Properties

Label 1350.2.q.h.1043.4
Level $1350$
Weight $2$
Character 1350.1043
Analytic conductor $10.780$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1350,2,Mod(143,1350)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1350, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([2, 9]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1350.143");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1350 = 2 \cdot 3^{3} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1350.q (of order \(12\), degree \(4\), 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: \(10.7798042729\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(4\) over \(\Q(\zeta_{12})\)
Coefficient field: 16.0.9349208943630483456.9
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 8 x^{15} + 48 x^{14} - 196 x^{13} + 642 x^{12} - 1668 x^{11} + 3580 x^{10} - 6328 x^{9} + 9297 x^{8} - 11276 x^{7} + 11224 x^{6} - 9024 x^{5} + 5736 x^{4} - 2780 x^{3} + \cdots + 25 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 90)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 1043.4
Root \(0.500000 - 2.74530i\) of defining polynomial
Character \(\chi\) \(=\) 1350.1043
Dual form 1350.2.q.h.1007.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.258819 - 0.965926i) q^{2} +(-0.866025 - 0.500000i) q^{4} +(2.56188 + 0.686453i) q^{7} +(-0.707107 + 0.707107i) q^{8} +O(q^{10})\) \(q+(0.258819 - 0.965926i) q^{2} +(-0.866025 - 0.500000i) q^{4} +(2.56188 + 0.686453i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-4.15512 + 2.39896i) q^{11} +(-0.581838 + 0.155903i) q^{13} +(1.32613 - 2.29692i) q^{14} +(0.500000 + 0.866025i) q^{16} +(4.40865 + 4.40865i) q^{17} +5.19145i q^{19} +(1.24179 + 4.63444i) q^{22} +(-0.681226 - 2.54237i) q^{23} +0.602363i q^{26} +(-1.87542 - 1.87542i) q^{28} +(0.920201 + 1.59383i) q^{29} +(-2.03888 + 3.53145i) q^{31} +(0.965926 - 0.258819i) q^{32} +(5.39948 - 3.11739i) q^{34} +(-0.632057 + 0.632057i) q^{37} +(5.01456 + 1.34365i) q^{38} +(5.58550 + 3.22479i) q^{41} +(0.644420 - 2.40501i) q^{43} +4.79792 q^{44} -2.63206 q^{46} +(-1.02538 + 3.82678i) q^{47} +(0.0298240 + 0.0172189i) q^{49} +(0.581838 + 0.155903i) q^{52} +(-1.31215 + 1.31215i) q^{53} +(-2.29692 + 1.32613i) q^{56} +(1.77769 - 0.476331i) q^{58} +(0.0645473 - 0.111799i) q^{59} +(6.27251 + 10.8643i) q^{61} +(2.88341 + 2.88341i) q^{62} -1.00000i q^{64} +(-2.85782 - 10.6655i) q^{67} +(-1.61368 - 6.02233i) q^{68} +10.4203i q^{71} +(-3.30021 - 3.30021i) q^{73} +(0.446932 + 0.774109i) q^{74} +(2.59573 - 4.49593i) q^{76} +(-12.2917 + 3.29355i) q^{77} +(3.62792 - 2.09458i) q^{79} +(4.56054 - 4.56054i) q^{82} +(11.1098 + 2.97686i) q^{83} +(-2.15627 - 1.24492i) q^{86} +(1.24179 - 4.63444i) q^{88} -2.04989 q^{89} -1.59762 q^{91} +(-0.681226 + 2.54237i) q^{92} +(3.43100 + 1.98089i) q^{94} +(16.7115 + 4.47782i) q^{97} +(0.0243512 - 0.0243512i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 8 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 8 q^{7} + 8 q^{16} - 8 q^{22} - 24 q^{23} + 16 q^{28} - 8 q^{31} + 24 q^{38} - 24 q^{41} - 32 q^{46} + 48 q^{47} - 24 q^{56} - 16 q^{58} - 24 q^{61} + 16 q^{67} - 24 q^{68} - 16 q^{73} + 16 q^{76} - 72 q^{77} + 16 q^{82} + 48 q^{83} + 48 q^{86} - 8 q^{88} - 24 q^{92} + 48 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1350\mathbb{Z}\right)^\times\).

\(n\) \(1001\) \(1027\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{3}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.258819 0.965926i 0.183013 0.683013i
\(3\) 0 0
\(4\) −0.866025 0.500000i −0.433013 0.250000i
\(5\) 0 0
\(6\) 0 0
\(7\) 2.56188 + 0.686453i 0.968299 + 0.259455i 0.708109 0.706103i \(-0.249548\pi\)
0.260189 + 0.965558i \(0.416215\pi\)
\(8\) −0.707107 + 0.707107i −0.250000 + 0.250000i
\(9\) 0 0
\(10\) 0 0
\(11\) −4.15512 + 2.39896i −1.25282 + 0.723314i −0.971668 0.236350i \(-0.924049\pi\)
−0.281149 + 0.959664i \(0.590715\pi\)
\(12\) 0 0
\(13\) −0.581838 + 0.155903i −0.161373 + 0.0432397i −0.338601 0.940930i \(-0.609954\pi\)
0.177228 + 0.984170i \(0.443287\pi\)
\(14\) 1.32613 2.29692i 0.354422 0.613877i
\(15\) 0 0
\(16\) 0.500000 + 0.866025i 0.125000 + 0.216506i
\(17\) 4.40865 + 4.40865i 1.06926 + 1.06926i 0.997416 + 0.0718393i \(0.0228869\pi\)
0.0718393 + 0.997416i \(0.477113\pi\)
\(18\) 0 0
\(19\) 5.19145i 1.19100i 0.803355 + 0.595501i \(0.203046\pi\)
−0.803355 + 0.595501i \(0.796954\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 1.24179 + 4.63444i 0.264751 + 0.988065i
\(23\) −0.681226 2.54237i −0.142046 0.530121i −0.999869 0.0161770i \(-0.994850\pi\)
0.857824 0.513944i \(-0.171816\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0.602363i 0.118133i
\(27\) 0 0
\(28\) −1.87542 1.87542i −0.354422 0.354422i
\(29\) 0.920201 + 1.59383i 0.170877 + 0.295968i 0.938727 0.344662i \(-0.112007\pi\)
−0.767850 + 0.640630i \(0.778673\pi\)
\(30\) 0 0
\(31\) −2.03888 + 3.53145i −0.366194 + 0.634266i −0.988967 0.148136i \(-0.952673\pi\)
0.622773 + 0.782402i \(0.286006\pi\)
\(32\) 0.965926 0.258819i 0.170753 0.0457532i
\(33\) 0 0
\(34\) 5.39948 3.11739i 0.926002 0.534628i
\(35\) 0 0
\(36\) 0 0
\(37\) −0.632057 + 0.632057i −0.103910 + 0.103910i −0.757150 0.653241i \(-0.773409\pi\)
0.653241 + 0.757150i \(0.273409\pi\)
\(38\) 5.01456 + 1.34365i 0.813469 + 0.217968i
\(39\) 0 0
\(40\) 0 0
\(41\) 5.58550 + 3.22479i 0.872309 + 0.503628i 0.868115 0.496363i \(-0.165332\pi\)
0.00419400 + 0.999991i \(0.498665\pi\)
\(42\) 0 0
\(43\) 0.644420 2.40501i 0.0982731 0.366760i −0.899222 0.437492i \(-0.855867\pi\)
0.997495 + 0.0707320i \(0.0225335\pi\)
\(44\) 4.79792 0.723314
\(45\) 0 0
\(46\) −2.63206 −0.388076
\(47\) −1.02538 + 3.82678i −0.149568 + 0.558194i 0.849942 + 0.526876i \(0.176637\pi\)
−0.999509 + 0.0313173i \(0.990030\pi\)
\(48\) 0 0
\(49\) 0.0298240 + 0.0172189i 0.00426058 + 0.00245984i
\(50\) 0 0
\(51\) 0 0
\(52\) 0.581838 + 0.155903i 0.0806865 + 0.0216199i
\(53\) −1.31215 + 1.31215i −0.180237 + 0.180237i −0.791459 0.611222i \(-0.790678\pi\)
