Properties

Label 224.2.u.a.141.1
Level $224$
Weight $2$
Character 224.141
Analytic conductor $1.789$
Analytic rank $1$
Dimension $4$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [224,2,Mod(29,224)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(224, base_ring=CyclotomicField(8))
 
chi = DirichletCharacter(H, H._module([0, 3, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("224.29");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 224 = 2^{5} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 224.u (of order \(8\), degree \(4\), 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: \(1.78864900528\)
Analytic rank: \(1\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{8})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 141.1
Root \(0.707107 - 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 224.141
Dual form 224.2.u.a.197.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.00000 - 1.00000i) q^{2} +(-1.00000 + 2.41421i) q^{3} +2.00000i q^{4} +(-3.41421 + 1.41421i) q^{5} +(3.41421 - 1.41421i) q^{6} +(0.707107 - 0.707107i) q^{7} +(2.00000 - 2.00000i) q^{8} +(-2.70711 - 2.70711i) q^{9} +O(q^{10})\) \(q+(-1.00000 - 1.00000i) q^{2} +(-1.00000 + 2.41421i) q^{3} +2.00000i q^{4} +(-3.41421 + 1.41421i) q^{5} +(3.41421 - 1.41421i) q^{6} +(0.707107 - 0.707107i) q^{7} +(2.00000 - 2.00000i) q^{8} +(-2.70711 - 2.70711i) q^{9} +(4.82843 + 2.00000i) q^{10} +(-2.29289 - 5.53553i) q^{11} +(-4.82843 - 2.00000i) q^{12} +(1.41421 + 0.585786i) q^{13} -1.41421 q^{14} -9.65685i q^{15} -4.00000 q^{16} +5.41421i q^{18} +(0.414214 + 0.171573i) q^{19} +(-2.82843 - 6.82843i) q^{20} +(1.00000 + 2.41421i) q^{21} +(-3.24264 + 7.82843i) q^{22} +(-1.00000 - 1.00000i) q^{23} +(2.82843 + 6.82843i) q^{24} +(6.12132 - 6.12132i) q^{25} +(-0.828427 - 2.00000i) q^{26} +(2.00000 - 0.828427i) q^{27} +(1.41421 + 1.41421i) q^{28} +(-3.29289 + 7.94975i) q^{29} +(-9.65685 + 9.65685i) q^{30} -8.82843 q^{31} +(4.00000 + 4.00000i) q^{32} +15.6569 q^{33} +(-1.41421 + 3.41421i) q^{35} +(5.41421 - 5.41421i) q^{36} +(-4.70711 + 1.94975i) q^{37} +(-0.242641 - 0.585786i) q^{38} +(-2.82843 + 2.82843i) q^{39} +(-4.00000 + 9.65685i) q^{40} +(-3.41421 - 3.41421i) q^{41} +(1.41421 - 3.41421i) q^{42} +(-1.87868 - 4.53553i) q^{43} +(11.0711 - 4.58579i) q^{44} +(13.0711 + 5.41421i) q^{45} +2.00000i q^{46} -8.82843i q^{47} +(4.00000 - 9.65685i) q^{48} -1.00000i q^{49} -12.2426 q^{50} +(-1.17157 + 2.82843i) q^{52} +(0.0502525 + 0.121320i) q^{53} +(-2.82843 - 1.17157i) q^{54} +(15.6569 + 15.6569i) q^{55} -2.82843i q^{56} +(-0.828427 + 0.828427i) q^{57} +(11.2426 - 4.65685i) q^{58} +(-5.00000 + 2.07107i) q^{59} +19.3137 q^{60} +(-1.17157 + 2.82843i) q^{61} +(8.82843 + 8.82843i) q^{62} -3.82843 q^{63} -8.00000i q^{64} -5.65685 q^{65} +(-15.6569 - 15.6569i) q^{66} +(4.70711 - 11.3640i) q^{67} +(3.41421 - 1.41421i) q^{69} +(4.82843 - 2.00000i) q^{70} +(-4.24264 + 4.24264i) q^{71} -10.8284 q^{72} +(3.17157 + 3.17157i) q^{73} +(6.65685 + 2.75736i) q^{74} +(8.65685 + 20.8995i) q^{75} +(-0.343146 + 0.828427i) q^{76} +(-5.53553 - 2.29289i) q^{77} +5.65685 q^{78} +9.89949i q^{79} +(13.6569 - 5.65685i) q^{80} -5.82843i q^{81} +6.82843i q^{82} +(3.24264 + 1.34315i) q^{83} +(-4.82843 + 2.00000i) q^{84} +(-2.65685 + 6.41421i) q^{86} +(-15.8995 - 15.8995i) q^{87} +(-15.6569 - 6.48528i) q^{88} +(-5.17157 + 5.17157i) q^{89} +(-7.65685 - 18.4853i) q^{90} +(1.41421 - 0.585786i) q^{91} +(2.00000 - 2.00000i) q^{92} +(8.82843 - 21.3137i) q^{93} +(-8.82843 + 8.82843i) q^{94} -1.65685 q^{95} +(-13.6569 + 5.65685i) q^{96} +1.17157 q^{97} +(-1.00000 + 1.00000i) q^{98} +(-8.77817 + 21.1924i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 4 q^{2} - 4 q^{3} - 8 q^{5} + 8 q^{6} + 8 q^{8} - 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 4 q^{2} - 4 q^{3} - 8 q^{5} + 8 q^{6} + 8 q^{8} - 8 q^{9} + 8 q^{10} - 12 q^{11} - 8 q^{12} - 16 q^{16} - 4 q^{19} + 4 q^{21} + 4 q^{22} - 4 q^{23} + 16 q^{25} + 8 q^{26} + 8 q^{27} - 16 q^{29} - 16 q^{30} - 24 q^{31} + 16 q^{32} + 40 q^{33} + 16 q^{36} - 16 q^{37} + 16 q^{38} - 16 q^{40} - 8 q^{41} - 16 q^{43} + 16 q^{44} + 24 q^{45} + 16 q^{48} - 32 q^{50} - 16 q^{52} + 20 q^{53} + 40 q^{55} + 8 q^{57} + 28 q^{58} - 20 q^{59} + 32 q^{60} - 16 q^{61} + 24 q^{62} - 4 q^{63} - 40 q^{66} + 16 q^{67} + 8 q^{69} + 8 q^{70} - 32 q^{72} + 24 q^{73} + 4 q^{74} + 12 q^{75} - 24 q^{76} - 8 q^{77} + 32 q^{80} - 4 q^{83} - 8 q^{84} + 12 q^{86} - 24 q^{87} - 40 q^{88} - 32 q^{89} - 8 q^{90} + 8 q^{92} + 24 q^{93} - 24 q^{94} + 16 q^{95} - 32 q^{96} + 16 q^{97} - 4 q^{98} - 4 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/224\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(129\) \(197\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{7}{8}\right)\)

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 −0.707107 0.707107i
\(3\) −1.00000 + 2.41421i −0.577350 + 1.39385i 0.317832 + 0.948147i \(0.397045\pi\)
−0.895182 + 0.445700i \(0.852955\pi\)
\(4\) 2.00000i 1.00000i
\(5\) −3.41421 + 1.41421i −1.52688 + 0.632456i −0.978956 0.204071i \(-0.934583\pi\)
−0.547927 + 0.836526i \(0.684583\pi\)
\(6\) 3.41421 1.41421i 1.39385 0.577350i
\(7\) 0.707107 0.707107i 0.267261 0.267261i
\(8\) 2.00000 2.00000i 0.707107 0.707107i
\(9\) −2.70711 2.70711i −0.902369 0.902369i
\(10\) 4.82843 + 2.00000i 1.52688 + 0.632456i
\(11\) −2.29289 5.53553i −0.691333 1.66903i −0.742077 0.670315i \(-0.766159\pi\)
0.0507438 0.998712i \(-0.483841\pi\)
\(12\) −4.82843 2.00000i −1.39385 0.577350i
\(13\) 1.41421 + 0.585786i 0.392232 + 0.162468i 0.570078 0.821590i \(-0.306913\pi\)
−0.177846 + 0.984058i \(0.556913\pi\)
\(14\) −1.41421 −0.377964
\(15\) 9.65685i 2.49339i
\(16\) −4.00000 −1.00000
\(17\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(18\) 5.41421i 1.27614i
\(19\) 0.414214 + 0.171573i 0.0950271 + 0.0393615i 0.429691 0.902976i \(-0.358623\pi\)
−0.334663 + 0.942338i \(0.608623\pi\)
\(20\) −2.82843 6.82843i −0.632456 1.52688i
\(21\) 1.00000 + 2.41421i 0.218218 + 0.526825i
\(22\) −3.24264 + 7.82843i −0.691333 + 1.66903i
\(23\) −1.00000 1.00000i −0.208514 0.208514i 0.595121 0.803636i \(-0.297104\pi\)
−0.803636 + 0.595121i \(0.797104\pi\)
\(24\) 2.82843 + 6.82843i 0.577350 + 1.39385i
\(25\) 6.12132 6.12132i 1.22426 1.22426i
\(26\) −0.828427 2.00000i −0.162468 0.392232i
\(27\) 2.00000 0.828427i 0.384900 0.159431i
\(28\) 1.41421 + 1.41421i 0.267261 + 0.267261i
\(29\) −3.29289 + 7.94975i −0.611475 + 1.47623i 0.249905 + 0.968270i \(0.419601\pi\)
−0.861380 + 0.507961i \(0.830399\pi\)
\(30\) −9.65685 + 9.65685i −1.76309 + 1.76309i
\(31\) −8.82843 −1.58563 −0.792816 0.609461i \(-0.791386\pi\)
−0.792816 + 0.609461i \(0.791386\pi\)
\(32\) 4.00000 + 4.00000i 0.707107 + 0.707107i
\(33\) 15.6569 2.72551
\(34\) 0 0
\(35\) −1.41421 + 3.41421i −0.239046 + 0.577107i
\(36\) 5.41421 5.41421i 0.902369 0.902369i
\(37\) −4.70711 + 1.94975i −0.773844 + 0.320537i −0.734428 0.678686i \(-0.762550\pi\)
−0.0394154 + 0.999223i \(0.512550\pi\)
\(38\) −0.242641 0.585786i −0.0393615 0.0950271i
\(39\) −2.82843 + 2.82843i −0.452911 + 0.452911i
\(40\) −4.00000 + 9.65685i −0.632456 + 1.52688i
\(41\) −3.41421 3.41421i −0.533211 0.533211i 0.388316 0.921526i \(-0.373057\pi\)
−0.921526 + 0.388316i \(0.873057\pi\)
