Properties

Label 483.2.e.a.344.3
Level $483$
Weight $2$
Character 483.344
Analytic conductor $3.857$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [483,2,Mod(344,483)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(483, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("483.344");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 483 = 3 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 483.e (of order \(2\), degree \(1\), 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: \(3.85677441763\)
Analytic rank: \(0\)
Dimension: \(48\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 344.3
Character \(\chi\) \(=\) 483.344
Dual form 483.2.e.a.344.45

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.35218i q^{2} +(1.12077 - 1.32055i) q^{3} -3.53277 q^{4} -2.32116 q^{5} +(-3.10619 - 2.63627i) q^{6} +1.00000i q^{7} +3.60535i q^{8} +(-0.487727 - 2.96009i) q^{9} +O(q^{10})\) \(q-2.35218i q^{2} +(1.12077 - 1.32055i) q^{3} -3.53277 q^{4} -2.32116 q^{5} +(-3.10619 - 2.63627i) q^{6} +1.00000i q^{7} +3.60535i q^{8} +(-0.487727 - 2.96009i) q^{9} +5.45980i q^{10} -3.27605 q^{11} +(-3.95944 + 4.66521i) q^{12} -0.766081 q^{13} +2.35218 q^{14} +(-2.60150 + 3.06522i) q^{15} +1.41491 q^{16} -1.00367 q^{17} +(-6.96267 + 1.14722i) q^{18} -3.84491i q^{19} +8.20013 q^{20} +(1.32055 + 1.12077i) q^{21} +7.70588i q^{22} +(3.66310 + 3.09543i) q^{23} +(4.76106 + 4.04079i) q^{24} +0.387798 q^{25} +1.80196i q^{26} +(-4.45559 - 2.67352i) q^{27} -3.53277i q^{28} +0.127170i q^{29} +(7.20996 + 6.11921i) q^{30} +4.13415 q^{31} +3.88257i q^{32} +(-3.67172 + 4.32621i) q^{33} +2.36083i q^{34} -2.32116i q^{35} +(1.72303 + 10.4573i) q^{36} -8.32017i q^{37} -9.04394 q^{38} +(-0.858604 + 1.01165i) q^{39} -8.36861i q^{40} -3.74563i q^{41} +(2.63627 - 3.10619i) q^{42} -5.48730i q^{43} +11.5735 q^{44} +(1.13209 + 6.87085i) q^{45} +(7.28101 - 8.61630i) q^{46} -9.48738i q^{47} +(1.58580 - 1.86847i) q^{48} -1.00000 q^{49} -0.912172i q^{50} +(-1.12489 + 1.32541i) q^{51} +2.70639 q^{52} -6.61336 q^{53} +(-6.28861 + 10.4804i) q^{54} +7.60426 q^{55} -3.60535 q^{56} +(-5.07741 - 4.30928i) q^{57} +0.299127 q^{58} +3.94915i q^{59} +(9.19050 - 10.8287i) q^{60} -12.6734i q^{61} -9.72427i q^{62} +(2.96009 - 0.487727i) q^{63} +11.9623 q^{64} +1.77820 q^{65} +(10.1760 + 8.63656i) q^{66} +4.09736i q^{67} +3.54575 q^{68} +(8.19319 - 1.36805i) q^{69} -5.45980 q^{70} -2.78937i q^{71} +(10.6722 - 1.75843i) q^{72} +1.11384 q^{73} -19.5706 q^{74} +(0.434634 - 0.512108i) q^{75} +13.5832i q^{76} -3.27605i q^{77} +(2.37959 + 2.01959i) q^{78} +11.9480i q^{79} -3.28424 q^{80} +(-8.52424 + 2.88743i) q^{81} -8.81042 q^{82} -10.7907 q^{83} +(-4.66521 - 3.95944i) q^{84} +2.32969 q^{85} -12.9071 q^{86} +(0.167935 + 0.142529i) q^{87} -11.8113i q^{88} +17.1066 q^{89} +(16.1615 - 2.66290i) q^{90} -0.766081i q^{91} +(-12.9409 - 10.9354i) q^{92} +(4.63345 - 5.45937i) q^{93} -22.3161 q^{94} +8.92467i q^{95} +(5.12714 + 4.35148i) q^{96} +4.16963i q^{97} +2.35218i q^{98} +(1.59782 + 9.69741i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q - 4 q^{3} - 40 q^{4} + 6 q^{6} + 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 48 q - 4 q^{3} - 40 q^{4} + 6 q^{6} + 4 q^{9} + 22 q^{12} - 8 q^{13} + 24 q^{16} - 14 q^{18} - 12 q^{24} + 88 q^{25} - 16 q^{27} - 8 q^{31} - 10 q^{36} + 8 q^{46} - 98 q^{48} - 48 q^{49} + 28 q^{52} - 28 q^{54} - 92 q^{58} + 92 q^{64} + 8 q^{69} + 8 q^{70} + 60 q^{72} + 40 q^{73} - 80 q^{75} + 114 q^{78} - 28 q^{81} - 20 q^{82} - 40 q^{85} - 28 q^{87} - 76 q^{93} - 12 q^{94} - 6 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/483\mathbb{Z}\right)^\times\).

\(n\) \(323\) \(346\) \(442\)
\(\chi(n)\) \(-1\) \(1\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.35218i 1.66324i −0.555341 0.831622i \(-0.687412\pi\)
0.555341 0.831622i \(-0.312588\pi\)
\(3\) 1.12077 1.32055i 0.647080 0.762422i
\(4\) −3.53277 −1.76638
\(5\) −2.32116 −1.03806 −0.519028 0.854757i \(-0.673706\pi\)
−0.519028 + 0.854757i \(0.673706\pi\)
\(6\) −3.10619 2.63627i −1.26810 1.07625i
\(7\) 1.00000i 0.377964i
\(8\) 3.60535i 1.27468i
\(9\) −0.487727 2.96009i −0.162576 0.986696i
\(10\) 5.45980i 1.72654i
\(11\) −3.27605 −0.987767 −0.493884 0.869528i \(-0.664423\pi\)
−0.493884 + 0.869528i \(0.664423\pi\)
\(12\) −3.95944 + 4.66521i −1.14299 + 1.34673i
\(13\) −0.766081 −0.212473 −0.106236 0.994341i \(-0.533880\pi\)
−0.106236 + 0.994341i \(0.533880\pi\)
\(14\) 2.35218 0.628648
\(15\) −2.60150 + 3.06522i −0.671705 + 0.791437i
\(16\) 1.41491 0.353728
\(17\) −1.00367 −0.243427 −0.121713 0.992565i \(-0.538839\pi\)
−0.121713 + 0.992565i \(0.538839\pi\)
\(18\) −6.96267 + 1.14722i −1.64112 + 0.270403i
\(19\) 3.84491i 0.882083i −0.897487 0.441042i \(-0.854609\pi\)
0.897487 0.441042i \(-0.145391\pi\)
\(20\) 8.20013 1.83360
\(21\) 1.32055 + 1.12077i 0.288169 + 0.244573i
\(22\) 7.70588i 1.64290i
\(23\) 3.66310 + 3.09543i 0.763810 + 0.645441i
\(24\) 4.76106 + 4.04079i 0.971848 + 0.824822i
\(25\) 0.387798 0.0775596
\(26\) 1.80196i 0.353394i
\(27\) −4.45559 2.67352i −0.857479 0.514520i
\(28\) 3.53277i 0.667630i
\(29\) 0.127170i 0.0236148i 0.999930 + 0.0118074i \(0.00375851\pi\)
−0.999930 + 0.0118074i \(0.996241\pi\)
\(30\) 7.20996 + 6.11921i 1.31635 + 1.11721i
\(31\) 4.13415 0.742515 0.371257 0.928530i \(-0.378927\pi\)
0.371257 + 0.928530i \(0.378927\pi\)
\(32\) 3.88257i 0.686348i
\(33\) −3.67172 + 4.32621i −0.639164 + 0.753096i
\(34\) 2.36083i 0.404878i
\(35\) 2.32116i 0.392348i
\(36\) 1.72303 + 10.4573i 0.287171 + 1.74288i
\(37\) 8.32017i 1.36783i −0.729563 0.683913i \(-0.760277\pi\)
0.729563 0.683913i \(-0.239723\pi\)
\(38\) −9.04394 −1.46712
\(39\) −0.858604 + 1.01165i −0.137487 + 0.161994i
\(40\) 8.36861i 1.32319i
\(41\) 3.74563i 0.584970i −0.956270 0.292485i \(-0.905518\pi\)
0.956270 0.292485i \(-0.0944821\pi\)
\(42\) 2.63627 3.10619i 0.406785 0.479295i
\(43\) 5.48730i 0.836806i −0.908262 0.418403i \(-0.862590\pi\)
0.908262 0.418403i \(-0.137410\pi\)
\(44\) 11.5735 1.74478
\(45\) 1.13209 + 6.87085i 0.168763 + 1.02425i
\(46\) 7.28101 8.61630i 1.07353 1.27040i
\(47\) 9.48738i 1.38388i −0.721957 0.691938i \(-0.756757\pi\)
0.721957 0.691938i \(-0.243243\pi\)
\(48\) 1.58580 1.86847i 0.228890 0.269690i
\(49\) −1.00000 −0.142857
\(50\) 0.912172i 0.129001i
\(51\) −1.12489 + 1.32541i −0.157517 + 0.185594i
