −0.869100 0.494636i \(-0.835301\pi\)
0.675627 + 0.737243i \(0.263873\pi\)
\(308\) 0.203099 + 0.103851i 0.0115726 + 0.00591747i
\(309\) 0 0
\(310\) 12.7834 6.15618i 0.726051 0.349648i
\(311\) −3.05055 + 13.3654i −0.172981 + 0.757880i 0.811779 + 0.583964i \(0.198499\pi\)
−0.984761 + 0.173916i \(0.944358\pi\)
\(312\) 0 0
\(313\) −22.0195 −1.24462 −0.622309 0.782772i \(-0.713805\pi\)
−0.622309 + 0.782772i \(0.713805\pi\)
\(314\) −0.770298 + 3.37490i −0.0434704 + 0.190456i
\(315\) 0 0
\(316\) −3.87295 16.9685i −0.217871 0.954554i
\(317\) −2.21593 9.70861i −0.124459 0.545290i −0.998258 0.0590026i \(-0.981208\pi\)
0.873799 0.486287i \(-0.161649\pi\)
\(318\) 0 0
\(319\) 0.290654 + 0.364468i 0.0162735 + 0.0204063i
\(320\) −0.203345 0.890913i −0.0113673 0.0498036i
\(321\) 0 0
\(322\) −2.91698 1.49155i −0.162557 0.0831208i
\(323\) −0.745409 + 3.26585i −0.0414756 + 0.181717i
\(324\) 0 0
\(325\) −4.30440 −0.238765
\(326\) 0.367510 1.61016i 0.0203545 0.0891788i
\(327\) 0 0
\(328\) 2.90208 + 3.63909i 0.160240 + 0.200935i
\(329\) −18.1958 + 21.7316i −1.00317 + 1.19810i
\(330\) 0 0
\(331\) 4.61336 20.2124i 0.253573 1.11098i −0.674411 0.738356i \(-0.735602\pi\)
0.927984 0.372620i \(-0.121540\pi\)
\(332\) 0.905547 1.13552i 0.0496983 0.0623197i
\(333\) 0 0
\(334\) −5.75778 7.22003i −0.315052 0.395062i
\(335\) −37.8905 18.2471i −2.07018 0.996945i
\(336\) 0 0
\(337\) −19.6965 + 9.48533i −1.07294 + 0.516699i −0.885052 0.465492i \(-0.845877\pi\)
−0.187885 + 0.982191i \(0.560163\pi\)
\(338\) 7.16364 + 3.44983i 0.389651 + 0.187646i
\(339\) 0 0
\(340\) 4.56139 + 2.19665i 0.247376 + 0.119130i
\(341\) −0.188767 + 0.236706i −0.0102223 + 0.0128184i
\(342\) 0 0
\(343\) −18.4728 1.32532i −0.997436 0.0715604i
\(344\) −15.8239 −0.853167
\(345\) 0 0
\(346\) −2.25487 1.08589i −0.121223 0.0583778i
\(347\) 2.04869 + 8.97591i 0.109980 + 0.481852i 0.999680 + 0.0253068i \(0.00805625\pi\)
−0.889700 + 0.456545i \(0.849087\pi\)
\(348\) 0 0
\(349\) −30.1787 + 14.5333i −1.61543 + 0.777950i −0.999948 0.0102001i \(-0.996753\pi\)
−0.615483 + 0.788150i \(0.711039\pi\)
\(350\) −18.5069 0.441916i −0.989236 0.0236214i
\(351\) 0 0
\(352\) −0.186771 0.234203i −0.00995491 0.0124831i
\(353\) 4.69848 2.26267i 0.250075 0.120430i −0.304648 0.952465i \(-0.598539\pi\)
0.554723 + 0.832035i \(0.312824\pi\)
\(354\) 0 0
\(355\) −9.68207 + 42.4199i −0.513871 + 2.25141i
\(356\) 12.2278 15.3332i 0.648072 0.812656i
\(357\) 0 0
\(358\) 1.91135 + 2.39676i 0.101018 + 0.126673i
\(359\) 14.7239 7.09065i 0.777097 0.374230i −0.00291421 0.999996i \(-0.500928\pi\)
0.780011 + 0.625766i \(0.215213\pi\)
\(360\) 0 0
\(361\) −0.316475 −0.0166566
\(362\) −7.98347 −0.419602
\(363\) 0 0
\(364\) 1.44974 + 0.741302i 0.0759872 + 0.0388548i
\(365\) −2.22292 9.73926i −0.116353 0.509776i
\(366\) 0 0
\(367\) −2.85353 3.57822i −0.148953 0.186781i 0.701757 0.712416i \(-0.252399\pi\)
−0.850710 + 0.525635i \(0.823828\pi\)
\(368\) −2.31059 2.89739i −0.120448 0.151037i
\(369\) 0 0
\(370\) −5.99410 26.2619i −0.311618 1.36529i
\(371\) −3.59956 17.7094i −0.186880 0.919424i
\(372\) 0 0
\(373\) 24.5427 1.27077 0.635387 0.772194i \(-0.280841\pi\)
0.635387 + 0.772194i \(0.280841\pi\)
\(374\) 0.0255507 0.00132120
\(375\) 0 0
\(376\) 21.5954 10.3998i 1.11370 0.536328i
\(377\) 2.07472 + 2.60162i 0.106853 + 0.133990i
\(378\) 0 0
\(379\) −2.14950 + 2.69539i −0.110412 + 0.138453i −0.833967 0.551815i \(-0.813936\pi\)
0.723555 + 0.690267i \(0.242507\pi\)
\(380\) 6.28338 27.5293i 0.322331 1.41222i
\(381\) 0 0
\(382\) −0.861184 + 0.414724i −0.0440620 + 0.0212191i
\(383\) 17.0160 + 21.3374i 0.869476 + 1.09029i 0.995165 + 0.0982187i \(0.0313145\pi\)
−0.125689 + 0.992070i \(0.540114\pi\)
\(384\) 0 0
\(385\) 0.518953 0.234822i 0.0264483 0.0119677i
\(386\) −8.35001 + 4.02115i −0.425004 + 0.204671i
\(387\) 0 0
\(388\) 3.59755 + 15.7619i 0.182638 + 0.800190i
\(389\) 5.02221 + 2.41857i 0.254636 + 0.122626i 0.556848 0.830615i \(-0.312011\pi\)
−0.302212 + 0.953241i \(0.597725\pi\)
\(390\) 0 0
\(391\) 1.55157 0.0784663
\(392\) 13.7705 + 7.46121i 0.695514 + 0.376848i
