Properties

Label 338.2.c.b.191.1
Level $338$
Weight $2$
Character 338.191
Analytic conductor $2.699$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [338,2,Mod(191,338)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(338, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("338.191");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 338 = 2 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 338.c (of order \(3\), 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: \(2.69894358832\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 26)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 191.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 338.191
Dual form 338.2.c.b.315.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} -3.00000 q^{5} +(0.500000 + 0.866025i) q^{6} +(1.50000 + 2.59808i) q^{7} +1.00000 q^{8} +(1.00000 + 1.73205i) q^{9} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} -3.00000 q^{5} +(0.500000 + 0.866025i) q^{6} +(1.50000 + 2.59808i) q^{7} +1.00000 q^{8} +(1.00000 + 1.73205i) q^{9} +(1.50000 - 2.59808i) q^{10} -1.00000 q^{12} -3.00000 q^{14} +(-1.50000 + 2.59808i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.50000 + 2.59808i) q^{17} -2.00000 q^{18} +(3.00000 + 5.19615i) q^{19} +(1.50000 + 2.59808i) q^{20} +3.00000 q^{21} +(-3.00000 + 5.19615i) q^{23} +(0.500000 - 0.866025i) q^{24} +4.00000 q^{25} +5.00000 q^{27} +(1.50000 - 2.59808i) q^{28} +(-1.50000 - 2.59808i) q^{30} +(-0.500000 - 0.866025i) q^{32} -3.00000 q^{34} +(-4.50000 - 7.79423i) q^{35} +(1.00000 - 1.73205i) q^{36} +(1.50000 - 2.59808i) q^{37} -6.00000 q^{38} -3.00000 q^{40} +(-1.50000 + 2.59808i) q^{42} +(-0.500000 - 0.866025i) q^{43} +(-3.00000 - 5.19615i) q^{45} +(-3.00000 - 5.19615i) q^{46} -3.00000 q^{47} +(0.500000 + 0.866025i) q^{48} +(-1.00000 + 1.73205i) q^{49} +(-2.00000 + 3.46410i) q^{50} +3.00000 q^{51} -6.00000 q^{53} +(-2.50000 + 4.33013i) q^{54} +(1.50000 + 2.59808i) q^{56} +6.00000 q^{57} +(-3.00000 - 5.19615i) q^{59} +3.00000 q^{60} +(4.00000 + 6.92820i) q^{61} +(-3.00000 + 5.19615i) q^{63} +1.00000 q^{64} +(6.00000 - 10.3923i) q^{67} +(1.50000 - 2.59808i) q^{68} +(3.00000 + 5.19615i) q^{69} +9.00000 q^{70} +(-7.50000 - 12.9904i) q^{71} +(1.00000 + 1.73205i) q^{72} -6.00000 q^{73} +(1.50000 + 2.59808i) q^{74} +(2.00000 - 3.46410i) q^{75} +(3.00000 - 5.19615i) q^{76} +10.0000 q^{79} +(1.50000 - 2.59808i) q^{80} +(-0.500000 + 0.866025i) q^{81} +6.00000 q^{83} +(-1.50000 - 2.59808i) q^{84} +(-4.50000 - 7.79423i) q^{85} +1.00000 q^{86} +(-3.00000 + 5.19615i) q^{89} +6.00000 q^{90} +6.00000 q^{92} +(1.50000 - 2.59808i) q^{94} +(-9.00000 - 15.5885i) q^{95} -1.00000 q^{96} +(6.00000 + 10.3923i) q^{97} +(-1.00000 - 1.73205i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - q^{2} + q^{3} - q^{4} - 6 q^{5} + q^{6} + 3 q^{7} + 2 q^{8} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - q^{2} + q^{3} - q^{4} - 6 q^{5} + q^{6} + 3 q^{7} + 2 q^{8} + 2 q^{9} + 3 q^{10} - 2 q^{12} - 6 q^{14} - 3 q^{15} - q^{16} + 3 q^{17} - 4 q^{18} + 6 q^{19} + 3 q^{20} + 6 q^{21} - 6 q^{23} + q^{24} + 8 q^{25} + 10 q^{27} + 3 q^{28} - 3 q^{30} - q^{32} - 6 q^{34} - 9 q^{35} + 2 q^{36} + 3 q^{37} - 12 q^{38} - 6 q^{40} - 3 q^{42} - q^{43} - 6 q^{45} - 6 q^{46} - 6 q^{47} + q^{48} - 2 q^{49} - 4 q^{50} + 6 q^{51} - 12 q^{53} - 5 q^{54} + 3 q^{56} + 12 q^{57} - 6 q^{59} + 6 q^{60} + 8 q^{61} - 6 q^{63} + 2 q^{64} + 12 q^{67} + 3 q^{68} + 6 q^{69} + 18 q^{70} - 15 q^{71} + 2 q^{72} - 12 q^{73} + 3 q^{74} + 4 q^{75} + 6 q^{76} + 20 q^{79} + 3 q^{80} - q^{81} + 12 q^{83} - 3 q^{84} - 9 q^{85} + 2 q^{86} - 6 q^{89} + 12 q^{90} + 12 q^{92} + 3 q^{94} - 18 q^{95} - 2 q^{96} + 12 q^{97} - 2 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/338\mathbb{Z}\right)^\times\).

\(n\) \(171\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 + 0.866025i −0.353553 + 0.612372i
\(3\) 0.500000 0.866025i 0.288675 0.500000i −0.684819 0.728714i \(-0.740119\pi\)
0.973494 + 0.228714i \(0.0734519\pi\)
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) −3.00000 −1.34164 −0.670820 0.741620i \(-0.734058\pi\)
−0.670820 + 0.741620i \(0.734058\pi\)
\(6\) 0.500000 + 0.866025i 0.204124 + 0.353553i
\(7\) 1.50000 + 2.59808i 0.566947 + 0.981981i 0.996866 + 0.0791130i \(0.0252088\pi\)
−0.429919 + 0.902867i \(0.641458\pi\)
\(8\) 1.00000 0.353553
\(9\) 1.00000 + 1.73205i 0.333333 + 0.577350i
\(10\) 1.50000 2.59808i 0.474342 0.821584i
\(11\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(12\) −1.00000 −0.288675
\(13\) 0 0
\(14\) −3.00000 −0.801784
\(15\) −1.50000 + 2.59808i −0.387298 + 0.670820i
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 1.50000 + 2.59808i 0.363803 + 0.630126i 0.988583 0.150675i \(-0.0481447\pi\)
−0.624780 + 0.780801i \(0.714811\pi\)
\(18\) −2.00000 −0.471405
\(19\) 3.00000 + 5.19615i 0.688247 + 1.19208i 0.972404 + 0.233301i \(0.0749529\pi\)
−0.284157 + 0.958778i \(0.591714\pi\)
\(20\) 1.50000 + 2.59808i 0.335410 + 0.580948i
\(21\) 3.00000 0.654654
\(22\) 0 0
\(23\) −3.00000 + 5.19615i −0.625543 + 1.08347i 0.362892 + 0.931831i \(0.381789\pi\)
−0.988436 + 0.151642i \(0.951544\pi\)
\(24\) 0.500000 0.866025i 0.102062 0.176777i
\(25\) 4.00000 0.800000
\(26\) 0 0
\(27\) 5.00000 0.962250
\(28\) 1.50000 2.59808i 0.283473 0.490990i
\(29\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(30\) −1.50000 2.59808i −0.273861 0.474342i
\(31\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) 0 0
\(34\) −3.00000 −0.514496
\(35\) −4.50000 7.79423i −0.760639 1.31747i
\(36\) 1.00000 1.73205i 0.166667 0.288675i
\(37\) 1.50000 2.59808i 0.246598 0.427121i −0.715981 0.698119i \(-0.754020\pi\)
0.962580 + 0.270998i \(0.0873538\pi\)
\(38\) −6.00000 −0.973329
\(39\) 0 0
\(40\) −3.00000 −0.474342
\(41\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(42\) −1.50000 + 2.59808i −0.231455 + 0.400892i
\(43\) −0.500000 0.866025i −0.0762493 0.132068i 0.825380 0.564578i \(-0.190961\pi\)
−0.901629 + 0.432511i \(0.857628\pi\)
\(44\) 0 0
\(45\) −3.00000 5.19615i −0.447214 0.774597i
\(46\) −3.00000 5.19615i −0.442326 0.766131i
\(47\) −3.00000 −0.437595 −0.218797 0.975770i \(-0.570213\pi\)
−0.218797 + 0.975770i \(0.570213\pi\)
\(48\) 0.500000 + 0.866025i 0.0721688 + 0.125000i
\(49\) −1.00000 + 1.73205i −0.142857 + 0.247436i
\(50\) −2.00000 + 3.46410i −0.282843 + 0.489898i
\(51\) 3.00000 0.420084
\(52\) 0 0
\(53\) −6.00000 −0.824163 −0.412082 0.911147i \(-0.635198\pi\)
−0.412082 + 0.911147i \(0.635198\pi\)
\(54\) −2.50000 + 4.33013i −0.340207 + 0.589256i
\(55\) 0 0
\(56\) 1.50000 + 2.59808i 0.200446 + 0.347183i
