Properties

Label 150.3.f.c.7.1
Level $150$
Weight $3$
Character 150.7
Analytic conductor $4.087$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [150,3,Mod(7,150)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(150, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 1]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("150.7");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 150.f (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: \(4.08720396540\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(i)\)
Coefficient field: \(\Q(i, \sqrt{6})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} + 9 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 7.1
Root \(-1.22474 + 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 150.7
Dual form 150.3.f.c.43.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.00000 + 1.00000i) q^{2} +(-1.22474 + 1.22474i) q^{3} +2.00000i q^{4} -2.44949 q^{6} +(7.22474 + 7.22474i) q^{7} +(-2.00000 + 2.00000i) q^{8} -3.00000i q^{9} +O(q^{10})\) \(q+(1.00000 + 1.00000i) q^{2} +(-1.22474 + 1.22474i) q^{3} +2.00000i q^{4} -2.44949 q^{6} +(7.22474 + 7.22474i) q^{7} +(-2.00000 + 2.00000i) q^{8} -3.00000i q^{9} -8.69694 q^{11} +(-2.44949 - 2.44949i) q^{12} +(-15.6742 + 15.6742i) q^{13} +14.4495i q^{14} -4.00000 q^{16} +(13.3485 + 13.3485i) q^{17} +(3.00000 - 3.00000i) q^{18} -4.30306i q^{19} -17.6969 q^{21} +(-8.69694 - 8.69694i) q^{22} +(28.0454 - 28.0454i) q^{23} -4.89898i q^{24} -31.3485 q^{26} +(3.67423 + 3.67423i) q^{27} +(-14.4495 + 14.4495i) q^{28} -20.6969i q^{29} +39.0908 q^{31} +(-4.00000 - 4.00000i) q^{32} +(10.6515 - 10.6515i) q^{33} +26.6969i q^{34} +6.00000 q^{36} +(12.4949 + 12.4949i) q^{37} +(4.30306 - 4.30306i) q^{38} -38.3939i q^{39} +62.6969 q^{41} +(-17.6969 - 17.6969i) q^{42} +(-11.8763 + 11.8763i) q^{43} -17.3939i q^{44} +56.0908 q^{46} +(-58.0454 - 58.0454i) q^{47} +(4.89898 - 4.89898i) q^{48} +55.3939i q^{49} -32.6969 q^{51} +(-31.3485 - 31.3485i) q^{52} +(0.606123 - 0.606123i) q^{53} +7.34847i q^{54} -28.8990 q^{56} +(5.27015 + 5.27015i) q^{57} +(20.6969 - 20.6969i) q^{58} -30.0000i q^{59} +69.7878 q^{61} +(39.0908 + 39.0908i) q^{62} +(21.6742 - 21.6742i) q^{63} -8.00000i q^{64} +21.3031 q^{66} +(-5.02270 - 5.02270i) q^{67} +(-26.6969 + 26.6969i) q^{68} +68.6969i q^{69} -38.6969 q^{71} +(6.00000 + 6.00000i) q^{72} +(-46.2929 + 46.2929i) q^{73} +24.9898i q^{74} +8.60612 q^{76} +(-62.8332 - 62.8332i) q^{77} +(38.3939 - 38.3939i) q^{78} -31.3939i q^{79} -9.00000 q^{81} +(62.6969 + 62.6969i) q^{82} +(39.4393 - 39.4393i) q^{83} -35.3939i q^{84} -23.7526 q^{86} +(25.3485 + 25.3485i) q^{87} +(17.3939 - 17.3939i) q^{88} -41.3939i q^{89} -226.485 q^{91} +(56.0908 + 56.0908i) q^{92} +(-47.8763 + 47.8763i) q^{93} -116.091i q^{94} +9.79796 q^{96} +(54.1237 + 54.1237i) q^{97} +(-55.3939 + 55.3939i) q^{98} +26.0908i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 4 q^{2} + 24 q^{7} - 8 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 4 q^{2} + 24 q^{7} - 8 q^{8} + 24 q^{11} - 48 q^{13} - 16 q^{16} + 24 q^{17} + 12 q^{18} - 12 q^{21} + 24 q^{22} + 24 q^{23} - 96 q^{26} - 48 q^{28} - 20 q^{31} - 16 q^{32} + 72 q^{33} + 24 q^{36} - 48 q^{37} + 76 q^{38} + 192 q^{41} - 12 q^{42} - 72 q^{43} + 48 q^{46} - 144 q^{47} - 72 q^{51} - 96 q^{52} + 120 q^{53} - 96 q^{56} - 72 q^{57} + 24 q^{58} + 44 q^{61} - 20 q^{62} + 72 q^{63} + 144 q^{66} + 24 q^{67} - 48 q^{68} - 96 q^{71} + 24 q^{72} - 48 q^{73} + 152 q^{76} + 72 q^{77} + 36 q^{78} - 36 q^{81} + 192 q^{82} - 48 q^{83} - 144 q^{86} + 72 q^{87} - 48 q^{88} - 612 q^{91} + 48 q^{92} - 216 q^{93} + 192 q^{97} - 104 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/150\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 + 1.00000i 0.500000 + 0.500000i
\(3\) −1.22474 + 1.22474i −0.408248 + 0.408248i
\(4\) 2.00000i 0.500000i
\(5\) 0 0
\(6\) −2.44949 −0.408248
\(7\) 7.22474 + 7.22474i 1.03211 + 1.03211i 0.999467 + 0.0326392i \(0.0103912\pi\)
0.0326392 + 0.999467i \(0.489609\pi\)
\(8\) −2.00000 + 2.00000i −0.250000 + 0.250000i
\(9\) 3.00000i 0.333333i
\(10\) 0 0
\(11\) −8.69694 −0.790631 −0.395315 0.918545i \(-0.629365\pi\)
−0.395315 + 0.918545i \(0.629365\pi\)
\(12\) −2.44949 2.44949i −0.204124 0.204124i
\(13\) −15.6742 + 15.6742i −1.20571 + 1.20571i −0.233307 + 0.972403i \(0.574955\pi\)
−0.972403 + 0.233307i \(0.925045\pi\)
\(14\) 14.4495i 1.03211i
\(15\) 0 0
\(16\) −4.00000 −0.250000
\(17\) 13.3485 + 13.3485i 0.785204 + 0.785204i 0.980704 0.195500i \(-0.0626329\pi\)
−0.195500 + 0.980704i \(0.562633\pi\)
\(18\) 3.00000 3.00000i 0.166667 0.166667i
\(19\) 4.30306i 0.226477i −0.993568 0.113238i \(-0.963878\pi\)
0.993568 0.113238i \(-0.0361224\pi\)
\(20\) 0 0
\(21\) −17.6969 −0.842711
\(22\) −8.69694 8.69694i −0.395315 0.395315i
\(23\) 28.0454 28.0454i 1.21937 1.21937i 0.251511 0.967854i \(-0.419072\pi\)
0.967854 0.251511i \(-0.0809275\pi\)
\(24\) 4.89898i 0.204124i
\(25\) 0 0
\(26\) −31.3485 −1.20571
\(27\) 3.67423 + 3.67423i 0.136083 + 0.136083i
\(28\) −14.4495 + 14.4495i −0.516053 + 0.516053i
\(29\) 20.6969i 0.713688i −0.934164 0.356844i \(-0.883853\pi\)
0.934164 0.356844i \(-0.116147\pi\)
\(30\) 0 0
\(31\) 39.0908 1.26099 0.630497 0.776192i \(-0.282851\pi\)
0.630497 + 0.776192i \(0.282851\pi\)
\(32\) −4.00000 4.00000i −0.125000 0.125000i
\(33\) 10.6515 10.6515i 0.322774 0.322774i
\(34\) 26.6969i 0.785204i
\(35\) 0 0
\(36\) 6.00000 0.166667
\(37\) 12.4949 + 12.4949i 0.337700 + 0.337700i 0.855501 0.517801i \(-0.173249\pi\)
−0.517801 + 0.855501i \(0.673249\pi\)
\(38\) 4.30306 4.30306i 0.113238 0.113238i
\(39\) 38.3939i 0.984458i
\(40\) 0 0
\(41\) 62.6969 1.52919 0.764597 0.644509i \(-0.222938\pi\)
0.764597 + 0.644509i \(0.222938\pi\)
\(42\) −17.6969 17.6969i −0.421356 0.421356i
\(43\) −11.8763 + 11.8763i −0.276192 + 0.276192i −0.831587 0.555395i \(-0.812567\pi\)
0.555395 + 0.831587i \(0.312567\pi\)
\(44\) 17.3939i 0.395315i
\(45\) 0 0
\(46\) 56.0908 1.21937
\(47\) −58.0454 58.0454i −1.23501 1.23501i −0.962016 0.272993i \(-0.911987\pi\)
−0.272993 0.962016i \(-0.588013\pi\)
\(48\) 4.89898 4.89898i 0.102062 0.102062i
\(49\) 55.3939i 1.13049i