\(393\) 0 0
\(394\) 3.43378 4.30582i 0.172991 0.216924i
\(395\) −39.1573 18.8572i −1.97022 0.948807i
\(396\) 0 0
\(397\) −1.96250 0.945088i −0.0984948 0.0474326i 0.383988 0.923338i \(-0.374551\pi\)
−0.482483 + 0.875906i \(0.660265\pi\)
\(398\) 7.82896 3.77023i 0.392430 0.188984i
\(399\) 0 0
\(400\) −18.8665 9.08562i −0.943324 0.454281i
\(401\) 0.819337 + 1.02742i 0.0409157 + 0.0513067i 0.801868 0.597501i \(-0.203839\pi\)
−0.760953 + 0.648807i \(0.775268\pi\)
\(402\) 0 0
\(403\) −1.34744 + 1.68964i −0.0671208 + 0.0841668i
\(404\) −2.54243 + 11.1391i −0.126490 + 0.554191i
\(405\) 0 0
\(406\) 8.65322 + 11.3987i 0.429452 + 0.565709i
\(407\) 0.358378 + 0.449391i 0.0177641 + 0.0222755i
\(408\) 0 0
\(409\) 3.02377 13.2480i 0.149516 0.655071i −0.843504 0.537123i \(-0.819511\pi\)
0.993020 0.117948i \(-0.0376317\pi\)
\(410\) 5.19684 0.256654
\(411\) 0 0
\(412\) 6.65400 29.1531i 0.327819 1.43627i
\(413\) −17.0735 + 7.72563i −0.840132 + 0.380154i
\(414\) 0 0
\(415\) −0.807019 3.53578i −0.0396150 0.173565i
\(416\) −1.33319 1.67177i −0.0653650 0.0819651i
\(417\) 0 0
\(418\) −0.0317110 0.138935i −0.00155103 0.00679552i
\(419\) 4.25773 + 18.6544i 0.208004 + 0.911325i 0.965893 + 0.258941i \(0.0833736\pi\)
−0.757889 + 0.652383i \(0.773769\pi\)
\(420\) 0 0
\(421\) 1.32787 5.81777i 0.0647163 0.283541i −0.932207 0.361926i \(-0.882119\pi\)
0.996923 + 0.0783853i \(0.0249764\pi\)
\(422\) −8.21020 −0.399666
\(423\) 0 0
\(424\) −3.40065 + 14.8992i −0.165150 + 0.723571i
\(425\) 7.89893 3.80393i 0.383155 0.184518i
\(426\) 0 0
\(427\) −3.63876 + 14.3539i −0.176092 + 0.694633i
\(428\) 11.5142 14.4384i 0.556562 0.697907i
\(429\) 0 0
\(430\) −11.0155 + 13.8129i −0.531212 + 0.666119i
\(431\) 5.39828 2.59968i 0.260026 0.125222i −0.299329 0.954150i \(-0.596763\pi\)
0.559356 + 0.828928i \(0.311049\pi\)
\(432\) 0 0
\(433\) −5.67798 2.73437i −0.272866 0.131406i 0.292447 0.956282i \(-0.405530\pi\)
−0.565313 + 0.824876i \(0.691245\pi\)
\(434\) −5.96683 + 7.12631i −0.286417 + 0.342074i
\(435\) 0 0
\(436\) −7.27208 3.50205i −0.348269 0.167718i
\(437\) −1.92565 8.43684i −0.0921165 0.403589i
\(438\) 0 0
\(439\) −1.98987 + 2.49521i −0.0949711 + 0.119090i −0.827046 0.562134i \(-0.809981\pi\)
0.732075 + 0.681224i \(0.238552\pi\)
\(440\) −0.481697 −0.0229640
\(441\) 0 0
\(442\) 0.182384 0.00867512
\(443\) −18.5532 + 23.2650i −0.881491 + 1.10535i 0.112254 + 0.993680i \(0.464193\pi\)
−0.993745 + 0.111675i \(0.964379\pi\)
\(444\) 0 0
\(445\) −10.8974 47.7444i −0.516584 2.26330i
\(446\) 8.79739 + 4.23660i 0.416568 + 0.200609i
\(447\) 0 0
\(448\) 0.361953 + 0.476794i 0.0171007 + 0.0225264i
\(449\) 27.0875 + 13.0446i 1.27834 + 0.615614i 0.944962 0.327180i \(-0.106098\pi\)
0.333375 + 0.942794i \(0.391813\pi\)
\(450\) 0 0
\(451\) −0.0999097 + 0.0481140i −0.00470456 + 0.00226560i
\(452\) 12.0786 15.1460i 0.568128 0.712410i
\(453\) 0 0
\(454\) 6.15560 7.71888i 0.288897 0.362265i
\(455\) 3.70434 1.67619i 0.173662 0.0785810i
\(456\) 0 0
\(457\) −26.6941 + 12.8552i −1.24870 + 0.601340i −0.937162 0.348895i \(-0.886557\pi\)
−0.311533 + 0.950235i \(0.600843\pi\)
\(458\) −1.18603 + 5.19634i −0.0554196 + 0.242809i
\(459\) 0 0
\(460\) −13.0789 −0.609806
\(461\) −1.09106 + 4.78027i −0.0508159 + 0.222639i −0.993960 0.109746i \(-0.964996\pi\)
0.943144 + 0.332385i \(0.107853\pi\)
\(462\) 0 0
\(463\) 3.59483 + 15.7500i 0.167066 + 0.731963i 0.987160 + 0.159734i \(0.0510638\pi\)
−0.820094 + 0.572228i \(0.806079\pi\)
\(464\) 3.60221 + 15.7823i 0.167228 + 0.732675i
\(465\) 0 0
\(466\) 2.11549 + 2.65274i 0.0979982 + 0.122886i
\(467\) −8.51045 37.2867i −0.393817 1.72542i −0.651014 0.759066i \(-0.725656\pi\)
0.257197 0.966359i \(-0.417201\pi\)
\(468\) 0 0
\(469\) 27.5412 + 0.657641i 1.27174 + 0.0303670i
\(470\) 5.95500 26.0905i 0.274684 1.20347i
\(471\) 0 0
\(472\) 15.8478 0.729453
\(473\) 0.0838885 0.367539i 0.00385720 0.0168995i
\(474\) 0 0
\(475\) −30.4876 38.2302i −1.39887 1.75412i
\(476\) −3.31551 0.0791691i −0.151966 0.00362871i
\(477\) 0 0
\(478\) 0.727979 3.18948i 0.0332970 0.145884i
