Properties

Label 1161.2.f.d.388.17
Level $1161$
Weight $2$
Character 1161.388
Analytic conductor $9.271$
Analytic rank $0$
Dimension $40$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1161,2,Mod(388,1161)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1161, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1161.388");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1161 = 3^{3} \cdot 43 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1161.f (of order \(3\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(9.27063167467\)
Analytic rank: \(0\)
Dimension: \(40\)
Relative dimension: \(20\) over \(\Q(\zeta_{3})\)
Twist minimal: no (minimal twist has level 387)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 388.17
Character \(\chi\) \(=\) 1161.388
Dual form 1161.2.f.d.775.17

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.911404 + 1.57860i) q^{2} +(-0.661315 + 1.14543i) q^{4} +(-0.216442 + 0.374888i) q^{5} +(0.345529 + 0.598473i) q^{7} +1.23472 q^{8} +O(q^{10})\) \(q+(0.911404 + 1.57860i) q^{2} +(-0.661315 + 1.14543i) q^{4} +(-0.216442 + 0.374888i) q^{5} +(0.345529 + 0.598473i) q^{7} +1.23472 q^{8} -0.789063 q^{10} +(1.26780 + 2.19589i) q^{11} +(3.60136 - 6.23773i) q^{13} +(-0.629833 + 1.09090i) q^{14} +(2.44795 + 4.23998i) q^{16} -4.46895 q^{17} +6.05843 q^{19} +(-0.286272 - 0.495838i) q^{20} +(-2.31095 + 4.00268i) q^{22} +(-2.05578 + 3.56072i) q^{23} +(2.40631 + 4.16784i) q^{25} +13.1292 q^{26} -0.914014 q^{28} +(3.23074 + 5.59581i) q^{29} +(1.26948 - 2.19881i) q^{31} +(-3.22744 + 5.59009i) q^{32} +(-4.07302 - 7.05468i) q^{34} -0.299147 q^{35} -9.14340 q^{37} +(5.52168 + 9.56383i) q^{38} +(-0.267244 + 0.462880i) q^{40} +(0.455380 - 0.788741i) q^{41} +(0.500000 + 0.866025i) q^{43} -3.35365 q^{44} -7.49459 q^{46} +(-4.79713 - 8.30887i) q^{47} +(3.26122 - 5.64860i) q^{49} +(-4.38623 + 7.59718i) q^{50} +(4.76326 + 8.25022i) q^{52} +8.85806 q^{53} -1.09761 q^{55} +(0.426630 + 0.738944i) q^{56} +(-5.88902 + 10.2001i) q^{58} +(-6.51130 + 11.2779i) q^{59} +(-0.396746 - 0.687184i) q^{61} +4.62805 q^{62} -1.97418 q^{64} +(1.55897 + 2.70021i) q^{65} +(-5.69986 + 9.87245i) q^{67} +(2.95539 - 5.11888i) q^{68} +(-0.272644 - 0.472233i) q^{70} +13.2707 q^{71} -4.01445 q^{73} +(-8.33334 - 14.4338i) q^{74} +(-4.00653 + 6.93952i) q^{76} +(-0.876120 + 1.51748i) q^{77} +(5.94290 + 10.2934i) q^{79} -2.11936 q^{80} +1.66014 q^{82} +(-4.88090 - 8.45396i) q^{83} +(0.967268 - 1.67536i) q^{85} +(-0.911404 + 1.57860i) q^{86} +(1.56537 + 2.71129i) q^{88} -8.04947 q^{89} +4.97749 q^{91} +(-2.71904 - 4.70951i) q^{92} +(8.74425 - 15.1455i) q^{94} +(-1.31130 + 2.27123i) q^{95} +(-7.49445 - 12.9808i) q^{97} +11.8892 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40 q - 6 q^{2} - 22 q^{4} - 17 q^{5} - 3 q^{7} + 30 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 40 q - 6 q^{2} - 22 q^{4} - 17 q^{5} - 3 q^{7} + 30 q^{8} - 4 q^{10} - 10 q^{11} + q^{13} - 10 q^{14} - 22 q^{16} + 40 q^{17} + 16 q^{19} - 30 q^{20} - 15 q^{22} - 19 q^{23} - 19 q^{25} + 50 q^{26} - 6 q^{28} - 25 q^{29} + 11 q^{31} - 36 q^{32} - 9 q^{34} + 18 q^{37} - 28 q^{38} - 12 q^{40} - 12 q^{41} + 20 q^{43} + 10 q^{44} + 8 q^{46} - 38 q^{47} - 37 q^{49} - 36 q^{50} + 8 q^{52} + 138 q^{53} - 18 q^{55} - 30 q^{56} + 27 q^{58} - 31 q^{59} - 19 q^{61} + 64 q^{62} + 22 q^{64} - 47 q^{65} - 9 q^{67} - 68 q^{68} + 6 q^{70} + 42 q^{71} - 4 q^{73} + 16 q^{74} - 37 q^{76} - 85 q^{77} + 4 q^{79} + 122 q^{80} + 2 q^{82} - 19 q^{83} + 6 q^{85} + 6 q^{86} - 60 q^{88} + 108 q^{89} - 6 q^{91} - 85 q^{92} + 19 q^{94} + 11 q^{95} - 2 q^{97} + 10 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1161\mathbb{Z}\right)^\times\).

\(n\) \(433\) \(947\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.911404 + 1.57860i 0.644460 + 1.11624i 0.984426 + 0.175800i \(0.0562511\pi\)
−0.339966 + 0.940438i \(0.610416\pi\)
\(3\) 0 0
\(4\) −0.661315 + 1.14543i −0.330658 + 0.572716i
\(5\) −0.216442 + 0.374888i −0.0967957 + 0.167655i −0.910357 0.413825i \(-0.864193\pi\)
0.813561 + 0.581480i \(0.197526\pi\)
\(6\) 0 0
\(7\) 0.345529 + 0.598473i 0.130598 + 0.226202i 0.923907 0.382617i \(-0.124977\pi\)
−0.793309 + 0.608819i \(0.791644\pi\)
\(8\) 1.23472 0.436538
\(9\) 0 0
\(10\) −0.789063 −0.249524
\(11\) 1.26780 + 2.19589i 0.382255 + 0.662084i 0.991384 0.130986i \(-0.0418144\pi\)
−0.609130 + 0.793071i \(0.708481\pi\)
\(12\) 0 0
\(13\) 3.60136 6.23773i 0.998837 1.73004i 0.457661 0.889127i \(-0.348687\pi\)
0.541176 0.840909i \(-0.317979\pi\)
\(14\) −0.629833 + 1.09090i −0.168330 + 0.291556i
\(15\) 0 0
\(16\) 2.44795 + 4.23998i 0.611989 + 1.06000i
\(17\) −4.46895 −1.08388 −0.541940 0.840417i \(-0.682310\pi\)
−0.541940 + 0.840417i \(0.682310\pi\)
\(18\) 0 0
\(19\) 6.05843 1.38990 0.694950 0.719058i \(-0.255427\pi\)
0.694950 + 0.719058i \(0.255427\pi\)
\(20\) −0.286272 0.495838i −0.0640124 0.110873i
\(21\) 0 0
\(22\) −2.31095 + 4.00268i −0.492696 + 0.853374i
\(23\) −2.05578 + 3.56072i −0.428660 + 0.742460i −0.996754 0.0805028i \(-0.974347\pi\)
0.568095 + 0.822963i \(0.307681\pi\)
\(24\) 0 0
\(25\) 2.40631 + 4.16784i 0.481261 + 0.833569i
\(26\) 13.1292 2.57484
\(27\) 0 0
\(28\) −0.914014 −0.172732
\(29\) 3.23074 + 5.59581i 0.599933 + 1.03912i 0.992830 + 0.119533i \(0.0381396\pi\)
−0.392897 + 0.919583i \(0.628527\pi\)
\(30\) 0 0
\(31\) 1.26948 2.19881i 0.228006 0.394918i −0.729211 0.684289i \(-0.760113\pi\)
0.957217 + 0.289371i \(0.0934461\pi\)
\(32\) −3.22744 + 5.59009i −0.570536 + 0.988197i
\(33\) 0 0
\(34\) −4.07302 7.05468i −0.698518 1.20987i
\(35\) −0.299147 −0.0505651
\(36\) 0 0
\(37\) −9.14340 −1.50317 −0.751583 0.659638i \(-0.770709\pi\)
−0.751583 + 0.659638i \(0.770709\pi\)
\(38\) 5.52168 + 9.56383i 0.895735 + 1.55146i
\(39\) 0 0
\(40\) −0.267244 + 0.462880i −0.0422550 + 0.0731877i
\(41\) 0.455380 0.788741i 0.0711184 0.123181i −0.828273 0.560324i \(-0.810677\pi\)
0.899392 + 0.437144i \(0.144010\pi\)
\(42\) 0 0
\(43\) 0.500000 + 0.866025i 0.0762493 + 0.132068i
