Properties

Label 1050.2.m.d.643.1
Level $1050$
Weight $2$
Character 1050.643
Analytic conductor $8.384$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1050,2,Mod(307,1050)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1050, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 1, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1050.307");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1050.m (of order \(4\), degree \(2\), 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: \(8.38429221223\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(i)\)
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: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{4} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 643.1
Root \(-0.965926 + 0.258819i\) of defining polynomial
Character \(\chi\) \(=\) 1050.643
Dual form 1050.2.m.d.307.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.707107 + 0.707107i) q^{2} +(-0.707107 + 0.707107i) q^{3} -1.00000i q^{4} -1.00000i q^{6} +(-2.63896 + 0.189469i) q^{7} +(0.707107 + 0.707107i) q^{8} -1.00000i q^{9} +O(q^{10})\) \(q+(-0.707107 + 0.707107i) q^{2} +(-0.707107 + 0.707107i) q^{3} -1.00000i q^{4} -1.00000i q^{6} +(-2.63896 + 0.189469i) q^{7} +(0.707107 + 0.707107i) q^{8} -1.00000i q^{9} -5.46410 q^{11} +(0.707107 + 0.707107i) q^{12} +(-2.63896 + 2.63896i) q^{13} +(1.73205 - 2.00000i) q^{14} -1.00000 q^{16} +(3.53553 + 3.53553i) q^{17} +(0.707107 + 0.707107i) q^{18} +7.46410 q^{19} +(1.73205 - 2.00000i) q^{21} +(3.86370 - 3.86370i) q^{22} +(-0.707107 - 0.707107i) q^{23} -1.00000 q^{24} -3.73205i q^{26} +(0.707107 + 0.707107i) q^{27} +(0.189469 + 2.63896i) q^{28} -7.73205i q^{29} -7.92820i q^{31} +(0.707107 - 0.707107i) q^{32} +(3.86370 - 3.86370i) q^{33} -5.00000 q^{34} -1.00000 q^{36} +(4.89898 - 4.89898i) q^{37} +(-5.27792 + 5.27792i) q^{38} -3.73205i q^{39} +5.73205i q^{41} +(0.189469 + 2.63896i) q^{42} +(-2.63896 - 2.63896i) q^{43} +5.46410i q^{44} +1.00000 q^{46} +(-5.93426 - 5.93426i) q^{47} +(0.707107 - 0.707107i) q^{48} +(6.92820 - 1.00000i) q^{49} -5.00000 q^{51} +(2.63896 + 2.63896i) q^{52} +(-2.50026 - 2.50026i) q^{53} -1.00000 q^{54} +(-2.00000 - 1.73205i) q^{56} +(-5.27792 + 5.27792i) q^{57} +(5.46739 + 5.46739i) q^{58} +7.19615 q^{59} -2.46410i q^{61} +(5.60609 + 5.60609i) q^{62} +(0.189469 + 2.63896i) q^{63} +1.00000i q^{64} +5.46410i q^{66} +(4.52004 - 4.52004i) q^{67} +(3.53553 - 3.53553i) q^{68} +1.00000 q^{69} -11.4641 q^{71} +(0.707107 - 0.707107i) q^{72} +(8.76268 - 8.76268i) q^{73} +6.92820i q^{74} -7.46410i q^{76} +(14.4195 - 1.03528i) q^{77} +(2.63896 + 2.63896i) q^{78} -12.3923i q^{79} -1.00000 q^{81} +(-4.05317 - 4.05317i) q^{82} +(-0.328169 + 0.328169i) q^{83} +(-2.00000 - 1.73205i) q^{84} +3.73205 q^{86} +(5.46739 + 5.46739i) q^{87} +(-3.86370 - 3.86370i) q^{88} +12.0000 q^{89} +(6.46410 - 7.46410i) q^{91} +(-0.707107 + 0.707107i) q^{92} +(5.60609 + 5.60609i) q^{93} +8.39230 q^{94} +1.00000i q^{96} +(-2.17209 - 2.17209i) q^{97} +(-4.19187 + 5.60609i) q^{98} +5.46410i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 16 q^{11} - 8 q^{16} + 32 q^{19} - 8 q^{24} - 40 q^{34} - 8 q^{36} + 8 q^{46} - 40 q^{51} - 8 q^{54} - 16 q^{56} + 16 q^{59} + 8 q^{69} - 64 q^{71} - 8 q^{81} - 16 q^{84} + 16 q^{86} + 96 q^{89} + 24 q^{91} - 16 q^{94}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(451\) \(701\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.707107 + 0.707107i −0.500000 + 0.500000i
\(3\) −0.707107 + 0.707107i −0.408248 + 0.408248i
\(4\) 1.00000i 0.500000i
\(5\) 0 0
\(6\) 1.00000i 0.408248i
\(7\) −2.63896 + 0.189469i −0.997433 + 0.0716124i
\(8\) 0.707107 + 0.707107i 0.250000 + 0.250000i
\(9\) 1.00000i 0.333333i
\(10\) 0 0
\(11\) −5.46410 −1.64749 −0.823744 0.566961i \(-0.808119\pi\)
−0.823744 + 0.566961i \(0.808119\pi\)
\(12\) 0.707107 + 0.707107i 0.204124 + 0.204124i
\(13\) −2.63896 + 2.63896i −0.731915 + 0.731915i −0.970999 0.239084i \(-0.923153\pi\)
0.239084 + 0.970999i \(0.423153\pi\)
\(14\) 1.73205 2.00000i 0.462910 0.534522i
\(15\) 0 0
\(16\) −1.00000 −0.250000
\(17\) 3.53553 + 3.53553i 0.857493 + 0.857493i 0.991042 0.133549i \(-0.0426374\pi\)
−0.133549 + 0.991042i \(0.542637\pi\)
\(18\) 0.707107 + 0.707107i 0.166667 + 0.166667i
\(19\) 7.46410 1.71238 0.856191 0.516659i \(-0.172825\pi\)
0.856191 + 0.516659i \(0.172825\pi\)
\(20\) 0 0
\(21\) 1.73205 2.00000i 0.377964 0.436436i
\(22\) 3.86370 3.86370i 0.823744 0.823744i
\(23\) −0.707107 0.707107i −0.147442 0.147442i 0.629532 0.776974i \(-0.283247\pi\)
−0.776974 + 0.629532i \(0.783247\pi\)
\(24\) −1.00000 −0.204124
\(25\) 0 0
\(26\) 3.73205i 0.731915i
\(27\) 0.707107 + 0.707107i 0.136083 + 0.136083i
\(28\) 0.189469 + 2.63896i 0.0358062 + 0.498716i
\(29\) 7.73205i 1.43581i −0.696143 0.717903i \(-0.745102\pi\)
0.696143 0.717903i \(-0.254898\pi\)
\(30\) 0 0
\(31\) 7.92820i 1.42395i −0.702206 0.711974i \(-0.747802\pi\)
0.702206 0.711974i \(-0.252198\pi\)
\(32\) 0.707107 0.707107i 0.125000 0.125000i
\(33\) 3.86370 3.86370i 0.672584 0.672584i
\(34\) −5.00000 −0.857493
\(35\) 0 0
\(36\) −1.00000 −0.166667
\(37\) 4.89898 4.89898i 0.805387 0.805387i −0.178545 0.983932i \(-0.557139\pi\)
0.983932 + 0.178545i \(0.0571389\pi\)
\(38\) −5.27792 + 5.27792i −0.856191 + 0.856191i
\(39\) 3.73205i 0.597606i
\(40\) 0 0
\(41\) 5.73205i 0.895196i 0.894235 + 0.447598i \(0.147720\pi\)
−0.894235 + 0.447598i \(0.852280\pi\)
\(42\) 0.189469 + 2.63896i 0.0292357 + 0.407200i
\(43\) −2.63896 2.63896i −0.402437 0.402437i 0.476654 0.879091i \(-0.341850\pi\)
−0.879091 + 0.476654i \(0.841850\pi\)
\(44\) 5.46410i 0.823744i
\(45\) 0 0
\(46\) 1.00000 0.147442
\(47\) −5.93426 5.93426i −0.865600 0.865600i 0.126382 0.991982i \(-0.459664\pi\)
−0.991982 + 0.126382i \(0.959664\pi\)
\(48\) 0.707107 0.707107i 0.102062 0.102062i
\(49\) 6.92820 1.00000i 0.989743 0.142857i
\(50\) 0 0
\(51\) −5.00000 −0.700140
\(52\) 2.63896 + 2.63896i 0.365958 + 0.365958i
\(53\) −2.50026 2.50026i −0.343437 0.343437i 0.514221 0.857658i \(-0.328081\pi\)
−0.857658 + 0.514221i \(0.828081\pi\)
\(54\) −1.00000 −0.136083
\(55\) 0 0
\(56\) −2.00000 1.73205i −0.267261 0.231455i
\(57\) −5.27792 + 5.27792i −0.699077 + 0.699077i
\(58\) 5.46739 + 5.46739i 0.717903 + 0.717903i
