Properties

Label 294.3.h.e.275.3
Level $294$
Weight $3$
Character 294.275
Analytic conductor $8.011$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [294,3,Mod(263,294)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(294, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 4]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("294.263");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 294.h (of order \(6\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(8.01091977219\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{24})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - x^{4} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 275.3
Root \(0.258819 + 0.965926i\) of defining polynomial
Character \(\chi\) \(=\) 294.275
Dual form 294.3.h.e.263.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.22474 + 0.707107i) q^{2} +(-2.28024 - 1.94949i) q^{3} +(1.00000 + 1.73205i) q^{4} +(-3.46410 - 2.00000i) q^{5} +(-1.41421 - 4.00000i) q^{6} +2.82843i q^{8} +(1.39898 + 8.89060i) q^{9} +O(q^{10})\) \(q+(1.22474 + 0.707107i) q^{2} +(-2.28024 - 1.94949i) q^{3} +(1.00000 + 1.73205i) q^{4} +(-3.46410 - 2.00000i) q^{5} +(-1.41421 - 4.00000i) q^{6} +2.82843i q^{8} +(1.39898 + 8.89060i) q^{9} +(-2.82843 - 4.89898i) q^{10} +(-8.57321 + 4.94975i) q^{11} +(1.09638 - 5.89898i) q^{12} +12.7279 q^{13} +(4.00000 + 11.3137i) q^{15} +(-2.00000 + 3.46410i) q^{16} +(-27.7128 + 16.0000i) q^{17} +(-4.57321 + 11.8780i) q^{18} +(-14.1421 + 24.4949i) q^{19} -8.00000i q^{20} -14.0000 q^{22} +(-1.22474 - 0.707107i) q^{23} +(5.51399 - 6.44949i) q^{24} +(-4.50000 - 7.79423i) q^{25} +(15.5885 + 9.00000i) q^{26} +(14.1421 - 23.0000i) q^{27} +56.5685i q^{29} +(-3.10102 + 16.6848i) q^{30} +(-4.89898 + 2.82843i) q^{32} +(29.1985 + 5.42679i) q^{33} -45.2548 q^{34} +(-14.0000 + 11.3137i) q^{36} +(25.0000 - 43.3013i) q^{37} +(-34.6410 + 20.0000i) q^{38} +(-29.0227 - 24.8130i) q^{39} +(5.65685 - 9.79796i) q^{40} +16.0000i q^{41} -52.0000 q^{43} +(-17.1464 - 9.89949i) q^{44} +(12.9350 - 33.5959i) q^{45} +(-1.00000 - 1.73205i) q^{46} +(-29.4449 - 17.0000i) q^{47} +(11.3137 - 4.00000i) q^{48} -12.7279i q^{50} +(94.3837 + 17.5420i) q^{51} +(12.7279 + 22.0454i) q^{52} +(39.1918 - 22.6274i) q^{53} +(33.5840 - 18.1691i) q^{54} +39.5980 q^{55} +(80.0000 - 28.2843i) q^{57} +(-40.0000 + 69.2820i) q^{58} +(-27.7128 + 16.0000i) q^{59} +(-15.5959 + 18.2419i) q^{60} +(16.2635 - 28.1691i) q^{61} -8.00000 q^{64} +(-44.0908 - 25.4558i) q^{65} +(31.9233 + 27.2929i) q^{66} +(6.00000 + 10.3923i) q^{67} +(-55.4256 - 32.0000i) q^{68} +(1.41421 + 4.00000i) q^{69} -89.0955i q^{71} +(-25.1464 + 3.95691i) q^{72} +(16.2635 + 28.1691i) q^{73} +(61.2372 - 35.3553i) q^{74} +(-4.93369 + 26.5454i) q^{75} -56.5685 q^{76} +(-18.0000 - 50.9117i) q^{78} +(20.0000 - 34.6410i) q^{79} +(13.8564 - 8.00000i) q^{80} +(-77.0857 + 24.8755i) q^{81} +(-11.3137 + 19.5959i) q^{82} +62.0000i q^{83} +128.000 q^{85} +(-63.6867 - 36.7696i) q^{86} +(110.280 - 128.990i) q^{87} +(-14.0000 - 24.2487i) q^{88} +(-48.4974 - 28.0000i) q^{89} +(39.5980 - 32.0000i) q^{90} -2.82843i q^{92} +(-24.0416 - 41.6413i) q^{94} +(97.9796 - 56.5685i) q^{95} +(16.6848 + 3.10102i) q^{96} +24.0416 q^{97} +(-56.0000 - 69.2965i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 8 q^{4} - 28 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 8 q^{4} - 28 q^{9} + 32 q^{15} - 16 q^{16} + 32 q^{18} - 112 q^{22} - 36 q^{25} - 64 q^{30} - 112 q^{36} + 200 q^{37} - 144 q^{39} - 416 q^{43} - 8 q^{46} + 128 q^{51} + 640 q^{57} - 320 q^{58} + 32 q^{60} - 64 q^{64} + 48 q^{67} - 64 q^{72} - 144 q^{78} + 160 q^{79} - 68 q^{81} + 1024 q^{85} - 112 q^{88} - 448 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/294\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(199\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.22474 + 0.707107i 0.612372 + 0.353553i
\(3\) −2.28024 1.94949i −0.760080 0.649830i
\(4\) 1.00000 + 1.73205i 0.250000 + 0.433013i
\(5\) −3.46410 2.00000i −0.692820 0.400000i 0.111847 0.993725i \(-0.464323\pi\)
−0.804668 + 0.593725i \(0.797657\pi\)
\(6\) −1.41421 4.00000i −0.235702 0.666667i
\(7\) 0 0
\(8\) 2.82843i 0.353553i
\(9\) 1.39898 + 8.89060i 0.155442 + 0.987845i
\(10\) −2.82843 4.89898i −0.282843 0.489898i
\(11\) −8.57321 + 4.94975i −0.779383 + 0.449977i −0.836212 0.548407i \(-0.815235\pi\)
0.0568285 + 0.998384i \(0.481901\pi\)
\(12\) 1.09638 5.89898i 0.0913647 0.491582i
\(13\) 12.7279 0.979071 0.489535 0.871983i \(-0.337166\pi\)
0.489535 + 0.871983i \(0.337166\pi\)
\(14\) 0 0
\(15\) 4.00000 + 11.3137i 0.266667 + 0.754247i
\(16\) −2.00000 + 3.46410i −0.125000 + 0.216506i
\(17\) −27.7128 + 16.0000i −1.63017 + 0.941176i −0.646125 + 0.763232i \(0.723612\pi\)
−0.984040 + 0.177945i \(0.943055\pi\)
\(18\) −4.57321 + 11.8780i −0.254067 + 0.659886i
\(19\) −14.1421 + 24.4949i −0.744323 + 1.28921i 0.206188 + 0.978512i \(0.433894\pi\)
−0.950510 + 0.310693i \(0.899439\pi\)
\(20\) 8.00000i 0.400000i
\(21\) 0 0
\(22\) −14.0000 −0.636364
\(23\) −1.22474 0.707107i −0.0532498 0.0307438i 0.473139 0.880988i \(-0.343121\pi\)
−0.526389 + 0.850244i \(0.676454\pi\)
\(24\) 5.51399 6.44949i 0.229750 0.268729i
\(25\) −4.50000 7.79423i −0.180000 0.311769i
\(26\) 15.5885 + 9.00000i 0.599556 + 0.346154i
\(27\) 14.1421 23.0000i 0.523783 0.851852i
\(28\) 0 0
\(29\) 56.5685i 1.95064i 0.220797 + 0.975320i \(0.429134\pi\)
−0.220797 + 0.975320i \(0.570866\pi\)
\(30\) −3.10102 + 16.6848i −0.103367 + 0.556161i
\(31\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(32\) −4.89898 + 2.82843i −0.153093 + 0.0883883i
\(33\) 29.1985 + 5.42679i 0.884802 + 0.164448i
\(34\) −45.2548 −1.33102
\(35\) 0 0
\(36\) −14.0000 + 11.3137i −0.388889 + 0.314270i
\(37\) 25.0000 43.3013i 0.675676 1.17030i −0.300595 0.953752i \(-0.597185\pi\)
0.976271 0.216553i \(-0.0694813\pi\)
\(38\) −34.6410 + 20.0000i −0.911606 + 0.526316i
\(39\) −29.0227 24.8130i −0.744172 0.636230i
\(40\) 5.65685 9.79796i 0.141421 0.244949i
\(41\) 16.0000i 0.390244i 0.980779 + 0.195122i \(0.0625103\pi\)
−0.980779 + 0.195122i \(0.937490\pi\)
\(42\) 0 0
\(43\) −52.0000 −1.20930 −0.604651 0.796490i \(-0.706687\pi\)
−0.604651 + 0.796490i \(0.706687\pi\)
\(44\) −17.1464 9.89949i −0.389692 0.224989i
\(45\) 12.9350 33.5959i 0.287445 0.746576i
\(46\) −1.00000 1.73205i −0.0217391 0.0376533i
\(47\) −29.4449 17.0000i −0.626486 0.361702i 0.152904 0.988241i \(-0.451138\pi\)
−0.779390 + 0.626539i \(0.784471\pi\)
\(48\) 11.3137 4.00000i 0.235702 0.0833333i
\(49\) 0 0
\(50\) 12.7279i 0.254558i
\(51\) 94.3837 + 17.5420i 1.85066 + 0.343961i
\(52\) 12.7279 + 22.0454i 0.244768 + 0.423950i
\(53\) 39.1918 22.6274i 0.739469 0.426932i −0.0824075 0.996599i \(-0.526261\pi\)
0.821876 + 0.569666i \(0.192928\pi\)
\(54\) 33.5840 18.1691i 0.621925 0.336465i
\(55\) 39.5980 0.719963
\(56\) 0 0
\(57\) 80.0000 28.2843i 1.40351 0.496215i
