Properties

Label 245.2.j.e.214.2
Level $245$
Weight $2$
Character 245.214
Analytic conductor $1.956$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [245,2,Mod(79,245)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(245, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("245.79");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 245 = 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 245.j (of order \(6\), degree \(2\), not 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: \(1.95633484952\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{12})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 35)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 214.2
Root \(0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 245.214
Dual form 245.2.j.e.79.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.73205 - 1.00000i) q^{2} +(0.866025 + 0.500000i) q^{3} +(1.00000 - 1.73205i) q^{4} +(0.133975 + 2.23205i) q^{5} +2.00000 q^{6} +(-1.00000 - 1.73205i) q^{9} +O(q^{10})\) \(q+(1.73205 - 1.00000i) q^{2} +(0.866025 + 0.500000i) q^{3} +(1.00000 - 1.73205i) q^{4} +(0.133975 + 2.23205i) q^{5} +2.00000 q^{6} +(-1.00000 - 1.73205i) q^{9} +(2.46410 + 3.73205i) q^{10} +(1.50000 - 2.59808i) q^{11} +(1.73205 - 1.00000i) q^{12} -1.00000i q^{13} +(-1.00000 + 2.00000i) q^{15} +(2.00000 + 3.46410i) q^{16} +(-6.06218 - 3.50000i) q^{17} +(-3.46410 - 2.00000i) q^{18} +(4.00000 + 2.00000i) q^{20} -6.00000i q^{22} +(-5.19615 + 3.00000i) q^{23} +(-4.96410 + 0.598076i) q^{25} +(-1.00000 - 1.73205i) q^{26} -5.00000i q^{27} +5.00000 q^{29} +(0.267949 + 4.46410i) q^{30} +(-1.00000 + 1.73205i) q^{31} +(6.92820 + 4.00000i) q^{32} +(2.59808 - 1.50000i) q^{33} -14.0000 q^{34} -4.00000 q^{36} +(1.73205 - 1.00000i) q^{37} +(0.500000 - 0.866025i) q^{39} +2.00000 q^{41} +4.00000i q^{43} +(-3.00000 - 5.19615i) q^{44} +(3.73205 - 2.46410i) q^{45} +(-6.00000 + 10.3923i) q^{46} +(-2.59808 + 1.50000i) q^{47} +4.00000i q^{48} +(-8.00000 + 6.00000i) q^{50} +(-3.50000 - 6.06218i) q^{51} +(-1.73205 - 1.00000i) q^{52} +(5.19615 + 3.00000i) q^{53} +(-5.00000 - 8.66025i) q^{54} +(6.00000 + 3.00000i) q^{55} +(8.66025 - 5.00000i) q^{58} +(5.00000 - 8.66025i) q^{59} +(2.46410 + 3.73205i) q^{60} +(4.00000 + 6.92820i) q^{61} +4.00000i q^{62} +8.00000 q^{64} +(2.23205 - 0.133975i) q^{65} +(3.00000 - 5.19615i) q^{66} +(-1.73205 - 1.00000i) q^{67} +(-12.1244 + 7.00000i) q^{68} -6.00000 q^{69} -8.00000 q^{71} +(5.19615 + 3.00000i) q^{73} +(2.00000 - 3.46410i) q^{74} +(-4.59808 - 1.96410i) q^{75} -2.00000i q^{78} +(-2.50000 - 4.33013i) q^{79} +(-7.46410 + 4.92820i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(3.46410 - 2.00000i) q^{82} +4.00000i q^{83} +(7.00000 - 14.0000i) q^{85} +(4.00000 + 6.92820i) q^{86} +(4.33013 + 2.50000i) q^{87} +(4.00000 - 8.00000i) q^{90} +12.0000i q^{92} +(-1.73205 + 1.00000i) q^{93} +(-3.00000 + 5.19615i) q^{94} +(4.00000 + 6.92820i) q^{96} +7.00000i q^{97} -6.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 4 q^{4} + 4 q^{5} + 8 q^{6} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 4 q^{4} + 4 q^{5} + 8 q^{6} - 4 q^{9} - 4 q^{10} + 6 q^{11} - 4 q^{15} + 8 q^{16} + 16 q^{20} - 6 q^{25} - 4 q^{26} + 20 q^{29} + 8 q^{30} - 4 q^{31} - 56 q^{34} - 16 q^{36} + 2 q^{39} + 8 q^{41} - 12 q^{44} + 8 q^{45} - 24 q^{46} - 32 q^{50} - 14 q^{51} - 20 q^{54} + 24 q^{55} + 20 q^{59} - 4 q^{60} + 16 q^{61} + 32 q^{64} + 2 q^{65} + 12 q^{66} - 24 q^{69} - 32 q^{71} + 8 q^{74} - 8 q^{75} - 10 q^{79} - 16 q^{80} - 2 q^{81} + 28 q^{85} + 16 q^{86} + 16 q^{90} - 12 q^{94} + 16 q^{96} - 24 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/245\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(197\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.73205 1.00000i 1.22474 0.707107i 0.258819 0.965926i \(-0.416667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(3\) 0.866025 + 0.500000i 0.500000 + 0.288675i 0.728714 0.684819i \(-0.240119\pi\)
−0.228714 + 0.973494i \(0.573452\pi\)
\(4\) 1.00000 1.73205i 0.500000 0.866025i
\(5\) 0.133975 + 2.23205i 0.0599153 + 0.998203i
\(6\) 2.00000 0.816497
\(7\) 0 0
\(8\) 0 0
\(9\) −1.00000 1.73205i −0.333333 0.577350i
\(10\) 2.46410 + 3.73205i 0.779217 + 1.18018i
\(11\) 1.50000 2.59808i 0.452267 0.783349i −0.546259 0.837616i \(-0.683949\pi\)
0.998526 + 0.0542666i \(0.0172821\pi\)
\(12\) 1.73205 1.00000i 0.500000 0.288675i
\(13\) 1.00000i 0.277350i −0.990338 0.138675i \(-0.955716\pi\)
0.990338 0.138675i \(-0.0442844\pi\)
\(14\) 0 0
\(15\) −1.00000 + 2.00000i −0.258199 + 0.516398i
\(16\) 2.00000 + 3.46410i 0.500000 + 0.866025i
\(17\) −6.06218 3.50000i −1.47029 0.848875i −0.470850 0.882213i \(-0.656053\pi\)
−0.999444 + 0.0333386i \(0.989386\pi\)
\(18\) −3.46410 2.00000i −0.816497 0.471405i
\(19\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(20\) 4.00000 + 2.00000i 0.894427 + 0.447214i
\(21\) 0 0
\(22\) 6.00000i 1.27920i
\(23\) −5.19615 + 3.00000i −1.08347 + 0.625543i −0.931831 0.362892i \(-0.881789\pi\)
−0.151642 + 0.988436i \(0.548456\pi\)
\(24\) 0 0
\(25\) −4.96410 + 0.598076i −0.992820 + 0.119615i
\(26\) −1.00000 1.73205i −0.196116 0.339683i
\(27\) 5.00000i 0.962250i
\(28\) 0 0
\(29\) 5.00000 0.928477 0.464238 0.885710i \(-0.346328\pi\)
0.464238 + 0.885710i \(0.346328\pi\)
\(30\) 0.267949 + 4.46410i 0.0489206 + 0.815030i
\(31\) −1.00000 + 1.73205i −0.179605 + 0.311086i −0.941745 0.336327i \(-0.890815\pi\)
0.762140 + 0.647412i \(0.224149\pi\)
\(32\) 6.92820 + 4.00000i 1.22474 + 0.707107i
\(33\) 2.59808 1.50000i 0.452267 0.261116i
\(34\) −14.0000 −2.40098
\(35\) 0 0
\(36\) −4.00000 −0.666667
\(37\) 1.73205 1.00000i 0.284747 0.164399i −0.350823 0.936442i \(-0.614098\pi\)
0.635571 + 0.772043i \(0.280765\pi\)
\(38\) 0 0
\(39\) 0.500000 0.866025i 0.0800641 0.138675i
\(40\) 0 0
\(41\) 2.00000 0.312348 0.156174 0.987730i \(-0.450084\pi\)
0.156174 + 0.987730i \(0.450084\pi\)
\(42\) 0 0
\(43\) 4.00000i 0.609994i 0.952353 + 0.304997i \(0.0986555\pi\)
−0.952353 + 0.304997i \(0.901344\pi\)
\(44\) −3.00000 5.19615i −0.452267 0.783349i
\(45\) 3.73205 2.46410i 0.556341 0.367327i
\(46\) −6.00000 + 10.3923i −0.884652 + 1.53226i
\(47\) −2.59808 + 1.50000i −0.378968 + 0.218797i −0.677369 0.735643i \(-0.736880\pi\)
0.298401 + 0.954441i \(0.403547\pi\)
\(48\) 4.00000i 0.577350i
\(49\) 0 0
\(50\) −8.00000 + 6.00000i −1.13137 + 0.848528i
\(51\) −3.50000 6.06218i −0.490098 0.848875i
\(52\) −1.73205 1.00000i −0.240192 0.138675i
\(53\) 5.19615 + 3.00000i 0.713746 + 0.412082i 0.812447 0.583036i \(-0.198135\pi\)
−0.0987002 + 0.995117i \(0.531468\pi\)
\(54\) −5.00000 8.66025i −0.680414 1.17851i
