Properties

Label 1950.2.y.k.199.3
Level $1950$
Weight $2$
Character 1950.199
Analytic conductor $15.571$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1950,2,Mod(49,1950)]
 
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, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1950.49");
 
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.y (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: 8.0.17284886784.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 2x^{7} + 2x^{6} + 30x^{5} + 185x^{4} + 36x^{3} + 8x^{2} + 208x + 2704 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 390)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 199.3
Root \(3.17270 - 3.17270i\) of defining polynomial
Character \(\chi\) \(=\) 1950.199
Dual form 1950.2.y.k.49.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.866025 - 0.500000i) q^{6} +(-1.16129 - 2.01141i) q^{7} -1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.866025 - 0.500000i) q^{6} +(-1.16129 - 2.01141i) q^{7} -1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +(4.62926 + 2.67270i) q^{11} -1.00000i q^{12} +(0.161290 + 3.60194i) q^{13} -2.32258 q^{14} +(-0.500000 + 0.866025i) q^{16} +(-3.46410 + 2.00000i) q^{17} +1.00000 q^{18} +(3.48387 - 2.01141i) q^{19} -2.32258i q^{21} +(4.62926 - 2.67270i) q^{22} +(4.27464 + 2.46797i) q^{23} +(-0.866025 - 0.500000i) q^{24} +(3.20002 + 1.66129i) q^{26} +1.00000i q^{27} +(-1.16129 + 2.01141i) q^{28} +(2.14539 - 3.71592i) q^{29} +3.47183i q^{31} +(0.500000 + 0.866025i) q^{32} +(2.67270 + 4.62926i) q^{33} +4.00000i q^{34} +(0.500000 - 0.866025i) q^{36} +(1.57463 - 2.72733i) q^{37} -4.02283i q^{38} +(-1.66129 + 3.20002i) q^{39} +(2.29078 + 1.32258i) q^{41} +(-2.01141 - 1.16129i) q^{42} +(10.6095 - 6.12539i) q^{43} -5.34541i q^{44} +(4.27464 - 2.46797i) q^{46} +1.81894 q^{47} +(-0.866025 + 0.500000i) q^{48} +(0.802812 - 1.39051i) q^{49} -4.00000 q^{51} +(3.03873 - 1.94065i) q^{52} +5.48693i q^{53} +(0.866025 + 0.500000i) q^{54} +(1.16129 + 2.01141i) q^{56} +4.02283 q^{57} +(-2.14539 - 3.71592i) q^{58} +(-5.87744 + 3.39334i) q^{59} +(-0.267949 - 0.464102i) q^{61} +(3.00670 + 1.73592i) q^{62} +(1.16129 - 2.01141i) q^{63} +1.00000 q^{64} +5.34541 q^{66} +(-2.05463 + 3.55872i) q^{67} +(3.46410 + 2.00000i) q^{68} +(2.46797 + 4.27464i) q^{69} +(13.7454 - 7.93593i) q^{71} +(-0.500000 - 0.866025i) q^{72} -13.5734 q^{73} +(-1.57463 - 2.72733i) q^{74} +(-3.48387 - 2.01141i) q^{76} -12.4151i q^{77} +(1.94065 + 3.03873i) q^{78} +7.96774 q^{79} +(-0.500000 + 0.866025i) q^{81} +(2.29078 - 1.32258i) q^{82} -11.3360 q^{83} +(-2.01141 + 1.16129i) q^{84} -12.2508i q^{86} +(3.71592 - 2.14539i) q^{87} +(-4.62926 - 2.67270i) q^{88} +(1.50670 + 0.869891i) q^{89} +(7.05769 - 4.50732i) q^{91} -4.93593i q^{92} +(-1.73592 + 3.00670i) q^{93} +(0.909471 - 1.57525i) q^{94} +1.00000i q^{96} +(-8.05463 - 13.9510i) q^{97} +(-0.802812 - 1.39051i) q^{98} +5.34541i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 4 q^{2} - 4 q^{4} - 2 q^{7} - 8 q^{8} + 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 4 q^{2} - 4 q^{4} - 2 q^{7} - 8 q^{8} + 4 q^{9} + 6 q^{11} - 6 q^{13} - 4 q^{14} - 4 q^{16} + 8 q^{18} + 6 q^{19} + 6 q^{22} - 6 q^{23} - 12 q^{26} - 2 q^{28} + 8 q^{29} + 4 q^{32} - 2 q^{33} + 4 q^{36} + 10 q^{37} - 6 q^{39} + 48 q^{43} - 6 q^{46} + 16 q^{47} - 14 q^{49} - 32 q^{51} - 6 q^{52} + 2 q^{56} - 8 q^{58} - 24 q^{59} - 16 q^{61} - 30 q^{62} + 2 q^{63} + 8 q^{64} - 4 q^{66} + 12 q^{67} - 4 q^{69} - 12 q^{71} - 4 q^{72} - 24 q^{73} - 10 q^{74} - 6 q^{76} + 6 q^{78} + 20 q^{79} - 4 q^{81} + 32 q^{83} - 6 q^{87} - 6 q^{88} - 42 q^{89} - 10 q^{91} - 4 q^{93} + 8 q^{94} - 36 q^{97} + 14 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(301\) \(1301\) \(1327\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 0.866025i 0.353553 0.612372i
\(3\) 0.866025 + 0.500000i 0.500000 + 0.288675i
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 0 0
\(6\) 0.866025 0.500000i 0.353553 0.204124i
\(7\) −1.16129 2.01141i −0.438926 0.760243i 0.558681 0.829383i \(-0.311308\pi\)
−0.997607 + 0.0691402i \(0.977974\pi\)
\(8\) −1.00000 −0.353553
\(9\) 0.500000 + 0.866025i 0.166667 + 0.288675i
\(10\) 0 0
\(11\) 4.62926 + 2.67270i 1.39577 + 0.805850i 0.993946 0.109865i \(-0.0350420\pi\)
0.401827 + 0.915716i \(0.368375\pi\)
\(12\) 1.00000i 0.288675i
\(13\) 0.161290 + 3.60194i 0.0447338 + 0.998999i
\(14\) −2.32258 −0.620736
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −3.46410 + 2.00000i −0.840168 + 0.485071i −0.857321 0.514782i \(-0.827873\pi\)
0.0171533 + 0.999853i \(0.494540\pi\)
\(18\) 1.00000 0.235702
\(19\) 3.48387 2.01141i 0.799254 0.461450i −0.0439559 0.999033i \(-0.513996\pi\)
0.843210 + 0.537584i \(0.180663\pi\)
\(20\) 0 0
\(21\) 2.32258i 0.506828i
\(22\) 4.62926 2.67270i 0.986961 0.569822i
\(23\) 4.27464 + 2.46797i 0.891325 + 0.514607i 0.874376 0.485250i \(-0.161271\pi\)
0.0169494 + 0.999856i \(0.494605\pi\)
\(24\) −0.866025 0.500000i −0.176777 0.102062i
\(25\) 0 0
\(26\) 3.20002 + 1.66129i 0.627575 + 0.325806i
\(27\) 1.00000i 0.192450i
\(28\) −1.16129 + 2.01141i −0.219463 + 0.380121i
\(29\) 2.14539 3.71592i 0.398388 0.690029i −0.595139 0.803623i \(-0.702903\pi\)
0.993527 + 0.113594i \(0.0362363\pi\)
\(30\) 0 0
\(31\) 3.47183i 0.623560i 0.950154 + 0.311780i \(0.100925\pi\)
−0.950154 + 0.311780i \(0.899075\pi\)
\(32\) 0.500000 + 0.866025i 0.0883883 + 0.153093i
\(33\) 2.67270 + 4.62926i 0.465258 + 0.805850i
\(34\) 4.00000i 0.685994i
\(35\) 0 0
\(36\) 0.500000 0.866025i 0.0833333 0.144338i
\(37\) 1.57463 2.72733i 0.258867 0.448371i −0.707072 0.707142i \(-0.749984\pi\)
0.965939 + 0.258771i \(0.0833175\pi\)
\(38\) 4.02283i 0.652589i
\(39\) −1.66129 + 3.20002i −0.266019 + 0.512413i
\(40\) 0 0
\(41\) 2.29078 + 1.32258i 0.357759 + 0.206552i 0.668097 0.744074i \(-0.267109\pi\)
−0.310338 + 0.950626i \(0.600442\pi\)
\(42\) −2.01141 1.16129i −0.310368 0.179191i
\(43\) 10.6095 6.12539i 1.61793 0.934113i 0.630478 0.776207i \(-0.282859\pi\)
0.987454 0.157906i \(-0.0504744\pi\)
\(44\) 5.34541i 0.805850i
\(45\) 0 0
\(46\) 4.27464 2.46797i 0.630262 0.363882i
\(47\) 1.81894 0.265320 0.132660 0.991162i \(-0.457648\pi\)
0.132660 + 0.991162i \(0.457648\pi\)
\(48\) −0.866025 + 0.500000i −0.125000 + 0.0721688i
\(49\) 0.802812 1.39051i 0.114687 0.198644i
\(50\) 0 0
\(51\) −4.00000 −0.560112
\(52\) 3.03873 1.94065i 0.421396 0.269120i
\(53\) 5.48693i 0.753687i 0.926277 + 0.376844i \(0.122991\pi\)
−0.926277 + 0.376844i \(0.877009\pi\)
\(54\) 0.866025 + 0.500000i 0.117851 + 0.0680414i
\(55\) 0 0
\(56\) 1.16129 + 2.01141i 0.155184 + 0.268786i