\(59\) 7.19615 0.936859 0.468430 0.883501i \(-0.344820\pi\)
0.468430 + 0.883501i \(0.344820\pi\)
\(60\) 0 0
\(61\) 2.46410i 0.315496i −0.987479 0.157748i \(-0.949577\pi\)
0.987479 0.157748i \(-0.0504233\pi\)
\(62\) 5.60609 + 5.60609i 0.711974 + 0.711974i
\(63\) 0.189469 + 2.63896i 0.0238708 + 0.332478i
\(64\) 1.00000i 0.125000i
\(65\) 0 0
\(66\) 5.46410i 0.672584i
\(67\) 4.52004 4.52004i 0.552211 0.552211i −0.374867 0.927078i \(-0.622312\pi\)
0.927078 + 0.374867i \(0.122312\pi\)
\(68\) 3.53553 3.53553i 0.428746 0.428746i
\(69\) 1.00000 0.120386
\(70\) 0 0
\(71\) −11.4641 −1.36054 −0.680269 0.732962i \(-0.738137\pi\)
−0.680269 + 0.732962i \(0.738137\pi\)
\(72\) 0.707107 0.707107i 0.0833333 0.0833333i
\(73\) 8.76268 8.76268i 1.02559 1.02559i 0.0259307 0.999664i \(-0.491745\pi\)
0.999664 0.0259307i \(-0.00825492\pi\)
\(74\) 6.92820i 0.805387i
\(75\) 0 0
\(76\) 7.46410i 0.856191i
\(77\) 14.4195 1.03528i 1.64326 0.117981i
\(78\) 2.63896 + 2.63896i 0.298803 + 0.298803i
\(79\) 12.3923i 1.39424i −0.716953 0.697122i \(-0.754464\pi\)
0.716953 0.697122i \(-0.245536\pi\)
\(80\) 0 0
\(81\) −1.00000 −0.111111
\(82\) −4.05317 4.05317i −0.447598 0.447598i
\(83\) −0.328169 + 0.328169i −0.0360213 + 0.0360213i −0.724888 0.688867i \(-0.758109\pi\)
0.688867 + 0.724888i \(0.258109\pi\)
\(84\) −2.00000 1.73205i −0.218218 0.188982i
\(85\) 0 0
\(86\) 3.73205 0.402437
\(87\) 5.46739 + 5.46739i 0.586165 + 0.586165i
\(88\) −3.86370 3.86370i −0.411872 0.411872i
\(89\) 12.0000 1.27200 0.635999 0.771690i \(-0.280588\pi\)
0.635999 + 0.771690i \(0.280588\pi\)
\(90\) 0 0
\(91\) 6.46410 7.46410i 0.677622 0.782450i
\(92\) −0.707107 + 0.707107i −0.0737210 + 0.0737210i
\(93\) 5.60609 + 5.60609i 0.581324 + 0.581324i
\(94\) 8.39230 0.865600
\(95\) 0 0
\(96\) 1.00000i 0.102062i
\(97\) −2.17209 2.17209i −0.220542 0.220542i 0.588185 0.808727i \(-0.299843\pi\)
−0.808727 + 0.588185i \(0.799843\pi\)
\(98\) −4.19187 + 5.60609i −0.423443 + 0.566300i
\(99\) 5.46410i 0.549163i
\(100\) 0 0
\(101\) 6.53590i 0.650346i 0.945655 + 0.325173i \(0.105423\pi\)
−0.945655 + 0.325173i \(0.894577\pi\)
\(102\) 3.53553 3.53553i 0.350070 0.350070i
\(103\) 2.91636 2.91636i 0.287357 0.287357i −0.548677 0.836034i \(-0.684868\pi\)
0.836034 + 0.548677i \(0.184868\pi\)
\(104\) −3.73205 −0.365958
\(105\) 0 0
\(106\) 3.53590 0.343437
\(107\) −6.31319 + 6.31319i −0.610319 + 0.610319i −0.943029 0.332710i \(-0.892037\pi\)
0.332710 + 0.943029i \(0.392037\pi\)
\(108\) 0.707107 0.707107i 0.0680414 0.0680414i
\(109\) 12.3923i 1.18697i 0.804846 + 0.593484i \(0.202248\pi\)
−0.804846 + 0.593484i \(0.797752\pi\)
\(110\) 0 0
\(111\) 6.92820i 0.657596i
\(112\) 2.63896 0.189469i 0.249358 0.0179031i
\(113\) −1.79315 1.79315i −0.168685 0.168685i 0.617716 0.786401i \(-0.288058\pi\)
−0.786401 + 0.617716i \(0.788058\pi\)
\(114\) 7.46410i 0.699077i
\(115\) 0 0
\(116\) −7.73205 −0.717903
\(117\) 2.63896 + 2.63896i 0.243972 + 0.243972i
\(118\) −5.08845 + 5.08845i −0.468430 + 0.468430i
\(119\) −10.0000 8.66025i −0.916698 0.793884i
\(120\) 0 0
\(121\) 18.8564 1.71422
\(122\) 1.74238 + 1.74238i 0.157748 + 0.157748i
\(123\) −4.05317 4.05317i −0.365462 0.365462i
\(124\) −7.92820 −0.711974
\(125\) 0 0
\(126\) −2.00000 1.73205i −0.178174 0.154303i
\(127\) 5.27792 5.27792i 0.468339 0.468339i −0.433037 0.901376i \(-0.642558\pi\)
0.901376 + 0.433037i \(0.142558\pi\)
\(128\) −0.707107 0.707107i −0.0625000 0.0625000i
\(129\) 3.73205 0.328589
\(130\) 0 0
\(131\) 14.3923i 1.25746i 0.777623 + 0.628731i \(0.216425\pi\)
−0.777623 + 0.628731i \(0.783575\pi\)
\(132\) −3.86370 3.86370i −0.336292 0.336292i
\(133\) −19.6975 + 1.41421i −1.70799 + 0.122628i
\(134\) 6.39230i 0.552211i
\(135\) 0 0
\(136\) 5.00000i 0.428746i
\(137\) −5.55532 + 5.55532i −0.474623 + 0.474623i −0.903407 0.428784i \(-0.858942\pi\)
0.428784 + 0.903407i \(0.358942\pi\)
\(138\) −0.707107 + 0.707107i −0.0601929 + 0.0601929i
\(139\) −19.8564 −1.68420 −0.842099 0.539323i \(-0.818680\pi\)
−0.842099 + 0.539323i \(0.818680\pi\)
\(140\) 0 0
\(141\) 8.39230 0.706760
\(142\) 8.10634 8.10634i 0.680269 0.680269i
\(143\) 14.4195 14.4195i 1.20582 1.20582i
\(144\) 1.00000i 0.0833333i
\(145\) 0 0
\(146\) 12.3923i 1.02559i
\(147\) −4.19187 + 5.60609i −0.345740 + 0.462382i
\(148\) −4.89898 4.89898i −0.402694 0.402694i
\(149\) 7.73205i 0.633434i 0.948520 + 0.316717i \(0.102581\pi\)
−0.948520 + 0.316717i \(0.897419\pi\)
\(150\) 0 0
\(151\) 16.0000 1.30206 0.651031 0.759051i \(-0.274337\pi\)
0.651031 + 0.759051i \(0.274337\pi\)
\(152\) 5.27792 + 5.27792i 0.428096 + 0.428096i
\(153\) 3.53553 3.53553i 0.285831 0.285831i
\(154\) −9.46410 + 10.9282i −0.762639 + 0.880620i
\(155\) 0 0
\(156\) −3.73205 −0.298803
\(157\) −5.65685 5.65685i −0.451466 0.451466i 0.444375 0.895841i \(-0.353426\pi\)
−0.895841 + 0.444375i \(0.853426\pi\)
\(158\) 8.76268 + 8.76268i 0.697122 + 0.697122i
\(159\) 3.53590 0.280415
\(160\) 0 0
\(161\) 2.00000 + 1.73205i 0.157622 + 0.136505i
\(162\) 0.707107 0.707107i 0.0555556 0.0555556i
\(163\) 0.568406 + 0.568406i 0.0445210 + 0.0445210i 0.729017 0.684496i \(-0.239978\pi\)
−0.684496 + 0.729017i \(0.739978\pi\)
\(164\) 5.73205 0.447598
\(165\) 0 0
\(166\) 0.464102i 0.0360213i
\(167\) −10.9348 10.9348i −0.846158 0.846158i 0.143493 0.989651i \(-0.454166\pi\)
−0.989651 + 0.143493i \(0.954166\pi\)
\(168\) 2.63896 0.189469i 0.203600 0.0146178i
\(169\) 0.928203i 0.0714002i
\(170\) 0 0
\(171\) 7.46410i 0.570794i
\(172\) −2.63896 + 2.63896i −0.201219 + 0.201219i
\(173\) 6.59059 6.59059i 0.501074 0.501074i −0.410698 0.911771i \(-0.634715\pi\)
0.911771 + 0.410698i \(0.134715\pi\)
\(174\) −7.73205 −0.586165
\(175\) 0 0
\(176\) 5.46410 0.411872
\(177\) −5.08845 + 5.08845i −0.382471 + 0.382471i
\(178\) −8.48528 + 8.48528i −0.635999 + 0.635999i
\(179\) 13.8564i 1.03568i −0.855479 0.517838i \(-0.826737\pi\)
0.855479 0.517838i \(-0.173263\pi\)
\(180\) 0 0
\(181\) 2.00000i 0.148659i −0.997234 0.0743294i \(-0.976318\pi\)
0.997234 0.0743294i \(-0.0236816\pi\)
\(182\) 0.707107 + 9.84873i 0.0524142 + 0.730036i
\(183\) 1.74238 + 1.74238i 0.128801 + 0.128801i
\(184\) 1.00000i 0.0737210i
\(185\) 0 0
\(186\) −7.92820 −0.581324
\(187\) −19.3185 19.3185i −1.41271 1.41271i
\(188\) −5.93426 + 5.93426i −0.432800 + 0.432800i