\(55\) 6.00000 + 3.00000i 0.809040 + 0.404520i
\(56\) 0 0
\(57\) 0 0
\(58\) 8.66025 5.00000i 1.13715 0.656532i
\(59\) 5.00000 8.66025i 0.650945 1.12747i −0.331949 0.943297i \(-0.607706\pi\)
0.982894 0.184172i \(-0.0589603\pi\)
\(60\) 2.46410 + 3.73205i 0.318114 + 0.481806i
\(61\) 4.00000 + 6.92820i 0.512148 + 0.887066i 0.999901 + 0.0140840i \(0.00448323\pi\)
−0.487753 + 0.872982i \(0.662183\pi\)
\(62\) 4.00000i 0.508001i
\(63\) 0 0
\(64\) 8.00000 1.00000
\(65\) 2.23205 0.133975i 0.276852 0.0166175i
\(66\) 3.00000 5.19615i 0.369274 0.639602i
\(67\) −1.73205 1.00000i −0.211604 0.122169i 0.390453 0.920623i \(-0.372318\pi\)
−0.602056 + 0.798454i \(0.705652\pi\)
\(68\) −12.1244 + 7.00000i −1.47029 + 0.848875i
\(69\) −6.00000 −0.722315
\(70\) 0 0
\(71\) −8.00000 −0.949425 −0.474713 0.880141i \(-0.657448\pi\)
−0.474713 + 0.880141i \(0.657448\pi\)
\(72\) 0 0
\(73\) 5.19615 + 3.00000i 0.608164 + 0.351123i 0.772246 0.635323i \(-0.219133\pi\)
−0.164083 + 0.986447i \(0.552466\pi\)
\(74\) 2.00000 3.46410i 0.232495 0.402694i
\(75\) −4.59808 1.96410i −0.530940 0.226795i
\(76\) 0 0
\(77\) 0 0
\(78\) 2.00000i 0.226455i
\(79\) −2.50000 4.33013i −0.281272 0.487177i 0.690426 0.723403i \(-0.257423\pi\)
−0.971698 + 0.236225i \(0.924090\pi\)
\(80\) −7.46410 + 4.92820i −0.834512 + 0.550990i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 3.46410 2.00000i 0.382546 0.220863i
\(83\) 4.00000i 0.439057i 0.975606 + 0.219529i \(0.0704519\pi\)
−0.975606 + 0.219529i \(0.929548\pi\)
\(84\) 0 0
\(85\) 7.00000 14.0000i 0.759257 1.51851i
\(86\) 4.00000 + 6.92820i 0.431331 + 0.747087i
\(87\) 4.33013 + 2.50000i 0.464238 + 0.268028i
\(88\) 0 0
\(89\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(90\) 4.00000 8.00000i 0.421637 0.843274i
\(91\) 0 0
\(92\) 12.0000i 1.25109i
\(93\) −1.73205 + 1.00000i −0.179605 + 0.103695i
\(94\) −3.00000 + 5.19615i −0.309426 + 0.535942i
\(95\) 0 0
\(96\) 4.00000 + 6.92820i 0.408248 + 0.707107i
\(97\) 7.00000i 0.710742i 0.934725 + 0.355371i \(0.115646\pi\)
−0.934725 + 0.355371i \(0.884354\pi\)
\(98\) 0 0
\(99\) −6.00000 −0.603023
\(100\) −3.92820 + 9.19615i −0.392820 + 0.919615i
\(101\) −6.00000 + 10.3923i −0.597022 + 1.03407i 0.396236 + 0.918149i \(0.370316\pi\)
−0.993258 + 0.115924i \(0.963017\pi\)
\(102\) −12.1244 7.00000i −1.20049 0.693103i
\(103\) 16.4545 9.50000i 1.62131 0.936063i 0.634738 0.772728i \(-0.281108\pi\)
0.986571 0.163335i \(-0.0522252\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 12.0000 1.16554
\(107\) −6.92820 + 4.00000i −0.669775 + 0.386695i −0.795991 0.605308i \(-0.793050\pi\)
0.126217 + 0.992003i \(0.459717\pi\)
\(108\) −8.66025 5.00000i −0.833333 0.481125i
\(109\) 2.50000 4.33013i 0.239457 0.414751i −0.721102 0.692829i \(-0.756364\pi\)
0.960558 + 0.278078i \(0.0896974\pi\)
\(110\) 13.3923 0.803848i 1.27691 0.0766439i
\(111\) 2.00000 0.189832
\(112\) 0 0
\(113\) 6.00000i 0.564433i −0.959351 0.282216i \(-0.908930\pi\)
0.959351 0.282216i \(-0.0910696\pi\)
\(114\) 0 0
\(115\) −7.39230 11.1962i −0.689336 1.04405i
\(116\) 5.00000 8.66025i 0.464238 0.804084i
\(117\) −1.73205 + 1.00000i −0.160128 + 0.0924500i
\(118\) 20.0000i 1.84115i
\(119\) 0 0
\(120\) 0 0
\(121\) 1.00000 + 1.73205i 0.0909091 + 0.157459i
\(122\) 13.8564 + 8.00000i 1.25450 + 0.724286i
\(123\) 1.73205 + 1.00000i 0.156174 + 0.0901670i
\(124\) 2.00000 + 3.46410i 0.179605 + 0.311086i
\(125\) −2.00000 11.0000i −0.178885 0.983870i
\(126\) 0 0
\(127\) 2.00000i 0.177471i 0.996055 + 0.0887357i \(0.0282826\pi\)
−0.996055 + 0.0887357i \(0.971717\pi\)
\(128\) 0 0
\(129\) −2.00000 + 3.46410i −0.176090 + 0.304997i
\(130\) 3.73205 2.46410i 0.327323 0.216116i
\(131\) −11.0000 19.0526i −0.961074 1.66463i −0.719811 0.694170i \(-0.755772\pi\)
−0.241264 0.970460i \(-0.577562\pi\)
\(132\) 6.00000i 0.522233i
\(133\) 0 0
\(134\) −4.00000 −0.345547
\(135\) 11.1603 0.669873i 0.960522 0.0576535i
\(136\) 0 0
\(137\) −10.3923 6.00000i −0.887875 0.512615i −0.0146279 0.999893i \(-0.504656\pi\)
−0.873247 + 0.487278i \(0.837990\pi\)
\(138\) −10.3923 + 6.00000i −0.884652 + 0.510754i
\(139\) 10.0000 0.848189 0.424094 0.905618i \(-0.360592\pi\)
0.424094 + 0.905618i \(0.360592\pi\)
\(140\) 0 0
\(141\) −3.00000 −0.252646
\(142\) −13.8564 + 8.00000i −1.16280 + 0.671345i
\(143\) −2.59808 1.50000i −0.217262 0.125436i
\(144\) 4.00000 6.92820i 0.333333 0.577350i
\(145\) 0.669873 + 11.1603i 0.0556299 + 0.926809i
\(146\) 12.0000 0.993127
\(147\) 0 0
\(148\) 4.00000i 0.328798i
\(149\) 5.00000 + 8.66025i 0.409616 + 0.709476i 0.994847 0.101391i \(-0.0323294\pi\)
−0.585231 + 0.810867i \(0.698996\pi\)
\(150\) −9.92820 + 1.19615i −0.810634 + 0.0976654i
\(151\) 6.50000 11.2583i 0.528962 0.916190i −0.470467 0.882418i \(-0.655915\pi\)
0.999430 0.0337724i \(-0.0107521\pi\)
\(152\) 0 0
\(153\) 14.0000i 1.13183i
\(154\) 0 0
\(155\) −4.00000 2.00000i −0.321288 0.160644i
\(156\) −1.00000 1.73205i −0.0800641 0.138675i
\(157\) 15.5885 + 9.00000i 1.24409 + 0.718278i 0.969925 0.243403i \(-0.0782638\pi\)
0.274169 + 0.961681i \(0.411597\pi\)
\(158\) −8.66025 5.00000i −0.688973 0.397779i
\(159\) 3.00000 + 5.19615i 0.237915 + 0.412082i
\(160\) −8.00000 + 16.0000i −0.632456 + 1.26491i
\(161\) 0 0
\(162\) 2.00000i 0.157135i
\(163\) 12.1244 7.00000i 0.949653 0.548282i 0.0566798 0.998392i \(-0.481949\pi\)
0.892973 + 0.450110i \(0.148615\pi\)
\(164\) 2.00000 3.46410i 0.156174 0.270501i
\(165\) 3.69615 + 5.59808i 0.287745 + 0.435810i
\(166\) 4.00000 + 6.92820i 0.310460 + 0.537733i
\(167\) 3.00000i 0.232147i −0.993241 0.116073i \(-0.962969\pi\)
0.993241 0.116073i \(-0.0370308\pi\)
\(168\) 0 0
\(169\) 12.0000 0.923077
\(170\) −1.87564 31.2487i −0.143855 2.39667i
\(171\) 0 0
\(172\) 6.92820 + 4.00000i 0.528271 + 0.304997i
\(173\) 7.79423 4.50000i 0.592584 0.342129i −0.173534 0.984828i \(-0.555519\pi\)
0.766119 + 0.642699i \(0.222185\pi\)
\(174\) 10.0000 0.758098
\(175\) 0 0
\(176\) 12.0000 0.904534
\(177\) 8.66025 5.00000i 0.650945 0.375823i
\(178\) 0 0
\(179\) −10.0000 + 17.3205i −0.747435 + 1.29460i 0.201613 + 0.979465i \(0.435382\pi\)
−0.949048 + 0.315130i \(0.897952\pi\)
\(180\) −0.535898 8.92820i −0.0399435 0.665469i
\(181\) −18.0000 −1.33793 −0.668965 0.743294i \(-0.733262\pi\)
−0.668965 + 0.743294i \(0.733262\pi\)
\(182\) 0 0
\(183\) 8.00000i 0.591377i
\(184\) 0 0
\(185\) 2.46410 + 3.73205i 0.181164 + 0.274386i
\(186\) −2.00000 + 3.46410i −0.146647 + 0.254000i
\(187\) −18.1865 + 10.5000i −1.32993 + 0.767836i
\(188\) 6.00000i 0.437595i
\(189\) 0 0
\(190\) 0 0
\(191\) 1.50000 + 2.59808i 0.108536 + 0.187990i 0.915177 0.403051i \(-0.132050\pi\)
−0.806641 + 0.591041i \(0.798717\pi\)