\(42\) 1.41421 3.41421i 0.218218 0.526825i
\(43\) −1.87868 4.53553i −0.286496 0.691662i 0.713463 0.700693i \(-0.247126\pi\)
−0.999959 + 0.00903020i \(0.997126\pi\)
\(44\) 11.0711 4.58579i 1.66903 0.691333i
\(45\) 13.0711 + 5.41421i 1.94852 + 0.807103i
\(46\) 2.00000i 0.294884i
\(47\) 8.82843i 1.28776i −0.765127 0.643879i \(-0.777324\pi\)
0.765127 0.643879i \(-0.222676\pi\)
\(48\) 4.00000 9.65685i 0.577350 1.39385i
\(49\) 1.00000i 0.142857i
\(50\) −12.2426 −1.73137
\(51\) 0 0
\(52\) −1.17157 + 2.82843i −0.162468 + 0.392232i
\(53\) 0.0502525 + 0.121320i 0.00690272 + 0.0166646i 0.927293 0.374336i \(-0.122129\pi\)
−0.920391 + 0.391000i \(0.872129\pi\)
\(54\) −2.82843 1.17157i −0.384900 0.159431i
\(55\) 15.6569 + 15.6569i 2.11117 + 2.11117i
\(56\) 2.82843i 0.377964i
\(57\) −0.828427 + 0.828427i −0.109728 + 0.109728i
\(58\) 11.2426 4.65685i 1.47623 0.611475i
\(59\) −5.00000 + 2.07107i −0.650945 + 0.269630i −0.683622 0.729836i \(-0.739596\pi\)
0.0326779 + 0.999466i \(0.489596\pi\)
\(60\) 19.3137 2.49339
\(61\) −1.17157 + 2.82843i −0.150005 + 0.362143i −0.980964 0.194190i \(-0.937792\pi\)
0.830959 + 0.556333i \(0.187792\pi\)
\(62\) 8.82843 + 8.82843i 1.12121 + 1.12121i
\(63\) −3.82843 −0.482336
\(64\) 8.00000i 1.00000i
\(65\) −5.65685 −0.701646
\(66\) −15.6569 15.6569i −1.92723 1.92723i
\(67\) 4.70711 11.3640i 0.575065 1.38833i −0.322131 0.946695i \(-0.604399\pi\)
0.897195 0.441634i \(-0.145601\pi\)
\(68\) 0 0
\(69\) 3.41421 1.41421i 0.411023 0.170251i
\(70\) 4.82843 2.00000i 0.577107 0.239046i
\(71\) −4.24264 + 4.24264i −0.503509 + 0.503509i −0.912526 0.409018i \(-0.865871\pi\)
0.409018 + 0.912526i \(0.365871\pi\)
\(72\) −10.8284 −1.27614
\(73\) 3.17157 + 3.17157i 0.371205 + 0.371205i 0.867916 0.496711i \(-0.165459\pi\)
−0.496711 + 0.867916i \(0.665459\pi\)
\(74\) 6.65685 + 2.75736i 0.773844 + 0.320537i
\(75\) 8.65685 + 20.8995i 0.999607 + 2.41327i
\(76\) −0.343146 + 0.828427i −0.0393615 + 0.0950271i
\(77\) −5.53553 2.29289i −0.630833 0.261299i
\(78\) 5.65685 0.640513
\(79\) 9.89949i 1.11378i 0.830586 + 0.556890i \(0.188006\pi\)
−0.830586 + 0.556890i \(0.811994\pi\)
\(80\) 13.6569 5.65685i 1.52688 0.632456i
\(81\) 5.82843i 0.647603i
\(82\) 6.82843i 0.754074i
\(83\) 3.24264 + 1.34315i 0.355926 + 0.147429i 0.553480 0.832863i \(-0.313300\pi\)
−0.197554 + 0.980292i \(0.563300\pi\)
\(84\) −4.82843 + 2.00000i −0.526825 + 0.218218i
\(85\) 0 0
\(86\) −2.65685 + 6.41421i −0.286496 + 0.691662i
\(87\) −15.8995 15.8995i −1.70460 1.70460i
\(88\) −15.6569 6.48528i −1.66903 0.691333i
\(89\) −5.17157 + 5.17157i −0.548186 + 0.548186i −0.925916 0.377730i \(-0.876705\pi\)
0.377730 + 0.925916i \(0.376705\pi\)
\(90\) −7.65685 18.4853i −0.807103 1.94852i
\(91\) 1.41421 0.585786i 0.148250 0.0614071i
\(92\) 2.00000 2.00000i 0.208514 0.208514i
\(93\) 8.82843 21.3137i 0.915465 2.21013i
\(94\) −8.82843 + 8.82843i −0.910583 + 0.910583i
\(95\) −1.65685 −0.169990
\(96\) −13.6569 + 5.65685i −1.39385 + 0.577350i
\(97\) 1.17157 0.118955 0.0594776 0.998230i \(-0.481057\pi\)
0.0594776 + 0.998230i \(0.481057\pi\)
\(98\) −1.00000 + 1.00000i −0.101015 + 0.101015i
\(99\) −8.77817 + 21.1924i −0.882240 + 2.12992i
\(100\) 12.2426 + 12.2426i 1.22426 + 1.22426i
\(101\) −3.41421 + 1.41421i −0.339727 + 0.140720i −0.546023 0.837770i \(-0.683859\pi\)
0.206296 + 0.978490i \(0.433859\pi\)
\(102\) 0 0
\(103\) −10.2426 + 10.2426i −1.00924 + 1.00924i −0.00928044 + 0.999957i \(0.502954\pi\)
−0.999957 + 0.00928044i \(0.997046\pi\)
\(104\) 4.00000 1.65685i 0.392232 0.162468i
\(105\) −6.82843 6.82843i −0.666386 0.666386i
\(106\) 0.0710678 0.171573i 0.00690272 0.0166646i
\(107\) −2.36396 5.70711i −0.228533 0.551727i 0.767466 0.641089i \(-0.221517\pi\)
−0.995999 + 0.0893623i \(0.971517\pi\)
\(108\) 1.65685 + 4.00000i 0.159431 + 0.384900i
\(109\) −8.53553 3.53553i −0.817556 0.338643i −0.0655916 0.997847i \(-0.520893\pi\)
−0.751964 + 0.659204i \(0.770893\pi\)
\(110\) 31.3137i 2.98564i
\(111\) 13.3137i 1.26368i
\(112\) −2.82843 + 2.82843i −0.267261 + 0.267261i
\(113\) 17.4142i 1.63819i 0.573657 + 0.819096i \(0.305524\pi\)
−0.573657 + 0.819096i \(0.694476\pi\)
\(114\) 1.65685 0.155179
\(115\) 4.82843 + 2.00000i 0.450253 + 0.186501i
\(116\) −15.8995 6.58579i −1.47623 0.611475i
\(117\) −2.24264 5.41421i −0.207332 0.500544i
\(118\) 7.07107 + 2.92893i 0.650945 + 0.269630i
\(119\) 0 0
\(120\) −19.3137 19.3137i −1.76309 1.76309i
\(121\) −17.6066 + 17.6066i −1.60060 + 1.60060i
\(122\) 4.00000 1.65685i 0.362143 0.150005i
\(123\) 11.6569 4.82843i 1.05106 0.435365i
\(124\) 17.6569i 1.58563i
\(125\) −5.17157 + 12.4853i −0.462560 + 1.11672i
\(126\) 3.82843 + 3.82843i 0.341063 + 0.341063i
\(127\) 14.9706 1.32842 0.664211 0.747545i \(-0.268768\pi\)
0.664211 + 0.747545i \(0.268768\pi\)
\(128\) −8.00000 + 8.00000i −0.707107 + 0.707107i
\(129\) 12.8284 1.12948
\(130\) 5.65685 + 5.65685i 0.496139 + 0.496139i
\(131\) 2.41421 5.82843i 0.210931 0.509232i −0.782636 0.622480i \(-0.786125\pi\)
0.993567 + 0.113248i \(0.0361253\pi\)
\(132\) 31.3137i 2.72551i
\(133\) 0.414214 0.171573i 0.0359169 0.0148773i
\(134\) −16.0711 + 6.65685i −1.38833 + 0.575065i
\(135\) −5.65685 + 5.65685i −0.486864 + 0.486864i
\(136\) 0 0
\(137\) 15.1421 + 15.1421i 1.29368 + 1.29368i 0.932494 + 0.361186i \(0.117628\pi\)
0.361186 + 0.932494i \(0.382372\pi\)
\(138\) −4.82843 2.00000i −0.411023 0.170251i
\(139\) 3.24264 + 7.82843i 0.275037 + 0.663999i 0.999684 0.0251215i \(-0.00799727\pi\)
−0.724647 + 0.689120i \(0.757997\pi\)
\(140\) −6.82843 2.82843i −0.577107 0.239046i
\(141\) 21.3137 + 8.82843i 1.79494 + 0.743488i
\(142\) 8.48528 0.712069
\(143\) 9.17157i 0.766965i
\(144\) 10.8284 + 10.8284i 0.902369 + 0.902369i
\(145\) 31.7990i 2.64076i
\(146\) 6.34315i 0.524962i
\(147\) 2.41421 + 1.00000i 0.199121 + 0.0824786i
\(148\) −3.89949 9.41421i −0.320537 0.773844i
\(149\) −0.0502525 0.121320i −0.00411685 0.00993895i 0.921808 0.387647i \(-0.126712\pi\)
−0.925925 + 0.377708i \(0.876712\pi\)
\(150\) 12.2426 29.5563i 0.999607 2.41327i
\(151\) −3.00000 3.00000i −0.244137 0.244137i 0.574422 0.818559i \(-0.305227\pi\)
−0.818559 + 0.574422i \(0.805227\pi\)
\(152\) 1.17157 0.485281i 0.0950271 0.0393615i
\(153\) 0 0
\(154\) 3.24264 + 7.82843i 0.261299 + 0.630833i
\(155\) 30.1421 12.4853i 2.42107 1.00284i
\(156\) −5.65685 5.65685i −0.452911 0.452911i
\(157\) −2.48528 + 6.00000i −0.198347 + 0.478852i −0.991490 0.130183i \(-0.958443\pi\)
0.793143 + 0.609036i \(0.208443\pi\)
\(158\) 9.89949 9.89949i 0.787562 0.787562i
\(159\) −0.343146 −0.0272132
\(160\) −19.3137 8.00000i −1.52688 0.632456i
\(161\) −1.41421 −0.111456
\(162\) −5.82843 + 5.82843i −0.457924 + 0.457924i
\(163\) 2.05025 4.94975i 0.160588 0.387694i −0.823020 0.568012i \(-0.807713\pi\)
0.983608 + 0.180318i \(0.0577127\pi\)
\(164\) 6.82843 6.82843i 0.533211 0.533211i
\(165\) −53.4558 + 22.1421i −4.16153 + 1.72376i
\(166\) −1.89949 4.58579i −0.147429 0.355926i
\(167\) 5.75736 5.75736i 0.445518 0.445518i −0.448344 0.893861i \(-0.647986\pi\)
0.893861 + 0.448344i \(0.147986\pi\)
\(168\) 6.82843 + 2.82843i 0.526825 + 0.218218i
\(169\) −7.53553 7.53553i −0.579656 0.579656i
\(170\) 0 0
\(171\) −0.656854 1.58579i −0.0502309 0.121268i
\(172\) 9.07107 3.75736i 0.691662 0.286496i
\(173\) 4.24264 + 1.75736i 0.322562 + 0.133610i 0.538088 0.842888i \(-0.319147\pi\)
