Properties

Label 1274.2.f.u.79.1
Level $1274$
Weight $2$
Character 1274.79
Analytic conductor $10.173$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1274,2,Mod(79,1274)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1274, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1274.79");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1274 = 2 \cdot 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1274.f (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: \(10.1729412175\)
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 182)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 79.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1274.79
Dual form 1274.2.f.u.1145.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{2} +(1.50000 + 2.59808i) q^{3} +(-0.500000 - 0.866025i) q^{4} +3.00000 q^{6} -1.00000 q^{8} +(-3.00000 + 5.19615i) q^{9} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{2} +(1.50000 + 2.59808i) q^{3} +(-0.500000 - 0.866025i) q^{4} +3.00000 q^{6} -1.00000 q^{8} +(-3.00000 + 5.19615i) q^{9} +(2.50000 + 4.33013i) q^{11} +(1.50000 - 2.59808i) q^{12} +1.00000 q^{13} +(-0.500000 + 0.866025i) q^{16} +(-2.00000 - 3.46410i) q^{17} +(3.00000 + 5.19615i) q^{18} +(1.00000 - 1.73205i) q^{19} +5.00000 q^{22} +(-2.50000 + 4.33013i) q^{23} +(-1.50000 - 2.59808i) q^{24} +(2.50000 + 4.33013i) q^{25} +(0.500000 - 0.866025i) q^{26} -9.00000 q^{27} +4.00000 q^{29} +(0.500000 + 0.866025i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-7.50000 + 12.9904i) q^{33} -4.00000 q^{34} +6.00000 q^{36} +(-3.50000 + 6.06218i) q^{37} +(-1.00000 - 1.73205i) q^{38} +(1.50000 + 2.59808i) q^{39} +9.00000 q^{41} -12.0000 q^{43} +(2.50000 - 4.33013i) q^{44} +(2.50000 + 4.33013i) q^{46} +(-3.50000 + 6.06218i) q^{47} -3.00000 q^{48} +5.00000 q^{50} +(6.00000 - 10.3923i) q^{51} +(-0.500000 - 0.866025i) q^{52} +(2.00000 + 3.46410i) q^{53} +(-4.50000 + 7.79423i) q^{54} +6.00000 q^{57} +(2.00000 - 3.46410i) q^{58} +(-3.00000 - 5.19615i) q^{59} +(6.50000 - 11.2583i) q^{61} +1.00000 q^{62} +1.00000 q^{64} +(7.50000 + 12.9904i) q^{66} +(-5.50000 - 9.52628i) q^{67} +(-2.00000 + 3.46410i) q^{68} -15.0000 q^{69} +(3.00000 - 5.19615i) q^{72} +(3.50000 + 6.06218i) q^{73} +(3.50000 + 6.06218i) q^{74} +(-7.50000 + 12.9904i) q^{75} -2.00000 q^{76} +3.00000 q^{78} +(8.50000 - 14.7224i) q^{79} +(-4.50000 - 7.79423i) q^{81} +(4.50000 - 7.79423i) q^{82} -4.00000 q^{83} +(-6.00000 + 10.3923i) q^{86} +(6.00000 + 10.3923i) q^{87} +(-2.50000 - 4.33013i) q^{88} +(7.00000 - 12.1244i) q^{89} +5.00000 q^{92} +(-1.50000 + 2.59808i) q^{93} +(3.50000 + 6.06218i) q^{94} +(-1.50000 + 2.59808i) q^{96} -5.00000 q^{97} -30.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + q^{2} + 3 q^{3} - q^{4} + 6 q^{6} - 2 q^{8} - 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + q^{2} + 3 q^{3} - q^{4} + 6 q^{6} - 2 q^{8} - 6 q^{9} + 5 q^{11} + 3 q^{12} + 2 q^{13} - q^{16} - 4 q^{17} + 6 q^{18} + 2 q^{19} + 10 q^{22} - 5 q^{23} - 3 q^{24} + 5 q^{25} + q^{26} - 18 q^{27} + 8 q^{29} + q^{31} + q^{32} - 15 q^{33} - 8 q^{34} + 12 q^{36} - 7 q^{37} - 2 q^{38} + 3 q^{39} + 18 q^{41} - 24 q^{43} + 5 q^{44} + 5 q^{46} - 7 q^{47} - 6 q^{48} + 10 q^{50} + 12 q^{51} - q^{52} + 4 q^{53} - 9 q^{54} + 12 q^{57} + 4 q^{58} - 6 q^{59} + 13 q^{61} + 2 q^{62} + 2 q^{64} + 15 q^{66} - 11 q^{67} - 4 q^{68} - 30 q^{69} + 6 q^{72} + 7 q^{73} + 7 q^{74} - 15 q^{75} - 4 q^{76} + 6 q^{78} + 17 q^{79} - 9 q^{81} + 9 q^{82} - 8 q^{83} - 12 q^{86} + 12 q^{87} - 5 q^{88} + 14 q^{89} + 10 q^{92} - 3 q^{93} + 7 q^{94} - 3 q^{96} - 10 q^{97} - 60 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1274\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(885\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\)

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
\(3\) 1.50000 + 2.59808i 0.866025 + 1.50000i 0.866025 + 0.500000i \(0.166667\pi\)
1.00000i \(0.5\pi\)
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(6\) 3.00000 1.22474
\(7\) 0 0
\(8\) −1.00000 −0.353553
\(9\) −3.00000 + 5.19615i −1.00000 + 1.73205i
\(10\) 0 0
\(11\) 2.50000 + 4.33013i 0.753778 + 1.30558i 0.945979 + 0.324227i \(0.105104\pi\)
−0.192201 + 0.981356i \(0.561563\pi\)
\(12\) 1.50000 2.59808i 0.433013 0.750000i
\(13\) 1.00000 0.277350
\(14\) 0 0
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −2.00000 3.46410i −0.485071 0.840168i 0.514782 0.857321i \(-0.327873\pi\)
−0.999853 + 0.0171533i \(0.994540\pi\)
\(18\) 3.00000 + 5.19615i 0.707107 + 1.22474i
\(19\) 1.00000 1.73205i 0.229416 0.397360i −0.728219 0.685344i \(-0.759652\pi\)
0.957635 + 0.287984i \(0.0929851\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 5.00000 1.06600
\(23\) −2.50000 + 4.33013i −0.521286 + 0.902894i 0.478407 + 0.878138i \(0.341214\pi\)
−0.999694 + 0.0247559i \(0.992119\pi\)
\(24\) −1.50000 2.59808i −0.306186 0.530330i
\(25\) 2.50000 + 4.33013i 0.500000 + 0.866025i
\(26\) 0.500000 0.866025i 0.0980581 0.169842i
\(27\) −9.00000 −1.73205
\(28\) 0 0
\(29\) 4.00000 0.742781 0.371391 0.928477i \(-0.378881\pi\)
0.371391 + 0.928477i \(0.378881\pi\)
\(30\) 0 0
\(31\) 0.500000 + 0.866025i 0.0898027 + 0.155543i 0.907428 0.420208i \(-0.138043\pi\)
−0.817625 + 0.575751i \(0.804710\pi\)
\(32\) 0.500000 + 0.866025i 0.0883883 + 0.153093i
\(33\) −7.50000 + 12.9904i −1.30558 + 2.26134i
\(34\) −4.00000 −0.685994
\(35\) 0 0
\(36\) 6.00000 1.00000
\(37\) −3.50000 + 6.06218i −0.575396 + 0.996616i 0.420602 + 0.907245i \(0.361819\pi\)
−0.995998 + 0.0893706i \(0.971514\pi\)
\(38\) −1.00000 1.73205i −0.162221 0.280976i
\(39\) 1.50000 + 2.59808i 0.240192 + 0.416025i
\(40\) 0 0
\(41\) 9.00000 1.40556 0.702782 0.711405i \(-0.251941\pi\)
0.702782 + 0.711405i \(0.251941\pi\)
\(42\) 0 0
\(43\) −12.0000 −1.82998 −0.914991 0.403473i \(-0.867803\pi\)
−0.914991 + 0.403473i \(0.867803\pi\)
\(44\) 2.50000 4.33013i 0.376889 0.652791i
\(45\) 0 0
\(46\) 2.50000 + 4.33013i 0.368605 + 0.638442i
\(47\) −3.50000 + 6.06218i −0.510527 + 0.884260i 0.489398 + 0.872060i \(0.337217\pi\)
−0.999926 + 0.0121990i \(0.996117\pi\)
\(48\) −3.00000 −0.433013
\(49\) 0 0
\(50\) 5.00000 0.707107