0.611222 + 0.791459i \(0.290678\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) −2.29692 + 1.32613i −0.306938 + 0.177211i
\(57\) 0 0
\(58\) 1.77769 0.476331i 0.233422 0.0625453i
\(59\) 0.0645473 0.111799i 0.00840334 0.0145550i −0.861793 0.507260i \(-0.830658\pi\)
0.870196 + 0.492705i \(0.163992\pi\)
\(60\) 0 0
\(61\) 6.27251 + 10.8643i 0.803113 + 1.39103i 0.917558 + 0.397603i \(0.130158\pi\)
−0.114445 + 0.993430i \(0.536509\pi\)
\(62\) 2.88341 + 2.88341i 0.366194 + 0.366194i
\(63\) 0 0
\(64\) 1.00000i 0.125000i
\(65\) 0 0
\(66\) 0 0
\(67\) −2.85782 10.6655i −0.349138 1.30300i −0.887703 0.460416i \(-0.847700\pi\)
0.538566 0.842584i \(-0.318966\pi\)
\(68\) −1.61368 6.02233i −0.195687 0.730315i
\(69\) 0 0
\(70\) 0 0
\(71\) 10.4203i 1.23666i 0.785919 + 0.618329i \(0.212190\pi\)
−0.785919 + 0.618329i \(0.787810\pi\)
\(72\) 0 0
\(73\) −3.30021 3.30021i −0.386261 0.386261i 0.487091 0.873351i \(-0.338058\pi\)
−0.873351 + 0.487091i \(0.838058\pi\)
\(74\) 0.446932 + 0.774109i 0.0519548 + 0.0899883i
\(75\) 0 0
\(76\) 2.59573 4.49593i 0.297750 0.515719i
\(77\) −12.2917 + 3.29355i −1.40077 + 0.375335i
\(78\) 0 0
\(79\) 3.62792 2.09458i 0.408173 0.235659i −0.281832 0.959464i \(-0.590942\pi\)
0.690004 + 0.723805i \(0.257609\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 4.56054 4.56054i 0.503628 0.503628i
\(83\) 11.1098 + 2.97686i 1.21946 + 0.326753i 0.810466 0.585785i \(-0.199214\pi\)
0.408992 + 0.912538i \(0.365881\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −2.15627 1.24492i −0.232517 0.134243i
\(87\) 0 0
\(88\) 1.24179 4.63444i 0.132376 0.494033i
\(89\) −2.04989 −0.217288 −0.108644 0.994081i \(-0.534651\pi\)
−0.108644 + 0.994081i \(0.534651\pi\)
\(90\) 0 0
\(91\) −1.59762 −0.167476
\(92\) −0.681226 + 2.54237i −0.0710228 + 0.265061i
\(93\) 0 0
\(94\) 3.43100 + 1.98089i 0.353881 + 0.204313i
\(95\) 0 0
\(96\) 0 0
\(97\) 16.7115 + 4.47782i 1.69679 + 0.454654i 0.972128 0.234450i \(-0.0753290\pi\)
0.724663 + 0.689104i \(0.241996\pi\)
\(98\) 0.0243512 0.0243512i 0.00245984 0.00245984i
\(99\) 0 0
\(100\) 0 0
\(101\) 10.3594 5.98097i 1.03079 0.595129i 0.113582 0.993529i \(-0.463768\pi\)
0.917212 + 0.398399i \(0.130434\pi\)
\(102\) 0 0
\(103\) 10.4055 2.78816i 1.02529 0.274725i 0.293285 0.956025i \(-0.405252\pi\)
0.732004 + 0.681300i \(0.238585\pi\)
\(104\) 0.301182 0.521662i 0.0295333 0.0511532i
\(105\) 0 0
\(106\) 0.927828 + 1.60704i 0.0901186 + 0.156090i
\(107\) 4.35367 + 4.35367i 0.420885 + 0.420885i 0.885508 0.464623i \(-0.153810\pi\)
−0.464623 + 0.885508i \(0.653810\pi\)
\(108\) 0 0
\(109\) 15.4546i 1.48028i −0.672452 0.740141i \(-0.734759\pi\)
0.672452 0.740141i \(-0.265241\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0.686453 + 2.56188i 0.0648637 + 0.242075i
\(113\) 1.53568 + 5.73124i 0.144465 + 0.539150i 0.999779 + 0.0210396i \(0.00669762\pi\)
−0.855314 + 0.518110i \(0.826636\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 1.84040i 0.170877i
\(117\) 0 0
\(118\) −0.0912837 0.0912837i −0.00840334 0.00840334i
\(119\) 8.26810 + 14.3208i 0.757935 + 1.31278i
\(120\) 0 0
\(121\) 6.01003 10.4097i 0.546367 0.946335i
\(122\) 12.1176 3.24689i 1.09707 0.293960i
\(123\) 0 0
\(124\) 3.53145 2.03888i 0.317133 0.183097i
\(125\) 0 0
\(126\) 0 0
\(127\) −2.51837 + 2.51837i −0.223469 + 0.223469i −0.809957 0.586489i \(-0.800510\pi\)
0.586489 + 0.809957i \(0.300510\pi\)
\(128\) −0.965926 0.258819i −0.0853766 0.0228766i
\(129\) 0 0
\(130\) 0 0
\(131\) −11.3102 6.52997i −0.988181 0.570526i −0.0834508 0.996512i \(-0.526594\pi\)
−0.904730 + 0.425985i \(0.859927\pi\)
\(132\) 0 0
\(133\) −3.56369 + 13.2999i −0.309011 + 1.15325i
\(134\) −11.0417 −0.953862
\(135\) 0 0
\(136\) −6.23478 −0.534628
\(137\) 0.840942 3.13844i 0.0718465 0.268135i −0.920653 0.390381i \(-0.872343\pi\)
0.992500 + 0.122246i \(0.0390098\pi\)
\(138\) 0 0
\(139\) −19.0478 10.9973i −1.61561 0.932775i −0.988036 0.154221i \(-0.950713\pi\)
−0.627578 0.778554i \(-0.715953\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 10.0652 + 2.69696i 0.844653 + 0.226324i
\(143\) 2.04360 2.04360i 0.170895 0.170895i
\(144\) 0 0
\(145\) 0 0
\(146\) −4.04192 + 2.33360i −0.334512 + 0.193130i
\(147\) 0 0
\(148\) 0.863406 0.231349i 0.0709715 0.0190168i
\(149\) −6.56668 + 11.3738i −0.537964 + 0.931780i 0.461050 + 0.887374i \(0.347473\pi\)
−0.999014 + 0.0444061i \(0.985860\pi\)
\(150\) 0 0
\(151\) −0.167899 0.290810i −0.0136634 0.0236658i 0.859113 0.511786i \(-0.171016\pi\)
−0.872776 + 0.488120i \(0.837683\pi\)
\(152\) −3.67091 3.67091i −0.297750 0.297750i
\(153\) 0 0
\(154\) 12.7253i 1.02543i
\(155\) 0 0
\(156\) 0 0
\(157\) 1.17992 + 4.40352i 0.0941678 + 0.351439i 0.996892 0.0787808i \(-0.0251027\pi\)
−0.902724 + 0.430220i \(0.858436\pi\)
\(158\) −1.08423 4.04642i −0.0862571 0.321916i
\(159\) 0 0
\(160\) 0 0
\(161\) 6.98088i 0.550170i
\(162\) 0 0
\(163\) −9.01496 9.01496i −0.706106 0.706106i 0.259608 0.965714i \(-0.416407\pi\)
−0.965714 + 0.259608i \(0.916407\pi\)
\(164\) −3.22479 5.58550i −0.251814 0.436154i
\(165\) 0 0
\(166\) 5.75085 9.96076i 0.446353 0.773105i
\(167\) −0.00858342 + 0.00229992i −0.000664205 + 0.000177973i −0.259151 0.965837i \(-0.583443\pi\)
0.258487 + 0.966015i \(0.416776\pi\)
\(168\) 0 0
\(169\) −10.9441 + 6.31858i −0.841854 + 0.486045i
\(170\) 0 0
\(171\) 0 0
\(172\) −1.76059 + 1.76059i −0.134243 + 0.134243i
\(173\) −10.0291 2.68729i −0.762500 0.204311i −0.143444 0.989658i \(-0.545818\pi\)
−0.619056 + 0.785347i \(0.712484\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −4.15512 2.39896i −0.313204 0.180829i
\(177\) 0 0
\(178\) −0.530550 + 1.98004i −0.0397664 + 0.148410i
\(179\) −1.46292 −0.109343 −0.0546717 0.998504i \(-0.517411\pi\)
−0.0546717 + 0.998504i \(0.517411\pi\)
\(180\) 0 0
\(181\) −8.68576 −0.645607 −0.322804 0.946466i \(-0.604625\pi\)
−0.322804 + 0.946466i \(0.604625\pi\)
\(182\) −0.413494 + 1.54318i −0.0306502 + 0.114388i
\(183\) 0 0