\(58\) −40.0000 + 69.2820i −0.689655 + 1.19452i
\(59\) −27.7128 + 16.0000i −0.469709 + 0.271186i −0.716118 0.697979i \(-0.754083\pi\)
0.246409 + 0.969166i \(0.420749\pi\)
\(60\) −15.5959 + 18.2419i −0.259932 + 0.304032i
\(61\) 16.2635 28.1691i 0.266614 0.461789i −0.701371 0.712796i \(-0.747428\pi\)
0.967985 + 0.251007i \(0.0807618\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) −8.00000 −0.125000
\(65\) −44.0908 25.4558i −0.678320 0.391628i
\(66\) 31.9233 + 27.2929i 0.483687 + 0.413528i
\(67\) 6.00000 + 10.3923i 0.0895522 + 0.155109i 0.907322 0.420437i \(-0.138123\pi\)
−0.817770 + 0.575546i \(0.804790\pi\)
\(68\) −55.4256 32.0000i −0.815083 0.470588i
\(69\) 1.41421 + 4.00000i 0.0204958 + 0.0579710i
\(70\) 0 0
\(71\) 89.0955i 1.25487i −0.778671 0.627433i \(-0.784106\pi\)
0.778671 0.627433i \(-0.215894\pi\)
\(72\) −25.1464 + 3.95691i −0.349256 + 0.0549571i
\(73\) 16.2635 + 28.1691i 0.222787 + 0.385879i 0.955653 0.294494i \(-0.0951512\pi\)
−0.732866 + 0.680373i \(0.761818\pi\)
\(74\) 61.2372 35.3553i 0.827530 0.477775i
\(75\) −4.93369 + 26.5454i −0.0657826 + 0.353939i
\(76\) −56.5685 −0.744323
\(77\) 0 0
\(78\) −18.0000 50.9117i −0.230769 0.652714i
\(79\) 20.0000 34.6410i 0.253165 0.438494i −0.711231 0.702959i \(-0.751862\pi\)
0.964395 + 0.264465i \(0.0851953\pi\)
\(80\) 13.8564 8.00000i 0.173205 0.100000i
\(81\) −77.0857 + 24.8755i −0.951675 + 0.307106i
\(82\) −11.3137 + 19.5959i −0.137972 + 0.238975i
\(83\) 62.0000i 0.746988i 0.927633 + 0.373494i \(0.121840\pi\)
−0.927633 + 0.373494i \(0.878160\pi\)
\(84\) 0 0
\(85\) 128.000 1.50588
\(86\) −63.6867 36.7696i −0.740543 0.427553i
\(87\) 110.280 128.990i 1.26758 1.48264i
\(88\) −14.0000 24.2487i −0.159091 0.275554i
\(89\) −48.4974 28.0000i −0.544915 0.314607i 0.202154 0.979354i \(-0.435206\pi\)
−0.747068 + 0.664747i \(0.768539\pi\)
\(90\) 39.5980 32.0000i 0.439978 0.355556i
\(91\) 0 0
\(92\) 2.82843i 0.0307438i
\(93\) 0 0
\(94\) −24.0416 41.6413i −0.255762 0.442993i
\(95\) 97.9796 56.5685i 1.03136 0.595458i
\(96\) 16.6848 + 3.10102i 0.173800 + 0.0323023i
\(97\) 24.0416 0.247852 0.123926 0.992291i \(-0.460451\pi\)
0.123926 + 0.992291i \(0.460451\pi\)
\(98\) 0 0
\(99\) −56.0000 69.2965i −0.565657 0.699964i
\(100\) 9.00000 15.5885i 0.0900000 0.155885i
\(101\) 31.1769 18.0000i 0.308682 0.178218i −0.337654 0.941270i \(-0.609633\pi\)
0.646337 + 0.763052i \(0.276300\pi\)
\(102\) 103.192 + 88.2238i 1.01168 + 0.864940i
\(103\) −36.7696 + 63.6867i −0.356986 + 0.618318i −0.987456 0.157896i \(-0.949529\pi\)
0.630470 + 0.776214i \(0.282862\pi\)
\(104\) 36.0000i 0.346154i
\(105\) 0 0
\(106\) 64.0000 0.603774
\(107\) −126.149 72.8320i −1.17896 0.680673i −0.223186 0.974776i \(-0.571646\pi\)
−0.955774 + 0.294103i \(0.904979\pi\)
\(108\) 53.9793 + 1.49490i 0.499808 + 0.0138416i
\(109\) 88.0000 + 152.420i 0.807339 + 1.39835i 0.914700 + 0.404133i \(0.132427\pi\)
−0.107361 + 0.994220i \(0.534240\pi\)
\(110\) 48.4974 + 28.0000i 0.440886 + 0.254545i
\(111\) −141.421 + 50.0000i −1.27407 + 0.450450i
\(112\) 0 0
\(113\) 16.9706i 0.150182i −0.997177 0.0750910i \(-0.976075\pi\)
0.997177 0.0750910i \(-0.0239247\pi\)
\(114\) 117.980 + 21.9275i 1.03491 + 0.192347i
\(115\) 2.82843 + 4.89898i 0.0245950 + 0.0425998i
\(116\) −97.9796 + 56.5685i −0.844652 + 0.487660i
\(117\) 17.8061 + 113.159i 0.152189 + 0.967170i
\(118\) −45.2548 −0.383516
\(119\) 0 0
\(120\) −32.0000 + 11.3137i −0.266667 + 0.0942809i
\(121\) −11.5000 + 19.9186i −0.0950413 + 0.164616i
\(122\) 39.8372 23.0000i 0.326534 0.188525i
\(123\) 31.1918 36.4838i 0.253592 0.296616i
\(124\) 0 0
\(125\) 136.000i 1.08800i
\(126\) 0 0
\(127\) −104.000 −0.818898 −0.409449 0.912333i \(-0.634279\pi\)
−0.409449 + 0.912333i \(0.634279\pi\)
\(128\) −9.79796 5.65685i −0.0765466 0.0441942i
\(129\) 118.572 + 101.373i 0.919166 + 0.785841i
\(130\) −36.0000 62.3538i −0.276923 0.479645i
\(131\) −25.9808 15.0000i −0.198326 0.114504i 0.397548 0.917581i \(-0.369861\pi\)
−0.595875 + 0.803077i \(0.703194\pi\)
\(132\) 19.7990 + 56.0000i 0.149992 + 0.424242i
\(133\) 0 0
\(134\) 16.9706i 0.126646i
\(135\) −94.9898 + 51.3901i −0.703628 + 0.380667i
\(136\) −45.2548 78.3837i −0.332756 0.576351i
\(137\) 58.7878 33.9411i 0.429108 0.247745i −0.269859 0.962900i \(-0.586977\pi\)
0.698966 + 0.715154i \(0.253644\pi\)
\(138\) −1.09638 + 5.89898i −0.00794476 + 0.0427462i
\(139\) 214.960 1.54648 0.773239 0.634115i \(-0.218635\pi\)
0.773239 + 0.634115i \(0.218635\pi\)
\(140\) 0 0
\(141\) 34.0000 + 96.1665i 0.241135 + 0.682032i
\(142\) 63.0000 109.119i 0.443662 0.768445i
\(143\) −109.119 + 63.0000i −0.763071 + 0.440559i
\(144\) −33.5959 12.9350i −0.233305 0.0898264i
\(145\) 113.137 195.959i 0.780256 1.35144i
\(146\) 46.0000i 0.315068i
\(147\) 0 0
\(148\) 100.000 0.675676
\(149\) 78.3837 + 45.2548i 0.526065 + 0.303724i 0.739413 0.673253i \(-0.235103\pi\)
−0.213348 + 0.976976i \(0.568437\pi\)
\(150\) −24.8130 + 29.0227i −0.165420 + 0.193485i
\(151\) −76.0000 131.636i −0.503311 0.871761i −0.999993 0.00382774i \(-0.998782\pi\)
0.496681 0.867933i \(-0.334552\pi\)
\(152\) −69.2820 40.0000i −0.455803 0.263158i
\(153\) −181.019 224.000i −1.18313 1.46405i
\(154\) 0 0
\(155\) 0 0
\(156\) 13.9546 75.0818i 0.0894525 0.481293i
\(157\) 85.5599 + 148.194i 0.544968 + 0.943912i 0.998609 + 0.0527273i \(0.0167914\pi\)
−0.453641 + 0.891184i \(0.649875\pi\)
\(158\) 48.9898 28.2843i 0.310062 0.179014i
\(159\) −133.479 24.8082i −0.839488 0.156026i
\(160\) 22.6274 0.141421
\(161\) 0 0
\(162\) −112.000 24.0416i −0.691358 0.148405i
\(163\) −122.000 + 211.310i −0.748466 + 1.29638i 0.200091 + 0.979777i \(0.435876\pi\)
−0.948558 + 0.316604i \(0.897457\pi\)
\(164\) −27.7128 + 16.0000i −0.168981 + 0.0975610i
\(165\) −90.2929 77.1959i −0.547229 0.467854i
\(166\) −43.8406 + 75.9342i −0.264100 + 0.457435i
\(167\) 226.000i 1.35329i −0.736308 0.676647i \(-0.763432\pi\)
0.736308 0.676647i \(-0.236568\pi\)
\(168\) 0 0
\(169\) −7.00000 −0.0414201
\(170\) 156.767 + 90.5097i 0.922161 + 0.532410i
\(171\) −237.559 91.4643i −1.38923 0.534879i
\(172\) −52.0000 90.0666i −0.302326 0.523643i
\(173\) 114.315 + 66.0000i 0.660782 + 0.381503i 0.792575 0.609774i \(-0.208740\pi\)
−0.131793 + 0.991277i \(0.542073\pi\)
\(174\) 226.274 80.0000i 1.30043 0.459770i
\(175\) 0 0
\(176\) 39.5980i 0.224989i
\(177\) 94.3837 + 17.5420i 0.533241 + 0.0991075i
\(178\) −39.5980 68.5857i −0.222461 0.385313i
\(179\) −194.734 + 112.430i −1.08790 + 0.628100i −0.933017 0.359832i \(-0.882834\pi\)
−0.154885 + 0.987933i \(0.549501\pi\)
\(180\) 71.1248 11.1918i 0.395138 0.0621769i
\(181\) −182.434 −1.00792 −0.503960 0.863727i \(-0.668124\pi\)
−0.503960 + 0.863727i \(0.668124\pi\)
\(182\) 0 0
\(183\) −92.0000 + 32.5269i −0.502732 + 0.177743i
\(184\) 2.00000 3.46410i 0.0108696 0.0188266i
\(185\) −173.205 + 100.000i −0.936244 + 0.540541i
\(186\) 0 0
\(187\) 158.392 274.343i 0.847016 1.46707i
\(188\) 68.0000i 0.361702i