\(51\) 6.00000 10.3923i 0.840168 1.45521i
\(52\) −0.500000 0.866025i −0.0693375 0.120096i
\(53\) 2.00000 + 3.46410i 0.274721 + 0.475831i 0.970065 0.242846i \(-0.0780811\pi\)
−0.695344 + 0.718677i \(0.744748\pi\)
\(54\) −4.50000 + 7.79423i −0.612372 + 1.06066i
\(55\) 0 0
\(56\) 0 0
\(57\) 6.00000 0.794719
\(58\) 2.00000 3.46410i 0.262613 0.454859i
\(59\) −3.00000 5.19615i −0.390567 0.676481i 0.601958 0.798528i \(-0.294388\pi\)
−0.992524 + 0.122047i \(0.961054\pi\)
\(60\) 0 0
\(61\) 6.50000 11.2583i 0.832240 1.44148i −0.0640184 0.997949i \(-0.520392\pi\)
0.896258 0.443533i \(-0.146275\pi\)
\(62\) 1.00000 0.127000
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 7.50000 + 12.9904i 0.923186 + 1.59901i
\(67\) −5.50000 9.52628i −0.671932 1.16382i −0.977356 0.211604i \(-0.932131\pi\)
0.305424 0.952217i \(-0.401202\pi\)
\(68\) −2.00000 + 3.46410i −0.242536 + 0.420084i
\(69\) −15.0000 −1.80579
\(70\) 0 0
\(71\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) 3.00000 5.19615i 0.353553 0.612372i
\(73\) 3.50000 + 6.06218i 0.409644 + 0.709524i 0.994850 0.101361i \(-0.0323196\pi\)
−0.585206 + 0.810885i \(0.698986\pi\)
\(74\) 3.50000 + 6.06218i 0.406867 + 0.704714i
\(75\) −7.50000 + 12.9904i −0.866025 + 1.50000i
\(76\) −2.00000 −0.229416
\(77\) 0 0
\(78\) 3.00000 0.339683
\(79\) 8.50000 14.7224i 0.956325 1.65640i 0.225018 0.974355i \(-0.427756\pi\)
0.731307 0.682048i \(-0.238911\pi\)
\(80\) 0 0
\(81\) −4.50000 7.79423i −0.500000 0.866025i
\(82\) 4.50000 7.79423i 0.496942 0.860729i
\(83\) −4.00000 −0.439057 −0.219529 0.975606i \(-0.570452\pi\)
−0.219529 + 0.975606i \(0.570452\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −6.00000 + 10.3923i −0.646997 + 1.12063i
\(87\) 6.00000 + 10.3923i 0.643268 + 1.11417i
\(88\) −2.50000 4.33013i −0.266501 0.461593i
\(89\) 7.00000 12.1244i 0.741999 1.28518i −0.209585 0.977790i \(-0.567211\pi\)
0.951584 0.307389i \(-0.0994552\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 5.00000 0.521286
\(93\) −1.50000 + 2.59808i −0.155543 + 0.269408i
\(94\) 3.50000 + 6.06218i 0.360997 + 0.625266i
\(95\) 0 0
\(96\) −1.50000 + 2.59808i −0.153093 + 0.265165i
\(97\) −5.00000 −0.507673 −0.253837 0.967247i \(-0.581693\pi\)
−0.253837 + 0.967247i \(0.581693\pi\)
\(98\) 0 0
\(99\) −30.0000 −3.01511
\(100\) 2.50000 4.33013i 0.250000 0.433013i
\(101\) 7.50000 + 12.9904i 0.746278 + 1.29259i 0.949595 + 0.313478i \(0.101494\pi\)
−0.203317 + 0.979113i \(0.565172\pi\)
\(102\) −6.00000 10.3923i −0.594089 1.02899i
\(103\) 3.00000 5.19615i 0.295599 0.511992i −0.679525 0.733652i \(-0.737814\pi\)
0.975124 + 0.221660i \(0.0711475\pi\)
\(104\) −1.00000 −0.0980581
\(105\) 0 0
\(106\) 4.00000 0.388514
\(107\) 4.00000 6.92820i 0.386695 0.669775i −0.605308 0.795991i \(-0.706950\pi\)
0.992003 + 0.126217i \(0.0402834\pi\)
\(108\) 4.50000 + 7.79423i 0.433013 + 0.750000i
\(109\) 9.00000 + 15.5885i 0.862044 + 1.49310i 0.869953 + 0.493135i \(0.164149\pi\)
−0.00790932 + 0.999969i \(0.502518\pi\)
\(110\) 0 0
\(111\) −21.0000 −1.99323
\(112\) 0 0
\(113\) 1.00000 0.0940721 0.0470360 0.998893i \(-0.485022\pi\)
0.0470360 + 0.998893i \(0.485022\pi\)
\(114\) 3.00000 5.19615i 0.280976 0.486664i
\(115\) 0 0
\(116\) −2.00000 3.46410i −0.185695 0.321634i
\(117\) −3.00000 + 5.19615i −0.277350 + 0.480384i
\(118\) −6.00000 −0.552345
\(119\) 0 0
\(120\) 0 0
\(121\) −7.00000 + 12.1244i −0.636364 + 1.10221i
\(122\) −6.50000 11.2583i −0.588482 1.01928i
\(123\) 13.5000 + 23.3827i 1.21725 + 2.10835i
\(124\) 0.500000 0.866025i 0.0449013 0.0777714i
\(125\) 0 0
\(126\) 0 0
\(127\) 9.00000 0.798621 0.399310 0.916816i \(-0.369250\pi\)
0.399310 + 0.916816i \(0.369250\pi\)
\(128\) 0.500000 0.866025i 0.0441942 0.0765466i
\(129\) −18.0000 31.1769i −1.58481 2.74497i
\(130\) 0 0
\(131\) 4.00000 6.92820i 0.349482 0.605320i −0.636676 0.771132i \(-0.719691\pi\)
0.986157 + 0.165812i \(0.0530244\pi\)
\(132\) 15.0000 1.30558
\(133\) 0 0
\(134\) −11.0000 −0.950255
\(135\) 0 0
\(136\) 2.00000 + 3.46410i 0.171499 + 0.297044i
\(137\) −9.00000 15.5885i −0.768922 1.33181i −0.938148 0.346235i \(-0.887460\pi\)
0.169226 0.985577i \(-0.445873\pi\)
\(138\) −7.50000 + 12.9904i −0.638442 + 1.10581i
\(139\) −4.00000 −0.339276 −0.169638 0.985506i \(-0.554260\pi\)
−0.169638 + 0.985506i \(0.554260\pi\)
\(140\) 0 0
\(141\) −21.0000 −1.76852
\(142\) 0 0
\(143\) 2.50000 + 4.33013i 0.209061 + 0.362103i
\(144\) −3.00000 5.19615i −0.250000 0.433013i
\(145\) 0 0
\(146\) 7.00000 0.579324
\(147\) 0 0
\(148\) 7.00000 0.575396
\(149\) −3.50000 + 6.06218i −0.286731 + 0.496633i −0.973028 0.230689i \(-0.925902\pi\)
0.686296 + 0.727322i \(0.259235\pi\)
\(150\) 7.50000 + 12.9904i 0.612372 + 1.06066i
\(151\) 6.00000 + 10.3923i 0.488273 + 0.845714i 0.999909 0.0134886i \(-0.00429367\pi\)
−0.511636 + 0.859202i \(0.670960\pi\)
\(152\) −1.00000 + 1.73205i −0.0811107 + 0.140488i
\(153\) 24.0000 1.94029
\(154\) 0 0
\(155\) 0 0
\(156\) 1.50000 2.59808i 0.120096 0.208013i
\(157\) 0.500000 + 0.866025i 0.0399043 + 0.0691164i 0.885288 0.465044i \(-0.153961\pi\)
−0.845383 + 0.534160i \(0.820628\pi\)
\(158\) −8.50000 14.7224i −0.676224 1.17125i
\(159\) −6.00000 + 10.3923i −0.475831 + 0.824163i
\(160\) 0 0
\(161\) 0 0
\(162\) −9.00000 −0.707107
\(163\) −2.00000 + 3.46410i −0.156652 + 0.271329i −0.933659 0.358162i \(-0.883403\pi\)
0.777007 + 0.629492i \(0.216737\pi\)
\(164\) −4.50000 7.79423i −0.351391 0.608627i
\(165\) 0 0
\(166\) −2.00000 + 3.46410i −0.155230 + 0.268866i
\(167\) −8.00000 −0.619059 −0.309529 0.950890i \(-0.600171\pi\)
−0.309529 + 0.950890i \(0.600171\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) 6.00000 + 10.3923i 0.458831 + 0.794719i
\(172\) 6.00000 + 10.3923i 0.457496 + 0.792406i
\(173\) 9.00000 15.5885i 0.684257 1.18517i −0.289412 0.957205i \(-0.593460\pi\)
0.973670 0.227964i \(-0.0732068\pi\)
\(174\) 12.0000 0.909718
\(175\) 0 0
\(176\) −5.00000 −0.376889
\(177\) 9.00000 15.5885i 0.676481 1.17170i
\(178\) −7.00000 12.1244i −0.524672 0.908759i
\(179\) 1.00000 + 1.73205i 0.0747435 + 0.129460i 0.900975 0.433872i \(-0.142853\pi\)
−0.826231 + 0.563331i \(0.809520\pi\)
\(180\) 0 0
