Properties

Label 90.3.g.a.37.1
Level $90$
Weight $3$
Character 90.37
Analytic conductor $2.452$
Analytic rank $0$
Dimension $2$
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] = [90,3,Mod(37,90)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(90, 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("90.37");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 90 = 2 \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 90.g (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: \(2.45232237924\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(i)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 37.1
Root \(1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 90.37
Dual form 90.3.g.a.73.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.00000 - 1.00000i) q^{2} +2.00000i q^{4} +(-3.00000 + 4.00000i) q^{5} +(8.00000 + 8.00000i) q^{7} +(2.00000 - 2.00000i) q^{8} +O(q^{10})\) \(q+(-1.00000 - 1.00000i) q^{2} +2.00000i q^{4} +(-3.00000 + 4.00000i) q^{5} +(8.00000 + 8.00000i) q^{7} +(2.00000 - 2.00000i) q^{8} +(7.00000 - 1.00000i) q^{10} +4.00000 q^{11} +(-3.00000 + 3.00000i) q^{13} -16.0000i q^{14} -4.00000 q^{16} +(19.0000 + 19.0000i) q^{17} -8.00000i q^{19} +(-8.00000 - 6.00000i) q^{20} +(-4.00000 - 4.00000i) q^{22} +(-20.0000 + 20.0000i) q^{23} +(-7.00000 - 24.0000i) q^{25} +6.00000 q^{26} +(-16.0000 + 16.0000i) q^{28} -38.0000i q^{29} -44.0000 q^{31} +(4.00000 + 4.00000i) q^{32} -38.0000i q^{34} +(-56.0000 + 8.00000i) q^{35} +(-3.00000 - 3.00000i) q^{37} +(-8.00000 + 8.00000i) q^{38} +(2.00000 + 14.0000i) q^{40} +70.0000 q^{41} +(36.0000 - 36.0000i) q^{43} +8.00000i q^{44} +40.0000 q^{46} +79.0000i q^{49} +(-17.0000 + 31.0000i) q^{50} +(-6.00000 - 6.00000i) q^{52} +(17.0000 - 17.0000i) q^{53} +(-12.0000 + 16.0000i) q^{55} +32.0000 q^{56} +(-38.0000 + 38.0000i) q^{58} -92.0000i q^{59} +72.0000 q^{61} +(44.0000 + 44.0000i) q^{62} -8.00000i q^{64} +(-3.00000 - 21.0000i) q^{65} +(44.0000 + 44.0000i) q^{67} +(-38.0000 + 38.0000i) q^{68} +(64.0000 + 48.0000i) q^{70} -88.0000 q^{71} +(55.0000 - 55.0000i) q^{73} +6.00000i q^{74} +16.0000 q^{76} +(32.0000 + 32.0000i) q^{77} +12.0000i q^{79} +(12.0000 - 16.0000i) q^{80} +(-70.0000 - 70.0000i) q^{82} +(-24.0000 + 24.0000i) q^{83} +(-133.000 + 19.0000i) q^{85} -72.0000 q^{86} +(8.00000 - 8.00000i) q^{88} +26.0000i q^{89} -48.0000 q^{91} +(-40.0000 - 40.0000i) q^{92} +(32.0000 + 24.0000i) q^{95} +(-57.0000 - 57.0000i) q^{97} +(79.0000 - 79.0000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 2 q^{2} - 6 q^{5} + 16 q^{7} + 4 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 2 q^{2} - 6 q^{5} + 16 q^{7} + 4 q^{8} + 14 q^{10} + 8 q^{11} - 6 q^{13} - 8 q^{16} + 38 q^{17} - 16 q^{20} - 8 q^{22} - 40 q^{23} - 14 q^{25} + 12 q^{26} - 32 q^{28} - 88 q^{31} + 8 q^{32} - 112 q^{35} - 6 q^{37} - 16 q^{38} + 4 q^{40} + 140 q^{41} + 72 q^{43} + 80 q^{46} - 34 q^{50} - 12 q^{52} + 34 q^{53} - 24 q^{55} + 64 q^{56} - 76 q^{58} + 144 q^{61} + 88 q^{62} - 6 q^{65} + 88 q^{67} - 76 q^{68} + 128 q^{70} - 176 q^{71} + 110 q^{73} + 32 q^{76} + 64 q^{77} + 24 q^{80} - 140 q^{82} - 48 q^{83} - 266 q^{85} - 144 q^{86} + 16 q^{88} - 96 q^{91} - 80 q^{92} + 64 q^{95} - 114 q^{97} + 158 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/90\mathbb{Z}\right)^\times\).

\(n\) \(11\) \(37\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{4}\right)\)

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
\(3\) 0 0
\(4\) 2.00000i 0.500000i
\(5\) −3.00000 + 4.00000i −0.600000 + 0.800000i
\(6\) 0 0
\(7\) 8.00000 + 8.00000i 1.14286 + 1.14286i 0.987925 + 0.154932i \(0.0495158\pi\)
0.154932 + 0.987925i \(0.450484\pi\)
\(8\) 2.00000 2.00000i 0.250000 0.250000i
\(9\) 0 0
\(10\) 7.00000 1.00000i 0.700000 0.100000i
\(11\) 4.00000 0.363636 0.181818 0.983332i \(-0.441802\pi\)
0.181818 + 0.983332i \(0.441802\pi\)
\(12\) 0 0
\(13\) −3.00000 + 3.00000i −0.230769 + 0.230769i −0.813014 0.582245i \(-0.802175\pi\)
0.582245 + 0.813014i \(0.302175\pi\)
\(14\) 16.0000i 1.14286i
\(15\) 0 0
\(16\) −4.00000 −0.250000
\(17\) 19.0000 + 19.0000i 1.11765 + 1.11765i 0.992086 + 0.125561i \(0.0400731\pi\)
0.125561 + 0.992086i \(0.459927\pi\)
\(18\) 0 0
\(19\) 8.00000i 0.421053i −0.977588 0.210526i \(-0.932482\pi\)
0.977588 0.210526i \(-0.0675178\pi\)
\(20\) −8.00000 6.00000i −0.400000 0.300000i
\(21\) 0 0
\(22\) −4.00000 4.00000i −0.181818 0.181818i
\(23\) −20.0000 + 20.0000i −0.869565 + 0.869565i −0.992424 0.122859i \(-0.960794\pi\)
0.122859 + 0.992424i \(0.460794\pi\)
\(24\) 0 0
\(25\) −7.00000 24.0000i −0.280000 0.960000i
