Properties

Label 1950.2.z.m.1849.4
Level $1950$
Weight $2$
Character 1950.1849
Analytic conductor $15.571$
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] = [1950,2,Mod(1699,1950)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1950, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 3, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1950.1699");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1950.z (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: \(15.5708283941\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: 8.0.1731891456.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 9x^{6} + 65x^{4} - 144x^{2} + 256 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 1849.4
Root \(2.21837 + 1.28078i\) of defining polynomial
Character \(\chi\) \(=\) 1950.1849
Dual form 1950.2.z.m.1699.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.866025 - 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{6} +(3.08440 + 1.78078i) q^{7} -1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(0.866025 - 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{6} +(3.08440 + 1.78078i) q^{7} -1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(0.280776 + 0.486319i) q^{11} +1.00000i q^{12} +(-2.21837 - 2.84233i) q^{13} +3.56155 q^{14} +(-0.500000 - 0.866025i) q^{16} +(2.70469 + 1.56155i) q^{17} -1.00000i q^{18} +(-1.21922 + 2.11176i) q^{19} -3.56155 q^{21} +(0.486319 + 0.280776i) q^{22} +(6.65511 - 3.84233i) q^{23} +(0.500000 + 0.866025i) q^{24} +(-3.34233 - 1.35234i) q^{26} +1.00000i q^{27} +(3.08440 - 1.78078i) q^{28} +(0.561553 + 0.972638i) q^{29} +4.00000 q^{31} +(-0.866025 - 0.500000i) q^{32} +(-0.486319 - 0.280776i) q^{33} +3.12311 q^{34} +(-0.500000 - 0.866025i) q^{36} +(0.486319 - 0.280776i) q^{37} +2.43845i q^{38} +(3.34233 + 1.35234i) q^{39} +(1.56155 + 2.70469i) q^{41} +(-3.08440 + 1.78078i) q^{42} +(0.379706 + 0.219224i) q^{43} +0.561553 q^{44} +(3.84233 - 6.65511i) q^{46} +4.00000i q^{47} +(0.866025 + 0.500000i) q^{48} +(2.84233 + 4.92306i) q^{49} -3.12311 q^{51} +(-3.57071 + 0.500000i) q^{52} -4.24621i q^{53} +(0.500000 + 0.866025i) q^{54} +(1.78078 - 3.08440i) q^{56} -2.43845i q^{57} +(0.972638 + 0.561553i) q^{58} +(-5.12311 + 8.87348i) q^{59} +(0.842329 - 1.45896i) q^{61} +(3.46410 - 2.00000i) q^{62} +(3.08440 - 1.78078i) q^{63} -1.00000 q^{64} -0.561553 q^{66} +(10.2258 - 5.90388i) q^{67} +(2.70469 - 1.56155i) q^{68} +(-3.84233 + 6.65511i) q^{69} +(-6.28078 + 10.8786i) q^{71} +(-0.866025 - 0.500000i) q^{72} -9.00000i q^{73} +(0.280776 - 0.486319i) q^{74} +(1.21922 + 2.11176i) q^{76} +2.00000i q^{77} +(3.57071 - 0.500000i) q^{78} +15.8078 q^{79} +(-0.500000 - 0.866025i) q^{81} +(2.70469 + 1.56155i) q^{82} -6.56155i q^{83} +(-1.78078 + 3.08440i) q^{84} +0.438447 q^{86} +(-0.972638 - 0.561553i) q^{87} +(0.486319 - 0.280776i) q^{88} +(5.12311 + 8.87348i) q^{89} +(-1.78078 - 12.7173i) q^{91} -7.68466i q^{92} +(-3.46410 + 2.00000i) q^{93} +(2.00000 + 3.46410i) q^{94} +1.00000 q^{96} +(2.43160 + 1.40388i) q^{97} +(4.92306 + 2.84233i) q^{98} +0.561553 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 4 q^{4} - 4 q^{6} + 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 4 q^{4} - 4 q^{6} + 4 q^{9} - 6 q^{11} + 12 q^{14} - 4 q^{16} - 18 q^{19} - 12 q^{21} + 4 q^{24} - 2 q^{26} - 12 q^{29} + 32 q^{31} - 8 q^{34} - 4 q^{36} + 2 q^{39} - 4 q^{41} - 12 q^{44} + 6 q^{46} - 2 q^{49} + 8 q^{51} + 4 q^{54} + 6 q^{56} - 8 q^{59} - 18 q^{61} - 8 q^{64} + 12 q^{66} - 6 q^{69} - 42 q^{71} - 6 q^{74} + 18 q^{76} + 44 q^{79} - 4 q^{81} - 6 q^{84} + 20 q^{86} + 8 q^{89} - 6 q^{91} + 16 q^{94} + 8 q^{96} - 12 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times\).

\(n\) \(301\) \(1301\) \(1327\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.866025 0.500000i 0.612372 0.353553i
\(3\) −0.866025 + 0.500000i −0.500000 + 0.288675i
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) 0 0
\(6\) −0.500000 + 0.866025i −0.204124 + 0.353553i
\(7\) 3.08440 + 1.78078i 1.16579 + 0.673070i 0.952685 0.303959i \(-0.0983085\pi\)
0.213107 + 0.977029i \(0.431642\pi\)
\(8\) 1.00000i 0.353553i
\(9\) 0.500000 0.866025i 0.166667 0.288675i
\(10\) 0 0
\(11\) 0.280776 + 0.486319i 0.0846573 + 0.146631i 0.905245 0.424890i \(-0.139687\pi\)
−0.820588 + 0.571520i \(0.806354\pi\)
\(12\) 1.00000i 0.288675i
\(13\) −2.21837 2.84233i −0.615265 0.788320i
\(14\) 3.56155 0.951865
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 2.70469 + 1.56155i 0.655983 + 0.378732i 0.790745 0.612146i \(-0.209693\pi\)
−0.134761 + 0.990878i \(0.543027\pi\)
\(18\) 1.00000i 0.235702i
\(19\) −1.21922 + 2.11176i −0.279709 + 0.484470i −0.971312 0.237807i \(-0.923571\pi\)
0.691603 + 0.722278i \(0.256905\pi\)
\(20\) 0 0
\(21\) −3.56155 −0.777195
\(22\) 0.486319 + 0.280776i 0.103684 + 0.0598617i
\(23\) 6.65511 3.84233i 1.38769 0.801181i 0.394632 0.918839i \(-0.370872\pi\)
0.993054 + 0.117658i \(0.0375387\pi\)
\(24\) 0.500000 + 0.866025i 0.102062 + 0.176777i
\(25\) 0 0
\(26\) −3.34233 1.35234i −0.655485 0.265217i
\(27\) 1.00000i 0.192450i
\(28\) 3.08440 1.78078i 0.582896 0.336535i
\(29\) 0.561553 + 0.972638i 0.104278 + 0.180614i 0.913443 0.406967i \(-0.133414\pi\)
−0.809165 + 0.587581i \(0.800080\pi\)
\(30\) 0 0
\(31\) 4.00000 0.718421 0.359211 0.933257i \(-0.383046\pi\)
0.359211 + 0.933257i \(0.383046\pi\)
\(32\) −0.866025 0.500000i −0.153093 0.0883883i
\(33\) −0.486319 0.280776i −0.0846573 0.0488769i
\(34\) 3.12311 0.535608
\(35\) 0 0
\(36\) −0.500000 0.866025i −0.0833333 0.144338i
\(37\) 0.486319 0.280776i 0.0799504 0.0461594i −0.459492 0.888182i \(-0.651968\pi\)
0.539442 + 0.842023i \(0.318635\pi\)
\(38\) 2.43845i 0.395568i
\(39\) 3.34233 + 1.35234i 0.535201 + 0.216548i
\(40\) 0 0
\(41\) 1.56155 + 2.70469i 0.243874 + 0.422401i 0.961814 0.273703i \(-0.0882485\pi\)
−0.717941 + 0.696104i \(0.754915\pi\)
\(42\) −3.08440 + 1.78078i −0.475933 + 0.274780i
\(43\) 0.379706 + 0.219224i 0.0579047 + 0.0334313i 0.528673 0.848826i \(-0.322690\pi\)
−0.470768 + 0.882257i \(0.656023\pi\)
\(44\) 0.561553 0.0846573
\(45\) 0 0
\(46\) 3.84233 6.65511i 0.566521 0.981242i
\(47\) 4.00000i 0.583460i 0.956501 + 0.291730i \(0.0942309\pi\)
−0.956501 + 0.291730i \(0.905769\pi\)
\(48\) 0.866025 + 0.500000i 0.125000 + 0.0721688i
\(49\) 2.84233 + 4.92306i 0.406047 + 0.703294i
\(50\) 0 0
\(51\) −3.12311 −0.437322
\(52\) −3.57071 + 0.500000i −0.495169 + 0.0693375i
\(53\) 4.24621i 0.583262i −0.956531 0.291631i \(-0.905802\pi\)
0.956531 0.291631i \(-0.0941979\pi\)
\(54\) 0.500000 + 0.866025i 0.0680414 + 0.117851i