\(181\) 5.00000 0.371647 0.185824 0.982583i \(-0.440505\pi\)
0.185824 + 0.982583i \(0.440505\pi\)
\(182\) 0 0
\(183\) 39.0000 2.88296
\(184\) 2.50000 4.33013i 0.184302 0.319221i
\(185\) 0 0
\(186\) 1.50000 + 2.59808i 0.109985 + 0.190500i
\(187\) 10.0000 17.3205i 0.731272 1.26660i
\(188\) 7.00000 0.510527
\(189\) 0 0
\(190\) 0 0
\(191\) 8.00000 13.8564i 0.578860 1.00261i −0.416751 0.909021i \(-0.636831\pi\)
0.995610 0.0935936i \(-0.0298354\pi\)
\(192\) 1.50000 + 2.59808i 0.108253 + 0.187500i
\(193\) −2.00000 3.46410i −0.143963 0.249351i 0.785022 0.619467i \(-0.212651\pi\)
−0.928986 + 0.370116i \(0.879318\pi\)
\(194\) −2.50000 + 4.33013i −0.179490 + 0.310885i
\(195\) 0 0
\(196\) 0 0
\(197\) 27.0000 1.92367 0.961835 0.273629i \(-0.0882242\pi\)
0.961835 + 0.273629i \(0.0882242\pi\)
\(198\) −15.0000 + 25.9808i −1.06600 + 1.84637i
\(199\) −10.0000 17.3205i −0.708881 1.22782i −0.965272 0.261245i \(-0.915867\pi\)
0.256391 0.966573i \(-0.417466\pi\)
\(200\) −2.50000 4.33013i −0.176777 0.306186i
\(201\) 16.5000 28.5788i 1.16382 2.01580i
\(202\) 15.0000 1.05540
\(203\) 0 0
\(204\) −12.0000 −0.840168
\(205\) 0 0
\(206\) −3.00000 5.19615i −0.209020 0.362033i
\(207\) −15.0000 25.9808i −1.04257 1.80579i
\(208\) −0.500000 + 0.866025i −0.0346688 + 0.0600481i
\(209\) 10.0000 0.691714
\(210\) 0 0
\(211\) −14.0000 −0.963800 −0.481900 0.876226i \(-0.660053\pi\)
−0.481900 + 0.876226i \(0.660053\pi\)
\(212\) 2.00000 3.46410i 0.137361 0.237915i
\(213\) 0 0
\(214\) −4.00000 6.92820i −0.273434 0.473602i
\(215\) 0 0
\(216\) 9.00000 0.612372
\(217\) 0 0
\(218\) 18.0000 1.21911
\(219\) −10.5000 + 18.1865i −0.709524 + 1.22893i
\(220\) 0 0
\(221\) −2.00000 3.46410i −0.134535 0.233021i
\(222\) −10.5000 + 18.1865i −0.704714 + 1.22060i
\(223\) −3.00000 −0.200895 −0.100447 0.994942i \(-0.532027\pi\)
−0.100447 + 0.994942i \(0.532027\pi\)
\(224\) 0 0
\(225\) −30.0000 −2.00000
\(226\) 0.500000 0.866025i 0.0332595 0.0576072i
\(227\) −6.00000 10.3923i −0.398234 0.689761i 0.595274 0.803523i \(-0.297043\pi\)
−0.993508 + 0.113761i \(0.963710\pi\)
\(228\) −3.00000 5.19615i −0.198680 0.344124i
\(229\) 8.00000 13.8564i 0.528655 0.915657i −0.470787 0.882247i \(-0.656030\pi\)
0.999442 0.0334101i \(-0.0106368\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −4.00000 −0.262613
\(233\) 10.5000 18.1865i 0.687878 1.19144i −0.284645 0.958633i \(-0.591876\pi\)
0.972523 0.232806i \(-0.0747909\pi\)
\(234\) 3.00000 + 5.19615i 0.196116 + 0.339683i
\(235\) 0 0
\(236\) −3.00000 + 5.19615i −0.195283 + 0.338241i
\(237\) 51.0000 3.31281
\(238\) 0 0
\(239\) −6.00000 −0.388108 −0.194054 0.980991i \(-0.562164\pi\)
−0.194054 + 0.980991i \(0.562164\pi\)
\(240\) 0 0
\(241\) −15.0000 25.9808i −0.966235 1.67357i −0.706260 0.707953i \(-0.749619\pi\)
−0.259975 0.965615i \(-0.583714\pi\)
\(242\) 7.00000 + 12.1244i 0.449977 + 0.779383i
\(243\) 0 0
\(244\) −13.0000 −0.832240
\(245\) 0 0
\(246\) 27.0000 1.72146
\(247\) 1.00000 1.73205i 0.0636285 0.110208i
\(248\) −0.500000 0.866025i −0.0317500 0.0549927i
\(249\) −6.00000 10.3923i −0.380235 0.658586i
\(250\) 0 0
\(251\) 13.0000 0.820553 0.410276 0.911961i \(-0.365432\pi\)
0.410276 + 0.911961i \(0.365432\pi\)
\(252\) 0 0
\(253\) −25.0000 −1.57174
\(254\) 4.50000 7.79423i 0.282355 0.489053i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 14.0000 24.2487i 0.873296 1.51259i 0.0147291 0.999892i \(-0.495311\pi\)
0.858567 0.512702i \(-0.171355\pi\)
\(258\) −36.0000 −2.24126
\(259\) 0 0
\(260\) 0 0
\(261\) −12.0000 + 20.7846i −0.742781 + 1.28654i
\(262\) −4.00000 6.92820i −0.247121 0.428026i
\(263\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(264\) 7.50000 12.9904i 0.461593 0.799503i
\(265\) 0 0
\(266\) 0 0
\(267\) 42.0000 2.57036
\(268\) −5.50000 + 9.52628i −0.335966 + 0.581910i
\(269\) 6.50000 + 11.2583i 0.396312 + 0.686433i 0.993268 0.115842i \(-0.0369565\pi\)
−0.596956 + 0.802274i \(0.703623\pi\)
\(270\) 0 0
\(271\) −0.500000 + 0.866025i −0.0303728 + 0.0526073i −0.880812 0.473466i \(-0.843003\pi\)
0.850439 + 0.526073i \(0.176336\pi\)
\(272\) 4.00000 0.242536
\(273\) 0 0
\(274\) −18.0000 −1.08742
\(275\) −12.5000 + 21.6506i −0.753778 + 1.30558i
\(276\) 7.50000 + 12.9904i 0.451447 + 0.781929i
\(277\) 5.00000 + 8.66025i 0.300421 + 0.520344i 0.976231 0.216731i \(-0.0695395\pi\)
−0.675810 + 0.737075i \(0.736206\pi\)
\(278\) −2.00000 + 3.46410i −0.119952 + 0.207763i
\(279\) −6.00000 −0.359211
\(280\) 0 0
\(281\) −16.0000 −0.954480 −0.477240 0.878773i \(-0.658363\pi\)
−0.477240 + 0.878773i \(0.658363\pi\)
\(282\) −10.5000 + 18.1865i −0.625266 + 1.08299i
\(283\) 1.50000 + 2.59808i 0.0891657 + 0.154440i 0.907159 0.420789i \(-0.138247\pi\)
−0.817993 + 0.575228i \(0.804913\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 5.00000 0.295656
\(287\) 0 0
\(288\) −6.00000 −0.353553
\(289\) 0.500000 0.866025i 0.0294118 0.0509427i
\(290\) 0 0
\(291\) −7.50000 12.9904i −0.439658 0.761510i
\(292\) 3.50000 6.06218i 0.204822 0.354762i
\(293\) 6.00000 0.350524 0.175262 0.984522i \(-0.443923\pi\)
0.175262 + 0.984522i \(0.443923\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 3.50000 6.06218i 0.203433 0.352357i
\(297\) −22.5000 38.9711i −1.30558 2.26134i
\(298\) 3.50000 + 6.06218i 0.202750 + 0.351173i
\(299\) −2.50000 + 4.33013i −0.144579 + 0.250418i
\(300\) 15.0000 0.866025
\(301\) 0 0
\(302\) 12.0000 0.690522
\(303\) −22.5000 + 38.9711i −1.29259 + 2.23883i
\(304\) 1.00000 + 1.73205i 0.0573539 + 0.0993399i
\(305\) 0 0
\(306\) 12.0000 20.7846i 0.685994 1.18818i
\(307\) −32.0000 −1.82634 −0.913168 0.407583i \(-0.866372\pi\)
−0.913168 + 0.407583i \(0.866372\pi\)
\(308\) 0 0
\(309\) 18.0000 1.02398
\(310\) 0 0
\(311\) 13.0000 + 22.5167i 0.737162 + 1.27680i 0.953768 + 0.300544i \(0.0971681\pi\)
−0.216606 + 0.976259i \(0.569499\pi\)
\(312\) −1.50000 2.59808i −0.0849208 0.147087i
\(313\) −15.0000 + 25.9808i −0.847850 + 1.46852i 0.0352727 + 0.999378i \(0.488770\pi\)
−0.883123 + 0.469142i \(0.844563\pi\)
\(314\) 1.00000 0.0564333
\(315\) 0 0
\(316\) −17.0000 −0.956325
\(317\) −5.50000 + 9.52628i −0.308911 + 0.535049i −0.978124 0.208021i \(-0.933298\pi\)
0.669214 + 0.743070i \(0.266631\pi\)