\(26\) 6.00000 0.230769
\(27\) 0 0
\(28\) −16.0000 + 16.0000i −0.571429 + 0.571429i
\(29\) 38.0000i 1.31034i −0.755479 0.655172i \(-0.772596\pi\)
0.755479 0.655172i \(-0.227404\pi\)
\(30\) 0 0
\(31\) −44.0000 −1.41935 −0.709677 0.704527i \(-0.751159\pi\)
−0.709677 + 0.704527i \(0.751159\pi\)
\(32\) 4.00000 + 4.00000i 0.125000 + 0.125000i
\(33\) 0 0
\(34\) 38.0000i 1.11765i
\(35\) −56.0000 + 8.00000i −1.60000 + 0.228571i
\(36\) 0 0
\(37\) −3.00000 3.00000i −0.0810811 0.0810811i 0.665403 0.746484i \(-0.268260\pi\)
−0.746484 + 0.665403i \(0.768260\pi\)
\(38\) −8.00000 + 8.00000i −0.210526 + 0.210526i
\(39\) 0 0
\(40\) 2.00000 + 14.0000i 0.0500000 + 0.350000i
\(41\) 70.0000 1.70732 0.853659 0.520833i \(-0.174379\pi\)
0.853659 + 0.520833i \(0.174379\pi\)
\(42\) 0 0
\(43\) 36.0000 36.0000i 0.837209 0.837209i −0.151281 0.988491i \(-0.548340\pi\)
0.988491 + 0.151281i \(0.0483400\pi\)
\(44\) 8.00000i 0.181818i
\(45\) 0 0
\(46\) 40.0000 0.869565
\(47\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(48\) 0 0
\(49\) 79.0000i 1.61224i
\(50\) −17.0000 + 31.0000i −0.340000 + 0.620000i
\(51\) 0 0
\(52\) −6.00000 6.00000i −0.115385 0.115385i
\(53\) 17.0000 17.0000i 0.320755 0.320755i −0.528302 0.849057i \(-0.677171\pi\)
0.849057 + 0.528302i \(0.177171\pi\)
\(54\) 0 0
\(55\) −12.0000 + 16.0000i −0.218182 + 0.290909i
\(56\) 32.0000 0.571429
\(57\) 0 0
\(58\) −38.0000 + 38.0000i −0.655172 + 0.655172i
\(59\) 92.0000i 1.55932i −0.626202 0.779661i \(-0.715391\pi\)
0.626202 0.779661i \(-0.284609\pi\)
\(60\) 0 0
\(61\) 72.0000 1.18033 0.590164 0.807283i \(-0.299063\pi\)
0.590164 + 0.807283i \(0.299063\pi\)
\(62\) 44.0000 + 44.0000i 0.709677 + 0.709677i
\(63\) 0 0
\(64\) 8.00000i 0.125000i
\(65\) −3.00000 21.0000i −0.0461538 0.323077i
\(66\) 0 0
\(67\) 44.0000 + 44.0000i 0.656716 + 0.656716i 0.954602 0.297885i \(-0.0962813\pi\)
−0.297885 + 0.954602i \(0.596281\pi\)
\(68\) −38.0000 + 38.0000i −0.558824 + 0.558824i
\(69\) 0 0
\(70\) 64.0000 + 48.0000i 0.914286 + 0.685714i
\(71\) −88.0000 −1.23944 −0.619718 0.784824i \(-0.712753\pi\)
−0.619718 + 0.784824i \(0.712753\pi\)
\(72\) 0 0
\(73\) 55.0000 55.0000i 0.753425 0.753425i −0.221692 0.975117i \(-0.571158\pi\)
0.975117 + 0.221692i \(0.0711580\pi\)
\(74\) 6.00000i 0.0810811i
\(75\) 0 0
\(76\) 16.0000 0.210526
\(77\) 32.0000 + 32.0000i 0.415584 + 0.415584i
\(78\) 0 0
\(79\) 12.0000i 0.151899i 0.997112 + 0.0759494i \(0.0241987\pi\)
−0.997112 + 0.0759494i \(0.975801\pi\)
\(80\) 12.0000 16.0000i 0.150000 0.200000i
\(81\) 0 0
\(82\) −70.0000 70.0000i −0.853659 0.853659i
\(83\) −24.0000 + 24.0000i −0.289157 + 0.289157i −0.836747 0.547590i \(-0.815545\pi\)
0.547590 + 0.836747i \(0.315545\pi\)
\(84\) 0 0
\(85\) −133.000 + 19.0000i −1.56471 + 0.223529i
\(86\) −72.0000 −0.837209
\(87\) 0 0
\(88\) 8.00000 8.00000i 0.0909091 0.0909091i
\(89\) 26.0000i 0.292135i 0.989275 + 0.146067i \(0.0466616\pi\)
−0.989275 + 0.146067i \(0.953338\pi\)
\(90\) 0 0
\(91\) −48.0000 −0.527473
\(92\) −40.0000 40.0000i −0.434783 0.434783i
\(93\) 0 0
\(94\) 0 0
\(95\) 32.0000 + 24.0000i 0.336842 + 0.252632i
\(96\) 0 0
\(97\) −57.0000 57.0000i −0.587629 0.587629i 0.349360 0.936989i \(-0.386399\pi\)
−0.936989 + 0.349360i \(0.886399\pi\)
\(98\) 79.0000 79.0000i 0.806122 0.806122i
\(99\) 0 0
\(100\) 48.0000 14.0000i 0.480000 0.140000i
\(101\) 56.0000 0.554455 0.277228 0.960804i \(-0.410584\pi\)
0.277228 + 0.960804i \(0.410584\pi\)
\(102\) 0 0
\(103\) 4.00000 4.00000i 0.0388350 0.0388350i −0.687423 0.726258i \(-0.741258\pi\)
0.726258 + 0.687423i \(0.241258\pi\)
\(104\) 12.0000i 0.115385i
\(105\) 0 0
\(106\) −34.0000 −0.320755
\(107\) −68.0000 68.0000i −0.635514 0.635514i 0.313932 0.949446i \(-0.398354\pi\)
−0.949446 + 0.313932i \(0.898354\pi\)
\(108\) 0 0
\(109\) 46.0000i 0.422018i −0.977484 0.211009i \(-0.932325\pi\)
0.977484 0.211009i \(-0.0676750\pi\)
\(110\) 28.0000 4.00000i 0.254545 0.0363636i
\(111\) 0 0
\(112\) −32.0000 32.0000i −0.285714 0.285714i
\(113\) 53.0000 53.0000i 0.469027 0.469027i −0.432573 0.901599i \(-0.642394\pi\)
0.901599 + 0.432573i \(0.142394\pi\)
\(114\) 0 0
\(115\) −20.0000 140.000i −0.173913 1.21739i
\(116\) 76.0000 0.655172
\(117\) 0 0
\(118\) −92.0000 + 92.0000i −0.779661 + 0.779661i
\(119\) 304.000i 2.55462i
\(120\) 0 0
\(121\) −105.000 −0.867769
\(122\) −72.0000 72.0000i −0.590164 0.590164i
\(123\) 0 0
\(124\) 88.0000i 0.709677i
\(125\) 117.000 + 44.0000i 0.936000 + 0.352000i
\(126\) 0 0
\(127\) 68.0000 + 68.0000i 0.535433 + 0.535433i 0.922184 0.386751i \(-0.126403\pi\)
−0.386751 + 0.922184i \(0.626403\pi\)
\(128\) −8.00000 + 8.00000i −0.0625000 + 0.0625000i
