Properties

Label 90.3.g.c.73.1
Level $90$
Weight $3$
Character 90.73
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 73.1
Root \(-1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 90.73
Dual form 90.3.g.c.37.1

$q$-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 \(\left(\mathbb{Z}/90\mathbb{Z}\right)^\times\).

\(n\) \(11\) \(37\)
\(\chi(n)\) \(1\) \(e\left(\frac{3}{4}\right)\)

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 0.154932 0.987925i \(-0.450484\pi\)
0.987925 0.154932i \(-0.0495158\pi\)
\(8\) −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 \(-0.558198\pi\)
−0.181818 + 0.983332i \(0.558198\pi\)
\(12\) 0 0
\(13\) −3.00000 3.00000i −0.230769 0.230769i 0.582245 0.813014i \(-0.302175\pi\)
−0.813014 + 0.582245i \(0.802175\pi\)
\(14\) 16.0000i 1.14286i
\(15\) 0 0
\(16\) −4.00000 −0.250000
\(17\) −19.0000 + 19.0000i −1.11765 + 1.11765i −0.125561 + 0.992086i \(0.540073\pi\)
−0.992086 + 0.125561i \(0.959927\pi\)
\(18\) 0 0
\(19\) 8.00000i 0.421053i 0.977588 + 0.210526i \(0.0675178\pi\)
−0.977588 + 0.210526i \(0.932482\pi\)
\(20\) 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 \(-0.0392063\pi\)
−0.122859 + 0.992424i \(0.539206\pi\)
\(24\) 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 −0.746484 0.665403i \(-0.768260\pi\)
0.665403 + 0.746484i \(0.268260\pi\)
\(38\) 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 \(-0.825621\pi\)
−0.853659 + 0.520833i \(0.825621\pi\)
\(42\) 0 0
\(43\) 36.0000 + 36.0000i 0.837209 + 0.837209i 0.988491 0.151281i \(-0.0483400\pi\)
−0.151281 + 0.988491i \(0.548340\pi\)
\(44\) 8.00000i 0.181818i
\(45\) 0 0
\(46\) 40.0000 0.869565
\(47\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(48\) 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 \(-0.322829\pi\)
−0.849057 + 0.528302i \(0.822829\pi\)
\(54\) 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 −0.297885 0.954602i \(-0.596281\pi\)
0.954602 + 0.297885i \(0.0962813\pi\)
\(68\) 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 \(-0.287247\pi\)
0.619718 + 0.784824i \(0.287247\pi\)
\(72\) 0 0
\(73\) 55.0000 + 55.0000i 0.753425 + 0.753425i 0.975117 0.221692i \(-0.0711580\pi\)
−0.221692 + 0.975117i \(0.571158\pi\)
\(74\) 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 \(-0.975801\pi\)
0.997112 0.0759494i \(-0.0241987\pi\)
\(80\) −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 \(-0.184455\pi\)
−0.547590 + 0.836747i \(0.684455\pi\)
\(84\) 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 −0.936989 0.349360i \(-0.886399\pi\)
0.349360 + 0.936989i \(0.386399\pi\)
\(98\) −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 \(-0.589416\pi\)
−0.277228 + 0.960804i \(0.589416\pi\)
\(102\) 0 0
\(103\) 4.00000 + 4.00000i 0.0388350 + 0.0388350i 0.726258 0.687423i \(-0.241258\pi\)
−0.687423 + 0.726258i \(0.741258\pi\)
\(104\) 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 \(-0.601646\pi\)
0.949446 + 0.313932i \(0.101646\pi\)
\(108\) 0 0
\(109\) 46.0000i 0.422018i 0.977484 + 0.211009i \(0.0676750\pi\)
−0.977484 + 0.211009i \(0.932325\pi\)
\(110\) −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 \(-0.357606\pi\)
−0.901599 + 0.432573i \(0.857606\pi\)
\(114\) 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 −0.386751 0.922184i \(-0.626403\pi\)
0.922184 + 0.386751i \(0.126403\pi\)
\(128\) 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 \(-0.446289\pi\)
0.167939 + 0.985797i \(0.446289\pi\)
\(132\) 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 \(-0.634095\pi\)
0.912570 + 0.408920i \(0.134095\pi\)
\(138\) 0 0
\(139\) 80.0000i 0.575540i −0.957700 0.287770i \(-0.907086\pi\)
0.957700 0.287770i \(-0.0929138\pi\)
\(140\) 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 −0.317639 0.948212i \(-0.602890\pi\)
0.948212 + 0.317639i \(0.102890\pi\)
\(158\) −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 0.0182386 0.999834i \(-0.494194\pi\)
−0.999834 + 0.0182386i \(0.994194\pi\)
\(164\) 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 \(-0.826201\pi\)
0.519277 + 0.854606i \(0.326201\pi\)
\(168\) 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 \(-0.196405\pi\)
−0.578610 + 0.815604i \(0.696405\pi\)
\(174\) 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 \(-0.724902\pi\)
−0.649215 + 0.760605i \(0.724902\pi\)
\(192\) 0 0
\(193\) 135.000 + 135.000i 0.699482 + 0.699482i 0.964299 0.264817i \(-0.0853115\pi\)
