Properties

Label 1050.2.bc.d.493.1
Level $1050$
Weight $2$
Character 1050.493
Analytic conductor $8.384$
Analytic rank $0$
Dimension $8$
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] = [1050,2,Mod(157,1050)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1050, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([0, 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("1050.157");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1050.bc (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: \(8.38429221223\)
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 493.1
Root \(0.965926 + 0.258819i\) of defining polynomial
Character \(\chi\) \(=\) 1050.493
Dual form 1050.2.bc.d.607.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.965926 - 0.258819i) q^{2} +(-0.258819 - 0.965926i) q^{3} +(0.866025 + 0.500000i) q^{4} +1.00000i q^{6} +(2.63896 - 0.189469i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-0.866025 + 0.500000i) q^{9} +O(q^{10})\) \(q+(-0.965926 - 0.258819i) q^{2} +(-0.258819 - 0.965926i) q^{3} +(0.866025 + 0.500000i) q^{4} +1.00000i q^{6} +(2.63896 - 0.189469i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-0.866025 + 0.500000i) q^{9} +(-0.500000 + 0.866025i) q^{11} +(0.258819 - 0.965926i) q^{12} +(1.60368 - 1.60368i) q^{13} +(-2.59808 - 0.500000i) q^{14} +(0.500000 + 0.866025i) q^{16} +(0.517638 - 0.138701i) q^{17} +(0.965926 - 0.258819i) q^{18} +(2.86603 + 4.96410i) q^{19} +(-0.866025 - 2.50000i) q^{21} +(0.707107 - 0.707107i) q^{22} +(2.05197 - 7.65806i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(-1.96410 + 1.13397i) q^{26} +(0.707107 + 0.707107i) q^{27} +(2.38014 + 1.15539i) q^{28} +6.92820i q^{29} +(-0.464102 - 0.267949i) q^{31} +(-0.258819 - 0.965926i) q^{32} +(0.965926 + 0.258819i) q^{33} -0.535898 q^{34} -1.00000 q^{36} +(9.58991 + 2.56961i) q^{37} +(-1.48356 - 5.53674i) q^{38} +(-1.96410 - 1.13397i) q^{39} -5.73205i q^{41} +(0.189469 + 2.63896i) q^{42} +(-3.48477 - 3.48477i) q^{43} +(-0.866025 + 0.500000i) q^{44} +(-3.96410 + 6.86603i) q^{46} +(-2.38014 + 8.88280i) q^{47} +(0.707107 - 0.707107i) q^{48} +(6.92820 - 1.00000i) q^{49} +(-0.267949 - 0.464102i) q^{51} +(2.19067 - 0.586988i) q^{52} +(-0.965926 + 0.258819i) q^{53} +(-0.500000 - 0.866025i) q^{54} +(-2.00000 - 1.73205i) q^{56} +(4.05317 - 4.05317i) q^{57} +(1.79315 - 6.69213i) q^{58} +(2.26795 - 3.92820i) q^{59} +(3.92820 - 2.26795i) q^{61} +(0.378937 + 0.378937i) q^{62} +(-2.19067 + 1.48356i) q^{63} +1.00000i q^{64} +(-0.866025 - 0.500000i) q^{66} +(-0.517638 - 1.93185i) q^{67} +(0.517638 + 0.138701i) q^{68} -7.92820 q^{69} +4.92820 q^{71} +(0.965926 + 0.258819i) q^{72} +(-1.03528 - 3.86370i) q^{73} +(-8.59808 - 4.96410i) q^{74} +5.73205i q^{76} +(-1.15539 + 2.38014i) q^{77} +(1.60368 + 1.60368i) q^{78} +(14.6603 - 8.46410i) q^{79} +(0.500000 - 0.866025i) q^{81} +(-1.48356 + 5.53674i) q^{82} +(7.34847 - 7.34847i) q^{83} +(0.500000 - 2.59808i) q^{84} +(2.46410 + 4.26795i) q^{86} +(6.69213 - 1.79315i) q^{87} +(0.965926 - 0.258819i) q^{88} +(-3.46410 - 6.00000i) q^{89} +(3.92820 - 4.53590i) q^{91} +(5.60609 - 5.60609i) q^{92} +(-0.138701 + 0.517638i) q^{93} +(4.59808 - 7.96410i) q^{94} +(-0.866025 + 0.500000i) q^{96} +(-7.72741 - 7.72741i) q^{97} +(-6.95095 - 0.827225i) q^{98} -1.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 4 q^{11} + 4 q^{16} + 16 q^{19} - 4 q^{24} + 12 q^{26} + 24 q^{31} - 32 q^{34} - 8 q^{36} + 12 q^{39} - 4 q^{46} - 16 q^{51} - 4 q^{54} - 16 q^{56} + 32 q^{59} - 24 q^{61} - 8 q^{69} - 16 q^{71} - 48 q^{74} + 48 q^{79} + 4 q^{81} + 4 q^{84} - 8 q^{86} - 24 q^{91} + 16 q^{94}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(451\) \(701\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(e\left(\frac{1}{6}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.965926 0.258819i −0.683013 0.183013i
\(3\) −0.258819 0.965926i −0.149429 0.557678i
\(4\) 0.866025 + 0.500000i 0.433013 + 0.250000i
\(5\) 0 0
\(6\) 1.00000i 0.408248i
\(7\) 2.63896 0.189469i 0.997433 0.0716124i
\(8\) −0.707107 0.707107i −0.250000 0.250000i
\(9\) −0.866025 + 0.500000i −0.288675 + 0.166667i
\(10\) 0 0
\(11\) −0.500000 + 0.866025i −0.150756 + 0.261116i −0.931505 0.363727i \(-0.881504\pi\)
0.780750 + 0.624844i \(0.214837\pi\)
\(12\) 0.258819 0.965926i 0.0747146 0.278839i
\(13\) 1.60368 1.60368i 0.444781 0.444781i −0.448834 0.893615i \(-0.648160\pi\)
0.893615 + 0.448834i \(0.148160\pi\)
\(14\) −2.59808 0.500000i −0.694365 0.133631i
\(15\) 0 0
\(16\) 0.500000 + 0.866025i 0.125000 + 0.216506i
\(17\) 0.517638 0.138701i 0.125546 0.0336399i −0.195499 0.980704i \(-0.562633\pi\)
0.321045 + 0.947064i \(0.395966\pi\)
\(18\) 0.965926 0.258819i 0.227671 0.0610042i
\(19\) 2.86603 + 4.96410i 0.657511 + 1.13884i 0.981258 + 0.192699i \(0.0617242\pi\)
−0.323747 + 0.946144i \(0.604943\pi\)
\(20\) 0 0
\(21\) −0.866025 2.50000i −0.188982 0.545545i
\(22\) 0.707107 0.707107i 0.150756 0.150756i
\(23\) 2.05197 7.65806i 0.427865 1.59682i −0.329720 0.944079i \(-0.606954\pi\)
0.757585 0.652736i \(-0.226379\pi\)
\(24\) −0.500000 + 0.866025i −0.102062 + 0.176777i
\(25\) 0 0
\(26\) −1.96410 + 1.13397i −0.385192 + 0.222391i
\(27\) 0.707107 + 0.707107i 0.136083 + 0.136083i
\(28\) 2.38014 + 1.15539i 0.449804 + 0.218349i
\(29\) 6.92820i 1.28654i 0.765641 + 0.643268i \(0.222422\pi\)
−0.765641 + 0.643268i \(0.777578\pi\)
\(30\) 0 0
\(31\) −0.464102 0.267949i −0.0833551 0.0481251i 0.457743 0.889085i \(-0.348658\pi\)
−0.541098 + 0.840959i \(0.681991\pi\)
\(32\) −0.258819 0.965926i −0.0457532 0.170753i
\(33\) 0.965926 + 0.258819i 0.168146 + 0.0450546i
\(34\) −0.535898 −0.0919058
\(35\) 0 0
\(36\) −1.00000 −0.166667
\(37\) 9.58991 + 2.56961i 1.57657 + 0.422441i 0.937862 0.347008i \(-0.112802\pi\)
0.638709 + 0.769449i \(0.279469\pi\)
\(38\) −1.48356 5.53674i −0.240666 0.898177i
\(39\) −1.96410 1.13397i −0.314508 0.181581i
\(40\) 0 0
\(41\) 5.73205i 0.895196i −0.894235 0.447598i \(-0.852280\pi\)
0.894235 0.447598i \(-0.147720\pi\)
\(42\) 0.189469 + 2.63896i 0.0292357 + 0.407200i
\(43\) −3.48477 3.48477i −0.531422 0.531422i 0.389574 0.920995i \(-0.372622\pi\)
−0.920995 + 0.389574i \(0.872622\pi\)
\(44\) −0.866025 + 0.500000i −0.130558 + 0.0753778i
\(45\) 0 0
\(46\) −3.96410 + 6.86603i −0.584475 + 1.01234i
\(47\) −2.38014 + 8.88280i −0.347179 + 1.29569i 0.542867 + 0.839819i \(0.317339\pi\)
−0.890046 + 0.455871i \(0.849328\pi\)
\(48\) 0.707107 0.707107i 0.102062 0.102062i
\(49\) 6.92820 1.00000i 0.989743 0.142857i
\(50\) 0 0
\(51\) −0.267949 0.464102i −0.0375204 0.0649872i
\(52\) 2.19067 0.586988i 0.303791 0.0814007i
\(53\) −0.965926 + 0.258819i −0.132680 + 0.0355515i −0.324548 0.945869i \(-0.605212\pi\)
0.191868 + 0.981421i \(0.438546\pi\)
\(54\) −0.500000 0.866025i −0.0680414 0.117851i
\(55\) 0 0
\(56\) −2.00000 1.73205i −0.267261 0.231455i
\(57\) 4.05317 4.05317i 0.536856 0.536856i
\(58\) 1.79315 6.69213i 0.235452 0.878720i