\(129\) 0 0
\(130\) −18.0000 + 24.0000i −0.138462 + 0.184615i
\(131\) −44.0000 −0.335878 −0.167939 0.985797i \(-0.553711\pi\)
−0.167939 + 0.985797i \(0.553711\pi\)
\(132\) 0 0
\(133\) 64.0000 64.0000i 0.481203 0.481203i
\(134\) 88.0000i 0.656716i
\(135\) 0 0
\(136\) 76.0000 0.558824
\(137\) −69.0000 69.0000i −0.503650 0.503650i 0.408920 0.912570i \(-0.365905\pi\)
−0.912570 + 0.408920i \(0.865905\pi\)
\(138\) 0 0
\(139\) 80.0000i 0.575540i 0.957700 + 0.287770i \(0.0929138\pi\)
−0.957700 + 0.287770i \(0.907086\pi\)
\(140\) −16.0000 112.000i −0.114286 0.800000i
\(141\) 0 0
\(142\) 88.0000 + 88.0000i 0.619718 + 0.619718i
\(143\) −12.0000 + 12.0000i −0.0839161 + 0.0839161i
\(144\) 0 0
\(145\) 152.000 + 114.000i 1.04828 + 0.786207i
\(146\) −110.000 −0.753425
\(147\) 0 0
\(148\) 6.00000 6.00000i 0.0405405 0.0405405i
\(149\) 168.000i 1.12752i 0.825940 + 0.563758i \(0.190645\pi\)
−0.825940 + 0.563758i \(0.809355\pi\)
\(150\) 0 0
\(151\) 4.00000 0.0264901 0.0132450 0.999912i \(-0.495784\pi\)
0.0132450 + 0.999912i \(0.495784\pi\)
\(152\) −16.0000 16.0000i −0.105263 0.105263i
\(153\) 0 0
\(154\) 64.0000i 0.415584i
\(155\) 132.000 176.000i 0.851613 1.13548i
\(156\) 0 0
\(157\) 99.0000 + 99.0000i 0.630573 + 0.630573i 0.948212 0.317639i \(-0.102890\pi\)
−0.317639 + 0.948212i \(0.602890\pi\)
\(158\) 12.0000 12.0000i 0.0759494 0.0759494i
\(159\) 0 0
\(160\) −28.0000 + 4.00000i −0.175000 + 0.0250000i
\(161\) −320.000 −1.98758
\(162\) 0 0
\(163\) −160.000 + 160.000i −0.981595 + 0.981595i −0.999834 0.0182386i \(-0.994194\pi\)
0.0182386 + 0.999834i \(0.494194\pi\)
\(164\) 140.000i 0.853659i
\(165\) 0 0
\(166\) 48.0000 0.289157
\(167\) 56.0000 + 56.0000i 0.335329 + 0.335329i 0.854606 0.519277i \(-0.173799\pi\)
−0.519277 + 0.854606i \(0.673799\pi\)
\(168\) 0 0
\(169\) 151.000i 0.893491i
\(170\) 152.000 + 114.000i 0.894118 + 0.670588i
\(171\) 0 0
\(172\) 72.0000 + 72.0000i 0.418605 + 0.418605i
\(173\) −41.0000 + 41.0000i −0.236994 + 0.236994i −0.815604 0.578610i \(-0.803595\pi\)
0.578610 + 0.815604i \(0.303595\pi\)
\(174\) 0 0
\(175\) 136.000 248.000i 0.777143 1.41714i
\(176\) −16.0000 −0.0909091
\(177\) 0 0
\(178\) 26.0000 26.0000i 0.146067 0.146067i
\(179\) 172.000i 0.960894i −0.877024 0.480447i \(-0.840474\pi\)
0.877024 0.480447i \(-0.159526\pi\)
\(180\) 0 0
\(181\) 62.0000 0.342541 0.171271 0.985224i \(-0.445213\pi\)
0.171271 + 0.985224i \(0.445213\pi\)
\(182\) 48.0000 + 48.0000i 0.263736 + 0.263736i
\(183\) 0 0
\(184\) 80.0000i 0.434783i
\(185\) 21.0000 3.00000i 0.113514 0.0162162i
\(186\) 0 0
\(187\) 76.0000 + 76.0000i 0.406417 + 0.406417i
\(188\) 0 0
\(189\) 0 0
\(190\) −8.00000 56.0000i −0.0421053 0.294737i
\(191\) 248.000 1.29843 0.649215 0.760605i \(-0.275098\pi\)
0.649215 + 0.760605i \(0.275098\pi\)
\(192\) 0 0
\(193\) 135.000 135.000i 0.699482 0.699482i −0.264817 0.964299i \(-0.585312\pi\)
0.964299 + 0.264817i \(0.0853115\pi\)
\(194\) 114.000i 0.587629i
\(195\) 0 0
\(196\) −158.000 −0.806122
\(197\) −153.000 153.000i −0.776650 0.776650i 0.202610 0.979260i \(-0.435058\pi\)
−0.979260 + 0.202610i \(0.935058\pi\)
\(198\) 0 0
\(199\) 252.000i 1.26633i −0.774016 0.633166i \(-0.781755\pi\)
0.774016 0.633166i \(-0.218245\pi\)
\(200\) −62.0000 34.0000i −0.310000 0.170000i
\(201\) 0 0
\(202\) −56.0000 56.0000i −0.277228 0.277228i
\(203\) 304.000 304.000i 1.49754 1.49754i
\(204\) 0 0
\(205\) −210.000 + 280.000i −1.02439 + 1.36585i
\(206\) −8.00000 −0.0388350
\(207\) 0 0
\(208\) 12.0000 12.0000i 0.0576923 0.0576923i
\(209\) 32.0000i 0.153110i
\(210\) 0 0
\(211\) −64.0000 −0.303318 −0.151659 0.988433i \(-0.548461\pi\)
−0.151659 + 0.988433i \(0.548461\pi\)
\(212\) 34.0000 + 34.0000i 0.160377 + 0.160377i
\(213\) 0 0
\(214\) 136.000i 0.635514i
\(215\) 36.0000 + 252.000i 0.167442 + 1.17209i
\(216\) 0 0
\(217\) −352.000 352.000i −1.62212 1.62212i
\(218\) −46.0000 + 46.0000i −0.211009 + 0.211009i
\(219\) 0 0
\(220\) −32.0000 24.0000i −0.145455 0.109091i
\(221\) −114.000 −0.515837
\(222\) 0 0
\(223\) −228.000 + 228.000i −1.02242 + 1.02242i −0.0226787 + 0.999743i \(0.507219\pi\)
−0.999743 + 0.0226787i \(0.992781\pi\)
\(224\) 64.0000i 0.285714i
\(225\) 0 0
\(226\) −106.000 −0.469027
\(227\) −100.000 100.000i −0.440529 0.440529i 0.451661 0.892190i \(-0.350832\pi\)
−0.892190 + 0.451661i \(0.850832\pi\)
\(228\) 0 0
\(229\) 312.000i 1.36245i −0.732076 0.681223i \(-0.761449\pi\)
0.732076 0.681223i \(-0.238551\pi\)
\(230\) −120.000 + 160.000i −0.521739 + 0.695652i
\(231\) 0 0
\(232\) −76.0000 76.0000i −0.327586 0.327586i
\(233\) −93.0000 + 93.0000i −0.399142 + 0.399142i −0.877930 0.478789i \(-0.841076\pi\)
