Properties

Label 21.5.b.a.8.1
Level $21$
Weight $5$
Character 21.8
Analytic conductor $2.171$
Analytic rank $0$
Dimension $8$
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] = [21,5,Mod(8,21)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(21, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0]))
 
N = Newforms(chi, 5, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("21.8");
 
S:= CuspForms(chi, 5);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 21 = 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 21.b (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: \(2.17076922476\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} + 82x^{6} + 2017x^{4} + 13020x^{2} + 756 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2\cdot 3^{3}\cdot 7^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 8.1
Root \(-6.02741i\) of defining polynomial
Character \(\chi\) \(=\) 21.8
Dual form 21.5.b.a.8.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-6.02741i q^{2} +(-8.92230 + 1.18010i) q^{3} -20.3296 q^{4} -15.7540i q^{5} +(7.11292 + 53.7783i) q^{6} -18.5203 q^{7} +26.0965i q^{8} +(78.2147 - 21.0583i) q^{9} +O(q^{10})\) \(q-6.02741i q^{2} +(-8.92230 + 1.18010i) q^{3} -20.3296 q^{4} -15.7540i q^{5} +(7.11292 + 53.7783i) q^{6} -18.5203 q^{7} +26.0965i q^{8} +(78.2147 - 21.0583i) q^{9} -94.9556 q^{10} -196.340i q^{11} +(181.387 - 23.9909i) q^{12} +151.709 q^{13} +111.629i q^{14} +(18.5912 + 140.562i) q^{15} -167.980 q^{16} +421.337i q^{17} +(-126.927 - 471.432i) q^{18} +196.481 q^{19} +320.272i q^{20} +(165.243 - 21.8557i) q^{21} -1183.42 q^{22} -143.456i q^{23} +(-30.7963 - 232.840i) q^{24} +376.813 q^{25} -914.409i q^{26} +(-673.004 + 280.190i) q^{27} +376.510 q^{28} -753.566i q^{29} +(847.222 - 112.057i) q^{30} -635.323 q^{31} +1430.03i q^{32} +(231.700 + 1751.80i) q^{33} +2539.57 q^{34} +291.768i q^{35} +(-1590.08 + 428.108i) q^{36} +1336.52 q^{37} -1184.27i q^{38} +(-1353.59 + 179.031i) q^{39} +411.123 q^{40} -2846.73i q^{41} +(-131.733 - 995.988i) q^{42} +99.0370 q^{43} +3991.52i q^{44} +(-331.752 - 1232.19i) q^{45} -864.666 q^{46} -512.989i q^{47} +(1498.77 - 198.233i) q^{48} +343.000 q^{49} -2271.20i q^{50} +(-497.218 - 3759.29i) q^{51} -3084.18 q^{52} +4252.16i q^{53} +(1688.82 + 4056.47i) q^{54} -3093.13 q^{55} -483.313i q^{56} +(-1753.06 + 231.866i) q^{57} -4542.05 q^{58} +2893.09i q^{59} +(-377.952 - 2857.56i) q^{60} +2661.40 q^{61} +3829.35i q^{62} +(-1448.56 + 390.006i) q^{63} +5931.68 q^{64} -2390.01i q^{65} +(10558.8 - 1396.55i) q^{66} +2567.47 q^{67} -8565.62i q^{68} +(169.292 + 1279.95i) q^{69} +1758.60 q^{70} +1769.31i q^{71} +(549.548 + 2041.13i) q^{72} -3531.14 q^{73} -8055.76i q^{74} +(-3362.03 + 444.675i) q^{75} -3994.38 q^{76} +3636.27i q^{77} +(1079.09 + 8158.63i) q^{78} +2251.95 q^{79} +2646.35i q^{80} +(5674.09 - 3294.15i) q^{81} -17158.4 q^{82} -2063.23i q^{83} +(-3359.33 + 444.318i) q^{84} +6637.72 q^{85} -596.936i q^{86} +(889.280 + 6723.54i) q^{87} +5123.78 q^{88} +3069.01i q^{89} +(-7426.92 + 1999.61i) q^{90} -2809.68 q^{91} +2916.40i q^{92} +(5668.54 - 749.743i) q^{93} -3091.99 q^{94} -3095.35i q^{95} +(-1687.57 - 12759.1i) q^{96} +3416.07 q^{97} -2067.40i q^{98} +(-4134.59 - 15356.7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 2 q^{3} - 36 q^{4} - 34 q^{6} + 64 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 2 q^{3} - 36 q^{4} - 34 q^{6} + 64 q^{9} - 4 q^{10} + 98 q^{12} + 420 q^{13} + 76 q^{15} - 444 q^{16} - 712 q^{18} - 372 q^{19} + 98 q^{21} - 16 q^{22} + 1146 q^{24} + 1056 q^{25} - 1862 q^{27} + 392 q^{28} + 2348 q^{30} - 2776 q^{31} + 1396 q^{33} + 2928 q^{34} - 3268 q^{36} - 2560 q^{37} - 2540 q^{39} - 1980 q^{40} - 2450 q^{42} + 4720 q^{43} + 9700 q^{45} + 7536 q^{46} - 2962 q^{48} + 2744 q^{49} + 4764 q^{51} - 20252 q^{52} + 4886 q^{54} + 184 q^{55} - 14144 q^{57} - 7504 q^{58} - 13828 q^{60} + 972 q^{61} - 6076 q^{63} + 22772 q^{64} + 36020 q^{66} + 10200 q^{67} - 5760 q^{69} + 10780 q^{70} + 14304 q^{72} - 32008 q^{73} + 2114 q^{75} + 17332 q^{76} - 29668 q^{78} - 23168 q^{79} - 17216 q^{81} - 31976 q^{82} - 14798 q^{84} + 32016 q^{85} + 50764 q^{87} + 29208 q^{88} - 24352 q^{90} + 11956 q^{91} + 31848 q^{93} - 64992 q^{94} + 28630 q^{96} + 28112 q^{97} - 32432 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/21\mathbb{Z}\right)^\times\).

\(n\) \(8\) \(10\)
\(\chi(n)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 6.02741i 1.50685i −0.657533 0.753426i \(-0.728400\pi\)
0.657533 0.753426i \(-0.271600\pi\)
\(3\) −8.92230 + 1.18010i −0.991366 + 0.131122i
\(4\) −20.3296 −1.27060
\(5\) 15.7540i 0.630159i −0.949065 0.315079i \(-0.897969\pi\)
0.949065 0.315079i \(-0.102031\pi\)
\(6\) 7.11292 + 53.7783i 0.197581 + 1.49384i
\(7\) −18.5203 −0.377964
\(8\) 26.0965i 0.407757i
\(9\) 78.2147 21.0583i 0.965614 0.259980i
\(10\) −94.9556 −0.949556
\(11\) 196.340i 1.62264i −0.584600 0.811322i \(-0.698748\pi\)
0.584600 0.811322i \(-0.301252\pi\)
\(12\) 181.387 23.9909i 1.25963 0.166604i
\(13\) 151.709 0.897684 0.448842 0.893611i \(-0.351837\pi\)
0.448842 + 0.893611i \(0.351837\pi\)
\(14\) 111.629i 0.569536i
\(15\) 18.5912 + 140.562i 0.0826276 + 0.624718i
\(16\) −167.980 −0.656173
\(17\) 421.337i 1.45791i 0.684560 + 0.728956i \(0.259994\pi\)
−0.684560 + 0.728956i \(0.740006\pi\)
\(18\) −126.927 471.432i −0.391751 1.45504i
\(19\) 196.481 0.544268 0.272134 0.962259i \(-0.412271\pi\)
0.272134 + 0.962259i \(0.412271\pi\)
\(20\) 320.272i 0.800681i
\(21\) 165.243 21.8557i 0.374701 0.0495594i
\(22\) −1183.42 −2.44508
\(23\) 143.456i 0.271183i −0.990765 0.135591i \(-0.956707\pi\)
0.990765 0.135591i \(-0.0432935\pi\)
\(24\) −30.7963 232.840i −0.0534659 0.404237i
\(25\) 376.813 0.602900
\(26\) 914.409i 1.35268i
\(27\) −673.004 + 280.190i −0.923188 + 0.384348i
\(28\) 376.510 0.480242
\(29\) 753.566i 0.896035i −0.894025 0.448018i \(-0.852130\pi\)
0.894025 0.448018i \(-0.147870\pi\)
\(30\) 847.222 112.057i 0.941357 0.124507i
\(31\) −635.323 −0.661107 −0.330553 0.943787i \(-0.607235\pi\)
−0.330553 + 0.943787i \(0.607235\pi\)
\(32\) 1430.03i 1.39651i
\(33\) 231.700 + 1751.80i 0.212764 + 1.60863i
\(34\) 2539.57 2.19686
\(35\) 291.768i 0.238178i
\(36\) −1590.08 + 428.108i −1.22691 + 0.330331i
\(37\) 1336.52 0.976276 0.488138 0.872767i \(-0.337676\pi\)
0.488138 + 0.872767i \(0.337676\pi\)
\(38\) 1184.27i 0.820131i
\(39\) −1353.59 + 179.031i −0.889933 + 0.117706i
\(40\) 411.123 0.256952