\(318\) 6.00000 + 10.3923i 0.336463 + 0.582772i
\(319\) 10.0000 + 17.3205i 0.559893 + 0.969762i
\(320\) 0 0
\(321\) 24.0000 1.33955
\(322\) 0 0
\(323\) −8.00000 −0.445132
\(324\) −4.50000 + 7.79423i −0.250000 + 0.433013i
\(325\) 2.50000 + 4.33013i 0.138675 + 0.240192i
\(326\) 2.00000 + 3.46410i 0.110770 + 0.191859i
\(327\) −27.0000 + 46.7654i −1.49310 + 2.58613i
\(328\) −9.00000 −0.496942
\(329\) 0 0
\(330\) 0 0
\(331\) −1.50000 + 2.59808i −0.0824475 + 0.142803i −0.904301 0.426896i \(-0.859607\pi\)
0.821853 + 0.569699i \(0.192940\pi\)
\(332\) 2.00000 + 3.46410i 0.109764 + 0.190117i
\(333\) −21.0000 36.3731i −1.15079 1.99323i
\(334\) −4.00000 + 6.92820i −0.218870 + 0.379094i
\(335\) 0 0
\(336\) 0 0
\(337\) 9.00000 0.490261 0.245131 0.969490i \(-0.421169\pi\)
0.245131 + 0.969490i \(0.421169\pi\)
\(338\) 0.500000 0.866025i 0.0271964 0.0471056i
\(339\) 1.50000 + 2.59808i 0.0814688 + 0.141108i
\(340\) 0 0
\(341\) −2.50000 + 4.33013i −0.135383 + 0.234490i
\(342\) 12.0000 0.648886
\(343\) 0 0
\(344\) 12.0000 0.646997
\(345\) 0 0
\(346\) −9.00000 15.5885i −0.483843 0.838041i
\(347\) −8.00000 13.8564i −0.429463 0.743851i 0.567363 0.823468i \(-0.307964\pi\)
−0.996826 + 0.0796169i \(0.974630\pi\)
\(348\) 6.00000 10.3923i 0.321634 0.557086i
\(349\) −2.00000 −0.107058 −0.0535288 0.998566i \(-0.517047\pi\)
−0.0535288 + 0.998566i \(0.517047\pi\)
\(350\) 0 0
\(351\) −9.00000 −0.480384
\(352\) −2.50000 + 4.33013i −0.133250 + 0.230797i
\(353\) 1.50000 + 2.59808i 0.0798369 + 0.138282i 0.903179 0.429263i \(-0.141227\pi\)
−0.823343 + 0.567545i \(0.807893\pi\)
\(354\) −9.00000 15.5885i −0.478345 0.828517i
\(355\) 0 0
\(356\) −14.0000 −0.741999
\(357\) 0 0
\(358\) 2.00000 0.105703
\(359\) 2.00000 3.46410i 0.105556 0.182828i −0.808409 0.588621i \(-0.799671\pi\)
0.913965 + 0.405793i \(0.133004\pi\)
\(360\) 0 0
\(361\) 7.50000 + 12.9904i 0.394737 + 0.683704i
\(362\) 2.50000 4.33013i 0.131397 0.227586i
\(363\) −42.0000 −2.20443
\(364\) 0 0
\(365\) 0 0
\(366\) 19.5000 33.7750i 1.01928 1.76545i
\(367\) 4.00000 + 6.92820i 0.208798 + 0.361649i 0.951336 0.308155i \(-0.0997115\pi\)
−0.742538 + 0.669804i \(0.766378\pi\)
\(368\) −2.50000 4.33013i −0.130322 0.225723i
\(369\) −27.0000 + 46.7654i −1.40556 + 2.43451i
\(370\) 0 0
\(371\) 0 0
\(372\) 3.00000 0.155543
\(373\) −2.00000 + 3.46410i −0.103556 + 0.179364i −0.913147 0.407630i \(-0.866355\pi\)
0.809591 + 0.586994i \(0.199689\pi\)
\(374\) −10.0000 17.3205i −0.517088 0.895622i
\(375\) 0 0
\(376\) 3.50000 6.06218i 0.180499 0.312633i
\(377\) 4.00000 0.206010
\(378\) 0 0
\(379\) −16.0000 −0.821865 −0.410932 0.911666i \(-0.634797\pi\)
−0.410932 + 0.911666i \(0.634797\pi\)
\(380\) 0 0
\(381\) 13.5000 + 23.3827i 0.691626 + 1.19793i
\(382\) −8.00000 13.8564i −0.409316 0.708955i
\(383\) −4.50000 + 7.79423i −0.229939 + 0.398266i −0.957790 0.287469i \(-0.907186\pi\)
0.727851 + 0.685736i \(0.240519\pi\)
\(384\) 3.00000 0.153093
\(385\) 0 0
\(386\) −4.00000 −0.203595
\(387\) 36.0000 62.3538i 1.82998 3.16962i
\(388\) 2.50000 + 4.33013i 0.126918 + 0.219829i
\(389\) −4.00000 6.92820i −0.202808 0.351274i 0.746624 0.665246i \(-0.231673\pi\)
−0.949432 + 0.313972i \(0.898340\pi\)
\(390\) 0 0
\(391\) 20.0000 1.01144
\(392\) 0 0
\(393\) 24.0000 1.21064
\(394\) 13.5000 23.3827i 0.680120 1.17800i
\(395\) 0 0
\(396\) 15.0000 + 25.9808i 0.753778 + 1.30558i
\(397\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(398\) −20.0000 −1.00251
\(399\) 0 0
\(400\) −5.00000 −0.250000
\(401\) 14.0000 24.2487i 0.699127 1.21092i −0.269643 0.962960i \(-0.586906\pi\)
0.968770 0.247962i \(-0.0797610\pi\)
\(402\) −16.5000 28.5788i −0.822945 1.42538i
\(403\) 0.500000 + 0.866025i 0.0249068 + 0.0431398i
\(404\) 7.50000 12.9904i 0.373139 0.646296i
\(405\) 0 0
\(406\) 0 0
\(407\) −35.0000 −1.73489
\(408\) −6.00000 + 10.3923i −0.297044 + 0.514496i
\(409\) −3.00000 5.19615i −0.148340 0.256933i 0.782274 0.622935i \(-0.214060\pi\)
−0.930614 + 0.366002i \(0.880726\pi\)
\(410\) 0 0
\(411\) 27.0000 46.7654i 1.33181 2.30677i
\(412\) −6.00000 −0.295599
\(413\) 0 0
\(414\) −30.0000 −1.47442
\(415\) 0 0
\(416\) 0.500000 + 0.866025i 0.0245145 + 0.0424604i
\(417\) −6.00000 10.3923i −0.293821 0.508913i
\(418\) 5.00000 8.66025i 0.244558 0.423587i
\(419\) 9.00000 0.439679 0.219839 0.975536i \(-0.429447\pi\)
0.219839 + 0.975536i \(0.429447\pi\)
\(420\) 0 0
\(421\) −35.0000 −1.70580 −0.852898 0.522078i \(-0.825157\pi\)
−0.852898 + 0.522078i \(0.825157\pi\)
\(422\) −7.00000 + 12.1244i −0.340755 + 0.590204i
\(423\) −21.0000 36.3731i −1.02105 1.76852i
\(424\) −2.00000 3.46410i −0.0971286 0.168232i
\(425\) 10.0000 17.3205i 0.485071 0.840168i
\(426\) 0 0
\(427\) 0 0
\(428\) −8.00000 −0.386695
\(429\) −7.50000 + 12.9904i −0.362103 + 0.627182i
\(430\) 0 0
\(431\) 3.00000 + 5.19615i 0.144505 + 0.250290i 0.929188 0.369607i \(-0.120508\pi\)
−0.784683 + 0.619897i \(0.787174\pi\)
\(432\) 4.50000 7.79423i 0.216506 0.375000i
\(433\) −26.0000 −1.24948 −0.624740 0.780833i \(-0.714795\pi\)
−0.624740 + 0.780833i \(0.714795\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 9.00000 15.5885i 0.431022 0.746552i
\(437\) 5.00000 + 8.66025i 0.239182 + 0.414276i
\(438\) 10.5000 + 18.1865i 0.501709 + 0.868986i
\(439\) −1.00000 + 1.73205i −0.0477274 + 0.0826663i −0.888902 0.458097i \(-0.848531\pi\)
0.841175 + 0.540763i \(0.181865\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) −4.00000 −0.190261
\(443\) 6.00000 10.3923i 0.285069 0.493753i −0.687557 0.726130i \(-0.741317\pi\)
0.972626 + 0.232377i \(0.0746503\pi\)
\(444\) 10.5000 + 18.1865i 0.498308 + 0.863095i
\(445\) 0 0
\(446\) −1.50000 + 2.59808i −0.0710271 + 0.123022i
\(447\) −21.0000 −0.993266
\(448\) 0 0
\(449\) 18.0000 0.849473 0.424736 0.905317i \(-0.360367\pi\)
0.424736 + 0.905317i \(0.360367\pi\)
\(450\) −15.0000 + 25.9808i −0.707107 + 1.22474i
\(451\) 22.5000 + 38.9711i 1.05948 + 1.83508i
\(452\) −0.500000 0.866025i −0.0235180 0.0407344i
\(453\) −18.0000 + 31.1769i −0.845714 + 1.46482i
\(454\) −12.0000 −0.563188
\(455\) 0 0
\(456\) −6.00000 −0.280976
\(457\) 5.00000 8.66025i 0.233890 0.405110i −0.725059 0.688686i \(-0.758188\pi\)
0.958950 + 0.283577i \(0.0915211\pi\)