\(184\) 2.27943 + 1.31603i 0.168042 + 0.0970189i
\(185\) 0 0
\(186\) 0 0
\(187\) −28.8947 7.74231i −2.11299 0.566174i
\(188\) 2.80140 2.80140i 0.204313 0.204313i
\(189\) 0 0
\(190\) 0 0
\(191\) 4.33795 2.50452i 0.313883 0.181220i −0.334780 0.942296i \(-0.608662\pi\)
0.648663 + 0.761076i \(0.275329\pi\)
\(192\) 0 0
\(193\) 3.25355 0.871785i 0.234195 0.0627524i −0.139812 0.990178i \(-0.544650\pi\)
0.374008 + 0.927426i \(0.377983\pi\)
\(194\) 8.65048 14.9831i 0.621069 1.07572i
\(195\) 0 0
\(196\) −0.0172189 0.0298240i −0.00122992 0.00213029i
\(197\) −15.5027 15.5027i −1.10452 1.10452i −0.993858 0.110665i \(-0.964702\pi\)
−0.110665 0.993858i \(-0.535298\pi\)
\(198\) 0 0
\(199\) 18.4607i 1.30864i 0.756217 + 0.654321i \(0.227045\pi\)
−0.756217 + 0.654321i \(0.772955\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) −3.09598 11.5544i −0.217832 0.812962i
\(203\) 1.26335 + 4.71488i 0.0886697 + 0.330920i
\(204\) 0 0
\(205\) 0 0
\(206\) 10.7726i 0.750564i
\(207\) 0 0
\(208\) −0.425935 0.425935i −0.0295333 0.0295333i
\(209\) −12.4541 21.5711i −0.861468 1.49211i
\(210\) 0 0
\(211\) 0.654465 1.13357i 0.0450552 0.0780380i −0.842618 0.538511i \(-0.818987\pi\)
0.887674 + 0.460473i \(0.152320\pi\)
\(212\) 1.79243 0.480279i 0.123104 0.0329857i
\(213\) 0 0
\(214\) 5.33213 3.07851i 0.364497 0.210442i
\(215\) 0 0
\(216\) 0 0
\(217\) −7.64754 + 7.64754i −0.519149 + 0.519149i
\(218\) −14.9280 3.99994i −1.01105 0.270910i
\(219\) 0 0
\(220\) 0 0
\(221\) −3.25245 1.87780i −0.218783 0.126315i
\(222\) 0 0
\(223\) −5.42903 + 20.2614i −0.363555 + 1.35681i 0.505814 + 0.862643i \(0.331192\pi\)
−0.869369 + 0.494163i \(0.835474\pi\)
\(224\) 2.65225 0.177211
\(225\) 0 0
\(226\) 5.93342 0.394685
\(227\) 1.54126 5.75206i 0.102297 0.381778i −0.895727 0.444604i \(-0.853345\pi\)
0.998025 + 0.0628257i \(0.0200112\pi\)
\(228\) 0 0
\(229\) 10.1822 + 5.87872i 0.672862 + 0.388477i 0.797160 0.603768i \(-0.206335\pi\)
−0.124298 + 0.992245i \(0.539668\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −1.77769 0.476331i −0.116711 0.0312727i
\(233\) 13.4322 13.4322i 0.879973 0.879973i −0.113558 0.993531i \(-0.536225\pi\)
0.993531 + 0.113558i \(0.0362249\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) −0.111799 + 0.0645473i −0.00727751 + 0.00420167i
\(237\) 0 0
\(238\) 15.9727 4.27988i 1.03536 0.277424i
\(239\) 2.27943 3.94809i 0.147444 0.255380i −0.782838 0.622225i \(-0.786229\pi\)
0.930282 + 0.366845i \(0.119562\pi\)
\(240\) 0 0
\(241\) 8.03104 + 13.9102i 0.517325 + 0.896032i 0.999798 + 0.0201215i \(0.00640532\pi\)
−0.482473 + 0.875911i \(0.660261\pi\)
\(242\) −8.49947 8.49947i −0.546367 0.546367i
\(243\) 0 0
\(244\) 12.5450i 0.803113i
\(245\) 0 0
\(246\) 0 0
\(247\) −0.809364 3.02059i −0.0514986 0.192195i
\(248\) −1.05540 3.93882i −0.0670181 0.250115i
\(249\) 0 0
\(250\) 0 0
\(251\) 18.9981i 1.19915i 0.800319 + 0.599574i \(0.204663\pi\)
−0.800319 + 0.599574i \(0.795337\pi\)
\(252\) 0 0
\(253\) 8.92963 + 8.92963i 0.561401 + 0.561401i
\(254\) 1.78075 + 3.08436i 0.111734 + 0.193530i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 3.23709 0.867374i 0.201924 0.0541053i −0.156439 0.987688i \(-0.550002\pi\)
0.358363 + 0.933582i \(0.383335\pi\)
\(258\) 0 0
\(259\) −2.05313 + 1.18538i −0.127575 + 0.0736557i
\(260\) 0 0
\(261\) 0 0
\(262\) −9.23478 + 9.23478i −0.570526 + 0.570526i
\(263\) −16.1748 4.33402i −0.997380 0.267247i −0.277032 0.960861i \(-0.589351\pi\)
−0.720347 + 0.693614i \(0.756018\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 11.9243 + 6.88452i 0.731128 + 0.422117i
\(267\) 0 0
\(268\) −2.85782 + 10.6655i −0.174569 + 0.651500i
\(269\) −0.535741 −0.0326647 −0.0163324 0.999867i \(-0.505199\pi\)
−0.0163324 + 0.999867i \(0.505199\pi\)
\(270\) 0 0
\(271\) −15.5412 −0.944063 −0.472032 0.881582i \(-0.656479\pi\)
−0.472032 + 0.881582i \(0.656479\pi\)
\(272\) −1.61368 + 6.02233i −0.0978437 + 0.365158i
\(273\) 0 0
\(274\) −2.81385 1.62458i −0.169991 0.0981442i
\(275\) 0 0
\(276\) 0 0
\(277\) −16.7200 4.48011i −1.00461 0.269184i −0.281232 0.959640i \(-0.590743\pi\)
−0.723374 + 0.690456i \(0.757410\pi\)
\(278\) −15.5525 + 15.5525i −0.932775 + 0.932775i
\(279\) 0 0
\(280\) 0 0
\(281\) 20.8909 12.0613i 1.24624 0.719519i 0.275886 0.961190i \(-0.411029\pi\)
0.970358 + 0.241671i \(0.0776955\pi\)
\(282\) 0 0
\(283\) −15.9876 + 4.28387i −0.950365 + 0.254649i −0.700517 0.713636i \(-0.747047\pi\)
−0.249848 + 0.968285i \(0.580381\pi\)
\(284\) 5.21013 9.02421i 0.309164 0.535489i
\(285\) 0 0
\(286\) −1.44505 2.50289i −0.0854474 0.147999i
\(287\) 12.0957 + 12.0957i 0.713987 + 0.713987i
\(288\) 0 0
\(289\) 21.8725i 1.28661i
\(290\) 0 0
\(291\) 0 0
\(292\) 1.20796 + 4.50818i 0.0706906 + 0.263821i
\(293\) 4.18032 + 15.6012i 0.244217 + 0.911431i 0.973775 + 0.227512i \(0.0730591\pi\)
−0.729558 + 0.683919i \(0.760274\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0.893864i 0.0519548i
\(297\) 0 0
\(298\) 9.28669 + 9.28669i 0.537964 + 0.537964i
\(299\) 0.792727 + 1.37304i 0.0458446 + 0.0794052i
\(300\) 0 0
\(301\) 3.30185 5.71897i 0.190315 0.329636i
\(302\) −0.324356 + 0.0869109i −0.0186646 + 0.00500116i
\(303\) 0 0
\(304\) −4.49593 + 2.59573i −0.257859 + 0.148875i
\(305\) 0 0
\(306\) 0 0
\(307\) 1.45642 1.45642i 0.0831222 0.0831222i −0.664323 0.747445i \(-0.731280\pi\)
0.747445 + 0.664323i \(0.231280\pi\)
\(308\) 12.2917 + 3.29355i 0.700384 + 0.187667i
\(309\) 0 0
\(310\) 0 0
\(311\) 1.81462 + 1.04767i 0.102898 + 0.0594081i 0.550566 0.834792i \(-0.314412\pi\)
−0.447668 + 0.894200i \(0.647745\pi\)
\(312\) 0 0
\(313\) 5.11217 19.0789i 0.288957 1.07840i −0.656942 0.753941i \(-0.728150\pi\)
0.945899 0.324461i \(-0.105183\pi\)
\(314\) 4.55886 0.257271
\(315\) 0 0
\(316\) −4.18916 −0.235659
\(317\) 8.82217 32.9248i 0.495503 1.84924i −0.0316937 0.999498i \(-0.510090\pi\)
0.527196 0.849743i \(-0.323243\pi\)
\(318\) 0 0
\(319\) −7.64709 4.41505i −0.428155 0.247195i
\(320\) 0 0
\(321\) 0 0
\(322\) −6.74301 1.80678i −0.375773 0.100688i