\(59\) 2.26795 3.92820i 0.295262 0.511409i −0.679784 0.733412i \(-0.737926\pi\)
0.975046 + 0.222004i \(0.0712598\pi\)
\(60\) 0 0
\(61\) 3.92820 2.26795i 0.502955 0.290381i −0.226978 0.973900i \(-0.572885\pi\)
0.729933 + 0.683519i \(0.239551\pi\)
\(62\) 0.378937 + 0.378937i 0.0481251 + 0.0481251i
\(63\) −2.19067 + 1.48356i −0.275999 + 0.186911i
\(64\) 1.00000i 0.125000i
\(65\) 0 0
\(66\) −0.866025 0.500000i −0.106600 0.0615457i
\(67\) −0.517638 1.93185i −0.0632396 0.236013i 0.927071 0.374887i \(-0.122318\pi\)
−0.990310 + 0.138874i \(0.955652\pi\)
\(68\) 0.517638 + 0.138701i 0.0627728 + 0.0168199i
\(69\) −7.92820 −0.954444
\(70\) 0 0
\(71\) 4.92820 0.584870 0.292435 0.956285i \(-0.405534\pi\)
0.292435 + 0.956285i \(0.405534\pi\)
\(72\) 0.965926 + 0.258819i 0.113835 + 0.0305021i
\(73\) −1.03528 3.86370i −0.121170 0.452212i 0.878504 0.477734i \(-0.158542\pi\)
−0.999674 + 0.0255221i \(0.991875\pi\)
\(74\) −8.59808 4.96410i −0.999506 0.577065i
\(75\) 0 0
\(76\) 5.73205i 0.657511i
\(77\) −1.15539 + 2.38014i −0.131669 + 0.271242i
\(78\) 1.60368 + 1.60368i 0.181581 + 0.181581i
\(79\) 14.6603 8.46410i 1.64941 0.952286i 0.672100 0.740460i \(-0.265393\pi\)
0.977308 0.211825i \(-0.0679408\pi\)
\(80\) 0 0
\(81\) 0.500000 0.866025i 0.0555556 0.0962250i
\(82\) −1.48356 + 5.53674i −0.163832 + 0.611430i
\(83\) 7.34847 7.34847i 0.806599 0.806599i −0.177518 0.984118i \(-0.556807\pi\)
0.984118 + 0.177518i \(0.0568069\pi\)
\(84\) 0.500000 2.59808i 0.0545545 0.283473i
\(85\) 0 0
\(86\) 2.46410 + 4.26795i 0.265711 + 0.460225i
\(87\) 6.69213 1.79315i 0.717472 0.192246i
\(88\) 0.965926 0.258819i 0.102968 0.0275902i
\(89\) −3.46410 6.00000i −0.367194 0.635999i 0.621932 0.783072i \(-0.286348\pi\)
−0.989126 + 0.147073i \(0.953015\pi\)
\(90\) 0 0
\(91\) 3.92820 4.53590i 0.411788 0.475491i
\(92\) 5.60609 5.60609i 0.584475 0.584475i
\(93\) −0.138701 + 0.517638i −0.0143826 + 0.0536766i
\(94\) 4.59808 7.96410i 0.474255 0.821434i
\(95\) 0 0
\(96\) −0.866025 + 0.500000i −0.0883883 + 0.0510310i
\(97\) −7.72741 7.72741i −0.784599 0.784599i 0.196004 0.980603i \(-0.437203\pi\)
−0.980603 + 0.196004i \(0.937203\pi\)
\(98\) −6.95095 0.827225i −0.702152 0.0835624i
\(99\) 1.00000i 0.100504i
\(100\) 0 0
\(101\) −12.9282 7.46410i −1.28640 0.742706i −0.308393 0.951259i \(-0.599791\pi\)
−0.978011 + 0.208553i \(0.933125\pi\)
\(102\) 0.138701 + 0.517638i 0.0137334 + 0.0512538i
\(103\) −2.31079 0.619174i −0.227689 0.0610090i 0.143171 0.989698i \(-0.454270\pi\)
−0.370860 + 0.928689i \(0.620937\pi\)
\(104\) −2.26795 −0.222391
\(105\) 0 0
\(106\) 1.00000 0.0971286
\(107\) −1.03528 0.277401i −0.100084 0.0268174i 0.208430 0.978037i \(-0.433165\pi\)
−0.308513 + 0.951220i \(0.599831\pi\)
\(108\) 0.258819 + 0.965926i 0.0249049 + 0.0929463i
\(109\) 2.66025 + 1.53590i 0.254806 + 0.147112i 0.621963 0.783047i \(-0.286335\pi\)
−0.367157 + 0.930159i \(0.619669\pi\)
\(110\) 0 0
\(111\) 9.92820i 0.942343i
\(112\) 1.48356 + 2.19067i 0.140184 + 0.206999i
\(113\) −0.656339 0.656339i −0.0617432 0.0617432i 0.675561 0.737304i \(-0.263902\pi\)
−0.737304 + 0.675561i \(0.763902\pi\)
\(114\) −4.96410 + 2.86603i −0.464931 + 0.268428i
\(115\) 0 0
\(116\) −3.46410 + 6.00000i −0.321634 + 0.557086i
\(117\) −0.586988 + 2.19067i −0.0542671 + 0.202528i
\(118\) −3.20736 + 3.20736i −0.295262 + 0.295262i
\(119\) 1.33975 0.464102i 0.122814 0.0425441i
\(120\) 0 0
\(121\) 5.00000 + 8.66025i 0.454545 + 0.787296i
\(122\) −4.38134 + 1.17398i −0.396668 + 0.106287i
\(123\) −5.53674 + 1.48356i −0.499231 + 0.133768i
\(124\) −0.267949 0.464102i −0.0240625 0.0416776i
\(125\) 0 0
\(126\) 2.50000 0.866025i 0.222718 0.0771517i
\(127\) 3.53553 3.53553i 0.313728 0.313728i −0.532624 0.846352i \(-0.678794\pi\)
0.846352 + 0.532624i \(0.178794\pi\)
\(128\) 0.258819 0.965926i 0.0228766 0.0853766i
\(129\) −2.46410 + 4.26795i −0.216952 + 0.375772i
\(130\) 0 0
\(131\) 17.4282 10.0622i 1.52271 0.879137i 0.523070 0.852290i \(-0.324787\pi\)
0.999640 0.0268466i \(-0.00854657\pi\)
\(132\) 0.707107 + 0.707107i 0.0615457 + 0.0615457i
\(133\) 8.50386 + 12.5570i 0.737379 + 1.08883i
\(134\) 2.00000i 0.172774i
\(135\) 0 0
\(136\) −0.464102 0.267949i −0.0397964 0.0229765i
\(137\) 1.31268 + 4.89898i 0.112150 + 0.418548i 0.999058 0.0433975i \(-0.0138182\pi\)
−0.886908 + 0.461946i \(0.847152\pi\)
\(138\) 7.65806 + 2.05197i 0.651897 + 0.174675i
\(139\) 10.3923 0.881464 0.440732 0.897639i \(-0.354719\pi\)
0.440732 + 0.897639i \(0.354719\pi\)
\(140\) 0 0
\(141\) 9.19615 0.774456
\(142\) −4.76028 1.27551i −0.399474 0.107039i
\(143\) 0.586988 + 2.19067i 0.0490864 + 0.183193i
\(144\) −0.866025 0.500000i −0.0721688 0.0416667i
\(145\) 0 0
\(146\) 4.00000i 0.331042i
\(147\) −2.75908 6.43331i −0.227565 0.530611i
\(148\) 7.02030 + 7.02030i 0.577065 + 0.577065i
\(149\) −11.1962 + 6.46410i −0.917225 + 0.529560i −0.882749 0.469846i \(-0.844310\pi\)
−0.0344760 + 0.999406i \(0.510976\pi\)
\(150\) 0 0
\(151\) −11.9282 + 20.6603i −0.970703 + 1.68131i −0.277262 + 0.960794i \(0.589427\pi\)
−0.693441 + 0.720513i \(0.743906\pi\)
\(152\) 1.48356 5.53674i 0.120333 0.449089i
\(153\) −0.378937 + 0.378937i −0.0306353 + 0.0306353i
\(154\) 1.73205 2.00000i 0.139573 0.161165i
\(155\) 0 0
\(156\) −1.13397 1.96410i −0.0907906 0.157254i
\(157\) −12.2289 + 3.27671i −0.975970 + 0.261510i −0.711346 0.702842i \(-0.751914\pi\)
−0.264623 + 0.964352i \(0.585248\pi\)
\(158\) −16.3514 + 4.38134i −1.30085 + 0.348561i
\(159\) 0.500000 + 0.866025i 0.0396526 + 0.0686803i
\(160\) 0 0
\(161\) 3.96410 20.5981i 0.312415 1.62336i
\(162\) −0.707107 + 0.707107i −0.0555556 + 0.0555556i
\(163\) 3.10583 11.5911i 0.243267 0.907886i −0.730979 0.682400i \(-0.760936\pi\)
0.974246 0.225486i \(-0.0723970\pi\)
\(164\) 2.86603 4.96410i 0.223799 0.387631i
\(165\) 0 0
\(166\) −9.00000 + 5.19615i −0.698535 + 0.403300i
\(167\) −12.1595 12.1595i −0.940932 0.940932i 0.0574186 0.998350i \(-0.481713\pi\)
−0.998350 + 0.0574186i \(0.981713\pi\)
\(168\) −1.15539 + 2.38014i −0.0891406 + 0.183632i
\(169\) 7.85641i 0.604339i
\(170\) 0 0
\(171\) −4.96410 2.86603i −0.379614 0.219170i
\(172\) −1.27551 4.76028i −0.0972569 0.362968i
\(173\) 22.7847 + 6.10514i 1.73229 + 0.464165i 0.980708 0.195476i \(-0.0626253\pi\)
0.751580 + 0.659642i \(0.229292\pi\)
\(174\) −6.92820 −0.525226
\(175\) 0 0
\(176\) −1.00000 −0.0753778
\(177\) −4.38134 1.17398i −0.329322 0.0882415i
\(178\) 1.79315 + 6.69213i 0.134402 + 0.501596i
\(179\) −7.79423 4.50000i −0.582568 0.336346i 0.179585 0.983742i \(-0.442524\pi\)
−0.762153 + 0.647397i \(0.775858\pi\)
\(180\) 0 0
\(181\) 6.39230i 0.475136i 0.971371 + 0.237568i \(0.0763503\pi\)
−0.971371 + 0.237568i \(0.923650\pi\)
\(182\) −4.96833 + 3.36465i −0.368277 + 0.249404i
\(183\) −3.20736 3.20736i −0.237095 0.237095i
\(184\) −6.86603 + 3.96410i −0.506170 + 0.292237i
\(185\) 0 0
\(186\) 0.267949 0.464102i 0.0196470 0.0340296i
\(187\) −0.138701 + 0.517638i −0.0101428 + 0.0378534i
\(188\) −6.50266 + 6.50266i −0.474255 + 0.474255i