\(192\) 6.92820 + 4.00000i 0.500000 + 0.288675i
\(193\) 13.8564 + 8.00000i 0.997406 + 0.575853i 0.907480 0.420096i \(-0.138004\pi\)
0.0899262 + 0.995948i \(0.471337\pi\)
\(194\) 7.00000 + 12.1244i 0.502571 + 0.870478i
\(195\) 2.00000 + 1.00000i 0.143223 + 0.0716115i
\(196\) 0 0
\(197\) 2.00000i 0.142494i 0.997459 + 0.0712470i \(0.0226979\pi\)
−0.997459 + 0.0712470i \(0.977302\pi\)
\(198\) −10.3923 + 6.00000i −0.738549 + 0.426401i
\(199\) −5.00000 + 8.66025i −0.354441 + 0.613909i −0.987022 0.160585i \(-0.948662\pi\)
0.632581 + 0.774494i \(0.281995\pi\)
\(200\) 0 0
\(201\) −1.00000 1.73205i −0.0705346 0.122169i
\(202\) 24.0000i 1.68863i
\(203\) 0 0
\(204\) −14.0000 −0.980196
\(205\) 0.267949 + 4.46410i 0.0187144 + 0.311786i
\(206\) 19.0000 32.9090i 1.32379 2.29288i
\(207\) 10.3923 + 6.00000i 0.722315 + 0.417029i
\(208\) 3.46410 2.00000i 0.240192 0.138675i
\(209\) 0 0
\(210\) 0 0
\(211\) −13.0000 −0.894957 −0.447478 0.894295i \(-0.647678\pi\)
−0.447478 + 0.894295i \(0.647678\pi\)
\(212\) 10.3923 6.00000i 0.713746 0.412082i
\(213\) −6.92820 4.00000i −0.474713 0.274075i
\(214\) −8.00000 + 13.8564i −0.546869 + 0.947204i
\(215\) −8.92820 + 0.535898i −0.608898 + 0.0365480i
\(216\) 0 0
\(217\) 0 0
\(218\) 10.0000i 0.677285i
\(219\) 3.00000 + 5.19615i 0.202721 + 0.351123i
\(220\) 11.1962 7.39230i 0.754844 0.498389i
\(221\) −3.50000 + 6.06218i −0.235435 + 0.407786i
\(222\) 3.46410 2.00000i 0.232495 0.134231i
\(223\) 21.0000i 1.40626i −0.711059 0.703132i \(-0.751784\pi\)
0.711059 0.703132i \(-0.248216\pi\)
\(224\) 0 0
\(225\) 6.00000 + 8.00000i 0.400000 + 0.533333i
\(226\) −6.00000 10.3923i −0.399114 0.691286i
\(227\) −14.7224 8.50000i −0.977162 0.564165i −0.0757500 0.997127i \(-0.524135\pi\)
−0.901412 + 0.432962i \(0.857468\pi\)
\(228\) 0 0
\(229\) −5.00000 8.66025i −0.330409 0.572286i 0.652183 0.758062i \(-0.273853\pi\)
−0.982592 + 0.185776i \(0.940520\pi\)
\(230\) −24.0000 12.0000i −1.58251 0.791257i
\(231\) 0 0
\(232\) 0 0
\(233\) −13.8564 + 8.00000i −0.907763 + 0.524097i −0.879711 0.475509i \(-0.842264\pi\)
−0.0280525 + 0.999606i \(0.508931\pi\)
\(234\) −2.00000 + 3.46410i −0.130744 + 0.226455i
\(235\) −3.69615 5.59808i −0.241110 0.365178i
\(236\) −10.0000 17.3205i −0.650945 1.12747i
\(237\) 5.00000i 0.324785i
\(238\) 0 0
\(239\) −15.0000 −0.970269 −0.485135 0.874439i \(-0.661229\pi\)
−0.485135 + 0.874439i \(0.661229\pi\)
\(240\) −8.92820 + 0.535898i −0.576313 + 0.0345921i
\(241\) −11.0000 + 19.0526i −0.708572 + 1.22728i 0.256814 + 0.966461i \(0.417327\pi\)
−0.965387 + 0.260822i \(0.916006\pi\)
\(242\) 3.46410 + 2.00000i 0.222681 + 0.128565i
\(243\) −13.8564 + 8.00000i −0.888889 + 0.513200i
\(244\) 16.0000 1.02430
\(245\) 0 0
\(246\) 4.00000 0.255031
\(247\) 0 0
\(248\) 0 0
\(249\) −2.00000 + 3.46410i −0.126745 + 0.219529i
\(250\) −14.4641 17.0526i −0.914790 1.07850i
\(251\) −18.0000 −1.13615 −0.568075 0.822977i \(-0.692312\pi\)
−0.568075 + 0.822977i \(0.692312\pi\)
\(252\) 0 0
\(253\) 18.0000i 1.13165i
\(254\) 2.00000 + 3.46410i 0.125491 + 0.217357i
\(255\) 13.0622 8.62436i 0.817985 0.540078i
\(256\) −8.00000 + 13.8564i −0.500000 + 0.866025i
\(257\) 19.0526 11.0000i 1.18847 0.686161i 0.230508 0.973070i \(-0.425961\pi\)
0.957958 + 0.286909i \(0.0926278\pi\)
\(258\) 8.00000i 0.498058i
\(259\) 0 0
\(260\) 2.00000 4.00000i 0.124035 0.248069i
\(261\) −5.00000 8.66025i −0.309492 0.536056i
\(262\) −38.1051 22.0000i −2.35414 1.35916i
\(263\) −20.7846 12.0000i −1.28163 0.739952i −0.304487 0.952517i \(-0.598485\pi\)
−0.977147 + 0.212565i \(0.931818\pi\)
\(264\) 0 0
\(265\) −6.00000 + 12.0000i −0.368577 + 0.737154i
\(266\) 0 0
\(267\) 0 0
\(268\) −3.46410 + 2.00000i −0.211604 + 0.122169i
\(269\) 5.00000 8.66025i 0.304855 0.528025i −0.672374 0.740212i \(-0.734725\pi\)
0.977229 + 0.212187i \(0.0680585\pi\)
\(270\) 18.6603 12.3205i 1.13563 0.749802i
\(271\) 4.00000 + 6.92820i 0.242983 + 0.420858i 0.961563 0.274586i \(-0.0885408\pi\)
−0.718580 + 0.695444i \(0.755208\pi\)
\(272\) 28.0000i 1.69775i
\(273\) 0 0
\(274\) −24.0000 −1.44989
\(275\) −5.89230 + 13.7942i −0.355319 + 0.831823i
\(276\) −6.00000 + 10.3923i −0.361158 + 0.625543i
\(277\) −1.73205 1.00000i −0.104069 0.0600842i 0.447062 0.894503i \(-0.352470\pi\)
−0.551131 + 0.834419i \(0.685804\pi\)
\(278\) 17.3205 10.0000i 1.03882 0.599760i
\(279\) 4.00000 0.239474
\(280\) 0 0
\(281\) 7.00000 0.417585 0.208792 0.977960i \(-0.433047\pi\)
0.208792 + 0.977960i \(0.433047\pi\)
\(282\) −5.19615 + 3.00000i −0.309426 + 0.178647i
\(283\) 9.52628 + 5.50000i 0.566279 + 0.326941i 0.755662 0.654962i \(-0.227315\pi\)
−0.189383 + 0.981903i \(0.560649\pi\)
\(284\) −8.00000 + 13.8564i −0.474713 + 0.822226i
\(285\) 0 0
\(286\) −6.00000 −0.354787
\(287\) 0 0
\(288\) 16.0000i 0.942809i
\(289\) 16.0000 + 27.7128i 0.941176 + 1.63017i
\(290\) 12.3205 + 18.6603i 0.723485 + 1.09577i
\(291\) −3.50000 + 6.06218i −0.205174 + 0.355371i
\(292\) 10.3923 6.00000i 0.608164 0.351123i
\(293\) 9.00000i 0.525786i 0.964825 + 0.262893i \(0.0846766\pi\)
−0.964825 + 0.262893i \(0.915323\pi\)
\(294\) 0 0
\(295\) 20.0000 + 10.0000i 1.16445 + 0.582223i
\(296\) 0 0
\(297\) −12.9904 7.50000i −0.753778 0.435194i
\(298\) 17.3205 + 10.0000i 1.00335 + 0.579284i
\(299\) 3.00000 + 5.19615i 0.173494 + 0.300501i
\(300\) −8.00000 + 6.00000i −0.461880 + 0.346410i
\(301\) 0 0
\(302\) 26.0000i 1.49613i
\(303\) −10.3923 + 6.00000i −0.597022 + 0.344691i
\(304\) 0 0
\(305\) −14.9282 + 9.85641i −0.854786 + 0.564376i
\(306\) 14.0000 + 24.2487i 0.800327 + 1.38621i
\(307\) 7.00000i 0.399511i 0.979846 + 0.199756i \(0.0640148\pi\)
−0.979846 + 0.199756i \(0.935985\pi\)
\(308\) 0 0
\(309\) 19.0000 1.08087
\(310\) −8.92820 + 0.535898i −0.507088 + 0.0304370i
\(311\) −6.00000 + 10.3923i −0.340229 + 0.589294i −0.984475 0.175525i \(-0.943838\pi\)
0.644246 + 0.764818i \(0.277171\pi\)
\(312\) 0 0
\(313\) −18.1865 + 10.5000i −1.02796 + 0.593495i −0.916401 0.400262i \(-0.868919\pi\)
−0.111563 + 0.993757i \(0.535586\pi\)
\(314\) 36.0000 2.03160
\(315\) 0 0
\(316\) −10.0000 −0.562544
\(317\) 10.3923 6.00000i 0.583690 0.336994i −0.178908 0.983866i \(-0.557257\pi\)
0.762598 + 0.646872i \(0.223923\pi\)
\(318\) 10.3923 + 6.00000i 0.582772 + 0.336463i
\(319\) 7.50000 12.9904i 0.419919 0.727322i
\(320\) 1.07180 + 17.8564i 0.0599153 + 0.998203i
\(321\) −8.00000 −0.446516
\(322\) 0 0
\(323\) 0 0
\(324\) 1.00000 + 1.73205i 0.0555556 + 0.0962250i
\(325\) 0.598076 + 4.96410i 0.0331753 + 0.275359i
\(326\) 14.0000 24.2487i 0.775388 1.34301i
\(327\) 4.33013 2.50000i 0.239457 0.138250i
\(328\) 0 0
\(329\) 0 0
\(330\) 12.0000 + 6.00000i 0.660578 + 0.330289i