0.478789 + 0.877930i \(0.341076\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 184.000 0.779661
\(237\) 0 0
\(238\) 304.000 304.000i 1.27731 1.27731i
\(239\) 96.0000i 0.401674i −0.979625 0.200837i \(-0.935634\pi\)
0.979625 0.200837i \(-0.0643661\pi\)
\(240\) 0 0
\(241\) 160.000 0.663900 0.331950 0.943297i \(-0.392293\pi\)
0.331950 + 0.943297i \(0.392293\pi\)
\(242\) 105.000 + 105.000i 0.433884 + 0.433884i
\(243\) 0 0
\(244\) 144.000i 0.590164i
\(245\) −316.000 237.000i −1.28980 0.967347i
\(246\) 0 0
\(247\) 24.0000 + 24.0000i 0.0971660 + 0.0971660i
\(248\) −88.0000 + 88.0000i −0.354839 + 0.354839i
\(249\) 0 0
\(250\) −73.0000 161.000i −0.292000 0.644000i
\(251\) 12.0000 0.0478088 0.0239044 0.999714i \(-0.492390\pi\)
0.0239044 + 0.999714i \(0.492390\pi\)
\(252\) 0 0
\(253\) −80.0000 + 80.0000i −0.316206 + 0.316206i
\(254\) 136.000i 0.535433i
\(255\) 0 0
\(256\) 16.0000 0.0625000
\(257\) 101.000 + 101.000i 0.392996 + 0.392996i 0.875754 0.482758i \(-0.160365\pi\)
−0.482758 + 0.875754i \(0.660365\pi\)
\(258\) 0 0
\(259\) 48.0000i 0.185328i
\(260\) 42.0000 6.00000i 0.161538 0.0230769i
\(261\) 0 0
\(262\) 44.0000 + 44.0000i 0.167939 + 0.167939i
\(263\) −208.000 + 208.000i −0.790875 + 0.790875i −0.981636 0.190762i \(-0.938904\pi\)
0.190762 + 0.981636i \(0.438904\pi\)
\(264\) 0 0
\(265\) 17.0000 + 119.000i 0.0641509 + 0.449057i
\(266\) −128.000 −0.481203
\(267\) 0 0
\(268\) −88.0000 + 88.0000i −0.328358 + 0.328358i
\(269\) 296.000i 1.10037i −0.835042 0.550186i \(-0.814557\pi\)
0.835042 0.550186i \(-0.185443\pi\)
\(270\) 0 0
\(271\) 108.000 0.398524 0.199262 0.979946i \(-0.436146\pi\)
0.199262 + 0.979946i \(0.436146\pi\)
\(272\) −76.0000 76.0000i −0.279412 0.279412i
\(273\) 0 0
\(274\) 138.000i 0.503650i
\(275\) −28.0000 96.0000i −0.101818 0.349091i
\(276\) 0 0
\(277\) −243.000 243.000i −0.877256 0.877256i 0.115994 0.993250i \(-0.462995\pi\)
−0.993250 + 0.115994i \(0.962995\pi\)
\(278\) 80.0000 80.0000i 0.287770 0.287770i
\(279\) 0 0
\(280\) −96.0000 + 128.000i −0.342857 + 0.457143i
\(281\) 378.000 1.34520 0.672598 0.740008i \(-0.265178\pi\)
0.672598 + 0.740008i \(0.265178\pi\)
\(282\) 0 0
\(283\) 92.0000 92.0000i 0.325088 0.325088i −0.525627 0.850715i \(-0.676169\pi\)
0.850715 + 0.525627i \(0.176169\pi\)
\(284\) 176.000i 0.619718i
\(285\) 0 0
\(286\) 24.0000 0.0839161
\(287\) 560.000 + 560.000i 1.95122 + 1.95122i
\(288\) 0 0
\(289\) 433.000i 1.49827i
\(290\) −38.0000 266.000i −0.131034 0.917241i
\(291\) 0 0
\(292\) 110.000 + 110.000i 0.376712 + 0.376712i
\(293\) −279.000 + 279.000i −0.952218 + 0.952218i −0.998909 0.0466910i \(-0.985132\pi\)
0.0466910 + 0.998909i \(0.485132\pi\)
\(294\) 0 0
\(295\) 368.000 + 276.000i 1.24746 + 0.935593i
\(296\) −12.0000 −0.0405405
\(297\) 0 0
\(298\) 168.000 168.000i 0.563758 0.563758i
\(299\) 120.000i 0.401338i
\(300\) 0 0
\(301\) 576.000 1.91362
\(302\) −4.00000 4.00000i −0.0132450 0.0132450i
\(303\) 0 0
\(304\) 32.0000i 0.105263i
\(305\) −216.000 + 288.000i −0.708197 + 0.944262i
\(306\) 0 0
\(307\) 216.000 + 216.000i 0.703583 + 0.703583i 0.965178 0.261595i \(-0.0842484\pi\)
−0.261595 + 0.965178i \(0.584248\pi\)
\(308\) −64.0000 + 64.0000i −0.207792 + 0.207792i
\(309\) 0 0
\(310\) −308.000 + 44.0000i −0.993548 + 0.141935i
\(311\) 272.000 0.874598 0.437299 0.899316i \(-0.355935\pi\)
0.437299 + 0.899316i \(0.355935\pi\)
\(312\) 0 0
\(313\) 15.0000 15.0000i 0.0479233 0.0479233i −0.682739 0.730662i \(-0.739211\pi\)
0.730662 + 0.682739i \(0.239211\pi\)
\(314\) 198.000i 0.630573i
\(315\) 0 0
\(316\) −24.0000 −0.0759494
\(317\) 87.0000 + 87.0000i 0.274448 + 0.274448i 0.830888 0.556440i \(-0.187833\pi\)
−0.556440 + 0.830888i \(0.687833\pi\)
\(318\) 0 0
\(319\) 152.000i 0.476489i
\(320\) 32.0000 + 24.0000i 0.100000 + 0.0750000i
\(321\) 0 0
\(322\) 320.000 + 320.000i 0.993789 + 0.993789i
\(323\) 152.000 152.000i 0.470588 0.470588i
\(324\) 0 0
\(325\) 93.0000 + 51.0000i 0.286154 + 0.156923i
\(326\) 320.000 0.981595
\(327\) 0 0
\(328\) 140.000 140.000i 0.426829 0.426829i
\(329\) 0 0
\(330\) 0 0
\(331\) −584.000 −1.76435 −0.882175 0.470921i \(-0.843922\pi\)
−0.882175 + 0.470921i \(0.843922\pi\)
\(332\) −48.0000 48.0000i −0.144578 0.144578i
\(333\) 0 0
\(334\) 112.000i 0.335329i
\(335\) −308.000 + 44.0000i −0.919403 + 0.131343i
\(336\) 0 0
\(337\) −129.000 129.000i −0.382789 0.382789i 0.489317 0.872106i \(-0.337246\pi\)
−0.872106 + 0.489317i \(0.837246\pi\)
\(338\) 151.000 151.000i 0.446746 0.446746i
\(339\) 0 0
\(340\) −38.0000 266.000i −0.111765 0.782353i
\(341\) −176.000 −0.516129
\(342\) 0 0