\(44\) −3.35365 −0.505582
\(45\) 0 0
\(46\) −7.49459 −1.10502
\(47\) −4.79713 8.30887i −0.699733 1.21197i −0.968559 0.248785i \(-0.919969\pi\)
0.268826 0.963189i \(-0.413364\pi\)
\(48\) 0 0
\(49\) 3.26122 5.64860i 0.465889 0.806943i
\(50\) −4.38623 + 7.59718i −0.620307 + 1.07440i
\(51\) 0 0
\(52\) 4.76326 + 8.25022i 0.660546 + 1.14410i
\(53\) 8.85806 1.21675 0.608374 0.793650i \(-0.291822\pi\)
0.608374 + 0.793650i \(0.291822\pi\)
\(54\) 0 0
\(55\) −1.09761 −0.148002
\(56\) 0.426630 + 0.738944i 0.0570108 + 0.0987456i
\(57\) 0 0
\(58\) −5.88902 + 10.2001i −0.773266 + 1.33934i
\(59\) −6.51130 + 11.2779i −0.847699 + 1.46826i 0.0355576 + 0.999368i \(0.488679\pi\)
−0.883257 + 0.468890i \(0.844654\pi\)
\(60\) 0 0
\(61\) −0.396746 0.687184i −0.0507981 0.0879849i 0.839508 0.543347i \(-0.182843\pi\)
−0.890306 + 0.455362i \(0.849510\pi\)
\(62\) 4.62805 0.587763
\(63\) 0 0
\(64\) −1.97418 −0.246772
\(65\) 1.55897 + 2.70021i 0.193366 + 0.334920i
\(66\) 0 0
\(67\) −5.69986 + 9.87245i −0.696349 + 1.20611i 0.273375 + 0.961908i \(0.411860\pi\)
−0.969724 + 0.244204i \(0.921473\pi\)
\(68\) 2.95539 5.11888i 0.358393 0.620755i
\(69\) 0 0
\(70\) −0.272644 0.472233i −0.0325872 0.0564427i
\(71\) 13.2707 1.57495 0.787473 0.616349i \(-0.211389\pi\)
0.787473 + 0.616349i \(0.211389\pi\)
\(72\) 0 0
\(73\) −4.01445 −0.469856 −0.234928 0.972013i \(-0.575485\pi\)
−0.234928 + 0.972013i \(0.575485\pi\)
\(74\) −8.33334 14.4338i −0.968731 1.67789i
\(75\) 0 0
\(76\) −4.00653 + 6.93952i −0.459581 + 0.796017i
\(77\) −0.876120 + 1.51748i −0.0998431 + 0.172933i
\(78\) 0 0
\(79\) 5.94290 + 10.2934i 0.668628 + 1.15810i 0.978288 + 0.207251i \(0.0664516\pi\)
−0.309659 + 0.950848i \(0.600215\pi\)
\(80\) −2.11936 −0.236951
\(81\) 0 0
\(82\) 1.66014 0.183332
\(83\) −4.88090 8.45396i −0.535748 0.927943i −0.999127 0.0417825i \(-0.986696\pi\)
0.463379 0.886160i \(-0.346637\pi\)
\(84\) 0 0
\(85\) 0.967268 1.67536i 0.104915 0.181718i
\(86\) −0.911404 + 1.57860i −0.0982792 + 0.170225i
\(87\) 0 0
\(88\) 1.56537 + 2.71129i 0.166869 + 0.289025i
\(89\) −8.04947 −0.853242 −0.426621 0.904431i \(-0.640296\pi\)
−0.426621 + 0.904431i \(0.640296\pi\)
\(90\) 0 0
\(91\) 4.97749 0.521783
\(92\) −2.71904 4.70951i −0.283479 0.491000i
\(93\) 0 0
\(94\) 8.74425 15.1455i 0.901900 1.56214i
\(95\) −1.31130 + 2.27123i −0.134536 + 0.233024i
\(96\) 0 0
\(97\) −7.49445 12.9808i −0.760947 1.31800i −0.942363 0.334592i \(-0.891402\pi\)
0.181417 0.983406i \(-0.441932\pi\)
\(98\) 11.8892 1.20099
\(99\) 0 0
\(100\) −6.36531 −0.636531
\(101\) −1.55310 2.69005i −0.154539 0.267670i 0.778352 0.627828i \(-0.216056\pi\)
−0.932891 + 0.360159i \(0.882723\pi\)
\(102\) 0 0
\(103\) −3.48129 + 6.02977i −0.343022 + 0.594131i −0.984992 0.172598i \(-0.944784\pi\)
0.641970 + 0.766729i \(0.278117\pi\)
\(104\) 4.44665 7.70183i 0.436030 0.755226i
\(105\) 0 0
\(106\) 8.07328 + 13.9833i 0.784146 + 1.35818i
\(107\) −8.10561 −0.783599 −0.391800 0.920051i \(-0.628147\pi\)
−0.391800 + 0.920051i \(0.628147\pi\)
\(108\) 0 0
\(109\) −0.0751888 −0.00720178 −0.00360089 0.999994i \(-0.501146\pi\)
−0.00360089 + 0.999994i \(0.501146\pi\)
\(110\) −1.00037 1.73269i −0.0953816 0.165206i
\(111\) 0 0
\(112\) −1.69168 + 2.93007i −0.159849 + 0.276866i
\(113\) 3.84430 6.65852i 0.361641 0.626380i −0.626590 0.779349i \(-0.715550\pi\)
0.988231 + 0.152969i \(0.0488833\pi\)
\(114\) 0 0
\(115\) −0.889913 1.54137i −0.0829848 0.143734i
\(116\) −8.54615 −0.793490
\(117\) 0 0
\(118\) −23.7377 −2.18523
\(119\) −1.54415 2.67455i −0.141552 0.245176i
\(120\) 0 0
\(121\) 2.28539 3.95841i 0.207763 0.359856i
\(122\) 0.723192 1.25260i 0.0654747 0.113405i
\(123\) 0 0
\(124\) 1.67906 + 2.90821i 0.150784 + 0.261165i
\(125\) −4.24772 −0.379927
\(126\) 0 0
\(127\) 0.411999 0.0365590 0.0182795 0.999833i \(-0.494181\pi\)
0.0182795 + 0.999833i \(0.494181\pi\)
\(128\) 4.65560 + 8.06373i 0.411501 + 0.712740i
\(129\) 0 0
\(130\) −2.84170 + 4.92197i −0.249234 + 0.431685i
\(131\) 1.51555 2.62501i 0.132414 0.229348i −0.792193 0.610271i \(-0.791060\pi\)
0.924607 + 0.380923i \(0.124394\pi\)
\(132\) 0 0
\(133\) 2.09336 + 3.62581i 0.181518 + 0.314398i
\(134\) −20.7795 −1.79508
\(135\) 0 0
\(136\) −5.51788 −0.473155
\(137\) −5.34442 9.25680i −0.456604 0.790862i 0.542174 0.840266i \(-0.317601\pi\)
−0.998779 + 0.0494039i \(0.984268\pi\)
\(138\) 0 0
\(139\) 11.3648 19.6844i 0.963951 1.66961i 0.251543 0.967846i \(-0.419062\pi\)
0.712408 0.701766i \(-0.247605\pi\)
\(140\) 0.197831 0.342653i 0.0167197 0.0289594i
\(141\) 0 0
\(142\) 12.0950 + 20.9492i 1.01499 + 1.75801i
\(143\) 18.2631 1.52724
\(144\) 0 0
\(145\) −2.79707 −0.232284
\(146\) −3.65879 6.33720i −0.302803 0.524471i
\(147\) 0 0
\(148\) 6.04667 10.4731i 0.497033 0.860887i
\(149\) 7.49268 12.9777i 0.613824 1.06317i −0.376766 0.926309i \(-0.622964\pi\)
0.990590 0.136866i \(-0.0437028\pi\)
\(150\) 0 0
\(151\) −4.01750 6.95851i −0.326939 0.566276i 0.654964 0.755660i \(-0.272684\pi\)
−0.981903 + 0.189385i \(0.939351\pi\)
\(152\) 7.48044 0.606744
\(153\) 0 0
\(154\) −3.19400 −0.257380
\(155\) 0.549538 + 0.951828i 0.0441399 + 0.0764526i
\(156\) 0 0
\(157\) −3.44630 + 5.96916i −0.275045 + 0.476391i −0.970146 0.242520i \(-0.922026\pi\)
0.695102 + 0.718911i \(0.255359\pi\)
\(158\) −10.8328 + 18.7629i −0.861809 + 1.49270i
\(159\) 0 0
\(160\) −1.39710 2.41985i −0.110451 0.191306i
\(161\) −2.84132 −0.223928
\(162\) 0 0
\(163\) 6.87193 0.538251 0.269125 0.963105i \(-0.413265\pi\)
0.269125 + 0.963105i \(0.413265\pi\)
\(164\) 0.602299 + 1.04321i 0.0470317 + 0.0814613i
\(165\) 0 0
\(166\) 8.89694 15.4100i 0.690536 1.19604i
\(167\) 7.79562 13.5024i 0.603243 1.04485i −0.389083 0.921203i \(-0.627208\pi\)
0.992327 0.123645i \(-0.0394584\pi\)
\(168\) 0 0
\(169\) −19.4396 33.6703i −1.49535 2.59002i
\(170\) 3.52629 0.270454
\(171\) 0 0
\(172\) −1.32263 −0.100850
\(173\) −1.53573 2.65997i −0.116760 0.202234i 0.801722 0.597697i \(-0.203917\pi\)
−0.918482 + 0.395463i \(0.870584\pi\)
\(174\) 0 0