\(55\) 0 0
\(56\) 1.78078 3.08440i 0.237966 0.412170i
\(57\) 2.43845i 0.322980i
\(58\) 0.972638 + 0.561553i 0.127714 + 0.0737355i
\(59\) −5.12311 + 8.87348i −0.666972 + 1.15523i 0.311775 + 0.950156i \(0.399076\pi\)
−0.978747 + 0.205073i \(0.934257\pi\)
\(60\) 0 0
\(61\) 0.842329 1.45896i 0.107849 0.186800i −0.807050 0.590484i \(-0.798937\pi\)
0.914899 + 0.403683i \(0.132270\pi\)
\(62\) 3.46410 2.00000i 0.439941 0.254000i
\(63\) 3.08440 1.78078i 0.388597 0.224357i
\(64\) −1.00000 −0.125000
\(65\) 0 0
\(66\) −0.561553 −0.0691224
\(67\) 10.2258 5.90388i 1.24928 0.721274i 0.278317 0.960489i \(-0.410224\pi\)
0.970967 + 0.239215i \(0.0768902\pi\)
\(68\) 2.70469 1.56155i 0.327992 0.189366i
\(69\) −3.84233 + 6.65511i −0.462562 + 0.801181i
\(70\) 0 0
\(71\) −6.28078 + 10.8786i −0.745391 + 1.29106i 0.204621 + 0.978841i \(0.434404\pi\)
−0.950012 + 0.312214i \(0.898929\pi\)
\(72\) −0.866025 0.500000i −0.102062 0.0589256i
\(73\) 9.00000i 1.05337i −0.850060 0.526685i \(-0.823435\pi\)
0.850060 0.526685i \(-0.176565\pi\)
\(74\) 0.280776 0.486319i 0.0326396 0.0565334i
\(75\) 0 0
\(76\) 1.21922 + 2.11176i 0.139855 + 0.242235i
\(77\) 2.00000i 0.227921i
\(78\) 3.57071 0.500000i 0.404304 0.0566139i
\(79\) 15.8078 1.77851 0.889256 0.457409i \(-0.151223\pi\)
0.889256 + 0.457409i \(0.151223\pi\)
\(80\) 0 0
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 2.70469 + 1.56155i 0.298683 + 0.172445i
\(83\) 6.56155i 0.720224i −0.932909 0.360112i \(-0.882738\pi\)
0.932909 0.360112i \(-0.117262\pi\)
\(84\) −1.78078 + 3.08440i −0.194299 + 0.336535i
\(85\) 0 0
\(86\) 0.438447 0.0472790
\(87\) −0.972638 0.561553i −0.104278 0.0602048i
\(88\) 0.486319 0.280776i 0.0518418 0.0299309i
\(89\) 5.12311 + 8.87348i 0.543048 + 0.940587i 0.998727 + 0.0504427i \(0.0160632\pi\)
−0.455679 + 0.890144i \(0.650603\pi\)
\(90\) 0 0
\(91\) −1.78078 12.7173i −0.186676 1.33313i
\(92\) 7.68466i 0.801181i
\(93\) −3.46410 + 2.00000i −0.359211 + 0.207390i
\(94\) 2.00000 + 3.46410i 0.206284 + 0.357295i
\(95\) 0 0
\(96\) 1.00000 0.102062
\(97\) 2.43160 + 1.40388i 0.246891 + 0.142543i 0.618340 0.785911i \(-0.287806\pi\)
−0.371449 + 0.928453i \(0.621139\pi\)
\(98\) 4.92306 + 2.84233i 0.497304 + 0.287119i
\(99\) 0.561553 0.0564382
\(100\) 0 0
\(101\) 3.12311 + 5.40938i 0.310761 + 0.538253i 0.978527 0.206118i \(-0.0660829\pi\)
−0.667767 + 0.744371i \(0.732750\pi\)
\(102\) −2.70469 + 1.56155i −0.267804 + 0.154617i
\(103\) 4.43845i 0.437333i 0.975800 + 0.218667i \(0.0701707\pi\)
−0.975800 + 0.218667i \(0.929829\pi\)
\(104\) −2.84233 + 2.21837i −0.278713 + 0.217529i
\(105\) 0 0
\(106\) −2.12311 3.67733i −0.206214 0.357174i
\(107\) 4.64996 2.68466i 0.449529 0.259536i −0.258102 0.966118i \(-0.583097\pi\)
0.707631 + 0.706582i \(0.249764\pi\)
\(108\) 0.866025 + 0.500000i 0.0833333 + 0.0481125i
\(109\) 2.80776 0.268935 0.134468 0.990918i \(-0.457068\pi\)
0.134468 + 0.990918i \(0.457068\pi\)
\(110\) 0 0
\(111\) −0.280776 + 0.486319i −0.0266501 + 0.0461594i
\(112\) 3.56155i 0.336535i
\(113\) 3.46410 + 2.00000i 0.325875 + 0.188144i 0.654008 0.756487i \(-0.273086\pi\)
−0.328133 + 0.944632i \(0.606419\pi\)
\(114\) −1.21922 2.11176i −0.114191 0.197784i
\(115\) 0 0
\(116\) 1.12311 0.104278
\(117\) −3.57071 + 0.500000i −0.330113 + 0.0462250i
\(118\) 10.2462i 0.943240i
\(119\) 5.56155 + 9.63289i 0.509827 + 0.883046i
\(120\) 0 0
\(121\) 5.34233 9.25319i 0.485666 0.841199i
\(122\) 1.68466i 0.152522i
\(123\) −2.70469 1.56155i −0.243874 0.140800i
\(124\) 2.00000 3.46410i 0.179605 0.311086i
\(125\) 0 0
\(126\) 1.78078 3.08440i 0.158644 0.274780i
\(127\) 18.8861 10.9039i 1.67587 0.967563i 0.711619 0.702565i \(-0.247962\pi\)
0.964249 0.264998i \(-0.0853713\pi\)
\(128\) −0.866025 + 0.500000i −0.0765466 + 0.0441942i
\(129\) −0.438447 −0.0386031
\(130\) 0 0
\(131\) 0.876894 0.0766146 0.0383073 0.999266i \(-0.487803\pi\)
0.0383073 + 0.999266i \(0.487803\pi\)
\(132\) −0.486319 + 0.280776i −0.0423286 + 0.0244384i
\(133\) −7.52113 + 4.34233i −0.652165 + 0.376528i
\(134\) 5.90388 10.2258i 0.510018 0.883377i
\(135\) 0 0
\(136\) 1.56155 2.70469i 0.133902 0.231925i
\(137\) −14.2829 8.24621i −1.22027 0.704521i −0.255292 0.966864i \(-0.582172\pi\)
−0.964975 + 0.262343i \(0.915505\pi\)
\(138\) 7.68466i 0.654162i
\(139\) 10.7808 18.6729i 0.914414 1.58381i 0.106656 0.994296i \(-0.465986\pi\)
0.807758 0.589515i \(-0.200681\pi\)
\(140\) 0 0
\(141\) −2.00000 3.46410i −0.168430 0.291730i
\(142\) 12.5616i 1.05414i
\(143\) 0.759413 1.87689i 0.0635053 0.156954i
\(144\) −1.00000 −0.0833333
\(145\) 0 0
\(146\) −4.50000 7.79423i −0.372423 0.645055i
\(147\) −4.92306 2.84233i −0.406047 0.234431i
\(148\) 0.561553i 0.0461594i
\(149\) −5.12311 + 8.87348i −0.419701 + 0.726944i −0.995909 0.0903593i \(-0.971198\pi\)
0.576208 + 0.817303i \(0.304532\pi\)
\(150\) 0 0
\(151\) −16.6847 −1.35778 −0.678889 0.734241i \(-0.737538\pi\)
−0.678889 + 0.734241i \(0.737538\pi\)
\(152\) 2.11176 + 1.21922i 0.171286 + 0.0988921i
\(153\) 2.70469 1.56155i 0.218661 0.126244i
\(154\) 1.00000 + 1.73205i 0.0805823 + 0.139573i
\(155\) 0 0
\(156\) 2.84233 2.21837i 0.227568 0.177612i
\(157\) 17.2462i 1.37640i 0.725522 + 0.688199i \(0.241598\pi\)
−0.725522 + 0.688199i \(0.758402\pi\)
\(158\) 13.6899 7.90388i 1.08911 0.628799i
\(159\) 2.12311 + 3.67733i 0.168373 + 0.291631i
\(160\) 0 0
\(161\) 27.3693 2.15700
\(162\) −0.866025 0.500000i −0.0680414 0.0392837i
\(163\) −14.2829 8.24621i −1.11872 0.645893i −0.177646 0.984094i \(-0.556848\pi\)
−0.941074 + 0.338201i \(0.890182\pi\)
\(164\) 3.12311 0.243874
\(165\) 0 0
\(166\) −3.28078 5.68247i −0.254638 0.441045i
\(167\) 20.5115 11.8423i 1.58723 0.916387i 0.593468 0.804858i \(-0.297759\pi\)
0.993761 0.111529i \(-0.0355748\pi\)
\(168\) 3.56155i 0.274780i
\(169\) −3.15767 + 12.6107i −0.242898 + 0.970052i
\(170\) 0 0
\(171\) 1.21922 + 2.11176i 0.0932364 + 0.161490i
\(172\) 0.379706 0.219224i 0.0289523 0.0167156i
\(173\) −7.68762 4.43845i −0.584479 0.337449i 0.178433 0.983952i \(-0.442897\pi\)
−0.762911 + 0.646503i \(0.776231\pi\)
\(174\) −1.12311 −0.0851424
\(175\) 0 0
\(176\) 0.280776 0.486319i 0.0211643 0.0366577i
\(177\) 10.2462i 0.770152i
\(178\) 8.87348 + 5.12311i 0.665095 + 0.383993i
\(179\) −7.84233 13.5833i −0.586163 1.01526i −0.994729 0.102536i \(-0.967304\pi\)
0.408566 0.912729i \(-0.366029\pi\)
\(180\) 0 0
\(181\) −15.4924 −1.15154 −0.575771 0.817611i \(-0.695298\pi\)
−0.575771 + 0.817611i \(0.695298\pi\)
\(182\) −7.90084 10.1231i −0.585649 0.750375i
\(183\) 1.68466i 0.124534i
\(184\) −3.84233 6.65511i −0.283260 0.490621i
\(185\) 0 0
