Properties

Label 950.2.q.c.943.1
Level $950$
Weight $2$
Character 950.943
Analytic conductor $7.586$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [950,2,Mod(107,950)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(950, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([3, 10]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("950.107");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 950.q (of order \(12\), 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: \(7.58578819202\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{12})\)
Coefficient field: \(\Q(\zeta_{24})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - x^{4} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 943.1
Root \(0.258819 - 0.965926i\) of defining polynomial
Character \(\chi\) \(=\) 950.943
Dual form 950.2.q.c.407.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.258819 + 0.965926i) q^{2} +(-0.965926 - 0.258819i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(0.500000 - 0.866025i) q^{6} +(-2.44949 + 2.44949i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-1.73205 - 1.00000i) q^{9} +O(q^{10})\) \(q+(-0.258819 + 0.965926i) q^{2} +(-0.965926 - 0.258819i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(0.500000 - 0.866025i) q^{6} +(-2.44949 + 2.44949i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-1.73205 - 1.00000i) q^{9} +(0.707107 + 0.707107i) q^{12} +(0.517638 + 1.93185i) q^{13} +(-1.73205 - 3.00000i) q^{14} +(0.500000 + 0.866025i) q^{16} +(-1.67303 - 0.448288i) q^{17} +(1.41421 - 1.41421i) q^{18} +(2.59808 - 3.50000i) q^{19} +(3.00000 - 1.73205i) q^{21} +(3.34607 - 0.896575i) q^{23} +(-0.866025 + 0.500000i) q^{24} -2.00000 q^{26} +(3.53553 + 3.53553i) q^{27} +(3.34607 - 0.896575i) q^{28} +(-1.73205 + 3.00000i) q^{29} -10.3923i q^{31} +(-0.965926 + 0.258819i) q^{32} +(0.866025 - 1.50000i) q^{34} +(1.00000 + 1.73205i) q^{36} +(-2.82843 - 2.82843i) q^{37} +(2.70831 + 3.41542i) q^{38} -2.00000i q^{39} +(6.00000 - 3.46410i) q^{41} +(0.896575 + 3.34607i) q^{42} +(0.896575 - 3.34607i) q^{43} +3.46410i q^{46} +(-1.79315 - 6.69213i) q^{47} +(-0.258819 - 0.965926i) q^{48} -5.00000i q^{49} +(1.50000 + 0.866025i) q^{51} +(0.517638 - 1.93185i) q^{52} +(-4.33013 + 2.50000i) q^{54} +3.46410i q^{56} +(-3.41542 + 2.70831i) q^{57} +(-2.44949 - 2.44949i) q^{58} +(-2.59808 - 4.50000i) q^{59} +(4.00000 - 6.92820i) q^{61} +(10.0382 + 2.68973i) q^{62} +(6.69213 - 1.79315i) q^{63} -1.00000i q^{64} +(7.72741 - 2.07055i) q^{67} +(1.22474 + 1.22474i) q^{68} -3.46410 q^{69} +(12.0000 - 6.92820i) q^{71} +(-1.93185 + 0.517638i) q^{72} +(-2.24144 + 8.36516i) q^{73} +(3.46410 - 2.00000i) q^{74} +(-4.00000 + 1.73205i) q^{76} +(1.93185 + 0.517638i) q^{78} +(0.500000 + 0.866025i) q^{81} +(1.79315 + 6.69213i) q^{82} +(-1.22474 - 1.22474i) q^{83} -3.46410 q^{84} +(3.00000 + 1.73205i) q^{86} +(2.44949 - 2.44949i) q^{87} +(-4.33013 + 7.50000i) q^{89} +(-6.00000 - 3.46410i) q^{91} +(-3.34607 - 0.896575i) q^{92} +(-2.68973 + 10.0382i) q^{93} +6.92820 q^{94} +1.00000 q^{96} +(1.81173 - 6.76148i) q^{97} +(4.82963 + 1.29410i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 4 q^{6}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 4 q^{6} + 4 q^{16} + 24 q^{21} - 16 q^{26} + 8 q^{36} + 48 q^{41} + 12 q^{51} + 32 q^{61} + 96 q^{71} - 32 q^{76} + 4 q^{81} + 24 q^{86} - 48 q^{91} + 8 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/950\mathbb{Z}\right)^\times\).

\(n\) \(77\) \(401\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(e\left(\frac{5}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.258819 + 0.965926i −0.183013 + 0.683013i
\(3\) −0.965926 0.258819i −0.557678 0.149429i −0.0310384 0.999518i \(-0.509881\pi\)
−0.526639 + 0.850089i \(0.676548\pi\)
\(4\) −0.866025 0.500000i −0.433013 0.250000i
\(5\) 0 0
\(6\) 0.500000 0.866025i 0.204124 0.353553i
\(7\) −2.44949 + 2.44949i −0.925820 + 0.925820i −0.997433 0.0716124i \(-0.977186\pi\)
0.0716124 + 0.997433i \(0.477186\pi\)
\(8\) 0.707107 0.707107i 0.250000 0.250000i
\(9\) −1.73205 1.00000i −0.577350 0.333333i
\(10\) 0 0
\(11\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(12\) 0.707107 + 0.707107i 0.204124 + 0.204124i
\(13\) 0.517638 + 1.93185i 0.143567 + 0.535799i 0.999815 + 0.0192343i \(0.00612285\pi\)
−0.856248 + 0.516565i \(0.827210\pi\)
\(14\) −1.73205 3.00000i −0.462910 0.801784i
\(15\) 0 0
\(16\) 0.500000 + 0.866025i 0.125000 + 0.216506i
\(17\) −1.67303 0.448288i −0.405770 0.108726i 0.0501604 0.998741i \(-0.484027\pi\)
−0.455930 + 0.890015i \(0.650693\pi\)
\(18\) 1.41421 1.41421i 0.333333 0.333333i
\(19\) 2.59808 3.50000i 0.596040 0.802955i
\(20\) 0 0
\(21\) 3.00000 1.73205i 0.654654 0.377964i
\(22\) 0 0
\(23\) 3.34607 0.896575i 0.697703 0.186949i 0.107501 0.994205i \(-0.465715\pi\)
0.590201 + 0.807256i \(0.299048\pi\)
\(24\) −0.866025 + 0.500000i −0.176777 + 0.102062i
\(25\) 0 0
\(26\) −2.00000 −0.392232
\(27\) 3.53553 + 3.53553i 0.680414 + 0.680414i
\(28\) 3.34607 0.896575i 0.632347 0.169437i
\(29\) −1.73205 + 3.00000i −0.321634 + 0.557086i −0.980825 0.194889i \(-0.937565\pi\)
0.659192 + 0.751975i \(0.270899\pi\)
\(30\) 0 0
\(31\) 10.3923i 1.86651i −0.359211 0.933257i \(-0.616954\pi\)
0.359211 0.933257i \(-0.383046\pi\)
\(32\) −0.965926 + 0.258819i −0.170753 + 0.0457532i
\(33\) 0 0
\(34\) 0.866025 1.50000i 0.148522 0.257248i
\(35\) 0 0
\(36\) 1.00000 + 1.73205i 0.166667 + 0.288675i
\(37\) −2.82843 2.82843i −0.464991 0.464991i 0.435297 0.900287i \(-0.356644\pi\)
−0.900287 + 0.435297i \(0.856644\pi\)
\(38\) 2.70831 + 3.41542i 0.439346 + 0.554054i
\(39\) 2.00000i 0.320256i
\(40\) 0 0
\(41\) 6.00000 3.46410i 0.937043 0.541002i 0.0480106 0.998847i \(-0.484712\pi\)
0.889032 + 0.457845i \(0.151379\pi\)
\(42\) 0.896575 + 3.34607i 0.138345 + 0.516309i
\(43\) 0.896575 3.34607i 0.136726 0.510270i −0.863258 0.504762i \(-0.831580\pi\)
0.999985 0.00550783i \(-0.00175320\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 3.46410i 0.510754i
\(47\) −1.79315 6.69213i −0.261558 0.976148i −0.964324 0.264726i \(-0.914718\pi\)
0.702766 0.711421i \(-0.251948\pi\)
\(48\) −0.258819 0.965926i −0.0373573 0.139419i
\(49\) 5.00000i 0.714286i
\(50\) 0 0
\(51\) 1.50000 + 0.866025i 0.210042 + 0.121268i
\(52\) 0.517638 1.93185i 0.0717835 0.267900i
\(53\) 0 0 0.965926 0.258819i \(-0.0833333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(54\) −4.33013 + 2.50000i −0.589256 + 0.340207i