\(331\) −6.00000 10.3923i −0.329790 0.571213i 0.652680 0.757634i \(-0.273645\pi\)
−0.982470 + 0.186421i \(0.940311\pi\)
\(332\) 6.92820 + 4.00000i 0.380235 + 0.219529i
\(333\) −3.46410 2.00000i −0.189832 0.109599i
\(334\) −3.00000 5.19615i −0.164153 0.284321i
\(335\) 2.00000 4.00000i 0.109272 0.218543i
\(336\) 0 0
\(337\) 18.0000i 0.980522i −0.871576 0.490261i \(-0.836901\pi\)
0.871576 0.490261i \(-0.163099\pi\)
\(338\) 20.7846 12.0000i 1.13053 0.652714i
\(339\) 3.00000 5.19615i 0.162938 0.282216i
\(340\) −17.2487 26.1244i −0.935443 1.41679i
\(341\) 3.00000 + 5.19615i 0.162459 + 0.281387i
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) −0.803848 13.3923i −0.0432777 0.721017i
\(346\) 9.00000 15.5885i 0.483843 0.838041i
\(347\) 15.5885 + 9.00000i 0.836832 + 0.483145i 0.856186 0.516667i \(-0.172828\pi\)
−0.0193540 + 0.999813i \(0.506161\pi\)
\(348\) 8.66025 5.00000i 0.464238 0.268028i
\(349\) 20.0000 1.07058 0.535288 0.844670i \(-0.320203\pi\)
0.535288 + 0.844670i \(0.320203\pi\)
\(350\) 0 0
\(351\) −5.00000 −0.266880
\(352\) 20.7846 12.0000i 1.10782 0.639602i
\(353\) 9.52628 + 5.50000i 0.507033 + 0.292735i 0.731613 0.681720i \(-0.238768\pi\)
−0.224580 + 0.974456i \(0.572101\pi\)
\(354\) 10.0000 17.3205i 0.531494 0.920575i
\(355\) −1.07180 17.8564i −0.0568851 0.947720i
\(356\) 0 0
\(357\) 0 0
\(358\) 40.0000i 2.11407i
\(359\) −10.0000 17.3205i −0.527780 0.914141i −0.999476 0.0323801i \(-0.989691\pi\)
0.471696 0.881761i \(-0.343642\pi\)
\(360\) 0 0
\(361\) 9.50000 16.4545i 0.500000 0.866025i
\(362\) −31.1769 + 18.0000i −1.63862 + 0.946059i
\(363\) 2.00000i 0.104973i
\(364\) 0 0
\(365\) −6.00000 + 12.0000i −0.314054 + 0.628109i
\(366\) 8.00000 + 13.8564i 0.418167 + 0.724286i
\(367\) 2.59808 + 1.50000i 0.135618 + 0.0782994i 0.566274 0.824217i \(-0.308384\pi\)
−0.430656 + 0.902516i \(0.641718\pi\)
\(368\) −20.7846 12.0000i −1.08347 0.625543i
\(369\) −2.00000 3.46410i −0.104116 0.180334i
\(370\) 8.00000 + 4.00000i 0.415900 + 0.207950i
\(371\) 0 0
\(372\) 4.00000i 0.207390i
\(373\) 20.7846 12.0000i 1.07619 0.621336i 0.146321 0.989237i \(-0.453257\pi\)
0.929865 + 0.367901i \(0.119923\pi\)
\(374\) −21.0000 + 36.3731i −1.08588 + 1.88081i
\(375\) 3.76795 10.5263i 0.194576 0.543575i
\(376\) 0 0
\(377\) 5.00000i 0.257513i
\(378\) 0 0
\(379\) −20.0000 −1.02733 −0.513665 0.857991i \(-0.671713\pi\)
−0.513665 + 0.857991i \(0.671713\pi\)
\(380\) 0 0
\(381\) −1.00000 + 1.73205i −0.0512316 + 0.0887357i
\(382\) 5.19615 + 3.00000i 0.265858 + 0.153493i
\(383\) −13.8564 + 8.00000i −0.708029 + 0.408781i −0.810331 0.585973i \(-0.800713\pi\)
0.102302 + 0.994753i \(0.467379\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 32.0000 1.62876
\(387\) 6.92820 4.00000i 0.352180 0.203331i
\(388\) 12.1244 + 7.00000i 0.615521 + 0.355371i
\(389\) 2.50000 4.33013i 0.126755 0.219546i −0.795663 0.605740i \(-0.792877\pi\)
0.922418 + 0.386194i \(0.126210\pi\)
\(390\) 4.46410 0.267949i 0.226049 0.0135681i
\(391\) 42.0000 2.12403
\(392\) 0 0
\(393\) 22.0000i 1.10975i
\(394\) 2.00000 + 3.46410i 0.100759 + 0.174519i
\(395\) 9.33013 6.16025i 0.469450 0.309956i
\(396\) −6.00000 + 10.3923i −0.301511 + 0.522233i
\(397\) 6.06218 3.50000i 0.304252 0.175660i −0.340099 0.940389i \(-0.610461\pi\)
0.644351 + 0.764730i \(0.277127\pi\)
\(398\) 20.0000i 1.00251i
\(399\) 0 0
\(400\) −12.0000 16.0000i −0.600000 0.800000i
\(401\) 1.50000 + 2.59808i 0.0749064 + 0.129742i 0.901046 0.433724i \(-0.142801\pi\)
−0.826139 + 0.563466i \(0.809468\pi\)
\(402\) −3.46410 2.00000i −0.172774 0.0997509i
\(403\) 1.73205 + 1.00000i 0.0862796 + 0.0498135i
\(404\) 12.0000 + 20.7846i 0.597022 + 1.03407i
\(405\) −2.00000 1.00000i −0.0993808 0.0496904i
\(406\) 0 0
\(407\) 6.00000i 0.297409i
\(408\) 0 0
\(409\) 10.0000 17.3205i 0.494468 0.856444i −0.505511 0.862820i \(-0.668696\pi\)
0.999980 + 0.00637586i \(0.00202951\pi\)
\(410\) 4.92820 + 7.46410i 0.243387 + 0.368626i
\(411\) −6.00000 10.3923i −0.295958 0.512615i
\(412\) 38.0000i 1.87213i
\(413\) 0 0
\(414\) 24.0000 1.17954
\(415\) −8.92820 + 0.535898i −0.438268 + 0.0263062i
\(416\) 4.00000 6.92820i 0.196116 0.339683i
\(417\) 8.66025 + 5.00000i 0.424094 + 0.244851i
\(418\) 0 0
\(419\) −30.0000 −1.46560 −0.732798 0.680446i \(-0.761786\pi\)
−0.732798 + 0.680446i \(0.761786\pi\)
\(420\) 0 0
\(421\) −3.00000 −0.146211 −0.0731055 0.997324i \(-0.523291\pi\)
−0.0731055 + 0.997324i \(0.523291\pi\)
\(422\) −22.5167 + 13.0000i −1.09609 + 0.632830i
\(423\) 5.19615 + 3.00000i 0.252646 + 0.145865i
\(424\) 0 0
\(425\) 32.1865 + 13.7487i 1.56128 + 0.666910i
\(426\) −16.0000 −0.775203
\(427\) 0 0
\(428\) 16.0000i 0.773389i
\(429\) −1.50000 2.59808i −0.0724207 0.125436i
\(430\) −14.9282 + 9.85641i −0.719902 + 0.475318i
\(431\) 11.5000 19.9186i 0.553936 0.959444i −0.444050 0.896002i \(-0.646459\pi\)
0.997985 0.0634424i \(-0.0202079\pi\)
\(432\) 17.3205 10.0000i 0.833333 0.481125i
\(433\) 26.0000i 1.24948i −0.780833 0.624740i \(-0.785205\pi\)
0.780833 0.624740i \(-0.214795\pi\)
\(434\) 0 0
\(435\) −5.00000 + 10.0000i −0.239732 + 0.479463i
\(436\) −5.00000 8.66025i −0.239457 0.414751i
\(437\) 0 0
\(438\) 10.3923 + 6.00000i 0.496564 + 0.286691i
\(439\) 15.0000 + 25.9808i 0.715911 + 1.23999i 0.962607 + 0.270901i \(0.0873217\pi\)
−0.246696 + 0.969093i \(0.579345\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 14.0000i 0.665912i
\(443\) 3.46410 2.00000i 0.164584 0.0950229i −0.415445 0.909618i \(-0.636374\pi\)
0.580030 + 0.814595i \(0.303041\pi\)
\(444\) 2.00000 3.46410i 0.0949158 0.164399i
\(445\) 0 0
\(446\) −21.0000 36.3731i −0.994379 1.72231i
\(447\) 10.0000i 0.472984i
\(448\) 0 0
\(449\) 5.00000 0.235965 0.117982 0.993016i \(-0.462357\pi\)
0.117982 + 0.993016i \(0.462357\pi\)
\(450\) 18.3923 + 7.85641i 0.867022 + 0.370355i
\(451\) 3.00000 5.19615i 0.141264 0.244677i
\(452\) −10.3923 6.00000i −0.488813 0.282216i
\(453\) 11.2583 6.50000i 0.528962 0.305397i
\(454\) −34.0000 −1.59570
\(455\) 0 0
\(456\) 0 0
\(457\) −32.9090 + 19.0000i −1.53942 + 0.888783i −0.540544 + 0.841316i \(0.681781\pi\)
−0.998873 + 0.0474665i \(0.984885\pi\)
\(458\) −17.3205 10.0000i −0.809334 0.467269i
\(459\) −17.5000 + 30.3109i −0.816830 + 1.41479i
\(460\) −26.7846 + 1.60770i −1.24884 + 0.0749592i
\(461\) 12.0000 0.558896 0.279448 0.960161i \(-0.409849\pi\)
0.279448 + 0.960161i \(0.409849\pi\)
\(462\) 0 0
\(463\) 36.0000i 1.67306i −0.547920 0.836531i \(-0.684580\pi\)
0.547920 0.836531i \(-0.315420\pi\)
\(464\) 10.0000 + 17.3205i 0.464238 + 0.804084i
\(465\) −2.46410 3.73205i −0.114270 0.173070i
\(466\) −16.0000 + 27.7128i −0.741186 + 1.28377i