\(186\) −2.00000 + 3.46410i −0.146647 + 0.254000i
\(187\) 1.75379i 0.128250i
\(188\) 3.46410 + 2.00000i 0.252646 + 0.145865i
\(189\) −1.78078 + 3.08440i −0.129532 + 0.224357i
\(190\) 0 0
\(191\) −7.96543 + 13.7965i −0.576359 + 0.998282i 0.419534 + 0.907740i \(0.362194\pi\)
−0.995893 + 0.0905428i \(0.971140\pi\)
\(192\) 0.866025 0.500000i 0.0625000 0.0360844i
\(193\) −2.59808 + 1.50000i −0.187014 + 0.107972i −0.590584 0.806976i \(-0.701102\pi\)
0.403570 + 0.914949i \(0.367769\pi\)
\(194\) 2.80776 0.201586
\(195\) 0 0
\(196\) 5.68466 0.406047
\(197\) 4.43674 2.56155i 0.316105 0.182503i −0.333550 0.942732i \(-0.608247\pi\)
0.649655 + 0.760229i \(0.274913\pi\)
\(198\) 0.486319 0.280776i 0.0345612 0.0199539i
\(199\) −2.21922 + 3.84381i −0.157317 + 0.272480i −0.933900 0.357534i \(-0.883618\pi\)
0.776584 + 0.630014i \(0.216951\pi\)
\(200\) 0 0
\(201\) −5.90388 + 10.2258i −0.416428 + 0.721274i
\(202\) 5.40938 + 3.12311i 0.380602 + 0.219741i
\(203\) 4.00000i 0.280745i
\(204\) −1.56155 + 2.70469i −0.109331 + 0.189366i
\(205\) 0 0
\(206\) 2.21922 + 3.84381i 0.154621 + 0.267811i
\(207\) 7.68466i 0.534121i
\(208\) −1.35234 + 3.34233i −0.0937682 + 0.231749i
\(209\) −1.36932 −0.0947176
\(210\) 0 0
\(211\) −0.561553 0.972638i −0.0386589 0.0669592i 0.846049 0.533106i \(-0.178975\pi\)
−0.884707 + 0.466147i \(0.845642\pi\)
\(212\) −3.67733 2.12311i −0.252560 0.145815i
\(213\) 12.5616i 0.860703i
\(214\) 2.68466 4.64996i 0.183519 0.317865i
\(215\) 0 0
\(216\) 1.00000 0.0680414
\(217\) 12.3376 + 7.12311i 0.837530 + 0.483548i
\(218\) 2.43160 1.40388i 0.164688 0.0950829i
\(219\) 4.50000 + 7.79423i 0.304082 + 0.526685i
\(220\) 0 0
\(221\) −1.56155 11.1517i −0.105041 0.750146i
\(222\) 0.561553i 0.0376890i
\(223\) 0.379706 0.219224i 0.0254270 0.0146803i −0.487233 0.873272i \(-0.661994\pi\)
0.512660 + 0.858592i \(0.328660\pi\)
\(224\) −1.78078 3.08440i −0.118983 0.206085i
\(225\) 0 0
\(226\) 4.00000 0.266076
\(227\) −25.7077 14.8423i −1.70628 0.985120i −0.939073 0.343718i \(-0.888314\pi\)
−0.767205 0.641402i \(-0.778353\pi\)
\(228\) −2.11176 1.21922i −0.139855 0.0807451i
\(229\) −9.49242 −0.627277 −0.313638 0.949542i \(-0.601548\pi\)
−0.313638 + 0.949542i \(0.601548\pi\)
\(230\) 0 0
\(231\) −1.00000 1.73205i −0.0657952 0.113961i
\(232\) 0.972638 0.561553i 0.0638568 0.0368677i
\(233\) 25.3693i 1.66200i 0.556273 + 0.831000i \(0.312231\pi\)
−0.556273 + 0.831000i \(0.687769\pi\)
\(234\) −2.84233 + 2.21837i −0.185809 + 0.145019i
\(235\) 0 0
\(236\) 5.12311 + 8.87348i 0.333486 + 0.577614i
\(237\) −13.6899 + 7.90388i −0.889256 + 0.513412i
\(238\) 9.63289 + 5.56155i 0.624408 + 0.360502i
\(239\) −27.0540 −1.74998 −0.874988 0.484144i \(-0.839131\pi\)
−0.874988 + 0.484144i \(0.839131\pi\)
\(240\) 0 0
\(241\) −7.78078 + 13.4767i −0.501204 + 0.868111i 0.498795 + 0.866720i \(0.333776\pi\)
−0.999999 + 0.00139067i \(0.999557\pi\)
\(242\) 10.6847i 0.686836i
\(243\) 0.866025 + 0.500000i 0.0555556 + 0.0320750i
\(244\) −0.842329 1.45896i −0.0539246 0.0934002i
\(245\) 0 0
\(246\) −3.12311 −0.199122
\(247\) 8.70700 1.21922i 0.554013 0.0775773i
\(248\) 4.00000i 0.254000i
\(249\) 3.28078 + 5.68247i 0.207911 + 0.360112i
\(250\) 0 0
\(251\) −11.9654 + 20.7247i −0.755252 + 1.30813i 0.189998 + 0.981785i \(0.439152\pi\)
−0.945249 + 0.326350i \(0.894181\pi\)
\(252\) 3.56155i 0.224357i
\(253\) 3.73720 + 2.15767i 0.234955 + 0.135652i
\(254\) 10.9039 18.8861i 0.684170 1.18502i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −11.7914 + 6.80776i −0.735527 + 0.424657i −0.820441 0.571732i \(-0.806272\pi\)
0.0849138 + 0.996388i \(0.472939\pi\)
\(258\) −0.379706 + 0.219224i −0.0236395 + 0.0136483i
\(259\) 2.00000 0.124274
\(260\) 0 0
\(261\) 1.12311 0.0695185
\(262\) 0.759413 0.438447i 0.0469167 0.0270874i
\(263\) −5.46925 + 3.15767i −0.337248 + 0.194710i −0.659054 0.752095i \(-0.729043\pi\)
0.321806 + 0.946806i \(0.395710\pi\)
\(264\) −0.280776 + 0.486319i −0.0172806 + 0.0299309i
\(265\) 0 0
\(266\) −4.34233 + 7.52113i −0.266245 + 0.461150i
\(267\) −8.87348 5.12311i −0.543048 0.313529i
\(268\) 11.8078i 0.721274i
\(269\) −1.68466 + 2.91791i −0.102715 + 0.177908i −0.912803 0.408401i \(-0.866086\pi\)
0.810087 + 0.586310i \(0.199420\pi\)
\(270\) 0 0
\(271\) −4.46543 7.73436i −0.271256 0.469829i 0.697928 0.716168i \(-0.254106\pi\)
−0.969184 + 0.246339i \(0.920772\pi\)
\(272\) 3.12311i 0.189366i
\(273\) 7.90084 + 10.1231i 0.478181 + 0.612678i
\(274\) −16.4924 −0.996344
\(275\) 0 0
\(276\) 3.84233 + 6.65511i 0.231281 + 0.400591i
\(277\) −4.33013 2.50000i −0.260172 0.150210i 0.364241 0.931305i \(-0.381328\pi\)
−0.624413 + 0.781094i \(0.714662\pi\)
\(278\) 21.5616i 1.29318i
\(279\) 2.00000 3.46410i 0.119737 0.207390i
\(280\) 0 0
\(281\) −1.75379 −0.104622 −0.0523111 0.998631i \(-0.516659\pi\)
−0.0523111 + 0.998631i \(0.516659\pi\)
\(282\) −3.46410 2.00000i −0.206284 0.119098i
\(283\) −25.6478 + 14.8078i −1.52460 + 0.880230i −0.525028 + 0.851085i \(0.675945\pi\)
−0.999575 + 0.0291454i \(0.990721\pi\)
\(284\) 6.28078 + 10.8786i 0.372696 + 0.645528i
\(285\) 0 0
\(286\) −0.280776 2.00514i −0.0166027 0.118567i
\(287\) 11.1231i 0.656576i
\(288\) −0.866025 + 0.500000i −0.0510310 + 0.0294628i
\(289\) −3.62311 6.27540i −0.213124 0.369141i
\(290\) 0 0
\(291\) −2.80776 −0.164594
\(292\) −7.79423 4.50000i −0.456123 0.263343i
\(293\) 17.5337 + 10.1231i 1.02433 + 0.591398i 0.915356 0.402646i \(-0.131910\pi\)
0.108976 + 0.994044i \(0.465243\pi\)
\(294\) −5.68466 −0.331536
\(295\) 0 0
\(296\) −0.280776 0.486319i −0.0163198 0.0282667i
\(297\) −0.486319 + 0.280776i −0.0282191 + 0.0162923i
\(298\) 10.2462i 0.593547i
\(299\) −25.6847 10.3923i −1.48538 0.601003i
\(300\) 0 0
\(301\) 0.780776 + 1.35234i 0.0450032 + 0.0779478i
\(302\) −14.4493 + 8.34233i −0.831466 + 0.480047i
\(303\) −5.40938 3.12311i −0.310761 0.179418i
\(304\) 2.43845 0.139855
\(305\) 0 0
\(306\) 1.56155 2.70469i 0.0892680 0.154617i
\(307\) 22.2462i 1.26966i 0.772653 + 0.634829i \(0.218930\pi\)
−0.772653 + 0.634829i \(0.781070\pi\)
\(308\) 1.73205 + 1.00000i 0.0986928 + 0.0569803i
\(309\) −2.21922 3.84381i −0.126247 0.218667i
\(310\) 0 0
\(311\) −10.3153 −0.584929 −0.292465 0.956276i \(-0.594475\pi\)
−0.292465 + 0.956276i \(0.594475\pi\)
\(312\) 1.35234 3.34233i 0.0765614 0.189222i
\(313\) 31.0000i 1.75222i −0.482108 0.876112i \(-0.660129\pi\)
0.482108 0.876112i \(-0.339871\pi\)
\(314\) 8.62311 + 14.9357i 0.486630 + 0.842868i
\(315\) 0 0
\(316\) 7.90388 13.6899i 0.444628 0.770118i
\(317\) 16.2462i 0.912478i 0.889857 + 0.456239i \(0.150804\pi\)
−0.889857 + 0.456239i \(0.849196\pi\)