\(55\) 0 0
\(56\) 3.46410i 0.462910i
\(57\) −3.41542 + 2.70831i −0.452383 + 0.358724i
\(58\) −2.44949 2.44949i −0.321634 0.321634i
\(59\) −2.59808 4.50000i −0.338241 0.585850i 0.645861 0.763455i \(-0.276498\pi\)
−0.984102 + 0.177605i \(0.943165\pi\)
\(60\) 0 0
\(61\) 4.00000 6.92820i 0.512148 0.887066i −0.487753 0.872982i \(-0.662183\pi\)
0.999901 0.0140840i \(-0.00448323\pi\)
\(62\) 10.0382 + 2.68973i 1.27485 + 0.341596i
\(63\) 6.69213 1.79315i 0.843129 0.225916i
\(64\) 1.00000i 0.125000i
\(65\) 0 0
\(66\) 0 0
\(67\) 7.72741 2.07055i 0.944053 0.252958i 0.246216 0.969215i \(-0.420813\pi\)
0.697837 + 0.716257i \(0.254146\pi\)
\(68\) 1.22474 + 1.22474i 0.148522 + 0.148522i
\(69\) −3.46410 −0.417029
\(70\) 0 0
\(71\) 12.0000 6.92820i 1.42414 0.822226i 0.427489 0.904021i \(-0.359398\pi\)
0.996649 + 0.0817942i \(0.0260650\pi\)
\(72\) −1.93185 + 0.517638i −0.227671 + 0.0610042i
\(73\) −2.24144 + 8.36516i −0.262341 + 0.979068i 0.701518 + 0.712652i \(0.252506\pi\)
−0.963858 + 0.266416i \(0.914160\pi\)
\(74\) 3.46410 2.00000i 0.402694 0.232495i
\(75\) 0 0
\(76\) −4.00000 + 1.73205i −0.458831 + 0.198680i
\(77\) 0 0
\(78\) 1.93185 + 0.517638i 0.218739 + 0.0586110i
\(79\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(80\) 0 0
\(81\) 0.500000 + 0.866025i 0.0555556 + 0.0962250i
\(82\) 1.79315 + 6.69213i 0.198020 + 0.739022i
\(83\) −1.22474 1.22474i −0.134433 0.134433i 0.636688 0.771121i \(-0.280304\pi\)
−0.771121 + 0.636688i \(0.780304\pi\)
\(84\) −3.46410 −0.377964
\(85\) 0 0
\(86\) 3.00000 + 1.73205i 0.323498 + 0.186772i
\(87\) 2.44949 2.44949i 0.262613 0.262613i
\(88\) 0 0
\(89\) −4.33013 + 7.50000i −0.458993 + 0.794998i −0.998908 0.0467209i \(-0.985123\pi\)
0.539915 + 0.841719i \(0.318456\pi\)
\(90\) 0 0
\(91\) −6.00000 3.46410i −0.628971 0.363137i
\(92\) −3.34607 0.896575i −0.348851 0.0934745i
\(93\) −2.68973 + 10.0382i −0.278912 + 1.04091i
\(94\) 6.92820 0.714590
\(95\) 0 0
\(96\) 1.00000 0.102062
\(97\) 1.81173 6.76148i 0.183954 0.686524i −0.810898 0.585187i \(-0.801021\pi\)
0.994852 0.101337i \(-0.0323122\pi\)
\(98\) 4.82963 + 1.29410i 0.487866 + 0.130723i
\(99\) 0 0
\(100\) 0 0
\(101\) −3.00000 + 5.19615i −0.298511 + 0.517036i −0.975796 0.218685i \(-0.929823\pi\)
0.677284 + 0.735721i \(0.263157\pi\)
\(102\) −1.22474 + 1.22474i −0.121268 + 0.121268i
\(103\) 2.82843 2.82843i 0.278693 0.278693i −0.553894 0.832587i \(-0.686859\pi\)
0.832587 + 0.553894i \(0.186859\pi\)
\(104\) 1.73205 + 1.00000i 0.169842 + 0.0980581i
\(105\) 0 0
\(106\) 0 0
\(107\) −10.6066 10.6066i −1.02538 1.02538i −0.999669 0.0257094i \(-0.991816\pi\)
−0.0257094 0.999669i \(-0.508184\pi\)
\(108\) −1.29410 4.82963i −0.124524 0.464731i
\(109\) 8.66025 + 15.0000i 0.829502 + 1.43674i 0.898430 + 0.439118i \(0.144709\pi\)
−0.0689276 + 0.997622i \(0.521958\pi\)
\(110\) 0 0
\(111\) 2.00000 + 3.46410i 0.189832 + 0.328798i
\(112\) −3.34607 0.896575i −0.316173 0.0847184i
\(113\) 6.36396 6.36396i 0.598671 0.598671i −0.341288 0.939959i \(-0.610863\pi\)
0.939959 + 0.341288i \(0.110863\pi\)
\(114\) −1.73205 4.00000i −0.162221 0.374634i
\(115\) 0 0
\(116\) 3.00000 1.73205i 0.278543 0.160817i
\(117\) 1.03528 3.86370i 0.0957113 0.357199i
\(118\) 5.01910 1.34486i 0.462045 0.123805i
\(119\) 5.19615 3.00000i 0.476331 0.275010i
\(120\) 0 0
\(121\) −11.0000 −1.00000
\(122\) 5.65685 + 5.65685i 0.512148 + 0.512148i
\(123\) −6.69213 + 1.79315i −0.603409 + 0.161683i
\(124\) −5.19615 + 9.00000i −0.466628 + 0.808224i
\(125\) 0 0
\(126\) 6.92820i 0.617213i
\(127\) −3.86370 + 1.03528i −0.342848 + 0.0918659i −0.426135 0.904660i \(-0.640125\pi\)
0.0832864 + 0.996526i \(0.473458\pi\)
\(128\) 0.965926 + 0.258819i 0.0853766 + 0.0228766i
\(129\) −1.73205 + 3.00000i −0.152499 + 0.264135i
\(130\) 0 0
\(131\) −7.50000 12.9904i −0.655278 1.13497i −0.981824 0.189794i \(-0.939218\pi\)
0.326546 0.945181i \(-0.394115\pi\)
\(132\) 0 0
\(133\) 2.20925 + 14.9372i 0.191567 + 1.29522i
\(134\) 8.00000i 0.691095i
\(135\) 0 0
\(136\) −1.50000 + 0.866025i −0.128624 + 0.0742611i
\(137\) −4.03459 15.0573i −0.344698 1.28643i −0.892964 0.450127i \(-0.851379\pi\)
0.548266 0.836304i \(-0.315288\pi\)
\(138\) 0.896575 3.34607i 0.0763216 0.284836i
\(139\) 13.8564 + 8.00000i 1.17529 + 0.678551i 0.954919 0.296866i \(-0.0959415\pi\)
0.220366 + 0.975417i \(0.429275\pi\)
\(140\) 0 0
\(141\) 6.92820i 0.583460i
\(142\) 3.58630 + 13.3843i 0.300956 + 1.12318i
\(143\) 0 0
\(144\) 2.00000i 0.166667i
\(145\) 0 0
\(146\) −7.50000 4.33013i −0.620704 0.358364i
\(147\) −1.29410 + 4.82963i −0.106735 + 0.398341i
\(148\) 1.03528 + 3.86370i 0.0850992 + 0.317594i
\(149\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(150\) 0 0
\(151\) 20.7846i 1.69143i 0.533637 + 0.845714i \(0.320825\pi\)
−0.533637 + 0.845714i \(0.679175\pi\)
\(152\) −0.637756 4.31199i −0.0517289 0.349749i
\(153\) 2.44949 + 2.44949i 0.198030 + 0.198030i
\(154\) 0 0
\(155\) 0 0
\(156\) −1.00000 + 1.73205i −0.0800641 + 0.138675i
\(157\) 16.7303 + 4.48288i 1.33523 + 0.357773i 0.854661 0.519187i \(-0.173765\pi\)
0.480565 + 0.876959i \(0.340432\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −6.00000 + 10.3923i −0.472866 + 0.819028i
\(162\) −0.965926 + 0.258819i −0.0758903 + 0.0203347i
\(163\) −12.2474 12.2474i −0.959294 0.959294i 0.0399091 0.999203i \(-0.487293\pi\)
−0.999203 + 0.0399091i \(0.987293\pi\)
\(164\) −6.92820 −0.541002
\(165\) 0 0
\(166\) 1.50000 0.866025i 0.116423 0.0672166i
\(167\) −17.3867 + 4.65874i −1.34542 + 0.360504i −0.858442 0.512910i \(-0.828568\pi\)
−0.486978 + 0.873414i \(0.661901\pi\)
\(168\) 0.896575 3.34607i 0.0691723 0.258155i
\(169\) 7.79423 4.50000i 0.599556 0.346154i
\(170\) 0 0
\(171\) −8.00000 + 3.46410i −0.611775 + 0.264906i
\(172\) −2.44949 + 2.44949i −0.186772 + 0.186772i
\(173\) −17.3867 4.65874i −1.32188 0.354198i −0.472200 0.881491i \(-0.656540\pi\)
−0.849683 + 0.527294i \(0.823207\pi\)
\(174\) 1.73205 + 3.00000i 0.131306 + 0.227429i
\(175\) 0 0
\(176\) 0 0
\(177\) 1.34486 + 5.01910i 0.101086 + 0.377258i
\(178\) −6.12372 6.12372i −0.458993 0.458993i
\(179\) −8.66025 −0.647298 −0.323649 0.946177i \(-0.604910\pi\)
−0.323649 + 0.946177i \(0.604910\pi\)
\(180\) 0 0
\(181\) −6.00000 3.46410i −0.445976 0.257485i 0.260153 0.965567i \(-0.416227\pi\)
−0.706129 + 0.708083i \(0.749560\pi\)
\(182\) 4.89898 4.89898i 0.363137 0.363137i