\(189\) 0 0
\(190\) 160.000 0.842105
\(191\) −8.57321 4.94975i −0.0448859 0.0259149i 0.477389 0.878692i \(-0.341583\pi\)
−0.522275 + 0.852777i \(0.674917\pi\)
\(192\) 18.2419 + 15.5959i 0.0950100 + 0.0812287i
\(193\) 80.0000 + 138.564i 0.414508 + 0.717949i 0.995377 0.0960486i \(-0.0306204\pi\)
−0.580869 + 0.813997i \(0.697287\pi\)
\(194\) 29.4449 + 17.0000i 0.151778 + 0.0876289i
\(195\) 50.9117 + 144.000i 0.261086 + 0.738462i
\(196\) 0 0
\(197\) 107.480i 0.545585i 0.962073 + 0.272792i \(0.0879472\pi\)
−0.962073 + 0.272792i \(0.912053\pi\)
\(198\) −19.5857 124.468i −0.0989177 0.628629i
\(199\) −110.309 191.060i −0.554315 0.960102i −0.997956 0.0638972i \(-0.979647\pi\)
0.443642 0.896204i \(-0.353686\pi\)
\(200\) 22.0454 12.7279i 0.110227 0.0636396i
\(201\) 6.57826 35.3939i 0.0327277 0.176089i
\(202\) 50.9117 0.252038
\(203\) 0 0
\(204\) 64.0000 + 181.019i 0.313725 + 0.887350i
\(205\) 32.0000 55.4256i 0.156098 0.270369i
\(206\) −90.0666 + 52.0000i −0.437217 + 0.252427i
\(207\) 4.57321 11.8780i 0.0220928 0.0573814i
\(208\) −25.4558 + 44.0908i −0.122384 + 0.211975i
\(209\) 280.000i 1.33971i
\(210\) 0 0
\(211\) −372.000 −1.76303 −0.881517 0.472153i \(-0.843477\pi\)
−0.881517 + 0.472153i \(0.843477\pi\)
\(212\) 78.3837 + 45.2548i 0.369734 + 0.213466i
\(213\) −173.691 + 203.159i −0.815449 + 0.953798i
\(214\) −103.000 178.401i −0.481308 0.833651i
\(215\) 180.133 + 104.000i 0.837829 + 0.483721i
\(216\) 65.0538 + 40.0000i 0.301175 + 0.185185i
\(217\) 0 0
\(218\) 248.902i 1.14175i
\(219\) 17.8309 95.9378i 0.0814195 0.438072i
\(220\) 39.5980 + 68.5857i 0.179991 + 0.311753i
\(221\) −352.727 + 203.647i −1.59605 + 0.921479i
\(222\) −208.560 38.7628i −0.939461 0.174607i
\(223\) 16.9706 0.0761012 0.0380506 0.999276i \(-0.487885\pi\)
0.0380506 + 0.999276i \(0.487885\pi\)
\(224\) 0 0
\(225\) 63.0000 50.9117i 0.280000 0.226274i
\(226\) 12.0000 20.7846i 0.0530973 0.0919673i
\(227\) 332.554 192.000i 1.46499 0.845815i 0.465759 0.884912i \(-0.345781\pi\)
0.999235 + 0.0390966i \(0.0124480\pi\)
\(228\) 128.990 + 110.280i 0.565745 + 0.483683i
\(229\) −125.158 + 216.780i −0.546541 + 0.946637i 0.451967 + 0.892035i \(0.350722\pi\)
−0.998508 + 0.0546023i \(0.982611\pi\)
\(230\) 8.00000i 0.0347826i
\(231\) 0 0
\(232\) −160.000 −0.689655
\(233\) 279.242 + 161.220i 1.19846 + 0.691933i 0.960212 0.279271i \(-0.0900928\pi\)
0.238250 + 0.971204i \(0.423426\pi\)
\(234\) −58.2075 + 151.182i −0.248750 + 0.646075i
\(235\) 68.0000 + 117.779i 0.289362 + 0.501189i
\(236\) −55.4256 32.0000i −0.234854 0.135593i
\(237\) −113.137 + 40.0000i −0.477372 + 0.168776i
\(238\) 0 0
\(239\) 284.257i 1.18936i 0.803963 + 0.594680i \(0.202721\pi\)
−0.803963 + 0.594680i \(0.797279\pi\)
\(240\) −47.1918 8.77101i −0.196633 0.0365459i
\(241\) 23.3345 + 40.4166i 0.0968238 + 0.167704i 0.910368 0.413799i \(-0.135798\pi\)
−0.813545 + 0.581503i \(0.802465\pi\)
\(242\) −28.1691 + 16.2635i −0.116401 + 0.0672044i
\(243\) 224.268 + 93.5556i 0.922916 + 0.385003i
\(244\) 65.0538 0.266614
\(245\) 0 0
\(246\) 64.0000 22.6274i 0.260163 0.0919814i
\(247\) −180.000 + 311.769i −0.728745 + 1.26222i
\(248\) 0 0
\(249\) 120.868 141.375i 0.485415 0.567770i
\(250\) −96.1665 + 166.565i −0.384666 + 0.666261i
\(251\) 224.000i 0.892430i 0.894926 + 0.446215i \(0.147228\pi\)
−0.894926 + 0.446215i \(0.852772\pi\)
\(252\) 0 0
\(253\) 14.0000 0.0553360
\(254\) −127.373 73.5391i −0.501470 0.289524i
\(255\) −291.871 249.535i −1.14459 0.978567i
\(256\) −8.00000 13.8564i −0.0312500 0.0541266i
\(257\) −103.923 60.0000i −0.404370 0.233463i 0.283998 0.958825i \(-0.408339\pi\)
−0.688368 + 0.725362i \(0.741672\pi\)
\(258\) 73.5391 + 208.000i 0.285035 + 0.806202i
\(259\) 0 0
\(260\) 101.823i 0.391628i
\(261\) −502.929 + 79.1382i −1.92693 + 0.303212i
\(262\) −21.2132 36.7423i −0.0809664 0.140238i
\(263\) 194.734 112.430i 0.740435 0.427490i −0.0817924 0.996649i \(-0.526064\pi\)
0.822227 + 0.569159i \(0.192731\pi\)
\(264\) −15.3493 + 82.5857i −0.0581412 + 0.312825i
\(265\) −181.019 −0.683092
\(266\) 0 0
\(267\) 56.0000 + 158.392i 0.209738 + 0.593228i
\(268\) −12.0000 + 20.7846i −0.0447761 + 0.0775545i
\(269\) 142.028 82.0000i 0.527986 0.304833i −0.212210 0.977224i \(-0.568066\pi\)
0.740196 + 0.672391i \(0.234733\pi\)
\(270\) −152.677 4.22821i −0.565469 0.0156600i
\(271\) −115.966 + 200.858i −0.427917 + 0.741174i −0.996688 0.0813220i \(-0.974086\pi\)
0.568771 + 0.822496i \(0.307419\pi\)
\(272\) 128.000i 0.470588i
\(273\) 0 0
\(274\) 96.0000 0.350365
\(275\) 77.1589 + 44.5477i 0.280578 + 0.161992i
\(276\) −5.51399 + 6.44949i −0.0199782 + 0.0233677i
\(277\) 232.000 + 401.836i 0.837545 + 1.45067i 0.891941 + 0.452151i \(0.149343\pi\)
−0.0543961 + 0.998519i \(0.517323\pi\)
\(278\) 263.272 + 152.000i 0.947021 + 0.546763i
\(279\) 0 0
\(280\) 0 0
\(281\) 39.5980i 0.140918i −0.997515 0.0704590i \(-0.977554\pi\)
0.997515 0.0704590i \(-0.0224464\pi\)
\(282\) −26.3587 + 141.821i −0.0934705 + 0.502912i
\(283\) 124.451 + 215.555i 0.439755 + 0.761679i 0.997670 0.0682194i \(-0.0217318\pi\)
−0.557915 + 0.829898i \(0.688398\pi\)
\(284\) 154.318 89.0955i 0.543373 0.313716i
\(285\) −333.697 62.0204i −1.17087 0.217615i
\(286\) −178.191 −0.623045
\(287\) 0 0
\(288\) −32.0000 39.5980i −0.111111 0.137493i
\(289\) 367.500 636.529i 1.27163 2.20252i
\(290\) 277.128 160.000i 0.955614 0.551724i
\(291\) −54.8207 46.8689i −0.188387 0.161062i
\(292\) −32.5269 + 56.3383i −0.111394 + 0.192939i
\(293\) 316.000i 1.07850i −0.842146 0.539249i \(-0.818708\pi\)
0.842146 0.539249i \(-0.181292\pi\)
\(294\) 0 0
\(295\) 128.000 0.433898
\(296\) 122.474 + 70.7107i 0.413765 + 0.238887i
\(297\) −7.39936 + 267.184i −0.0249137 + 0.899609i
\(298\) 64.0000 + 110.851i 0.214765 + 0.371984i
\(299\) −15.5885 9.00000i −0.0521353 0.0301003i
\(300\) −50.9117 + 18.0000i −0.169706 + 0.0600000i
\(301\) 0 0
\(302\) 214.960i 0.711790i
\(303\) −106.182 19.7348i −0.350434 0.0651313i
\(304\) −56.5685 97.9796i −0.186081 0.322301i
\(305\) −112.677 + 65.0538i −0.369431 + 0.213291i
\(306\) −63.3106 402.343i −0.206897 1.31485i
\(307\) 345.068 1.12400 0.562000 0.827137i \(-0.310032\pi\)
0.562000 + 0.827137i \(0.310032\pi\)
\(308\) 0 0
\(309\) 208.000 73.5391i 0.673139 0.237991i
\(310\) 0 0
\(311\) 458.993 265.000i 1.47586 0.852090i 0.476234 0.879319i \(-0.342002\pi\)
0.999629 + 0.0272286i \(0.00866819\pi\)
\(312\) 70.1816 82.0886i 0.224941 0.263104i
\(313\) 74.2462 128.598i 0.237208 0.410857i −0.722704 0.691158i \(-0.757101\pi\)
0.959912 + 0.280301i \(0.0904343\pi\)
\(314\) 242.000i 0.770701i
\(315\) 0 0
\(316\) 80.0000 0.253165
\(317\) −97.9796 56.5685i −0.309084 0.178450i 0.337433 0.941350i \(-0.390441\pi\)
−0.646516 + 0.762900i \(0.723775\pi\)
\(318\) −145.935 124.767i −0.458916 0.392350i
\(319\) −280.000 484.974i −0.877743 1.52030i
\(320\) 27.7128 + 16.0000i 0.0866025 + 0.0500000i
\(321\) 145.664 + 412.000i 0.453782 + 1.28349i