\(318\) 3.67733 + 2.12311i 0.206214 + 0.119058i
\(319\) −0.315342 + 0.546188i −0.0176557 + 0.0305806i
\(320\) 0 0
\(321\) −2.68466 + 4.64996i −0.149843 + 0.259536i
\(322\) 23.7025 13.6847i 1.32089 0.762616i
\(323\) −6.59524 + 3.80776i −0.366969 + 0.211870i
\(324\) −1.00000 −0.0555556
\(325\) 0 0
\(326\) −16.4924 −0.913431
\(327\) −2.43160 + 1.40388i −0.134468 + 0.0776349i
\(328\) 2.70469 1.56155i 0.149341 0.0862223i
\(329\) −7.12311 + 12.3376i −0.392710 + 0.680193i
\(330\) 0 0
\(331\) 8.34233 14.4493i 0.458536 0.794207i −0.540348 0.841442i \(-0.681707\pi\)
0.998884 + 0.0472342i \(0.0150407\pi\)
\(332\) −5.68247 3.28078i −0.311866 0.180056i
\(333\) 0.561553i 0.0307729i
\(334\) 11.8423 20.5115i 0.647983 1.12234i
\(335\) 0 0
\(336\) 1.78078 + 3.08440i 0.0971493 + 0.168268i
\(337\) 8.05398i 0.438728i 0.975643 + 0.219364i \(0.0703982\pi\)
−0.975643 + 0.219364i \(0.929602\pi\)
\(338\) 3.57071 + 12.5000i 0.194221 + 0.679910i
\(339\) −4.00000 −0.217250
\(340\) 0 0
\(341\) 1.12311 + 1.94528i 0.0608196 + 0.105343i
\(342\) 2.11176 + 1.21922i 0.114191 + 0.0659281i
\(343\) 4.68466i 0.252948i
\(344\) 0.219224 0.379706i 0.0118197 0.0204724i
\(345\) 0 0
\(346\) −8.87689 −0.477225
\(347\) 21.4842 + 12.4039i 1.15333 + 0.665875i 0.949696 0.313172i \(-0.101392\pi\)
0.203633 + 0.979047i \(0.434725\pi\)
\(348\) −0.972638 + 0.561553i −0.0521389 + 0.0301024i
\(349\) −9.62311 16.6677i −0.515113 0.892202i −0.999846 0.0175398i \(-0.994417\pi\)
0.484733 0.874662i \(-0.338917\pi\)
\(350\) 0 0
\(351\) 2.84233 2.21837i 0.151712 0.118408i
\(352\) 0.561553i 0.0299309i
\(353\) −1.94528 + 1.12311i −0.103537 + 0.0597769i −0.550874 0.834588i \(-0.685706\pi\)
0.447338 + 0.894365i \(0.352372\pi\)
\(354\) −5.12311 8.87348i −0.272290 0.471620i
\(355\) 0 0
\(356\) 10.2462 0.543048
\(357\) −9.63289 5.56155i −0.509827 0.294349i
\(358\) −13.5833 7.84233i −0.717900 0.414480i
\(359\) 4.87689 0.257393 0.128696 0.991684i \(-0.458921\pi\)
0.128696 + 0.991684i \(0.458921\pi\)
\(360\) 0 0
\(361\) 6.52699 + 11.3051i 0.343526 + 0.595004i
\(362\) −13.4168 + 7.74621i −0.705173 + 0.407132i
\(363\) 10.6847i 0.560799i
\(364\) −11.9039 4.81645i −0.623933 0.252450i
\(365\) 0 0
\(366\) 0.842329 + 1.45896i 0.0440293 + 0.0762609i
\(367\) −8.82674 + 5.09612i −0.460752 + 0.266015i −0.712360 0.701814i \(-0.752374\pi\)
0.251609 + 0.967829i \(0.419040\pi\)
\(368\) −6.65511 3.84233i −0.346922 0.200295i
\(369\) 3.12311 0.162582
\(370\) 0 0
\(371\) 7.56155 13.0970i 0.392576 0.679962i
\(372\) 4.00000i 0.207390i
\(373\) −8.22068 4.74621i −0.425651 0.245750i 0.271841 0.962342i \(-0.412367\pi\)
−0.697492 + 0.716593i \(0.745701\pi\)
\(374\) 0.876894 + 1.51883i 0.0453431 + 0.0785366i
\(375\) 0 0
\(376\) 4.00000 0.206284
\(377\) 1.51883 3.75379i 0.0782235 0.193330i
\(378\) 3.56155i 0.183187i
\(379\) −12.0270 20.8314i −0.617785 1.07003i −0.989889 0.141844i \(-0.954697\pi\)
0.372104 0.928191i \(-0.378636\pi\)
\(380\) 0 0
\(381\) −10.9039 + 18.8861i −0.558623 + 0.967563i
\(382\) 15.9309i 0.815094i
\(383\) −4.70983 2.71922i −0.240661 0.138946i 0.374819 0.927098i \(-0.377705\pi\)
−0.615481 + 0.788152i \(0.711038\pi\)
\(384\) 0.500000 0.866025i 0.0255155 0.0441942i
\(385\) 0 0
\(386\) −1.50000 + 2.59808i −0.0763480 + 0.132239i
\(387\) 0.379706 0.219224i 0.0193016 0.0111438i
\(388\) 2.43160 1.40388i 0.123446 0.0712713i
\(389\) −11.3693 −0.576447 −0.288224 0.957563i \(-0.593065\pi\)
−0.288224 + 0.957563i \(0.593065\pi\)
\(390\) 0 0
\(391\) 24.0000 1.21373
\(392\) 4.92306 2.84233i 0.248652 0.143559i
\(393\) −0.759413 + 0.438447i −0.0383073 + 0.0221167i
\(394\) 2.56155 4.43674i 0.129049 0.223520i
\(395\) 0 0
\(396\) 0.280776 0.486319i 0.0141095 0.0244384i
\(397\) 8.49377 + 4.90388i 0.426290 + 0.246119i 0.697765 0.716327i \(-0.254178\pi\)
−0.271475 + 0.962446i \(0.587511\pi\)
\(398\) 4.43845i 0.222479i
\(399\) 4.34233 7.52113i 0.217388 0.376528i
\(400\) 0 0
\(401\) 6.31534 + 10.9385i 0.315373 + 0.546242i 0.979517 0.201363i \(-0.0645370\pi\)
−0.664144 + 0.747605i \(0.731204\pi\)
\(402\) 11.8078i 0.588918i
\(403\) −8.87348 11.3693i −0.442019 0.566346i
\(404\) 6.24621 0.310761
\(405\) 0 0
\(406\) 2.00000 + 3.46410i 0.0992583 + 0.171920i
\(407\) 0.273094 + 0.157671i 0.0135368 + 0.00781545i
\(408\) 3.12311i 0.154617i
\(409\) 8.12311 14.0696i 0.401662 0.695699i −0.592265 0.805743i \(-0.701766\pi\)
0.993927 + 0.110045i \(0.0350994\pi\)
\(410\) 0 0
\(411\) 16.4924 0.813511
\(412\) 3.84381 + 2.21922i 0.189371 + 0.109333i
\(413\) −31.6034 + 18.2462i −1.55510 + 0.897837i
\(414\) −3.84233 6.65511i −0.188840 0.327081i
\(415\) 0 0
\(416\) 0.500000 + 3.57071i 0.0245145 + 0.175069i
\(417\) 21.5616i 1.05587i
\(418\) −1.18586 + 0.684658i −0.0580025 + 0.0334877i
\(419\) −5.96543 10.3324i −0.291431 0.504773i 0.682718 0.730682i \(-0.260798\pi\)
−0.974148 + 0.225910i \(0.927465\pi\)
\(420\) 0 0
\(421\) 31.2462 1.52285 0.761424 0.648255i \(-0.224501\pi\)
0.761424 + 0.648255i \(0.224501\pi\)
\(422\) −0.972638 0.561553i −0.0473473 0.0273360i
\(423\) 3.46410 + 2.00000i 0.168430 + 0.0972433i
\(424\) −4.24621 −0.206214
\(425\) 0 0
\(426\) −6.28078 10.8786i −0.304305 0.527071i
\(427\) 5.19615 3.00000i 0.251459 0.145180i
\(428\) 5.36932i 0.259536i
\(429\) 0.280776 + 2.00514i 0.0135560 + 0.0968093i
\(430\) 0 0
\(431\) −9.15767 15.8616i −0.441109 0.764024i 0.556663 0.830739i \(-0.312082\pi\)
−0.997772 + 0.0667146i \(0.978748\pi\)
\(432\) 0.866025 0.500000i 0.0416667 0.0240563i
\(433\) −11.8513 6.84233i −0.569535 0.328821i 0.187428 0.982278i \(-0.439985\pi\)
−0.756964 + 0.653457i \(0.773318\pi\)
\(434\) 14.2462 0.683840
\(435\) 0 0
\(436\) 1.40388 2.43160i 0.0672338 0.116452i
\(437\) 18.7386i 0.896390i
\(438\) 7.79423 + 4.50000i 0.372423 + 0.215018i
\(439\) −3.46543 6.00231i −0.165396 0.286475i 0.771400 0.636351i \(-0.219557\pi\)
−0.936796 + 0.349876i \(0.886224\pi\)
\(440\) 0 0
\(441\) 5.68466 0.270698
\(442\) −6.92820 8.87689i −0.329541 0.422231i
\(443\) 2.80776i 0.133401i 0.997773 + 0.0667004i \(0.0212472\pi\)
−0.997773 + 0.0667004i \(0.978753\pi\)
\(444\) 0.280776 + 0.486319i 0.0133251 + 0.0230797i
\(445\) 0 0
\(446\) 0.219224 0.379706i 0.0103805 0.0179796i
\(447\) 10.2462i 0.484629i
\(448\) −3.08440 1.78078i −0.145724 0.0841338i
\(449\) −1.56155 + 2.70469i −0.0736942 + 0.127642i −0.900518 0.434819i \(-0.856812\pi\)
0.826823 + 0.562462i \(0.190146\pi\)
\(450\) 0 0
\(451\) −0.876894 + 1.51883i −0.0412913 + 0.0715187i
\(452\) 3.46410 2.00000i 0.162938 0.0940721i
\(453\) 14.4493 8.34233i 0.678889 0.391957i
\(454\) −29.6847 −1.39317
\(455\) 0 0
\(456\) −2.43845 −0.114191