\(343\) −240.000 + 240.000i −0.699708 + 0.699708i
\(344\) 144.000i 0.418605i
\(345\) 0 0
\(346\) 82.0000 0.236994
\(347\) −260.000 260.000i −0.749280 0.749280i 0.225064 0.974344i \(-0.427741\pi\)
−0.974344 + 0.225064i \(0.927741\pi\)
\(348\) 0 0
\(349\) 136.000i 0.389685i 0.980835 + 0.194842i \(0.0624195\pi\)
−0.980835 + 0.194842i \(0.937580\pi\)
\(350\) −384.000 + 112.000i −1.09714 + 0.320000i
\(351\) 0 0
\(352\) 16.0000 + 16.0000i 0.0454545 + 0.0454545i
\(353\) −75.0000 + 75.0000i −0.212465 + 0.212465i −0.805314 0.592849i \(-0.798003\pi\)
0.592849 + 0.805314i \(0.298003\pi\)
\(354\) 0 0
\(355\) 264.000 352.000i 0.743662 0.991549i
\(356\) −52.0000 −0.146067
\(357\) 0 0
\(358\) −172.000 + 172.000i −0.480447 + 0.480447i
\(359\) 32.0000i 0.0891365i 0.999006 + 0.0445682i \(0.0141912\pi\)
−0.999006 + 0.0445682i \(0.985809\pi\)
\(360\) 0 0
\(361\) 297.000 0.822715
\(362\) −62.0000 62.0000i −0.171271 0.171271i
\(363\) 0 0
\(364\) 96.0000i 0.263736i
\(365\) 55.0000 + 385.000i 0.150685 + 1.05479i
\(366\) 0 0
\(367\) −16.0000 16.0000i −0.0435967 0.0435967i 0.684972 0.728569i \(-0.259814\pi\)
−0.728569 + 0.684972i \(0.759814\pi\)
\(368\) 80.0000 80.0000i 0.217391 0.217391i
\(369\) 0 0
\(370\) −24.0000 18.0000i −0.0648649 0.0486486i
\(371\) 272.000 0.733154
\(372\) 0 0
\(373\) −251.000 + 251.000i −0.672922 + 0.672922i −0.958389 0.285466i \(-0.907851\pi\)
0.285466 + 0.958389i \(0.407851\pi\)
\(374\) 152.000i 0.406417i
\(375\) 0 0
\(376\) 0 0
\(377\) 114.000 + 114.000i 0.302387 + 0.302387i
\(378\) 0 0
\(379\) 560.000i 1.47757i −0.673940 0.738786i \(-0.735399\pi\)
0.673940 0.738786i \(-0.264601\pi\)
\(380\) −48.0000 + 64.0000i −0.126316 + 0.168421i
\(381\) 0 0
\(382\) −248.000 248.000i −0.649215 0.649215i
\(383\) −300.000 + 300.000i −0.783290 + 0.783290i −0.980384 0.197095i \(-0.936849\pi\)
0.197095 + 0.980384i \(0.436849\pi\)
\(384\) 0 0
\(385\) −224.000 + 32.0000i −0.581818 + 0.0831169i
\(386\) −270.000 −0.699482
\(387\) 0 0
\(388\) 114.000 114.000i 0.293814 0.293814i
\(389\) 24.0000i 0.0616967i −0.999524 0.0308483i \(-0.990179\pi\)
0.999524 0.0308483i \(-0.00982089\pi\)
\(390\) 0 0
\(391\) −760.000 −1.94373
\(392\) 158.000 + 158.000i 0.403061 + 0.403061i
\(393\) 0 0
\(394\) 306.000i 0.776650i
\(395\) −48.0000 36.0000i −0.121519 0.0911392i
\(396\) 0 0
\(397\) −299.000 299.000i −0.753149 0.753149i 0.221917 0.975066i \(-0.428769\pi\)
−0.975066 + 0.221917i \(0.928769\pi\)
\(398\) −252.000 + 252.000i −0.633166 + 0.633166i
\(399\) 0 0
\(400\) 28.0000 + 96.0000i 0.0700000 + 0.240000i
\(401\) −144.000 −0.359102 −0.179551 0.983749i \(-0.557465\pi\)
−0.179551 + 0.983749i \(0.557465\pi\)
\(402\) 0 0
\(403\) 132.000 132.000i 0.327543 0.327543i
\(404\) 112.000i 0.277228i
\(405\) 0 0
\(406\) −608.000 −1.49754
\(407\) −12.0000 12.0000i −0.0294840 0.0294840i
\(408\) 0 0
\(409\) 354.000i 0.865526i −0.901508 0.432763i \(-0.857539\pi\)
0.901508 0.432763i \(-0.142461\pi\)
\(410\) 490.000 70.0000i 1.19512 0.170732i
\(411\) 0 0
\(412\) 8.00000 + 8.00000i 0.0194175 + 0.0194175i
\(413\) 736.000 736.000i 1.78208 1.78208i
\(414\) 0 0
\(415\) −24.0000 168.000i −0.0578313 0.404819i
\(416\) −24.0000 −0.0576923
\(417\) 0 0
\(418\) −32.0000 + 32.0000i −0.0765550 + 0.0765550i
\(419\) 468.000i 1.11695i −0.829523 0.558473i \(-0.811388\pi\)
0.829523 0.558473i \(-0.188612\pi\)
\(420\) 0 0
\(421\) 104.000 0.247031 0.123515 0.992343i \(-0.460583\pi\)
0.123515 + 0.992343i \(0.460583\pi\)
\(422\) 64.0000 + 64.0000i 0.151659 + 0.151659i
\(423\) 0 0
\(424\) 68.0000i 0.160377i
\(425\) 323.000 589.000i 0.760000 1.38588i
\(426\) 0 0
\(427\) 576.000 + 576.000i 1.34895 + 1.34895i
\(428\) 136.000 136.000i 0.317757 0.317757i
\(429\) 0 0
\(430\) 216.000 288.000i 0.502326 0.669767i
\(431\) −680.000 −1.57773 −0.788863 0.614569i \(-0.789330\pi\)
−0.788863 + 0.614569i \(0.789330\pi\)
\(432\) 0 0
\(433\) 41.0000 41.0000i 0.0946882 0.0946882i −0.658176 0.752864i \(-0.728672\pi\)
0.752864 + 0.658176i \(0.228672\pi\)
\(434\) 704.000i 1.62212i
\(435\) 0 0
\(436\) 92.0000 0.211009
\(437\) 160.000 + 160.000i 0.366133 + 0.366133i
\(438\) 0 0
\(439\) 364.000i 0.829157i −0.910014 0.414579i \(-0.863929\pi\)
0.910014 0.414579i \(-0.136071\pi\)
\(440\) 8.00000 + 56.0000i 0.0181818 + 0.127273i
\(441\) 0 0
\(442\) 114.000 + 114.000i 0.257919 + 0.257919i
\(443\) −372.000 + 372.000i −0.839729 + 0.839729i −0.988823 0.149094i \(-0.952364\pi\)
0.149094 + 0.988823i \(0.452364\pi\)
\(444\) 0 0
\(445\) −104.000 78.0000i −0.233708 0.175281i
\(446\) 456.000 1.02242
\(447\) 0 0
\(448\) 64.0000 64.0000i 0.142857 0.142857i