\(41\) 2846.73i 1.69347i −0.532012 0.846737i \(-0.678564\pi\)
0.532012 0.846737i \(-0.321436\pi\)
\(42\) −131.733 995.988i −0.0746787 0.564619i
\(43\) 99.0370 0.0535624 0.0267812 0.999641i \(-0.491474\pi\)
0.0267812 + 0.999641i \(0.491474\pi\)
\(44\) 3991.52i 2.06173i
\(45\) −331.752 1232.19i −0.163828 0.608490i
\(46\) −864.666 −0.408632
\(47\) 512.989i 0.232227i −0.993236 0.116113i \(-0.962956\pi\)
0.993236 0.116113i \(-0.0370436\pi\)
\(48\) 1498.77 198.233i 0.650507 0.0860386i
\(49\) 343.000 0.142857
\(50\) 2271.20i 0.908481i
\(51\) −497.218 3759.29i −0.191164 1.44532i
\(52\) −3084.18 −1.14060
\(53\) 4252.16i 1.51376i 0.653553 + 0.756881i \(0.273278\pi\)
−0.653553 + 0.756881i \(0.726722\pi\)
\(54\) 1688.82 + 4056.47i 0.579156 + 1.39111i
\(55\) −3093.13 −1.02252
\(56\) 483.313i 0.154118i
\(57\) −1753.06 + 231.866i −0.539569 + 0.0713654i
\(58\) −4542.05 −1.35019
\(59\) 2893.09i 0.831110i 0.909568 + 0.415555i \(0.136413\pi\)
−0.909568 + 0.415555i \(0.863587\pi\)
\(60\) −377.952 2857.56i −0.104987 0.793768i
\(61\) 2661.40 0.715238 0.357619 0.933868i \(-0.383589\pi\)
0.357619 + 0.933868i \(0.383589\pi\)
\(62\) 3829.35i 0.996190i
\(63\) −1448.56 + 390.006i −0.364968 + 0.0982630i
\(64\) 5931.68 1.44816
\(65\) 2390.01i 0.565683i
\(66\) 10558.8 1396.55i 2.42397 0.320604i
\(67\) 2567.47 0.571947 0.285974 0.958237i \(-0.407683\pi\)
0.285974 + 0.958237i \(0.407683\pi\)
\(68\) 8565.62i 1.85243i
\(69\) 169.292 + 1279.95i 0.0355580 + 0.268842i
\(70\) 1758.60 0.358898
\(71\) 1769.31i 0.350983i 0.984481 + 0.175492i \(0.0561515\pi\)
−0.984481 + 0.175492i \(0.943849\pi\)
\(72\) 549.548 + 2041.13i 0.106009 + 0.393736i
\(73\) −3531.14 −0.662628 −0.331314 0.943521i \(-0.607492\pi\)
−0.331314 + 0.943521i \(0.607492\pi\)
\(74\) 8055.76i 1.47110i
\(75\) −3362.03 + 444.675i −0.597695 + 0.0790534i
\(76\) −3994.38 −0.691548
\(77\) 3636.27i 0.613302i
\(78\) 1079.09 + 8158.63i 0.177365 + 1.34100i
\(79\) 2251.95 0.360832 0.180416 0.983590i \(-0.442256\pi\)
0.180416 + 0.983590i \(0.442256\pi\)
\(80\) 2646.35i 0.413493i
\(81\) 5674.09 3294.15i 0.864821 0.502080i
\(82\) −17158.4 −2.55181
\(83\) 2063.23i 0.299496i −0.988724 0.149748i \(-0.952154\pi\)
0.988724 0.149748i \(-0.0478463\pi\)
\(84\) −3359.33 + 444.318i −0.476096 + 0.0629703i
\(85\) 6637.72 0.918716
\(86\) 596.936i 0.0807107i
\(87\) 889.280 + 6723.54i 0.117490 + 0.888299i
\(88\) 5123.78 0.661645
\(89\) 3069.01i 0.387453i 0.981056 + 0.193726i \(0.0620574\pi\)
−0.981056 + 0.193726i \(0.937943\pi\)
\(90\) −7426.92 + 1999.61i −0.916904 + 0.246865i
\(91\) −2809.68 −0.339293
\(92\) 2916.40i 0.344566i
\(93\) 5668.54 749.743i 0.655399 0.0866855i
\(94\) −3091.99 −0.349931
\(95\) 3095.35i 0.342975i
\(96\) −1687.57 12759.1i −0.183113 1.38445i
\(97\) 3416.07 0.363064 0.181532 0.983385i \(-0.441894\pi\)
0.181532 + 0.983385i \(0.441894\pi\)
\(98\) 2067.40i 0.215265i
\(99\) −4134.59 15356.7i −0.421854 1.56685i
\(100\) −7660.46 −0.766046
\(101\) 868.123i 0.0851017i 0.999094 + 0.0425509i \(0.0135484\pi\)
−0.999094 + 0.0425509i \(0.986452\pi\)
\(102\) −22658.8 + 2996.93i −2.17789 + 0.288056i
\(103\) 2420.92 0.228195 0.114098 0.993470i \(-0.463602\pi\)
0.114098 + 0.993470i \(0.463602\pi\)
\(104\) 3959.06i 0.366037i
\(105\) −344.314 2603.24i −0.0312303 0.236121i
\(106\) 25629.5 2.28102
\(107\) 5171.46i 0.451695i −0.974163 0.225848i \(-0.927485\pi\)
0.974163 0.225848i \(-0.0725152\pi\)
\(108\) 13681.9 5696.16i 1.17300 0.488353i
\(109\) 18184.1 1.53052 0.765258 0.643723i \(-0.222611\pi\)
0.765258 + 0.643723i \(0.222611\pi\)
\(110\) 18643.6i 1.54079i
\(111\) −11924.8 + 1577.22i −0.967847 + 0.128011i
\(112\) 3111.04 0.248010
\(113\) 8272.19i 0.647834i 0.946086 + 0.323917i \(0.105000\pi\)
−0.946086 + 0.323917i \(0.895000\pi\)
\(114\) 1397.55 + 10566.4i 0.107537 + 0.813050i
\(115\) −2260.00 −0.170888
\(116\) 15319.7i 1.13850i
\(117\) 11865.8 3194.73i 0.866816 0.233379i
\(118\) 17437.9 1.25236
\(119\) 7803.26i 0.551039i
\(120\) −3668.16 + 485.164i −0.254733 + 0.0336920i
\(121\) −23908.4 −1.63297
\(122\) 16041.3i 1.07776i
\(123\) 3359.42 + 25399.4i 0.222051 + 1.67885i
\(124\) 12915.9 0.840003
\(125\) 15782.5i 1.01008i
\(126\) 2350.72 + 8731.04i 0.148068 + 0.549952i
\(127\) −23527.3 −1.45870 −0.729348 0.684143i \(-0.760176\pi\)
−0.729348 + 0.684143i \(0.760176\pi\)
\(128\) 12872.2i 0.785656i
\(129\) −883.637 + 116.873i −0.0531000 + 0.00702321i
\(130\) −14405.6 −0.852400
\(131\) 19736.1i 1.15005i 0.818134 + 0.575027i \(0.195008\pi\)
−0.818134 + 0.575027i \(0.804992\pi\)
\(132\) −4710.38 35613.5i −0.270339 2.04393i
\(133\) −3638.87 −0.205714
\(134\) 15475.2i 0.861840i
\(135\) 4414.10 + 10602.5i 0.242200 + 0.581755i
\(136\) −10995.4 −0.594474
\(137\) 13653.6i 0.727457i −0.931505 0.363728i \(-0.881504\pi\)
0.931505 0.363728i \(-0.118496\pi\)
\(138\) 7714.81 1020.39i 0.405104 0.0535806i
\(139\) 6654.45 0.344416 0.172208 0.985061i \(-0.444910\pi\)
0.172208 + 0.985061i \(0.444910\pi\)
\(140\) 5931.53i 0.302629i
\(141\) 605.376 + 4577.04i 0.0304500 + 0.230222i
\(142\) 10664.3 0.528880
\(143\) 29786.4i 1.45662i
\(144\) −13138.5 + 3537.38i −0.633609 + 0.170591i
\(145\) −11871.6 −0.564644
\(146\) 21283.6i 0.998482i
\(147\) −3060.35 + 404.773i −0.141624 + 0.0187317i
\(148\) −27171.0 −1.24046
\(149\) 25398.8i 1.14404i 0.820239 + 0.572020i \(0.193840\pi\)
−0.820239 + 0.572020i \(0.806160\pi\)
\(150\) 2680.24 + 20264.3i 0.119122 + 0.900638i
\(151\) −2253.44 −0.0988307 −0.0494154 0.998778i \(-0.515736\pi\)
−0.0494154 + 0.998778i \(0.515736\pi\)
\(152\) 5127.45i 0.221929i
\(153\) 8872.65 + 32954.7i 0.379027 + 1.40778i
\(154\) 21917.3 0.924155
\(155\) 10008.9i 0.416602i
\(156\) 27518.0 3639.63i 1.13075 0.149557i
\(157\) −41471.1 −1.68246 −0.841232 0.540674i \(-0.818169\pi\)
−0.841232 + 0.540674i \(0.818169\pi\)
\(158\) 13573.4i 0.543720i
\(159\) −5017.96 37939.0i −0.198487 1.50069i
\(160\) 22528.6 0.880024
\(161\) 2656.84i 0.102498i
\(162\) −19855.2 34200.1i −0.756560 1.30316i
\(163\) 43022.4 1.61927 0.809635 0.586934i \(-0.199665\pi\)
0.809635 + 0.586934i \(0.199665\pi\)
\(164\) 57873.0i 2.15173i
\(165\) 27597.8 3650.20i 1.01369 0.134075i
\(166\) −12435.9 −0.451296
\(167\) 13076.2i 0.468867i 0.972132 + 0.234433i \(0.0753234\pi\)
−0.972132 + 0.234433i \(0.924677\pi\)
\(168\) 570.356 + 4312.26i 0.0202082 + 0.152787i
\(169\) −5545.52 −0.194164
\(170\) 40008.2i 1.38437i
\(171\) 15367.7 4137.56i 0.525553 0.141498i
\(172\) −2013.38 −0.0680566