−0.215526 + 0.976498i \(0.569147\pi\)
\(174\) 31.7990i 2.41068i
\(175\) 8.65685i 0.654397i
\(176\) 9.17157 + 22.1421i 0.691333 + 1.66903i
\(177\) 14.1421i 1.06299i
\(178\) 10.3431 0.775252
\(179\) −10.5355 4.36396i −0.787463 0.326178i −0.0475398 0.998869i \(-0.515138\pi\)
−0.739923 + 0.672692i \(0.765138\pi\)
\(180\) −10.8284 + 26.1421i −0.807103 + 1.94852i
\(181\) −5.41421 13.0711i −0.402435 0.971565i −0.987073 0.160270i \(-0.948763\pi\)
0.584638 0.811294i \(-0.301237\pi\)
\(182\) −2.00000 0.828427i −0.148250 0.0614071i
\(183\) −5.65685 5.65685i −0.418167 0.418167i
\(184\) −4.00000 −0.294884
\(185\) 13.3137 13.3137i 0.978843 0.978843i
\(186\) −30.1421 + 12.4853i −2.21013 + 0.915465i
\(187\) 0 0
\(188\) 17.6569 1.28776
\(189\) 0.828427 2.00000i 0.0602592 0.145479i
\(190\) 1.65685 + 1.65685i 0.120201 + 0.120201i
\(191\) 3.07107 0.222215 0.111107 0.993808i \(-0.464560\pi\)
0.111107 + 0.993808i \(0.464560\pi\)
\(192\) 19.3137 + 8.00000i 1.39385 + 0.577350i
\(193\) 1.41421 0.101797 0.0508987 0.998704i \(-0.483791\pi\)
0.0508987 + 0.998704i \(0.483791\pi\)
\(194\) −1.17157 1.17157i −0.0841140 0.0841140i
\(195\) 5.65685 13.6569i 0.405096 0.977988i
\(196\) 2.00000 0.142857
\(197\) 12.6066 5.22183i 0.898183 0.372040i 0.114662 0.993405i \(-0.463422\pi\)
0.783521 + 0.621365i \(0.213422\pi\)
\(198\) 29.9706 12.4142i 2.12992 0.882240i
\(199\) 0.928932 0.928932i 0.0658503 0.0658503i −0.673415 0.739265i \(-0.735173\pi\)
0.739265 + 0.673415i \(0.235173\pi\)
\(200\) 24.4853i 1.73137i
\(201\) 22.7279 + 22.7279i 1.60310 + 1.60310i
\(202\) 4.82843 + 2.00000i 0.339727 + 0.140720i
\(203\) 3.29289 + 7.94975i 0.231116 + 0.557963i
\(204\) 0 0
\(205\) 16.4853 + 6.82843i 1.15138 + 0.476918i
\(206\) 20.4853 1.42728
\(207\) 5.41421i 0.376314i
\(208\) −5.65685 2.34315i −0.392232 0.162468i
\(209\) 2.68629i 0.185815i
\(210\) 13.6569i 0.942412i
\(211\) −4.12132 1.70711i −0.283723 0.117522i 0.236283 0.971684i \(-0.424071\pi\)
−0.520007 + 0.854162i \(0.674071\pi\)
\(212\) −0.242641 + 0.100505i −0.0166646 + 0.00690272i
\(213\) −6.00000 14.4853i −0.411113 0.992515i
\(214\) −3.34315 + 8.07107i −0.228533 + 0.551727i
\(215\) 12.8284 + 12.8284i 0.874891 + 0.874891i
\(216\) 2.34315 5.65685i 0.159431 0.384900i
\(217\) −6.24264 + 6.24264i −0.423778 + 0.423778i
\(218\) 5.00000 + 12.0711i 0.338643 + 0.817556i
\(219\) −10.8284 + 4.48528i −0.731717 + 0.303087i
\(220\) −31.3137 + 31.3137i −2.11117 + 2.11117i
\(221\) 0 0
\(222\) −13.3137 + 13.3137i −0.893558 + 0.893558i
\(223\) −23.3137 −1.56120 −0.780601 0.625030i \(-0.785087\pi\)
−0.780601 + 0.625030i \(0.785087\pi\)
\(224\) 5.65685 0.377964
\(225\) −33.1421 −2.20948
\(226\) 17.4142 17.4142i 1.15838 1.15838i
\(227\) −11.0000 + 26.5563i −0.730096 + 1.76261i −0.0878156 + 0.996137i \(0.527989\pi\)
−0.642280 + 0.766470i \(0.722011\pi\)
\(228\) −1.65685 1.65685i −0.109728 0.109728i
\(229\) 8.00000 3.31371i 0.528655 0.218976i −0.102359 0.994748i \(-0.532639\pi\)
0.631014 + 0.775771i \(0.282639\pi\)
\(230\) −2.82843 6.82843i −0.186501 0.450253i
\(231\) 11.0711 11.0711i 0.728423 0.728423i
\(232\) 9.31371 + 22.4853i 0.611475 + 1.47623i
\(233\) −1.82843 1.82843i −0.119784 0.119784i 0.644674 0.764458i \(-0.276993\pi\)
−0.764458 + 0.644674i \(0.776993\pi\)
\(234\) −3.17157 + 7.65685i −0.207332 + 0.500544i
\(235\) 12.4853 + 30.1421i 0.814450 + 1.96626i
\(236\) −4.14214 10.0000i −0.269630 0.650945i
\(237\) −23.8995 9.89949i −1.55244 0.643041i
\(238\) 0 0
\(239\) 6.00000i 0.388108i 0.980991 + 0.194054i \(0.0621637\pi\)
−0.980991 + 0.194054i \(0.937836\pi\)
\(240\) 38.6274i 2.49339i
\(241\) 23.7990i 1.53303i −0.642228 0.766514i \(-0.721990\pi\)
0.642228 0.766514i \(-0.278010\pi\)
\(242\) 35.2132 2.26359
\(243\) 20.0711 + 8.31371i 1.28756 + 0.533325i
\(244\) −5.65685 2.34315i −0.362143 0.150005i
\(245\) 1.41421 + 3.41421i 0.0903508 + 0.218126i
\(246\) −16.4853 6.82843i −1.05106 0.435365i
\(247\) 0.485281 + 0.485281i 0.0308777 + 0.0308777i
\(248\) −17.6569 + 17.6569i −1.12121 + 1.12121i
\(249\) −6.48528 + 6.48528i −0.410988 + 0.410988i
\(250\) 17.6569 7.31371i 1.11672 0.462560i
\(251\) 2.65685 1.10051i 0.167699 0.0694633i −0.297255 0.954798i \(-0.596071\pi\)
0.464954 + 0.885335i \(0.346071\pi\)
\(252\) 7.65685i 0.482336i
\(253\) −3.24264 + 7.82843i −0.203863 + 0.492169i
\(254\) −14.9706 14.9706i −0.939337 0.939337i
\(255\) 0 0
\(256\) 16.0000 1.00000
\(257\) −28.1421 −1.75546 −0.877729 0.479157i \(-0.840942\pi\)
−0.877729 + 0.479157i \(0.840942\pi\)
\(258\) −12.8284 12.8284i −0.798663 0.798663i
\(259\) −1.94975 + 4.70711i −0.121151 + 0.292485i
\(260\) 11.3137i 0.701646i
\(261\) 30.4350 12.6066i 1.88388 0.780329i
\(262\) −8.24264 + 3.41421i −0.509232 + 0.210931i
\(263\) −9.65685 + 9.65685i −0.595467 + 0.595467i −0.939103 0.343636i \(-0.888341\pi\)
0.343636 + 0.939103i \(0.388341\pi\)
\(264\) 31.3137 31.3137i 1.92723 1.92723i
\(265\) −0.343146 0.343146i −0.0210793 0.0210793i
\(266\) −0.585786 0.242641i −0.0359169 0.0148773i
\(267\) −7.31371 17.6569i −0.447592 1.08058i
\(268\) 22.7279 + 9.41421i 1.38833 + 0.575065i
\(269\) −14.2426 5.89949i −0.868389 0.359699i −0.0964064 0.995342i \(-0.530735\pi\)
−0.771983 + 0.635644i \(0.780735\pi\)
\(270\) 11.3137 0.688530
\(271\) 11.5147i 0.699469i 0.936849 + 0.349735i \(0.113728\pi\)
−0.936849 + 0.349735i \(0.886272\pi\)
\(272\) 0 0
\(273\) 4.00000i 0.242091i
\(274\) 30.2843i 1.82954i
\(275\) −47.9203 19.8492i −2.88970 1.19695i
\(276\) 2.82843 + 6.82843i 0.170251 + 0.411023i
\(277\) −8.36396 20.1924i −0.502542 1.21324i −0.948095 0.317988i \(-0.896993\pi\)
0.445553 0.895255i \(-0.353007\pi\)
\(278\) 4.58579 11.0711i 0.275037 0.663999i
\(279\) 23.8995 + 23.8995i 1.43083 + 1.43083i
\(280\) 4.00000 + 9.65685i 0.239046 + 0.577107i
\(281\) −1.34315 + 1.34315i −0.0801254 + 0.0801254i −0.746034 0.665908i \(-0.768044\pi\)
0.665908 + 0.746034i \(0.268044\pi\)
\(282\) −12.4853 30.1421i −0.743488 1.79494i
\(283\) 12.8995 5.34315i 0.766795 0.317617i 0.0352218 0.999380i \(-0.488786\pi\)
0.731574 + 0.681762i \(0.238786\pi\)
\(284\) −8.48528 8.48528i −0.503509 0.503509i
\(285\) 1.65685 4.00000i 0.0981436 0.236940i
\(286\) −9.17157 + 9.17157i −0.542326 + 0.542326i
\(287\) −4.82843 −0.285013
\(288\) 21.6569i 1.27614i
\(289\) 17.0000 1.00000
\(290\) −31.7990 + 31.7990i −1.86730 + 1.86730i
\(291\) −1.17157 + 2.82843i −0.0686788 + 0.165805i
\(292\) −6.34315 + 6.34315i −0.371205 + 0.371205i
\(293\) 14.8284 6.14214i 0.866286 0.358827i 0.0951233 0.995466i \(-0.469675\pi\)
0.771163 + 0.636638i \(0.219675\pi\)
\(294\) −1.41421 3.41421i −0.0824786 0.199121i
\(295\) 14.1421 14.1421i 0.823387 0.823387i
\(296\) −5.51472 + 13.3137i −0.320537 + 0.773844i
\(297\) −9.17157 9.17157i −0.532189 0.532189i
\(298\) −0.0710678 + 0.171573i −0.00411685 + 0.00993895i
\(299\) −0.828427 2.00000i −0.0479092 0.115663i
\(300\) −41.7990 + 17.3137i −2.41327 + 0.999607i
\(301\) −4.53553 1.87868i −0.261424 0.108285i
\(302\) 6.00000i 0.345261i
\(303\) 9.65685i 0.554772i
\(304\) −1.65685 0.686292i −0.0950271 0.0393615i
\(305\) 11.3137i 0.647821i
\(306\) 0 0
\(307\) −29.1421 12.0711i −1.66323 0.688932i −0.664912 0.746921i \(-0.731531\pi\)
−0.998317 + 0.0579892i \(0.981531\pi\)
\(308\) 4.58579 11.0711i 0.261299 0.630833i
\(309\) −14.4853 34.9706i −0.824039 1.98941i