\(322\) 0 0
\(323\) 905.097i 2.80216i
\(324\) −120.171 108.641i −0.370899 0.335311i
\(325\) −57.2756 99.2043i −0.176233 0.305244i
\(326\) −298.838 + 172.534i −0.916680 + 0.529246i
\(327\) 96.4811 519.110i 0.295049 1.58749i
\(328\) −45.2548 −0.137972
\(329\) 0 0
\(330\) −56.0000 158.392i −0.169697 0.479976i
\(331\) −26.0000 + 45.0333i −0.0785498 + 0.136052i −0.902624 0.430429i \(-0.858362\pi\)
0.824075 + 0.566481i \(0.191696\pi\)
\(332\) −107.387 + 62.0000i −0.323455 + 0.186747i
\(333\) 419.949 + 161.688i 1.26111 + 0.485548i
\(334\) 159.806 276.792i 0.478461 0.828720i
\(335\) 48.0000i 0.143284i
\(336\) 0 0
\(337\) 80.0000 0.237389 0.118694 0.992931i \(-0.462129\pi\)
0.118694 + 0.992931i \(0.462129\pi\)
\(338\) −8.57321 4.94975i −0.0253645 0.0146442i
\(339\) −33.0839 + 38.6969i −0.0975927 + 0.114150i
\(340\) 128.000 + 221.703i 0.376471 + 0.652066i
\(341\) 0 0
\(342\) −226.274 280.000i −0.661620 0.818713i
\(343\) 0 0
\(344\) 147.078i 0.427553i
\(345\) 3.10102 16.6848i 0.00898847 0.0483618i
\(346\) 93.3381 + 161.666i 0.269763 + 0.467244i
\(347\) 187.386 108.187i 0.540017 0.311779i −0.205069 0.978748i \(-0.565742\pi\)
0.745086 + 0.666969i \(0.232408\pi\)
\(348\) 333.697 + 62.0204i 0.958898 + 0.178220i
\(349\) −12.7279 −0.0364697 −0.0182348 0.999834i \(-0.505805\pi\)
−0.0182348 + 0.999834i \(0.505805\pi\)
\(350\) 0 0
\(351\) 180.000 292.742i 0.512821 0.834023i
\(352\) 28.0000 48.4974i 0.0795455 0.137777i
\(353\) 55.4256 32.0000i 0.157013 0.0906516i −0.419435 0.907785i \(-0.637772\pi\)
0.576448 + 0.817134i \(0.304438\pi\)
\(354\) 103.192 + 88.2238i 0.291502 + 0.249220i
\(355\) −178.191 + 308.636i −0.501946 + 0.869396i
\(356\) 112.000i 0.314607i
\(357\) 0 0
\(358\) −318.000 −0.888268
\(359\) 155.543 + 89.8026i 0.433266 + 0.250146i 0.700737 0.713420i \(-0.252855\pi\)
−0.267471 + 0.963566i \(0.586188\pi\)
\(360\) 95.0236 + 36.5857i 0.263954 + 0.101627i
\(361\) −219.500 380.185i −0.608033 1.05314i
\(362\) −223.435 129.000i −0.617223 0.356354i
\(363\) 65.0538 23.0000i 0.179212 0.0633609i
\(364\) 0 0
\(365\) 130.108i 0.356459i
\(366\) −135.677 25.2167i −0.370701 0.0688980i
\(367\) 65.0538 + 112.677i 0.177258 + 0.307021i 0.940941 0.338572i \(-0.109944\pi\)
−0.763682 + 0.645592i \(0.776611\pi\)
\(368\) 4.89898 2.82843i 0.0133124 0.00768594i
\(369\) −142.250 + 22.3837i −0.385500 + 0.0606604i
\(370\) −282.843 −0.764440
\(371\) 0 0
\(372\) 0 0
\(373\) 7.00000 12.1244i 0.0187668 0.0325050i −0.856490 0.516164i \(-0.827359\pi\)
0.875256 + 0.483659i \(0.160693\pi\)
\(374\) 387.979 224.000i 1.03738 0.598930i
\(375\) 265.131 310.112i 0.707015 0.826967i
\(376\) 48.0833 83.2827i 0.127881 0.221496i
\(377\) 720.000i 1.90981i
\(378\) 0 0
\(379\) 148.000 0.390501 0.195251 0.980753i \(-0.437448\pi\)
0.195251 + 0.980753i \(0.437448\pi\)
\(380\) 195.959 + 113.137i 0.515682 + 0.297729i
\(381\) 237.145 + 202.747i 0.622427 + 0.532144i
\(382\) −7.00000 12.1244i −0.0183246 0.0317392i
\(383\) 96.9948 + 56.0000i 0.253250 + 0.146214i 0.621252 0.783611i \(-0.286624\pi\)
−0.368001 + 0.929825i \(0.619958\pi\)
\(384\) 11.3137 + 32.0000i 0.0294628 + 0.0833333i
\(385\) 0 0
\(386\) 226.274i 0.586203i
\(387\) −72.7469 462.311i −0.187977 1.19460i
\(388\) 24.0416 + 41.6413i 0.0619630 + 0.107323i
\(389\) 372.322 214.960i 0.957127 0.552598i 0.0618394 0.998086i \(-0.480303\pi\)
0.895288 + 0.445489i \(0.146970\pi\)
\(390\) −39.4695 + 212.363i −0.101204 + 0.544521i
\(391\) 45.2548 0.115741
\(392\) 0 0
\(393\) 30.0000 + 84.8528i 0.0763359 + 0.215910i
\(394\) −76.0000 + 131.636i −0.192893 + 0.334101i
\(395\) −138.564 + 80.0000i −0.350795 + 0.202532i
\(396\) 64.0250 166.291i 0.161679 0.419928i
\(397\) 17.6777 30.6186i 0.0445281 0.0771250i −0.842902 0.538067i \(-0.819155\pi\)
0.887430 + 0.460942i \(0.152488\pi\)
\(398\) 312.000i 0.783920i
\(399\) 0 0
\(400\) 36.0000 0.0900000
\(401\) −117.576 67.8823i −0.293206 0.169282i 0.346181 0.938168i \(-0.387478\pi\)
−0.639387 + 0.768885i \(0.720812\pi\)
\(402\) 33.0839 38.6969i 0.0822984 0.0962610i
\(403\) 0 0
\(404\) 62.3538 + 36.0000i 0.154341 + 0.0891089i
\(405\) 316.784 + 68.0000i 0.782182 + 0.167901i
\(406\) 0 0
\(407\) 494.975i 1.21615i
\(408\) −49.6163 + 266.957i −0.121609 + 0.654307i
\(409\) 163.342 + 282.916i 0.399368 + 0.691726i 0.993648 0.112532i \(-0.0358961\pi\)
−0.594280 + 0.804258i \(0.702563\pi\)
\(410\) 78.3837 45.2548i 0.191180 0.110378i
\(411\) −200.218 37.2122i −0.487148 0.0905407i
\(412\) −147.078 −0.356986
\(413\) 0 0
\(414\) 14.0000 11.3137i 0.0338164 0.0273278i
\(415\) 124.000 214.774i 0.298795 0.517528i
\(416\) −62.3538 + 36.0000i −0.149889 + 0.0865385i
\(417\) −490.161 419.063i −1.17545 1.00495i
\(418\) 197.990 342.929i 0.473660 0.820403i
\(419\) 352.000i 0.840095i 0.907502 + 0.420048i \(0.137987\pi\)
−0.907502 + 0.420048i \(0.862013\pi\)
\(420\) 0 0
\(421\) 240.000 0.570071 0.285036 0.958517i \(-0.407995\pi\)
0.285036 + 0.958517i \(0.407995\pi\)
\(422\) −455.605 263.044i −1.07963 0.623326i
\(423\) 109.948 285.565i 0.259923 0.675095i
\(424\) 64.0000 + 110.851i 0.150943 + 0.261442i
\(425\) 249.415 + 144.000i 0.586860 + 0.338824i
\(426\) −356.382 + 126.000i −0.836577 + 0.295775i
\(427\) 0 0
\(428\) 291.328i 0.680673i
\(429\) 371.636 + 69.0717i 0.866284 + 0.161006i
\(430\) 147.078 + 254.747i 0.342042 + 0.592435i
\(431\) −635.643 + 366.988i −1.47481 + 0.851481i −0.999597 0.0283901i \(-0.990962\pi\)
−0.475212 + 0.879871i \(0.657629\pi\)
\(432\) 51.3901 + 94.9898i 0.118958 + 0.219884i
\(433\) −428.507 −0.989623 −0.494811 0.869000i \(-0.664763\pi\)
−0.494811 + 0.869000i \(0.664763\pi\)
\(434\) 0 0
\(435\) −640.000 + 226.274i −1.47126 + 0.520171i
\(436\) −176.000 + 304.841i −0.403670 + 0.699176i
\(437\) 34.6410 20.0000i 0.0792701 0.0457666i
\(438\) 89.6765 104.891i 0.204741 0.239477i
\(439\) −203.647 + 352.727i −0.463888 + 0.803477i −0.999151 0.0412083i \(-0.986879\pi\)
0.535263 + 0.844686i \(0.320213\pi\)
\(440\) 112.000i 0.254545i
\(441\) 0 0
\(442\) −576.000 −1.30317
\(443\) 344.153 + 198.697i 0.776870 + 0.448526i 0.835320 0.549764i \(-0.185282\pi\)
−0.0584500 + 0.998290i \(0.518616\pi\)
\(444\) −228.024 194.949i −0.513567 0.439074i
\(445\) 112.000 + 193.990i 0.251685 + 0.435932i
\(446\) 20.7846 + 12.0000i 0.0466023 + 0.0269058i
\(447\) −90.5097 256.000i −0.202482 0.572707i
\(448\) 0 0
\(449\) 16.9706i 0.0377964i −0.999821 0.0188982i \(-0.993984\pi\)
0.999821 0.0188982i \(-0.00601583\pi\)
\(450\) 113.159 17.8061i 0.251464 0.0395691i
\(451\) −79.1960 137.171i −0.175601 0.304150i
\(452\) 29.3939 16.9706i 0.0650307 0.0375455i
\(453\) −83.3246 + 448.322i −0.183940 + 0.989674i
\(454\) 543.058 1.19616
\(455\) 0 0
\(456\) 80.0000 + 226.274i 0.175439 + 0.496215i
\(457\) 63.0000 109.119i 0.137856 0.238773i −0.788829 0.614613i \(-0.789312\pi\)
0.926685 + 0.375840i \(0.122646\pi\)
\(458\) −306.573 + 177.000i −0.669373 + 0.386463i
\(459\) −23.9184 + 863.669i −0.0521097 + 1.88163i