\(189\) 2.00000 + 1.73205i 0.145479 + 0.125988i
\(190\) 0 0
\(191\) 5.46410 + 9.46410i 0.395369 + 0.684798i 0.993148 0.116862i \(-0.0372836\pi\)
−0.597780 + 0.801660i \(0.703950\pi\)
\(192\) 0.965926 0.258819i 0.0697097 0.0186787i
\(193\) −18.1445 + 4.86181i −1.30607 + 0.349961i −0.843743 0.536747i \(-0.819653\pi\)
−0.462329 + 0.886708i \(0.652986\pi\)
\(194\) 5.46410 + 9.46410i 0.392300 + 0.679483i
\(195\) 0 0
\(196\) 6.50000 + 2.59808i 0.464286 + 0.185577i
\(197\) −7.67664 + 7.67664i −0.546938 + 0.546938i −0.925554 0.378616i \(-0.876400\pi\)
0.378616 + 0.925554i \(0.376400\pi\)
\(198\) −0.258819 + 0.965926i −0.0183935 + 0.0686454i
\(199\) 9.73205 16.8564i 0.689887 1.19492i −0.281987 0.959418i \(-0.590994\pi\)
0.971874 0.235501i \(-0.0756730\pi\)
\(200\) 0 0
\(201\) −1.73205 + 1.00000i −0.122169 + 0.0705346i
\(202\) 10.5558 + 10.5558i 0.742706 + 0.742706i
\(203\) 1.31268 + 18.2832i 0.0921319 + 1.28323i
\(204\) 0.535898i 0.0375204i
\(205\) 0 0
\(206\) 2.07180 + 1.19615i 0.144349 + 0.0833399i
\(207\) 2.05197 + 7.65806i 0.142622 + 0.532272i
\(208\) 2.19067 + 0.586988i 0.151896 + 0.0407003i
\(209\) −5.73205 −0.396494
\(210\) 0 0
\(211\) 21.7846 1.49971 0.749857 0.661600i \(-0.230122\pi\)
0.749857 + 0.661600i \(0.230122\pi\)
\(212\) −0.965926 0.258819i −0.0663401 0.0177758i
\(213\) −1.27551 4.76028i −0.0873967 0.326169i
\(214\) 0.928203 + 0.535898i 0.0634507 + 0.0366333i
\(215\) 0 0
\(216\) 1.00000i 0.0680414i
\(217\) −1.27551 0.619174i −0.0865875 0.0420323i
\(218\) −2.17209 2.17209i −0.147112 0.147112i
\(219\) −3.46410 + 2.00000i −0.234082 + 0.135147i
\(220\) 0 0
\(221\) 0.607695 1.05256i 0.0408780 0.0708028i
\(222\) −2.56961 + 9.58991i −0.172461 + 0.643632i
\(223\) −17.9043 + 17.9043i −1.19896 + 1.19896i −0.224483 + 0.974478i \(0.572069\pi\)
−0.974478 + 0.224483i \(0.927931\pi\)
\(224\) −0.866025 2.50000i −0.0578638 0.167038i
\(225\) 0 0
\(226\) 0.464102 + 0.803848i 0.0308716 + 0.0534711i
\(227\) 3.34607 0.896575i 0.222086 0.0595078i −0.146060 0.989276i \(-0.546659\pi\)
0.368146 + 0.929768i \(0.379993\pi\)
\(228\) 5.53674 1.48356i 0.366679 0.0982514i
\(229\) 5.46410 + 9.46410i 0.361078 + 0.625405i 0.988139 0.153565i \(-0.0490755\pi\)
−0.627061 + 0.778971i \(0.715742\pi\)
\(230\) 0 0
\(231\) 2.59808 + 0.500000i 0.170941 + 0.0328976i
\(232\) 4.89898 4.89898i 0.321634 0.321634i
\(233\) −6.69213 + 24.9754i −0.438416 + 1.63619i 0.294341 + 0.955700i \(0.404900\pi\)
−0.732757 + 0.680490i \(0.761767\pi\)
\(234\) 1.13397 1.96410i 0.0741302 0.128397i
\(235\) 0 0
\(236\) 3.92820 2.26795i 0.255704 0.147631i
\(237\) −11.9700 11.9700i −0.777538 0.777538i
\(238\) −1.41421 + 0.101536i −0.0916698 + 0.00658160i
\(239\) 24.0000i 1.55243i 0.630468 + 0.776215i \(0.282863\pi\)
−0.630468 + 0.776215i \(0.717137\pi\)
\(240\) 0 0
\(241\) −22.2846 12.8660i −1.43548 0.828774i −0.437947 0.899001i \(-0.644294\pi\)
−0.997531 + 0.0702273i \(0.977628\pi\)
\(242\) −2.58819 9.65926i −0.166375 0.620921i
\(243\) −0.965926 0.258819i −0.0619642 0.0166032i
\(244\) 4.53590 0.290381
\(245\) 0 0
\(246\) 5.73205 0.365462
\(247\) 12.5570 + 3.36465i 0.798985 + 0.214087i
\(248\) 0.138701 + 0.517638i 0.00880750 + 0.0328701i
\(249\) −9.00000 5.19615i −0.570352 0.329293i
\(250\) 0 0
\(251\) 24.6603i 1.55654i 0.627929 + 0.778271i \(0.283903\pi\)
−0.627929 + 0.778271i \(0.716097\pi\)
\(252\) −2.63896 + 0.189469i −0.166239 + 0.0119354i
\(253\) 5.60609 + 5.60609i 0.352452 + 0.352452i
\(254\) −4.33013 + 2.50000i −0.271696 + 0.156864i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −4.76028 + 17.7656i −0.296938 + 1.10819i 0.642728 + 0.766094i \(0.277803\pi\)
−0.939666 + 0.342093i \(0.888864\pi\)
\(258\) 3.48477 3.48477i 0.216952 0.216952i
\(259\) 25.7942 + 4.96410i 1.60278 + 0.308454i
\(260\) 0 0
\(261\) −3.46410 6.00000i −0.214423 0.371391i
\(262\) −19.4386 + 5.20857i −1.20092 + 0.321786i
\(263\) 2.07055 0.554803i 0.127676 0.0342106i −0.194415 0.980919i \(-0.562281\pi\)
0.322091 + 0.946709i \(0.395614\pi\)
\(264\) −0.500000 0.866025i −0.0307729 0.0533002i
\(265\) 0 0
\(266\) −4.96410 14.3301i −0.304369 0.878636i
\(267\) −4.89898 + 4.89898i −0.299813 + 0.299813i
\(268\) 0.517638 1.93185i 0.0316198 0.118007i
\(269\) 4.66025 8.07180i 0.284141 0.492146i −0.688260 0.725464i \(-0.741625\pi\)
0.972400 + 0.233318i \(0.0749584\pi\)
\(270\) 0 0
\(271\) −6.92820 + 4.00000i −0.420858 + 0.242983i −0.695444 0.718580i \(-0.744792\pi\)
0.274586 + 0.961563i \(0.411459\pi\)
\(272\) 0.378937 + 0.378937i 0.0229765 + 0.0229765i
\(273\) −5.39804 2.62038i −0.326704 0.158592i
\(274\) 5.07180i 0.306398i
\(275\) 0 0
\(276\) −6.86603 3.96410i −0.413286 0.238611i
\(277\) −5.69402 21.2504i −0.342120 1.27681i −0.895940 0.444174i \(-0.853497\pi\)
0.553820 0.832636i \(-0.313170\pi\)
\(278\) −10.0382 2.68973i −0.602051 0.161319i
\(279\) 0.535898 0.0320834
\(280\) 0 0
\(281\) −14.0718 −0.839453 −0.419727 0.907651i \(-0.637874\pi\)
−0.419727 + 0.907651i \(0.637874\pi\)
\(282\) −8.88280 2.38014i −0.528963 0.141735i
\(283\) 5.03768 + 18.8009i 0.299459 + 1.11760i 0.937611 + 0.347686i \(0.113032\pi\)
−0.638152 + 0.769910i \(0.720301\pi\)
\(284\) 4.26795 + 2.46410i 0.253256 + 0.146218i
\(285\) 0 0
\(286\) 2.26795i 0.134107i
\(287\) −1.08604 15.1266i −0.0641072 0.892898i
\(288\) 0.707107 + 0.707107i 0.0416667 + 0.0416667i
\(289\) −14.4737 + 8.35641i −0.851395 + 0.491553i
\(290\) 0 0
\(291\) −5.46410 + 9.46410i −0.320311 + 0.554795i
\(292\) 1.03528 3.86370i 0.0605850 0.226106i
\(293\) 1.22474 1.22474i 0.0715504 0.0715504i −0.670426 0.741976i \(-0.733889\pi\)
0.741976 + 0.670426i \(0.233889\pi\)
\(294\) 1.00000 + 6.92820i 0.0583212 + 0.404061i
\(295\) 0 0
\(296\) −4.96410 8.59808i −0.288533 0.499753i
\(297\) −0.965926 + 0.258819i −0.0560487 + 0.0150182i
\(298\) 12.4877 3.34607i 0.723392 0.193832i
\(299\) −8.99038 15.5718i −0.519927 0.900540i
\(300\) 0 0
\(301\) −9.85641 8.53590i −0.568114 0.492001i
\(302\) 16.8690 16.8690i 0.970703 0.970703i
\(303\) −3.86370 + 14.4195i −0.221964 + 0.828381i
\(304\) −2.86603 + 4.96410i −0.164378 + 0.284711i
\(305\) 0 0
\(306\) 0.464102 0.267949i 0.0265309 0.0153176i
\(307\) −1.13681 1.13681i −0.0648813 0.0648813i 0.673922 0.738803i \(-0.264609\pi\)
−0.738803 + 0.673922i \(0.764609\pi\)
\(308\) −2.19067 + 1.48356i −0.124825 + 0.0845339i
\(309\) 2.39230i 0.136093i
\(310\) 0 0
\(311\) −23.7846 13.7321i −1.34870 0.778673i −0.360636 0.932707i \(-0.617440\pi\)
−0.988066 + 0.154034i \(0.950774\pi\)
\(312\) 0.586988 + 2.19067i 0.0332317 + 0.124022i
\(313\) −30.1146 8.06918i −1.70218 0.456097i −0.728691 0.684843i \(-0.759871\pi\)
−0.973486 + 0.228746i \(0.926538\pi\)
\(314\) 12.6603 0.714459
\(315\) 0 0
\(316\) 16.9282 0.952286
\(317\) 13.5230 + 3.62347i 0.759525 + 0.203514i 0.617739 0.786383i \(-0.288049\pi\)
0.141786 + 0.989897i \(0.454715\pi\)
\(318\) −0.258819 0.965926i −0.0145139 0.0541664i
\(319\) −6.00000 3.46410i −0.335936 0.193952i
\(320\) 0 0
\(321\) 1.07180i 0.0598219i
\(322\) −9.16020 + 18.8702i −0.510478 + 1.05160i