\(173\) 20091.4i 0.671303i −0.941986 0.335652i \(-0.891043\pi\)
0.941986 0.335652i \(-0.108957\pi\)
\(174\) 40525.5 5360.06i 1.33854 0.177040i
\(175\) −6978.67 −0.227875
\(176\) 32981.2i 1.06473i
\(177\) −3414.13 25813.1i −0.108977 0.823935i
\(178\) 18498.2 0.583834
\(179\) 40066.7i 1.25048i −0.780431 0.625242i \(-0.785000\pi\)
0.780431 0.625242i \(-0.215000\pi\)
\(180\) 6744.40 + 25050.0i 0.208161 + 0.773149i
\(181\) −63926.2 −1.95129 −0.975645 0.219354i \(-0.929605\pi\)
−0.975645 + 0.219354i \(0.929605\pi\)
\(182\) 16935.1i 0.511264i
\(183\) −23745.8 + 3140.71i −0.709063 + 0.0937834i
\(184\) 3743.69 0.110577
\(185\) 21055.5i 0.615209i
\(186\) −4519.01 34166.6i −0.130622 0.987589i
\(187\) 82725.2 2.36567
\(188\) 10428.9i 0.295068i
\(189\) 12464.2 5189.19i 0.348932 0.145270i
\(190\) −18656.9 −0.516812
\(191\) 57708.3i 1.58187i 0.611899 + 0.790936i \(0.290406\pi\)
−0.611899 + 0.790936i \(0.709594\pi\)
\(192\) −52924.2 + 6999.95i −1.43566 + 0.189886i
\(193\) −2395.62 −0.0643137 −0.0321568 0.999483i \(-0.510238\pi\)
−0.0321568 + 0.999483i \(0.510238\pi\)
\(194\) 20590.0i 0.547084i
\(195\) 2820.44 + 21324.4i 0.0741734 + 0.560799i
\(196\) −6973.06 −0.181515
\(197\) 2034.61i 0.0524263i 0.999656 + 0.0262132i \(0.00834487\pi\)
−0.999656 + 0.0262132i \(0.991655\pi\)
\(198\) −92560.9 + 24920.9i −2.36101 + 0.635672i
\(199\) 25978.9 0.656016 0.328008 0.944675i \(-0.393623\pi\)
0.328008 + 0.944675i \(0.393623\pi\)
\(200\) 9833.47i 0.245837i
\(201\) −22907.7 + 3029.87i −0.567009 + 0.0749948i
\(202\) 5232.53 0.128236
\(203\) 13956.2i 0.338670i
\(204\) 10108.3 + 76425.0i 0.242894 + 1.83643i
\(205\) −44847.3 −1.06716
\(206\) 14591.9i 0.343856i
\(207\) −3020.94 11220.4i −0.0705020 0.261858i
\(208\) −25484.0 −0.589035
\(209\) 38577.0i 0.883153i
\(210\) −15690.8 + 2075.32i −0.355800 + 0.0470594i
\(211\) 60437.2 1.35750 0.678749 0.734370i \(-0.262522\pi\)
0.678749 + 0.734370i \(0.262522\pi\)
\(212\) 86444.8i 1.92339i
\(213\) −2087.95 15786.3i −0.0460216 0.347953i
\(214\) −31170.5 −0.680638
\(215\) 1560.22i 0.0337528i
\(216\) −7311.96 17563.0i −0.156721 0.376437i
\(217\) 11766.4 0.249875
\(218\) 109603.i 2.30626i
\(219\) 31505.9 4167.09i 0.656907 0.0868850i
\(220\) 62882.2 1.29922
\(221\) 63920.4i 1.30874i
\(222\) 9506.58 + 71875.9i 0.192894 + 1.45840i
\(223\) 11036.5 0.221933 0.110966 0.993824i \(-0.464605\pi\)
0.110966 + 0.993824i \(0.464605\pi\)
\(224\) 26484.5i 0.527832i
\(225\) 29472.3 7935.05i 0.582169 0.156742i
\(226\) 49859.8 0.976189
\(227\) 73080.6i 1.41824i 0.705087 + 0.709121i \(0.250908\pi\)
−0.705087 + 0.709121i \(0.749092\pi\)
\(228\) 35639.0 4713.75i 0.685577 0.0906770i
\(229\) 15706.6 0.299509 0.149755 0.988723i \(-0.452152\pi\)
0.149755 + 0.988723i \(0.452152\pi\)
\(230\) 13621.9i 0.257503i
\(231\) −4291.15 32443.8i −0.0804173 0.608007i
\(232\) 19665.4 0.365365
\(233\) 58490.4i 1.07739i 0.842501 + 0.538694i \(0.181082\pi\)
−0.842501 + 0.538694i \(0.818918\pi\)
\(234\) −19255.9 71520.3i −0.351668 1.30616i
\(235\) −8081.61 −0.146340
\(236\) 58815.6i 1.05601i
\(237\) −20092.6 + 2657.52i −0.357716 + 0.0473129i
\(238\) −47033.4 −0.830334
\(239\) 13382.2i 0.234277i 0.993116 + 0.117139i \(0.0373722\pi\)
−0.993116 + 0.117139i \(0.962628\pi\)
\(240\) −3122.95 23611.6i −0.0542179 0.409923i
\(241\) −310.843 −0.00535189 −0.00267595 0.999996i \(-0.500852\pi\)
−0.00267595 + 0.999996i \(0.500852\pi\)
\(242\) 144105.i 2.46065i
\(243\) −46738.5 + 36087.3i −0.791521 + 0.611142i
\(244\) −54105.3 −0.908783
\(245\) 5403.61i 0.0900227i
\(246\) 153092. 20248.6i 2.52978 0.334599i
\(247\) 29807.8 0.488580
\(248\) 16579.7i 0.269571i
\(249\) 2434.81 + 18408.7i 0.0392705 + 0.296910i
\(250\) −95127.7 −1.52204
\(251\) 82720.9i 1.31301i −0.754322 0.656505i \(-0.772034\pi\)
0.754322 0.656505i \(-0.227966\pi\)
\(252\) 29448.6 7928.68i 0.463729 0.124853i
\(253\) −28166.1 −0.440033
\(254\) 141809.i 2.19804i
\(255\) −59223.7 + 7833.15i −0.910784 + 0.120464i
\(256\) 17320.9 0.264297
\(257\) 10849.5i 0.164265i 0.996621 + 0.0821324i \(0.0261730\pi\)
−0.996621 + 0.0821324i \(0.973827\pi\)
\(258\) 704.442 + 5326.04i 0.0105829 + 0.0800138i
\(259\) −24752.7 −0.368998
\(260\) 48588.0i 0.718758i
\(261\) −15868.8 58940.0i −0.232951 0.865224i
\(262\) 118957. 1.73296
\(263\) 40082.3i 0.579484i −0.957105 0.289742i \(-0.906431\pi\)
0.957105 0.289742i \(-0.0935695\pi\)
\(264\) −45715.8 + 6046.55i −0.655932 + 0.0867561i
\(265\) 66988.3 0.953910
\(266\) 21933.0i 0.309980i
\(267\) −3621.73 27382.7i −0.0508036 0.384108i
\(268\) −52195.8 −0.726717
\(269\) 75313.8i 1.04081i −0.853921 0.520403i \(-0.825782\pi\)
0.853921 0.520403i \(-0.174218\pi\)
\(270\) 63905.5 26605.6i 0.876618 0.364960i
\(271\) −113072. −1.53963 −0.769814 0.638268i \(-0.779651\pi\)
−0.769814 + 0.638268i \(0.779651\pi\)
\(272\) 70776.2i 0.956642i
\(273\) 25068.8 3315.70i 0.336363 0.0444887i
\(274\) −82296.0 −1.09617
\(275\) 73983.4i 0.978292i
\(276\) −3441.64 26021.0i −0.0451801 0.341591i
\(277\) −52989.5 −0.690606 −0.345303 0.938491i \(-0.612224\pi\)
−0.345303 + 0.938491i \(0.612224\pi\)
\(278\) 40109.1i 0.518983i
\(279\) −49691.7 + 13378.9i −0.638374 + 0.171874i
\(280\) −7614.10 −0.0971186
\(281\) 48221.1i 0.610695i −0.952241 0.305347i \(-0.901227\pi\)
0.952241 0.305347i \(-0.0987726\pi\)
\(282\) 27587.7 3648.85i 0.346910 0.0458836i
\(283\) 63901.6 0.797882 0.398941 0.916977i \(-0.369378\pi\)
0.398941 + 0.916977i \(0.369378\pi\)
\(284\) 35969.4i 0.445960i
\(285\) 3652.81 + 27617.6i 0.0449715 + 0.340014i
\(286\) −179535. −2.19491
\(287\) 52722.2i 0.640073i
\(288\) 30114.0 + 111849.i 0.363065 + 1.34849i
\(289\) −94003.5 −1.12551
\(290\) 71555.2i 0.850835i
\(291\) −30479.2 + 4031.29i −0.359930 + 0.0476056i
\(292\) 71786.9 0.841937
\(293\) 76356.1i 0.889423i 0.895674 + 0.444711i \(0.146694\pi\)
−0.895674 + 0.444711i \(0.853306\pi\)
\(294\) 2439.73 + 18446.0i 0.0282259 + 0.213406i
\(295\) 45577.7 0.523731
\(296\) 34878.5i 0.398083i
\(297\) 55012.4 + 132138.i 0.623660 + 1.49801i
\(298\) 153089. 1.72390
\(299\) 21763.5i 0.243436i
\(300\) 68348.9 9040.09i 0.759432 0.100445i
\(301\) −1834.19 −0.0202447
\(302\) 13582.4i 0.148923i
\(303\) −1024.47 7745.65i −0.0111587 0.0843670i
\(304\) −33004.9 −0.357134
\(305\) 41927.6i 0.450713i
\(306\) 198632. 53479.1i 2.12132 0.571138i
\(307\) 88506.5 0.939071 0.469535 0.882914i \(-0.344421\pi\)
0.469535 + 0.882914i \(0.344421\pi\)
\(308\) 73924.0i 0.779263i
\(309\) −21600.2 + 2856.92i −0.226225 + 0.0299214i
\(310\) 60327.5 0.627757
