Properties

Label 1950.2.i.m.451.1
Level $1950$
Weight $2$
Character 1950.451
Analytic conductor $15.571$
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] = [1950,2,Mod(451,1950)]
 
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, 0, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1950.451");
 
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.i (of order \(3\), degree \(2\), 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: \(2\)
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 78)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 451.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1950.451
Dual form 1950.2.i.m.601.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{6} +(1.00000 + 1.73205i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{6} +(1.00000 + 1.73205i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-3.00000 + 5.19615i) q^{11} -1.00000 q^{12} +(3.50000 + 0.866025i) q^{13} -2.00000 q^{14} +(-0.500000 + 0.866025i) q^{16} +(-1.50000 - 2.59808i) q^{17} +1.00000 q^{18} +(-1.00000 - 1.73205i) q^{19} +2.00000 q^{21} +(-3.00000 - 5.19615i) q^{22} +(-3.00000 + 5.19615i) q^{23} +(0.500000 - 0.866025i) q^{24} +(-2.50000 + 2.59808i) q^{26} -1.00000 q^{27} +(1.00000 - 1.73205i) q^{28} +(-1.50000 + 2.59808i) q^{29} -4.00000 q^{31} +(-0.500000 - 0.866025i) q^{32} +(3.00000 + 5.19615i) q^{33} +3.00000 q^{34} +(-0.500000 + 0.866025i) q^{36} +(-3.50000 + 6.06218i) q^{37} +2.00000 q^{38} +(2.50000 - 2.59808i) q^{39} +(1.50000 - 2.59808i) q^{41} +(-1.00000 + 1.73205i) q^{42} +(-5.00000 - 8.66025i) q^{43} +6.00000 q^{44} +(-3.00000 - 5.19615i) q^{46} -6.00000 q^{47} +(0.500000 + 0.866025i) q^{48} +(1.50000 - 2.59808i) q^{49} -3.00000 q^{51} +(-1.00000 - 3.46410i) q^{52} -3.00000 q^{53} +(0.500000 - 0.866025i) q^{54} +(1.00000 + 1.73205i) q^{56} -2.00000 q^{57} +(-1.50000 - 2.59808i) q^{58} +(3.50000 + 6.06218i) q^{61} +(2.00000 - 3.46410i) q^{62} +(1.00000 - 1.73205i) q^{63} +1.00000 q^{64} -6.00000 q^{66} +(-5.00000 + 8.66025i) q^{67} +(-1.50000 + 2.59808i) q^{68} +(3.00000 + 5.19615i) q^{69} +(-3.00000 - 5.19615i) q^{71} +(-0.500000 - 0.866025i) q^{72} +13.0000 q^{73} +(-3.50000 - 6.06218i) q^{74} +(-1.00000 + 1.73205i) q^{76} -12.0000 q^{77} +(1.00000 + 3.46410i) q^{78} -4.00000 q^{79} +(-0.500000 + 0.866025i) q^{81} +(1.50000 + 2.59808i) q^{82} +6.00000 q^{83} +(-1.00000 - 1.73205i) q^{84} +10.0000 q^{86} +(1.50000 + 2.59808i) q^{87} +(-3.00000 + 5.19615i) q^{88} +(-9.00000 + 15.5885i) q^{89} +(2.00000 + 6.92820i) q^{91} +6.00000 q^{92} +(-2.00000 + 3.46410i) q^{93} +(3.00000 - 5.19615i) q^{94} -1.00000 q^{96} +(7.00000 + 12.1244i) q^{97} +(1.50000 + 2.59808i) q^{98} +6.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - q^{2} + q^{3} - q^{4} + q^{6} + 2 q^{7} + 2 q^{8} - q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - q^{2} + q^{3} - q^{4} + q^{6} + 2 q^{7} + 2 q^{8} - q^{9} - 6 q^{11} - 2 q^{12} + 7 q^{13} - 4 q^{14} - q^{16} - 3 q^{17} + 2 q^{18} - 2 q^{19} + 4 q^{21} - 6 q^{22} - 6 q^{23} + q^{24} - 5 q^{26} - 2 q^{27} + 2 q^{28} - 3 q^{29} - 8 q^{31} - q^{32} + 6 q^{33} + 6 q^{34} - q^{36} - 7 q^{37} + 4 q^{38} + 5 q^{39} + 3 q^{41} - 2 q^{42} - 10 q^{43} + 12 q^{44} - 6 q^{46} - 12 q^{47} + q^{48} + 3 q^{49} - 6 q^{51} - 2 q^{52} - 6 q^{53} + q^{54} + 2 q^{56} - 4 q^{57} - 3 q^{58} + 7 q^{61} + 4 q^{62} + 2 q^{63} + 2 q^{64} - 12 q^{66} - 10 q^{67} - 3 q^{68} + 6 q^{69} - 6 q^{71} - q^{72} + 26 q^{73} - 7 q^{74} - 2 q^{76} - 24 q^{77} + 2 q^{78} - 8 q^{79} - q^{81} + 3 q^{82} + 12 q^{83} - 2 q^{84} + 20 q^{86} + 3 q^{87} - 6 q^{88} - 18 q^{89} + 4 q^{91} + 12 q^{92} - 4 q^{93} + 6 q^{94} - 2 q^{96} + 14 q^{97} + 3 q^{98} + 12 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(301\) \(1301\) \(1327\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 + 0.866025i −0.353553 + 0.612372i
\(3\) 0.500000 0.866025i 0.288675 0.500000i
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 0 0
\(6\) 0.500000 + 0.866025i 0.204124 + 0.353553i
\(7\) 1.00000 + 1.73205i 0.377964 + 0.654654i 0.990766 0.135583i \(-0.0432908\pi\)
−0.612801 + 0.790237i \(0.709957\pi\)
\(8\) 1.00000 0.353553
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) 0 0
\(11\) −3.00000 + 5.19615i −0.904534 + 1.56670i −0.0829925 + 0.996550i \(0.526448\pi\)
−0.821541 + 0.570149i \(0.806886\pi\)
\(12\) −1.00000 −0.288675
\(13\) 3.50000 + 0.866025i 0.970725 + 0.240192i
\(14\) −2.00000 −0.534522
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −1.50000 2.59808i −0.363803 0.630126i 0.624780 0.780801i \(-0.285189\pi\)
−0.988583 + 0.150675i \(0.951855\pi\)
\(18\) 1.00000 0.235702
\(19\) −1.00000 1.73205i −0.229416 0.397360i 0.728219 0.685344i \(-0.240348\pi\)
−0.957635 + 0.287984i \(0.907015\pi\)
\(20\) 0 0
\(21\) 2.00000 0.436436
\(22\) −3.00000 5.19615i −0.639602 1.10782i
\(23\) −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
\(25\) 0 0
\(26\) −2.50000 + 2.59808i −0.490290 + 0.509525i
\(27\) −1.00000 −0.192450
\(28\) 1.00000 1.73205i 0.188982 0.327327i
\(29\) −1.50000 + 2.59808i −0.278543 + 0.482451i −0.971023 0.238987i \(-0.923185\pi\)
0.692480 + 0.721437i \(0.256518\pi\)
\(30\) 0 0
\(31\) −4.00000 −0.718421 −0.359211 0.933257i \(-0.616954\pi\)
−0.359211 + 0.933257i \(0.616954\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) 3.00000 + 5.19615i 0.522233 + 0.904534i
\(34\) 3.00000 0.514496
\(35\) 0 0
\(36\) −0.500000 + 0.866025i −0.0833333 + 0.144338i
\(37\) −3.50000 + 6.06218i −0.575396 + 0.996616i 0.420602 + 0.907245i \(0.361819\pi\)
−0.995998 + 0.0893706i \(0.971514\pi\)
\(38\) 2.00000 0.324443
\(39\) 2.50000 2.59808i 0.400320 0.416025i
\(40\) 0 0
\(41\) 1.50000 2.59808i 0.234261 0.405751i −0.724797 0.688963i \(-0.758066\pi\)
0.959058 + 0.283211i \(0.0913998\pi\)
\(42\) −1.00000 + 1.73205i −0.154303 + 0.267261i
\(43\) −5.00000 8.66025i −0.762493 1.32068i −0.941562 0.336840i \(-0.890642\pi\)
0.179069 0.983836i \(-0.442691\pi\)
\(44\) 6.00000 0.904534
\(45\) 0 0
\(46\) −3.00000 5.19615i −0.442326 0.766131i
\(47\) −6.00000 −0.875190 −0.437595 0.899172i \(-0.644170\pi\)
−0.437595 + 0.899172i \(0.644170\pi\)
\(48\) 0.500000 + 0.866025i 0.0721688 + 0.125000i
\(49\) 1.50000 2.59808i 0.214286 0.371154i
\(50\) 0 0
\(51\) −3.00000 −0.420084
\(52\) −1.00000 3.46410i −0.138675 0.480384i
\(53\) −3.00000 −0.412082 −0.206041 0.978543i \(-0.566058\pi\)
−0.206041 + 0.978543i \(0.566058\pi\)
\(54\) 0.500000 0.866025i 0.0680414 0.117851i
\(55\) 0 0
\(56\) 1.00000 + 1.73205i 0.133631 + 0.231455i
\(57\) −2.00000 −0.264906