\(189\) −2.00000 1.73205i −0.145479 0.125988i
\(190\) 0 0
\(191\) 6.26795 0.453533 0.226766 0.973949i \(-0.427185\pi\)
0.226766 + 0.973949i \(0.427185\pi\)
\(192\) −0.707107 0.707107i −0.0510310 0.0510310i
\(193\) −12.6264 12.6264i −0.908867 0.908867i 0.0873137 0.996181i \(-0.472172\pi\)
−0.996181 + 0.0873137i \(0.972172\pi\)
\(194\) 3.07180 0.220542
\(195\) 0 0
\(196\) −1.00000 6.92820i −0.0714286 0.494872i
\(197\) −5.22715 + 5.22715i −0.372419 + 0.372419i −0.868358 0.495939i \(-0.834824\pi\)
0.495939 + 0.868358i \(0.334824\pi\)
\(198\) −3.86370 3.86370i −0.274581 0.274581i
\(199\) 16.0000 1.13421 0.567105 0.823646i \(-0.308063\pi\)
0.567105 + 0.823646i \(0.308063\pi\)
\(200\) 0 0
\(201\) 6.39230i 0.450878i
\(202\) −4.62158 4.62158i −0.325173 0.325173i
\(203\) 1.46498 + 20.4046i 0.102822 + 1.43212i
\(204\) 5.00000i 0.350070i
\(205\) 0 0
\(206\) 4.12436i 0.287357i
\(207\) −0.707107 + 0.707107i −0.0491473 + 0.0491473i
\(208\) 2.63896 2.63896i 0.182979 0.182979i
\(209\) −40.7846 −2.82113
\(210\) 0 0
\(211\) −10.3205 −0.710493 −0.355247 0.934773i \(-0.615603\pi\)
−0.355247 + 0.934773i \(0.615603\pi\)
\(212\) −2.50026 + 2.50026i −0.171718 + 0.171718i
\(213\) 8.10634 8.10634i 0.555438 0.555438i
\(214\) 8.92820i 0.610319i
\(215\) 0 0
\(216\) 1.00000i 0.0680414i
\(217\) 1.50215 + 20.9222i 0.101972 + 1.42029i
\(218\) −8.76268 8.76268i −0.593484 0.593484i
\(219\) 12.3923i 0.837394i
\(220\) 0 0
\(221\) −18.6603 −1.25522
\(222\) −4.89898 4.89898i −0.328798 0.328798i
\(223\) −8.19428 + 8.19428i −0.548729 + 0.548729i −0.926073 0.377344i \(-0.876837\pi\)
0.377344 + 0.926073i \(0.376837\pi\)
\(224\) −1.73205 + 2.00000i −0.115728 + 0.133631i
\(225\) 0 0
\(226\) 2.53590 0.168685
\(227\) −0.984508 0.984508i −0.0653441 0.0653441i 0.673680 0.739024i \(-0.264713\pi\)
−0.739024 + 0.673680i \(0.764713\pi\)
\(228\) 5.27792 + 5.27792i 0.349539 + 0.349539i
\(229\) 15.0718 0.995972 0.497986 0.867185i \(-0.334073\pi\)
0.497986 + 0.867185i \(0.334073\pi\)
\(230\) 0 0
\(231\) −9.46410 + 10.9282i −0.622692 + 0.719023i
\(232\) 5.46739 5.46739i 0.358951 0.358951i
\(233\) −7.34847 7.34847i −0.481414 0.481414i 0.424169 0.905583i \(-0.360566\pi\)
−0.905583 + 0.424169i \(0.860566\pi\)
\(234\) −3.73205 −0.243972
\(235\) 0 0
\(236\) 7.19615i 0.468430i
\(237\) 8.76268 + 8.76268i 0.569197 + 0.569197i
\(238\) 13.1948 0.947343i 0.855291 0.0614072i
\(239\) 8.53590i 0.552141i 0.961137 + 0.276071i \(0.0890324\pi\)
−0.961137 + 0.276071i \(0.910968\pi\)
\(240\) 0 0
\(241\) 0.928203i 0.0597908i −0.999553 0.0298954i \(-0.990483\pi\)
0.999553 0.0298954i \(-0.00951742\pi\)
\(242\) −13.3335 + 13.3335i −0.857109 + 0.857109i
\(243\) 0.707107 0.707107i 0.0453609 0.0453609i
\(244\) −2.46410 −0.157748
\(245\) 0 0
\(246\) 5.73205 0.365462
\(247\) −19.6975 + 19.6975i −1.25332 + 1.25332i
\(248\) 5.60609 5.60609i 0.355987 0.355987i
\(249\) 0.464102i 0.0294112i
\(250\) 0 0
\(251\) 20.2679i 1.27930i −0.768666 0.639651i \(-0.779079\pi\)
0.768666 0.639651i \(-0.220921\pi\)
\(252\) 2.63896 0.189469i 0.166239 0.0119354i
\(253\) 3.86370 + 3.86370i 0.242909 + 0.242909i
\(254\) 7.46410i 0.468339i
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) −16.9198 16.9198i −1.05543 1.05543i −0.998371 0.0570569i \(-0.981828\pi\)
−0.0570569 0.998371i \(-0.518172\pi\)
\(258\) −2.63896 + 2.63896i −0.164294 + 0.164294i
\(259\) −12.0000 + 13.8564i −0.745644 + 0.860995i
\(260\) 0 0
\(261\) −7.73205 −0.478602
\(262\) −10.1769 10.1769i −0.628731 0.628731i
\(263\) 4.94975 + 4.94975i 0.305215 + 0.305215i 0.843050 0.537835i \(-0.180758\pi\)
−0.537835 + 0.843050i \(0.680758\pi\)
\(264\) 5.46410 0.336292
\(265\) 0 0
\(266\) 12.9282 14.9282i 0.792679 0.915307i
\(267\) −8.48528 + 8.48528i −0.519291 + 0.519291i
\(268\) −4.52004 4.52004i −0.276106 0.276106i
\(269\) −21.8564 −1.33261 −0.666304 0.745680i \(-0.732125\pi\)
−0.666304 + 0.745680i \(0.732125\pi\)
\(270\) 0 0
\(271\) 2.92820i 0.177876i 0.996037 + 0.0889378i \(0.0283472\pi\)
−0.996037 + 0.0889378i \(0.971653\pi\)
\(272\) −3.53553 3.53553i −0.214373 0.214373i
\(273\) 0.707107 + 9.84873i 0.0427960 + 0.596072i
\(274\) 7.85641i 0.474623i
\(275\) 0 0
\(276\) 1.00000i 0.0601929i
\(277\) 5.93426 5.93426i 0.356555 0.356555i −0.505987 0.862541i \(-0.668871\pi\)
0.862541 + 0.505987i \(0.168871\pi\)
\(278\) 14.0406 14.0406i 0.842099 0.842099i
\(279\) −7.92820 −0.474649
\(280\) 0 0
\(281\) 13.8564 0.826604 0.413302 0.910594i \(-0.364375\pi\)
0.413302 + 0.910594i \(0.364375\pi\)
\(282\) −5.93426 + 5.93426i −0.353380 + 0.353380i
\(283\) −16.1112 + 16.1112i −0.957709 + 0.957709i −0.999141 0.0414327i \(-0.986808\pi\)
0.0414327 + 0.999141i \(0.486808\pi\)
\(284\) 11.4641i 0.680269i
\(285\) 0 0
\(286\) 20.3923i 1.20582i
\(287\) −1.08604 15.1266i −0.0641072 0.892898i
\(288\) −0.707107 0.707107i −0.0416667 0.0416667i
\(289\) 8.00000i 0.470588i
\(290\) 0 0
\(291\) 3.07180 0.180072
\(292\) −8.76268 8.76268i −0.512797 0.512797i
\(293\) −1.31268 + 1.31268i −0.0766874 + 0.0766874i −0.744410 0.667723i \(-0.767269\pi\)
0.667723 + 0.744410i \(0.267269\pi\)
\(294\) −1.00000 6.92820i −0.0583212 0.404061i
\(295\) 0 0
\(296\) 6.92820 0.402694
\(297\) −3.86370 3.86370i −0.224195 0.224195i
\(298\) −5.46739 5.46739i −0.316717 0.316717i
\(299\) 3.73205 0.215830
\(300\) 0 0
\(301\) 7.46410 + 6.46410i 0.430224 + 0.372585i
\(302\) −11.3137 + 11.3137i −0.651031 + 0.651031i
\(303\) −4.62158 4.62158i −0.265503 0.265503i
\(304\) −7.46410 −0.428096
\(305\) 0 0
\(306\) 5.00000i 0.285831i
\(307\) −3.58630 3.58630i −0.204681 0.204681i 0.597321 0.802002i \(-0.296232\pi\)
−0.802002 + 0.597321i \(0.796232\pi\)
\(308\) −1.03528 14.4195i −0.0589903 0.821629i
\(309\) 4.12436i 0.234626i
\(310\) 0 0
\(311\) 25.8564i 1.46618i −0.680130 0.733091i \(-0.738077\pi\)
0.680130 0.733091i \(-0.261923\pi\)
\(312\) 2.63896 2.63896i 0.149402 0.149402i
\(313\) 21.3891 21.3891i 1.20898 1.20898i 0.237625 0.971357i \(-0.423631\pi\)
0.971357 0.237625i \(-0.0763688\pi\)
\(314\) 8.00000 0.451466
\(315\) 0 0
\(316\) −12.3923 −0.697122
\(317\) 19.3693 19.3693i 1.08789 1.08789i 0.0921415 0.995746i \(-0.470629\pi\)
0.995746 0.0921415i \(-0.0293712\pi\)
\(318\) −2.50026 + 2.50026i −0.140207 + 0.140207i
\(319\) 42.2487i 2.36547i
\(320\) 0 0
\(321\) 8.92820i 0.498324i