\(311\) 23502.0i 0.242987i −0.992592 0.121494i \(-0.961232\pi\)
0.992592 0.121494i \(-0.0387684\pi\)
\(312\) −4672.07 35323.9i −0.0479954 0.362877i
\(313\) 158727. 1.62018 0.810089 0.586307i \(-0.199419\pi\)
0.810089 + 0.586307i \(0.199419\pi\)
\(314\) 249963.i 2.53522i
\(315\) 6144.14 + 22820.5i 0.0619213 + 0.229988i
\(316\) −45781.3 −0.458473
\(317\) 173185.i 1.72342i −0.507403 0.861709i \(-0.669394\pi\)
0.507403 0.861709i \(-0.330606\pi\)
\(318\) −228674. + 30245.3i −2.26132 + 0.299091i
\(319\) −147955. −1.45395
\(320\) 93447.4i 0.912573i
\(321\) 6102.82 + 46141.3i 0.0592271 + 0.447796i
\(322\) 16013.8 0.154449
\(323\) 82784.5i 0.793494i
\(324\) −115352. + 66968.8i −1.09884 + 0.637944i
\(325\) 57165.7 0.541214
\(326\) 259313.i 2.44000i
\(327\) −162244. + 21459.0i −1.51730 + 0.200684i
\(328\) 74289.5 0.690526
\(329\) 9500.68i 0.0877734i
\(330\) −22001.2 166343.i −0.202031 1.52749i
\(331\) 84106.5 0.767668 0.383834 0.923402i \(-0.374603\pi\)
0.383834 + 0.923402i \(0.374603\pi\)
\(332\) 41944.7i 0.380540i
\(333\) 104536. 28144.9i 0.942706 0.253812i
\(334\) 78815.7 0.706512
\(335\) 40447.9i 0.360418i
\(336\) −27757.6 + 3671.32i −0.245869 + 0.0325195i
\(337\) 3077.59 0.0270989 0.0135494 0.999908i \(-0.495687\pi\)
0.0135494 + 0.999908i \(0.495687\pi\)
\(338\) 33425.1i 0.292576i
\(339\) −9761.98 73806.9i −0.0849451 0.642240i
\(340\) −134942. −1.16732
\(341\) 124739.i 1.07274i
\(342\) −24938.7 92627.3i −0.213217 0.791930i
\(343\) −6352.45 −0.0539949
\(344\) 2584.51i 0.0218405i
\(345\) 20164.4 2667.02i 0.169413 0.0224072i
\(346\) −121099. −1.01155
\(347\) 102480.i 0.851101i 0.904935 + 0.425551i \(0.139920\pi\)
−0.904935 + 0.425551i \(0.860080\pi\)
\(348\) −18078.7 136687.i −0.149283 1.12867i
\(349\) 81452.0 0.668730 0.334365 0.942444i \(-0.391478\pi\)
0.334365 + 0.942444i \(0.391478\pi\)
\(350\) 42063.3i 0.343374i
\(351\) −102100. + 42507.2i −0.828731 + 0.345023i
\(352\) 280772. 2.26604
\(353\) 198402.i 1.59220i 0.605167 + 0.796099i \(0.293106\pi\)
−0.605167 + 0.796099i \(0.706894\pi\)
\(354\) −155586. + 20578.4i −1.24155 + 0.164212i
\(355\) 27873.6 0.221175
\(356\) 62391.9i 0.492298i
\(357\) 9208.61 + 69623.0i 0.0722533 + 0.546281i
\(358\) −241498. −1.88429
\(359\) 20290.7i 0.157437i −0.996897 0.0787186i \(-0.974917\pi\)
0.996897 0.0787186i \(-0.0250829\pi\)
\(360\) 32155.8 8657.56i 0.248116 0.0668022i
\(361\) −91716.4 −0.703773
\(362\) 385309.i 2.94031i
\(363\) 213318. 28214.2i 1.61888 0.214119i
\(364\) 57119.8 0.431106
\(365\) 55629.5i 0.417561i
\(366\) 18930.3 + 143126.i 0.141318 + 1.06845i
\(367\) −196750. −1.46077 −0.730385 0.683036i \(-0.760659\pi\)
−0.730385 + 0.683036i \(0.760659\pi\)
\(368\) 24097.7i 0.177943i
\(369\) −59947.4 222656.i −0.440269 1.63524i
\(370\) −126910. −0.927028
\(371\) 78751.1i 0.572148i
\(372\) −115239. + 15242.0i −0.832751 + 0.110143i
\(373\) −144072. −1.03553 −0.517765 0.855523i \(-0.673236\pi\)
−0.517765 + 0.855523i \(0.673236\pi\)
\(374\) 498618.i 3.56472i
\(375\) 18624.9 + 140816.i 0.132444 + 1.00136i
\(376\) 13387.2 0.0946921
\(377\) 114322.i 0.804356i
\(378\) −31277.3 75126.9i −0.218900 0.525789i
\(379\) 134879. 0.939004 0.469502 0.882931i \(-0.344433\pi\)
0.469502 + 0.882931i \(0.344433\pi\)
\(380\) 62927.3i 0.435785i
\(381\) 209918. 27764.5i 1.44610 0.191267i
\(382\) 347831. 2.38365
\(383\) 10393.5i 0.0708540i −0.999372 0.0354270i \(-0.988721\pi\)
0.999372 0.0354270i \(-0.0112791\pi\)
\(384\) 15190.4 + 114849.i 0.103017 + 0.778873i
\(385\) 57285.6 0.386477
\(386\) 14439.4i 0.0969112i
\(387\) 7746.15 2085.55i 0.0517207 0.0139251i
\(388\) −69447.5 −0.461310
\(389\) 22075.3i 0.145884i −0.997336 0.0729421i \(-0.976761\pi\)
0.997336 0.0729421i \(-0.0232388\pi\)
\(390\) 128531. 17000.0i 0.845041 0.111768i
\(391\) 60443.2 0.395361
\(392\) 8951.08i 0.0582510i
\(393\) −23290.5 176091.i −0.150797 1.14012i
\(394\) 12263.4 0.0789987
\(395\) 35477.1i 0.227381i
\(396\) 84054.8 + 312196.i 0.536009 + 1.99084i
\(397\) 39063.7 0.247852 0.123926 0.992291i \(-0.460452\pi\)
0.123926 + 0.992291i \(0.460452\pi\)
\(398\) 156585.i 0.988518i
\(399\) 32467.1 4294.22i 0.203938 0.0269736i
\(400\) −63297.0 −0.395607
\(401\) 42017.8i 0.261303i −0.991428 0.130652i \(-0.958293\pi\)
0.991428 0.130652i \(-0.0417069\pi\)
\(402\) 18262.2 + 138074.i 0.113006 + 0.854399i
\(403\) −96384.0 −0.593465
\(404\) 17648.6i 0.108130i
\(405\) −51895.9 89389.4i −0.316390 0.544975i
\(406\) 84119.9 0.510325
\(407\) 262413.i 1.58415i
\(408\) 98104.1 12975.6i 0.589341 0.0779485i
\(409\) 279559. 1.67120 0.835598 0.549342i \(-0.185122\pi\)
0.835598 + 0.549342i \(0.185122\pi\)
\(410\) 270313.i 1.60805i
\(411\) 16112.6 + 121822.i 0.0953855 + 0.721176i
\(412\) −49216.5 −0.289945
\(413\) 53580.9i 0.314130i
\(414\) −67629.6 + 18208.4i −0.394581 + 0.106236i
\(415\) −32504.0 −0.188730
\(416\) 216947.i 1.25363i
\(417\) −59373.0 + 7852.90i −0.341442 + 0.0451604i
\(418\) −232519. −1.33078
\(419\) 230293.i 1.31175i 0.754868 + 0.655876i \(0.227701\pi\)
−0.754868 + 0.655876i \(0.772299\pi\)
\(420\) 6999.77 + 52922.8i 0.0396813 + 0.300016i
\(421\) −50251.7 −0.283522 −0.141761 0.989901i \(-0.545276\pi\)
−0.141761 + 0.989901i \(0.545276\pi\)
\(422\) 364279.i 2.04555i
\(423\) −10802.7 40123.3i −0.0603742 0.224241i
\(424\) −110966. −0.617247
\(425\) 158765.i 0.878975i
\(426\) −95150.3 + 12584.9i −0.524314 + 0.0693477i
\(427\) −49289.8 −0.270335
\(428\) 105134.i 0.573925i
\(429\) 35150.9 + 265763.i 0.190995 + 1.44405i
\(430\) −9404.11 −0.0508605
\(431\) 89839.7i 0.483631i −0.970322 0.241815i \(-0.922257\pi\)
0.970322 0.241815i \(-0.0777428\pi\)
\(432\) 113051. 47066.3i 0.605771 0.252199i
\(433\) −204051. −1.08833 −0.544167 0.838977i \(-0.683154\pi\)
−0.544167 + 0.838977i \(0.683154\pi\)
\(434\) 70920.6i 0.376524i
\(435\) 105922. 14009.7i 0.559769 0.0740372i
\(436\) −369675. −1.94468
\(437\) 28186.3i 0.147596i
\(438\) −25116.8 189899.i −0.130923 0.989862i
\(439\) −195110. −1.01239 −0.506197 0.862418i \(-0.668949\pi\)
−0.506197 + 0.862418i \(0.668949\pi\)
\(440\) 80719.8i 0.416941i
\(441\) 26827.7 7223.01i 0.137945 0.0371399i
\(442\) 385274. 1.97208
\(443\) 302752.i 1.54269i 0.636416 + 0.771346i \(0.280416\pi\)
−0.636416 + 0.771346i \(0.719584\pi\)
\(444\) 242428. 32064.4i 1.22975 0.162651i
\(445\) 48349.1 0.244157
\(446\) 66521.5i 0.334420i
\(447\) −29973.1 226616.i −0.150009 1.13416i
\(448\) −109856. −0.547354
\(449\) 162997.i 0.808512i 0.914646 + 0.404256i \(0.132470\pi\)