\(58\) −1.50000 2.59808i −0.196960 0.341144i
\(59\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(60\) 0 0
\(61\) 3.50000 + 6.06218i 0.448129 + 0.776182i 0.998264 0.0588933i \(-0.0187572\pi\)
−0.550135 + 0.835076i \(0.685424\pi\)
\(62\) 2.00000 3.46410i 0.254000 0.439941i
\(63\) 1.00000 1.73205i 0.125988 0.218218i
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) −6.00000 −0.738549
\(67\) −5.00000 + 8.66025i −0.610847 + 1.05802i 0.380251 + 0.924883i \(0.375838\pi\)
−0.991098 + 0.133135i \(0.957496\pi\)
\(68\) −1.50000 + 2.59808i −0.181902 + 0.315063i
\(69\) 3.00000 + 5.19615i 0.361158 + 0.625543i
\(70\) 0 0
\(71\) −3.00000 5.19615i −0.356034 0.616670i 0.631260 0.775571i \(-0.282538\pi\)
−0.987294 + 0.158901i \(0.949205\pi\)
\(72\) −0.500000 0.866025i −0.0589256 0.102062i
\(73\) 13.0000 1.52153 0.760767 0.649025i \(-0.224823\pi\)
0.760767 + 0.649025i \(0.224823\pi\)
\(74\) −3.50000 6.06218i −0.406867 0.704714i
\(75\) 0 0
\(76\) −1.00000 + 1.73205i −0.114708 + 0.198680i
\(77\) −12.0000 −1.36753
\(78\) 1.00000 + 3.46410i 0.113228 + 0.392232i
\(79\) −4.00000 −0.450035 −0.225018 0.974355i \(-0.572244\pi\)
−0.225018 + 0.974355i \(0.572244\pi\)
\(80\) 0 0
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 1.50000 + 2.59808i 0.165647 + 0.286910i
\(83\) 6.00000 0.658586 0.329293 0.944228i \(-0.393190\pi\)
0.329293 + 0.944228i \(0.393190\pi\)
\(84\) −1.00000 1.73205i −0.109109 0.188982i
\(85\) 0 0
\(86\) 10.0000 1.07833
\(87\) 1.50000 + 2.59808i 0.160817 + 0.278543i
\(88\) −3.00000 + 5.19615i −0.319801 + 0.553912i
\(89\) −9.00000 + 15.5885i −0.953998 + 1.65237i −0.217354 + 0.976093i \(0.569742\pi\)
−0.736644 + 0.676280i \(0.763591\pi\)
\(90\) 0 0
\(91\) 2.00000 + 6.92820i 0.209657 + 0.726273i
\(92\) 6.00000 0.625543
\(93\) −2.00000 + 3.46410i −0.207390 + 0.359211i
\(94\) 3.00000 5.19615i 0.309426 0.535942i
\(95\) 0 0
\(96\) −1.00000 −0.102062
\(97\) 7.00000 + 12.1244i 0.710742 + 1.23104i 0.964579 + 0.263795i \(0.0849741\pi\)
−0.253837 + 0.967247i \(0.581693\pi\)
\(98\) 1.50000 + 2.59808i 0.151523 + 0.262445i
\(99\) 6.00000 0.603023
\(100\) 0 0
\(101\) −7.50000 + 12.9904i −0.746278 + 1.29259i 0.203317 + 0.979113i \(0.434828\pi\)
−0.949595 + 0.313478i \(0.898506\pi\)
\(102\) 1.50000 2.59808i 0.148522 0.257248i
\(103\) −14.0000 −1.37946 −0.689730 0.724066i \(-0.742271\pi\)
−0.689730 + 0.724066i \(0.742271\pi\)
\(104\) 3.50000 + 0.866025i 0.343203 + 0.0849208i
\(105\) 0 0
\(106\) 1.50000 2.59808i 0.145693 0.252347i
\(107\) −3.00000 + 5.19615i −0.290021 + 0.502331i −0.973814 0.227345i \(-0.926996\pi\)
0.683793 + 0.729676i \(0.260329\pi\)
\(108\) 0.500000 + 0.866025i 0.0481125 + 0.0833333i
\(109\) 14.0000 1.34096 0.670478 0.741929i \(-0.266089\pi\)
0.670478 + 0.741929i \(0.266089\pi\)
\(110\) 0 0
\(111\) 3.50000 + 6.06218i 0.332205 + 0.575396i
\(112\) −2.00000 −0.188982
\(113\) −1.50000 2.59808i −0.141108 0.244406i 0.786806 0.617200i \(-0.211733\pi\)
−0.927914 + 0.372794i \(0.878400\pi\)
\(114\) 1.00000 1.73205i 0.0936586 0.162221i
\(115\) 0 0
\(116\) 3.00000 0.278543
\(117\) −1.00000 3.46410i −0.0924500 0.320256i
\(118\) 0 0
\(119\) 3.00000 5.19615i 0.275010 0.476331i
\(120\) 0 0
\(121\) −12.5000 21.6506i −1.13636 1.96824i
\(122\) −7.00000 −0.633750
\(123\) −1.50000 2.59808i −0.135250 0.234261i
\(124\) 2.00000 + 3.46410i 0.179605 + 0.311086i
\(125\) 0 0
\(126\) 1.00000 + 1.73205i 0.0890871 + 0.154303i
\(127\) −2.00000 + 3.46410i −0.177471 + 0.307389i −0.941014 0.338368i \(-0.890125\pi\)
0.763542 + 0.645758i \(0.223458\pi\)
\(128\) −0.500000 + 0.866025i −0.0441942 + 0.0765466i
\(129\) −10.0000 −0.880451
\(130\) 0 0
\(131\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(132\) 3.00000 5.19615i 0.261116 0.452267i
\(133\) 2.00000 3.46410i 0.173422 0.300376i
\(134\) −5.00000 8.66025i −0.431934 0.748132i
\(135\) 0 0
\(136\) −1.50000 2.59808i −0.128624 0.222783i
\(137\) 4.50000 + 7.79423i 0.384461 + 0.665906i 0.991694 0.128618i \(-0.0410540\pi\)
−0.607233 + 0.794524i \(0.707721\pi\)
\(138\) −6.00000 −0.510754
\(139\) 2.00000 + 3.46410i 0.169638 + 0.293821i 0.938293 0.345843i \(-0.112407\pi\)
−0.768655 + 0.639664i \(0.779074\pi\)
\(140\) 0 0
\(141\) −3.00000 + 5.19615i −0.252646 + 0.437595i
\(142\) 6.00000 0.503509
\(143\) −15.0000 + 15.5885i −1.25436 + 1.30357i
\(144\) 1.00000 0.0833333
\(145\) 0 0
\(146\) −6.50000 + 11.2583i −0.537944 + 0.931746i
\(147\) −1.50000 2.59808i −0.123718 0.214286i
\(148\) 7.00000 0.575396
\(149\) 4.50000 + 7.79423i 0.368654 + 0.638528i 0.989355 0.145519i \(-0.0464853\pi\)
−0.620701 + 0.784047i \(0.713152\pi\)
\(150\) 0 0
\(151\) −10.0000 −0.813788 −0.406894 0.913475i \(-0.633388\pi\)
−0.406894 + 0.913475i \(0.633388\pi\)
\(152\) −1.00000 1.73205i −0.0811107 0.140488i
\(153\) −1.50000 + 2.59808i −0.121268 + 0.210042i
\(154\) 6.00000 10.3923i 0.483494 0.837436i
\(155\) 0 0
\(156\) −3.50000 0.866025i −0.280224 0.0693375i
\(157\) −5.00000 −0.399043 −0.199522 0.979893i \(-0.563939\pi\)
−0.199522 + 0.979893i \(0.563939\pi\)
\(158\) 2.00000 3.46410i 0.159111 0.275589i
\(159\) −1.50000 + 2.59808i −0.118958 + 0.206041i
\(160\) 0 0
\(161\) −12.0000 −0.945732
\(162\) −0.500000 0.866025i −0.0392837 0.0680414i
\(163\) −2.00000 3.46410i −0.156652 0.271329i 0.777007 0.629492i \(-0.216737\pi\)
−0.933659 + 0.358162i \(0.883403\pi\)
\(164\) −3.00000 −0.234261
\(165\) 0 0
\(166\) −3.00000 + 5.19615i −0.232845 + 0.403300i
\(167\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(168\) 2.00000 0.154303
\(169\) 11.5000 + 6.06218i 0.884615 + 0.466321i
\(170\) 0 0
\(171\) −1.00000 + 1.73205i −0.0764719 + 0.132453i
\(172\) −5.00000 + 8.66025i −0.381246 + 0.660338i
\(173\) −3.00000 5.19615i −0.228086 0.395056i 0.729155 0.684349i \(-0.239913\pi\)
−0.957241 + 0.289292i \(0.906580\pi\)
\(174\) −3.00000 −0.227429
\(175\) 0 0
\(176\) −3.00000 5.19615i −0.226134 0.391675i
\(177\) 0 0
\(178\) −9.00000 15.5885i −0.674579 1.16840i
\(179\) −3.00000 + 5.19615i −0.224231 + 0.388379i −0.956088 0.293079i \(-0.905320\pi\)
0.731858 + 0.681457i \(0.238654\pi\)
\(180\) 0 0
\(181\) −7.00000 −0.520306 −0.260153 0.965567i \(-0.583773\pi\)
−0.260153 + 0.965567i \(0.583773\pi\)
\(182\) −7.00000 1.73205i −0.518875 0.128388i
\(183\) 7.00000 0.517455
\(184\) −3.00000 + 5.19615i −0.221163 + 0.383065i
\(185\) 0 0
\(186\) −2.00000 3.46410i −0.146647 0.254000i
\(187\) 18.0000 1.31629
\(188\) 3.00000 + 5.19615i 0.218797 + 0.378968i
\(189\) −1.00000 1.73205i −0.0727393 0.125988i
\(190\) 0 0
\(191\) 6.00000 + 10.3923i 0.434145 + 0.751961i 0.997225 0.0744412i \(-0.0237173\pi\)