\(310\) −42.6274 17.6569i −2.42107 1.00284i
\(311\) 19.3137 + 19.3137i 1.09518 + 1.09518i 0.994966 + 0.100214i \(0.0319528\pi\)
0.100214 + 0.994966i \(0.468047\pi\)
\(312\) 11.3137i 0.640513i
\(313\) −4.92893 + 4.92893i −0.278600 + 0.278600i −0.832550 0.553950i \(-0.813120\pi\)
0.553950 + 0.832550i \(0.313120\pi\)
\(314\) 8.48528 3.51472i 0.478852 0.198347i
\(315\) 13.0711 5.41421i 0.736471 0.305056i
\(316\) −19.7990 −1.11378
\(317\) 4.36396 10.5355i 0.245104 0.591735i −0.752671 0.658397i \(-0.771235\pi\)
0.997776 + 0.0666621i \(0.0212350\pi\)
\(318\) 0.343146 + 0.343146i 0.0192427 + 0.0192427i
\(319\) 51.5563 2.88660
\(320\) 11.3137 + 27.3137i 0.632456 + 1.52688i
\(321\) 16.1421 0.900966
\(322\) 1.41421 + 1.41421i 0.0788110 + 0.0788110i
\(323\) 0 0
\(324\) 11.6569 0.647603
\(325\) 12.2426 5.07107i 0.679100 0.281292i
\(326\) −7.00000 + 2.89949i −0.387694 + 0.160588i
\(327\) 17.0711 17.0711i 0.944032 0.944032i
\(328\) −13.6569 −0.754074
\(329\) −6.24264 6.24264i −0.344168 0.344168i
\(330\) 75.5980 + 31.3137i 4.16153 + 1.72376i
\(331\) 5.12132 + 12.3640i 0.281493 + 0.679585i 0.999871 0.0160685i \(-0.00511500\pi\)
−0.718378 + 0.695653i \(0.755115\pi\)
\(332\) −2.68629 + 6.48528i −0.147429 + 0.355926i
\(333\) 18.0208 + 7.46447i 0.987535 + 0.409050i
\(334\) −11.5147 −0.630057
\(335\) 45.4558i 2.48352i
\(336\) −4.00000 9.65685i −0.218218 0.526825i
\(337\) 7.27208i 0.396135i −0.980188 0.198068i \(-0.936533\pi\)
0.980188 0.198068i \(-0.0634666\pi\)
\(338\) 15.0711i 0.819758i
\(339\) −42.0416 17.4142i −2.28339 0.945810i
\(340\) 0 0
\(341\) 20.2426 + 48.8701i 1.09620 + 2.64646i
\(342\) −0.928932 + 2.24264i −0.0502309 + 0.121268i
\(343\) −0.707107 0.707107i −0.0381802 0.0381802i
\(344\) −12.8284 5.31371i −0.691662 0.286496i
\(345\) −9.65685 + 9.65685i −0.519908 + 0.519908i
\(346\) −2.48528 6.00000i −0.133610 0.322562i
\(347\) −2.12132 + 0.878680i −0.113878 + 0.0471700i −0.438895 0.898538i \(-0.644630\pi\)
0.325017 + 0.945708i \(0.394630\pi\)
\(348\) 31.7990 31.7990i 1.70460 1.70460i
\(349\) −3.31371 + 8.00000i −0.177379 + 0.428230i −0.987415 0.158149i \(-0.949447\pi\)
0.810036 + 0.586380i \(0.199447\pi\)
\(350\) −8.65685 + 8.65685i −0.462728 + 0.462728i
\(351\) 3.31371 0.176873
\(352\) 12.9706 31.3137i 0.691333 1.66903i
\(353\) 27.4558 1.46133 0.730664 0.682738i \(-0.239211\pi\)
0.730664 + 0.682738i \(0.239211\pi\)
\(354\) −14.1421 + 14.1421i −0.751646 + 0.751646i
\(355\) 8.48528 20.4853i 0.450352 1.08725i
\(356\) −10.3431 10.3431i −0.548186 0.548186i
\(357\) 0 0
\(358\) 6.17157 + 14.8995i 0.326178 + 0.787463i
\(359\) 11.9706 11.9706i 0.631782 0.631782i −0.316733 0.948515i \(-0.602586\pi\)
0.948515 + 0.316733i \(0.102586\pi\)
\(360\) 36.9706 15.3137i 1.94852 0.807103i
\(361\) −13.2929 13.2929i −0.699626 0.699626i
\(362\) −7.65685 + 18.4853i −0.402435 + 0.971565i
\(363\) −24.8995 60.1127i −1.30688 3.15510i
\(364\) 1.17157 + 2.82843i 0.0614071 + 0.148250i
\(365\) −15.3137 6.34315i −0.801556 0.332015i
\(366\) 11.3137i 0.591377i
\(367\) 12.4853i 0.651726i 0.945417 + 0.325863i \(0.105655\pi\)
−0.945417 + 0.325863i \(0.894345\pi\)
\(368\) 4.00000 + 4.00000i 0.208514 + 0.208514i
\(369\) 18.4853i 0.962305i
\(370\) −26.6274 −1.38429
\(371\) 0.121320 + 0.0502525i 0.00629864 + 0.00260898i
\(372\) 42.6274 + 17.6569i 2.21013 + 0.915465i
\(373\) 7.39340 + 17.8492i 0.382816 + 0.924199i 0.991419 + 0.130724i \(0.0417302\pi\)
−0.608603 + 0.793475i \(0.708270\pi\)
\(374\) 0 0
\(375\) −24.9706 24.9706i −1.28947 1.28947i
\(376\) −17.6569 17.6569i −0.910583 0.910583i
\(377\) −9.31371 + 9.31371i −0.479680 + 0.479680i
\(378\) −2.82843 + 1.17157i −0.145479 + 0.0602592i
\(379\) −19.2635 + 7.97918i −0.989497 + 0.409863i −0.817935 0.575310i \(-0.804881\pi\)
−0.171562 + 0.985173i \(0.554881\pi\)
\(380\) 3.31371i 0.169990i
\(381\) −14.9706 + 36.1421i −0.766965 + 1.85162i
\(382\) −3.07107 3.07107i −0.157129 0.157129i
\(383\) −12.8284 −0.655502 −0.327751 0.944764i \(-0.606291\pi\)
−0.327751 + 0.944764i \(0.606291\pi\)
\(384\) −11.3137 27.3137i −0.577350 1.39385i
\(385\) 22.1421 1.12847
\(386\) −1.41421 1.41421i −0.0719816 0.0719816i
\(387\) −7.19239 + 17.3640i −0.365610 + 0.882660i
\(388\) 2.34315i 0.118955i
\(389\) 12.0208 4.97918i 0.609480 0.252455i −0.0565264 0.998401i \(-0.518003\pi\)
0.666006 + 0.745946i \(0.268003\pi\)
\(390\) −19.3137 + 8.00000i −0.977988 + 0.405096i
\(391\) 0 0
\(392\) −2.00000 2.00000i −0.101015 0.101015i
\(393\) 11.6569 + 11.6569i 0.588011 + 0.588011i
\(394\) −17.8284 7.38478i −0.898183 0.372040i
\(395\) −14.0000 33.7990i −0.704416 1.70061i
\(396\) −42.3848 17.5563i −2.12992 0.882240i
\(397\) −1.65685 0.686292i −0.0831551 0.0344440i 0.340718 0.940165i \(-0.389330\pi\)
−0.423873 + 0.905722i \(0.639330\pi\)
\(398\) −1.85786 −0.0931263
\(399\) 1.17157i 0.0586520i
\(400\) −24.4853 + 24.4853i −1.22426 + 1.22426i
\(401\) 32.2426i 1.61012i 0.593193 + 0.805060i \(0.297867\pi\)
−0.593193 + 0.805060i \(0.702133\pi\)
\(402\) 45.4558i 2.26713i
\(403\) −12.4853 5.17157i −0.621936 0.257614i
\(404\) −2.82843 6.82843i −0.140720 0.339727i
\(405\) 8.24264 + 19.8995i 0.409580 + 0.988814i
\(406\) 4.65685 11.2426i 0.231116 0.557963i
\(407\) 21.5858 + 21.5858i 1.06997 + 1.06997i
\(408\) 0 0
\(409\) 15.7574 15.7574i 0.779151 0.779151i −0.200535 0.979686i \(-0.564268\pi\)
0.979686 + 0.200535i \(0.0642681\pi\)
\(410\) −9.65685 23.3137i −0.476918 1.15138i
\(411\) −51.6985 + 21.4142i −2.55010 + 1.05629i
\(412\) −20.4853 20.4853i −1.00924 1.00924i
\(413\) −2.07107 + 5.00000i −0.101911 + 0.246034i
\(414\) 5.41421 5.41421i 0.266094 0.266094i
\(415\) −12.9706 −0.636700
\(416\) 3.31371 + 8.00000i 0.162468 + 0.392232i
\(417\) −22.1421 −1.08431
\(418\) −2.68629 + 2.68629i −0.131391 + 0.131391i
\(419\) 1.24264 3.00000i 0.0607070 0.146560i −0.890615 0.454758i \(-0.849726\pi\)
0.951322 + 0.308198i \(0.0997259\pi\)
\(420\) 13.6569 13.6569i 0.666386 0.666386i
\(421\) 23.6066 9.77817i 1.15052 0.476559i 0.275809 0.961212i \(-0.411054\pi\)
0.874706 + 0.484653i \(0.161054\pi\)
\(422\) 2.41421 + 5.82843i 0.117522 + 0.283723i
\(423\) −23.8995 + 23.8995i −1.16203 + 1.16203i
\(424\) 0.343146 + 0.142136i 0.0166646 + 0.00690272i
\(425\) 0 0
\(426\) −8.48528 + 20.4853i −0.411113 + 0.992515i
\(427\) 1.17157 + 2.82843i 0.0566964 + 0.136877i
\(428\) 11.4142 4.72792i 0.551727 0.228533i
\(429\) 22.1421 + 9.17157i 1.06903 + 0.442808i
\(430\) 25.6569i 1.23728i
\(431\) 21.6569i 1.04317i 0.853198 + 0.521587i \(0.174660\pi\)
−0.853198 + 0.521587i \(0.825340\pi\)
\(432\) −8.00000 + 3.31371i −0.384900 + 0.159431i
\(433\) 24.2843i 1.16703i 0.812103 + 0.583514i \(0.198323\pi\)
−0.812103 + 0.583514i \(0.801677\pi\)
\(434\) 12.4853 0.599313
\(435\) 76.7696 + 31.7990i 3.68082 + 1.52464i
\(436\) 7.07107 17.0711i 0.338643 0.817556i
\(437\) −0.242641 0.585786i −0.0116071 0.0280220i
\(438\) 15.3137 + 6.34315i 0.731717 + 0.303087i
\(439\) −18.0000 18.0000i −0.859093 0.859093i 0.132138 0.991231i \(-0.457816\pi\)
−0.991231 + 0.132138i \(0.957816\pi\)
\(440\) 62.6274 2.98564
\(441\) −2.70711 + 2.70711i −0.128910 + 0.128910i
\(442\) 0 0
\(443\) 14.1924 5.87868i 0.674301 0.279304i −0.0191415 0.999817i \(-0.506093\pi\)
0.693442 + 0.720512i \(0.256093\pi\)
\(444\) 26.6274 1.26368
\(445\) 10.3431 24.9706i 0.490312 1.18372i