\(52\) 2.70639 0.375308
\(53\) −6.61336 −0.908415 −0.454208 0.890896i \(-0.650078\pi\)
−0.454208 + 0.890896i \(0.650078\pi\)
\(54\) −6.28861 + 10.4804i −0.855772 + 1.42620i
\(55\) 7.60426 1.02536
\(56\) −3.60535 −0.481785
\(57\) −5.07741 4.30928i −0.672520 0.570778i
\(58\) 0.299127 0.0392773
\(59\) 3.94915i 0.514136i 0.966393 + 0.257068i \(0.0827565\pi\)
−0.966393 + 0.257068i \(0.917244\pi\)
\(60\) 9.19050 10.8287i 1.18649 1.39798i
\(61\) 12.6734i 1.62266i −0.584590 0.811329i \(-0.698745\pi\)
0.584590 0.811329i \(-0.301255\pi\)
\(62\) 9.72427i 1.23498i
\(63\) 2.96009 0.487727i 0.372936 0.0614479i
\(64\) 11.9623 1.49529
\(65\) 1.77820 0.220558
\(66\) 10.1760 + 8.63656i 1.25258 + 1.06309i
\(67\) 4.09736i 0.500572i 0.968172 + 0.250286i \(0.0805246\pi\)
−0.968172 + 0.250286i \(0.919475\pi\)
\(68\) 3.54575 0.429985
\(69\) 8.19319 1.36805i 0.986345 0.164694i
\(70\) −5.45980 −0.652571
\(71\) 2.78937i 0.331037i −0.986207 0.165519i \(-0.947070\pi\)
0.986207 0.165519i \(-0.0529298\pi\)
\(72\) 10.6722 1.75843i 1.25773 0.207233i
\(73\) 1.11384 0.130365 0.0651826 0.997873i \(-0.479237\pi\)
0.0651826 + 0.997873i \(0.479237\pi\)
\(74\) −19.5706 −2.27503
\(75\) 0.434634 0.512108i 0.0501872 0.0591332i
\(76\) 13.5832i 1.55810i
\(77\) 3.27605i 0.373341i
\(78\) 2.37959 + 2.01959i 0.269435 + 0.228674i
\(79\) 11.9480i 1.34425i 0.740436 + 0.672127i \(0.234619\pi\)
−0.740436 + 0.672127i \(0.765381\pi\)
\(80\) −3.28424 −0.367190
\(81\) −8.52424 + 2.88743i −0.947138 + 0.320826i
\(82\) −8.81042 −0.972948
\(83\) −10.7907 −1.18444 −0.592219 0.805777i \(-0.701748\pi\)
−0.592219 + 0.805777i \(0.701748\pi\)
\(84\) −4.66521 3.95944i −0.509016 0.432010i
\(85\) 2.32969 0.252691
\(86\) −12.9071 −1.39181
\(87\) 0.167935 + 0.142529i 0.0180045 + 0.0152807i
\(88\) 11.8113i 1.25909i
\(89\) 17.1066 1.81329 0.906647 0.421889i \(-0.138633\pi\)
0.906647 + 0.421889i \(0.138633\pi\)
\(90\) 16.1615 2.66290i 1.70357 0.280694i
\(91\) 0.766081i 0.0803071i
\(92\) −12.9409 10.9354i −1.34918 1.14010i
\(93\) 4.63345 5.45937i 0.480466 0.566110i
\(94\) −22.3161 −2.30173
\(95\) 8.92467i 0.915652i
\(96\) 5.12714 + 4.35148i 0.523287 + 0.444122i
\(97\) 4.16963i 0.423361i 0.977339 + 0.211681i \(0.0678937\pi\)
−0.977339 + 0.211681i \(0.932106\pi\)
\(98\) 2.35218i 0.237606i
\(99\) 1.59782 + 9.69741i 0.160587 + 0.974626i
\(100\) −1.37000 −0.137000
\(101\) 2.31150i 0.230003i 0.993365 + 0.115001i \(0.0366872\pi\)
−0.993365 + 0.115001i \(0.963313\pi\)
\(102\) 3.11760 + 2.64596i 0.308688 + 0.261989i
\(103\) 3.40410i 0.335416i −0.985837 0.167708i \(-0.946363\pi\)
0.985837 0.167708i \(-0.0536366\pi\)
\(104\) 2.76199i 0.270835i
\(105\) −3.06522 2.60150i −0.299135 0.253881i
\(106\) 15.5558i 1.51092i
\(107\) −8.25153 −0.797705 −0.398853 0.917015i \(-0.630591\pi\)
−0.398853 + 0.917015i \(0.630591\pi\)
\(108\) 15.7406 + 9.44493i 1.51464 + 0.908839i
\(109\) 11.9034i 1.14014i 0.821595 + 0.570071i \(0.193084\pi\)
−0.821595 + 0.570071i \(0.806916\pi\)
\(110\) 17.8866i 1.70542i
\(111\) −10.9872 9.32503i −1.04286 0.885093i
\(112\) 1.41491i 0.133697i
\(113\) 9.80907 0.922759 0.461380 0.887203i \(-0.347355\pi\)
0.461380 + 0.887203i \(0.347355\pi\)
\(114\) −10.1362 + 11.9430i −0.949344 + 1.11857i
\(115\) −8.50266 7.18499i −0.792877 0.670004i
\(116\) 0.449261i 0.0417129i
\(117\) 0.373639 + 2.26767i 0.0345429 + 0.209646i
\(118\) 9.28914 0.855134
\(119\) 1.00367i 0.0920067i
\(120\) −11.0512 9.37933i −1.00883 0.856211i
\(121\) −0.267471 −0.0243155
\(122\) −29.8101 −2.69888
\(123\) −4.94631 4.19801i −0.445994 0.378522i
\(124\) −14.6050 −1.31157
\(125\) 10.7057 0.957544
\(126\) −1.14722 6.96267i −0.102203 0.620284i
\(127\) 10.7940 0.957814 0.478907 0.877866i \(-0.341033\pi\)
0.478907 + 0.877866i \(0.341033\pi\)
\(128\) 20.3725i 1.80069i
\(129\) −7.24628 6.15003i −0.637999 0.541480i
\(130\) 4.18265i 0.366843i
\(131\) 22.6807i 1.98162i −0.135263 0.990810i \(-0.543188\pi\)
0.135263 0.990810i \(-0.456812\pi\)
\(132\) 12.9713 15.2835i 1.12901 1.33026i
\(133\) 3.84491 0.333396
\(134\) 9.63773 0.832573
\(135\) 10.3422 + 6.20568i 0.890111 + 0.534100i
\(136\) 3.61860i 0.310292i
\(137\) −18.5836 −1.58771 −0.793854 0.608109i \(-0.791929\pi\)
−0.793854 + 0.608109i \(0.791929\pi\)
\(138\) −3.21791 19.2719i −0.273927 1.64053i
\(139\) −19.7545 −1.67556 −0.837779 0.546009i \(-0.816146\pi\)
−0.837779 + 0.546009i \(0.816146\pi\)
\(140\) 8.20013i 0.693037i
\(141\) −12.5286 10.6332i −1.05510 0.895478i
\(142\) −6.56110 −0.550596
\(143\) 2.50972 0.209873
\(144\) −0.690092 4.18827i −0.0575077 0.349022i
\(145\) 0.295182i 0.0245135i
\(146\) 2.61996i 0.216829i
\(147\) −1.12077 + 1.32055i −0.0924400 + 0.108917i
\(148\) 29.3932i 2.41611i
\(149\) 20.1542 1.65110 0.825548 0.564331i \(-0.190866\pi\)
0.825548 + 0.564331i \(0.190866\pi\)
\(150\) −1.20457 1.02234i −0.0983530 0.0834737i
\(151\) 17.4899 1.42330 0.711652 0.702532i \(-0.247947\pi\)
0.711652 + 0.702532i \(0.247947\pi\)
\(152\) 13.8623 1.12438
\(153\) 0.489520 + 2.97096i 0.0395753 + 0.240188i
\(154\) −7.70588 −0.620958
\(155\) −9.59603 −0.770772
\(156\) 3.03325 3.57393i 0.242854 0.286143i
\(157\) 14.6196i 1.16677i −0.812196 0.583385i \(-0.801728\pi\)
0.812196 0.583385i \(-0.198272\pi\)
\(158\) 28.1039 2.23582
\(159\) −7.41209 + 8.73331i −0.587817 + 0.692596i
\(160\) 9.01207i 0.712467i
\(161\) −3.09543 + 3.66310i −0.243954 + 0.288693i
\(162\) 6.79177 + 20.0506i 0.533612 + 1.57532i
\(163\) 24.1271 1.88978 0.944891 0.327385i \(-0.106168\pi\)
0.944891 + 0.327385i \(0.106168\pi\)
\(164\) 13.2325i 1.03328i
\(165\) 8.52266 10.0418i 0.663488 0.781756i
\(166\) 25.3818i 1.97001i
\(167\) 12.4111i 0.960399i −0.877159 0.480199i \(-0.840564\pi\)
0.877159 0.480199i \(-0.159436\pi\)
\(168\) −4.04079 + 4.76106i −0.311753 + 0.367324i
\(169\) −12.4131 −0.954855
\(170\) 5.47986i 0.420286i
\(171\) −11.3813 + 1.87527i −0.870348 + 0.143405i
\(172\) 19.3854i 1.47812i
\(173\) 7.37839i 0.560969i 0.959859 + 0.280484i \(0.0904951\pi\)
−0.959859 + 0.280484i \(0.909505\pi\)
\(174\) 0.335254 0.395013i 0.0254155 0.0299459i
\(175\) 0.387798i 0.0293148i
\(176\) −4.63533 −0.349401
\(177\) 5.21507 + 4.42611i 0.391989 + 0.332687i
\(178\) 40.2378i 3.01595i
\(179\) 20.7984i 1.55454i 0.629164 + 0.777272i \(0.283397\pi\)
−0.629164 + 0.777272i \(0.716603\pi\)
\(180\) −3.99943 24.2731i −0.298100 1.80921i
\(181\) 15.9327i 1.18427i −0.805838 0.592136i \(-0.798285\pi\)