\(57\) 4.02283 0.532836
\(58\) −2.14539 3.71592i −0.281703 0.487924i
\(59\) −5.87744 + 3.39334i −0.765177 + 0.441775i −0.831152 0.556046i \(-0.812318\pi\)
0.0659742 + 0.997821i \(0.478984\pi\)
\(60\) 0 0
\(61\) −0.267949 0.464102i −0.0343074 0.0594221i 0.848362 0.529417i \(-0.177589\pi\)
−0.882669 + 0.469995i \(0.844256\pi\)
\(62\) 3.00670 + 1.73592i 0.381851 + 0.220462i
\(63\) 1.16129 2.01141i 0.146309 0.253414i
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 5.34541 0.657974
\(67\) −2.05463 + 3.55872i −0.251013 + 0.434767i −0.963805 0.266608i \(-0.914097\pi\)
0.712792 + 0.701376i \(0.247430\pi\)
\(68\) 3.46410 + 2.00000i 0.420084 + 0.242536i
\(69\) 2.46797 + 4.27464i 0.297108 + 0.514607i
\(70\) 0 0
\(71\) 13.7454 7.93593i 1.63128 0.941822i 0.647586 0.761992i \(-0.275779\pi\)
0.983698 0.179830i \(-0.0575547\pi\)
\(72\) −0.500000 0.866025i −0.0589256 0.102062i
\(73\) −13.5734 −1.58864 −0.794321 0.607498i \(-0.792173\pi\)
−0.794321 + 0.607498i \(0.792173\pi\)
\(74\) −1.57463 2.72733i −0.183047 0.317046i
\(75\) 0 0
\(76\) −3.48387 2.01141i −0.399627 0.230725i
\(77\) 12.4151i 1.41484i
\(78\) 1.94065 + 3.03873i 0.219736 + 0.344068i
\(79\) 7.96774 0.896441 0.448220 0.893923i \(-0.352058\pi\)
0.448220 + 0.893923i \(0.352058\pi\)
\(80\) 0 0
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 2.29078 1.32258i 0.252974 0.146054i
\(83\) −11.3360 −1.24428 −0.622142 0.782904i \(-0.713737\pi\)
−0.622142 + 0.782904i \(0.713737\pi\)
\(84\) −2.01141 + 1.16129i −0.219463 + 0.126707i
\(85\) 0 0
\(86\) 12.2508i 1.32104i
\(87\) 3.71592 2.14539i 0.398388 0.230010i
\(88\) −4.62926 2.67270i −0.493480 0.284911i
\(89\) 1.50670 + 0.869891i 0.159709 + 0.0922083i 0.577725 0.816232i \(-0.303941\pi\)
−0.418015 + 0.908440i \(0.637274\pi\)
\(90\) 0 0
\(91\) 7.05769 4.50732i 0.739847 0.472495i
\(92\) 4.93593i 0.514607i
\(93\) −1.73592 + 3.00670i −0.180006 + 0.311780i
\(94\) 0.909471 1.57525i 0.0938048 0.162475i
\(95\) 0 0
\(96\) 1.00000i 0.102062i
\(97\) −8.05463 13.9510i −0.817824 1.41651i −0.907282 0.420522i \(-0.861847\pi\)
0.0894586 0.995991i \(-0.471486\pi\)
\(98\) −0.802812 1.39051i −0.0810962 0.140463i
\(99\) 5.34541i 0.537233i
\(100\) 0 0
\(101\) 6.34541 10.9906i 0.631391 1.09360i −0.355876 0.934533i \(-0.615817\pi\)
0.987267 0.159069i \(-0.0508492\pi\)
\(102\) −2.00000 + 3.46410i −0.198030 + 0.342997i
\(103\) 4.79612i 0.472575i 0.971683 + 0.236288i \(0.0759308\pi\)
−0.971683 + 0.236288i \(0.924069\pi\)
\(104\) −0.161290 3.60194i −0.0158158 0.353199i
\(105\) 0 0
\(106\) 4.75182 + 2.74346i 0.461537 + 0.266469i
\(107\) −2.66025 1.53590i −0.257176 0.148481i 0.365869 0.930666i \(-0.380772\pi\)
−0.623046 + 0.782185i \(0.714105\pi\)
\(108\) 0.866025 0.500000i 0.0833333 0.0481125i
\(109\) 6.69081i 0.640864i 0.947272 + 0.320432i \(0.103828\pi\)
−0.947272 + 0.320432i \(0.896172\pi\)
\(110\) 0 0
\(111\) 2.72733 1.57463i 0.258867 0.149457i
\(112\) 2.32258 0.219463
\(113\) 6.15720 3.55486i 0.579220 0.334413i −0.181603 0.983372i \(-0.558129\pi\)
0.760823 + 0.648959i \(0.224795\pi\)
\(114\) 2.01141 3.48387i 0.188386 0.326294i
\(115\) 0 0
\(116\) −4.29078 −0.398388
\(117\) −3.03873 + 1.94065i −0.280931 + 0.179413i
\(118\) 6.78668i 0.624765i
\(119\) 8.04565 + 4.64516i 0.737544 + 0.425821i
\(120\) 0 0
\(121\) 8.78668 + 15.2190i 0.798789 + 1.38354i
\(122\) −0.535898 −0.0485180
\(123\) 1.32258 + 2.29078i 0.119253 + 0.206552i
\(124\) 3.00670 1.73592i 0.270009 0.155890i
\(125\) 0 0
\(126\) −1.16129 2.01141i −0.103456 0.179191i
\(127\) −1.84644 1.06604i −0.163845 0.0945961i 0.415835 0.909440i \(-0.363489\pi\)
−0.579680 + 0.814844i \(0.696823\pi\)
\(128\) 0.500000 0.866025i 0.0441942 0.0765466i
\(129\) 12.2508 1.07862
\(130\) 0 0
\(131\) 1.25851 0.109957 0.0549785 0.998488i \(-0.482491\pi\)
0.0549785 + 0.998488i \(0.482491\pi\)
\(132\) 2.67270 4.62926i 0.232629 0.402925i
\(133\) −8.09156 4.67167i −0.701628 0.405085i
\(134\) 2.05463 + 3.55872i 0.177493 + 0.307427i
\(135\) 0 0
\(136\) 3.46410 2.00000i 0.297044 0.171499i
\(137\) 9.85744 + 17.0736i 0.842178 + 1.45870i 0.888049 + 0.459748i \(0.152060\pi\)
−0.0458713 + 0.998947i \(0.514606\pi\)
\(138\) 4.93593 0.420175
\(139\) 2.83871 + 4.91679i 0.240776 + 0.417037i 0.960936 0.276772i \(-0.0892647\pi\)
−0.720159 + 0.693809i \(0.755931\pi\)
\(140\) 0 0
\(141\) 1.57525 + 0.909471i 0.132660 + 0.0765913i
\(142\) 15.8719i 1.33194i
\(143\) −8.88027 + 17.1054i −0.742605 + 1.43043i
\(144\) −1.00000 −0.0833333
\(145\) 0 0
\(146\) −6.78668 + 11.7549i −0.561670 + 0.972841i
\(147\) 1.39051 0.802812i 0.114687 0.0662148i
\(148\) −3.14925 −0.258867
\(149\) 16.8680 9.73875i 1.38188 0.797829i 0.389499 0.921027i \(-0.372648\pi\)
0.992382 + 0.123198i \(0.0393150\pi\)
\(150\) 0 0
\(151\) 14.5170i 1.18138i 0.806899 + 0.590690i \(0.201144\pi\)
−0.806899 + 0.590690i \(0.798856\pi\)
\(152\) −3.48387 + 2.01141i −0.282579 + 0.163147i
\(153\) −3.46410 2.00000i −0.280056 0.161690i
\(154\) −10.7518 6.20757i −0.866406 0.500220i
\(155\) 0 0
\(156\) 3.60194 0.161290i 0.288386 0.0129135i
\(157\) 24.3829i 1.94596i 0.230879 + 0.972982i \(0.425840\pi\)
−0.230879 + 0.972982i \(0.574160\pi\)
\(158\) 3.98387 6.90026i 0.316940 0.548956i
\(159\) −2.74346 + 4.75182i −0.217571 + 0.376844i
\(160\) 0 0
\(161\) 11.4641i 0.903498i
\(162\) 0.500000 + 0.866025i 0.0392837 + 0.0680414i
\(163\) −11.8134 20.4614i −0.925295 1.60266i −0.791086 0.611704i \(-0.790484\pi\)
−0.134208 0.990953i \(-0.542849\pi\)
\(164\) 2.64516i 0.206552i
\(165\) 0 0
\(166\) −5.66799 + 9.81724i −0.439921 + 0.761966i
\(167\) −8.37357 + 14.5035i −0.647967 + 1.12231i 0.335641 + 0.941990i \(0.391047\pi\)
−0.983608 + 0.180321i \(0.942286\pi\)
\(168\) 2.32258i 0.179191i
\(169\) −12.9480 + 1.16191i −0.995998 + 0.0893780i
\(170\) 0 0
\(171\) 3.48387 + 2.01141i 0.266418 + 0.153817i
\(172\) −10.6095 6.12539i −0.808966 0.467057i
\(173\) 13.9708 8.06604i 1.06218 0.613250i 0.136146 0.990689i \(-0.456529\pi\)
0.926034 + 0.377439i \(0.123195\pi\)
\(174\) 4.29078i 0.325283i
\(175\) 0 0
\(176\) −4.62926 + 2.67270i −0.348943 + 0.201463i
\(177\) −6.78668 −0.510118
\(178\) 1.50670 0.869891i 0.112932 0.0652011i
\(179\) −3.66412 + 6.34644i −0.273869 + 0.474355i −0.969849 0.243706i \(-0.921637\pi\)
0.695980 + 0.718061i \(0.254970\pi\)
\(180\) 0 0
\(181\) −19.5734 −1.45488 −0.727438 0.686173i \(-0.759289\pi\)
−0.727438 + 0.686173i \(0.759289\pi\)
\(182\) −0.374609 8.36580i −0.0277678 0.620114i
\(183\) 0.535898i 0.0396147i
\(184\) −4.27464 2.46797i −0.315131 0.181941i
\(185\) 0 0
\(186\) 1.73592 + 3.00670i 0.127284 + 0.220462i
\(187\) −21.3816 −1.56358