\(467\) 23.3827 13.5000i 1.08202 0.624705i 0.150581 0.988598i \(-0.451886\pi\)
0.931441 + 0.363892i \(0.118552\pi\)
\(468\) 4.00000i 0.184900i
\(469\) 0 0
\(470\) −12.0000 6.00000i −0.553519 0.276759i
\(471\) 9.00000 + 15.5885i 0.414698 + 0.718278i
\(472\) 0 0
\(473\) 10.3923 + 6.00000i 0.477839 + 0.275880i
\(474\) −5.00000 8.66025i −0.229658 0.397779i
\(475\) 0 0
\(476\) 0 0
\(477\) 12.0000i 0.549442i
\(478\) −25.9808 + 15.0000i −1.18833 + 0.686084i
\(479\) −15.0000 + 25.9808i −0.685367 + 1.18709i 0.287954 + 0.957644i \(0.407025\pi\)
−0.973321 + 0.229447i \(0.926308\pi\)
\(480\) −14.9282 + 9.85641i −0.681376 + 0.449881i
\(481\) −1.00000 1.73205i −0.0455961 0.0789747i
\(482\) 44.0000i 2.00415i
\(483\) 0 0
\(484\) 4.00000 0.181818
\(485\) −15.6244 + 0.937822i −0.709465 + 0.0425843i
\(486\) −16.0000 + 27.7128i −0.725775 + 1.25708i
\(487\) −36.3731 21.0000i −1.64822 0.951601i −0.977779 0.209639i \(-0.932771\pi\)
−0.670442 0.741962i \(-0.733896\pi\)
\(488\) 0 0
\(489\) 14.0000 0.633102
\(490\) 0 0
\(491\) 7.00000 0.315906 0.157953 0.987447i \(-0.449511\pi\)
0.157953 + 0.987447i \(0.449511\pi\)
\(492\) 3.46410 2.00000i 0.156174 0.0901670i
\(493\) −30.3109 17.5000i −1.36513 0.788160i
\(494\) 0 0
\(495\) −0.803848 13.3923i −0.0361303 0.601939i
\(496\) −8.00000 −0.359211
\(497\) 0 0
\(498\) 8.00000i 0.358489i
\(499\) −17.5000 30.3109i −0.783408 1.35690i −0.929946 0.367697i \(-0.880146\pi\)
0.146538 0.989205i \(-0.453187\pi\)
\(500\) −21.0526 7.53590i −0.941499 0.337016i
\(501\) 1.50000 2.59808i 0.0670151 0.116073i
\(502\) −31.1769 + 18.0000i −1.39149 + 0.803379i
\(503\) 9.00000i 0.401290i 0.979664 + 0.200645i \(0.0643038\pi\)
−0.979664 + 0.200645i \(0.935696\pi\)
\(504\) 0 0
\(505\) −24.0000 12.0000i −1.06799 0.533993i
\(506\) 18.0000 + 31.1769i 0.800198 + 1.38598i
\(507\) 10.3923 + 6.00000i 0.461538 + 0.266469i
\(508\) 3.46410 + 2.00000i 0.153695 + 0.0887357i
\(509\) −15.0000 25.9808i −0.664863 1.15158i −0.979322 0.202306i \(-0.935156\pi\)
0.314459 0.949271i \(-0.398177\pi\)
\(510\) 14.0000 28.0000i 0.619930 1.23986i
\(511\) 0 0
\(512\) 32.0000i 1.41421i
\(513\) 0 0
\(514\) 22.0000 38.1051i 0.970378 1.68074i
\(515\) 23.4090 + 35.4545i 1.03152 + 1.56231i
\(516\) 4.00000 + 6.92820i 0.176090 + 0.304997i
\(517\) 9.00000i 0.395820i
\(518\) 0 0
\(519\) 9.00000 0.395056
\(520\) 0 0
\(521\) 14.0000 24.2487i 0.613351 1.06236i −0.377320 0.926083i \(-0.623154\pi\)
0.990671 0.136272i \(-0.0435123\pi\)
\(522\) −17.3205 10.0000i −0.758098 0.437688i
\(523\) 3.46410 2.00000i 0.151475 0.0874539i −0.422347 0.906434i \(-0.638794\pi\)
0.573822 + 0.818980i \(0.305460\pi\)
\(524\) −44.0000 −1.92215
\(525\) 0 0
\(526\) −48.0000 −2.09290
\(527\) 12.1244 7.00000i 0.528145 0.304925i
\(528\) 10.3923 + 6.00000i 0.452267 + 0.261116i
\(529\) 6.50000 11.2583i 0.282609 0.489493i
\(530\) 1.60770 + 26.7846i 0.0698338 + 1.16345i
\(531\) −20.0000 −0.867926
\(532\) 0 0
\(533\) 2.00000i 0.0866296i
\(534\) 0 0
\(535\) −9.85641 14.9282i −0.426130 0.645403i
\(536\) 0 0
\(537\) −17.3205 + 10.0000i −0.747435 + 0.431532i
\(538\) 20.0000i 0.862261i
\(539\) 0 0
\(540\) 10.0000 20.0000i 0.430331 0.860663i
\(541\) −13.5000 23.3827i −0.580410 1.00530i −0.995431 0.0954880i \(-0.969559\pi\)
0.415020 0.909812i \(-0.363774\pi\)
\(542\) 13.8564 + 8.00000i 0.595184 + 0.343629i
\(543\) −15.5885 9.00000i −0.668965 0.386227i
\(544\) −28.0000 48.4974i −1.20049 2.07931i
\(545\) 10.0000 + 5.00000i 0.428353 + 0.214176i
\(546\) 0 0
\(547\) 32.0000i 1.36822i 0.729378 + 0.684111i \(0.239809\pi\)
−0.729378 + 0.684111i \(0.760191\pi\)
\(548\) −20.7846 + 12.0000i −0.887875 + 0.512615i
\(549\) 8.00000 13.8564i 0.341432 0.591377i
\(550\) 3.58846 + 29.7846i 0.153012 + 1.27002i
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) −4.00000 −0.169944
\(555\) 0.267949 + 4.46410i 0.0113738 + 0.189491i
\(556\) 10.0000 17.3205i 0.424094 0.734553i
\(557\) 24.2487 + 14.0000i 1.02745 + 0.593199i 0.916253 0.400599i \(-0.131198\pi\)
0.111198 + 0.993798i \(0.464531\pi\)
\(558\) 6.92820 4.00000i 0.293294 0.169334i
\(559\) 4.00000 0.169182
\(560\) 0 0
\(561\) −21.0000 −0.886621
\(562\) 12.1244 7.00000i 0.511435 0.295277i
\(563\) −20.7846 12.0000i −0.875967 0.505740i −0.00664037 0.999978i \(-0.502114\pi\)
−0.869326 + 0.494238i \(0.835447\pi\)
\(564\) −3.00000 + 5.19615i −0.126323 + 0.218797i
\(565\) 13.3923 0.803848i 0.563418 0.0338181i
\(566\) 22.0000 0.924729
\(567\) 0 0
\(568\) 0 0
\(569\) −15.0000 25.9808i −0.628833 1.08917i −0.987786 0.155815i \(-0.950200\pi\)
0.358954 0.933355i \(-0.383134\pi\)
\(570\) 0 0
\(571\) −6.00000 + 10.3923i −0.251092 + 0.434904i −0.963827 0.266529i \(-0.914123\pi\)
0.712735 + 0.701434i \(0.247456\pi\)
\(572\) −5.19615 + 3.00000i −0.217262 + 0.125436i
\(573\) 3.00000i 0.125327i
\(574\) 0 0
\(575\) 24.0000 18.0000i 1.00087 0.750652i
\(576\) −8.00000 13.8564i −0.333333 0.577350i
\(577\) 37.2391 + 21.5000i 1.55028 + 0.895057i 0.998118 + 0.0613223i \(0.0195318\pi\)
0.552166 + 0.833734i \(0.313802\pi\)
\(578\) 55.4256 + 32.0000i 2.30540 + 1.33102i
\(579\) 8.00000 + 13.8564i 0.332469 + 0.575853i
\(580\) 20.0000 + 10.0000i 0.830455 + 0.415227i
\(581\) 0 0
\(582\) 14.0000i 0.580319i
\(583\) 15.5885 9.00000i 0.645608 0.372742i
\(584\) 0 0
\(585\) −2.46410 3.73205i −0.101878 0.154301i
\(586\) 9.00000 + 15.5885i 0.371787 + 0.643953i
\(587\) 12.0000i 0.495293i 0.968850 + 0.247647i \(0.0796572\pi\)
−0.968850 + 0.247647i \(0.920343\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 44.6410 2.67949i 1.83784 0.110313i
\(591\) −1.00000 + 1.73205i −0.0411345 + 0.0712470i
\(592\) 6.92820 + 4.00000i 0.284747 + 0.164399i
\(593\) −35.5070 + 20.5000i −1.45810 + 0.841834i −0.998918 0.0465084i \(-0.985191\pi\)
−0.459182 + 0.888342i \(0.651857\pi\)
\(594\) −30.0000 −1.23091
\(595\) 0 0
\(596\) 20.0000 0.819232
\(597\) −8.66025 + 5.00000i −0.354441 + 0.204636i
\(598\) 10.3923 + 6.00000i 0.424973 + 0.245358i
\(599\) 12.5000 21.6506i 0.510736 0.884621i −0.489186 0.872179i \(-0.662706\pi\)
0.999923 0.0124417i \(-0.00396043\pi\)
\(600\) 0 0
\(601\) −8.00000 −0.326327 −0.163163 0.986599i \(-0.552170\pi\)
−0.163163 + 0.986599i \(0.552170\pi\)
\(602\) 0 0
\(603\) 4.00000i 0.162893i
\(604\) −13.0000 22.5167i −0.528962 0.916190i
\(605\) −3.73205 + 2.46410i −0.151729 + 0.100180i
\(606\) −12.0000 + 20.7846i −0.487467 + 0.844317i
\(607\) 23.3827 13.5000i 0.949074 0.547948i 0.0562808 0.998415i \(-0.482076\pi\)
0.892793 + 0.450467i \(0.148742\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) −16.0000 + 32.0000i −0.647821 + 1.29564i
\(611\) 1.50000 + 2.59808i 0.0606835 + 0.105107i
\(612\) 24.2487 + 14.0000i 0.980196 + 0.565916i