\(50\) 0 0
\(51\) −32.6969 −0.641116
\(52\) −31.3485 31.3485i −0.602855 0.602855i
\(53\) 0.606123 0.606123i 0.0114363 0.0114363i −0.701366 0.712802i \(-0.747426\pi\)
0.712802 + 0.701366i \(0.247426\pi\)
\(54\) 7.34847i 0.136083i
\(55\) 0 0
\(56\) −28.8990 −0.516053
\(57\) 5.27015 + 5.27015i 0.0924588 + 0.0924588i
\(58\) 20.6969 20.6969i 0.356844 0.356844i
\(59\) 30.0000i 0.508475i −0.967142 0.254237i \(-0.918176\pi\)
0.967142 0.254237i \(-0.0818244\pi\)
\(60\) 0 0
\(61\) 69.7878 1.14406 0.572031 0.820232i \(-0.306156\pi\)
0.572031 + 0.820232i \(0.306156\pi\)
\(62\) 39.0908 + 39.0908i 0.630497 + 0.630497i
\(63\) 21.6742 21.6742i 0.344035 0.344035i
\(64\) 8.00000i 0.125000i
\(65\) 0 0
\(66\) 21.3031 0.322774
\(67\) −5.02270 5.02270i −0.0749657 0.0749657i 0.668630 0.743595i \(-0.266881\pi\)
−0.743595 + 0.668630i \(0.766881\pi\)
\(68\) −26.6969 + 26.6969i −0.392602 + 0.392602i
\(69\) 68.6969i 0.995608i
\(70\) 0 0
\(71\) −38.6969 −0.545027 −0.272514 0.962152i \(-0.587855\pi\)
−0.272514 + 0.962152i \(0.587855\pi\)
\(72\) 6.00000 + 6.00000i 0.0833333 + 0.0833333i
\(73\) −46.2929 + 46.2929i −0.634149 + 0.634149i −0.949106 0.314957i \(-0.898010\pi\)
0.314957 + 0.949106i \(0.398010\pi\)
\(74\) 24.9898i 0.337700i
\(75\) 0 0
\(76\) 8.60612 0.113238
\(77\) −62.8332 62.8332i −0.816015 0.816015i
\(78\) 38.3939 38.3939i 0.492229 0.492229i
\(79\) 31.3939i 0.397391i −0.980061 0.198695i \(-0.936330\pi\)
0.980061 0.198695i \(-0.0636705\pi\)
\(80\) 0 0
\(81\) −9.00000 −0.111111
\(82\) 62.6969 + 62.6969i 0.764597 + 0.764597i
\(83\) 39.4393 39.4393i 0.475172 0.475172i −0.428412 0.903584i \(-0.640927\pi\)
0.903584 + 0.428412i \(0.140927\pi\)
\(84\) 35.3939i 0.421356i
\(85\) 0 0
\(86\) −23.7526 −0.276192
\(87\) 25.3485 + 25.3485i 0.291362 + 0.291362i
\(88\) 17.3939 17.3939i 0.197658 0.197658i
\(89\) 41.3939i 0.465100i −0.972584 0.232550i \(-0.925293\pi\)
0.972584 0.232550i \(-0.0747069\pi\)
\(90\) 0 0
\(91\) −226.485 −2.48884
\(92\) 56.0908 + 56.0908i 0.609683 + 0.609683i
\(93\) −47.8763 + 47.8763i −0.514799 + 0.514799i
\(94\) 116.091i 1.23501i
\(95\) 0 0
\(96\) 9.79796 0.102062
\(97\) 54.1237 + 54.1237i 0.557977 + 0.557977i 0.928731 0.370754i \(-0.120901\pi\)
−0.370754 + 0.928731i \(0.620901\pi\)
\(98\) −55.3939 + 55.3939i −0.565244 + 0.565244i
\(99\) 26.0908i 0.263544i
\(100\) 0 0
\(101\) −42.8786 −0.424540 −0.212270 0.977211i \(-0.568086\pi\)
−0.212270 + 0.977211i \(0.568086\pi\)
\(102\) −32.6969 32.6969i −0.320558 0.320558i
\(103\) 60.9898 60.9898i 0.592134 0.592134i −0.346073 0.938207i \(-0.612485\pi\)
0.938207 + 0.346073i \(0.112485\pi\)
\(104\) 62.6969i 0.602855i
\(105\) 0 0
\(106\) 1.21225 0.0114363
\(107\) 45.9092 + 45.9092i 0.429058 + 0.429058i 0.888307 0.459250i \(-0.151882\pi\)
−0.459250 + 0.888307i \(0.651882\pi\)
\(108\) −7.34847 + 7.34847i −0.0680414 + 0.0680414i
\(109\) 145.000i 1.33028i 0.746721 + 0.665138i \(0.231627\pi\)
−0.746721 + 0.665138i \(0.768373\pi\)
\(110\) 0 0
\(111\) −30.6061 −0.275731
\(112\) −28.8990 28.8990i −0.258027 0.258027i
\(113\) −130.788 + 130.788i −1.15741 + 1.15741i −0.172384 + 0.985030i \(0.555147\pi\)
−0.985030 + 0.172384i \(0.944853\pi\)
\(114\) 10.5403i 0.0924588i
\(115\) 0 0
\(116\) 41.3939 0.356844
\(117\) 47.0227 + 47.0227i 0.401903 + 0.401903i
\(118\) 30.0000 30.0000i 0.254237 0.254237i
\(119\) 192.879i 1.62083i
\(120\) 0 0
\(121\) −45.3633 −0.374903
\(122\) 69.7878 + 69.7878i 0.572031 + 0.572031i
\(123\) −76.7878 + 76.7878i −0.624291 + 0.624291i
\(124\) 78.1816i 0.630497i
\(125\) 0 0
\(126\) 43.3485 0.344035
\(127\) −21.3031 21.3031i −0.167741 0.167741i 0.618245 0.785986i \(-0.287844\pi\)
−0.785986 + 0.618245i \(0.787844\pi\)
\(128\) 8.00000 8.00000i 0.0625000 0.0625000i
\(129\) 29.0908i 0.225510i
\(130\) 0 0
\(131\) 108.272 0.826507 0.413254 0.910616i \(-0.364392\pi\)
0.413254 + 0.910616i \(0.364392\pi\)
\(132\) 21.3031 + 21.3031i 0.161387 + 0.161387i
\(133\) 31.0885 31.0885i 0.233748 0.233748i
\(134\) 10.0454i 0.0749657i
\(135\) 0 0
\(136\) −53.3939 −0.392602
\(137\) −76.6515 76.6515i −0.559500 0.559500i 0.369665 0.929165i \(-0.379472\pi\)
−0.929165 + 0.369665i \(0.879472\pi\)
\(138\) −68.6969 + 68.6969i −0.497804 + 0.497804i
\(139\) 152.788i 1.09919i −0.835430 0.549596i \(-0.814782\pi\)
0.835430 0.549596i \(-0.185218\pi\)
\(140\) 0 0
\(141\) 142.182 1.00838
\(142\) −38.6969 38.6969i −0.272514 0.272514i
\(143\) 136.318 136.318i 0.953272 0.953272i
\(144\) 12.0000i 0.0833333i
\(145\) 0 0
\(146\) −92.5857 −0.634149
\(147\) −67.8434 67.8434i −0.461520 0.461520i
\(148\) −24.9898 + 24.9898i −0.168850 + 0.168850i
\(149\) 112.788i 0.756965i 0.925608 + 0.378482i \(0.123554\pi\)
−0.925608 + 0.378482i \(0.876446\pi\)
\(150\) 0 0
\(151\) −167.879 −1.11178 −0.555889 0.831256i \(-0.687622\pi\)
−0.555889 + 0.831256i \(0.687622\pi\)
\(152\) 8.60612 + 8.60612i 0.0566192 + 0.0566192i
\(153\) 40.0454 40.0454i 0.261735 0.261735i
\(154\) 125.666i 0.816015i
\(155\) 0 0
\(156\) 76.7878 0.492229
\(157\) −114.866 114.866i −0.731631 0.731631i 0.239312 0.970943i \(-0.423078\pi\)
−0.970943 + 0.239312i \(0.923078\pi\)
\(158\) 31.3939 31.3939i 0.198695 0.198695i
\(159\) 1.48469i 0.00933769i
\(160\) 0 0
\(161\) 405.242 2.51703
\(162\) −9.00000 9.00000i −0.0555556 0.0555556i
\(163\) 10.1441 10.1441i 0.0622340 0.0622340i −0.675305 0.737539i \(-0.735988\pi\)
0.737539 + 0.675305i \(0.235988\pi\)
\(164\) 125.394i 0.764597i
\(165\) 0 0
\(166\) 78.8786 0.475172
\(167\) 155.666 + 155.666i 0.932134 + 0.932134i 0.997839 0.0657054i \(-0.0209298\pi\)
−0.0657054 + 0.997839i \(0.520930\pi\)
\(168\) 35.3939 35.3939i 0.210678 0.210678i
\(169\) 322.363i 1.90747i
\(170\) 0 0
\(171\) −12.9092 −0.0754923
\(172\) −23.7526 23.7526i −0.138096 0.138096i
\(173\) −86.8332 + 86.8332i −0.501926 + 0.501926i −0.912036 0.410110i \(-0.865490\pi\)
0.410110 + 0.912036i \(0.365490\pi\)
\(174\) 50.6969i 0.291362i
\(175\) 0 0
\(176\) 34.7878 0.197658
\(177\) 36.7423 + 36.7423i 0.207584 + 0.207584i
\(178\) 41.3939 41.3939i 0.232550 0.232550i
\(179\) 241.151i 1.34721i −0.739090 0.673606i \(-0.764744\pi\)
0.739090 0.673606i \(-0.235256\pi\)
\(180\) 0 0
\(181\) 41.1816 0.227523 0.113761 0.993508i \(-0.463710\pi\)