\(458\) −8.00000 13.8564i −0.373815 0.647467i
\(459\) 18.0000 + 31.1769i 0.840168 + 1.45521i
\(460\) 0 0
\(461\) −12.0000 −0.558896 −0.279448 0.960161i \(-0.590151\pi\)
−0.279448 + 0.960161i \(0.590151\pi\)
\(462\) 0 0
\(463\) 12.0000 0.557687 0.278844 0.960337i \(-0.410049\pi\)
0.278844 + 0.960337i \(0.410049\pi\)
\(464\) −2.00000 + 3.46410i −0.0928477 + 0.160817i
\(465\) 0 0
\(466\) −10.5000 18.1865i −0.486403 0.842475i
\(467\) −18.0000 + 31.1769i −0.832941 + 1.44270i 0.0627555 + 0.998029i \(0.480011\pi\)
−0.895696 + 0.444667i \(0.853322\pi\)
\(468\) 6.00000 0.277350
\(469\) 0 0
\(470\) 0 0
\(471\) −1.50000 + 2.59808i −0.0691164 + 0.119713i
\(472\) 3.00000 + 5.19615i 0.138086 + 0.239172i
\(473\) −30.0000 51.9615i −1.37940 2.38919i
\(474\) 25.5000 44.1673i 1.17125 2.02867i
\(475\) 10.0000 0.458831
\(476\) 0 0
\(477\) −24.0000 −1.09888
\(478\) −3.00000 + 5.19615i −0.137217 + 0.237666i
\(479\) −8.00000 13.8564i −0.365529 0.633115i 0.623332 0.781958i \(-0.285779\pi\)
−0.988861 + 0.148842i \(0.952445\pi\)
\(480\) 0 0
\(481\) −3.50000 + 6.06218i −0.159586 + 0.276412i
\(482\) −30.0000 −1.36646
\(483\) 0 0
\(484\) 14.0000 0.636364
\(485\) 0 0
\(486\) 0 0
\(487\) 13.0000 + 22.5167i 0.589086 + 1.02033i 0.994352 + 0.106129i \(0.0338455\pi\)
−0.405266 + 0.914199i \(0.632821\pi\)
\(488\) −6.50000 + 11.2583i −0.294241 + 0.509641i
\(489\) −12.0000 −0.542659
\(490\) 0 0
\(491\) 28.0000 1.26362 0.631811 0.775122i \(-0.282312\pi\)
0.631811 + 0.775122i \(0.282312\pi\)
\(492\) 13.5000 23.3827i 0.608627 1.05417i
\(493\) −8.00000 13.8564i −0.360302 0.624061i
\(494\) −1.00000 1.73205i −0.0449921 0.0779287i
\(495\) 0 0
\(496\) −1.00000 −0.0449013
\(497\) 0 0
\(498\) −12.0000 −0.537733
\(499\) −0.500000 + 0.866025i −0.0223831 + 0.0387686i −0.877000 0.480490i \(-0.840459\pi\)
0.854617 + 0.519259i \(0.173792\pi\)
\(500\) 0 0
\(501\) −12.0000 20.7846i −0.536120 0.928588i
\(502\) 6.50000 11.2583i 0.290109 0.502484i
\(503\) 40.0000 1.78351 0.891756 0.452517i \(-0.149474\pi\)
0.891756 + 0.452517i \(0.149474\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) −12.5000 + 21.6506i −0.555693 + 0.962488i
\(507\) 1.50000 + 2.59808i 0.0666173 + 0.115385i
\(508\) −4.50000 7.79423i −0.199655 0.345813i
\(509\) 3.00000 5.19615i 0.132973 0.230315i −0.791849 0.610718i \(-0.790881\pi\)
0.924821 + 0.380402i \(0.124214\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −1.00000 −0.0441942
\(513\) −9.00000 + 15.5885i −0.397360 + 0.688247i
\(514\) −14.0000 24.2487i −0.617514 1.06956i
\(515\) 0 0
\(516\) −18.0000 + 31.1769i −0.792406 + 1.37249i
\(517\) −35.0000 −1.53930
\(518\) 0 0
\(519\) 54.0000 2.37034
\(520\) 0 0
\(521\) −7.00000 12.1244i −0.306676 0.531178i 0.670957 0.741496i \(-0.265883\pi\)
−0.977633 + 0.210318i \(0.932550\pi\)
\(522\) 12.0000 + 20.7846i 0.525226 + 0.909718i
\(523\) −6.50000 + 11.2583i −0.284225 + 0.492292i −0.972421 0.233233i \(-0.925070\pi\)
0.688196 + 0.725525i \(0.258403\pi\)
\(524\) −8.00000 −0.349482
\(525\) 0 0
\(526\) 0 0
\(527\) 2.00000 3.46410i 0.0871214 0.150899i
\(528\) −7.50000 12.9904i −0.326396 0.565334i
\(529\) −1.00000 1.73205i −0.0434783 0.0753066i
\(530\) 0 0
\(531\) 36.0000 1.56227
\(532\) 0 0
\(533\) 9.00000 0.389833
\(534\) 21.0000 36.3731i 0.908759 1.57402i
\(535\) 0 0
\(536\) 5.50000 + 9.52628i 0.237564 + 0.411473i
\(537\) −3.00000 + 5.19615i −0.129460 + 0.224231i
\(538\) 13.0000 0.560470
\(539\) 0 0
\(540\) 0 0
\(541\) −9.00000 + 15.5885i −0.386940 + 0.670200i −0.992036 0.125952i \(-0.959801\pi\)
0.605096 + 0.796152i \(0.293135\pi\)
\(542\) 0.500000 + 0.866025i 0.0214768 + 0.0371990i
\(543\) 7.50000 + 12.9904i 0.321856 + 0.557471i
\(544\) 2.00000 3.46410i 0.0857493 0.148522i
\(545\) 0 0
\(546\) 0 0
\(547\) −32.0000 −1.36822 −0.684111 0.729378i \(-0.739809\pi\)
−0.684111 + 0.729378i \(0.739809\pi\)
\(548\) −9.00000 + 15.5885i −0.384461 + 0.665906i
\(549\) 39.0000 + 67.5500i 1.66448 + 2.88296i
\(550\) 12.5000 + 21.6506i 0.533002 + 0.923186i
\(551\) 4.00000 6.92820i 0.170406 0.295151i
\(552\) 15.0000 0.638442
\(553\) 0 0
\(554\) 10.0000 0.424859
\(555\) 0 0
\(556\) 2.00000 + 3.46410i 0.0848189 + 0.146911i
\(557\) 4.50000 + 7.79423i 0.190671 + 0.330252i 0.945473 0.325701i \(-0.105600\pi\)
−0.754802 + 0.655953i \(0.772267\pi\)
\(558\) −3.00000 + 5.19615i −0.127000 + 0.219971i
\(559\) −12.0000 −0.507546
\(560\) 0 0
\(561\) 60.0000 2.53320
\(562\) −8.00000 + 13.8564i −0.337460 + 0.584497i
\(563\) 17.5000 + 30.3109i 0.737537 + 1.27745i 0.953601 + 0.301073i \(0.0973446\pi\)
−0.216064 + 0.976379i \(0.569322\pi\)
\(564\) 10.5000 + 18.1865i 0.442130 + 0.765791i
\(565\) 0 0
\(566\) 3.00000 0.126099
\(567\) 0 0
\(568\) 0 0
\(569\) −10.5000 + 18.1865i −0.440183 + 0.762419i −0.997703 0.0677445i \(-0.978420\pi\)
0.557520 + 0.830164i \(0.311753\pi\)
\(570\) 0 0
\(571\) −11.0000 19.0526i −0.460336 0.797325i 0.538642 0.842535i \(-0.318938\pi\)
−0.998978 + 0.0452101i \(0.985604\pi\)
\(572\) 2.50000 4.33013i 0.104530 0.181052i
\(573\) 48.0000 2.00523
\(574\) 0 0
\(575\) −25.0000 −1.04257
\(576\) −3.00000 + 5.19615i −0.125000 + 0.216506i
\(577\) 1.00000 + 1.73205i 0.0416305 + 0.0721062i 0.886090 0.463513i \(-0.153411\pi\)
−0.844459 + 0.535620i \(0.820078\pi\)
\(578\) −0.500000 0.866025i −0.0207973 0.0360219i
\(579\) 6.00000 10.3923i 0.249351 0.431889i
\(580\) 0 0
\(581\) 0 0
\(582\) −15.0000 −0.621770
\(583\) −10.0000 + 17.3205i −0.414158 + 0.717342i
\(584\) −3.50000 6.06218i −0.144831 0.250855i
\(585\) 0 0
\(586\) 3.00000 5.19615i 0.123929 0.214651i
\(587\) −18.0000 −0.742940 −0.371470 0.928445i \(-0.621146\pi\)
−0.371470 + 0.928445i \(0.621146\pi\)
\(588\) 0 0
\(589\) 2.00000 0.0824086
\(590\) 0 0
\(591\) 40.5000 + 70.1481i 1.66595 + 2.88551i
\(592\) −3.50000 6.06218i −0.143849 0.249154i
\(593\) −23.0000 + 39.8372i −0.944497 + 1.63592i −0.187741 + 0.982219i \(0.560117\pi\)
−0.756756 + 0.653698i \(0.773217\pi\)
\(594\) −45.0000 −1.84637
\(595\) 0 0
\(596\) 7.00000 0.286731
\(597\) 30.0000 51.9615i 1.22782 2.12664i
\(598\) 2.50000 + 4.33013i 0.102233 + 0.177072i
\(599\) 4.50000 + 7.79423i 0.183865 + 0.318464i 0.943193 0.332244i \(-0.107806\pi\)