0.805838 0.592136i \(-0.201715\pi\)
\(182\) −1.80196 −0.133570
\(183\) −16.7359 14.2040i −1.23715 1.04999i
\(184\) −11.1601 + 13.2068i −0.822733 + 0.973617i
\(185\) 19.3125i 1.41988i
\(186\) −12.8414 10.8987i −0.941580 0.799133i
\(187\) 3.28809 0.240449
\(188\) 33.5167i 2.44446i
\(189\) 2.67352 4.45559i 0.194470 0.324096i
\(190\) 20.9925 1.52295
\(191\) −10.1089 −0.731452 −0.365726 0.930722i \(-0.619179\pi\)
−0.365726 + 0.930722i \(0.619179\pi\)
\(192\) 13.4071 15.7969i 0.967573 1.14004i
\(193\) 19.4873 1.40273 0.701365 0.712802i \(-0.252574\pi\)
0.701365 + 0.712802i \(0.252574\pi\)
\(194\) 9.80773 0.704154
\(195\) 1.99296 2.34821i 0.142719 0.168159i
\(196\) 3.53277 0.252341
\(197\) 14.8199i 1.05588i 0.849283 + 0.527939i \(0.177035\pi\)
−0.849283 + 0.527939i \(0.822965\pi\)
\(198\) 22.8101 3.75837i 1.62104 0.267096i
\(199\) 14.8695i 1.05407i −0.849843 0.527036i \(-0.823303\pi\)
0.849843 0.527036i \(-0.176697\pi\)
\(200\) 1.39815i 0.0988640i
\(201\) 5.41078 + 4.59221i 0.381647 + 0.323910i
\(202\) 5.43707 0.382551
\(203\) −0.127170 −0.00892557
\(204\) 3.97399 4.68235i 0.278235 0.327830i
\(205\) 8.69423i 0.607231i
\(206\) −8.00708 −0.557879
\(207\) 7.37614 12.3528i 0.512677 0.858582i
\(208\) −1.08394 −0.0751575
\(209\) 12.5961i 0.871293i
\(210\) −6.11921 + 7.20996i −0.422266 + 0.497535i
\(211\) −16.1684 −1.11308 −0.556538 0.830822i \(-0.687871\pi\)
−0.556538 + 0.830822i \(0.687871\pi\)
\(212\) 23.3635 1.60461
\(213\) −3.68351 3.12625i −0.252390 0.214207i
\(214\) 19.4091i 1.32678i
\(215\) 12.7369i 0.868651i
\(216\) 9.63899 16.0640i 0.655850 1.09301i
\(217\) 4.13415i 0.280644i
\(218\) 27.9991 1.89634
\(219\) 1.24837 1.47089i 0.0843567 0.0993934i
\(220\) −26.8641 −1.81118
\(221\) 0.768896 0.0517215
\(222\) −21.9342 + 25.8440i −1.47213 + 1.73453i
\(223\) −7.23975 −0.484809 −0.242405 0.970175i \(-0.577936\pi\)
−0.242405 + 0.970175i \(0.577936\pi\)
\(224\) −3.88257 −0.259415
\(225\) −0.189140 1.14792i −0.0126093 0.0765278i
\(226\) 23.0727i 1.53478i
\(227\) 23.7493 1.57630 0.788150 0.615484i \(-0.211039\pi\)
0.788150 + 0.615484i \(0.211039\pi\)
\(228\) 17.9373 + 15.2237i 1.18793 + 1.00821i
\(229\) 0.372945i 0.0246449i 0.999924 + 0.0123225i \(0.00392246\pi\)
−0.999924 + 0.0123225i \(0.996078\pi\)
\(230\) −16.9004 + 19.9998i −1.11438 + 1.31875i
\(231\) −4.32621 3.67172i −0.284644 0.241581i
\(232\) −0.458492 −0.0301015
\(233\) 14.8258i 0.971269i −0.874162 0.485635i \(-0.838589\pi\)
0.874162 0.485635i \(-0.161411\pi\)
\(234\) 5.33397 0.878867i 0.348692 0.0574533i
\(235\) 22.0218i 1.43654i
\(236\) 13.9514i 0.908162i
\(237\) 15.7780 + 13.3910i 1.02489 + 0.869840i
\(238\) −2.36083 −0.153030
\(239\) 9.40671i 0.608469i −0.952597 0.304235i \(-0.901599\pi\)
0.952597 0.304235i \(-0.0984007\pi\)
\(240\) −3.68090 + 4.33702i −0.237601 + 0.279954i
\(241\) 19.5410i 1.25875i 0.777103 + 0.629373i \(0.216688\pi\)
−0.777103 + 0.629373i \(0.783312\pi\)
\(242\) 0.629141i 0.0404427i
\(243\) −5.74075 + 14.4929i −0.368269 + 0.929719i
\(244\) 44.7720i 2.86624i
\(245\) 2.32116 0.148294
\(246\) −9.87450 + 11.6346i −0.629575 + 0.741797i
\(247\) 2.94551i 0.187419i
\(248\) 14.9051i 0.946472i
\(249\) −12.0940 + 14.2498i −0.766426 + 0.903042i
\(250\) 25.1817i 1.59263i
\(251\) 8.79157 0.554919 0.277459 0.960737i \(-0.410508\pi\)
0.277459 + 0.960737i \(0.410508\pi\)
\(252\) −10.4573 + 1.72303i −0.658748 + 0.108541i
\(253\) −12.0005 10.1408i −0.754467 0.637546i
\(254\) 25.3895i 1.59308i
\(255\) 2.61106 3.07649i 0.163511 0.192657i
\(256\) −23.9951 −1.49970
\(257\) 26.6743i 1.66390i 0.554852 + 0.831949i \(0.312775\pi\)
−0.554852 + 0.831949i \(0.687225\pi\)
\(258\) −14.4660 + 17.0446i −0.900614 + 1.06115i
\(259\) 8.32017 0.516990
\(260\) −6.28196 −0.389591
\(261\) 0.376434 0.0620242i 0.0233007 0.00383920i
\(262\) −53.3491 −3.29592
\(263\) 7.17412 0.442375 0.221188 0.975231i \(-0.429007\pi\)
0.221188 + 0.975231i \(0.429007\pi\)
\(264\) −15.5975 13.2378i −0.959960 0.814733i
\(265\) 15.3507 0.942986
\(266\) 9.04394i 0.554519i
\(267\) 19.1726 22.5902i 1.17335 1.38250i
\(268\) 14.4750i 0.884202i
\(269\) 4.03811i 0.246208i 0.992394 + 0.123104i \(0.0392848\pi\)
−0.992394 + 0.123104i \(0.960715\pi\)
\(270\) 14.5969 24.3266i 0.888339 1.48047i
\(271\) 7.05323 0.428453 0.214227 0.976784i \(-0.431277\pi\)
0.214227 + 0.976784i \(0.431277\pi\)
\(272\) −1.42011 −0.0861069
\(273\) −1.01165 0.858604i −0.0612279 0.0519651i
\(274\) 43.7121i 2.64075i
\(275\) −1.27045 −0.0766108
\(276\) −28.9447 + 4.83302i −1.74226 + 0.290913i
\(277\) 10.9219 0.656234 0.328117 0.944637i \(-0.393586\pi\)
0.328117 + 0.944637i \(0.393586\pi\)
\(278\) 46.4663i 2.78686i
\(279\) −2.01634 12.2374i −0.120715 0.732636i
\(280\) 8.36861 0.500120
\(281\) 18.6481 1.11245 0.556226 0.831031i \(-0.312249\pi\)
0.556226 + 0.831031i \(0.312249\pi\)
\(282\) −25.0113 + 29.4696i −1.48940 + 1.75489i
\(283\) 15.6604i 0.930917i −0.885070 0.465458i \(-0.845889\pi\)
0.885070 0.465458i \(-0.154111\pi\)
\(284\) 9.85419i 0.584738i
\(285\) 11.7855 + 10.0025i 0.698113 + 0.592499i
\(286\) 5.90333i 0.349071i
\(287\) 3.74563 0.221098
\(288\) 11.4927 1.89363i 0.677216 0.111584i
\(289\) −15.9926 −0.940743
\(290\) −0.694322 −0.0407720
\(291\) 5.50622 + 4.67321i 0.322780 + 0.273949i
\(292\) −3.93494 −0.230275
\(293\) 15.4374 0.901865 0.450933 0.892558i \(-0.351091\pi\)
0.450933 + 0.892558i \(0.351091\pi\)
\(294\) 3.10619 + 2.63627i 0.181156 + 0.153750i
\(295\) 9.16663i 0.533702i
\(296\) 29.9971 1.74355
\(297\) 14.5968 + 8.75860i 0.846989 + 0.508226i
\(298\) 47.4064i 2.74618i
\(299\) −2.80623 2.37135i −0.162289 0.137139i
\(300\) −1.53546 + 1.80916i −0.0886499 + 0.104452i
\(301\) 5.48730 0.316283
\(302\) 41.1394i 2.36730i
\(303\) 3.05246 + 2.59067i 0.175359 + 0.148830i
\(304\) 5.44022i 0.312018i
\(305\) 29.4169i 1.68441i
\(306\) 6.98826 1.15144i 0.399492 0.0658234i
\(307\) 8.05965 0.459989 0.229994 0.973192i \(-0.426129\pi\)
0.229994 + 0.973192i \(0.426129\pi\)
\(308\) 11.5735i 0.659464i
\(309\) −4.49530 3.81523i −0.255729 0.217041i
\(310\) 22.5716i 1.28198i
\(311\) 5.39149i 0.305723i −0.988248 0.152862i \(-0.951151\pi\)
0.988248 0.152862i \(-0.0488489\pi\)
\(312\) −3.64736 3.09557i −0.206491 0.175252i
\(313\) 0.965127i 0.0545522i 0.999628 + 0.0272761i \(0.00868333\pi\)
−0.999628 + 0.0272761i \(0.991317\pi\)
\(314\) −34.3879 −1.94062