0.113761 + 0.993508i \(0.463710\pi\)
\(182\) −226.485 226.485i −1.24442 1.24442i
\(183\) −85.4722 + 85.4722i −0.467061 + 0.467061i
\(184\) 112.182i 0.609683i
\(185\) 0 0
\(186\) −95.7526 −0.514799
\(187\) −116.091 116.091i −0.620806 0.620806i
\(188\) 116.091 116.091i 0.617504 0.617504i
\(189\) 53.0908i 0.280904i
\(190\) 0 0
\(191\) −110.091 −0.576392 −0.288196 0.957571i \(-0.593055\pi\)
−0.288196 + 0.957571i \(0.593055\pi\)
\(192\) 9.79796 + 9.79796i 0.0510310 + 0.0510310i
\(193\) 266.487 266.487i 1.38076 1.38076i 0.537494 0.843268i \(-0.319371\pi\)
0.843268 0.537494i \(-0.180629\pi\)
\(194\) 108.247i 0.557977i
\(195\) 0 0
\(196\) −110.788 −0.565244
\(197\) −39.4393 39.4393i −0.200199 0.200199i 0.599886 0.800085i \(-0.295213\pi\)
−0.800085 + 0.599886i \(0.795213\pi\)
\(198\) −26.0908 + 26.0908i −0.131772 + 0.131772i
\(199\) 92.9092i 0.466880i −0.972371 0.233440i \(-0.925002\pi\)
0.972371 0.233440i \(-0.0749983\pi\)
\(200\) 0 0
\(201\) 12.3031 0.0612093
\(202\) −42.8786 42.8786i −0.212270 0.212270i
\(203\) 149.530 149.530i 0.736601 0.736601i
\(204\) 65.3939i 0.320558i
\(205\) 0 0
\(206\) 121.980 0.592134
\(207\) −84.1362 84.1362i −0.406455 0.406455i
\(208\) 62.6969 62.6969i 0.301428 0.301428i
\(209\) 37.4235i 0.179060i
\(210\) 0 0
\(211\) 293.272 1.38992 0.694958 0.719050i \(-0.255423\pi\)
0.694958 + 0.719050i \(0.255423\pi\)
\(212\) 1.21225 + 1.21225i 0.00571814 + 0.00571814i
\(213\) 47.3939 47.3939i 0.222506 0.222506i
\(214\) 91.8184i 0.429058i
\(215\) 0 0
\(216\) −14.6969 −0.0680414
\(217\) 282.421 + 282.421i 1.30148 + 1.30148i
\(218\) −145.000 + 145.000i −0.665138 + 0.665138i
\(219\) 113.394i 0.517780i
\(220\) 0 0
\(221\) −418.454 −1.89346
\(222\) −30.6061 30.6061i −0.137865 0.137865i
\(223\) −74.8207 + 74.8207i −0.335519 + 0.335519i −0.854678 0.519159i \(-0.826245\pi\)
0.519159 + 0.854678i \(0.326245\pi\)
\(224\) 57.7980i 0.258027i
\(225\) 0 0
\(226\) −261.576 −1.15741
\(227\) −47.1214 47.1214i −0.207583 0.207583i 0.595656 0.803240i \(-0.296892\pi\)
−0.803240 + 0.595656i \(0.796892\pi\)
\(228\) −10.5403 + 10.5403i −0.0462294 + 0.0462294i
\(229\) 275.000i 1.20087i 0.799672 + 0.600437i \(0.205007\pi\)
−0.799672 + 0.600437i \(0.794993\pi\)
\(230\) 0 0
\(231\) 153.909 0.666274
\(232\) 41.3939 + 41.3939i 0.178422 + 0.178422i
\(233\) −187.757 + 187.757i −0.805825 + 0.805825i −0.983999 0.178174i \(-0.942981\pi\)
0.178174 + 0.983999i \(0.442981\pi\)
\(234\) 94.0454i 0.401903i
\(235\) 0 0
\(236\) 60.0000 0.254237
\(237\) 38.4495 + 38.4495i 0.162234 + 0.162234i
\(238\) −192.879 + 192.879i −0.810414 + 0.810414i
\(239\) 17.6663i 0.0739177i −0.999317 0.0369588i \(-0.988233\pi\)
0.999317 0.0369588i \(-0.0117670\pi\)
\(240\) 0 0
\(241\) 167.000 0.692946 0.346473 0.938060i \(-0.387379\pi\)
0.346473 + 0.938060i \(0.387379\pi\)
\(242\) −45.3633 45.3633i −0.187451 0.187451i
\(243\) 11.0227 11.0227i 0.0453609 0.0453609i
\(244\) 139.576i 0.572031i
\(245\) 0 0
\(246\) −153.576 −0.624291
\(247\) 67.4472 + 67.4472i 0.273066 + 0.273066i
\(248\) −78.1816 + 78.1816i −0.315249 + 0.315249i
\(249\) 96.6061i 0.387976i
\(250\) 0 0
\(251\) 26.4245 0.105277 0.0526384 0.998614i \(-0.483237\pi\)
0.0526384 + 0.998614i \(0.483237\pi\)
\(252\) 43.3485 + 43.3485i 0.172018 + 0.172018i
\(253\) −243.909 + 243.909i −0.964068 + 0.964068i
\(254\) 42.6061i 0.167741i
\(255\) 0 0
\(256\) 16.0000 0.0625000
\(257\) 241.485 + 241.485i 0.939629 + 0.939629i 0.998279 0.0586495i \(-0.0186794\pi\)
−0.0586495 + 0.998279i \(0.518679\pi\)
\(258\) 29.0908 29.0908i 0.112755 0.112755i
\(259\) 180.545i 0.697085i
\(260\) 0 0
\(261\) −62.0908 −0.237896
\(262\) 108.272 + 108.272i 0.413254 + 0.413254i
\(263\) −142.182 + 142.182i −0.540615 + 0.540615i −0.923709 0.383095i \(-0.874858\pi\)
0.383095 + 0.923709i \(0.374858\pi\)
\(264\) 42.6061i 0.161387i
\(265\) 0 0
\(266\) 62.1770 0.233748
\(267\) 50.6969 + 50.6969i 0.189876 + 0.189876i
\(268\) 10.0454 10.0454i 0.0374829 0.0374829i
\(269\) 521.605i 1.93905i −0.244988 0.969526i \(-0.578784\pi\)
0.244988 0.969526i \(-0.421216\pi\)
\(270\) 0 0
\(271\) 39.2122 0.144695 0.0723473 0.997379i \(-0.476951\pi\)
0.0723473 + 0.997379i \(0.476951\pi\)
\(272\) −53.3939 53.3939i −0.196301 0.196301i
\(273\) 277.386 277.386i 1.01607 1.01607i
\(274\) 153.303i 0.559500i
\(275\) 0 0
\(276\) −137.394 −0.497804
\(277\) −69.5880 69.5880i −0.251220 0.251220i 0.570251 0.821471i \(-0.306846\pi\)
−0.821471 + 0.570251i \(0.806846\pi\)
\(278\) 152.788 152.788i 0.549596 0.549596i
\(279\) 117.272i 0.420331i
\(280\) 0 0
\(281\) −519.848 −1.84999 −0.924996 0.379976i \(-0.875932\pi\)
−0.924996 + 0.379976i \(0.875932\pi\)
\(282\) 142.182 + 142.182i 0.504190 + 0.504190i
\(283\) −153.427 + 153.427i −0.542144 + 0.542144i −0.924157 0.382013i \(-0.875231\pi\)
0.382013 + 0.924157i \(0.375231\pi\)
\(284\) 77.3939i 0.272514i
\(285\) 0 0
\(286\) 272.636 0.953272
\(287\) 452.969 + 452.969i 1.57829 + 1.57829i
\(288\) −12.0000 + 12.0000i −0.0416667 + 0.0416667i
\(289\) 67.3633i 0.233091i
\(290\) 0 0
\(291\) −132.576 −0.455586
\(292\) −92.5857 92.5857i −0.317074 0.317074i
\(293\) −19.6209 + 19.6209i −0.0669656 + 0.0669656i −0.739796 0.672831i \(-0.765078\pi\)
0.672831 + 0.739796i \(0.265078\pi\)
\(294\) 135.687i 0.461520i
\(295\) 0 0
\(296\) −49.9796 −0.168850
\(297\) −31.9546 31.9546i −0.107591 0.107591i
\(298\) −112.788 + 112.788i −0.378482 + 0.378482i
\(299\) 879.181i 2.94040i
\(300\) 0 0
\(301\) −171.606 −0.570120
\(302\) −167.879 167.879i −0.555889 0.555889i
\(303\) 52.5153 52.5153i 0.173318 0.173318i
\(304\) 17.2122i 0.0566192i
\(305\) 0 0
\(306\) 80.0908 0.261735
\(307\) −10.9115 10.9115i −0.0355423 0.0355423i 0.689112 0.724655i \(-0.258001\pi\)
−0.724655 + 0.689112i \(0.758001\pi\)
\(308\) 125.666 125.666i 0.408008 0.408008i
\(309\) 149.394i 0.483475i
\(310\) 0 0
\(311\) 64.7878 0.208321 0.104160 0.994561i \(-0.466784\pi\)
0.104160 + 0.994561i \(0.466784\pi\)
\(312\) 76.7878 + 76.7878i 0.246115 + 0.246115i
\(313\) −25.4472 + 25.4472i −0.0813009 + 0.0813009i −0.746588 0.665287i \(-0.768309\pi\)
0.665287 + 0.746588i \(0.268309\pi\)
\(314\) 229.732i 0.731631i
\(315\) 0 0
\(316\) 62.7878 0.198695