\(57\) 6.00000 0.794719
\(58\) 0 0
\(59\) −3.00000 5.19615i −0.390567 0.676481i 0.601958 0.798528i \(-0.294388\pi\)
−0.992524 + 0.122047i \(0.961054\pi\)
\(60\) 3.00000 0.387298
\(61\) 4.00000 + 6.92820i 0.512148 + 0.887066i 0.999901 + 0.0140840i \(0.00448323\pi\)
−0.487753 + 0.872982i \(0.662183\pi\)
\(62\) 0 0
\(63\) −3.00000 + 5.19615i −0.377964 + 0.654654i
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 0 0
\(67\) 6.00000 10.3923i 0.733017 1.26962i −0.222571 0.974916i \(-0.571445\pi\)
0.955588 0.294706i \(-0.0952216\pi\)
\(68\) 1.50000 2.59808i 0.181902 0.315063i
\(69\) 3.00000 + 5.19615i 0.361158 + 0.625543i
\(70\) 9.00000 1.07571
\(71\) −7.50000 12.9904i −0.890086 1.54167i −0.839771 0.542941i \(-0.817311\pi\)
−0.0503155 0.998733i \(-0.516023\pi\)
\(72\) 1.00000 + 1.73205i 0.117851 + 0.204124i
\(73\) −6.00000 −0.702247 −0.351123 0.936329i \(-0.614200\pi\)
−0.351123 + 0.936329i \(0.614200\pi\)
\(74\) 1.50000 + 2.59808i 0.174371 + 0.302020i
\(75\) 2.00000 3.46410i 0.230940 0.400000i
\(76\) 3.00000 5.19615i 0.344124 0.596040i
\(77\) 0 0
\(78\) 0 0
\(79\) 10.0000 1.12509 0.562544 0.826767i \(-0.309823\pi\)
0.562544 + 0.826767i \(0.309823\pi\)
\(80\) 1.50000 2.59808i 0.167705 0.290474i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 0 0
\(83\) 6.00000 0.658586 0.329293 0.944228i \(-0.393190\pi\)
0.329293 + 0.944228i \(0.393190\pi\)
\(84\) −1.50000 2.59808i −0.163663 0.283473i
\(85\) −4.50000 7.79423i −0.488094 0.845403i
\(86\) 1.00000 0.107833
\(87\) 0 0
\(88\) 0 0
\(89\) −3.00000 + 5.19615i −0.317999 + 0.550791i −0.980071 0.198650i \(-0.936344\pi\)
0.662071 + 0.749441i \(0.269678\pi\)
\(90\) 6.00000 0.632456
\(91\) 0 0
\(92\) 6.00000 0.625543
\(93\) 0 0
\(94\) 1.50000 2.59808i 0.154713 0.267971i
\(95\) −9.00000 15.5885i −0.923381 1.59934i
\(96\) −1.00000 −0.102062
\(97\) 6.00000 + 10.3923i 0.609208 + 1.05518i 0.991371 + 0.131084i \(0.0418458\pi\)
−0.382164 + 0.924095i \(0.624821\pi\)
\(98\) −1.00000 1.73205i −0.101015 0.174964i
\(99\) 0 0
\(100\) −2.00000 3.46410i −0.200000 0.346410i
\(101\) 6.00000 10.3923i 0.597022 1.03407i −0.396236 0.918149i \(-0.629684\pi\)
0.993258 0.115924i \(-0.0369830\pi\)
\(102\) −1.50000 + 2.59808i −0.148522 + 0.257248i
\(103\) −14.0000 −1.37946 −0.689730 0.724066i \(-0.742271\pi\)
−0.689730 + 0.724066i \(0.742271\pi\)
\(104\) 0 0
\(105\) −9.00000 −0.878310
\(106\) 3.00000 5.19615i 0.291386 0.504695i
\(107\) 6.00000 10.3923i 0.580042 1.00466i −0.415432 0.909624i \(-0.636370\pi\)
0.995474 0.0950377i \(-0.0302972\pi\)
\(108\) −2.50000 4.33013i −0.240563 0.416667i
\(109\) 9.00000 0.862044 0.431022 0.902342i \(-0.358153\pi\)
0.431022 + 0.902342i \(0.358153\pi\)
\(110\) 0 0
\(111\) −1.50000 2.59808i −0.142374 0.246598i
\(112\) −3.00000 −0.283473
\(113\) 3.00000 + 5.19615i 0.282216 + 0.488813i 0.971930 0.235269i \(-0.0755971\pi\)
−0.689714 + 0.724082i \(0.742264\pi\)
\(114\) −3.00000 + 5.19615i −0.280976 + 0.486664i
\(115\) 9.00000 15.5885i 0.839254 1.45363i
\(116\) 0 0
\(117\) 0 0
\(118\) 6.00000 0.552345
\(119\) −4.50000 + 7.79423i −0.412514 + 0.714496i
\(120\) −1.50000 + 2.59808i −0.136931 + 0.237171i
\(121\) 5.50000 + 9.52628i 0.500000 + 0.866025i
\(122\) −8.00000 −0.724286
\(123\) 0 0
\(124\) 0 0
\(125\) 3.00000 0.268328
\(126\) −3.00000 5.19615i −0.267261 0.462910i
\(127\) −1.00000 + 1.73205i −0.0887357 + 0.153695i −0.906977 0.421180i \(-0.861616\pi\)
0.818241 + 0.574875i \(0.194949\pi\)
\(128\) −0.500000 + 0.866025i −0.0441942 + 0.0765466i
\(129\) −1.00000 −0.0880451
\(130\) 0 0
\(131\) −3.00000 −0.262111 −0.131056 0.991375i \(-0.541837\pi\)
−0.131056 + 0.991375i \(0.541837\pi\)
\(132\) 0 0
\(133\) −9.00000 + 15.5885i −0.780399 + 1.35169i
\(134\) 6.00000 + 10.3923i 0.518321 + 0.897758i
\(135\) −15.0000 −1.29099
\(136\) 1.50000 + 2.59808i 0.128624 + 0.222783i
\(137\) 9.00000 + 15.5885i 0.768922 + 1.33181i 0.938148 + 0.346235i \(0.112540\pi\)
−0.169226 + 0.985577i \(0.554127\pi\)
\(138\) −6.00000 −0.510754
\(139\) −2.50000 4.33013i −0.212047 0.367277i 0.740308 0.672268i \(-0.234680\pi\)
−0.952355 + 0.304991i \(0.901346\pi\)
\(140\) −4.50000 + 7.79423i −0.380319 + 0.658733i
\(141\) −1.50000 + 2.59808i −0.126323 + 0.218797i
\(142\) 15.0000 1.25877
\(143\) 0 0
\(144\) −2.00000 −0.166667
\(145\) 0 0
\(146\) 3.00000 5.19615i 0.248282 0.430037i
\(147\) 1.00000 + 1.73205i 0.0824786 + 0.142857i
\(148\) −3.00000 −0.246598
\(149\) 3.00000 + 5.19615i 0.245770 + 0.425685i 0.962348 0.271821i \(-0.0876260\pi\)
−0.716578 + 0.697507i \(0.754293\pi\)
\(150\) 2.00000 + 3.46410i 0.163299 + 0.282843i
\(151\) 15.0000 1.22068 0.610341 0.792139i \(-0.291032\pi\)
0.610341 + 0.792139i \(0.291032\pi\)
\(152\) 3.00000 + 5.19615i 0.243332 + 0.421464i
\(153\) −3.00000 + 5.19615i −0.242536 + 0.420084i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −22.0000 −1.75579 −0.877896 0.478852i \(-0.841053\pi\)
−0.877896 + 0.478852i \(0.841053\pi\)
\(158\) −5.00000 + 8.66025i −0.397779 + 0.688973i
\(159\) −3.00000 + 5.19615i −0.237915 + 0.412082i
\(160\) 1.50000 + 2.59808i 0.118585 + 0.205396i
\(161\) −18.0000 −1.41860
\(162\) −0.500000 0.866025i −0.0392837 0.0680414i
\(163\) 3.00000 + 5.19615i 0.234978 + 0.406994i 0.959266 0.282503i \(-0.0911648\pi\)
−0.724288 + 0.689497i \(0.757831\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) −3.00000 + 5.19615i −0.232845 + 0.403300i
\(167\) −6.00000 + 10.3923i −0.464294 + 0.804181i −0.999169 0.0407502i \(-0.987025\pi\)
0.534875 + 0.844931i \(0.320359\pi\)
\(168\) 3.00000 0.231455
\(169\) 0 0
\(170\) 9.00000 0.690268
\(171\) −6.00000 + 10.3923i −0.458831 + 0.794719i
\(172\) −0.500000 + 0.866025i −0.0381246 + 0.0660338i
\(173\) −3.00000 5.19615i −0.228086 0.395056i 0.729155 0.684349i \(-0.239913\pi\)
−0.957241 + 0.289292i \(0.906580\pi\)
\(174\) 0 0
\(175\) 6.00000 + 10.3923i 0.453557 + 0.785584i
\(176\) 0 0
\(177\) −6.00000 −0.450988
\(178\) −3.00000 5.19615i −0.224860 0.389468i
\(179\) 7.50000 12.9904i 0.560576 0.970947i −0.436870 0.899525i \(-0.643913\pi\)
0.997446 0.0714220i \(-0.0227537\pi\)
\(180\) −3.00000 + 5.19615i −0.223607 + 0.387298i
\(181\) −2.00000 −0.148659 −0.0743294 0.997234i \(-0.523682\pi\)
−0.0743294 + 0.997234i \(0.523682\pi\)
\(182\) 0 0
\(183\) 8.00000 0.591377
\(184\) −3.00000 + 5.19615i −0.221163 + 0.383065i
\(185\) −4.50000 + 7.79423i −0.330847 + 0.573043i
\(186\) 0 0
\(187\) 0 0
\(188\) 1.50000 + 2.59808i 0.109399 + 0.189484i
\(189\) 7.50000 + 12.9904i 0.545545 + 0.944911i
\(190\) 18.0000 1.30586
\(191\) −6.00000 10.3923i −0.434145 0.751961i 0.563081 0.826402i \(-0.309616\pi\)
−0.997225 + 0.0744412i \(0.976283\pi\)
