Properties

Label 450.3.g.d.307.1
Level $450$
Weight $3$
Character 450.307
Analytic conductor $12.262$
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] = [450,3,Mod(307,450)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(450, 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("450.307");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 450 = 2 \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 450.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: \(12.2616118962\)
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: no (minimal twist has level 90)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 307.1
Root \(1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 450.307
Dual form 450.3.g.d.343.1

$q$-expansion

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

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/450\mathbb{Z}\right)^\times\).

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

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
\(3\) 0 0
\(4\) 2.00000i 0.500000i
\(5\) 0 0
\(6\) 0 0
\(7\) −8.00000 8.00000i −1.14286 1.14286i −0.987925 0.154932i \(-0.950484\pi\)
−0.154932 0.987925i \(-0.549516\pi\)
\(8\) −2.00000 + 2.00000i −0.250000 + 0.250000i
\(9\) 0 0
\(10\) 0 0
\(11\) 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 −0.582245 0.813014i \(-0.697825\pi\)
0.813014 + 0.582245i \(0.197825\pi\)
\(14\) 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 \(-0.959927\pi\)
−0.125561 0.992086i \(-0.540073\pi\)
\(18\) 0 0
\(19\) 8.00000i 0.421053i −0.977588 0.210526i \(-0.932482\pi\)
0.977588 0.210526i \(-0.0675178\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 4.00000 + 4.00000i 0.181818 + 0.181818i
\(23\) 20.0000 20.0000i 0.869565 0.869565i −0.122859 0.992424i \(-0.539206\pi\)
0.992424 + 0.122859i \(0.0392063\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 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
\(35\) 0 0
\(36\) 0 0
\(37\) 3.00000 + 3.00000i 0.0810811 + 0.0810811i 0.746484 0.665403i \(-0.231740\pi\)
−0.665403 + 0.746484i \(0.731740\pi\)
\(38\) 8.00000 8.00000i 0.210526 0.210526i
\(39\) 0 0
\(40\) 0 0
\(41\) 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 −0.988491 0.151281i \(-0.951660\pi\)
0.151281 + 0.988491i \(0.451660\pi\)
\(44\) 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
\(50\) 0 0
\(51\) 0 0
\(52\) 6.00000 + 6.00000i 0.115385 + 0.115385i
\(53\) −17.0000 + 17.0000i −0.320755 + 0.320755i −0.849057 0.528302i \(-0.822829\pi\)
0.528302 + 0.849057i \(0.322829\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 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
\(65\) 0 0
\(66\) 0 0
\(67\) −44.0000 44.0000i −0.656716 0.656716i 0.297885 0.954602i \(-0.403719\pi\)
−0.954602 + 0.297885i \(0.903719\pi\)
\(68\) 38.0000 38.0000i 0.558824 0.558824i
\(69\) 0 0
\(70\) 0 0
\(71\) −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 −0.975117 0.221692i \(-0.928842\pi\)
0.221692 + 0.975117i \(0.428842\pi\)
\(74\) 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 \(0.975801\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 70.0000 + 70.0000i 0.853659 + 0.853659i
\(83\) 24.0000 24.0000i 0.289157 0.289157i −0.547590 0.836747i \(-0.684455\pi\)
0.836747 + 0.547590i \(0.184455\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −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