\(479\) −19.7900 + 24.8158i −0.904226 + 1.13386i 0.0862630 + 0.996272i \(0.472507\pi\)
−0.990489 + 0.137591i \(0.956064\pi\)
\(480\) 0 0
\(481\) 2.55814 + 3.20781i 0.116641 + 0.146263i
\(482\) −0.374117 0.180165i −0.0170405 0.00820629i
\(483\) 0 0
\(484\) −16.0258 + 7.71764i −0.728448 + 0.350802i
\(485\) 36.3729 + 17.5163i 1.65161 + 0.795372i
\(486\) 0 0
\(487\) −8.30514 3.99954i −0.376342 0.181237i 0.236144 0.971718i \(-0.424116\pi\)
−0.612486 + 0.790481i \(0.709830\pi\)
\(488\) 7.80766 9.79050i 0.353436 0.443195i
\(489\) 0 0
\(490\) 16.0990 6.82652i 0.727280 0.308391i
\(491\) −9.72710 −0.438978 −0.219489 0.975615i \(-0.570439\pi\)
−0.219489 + 0.975615i \(0.570439\pi\)
\(492\) 0 0
\(493\) −6.10640 2.94069i −0.275019 0.132442i
\(494\) −0.226357 0.991733i −0.0101843 0.0446202i
\(495\) 0 0
\(496\) −9.47235 + 4.56164i −0.425321 + 0.204824i
\(497\) −5.67727 27.9314i −0.254660 1.25290i
\(498\) 0 0
\(499\) −11.6707 14.6346i −0.522453 0.655136i 0.448675 0.893695i \(-0.351896\pi\)
−0.971128 + 0.238560i \(0.923325\pi\)
\(500\) −37.1548 + 17.8928i −1.66161 + 0.800191i
\(501\) 0 0
\(502\) 1.43261 6.27669i 0.0639406 0.280142i
\(503\) 11.4601 14.3705i 0.510981 0.640749i −0.457686 0.889114i \(-0.651322\pi\)
0.968667 + 0.248364i \(0.0798930\pi\)
\(504\) 0 0
\(505\) 17.7885 + 22.3060i 0.791576 + 0.992605i
\(506\) −0.0594698 + 0.0286392i −0.00264376 + 0.00127317i
\(507\) 0 0
\(508\) 2.31872 0.102877
\(509\) −11.0967 −0.491855 −0.245927 0.969288i \(-0.579092\pi\)
−0.245927 + 0.969288i \(0.579092\pi\)
\(510\) 0 0
\(511\) 3.95679 + 5.21221i 0.175038 + 0.230575i
\(512\) −4.15790 18.2170i −0.183755 0.805083i
\(513\) 0 0
\(514\) 1.53092 + 1.91972i 0.0675261 + 0.0846751i
\(515\) −46.5557 58.3790i −2.05149 2.57249i
\(516\) 0 0
\(517\) 0.127069 + 0.556726i 0.00558849 + 0.0244848i
\(518\) 10.6695 + 14.0547i 0.468790 + 0.617528i
\(519\) 0 0
\(520\) −3.43841 −0.150784
\(521\) −14.5769 −0.638627 −0.319313 0.947649i \(-0.603452\pi\)
−0.319313 + 0.947649i \(0.603452\pi\)
\(522\) 0 0
\(523\) 0.404037 0.194574i 0.0176673 0.00850813i −0.425029 0.905180i \(-0.639736\pi\)
0.442697 + 0.896671i \(0.354022\pi\)
\(524\) 5.25592 + 6.59072i 0.229606 + 0.287917i
\(525\) 0 0
\(526\) −2.54391 + 3.18996i −0.110920 + 0.139089i
\(527\) 0.979482 4.29139i 0.0426669 0.186936i
\(528\) 0 0
\(529\) 17.1110 8.24021i 0.743955 0.358270i
\(530\) 10.6385 + 13.3403i 0.462107 + 0.579464i
\(531\) 0 0
\(532\) 3.68438 + 18.1267i 0.159738 + 0.785892i
\(533\) −0.713167 + 0.343443i −0.0308907 + 0.0148762i
\(534\) 0 0
\(535\) −10.2614 44.9583i −0.443641 1.94372i
\(536\) −20.9901 10.1083i −0.906634 0.436612i
\(537\) 0 0
\(538\) 13.8590 0.597502
\(539\) −0.246303 + 0.280290i −0.0106090 + 0.0120730i
\(540\) 0 0
\(541\) −11.5661 + 14.5034i −0.497266 + 0.623552i −0.965610 0.259994i \(-0.916279\pi\)
0.468344 + 0.883546i \(0.344851\pi\)
\(542\) 2.33733 + 1.12560i 0.100397 + 0.0483485i
\(543\) 0 0
\(544\) 3.92390 + 1.88965i 0.168236 + 0.0810181i
\(545\) −18.1589 + 8.74487i −0.777843 + 0.374589i
\(546\) 0 0
\(547\) 6.21231 + 2.99169i 0.265619 + 0.127915i 0.561953 0.827169i \(-0.310050\pi\)
−0.296334 + 0.955084i \(0.595764\pi\)
\(548\) −3.38839 4.24890i −0.144745 0.181504i
\(549\) 0 0
\(550\) −0.232543 + 0.291600i −0.00991566 + 0.0124338i
\(551\) −8.41166 + 36.8539i −0.358349 + 1.57003i
\(552\) 0 0
\(553\) 28.4620 + 0.679628i 1.21033 + 0.0289007i
\(554\) 7.78029 + 9.75618i 0.330553 + 0.414500i
\(555\) 0 0
\(556\) −6.30620 + 27.6292i −0.267442 + 1.17174i
\(557\) 40.3244 1.70860 0.854299 0.519781i \(-0.173987\pi\)
0.854299 + 0.519781i \(0.173987\pi\)
\(558\) 0 0
\(559\) 0.598805 2.62354i 0.0253268 0.110964i
\(560\) 19.7744 + 0.472182i 0.835622 + 0.0199533i
\(561\) 0 0
\(562\) 2.36364 + 10.3558i 0.0997041 + 0.436832i
\(563\) −3.30611 4.14573i −0.139336 0.174722i 0.707267 0.706946i \(-0.249928\pi\)
−0.846603 + 0.532225i \(0.821356\pi\)
\(564\) 0 0
\(565\) −10.7644 47.1618i −0.452860 1.98411i
\(566\) −1.52574 6.68470i −0.0641316 0.280979i
\(567\) 0 0
\(568\) −5.36355 + 23.4993i −0.225050 + 0.986007i
