Properties

Label 351.2.r.a.316.1
Level $351$
Weight $2$
Character 351.316
Analytic conductor $2.803$
Analytic rank $0$
Dimension $2$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [351,2,Mod(10,351)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(351, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("351.10");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 351 = 3^{3} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 351.r (of order \(6\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.80274911095\)
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 117)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 316.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 351.316
Dual form 351.2.r.a.10.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.50000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{4} +(1.50000 - 0.866025i) q^{5} -1.73205i q^{7} +1.73205i q^{8} +(1.50000 - 2.59808i) q^{10} +(3.00000 - 1.73205i) q^{11} +(-2.50000 - 2.59808i) q^{13} +(-1.50000 - 2.59808i) q^{14} +(2.50000 + 4.33013i) q^{16} +(1.50000 + 2.59808i) q^{17} +(-1.50000 + 0.866025i) q^{19} -1.73205i q^{20} +(3.00000 - 5.19615i) q^{22} +3.00000 q^{23} +(-1.00000 + 1.73205i) q^{25} +(-6.00000 - 1.73205i) q^{26} +(-1.50000 - 0.866025i) q^{28} +(-3.00000 - 5.19615i) q^{29} +(-7.50000 + 4.33013i) q^{31} +(4.50000 + 2.59808i) q^{32} +(4.50000 + 2.59808i) q^{34} +(-1.50000 - 2.59808i) q^{35} +(-4.50000 - 2.59808i) q^{37} +(-1.50000 + 2.59808i) q^{38} +(1.50000 + 2.59808i) q^{40} +12.1244i q^{41} -1.00000 q^{43} -3.46410i q^{44} +(4.50000 - 2.59808i) q^{46} +(4.50000 + 2.59808i) q^{47} +4.00000 q^{49} +3.46410i q^{50} +(-3.50000 + 0.866025i) q^{52} -6.00000 q^{53} +(3.00000 - 5.19615i) q^{55} +3.00000 q^{56} +(-9.00000 - 5.19615i) q^{58} +(-3.00000 - 1.73205i) q^{59} -5.00000 q^{61} +(-7.50000 + 12.9904i) q^{62} -1.00000 q^{64} +(-6.00000 - 1.73205i) q^{65} +12.1244i q^{67} +3.00000 q^{68} +(-4.50000 - 2.59808i) q^{70} +(7.50000 - 4.33013i) q^{71} +6.92820i q^{73} -9.00000 q^{74} +1.73205i q^{76} +(-3.00000 - 5.19615i) q^{77} +(5.50000 - 9.52628i) q^{79} +(7.50000 + 4.33013i) q^{80} +(10.5000 + 18.1865i) q^{82} +(4.50000 + 2.59808i) q^{83} +(4.50000 + 2.59808i) q^{85} +(-1.50000 + 0.866025i) q^{86} +(3.00000 + 5.19615i) q^{88} +(-13.5000 - 7.79423i) q^{89} +(-4.50000 + 4.33013i) q^{91} +(1.50000 - 2.59808i) q^{92} +9.00000 q^{94} +(-1.50000 + 2.59808i) q^{95} -15.5885i q^{97} +(6.00000 - 3.46410i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 3 q^{2} + q^{4} + 3 q^{5} + 3 q^{10} + 6 q^{11} - 5 q^{13} - 3 q^{14} + 5 q^{16} + 3 q^{17} - 3 q^{19} + 6 q^{22} + 6 q^{23} - 2 q^{25} - 12 q^{26} - 3 q^{28} - 6 q^{29} - 15 q^{31} + 9 q^{32} + 9 q^{34}+ \cdots + 12 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/351\mathbb{Z}\right)^\times\).

\(n\) \(28\) \(326\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.50000 0.866025i 1.06066 0.612372i 0.135045 0.990839i \(-0.456882\pi\)
0.925615 + 0.378467i \(0.123549\pi\)
\(3\) 0 0
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) 1.50000 0.866025i 0.670820 0.387298i −0.125567 0.992085i \(-0.540075\pi\)
0.796387 + 0.604787i \(0.206742\pi\)
\(6\) 0 0
\(7\) 1.73205i 0.654654i −0.944911 0.327327i \(-0.893852\pi\)
0.944911 0.327327i \(-0.106148\pi\)
\(8\) 1.73205i 0.612372i
\(9\) 0 0
\(10\) 1.50000 2.59808i 0.474342 0.821584i
\(11\) 3.00000 1.73205i 0.904534 0.522233i 0.0258656 0.999665i \(-0.491766\pi\)
0.878668 + 0.477432i \(0.158432\pi\)
\(12\) 0 0
\(13\) −2.50000 2.59808i −0.693375 0.720577i
