Properties

Label 210.3.e.a.71.1
Level $210$
Weight $3$
Character 210.71
Analytic conductor $5.722$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [210,3,Mod(71,210)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(210, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0, 0]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("210.71");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 210.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: \(5.72208555157\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 8 x^{15} + 34 x^{14} - 80 x^{13} + 97 x^{12} - 80 x^{11} + 498 x^{10} - 3288 x^{9} + 11844 x^{8} - 29592 x^{7} + 40338 x^{6} - 58320 x^{5} + 636417 x^{4} + \cdots + 43046721 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{8}\cdot 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 71.1
Root \(2.97371 + 0.396304i\) of defining polynomial
Character \(\chi\) \(=\) 210.71
Dual form 210.3.e.a.71.9

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.41421i q^{2} +(-2.97371 - 0.396304i) q^{3} -2.00000 q^{4} +2.23607i q^{5} +(-0.560459 + 4.20546i) q^{6} -2.64575 q^{7} +2.82843i q^{8} +(8.68589 + 2.35699i) q^{9} +O(q^{10})\) \(q-1.41421i q^{2} +(-2.97371 - 0.396304i) q^{3} -2.00000 q^{4} +2.23607i q^{5} +(-0.560459 + 4.20546i) q^{6} -2.64575 q^{7} +2.82843i q^{8} +(8.68589 + 2.35699i) q^{9} +3.16228 q^{10} +2.01787i q^{11} +(5.94742 + 0.792609i) q^{12} +11.6017 q^{13} +3.74166i q^{14} +(0.886164 - 6.64941i) q^{15} +4.00000 q^{16} +17.3916i q^{17} +(3.33328 - 12.2837i) q^{18} +36.1315 q^{19} -4.47214i q^{20} +(7.86769 + 1.04852i) q^{21} +2.85370 q^{22} -32.2831i q^{23} +(1.12092 - 8.41092i) q^{24} -5.00000 q^{25} -16.4072i q^{26} +(-24.8952 - 10.4512i) q^{27} +5.29150 q^{28} +46.1442i q^{29} +(-9.40369 - 1.25322i) q^{30} +34.0124 q^{31} -5.65685i q^{32} +(0.799692 - 6.00057i) q^{33} +24.5954 q^{34} -5.91608i q^{35} +(-17.3718 - 4.71398i) q^{36} +31.4813 q^{37} -51.0976i q^{38} +(-34.4999 - 4.59779i) q^{39} -6.32456 q^{40} +32.1651i q^{41} +(1.48284 - 11.1266i) q^{42} -51.7542 q^{43} -4.03575i q^{44} +(-5.27038 + 19.4222i) q^{45} -45.6552 q^{46} +92.3399i q^{47} +(-11.8948 - 1.58522i) q^{48} +7.00000 q^{49} +7.07107i q^{50} +(6.89236 - 51.7175i) q^{51} -23.2033 q^{52} -18.3315i q^{53} +(-14.7803 + 35.2071i) q^{54} -4.51210 q^{55} -7.48331i q^{56} +(-107.445 - 14.3191i) q^{57} +65.2577 q^{58} +45.4634i q^{59} +(-1.77233 + 13.2988i) q^{60} +28.1445 q^{61} -48.1007i q^{62} +(-22.9807 - 6.23600i) q^{63} -8.00000 q^{64} +25.9421i q^{65} +(-8.48608 - 1.13094i) q^{66} -33.7430 q^{67} -34.7832i q^{68} +(-12.7939 + 96.0005i) q^{69} -8.36660 q^{70} -25.2759i q^{71} +(-6.66657 + 24.5674i) q^{72} +48.5331 q^{73} -44.5212i q^{74} +(14.8685 + 1.98152i) q^{75} -72.2630 q^{76} -5.33879i q^{77} +(-6.50225 + 48.7903i) q^{78} +32.9331 q^{79} +8.94427i q^{80} +(69.8892 + 40.9450i) q^{81} +45.4883 q^{82} -82.4176i q^{83} +(-15.7354 - 2.09705i) q^{84} -38.8888 q^{85} +73.1915i q^{86} +(18.2871 - 137.219i) q^{87} -5.70741 q^{88} +48.8676i q^{89} +(27.4672 + 7.45345i) q^{90} -30.6951 q^{91} +64.5661i q^{92} +(-101.143 - 13.4792i) q^{93} +130.588 q^{94} +80.7925i q^{95} +(-2.24184 + 16.8218i) q^{96} -14.5167 q^{97} -9.89949i q^{98} +(-4.75610 + 17.5270i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 8 q^{3} - 32 q^{4} + 16 q^{6} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 8 q^{3} - 32 q^{4} + 16 q^{6} - 4 q^{9} + 16 q^{12} - 20 q^{15} + 64 q^{16} - 32 q^{18} + 48 q^{19} + 28 q^{21} - 96 q^{22} - 32 q^{24} - 80 q^{25} + 64 q^{27} - 88 q^{33} + 160 q^{34} + 8 q^{36} + 80 q^{37} + 156 q^{39} - 336 q^{43} - 80 q^{45} + 32 q^{46} - 32 q^{48} + 112 q^{49} + 84 q^{51} - 32 q^{54} - 80 q^{55} - 264 q^{57} + 96 q^{58} + 40 q^{60} + 112 q^{61} + 112 q^{63} - 128 q^{64} + 240 q^{67} + 8 q^{69} + 64 q^{72} + 48 q^{73} + 40 q^{75} - 96 q^{76} + 208 q^{78} + 8 q^{79} - 124 q^{81} - 608 q^{82} - 56 q^{84} + 120 q^{85} - 120 q^{87} + 192 q^{88} + 160 q^{90} - 56 q^{91} + 104 q^{93} + 32 q^{94} + 64 q^{96} - 192 q^{97} - 52 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/210\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(71\) \(127\)
\(\chi(n)\) \(1\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.41421i 0.707107i
\(3\) −2.97371 0.396304i −0.991236 0.132101i
\(4\) −2.00000 −0.500000
\(5\) 2.23607i 0.447214i
\(6\) −0.560459 + 4.20546i −0.0934098 + 0.700910i
\(7\) −2.64575 −0.377964
\(8\) 2.82843i 0.353553i
\(9\) 8.68589 + 2.35699i 0.965098 + 0.261888i
\(10\) 3.16228 0.316228
\(11\) 2.01787i 0.183443i 0.995785 + 0.0917215i \(0.0292369\pi\)
−0.995785 + 0.0917215i \(0.970763\pi\)
\(12\) 5.94742 + 0.792609i 0.495618 + 0.0660507i
\(13\) 11.6017 0.892435 0.446218 0.894925i \(-0.352771\pi\)
0.446218 + 0.894925i \(0.352771\pi\)
\(14\) 3.74166i 0.267261i
\(15\) 0.886164 6.64941i 0.0590776 0.443294i
\(16\) 4.00000 0.250000
\(17\) 17.3916i 1.02303i 0.859273 + 0.511517i \(0.170916\pi\)
−0.859273 + 0.511517i \(0.829084\pi\)
\(18\) 3.33328 12.2837i 0.185182 0.682428i
\(19\) 36.1315 1.90166 0.950829 0.309718i \(-0.100234\pi\)
0.950829 + 0.309718i \(0.100234\pi\)
\(20\) 4.47214i 0.223607i
\(21\) 7.86769 + 1.04852i 0.374652 + 0.0499297i
\(22\) 2.85370 0.129714
\(23\) 32.2831i 1.40361i −0.712368 0.701806i \(-0.752377\pi\)
0.712368 0.701806i \(-0.247623\pi\)
\(24\) 1.12092 8.41092i 0.0467049 0.350455i
\(25\) −5.00000 −0.200000
\(26\) 16.4072i 0.631047i
\(27\) −24.8952 10.4512i −0.922045 0.387083i
\(28\) 5.29150 0.188982
\(29\) 46.1442i 1.59118i 0.605837 + 0.795589i \(0.292839\pi\)
−0.605837 + 0.795589i \(0.707161\pi\)
\(30\) −9.40369 1.25322i −0.313456 0.0417742i
\(31\) 34.0124 1.09717 0.548586 0.836094i \(-0.315166\pi\)
0.548586 + 0.836094i \(0.315166\pi\)
\(32\) 5.65685i 0.176777i
\(33\) 0.799692 6.00057i 0.0242331 0.181835i
\(34\) 24.5954 0.723394
\(35\) 5.91608i 0.169031i
\(36\) −17.3718 4.71398i −0.482549 0.130944i
\(37\) 31.4813 0.850845 0.425423 0.904995i \(-0.360125\pi\)
0.425423 + 0.904995i \(0.360125\pi\)
\(38\) 51.0976i 1.34467i
\(39\) −34.4999 4.59779i −0.884614 0.117892i
\(40\) −6.32456 −0.158114
\(41\) 32.1651i 0.784514i 0.919856 + 0.392257i \(0.128306\pi\)
−0.919856 + 0.392257i \(0.871694\pi\)
\(42\) 1.48284 11.1266i 0.0353056 0.264919i
\(43\) −51.7542 −1.20359 −0.601793 0.798652i \(-0.705547\pi\)
−0.601793 + 0.798652i \(0.705547\pi\)
\(44\) 4.03575i 0.0917215i
\(45\) −5.27038 + 19.4222i −0.117120 + 0.431605i