\(323\) 2.17209 + 2.17209i 0.120858 + 0.120858i
\(324\) 0.866025 0.500000i 0.0481125 0.0277778i
\(325\) 0 0
\(326\) −6.00000 + 10.3923i −0.332309 + 0.575577i
\(327\) 0.795040 2.96713i 0.0439658 0.164083i
\(328\) −4.05317 + 4.05317i −0.223799 + 0.223799i
\(329\) −4.59808 + 23.8923i −0.253500 + 1.31723i
\(330\) 0 0
\(331\) 7.89230 + 13.6699i 0.433800 + 0.751364i 0.997197 0.0748224i \(-0.0238390\pi\)
−0.563397 + 0.826187i \(0.690506\pi\)
\(332\) 10.0382 2.68973i 0.550918 0.147618i
\(333\) −9.58991 + 2.56961i −0.525524 + 0.140814i
\(334\) 8.59808 + 14.8923i 0.470466 + 0.814871i
\(335\) 0 0
\(336\) 1.73205 2.00000i 0.0944911 0.109109i
\(337\) −17.6269 + 17.6269i −0.960199 + 0.960199i −0.999238 0.0390392i \(-0.987570\pi\)
0.0390392 + 0.999238i \(0.487570\pi\)
\(338\) 2.03339 7.58871i 0.110602 0.412771i
\(339\) −0.464102 + 0.803848i −0.0252065 + 0.0436590i
\(340\) 0 0
\(341\) 0.464102 0.267949i 0.0251325 0.0145103i
\(342\) 4.05317 + 4.05317i 0.219170 + 0.219170i
\(343\) 18.0938 3.95164i 0.976972 0.213368i
\(344\) 4.92820i 0.265711i
\(345\) 0 0
\(346\) −20.4282 11.7942i −1.09823 0.634062i
\(347\) 2.82843 + 10.5558i 0.151838 + 0.566667i 0.999355 + 0.0358994i \(0.0114296\pi\)
−0.847517 + 0.530767i \(0.821904\pi\)
\(348\) 6.69213 + 1.79315i 0.358736 + 0.0961230i
\(349\) −25.8564 −1.38406 −0.692031 0.721868i \(-0.743284\pi\)
−0.692031 + 0.721868i \(0.743284\pi\)
\(350\) 0 0
\(351\) 2.26795 0.121054
\(352\) 0.965926 + 0.258819i 0.0514840 + 0.0137951i
\(353\) 1.79315 + 6.69213i 0.0954398 + 0.356186i 0.997086 0.0762887i \(-0.0243071\pi\)
−0.901646 + 0.432475i \(0.857640\pi\)
\(354\) 3.92820 + 2.26795i 0.208782 + 0.120540i
\(355\) 0 0
\(356\) 6.92820i 0.367194i
\(357\) −0.795040 1.17398i −0.0420780 0.0621334i
\(358\) 6.36396 + 6.36396i 0.336346 + 0.336346i
\(359\) 16.3923 9.46410i 0.865153 0.499496i −0.000581665 1.00000i \(-0.500185\pi\)
0.865734 + 0.500504i \(0.166852\pi\)
\(360\) 0 0
\(361\) −6.92820 + 12.0000i −0.364642 + 0.631579i
\(362\) 1.65445 6.17449i 0.0869560 0.324524i
\(363\) 7.07107 7.07107i 0.371135 0.371135i
\(364\) 5.66987 1.96410i 0.297182 0.102947i
\(365\) 0 0
\(366\) 2.26795 + 3.92820i 0.118548 + 0.205330i
\(367\) −14.0220 + 3.75719i −0.731943 + 0.196124i −0.605494 0.795849i \(-0.707025\pi\)
−0.126449 + 0.991973i \(0.540358\pi\)
\(368\) 7.65806 2.05197i 0.399204 0.106966i
\(369\) 2.86603 + 4.96410i 0.149199 + 0.258421i
\(370\) 0 0
\(371\) −2.50000 + 0.866025i −0.129794 + 0.0449618i
\(372\) −0.378937 + 0.378937i −0.0196470 + 0.0196470i
\(373\) 6.72930 25.1141i 0.348430 1.30036i −0.540124 0.841585i \(-0.681623\pi\)
0.888554 0.458772i \(-0.151711\pi\)
\(374\) 0.267949 0.464102i 0.0138553 0.0239981i
\(375\) 0 0
\(376\) 7.96410 4.59808i 0.410717 0.237128i
\(377\) 11.1106 + 11.1106i 0.572227 + 0.572227i
\(378\) −1.48356 2.19067i −0.0763063 0.112676i
\(379\) 9.92820i 0.509978i −0.966944 0.254989i \(-0.917928\pi\)
0.966944 0.254989i \(-0.0820718\pi\)
\(380\) 0 0
\(381\) −4.33013 2.50000i −0.221839 0.128079i
\(382\) −2.82843 10.5558i −0.144715 0.540083i
\(383\) 28.9592 + 7.75959i 1.47975 + 0.396497i 0.906261 0.422719i \(-0.138924\pi\)
0.573485 + 0.819216i \(0.305591\pi\)
\(384\) −1.00000 −0.0510310
\(385\) 0 0
\(386\) 18.7846 0.956111
\(387\) 4.76028 + 1.27551i 0.241979 + 0.0648380i
\(388\) −2.82843 10.5558i −0.143592 0.535891i
\(389\) −28.2679 16.3205i −1.43324 0.827483i −0.435875 0.900007i \(-0.643561\pi\)
−0.997367 + 0.0725245i \(0.976894\pi\)
\(390\) 0 0
\(391\) 4.24871i 0.214867i
\(392\) −5.60609 4.19187i −0.283150 0.211722i
\(393\) −14.2301 14.2301i −0.717812 0.717812i
\(394\) 9.40192 5.42820i 0.473662 0.273469i
\(395\) 0 0
\(396\) 0.500000 0.866025i 0.0251259 0.0435194i
\(397\) 3.30890 12.3490i 0.166069 0.619778i −0.831832 0.555027i \(-0.812708\pi\)
0.997901 0.0647510i \(-0.0206253\pi\)
\(398\) −13.7632 + 13.7632i −0.689887 + 0.689887i
\(399\) 9.92820 11.4641i 0.497032 0.573923i
\(400\) 0 0
\(401\) 5.96410 + 10.3301i 0.297833 + 0.515862i 0.975640 0.219378i \(-0.0704028\pi\)
−0.677807 + 0.735240i \(0.737069\pi\)
\(402\) 1.93185 0.517638i 0.0963520 0.0258174i
\(403\) −1.17398 + 0.314566i −0.0584800 + 0.0156697i
\(404\) −7.46410 12.9282i −0.371353 0.643202i
\(405\) 0 0
\(406\) 3.46410 18.0000i 0.171920 0.893325i
\(407\) −7.02030 + 7.02030i −0.347983 + 0.347983i
\(408\) −0.138701 + 0.517638i −0.00686671 + 0.0256269i
\(409\) −6.39230 + 11.0718i −0.316079 + 0.547465i −0.979666 0.200634i \(-0.935700\pi\)
0.663587 + 0.748099i \(0.269033\pi\)
\(410\) 0 0
\(411\) 4.39230 2.53590i 0.216656 0.125087i
\(412\) −1.69161 1.69161i −0.0833399 0.0833399i
\(413\) 5.24075 10.7961i 0.257881 0.531240i
\(414\) 7.92820i 0.389650i
\(415\) 0 0
\(416\) −1.96410 1.13397i −0.0962980 0.0555977i
\(417\) −2.68973 10.0382i −0.131716 0.491573i
\(418\) 5.53674 + 1.48356i 0.270811 + 0.0725635i
\(419\) 27.0526 1.32160 0.660802 0.750560i \(-0.270216\pi\)
0.660802 + 0.750560i \(0.270216\pi\)
\(420\) 0 0
\(421\) 13.8564 0.675320 0.337660 0.941268i \(-0.390365\pi\)
0.337660 + 0.941268i \(0.390365\pi\)
\(422\) −21.0423 5.63827i −1.02432 0.274467i
\(423\) −2.38014 8.88280i −0.115726 0.431897i
\(424\) 0.866025 + 0.500000i 0.0420579 + 0.0242821i
\(425\) 0 0
\(426\) 4.92820i 0.238772i
\(427\) 9.93666 6.72930i 0.480869 0.325653i
\(428\) −0.757875 0.757875i −0.0366333 0.0366333i
\(429\) 1.96410 1.13397i 0.0948277 0.0547488i
\(430\) 0 0
\(431\) −10.8564 + 18.8038i −0.522935 + 0.905749i 0.476709 + 0.879061i \(0.341830\pi\)
−0.999644 + 0.0266884i \(0.991504\pi\)
\(432\) −0.258819 + 0.965926i −0.0124524 + 0.0464731i
\(433\) 11.3137 11.3137i 0.543702 0.543702i −0.380910 0.924612i \(-0.624389\pi\)
0.924612 + 0.380910i \(0.124389\pi\)
\(434\) 1.07180 + 0.928203i 0.0514479 + 0.0445552i
\(435\) 0 0
\(436\) 1.53590 + 2.66025i 0.0735562 + 0.127403i
\(437\) 43.8964 11.7620i 2.09985 0.562653i
\(438\) 3.86370 1.03528i 0.184615 0.0494674i
\(439\) −10.0000 17.3205i −0.477274 0.826663i 0.522387 0.852709i \(-0.325042\pi\)
−0.999661 + 0.0260459i \(0.991708\pi\)
\(440\) 0 0
\(441\) −5.50000 + 4.33013i −0.261905 + 0.206197i
\(442\) −0.859411 + 0.859411i −0.0408780 + 0.0408780i
\(443\) −0.0371647 + 0.138701i −0.00176575 + 0.00658987i −0.966803 0.255523i \(-0.917752\pi\)
0.965037 + 0.262112i \(0.0844191\pi\)
\(444\) 4.96410 8.59808i 0.235586 0.408047i
\(445\) 0 0
\(446\) 21.9282 12.6603i 1.03833 0.599480i
\(447\) 9.14162 + 9.14162i 0.432384 + 0.432384i
\(448\) 0.189469 + 2.63896i 0.00895155 + 0.124679i
\(449\) 0.0717968i 0.00338830i 0.999999 + 0.00169415i \(0.000539265\pi\)
−0.999999 + 0.00169415i \(0.999461\pi\)
\(450\) 0 0
\(451\) 4.96410 + 2.86603i 0.233750 + 0.134956i
\(452\) −0.240237 0.896575i −0.0112998 0.0421714i
\(453\) 23.0435 + 6.17449i 1.08268 + 0.290103i
\(454\) −3.46410 −0.162578
\(455\) 0 0
\(456\) −5.73205 −0.268428
\(457\) 11.4524 + 3.06866i 0.535721 + 0.143546i 0.516529 0.856270i \(-0.327224\pi\)
0.0191922 + 0.999816i \(0.493891\pi\)