\(457\) 3.90368 2.25379i 0.182606 0.105428i −0.405910 0.913913i \(-0.633045\pi\)
0.588517 + 0.808485i \(0.299712\pi\)
\(458\) −8.22068 + 4.74621i −0.384127 + 0.221776i
\(459\) −1.56155 + 2.70469i −0.0728870 + 0.126244i
\(460\) 0 0
\(461\) −5.31534 + 9.20644i −0.247560 + 0.428787i −0.962848 0.270043i \(-0.912962\pi\)
0.715288 + 0.698830i \(0.246295\pi\)
\(462\) −1.73205 1.00000i −0.0805823 0.0465242i
\(463\) 27.8078i 1.29234i −0.763195 0.646168i \(-0.776370\pi\)
0.763195 0.646168i \(-0.223630\pi\)
\(464\) 0.561553 0.972638i 0.0260694 0.0451536i
\(465\) 0 0
\(466\) 12.6847 + 21.9705i 0.587605 + 1.01776i
\(467\) 3.43845i 0.159112i −0.996830 0.0795562i \(-0.974650\pi\)
0.996830 0.0795562i \(-0.0253503\pi\)
\(468\) −1.35234 + 3.34233i −0.0625121 + 0.154499i
\(469\) 42.0540 1.94187
\(470\) 0 0
\(471\) −8.62311 14.9357i −0.397332 0.688199i
\(472\) 8.87348 + 5.12311i 0.408435 + 0.235810i
\(473\) 0.246211i 0.0113208i
\(474\) −7.90388 + 13.6899i −0.363037 + 0.628799i
\(475\) 0 0
\(476\) 11.1231 0.509827
\(477\) −3.67733 2.12311i −0.168373 0.0972103i
\(478\) −23.4294 + 13.5270i −1.07164 + 0.618710i
\(479\) −5.80776 10.0593i −0.265364 0.459623i 0.702295 0.711886i \(-0.252159\pi\)
−0.967659 + 0.252263i \(0.918825\pi\)
\(480\) 0 0
\(481\) −1.87689 0.759413i −0.0855790 0.0346262i
\(482\) 15.5616i 0.708809i
\(483\) −23.7025 + 13.6847i −1.07850 + 0.622674i
\(484\) −5.34233 9.25319i −0.242833 0.420599i
\(485\) 0 0
\(486\) 1.00000 0.0453609
\(487\) −36.9660 21.3423i −1.67509 0.967113i −0.964718 0.263286i \(-0.915194\pi\)
−0.710372 0.703827i \(-0.751473\pi\)
\(488\) −1.45896 0.842329i −0.0660439 0.0381305i
\(489\) 16.4924 0.745813
\(490\) 0 0
\(491\) −15.6501 27.1068i −0.706279 1.22331i −0.966228 0.257689i \(-0.917039\pi\)
0.259949 0.965622i \(-0.416294\pi\)
\(492\) −2.70469 + 1.56155i −0.121937 + 0.0704002i
\(493\) 3.50758i 0.157973i
\(494\) 6.93087 5.40938i 0.311835 0.243379i
\(495\) 0 0
\(496\) −2.00000 3.46410i −0.0898027 0.155543i
\(497\) −38.7448 + 22.3693i −1.73794 + 1.00340i
\(498\) 5.68247 + 3.28078i 0.254638 + 0.147015i
\(499\) −6.05398 −0.271013 −0.135507 0.990776i \(-0.543266\pi\)
−0.135507 + 0.990776i \(0.543266\pi\)
\(500\) 0 0
\(501\) −11.8423 + 20.5115i −0.529076 + 0.916387i
\(502\) 23.9309i 1.06809i
\(503\) −21.0577 12.1577i −0.938917 0.542084i −0.0492961 0.998784i \(-0.515698\pi\)
−0.889621 + 0.456700i \(0.849031\pi\)
\(504\) −1.78078 3.08440i −0.0793221 0.137390i
\(505\) 0 0
\(506\) 4.31534 0.191840
\(507\) −3.57071 12.5000i −0.158581 0.555144i
\(508\) 21.8078i 0.967563i
\(509\) −8.12311 14.0696i −0.360050 0.623625i 0.627918 0.778279i \(-0.283907\pi\)
−0.987969 + 0.154654i \(0.950574\pi\)
\(510\) 0 0
\(511\) 16.0270 27.7596i 0.708992 1.22801i
\(512\) 1.00000i 0.0441942i
\(513\) −2.11176 1.21922i −0.0932364 0.0538300i
\(514\) −6.80776 + 11.7914i −0.300278 + 0.520096i
\(515\) 0 0
\(516\) −0.219224 + 0.379706i −0.00965078 + 0.0167156i
\(517\) −1.94528 + 1.12311i −0.0855531 + 0.0493941i
\(518\) 1.73205 1.00000i 0.0761019 0.0439375i
\(519\) 8.87689 0.389652
\(520\) 0 0
\(521\) 34.7386 1.52193 0.760964 0.648795i \(-0.224727\pi\)
0.760964 + 0.648795i \(0.224727\pi\)
\(522\) 0.972638 0.561553i 0.0425712 0.0245785i
\(523\) −21.5908 + 12.4654i −0.944098 + 0.545075i −0.891243 0.453527i \(-0.850166\pi\)
−0.0528556 + 0.998602i \(0.516832\pi\)
\(524\) 0.438447 0.759413i 0.0191537 0.0331751i
\(525\) 0 0
\(526\) −3.15767 + 5.46925i −0.137681 + 0.238470i
\(527\) 10.8188 + 6.24621i 0.471272 + 0.272089i
\(528\) 0.561553i 0.0244384i
\(529\) 18.0270 31.2237i 0.783782 1.35755i
\(530\) 0 0
\(531\) 5.12311 + 8.87348i 0.222324 + 0.385076i
\(532\) 8.68466i 0.376528i
\(533\) 4.22351 10.4384i 0.182941 0.452139i
\(534\) −10.2462 −0.443397
\(535\) 0 0
\(536\) −5.90388 10.2258i −0.255009 0.441688i
\(537\) 13.5833 + 7.84233i 0.586163 + 0.338421i
\(538\) 3.36932i 0.145262i
\(539\) −1.59612 + 2.76456i −0.0687497 + 0.119078i
\(540\) 0 0
\(541\) −22.3153 −0.959411 −0.479706 0.877429i \(-0.659257\pi\)
−0.479706 + 0.877429i \(0.659257\pi\)
\(542\) −7.73436 4.46543i −0.332219 0.191807i
\(543\) 13.4168 7.74621i 0.575771 0.332422i
\(544\) −1.56155 2.70469i −0.0669510 0.115963i
\(545\) 0 0
\(546\) 11.9039 + 4.81645i 0.509439 + 0.206125i
\(547\) 30.9309i 1.32251i −0.750162 0.661254i \(-0.770024\pi\)
0.750162 0.661254i \(-0.229976\pi\)
\(548\) −14.2829 + 8.24621i −0.610133 + 0.352261i
\(549\) −0.842329 1.45896i −0.0359497 0.0622668i
\(550\) 0 0
\(551\) −2.73863 −0.116670
\(552\) 6.65511 + 3.84233i 0.283260 + 0.163540i
\(553\) 48.7574 + 28.1501i 2.07338 + 1.19706i
\(554\) −5.00000 −0.212430
\(555\) 0 0
\(556\) −10.7808 18.6729i −0.457207 0.791905i
\(557\) −27.3799 + 15.8078i −1.16012 + 0.669796i −0.951333 0.308164i \(-0.900285\pi\)
−0.208788 + 0.977961i \(0.566952\pi\)
\(558\) 4.00000i 0.169334i
\(559\) −0.219224 1.56557i −0.00927217 0.0662165i
\(560\) 0 0
\(561\) −0.876894 1.51883i −0.0370225 0.0641249i
\(562\) −1.51883 + 0.876894i −0.0640678 + 0.0369896i
\(563\) 18.0201 + 10.4039i 0.759455 + 0.438471i 0.829100 0.559100i \(-0.188853\pi\)
−0.0696453 + 0.997572i \(0.522187\pi\)
\(564\) −4.00000 −0.168430
\(565\) 0 0
\(566\) −14.8078 + 25.6478i −0.622417 + 1.07806i
\(567\) 3.56155i 0.149571i
\(568\) 10.8786 + 6.28078i 0.456457 + 0.263536i
\(569\) −5.75379 9.96585i −0.241211 0.417790i 0.719848 0.694131i \(-0.244211\pi\)
−0.961060 + 0.276341i \(0.910878\pi\)
\(570\) 0 0
\(571\) 21.4233 0.896537 0.448268 0.893899i \(-0.352041\pi\)
0.448268 + 0.893899i \(0.352041\pi\)
\(572\) −1.24573 1.59612i −0.0520867 0.0667370i
\(573\) 15.9309i 0.665522i
\(574\) 5.56155 + 9.63289i 0.232135 + 0.402069i
\(575\) 0 0
\(576\) −0.500000 + 0.866025i −0.0208333 + 0.0360844i
\(577\) 23.0000i 0.957503i 0.877951 + 0.478751i \(0.158910\pi\)
−0.877951 + 0.478751i \(0.841090\pi\)
\(578\) −6.27540 3.62311i −0.261022 0.150701i
\(579\) 1.50000 2.59808i 0.0623379 0.107972i
\(580\) 0 0
\(581\) 11.6847 20.2384i 0.484761 0.839631i
\(582\) −2.43160 + 1.40388i −0.100793 + 0.0581928i
\(583\) 2.06501 1.19224i 0.0855241 0.0493774i
\(584\) −9.00000 −0.372423
\(585\) 0 0
\(586\) 20.2462 0.836363
\(587\) −15.5286 + 8.96543i −0.640933 + 0.370043i −0.784974 0.619529i \(-0.787324\pi\)
0.144041 + 0.989572i \(0.453990\pi\)
\(588\) −4.92306 + 2.84233i −0.203024 + 0.117216i
\(589\) −4.87689 + 8.44703i −0.200949 + 0.348054i
\(590\) 0 0
\(591\) −2.56155 + 4.43674i −0.105368 + 0.182503i
\(592\) −0.486319 0.280776i −0.0199876 0.0115398i
\(593\) 38.9848i 1.60092i 0.599389 + 0.800458i \(0.295410\pi\)
−0.599389 + 0.800458i \(0.704590\pi\)
\(594\) −0.280776 + 0.486319i −0.0115204 + 0.0199539i