\(188\) −0.909471 1.57525i −0.0663300 0.114887i
\(189\) 2.01141 1.16129i 0.146309 0.0844714i
\(190\) 0 0
\(191\) 8.51873 + 14.7549i 0.616394 + 1.06763i 0.990138 + 0.140094i \(0.0447404\pi\)
−0.373744 + 0.927532i \(0.621926\pi\)
\(192\) 0.866025 + 0.500000i 0.0625000 + 0.0360844i
\(193\) 3.07746 5.33031i 0.221520 0.383684i −0.733750 0.679420i \(-0.762231\pi\)
0.955270 + 0.295736i \(0.0955648\pi\)
\(194\) −16.1093 −1.15658
\(195\) 0 0
\(196\) −1.60562 −0.114687
\(197\) 6.89334 11.9396i 0.491130 0.850662i −0.508818 0.860874i \(-0.669917\pi\)
0.999948 + 0.0102119i \(0.00325060\pi\)
\(198\) 4.62926 + 2.67270i 0.328987 + 0.189941i
\(199\) −1.14152 1.97717i −0.0809203 0.140158i 0.822725 0.568439i \(-0.192453\pi\)
−0.903646 + 0.428281i \(0.859119\pi\)
\(200\) 0 0
\(201\) −3.55872 + 2.05463i −0.251013 + 0.144922i
\(202\) −6.34541 10.9906i −0.446461 0.773293i
\(203\) −9.96567 −0.699453
\(204\) 2.00000 + 3.46410i 0.140028 + 0.242536i
\(205\) 0 0
\(206\) 4.15356 + 2.39806i 0.289392 + 0.167081i
\(207\) 4.93593i 0.343071i
\(208\) −3.20002 1.66129i −0.221881 0.115190i
\(209\) 21.5036 1.48744
\(210\) 0 0
\(211\) −11.2387 + 19.4661i −0.773707 + 1.34010i 0.161811 + 0.986822i \(0.448267\pi\)
−0.935518 + 0.353278i \(0.885067\pi\)
\(212\) 4.75182 2.74346i 0.326356 0.188422i
\(213\) 15.8719 1.08752
\(214\) −2.66025 + 1.53590i −0.181851 + 0.104992i
\(215\) 0 0
\(216\) 1.00000i 0.0680414i
\(217\) 6.98329 4.03180i 0.474057 0.273697i
\(218\) 5.79441 + 3.34541i 0.392447 + 0.226579i
\(219\) −11.7549 6.78668i −0.794321 0.458601i
\(220\) 0 0
\(221\) −7.76261 12.1549i −0.522170 0.817628i
\(222\) 3.14925i 0.211364i
\(223\) 0.689457 1.19417i 0.0461694 0.0799678i −0.842017 0.539451i \(-0.818632\pi\)
0.888187 + 0.459483i \(0.151965\pi\)
\(224\) 1.16129 2.01141i 0.0775919 0.134393i
\(225\) 0 0
\(226\) 7.10972i 0.472931i
\(227\) −9.66025 16.7321i −0.641174 1.11055i −0.985171 0.171575i \(-0.945115\pi\)
0.343998 0.938971i \(-0.388219\pi\)
\(228\) −2.01141 3.48387i −0.133209 0.230725i
\(229\) 15.7626i 1.04162i 0.853672 + 0.520811i \(0.174370\pi\)
−0.853672 + 0.520811i \(0.825630\pi\)
\(230\) 0 0
\(231\) 6.20757 10.7518i 0.408428 0.707418i
\(232\) −2.14539 + 3.71592i −0.140852 + 0.243962i
\(233\) 16.5549i 1.08455i 0.840201 + 0.542275i \(0.182437\pi\)
−0.840201 + 0.542275i \(0.817563\pi\)
\(234\) 0.161290 + 3.60194i 0.0105438 + 0.235466i
\(235\) 0 0
\(236\) 5.87744 + 3.39334i 0.382589 + 0.220888i
\(237\) 6.90026 + 3.98387i 0.448220 + 0.258780i
\(238\) 8.04565 4.64516i 0.521522 0.301101i
\(239\) 26.2006i 1.69477i −0.530976 0.847387i \(-0.678175\pi\)
0.530976 0.847387i \(-0.321825\pi\)
\(240\) 0 0
\(241\) −13.5529 + 7.82479i −0.873021 + 0.504039i −0.868351 0.495950i \(-0.834820\pi\)
−0.00466988 + 0.999989i \(0.501486\pi\)
\(242\) 17.5734 1.12966
\(243\) −0.866025 + 0.500000i −0.0555556 + 0.0320750i
\(244\) −0.267949 + 0.464102i −0.0171537 + 0.0297111i
\(245\) 0 0
\(246\) 2.64516 0.168649
\(247\) 7.80691 + 12.2243i 0.496742 + 0.777812i
\(248\) 3.47183i 0.220462i
\(249\) −9.81724 5.66799i −0.622142 0.359194i
\(250\) 0 0
\(251\) −14.1708 24.5446i −0.894454 1.54924i −0.834479 0.551040i \(-0.814231\pi\)
−0.0599750 0.998200i \(-0.519102\pi\)
\(252\) −2.32258 −0.146309
\(253\) 13.1923 + 22.8497i 0.829392 + 1.43655i
\(254\) −1.84644 + 1.06604i −0.115856 + 0.0668895i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −10.8334 6.25465i −0.675767 0.390154i 0.122491 0.992470i \(-0.460912\pi\)
−0.798258 + 0.602315i \(0.794245\pi\)
\(258\) 6.12539 10.6095i 0.381350 0.660518i
\(259\) −7.31439 −0.454494
\(260\) 0 0
\(261\) 4.29078 0.265592
\(262\) 0.629257 1.08991i 0.0388756 0.0673346i
\(263\) −9.27159 5.35295i −0.571711 0.330077i 0.186122 0.982527i \(-0.440408\pi\)
−0.757832 + 0.652449i \(0.773741\pi\)
\(264\) −2.67270 4.62926i −0.164493 0.284911i
\(265\) 0 0
\(266\) −8.09156 + 4.67167i −0.496126 + 0.286438i
\(267\) 0.869891 + 1.50670i 0.0532365 + 0.0922083i
\(268\) 4.10926 0.251013
\(269\) 3.76261 + 6.51703i 0.229410 + 0.397350i 0.957633 0.287990i \(-0.0929869\pi\)
−0.728223 + 0.685340i \(0.759654\pi\)
\(270\) 0 0
\(271\) 8.52920 + 4.92434i 0.518112 + 0.299132i 0.736162 0.676805i \(-0.236636\pi\)
−0.218050 + 0.975938i \(0.569970\pi\)
\(272\) 4.00000i 0.242536i
\(273\) 8.36580 0.374609i 0.506321 0.0226723i
\(274\) 19.7149 1.19102
\(275\) 0 0
\(276\) 2.46797 4.27464i 0.148554 0.257303i
\(277\) −0.825410 + 0.476550i −0.0495941 + 0.0286331i −0.524592 0.851354i \(-0.675782\pi\)
0.474998 + 0.879987i \(0.342449\pi\)
\(278\) 5.67742 0.340509
\(279\) −3.00670 + 1.73592i −0.180006 + 0.103927i
\(280\) 0 0
\(281\) 5.57336i 0.332479i −0.986085 0.166239i \(-0.946838\pi\)
0.986085 0.166239i \(-0.0531625\pi\)
\(282\) 1.57525 0.909471i 0.0938048 0.0541582i
\(283\) −19.0642 11.0067i −1.13325 0.654280i −0.188497 0.982074i \(-0.560362\pi\)
−0.944749 + 0.327794i \(0.893695\pi\)
\(284\) −13.7454 7.93593i −0.815642 0.470911i
\(285\) 0 0
\(286\) 10.3736 + 16.2432i 0.613402 + 0.960483i
\(287\) 6.14359i 0.362645i
\(288\) −0.500000 + 0.866025i −0.0294628 + 0.0510310i
\(289\) −0.500000 + 0.866025i −0.0294118 + 0.0509427i
\(290\) 0 0
\(291\) 16.1093i 0.944342i
\(292\) 6.78668 + 11.7549i 0.397160 + 0.687902i
\(293\) −3.42151 5.92623i −0.199887 0.346214i 0.748605 0.663016i \(-0.230724\pi\)
−0.948491 + 0.316803i \(0.897391\pi\)
\(294\) 1.60562i 0.0936419i
\(295\) 0 0
\(296\) −1.57463 + 2.72733i −0.0915233 + 0.158523i
\(297\) −2.67270 + 4.62926i −0.155086 + 0.268617i
\(298\) 19.4775i 1.12830i
\(299\) −8.20002 + 15.7951i −0.474219 + 0.913453i
\(300\) 0 0
\(301\) −24.6414 14.2267i −1.42031 0.820014i
\(302\) 12.5721 + 7.25851i 0.723444 + 0.417681i
\(303\) 10.9906 6.34541i 0.631391 0.364534i
\(304\) 4.02283i 0.230725i
\(305\) 0 0
\(306\) −3.46410 + 2.00000i −0.198030 + 0.114332i
\(307\) 4.75442 0.271349 0.135675 0.990753i \(-0.456680\pi\)
0.135675 + 0.990753i \(0.456680\pi\)
\(308\) −10.7518 + 6.20757i −0.612642 + 0.353709i
\(309\) −2.39806 + 4.15356i −0.136421 + 0.236288i
\(310\) 0 0
\(311\) 1.93639 0.109803 0.0549013 0.998492i \(-0.482516\pi\)
0.0549013 + 0.998492i \(0.482516\pi\)
\(312\) 1.66129 3.20002i 0.0940520 0.181165i
\(313\) 25.5545i 1.44443i −0.691671 0.722213i \(-0.743125\pi\)
0.691671 0.722213i \(-0.256875\pi\)
\(314\) 21.1162 + 12.1914i 1.19166 + 0.688002i
\(315\) 0 0
\(316\) −3.98387 6.90026i −0.224110 0.388170i
\(317\) 12.6667 0.711435 0.355717 0.934594i \(-0.384237\pi\)
0.355717 + 0.934594i \(0.384237\pi\)
\(318\) 2.74346 + 4.75182i 0.153846 + 0.266469i
\(319\) 19.8631 11.4680i 1.11212 0.642083i
\(320\) 0 0
\(321\) −1.53590 2.66025i −0.0857255 0.148481i