\(175\) −1.66290 + 2.88022i −0.125703 + 0.217724i
\(176\) −6.20701 + 10.7509i −0.467871 + 0.810376i
\(177\) 0 0
\(178\) −7.33632 12.7069i −0.549880 0.952420i
\(179\) −6.81694 −0.509522 −0.254761 0.967004i \(-0.581997\pi\)
−0.254761 + 0.967004i \(0.581997\pi\)
\(180\) 0 0
\(181\) −6.26156 −0.465418 −0.232709 0.972546i \(-0.574759\pi\)
−0.232709 + 0.972546i \(0.574759\pi\)
\(182\) 4.53651 + 7.85746i 0.336268 + 0.582434i
\(183\) 0 0
\(184\) −2.53830 + 4.39647i −0.187126 + 0.324112i
\(185\) 1.97901 3.42775i 0.145500 0.252013i
\(186\) 0 0
\(187\) −5.66572 9.81331i −0.414318 0.717620i
\(188\) 12.6897 0.925488
\(189\) 0 0
\(190\) −4.78049 −0.346813
\(191\) −4.89485 8.47813i −0.354179 0.613456i 0.632798 0.774317i \(-0.281906\pi\)
−0.986977 + 0.160861i \(0.948573\pi\)
\(192\) 0 0
\(193\) −3.22778 + 5.59068i −0.232341 + 0.402426i −0.958496 0.285104i \(-0.907972\pi\)
0.726156 + 0.687530i \(0.241305\pi\)
\(194\) 13.6610 23.6615i 0.980799 1.69879i
\(195\) 0 0
\(196\) 4.31339 + 7.47101i 0.308099 + 0.533643i
\(197\) 9.52049 0.678307 0.339154 0.940731i \(-0.389859\pi\)
0.339154 + 0.940731i \(0.389859\pi\)
\(198\) 0 0
\(199\) 16.8531 1.19469 0.597344 0.801985i \(-0.296223\pi\)
0.597344 + 0.801985i \(0.296223\pi\)
\(200\) 2.97110 + 5.14610i 0.210089 + 0.363884i
\(201\) 0 0
\(202\) 2.83100 4.90344i 0.199189 0.345005i
\(203\) −2.23263 + 3.86702i −0.156700 + 0.271412i
\(204\) 0 0
\(205\) 0.197126 + 0.341433i 0.0137679 + 0.0238467i
\(206\) −12.6915 −0.884256
\(207\) 0 0
\(208\) 35.2638 2.44511
\(209\) 7.68085 + 13.3036i 0.531296 + 0.920231i
\(210\) 0 0
\(211\) −0.656265 + 1.13668i −0.0451792 + 0.0782526i −0.887731 0.460363i \(-0.847719\pi\)
0.842552 + 0.538616i \(0.181053\pi\)
\(212\) −5.85797 + 10.1463i −0.402327 + 0.696851i
\(213\) 0 0
\(214\) −7.38749 12.7955i −0.504998 0.874683i
\(215\) −0.432883 −0.0295224
\(216\) 0 0
\(217\) 1.75457 0.119108
\(218\) −0.0685274 0.118693i −0.00464126 0.00803890i
\(219\) 0 0
\(220\) 0.725869 1.25724i 0.0489381 0.0847633i
\(221\) −16.0943 + 27.8761i −1.08262 + 1.87515i
\(222\) 0 0
\(223\) 0.949986 + 1.64542i 0.0636157 + 0.110186i 0.896079 0.443894i \(-0.146403\pi\)
−0.832463 + 0.554080i \(0.813070\pi\)
\(224\) −4.46069 −0.298042
\(225\) 0 0
\(226\) 14.0148 0.932252
\(227\) −6.36963 11.0325i −0.422767 0.732254i 0.573442 0.819246i \(-0.305608\pi\)
−0.996209 + 0.0869919i \(0.972275\pi\)
\(228\) 0 0
\(229\) −11.8720 + 20.5630i −0.784526 + 1.35884i 0.144756 + 0.989467i \(0.453760\pi\)
−0.929282 + 0.369371i \(0.879573\pi\)
\(230\) 1.62214 2.80963i 0.106961 0.185262i
\(231\) 0 0
\(232\) 3.98904 + 6.90923i 0.261894 + 0.453613i
\(233\) 7.78814 0.510218 0.255109 0.966912i \(-0.417889\pi\)
0.255109 + 0.966912i \(0.417889\pi\)
\(234\) 0 0
\(235\) 4.15319 0.270925
\(236\) −8.61204 14.9165i −0.560596 0.970981i
\(237\) 0 0
\(238\) 2.81469 4.87519i 0.182449 0.316012i
\(239\) −1.70650 + 2.95575i −0.110385 + 0.191192i −0.915925 0.401349i \(-0.868542\pi\)
0.805541 + 0.592540i \(0.201875\pi\)
\(240\) 0 0
\(241\) 6.16770 + 10.6828i 0.397296 + 0.688137i 0.993391 0.114777i \(-0.0366152\pi\)
−0.596095 + 0.802914i \(0.703282\pi\)
\(242\) 8.33166 0.535579
\(243\) 0 0
\(244\) 1.04950 0.0671871
\(245\) 1.41173 + 2.44518i 0.0901920 + 0.156217i
\(246\) 0 0
\(247\) 21.8186 37.7909i 1.38828 2.40458i
\(248\) 1.56745 2.71490i 0.0995331 0.172396i
\(249\) 0 0
\(250\) −3.87139 6.70544i −0.244848 0.424089i
\(251\) −7.32241 −0.462186 −0.231093 0.972932i \(-0.574230\pi\)
−0.231093 + 0.972932i \(0.574230\pi\)
\(252\) 0 0
\(253\) −10.4252 −0.655429
\(254\) 0.375498 + 0.650381i 0.0235608 + 0.0408086i
\(255\) 0 0
\(256\) −10.4604 + 18.1180i −0.653778 + 1.13238i
\(257\) 2.49747 4.32575i 0.155788 0.269833i −0.777558 0.628812i \(-0.783542\pi\)
0.933346 + 0.358979i \(0.116875\pi\)
\(258\) 0 0
\(259\) −3.15931 5.47208i −0.196310 0.340019i
\(260\) −4.12388 −0.255752
\(261\) 0 0
\(262\) 5.52511 0.341342
\(263\) −9.05500 15.6837i −0.558355 0.967099i −0.997634 0.0687485i \(-0.978099\pi\)
0.439279 0.898351i \(-0.355234\pi\)
\(264\) 0 0
\(265\) −1.91725 + 3.32078i −0.117776 + 0.203994i
\(266\) −3.81580 + 6.60916i −0.233962 + 0.405234i
\(267\) 0 0
\(268\) −7.53881 13.0576i −0.460506 0.797620i
\(269\) −12.3502 −0.753004 −0.376502 0.926416i \(-0.622873\pi\)
−0.376502 + 0.926416i \(0.622873\pi\)
\(270\) 0 0
\(271\) −11.1352 −0.676418 −0.338209 0.941071i \(-0.609821\pi\)
−0.338209 + 0.941071i \(0.609821\pi\)
\(272\) −10.9398 18.9483i −0.663322 1.14891i
\(273\) 0 0
\(274\) 9.74185 16.8734i 0.588527 1.01936i
\(275\) −6.10141 + 10.5679i −0.367929 + 0.637271i
\(276\) 0 0
\(277\) −7.92554 13.7274i −0.476200 0.824802i 0.523429 0.852070i \(-0.324653\pi\)
−0.999628 + 0.0272677i \(0.991319\pi\)
\(278\) 41.4318 2.48491
\(279\) 0 0
\(280\) −0.369362 −0.0220736
\(281\) −4.44576 7.70028i −0.265212 0.459360i 0.702407 0.711775i \(-0.252109\pi\)
−0.967619 + 0.252415i \(0.918775\pi\)
\(282\) 0 0
\(283\) 3.93496 6.81556i 0.233909 0.405143i −0.725046 0.688701i \(-0.758181\pi\)
0.958955 + 0.283558i \(0.0915148\pi\)
\(284\) −8.77614 + 15.2007i −0.520768 + 0.901997i
\(285\) 0 0
\(286\) 16.6451 + 28.8302i 0.984245 + 1.70476i
\(287\) 0.629388 0.0371516
\(288\) 0 0
\(289\) 2.97154 0.174796
\(290\) −2.54926 4.41545i −0.149698 0.259284i
\(291\) 0 0
\(292\) 2.65482 4.59828i 0.155361 0.269094i
\(293\) −16.7554 + 29.0212i −0.978859 + 1.69543i −0.312298 + 0.949984i \(0.601099\pi\)
−0.666561 + 0.745450i \(0.732235\pi\)
\(294\) 0 0
\(295\) −2.81863 4.88202i −0.164107 0.284242i
\(296\) −11.2895 −0.656189
\(297\) 0 0
\(298\) 27.3154 1.58234
\(299\) 14.8072 + 25.6468i 0.856322 + 1.48319i
\(300\) 0 0
\(301\) −0.345529 + 0.598473i −0.0199160 + 0.0344954i
\(302\) 7.32313 12.6840i 0.421399 0.729884i
\(303\) 0 0
\(304\) 14.8308 + 25.6876i 0.850603 + 1.47329i
\(305\) 0.343489 0.0196681
\(306\) 0 0
\(307\) 12.9225 0.737524 0.368762 0.929524i \(-0.379782\pi\)
0.368762 + 0.929524i \(0.379782\pi\)
\(308\) −1.15878 2.00707i −0.0660277 0.114363i
\(309\) 0 0
\(310\) −1.00170 + 1.73500i −0.0568929 + 0.0985413i