\(46\) −45.6552 −0.992503
\(47\) 92.3399i 1.96468i 0.187110 + 0.982339i \(0.440088\pi\)
−0.187110 + 0.982339i \(0.559912\pi\)
\(48\) −11.8948 1.58522i −0.247809 0.0330254i
\(49\) 7.00000 0.142857
\(50\) 7.07107i 0.141421i
\(51\) 6.89236 51.7175i 0.135144 1.01407i
\(52\) −23.2033 −0.446218
\(53\) 18.3315i 0.345877i −0.984933 0.172939i \(-0.944674\pi\)
0.984933 0.172939i \(-0.0553262\pi\)
\(54\) −14.7803 + 35.2071i −0.273709 + 0.651984i
\(55\) −4.51210 −0.0820382
\(56\) 7.48331i 0.133631i
\(57\) −107.445 14.3191i −1.88499 0.251212i
\(58\) 65.2577 1.12513
\(59\) 45.4634i 0.770566i 0.922798 + 0.385283i \(0.125896\pi\)
−0.922798 + 0.385283i \(0.874104\pi\)
\(60\) −1.77233 + 13.2988i −0.0295388 + 0.221647i
\(61\) 28.1445 0.461385 0.230693 0.973027i \(-0.425901\pi\)
0.230693 + 0.973027i \(0.425901\pi\)
\(62\) 48.1007i 0.775818i
\(63\) −22.9807 6.23600i −0.364773 0.0989842i
\(64\) −8.00000 −0.125000
\(65\) 25.9421i 0.399109i
\(66\) −8.48608 1.13094i −0.128577 0.0171354i
\(67\) −33.7430 −0.503626 −0.251813 0.967776i \(-0.581027\pi\)
−0.251813 + 0.967776i \(0.581027\pi\)
\(68\) 34.7832i 0.511517i
\(69\) −12.7939 + 96.0005i −0.185419 + 1.39131i
\(70\) −8.36660 −0.119523
\(71\) 25.2759i 0.355999i −0.984031 0.177999i \(-0.943038\pi\)
0.984031 0.177999i \(-0.0569625\pi\)
\(72\) −6.66657 + 24.5674i −0.0925912 + 0.341214i
\(73\) 48.5331 0.664837 0.332418 0.943132i \(-0.392135\pi\)
0.332418 + 0.943132i \(0.392135\pi\)
\(74\) 44.5212i 0.601638i
\(75\) 14.8685 + 1.98152i 0.198247 + 0.0264203i
\(76\) −72.2630 −0.950829
\(77\) 5.33879i 0.0693349i
\(78\) −6.50225 + 48.7903i −0.0833622 + 0.625517i
\(79\) 32.9331 0.416875 0.208437 0.978036i \(-0.433162\pi\)
0.208437 + 0.978036i \(0.433162\pi\)
\(80\) 8.94427i 0.111803i
\(81\) 69.8892 + 40.9450i 0.862830 + 0.505494i
\(82\) 45.4883 0.554735
\(83\) 82.4176i 0.992983i −0.868041 0.496492i \(-0.834621\pi\)
0.868041 0.496492i \(-0.165379\pi\)
\(84\) −15.7354 2.09705i −0.187326 0.0249648i
\(85\) −38.8888 −0.457515
\(86\) 73.1915i 0.851064i
\(87\) 18.2871 137.219i 0.210197 1.57723i
\(88\) −5.70741 −0.0648569
\(89\) 48.8676i 0.549075i 0.961576 + 0.274537i \(0.0885247\pi\)
−0.961576 + 0.274537i \(0.911475\pi\)
\(90\) 27.4672 + 7.45345i 0.305191 + 0.0828161i
\(91\) −30.6951 −0.337309
\(92\) 64.5661i 0.701806i
\(93\) −101.143 13.4792i −1.08756 0.144938i
\(94\) 130.588 1.38924
\(95\) 80.7925i 0.850447i
\(96\) −2.24184 + 16.8218i −0.0233525 + 0.175227i
\(97\) −14.5167 −0.149657 −0.0748283 0.997196i \(-0.523841\pi\)
−0.0748283 + 0.997196i \(0.523841\pi\)
\(98\) 9.89949i 0.101015i
\(99\) −4.75610 + 17.5270i −0.0480414 + 0.177041i
\(100\) 10.0000 0.100000
\(101\) 68.8829i 0.682009i −0.940062 0.341004i \(-0.889233\pi\)
0.940062 0.341004i \(-0.110767\pi\)
\(102\) −73.1396 9.74727i −0.717055 0.0955615i
\(103\) −43.5237 −0.422560 −0.211280 0.977426i \(-0.567763\pi\)
−0.211280 + 0.977426i \(0.567763\pi\)
\(104\) 32.8144i 0.315523i
\(105\) −2.34457 + 17.5927i −0.0223292 + 0.167549i
\(106\) −25.9247 −0.244572
\(107\) 207.704i 1.94116i −0.240781 0.970579i \(-0.577404\pi\)
0.240781 0.970579i \(-0.422596\pi\)
\(108\) 49.7904 + 20.9025i 0.461022 + 0.193542i
\(109\) −151.884 −1.39343 −0.696715 0.717348i \(-0.745356\pi\)
−0.696715 + 0.717348i \(0.745356\pi\)
\(110\) 6.38107i 0.0580098i
\(111\) −93.6161 12.4762i −0.843389 0.112398i
\(112\) −10.5830 −0.0944911
\(113\) 38.2266i 0.338289i 0.985591 + 0.169144i \(0.0541004\pi\)
−0.985591 + 0.169144i \(0.945900\pi\)
\(114\) −20.2502 + 151.949i −0.177633 + 1.33289i
\(115\) 72.1871 0.627714
\(116\) 92.2883i 0.795589i
\(117\) 100.771 + 27.3450i 0.861288 + 0.233718i
\(118\) 64.2949 0.544872
\(119\) 46.0138i 0.386671i
\(120\) 18.8074 + 2.50645i 0.156728 + 0.0208871i
\(121\) 116.928 0.966349
\(122\) 39.8023i 0.326248i
\(123\) 12.7472 95.6495i 0.103635 0.777638i
\(124\) −68.0247 −0.548586
\(125\) 11.1803i 0.0894427i
\(126\) −8.81904 + 32.4996i −0.0699924 + 0.257933i
\(127\) 101.520 0.799371 0.399685 0.916652i \(-0.369119\pi\)
0.399685 + 0.916652i \(0.369119\pi\)
\(128\) 11.3137i 0.0883883i
\(129\) 153.902 + 20.5104i 1.19304 + 0.158996i
\(130\) 36.6877 0.282213
\(131\) 224.148i 1.71105i −0.517758 0.855527i \(-0.673233\pi\)
0.517758 0.855527i \(-0.326767\pi\)
\(132\) −1.59938 + 12.0011i −0.0121165 + 0.0909177i
\(133\) −95.5949 −0.718759
\(134\) 47.7198i 0.356118i
\(135\) 23.3697 55.6674i 0.173109 0.412351i
\(136\) −49.1908 −0.361697
\(137\) 122.440i 0.893726i 0.894602 + 0.446863i \(0.147459\pi\)
−0.894602 + 0.446863i \(0.852541\pi\)
\(138\) 135.765 + 18.0933i 0.983805 + 0.131111i
\(139\) 132.544 0.953551 0.476776 0.879025i \(-0.341805\pi\)
0.476776 + 0.879025i \(0.341805\pi\)
\(140\) 11.8322i 0.0845154i
\(141\) 36.5947 274.592i 0.259537 1.94746i
\(142\) −35.7455 −0.251729
\(143\) 23.4107i 0.163711i
\(144\) 34.7435 + 9.42795i 0.241275 + 0.0654719i
\(145\) −103.181 −0.711597
\(146\) 68.6361i 0.470111i
\(147\) −20.8160 2.77413i −0.141605 0.0188716i
\(148\) −62.9626 −0.425423
\(149\) 11.7097i 0.0785885i −0.999228 0.0392943i \(-0.987489\pi\)
0.999228 0.0392943i \(-0.0125110\pi\)
\(150\) 2.80230 21.0273i 0.0186820 0.140182i
\(151\) −73.1995 −0.484765 −0.242382 0.970181i \(-0.577929\pi\)
−0.242382 + 0.970181i \(0.577929\pi\)
\(152\) 102.195i 0.672337i
\(153\) −40.9917 + 151.061i −0.267920 + 0.987329i
\(154\) −7.55019 −0.0490272
\(155\) 76.0539i 0.490671i
\(156\) 68.9999 + 9.19557i 0.442307 + 0.0589460i
\(157\) 290.488 1.85024 0.925120 0.379675i \(-0.123964\pi\)
0.925120 + 0.379675i \(0.123964\pi\)
\(158\) 46.5745i 0.294775i
\(159\) −7.26485 + 54.5125i −0.0456909 + 0.342846i
\(160\) 12.6491 0.0790569
\(161\) 85.4130i 0.530515i
\(162\) 57.9050 98.8383i 0.357439 0.610113i
\(163\) 22.7666 0.139672 0.0698361 0.997558i \(-0.477752\pi\)
0.0698361 + 0.997558i \(0.477752\pi\)
\(164\) 64.3301i 0.392257i
\(165\) 13.4177 + 1.78817i 0.0813192 + 0.0108374i
\(166\) −116.556 −0.702145
\(167\) 235.762i 1.41175i 0.708338 + 0.705874i \(0.249445\pi\)
−0.708338 + 0.705874i \(0.750555\pi\)
\(168\) −2.96567 + 22.2532i −0.0176528 + 0.132460i
\(169\) −34.4016 −0.203560
\(170\) 54.9970i 0.323512i
\(171\) 313.834 + 85.1615i 1.83529 + 0.498020i
\(172\) 103.508 0.601793
\(173\) 136.011i 0.786189i −0.919498 0.393095i \(-0.871404\pi\)
0.919498 0.393095i \(-0.128596\pi\)
\(174\) −194.057 25.8619i −1.11527 0.148632i
\(175\) 13.2288 0.0755929
\(176\) 8.07149i 0.0458607i