\(569\) 42.7802 1.79344 0.896720 0.442598i \(-0.145943\pi\)
0.896720 + 0.442598i \(0.145943\pi\)
\(570\) 0 0
\(571\) −2.89677 + 12.6916i −0.121226 + 0.531127i 0.877449 + 0.479670i \(0.159244\pi\)
−0.998675 + 0.0514567i \(0.983614\pi\)
\(572\) 0.0295566 0.0142337i 0.00123582 0.000595141i
\(573\) 0 0
\(574\) −3.10154 + 1.40343i −0.129456 + 0.0585779i
\(575\) −14.1212 + 17.7074i −0.588895 + 0.738451i
\(576\) 0 0
\(577\) 13.5274 16.9629i 0.563154 0.706173i −0.415983 0.909372i \(-0.636563\pi\)
0.979137 + 0.203199i \(0.0651339\pi\)
\(578\) 9.13865 4.40094i 0.380118 0.183055i
\(579\) 0 0
\(580\) 51.4736 + 24.7884i 2.13732 + 1.02928i
\(581\) 1.43649 + 1.89226i 0.0595957 + 0.0785043i
\(582\) 0 0
\(583\) −0.328034 0.157973i −0.0135858 0.00654257i
\(584\) −1.23143 5.39524i −0.0509568 0.223257i
\(585\) 0 0
\(586\) −12.6153 + 15.8190i −0.521132 + 0.653478i
\(587\) 6.07713 0.250830 0.125415 0.992104i \(-0.459974\pi\)
0.125415 + 0.992104i \(0.459974\pi\)
\(588\) 0 0
\(589\) −24.5505 −1.01159
\(590\) 11.0321 13.8338i 0.454184 0.569529i
\(591\) 0 0
\(592\) 4.44154 + 19.4597i 0.182546 + 0.799788i
\(593\) 21.0947 + 10.1587i 0.866257 + 0.417167i 0.813586 0.581445i \(-0.197512\pi\)
0.0526709 + 0.998612i \(0.483227\pi\)
\(594\) 0 0
\(595\) −5.31648 + 6.34958i −0.217954 + 0.260307i
\(596\) −23.7106 11.4184i −0.971224 0.467717i
\(597\) 0 0
\(598\) −0.424502 + 0.204430i −0.0173592 + 0.00835975i
\(599\) 1.68654 2.11485i 0.0689102 0.0864106i −0.746182 0.665742i \(-0.768115\pi\)
0.815092 + 0.579332i \(0.196686\pi\)
\(600\) 0 0
\(601\) 21.0204 26.3587i 0.857439 1.07519i −0.138951 0.990299i \(-0.544373\pi\)
0.996390 0.0848950i \(-0.0270555\pi\)
\(602\) 2.84393 11.2185i 0.115910 0.457232i
\(603\) 0 0
\(604\) 7.00946 3.37558i 0.285211 0.137350i
\(605\) −9.88357 + 43.3027i −0.401824 + 1.76051i
\(606\) 0 0
\(607\) 17.5455 0.712148 0.356074 0.934458i \(-0.384115\pi\)
0.356074 + 0.934458i \(0.384115\pi\)
\(608\) 5.40523 23.6819i 0.219211 0.960427i
\(609\) 0 0
\(610\) −3.11116 13.6309i −0.125967 0.551898i
\(611\) 0.907034 + 3.97397i 0.0366947 + 0.160770i
\(612\) 0 0
\(613\) 13.9667 + 17.5137i 0.564110 + 0.707372i 0.979312 0.202358i \(-0.0648603\pi\)
−0.415201 + 0.909730i \(0.636289\pi\)
\(614\) 0.748298 + 3.27851i 0.0301989 + 0.132310i
\(615\) 0 0
\(616\) 0.287483 0.130084i 0.0115830 0.00524124i
\(617\) −1.16088 + 5.08614i −0.0467352 + 0.204760i −0.992905 0.118910i \(-0.962060\pi\)
0.946170 + 0.323671i \(0.104917\pi\)
\(618\) 0 0
\(619\) 4.76208 0.191404 0.0957020 0.995410i \(-0.469490\pi\)
0.0957020 + 0.995410i \(0.469490\pi\)
\(620\) −8.25649 + 36.1741i −0.331589 + 1.45278i
\(621\) 0 0
\(622\) 5.28666 + 6.62926i 0.211976 + 0.265809i
\(623\) 19.3972 + 25.5516i 0.777134 + 1.02370i
\(624\) 0 0
\(625\) −10.3278 + 45.2492i −0.413114 + 1.80997i
\(626\) −8.49145 + 10.6479i −0.339386 + 0.425577i
\(627\) 0 0
\(628\) −5.64422 7.07763i −0.225229 0.282428i
\(629\) −7.52923 3.62589i −0.300210 0.144574i
\(630\) 0 0
\(631\) 11.6595 5.61490i 0.464155 0.223525i −0.187165 0.982329i \(-0.559930\pi\)
0.651320 + 0.758803i \(0.274216\pi\)
\(632\) −21.6919 10.4463i −0.862857 0.415530i
\(633\) 0 0
\(634\) −5.54931 2.67240i −0.220391 0.106135i
\(635\) 3.61002 4.52682i 0.143259 0.179641i
\(636\) 0 0
\(637\) −1.75814 + 2.00074i −0.0696600 + 0.0792723i
\(638\) 0.288331 0.0114151
\(639\) 0 0
\(640\) −41.4086 19.9413i −1.63682 0.788250i
\(641\) 0.803931 + 3.52225i 0.0317534 + 0.139121i 0.988320 0.152394i \(-0.0486981\pi\)
−0.956567 + 0.291514i \(0.905841\pi\)
\(642\) 0 0
\(643\) 27.2244 13.1106i 1.07363 0.517032i 0.188353 0.982101i \(-0.439685\pi\)
0.885274 + 0.465070i \(0.153971\pi\)
\(644\) 7.80565 3.53200i 0.307586 0.139180i
\(645\) 0 0
\(646\) 1.29181 + 1.61987i 0.0508254 + 0.0637330i
\(647\) 1.40985 0.678946i 0.0554268 0.0266921i −0.405965 0.913889i \(-0.633065\pi\)
0.461392 + 0.887196i \(0.347350\pi\)
\(648\) 0 0
\(649\) −0.0840152 + 0.368094i −0.00329788 + 0.0144490i
\(650\) −1.65992 + 2.08147i −0.0651073 + 0.0816420i
\(651\) 0 0
\(652\) 2.69286 + 3.37674i 0.105461 + 0.132243i