\(192\) 0.500000 0.866025i 0.0360844 0.0625000i
\(193\) 3.00000 5.19615i 0.215945 0.374027i −0.737620 0.675216i \(-0.764050\pi\)
0.953564 + 0.301189i \(0.0973836\pi\)
\(194\) −12.0000 −0.861550
\(195\) 0 0
\(196\) 2.00000 0.142857
\(197\) −1.50000 + 2.59808i −0.106871 + 0.185105i −0.914501 0.404584i \(-0.867416\pi\)
0.807630 + 0.589689i \(0.200750\pi\)
\(198\) 0 0
\(199\) −10.0000 17.3205i −0.708881 1.22782i −0.965272 0.261245i \(-0.915867\pi\)
0.256391 0.966573i \(-0.417466\pi\)
\(200\) 4.00000 0.282843
\(201\) −6.00000 10.3923i −0.423207 0.733017i
\(202\) 6.00000 + 10.3923i 0.422159 + 0.731200i
\(203\) 0 0
\(204\) −1.50000 2.59808i −0.105021 0.181902i
\(205\) 0 0
\(206\) 7.00000 12.1244i 0.487713 0.844744i
\(207\) −12.0000 −0.834058
\(208\) 0 0
\(209\) 0 0
\(210\) 4.50000 7.79423i 0.310530 0.537853i
\(211\) 11.5000 19.9186i 0.791693 1.37125i −0.133226 0.991086i \(-0.542533\pi\)
0.924918 0.380166i \(-0.124133\pi\)
\(212\) 3.00000 + 5.19615i 0.206041 + 0.356873i
\(213\) −15.0000 −1.02778
\(214\) 6.00000 + 10.3923i 0.410152 + 0.710403i
\(215\) 1.50000 + 2.59808i 0.102299 + 0.177187i
\(216\) 5.00000 0.340207
\(217\) 0 0
\(218\) −4.50000 + 7.79423i −0.304778 + 0.527892i
\(219\) −3.00000 + 5.19615i −0.202721 + 0.351123i
\(220\) 0 0
\(221\) 0 0
\(222\) 3.00000 0.201347
\(223\) 4.50000 7.79423i 0.301342 0.521940i −0.675098 0.737728i \(-0.735899\pi\)
0.976440 + 0.215788i \(0.0692320\pi\)
\(224\) 1.50000 2.59808i 0.100223 0.173591i
\(225\) 4.00000 + 6.92820i 0.266667 + 0.461880i
\(226\) −6.00000 −0.399114
\(227\) 6.00000 + 10.3923i 0.398234 + 0.689761i 0.993508 0.113761i \(-0.0362899\pi\)
−0.595274 + 0.803523i \(0.702957\pi\)
\(228\) −3.00000 5.19615i −0.198680 0.344124i
\(229\) −9.00000 −0.594737 −0.297368 0.954763i \(-0.596109\pi\)
−0.297368 + 0.954763i \(0.596109\pi\)
\(230\) 9.00000 + 15.5885i 0.593442 + 1.02787i
\(231\) 0 0
\(232\) 0 0
\(233\) 21.0000 1.37576 0.687878 0.725826i \(-0.258542\pi\)
0.687878 + 0.725826i \(0.258542\pi\)
\(234\) 0 0
\(235\) 9.00000 0.587095
\(236\) −3.00000 + 5.19615i −0.195283 + 0.338241i
\(237\) 5.00000 8.66025i 0.324785 0.562544i
\(238\) −4.50000 7.79423i −0.291692 0.505225i
\(239\) 9.00000 0.582162 0.291081 0.956698i \(-0.405985\pi\)
0.291081 + 0.956698i \(0.405985\pi\)
\(240\) −1.50000 2.59808i −0.0968246 0.167705i
\(241\) −15.0000 25.9808i −0.966235 1.67357i −0.706260 0.707953i \(-0.749619\pi\)
−0.259975 0.965615i \(-0.583714\pi\)
\(242\) −11.0000 −0.707107
\(243\) 8.00000 + 13.8564i 0.513200 + 0.888889i
\(244\) 4.00000 6.92820i 0.256074 0.443533i
\(245\) 3.00000 5.19615i 0.191663 0.331970i
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 3.00000 5.19615i 0.190117 0.329293i
\(250\) −1.50000 + 2.59808i −0.0948683 + 0.164317i
\(251\) 6.00000 + 10.3923i 0.378717 + 0.655956i 0.990876 0.134778i \(-0.0430322\pi\)
−0.612159 + 0.790735i \(0.709699\pi\)
\(252\) 6.00000 0.377964
\(253\) 0 0
\(254\) −1.00000 1.73205i −0.0627456 0.108679i
\(255\) −9.00000 −0.563602
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 1.50000 2.59808i 0.0935674 0.162064i −0.815442 0.578838i \(-0.803506\pi\)
0.909010 + 0.416775i \(0.136840\pi\)
\(258\) 0.500000 0.866025i 0.0311286 0.0539164i
\(259\) 9.00000 0.559233
\(260\) 0 0
\(261\) 0 0
\(262\) 1.50000 2.59808i 0.0926703 0.160510i
\(263\) −12.0000 + 20.7846i −0.739952 + 1.28163i 0.212565 + 0.977147i \(0.431818\pi\)
−0.952517 + 0.304487i \(0.901515\pi\)
\(264\) 0 0
\(265\) 18.0000 1.10573
\(266\) −9.00000 15.5885i −0.551825 0.955790i
\(267\) 3.00000 + 5.19615i 0.183597 + 0.317999i
\(268\) −12.0000 −0.733017
\(269\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(270\) 7.50000 12.9904i 0.456435 0.790569i
\(271\) 7.50000 12.9904i 0.455593 0.789109i −0.543130 0.839649i \(-0.682761\pi\)
0.998722 + 0.0505395i \(0.0160941\pi\)
\(272\) −3.00000 −0.181902
\(273\) 0 0
\(274\) −18.0000 −1.08742
\(275\) 0 0
\(276\) 3.00000 5.19615i 0.180579 0.312772i
\(277\) 4.00000 + 6.92820i 0.240337 + 0.416275i 0.960810 0.277207i \(-0.0894088\pi\)
−0.720473 + 0.693482i \(0.756075\pi\)
\(278\) 5.00000 0.299880
\(279\) 0 0
\(280\) −4.50000 7.79423i −0.268926 0.465794i
\(281\) 30.0000 1.78965 0.894825 0.446417i \(-0.147300\pi\)
0.894825 + 0.446417i \(0.147300\pi\)
\(282\) −1.50000 2.59808i −0.0893237 0.154713i
\(283\) 2.00000 3.46410i 0.118888 0.205919i −0.800439 0.599414i \(-0.795400\pi\)
0.919327 + 0.393494i \(0.128734\pi\)
\(284\) −7.50000 + 12.9904i −0.445043 + 0.770837i
\(285\) −18.0000 −1.06623
\(286\) 0 0
\(287\) 0 0
\(288\) 1.00000 1.73205i 0.0589256 0.102062i
\(289\) 4.00000 6.92820i 0.235294 0.407541i
\(290\) 0 0
\(291\) 12.0000 0.703452
\(292\) 3.00000 + 5.19615i 0.175562 + 0.304082i
\(293\) −4.50000 7.79423i −0.262893 0.455344i 0.704117 0.710084i \(-0.251343\pi\)
−0.967009 + 0.254741i \(0.918010\pi\)
\(294\) −2.00000 −0.116642
\(295\) 9.00000 + 15.5885i 0.524000 + 0.907595i
\(296\) 1.50000 2.59808i 0.0871857 0.151010i
\(297\) 0 0
\(298\) −6.00000 −0.347571
\(299\) 0 0
\(300\) −4.00000 −0.230940
\(301\) 1.50000 2.59808i 0.0864586 0.149751i
\(302\) −7.50000 + 12.9904i −0.431577 + 0.747512i
\(303\) −6.00000 10.3923i −0.344691 0.597022i
\(304\) −6.00000 −0.344124
\(305\) −12.0000 20.7846i −0.687118 1.19012i
\(306\) −3.00000 5.19615i −0.171499 0.297044i
\(307\) −18.0000 −1.02731 −0.513657 0.857996i \(-0.671710\pi\)
−0.513657 + 0.857996i \(0.671710\pi\)
\(308\) 0 0
\(309\) −7.00000 + 12.1244i −0.398216 + 0.689730i
\(310\) 0 0
\(311\) 18.0000 1.02069 0.510343 0.859971i \(-0.329518\pi\)
0.510343 + 0.859971i \(0.329518\pi\)
\(312\) 0 0
\(313\) 19.0000 1.07394 0.536972 0.843600i \(-0.319568\pi\)
0.536972 + 0.843600i \(0.319568\pi\)
\(314\) 11.0000 19.0526i 0.620766 1.07520i
\(315\) 9.00000 15.5885i 0.507093 0.878310i
\(316\) −5.00000 8.66025i −0.281272 0.487177i
\(317\) 18.0000 1.01098 0.505490 0.862832i \(-0.331312\pi\)
0.505490 + 0.862832i \(0.331312\pi\)
\(318\) −3.00000 5.19615i −0.168232 0.291386i
\(319\) 0 0
\(320\) −3.00000 −0.167705
\(321\) −6.00000 10.3923i −0.334887 0.580042i
\(322\) 9.00000 15.5885i 0.501550 0.868711i
\(323\) −9.00000 + 15.5885i −0.500773 + 0.867365i
\(324\) 1.00000 0.0555556
\(325\) 0 0
\(326\) −6.00000 −0.332309
\(327\) 4.50000 7.79423i 0.248851 0.431022i
\(328\) 0 0
\(329\) −4.50000 7.79423i −0.248093 0.429710i
\(330\) 0 0
\(331\) −15.0000 25.9808i −0.824475 1.42803i −0.902320 0.431066i \(-0.858137\pi\)
0.0778456 0.996965i \(-0.475196\pi\)
\(332\) −3.00000 5.19615i −0.164646 0.285176i
\(333\) 6.00000 0.328798
\(334\) −6.00000 10.3923i −0.328305 0.568642i
\(335\) −18.0000 + 31.1769i −0.983445 + 1.70338i
\(336\) −1.50000 + 2.59808i −0.0818317 + 0.141737i