\(183\) −5.65685 + 5.65685i −0.418167 + 0.418167i
\(184\) 1.73205 3.00000i 0.127688 0.221163i
\(185\) 0 0
\(186\) −9.00000 5.19615i −0.659912 0.381000i
\(187\) 0 0
\(188\) −1.79315 + 6.69213i −0.130779 + 0.488074i
\(189\) −17.3205 −1.25988
\(190\) 0 0
\(191\) 6.00000 0.434145 0.217072 0.976156i \(-0.430349\pi\)
0.217072 + 0.976156i \(0.430349\pi\)
\(192\) −0.258819 + 0.965926i −0.0186787 + 0.0697097i
\(193\) −10.6252 2.84701i −0.764817 0.204932i −0.144737 0.989470i \(-0.546234\pi\)
−0.620081 + 0.784538i \(0.712900\pi\)
\(194\) 6.06218 + 3.50000i 0.435239 + 0.251285i
\(195\) 0 0
\(196\) −2.50000 + 4.33013i −0.178571 + 0.309295i
\(197\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(198\) 0 0
\(199\) 3.46410 + 2.00000i 0.245564 + 0.141776i 0.617731 0.786389i \(-0.288052\pi\)
−0.372168 + 0.928166i \(0.621385\pi\)
\(200\) 0 0
\(201\) −8.00000 −0.564276
\(202\) −4.24264 4.24264i −0.298511 0.298511i
\(203\) −3.10583 11.5911i −0.217986 0.813536i
\(204\) −0.866025 1.50000i −0.0606339 0.105021i
\(205\) 0 0
\(206\) 2.00000 + 3.46410i 0.139347 + 0.241355i
\(207\) −6.69213 1.79315i −0.465135 0.124633i
\(208\) −1.41421 + 1.41421i −0.0980581 + 0.0980581i
\(209\) 0 0
\(210\) 0 0
\(211\) −4.50000 + 2.59808i −0.309793 + 0.178859i −0.646834 0.762631i \(-0.723907\pi\)
0.337041 + 0.941490i \(0.390574\pi\)
\(212\) 0 0
\(213\) −13.3843 + 3.58630i −0.917074 + 0.245729i
\(214\) 12.9904 7.50000i 0.888004 0.512689i
\(215\) 0 0
\(216\) 5.00000 0.340207
\(217\) 25.4558 + 25.4558i 1.72806 + 1.72806i
\(218\) −16.7303 + 4.48288i −1.13312 + 0.303619i
\(219\) 4.33013 7.50000i 0.292603 0.506803i
\(220\) 0 0
\(221\) 3.46410i 0.233021i
\(222\) −3.86370 + 1.03528i −0.259315 + 0.0694832i
\(223\) 1.93185 + 0.517638i 0.129366 + 0.0346636i 0.322921 0.946426i \(-0.395335\pi\)
−0.193555 + 0.981089i \(0.562002\pi\)
\(224\) 1.73205 3.00000i 0.115728 0.200446i
\(225\) 0 0
\(226\) 4.50000 + 7.79423i 0.299336 + 0.518464i
\(227\) −19.0919 19.0919i −1.26717 1.26717i −0.947542 0.319631i \(-0.896441\pi\)
−0.319631 0.947542i \(-0.603559\pi\)
\(228\) 4.31199 0.637756i 0.285569 0.0422365i
\(229\) 22.0000i 1.45380i −0.686743 0.726900i \(-0.740960\pi\)
0.686743 0.726900i \(-0.259040\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0.896575 + 3.34607i 0.0588631 + 0.219680i
\(233\) −5.82774 + 21.7494i −0.381788 + 1.42485i 0.461380 + 0.887202i \(0.347354\pi\)
−0.843168 + 0.537650i \(0.819312\pi\)
\(234\) 3.46410 + 2.00000i 0.226455 + 0.130744i
\(235\) 0 0
\(236\) 5.19615i 0.338241i
\(237\) 0 0
\(238\) 1.55291 + 5.79555i 0.100660 + 0.375670i
\(239\) 18.0000i 1.16432i −0.813073 0.582162i \(-0.802207\pi\)
0.813073 0.582162i \(-0.197793\pi\)
\(240\) 0 0
\(241\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(242\) 2.84701 10.6252i 0.183013 0.683013i
\(243\) −4.14110 15.4548i −0.265652 0.991427i
\(244\) −6.92820 + 4.00000i −0.443533 + 0.256074i
\(245\) 0 0
\(246\) 6.92820i 0.441726i
\(247\) 8.10634 + 3.20736i 0.515794 + 0.204080i
\(248\) −7.34847 7.34847i −0.466628 0.466628i
\(249\) 0.866025 + 1.50000i 0.0548821 + 0.0950586i
\(250\) 0 0
\(251\) −6.00000 + 10.3923i −0.378717 + 0.655956i −0.990876 0.134778i \(-0.956968\pi\)
0.612159 + 0.790735i \(0.290301\pi\)
\(252\) −6.69213 1.79315i −0.421565 0.112958i
\(253\) 0 0
\(254\) 4.00000i 0.250982i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −8.69333 + 2.32937i −0.542275 + 0.145302i −0.519551 0.854440i \(-0.673901\pi\)
−0.0227244 + 0.999742i \(0.507234\pi\)
\(258\) −2.44949 2.44949i −0.152499 0.152499i
\(259\) 13.8564 0.860995
\(260\) 0 0
\(261\) 6.00000 3.46410i 0.371391 0.214423i
\(262\) 14.4889 3.88229i 0.895126 0.239848i
\(263\) 6.27603 23.4225i 0.386996 1.44429i −0.447999 0.894034i \(-0.647863\pi\)
0.834996 0.550257i \(-0.185470\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) −15.0000 1.73205i −0.919709 0.106199i
\(267\) 6.12372 6.12372i 0.374766 0.374766i
\(268\) −7.72741 2.07055i −0.472026 0.126479i
\(269\) 12.1244 + 21.0000i 0.739235 + 1.28039i 0.952840 + 0.303473i \(0.0981461\pi\)
−0.213605 + 0.976920i \(0.568521\pi\)
\(270\) 0 0
\(271\) −1.00000 1.73205i −0.0607457 0.105215i 0.834053 0.551684i \(-0.186015\pi\)
−0.894799 + 0.446469i \(0.852681\pi\)
\(272\) −0.448288 1.67303i −0.0271814 0.101443i
\(273\) 4.89898 + 4.89898i 0.296500 + 0.296500i
\(274\) 15.5885 0.941733
\(275\) 0 0
\(276\) 3.00000 + 1.73205i 0.180579 + 0.104257i
\(277\) 17.1464 17.1464i 1.03023 1.03023i 0.0307004 0.999529i \(-0.490226\pi\)
0.999529 0.0307004i \(-0.00977377\pi\)
\(278\) −11.3137 + 11.3137i −0.678551 + 0.678551i
\(279\) −10.3923 + 18.0000i −0.622171 + 1.07763i
\(280\) 0 0
\(281\) −10.5000 6.06218i −0.626377 0.361639i 0.152970 0.988231i \(-0.451116\pi\)
−0.779348 + 0.626592i \(0.784449\pi\)
\(282\) −6.69213 1.79315i −0.398511 0.106781i
\(283\) 0.896575 3.34607i 0.0532959 0.198903i −0.934144 0.356895i \(-0.883835\pi\)
0.987440 + 0.157992i \(0.0505021\pi\)
\(284\) −13.8564 −0.822226
\(285\) 0 0
\(286\) 0 0
\(287\) −6.21166 + 23.1822i −0.366663 + 1.36840i
\(288\) 1.93185 + 0.517638i 0.113835 + 0.0305021i
\(289\) −12.1244 7.00000i −0.713197 0.411765i
\(290\) 0 0
\(291\) −3.50000 + 6.06218i −0.205174 + 0.355371i
\(292\) 6.12372 6.12372i 0.358364 0.358364i
\(293\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(294\) −4.33013 2.50000i −0.252538 0.145803i
\(295\) 0 0
\(296\) −4.00000 −0.232495
\(297\) 0 0
\(298\) 0 0
\(299\) 3.46410 + 6.00000i 0.200334 + 0.346989i
\(300\) 0 0
\(301\) 6.00000 + 10.3923i 0.345834 + 0.599002i
\(302\) −20.0764 5.37945i −1.15527 0.309553i
\(303\) 4.24264 4.24264i 0.243733 0.243733i
\(304\) 4.33013 + 0.500000i 0.248350 + 0.0286770i
\(305\) 0 0
\(306\) −3.00000 + 1.73205i −0.171499 + 0.0990148i
\(307\) −2.84701 + 10.6252i −0.162487 + 0.606411i 0.835860 + 0.548943i \(0.184970\pi\)
−0.998347 + 0.0574685i \(0.981697\pi\)
\(308\) 0 0
\(309\) −3.46410 + 2.00000i −0.197066 + 0.113776i
\(310\) 0 0
\(311\) 30.0000 1.70114 0.850572 0.525859i \(-0.176256\pi\)
0.850572 + 0.525859i \(0.176256\pi\)
\(312\) −1.41421 1.41421i −0.0800641 0.0800641i
\(313\) 18.4034 4.93117i 1.04022 0.278726i 0.302015 0.953303i \(-0.402341\pi\)
0.738204 + 0.674577i \(0.235674\pi\)
\(314\) −8.66025 + 15.0000i −0.488726 + 0.846499i
\(315\) 0 0
\(316\) 0 0
\(317\) 11.5911 3.10583i 0.651022 0.174441i 0.0818309 0.996646i \(-0.473923\pi\)