−0.563081 + 0.826402i \(0.690384\pi\)
\(192\) 0.500000 0.866025i 0.0360844 0.0625000i
\(193\) 11.5000 19.9186i 0.827788 1.43377i −0.0719816 0.997406i \(-0.522932\pi\)
0.899770 0.436365i \(-0.143734\pi\)
\(194\) −14.0000 −1.00514
\(195\) 0 0
\(196\) −3.00000 −0.214286
\(197\) 3.00000 5.19615i 0.213741 0.370211i −0.739141 0.673550i \(-0.764768\pi\)
0.952882 + 0.303340i \(0.0981018\pi\)
\(198\) −3.00000 + 5.19615i −0.213201 + 0.369274i
\(199\) 5.00000 + 8.66025i 0.354441 + 0.613909i 0.987022 0.160585i \(-0.0513380\pi\)
−0.632581 + 0.774494i \(0.718005\pi\)
\(200\) 0 0
\(201\) 5.00000 + 8.66025i 0.352673 + 0.610847i
\(202\) −7.50000 12.9904i −0.527698 0.914000i
\(203\) −6.00000 −0.421117
\(204\) 1.50000 + 2.59808i 0.105021 + 0.181902i
\(205\) 0 0
\(206\) 7.00000 12.1244i 0.487713 0.844744i
\(207\) 6.00000 0.417029
\(208\) −2.50000 + 2.59808i −0.173344 + 0.180144i
\(209\) 12.0000 0.830057
\(210\) 0 0
\(211\) 8.00000 13.8564i 0.550743 0.953914i −0.447478 0.894295i \(-0.647678\pi\)
0.998221 0.0596196i \(-0.0189888\pi\)
\(212\) 1.50000 + 2.59808i 0.103020 + 0.178437i
\(213\) −6.00000 −0.411113
\(214\) −3.00000 5.19615i −0.205076 0.355202i
\(215\) 0 0
\(216\) −1.00000 −0.0680414
\(217\) −4.00000 6.92820i −0.271538 0.470317i
\(218\) −7.00000 + 12.1244i −0.474100 + 0.821165i
\(219\) 6.50000 11.2583i 0.439229 0.760767i
\(220\) 0 0
\(221\) −3.00000 10.3923i −0.201802 0.699062i
\(222\) −7.00000 −0.469809
\(223\) 4.00000 6.92820i 0.267860 0.463947i −0.700449 0.713702i \(-0.747017\pi\)
0.968309 + 0.249756i \(0.0803503\pi\)
\(224\) 1.00000 1.73205i 0.0668153 0.115728i
\(225\) 0 0
\(226\) 3.00000 0.199557
\(227\) 9.00000 + 15.5885i 0.597351 + 1.03464i 0.993210 + 0.116331i \(0.0371134\pi\)
−0.395860 + 0.918311i \(0.629553\pi\)
\(228\) 1.00000 + 1.73205i 0.0662266 + 0.114708i
\(229\) −22.0000 −1.45380 −0.726900 0.686743i \(-0.759040\pi\)
−0.726900 + 0.686743i \(0.759040\pi\)
\(230\) 0 0
\(231\) −6.00000 + 10.3923i −0.394771 + 0.683763i
\(232\) −1.50000 + 2.59808i −0.0984798 + 0.170572i
\(233\) 6.00000 0.393073 0.196537 0.980497i \(-0.437031\pi\)
0.196537 + 0.980497i \(0.437031\pi\)
\(234\) 3.50000 + 0.866025i 0.228802 + 0.0566139i
\(235\) 0 0
\(236\) 0 0
\(237\) −2.00000 + 3.46410i −0.129914 + 0.225018i
\(238\) 3.00000 + 5.19615i 0.194461 + 0.336817i
\(239\) 6.00000 0.388108 0.194054 0.980991i \(-0.437836\pi\)
0.194054 + 0.980991i \(0.437836\pi\)
\(240\) 0 0
\(241\) 0.500000 + 0.866025i 0.0322078 + 0.0557856i 0.881680 0.471848i \(-0.156413\pi\)
−0.849472 + 0.527633i \(0.823079\pi\)
\(242\) 25.0000 1.60706
\(243\) 0.500000 + 0.866025i 0.0320750 + 0.0555556i
\(244\) 3.50000 6.06218i 0.224065 0.388091i
\(245\) 0 0
\(246\) 3.00000 0.191273
\(247\) −2.00000 6.92820i −0.127257 0.440831i
\(248\) −4.00000 −0.254000
\(249\) 3.00000 5.19615i 0.190117 0.329293i
\(250\) 0 0
\(251\) 6.00000 + 10.3923i 0.378717 + 0.655956i 0.990876 0.134778i \(-0.0430322\pi\)
−0.612159 + 0.790735i \(0.709699\pi\)
\(252\) −2.00000 −0.125988
\(253\) −18.0000 31.1769i −1.13165 1.96008i
\(254\) −2.00000 3.46410i −0.125491 0.217357i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −1.50000 + 2.59808i −0.0935674 + 0.162064i −0.909010 0.416775i \(-0.863160\pi\)
0.815442 + 0.578838i \(0.196494\pi\)
\(258\) 5.00000 8.66025i 0.311286 0.539164i
\(259\) −14.0000 −0.869918
\(260\) 0 0
\(261\) 3.00000 0.185695
\(262\) 0 0
\(263\) −3.00000 + 5.19615i −0.184988 + 0.320408i −0.943572 0.331166i \(-0.892558\pi\)
0.758585 + 0.651575i \(0.225891\pi\)
\(264\) 3.00000 + 5.19615i 0.184637 + 0.319801i
\(265\) 0 0
\(266\) 2.00000 + 3.46410i 0.122628 + 0.212398i
\(267\) 9.00000 + 15.5885i 0.550791 + 0.953998i
\(268\) 10.0000 0.610847
\(269\) −9.00000 15.5885i −0.548740 0.950445i −0.998361 0.0572259i \(-0.981774\pi\)
0.449622 0.893219i \(-0.351559\pi\)
\(270\) 0 0
\(271\) 8.00000 13.8564i 0.485965 0.841717i −0.513905 0.857847i \(-0.671801\pi\)
0.999870 + 0.0161307i \(0.00513477\pi\)
\(272\) 3.00000 0.181902
\(273\) 7.00000 + 1.73205i 0.423659 + 0.104828i
\(274\) −9.00000 −0.543710
\(275\) 0 0
\(276\) 3.00000 5.19615i 0.180579 0.312772i
\(277\) 8.50000 + 14.7224i 0.510716 + 0.884585i 0.999923 + 0.0124177i \(0.00395278\pi\)
−0.489207 + 0.872167i \(0.662714\pi\)
\(278\) −4.00000 −0.239904
\(279\) 2.00000 + 3.46410i 0.119737 + 0.207390i
\(280\) 0 0
\(281\) 9.00000 0.536895 0.268447 0.963294i \(-0.413489\pi\)
0.268447 + 0.963294i \(0.413489\pi\)
\(282\) −3.00000 5.19615i −0.178647 0.309426i
\(283\) 7.00000 12.1244i 0.416107 0.720718i −0.579437 0.815017i \(-0.696728\pi\)
0.995544 + 0.0942988i \(0.0300609\pi\)
\(284\) −3.00000 + 5.19615i −0.178017 + 0.308335i
\(285\) 0 0
\(286\) −6.00000 20.7846i −0.354787 1.22902i
\(287\) 6.00000 0.354169
\(288\) −0.500000 + 0.866025i −0.0294628 + 0.0510310i
\(289\) 4.00000 6.92820i 0.235294 0.407541i
\(290\) 0 0
\(291\) 14.0000 0.820695
\(292\) −6.50000 11.2583i −0.380384 0.658844i
\(293\) −10.5000 18.1865i −0.613417 1.06247i −0.990660 0.136355i \(-0.956461\pi\)
0.377244 0.926114i \(-0.376872\pi\)
\(294\) 3.00000 0.174964
\(295\) 0 0
\(296\) −3.50000 + 6.06218i −0.203433 + 0.352357i
\(297\) 3.00000 5.19615i 0.174078 0.301511i
\(298\) −9.00000 −0.521356
\(299\) −15.0000 + 15.5885i −0.867472 + 0.901504i
\(300\) 0 0
\(301\) 10.0000 17.3205i 0.576390 0.998337i
\(302\) 5.00000 8.66025i 0.287718 0.498342i
\(303\) 7.50000 + 12.9904i 0.430864 + 0.746278i
\(304\) 2.00000 0.114708
\(305\) 0 0
\(306\) −1.50000 2.59808i −0.0857493 0.148522i
\(307\) 10.0000 0.570730 0.285365 0.958419i \(-0.407885\pi\)
0.285365 + 0.958419i \(0.407885\pi\)
\(308\) 6.00000 + 10.3923i 0.341882 + 0.592157i
\(309\) −7.00000 + 12.1244i −0.398216 + 0.689730i
\(310\) 0 0
\(311\) −30.0000 −1.70114 −0.850572 0.525859i \(-0.823744\pi\)
−0.850572 + 0.525859i \(0.823744\pi\)
\(312\) 2.50000 2.59808i 0.141535 0.147087i
\(313\) 10.0000 0.565233 0.282617 0.959233i \(-0.408798\pi\)
0.282617 + 0.959233i \(0.408798\pi\)
\(314\) 2.50000 4.33013i 0.141083 0.244363i
\(315\) 0 0
\(316\) 2.00000 + 3.46410i 0.112509 + 0.194871i
\(317\) −3.00000 −0.168497 −0.0842484 0.996445i \(-0.526849\pi\)
−0.0842484 + 0.996445i \(0.526849\pi\)
\(318\) −1.50000 2.59808i −0.0841158 0.145693i
\(319\) −9.00000 15.5885i −0.503903 0.872786i
\(320\) 0 0
\(321\) 3.00000 + 5.19615i 0.167444 + 0.290021i
\(322\) 6.00000 10.3923i 0.334367 0.579141i
\(323\) −3.00000 + 5.19615i −0.166924 + 0.289122i
\(324\) 1.00000 0.0555556
\(325\) 0 0
\(326\) 4.00000 0.221540
\(327\) 7.00000 12.1244i 0.387101 0.670478i
\(328\) 1.50000 2.59808i 0.0828236 0.143455i
\(329\) −6.00000 10.3923i −0.330791 0.572946i