\(337\) −13.0000 −0.708155 −0.354078 0.935216i \(-0.615205\pi\)
−0.354078 + 0.935216i \(0.615205\pi\)
\(338\) 0 0
\(339\) 6.00000 0.325875
\(340\) −4.50000 + 7.79423i −0.244047 + 0.422701i
\(341\) 0 0
\(342\) −6.00000 10.3923i −0.324443 0.561951i
\(343\) 15.0000 0.809924
\(344\) −0.500000 0.866025i −0.0269582 0.0466930i
\(345\) −9.00000 15.5885i −0.484544 0.839254i
\(346\) 6.00000 0.322562
\(347\) −16.5000 28.5788i −0.885766 1.53419i −0.844833 0.535031i \(-0.820300\pi\)
−0.0409337 0.999162i \(-0.513033\pi\)
\(348\) 0 0
\(349\) −10.5000 + 18.1865i −0.562052 + 0.973503i 0.435265 + 0.900302i \(0.356655\pi\)
−0.997317 + 0.0732005i \(0.976679\pi\)
\(350\) −12.0000 −0.641427
\(351\) 0 0
\(352\) 0 0
\(353\) −3.00000 + 5.19615i −0.159674 + 0.276563i −0.934751 0.355303i \(-0.884378\pi\)
0.775077 + 0.631867i \(0.217711\pi\)
\(354\) 3.00000 5.19615i 0.159448 0.276172i
\(355\) 22.5000 + 38.9711i 1.19418 + 2.06837i
\(356\) 6.00000 0.317999
\(357\) 4.50000 + 7.79423i 0.238165 + 0.412514i
\(358\) 7.50000 + 12.9904i 0.396387 + 0.686563i
\(359\) −24.0000 −1.26667 −0.633336 0.773877i \(-0.718315\pi\)
−0.633336 + 0.773877i \(0.718315\pi\)
\(360\) −3.00000 5.19615i −0.158114 0.273861i
\(361\) −8.50000 + 14.7224i −0.447368 + 0.774865i
\(362\) 1.00000 1.73205i 0.0525588 0.0910346i
\(363\) 11.0000 0.577350
\(364\) 0 0
\(365\) 18.0000 0.942163
\(366\) −4.00000 + 6.92820i −0.209083 + 0.362143i
\(367\) −4.00000 + 6.92820i −0.208798 + 0.361649i −0.951336 0.308155i \(-0.900289\pi\)
0.742538 + 0.669804i \(0.233622\pi\)
\(368\) −3.00000 5.19615i −0.156386 0.270868i
\(369\) 0 0
\(370\) −4.50000 7.79423i −0.233944 0.405203i
\(371\) −9.00000 15.5885i −0.467257 0.809312i
\(372\) 0 0
\(373\) −2.00000 3.46410i −0.103556 0.179364i 0.809591 0.586994i \(-0.199689\pi\)
−0.913147 + 0.407630i \(0.866355\pi\)
\(374\) 0 0
\(375\) 1.50000 2.59808i 0.0774597 0.134164i
\(376\) −3.00000 −0.154713
\(377\) 0 0
\(378\) −15.0000 −0.771517
\(379\) 3.00000 5.19615i 0.154100 0.266908i −0.778631 0.627482i \(-0.784086\pi\)
0.932731 + 0.360573i \(0.117419\pi\)
\(380\) −9.00000 + 15.5885i −0.461690 + 0.799671i
\(381\) 1.00000 + 1.73205i 0.0512316 + 0.0887357i
\(382\) 12.0000 0.613973
\(383\) 4.50000 + 7.79423i 0.229939 + 0.398266i 0.957790 0.287469i \(-0.0928139\pi\)
−0.727851 + 0.685736i \(0.759481\pi\)
\(384\) 0.500000 + 0.866025i 0.0255155 + 0.0441942i
\(385\) 0 0
\(386\) 3.00000 + 5.19615i 0.152696 + 0.264477i
\(387\) 1.00000 1.73205i 0.0508329 0.0880451i
\(388\) 6.00000 10.3923i 0.304604 0.527589i
\(389\) 30.0000 1.52106 0.760530 0.649303i \(-0.224939\pi\)
0.760530 + 0.649303i \(0.224939\pi\)
\(390\) 0 0
\(391\) −18.0000 −0.910299
\(392\) −1.00000 + 1.73205i −0.0505076 + 0.0874818i
\(393\) −1.50000 + 2.59808i −0.0756650 + 0.131056i
\(394\) −1.50000 2.59808i −0.0755689 0.130889i
\(395\) −30.0000 −1.50946
\(396\) 0 0
\(397\) 9.00000 + 15.5885i 0.451697 + 0.782362i 0.998492 0.0549046i \(-0.0174855\pi\)
−0.546795 + 0.837267i \(0.684152\pi\)
\(398\) 20.0000 1.00251
\(399\) 9.00000 + 15.5885i 0.450564 + 0.780399i
\(400\) −2.00000 + 3.46410i −0.100000 + 0.173205i
\(401\) 15.0000 25.9808i 0.749064 1.29742i −0.199207 0.979957i \(-0.563837\pi\)
0.948272 0.317460i \(-0.102830\pi\)
\(402\) 12.0000 0.598506
\(403\) 0 0
\(404\) −12.0000 −0.597022
\(405\) 1.50000 2.59808i 0.0745356 0.129099i
\(406\) 0 0
\(407\) 0 0
\(408\) 3.00000 0.148522
\(409\) 3.00000 + 5.19615i 0.148340 + 0.256933i 0.930614 0.366002i \(-0.119274\pi\)
−0.782274 + 0.622935i \(0.785940\pi\)
\(410\) 0 0
\(411\) 18.0000 0.887875
\(412\) 7.00000 + 12.1244i 0.344865 + 0.597324i
\(413\) 9.00000 15.5885i 0.442861 0.767058i
\(414\) 6.00000 10.3923i 0.294884 0.510754i
\(415\) −18.0000 −0.883585
\(416\) 0 0
\(417\) −5.00000 −0.244851
\(418\) 0 0
\(419\) −7.50000 + 12.9904i −0.366399 + 0.634622i −0.989000 0.147918i \(-0.952743\pi\)
0.622601 + 0.782540i \(0.286076\pi\)
\(420\) 4.50000 + 7.79423i 0.219578 + 0.380319i
\(421\) −15.0000 −0.731055 −0.365528 0.930800i \(-0.619111\pi\)
−0.365528 + 0.930800i \(0.619111\pi\)
\(422\) 11.5000 + 19.9186i 0.559811 + 0.969622i
\(423\) −3.00000 5.19615i −0.145865 0.252646i
\(424\) −6.00000 −0.291386
\(425\) 6.00000 + 10.3923i 0.291043 + 0.504101i
\(426\) 7.50000 12.9904i 0.363376 0.629386i
\(427\) −12.0000 + 20.7846i −0.580721 + 1.00584i
\(428\) −12.0000 −0.580042
\(429\) 0 0
\(430\) −3.00000 −0.144673
\(431\) 7.50000 12.9904i 0.361262 0.625725i −0.626907 0.779094i \(-0.715679\pi\)
0.988169 + 0.153370i \(0.0490126\pi\)
\(432\) −2.50000 + 4.33013i −0.120281 + 0.208333i
\(433\) −5.50000 9.52628i −0.264313 0.457804i 0.703070 0.711120i \(-0.251812\pi\)
−0.967383 + 0.253317i \(0.918479\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −4.50000 7.79423i −0.215511 0.373276i
\(437\) −36.0000 −1.72211
\(438\) −3.00000 5.19615i −0.143346 0.248282i
\(439\) −5.00000 + 8.66025i −0.238637 + 0.413331i −0.960323 0.278889i \(-0.910034\pi\)
0.721686 + 0.692220i \(0.243367\pi\)
\(440\) 0 0
\(441\) −4.00000 −0.190476
\(442\) 0 0
\(443\) −21.0000 −0.997740 −0.498870 0.866677i \(-0.666252\pi\)
−0.498870 + 0.866677i \(0.666252\pi\)
\(444\) −1.50000 + 2.59808i −0.0711868 + 0.123299i
\(445\) 9.00000 15.5885i 0.426641 0.738964i
\(446\) 4.50000 + 7.79423i 0.213081 + 0.369067i
\(447\) 6.00000 0.283790
\(448\) 1.50000 + 2.59808i 0.0708683 + 0.122748i
\(449\) 12.0000 + 20.7846i 0.566315 + 0.980886i 0.996926 + 0.0783487i \(0.0249648\pi\)
−0.430611 + 0.902538i \(0.641702\pi\)
\(450\) −8.00000 −0.377124
\(451\) 0 0
\(452\) 3.00000 5.19615i 0.141108 0.244406i
\(453\) 7.50000 12.9904i 0.352381 0.610341i
\(454\) −12.0000 −0.563188
\(455\) 0 0
\(456\) 6.00000 0.280976
\(457\) −9.00000 + 15.5885i −0.421002 + 0.729197i −0.996038 0.0889312i \(-0.971655\pi\)
0.575036 + 0.818128i \(0.304988\pi\)
\(458\) 4.50000 7.79423i 0.210271 0.364200i
\(459\) 7.50000 + 12.9904i 0.350070 + 0.606339i
\(460\) −18.0000 −0.839254
\(461\) 7.50000 + 12.9904i 0.349310 + 0.605022i 0.986127 0.165992i \(-0.0530827\pi\)
−0.636817 + 0.771015i \(0.719749\pi\)
\(462\) 0 0
\(463\) 24.0000 1.11537 0.557687 0.830051i \(-0.311689\pi\)
0.557687 + 0.830051i \(0.311689\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) −10.5000 + 18.1865i −0.486403 + 0.842475i
\(467\) 12.0000 0.555294 0.277647 0.960683i \(-0.410445\pi\)
0.277647 + 0.960683i \(0.410445\pi\)
\(468\) 0 0
\(469\) 36.0000 1.66233
\(470\) −4.50000 + 7.79423i −0.207570 + 0.359521i
\(471\) −11.0000 + 19.0526i −0.506853 + 0.877896i
\(472\) −3.00000 5.19615i −0.138086 0.239172i
\(473\) 0 0
\(474\) 5.00000 + 8.66025i 0.229658 + 0.397779i