\(14\) −1.50000 2.59808i −0.400892 0.694365i
\(15\) 0 0
\(16\) 2.50000 + 4.33013i 0.625000 + 1.08253i
\(17\) 1.50000 + 2.59808i 0.363803 + 0.630126i 0.988583 0.150675i \(-0.0481447\pi\)
−0.624780 + 0.780801i \(0.714811\pi\)
\(18\) 0 0
\(19\) −1.50000 + 0.866025i −0.344124 + 0.198680i −0.662094 0.749421i \(-0.730332\pi\)
0.317970 + 0.948101i \(0.396999\pi\)
\(20\) 1.73205i 0.387298i
\(21\) 0 0
\(22\) 3.00000 5.19615i 0.639602 1.10782i
\(23\) 3.00000 0.625543 0.312772 0.949828i \(-0.398743\pi\)
0.312772 + 0.949828i \(0.398743\pi\)
\(24\) 0 0
\(25\) −1.00000 + 1.73205i −0.200000 + 0.346410i
\(26\) −6.00000 1.73205i −1.17670 0.339683i
\(27\) 0 0
\(28\) −1.50000 0.866025i −0.283473 0.163663i
\(29\) −3.00000 5.19615i −0.557086 0.964901i −0.997738 0.0672232i \(-0.978586\pi\)
0.440652 0.897678i \(-0.354747\pi\)
\(30\) 0 0
\(31\) −7.50000 + 4.33013i −1.34704 + 0.777714i −0.987829 0.155543i \(-0.950287\pi\)
−0.359211 + 0.933257i \(0.616954\pi\)
\(32\) 4.50000 + 2.59808i 0.795495 + 0.459279i
\(33\) 0 0
\(34\) 4.50000 + 2.59808i 0.771744 + 0.445566i
\(35\) −1.50000 2.59808i −0.253546 0.439155i
\(36\) 0 0
\(37\) −4.50000 2.59808i −0.739795 0.427121i 0.0821995 0.996616i \(-0.473806\pi\)
−0.821995 + 0.569495i \(0.807139\pi\)
\(38\) −1.50000 + 2.59808i −0.243332 + 0.421464i
\(39\) 0 0
\(40\) 1.50000 + 2.59808i 0.237171 + 0.410792i
\(41\) 12.1244i 1.89351i 0.321960 + 0.946753i \(0.395658\pi\)
−0.321960 + 0.946753i \(0.604342\pi\)
\(42\) 0 0
\(43\) −1.00000 −0.152499 −0.0762493 0.997089i \(-0.524294\pi\)
−0.0762493 + 0.997089i \(0.524294\pi\)
\(44\) 3.46410i 0.522233i
\(45\) 0 0
\(46\) 4.50000 2.59808i 0.663489 0.383065i
\(47\) 4.50000 + 2.59808i 0.656392 + 0.378968i 0.790901 0.611944i \(-0.209612\pi\)
−0.134509 + 0.990912i \(0.542946\pi\)
\(48\) 0 0
\(49\) 4.00000 0.571429
\(50\) 3.46410i 0.489898i
\(51\) 0 0
\(52\) −3.50000 + 0.866025i −0.485363 + 0.120096i
\(53\) −6.00000 −0.824163 −0.412082 0.911147i \(-0.635198\pi\)
−0.412082 + 0.911147i \(0.635198\pi\)
\(54\) 0 0
\(55\) 3.00000 5.19615i 0.404520 0.700649i
\(56\) 3.00000 0.400892
\(57\) 0 0
\(58\) −9.00000 5.19615i −1.18176 0.682288i
\(59\) −3.00000 1.73205i −0.390567 0.225494i 0.291839 0.956467i \(-0.405733\pi\)
−0.682406 + 0.730974i \(0.739066\pi\)
\(60\) 0 0
\(61\) −5.00000 −0.640184 −0.320092 0.947386i \(-0.603714\pi\)
−0.320092 + 0.947386i \(0.603714\pi\)
\(62\) −7.50000 + 12.9904i −0.952501 + 1.64978i
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) −6.00000 1.73205i −0.744208 0.214834i
\(66\) 0 0
\(67\) 12.1244i 1.48123i 0.671932 + 0.740613i \(0.265465\pi\)
−0.671932 + 0.740613i \(0.734535\pi\)
\(68\) 3.00000 0.363803
\(69\) 0 0
\(70\) −4.50000 2.59808i −0.537853 0.310530i
\(71\) 7.50000 4.33013i 0.890086 0.513892i 0.0161155 0.999870i \(-0.494870\pi\)
0.873971 + 0.485979i \(0.161537\pi\)
\(72\) 0 0
\(73\) 6.92820i 0.810885i 0.914121 + 0.405442i \(0.132883\pi\)
−0.914121 + 0.405442i \(0.867117\pi\)
\(74\) −9.00000 −1.04623
\(75\) 0 0
\(76\) 1.73205i 0.198680i
\(77\) −3.00000 5.19615i −0.341882 0.592157i
\(78\) 0 0
\(79\) 5.50000 9.52628i 0.618798 1.07179i −0.370907 0.928670i \(-0.620953\pi\)
0.989705 0.143120i \(-0.0457135\pi\)
\(80\) 7.50000 + 4.33013i 0.838525 + 0.484123i
\(81\) 0 0
\(82\) 10.5000 + 18.1865i 1.15953 + 2.00837i
\(83\) 4.50000 + 2.59808i 0.493939 + 0.285176i 0.726207 0.687476i \(-0.241281\pi\)
−0.232268 + 0.972652i \(0.574615\pi\)
\(84\) 0 0
\(85\) 4.50000 + 2.59808i 0.488094 + 0.281801i
\(86\) −1.50000 + 0.866025i −0.161749 + 0.0933859i
\(87\) 0 0
\(88\) 3.00000 + 5.19615i 0.319801 + 0.553912i