\(458\) −2.82843 10.5558i −0.132164 0.493242i
\(459\) 0.464102 + 0.267949i 0.0216624 + 0.0125068i
\(460\) 0 0
\(461\) 30.6410i 1.42709i 0.700607 + 0.713547i \(0.252913\pi\)
−0.700607 + 0.713547i \(0.747087\pi\)
\(462\) −2.38014 1.15539i −0.110734 0.0537538i
\(463\) −23.1315 23.1315i −1.07501 1.07501i −0.996949 0.0780612i \(-0.975127\pi\)
−0.0780612 0.996949i \(-0.524873\pi\)
\(464\) −6.00000 + 3.46410i −0.278543 + 0.160817i
\(465\) 0 0
\(466\) 12.9282 22.3923i 0.598887 1.03730i
\(467\) 3.72500 13.9019i 0.172373 0.643303i −0.824612 0.565699i \(-0.808606\pi\)
0.996984 0.0776040i \(-0.0247270\pi\)
\(468\) −1.60368 + 1.60368i −0.0741302 + 0.0741302i
\(469\) −1.73205 5.00000i −0.0799787 0.230879i
\(470\) 0 0
\(471\) 6.33013 + 10.9641i 0.291677 + 0.505199i
\(472\) −4.38134 + 1.17398i −0.201668 + 0.0540367i
\(473\) 4.76028 1.27551i 0.218878 0.0586481i
\(474\) 8.46410 + 14.6603i 0.388769 + 0.673368i
\(475\) 0 0
\(476\) 1.39230 + 0.267949i 0.0638162 + 0.0122814i
\(477\) 0.707107 0.707107i 0.0323762 0.0323762i
\(478\) 6.21166 23.1822i 0.284115 1.06033i
\(479\) 21.4641 37.1769i 0.980720 1.69866i 0.321122 0.947038i \(-0.395940\pi\)
0.659598 0.751619i \(-0.270727\pi\)
\(480\) 0 0
\(481\) 19.5000 11.2583i 0.889123 0.513336i
\(482\) 18.1953 + 18.1953i 0.828774 + 0.828774i
\(483\) −20.9222 + 1.50215i −0.951993 + 0.0683500i
\(484\) 10.0000i 0.454545i
\(485\) 0 0
\(486\) 0.866025 + 0.500000i 0.0392837 + 0.0226805i
\(487\) 5.65685 + 21.1117i 0.256337 + 0.956661i 0.967342 + 0.253475i \(0.0815734\pi\)
−0.711006 + 0.703186i \(0.751760\pi\)
\(488\) −4.38134 1.17398i −0.198334 0.0531434i
\(489\) −12.0000 −0.542659
\(490\) 0 0
\(491\) 43.7128 1.97273 0.986366 0.164568i \(-0.0526229\pi\)
0.986366 + 0.164568i \(0.0526229\pi\)
\(492\) −5.53674 1.48356i −0.249615 0.0668842i
\(493\) 0.960947 + 3.58630i 0.0432789 + 0.161519i
\(494\) −11.2583 6.50000i −0.506536 0.292449i
\(495\) 0 0
\(496\) 0.535898i 0.0240625i
\(497\) 13.0053 0.933740i 0.583368 0.0418840i
\(498\) 7.34847 + 7.34847i 0.329293 + 0.329293i
\(499\) −24.2487 + 14.0000i −1.08552 + 0.626726i −0.932381 0.361478i \(-0.882272\pi\)
−0.153141 + 0.988204i \(0.548939\pi\)
\(500\) 0 0
\(501\) −8.59808 + 14.8923i −0.384134 + 0.665339i
\(502\) 6.38254 23.8200i 0.284867 1.06314i
\(503\) 24.3190 24.3190i 1.08433 1.08433i 0.0882321 0.996100i \(-0.471878\pi\)
0.996100 0.0882321i \(-0.0281217\pi\)
\(504\) 2.59808 + 0.500000i 0.115728 + 0.0222718i
\(505\) 0 0
\(506\) −3.96410 6.86603i −0.176226 0.305232i
\(507\) 7.58871 2.03339i 0.337026 0.0903059i
\(508\) 4.82963 1.29410i 0.214280 0.0574162i
\(509\) 5.19615 + 9.00000i 0.230315 + 0.398918i 0.957901 0.287099i \(-0.0926909\pi\)
−0.727586 + 0.686017i \(0.759358\pi\)
\(510\) 0 0
\(511\) −3.46410 10.0000i −0.153243 0.442374i
\(512\) 0.707107 0.707107i 0.0312500 0.0312500i
\(513\) −1.48356 + 5.53674i −0.0655009 + 0.244453i
\(514\) 9.19615 15.9282i 0.405625 0.702563i
\(515\) 0 0
\(516\) −4.26795 + 2.46410i −0.187886 + 0.108476i
\(517\) −6.50266 6.50266i −0.285987 0.285987i
\(518\) −23.6305 11.4710i −1.03826 0.504006i
\(519\) 23.5885i 1.03542i
\(520\) 0 0
\(521\) −6.82051 3.93782i −0.298812 0.172519i 0.343097 0.939300i \(-0.388524\pi\)
−0.641909 + 0.766781i \(0.721857\pi\)
\(522\) 1.79315 + 6.69213i 0.0784841 + 0.292907i
\(523\) −32.7028 8.76268i −1.42999 0.383165i −0.540975 0.841039i \(-0.681945\pi\)
−0.889017 + 0.457873i \(0.848611\pi\)
\(524\) 20.1244 0.879137
\(525\) 0 0
\(526\) −2.14359 −0.0934651
\(527\) −0.277401 0.0743295i −0.0120838 0.00323784i
\(528\) 0.258819 + 0.965926i 0.0112637 + 0.0420365i
\(529\) −34.5167 19.9282i −1.50072 0.866444i
\(530\) 0 0
\(531\) 4.53590i 0.196841i
\(532\) 1.08604 + 15.1266i 0.0470860 + 0.655823i
\(533\) −9.19239 9.19239i −0.398167 0.398167i
\(534\) 6.00000 3.46410i 0.259645 0.149906i
\(535\) 0 0
\(536\) −1.00000 + 1.73205i −0.0431934 + 0.0748132i
\(537\) −2.32937 + 8.69333i −0.100520 + 0.375145i
\(538\) −6.59059 + 6.59059i −0.284141 + 0.284141i
\(539\) −2.59808 + 6.50000i −0.111907 + 0.279975i
\(540\) 0 0
\(541\) −8.53590 14.7846i −0.366987 0.635640i 0.622106 0.782933i \(-0.286277\pi\)
−0.989093 + 0.147293i \(0.952944\pi\)
\(542\) 7.72741 2.07055i 0.331921 0.0889378i
\(543\) 6.17449 1.65445i 0.264973 0.0709993i
\(544\) −0.267949 0.464102i −0.0114882 0.0198982i
\(545\) 0 0
\(546\) 4.53590 + 3.92820i 0.194119 + 0.168112i
\(547\) −21.0101 + 21.0101i −0.898328 + 0.898328i −0.995288 0.0969599i \(-0.969088\pi\)
0.0969599 + 0.995288i \(0.469088\pi\)
\(548\) −1.31268 + 4.89898i −0.0560748 + 0.209274i
\(549\) −2.26795 + 3.92820i −0.0967937 + 0.167652i
\(550\) 0 0
\(551\) −34.3923 + 19.8564i −1.46516 + 0.845911i
\(552\) 5.60609 + 5.60609i 0.238611 + 0.238611i
\(553\) 37.0841 25.1141i 1.57698 1.06796i
\(554\) 22.0000i 0.934690i
\(555\) 0 0
\(556\) 9.00000 + 5.19615i 0.381685 + 0.220366i
\(557\) 5.91567 + 22.0776i 0.250655 + 0.935458i 0.970456 + 0.241277i \(0.0775663\pi\)
−0.719801 + 0.694180i \(0.755767\pi\)
\(558\) −0.517638 0.138701i −0.0219134 0.00587167i
\(559\) −11.1769 −0.472733
\(560\) 0 0
\(561\) 0.535898 0.0226256
\(562\) 13.5923 + 3.64205i 0.573357 + 0.153631i
\(563\) −4.76028 17.7656i −0.200622 0.748731i −0.990740 0.135776i \(-0.956647\pi\)
0.790118 0.612955i \(-0.210019\pi\)
\(564\) 7.96410 + 4.59808i 0.335349 + 0.193614i
\(565\) 0 0
\(566\) 19.4641i 0.818137i
\(567\) 1.15539 2.38014i 0.0485220 0.0999565i
\(568\) −3.48477 3.48477i −0.146218 0.146218i
\(569\) −8.47372 + 4.89230i −0.355237 + 0.205096i −0.666989 0.745067i \(-0.732417\pi\)
0.311752 + 0.950163i \(0.399084\pi\)
\(570\) 0 0
\(571\) −6.92820 + 12.0000i −0.289936 + 0.502184i −0.973794 0.227431i \(-0.926967\pi\)
0.683858 + 0.729615i \(0.260301\pi\)
\(572\) −0.586988 + 2.19067i −0.0245432 + 0.0915965i
\(573\) 7.72741 7.72741i 0.322817 0.322817i
\(574\) −2.86603 + 14.8923i −0.119626 + 0.621593i
\(575\) 0 0
\(576\) −0.500000 0.866025i −0.0208333 0.0360844i
\(577\) 33.7381 9.04008i 1.40453 0.376344i 0.524563 0.851372i \(-0.324229\pi\)
0.879971 + 0.475028i \(0.157562\pi\)
\(578\) 16.1433 4.32559i 0.671474 0.179921i
\(579\) 9.39230 + 16.2679i 0.390331 + 0.676073i
\(580\) 0 0
\(581\) 18.0000 20.7846i 0.746766 0.862291i
\(582\) 7.72741 7.72741i 0.320311 0.320311i
\(583\) 0.258819 0.965926i 0.0107192 0.0400046i
\(584\) −2.00000 + 3.46410i −0.0827606 + 0.143346i
\(585\) 0 0
\(586\) −1.50000 + 0.866025i −0.0619644 + 0.0357752i
\(587\) −9.41902 9.41902i −0.388765 0.388765i 0.485482 0.874247i \(-0.338644\pi\)
−0.874247 + 0.485482i \(0.838644\pi\)
\(588\) 0.827225 6.95095i 0.0341142 0.286652i
\(589\) 3.07180i 0.126571i
\(590\) 0 0
\(591\) 9.40192 + 5.42820i 0.386743 + 0.223286i
\(592\) 2.56961 + 9.58991i 0.105610 + 0.394143i
\(593\) −20.8714 5.59248i −0.857087 0.229656i −0.196591 0.980486i \(-0.562987\pi\)
−0.660496 + 0.750830i \(0.729654\pi\)
\(594\) 1.00000 0.0410305
\(595\) 0 0
\(596\) −12.9282 −0.529560
\(597\) −18.8009 5.03768i −0.769469 0.206179i
\(598\) 4.65376 + 17.3681i 0.190307 + 0.710234i