\(322\) −9.92820 5.73205i −0.553277 0.319435i
\(323\) −8.04565 + 13.9355i −0.447672 + 0.775391i
\(324\) 1.00000 0.0555556
\(325\) 0 0
\(326\) −23.6267 −1.30856
\(327\) −3.34541 + 5.79441i −0.185001 + 0.320432i
\(328\) −2.29078 1.32258i −0.126487 0.0730272i
\(329\) −2.11232 3.65864i −0.116456 0.201708i
\(330\) 0 0
\(331\) −20.5231 + 11.8490i −1.12805 + 0.651282i −0.943445 0.331530i \(-0.892435\pi\)
−0.184609 + 0.982812i \(0.559102\pi\)
\(332\) 5.66799 + 9.81724i 0.311071 + 0.538791i
\(333\) 3.14925 0.172578
\(334\) 8.37357 + 14.5035i 0.458182 + 0.793594i
\(335\) 0 0
\(336\) 2.01141 + 1.16129i 0.109732 + 0.0633536i
\(337\) 19.5554i 1.06525i 0.846351 + 0.532625i \(0.178795\pi\)
−0.846351 + 0.532625i \(0.821205\pi\)
\(338\) −5.46774 + 11.7942i −0.297406 + 0.641521i
\(339\) 7.10972 0.386147
\(340\) 0 0
\(341\) −9.27918 + 16.0720i −0.502496 + 0.870348i
\(342\) 3.48387 2.01141i 0.188386 0.108765i
\(343\) −19.9872 −1.07921
\(344\) −10.6095 + 6.12539i −0.572025 + 0.330259i
\(345\) 0 0
\(346\) 16.1321i 0.867266i
\(347\) −19.9510 + 11.5187i −1.07103 + 0.618358i −0.928462 0.371427i \(-0.878868\pi\)
−0.142565 + 0.989785i \(0.545535\pi\)
\(348\) −3.71592 2.14539i −0.199194 0.115005i
\(349\) −13.2679 7.66025i −0.710217 0.410044i 0.100924 0.994894i \(-0.467820\pi\)
−0.811141 + 0.584850i \(0.801153\pi\)
\(350\) 0 0
\(351\) −3.60194 + 0.161290i −0.192257 + 0.00860902i
\(352\) 5.34541i 0.284911i
\(353\) 14.2039 24.6018i 0.755996 1.30942i −0.188881 0.982000i \(-0.560486\pi\)
0.944877 0.327424i \(-0.106181\pi\)
\(354\) −3.39334 + 5.87744i −0.180354 + 0.312382i
\(355\) 0 0
\(356\) 1.73978i 0.0922083i
\(357\) 4.64516 + 8.04565i 0.245848 + 0.425821i
\(358\) 3.66412 + 6.34644i 0.193655 + 0.335420i
\(359\) 23.5734i 1.24415i −0.782956 0.622077i \(-0.786289\pi\)
0.782956 0.622077i \(-0.213711\pi\)
\(360\) 0 0
\(361\) −1.40844 + 2.43948i −0.0741282 + 0.128394i
\(362\) −9.78668 + 16.9510i −0.514377 + 0.890926i
\(363\) 17.5734i 0.922362i
\(364\) −7.43230 3.85848i −0.389558 0.202239i
\(365\) 0 0
\(366\) −0.464102 0.267949i −0.0242590 0.0140059i
\(367\) −23.8078 13.7454i −1.24276 0.717506i −0.273103 0.961985i \(-0.588050\pi\)
−0.969655 + 0.244479i \(0.921383\pi\)
\(368\) −4.27464 + 2.46797i −0.222831 + 0.128652i
\(369\) 2.64516i 0.137701i
\(370\) 0 0
\(371\) 11.0365 6.37191i 0.572985 0.330813i
\(372\) 3.47183 0.180006
\(373\) −22.8129 + 13.1710i −1.18121 + 0.681971i −0.956294 0.292408i \(-0.905544\pi\)
−0.224914 + 0.974379i \(0.572210\pi\)
\(374\) −10.6908 + 18.5170i −0.552809 + 0.957493i
\(375\) 0 0
\(376\) −1.81894 −0.0938048
\(377\) 13.7306 + 7.12822i 0.707160 + 0.367122i
\(378\) 2.32258i 0.119461i
\(379\) −0.388456 0.224275i −0.0199537 0.0115202i 0.489990 0.871728i \(-0.337000\pi\)
−0.509944 + 0.860208i \(0.670334\pi\)
\(380\) 0 0
\(381\) −1.06604 1.84644i −0.0546151 0.0945961i
\(382\) 17.0375 0.871713
\(383\) −6.06133 10.4985i −0.309719 0.536450i 0.668582 0.743639i \(-0.266902\pi\)
−0.978301 + 0.207189i \(0.933568\pi\)
\(384\) 0.866025 0.500000i 0.0441942 0.0255155i
\(385\) 0 0
\(386\) −3.07746 5.33031i −0.156638 0.271306i
\(387\) 10.6095 + 6.12539i 0.539311 + 0.311371i
\(388\) −8.05463 + 13.9510i −0.408912 + 0.708256i
\(389\) −18.6195 −0.944045 −0.472022 0.881587i \(-0.656476\pi\)
−0.472022 + 0.881587i \(0.656476\pi\)
\(390\) 0 0
\(391\) −19.7437 −0.998484
\(392\) −0.802812 + 1.39051i −0.0405481 + 0.0702314i
\(393\) 1.08991 + 0.629257i 0.0549785 + 0.0317418i
\(394\) −6.89334 11.9396i −0.347281 0.601509i
\(395\) 0 0
\(396\) 4.62926 2.67270i 0.232629 0.134308i
\(397\) 5.65208 + 9.78970i 0.283670 + 0.491331i 0.972286 0.233796i \(-0.0751147\pi\)
−0.688616 + 0.725126i \(0.741781\pi\)
\(398\) −2.28304 −0.114439
\(399\) −4.67167 8.09156i −0.233876 0.405085i
\(400\) 0 0
\(401\) −1.30406 0.752899i −0.0651216 0.0375980i 0.467086 0.884212i \(-0.345304\pi\)
−0.532207 + 0.846614i \(0.678637\pi\)
\(402\) 4.10926i 0.204951i
\(403\) −12.5053 + 0.559971i −0.622935 + 0.0278942i
\(404\) −12.6908 −0.631391
\(405\) 0 0
\(406\) −4.98283 + 8.63052i −0.247294 + 0.428326i
\(407\) 14.5787 8.41702i 0.722640 0.417216i
\(408\) 4.00000 0.198030
\(409\) −9.64697 + 5.56968i −0.477012 + 0.275403i −0.719170 0.694834i \(-0.755478\pi\)
0.242158 + 0.970237i \(0.422145\pi\)
\(410\) 0 0
\(411\) 19.7149i 0.972464i
\(412\) 4.15356 2.39806i 0.204631 0.118144i
\(413\) 13.6508 + 7.88130i 0.671713 + 0.387814i
\(414\) 4.27464 + 2.46797i 0.210087 + 0.121294i
\(415\) 0 0
\(416\) −3.03873 + 1.94065i −0.148986 + 0.0951483i
\(417\) 5.67742i 0.278024i
\(418\) 10.7518 18.6227i 0.525889 0.910866i
\(419\) −7.75488 + 13.4318i −0.378851 + 0.656188i −0.990895 0.134635i \(-0.957014\pi\)
0.612045 + 0.790823i \(0.290347\pi\)
\(420\) 0 0
\(421\) 39.4452i 1.92244i −0.275778 0.961221i \(-0.588935\pi\)
0.275778 0.961221i \(-0.411065\pi\)
\(422\) 11.2387 + 19.4661i 0.547094 + 0.947594i
\(423\) 0.909471 + 1.57525i 0.0442200 + 0.0765913i
\(424\) 5.48693i 0.266469i
\(425\) 0 0
\(426\) 7.93593 13.7454i 0.384497 0.665969i
\(427\) −0.622333 + 1.07791i −0.0301168 + 0.0521639i
\(428\) 3.07180i 0.148481i
\(429\) −16.2432 + 10.3736i −0.784231 + 0.500841i
\(430\) 0 0
\(431\) 1.86621 + 1.07746i 0.0898921 + 0.0518993i 0.544272 0.838909i \(-0.316806\pi\)
−0.454380 + 0.890808i \(0.650139\pi\)
\(432\) −0.866025 0.500000i −0.0416667 0.0240563i
\(433\) 1.15994 0.669689i 0.0557429 0.0321832i −0.471870 0.881668i \(-0.656421\pi\)
0.527612 + 0.849485i \(0.323087\pi\)
\(434\) 8.06361i 0.387066i
\(435\) 0 0
\(436\) 5.79441 3.34541i 0.277502 0.160216i
\(437\) 19.8564 0.949861
\(438\) −11.7549 + 6.78668i −0.561670 + 0.324280i
\(439\) 15.8490 27.4513i 0.756434 1.31018i −0.188225 0.982126i \(-0.560273\pi\)
0.944658 0.328055i \(-0.106393\pi\)
\(440\) 0 0
\(441\) 1.60562 0.0764583
\(442\) −14.4078 + 0.645159i −0.685308 + 0.0306871i
\(443\) 28.0904i 1.33461i 0.744782 + 0.667307i \(0.232553\pi\)
−0.744782 + 0.667307i \(0.767447\pi\)
\(444\) −2.72733 1.57463i −0.129434 0.0747285i
\(445\) 0 0
\(446\) −0.689457 1.19417i −0.0326467 0.0565458i
\(447\) 19.4775 0.921254
\(448\) −1.16129 2.01141i −0.0548658 0.0950303i
\(449\) −25.0426 + 14.4583i −1.18183 + 0.682332i −0.956438 0.291936i \(-0.905701\pi\)
−0.225395 + 0.974267i \(0.572367\pi\)
\(450\) 0 0
\(451\) 7.06973 + 12.2451i 0.332900 + 0.576600i
\(452\) −6.15720 3.55486i −0.289610 0.167206i
\(453\) −7.25851 + 12.5721i −0.341035 + 0.590690i
\(454\) −19.3205 −0.906756
\(455\) 0 0
\(456\) −4.02283 −0.188386
\(457\) −4.84950 + 8.39958i −0.226850 + 0.392916i −0.956873 0.290507i \(-0.906176\pi\)
0.730023 + 0.683423i \(0.239509\pi\)
\(458\) 13.6508 + 7.88130i 0.637861 + 0.368269i