\(95\) 0 0
\(96\) 0 0
\(97\) 57.0000 + 57.0000i 0.587629 + 0.587629i 0.936989 0.349360i \(-0.113601\pi\)
−0.349360 + 0.936989i \(0.613601\pi\)
\(98\) −79.0000 + 79.0000i −0.806122 + 0.806122i
\(99\) 0 0
\(100\) 0 0
\(101\) 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 −0.726258 0.687423i \(-0.758742\pi\)
0.687423 + 0.726258i \(0.258742\pi\)
\(104\) 12.0000i 0.115385i
\(105\) 0 0
\(106\) −34.0000 −0.320755
\(107\) 68.0000 + 68.0000i 0.635514 + 0.635514i 0.949446 0.313932i \(-0.101646\pi\)
−0.313932 + 0.949446i \(0.601646\pi\)
\(108\) 0 0
\(109\) 46.0000i 0.422018i −0.977484 0.211009i \(-0.932325\pi\)
0.977484 0.211009i \(-0.0676750\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 32.0000 + 32.0000i 0.285714 + 0.285714i
\(113\) −53.0000 + 53.0000i −0.469027 + 0.469027i −0.901599 0.432573i \(-0.857606\pi\)
0.432573 + 0.901599i \(0.357606\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 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
\(125\) 0 0
\(126\) 0 0
\(127\) −68.0000 68.0000i −0.535433 0.535433i 0.386751 0.922184i \(-0.373597\pi\)
−0.922184 + 0.386751i \(0.873597\pi\)
\(128\) 8.00000 8.00000i 0.0625000 0.0625000i
\(129\) 0 0
\(130\) 0 0
\(131\) −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 0.912570 0.408920i \(-0.134095\pi\)
−0.408920 + 0.912570i \(0.634095\pi\)
\(138\) 0 0
\(139\) 80.0000i 0.575540i 0.957700 + 0.287770i \(0.0929138\pi\)
−0.957700 + 0.287770i \(0.907086\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −88.0000 88.0000i −0.619718 0.619718i
\(143\) 12.0000 12.0000i 0.0839161 0.0839161i
\(144\) 0 0
\(145\) 0 0
\(146\) −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
\(155\) 0 0
\(156\) 0 0
\(157\) −99.0000 99.0000i −0.630573 0.630573i 0.317639 0.948212i \(-0.397110\pi\)
−0.948212 + 0.317639i \(0.897110\pi\)
\(158\) −12.0000 + 12.0000i −0.0759494 + 0.0759494i
\(159\) 0 0
\(160\) 0 0
\(161\) −320.000 −1.98758
\(162\) 0 0
\(163\) 160.000 160.000i 0.981595 0.981595i −0.0182386 0.999834i \(-0.505806\pi\)
0.999834 + 0.0182386i \(0.00580584\pi\)
\(164\) 140.000i 0.853659i
\(165\) 0 0
\(166\) 48.0000 0.289157
\(167\) −56.0000 56.0000i −0.335329 0.335329i 0.519277 0.854606i \(-0.326201\pi\)
−0.854606 + 0.519277i \(0.826201\pi\)
\(168\) 0 0
\(169\) 151.000i 0.893491i
\(170\) 0 0
\(171\) 0 0
\(172\) −72.0000 72.0000i −0.418605 0.418605i
\(173\) 41.0000 41.0000i 0.236994 0.236994i −0.578610 0.815604i \(-0.696405\pi\)
0.815604 + 0.578610i \(0.196405\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −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
\(185\) 0 0
\(186\) 0 0
\(187\) −76.0000 76.0000i −0.406417 0.406417i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 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 −0.964299 0.264817i \(-0.914688\pi\)
0.264817 + 0.964299i \(0.414688\pi\)
\(194\) 114.000i 0.587629i
\(195\) 0 0
\(196\) −158.000 −0.806122
\(197\) 153.000 + 153.000i 0.776650 + 0.776650i 0.979260 0.202610i \(-0.0649423\pi\)
−0.202610 + 0.979260i \(0.564942\pi\)
\(198\) 0 0
\(199\) 252.000i 1.26633i −0.774016 0.633166i \(-0.781755\pi\)
0.774016 0.633166i \(-0.218245\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 56.0000 + 56.0000i 0.277228 + 0.277228i
\(203\) −304.000 + 304.000i −1.49754 + 1.49754i
\(204\) 0 0
\(205\) 0 0