−0.914646 + 0.404256i \(0.867530\pi\)
\(450\) −47827.8 177642.i −0.236187 0.877242i
\(451\) −558927. −2.74790
\(452\) 168171.i 0.823139i
\(453\) 20105.9 2659.28i 0.0979774 0.0129589i
\(454\) 440486. 2.13708
\(455\) 44263.6i 0.213808i
\(456\) −6050.88 45748.6i −0.0290997 0.220013i
\(457\) −156346. −0.748607 −0.374304 0.927306i \(-0.622118\pi\)
−0.374304 + 0.927306i \(0.622118\pi\)
\(458\) 94669.9i 0.451316i
\(459\) −118054. 283561.i −0.560346 1.34593i
\(460\) 45944.9 0.217131
\(461\) 140167.i 0.659543i 0.944061 + 0.329772i \(0.106972\pi\)
−0.944061 + 0.329772i \(0.893028\pi\)
\(462\) −195552. + 25864.5i −0.916176 + 0.121177i
\(463\) 46832.0 0.218464 0.109232 0.994016i \(-0.465161\pi\)
0.109232 + 0.994016i \(0.465161\pi\)
\(464\) 126584.i 0.587954i
\(465\) −11811.4 89302.0i −0.0546256 0.413005i
\(466\) 352545. 1.62347
\(467\) 364198.i 1.66995i −0.550285 0.834977i \(-0.685481\pi\)
0.550285 0.834977i \(-0.314519\pi\)
\(468\) −241228. + 64947.7i −1.10138 + 0.296532i
\(469\) −47550.2 −0.216176
\(470\) 48711.1i 0.220512i
\(471\) 370017. 48939.9i 1.66794 0.220608i
\(472\) −75499.5 −0.338891
\(473\) 19444.9i 0.0869128i
\(474\) 16018.0 + 121106.i 0.0712936 + 0.539026i
\(475\) 74036.4 0.328139
\(476\) 158637.i 0.700151i
\(477\) 89543.4 + 332581.i 0.393547 + 1.46171i
\(478\) 80659.7 0.353021
\(479\) 139602.i 0.608445i 0.952601 + 0.304223i \(0.0983967\pi\)
−0.952601 + 0.304223i \(0.901603\pi\)
\(480\) −201007. + 26585.9i −0.872426 + 0.115390i
\(481\) 202762. 0.876387
\(482\) 1873.58i 0.00806451i
\(483\) −3135.33 23705.1i −0.0134397 0.101613i
\(484\) 486048. 2.07486
\(485\) 53816.7i 0.228788i
\(486\) 217513. + 281712.i 0.920900 + 1.19270i
\(487\) −122130. −0.514950 −0.257475 0.966285i \(-0.582891\pi\)
−0.257475 + 0.966285i \(0.582891\pi\)
\(488\) 69453.1i 0.291643i
\(489\) −383858. + 50770.6i −1.60529 + 0.212322i
\(490\) −32569.8 −0.135651
\(491\) 239214.i 0.992257i 0.868249 + 0.496129i \(0.165246\pi\)
−0.868249 + 0.496129i \(0.834754\pi\)
\(492\) −68295.7 516360.i −0.282139 2.13315i
\(493\) 317505. 1.30634
\(494\) 179664.i 0.736218i
\(495\) −241929. + 65136.2i −0.987363 + 0.265835i
\(496\) 106722. 0.433800
\(497\) 32768.0i 0.132659i
\(498\) 110957. 14675.6i 0.447400 0.0591748i
\(499\) 28578.8 0.114774 0.0573869 0.998352i \(-0.481723\pi\)
0.0573869 + 0.998352i \(0.481723\pi\)
\(500\) 320853.i 1.28341i
\(501\) −15431.2 116670.i −0.0614787 0.464818i
\(502\) −498593. −1.97851
\(503\) 394825.i 1.56052i 0.625457 + 0.780258i \(0.284912\pi\)
−0.625457 + 0.780258i \(0.715088\pi\)
\(504\) −10177.8 37802.2i −0.0400675 0.148818i
\(505\) 13676.4 0.0536276
\(506\) 169769.i 0.663065i
\(507\) 49478.8 6544.25i 0.192488 0.0254591i
\(508\) 478301. 1.85342
\(509\) 370203.i 1.42891i −0.699681 0.714455i \(-0.746675\pi\)
0.699681 0.714455i \(-0.253325\pi\)
\(510\) 47213.6 + 356965.i 0.181521 + 1.37242i
\(511\) 65397.7 0.250450
\(512\) 310355.i 1.18391i
\(513\) −132232. + 55051.9i −0.502462 + 0.209188i
\(514\) 65394.5 0.247523
\(515\) 38139.1i 0.143799i
\(516\) 17964.0 2375.99i 0.0674690 0.00892370i
\(517\) −100720. −0.376821
\(518\) 149195.i 0.556025i
\(519\) 23709.8 + 179262.i 0.0880226 + 0.665508i
\(520\) 62370.8 0.230661
\(521\) 319934.i 1.17865i −0.807896 0.589325i \(-0.799394\pi\)
0.807896 0.589325i \(-0.200606\pi\)
\(522\) −355255. + 95648.0i −1.30376 + 0.351022i
\(523\) 365694. 1.33695 0.668474 0.743736i \(-0.266948\pi\)
0.668474 + 0.743736i \(0.266948\pi\)
\(524\) 401227.i 1.46126i
\(525\) 62265.7 8235.50i 0.225907 0.0298794i
\(526\) −241592. −0.873196
\(527\) 267685.i 0.963835i
\(528\) −38921.0 294268.i −0.139610 1.05554i
\(529\) 259261. 0.926460
\(530\) 403766.i 1.43740i
\(531\) 60923.8 + 226283.i 0.216072 + 0.802532i
\(532\) 73976.9 0.261380
\(533\) 431873.i 1.52020i
\(534\) −165046. + 21829.7i −0.578793 + 0.0765534i
\(535\) −81471.0 −0.284640
\(536\) 67001.9i 0.233216i
\(537\) 47282.6 + 357487.i 0.163966 + 1.23969i
\(538\) −453947. −1.56834
\(539\) 67344.6i 0.231806i
\(540\) −89737.0 215545.i −0.307740 0.739179i
\(541\) −398244. −1.36068 −0.680339 0.732898i \(-0.738167\pi\)
−0.680339 + 0.732898i \(0.738167\pi\)
\(542\) 681530.i 2.31999i
\(543\) 570369. 75439.1i 1.93444 0.255857i
\(544\) −602523. −2.03599
\(545\) 286471.i 0.964468i
\(546\) −19985.0 151100.i −0.0670378 0.506849i
\(547\) 310182. 1.03667 0.518336 0.855177i \(-0.326552\pi\)
0.518336 + 0.855177i \(0.326552\pi\)
\(548\) 277573.i 0.924308i
\(549\) 208161. 56044.7i 0.690644 0.185947i
\(550\) −445928. −1.47414
\(551\) 148061.i 0.487683i
\(552\) −33402.3 + 4417.91i −0.109622 + 0.0144990i
\(553\) −41706.7 −0.136382
\(554\) 319389.i 1.04064i
\(555\) 24847.5 + 187864.i 0.0806673 + 0.609897i
\(556\) −135283. −0.437615
\(557\) 446126.i 1.43796i 0.695030 + 0.718980i \(0.255391\pi\)
−0.695030 + 0.718980i \(0.744609\pi\)
\(558\) 80639.8 + 299512.i 0.258989 + 0.961935i
\(559\) 15024.8 0.0480821
\(560\) 49011.2i 0.156286i
\(561\) −738099. + 97623.7i −2.34525 + 0.310191i
\(562\) −290648. −0.920226
\(563\) 489563.i 1.54451i −0.635310 0.772257i \(-0.719128\pi\)
0.635310 0.772257i \(-0.280872\pi\)
\(564\) −12307.1 93049.5i −0.0386898 0.292520i
\(565\) 130320. 0.408238
\(566\) 385161.i 1.20229i
\(567\) −105086. + 61008.4i −0.326872 + 0.189768i
\(568\) −46172.6 −0.143116
\(569\) 444748.i 1.37369i 0.726803 + 0.686846i \(0.241005\pi\)
−0.726803 + 0.686846i \(0.758995\pi\)
\(570\) 166463. 22017.0i 0.512350 0.0677654i
\(571\) 48894.3 0.149964 0.0749818 0.997185i \(-0.476110\pi\)
0.0749818 + 0.997185i \(0.476110\pi\)
\(572\) 605547.i 1.85079i
\(573\) −68101.4 514890.i −0.207418 1.56821i
\(574\) 317778. 0.964495
\(575\) 54055.9i 0.163496i
\(576\) 463945. 124911.i 1.39837 0.376493i
\(577\) −80474.7 −0.241717 −0.120859 0.992670i \(-0.538565\pi\)
−0.120859 + 0.992670i \(0.538565\pi\)
\(578\) 566598.i 1.69597i
\(579\) 21374.4 2827.06i 0.0637584 0.00843293i
\(580\) 241346. 0.717438
\(581\) 38211.5i 0.113199i
\(582\) 24298.2 + 183710.i 0.0717347 + 0.542360i
\(583\) 834868. 2.45630
\(584\) 92150.4i 0.270191i
\(585\) −50329.7 186934.i −0.147066 0.546232i
\(586\) 460229. 1.34023
\(587\) 54845.0i 0.159170i 0.996828 + 0.0795849i \(0.0253595\pi\)
−0.996828 + 0.0795849i \(0.974641\pi\)
\(588\) 62215.7 8228.89i 0.179947 0.0238005i
\(589\) −124829. −0.359819
\(590\) 274715.i 0.789185i
\(591\) −2401.04 18153.4i −0.00687424 0.0519737i
\(592\) −224509. −0.640605
\(593\) 192797.i 0.548265i 0.961692 + 0.274133i \(0.0883907\pi\)
−0.961692 + 0.274133i \(0.911609\pi\)