\(330\) 0 0
\(331\) 2.00000 + 3.46410i 0.109930 + 0.190404i 0.915742 0.401768i \(-0.131604\pi\)
−0.805812 + 0.592172i \(0.798271\pi\)
\(332\) −3.00000 5.19615i −0.164646 0.285176i
\(333\) 7.00000 0.383598
\(334\) 0 0
\(335\) 0 0
\(336\) −1.00000 + 1.73205i −0.0545545 + 0.0944911i
\(337\) −23.0000 −1.25289 −0.626445 0.779466i \(-0.715491\pi\)
−0.626445 + 0.779466i \(0.715491\pi\)
\(338\) −11.0000 + 6.92820i −0.598321 + 0.376845i
\(339\) −3.00000 −0.162938
\(340\) 0 0
\(341\) 12.0000 20.7846i 0.649836 1.12555i
\(342\) −1.00000 1.73205i −0.0540738 0.0936586i
\(343\) 20.0000 1.07990
\(344\) −5.00000 8.66025i −0.269582 0.466930i
\(345\) 0 0
\(346\) 6.00000 0.322562
\(347\) −15.0000 25.9808i −0.805242 1.39472i −0.916127 0.400887i \(-0.868702\pi\)
0.110885 0.993833i \(-0.464631\pi\)
\(348\) 1.50000 2.59808i 0.0804084 0.139272i
\(349\) 5.00000 8.66025i 0.267644 0.463573i −0.700609 0.713545i \(-0.747088\pi\)
0.968253 + 0.249973i \(0.0804216\pi\)
\(350\) 0 0
\(351\) −3.50000 0.866025i −0.186816 0.0462250i
\(352\) 6.00000 0.319801
\(353\) −7.50000 + 12.9904i −0.399185 + 0.691408i −0.993626 0.112731i \(-0.964040\pi\)
0.594441 + 0.804139i \(0.297373\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 18.0000 0.953998
\(357\) −3.00000 5.19615i −0.158777 0.275010i
\(358\) −3.00000 5.19615i −0.158555 0.274625i
\(359\) 6.00000 0.316668 0.158334 0.987386i \(-0.449388\pi\)
0.158334 + 0.987386i \(0.449388\pi\)
\(360\) 0 0
\(361\) 7.50000 12.9904i 0.394737 0.683704i
\(362\) 3.50000 6.06218i 0.183956 0.318621i
\(363\) −25.0000 −1.31216
\(364\) 5.00000 5.19615i 0.262071 0.272352i
\(365\) 0 0
\(366\) −3.50000 + 6.06218i −0.182948 + 0.316875i
\(367\) 1.00000 1.73205i 0.0521996 0.0904123i −0.838745 0.544524i \(-0.816710\pi\)
0.890945 + 0.454112i \(0.150043\pi\)
\(368\) −3.00000 5.19615i −0.156386 0.270868i
\(369\) −3.00000 −0.156174
\(370\) 0 0
\(371\) −3.00000 5.19615i −0.155752 0.269771i
\(372\) 4.00000 0.207390
\(373\) 14.5000 + 25.1147i 0.750782 + 1.30039i 0.947444 + 0.319921i \(0.103656\pi\)
−0.196663 + 0.980471i \(0.563010\pi\)
\(374\) −9.00000 + 15.5885i −0.465379 + 0.806060i
\(375\) 0 0
\(376\) −6.00000 −0.309426
\(377\) −7.50000 + 7.79423i −0.386270 + 0.401423i
\(378\) 2.00000 0.102869
\(379\) −10.0000 + 17.3205i −0.513665 + 0.889695i 0.486209 + 0.873843i \(0.338379\pi\)
−0.999874 + 0.0158521i \(0.994954\pi\)
\(380\) 0 0
\(381\) 2.00000 + 3.46410i 0.102463 + 0.177471i
\(382\) −12.0000 −0.613973
\(383\) 12.0000 + 20.7846i 0.613171 + 1.06204i 0.990702 + 0.136047i \(0.0434398\pi\)
−0.377531 + 0.925997i \(0.623227\pi\)
\(384\) 0.500000 + 0.866025i 0.0255155 + 0.0441942i
\(385\) 0 0
\(386\) 11.5000 + 19.9186i 0.585335 + 1.01383i
\(387\) −5.00000 + 8.66025i −0.254164 + 0.440225i
\(388\) 7.00000 12.1244i 0.355371 0.615521i
\(389\) 39.0000 1.97738 0.988689 0.149979i \(-0.0479205\pi\)
0.988689 + 0.149979i \(0.0479205\pi\)
\(390\) 0 0
\(391\) 18.0000 0.910299
\(392\) 1.50000 2.59808i 0.0757614 0.131223i
\(393\) 0 0
\(394\) 3.00000 + 5.19615i 0.151138 + 0.261778i
\(395\) 0 0
\(396\) −3.00000 5.19615i −0.150756 0.261116i
\(397\) 7.00000 + 12.1244i 0.351320 + 0.608504i 0.986481 0.163876i \(-0.0523996\pi\)
−0.635161 + 0.772380i \(0.719066\pi\)
\(398\) −10.0000 −0.501255
\(399\) −2.00000 3.46410i −0.100125 0.173422i
\(400\) 0 0
\(401\) 1.50000 2.59808i 0.0749064 0.129742i −0.826139 0.563466i \(-0.809468\pi\)
0.901046 + 0.433724i \(0.142801\pi\)
\(402\) −10.0000 −0.498755
\(403\) −14.0000 3.46410i −0.697390 0.172559i
\(404\) 15.0000 0.746278
\(405\) 0 0
\(406\) 3.00000 5.19615i 0.148888 0.257881i
\(407\) −21.0000 36.3731i −1.04093 1.80295i
\(408\) −3.00000 −0.148522
\(409\) 0.500000 + 0.866025i 0.0247234 + 0.0428222i 0.878122 0.478436i \(-0.158796\pi\)
−0.853399 + 0.521258i \(0.825463\pi\)
\(410\) 0 0
\(411\) 9.00000 0.443937
\(412\) 7.00000 + 12.1244i 0.344865 + 0.597324i
\(413\) 0 0
\(414\) −3.00000 + 5.19615i −0.147442 + 0.255377i
\(415\) 0 0
\(416\) −1.00000 3.46410i −0.0490290 0.169842i
\(417\) 4.00000 0.195881
\(418\) −6.00000 + 10.3923i −0.293470 + 0.508304i
\(419\) −12.0000 + 20.7846i −0.586238 + 1.01539i 0.408481 + 0.912767i \(0.366058\pi\)
−0.994720 + 0.102628i \(0.967275\pi\)
\(420\) 0 0
\(421\) 29.0000 1.41337 0.706687 0.707527i \(-0.250189\pi\)
0.706687 + 0.707527i \(0.250189\pi\)
\(422\) 8.00000 + 13.8564i 0.389434 + 0.674519i
\(423\) 3.00000 + 5.19615i 0.145865 + 0.252646i
\(424\) −3.00000 −0.145693
\(425\) 0 0
\(426\) 3.00000 5.19615i 0.145350 0.251754i
\(427\) −7.00000 + 12.1244i −0.338754 + 0.586739i
\(428\) 6.00000 0.290021
\(429\) 6.00000 + 20.7846i 0.289683 + 1.00349i
\(430\) 0 0
\(431\) 3.00000 5.19615i 0.144505 0.250290i −0.784683 0.619897i \(-0.787174\pi\)
0.929188 + 0.369607i \(0.120508\pi\)
\(432\) 0.500000 0.866025i 0.0240563 0.0416667i
\(433\) −6.50000 11.2583i −0.312370 0.541041i 0.666505 0.745501i \(-0.267790\pi\)
−0.978875 + 0.204460i \(0.934456\pi\)
\(434\) 8.00000 0.384012
\(435\) 0 0
\(436\) −7.00000 12.1244i −0.335239 0.580651i
\(437\) 12.0000 0.574038
\(438\) 6.50000 + 11.2583i 0.310582 + 0.537944i
\(439\) −7.00000 + 12.1244i −0.334092 + 0.578664i −0.983310 0.181938i \(-0.941763\pi\)
0.649218 + 0.760602i \(0.275096\pi\)
\(440\) 0 0
\(441\) −3.00000 −0.142857
\(442\) 10.5000 + 2.59808i 0.499434 + 0.123578i
\(443\) 36.0000 1.71041 0.855206 0.518289i \(-0.173431\pi\)
0.855206 + 0.518289i \(0.173431\pi\)
\(444\) 3.50000 6.06218i 0.166103 0.287698i
\(445\) 0 0
\(446\) 4.00000 + 6.92820i 0.189405 + 0.328060i
\(447\) 9.00000 0.425685
\(448\) 1.00000 + 1.73205i 0.0472456 + 0.0818317i
\(449\) −9.00000 15.5885i −0.424736 0.735665i 0.571660 0.820491i \(-0.306300\pi\)
−0.996396 + 0.0848262i \(0.972967\pi\)
\(450\) 0 0
\(451\) 9.00000 + 15.5885i 0.423793 + 0.734032i
\(452\) −1.50000 + 2.59808i −0.0705541 + 0.122203i
\(453\) −5.00000 + 8.66025i −0.234920 + 0.406894i
\(454\) −18.0000 −0.844782
\(455\) 0 0
\(456\) −2.00000 −0.0936586
\(457\) 5.50000 9.52628i 0.257279 0.445621i −0.708233 0.705979i \(-0.750507\pi\)
0.965512 + 0.260358i \(0.0838407\pi\)
\(458\) 11.0000 19.0526i 0.513996 0.890268i
\(459\) 1.50000 + 2.59808i 0.0700140 + 0.121268i
\(460\) 0 0
\(461\) −7.50000 12.9904i −0.349310 0.605022i 0.636817 0.771015i \(-0.280251\pi\)
−0.986127 + 0.165992i \(0.946917\pi\)
\(462\) −6.00000 10.3923i −0.279145 0.483494i
\(463\) −38.0000 −1.76601 −0.883005 0.469364i \(-0.844483\pi\)
−0.883005 + 0.469364i \(0.844483\pi\)
\(464\) −1.50000 2.59808i −0.0696358 0.120613i
\(465\) 0 0
\(466\) −3.00000 + 5.19615i −0.138972 + 0.240707i