\(460\) −5.65685 + 9.79796i −0.0122975 + 0.0212999i
\(461\) 580.000i 1.25813i −0.777351 0.629067i \(-0.783437\pi\)
0.777351 0.629067i \(-0.216563\pi\)
\(462\) 0 0
\(463\) 112.000 0.241901 0.120950 0.992659i \(-0.461406\pi\)
0.120950 + 0.992659i \(0.461406\pi\)
\(464\) −195.959 113.137i −0.422326 0.243830i
\(465\) 0 0
\(466\) 228.000 + 394.908i 0.489270 + 0.847441i
\(467\) 110.851 + 64.0000i 0.237369 + 0.137045i 0.613967 0.789332i \(-0.289573\pi\)
−0.376598 + 0.926377i \(0.622906\pi\)
\(468\) −178.191 + 144.000i −0.380750 + 0.307692i
\(469\) 0 0
\(470\) 192.333i 0.409219i
\(471\) 93.8059 504.716i 0.199163 1.07158i
\(472\) −45.2548 78.3837i −0.0958789 0.166067i
\(473\) 445.807 257.387i 0.942510 0.544158i
\(474\) −166.848 31.0102i −0.352001 0.0654224i
\(475\) 254.558 0.535913
\(476\) 0 0
\(477\) 256.000 + 316.784i 0.536688 + 0.664117i
\(478\) −201.000 + 348.142i −0.420502 + 0.728331i
\(479\) −417.424 + 241.000i −0.871449 + 0.503132i −0.867830 0.496862i \(-0.834486\pi\)
−0.00361975 + 0.999993i \(0.501152\pi\)
\(480\) −51.5959 44.1119i −0.107491 0.0918998i
\(481\) 318.198 551.135i 0.661534 1.14581i
\(482\) 66.0000i 0.136929i
\(483\) 0 0
\(484\) −46.0000 −0.0950413
\(485\) −83.2827 48.0833i −0.171717 0.0991407i
\(486\) 208.518 + 273.164i 0.429049 + 0.562065i
\(487\) 60.0000 + 103.923i 0.123203 + 0.213394i 0.921029 0.389494i \(-0.127350\pi\)
−0.797826 + 0.602888i \(0.794017\pi\)
\(488\) 79.6743 + 46.0000i 0.163267 + 0.0942623i
\(489\) 690.136 244.000i 1.41132 0.498978i
\(490\) 0 0
\(491\) 623.668i 1.27020i 0.772430 + 0.635100i \(0.219041\pi\)
−0.772430 + 0.635100i \(0.780959\pi\)
\(492\) 94.3837 + 17.5420i 0.191837 + 0.0356545i
\(493\) −905.097 1567.67i −1.83590 3.17986i
\(494\) −440.908 + 254.558i −0.892527 + 0.515300i
\(495\) 55.3968 + 352.050i 0.111913 + 0.711212i
\(496\) 0 0
\(497\) 0 0
\(498\) 248.000 87.6812i 0.497992 0.176067i
\(499\) −142.000 + 245.951i −0.284569 + 0.492888i −0.972505 0.232884i \(-0.925184\pi\)
0.687935 + 0.725772i \(0.258517\pi\)
\(500\) −235.559 + 136.000i −0.471118 + 0.272000i
\(501\) −440.585 + 515.334i −0.879411 + 1.02861i
\(502\) −158.392 + 274.343i −0.315522 + 0.546500i
\(503\) 16.0000i 0.0318091i −0.999874 0.0159046i \(-0.994937\pi\)
0.999874 0.0159046i \(-0.00506280\pi\)
\(504\) 0 0
\(505\) −144.000 −0.285149
\(506\) 17.1464 + 9.89949i 0.0338862 + 0.0195642i
\(507\) 15.9617 + 13.6464i 0.0314826 + 0.0269160i
\(508\) −104.000 180.133i −0.204724 0.354593i
\(509\) −308.305 178.000i −0.605707 0.349705i 0.165576 0.986197i \(-0.447052\pi\)
−0.771284 + 0.636492i \(0.780385\pi\)
\(510\) −181.019 512.000i −0.354940 1.00392i
\(511\) 0 0
\(512\) 22.6274i 0.0441942i
\(513\) 363.383 + 671.679i 0.708348 + 1.30932i
\(514\) −84.8528 146.969i −0.165083 0.285933i
\(515\) 254.747 147.078i 0.494654 0.285589i
\(516\) −57.0116 + 306.747i −0.110488 + 0.594471i
\(517\) 336.583 0.651031
\(518\) 0 0
\(519\) −132.000 373.352i −0.254335 0.719369i
\(520\) 72.0000 124.708i 0.138462 0.239822i
\(521\) −214.774 + 124.000i −0.412235 + 0.238004i −0.691749 0.722138i \(-0.743160\pi\)
0.279515 + 0.960141i \(0.409826\pi\)
\(522\) −671.918 258.700i −1.28720 0.495594i
\(523\) −25.4558 + 44.0908i −0.0486727 + 0.0843037i −0.889335 0.457256i \(-0.848832\pi\)
0.840663 + 0.541559i \(0.182166\pi\)
\(524\) 60.0000i 0.114504i
\(525\) 0 0
\(526\) 318.000 0.604563
\(527\) 0 0
\(528\) −77.1959 + 90.2929i −0.146204 + 0.171009i
\(529\) −263.500 456.395i −0.498110 0.862751i
\(530\) −221.703 128.000i −0.418307 0.241509i
\(531\) −181.019 224.000i −0.340903 0.421846i
\(532\) 0 0
\(533\) 203.647i 0.382076i
\(534\) −43.4143 + 233.588i −0.0813002 + 0.437430i
\(535\) 291.328 + 504.595i 0.544538 + 0.943168i
\(536\) −29.3939 + 16.9706i −0.0548393 + 0.0316615i
\(537\) 663.222 + 123.266i 1.23505 + 0.229545i
\(538\) 231.931 0.431099
\(539\) 0 0
\(540\) −184.000 113.137i −0.340741 0.209513i
\(541\) −200.000 + 346.410i −0.369686 + 0.640315i −0.989516 0.144421i \(-0.953868\pi\)
0.619831 + 0.784736i \(0.287201\pi\)
\(542\) −284.056 + 164.000i −0.524089 + 0.302583i
\(543\) 415.992 + 355.652i 0.766100 + 0.654977i
\(544\) 90.5097 156.767i 0.166378 0.288175i
\(545\) 704.000i 1.29174i
\(546\) 0 0
\(547\) 820.000 1.49909 0.749543 0.661956i \(-0.230273\pi\)
0.749543 + 0.661956i \(0.230273\pi\)
\(548\) 117.576 + 67.8823i 0.214554 + 0.123873i
\(549\) 273.193 + 105.184i 0.497619 + 0.191592i
\(550\) 63.0000 + 109.119i 0.114545 + 0.198399i
\(551\) −1385.64 800.000i −2.51477 1.45191i
\(552\) −11.3137 + 4.00000i −0.0204958 + 0.00724638i
\(553\) 0 0
\(554\) 656.195i 1.18447i
\(555\) 589.898 + 109.638i 1.06288 + 0.197545i
\(556\) 214.960 + 372.322i 0.386620 + 0.669645i
\(557\) −911.210 + 526.087i −1.63592 + 0.944502i −0.653709 + 0.756746i \(0.726788\pi\)
−0.982216 + 0.187756i \(0.939879\pi\)
\(558\) 0 0
\(559\) −661.852 −1.18399
\(560\) 0 0
\(561\) −896.000 + 316.784i −1.59715 + 0.564677i
\(562\) 28.0000 48.4974i 0.0498221 0.0862943i
\(563\) −942.236 + 544.000i −1.67360 + 0.966252i −0.708000 + 0.706212i \(0.750402\pi\)
−0.965598 + 0.260040i \(0.916264\pi\)
\(564\) −132.565 + 155.056i −0.235045 + 0.274922i
\(565\) −33.9411 + 58.7878i −0.0600728 + 0.104049i
\(566\) 352.000i 0.621908i
\(567\) 0 0
\(568\) 252.000 0.443662
\(569\) −436.009 251.730i −0.766273 0.442408i 0.0652707 0.997868i \(-0.479209\pi\)
−0.831543 + 0.555460i \(0.812542\pi\)
\(570\) −364.838 311.918i −0.640067 0.547225i
\(571\) −410.000 710.141i −0.718039 1.24368i −0.961776 0.273838i \(-0.911707\pi\)
0.243737 0.969841i \(-0.421627\pi\)
\(572\) −218.238 126.000i −0.381536 0.220280i
\(573\) 9.89949 + 28.0000i 0.0172766 + 0.0488656i
\(574\) 0 0
\(575\) 12.7279i 0.0221355i
\(576\) −11.1918 71.1248i −0.0194303 0.123481i
\(577\) −146.371 253.522i −0.253676 0.439380i 0.710859 0.703335i \(-0.248306\pi\)
−0.964535 + 0.263955i \(0.914973\pi\)
\(578\) 900.187 519.723i 1.55742 0.899176i
\(579\) 87.7101 471.918i 0.151486 0.815058i
\(580\) 452.548 0.780256
\(581\) 0 0
\(582\) −34.0000 96.1665i −0.0584192 0.165235i
\(583\) −224.000 + 387.979i −0.384220 + 0.665488i
\(584\) −79.6743 + 46.0000i −0.136429 + 0.0787671i
\(585\) 164.636 427.606i 0.281429 0.730951i
\(586\) 223.446 387.019i 0.381307 0.660443i
\(587\) 480.000i 0.817717i −0.912598 0.408859i \(-0.865927\pi\)
0.912598 0.408859i \(-0.134073\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 156.767 + 90.5097i 0.265707 + 0.153406i
\(591\) 209.532 245.081i 0.354537 0.414688i
\(592\) 100.000 + 173.205i 0.168919 + 0.292576i
\(593\) 928.379 + 536.000i 1.56556 + 0.903879i 0.996676 + 0.0814631i \(0.0259593\pi\)
0.568887 + 0.822416i \(0.307374\pi\)
\(594\) −197.990 + 322.000i −0.333316 + 0.542088i
\(595\) 0 0
\(596\) 181.019i 0.303724i
\(597\) −120.940 + 650.709i −0.202579 + 1.08996i
\(598\) −12.7279 22.0454i −0.0212842 0.0368652i
\(599\) 353.951 204.354i 0.590904 0.341158i −0.174551 0.984648i \(-0.555847\pi\)