\(446\) 23.3137 + 23.3137i 1.10394 + 1.10394i
\(447\) 0.343146 0.0162302
\(448\) −5.65685 5.65685i −0.267261 0.267261i
\(449\) −33.4558 −1.57888 −0.789439 0.613828i \(-0.789629\pi\)
−0.789439 + 0.613828i \(0.789629\pi\)
\(450\) 33.1421 + 33.1421i 1.56234 + 1.56234i
\(451\) −11.0711 + 26.7279i −0.521316 + 1.25857i
\(452\) −34.8284 −1.63819
\(453\) 10.2426 4.24264i 0.481241 0.199337i
\(454\) 37.5563 15.5563i 1.76261 0.730096i
\(455\) −4.00000 + 4.00000i −0.187523 + 0.187523i
\(456\) 3.31371i 0.155179i
\(457\) 8.00000 + 8.00000i 0.374224 + 0.374224i 0.869013 0.494789i \(-0.164755\pi\)
−0.494789 + 0.869013i \(0.664755\pi\)
\(458\) −11.3137 4.68629i −0.528655 0.218976i
\(459\) 0 0
\(460\) −4.00000 + 9.65685i −0.186501 + 0.450253i
\(461\) −8.48528 3.51472i −0.395199 0.163697i 0.176229 0.984349i \(-0.443610\pi\)
−0.571428 + 0.820652i \(0.693610\pi\)
\(462\) −22.1421 −1.03015
\(463\) 28.0416i 1.30321i −0.758561 0.651603i \(-0.774097\pi\)
0.758561 0.651603i \(-0.225903\pi\)
\(464\) 13.1716 31.7990i 0.611475 1.47623i
\(465\) 85.2548i 3.95360i
\(466\) 3.65685i 0.169401i
\(467\) 3.34315 + 1.38478i 0.154702 + 0.0640798i 0.458691 0.888596i \(-0.348318\pi\)
−0.303989 + 0.952676i \(0.598318\pi\)
\(468\) 10.8284 4.48528i 0.500544 0.207332i
\(469\) −4.70711 11.3640i −0.217354 0.524739i
\(470\) 17.6569 42.6274i 0.814450 1.96626i
\(471\) −12.0000 12.0000i −0.552931 0.552931i
\(472\) −5.85786 + 14.1421i −0.269630 + 0.650945i
\(473\) −20.7990 + 20.7990i −0.956339 + 0.956339i
\(474\) 14.0000 + 33.7990i 0.643041 + 1.55244i
\(475\) 3.58579 1.48528i 0.164527 0.0681494i
\(476\) 0 0
\(477\) 0.192388 0.464466i 0.00880885 0.0212664i
\(478\) 6.00000 6.00000i 0.274434 0.274434i
\(479\) −29.3137 −1.33938 −0.669689 0.742642i \(-0.733572\pi\)
−0.669689 + 0.742642i \(0.733572\pi\)
\(480\) 38.6274 38.6274i 1.76309 1.76309i
\(481\) −7.79899 −0.355603
\(482\) −23.7990 + 23.7990i −1.08401 + 1.08401i
\(483\) 1.41421 3.41421i 0.0643489 0.155352i
\(484\) −35.2132 35.2132i −1.60060 1.60060i
\(485\) −4.00000 + 1.65685i −0.181631 + 0.0752339i
\(486\) −11.7574 28.3848i −0.533325 1.28756i
\(487\) −0.857864 + 0.857864i −0.0388735 + 0.0388735i −0.726276 0.687403i \(-0.758751\pi\)
0.687403 + 0.726276i \(0.258751\pi\)
\(488\) 3.31371 + 8.00000i 0.150005 + 0.362143i
\(489\) 9.89949 + 9.89949i 0.447671 + 0.447671i
\(490\) 2.00000 4.82843i 0.0903508 0.218126i
\(491\) 6.46447 + 15.6066i 0.291737 + 0.704316i 0.999999 0.00163420i \(-0.000520184\pi\)
−0.708261 + 0.705950i \(0.750520\pi\)
\(492\) 9.65685 + 23.3137i 0.435365 + 1.05106i
\(493\) 0 0
\(494\) 0.970563i 0.0436677i
\(495\) 84.7696i 3.81011i
\(496\) 35.3137 1.58563
\(497\) 6.00000i 0.269137i
\(498\) 12.9706 0.581225
\(499\) 14.5355 + 6.02082i 0.650700 + 0.269529i 0.683519 0.729933i \(-0.260449\pi\)
−0.0328193 + 0.999461i \(0.510449\pi\)
\(500\) −24.9706 10.3431i −1.11672 0.462560i
\(501\) 8.14214 + 19.6569i 0.363764 + 0.878203i
\(502\) −3.75736 1.55635i −0.167699 0.0694633i
\(503\) 5.17157 + 5.17157i 0.230589 + 0.230589i 0.812939 0.582349i \(-0.197866\pi\)
−0.582349 + 0.812939i \(0.697866\pi\)
\(504\) −7.65685 + 7.65685i −0.341063 + 0.341063i
\(505\) 9.65685 9.65685i 0.429724 0.429724i
\(506\) 11.0711 4.58579i 0.492169 0.203863i
\(507\) 25.7279 10.6569i 1.14262 0.473288i
\(508\) 29.9411i 1.32842i
\(509\) 3.31371 8.00000i 0.146878 0.354594i −0.833269 0.552868i \(-0.813534\pi\)
0.980147 + 0.198274i \(0.0635335\pi\)
\(510\) 0 0
\(511\) 4.48528 0.198417
\(512\) −16.0000 16.0000i −0.707107 0.707107i
\(513\) 0.970563 0.0428514
\(514\) 28.1421 + 28.1421i 1.24130 + 1.24130i
\(515\) 20.4853 49.4558i 0.902689 2.17928i
\(516\) 25.6569i 1.12948i
\(517\) −48.8701 + 20.2426i −2.14930 + 0.890270i
\(518\) 6.65685 2.75736i 0.292485 0.121151i
\(519\) −8.48528 + 8.48528i −0.372463 + 0.372463i
\(520\) −11.3137 + 11.3137i −0.496139 + 0.496139i
\(521\) −16.7279 16.7279i −0.732864 0.732864i 0.238323 0.971186i \(-0.423402\pi\)
−0.971186 + 0.238323i \(0.923402\pi\)
\(522\) −43.0416 17.8284i −1.88388 0.780329i
\(523\) −1.00000 2.41421i −0.0437269 0.105566i 0.900507 0.434841i \(-0.143196\pi\)
−0.944234 + 0.329275i \(0.893196\pi\)
\(524\) 11.6569 + 4.82843i 0.509232 + 0.210931i
\(525\) 20.8995 + 8.65685i 0.912129 + 0.377816i
\(526\) 19.3137 0.842118
\(527\) 0 0
\(528\) −62.6274 −2.72551
\(529\) 21.0000i 0.913043i
\(530\) 0.686292i 0.0298106i
\(531\) 19.1421 + 7.92893i 0.830698 + 0.344086i
\(532\) 0.343146 + 0.828427i 0.0148773 + 0.0359169i
\(533\) −2.82843 6.82843i −0.122513 0.295772i
\(534\) −10.3431 + 24.9706i −0.447592 + 1.08058i
\(535\) 16.1421 + 16.1421i 0.697885 + 0.697885i
\(536\) −13.3137 32.1421i −0.575065 1.38833i
\(537\) 21.0711 21.0711i 0.909284 0.909284i
\(538\) 8.34315 + 20.1421i 0.359699 + 0.868389i
\(539\) −5.53553 + 2.29289i −0.238432 + 0.0987619i
\(540\) −11.3137 11.3137i −0.486864 0.486864i
\(541\) 4.87868 11.7782i 0.209751 0.506383i −0.783633 0.621224i \(-0.786636\pi\)
0.993384 + 0.114841i \(0.0366357\pi\)
\(542\) 11.5147 11.5147i 0.494600 0.494600i
\(543\) 36.9706 1.58656
\(544\) 0 0
\(545\) 34.1421 1.46249
\(546\) 4.00000 4.00000i 0.171184 0.171184i
\(547\) −6.77817 + 16.3640i −0.289814 + 0.699672i −0.999991 0.00435101i \(-0.998615\pi\)
0.710177 + 0.704023i \(0.248615\pi\)
\(548\) −30.2843 + 30.2843i −1.29368 + 1.29368i
\(549\) 10.8284 4.48528i 0.462146 0.191427i
\(550\) 28.0711 + 67.7696i 1.19695 + 2.88970i
\(551\) −2.72792 + 2.72792i −0.116213 + 0.116213i
\(552\) 4.00000 9.65685i 0.170251 0.411023i
\(553\) 7.00000 + 7.00000i 0.297670 + 0.297670i
\(554\) −11.8284 + 28.5563i −0.502542 + 1.21324i
\(555\) 18.8284 + 45.4558i 0.799222 + 1.92949i
\(556\) −15.6569 + 6.48528i −0.663999 + 0.275037i
\(557\) 20.1924 + 8.36396i 0.855579 + 0.354392i 0.766977 0.641675i \(-0.221760\pi\)
0.0886020 + 0.996067i \(0.471760\pi\)
\(558\) 47.7990i 2.02349i
\(559\) 7.51472i 0.317839i
\(560\) 5.65685 13.6569i 0.239046 0.577107i
\(561\) 0 0
\(562\) 2.68629 0.113314
\(563\) 14.3137 + 5.92893i 0.603251 + 0.249875i 0.663340 0.748318i \(-0.269138\pi\)
−0.0600889 + 0.998193i \(0.519138\pi\)
\(564\) −17.6569 + 42.6274i −0.743488 + 1.79494i
\(565\) −24.6274 59.4558i −1.03608 2.50133i
\(566\) −18.2426 7.55635i −0.766795 0.317617i
\(567\) −4.12132 4.12132i −0.173079 0.173079i
\(568\) 16.9706i 0.712069i
\(569\) 19.7990 19.7990i 0.830017 0.830017i −0.157502 0.987519i \(-0.550344\pi\)
0.987519 + 0.157502i \(0.0503440\pi\)
\(570\) −5.65685 + 2.34315i −0.236940 + 0.0981436i
\(571\) −7.87868 + 3.26346i −0.329712 + 0.136571i −0.541398 0.840766i \(-0.682105\pi\)
0.211685 + 0.977338i \(0.432105\pi\)
\(572\) 18.3431 0.766965
\(573\) −3.07107 + 7.41421i −0.128296 + 0.309733i
\(574\) 4.82843 + 4.82843i 0.201535 + 0.201535i
\(575\) −12.2426 −0.510553
\(576\) −21.6569 + 21.6569i −0.902369 + 0.902369i
\(577\) 4.14214 0.172439 0.0862197 0.996276i \(-0.472521\pi\)
0.0862197 + 0.996276i \(0.472521\pi\)
\(578\) −17.0000 17.0000i −0.707107 0.707107i
\(579\) −1.41421 + 3.41421i −0.0587727 + 0.141890i
\(580\) 63.5980 2.64076
\(581\) 3.24264 1.34315i 0.134527 0.0557231i
\(582\) 4.00000 1.65685i 0.165805 0.0686788i
\(583\) 0.556349 0.556349i 0.0230416 0.0230416i
\(584\) 12.6863 0.524962
\(585\) 15.3137 + 15.3137i 0.633144 + 0.633144i
\(586\) −20.9706 8.68629i −0.866286 0.358827i