−0.759328 + 0.650708i \(0.774472\pi\)
\(600\) 7.50000 12.9904i 0.306186 0.530330i
\(601\) −26.0000 −1.06056 −0.530281 0.847822i \(-0.677914\pi\)
−0.530281 + 0.847822i \(0.677914\pi\)
\(602\) 0 0
\(603\) 66.0000 2.68773
\(604\) 6.00000 10.3923i 0.244137 0.422857i
\(605\) 0 0
\(606\) 22.5000 + 38.9711i 0.914000 + 1.58309i
\(607\) 11.0000 19.0526i 0.446476 0.773320i −0.551678 0.834058i \(-0.686012\pi\)
0.998154 + 0.0607380i \(0.0193454\pi\)
\(608\) 2.00000 0.0811107
\(609\) 0 0
\(610\) 0 0
\(611\) −3.50000 + 6.06218i −0.141595 + 0.245249i
\(612\) −12.0000 20.7846i −0.485071 0.840168i
\(613\) 11.5000 + 19.9186i 0.464481 + 0.804504i 0.999178 0.0405396i \(-0.0129077\pi\)
−0.534697 + 0.845044i \(0.679574\pi\)
\(614\) −16.0000 + 27.7128i −0.645707 + 1.11840i
\(615\) 0 0
\(616\) 0 0
\(617\) 6.00000 0.241551 0.120775 0.992680i \(-0.461462\pi\)
0.120775 + 0.992680i \(0.461462\pi\)
\(618\) 9.00000 15.5885i 0.362033 0.627060i
\(619\) 3.00000 + 5.19615i 0.120580 + 0.208851i 0.919997 0.391926i \(-0.128191\pi\)
−0.799416 + 0.600777i \(0.794858\pi\)
\(620\) 0 0
\(621\) 22.5000 38.9711i 0.902894 1.56386i
\(622\) 26.0000 1.04251
\(623\) 0 0
\(624\) −3.00000 −0.120096
\(625\) −12.5000 + 21.6506i −0.500000 + 0.866025i
\(626\) 15.0000 + 25.9808i 0.599521 + 1.03840i
\(627\) 15.0000 + 25.9808i 0.599042 + 1.03757i
\(628\) 0.500000 0.866025i 0.0199522 0.0345582i
\(629\) 28.0000 1.11643
\(630\) 0 0
\(631\) −26.0000 −1.03504 −0.517522 0.855670i \(-0.673145\pi\)
−0.517522 + 0.855670i \(0.673145\pi\)
\(632\) −8.50000 + 14.7224i −0.338112 + 0.585627i
\(633\) −21.0000 36.3731i −0.834675 1.44570i
\(634\) 5.50000 + 9.52628i 0.218433 + 0.378337i
\(635\) 0 0
\(636\) 12.0000 0.475831
\(637\) 0 0
\(638\) 20.0000 0.791808
\(639\) 0 0
\(640\) 0 0
\(641\) 16.5000 + 28.5788i 0.651711 + 1.12880i 0.982708 + 0.185164i \(0.0592817\pi\)
−0.330997 + 0.943632i \(0.607385\pi\)
\(642\) 12.0000 20.7846i 0.473602 0.820303i
\(643\) 36.0000 1.41970 0.709851 0.704352i \(-0.248762\pi\)
0.709851 + 0.704352i \(0.248762\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −4.00000 + 6.92820i −0.157378 + 0.272587i
\(647\) −6.00000 10.3923i −0.235884 0.408564i 0.723645 0.690172i \(-0.242465\pi\)
−0.959529 + 0.281609i \(0.909132\pi\)
\(648\) 4.50000 + 7.79423i 0.176777 + 0.306186i
\(649\) 15.0000 25.9808i 0.588802 1.01983i
\(650\) 5.00000 0.196116
\(651\) 0 0
\(652\) 4.00000 0.156652
\(653\) 6.00000 10.3923i 0.234798 0.406682i −0.724416 0.689363i \(-0.757890\pi\)
0.959214 + 0.282681i \(0.0912238\pi\)
\(654\) 27.0000 + 46.7654i 1.05578 + 1.82867i
\(655\) 0 0
\(656\) −4.50000 + 7.79423i −0.175695 + 0.304314i
\(657\) −42.0000 −1.63858
\(658\) 0 0
\(659\) 26.0000 1.01282 0.506408 0.862294i \(-0.330973\pi\)
0.506408 + 0.862294i \(0.330973\pi\)
\(660\) 0 0
\(661\) −10.0000 17.3205i −0.388955 0.673690i 0.603354 0.797473i \(-0.293830\pi\)
−0.992309 + 0.123784i \(0.960497\pi\)
\(662\) 1.50000 + 2.59808i 0.0582992 + 0.100977i
\(663\) 6.00000 10.3923i 0.233021 0.403604i
\(664\) 4.00000 0.155230
\(665\) 0 0
\(666\) −42.0000 −1.62747
\(667\) −10.0000 + 17.3205i −0.387202 + 0.670653i
\(668\) 4.00000 + 6.92820i 0.154765 + 0.268060i
\(669\) −4.50000 7.79423i −0.173980 0.301342i
\(670\) 0 0
\(671\) 65.0000 2.50930
\(672\) 0 0
\(673\) −9.00000 −0.346925 −0.173462 0.984841i \(-0.555495\pi\)
−0.173462 + 0.984841i \(0.555495\pi\)
\(674\) 4.50000 7.79423i 0.173334 0.300222i
\(675\) −22.5000 38.9711i −0.866025 1.50000i
\(676\) −0.500000 0.866025i −0.0192308 0.0333087i
\(677\) 1.50000 2.59808i 0.0576497 0.0998522i −0.835760 0.549095i \(-0.814973\pi\)
0.893410 + 0.449242i \(0.148306\pi\)
\(678\) 3.00000 0.115214
\(679\) 0 0
\(680\) 0 0
\(681\) 18.0000 31.1769i 0.689761 1.19470i
\(682\) 2.50000 + 4.33013i 0.0957299 + 0.165809i
\(683\) −1.50000 2.59808i −0.0573959 0.0994126i 0.835900 0.548882i \(-0.184946\pi\)
−0.893296 + 0.449469i \(0.851613\pi\)
\(684\) 6.00000 10.3923i 0.229416 0.397360i
\(685\) 0 0
\(686\) 0 0
\(687\) 48.0000 1.83131
\(688\) 6.00000 10.3923i 0.228748 0.396203i
\(689\) 2.00000 + 3.46410i 0.0761939 + 0.131972i
\(690\) 0 0
\(691\) −18.0000 + 31.1769i −0.684752 + 1.18603i 0.288762 + 0.957401i \(0.406756\pi\)
−0.973515 + 0.228625i \(0.926577\pi\)
\(692\) −18.0000 −0.684257
\(693\) 0 0
\(694\) −16.0000 −0.607352
\(695\) 0 0
\(696\) −6.00000 10.3923i −0.227429 0.393919i
\(697\) −18.0000 31.1769i −0.681799 1.18091i
\(698\) −1.00000 + 1.73205i −0.0378506 + 0.0655591i
\(699\) 63.0000 2.38288
\(700\) 0 0
\(701\) −12.0000 −0.453234 −0.226617 0.973984i \(-0.572767\pi\)
−0.226617 + 0.973984i \(0.572767\pi\)
\(702\) −4.50000 + 7.79423i −0.169842 + 0.294174i
\(703\) 7.00000 + 12.1244i 0.264010 + 0.457279i
\(704\) 2.50000 + 4.33013i 0.0942223 + 0.163198i
\(705\) 0 0
\(706\) 3.00000 0.112906
\(707\) 0 0
\(708\) −18.0000 −0.676481
\(709\) −14.5000 + 25.1147i −0.544559 + 0.943204i 0.454076 + 0.890963i \(0.349970\pi\)
−0.998635 + 0.0522406i \(0.983364\pi\)
\(710\) 0 0
\(711\) 51.0000 + 88.3346i 1.91265 + 3.31281i
\(712\) −7.00000 + 12.1244i −0.262336 + 0.454379i
\(713\) −5.00000 −0.187251
\(714\) 0 0
\(715\) 0 0
\(716\) 1.00000 1.73205i 0.0373718 0.0647298i
\(717\) −9.00000 15.5885i −0.336111 0.582162i
\(718\) −2.00000 3.46410i −0.0746393 0.129279i
\(719\) −9.00000 + 15.5885i −0.335643 + 0.581351i −0.983608 0.180319i \(-0.942287\pi\)
0.647965 + 0.761670i \(0.275620\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 15.0000 0.558242
\(723\) 45.0000 77.9423i 1.67357 2.89870i
\(724\) −2.50000 4.33013i −0.0929118 0.160928i
\(725\) 10.0000 + 17.3205i 0.371391 + 0.643268i
\(726\) −21.0000 + 36.3731i −0.779383 + 1.34993i
\(727\) −14.0000 −0.519231 −0.259616 0.965712i \(-0.583596\pi\)
−0.259616 + 0.965712i \(0.583596\pi\)
\(728\) 0 0
\(729\) −27.0000 −1.00000
\(730\) 0 0
\(731\) 24.0000 + 41.5692i 0.887672 + 1.53749i
\(732\) −19.5000 33.7750i −0.720741 1.24836i
\(733\) 10.0000 17.3205i 0.369358 0.639748i −0.620107 0.784517i \(-0.712911\pi\)
0.989465 + 0.144770i \(0.0462441\pi\)
\(734\) 8.00000 0.295285
\(735\) 0 0
\(736\) −5.00000 −0.184302
\(737\) 27.5000 47.6314i 1.01298 1.75453i
\(738\) 27.0000 + 46.7654i 0.993884 + 1.72146i