\(599\) 12.2487 + 7.07180i 0.500469 + 0.288946i 0.728907 0.684613i \(-0.240029\pi\)
−0.228438 + 0.973558i \(0.573362\pi\)
\(600\) 0 0
\(601\) 12.7846i 0.521495i −0.965407 0.260748i \(-0.916031\pi\)
0.965407 0.260748i \(-0.0839690\pi\)
\(602\) 7.31130 + 10.7961i 0.297987 + 0.440015i
\(603\) 1.41421 + 1.41421i 0.0575912 + 0.0575912i
\(604\) −20.6603 + 11.9282i −0.840654 + 0.485352i
\(605\) 0 0
\(606\) 7.46410 12.9282i 0.303208 0.525172i
\(607\) 4.93117 18.4034i 0.200150 0.746969i −0.790724 0.612173i \(-0.790295\pi\)
0.990873 0.134796i \(-0.0430379\pi\)
\(608\) 4.05317 4.05317i 0.164378 0.164378i
\(609\) 17.3205 6.00000i 0.701862 0.243132i
\(610\) 0 0
\(611\) 10.4282 + 18.0622i 0.421880 + 0.730718i
\(612\) −0.517638 + 0.138701i −0.0209243 + 0.00560664i
\(613\) 3.93305 1.05386i 0.158855 0.0425649i −0.178515 0.983937i \(-0.557129\pi\)
0.337370 + 0.941372i \(0.390463\pi\)
\(614\) 0.803848 + 1.39230i 0.0324406 + 0.0561889i
\(615\) 0 0
\(616\) 2.50000 0.866025i 0.100728 0.0348932i
\(617\) −11.9700 + 11.9700i −0.481896 + 0.481896i −0.905737 0.423841i \(-0.860682\pi\)
0.423841 + 0.905737i \(0.360682\pi\)
\(618\) 0.619174 2.31079i 0.0249068 0.0929536i
\(619\) −9.79423 + 16.9641i −0.393663 + 0.681845i −0.992930 0.118705i \(-0.962126\pi\)
0.599266 + 0.800550i \(0.295459\pi\)
\(620\) 0 0
\(621\) 6.86603 3.96410i 0.275524 0.159074i
\(622\) 19.4201 + 19.4201i 0.778673 + 0.778673i
\(623\) −10.2784 15.1774i −0.411797 0.608070i
\(624\) 2.26795i 0.0907906i
\(625\) 0 0
\(626\) 27.0000 + 15.5885i 1.07914 + 0.623040i
\(627\) 1.48356 + 5.53674i 0.0592478 + 0.221116i
\(628\) −12.2289 3.27671i −0.487985 0.130755i
\(629\) 5.32051 0.212143
\(630\) 0 0
\(631\) 1.21539 0.0483839 0.0241920 0.999707i \(-0.492299\pi\)
0.0241920 + 0.999707i \(0.492299\pi\)
\(632\) −16.3514 4.38134i −0.650423 0.174280i
\(633\) −5.63827 21.0423i −0.224101 0.836357i
\(634\) −12.1244 7.00000i −0.481520 0.278006i
\(635\) 0 0
\(636\) 1.00000i 0.0396526i
\(637\) 9.50695 12.7143i 0.376679 0.503760i
\(638\) 4.89898 + 4.89898i 0.193952 + 0.193952i
\(639\) −4.26795 + 2.46410i −0.168837 + 0.0974784i
\(640\) 0 0
\(641\) −9.03590 + 15.6506i −0.356897 + 0.618163i −0.987441 0.157991i \(-0.949498\pi\)
0.630544 + 0.776153i \(0.282832\pi\)
\(642\) 0.277401 1.03528i 0.0109482 0.0408591i
\(643\) 4.72311 4.72311i 0.186261 0.186261i −0.607816 0.794078i \(-0.707954\pi\)
0.794078 + 0.607816i \(0.207954\pi\)
\(644\) 13.7321 15.8564i 0.541119 0.624830i
\(645\) 0 0
\(646\) −1.53590 2.66025i −0.0604291 0.104666i
\(647\) −34.3758 + 9.21097i −1.35145 + 0.362121i −0.860671 0.509162i \(-0.829955\pi\)
−0.490782 + 0.871283i \(0.663289\pi\)
\(648\) −0.965926 + 0.258819i −0.0379452 + 0.0101674i
\(649\) 2.26795 + 3.92820i 0.0890248 + 0.154195i
\(650\) 0 0
\(651\) −0.267949 + 1.39230i −0.0105018 + 0.0545687i
\(652\) 8.48528 8.48528i 0.332309 0.332309i
\(653\) −7.94906 + 29.6663i −0.311071 + 1.16093i 0.616522 + 0.787338i \(0.288541\pi\)
−0.927592 + 0.373594i \(0.878125\pi\)
\(654\) −1.53590 + 2.66025i −0.0600584 + 0.104024i
\(655\) 0 0
\(656\) 4.96410 2.86603i 0.193816 0.111899i
\(657\) 2.82843 + 2.82843i 0.110347 + 0.110347i
\(658\) 10.6252 21.8881i 0.414213 0.853288i
\(659\) 15.7128i 0.612084i 0.952018 + 0.306042i \(0.0990048\pi\)
−0.952018 + 0.306042i \(0.900995\pi\)
\(660\) 0 0
\(661\) −19.8564 11.4641i −0.772325 0.445902i 0.0613786 0.998115i \(-0.480450\pi\)
−0.833703 + 0.552213i \(0.813784\pi\)
\(662\) −4.08536 15.2468i −0.158782 0.592582i
\(663\) −1.17398 0.314566i −0.0455935 0.0122167i
\(664\) −10.3923 −0.403300
\(665\) 0 0
\(666\) 9.92820 0.384710
\(667\) 53.0566 + 14.2165i 2.05436 + 0.550464i
\(668\) −4.45069 16.6102i −0.172202 0.642668i
\(669\) 21.9282 + 12.6603i 0.847793 + 0.489474i
\(670\) 0 0
\(671\) 4.53590i 0.175106i
\(672\) −2.19067 + 1.48356i −0.0845070 + 0.0572297i
\(673\) 11.8685 + 11.8685i 0.457497 + 0.457497i 0.897833 0.440336i \(-0.145141\pi\)
−0.440336 + 0.897833i \(0.645141\pi\)
\(674\) 21.5885 12.4641i 0.831556 0.480099i
\(675\) 0 0
\(676\) −3.92820 + 6.80385i −0.151085 + 0.261686i
\(677\) −0.512659 + 1.91327i −0.0197031 + 0.0735329i −0.975077 0.221865i \(-0.928786\pi\)
0.955374 + 0.295398i \(0.0954522\pi\)
\(678\) 0.656339 0.656339i 0.0252065 0.0252065i
\(679\) −21.8564 18.9282i −0.838772 0.726398i
\(680\) 0 0
\(681\) −1.73205 3.00000i −0.0663723 0.114960i
\(682\) −0.517638 + 0.138701i −0.0198214 + 0.00531112i
\(683\) 40.4302 10.8332i 1.54702 0.414522i 0.618492 0.785791i \(-0.287744\pi\)
0.928526 + 0.371269i \(0.121077\pi\)
\(684\) −2.86603 4.96410i −0.109585 0.189807i
\(685\) 0 0
\(686\) −18.5000 0.866025i −0.706333 0.0330650i
\(687\) 7.72741 7.72741i 0.294819 0.294819i
\(688\) 1.27551 4.76028i 0.0486285 0.181484i
\(689\) −1.13397 + 1.96410i −0.0432010 + 0.0748263i
\(690\) 0 0
\(691\) −7.14359 + 4.12436i −0.271755 + 0.156898i −0.629685 0.776851i \(-0.716816\pi\)
0.357930 + 0.933748i \(0.383483\pi\)
\(692\) 16.6796 + 16.6796i 0.634062 + 0.634062i
\(693\) −0.189469 2.63896i −0.00719732 0.100246i
\(694\) 10.9282i 0.414829i
\(695\) 0 0
\(696\) −6.00000 3.46410i −0.227429 0.131306i
\(697\) −0.795040 2.96713i −0.0301143 0.112388i
\(698\) 24.9754 + 6.69213i 0.945332 + 0.253301i
\(699\) 25.8564 0.977979
\(700\) 0 0
\(701\) −31.8564 −1.20320 −0.601600 0.798798i \(-0.705470\pi\)
−0.601600 + 0.798798i \(0.705470\pi\)
\(702\) −2.19067 0.586988i −0.0826815 0.0221545i
\(703\) 14.7291 + 54.9698i 0.555519 + 2.07323i
\(704\) −0.866025 0.500000i −0.0326396 0.0188445i
\(705\) 0 0
\(706\) 6.92820i 0.260746i
\(707\) −35.5312 17.2480i −1.33629 0.648676i
\(708\) −3.20736 3.20736i −0.120540 0.120540i
\(709\) −11.3205 + 6.53590i −0.425151 + 0.245461i −0.697279 0.716800i \(-0.745606\pi\)
0.272128 + 0.962261i \(0.412273\pi\)
\(710\) 0 0
\(711\) −8.46410 + 14.6603i −0.317429 + 0.549802i
\(712\) −1.79315 + 6.69213i −0.0672012 + 0.250798i
\(713\) −3.00429 + 3.00429i −0.112512 + 0.112512i
\(714\) 0.464102 + 1.33975i 0.0173686 + 0.0501387i
\(715\) 0 0
\(716\) −4.50000 7.79423i −0.168173 0.291284i
\(717\) 23.1822 6.21166i 0.865756 0.231979i
\(718\) −18.2832 + 4.89898i −0.682324 + 0.182828i
\(719\) −7.19615 12.4641i −0.268371 0.464833i 0.700070 0.714074i \(-0.253152\pi\)
−0.968441 + 0.249242i \(0.919819\pi\)
\(720\) 0 0
\(721\) −6.21539 1.19615i −0.231473 0.0445470i
\(722\) 9.79796 9.79796i 0.364642 0.364642i
\(723\) −6.65994 + 24.8553i −0.247686 + 0.924377i
\(724\) −3.19615 + 5.53590i −0.118784 + 0.205740i
\(725\) 0 0
\(726\) −8.66025 + 5.00000i −0.321412 + 0.185567i
\(727\) −23.0943 23.0943i −0.856520 0.856520i 0.134407 0.990926i \(-0.457087\pi\)
−0.990926 + 0.134407i \(0.957087\pi\)
\(728\) −5.98502 + 0.429705i −0.221820 + 0.0159259i
\(729\) 1.00000i 0.0370370i
\(730\) 0 0
\(731\) −2.28719 1.32051i −0.0845947 0.0488408i
\(732\) −1.17398 4.38134i −0.0433914 0.161939i
\(733\) −22.2671 5.96644i −0.822453 0.220376i −0.177034 0.984205i \(-0.556650\pi\)
−0.645418 + 0.763829i \(0.723317\pi\)
\(734\) 14.5167 0.535820
\(735\) 0 0