\(317\) −431.060 431.060i −1.35981 1.35981i −0.874143 0.485668i \(-0.838576\pi\)
−0.485668 0.874143i \(-0.661424\pi\)
\(318\) −1.48469 + 1.48469i −0.00466884 + 0.00466884i
\(319\) 180.000i 0.564263i
\(320\) 0 0
\(321\) −112.454 −0.350324
\(322\) 405.242 + 405.242i 1.25852 + 1.25852i
\(323\) 57.4393 57.4393i 0.177831 0.177831i
\(324\) 18.0000i 0.0555556i
\(325\) 0 0
\(326\) 20.2883 0.0622340
\(327\) −177.588 177.588i −0.543083 0.543083i
\(328\) −125.394 + 125.394i −0.382298 + 0.382298i
\(329\) 838.727i 2.54932i
\(330\) 0 0
\(331\) 295.939 0.894075 0.447037 0.894515i \(-0.352479\pi\)
0.447037 + 0.894515i \(0.352479\pi\)
\(332\) 78.8786 + 78.8786i 0.237586 + 0.237586i
\(333\) 37.4847 37.4847i 0.112567 0.112567i
\(334\) 311.333i 0.932134i
\(335\) 0 0
\(336\) 70.7878 0.210678
\(337\) −141.538 141.538i −0.419994 0.419994i 0.465208 0.885202i \(-0.345980\pi\)
−0.885202 + 0.465208i \(0.845980\pi\)
\(338\) 322.363 322.363i 0.953737 0.953737i
\(339\) 320.363i 0.945024i
\(340\) 0 0
\(341\) −339.970 −0.996981
\(342\) −12.9092 12.9092i −0.0377462 0.0377462i
\(343\) −46.1941 + 46.1941i −0.134677 + 0.134677i
\(344\) 47.5051i 0.138096i
\(345\) 0 0
\(346\) −173.666 −0.501926
\(347\) −362.227 362.227i −1.04388 1.04388i −0.998992 0.0448900i \(-0.985706\pi\)
−0.0448900 0.998992i \(-0.514294\pi\)
\(348\) −50.6969 + 50.6969i −0.145681 + 0.145681i
\(349\) 403.939i 1.15742i 0.815534 + 0.578709i \(0.196443\pi\)
−0.815534 + 0.578709i \(0.803557\pi\)
\(350\) 0 0
\(351\) −115.182 −0.328153
\(352\) 34.7878 + 34.7878i 0.0988288 + 0.0988288i
\(353\) 18.7423 18.7423i 0.0530945 0.0530945i −0.680061 0.733156i \(-0.738047\pi\)
0.733156 + 0.680061i \(0.238047\pi\)
\(354\) 73.4847i 0.207584i
\(355\) 0 0
\(356\) 82.7878 0.232550
\(357\) −236.227 236.227i −0.661700 0.661700i
\(358\) 241.151 241.151i 0.673606 0.673606i
\(359\) 383.728i 1.06888i 0.845207 + 0.534439i \(0.179477\pi\)
−0.845207 + 0.534439i \(0.820523\pi\)
\(360\) 0 0
\(361\) 342.484 0.948708
\(362\) 41.1816 + 41.1816i 0.113761 + 0.113761i
\(363\) 55.5584 55.5584i 0.153054 0.153054i
\(364\) 452.969i 1.24442i
\(365\) 0 0
\(366\) −170.944 −0.467061
\(367\) −387.341 387.341i −1.05542 1.05542i −0.998371 0.0570527i \(-0.981830\pi\)
−0.0570527 0.998371i \(-0.518170\pi\)
\(368\) −112.182 + 112.182i −0.304841 + 0.304841i
\(369\) 188.091i 0.509731i
\(370\) 0 0
\(371\) 8.75817 0.0236069
\(372\) −95.7526 95.7526i −0.257399 0.257399i
\(373\) 419.815 419.815i 1.12551 1.12551i 0.134611 0.990899i \(-0.457022\pi\)
0.990899 0.134611i \(-0.0429785\pi\)
\(374\) 232.182i 0.620806i
\(375\) 0 0
\(376\) 232.182 0.617504
\(377\) 324.409 + 324.409i 0.860500 + 0.860500i
\(378\) −53.0908 + 53.0908i −0.140452 + 0.140452i
\(379\) 472.181i 1.24586i −0.782278 0.622930i \(-0.785942\pi\)
0.782278 0.622930i \(-0.214058\pi\)
\(380\) 0 0
\(381\) 52.1816 0.136960
\(382\) −110.091 110.091i −0.288196 0.288196i
\(383\) 67.8184 67.8184i 0.177071 0.177071i −0.613006 0.790078i \(-0.710040\pi\)
0.790078 + 0.613006i \(0.210040\pi\)
\(384\) 19.5959i 0.0510310i
\(385\) 0 0
\(386\) 532.974 1.38076
\(387\) 35.6288 + 35.6288i 0.0920642 + 0.0920642i
\(388\) −108.247 + 108.247i −0.278988 + 0.278988i
\(389\) 603.242i 1.55075i 0.631501 + 0.775375i \(0.282439\pi\)
−0.631501 + 0.775375i \(0.717561\pi\)
\(390\) 0 0
\(391\) 748.727 1.91490
\(392\) −110.788 110.788i −0.282622 0.282622i
\(393\) −132.606 + 132.606i −0.337420 + 0.337420i
\(394\) 78.8786i 0.200199i
\(395\) 0 0
\(396\) −52.1816 −0.131772
\(397\) −188.648 188.648i −0.475184 0.475184i 0.428403 0.903588i \(-0.359076\pi\)
−0.903588 + 0.428403i \(0.859076\pi\)
\(398\) 92.9092 92.9092i 0.233440 0.233440i
\(399\) 76.1510i 0.190855i
\(400\) 0 0
\(401\) 302.697 0.754855 0.377428 0.926039i \(-0.376809\pi\)
0.377428 + 0.926039i \(0.376809\pi\)
\(402\) 12.3031 + 12.3031i 0.0306046 + 0.0306046i
\(403\) −612.719 + 612.719i −1.52039 + 1.52039i
\(404\) 85.7571i 0.212270i
\(405\) 0 0
\(406\) 299.060 0.736601
\(407\) −108.667 108.667i −0.266996 0.266996i
\(408\) 65.3939 65.3939i 0.160279 0.160279i
\(409\) 20.8184i 0.0509007i −0.999676 0.0254503i \(-0.991898\pi\)
0.999676 0.0254503i \(-0.00810197\pi\)
\(410\) 0 0
\(411\) 187.757 0.456830
\(412\) 121.980 + 121.980i 0.296067 + 0.296067i
\(413\) 216.742 216.742i 0.524800 0.524800i
\(414\) 168.272i 0.406455i
\(415\) 0 0
\(416\) 125.394 0.301428
\(417\) 187.126 + 187.126i 0.448743 + 0.448743i
\(418\) −37.4235 + 37.4235i −0.0895298 + 0.0895298i
\(419\) 466.515i 1.11340i 0.830713 + 0.556701i \(0.187933\pi\)
−0.830713 + 0.556701i \(0.812067\pi\)
\(420\) 0 0
\(421\) −636.120 −1.51097 −0.755487 0.655163i \(-0.772600\pi\)
−0.755487 + 0.655163i \(0.772600\pi\)
\(422\) 293.272 + 293.272i 0.694958 + 0.694958i
\(423\) −174.136 + 174.136i −0.411670 + 0.411670i
\(424\) 2.42449i 0.00571814i
\(425\) 0 0
\(426\) 94.7878 0.222506
\(427\) 504.199 + 504.199i 1.18079 + 1.18079i
\(428\) −91.8184 + 91.8184i −0.214529 + 0.214529i
\(429\) 333.909i 0.778343i
\(430\) 0 0
\(431\) 165.242 0.383392 0.191696 0.981454i \(-0.438601\pi\)
0.191696 + 0.981454i \(0.438601\pi\)
\(432\) −14.6969 14.6969i −0.0340207 0.0340207i
\(433\) 282.619 282.619i 0.652699 0.652699i −0.300943 0.953642i \(-0.597301\pi\)
0.953642 + 0.300943i \(0.0973015\pi\)
\(434\) 564.842i 1.30148i
\(435\) 0 0
\(436\) −290.000 −0.665138
\(437\) −120.681 120.681i −0.276158 0.276158i
\(438\) 113.394 113.394i 0.258890 0.258890i
\(439\) 272.909i 0.621661i −0.950465 0.310831i \(-0.899393\pi\)
0.950465 0.310831i \(-0.100607\pi\)
\(440\) 0 0
\(441\) 166.182 0.376829
\(442\) −418.454 418.454i −0.946729 0.946729i
\(443\) 176.636 176.636i 0.398726 0.398726i −0.479057 0.877784i \(-0.659021\pi\)
0.877784 + 0.479057i \(0.159021\pi\)
\(444\) 61.2122i 0.137865i
\(445\) 0 0
\(446\) −149.641 −0.335519
\(447\) −138.136 138.136i −0.309030 0.309030i
\(448\) 57.7980 57.7980i 0.129013 0.129013i
\(449\) 751.151i 1.67294i −0.548011 0.836471i \(-0.684615\pi\)
0.548011 0.836471i \(-0.315385\pi\)
\(450\) 0 0
\(451\) −545.271 −1.20903
\(452\) −261.576 261.576i −0.578707 0.578707i
\(453\) 205.608 205.608i 0.453882 0.453882i
\(454\) 94.2429i 0.207583i
\(455\) 0 0
\(456\) −21.0806 −0.0462294