\(739\) 8.00000 + 13.8564i 0.294285 + 0.509716i 0.974818 0.223001i \(-0.0715853\pi\)
−0.680534 + 0.732717i \(0.738252\pi\)
\(740\) 0 0
\(741\) 6.00000 0.220416
\(742\) 0 0
\(743\) −36.0000 −1.32071 −0.660356 0.750953i \(-0.729595\pi\)
−0.660356 + 0.750953i \(0.729595\pi\)
\(744\) 1.50000 2.59808i 0.0549927 0.0952501i
\(745\) 0 0
\(746\) 2.00000 + 3.46410i 0.0732252 + 0.126830i
\(747\) 12.0000 20.7846i 0.439057 0.760469i
\(748\) −20.0000 −0.731272
\(749\) 0 0
\(750\) 0 0
\(751\) −12.5000 + 21.6506i −0.456131 + 0.790043i −0.998752 0.0499348i \(-0.984099\pi\)
0.542621 + 0.839978i \(0.317432\pi\)
\(752\) −3.50000 6.06218i −0.127632 0.221065i
\(753\) 19.5000 + 33.7750i 0.710620 + 1.23083i
\(754\) 2.00000 3.46410i 0.0728357 0.126155i
\(755\) 0 0
\(756\) 0 0
\(757\) −18.0000 −0.654221 −0.327111 0.944986i \(-0.606075\pi\)
−0.327111 + 0.944986i \(0.606075\pi\)
\(758\) −8.00000 + 13.8564i −0.290573 + 0.503287i
\(759\) −37.5000 64.9519i −1.36116 2.35760i
\(760\) 0 0
\(761\) −16.5000 + 28.5788i −0.598125 + 1.03598i 0.394973 + 0.918693i \(0.370754\pi\)
−0.993098 + 0.117289i \(0.962579\pi\)
\(762\) 27.0000 0.978107
\(763\) 0 0
\(764\) −16.0000 −0.578860
\(765\) 0 0
\(766\) 4.50000 + 7.79423i 0.162592 + 0.281617i
\(767\) −3.00000 5.19615i −0.108324 0.187622i
\(768\) 1.50000 2.59808i 0.0541266 0.0937500i
\(769\) 1.00000 0.0360609 0.0180305 0.999837i \(-0.494260\pi\)
0.0180305 + 0.999837i \(0.494260\pi\)
\(770\) 0 0
\(771\) 84.0000 3.02519
\(772\) −2.00000 + 3.46410i −0.0719816 + 0.124676i
\(773\) 17.0000 + 29.4449i 0.611448 + 1.05906i 0.990997 + 0.133887i \(0.0427458\pi\)
−0.379549 + 0.925172i \(0.623921\pi\)
\(774\) −36.0000 62.3538i −1.29399 2.24126i
\(775\) −2.50000 + 4.33013i −0.0898027 + 0.155543i
\(776\) 5.00000 0.179490
\(777\) 0 0
\(778\) −8.00000 −0.286814
\(779\) 9.00000 15.5885i 0.322458 0.558514i
\(780\) 0 0
\(781\) 0 0
\(782\) 10.0000 17.3205i 0.357599 0.619380i
\(783\) −36.0000 −1.28654
\(784\) 0 0
\(785\) 0 0
\(786\) 12.0000 20.7846i 0.428026 0.741362i
\(787\) 4.00000 + 6.92820i 0.142585 + 0.246964i 0.928469 0.371409i \(-0.121125\pi\)
−0.785885 + 0.618373i \(0.787792\pi\)
\(788\) −13.5000 23.3827i −0.480918 0.832974i
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 30.0000 1.06600
\(793\) 6.50000 11.2583i 0.230822 0.399795i
\(794\) 0 0
\(795\) 0 0
\(796\) −10.0000 + 17.3205i −0.354441 + 0.613909i
\(797\) −3.00000 −0.106265 −0.0531327 0.998587i \(-0.516921\pi\)
−0.0531327 + 0.998587i \(0.516921\pi\)
\(798\) 0 0
\(799\) 28.0000 0.990569
\(800\) −2.50000 + 4.33013i −0.0883883 + 0.153093i
\(801\) 42.0000 + 72.7461i 1.48400 + 2.57036i
\(802\) −14.0000 24.2487i −0.494357 0.856252i
\(803\) −17.5000 + 30.3109i −0.617562 + 1.06965i
\(804\) −33.0000 −1.16382
\(805\) 0 0
\(806\) 1.00000 0.0352235
\(807\) −19.5000 + 33.7750i −0.686433 + 1.18894i
\(808\) −7.50000 12.9904i −0.263849 0.457000i
\(809\) −3.00000 5.19615i −0.105474 0.182687i 0.808458 0.588555i \(-0.200303\pi\)
−0.913932 + 0.405868i \(0.866969\pi\)
\(810\) 0 0
\(811\) −52.0000 −1.82597 −0.912983 0.407997i \(-0.866228\pi\)
−0.912983 + 0.407997i \(0.866228\pi\)
\(812\) 0 0
\(813\) −3.00000 −0.105215
\(814\) −17.5000 + 30.3109i −0.613375 + 1.06240i
\(815\) 0 0
\(816\) 6.00000 + 10.3923i 0.210042 + 0.363803i
\(817\) −12.0000 + 20.7846i −0.419827 + 0.727161i
\(818\) −6.00000 −0.209785
\(819\) 0 0
\(820\) 0 0
\(821\) −3.00000 + 5.19615i −0.104701 + 0.181347i −0.913616 0.406578i \(-0.866722\pi\)
0.808915 + 0.587925i \(0.200055\pi\)
\(822\) −27.0000 46.7654i −0.941733 1.63113i
\(823\) 7.50000 + 12.9904i 0.261434 + 0.452816i 0.966623 0.256203i \(-0.0824714\pi\)
−0.705190 + 0.709019i \(0.749138\pi\)
\(824\) −3.00000 + 5.19615i −0.104510 + 0.181017i
\(825\) −75.0000 −2.61116
\(826\) 0 0
\(827\) −36.0000 −1.25184 −0.625921 0.779886i \(-0.715277\pi\)
−0.625921 + 0.779886i \(0.715277\pi\)
\(828\) −15.0000 + 25.9808i −0.521286 + 0.902894i
\(829\) −27.0000 46.7654i −0.937749 1.62423i −0.769657 0.638457i \(-0.779573\pi\)
−0.168091 0.985771i \(-0.553760\pi\)
\(830\) 0 0
\(831\) −15.0000 + 25.9808i −0.520344 + 0.901263i
\(832\) 1.00000 0.0346688
\(833\) 0 0
\(834\) −12.0000 −0.415526
\(835\) 0 0
\(836\) −5.00000 8.66025i −0.172929 0.299521i
\(837\) −4.50000 7.79423i −0.155543 0.269408i
\(838\) 4.50000 7.79423i 0.155450 0.269247i
\(839\) −47.0000 −1.62262 −0.811310 0.584616i \(-0.801245\pi\)
−0.811310 + 0.584616i \(0.801245\pi\)
\(840\) 0 0
\(841\) −13.0000 −0.448276
\(842\) −17.5000 + 30.3109i −0.603090 + 1.04458i
\(843\) −24.0000 41.5692i −0.826604 1.43172i
\(844\) 7.00000 + 12.1244i 0.240950 + 0.417338i
\(845\) 0 0
\(846\) −42.0000 −1.44399
\(847\) 0 0
\(848\) −4.00000 −0.137361
\(849\) −4.50000 + 7.79423i −0.154440 + 0.267497i
\(850\) −10.0000 17.3205i −0.342997 0.594089i
\(851\) −17.5000 30.3109i −0.599892 1.03904i
\(852\) 0 0
\(853\) 16.0000 0.547830 0.273915 0.961754i \(-0.411681\pi\)
0.273915 + 0.961754i \(0.411681\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) −4.00000 + 6.92820i −0.136717 + 0.236801i
\(857\) 1.00000 + 1.73205i 0.0341593 + 0.0591657i 0.882600 0.470125i \(-0.155791\pi\)
−0.848440 + 0.529291i \(0.822458\pi\)
\(858\) 7.50000 + 12.9904i 0.256046 + 0.443484i
\(859\) 14.5000 25.1147i 0.494734 0.856904i −0.505248 0.862974i \(-0.668599\pi\)
0.999982 + 0.00607046i \(0.00193230\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 6.00000 0.204361
\(863\) 12.0000 20.7846i 0.408485 0.707516i −0.586235 0.810141i \(-0.699391\pi\)
0.994720 + 0.102624i \(0.0327240\pi\)
\(864\) −4.50000 7.79423i −0.153093 0.265165i
\(865\) 0 0
\(866\) −13.0000 + 22.5167i −0.441758 + 0.765147i
\(867\) 3.00000 0.101885
\(868\) 0 0
\(869\) 85.0000 2.88343
\(870\) 0 0
\(871\) −5.50000 9.52628i −0.186360 0.322786i
\(872\) −9.00000 15.5885i −0.304778 0.527892i
\(873\) 15.0000 25.9808i 0.507673 0.879316i
\(874\) 10.0000 0.338255
\(875\) 0 0
\(876\) 21.0000 0.709524
\(877\) −6.50000 + 11.2583i −0.219489 + 0.380167i −0.954652 0.297724i \(-0.903772\pi\)
0.735163 + 0.677891i \(0.237106\pi\)
\(878\) 1.00000 + 1.73205i 0.0337484 + 0.0584539i
\(879\) 9.00000 + 15.5885i 0.303562 + 0.525786i
\(880\) 0 0