\(587\) −14.7574 35.6274i −0.609101 1.47050i −0.863979 0.503528i \(-0.832035\pi\)
0.254878 0.966973i \(-0.417965\pi\)
\(588\) −2.00000 + 4.82843i −0.0824786 + 0.199121i
\(589\) −3.65685 1.51472i −0.150678 0.0624129i
\(590\) −28.2843 −1.16445
\(591\) 35.6569i 1.46673i
\(592\) 18.8284 7.79899i 0.773844 0.320537i
\(593\) 23.1716i 0.951542i −0.879569 0.475771i \(-0.842169\pi\)
0.879569 0.475771i \(-0.157831\pi\)
\(594\) 18.3431i 0.752628i
\(595\) 0 0
\(596\) 0.242641 0.100505i 0.00993895 0.00411685i
\(597\) 1.31371 + 3.17157i 0.0537665 + 0.129804i
\(598\) −1.17157 + 2.82843i −0.0479092 + 0.115663i
\(599\) −19.3137 19.3137i −0.789137 0.789137i 0.192216 0.981353i \(-0.438433\pi\)
−0.981353 + 0.192216i \(0.938433\pi\)
\(600\) 59.1127 + 24.4853i 2.41327 + 0.999607i
\(601\) 1.31371 1.31371i 0.0535873 0.0535873i −0.679805 0.733393i \(-0.737936\pi\)
0.733393 + 0.679805i \(0.237936\pi\)
\(602\) 2.65685 + 6.41421i 0.108285 + 0.261424i
\(603\) −43.5061 + 18.0208i −1.77171 + 0.733864i
\(604\) 6.00000 6.00000i 0.244137 0.244137i
\(605\) 35.2132 85.0122i 1.43162 3.45624i
\(606\) −9.65685 + 9.65685i −0.392283 + 0.392283i
\(607\) −26.3431 −1.06924 −0.534618 0.845094i \(-0.679544\pi\)
−0.534618 + 0.845094i \(0.679544\pi\)
\(608\) 0.970563 + 2.34315i 0.0393615 + 0.0950271i
\(609\) −22.4853 −0.911150
\(610\) −11.3137 + 11.3137i −0.458079 + 0.458079i
\(611\) 5.17157 12.4853i 0.209219 0.505100i
\(612\) 0 0
\(613\) −33.7487 + 13.9792i −1.36310 + 0.564614i −0.939908 0.341427i \(-0.889090\pi\)
−0.423190 + 0.906041i \(0.639090\pi\)
\(614\) 17.0711 + 41.2132i 0.688932 + 1.66323i
\(615\) −32.9706 + 32.9706i −1.32950 + 1.32950i
\(616\) −15.6569 + 6.48528i −0.630833 + 0.261299i
\(617\) −6.97056 6.97056i −0.280624 0.280624i 0.552734 0.833358i \(-0.313585\pi\)
−0.833358 + 0.552734i \(0.813585\pi\)
\(618\) −20.4853 + 49.4558i −0.824039 + 1.98941i
\(619\) 2.89949 + 7.00000i 0.116541 + 0.281354i 0.971377 0.237544i \(-0.0763425\pi\)
−0.854836 + 0.518898i \(0.826342\pi\)
\(620\) 24.9706 + 60.2843i 1.00284 + 2.42107i
\(621\) −2.82843 1.17157i −0.113501 0.0470136i
\(622\) 38.6274i 1.54882i
\(623\) 7.31371i 0.293018i
\(624\) 11.3137 11.3137i 0.452911 0.452911i
\(625\) 6.65685i 0.266274i
\(626\) 9.85786 0.394000
\(627\) 6.48528 + 2.68629i 0.258997 + 0.107280i
\(628\) −12.0000 4.97056i −0.478852 0.198347i
\(629\) 0 0
\(630\) −18.4853 7.65685i −0.736471 0.305056i
\(631\) −11.7574 11.7574i −0.468053 0.468053i 0.433230 0.901283i \(-0.357374\pi\)
−0.901283 + 0.433230i \(0.857374\pi\)
\(632\) 19.7990 + 19.7990i 0.787562 + 0.787562i
\(633\) 8.24264 8.24264i 0.327616 0.327616i
\(634\) −14.8995 + 6.17157i −0.591735 + 0.245104i
\(635\) −51.1127 + 21.1716i −2.02835 + 0.840168i
\(636\) 0.686292i 0.0272132i
\(637\) 0.585786 1.41421i 0.0232097 0.0560332i
\(638\) −51.5563 51.5563i −2.04114 2.04114i
\(639\) 22.9706 0.908701
\(640\) 16.0000 38.6274i 0.632456 1.52688i
\(641\) 38.1838 1.50817 0.754084 0.656778i \(-0.228081\pi\)
0.754084 + 0.656778i \(0.228081\pi\)
\(642\) −16.1421 16.1421i −0.637079 0.637079i
\(643\) 12.5563 30.3137i 0.495174 1.19546i −0.456881 0.889528i \(-0.651033\pi\)
0.952055 0.305928i \(-0.0989667\pi\)
\(644\) 2.82843i 0.111456i
\(645\) −43.7990 + 18.1421i −1.72458 + 0.714346i
\(646\) 0 0
\(647\) 19.5563 19.5563i 0.768839 0.768839i −0.209063 0.977902i \(-0.567041\pi\)
0.977902 + 0.209063i \(0.0670413\pi\)
\(648\) −11.6569 11.6569i −0.457924 0.457924i
\(649\) 22.9289 + 22.9289i 0.900039 + 0.900039i
\(650\) −17.3137 7.17157i −0.679100 0.281292i
\(651\) −8.82843 21.3137i −0.346013 0.835350i
\(652\) 9.89949 + 4.10051i 0.387694 + 0.160588i
\(653\) −8.77817 3.63604i −0.343517 0.142289i 0.204254 0.978918i \(-0.434523\pi\)
−0.547770 + 0.836629i \(0.684523\pi\)
\(654\) −34.1421 −1.33506
\(655\) 23.3137i 0.910942i
\(656\) 13.6569 + 13.6569i 0.533211 + 0.533211i
\(657\) 17.1716i 0.669927i
\(658\) 12.4853i 0.486727i
\(659\) −25.4350 10.5355i −0.990808 0.410406i −0.172390 0.985029i \(-0.555149\pi\)
−0.818418 + 0.574623i \(0.805149\pi\)
\(660\) −44.2843 106.912i −1.72376 4.16153i
\(661\) 12.8701 + 31.0711i 0.500587 + 1.20852i 0.949165 + 0.314780i \(0.101931\pi\)
−0.448577 + 0.893744i \(0.648069\pi\)
\(662\) 7.24264 17.4853i 0.281493 0.679585i
\(663\) 0 0
\(664\) 9.17157 3.79899i 0.355926 0.147429i
\(665\) −1.17157 + 1.17157i −0.0454316 + 0.0454316i
\(666\) −10.5563 25.4853i −0.409050 0.987535i
\(667\) 11.2426 4.65685i 0.435317 0.180314i
\(668\) 11.5147 + 11.5147i 0.445518 + 0.445518i
\(669\) 23.3137 56.2843i 0.901360 2.17608i
\(670\) 45.4558 45.4558i 1.75611 1.75611i
\(671\) 18.3431 0.708129
\(672\) −5.65685 + 13.6569i −0.218218 + 0.526825i
\(673\) 25.4558 0.981251 0.490625 0.871371i \(-0.336768\pi\)
0.490625 + 0.871371i \(0.336768\pi\)
\(674\) −7.27208 + 7.27208i −0.280110 + 0.280110i
\(675\) 7.17157 17.3137i 0.276034 0.666405i
\(676\) 15.0711 15.0711i 0.579656 0.579656i
\(677\) 44.6274 18.4853i 1.71517 0.710447i 0.715238 0.698881i \(-0.246318\pi\)
0.999933 0.0115660i \(-0.00368164\pi\)
\(678\) 24.6274 + 59.4558i 0.945810 + 2.28339i
\(679\) 0.828427 0.828427i 0.0317921 0.0317921i
\(680\) 0 0
\(681\) −53.1127 53.1127i −2.03528 2.03528i
\(682\) 28.6274 69.1127i 1.09620 2.64646i
\(683\) −3.63604 8.77817i −0.139129 0.335888i 0.838922 0.544251i \(-0.183186\pi\)
−0.978051 + 0.208364i \(0.933186\pi\)
\(684\) 3.17157 1.31371i 0.121268 0.0502309i
\(685\) −73.1127 30.2843i −2.79349 1.15710i
\(686\) 1.41421i 0.0539949i
\(687\) 22.6274i 0.863290i
\(688\) 7.51472 + 18.1421i 0.286496 + 0.691662i
\(689\) 0.201010i 0.00765788i
\(690\) 19.3137 0.735260
\(691\) −2.89949 1.20101i −0.110302 0.0456886i 0.326850 0.945076i \(-0.394013\pi\)
−0.437152 + 0.899388i \(0.644013\pi\)
\(692\) −3.51472 + 8.48528i −0.133610 + 0.322562i
\(693\) 8.77817 + 21.1924i 0.333455 + 0.805032i
\(694\) 3.00000 + 1.24264i 0.113878 + 0.0471700i
\(695\) −22.1421 22.1421i −0.839899 0.839899i
\(696\) −63.5980 −2.41068
\(697\) 0 0
\(698\) 11.3137 4.68629i 0.428230 0.177379i
\(699\) 6.24264 2.58579i 0.236118 0.0978034i
\(700\) 17.3137 0.654397
\(701\) −3.22183 + 7.77817i −0.121687 + 0.293778i −0.972971 0.230927i \(-0.925824\pi\)
0.851284 + 0.524704i \(0.175824\pi\)
\(702\) −3.31371 3.31371i −0.125068 0.125068i
\(703\) −2.28427 −0.0861529
\(704\) −44.2843 + 18.3431i −1.66903 + 0.691333i
\(705\) −85.2548 −3.21088
\(706\) −27.4558 27.4558i −1.03331 1.03331i
\(707\) −1.41421 + 3.41421i −0.0531870 + 0.128405i
\(708\) 28.2843 1.06299
\(709\) −9.46447 + 3.92031i −0.355445 + 0.147230i −0.553259 0.833009i \(-0.686616\pi\)
0.197813 + 0.980240i \(0.436616\pi\)
\(710\) −28.9706 + 12.0000i −1.08725 + 0.450352i
\(711\) 26.7990 26.7990i 1.00504 1.00504i
\(712\) 20.6863i 0.775252i
\(713\) 8.82843 + 8.82843i 0.330627 + 0.330627i
\(714\) 0 0
\(715\) 12.9706 + 31.3137i 0.485072 + 1.17107i
\(716\) 8.72792 21.0711i 0.326178 0.787463i
\(717\) −14.4853 6.00000i −0.540963 0.224074i
\(718\) −23.9411 −0.893475
\(719\) 10.6863i 0.398531i −0.979945 0.199266i \(-0.936144\pi\)
0.979945 0.199266i \(-0.0638557\pi\)
\(720\) −52.2843 21.6569i −1.94852 0.807103i
\(721\) 14.4853i 0.539460i
\(722\) 26.5858i 0.989421i
\(723\) 57.4558 + 23.7990i 2.13681 + 0.885094i
\(724\) 26.1421 10.8284i 0.971565 0.402435i
\(725\) 28.5061 + 68.8198i 1.05869 + 2.55590i
\(726\) −35.2132 + 85.0122i −1.30688 + 3.15510i