0.765455 + 0.643490i \(0.222514\pi\)
\(600\) −75.0818 13.9546i −0.125136 0.0232577i
\(601\) 326.683 0.543566 0.271783 0.962359i \(-0.412387\pi\)
0.271783 + 0.962359i \(0.412387\pi\)
\(602\) 0 0
\(603\) −84.0000 + 67.8823i −0.139303 + 0.112574i
\(604\) 152.000 263.272i 0.251656 0.435880i
\(605\) 79.6743 46.0000i 0.131693 0.0760331i
\(606\) −116.091 99.2518i −0.191569 0.163782i
\(607\) −127.279 + 220.454i −0.209686 + 0.363186i −0.951616 0.307291i \(-0.900577\pi\)
0.741930 + 0.670478i \(0.233911\pi\)
\(608\) 160.000i 0.263158i
\(609\) 0 0
\(610\) −184.000 −0.301639
\(611\) −374.772 216.375i −0.613375 0.354132i
\(612\) 206.960 537.535i 0.338170 0.878325i
\(613\) 168.000 + 290.985i 0.274062 + 0.474689i 0.969898 0.243511i \(-0.0782993\pi\)
−0.695836 + 0.718201i \(0.744966\pi\)
\(614\) 422.620 + 244.000i 0.688307 + 0.397394i
\(615\) −181.019 + 64.0000i −0.294340 + 0.104065i
\(616\) 0 0
\(617\) 384.666i 0.623446i 0.950173 + 0.311723i \(0.100906\pi\)
−0.950173 + 0.311723i \(0.899094\pi\)
\(618\) 306.747 + 57.0116i 0.496354 + 0.0922517i
\(619\) 308.299 + 533.989i 0.498059 + 0.862664i 0.999997 0.00223976i \(-0.000712938\pi\)
−0.501938 + 0.864903i \(0.667380\pi\)
\(620\) 0 0
\(621\) −33.5840 + 18.1691i −0.0540805 + 0.0292579i
\(622\) 749.533 1.20504
\(623\) 0 0
\(624\) 144.000 50.9117i 0.230769 0.0815892i
\(625\) 159.500 276.262i 0.255200 0.442019i
\(626\) 181.865 105.000i 0.290520 0.167732i
\(627\) −545.857 + 638.467i −0.870586 + 1.01829i
\(628\) −171.120 + 296.388i −0.272484 + 0.471956i
\(629\) 1600.00i 2.54372i
\(630\) 0 0
\(631\) −712.000 −1.12837 −0.564184 0.825649i \(-0.690809\pi\)
−0.564184 + 0.825649i \(0.690809\pi\)
\(632\) 97.9796 + 56.5685i 0.155031 + 0.0895072i
\(633\) 848.249 + 725.210i 1.34005 + 1.14567i
\(634\) −80.0000 138.564i −0.126183 0.218555i
\(635\) 360.267 + 208.000i 0.567349 + 0.327559i
\(636\) −90.5097 256.000i −0.142311 0.402516i
\(637\) 0 0
\(638\) 791.960i 1.24132i
\(639\) 792.112 124.643i 1.23961 0.195059i
\(640\) 22.6274 + 39.1918i 0.0353553 + 0.0612372i
\(641\) 489.898 282.843i 0.764271 0.441252i −0.0665559 0.997783i \(-0.521201\pi\)
0.830827 + 0.556530i \(0.187868\pi\)
\(642\) −112.927 + 607.595i −0.175898 + 0.946409i
\(643\) −837.214 −1.30204 −0.651022 0.759059i \(-0.725659\pi\)
−0.651022 + 0.759059i \(0.725659\pi\)
\(644\) 0 0
\(645\) −208.000 588.313i −0.322481 0.912113i
\(646\) 640.000 1108.51i 0.990712 1.71596i
\(647\) −805.404 + 465.000i −1.24483 + 0.718702i −0.970073 0.242813i \(-0.921930\pi\)
−0.274755 + 0.961514i \(0.588597\pi\)
\(648\) −70.3587 218.031i −0.108578 0.336468i
\(649\) 158.392 274.343i 0.244055 0.422716i
\(650\) 162.000i 0.249231i
\(651\) 0 0
\(652\) −488.000 −0.748466
\(653\) −455.605 263.044i −0.697711 0.402823i 0.108783 0.994065i \(-0.465304\pi\)
−0.806494 + 0.591242i \(0.798638\pi\)
\(654\) 485.231 567.555i 0.741944 0.867821i
\(655\) 60.0000 + 103.923i 0.0916031 + 0.158661i
\(656\) −55.4256 32.0000i −0.0844903 0.0487805i
\(657\) −227.688 + 184.000i −0.346558 + 0.280061i
\(658\) 0 0
\(659\) 46.6690i 0.0708180i −0.999373 0.0354090i \(-0.988727\pi\)
0.999373 0.0354090i \(-0.0112734\pi\)
\(660\) 43.4143 233.588i 0.0657792 0.353921i
\(661\) −248.194 429.885i −0.375483 0.650356i 0.614916 0.788593i \(-0.289190\pi\)
−0.990399 + 0.138236i \(0.955857\pi\)
\(662\) −63.6867 + 36.7696i −0.0962035 + 0.0555431i
\(663\) 1201.31 + 223.273i 1.81193 + 0.336762i
\(664\) −175.362 −0.264100
\(665\) 0 0
\(666\) 400.000 + 494.975i 0.600601 + 0.743205i
\(667\) 40.0000 69.2820i 0.0599700 0.103871i
\(668\) 391.443 226.000i 0.585993 0.338323i
\(669\) −38.6969 33.0839i −0.0578430 0.0494528i
\(670\) 33.9411 58.7878i 0.0506584 0.0877429i
\(671\) 322.000i 0.479881i
\(672\) 0 0
\(673\) −498.000 −0.739970 −0.369985 0.929038i \(-0.620637\pi\)
−0.369985 + 0.929038i \(0.620637\pi\)
\(674\) 97.9796 + 56.5685i 0.145370 + 0.0839296i
\(675\) −242.907 6.72704i −0.359862 0.00996598i
\(676\) −7.00000 12.1244i −0.0103550 0.0179354i
\(677\) −883.346 510.000i −1.30479 0.753323i −0.323572 0.946203i \(-0.604884\pi\)
−0.981222 + 0.192880i \(0.938217\pi\)
\(678\) −67.8823 + 24.0000i −0.100121 + 0.0353982i
\(679\) 0 0
\(680\) 362.039i 0.532410i
\(681\) −1132.60 210.504i −1.66315 0.309111i
\(682\) 0 0
\(683\) 400.492 231.224i 0.586371 0.338542i −0.177290 0.984159i \(-0.556733\pi\)
0.763661 + 0.645617i \(0.223400\pi\)
\(684\) −79.1382 502.929i −0.115699 0.735276i
\(685\) −271.529 −0.396393
\(686\) 0 0
\(687\) 708.000 250.316i 1.03057 0.364361i
\(688\) 104.000 180.133i 0.151163 0.261822i
\(689\) 498.831 288.000i 0.723992 0.417997i
\(690\) 15.5959 18.2419i 0.0226028 0.0264376i
\(691\) 271.529 470.302i 0.392951 0.680611i −0.599886 0.800085i \(-0.704788\pi\)
0.992837 + 0.119474i \(0.0381209\pi\)
\(692\) 264.000i 0.381503i
\(693\) 0 0
\(694\) 306.000 0.440922
\(695\) −744.645 429.921i −1.07143 0.618591i
\(696\) 364.838 + 311.918i 0.524193 + 0.448159i
\(697\) −256.000 443.405i −0.367288 0.636162i
\(698\) −15.5885 9.00000i −0.0223330 0.0128940i
\(699\) −322.441 912.000i −0.461289 1.30472i
\(700\) 0 0
\(701\) 797.616i 1.13783i −0.822398 0.568913i \(-0.807364\pi\)
0.822398 0.568913i \(-0.192636\pi\)
\(702\) 427.454 231.255i 0.608909 0.329423i
\(703\) 707.107 + 1224.74i 1.00584 + 1.74217i
\(704\) 68.5857 39.5980i 0.0974229 0.0562471i
\(705\) 74.5536 401.131i 0.105750 0.568980i
\(706\) 90.5097 0.128201
\(707\) 0 0
\(708\) 64.0000 + 181.019i 0.0903955 + 0.255677i
\(709\) −440.000 + 762.102i −0.620592 + 1.07490i 0.368783 + 0.929515i \(0.379774\pi\)
−0.989376 + 0.145382i \(0.953559\pi\)
\(710\) −436.477 + 252.000i −0.614756 + 0.354930i
\(711\) 335.959 + 129.350i 0.472516 + 0.181927i
\(712\) 79.1960 137.171i 0.111230 0.192656i
\(713\) 0 0
\(714\) 0 0
\(715\) 504.000 0.704895
\(716\) −389.469 224.860i −0.543951 0.314050i
\(717\) 554.156 648.174i 0.772881 0.904008i
\(718\) 127.000 + 219.970i 0.176880 + 0.306366i
\(719\) 568.113 + 328.000i 0.790143 + 0.456189i 0.840013 0.542567i \(-0.182547\pi\)
−0.0498700 + 0.998756i \(0.515881\pi\)
\(720\) 90.5097 + 112.000i 0.125708 + 0.155556i
\(721\) 0 0
\(722\) 620.840i 0.859889i
\(723\) 25.5834 137.650i 0.0353851 0.190387i
\(724\) −182.434 315.984i −0.251980 0.436442i
\(725\) 440.908 254.558i 0.608149 0.351115i
\(726\) 95.9378 + 17.8309i 0.132146 + 0.0245604i
\(727\) −786.303 −1.08157 −0.540786 0.841160i \(-0.681873\pi\)
−0.540786 + 0.841160i \(0.681873\pi\)
\(728\) 0 0
\(729\) −329.000 650.538i −0.451303 0.892371i
\(730\) 92.0000 159.349i 0.126027 0.218286i
\(731\) 1441.07 832.000i 1.97136 1.13817i
\(732\) −148.338 126.822i −0.202648 0.173254i
\(733\) −617.304 + 1069.20i −0.842161 + 1.45867i 0.0459025 + 0.998946i \(0.485384\pi\)
−0.888064 + 0.459720i \(0.847950\pi\)
\(734\) 184.000i 0.250681i
\(735\) 0 0
\(736\) 8.00000 0.0108696
\(737\) −102.879 59.3970i −0.139591 0.0805929i
\(738\) −190.047 73.1714i −0.257517 0.0991483i