\(322\) −2.63896 + 0.189469i −0.147063 + 0.0105587i
\(323\) 26.3896 + 26.3896i 1.46836 + 1.46836i
\(324\) 1.00000i 0.0555556i
\(325\) 0 0
\(326\) −0.803848 −0.0445210
\(327\) −8.76268 8.76268i −0.484577 0.484577i
\(328\) −4.05317 + 4.05317i −0.223799 + 0.223799i
\(329\) 16.7846 + 14.5359i 0.925365 + 0.801390i
\(330\) 0 0
\(331\) −30.3205 −1.66657 −0.833283 0.552847i \(-0.813541\pi\)
−0.833283 + 0.552847i \(0.813541\pi\)
\(332\) 0.328169 + 0.328169i 0.0180106 + 0.0180106i
\(333\) −4.89898 4.89898i −0.268462 0.268462i
\(334\) 15.4641 0.846158
\(335\) 0 0
\(336\) −1.73205 + 2.00000i −0.0944911 + 0.109109i
\(337\) 15.7458 15.7458i 0.857729 0.857729i −0.133341 0.991070i \(-0.542571\pi\)
0.991070 + 0.133341i \(0.0425705\pi\)
\(338\) 0.656339 + 0.656339i 0.0357001 + 0.0357001i
\(339\) 2.53590 0.137731
\(340\) 0 0
\(341\) 43.3205i 2.34594i
\(342\) 5.27792 + 5.27792i 0.285397 + 0.285397i
\(343\) −18.0938 + 3.95164i −0.976972 + 0.213368i
\(344\) 3.73205i 0.201219i
\(345\) 0 0
\(346\) 9.32051i 0.501074i
\(347\) 3.20736 3.20736i 0.172180 0.172180i −0.615756 0.787937i \(-0.711149\pi\)
0.787937 + 0.615756i \(0.211149\pi\)
\(348\) 5.46739 5.46739i 0.293083 0.293083i
\(349\) −4.60770 −0.246644 −0.123322 0.992367i \(-0.539355\pi\)
−0.123322 + 0.992367i \(0.539355\pi\)
\(350\) 0 0
\(351\) −3.73205 −0.199202
\(352\) −3.86370 + 3.86370i −0.205936 + 0.205936i
\(353\) −9.14162 + 9.14162i −0.486559 + 0.486559i −0.907219 0.420659i \(-0.861799\pi\)
0.420659 + 0.907219i \(0.361799\pi\)
\(354\) 7.19615i 0.382471i
\(355\) 0 0
\(356\) 12.0000i 0.635999i
\(357\) 13.1948 0.947343i 0.698342 0.0501387i
\(358\) 9.79796 + 9.79796i 0.517838 + 0.517838i
\(359\) 36.1244i 1.90657i −0.302071 0.953285i \(-0.597678\pi\)
0.302071 0.953285i \(-0.402322\pi\)
\(360\) 0 0
\(361\) 36.7128 1.93225
\(362\) 1.41421 + 1.41421i 0.0743294 + 0.0743294i
\(363\) −13.3335 + 13.3335i −0.699827 + 0.699827i
\(364\) −7.46410 6.46410i −0.391225 0.338811i
\(365\) 0 0
\(366\) −2.46410 −0.128801
\(367\) 7.63947 + 7.63947i 0.398777 + 0.398777i 0.877802 0.479024i \(-0.159009\pi\)
−0.479024 + 0.877802i \(0.659009\pi\)
\(368\) 0.707107 + 0.707107i 0.0368605 + 0.0368605i
\(369\) 5.73205 0.298399
\(370\) 0 0
\(371\) 7.07180 + 6.12436i 0.367149 + 0.317961i
\(372\) 5.60609 5.60609i 0.290662 0.290662i
\(373\) 10.8332 + 10.8332i 0.560924 + 0.560924i 0.929570 0.368646i \(-0.120179\pi\)
−0.368646 + 0.929570i \(0.620179\pi\)
\(374\) 27.3205 1.41271
\(375\) 0 0
\(376\) 8.39230i 0.432800i
\(377\) 20.4046 + 20.4046i 1.05089 + 1.05089i
\(378\) 2.63896 0.189469i 0.135733 0.00974522i
\(379\) 19.3923i 0.996116i −0.867144 0.498058i \(-0.834047\pi\)
0.867144 0.498058i \(-0.165953\pi\)
\(380\) 0 0
\(381\) 7.46410i 0.382398i
\(382\) −4.43211 + 4.43211i −0.226766 + 0.226766i
\(383\) 21.0101 21.0101i 1.07357 1.07357i 0.0764978 0.997070i \(-0.475626\pi\)
0.997070 0.0764978i \(-0.0243738\pi\)
\(384\) 1.00000 0.0510310
\(385\) 0 0
\(386\) 17.8564 0.908867
\(387\) −2.63896 + 2.63896i −0.134146 + 0.134146i
\(388\) −2.17209 + 2.17209i −0.110271 + 0.110271i
\(389\) 26.9282i 1.36531i −0.730739 0.682657i \(-0.760824\pi\)
0.730739 0.682657i \(-0.239176\pi\)
\(390\) 0 0
\(391\) 5.00000i 0.252861i
\(392\) 5.60609 + 4.19187i 0.283150 + 0.211722i
\(393\) −10.1769 10.1769i −0.513357 0.513357i
\(394\) 7.39230i 0.372419i
\(395\) 0 0
\(396\) 5.46410 0.274581
\(397\) 7.15900 + 7.15900i 0.359300 + 0.359300i 0.863555 0.504255i \(-0.168233\pi\)
−0.504255 + 0.863555i \(0.668233\pi\)
\(398\) −11.3137 + 11.3137i −0.567105 + 0.567105i
\(399\) 12.9282 14.9282i 0.647220 0.747345i
\(400\) 0 0
\(401\) −13.3205 −0.665194 −0.332597 0.943069i \(-0.607925\pi\)
−0.332597 + 0.943069i \(0.607925\pi\)
\(402\) −4.52004 4.52004i −0.225439 0.225439i
\(403\) 20.9222 + 20.9222i 1.04221 + 1.04221i
\(404\) 6.53590 0.325173
\(405\) 0 0
\(406\) −15.4641 13.3923i −0.767470 0.664649i
\(407\) −26.7685 + 26.7685i −1.32687 + 1.32687i
\(408\) −3.53553 3.53553i −0.175035 0.175035i
\(409\) −20.3923 −1.00833 −0.504167 0.863606i \(-0.668201\pi\)
−0.504167 + 0.863606i \(0.668201\pi\)
\(410\) 0 0
\(411\) 7.85641i 0.387528i
\(412\) −2.91636 2.91636i −0.143679 0.143679i
\(413\) −18.9903 + 1.36345i −0.934454 + 0.0670908i
\(414\) 1.00000i 0.0491473i
\(415\) 0 0
\(416\) 3.73205i 0.182979i
\(417\) 14.0406 14.0406i 0.687571 0.687571i
\(418\) 28.8391 28.8391i 1.41057 1.41057i
\(419\) −17.3397 −0.847102 −0.423551 0.905872i \(-0.639217\pi\)
−0.423551 + 0.905872i \(0.639217\pi\)
\(420\) 0 0
\(421\) −29.3205 −1.42899 −0.714497 0.699638i \(-0.753344\pi\)
−0.714497 + 0.699638i \(0.753344\pi\)
\(422\) 7.29770 7.29770i 0.355247 0.355247i
\(423\) −5.93426 + 5.93426i −0.288533 + 0.288533i
\(424\) 3.53590i 0.171718i
\(425\) 0 0
\(426\) 11.4641i 0.555438i
\(427\) 0.466870 + 6.50266i 0.0225934 + 0.314686i
\(428\) 6.31319 + 6.31319i 0.305160 + 0.305160i
\(429\) 20.3923i 0.984550i
\(430\) 0 0
\(431\) −6.80385 −0.327730 −0.163865 0.986483i \(-0.552396\pi\)
−0.163865 + 0.986483i \(0.552396\pi\)
\(432\) −0.707107 0.707107i −0.0340207 0.0340207i
\(433\) 0.378937 0.378937i 0.0182106 0.0182106i −0.697943 0.716153i \(-0.745901\pi\)
0.716153 + 0.697943i \(0.245901\pi\)
\(434\) −15.8564 13.7321i −0.761132 0.659160i
\(435\) 0 0
\(436\) 12.3923 0.593484
\(437\) −5.27792 5.27792i −0.252477 0.252477i
\(438\) −8.76268 8.76268i −0.418697 0.418697i
\(439\) 39.7846 1.89882 0.949408 0.314046i \(-0.101684\pi\)
0.949408 + 0.314046i \(0.101684\pi\)
\(440\) 0 0
\(441\) −1.00000 6.92820i −0.0476190 0.329914i
\(442\) 13.1948 13.1948i 0.627612 0.627612i
\(443\) −7.24693 7.24693i −0.344312 0.344312i 0.513674 0.857986i \(-0.328284\pi\)
−0.857986 + 0.513674i \(0.828284\pi\)
\(444\) 6.92820 0.328798
\(445\) 0 0
\(446\) 11.5885i 0.548729i
\(447\) −5.46739 5.46739i −0.258598 0.258598i
\(448\) −0.189469 2.63896i −0.00895155 0.124679i
\(449\) 30.7846i 1.45282i 0.687264 + 0.726408i \(0.258812\pi\)
−0.687264 + 0.726408i \(0.741188\pi\)
\(450\) 0 0
\(451\) 31.3205i 1.47483i
\(452\) −1.79315 + 1.79315i −0.0843427 + 0.0843427i
\(453\) −11.3137 + 11.3137i −0.531564 + 0.531564i
\(454\) 1.39230 0.0653441
\(455\) 0 0
\(456\) −7.46410 −0.349539
\(457\) 16.1248 16.1248i 0.754284 0.754284i −0.220991 0.975276i \(-0.570929\pi\)
0.975276 + 0.220991i \(0.0709293\pi\)