\(595\) 0 0
\(596\) 5.12311 + 8.87348i 0.209851 + 0.363472i
\(597\) 4.43845i 0.181654i
\(598\) −27.4397 + 3.84233i −1.12209 + 0.157125i
\(599\) 18.3153 0.748345 0.374172 0.927359i \(-0.377927\pi\)
0.374172 + 0.927359i \(0.377927\pi\)
\(600\) 0 0
\(601\) 2.90388 + 5.02967i 0.118452 + 0.205165i 0.919154 0.393898i \(-0.128874\pi\)
−0.800703 + 0.599062i \(0.795540\pi\)
\(602\) 1.35234 + 0.780776i 0.0551174 + 0.0318221i
\(603\) 11.8078i 0.480849i
\(604\) −8.34233 + 14.4493i −0.339445 + 0.587935i
\(605\) 0 0
\(606\) −6.24621 −0.253735
\(607\) 34.0948 + 19.6847i 1.38387 + 0.798976i 0.992615 0.121308i \(-0.0387089\pi\)
0.391252 + 0.920284i \(0.372042\pi\)
\(608\) 2.11176 1.21922i 0.0856431 0.0494460i
\(609\) −2.00000 3.46410i −0.0810441 0.140372i
\(610\) 0 0
\(611\) 11.3693 8.87348i 0.459953 0.358983i
\(612\) 3.12311i 0.126244i
\(613\) 31.6501 18.2732i 1.27834 0.738048i 0.301794 0.953373i \(-0.402415\pi\)
0.976542 + 0.215326i \(0.0690813\pi\)
\(614\) 11.1231 + 19.2658i 0.448892 + 0.777504i
\(615\) 0 0
\(616\) 2.00000 0.0805823
\(617\) −41.0230 23.6847i −1.65153 0.953508i −0.976446 0.215763i \(-0.930776\pi\)
−0.675079 0.737745i \(-0.735891\pi\)
\(618\) −3.84381 2.21922i −0.154621 0.0892703i
\(619\) 12.3002 0.494386 0.247193 0.968966i \(-0.420492\pi\)
0.247193 + 0.968966i \(0.420492\pi\)
\(620\) 0 0
\(621\) 3.84233 + 6.65511i 0.154187 + 0.267060i
\(622\) −8.93335 + 5.15767i −0.358195 + 0.206804i
\(623\) 36.4924i 1.46204i
\(624\) −0.500000 3.57071i −0.0200160 0.142943i
\(625\) 0 0
\(626\) −15.5000 26.8468i −0.619505 1.07301i
\(627\) 1.18586 0.684658i 0.0473588 0.0273426i
\(628\) 14.9357 + 8.62311i 0.595998 + 0.344099i
\(629\) 1.75379 0.0699281
\(630\) 0 0
\(631\) −16.4654 + 28.5190i −0.655479 + 1.13532i 0.326295 + 0.945268i \(0.394200\pi\)
−0.981774 + 0.190054i \(0.939134\pi\)
\(632\) 15.8078i 0.628799i
\(633\) 0.972638 + 0.561553i 0.0386589 + 0.0223197i
\(634\) 8.12311 + 14.0696i 0.322610 + 0.558776i
\(635\) 0 0
\(636\) 4.24621 0.168373
\(637\) 7.68762 19.0000i 0.304594 0.752807i
\(638\) 0.630683i 0.0249690i
\(639\) 6.28078 + 10.8786i 0.248464 + 0.430352i
\(640\) 0 0
\(641\) −19.1231 + 33.1222i −0.755317 + 1.30825i 0.189899 + 0.981804i \(0.439184\pi\)
−0.945216 + 0.326444i \(0.894149\pi\)
\(642\) 5.36932i 0.211910i
\(643\) 21.2578 + 12.2732i 0.838326 + 0.484008i 0.856695 0.515824i \(-0.172514\pi\)
−0.0183689 + 0.999831i \(0.505847\pi\)
\(644\) 13.6847 23.7025i 0.539251 0.934010i
\(645\) 0 0
\(646\) −3.80776 + 6.59524i −0.149814 + 0.259486i
\(647\) 28.0794 16.2116i 1.10391 0.637346i 0.166668 0.986013i \(-0.446699\pi\)
0.937247 + 0.348667i \(0.113366\pi\)
\(648\) −0.866025 + 0.500000i −0.0340207 + 0.0196419i
\(649\) −5.75379 −0.225856
\(650\) 0 0
\(651\) −14.2462 −0.558353
\(652\) −14.2829 + 8.24621i −0.559360 + 0.322947i
\(653\) 32.5760 18.8078i 1.27480 0.736005i 0.298911 0.954281i \(-0.403377\pi\)
0.975887 + 0.218276i \(0.0700435\pi\)
\(654\) −1.40388 + 2.43160i −0.0548961 + 0.0950829i
\(655\) 0 0
\(656\) 1.56155 2.70469i 0.0609684 0.105600i
\(657\) −7.79423 4.50000i −0.304082 0.175562i
\(658\) 14.2462i 0.555375i
\(659\) 9.15767 15.8616i 0.356732 0.617878i −0.630681 0.776042i \(-0.717224\pi\)
0.987413 + 0.158164i \(0.0505575\pi\)
\(660\) 0 0
\(661\) 24.2732 + 42.0424i 0.944118 + 1.63526i 0.757508 + 0.652826i \(0.226417\pi\)
0.186610 + 0.982434i \(0.440250\pi\)
\(662\) 16.6847i 0.648468i
\(663\) 6.92820 + 8.87689i 0.269069 + 0.344750i
\(664\) −6.56155 −0.254638
\(665\) 0 0
\(666\) −0.280776 0.486319i −0.0108799 0.0188445i
\(667\) 7.47439 + 4.31534i 0.289410 + 0.167091i
\(668\) 23.6847i 0.916387i
\(669\) −0.219224 + 0.379706i −0.00847567 + 0.0146803i
\(670\) 0 0
\(671\) 0.946025 0.0365209
\(672\) 3.08440 + 1.78078i 0.118983 + 0.0686949i
\(673\) −24.9015 + 14.3769i −0.959883 + 0.554189i −0.896137 0.443778i \(-0.853638\pi\)
−0.0637458 + 0.997966i \(0.520305\pi\)
\(674\) 4.02699 + 6.97495i 0.155114 + 0.268665i
\(675\) 0 0
\(676\) 9.34233 + 9.03996i 0.359320 + 0.347691i
\(677\) 11.6155i 0.446421i 0.974770 + 0.223211i \(0.0716537\pi\)
−0.974770 + 0.223211i \(0.928346\pi\)
\(678\) −3.46410 + 2.00000i −0.133038 + 0.0768095i
\(679\) 5.00000 + 8.66025i 0.191882 + 0.332350i
\(680\) 0 0
\(681\) 29.6847 1.13752
\(682\) 1.94528 + 1.12311i 0.0744885 + 0.0430059i
\(683\) 13.3701 + 7.71922i 0.511592 + 0.295368i 0.733488 0.679703i \(-0.237891\pi\)
−0.221896 + 0.975070i \(0.571224\pi\)
\(684\) 2.43845 0.0932364
\(685\) 0 0
\(686\) −2.34233 4.05703i −0.0894305 0.154898i
\(687\) 8.22068 4.74621i 0.313638 0.181079i
\(688\) 0.438447i 0.0167156i
\(689\) −12.0691 + 9.41967i −0.459797 + 0.358861i
\(690\) 0 0
\(691\) 2.41146 + 4.17677i 0.0917362 + 0.158892i 0.908242 0.418446i \(-0.137425\pi\)
−0.816506 + 0.577338i \(0.804092\pi\)
\(692\) −7.68762 + 4.43845i −0.292239 + 0.168724i
\(693\) 1.73205 + 1.00000i 0.0657952 + 0.0379869i
\(694\) 24.8078 0.941690
\(695\) 0 0
\(696\) −0.561553 + 0.972638i −0.0212856 + 0.0368677i
\(697\) 9.75379i 0.369451i
\(698\) −16.6677 9.62311i −0.630882 0.364240i
\(699\) −12.6847 21.9705i −0.479778 0.831000i
\(700\) 0 0
\(701\) −0.876894 −0.0331198 −0.0165599 0.999863i \(-0.505271\pi\)
−0.0165599 + 0.999863i \(0.505271\pi\)
\(702\) 1.35234 3.34233i 0.0510410 0.126148i
\(703\) 1.36932i 0.0516448i
\(704\) −0.280776 0.486319i −0.0105822 0.0183288i
\(705\) 0 0
\(706\) −1.12311 + 1.94528i −0.0422686 + 0.0732114i
\(707\) 22.2462i 0.836655i
\(708\) −8.87348 5.12311i −0.333486 0.192538i
\(709\) −14.3769 + 24.9015i −0.539936 + 0.935196i 0.458971 + 0.888451i \(0.348218\pi\)
−0.998907 + 0.0467448i \(0.985115\pi\)
\(710\) 0 0
\(711\) 7.90388 13.6899i 0.296419 0.513412i
\(712\) 8.87348 5.12311i 0.332548 0.191997i
\(713\) 26.6204 15.3693i 0.996943 0.575585i
\(714\) −11.1231 −0.416272
\(715\) 0 0
\(716\) −15.6847 −0.586163
\(717\) 23.4294 13.5270i 0.874988 0.505175i
\(718\) 4.22351 2.43845i 0.157620 0.0910020i
\(719\) −8.71922 + 15.1021i −0.325172 + 0.563215i −0.981547 0.191220i \(-0.938756\pi\)
0.656375 + 0.754435i \(0.272089\pi\)
\(720\) 0 0
\(721\) −7.90388 + 13.6899i −0.294356 + 0.509839i
\(722\) 11.3051 + 6.52699i 0.420731 + 0.242909i
\(723\) 15.5616i 0.578740i
\(724\) −7.74621 + 13.4168i −0.287886 + 0.498633i
\(725\) 0 0
\(726\) 5.34233 + 9.25319i 0.198272 + 0.343418i
\(727\) 50.7926i 1.88379i −0.335902 0.941897i \(-0.609041\pi\)
0.335902 0.941897i \(-0.390959\pi\)
\(728\) −12.7173 + 1.78078i −0.471334 + 0.0660000i
\(729\) −1.00000 −0.0370370
\(730\) 0 0
\(731\) 0.684658 + 1.18586i 0.0253230 + 0.0438607i
\(732\) 1.45896 + 0.842329i 0.0539246 + 0.0311334i