\(177\) 18.0173 135.195i 0.101793 0.763813i
\(178\) 69.1093 0.388254
\(179\) 12.3778i 0.0691495i −0.999402 0.0345748i \(-0.988992\pi\)
0.999402 0.0345748i \(-0.0110077\pi\)
\(180\) 10.5408 38.8445i 0.0585598 0.215803i
\(181\) −55.8191 −0.308393 −0.154196 0.988040i \(-0.549279\pi\)
−0.154196 + 0.988040i \(0.549279\pi\)
\(182\) 43.4094i 0.238513i
\(183\) −83.6935 11.1538i −0.457342 0.0609496i
\(184\) 91.3103 0.496252
\(185\) 70.3943i 0.380510i
\(186\) −19.0625 + 143.038i −0.102487 + 0.769019i
\(187\) −35.0940 −0.187668
\(188\) 184.680i 0.982339i
\(189\) 65.8665 + 27.6514i 0.348500 + 0.146304i
\(190\) 114.258 0.601357
\(191\) 198.559i 1.03958i 0.854295 + 0.519788i \(0.173989\pi\)
−0.854295 + 0.519788i \(0.826011\pi\)
\(192\) 23.7897 + 3.17044i 0.123905 + 0.0165127i
\(193\) 44.6577 0.231387 0.115694 0.993285i \(-0.463091\pi\)
0.115694 + 0.993285i \(0.463091\pi\)
\(194\) 20.5297i 0.105823i
\(195\) 10.2810 77.1442i 0.0527229 0.395611i
\(196\) −14.0000 −0.0714286
\(197\) 0.952715i 0.00483612i −0.999997 0.00241806i \(-0.999230\pi\)
0.999997 0.00241806i \(-0.000769693\pi\)
\(198\) 24.7869 + 6.72614i 0.125187 + 0.0339704i
\(199\) −131.143 −0.659011 −0.329505 0.944154i \(-0.606882\pi\)
−0.329505 + 0.944154i \(0.606882\pi\)
\(200\) 14.1421i 0.0707107i
\(201\) 100.342 + 13.3725i 0.499213 + 0.0665298i
\(202\) −97.4151 −0.482253
\(203\) 122.086i 0.601409i
\(204\) −13.7847 + 103.435i −0.0675722 + 0.507034i
\(205\) −71.9233 −0.350845
\(206\) 61.5518i 0.298795i
\(207\) 76.0908 280.407i 0.367588 1.35462i
\(208\) 46.4066 0.223109
\(209\) 72.9087i 0.348846i
\(210\) 24.8798 + 3.31572i 0.118475 + 0.0157891i
\(211\) −101.671 −0.481855 −0.240928 0.970543i \(-0.577452\pi\)
−0.240928 + 0.970543i \(0.577452\pi\)
\(212\) 36.6630i 0.172939i
\(213\) −10.0170 + 75.1632i −0.0470279 + 0.352879i
\(214\) −293.738 −1.37261
\(215\) 115.726i 0.538260i
\(216\) 29.5606 70.4143i 0.136855 0.325992i
\(217\) −89.9882 −0.414692
\(218\) 214.796i 0.985304i
\(219\) −144.323 19.2339i −0.659010 0.0878259i
\(220\) 9.02420 0.0410191
\(221\) 201.771i 0.912992i
\(222\) −17.6440 + 132.393i −0.0794773 + 0.596366i
\(223\) −368.065 −1.65051 −0.825257 0.564757i \(-0.808970\pi\)
−0.825257 + 0.564757i \(0.808970\pi\)
\(224\) 14.9666i 0.0668153i
\(225\) −43.4294 11.7849i −0.193020 0.0523775i
\(226\) 54.0606 0.239206
\(227\) 311.633i 1.37283i 0.727210 + 0.686415i \(0.240817\pi\)
−0.727210 + 0.686415i \(0.759183\pi\)
\(228\) 214.889 + 28.6381i 0.942496 + 0.125606i
\(229\) −121.083 −0.528748 −0.264374 0.964420i \(-0.585165\pi\)
−0.264374 + 0.964420i \(0.585165\pi\)
\(230\) 102.088i 0.443861i
\(231\) −2.11579 + 15.8760i −0.00915925 + 0.0687273i
\(232\) −130.515 −0.562566
\(233\) 188.437i 0.808744i −0.914595 0.404372i \(-0.867490\pi\)
0.914595 0.404372i \(-0.132510\pi\)
\(234\) 38.6716 142.511i 0.165263 0.609022i
\(235\) −206.478 −0.878631
\(236\) 90.9268i 0.385283i
\(237\) −97.9335 13.0515i −0.413221 0.0550698i
\(238\) −65.0733 −0.273417
\(239\) 242.788i 1.01585i −0.861402 0.507924i \(-0.830413\pi\)
0.861402 0.507924i \(-0.169587\pi\)
\(240\) 3.54465 26.5977i 0.0147694 0.110824i
\(241\) −217.929 −0.904272 −0.452136 0.891949i \(-0.649338\pi\)
−0.452136 + 0.891949i \(0.649338\pi\)
\(242\) 165.361i 0.683312i
\(243\) −191.603 149.456i −0.788492 0.615045i
\(244\) −56.2890 −0.230693
\(245\) 15.6525i 0.0638877i
\(246\) −135.269 18.0272i −0.549873 0.0732813i
\(247\) 419.185 1.69711
\(248\) 96.2015i 0.387909i
\(249\) −32.6625 + 245.086i −0.131175 + 0.984281i
\(250\) −15.8114 −0.0632456
\(251\) 44.7224i 0.178177i 0.996024 + 0.0890885i \(0.0283954\pi\)
−0.996024 + 0.0890885i \(0.971605\pi\)
\(252\) 45.9614 + 12.4720i 0.182386 + 0.0494921i
\(253\) 65.1431 0.257483
\(254\) 143.571i 0.565241i
\(255\) 115.644 + 15.4118i 0.453505 + 0.0604384i
\(256\) 16.0000 0.0625000
\(257\) 163.933i 0.637872i 0.947776 + 0.318936i \(0.103325\pi\)
−0.947776 + 0.318936i \(0.896675\pi\)
\(258\) 29.0061 217.650i 0.112427 0.843606i
\(259\) −83.2916 −0.321589
\(260\) 51.8842i 0.199555i
\(261\) −108.761 + 400.803i −0.416710 + 1.53564i
\(262\) −316.993 −1.20990
\(263\) 516.880i 1.96532i 0.185404 + 0.982662i \(0.440641\pi\)
−0.185404 + 0.982662i \(0.559359\pi\)
\(264\) 16.9722 + 2.26187i 0.0642885 + 0.00856769i
\(265\) 40.9905 0.154681
\(266\) 135.192i 0.508239i
\(267\) 19.3665 145.318i 0.0725336 0.544263i
\(268\) 67.4859 0.251813
\(269\) 425.762i 1.58276i −0.611325 0.791380i \(-0.709363\pi\)
0.611325 0.791380i \(-0.290637\pi\)
\(270\) −78.7256 33.0498i −0.291576 0.122406i
\(271\) −38.4253 −0.141791 −0.0708953 0.997484i \(-0.522586\pi\)
−0.0708953 + 0.997484i \(0.522586\pi\)
\(272\) 69.5663i 0.255759i
\(273\) 91.2783 + 12.1646i 0.334353 + 0.0445590i
\(274\) 173.157 0.631960
\(275\) 10.0894i 0.0366886i
\(276\) 25.5878 192.001i 0.0927096 0.695655i
\(277\) −365.774 −1.32048 −0.660242 0.751053i \(-0.729546\pi\)
−0.660242 + 0.751053i \(0.729546\pi\)
\(278\) 187.445i 0.674263i
\(279\) 295.427 + 80.1667i 1.05888 + 0.287336i
\(280\) 16.7332 0.0597614
\(281\) 402.773i 1.43336i −0.697404 0.716678i \(-0.745662\pi\)
0.697404 0.716678i \(-0.254338\pi\)
\(282\) −388.331 51.7527i −1.37706 0.183520i
\(283\) −390.233 −1.37892 −0.689458 0.724326i \(-0.742151\pi\)
−0.689458 + 0.724326i \(0.742151\pi\)
\(284\) 50.5518i 0.177999i
\(285\) 32.0184 240.253i 0.112345 0.842994i
\(286\) 33.1077 0.115761
\(287\) 85.1008i 0.296518i
\(288\) 13.3331 49.1348i 0.0462956 0.170607i
\(289\) −13.4671 −0.0465989
\(290\) 145.921i 0.503175i
\(291\) 43.1684 + 5.75302i 0.148345 + 0.0197698i
\(292\) −97.0662 −0.332418
\(293\) 22.6093i 0.0771650i 0.999255 + 0.0385825i \(0.0122842\pi\)
−0.999255 + 0.0385825i \(0.987716\pi\)
\(294\) −3.92321 + 29.4382i −0.0133443 + 0.100130i
\(295\) −101.659 −0.344608
\(296\) 89.0425i 0.300819i
\(297\) 21.0893 50.2354i 0.0710077 0.169143i
\(298\) −16.5600 −0.0555705
\(299\) 374.537i 1.25263i
\(300\) −29.7371 3.96304i −0.0991236 0.0132101i
\(301\) 136.929 0.454913
\(302\) 103.520i 0.342780i
\(303\) −27.2986 + 204.838i −0.0900944 + 0.676032i
\(304\) 144.526 0.475414
\(305\) 62.9330i 0.206338i
\(306\) 213.633 + 57.9711i 0.698147 + 0.189448i
\(307\) 332.914 1.08441 0.542206 0.840246i \(-0.317589\pi\)
0.542206 + 0.840246i \(0.317589\pi\)
\(308\) 10.6776i 0.0346675i
\(309\) 129.427 + 17.2486i 0.418857 + 0.0558208i
\(310\) 107.556 0.346956
\(311\) 145.028i 0.466328i 0.972437 + 0.233164i \(0.0749080\pi\)
−0.972437 + 0.233164i \(0.925092\pi\)