\(613\) −38.1051 22.0000i −1.53905 0.888572i −0.998895 0.0470071i \(-0.985032\pi\)
−0.540157 0.841564i \(-0.681635\pi\)
\(614\) 7.00000 + 12.1244i 0.282497 + 0.489299i
\(615\) −2.00000 + 4.00000i −0.0806478 + 0.161296i
\(616\) 0 0
\(617\) 22.0000i 0.885687i 0.896599 + 0.442843i \(0.146030\pi\)
−0.896599 + 0.442843i \(0.853970\pi\)
\(618\) 32.9090 19.0000i 1.32379 0.764292i
\(619\) 5.00000 8.66025i 0.200967 0.348085i −0.747873 0.663842i \(-0.768925\pi\)
0.948840 + 0.315757i \(0.102258\pi\)
\(620\) −7.46410 + 4.92820i −0.299766 + 0.197921i
\(621\) 15.0000 + 25.9808i 0.601929 + 1.04257i
\(622\) 24.0000i 0.962312i
\(623\) 0 0
\(624\) 4.00000 0.160128
\(625\) 24.2846 5.93782i 0.971384 0.237513i
\(626\) −21.0000 + 36.3731i −0.839329 + 1.45376i
\(627\) 0 0
\(628\) 31.1769 18.0000i 1.24409 0.718278i
\(629\) −14.0000 −0.558217
\(630\) 0 0
\(631\) 37.0000 1.47295 0.736473 0.676467i \(-0.236490\pi\)
0.736473 + 0.676467i \(0.236490\pi\)
\(632\) 0 0
\(633\) −11.2583 6.50000i −0.447478 0.258352i
\(634\) 12.0000 20.7846i 0.476581 0.825462i
\(635\) −4.46410 + 0.267949i −0.177152 + 0.0106332i
\(636\) 12.0000 0.475831
\(637\) 0 0
\(638\) 30.0000i 1.18771i
\(639\) 8.00000 + 13.8564i 0.316475 + 0.548151i
\(640\) 0 0
\(641\) −11.0000 + 19.0526i −0.434474 + 0.752531i −0.997253 0.0740768i \(-0.976399\pi\)
0.562779 + 0.826608i \(0.309732\pi\)
\(642\) −13.8564 + 8.00000i −0.546869 + 0.315735i
\(643\) 1.00000i 0.0394362i −0.999806 0.0197181i \(-0.993723\pi\)
0.999806 0.0197181i \(-0.00627687\pi\)
\(644\) 0 0
\(645\) −8.00000 4.00000i −0.315000 0.157500i
\(646\) 0 0
\(647\) 6.92820 + 4.00000i 0.272376 + 0.157256i 0.629967 0.776622i \(-0.283068\pi\)
−0.357591 + 0.933878i \(0.616402\pi\)
\(648\) 0 0
\(649\) −15.0000 25.9808i −0.588802 1.01983i
\(650\) 6.00000 + 8.00000i 0.235339 + 0.313786i
\(651\) 0 0
\(652\) 28.0000i 1.09656i
\(653\) 3.46410 2.00000i 0.135561 0.0782660i −0.430686 0.902502i \(-0.641728\pi\)
0.566247 + 0.824236i \(0.308395\pi\)
\(654\) 5.00000 8.66025i 0.195515 0.338643i
\(655\) 41.0526 27.1051i 1.60406 1.05908i
\(656\) 4.00000 + 6.92820i 0.156174 + 0.270501i
\(657\) 12.0000i 0.468165i
\(658\) 0 0
\(659\) 15.0000 0.584317 0.292159 0.956370i \(-0.405627\pi\)
0.292159 + 0.956370i \(0.405627\pi\)
\(660\) 13.3923 0.803848i 0.521295 0.0312897i
\(661\) −6.00000 + 10.3923i −0.233373 + 0.404214i −0.958799 0.284087i \(-0.908310\pi\)
0.725426 + 0.688301i \(0.241643\pi\)
\(662\) −20.7846 12.0000i −0.807817 0.466393i
\(663\) −6.06218 + 3.50000i −0.235435 + 0.135929i
\(664\) 0 0
\(665\) 0 0
\(666\) −8.00000 −0.309994
\(667\) −25.9808 + 15.0000i −1.00598 + 0.580802i
\(668\) −5.19615 3.00000i −0.201045 0.116073i
\(669\) 10.5000 18.1865i 0.405953 0.703132i
\(670\) −0.535898 8.92820i −0.0207036 0.344927i
\(671\) 24.0000 0.926510
\(672\) 0 0
\(673\) 24.0000i 0.925132i 0.886585 + 0.462566i \(0.153071\pi\)
−0.886585 + 0.462566i \(0.846929\pi\)
\(674\) −18.0000 31.1769i −0.693334 1.20089i
\(675\) 2.99038 + 24.8205i 0.115100 + 0.955342i
\(676\) 12.0000 20.7846i 0.461538 0.799408i
\(677\) −37.2391 + 21.5000i −1.43121 + 0.826312i −0.997214 0.0746002i \(-0.976232\pi\)
−0.434001 + 0.900912i \(0.642899\pi\)
\(678\) 12.0000i 0.460857i
\(679\) 0 0
\(680\) 0 0
\(681\) −8.50000 14.7224i −0.325721 0.564165i
\(682\) 10.3923 + 6.00000i 0.397942 + 0.229752i
\(683\) 13.8564 + 8.00000i 0.530201 + 0.306111i 0.741098 0.671397i \(-0.234305\pi\)
−0.210898 + 0.977508i \(0.567639\pi\)
\(684\) 0 0
\(685\) 12.0000 24.0000i 0.458496 0.916993i
\(686\) 0 0
\(687\) 10.0000i 0.381524i
\(688\) −13.8564 + 8.00000i −0.528271 + 0.304997i
\(689\) 3.00000 5.19615i 0.114291 0.197958i
\(690\) −14.7846 22.3923i −0.562840 0.852460i
\(691\) 4.00000 + 6.92820i 0.152167 + 0.263561i 0.932024 0.362397i \(-0.118041\pi\)
−0.779857 + 0.625958i \(0.784708\pi\)
\(692\) 18.0000i 0.684257i
\(693\) 0 0
\(694\) 36.0000 1.36654
\(695\) 1.33975 + 22.3205i 0.0508195 + 0.846665i
\(696\) 0 0
\(697\) −12.1244 7.00000i −0.459243 0.265144i
\(698\) 34.6410 20.0000i 1.31118 0.757011i
\(699\) −16.0000 −0.605176
\(700\) 0 0
\(701\) −13.0000 −0.491003 −0.245502 0.969396i \(-0.578953\pi\)
−0.245502 + 0.969396i \(0.578953\pi\)
\(702\) −8.66025 + 5.00000i −0.326860 + 0.188713i
\(703\) 0 0
\(704\) 12.0000 20.7846i 0.452267 0.783349i
\(705\) −0.401924 6.69615i −0.0151373 0.252192i
\(706\) 22.0000 0.827981
\(707\) 0 0
\(708\) 20.0000i 0.751646i
\(709\) 17.5000 + 30.3109i 0.657226 + 1.13835i 0.981331 + 0.192328i \(0.0616038\pi\)
−0.324104 + 0.946021i \(0.605063\pi\)
\(710\) −19.7128 29.8564i −0.739809 1.12049i
\(711\) −5.00000 + 8.66025i −0.187515 + 0.324785i
\(712\) 0 0
\(713\) 12.0000i 0.449404i
\(714\) 0 0
\(715\) 3.00000 6.00000i 0.112194 0.224387i
\(716\) 20.0000 + 34.6410i 0.747435 + 1.29460i
\(717\) −12.9904 7.50000i −0.485135 0.280093i
\(718\) −34.6410 20.0000i −1.29279 0.746393i
\(719\) 15.0000 + 25.9808i 0.559406 + 0.968919i 0.997546 + 0.0700124i \(0.0223039\pi\)
−0.438141 + 0.898906i \(0.644363\pi\)
\(720\) 16.0000 + 8.00000i 0.596285 + 0.298142i
\(721\) 0 0
\(722\) 38.0000i 1.41421i
\(723\) −19.0526 + 11.0000i −0.708572 + 0.409094i
\(724\) −18.0000 + 31.1769i −0.668965 + 1.15868i
\(725\) −24.8205 + 2.99038i −0.921811 + 0.111060i
\(726\) 2.00000 + 3.46410i 0.0742270 + 0.128565i
\(727\) 28.0000i 1.03846i −0.854634 0.519231i \(-0.826218\pi\)
0.854634 0.519231i \(-0.173782\pi\)
\(728\) 0 0
\(729\) −13.0000 −0.481481
\(730\) 1.60770 + 26.7846i 0.0595035 + 0.991343i
\(731\) 14.0000 24.2487i 0.517809 0.896871i
\(732\) 13.8564 + 8.00000i 0.512148 + 0.295689i
\(733\) −0.866025 + 0.500000i −0.0319874 + 0.0184679i −0.515908 0.856644i \(-0.672546\pi\)
0.483921 + 0.875112i \(0.339212\pi\)
\(734\) 6.00000 0.221464
\(735\) 0 0
\(736\) −48.0000 −1.76930
\(737\) −5.19615 + 3.00000i −0.191403 + 0.110506i
\(738\) −6.92820 4.00000i −0.255031 0.147242i
\(739\) −17.5000 + 30.3109i −0.643748 + 1.11500i 0.340841 + 0.940121i \(0.389288\pi\)
−0.984589 + 0.174883i \(0.944045\pi\)
\(740\) 8.92820 0.535898i 0.328207 0.0197000i
\(741\) 0 0
\(742\) 0 0
\(743\) 14.0000i 0.513610i 0.966463 + 0.256805i \(0.0826698\pi\)
−0.966463 + 0.256805i \(0.917330\pi\)
\(744\) 0 0
\(745\) −18.6603 + 12.3205i −0.683659 + 0.451388i
\(746\) 24.0000 41.5692i 0.878702 1.52196i
\(747\) 6.92820 4.00000i 0.253490 0.146352i
\(748\) 42.0000i 1.53567i
\(749\) 0 0
\(750\) −4.00000 22.0000i −0.146059 0.803326i
\(751\) 16.5000 + 28.5788i 0.602094 + 1.04286i 0.992504 + 0.122216i \(0.0389999\pi\)
−0.390410 + 0.920641i \(0.627667\pi\)
\(752\) −10.3923 6.00000i −0.378968 0.218797i
\(753\) −15.5885 9.00000i −0.568075 0.327978i
\(754\) −5.00000 8.66025i −0.182089 0.315388i