\(315\) −6.87085 + 1.13209i −0.387128 + 0.0637863i
\(316\) 42.2095i 2.37447i
\(317\) 17.4142i 0.978078i 0.872262 + 0.489039i \(0.162652\pi\)
−0.872262 + 0.489039i \(0.837348\pi\)
\(318\) 20.5423 + 17.4346i 1.15196 + 0.977684i
\(319\) 0.416615i 0.0233260i
\(320\) −27.7665 −1.55220
\(321\) −9.24810 + 10.8966i −0.516179 + 0.608188i
\(322\) 8.61630 + 7.28101i 0.480167 + 0.405755i
\(323\) 3.85904i 0.214723i
\(324\) 30.1142 10.2006i 1.67301 0.566702i
\(325\) −0.297085 −0.0164793
\(326\) 56.7514i 3.14317i
\(327\) 15.7191 + 13.3411i 0.869270 + 0.737763i
\(328\) 13.5043 0.745652
\(329\) 9.48738 0.523056
\(330\) −23.6202 20.0469i −1.30025 1.10354i
\(331\) 7.31973 0.402329 0.201164 0.979557i \(-0.435527\pi\)
0.201164 + 0.979557i \(0.435527\pi\)
\(332\) 38.1212 2.09217
\(333\) −24.6284 + 4.05797i −1.34963 + 0.222376i
\(334\) −29.1932 −1.59738
\(335\) 9.51063i 0.519621i
\(336\) 1.86847 + 1.58580i 0.101933 + 0.0865124i
\(337\) 0.741689i 0.0404024i −0.999796 0.0202012i \(-0.993569\pi\)
0.999796 0.0202012i \(-0.00643067\pi\)
\(338\) 29.1979i 1.58816i
\(339\) 10.9938 12.9534i 0.597099 0.703532i
\(340\) −8.23026 −0.446349
\(341\) −13.5437 −0.733432
\(342\) 4.41098 + 26.7709i 0.238518 + 1.44760i
\(343\) 1.00000i 0.0539949i
\(344\) 19.7837 1.06666
\(345\) −19.0177 + 3.17548i −1.02388 + 0.170962i
\(346\) 17.3553 0.933028
\(347\) 19.6024i 1.05231i −0.850389 0.526155i \(-0.823633\pi\)
0.850389 0.526155i \(-0.176367\pi\)
\(348\) −0.593274 0.503521i −0.0318028 0.0269916i
\(349\) −21.2917 −1.13972 −0.569860 0.821741i \(-0.693003\pi\)
−0.569860 + 0.821741i \(0.693003\pi\)
\(350\) 0.912172 0.0487577
\(351\) 3.41334 + 2.04813i 0.182191 + 0.109321i
\(352\) 12.7195i 0.677952i
\(353\) 22.0203i 1.17202i −0.810302 0.586012i \(-0.800697\pi\)
0.810302 0.586012i \(-0.199303\pi\)
\(354\) 10.4110 12.2668i 0.553340 0.651974i
\(355\) 6.47458i 0.343635i
\(356\) −60.4336 −3.20297
\(357\) −1.32541 1.12489i −0.0701480 0.0595357i
\(358\) 48.9216 2.58559
\(359\) −0.352075 −0.0185818 −0.00929090 0.999957i \(-0.502957\pi\)
−0.00929090 + 0.999957i \(0.502957\pi\)
\(360\) −24.7718 + 4.08160i −1.30559 + 0.215119i
\(361\) 4.21665 0.221929
\(362\) −37.4767 −1.96973
\(363\) −0.299775 + 0.353210i −0.0157341 + 0.0185387i
\(364\) 2.70639i 0.141853i
\(365\) −2.58541 −0.135326
\(366\) −33.4104 + 39.3658i −1.74639 + 2.05768i
\(367\) 28.8036i 1.50354i −0.659427 0.751769i \(-0.729201\pi\)
0.659427 0.751769i \(-0.270799\pi\)
\(368\) 5.18297 + 4.37976i 0.270181 + 0.228311i
\(369\) −11.0874 + 1.82685i −0.577187 + 0.0951019i
\(370\) 45.4265 2.36161
\(371\) 6.61336i 0.343349i
\(372\) −16.3689 + 19.2867i −0.848688 + 0.999968i
\(373\) 18.4620i 0.955924i 0.878381 + 0.477962i \(0.158624\pi\)
−0.878381 + 0.477962i \(0.841376\pi\)
\(374\) 7.73420i 0.399926i
\(375\) 11.9986 14.1374i 0.619608 0.730053i
\(376\) 34.2053 1.76401
\(377\) 0.0974223i 0.00501751i
\(378\) −10.4804 6.28861i −0.539052 0.323451i
\(379\) 0.262031i 0.0134596i −0.999977 0.00672980i \(-0.997858\pi\)
0.999977 0.00672980i \(-0.00214218\pi\)
\(380\) 31.5288i 1.61739i
\(381\) 12.0977 14.2541i 0.619782 0.730259i
\(382\) 23.7779i 1.21658i
\(383\) −0.961680 −0.0491396 −0.0245698 0.999698i \(-0.507822\pi\)
−0.0245698 + 0.999698i \(0.507822\pi\)
\(384\) −26.9030 22.8330i −1.37289 1.16519i
\(385\) 7.60426i 0.387549i
\(386\) 45.8378i 2.33308i
\(387\) −16.2429 + 2.67631i −0.825673 + 0.136044i
\(388\) 14.7303i 0.747819i
\(389\) −10.9789 −0.556651 −0.278326 0.960487i \(-0.589779\pi\)
−0.278326 + 0.960487i \(0.589779\pi\)
\(390\) −5.52342 4.68781i −0.279689 0.237376i
\(391\) −3.67656 3.10680i −0.185932 0.157118i
\(392\) 3.60535i 0.182098i
\(393\) −29.9511 25.4199i −1.51083 1.28227i
\(394\) 34.8592 1.75618
\(395\) 27.7332i 1.39541i
\(396\) −5.64473 34.2587i −0.283658 1.72156i
\(397\) −8.73814 −0.438555 −0.219277 0.975663i \(-0.570370\pi\)
−0.219277 + 0.975663i \(0.570370\pi\)
\(398\) −34.9759 −1.75318
\(399\) 4.30928 5.07741i 0.215734 0.254189i
\(400\) 0.548700 0.0274350
\(401\) −25.0351 −1.25019 −0.625096 0.780548i \(-0.714940\pi\)
−0.625096 + 0.780548i \(0.714940\pi\)
\(402\) 10.8017 12.7272i 0.538741 0.634773i
\(403\) −3.16709 −0.157764
\(404\) 8.16598i 0.406273i
\(405\) 19.7862 6.70220i 0.983182 0.333035i
\(406\) 0.299127i 0.0148454i
\(407\) 27.2573i 1.35109i
\(408\) −4.77856 4.05563i −0.236574 0.200784i
\(409\) −20.1381 −0.995765 −0.497883 0.867244i \(-0.665889\pi\)
−0.497883 + 0.867244i \(0.665889\pi\)
\(410\) 20.4504 1.00997
\(411\) −20.8281 + 24.5407i −1.02737 + 1.21050i
\(412\) 12.0259i 0.592474i
\(413\) −3.94915 −0.194325
\(414\) −29.0561 17.3500i −1.42803 0.852707i
\(415\) 25.0471 1.22951
\(416\) 2.97436i 0.145830i
\(417\) −22.1404 + 26.0869i −1.08422 + 1.27748i
\(418\) 29.6284 1.44917
\(419\) 4.76560 0.232815 0.116407 0.993202i \(-0.462862\pi\)
0.116407 + 0.993202i \(0.462862\pi\)
\(420\) 10.8287 + 9.19050i 0.528387 + 0.448450i
\(421\) 21.4790i 1.04682i −0.852081 0.523410i \(-0.824660\pi\)
0.852081 0.523410i \(-0.175340\pi\)
\(422\) 38.0310i 1.85132i
\(423\) −28.0835 + 4.62725i −1.36547 + 0.224985i
\(424\) 23.8435i 1.15794i
\(425\) −0.389223 −0.0188801
\(426\) −7.35352 + 8.66429i −0.356279 + 0.419786i
\(427\) 12.6734 0.613307
\(428\) 29.1507 1.40905
\(429\) 2.81283 3.31422i 0.135805 0.160012i
\(430\) 29.9596 1.44478
\(431\) −20.8314 −1.00341 −0.501707 0.865038i \(-0.667294\pi\)
−0.501707 + 0.865038i \(0.667294\pi\)
\(432\) −6.30427 3.78280i −0.303314 0.182000i
\(433\) 30.1525i 1.44904i 0.689254 + 0.724520i \(0.257938\pi\)
−0.689254 + 0.724520i \(0.742062\pi\)
\(434\) 9.72427 0.466780
\(435\) −0.389804 0.330832i −0.0186897 0.0158622i
\(436\) 42.0521i 2.01393i
\(437\) 11.9016 14.0843i 0.569333 0.673744i
\(438\) −3.45980 2.93638i −0.165316 0.140306i
\(439\) −20.0251 −0.955745 −0.477873 0.878429i \(-0.658592\pi\)
−0.477873 + 0.878429i \(0.658592\pi\)
\(440\) 27.4160i 1.30701i
\(441\) 0.487727 + 2.96009i 0.0232251 + 0.140957i
\(442\) 1.80858i 0.0860256i
\(443\) 1.85078i 0.0879333i 0.999033 + 0.0439667i \(0.0139995\pi\)
−0.999033 + 0.0439667i \(0.986000\pi\)
\(444\) 38.8153 + 32.9432i 1.84209 + 1.56341i
\(445\) −39.7072 −1.88230
\(446\) 17.0292i 0.806357i
\(447\) 22.5883 26.6147i 1.06839 1.25883i
\(448\) 11.9623i 0.565167i
\(449\) 35.0747i 1.65528i 0.561261 + 0.827639i \(0.310316\pi\)
−0.561261 + 0.827639i \(0.689684\pi\)
\(450\) −2.70011 + 0.444891i −0.127284 + 0.0209724i