\(312\) 13.0045 97.5806i 0.0416811 0.312758i
\(313\) 345.934 1.10522 0.552611 0.833440i \(-0.313632\pi\)
0.552611 + 0.833440i \(0.313632\pi\)
\(314\) 410.812i 1.30832i
\(315\) 13.9441 51.3864i 0.0442671 0.163131i
\(316\) −65.8662 −0.208437
\(317\) 155.393i 0.490199i 0.969498 + 0.245099i \(0.0788206\pi\)
−0.969498 + 0.245099i \(0.921179\pi\)
\(318\) 77.0924 + 10.2741i 0.242429 + 0.0323083i
\(319\) −93.1131 −0.291890
\(320\) 17.8885i 0.0559017i
\(321\) −82.3140 + 617.651i −0.256430 + 1.92415i
\(322\) 120.792 0.375131
\(323\) 628.384i 1.94546i
\(324\) −139.778 81.8901i −0.431415 0.252747i
\(325\) −58.0083 −0.178487
\(326\) 32.1968i 0.0987632i
\(327\) 451.659 + 60.1923i 1.38122 + 0.184074i
\(328\) −90.9765 −0.277367
\(329\) 244.308i 0.742578i
\(330\) 2.52885 18.9755i 0.00766317 0.0575014i
\(331\) 142.477 0.430443 0.215221 0.976565i \(-0.430953\pi\)
0.215221 + 0.976565i \(0.430953\pi\)
\(332\) 164.835i 0.496492i
\(333\) 273.443 + 74.2010i 0.821149 + 0.222826i
\(334\) 333.418 0.998256
\(335\) 75.4516i 0.225229i
\(336\) 31.4708 + 4.19409i 0.0936630 + 0.0124824i
\(337\) −226.965 −0.673487 −0.336743 0.941596i \(-0.609325\pi\)
−0.336743 + 0.941596i \(0.609325\pi\)
\(338\) 48.6512i 0.143938i
\(339\) 15.1494 113.675i 0.0446884 0.335324i
\(340\) 77.7775 0.228757
\(341\) 68.6326i 0.201269i
\(342\) 120.437 443.828i 0.352154 1.29774i
\(343\) −18.5203 −0.0539949
\(344\) 146.383i 0.425532i
\(345\) −214.664 28.6081i −0.622213 0.0829220i
\(346\) −192.348 −0.555920
\(347\) 91.8895i 0.264811i −0.991196 0.132406i \(-0.957730\pi\)
0.991196 0.132406i \(-0.0422701\pi\)
\(348\) −36.5743 + 274.439i −0.105098 + 0.788617i
\(349\) 442.343 1.26746 0.633729 0.773555i \(-0.281524\pi\)
0.633729 + 0.773555i \(0.281524\pi\)
\(350\) 18.7083i 0.0534522i
\(351\) −288.826 121.252i −0.822865 0.345447i
\(352\) 11.4148 0.0324284
\(353\) 88.1350i 0.249674i 0.992177 + 0.124837i \(0.0398408\pi\)
−0.992177 + 0.124837i \(0.960159\pi\)
\(354\) −191.194 25.4804i −0.540097 0.0719784i
\(355\) 56.5186 0.159207
\(356\) 97.7353i 0.274537i
\(357\) −18.2355 + 136.832i −0.0510797 + 0.383282i
\(358\) −17.5048 −0.0488961
\(359\) 21.1772i 0.0589894i 0.999565 + 0.0294947i \(0.00938981\pi\)
−0.999565 + 0.0294947i \(0.990610\pi\)
\(360\) −54.9344 14.9069i −0.152595 0.0414081i
\(361\) 944.484 2.61630
\(362\) 78.9401i 0.218067i
\(363\) −347.710 46.3392i −0.957880 0.127656i
\(364\) 61.3902 0.168654
\(365\) 108.523i 0.297324i
\(366\) −15.7738 + 118.360i −0.0430979 + 0.323389i
\(367\) −306.468 −0.835064 −0.417532 0.908662i \(-0.637105\pi\)
−0.417532 + 0.908662i \(0.637105\pi\)
\(368\) 129.132i 0.350903i
\(369\) −75.8126 + 279.382i −0.205454 + 0.757133i
\(370\) 99.5525 0.269061
\(371\) 48.5006i 0.130729i
\(372\) 202.286 + 26.9585i 0.543779 + 0.0724691i
\(373\) 536.875 1.43934 0.719671 0.694315i \(-0.244292\pi\)
0.719671 + 0.694315i \(0.244292\pi\)
\(374\) 49.6304i 0.132702i
\(375\) −4.43082 + 33.2471i −0.0118155 + 0.0886589i
\(376\) −261.177 −0.694619
\(377\) 535.349i 1.42002i
\(378\) 39.1050 93.1493i 0.103452 0.246427i
\(379\) 457.399 1.20686 0.603429 0.797417i \(-0.293801\pi\)
0.603429 + 0.797417i \(0.293801\pi\)
\(380\) 161.585i 0.425223i
\(381\) −301.891 40.2329i −0.792365 0.105598i
\(382\) 280.805 0.735092
\(383\) 274.471i 0.716633i −0.933600 0.358317i \(-0.883351\pi\)
0.933600 0.358317i \(-0.116649\pi\)
\(384\) 4.48367 33.6437i 0.0116762 0.0876137i
\(385\) 11.9379 0.0310075
\(386\) 63.1556i 0.163615i
\(387\) −449.531 121.984i −1.16158 0.315204i
\(388\) 29.0334 0.0748283
\(389\) 507.661i 1.30504i −0.757771 0.652521i \(-0.773712\pi\)
0.757771 0.652521i \(-0.226288\pi\)
\(390\) −109.098 14.5395i −0.279740 0.0372807i
\(391\) 561.454 1.43594
\(392\) 19.7990i 0.0505076i
\(393\) −88.8309 + 666.551i −0.226033 + 1.69606i
\(394\) −1.34734 −0.00341965
\(395\) 73.6407i 0.186432i
\(396\) 9.51220 35.0540i 0.0240207 0.0885203i
\(397\) −552.511 −1.39171 −0.695857 0.718180i \(-0.744975\pi\)
−0.695857 + 0.718180i \(0.744975\pi\)
\(398\) 185.464i 0.465991i
\(399\) 284.271 + 37.8847i 0.712460 + 0.0949491i
\(400\) −20.0000 −0.0500000
\(401\) 240.320i 0.599302i −0.954049 0.299651i \(-0.903130\pi\)
0.954049 0.299651i \(-0.0968702\pi\)
\(402\) 18.9116 141.905i 0.0470437 0.352997i
\(403\) 394.600 0.979155
\(404\) 137.766i 0.341004i
\(405\) −91.5559 + 156.277i −0.226064 + 0.385869i
\(406\) −172.656 −0.425260
\(407\) 63.5252i 0.156082i
\(408\) 146.279 + 19.4945i 0.358527 + 0.0477807i
\(409\) −441.083 −1.07844 −0.539222 0.842164i \(-0.681281\pi\)
−0.539222 + 0.842164i \(0.681281\pi\)
\(410\) 101.715i 0.248085i
\(411\) 48.5237 364.102i 0.118063 0.885894i
\(412\) 87.0474 0.211280
\(413\) 120.285i 0.291247i
\(414\) −396.556 107.609i −0.957864 0.259924i
\(415\) 184.291 0.444076
\(416\) 65.6289i 0.157762i
\(417\) −394.146 52.5276i −0.945195 0.125966i
\(418\) 103.109 0.246671
\(419\) 412.950i 0.985561i −0.870154 0.492780i \(-0.835981\pi\)
0.870154 0.492780i \(-0.164019\pi\)
\(420\) 4.68914 35.1854i 0.0111646 0.0837747i
\(421\) −147.333 −0.349959 −0.174980 0.984572i \(-0.555986\pi\)
−0.174980 + 0.984572i \(0.555986\pi\)
\(422\) 143.785i 0.340723i
\(423\) −217.644 + 802.053i −0.514525 + 1.89611i
\(424\) 51.8493 0.122286
\(425\) 86.9579i 0.204607i
\(426\) 106.297 + 14.1661i 0.249523 + 0.0332538i
\(427\) −74.4633 −0.174387
\(428\) 415.408i 0.970579i
\(429\) 9.27775 69.6165i 0.0216265 0.162276i
\(430\) −163.661 −0.380608
\(431\) 50.5951i 0.117390i 0.998276 + 0.0586950i \(0.0186939\pi\)
−0.998276 + 0.0586950i \(0.981306\pi\)
\(432\) −99.5808 41.8050i −0.230511 0.0967708i
\(433\) 653.464 1.50915 0.754577 0.656211i \(-0.227842\pi\)
0.754577 + 0.656211i \(0.227842\pi\)
\(434\) 127.263i 0.293232i
\(435\) 306.832 + 40.8913i 0.705360 + 0.0940029i
\(436\) 303.768 0.696715
\(437\) 1166.44i 2.66919i
\(438\) −27.2008 + 204.104i −0.0621023 + 0.465991i
\(439\) −760.655 −1.73270 −0.866350 0.499438i \(-0.833540\pi\)
−0.866350 + 0.499438i \(0.833540\pi\)
\(440\) 12.7621i 0.0290049i
\(441\) 60.8012 + 16.4989i 0.137871 + 0.0374125i
\(442\) 285.347 0.645583
\(443\) 543.566i 1.22701i −0.789690 0.613506i \(-0.789759\pi\)
0.789690 0.613506i \(-0.210241\pi\)
\(444\) 187.232 + 24.9523i 0.421694 + 0.0561990i
\(445\) −109.271 −0.245554
\(446\) 520.522i 1.16709i
\(447\) −4.64060 + 34.8212i −0.0103817 + 0.0778998i
\(448\) 21.1660 0.0472456
\(449\) 691.105i 1.53921i −0.638521 0.769604i \(-0.720454\pi\)
0.638521 0.769604i \(-0.279546\pi\)