\(323\) −22.8873 + 22.8873i −1.27348 + 1.27348i
\(324\) 0 0
\(325\) 0 0
\(326\) −11.0410 + 6.37454i −0.611506 + 0.353053i
\(327\) 0 0
\(328\) −6.22982 + 1.66927i −0.343984 + 0.0921703i
\(329\) −5.25381 + 9.09987i −0.289652 + 0.501692i
\(330\) 0 0
\(331\) −12.0140 20.8088i −0.660348 1.14376i −0.980524 0.196399i \(-0.937075\pi\)
0.320176 0.947358i \(-0.396258\pi\)
\(332\) −8.13293 8.13293i −0.446353 0.446353i
\(333\) 0 0
\(334\) 0.00888621i 0.000486232i
\(335\) 0 0
\(336\) 0 0
\(337\) −3.17090 11.8340i −0.172730 0.644637i −0.996927 0.0783338i \(-0.975040\pi\)
0.824197 0.566303i \(-0.191627\pi\)
\(338\) 3.27074 + 12.2066i 0.177905 + 0.663949i
\(339\) 0 0
\(340\) 0 0
\(341\) 19.5648i 1.05949i
\(342\) 0 0
\(343\) −13.0634 13.0634i −0.705357 0.705357i
\(344\) 1.24492 + 2.15627i 0.0671217 + 0.116258i
\(345\) 0 0
\(346\) −5.19145 + 8.99186i −0.279094 + 0.483405i
\(347\) −17.9559 + 4.81127i −0.963924 + 0.258283i −0.706260 0.707952i \(-0.749619\pi\)
−0.257663 + 0.966235i \(0.582953\pi\)
\(348\) 0 0
\(349\) 27.2305 15.7215i 1.45761 0.841553i 0.458720 0.888581i \(-0.348308\pi\)
0.998894 + 0.0470278i \(0.0149749\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −3.39264 + 3.39264i −0.180829 + 0.180829i
\(353\) 11.7440 + 3.14681i 0.625073 + 0.167488i 0.557433 0.830222i \(-0.311786\pi\)
0.0676398 + 0.997710i \(0.478453\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 1.77526 + 1.02494i 0.0940883 + 0.0543219i
\(357\) 0 0
\(358\) −0.378631 + 1.41307i −0.0200112 + 0.0746830i
\(359\) 4.31606 0.227793 0.113896 0.993493i \(-0.463667\pi\)
0.113896 + 0.993493i \(0.463667\pi\)
\(360\) 0 0
\(361\) −7.95119 −0.418484
\(362\) −2.24804 + 8.38980i −0.118154 + 0.440958i
\(363\) 0 0
\(364\) 1.38358 + 0.798810i 0.0725192 + 0.0418690i
\(365\) 0 0
\(366\) 0 0
\(367\) 19.2008 + 5.14485i 1.00228 + 0.268559i 0.722399 0.691477i \(-0.243040\pi\)
0.279877 + 0.960036i \(0.409706\pi\)
\(368\) 1.86115 1.86115i 0.0970189 0.0970189i
\(369\) 0 0
\(370\) 0 0
\(371\) −4.26229 + 2.46083i −0.221287 + 0.127760i
\(372\) 0 0
\(373\) −2.53800 + 0.680056i −0.131413 + 0.0352120i −0.323926 0.946082i \(-0.605003\pi\)
0.192513 + 0.981294i \(0.438336\pi\)
\(374\) −14.9570 + 25.9063i −0.773408 + 1.33958i
\(375\) 0 0
\(376\) −1.98089 3.43100i −0.102157 0.176940i
\(377\) −0.783892 0.783892i −0.0403725 0.0403725i
\(378\) 0 0
\(379\) 3.03124i 0.155705i 0.996965 + 0.0778523i \(0.0248063\pi\)
−0.996965 + 0.0778523i \(0.975194\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) −1.29643 4.83835i −0.0663313 0.247552i
\(383\) −6.14717 22.9416i −0.314106 1.17226i −0.924819 0.380407i \(-0.875784\pi\)
0.610713 0.791852i \(-0.290883\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 3.36832i 0.171443i
\(387\) 0 0
\(388\) −12.2336 12.2336i −0.621069 0.621069i
\(389\) −3.33254 5.77213i −0.168966 0.292659i 0.769090 0.639140i \(-0.220710\pi\)
−0.938057 + 0.346482i \(0.887376\pi\)
\(390\) 0 0
\(391\) 8.20515 14.2117i 0.414952 0.718718i
\(392\) −0.0332644 + 0.00891317i −0.00168011 + 0.000450183i
\(393\) 0 0
\(394\) −18.9869 + 10.9621i −0.956545 + 0.552261i
\(395\) 0 0
\(396\) 0 0
\(397\) 13.2242 13.2242i 0.663703 0.663703i −0.292548 0.956251i \(-0.594503\pi\)
0.956251 + 0.292548i \(0.0945031\pi\)
\(398\) 17.8316 + 4.77797i 0.893819 + 0.239498i
\(399\) 0 0
\(400\) 0 0
\(401\) −4.66934 2.69585i −0.233176 0.134624i 0.378860 0.925454i \(-0.376316\pi\)
−0.612036 + 0.790830i \(0.709649\pi\)
\(402\) 0 0
\(403\) 0.635736 2.37260i 0.0316683 0.118188i
\(404\) −11.9619 −0.595129
\(405\) 0 0
\(406\) 4.88121 0.242250
\(407\) 1.10999 4.14256i 0.0550204 0.205339i
\(408\) 0 0
\(409\) −7.43574 4.29303i −0.367674 0.212277i 0.304768 0.952427i \(-0.401421\pi\)
−0.672442 + 0.740150i \(0.734754\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) −10.4055 2.78816i −0.512644 0.137363i
\(413\) 0.242107 0.242107i 0.0119133 0.0119133i
\(414\) 0 0
\(415\) 0 0
\(416\) −0.521662 + 0.301182i −0.0255766 + 0.0147666i
\(417\) 0 0
\(418\) −24.0595 + 6.44672i −1.17679 + 0.315319i
\(419\) −7.72749 + 13.3844i −0.377512 + 0.653871i −0.990700 0.136067i \(-0.956554\pi\)
0.613187 + 0.789938i \(0.289887\pi\)
\(420\) 0 0
\(421\) 9.45129 + 16.3701i 0.460628 + 0.797831i 0.998992 0.0448812i \(-0.0142909\pi\)
−0.538364 + 0.842712i \(0.680958\pi\)
\(422\) −0.925553 0.925553i −0.0450552 0.0450552i
\(423\) 0 0
\(424\) 1.85566i 0.0901186i
\(425\) 0 0
\(426\) 0 0
\(427\) 8.61157 + 32.1388i 0.416743 + 1.55531i
\(428\) −1.59355 5.94722i −0.0770273 0.287470i
\(429\) 0 0
\(430\) 0 0
\(431\) 3.91428i 0.188544i −0.995546 0.0942720i \(-0.969948\pi\)
0.995546 0.0942720i \(-0.0300523\pi\)
\(432\) 0 0
\(433\) 27.2049 + 27.2049i 1.30738 + 1.30738i 0.923297 + 0.384086i \(0.125483\pi\)
0.384086 + 0.923297i \(0.374517\pi\)
\(434\) 5.40762 + 9.36628i 0.259574 + 0.449596i
\(435\) 0 0
\(436\) −7.72730 + 13.3841i −0.370070 + 0.640981i
\(437\) 13.1986 3.53656i 0.631375 0.169176i
\(438\) 0 0
\(439\) −13.2725 + 7.66286i −0.633460 + 0.365728i −0.782091 0.623164i \(-0.785847\pi\)
0.148631 + 0.988893i \(0.452513\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) −2.65561 + 2.65561i −0.126315 + 0.126315i
\(443\) −26.8719 7.20031i −1.27672 0.342097i −0.444120 0.895967i \(-0.646484\pi\)
−0.832603 + 0.553870i \(0.813150\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 18.1659 + 10.4881i 0.860180 + 0.496625i
\(447\) 0 0
\(448\) 0.686453 2.56188i 0.0324319 0.121037i
\(449\) 24.3627 1.14975 0.574874 0.818242i \(-0.305051\pi\)
0.574874 + 0.818242i \(0.305051\pi\)
\(450\) 0 0
\(451\) −30.9446 −1.45712
\(452\) 1.53568 5.73124i 0.0722324 0.269575i
\(453\) 0 0
\(454\) −5.15716 2.97749i −0.242037 0.139740i
\(455\) 0 0
\(456\) 0 0
\(457\) 12.6705 + 3.39506i 0.592702 + 0.158814i 0.542688 0.839935i \(-0.317407\pi\)
0.0500141 + 0.998749i \(0.484073\pi\)
\(458\) 8.31377 8.31377i 0.388477 0.388477i
\(459\) 0 0
\(460\) 0 0
\(461\) −34.7684 + 20.0736i −1.61933 + 0.934919i −0.632233 + 0.774778i \(0.717861\pi\)