\(457\) −26.4245 26.4245i −0.0578216 0.0578216i 0.677605 0.735426i \(-0.263018\pi\)
−0.735426 + 0.677605i \(0.763018\pi\)
\(458\) −275.000 + 275.000i −0.600437 + 0.600437i
\(459\) 98.0908i 0.213705i
\(460\) 0 0
\(461\) −38.6969 −0.0839413 −0.0419706 0.999119i \(-0.513364\pi\)
−0.0419706 + 0.999119i \(0.513364\pi\)
\(462\) 153.909 + 153.909i 0.333137 + 0.333137i
\(463\) −203.505 + 203.505i −0.439536 + 0.439536i −0.891856 0.452320i \(-0.850597\pi\)
0.452320 + 0.891856i \(0.350597\pi\)
\(464\) 82.7878i 0.178422i
\(465\) 0 0
\(466\) −375.514 −0.805825
\(467\) 557.530 + 557.530i 1.19385 + 1.19385i 0.975976 + 0.217879i \(0.0699137\pi\)
0.217879 + 0.975976i \(0.430086\pi\)
\(468\) −94.0454 + 94.0454i −0.200952 + 0.200952i
\(469\) 72.5755i 0.154745i
\(470\) 0 0
\(471\) 281.363 0.597374
\(472\) 60.0000 + 60.0000i 0.127119 + 0.127119i
\(473\) 103.287 103.287i 0.218366 0.218366i
\(474\) 76.8990i 0.162234i
\(475\) 0 0
\(476\) −385.757 −0.810414
\(477\) −1.81837 1.81837i −0.00381209 0.00381209i
\(478\) 17.6663 17.6663i 0.0369588 0.0369588i
\(479\) 265.818i 0.554944i −0.960734 0.277472i \(-0.910503\pi\)
0.960734 0.277472i \(-0.0894966\pi\)
\(480\) 0 0
\(481\) −391.696 −0.814337
\(482\) 167.000 + 167.000i 0.346473 + 0.346473i
\(483\) −496.318 + 496.318i −1.02757 + 1.02757i
\(484\) 90.7265i 0.187451i
\(485\) 0 0
\(486\) 22.0454 0.0453609
\(487\) −304.083 304.083i −0.624400 0.624400i 0.322253 0.946653i \(-0.395560\pi\)
−0.946653 + 0.322253i \(0.895560\pi\)
\(488\) −139.576 + 139.576i −0.286015 + 0.286015i
\(489\) 24.8480i 0.0508138i
\(490\) 0 0
\(491\) 169.212 0.344628 0.172314 0.985042i \(-0.444876\pi\)
0.172314 + 0.985042i \(0.444876\pi\)
\(492\) −153.576 153.576i −0.312145 0.312145i
\(493\) 276.272 276.272i 0.560390 0.560390i
\(494\) 134.894i 0.273066i
\(495\) 0 0
\(496\) −156.363 −0.315249
\(497\) −279.576 279.576i −0.562526 0.562526i
\(498\) −96.6061 + 96.6061i −0.193988 + 0.193988i
\(499\) 699.636i 1.40208i 0.713124 + 0.701038i \(0.247280\pi\)
−0.713124 + 0.701038i \(0.752720\pi\)
\(500\) 0 0
\(501\) −381.303 −0.761084
\(502\) 26.4245 + 26.4245i 0.0526384 + 0.0526384i
\(503\) −279.848 + 279.848i −0.556358 + 0.556358i −0.928268 0.371911i \(-0.878703\pi\)
0.371911 + 0.928268i \(0.378703\pi\)
\(504\) 86.6969i 0.172018i
\(505\) 0 0
\(506\) −487.818 −0.964068
\(507\) 394.813 + 394.813i 0.778723 + 0.778723i
\(508\) 42.6061 42.6061i 0.0838703 0.0838703i
\(509\) 193.696i 0.380542i 0.981732 + 0.190271i \(0.0609367\pi\)
−0.981732 + 0.190271i \(0.939063\pi\)
\(510\) 0 0
\(511\) −668.908 −1.30902
\(512\) 16.0000 + 16.0000i 0.0312500 + 0.0312500i
\(513\) 15.8105 15.8105i 0.0308196 0.0308196i
\(514\) 482.969i 0.939629i
\(515\) 0 0
\(516\) 58.1816 0.112755
\(517\) 504.817 + 504.817i 0.976436 + 0.976436i
\(518\) −180.545 + 180.545i −0.348542 + 0.348542i
\(519\) 212.697i 0.409821i
\(520\) 0 0
\(521\) 167.121 0.320771 0.160385 0.987054i \(-0.448726\pi\)
0.160385 + 0.987054i \(0.448726\pi\)
\(522\) −62.0908 62.0908i −0.118948 0.118948i
\(523\) 675.860 675.860i 1.29228 1.29228i 0.358900 0.933376i \(-0.383152\pi\)
0.933376 0.358900i \(-0.116848\pi\)
\(524\) 216.545i 0.413254i
\(525\) 0 0
\(526\) −284.363 −0.540615
\(527\) 521.803 + 521.803i 0.990138 + 0.990138i
\(528\) −42.6061 + 42.6061i −0.0806934 + 0.0806934i
\(529\) 1044.09i 1.97370i
\(530\) 0 0
\(531\) −90.0000 −0.169492
\(532\) 62.1770 + 62.1770i 0.116874 + 0.116874i
\(533\) −982.727 + 982.727i −1.84376 + 1.84376i
\(534\) 101.394i 0.189876i
\(535\) 0 0
\(536\) 20.0908 0.0374829
\(537\) 295.348 + 295.348i 0.549997 + 0.549997i
\(538\) 521.605 521.605i 0.969526 0.969526i
\(539\) 481.757i 0.893798i
\(540\) 0 0
\(541\) −131.120 −0.242367 −0.121183 0.992630i \(-0.538669\pi\)
−0.121183 + 0.992630i \(0.538669\pi\)
\(542\) 39.2122 + 39.2122i 0.0723473 + 0.0723473i
\(543\) −50.4370 + 50.4370i −0.0928858 + 0.0928858i
\(544\) 106.788i 0.196301i
\(545\) 0 0
\(546\) 554.772 1.01607
\(547\) 423.959 + 423.959i 0.775062 + 0.775062i 0.978987 0.203924i \(-0.0653696\pi\)
−0.203924 + 0.978987i \(0.565370\pi\)
\(548\) 153.303 153.303i 0.279750 0.279750i
\(549\) 209.363i 0.381354i
\(550\) 0 0
\(551\) −89.0602 −0.161634
\(552\) −137.394 137.394i −0.248902 0.248902i
\(553\) 226.813 226.813i 0.410150 0.410150i
\(554\) 139.176i 0.251220i
\(555\) 0 0
\(556\) 305.576 0.549596
\(557\) −341.741 341.741i −0.613539 0.613539i 0.330327 0.943866i \(-0.392841\pi\)
−0.943866 + 0.330327i \(0.892841\pi\)
\(558\) 117.272 117.272i 0.210166 0.210166i
\(559\) 372.303i 0.666016i
\(560\) 0 0
\(561\) 284.363 0.506886
\(562\) −519.848 519.848i −0.924996 0.924996i
\(563\) 13.6209 13.6209i 0.0241935 0.0241935i −0.694907 0.719100i \(-0.744554\pi\)
0.719100 + 0.694907i \(0.244554\pi\)
\(564\) 284.363i 0.504190i
\(565\) 0 0
\(566\) −306.854 −0.542144
\(567\) −65.0227 65.0227i −0.114678 0.114678i
\(568\) 77.3939 77.3939i 0.136257 0.136257i
\(569\) 22.9990i 0.0404200i 0.999796 + 0.0202100i \(0.00643348\pi\)
−0.999796 + 0.0202100i \(0.993567\pi\)
\(570\) 0 0
\(571\) −660.666 −1.15703 −0.578517 0.815670i \(-0.696368\pi\)
−0.578517 + 0.815670i \(0.696368\pi\)
\(572\) 272.636 + 272.636i 0.476636 + 0.476636i
\(573\) 134.833 134.833i 0.235311 0.235311i
\(574\) 905.939i 1.57829i
\(575\) 0 0
\(576\) −24.0000 −0.0416667
\(577\) 421.547 + 421.547i 0.730584 + 0.730584i 0.970736 0.240151i \(-0.0771970\pi\)
−0.240151 + 0.970736i \(0.577197\pi\)
\(578\) −67.3633 + 67.3633i −0.116545 + 0.116545i
\(579\) 652.757i 1.12739i
\(580\) 0 0
\(581\) 569.878 0.980856
\(582\) −132.576 132.576i −0.227793 0.227793i
\(583\) −5.27142 + 5.27142i −0.00904188 + 0.00904188i
\(584\) 185.171i 0.317074i
\(585\) 0 0
\(586\) −39.2418 −0.0669656
\(587\) −441.514 441.514i −0.752154 0.752154i 0.222727 0.974881i \(-0.428504\pi\)
−0.974881 + 0.222727i \(0.928504\pi\)
\(588\) 135.687 135.687i 0.230760 0.230760i
\(589\) 168.210i 0.285586i
\(590\) 0 0
\(591\) 96.6061 0.163462
\(592\) −49.9796 49.9796i −0.0844250 0.0844250i
\(593\) 171.303 171.303i 0.288875 0.288875i −0.547760 0.836635i \(-0.684519\pi\)
0.836635 + 0.547760i \(0.184519\pi\)
\(594\) 63.9092i 0.107591i
\(595\) 0 0
\(596\) −225.576 −0.378482