\(459\) −2.00000 3.46410i −0.0933520 0.161690i
\(460\) 0 0
\(461\) 10.3905 5.99896i 0.483934 0.279400i −0.238120 0.971236i \(-0.576531\pi\)
0.722055 + 0.691836i \(0.243198\pi\)
\(462\) −6.20757 10.7518i −0.288802 0.500220i
\(463\) 6.42664 0.298671 0.149336 0.988787i \(-0.452287\pi\)
0.149336 + 0.988787i \(0.452287\pi\)
\(464\) 2.14539 + 3.71592i 0.0995971 + 0.172507i
\(465\) 0 0
\(466\) 14.3370 + 8.27747i 0.664149 + 0.383447i
\(467\) 26.2642i 1.21536i 0.794182 + 0.607681i \(0.207900\pi\)
−0.794182 + 0.607681i \(0.792100\pi\)
\(468\) 3.20002 + 1.66129i 0.147921 + 0.0767932i
\(469\) 9.54409 0.440705
\(470\) 0 0
\(471\) −12.1914 + 21.1162i −0.561752 + 0.972982i
\(472\) 5.87744 3.39334i 0.270531 0.156191i
\(473\) 65.4854 3.01102
\(474\) 6.90026 3.98387i 0.316940 0.182985i
\(475\) 0 0
\(476\) 9.29032i 0.425821i
\(477\) −4.75182 + 2.74346i −0.217571 + 0.125615i
\(478\) −22.6904 13.1003i −1.03783 0.599193i
\(479\) 22.2418 + 12.8413i 1.01625 + 0.586735i 0.913017 0.407922i \(-0.133747\pi\)
0.103237 + 0.994657i \(0.467080\pi\)
\(480\) 0 0
\(481\) 10.0777 + 5.23182i 0.459502 + 0.238551i
\(482\) 15.6496i 0.712818i
\(483\) 5.73205 9.92820i 0.260817 0.451749i
\(484\) 8.78668 15.2190i 0.399395 0.691772i
\(485\) 0 0
\(486\) 1.00000i 0.0453609i
\(487\) −4.68946 8.12238i −0.212500 0.368060i 0.739997 0.672611i \(-0.234827\pi\)
−0.952496 + 0.304551i \(0.901494\pi\)
\(488\) 0.267949 + 0.464102i 0.0121295 + 0.0210089i
\(489\) 23.6267i 1.06844i
\(490\) 0 0
\(491\) −3.86927 + 6.70177i −0.174618 + 0.302447i −0.940029 0.341095i \(-0.889202\pi\)
0.765411 + 0.643541i \(0.222536\pi\)
\(492\) 1.32258 2.29078i 0.0596265 0.103276i
\(493\) 17.1631i 0.772987i
\(494\) 14.4900 0.648841i 0.651935 0.0291927i
\(495\) 0 0
\(496\) −3.00670 1.73592i −0.135005 0.0779450i
\(497\) −31.9249 18.4318i −1.43203 0.826781i
\(498\) −9.81724 + 5.66799i −0.439921 + 0.253989i
\(499\) 3.18106i 0.142404i −0.997462 0.0712019i \(-0.977317\pi\)
0.997462 0.0712019i \(-0.0226834\pi\)
\(500\) 0 0
\(501\) −14.5035 + 8.37357i −0.647967 + 0.374104i
\(502\) −28.3416 −1.26495
\(503\) 30.3765 17.5379i 1.35442 0.781975i 0.365556 0.930789i \(-0.380879\pi\)
0.988865 + 0.148814i \(0.0475456\pi\)
\(504\) −1.16129 + 2.01141i −0.0517280 + 0.0895955i
\(505\) 0 0
\(506\) 26.3846 1.17294
\(507\) −11.7942 5.46774i −0.523800 0.242831i
\(508\) 2.13209i 0.0945961i
\(509\) 16.2697 + 9.39334i 0.721144 + 0.416353i 0.815173 0.579217i \(-0.196642\pi\)
−0.0940298 + 0.995569i \(0.529975\pi\)
\(510\) 0 0
\(511\) 15.7626 + 27.3016i 0.697297 + 1.20775i
\(512\) −1.00000 −0.0441942
\(513\) 2.01141 + 3.48387i 0.0888061 + 0.153817i
\(514\) −10.8334 + 6.25465i −0.477839 + 0.275881i
\(515\) 0 0
\(516\) −6.12539 10.6095i −0.269655 0.467057i
\(517\) 8.42035 + 4.86149i 0.370327 + 0.213808i
\(518\) −3.65720 + 6.33445i −0.160688 + 0.278320i
\(519\) 16.1321 0.708120
\(520\) 0 0
\(521\) 5.28512 0.231545 0.115773 0.993276i \(-0.463066\pi\)
0.115773 + 0.993276i \(0.463066\pi\)
\(522\) 2.14539 3.71592i 0.0939011 0.162641i
\(523\) −17.9721 10.3762i −0.785863 0.453718i 0.0526409 0.998614i \(-0.483236\pi\)
−0.838504 + 0.544895i \(0.816569\pi\)
\(524\) −0.629257 1.08991i −0.0274892 0.0476127i
\(525\) 0 0
\(526\) −9.27159 + 5.35295i −0.404260 + 0.233400i
\(527\) −6.94367 12.0268i −0.302471 0.523895i
\(528\) −5.34541 −0.232629
\(529\) 0.681725 + 1.18078i 0.0296402 + 0.0513384i
\(530\) 0 0
\(531\) −5.87744 3.39334i −0.255059 0.147258i
\(532\) 9.34333i 0.405085i
\(533\) −4.39438 + 8.46456i −0.190342 + 0.366641i
\(534\) 1.73978 0.0752877
\(535\) 0 0
\(536\) 2.05463 3.55872i 0.0887465 0.153713i
\(537\) −6.34644 + 3.66412i −0.273869 + 0.158118i
\(538\) 7.52522 0.324435
\(539\) 7.43284 4.29135i 0.320155 0.184842i
\(540\) 0 0
\(541\) 28.7365i 1.23548i −0.786384 0.617739i \(-0.788049\pi\)
0.786384 0.617739i \(-0.211951\pi\)
\(542\) 8.52920 4.92434i 0.366361 0.211518i
\(543\) −16.9510 9.78668i −0.727438 0.419987i
\(544\) −3.46410 2.00000i −0.148522 0.0857493i
\(545\) 0 0
\(546\) 3.85848 7.43230i 0.165128 0.318073i
\(547\) 18.3768i 0.785737i 0.919595 + 0.392869i \(0.128517\pi\)
−0.919595 + 0.392869i \(0.871483\pi\)
\(548\) 9.85744 17.0736i 0.421089 0.729348i
\(549\) 0.267949 0.464102i 0.0114358 0.0198074i
\(550\) 0 0
\(551\) 17.2610i 0.735345i
\(552\) −2.46797 4.27464i −0.105044 0.181941i
\(553\) −9.25285 16.0264i −0.393471 0.681512i
\(554\) 0.953101i 0.0404934i
\(555\) 0 0
\(556\) 2.83871 4.91679i 0.120388 0.208518i
\(557\) −13.2693 + 22.9831i −0.562238 + 0.973826i 0.435062 + 0.900400i \(0.356726\pi\)
−0.997301 + 0.0734252i \(0.976607\pi\)
\(558\) 3.47183i 0.146974i
\(559\) 23.7745 + 37.2268i 1.00555 + 1.57453i
\(560\) 0 0
\(561\) −18.5170 10.6908i −0.781790 0.451366i
\(562\) −4.82667 2.78668i −0.203601 0.117549i
\(563\) −5.24908 + 3.03056i −0.221222 + 0.127723i −0.606516 0.795071i \(-0.707433\pi\)
0.385294 + 0.922794i \(0.374100\pi\)
\(564\) 1.81894i 0.0765913i
\(565\) 0 0
\(566\) −19.0642 + 11.0067i −0.801326 + 0.462646i
\(567\) 2.32258 0.0975392
\(568\) −13.7454 + 7.93593i −0.576746 + 0.332984i
\(569\) 7.24818 12.5542i 0.303860 0.526300i −0.673147 0.739509i \(-0.735058\pi\)
0.977007 + 0.213208i \(0.0683913\pi\)
\(570\) 0 0
\(571\) −2.90413 −0.121534 −0.0607670 0.998152i \(-0.519355\pi\)
−0.0607670 + 0.998152i \(0.519355\pi\)
\(572\) 19.2538 0.862160i 0.805044 0.0360487i
\(573\) 17.0375i 0.711750i
\(574\) −5.32051 3.07180i −0.222074 0.128214i
\(575\) 0 0
\(576\) 0.500000 + 0.866025i 0.0208333 + 0.0360844i
\(577\) 18.8180 0.783405 0.391702 0.920092i \(-0.371886\pi\)
0.391702 + 0.920092i \(0.371886\pi\)
\(578\) 0.500000 + 0.866025i 0.0207973 + 0.0360219i
\(579\) 5.33031 3.07746i 0.221520 0.127895i
\(580\) 0 0
\(581\) 13.1643 + 22.8013i 0.546149 + 0.945958i
\(582\) −13.9510 8.05463i −0.578289 0.333875i
\(583\) −14.6649 + 25.4004i −0.607359 + 1.05198i
\(584\) 13.5734 0.561670
\(585\) 0 0
\(586\) −6.84302 −0.282682
\(587\) 1.96820 3.40901i 0.0812361 0.140705i −0.822545 0.568700i \(-0.807447\pi\)
0.903781 + 0.427995i \(0.140780\pi\)
\(588\) −1.39051 0.802812i −0.0573437 0.0331074i
\(589\) 6.98329 + 12.0954i 0.287741 + 0.498383i
\(590\) 0 0
\(591\) 11.9396 6.89334i 0.491130 0.283554i
\(592\) 1.57463 + 2.72733i 0.0647168 + 0.112093i
\(593\) 20.1227 0.826338 0.413169 0.910654i \(-0.364422\pi\)
0.413169 + 0.910654i \(0.364422\pi\)
\(594\) 2.67270 + 4.62926i 0.109662 + 0.189941i
\(595\) 0 0
\(596\) −16.8680 9.73875i −0.690940 0.398915i
\(597\) 2.28304i 0.0934388i
\(598\) 9.57893 + 14.9990i 0.391712 + 0.613353i
\(599\) −48.1172 −1.96601 −0.983007 0.183567i \(-0.941236\pi\)