−0.987094 + 0.160141i \(0.948805\pi\)
\(462\) 0 0
\(463\) 11.5688 3.09986i 0.537649 0.144063i 0.0202307 0.999795i \(-0.493560\pi\)
0.517418 + 0.855733i \(0.326893\pi\)
\(464\) −0.920201 + 1.59383i −0.0427192 + 0.0739919i
\(465\) 0 0
\(466\) −9.49800 16.4510i −0.439986 0.762079i
\(467\) 8.63124 + 8.63124i 0.399406 + 0.399406i 0.878024 0.478617i \(-0.158862\pi\)
−0.478617 + 0.878024i \(0.658862\pi\)
\(468\) 0 0
\(469\) 29.2855i 1.35228i
\(470\) 0 0
\(471\) 0 0
\(472\) 0.0334121 + 0.124696i 0.00153792 + 0.00573959i
\(473\) 3.09188 + 11.5390i 0.142165 + 0.530565i
\(474\) 0 0
\(475\) 0 0
\(476\) 16.5362i 0.757935i
\(477\) 0 0
\(478\) −3.22360 3.22360i −0.147444 0.147444i
\(479\) −5.13488 8.89388i −0.234619 0.406372i 0.724543 0.689230i \(-0.242051\pi\)
−0.959162 + 0.282858i \(0.908718\pi\)
\(480\) 0 0
\(481\) 0.269215 0.466295i 0.0122752 0.0212612i
\(482\) 15.5148 4.15717i 0.706678 0.189354i
\(483\) 0 0
\(484\) −10.4097 + 6.01003i −0.473167 + 0.273183i
\(485\) 0 0
\(486\) 0 0
\(487\) −17.5218 + 17.5218i −0.793987 + 0.793987i −0.982140 0.188153i \(-0.939750\pi\)
0.188153 + 0.982140i \(0.439750\pi\)
\(488\) −12.1176 3.24689i −0.548536 0.146980i
\(489\) 0 0
\(490\) 0 0
\(491\) 7.70100 + 4.44617i 0.347541 + 0.200653i 0.663602 0.748086i \(-0.269027\pi\)
−0.316061 + 0.948739i \(0.602360\pi\)
\(492\) 0 0
\(493\) −2.96982 + 11.0835i −0.133754 + 0.499176i
\(494\) −3.12714 −0.140697
\(495\) 0 0
\(496\) −4.07776 −0.183097
\(497\) −7.15302 + 26.6954i −0.320857 + 1.19745i
\(498\) 0 0
\(499\) 25.4186 + 14.6754i 1.13789 + 0.656963i 0.945908 0.324435i \(-0.105174\pi\)
0.191985 + 0.981398i \(0.438507\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 18.3507 + 4.91707i 0.819034 + 0.219459i
\(503\) 10.0766 10.0766i 0.449293 0.449293i −0.445826 0.895120i \(-0.647090\pi\)
0.895120 + 0.445826i \(0.147090\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 10.9365 6.31420i 0.486188 0.280701i
\(507\) 0 0
\(508\) 3.44015 0.921786i 0.152632 0.0408976i
\(509\) 15.0024 25.9849i 0.664970 1.15176i −0.314323 0.949316i \(-0.601777\pi\)
0.979293 0.202446i \(-0.0648892\pi\)
\(510\) 0 0
\(511\) −6.18930 10.7202i −0.273799 0.474233i
\(512\) 0.707107 + 0.707107i 0.0312500 + 0.0312500i
\(513\) 0 0
\(514\) 3.35128i 0.147819i
\(515\) 0 0
\(516\) 0 0
\(517\) −4.91971 18.3606i −0.216369 0.807499i
\(518\) 0.613596 + 2.28997i 0.0269598 + 0.100615i
\(519\) 0 0
\(520\) 0 0
\(521\) 6.40485i 0.280602i −0.990109 0.140301i \(-0.955193\pi\)
0.990109 0.140301i \(-0.0448070\pi\)
\(522\) 0 0
\(523\) −16.0596 16.0596i −0.702237 0.702237i 0.262653 0.964890i \(-0.415403\pi\)
−0.964890 + 0.262653i \(0.915403\pi\)
\(524\) 6.52997 + 11.3102i 0.285263 + 0.494090i
\(525\) 0 0
\(526\) −8.37268 + 14.5019i −0.365066 + 0.632313i
\(527\) −24.5576 + 6.58020i −1.06975 + 0.286638i
\(528\) 0 0
\(529\) 13.9190 8.03614i 0.605174 0.349397i
\(530\) 0 0
\(531\) 0 0
\(532\) 9.73618 9.73618i 0.422117 0.422117i
\(533\) −3.75261 1.00551i −0.162544 0.0435535i
\(534\) 0 0
\(535\) 0 0
\(536\) 9.56244 + 5.52087i 0.413034 + 0.238465i
\(537\) 0 0
\(538\) −0.138660 + 0.517486i −0.00597806 + 0.0223104i
\(539\) −0.165230 −0.00711696
\(540\) 0 0
\(541\) 44.6389 1.91917 0.959587 0.281412i \(-0.0908026\pi\)
0.959587 + 0.281412i \(0.0908026\pi\)
\(542\) −4.02237 + 15.0117i −0.172776 + 0.644807i
\(543\) 0 0
\(544\) 5.39948 + 3.11739i 0.231501 + 0.133657i
\(545\) 0 0
\(546\) 0 0
\(547\) −5.15053 1.38008i −0.220221 0.0590080i 0.147022 0.989133i \(-0.453031\pi\)
−0.367242 + 0.930125i \(0.619698\pi\)
\(548\) −2.29750 + 2.29750i −0.0981442 + 0.0981442i
\(549\) 0 0
\(550\) 0 0
\(551\) −8.27432 + 4.77718i −0.352498 + 0.203515i
\(552\) 0 0
\(553\) 10.7321 2.87566i 0.456376 0.122286i
\(554\) −8.65490 + 14.9907i −0.367712 + 0.636895i
\(555\) 0 0
\(556\) 10.9973 + 19.0478i 0.466388 + 0.807807i
\(557\) 4.10329 + 4.10329i 0.173862 + 0.173862i 0.788674 0.614812i \(-0.210768\pi\)
−0.614812 + 0.788674i \(0.710768\pi\)
\(558\) 0 0
\(559\) 1.49979i 0.0634344i
\(560\) 0 0
\(561\) 0 0
\(562\) −6.24341 23.3007i −0.263362 0.982882i
\(563\) 1.53547 + 5.73047i 0.0647125 + 0.241510i 0.990704 0.136033i \(-0.0434354\pi\)
−0.925992 + 0.377544i \(0.876769\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 16.5516i 0.695715i
\(567\) 0 0
\(568\) −7.36824 7.36824i −0.309164 0.309164i
\(569\) −17.6714 30.6077i −0.740822 1.28314i −0.952122 0.305720i \(-0.901103\pi\)
0.211300 0.977421i \(-0.432230\pi\)
\(570\) 0 0
\(571\) 1.50529 2.60725i 0.0629946 0.109110i −0.832808 0.553562i \(-0.813268\pi\)
0.895803 + 0.444452i \(0.146602\pi\)
\(572\) −2.79162 + 0.748011i −0.116723 + 0.0312759i
\(573\) 0 0
\(574\) 14.8142 8.55296i 0.618331 0.356993i
\(575\) 0 0
\(576\) 0 0
\(577\) 11.5350 11.5350i 0.480208 0.480208i −0.424990 0.905198i \(-0.639722\pi\)
0.905198 + 0.424990i \(0.139722\pi\)
\(578\) 21.1272 + 5.66101i 0.878774 + 0.235467i
\(579\) 0 0
\(580\) 0 0
\(581\) 26.4185 + 15.2527i 1.09602 + 0.632789i
\(582\) 0 0
\(583\) 2.30434 8.59992i 0.0954361 0.356172i
\(584\) 4.66721 0.193130
\(585\) 0 0
\(586\) 16.1515 0.667214
\(587\) −2.95165 + 11.0157i −0.121828 + 0.454666i −0.999707 0.0242156i \(-0.992291\pi\)
0.877879 + 0.478882i \(0.158958\pi\)
\(588\) 0 0
\(589\) −18.3333 10.5848i −0.755412 0.436137i
\(590\) 0 0
\(591\) 0 0
\(592\) −0.863406 0.231349i −0.0354858 0.00950838i
\(593\) 23.4664 23.4664i 0.963651 0.963651i −0.0357109 0.999362i \(-0.511370\pi\)
0.999362 + 0.0357109i \(0.0113696\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 11.3738 6.56668i 0.465890 0.268982i
\(597\) 0 0
\(598\) 1.53143 0.410346i 0.0626249 0.0167803i
\(599\) 17.2683 29.9097i 0.705566 1.22208i −0.260922 0.965360i \(-0.584026\pi\)
0.966487 0.256715i \(-0.0826403\pi\)
\(600\) 0 0
\(601\) −1.57759 2.73247i −0.0643513 0.111460i 0.832055 0.554694i \(-0.187164\pi\)
−0.896406 + 0.443234i \(0.853831\pi\)
\(602\) −4.66952 4.66952i −0.190315 0.190315i
\(603\) 0 0
\(604\) 0.335798i 0.0136634i
\(605\) 0 0
\(606\) 0 0