\(450\) −16.6664 + 61.4185i −0.0370365 + 0.136486i
\(451\) −64.9050 −0.143914
\(452\) 76.4532i 0.169144i
\(453\) 217.674 + 29.0093i 0.480516 + 0.0640381i
\(454\) 440.715 0.970738
\(455\) 68.6363i 0.150849i
\(456\) 40.5004 303.899i 0.0888167 0.666445i
\(457\) 32.4937 0.0711022 0.0355511 0.999368i \(-0.488681\pi\)
0.0355511 + 0.999368i \(0.488681\pi\)
\(458\) 171.238i 0.373882i
\(459\) 181.764 432.967i 0.395999 0.943283i
\(460\) −144.374 −0.313857
\(461\) 18.9876i 0.0411879i −0.999788 0.0205940i \(-0.993444\pi\)
0.999788 0.0205940i \(-0.00655573\pi\)
\(462\) 22.4521 + 2.99217i 0.0485975 + 0.00647656i
\(463\) 772.969 1.66948 0.834740 0.550645i \(-0.185618\pi\)
0.834740 + 0.550645i \(0.185618\pi\)
\(464\) 184.577i 0.397795i
\(465\) 30.1405 226.162i 0.0648183 0.486370i
\(466\) −266.491 −0.571868
\(467\) 335.729i 0.718905i 0.933163 + 0.359453i \(0.117037\pi\)
−0.933163 + 0.359453i \(0.882963\pi\)
\(468\) −201.541 54.6899i −0.430644 0.116859i
\(469\) 89.2755 0.190353
\(470\) 292.004i 0.621286i
\(471\) −863.826 115.122i −1.83402 0.244419i
\(472\) −128.590 −0.272436
\(473\) 104.433i 0.220790i
\(474\) −18.4577 + 138.499i −0.0389402 + 0.292192i
\(475\) −180.657 −0.380331
\(476\) 92.0276i 0.193335i
\(477\) 43.2071 159.225i 0.0905809 0.333806i
\(478\) −343.353 −0.718313
\(479\) 937.543i 1.95729i 0.205551 + 0.978646i \(0.434101\pi\)
−0.205551 + 0.978646i \(0.565899\pi\)
\(480\) −37.6148 5.01290i −0.0783641 0.0104435i
\(481\) 365.235 0.759324
\(482\) 308.199i 0.639417i
\(483\) 33.8495 253.993i 0.0700819 0.525866i
\(484\) −233.856 −0.483174
\(485\) 32.4603i 0.0669284i
\(486\) −211.363 + 270.968i −0.434903 + 0.557548i
\(487\) 752.244 1.54465 0.772325 0.635228i \(-0.219094\pi\)
0.772325 + 0.635228i \(0.219094\pi\)
\(488\) 79.6046i 0.163124i
\(489\) −67.7012 9.02249i −0.138448 0.0184509i
\(490\) 22.1359 0.0451754
\(491\) 854.568i 1.74047i −0.492641 0.870233i \(-0.663968\pi\)
0.492641 0.870233i \(-0.336032\pi\)
\(492\) −25.4943 + 191.299i −0.0518177 + 0.388819i
\(493\) −802.520 −1.62783
\(494\) 592.817i 1.20003i
\(495\) −39.1916 10.6350i −0.0791749 0.0214848i
\(496\) 136.049 0.274293
\(497\) 66.8738i 0.134555i
\(498\) 346.604 + 46.1917i 0.695992 + 0.0927544i
\(499\) −364.673 −0.730807 −0.365404 0.930849i \(-0.619069\pi\)
−0.365404 + 0.930849i \(0.619069\pi\)
\(500\) 22.3607i 0.0447214i
\(501\) 93.4334 701.087i 0.186494 1.39937i
\(502\) 63.2471 0.125990
\(503\) 251.341i 0.499683i −0.968287 0.249842i \(-0.919621\pi\)
0.968287 0.249842i \(-0.0803785\pi\)
\(504\) 17.6381 64.9992i 0.0349962 0.128967i
\(505\) 154.027 0.305004
\(506\) 92.1263i 0.182068i
\(507\) 102.300 + 13.6335i 0.201776 + 0.0268905i
\(508\) −203.040 −0.399685
\(509\) 377.854i 0.742345i 0.928564 + 0.371173i \(0.121044\pi\)
−0.928564 + 0.371173i \(0.878956\pi\)
\(510\) 21.7956 163.545i 0.0427364 0.320677i
\(511\) −128.406 −0.251285
\(512\) 22.6274i 0.0441942i
\(513\) −899.501 377.619i −1.75341 0.736100i
\(514\) 231.836 0.451043
\(515\) 97.3220i 0.188975i
\(516\) −307.804 41.0209i −0.596519 0.0794978i
\(517\) −186.330 −0.360406
\(518\) 117.792i 0.227398i
\(519\) −53.9017 + 404.456i −0.103857 + 0.779299i
\(520\) −73.3753 −0.141106
\(521\) 959.258i 1.84119i −0.390524 0.920593i \(-0.627706\pi\)
0.390524 0.920593i \(-0.372294\pi\)
\(522\) 566.821 + 153.812i 1.08586 + 0.294658i
\(523\) −372.766 −0.712745 −0.356372 0.934344i \(-0.615987\pi\)
−0.356372 + 0.934344i \(0.615987\pi\)
\(524\) 448.296i 0.855527i
\(525\) −39.3385 5.24261i −0.0749304 0.00998593i
\(526\) 730.979 1.38969
\(527\) 591.529i 1.12245i
\(528\) 3.19877 24.0023i 0.00605827 0.0454588i
\(529\) −513.197 −0.970126
\(530\) 57.9693i 0.109376i
\(531\) −107.157 + 394.890i −0.201802 + 0.743672i
\(532\) 191.190 0.359379
\(533\) 373.168i 0.700128i
\(534\) −205.511 27.3883i −0.384852 0.0512890i
\(535\) 464.440 0.868113
\(536\) 95.4395i 0.178059i
\(537\) −4.90536 + 36.8079i −0.00913475 + 0.0685435i
\(538\) −602.119 −1.11918
\(539\) 14.1251i 0.0262061i
\(540\) −46.7394 + 111.335i −0.0865545 + 0.206175i
\(541\) −425.367 −0.786262 −0.393131 0.919483i \(-0.628608\pi\)
−0.393131 + 0.919483i \(0.628608\pi\)
\(542\) 54.3415i 0.100261i
\(543\) 165.990 + 22.1213i 0.305690 + 0.0407391i
\(544\) 98.3816 0.180849
\(545\) 339.623i 0.623161i
\(546\) 17.2033 129.087i 0.0315080 0.236423i
\(547\) −163.904 −0.299641 −0.149821 0.988713i \(-0.547870\pi\)
−0.149821 + 0.988713i \(0.547870\pi\)
\(548\) 244.881i 0.446863i
\(549\) 244.460 + 66.3362i 0.445282 + 0.120831i
\(550\) −14.2685 −0.0259428
\(551\) 1667.26i 3.02588i
\(552\) −271.530 36.1867i −0.491903 0.0655556i
\(553\) −87.1328 −0.157564
\(554\) 517.283i 0.933723i
\(555\) 27.8976 209.332i 0.0502659 0.377175i
\(556\) −265.087 −0.476776
\(557\) 706.900i 1.26912i 0.772873 + 0.634560i \(0.218819\pi\)
−0.772873 + 0.634560i \(0.781181\pi\)
\(558\) 113.373 417.797i 0.203177 0.748741i
\(559\) −600.435 −1.07412
\(560\) 23.6643i 0.0422577i
\(561\) 104.359 + 13.9079i 0.186024 + 0.0247913i
\(562\) −569.607 −1.01354
\(563\) 456.163i 0.810237i 0.914264 + 0.405118i \(0.132770\pi\)
−0.914264 + 0.405118i \(0.867230\pi\)
\(564\) −73.1894 + 549.184i −0.129768 + 0.973730i
\(565\) −85.4773 −0.151287
\(566\) 551.873i 0.975040i
\(567\) −184.909 108.330i −0.326119 0.191059i
\(568\) 71.4911 0.125865
\(569\) 429.044i 0.754032i −0.926207 0.377016i \(-0.876950\pi\)
0.926207 0.377016i \(-0.123050\pi\)
\(570\) −339.769 45.2809i −0.596087 0.0794401i
\(571\) −739.819 −1.29566 −0.647828 0.761787i \(-0.724322\pi\)
−0.647828 + 0.761787i \(0.724322\pi\)
\(572\) 46.8213i 0.0818555i
\(573\) 78.6899 590.457i 0.137330 1.03047i
\(574\) −120.351 −0.209670
\(575\) 161.415i 0.280722i
\(576\) −69.4871 18.8559i −0.120637 0.0327359i
\(577\) −826.999 −1.43327 −0.716637 0.697446i \(-0.754320\pi\)
−0.716637 + 0.697446i \(0.754320\pi\)
\(578\) 19.0453i 0.0329504i
\(579\) −132.799 17.6981i −0.229359 0.0305666i
\(580\) 206.363 0.355798
\(581\) 218.057i 0.375312i
\(582\) 8.13601 61.0493i 0.0139794 0.104896i
\(583\) 36.9906 0.0634488
\(584\) 137.272i 0.235055i
\(585\) −61.1452 + 225.330i −0.104522 + 0.385180i
\(586\) 31.9744 0.0545639
\(587\) 419.920i 0.715366i −0.933843 0.357683i \(-0.883567\pi\)
0.933843 0.357683i \(-0.116433\pi\)
\(588\) 41.6319 + 5.54826i 0.0708026 + 0.00943582i
\(589\) 1228.92 2.08645
\(590\) 143.768i 0.243674i
\(591\) −0.377565 + 2.83310i −0.000638858 + 0.00479374i
\(592\) 125.925 0.212711