\(653\) 8.46598 4.07700i 0.331299 0.159545i −0.260838 0.965383i \(-0.583999\pi\)
0.592137 + 0.805837i \(0.298284\pi\)
\(654\) 0 0
\(655\) 21.0499 0.822489
\(656\) −3.85079 −0.150348
\(657\) 0 0
\(658\) 3.49183 + 17.1793i 0.136126 + 0.669721i
\(659\) 5.36045 + 23.4857i 0.208813 + 0.914871i 0.965358 + 0.260929i \(0.0840289\pi\)
−0.756545 + 0.653942i \(0.773114\pi\)
\(660\) 0 0
\(661\) 21.9239 + 27.4917i 0.852742 + 1.06930i 0.996816 + 0.0797377i \(0.0254083\pi\)
−0.144074 + 0.989567i \(0.546020\pi\)
\(662\) −7.99502 10.0254i −0.310735 0.389650i
\(663\) 0 0
\(664\) −0.447063 1.95871i −0.0173494 0.0760127i
\(665\) 41.1248 + 21.0285i 1.59475 + 0.815449i
\(666\) 0 0
\(667\) 17.5089 0.677948
\(668\) 24.1497 0.934381
\(669\) 0 0
\(670\) −23.4355 + 11.2859i −0.905393 + 0.436014i
\(671\) 0.186011 + 0.233251i 0.00718088 + 0.00900454i
\(672\) 0 0
\(673\) −4.23581 + 5.31154i −0.163278 + 0.204745i −0.856739 0.515749i \(-0.827514\pi\)
0.693461 + 0.720494i \(0.256085\pi\)
\(674\) −3.00881 + 13.1824i −0.115895 + 0.507769i
\(675\) 0 0
\(676\) −18.7336 + 9.02160i −0.720521 + 0.346985i
\(677\) −8.78740 11.0190i −0.337727 0.423496i 0.583747 0.811935i \(-0.301586\pi\)
−0.921474 + 0.388439i \(0.873014\pi\)
\(678\) 0 0
\(679\) −26.4381 0.631301i −1.01460 0.0242271i
\(680\) 6.30976 3.03862i 0.241968 0.116526i
\(681\) 0 0
\(682\) 0.0416689 + 0.182563i 0.00159558 + 0.00699071i
\(683\) −30.7166 14.7924i −1.17534 0.566014i −0.258789 0.965934i \(-0.583324\pi\)
−0.916550 + 0.399920i \(0.869038\pi\)
\(684\) 0 0
\(685\) −13.5705 −0.518501
\(686\) −7.76458 + 8.42176i −0.296453 + 0.321544i
\(687\) 0 0
\(688\) 8.16229 10.2352i 0.311185 0.390213i
\(689\) −2.34155 1.12763i −0.0892058 0.0429593i
\(690\) 0 0
\(691\) 10.9171 + 5.25738i 0.415305 + 0.200000i 0.629855 0.776713i \(-0.283114\pi\)
−0.214550 + 0.976713i \(0.568829\pi\)
\(692\) 5.89670 2.83970i 0.224159 0.107949i
\(693\) 0 0
\(694\) 5.13050 + 2.47072i 0.194751 + 0.0937873i
\(695\) 44.1222 + 55.3275i 1.67365 + 2.09869i
\(696\) 0 0
\(697\) 1.00521 1.26049i 0.0380750 0.0477445i
\(698\) −4.61006 + 20.1980i −0.174493 + 0.764505i
\(699\) 0 0
\(700\) 31.0787 37.1180i 1.17466 1.40293i
\(701\) −25.7952 32.3461i −0.974270 1.22170i −0.975116 0.221696i \(-0.928841\pi\)
0.000845631 1.00000i \(-0.499731\pi\)
\(702\) 0 0
\(703\) −10.3716 + 45.4411i −0.391173 + 1.71384i
\(704\) 0.0120605 0.000454547
\(705\) 0 0
\(706\) 0.717733 3.14460i 0.0270122 0.118348i
\(707\) −16.6402 8.50869i −0.625820 0.320002i
\(708\) 0 0
\(709\) −2.85073 12.4899i −0.107061 0.469067i −0.999828 0.0185474i \(-0.994096\pi\)
0.892766 0.450520i \(-0.148761\pi\)
\(710\) 16.7792 + 21.0404i 0.629711 + 0.789633i
\(711\) 0 0
\(712\) −6.03678 26.4489i −0.226238 0.991213i
\(713\) 2.53035 + 11.0862i 0.0947622 + 0.415181i
\(714\) 0 0
\(715\) 0.0182283 0.0798635i 0.000681701 0.00298673i
\(716\) −8.01674 −0.299600
\(717\) 0 0
\(718\) 2.24920 9.85438i 0.0839393 0.367762i
\(719\) −31.7889 + 15.3087i −1.18552 + 0.570918i −0.919516 0.393052i \(-0.871419\pi\)
−0.266008 + 0.963971i \(0.585705\pi\)
\(720\) 0 0
\(721\) 43.5505 + 22.2688i 1.62191 + 0.829334i
\(722\) −0.122043 + 0.153037i −0.00454197 + 0.00569545i
\(723\) 0 0
\(724\) 13.0169 16.3227i 0.483769 0.606628i
\(725\) 89.1366 42.9259i 3.31045 1.59423i
\(726\) 0 0
\(727\) −30.3425 14.6122i −1.12534 0.541935i −0.223802 0.974635i \(-0.571847\pi\)
−0.901538 + 0.432699i \(0.857561\pi\)
\(728\) 2.05209 0.928555i 0.0760554 0.0344145i
\(729\) 0 0
\(730\) −5.56683 2.68084i −0.206038 0.0992224i
\(731\) 1.21964 + 5.34359i 0.0451100 + 0.197640i
\(732\) 0 0
\(733\) −30.3410 + 38.0464i −1.12067 + 1.40528i −0.217466 + 0.976068i \(0.569779\pi\)
−0.903205 + 0.429209i \(0.858792\pi\)
\(734\) −2.83072 −0.104484
\(735\) 0 0
\(736\) −11.2510 −0.414718
\(737\) 0.346061 0.433946i 0.0127473 0.0159846i
\(738\) 0 0
\(739\) −4.27327 18.7224i −0.157195 0.688715i −0.990684 0.136180i \(-0.956518\pi\)
0.833489 0.552535i \(-0.186340\pi\)
\(740\) 63.4672 + 30.5642i 2.33310 + 1.12356i
\(741\) 0 0
\(742\) −9.95178 5.08867i −0.365341 0.186811i