\(881\) −6.00000 −0.202145 −0.101073 0.994879i \(-0.532227\pi\)
−0.101073 + 0.994879i \(0.532227\pi\)
\(882\) 0 0
\(883\) 30.0000 1.00958 0.504790 0.863242i \(-0.331570\pi\)
0.504790 + 0.863242i \(0.331570\pi\)
\(884\) −2.00000 + 3.46410i −0.0672673 + 0.116510i
\(885\) 0 0
\(886\) −6.00000 10.3923i −0.201574 0.349136i
\(887\) 27.0000 46.7654i 0.906571 1.57023i 0.0877772 0.996140i \(-0.472024\pi\)
0.818794 0.574087i \(-0.194643\pi\)
\(888\) 21.0000 0.704714
\(889\) 0 0
\(890\) 0 0
\(891\) 22.5000 38.9711i 0.753778 1.30558i
\(892\) 1.50000 + 2.59808i 0.0502237 + 0.0869900i
\(893\) 7.00000 + 12.1244i 0.234246 + 0.405726i
\(894\) −10.5000 + 18.1865i −0.351173 + 0.608249i
\(895\) 0 0
\(896\) 0 0
\(897\) −15.0000 −0.500835
\(898\) 9.00000 15.5885i 0.300334 0.520194i
\(899\) 2.00000 + 3.46410i 0.0667037 + 0.115534i
\(900\) 15.0000 + 25.9808i 0.500000 + 0.866025i
\(901\) 8.00000 13.8564i 0.266519 0.461624i
\(902\) 45.0000 1.49834
\(903\) 0 0
\(904\) −1.00000 −0.0332595
\(905\) 0 0
\(906\) 18.0000 + 31.1769i 0.598010 + 1.03578i
\(907\) −7.00000 12.1244i −0.232431 0.402583i 0.726092 0.687598i \(-0.241335\pi\)
−0.958523 + 0.285015i \(0.908001\pi\)
\(908\) −6.00000 + 10.3923i −0.199117 + 0.344881i
\(909\) −90.0000 −2.98511
\(910\) 0 0
\(911\) 28.0000 0.927681 0.463841 0.885919i \(-0.346471\pi\)
0.463841 + 0.885919i \(0.346471\pi\)
\(912\) −3.00000 + 5.19615i −0.0993399 + 0.172062i
\(913\) −10.0000 17.3205i −0.330952 0.573225i
\(914\) −5.00000 8.66025i −0.165385 0.286456i
\(915\) 0 0
\(916\) −16.0000 −0.528655
\(917\) 0 0
\(918\) 36.0000 1.18818
\(919\) −15.5000 + 26.8468i −0.511298 + 0.885594i 0.488616 + 0.872499i \(0.337502\pi\)
−0.999914 + 0.0130951i \(0.995832\pi\)
\(920\) 0 0
\(921\) −48.0000 83.1384i −1.58165 2.73950i
\(922\) −6.00000 + 10.3923i −0.197599 + 0.342252i
\(923\) 0 0
\(924\) 0 0
\(925\) −35.0000 −1.15079
\(926\) 6.00000 10.3923i 0.197172 0.341512i
\(927\) 18.0000 + 31.1769i 0.591198 + 1.02398i
\(928\) 2.00000 + 3.46410i 0.0656532 + 0.113715i
\(929\) −14.5000 + 25.1147i −0.475730 + 0.823988i −0.999613 0.0278019i \(-0.991149\pi\)
0.523884 + 0.851790i \(0.324483\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) −21.0000 −0.687878
\(933\) −39.0000 + 67.5500i −1.27680 + 2.21149i
\(934\) 18.0000 + 31.1769i 0.588978 + 1.02014i
\(935\) 0 0
\(936\) 3.00000 5.19615i 0.0980581 0.169842i
\(937\) 8.00000 0.261349 0.130674 0.991425i \(-0.458286\pi\)
0.130674 + 0.991425i \(0.458286\pi\)
\(938\) 0 0
\(939\) −90.0000 −2.93704
\(940\) 0 0
\(941\) 3.00000 + 5.19615i 0.0977972 + 0.169390i 0.910773 0.412908i \(-0.135487\pi\)
−0.812975 + 0.582298i \(0.802154\pi\)
\(942\) 1.50000 + 2.59808i 0.0488726 + 0.0846499i
\(943\) −22.5000 + 38.9711i −0.732701 + 1.26908i
\(944\) 6.00000 0.195283
\(945\) 0 0
\(946\) −60.0000 −1.95077
\(947\) 8.00000 13.8564i 0.259965 0.450273i −0.706267 0.707945i \(-0.749622\pi\)
0.966232 + 0.257673i \(0.0829556\pi\)
\(948\) −25.5000 44.1673i −0.828201 1.43449i
\(949\) 3.50000 + 6.06218i 0.113615 + 0.196787i
\(950\) 5.00000 8.66025i 0.162221 0.280976i
\(951\) −33.0000 −1.07010
\(952\) 0 0
\(953\) 6.00000 0.194359 0.0971795 0.995267i \(-0.469018\pi\)
0.0971795 + 0.995267i \(0.469018\pi\)
\(954\) −12.0000 + 20.7846i −0.388514 + 0.672927i
\(955\) 0 0
\(956\) 3.00000 + 5.19615i 0.0970269 + 0.168056i
\(957\) −30.0000 + 51.9615i −0.969762 + 1.67968i
\(958\) −16.0000 −0.516937
\(959\) 0 0
\(960\) 0 0
\(961\) 15.0000 25.9808i 0.483871 0.838089i
\(962\) 3.50000 + 6.06218i 0.112845 + 0.195452i
\(963\) 24.0000 + 41.5692i 0.773389 + 1.33955i
\(964\) −15.0000 + 25.9808i −0.483117 + 0.836784i
\(965\) 0 0
\(966\) 0 0
\(967\) 2.00000 0.0643157 0.0321578 0.999483i \(-0.489762\pi\)
0.0321578 + 0.999483i \(0.489762\pi\)
\(968\) 7.00000 12.1244i 0.224989 0.389692i
\(969\) −12.0000 20.7846i −0.385496 0.667698i
\(970\) 0 0
\(971\) 4.50000 7.79423i 0.144412 0.250129i −0.784741 0.619823i \(-0.787204\pi\)
0.929153 + 0.369694i \(0.120538\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 26.0000 0.833094
\(975\) −7.50000 + 12.9904i −0.240192 + 0.416025i
\(976\) 6.50000 + 11.2583i 0.208060 + 0.360370i
\(977\) 13.0000 + 22.5167i 0.415907 + 0.720372i 0.995523 0.0945177i \(-0.0301309\pi\)
−0.579616 + 0.814890i \(0.696798\pi\)
\(978\) −6.00000 + 10.3923i −0.191859 + 0.332309i
\(979\) 70.0000 2.23721
\(980\) 0 0
\(981\) −108.000 −3.44817
\(982\) 14.0000 24.2487i 0.446758 0.773807i
\(983\) −28.0000 48.4974i −0.893061 1.54683i −0.836186 0.548446i \(-0.815220\pi\)
−0.0568755 0.998381i \(-0.518114\pi\)
\(984\) −13.5000 23.3827i −0.430364 0.745413i
\(985\) 0 0
\(986\) −16.0000 −0.509544
\(987\) 0 0
\(988\) −2.00000 −0.0636285
\(989\) 30.0000 51.9615i 0.953945 1.65228i
\(990\) 0 0
\(991\) −29.5000 51.0955i −0.937098 1.62310i −0.770849 0.637018i \(-0.780168\pi\)
−0.166250 0.986084i \(-0.553166\pi\)
\(992\) −0.500000 + 0.866025i −0.0158750 + 0.0274963i
\(993\) −9.00000 −0.285606
\(994\) 0 0
\(995\) 0 0
\(996\) −6.00000 + 10.3923i −0.190117 + 0.329293i
\(997\) 16.5000 + 28.5788i 0.522560 + 0.905101i 0.999655 + 0.0262493i \(0.00835636\pi\)
−0.477095 + 0.878852i \(0.658310\pi\)
\(998\) 0.500000 + 0.866025i 0.0158272 + 0.0274136i
\(999\) 31.5000 54.5596i 0.996616 1.72619i
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 1274.2.f.u.79.1 2
7.2 even 3 1274.2.a.a.1.1 1
7.3 odd 6 1274.2.f.m.1145.1 2
7.4 even 3 inner 1274.2.f.u.1145.1 2
7.5 odd 6 182.2.a.b.1.1 1
7.6 odd 2 1274.2.f.m.79.1 2
21.5 even 6 1638.2.a.q.1.1 1
28.19 even 6 1456.2.a.b.1.1 1
35.19 odd 6 4550.2.a.o.1.1 1
56.5 odd 6 5824.2.a.a.1.1 1
56.19 even 6 5824.2.a.be.1.1 1
91.5 even 12 2366.2.d.i.337.2 2
91.12 odd 6 2366.2.a.o.1.1 1
91.47 even 12 2366.2.d.i.337.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
182.2.a.b.1.1 1 7.5 odd 6
1274.2.a.a.1.1 1 7.2 even 3
1274.2.f.m.79.1 2 7.6 odd 2
1274.2.f.m.1145.1 2 7.3 odd 6
1274.2.f.u.79.1 2 1.1 even 1 trivial
1274.2.f.u.1145.1 2 7.4 even 3 inner
1456.2.a.b.1.1 1 28.19 even 6
1638.2.a.q.1.1 1 21.5 even 6
2366.2.a.o.1.1 1 91.12 odd 6
2366.2.d.i.337.1 2 91.47 even 12
2366.2.d.i.337.2 2 91.5 even 12
4550.2.a.o.1.1 1 35.19 odd 6
5824.2.a.a.1.1 1 56.5 odd 6
5824.2.a.be.1.1 1 56.19 even 6