\(206\) −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
\(215\) 0 0
\(216\) 0 0
\(217\) 352.000 + 352.000i 1.62212 + 1.62212i
\(218\) 46.0000 46.0000i 0.211009 0.211009i
\(219\) 0 0
\(220\) 0 0
\(221\) −114.000 −0.515837
\(222\) 0 0
\(223\) 228.000 228.000i 1.02242 1.02242i 0.0226787 0.999743i \(-0.492781\pi\)
0.999743 0.0226787i \(-0.00721948\pi\)
\(224\) 64.0000i 0.285714i
\(225\) 0 0
\(226\) −106.000 −0.469027
\(227\) 100.000 + 100.000i 0.440529 + 0.440529i 0.892190 0.451661i \(-0.149168\pi\)
−0.451661 + 0.892190i \(0.649168\pi\)
\(228\) 0 0
\(229\) 312.000i 1.36245i −0.732076 0.681223i \(-0.761449\pi\)
0.732076 0.681223i \(-0.238551\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 76.0000 + 76.0000i 0.327586 + 0.327586i
\(233\) 93.0000 93.0000i 0.399142 0.399142i −0.478789 0.877930i \(-0.658924\pi\)
0.877930 + 0.478789i \(0.158924\pi\)
\(234\) 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
\(245\) 0 0
\(246\) 0 0
\(247\) −24.0000 24.0000i −0.0971660 0.0971660i
\(248\) 88.0000 88.0000i 0.354839 0.354839i
\(249\) 0 0
\(250\) 0 0
\(251\) 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 0.482758 0.875754i \(-0.339635\pi\)
−0.875754 + 0.482758i \(0.839635\pi\)
\(258\) 0 0
\(259\) 48.0000i 0.185328i
\(260\) 0 0
\(261\) 0 0
\(262\) −44.0000 44.0000i −0.167939 0.167939i
\(263\) 208.000 208.000i 0.790875 0.790875i −0.190762 0.981636i \(-0.561096\pi\)
0.981636 + 0.190762i \(0.0610958\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) −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
\(275\) 0 0
\(276\) 0 0
\(277\) 243.000 + 243.000i 0.877256 + 0.877256i 0.993250 0.115994i \(-0.0370052\pi\)
−0.115994 + 0.993250i \(0.537005\pi\)
\(278\) −80.0000 + 80.0000i −0.287770 + 0.287770i
\(279\) 0 0
\(280\) 0 0
\(281\) 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 −0.850715 0.525627i \(-0.823831\pi\)
0.525627 + 0.850715i \(0.323831\pi\)
\(284\) 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
\(290\) 0 0
\(291\) 0 0
\(292\) −110.000 110.000i −0.376712 0.376712i
\(293\) 279.000 279.000i 0.952218 0.952218i −0.0466910 0.998909i \(-0.514868\pi\)
0.998909 + 0.0466910i \(0.0148676\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) −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
\(305\) 0 0
\(306\) 0 0
\(307\) −216.000 216.000i −0.703583 0.703583i 0.261595 0.965178i \(-0.415752\pi\)
−0.965178 + 0.261595i \(0.915752\pi\)
\(308\) 64.0000 64.0000i 0.207792 0.207792i
\(309\) 0 0
\(310\) 0 0
\(311\) 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 −0.730662 0.682739i \(-0.760789\pi\)
0.682739 + 0.730662i \(0.260789\pi\)
\(314\) 198.000i 0.630573i
\(315\) 0 0
\(316\) −24.0000 −0.0759494
\(317\) −87.0000 87.0000i −0.274448 0.274448i 0.556440 0.830888i \(-0.312167\pi\)
−0.830888 + 0.556440i \(0.812167\pi\)
\(318\) 0 0
\(319\) 152.000i 0.476489i
\(320\) 0 0
\(321\) 0 0
\(322\) −320.000 320.000i −0.993789 0.993789i
\(323\) −152.000 + 152.000i −0.470588 + 0.470588i
\(324\) 0 0
\(325\) 0 0
\(326\) 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
\(335\) 0 0
\(336\) 0 0
\(337\) 129.000 + 129.000i 0.382789 + 0.382789i 0.872106 0.489317i \(-0.162754\pi\)
−0.489317 + 0.872106i \(0.662754\pi\)
\(338\) −151.000 + 151.000i −0.446746 + 0.446746i
\(339\) 0 0
\(340\) 0 0
\(341\) −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 0.974344 0.225064i \(-0.0722592\pi\)