\(736\) −7.92820 −0.292237
\(737\) 1.93185 + 0.517638i 0.0711607 + 0.0190674i
\(738\) −1.48356 5.53674i −0.0546107 0.203810i
\(739\) −5.25833 3.03590i −0.193431 0.111677i 0.400157 0.916447i \(-0.368956\pi\)
−0.593588 + 0.804769i \(0.702289\pi\)
\(740\) 0 0
\(741\) 13.0000i 0.477567i
\(742\) 2.63896 0.189469i 0.0968792 0.00695561i
\(743\) −23.8893 23.8893i −0.876414 0.876414i 0.116747 0.993162i \(-0.462753\pi\)
−0.993162 + 0.116747i \(0.962753\pi\)
\(744\) 0.464102 0.267949i 0.0170148 0.00982349i
\(745\) 0 0
\(746\) −13.0000 + 22.5167i −0.475964 + 0.824394i
\(747\) −2.68973 + 10.0382i −0.0984119 + 0.367278i
\(748\) −0.378937 + 0.378937i −0.0138553 + 0.0138553i
\(749\) −2.78461 0.535898i −0.101747 0.0195813i
\(750\) 0 0
\(751\) −6.92820 12.0000i −0.252814 0.437886i 0.711486 0.702701i \(-0.248023\pi\)
−0.964299 + 0.264814i \(0.914689\pi\)
\(752\) −8.88280 + 2.38014i −0.323922 + 0.0867948i
\(753\) 23.8200 6.38254i 0.868048 0.232593i
\(754\) −7.85641 13.6077i −0.286113 0.495563i
\(755\) 0 0
\(756\) 0.866025 + 2.50000i 0.0314970 + 0.0909241i
\(757\) −12.5249 + 12.5249i −0.455223 + 0.455223i −0.897084 0.441860i \(-0.854319\pi\)
0.441860 + 0.897084i \(0.354319\pi\)
\(758\) −2.56961 + 9.58991i −0.0933324 + 0.348321i
\(759\) 3.96410 6.86603i 0.143888 0.249221i
\(760\) 0 0
\(761\) 21.1077 12.1865i 0.765153 0.441761i −0.0659896 0.997820i \(-0.521020\pi\)
0.831143 + 0.556059i \(0.187687\pi\)
\(762\) 3.53553 + 3.53553i 0.128079 + 0.128079i
\(763\) 7.31130 + 3.54914i 0.264687 + 0.128487i
\(764\) 10.9282i 0.395369i
\(765\) 0 0
\(766\) −25.9641 14.9904i −0.938121 0.541624i
\(767\) −2.66252 9.93666i −0.0961380 0.358792i
\(768\) 0.965926 + 0.258819i 0.0348548 + 0.00933933i
\(769\) −21.1962 −0.764353 −0.382176 0.924089i \(-0.624825\pi\)
−0.382176 + 0.924089i \(0.624825\pi\)
\(770\) 0 0
\(771\) 18.3923 0.662383
\(772\) −18.1445 4.86181i −0.653036 0.174981i
\(773\) −9.41404 35.1337i −0.338600 1.26367i −0.899914 0.436068i \(-0.856371\pi\)
0.561314 0.827603i \(-0.310296\pi\)
\(774\) −4.26795 2.46410i −0.153408 0.0885703i
\(775\) 0 0
\(776\) 10.9282i 0.392300i
\(777\) −1.88108 26.2001i −0.0674835 0.939924i
\(778\) 23.0807 + 23.0807i 0.827483 + 0.827483i
\(779\) 28.4545 16.4282i 1.01949 0.588601i
\(780\) 0 0
\(781\) −2.46410 + 4.26795i −0.0881725 + 0.152719i
\(782\) −1.09965 + 4.10394i −0.0393233 + 0.146757i
\(783\) −4.89898 + 4.89898i −0.175075 + 0.175075i
\(784\) 4.33013 + 5.50000i 0.154647 + 0.196429i
\(785\) 0 0
\(786\) 10.0622 + 17.4282i 0.358906 + 0.621643i
\(787\) −17.7656 + 4.76028i −0.633275 + 0.169686i −0.561156 0.827710i \(-0.689643\pi\)
−0.0721198 + 0.997396i \(0.522976\pi\)
\(788\) −10.4865 + 2.80984i −0.373566 + 0.100097i
\(789\) −1.07180 1.85641i −0.0381570 0.0660898i
\(790\) 0 0
\(791\) −1.85641 1.60770i −0.0660062 0.0571631i
\(792\) −0.707107 + 0.707107i −0.0251259 + 0.0251259i
\(793\) 2.66252 9.93666i 0.0945489 0.352861i
\(794\) −6.39230 + 11.0718i −0.226854 + 0.392923i
\(795\) 0 0
\(796\) 16.8564 9.73205i 0.597459 0.344943i
\(797\) −1.51575 1.51575i −0.0536906 0.0536906i 0.679752 0.733442i \(-0.262088\pi\)
−0.733442 + 0.679752i \(0.762088\pi\)
\(798\) −12.5570 + 8.50386i −0.444514 + 0.301034i
\(799\) 4.92820i 0.174347i
\(800\) 0 0
\(801\) 6.00000 + 3.46410i 0.212000 + 0.122398i
\(802\) −3.08725 11.5218i −0.109014 0.406847i
\(803\) 3.86370 + 1.03528i 0.136347 + 0.0365341i
\(804\) −2.00000 −0.0705346
\(805\) 0 0
\(806\) 1.21539 0.0428103
\(807\) −9.00292 2.41233i −0.316918 0.0849179i
\(808\) 3.86370 + 14.4195i 0.135925 + 0.507278i
\(809\) 37.7942 + 21.8205i 1.32877 + 0.767168i 0.985110 0.171924i \(-0.0549985\pi\)
0.343664 + 0.939093i \(0.388332\pi\)
\(810\) 0 0
\(811\) 42.5167i 1.49296i −0.665407 0.746481i \(-0.731742\pi\)
0.665407 0.746481i \(-0.268258\pi\)
\(812\) −8.00481 + 16.4901i −0.280914 + 0.578689i
\(813\) 5.65685 + 5.65685i 0.198395 + 0.198395i
\(814\) 8.59808 4.96410i 0.301362 0.173992i
\(815\) 0 0
\(816\) 0.267949 0.464102i 0.00938010 0.0162468i
\(817\) 7.31130 27.2862i 0.255790 0.954622i
\(818\) 9.04008 9.04008i 0.316079 0.316079i
\(819\) −1.13397 + 5.89230i −0.0396243 + 0.205894i
\(820\) 0 0
\(821\) −1.92820 3.33975i −0.0672948 0.116558i 0.830415 0.557146i \(-0.188103\pi\)
−0.897710 + 0.440588i \(0.854770\pi\)
\(822\) −4.89898 + 1.31268i −0.170872 + 0.0457849i
\(823\) 19.0411 5.10205i 0.663732 0.177846i 0.0888021 0.996049i \(-0.471696\pi\)
0.574929 + 0.818203i \(0.305029\pi\)
\(824\) 1.19615 + 2.07180i 0.0416699 + 0.0721745i
\(825\) 0 0
\(826\) −7.85641 + 9.07180i −0.273359 + 0.315648i
\(827\) −11.4152 + 11.4152i −0.396947 + 0.396947i −0.877155 0.480208i \(-0.840561\pi\)
0.480208 + 0.877155i \(0.340561\pi\)
\(828\) −2.05197 + 7.65806i −0.0713109 + 0.266136i
\(829\) −11.7321 + 20.3205i −0.407471 + 0.705760i −0.994606 0.103729i \(-0.966923\pi\)
0.587135 + 0.809489i \(0.300256\pi\)
\(830\) 0 0
\(831\) −19.0526 + 11.0000i −0.660926 + 0.381586i
\(832\) 1.60368 + 1.60368i 0.0555977 + 0.0555977i
\(833\) 3.44760 1.47858i 0.119452 0.0512299i
\(834\) 10.3923i 0.359856i
\(835\) 0 0
\(836\) −4.96410 2.86603i −0.171687 0.0991236i
\(837\) −0.138701 0.517638i −0.00479420 0.0178922i
\(838\) −26.1308 7.00172i −0.902672 0.241870i
\(839\) −15.4641 −0.533880 −0.266940 0.963713i \(-0.586013\pi\)
−0.266940 + 0.963713i \(0.586013\pi\)
\(840\) 0 0
\(841\) −19.0000 −0.655172
\(842\) −13.3843 3.58630i −0.461252 0.123592i
\(843\) 3.64205 + 13.5923i 0.125439 + 0.468144i
\(844\) 18.8660 + 10.8923i 0.649395 + 0.374929i
\(845\) 0 0
\(846\) 9.19615i 0.316170i
\(847\) 14.8356 + 21.9067i 0.509759 + 0.752723i
\(848\) −0.707107 0.707107i −0.0242821 0.0242821i
\(849\) 16.8564 9.73205i 0.578510 0.334003i
\(850\) 0 0
\(851\) 39.3564 68.1673i 1.34912 2.33674i
\(852\) 1.27551 4.76028i 0.0436984 0.163084i
\(853\) −22.7153 + 22.7153i −0.777759 + 0.777759i −0.979449 0.201691i \(-0.935356\pi\)
0.201691 + 0.979449i \(0.435356\pi\)
\(854\) −11.3397 + 3.92820i −0.388038 + 0.134420i
\(855\) 0 0
\(856\) 0.535898 + 0.928203i 0.0183166 + 0.0317253i
\(857\) −15.4548 + 4.14110i −0.527926 + 0.141457i −0.512931 0.858430i \(-0.671440\pi\)
−0.0149958 + 0.999888i \(0.504773\pi\)
\(858\) −2.19067 + 0.586988i −0.0747883 + 0.0200395i
\(859\) 17.1962 + 29.7846i 0.586725 + 1.01624i 0.994658 + 0.103226i \(0.0329164\pi\)
−0.407933 + 0.913012i \(0.633750\pi\)
\(860\) 0 0
\(861\) −14.3301 + 4.96410i −0.488369 + 0.169176i
\(862\) 15.3533 15.3533i 0.522935 0.522935i
\(863\) −7.67166 + 28.6310i −0.261146 + 0.974611i 0.703421 + 0.710774i \(0.251655\pi\)
−0.964567 + 0.263838i \(0.915012\pi\)
\(864\) 0.500000 0.866025i 0.0170103 0.0294628i
\(865\) 0 0
\(866\) −13.8564 + 8.00000i −0.470860 + 0.271851i
\(867\) 11.8177 + 11.8177i 0.401352 + 0.401352i
\(868\) −0.795040 1.17398i −0.0269854 0.0398474i
\(869\) 16.9282i 0.574250i
\(870\) 0 0
\(871\) −3.92820 2.26795i −0.133102 0.0768465i
\(872\) −0.795040 2.96713i −0.0269234 0.100480i
\(873\) 10.5558 + 2.82843i 0.357261 + 0.0957278i