\(467\) 18.0000 0.832941 0.416470 0.909149i \(-0.363267\pi\)
0.416470 + 0.909149i \(0.363267\pi\)
\(468\) −2.50000 + 2.59808i −0.115563 + 0.120096i
\(469\) −20.0000 −0.923514
\(470\) 0 0
\(471\) −2.50000 + 4.33013i −0.115194 + 0.199522i
\(472\) 0 0
\(473\) 60.0000 2.75880
\(474\) −2.00000 3.46410i −0.0918630 0.159111i
\(475\) 0 0
\(476\) −6.00000 −0.275010
\(477\) 1.50000 + 2.59808i 0.0686803 + 0.118958i
\(478\) −3.00000 + 5.19615i −0.137217 + 0.237666i
\(479\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(480\) 0 0
\(481\) −17.5000 + 18.1865i −0.797931 + 0.829235i
\(482\) −1.00000 −0.0455488
\(483\) −6.00000 + 10.3923i −0.273009 + 0.472866i
\(484\) −12.5000 + 21.6506i −0.568182 + 0.984120i
\(485\) 0 0
\(486\) −1.00000 −0.0453609
\(487\) 1.00000 + 1.73205i 0.0453143 + 0.0784867i 0.887793 0.460243i \(-0.152238\pi\)
−0.842479 + 0.538730i \(0.818904\pi\)
\(488\) 3.50000 + 6.06218i 0.158438 + 0.274422i
\(489\) −4.00000 −0.180886
\(490\) 0 0
\(491\) 9.00000 15.5885i 0.406164 0.703497i −0.588292 0.808649i \(-0.700199\pi\)
0.994456 + 0.105151i \(0.0335327\pi\)
\(492\) −1.50000 + 2.59808i −0.0676252 + 0.117130i
\(493\) 9.00000 0.405340
\(494\) 7.00000 + 1.73205i 0.314945 + 0.0779287i
\(495\) 0 0
\(496\) 2.00000 3.46410i 0.0898027 0.155543i
\(497\) 6.00000 10.3923i 0.269137 0.466159i
\(498\) 3.00000 + 5.19615i 0.134433 + 0.232845i
\(499\) 32.0000 1.43252 0.716258 0.697835i \(-0.245853\pi\)
0.716258 + 0.697835i \(0.245853\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) −12.0000 −0.535586
\(503\) 3.00000 + 5.19615i 0.133763 + 0.231685i 0.925124 0.379664i \(-0.123960\pi\)
−0.791361 + 0.611349i \(0.790627\pi\)
\(504\) 1.00000 1.73205i 0.0445435 0.0771517i
\(505\) 0 0
\(506\) 36.0000 1.60040
\(507\) 11.0000 6.92820i 0.488527 0.307692i
\(508\) 4.00000 0.177471
\(509\) −1.50000 + 2.59808i −0.0664863 + 0.115158i −0.897352 0.441315i \(-0.854512\pi\)
0.830866 + 0.556473i \(0.187846\pi\)
\(510\) 0 0
\(511\) 13.0000 + 22.5167i 0.575086 + 0.996078i
\(512\) 1.00000 0.0441942
\(513\) 1.00000 + 1.73205i 0.0441511 + 0.0764719i
\(514\) −1.50000 2.59808i −0.0661622 0.114596i
\(515\) 0 0
\(516\) 5.00000 + 8.66025i 0.220113 + 0.381246i
\(517\) 18.0000 31.1769i 0.791639 1.37116i
\(518\) 7.00000 12.1244i 0.307562 0.532714i
\(519\) −6.00000 −0.263371
\(520\) 0 0
\(521\) 33.0000 1.44576 0.722878 0.690976i \(-0.242819\pi\)
0.722878 + 0.690976i \(0.242819\pi\)
\(522\) −1.50000 + 2.59808i −0.0656532 + 0.113715i
\(523\) −17.0000 + 29.4449i −0.743358 + 1.28753i 0.207600 + 0.978214i \(0.433435\pi\)
−0.950958 + 0.309320i \(0.899899\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) −3.00000 5.19615i −0.130806 0.226563i
\(527\) 6.00000 + 10.3923i 0.261364 + 0.452696i
\(528\) −6.00000 −0.261116
\(529\) −6.50000 11.2583i −0.282609 0.489493i
\(530\) 0 0
\(531\) 0 0
\(532\) −4.00000 −0.173422
\(533\) 7.50000 7.79423i 0.324861 0.337606i
\(534\) −18.0000 −0.778936
\(535\) 0 0
\(536\) −5.00000 + 8.66025i −0.215967 + 0.374066i
\(537\) 3.00000 + 5.19615i 0.129460 + 0.224231i
\(538\) 18.0000 0.776035
\(539\) 9.00000 + 15.5885i 0.387657 + 0.671442i
\(540\) 0 0
\(541\) 29.0000 1.24681 0.623404 0.781900i \(-0.285749\pi\)
0.623404 + 0.781900i \(0.285749\pi\)
\(542\) 8.00000 + 13.8564i 0.343629 + 0.595184i
\(543\) −3.50000 + 6.06218i −0.150199 + 0.260153i
\(544\) −1.50000 + 2.59808i −0.0643120 + 0.111392i
\(545\) 0 0
\(546\) −5.00000 + 5.19615i −0.213980 + 0.222375i
\(547\) 34.0000 1.45374 0.726868 0.686778i \(-0.240975\pi\)
0.726868 + 0.686778i \(0.240975\pi\)
\(548\) 4.50000 7.79423i 0.192230 0.332953i
\(549\) 3.50000 6.06218i 0.149376 0.258727i
\(550\) 0 0
\(551\) 6.00000 0.255609
\(552\) 3.00000 + 5.19615i 0.127688 + 0.221163i
\(553\) −4.00000 6.92820i −0.170097 0.294617i
\(554\) −17.0000 −0.722261
\(555\) 0 0
\(556\) 2.00000 3.46410i 0.0848189 0.146911i
\(557\) 1.50000 2.59808i 0.0635570 0.110084i −0.832496 0.554031i \(-0.813089\pi\)
0.896053 + 0.443947i \(0.146422\pi\)
\(558\) −4.00000 −0.169334
\(559\) −10.0000 34.6410i −0.422955 1.46516i
\(560\) 0 0
\(561\) 9.00000 15.5885i 0.379980 0.658145i
\(562\) −4.50000 + 7.79423i −0.189821 + 0.328780i
\(563\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(564\) 6.00000 0.252646
\(565\) 0 0
\(566\) 7.00000 + 12.1244i 0.294232 + 0.509625i
\(567\) −2.00000 −0.0839921
\(568\) −3.00000 5.19615i −0.125877 0.218026i
\(569\) −3.00000 + 5.19615i −0.125767 + 0.217834i −0.922032 0.387113i \(-0.873472\pi\)
0.796266 + 0.604947i \(0.206806\pi\)
\(570\) 0 0
\(571\) −22.0000 −0.920671 −0.460336 0.887745i \(-0.652271\pi\)
−0.460336 + 0.887745i \(0.652271\pi\)
\(572\) 21.0000 + 5.19615i 0.878054 + 0.217262i
\(573\) 12.0000 0.501307
\(574\) −3.00000 + 5.19615i −0.125218 + 0.216883i
\(575\) 0 0
\(576\) −0.500000 0.866025i −0.0208333 0.0360844i
\(577\) −11.0000 −0.457936 −0.228968 0.973434i \(-0.573535\pi\)
−0.228968 + 0.973434i \(0.573535\pi\)
\(578\) 4.00000 + 6.92820i 0.166378 + 0.288175i
\(579\) −11.5000 19.9186i −0.477924 0.827788i
\(580\) 0 0
\(581\) 6.00000 + 10.3923i 0.248922 + 0.431145i
\(582\) −7.00000 + 12.1244i −0.290159 + 0.502571i
\(583\) 9.00000 15.5885i 0.372742 0.645608i
\(584\) 13.0000 0.537944
\(585\) 0 0
\(586\) 21.0000 0.867502
\(587\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(588\) −1.50000 + 2.59808i −0.0618590 + 0.107143i
\(589\) 4.00000 + 6.92820i 0.164817 + 0.285472i
\(590\) 0 0
\(591\) −3.00000 5.19615i −0.123404 0.213741i
\(592\) −3.50000 6.06218i −0.143849 0.249154i
\(593\) −9.00000 −0.369586 −0.184793 0.982777i \(-0.559161\pi\)
−0.184793 + 0.982777i \(0.559161\pi\)
\(594\) 3.00000 + 5.19615i 0.123091 + 0.213201i
\(595\) 0 0
\(596\) 4.50000 7.79423i 0.184327 0.319264i
\(597\) 10.0000 0.409273
\(598\) −6.00000 20.7846i −0.245358 0.849946i
\(599\) 24.0000 0.980613 0.490307 0.871550i \(-0.336885\pi\)
0.490307 + 0.871550i \(0.336885\pi\)
\(600\) 0 0
\(601\) 18.5000 32.0429i 0.754631 1.30706i −0.190927 0.981604i \(-0.561149\pi\)
0.945558 0.325455i \(-0.105517\pi\)
\(602\) 10.0000 + 17.3205i 0.407570 + 0.705931i
\(603\) 10.0000 0.407231
\(604\) 5.00000 + 8.66025i 0.203447 + 0.352381i
\(605\) 0 0
\(606\) −15.0000 −0.609333
\(607\) 16.0000 + 27.7128i 0.649420 + 1.12483i 0.983262 + 0.182199i \(0.0583216\pi\)
−0.333842 + 0.942629i \(0.608345\pi\)
\(608\) −1.00000 + 1.73205i −0.0405554 + 0.0702439i
\(609\) −3.00000 + 5.19615i −0.121566 + 0.210559i
\(610\) 0 0
\(611\) −21.0000 5.19615i −0.849569 0.210214i
\(612\) 3.00000 0.121268
\(613\) −15.5000 + 26.8468i −0.626039 + 1.08433i 0.362300 + 0.932062i \(0.381992\pi\)
−0.988339 + 0.152270i \(0.951342\pi\)