\(451\) 12.2709i 0.577814i
\(452\) −34.6532 −1.62995
\(453\) 19.6022 23.0963i 0.920991 1.08516i
\(454\) 55.8628i 2.62177i
\(455\) 1.77820i 0.0833632i
\(456\) 15.5365 18.3059i 0.727562 0.857251i
\(457\) 25.3967i 1.18801i 0.804461 + 0.594005i \(0.202454\pi\)
−0.804461 + 0.594005i \(0.797546\pi\)
\(458\) 0.877236 0.0409905
\(459\) 4.47196 + 2.68335i 0.208733 + 0.125248i
\(460\) 30.0379 + 25.3829i 1.40053 + 1.18348i
\(461\) 1.87688i 0.0874152i 0.999044 + 0.0437076i \(0.0139170\pi\)
−0.999044 + 0.0437076i \(0.986083\pi\)
\(462\) −8.63656 + 10.1760i −0.401809 + 0.473432i
\(463\) −8.06674 −0.374893 −0.187447 0.982275i \(-0.560021\pi\)
−0.187447 + 0.982275i \(0.560021\pi\)
\(464\) 0.179934i 0.00835324i
\(465\) −10.7550 + 12.6721i −0.498751 + 0.587654i
\(466\) −34.8730 −1.61546
\(467\) 0.441999 0.0204533 0.0102266 0.999948i \(-0.496745\pi\)
0.0102266 + 0.999948i \(0.496745\pi\)
\(468\) −1.31998 8.01114i −0.0610160 0.370315i
\(469\) −4.09736 −0.189198
\(470\) 51.7992 2.38932
\(471\) −19.3059 16.3853i −0.889571 0.754993i
\(472\) −14.2381 −0.655361
\(473\) 17.9767i 0.826569i
\(474\) 31.4981 37.1127i 1.44676 1.70464i
\(475\) 1.49105i 0.0684140i
\(476\) 3.54575i 0.162519i
\(477\) 3.22552 + 19.5761i 0.147686 + 0.896330i
\(478\) −22.1263 −1.01203
\(479\) −9.36305 −0.427809 −0.213904 0.976855i \(-0.568618\pi\)
−0.213904 + 0.976855i \(0.568618\pi\)
\(480\) −11.9009 10.1005i −0.543201 0.461023i
\(481\) 6.37392i 0.290626i
\(482\) 45.9640 2.09360
\(483\) 1.36805 + 8.19319i 0.0622486 + 0.372803i
\(484\) 0.944913 0.0429506
\(485\) 9.67838i 0.439473i
\(486\) 34.0899 + 13.5033i 1.54635 + 0.612522i
\(487\) 33.8470 1.53376 0.766878 0.641793i \(-0.221809\pi\)
0.766878 + 0.641793i \(0.221809\pi\)
\(488\) 45.6919 2.06838
\(489\) 27.0411 31.8612i 1.22284 1.44081i
\(490\) 5.45980i 0.246649i
\(491\) 24.1720i 1.09087i −0.838154 0.545433i \(-0.816365\pi\)
0.838154 0.545433i \(-0.183635\pi\)
\(492\) 17.4742 + 14.8306i 0.787797 + 0.668615i
\(493\) 0.127637i 0.00574849i
\(494\) 6.92839 0.311723
\(495\) −3.70880 22.5093i −0.166698 1.01172i
\(496\) 5.84946 0.262648
\(497\) 2.78937 0.125120
\(498\) 33.5181 + 28.4473i 1.50198 + 1.27475i
\(499\) −21.4157 −0.958700 −0.479350 0.877624i \(-0.659128\pi\)
−0.479350 + 0.877624i \(0.659128\pi\)
\(500\) −37.8207 −1.69139
\(501\) −16.3895 13.9100i −0.732229 0.621454i
\(502\) 20.6794i 0.922966i
\(503\) 13.6310 0.607774 0.303887 0.952708i \(-0.401715\pi\)
0.303887 + 0.952708i \(0.401715\pi\)
\(504\) 1.75843 + 10.6722i 0.0783266 + 0.475376i
\(505\) 5.36536i 0.238756i
\(506\) −23.8530 + 28.2274i −1.06039 + 1.25486i
\(507\) −13.9123 + 16.3922i −0.617868 + 0.728003i
\(508\) −38.1328 −1.69187
\(509\) 12.3478i 0.547307i 0.961828 + 0.273654i \(0.0882322\pi\)
−0.961828 + 0.273654i \(0.911768\pi\)
\(510\) −7.23646 6.14169i −0.320436 0.271959i
\(511\) 1.11384i 0.0492734i
\(512\) 15.6960i 0.693672i
\(513\) −10.2795 + 17.1314i −0.453849 + 0.756368i
\(514\) 62.7429 2.76747
\(515\) 7.90148i 0.348181i
\(516\) 25.5994 + 21.7266i 1.12695 + 0.956462i
\(517\) 31.0812i 1.36695i
\(518\) 19.5706i 0.859881i
\(519\) 9.74357 + 8.26951i 0.427695 + 0.362991i
\(520\) 6.41103i 0.281142i
\(521\) 39.8081 1.74402 0.872012 0.489484i \(-0.162815\pi\)
0.872012 + 0.489484i \(0.162815\pi\)
\(522\) −0.145892 0.885442i −0.00638553 0.0387547i
\(523\) 10.2398i 0.447756i 0.974617 + 0.223878i \(0.0718718\pi\)
−0.974617 + 0.223878i \(0.928128\pi\)
\(524\) 80.1255i 3.50030i
\(525\) 0.512108 + 0.434634i 0.0223502 + 0.0189690i
\(526\) 16.8748i 0.735778i
\(527\) −4.14934 −0.180748
\(528\) −5.19516 + 6.12121i −0.226090 + 0.266391i
\(529\) 3.83668 + 22.6777i 0.166812 + 0.985989i
\(530\) 36.1077i 1.56842i
\(531\) 11.6898 1.92611i 0.507296 0.0835861i
\(532\) −13.5832 −0.588906
\(533\) 2.86946i 0.124290i
\(534\) −53.1363 45.0976i −2.29943 1.95156i
\(535\) 19.1531 0.828062
\(536\) −14.7724 −0.638071
\(537\) 27.4654 + 23.3103i 1.18522 + 1.00591i
\(538\) 9.49837 0.409504
\(539\) 3.27605 0.141110
\(540\) −36.5364 21.9232i −1.57228 0.943425i
\(541\) −37.8124 −1.62568 −0.812842 0.582484i \(-0.802081\pi\)
−0.812842 + 0.582484i \(0.802081\pi\)
\(542\) 16.5905i 0.712623i
\(543\) −21.0401 17.8570i −0.902915 0.766318i
\(544\) 3.89683i 0.167075i
\(545\) 27.6298i 1.18353i
\(546\) −2.01959 + 2.37959i −0.0864307 + 0.101837i
\(547\) −41.2938 −1.76560 −0.882798 0.469753i \(-0.844343\pi\)
−0.882798 + 0.469753i \(0.844343\pi\)
\(548\) 65.6517 2.80450
\(549\) −37.5143 + 6.18115i −1.60107 + 0.263805i
\(550\) 2.98832i 0.127423i
\(551\) 0.488957 0.0208303
\(552\) 4.93231 + 29.5393i 0.209933 + 1.25728i
\(553\) −11.9480 −0.508080
\(554\) 25.6903i 1.09148i
\(555\) 25.5032 + 21.6449i 1.08255 + 0.918776i
\(556\) 69.7882 2.95968
\(557\) 16.0587 0.680428 0.340214 0.940348i \(-0.389500\pi\)
0.340214 + 0.940348i \(0.389500\pi\)
\(558\) −28.7847 + 4.74280i −1.21855 + 0.200779i
\(559\) 4.20372i 0.177798i
\(560\) 3.28424i 0.138785i
\(561\) 3.68521 4.34210i 0.155590 0.183324i
\(562\) 43.8638i 1.85028i
\(563\) −29.6673 −1.25033 −0.625163 0.780494i \(-0.714968\pi\)
−0.625163 + 0.780494i \(0.714968\pi\)
\(564\) 44.2606 + 37.5647i 1.86371 + 1.58176i
\(565\) −22.7684 −0.957876
\(566\) −36.8362 −1.54834
\(567\) −2.88743 8.52424i −0.121261 0.357985i
\(568\) 10.0566 0.421968
\(569\) 34.6871 1.45416 0.727080 0.686553i \(-0.240877\pi\)
0.727080 + 0.686553i \(0.240877\pi\)
\(570\) 23.5278 27.7217i 0.985472 1.16113i
\(571\) 27.6815i 1.15843i −0.815173 0.579217i \(-0.803358\pi\)
0.815173 0.579217i \(-0.196642\pi\)
\(572\) −8.86626 −0.370717
\(573\) −11.3298 + 13.3493i −0.473308 + 0.557676i
\(574\) 8.81042i 0.367740i
\(575\) 1.42054 + 1.20040i 0.0592408 + 0.0500601i
\(576\) −5.83436 35.4096i −0.243098 1.47540i
\(577\) −14.6019 −0.607887 −0.303943 0.952690i \(-0.598303\pi\)
−0.303943 + 0.952690i \(0.598303\pi\)
\(578\) 37.6176i 1.56469i
\(579\) 21.8409 25.7341i 0.907678 1.06947i
\(580\) 1.04281i 0.0433003i
\(581\) 10.7907i 0.447676i
\(582\) 10.9923 12.9516i 0.455644 0.536863i
\(583\) 21.6657 0.897303
\(584\) 4.01579i 0.166175i
\(585\) −0.867276 5.26362i −0.0358575 0.217624i
\(586\) 36.3117i 1.50002i
\(587\) 24.1786i 0.997959i −0.866614 0.498980i \(-0.833708\pi\)
0.866614 0.498980i \(-0.166292\pi\)
\(588\) 3.95944 4.66521i 0.163284 0.192390i
\(589\) 15.8954i 0.654960i
\(590\) −21.5616 −0.887677
\(591\) 19.5705 + 16.6098i 0.805025 + 0.683237i