\(743\) −41.0343 19.7611i −1.50540 0.724963i −0.514243 0.857644i \(-0.671927\pi\)
−0.991159 + 0.132681i \(0.957641\pi\)
\(744\) 0 0
\(745\) −59.2071 + 28.5127i −2.16918 + 1.04462i
\(746\) 9.46447 11.8681i 0.346519 0.434521i
\(747\) 0 0
\(748\) −0.0416600 + 0.0522400i −0.00152324 + 0.00191008i
\(749\) 18.2653 + 24.0606i 0.667400 + 0.879154i
\(750\) 0 0
\(751\) −25.5628 + 12.3104i −0.932799 + 0.449212i −0.837623 0.546248i \(-0.816056\pi\)
−0.0951758 + 0.995460i \(0.530341\pi\)
\(752\) −4.41257 + 19.3327i −0.160910 + 0.704992i
\(753\) 0 0
\(754\) 2.05814 0.0749529
\(755\) 4.32292 18.9400i 0.157327 0.689296i
\(756\) 0 0
\(757\) −7.68780 33.6824i −0.279418 1.22421i −0.898532 0.438908i \(-0.855365\pi\)
0.619114 0.785301i \(-0.287492\pi\)
\(758\) 0.474485 + 2.07886i 0.0172341 + 0.0755075i
\(759\) 0 0
\(760\) −24.3539 30.5388i −0.883407 1.10776i
\(761\) −6.67421 29.2416i −0.241940 1.06001i −0.939249 0.343238i \(-0.888476\pi\)
0.697309 0.716771i \(-0.254381\pi\)
\(762\) 0 0
\(763\) 8.47589 10.1229i 0.306848 0.366475i
\(764\) 0.556216 2.43694i 0.0201232 0.0881655i
\(765\) 0 0
\(766\) 16.8800 0.609898
\(767\) −0.599710 + 2.62750i −0.0216543 + 0.0948735i
\(768\) 0 0
\(769\) 0.272327 + 0.341488i 0.00982038 + 0.0123144i 0.786717 0.617313i \(-0.211779\pi\)
−0.776897 + 0.629628i \(0.783207\pi\)
\(770\) 0.0865725 0.341504i 0.00311986 0.0123070i
\(771\) 0 0
\(772\) 5.39305 23.6285i 0.194100 0.850408i
\(773\) 25.7298 32.2642i 0.925438 1.16046i −0.0612962 0.998120i \(-0.519523\pi\)
0.986734 0.162343i \(-0.0519051\pi\)
\(774\) 0 0
\(775\) 40.0613 + 50.2353i 1.43905 + 1.80451i
\(776\) 20.1494 + 9.70344i 0.723321 + 0.348333i
\(777\) 0 0
\(778\) 3.10627 1.49590i 0.111365 0.0536306i
\(779\) −8.10162 3.90154i −0.290271 0.139787i
\(780\) 0 0
\(781\) −0.517380 0.249157i −0.0185133 0.00891554i
\(782\) 0.598336 0.750290i 0.0213965 0.0268303i
\(783\) 0 0
\(784\) −11.9292 + 5.05835i −0.426041 + 0.180655i
\(785\) −22.6051 −0.806810
\(786\) 0 0
\(787\) 10.6071 + 5.10813i 0.378104 + 0.182085i 0.613276 0.789869i \(-0.289851\pi\)
−0.235173 + 0.971954i \(0.575566\pi\)
\(788\) 3.20480 + 14.0411i 0.114166 + 0.500194i
\(789\) 0 0
\(790\) −24.2190 + 11.6633i −0.861675 + 0.414961i
\(791\) 19.1605 + 25.2398i 0.681270 + 0.897424i
\(792\) 0 0
\(793\) 1.32777 + 1.66497i 0.0471505 + 0.0591248i
\(794\) −1.21382 + 0.584543i −0.0430767 + 0.0207447i
\(795\) 0 0
\(796\) −5.05652 + 22.1541i −0.179224 + 0.785230i
\(797\) −0.111693 + 0.140059i −0.00395637 + 0.00496113i −0.783806 0.621006i \(-0.786724\pi\)
0.779849 + 0.625967i \(0.215296\pi\)
\(798\) 0 0
\(799\) −5.17640 6.49100i −0.183128 0.229635i
\(800\) −57.2781 + 27.5837i −2.02509 + 0.975230i
\(801\) 0 0
\(802\) 0.812788 0.0287005
\(803\) 0.131843 0.00465263
\(804\) 0 0
\(805\) 5.25713 20.7379i 0.185289 0.730914i
\(806\) 0.297437 + 1.30316i 0.0104768 + 0.0459018i
\(807\) 0 0
\(808\) 9.85424 + 12.3568i 0.346671 + 0.434711i
\(809\) −7.48548 9.38649i −0.263175 0.330011i 0.632633 0.774452i \(-0.281974\pi\)
−0.895809 + 0.444440i \(0.853403\pi\)
\(810\) 0 0
\(811\) 2.12740 + 9.32076i 0.0747032 + 0.327296i 0.998447 0.0557157i \(-0.0177440\pi\)
−0.923744 + 0.383012i \(0.874887\pi\)
\(812\) −37.4143 0.893394i −1.31298 0.0313520i
\(813\) 0 0
\(814\) 0.355513 0.0124607
\(815\) 10.7849 0.377778
\(816\) 0 0
\(817\) 27.5426 13.2638i 0.963595 0.464043i
\(818\) −5.24024 6.57105i −0.183221 0.229751i
\(819\) 0 0
\(820\) −8.47335 + 10.6253i −0.295902 + 0.371050i
\(821\) 9.56885 41.9239i 0.333955 1.46315i −0.477444 0.878662i \(-0.658437\pi\)
0.811400 0.584492i \(-0.198706\pi\)
\(822\) 0 0
\(823\) 5.41216 2.60636i 0.188656 0.0908519i −0.337171 0.941443i \(-0.609470\pi\)
0.525827 + 0.850591i \(0.323756\pi\)
\(824\) −25.7904 32.3401i −0.898449 1.12662i
\(825\) 0 0
\(826\) −2.84823 + 11.2354i −0.0991024 + 0.390931i
\(827\) 28.3668 13.6607i 0.986410 0.475030i 0.130105 0.991500i \(-0.458469\pi\)
0.856305 + 0.516470i \(0.172754\pi\)
\(828\) 0 0
\(829\) 5.58609 + 24.4743i 0.194013 + 0.850026i 0.974416 + 0.224750i \(0.0721565\pi\)
−0.780404 + 0.625276i \(0.784986\pi\)