−0.225064 + 0.974344i \(0.572259\pi\)
\(348\) 0 0
\(349\) 136.000i 0.389685i 0.980835 + 0.194842i \(0.0624195\pi\)
−0.980835 + 0.194842i \(0.937580\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −16.0000 16.0000i −0.0454545 0.0454545i
\(353\) 75.0000 75.0000i 0.212465 0.212465i −0.592849 0.805314i \(-0.701997\pi\)
0.805314 + 0.592849i \(0.201997\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −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
\(365\) 0 0
\(366\) 0 0
\(367\) 16.0000 + 16.0000i 0.0435967 + 0.0435967i 0.728569 0.684972i \(-0.240186\pi\)
−0.684972 + 0.728569i \(0.740186\pi\)
\(368\) −80.0000 + 80.0000i −0.217391 + 0.217391i
\(369\) 0 0
\(370\) 0 0
\(371\) 272.000 0.733154
\(372\) 0 0
\(373\) 251.000 251.000i 0.672922 0.672922i −0.285466 0.958389i \(-0.592149\pi\)
0.958389 + 0.285466i \(0.0921485\pi\)
\(374\) 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 \(-0.264601\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 248.000 + 248.000i 0.649215 + 0.649215i
\(383\) 300.000 300.000i 0.783290 0.783290i −0.197095 0.980384i \(-0.563151\pi\)
0.980384 + 0.197095i \(0.0631506\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −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
\(395\) 0 0
\(396\) 0 0
\(397\) 299.000 + 299.000i 0.753149 + 0.753149i 0.975066 0.221917i \(-0.0712314\pi\)
−0.221917 + 0.975066i \(0.571231\pi\)
\(398\) 252.000 252.000i 0.633166 0.633166i
\(399\) 0 0
\(400\) 0 0
\(401\) −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 \(-0.142461\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) −8.00000 8.00000i −0.0194175 0.0194175i
\(413\) −736.000 + 736.000i −1.78208 + 1.78208i
\(414\) 0 0
\(415\) 0 0
\(416\) −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
\(425\) 0 0
\(426\) 0 0
\(427\) −576.000 576.000i −1.34895 1.34895i
\(428\) −136.000 + 136.000i −0.317757 + 0.317757i
\(429\) 0 0
\(430\) 0 0
\(431\) −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 −0.752864 0.658176i \(-0.771328\pi\)
0.658176 + 0.752864i \(0.271328\pi\)
\(434\) 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 \(-0.136071\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) −114.000 114.000i −0.257919 0.257919i
\(443\) 372.000 372.000i 0.839729 0.839729i −0.149094 0.988823i \(-0.547636\pi\)
0.988823 + 0.149094i \(0.0476357\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 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
\(455\) 0 0
\(456\) 0 0
\(457\) −129.000 129.000i −0.282276 0.282276i 0.551740 0.834016i \(-0.313964\pi\)
−0.834016 + 0.551740i \(0.813964\pi\)
\(458\) 312.000 312.000i 0.681223 0.681223i
\(459\) 0 0
\(460\) 0 0
\(461\) 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 \(-0.415747\pi\)
0.965174 0.261608i \(-0.0842526\pi\)
\(464\) 152.000i 0.327586i
\(465\) 0 0
\(466\) 186.000 0.399142
\(467\) 272.000 + 272.000i 0.582441 + 0.582441i 0.935573 0.353132i \(-0.114883\pi\)
−0.353132 + 0.935573i \(0.614883\pi\)
\(468\) 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
\(475\) 0 0
\(476\) −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
\(485\) 0 0
\(486\) 0 0
\(487\) −252.000 252.000i −0.517454 0.517454i 0.399346 0.916800i \(-0.369237\pi\)
−0.916800 + 0.399346i \(0.869237\pi\)
\(488\) −144.000 + 144.000i −0.295082 + 0.295082i
\(489\) 0 0
\(490\) 0 0