\(607\) −1.32070 4.92890i −0.0536054 0.200058i 0.933930 0.357456i \(-0.116356\pi\)
−0.987535 + 0.157399i \(0.949689\pi\)
\(608\) 1.34365 + 5.01456i 0.0544921 + 0.203367i
\(609\) 0 0
\(610\) 0 0
\(611\) 2.38643i 0.0965446i
\(612\) 0 0
\(613\) 9.09622 + 9.09622i 0.367393 + 0.367393i 0.866525 0.499133i \(-0.166348\pi\)
−0.499133 + 0.866525i \(0.666348\pi\)
\(614\) −1.02984 1.78374i −0.0415611 0.0719859i
\(615\) 0 0
\(616\) 6.36265 11.0204i 0.256358 0.444026i
\(617\) 23.2998 6.24315i 0.938013 0.251340i 0.242745 0.970090i \(-0.421952\pi\)
0.695268 + 0.718751i \(0.255286\pi\)
\(618\) 0 0
\(619\) 26.9280 15.5469i 1.08233 0.624883i 0.150806 0.988563i \(-0.451813\pi\)
0.931524 + 0.363680i \(0.118480\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 1.48163 1.48163i 0.0594081 0.0594081i
\(623\) −5.25156 1.40715i −0.210399 0.0563764i
\(624\) 0 0
\(625\) 0 0
\(626\) −17.1057 9.87595i −0.683679 0.394723i
\(627\) 0 0
\(628\) 1.17992 4.40352i 0.0470839 0.175719i
\(629\) −5.57304 −0.222212
\(630\) 0 0
\(631\) 46.1604 1.83762 0.918809 0.394703i \(-0.129153\pi\)
0.918809 + 0.394703i \(0.129153\pi\)
\(632\) −1.08423 + 4.04642i −0.0431285 + 0.160958i
\(633\) 0 0
\(634\) −29.5196 17.0431i −1.17237 0.676869i
\(635\) 0 0
\(636\) 0 0
\(637\) −0.0200372 0.00536896i −0.000793905 0.000212726i
\(638\) −6.24383 + 6.24383i −0.247195 + 0.247195i
\(639\) 0 0
\(640\) 0 0
\(641\) 3.41084 1.96925i 0.134720 0.0777808i −0.431125 0.902292i \(-0.641883\pi\)
0.565845 + 0.824511i \(0.308550\pi\)
\(642\) 0 0
\(643\) 29.9917 8.03625i 1.18276 0.316919i 0.386737 0.922190i \(-0.373602\pi\)
0.796019 + 0.605271i \(0.206935\pi\)
\(644\) −3.49044 + 6.04562i −0.137543 + 0.238231i
\(645\) 0 0
\(646\) 16.1838 + 28.0311i 0.636742 + 1.10287i
\(647\) −18.0986 18.0986i −0.711531 0.711531i 0.255325 0.966855i \(-0.417818\pi\)
−0.966855 + 0.255325i \(0.917818\pi\)
\(648\) 0 0
\(649\) 0.619386i 0.0243130i
\(650\) 0 0
\(651\) 0 0
\(652\) 3.29971 + 12.3147i 0.129226 + 0.482280i
\(653\) 3.63685 + 13.5729i 0.142321 + 0.531148i 0.999860 + 0.0167299i \(0.00532554\pi\)
−0.857539 + 0.514419i \(0.828008\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 6.44958i 0.251814i
\(657\) 0 0
\(658\) 7.43002 + 7.43002i 0.289652 + 0.289652i
\(659\) 18.2709 + 31.6462i 0.711734 + 1.23276i 0.964206 + 0.265155i \(0.0854233\pi\)
−0.252471 + 0.967604i \(0.581243\pi\)
\(660\) 0 0
\(661\) −17.9365 + 31.0670i −0.697650 + 1.20836i 0.271629 + 0.962402i \(0.412438\pi\)
−0.969279 + 0.245963i \(0.920896\pi\)
\(662\) −23.2092 + 6.21890i −0.902053 + 0.241704i
\(663\) 0 0
\(664\) −9.96076 + 5.75085i −0.386553 + 0.223176i
\(665\) 0 0
\(666\) 0 0
\(667\) 3.42525 3.42525i 0.132626 0.132626i
\(668\) 0.00858342 + 0.00229992i 0.000332102 + 8.89866e-5i
\(669\) 0 0
\(670\) 0 0
\(671\) −52.1261 30.0950i −2.01231 1.16181i
\(672\) 0 0
\(673\) 6.49200 24.2285i 0.250248 0.933939i −0.720424 0.693534i \(-0.756053\pi\)
0.970673 0.240406i \(-0.0772804\pi\)
\(674\) −12.2514 −0.471907
\(675\) 0 0
\(676\) 12.6372 0.486045
\(677\) 1.40152 5.23054i 0.0538647 0.201026i −0.933750 0.357927i \(-0.883484\pi\)
0.987614 + 0.156901i \(0.0501504\pi\)
\(678\) 0 0
\(679\) 39.7389 + 22.9433i 1.52504 + 0.880481i
\(680\) 0 0
\(681\) 0 0
\(682\) −18.8981 5.06374i −0.723647 0.193901i
\(683\) 14.3302 14.3302i 0.548331 0.548331i −0.377627 0.925958i \(-0.623260\pi\)
0.925958 + 0.377627i \(0.123260\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) −15.9993 + 9.23721i −0.610857 + 0.352678i
\(687\) 0 0
\(688\) 2.40501 0.644420i 0.0916900 0.0245683i
\(689\) 0.558889 0.968025i 0.0212920 0.0368788i
\(690\) 0 0
\(691\) −5.85991 10.1497i −0.222921 0.386111i 0.732772 0.680474i \(-0.238226\pi\)
−0.955694 + 0.294363i \(0.904893\pi\)
\(692\) 7.34182 + 7.34182i 0.279094 + 0.279094i
\(693\) 0 0
\(694\) 18.5893i 0.705641i
\(695\) 0 0
\(696\) 0 0
\(697\) 10.4076 + 38.8415i 0.394214 + 1.47123i
\(698\) −8.13805 30.3716i −0.308030 1.14958i
\(699\) 0 0
\(700\) 0 0
\(701\) 30.7235i 1.16041i 0.814471 + 0.580205i \(0.197028\pi\)
−0.814471 + 0.580205i \(0.802972\pi\)
\(702\) 0 0
\(703\) −3.28129 3.28129i −0.123756 0.123756i
\(704\) 2.39896 + 4.15512i 0.0904143 + 0.156602i
\(705\) 0 0
\(706\) 6.07917 10.5294i 0.228792 0.396280i
\(707\) 30.6451 8.21132i 1.15253 0.308818i
\(708\) 0 0
\(709\) −27.4879 + 15.8701i −1.03233 + 0.596015i −0.917651 0.397387i \(-0.869917\pi\)
−0.114678 + 0.993403i \(0.536584\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 1.44949 1.44949i 0.0543219 0.0543219i
\(713\) 10.3672 + 2.77788i 0.388254 + 0.104032i
\(714\) 0 0
\(715\) 0 0
\(716\) 1.26692 + 0.731458i 0.0473471 + 0.0273359i
\(717\) 0 0
\(718\) 1.11708 4.16899i 0.0416890 0.155585i
\(719\) 7.79879 0.290846 0.145423 0.989370i \(-0.453546\pi\)
0.145423 + 0.989370i \(0.453546\pi\)
\(720\) 0 0
\(721\) 28.5717 1.06407
\(722\) −2.05792 + 7.68026i −0.0765878 + 0.285830i
\(723\) 0 0
\(724\) 7.52209 + 4.34288i 0.279556 + 0.161402i
\(725\) 0 0
\(726\) 0 0
\(727\) 42.7863 + 11.4645i 1.58685 + 0.425196i 0.941039 0.338297i \(-0.109851\pi\)
0.645815 + 0.763494i \(0.276518\pi\)
\(728\) 1.12969 1.12969i 0.0418690 0.0418690i
\(729\) 0 0
\(730\) 0 0
\(731\) 13.4439 7.76182i 0.497239 0.287081i
\(732\) 0 0
\(733\) −26.9304 + 7.21598i −0.994697 + 0.266528i −0.719222 0.694780i \(-0.755502\pi\)
−0.275475 + 0.961308i \(0.588835\pi\)
\(734\) 9.93909 17.2150i 0.366858 0.635418i
\(735\) 0 0
\(736\) −1.31603 2.27943i −0.0485095 0.0840208i
\(737\) 37.4607 + 37.4607i 1.37988 + 1.37988i
\(738\) 0 0
\(739\) 10.8068i 0.397536i −0.980047 0.198768i \(-0.936306\pi\)
0.980047 0.198768i \(-0.0636941\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 1.27382 + 4.75396i 0.0467634 + 0.174523i
\(743\) −5.75762 21.4877i −0.211227 0.788309i −0.987461 0.157864i \(-0.949539\pi\)
0.776234 0.630445i \(-0.217127\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 2.62754i 0.0962009i
\(747\) 0 0
\(748\) 21.1524 + 21.1524i 0.773408 + 0.773408i
\(749\) 8.16498 + 14.1422i 0.298342 + 0.516743i
\(750\) 0 0