\(475\) 12.0000 + 20.7846i 0.550598 + 0.953663i
\(476\) 9.00000 0.412514
\(477\) −6.00000 10.3923i −0.274721 0.475831i
\(478\) −4.50000 + 7.79423i −0.205825 + 0.356500i
\(479\) 19.5000 33.7750i 0.890978 1.54322i 0.0522726 0.998633i \(-0.483354\pi\)
0.838705 0.544586i \(-0.183313\pi\)
\(480\) 3.00000 0.136931
\(481\) 0 0
\(482\) 30.0000 1.36646
\(483\) −9.00000 + 15.5885i −0.409514 + 0.709299i
\(484\) 5.50000 9.52628i 0.250000 0.433013i
\(485\) −18.0000 31.1769i −0.817338 1.41567i
\(486\) −16.0000 −0.725775
\(487\) 6.00000 + 10.3923i 0.271886 + 0.470920i 0.969345 0.245705i \(-0.0790193\pi\)
−0.697459 + 0.716625i \(0.745686\pi\)
\(488\) 4.00000 + 6.92820i 0.181071 + 0.313625i
\(489\) 6.00000 0.271329
\(490\) 3.00000 + 5.19615i 0.135526 + 0.234738i
\(491\) 13.5000 23.3827i 0.609246 1.05525i −0.382118 0.924113i \(-0.624805\pi\)
0.991365 0.131132i \(-0.0418613\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 22.5000 38.9711i 1.00926 1.74809i
\(498\) 3.00000 + 5.19615i 0.134433 + 0.232845i
\(499\) −36.0000 −1.61158 −0.805791 0.592200i \(-0.798259\pi\)
−0.805791 + 0.592200i \(0.798259\pi\)
\(500\) −1.50000 2.59808i −0.0670820 0.116190i
\(501\) 6.00000 + 10.3923i 0.268060 + 0.464294i
\(502\) −12.0000 −0.535586
\(503\) 3.00000 + 5.19615i 0.133763 + 0.231685i 0.925124 0.379664i \(-0.123960\pi\)
−0.791361 + 0.611349i \(0.790627\pi\)
\(504\) −3.00000 + 5.19615i −0.133631 + 0.231455i
\(505\) −18.0000 + 31.1769i −0.800989 + 1.38735i
\(506\) 0 0
\(507\) 0 0
\(508\) 2.00000 0.0887357
\(509\) 3.00000 5.19615i 0.132973 0.230315i −0.791849 0.610718i \(-0.790881\pi\)
0.924821 + 0.380402i \(0.124214\pi\)
\(510\) 4.50000 7.79423i 0.199263 0.345134i
\(511\) −9.00000 15.5885i −0.398137 0.689593i
\(512\) 1.00000 0.0441942
\(513\) 15.0000 + 25.9808i 0.662266 + 1.14708i
\(514\) 1.50000 + 2.59808i 0.0661622 + 0.114596i
\(515\) 42.0000 1.85074
\(516\) 0.500000 + 0.866025i 0.0220113 + 0.0381246i
\(517\) 0 0
\(518\) −4.50000 + 7.79423i −0.197719 + 0.342459i
\(519\) −6.00000 −0.263371
\(520\) 0 0
\(521\) 27.0000 1.18289 0.591446 0.806345i \(-0.298557\pi\)
0.591446 + 0.806345i \(0.298557\pi\)
\(522\) 0 0
\(523\) 8.00000 13.8564i 0.349816 0.605898i −0.636401 0.771358i \(-0.719578\pi\)
0.986216 + 0.165460i \(0.0529109\pi\)
\(524\) 1.50000 + 2.59808i 0.0655278 + 0.113497i
\(525\) 12.0000 0.523723
\(526\) −12.0000 20.7846i −0.523225 0.906252i
\(527\) 0 0
\(528\) 0 0
\(529\) −6.50000 11.2583i −0.282609 0.489493i
\(530\) −9.00000 + 15.5885i −0.390935 + 0.677119i
\(531\) 6.00000 10.3923i 0.260378 0.450988i
\(532\) 18.0000 0.780399
\(533\) 0 0
\(534\) −6.00000 −0.259645
\(535\) −18.0000 + 31.1769i −0.778208 + 1.34790i
\(536\) 6.00000 10.3923i 0.259161 0.448879i
\(537\) −7.50000 12.9904i −0.323649 0.560576i
\(538\) 0 0
\(539\) 0 0
\(540\) 7.50000 + 12.9904i 0.322749 + 0.559017i
\(541\) 15.0000 0.644900 0.322450 0.946586i \(-0.395494\pi\)
0.322450 + 0.946586i \(0.395494\pi\)
\(542\) 7.50000 + 12.9904i 0.322153 + 0.557985i
\(543\) −1.00000 + 1.73205i −0.0429141 + 0.0743294i
\(544\) 1.50000 2.59808i 0.0643120 0.111392i
\(545\) −27.0000 −1.15655
\(546\) 0 0
\(547\) −37.0000 −1.58201 −0.791003 0.611812i \(-0.790441\pi\)
−0.791003 + 0.611812i \(0.790441\pi\)
\(548\) 9.00000 15.5885i 0.384461 0.665906i
\(549\) −8.00000 + 13.8564i −0.341432 + 0.591377i
\(550\) 0 0
\(551\) 0 0
\(552\) 3.00000 + 5.19615i 0.127688 + 0.221163i
\(553\) 15.0000 + 25.9808i 0.637865 + 1.10481i
\(554\) −8.00000 −0.339887
\(555\) 4.50000 + 7.79423i 0.191014 + 0.330847i
\(556\) −2.50000 + 4.33013i −0.106024 + 0.183638i
\(557\) −13.5000 + 23.3827i −0.572013 + 0.990756i 0.424346 + 0.905500i \(0.360504\pi\)
−0.996359 + 0.0852559i \(0.972829\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 9.00000 0.380319
\(561\) 0 0
\(562\) −15.0000 + 25.9808i −0.632737 + 1.09593i
\(563\) 19.5000 + 33.7750i 0.821827 + 1.42345i 0.904320 + 0.426855i \(0.140378\pi\)
−0.0824933 + 0.996592i \(0.526288\pi\)
\(564\) 3.00000 0.126323
\(565\) −9.00000 15.5885i −0.378633 0.655811i
\(566\) 2.00000 + 3.46410i 0.0840663 + 0.145607i
\(567\) −3.00000 −0.125988
\(568\) −7.50000 12.9904i −0.314693 0.545064i
\(569\) 22.5000 38.9711i 0.943249 1.63376i 0.184030 0.982921i \(-0.441086\pi\)
0.759220 0.650835i \(-0.225581\pi\)
\(570\) 9.00000 15.5885i 0.376969 0.652929i
\(571\) 23.0000 0.962520 0.481260 0.876578i \(-0.340179\pi\)
0.481260 + 0.876578i \(0.340179\pi\)
\(572\) 0 0
\(573\) −12.0000 −0.501307
\(574\) 0 0
\(575\) −12.0000 + 20.7846i −0.500435 + 0.866778i
\(576\) 1.00000 + 1.73205i 0.0416667 + 0.0721688i
\(577\) −42.0000 −1.74848 −0.874241 0.485491i \(-0.838641\pi\)
−0.874241 + 0.485491i \(0.838641\pi\)
\(578\) 4.00000 + 6.92820i 0.166378 + 0.288175i
\(579\) −3.00000 5.19615i −0.124676 0.215945i
\(580\) 0 0
\(581\) 9.00000 + 15.5885i 0.373383 + 0.646718i
\(582\) −6.00000 + 10.3923i −0.248708 + 0.430775i
\(583\) 0 0
\(584\) −6.00000 −0.248282
\(585\) 0 0
\(586\) 9.00000 0.371787
\(587\) −9.00000 + 15.5885i −0.371470 + 0.643404i −0.989792 0.142520i \(-0.954479\pi\)
0.618322 + 0.785925i \(0.287813\pi\)
\(588\) 1.00000 1.73205i 0.0412393 0.0714286i
\(589\) 0 0
\(590\) −18.0000 −0.741048
\(591\) 1.50000 + 2.59808i 0.0617018 + 0.106871i
\(592\) 1.50000 + 2.59808i 0.0616496 + 0.106780i
\(593\) −36.0000 −1.47834 −0.739171 0.673517i \(-0.764783\pi\)
−0.739171 + 0.673517i \(0.764783\pi\)
\(594\) 0 0
\(595\) 13.5000 23.3827i 0.553446 0.958597i
\(596\) 3.00000 5.19615i 0.122885 0.212843i
\(597\) −20.0000 −0.818546
\(598\) 0 0
\(599\) −30.0000 −1.22577 −0.612883 0.790173i \(-0.709990\pi\)
−0.612883 + 0.790173i \(0.709990\pi\)
\(600\) 2.00000 3.46410i 0.0816497 0.141421i
\(601\) −18.5000 + 32.0429i −0.754631 + 1.30706i 0.190927 + 0.981604i \(0.438851\pi\)
−0.945558 + 0.325455i \(0.894483\pi\)
\(602\) 1.50000 + 2.59808i 0.0611354 + 0.105890i
\(603\) 24.0000 0.977356
\(604\) −7.50000 12.9904i −0.305171 0.528571i
\(605\) −16.5000 28.5788i −0.670820 1.16190i
\(606\) 12.0000 0.487467
\(607\) 11.0000 + 19.0526i 0.446476 + 0.773320i 0.998154 0.0607380i \(-0.0193454\pi\)
−0.551678 + 0.834058i \(0.686012\pi\)
\(608\) 3.00000 5.19615i 0.121666 0.210732i
\(609\) 0 0
\(610\) 24.0000 0.971732
\(611\) 0 0
\(612\) 6.00000 0.242536
\(613\) −3.00000 + 5.19615i −0.121169 + 0.209871i −0.920229 0.391381i \(-0.871998\pi\)
0.799060 + 0.601251i \(0.205331\pi\)
\(614\) 9.00000 15.5885i 0.363210 0.629099i
\(615\) 0 0
\(616\) 0 0
\(617\) 6.00000 + 10.3923i 0.241551 + 0.418378i 0.961156 0.276005i \(-0.0890106\pi\)
−0.719605 + 0.694383i \(0.755677\pi\)
\(618\) −7.00000 12.1244i −0.281581 0.487713i
\(619\) −24.0000 −0.964641 −0.482321 0.875995i \(-0.660206\pi\)