\(830\) −2.02100 0.973264i −0.0701501 0.0337825i
\(831\) 0 0
\(832\) 0.0860893 0.00298461
\(833\) 1.45822 5.22525i 0.0505242 0.181044i
\(834\) 0 0
\(835\) 37.5987 47.1473i 1.30116 1.63160i
\(836\) 0.335765 + 0.161696i 0.0116127 + 0.00559236i
\(837\) 0 0
\(838\) 10.6626 + 5.13482i 0.368332 + 0.177379i
\(839\) −1.82613 + 0.879416i −0.0630449 + 0.0303608i −0.465141 0.885237i \(-0.653996\pi\)
0.402096 + 0.915598i \(0.368282\pi\)
\(840\) 0 0
\(841\) −42.7804 20.6020i −1.47519 0.710412i
\(842\) −2.30122 2.88564i −0.0793052 0.0994456i
\(843\) 0 0
\(844\) 13.3866 16.7862i 0.460785 0.577806i
\(845\) −11.5535 + 50.6191i −0.397452 + 1.74135i
\(846\) 0 0
\(847\) −5.79542 28.5127i −0.199133 0.979709i
\(848\) −7.88298 9.88494i −0.270703 0.339450i
\(849\) 0 0
\(850\) 1.20663 5.28659i 0.0413870 0.181328i
\(851\) 21.5886 0.740047
\(852\) 0 0
\(853\) −1.58776 + 6.95644i −0.0543640 + 0.238184i −0.994809 0.101762i \(-0.967552\pi\)
0.940445 + 0.339947i \(0.110409\pi\)
\(854\) 5.53785 + 7.29491i 0.189501 + 0.249627i
\(855\) 0 0
\(856\) −5.68451 24.9055i −0.194293 0.851251i
\(857\) −22.6118 28.3544i −0.772406 0.968567i 0.227580 0.973759i \(-0.426919\pi\)
−0.999987 + 0.00519271i \(0.998347\pi\)
\(858\) 0 0
\(859\) 0.00122908 + 0.00538497i 4.19358e−5 + 0.000183733i 0.974949 0.222429i \(-0.0713986\pi\)
−0.974907 + 0.222613i \(0.928541\pi\)
\(860\) −10.2809 45.0435i −0.350575 1.53597i
\(861\) 0 0
\(862\) 0.824634 3.61296i 0.0280871 0.123058i
\(863\) −2.81750 −0.0959087 −0.0479543 0.998850i \(-0.515270\pi\)
−0.0479543 + 0.998850i \(0.515270\pi\)
\(864\) 0 0
\(865\) 3.63665 15.9332i 0.123650 0.541745i
\(866\) −3.51187 + 1.69123i −0.119338 + 0.0574702i
\(867\) 0 0
\(868\) −4.84135 23.8188i −0.164326 0.808464i
\(869\) 0.357631 0.448455i 0.0121318 0.0152128i
\(870\) 0 0
\(871\) 2.47022 3.09756i 0.0837003 0.104957i
\(872\) −10.0595 + 4.84438i −0.340656 + 0.164051i
\(873\) 0 0
\(874\) −4.82238 2.32233i −0.163119 0.0785541i
\(875\) −13.4363 66.1048i −0.454229 2.23475i
\(876\) 0 0
\(877\) 25.3716 + 12.2183i 0.856738 + 0.412583i 0.810074 0.586327i \(-0.199427\pi\)
0.0466640 + 0.998911i \(0.485141\pi\)
\(878\) 0.439248 + 1.92447i 0.0148239 + 0.0649477i
\(879\) 0 0
\(880\) 0.248470 0.311571i 0.00837591 0.0105031i
\(881\) −13.3084 −0.448373 −0.224186 0.974546i \(-0.571972\pi\)
−0.224186 + 0.974546i \(0.571972\pi\)
\(882\) 0 0
\(883\) −46.3470 −1.55970 −0.779850 0.625966i \(-0.784705\pi\)
−0.779850 + 0.625966i \(0.784705\pi\)
\(884\) −0.297374 + 0.372895i −0.0100018 + 0.0125418i
\(885\) 0 0
\(886\) 4.09548 + 17.9435i 0.137591 + 0.602823i
\(887\) −3.36077 1.61846i −0.112844 0.0543426i 0.376610 0.926372i \(-0.377090\pi\)
−0.489454 + 0.872029i \(0.662804\pi\)
\(888\) 0 0
\(889\) −0.932022 + 3.67656i −0.0312590 + 0.123308i
\(890\) −27.2900 13.1422i −0.914764 0.440527i
\(891\) 0 0
\(892\) −23.0060 + 11.0791i −0.770296 + 0.370955i
\(893\) −28.8711 + 36.2032i −0.966133 + 1.21149i
\(894\) 0 0
\(895\) −12.4813 + 15.6510i −0.417203 + 0.523156i
\(896\) 30.0984 + 0.718702i 1.00552 + 0.0240102i
\(897\) 0 0
\(898\) 16.7538 8.06819i 0.559081 0.269239i
\(899\) 11.0531 48.4268i 0.368641 1.61512i
\(900\) 0 0
\(901\) 5.29345 0.176350
\(902\) −0.0152621 + 0.0668674i −0.000508171 + 0.00222644i
\(903\) 0 0
\(904\) −5.96311 26.1261i −0.198330 0.868941i
\(905\) −11.6006 50.8256i −0.385617 1.68950i
\(906\) 0 0
\(907\) 8.37496 + 10.5019i 0.278086 + 0.348709i 0.901185 0.433434i \(-0.142698\pi\)
−0.623099 + 0.782143i \(0.714127\pi\)
\(908\) 5.74511 + 25.1710i 0.190658 + 0.835328i
\(909\) 0 0
\(910\) 0.617964 2.43770i 0.0204853 0.0808088i
\(911\) −12.6197 + 55.2907i −0.418111 + 1.83186i 0.124941 + 0.992164i \(0.460126\pi\)
−0.543052 + 0.839699i \(0.682731\pi\)
\(912\) 0 0
\(913\) 0.0478647 0.00158409
\(914\) −4.07774 + 17.8658i −0.134880 + 0.590947i
\(915\) 0 0
\(916\) −8.69043 10.8974i −0.287140 0.360062i
\(917\) −12.5629 + 5.68461i −0.414863 + 0.187722i
\(918\) 0 0
\(919\) −4.34213 + 19.0241i −0.143234 + 0.627548i 0.851438 + 0.524455i \(0.175731\pi\)
−0.994672 + 0.103093i \(0.967126\pi\)