\(89\) −13.5000 7.79423i −1.43100 0.826187i −0.433800 0.901009i \(-0.642828\pi\)
−0.997197 + 0.0748225i \(0.976161\pi\)
\(90\) 0 0
\(91\) −4.50000 + 4.33013i −0.471728 + 0.453921i
\(92\) 1.50000 2.59808i 0.156386 0.270868i
\(93\) 0 0
\(94\) 9.00000 0.928279
\(95\) −1.50000 + 2.59808i −0.153897 + 0.266557i
\(96\) 0 0
\(97\) 15.5885i 1.58277i −0.611319 0.791384i \(-0.709361\pi\)
0.611319 0.791384i \(-0.290639\pi\)
\(98\) 6.00000 3.46410i 0.606092 0.349927i
\(99\) 0 0
\(100\) 1.00000 + 1.73205i 0.100000 + 0.173205i
\(101\) −3.00000 5.19615i −0.298511 0.517036i 0.677284 0.735721i \(-0.263157\pi\)
−0.975796 + 0.218685i \(0.929823\pi\)
\(102\) 0 0
\(103\) 6.50000 + 11.2583i 0.640464 + 1.10932i 0.985329 + 0.170664i \(0.0545913\pi\)
−0.344865 + 0.938652i \(0.612075\pi\)
\(104\) 4.50000 4.33013i 0.441261 0.424604i
\(105\) 0 0
\(106\) −9.00000 + 5.19615i −0.874157 + 0.504695i
\(107\) 7.50000 12.9904i 0.725052 1.25583i −0.233900 0.972261i \(-0.575149\pi\)
0.958952 0.283567i \(-0.0915178\pi\)
\(108\) 0 0
\(109\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(110\) 10.3923i 0.990867i
\(111\) 0 0
\(112\) 7.50000 4.33013i 0.708683 0.409159i
\(113\) 3.00000 5.19615i 0.282216 0.488813i −0.689714 0.724082i \(-0.742264\pi\)
0.971930 + 0.235269i \(0.0755971\pi\)
\(114\) 0 0
\(115\) 4.50000 2.59808i 0.419627 0.242272i
\(116\) −6.00000 −0.557086
\(117\) 0 0
\(118\) −6.00000 −0.552345
\(119\) 4.50000 2.59808i 0.412514 0.238165i
\(120\) 0 0
\(121\) 0.500000 0.866025i 0.0454545 0.0787296i
\(122\) −7.50000 + 4.33013i −0.679018 + 0.392031i
\(123\) 0 0
\(124\) 8.66025i 0.777714i
\(125\) 12.1244i 1.08444i
\(126\) 0 0
\(127\) 2.50000 4.33013i 0.221839 0.384237i −0.733527 0.679660i \(-0.762127\pi\)
0.955366 + 0.295423i \(0.0954607\pi\)
\(128\) −10.5000 + 6.06218i −0.928078 + 0.535826i
\(129\) 0 0
\(130\) −10.5000 + 2.59808i −0.920911 + 0.227866i
\(131\) 7.50000 + 12.9904i 0.655278 + 1.13497i 0.981824 + 0.189794i \(0.0607819\pi\)
−0.326546 + 0.945181i \(0.605885\pi\)
\(132\) 0 0
\(133\) 1.50000 + 2.59808i 0.130066 + 0.225282i
\(134\) 10.5000 + 18.1865i 0.907062 + 1.57108i
\(135\) 0 0
\(136\) −4.50000 + 2.59808i −0.385872 + 0.222783i
\(137\) 5.19615i 0.443937i −0.975054 0.221969i \(-0.928752\pi\)
0.975054 0.221969i \(-0.0712483\pi\)
\(138\) 0 0
\(139\) 8.00000 13.8564i 0.678551 1.17529i −0.296866 0.954919i \(-0.595942\pi\)
0.975417 0.220366i \(-0.0707252\pi\)
\(140\) −3.00000 −0.253546
\(141\) 0 0
\(142\) 7.50000 12.9904i 0.629386 1.09013i
\(143\) −12.0000 3.46410i −1.00349 0.289683i
\(144\) 0 0
\(145\) −9.00000 5.19615i −0.747409 0.431517i
\(146\) 6.00000 + 10.3923i 0.496564 + 0.860073i
\(147\) 0 0
\(148\) −4.50000 + 2.59808i −0.369898 + 0.213561i
\(149\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(150\) 0 0
\(151\) −10.5000 6.06218i −0.854478 0.493333i 0.00768132 0.999970i \(-0.497555\pi\)
−0.862159 + 0.506637i \(0.830888\pi\)
\(152\) −1.50000 2.59808i −0.121666 0.210732i
\(153\) 0 0
\(154\) −9.00000 5.19615i −0.725241 0.418718i
\(155\) −7.50000 + 12.9904i −0.602414 + 1.04341i
\(156\) 0 0
\(157\) −11.5000 19.9186i −0.917800 1.58968i −0.802749 0.596316i \(-0.796630\pi\)
−0.115050 0.993360i \(-0.536703\pi\)
\(158\) 19.0526i 1.51574i
\(159\) 0 0
\(160\) 9.00000 0.711512
\(161\) 5.19615i 0.409514i
\(162\) 0 0
\(163\) 10.5000 6.06218i 0.822423 0.474826i −0.0288280 0.999584i \(-0.509178\pi\)
0.851251 + 0.524758i \(0.175844\pi\)
\(164\) 10.5000 + 6.06218i 0.819912 + 0.473377i
\(165\) 0 0
\(166\) 9.00000 0.698535
\(167\) 5.19615i 0.402090i −0.979582 0.201045i \(-0.935566\pi\)
0.979582 0.201045i \(-0.0644338\pi\)
\(168\) 0 0