\(491\) −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 \(0.661683\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 12.0000 + 12.0000i 0.0239044 + 0.0239044i
\(503\) −480.000 + 480.000i −0.954274 + 0.954274i −0.998999 0.0447250i \(-0.985759\pi\)
0.0447250 + 0.998999i \(0.485759\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 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
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 48.0000 48.0000i 0.0926641 0.0926641i
\(519\) 0 0
\(520\) 0 0
\(521\) 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 \(0.518179\pi\)
−0.998370 + 0.0570797i \(0.981821\pi\)
\(524\) 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
\(530\) 0 0
\(531\) 0 0
\(532\) −128.000 128.000i −0.240602 0.240602i
\(533\) 210.000 210.000i 0.393996 0.393996i
\(534\) 0 0
\(535\) 0 0
\(536\) 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
\(545\) 0 0
\(546\) 0 0
\(547\) 420.000 + 420.000i 0.767824 + 0.767824i 0.977723 0.209899i \(-0.0673134\pi\)
−0.209899 + 0.977723i \(0.567313\pi\)
\(548\) −138.000 + 138.000i −0.251825 + 0.251825i
\(549\) 0 0
\(550\) 0 0
\(551\) −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 0.225573 0.974226i \(-0.427575\pi\)
−0.974226 + 0.225573i \(0.927575\pi\)
\(558\) 0 0
\(559\) 216.000i 0.386404i
\(560\) 0 0
\(561\) 0 0
\(562\) 378.000 + 378.000i 0.672598 + 0.672598i
\(563\) −228.000 + 228.000i −0.404973 + 0.404973i −0.879981 0.475008i \(-0.842445\pi\)
0.475008 + 0.879981i \(0.342445\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) −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
\(575\) 0 0
\(576\) 0 0
\(577\) 113.000 + 113.000i 0.195841 + 0.195841i 0.798214 0.602374i \(-0.205778\pi\)
−0.602374 + 0.798214i \(0.705778\pi\)
\(578\) −433.000 + 433.000i −0.749135 + 0.749135i
\(579\) 0 0
\(580\) 0 0
\(581\) −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 \(-0.941763\pi\)
−0.181937 0.983310i \(-0.558237\pi\)
\(588\) 0 0
\(589\) 352.000i 0.597623i
\(590\) 0 0
\(591\) 0 0
\(592\) −12.0000 12.0000i −0.0202703 0.0202703i
\(593\) 149.000 149.000i 0.251265 0.251265i −0.570224 0.821489i \(-0.693144\pi\)
0.821489 + 0.570224i \(0.193144\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −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
\(605\) 0 0
\(606\) 0 0
\(607\) 528.000 + 528.000i 0.869852 + 0.869852i 0.992456 0.122604i \(-0.0391245\pi\)
−0.122604 + 0.992456i \(0.539124\pi\)
\(608\) −32.0000 + 32.0000i −0.0526316 + 0.0526316i
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) −771.000 + 771.000i −1.25775 + 1.25775i −0.305583 + 0.952165i \(0.598852\pi\)
−0.952165 + 0.305583i \(0.901148\pi\)
\(614\) 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 \(-0.968466\pi\)
−0.0989065 0.995097i \(-0.531534\pi\)
\(618\) 0 0
\(619\) 600.000i 0.969305i 0.874707 + 0.484653i \(0.161054\pi\)
−0.874707 + 0.484653i \(0.838946\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 272.000 + 272.000i 0.437299 + 0.437299i
\(623\) 208.000 208.000i 0.333868 0.333868i
\(624\) 0 0
\(625\) 0 0
\(626\) −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
\(635\) 0 0
\(636\) 0 0
\(637\) 237.000 + 237.000i 0.372057 + 0.372057i
\(638\) 152.000 152.000i 0.238245 0.238245i
\(639\) 0 0
\(640\) 0 0
\(641\) −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 −0.564297 0.825572i \(-0.690853\pi\)