\(874\) −45.4449 −1.53720
\(875\) 0 0
\(876\) −4.00000 −0.135147
\(877\) −9.58991 2.56961i −0.323828 0.0867695i 0.0932428 0.995643i \(-0.470277\pi\)
−0.417071 + 0.908874i \(0.636943\pi\)
\(878\) 5.17638 + 19.3185i 0.174694 + 0.651968i
\(879\) −1.50000 0.866025i −0.0505937 0.0292103i
\(880\) 0 0
\(881\) 28.9090i 0.973968i 0.873411 + 0.486984i \(0.161903\pi\)
−0.873411 + 0.486984i \(0.838097\pi\)
\(882\) 6.43331 2.75908i 0.216621 0.0929029i
\(883\) 14.9000 + 14.9000i 0.501425 + 0.501425i 0.911881 0.410455i \(-0.134630\pi\)
−0.410455 + 0.911881i \(0.634630\pi\)
\(884\) 1.05256 0.607695i 0.0354014 0.0204390i
\(885\) 0 0
\(886\) 0.0717968 0.124356i 0.00241206 0.00417781i
\(887\) 0.896575 3.34607i 0.0301041 0.112350i −0.949239 0.314556i \(-0.898144\pi\)
0.979343 + 0.202206i \(0.0648111\pi\)
\(888\) −7.02030 + 7.02030i −0.235586 + 0.235586i
\(889\) 8.66025 10.0000i 0.290456 0.335389i
\(890\) 0 0
\(891\) 0.500000 + 0.866025i 0.0167506 + 0.0290129i
\(892\) −24.4577 + 6.55343i −0.818905 + 0.219425i
\(893\) −50.9167 + 13.6431i −1.70386 + 0.456548i
\(894\) −6.46410 11.1962i −0.216192 0.374455i
\(895\) 0 0
\(896\) 0.500000 2.59808i 0.0167038 0.0867956i
\(897\) −12.7143 + 12.7143i −0.424519 + 0.424519i
\(898\) 0.0185824 0.0693504i 0.000620102 0.00231425i
\(899\) 1.85641 3.21539i 0.0619146 0.107239i
\(900\) 0 0
\(901\) −0.464102 + 0.267949i −0.0154615 + 0.00892668i
\(902\) −4.05317 4.05317i −0.134956 0.134956i
\(903\) −5.69402 + 11.7298i −0.189485 + 0.390344i
\(904\) 0.928203i 0.0308716i
\(905\) 0 0
\(906\) −20.6603 11.9282i −0.686391 0.396288i
\(907\) 7.72741 + 28.8391i 0.256584 + 0.957586i 0.967202 + 0.254008i \(0.0817488\pi\)
−0.710618 + 0.703578i \(0.751585\pi\)
\(908\) 3.34607 + 0.896575i 0.111043 + 0.0297539i
\(909\) 14.9282 0.495137
\(910\) 0 0
\(911\) −57.7128 −1.91211 −0.956055 0.293186i \(-0.905284\pi\)
−0.956055 + 0.293186i \(0.905284\pi\)
\(912\) 5.53674 + 1.48356i 0.183340 + 0.0491257i
\(913\) 2.68973 + 10.0382i 0.0890170 + 0.332216i
\(914\) −10.2679 5.92820i −0.339634 0.196088i
\(915\) 0 0
\(916\) 10.9282i 0.361078i
\(917\) 44.0858 29.8558i 1.45584 0.985924i
\(918\) −0.378937 0.378937i −0.0125068 0.0125068i
\(919\) −2.78461 + 1.60770i −0.0918558 + 0.0530330i −0.545224 0.838290i \(-0.683556\pi\)
0.453368 + 0.891323i \(0.350222\pi\)
\(920\) 0 0
\(921\) −0.803848 + 1.39230i −0.0264877 + 0.0458780i
\(922\) 7.93048 29.5969i 0.261176 0.974724i
\(923\) 7.90327 7.90327i 0.260139 0.260139i
\(924\) 2.00000 + 1.73205i 0.0657952 + 0.0569803i
\(925\) 0 0
\(926\) 16.3564 + 28.3301i 0.537505 + 0.930986i
\(927\) 2.31079 0.619174i 0.0758963 0.0203363i
\(928\) 6.69213 1.79315i 0.219680 0.0588631i
\(929\) −4.06218 7.03590i −0.133276 0.230840i 0.791662 0.610960i \(-0.209216\pi\)
−0.924937 + 0.380119i \(0.875883\pi\)
\(930\) 0 0
\(931\) 24.8205 + 31.5263i 0.813459 + 1.03323i
\(932\) −18.2832 + 18.2832i −0.598887 + 0.598887i
\(933\) −7.10823 + 26.5283i −0.232713 + 0.868497i
\(934\) −7.19615 + 12.4641i −0.235465 + 0.407838i
\(935\) 0 0
\(936\) 1.96410 1.13397i 0.0641987 0.0370651i
\(937\) −21.4906 21.4906i −0.702067 0.702067i 0.262787 0.964854i \(-0.415359\pi\)
−0.964854 + 0.262787i \(0.915359\pi\)
\(938\) 0.378937 + 5.27792i 0.0123727 + 0.172330i
\(939\) 31.1769i 1.01742i
\(940\) 0 0
\(941\) 41.3205 + 23.8564i 1.34701 + 0.777697i 0.987825 0.155570i \(-0.0497213\pi\)
0.359185 + 0.933266i \(0.383055\pi\)
\(942\) −3.27671 12.2289i −0.106761 0.398438i
\(943\) −43.8964 11.7620i −1.42946 0.383023i
\(944\) 4.53590 0.147631
\(945\) 0 0
\(946\) −4.92820 −0.160230
\(947\) −44.2939 11.8685i −1.43936 0.385675i −0.547049 0.837100i \(-0.684249\pi\)
−0.892309 + 0.451426i \(0.850916\pi\)
\(948\) −4.38134 16.3514i −0.142299 0.531068i
\(949\) −7.85641 4.53590i −0.255030 0.147241i
\(950\) 0 0
\(951\) 14.0000i 0.453981i
\(952\) −1.27551 0.619174i −0.0413396 0.0200675i
\(953\) 26.5654 + 26.5654i 0.860539 + 0.860539i 0.991401 0.130861i \(-0.0417743\pi\)
−0.130861 + 0.991401i \(0.541774\pi\)
\(954\) −0.866025 + 0.500000i −0.0280386 + 0.0161881i
\(955\) 0 0
\(956\) −12.0000 + 20.7846i −0.388108 + 0.672222i
\(957\) −1.79315 + 6.69213i −0.0579643 + 0.216326i
\(958\) −30.3548 + 30.3548i −0.980720 + 0.980720i
\(959\) 4.39230 + 12.6795i 0.141835 + 0.409442i
\(960\) 0 0
\(961\) −15.3564 26.5981i −0.495368 0.858002i
\(962\) −21.7494 + 5.82774i −0.701230 + 0.187894i
\(963\) 1.03528 0.277401i 0.0333613 0.00893914i
\(964\) −12.8660 22.2846i −0.414387 0.717739i
\(965\) 0 0
\(966\) 20.5981 + 3.96410i 0.662732 + 0.127543i
\(967\) −1.51575 + 1.51575i −0.0487432 + 0.0487432i −0.731058 0.682315i \(-0.760973\pi\)
0.682315 + 0.731058i \(0.260973\pi\)
\(968\) 2.58819 9.65926i 0.0831876 0.310460i
\(969\) 1.53590 2.66025i 0.0493402 0.0854597i
\(970\) 0 0
\(971\) 17.2128 9.93782i 0.552385 0.318920i −0.197698 0.980263i \(-0.563347\pi\)
0.750084 + 0.661343i \(0.230013\pi\)
\(972\) −0.707107 0.707107i −0.0226805 0.0226805i
\(973\) 27.4249 1.96902i 0.879201 0.0631238i
\(974\) 21.8564i 0.700324i
\(975\) 0 0
\(976\) 3.92820 + 2.26795i 0.125739 + 0.0725953i
\(977\) 7.76457 + 28.9778i 0.248411 + 0.927081i 0.971638 + 0.236472i \(0.0759910\pi\)
−0.723228 + 0.690610i \(0.757342\pi\)
\(978\) 11.5911 + 3.10583i 0.370643 + 0.0993134i
\(979\) 6.92820 0.221426
\(980\) 0 0
\(981\) −3.07180 −0.0980749
\(982\) −42.2233 11.3137i −1.34740 0.361035i
\(983\) 8.25002 + 30.7895i 0.263135 + 0.982033i 0.963382 + 0.268132i \(0.0864064\pi\)
−0.700247 + 0.713900i \(0.746927\pi\)
\(984\) 4.96410 + 2.86603i 0.158250 + 0.0913656i
\(985\) 0 0
\(986\) 3.71281i 0.118240i
\(987\) 24.2683 1.74238i 0.772467 0.0554607i
\(988\) 9.19239 + 9.19239i 0.292449 + 0.292449i
\(989\) −33.8372 + 19.5359i −1.07596 + 0.621205i
\(990\) 0 0
\(991\) 8.39230 14.5359i 0.266590 0.461748i −0.701389 0.712779i \(-0.747436\pi\)
0.967979 + 0.251031i \(0.0807696\pi\)
\(992\) −0.138701 + 0.517638i −0.00440375 + 0.0164350i
\(993\) 11.1614 11.1614i 0.354196 0.354196i
\(994\) −12.8038 2.46410i −0.406113 0.0781566i
\(995\) 0 0
\(996\) −5.19615 9.00000i −0.164646 0.285176i
\(997\) −49.9507 + 13.3843i −1.58196 + 0.423884i −0.939531 0.342465i \(-0.888738\pi\)
−0.642425 + 0.766348i \(0.722072\pi\)
\(998\) 27.0459 7.24693i 0.856124 0.229398i
\(999\) 4.96410 + 8.59808i 0.157057 + 0.272031i
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 1050.2.bc.d.493.1 yes 8
5.2 odd 4 1050.2.bc.a.157.2 yes 8
5.3 odd 4 1050.2.bc.a.157.1 8
5.4 even 2 inner 1050.2.bc.d.493.2 yes 8
7.5 odd 6 1050.2.bc.a.943.2 yes 8
35.12 even 12 inner 1050.2.bc.d.607.1 yes 8
35.19 odd 6 1050.2.bc.a.943.1 yes 8
35.33 even 12 inner 1050.2.bc.d.607.2 yes 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1050.2.bc.a.157.1 8 5.3 odd 4
1050.2.bc.a.157.2 yes 8 5.2 odd 4
1050.2.bc.a.943.1 yes 8 35.19 odd 6
1050.2.bc.a.943.2 yes 8 7.5 odd 6
1050.2.bc.d.493.1 yes 8 1.1 even 1 trivial
1050.2.bc.d.493.2 yes 8 5.4 even 2 inner
1050.2.bc.d.607.1 yes 8 35.12 even 12 inner
1050.2.bc.d.607.2 yes 8 35.33 even 12 inner