−0.482321 + 0.875995i \(0.660206\pi\)
\(620\) 0 0
\(621\) −15.0000 + 25.9808i −0.601929 + 1.04257i
\(622\) −9.00000 + 15.5885i −0.360867 + 0.625040i
\(623\) −18.0000 −0.721155
\(624\) 0 0
\(625\) −29.0000 −1.16000
\(626\) −9.50000 + 16.4545i −0.379696 + 0.657653i
\(627\) 0 0
\(628\) 11.0000 + 19.0526i 0.438948 + 0.760280i
\(629\) 9.00000 0.358854
\(630\) 9.00000 + 15.5885i 0.358569 + 0.621059i
\(631\) −7.50000 12.9904i −0.298570 0.517139i 0.677239 0.735763i \(-0.263176\pi\)
−0.975809 + 0.218624i \(0.929843\pi\)
\(632\) 10.0000 0.397779
\(633\) −11.5000 19.9186i −0.457084 0.791693i
\(634\) −9.00000 + 15.5885i −0.357436 + 0.619097i
\(635\) 3.00000 5.19615i 0.119051 0.206203i
\(636\) 6.00000 0.237915
\(637\) 0 0
\(638\) 0 0
\(639\) 15.0000 25.9808i 0.593391 1.02778i
\(640\) 1.50000 2.59808i 0.0592927 0.102698i
\(641\) −9.00000 15.5885i −0.355479 0.615707i 0.631721 0.775196i \(-0.282349\pi\)
−0.987200 + 0.159489i \(0.949015\pi\)
\(642\) 12.0000 0.473602
\(643\) −18.0000 31.1769i −0.709851 1.22950i −0.964912 0.262573i \(-0.915429\pi\)
0.255062 0.966925i \(-0.417904\pi\)
\(644\) 9.00000 + 15.5885i 0.354650 + 0.614271i
\(645\) 3.00000 0.118125
\(646\) −9.00000 15.5885i −0.354100 0.613320i
\(647\) −21.0000 + 36.3731i −0.825595 + 1.42997i 0.0758684 + 0.997118i \(0.475827\pi\)
−0.901464 + 0.432855i \(0.857506\pi\)
\(648\) −0.500000 + 0.866025i −0.0196419 + 0.0340207i
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 3.00000 5.19615i 0.117489 0.203497i
\(653\) 18.0000 31.1769i 0.704394 1.22005i −0.262515 0.964928i \(-0.584552\pi\)
0.966910 0.255119i \(-0.0821147\pi\)
\(654\) 4.50000 + 7.79423i 0.175964 + 0.304778i
\(655\) 9.00000 0.351659
\(656\) 0 0
\(657\) −6.00000 10.3923i −0.234082 0.405442i
\(658\) 9.00000 0.350857
\(659\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(660\) 0 0
\(661\) 15.0000 25.9808i 0.583432 1.01053i −0.411636 0.911348i \(-0.635043\pi\)
0.995069 0.0991864i \(-0.0316240\pi\)
\(662\) 30.0000 1.16598
\(663\) 0 0
\(664\) 6.00000 0.232845
\(665\) 27.0000 46.7654i 1.04702 1.81348i
\(666\) −3.00000 + 5.19615i −0.116248 + 0.201347i
\(667\) 0 0
\(668\) 12.0000 0.464294
\(669\) −4.50000 7.79423i −0.173980 0.301342i
\(670\) −18.0000 31.1769i −0.695401 1.20447i
\(671\) 0 0
\(672\) −1.50000 2.59808i −0.0578638 0.100223i
\(673\) −0.500000 + 0.866025i −0.0192736 + 0.0333828i −0.875501 0.483216i \(-0.839469\pi\)
0.856228 + 0.516599i \(0.172802\pi\)
\(674\) 6.50000 11.2583i 0.250371 0.433655i
\(675\) 20.0000 0.769800
\(676\) 0 0
\(677\) 18.0000 0.691796 0.345898 0.938272i \(-0.387574\pi\)
0.345898 + 0.938272i \(0.387574\pi\)
\(678\) −3.00000 + 5.19615i −0.115214 + 0.199557i
\(679\) −18.0000 + 31.1769i −0.690777 + 1.19646i
\(680\) −4.50000 7.79423i −0.172567 0.298895i
\(681\) 12.0000 0.459841
\(682\) 0 0
\(683\) 3.00000 + 5.19615i 0.114792 + 0.198825i 0.917697 0.397282i \(-0.130047\pi\)
−0.802905 + 0.596107i \(0.796713\pi\)
\(684\) 12.0000 0.458831
\(685\) −27.0000 46.7654i −1.03162 1.78681i
\(686\) −7.50000 + 12.9904i −0.286351 + 0.495975i
\(687\) −4.50000 + 7.79423i −0.171686 + 0.297368i
\(688\) 1.00000 0.0381246
\(689\) 0 0
\(690\) 18.0000 0.685248
\(691\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(692\) −3.00000 + 5.19615i −0.114043 + 0.197528i
\(693\) 0 0
\(694\) 33.0000 1.25266
\(695\) 7.50000 + 12.9904i 0.284491 + 0.492753i
\(696\) 0 0
\(697\) 0 0
\(698\) −10.5000 18.1865i −0.397431 0.688370i
\(699\) 10.5000 18.1865i 0.397146 0.687878i
\(700\) 6.00000 10.3923i 0.226779 0.392792i
\(701\) −42.0000 −1.58632 −0.793159 0.609015i \(-0.791565\pi\)
−0.793159 + 0.609015i \(0.791565\pi\)
\(702\) 0 0
\(703\) 18.0000 0.678883
\(704\) 0 0
\(705\) 4.50000 7.79423i 0.169480 0.293548i
\(706\) −3.00000 5.19615i −0.112906 0.195560i
\(707\) 36.0000 1.35392
\(708\) 3.00000 + 5.19615i 0.112747 + 0.195283i
\(709\) −3.00000 5.19615i −0.112667 0.195146i 0.804178 0.594389i \(-0.202606\pi\)
−0.916845 + 0.399244i \(0.869273\pi\)
\(710\) −45.0000 −1.68882
\(711\) 10.0000 + 17.3205i 0.375029 + 0.649570i
\(712\) −3.00000 + 5.19615i −0.112430 + 0.194734i
\(713\) 0 0
\(714\) −9.00000 −0.336817
\(715\) 0 0
\(716\) −15.0000 −0.560576
\(717\) 4.50000 7.79423i 0.168056 0.291081i
\(718\) 12.0000 20.7846i 0.447836 0.775675i
\(719\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(720\) 6.00000 0.223607
\(721\) −21.0000 36.3731i −0.782081 1.35460i
\(722\) −8.50000 14.7224i −0.316337 0.547912i
\(723\) −30.0000 −1.11571
\(724\) 1.00000 + 1.73205i 0.0371647 + 0.0643712i
\(725\) 0 0
\(726\) −5.50000 + 9.52628i −0.204124 + 0.353553i
\(727\) −28.0000 −1.03846 −0.519231 0.854634i \(-0.673782\pi\)
−0.519231 + 0.854634i \(0.673782\pi\)
\(728\) 0 0
\(729\) 13.0000 0.481481
\(730\) −9.00000 + 15.5885i −0.333105 + 0.576955i
\(731\) 1.50000 2.59808i 0.0554795 0.0960933i
\(732\) −4.00000 6.92820i −0.147844 0.256074i
\(733\) −9.00000 −0.332423 −0.166211 0.986090i \(-0.553153\pi\)
−0.166211 + 0.986090i \(0.553153\pi\)
\(734\) −4.00000 6.92820i −0.147643 0.255725i
\(735\) −3.00000 5.19615i −0.110657 0.191663i
\(736\) 6.00000 0.221163
\(737\) 0 0
\(738\) 0 0
\(739\) −18.0000 + 31.1769i −0.662141 + 1.14686i 0.317911 + 0.948120i \(0.397019\pi\)
−0.980052 + 0.198741i \(0.936315\pi\)
\(740\) 9.00000 0.330847
\(741\) 0 0
\(742\) 18.0000 0.660801
\(743\) 19.5000 33.7750i 0.715386 1.23908i −0.247425 0.968907i \(-0.579584\pi\)
0.962811 0.270177i \(-0.0870823\pi\)
\(744\) 0 0
\(745\) −9.00000 15.5885i −0.329734 0.571117i
\(746\) 4.00000 0.146450
\(747\) 6.00000 + 10.3923i 0.219529 + 0.380235i
\(748\) 0 0
\(749\) 36.0000 1.31541
\(750\) 1.50000 + 2.59808i 0.0547723 + 0.0948683i
\(751\) 16.0000 27.7128i 0.583848 1.01125i −0.411170 0.911559i \(-0.634880\pi\)
0.995018 0.0996961i \(-0.0317870\pi\)
\(752\) 1.50000 2.59808i 0.0546994 0.0947421i
\(753\) 12.0000 0.437304
\(754\) 0 0
\(755\) −45.0000 −1.63772
\(756\) 7.50000 12.9904i 0.272772 0.472456i
\(757\) 1.00000 1.73205i 0.0363456 0.0629525i −0.847280 0.531146i \(-0.821762\pi\)
0.883626 + 0.468193i \(0.155095\pi\)
\(758\) 3.00000 + 5.19615i 0.108965 + 0.188733i
\(759\) 0 0
\(760\) −9.00000 15.5885i −0.326464 0.565453i
\(761\) −15.0000 25.9808i −0.543750 0.941802i −0.998684 0.0512772i \(-0.983671\pi\)
0.454935 0.890525i \(-0.349663\pi\)
\(762\) −2.00000 −0.0724524
\(763\) 13.5000 + 23.3827i 0.488733 + 0.846510i
\(764\) −6.00000 + 10.3923i −0.217072 + 0.375980i
\(765\) 9.00000 15.5885i 0.325396 0.563602i
\(766\) −9.00000 −0.325183
\(767\) 0 0
\(768\) −1.00000 −0.0360844
\(769\) −12.0000 + 20.7846i −0.432731 + 0.749512i −0.997107 0.0760054i \(-0.975783\pi\)
0.564376 + 0.825518i \(0.309117\pi\)