0.825572 + 0.564297i \(0.190853\pi\)
\(644\) 640.000i 0.993789i
\(645\) 0 0
\(646\) −304.000 −0.470588
\(647\) 328.000 + 328.000i 0.506955 + 0.506955i 0.913591 0.406635i \(-0.133298\pi\)
−0.406635 + 0.913591i \(0.633298\pi\)
\(648\) 0 0
\(649\) 368.000i 0.567026i
\(650\) 0 0
\(651\) 0 0
\(652\) 320.000 + 320.000i 0.490798 + 0.490798i
\(653\) −81.0000 + 81.0000i −0.124043 + 0.124043i −0.766403 0.642360i \(-0.777955\pi\)
0.642360 + 0.766403i \(0.277955\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) −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
\(665\) 0 0
\(666\) 0 0
\(667\) −760.000 760.000i −1.13943 1.13943i
\(668\) 112.000 112.000i 0.167665 0.167665i
\(669\) 0 0
\(670\) 0 0
\(671\) 288.000 0.429210
\(672\) 0 0
\(673\) −73.0000 + 73.0000i −0.108470 + 0.108470i −0.759259 0.650789i \(-0.774438\pi\)
0.650789 + 0.759259i \(0.274438\pi\)
\(674\) 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 \(0.0900029\pi\)
0.279000 + 0.960291i \(0.409997\pi\)
\(678\) 0 0
\(679\) 912.000i 1.34315i
\(680\) 0 0
\(681\) 0 0
\(682\) −176.000 176.000i −0.258065 0.258065i
\(683\) 744.000 744.000i 1.08931 1.08931i 0.0937126 0.995599i \(-0.470127\pi\)
0.995599 0.0937126i \(-0.0298735\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 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
\(695\) 0 0
\(696\) 0 0
\(697\) −1330.00 1330.00i −1.90818 1.90818i
\(698\) −136.000 + 136.000i −0.194842 + 0.194842i
\(699\) 0 0
\(700\) 0 0
\(701\) 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 \(0.891985\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −52.0000 52.0000i −0.0730337 0.0730337i
\(713\) −880.000 + 880.000i −1.23422 + 1.23422i
\(714\) 0 0
\(715\) 0 0
\(716\) 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
\(725\) 0 0
\(726\) 0 0
\(727\) 60.0000 + 60.0000i 0.0825309 + 0.0825309i 0.747167 0.664636i \(-0.231413\pi\)
−0.664636 + 0.747167i \(0.731413\pi\)
\(728\) 96.0000 96.0000i 0.131868 0.131868i
\(729\) 0 0
\(730\) 0 0
\(731\) 1368.00 1.87141
\(732\) 0 0
\(733\) 581.000 581.000i 0.792633 0.792633i −0.189289 0.981922i \(-0.560618\pi\)
0.981922 + 0.189289i \(0.0606181\pi\)
\(734\) 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 \(0.712743\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 272.000 + 272.000i 0.366577 + 0.366577i
\(743\) −380.000 + 380.000i −0.511440 + 0.511440i −0.914968 0.403527i \(-0.867784\pi\)
0.403527 + 0.914968i \(0.367784\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 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
\(755\) 0 0
\(756\) 0 0
\(757\) −285.000 285.000i −0.376486 0.376486i 0.493347 0.869833i \(-0.335773\pi\)
−0.869833 + 0.493347i \(0.835773\pi\)
\(758\) 560.000 560.000i 0.738786 0.738786i
\(759\) 0 0
\(760\) 0 0
\(761\) 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 \(-0.245486\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −270.000 270.000i −0.349741 0.349741i
\(773\) 897.000 897.000i 1.16041 1.16041i 0.176029 0.984385i \(-0.443675\pi\)
0.984385 0.176029i \(-0.0563252\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) −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 0.971867i
\(783\) 0 0
\(784\) 316.000i 0.403061i
\(785\) 0 0
\(786\) 0 0
\(787\) −328.000 328.000i −0.416773 0.416773i 0.467317 0.884090i \(-0.345221\pi\)
−0.884090 + 0.467317i \(0.845221\pi\)
\(788\)