\(311\) −6.78105 + 11.7451i −0.384518 + 0.666005i −0.991702 0.128556i \(-0.958966\pi\)
0.607184 + 0.794561i \(0.292299\pi\)
\(312\) 0 0
\(313\) 11.6910 + 20.2493i 0.660812 + 1.14456i 0.980403 + 0.197004i \(0.0631211\pi\)
−0.319591 + 0.947556i \(0.603546\pi\)
\(314\) −12.5639 −0.709021
\(315\) 0 0
\(316\) −15.7205 −0.884348
\(317\) 0.805713 + 1.39554i 0.0452533 + 0.0783811i 0.887765 0.460297i \(-0.152257\pi\)
−0.842512 + 0.538678i \(0.818924\pi\)
\(318\) 0 0
\(319\) −8.19183 + 14.1887i −0.458655 + 0.794413i
\(320\) 0.427295 0.740096i 0.0238865 0.0413726i
\(321\) 0 0
\(322\) −2.58960 4.48531i −0.144312 0.249957i
\(323\) −27.0748 −1.50648
\(324\) 0 0
\(325\) 34.6639 1.92281
\(326\) 6.26310 + 10.8480i 0.346881 + 0.600816i
\(327\) 0 0
\(328\) 0.562265 0.973871i 0.0310459 0.0537730i
\(329\) 3.31509 5.74191i 0.182767 0.316562i
\(330\) 0 0
\(331\) −17.1277 29.6660i −0.941422 1.63059i −0.762762 0.646679i \(-0.776157\pi\)
−0.178660 0.983911i \(-0.557176\pi\)
\(332\) 12.9112 0.708597
\(333\) 0 0
\(334\) 28.4198 1.55506
\(335\) −2.46737 4.27362i −0.134807 0.233493i
\(336\) 0 0
\(337\) −7.67840 + 13.2994i −0.418269 + 0.724464i −0.995766 0.0919297i \(-0.970697\pi\)
0.577496 + 0.816393i \(0.304030\pi\)
\(338\) 35.4346 61.3745i 1.92739 3.33833i
\(339\) 0 0
\(340\) 1.27934 + 2.21588i 0.0693818 + 0.120173i
\(341\) 6.43778 0.348625
\(342\) 0 0
\(343\) 9.34478 0.504571
\(344\) 0.617358 + 1.06929i 0.0332857 + 0.0576525i
\(345\) 0 0
\(346\) 2.79935 4.84861i 0.150494 0.260663i
\(347\) −0.967222 + 1.67528i −0.0519232 + 0.0899336i −0.890819 0.454359i \(-0.849868\pi\)
0.838896 + 0.544292i \(0.183202\pi\)
\(348\) 0 0
\(349\) −2.79439 4.84003i −0.149580 0.259081i 0.781492 0.623915i \(-0.214459\pi\)
−0.931072 + 0.364834i \(0.881126\pi\)
\(350\) −6.06228 −0.324043
\(351\) 0 0
\(352\) −16.3669 −0.872360
\(353\) −2.26919 3.93036i −0.120777 0.209192i 0.799297 0.600936i \(-0.205205\pi\)
−0.920074 + 0.391744i \(0.871872\pi\)
\(354\) 0 0
\(355\) −2.87234 + 4.97504i −0.152448 + 0.264048i
\(356\) 5.32323 9.22011i 0.282131 0.488665i
\(357\) 0 0
\(358\) −6.21298 10.7612i −0.328366 0.568747i
\(359\) 11.5921 0.611809 0.305904 0.952062i \(-0.401041\pi\)
0.305904 + 0.952062i \(0.401041\pi\)
\(360\) 0 0
\(361\) 17.7046 0.931821
\(362\) −5.70681 9.88449i −0.299943 0.519517i
\(363\) 0 0
\(364\) −3.29169 + 5.70137i −0.172531 + 0.298833i
\(365\) 0.868894 1.50497i 0.0454800 0.0787737i
\(366\) 0 0
\(367\) 3.61750 + 6.26569i 0.188832 + 0.327066i 0.944861 0.327472i \(-0.106197\pi\)
−0.756029 + 0.654538i \(0.772863\pi\)
\(368\) −20.1298 −1.04934
\(369\) 0 0
\(370\) 7.21472 0.375076
\(371\) 3.06072 + 5.30132i 0.158904 + 0.275231i
\(372\) 0 0
\(373\) −5.87996 + 10.1844i −0.304453 + 0.527328i −0.977139 0.212600i \(-0.931807\pi\)
0.672686 + 0.739928i \(0.265140\pi\)
\(374\) 10.3275 17.8878i 0.534023 0.924955i
\(375\) 0 0
\(376\) −5.92309 10.2591i −0.305460 0.529072i
\(377\) 46.5402 2.39694
\(378\) 0 0
\(379\) −5.11108 −0.262539 −0.131269 0.991347i \(-0.541905\pi\)
−0.131269 + 0.991347i \(0.541905\pi\)
\(380\) −1.73436 3.00400i −0.0889709 0.154102i
\(381\) 0 0
\(382\) 8.92237 15.4540i 0.456508 0.790696i
\(383\) 8.07593 13.9879i 0.412661 0.714749i −0.582519 0.812817i \(-0.697933\pi\)
0.995180 + 0.0980678i \(0.0312662\pi\)
\(384\) 0 0
\(385\) −0.379258 0.656893i −0.0193288 0.0334784i
\(386\) −11.7672 −0.598937
\(387\) 0 0
\(388\) 19.8248 1.00645
\(389\) 8.61616 + 14.9236i 0.436857 + 0.756658i 0.997445 0.0714365i \(-0.0227583\pi\)
−0.560588 + 0.828095i \(0.689425\pi\)
\(390\) 0 0
\(391\) 9.18718 15.9127i 0.464616 0.804738i
\(392\) 4.02668 6.97441i 0.203378 0.352261i
\(393\) 0 0
\(394\) 8.67702 + 15.0290i 0.437142 + 0.757152i
\(395\) −5.14516 −0.258881
\(396\) 0 0
\(397\) −29.6151 −1.48634 −0.743170 0.669103i \(-0.766679\pi\)
−0.743170 + 0.669103i \(0.766679\pi\)
\(398\) 15.3600 + 26.6043i 0.769929 + 1.33356i
\(399\) 0 0
\(400\) −11.7811 + 20.4054i −0.589053 + 1.02027i
\(401\) −7.15251 + 12.3885i −0.357179 + 0.618653i −0.987488 0.157692i \(-0.949595\pi\)
0.630309 + 0.776344i \(0.282928\pi\)
\(402\) 0 0
\(403\) −9.14372 15.8374i −0.455481 0.788917i
\(404\) 4.10835 0.204398
\(405\) 0 0
\(406\) −8.13931 −0.403947
\(407\) −11.5920 20.0779i −0.574592 0.995223i
\(408\) 0 0
\(409\) −8.43314 + 14.6066i −0.416992 + 0.722251i −0.995635 0.0933297i \(-0.970249\pi\)
0.578644 + 0.815581i \(0.303582\pi\)
\(410\) −0.359324 + 0.622367i −0.0177457 + 0.0307365i
\(411\) 0 0
\(412\) −4.60446 7.97516i −0.226846 0.392908i
\(413\) −8.99937 −0.442830
\(414\) 0 0
\(415\) 4.22572 0.207432
\(416\) 23.2463 + 40.2638i 1.13974 + 1.97409i
\(417\) 0 0
\(418\) −14.0007 + 24.2500i −0.684798 + 1.18610i
\(419\) −0.720706 + 1.24830i −0.0352088 + 0.0609835i −0.883093 0.469198i \(-0.844543\pi\)
0.847884 + 0.530182i \(0.177876\pi\)
\(420\) 0 0
\(421\) 0.693490 + 1.20116i 0.0337986 + 0.0585409i 0.882430 0.470444i \(-0.155906\pi\)
−0.848631 + 0.528985i \(0.822573\pi\)
\(422\) −2.39249 −0.116465
\(423\) 0 0
\(424\) 10.9372 0.531157
\(425\) −10.7537 18.6259i −0.521630 0.903489i
\(426\) 0 0
\(427\) 0.274174 0.474884i 0.0132682 0.0229812i
\(428\) 5.36036 9.28442i 0.259103 0.448780i
\(429\) 0 0
\(430\) −0.394532 0.683349i −0.0190260 0.0329540i
\(431\) 19.8758 0.957383 0.478692 0.877983i \(-0.341111\pi\)
0.478692 + 0.877983i \(0.341111\pi\)
\(432\) 0 0
\(433\) −3.09155 −0.148570 −0.0742851 0.997237i \(-0.523667\pi\)
−0.0742851 + 0.997237i \(0.523667\pi\)
\(434\) 1.59912 + 2.76976i 0.0767604 + 0.132953i
\(435\) 0 0
\(436\) 0.0497235 0.0861236i 0.00238132 0.00412457i
\(437\) −12.4548 + 21.5724i −0.595794 + 1.03195i
\(438\) 0 0
\(439\) −4.45099 7.70933i −0.212434 0.367946i 0.740042 0.672561i \(-0.234806\pi\)
−0.952476 + 0.304614i \(0.901472\pi\)
\(440\) −1.35524 −0.0646086
\(441\) 0 0
\(442\) −58.6736 −2.79082
\(443\) −5.48826 9.50594i −0.260755 0.451641i 0.705688 0.708523i \(-0.250638\pi\)
−0.966443 + 0.256882i \(0.917305\pi\)
\(444\) 0 0
\(445\) 1.74224 3.01765i 0.0825901 0.143050i