\(755\) 26.0000 + 13.0000i 0.946237 + 0.473118i
\(756\) 0 0
\(757\) 32.0000i 1.16306i 0.813525 + 0.581530i \(0.197546\pi\)
−0.813525 + 0.581530i \(0.802454\pi\)
\(758\) −34.6410 + 20.0000i −1.25822 + 0.726433i
\(759\) −9.00000 + 15.5885i −0.326679 + 0.565825i
\(760\) 0 0
\(761\) −1.00000 1.73205i −0.0362500 0.0627868i 0.847331 0.531065i \(-0.178208\pi\)
−0.883581 + 0.468278i \(0.844875\pi\)
\(762\) 4.00000i 0.144905i
\(763\) 0 0
\(764\) 6.00000 0.217072
\(765\) −31.2487 + 1.87564i −1.12980 + 0.0678141i
\(766\) −16.0000 + 27.7128i −0.578103 + 1.00130i
\(767\) −8.66025 5.00000i −0.312704 0.180540i
\(768\) −13.8564 + 8.00000i −0.500000 + 0.288675i
\(769\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(770\) 0 0
\(771\) 22.0000 0.792311
\(772\) 27.7128 16.0000i 0.997406 0.575853i
\(773\) 18.1865 + 10.5000i 0.654124 + 0.377659i 0.790034 0.613062i \(-0.210063\pi\)
−0.135910 + 0.990721i \(0.543396\pi\)
\(774\) 8.00000 13.8564i 0.287554 0.498058i
\(775\) 3.92820 9.19615i 0.141105 0.330336i
\(776\) 0 0
\(777\) 0 0
\(778\) 10.0000i 0.358517i
\(779\) 0 0
\(780\) 3.73205 2.46410i 0.133629 0.0882290i
\(781\) −12.0000 + 20.7846i −0.429394 + 0.743732i
\(782\) 72.7461 42.0000i 2.60140 1.50192i
\(783\) 25.0000i 0.893427i
\(784\) 0 0
\(785\) −18.0000 + 36.0000i −0.642448 + 1.28490i
\(786\) −22.0000 38.1051i −0.784714 1.35916i
\(787\) −14.7224 8.50000i −0.524798 0.302992i 0.214097 0.976812i \(-0.431319\pi\)
−0.738896 + 0.673820i \(0.764652\pi\)
\(788\) 3.46410 + 2.00000i 0.123404 + 0.0712470i
\(789\) −12.0000 20.7846i −0.427211 0.739952i
\(790\) 10.0000 20.0000i 0.355784 0.711568i
\(791\) 0 0
\(792\) 0 0
\(793\) 6.92820 4.00000i 0.246028 0.142044i
\(794\) 7.00000 12.1244i 0.248421 0.430277i
\(795\) −11.1962 + 7.39230i −0.397087 + 0.262178i
\(796\) 10.0000 + 17.3205i 0.354441 + 0.613909i
\(797\) 13.0000i 0.460484i −0.973133 0.230242i \(-0.926048\pi\)
0.973133 0.230242i \(-0.0739517\pi\)
\(798\) 0 0
\(799\) 21.0000 0.742927
\(800\) −36.7846 15.7128i −1.30053 0.555532i
\(801\) 0 0
\(802\) 5.19615 + 3.00000i 0.183483 + 0.105934i
\(803\) 15.5885 9.00000i 0.550105 0.317603i
\(804\) −4.00000 −0.141069
\(805\) 0 0
\(806\) 4.00000 0.140894
\(807\) 8.66025 5.00000i 0.304855 0.176008i
\(808\) 0 0
\(809\) 22.5000 38.9711i 0.791058 1.37015i −0.134255 0.990947i \(-0.542864\pi\)
0.925312 0.379206i \(-0.123803\pi\)
\(810\) −4.46410 + 0.267949i −0.156853 + 0.00941477i
\(811\) −38.0000 −1.33436 −0.667180 0.744896i \(-0.732499\pi\)
−0.667180 + 0.744896i \(0.732499\pi\)
\(812\) 0 0
\(813\) 8.00000i 0.280572i
\(814\) −6.00000 10.3923i −0.210300 0.364250i
\(815\) 17.2487 + 26.1244i 0.604196 + 0.915096i
\(816\) 14.0000 24.2487i 0.490098 0.848875i
\(817\) 0 0
\(818\) 40.0000i 1.39857i
\(819\) 0 0
\(820\) 8.00000 + 4.00000i 0.279372 + 0.139686i
\(821\) 11.5000 + 19.9186i 0.401353 + 0.695163i 0.993889 0.110380i \(-0.0352068\pi\)
−0.592537 + 0.805543i \(0.701873\pi\)
\(822\) −20.7846 12.0000i −0.724947 0.418548i
\(823\) 22.5167 + 13.0000i 0.784881 + 0.453152i 0.838157 0.545428i \(-0.183633\pi\)
−0.0532760 + 0.998580i \(0.516966\pi\)
\(824\) 0 0
\(825\) −12.0000 + 9.00000i −0.417786 + 0.313340i
\(826\) 0 0
\(827\) 18.0000i 0.625921i −0.949766 0.312961i \(-0.898679\pi\)
0.949766 0.312961i \(-0.101321\pi\)
\(828\) 20.7846 12.0000i 0.722315 0.417029i
\(829\) −15.0000 + 25.9808i −0.520972 + 0.902349i 0.478731 + 0.877962i \(0.341097\pi\)
−0.999703 + 0.0243876i \(0.992236\pi\)
\(830\) −14.9282 + 9.85641i −0.518165 + 0.342121i
\(831\) −1.00000 1.73205i −0.0346896 0.0600842i
\(832\) 8.00000i 0.277350i
\(833\) 0 0
\(834\) 20.0000 0.692543
\(835\) 6.69615 0.401924i 0.231730 0.0139091i
\(836\) 0 0
\(837\) 8.66025 + 5.00000i 0.299342 + 0.172825i
\(838\) −51.9615 + 30.0000i −1.79498 + 1.03633i
\(839\) −30.0000 −1.03572 −0.517858 0.855467i \(-0.673270\pi\)
−0.517858 + 0.855467i \(0.673270\pi\)
\(840\) 0 0
\(841\) −4.00000 −0.137931
\(842\) −5.19615 + 3.00000i −0.179071 + 0.103387i
\(843\) 6.06218 + 3.50000i 0.208792 + 0.120546i
\(844\) −13.0000 + 22.5167i −0.447478 + 0.775055i
\(845\) 1.60770 + 26.7846i 0.0553064 + 0.921419i
\(846\) 12.0000 0.412568
\(847\) 0 0
\(848\) 24.0000i 0.824163i
\(849\) 5.50000 + 9.52628i 0.188760 + 0.326941i
\(850\) 69.4974 8.37307i 2.38374 0.287194i
\(851\) −6.00000 + 10.3923i −0.205677 + 0.356244i
\(852\) −13.8564 + 8.00000i −0.474713 + 0.274075i
\(853\) 54.0000i 1.84892i 0.381273 + 0.924462i \(0.375486\pi\)
−0.381273 + 0.924462i \(0.624514\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −36.3731 21.0000i −1.24248 0.717346i −0.272882 0.962048i \(-0.587977\pi\)
−0.969599 + 0.244701i \(0.921310\pi\)
\(858\) −5.19615 3.00000i −0.177394 0.102418i
\(859\) 20.0000 + 34.6410i 0.682391 + 1.18194i 0.974249 + 0.225475i \(0.0723932\pi\)
−0.291858 + 0.956462i \(0.594273\pi\)
\(860\) −8.00000 + 16.0000i −0.272798 + 0.545595i
\(861\) 0 0
\(862\) 46.0000i 1.56677i
\(863\) 46.7654 27.0000i 1.59191 0.919091i 0.598933 0.800799i \(-0.295592\pi\)
0.992979 0.118291i \(-0.0377417\pi\)
\(864\) 20.0000 34.6410i 0.680414 1.17851i
\(865\) 11.0885 + 16.7942i 0.377019 + 0.571021i
\(866\) −26.0000 45.0333i −0.883516 1.53029i
\(867\) 32.0000i 1.08678i
\(868\) 0 0
\(869\) −15.0000 −0.508840
\(870\) 1.33975 + 22.3205i 0.0454216 + 0.756736i
\(871\) −1.00000 + 1.73205i −0.0338837 + 0.0586883i
\(872\) 0 0
\(873\) 12.1244 7.00000i 0.410347 0.236914i
\(874\) 0 0
\(875\) 0 0
\(876\) 12.0000 0.405442
\(877\) 27.7128 16.0000i 0.935795 0.540282i 0.0471555 0.998888i \(-0.484984\pi\)
0.888640 + 0.458606i \(0.151651\pi\)
\(878\) 51.9615 + 30.0000i 1.75362 + 1.01245i
\(879\) −4.50000 + 7.79423i −0.151781 + 0.262893i
\(880\) 1.60770 + 26.7846i 0.0541954 + 0.902909i
\(881\) 32.0000 1.07811 0.539054 0.842271i \(-0.318782\pi\)
0.539054 + 0.842271i \(0.318782\pi\)
\(882\) 0 0
\(883\) 36.0000i 1.21150i −0.795656 0.605748i \(-0.792874\pi\)
0.795656 0.605748i \(-0.207126\pi\)
\(884\) 7.00000 + 12.1244i 0.235435 + 0.407786i
\(885\) 12.3205 + 18.6603i 0.414149 + 0.627258i
\(886\) 4.00000 6.92820i 0.134383 0.232758i
\(887\) −24.2487 + 14.0000i −0.814192 + 0.470074i −0.848410 0.529340i \(-0.822439\pi\)
0.0342175 + 0.999414i \(0.489106\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 1.50000 + 2.59808i 0.0502519 + 0.0870388i
\(892\) −36.3731 21.0000i −1.21786 0.703132i
\(893\) 0 0
\(894\) 10.0000 + 17.3205i 0.334450 + 0.579284i
\(895\) −40.0000 20.0000i −1.33705 0.668526i
\(896\) 0 0
\(897\) 6.00000i 0.200334i
\(898\) 8.66025 5.00000i 0.288996 0.166852i
\(899\) −5.00000 + 8.66025i −0.166759 + 0.288836i
\(900\) 19.8564 2.39230i 0.661880 0.0797435i