\(594\) 796447. 331582.i 2.25727 0.939763i
\(595\) −122932. −0.347242
\(596\) 516349.i 1.45362i
\(597\) −231791. + 30657.6i −0.650352 + 0.0860180i
\(598\) −131177. −0.366823
\(599\) 466565.i 1.30035i 0.759786 + 0.650173i \(0.225304\pi\)
−0.759786 + 0.650173i \(0.774696\pi\)
\(600\) −11604.4 87737.2i −0.0322346 0.243714i
\(601\) 125070. 0.346261 0.173130 0.984899i \(-0.444612\pi\)
0.173130 + 0.984899i \(0.444612\pi\)
\(602\) 11055.4i 0.0305058i
\(603\) 200814. 54066.7i 0.552280 0.148695i
\(604\) 45811.6 0.125575
\(605\) 376652.i 1.02903i
\(606\) −46686.2 + 6174.89i −0.127129 + 0.0168145i
\(607\) −385152. −1.04533 −0.522667 0.852537i \(-0.675063\pi\)
−0.522667 + 0.852537i \(0.675063\pi\)
\(608\) 280973.i 0.760076i
\(609\) −16469.7 124522.i −0.0444070 0.335746i
\(610\) −252715. −0.679158
\(611\) 77824.8i 0.208466i
\(612\) −180378. 669958.i −0.481593 1.78873i
\(613\) −135252. −0.359933 −0.179967 0.983673i \(-0.557599\pi\)
−0.179967 + 0.983673i \(0.557599\pi\)
\(614\) 533464.i 1.41504i
\(615\) 400141. 52924.1i 1.05794 0.139928i
\(616\) −94893.7 −0.250078
\(617\) 378025.i 0.993003i −0.868036 0.496502i \(-0.834618\pi\)
0.868036 0.496502i \(-0.165382\pi\)
\(618\) 17219.8 + 130193.i 0.0450871 + 0.340888i
\(619\) −286244. −0.747059 −0.373529 0.927618i \(-0.621853\pi\)
−0.373529 + 0.927618i \(0.621853\pi\)
\(620\) 203476.i 0.529335i
\(621\) 40194.8 + 96546.3i 0.104229 + 0.250353i
\(622\) −141656. −0.366146
\(623\) 56838.9i 0.146443i
\(624\) 227376. 30073.6i 0.583950 0.0772354i
\(625\) −13129.4 −0.0336112
\(626\) 956713.i 2.44137i
\(627\) 45524.6 + 344195.i 0.115801 + 0.875528i
\(628\) 843091. 2.13774
\(629\) 563125.i 1.42332i
\(630\) 137549. 37033.2i 0.346557 0.0933062i
\(631\) −104005. −0.261214 −0.130607 0.991434i \(-0.541693\pi\)
−0.130607 + 0.991434i \(0.541693\pi\)
\(632\) 58767.9i 0.147132i
\(633\) −539238. + 71321.7i −1.34578 + 0.177998i
\(634\) −1.04385e6 −2.59694
\(635\) 370648.i 0.919210i
\(636\) 102013. + 771286.i 0.252198 + 1.90678i
\(637\) 52036.0 0.128241
\(638\) 891785.i 2.19088i
\(639\) 37258.7 + 138386.i 0.0912485 + 0.338914i
\(640\) −202788. −0.495088
\(641\) 313789.i 0.763699i −0.924224 0.381850i \(-0.875287\pi\)
0.924224 0.381850i \(-0.124713\pi\)
\(642\) 278112. 36784.2i 0.674761 0.0892465i
\(643\) −17439.4 −0.0421803 −0.0210902 0.999778i \(-0.506714\pi\)
−0.0210902 + 0.999778i \(0.506714\pi\)
\(644\) 54012.5i 0.130234i
\(645\) 1841.22 + 13920.8i 0.00442573 + 0.0334614i
\(646\) 498976. 1.19568
\(647\) 470170.i 1.12317i 0.827419 + 0.561586i \(0.189808\pi\)
−0.827419 + 0.561586i \(0.810192\pi\)
\(648\) 85965.5 + 148074.i 0.204727 + 0.352637i
\(649\) 568030. 1.34860
\(650\) 344561.i 0.815529i
\(651\) −104983. + 13885.4i −0.247717 + 0.0327641i
\(652\) −874629. −2.05745
\(653\) 426505.i 1.00022i −0.865961 0.500112i \(-0.833292\pi\)
0.865961 0.500112i \(-0.166708\pi\)
\(654\) 129342. + 977908.i 0.302401 + 2.28635i
\(655\) 310921. 0.724716
\(656\) 478194.i 1.11121i
\(657\) −276188. + 74360.1i −0.639843 + 0.172270i
\(658\) 57264.5 0.132262
\(659\) 201868.i 0.464833i −0.972616 0.232416i \(-0.925337\pi\)
0.972616 0.232416i \(-0.0746632\pi\)
\(660\) −561054. + 74207.1i −1.28800 + 0.170356i
\(661\) −64778.0 −0.148260 −0.0741301 0.997249i \(-0.523618\pi\)
−0.0741301 + 0.997249i \(0.523618\pi\)
\(662\) 506944.i 1.15676i
\(663\) −75432.2 570316.i −0.171605 1.29744i
\(664\) 53843.0 0.122122
\(665\) 57326.7i 0.129632i
\(666\) −169641. 630079.i −0.382457 1.42052i
\(667\) −108103. −0.242989
\(668\) 265835.i 0.595743i
\(669\) −98470.9 + 13024.1i −0.220017 + 0.0291002i
\(670\) −243796. −0.543096
\(671\) 522539.i 1.16058i
\(672\) 31254.3 + 236302.i 0.0692103 + 0.523275i
\(673\) −417567. −0.921925 −0.460963 0.887420i \(-0.652496\pi\)
−0.460963 + 0.887420i \(0.652496\pi\)
\(674\) 18549.9i 0.0408340i
\(675\) −253596. + 105579.i −0.556590 + 0.231724i
\(676\) 112738. 0.246705
\(677\) 291796.i 0.636652i −0.947981 0.318326i \(-0.896879\pi\)
0.947981 0.318326i \(-0.103121\pi\)
\(678\) −444864. + 58839.4i −0.967761 + 0.128000i
\(679\) −63266.5 −0.137225
\(680\) 173221.i 0.374613i
\(681\) −86242.2 652047.i −0.185963 1.40600i
\(682\) 751855. 1.61646
\(683\) 493655.i 1.05823i −0.848549 0.529117i \(-0.822523\pi\)
0.848549 0.529117i \(-0.177477\pi\)
\(684\) −312419. + 84115.0i −0.667768 + 0.179788i
\(685\) −215099. −0.458413
\(686\) 38288.8i 0.0813623i
\(687\) −140139. + 18535.3i −0.296923 + 0.0392722i
\(688\) −16636.2 −0.0351462
\(689\) 645089.i 1.35888i
\(690\) −16075.2 121539.i −0.0337643 0.255280i
\(691\) −56687.4 −0.118722 −0.0593609 0.998237i \(-0.518906\pi\)
−0.0593609 + 0.998237i \(0.518906\pi\)
\(692\) 408452.i 0.852959i
\(693\) 76573.8 + 284410.i 0.159446 + 0.592213i
\(694\) 617690. 1.28248
\(695\) 104834.i 0.217036i
\(696\) −175460. + 23207.1i −0.362210 + 0.0479073i
\(697\) 1.19943e6 2.46894
\(698\) 490944.i 1.00768i
\(699\) −69024.3 521868.i −0.141269 1.06809i
\(700\) 141874. 0.289538
\(701\) 441765.i 0.898992i 0.893282 + 0.449496i \(0.148396\pi\)
−0.893282 + 0.449496i \(0.851604\pi\)
\(702\) 256208. + 615401.i 0.519899 + 1.24877i
\(703\) 262601. 0.531355
\(704\) 1.16463e6i 2.34985i
\(705\) 72106.5 9537.08i 0.145076 0.0191883i
\(706\) 1.19585e6 2.39921
\(707\) 16077.9i 0.0321654i
\(708\) 69408.0 + 524770.i 0.138466 + 1.04689i
\(709\) −590139. −1.17398 −0.586992 0.809593i \(-0.699688\pi\)
−0.586992 + 0.809593i \(0.699688\pi\)
\(710\) 168005.i 0.333278i
\(711\) 176136. 47422.4i 0.348424 0.0938089i
\(712\) −80090.4 −0.157987
\(713\) 91140.8i 0.179281i
\(714\) 419646. 55504.0i 0.823165 0.108875i
\(715\) −469255. −0.917902
\(716\) 814542.i 1.58887i
\(717\) −15792.2 119400.i −0.0307189 0.232255i
\(718\) −122300. −0.237234
\(719\) 918202.i 1.77615i 0.459695 + 0.888077i \(0.347959\pi\)
−0.459695 + 0.888077i \(0.652041\pi\)
\(720\) 55727.8 + 206984.i 0.107500 + 0.399274i
\(721\) −44836.1 −0.0862497
\(722\) 552812.i 1.06048i
\(723\) 2773.44 366.825i 0.00530569 0.000701750i
\(724\) 1.29960e6 2.47931
\(725\) 283953.i 0.540220i
\(726\) −170058. 1.28575e6i −0.322645 2.43940i
\(727\) −242969. −0.459708 −0.229854 0.973225i \(-0.573825\pi\)
−0.229854 + 0.973225i \(0.573825\pi\)
\(728\) 73322.7i 0.138349i
\(729\) 374428. 377138.i 0.704553 0.709651i
\(730\) 335302. 0.629202
\(731\) 41727.9i 0.0780893i
\(732\) 482744. 63849.5i 0.900937 0.119161i
\(733\) −145455. −0.270721 −0.135361 0.990796i \(-0.543219\pi\)
−0.135361 + 0.990796i \(0.543219\pi\)
\(734\) 1.18589e6i 2.20116i