\(733\) 47.9848i 1.77236i 0.463340 + 0.886180i \(0.346651\pi\)
−0.463340 + 0.886180i \(0.653349\pi\)
\(734\) −5.09612 + 8.82674i −0.188101 + 0.325801i
\(735\) 0 0
\(736\) −7.68466 −0.283260
\(737\) 5.74234 + 3.31534i 0.211522 + 0.122122i
\(738\) 2.70469 1.56155i 0.0995610 0.0574816i
\(739\) −6.56155 11.3649i −0.241371 0.418066i 0.719734 0.694250i \(-0.244264\pi\)
−0.961105 + 0.276183i \(0.910930\pi\)
\(740\) 0 0
\(741\) −6.93087 + 5.40938i −0.254612 + 0.198718i
\(742\) 15.1231i 0.555187i
\(743\) −9.63289 + 5.56155i −0.353397 + 0.204034i −0.666180 0.745791i \(-0.732072\pi\)
0.312784 + 0.949824i \(0.398739\pi\)
\(744\) 2.00000 + 3.46410i 0.0733236 + 0.127000i
\(745\) 0 0
\(746\) −9.49242 −0.347542
\(747\) −5.68247 3.28078i −0.207911 0.120037i
\(748\) 1.51883 + 0.876894i 0.0555338 + 0.0320624i
\(749\) 19.1231 0.698743
\(750\) 0 0
\(751\) −25.1231 43.5145i −0.916755 1.58787i −0.804311 0.594208i \(-0.797465\pi\)
−0.112444 0.993658i \(-0.535868\pi\)
\(752\) 3.46410 2.00000i 0.126323 0.0729325i
\(753\) 23.9309i 0.872089i
\(754\) −0.561553 4.01029i −0.0204505 0.146046i
\(755\) 0 0
\(756\) 1.78078 + 3.08440i 0.0647662 + 0.112178i
\(757\) −26.5737 + 15.3423i −0.965837 + 0.557626i −0.897965 0.440068i \(-0.854954\pi\)
−0.0678727 + 0.997694i \(0.521621\pi\)
\(758\) −20.8314 12.0270i −0.756629 0.436840i
\(759\) −4.31534 −0.156637
\(760\) 0 0
\(761\) 11.4924 19.9055i 0.416600 0.721572i −0.578995 0.815331i \(-0.696555\pi\)
0.995595 + 0.0937588i \(0.0298882\pi\)
\(762\) 21.8078i 0.790012i
\(763\) 8.66025 + 5.00000i 0.313522 + 0.181012i
\(764\) 7.96543 + 13.7965i 0.288179 + 0.499141i
\(765\) 0 0
\(766\) −5.43845 −0.196499
\(767\) 36.5863 5.12311i 1.32105 0.184985i
\(768\) 1.00000i 0.0360844i
\(769\) −4.65767 8.06732i −0.167960 0.290915i 0.769743 0.638354i \(-0.220385\pi\)
−0.937702 + 0.347439i \(0.887051\pi\)
\(770\) 0 0
\(771\) 6.80776 11.7914i 0.245176 0.424657i
\(772\) 3.00000i 0.107972i
\(773\) −25.6478 14.8078i −0.922487 0.532598i −0.0380595 0.999275i \(-0.512118\pi\)
−0.884428 + 0.466677i \(0.845451\pi\)
\(774\) 0.219224 0.379706i 0.00787983 0.0136483i
\(775\) 0 0
\(776\) 1.40388 2.43160i 0.0503964 0.0872892i
\(777\) −1.73205 + 1.00000i −0.0621370 + 0.0358748i
\(778\) −9.84612 + 5.68466i −0.353000 + 0.203805i
\(779\) −7.61553 −0.272855
\(780\) 0 0
\(781\) −7.05398 −0.252411
\(782\) 20.7846 12.0000i 0.743256 0.429119i
\(783\) −0.972638 + 0.561553i −0.0347592 + 0.0200683i
\(784\) 2.84233 4.92306i 0.101512 0.175824i
\(785\) 0 0
\(786\) −0.438447 + 0.759413i −0.0156389 + 0.0270874i
\(787\) 10.3923 + 6.00000i 0.370446 + 0.213877i 0.673653 0.739048i \(-0.264724\pi\)
−0.303207 + 0.952925i \(0.598058\pi\)
\(788\) 5.12311i 0.182503i
\(789\) 3.15767 5.46925i 0.112416 0.194710i
\(790\) 0 0
\(791\) 7.12311 + 12.3376i 0.253268 + 0.438674i
\(792\) 0.561553i 0.0199539i
\(793\) −6.01543 + 0.842329i −0.213614 + 0.0299120i
\(794\) 9.80776 0.348065
\(795\) 0 0
\(796\) 2.21922 + 3.84381i 0.0786583 + 0.136240i
\(797\) 22.7299 + 13.1231i 0.805134 + 0.464844i 0.845263 0.534350i \(-0.179444\pi\)
−0.0401293 + 0.999194i \(0.512777\pi\)
\(798\) 8.68466i 0.307434i
\(799\) −6.24621 + 10.8188i −0.220975 + 0.382740i
\(800\) 0 0
\(801\) 10.2462 0.362032
\(802\) 10.9385 + 6.31534i 0.386252 + 0.223002i
\(803\) 4.37687 2.52699i 0.154456 0.0891755i
\(804\) 5.90388 + 10.2258i 0.208214 + 0.360637i
\(805\) 0 0
\(806\) −13.3693 5.40938i −0.470914 0.190537i
\(807\) 3.36932i 0.118606i
\(808\) 5.40938 3.12311i 0.190301 0.109870i
\(809\) 15.8078 + 27.3799i 0.555771 + 0.962624i 0.997843 + 0.0656446i \(0.0209103\pi\)
−0.442072 + 0.896980i \(0.645756\pi\)
\(810\) 0 0
\(811\) −16.9309 −0.594523 −0.297262 0.954796i \(-0.596073\pi\)
−0.297262 + 0.954796i \(0.596073\pi\)
\(812\) 3.46410 + 2.00000i 0.121566 + 0.0701862i
\(813\) 7.73436 + 4.46543i 0.271256 + 0.156610i
\(814\) 0.315342 0.0110527
\(815\) 0 0
\(816\) 1.56155 + 2.70469i 0.0546653 + 0.0946830i
\(817\) −0.925894 + 0.534565i −0.0323929 + 0.0187021i
\(818\) 16.2462i 0.568035i
\(819\) −11.9039 4.81645i −0.415955 0.168300i
\(820\) 0 0
\(821\) −19.4924 33.7619i −0.680290 1.17830i −0.974892 0.222677i \(-0.928520\pi\)
0.294602 0.955620i \(-0.404813\pi\)
\(822\) 14.2829 8.24621i 0.498172 0.287620i
\(823\) 43.9877 + 25.3963i 1.53331 + 0.885260i 0.999206 + 0.0398436i \(0.0126860\pi\)
0.534109 + 0.845416i \(0.320647\pi\)
\(824\) 4.43845 0.154621
\(825\) 0 0
\(826\) −18.2462 + 31.6034i −0.634867 + 1.09962i
\(827\) 6.06913i 0.211044i 0.994417 + 0.105522i \(0.0336514\pi\)
−0.994417 + 0.105522i \(0.966349\pi\)
\(828\) −6.65511 3.84233i −0.231281 0.133530i
\(829\) 6.27320 + 10.8655i 0.217877 + 0.377374i 0.954159 0.299301i \(-0.0967534\pi\)
−0.736282 + 0.676675i \(0.763420\pi\)
\(830\) 0 0
\(831\) 5.00000 0.173448
\(832\) 2.21837 + 2.84233i 0.0769081 + 0.0985400i
\(833\) 17.7538i 0.615132i
\(834\) 10.7808 + 18.6729i 0.373308 + 0.646588i
\(835\) 0 0
\(836\) −0.684658 + 1.18586i −0.0236794 + 0.0410139i
\(837\) 4.00000i 0.138260i
\(838\) −10.3324 5.96543i −0.356928 0.206073i
\(839\) 6.84233 11.8513i 0.236223 0.409151i −0.723404 0.690425i \(-0.757424\pi\)
0.959628 + 0.281274i \(0.0907569\pi\)
\(840\) 0 0
\(841\) 13.8693 24.0224i 0.478252 0.828357i
\(842\) 27.0600 15.6231i 0.932550 0.538408i
\(843\) 1.51883 0.876894i 0.0523111 0.0302018i
\(844\) −1.12311 −0.0386589
\(845\) 0 0
\(846\) 4.00000 0.137523
\(847\) 32.9557 19.0270i 1.13237 0.653775i
\(848\) −3.67733 + 2.12311i −0.126280 + 0.0729077i
\(849\) 14.8078 25.6478i 0.508201 0.880230i
\(850\) 0 0
\(851\) 2.15767 3.73720i 0.0739640 0.128109i
\(852\) −10.8786 6.28078i −0.372696 0.215176i
\(853\) 18.9848i 0.650029i −0.945709 0.325014i \(-0.894631\pi\)
0.945709 0.325014i \(-0.105369\pi\)
\(854\) 3.00000 5.19615i 0.102658 0.177809i
\(855\) 0 0
\(856\) −2.68466 4.64996i −0.0917597 0.158933i
\(857\) 56.2462i 1.92133i −0.277703 0.960667i \(-0.589573\pi\)
0.277703 0.960667i \(-0.410427\pi\)
\(858\) 1.24573 + 1.59612i 0.0425286 + 0.0544906i
\(859\) −27.4233 −0.935671 −0.467835 0.883816i \(-0.654966\pi\)
−0.467835 + 0.883816i \(0.654966\pi\)
\(860\) 0 0
\(861\) −5.56155 9.63289i −0.189537 0.328288i
\(862\) −15.8616 9.15767i −0.540247 0.311912i
\(863\) 2.06913i 0.0704340i −0.999380 0.0352170i \(-0.988788\pi\)
0.999380 0.0352170i \(-0.0112122\pi\)
\(864\) 0.500000 0.866025i 0.0170103 0.0294628i
\(865\) 0 0
\(866\) −13.6847 −0.465024
\(867\) 6.27540 + 3.62311i 0.213124 + 0.123047i
\(868\) 12.3376 7.12311i 0.418765 0.241774i
\(869\) 4.43845 + 7.68762i 0.150564 + 0.260785i
\(870\) 0 0
\(871\) −39.4654 15.9682i −1.33724 0.541061i
\(872\) 2.80776i 0.0950829i