\(751\) −20.6235 + 35.7209i −0.752561 + 1.30347i 0.194017 + 0.980998i \(0.437848\pi\)
−0.946578 + 0.322476i \(0.895485\pi\)
\(752\) −3.82678 + 1.02538i −0.139548 + 0.0373919i
\(753\) 0 0
\(754\) −0.960067 + 0.554295i −0.0349636 + 0.0201862i
\(755\) 0 0
\(756\) 0 0
\(757\) 20.5246 20.5246i 0.745978 0.745978i −0.227743 0.973721i \(-0.573135\pi\)
0.973721 + 0.227743i \(0.0731346\pi\)
\(758\) 2.92796 + 0.784544i 0.106348 + 0.0284959i
\(759\) 0 0
\(760\) 0 0
\(761\) −39.8188 22.9894i −1.44343 0.833365i −0.445353 0.895355i \(-0.646922\pi\)
−0.998077 + 0.0619904i \(0.980255\pi\)
\(762\) 0 0
\(763\) 10.6089 39.5928i 0.384066 1.43335i
\(764\) −5.00903 −0.181220
\(765\) 0 0
\(766\) −23.7508 −0.858153
\(767\) −0.0201262 + 0.0751122i −0.000726717 + 0.00271214i
\(768\) 0 0
\(769\) 26.6702 + 15.3980i 0.961752 + 0.555268i 0.896712 0.442615i \(-0.145949\pi\)
0.0650399 + 0.997883i \(0.479283\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −3.25355 0.871785i −0.117098 0.0313762i
\(773\) 29.6376 29.6376i 1.06599 1.06599i 0.0683287 0.997663i \(-0.478233\pi\)
0.997663 0.0683287i \(-0.0217667\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) −14.9831 + 8.65048i −0.537861 + 0.310534i
\(777\) 0 0
\(778\) −6.43797 + 1.72505i −0.230813 + 0.0618460i
\(779\) −16.7414 + 28.9969i −0.599821 + 1.03892i
\(780\) 0 0
\(781\) −24.9978 43.2975i −0.894492 1.54931i
\(782\) −11.6038 11.6038i −0.414952 0.414952i
\(783\) 0 0
\(784\) 0.0344378i 0.00122992i
\(785\) 0 0
\(786\) 0 0
\(787\) 6.98316 + 26.0615i 0.248923 + 0.928993i 0.971371 + 0.237568i \(0.0763501\pi\)
−0.722448 + 0.691425i \(0.756983\pi\)
\(788\) 5.67439 + 21.1771i 0.202142 + 0.754403i
\(789\) 0 0
\(790\) 0 0
\(791\) 15.7369i 0.559540i
\(792\) 0 0
\(793\) −5.34337 5.34337i −0.189749 0.189749i
\(794\) −9.35091 16.1963i −0.331852 0.574784i
\(795\) 0 0
\(796\) 9.23033 15.9874i 0.327161 0.566659i
\(797\) 6.28188 1.68322i 0.222515 0.0596228i −0.145839 0.989308i \(-0.546588\pi\)
0.368354 + 0.929686i \(0.379921\pi\)
\(798\) 0 0
\(799\) −21.3915 + 12.3504i −0.756778 + 0.436926i
\(800\) 0 0
\(801\) 0 0
\(802\) −3.81250 + 3.81250i −0.134624 + 0.134624i
\(803\) 21.6299 + 5.79571i 0.763302 + 0.204526i
\(804\) 0 0
\(805\) 0 0
\(806\) −2.12721 1.22815i −0.0749279 0.0432596i
\(807\) 0 0
\(808\) −3.09598 + 11.5544i −0.108916 + 0.406481i
\(809\) 5.79431 0.203717 0.101859 0.994799i \(-0.467521\pi\)
0.101859 + 0.994799i \(0.467521\pi\)
\(810\) 0 0
\(811\) 1.90498 0.0668929 0.0334465 0.999441i \(-0.489352\pi\)
0.0334465 + 0.999441i \(0.489352\pi\)
\(812\) 1.26335 4.71488i 0.0443349 0.165460i
\(813\) 0 0
\(814\) −3.71411 2.14434i −0.130180 0.0751592i
\(815\) 0 0
\(816\) 0 0
\(817\) 12.4855 + 3.34547i 0.436812 + 0.117043i
\(818\) −6.07126 + 6.07126i −0.212277 + 0.212277i
\(819\) 0 0
\(820\) 0 0
\(821\) 33.4503 19.3125i 1.16742 0.674012i 0.214351 0.976757i \(-0.431236\pi\)
0.953072 + 0.302745i \(0.0979030\pi\)
\(822\) 0 0
\(823\) −20.6711 + 5.53879i −0.720548 + 0.193070i −0.600416 0.799688i \(-0.704998\pi\)
−0.120132 + 0.992758i \(0.538332\pi\)
\(824\) −5.38631 + 9.32936i −0.187641 + 0.325004i
\(825\) 0 0
\(826\) −0.171196 0.296520i −0.00595666 0.0103172i
\(827\) 23.1603 + 23.1603i 0.805364 + 0.805364i 0.983928 0.178564i \(-0.0571453\pi\)
−0.178564 + 0.983928i \(0.557145\pi\)
\(828\) 0 0
\(829\) 34.1116i 1.18475i −0.805664 0.592373i \(-0.798191\pi\)
0.805664 0.592373i \(-0.201809\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0.155903 + 0.581838i 0.00540497 + 0.0201716i
\(833\) 0.0555716 + 0.207396i 0.00192544 + 0.00718585i
\(834\) 0 0
\(835\) 0 0
\(836\) 24.9082i 0.861468i
\(837\) 0 0
\(838\) 10.9283 + 10.9283i 0.377512 + 0.377512i
\(839\) −18.8058 32.5726i −0.649249 1.12453i −0.983303 0.181978i \(-0.941750\pi\)
0.334054 0.942554i \(-0.391583\pi\)
\(840\) 0 0
\(841\) 12.8065 22.1814i 0.441602 0.764877i
\(842\) 18.2585 4.89235i 0.629229 0.168602i
\(843\) 0 0
\(844\) −1.13357 + 0.654465i −0.0390190 + 0.0225276i
\(845\) 0 0
\(846\) 0 0
\(847\) 22.5427 22.5427i 0.774577 0.774577i
\(848\) −1.79243 0.480279i −0.0615521 0.0164928i
\(849\) 0 0
\(850\) 0 0
\(851\) 2.03750 + 1.17635i 0.0698445 + 0.0403248i
\(852\) 0 0
\(853\) 1.98742 7.41714i 0.0680478 0.253958i −0.923519 0.383552i \(-0.874701\pi\)
0.991567 + 0.129594i \(0.0413674\pi\)
\(854\) 33.2726 1.13856
\(855\) 0 0
\(856\) −6.15702 −0.210442
\(857\) 1.87635 7.00264i 0.0640949 0.239206i −0.926445 0.376430i \(-0.877152\pi\)
0.990540 + 0.137224i \(0.0438182\pi\)
\(858\) 0 0
\(859\) −1.50446 0.868601i −0.0513316 0.0296363i 0.474115 0.880463i \(-0.342768\pi\)
−0.525446 + 0.850827i \(0.676102\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) −3.78090 1.01309i −0.128778 0.0345060i
\(863\) −36.4612 + 36.4612i −1.24115 + 1.24115i −0.281630 + 0.959523i \(0.590875\pi\)
−0.959523 + 0.281630i \(0.909125\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 33.3190 19.2368i 1.13223 0.653692i
\(867\) 0 0
\(868\) 10.4467 2.79919i 0.354585 0.0950108i
\(869\) −10.0496 + 17.4065i −0.340911 + 0.590474i
\(870\) 0 0
\(871\) 3.32557 + 5.76006i 0.112683 + 0.195172i
\(872\) 10.9280 + 10.9280i 0.370070 + 0.370070i
\(873\) 0 0
\(874\) 13.6642i 0.462199i
\(875\) 0 0
\(876\) 0 0
\(877\) −2.68194 10.0092i −0.0905628 0.337985i 0.905747 0.423820i \(-0.139311\pi\)
−0.996309 + 0.0858347i \(0.972644\pi\)
\(878\) 3.96659 + 14.8035i 0.133866 + 0.499594i
\(879\) 0 0
\(880\) 0 0
\(881\) 1.17719i 0.0396604i −0.999803 0.0198302i \(-0.993687\pi\)
0.999803 0.0198302i \(-0.00631257\pi\)
\(882\) 0 0
\(883\) 22.1929 + 22.1929i 0.746850 + 0.746850i 0.973886 0.227036i \(-0.0729035\pi\)
−0.227036 + 0.973886i \(0.572903\pi\)
\(884\) 1.87780 + 3.25245i 0.0631573 + 0.109392i
\(885\) 0 0
\(886\) −13.9099 + 24.0927i −0.467313 + 0.809410i
\(887\) 8.80492 2.35927i 0.295640 0.0792166i −0.107950 0.994156i \(-0.534429\pi\)
0.403590 + 0.914940i \(0.367762\pi\)
\(888\) 0 0
\(889\) −8.18049 + 4.72301i −0.274365 + 0.158405i
\(890\) 0 0
\(891\) 0 0
\(892\) 14.8324 14.8324i 0.496625 0.496625i