\(458\) −10.6574 + 10.6574i −0.497986 + 0.497986i
\(459\) 5.00000i 0.233380i
\(460\) 0 0
\(461\) 11.6077i 0.540624i 0.962773 + 0.270312i \(0.0871269\pi\)
−0.962773 + 0.270312i \(0.912873\pi\)
\(462\) −1.03528 14.4195i −0.0481654 0.670858i
\(463\) −15.0759 15.0759i −0.700635 0.700635i 0.263912 0.964547i \(-0.414987\pi\)
−0.964547 + 0.263912i \(0.914987\pi\)
\(464\) 7.73205i 0.358951i
\(465\) 0 0
\(466\) 10.3923 0.481414
\(467\) 15.2282 + 15.2282i 0.704676 + 0.704676i 0.965411 0.260734i \(-0.0839647\pi\)
−0.260734 + 0.965411i \(0.583965\pi\)
\(468\) 2.63896 2.63896i 0.121986 0.121986i
\(469\) −11.0718 + 12.7846i −0.511248 + 0.590338i
\(470\) 0 0
\(471\) 8.00000 0.368621
\(472\) 5.08845 + 5.08845i 0.234215 + 0.234215i
\(473\) 14.4195 + 14.4195i 0.663011 + 0.663011i
\(474\) −12.3923 −0.569197
\(475\) 0 0
\(476\) −8.66025 + 10.0000i −0.396942 + 0.458349i
\(477\) −2.50026 + 2.50026i −0.114479 + 0.114479i
\(478\) −6.03579 6.03579i −0.276071 0.276071i
\(479\) −0.928203 −0.0424107 −0.0212053 0.999775i \(-0.506750\pi\)
−0.0212053 + 0.999775i \(0.506750\pi\)
\(480\) 0 0
\(481\) 25.8564i 1.17895i
\(482\) 0.656339 + 0.656339i 0.0298954 + 0.0298954i
\(483\) −2.63896 + 0.189469i −0.120077 + 0.00862112i
\(484\) 18.8564i 0.857109i
\(485\) 0 0
\(486\) 1.00000i 0.0453609i
\(487\) −26.8701 + 26.8701i −1.21760 + 1.21760i −0.249128 + 0.968471i \(0.580144\pi\)
−0.968471 + 0.249128i \(0.919856\pi\)
\(488\) 1.74238 1.74238i 0.0788740 0.0788740i
\(489\) −0.803848 −0.0363512
\(490\) 0 0
\(491\) 9.32051 0.420629 0.210314 0.977634i \(-0.432551\pi\)
0.210314 + 0.977634i \(0.432551\pi\)
\(492\) −4.05317 + 4.05317i −0.182731 + 0.182731i
\(493\) 27.3369 27.3369i 1.23119 1.23119i
\(494\) 27.8564i 1.25332i
\(495\) 0 0
\(496\) 7.92820i 0.355987i
\(497\) 30.2533 2.17209i 1.35705 0.0974315i
\(498\) 0.328169 + 0.328169i 0.0147056 + 0.0147056i
\(499\) 3.39230i 0.151860i 0.997113 + 0.0759302i \(0.0241926\pi\)
−0.997113 + 0.0759302i \(0.975807\pi\)
\(500\) 0 0
\(501\) 15.4641 0.690885
\(502\) 14.3316 + 14.3316i 0.639651 + 0.639651i
\(503\) −20.0764 + 20.0764i −0.895162 + 0.895162i −0.995003 0.0998413i \(-0.968166\pi\)
0.0998413 + 0.995003i \(0.468166\pi\)
\(504\) −1.73205 + 2.00000i −0.0771517 + 0.0890871i
\(505\) 0 0
\(506\) −5.46410 −0.242909
\(507\) 0.656339 + 0.656339i 0.0291490 + 0.0291490i
\(508\) −5.27792 5.27792i −0.234170 0.234170i
\(509\) 19.8564 0.880120 0.440060 0.897968i \(-0.354957\pi\)
0.440060 + 0.897968i \(0.354957\pi\)
\(510\) 0 0
\(511\) −21.4641 + 24.7846i −0.949516 + 1.09641i
\(512\) −0.707107 + 0.707107i −0.0312500 + 0.0312500i
\(513\) 5.27792 + 5.27792i 0.233026 + 0.233026i
\(514\) 23.9282 1.05543
\(515\) 0 0
\(516\) 3.73205i 0.164294i
\(517\) 32.4254 + 32.4254i 1.42607 + 1.42607i
\(518\) −1.31268 18.2832i −0.0576757 0.803319i
\(519\) 9.32051i 0.409125i
\(520\) 0 0
\(521\) 11.5885i 0.507700i −0.967244 0.253850i \(-0.918303\pi\)
0.967244 0.253850i \(-0.0816969\pi\)
\(522\) 5.46739 5.46739i 0.239301 0.239301i
\(523\) −22.9048 + 22.9048i −1.00156 + 1.00156i −0.00155899 + 0.999999i \(0.500496\pi\)
−0.999999 + 0.00155899i \(0.999504\pi\)
\(524\) 14.3923 0.628731
\(525\) 0 0
\(526\) −7.00000 −0.305215
\(527\) 28.0304 28.0304i 1.22102 1.22102i
\(528\) −3.86370 + 3.86370i −0.168146 + 0.168146i
\(529\) 22.0000i 0.956522i
\(530\) 0 0
\(531\) 7.19615i 0.312286i
\(532\) 1.41421 + 19.6975i 0.0613139 + 0.853993i
\(533\) −15.1266 15.1266i −0.655208 0.655208i
\(534\) 12.0000i 0.519291i
\(535\) 0 0
\(536\) 6.39230 0.276106
\(537\) 9.79796 + 9.79796i 0.422813 + 0.422813i
\(538\) 15.4548 15.4548i 0.666304 0.666304i
\(539\) −37.8564 + 5.46410i −1.63059 + 0.235356i
\(540\) 0 0
\(541\) 5.32051 0.228747 0.114373 0.993438i \(-0.463514\pi\)
0.114373 + 0.993438i \(0.463514\pi\)
\(542\) −2.07055 2.07055i −0.0889378 0.0889378i
\(543\) 1.41421 + 1.41421i 0.0606897 + 0.0606897i
\(544\) 5.00000 0.214373
\(545\) 0 0
\(546\) −7.46410 6.46410i −0.319434 0.276638i
\(547\) 28.0948 28.0948i 1.20125 1.20125i 0.227459 0.973788i \(-0.426958\pi\)
0.973788 0.227459i \(-0.0730419\pi\)
\(548\) 5.55532 + 5.55532i 0.237311 + 0.237311i
\(549\) −2.46410 −0.105165
\(550\) 0 0
\(551\) 57.7128i 2.45865i
\(552\) 0.707107 + 0.707107i 0.0300965 + 0.0300965i
\(553\) 2.34795 + 32.7028i 0.0998452 + 1.39066i
\(554\) 8.39230i 0.356555i
\(555\) 0 0
\(556\) 19.8564i 0.842099i
\(557\) 11.4152 11.4152i 0.483679 0.483679i −0.422625 0.906305i \(-0.638891\pi\)
0.906305 + 0.422625i \(0.138891\pi\)
\(558\) 5.60609 5.60609i 0.237325 0.237325i
\(559\) 13.9282 0.589100
\(560\) 0 0
\(561\) 27.3205 1.15347
\(562\) −9.79796 + 9.79796i −0.413302 + 0.413302i
\(563\) 24.3698 24.3698i 1.02706 1.02706i 0.0274412 0.999623i \(-0.491264\pi\)
0.999623 0.0274412i \(-0.00873590\pi\)
\(564\) 8.39230i 0.353380i
\(565\) 0 0
\(566\) 22.7846i 0.957709i
\(567\) 2.63896 0.189469i 0.110826 0.00795694i
\(568\) −8.10634 8.10634i −0.340135 0.340135i
\(569\) 11.6077i 0.486620i −0.969949 0.243310i \(-0.921767\pi\)
0.969949 0.243310i \(-0.0782332\pi\)
\(570\) 0 0
\(571\) −42.4641 −1.77707 −0.888534 0.458811i \(-0.848275\pi\)
−0.888534 + 0.458811i \(0.848275\pi\)
\(572\) −14.4195 14.4195i −0.602911 0.602911i
\(573\) −4.43211 + 4.43211i −0.185154 + 0.185154i
\(574\) 11.4641 + 9.92820i 0.478502 + 0.414395i
\(575\) 0 0
\(576\) 1.00000 0.0416667
\(577\) 16.5916 + 16.5916i 0.690718 + 0.690718i 0.962390 0.271672i \(-0.0875765\pi\)
−0.271672 + 0.962390i \(0.587576\pi\)
\(578\) −5.65685 5.65685i −0.235294 0.235294i
\(579\) 17.8564 0.742087
\(580\) 0 0
\(581\) 0.803848 0.928203i 0.0333492 0.0385084i
\(582\) −2.17209 + 2.17209i −0.0900360 + 0.0900360i
\(583\) 13.6617 + 13.6617i 0.565808 + 0.565808i
\(584\) 12.3923 0.512797
\(585\) 0 0
\(586\) 1.85641i 0.0766874i
\(587\) 25.6825 + 25.6825i 1.06003 + 1.06003i 0.998079 + 0.0619500i \(0.0197319\pi\)
0.0619500 + 0.998079i \(0.480268\pi\)
\(588\) 5.60609 + 4.19187i 0.231191 + 0.172870i
\(589\) 59.1769i 2.43834i
\(590\) 0 0
\(591\) 7.39230i 0.304079i
\(592\) −4.89898 + 4.89898i −0.201347 + 0.201347i
\(593\) −7.07107 + 7.07107i −0.290374 + 0.290374i −0.837228 0.546854i \(-0.815825\pi\)
0.546854 + 0.837228i \(0.315825\pi\)
\(594\) 5.46410 0.224195
\(595\) 0 0
\(596\) 7.73205 0.316717
\(597\) −11.3137 + 11.3137i −0.463039 + 0.463039i