−0.983007 + 0.183567i \(0.941236\pi\)
\(600\) 0 0
\(601\) 2.12109 3.67383i 0.0865209 0.149859i −0.819517 0.573054i \(-0.805758\pi\)
0.906038 + 0.423196i \(0.139092\pi\)
\(602\) −24.6414 + 14.2267i −1.00431 + 0.579837i
\(603\) −4.10926 −0.167342
\(604\) 12.5721 7.25851i 0.511552 0.295345i
\(605\) 0 0
\(606\) 12.6908i 0.515529i
\(607\) 10.4516 6.03424i 0.424218 0.244922i −0.272663 0.962110i \(-0.587904\pi\)
0.696880 + 0.717188i \(0.254571\pi\)
\(608\) 3.48387 + 2.01141i 0.141290 + 0.0815736i
\(609\) −8.63052 4.98283i −0.349726 0.201915i
\(610\) 0 0
\(611\) 0.293377 + 6.55172i 0.0118688 + 0.265054i
\(612\) 4.00000i 0.161690i
\(613\) 20.8711 36.1497i 0.842974 1.46007i −0.0443946 0.999014i \(-0.514136\pi\)
0.887369 0.461060i \(-0.152531\pi\)
\(614\) 2.37721 4.11745i 0.0959364 0.166167i
\(615\) 0 0
\(616\) 12.4151i 0.500220i
\(617\) −16.7293 28.9760i −0.673497 1.16653i −0.976906 0.213670i \(-0.931458\pi\)
0.303409 0.952860i \(-0.401875\pi\)
\(618\) 2.39806 + 4.15356i 0.0964640 + 0.167081i
\(619\) 38.0978i 1.53128i −0.643270 0.765639i \(-0.722423\pi\)
0.643270 0.765639i \(-0.277577\pi\)
\(620\) 0 0
\(621\) −2.46797 + 4.27464i −0.0990361 + 0.171536i
\(622\) 0.968196 1.67696i 0.0388211 0.0672401i
\(623\) 4.04078i 0.161891i
\(624\) −1.94065 3.03873i −0.0776883 0.121646i
\(625\) 0 0
\(626\) −22.1308 12.7772i −0.884526 0.510681i
\(627\) 18.6227 + 10.7518i 0.743719 + 0.429386i
\(628\) 21.1162 12.1914i 0.842628 0.486491i
\(629\) 12.5970i 0.502276i
\(630\) 0 0
\(631\) −21.4775 + 12.4000i −0.855005 + 0.493638i −0.862337 0.506335i \(-0.831000\pi\)
0.00733109 + 0.999973i \(0.497666\pi\)
\(632\) −7.96774 −0.316940
\(633\) −19.4661 + 11.2387i −0.773707 + 0.446700i
\(634\) 6.33337 10.9697i 0.251530 0.435663i
\(635\) 0 0
\(636\) 5.48693 0.217571
\(637\) 5.13802 + 2.66741i 0.203576 + 0.105686i
\(638\) 22.9359i 0.908042i
\(639\) 13.7454 + 7.93593i 0.543761 + 0.313941i
\(640\) 0 0
\(641\) 2.04259 + 3.53788i 0.0806776 + 0.139738i 0.903541 0.428501i \(-0.140958\pi\)
−0.822864 + 0.568239i \(0.807625\pi\)
\(642\) −3.07180 −0.121234
\(643\) 18.2908 + 31.6806i 0.721318 + 1.24936i 0.960472 + 0.278377i \(0.0897966\pi\)
−0.239154 + 0.970982i \(0.576870\pi\)
\(644\) −9.92820 + 5.73205i −0.391226 + 0.225874i
\(645\) 0 0
\(646\) 8.04565 + 13.9355i 0.316552 + 0.548284i
\(647\) 14.9251 + 8.61704i 0.586768 + 0.338771i 0.763818 0.645431i \(-0.223322\pi\)
−0.177050 + 0.984202i \(0.556656\pi\)
\(648\) 0.500000 0.866025i 0.0196419 0.0340207i
\(649\) −36.2776 −1.42402
\(650\) 0 0
\(651\) 8.06361 0.316038
\(652\) −11.8134 + 20.4614i −0.462647 + 0.801329i
\(653\) −18.9897 10.9637i −0.743123 0.429042i 0.0800806 0.996788i \(-0.474482\pi\)
−0.823204 + 0.567746i \(0.807816\pi\)
\(654\) 3.34541 + 5.79441i 0.130816 + 0.226579i
\(655\) 0 0
\(656\) −2.29078 + 1.32258i −0.0894397 + 0.0516381i
\(657\) −6.78668 11.7549i −0.264774 0.458601i
\(658\) −4.22464 −0.164694
\(659\) −24.2379 41.9813i −0.944176 1.63536i −0.757393 0.652960i \(-0.773527\pi\)
−0.186783 0.982401i \(-0.559806\pi\)
\(660\) 0 0
\(661\) −25.8267 14.9110i −1.00454 0.579972i −0.0949524 0.995482i \(-0.530270\pi\)
−0.909589 + 0.415510i \(0.863603\pi\)
\(662\) 23.6981i 0.921052i
\(663\) −0.645159 14.4078i −0.0250559 0.559551i
\(664\) 11.3360 0.439921
\(665\) 0 0
\(666\) 1.57463 2.72733i 0.0610155 0.105682i
\(667\) 18.3415 10.5895i 0.710187 0.410027i
\(668\) 16.7471 0.647967
\(669\) 1.19417 0.689457i 0.0461694 0.0266559i
\(670\) 0 0
\(671\) 2.86459i 0.110586i
\(672\) 2.01141 1.16129i 0.0775919 0.0447977i
\(673\) 26.5627 + 15.3360i 1.02392 + 0.591158i 0.915236 0.402919i \(-0.132004\pi\)
0.108680 + 0.994077i \(0.465338\pi\)
\(674\) 16.9355 + 9.77770i 0.652330 + 0.376623i
\(675\) 0 0
\(676\) 7.48023 + 10.6323i 0.287701 + 0.408935i
\(677\) 21.0831i 0.810290i 0.914252 + 0.405145i \(0.132779\pi\)
−0.914252 + 0.405145i \(0.867221\pi\)
\(678\) 3.55486 6.15720i 0.136524 0.236466i
\(679\) −18.7075 + 32.4024i −0.717929 + 1.24349i
\(680\) 0 0
\(681\) 19.3205i 0.740363i
\(682\) 9.27918 + 16.0720i 0.355318 + 0.615429i
\(683\) 6.66799 + 11.5493i 0.255143 + 0.441921i 0.964934 0.262491i \(-0.0845440\pi\)
−0.709791 + 0.704412i \(0.751211\pi\)
\(684\) 4.02283i 0.153817i
\(685\) 0 0
\(686\) −9.99362 + 17.3095i −0.381558 + 0.660878i
\(687\) −7.88130 + 13.6508i −0.300691 + 0.520811i
\(688\) 12.2508i 0.467057i
\(689\) −19.7636 + 0.884986i −0.752933 + 0.0337153i
\(690\) 0 0
\(691\) −30.2289 17.4527i −1.14996 0.663932i −0.201085 0.979574i \(-0.564447\pi\)
−0.948878 + 0.315642i \(0.897780\pi\)
\(692\) −13.9708 8.06604i −0.531090 0.306625i
\(693\) 10.7518 6.20757i 0.408428 0.235806i
\(694\) 23.0375i 0.874490i
\(695\) 0 0
\(696\) −3.71592 + 2.14539i −0.140852 + 0.0813207i
\(697\) −10.5806 −0.400770
\(698\) −13.2679 + 7.66025i −0.502199 + 0.289945i
\(699\) −8.27747 + 14.3370i −0.313083 + 0.542275i
\(700\) 0 0
\(701\) 39.6715 1.49837 0.749186 0.662360i \(-0.230445\pi\)
0.749186 + 0.662360i \(0.230445\pi\)
\(702\) −1.66129 + 3.20002i −0.0627013 + 0.120777i
\(703\) 12.6689i 0.477817i
\(704\) 4.62926 + 2.67270i 0.174472 + 0.100731i
\(705\) 0 0
\(706\) −14.2039 24.6018i −0.534570 0.925903i
\(707\) −29.4754 −1.10854
\(708\) 3.39334 + 5.87744i 0.127530 + 0.220888i
\(709\) −2.45467 + 1.41720i −0.0921869 + 0.0532242i −0.545385 0.838186i \(-0.683616\pi\)
0.453198 + 0.891410i \(0.350283\pi\)
\(710\) 0 0
\(711\) 3.98387 + 6.90026i 0.149407 + 0.258780i
\(712\) −1.50670 0.869891i −0.0564658 0.0326005i
\(713\) −8.56837 + 14.8409i −0.320888 + 0.555794i
\(714\) 9.29032 0.347681
\(715\) 0 0
\(716\) 7.32824 0.273869
\(717\) 13.1003 22.6904i 0.489239 0.847387i
\(718\) −20.4151 11.7867i −0.761886 0.439875i
\(719\) 21.8564 + 37.8564i 0.815106 + 1.41181i 0.909251 + 0.416247i \(0.136655\pi\)
−0.0941451 + 0.995558i \(0.530012\pi\)
\(720\) 0 0
\(721\) 9.64697 5.56968i 0.359272 0.207426i
\(722\) 1.40844 + 2.43948i 0.0524165 + 0.0907881i
\(723\) −15.6496 −0.582014
\(724\) 9.78668 + 16.9510i 0.363719 + 0.629980i
\(725\) 0 0
\(726\) 15.2190 + 8.78668i 0.564829 + 0.326104i
\(727\) 16.2568i 0.602932i −0.953477 0.301466i \(-0.902524\pi\)
0.953477 0.301466i \(-0.0974759\pi\)
\(728\) −7.05769 + 4.50732i −0.261575 + 0.167052i
\(729\) −1.00000 −0.0370370
\(730\) 0 0
\(731\) −24.5016 + 42.4380i −0.906223 + 1.56962i
\(732\) −0.464102 + 0.267949i −0.0171537 + 0.00990369i
\(733\) 4.96774 0.183488 0.0917438 0.995783i \(-0.470756\pi\)
0.0917438 + 0.995783i \(0.470756\pi\)
\(734\) −23.8078 + 13.7454i −0.878762 + 0.507354i
\(735\) 0 0
\(736\) 4.93593i 0.181941i
\(737\) −19.0228 + 10.9828i −0.700715 + 0.404558i
\(738\) 2.29078 + 1.32258i 0.0843246 + 0.0486848i