0.569191 + 0.822206i \(0.307257\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 7.50000 + 12.9904i 0.418609 + 0.725052i
\(322\) −8.48528 8.48528i −0.472866 0.472866i
\(323\) −5.91567 + 4.69093i −0.329157 + 0.261010i
\(324\) 1.00000i 0.0555556i
\(325\) 0 0
\(326\) 15.0000 8.66025i 0.830773 0.479647i
\(327\) −4.48288 16.7303i −0.247904 0.925189i
\(328\) 1.79315 6.69213i 0.0990102 0.369511i
\(329\) 20.7846 + 12.0000i 1.14589 + 0.661581i
\(330\) 0 0
\(331\) 5.19615i 0.285606i −0.989751 0.142803i \(-0.954388\pi\)
0.989751 0.142803i \(-0.0456116\pi\)
\(332\) 0.448288 + 1.67303i 0.0246030 + 0.0918196i
\(333\) 2.07055 + 7.72741i 0.113466 + 0.423459i
\(334\) 18.0000i 0.984916i
\(335\) 0 0
\(336\) 3.00000 + 1.73205i 0.163663 + 0.0944911i
\(337\) −5.69402 + 21.2504i −0.310173 + 1.15758i 0.618227 + 0.785999i \(0.287851\pi\)
−0.928400 + 0.371582i \(0.878816\pi\)
\(338\) 2.32937 + 8.69333i 0.126701 + 0.472855i
\(339\) −7.79423 + 4.50000i −0.423324 + 0.244406i
\(340\) 0 0
\(341\) 0 0
\(342\) −1.27551 8.62398i −0.0689718 0.466332i
\(343\) −4.89898 4.89898i −0.264520 0.264520i
\(344\) −1.73205 3.00000i −0.0933859 0.161749i
\(345\) 0 0
\(346\) 9.00000 15.5885i 0.483843 0.838041i
\(347\) 3.34607 + 0.896575i 0.179626 + 0.0481307i 0.347511 0.937676i \(-0.387027\pi\)
−0.167885 + 0.985807i \(0.553694\pi\)
\(348\) −3.34607 + 0.896575i −0.179368 + 0.0480615i
\(349\) 28.0000i 1.49881i 0.662114 + 0.749403i \(0.269659\pi\)
−0.662114 + 0.749403i \(0.730341\pi\)
\(350\) 0 0
\(351\) −5.00000 + 8.66025i −0.266880 + 0.462250i
\(352\) 0 0
\(353\) −3.67423 3.67423i −0.195560 0.195560i 0.602534 0.798093i \(-0.294158\pi\)
−0.798093 + 0.602534i \(0.794158\pi\)
\(354\) −5.19615 −0.276172
\(355\) 0 0
\(356\) 7.50000 4.33013i 0.397499 0.229496i
\(357\) −5.79555 + 1.55291i −0.306733 + 0.0821889i
\(358\) 2.24144 8.36516i 0.118464 0.442113i
\(359\) 10.3923 6.00000i 0.548485 0.316668i −0.200026 0.979791i \(-0.564103\pi\)
0.748511 + 0.663123i \(0.230769\pi\)
\(360\) 0 0
\(361\) −5.50000 18.1865i −0.289474 0.957186i
\(362\) 4.89898 4.89898i 0.257485 0.257485i
\(363\) 10.6252 + 2.84701i 0.557678 + 0.149429i
\(364\) 3.46410 + 6.00000i 0.181568 + 0.314485i
\(365\) 0 0
\(366\) −4.00000 6.92820i −0.209083 0.362143i
\(367\) 7.17260 + 26.7685i 0.374407 + 1.39731i 0.854209 + 0.519929i \(0.174042\pi\)
−0.479803 + 0.877376i \(0.659292\pi\)
\(368\) 2.44949 + 2.44949i 0.127688 + 0.127688i
\(369\) −13.8564 −0.721336
\(370\) 0 0
\(371\) 0 0
\(372\) 7.34847 7.34847i 0.381000 0.381000i
\(373\) 7.07107 7.07107i 0.366126 0.366126i −0.499936 0.866062i \(-0.666643\pi\)
0.866062 + 0.499936i \(0.166643\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) −6.00000 3.46410i −0.309426 0.178647i
\(377\) −6.69213 1.79315i −0.344662 0.0923520i
\(378\) 4.48288 16.7303i 0.230574 0.860515i
\(379\) 5.19615 0.266908 0.133454 0.991055i \(-0.457393\pi\)
0.133454 + 0.991055i \(0.457393\pi\)
\(380\) 0 0
\(381\) 4.00000 0.204926
\(382\) −1.55291 + 5.79555i −0.0794540 + 0.296526i
\(383\) −23.1822 6.21166i −1.18456 0.317401i −0.387824 0.921733i \(-0.626773\pi\)
−0.796732 + 0.604333i \(0.793440\pi\)
\(384\) −0.866025 0.500000i −0.0441942 0.0255155i
\(385\) 0 0
\(386\) 5.50000 9.52628i 0.279943 0.484875i
\(387\) −4.89898 + 4.89898i −0.249029 + 0.249029i
\(388\) −4.94975 + 4.94975i −0.251285 + 0.251285i
\(389\) −25.9808 15.0000i −1.31728 0.760530i −0.333987 0.942578i \(-0.608394\pi\)
−0.983290 + 0.182047i \(0.941728\pi\)
\(390\) 0 0
\(391\) −6.00000 −0.303433
\(392\) −3.53553 3.53553i −0.178571 0.178571i
\(393\) 3.88229 + 14.4889i 0.195835 + 0.730868i
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 30.1146 + 8.06918i 1.51141 + 0.404980i 0.916903 0.399111i \(-0.130681\pi\)
0.594505 + 0.804092i \(0.297348\pi\)
\(398\) −2.82843 + 2.82843i −0.141776 + 0.141776i
\(399\) 1.73205 15.0000i 0.0867110 0.750939i
\(400\) 0 0
\(401\) −30.0000 + 17.3205i −1.49813 + 0.864945i −0.999998 0.00215698i \(-0.999313\pi\)
−0.498131 + 0.867102i \(0.665980\pi\)
\(402\) 2.07055 7.72741i 0.103270 0.385408i
\(403\) 20.0764 5.37945i 1.00008 0.267970i
\(404\) 5.19615 3.00000i 0.258518 0.149256i
\(405\) 0 0
\(406\) 12.0000 0.595550
\(407\) 0 0
\(408\) 1.67303 0.448288i 0.0828275 0.0221936i
\(409\) 3.46410 6.00000i 0.171289 0.296681i −0.767582 0.640951i \(-0.778540\pi\)
0.938871 + 0.344270i \(0.111874\pi\)
\(410\) 0 0
\(411\) 15.5885i 0.768922i
\(412\) −3.86370 + 1.03528i −0.190351 + 0.0510044i
\(413\) 17.3867 + 4.65874i 0.855542 + 0.229242i
\(414\) 3.46410 6.00000i 0.170251 0.294884i
\(415\) 0 0
\(416\) −1.00000 1.73205i −0.0490290 0.0849208i
\(417\) −11.3137 11.3137i −0.554035 0.554035i
\(418\) 0 0
\(419\) 21.0000i 1.02592i −0.858413 0.512959i \(-0.828549\pi\)
0.858413 0.512959i \(-0.171451\pi\)
\(420\) 0 0
\(421\) 33.0000 19.0526i 1.60832 0.928565i 0.618576 0.785725i \(-0.287710\pi\)
0.989746 0.142840i \(-0.0456234\pi\)
\(422\) −1.34486 5.01910i −0.0654669 0.244326i
\(423\) −3.58630 + 13.3843i −0.174372 + 0.650765i
\(424\) 0 0
\(425\) 0 0
\(426\) 13.8564i 0.671345i
\(427\) 7.17260 + 26.7685i 0.347107 + 1.29542i
\(428\) 3.88229 + 14.4889i 0.187657 + 0.700347i
\(429\) 0 0
\(430\) 0 0
\(431\) 21.0000 + 12.1244i 1.01153 + 0.584010i 0.911641 0.410988i \(-0.134816\pi\)
0.0998939 + 0.994998i \(0.468150\pi\)
\(432\) −1.29410 + 4.82963i −0.0622622 + 0.232366i
\(433\) 9.05867 + 33.8074i 0.435332 + 1.62468i 0.740271 + 0.672308i \(0.234697\pi\)
−0.304939 + 0.952372i \(0.598636\pi\)
\(434\) −31.1769 + 18.0000i −1.49654 + 0.864028i
\(435\) 0 0
\(436\) 17.3205i 0.829502i
\(437\) 5.55532 14.0406i 0.265747 0.671653i
\(438\) 6.12372 + 6.12372i 0.292603 + 0.292603i
\(439\) −3.46410 6.00000i −0.165333 0.286364i 0.771441 0.636301i \(-0.219536\pi\)
−0.936773 + 0.349937i \(0.886203\pi\)
\(440\) 0 0
\(441\) −5.00000 + 8.66025i −0.238095 + 0.412393i
\(442\) 3.34607 + 0.896575i 0.159156 + 0.0426457i
\(443\) 23.4225 6.27603i 1.11283 0.298183i 0.344854 0.938656i \(-0.387928\pi\)
0.767980 + 0.640473i \(0.221262\pi\)
\(444\) 4.00000i 0.189832i
\(445\) 0 0
\(446\) −1.00000 + 1.73205i −0.0473514 + 0.0820150i
\(447\) 0 0
\(448\) 2.44949 + 2.44949i 0.115728 + 0.115728i
\(449\) −25.9808 −1.22611 −0.613054 0.790041i \(-0.710059\pi\)
−0.613054 + 0.790041i \(0.710059\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) −8.69333 + 2.32937i −0.408900 + 0.109564i
\(453\) 5.37945 20.0764i 0.252749 0.943271i
\(454\) 23.3827 13.5000i 1.09740 0.633586i
\(455\) 0 0