\(598\) −2.63896 + 2.63896i −0.107915 + 0.107915i
\(599\) 14.5167i 0.593135i −0.955012 0.296567i \(-0.904158\pi\)
0.955012 0.296567i \(-0.0958419\pi\)
\(600\) 0 0
\(601\) 25.3205i 1.03285i −0.856334 0.516423i \(-0.827263\pi\)
0.856334 0.516423i \(-0.172737\pi\)
\(602\) −9.84873 + 0.707107i −0.401404 + 0.0288195i
\(603\) −4.52004 4.52004i −0.184070 0.184070i
\(604\) 16.0000i 0.651031i
\(605\) 0 0
\(606\) 6.53590 0.265503
\(607\) 9.62209 + 9.62209i 0.390549 + 0.390549i 0.874883 0.484334i \(-0.160938\pi\)
−0.484334 + 0.874883i \(0.660938\pi\)
\(608\) 5.27792 5.27792i 0.214048 0.214048i
\(609\) −15.4641 13.3923i −0.626637 0.542684i
\(610\) 0 0
\(611\) 31.3205 1.26709
\(612\) −3.53553 3.53553i −0.142915 0.142915i
\(613\) 3.20736 + 3.20736i 0.129544 + 0.129544i 0.768906 0.639362i \(-0.220801\pi\)
−0.639362 + 0.768906i \(0.720801\pi\)
\(614\) 5.07180 0.204681
\(615\) 0 0
\(616\) 10.9282 + 9.46410i 0.440310 + 0.381320i
\(617\) 32.2223 32.2223i 1.29722 1.29722i 0.367000 0.930221i \(-0.380385\pi\)
0.930221 0.367000i \(-0.119615\pi\)
\(618\) −2.91636 2.91636i −0.117313 0.117313i
\(619\) −10.0000 −0.401934 −0.200967 0.979598i \(-0.564408\pi\)
−0.200967 + 0.979598i \(0.564408\pi\)
\(620\) 0 0
\(621\) 1.00000i 0.0401286i
\(622\) 18.2832 + 18.2832i 0.733091 + 0.733091i
\(623\) −31.6675 + 2.27362i −1.26873 + 0.0910908i
\(624\) 3.73205i 0.149402i
\(625\) 0 0
\(626\) 30.2487i 1.20898i
\(627\) 28.8391 28.8391i 1.15172 1.15172i
\(628\) −5.65685 + 5.65685i −0.225733 + 0.225733i
\(629\) 34.6410 1.38123
\(630\) 0 0
\(631\) −2.00000 −0.0796187 −0.0398094 0.999207i \(-0.512675\pi\)
−0.0398094 + 0.999207i \(0.512675\pi\)
\(632\) 8.76268 8.76268i 0.348561 0.348561i
\(633\) 7.29770 7.29770i 0.290058 0.290058i
\(634\) 27.3923i 1.08789i
\(635\) 0 0
\(636\) 3.53590i 0.140207i
\(637\) −15.6443 + 20.9222i −0.619849 + 0.828968i
\(638\) −29.8744 29.8744i −1.18274 1.18274i
\(639\) 11.4641i 0.453513i
\(640\) 0 0
\(641\) −14.9282 −0.589629 −0.294814 0.955555i \(-0.595258\pi\)
−0.294814 + 0.955555i \(0.595258\pi\)
\(642\) 6.31319 + 6.31319i 0.249162 + 0.249162i
\(643\) −4.41851 + 4.41851i −0.174249 + 0.174249i −0.788843 0.614594i \(-0.789320\pi\)
0.614594 + 0.788843i \(0.289320\pi\)
\(644\) 1.73205 2.00000i 0.0682524 0.0788110i
\(645\) 0 0
\(646\) −37.3205 −1.46836
\(647\) −27.8038 27.8038i −1.09308 1.09308i −0.995198 0.0978821i \(-0.968793\pi\)
−0.0978821 0.995198i \(-0.531207\pi\)
\(648\) −0.707107 0.707107i −0.0277778 0.0277778i
\(649\) −39.3205 −1.54346
\(650\) 0 0
\(651\) −15.8564 13.7321i −0.621462 0.538202i
\(652\) 0.568406 0.568406i 0.0222605 0.0222605i
\(653\) −16.3142 16.3142i −0.638425 0.638425i 0.311742 0.950167i \(-0.399088\pi\)
−0.950167 + 0.311742i \(0.899088\pi\)
\(654\) 12.3923 0.484577
\(655\) 0 0
\(656\) 5.73205i 0.223799i
\(657\) −8.76268 8.76268i −0.341865 0.341865i
\(658\) −22.1469 + 1.59008i −0.863378 + 0.0619877i
\(659\) 7.85641i 0.306042i 0.988223 + 0.153021i \(0.0489002\pi\)
−0.988223 + 0.153021i \(0.951100\pi\)
\(660\) 0 0
\(661\) 4.92820i 0.191685i −0.995397 0.0958424i \(-0.969446\pi\)
0.995397 0.0958424i \(-0.0305545\pi\)
\(662\) 21.4398 21.4398i 0.833283 0.833283i
\(663\) 13.1948 13.1948i 0.512443 0.512443i
\(664\) −0.464102 −0.0180106
\(665\) 0 0
\(666\) 6.92820 0.268462
\(667\) −5.46739 + 5.46739i −0.211698 + 0.211698i
\(668\) −10.9348 + 10.9348i −0.423079 + 0.423079i
\(669\) 11.5885i 0.448036i
\(670\) 0 0
\(671\) 13.4641i 0.519776i
\(672\) −0.189469 2.63896i −0.00730891 0.101800i
\(673\) 28.3722 + 28.3722i 1.09367 + 1.09367i 0.995134 + 0.0985345i \(0.0314155\pi\)
0.0985345 + 0.995134i \(0.468585\pi\)
\(674\) 22.2679i 0.857729i
\(675\) 0 0
\(676\) −0.928203 −0.0357001
\(677\) −20.7327 20.7327i −0.796824 0.796824i 0.185770 0.982593i \(-0.440522\pi\)
−0.982593 + 0.185770i \(0.940522\pi\)
\(678\) −1.79315 + 1.79315i −0.0688655 + 0.0688655i
\(679\) 6.14359 + 5.32051i 0.235769 + 0.204182i
\(680\) 0 0
\(681\) 1.39230 0.0533532
\(682\) −30.6322 30.6322i −1.17297 1.17297i
\(683\) 24.6980 + 24.6980i 0.945042 + 0.945042i 0.998567 0.0535250i \(-0.0170457\pi\)
−0.0535250 + 0.998567i \(0.517046\pi\)
\(684\) −7.46410 −0.285397
\(685\) 0 0
\(686\) 10.0000 15.5885i 0.381802 0.595170i
\(687\) −10.6574 + 10.6574i −0.406604 + 0.406604i
\(688\) 2.63896 + 2.63896i 0.100609 + 0.100609i
\(689\) 13.1962 0.502733
\(690\) 0 0
\(691\) 51.1769i 1.94686i 0.228981 + 0.973431i \(0.426460\pi\)
−0.228981 + 0.973431i \(0.573540\pi\)
\(692\) −6.59059 6.59059i −0.250537 0.250537i
\(693\) −1.03528 14.4195i −0.0393269 0.547753i
\(694\) 4.53590i 0.172180i
\(695\) 0 0
\(696\) 7.73205i 0.293083i
\(697\) −20.2659 + 20.2659i −0.767624 + 0.767624i
\(698\) 3.25813 3.25813i 0.123322 0.123322i
\(699\) 10.3923 0.393073
\(700\) 0 0
\(701\) −19.9808 −0.754663 −0.377331 0.926078i \(-0.623158\pi\)
−0.377331 + 0.926078i \(0.623158\pi\)
\(702\) 2.63896 2.63896i 0.0996011 0.0996011i
\(703\) 36.5665 36.5665i 1.37913 1.37913i
\(704\) 5.46410i 0.205936i
\(705\) 0 0
\(706\) 12.9282i 0.486559i
\(707\) −1.23835 17.2480i −0.0465729 0.648676i
\(708\) 5.08845 + 5.08845i 0.191236 + 0.191236i
\(709\) 15.0718i 0.566033i 0.959115 + 0.283017i \(0.0913352\pi\)
−0.959115 + 0.283017i \(0.908665\pi\)
\(710\) 0 0
\(711\) −12.3923 −0.464748
\(712\) 8.48528 + 8.48528i 0.317999 + 0.317999i
\(713\) −5.60609 + 5.60609i −0.209950 + 0.209950i
\(714\) −8.66025 + 10.0000i −0.324102 + 0.374241i
\(715\) 0 0
\(716\) −13.8564 −0.517838
\(717\) −6.03579 6.03579i −0.225411 0.225411i
\(718\) 25.5438 + 25.5438i 0.953285 + 0.953285i
\(719\) 19.3205 0.720533 0.360267 0.932849i \(-0.382686\pi\)
0.360267 + 0.932849i \(0.382686\pi\)
\(720\) 0 0
\(721\) −7.14359 + 8.24871i −0.266041 + 0.307198i
\(722\) −25.9599 + 25.9599i −0.966127 + 0.966127i
\(723\) 0.656339 + 0.656339i 0.0244095 + 0.0244095i
\(724\) −2.00000 −0.0743294
\(725\) 0 0
\(726\) 18.8564i 0.699827i
\(727\) 3.49837 + 3.49837i 0.129747 + 0.129747i 0.768998 0.639251i \(-0.220755\pi\)
−0.639251 + 0.768998i \(0.720755\pi\)
\(728\) 9.84873 0.707107i 0.365018 0.0262071i
\(729\) 1.00000i 0.0370370i
\(730\) 0 0
\(731\) 18.6603i 0.690174i
\(732\) 1.74238 1.74238i 0.0644003 0.0644003i
\(733\) −0.189469 + 0.189469i −0.00699819 + 0.00699819i −0.710597 0.703599i \(-0.751575\pi\)
0.703599 + 0.710597i \(0.251575\pi\)