\(893\) −19.8666 5.32323i −0.664809 0.178135i
\(894\) 0 0
\(895\) 0 0
\(896\) −2.29692 1.32613i −0.0767346 0.0443028i
\(897\) 0 0
\(898\) 6.30553 23.5326i 0.210418 0.785292i
\(899\) −7.50472 −0.250296
\(900\) 0 0
\(901\) −11.5696 −0.385439
\(902\) −8.00905 + 29.8902i −0.266672 + 0.995234i
\(903\) 0 0
\(904\) −5.13849 2.96671i −0.170904 0.0986713i
\(905\) 0 0
\(906\) 0 0
\(907\) −7.35203 1.96997i −0.244120 0.0654118i 0.134684 0.990889i \(-0.456998\pi\)
−0.378804 + 0.925477i \(0.623665\pi\)
\(908\) −4.21080 + 4.21080i −0.139740 + 0.139740i
\(909\) 0 0
\(910\) 0 0
\(911\) −39.2522 + 22.6623i −1.30048 + 0.750835i −0.980487 0.196583i \(-0.937015\pi\)
−0.319997 + 0.947418i \(0.603682\pi\)
\(912\) 0 0
\(913\) −53.3039 + 14.2827i −1.76410 + 0.472690i
\(914\) 6.55874 11.3601i 0.216944 0.375758i
\(915\) 0 0
\(916\) −5.87872 10.1822i −0.194238 0.336431i
\(917\) −24.4930 24.4930i −0.808829 0.808829i
\(918\) 0 0
\(919\) 19.9726i 0.658836i −0.944184 0.329418i \(-0.893148\pi\)
0.944184 0.329418i \(-0.106852\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 10.3908 + 38.7791i 0.342204 + 1.27712i
\(923\) −1.62455 6.06291i −0.0534728 0.199563i
\(924\) 0 0
\(925\) 0 0
\(926\) 11.9769i 0.393586i
\(927\) 0 0
\(928\) 1.30136 + 1.30136i 0.0427192 + 0.0427192i
\(929\) 24.8920 + 43.1142i 0.816681 + 1.41453i 0.908115 + 0.418721i \(0.137522\pi\)
−0.0914341 + 0.995811i \(0.529145\pi\)
\(930\) 0 0
\(931\) −0.0893912 + 0.154830i −0.00292968 + 0.00507435i
\(932\) −18.3487 + 4.91653i −0.601033 + 0.161046i
\(933\) 0 0
\(934\) 10.5711 6.10321i 0.345896 0.199703i
\(935\) 0 0
\(936\) 0 0
\(937\) −28.6750 + 28.6750i −0.936771 + 0.936771i −0.998117 0.0613453i \(-0.980461\pi\)
0.0613453 + 0.998117i \(0.480461\pi\)
\(938\) −28.2876 7.57964i −0.923623 0.247484i
\(939\) 0 0
\(940\) 0 0
\(941\) 42.4585 + 24.5134i 1.38411 + 0.799115i 0.992643 0.121078i \(-0.0386353\pi\)
0.391464 + 0.920193i \(0.371969\pi\)
\(942\) 0 0
\(943\) 4.39363 16.3972i 0.143076 0.533967i
\(944\) 0.129095 0.00420167
\(945\) 0 0
\(946\) 11.9461 0.388401
\(947\) 11.6667 43.5407i 0.379117 1.41488i −0.468119 0.883665i \(-0.655068\pi\)
0.847236 0.531217i \(-0.178265\pi\)
\(948\) 0 0
\(949\) 2.43470 + 1.40568i 0.0790339 + 0.0456302i
\(950\) 0 0
\(951\) 0 0
\(952\) −15.9727 4.27988i −0.517679 0.138712i
\(953\) −2.71971 + 2.71971i −0.0881001 + 0.0881001i −0.749783 0.661683i \(-0.769842\pi\)
0.661683 + 0.749783i \(0.269842\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) −3.94809 + 2.27943i −0.127690 + 0.0737220i
\(957\) 0 0
\(958\) −9.91983 + 2.65801i −0.320495 + 0.0858764i
\(959\) 4.30878 7.46303i 0.139138 0.240994i
\(960\) 0 0
\(961\) 7.18593 + 12.4464i 0.231804 + 0.401497i
\(962\) −0.380728 0.380728i −0.0122752 0.0122752i
\(963\) 0 0
\(964\) 16.0621i 0.517325i
\(965\) 0 0
\(966\) 0 0
\(967\) −8.10886 30.2627i −0.260763 0.973182i −0.964793 0.263011i \(-0.915284\pi\)
0.704029 0.710171i \(-0.251382\pi\)
\(968\) 3.11102 + 11.6105i 0.0999920 + 0.373175i
\(969\) 0 0
\(970\) 0 0
\(971\) 31.9680i 1.02590i 0.858418 + 0.512951i \(0.171448\pi\)
−0.858418 + 0.512951i \(0.828552\pi\)
\(972\) 0 0
\(973\) −41.2491 41.2491i −1.32238 1.32238i
\(974\) 12.3898 + 21.4597i 0.396993 + 0.687613i
\(975\) 0 0
\(976\) −6.27251 + 10.8643i −0.200778 + 0.347758i
\(977\) −8.45932 + 2.26667i −0.270638 + 0.0725171i −0.391585 0.920142i \(-0.628073\pi\)
0.120948 + 0.992659i \(0.461407\pi\)
\(978\) 0 0
\(979\) 8.51754 4.91760i 0.272222 0.157167i
\(980\) 0 0
\(981\) 0 0
\(982\) 6.28784 6.28784i 0.200653 0.200653i
\(983\) 40.7397 + 10.9162i 1.29940 + 0.348172i 0.841222 0.540691i \(-0.181837\pi\)
0.458174 + 0.888863i \(0.348504\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 9.93720 + 5.73725i 0.316465 + 0.182711i
\(987\) 0 0
\(988\) −0.809364 + 3.02059i −0.0257493 + 0.0960977i
\(989\) −6.55342 −0.208387
\(990\) 0 0
\(991\) −13.9120 −0.441929 −0.220964 0.975282i \(-0.570920\pi\)
−0.220964 + 0.975282i \(0.570920\pi\)
\(992\) −1.05540 + 3.93882i −0.0335091 + 0.125058i
\(993\) 0 0
\(994\) 23.9345 + 13.8186i 0.759156 + 0.438299i
\(995\) 0 0
\(996\) 0 0
\(997\) −29.2374 7.83414i −0.925958 0.248110i −0.235828 0.971795i \(-0.575780\pi\)
−0.690130 + 0.723685i \(0.742447\pi\)
\(998\) 20.7542 20.7542i 0.656963 0.656963i
\(999\) 0 0
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 1350.2.q.h.1043.4 16
3.2 odd 2 450.2.p.h.293.2 16
5.2 odd 4 inner 1350.2.q.h.557.3 16
5.3 odd 4 270.2.m.b.17.1 16
5.4 even 2 270.2.m.b.233.1 16
9.2 odd 6 inner 1350.2.q.h.143.3 16
9.7 even 3 450.2.p.h.443.2 16
15.2 even 4 450.2.p.h.257.2 16
15.8 even 4 90.2.l.b.77.3 yes 16
15.14 odd 2 90.2.l.b.23.3 16
45.2 even 12 inner 1350.2.q.h.1007.4 16
45.4 even 6 810.2.f.c.323.4 16
45.7 odd 12 450.2.p.h.407.2 16
45.13 odd 12 810.2.f.c.647.5 16
45.14 odd 6 810.2.f.c.323.5 16
45.23 even 12 810.2.f.c.647.4 16
45.29 odd 6 270.2.m.b.143.1 16
45.34 even 6 90.2.l.b.83.3 yes 16
45.38 even 12 270.2.m.b.197.1 16
45.43 odd 12 90.2.l.b.47.3 yes 16
60.23 odd 4 720.2.cu.b.257.3 16
60.59 even 2 720.2.cu.b.113.4 16
180.43 even 12 720.2.cu.b.497.4 16
180.79 odd 6 720.2.cu.b.353.3 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
90.2.l.b.23.3 16 15.14 odd 2
90.2.l.b.47.3 yes 16 45.43 odd 12
90.2.l.b.77.3 yes 16 15.8 even 4
90.2.l.b.83.3 yes 16 45.34 even 6
270.2.m.b.17.1 16 5.3 odd 4
270.2.m.b.143.1 16 45.29 odd 6
270.2.m.b.197.1 16 45.38 even 12
270.2.m.b.233.1 16 5.4 even 2
450.2.p.h.257.2 16 15.2 even 4
450.2.p.h.293.2 16 3.2 odd 2
450.2.p.h.407.2 16 45.7 odd 12
450.2.p.h.443.2 16 9.7 even 3
720.2.cu.b.113.4 16 60.59 even 2
720.2.cu.b.257.3 16 60.23 odd 4
720.2.cu.b.353.3 16 180.79 odd 6
720.2.cu.b.497.4 16 180.43 even 12
810.2.f.c.323.4 16 45.4 even 6
810.2.f.c.323.5 16 45.14 odd 6
810.2.f.c.647.4 16 45.23 even 12
810.2.f.c.647.5 16 45.13 odd 12
1350.2.q.h.143.3 16 9.2 odd 6 inner
1350.2.q.h.557.3 16 5.2 odd 4 inner
1350.2.q.h.1007.4 16 45.2 even 12 inner
1350.2.q.h.1043.4 16 1.1 even 1 trivial