\(446\) −1.73164 + 2.99929i −0.0819956 + 0.142021i
\(447\) 0 0
\(448\) −0.682136 1.18149i −0.0322279 0.0558204i
\(449\) −18.7937 −0.886931 −0.443465 0.896292i \(-0.646251\pi\)
−0.443465 + 0.896292i \(0.646251\pi\)
\(450\) 0 0
\(451\) 2.30931 0.108741
\(452\) 5.08458 + 8.80675i 0.239159 + 0.414235i
\(453\) 0 0
\(454\) 11.6106 20.1102i 0.544913 0.943818i
\(455\) −1.07734 + 1.86600i −0.0505063 + 0.0874795i
\(456\) 0 0
\(457\) −9.85804 17.0746i −0.461140 0.798717i 0.537879 0.843022i \(-0.319226\pi\)
−0.999018 + 0.0443053i \(0.985893\pi\)
\(458\) −43.2809 −2.02238
\(459\) 0 0
\(460\) 2.35405 0.109758
\(461\) −20.0872 34.7921i −0.935556 1.62043i −0.773639 0.633627i \(-0.781565\pi\)
−0.161918 0.986804i \(-0.551768\pi\)
\(462\) 0 0
\(463\) −11.1465 + 19.3064i −0.518024 + 0.897243i 0.481757 + 0.876305i \(0.339999\pi\)
−0.999781 + 0.0209385i \(0.993335\pi\)
\(464\) −15.8174 + 27.3966i −0.734305 + 1.27185i
\(465\) 0 0
\(466\) 7.09814 + 12.2943i 0.328815 + 0.569524i
\(467\) −2.81433 −0.130232 −0.0651158 0.997878i \(-0.520742\pi\)
−0.0651158 + 0.997878i \(0.520742\pi\)
\(468\) 0 0
\(469\) −7.87786 −0.363766
\(470\) 3.78524 + 6.55623i 0.174600 + 0.302416i
\(471\) 0 0
\(472\) −8.03960 + 13.9250i −0.370053 + 0.640950i
\(473\) −1.26780 + 2.19589i −0.0582933 + 0.100967i
\(474\) 0 0
\(475\) 14.5784 + 25.2506i 0.668905 + 1.15858i
\(476\) 4.08468 0.187221
\(477\) 0 0
\(478\) −6.22126 −0.284554
\(479\) 7.84457 + 13.5872i 0.358428 + 0.620815i 0.987698 0.156371i \(-0.0499797\pi\)
−0.629271 + 0.777186i \(0.716646\pi\)
\(480\) 0 0
\(481\) −32.9287 + 57.0341i −1.50142 + 2.60053i
\(482\) −11.2425 + 19.4726i −0.512083 + 0.886954i
\(483\) 0 0
\(484\) 3.02273 + 5.23552i 0.137397 + 0.237978i
\(485\) 6.48845 0.294625
\(486\) 0 0
\(487\) −8.31905 −0.376972 −0.188486 0.982076i \(-0.560358\pi\)
−0.188486 + 0.982076i \(0.560358\pi\)
\(488\) −0.489868 0.848476i −0.0221753 0.0384087i
\(489\) 0 0
\(490\) −2.57331 + 4.45710i −0.116250 + 0.201351i
\(491\) 10.7300 18.5849i 0.484237 0.838723i −0.515599 0.856830i \(-0.672431\pi\)
0.999836 + 0.0181071i \(0.00576397\pi\)
\(492\) 0 0
\(493\) −14.4380 25.0074i −0.650256 1.12628i
\(494\) 79.5422 3.57877
\(495\) 0 0
\(496\) 12.4305 0.558148
\(497\) 4.58542 + 7.94218i 0.205684 + 0.356256i
\(498\) 0 0
\(499\) 4.43186 7.67620i 0.198397 0.343634i −0.749612 0.661878i \(-0.769760\pi\)
0.948009 + 0.318244i \(0.103093\pi\)
\(500\) 2.80908 4.86547i 0.125626 0.217590i
\(501\) 0 0
\(502\) −6.67367 11.5591i −0.297861 0.515910i
\(503\) 18.4384 0.822126 0.411063 0.911607i \(-0.365158\pi\)
0.411063 + 0.911607i \(0.365158\pi\)
\(504\) 0 0
\(505\) 1.34462 0.0598349
\(506\) −9.50160 16.4573i −0.422398 0.731614i
\(507\) 0 0
\(508\) −0.272461 + 0.471917i −0.0120885 + 0.0209379i
\(509\) −2.69763 + 4.67243i −0.119570 + 0.207102i −0.919597 0.392862i \(-0.871485\pi\)
0.800027 + 0.599964i \(0.204818\pi\)
\(510\) 0 0
\(511\) −1.38711 2.40254i −0.0613621 0.106282i
\(512\) −19.5124 −0.862333
\(513\) 0 0
\(514\) 9.10483 0.401597
\(515\) −1.50699 2.61019i −0.0664061 0.115019i
\(516\) 0 0
\(517\) 12.1636 21.0679i 0.534953 0.926565i
\(518\) 5.75881 9.97456i 0.253028 0.438257i
\(519\) 0 0
\(520\) 1.92488 + 3.33399i 0.0844116 + 0.146205i
\(521\) −34.0231 −1.49058 −0.745290 0.666741i \(-0.767689\pi\)
−0.745290 + 0.666741i \(0.767689\pi\)
\(522\) 0 0
\(523\) 17.5996 0.769576 0.384788 0.923005i \(-0.374275\pi\)
0.384788 + 0.923005i \(0.374275\pi\)
\(524\) 2.00451 + 3.47191i 0.0875674 + 0.151671i
\(525\) 0 0
\(526\) 16.5055 28.5884i 0.719675 1.24651i
\(527\) −5.67326 + 9.82637i −0.247131 + 0.428043i
\(528\) 0 0
\(529\) 3.04754 + 5.27849i 0.132502 + 0.229500i
\(530\) −6.98957 −0.303608
\(531\) 0 0
\(532\) −5.53749 −0.240081
\(533\) −3.27997 5.68108i −0.142071 0.246075i
\(534\) 0 0
\(535\) 1.75439 3.03870i 0.0758490 0.131374i
\(536\) −7.03770 + 12.1897i −0.303983 + 0.526513i
\(537\) 0 0
\(538\) −11.2560 19.4960i −0.485281 0.840531i
\(539\) 16.5382 0.712352
\(540\) 0 0
\(541\) 19.6744 0.845868 0.422934 0.906160i \(-0.361000\pi\)
0.422934 + 0.906160i \(0.361000\pi\)
\(542\) −10.1487 17.5781i −0.435924 0.755043i
\(543\) 0 0
\(544\) 14.4233 24.9818i 0.618392 1.07109i
\(545\) 0.0162740 0.0281874i 0.000697101 0.00120741i
\(546\) 0 0
\(547\) 7.16166 + 12.4044i 0.306211 + 0.530372i 0.977530 0.210796i \(-0.0676055\pi\)
−0.671320 + 0.741168i \(0.734272\pi\)
\(548\) 14.1374 0.603919
\(549\) 0 0
\(550\) −22.2434 −0.948461
\(551\) 19.5732 + 33.9018i 0.833847 + 1.44427i
\(552\) 0 0
\(553\) −4.10689 + 7.11333i −0.174643 + 0.302490i
\(554\) 14.4467 25.0225i 0.613783 1.06310i
\(555\) 0 0
\(556\) 15.0314 + 26.0352i 0.637475 + 1.10414i
\(557\) −1.21426 −0.0514499 −0.0257250 0.999669i \(-0.508189\pi\)
−0.0257250 + 0.999669i \(0.508189\pi\)
\(558\) 0 0
\(559\) 7.20272 0.304642
\(560\) −0.732299 1.26838i −0.0309453 0.0535988i
\(561\) 0 0
\(562\) 8.10377 14.0361i 0.341837 0.592079i
\(563\) 15.8136 27.3900i 0.666464 1.15435i −0.312422 0.949943i \(-0.601140\pi\)
0.978886 0.204406i \(-0.0655264\pi\)
\(564\) 0 0
\(565\) 1.66413 + 2.88236i 0.0700105 + 0.121262i
\(566\) 14.3454 0.602981
\(567\) 0 0
\(568\) 16.3856 0.687524
\(569\) −23.5071 40.7155i −0.985468 1.70688i −0.639836 0.768511i \(-0.720998\pi\)
−0.345632 0.938370i \(-0.612336\pi\)
\(570\) 0 0
\(571\) −15.8025 + 27.3707i −0.661314 + 1.14543i 0.318956 + 0.947769i \(0.396668\pi\)
−0.980271 + 0.197661i \(0.936666\pi\)
\(572\) −12.0777 + 20.9192i −0.504993 + 0.874674i
\(573\) 0 0
\(574\) 0.573627 + 0.993550i 0.0239427 + 0.0414700i
\(575\) −19.7873 −0.825189
\(576\) 0 0
\(577\) −35.2559 −1.46772 −0.733860 0.679300i \(-0.762283\pi\)
−0.733860 + 0.679300i \(0.762283\pi\)
\(578\) 2.70827 + 4.69087i 0.112649 + 0.195114i
\(579\) 0 0
\(580\) 1.84974 3.20385i 0.0768064 0.133033i
\(581\) 3.37298 5.84217i 0.139935 0.242374i
\(582\) 0 0
\(583\) 11.2302 + 19.4513i 0.465108 + 0.805590i
\(584\) −4.95670 −0.205110
\(585\) 0 0
\(586\) −61.0837 −2.52334
\(587\) −14.2400 24.6645i −0.587749 1.01801i −0.994527 0.104484i \(-0.966681\pi\)