\(734\) −10.8038 −0.398777
\(735\) 0 0
\(736\) −1.00000 −0.0368605
\(737\) −24.6980 + 24.6980i −0.909761 + 0.909761i
\(738\) −4.05317 + 4.05317i −0.149199 + 0.149199i
\(739\) 12.3205i 0.453217i 0.973986 + 0.226609i \(0.0727638\pi\)
−0.973986 + 0.226609i \(0.927236\pi\)
\(740\) 0 0
\(741\) 27.8564i 1.02333i
\(742\) −9.33109 + 0.669942i −0.342555 + 0.0245943i
\(743\) 25.2020 + 25.2020i 0.924572 + 0.924572i 0.997348 0.0727764i \(-0.0231860\pi\)
−0.0727764 + 0.997348i \(0.523186\pi\)
\(744\) 7.92820i 0.290662i
\(745\) 0 0
\(746\) −15.3205 −0.560924
\(747\) 0.328169 + 0.328169i 0.0120071 + 0.0120071i
\(748\) −19.3185 + 19.3185i −0.706355 + 0.706355i
\(749\) 15.4641 17.8564i 0.565046 0.652459i
\(750\) 0 0
\(751\) −37.1769 −1.35660 −0.678302 0.734783i \(-0.737284\pi\)
−0.678302 + 0.734783i \(0.737284\pi\)
\(752\) 5.93426 + 5.93426i 0.216400 + 0.216400i
\(753\) 14.3316 + 14.3316i 0.522273 + 0.522273i
\(754\) −28.8564 −1.05089
\(755\) 0 0
\(756\) −1.73205 + 2.00000i −0.0629941 + 0.0727393i
\(757\) −25.5302 + 25.5302i −0.927910 + 0.927910i −0.997571 0.0696608i \(-0.977808\pi\)
0.0696608 + 0.997571i \(0.477808\pi\)
\(758\) 13.7124 + 13.7124i 0.498058 + 0.498058i
\(759\) −5.46410 −0.198334
\(760\) 0 0
\(761\) 13.8564i 0.502294i 0.967949 + 0.251147i \(0.0808078\pi\)
−0.967949 + 0.251147i \(0.919192\pi\)
\(762\) −5.27792 5.27792i −0.191199 0.191199i
\(763\) −2.34795 32.7028i −0.0850016 1.18392i
\(764\) 6.26795i 0.226766i
\(765\) 0 0
\(766\) 29.7128i 1.07357i
\(767\) −18.9903 + 18.9903i −0.685702 + 0.685702i
\(768\) −0.707107 + 0.707107i −0.0255155 + 0.0255155i
\(769\) 15.3205 0.552472 0.276236 0.961090i \(-0.410913\pi\)
0.276236 + 0.961090i \(0.410913\pi\)
\(770\) 0 0
\(771\) 23.9282 0.861753
\(772\) −12.6264 + 12.6264i −0.454434 + 0.454434i
\(773\) 5.37945 5.37945i 0.193485 0.193485i −0.603715 0.797200i \(-0.706313\pi\)
0.797200 + 0.603715i \(0.206313\pi\)
\(774\) 3.73205i 0.134146i
\(775\) 0 0
\(776\) 3.07180i 0.110271i
\(777\) −1.31268 18.2832i −0.0470920 0.655908i
\(778\) 19.0411 + 19.0411i 0.682657 + 0.682657i
\(779\) 42.7846i 1.53292i
\(780\) 0 0
\(781\) 62.6410 2.24147
\(782\) 3.53553 + 3.53553i 0.126430 + 0.126430i
\(783\) 5.46739 5.46739i 0.195388 0.195388i
\(784\) −6.92820 + 1.00000i −0.247436 + 0.0357143i
\(785\) 0 0
\(786\) 14.3923 0.513357
\(787\) 13.0053 + 13.0053i 0.463590 + 0.463590i 0.899830 0.436240i \(-0.143690\pi\)
−0.436240 + 0.899830i \(0.643690\pi\)
\(788\) 5.22715 + 5.22715i 0.186209 + 0.186209i
\(789\) −7.00000 −0.249207
\(790\) 0 0
\(791\) 5.07180 + 4.39230i 0.180332 + 0.156172i
\(792\) −3.86370 + 3.86370i −0.137291 + 0.137291i
\(793\) 6.50266 + 6.50266i 0.230916 + 0.230916i
\(794\) −10.1244 −0.359300
\(795\) 0 0
\(796\) 16.0000i 0.567105i
\(797\) −27.8038 27.8038i −0.984861 0.984861i 0.0150261 0.999887i \(-0.495217\pi\)
−0.999887 + 0.0150261i \(0.995217\pi\)
\(798\) 1.41421 + 19.6975i 0.0500626 + 0.697282i
\(799\) 41.9615i 1.48449i
\(800\) 0 0
\(801\) 12.0000i 0.423999i
\(802\) 9.41902 9.41902i 0.332597 0.332597i
\(803\) −47.8802 + 47.8802i −1.68966 + 1.68966i
\(804\) 6.39230 0.225439
\(805\) 0 0
\(806\) −29.5885 −1.04221
\(807\) 15.4548 15.4548i 0.544035 0.544035i
\(808\) −4.62158 + 4.62158i −0.162587 + 0.162587i
\(809\) 2.53590i 0.0891574i −0.999006 0.0445787i \(-0.985805\pi\)
0.999006 0.0445787i \(-0.0141946\pi\)
\(810\) 0 0
\(811\) 6.53590i 0.229506i −0.993394 0.114753i \(-0.963392\pi\)
0.993394 0.114753i \(-0.0366077\pi\)
\(812\) 20.4046 1.46498i 0.716060 0.0514108i
\(813\) −2.07055 2.07055i −0.0726174 0.0726174i
\(814\) 37.8564i 1.32687i
\(815\) 0 0
\(816\) 5.00000 0.175035
\(817\) −19.6975 19.6975i −0.689127 0.689127i
\(818\) 14.4195 14.4195i 0.504167 0.504167i
\(819\) −7.46410 6.46410i −0.260817 0.225874i
\(820\) 0 0
\(821\) −0.784610 −0.0273831 −0.0136915 0.999906i \(-0.504358\pi\)
−0.0136915 + 0.999906i \(0.504358\pi\)
\(822\) 5.55532 + 5.55532i 0.193764 + 0.193764i
\(823\) −32.9058 32.9058i −1.14703 1.14703i −0.987135 0.159891i \(-0.948886\pi\)
−0.159891 0.987135i \(-0.551114\pi\)
\(824\) 4.12436 0.143679
\(825\) 0 0
\(826\) 12.4641 14.3923i 0.433682 0.500772i
\(827\) −7.17260 + 7.17260i −0.249416 + 0.249416i −0.820731 0.571315i \(-0.806433\pi\)
0.571315 + 0.820731i \(0.306433\pi\)
\(828\) 0.707107 + 0.707107i 0.0245737 + 0.0245737i
\(829\) −12.1769 −0.422922 −0.211461 0.977386i \(-0.567822\pi\)
−0.211461 + 0.977386i \(0.567822\pi\)
\(830\) 0 0
\(831\) 8.39230i 0.291126i
\(832\) −2.63896 2.63896i −0.0914894 0.0914894i
\(833\) 28.0304 + 20.9594i 0.971197 + 0.726199i
\(834\) 19.8564i 0.687571i
\(835\) 0 0
\(836\) 40.7846i 1.41057i
\(837\) 5.60609 5.60609i 0.193775 0.193775i
\(838\) 12.2611 12.2611i 0.423551 0.423551i
\(839\) 18.6795 0.644888 0.322444 0.946589i \(-0.395496\pi\)
0.322444 + 0.946589i \(0.395496\pi\)
\(840\) 0 0
\(841\) −30.7846 −1.06154
\(842\) 20.7327 20.7327i 0.714497 0.714497i
\(843\) −9.79796 + 9.79796i −0.337460 + 0.337460i
\(844\) 10.3205i 0.355247i
\(845\) 0 0
\(846\) 8.39230i 0.288533i
\(847\) −49.7613 + 3.57270i −1.70982 + 0.122759i
\(848\) 2.50026 + 2.50026i 0.0858592 + 0.0858592i
\(849\) 22.7846i 0.781966i
\(850\) 0 0
\(851\) −6.92820 −0.237496
\(852\) −8.10634 8.10634i −0.277719 0.277719i
\(853\) −12.2611 + 12.2611i −0.419810 + 0.419810i −0.885138 0.465328i \(-0.845936\pi\)
0.465328 + 0.885138i \(0.345936\pi\)
\(854\) −4.92820 4.26795i −0.168640 0.146046i
\(855\) 0 0
\(856\) −8.92820 −0.305160
\(857\) 9.69642 + 9.69642i 0.331224 + 0.331224i 0.853051 0.521828i \(-0.174750\pi\)
−0.521828 + 0.853051i \(0.674750\pi\)
\(858\) −14.4195 14.4195i −0.492275 0.492275i
\(859\) 46.6410 1.59137 0.795685 0.605710i \(-0.207111\pi\)
0.795685 + 0.605710i \(0.207111\pi\)
\(860\) 0 0
\(861\) 11.4641 + 9.92820i 0.390696 + 0.338352i
\(862\) 4.81105 4.81105i 0.163865 0.163865i
\(863\) −31.4644 31.4644i −1.07106 1.07106i −0.997274 0.0737877i \(-0.976491\pi\)
−0.0737877 0.997274i \(-0.523509\pi\)
\(864\) 1.00000 0.0340207
\(865\) 0 0
\(866\) 0.535898i 0.0182106i
\(867\) −5.65685 5.65685i −0.192117 0.192117i
\(868\) 20.9222 1.50215i 0.710146 0.0509862i
\(869\) 67.7128i 2.29700i
\(870\) 0 0
\(871\) 23.8564i 0.808343i
\(872\) −8.76268 + 8.76268i −0.296742 + 0.296742i
\(873\) −2.17209 + 2.17209i −0.0735141 + 0.0735141i
\(874\) 7.46410 0.252477