\(597\) 113.790 + 113.790i 0.190603 + 0.190603i
\(598\) −879.181 + 879.181i −1.47020 + 1.47020i
\(599\) 64.1816i 0.107148i 0.998564 + 0.0535740i \(0.0170613\pi\)
−0.998564 + 0.0535740i \(0.982939\pi\)
\(600\) 0 0
\(601\) 469.545 0.781273 0.390636 0.920545i \(-0.372255\pi\)
0.390636 + 0.920545i \(0.372255\pi\)
\(602\) −171.606 171.606i −0.285060 0.285060i
\(603\) −15.0681 + 15.0681i −0.0249886 + 0.0249886i
\(604\) 335.757i 0.555889i
\(605\) 0 0
\(606\) 105.031 0.173318
\(607\) −121.930 121.930i −0.200872 0.200872i 0.599501 0.800374i \(-0.295366\pi\)
−0.800374 + 0.599501i \(0.795366\pi\)
\(608\) −17.2122 + 17.2122i −0.0283096 + 0.0283096i
\(609\) 366.272i 0.601433i
\(610\) 0 0
\(611\) 1819.63 2.97813
\(612\) 80.0908 + 80.0908i 0.130867 + 0.130867i
\(613\) −542.252 + 542.252i −0.884587 + 0.884587i −0.993997 0.109409i \(-0.965104\pi\)
0.109409 + 0.993997i \(0.465104\pi\)
\(614\) 21.8230i 0.0355423i
\(615\) 0 0
\(616\) 251.333 0.408008
\(617\) −117.364 117.364i −0.190218 0.190218i 0.605572 0.795790i \(-0.292944\pi\)
−0.795790 + 0.605572i \(0.792944\pi\)
\(618\) −149.394 + 149.394i −0.241738 + 0.241738i
\(619\) 295.697i 0.477701i −0.971056 0.238851i \(-0.923229\pi\)
0.971056 0.238851i \(-0.0767706\pi\)
\(620\) 0 0
\(621\) 206.091 0.331869
\(622\) 64.7878 + 64.7878i 0.104160 + 0.104160i
\(623\) 299.060 299.060i 0.480032 0.480032i
\(624\) 153.576i 0.246115i
\(625\) 0 0
\(626\) −50.8944 −0.0813009
\(627\) −45.8342 45.8342i −0.0731008 0.0731008i
\(628\) 229.732 229.732i 0.365816 0.365816i
\(629\) 333.576i 0.530327i
\(630\) 0 0
\(631\) 897.454 1.42227 0.711136 0.703054i \(-0.248181\pi\)
0.711136 + 0.703054i \(0.248181\pi\)
\(632\) 62.7878 + 62.7878i 0.0993477 + 0.0993477i
\(633\) −359.184 + 359.184i −0.567431 + 0.567431i
\(634\) 862.120i 1.35981i
\(635\) 0 0
\(636\) −2.96938 −0.00466884
\(637\) −868.257 868.257i −1.36304 1.36304i
\(638\) −180.000 + 180.000i −0.282132 + 0.282132i
\(639\) 116.091i 0.181676i
\(640\) 0 0
\(641\) −226.120 −0.352762 −0.176381 0.984322i \(-0.556439\pi\)
−0.176381 + 0.984322i \(0.556439\pi\)
\(642\) −112.454 112.454i −0.175162 0.175162i
\(643\) 472.454 472.454i 0.734765 0.734765i −0.236794 0.971560i \(-0.576097\pi\)
0.971560 + 0.236794i \(0.0760968\pi\)
\(644\) 810.484i 1.25852i
\(645\) 0 0
\(646\) 114.879 0.177831
\(647\) −583.151 583.151i −0.901315 0.901315i 0.0942347 0.995550i \(-0.469960\pi\)
−0.995550 + 0.0942347i \(0.969960\pi\)
\(648\) 18.0000 18.0000i 0.0277778 0.0277778i
\(649\) 260.908i 0.402016i
\(650\) 0 0
\(651\) −691.788 −1.06265
\(652\) 20.2883 + 20.2883i 0.0311170 + 0.0311170i
\(653\) 36.1975 36.1975i 0.0554325 0.0554325i −0.678847 0.734280i \(-0.737520\pi\)
0.734280 + 0.678847i \(0.237520\pi\)
\(654\) 355.176i 0.543083i
\(655\) 0 0
\(656\) −250.788 −0.382298
\(657\) 138.879 + 138.879i 0.211383 + 0.211383i
\(658\) 838.727 838.727i 1.27466 1.27466i
\(659\) 615.787i 0.934426i −0.884145 0.467213i \(-0.845258\pi\)
0.884145 0.467213i \(-0.154742\pi\)
\(660\) 0 0
\(661\) −426.849 −0.645762 −0.322881 0.946439i \(-0.604651\pi\)
−0.322881 + 0.946439i \(0.604651\pi\)
\(662\) 295.939 + 295.939i 0.447037 + 0.447037i
\(663\) 512.499 512.499i 0.773001 0.773001i
\(664\) 157.757i 0.237586i
\(665\) 0 0
\(666\) 74.9694 0.112567
\(667\) −580.454 580.454i −0.870246 0.870246i
\(668\) −311.333 + 311.333i −0.466067 + 0.466067i
\(669\) 183.272i 0.273950i
\(670\) 0 0
\(671\) −606.940 −0.904530
\(672\) 70.7878 + 70.7878i 0.105339 + 0.105339i
\(673\) −350.474 + 350.474i −0.520764 + 0.520764i −0.917802 0.397038i \(-0.870038\pi\)
0.397038 + 0.917802i \(0.370038\pi\)
\(674\) 283.076i 0.419994i
\(675\) 0 0
\(676\) 644.727 0.953737
\(677\) −208.985 208.985i −0.308693 0.308693i 0.535709 0.844402i \(-0.320044\pi\)
−0.844402 + 0.535709i \(0.820044\pi\)
\(678\) 320.363 320.363i 0.472512 0.472512i
\(679\) 782.060i 1.15178i
\(680\) 0 0
\(681\) 115.423 0.169491
\(682\) −339.970 339.970i −0.498490 0.498490i
\(683\) 701.271 701.271i 1.02675 1.02675i 0.0271195 0.999632i \(-0.491367\pi\)
0.999632 0.0271195i \(-0.00863347\pi\)
\(684\) 25.8184i 0.0377462i
\(685\) 0 0
\(686\) −92.3883 −0.134677
\(687\) −336.805 336.805i −0.490254 0.490254i
\(688\) 47.5051 47.5051i 0.0690481 0.0690481i
\(689\) 19.0010i 0.0275777i
\(690\) 0 0
\(691\) −132.910 −0.192345 −0.0961724 0.995365i \(-0.530660\pi\)
−0.0961724 + 0.995365i \(0.530660\pi\)
\(692\) −173.666 173.666i −0.250963 0.250963i
\(693\) −188.499 + 188.499i −0.272005 + 0.272005i
\(694\) 724.454i 1.04388i
\(695\) 0 0
\(696\) −101.394 −0.145681
\(697\) 836.908 + 836.908i 1.20073 + 1.20073i
\(698\) −403.939 + 403.939i −0.578709 + 0.578709i
\(699\) 459.909i 0.657953i
\(700\) 0 0
\(701\) 158.758 0.226474 0.113237 0.993568i \(-0.463878\pi\)
0.113237 + 0.993568i \(0.463878\pi\)
\(702\) −115.182 115.182i −0.164076 0.164076i
\(703\) 53.7663 53.7663i 0.0764812 0.0764812i
\(704\) 69.5755i 0.0988288i
\(705\) 0 0
\(706\) 37.4847 0.0530945
\(707\) −309.787 309.787i −0.438171 0.438171i
\(708\) −73.4847 + 73.4847i −0.103792 + 0.103792i
\(709\) 674.514i 0.951360i 0.879618 + 0.475680i \(0.157798\pi\)
−0.879618 + 0.475680i \(0.842202\pi\)
\(710\) 0 0
\(711\) −94.1816 −0.132464
\(712\) 82.7878 + 82.7878i 0.116275 + 0.116275i
\(713\) 1096.32 1096.32i 1.53761 1.53761i
\(714\) 472.454i 0.661700i
\(715\) 0 0
\(716\) 482.302 0.673606
\(717\) 21.6367 + 21.6367i 0.0301768 + 0.0301768i
\(718\) −383.728 + 383.728i −0.534439 + 0.534439i
\(719\) 103.485i 0.143929i −0.997407 0.0719643i \(-0.977073\pi\)
0.997407 0.0719643i \(-0.0229268\pi\)
\(720\) 0 0
\(721\) 881.271 1.22229
\(722\) 342.484 + 342.484i 0.474354 + 0.474354i
\(723\) −204.532 + 204.532i −0.282894 + 0.282894i
\(724\) 82.3633i 0.113761i
\(725\) 0 0
\(726\) 111.117 0.153054
\(727\) 658.392 + 658.392i 0.905628 + 0.905628i 0.995916 0.0902877i \(-0.0287787\pi\)
−0.0902877 + 0.995916i \(0.528779\pi\)
\(728\) 452.969 452.969i 0.622211 0.622211i
\(729\) 27.0000i 0.0370370i
\(730\) 0 0
\(731\) −317.060 −0.433735
\(732\) −170.944 170.944i −0.233531 0.233531i
\(733\) 165.970 165.970i 0.226426 0.226426i −0.584772 0.811198i \(-0.698816\pi\)
0.811198 + 0.584772i \(0.198816\pi\)
\(734\) 774.681i 1.05542i
\(735\) 0 0