\(593\) 831.323i 1.40189i −0.713213 0.700947i \(-0.752761\pi\)
0.713213 0.700947i \(-0.247239\pi\)
\(594\) −71.0435 29.8248i −0.119602 0.0502100i
\(595\) 102.890 0.172924
\(596\) 23.4194i 0.0392943i
\(597\) 389.982 + 51.9726i 0.653235 + 0.0870563i
\(598\) −529.675 −0.885745
\(599\) 902.352i 1.50643i 0.657774 + 0.753216i \(0.271498\pi\)
−0.657774 + 0.753216i \(0.728502\pi\)
\(600\) −5.60459 + 42.0546i −0.00934098 + 0.0700910i
\(601\) −149.891 −0.249403 −0.124702 0.992194i \(-0.539797\pi\)
−0.124702 + 0.992194i \(0.539797\pi\)
\(602\) 193.647i 0.321672i
\(603\) −293.088 79.5318i −0.486049 0.131893i
\(604\) 146.399 0.242382
\(605\) 261.459i 0.432164i
\(606\) 289.684 + 38.6060i 0.478027 + 0.0637063i
\(607\) 14.9805 0.0246795 0.0123398 0.999924i \(-0.496072\pi\)
0.0123398 + 0.999924i \(0.496072\pi\)
\(608\) 204.391i 0.336169i
\(609\) −48.3832 + 363.048i −0.0794470 + 0.596138i
\(610\) 89.0007 0.145903
\(611\) 1071.30i 1.75335i
\(612\) 81.9835 302.123i 0.133960 0.493664i
\(613\) 289.923 0.472958 0.236479 0.971637i \(-0.424006\pi\)
0.236479 + 0.971637i \(0.424006\pi\)
\(614\) 470.812i 0.766795i
\(615\) 213.879 + 28.5035i 0.347770 + 0.0463472i
\(616\) 15.1004 0.0245136
\(617\) 1118.36i 1.81257i −0.422662 0.906287i \(-0.638904\pi\)
0.422662 0.906287i \(-0.361096\pi\)
\(618\) 24.3933 183.037i 0.0394713 0.296177i
\(619\) −963.589 −1.55669 −0.778343 0.627839i \(-0.783940\pi\)
−0.778343 + 0.627839i \(0.783940\pi\)
\(620\) 152.108i 0.245335i
\(621\) −337.398 + 803.694i −0.543315 + 1.29419i
\(622\) 205.101 0.329744
\(623\) 129.292i 0.207531i
\(624\) −138.000 18.3911i −0.221153 0.0294730i
\(625\) 25.0000 0.0400000
\(626\) 489.225i 0.781509i
\(627\) 28.8941 216.809i 0.0460830 0.345788i
\(628\) −580.975 −0.925120
\(629\) 547.509i 0.870444i
\(630\) −72.6713 19.7200i −0.115351 0.0313015i
\(631\) 408.113 0.646772 0.323386 0.946267i \(-0.395179\pi\)
0.323386 + 0.946267i \(0.395179\pi\)
\(632\) 93.1489i 0.147388i
\(633\) 302.341 + 40.2928i 0.477632 + 0.0636538i
\(634\) 219.759 0.346623
\(635\) 227.006i 0.357489i
\(636\) 14.5297 109.025i 0.0228454 0.171423i
\(637\) 81.2116 0.127491
\(638\) 131.682i 0.206398i
\(639\) 59.5750 219.544i 0.0932316 0.343574i
\(640\) −25.2982 −0.0395285
\(641\) 548.724i 0.856044i −0.903768 0.428022i \(-0.859211\pi\)
0.903768 0.428022i \(-0.140789\pi\)
\(642\) 873.491 + 116.410i 1.36058 + 0.181323i
\(643\) −106.614 −0.165807 −0.0829033 0.996558i \(-0.526419\pi\)
−0.0829033 + 0.996558i \(0.526419\pi\)
\(644\) 170.826i 0.265258i
\(645\) −45.8627 + 344.135i −0.0711050 + 0.533543i
\(646\) 888.669 1.37565
\(647\) 316.788i 0.489625i 0.969570 + 0.244813i \(0.0787265\pi\)
−0.969570 + 0.244813i \(0.921274\pi\)
\(648\) −115.810 + 197.677i −0.178719 + 0.305056i
\(649\) −91.7393 −0.141355
\(650\) 82.0361i 0.126209i
\(651\) 267.599 + 35.6627i 0.411058 + 0.0547815i
\(652\) −45.5332 −0.0698361
\(653\) 407.664i 0.624293i −0.950034 0.312147i \(-0.898952\pi\)
0.950034 0.312147i \(-0.101048\pi\)
\(654\) 85.1247 638.742i 0.130160 0.976669i
\(655\) 501.210 0.765207
\(656\) 128.660i 0.196128i
\(657\) 421.553 + 114.392i 0.641633 + 0.174112i
\(658\) −345.504 −0.525082
\(659\) 442.719i 0.671804i −0.941897 0.335902i \(-0.890959\pi\)
0.941897 0.335902i \(-0.109041\pi\)
\(660\) −26.8353 3.57633i −0.0406596 0.00541868i
\(661\) 300.069 0.453962 0.226981 0.973899i \(-0.427114\pi\)
0.226981 + 0.973899i \(0.427114\pi\)
\(662\) 201.492i 0.304369i
\(663\) 79.9628 600.009i 0.120608 0.904990i
\(664\) 233.112 0.351073
\(665\) 213.757i 0.321439i
\(666\) 104.936 386.706i 0.157562 0.580640i
\(667\) 1489.68 2.23340
\(668\) 471.524i 0.705874i
\(669\) 1094.52 + 145.866i 1.63605 + 0.218035i
\(670\) −106.705 −0.159261
\(671\) 56.7920i 0.0846378i
\(672\) 5.93134 44.5064i 0.00882640 0.0662298i
\(673\) 199.000 0.295691 0.147845 0.989011i \(-0.452766\pi\)
0.147845 + 0.989011i \(0.452766\pi\)
\(674\) 320.977i 0.476227i
\(675\) 124.476 + 52.2562i 0.184409 + 0.0774167i
\(676\) 68.8031 0.101780
\(677\) 235.136i 0.347321i −0.984806 0.173660i \(-0.944441\pi\)
0.984806 0.173660i \(-0.0555595\pi\)
\(678\) −160.760 21.4245i −0.237110 0.0315995i
\(679\) 38.4075 0.0565648
\(680\) 109.994i 0.161756i
\(681\) 123.501 926.704i 0.181353 1.36080i
\(682\) 97.0612 0.142318
\(683\) 698.860i 1.02322i −0.859218 0.511610i \(-0.829049\pi\)
0.859218 0.511610i \(-0.170951\pi\)
\(684\) −627.668 170.323i −0.917643 0.249010i
\(685\) −273.785 −0.399686
\(686\) 26.1916i 0.0381802i
\(687\) 360.067 + 47.9859i 0.524114 + 0.0698484i
\(688\) −207.017 −0.300897
\(689\) 212.676i 0.308673i
\(690\) −40.4579 + 303.580i −0.0586347 + 0.439971i
\(691\) 326.641 0.472708 0.236354 0.971667i \(-0.424047\pi\)
0.236354 + 0.971667i \(0.424047\pi\)
\(692\) 272.022i 0.393095i
\(693\) 12.5835 46.3721i 0.0181580 0.0669150i
\(694\) −129.951 −0.187250
\(695\) 296.377i 0.426441i
\(696\) 388.115 + 51.7238i 0.557636 + 0.0743159i
\(697\) −559.401 −0.802584
\(698\) 625.567i 0.896228i
\(699\) −74.6785 + 560.358i −0.106836 + 0.801656i
\(700\) −26.4575 −0.0377964
\(701\) 482.417i 0.688185i 0.938936 + 0.344092i \(0.111813\pi\)
−0.938936 + 0.344092i \(0.888187\pi\)
\(702\) −171.476 + 408.461i −0.244268 + 0.581853i
\(703\) 1137.47 1.61802
\(704\) 16.1430i 0.0229304i
\(705\) 614.006 + 81.8282i 0.870931 + 0.116068i
\(706\) 124.642 0.176546
\(707\) 182.247i 0.257775i
\(708\) −36.0347 + 270.390i −0.0508964 + 0.381906i
\(709\) −415.186 −0.585594 −0.292797 0.956175i \(-0.594586\pi\)
−0.292797 + 0.956175i \(0.594586\pi\)
\(710\) 79.9294i 0.112577i
\(711\) 286.053 + 77.6229i 0.402325 + 0.109174i
\(712\) −138.219 −0.194127
\(713\) 1098.02i 1.54000i
\(714\) 193.509 + 25.7888i 0.271021 + 0.0361188i
\(715\) −52.3478 −0.0732138
\(716\) 24.7555i 0.0345748i
\(717\) −96.2178 + 721.979i −0.134195 + 1.00694i
\(718\) 29.9491 0.0417118
\(719\) 1341.45i 1.86571i 0.360249 + 0.932856i \(0.382692\pi\)
−0.360249 + 0.932856i \(0.617308\pi\)
\(720\) −21.0815 + 77.6889i −0.0292799 + 0.107901i
\(721\) 115.153 0.159713
\(722\) 1335.70i 1.85000i
\(723\) 648.059 + 86.3664i 0.896347 + 0.119456i
\(724\) 111.638 0.154196
\(725\) 230.721i 0.318236i
\(726\) −65.5335 + 491.737i −0.0902665 + 0.677323i
\(727\) 5.22241 0.00718351 0.00359175 0.999994i \(-0.498857\pi\)
0.00359175 + 0.999994i \(0.498857\pi\)
\(728\) 86.8188i 0.119257i
\(729\) 510.543 + 520.372i 0.700333 + 0.713816i
\(730\) 153.475 0.210240
\(731\) 900.088i 1.23131i
\(732\) 167.387 + 22.3076i 0.228671 + 0.0304748i