\(875\) 0 0
\(876\) 12.3923 0.418697
\(877\) 16.9706 16.9706i 0.573055 0.573055i −0.359926 0.932981i \(-0.617198\pi\)
0.932981 + 0.359926i \(0.117198\pi\)
\(878\) −28.1320 + 28.1320i −0.949408 + 0.949408i
\(879\) 1.85641i 0.0626150i
\(880\) 0 0
\(881\) 6.51666i 0.219552i −0.993956 0.109776i \(-0.964987\pi\)
0.993956 0.109776i \(-0.0350133\pi\)
\(882\) 5.60609 + 4.19187i 0.188767 + 0.141148i
\(883\) 13.5737 + 13.5737i 0.456792 + 0.456792i 0.897601 0.440809i \(-0.145308\pi\)
−0.440809 + 0.897601i \(0.645308\pi\)
\(884\) 18.6603i 0.627612i
\(885\) 0 0
\(886\) 10.2487 0.344312
\(887\) 4.89898 + 4.89898i 0.164492 + 0.164492i 0.784553 0.620062i \(-0.212892\pi\)
−0.620062 + 0.784553i \(0.712892\pi\)
\(888\) −4.89898 + 4.89898i −0.164399 + 0.164399i
\(889\) −12.9282 + 14.9282i −0.433598 + 0.500676i
\(890\) 0 0
\(891\) 5.46410 0.183054
\(892\) 8.19428 + 8.19428i 0.274365 + 0.274365i
\(893\) −44.2939 44.2939i −1.48224 1.48224i
\(894\) 7.73205 0.258598
\(895\) 0 0
\(896\) 2.00000 + 1.73205i 0.0668153 + 0.0578638i
\(897\) −2.63896 + 2.63896i −0.0881123 + 0.0881123i
\(898\) −21.7680 21.7680i −0.726408 0.726408i
\(899\) −61.3013 −2.04451
\(900\) 0 0
\(901\) 17.6795i 0.588989i
\(902\) 22.1469 + 22.1469i 0.737413 + 0.737413i
\(903\) −9.84873 + 0.707107i −0.327745 + 0.0235310i
\(904\) 2.53590i 0.0843427i
\(905\) 0 0
\(906\) 16.0000i 0.531564i
\(907\) −22.9928 + 22.9928i −0.763462 + 0.763462i −0.976946 0.213485i \(-0.931519\pi\)
0.213485 + 0.976946i \(0.431519\pi\)
\(908\) −0.984508 + 0.984508i −0.0326721 + 0.0326721i
\(909\) 6.53590 0.216782
\(910\) 0 0
\(911\) 22.5167 0.746010 0.373005 0.927829i \(-0.378327\pi\)
0.373005 + 0.927829i \(0.378327\pi\)
\(912\) 5.27792 5.27792i 0.174769 0.174769i
\(913\) 1.79315 1.79315i 0.0593446 0.0593446i
\(914\) 22.8038i 0.754284i
\(915\) 0 0
\(916\) 15.0718i 0.497986i
\(917\) −2.72689 37.9807i −0.0900499 1.25423i
\(918\) −3.53553 3.53553i −0.116690 0.116690i
\(919\) 1.60770i 0.0530330i 0.999648 + 0.0265165i \(0.00844145\pi\)
−0.999648 + 0.0265165i \(0.991559\pi\)
\(920\) 0 0
\(921\) 5.07180 0.167121
\(922\) −8.20788 8.20788i −0.270312 0.270312i
\(923\) 30.2533 30.2533i 0.995799 0.995799i
\(924\) 10.9282 + 9.46410i 0.359511 + 0.311346i
\(925\) 0 0
\(926\) 21.3205 0.700635
\(927\) −2.91636 2.91636i −0.0957858 0.0957858i
\(928\) −5.46739 5.46739i −0.179476 0.179476i
\(929\) −16.9090 −0.554765 −0.277383 0.960760i \(-0.589467\pi\)
−0.277383 + 0.960760i \(0.589467\pi\)
\(930\) 0 0
\(931\) 51.7128 7.46410i 1.69482 0.244626i
\(932\) −7.34847 + 7.34847i −0.240707 + 0.240707i
\(933\) 18.2832 + 18.2832i 0.598566 + 0.598566i
\(934\) −21.5359 −0.704676
\(935\) 0 0
\(936\) 3.73205i 0.121986i
\(937\) 19.7990 + 19.7990i 0.646805 + 0.646805i 0.952219 0.305415i \(-0.0987951\pi\)
−0.305415 + 0.952219i \(0.598795\pi\)
\(938\) −1.21114 16.8690i −0.0395452 0.550793i
\(939\) 30.2487i 0.987129i
\(940\) 0 0
\(941\) 13.0718i 0.426128i 0.977038 + 0.213064i \(0.0683443\pi\)
−0.977038 + 0.213064i \(0.931656\pi\)
\(942\) −5.65685 + 5.65685i −0.184310 + 0.184310i
\(943\) 4.05317 4.05317i 0.131989 0.131989i
\(944\) −7.19615 −0.234215
\(945\) 0 0
\(946\) −20.3923 −0.663011
\(947\) −42.3992 + 42.3992i −1.37779 + 1.37779i −0.529444 + 0.848345i \(0.677599\pi\)
−0.848345 + 0.529444i \(0.822401\pi\)
\(948\) 8.76268 8.76268i 0.284599 0.284599i
\(949\) 46.2487i 1.50130i
\(950\) 0 0
\(951\) 27.3923i 0.888256i
\(952\) −0.947343 13.1948i −0.0307036 0.427646i
\(953\) −31.1127 31.1127i −1.00784 1.00784i −0.999969 0.00787013i \(-0.997495\pi\)
−0.00787013 0.999969i \(-0.502505\pi\)
\(954\) 3.53590i 0.114479i
\(955\) 0 0
\(956\) 8.53590 0.276071
\(957\) −29.8744 29.8744i −0.965701 0.965701i
\(958\) 0.656339 0.656339i 0.0212053 0.0212053i
\(959\) 13.6077 15.7128i 0.439415 0.507393i
\(960\) 0 0
\(961\) −31.8564 −1.02763
\(962\) −18.2832 18.2832i −0.589475 0.589475i
\(963\) 6.31319 + 6.31319i 0.203440 + 0.203440i
\(964\) −0.928203 −0.0298954
\(965\) 0 0
\(966\) 1.73205 2.00000i 0.0557278 0.0643489i
\(967\) 10.6574 10.6574i 0.342718 0.342718i −0.514670 0.857388i \(-0.672086\pi\)
0.857388 + 0.514670i \(0.172086\pi\)
\(968\) 13.3335 + 13.3335i 0.428555 + 0.428555i
\(969\) −37.3205 −1.19891
\(970\) 0 0
\(971\) 11.4641i 0.367901i −0.982936 0.183950i \(-0.941111\pi\)
0.982936 0.183950i \(-0.0588885\pi\)
\(972\) −0.707107 0.707107i −0.0226805 0.0226805i
\(973\) 52.4002 3.76217i 1.67987 0.120610i
\(974\) 38.0000i 1.21760i
\(975\) 0 0
\(976\) 2.46410i 0.0788740i
\(977\) −23.1822 + 23.1822i −0.741665 + 0.741665i −0.972898 0.231233i \(-0.925724\pi\)
0.231233 + 0.972898i \(0.425724\pi\)
\(978\) 0.568406 0.568406i 0.0181756 0.0181756i
\(979\) −65.5692 −2.09560
\(980\) 0 0
\(981\) 12.3923 0.395656
\(982\) −6.59059 + 6.59059i −0.210314 + 0.210314i
\(983\) −5.10205 + 5.10205i −0.162730 + 0.162730i −0.783775 0.621045i \(-0.786708\pi\)
0.621045 + 0.783775i \(0.286708\pi\)
\(984\) 5.73205i 0.182731i
\(985\) 0 0
\(986\) 38.6603i 1.23119i
\(987\) −22.1469 + 1.59008i −0.704945 + 0.0506128i
\(988\) 19.6975 + 19.6975i 0.626659 + 0.626659i
\(989\) 3.73205i 0.118672i
\(990\) 0 0
\(991\) 15.3205 0.486672 0.243336 0.969942i \(-0.421758\pi\)
0.243336 + 0.969942i \(0.421758\pi\)
\(992\) −5.60609 5.60609i −0.177993 0.177993i
\(993\) 21.4398 21.4398i 0.680373 0.680373i
\(994\) −19.8564 + 22.9282i −0.629807 + 0.727238i
\(995\) 0 0
\(996\) −0.464102 −0.0147056
\(997\) −16.9706 16.9706i −0.537463 0.537463i 0.385320 0.922783i \(-0.374091\pi\)
−0.922783 + 0.385320i \(0.874091\pi\)
\(998\) −2.39872 2.39872i −0.0759302 0.0759302i
\(999\) 6.92820 0.219199
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 1050.2.m.d.643.1 yes 8
5.2 odd 4 1050.2.m.c.307.2 8
5.3 odd 4 1050.2.m.c.307.3 yes 8
5.4 even 2 inner 1050.2.m.d.643.4 yes 8
7.6 odd 2 1050.2.m.c.643.2 yes 8
35.13 even 4 inner 1050.2.m.d.307.4 yes 8
35.27 even 4 inner 1050.2.m.d.307.1 yes 8
35.34 odd 2 1050.2.m.c.643.3 yes 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1050.2.m.c.307.2 8 5.2 odd 4
1050.2.m.c.307.3 yes 8 5.3 odd 4
1050.2.m.c.643.2 yes 8 7.6 odd 2
1050.2.m.c.643.3 yes 8 35.34 odd 2
1050.2.m.d.307.1 yes 8 35.27 even 4 inner
1050.2.m.d.307.4 yes 8 35.13 even 4 inner
1050.2.m.d.643.1 yes 8 1.1 even 1 trivial
1050.2.m.d.643.4 yes 8 5.4 even 2 inner