\(456\) −0.500000 + 4.33013i −0.0234146 + 0.202777i
\(457\) −13.4722 + 13.4722i −0.630203 + 0.630203i −0.948119 0.317916i \(-0.897017\pi\)
0.317916 + 0.948119i \(0.397017\pi\)
\(458\) 21.2504 + 5.69402i 0.992964 + 0.266064i
\(459\) −4.33013 7.50000i −0.202113 0.350070i
\(460\) 0 0
\(461\) −9.00000 15.5885i −0.419172 0.726027i 0.576685 0.816967i \(-0.304346\pi\)
−0.995856 + 0.0909401i \(0.971013\pi\)
\(462\) 0 0
\(463\) 7.34847 + 7.34847i 0.341512 + 0.341512i 0.856936 0.515423i \(-0.172365\pi\)
−0.515423 + 0.856936i \(0.672365\pi\)
\(464\) −3.46410 −0.160817
\(465\) 0 0
\(466\) −19.5000 11.2583i −0.903320 0.521532i
\(467\) 25.7196 25.7196i 1.19016 1.19016i 0.213142 0.977021i \(-0.431630\pi\)
0.977021 0.213142i \(-0.0683696\pi\)
\(468\) −2.82843 + 2.82843i −0.130744 + 0.130744i
\(469\) −13.8564 + 24.0000i −0.639829 + 1.10822i
\(470\) 0 0
\(471\) −15.0000 8.66025i −0.691164 0.399043i
\(472\) −5.01910 1.34486i −0.231023 0.0619023i
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) −6.00000 −0.275010
\(477\) 0 0
\(478\) 17.3867 + 4.65874i 0.795248 + 0.213086i
\(479\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(480\) 0 0
\(481\) 4.00000 6.92820i 0.182384 0.315899i
\(482\) 0 0
\(483\) 8.48528 8.48528i 0.386094 0.386094i
\(484\) 9.52628 + 5.50000i 0.433013 + 0.250000i
\(485\) 0 0
\(486\) 16.0000 0.725775
\(487\) −11.3137 11.3137i −0.512673 0.512673i 0.402671 0.915345i \(-0.368082\pi\)
−0.915345 + 0.402671i \(0.868082\pi\)
\(488\) −2.07055 7.72741i −0.0937295 0.349803i
\(489\) 8.66025 + 15.0000i 0.391630 + 0.678323i
\(490\) 0 0
\(491\) 12.0000 + 20.7846i 0.541552 + 0.937996i 0.998815 + 0.0486647i \(0.0154966\pi\)
−0.457263 + 0.889332i \(0.651170\pi\)
\(492\) 6.69213 + 1.79315i 0.301705 + 0.0808415i
\(493\) 4.24264 4.24264i 0.191079 0.191079i
\(494\) −5.19615 + 7.00000i −0.233786 + 0.314945i
\(495\) 0 0
\(496\) 9.00000 5.19615i 0.404112 0.233314i
\(497\) −12.4233 + 46.3644i −0.557262 + 2.07973i
\(498\) −1.67303 + 0.448288i −0.0749704 + 0.0200883i
\(499\) 26.8468 15.5000i 1.20183 0.693875i 0.240866 0.970558i \(-0.422569\pi\)
0.960961 + 0.276683i \(0.0892352\pi\)
\(500\) 0 0
\(501\) 18.0000 0.804181
\(502\) −8.48528 8.48528i −0.378717 0.378717i
\(503\) 40.1528 10.7589i 1.79032 0.479716i 0.797923 0.602760i \(-0.205932\pi\)
0.992401 + 0.123044i \(0.0392655\pi\)
\(504\) 3.46410 6.00000i 0.154303 0.267261i
\(505\) 0 0
\(506\) 0 0
\(507\) −8.69333 + 2.32937i −0.386084 + 0.103451i
\(508\) 3.86370 + 1.03528i 0.171424 + 0.0459330i
\(509\) 12.1244 21.0000i 0.537403 0.930809i −0.461640 0.887067i \(-0.652739\pi\)
0.999043 0.0437414i \(-0.0139278\pi\)
\(510\) 0 0
\(511\) −15.0000 25.9808i −0.663561 1.14932i
\(512\) −0.707107 0.707107i −0.0312500 0.0312500i
\(513\) 21.5600 3.18878i 0.951895 0.140788i
\(514\) 9.00000i 0.396973i
\(515\) 0 0
\(516\) 3.00000 1.73205i 0.132068 0.0762493i
\(517\) 0 0
\(518\) −3.58630 + 13.3843i −0.157573 + 0.588071i
\(519\) 15.5885 + 9.00000i 0.684257 + 0.395056i
\(520\) 0 0
\(521\) 20.7846i 0.910590i −0.890341 0.455295i \(-0.849534\pi\)
0.890341 0.455295i \(-0.150466\pi\)
\(522\) 1.79315 + 6.69213i 0.0784841 + 0.292907i
\(523\) 7.50575 + 28.0118i 0.328204 + 1.22487i 0.911052 + 0.412292i \(0.135272\pi\)
−0.582848 + 0.812581i \(0.698062\pi\)
\(524\) 15.0000i 0.655278i
\(525\) 0 0
\(526\) 21.0000 + 12.1244i 0.915644 + 0.528647i
\(527\) −4.65874 + 17.3867i −0.202938 + 0.757375i
\(528\) 0 0
\(529\) −9.52628 + 5.50000i −0.414186 + 0.239130i
\(530\) 0 0
\(531\) 10.3923i 0.450988i
\(532\) 5.55532 14.0406i 0.240854 0.608737i
\(533\) 9.79796 + 9.79796i 0.424397 + 0.424397i
\(534\) 4.33013 + 7.50000i 0.187383 + 0.324557i
\(535\) 0 0
\(536\) 4.00000 6.92820i 0.172774 0.299253i
\(537\) 8.36516 + 2.24144i 0.360983 + 0.0967252i
\(538\) −23.4225 + 6.27603i −1.00981 + 0.270579i
\(539\) 0 0
\(540\) 0 0
\(541\) −1.00000 + 1.73205i −0.0429934 + 0.0744667i −0.886721 0.462304i \(-0.847023\pi\)
0.843728 + 0.536771i \(0.180356\pi\)
\(542\) 1.93185 0.517638i 0.0829801 0.0222345i
\(543\) 4.89898 + 4.89898i 0.210235 + 0.210235i
\(544\) 1.73205 0.0742611
\(545\) 0 0
\(546\) −6.00000 + 3.46410i −0.256776 + 0.148250i
\(547\) 6.76148 1.81173i 0.289100 0.0774641i −0.111355 0.993781i \(-0.535519\pi\)
0.400455 + 0.916317i \(0.368852\pi\)
\(548\) −4.03459 + 15.0573i −0.172349 + 0.643216i
\(549\) −13.8564 + 8.00000i −0.591377 + 0.341432i
\(550\) 0 0
\(551\) 6.00000 + 13.8564i 0.255609 + 0.590303i
\(552\) −2.44949 + 2.44949i −0.104257 + 0.104257i
\(553\) 0 0
\(554\) 12.1244 + 21.0000i 0.515115 + 0.892205i
\(555\) 0 0
\(556\) −8.00000 13.8564i −0.339276 0.587643i
\(557\) −6.27603 23.4225i −0.265924 0.992441i −0.961682 0.274166i \(-0.911598\pi\)
0.695759 0.718276i \(-0.255068\pi\)
\(558\) −14.6969 14.6969i −0.622171 0.622171i
\(559\) 6.92820 0.293032
\(560\) 0 0
\(561\) 0 0
\(562\) 8.57321 8.57321i 0.361639 0.361639i
\(563\) 14.8492 14.8492i 0.625821 0.625821i −0.321193 0.947014i \(-0.604084\pi\)
0.947014 + 0.321193i \(0.104084\pi\)
\(564\) 3.46410 6.00000i 0.145865 0.252646i
\(565\) 0 0
\(566\) 3.00000 + 1.73205i 0.126099 + 0.0728035i
\(567\) −3.34607 0.896575i −0.140522 0.0376526i
\(568\) 3.58630 13.3843i 0.150478 0.561591i
\(569\) −39.8372 −1.67006 −0.835030 0.550204i \(-0.814550\pi\)
−0.835030 + 0.550204i \(0.814550\pi\)
\(570\) 0 0
\(571\) −7.00000 −0.292941 −0.146470 0.989215i \(-0.546791\pi\)
−0.146470 + 0.989215i \(0.546791\pi\)
\(572\) 0 0
\(573\) −5.79555 1.55291i −0.242113 0.0648739i
\(574\) −20.7846 12.0000i −0.867533 0.500870i
\(575\) 0 0
\(576\) −1.00000 + 1.73205i −0.0416667 + 0.0721688i
\(577\) 29.3939 29.3939i 1.22368 1.22368i 0.257370 0.966313i \(-0.417144\pi\)
0.966313 0.257370i \(-0.0828560\pi\)
\(578\) 9.89949 9.89949i 0.411765 0.411765i
\(579\) 9.52628 + 5.50000i 0.395899 + 0.228572i
\(580\) 0 0
\(581\) 6.00000 0.248922
\(582\) −4.94975 4.94975i −0.205174 0.205174i
\(583\) 0 0
\(584\) 4.33013 + 7.50000i 0.179182 + 0.310352i
\(585\) 0 0
\(586\) 0 0
\(587\) 28.4416 + 7.62089i 1.17391 + 0.314548i 0.792508 0.609862i \(-0.208775\pi\)
0.381401 + 0.924410i \(0.375442\pi\)
\(588\) 3.53553 3.53553i 0.145803 0.145803i
\(589\) −36.3731 27.0000i −1.49873 1.11252i
\(590\) 0 0
\(591\) 0 0
\(592\) 1.03528 3.86370i 0.0425496 0.158797i
\(593\) 20.0764 5.37945i 0.824439 0.220908i 0.178153 0.984003i \(-0.442988\pi\)
0.646286 + 0.763095i \(0.276321\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −2.82843 2.82843i −0.115760 0.115760i