\(873\) 2.43160 1.40388i 0.0822970 0.0475142i
\(874\) 9.36932 + 16.2281i 0.316922 + 0.548925i
\(875\) 0 0
\(876\) 9.00000 0.304082
\(877\) −37.6655 21.7462i −1.27188 0.734317i −0.296534 0.955022i \(-0.595831\pi\)
−0.975341 + 0.220705i \(0.929164\pi\)
\(878\) −6.00231 3.46543i −0.202568 0.116953i
\(879\) −20.2462 −0.682888
\(880\) 0 0
\(881\) −24.5616 42.5419i −0.827500 1.43327i −0.899994 0.435903i \(-0.856429\pi\)
0.0724940 0.997369i \(-0.476904\pi\)
\(882\) 4.92306 2.84233i 0.165768 0.0957062i
\(883\) 34.2462i 1.15248i −0.817282 0.576238i \(-0.804520\pi\)
0.817282 0.576238i \(-0.195480\pi\)
\(884\) −10.4384 4.22351i −0.351083 0.142052i
\(885\) 0 0
\(886\) 1.40388 + 2.43160i 0.0471643 + 0.0816910i
\(887\) −35.8269 + 20.6847i −1.20295 + 0.694523i −0.961210 0.275818i \(-0.911051\pi\)
−0.241739 + 0.970341i \(0.577718\pi\)
\(888\) 0.486319 + 0.280776i 0.0163198 + 0.00942224i
\(889\) 77.6695 2.60495
\(890\) 0 0
\(891\) 0.280776 0.486319i 0.00940636 0.0162923i
\(892\) 0.438447i 0.0146803i
\(893\) −8.44703 4.87689i −0.282669 0.163199i
\(894\) −5.12311 8.87348i −0.171342 0.296774i
\(895\) 0 0
\(896\) −3.56155 −0.118983
\(897\) 27.4397 3.84233i 0.916186 0.128292i
\(898\) 3.12311i 0.104219i
\(899\) 2.24621 + 3.89055i 0.0749153 + 0.129757i
\(900\) 0 0
\(901\) 6.63068 11.4847i 0.220900 0.382610i
\(902\) 1.75379i 0.0583948i
\(903\) −1.35234 0.780776i −0.0450032 0.0259826i
\(904\) 2.00000 3.46410i 0.0665190 0.115214i
\(905\) 0 0
\(906\) 8.34233 14.4493i 0.277155 0.480047i
\(907\) −3.34436 + 1.93087i −0.111048 + 0.0641135i −0.554495 0.832187i \(-0.687089\pi\)
0.443447 + 0.896300i \(0.353755\pi\)
\(908\) −25.7077 + 14.8423i −0.853139 + 0.492560i
\(909\) 6.24621 0.207174
\(910\) 0 0
\(911\) 39.6847 1.31481 0.657406 0.753537i \(-0.271654\pi\)
0.657406 + 0.753537i \(0.271654\pi\)
\(912\) −2.11176 + 1.21922i −0.0699273 + 0.0403725i
\(913\) 3.19101 1.84233i 0.105607 0.0609722i
\(914\) 2.25379 3.90368i 0.0745487 0.129122i
\(915\) 0 0
\(916\) −4.74621 + 8.22068i −0.156819 + 0.271619i
\(917\) 2.70469 + 1.56155i 0.0893167 + 0.0515670i
\(918\) 3.12311i 0.103078i
\(919\) 13.6577 23.6558i 0.450525 0.780332i −0.547894 0.836548i \(-0.684570\pi\)
0.998419 + 0.0562158i \(0.0179035\pi\)
\(920\) 0 0
\(921\) −11.1231 19.2658i −0.366519 0.634829i
\(922\) 10.6307i 0.350103i
\(923\) 44.8537 6.28078i 1.47638 0.206734i
\(924\) −2.00000 −0.0657952
\(925\) 0 0
\(926\) −13.9039 24.0822i −0.456910 0.791391i
\(927\) 3.84381 + 2.21922i 0.126247 + 0.0728889i
\(928\) 1.12311i 0.0368677i
\(929\) −24.9309 + 43.1815i −0.817955 + 1.41674i 0.0892310 + 0.996011i \(0.471559\pi\)
−0.907186 + 0.420729i \(0.861774\pi\)
\(930\) 0 0
\(931\) −13.8617 −0.454300
\(932\) 21.9705 + 12.6847i 0.719667 + 0.415500i
\(933\) 8.93335 5.15767i 0.292465 0.168855i
\(934\) −1.71922 2.97778i −0.0562547 0.0974360i
\(935\) 0 0
\(936\) 0.500000 + 3.57071i 0.0163430 + 0.116712i
\(937\) 11.2462i 0.367398i −0.982983 0.183699i \(-0.941193\pi\)
0.982983 0.183699i \(-0.0588071\pi\)
\(938\) 36.4198 21.0270i 1.18915 0.686555i
\(939\) 15.5000 + 26.8468i 0.505823 + 0.876112i
\(940\) 0 0
\(941\) 34.6307 1.12893 0.564464 0.825458i \(-0.309083\pi\)
0.564464 + 0.825458i \(0.309083\pi\)
\(942\) −14.9357 8.62311i −0.486630 0.280956i
\(943\) 20.7846 + 12.0000i 0.676840 + 0.390774i
\(944\) 10.2462 0.333486
\(945\) 0 0
\(946\) 0.123106 + 0.213225i 0.00400251 + 0.00693255i
\(947\) 40.4170 23.3348i 1.31338 0.758278i 0.330722 0.943728i \(-0.392708\pi\)
0.982654 + 0.185451i \(0.0593745\pi\)
\(948\) 15.8078i 0.513412i
\(949\) −25.5810 + 19.9653i −0.830393 + 0.648102i
\(950\) 0 0
\(951\) −8.12311 14.0696i −0.263410 0.456239i
\(952\) 9.63289 5.56155i 0.312204 0.180251i
\(953\) −7.14143 4.12311i −0.231334 0.133560i 0.379854 0.925047i \(-0.375974\pi\)
−0.611187 + 0.791486i \(0.709308\pi\)
\(954\) −4.24621 −0.137476
\(955\) 0 0
\(956\) −13.5270 + 23.4294i −0.437494 + 0.757762i
\(957\) 0.630683i 0.0203871i
\(958\) −10.0593 5.80776i −0.325003 0.187640i
\(959\) −29.3693 50.8691i −0.948385 1.64265i
\(960\) 0 0
\(961\) −15.0000 −0.483871
\(962\) −2.00514 + 0.280776i −0.0646485 + 0.00905259i
\(963\) 5.36932i 0.173024i
\(964\) 7.78078 + 13.4767i 0.250602 + 0.434055i
\(965\) 0 0
\(966\) −13.6847 + 23.7025i −0.440297 + 0.762616i
\(967\) 16.6307i 0.534807i 0.963585 + 0.267403i \(0.0861656\pi\)
−0.963585 + 0.267403i \(0.913834\pi\)
\(968\) −9.25319 5.34233i −0.297409 0.171709i
\(969\) 3.80776 6.59524i 0.122323 0.211870i
\(970\) 0 0
\(971\) −7.31534 + 12.6705i −0.234760 + 0.406617i −0.959203 0.282718i \(-0.908764\pi\)
0.724443 + 0.689335i \(0.242097\pi\)
\(972\) 0.866025 0.500000i 0.0277778 0.0160375i
\(973\) 66.5044 38.3963i 2.13203 1.23093i
\(974\) −42.6847 −1.36770
\(975\) 0 0
\(976\) −1.68466 −0.0539246
\(977\) −40.0504 + 23.1231i −1.28133 + 0.739774i −0.977091 0.212823i \(-0.931734\pi\)
−0.304235 + 0.952597i \(0.598401\pi\)
\(978\) 14.2829 8.24621i 0.456715 0.263685i
\(979\) −2.87689 + 4.98293i −0.0919459 + 0.159255i
\(980\) 0 0
\(981\) 1.40388 2.43160i 0.0448225 0.0776349i
\(982\) −27.1068 15.6501i −0.865011 0.499415i
\(983\) 22.2462i 0.709544i 0.934953 + 0.354772i \(0.115441\pi\)
−0.934953 + 0.354772i \(0.884559\pi\)
\(984\) −1.56155 + 2.70469i −0.0497805 + 0.0862223i
\(985\) 0 0
\(986\) 1.75379 + 3.03765i 0.0558520 + 0.0967385i
\(987\) 14.2462i 0.453462i
\(988\) 3.29762 8.15009i 0.104911 0.259289i
\(989\) 3.36932 0.107138
\(990\) 0 0
\(991\) 9.97301 + 17.2738i 0.316803 + 0.548719i 0.979819 0.199886i \(-0.0640572\pi\)
−0.663016 + 0.748605i \(0.730724\pi\)
\(992\) −3.46410 2.00000i −0.109985 0.0635001i
\(993\) 16.6847i 0.529472i
\(994\) −22.3693 + 38.7448i −0.709512 + 1.22891i
\(995\) 0 0
\(996\) 6.56155 0.207911
\(997\) −23.9625 13.8348i −0.758900 0.438151i 0.0700008 0.997547i \(-0.477700\pi\)
−0.828901 + 0.559396i \(0.811033\pi\)
\(998\) −5.24290 + 3.02699i −0.165961 + 0.0958176i
\(999\) 0.280776 + 0.486319i 0.00888337 + 0.0153865i
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 1950.2.z.m.1849.4 8
5.2 odd 4 1950.2.i.bg.601.1 yes 4
5.3 odd 4 1950.2.i.z.601.2 yes 4
5.4 even 2 inner 1950.2.z.m.1849.1 8
13.9 even 3 inner 1950.2.z.m.1699.1 8
65.9 even 6 inner 1950.2.z.m.1699.4 8
65.22 odd 12 1950.2.i.bg.451.1 yes 4
65.48 odd 12 1950.2.i.z.451.2 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1950.2.i.z.451.2 4 65.48 odd 12
1950.2.i.z.601.2 yes 4 5.3 odd 4
1950.2.i.bg.451.1 yes 4 65.22 odd 12
1950.2.i.bg.601.1 yes 4 5.2 odd 4
1950.2.z.m.1699.1 8 13.9 even 3 inner
1950.2.z.m.1699.4 8 65.9 even 6 inner
1950.2.z.m.1849.1 8 5.4 even 2 inner
1950.2.z.m.1849.4 8 1.1 even 1 trivial