\(169\) −0.500000 + 12.9904i −0.0384615 + 0.999260i
\(170\) 9.00000 0.690268
\(171\) 0 0
\(172\) −0.500000 + 0.866025i −0.0381246 + 0.0660338i
\(173\) 21.0000 1.59660 0.798300 0.602260i \(-0.205733\pi\)
0.798300 + 0.602260i \(0.205733\pi\)
\(174\) 0 0
\(175\) 3.00000 + 1.73205i 0.226779 + 0.130931i
\(176\) 15.0000 + 8.66025i 1.13067 + 0.652791i
\(177\) 0 0
\(178\) −27.0000 −2.02374
\(179\) 1.50000 2.59808i 0.112115 0.194189i −0.804508 0.593942i \(-0.797571\pi\)
0.916623 + 0.399753i \(0.130904\pi\)
\(180\) 0 0
\(181\) −22.0000 −1.63525 −0.817624 0.575753i \(-0.804709\pi\)
−0.817624 + 0.575753i \(0.804709\pi\)
\(182\) −3.00000 + 10.3923i −0.222375 + 0.770329i
\(183\) 0 0
\(184\) 5.19615i 0.383065i
\(185\) −9.00000 −0.661693
\(186\) 0 0
\(187\) 9.00000 + 5.19615i 0.658145 + 0.379980i
\(188\) 4.50000 2.59808i 0.328196 0.189484i
\(189\) 0 0
\(190\) 5.19615i 0.376969i
\(191\) −3.00000 −0.217072 −0.108536 0.994092i \(-0.534616\pi\)
−0.108536 + 0.994092i \(0.534616\pi\)
\(192\) 0 0
\(193\) 5.19615i 0.374027i −0.982357 0.187014i \(-0.940119\pi\)
0.982357 0.187014i \(-0.0598809\pi\)
\(194\) −13.5000 23.3827i −0.969244 1.67878i
\(195\) 0 0
\(196\) 2.00000 3.46410i 0.142857 0.247436i
\(197\) −7.50000 4.33013i −0.534353 0.308509i 0.208434 0.978036i \(-0.433163\pi\)
−0.742787 + 0.669528i \(0.766497\pi\)
\(198\) 0 0
\(199\) −6.50000 11.2583i −0.460773 0.798082i 0.538227 0.842800i \(-0.319094\pi\)
−0.999000 + 0.0447181i \(0.985761\pi\)
\(200\) −3.00000 1.73205i −0.212132 0.122474i
\(201\) 0 0
\(202\) −9.00000 5.19615i −0.633238 0.365600i
\(203\) −9.00000 + 5.19615i −0.631676 + 0.364698i
\(204\) 0 0
\(205\) 10.5000 + 18.1865i 0.733352 + 1.27020i
\(206\) 19.5000 + 11.2583i 1.35863 + 0.784405i
\(207\) 0 0
\(208\) 5.00000 17.3205i 0.346688 1.20096i
\(209\) −3.00000 + 5.19615i −0.207514 + 0.359425i
\(210\) 0 0
\(211\) 13.0000 0.894957 0.447478 0.894295i \(-0.352322\pi\)
0.447478 + 0.894295i \(0.352322\pi\)
\(212\) −3.00000 + 5.19615i −0.206041 + 0.356873i
\(213\) 0 0
\(214\) 25.9808i 1.77601i
\(215\) −1.50000 + 0.866025i −0.102299 + 0.0590624i
\(216\) 0 0
\(217\) 7.50000 + 12.9904i 0.509133 + 0.881845i
\(218\) 0 0
\(219\) 0 0
\(220\) −3.00000 5.19615i −0.202260 0.350325i
\(221\) 3.00000 10.3923i 0.201802 0.699062i
\(222\) 0 0
\(223\) 3.00000 1.73205i 0.200895 0.115987i −0.396178 0.918174i \(-0.629664\pi\)
0.597073 + 0.802187i \(0.296330\pi\)
\(224\) 4.50000 7.79423i 0.300669 0.520774i
\(225\) 0 0
\(226\) 10.3923i 0.691286i
\(227\) 12.1244i 0.804722i −0.915481 0.402361i \(-0.868190\pi\)
0.915481 0.402361i \(-0.131810\pi\)
\(228\) 0 0
\(229\) −7.50000 + 4.33013i −0.495614 + 0.286143i −0.726900 0.686743i \(-0.759040\pi\)
0.231287 + 0.972886i \(0.425707\pi\)
\(230\) 4.50000 7.79423i 0.296721 0.513936i
\(231\) 0 0
\(232\) 9.00000 5.19615i 0.590879 0.341144i
\(233\) 18.0000 1.17922 0.589610 0.807688i \(-0.299282\pi\)
0.589610 + 0.807688i \(0.299282\pi\)
\(234\) 0 0
\(235\) 9.00000 0.587095
\(236\) −3.00000 + 1.73205i −0.195283 + 0.112747i
\(237\) 0 0
\(238\) 4.50000 7.79423i 0.291692 0.505225i
\(239\) −4.50000 + 2.59808i −0.291081 + 0.168056i −0.638429 0.769681i \(-0.720415\pi\)
0.347348 + 0.937736i \(0.387082\pi\)
\(240\) 0 0
\(241\) 5.19615i 0.334714i 0.985896 + 0.167357i \(0.0535232\pi\)
−0.985896 + 0.167357i \(0.946477\pi\)
\(242\) 1.73205i 0.111340i
\(243\) 0 0
\(244\) −2.50000 + 4.33013i −0.160046 + 0.277208i
\(245\) 6.00000 3.46410i 0.383326 0.221313i
\(246\) 0 0
\(247\) 6.00000 + 1.73205i 0.381771 + 0.110208i
\(248\) −7.50000 12.9904i −0.476250 0.824890i
\(249\) 0 0