\(614\) −5.00000 + 8.66025i −0.201784 + 0.349499i
\(615\) 0 0
\(616\) −12.0000 −0.483494
\(617\) −7.50000 12.9904i −0.301939 0.522973i 0.674636 0.738150i \(-0.264300\pi\)
−0.976575 + 0.215177i \(0.930967\pi\)
\(618\) −7.00000 12.1244i −0.281581 0.487713i
\(619\) 8.00000 0.321547 0.160774 0.986991i \(-0.448601\pi\)
0.160774 + 0.986991i \(0.448601\pi\)
\(620\) 0 0
\(621\) 3.00000 5.19615i 0.120386 0.208514i
\(622\) 15.0000 25.9808i 0.601445 1.04173i
\(623\) −36.0000 −1.44231
\(624\) 1.00000 + 3.46410i 0.0400320 + 0.138675i
\(625\) 0 0
\(626\) −5.00000 + 8.66025i −0.199840 + 0.346133i
\(627\) 6.00000 10.3923i 0.239617 0.415029i
\(628\) 2.50000 + 4.33013i 0.0997609 + 0.172791i
\(629\) 21.0000 0.837325
\(630\) 0 0
\(631\) −10.0000 17.3205i −0.398094 0.689519i 0.595397 0.803432i \(-0.296995\pi\)
−0.993491 + 0.113913i \(0.963661\pi\)
\(632\) −4.00000 −0.159111
\(633\) −8.00000 13.8564i −0.317971 0.550743i
\(634\) 1.50000 2.59808i 0.0595726 0.103183i
\(635\) 0 0
\(636\) 3.00000 0.118958
\(637\) 7.50000 7.79423i 0.297161 0.308819i
\(638\) 18.0000 0.712627
\(639\) −3.00000 + 5.19615i −0.118678 + 0.205557i
\(640\) 0 0
\(641\) 1.50000 + 2.59808i 0.0592464 + 0.102618i 0.894127 0.447813i \(-0.147797\pi\)
−0.834881 + 0.550431i \(0.814464\pi\)
\(642\) −6.00000 −0.236801
\(643\) −8.00000 13.8564i −0.315489 0.546443i 0.664052 0.747686i \(-0.268835\pi\)
−0.979541 + 0.201243i \(0.935502\pi\)
\(644\) 6.00000 + 10.3923i 0.236433 + 0.409514i
\(645\) 0 0
\(646\) −3.00000 5.19615i −0.118033 0.204440i
\(647\) 12.0000 20.7846i 0.471769 0.817127i −0.527710 0.849425i \(-0.676949\pi\)
0.999478 + 0.0322975i \(0.0102824\pi\)
\(648\) −0.500000 + 0.866025i −0.0196419 + 0.0340207i
\(649\) 0 0
\(650\) 0 0
\(651\) −8.00000 −0.313545
\(652\) −2.00000 + 3.46410i −0.0783260 + 0.135665i
\(653\) 21.0000 36.3731i 0.821794 1.42339i −0.0825519 0.996587i \(-0.526307\pi\)
0.904345 0.426801i \(-0.140360\pi\)
\(654\) 7.00000 + 12.1244i 0.273722 + 0.474100i
\(655\) 0 0
\(656\) 1.50000 + 2.59808i 0.0585652 + 0.101438i
\(657\) −6.50000 11.2583i −0.253589 0.439229i
\(658\) 12.0000 0.467809
\(659\) −12.0000 20.7846i −0.467454 0.809653i 0.531855 0.846836i \(-0.321495\pi\)
−0.999309 + 0.0371821i \(0.988162\pi\)
\(660\) 0 0
\(661\) −2.50000 + 4.33013i −0.0972387 + 0.168422i −0.910541 0.413419i \(-0.864334\pi\)
0.813302 + 0.581842i \(0.197668\pi\)
\(662\) −4.00000 −0.155464
\(663\) −10.5000 2.59808i −0.407786 0.100901i
\(664\) 6.00000 0.232845
\(665\) 0 0
\(666\) −3.50000 + 6.06218i −0.135622 + 0.234905i
\(667\) −9.00000 15.5885i −0.348481 0.603587i
\(668\) 0 0
\(669\) −4.00000 6.92820i −0.154649 0.267860i
\(670\) 0 0
\(671\) −42.0000 −1.62139
\(672\) −1.00000 1.73205i −0.0385758 0.0668153i
\(673\) −6.50000 + 11.2583i −0.250557 + 0.433977i −0.963679 0.267063i \(-0.913947\pi\)
0.713123 + 0.701039i \(0.247280\pi\)
\(674\) 11.5000 19.9186i 0.442963 0.767235i
\(675\) 0 0
\(676\) −0.500000 12.9904i −0.0192308 0.499630i
\(677\) −18.0000 −0.691796 −0.345898 0.938272i \(-0.612426\pi\)
−0.345898 + 0.938272i \(0.612426\pi\)
\(678\) 1.50000 2.59808i 0.0576072 0.0997785i
\(679\) −14.0000 + 24.2487i −0.537271 + 0.930580i
\(680\) 0 0
\(681\) 18.0000 0.689761
\(682\) 12.0000 + 20.7846i 0.459504 + 0.795884i
\(683\) −24.0000 41.5692i −0.918334 1.59060i −0.801945 0.597398i \(-0.796201\pi\)
−0.116390 0.993204i \(-0.537132\pi\)
\(684\) 2.00000 0.0764719
\(685\) 0 0
\(686\) −10.0000 + 17.3205i −0.381802 + 0.661300i
\(687\) −11.0000 + 19.0526i −0.419676 + 0.726900i
\(688\) 10.0000 0.381246
\(689\) −10.5000 2.59808i −0.400018 0.0989788i
\(690\) 0 0
\(691\) −13.0000 + 22.5167i −0.494543 + 0.856574i −0.999980 0.00628943i \(-0.997998\pi\)
0.505437 + 0.862864i \(0.331331\pi\)
\(692\) −3.00000 + 5.19615i −0.114043 + 0.197528i
\(693\) 6.00000 + 10.3923i 0.227921 + 0.394771i
\(694\) 30.0000 1.13878
\(695\) 0 0
\(696\) 1.50000 + 2.59808i 0.0568574 + 0.0984798i
\(697\) −9.00000 −0.340899
\(698\) 5.00000 + 8.66025i 0.189253 + 0.327795i
\(699\) 3.00000 5.19615i 0.113470 0.196537i
\(700\) 0 0
\(701\) −30.0000 −1.13308 −0.566542 0.824033i \(-0.691719\pi\)
−0.566542 + 0.824033i \(0.691719\pi\)
\(702\) 2.50000 2.59808i 0.0943564 0.0980581i
\(703\) 14.0000 0.528020
\(704\) −3.00000 + 5.19615i −0.113067 + 0.195837i
\(705\) 0 0
\(706\) −7.50000 12.9904i −0.282266 0.488899i
\(707\) −30.0000 −1.12827
\(708\) 0 0
\(709\) −2.50000 4.33013i −0.0938895 0.162621i 0.815255 0.579102i \(-0.196597\pi\)
−0.909145 + 0.416481i \(0.863263\pi\)
\(710\) 0 0
\(711\) 2.00000 + 3.46410i 0.0750059 + 0.129914i
\(712\) −9.00000 + 15.5885i −0.337289 + 0.584202i
\(713\) 12.0000 20.7846i 0.449404 0.778390i
\(714\) 6.00000 0.224544
\(715\) 0 0
\(716\) 6.00000 0.224231
\(717\) 3.00000 5.19615i 0.112037 0.194054i
\(718\) −3.00000 + 5.19615i −0.111959 + 0.193919i
\(719\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(720\) 0 0
\(721\) −14.0000 24.2487i −0.521387 0.903069i
\(722\) 7.50000 + 12.9904i 0.279121 + 0.483452i
\(723\) 1.00000 0.0371904
\(724\) 3.50000 + 6.06218i 0.130076 + 0.225299i
\(725\) 0 0
\(726\) 12.5000 21.6506i 0.463919 0.803530i
\(727\) −14.0000 −0.519231 −0.259616 0.965712i \(-0.583596\pi\)
−0.259616 + 0.965712i \(0.583596\pi\)
\(728\) 2.00000 + 6.92820i 0.0741249 + 0.256776i
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −15.0000 + 25.9808i −0.554795 + 0.960933i
\(732\) −3.50000 6.06218i −0.129364 0.224065i
\(733\) 31.0000 1.14501 0.572506 0.819901i \(-0.305971\pi\)
0.572506 + 0.819901i \(0.305971\pi\)
\(734\) 1.00000 + 1.73205i 0.0369107 + 0.0639312i
\(735\) 0 0
\(736\) 6.00000 0.221163
\(737\) −30.0000 51.9615i −1.10506 1.91403i
\(738\) 1.50000 2.59808i 0.0552158 0.0956365i
\(739\) 8.00000 13.8564i 0.294285 0.509716i −0.680534 0.732717i \(-0.738252\pi\)
0.974818 + 0.223001i \(0.0715853\pi\)
\(740\) 0 0
\(741\) −7.00000 1.73205i −0.257151 0.0636285i
\(742\) 6.00000 0.220267
\(743\) −18.0000 + 31.1769i −0.660356 + 1.14377i 0.320166 + 0.947361i \(0.396261\pi\)
−0.980522 + 0.196409i \(0.937072\pi\)
\(744\) −2.00000 + 3.46410i −0.0733236 + 0.127000i
\(745\) 0 0
\(746\) −29.0000 −1.06177
\(747\) −3.00000 5.19615i −0.109764 0.190117i
\(748\) −9.00000 15.5885i −0.329073 0.569970i
\(749\) −12.0000 −0.438470
\(750\) 0 0
\(751\) −7.00000 + 12.1244i −0.255434 + 0.442424i −0.965013 0.262201i \(-0.915552\pi\)
0.709580 + 0.704625i \(0.248885\pi\)
\(752\) 3.00000 5.19615i 0.109399 0.189484i
\(753\) 12.0000 0.437304
\(754\) −3.00000 10.3923i −0.109254 0.378465i
\(755\) 0 0
\(756\) −1.00000 + 1.73205i −0.0363696 + 0.0629941i