\(592\) 11.7723i 0.483839i
\(593\) 11.7606i 0.482950i −0.970407 0.241475i \(-0.922369\pi\)
0.970407 0.241475i \(-0.0776311\pi\)
\(594\) 20.6018 34.3342i 0.845304 1.40875i
\(595\) 2.32969i 0.0955081i
\(596\) −71.2001 −2.91647
\(597\) −19.6360 16.6654i −0.803649 0.682069i
\(598\) −5.57784 + 6.60078i −0.228095 + 0.269926i
\(599\) 6.11753i 0.249956i −0.992160 0.124978i \(-0.960114\pi\)
0.992160 0.124978i \(-0.0398860\pi\)
\(600\) 1.84633 + 1.56701i 0.0753761 + 0.0639729i
\(601\) −16.9148 −0.689969 −0.344985 0.938608i \(-0.612116\pi\)
−0.344985 + 0.938608i \(0.612116\pi\)
\(602\) 12.9071i 0.526056i
\(603\) 12.1285 1.99839i 0.493912 0.0813809i
\(604\) −61.7876 −2.51410
\(605\) 0.620844 0.0252409
\(606\) 6.09373 7.17994i 0.247541 0.291665i
\(607\) 29.5858 1.20085 0.600426 0.799680i \(-0.294998\pi\)
0.600426 + 0.799680i \(0.294998\pi\)
\(608\) 14.9281 0.605416
\(609\) −0.142529 + 0.167935i −0.00577556 + 0.00680506i
\(610\) 69.1940 2.80158
\(611\) 7.26810i 0.294036i
\(612\) −1.72936 10.4957i −0.0699052 0.424265i
\(613\) 6.33400i 0.255828i −0.991785 0.127914i \(-0.959172\pi\)
0.991785 0.127914i \(-0.0408281\pi\)
\(614\) 18.9578i 0.765074i
\(615\) 11.4812 + 9.74427i 0.462967 + 0.392927i
\(616\) 11.8113 0.475892
\(617\) −7.78616 −0.313459 −0.156730 0.987642i \(-0.550095\pi\)
−0.156730 + 0.987642i \(0.550095\pi\)
\(618\) −8.97413 + 10.5738i −0.360992 + 0.425340i
\(619\) 36.6343i 1.47245i 0.676734 + 0.736227i \(0.263395\pi\)
−0.676734 + 0.736227i \(0.736605\pi\)
\(620\) 33.9005 1.36148
\(621\) −8.04560 23.5853i −0.322859 0.946447i
\(622\) −12.6818 −0.508493
\(623\) 17.1066i 0.685361i
\(624\) −1.21485 + 1.43140i −0.0486329 + 0.0573018i
\(625\) −26.7886 −1.07154
\(626\) 2.27016 0.0907337
\(627\) 16.6339 + 14.1174i 0.664293 + 0.563796i
\(628\) 51.6476i 2.06096i
\(629\) 8.35074i 0.332966i
\(630\) 2.66290 + 16.1615i 0.106092 + 0.643889i
\(631\) 8.74385i 0.348087i 0.984738 + 0.174044i \(0.0556834\pi\)
−0.984738 + 0.174044i \(0.944317\pi\)
\(632\) −43.0767 −1.71350
\(633\) −18.1211 + 21.3512i −0.720249 + 0.848634i
\(634\) 40.9614 1.62678
\(635\) −25.0547 −0.994264
\(636\) 26.1852 30.8527i 1.03831 1.22339i
\(637\) 0.766081 0.0303532
\(638\) −0.979955 −0.0387968
\(639\) −8.25677 + 1.36045i −0.326633 + 0.0538186i
\(640\) 47.2878i 1.86922i
\(641\) 21.4101 0.845647 0.422824 0.906212i \(-0.361039\pi\)
0.422824 + 0.906212i \(0.361039\pi\)
\(642\) 25.6308 + 21.7532i 1.01157 + 0.858532i
\(643\) 11.5802i 0.456678i −0.973582 0.228339i \(-0.926671\pi\)
0.973582 0.228339i \(-0.0733294\pi\)
\(644\) 10.9354 12.9409i 0.430916 0.509943i
\(645\) 16.8198 + 14.2752i 0.662279 + 0.562086i
\(646\) 9.07717 0.357136
\(647\) 2.17115i 0.0853567i −0.999089 0.0426783i \(-0.986411\pi\)
0.999089 0.0426783i \(-0.0135891\pi\)
\(648\) −10.4102 30.7329i −0.408952 1.20730i
\(649\) 12.9376i 0.507847i
\(650\) 0.698798i 0.0274091i
\(651\) 5.45937 + 4.63345i 0.213969 + 0.181599i
\(652\) −85.2355 −3.33808
\(653\) 19.2199i 0.752131i −0.926593 0.376066i \(-0.877277\pi\)
0.926593 0.376066i \(-0.122723\pi\)
\(654\) 31.3807 36.9743i 1.22708 1.44581i
\(655\) 52.6455i 2.05703i
\(656\) 5.29975i 0.206920i
\(657\) −0.543251 3.29707i −0.0211942 0.128631i
\(658\) 22.3161i 0.869970i
\(659\) −18.2933 −0.712605 −0.356302 0.934371i \(-0.615963\pi\)
−0.356302 + 0.934371i \(0.615963\pi\)
\(660\) −30.1086 + 35.4755i −1.17197 + 1.38088i
\(661\) 44.6466i 1.73655i 0.496082 + 0.868275i \(0.334771\pi\)
−0.496082 + 0.868275i \(0.665229\pi\)
\(662\) 17.2174i 0.669171i
\(663\) 0.861759 1.01537i 0.0334679 0.0394336i
\(664\) 38.9044i 1.50979i
\(665\) −8.92467 −0.346084
\(666\) 9.54510 + 57.9306i 0.369865 + 2.24476i
\(667\) −0.393645 + 0.465836i −0.0152420 + 0.0180373i
\(668\) 43.8455i 1.69643i
\(669\) −8.11413 + 9.56048i −0.313710 + 0.369629i
\(670\) −22.3708 −0.864258
\(671\) 41.5186i 1.60281i
\(672\) −4.35148 + 5.12714i −0.167862 + 0.197784i
\(673\) −25.6694 −0.989483 −0.494742 0.869040i \(-0.664737\pi\)
−0.494742 + 0.869040i \(0.664737\pi\)
\(674\) −1.74459 −0.0671990
\(675\) −1.72787 1.03679i −0.0665057 0.0399059i
\(676\) 43.8527 1.68664
\(677\) 0.371620 0.0142825 0.00714126 0.999975i \(-0.497727\pi\)
0.00714126 + 0.999975i \(0.497727\pi\)
\(678\) −30.4688 25.8593i −1.17015 0.993122i
\(679\) −4.16963 −0.160016
\(680\) 8.39936i 0.322101i
\(681\) 26.6177 31.3623i 1.01999 1.20181i
\(682\) 31.8572i 1.21988i
\(683\) 20.9096i 0.800085i −0.916497 0.400043i \(-0.868995\pi\)
0.916497 0.400043i \(-0.131005\pi\)
\(684\) 40.2074 6.62489i 1.53737 0.253309i
\(685\) 43.1357 1.64813
\(686\) −2.35218 −0.0898068
\(687\) 0.492495 + 0.417988i 0.0187898 + 0.0159472i
\(688\) 7.76405i 0.296002i
\(689\) 5.06637 0.193013
\(690\) 7.46930 + 44.7332i 0.284351 + 1.70296i
\(691\) −20.1908 −0.768093 −0.384046 0.923314i \(-0.625470\pi\)
−0.384046 + 0.923314i \(0.625470\pi\)
\(692\) 26.0661i 0.990886i
\(693\) −9.69741 + 1.59782i −0.368374 + 0.0606962i
\(694\) −46.1083 −1.75025
\(695\) 45.8535 1.73932
\(696\) −0.513866 + 0.605463i −0.0194780 + 0.0229500i
\(697\) 3.75940i 0.142397i
\(698\) 50.0821i 1.89564i
\(699\) −19.5782 16.6164i −0.740517 0.628488i
\(700\) 1.37000i 0.0517811i
\(701\) −30.1302 −1.13800 −0.569002 0.822336i \(-0.692670\pi\)
−0.569002 + 0.822336i \(0.692670\pi\)
\(702\) 4.81759 8.02881i 0.181828 0.303028i
\(703\) −31.9903 −1.20654
\(704\) −39.1893 −1.47700
\(705\) 29.0809 + 24.6814i 1.09525 + 0.929556i
\(706\) −51.7959 −1.94936
\(707\) −2.31150 −0.0869328
\(708\) −18.4236 15.6364i −0.692403 0.587653i
\(709\) 3.99204i 0.149924i −0.997186 0.0749620i \(-0.976116\pi\)
0.997186 0.0749620i \(-0.0238836\pi\)
\(710\) 15.2294 0.571549
\(711\) 35.3671 5.82736i 1.32637 0.218543i
\(712\) 61.6753i 2.31138i
\(713\) 15.1438 + 12.7969i 0.567140 + 0.479249i
\(714\) −2.64596 + 3.11760i −0.0990224 + 0.116673i
\(715\) −5.82547 −0.217860
\(716\) 73.4759i 2.74592i
\(717\) −12.4221 10.5428i −0.463911 0.393728i
\(718\) 0.828145i 0.0309061i
\(719\) 8.37285i 0.312255i −0.987737 0.156127i \(-0.950099\pi\)
0.987737 0.156127i \(-0.0499010\pi\)
\(720\) 1.60182 + 9.72165i 0.0596961 + 0.362305i
\(721\) 3.40410 0.126775
\(722\) 9.91834i 0.369122i
\(723\) 25.8049 + 21.9011i 0.959696 + 0.814509i
\(724\) 56.2867i 2.09188i
\(725\) 0.0493162i 0.00183156i
\(726\) 0.830815 + 0.705125i 0.0308344 + 0.0261697i
\(727\) 41.7377i 1.54797i −0.633206 0.773984i \(-0.718261\pi\)