\(739\) −43.0306 24.8437i −1.58291 0.913892i −0.994432 0.105377i \(-0.966395\pi\)
−0.588475 0.808515i \(-0.700271\pi\)
\(740\) 0 0
\(741\) 0.648841 + 14.4900i 0.0238358 + 0.532303i
\(742\) 12.7438i 0.467841i
\(743\) 10.7710 18.6559i 0.395150 0.684420i −0.597970 0.801518i \(-0.704026\pi\)
0.993120 + 0.117098i \(0.0373593\pi\)
\(744\) 1.73592 3.00670i 0.0636418 0.110231i
\(745\) 0 0
\(746\) 26.3421i 0.964452i
\(747\) −5.66799 9.81724i −0.207381 0.359194i
\(748\) 10.6908 + 18.5170i 0.390895 + 0.677050i
\(749\) 7.13449i 0.260689i
\(750\) 0 0
\(751\) −3.17436 + 5.49816i −0.115834 + 0.200631i −0.918113 0.396319i \(-0.870287\pi\)
0.802279 + 0.596950i \(0.203621\pi\)
\(752\) −0.909471 + 1.57525i −0.0331650 + 0.0574435i
\(753\) 28.3416i 1.03283i
\(754\) 13.0385 8.32690i 0.474834 0.303248i
\(755\) 0 0
\(756\) −2.01141 1.16129i −0.0731544 0.0422357i
\(757\) 41.6651 + 24.0554i 1.51434 + 0.874307i 0.999859 + 0.0168078i \(0.00535036\pi\)
0.514485 + 0.857499i \(0.327983\pi\)
\(758\) −0.388456 + 0.224275i −0.0141094 + 0.00814604i
\(759\) 26.3846i 0.957699i
\(760\) 0 0
\(761\) 29.1734 16.8433i 1.05754 0.610569i 0.132786 0.991145i \(-0.457608\pi\)
0.924750 + 0.380576i \(0.124274\pi\)
\(762\) −2.13209 −0.0772374
\(763\) 13.4580 7.76997i 0.487212 0.281292i
\(764\) 8.51873 14.7549i 0.308197 0.533813i
\(765\) 0 0
\(766\) −12.1227 −0.438009
\(767\) −13.1706 20.6229i −0.475562 0.744649i
\(768\) 1.00000i 0.0360844i
\(769\) 5.18651 + 2.99443i 0.187030 + 0.107982i 0.590592 0.806971i \(-0.298894\pi\)
−0.403561 + 0.914953i \(0.632228\pi\)
\(770\) 0 0
\(771\) −6.25465 10.8334i −0.225256 0.390154i
\(772\) −6.15491 −0.221520
\(773\) −6.74409 11.6811i −0.242568 0.420140i 0.718877 0.695137i \(-0.244656\pi\)
−0.961445 + 0.274997i \(0.911323\pi\)
\(774\) 10.6095 6.12539i 0.381350 0.220173i
\(775\) 0 0
\(776\) 8.05463 + 13.9510i 0.289144 + 0.500813i
\(777\) −6.33445 3.65720i −0.227247 0.131201i
\(778\) −9.30974 + 16.1249i −0.333770 + 0.578107i
\(779\) 10.6410 0.381254
\(780\) 0 0
\(781\) 84.8416 3.03587
\(782\) −9.87187 + 17.0986i −0.353017 + 0.611444i
\(783\) 3.71592 + 2.14539i 0.132796 + 0.0766699i
\(784\) 0.802812 + 1.39051i 0.0286718 + 0.0496611i
\(785\) 0 0
\(786\) 1.08991 0.629257i 0.0388756 0.0224449i
\(787\) −27.3244 47.3272i −0.974009 1.68703i −0.683168 0.730261i \(-0.739398\pi\)
−0.290841 0.956772i \(-0.593935\pi\)
\(788\) −13.7867 −0.491130
\(789\) −5.35295 9.27159i −0.190570 0.330077i
\(790\) 0 0
\(791\) −14.3006 8.25644i −0.508470 0.293565i
\(792\) 5.34541i 0.189941i
\(793\) 1.62845 1.03999i 0.0578279 0.0369312i
\(794\) 11.3042 0.401170
\(795\) 0 0
\(796\) −1.14152 + 1.97717i −0.0404602 + 0.0700791i
\(797\) 33.1899 19.1622i 1.17565 0.678760i 0.220643 0.975355i \(-0.429185\pi\)
0.955003 + 0.296595i \(0.0958512\pi\)
\(798\) −9.34333 −0.330750
\(799\) −6.30100 + 3.63788i −0.222913 + 0.128699i
\(800\) 0 0
\(801\) 1.73978i 0.0614722i
\(802\) −1.30406 + 0.752899i −0.0460479 + 0.0265858i
\(803\) −62.8346 36.2776i −2.21738 1.28021i
\(804\) 3.55872 + 2.05463i 0.125507 + 0.0724612i
\(805\) 0 0
\(806\) −5.76772 + 11.1099i −0.203159 + 0.391331i
\(807\) 7.52522i 0.264900i
\(808\) −6.34541 + 10.9906i −0.223231 + 0.386647i
\(809\) 5.69081 9.85677i 0.200078 0.346546i −0.748475 0.663163i \(-0.769214\pi\)
0.948553 + 0.316617i \(0.102547\pi\)
\(810\) 0 0
\(811\) 10.8899i 0.382397i −0.981551 0.191198i \(-0.938763\pi\)
0.981551 0.191198i \(-0.0612374\pi\)
\(812\) 4.98283 + 8.63052i 0.174863 + 0.302872i
\(813\) 4.92434 + 8.52920i 0.172704 + 0.299132i
\(814\) 16.8340i 0.590033i
\(815\) 0 0
\(816\) 2.00000 3.46410i 0.0700140 0.121268i
\(817\) 24.6414 42.6801i 0.862093 1.49319i
\(818\) 11.1394i 0.389479i
\(819\) 7.43230 + 3.85848i 0.259705 + 0.134826i
\(820\) 0 0
\(821\) −1.46194 0.844051i −0.0510220 0.0294576i 0.474272 0.880378i \(-0.342711\pi\)
−0.525294 + 0.850921i \(0.676045\pi\)
\(822\) 17.0736 + 9.85744i 0.595510 + 0.343818i
\(823\) 5.87006 3.38908i 0.204617 0.118136i −0.394190 0.919029i \(-0.628975\pi\)
0.598807 + 0.800893i \(0.295641\pi\)
\(824\) 4.79612i 0.167081i
\(825\) 0 0
\(826\) 13.6508 7.88130i 0.474973 0.274226i
\(827\) 30.2298 1.05119 0.525597 0.850733i \(-0.323842\pi\)
0.525597 + 0.850733i \(0.323842\pi\)
\(828\) 4.27464 2.46797i 0.148554 0.0857678i
\(829\) 5.22023 9.04170i 0.181306 0.314031i −0.761020 0.648729i \(-0.775301\pi\)
0.942326 + 0.334698i \(0.108634\pi\)
\(830\) 0 0
\(831\) −0.953101 −0.0330627
\(832\) 0.161290 + 3.60194i 0.00559172 + 0.124875i
\(833\) 6.42249i 0.222526i
\(834\) 4.91679 + 2.83871i 0.170255 + 0.0982965i
\(835\) 0 0
\(836\) −10.7518 18.6227i −0.371859 0.644079i
\(837\) −3.47183 −0.120004
\(838\) 7.75488 + 13.4318i 0.267888 + 0.463995i
\(839\) −9.69647 + 5.59826i −0.334759 + 0.193273i −0.657952 0.753060i \(-0.728577\pi\)
0.323193 + 0.946333i \(0.395244\pi\)
\(840\) 0 0
\(841\) 5.29462 + 9.17056i 0.182573 + 0.316226i
\(842\) −34.1606 19.7226i −1.17725 0.679686i
\(843\) 2.78668 4.82667i 0.0959784 0.166239i
\(844\) 22.4775 0.773707
\(845\) 0 0
\(846\) 1.81894 0.0625365
\(847\) 20.4078 35.3473i 0.701219 1.21455i
\(848\) −4.75182 2.74346i −0.163178 0.0942109i
\(849\) −11.0067 19.0642i −0.377749 0.654280i
\(850\) 0 0
\(851\) 13.4619 7.77225i 0.461469 0.266429i
\(852\) −7.93593 13.7454i −0.271881 0.470911i
\(853\) 21.8185 0.747051 0.373525 0.927620i \(-0.378149\pi\)
0.373525 + 0.927620i \(0.378149\pi\)
\(854\) 0.622333 + 1.07791i 0.0212958 + 0.0368854i
\(855\) 0 0
\(856\) 2.66025 + 1.53590i 0.0909256 + 0.0524959i
\(857\) 9.42369i 0.321907i −0.986962 0.160954i \(-0.948543\pi\)
0.986962 0.160954i \(-0.0514569\pi\)
\(858\) 0.862160 + 19.2538i 0.0294336 + 0.657315i
\(859\) −24.4775 −0.835161 −0.417581 0.908640i \(-0.637122\pi\)
−0.417581 + 0.908640i \(0.637122\pi\)
\(860\) 0 0
\(861\) 3.07180 5.32051i 0.104687 0.181322i
\(862\) 1.86621 1.07746i 0.0635633 0.0366983i
\(863\) −29.7873 −1.01397 −0.506986 0.861954i \(-0.669240\pi\)
−0.506986 + 0.861954i \(0.669240\pi\)
\(864\) −0.866025 + 0.500000i −0.0294628 + 0.0170103i
\(865\) 0 0
\(866\) 1.33938i 0.0455139i
\(867\) −0.866025 + 0.500000i −0.0294118 + 0.0169809i
\(868\) −6.98329 4.03180i −0.237028 0.136848i
\(869\) 36.8847 + 21.2954i 1.25123 + 0.722397i
\(870\) 0 0
\(871\) −13.1497 6.82667i −0.445561 0.231313i
\(872\) 6.69081i 0.226579i
\(873\) 8.05463 13.9510i 0.272608 0.472171i
\(874\) 9.92820 17.1962i 0.335826 0.581669i
\(875\) 0 0
\(876\) 13.5734i 0.458601i
\(877\) 0.954895 + 1.65393i 0.0322445 + 0.0558491i 0.881697 0.471815i \(-0.156401\pi\)
−0.849453 + 0.527665i \(0.823068\pi\)
\(878\) −15.8490 27.4513i −0.534879 0.926438i
\(879\) 6.84302i 0.230809i