\(770\) 0 0
\(771\) −1.50000 2.59808i −0.0540212 0.0935674i
\(772\) −6.00000 −0.215945
\(773\) −10.5000 18.1865i −0.377659 0.654124i 0.613062 0.790034i \(-0.289937\pi\)
−0.990721 + 0.135910i \(0.956604\pi\)
\(774\) 1.00000 + 1.73205i 0.0359443 + 0.0622573i
\(775\) 0 0
\(776\) 6.00000 + 10.3923i 0.215387 + 0.373062i
\(777\) 4.50000 7.79423i 0.161437 0.279616i
\(778\) −15.0000 + 25.9808i −0.537776 + 0.931455i
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 9.00000 15.5885i 0.321839 0.557442i
\(783\) 0 0
\(784\) −1.00000 1.73205i −0.0357143 0.0618590i
\(785\) 66.0000 2.35564
\(786\) −1.50000 2.59808i −0.0535032 0.0926703i
\(787\) −6.00000 10.3923i −0.213877 0.370446i 0.739048 0.673653i \(-0.235276\pi\)
−0.952925 + 0.303207i \(0.901942\pi\)
\(788\) 3.00000 0.106871
\(789\) 12.0000 + 20.7846i 0.427211 + 0.739952i
\(790\) 15.0000 25.9808i 0.533676 0.924354i
\(791\) −9.00000 + 15.5885i −0.320003 + 0.554262i
\(792\) 0 0
\(793\) 0 0
\(794\) −18.0000 −0.638796
\(795\) 9.00000 15.5885i 0.319197 0.552866i
\(796\) −10.0000 + 17.3205i −0.354441 + 0.613909i
\(797\) 9.00000 + 15.5885i 0.318796 + 0.552171i 0.980237 0.197826i \(-0.0633881\pi\)
−0.661441 + 0.749997i \(0.730055\pi\)
\(798\) −18.0000 −0.637193
\(799\) −4.50000 7.79423i −0.159199 0.275740i
\(800\) −2.00000 3.46410i −0.0707107 0.122474i
\(801\) −12.0000 −0.423999
\(802\) 15.0000 + 25.9808i 0.529668 + 0.917413i
\(803\) 0 0
\(804\) −6.00000 + 10.3923i −0.211604 + 0.366508i
\(805\) 54.0000 1.90325
\(806\) 0 0
\(807\) 0 0
\(808\) 6.00000 10.3923i 0.211079 0.365600i
\(809\) −7.50000 + 12.9904i −0.263686 + 0.456717i −0.967219 0.253946i \(-0.918272\pi\)
0.703533 + 0.710663i \(0.251605\pi\)
\(810\) 1.50000 + 2.59808i 0.0527046 + 0.0912871i
\(811\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(812\) 0 0
\(813\) −7.50000 12.9904i −0.263036 0.455593i
\(814\) 0 0
\(815\) −9.00000 15.5885i −0.315256 0.546040i
\(816\) −1.50000 + 2.59808i −0.0525105 + 0.0909509i
\(817\) 3.00000 5.19615i 0.104957 0.181790i
\(818\) −6.00000 −0.209785
\(819\) 0 0
\(820\) 0 0
\(821\) −22.5000 + 38.9711i −0.785255 + 1.36010i 0.143591 + 0.989637i \(0.454135\pi\)
−0.928846 + 0.370465i \(0.879198\pi\)
\(822\) −9.00000 + 15.5885i −0.313911 + 0.543710i
\(823\) 7.00000 + 12.1244i 0.244005 + 0.422628i 0.961851 0.273573i \(-0.0882054\pi\)
−0.717847 + 0.696201i \(0.754872\pi\)
\(824\) −14.0000 −0.487713
\(825\) 0 0
\(826\) 9.00000 + 15.5885i 0.313150 + 0.542392i
\(827\) −18.0000 −0.625921 −0.312961 0.949766i \(-0.601321\pi\)
−0.312961 + 0.949766i \(0.601321\pi\)
\(828\) 6.00000 + 10.3923i 0.208514 + 0.361158i
\(829\) −10.0000 + 17.3205i −0.347314 + 0.601566i −0.985771 0.168091i \(-0.946240\pi\)
0.638457 + 0.769657i \(0.279573\pi\)
\(830\) 9.00000 15.5885i 0.312395 0.541083i
\(831\) 8.00000 0.277517
\(832\) 0 0
\(833\) −6.00000 −0.207888
\(834\) 2.50000 4.33013i 0.0865679 0.149940i
\(835\) 18.0000 31.1769i 0.622916 1.07892i
\(836\) 0 0
\(837\) 0 0
\(838\) −7.50000 12.9904i −0.259083 0.448745i
\(839\) 12.0000 + 20.7846i 0.414286 + 0.717564i 0.995353 0.0962912i \(-0.0306980\pi\)
−0.581067 + 0.813856i \(0.697365\pi\)
\(840\) −9.00000 −0.310530
\(841\) 14.5000 + 25.1147i 0.500000 + 0.866025i
\(842\) 7.50000 12.9904i 0.258467 0.447678i
\(843\) 15.0000 25.9808i 0.516627 0.894825i
\(844\) −23.0000 −0.791693
\(845\) 0 0
\(846\) 6.00000 0.206284
\(847\) −16.5000 + 28.5788i −0.566947 + 0.981981i
\(848\) 3.00000 5.19615i 0.103020 0.178437i
\(849\) −2.00000 3.46410i −0.0686398 0.118888i
\(850\) −12.0000 −0.411597
\(851\) 9.00000 + 15.5885i 0.308516 + 0.534365i
\(852\) 7.50000 + 12.9904i 0.256946 + 0.445043i
\(853\) 39.0000 1.33533 0.667667 0.744460i \(-0.267293\pi\)
0.667667 + 0.744460i \(0.267293\pi\)
\(854\) −12.0000 20.7846i −0.410632 0.711235i
\(855\) 18.0000 31.1769i 0.615587 1.06623i
\(856\) 6.00000 10.3923i 0.205076 0.355202i
\(857\) −18.0000 −0.614868 −0.307434 0.951569i \(-0.599470\pi\)
−0.307434 + 0.951569i \(0.599470\pi\)
\(858\) 0 0
\(859\) 40.0000 1.36478 0.682391 0.730987i \(-0.260940\pi\)
0.682391 + 0.730987i \(0.260940\pi\)
\(860\) 1.50000 2.59808i 0.0511496 0.0885937i
\(861\) 0 0
\(862\) 7.50000 + 12.9904i 0.255451 + 0.442454i
\(863\) −39.0000 −1.32758 −0.663788 0.747921i \(-0.731052\pi\)
−0.663788 + 0.747921i \(0.731052\pi\)
\(864\) −2.50000 4.33013i −0.0850517 0.147314i
\(865\) 9.00000 + 15.5885i 0.306009 + 0.530023i
\(866\) 11.0000 0.373795
\(867\) −4.00000 6.92820i −0.135847 0.235294i
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 0 0
\(872\) 9.00000 0.304778
\(873\) −12.0000 + 20.7846i −0.406138 + 0.703452i
\(874\) 18.0000 31.1769i 0.608859 1.05457i
\(875\) 4.50000 + 7.79423i 0.152128 + 0.263493i
\(876\) 6.00000 0.202721
\(877\) −1.50000 2.59808i −0.0506514 0.0877308i 0.839588 0.543224i \(-0.182796\pi\)
−0.890239 + 0.455493i \(0.849463\pi\)
\(878\) −5.00000 8.66025i −0.168742 0.292269i
\(879\) −9.00000 −0.303562
\(880\) 0 0
\(881\) −16.5000 + 28.5788i −0.555899 + 0.962846i 0.441934 + 0.897048i \(0.354293\pi\)
−0.997833 + 0.0657979i \(0.979041\pi\)
\(882\) 2.00000 3.46410i 0.0673435 0.116642i
\(883\) 11.0000 0.370179 0.185090 0.982722i \(-0.440742\pi\)
0.185090 + 0.982722i \(0.440742\pi\)
\(884\) 0 0
\(885\) 18.0000 0.605063
\(886\) 10.5000 18.1865i 0.352754 0.610989i
\(887\) 6.00000 10.3923i 0.201460 0.348939i −0.747539 0.664218i \(-0.768765\pi\)
0.948999 + 0.315279i \(0.102098\pi\)
\(888\) −1.50000 2.59808i −0.0503367 0.0871857i
\(889\) −6.00000 −0.201234
\(890\) 9.00000 + 15.5885i 0.301681 + 0.522526i
\(891\) 0 0
\(892\) −9.00000 −0.301342
\(893\) −9.00000 15.5885i −0.301174 0.521648i
\(894\) −3.00000 + 5.19615i −0.100335 + 0.173785i
\(895\) −22.5000 + 38.9711i −0.752092 + 1.30266i
\(896\) −3.00000 −0.100223
\(897\) 0 0
\(898\) −24.0000 −0.800890
\(899\) 0 0
\(900\) 4.00000 6.92820i 0.133333 0.230940i
\(901\) −9.00000 15.5885i −0.299833 0.519327i
\(902\) 0 0
\(903\) −1.50000 2.59808i −0.0499169 0.0864586i
\(904\) 3.00000 + 5.19615i 0.0997785 + 0.172821i
\(905\) 6.00000 0.199447
\(906\) 7.50000 + 12.9904i 0.249171 + 0.431577i
\(907\) −8.50000 + 14.7224i −0.282238 + 0.488850i −0.971936 0.235247i \(-0.924410\pi\)
0.689698 + 0.724097i \(0.257743\pi\)
\(908\) 6.00000 10.3923i 0.199117 0.344881i
\(909\) 24.0000 0.796030
\(910\) 0 0
\(911\) 12.0000 0.397578 0.198789 0.980042i \(-0.436299\pi\)
0.198789 + 0.980042i \(0.436299\pi\)
\(912\) −3.00000 + 5.19615i −0.0993399 + 0.172062i
\(913\) 0 0
\(914\) −9.00000 15.5885i −0.297694 0.515620i
\(915\) −24.0000 −0.793416
\(916\) 4.50000 + 7.79423i 0.148684 + 0.257529i
\(917\) −4.50000 7.79423i −0.148603 0.257388i