0.633206 0.773984i \(-0.281739\pi\)
\(728\) 2.76199 0.102366
\(729\) 12.7046 + 23.8242i 0.470539 + 0.882379i
\(730\) 6.08135i 0.225081i
\(731\) 5.50747i 0.203701i
\(732\) 59.1239 + 50.1794i 2.18528 + 1.85468i
\(733\) 14.0758i 0.519900i −0.965622 0.259950i \(-0.916294\pi\)
0.965622 0.259950i \(-0.0837061\pi\)
\(734\) −67.7515 −2.50075
\(735\) 2.60150 3.06522i 0.0959578 0.113062i
\(736\) −12.0182 + 14.2223i −0.442997 + 0.524239i
\(737\) 13.4232i 0.494448i
\(738\) 4.29708 + 26.0796i 0.158178 + 0.960004i
\(739\) 4.14958 0.152645 0.0763225 0.997083i \(-0.475682\pi\)
0.0763225 + 0.997083i \(0.475682\pi\)
\(740\) 68.2264i 2.50805i
\(741\) 3.88971 + 3.30126i 0.142892 + 0.121275i
\(742\) −15.5558 −0.571073
\(743\) −41.3281 −1.51618 −0.758090 0.652150i \(-0.773867\pi\)
−0.758090 + 0.652150i \(0.773867\pi\)
\(744\) 19.6829 + 16.7052i 0.721611 + 0.612443i
\(745\) −46.7812 −1.71393
\(746\) 43.4259 1.58994
\(747\) 5.26294 + 31.9416i 0.192561 + 1.16868i
\(748\) −11.6161 −0.424725
\(749\) 8.25153i 0.301504i
\(750\) −33.2538 28.2230i −1.21426 1.03056i
\(751\) 11.0978i 0.404963i 0.979286 + 0.202481i \(0.0649006\pi\)
−0.979286 + 0.202481i \(0.935099\pi\)
\(752\) 13.4238i 0.489516i
\(753\) 9.85337 11.6097i 0.359077 0.423083i
\(754\) −0.229155 −0.00834534
\(755\) −40.5968 −1.47747
\(756\) −9.44493 + 15.7406i −0.343509 + 0.572479i
\(757\) 41.3684i 1.50356i −0.659413 0.751781i \(-0.729195\pi\)
0.659413 0.751781i \(-0.270805\pi\)
\(758\) −0.616344 −0.0223866
\(759\) −26.8413 + 4.48182i −0.974279 + 0.162680i
\(760\) −32.1766 −1.16717
\(761\) 14.6649i 0.531604i 0.964028 + 0.265802i \(0.0856367\pi\)
−0.964028 + 0.265802i \(0.914363\pi\)
\(762\) −33.5282 28.4559i −1.21460 1.03085i
\(763\) −11.9034 −0.430933
\(764\) 35.7123 1.29203
\(765\) −1.13625 6.89609i −0.0410814 0.249329i
\(766\) 2.26205i 0.0817311i
\(767\) 3.02537i 0.109240i
\(768\) −26.8931 + 31.6869i −0.970423 + 1.14340i
\(769\) 0.965100i 0.0348024i −0.999849 0.0174012i \(-0.994461\pi\)
0.999849 0.0174012i \(-0.00553925\pi\)
\(770\) 17.8866 0.644588
\(771\) 35.2249 + 29.8959i 1.26859 + 1.07667i
\(772\) −68.8443 −2.47776
\(773\) 21.8868 0.787213 0.393607 0.919279i \(-0.371227\pi\)
0.393607 + 0.919279i \(0.371227\pi\)
\(774\) 6.29517 + 38.2063i 0.226275 + 1.37330i
\(775\) 1.60321 0.0575892
\(776\) −15.0330 −0.539652
\(777\) 9.32503 10.9872i 0.334534 0.394165i
\(778\) 25.8243i 0.925847i
\(779\) −14.4016 −0.515992
\(780\) −7.04067 + 8.29567i −0.252096 + 0.297033i
\(781\) 9.13812i 0.326988i
\(782\) −7.30776 + 8.64796i −0.261325 + 0.309250i
\(783\) 0.339991 0.566617i 0.0121503 0.0202492i
\(784\) −1.41491 −0.0505326
\(785\) 33.9344i 1.21117i
\(786\) −59.7923 + 70.4504i −2.13272 + 2.51288i
\(787\) 31.4075i 1.11956i −0.828642 0.559778i \(-0.810886\pi\)
0.828642 0.559778i \(-0.189114\pi\)
\(788\) 52.3554i 1.86508i
\(789\) 8.04057 9.47382i 0.286252 0.337277i
\(790\) −65.2337 −2.32091
\(791\) 9.80907i 0.348770i
\(792\) −34.9626 + 5.76071i −1.24234 + 0.204698i
\(793\) 9.70882i 0.344770i
\(794\) 20.5537i 0.729424i
\(795\) 17.2047 20.2714i 0.610187 0.718954i
\(796\) 52.5306i 1.86190i
\(797\) 10.1893 0.360923 0.180462 0.983582i \(-0.442241\pi\)
0.180462 + 0.983582i \(0.442241\pi\)
\(798\) −11.9430 10.1362i −0.422778 0.358818i
\(799\) 9.52224i 0.336873i
\(800\) 1.50565i 0.0532328i
\(801\) −8.34335 50.6370i −0.294798 1.78917i
\(802\) 58.8871i 2.07938i
\(803\) −3.64900 −0.128771
\(804\) −19.1150 16.2232i −0.674135 0.572149i
\(805\) 7.18499 8.50266i 0.253238 0.299680i
\(806\) 7.44958i 0.262400i
\(807\) 5.33254 + 4.52581i 0.187714 + 0.159316i
\(808\) −8.33376 −0.293181
\(809\) 12.6327i 0.444140i 0.975031 + 0.222070i \(0.0712814\pi\)
−0.975031 + 0.222070i \(0.928719\pi\)
\(810\) −15.7648 46.5407i −0.553919 1.63527i
\(811\) −7.42142 −0.260601 −0.130301 0.991475i \(-0.541594\pi\)
−0.130301 + 0.991475i \(0.541594\pi\)
\(812\) 0.449261 0.0157660
\(813\) 7.90509 9.31418i 0.277244 0.326662i
\(814\) 64.1142 2.24720
\(815\) −56.0030 −1.96170
\(816\) −1.59163 + 1.87533i −0.0557180 + 0.0656499i
\(817\) −21.0982 −0.738132
\(818\) 47.3685i 1.65620i
\(819\) −2.26767 + 0.373639i −0.0792387 + 0.0130560i
\(820\) 30.7147i 1.07260i
\(821\) 14.3680i 0.501447i 0.968059 + 0.250723i \(0.0806685\pi\)
−0.968059 + 0.250723i \(0.919332\pi\)
\(822\) 57.7243 + 48.9915i 2.01336 + 1.70877i
\(823\) −19.4089 −0.676551 −0.338275 0.941047i \(-0.609844\pi\)
−0.338275 + 0.941047i \(0.609844\pi\)
\(824\) 12.2730 0.427550
\(825\) −1.42389 + 1.67769i −0.0495733 + 0.0584098i
\(826\) 9.28914i 0.323210i
\(827\) −39.6194 −1.37770 −0.688851 0.724903i \(-0.741885\pi\)
−0.688851 + 0.724903i \(0.741885\pi\)
\(828\) −26.0582 + 43.6397i −0.905584 + 1.51658i
\(829\) 43.8031 1.52135 0.760673 0.649135i \(-0.224869\pi\)
0.760673 + 0.649135i \(0.224869\pi\)
\(830\) 58.9153i 2.04498i
\(831\) 12.2410 14.4230i 0.424636 0.500327i
\(832\) −9.16412 −0.317709
\(833\) 1.00367 0.0347753
\(834\) 61.3613 + 52.0783i 2.12477 + 1.80332i
\(835\) 28.8082i 0.996947i
\(836\) 44.4992i 1.53904i
\(837\) −18.4201 11.0527i −0.636691 0.382038i
\(838\) 11.2096i 0.387228i
\(839\) 30.9005 1.06680 0.533402 0.845862i \(-0.320913\pi\)
0.533402 + 0.845862i \(0.320913\pi\)
\(840\) 9.37933 11.0512i 0.323617 0.381303i
\(841\) 28.9838 0.999442
\(842\) −50.5224 −1.74112
\(843\) 20.9003 24.6258i 0.719845 0.848159i
\(844\) 57.1191 1.96612
\(845\) 28.8129 0.991193
\(846\) 10.8842 + 66.0575i 0.374205 + 2.27110i
\(847\) 0.267471i 0.00919041i
\(848\) −9.35733 −0.321332
\(849\) −20.6805 17.5518i −0.709752 0.602377i
\(850\) 0.915524i 0.0314022i
\(851\) 25.7545 30.4776i 0.882851 1.04476i
\(852\) 13.0130 + 11.0443i 0.445818 + 0.378372i
\(853\) 31.5467 1.08014 0.540069 0.841621i \(-0.318398\pi\)
0.540069 + 0.841621i \(0.318398\pi\)
\(854\) 29.8101i 1.02008i
\(855\) 26.4178 4.35281i 0.903470 0.148863i
\(856\) 29.7497i 1.01682i
\(857\) 6.90528i 0.235880i −0.993021 0.117940i \(-0.962371\pi\)
0.993021 0.117940i \(-0.0376290\pi\)
\(858\) −7.79566 6.61630i −0.266140 0.225877i
\(859\) 28.9561 0.987969 0.493985 0.869471i \(-0.335540\pi\)
0.493985 + 0.869471i \(0.335540\pi\)
\(860\) 44.9966i 1.53437i
\(861\) 4.19801 4.94631i 0.143068 0.168570i
\(862\) 48.9993i 1.66892i
\(863\) 58.5614i 1.99345i −0.0808526 0.996726i \(-0.525764\pi\)
0.0808526 0.996726i \(-0.474236\pi\)
\(864\) 10.3801 17.2991i 0.353139 0.588528i
\(865\) 17.1264i 0.582317i