\(735\) 6376.78 + 48212.6i 0.0118039 + 0.0892454i
\(736\) 205146. 0.378710
\(737\) 504097.i 0.928067i
\(738\) −1.34204e6 + 361327.i −2.46407 + 0.663419i
\(739\) −971847. −1.77955 −0.889773 0.456404i \(-0.849137\pi\)
−0.889773 + 0.456404i \(0.849137\pi\)
\(740\) 428051.i 0.781685i
\(741\) −265954. + 35176.1i −0.484362 + 0.0640636i
\(742\) −474665. −0.862143
\(743\) 26014.8i 0.0471241i −0.999722 0.0235620i \(-0.992499\pi\)
0.999722 0.0235620i \(-0.00750072\pi\)
\(744\) 19565.6 + 147929.i 0.0353466 + 0.267244i
\(745\) 400133. 0.720927
\(746\) 868381.i 1.56039i
\(747\) −43448.2 161375.i −0.0778629 0.289198i
\(748\) −1.68177e6 −3.00583
\(749\) 95776.8i 0.170725i
\(750\) 848757. 112260.i 1.50890 0.199573i
\(751\) 424520. 0.752694 0.376347 0.926479i \(-0.377180\pi\)
0.376347 + 0.926479i \(0.377180\pi\)
\(752\) 86171.9i 0.152381i
\(753\) 97618.7 + 738061.i 0.172164 + 1.30167i
\(754\) −689067. −1.21205
\(755\) 35500.6i 0.0622790i
\(756\) −253393. + 105494.i −0.443354 + 0.184580i
\(757\) 241891. 0.422112 0.211056 0.977474i \(-0.432310\pi\)
0.211056 + 0.977474i \(0.432310\pi\)
\(758\) 812974.i 1.41494i
\(759\) 251306. 33238.7i 0.436234 0.0576980i
\(760\) 80777.6 0.139850
\(761\) 57363.8i 0.0990531i −0.998773 0.0495266i \(-0.984229\pi\)
0.998773 0.0495266i \(-0.0157712\pi\)
\(762\) −167348. 1.26526e6i −0.288211 2.17906i
\(763\) −336774. −0.578481
\(764\) 1.17319e6i 2.00993i
\(765\) 519168. 139779.i 0.887125 0.238847i
\(766\) −62645.8 −0.106766
\(767\) 438907.i 0.746074i
\(768\) −154543. + 20440.4i −0.262015 + 0.0346551i
\(769\) 919966. 1.55568 0.777838 0.628465i \(-0.216316\pi\)
0.777838 + 0.628465i \(0.216316\pi\)
\(770\) 345284.i 0.582364i
\(771\) −12803.5 96802.7i −0.0215387 0.162847i
\(772\) 48702.1 0.0817171
\(773\) 620899.i 1.03911i −0.854437 0.519556i \(-0.826097\pi\)
0.854437 0.519556i \(-0.173903\pi\)
\(774\) −12570.5 46689.2i −0.0209831 0.0779354i
\(775\) −239398. −0.398581
\(776\) 89147.3i 0.148042i
\(777\) 220851. 29210.6i 0.365812 0.0483837i
\(778\) −133057. −0.219826
\(779\) 559327.i 0.921703i
\(780\) −57338.6 433517.i −0.0942449 0.712552i
\(781\) 347386. 0.569521
\(782\) 364316.i 0.595750i
\(783\) 211141. + 507153.i 0.344389 + 0.827209i
\(784\) −57617.2 −0.0937389
\(785\) 653334.i 1.06022i
\(786\) −1.06137e6 + 140381.i −1.71800 + 0.227229i
\(787\) −559334. −0.903071 −0.451536 0.892253i \(-0.649124\pi\)
−0.451536 + 0.892253i \(0.649124\pi\)
\(788\) 41363.0i 0.0666130i
\(789\) 47301.0 + 357626.i 0.0759830 + 0.574481i
\(790\) −213835. −0.342630
\(791\) 153203.i 0.244858i
\(792\) 400755. 107898.i 0.638893 0.172014i
\(793\) 403757. 0.642058
\(794\) 235453.i 0.373476i
\(795\) −597690. + 79052.7i −0.945674 + 0.125078i
\(796\) −528141. −0.833535
\(797\) 280663.i 0.441843i −0.975292 0.220922i \(-0.929093\pi\)
0.975292 0.220922i \(-0.0709065\pi\)
\(798\) −25883.0 195692.i −0.0406452 0.307304i
\(799\) 216141. 0.338566
\(800\) 538853.i 0.841957i
\(801\) 64628.4 + 240042.i 0.100730 + 0.374130i
\(802\) −253258. −0.393745
\(803\) 693305.i 1.07521i
\(804\) 465706. 61596.0i 0.720443 0.0952885i
\(805\) 41855.7 0.0645897
\(806\) 580946.i 0.894263i
\(807\) 88877.5 + 671972.i 0.136472 + 1.03182i
\(808\) −22654.9 −0.0347008
\(809\) 572672.i 0.875002i 0.899218 + 0.437501i \(0.144136\pi\)
−0.899218 + 0.437501i \(0.855864\pi\)
\(810\) −538787. + 312797.i −0.821196 + 0.476753i
\(811\) −980201. −1.49030 −0.745149 0.666898i \(-0.767622\pi\)
−0.745149 + 0.666898i \(0.767622\pi\)
\(812\) 283725.i 0.430314i
\(813\) 1.00886e6 133436.i 1.52634 0.201879i
\(814\) −1.58167e6 −2.38708
\(815\) 677773.i 1.02040i
\(816\) 83522.8 + 631486.i 0.125437 + 0.948383i
\(817\) 19458.8 0.0291523
\(818\) 1.68502e6i 2.51824i
\(819\) −219759. + 59167.2i −0.327626 + 0.0882091i
\(820\) 911728. 1.35593
\(821\) 263704.i 0.391228i 0.980681 + 0.195614i \(0.0626700\pi\)
−0.980681 + 0.195614i \(0.937330\pi\)
\(822\) 734270. 97117.3i 1.08671 0.143732i
\(823\) −148647. −0.219461 −0.109730 0.993961i \(-0.534999\pi\)
−0.109730 + 0.993961i \(0.534999\pi\)
\(824\) 63177.5i 0.0930482i
\(825\) 87307.5 + 660101.i 0.128276 + 0.969846i
\(826\) −322954. −0.473348
\(827\) 30591.1i 0.0447285i −0.999750 0.0223642i \(-0.992881\pi\)
0.999750 0.0223642i \(-0.00711935\pi\)
\(828\) 61414.6 + 228106.i 0.0895800 + 0.332717i
\(829\) 285462. 0.415374 0.207687 0.978195i \(-0.433407\pi\)
0.207687 + 0.978195i \(0.433407\pi\)
\(830\) 195915.i 0.284388i
\(831\) 472788. 62532.7i 0.684643 0.0905535i
\(832\) 899886. 1.29999
\(833\) 144518.i 0.208273i
\(834\) 47332.6 + 357865.i 0.0680500 + 0.514502i
\(835\) 206002. 0.295460
\(836\) 784256.i 1.12214i
\(837\) 427575. 178011.i 0.610326 0.254095i
\(838\) 1.38807e6 1.97662
\(839\) 1.03015e6i 1.46345i −0.681602 0.731723i \(-0.738716\pi\)
0.681602 0.731723i \(-0.261284\pi\)
\(840\) 67935.2 8985.37i 0.0962801 0.0127344i
\(841\) 139420. 0.197121
\(842\) 302887.i 0.427225i
\(843\) 56905.5 + 430243.i 0.0800754 + 0.605422i
\(844\) −1.22867e6 −1.72484
\(845\) 87363.9i 0.122354i
\(846\) −241839. + 65112.2i −0.337898 + 0.0909750i
\(847\) 442789. 0.617206
\(848\) 714278.i 0.993289i
\(849\) −570149. + 75410.1i −0.790994 + 0.104620i
\(850\) 956941. 1.32449
\(851\) 191732.i 0.264749i
\(852\) 42447.3 + 320929.i 0.0584751 + 0.442110i
\(853\) −1.02297e6 −1.40593 −0.702967 0.711223i \(-0.748142\pi\)
−0.702967 + 0.711223i \(0.748142\pi\)
\(854\) 297090.i 0.407354i
\(855\) −65182.9 242102.i −0.0891665 0.331181i
\(856\) 134957. 0.184182
\(857\) 838435.i 1.14158i −0.821095 0.570792i \(-0.806636\pi\)
0.821095 0.570792i \(-0.193364\pi\)
\(858\) 1.60186e6 211869.i 2.17596 0.287801i
\(859\) 272504. 0.369306 0.184653 0.982804i \(-0.440884\pi\)
0.184653 + 0.982804i \(0.440884\pi\)
\(860\) 31718.8i 0.0428864i
\(861\) −62217.3 470403.i −0.0839275 0.634547i
\(862\) −541501. −0.728760
\(863\) 600703.i 0.806563i 0.915076 + 0.403281i \(0.132130\pi\)
−0.915076 + 0.403281i \(0.867870\pi\)
\(864\) −400679. 962415.i −0.536747 1.28924i
\(865\) −316520. −0.423028
\(866\) 1.22990e6i 1.63996i
\(867\) 838727. 110933.i 1.11579 0.147579i
\(868\) −239206. −0.317491
\(869\) 442148.i 0.585501i
\(870\) −84442.1 638437.i −0.111563 0.843489i
\(871\) 389507. 0.513428
\(872\) 474540.i 0.624079i
\(873\) 267187. 71936.8i 0.350580 0.0943893i
\(874\) −169890. −0.222405
\(875\) 292296.i 0.381775i
\(876\) −640504. + 84715.5i −0.834667 + 0.110396i
\(877\) −446820. −0.580943 −0.290472 0.956884i \(-0.593812\pi\)
−0.290472 + 0.956884i \(0.593812\pi\)