\(736\) −224.363 −0.304841
\(737\) 43.6821 + 43.6821i 0.0592702 + 0.0592702i
\(738\) 188.091 188.091i 0.254866 0.254866i
\(739\) 122.545i 0.165825i 0.996557 + 0.0829126i \(0.0264222\pi\)
−0.996557 + 0.0829126i \(0.973578\pi\)
\(740\) 0 0
\(741\) −165.211 −0.222957
\(742\) 8.75817 + 8.75817i 0.0118035 + 0.0118035i
\(743\) −541.485 + 541.485i −0.728782 + 0.728782i −0.970377 0.241595i \(-0.922329\pi\)
0.241595 + 0.970377i \(0.422329\pi\)
\(744\) 191.505i 0.257399i
\(745\) 0 0
\(746\) 839.630 1.12551
\(747\) −118.318 118.318i −0.158391 0.158391i
\(748\) 232.182 232.182i 0.310403 0.310403i
\(749\) 663.364i 0.885667i
\(750\) 0 0
\(751\) −495.212 −0.659404 −0.329702 0.944085i \(-0.606948\pi\)
−0.329702 + 0.944085i \(0.606948\pi\)
\(752\) 232.182 + 232.182i 0.308752 + 0.308752i
\(753\) −32.3633 + 32.3633i −0.0429791 + 0.0429791i
\(754\) 648.817i 0.860500i
\(755\) 0 0
\(756\) −106.182 −0.140452
\(757\) −565.547 565.547i −0.747090 0.747090i 0.226842 0.973932i \(-0.427160\pi\)
−0.973932 + 0.226842i \(0.927160\pi\)
\(758\) 472.181 472.181i 0.622930 0.622930i
\(759\) 597.453i 0.787158i
\(760\) 0 0
\(761\) −737.271 −0.968819 −0.484410 0.874841i \(-0.660966\pi\)
−0.484410 + 0.874841i \(0.660966\pi\)
\(762\) 52.1816 + 52.1816i 0.0684798 + 0.0684798i
\(763\) −1047.59 + 1047.59i −1.37299 + 1.37299i
\(764\) 220.182i 0.288196i
\(765\) 0 0
\(766\) 135.637 0.177071
\(767\) 470.227 + 470.227i 0.613073 + 0.613073i
\(768\) −19.5959 + 19.5959i −0.0255155 + 0.0255155i
\(769\) 1014.27i 1.31895i 0.751727 + 0.659474i \(0.229221\pi\)
−0.751727 + 0.659474i \(0.770779\pi\)
\(770\) 0 0
\(771\) −591.514 −0.767204
\(772\) 532.974 + 532.974i 0.690381 + 0.690381i
\(773\) −6.39491 + 6.39491i −0.00827284 + 0.00827284i −0.711231 0.702958i \(-0.751862\pi\)
0.702958 + 0.711231i \(0.251862\pi\)
\(774\) 71.2577i 0.0920642i
\(775\) 0 0
\(776\) −216.495 −0.278988
\(777\) −221.121 221.121i −0.284584 0.284584i
\(778\) −603.242 + 603.242i −0.775375 + 0.775375i
\(779\) 269.789i 0.346327i
\(780\) 0 0
\(781\) 336.545 0.430915
\(782\) 748.727 + 748.727i 0.957451 + 0.957451i
\(783\) 76.0454 76.0454i 0.0971206 0.0971206i
\(784\) 221.576i 0.282622i
\(785\) 0 0
\(786\) −265.212 −0.337420
\(787\) −565.806 565.806i −0.718940 0.718940i 0.249448 0.968388i \(-0.419751\pi\)
−0.968388 + 0.249448i \(0.919751\pi\)
\(788\) 78.8786 78.8786i 0.100100 0.100100i
\(789\) 348.272i 0.441410i
\(790\) 0 0
\(791\) −1889.82 −2.38915
\(792\) −52.1816 52.1816i −0.0658859 0.0658859i
\(793\) −1093.87 + 1093.87i −1.37941 + 1.37941i
\(794\) 377.296i 0.475184i
\(795\) 0 0
\(796\) 185.818 0.233440
\(797\) 352.182 + 352.182i 0.441884 + 0.441884i 0.892645 0.450761i \(-0.148847\pi\)
−0.450761 + 0.892645i \(0.648847\pi\)
\(798\) −76.1510 + 76.1510i −0.0954273 + 0.0954273i
\(799\) 1549.63i 1.93947i
\(800\) 0 0
\(801\) −124.182 −0.155033
\(802\) 302.697 + 302.697i 0.377428 + 0.377428i
\(803\) 402.606 402.606i 0.501377 0.501377i
\(804\) 24.6061i 0.0306046i
\(805\) 0 0
\(806\) −1225.44 −1.52039
\(807\) 638.833 + 638.833i 0.791615 + 0.791615i
\(808\) 85.7571 85.7571i 0.106135 0.106135i
\(809\) 563.728i 0.696820i 0.937342 + 0.348410i \(0.113278\pi\)
−0.937342 + 0.348410i \(0.886722\pi\)
\(810\) 0 0
\(811\) −205.091 −0.252886 −0.126443 0.991974i \(-0.540356\pi\)
−0.126443 + 0.991974i \(0.540356\pi\)
\(812\) 299.060 + 299.060i 0.368301 + 0.368301i
\(813\) −48.0250 + 48.0250i −0.0590713 + 0.0590713i
\(814\) 217.335i 0.266996i
\(815\) 0 0
\(816\) 130.788 0.160279
\(817\) 51.1043 + 51.1043i 0.0625512 + 0.0625512i
\(818\) 20.8184 20.8184i 0.0254503 0.0254503i
\(819\) 679.454i 0.829614i
\(820\) 0 0
\(821\) 867.576 1.05673 0.528365 0.849017i \(-0.322805\pi\)
0.528365 + 0.849017i \(0.322805\pi\)
\(822\) 187.757 + 187.757i 0.228415 + 0.228415i
\(823\) 80.8094 80.8094i 0.0981889 0.0981889i −0.656306 0.754495i \(-0.727882\pi\)
0.754495 + 0.656306i \(0.227882\pi\)
\(824\) 243.959i 0.296067i
\(825\) 0 0
\(826\) 433.485 0.524800
\(827\) −935.939 935.939i −1.13173 1.13173i −0.989890 0.141838i \(-0.954699\pi\)
−0.141838 0.989890i \(-0.545301\pi\)
\(828\) 168.272 168.272i 0.203228 0.203228i
\(829\) 1097.39i 1.32375i 0.749613 + 0.661877i \(0.230240\pi\)
−0.749613 + 0.661877i \(0.769760\pi\)
\(830\) 0 0
\(831\) 170.455 0.205120
\(832\) 125.394 + 125.394i 0.150714 + 0.150714i
\(833\) −739.423 + 739.423i −0.887663 + 0.887663i
\(834\) 374.252i 0.448743i
\(835\) 0 0
\(836\) −74.8469 −0.0895298
\(837\) 143.629 + 143.629i 0.171600 + 0.171600i
\(838\) −466.515 + 466.515i −0.556701 + 0.556701i
\(839\) 1047.18i 1.24813i 0.781373 + 0.624065i \(0.214520\pi\)
−0.781373 + 0.624065i \(0.785480\pi\)
\(840\) 0 0
\(841\) 412.637 0.490650
\(842\) −636.120 636.120i −0.755487 0.755487i
\(843\) 636.681 636.681i 0.755256 0.755256i
\(844\) 586.545i 0.694958i
\(845\) 0 0
\(846\) −348.272 −0.411670
\(847\) −327.738 327.738i −0.386940 0.386940i
\(848\) −2.42449 + 2.42449i −0.00285907 + 0.00285907i
\(849\) 375.817i 0.442659i
\(850\) 0 0
\(851\) 700.849 0.823559
\(852\) 94.7878 + 94.7878i 0.111253 + 0.111253i
\(853\) −902.612 + 902.612i −1.05816 + 1.05816i −0.0599610 + 0.998201i \(0.519098\pi\)
−0.998201 + 0.0599610i \(0.980902\pi\)
\(854\) 1008.40i 1.18079i
\(855\) 0 0
\(856\) −183.637 −0.214529
\(857\) 928.454 + 928.454i 1.08338 + 1.08338i 0.996192 + 0.0871848i \(0.0277871\pi\)
0.0871848 + 0.996192i \(0.472213\pi\)
\(858\) −333.909 + 333.909i −0.389172 + 0.389172i
\(859\) 581.151i 0.676544i 0.941048 + 0.338272i \(0.109842\pi\)
−0.941048 + 0.338272i \(0.890158\pi\)
\(860\) 0 0
\(861\) −1109.54 −1.28867
\(862\) 165.242 + 165.242i 0.191696 + 0.191696i
\(863\) −317.271 + 317.271i −0.367638 + 0.367638i −0.866615 0.498977i \(-0.833709\pi\)
0.498977 + 0.866615i \(0.333709\pi\)
\(864\) 29.3939i 0.0340207i
\(865\) 0 0
\(866\) 565.237 0.652699
\(867\) −82.5028 82.5028i −0.0951589 0.0951589i
\(868\) −564.842 + 564.842i −0.650740 + 0.650740i
\(869\) 273.031i 0.314189i
\(870\) 0 0
\(871\) 157.454 0.180774
\(872\) −290.000 290.000i −0.332569 0.332569i
\(873\) 162.371 162.371i 0.185992 0.185992i
\(874\) 241.362i 0.276158i
\(875\) 0 0
\(876\) 226.788 0.258890
\(877\) 1109.75 + 1109.75i 1.26540 + 1.26540i 0.948439 + 0.316958i \(0.102662\pi\)