\(757\) −17.0000 + 29.4449i −0.617876 + 1.07019i 0.371997 + 0.928234i \(0.378673\pi\)
−0.989873 + 0.141958i \(0.954660\pi\)
\(758\) −10.0000 17.3205i −0.363216 0.629109i
\(759\) −36.0000 −1.30672
\(760\) 0 0
\(761\) 15.0000 + 25.9808i 0.543750 + 0.941802i 0.998684 + 0.0512772i \(0.0163292\pi\)
−0.454935 + 0.890525i \(0.650337\pi\)
\(762\) −4.00000 −0.144905
\(763\) 14.0000 + 24.2487i 0.506834 + 0.877862i
\(764\) 6.00000 10.3923i 0.217072 0.375980i
\(765\) 0 0
\(766\) −24.0000 −0.867155
\(767\) 0 0
\(768\) −1.00000 −0.0360844
\(769\) −7.00000 + 12.1244i −0.252426 + 0.437215i −0.964193 0.265200i \(-0.914562\pi\)
0.711767 + 0.702416i \(0.247895\pi\)
\(770\) 0 0
\(771\) 1.50000 + 2.59808i 0.0540212 + 0.0935674i
\(772\) −23.0000 −0.827788
\(773\) −15.0000 25.9808i −0.539513 0.934463i −0.998930 0.0462427i \(-0.985275\pi\)
0.459418 0.888220i \(-0.348058\pi\)
\(774\) −5.00000 8.66025i −0.179721 0.311286i
\(775\) 0 0
\(776\) 7.00000 + 12.1244i 0.251285 + 0.435239i
\(777\) −7.00000 + 12.1244i −0.251124 + 0.434959i
\(778\) −19.5000 + 33.7750i −0.699109 + 1.21089i
\(779\) −6.00000 −0.214972
\(780\) 0 0
\(781\) 36.0000 1.28818
\(782\) −9.00000 + 15.5885i −0.321839 + 0.557442i
\(783\) 1.50000 2.59808i 0.0536056 0.0928477i
\(784\) 1.50000 + 2.59808i 0.0535714 + 0.0927884i
\(785\) 0 0
\(786\) 0 0
\(787\) −14.0000 24.2487i −0.499046 0.864373i 0.500953 0.865474i \(-0.332983\pi\)
−0.999999 + 0.00110111i \(0.999650\pi\)
\(788\) −6.00000 −0.213741
\(789\) 3.00000 + 5.19615i 0.106803 + 0.184988i
\(790\) 0 0
\(791\) 3.00000 5.19615i 0.106668 0.184754i
\(792\) 6.00000 0.213201
\(793\) 7.00000 + 24.2487i 0.248577 + 0.861097i
\(794\) −14.0000 −0.496841
\(795\) 0 0
\(796\) 5.00000 8.66025i 0.177220 0.306955i
\(797\) 15.0000 + 25.9808i 0.531327 + 0.920286i 0.999331 + 0.0365596i \(0.0116399\pi\)
−0.468004 + 0.883726i \(0.655027\pi\)
\(798\) 4.00000 0.141598
\(799\) 9.00000 + 15.5885i 0.318397 + 0.551480i
\(800\) 0 0
\(801\) 18.0000 0.635999
\(802\) 1.50000 + 2.59808i 0.0529668 + 0.0917413i
\(803\) −39.0000 + 67.5500i −1.37628 + 2.38379i
\(804\) 5.00000 8.66025i 0.176336 0.305424i
\(805\) 0 0
\(806\) 10.0000 10.3923i 0.352235 0.366053i
\(807\) −18.0000 −0.633630
\(808\) −7.50000 + 12.9904i −0.263849 + 0.457000i
\(809\) 25.5000 44.1673i 0.896532 1.55284i 0.0646355 0.997909i \(-0.479412\pi\)
0.831897 0.554930i \(-0.187255\pi\)
\(810\) 0 0
\(811\) −4.00000 −0.140459 −0.0702295 0.997531i \(-0.522373\pi\)
−0.0702295 + 0.997531i \(0.522373\pi\)
\(812\) 3.00000 + 5.19615i 0.105279 + 0.182349i
\(813\) −8.00000 13.8564i −0.280572 0.485965i
\(814\) 42.0000 1.47210
\(815\) 0 0
\(816\) 1.50000 2.59808i 0.0525105 0.0909509i
\(817\) −10.0000 + 17.3205i −0.349856 + 0.605968i
\(818\) −1.00000 −0.0349642
\(819\) 5.00000 5.19615i 0.174714 0.181568i
\(820\) 0 0
\(821\) −9.00000 + 15.5885i −0.314102 + 0.544041i −0.979246 0.202674i \(-0.935037\pi\)
0.665144 + 0.746715i \(0.268370\pi\)
\(822\) −4.50000 + 7.79423i −0.156956 + 0.271855i
\(823\) −20.0000 34.6410i −0.697156 1.20751i −0.969448 0.245295i \(-0.921115\pi\)
0.272292 0.962215i \(-0.412218\pi\)
\(824\) −14.0000 −0.487713
\(825\) 0 0
\(826\) 0 0
\(827\) 48.0000 1.66912 0.834562 0.550914i \(-0.185721\pi\)
0.834562 + 0.550914i \(0.185721\pi\)
\(828\) −3.00000 5.19615i −0.104257 0.180579i
\(829\) −8.50000 + 14.7224i −0.295217 + 0.511331i −0.975035 0.222049i \(-0.928725\pi\)
0.679818 + 0.733381i \(0.262059\pi\)
\(830\) 0 0
\(831\) 17.0000 0.589723
\(832\) 3.50000 + 0.866025i 0.121341 + 0.0300240i
\(833\) −9.00000 −0.311832
\(834\) −2.00000 + 3.46410i −0.0692543 + 0.119952i
\(835\) 0 0
\(836\) −6.00000 10.3923i −0.207514 0.359425i
\(837\) 4.00000 0.138260
\(838\) −12.0000 20.7846i −0.414533 0.717992i
\(839\) 6.00000 + 10.3923i 0.207143 + 0.358782i 0.950813 0.309764i \(-0.100250\pi\)
−0.743670 + 0.668546i \(0.766917\pi\)
\(840\) 0 0
\(841\) 10.0000 + 17.3205i 0.344828 + 0.597259i
\(842\) −14.5000 + 25.1147i −0.499703 + 0.865511i
\(843\) 4.50000 7.79423i 0.154988 0.268447i
\(844\) −16.0000 −0.550743
\(845\) 0 0
\(846\) −6.00000 −0.206284
\(847\) 25.0000 43.3013i 0.859010 1.48785i
\(848\) 1.50000 2.59808i 0.0515102 0.0892183i
\(849\) −7.00000 12.1244i −0.240239 0.416107i
\(850\) 0 0
\(851\) −21.0000 36.3731i −0.719871 1.24685i
\(852\) 3.00000 + 5.19615i 0.102778 + 0.178017i
\(853\) 19.0000 0.650548 0.325274 0.945620i \(-0.394544\pi\)
0.325274 + 0.945620i \(0.394544\pi\)
\(854\) −7.00000 12.1244i −0.239535 0.414887i
\(855\) 0 0
\(856\) −3.00000 + 5.19615i −0.102538 + 0.177601i
\(857\) −21.0000 −0.717346 −0.358673 0.933463i \(-0.616771\pi\)
−0.358673 + 0.933463i \(0.616771\pi\)
\(858\) −21.0000 5.19615i −0.716928 0.177394i
\(859\) 26.0000 0.887109 0.443554 0.896248i \(-0.353717\pi\)
0.443554 + 0.896248i \(0.353717\pi\)
\(860\) 0 0
\(861\) 3.00000 5.19615i 0.102240 0.177084i
\(862\) 3.00000 + 5.19615i 0.102180 + 0.176982i
\(863\) −18.0000 −0.612727 −0.306364 0.951915i \(-0.599112\pi\)
−0.306364 + 0.951915i \(0.599112\pi\)
\(864\) 0.500000 + 0.866025i 0.0170103 + 0.0294628i
\(865\) 0 0
\(866\) 13.0000 0.441758
\(867\) −4.00000 6.92820i −0.135847 0.235294i
\(868\) −4.00000 + 6.92820i −0.135769 + 0.235159i
\(869\) 12.0000 20.7846i 0.407072 0.705070i
\(870\) 0 0
\(871\) −25.0000 + 25.9808i −0.847093 + 0.880325i
\(872\) 14.0000 0.474100
\(873\) 7.00000 12.1244i 0.236914 0.410347i
\(874\) −6.00000 + 10.3923i −0.202953 + 0.351525i
\(875\) 0 0
\(876\) −13.0000 −0.439229
\(877\) 20.5000 + 35.5070i 0.692236 + 1.19899i 0.971104 + 0.238658i \(0.0767075\pi\)
−0.278868 + 0.960329i \(0.589959\pi\)
\(878\) −7.00000 12.1244i −0.236239 0.409177i
\(879\) −21.0000 −0.708312
\(880\) 0 0
\(881\) −16.5000 + 28.5788i −0.555899 + 0.962846i 0.441934 + 0.897048i \(0.354293\pi\)
−0.997833 + 0.0657979i \(0.979041\pi\)
\(882\) 1.50000 2.59808i 0.0505076 0.0874818i
\(883\) −8.00000 −0.269221 −0.134611 0.990899i \(-0.542978\pi\)
−0.134611 + 0.990899i \(0.542978\pi\)
\(884\) −7.50000 + 7.79423i −0.252252 + 0.262148i
\(885\) 0 0
\(886\) −18.0000 + 31.1769i −0.604722 + 1.04741i
\(887\) −24.0000 + 41.5692i −0.805841 + 1.39576i 0.109881 + 0.993945i \(0.464953\pi\)
−0.915722 + 0.401813i \(0.868380\pi\)
\(888\) 3.50000 + 6.06218i 0.117452 + 0.203433i
\(889\) −8.00000 −0.268311
\(890\) 0 0
\(891\) −3.00000 5.19615i −0.100504 0.174078i
\(892\) −8.00000 −0.267860
\(893\) 6.00000 + 10.3923i 0.200782 + 0.347765i
\(894\) −4.50000 + 7.79423i −0.150503 + 0.260678i
\(895\) 0 0
\(896\) −2.00000 −0.0668153
\(897\) 6.00000 + 20.7846i 0.200334 + 0.693978i
\(898\) 18.0000 0.600668
\(899\) 6.00000 10.3923i 0.200111 0.346603i