\(598\) −6.69213 + 1.79315i −0.273662 + 0.0733274i
\(599\) 13.8564 24.0000i 0.566157 0.980613i −0.430784 0.902455i \(-0.641763\pi\)
0.996941 0.0781581i \(-0.0249039\pi\)
\(600\) 0 0
\(601\) 22.5167i 0.918474i −0.888314 0.459237i \(-0.848123\pi\)
0.888314 0.459237i \(-0.151877\pi\)
\(602\) −11.5911 + 3.10583i −0.472418 + 0.126584i
\(603\) −15.4548 4.14110i −0.629369 0.168639i
\(604\) 10.3923 18.0000i 0.422857 0.732410i
\(605\) 0 0
\(606\) 3.00000 + 5.19615i 0.121867 + 0.211079i
\(607\) −24.0416 24.0416i −0.975820 0.975820i 0.0238948 0.999714i \(-0.492393\pi\)
−0.999714 + 0.0238948i \(0.992393\pi\)
\(608\) −1.60368 + 4.05317i −0.0650379 + 0.164378i
\(609\) 12.0000i 0.486265i
\(610\) 0 0
\(611\) 12.0000 6.92820i 0.485468 0.280285i
\(612\) −0.896575 3.34607i −0.0362419 0.135257i
\(613\) 0.896575 3.34607i 0.0362123 0.135146i −0.945453 0.325758i \(-0.894380\pi\)
0.981665 + 0.190612i \(0.0610472\pi\)
\(614\) −9.52628 5.50000i −0.384449 0.221962i
\(615\) 0 0
\(616\) 0 0
\(617\) 11.2072 + 41.8258i 0.451185 + 1.68384i 0.699069 + 0.715054i \(0.253598\pi\)
−0.247884 + 0.968790i \(0.579735\pi\)
\(618\) −1.03528 3.86370i −0.0416449 0.155421i
\(619\) 44.0000i 1.76851i −0.467005 0.884255i \(-0.654667\pi\)
0.467005 0.884255i \(-0.345333\pi\)
\(620\) 0 0
\(621\) 15.0000 + 8.66025i 0.601929 + 0.347524i
\(622\) −7.76457 + 28.9778i −0.311331 + 1.16190i
\(623\) −7.76457 28.9778i −0.311081 1.16097i
\(624\) 1.73205 1.00000i 0.0693375 0.0400320i
\(625\) 0 0
\(626\) 19.0526i 0.761493i
\(627\) 0 0
\(628\) −12.2474 12.2474i −0.488726 0.488726i
\(629\) 3.46410 + 6.00000i 0.138123 + 0.239236i
\(630\) 0 0
\(631\) 4.00000 6.92820i 0.159237 0.275807i −0.775356 0.631524i \(-0.782430\pi\)
0.934594 + 0.355716i \(0.115763\pi\)
\(632\) 0 0
\(633\) 5.01910 1.34486i 0.199491 0.0534535i
\(634\) 12.0000i 0.476581i
\(635\) 0 0
\(636\) 0 0
\(637\) 9.65926 2.58819i 0.382714 0.102548i
\(638\) 0 0
\(639\) −27.7128 −1.09630
\(640\) 0 0
\(641\) −10.5000 + 6.06218i −0.414725 + 0.239442i −0.692818 0.721113i \(-0.743631\pi\)
0.278093 + 0.960554i \(0.410298\pi\)
\(642\) −14.4889 + 3.88229i −0.571831 + 0.153222i
\(643\) −2.24144 + 8.36516i −0.0883937 + 0.329890i −0.995935 0.0900726i \(-0.971290\pi\)
0.907541 + 0.419962i \(0.137957\pi\)
\(644\) 10.3923 6.00000i 0.409514 0.236433i
\(645\) 0 0
\(646\) −3.00000 6.92820i −0.118033 0.272587i
\(647\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(648\) 0.965926 + 0.258819i 0.0379452 + 0.0101674i
\(649\) 0 0
\(650\) 0 0
\(651\) −18.0000 31.1769i −0.705476 1.22192i
\(652\) 4.48288 + 16.7303i 0.175563 + 0.655210i
\(653\) −34.2929 34.2929i −1.34198 1.34198i −0.894084 0.447899i \(-0.852172\pi\)
−0.447899 0.894084i \(-0.647828\pi\)
\(654\) 17.3205 0.677285
\(655\) 0 0
\(656\) 6.00000 + 3.46410i 0.234261 + 0.135250i
\(657\) 12.2474 12.2474i 0.477818 0.477818i
\(658\) −16.9706 + 16.9706i −0.661581 + 0.661581i
\(659\) 0.866025 1.50000i 0.0337356 0.0584317i −0.848665 0.528931i \(-0.822593\pi\)
0.882400 + 0.470500i \(0.155926\pi\)
\(660\) 0 0
\(661\) −6.00000 3.46410i −0.233373 0.134738i 0.378754 0.925497i \(-0.376353\pi\)
−0.612127 + 0.790759i \(0.709686\pi\)
\(662\) 5.01910 + 1.34486i 0.195073 + 0.0522696i
\(663\) −0.896575 + 3.34607i −0.0348201 + 0.129950i
\(664\) −1.73205 −0.0672166
\(665\) 0 0
\(666\) −8.00000 −0.309994
\(667\) −3.10583 + 11.5911i −0.120258 + 0.448810i
\(668\) 17.3867 + 4.65874i 0.672710 + 0.180252i
\(669\) −1.73205 1.00000i −0.0669650 0.0386622i
\(670\) 0 0
\(671\) 0 0
\(672\) −2.44949 + 2.44949i −0.0944911 + 0.0944911i
\(673\) −32.5269 + 32.5269i −1.25382 + 1.25382i −0.299827 + 0.953994i \(0.596929\pi\)
−0.953994 + 0.299827i \(0.903071\pi\)
\(674\) −19.0526 11.0000i −0.733877 0.423704i
\(675\) 0 0
\(676\) −9.00000 −0.346154
\(677\) −21.2132 21.2132i −0.815290 0.815290i 0.170132 0.985421i \(-0.445581\pi\)
−0.985421 + 0.170132i \(0.945581\pi\)
\(678\) −2.32937 8.69333i −0.0894590 0.333865i
\(679\) 12.1244 + 21.0000i 0.465290 + 0.805906i
\(680\) 0 0
\(681\) 13.5000 + 23.3827i 0.517321 + 0.896026i
\(682\) 0 0
\(683\) −23.3345 + 23.3345i −0.892871 + 0.892871i −0.994792 0.101922i \(-0.967501\pi\)
0.101922 + 0.994792i \(0.467501\pi\)
\(684\) 8.66025 + 1.00000i 0.331133 + 0.0382360i
\(685\) 0 0
\(686\) 6.00000 3.46410i 0.229081 0.132260i
\(687\) −5.69402 + 21.2504i −0.217240 + 0.810752i
\(688\) 3.34607 0.896575i 0.127568 0.0341816i
\(689\) 0 0
\(690\) 0 0
\(691\) 43.0000 1.63580 0.817899 0.575362i \(-0.195139\pi\)
0.817899 + 0.575362i \(0.195139\pi\)
\(692\) 12.7279 + 12.7279i 0.483843 + 0.483843i
\(693\) 0 0
\(694\) −1.73205 + 3.00000i −0.0657477 + 0.113878i
\(695\) 0 0
\(696\) 3.46410i 0.131306i
\(697\) −11.5911 + 3.10583i −0.439045 + 0.117642i
\(698\) −27.0459 7.24693i −1.02370 0.274300i
\(699\) 11.2583 19.5000i 0.425829 0.737558i
\(700\) 0 0
\(701\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(702\) −7.07107 7.07107i −0.266880 0.266880i
\(703\) −17.2480 + 2.55103i −0.650519 + 0.0962138i
\(704\) 0 0
\(705\) 0 0
\(706\) 4.50000 2.59808i 0.169360 0.0977799i
\(707\) −5.37945 20.0764i −0.202315 0.755050i
\(708\) 1.34486 5.01910i 0.0505431 0.188629i
\(709\) 6.92820 + 4.00000i 0.260194 + 0.150223i 0.624423 0.781086i \(-0.285334\pi\)
−0.364229 + 0.931309i \(0.618667\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 2.24144 + 8.36516i 0.0840015 + 0.313498i
\(713\) −9.31749 34.7733i −0.348943 1.30227i
\(714\) 6.00000i 0.224544i
\(715\) 0 0
\(716\) 7.50000 + 4.33013i 0.280288 + 0.161824i
\(717\) −4.65874 + 17.3867i −0.173984 + 0.649317i
\(718\) 3.10583 + 11.5911i 0.115908 + 0.432576i
\(719\) −31.1769 + 18.0000i −1.16270 + 0.671287i −0.951950 0.306253i \(-0.900925\pi\)
−0.210752 + 0.977539i \(0.567591\pi\)
\(720\) 0 0
\(721\) 13.8564i 0.516040i
\(722\) 18.9903 0.605571i 0.706748 0.0225370i
\(723\) 0 0
\(724\) 3.46410 + 6.00000i 0.128742 + 0.222988i
\(725\) 0 0
\(726\) −5.50000 + 9.52628i −0.204124 + 0.353553i
\(727\) −10.0382 2.68973i −0.372296 0.0997564i 0.0678194 0.997698i \(-0.478396\pi\)
−0.440115 + 0.897941i \(0.645062\pi\)
\(728\) −6.69213 + 1.79315i −0.248027 + 0.0664586i
\(729\) 13.0000i 0.481481i
\(730\) 0 0
\(731\) −3.00000 + 5.19615i −0.110959 + 0.192187i
\(732\) 7.72741 2.07055i 0.285613 0.0765298i
\(733\) −7.34847 7.34847i −0.271422 0.271422i 0.558251 0.829672i \(-0.311473\pi\)
−0.829672 + 0.558251i \(0.811473\pi\)