\(449\) 176.000i 0.391982i −0.980606 0.195991i \(-0.937208\pi\)
0.980606 0.195991i \(-0.0627924\pi\)
\(450\) 0 0
\(451\) 280.000 0.620843
\(452\) 106.000 + 106.000i 0.234513 + 0.234513i
\(453\) 0 0
\(454\) 200.000i 0.440529i
\(455\) 144.000 192.000i 0.316484 0.421978i
\(456\) 0 0
\(457\) 129.000 + 129.000i 0.282276 + 0.282276i 0.834016 0.551740i \(-0.186036\pi\)
−0.551740 + 0.834016i \(0.686036\pi\)
\(458\) −312.000 + 312.000i −0.681223 + 0.681223i
\(459\) 0 0
\(460\) 280.000 40.0000i 0.608696 0.0869565i
\(461\) 568.000 1.23210 0.616052 0.787705i \(-0.288731\pi\)
0.616052 + 0.787705i \(0.288731\pi\)
\(462\) 0 0
\(463\) −568.000 + 568.000i −1.22678 + 1.22678i −0.261608 + 0.965174i \(0.584253\pi\)
−0.965174 + 0.261608i \(0.915747\pi\)
\(464\) 152.000i 0.327586i
\(465\) 0 0
\(466\) 186.000 0.399142
\(467\) −272.000 272.000i −0.582441 0.582441i 0.353132 0.935573i \(-0.385117\pi\)
−0.935573 + 0.353132i \(0.885117\pi\)
\(468\) 0 0
\(469\) 704.000i 1.50107i
\(470\) 0 0
\(471\) 0 0
\(472\) −184.000 184.000i −0.389831 0.389831i
\(473\) 144.000 144.000i 0.304440 0.304440i
\(474\) 0 0
\(475\) −192.000 + 56.0000i −0.404211 + 0.117895i
\(476\) −608.000 −1.27731
\(477\) 0 0
\(478\) −96.0000 + 96.0000i −0.200837 + 0.200837i
\(479\) 928.000i 1.93737i 0.248294 + 0.968685i \(0.420130\pi\)
−0.248294 + 0.968685i \(0.579870\pi\)
\(480\) 0 0
\(481\) 18.0000 0.0374220
\(482\) −160.000 160.000i −0.331950 0.331950i
\(483\) 0 0
\(484\) 210.000i 0.433884i
\(485\) 399.000 57.0000i 0.822680 0.117526i
\(486\) 0 0
\(487\) 252.000 + 252.000i 0.517454 + 0.517454i 0.916800 0.399346i \(-0.130763\pi\)
−0.399346 + 0.916800i \(0.630763\pi\)
\(488\) 144.000 144.000i 0.295082 0.295082i
\(489\) 0 0
\(490\) 79.0000 + 553.000i 0.161224 + 1.12857i
\(491\) −844.000 −1.71894 −0.859470 0.511185i \(-0.829207\pi\)
−0.859470 + 0.511185i \(0.829207\pi\)
\(492\) 0 0
\(493\) 722.000 722.000i 1.46450 1.46450i
\(494\) 48.0000i 0.0971660i
\(495\) 0 0
\(496\) 176.000 0.354839
\(497\) −704.000 704.000i −1.41650 1.41650i
\(498\) 0 0
\(499\) 872.000i 1.74749i 0.486380 + 0.873747i \(0.338317\pi\)
−0.486380 + 0.873747i \(0.661683\pi\)
\(500\) −88.0000 + 234.000i −0.176000 + 0.468000i
\(501\) 0 0
\(502\) −12.0000 12.0000i −0.0239044 0.0239044i
\(503\) 480.000 480.000i 0.954274 0.954274i −0.0447250 0.998999i \(-0.514241\pi\)
0.998999 + 0.0447250i \(0.0142412\pi\)
\(504\) 0 0
\(505\) −168.000 + 224.000i −0.332673 + 0.443564i
\(506\) 160.000 0.316206
\(507\) 0 0
\(508\) −136.000 + 136.000i −0.267717 + 0.267717i
\(509\) 694.000i 1.36346i 0.731605 + 0.681729i \(0.238772\pi\)
−0.731605 + 0.681729i \(0.761228\pi\)
\(510\) 0 0
\(511\) 880.000 1.72211
\(512\) −16.0000 16.0000i −0.0312500 0.0312500i
\(513\) 0 0
\(514\) 202.000i 0.392996i
\(515\) 4.00000 + 28.0000i 0.00776699 + 0.0543689i
\(516\) 0 0
\(517\) 0 0
\(518\) −48.0000 + 48.0000i −0.0926641 + 0.0926641i
\(519\) 0 0
\(520\) −48.0000 36.0000i −0.0923077 0.0692308i
\(521\) 528.000 1.01344 0.506718 0.862112i \(-0.330859\pi\)
0.506718 + 0.862112i \(0.330859\pi\)
\(522\) 0 0
\(523\) 552.000 552.000i 1.05545 1.05545i 0.0570797 0.998370i \(-0.481821\pi\)
0.998370 0.0570797i \(-0.0181789\pi\)
\(524\) 88.0000i 0.167939i
\(525\) 0 0
\(526\) 416.000 0.790875
\(527\) −836.000 836.000i −1.58634 1.58634i
\(528\) 0 0
\(529\) 271.000i 0.512287i
\(530\) 102.000 136.000i 0.192453 0.256604i
\(531\) 0 0
\(532\) 128.000 + 128.000i 0.240602 + 0.240602i
\(533\) −210.000 + 210.000i −0.393996 + 0.393996i
\(534\) 0 0
\(535\) 476.000 68.0000i 0.889720 0.127103i
\(536\) 176.000 0.328358
\(537\) 0 0
\(538\) −296.000 + 296.000i −0.550186 + 0.550186i
\(539\) 316.000i 0.586271i
\(540\) 0 0
\(541\) −782.000 −1.44547 −0.722736 0.691125i \(-0.757116\pi\)
−0.722736 + 0.691125i \(0.757116\pi\)
\(542\) −108.000 108.000i −0.199262 0.199262i
\(543\) 0 0
\(544\) 152.000i 0.279412i
\(545\) 184.000 + 138.000i 0.337615 + 0.253211i
\(546\) 0 0
\(547\) −420.000 420.000i −0.767824 0.767824i 0.209899 0.977723i \(-0.432687\pi\)
−0.977723 + 0.209899i \(0.932687\pi\)
\(548\) 138.000 138.000i 0.251825 0.251825i
\(549\) 0 0
\(550\) −68.0000 + 124.000i −0.123636 + 0.225455i
\(551\) −304.000 −0.551724
\(552\) 0 0
\(553\) −96.0000 + 96.0000i −0.173599 + 0.173599i
\(554\) 486.000i 0.877256i
\(555\) 0 0
\(556\) −160.000 −0.287770
\(557\) 417.000 + 417.000i 0.748654 + 0.748654i 0.974226 0.225573i \(-0.0724254\pi\)
−0.225573 + 0.974226i \(0.572425\pi\)
\(558\) 0 0
\(559\) 216.000i 0.386404i
\(560\) 224.000 32.0000i 0.400000 0.0571429i
\(561\) 0 0
\(562\) −378.000 378.000i −0.672598 0.672598i
\(563\) 228.000 228.000i 0.404973 0.404973i −0.475008 0.879981i \(-0.657555\pi\)