0.406777 0.913527i \(-0.366652\pi\)
\(588\) 0 0
\(589\) 7.69107 13.3213i 0.316905 0.548896i
\(590\) 5.13783 8.89898i 0.211521 0.366365i
\(591\) 0 0
\(592\) −22.3826 38.7679i −0.919921 1.59335i
\(593\) 4.79696 0.196987 0.0984937 0.995138i \(-0.468598\pi\)
0.0984937 + 0.995138i \(0.468598\pi\)
\(594\) 0 0
\(595\) 1.33688 0.0548065
\(596\) 9.91004 + 17.1647i 0.405931 + 0.703093i
\(597\) 0 0
\(598\) −26.9907 + 46.7492i −1.10373 + 1.91172i
\(599\) 2.53206 4.38566i 0.103457 0.179193i −0.809650 0.586914i \(-0.800343\pi\)
0.913107 + 0.407720i \(0.133676\pi\)
\(600\) 0 0
\(601\) 17.9645 + 31.1154i 0.732785 + 1.26922i 0.955688 + 0.294381i \(0.0951134\pi\)
−0.222903 + 0.974841i \(0.571553\pi\)
\(602\) −1.25967 −0.0513401
\(603\) 0 0
\(604\) 10.6273 0.432420
\(605\) 0.989308 + 1.71353i 0.0402211 + 0.0696649i
\(606\) 0 0
\(607\) 2.62783 4.55154i 0.106660 0.184741i −0.807755 0.589518i \(-0.799318\pi\)
0.914415 + 0.404777i \(0.132651\pi\)
\(608\) −19.5532 + 33.8672i −0.792987 + 1.37349i
\(609\) 0 0
\(610\) 0.313058 + 0.542232i 0.0126753 + 0.0219543i
\(611\) −69.1047 −2.79568
\(612\) 0 0
\(613\) −21.9713 −0.887412 −0.443706 0.896172i \(-0.646337\pi\)
−0.443706 + 0.896172i \(0.646337\pi\)
\(614\) 11.7776 + 20.3994i 0.475305 + 0.823252i
\(615\) 0 0
\(616\) −1.08176 + 1.87366i −0.0435853 + 0.0754919i
\(617\) −15.8691 + 27.4860i −0.638864 + 1.10654i 0.346818 + 0.937932i \(0.387262\pi\)
−0.985682 + 0.168613i \(0.946071\pi\)
\(618\) 0 0
\(619\) 18.2257 + 31.5679i 0.732554 + 1.26882i 0.955788 + 0.294055i \(0.0950050\pi\)
−0.223235 + 0.974765i \(0.571662\pi\)
\(620\) −1.45367 −0.0583808
\(621\) 0 0
\(622\) −24.7211 −0.991226
\(623\) −2.78132 4.81739i −0.111431 0.193005i
\(624\) 0 0
\(625\) −11.1121 + 19.2468i −0.444486 + 0.769872i
\(626\) −21.3104 + 36.9106i −0.851734 + 1.47525i
\(627\) 0 0
\(628\) −4.55818 7.89500i −0.181891 0.315045i
\(629\) 40.8614 1.62925
\(630\) 0 0
\(631\) −6.25533 −0.249021 −0.124510 0.992218i \(-0.539736\pi\)
−0.124510 + 0.992218i \(0.539736\pi\)
\(632\) 7.33779 + 12.7094i 0.291882 + 0.505554i
\(633\) 0 0
\(634\) −1.46866 + 2.54379i −0.0583279 + 0.101027i
\(635\) −0.0891738 + 0.154454i −0.00353876 + 0.00612930i
\(636\) 0 0
\(637\) −23.4896 40.6852i −0.930693 1.61201i
\(638\) −29.8643 −1.18234
\(639\) 0 0
\(640\) −4.03066 −0.159326
\(641\) 19.6607 + 34.0533i 0.776550 + 1.34502i 0.933919 + 0.357484i \(0.116365\pi\)
−0.157370 + 0.987540i \(0.550301\pi\)
\(642\) 0 0
\(643\) −4.50051 + 7.79512i −0.177483 + 0.307410i −0.941018 0.338357i \(-0.890129\pi\)
0.763535 + 0.645767i \(0.223462\pi\)
\(644\) 1.87901 3.25454i 0.0740434 0.128247i
\(645\) 0 0
\(646\) −24.6761 42.7403i −0.970869 1.68160i
\(647\) −49.7161 −1.95454 −0.977271 0.211996i \(-0.932004\pi\)
−0.977271 + 0.211996i \(0.932004\pi\)
\(648\) 0 0
\(649\) −33.0200 −1.29615
\(650\) 31.5928 + 54.7203i 1.23917 + 2.14631i
\(651\) 0 0
\(652\) −4.54451 + 7.87132i −0.177977 + 0.308265i
\(653\) −13.9053 + 24.0846i −0.544155 + 0.942504i 0.454505 + 0.890744i \(0.349816\pi\)
−0.998660 + 0.0517595i \(0.983517\pi\)
\(654\) 0 0
\(655\) 0.656055 + 1.13632i 0.0256342 + 0.0443998i
\(656\) 4.45900 0.174095
\(657\) 0 0
\(658\) 12.0856 0.471144
\(659\) 4.38026 + 7.58682i 0.170631 + 0.295541i 0.938640 0.344897i \(-0.112086\pi\)
−0.768010 + 0.640438i \(0.778753\pi\)
\(660\) 0 0
\(661\) 2.31545 4.01048i 0.0900606 0.155990i −0.817476 0.575963i \(-0.804627\pi\)
0.907536 + 0.419973i \(0.137961\pi\)
\(662\) 31.2205 54.0754i 1.21342 2.10170i
\(663\) 0 0
\(664\) −6.02652 10.4382i −0.233874 0.405082i
\(665\) −1.81236 −0.0702805
\(666\) 0 0
\(667\) −26.5668 −1.02867
\(668\) 10.3107 + 17.8587i 0.398934 + 0.690974i
\(669\) 0 0
\(670\) 4.49755 7.78999i 0.173756 0.300953i
\(671\) 1.00598 1.74242i 0.0388356 0.0672653i
\(672\) 0 0
\(673\) −5.26726 9.12317i −0.203038 0.351672i 0.746468 0.665422i \(-0.231748\pi\)
−0.949506 + 0.313749i \(0.898415\pi\)
\(674\) −27.9925 −1.07823
\(675\) 0 0
\(676\) 51.4227 1.97780
\(677\) −1.01209 1.75299i −0.0388978 0.0673730i 0.845921 0.533308i \(-0.179051\pi\)
−0.884819 + 0.465935i \(0.845718\pi\)
\(678\) 0 0
\(679\) 5.17910 8.97046i 0.198756 0.344255i
\(680\) 1.19430 2.06859i 0.0457993 0.0793267i
\(681\) 0 0
\(682\) 5.86742 + 10.1627i 0.224675 + 0.389148i
\(683\) 30.3719 1.16215 0.581075 0.813850i \(-0.302632\pi\)
0.581075 + 0.813850i \(0.302632\pi\)
\(684\) 0 0
\(685\) 4.62702 0.176789
\(686\) 8.51688 + 14.7517i 0.325176 + 0.563221i
\(687\) 0 0
\(688\) −2.44795 + 4.23998i −0.0933274 + 0.161648i
\(689\) 31.9011 55.2543i 1.21533 2.10502i
\(690\) 0 0
\(691\) 9.17681 + 15.8947i 0.349102 + 0.604663i 0.986090 0.166211i \(-0.0531532\pi\)
−0.636988 + 0.770874i \(0.719820\pi\)
\(692\) 4.06241 0.154430
\(693\) 0 0
\(694\) −3.52612 −0.133850
\(695\) 4.91964 + 8.52106i 0.186613 + 0.323222i
\(696\) 0 0
\(697\) −2.03507 + 3.52485i −0.0770838 + 0.133513i
\(698\) 5.09364 8.82245i 0.192797 0.333935i
\(699\) 0 0
\(700\) −2.19940 3.80947i −0.0831294 0.143984i
\(701\) 4.98491 0.188277 0.0941387 0.995559i \(-0.469990\pi\)
0.0941387 + 0.995559i \(0.469990\pi\)
\(702\) 0 0
\(703\) −55.3947 −2.08925
\(704\) −2.50286 4.33507i −0.0943299 0.163384i
\(705\) 0 0
\(706\) 4.13630 7.16429i 0.155672 0.269632i
\(707\) 1.07328 1.85898i 0.0403649 0.0699140i
\(708\) 0 0
\(709\) −13.9418 24.1480i −0.523597 0.906896i −0.999623 0.0274647i \(-0.991257\pi\)
0.476026 0.879431i \(-0.342077\pi\)
\(710\) −10.4715 −0.392987
\(711\) 0 0
\(712\) −9.93880 −0.372472
\(713\) 5.21955 + 9.04053i 0.195474 + 0.338571i
\(714\) 0 0
\(715\) −3.95290 + 6.84663i −0.147830 + 0.256049i
\(716\) 4.50814 7.80833i 0.168477 0.291811i
\(717\) 0 0
\(718\) 10.5651 + 18.2993i 0.394286 + 0.682924i
\(719\) 10.7704 0.401668 0.200834 0.979625i \(-0.435635\pi\)
0.200834 + 0.979625i \(0.435635\pi\)
\(720\) 0 0
\(721\) −4.81155 −0.179191
\(722\) 16.1361 + 27.9485i 0.600522 + 1.04013i
\(723\) 0 0
\(724\) 4.14087 7.17219i 0.153894 0.266552i
\(725\) −15.5483 + 26.9304i −0.577449 + 1.00017i
\(726\) 0 0