−0.264817 + 0.964299i \(0.585312\pi\)
\(194\) 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 \(-0.564942\pi\)
0.979260 + 0.202610i \(0.0649423\pi\)
\(198\) 0 0
\(199\) 252.000i 1.26633i 0.774016 + 0.633166i \(0.218245\pi\)
−0.774016 + 0.633166i \(0.781755\pi\)
\(200\) 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 −0.999743 0.0226787i \(-0.992781\pi\)
−0.0226787 0.999743i \(-0.507219\pi\)
\(224\) 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 \(-0.649168\pi\)
0.892190 + 0.451661i \(0.149168\pi\)
\(228\) 0 0
\(229\) 312.000i 1.36245i 0.732076 + 0.681223i \(0.238551\pi\)
−0.732076 + 0.681223i \(0.761449\pi\)
\(230\) 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 \(-0.158924\pi\)
−0.478789 + 0.877930i \(0.658924\pi\)
\(234\) 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 \(-0.507610\pi\)
−0.0239044 + 0.999714i \(0.507610\pi\)
\(252\) 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 \(-0.839635\pi\)
0.482758 + 0.875754i \(0.339635\pi\)
\(258\) 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 \(-0.0610958\pi\)
−0.190762 + 0.981636i \(0.561096\pi\)
\(264\) 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 −0.993250 0.115994i \(-0.962995\pi\)
0.115994 + 0.993250i \(0.462995\pi\)
\(278\) −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 \(-0.734822\pi\)
−0.672598 + 0.740008i \(0.734822\pi\)
\(282\) 0 0
\(283\) 92.0000 + 92.0000i 0.325088 + 0.325088i 0.850715 0.525627i \(-0.176169\pi\)
−0.525627 + 0.850715i \(0.676169\pi\)
\(284\) 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 \(-0.0148676\pi\)
−0.0466910 + 0.998909i \(0.514868\pi\)
\(294\) 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 −0.261595 0.965178i \(-0.584248\pi\)
0.965178 + 0.261595i \(0.0842484\pi\)
\(308\) 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 \(-0.644065\pi\)
−0.437299 + 0.899316i \(0.644065\pi\)
\(312\) 0 0
\(313\) 15.0000 + 15.0000i 0.0479233 + 0.0479233i 0.730662 0.682739i \(-0.239211\pi\)
−0.682739 + 0.730662i \(0.739211\pi\)
\(314\) 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 \(-0.812167\pi\)
0.556440 + 0.830888i \(0.312167\pi\)
\(318\) 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 −0.872106 0.489317i \(-0.837246\pi\)
0.489317 + 0.872106i \(0.337246\pi\)
\(338\) −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 \(-0.572259\pi\)
0.974344 + 0.225064i \(0.0722592\pi\)
\(348\) 0 0
\(349\) 136.000i 0.389685i −0.980835 0.194842i \(-0.937580\pi\)
0.980835 0.194842i \(-0.0624195\pi\)
\(350\) 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 \(-0.201997\pi\)
−0.592849 + 0.805314i \(0.701997\pi\)
\(354\) 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 −0.728569 0.684972i \(-0.759814\pi\)
0.684972 + 0.728569i \(0.259814\pi\)
\(368\) −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 0.285466 0.958389i \(-0.407851\pi\)
−0.958389 + 0.285466i \(0.907851\pi\)
\(374\) 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 \(0.264601\pi\)
−0.673940 + 0.738786i \(0.735399\pi\)
\(380\) 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 \(-0.0631506\pi\)
−0.197095 + 0.980384i \(0.563151\pi\)
\(384\) 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 −0.975066 0.221917i \(-0.928769\pi\)
0.221917 + 0.975066i \(0.428769\pi\)
\(398\) 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 \(-0.442535\pi\)
0.179551 + 0.983749i \(0.442535\pi\)
\(402\) 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 \(0.142461\pi\)
−0.901508 + 0.432763i \(0.857539\pi\)
\(410\) −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 \(-0.210670\pi\)
0.788863 + 0.614569i \(0.210670\pi\)
\(432\) 0 0
\(433\) 41.0000 + 41.0000i 0.0946882 + 0.0946882i 0.752864 0.658176i \(-0.228672\pi\)
−0.658176 + 0.752864i \(0.728672\pi\)
\(434\) 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 \(0.136071\pi\)
−0.910014 + 0.414579i \(0.863929\pi\)
\(440\) −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 \(-0.0476357\pi\)
−0.149094 + 0.988823i \(0.547636\pi\)
\(444\) 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 −0.551740 0.834016i \(-0.686036\pi\)
0.834016 + 0.551740i \(0.186036\pi\)
\(458\) 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 \(-0.711269\pi\)
−0.616052 + 0.787705i \(0.711269\pi\)
\(462\) 0 0
\(463\) −568.000 568.000i −1.22678 1.22678i −0.965174 0.261608i \(-0.915747\pi\)
−0.261608 0.965174i \(-0.584253\pi\)
\(464\) 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 \(-0.614883\pi\)