\(250\) 10.5000 + 18.1865i 0.664078 + 1.15022i
\(251\) 4.50000 + 7.79423i 0.284037 + 0.491967i 0.972375 0.233423i \(-0.0749927\pi\)
−0.688338 + 0.725390i \(0.741659\pi\)
\(252\) 0 0
\(253\) 9.00000 5.19615i 0.565825 0.326679i
\(254\) 8.66025i 0.543393i
\(255\) 0 0
\(256\) −9.50000 + 16.4545i −0.593750 + 1.02841i
\(257\) −3.00000 −0.187135 −0.0935674 0.995613i \(-0.529827\pi\)
−0.0935674 + 0.995613i \(0.529827\pi\)
\(258\) 0 0
\(259\) −4.50000 + 7.79423i −0.279616 + 0.484310i
\(260\) −4.50000 + 4.33013i −0.279078 + 0.268543i
\(261\) 0 0
\(262\) 22.5000 + 12.9904i 1.39005 + 0.802548i
\(263\) 12.0000 + 20.7846i 0.739952 + 1.28163i 0.952517 + 0.304487i \(0.0984850\pi\)
−0.212565 + 0.977147i \(0.568182\pi\)
\(264\) 0 0
\(265\) −9.00000 + 5.19615i −0.552866 + 0.319197i
\(266\) 4.50000 + 2.59808i 0.275913 + 0.159298i
\(267\) 0 0
\(268\) 10.5000 + 6.06218i 0.641390 + 0.370306i
\(269\) 1.50000 + 2.59808i 0.0914566 + 0.158408i 0.908124 0.418701i \(-0.137514\pi\)
−0.816668 + 0.577108i \(0.804181\pi\)
\(270\) 0 0
\(271\) 13.5000 + 7.79423i 0.820067 + 0.473466i 0.850439 0.526073i \(-0.176336\pi\)
−0.0303728 + 0.999539i \(0.509669\pi\)
\(272\) −7.50000 + 12.9904i −0.454754 + 0.787658i
\(273\) 0 0
\(274\) −4.50000 7.79423i −0.271855 0.470867i
\(275\) 6.92820i 0.417786i
\(276\) 0 0
\(277\) 23.0000 1.38194 0.690968 0.722885i \(-0.257185\pi\)
0.690968 + 0.722885i \(0.257185\pi\)
\(278\) 27.7128i 1.66210i
\(279\) 0 0
\(280\) 4.50000 2.59808i 0.268926 0.155265i
\(281\) −4.50000 2.59808i −0.268447 0.154988i 0.359734 0.933055i \(-0.382867\pi\)
−0.628182 + 0.778067i \(0.716201\pi\)
\(282\) 0 0
\(283\) −23.0000 −1.36721 −0.683604 0.729853i \(-0.739588\pi\)
−0.683604 + 0.729853i \(0.739588\pi\)
\(284\) 8.66025i 0.513892i
\(285\) 0 0
\(286\) −21.0000 + 5.19615i −1.24176 + 0.307255i
\(287\) 21.0000 1.23959
\(288\) 0 0
\(289\) 4.00000 6.92820i 0.235294 0.407541i
\(290\) −18.0000 −1.05700
\(291\) 0 0
\(292\) 6.00000 + 3.46410i 0.351123 + 0.202721i
\(293\) −12.0000 6.92820i −0.701047 0.404750i 0.106690 0.994292i \(-0.465975\pi\)
−0.807737 + 0.589542i \(0.799308\pi\)
\(294\) 0 0
\(295\) −6.00000 −0.349334
\(296\) 4.50000 7.79423i 0.261557 0.453030i
\(297\) 0 0
\(298\) 0 0
\(299\) −7.50000 7.79423i −0.433736 0.450752i
\(300\) 0 0
\(301\) 1.73205i 0.0998337i
\(302\) −21.0000 −1.20841
\(303\) 0 0
\(304\) −7.50000 4.33013i −0.430155 0.248350i
\(305\) −7.50000 + 4.33013i −0.429449 + 0.247942i
\(306\) 0 0
\(307\) 24.2487i 1.38395i 0.721923 + 0.691974i \(0.243259\pi\)
−0.721923 + 0.691974i \(0.756741\pi\)
\(308\) −6.00000 −0.341882
\(309\) 0 0
\(310\) 25.9808i 1.47561i
\(311\) 13.5000 + 23.3827i 0.765515 + 1.32591i 0.939974 + 0.341246i \(0.110849\pi\)
−0.174459 + 0.984664i \(0.555818\pi\)
\(312\) 0 0
\(313\) −9.50000 + 16.4545i −0.536972 + 0.930062i 0.462093 + 0.886831i \(0.347098\pi\)
−0.999065 + 0.0432311i \(0.986235\pi\)
\(314\) −34.5000 19.9186i −1.94695 1.12407i
\(315\) 0 0
\(316\) −5.50000 9.52628i −0.309399 0.535895i
\(317\) 7.50000 + 4.33013i 0.421242 + 0.243204i 0.695609 0.718421i \(-0.255135\pi\)
−0.274367 + 0.961625i \(0.588468\pi\)
\(318\) 0 0
\(319\) −18.0000 10.3923i −1.00781 0.581857i
\(320\) −1.50000 + 0.866025i −0.0838525 + 0.0484123i
\(321\) 0 0
\(322\) −4.50000 7.79423i −0.250775 0.434355i
\(323\) −4.50000 2.59808i −0.250387 0.144561i
\(324\) 0 0
\(325\) 7.00000 1.73205i 0.388290 0.0960769i
\(326\) 10.5000 18.1865i 0.581541 1.00726i
\(327\) 0 0
\(328\) −21.0000 −1.15953
\(329\) 4.50000 7.79423i 0.248093 0.429710i
\(330\) 0 0
\(331\) 15.5885i 0.856819i −0.903585 0.428410i \(-0.859074\pi\)
0.903585 0.428410i \(-0.140926\pi\)