\(733\) −163.268 −0.222739 −0.111370 0.993779i \(-0.535524\pi\)
−0.111370 + 0.993779i \(0.535524\pi\)
\(734\) 433.412i 0.590479i
\(735\) 6.20314 46.5459i 0.00843965 0.0633278i
\(736\) −182.621 −0.248126
\(737\) 68.0890i 0.0923867i
\(738\) 395.106 + 107.215i 0.535374 + 0.145278i
\(739\) −995.463 −1.34704 −0.673520 0.739169i \(-0.735219\pi\)
−0.673520 + 0.739169i \(0.735219\pi\)
\(740\) 140.789i 0.190255i
\(741\) −1246.53 166.125i −1.68223 0.224190i
\(742\) 68.5902 0.0924396
\(743\) 1330.52i 1.79074i 0.445321 + 0.895371i \(0.353089\pi\)
−0.445321 + 0.895371i \(0.646911\pi\)
\(744\) 38.1251 286.075i 0.0512434 0.384510i
\(745\) 26.1837 0.0351459
\(746\) 759.256i 1.01777i
\(747\) 194.257 715.870i 0.260050 0.958327i
\(748\) 70.1880 0.0938342
\(749\) 549.533i 0.733689i
\(750\) 47.0185 + 6.26612i 0.0626913 + 0.00835483i
\(751\) −1291.88 −1.72021 −0.860107 0.510113i \(-0.829603\pi\)
−0.860107 + 0.510113i \(0.829603\pi\)
\(752\) 369.359i 0.491169i
\(753\) 17.7237 132.991i 0.0235374 0.176615i
\(754\) 757.098 1.00411
\(755\) 163.679i 0.216793i
\(756\) −131.733 55.3028i −0.174250 0.0731519i
\(757\) −608.247 −0.803497 −0.401748 0.915750i \(-0.631597\pi\)
−0.401748 + 0.915750i \(0.631597\pi\)
\(758\) 646.860i 0.853378i
\(759\) −193.717 25.8165i −0.255226 0.0340138i
\(760\) −228.516 −0.300678
\(761\) 19.5785i 0.0257273i −0.999917 0.0128637i \(-0.995905\pi\)
0.999917 0.0128637i \(-0.00409475\pi\)
\(762\) −56.8979 + 426.939i −0.0746691 + 0.560287i
\(763\) 401.847 0.526667
\(764\) 397.118i 0.519788i
\(765\) −337.783 91.6603i −0.441547 0.119817i
\(766\) −388.160 −0.506736
\(767\) 527.451i 0.687680i
\(768\) −47.5793 6.34087i −0.0619523 0.00825634i
\(769\) 1084.91 1.41081 0.705405 0.708804i \(-0.250765\pi\)
0.705405 + 0.708804i \(0.250765\pi\)
\(770\) 16.8827i 0.0219256i
\(771\) 64.9674 487.489i 0.0842638 0.632282i
\(772\) −89.3154 −0.115694
\(773\) 564.003i 0.729628i −0.931080 0.364814i \(-0.881133\pi\)
0.931080 0.364814i \(-0.118867\pi\)
\(774\) −172.512 + 635.733i −0.222883 + 0.821361i
\(775\) −170.062 −0.219435
\(776\) 41.0594i 0.0529116i
\(777\) 247.685 + 33.0088i 0.318771 + 0.0424824i
\(778\) −717.941 −0.922804
\(779\) 1162.17i 1.49188i
\(780\) −20.5619 + 154.288i −0.0263614 + 0.197806i
\(781\) 51.0036 0.0653055
\(782\) 794.015i 1.01536i
\(783\) 482.264 1148.77i 0.615918 1.46714i
\(784\) 28.0000 0.0357143
\(785\) 649.550i 0.827453i
\(786\) 942.645 + 125.626i 1.19929 + 0.159829i
\(787\) 1360.30 1.72846 0.864232 0.503094i \(-0.167805\pi\)
0.864232 + 0.503094i \(0.167805\pi\)
\(788\) 1.90543i 0.00241806i
\(789\) 204.842 1537.05i 0.259622 1.94810i
\(790\) 104.144 0.131827
\(791\) 101.138i 0.127861i
\(792\) −49.5739 13.4523i −0.0625933 0.0169852i
\(793\) 326.523 0.411756
\(794\) 781.368i 0.984091i
\(795\) −121.894 16.2447i −0.153325 0.0204336i
\(796\) 262.286 0.329505
\(797\) 81.4055i 0.102140i −0.998695 0.0510700i \(-0.983737\pi\)
0.998695 0.0510700i \(-0.0162631\pi\)
\(798\) 53.5770 402.021i 0.0671392 0.503785i
\(799\) −1605.94 −2.00993
\(800\) 28.2843i 0.0353553i
\(801\) −115.180 + 424.459i −0.143796 + 0.529911i
\(802\) −339.864 −0.423770
\(803\) 97.9336i 0.121960i
\(804\) −200.683 26.7450i −0.249606 0.0332649i
\(805\) −190.989 −0.237254
\(806\) 558.048i 0.692367i
\(807\) −168.731 + 1266.09i −0.209085 + 1.56889i
\(808\) 194.830 0.241127
\(809\) 907.697i 1.12200i 0.827816 + 0.560999i \(0.189583\pi\)
−0.827816 + 0.560999i \(0.810417\pi\)
\(810\) 221.009 + 129.480i 0.272851 + 0.159851i
\(811\) −451.340 −0.556523 −0.278261 0.960505i \(-0.589758\pi\)
−0.278261 + 0.960505i \(0.589758\pi\)
\(812\) 244.172i 0.300704i
\(813\) 114.266 + 15.2281i 0.140548 + 0.0187307i
\(814\) 89.8382 0.110366
\(815\) 50.9076i 0.0624633i
\(816\) 27.5694 206.870i 0.0337861 0.253517i
\(817\) −1869.96 −2.28881
\(818\) 623.786i 0.762574i
\(819\) −266.614 72.3480i −0.325536 0.0883370i
\(820\) 143.847 0.175423
\(821\) 248.662i 0.302878i 0.988467 + 0.151439i \(0.0483906\pi\)
−0.988467 + 0.151439i \(0.951609\pi\)
\(822\) −514.918 68.6229i −0.626421 0.0834828i
\(823\) −596.005 −0.724186 −0.362093 0.932142i \(-0.617938\pi\)
−0.362093 + 0.932142i \(0.617938\pi\)
\(824\) 123.104i 0.149398i
\(825\) −3.99846 + 30.0028i −0.00484662 + 0.0363671i
\(826\) −170.108 −0.205942
\(827\) 758.271i 0.916894i −0.888722 0.458447i \(-0.848406\pi\)
0.888722 0.458447i \(-0.151594\pi\)
\(828\) −152.182 + 560.814i −0.183794 + 0.677312i
\(829\) 509.182 0.614212 0.307106 0.951675i \(-0.400639\pi\)
0.307106 + 0.951675i \(0.400639\pi\)
\(830\) 260.627i 0.314009i
\(831\) 1087.71 + 144.958i 1.30891 + 0.174438i
\(832\) −92.8133 −0.111554
\(833\) 121.741i 0.146148i
\(834\) −74.2853 + 557.407i −0.0890711 + 0.668353i
\(835\) −527.179 −0.631353
\(836\) 145.817i 0.174423i
\(837\) −846.745 355.472i −1.01164 0.424697i
\(838\) −584.000 −0.696897
\(839\) 766.956i 0.914131i −0.889433 0.457065i \(-0.848901\pi\)
0.889433 0.457065i \(-0.151099\pi\)
\(840\) −49.7597 6.63144i −0.0592377 0.00789457i
\(841\) −1288.28 −1.53185
\(842\) 208.360i 0.247459i
\(843\) −159.621 + 1197.73i −0.189348 + 1.42079i
\(844\) 203.343 0.240928
\(845\) 76.9242i 0.0910346i
\(846\) 1134.27 + 307.795i 1.34075 + 0.363824i
\(847\) −309.363 −0.365245
\(848\) 73.3260i 0.0864693i
\(849\) 1160.44 + 154.651i 1.36683 + 0.182157i
\(850\) −122.977 −0.144679
\(851\) 1016.31i 1.19426i
\(852\) 20.0339 150.326i 0.0235140 0.176439i
\(853\) 735.107 0.861790 0.430895 0.902402i \(-0.358198\pi\)
0.430895 + 0.902402i \(0.358198\pi\)
\(854\) 105.307i 0.123310i
\(855\) −190.427 + 701.754i −0.222721 + 0.820765i
\(856\) 587.476 0.686303
\(857\) 514.911i 0.600830i −0.953809 0.300415i \(-0.902875\pi\)
0.953809 0.300415i \(-0.0971252\pi\)
\(858\) −98.4526 13.1207i −0.114747 0.0152922i
\(859\) 1414.99 1.64726 0.823628 0.567131i \(-0.191947\pi\)
0.823628 + 0.567131i \(0.191947\pi\)
\(860\) 231.452i 0.269130i
\(861\) −33.7258 + 253.065i −0.0391705 + 0.293920i
\(862\) 71.5523 0.0830073
\(863\) 249.645i 0.289276i −0.989485 0.144638i \(-0.953798\pi\)
0.989485 0.144638i \(-0.0462017\pi\)
\(864\) −59.1212 + 140.829i −0.0684273 + 0.162996i
\(865\) 304.129 0.351595
\(866\) 924.138i 1.06713i
\(867\) 40.0472 + 5.33707i 0.0461906 + 0.00615579i
\(868\) 179.976 0.207346
\(869\) 66.4548i 0.0764728i
\(870\) 57.8290 433.926i 0.0664701 0.498765i
\(871\) −391.474 −0.449454
\(872\) 429.593i 0.492652i
\(873\) −126.090 34.2156i −0.144433 0.0391932i