\(901\) −21.0000 36.3731i −0.699611 1.21176i
\(902\) 12.0000i 0.399556i
\(903\) 0 0
\(904\) 0 0
\(905\) −2.41154 40.1769i −0.0801624 1.33553i
\(906\) 13.0000 22.5167i 0.431896 0.748066i
\(907\) 32.9090 + 19.0000i 1.09272 + 0.630885i 0.934300 0.356487i \(-0.116025\pi\)
0.158424 + 0.987371i \(0.449359\pi\)
\(908\) −29.4449 + 17.0000i −0.977162 + 0.564165i
\(909\) 24.0000 0.796030
\(910\) 0 0
\(911\) 12.0000 0.397578 0.198789 0.980042i \(-0.436299\pi\)
0.198789 + 0.980042i \(0.436299\pi\)
\(912\) 0 0
\(913\) 10.3923 + 6.00000i 0.343935 + 0.198571i
\(914\) −38.0000 + 65.8179i −1.25693 + 2.17706i
\(915\) −17.8564 + 1.07180i −0.590315 + 0.0354325i
\(916\) −20.0000 −0.660819
\(917\) 0 0
\(918\) 70.0000i 2.31034i
\(919\) −2.50000 4.33013i −0.0824674 0.142838i 0.821842 0.569716i \(-0.192947\pi\)
−0.904309 + 0.426878i \(0.859613\pi\)
\(920\) 0 0
\(921\) −3.50000 + 6.06218i −0.115329 + 0.199756i
\(922\) 20.7846 12.0000i 0.684505 0.395199i
\(923\) 8.00000i 0.263323i
\(924\) 0 0
\(925\) −8.00000 + 6.00000i −0.263038 + 0.197279i
\(926\) −36.0000 62.3538i −1.18303 2.04907i
\(927\) −32.9090 19.0000i −1.08087 0.624042i
\(928\) 34.6410 + 20.0000i 1.13715 + 0.656532i
\(929\) −25.0000 43.3013i −0.820223 1.42067i −0.905516 0.424313i \(-0.860516\pi\)
0.0852924 0.996356i \(-0.472818\pi\)
\(930\) −8.00000 4.00000i −0.262330 0.131165i
\(931\) 0 0
\(932\) 32.0000i 1.04819i
\(933\) −10.3923 + 6.00000i −0.340229 + 0.196431i
\(934\) 27.0000 46.7654i 0.883467 1.53021i
\(935\) −25.8731 39.1865i −0.846140 1.28154i
\(936\) 0 0
\(937\) 13.0000i 0.424691i −0.977195 0.212346i \(-0.931890\pi\)
0.977195 0.212346i \(-0.0681103\pi\)
\(938\) 0 0
\(939\) −21.0000 −0.685309
\(940\) −13.3923 + 0.803848i −0.436809 + 0.0262186i
\(941\) 24.0000 41.5692i 0.782378 1.35512i −0.148176 0.988961i \(-0.547340\pi\)
0.930553 0.366157i \(-0.119327\pi\)
\(942\) 31.1769 + 18.0000i 1.01580 + 0.586472i
\(943\) −10.3923 + 6.00000i −0.338420 + 0.195387i
\(944\) 40.0000 1.30189
\(945\) 0 0
\(946\) 24.0000 0.780307
\(947\) 36.3731 21.0000i 1.18197 0.682408i 0.225497 0.974244i \(-0.427599\pi\)
0.956469 + 0.291835i \(0.0942660\pi\)
\(948\) −8.66025 5.00000i −0.281272 0.162392i
\(949\) 3.00000 5.19615i 0.0973841 0.168674i
\(950\) 0 0
\(951\) 12.0000 0.389127
\(952\) 0 0
\(953\) 6.00000i 0.194359i −0.995267 0.0971795i \(-0.969018\pi\)
0.995267 0.0971795i \(-0.0309821\pi\)
\(954\) −12.0000 20.7846i −0.388514 0.672927i
\(955\) −5.59808 + 3.69615i −0.181149 + 0.119605i
\(956\) −15.0000 + 25.9808i −0.485135 + 0.840278i
\(957\) 12.9904 7.50000i 0.419919 0.242441i
\(958\) 60.0000i 1.93851i
\(959\) 0 0
\(960\) −8.00000 + 16.0000i −0.258199 + 0.516398i
\(961\) 13.5000 + 23.3827i 0.435484 + 0.754280i
\(962\) −3.46410 2.00000i −0.111687 0.0644826i
\(963\) 13.8564 + 8.00000i 0.446516 + 0.257796i
\(964\) 22.0000 + 38.1051i 0.708572 + 1.22728i
\(965\) −16.0000 + 32.0000i −0.515058 + 1.03012i
\(966\) 0 0
\(967\) 8.00000i 0.257263i −0.991692 0.128631i \(-0.958942\pi\)
0.991692 0.128631i \(-0.0410584\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) −26.1244 + 17.2487i −0.838803 + 0.553823i
\(971\) −11.0000 19.0526i −0.353007 0.611426i 0.633768 0.773523i \(-0.281507\pi\)
−0.986775 + 0.162098i \(0.948174\pi\)
\(972\) 32.0000i 1.02640i
\(973\) 0 0
\(974\) −84.0000 −2.69153
\(975\) −1.96410 + 4.59808i −0.0629016 + 0.147256i
\(976\) −16.0000 + 27.7128i −0.512148 + 0.887066i
\(977\) −10.3923 6.00000i −0.332479 0.191957i 0.324462 0.945899i \(-0.394817\pi\)
−0.656941 + 0.753942i \(0.728150\pi\)
\(978\) 24.2487 14.0000i 0.775388 0.447671i
\(979\) 0 0
\(980\) 0 0
\(981\) −10.0000 −0.319275
\(982\) 12.1244 7.00000i 0.386904 0.223379i
\(983\) 44.1673 + 25.5000i 1.40872 + 0.813324i 0.995265 0.0972017i \(-0.0309892\pi\)
0.413453 + 0.910525i \(0.364323\pi\)
\(984\) 0 0
\(985\) −4.46410 + 0.267949i −0.142238 + 0.00853757i
\(986\) −70.0000 −2.22925
\(987\) 0 0
\(988\) 0 0
\(989\) −12.0000 20.7846i −0.381578 0.660912i
\(990\) −14.7846 22.3923i −0.469886 0.711674i
\(991\) 4.00000 6.92820i 0.127064 0.220082i −0.795474 0.605988i \(-0.792778\pi\)
0.922538 + 0.385906i \(0.126111\pi\)
\(992\) −13.8564 + 8.00000i −0.439941 + 0.254000i
\(993\) 12.0000i 0.380808i
\(994\) 0 0
\(995\) −20.0000 10.0000i −0.634043 0.317021i
\(996\) 4.00000 + 6.92820i 0.126745 + 0.219529i
\(997\) 11.2583 + 6.50000i 0.356555 + 0.205857i 0.667568 0.744548i \(-0.267335\pi\)
−0.311014 + 0.950405i \(0.600668\pi\)
\(998\) −60.6218 35.0000i −1.91895 1.10791i
\(999\) −5.00000 8.66025i −0.158193 0.273998i
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 245.2.j.e.214.2 4
5.4 even 2 inner 245.2.j.e.214.1 4
7.2 even 3 inner 245.2.j.e.79.1 4
7.3 odd 6 245.2.b.a.99.2 2
7.4 even 3 35.2.b.a.29.2 yes 2
7.5 odd 6 245.2.j.d.79.1 4
7.6 odd 2 245.2.j.d.214.2 4
21.11 odd 6 315.2.d.a.64.1 2
21.17 even 6 2205.2.d.b.1324.1 2
28.11 odd 6 560.2.g.b.449.2 2
35.3 even 12 1225.2.a.i.1.1 1
35.4 even 6 35.2.b.a.29.1 2
35.9 even 6 inner 245.2.j.e.79.2 4
35.17 even 12 1225.2.a.a.1.1 1
35.18 odd 12 175.2.a.c.1.1 1
35.19 odd 6 245.2.j.d.79.2 4
35.24 odd 6 245.2.b.a.99.1 2
35.32 odd 12 175.2.a.a.1.1 1
35.34 odd 2 245.2.j.d.214.1 4
56.11 odd 6 2240.2.g.g.449.1 2
56.53 even 6 2240.2.g.h.449.2 2
84.11 even 6 5040.2.t.p.1009.2 2
105.32 even 12 1575.2.a.k.1.1 1
105.53 even 12 1575.2.a.a.1.1 1
105.59 even 6 2205.2.d.b.1324.2 2
105.74 odd 6 315.2.d.a.64.2 2
140.39 odd 6 560.2.g.b.449.1 2
140.67 even 12 2800.2.a.w.1.1 1
140.123 even 12 2800.2.a.l.1.1 1
280.109 even 6 2240.2.g.h.449.1 2
280.179 odd 6 2240.2.g.g.449.2 2
420.179 even 6 5040.2.t.p.1009.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
35.2.b.a.29.1 2 35.4 even 6
35.2.b.a.29.2 yes 2 7.4 even 3
175.2.a.a.1.1 1 35.32 odd 12
175.2.a.c.1.1 1 35.18 odd 12
245.2.b.a.99.1 2 35.24 odd 6
245.2.b.a.99.2 2 7.3 odd 6
245.2.j.d.79.1 4 7.5 odd 6
245.2.j.d.79.2 4 35.19 odd 6
245.2.j.d.214.1 4 35.34 odd 2
245.2.j.d.214.2 4 7.6 odd 2
245.2.j.e.79.1 4 7.2 even 3 inner
245.2.j.e.79.2 4 35.9 even 6 inner
245.2.j.e.214.1 4 5.4 even 2 inner
245.2.j.e.214.2 4 1.1 even 1 trivial
315.2.d.a.64.1 2 21.11 odd 6
315.2.d.a.64.2 2 105.74 odd 6
560.2.g.b.449.1 2 140.39 odd 6
560.2.g.b.449.2 2 28.11 odd 6
1225.2.a.a.1.1 1 35.17 even 12
1225.2.a.i.1.1 1 35.3 even 12
1575.2.a.a.1.1 1 105.53 even 12
1575.2.a.k.1.1 1 105.32 even 12
2205.2.d.b.1324.1 2 21.17 even 6
2205.2.d.b.1324.2 2 105.59 even 6
2240.2.g.g.449.1 2 56.11 odd 6
2240.2.g.g.449.2 2 280.179 odd 6
2240.2.g.h.449.1 2 280.109 even 6
2240.2.g.h.449.2 2 56.53 even 6
2800.2.a.l.1.1 1 140.123 even 12
2800.2.a.w.1.1 1 140.67 even 12
5040.2.t.p.1009.1 2 420.179 even 6
5040.2.t.p.1009.2 2 84.11 even 6