0.935573 + 0.353132i \(0.114883\pi\)
\(468\) 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 −0.399346 0.916800i \(-0.630763\pi\)
0.916800 + 0.399346i \(0.130763\pi\)
\(488\) −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 \(-0.170793\pi\)
0.859470 + 0.511185i \(0.170793\pi\)
\(492\) 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 \(-0.661683\pi\)
0.486380 0.873747i \(-0.338317\pi\)
\(500\) 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 \(-0.485759\pi\)
−0.998999 + 0.0447250i \(0.985759\pi\)
\(504\) 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 \(-0.669141\pi\)
−0.506718 + 0.862112i \(0.669141\pi\)
\(522\) 0 0
\(523\) 552.000 + 552.000i 1.05545 + 1.05545i 0.998370 + 0.0570797i \(0.0181789\pi\)
0.0570797 + 0.998370i \(0.481821\pi\)
\(524\) 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 −0.977723 0.209899i \(-0.932687\pi\)
0.209899 + 0.977723i \(0.432687\pi\)
\(548\) −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 \(-0.927575\pi\)
0.225573 + 0.974226i \(0.427575\pi\)
\(558\) 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 \(-0.342445\pi\)
−0.879981 + 0.475008i \(0.842445\pi\)
\(564\) 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 −0.798214 0.602374i \(-0.794222\pi\)
0.602374 + 0.798214i \(0.294222\pi\)
\(578\) −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 −0.181937 + 0.983310i \(0.558237\pi\)
−0.983310 + 0.181937i \(0.941763\pi\)
\(588\) 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 \(-0.193144\pi\)
−0.570224 + 0.821489i \(0.693144\pi\)
\(594\) 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 −0.992456 0.122604i \(-0.960876\pi\)
0.122604 + 0.992456i \(0.460876\pi\)
\(608\) −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 0.952165 + 0.305583i \(0.0988515\pi\)
0.305583 + 0.952165i \(0.401148\pi\)
\(614\) 432.000i 0.703583i
\(615\) 0 0
\(616\) 128.000 0.207792
\(617\) −675.000 + 675.000i −1.09400 + 1.09400i −0.0989065 + 0.995097i \(0.531534\pi\)
−0.995097 + 0.0989065i \(0.968466\pi\)
\(618\) 0 0
\(619\) 600.000i 0.969305i −0.874707 0.484653i \(-0.838946\pi\)
0.874707 0.484653i \(-0.161054\pi\)
\(620\) −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 \(-0.317917\pi\)
0.541342 + 0.840803i \(0.317917\pi\)
\(642\) 0 0
\(643\) −168.000 168.000i −0.261275 0.261275i 0.564297 0.825572i \(-0.309147\pi\)
−0.825572 + 0.564297i \(0.809147\pi\)
\(644\) 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 \(-0.633298\pi\)
0.913591 + 0.406635i \(0.133298\pi\)
\(648\) 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 \(-0.277955\pi\)
−0.766403 + 0.642360i \(0.777955\pi\)
\(654\) 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 0.759259 0.650789i \(-0.225562\pi\)
−0.650789 + 0.759259i \(0.725562\pi\)
\(674\) 258.000i 0.382789i
\(675\) 0 0
\(676\) −302.000 −0.446746
\(677\) 839.000 839.000i 1.23929 1.23929i 0.279000 0.960291i \(-0.409997\pi\)
0.960291 0.279000i \(-0.0900029\pi\)
\(678\) 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 0.995599 + 0.0937126i \(0.0298735\pi\)
0.0937126 + 0.995599i \(0.470127\pi\)
\(684\) 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 \(-0.568178\pi\)
−0.212553 + 0.977149i \(0.568178\pi\)
\(702\) 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 \(-0.891985\pi\)
0.942975 0.332863i \(-0.108015\pi\)
\(710\) 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 −0.747167 0.664636i \(-0.768587\pi\)
0.664636 + 0.747167i \(0.268587\pi\)
\(728\) 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 0.189289 0.981922i \(-0.439382\pi\)
−0.981922 + 0.189289i \(0.939382\pi\)
\(734\) 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 \(-0.712743\pi\)
0.619693 0.784844i \(-0.287257\pi\)
\(740\) −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 \(-0.367784\pi\)
−0.914968 + 0.403527i \(0.867784\pi\)
\(744\) 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 −0.493347 0.869833i \(-0.664227\pi\)
0.869833 + 0.493347i \(0.164227\pi\)
\(758\) 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 \(-0.564009\pi\)
−0.199737 + 0.979850i \(0.564009\pi\)
\(762\) 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 \(0.245486\pi\)
−0.717062 + 0.697009i \(0.754514\pi\)
\(770\) −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 0.984385 + 0.176029i \(0.0563252\pi\)
0.176029 + 0.984385i \(0.443675\pi\)
\(774\) 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