\(739\) 78.0000 + 135.100i 0.105548 + 0.182815i 0.913962 0.405800i \(-0.133007\pi\)
−0.808414 + 0.588614i \(0.799674\pi\)
\(740\) −346.410 200.000i −0.468122 0.270270i
\(741\) 1018.23 360.000i 1.37413 0.485830i
\(742\) 0 0
\(743\) 858.428i 1.15535i −0.816266 0.577677i \(-0.803959\pi\)
0.816266 0.577677i \(-0.196041\pi\)
\(744\) 0 0
\(745\) −181.019 313.535i −0.242979 0.420852i
\(746\) 17.1464 9.89949i 0.0229845 0.0132701i
\(747\) −551.218 + 86.7367i −0.737908 + 0.116113i
\(748\) 633.568 0.847016
\(749\) 0 0
\(750\) 544.000 192.333i 0.725333 0.256444i
\(751\) −40.0000 + 69.2820i −0.0532623 + 0.0922530i −0.891427 0.453164i \(-0.850295\pi\)
0.838165 + 0.545417i \(0.183629\pi\)
\(752\) 117.779 68.0000i 0.156622 0.0904255i
\(753\) 436.686 510.774i 0.579928 0.678318i
\(754\) −509.117 + 881.816i −0.675221 + 1.16952i
\(755\) 608.000i 0.805298i
\(756\) 0 0
\(757\) −16.0000 −0.0211361 −0.0105680 0.999944i \(-0.503364\pi\)
−0.0105680 + 0.999944i \(0.503364\pi\)
\(758\) 181.262 + 104.652i 0.239132 + 0.138063i
\(759\) −31.9233 27.2929i −0.0420597 0.0359590i
\(760\) 160.000 + 277.128i 0.210526 + 0.364642i
\(761\) −588.897 340.000i −0.773847 0.446781i 0.0603985 0.998174i \(-0.480763\pi\)
−0.834245 + 0.551394i \(0.814096\pi\)
\(762\) 147.078 + 416.000i 0.193016 + 0.545932i
\(763\) 0 0
\(764\) 19.7990i 0.0259149i
\(765\) 179.069 + 1138.00i 0.234078 + 1.48758i
\(766\) 79.1960 + 137.171i 0.103389 + 0.179075i
\(767\) −352.727 + 203.647i −0.459878 + 0.265511i
\(768\) −8.77101 + 47.1918i −0.0114206 + 0.0614477i
\(769\) −1336.43 −1.73788 −0.868941 0.494915i \(-0.835199\pi\)
−0.868941 + 0.494915i \(0.835199\pi\)
\(770\) 0 0
\(771\) 120.000 + 339.411i 0.155642 + 0.440222i
\(772\) −160.000 + 277.128i −0.207254 + 0.358974i
\(773\) −1001.13 + 578.000i −1.29512 + 0.747736i −0.979556 0.201169i \(-0.935526\pi\)
−0.315560 + 0.948905i \(0.602193\pi\)
\(774\) 237.807 617.653i 0.307244 0.798002i
\(775\) 0 0
\(776\) 68.0000i 0.0876289i
\(777\) 0 0
\(778\) 608.000 0.781491
\(779\) −391.918 226.274i −0.503104 0.290467i
\(780\) −198.504 + 232.182i −0.254492 + 0.297669i
\(781\) 441.000 + 763.834i 0.564661 + 0.978021i
\(782\) 55.4256 + 32.0000i 0.0708768 + 0.0409207i
\(783\) 1301.08 + 800.000i 1.66166 + 1.02171i
\(784\) 0 0
\(785\) 684.479i 0.871948i
\(786\) −23.2577 + 125.136i −0.0295899 + 0.159206i
\(787\) 260.215 + 450.706i 0.330642 + 0.572689i 0.982638 0.185534i \(-0.0594014\pi\)
−0.651996 + 0.758223i \(0.726068\pi\)
\(788\) −186.161 + 107.480i −0.236245 + 0.136396i
\(789\) −663.222 123.266i −0.840586 0.156230i
\(790\) −226.274 −0.286423
\(791\) 0 0
\(792\) 196.000 158.392i 0.247475 0.199990i
\(793\) 207.000 358.535i 0.261034 0.452124i
\(794\) 43.3013 25.0000i 0.0545356 0.0314861i
\(795\) 412.767 + 352.895i 0.519204 + 0.443894i
\(796\) 220.617 382.120i 0.277157 0.480051i
\(797\) 60.0000i 0.0752823i −0.999291 0.0376412i \(-0.988016\pi\)
0.999291 0.0376412i \(-0.0119844\pi\)
\(798\) 0 0
\(799\) 1088.00 1.36170
\(800\) 44.0908 + 25.4558i 0.0551135 + 0.0318198i
\(801\) 181.090 470.343i 0.226080 0.587195i
\(802\) −96.0000 166.277i −0.119701 0.207328i
\(803\) −278.860 161.000i −0.347273 0.200498i
\(804\) 67.8823 24.0000i 0.0844307 0.0298507i
\(805\) 0 0
\(806\) 0 0
\(807\) −483.716 89.9029i −0.599401 0.111404i
\(808\) 50.9117 + 88.1816i 0.0630095 + 0.109136i
\(809\) −553.585 + 319.612i −0.684283 + 0.395071i −0.801467 0.598039i \(-0.795947\pi\)
0.117184 + 0.993110i \(0.462613\pi\)
\(810\) 339.896 + 307.283i 0.419625 + 0.379361i
\(811\) 458.205 0.564988 0.282494 0.959269i \(-0.408838\pi\)
0.282494 + 0.959269i \(0.408838\pi\)
\(812\) 0 0
\(813\) 656.000 231.931i 0.806888 0.285278i
\(814\) −350.000 + 606.218i −0.429975 + 0.744739i
\(815\) 845.241 488.000i 1.03711 0.598773i
\(816\) −249.535 + 291.871i −0.305802 + 0.357685i
\(817\) 735.391 1273.73i 0.900111 1.55904i
\(818\) 462.000i 0.564792i
\(819\) 0 0
\(820\) 128.000 0.156098
\(821\) 323.333 + 186.676i 0.393828 + 0.227377i 0.683817 0.729653i \(-0.260318\pi\)
−0.289990 + 0.957030i \(0.593652\pi\)
\(822\) −218.903 187.151i −0.266305 0.227678i
\(823\) 700.000 + 1212.44i 0.850547 + 1.47319i 0.880716 + 0.473645i \(0.157062\pi\)
−0.0301688 + 0.999545i \(0.509604\pi\)
\(824\) −180.133 104.000i −0.218608 0.126214i
\(825\) −89.0955 252.000i −0.107994 0.305455i
\(826\) 0 0
\(827\) 55.1543i 0.0666921i −0.999444 0.0333460i \(-0.989384\pi\)
0.999444 0.0333460i \(-0.0106163\pi\)
\(828\) 25.1464 3.95691i 0.0303701 0.00477888i
\(829\) −548.008 949.177i −0.661047 1.14497i −0.980341 0.197311i \(-0.936779\pi\)
0.319294 0.947656i \(-0.396554\pi\)
\(830\) 303.737 175.362i 0.365948 0.211280i
\(831\) 254.359 1368.56i 0.306088 1.64689i
\(832\) −101.823 −0.122384
\(833\) 0 0
\(834\) −304.000 859.842i −0.364508 1.03099i
\(835\) −452.000 + 782.887i −0.541317 + 0.937589i
\(836\) 484.974 280.000i 0.580113 0.334928i
\(837\) 0 0
\(838\) −248.902 + 431.110i −0.297019 + 0.514451i
\(839\) 1250.00i 1.48987i −0.667138 0.744934i \(-0.732481\pi\)
0.667138 0.744934i \(-0.267519\pi\)
\(840\) 0 0
\(841\) −2359.00 −2.80499
\(842\) 293.939 + 169.706i 0.349096 + 0.201551i
\(843\) −77.1959 + 90.2929i −0.0915728 + 0.107109i
\(844\) −372.000 644.323i −0.440758 0.763416i
\(845\) 24.2487 + 14.0000i 0.0286967 + 0.0165680i
\(846\) 336.583 272.000i 0.397852 0.321513i
\(847\) 0 0
\(848\) 181.019i 0.213466i
\(849\) 136.445 734.133i 0.160712 0.864703i
\(850\) 203.647 + 352.727i 0.239584 + 0.414972i
\(851\) −61.2372 + 35.3553i −0.0719592 + 0.0415456i
\(852\) −525.572 97.6821i −0.616869 0.114650i
\(853\) 250.316 0.293453 0.146727 0.989177i \(-0.453126\pi\)
0.146727 + 0.989177i \(0.453126\pi\)
\(854\) 0 0
\(855\) 640.000 + 791.960i 0.748538 + 0.926269i
\(856\) 206.000 356.802i 0.240654 0.416825i
\(857\) −221.703 + 128.000i −0.258696 + 0.149358i −0.623740 0.781632i \(-0.714387\pi\)
0.365044 + 0.930990i \(0.381054\pi\)
\(858\) 406.318 + 347.381i 0.473564 + 0.404873i
\(859\) −393.151 + 680.958i −0.457685 + 0.792734i −0.998838 0.0481904i \(-0.984655\pi\)
0.541153 + 0.840924i \(0.317988\pi\)
\(860\) 416.000i 0.483721i
\(861\) 0 0
\(862\) −1038.00 −1.20418
\(863\) 1402.33 + 809.637i 1.62495 + 0.938166i 0.985568 + 0.169277i \(0.0541434\pi\)
0.639383 + 0.768889i \(0.279190\pi\)
\(864\) −4.22821 + 152.677i −0.00489376 + 0.176709i
\(865\) −264.000 457.261i −0.305202 0.528626i
\(866\) −524.811 303.000i −0.606018 0.349885i
\(867\) −2078.89 + 735.000i −2.39780 + 0.847751i
\(868\) 0 0
\(869\) 395.980i 0.455673i
\(870\) −943.837 175.420i −1.08487 0.201632i
\(871\) 76.3675 + 132.272i 0.0876780 + 0.151863i
\(872\) −431.110 + 248.902i −0.494392 + 0.285438i
\(873\) 33.6337 + 213.745i 0.0385266 + 0.244839i
\(874\) 56.5685 0.0647237
\(875\) 0 0
\(876\) 184.000 65.0538i 0.210046 0.0742624i
\(877\) 632.000 1094.66i 0.720639 1.24818i −0.240106 0.970747i \(-0.577182\pi\)
0.960744 0.277436i \(-0.0894846\pi\)