\(727\) −1.23443 2.13810i −0.0457826 0.0792977i 0.842226 0.539125i \(-0.181245\pi\)
−0.888009 + 0.459827i \(0.847911\pi\)
\(728\) 6.14578 0.227778
\(729\) 0 0
\(730\) 3.16766 0.117240
\(731\) −2.23448 3.87023i −0.0826451 0.143146i
\(732\) 0 0
\(733\) 6.20513 10.7476i 0.229192 0.396972i −0.728377 0.685177i \(-0.759725\pi\)
0.957569 + 0.288205i \(0.0930584\pi\)
\(734\) −6.59400 + 11.4211i −0.243389 + 0.421562i
\(735\) 0 0
\(736\) −13.2698 22.9840i −0.489131 0.847200i
\(737\) −28.9050 −1.06473
\(738\) 0 0
\(739\) 38.5237 1.41712 0.708559 0.705651i \(-0.249346\pi\)
0.708559 + 0.705651i \(0.249346\pi\)
\(740\) 2.61750 + 4.53365i 0.0962213 + 0.166660i
\(741\) 0 0
\(742\) −5.57910 + 9.66328i −0.204815 + 0.354750i
\(743\) 18.4038 31.8762i 0.675168 1.16943i −0.301251 0.953545i \(-0.597404\pi\)
0.976420 0.215881i \(-0.0692624\pi\)
\(744\) 0 0
\(745\) 3.24345 + 5.61783i 0.118831 + 0.205821i
\(746\) −21.4361 −0.784831
\(747\) 0 0
\(748\) 14.9873 0.547990
\(749\) −2.80072 4.85099i −0.102336 0.177251i
\(750\) 0 0
\(751\) −7.09925 + 12.2963i −0.259055 + 0.448697i −0.965989 0.258583i \(-0.916745\pi\)
0.706934 + 0.707280i \(0.250078\pi\)
\(752\) 23.4863 40.6795i 0.856458 1.48343i
\(753\) 0 0
\(754\) 42.4169 + 73.4683i 1.54473 + 2.67556i
\(755\) 3.47822 0.126585
\(756\) 0 0
\(757\) 10.5676 0.384085 0.192042 0.981387i \(-0.438489\pi\)
0.192042 + 0.981387i \(0.438489\pi\)
\(758\) −4.65826 8.06835i −0.169196 0.293056i
\(759\) 0 0
\(760\) −1.61908 + 2.80433i −0.0587302 + 0.101724i
\(761\) 13.7421 23.8020i 0.498151 0.862823i −0.501847 0.864957i \(-0.667346\pi\)
0.999998 + 0.00213360i \(0.000679147\pi\)
\(762\) 0 0
\(763\) −0.0259799 0.0449985i −0.000940535 0.00162906i
\(764\) 12.9482 0.468448
\(765\) 0 0
\(766\) 29.4417 1.06377
\(767\) 46.8990 + 81.2315i 1.69343 + 2.93310i
\(768\) 0 0
\(769\) 5.50415 9.53346i 0.198485 0.343785i −0.749553 0.661945i \(-0.769731\pi\)
0.948037 + 0.318159i \(0.103065\pi\)
\(770\) 0.691314 1.19739i 0.0249132 0.0431510i
\(771\) 0 0
\(772\) −4.26916 7.39440i −0.153650 0.266130i
\(773\) 40.1139 1.44280 0.721398 0.692521i \(-0.243500\pi\)
0.721398 + 0.692521i \(0.243500\pi\)
\(774\) 0 0
\(775\) 12.2191 0.438921
\(776\) −9.25352 16.0276i −0.332182 0.575356i
\(777\) 0 0
\(778\) −15.7056 + 27.2029i −0.563073 + 0.975272i
\(779\) 2.75889 4.77854i 0.0988475 0.171209i
\(780\) 0 0
\(781\) 16.8246 + 29.1410i 0.602031 + 1.04275i
\(782\) 33.4929 1.19771
\(783\) 0 0
\(784\) 31.9333 1.14047
\(785\) −1.49185 2.58395i −0.0532462 0.0922252i
\(786\) 0 0
\(787\) 7.84526 13.5884i 0.279653 0.484374i −0.691645 0.722237i \(-0.743114\pi\)
0.971299 + 0.237864i \(0.0764472\pi\)
\(788\) −6.29605 + 10.9051i −0.224287 + 0.388477i
\(789\) 0 0
\(790\) −4.68932 8.12215i −0.166839 0.288973i
\(791\) 5.31326 0.188918
\(792\) 0 0
\(793\) −5.71529 −0.202956
\(794\) −26.9913 46.7504i −0.957887 1.65911i
\(795\) 0 0
\(796\) −11.1452 + 19.3041i −0.395033 + 0.684216i
\(797\) −21.3861 + 37.0417i −0.757533 + 1.31209i 0.186572 + 0.982441i \(0.440262\pi\)
−0.944105 + 0.329645i \(0.893071\pi\)
\(798\) 0 0
\(799\) 21.4381 + 37.1320i 0.758427 + 1.31363i
\(800\) −31.0648 −1.09831
\(801\) 0 0
\(802\) −26.0753 −0.920751
\(803\) −5.08950 8.81527i −0.179605 0.311084i
\(804\) 0 0
\(805\) 0.614981 1.06518i 0.0216752 0.0375426i
\(806\) 16.6673 28.8685i 0.587079 1.01685i
\(807\) 0 0
\(808\) −1.91764 3.32144i −0.0674622 0.116848i
\(809\) −45.5750 −1.60233 −0.801166 0.598442i \(-0.795787\pi\)
−0.801166 + 0.598442i \(0.795787\pi\)
\(810\) 0 0
\(811\) 19.9527 0.700634 0.350317 0.936631i \(-0.386074\pi\)
0.350317 + 0.936631i \(0.386074\pi\)
\(812\) −2.95294 5.11464i −0.103628 0.179489i
\(813\) 0 0
\(814\) 21.1299 36.5981i 0.740603 1.28276i
\(815\) −1.48737 + 2.57620i −0.0521003 + 0.0902404i
\(816\) 0 0
\(817\) 3.02922 + 5.24676i 0.105979 + 0.183561i
\(818\) −30.7440 −1.07494
\(819\) 0 0
\(820\) −0.521451 −0.0182098
\(821\) 23.5697 + 40.8238i 0.822587 + 1.42476i 0.903750 + 0.428061i \(0.140803\pi\)
−0.0811632 + 0.996701i \(0.525864\pi\)
\(822\) 0 0
\(823\) −11.1261 + 19.2710i −0.387831 + 0.671744i −0.992158 0.124993i \(-0.960109\pi\)
0.604326 + 0.796737i \(0.293442\pi\)
\(824\) −4.29840 + 7.44505i −0.149742 + 0.259361i
\(825\) 0 0
\(826\) −8.20206 14.2064i −0.285386 0.494303i
\(827\) 46.9285 1.63186 0.815931 0.578149i \(-0.196225\pi\)
0.815931 + 0.578149i \(0.196225\pi\)
\(828\) 0 0
\(829\) 48.4646 1.68324 0.841622 0.540067i \(-0.181601\pi\)
0.841622 + 0.540067i \(0.181601\pi\)
\(830\) 3.85134 + 6.67071i 0.133682 + 0.231544i
\(831\) 0 0
\(832\) −7.10973 + 12.3144i −0.246485 + 0.426925i
\(833\) −14.5742 + 25.2433i −0.504967 + 0.874629i
\(834\) 0 0
\(835\) 3.37459 + 5.84497i 0.116783 + 0.202273i
\(836\) −20.3179 −0.702708
\(837\) 0 0
\(838\) −2.62742 −0.0907627
\(839\) 4.63098 + 8.02109i 0.159879 + 0.276919i 0.934825 0.355109i \(-0.115556\pi\)
−0.774946 + 0.632028i \(0.782223\pi\)
\(840\) 0 0
\(841\) −6.37537 + 11.0425i −0.219840 + 0.380775i
\(842\) −1.26410 + 2.18948i −0.0435637 + 0.0754546i
\(843\) 0 0
\(844\) −0.867996 1.50341i −0.0298777 0.0517496i
\(845\) 16.8301 0.578974
\(846\) 0 0
\(847\) 3.15867 0.108533
\(848\) 21.6841 + 37.5580i 0.744636 + 1.28975i
\(849\) 0 0
\(850\) 19.6019 33.9514i 0.672339 1.16452i
\(851\) 18.7968 32.5571i 0.644347 1.11604i
\(852\) 0 0
\(853\) 15.3881 + 26.6529i 0.526877 + 0.912578i 0.999509 + 0.0313185i \(0.00997062\pi\)
−0.472632 + 0.881260i \(0.656696\pi\)
\(854\) 0.999534 0.0342034
\(855\) 0 0
\(856\) −10.0081 −0.342071
\(857\) −10.2118 17.6873i −0.348828 0.604188i 0.637213 0.770687i \(-0.280087\pi\)
−0.986042 + 0.166499i \(0.946754\pi\)
\(858\) 0 0
\(859\) 17.8263 30.8761i 0.608226 1.05348i −0.383306 0.923621i \(-0.625215\pi\)
0.991533 0.129858i \(-0.0414521\pi\)
\(860\) 0.286272 0.495838i 0.00976180 0.0169079i
\(861\) 0 0
\(862\) 18.1149 + 31.3759i 0.616995 + 1.06867i
\(863\) −9.21342 −0.313628 −0.156814 0.987628i \(-0.550122\pi\)
−0.156814 + 0.987628i \(0.550122\pi\)
\(864\) 0 0
\(865\) 1.32959 0.0452073
\(866\) −2.81765 4.88031i −0.0957476 0.165840i