\(332\) 4.50000 2.59808i 0.246970 0.142588i
\(333\) 0 0
\(334\) −4.50000 7.79423i −0.246229 0.426481i
\(335\) 10.5000 + 18.1865i 0.573676 + 0.993636i
\(336\) 0 0
\(337\) 14.5000 + 25.1147i 0.789865 + 1.36809i 0.926049 + 0.377403i \(0.123183\pi\)
−0.136184 + 0.990684i \(0.543484\pi\)
\(338\) 10.5000 + 19.9186i 0.571125 + 1.08343i
\(339\) 0 0
\(340\) 4.50000 2.59808i 0.244047 0.140900i
\(341\) −15.0000 + 25.9808i −0.812296 + 1.40694i
\(342\) 0 0
\(343\) 19.0526i 1.02874i
\(344\) 1.73205i 0.0933859i
\(345\) 0 0
\(346\) 31.5000 18.1865i 1.69345 0.977714i
\(347\) −6.00000 + 10.3923i −0.322097 + 0.557888i −0.980921 0.194409i \(-0.937721\pi\)
0.658824 + 0.752297i \(0.271054\pi\)
\(348\) 0 0
\(349\) −24.0000 + 13.8564i −1.28469 + 0.741716i −0.977702 0.209997i \(-0.932655\pi\)
−0.306988 + 0.951713i \(0.599321\pi\)
\(350\) 6.00000 0.320713
\(351\) 0 0
\(352\) 18.0000 0.959403
\(353\) −6.00000 + 3.46410i −0.319348 + 0.184376i −0.651102 0.758990i \(-0.725693\pi\)
0.331754 + 0.943366i \(0.392360\pi\)
\(354\) 0 0
\(355\) 7.50000 12.9904i 0.398059 0.689458i
\(356\) −13.5000 + 7.79423i −0.715499 + 0.413093i
\(357\) 0 0
\(358\) 5.19615i 0.274625i
\(359\) 10.3923i 0.548485i 0.961661 + 0.274242i \(0.0884271\pi\)
−0.961661 + 0.274242i \(0.911573\pi\)
\(360\) 0 0
\(361\) −8.00000 + 13.8564i −0.421053 + 0.729285i
\(362\) −33.0000 + 19.0526i −1.73444 + 1.00138i
\(363\) 0 0
\(364\) 1.50000 + 6.06218i 0.0786214 + 0.317744i
\(365\) 6.00000 + 10.3923i 0.314054 + 0.543958i
\(366\) 0 0
\(367\) −4.00000 6.92820i −0.208798 0.361649i 0.742538 0.669804i \(-0.233622\pi\)
−0.951336 + 0.308155i \(0.900289\pi\)
\(368\) 7.50000 + 12.9904i 0.390965 + 0.677170i
\(369\) 0 0
\(370\) −13.5000 + 7.79423i −0.701832 + 0.405203i
\(371\) 10.3923i 0.539542i
\(372\) 0 0
\(373\) 7.00000 12.1244i 0.362446 0.627775i −0.625917 0.779890i \(-0.715275\pi\)
0.988363 + 0.152115i \(0.0486083\pi\)
\(374\) 18.0000 0.930758
\(375\) 0 0
\(376\) −4.50000 + 7.79423i −0.232070 + 0.401957i
\(377\) −6.00000 + 20.7846i −0.309016 + 1.07046i
\(378\) 0 0
\(379\) −10.5000 6.06218i −0.539349 0.311393i 0.205466 0.978664i \(-0.434129\pi\)
−0.744815 + 0.667271i \(0.767462\pi\)
\(380\) 1.50000 + 2.59808i 0.0769484 + 0.133278i
\(381\) 0 0
\(382\) −4.50000 + 2.59808i −0.230240 + 0.132929i
\(383\) 3.00000 + 1.73205i 0.153293 + 0.0885037i 0.574684 0.818375i \(-0.305125\pi\)
−0.421392 + 0.906879i \(0.638458\pi\)
\(384\) 0 0
\(385\) −9.00000 5.19615i −0.458682 0.264820i
\(386\) −4.50000 7.79423i −0.229044 0.396716i
\(387\) 0 0
\(388\) −13.5000 7.79423i −0.685359 0.395692i
\(389\) 1.50000 2.59808i 0.0760530 0.131728i −0.825491 0.564416i \(-0.809102\pi\)
0.901544 + 0.432688i \(0.142435\pi\)
\(390\) 0 0
\(391\) 4.50000 + 7.79423i 0.227575 + 0.394171i
\(392\) 6.92820i 0.349927i
\(393\) 0 0
\(394\) −15.0000 −0.755689
\(395\) 19.0526i 0.958638i
\(396\) 0 0
\(397\) −22.5000 + 12.9904i −1.12924 + 0.651969i −0.943744 0.330676i \(-0.892723\pi\)
−0.185498 + 0.982645i \(0.559390\pi\)
\(398\) −19.5000 11.2583i −0.977447 0.564329i
\(399\) 0 0
\(400\) −10.0000 −0.500000
\(401\) 29.4449i 1.47041i −0.677847 0.735203i \(-0.737087\pi\)
0.677847 0.735203i \(-0.262913\pi\)
\(402\) 0 0
\(403\) 30.0000 + 8.66025i 1.49441 + 0.431398i
\(404\) −6.00000 −0.298511
\(405\) 0 0
\(406\) −9.00000 + 15.5885i −0.446663 + 0.773642i
\(407\) −18.0000 −0.892227
\(408\) 0 0
\(409\) 6.00000 + 3.46410i 0.296681 + 0.171289i 0.640951 0.767582i \(-0.278540\pi\)
−0.344270 + 0.938871i \(0.611874\pi\)
\(410\) 31.5000 + 18.1865i 1.55567 + 0.898169i
\(411\) 0 0
\(412\) 13.0000 0.640464