\(878\) 1.17600e6i 1.52553i
\(879\) −90107.5 681271.i −0.116623 0.881744i
\(880\) 519585. 0.670952
\(881\) 437687.i 0.563913i −0.959427 0.281956i \(-0.909017\pi\)
0.959427 0.281956i \(-0.0909833\pi\)
\(882\) −43536.0 161701.i −0.0559644 0.207862i
\(883\) −80288.7 −0.102975 −0.0514876 0.998674i \(-0.516396\pi\)
−0.0514876 + 0.998674i \(0.516396\pi\)
\(884\) 1.29948e6i 1.66289i
\(885\) −406658. + 53786.1i −0.519210 + 0.0686726i
\(886\) 1.82481e6 2.32461
\(887\) 1.44826e6i 1.84076i −0.391022 0.920381i \(-0.627878\pi\)
0.391022 0.920381i \(-0.372122\pi\)
\(888\) −41160.0 311196.i −0.0521974 0.394646i
\(889\) 435732. 0.551335
\(890\) 291420.i 0.367908i
\(891\) −646772. 1.11405e6i −0.814697 1.40330i
\(892\) −224368. −0.281988
\(893\) 100792.i 0.126393i
\(894\) −1.36591e6 + 180660.i −1.70902 + 0.226041i
\(895\) −631210. −0.788003
\(896\) 238396.i 0.296950i
\(897\) 25683.0 + 194180.i 0.0319198 + 0.241335i
\(898\) 982448. 1.21831
\(899\) 478758.i 0.592375i
\(900\) −599161. + 161317.i −0.739705 + 0.199156i
\(901\) −1.79159e6 −2.20693
\(902\) 3.36888e6i 4.14069i
\(903\) 16365.2 2164.52i 0.0200699 0.00265452i
\(904\) −215875. −0.264159
\(905\) 1.00709e6i 1.22962i
\(906\) −16028.5 121186.i −0.0195271 0.147637i
\(907\) −903376. −1.09813 −0.549065 0.835779i \(-0.685016\pi\)
−0.549065 + 0.835779i \(0.685016\pi\)
\(908\) 1.48570e6i 1.80202i
\(909\) 18281.2 + 67900.0i 0.0221247 + 0.0821754i
\(910\) 266795. 0.322177
\(911\) 1.15959e6i 1.39723i 0.715499 + 0.698614i \(0.246200\pi\)
−0.715499 + 0.698614i \(0.753800\pi\)
\(912\) 294479. 38948.9i 0.354050 0.0468280i
\(913\) −405094. −0.485976
\(914\) 942360.i 1.12804i
\(915\) 49478.6 + 374091.i 0.0590984 + 0.446822i
\(916\) −319309. −0.380557
\(917\) 365517.i 0.434680i
\(918\) −1.70914e6 + 711561.i −2.02811 + 0.844358i
\(919\) 1.39808e6 1.65539 0.827697 0.561176i \(-0.189651\pi\)
0.827697 + 0.561176i \(0.189651\pi\)
\(920\) 58977.9i 0.0696809i
\(921\) −789681. + 104446.i −0.930963 + 0.123133i
\(922\) 844842. 0.993834
\(923\) 268419.i 0.315072i
\(924\) 87237.4 + 659571.i 0.102178 + 0.772535i
\(925\) 503618. 0.588597
\(926\) 282276.i 0.329194i
\(927\) 189352. 50980.7i 0.220349 0.0593261i
\(928\) 1.07762e6 1.25132
\(929\) 1.23771e6i 1.43413i −0.697006 0.717066i \(-0.745485\pi\)
0.697006 0.717066i \(-0.254515\pi\)
\(930\) −538260. + 71192.3i −0.622338 + 0.0823127i
\(931\) 67392.9 0.0777525
\(932\) 1.18909e6i 1.36893i
\(933\) 27734.6 + 209691.i 0.0318609 + 0.240889i
\(934\) −2.19517e6 −2.51637
\(935\) 1.30325e6i 1.49075i
\(936\) 83371.2 + 309656.i 0.0951621 + 0.353450i
\(937\) 1.41105e6 1.60718 0.803589 0.595185i \(-0.202921\pi\)
0.803589 + 0.595185i \(0.202921\pi\)
\(938\) 286605.i 0.325745i
\(939\) −1.41621e6 + 187313.i −1.60619 + 0.212441i
\(940\) 164296. 0.185939
\(941\) 1.68557e6i 1.90356i 0.306775 + 0.951782i \(0.400750\pi\)
−0.306775 + 0.951782i \(0.599250\pi\)
\(942\) −294980. 2.23024e6i −0.332423 2.51334i
\(943\) −408380. −0.459241
\(944\) 485983.i 0.545352i
\(945\) −81750.3 196361.i −0.0915431 0.219883i
\(946\) −117202. −0.130965
\(947\) 1.28636e6i 1.43437i 0.696883 + 0.717185i \(0.254570\pi\)
−0.696883 + 0.717185i \(0.745430\pi\)
\(948\) 408475. 54026.4i 0.454515 0.0601159i
\(949\) −535705. −0.594830
\(950\) 446247.i 0.494457i
\(951\) 204375. + 1.54520e6i 0.225978 + 1.70854i
\(952\) 203637. 0.224690
\(953\) 261159.i 0.287553i −0.989610 0.143777i \(-0.954075\pi\)
0.989610 0.143777i \(-0.0459247\pi\)
\(954\) 2.00460e6 539715.i 2.20258 0.593017i
\(955\) 909134. 0.996830
\(956\) 272054.i 0.297673i
\(957\) 1.32010e6 174601.i 1.44139 0.190644i
\(958\) 841440. 0.916837
\(959\) 252869.i 0.274953i
\(960\) 110277. + 833766.i 0.119658 + 0.904694i
\(961\) −519885. −0.562938
\(962\) 1.22213e6i 1.32059i
\(963\) −108902. 404484.i −0.117432 0.436163i
\(964\) 6319.33 0.00680013
\(965\) 37740.5i 0.0405278i
\(966\) −142880. + 18897.9i −0.153115 + 0.0202516i
\(967\) −522045. −0.558284 −0.279142 0.960250i \(-0.590050\pi\)
−0.279142 + 0.960250i \(0.590050\pi\)
\(968\) 623924.i 0.665857i
\(969\) −97693.7 738628.i −0.104044 0.786644i
\(970\) −324375. −0.344750
\(971\) 527907.i 0.559911i −0.960013 0.279956i \(-0.909680\pi\)
0.960013 0.279956i \(-0.0903198\pi\)
\(972\) 950177. 733642.i 1.00571 0.776518i
\(973\) −123242. −0.130177
\(974\) 736129.i 0.775954i
\(975\) −510049. + 67461.1i −0.536541 + 0.0709649i
\(976\) −447063. −0.469320
\(977\) 730919.i 0.765737i −0.923803 0.382869i \(-0.874936\pi\)
0.923803 0.382869i \(-0.125064\pi\)
\(978\) 306015. + 2.31367e6i 0.319937 + 2.41893i
\(979\) 602570. 0.628698
\(980\) 109853.i 0.114383i
\(981\) 1.42226e6 382926.i 1.47789 0.397903i
\(982\) 1.44184e6 1.49518
\(983\) 163325.i 0.169023i −0.996423 0.0845115i \(-0.973067\pi\)
0.996423 0.0845115i \(-0.0269330\pi\)
\(984\) −662833. + 87668.8i −0.684564 + 0.0905430i
\(985\) 32053.2 0.0330369
\(986\) 1.91373e6i 1.96846i
\(987\) −11211.7 84767.9i −0.0115090 0.0870156i
\(988\) −605981. −0.620791
\(989\) 14207.4i 0.0145252i
\(990\) 392603. + 1.45820e6i 0.400574 + 1.48781i
\(991\) 1.24036e6 1.26299 0.631494 0.775381i \(-0.282442\pi\)
0.631494 + 0.775381i \(0.282442\pi\)
\(992\) 908530.i 0.923243i
\(993\) −750423. + 99253.8i −0.761040 + 0.100658i
\(994\) −197506. −0.199898
\(995\) 409270.i 0.413394i
\(996\) −49498.8 374243.i −0.0498972 0.377255i
\(997\) −881732. −0.887046 −0.443523 0.896263i \(-0.646272\pi\)
−0.443523 + 0.896263i \(0.646272\pi\)
\(998\) 172256.i 0.172947i
\(999\) −899485. + 374480.i −0.901286 + 0.375230i
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 21.5.b.a.8.1 8
3.2 odd 2 inner 21.5.b.a.8.8 yes 8
4.3 odd 2 336.5.d.b.113.7 8
7.2 even 3 147.5.h.e.116.1 16
7.3 odd 6 147.5.h.c.128.8 16
7.4 even 3 147.5.h.e.128.8 16
7.5 odd 6 147.5.h.c.116.1 16
7.6 odd 2 147.5.b.e.50.1 8
12.11 even 2 336.5.d.b.113.8 8
21.2 odd 6 147.5.h.e.116.8 16
21.5 even 6 147.5.h.c.116.8 16
21.11 odd 6 147.5.h.e.128.1 16
21.17 even 6 147.5.h.c.128.1 16
21.20 even 2 147.5.b.e.50.8 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
21.5.b.a.8.1 8 1.1 even 1 trivial
21.5.b.a.8.8 yes 8 3.2 odd 2 inner
147.5.b.e.50.1 8 7.6 odd 2
147.5.b.e.50.8 8 21.20 even 2
147.5.h.c.116.1 16 7.5 odd 6
147.5.h.c.116.8 16 21.5 even 6
147.5.h.c.128.1 16 21.17 even 6
147.5.h.c.128.8 16 7.3 odd 6
147.5.h.e.116.1 16 7.2 even 3
147.5.h.e.116.8 16 21.2 odd 6
147.5.h.e.128.1 16 21.11 odd 6
147.5.h.e.128.8 16 7.4 even 3
336.5.d.b.113.7 8 4.3 odd 2
336.5.d.b.113.8 8 12.11 even 2