0.879981 + 0.475008i \(0.157555\pi\)
\(564\) 0 0
\(565\) 53.0000 + 371.000i 0.0938053 + 0.656637i
\(566\) −184.000 −0.325088
\(567\) 0 0
\(568\) −176.000 + 176.000i −0.309859 + 0.309859i
\(569\) 368.000i 0.646749i 0.946271 + 0.323374i \(0.104817\pi\)
−0.946271 + 0.323374i \(0.895183\pi\)
\(570\) 0 0
\(571\) −736.000 −1.28897 −0.644483 0.764618i \(-0.722928\pi\)
−0.644483 + 0.764618i \(0.722928\pi\)
\(572\) −24.0000 24.0000i −0.0419580 0.0419580i
\(573\) 0 0
\(574\) 1120.00i 1.95122i
\(575\) 620.000 + 340.000i 1.07826 + 0.591304i
\(576\) 0 0
\(577\) −113.000 113.000i −0.195841 0.195841i 0.602374 0.798214i \(-0.294222\pi\)
−0.798214 + 0.602374i \(0.794222\pi\)
\(578\) 433.000 433.000i 0.749135 0.749135i
\(579\) 0 0
\(580\) −228.000 + 304.000i −0.393103 + 0.524138i
\(581\) −384.000 −0.660929
\(582\) 0 0
\(583\) 68.0000 68.0000i 0.116638 0.116638i
\(584\) 220.000i 0.376712i
\(585\) 0 0
\(586\) 558.000 0.952218
\(587\) 684.000 + 684.000i 1.16525 + 1.16525i 0.983310 + 0.181937i \(0.0582366\pi\)
0.181937 + 0.983310i \(0.441763\pi\)
\(588\) 0 0
\(589\) 352.000i 0.597623i
\(590\) −92.0000 644.000i −0.155932 1.09153i
\(591\) 0 0
\(592\) 12.0000 + 12.0000i 0.0202703 + 0.0202703i
\(593\) −149.000 + 149.000i −0.251265 + 0.251265i −0.821489 0.570224i \(-0.806856\pi\)
0.570224 + 0.821489i \(0.306856\pi\)
\(594\) 0 0
\(595\) −1216.00 912.000i −2.04370 1.53277i
\(596\) −336.000 −0.563758
\(597\) 0 0
\(598\) −120.000 + 120.000i −0.200669 + 0.200669i
\(599\) 152.000i 0.253756i −0.991918 0.126878i \(-0.959504\pi\)
0.991918 0.126878i \(-0.0404957\pi\)
\(600\) 0 0
\(601\) 320.000 0.532446 0.266223 0.963911i \(-0.414224\pi\)
0.266223 + 0.963911i \(0.414224\pi\)
\(602\) −576.000 576.000i −0.956811 0.956811i
\(603\) 0 0
\(604\) 8.00000i 0.0132450i
\(605\) 315.000 420.000i 0.520661 0.694215i
\(606\) 0 0
\(607\) −528.000 528.000i −0.869852 0.869852i 0.122604 0.992456i \(-0.460876\pi\)
−0.992456 + 0.122604i \(0.960876\pi\)
\(608\) 32.0000 32.0000i 0.0526316 0.0526316i
\(609\) 0 0
\(610\) 504.000 72.0000i 0.826230 0.118033i
\(611\) 0 0
\(612\) 0 0
\(613\) 771.000 771.000i 1.25775 1.25775i 0.305583 0.952165i \(-0.401148\pi\)
0.952165 0.305583i \(-0.0988515\pi\)
\(614\) 432.000i 0.703583i
\(615\) 0 0
\(616\) 128.000 0.207792
\(617\) 675.000 + 675.000i 1.09400 + 1.09400i 0.995097 + 0.0989065i \(0.0315345\pi\)
0.0989065 + 0.995097i \(0.468466\pi\)
\(618\) 0 0
\(619\) 600.000i 0.969305i 0.874707 + 0.484653i \(0.161054\pi\)
−0.874707 + 0.484653i \(0.838946\pi\)
\(620\) 352.000 + 264.000i 0.567742 + 0.425806i
\(621\) 0 0
\(622\) −272.000 272.000i −0.437299 0.437299i
\(623\) −208.000 + 208.000i −0.333868 + 0.333868i
\(624\) 0 0
\(625\) −527.000 + 336.000i −0.843200 + 0.537600i
\(626\) −30.0000 −0.0479233
\(627\) 0 0
\(628\) −198.000 + 198.000i −0.315287 + 0.315287i
\(629\) 114.000i 0.181240i
\(630\) 0 0
\(631\) −20.0000 −0.0316957 −0.0158479 0.999874i \(-0.505045\pi\)
−0.0158479 + 0.999874i \(0.505045\pi\)
\(632\) 24.0000 + 24.0000i 0.0379747 + 0.0379747i
\(633\) 0 0
\(634\) 174.000i 0.274448i
\(635\) −476.000 + 68.0000i −0.749606 + 0.107087i
\(636\) 0 0
\(637\) −237.000 237.000i −0.372057 0.372057i
\(638\) −152.000 + 152.000i −0.238245 + 0.238245i
\(639\) 0 0
\(640\) −8.00000 56.0000i −0.0125000 0.0875000i
\(641\) −694.000 −1.08268 −0.541342 0.840803i \(-0.682083\pi\)
−0.541342 + 0.840803i \(0.682083\pi\)
\(642\) 0 0
\(643\) −168.000 + 168.000i −0.261275 + 0.261275i −0.825572 0.564297i \(-0.809147\pi\)
0.564297 + 0.825572i \(0.309147\pi\)
\(644\) 640.000i 0.993789i
\(645\) 0 0
\(646\) −304.000 −0.470588
\(647\) −328.000 328.000i −0.506955 0.506955i 0.406635 0.913591i \(-0.366702\pi\)
−0.913591 + 0.406635i \(0.866702\pi\)
\(648\) 0 0
\(649\) 368.000i 0.567026i
\(650\) −42.0000 144.000i −0.0646154 0.221538i
\(651\) 0 0
\(652\) −320.000 320.000i −0.490798 0.490798i
\(653\) 81.0000 81.0000i 0.124043 0.124043i −0.642360 0.766403i \(-0.722045\pi\)
0.766403 + 0.642360i \(0.222045\pi\)
\(654\) 0 0
\(655\) 132.000 176.000i 0.201527 0.268702i
\(656\) −280.000 −0.426829
\(657\) 0 0
\(658\) 0 0
\(659\) 500.000i 0.758725i 0.925248 + 0.379363i \(0.123857\pi\)
−0.925248 + 0.379363i \(0.876143\pi\)
\(660\) 0 0
\(661\) −568.000 −0.859304 −0.429652 0.902995i \(-0.641364\pi\)
−0.429652 + 0.902995i \(0.641364\pi\)
\(662\) 584.000 + 584.000i 0.882175 + 0.882175i
\(663\) 0 0
\(664\) 96.0000i 0.144578i
\(665\) 64.0000 + 448.000i 0.0962406 + 0.673684i
\(666\) 0 0
\(667\) 760.000 + 760.000i 1.13943 + 1.13943i
\(668\) −112.000 + 112.000i −0.167665 + 0.167665i
\(669\) 0 0