\(734\) −27.7128 −1.02290
\(735\) 0 0
\(736\) −3.00000 + 1.73205i −0.110581 + 0.0638442i
\(737\) 0 0
\(738\) 3.58630 13.3843i 0.132014 0.492681i
\(739\) −21.6506 + 12.5000i −0.796431 + 0.459820i −0.842222 0.539131i \(-0.818753\pi\)
0.0457903 + 0.998951i \(0.485419\pi\)
\(740\) 0 0
\(741\) −7.00000 5.19615i −0.257151 0.190885i
\(742\) 0 0
\(743\) −5.79555 1.55291i −0.212618 0.0569709i 0.150938 0.988543i \(-0.451771\pi\)
−0.363556 + 0.931572i \(0.618437\pi\)
\(744\) 5.19615 + 9.00000i 0.190500 + 0.329956i
\(745\) 0 0
\(746\) 5.00000 + 8.66025i 0.183063 + 0.317074i
\(747\) 0.896575 + 3.34607i 0.0328040 + 0.122426i
\(748\) 0 0
\(749\) 51.9615 1.89863
\(750\) 0 0
\(751\) −9.00000 5.19615i −0.328415 0.189610i 0.326722 0.945120i \(-0.394056\pi\)
−0.655137 + 0.755510i \(0.727389\pi\)
\(752\) 4.89898 4.89898i 0.178647 0.178647i
\(753\) 8.48528 8.48528i 0.309221 0.309221i
\(754\) 3.46410 6.00000i 0.126155 0.218507i
\(755\) 0 0
\(756\) 15.0000 + 8.66025i 0.545545 + 0.314970i
\(757\) −33.4607 8.96575i −1.21615 0.325866i −0.406977 0.913439i \(-0.633417\pi\)
−0.809171 + 0.587573i \(0.800084\pi\)
\(758\) −1.34486 + 5.01910i −0.0488476 + 0.182302i
\(759\) 0 0
\(760\) 0 0
\(761\) −18.0000 −0.652499 −0.326250 0.945284i \(-0.605785\pi\)
−0.326250 + 0.945284i \(0.605785\pi\)
\(762\) −1.03528 + 3.86370i −0.0375041 + 0.139967i
\(763\) −57.9555 15.5291i −2.09813 0.562193i
\(764\) −5.19615 3.00000i −0.187990 0.108536i
\(765\) 0 0
\(766\) 12.0000 20.7846i 0.433578 0.750978i
\(767\) 7.34847 7.34847i 0.265338 0.265338i
\(768\) 0.707107 0.707107i 0.0255155 0.0255155i
\(769\) 19.9186 + 11.5000i 0.718283 + 0.414701i 0.814120 0.580696i \(-0.197220\pi\)
−0.0958377 + 0.995397i \(0.530553\pi\)
\(770\) 0 0
\(771\) 9.00000 0.324127
\(772\) 7.77817 + 7.77817i 0.279943 + 0.279943i
\(773\) 4.65874 + 17.3867i 0.167563 + 0.625355i 0.997699 + 0.0677939i \(0.0215960\pi\)
−0.830136 + 0.557561i \(0.811737\pi\)
\(774\) −3.46410 6.00000i −0.124515 0.215666i
\(775\) 0 0
\(776\) −3.50000 6.06218i −0.125643 0.217620i
\(777\) −13.3843 3.58630i −0.480158 0.128658i
\(778\) 21.2132 21.2132i 0.760530 0.760530i
\(779\) 3.46410 30.0000i 0.124114 1.07486i
\(780\) 0 0
\(781\) 0 0
\(782\) 1.55291 5.79555i 0.0555321 0.207249i
\(783\) −16.7303 + 4.48288i −0.597893 + 0.160205i
\(784\) 4.33013 2.50000i 0.154647 0.0892857i
\(785\) 0 0
\(786\) −15.0000 −0.535032
\(787\) 9.19239 + 9.19239i 0.327673 + 0.327673i 0.851701 0.524028i \(-0.175571\pi\)
−0.524028 + 0.851701i \(0.675571\pi\)
\(788\) 0 0
\(789\) −12.1244 + 21.0000i −0.431638 + 0.747620i
\(790\) 0 0
\(791\) 31.1769i 1.10852i
\(792\) 0 0
\(793\) 15.4548 + 4.14110i 0.548817 + 0.147055i
\(794\) −15.5885 + 27.0000i −0.553214 + 0.958194i
\(795\) 0 0
\(796\) −2.00000 3.46410i −0.0708881 0.122782i
\(797\) −8.48528 8.48528i −0.300564 0.300564i 0.540670 0.841235i \(-0.318171\pi\)
−0.841235 + 0.540670i \(0.818171\pi\)
\(798\) 14.0406 + 5.55532i 0.497032 + 0.196656i
\(799\) 12.0000i 0.424529i
\(800\) 0 0
\(801\) 15.0000 8.66025i 0.529999 0.305995i
\(802\) −8.96575 33.4607i −0.316592 1.18154i
\(803\) 0 0
\(804\) 6.92820 + 4.00000i 0.244339 + 0.141069i
\(805\) 0 0
\(806\) 20.7846i 0.732107i
\(807\) −6.27603 23.4225i −0.220927 0.824510i
\(808\) 1.55291 + 5.79555i 0.0546313 + 0.203887i
\(809\) 51.0000i 1.79306i −0.442978 0.896532i \(-0.646078\pi\)
0.442978 0.896532i \(-0.353922\pi\)
\(810\) 0 0
\(811\) −15.0000 8.66025i −0.526721 0.304103i 0.212959 0.977061i \(-0.431690\pi\)
−0.739680 + 0.672958i \(0.765023\pi\)
\(812\) −3.10583 + 11.5911i −0.108993 + 0.406768i
\(813\) 0.517638 + 1.93185i 0.0181544 + 0.0677530i
\(814\) 0 0
\(815\) 0 0
\(816\) 1.73205i 0.0606339i
\(817\) −9.38186 11.8313i −0.328230 0.413926i
\(818\) 4.89898 + 4.89898i 0.171289 + 0.171289i
\(819\) 6.92820 + 12.0000i 0.242091 + 0.419314i
\(820\) 0 0
\(821\) −21.0000 + 36.3731i −0.732905 + 1.26943i 0.222731 + 0.974880i \(0.428503\pi\)
−0.955636 + 0.294549i \(0.904831\pi\)
\(822\) −15.0573 4.03459i −0.525183 0.140722i
\(823\) −26.7685 + 7.17260i −0.933092 + 0.250021i −0.693173 0.720772i \(-0.743788\pi\)
−0.239919 + 0.970793i \(0.577121\pi\)
\(824\) 4.00000i 0.139347i
\(825\) 0 0
\(826\) −9.00000 + 15.5885i −0.313150 + 0.542392i
\(827\) −34.7733 + 9.31749i −1.20919 + 0.324001i −0.806443 0.591312i \(-0.798610\pi\)
−0.402744 + 0.915313i \(0.631944\pi\)
\(828\) 4.89898 + 4.89898i 0.170251 + 0.170251i
\(829\) 45.0333 1.56407 0.782036 0.623233i \(-0.214181\pi\)
0.782036 + 0.623233i \(0.214181\pi\)
\(830\) 0 0
\(831\) −21.0000 + 12.1244i −0.728482 + 0.420589i
\(832\) 1.93185 0.517638i 0.0669749 0.0179459i
\(833\) −2.24144 + 8.36516i −0.0776612 + 0.289836i
\(834\) 13.8564 8.00000i 0.479808 0.277017i
\(835\) 0 0
\(836\) 0 0
\(837\) 36.7423 36.7423i 1.27000 1.27000i
\(838\) 20.2844 + 5.43520i 0.700714 + 0.187756i
\(839\) 24.2487 + 42.0000i 0.837158 + 1.45000i 0.892261 + 0.451520i \(0.149118\pi\)
−0.0551024 + 0.998481i \(0.517549\pi\)
\(840\) 0 0
\(841\) 8.50000 + 14.7224i 0.293103 + 0.507670i
\(842\) 9.86233 + 36.8067i 0.339878 + 1.26844i
\(843\) 8.57321 + 8.57321i 0.295277 + 0.295277i
\(844\) 5.19615 0.178859
\(845\) 0 0
\(846\) −12.0000 6.92820i −0.412568 0.238197i
\(847\) 26.9444 26.9444i 0.925820 0.925820i
\(848\) 0 0
\(849\) −1.73205 + 3.00000i −0.0594438 + 0.102960i
\(850\) 0 0
\(851\) −12.0000 6.92820i −0.411355 0.237496i
\(852\) 13.3843 + 3.58630i 0.458537 + 0.122865i
\(853\) −5.37945 + 20.0764i −0.184189 + 0.687403i 0.810614 + 0.585581i \(0.199134\pi\)
−0.994803 + 0.101821i \(0.967533\pi\)
\(854\) −27.7128 −0.948313
\(855\) 0 0
\(856\) −15.0000 −0.512689
\(857\) −7.76457 + 28.9778i −0.265233 + 0.989862i 0.696875 + 0.717193i \(0.254573\pi\)
−0.962108 + 0.272669i \(0.912093\pi\)
\(858\) 0 0
\(859\) −0.866025 0.500000i −0.0295484 0.0170598i 0.485153 0.874429i \(-0.338764\pi\)
−0.514701 + 0.857369i \(0.672097\pi\)
\(860\) 0 0
\(861\) 12.0000 20.7846i 0.408959 0.708338i
\(862\) −17.1464 + 17.1464i −0.584010 + 0.584010i
\(863\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(864\) −4.33013 2.50000i −0.147314 0.0850517i
\(865\) 0 0
\(866\) −35.0000 −1.18935
\(867\) 9.89949 + 9.89949i 0.336204 + 0.336204i
\(868\) −9.31749 34.7733i −0.316256 1.18028i
\(869\) 0 0
\(870\) 0 0
\(871\) 8.00000 + 13.8564i 0.271070 + 0.469506i
\(872\) 16.7303 + 4.48288i 0.566560 + 0.151809i
\(873\) −9.89949 + 9.89949i −0.335047 + 0.335047i