\(866\) 70.9243 2.41011
\(867\) −17.9241 + 21.1191i −0.608736 + 0.717244i
\(868\) 14.6050i 0.495725i
\(869\) 39.1423i 1.32781i
\(870\) −0.778179 + 0.916890i −0.0263827 + 0.0310855i
\(871\) 3.13891i 0.106358i
\(872\) −42.9161 −1.45332
\(873\) 12.3425 2.03364i 0.417729 0.0688283i
\(874\) −33.1289 27.9948i −1.12060 0.946940i
\(875\) 10.7057i 0.361918i
\(876\) −4.41019 + 5.19631i −0.149006 + 0.175567i
\(877\) 36.9482 1.24765 0.623827 0.781563i \(-0.285577\pi\)
0.623827 + 0.781563i \(0.285577\pi\)
\(878\) 47.1027i 1.58964i
\(879\) 17.3019 20.3860i 0.583579 0.687602i
\(880\) 10.7594 0.362698
\(881\) 4.26098 0.143556 0.0717781 0.997421i \(-0.477133\pi\)
0.0717781 + 0.997421i \(0.477133\pi\)
\(882\) 6.96267 1.14722i 0.234445 0.0386291i
\(883\) 14.3118 0.481629 0.240815 0.970571i \(-0.422585\pi\)
0.240815 + 0.970571i \(0.422585\pi\)
\(884\) −2.71633 −0.0913601
\(885\) −12.1050 10.2737i −0.406906 0.345348i
\(886\) 4.35338 0.146255
\(887\) 54.9604i 1.84539i −0.385529 0.922696i \(-0.625981\pi\)
0.385529 0.922696i \(-0.374019\pi\)
\(888\) 33.6200 39.6128i 1.12821 1.32932i
\(889\) 10.7940i 0.362020i
\(890\) 93.3986i 3.13073i
\(891\) 27.9259 9.45938i 0.935552 0.316901i
\(892\) 25.5763 0.856359
\(893\) −36.4781 −1.22069
\(894\) −62.6027 53.1319i −2.09375 1.77700i
\(895\) 48.2764i 1.61370i
\(896\) 20.3725 0.680597
\(897\) −6.27665 + 1.04804i −0.209571 + 0.0349930i
\(898\) 82.5021 2.75313
\(899\) 0.525739i 0.0175344i
\(900\) 0.668187 + 4.05532i 0.0222729 + 0.135177i
\(901\) 6.63766 0.221133
\(902\) 28.8634 0.961046
\(903\) 6.15003 7.24628i 0.204660 0.241141i
\(904\) 35.3651i 1.17623i
\(905\) 36.9825i 1.22934i
\(906\) −54.3267 46.1080i −1.80489 1.53183i
\(907\) 37.0857i 1.23141i −0.787976 0.615706i \(-0.788871\pi\)
0.787976 0.615706i \(-0.211129\pi\)
\(908\) −83.9009 −2.78435
\(909\) 6.84224 1.12738i 0.226943 0.0373929i
\(910\) 4.18265 0.138653
\(911\) −28.1021 −0.931065 −0.465532 0.885031i \(-0.654137\pi\)
−0.465532 + 0.885031i \(0.654137\pi\)
\(912\) −7.18410 6.09726i −0.237889 0.201900i
\(913\) 35.3511 1.16995
\(914\) 59.7378 1.97595
\(915\) 38.8467 + 32.9698i 1.28423 + 1.08995i
\(916\) 1.31753i 0.0435324i
\(917\) 22.6807 0.748982
\(918\) 6.31172 10.5189i 0.208318 0.347175i
\(919\) 3.96456i 0.130779i 0.997860 + 0.0653894i \(0.0208290\pi\)
−0.997860 + 0.0653894i \(0.979171\pi\)
\(920\) 25.9044 30.6551i 0.854043 1.01067i
\(921\) 9.03306 10.6432i 0.297649 0.350706i
\(922\) 4.41478 0.145393
\(923\) 2.13688i 0.0703363i
\(924\) 15.2835 + 12.9713i 0.502790 + 0.426725i
\(925\) 3.22654i 0.106088i
\(926\) 18.9744i 0.623539i
\(927\) −10.0764 + 1.66027i −0.330954 + 0.0545306i
\(928\) −0.493745 −0.0162080
\(929\) 19.0657i 0.625524i 0.949832 + 0.312762i \(0.101254\pi\)
−0.949832 + 0.312762i \(0.898746\pi\)
\(930\) 29.8071 + 25.2977i 0.977412 + 0.829545i
\(931\) 3.84491i 0.126012i
\(932\) 52.3760i 1.71563i
\(933\) −7.11976 6.04265i −0.233090 0.197827i
\(934\) 1.03966i 0.0340188i
\(935\) −7.63220 −0.249600
\(936\) −8.17574 + 1.34710i −0.267232 + 0.0440313i
\(937\) 40.6610i 1.32834i 0.747583 + 0.664169i \(0.231214\pi\)
−0.747583 + 0.664169i \(0.768786\pi\)
\(938\) 9.63773i 0.314683i
\(939\) 1.27450 + 1.08169i 0.0415918 + 0.0352996i
\(940\) 77.7977i 2.53748i
\(941\) −43.8790 −1.43041 −0.715207 0.698913i \(-0.753667\pi\)
−0.715207 + 0.698913i \(0.753667\pi\)
\(942\) −38.5411 + 45.4111i −1.25574 + 1.47957i
\(943\) 11.5943 13.7207i 0.377563 0.446806i
\(944\) 5.58771i 0.181864i
\(945\) −6.20568 + 10.3422i −0.201871 + 0.336430i
\(946\) 42.2845 1.37479
\(947\) 26.8733i 0.873263i 0.899640 + 0.436632i \(0.143829\pi\)
−0.899640 + 0.436632i \(0.856171\pi\)
\(948\) −55.7399 47.3073i −1.81035 1.53647i
\(949\) −0.853293 −0.0276990
\(950\) −3.50722 −0.113789
\(951\) 22.9964 + 19.5174i 0.745709 + 0.632895i
\(952\) 3.61860 0.117279
\(953\) −10.7844 −0.349340 −0.174670 0.984627i \(-0.555886\pi\)
−0.174670 + 0.984627i \(0.555886\pi\)
\(954\) 46.0467 7.58701i 1.49082 0.245639i
\(955\) 23.4643 0.759288
\(956\) 33.2317i 1.07479i
\(957\) −0.550163 0.466932i −0.0177842 0.0150938i
\(958\) 22.0236i 0.711551i
\(959\) 18.5836i 0.600097i
\(960\) −31.1200 + 36.6672i −1.00439 + 1.18343i
\(961\) −13.9088 −0.448672
\(962\) 14.9926 0.483382
\(963\) 4.02450 + 24.4252i 0.129688 + 0.787093i
\(964\) 69.0338i 2.22343i
\(965\) −45.2333 −1.45611
\(966\) 19.2719 3.21791i 0.620063 0.103535i
\(967\) 0.647803 0.0208319 0.0104160 0.999946i \(-0.496684\pi\)
0.0104160 + 0.999946i \(0.496684\pi\)
\(968\) 0.964327i 0.0309946i
\(969\) 5.09607 + 4.32511i 0.163709 + 0.138943i
\(970\) −22.7653 −0.730951
\(971\) 52.4789 1.68413 0.842064 0.539377i \(-0.181340\pi\)
0.842064 + 0.539377i \(0.181340\pi\)
\(972\) 20.2807 51.2000i 0.650505 1.64224i
\(973\) 19.7545i 0.633302i
\(974\) 79.6145i 2.55101i
\(975\) −0.332965 + 0.392316i −0.0106634 + 0.0125642i
\(976\) 17.9317i 0.573980i
\(977\) 36.7055 1.17431 0.587156 0.809474i \(-0.300247\pi\)
0.587156 + 0.809474i \(0.300247\pi\)
\(978\) −74.9433 63.6056i −2.39642 2.03388i
\(979\) −56.0421 −1.79111
\(980\) −8.20013 −0.261944
\(981\) 35.2352 5.80563i 1.12497 0.185360i
\(982\) −56.8569 −1.81438
\(983\) 51.3552 1.63798 0.818989 0.573810i \(-0.194535\pi\)
0.818989 + 0.573810i \(0.194535\pi\)
\(984\) 15.1353 17.8332i 0.482496 0.568502i
\(985\) 34.3995i 1.09606i
\(986\) −0.300226 −0.00956114
\(987\) 10.6332 12.5286i 0.338459 0.398790i
\(988\) 10.4058i 0.331053i
\(989\) 16.9855 20.1006i 0.540109 0.639161i
\(990\) −52.9459 + 8.72379i −1.68273 + 0.277260i
\(991\) 9.34773 0.296941 0.148470 0.988917i \(-0.452565\pi\)
0.148470 + 0.988917i \(0.452565\pi\)
\(992\) 16.0511i 0.509623i
\(993\) 8.20377 9.66610i 0.260339 0.306745i
\(994\) 6.56110i 0.208106i
\(995\) 34.5146i 1.09419i
\(996\) 42.7253 50.3411i 1.35380 1.59512i
\(997\) 20.3833 0.645546 0.322773 0.946476i \(-0.395385\pi\)
0.322773 + 0.946476i \(0.395385\pi\)
\(998\) 50.3737i 1.59455i
\(999\) −22.2441 + 37.0712i −0.703774 + 1.17288i
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 483.2.e.a.344.3 48
3.2 odd 2 inner 483.2.e.a.344.46 yes 48
23.22 odd 2 inner 483.2.e.a.344.4 yes 48
69.68 even 2 inner 483.2.e.a.344.45 yes 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
483.2.e.a.344.3 48 1.1 even 1 trivial
483.2.e.a.344.4 yes 48 23.22 odd 2 inner
483.2.e.a.344.45 yes 48 69.68 even 2 inner
483.2.e.a.344.46 yes 48 3.2 odd 2 inner