\(918\) −15.0000 −0.495074
\(919\) 10.0000 + 17.3205i 0.329870 + 0.571351i 0.982486 0.186338i \(-0.0596619\pi\)
−0.652616 + 0.757689i \(0.726329\pi\)
\(920\) 9.00000 15.5885i 0.296721 0.513936i
\(921\) −9.00000 + 15.5885i −0.296560 + 0.513657i
\(922\) −15.0000 −0.493999
\(923\) 0 0
\(924\) 0 0
\(925\) 6.00000 10.3923i 0.197279 0.341697i
\(926\) −12.0000 + 20.7846i −0.394344 + 0.683025i
\(927\) −14.0000 24.2487i −0.459820 0.796432i
\(928\) 0 0
\(929\) 18.0000 + 31.1769i 0.590561 + 1.02288i 0.994157 + 0.107944i \(0.0344268\pi\)
−0.403596 + 0.914937i \(0.632240\pi\)
\(930\) 0 0
\(931\) −12.0000 −0.393284
\(932\) −10.5000 18.1865i −0.343939 0.595720i
\(933\) 9.00000 15.5885i 0.294647 0.510343i
\(934\) −6.00000 + 10.3923i −0.196326 + 0.340047i
\(935\) 0 0
\(936\) 0 0
\(937\) −2.00000 −0.0653372 −0.0326686 0.999466i \(-0.510401\pi\)
−0.0326686 + 0.999466i \(0.510401\pi\)
\(938\) −18.0000 + 31.1769i −0.587721 + 1.01796i
\(939\) 9.50000 16.4545i 0.310021 0.536972i
\(940\) −4.50000 7.79423i −0.146774 0.254220i
\(941\) −45.0000 −1.46696 −0.733479 0.679712i \(-0.762105\pi\)
−0.733479 + 0.679712i \(0.762105\pi\)
\(942\) −11.0000 19.0526i −0.358399 0.620766i
\(943\) 0 0
\(944\) 6.00000 0.195283
\(945\) −22.5000 38.9711i −0.731925 1.26773i
\(946\) 0 0
\(947\) 24.0000 41.5692i 0.779895 1.35082i −0.152106 0.988364i \(-0.548606\pi\)
0.932002 0.362454i \(-0.118061\pi\)
\(948\) −10.0000 −0.324785
\(949\) 0 0
\(950\) −24.0000 −0.778663
\(951\) 9.00000 15.5885i 0.291845 0.505490i
\(952\) −4.50000 + 7.79423i −0.145846 + 0.252612i
\(953\) 4.50000 + 7.79423i 0.145769 + 0.252480i 0.929660 0.368419i \(-0.120101\pi\)
−0.783890 + 0.620899i \(0.786768\pi\)
\(954\) 12.0000 0.388514
\(955\) 18.0000 + 31.1769i 0.582466 + 1.00886i
\(956\) −4.50000 7.79423i −0.145540 0.252083i
\(957\) 0 0
\(958\) 19.5000 + 33.7750i 0.630016 + 1.09122i
\(959\) −27.0000 + 46.7654i −0.871875 + 1.51013i
\(960\) −1.50000 + 2.59808i −0.0484123 + 0.0838525i
\(961\) −31.0000 −1.00000
\(962\) 0 0
\(963\) 24.0000 0.773389
\(964\) −15.0000 + 25.9808i −0.483117 + 0.836784i
\(965\) −9.00000 + 15.5885i −0.289720 + 0.501810i
\(966\) −9.00000 15.5885i −0.289570 0.501550i
\(967\) 3.00000 0.0964735 0.0482367 0.998836i \(-0.484640\pi\)
0.0482367 + 0.998836i \(0.484640\pi\)
\(968\) 5.50000 + 9.52628i 0.176777 + 0.306186i
\(969\) 9.00000 + 15.5885i 0.289122 + 0.500773i
\(970\) 36.0000 1.15589
\(971\) −13.5000 23.3827i −0.433236 0.750386i 0.563914 0.825833i \(-0.309295\pi\)
−0.997150 + 0.0754473i \(0.975962\pi\)
\(972\) 8.00000 13.8564i 0.256600 0.444444i
\(973\) 7.50000 12.9904i 0.240439 0.416452i
\(974\) −12.0000 −0.384505
\(975\) 0 0
\(976\) −8.00000 −0.256074
\(977\) 6.00000 10.3923i 0.191957 0.332479i −0.753942 0.656941i \(-0.771850\pi\)
0.945899 + 0.324462i \(0.105183\pi\)
\(978\) −3.00000 + 5.19615i −0.0959294 + 0.166155i
\(979\) 0 0
\(980\) −6.00000 −0.191663
\(981\) 9.00000 + 15.5885i 0.287348 + 0.497701i
\(982\) 13.5000 + 23.3827i 0.430802 + 0.746171i
\(983\) 9.00000 0.287055 0.143528 0.989646i \(-0.454155\pi\)
0.143528 + 0.989646i \(0.454155\pi\)
\(984\) 0 0
\(985\) 4.50000 7.79423i 0.143382 0.248345i
\(986\) 0 0
\(987\) −9.00000 −0.286473
\(988\) 0 0
\(989\) 6.00000 0.190789
\(990\) 0 0
\(991\) −1.00000 + 1.73205i −0.0317660 + 0.0550204i −0.881471 0.472237i \(-0.843446\pi\)
0.849705 + 0.527258i \(0.176780\pi\)
\(992\) 0 0
\(993\) −30.0000 −0.952021
\(994\) 22.5000 + 38.9711i 0.713657 + 1.23609i
\(995\) 30.0000 + 51.9615i 0.951064 + 1.64729i
\(996\) −6.00000 −0.190117
\(997\) −4.00000 6.92820i −0.126681 0.219418i 0.795708 0.605681i \(-0.207099\pi\)
−0.922389 + 0.386263i \(0.873766\pi\)
\(998\) 18.0000 31.1769i 0.569780 0.986888i
\(999\) 7.50000 12.9904i 0.237289 0.410997i
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 338.2.c.b.191.1 2
13.2 odd 12 338.2.e.c.23.1 4
13.3 even 3 inner 338.2.c.b.315.1 2
13.4 even 6 338.2.a.b.1.1 1
13.5 odd 4 338.2.e.c.147.2 4
13.6 odd 12 26.2.b.a.25.1 2
13.7 odd 12 26.2.b.a.25.2 yes 2
13.8 odd 4 338.2.e.c.147.1 4
13.9 even 3 338.2.a.d.1.1 1
13.10 even 6 338.2.c.f.315.1 2
13.11 odd 12 338.2.e.c.23.2 4
13.12 even 2 338.2.c.f.191.1 2
39.17 odd 6 3042.2.a.j.1.1 1
39.20 even 12 234.2.b.b.181.1 2
39.32 even 12 234.2.b.b.181.2 2
39.35 odd 6 3042.2.a.g.1.1 1
52.7 even 12 208.2.f.a.129.1 2
52.19 even 12 208.2.f.a.129.2 2
52.35 odd 6 2704.2.a.j.1.1 1
52.43 odd 6 2704.2.a.k.1.1 1
65.4 even 6 8450.2.a.u.1.1 1
65.7 even 12 650.2.c.a.649.2 2
65.9 even 6 8450.2.a.h.1.1 1
65.19 odd 12 650.2.d.b.51.2 2
65.32 even 12 650.2.c.d.649.2 2
65.33 even 12 650.2.c.d.649.1 2
65.58 even 12 650.2.c.a.649.1 2
65.59 odd 12 650.2.d.b.51.1 2
91.6 even 12 1274.2.d.c.883.1 2
91.19 even 12 1274.2.n.c.753.1 4
91.20 even 12 1274.2.d.c.883.2 2
91.32 odd 12 1274.2.n.d.961.2 4
91.33 even 12 1274.2.n.c.753.2 4
91.45 even 12 1274.2.n.c.961.2 4
91.46 odd 12 1274.2.n.d.961.1 4
91.58 odd 12 1274.2.n.d.753.1 4
91.59 even 12 1274.2.n.c.961.1 4
91.72 odd 12 1274.2.n.d.753.2 4
104.19 even 12 832.2.f.b.129.1 2
104.45 odd 12 832.2.f.d.129.1 2
104.59 even 12 832.2.f.b.129.2 2
104.85 odd 12 832.2.f.d.129.2 2
156.59 odd 12 1872.2.c.f.1585.2 2
156.71 odd 12 1872.2.c.f.1585.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
26.2.b.a.25.1 2 13.6 odd 12
26.2.b.a.25.2 yes 2 13.7 odd 12
208.2.f.a.129.1 2 52.7 even 12
208.2.f.a.129.2 2 52.19 even 12
234.2.b.b.181.1 2 39.20 even 12
234.2.b.b.181.2 2 39.32 even 12
338.2.a.b.1.1 1 13.4 even 6
338.2.a.d.1.1 1 13.9 even 3
338.2.c.b.191.1 2 1.1 even 1 trivial
338.2.c.b.315.1 2 13.3 even 3 inner
338.2.c.f.191.1 2 13.12 even 2
338.2.c.f.315.1 2 13.10 even 6
338.2.e.c.23.1 4 13.2 odd 12
338.2.e.c.23.2 4 13.11 odd 12
338.2.e.c.147.1 4 13.8 odd 4
338.2.e.c.147.2 4 13.5 odd 4
650.2.c.a.649.1 2 65.58 even 12
650.2.c.a.649.2 2 65.7 even 12
650.2.c.d.649.1 2 65.33 even 12
650.2.c.d.649.2 2 65.32 even 12
650.2.d.b.51.1 2 65.59 odd 12
650.2.d.b.51.2 2 65.19 odd 12
832.2.f.b.129.1 2 104.19 even 12
832.2.f.b.129.2 2 104.59 even 12
832.2.f.d.129.1 2 104.45 odd 12
832.2.f.d.129.2 2 104.85 odd 12
1274.2.d.c.883.1 2 91.6 even 12
1274.2.d.c.883.2 2 91.20 even 12
1274.2.n.c.753.1 4 91.19 even 12
1274.2.n.c.753.2 4 91.33 even 12
1274.2.n.c.961.1 4 91.59 even 12
1274.2.n.c.961.2 4 91.45 even 12
1274.2.n.d.753.1 4 91.58 odd 12
1274.2.n.d.753.2 4 91.72 odd 12
1274.2.n.d.961.1 4 91.46 odd 12
1274.2.n.d.961.2 4 91.32 odd 12
1872.2.c.f.1585.1 2 156.71 odd 12
1872.2.c.f.1585.2 2 156.59 odd 12
2704.2.a.j.1.1 1 52.35 odd 6
2704.2.a.k.1.1 1 52.43 odd 6
3042.2.a.g.1.1 1 39.35 odd 6
3042.2.a.j.1.1 1 39.17 odd 6
8450.2.a.h.1.1 1 65.9 even 6
8450.2.a.u.1.1 1 65.4 even 6