\(874\) 12.1244 + 9.00000i 0.410112 + 0.304430i
\(875\) 0 0
\(876\) −7.50000 + 4.33013i −0.253402 + 0.146301i
\(877\) −0.517638 + 1.93185i −0.0174794 + 0.0652340i −0.974115 0.226054i \(-0.927417\pi\)
0.956635 + 0.291288i \(0.0940839\pi\)
\(878\) 6.69213 1.79315i 0.225848 0.0605159i
\(879\) 0 0
\(880\) 0 0
\(881\) −45.0000 −1.51609 −0.758044 0.652203i \(-0.773845\pi\)
−0.758044 + 0.652203i \(0.773845\pi\)
\(882\) −7.07107 7.07107i −0.238095 0.238095i
\(883\) 1.67303 0.448288i 0.0563020 0.0150861i −0.230558 0.973059i \(-0.574055\pi\)
0.286860 + 0.957972i \(0.407389\pi\)
\(884\) −1.73205 + 3.00000i −0.0582552 + 0.100901i
\(885\) 0 0
\(886\) 24.2487i 0.814651i
\(887\) 0 0 −0.258819 0.965926i \(-0.583333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(888\) 3.86370 + 1.03528i 0.129657 + 0.0347416i
\(889\) 6.92820 12.0000i 0.232364 0.402467i
\(890\) 0 0
\(891\) 0 0
\(892\) −1.41421 1.41421i −0.0473514 0.0473514i
\(893\) −28.0812 11.1106i −0.939702 0.371803i
\(894\) 0 0
\(895\) 0 0
\(896\) −3.00000 + 1.73205i −0.100223 + 0.0578638i
\(897\) −1.79315 6.69213i −0.0598716 0.223444i
\(898\) 6.72432 25.0955i 0.224393 0.837447i
\(899\) 31.1769 + 18.0000i 1.03981 + 0.600334i
\(900\) 0 0
\(901\) 0 0
\(902\) 0 0
\(903\) −3.10583 11.5911i −0.103356 0.385728i
\(904\) 9.00000i 0.299336i
\(905\) 0 0
\(906\) 18.0000 + 10.3923i 0.598010 + 0.345261i
\(907\) 9.57630 35.7393i 0.317976 1.18670i −0.603211 0.797582i \(-0.706112\pi\)
0.921187 0.389121i \(-0.127221\pi\)
\(908\) 6.98811 + 26.0800i 0.231909 + 0.865495i
\(909\) 10.3923 6.00000i 0.344691 0.199007i
\(910\) 0 0
\(911\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(912\) −4.05317 1.60368i −0.134214 0.0531032i
\(913\) 0 0
\(914\) −9.52628 16.5000i −0.315101 0.545771i
\(915\) 0 0
\(916\) −11.0000 + 19.0526i −0.363450 + 0.629514i
\(917\) 50.1910 + 13.4486i 1.65745 + 0.444113i
\(918\) 8.36516 2.24144i 0.276092 0.0739785i
\(919\) 32.0000i 1.05558i 0.849374 + 0.527791i \(0.176980\pi\)
−0.849374 + 0.527791i \(0.823020\pi\)
\(920\) 0 0
\(921\) 5.50000 9.52628i 0.181231 0.313902i
\(922\) 17.3867 4.65874i 0.572599 0.153428i
\(923\) 19.5959 + 19.5959i 0.645007 + 0.645007i
\(924\) 0 0
\(925\) 0 0
\(926\) −9.00000 + 5.19615i −0.295758 + 0.170756i
\(927\) −7.72741 + 2.07055i −0.253801 + 0.0680059i
\(928\) 0.896575 3.34607i 0.0294315 0.109840i
\(929\) −18.1865 + 10.5000i −0.596681 + 0.344494i −0.767735 0.640768i \(-0.778616\pi\)
0.171054 + 0.985262i \(0.445283\pi\)
\(930\) 0 0
\(931\) −17.5000 12.9904i −0.573539 0.425743i
\(932\) 15.9217 15.9217i 0.521532 0.521532i
\(933\) −28.9778 7.76457i −0.948690 0.254201i
\(934\) 18.1865 + 31.5000i 0.595082 + 1.03071i
\(935\) 0 0
\(936\) −2.00000 3.46410i −0.0653720 0.113228i
\(937\) 11.2072 + 41.8258i 0.366123 + 1.36639i 0.865892 + 0.500231i \(0.166752\pi\)
−0.499769 + 0.866159i \(0.666582\pi\)
\(938\) −19.5959 19.5959i −0.639829 0.639829i
\(939\) −19.0526 −0.621757
\(940\) 0 0
\(941\) 12.0000 + 6.92820i 0.391189 + 0.225853i 0.682675 0.730722i \(-0.260816\pi\)
−0.291486 + 0.956575i \(0.594150\pi\)
\(942\) 12.2474 12.2474i 0.399043 0.399043i
\(943\) 16.9706 16.9706i 0.552638 0.552638i
\(944\) 2.59808 4.50000i 0.0845602 0.146463i
\(945\) 0 0
\(946\) 0 0
\(947\) −56.8831 15.2418i −1.84845 0.495291i −0.849001 0.528392i \(-0.822795\pi\)
−0.999452 + 0.0331004i \(0.989462\pi\)
\(948\) 0 0
\(949\) −17.3205 −0.562247
\(950\) 0 0
\(951\) −12.0000 −0.389127
\(952\) 1.55291 5.79555i 0.0503302 0.187835i
\(953\) 5.79555 + 1.55291i 0.187736 + 0.0503038i 0.351462 0.936202i \(-0.385685\pi\)
−0.163726 + 0.986506i \(0.552351\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) −9.00000 + 15.5885i −0.291081 + 0.504167i
\(957\) 0 0
\(958\) 0 0
\(959\) 46.7654 + 27.0000i 1.51013 + 0.871875i
\(960\) 0 0
\(961\) −77.0000 −2.48387
\(962\) 5.65685 + 5.65685i 0.182384 + 0.182384i
\(963\) 7.76457 + 28.9778i 0.250210 + 0.933796i
\(964\) 0 0
\(965\) 0 0
\(966\) 6.00000 + 10.3923i 0.193047 + 0.334367i
\(967\) 26.7685 + 7.17260i 0.860818 + 0.230655i 0.662113 0.749404i \(-0.269660\pi\)
0.198705 + 0.980059i \(0.436327\pi\)
\(968\) −7.77817 + 7.77817i −0.250000 + 0.250000i
\(969\) 6.92820 3.00000i 0.222566 0.0963739i
\(970\) 0 0
\(971\) 25.5000 14.7224i 0.818334 0.472465i −0.0315077 0.999504i \(-0.510031\pi\)
0.849842 + 0.527038i \(0.176698\pi\)
\(972\) −4.14110 + 15.4548i −0.132826 + 0.495713i
\(973\) −53.5370 + 14.3452i −1.71632 + 0.459886i
\(974\) 13.8564 8.00000i 0.443988 0.256337i
\(975\) 0 0
\(976\) 8.00000 0.256074
\(977\) 4.24264 + 4.24264i 0.135734 + 0.135734i 0.771709 0.635975i \(-0.219402\pi\)
−0.635975 + 0.771709i \(0.719402\pi\)
\(978\) −16.7303 + 4.48288i −0.534977 + 0.143347i
\(979\) 0 0
\(980\) 0 0
\(981\) 34.6410i 1.10600i
\(982\) −23.1822 + 6.21166i −0.739774 + 0.198222i
\(983\) −57.9555 15.5291i −1.84849 0.495303i −0.849040 0.528328i \(-0.822819\pi\)
−0.999455 + 0.0330251i \(0.989486\pi\)
\(984\) −3.46410 + 6.00000i −0.110432 + 0.191273i
\(985\) 0 0
\(986\) 3.00000 + 5.19615i 0.0955395 + 0.165479i
\(987\) −16.9706 16.9706i −0.540179 0.540179i
\(988\) −5.41662 6.83083i −0.172326 0.217318i
\(989\) 12.0000i 0.381578i
\(990\) 0 0
\(991\) −42.0000 + 24.2487i −1.33417 + 0.770286i −0.985936 0.167121i \(-0.946553\pi\)
−0.348238 + 0.937406i \(0.613220\pi\)
\(992\) 2.68973 + 10.0382i 0.0853989 + 0.318713i
\(993\) −1.34486 + 5.01910i −0.0426779 + 0.159276i
\(994\) −41.5692 24.0000i −1.31850 0.761234i
\(995\) 0 0
\(996\) 1.73205i 0.0548821i
\(997\) −6.27603 23.4225i −0.198764 0.741797i −0.991260 0.131920i \(-0.957886\pi\)
0.792497 0.609876i \(-0.208781\pi\)
\(998\) 8.02339 + 29.9437i 0.253976 + 0.947851i
\(999\) 20.0000i 0.632772i
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 950.2.q.c.943.1 yes 8
5.2 odd 4 inner 950.2.q.c.107.1 8
5.3 odd 4 inner 950.2.q.c.107.2 yes 8
5.4 even 2 inner 950.2.q.c.943.2 yes 8
19.8 odd 6 inner 950.2.q.c.293.1 yes 8
95.8 even 12 inner 950.2.q.c.407.2 yes 8
95.27 even 12 inner 950.2.q.c.407.1 yes 8
95.84 odd 6 inner 950.2.q.c.293.2 yes 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
950.2.q.c.107.1 8 5.2 odd 4 inner
950.2.q.c.107.2 yes 8 5.3 odd 4 inner
950.2.q.c.293.1 yes 8 19.8 odd 6 inner
950.2.q.c.293.2 yes 8 95.84 odd 6 inner
950.2.q.c.407.1 yes 8 95.27 even 12 inner
950.2.q.c.407.2 yes 8 95.8 even 12 inner
950.2.q.c.943.1 yes 8 1.1 even 1 trivial
950.2.q.c.943.2 yes 8 5.4 even 2 inner