\(878\) −498.831 + 288.000i −0.568144 + 0.328018i
\(879\) −616.039 + 720.556i −0.700840 + 0.819745i
\(880\) −79.1960 + 137.171i −0.0899954 + 0.155877i
\(881\) 264.000i 0.299659i 0.988712 + 0.149830i \(0.0478726\pi\)
−0.988712 + 0.149830i \(0.952127\pi\)
\(882\) 0 0
\(883\) 1148.00 1.30011 0.650057 0.759886i \(-0.274745\pi\)
0.650057 + 0.759886i \(0.274745\pi\)
\(884\) −705.453 407.294i −0.798024 0.460739i
\(885\) −291.871 249.535i −0.329797 0.281960i
\(886\) 281.000 + 486.706i 0.317156 + 0.549330i
\(887\) 1110.24 + 641.000i 1.25168 + 0.722661i 0.971444 0.237269i \(-0.0762523\pi\)
0.280241 + 0.959930i \(0.409586\pi\)
\(888\) −141.421 400.000i −0.159258 0.450450i
\(889\) 0 0
\(890\) 316.784i 0.355937i
\(891\) 537.745 594.818i 0.603529 0.667585i
\(892\) 16.9706 + 29.3939i 0.0190253 + 0.0329528i
\(893\) 832.827 480.833i 0.932616 0.538446i
\(894\) 70.1681 377.535i 0.0784878 0.422298i
\(895\) 899.440 1.00496
\(896\) 0 0
\(897\) 18.0000 + 50.9117i 0.0200669 + 0.0567577i
\(898\) 12.0000 20.7846i 0.0133630 0.0231454i
\(899\) 0 0
\(900\) 151.182 + 58.2075i 0.167980 + 0.0646750i
\(901\) −724.077 + 1254.14i −0.803637 + 1.39194i
\(902\) 224.000i 0.248337i
\(903\) 0 0
\(904\) 48.0000 0.0530973
\(905\) 631.968 + 364.867i 0.698308 + 0.403168i
\(906\) −419.063 + 490.161i −0.462542 + 0.541017i
\(907\) −434.000 751.710i −0.478501 0.828787i 0.521196 0.853437i \(-0.325486\pi\)
−0.999696 + 0.0246500i \(0.992153\pi\)
\(908\) 665.108 + 384.000i 0.732497 + 0.422907i
\(909\) 203.647 + 252.000i 0.224034 + 0.277228i
\(910\) 0 0
\(911\) 1231.78i 1.35212i 0.736847 + 0.676059i \(0.236314\pi\)
−0.736847 + 0.676059i \(0.763686\pi\)
\(912\) −62.0204 + 333.697i −0.0680048 + 0.365895i
\(913\) −306.884 531.539i −0.336127 0.582190i
\(914\) 154.318 89.0955i 0.168838 0.0974786i
\(915\) 383.751 + 71.3235i 0.419400 + 0.0779491i
\(916\) −500.632 −0.546541
\(917\) 0 0
\(918\) −640.000 + 1040.86i −0.697168 + 1.13384i
\(919\) 64.0000 110.851i 0.0696409 0.120622i −0.829102 0.559097i \(-0.811148\pi\)
0.898743 + 0.438475i \(0.144481\pi\)
\(920\) −13.8564 + 8.00000i −0.0150613 + 0.00869565i
\(921\) −786.838 672.707i −0.854330 0.730409i
\(922\) 410.122 710.352i 0.444818 0.770447i
\(923\) 1134.00i 1.22860i
\(924\) 0 0
\(925\) −450.000 −0.486486
\(926\) 137.171 + 79.1960i 0.148133 + 0.0855248i
\(927\) −617.653 237.807i −0.666293 0.256534i
\(928\) −160.000 277.128i −0.172414 0.298629i
\(929\) 1274.79 + 736.000i 1.37222 + 0.792250i 0.991207 0.132321i \(-0.0422430\pi\)
0.381010 + 0.924571i \(0.375576\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 644.881i 0.691933i
\(933\) −1563.23 290.540i −1.67549 0.311404i
\(934\) 90.5097 + 156.767i 0.0969054 + 0.167845i
\(935\) −1097.37 + 633.568i −1.17366 + 0.677612i
\(936\) −320.062 + 50.3633i −0.341946 + 0.0538069i
\(937\) 507.703 0.541838 0.270919 0.962602i \(-0.412672\pi\)
0.270919 + 0.962602i \(0.412672\pi\)
\(938\) 0 0
\(939\) −420.000 + 148.492i −0.447284 + 0.158139i
\(940\) −136.000 + 235.559i −0.144681 + 0.250595i
\(941\) 959.556 554.000i 1.01972 0.588735i 0.105697 0.994398i \(-0.466293\pi\)
0.914023 + 0.405663i \(0.132959\pi\)
\(942\) 471.777 551.818i 0.500824 0.585794i
\(943\) 11.3137 19.5959i 0.0119976 0.0207804i
\(944\) 128.000i 0.135593i
\(945\) 0 0
\(946\) 728.000 0.769556
\(947\) 216.780 + 125.158i 0.228912 + 0.132163i 0.610070 0.792347i \(-0.291141\pi\)
−0.381158 + 0.924510i \(0.624475\pi\)
\(948\) −182.419 155.959i −0.192425 0.164514i
\(949\) 207.000 + 358.535i 0.218124 + 0.377802i
\(950\) 311.769 + 180.000i 0.328178 + 0.189474i
\(951\) 113.137 + 320.000i 0.118966 + 0.336488i
\(952\) 0 0
\(953\) 497.803i 0.522354i −0.965291 0.261177i \(-0.915889\pi\)
0.965291 0.261177i \(-0.0841106\pi\)
\(954\) 89.5347 + 568.999i 0.0938519 + 0.596435i
\(955\) 19.7990 + 34.2929i 0.0207319 + 0.0359088i
\(956\) −492.347 + 284.257i −0.515008 + 0.297340i
\(957\) −306.985 + 1651.71i −0.320779 + 1.72593i
\(958\) −681.651 −0.711535
\(959\) 0 0
\(960\) −32.0000 90.5097i −0.0333333 0.0942809i
\(961\) 480.500 832.250i 0.500000 0.866025i
\(962\) 779.423 450.000i 0.810211 0.467775i
\(963\) 471.041 1223.43i 0.489139 1.27044i
\(964\) −46.6690 + 80.8332i −0.0484119 + 0.0838518i
\(965\) 640.000i 0.663212i
\(966\) 0 0
\(967\) −384.000 −0.397104 −0.198552 0.980090i \(-0.563624\pi\)
−0.198552 + 0.980090i \(0.563624\pi\)
\(968\) −56.3383 32.5269i −0.0582007 0.0336022i
\(969\) −1764.48 + 2063.84i −1.82093 + 2.12986i
\(970\) −68.0000 117.779i −0.0701031 0.121422i
\(971\) −289.252 167.000i −0.297891 0.171988i 0.343604 0.939115i \(-0.388352\pi\)
−0.641495 + 0.767127i \(0.721686\pi\)
\(972\) 62.2254 + 482.000i 0.0640179 + 0.495885i
\(973\) 0 0
\(974\) 169.706i 0.174236i
\(975\) −62.7957 + 337.868i −0.0644058 + 0.346531i
\(976\) 65.0538 + 112.677i 0.0666535 + 0.115447i
\(977\) −44.0908 + 25.4558i −0.0451288 + 0.0260551i −0.522395 0.852704i \(-0.674961\pi\)
0.477266 + 0.878759i \(0.341628\pi\)
\(978\) 1017.77 + 189.162i 1.04067 + 0.193417i
\(979\) 554.372 0.566263
\(980\) 0 0
\(981\) −1232.00 + 995.606i −1.25586 + 1.01489i
\(982\) −441.000 + 763.834i −0.449084 + 0.777835i
\(983\) −969.948 + 560.000i −0.986723 + 0.569685i −0.904293 0.426912i \(-0.859601\pi\)
−0.0824297 + 0.996597i \(0.526268\pi\)
\(984\) 103.192 + 88.2238i 0.104870 + 0.0896584i
\(985\) 214.960 372.322i 0.218234 0.377992i
\(986\) 2560.00i 2.59635i
\(987\) 0 0
\(988\) −720.000 −0.728745
\(989\) 63.6867 + 36.7696i 0.0643951 + 0.0371785i
\(990\) −181.090 + 470.343i −0.182919 + 0.475094i
\(991\) −508.000 879.882i −0.512614 0.887873i −0.999893 0.0146266i \(-0.995344\pi\)
0.487280 0.873246i \(-0.337989\pi\)
\(992\) 0 0
\(993\) 147.078 52.0000i 0.148115 0.0523666i
\(994\) 0 0
\(995\) 882.469i 0.886904i
\(996\) 365.737 + 67.9753i 0.367206 + 0.0682483i
\(997\) 610.233 + 1056.95i 0.612069 + 1.06014i 0.990891 + 0.134666i \(0.0429960\pi\)
−0.378822 + 0.925470i \(0.623671\pi\)
\(998\) −347.828 + 200.818i −0.348525 + 0.201221i
\(999\) −642.376 1187.37i −0.643019 1.18856i
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 294.3.h.e.275.3 8
3.2 odd 2 inner 294.3.h.e.275.1 8
7.2 even 3 294.3.b.g.197.2 yes 4
7.3 odd 6 inner 294.3.h.e.263.2 8
7.4 even 3 inner 294.3.h.e.263.1 8
7.5 odd 6 294.3.b.g.197.1 4
7.6 odd 2 inner 294.3.h.e.275.4 8
21.2 odd 6 294.3.b.g.197.4 yes 4
21.5 even 6 294.3.b.g.197.3 yes 4
21.11 odd 6 inner 294.3.h.e.263.3 8
21.17 even 6 inner 294.3.h.e.263.4 8
21.20 even 2 inner 294.3.h.e.275.2 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
294.3.b.g.197.1 4 7.5 odd 6
294.3.b.g.197.2 yes 4 7.2 even 3
294.3.b.g.197.3 yes 4 21.5 even 6
294.3.b.g.197.4 yes 4 21.2 odd 6
294.3.h.e.263.1 8 7.4 even 3 inner
294.3.h.e.263.2 8 7.3 odd 6 inner
294.3.h.e.263.3 8 21.11 odd 6 inner
294.3.h.e.263.4 8 21.17 even 6 inner
294.3.h.e.275.1 8 3.2 odd 2 inner
294.3.h.e.275.2 8 21.20 even 2 inner
294.3.h.e.275.3 8 1.1 even 1 trivial
294.3.h.e.275.4 8 7.6 odd 2 inner