\(413\) −3.00000 + 5.19615i −0.147620 + 0.255686i
\(414\) 0 0
\(415\) 9.00000 0.441793
\(416\) −4.50000 18.1865i −0.220631 0.891668i
\(417\) 0 0
\(418\) 10.3923i 0.508304i
\(419\) −9.00000 −0.439679 −0.219839 0.975536i \(-0.570553\pi\)
−0.219839 + 0.975536i \(0.570553\pi\)
\(420\) 0 0
\(421\) −7.50000 4.33013i −0.365528 0.211037i 0.305975 0.952039i \(-0.401018\pi\)
−0.671503 + 0.741002i \(0.734351\pi\)
\(422\) 19.5000 11.2583i 0.949245 0.548047i
\(423\) 0 0
\(424\) 10.3923i 0.504695i
\(425\) −6.00000 −0.291043
\(426\) 0 0
\(427\) 8.66025i 0.419099i
\(428\) −7.50000 12.9904i −0.362526 0.627914i
\(429\) 0 0
\(430\) −1.50000 + 2.59808i −0.0723364 + 0.125290i
\(431\) −19.5000 11.2583i −0.939282 0.542295i −0.0495468 0.998772i \(-0.515778\pi\)
−0.889735 + 0.456477i \(0.849111\pi\)
\(432\) 0 0
\(433\) 2.50000 + 4.33013i 0.120142 + 0.208093i 0.919824 0.392332i \(-0.128332\pi\)
−0.799681 + 0.600425i \(0.794998\pi\)
\(434\) 22.5000 + 12.9904i 1.08003 + 0.623558i
\(435\) 0 0
\(436\) 0 0
\(437\) −4.50000 + 2.59808i −0.215264 + 0.124283i
\(438\) 0 0
\(439\) −4.00000 6.92820i −0.190910 0.330665i 0.754642 0.656136i \(-0.227810\pi\)
−0.945552 + 0.325471i \(0.894477\pi\)
\(440\) 9.00000 + 5.19615i 0.429058 + 0.247717i
\(441\) 0 0
\(442\) −4.50000 18.1865i −0.214043 0.865045i
\(443\) 10.5000 18.1865i 0.498870 0.864068i −0.501129 0.865373i \(-0.667082\pi\)
0.999999 + 0.00130426i \(0.000415158\pi\)
\(444\) 0 0
\(445\) −27.0000 −1.27992
\(446\) 3.00000 5.19615i 0.142054 0.246045i
\(447\) 0 0
\(448\) 1.73205i 0.0818317i
\(449\) −13.5000 + 7.79423i −0.637104 + 0.367832i −0.783498 0.621394i \(-0.786567\pi\)
0.146394 + 0.989226i \(0.453233\pi\)
\(450\) 0 0
\(451\) 21.0000 + 36.3731i 0.988851 + 1.71274i
\(452\) −3.00000 5.19615i −0.141108 0.244406i
\(453\) 0 0
\(454\) −10.5000 18.1865i −0.492789 0.853536i
\(455\) −3.00000 + 10.3923i −0.140642 + 0.487199i
\(456\) 0 0
\(457\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(458\) −7.50000 + 12.9904i −0.350452 + 0.607001i
\(459\) 0 0
\(460\) 5.19615i 0.242272i
\(461\) 1.73205i 0.0806696i 0.999186 + 0.0403348i \(0.0128425\pi\)
−0.999186 + 0.0403348i \(0.987158\pi\)
\(462\) 0 0
\(463\) 22.5000 12.9904i 1.04566 0.603714i 0.124231 0.992253i \(-0.460353\pi\)
0.921432 + 0.388539i \(0.127020\pi\)
\(464\) 15.0000 25.9808i 0.696358 1.20613i
\(465\) 0 0
\(466\) 27.0000 15.5885i 1.25075 0.722121i
\(467\) 12.0000 0.555294 0.277647 0.960683i \(-0.410445\pi\)
0.277647 + 0.960683i \(0.410445\pi\)
\(468\) 0 0
\(469\) 21.0000 0.969690
\(470\) 13.5000 7.79423i 0.622709 0.359521i
\(471\) 0 0
\(472\) 3.00000 5.19615i 0.138086 0.239172i
\(473\) −3.00000 + 1.73205i −0.137940 + 0.0796398i
\(474\) 0 0
\(475\) 3.46410i 0.158944i
\(476\) 5.19615i 0.238165i
\(477\) 0 0
\(478\) −4.50000 + 7.79423i −0.205825 + 0.356500i
\(479\) 21.0000 12.1244i 0.959514 0.553976i 0.0634909 0.997982i \(-0.479777\pi\)
0.896024 + 0.444006i \(0.146443\pi\)
\(480\) 0 0
\(481\) 4.50000 + 18.1865i 0.205182 + 0.829235i
\(482\) 4.50000 + 7.79423i 0.204969 + 0.355017i
\(483\) 0 0
\(484\) −0.500000 0.866025i −0.0227273 0.0393648i
\(485\) −13.5000 23.3827i −0.613003 1.06175i
\(486\) 0 0
\(487\) −7.50000 + 4.33013i −0.339857 + 0.196217i −0.660209 0.751082i \(-0.729532\pi\)
0.320352 + 0.947299i \(0.396199\pi\)
\(488\) 8.66025i 0.392031i
\(489\) 0 0
\(490\) 6.00000 10.3923i 0.271052 0.469476i
\(491\) 3.00000 0.135388 0.0676941 0.997706i \(-0.478436\pi\)
0.0676941 + 0.997706i \(0.478436\pi\)
\(492\) 0 0
\(493\) 9.00000 15.5885i 0.405340 0.702069i
\(494\) 10.5000 2.59808i 0.472417 0.116893i
\(495\) 0 0