\(874\) −1649.59 −1.88740
\(875\) 29.5804i 0.0338062i
\(876\) 288.646 + 38.4677i 0.329505 + 0.0439130i
\(877\) 767.333 0.874952 0.437476 0.899230i \(-0.355872\pi\)
0.437476 + 0.899230i \(0.355872\pi\)
\(878\) 1075.73i 1.22520i
\(879\) 8.96018 67.2336i 0.0101936 0.0764887i
\(880\) −18.0484 −0.0205095
\(881\) 1200.08i 1.36217i 0.732203 + 0.681087i \(0.238492\pi\)
−0.732203 + 0.681087i \(0.761508\pi\)
\(882\) 23.3330 85.9859i 0.0264546 0.0974897i
\(883\) −370.168 −0.419217 −0.209608 0.977785i \(-0.567219\pi\)
−0.209608 + 0.977785i \(0.567219\pi\)
\(884\) 403.542i 0.456496i
\(885\) 302.305 + 40.2880i 0.341588 + 0.0455232i
\(886\) −768.718 −0.867628
\(887\) 797.714i 0.899339i −0.893195 0.449670i \(-0.851542\pi\)
0.893195 0.449670i \(-0.148458\pi\)
\(888\) 35.2879 264.786i 0.0397387 0.298183i
\(889\) −268.597 −0.302134
\(890\) 154.533i 0.173633i
\(891\) −82.6219 + 141.028i −0.0927294 + 0.158280i
\(892\) 736.129 0.825257
\(893\) 3336.38i 3.73614i
\(894\) 49.2446 + 6.56280i 0.0550835 + 0.00734094i
\(895\) 27.6775 0.0309246
\(896\) 29.9333i 0.0334077i
\(897\) −148.431 + 1113.76i −0.165475 + 1.24165i
\(898\) −977.369 −1.08838
\(899\) 1569.47i 1.74580i
\(900\) 86.8589 + 23.5699i 0.0965098 + 0.0261888i
\(901\) 318.814 0.353844
\(902\) 91.7895i 0.101762i
\(903\) −407.186 54.2655i −0.450926 0.0600947i
\(904\) −108.121 −0.119603
\(905\) 124.815i 0.137917i
\(906\) 41.0253 307.837i 0.0452818 0.339776i
\(907\) −60.6349 −0.0668522 −0.0334261 0.999441i \(-0.510642\pi\)
−0.0334261 + 0.999441i \(0.510642\pi\)
\(908\) 623.265i 0.686415i
\(909\) 162.356 598.309i 0.178610 0.658206i
\(910\) −97.0664 −0.106666
\(911\) 1640.58i 1.80085i −0.435009 0.900426i \(-0.643255\pi\)
0.435009 0.900426i \(-0.356745\pi\)
\(912\) −429.778 57.2763i −0.471248 0.0628029i
\(913\) 166.308 0.182156
\(914\) 45.9530i 0.0502768i
\(915\) 24.9406 187.144i 0.0272575 0.204529i
\(916\) 242.167 0.264374
\(917\) 593.040i 0.646718i
\(918\) −612.308 257.053i −0.667002 0.280014i
\(919\) 904.955 0.984717 0.492358 0.870393i \(-0.336135\pi\)
0.492358 + 0.870393i \(0.336135\pi\)
\(920\) 204.176i 0.221931i
\(921\) −989.990 131.935i −1.07491 0.143252i
\(922\) −26.8526 −0.0291243
\(923\) 293.242i 0.317706i
\(924\) 4.23157 31.7520i 0.00457962 0.0343636i
\(925\) −157.406 −0.170169
\(926\) 1093.14i 1.18050i
\(927\) −378.042 102.585i −0.407812 0.110663i
\(928\) 261.031 0.281283
\(929\) 320.892i 0.345417i 0.984973 + 0.172709i \(0.0552519\pi\)
−0.984973 + 0.172709i \(0.944748\pi\)
\(930\) −319.842 42.6251i −0.343916 0.0458335i
\(931\) 252.920 0.271665
\(932\) 376.875i 0.404372i
\(933\) 57.4753 431.271i 0.0616027 0.462242i
\(934\) 474.792 0.508343
\(935\) 78.4726i 0.0839279i
\(936\) −77.3432 + 285.022i −0.0826317 + 0.304511i
\(937\) −862.831 −0.920845 −0.460422 0.887700i \(-0.652302\pi\)
−0.460422 + 0.887700i \(0.652302\pi\)
\(938\) 126.255i 0.134600i
\(939\) −1028.71 137.095i −1.09554 0.146001i
\(940\) 412.956 0.439315
\(941\) 1297.26i 1.37859i −0.724479 0.689297i \(-0.757920\pi\)
0.724479 0.689297i \(-0.242080\pi\)
\(942\) −162.806 + 1221.63i −0.172831 + 1.29685i
\(943\) 1038.39 1.10115
\(944\) 181.854i 0.192641i
\(945\) −61.8304 + 147.282i −0.0654290 + 0.155854i
\(946\) −147.691 −0.156122
\(947\) 969.136i 1.02337i −0.859172 0.511687i \(-0.829021\pi\)
0.859172 0.511687i \(-0.170979\pi\)
\(948\) 195.867 + 26.1031i 0.206611 + 0.0275349i
\(949\) 563.064 0.593324
\(950\) 255.488i 0.268935i
\(951\) 61.5829 462.094i 0.0647560 0.485903i
\(952\) 130.147 0.136709
\(953\) 1341.41i 1.40756i 0.710416 + 0.703782i \(0.248507\pi\)
−0.710416 + 0.703782i \(0.751493\pi\)
\(954\) −225.179 61.1041i −0.236036 0.0640504i
\(955\) −443.992 −0.464913
\(956\) 485.575i 0.507924i
\(957\) 276.891 + 36.9011i 0.289332 + 0.0385592i
\(958\) 1325.89 1.38401
\(959\) 323.947i 0.337797i
\(960\) −7.08931 + 53.1953i −0.00738470 + 0.0554118i
\(961\) 195.840 0.203788
\(962\) 516.520i 0.536923i
\(963\) 489.556 1804.09i 0.508365 1.87341i
\(964\) 435.859 0.452136
\(965\) 99.8577i 0.103479i
\(966\) −359.201 47.8705i −0.371843 0.0495554i
\(967\) −454.329 −0.469834 −0.234917 0.972015i \(-0.575482\pi\)
−0.234917 + 0.972015i \(0.575482\pi\)
\(968\) 330.723i 0.341656i
\(969\) 249.031 1868.63i 0.256998 1.92841i
\(970\) −45.9058 −0.0473255
\(971\) 1594.23i 1.64185i 0.571037 + 0.820924i \(0.306541\pi\)
−0.571037 + 0.820924i \(0.693459\pi\)
\(972\) 383.207 + 298.912i 0.394246 + 0.307523i
\(973\) −350.677 −0.360408
\(974\) 1063.83i 1.09223i
\(975\) 172.500 + 22.9889i 0.176923 + 0.0235784i
\(976\) 112.578 0.115346
\(977\) 544.109i 0.556918i −0.960448 0.278459i \(-0.910176\pi\)
0.960448 0.278459i \(-0.0898237\pi\)
\(978\) −12.7597 + 95.7439i −0.0130468 + 0.0978977i
\(979\) −98.6087 −0.100724
\(980\) 31.3050i 0.0319438i
\(981\) −1319.25 357.989i −1.34480 0.364922i
\(982\) −1208.54 −1.23069
\(983\) 605.161i 0.615627i −0.951447 0.307813i \(-0.900403\pi\)
0.951447 0.307813i \(-0.0995973\pi\)
\(984\) 270.538 + 36.0544i 0.274937 + 0.0366406i
\(985\) 2.13034 0.00216278
\(986\) 1134.93i 1.15105i
\(987\) −96.8205 + 726.502i −0.0980957 + 0.736071i
\(988\) −838.370 −0.848553
\(989\) 1670.79i 1.68937i
\(990\) −15.0401 + 55.4253i −0.0151920 + 0.0559851i
\(991\) −1002.42 −1.01152 −0.505761 0.862674i \(-0.668788\pi\)
−0.505761 + 0.862674i \(0.668788\pi\)
\(992\) 192.403i 0.193955i
\(993\) −423.684 56.4641i −0.426670 0.0568621i
\(994\) 94.5738 0.0951446
\(995\) 293.245i 0.294719i
\(996\) 65.3249 490.172i 0.0655873 0.492141i
\(997\) −9.04315 −0.00907036 −0.00453518 0.999990i \(-0.501444\pi\)
−0.00453518 + 0.999990i \(0.501444\pi\)
\(998\) 515.725i 0.516759i
\(999\) −783.733 329.019i −0.784517 0.329348i
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 210.3.e.a.71.1 16
3.2 odd 2 inner 210.3.e.a.71.9 yes 16
4.3 odd 2 1680.3.l.c.1121.16 16
5.2 odd 4 1050.3.c.c.449.22 32
5.3 odd 4 1050.3.c.c.449.11 32
5.4 even 2 1050.3.e.d.701.16 16
12.11 even 2 1680.3.l.c.1121.15 16
15.2 even 4 1050.3.c.c.449.12 32
15.8 even 4 1050.3.c.c.449.21 32
15.14 odd 2 1050.3.e.d.701.8 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
210.3.e.a.71.1 16 1.1 even 1 trivial
210.3.e.a.71.9 yes 16 3.2 odd 2 inner
1050.3.c.c.449.11 32 5.3 odd 4
1050.3.c.c.449.12 32 15.2 even 4
1050.3.c.c.449.21 32 15.8 even 4
1050.3.c.c.449.22 32 5.2 odd 4
1050.3.e.d.701.8 16 15.14 odd 2
1050.3.e.d.701.16 16 5.4 even 2
1680.3.l.c.1121.15 16 12.11 even 2
1680.3.l.c.1121.16 16 4.3 odd 2