\(867\) 0 0
\(868\) −1.16032 + 2.00974i −0.0393840 + 0.0682151i
\(869\) −15.0688 + 26.0999i −0.511173 + 0.885377i
\(870\) 0 0
\(871\) 41.0545 + 71.1084i 1.39108 + 2.40942i
\(872\) −0.0928368 −0.00314385
\(873\) 0 0
\(874\) −45.4054 −1.53586
\(875\) −1.46771 2.54215i −0.0496176 0.0859402i
\(876\) 0 0
\(877\) 28.9184 50.0881i 0.976504 1.69135i 0.301622 0.953428i \(-0.402472\pi\)
0.674881 0.737926i \(-0.264195\pi\)
\(878\) 8.11330 14.0526i 0.273810 0.474254i
\(879\) 0 0
\(880\) −2.68691 4.65387i −0.0905758 0.156882i
\(881\) 28.9309 0.974706 0.487353 0.873205i \(-0.337962\pi\)
0.487353 + 0.873205i \(0.337962\pi\)
\(882\) 0 0
\(883\) 43.7957 1.47384 0.736922 0.675978i \(-0.236278\pi\)
0.736922 + 0.675978i \(0.236278\pi\)
\(884\) −21.2868 36.8698i −0.715953 1.24007i
\(885\) 0 0
\(886\) 10.0040 17.3275i 0.336092 0.582129i
\(887\) −15.0762 + 26.1128i −0.506210 + 0.876781i 0.493764 + 0.869596i \(0.335620\pi\)
−0.999974 + 0.00718527i \(0.997713\pi\)
\(888\) 0 0
\(889\) 0.142358 + 0.246571i 0.00477452 + 0.00826971i
\(890\) 6.35154 0.212904
\(891\) 0 0
\(892\) −2.51296 −0.0841401
\(893\) −29.0631 50.3387i −0.972559 1.68452i
\(894\) 0 0
\(895\) 1.47547 2.55559i 0.0493195 0.0854239i
\(896\) −3.21729 + 5.57250i −0.107482 + 0.186164i
\(897\) 0 0
\(898\) −17.1287 29.6677i −0.571591 0.990025i
\(899\) 16.4055 0.547153
\(900\) 0 0
\(901\) −39.5863 −1.31881
\(902\) 2.10472 + 3.64548i 0.0700795 + 0.121381i
\(903\) 0 0
\(904\) 4.74661 8.22137i 0.157870 0.273439i
\(905\) 1.35526 2.34738i 0.0450505 0.0780297i
\(906\) 0 0
\(907\) 20.8491 + 36.1118i 0.692284 + 1.19907i 0.971088 + 0.238723i \(0.0767289\pi\)
−0.278803 + 0.960348i \(0.589938\pi\)
\(908\) 16.8493 0.559165
\(909\) 0 0
\(910\) −3.92756 −0.130197
\(911\) 4.40486 + 7.62944i 0.145939 + 0.252775i 0.929723 0.368260i \(-0.120046\pi\)
−0.783784 + 0.621034i \(0.786713\pi\)
\(912\) 0 0
\(913\) 12.3760 21.4358i 0.409584 0.709421i
\(914\) 17.9693 31.1238i 0.594372 1.02948i
\(915\) 0 0
\(916\) −15.7023 27.1972i −0.518819 0.898621i
\(917\) 2.09466 0.0691718
\(918\) 0 0
\(919\) −10.9520 −0.361273 −0.180636 0.983550i \(-0.557816\pi\)
−0.180636 + 0.983550i \(0.557816\pi\)
\(920\) −1.09879 1.90316i −0.0362260 0.0627453i
\(921\) 0 0
\(922\) 36.6152 63.4194i 1.20586 2.08861i
\(923\) 47.7927 82.7793i 1.57312 2.72472i
\(924\) 0 0
\(925\) −22.0018 38.1083i −0.723416 1.25299i
\(926\) −40.6360 −1.33538
\(927\) 0 0
\(928\) −41.7080 −1.36913
\(929\) 14.1039 + 24.4287i 0.462735 + 0.801481i 0.999096 0.0425081i \(-0.0135348\pi\)
−0.536361 + 0.843989i \(0.680201\pi\)
\(930\) 0 0
\(931\) 19.7579 34.2217i 0.647538 1.12157i
\(932\) −5.15041 + 8.92078i −0.168707 + 0.292210i
\(933\) 0 0
\(934\) −2.56499 4.44270i −0.0839291 0.145369i
\(935\) 4.90519 0.160417
\(936\) 0 0
\(937\) −32.3092 −1.05550 −0.527748 0.849401i \(-0.676963\pi\)
−0.527748 + 0.849401i \(0.676963\pi\)
\(938\) −7.17992 12.4360i −0.234433 0.406049i
\(939\) 0 0
\(940\) −2.74657 + 4.75720i −0.0895833 + 0.155163i
\(941\) 11.5701 20.0400i 0.377175 0.653286i −0.613475 0.789714i \(-0.710229\pi\)
0.990650 + 0.136428i \(0.0435623\pi\)
\(942\) 0 0
\(943\) 1.87232 + 3.24296i 0.0609712 + 0.105605i
\(944\) −63.7575 −2.07513
\(945\) 0 0
\(946\) −4.62190 −0.150271
\(947\) 13.1368 + 22.7537i 0.426890 + 0.739396i 0.996595 0.0824539i \(-0.0262757\pi\)
−0.569705 + 0.821850i \(0.692942\pi\)
\(948\) 0 0
\(949\) −14.4575 + 25.0411i −0.469309 + 0.812868i
\(950\) −26.5737 + 46.0270i −0.862165 + 1.49331i
\(951\) 0 0
\(952\) −1.90659 3.30231i −0.0617929 0.107028i
\(953\) 8.01441 0.259612 0.129806 0.991539i \(-0.458565\pi\)
0.129806 + 0.991539i \(0.458565\pi\)
\(954\) 0 0
\(955\) 4.23780 0.137132
\(956\) −2.25707 3.90936i −0.0729989 0.126438i
\(957\) 0 0
\(958\) −14.2991 + 24.7669i −0.461985 + 0.800181i
\(959\) 3.69330 6.39698i 0.119263 0.206569i
\(960\) 0 0
\(961\) 12.2768 + 21.2641i 0.396027 + 0.685938i
\(962\) −120.045 −3.87042
\(963\) 0 0
\(964\) −16.3152 −0.525476
\(965\) −1.39725 2.42011i −0.0449791 0.0779061i
\(966\) 0 0
\(967\) −12.2344 + 21.1906i −0.393432 + 0.681445i −0.992900 0.118954i \(-0.962046\pi\)
0.599467 + 0.800399i \(0.295379\pi\)
\(968\) 2.82181 4.88751i 0.0906963 0.157091i
\(969\) 0 0
\(970\) 5.91360 + 10.2427i 0.189874 + 0.328872i
\(971\) 20.7426 0.665662 0.332831 0.942987i \(-0.391996\pi\)
0.332831 + 0.942987i \(0.391996\pi\)
\(972\) 0 0
\(973\) 15.7075 0.503559
\(974\) −7.58202 13.1324i −0.242943 0.420790i
\(975\) 0 0
\(976\) 1.94243 3.36439i 0.0621757 0.107692i
\(977\) −2.31165 + 4.00389i −0.0739562 + 0.128096i −0.900632 0.434583i \(-0.856896\pi\)
0.826676 + 0.562679i \(0.190229\pi\)
\(978\) 0 0
\(979\) −10.2051 17.6757i −0.326156 0.564918i
\(980\) −3.73439 −0.119291
\(981\) 0 0
\(982\) 39.1174 1.24829
\(983\) −21.9604 38.0364i −0.700427 1.21317i −0.968317 0.249725i \(-0.919660\pi\)
0.267890 0.963449i \(-0.413674\pi\)
\(984\) 0 0
\(985\) −2.06063 + 3.56912i −0.0656572 + 0.113722i
\(986\) 26.3178 45.5837i 0.838128 1.45168i
\(987\) 0 0
\(988\) 28.8579 + 49.9834i 0.918093 + 1.59018i
\(989\) −4.11156 −0.130740
\(990\) 0 0
\(991\) 30.0775 0.955442 0.477721 0.878511i \(-0.341463\pi\)
0.477721 + 0.878511i \(0.341463\pi\)
\(992\) 8.19435 + 14.1930i 0.260171 + 0.450629i
\(993\) 0 0
\(994\) −8.35835 + 14.4771i −0.265111 + 0.459185i
\(995\) −3.64772 + 6.31804i −0.115641 + 0.200295i
\(996\) 0 0
\(997\) 12.7130 + 22.0196i 0.402625 + 0.697367i 0.994042 0.108999i \(-0.0347646\pi\)
−0.591417 + 0.806366i \(0.701431\pi\)
\(998\) 16.1568 0.511436
\(999\) 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 1161.2.f.d.388.17 40
3.2 odd 2 387.2.f.d.130.4 40
9.2 odd 6 387.2.f.d.259.4 yes 40
9.4 even 3 3483.2.a.u.1.4 20
9.5 odd 6 3483.2.a.t.1.17 20
9.7 even 3 inner 1161.2.f.d.775.17 40
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
387.2.f.d.130.4 40 3.2 odd 2
387.2.f.d.259.4 yes 40 9.2 odd 6
1161.2.f.d.388.17 40 1.1 even 1 trivial
1161.2.f.d.775.17 40 9.7 even 3 inner
3483.2.a.t.1.17 20 9.5 odd 6
3483.2.a.u.1.4 20 9.4 even 3