\(900\) 0 0
\(901\) 4.50000 + 7.79423i 0.149917 + 0.259663i
\(902\) −18.0000 −0.599334
\(903\) −10.0000 17.3205i −0.332779 0.576390i
\(904\) −1.50000 2.59808i −0.0498893 0.0864107i
\(905\) 0 0
\(906\) −5.00000 8.66025i −0.166114 0.287718i
\(907\) 22.0000 38.1051i 0.730498 1.26526i −0.226173 0.974087i \(-0.572621\pi\)
0.956671 0.291172i \(-0.0940453\pi\)
\(908\) 9.00000 15.5885i 0.298675 0.517321i
\(909\) 15.0000 0.497519
\(910\) 0 0
\(911\) −24.0000 −0.795155 −0.397578 0.917568i \(-0.630149\pi\)
−0.397578 + 0.917568i \(0.630149\pi\)
\(912\) 1.00000 1.73205i 0.0331133 0.0573539i
\(913\) −18.0000 + 31.1769i −0.595713 + 1.03181i
\(914\) 5.50000 + 9.52628i 0.181924 + 0.315101i
\(915\) 0 0
\(916\) 11.0000 + 19.0526i 0.363450 + 0.629514i
\(917\) 0 0
\(918\) −3.00000 −0.0990148
\(919\) 8.00000 + 13.8564i 0.263896 + 0.457081i 0.967274 0.253735i \(-0.0816592\pi\)
−0.703378 + 0.710816i \(0.748326\pi\)
\(920\) 0 0
\(921\) 5.00000 8.66025i 0.164756 0.285365i
\(922\) 15.0000 0.493999
\(923\) −6.00000 20.7846i −0.197492 0.684134i
\(924\) 12.0000 0.394771
\(925\) 0 0
\(926\) 19.0000 32.9090i 0.624379 1.08146i
\(927\) 7.00000 + 12.1244i 0.229910 + 0.398216i
\(928\) 3.00000 0.0984798
\(929\) −16.5000 28.5788i −0.541347 0.937641i −0.998827 0.0484211i \(-0.984581\pi\)
0.457480 0.889220i \(-0.348752\pi\)
\(930\) 0 0
\(931\) −6.00000 −0.196642
\(932\) −3.00000 5.19615i −0.0982683 0.170206i
\(933\) −15.0000 + 25.9808i −0.491078 + 0.850572i
\(934\) −9.00000 + 15.5885i −0.294489 + 0.510070i
\(935\) 0 0
\(936\) −1.00000 3.46410i −0.0326860 0.113228i
\(937\) −47.0000 −1.53542 −0.767712 0.640796i \(-0.778605\pi\)
−0.767712 + 0.640796i \(0.778605\pi\)
\(938\) 10.0000 17.3205i 0.326512 0.565535i
\(939\) 5.00000 8.66025i 0.163169 0.282617i
\(940\) 0 0
\(941\) 42.0000 1.36916 0.684580 0.728937i \(-0.259985\pi\)
0.684580 + 0.728937i \(0.259985\pi\)
\(942\) −2.50000 4.33013i −0.0814544 0.141083i
\(943\) 9.00000 + 15.5885i 0.293080 + 0.507630i
\(944\) 0 0
\(945\) 0 0
\(946\) −30.0000 + 51.9615i −0.975384 + 1.68941i
\(947\) 12.0000 20.7846i 0.389948 0.675409i −0.602494 0.798123i \(-0.705826\pi\)
0.992442 + 0.122714i \(0.0391598\pi\)
\(948\) 4.00000 0.129914
\(949\) 45.5000 + 11.2583i 1.47699 + 0.365461i
\(950\) 0 0
\(951\) −1.50000 + 2.59808i −0.0486408 + 0.0842484i
\(952\) 3.00000 5.19615i 0.0972306 0.168408i
\(953\) 27.0000 + 46.7654i 0.874616 + 1.51488i 0.857171 + 0.515031i \(0.172220\pi\)
0.0174443 + 0.999848i \(0.494447\pi\)
\(954\) −3.00000 −0.0971286
\(955\) 0 0
\(956\) −3.00000 5.19615i −0.0970269 0.168056i
\(957\) −18.0000 −0.581857
\(958\) 0 0
\(959\) −9.00000 + 15.5885i −0.290625 + 0.503378i
\(960\) 0 0
\(961\) −15.0000 −0.483871
\(962\) −7.00000 24.2487i −0.225689 0.781810i
\(963\) 6.00000 0.193347
\(964\) 0.500000 0.866025i 0.0161039 0.0278928i
\(965\) 0 0
\(966\) −6.00000 10.3923i −0.193047 0.334367i
\(967\) 22.0000 0.707472 0.353736 0.935345i \(-0.384911\pi\)
0.353736 + 0.935345i \(0.384911\pi\)
\(968\) −12.5000 21.6506i −0.401765 0.695878i
\(969\) 3.00000 + 5.19615i 0.0963739 + 0.166924i
\(970\) 0 0
\(971\) −30.0000 51.9615i −0.962746 1.66752i −0.715553 0.698558i \(-0.753825\pi\)
−0.247193 0.968966i \(-0.579508\pi\)
\(972\) 0.500000 0.866025i 0.0160375 0.0277778i
\(973\) −4.00000 + 6.92820i −0.128234 + 0.222108i
\(974\) −2.00000 −0.0640841
\(975\) 0 0
\(976\) −7.00000 −0.224065
\(977\) −1.50000 + 2.59808i −0.0479893 + 0.0831198i −0.889022 0.457864i \(-0.848615\pi\)
0.841033 + 0.540984i \(0.181948\pi\)
\(978\) 2.00000 3.46410i 0.0639529 0.110770i
\(979\) −54.0000 93.5307i −1.72585 2.98926i
\(980\) 0 0
\(981\) −7.00000 12.1244i −0.223493 0.387101i
\(982\) 9.00000 + 15.5885i 0.287202 + 0.497448i
\(983\) 36.0000 1.14822 0.574111 0.818778i \(-0.305348\pi\)
0.574111 + 0.818778i \(0.305348\pi\)
\(984\) −1.50000 2.59808i −0.0478183 0.0828236i
\(985\) 0 0
\(986\) −4.50000 + 7.79423i −0.143309 + 0.248219i
\(987\) −12.0000 −0.381964
\(988\) −5.00000 + 5.19615i −0.159071 + 0.165312i
\(989\) 60.0000 1.90789
\(990\) 0 0
\(991\) −19.0000 + 32.9090i −0.603555 + 1.04539i 0.388723 + 0.921355i \(0.372916\pi\)
−0.992278 + 0.124033i \(0.960417\pi\)
\(992\) 2.00000 + 3.46410i 0.0635001 + 0.109985i
\(993\) 4.00000 0.126936
\(994\) 6.00000 + 10.3923i 0.190308 + 0.329624i
\(995\) 0 0
\(996\) −6.00000 −0.190117
\(997\) 2.50000 + 4.33013i 0.0791758 + 0.137136i 0.902895 0.429862i \(-0.141438\pi\)
−0.823719 + 0.566999i \(0.808104\pi\)
\(998\) −16.0000 + 27.7128i −0.506471 + 0.877234i
\(999\) 3.50000 6.06218i 0.110735 0.191799i
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.i.m.451.1 2
5.2 odd 4 1950.2.z.g.1699.1 4
5.3 odd 4 1950.2.z.g.1699.2 4
5.4 even 2 78.2.e.a.61.1 yes 2
13.3 even 3 inner 1950.2.i.m.601.1 2
15.14 odd 2 234.2.h.a.217.1 2
20.19 odd 2 624.2.q.g.529.1 2
60.59 even 2 1872.2.t.c.1153.1 2
65.3 odd 12 1950.2.z.g.1849.1 4
65.4 even 6 1014.2.a.f.1.1 1
65.9 even 6 1014.2.a.c.1.1 1
65.19 odd 12 1014.2.b.c.337.2 2
65.24 odd 12 1014.2.i.b.361.1 4
65.29 even 6 78.2.e.a.55.1 2
65.34 odd 4 1014.2.i.b.823.2 4
65.42 odd 12 1950.2.z.g.1849.2 4
65.44 odd 4 1014.2.i.b.823.1 4
65.49 even 6 1014.2.e.a.991.1 2
65.54 odd 12 1014.2.i.b.361.2 4
65.59 odd 12 1014.2.b.c.337.1 2
65.64 even 2 1014.2.e.a.529.1 2
195.29 odd 6 234.2.h.a.55.1 2
195.59 even 12 3042.2.b.h.1351.2 2
195.74 odd 6 3042.2.a.i.1.1 1
195.134 odd 6 3042.2.a.h.1.1 1
195.149 even 12 3042.2.b.h.1351.1 2
260.139 odd 6 8112.2.a.m.1.1 1
260.159 odd 6 624.2.q.g.289.1 2
260.199 odd 6 8112.2.a.c.1.1 1
780.419 even 6 1872.2.t.c.289.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
78.2.e.a.55.1 2 65.29 even 6
78.2.e.a.61.1 yes 2 5.4 even 2
234.2.h.a.55.1 2 195.29 odd 6
234.2.h.a.217.1 2 15.14 odd 2
624.2.q.g.289.1 2 260.159 odd 6
624.2.q.g.529.1 2 20.19 odd 2
1014.2.a.c.1.1 1 65.9 even 6
1014.2.a.f.1.1 1 65.4 even 6
1014.2.b.c.337.1 2 65.59 odd 12
1014.2.b.c.337.2 2 65.19 odd 12
1014.2.e.a.529.1 2 65.64 even 2
1014.2.e.a.991.1 2 65.49 even 6
1014.2.i.b.361.1 4 65.24 odd 12
1014.2.i.b.361.2 4 65.54 odd 12
1014.2.i.b.823.1 4 65.44 odd 4
1014.2.i.b.823.2 4 65.34 odd 4
1872.2.t.c.289.1 2 780.419 even 6
1872.2.t.c.1153.1 2 60.59 even 2
1950.2.i.m.451.1 2 1.1 even 1 trivial
1950.2.i.m.601.1 2 13.3 even 3 inner
1950.2.z.g.1699.1 4 5.2 odd 4
1950.2.z.g.1699.2 4 5.3 odd 4
1950.2.z.g.1849.1 4 65.3 odd 12
1950.2.z.g.1849.2 4 65.42 odd 12
3042.2.a.h.1.1 1 195.134 odd 6
3042.2.a.i.1.1 1 195.74 odd 6
3042.2.b.h.1351.1 2 195.149 even 12
3042.2.b.h.1351.2 2 195.59 even 12
8112.2.a.c.1.1 1 260.199 odd 6
8112.2.a.m.1.1 1 260.139 odd 6