\(920\) −11.2802 + 14.1449i −0.371897 + 0.466344i
\(921\) 0 0
\(922\) 1.89083 + 2.37103i 0.0622713 + 0.0780857i
\(923\) −3.69312 1.77851i −0.121560 0.0585404i
\(924\) 0 0
\(925\) 109.906 52.9279i 3.61368 1.74026i
\(926\) 9.00246 + 4.33535i 0.295839 + 0.142469i
\(927\) 0 0
\(928\) 44.2798 + 21.3240i 1.45356 + 0.699995i
\(929\) −11.3823 + 14.2729i −0.373440 + 0.468278i −0.932668 0.360735i \(-0.882526\pi\)
0.559229 + 0.829013i \(0.311097\pi\)
\(930\) 0 0
\(931\) −30.2226 1.44416i −0.990507 0.0473304i
\(932\) −8.87295 −0.290643
\(933\) 0 0
\(934\) −21.3126 10.2636i −0.697369 0.335835i
\(935\) 0.0371272 + 0.162665i 0.00121419 + 0.00531971i
\(936\) 0 0
\(937\) 15.0554 7.25031i 0.491839 0.236857i −0.171489 0.985186i \(-0.554858\pi\)
0.663328 + 0.748329i \(0.269143\pi\)
\(938\) 10.9388 13.0644i 0.357165 0.426569i
\(939\) 0 0
\(940\) 43.6341 + 54.7155i 1.42319 + 1.78462i
\(941\) −24.8825 + 11.9828i −0.811145 + 0.390627i −0.793010 0.609209i \(-0.791487\pi\)
−0.0181350 + 0.999836i \(0.505773\pi\)
\(942\) 0 0
\(943\) −0.926790 + 4.06053i −0.0301804 + 0.132229i
\(944\) −8.17462 + 10.2507i −0.266061 + 0.333630i
\(945\) 0 0
\(946\) −0.145380 0.182301i −0.00472671 0.00592711i
\(947\) 50.1247 24.1388i 1.62883 0.784405i 0.628858 0.777520i \(-0.283523\pi\)
0.999976 0.00688524i \(-0.00219166\pi\)
\(948\) 0 0
\(949\) 0.941109 0.0305497
\(950\) −30.2439 −0.981243
\(951\) 0 0
\(952\) −2.94516 + 3.51746i −0.0954531 + 0.114002i
\(953\) −8.39722 36.7906i −0.272013 1.19177i −0.907633 0.419764i \(-0.862113\pi\)
0.635621 0.772002i \(-0.280744\pi\)
\(954\) 0 0
\(955\) −3.89165 4.87997i −0.125931 0.157912i
\(956\) 5.33413 + 6.68879i 0.172518 + 0.216331i
\(957\) 0 0
\(958\) 4.36848 + 19.1396i 0.141139 + 0.618372i
\(959\) 8.09904 3.66476i 0.261532 0.118341i
\(960\) 0 0
\(961\) 1.25990 0.0406421
\(962\) 2.53769 0.0818186
\(963\) 0 0
\(964\) 0.978348 0.471148i 0.0315105 0.0151746i
\(965\) −37.7333 47.3160i −1.21468 1.52316i
\(966\) 0 0
\(967\) −13.4557 + 16.8729i −0.432705 + 0.542595i −0.949604 0.313451i \(-0.898515\pi\)
0.516899 + 0.856046i \(0.327086\pi\)
\(968\) −5.47518 + 23.9883i −0.175979 + 0.771014i
\(969\) 0 0
\(970\) 22.4969 10.8339i 0.722331 0.347856i
\(971\) −3.96219 4.96843i −0.127153 0.159444i 0.714180 0.699962i \(-0.246800\pi\)
−0.841333 + 0.540518i \(0.818228\pi\)
\(972\) 0 0
\(973\) −41.2741 21.1048i −1.32319 0.676589i
\(974\) −5.13678 + 2.47374i −0.164593 + 0.0792639i
\(975\) 0 0
\(976\) 2.30533 + 10.1003i 0.0737917 + 0.323302i
\(977\) −5.95871 2.86956i −0.190636 0.0918055i 0.336131 0.941815i \(-0.390882\pi\)
−0.526767 + 0.850010i \(0.676596\pi\)
\(978\) 0 0
\(979\) 0.646328 0.0206567
\(980\) −12.2920 + 44.0459i −0.392652 + 1.40700i
\(981\) 0 0
\(982\) −3.75109 + 4.70371i −0.119702 + 0.150102i
\(983\) −19.0045 9.15210i −0.606151 0.291907i 0.105523 0.994417i \(-0.466348\pi\)
−0.711674 + 0.702510i \(0.752063\pi\)
\(984\) 0 0
\(985\) 32.4019 + 15.6039i 1.03241 + 0.497183i
\(986\) −3.77685 + 1.81883i −0.120279 + 0.0579235i
\(987\) 0 0
\(988\) 2.39673 + 1.15420i 0.0762500 + 0.0367201i
\(989\) −8.82822 11.0702i −0.280721 0.352013i
\(990\) 0 0
\(991\) 0.0140925 0.0176715i 0.000447664 0.000561353i −0.781608 0.623770i \(-0.785600\pi\)
0.782055 + 0.623209i \(0.214171\pi\)
\(992\) −7.10259 + 31.1185i −0.225507 + 0.988013i
\(993\) 0 0
\(994\) −15.6961 8.02592i −0.497849 0.254567i
\(995\) 35.3787 + 44.3635i 1.12158 + 1.40642i
\(996\) 0 0
\(997\) 13.5212 59.2405i 0.428222 1.87616i −0.0513814 0.998679i \(-0.516362\pi\)
0.479604 0.877485i \(-0.340780\pi\)
\(998\) −11.5774 −0.366478
\(999\) 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 441.2.u.d.190.4 36
3.2 odd 2 147.2.i.b.43.3 36
49.8 even 7 inner 441.2.u.d.253.4 36
147.8 odd 14 147.2.i.b.106.3 yes 36
147.20 even 14 7203.2.a.g.1.7 18
147.29 odd 14 7203.2.a.h.1.7 18
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
147.2.i.b.43.3 36 3.2 odd 2
147.2.i.b.106.3 yes 36 147.8 odd 14
441.2.u.d.190.4 36 1.1 even 1 trivial
441.2.u.d.253.4 36 49.8 even 7 inner
7203.2.a.g.1.7 18 147.20 even 14
7203.2.a.h.1.7 18 147.29 odd 14