\(880\) 0 0
\(881\) 3.18412 5.51505i 0.107276 0.185807i −0.807390 0.590018i \(-0.799121\pi\)
0.914666 + 0.404211i \(0.132454\pi\)
\(882\) 0.802812 1.39051i 0.0270321 0.0468209i
\(883\) 34.9897i 1.17750i 0.808316 + 0.588749i \(0.200379\pi\)
−0.808316 + 0.588749i \(0.799621\pi\)
\(884\) −6.64516 + 12.8001i −0.223501 + 0.430513i
\(885\) 0 0
\(886\) 24.3270 + 14.0452i 0.817281 + 0.471858i
\(887\) −18.5331 10.7001i −0.622279 0.359273i 0.155477 0.987840i \(-0.450309\pi\)
−0.777756 + 0.628567i \(0.783642\pi\)
\(888\) −2.72733 + 1.57463i −0.0915233 + 0.0528410i
\(889\) 4.95194i 0.166083i
\(890\) 0 0
\(891\) −4.62926 + 2.67270i −0.155086 + 0.0895389i
\(892\) −1.37891 −0.0461694
\(893\) 6.33696 3.65864i 0.212058 0.122432i
\(894\) 9.73875 16.8680i 0.325712 0.564150i
\(895\) 0 0
\(896\) −2.32258 −0.0775919
\(897\) −14.9990 + 9.57893i −0.500801 + 0.319831i
\(898\) 28.9167i 0.964963i
\(899\) 12.9011 + 7.44843i 0.430274 + 0.248419i
\(900\) 0 0
\(901\) −10.9739 19.0073i −0.365592 0.633224i
\(902\) 14.1395 0.470792
\(903\) −14.2267 24.6414i −0.473435 0.820014i
\(904\) −6.15720 + 3.55486i −0.204785 + 0.118233i
\(905\) 0 0
\(906\) 7.25851 + 12.5721i 0.241148 + 0.417681i
\(907\) 28.1192 + 16.2347i 0.933684 + 0.539063i 0.887975 0.459892i \(-0.152112\pi\)
0.0457093 + 0.998955i \(0.485445\pi\)
\(908\) −9.66025 + 16.7321i −0.320587 + 0.555273i
\(909\) 12.6908 0.420928
\(910\) 0 0
\(911\) 34.4380 1.14098 0.570490 0.821304i \(-0.306753\pi\)
0.570490 + 0.821304i \(0.306753\pi\)
\(912\) −2.01141 + 3.48387i −0.0666045 + 0.115362i
\(913\) −52.4771 30.2977i −1.73674 1.00271i
\(914\) 4.84950 + 8.39958i 0.160407 + 0.277833i
\(915\) 0 0
\(916\) 13.6508 7.88130i 0.451036 0.260406i
\(917\) −1.46150 2.53139i −0.0482630 0.0835939i
\(918\) −4.00000 −0.132020
\(919\) 18.2413 + 31.5949i 0.601727 + 1.04222i 0.992560 + 0.121759i \(0.0388536\pi\)
−0.390833 + 0.920462i \(0.627813\pi\)
\(920\) 0 0
\(921\) 4.11745 + 2.37721i 0.135675 + 0.0783317i
\(922\) 11.9979i 0.395131i
\(923\) 30.8018 + 48.2303i 1.01385 + 1.58752i
\(924\) −12.4151 −0.408428
\(925\) 0 0
\(926\) 3.21332 5.56563i 0.105596 0.182898i
\(927\) −4.15356 + 2.39806i −0.136421 + 0.0787626i
\(928\) 4.29078 0.140852
\(929\) −43.2233 + 24.9550i −1.41811 + 0.818747i −0.996133 0.0878597i \(-0.971997\pi\)
−0.421978 + 0.906606i \(0.638664\pi\)
\(930\) 0 0
\(931\) 6.45914i 0.211690i
\(932\) 14.3370 8.27747i 0.469624 0.271138i
\(933\) 1.67696 + 0.968196i 0.0549013 + 0.0316973i
\(934\) 22.7454 + 13.1321i 0.744254 + 0.429695i
\(935\) 0 0
\(936\) 3.03873 1.94065i 0.0993239 0.0634322i
\(937\) 15.8873i 0.519017i −0.965741 0.259508i \(-0.916440\pi\)
0.965741 0.259508i \(-0.0835605\pi\)
\(938\) 4.77204 8.26542i 0.155813 0.269876i
\(939\) 12.7772 22.1308i 0.416970 0.722213i
\(940\) 0 0
\(941\) 6.99273i 0.227956i 0.993483 + 0.113978i \(0.0363594\pi\)
−0.993483 + 0.113978i \(0.963641\pi\)
\(942\) 12.1914 + 21.1162i 0.397218 + 0.688002i
\(943\) 6.52817 + 11.3071i 0.212586 + 0.368210i
\(944\) 6.78668i 0.220888i
\(945\) 0 0
\(946\) 32.7427 56.7120i 1.06456 1.84387i
\(947\) 26.1532 45.2987i 0.849865 1.47201i −0.0314631 0.999505i \(-0.510017\pi\)
0.881328 0.472505i \(-0.156650\pi\)
\(948\) 7.96774i 0.258780i
\(949\) −2.18925 48.8905i −0.0710659 1.58705i
\(950\) 0 0
\(951\) 10.9697 + 6.33337i 0.355717 + 0.205374i
\(952\) −8.04565 4.64516i −0.260761 0.150550i
\(953\) 25.0132 14.4414i 0.810256 0.467802i −0.0367885 0.999323i \(-0.511713\pi\)
0.847045 + 0.531521i \(0.178379\pi\)
\(954\) 5.48693i 0.177646i
\(955\) 0 0
\(956\) −22.6904 + 13.1003i −0.733859 + 0.423693i
\(957\) 22.9359 0.741413
\(958\) 22.2418 12.8413i 0.718600 0.414884i
\(959\) 22.8947 39.6548i 0.739308 1.28052i
\(960\) 0 0
\(961\) 18.9464 0.611173
\(962\) 9.56973 6.11160i 0.308540 0.197046i
\(963\) 3.07180i 0.0989873i
\(964\) 13.5529 + 7.82479i 0.436510 + 0.252019i
\(965\) 0 0
\(966\) −5.73205 9.92820i −0.184426 0.319435i
\(967\) −10.8610 −0.349265 −0.174633 0.984634i \(-0.555874\pi\)
−0.174633 + 0.984634i \(0.555874\pi\)
\(968\) −8.78668 15.2190i −0.282415 0.489156i
\(969\) −13.9355 + 8.04565i −0.447672 + 0.258464i
\(970\) 0 0
\(971\) 12.4990 + 21.6488i 0.401111 + 0.694744i 0.993860 0.110643i \(-0.0352909\pi\)
−0.592749 + 0.805387i \(0.701958\pi\)
\(972\) 0.866025 + 0.500000i 0.0277778 + 0.0160375i
\(973\) 6.59313 11.4196i 0.211366 0.366097i
\(974\) −9.37891 −0.300520
\(975\) 0 0
\(976\) 0.535898 0.0171537
\(977\) 21.3827 37.0359i 0.684092 1.18488i −0.289629 0.957139i \(-0.593532\pi\)
0.973721 0.227743i \(-0.0731346\pi\)
\(978\) −20.4614 11.8134i −0.654282 0.377750i
\(979\) 4.64992 + 8.05390i 0.148612 + 0.257404i
\(980\) 0 0
\(981\) −5.79441 + 3.34541i −0.185001 + 0.106811i
\(982\) 3.86927 + 6.70177i 0.123473 + 0.213862i
\(983\) −10.1288 −0.323058 −0.161529 0.986868i \(-0.551642\pi\)
−0.161529 + 0.986868i \(0.551642\pi\)
\(984\) −1.32258 2.29078i −0.0421623 0.0730272i
\(985\) 0 0
\(986\) 14.8637 + 8.58155i 0.473356 + 0.273292i
\(987\) 4.22464i 0.134472i
\(988\) 6.68308 12.8731i 0.212617 0.409548i
\(989\) 60.4691 1.92280
\(990\) 0 0
\(991\) −10.1241 + 17.5355i −0.321604 + 0.557035i −0.980819 0.194920i \(-0.937555\pi\)
0.659215 + 0.751954i \(0.270889\pi\)
\(992\) −3.00670 + 1.73592i −0.0954627 + 0.0551154i
\(993\) −23.6981 −0.752036
\(994\) −31.9249 + 18.4318i −1.01260 + 0.584622i
\(995\) 0 0
\(996\) 11.3360i 0.359194i
\(997\) −18.0100 + 10.3981i −0.570381 + 0.329310i −0.757302 0.653065i \(-0.773483\pi\)
0.186920 + 0.982375i \(0.440149\pi\)
\(998\) −2.75488 1.59053i −0.0872041 0.0503473i
\(999\) 2.72733 + 1.57463i 0.0862890 + 0.0498190i
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.y.k.199.3 8
5.2 odd 4 1950.2.bc.g.901.4 8
5.3 odd 4 390.2.bb.c.121.1 8
5.4 even 2 1950.2.y.j.199.2 8
13.10 even 6 1950.2.y.j.49.2 8
15.8 even 4 1170.2.bs.f.901.3 8
65.23 odd 12 390.2.bb.c.361.1 yes 8
65.33 even 12 5070.2.a.bz.1.2 4
65.43 odd 12 5070.2.b.ba.1351.3 8
65.48 odd 12 5070.2.b.ba.1351.6 8
65.49 even 6 inner 1950.2.y.k.49.3 8
65.58 even 12 5070.2.a.ca.1.3 4
65.62 odd 12 1950.2.bc.g.751.4 8
195.23 even 12 1170.2.bs.f.361.3 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
390.2.bb.c.121.1 8 5.3 odd 4
390.2.bb.c.361.1 yes 8 65.23 odd 12
1170.2.bs.f.361.3 8 195.23 even 12
1170.2.bs.f.901.3 8 15.8 even 4
1950.2.y.j.49.2 8 13.10 even 6
1950.2.y.j.199.2 8 5.4 even 2
1950.2.y.k.49.3 8 65.49 even 6 inner
1950.2.y.k.199.3 8 1.1 even 1 trivial
1950.2.bc.g.751.4 8 65.62 odd 12
1950.2.bc.g.901.4 8 5.2 odd 4
5070.2.a.bz.1.2 4 65.33 even 12
5070.2.a.ca.1.3 4 65.58 even 12
5070.2.b.ba.1351.3 8 65.43 odd 12
5070.2.b.ba.1351.6 8 65.48 odd 12