\(727\) −23.2132 23.2132i −0.860930 0.860930i 0.130516 0.991446i \(-0.458337\pi\)
−0.991446 + 0.130516i \(0.958337\pi\)
\(728\) 1.65685 4.00000i 0.0614071 0.148250i
\(729\) −27.7782 + 27.7782i −1.02882 + 1.02882i
\(730\) 8.97056 + 21.6569i 0.332015 + 0.801556i
\(731\) 0 0
\(732\) 11.3137 11.3137i 0.418167 0.418167i
\(733\) −3.85786 + 9.31371i −0.142493 + 0.344010i −0.978973 0.203988i \(-0.934610\pi\)
0.836480 + 0.547998i \(0.184610\pi\)
\(734\) 12.4853 12.4853i 0.460840 0.460840i
\(735\) −9.65685 −0.356198
\(736\) 8.00000i 0.294884i
\(737\) −73.6985 −2.71472
\(738\) 18.4853 18.4853i 0.680453 0.680453i
\(739\) −16.1924 + 39.0919i −0.595647 + 1.43802i 0.282331 + 0.959317i \(0.408892\pi\)
−0.877978 + 0.478701i \(0.841108\pi\)
\(740\) 26.6274 + 26.6274i 0.978843 + 0.978843i
\(741\) −1.65685 + 0.686292i −0.0608661 + 0.0252115i
\(742\) −0.0710678 0.171573i −0.00260898 0.00629864i
\(743\) −1.48528 + 1.48528i −0.0544897 + 0.0544897i −0.733827 0.679337i \(-0.762268\pi\)
0.679337 + 0.733827i \(0.262268\pi\)
\(744\) −24.9706 60.2843i −0.915465 2.21013i
\(745\) 0.343146 + 0.343146i 0.0125719 + 0.0125719i
\(746\) 10.4558 25.2426i 0.382816 0.924199i
\(747\) −5.14214 12.4142i −0.188141 0.454212i
\(748\) 0 0
\(749\) −5.70711 2.36396i −0.208533 0.0863773i
\(750\) 49.9411i 1.82359i
\(751\) 26.2843i 0.959127i −0.877507 0.479563i \(-0.840795\pi\)
0.877507 0.479563i \(-0.159205\pi\)
\(752\) 35.3137i 1.28776i
\(753\) 7.51472i 0.273852i
\(754\) 18.6274 0.678371
\(755\) 14.4853 + 6.00000i 0.527173 + 0.218362i
\(756\) 4.00000 + 1.65685i 0.145479 + 0.0602592i
\(757\) 3.46447 + 8.36396i 0.125918 + 0.303993i 0.974250 0.225472i \(-0.0723925\pi\)
−0.848331 + 0.529466i \(0.822392\pi\)
\(758\) 27.2426 + 11.2843i 0.989497 + 0.409863i
\(759\) −15.6569 15.6569i −0.568308 0.568308i
\(760\) −3.31371 + 3.31371i −0.120201 + 0.120201i
\(761\) −7.41421 + 7.41421i −0.268765 + 0.268765i −0.828602 0.559837i \(-0.810864\pi\)
0.559837 + 0.828602i \(0.310864\pi\)
\(762\) 51.1127 21.1716i 1.85162 0.766965i
\(763\) −8.53553 + 3.53553i −0.309007 + 0.127995i
\(764\) 6.14214i 0.222215i
\(765\) 0 0
\(766\) 12.8284 + 12.8284i 0.463510 + 0.463510i
\(767\) −8.28427 −0.299128
\(768\) −16.0000 + 38.6274i −0.577350 + 1.39385i
\(769\) 45.9411 1.65668 0.828340 0.560226i \(-0.189286\pi\)
0.828340 + 0.560226i \(0.189286\pi\)
\(770\) −22.1421 22.1421i −0.797947 0.797947i
\(771\) 28.1421 67.9411i 1.01351 2.44684i
\(772\) 2.82843i 0.101797i
\(773\) −0.828427 + 0.343146i −0.0297965 + 0.0123421i −0.397532 0.917588i \(-0.630133\pi\)
0.367735 + 0.929930i \(0.380133\pi\)
\(774\) 24.5563 10.1716i 0.882660 0.365610i
\(775\) −54.0416 + 54.0416i −1.94123 + 1.94123i
\(776\) 2.34315 2.34315i 0.0841140 0.0841140i
\(777\) −9.41421 9.41421i −0.337733 0.337733i
\(778\) −17.0000 7.04163i −0.609480 0.252455i
\(779\) −0.828427 2.00000i −0.0296815 0.0716574i
\(780\) 27.3137 + 11.3137i 0.977988 + 0.405096i
\(781\) 33.2132 + 13.7574i 1.18846 + 0.492277i
\(782\) 0 0
\(783\) 18.6274i 0.665690i
\(784\) 4.00000i 0.142857i
\(785\) 24.0000i 0.856597i
\(786\) 23.3137i 0.831572i
\(787\) 5.24264 + 2.17157i 0.186880 + 0.0774082i 0.474161 0.880438i \(-0.342751\pi\)
−0.287281 + 0.957846i \(0.592751\pi\)
\(788\) 10.4437 + 25.2132i 0.372040 + 0.898183i
\(789\) −13.6569 32.9706i −0.486197 1.17378i
\(790\) −19.7990 + 47.7990i −0.704416 + 1.70061i
\(791\) 12.3137 + 12.3137i 0.437825 + 0.437825i
\(792\) 24.8284 + 59.9411i 0.882240 + 2.12992i
\(793\) −3.31371 + 3.31371i −0.117673 + 0.117673i
\(794\) 0.970563 + 2.34315i 0.0344440 + 0.0831551i
\(795\) 1.17157 0.485281i 0.0415514 0.0172112i
\(796\) 1.85786 + 1.85786i 0.0658503 + 0.0658503i
\(797\) −19.5563 + 47.2132i −0.692721 + 1.67238i 0.0465029 + 0.998918i \(0.485192\pi\)
−0.739224 + 0.673459i \(0.764808\pi\)
\(798\) 1.17157 1.17157i 0.0414732 0.0414732i
\(799\) 0 0
\(800\) 48.9706 1.73137
\(801\) 28.0000 0.989331
\(802\) 32.2426 32.2426i 1.13853 1.13853i
\(803\) 10.2843 24.8284i 0.362924 0.876176i
\(804\) −45.4558 + 45.4558i −1.60310 + 1.60310i
\(805\) 4.82843 2.00000i 0.170180 0.0704907i
\(806\) 7.31371 + 17.6569i 0.257614 + 0.621936i
\(807\) 28.4853 28.4853i 1.00273 1.00273i
\(808\) −4.00000 + 9.65685i −0.140720 + 0.339727i
\(809\) −25.4558 25.4558i −0.894980 0.894980i 0.100007 0.994987i \(-0.468114\pi\)
−0.994987 + 0.100007i \(0.968114\pi\)
\(810\) 11.6569 28.1421i 0.409580 0.988814i
\(811\) 19.3848 + 46.7990i 0.680692 + 1.64333i 0.762739 + 0.646706i \(0.223854\pi\)
−0.0820475 + 0.996628i \(0.526146\pi\)
\(812\) −15.8995 + 6.58579i −0.557963 + 0.231116i
\(813\) −27.7990 11.5147i −0.974953 0.403839i
\(814\) 43.1716i 1.51316i
\(815\) 19.7990i 0.693528i
\(816\) 0 0
\(817\) 2.20101i 0.0770036i
\(818\) −31.5147 −1.10189
\(819\) −5.41421 2.24264i −0.189188 0.0783642i
\(820\) −13.6569 + 32.9706i −0.476918 + 1.15138i
\(821\) 8.60660 + 20.7782i 0.300372 + 0.725163i 0.999944 + 0.0106005i \(0.00337432\pi\)
−0.699571 + 0.714563i \(0.746626\pi\)
\(822\) 73.1127 + 30.2843i 2.55010 + 1.05629i
\(823\) 27.1127 + 27.1127i 0.945089 + 0.945089i 0.998569 0.0534797i \(-0.0170312\pi\)
−0.0534797 + 0.998569i \(0.517031\pi\)
\(824\) 40.9706i 1.42728i
\(825\) 95.8406 95.8406i 3.33674 3.33674i
\(826\) 7.07107 2.92893i 0.246034 0.101911i
\(827\) 4.53553 1.87868i 0.157716 0.0653281i −0.302429 0.953172i \(-0.597797\pi\)
0.460145 + 0.887844i \(0.347797\pi\)
\(828\) −10.8284 −0.376314
\(829\) −11.0711 + 26.7279i −0.384514 + 0.928299i 0.606566 + 0.795033i \(0.292547\pi\)
−0.991080 + 0.133266i \(0.957453\pi\)
\(830\) 12.9706 + 12.9706i 0.450215 + 0.450215i
\(831\) 57.1127 1.98122
\(832\) 4.68629 11.3137i 0.162468 0.392232i
\(833\) 0 0
\(834\) 22.1421 + 22.1421i 0.766719 + 0.766719i
\(835\) −11.5147 + 27.7990i −0.398483 + 0.962024i
\(836\) 5.37258 0.185815
\(837\) −17.6569 + 7.31371i −0.610310 + 0.252799i
\(838\) −4.24264 + 1.75736i −0.146560 + 0.0607070i
\(839\) 28.5858 28.5858i 0.986891 0.986891i −0.0130242 0.999915i \(-0.504146\pi\)
0.999915 + 0.0130242i \(0.00414586\pi\)
\(840\) −27.3137 −0.942412
\(841\) −31.8492 31.8492i −1.09825 1.09825i
\(842\) −33.3848 13.8284i −1.15052 0.476559i
\(843\) −1.89949 4.58579i −0.0654221 0.157943i
\(844\) 3.41421 8.24264i 0.117522 0.283723i
\(845\) 36.3848 + 15.0711i 1.25167 + 0.518460i
\(846\) 47.7990 1.64336
\(847\) 24.8995i 0.855557i
\(848\) −0.201010 0.485281i −0.00690272 0.0166646i
\(849\) 36.4853i 1.25217i
\(850\) 0 0
\(851\) 6.65685 + 2.75736i 0.228194 + 0.0945211i
\(852\) 28.9706 12.0000i 0.992515 0.411113i
\(853\) −20.6863 49.9411i −0.708285 1.70995i −0.704242 0.709960i \(-0.748713\pi\)
−0.00404287 0.999992i \(-0.501287\pi\)
\(854\) 1.65685 4.00000i 0.0566964 0.136877i
\(855\) 4.48528 + 4.48528i 0.153393 + 0.153393i
\(856\) −16.1421 6.68629i −0.551727 0.228533i
\(857\) −32.3848 + 32.3848i −1.10624 + 1.10624i −0.112603 + 0.993640i \(0.535919\pi\)
−0.993640 + 0.112603i \(0.964081\pi\)
\(858\) −12.9706 31.3137i −0.442808 1.06903i
\(859\) 13.5858 5.62742i 0.463541 0.192005i −0.138675 0.990338i \(-0.544284\pi\)
0.602216 + 0.798333i \(0.294284\pi\)
\(860\) −25.6569 + 25.6569i −0.874891 + 0.874891i
\(861\) 4.82843 11.6569i 0.164552 0.397265i
\(862\) 21.6569 21.6569i 0.737635 0.737635i
\(863\) −29.6985 −1.01095 −0.505474 0.862842i \(-0.668682\pi\)
−0.505474 + 0.862842i \(0.668682\pi\)