\(670\) 352.000 + 264.000i 0.525373 + 0.394030i
\(671\) 288.000 0.429210
\(672\) 0 0
\(673\) 73.0000 73.0000i 0.108470 0.108470i −0.650789 0.759259i \(-0.725562\pi\)
0.759259 + 0.650789i \(0.225562\pi\)
\(674\) 258.000i 0.382789i
\(675\) 0 0
\(676\) −302.000 −0.446746
\(677\) −839.000 839.000i −1.23929 1.23929i −0.960291 0.279000i \(-0.909997\pi\)
−0.279000 0.960291i \(-0.590003\pi\)
\(678\) 0 0
\(679\) 912.000i 1.34315i
\(680\) −228.000 + 304.000i −0.335294 + 0.447059i
\(681\) 0 0
\(682\) 176.000 + 176.000i 0.258065 + 0.258065i
\(683\) −744.000 + 744.000i −1.08931 + 1.08931i −0.0937126 + 0.995599i \(0.529873\pi\)
−0.995599 + 0.0937126i \(0.970127\pi\)
\(684\) 0 0
\(685\) 483.000 69.0000i 0.705109 0.100730i
\(686\) 480.000 0.699708
\(687\) 0 0
\(688\) −144.000 + 144.000i −0.209302 + 0.209302i
\(689\) 102.000i 0.148041i
\(690\) 0 0
\(691\) 504.000 0.729378 0.364689 0.931129i \(-0.381175\pi\)
0.364689 + 0.931129i \(0.381175\pi\)
\(692\) −82.0000 82.0000i −0.118497 0.118497i
\(693\) 0 0
\(694\) 520.000i 0.749280i
\(695\) −320.000 240.000i −0.460432 0.345324i
\(696\) 0 0
\(697\) 1330.00 + 1330.00i 1.90818 + 1.90818i
\(698\) 136.000 136.000i 0.194842 0.194842i
\(699\) 0 0
\(700\) 496.000 + 272.000i 0.708571 + 0.388571i
\(701\) 298.000 0.425107 0.212553 0.977149i \(-0.431822\pi\)
0.212553 + 0.977149i \(0.431822\pi\)
\(702\) 0 0
\(703\) −24.0000 + 24.0000i −0.0341394 + 0.0341394i
\(704\) 32.0000i 0.0454545i
\(705\) 0 0
\(706\) 150.000 0.212465
\(707\) 448.000 + 448.000i 0.633663 + 0.633663i
\(708\) 0 0
\(709\) 472.000i 0.665726i 0.942975 + 0.332863i \(0.108015\pi\)
−0.942975 + 0.332863i \(0.891985\pi\)
\(710\) −616.000 + 88.0000i −0.867606 + 0.123944i
\(711\) 0 0
\(712\) 52.0000 + 52.0000i 0.0730337 + 0.0730337i
\(713\) 880.000 880.000i 1.23422 1.23422i
\(714\) 0 0
\(715\) −12.0000 84.0000i −0.0167832 0.117483i
\(716\) 344.000 0.480447
\(717\) 0 0
\(718\) 32.0000 32.0000i 0.0445682 0.0445682i
\(719\) 872.000i 1.21280i −0.795161 0.606398i \(-0.792614\pi\)
0.795161 0.606398i \(-0.207386\pi\)
\(720\) 0 0
\(721\) 64.0000 0.0887656
\(722\) −297.000 297.000i −0.411357 0.411357i
\(723\) 0 0
\(724\) 124.000i 0.171271i
\(725\) −912.000 + 266.000i −1.25793 + 0.366897i
\(726\) 0 0
\(727\) −60.0000 60.0000i −0.0825309 0.0825309i 0.664636 0.747167i \(-0.268587\pi\)
−0.747167 + 0.664636i \(0.768587\pi\)
\(728\) −96.0000 + 96.0000i −0.131868 + 0.131868i
\(729\) 0 0
\(730\) 330.000 440.000i 0.452055 0.602740i
\(731\) 1368.00 1.87141
\(732\) 0 0
\(733\) −581.000 + 581.000i −0.792633 + 0.792633i −0.981922 0.189289i \(-0.939382\pi\)
0.189289 + 0.981922i \(0.439382\pi\)
\(734\) 32.0000i 0.0435967i
\(735\) 0 0
\(736\) −160.000 −0.217391
\(737\) 176.000 + 176.000i 0.238806 + 0.238806i
\(738\) 0 0
\(739\) 1160.00i 1.56969i 0.619693 + 0.784844i \(0.287257\pi\)
−0.619693 + 0.784844i \(0.712743\pi\)
\(740\) 6.00000 + 42.0000i 0.00810811 + 0.0567568i
\(741\) 0 0
\(742\) −272.000 272.000i −0.366577 0.366577i
\(743\) 380.000 380.000i 0.511440 0.511440i −0.403527 0.914968i \(-0.632216\pi\)
0.914968 + 0.403527i \(0.132216\pi\)
\(744\) 0 0
\(745\) −672.000 504.000i −0.902013 0.676510i
\(746\) 502.000 0.672922
\(747\) 0 0
\(748\) −152.000 + 152.000i −0.203209 + 0.203209i
\(749\) 1088.00i 1.45260i
\(750\) 0 0
\(751\) 780.000 1.03862 0.519308 0.854587i \(-0.326190\pi\)
0.519308 + 0.854587i \(0.326190\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 228.000i 0.302387i
\(755\) −12.0000 + 16.0000i −0.0158940 + 0.0211921i
\(756\) 0 0
\(757\) 285.000 + 285.000i 0.376486 + 0.376486i 0.869833 0.493347i \(-0.164227\pi\)
−0.493347 + 0.869833i \(0.664227\pi\)
\(758\) −560.000 + 560.000i −0.738786 + 0.738786i
\(759\) 0 0
\(760\) 112.000 16.0000i 0.147368 0.0210526i
\(761\) 304.000 0.399474 0.199737 0.979850i \(-0.435991\pi\)
0.199737 + 0.979850i \(0.435991\pi\)
\(762\) 0 0
\(763\) 368.000 368.000i 0.482307 0.482307i
\(764\) 496.000i 0.649215i
\(765\) 0 0
\(766\) 600.000 0.783290
\(767\) 276.000 + 276.000i 0.359844 + 0.359844i
\(768\) 0 0
\(769\) 1072.00i 1.39402i −0.717062 0.697009i \(-0.754514\pi\)
0.717062 0.697009i \(-0.245486\pi\)
\(770\) 256.000 + 192.000i 0.332468 + 0.249351i
\(771\) 0 0
\(772\) 270.000 + 270.000i 0.349741 + 0.349741i
\(773\) −897.000 + 897.000i −1.16041 + 1.16041i −0.176029 + 0.984385i \(0.556325\pi\)
−0.984385 + 0.176029i \(0.943675\pi\)
\(774\) 0 0
\(775\) 308.000 + 1056.00i 0.397419 + 1.36258i
\(776\) −228.000 −0.293814
\(777\) 0 0
\(778\) −24.0000 + 24.0000i −0.0308483 + 0.0308483i
\(779\) 560.000i 0.718870i
\(780\) 0 0
\(781\) −352.000 −0.450704
\(782\) 760.000 + 760.000i 0.971867