0.316958 + 0.948439i \(0.397338\pi\)
\(878\) 272.909 272.909i 0.310831 0.310831i
\(879\) 48.0612i 0.0546772i
\(880\) 0 0
\(881\) 119.455 0.135590 0.0677952 0.997699i \(-0.478404\pi\)
0.0677952 + 0.997699i \(0.478404\pi\)
\(882\) 166.182 + 166.182i 0.188415 + 0.188415i
\(883\) 252.619 252.619i 0.286091 0.286091i −0.549441 0.835532i \(-0.685159\pi\)
0.835532 + 0.549441i \(0.185159\pi\)
\(884\) 836.908i 0.946729i
\(885\) 0 0
\(886\) 353.271 0.398726
\(887\) 516.347 + 516.347i 0.582128 + 0.582128i 0.935488 0.353360i \(-0.114961\pi\)
−0.353360 + 0.935488i \(0.614961\pi\)
\(888\) 61.2122 61.2122i 0.0689327 0.0689327i
\(889\) 307.818i 0.346252i
\(890\) 0 0
\(891\) 78.2724 0.0878479
\(892\) −149.641 149.641i −0.167759 0.167759i
\(893\) −249.773 + 249.773i −0.279701 + 0.279701i
\(894\) 276.272i 0.309030i
\(895\) 0 0
\(896\) 115.596 0.129013
\(897\) −1076.77 1076.77i −1.20041 1.20041i
\(898\) 751.151 751.151i 0.836471 0.836471i
\(899\) 809.060i 0.899956i
\(900\) 0 0
\(901\) 16.1816 0.0179596
\(902\) −545.271 545.271i −0.604514 0.604514i
\(903\) 210.174 210.174i 0.232751 0.232751i
\(904\) 523.151i 0.578707i
\(905\) 0 0
\(906\) 411.217 0.453882
\(907\) 983.160 + 983.160i 1.08397 + 1.08397i 0.996135 + 0.0878342i \(0.0279946\pi\)
0.0878342 + 0.996135i \(0.472005\pi\)
\(908\) 94.2429 94.2429i 0.103792 0.103792i
\(909\) 128.636i 0.141513i
\(910\) 0 0
\(911\) −1698.00 −1.86389 −0.931943 0.362605i \(-0.881887\pi\)
−0.931943 + 0.362605i \(0.881887\pi\)
\(912\) −21.0806 21.0806i −0.0231147 0.0231147i
\(913\) −343.001 + 343.001i −0.375686 + 0.375686i
\(914\) 52.8490i 0.0578216i
\(915\) 0 0
\(916\) −550.000 −0.600437
\(917\) 782.241 + 782.241i 0.853043 + 0.853043i
\(918\) −98.0908 + 98.0908i −0.106853 + 0.106853i
\(919\) 581.272i 0.632505i 0.948675 + 0.316253i \(0.102425\pi\)
−0.948675 + 0.316253i \(0.897575\pi\)
\(920\) 0 0
\(921\) 26.7276 0.0290201
\(922\) −38.6969 38.6969i −0.0419706 0.0419706i
\(923\) 606.545 606.545i 0.657145 0.657145i
\(924\) 307.818i 0.333137i
\(925\) 0 0
\(926\) −407.010 −0.439536
\(927\) −182.969 182.969i −0.197378 0.197378i
\(928\) −82.7878 + 82.7878i −0.0892109 + 0.0892109i
\(929\) 1328.57i 1.43011i −0.699067 0.715056i \(-0.746401\pi\)
0.699067 0.715056i \(-0.253599\pi\)
\(930\) 0 0
\(931\) 238.363 0.256029
\(932\) −375.514 375.514i −0.402912 0.402912i
\(933\) −79.3485 + 79.3485i −0.0850466 + 0.0850466i
\(934\) 1115.06i 1.19385i
\(935\) 0 0
\(936\) −188.091 −0.200952
\(937\) −626.487 626.487i −0.668609 0.668609i 0.288785 0.957394i \(-0.406749\pi\)
−0.957394 + 0.288785i \(0.906749\pi\)
\(938\) 72.5755 72.5755i 0.0773726 0.0773726i
\(939\) 62.3326i 0.0663819i
\(940\) 0 0
\(941\) 762.422 0.810226 0.405113 0.914267i \(-0.367232\pi\)
0.405113 + 0.914267i \(0.367232\pi\)
\(942\) 281.363 + 281.363i 0.298687 + 0.298687i
\(943\) 1758.36 1758.36i 1.86465 1.86465i
\(944\) 120.000i 0.127119i
\(945\) 0 0
\(946\) 206.574 0.218366
\(947\) −614.983 614.983i −0.649401 0.649401i 0.303447 0.952848i \(-0.401862\pi\)
−0.952848 + 0.303447i \(0.901862\pi\)
\(948\) −76.8990 + 76.8990i −0.0811171 + 0.0811171i
\(949\) 1451.21i 1.52920i
\(950\) 0 0
\(951\) 1055.88 1.11028
\(952\) −385.757 385.757i −0.405207 0.405207i
\(953\) −328.454 + 328.454i −0.344653 + 0.344653i −0.858113 0.513460i \(-0.828363\pi\)
0.513460 + 0.858113i \(0.328363\pi\)
\(954\) 3.63674i 0.00381209i
\(955\) 0 0
\(956\) 35.3326 0.0369588
\(957\) −220.454 220.454i −0.230360 0.230360i
\(958\) 265.818 265.818i 0.277472 0.277472i
\(959\) 1107.58i 1.15493i
\(960\) 0 0
\(961\) 567.092 0.590106
\(962\) −391.696 391.696i −0.407168 0.407168i
\(963\) 137.728 137.728i 0.143019 0.143019i
\(964\) 334.000i 0.346473i
\(965\) 0 0
\(966\) −992.636 −1.02757
\(967\) 172.009 + 172.009i 0.177879 + 0.177879i 0.790431 0.612551i \(-0.209857\pi\)
−0.612551 + 0.790431i \(0.709857\pi\)
\(968\) 90.7265 90.7265i 0.0937257 0.0937257i
\(969\) 140.697i 0.145198i
\(970\) 0 0
\(971\) −1273.82 −1.31186 −0.655931 0.754821i \(-0.727724\pi\)
−0.655931 + 0.754821i \(0.727724\pi\)
\(972\) 22.0454 + 22.0454i 0.0226805 + 0.0226805i
\(973\) 1103.85 1103.85i 1.13448 1.13448i
\(974\) 608.166i 0.624400i
\(975\) 0 0
\(976\) −279.151 −0.286015
\(977\) −1013.86 1013.86i −1.03773 1.03773i −0.999260 0.0384719i \(-0.987751\pi\)
−0.0384719 0.999260i \(-0.512249\pi\)
\(978\) −24.8480 + 24.8480i −0.0254069 + 0.0254069i
\(979\) 360.000i 0.367722i
\(980\) 0 0
\(981\) 435.000 0.443425
\(982\) 169.212 + 169.212i 0.172314 + 0.172314i
\(983\) −856.332 + 856.332i −0.871141 + 0.871141i −0.992597 0.121456i \(-0.961244\pi\)
0.121456 + 0.992597i \(0.461244\pi\)
\(984\) 307.151i 0.312145i
\(985\) 0 0
\(986\) 552.545 0.560390
\(987\) 1027.23 + 1027.23i 1.04076 + 1.04076i
\(988\) −134.894 + 134.894i −0.136533 + 0.136533i
\(989\) 666.150i 0.673559i
\(990\) 0 0
\(991\) 688.605 0.694859 0.347429 0.937706i \(-0.387055\pi\)
0.347429 + 0.937706i \(0.387055\pi\)
\(992\) −156.363 156.363i −0.157624 0.157624i
\(993\) −362.449 + 362.449i −0.365005 + 0.365005i
\(994\) 559.151i 0.562526i
\(995\) 0 0
\(996\) −193.212 −0.193988
\(997\) −1260.82 1260.82i −1.26461 1.26461i −0.948833 0.315778i \(-0.897734\pi\)
−0.315778 0.948833i \(-0.602266\pi\)
\(998\) −699.636 + 699.636i −0.701038 + 0.701038i
\(999\) 91.8184i 0.0919103i
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 150.3.f.c.7.1 yes 4
3.2 odd 2 450.3.g.g.307.2 4
4.3 odd 2 1200.3.bg.a.1057.2 4
5.2 odd 4 150.3.f.a.43.2 yes 4
5.3 odd 4 inner 150.3.f.c.43.1 yes 4
5.4 even 2 150.3.f.a.7.2 4
15.2 even 4 450.3.g.h.343.1 4
15.8 even 4 450.3.g.g.343.2 4
15.14 odd 2 450.3.g.h.307.1 4
20.3 even 4 1200.3.bg.a.193.2 4
20.7 even 4 1200.3.bg.p.193.1 4
20.19 odd 2 1200.3.bg.p.1057.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
150.3.f.a.7.2 4 5.4 even 2
150.3.f.a.43.2 yes 4 5.2 odd 4
150.3.f.c.7.1 yes 4 1.1 even 1 trivial
150.3.f.c.43.1 yes 4 5.3 odd 4 inner
450.3.g.g.307.2 4 3.2 odd 2
450.3.g.g.343.2 4 15.8 even 4
450.3.g.h.307.1 4 15.14 odd 2
450.3.g.h.343.1 4 15.2 even 4
1200.3.bg.a.193.2 4 20.3 even 4
1200.3.bg.a.1057.2 4 4.3 odd 2
1200.3.bg.p.193.1 4 20.7 even 4
1200.3.bg.p.1057.1 4 20.19 odd 2