\(864\) 11.3137 + 4.68629i 0.384900 + 0.159431i
\(865\) −16.9706 −0.577016
\(866\) 24.2843 24.2843i 0.825213 0.825213i
\(867\) −17.0000 + 41.0416i −0.577350 + 1.39385i
\(868\) −12.4853 12.4853i −0.423778 0.423778i
\(869\) 54.7990 22.6985i 1.85893 0.769993i
\(870\) −44.9706 108.569i −1.52464 3.68082i
\(871\) 13.3137 13.3137i 0.451118 0.451118i
\(872\) −24.1421 + 10.0000i −0.817556 + 0.338643i
\(873\) −3.17157 3.17157i −0.107341 0.107341i
\(874\) −0.343146 + 0.828427i −0.0116071 + 0.0280220i
\(875\) 5.17157 + 12.4853i 0.174831 + 0.422080i
\(876\) −8.97056 21.6569i −0.303087 0.731717i
\(877\) −3.19239 1.32233i −0.107799 0.0446519i 0.328132 0.944632i \(-0.393581\pi\)
−0.435931 + 0.899980i \(0.643581\pi\)
\(878\) 36.0000i 1.21494i
\(879\) 41.9411i 1.41464i
\(880\) −62.6274 62.6274i −2.11117 2.11117i
\(881\) 23.4558i 0.790247i −0.918628 0.395124i \(-0.870702\pi\)
0.918628 0.395124i \(-0.129298\pi\)
\(882\) 5.41421 0.182306
\(883\) −31.3345 12.9792i −1.05449 0.436784i −0.212998 0.977053i \(-0.568323\pi\)
−0.841493 + 0.540268i \(0.818323\pi\)
\(884\) 0 0
\(885\) 20.0000 + 48.2843i 0.672293 + 1.62306i
\(886\) −20.0711 8.31371i −0.674301 0.279304i
\(887\) 15.2721 + 15.2721i 0.512786 + 0.512786i 0.915379 0.402593i \(-0.131891\pi\)
−0.402593 + 0.915379i \(0.631891\pi\)
\(888\) −26.6274 26.6274i −0.893558 0.893558i
\(889\) 10.5858 10.5858i 0.355036 0.355036i
\(890\) −35.3137 + 14.6274i −1.18372 + 0.490312i
\(891\) −32.2635 + 13.3640i −1.08087 + 0.447710i
\(892\) 46.6274i 1.56120i
\(893\) 1.51472 3.65685i 0.0506881 0.122372i
\(894\) −0.343146 0.343146i −0.0114765 0.0114765i
\(895\) 42.1421 1.40866
\(896\) 11.3137i 0.377964i
\(897\) 5.65685 0.188877
\(898\) 33.4558 + 33.4558i 1.11644 + 1.11644i
\(899\) 29.0711 70.1838i 0.969574 2.34076i
\(900\) 66.2843i 2.20948i
\(901\) 0 0
\(902\) 37.7990 15.6569i 1.25857 0.521316i
\(903\) 9.07107 9.07107i 0.301866 0.301866i
\(904\) 34.8284 + 34.8284i 1.15838 + 1.15838i
\(905\) 36.9706 + 36.9706i 1.22894 + 1.22894i
\(906\) −14.4853 6.00000i −0.481241 0.199337i
\(907\) 6.77817 + 16.3640i 0.225066 + 0.543356i 0.995564 0.0940854i \(-0.0299927\pi\)
−0.770499 + 0.637442i \(0.779993\pi\)
\(908\) −53.1127 22.0000i −1.76261 0.730096i
\(909\) 13.0711 + 5.41421i 0.433540 + 0.179578i
\(910\) 8.00000 0.265197
\(911\) 41.3137i 1.36878i −0.729114 0.684392i \(-0.760068\pi\)
0.729114 0.684392i \(-0.239932\pi\)
\(912\) 3.31371 3.31371i 0.109728 0.109728i
\(913\) 21.0294i 0.695973i
\(914\) 16.0000i 0.529233i
\(915\) 27.3137 + 11.3137i 0.902963 + 0.374020i
\(916\) 6.62742 + 16.0000i 0.218976 + 0.528655i
\(917\) −2.41421 5.82843i −0.0797244 0.192472i
\(918\) 0 0
\(919\) −23.0711 23.0711i −0.761044 0.761044i 0.215467 0.976511i \(-0.430873\pi\)
−0.976511 + 0.215467i \(0.930873\pi\)
\(920\) 13.6569 5.65685i 0.450253 0.186501i
\(921\) 58.2843 58.2843i 1.92053 1.92053i
\(922\) 4.97056 + 12.0000i 0.163697 + 0.395199i
\(923\) −8.48528 + 3.51472i −0.279296 + 0.115688i
\(924\) 22.1421 + 22.1421i 0.728423 + 0.728423i
\(925\) −16.8787 + 40.7487i −0.554968 + 1.33981i
\(926\) −28.0416 + 28.0416i −0.921505 + 0.921505i
\(927\) 55.4558 1.82141
\(928\) −44.9706 + 18.6274i −1.47623 + 0.611475i
\(929\) −25.9411 −0.851101 −0.425550 0.904935i \(-0.639919\pi\)
−0.425550 + 0.904935i \(0.639919\pi\)
\(930\) 85.2548 85.2548i 2.79562 2.79562i
\(931\) 0.171573 0.414214i 0.00562307 0.0135753i
\(932\) 3.65685 3.65685i 0.119784 0.119784i
\(933\) −65.9411 + 27.3137i −2.15882 + 0.894211i
\(934\) −1.95837 4.72792i −0.0640798 0.154702i
\(935\) 0 0
\(936\) −15.3137 6.34315i −0.500544 0.207332i
\(937\) −8.14214 8.14214i −0.265992 0.265992i 0.561491 0.827483i \(-0.310228\pi\)
−0.827483 + 0.561491i \(0.810228\pi\)
\(938\) −6.65685 + 16.0711i −0.217354 + 0.524739i
\(939\) −6.97056 16.8284i −0.227476 0.549175i
\(940\) −60.2843 + 24.9706i −1.96626 + 0.814450i
\(941\) −32.9706 13.6569i −1.07481 0.445201i −0.226124 0.974099i \(-0.572605\pi\)
−0.848686 + 0.528898i \(0.822605\pi\)
\(942\) 24.0000i 0.781962i
\(943\) 6.82843i 0.222364i
\(944\) 20.0000 8.28427i 0.650945 0.269630i
\(945\) 8.00000i 0.260240i
\(946\) 41.5980 1.35247
\(947\) 38.7487 + 16.0503i 1.25916 + 0.521563i 0.909653 0.415369i \(-0.136347\pi\)
0.349512 + 0.936932i \(0.386347\pi\)
\(948\) 19.7990 47.7990i 0.643041 1.55244i
\(949\) 2.62742 + 6.34315i 0.0852896 + 0.205907i
\(950\) −5.07107 2.10051i −0.164527 0.0681494i
\(951\) 21.0711 + 21.0711i 0.683276 + 0.683276i
\(952\) 0 0
\(953\) 27.9706 27.9706i 0.906055 0.906055i −0.0898958 0.995951i \(-0.528653\pi\)
0.995951 + 0.0898958i \(0.0286534\pi\)
\(954\) −0.656854 + 0.272078i −0.0212664 + 0.00880885i
\(955\) −10.4853 + 4.34315i −0.339296 + 0.140541i
\(956\) −12.0000 −0.388108
\(957\) −51.5563 + 124.468i −1.66658 + 4.02348i
\(958\) 29.3137 + 29.3137i 0.947083 + 0.947083i
\(959\) 21.4142 0.691501
\(960\) −77.2548 −2.49339
\(961\) 46.9411 1.51423
\(962\) 7.79899 + 7.79899i 0.251450 + 0.251450i
\(963\) −9.05025 + 21.8492i −0.291640 + 0.704082i
\(964\) 47.5980 1.53303
\(965\) −4.82843 + 2.00000i −0.155433 + 0.0643823i
\(966\) −4.82843 + 2.00000i −0.155352 + 0.0643489i
\(967\) 18.6569 18.6569i 0.599964 0.599964i −0.340339 0.940303i \(-0.610542\pi\)
0.940303 + 0.340339i \(0.110542\pi\)
\(968\) 70.4264i 2.26359i
\(969\) 0 0
\(970\) 5.65685 + 2.34315i 0.181631 + 0.0752339i
\(971\) 4.55635 + 11.0000i 0.146220 + 0.353007i 0.979973 0.199131i \(-0.0638121\pi\)
−0.833753 + 0.552138i \(0.813812\pi\)
\(972\) −16.6274 + 40.1421i −0.533325 + 1.28756i
\(973\) 7.82843 + 3.24264i 0.250968 + 0.103954i
\(974\) 1.71573 0.0549755
\(975\) 34.6274i 1.10896i
\(976\) 4.68629 11.3137i 0.150005 0.362143i
\(977\) 58.8284i 1.88209i 0.338284 + 0.941044i \(0.390154\pi\)
−0.338284 + 0.941044i \(0.609846\pi\)
\(978\) 19.7990i 0.633102i
\(979\) 40.4853 + 16.7696i 1.29392 + 0.535957i
\(980\) −6.82843 + 2.82843i −0.218126 + 0.0903508i
\(981\) 13.5355 + 32.6777i 0.432156 + 1.04332i
\(982\) 9.14214 22.0711i 0.291737 0.704316i
\(983\) −3.41421 3.41421i −0.108897 0.108897i 0.650559 0.759456i \(-0.274535\pi\)
−0.759456 + 0.650559i \(0.774535\pi\)
\(984\) 13.6569 32.9706i 0.435365 1.05106i
\(985\) −35.6569 + 35.6569i −1.13612 + 1.13612i
\(986\) 0 0
\(987\) 21.3137 8.82843i 0.678423 0.281012i
\(988\) −0.970563 + 0.970563i −0.0308777 + 0.0308777i
\(989\) −2.65685 + 6.41421i −0.0844831 + 0.203960i
\(990\) −84.7696 + 84.7696i −2.69415 + 2.69415i
\(991\) −26.1838 −0.831755 −0.415877 0.909421i \(-0.636525\pi\)
−0.415877 + 0.909421i \(0.636525\pi\)
\(992\) −35.3137 35.3137i −1.12121 1.12121i
\(993\) −34.9706 −1.10976
\(994\) 6.00000 6.00000i 0.190308 0.190308i
\(995\) −1.85786 + 4.48528i −0.0588983 + 0.142193i
\(996\) −12.9706 12.9706i −0.410988 0.410988i
\(997\) 10.7279 4.44365i 0.339757 0.140732i −0.206280 0.978493i \(-0.566136\pi\)
0.546037 + 0.837761i \(0.316136\pi\)
\(998\) −8.51472 20.5563i −0.269529 0.650700i
\(999\) −7.79899 + 7.79899i −0.246749 + 0.246749i
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 224.2.u.a.141.1 4
4.3 odd 2 896.2.u.a.785.1 4
32.5 even 8 inner 224.2.u.a.197.1 yes 4
32.27 odd 8 896.2.u.a.113.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
224.2.u.a.141.1 4 1.1 even 1 trivial
224.2.u.a.197.1 yes 4 32.5 even 8 inner
896.2.u.a.113.1 4 32.27 odd 8
896.2.u.a.785.1 4 4.3 odd 2