\(496\) −37.5000 21.6506i −1.68380 0.972142i
\(497\) −7.50000 12.9904i −0.336421 0.582698i
\(498\) 0 0
\(499\) 22.5000 12.9904i 1.00724 0.581529i 0.0968564 0.995298i \(-0.469121\pi\)
0.910382 + 0.413769i \(0.135788\pi\)
\(500\) 10.5000 + 6.06218i 0.469574 + 0.271109i
\(501\) 0 0
\(502\) 13.5000 + 7.79423i 0.602534 + 0.347873i
\(503\) 10.5000 + 18.1865i 0.468172 + 0.810897i 0.999338 0.0363700i \(-0.0115795\pi\)
−0.531167 + 0.847267i \(0.678246\pi\)
\(504\) 0 0
\(505\) −9.00000 5.19615i −0.400495 0.231226i
\(506\) 9.00000 15.5885i 0.400099 0.692991i
\(507\) 0 0
\(508\) −2.50000 4.33013i −0.110920 0.192118i
\(509\) 1.73205i 0.0767718i −0.999263 0.0383859i \(-0.987778\pi\)
0.999263 0.0383859i \(-0.0122216\pi\)
\(510\) 0 0
\(511\) 12.0000 0.530849
\(512\) 8.66025i 0.382733i
\(513\) 0 0
\(514\) −4.50000 + 2.59808i −0.198486 + 0.114596i
\(515\) 19.5000 + 11.2583i 0.859273 + 0.496101i
\(516\) 0 0
\(517\) 18.0000 0.791639
\(518\) 15.5885i 0.684917i
\(519\) 0 0
\(520\) 3.00000 10.3923i 0.131559 0.455733i
\(521\) −6.00000 −0.262865 −0.131432 0.991325i \(-0.541958\pi\)
−0.131432 + 0.991325i \(0.541958\pi\)
\(522\) 0 0
\(523\) 12.5000 21.6506i 0.546587 0.946716i −0.451918 0.892059i \(-0.649260\pi\)
0.998505 0.0546569i \(-0.0174065\pi\)
\(524\) 15.0000 0.655278
\(525\) 0 0
\(526\) 36.0000 + 20.7846i 1.56967 + 0.906252i
\(527\) −22.5000 12.9904i −0.980115 0.565870i
\(528\) 0 0
\(529\) −14.0000 −0.608696
\(530\) −9.00000 + 15.5885i −0.390935 + 0.677119i
\(531\) 0 0
\(532\) 3.00000 0.130066
\(533\) 31.5000 30.3109i 1.36442 1.31291i
\(534\) 0 0
\(535\) 25.9808i 1.12325i
\(536\) −21.0000 −0.907062
\(537\) 0 0
\(538\) 4.50000 + 2.59808i 0.194009 + 0.112011i
\(539\) 12.0000 6.92820i 0.516877 0.298419i
\(540\) 0 0
\(541\) 13.8564i 0.595733i −0.954607 0.297867i \(-0.903725\pi\)
0.954607 0.297867i \(-0.0962751\pi\)
\(542\) 27.0000 1.15975
\(543\) 0 0
\(544\) 15.5885i 0.668350i
\(545\) 0 0
\(546\) 0 0
\(547\) −8.50000 + 14.7224i −0.363434 + 0.629486i −0.988524 0.151067i \(-0.951729\pi\)
0.625090 + 0.780553i \(0.285062\pi\)
\(548\) −4.50000 2.59808i −0.192230 0.110984i
\(549\) 0 0
\(550\) 6.00000 + 10.3923i 0.255841 + 0.443129i
\(551\) 9.00000 + 5.19615i 0.383413 + 0.221364i
\(552\) 0 0
\(553\) −16.5000 9.52628i −0.701651 0.405099i
\(554\) 34.5000 19.9186i 1.46576 0.846260i
\(555\) 0 0
\(556\) −8.00000 13.8564i −0.339276 0.587643i
\(557\) 16.5000 + 9.52628i 0.699127 + 0.403641i 0.807022 0.590521i \(-0.201078\pi\)
−0.107895 + 0.994162i \(0.534411\pi\)
\(558\) 0 0
\(559\) 2.50000 + 2.59808i 0.105739 + 0.109887i
\(560\) 7.50000 12.9904i 0.316933 0.548944i
\(561\) 0 0
\(562\) −9.00000 −0.379642
\(563\) 12.0000 20.7846i 0.505740 0.875967i −0.494238 0.869326i \(-0.664553\pi\)
0.999978 0.00664037i \(-0.00211371\pi\)
\(564\) 0 0
\(565\) 10.3923i 0.437208i
\(566\) −34.5000 + 19.9186i −1.45014 + 0.837241i
\(567\) 0 0
\(568\) 7.50000 + 12.9904i 0.314693 + 0.545064i
\(569\) −9.00000 15.5885i −0.377300 0.653502i 0.613369 0.789797i \(-0.289814\pi\)
−0.990668 + 0.136295i \(0.956481\pi\)
\(570\) 0 0
\(571\) 2.50000 + 4.33013i 0.104622 + 0.181210i 0.913584 0.406651i \(-0.133303\pi\)
−0.808962 + 0.587861i \(0.799970\pi\)
\(572\) −9.00000 + 8.66025i −0.376309 + 0.362103i
\(573\) 0 0
\(574\) 31.5000 18.1865i 1.31478 0.759091i
\(575\) −3.00000 + 5.19615i −0.125109 + 0.216695i
\(576\) 0 0
\(577\) 6.92820i 0.288425i 0.989547 + 0.144212i \(0.0460649\pi\)
−0.989547 + 0.144212i \(0.953935\pi\)
\(578\) 13.8564i 0.576351i
\(579\) 0 0
\(580\) −9.00000 + 5.19615i −0.373705 + 0.215758i
\(581\) 4.50000 7.79423i 0.186691 0.323359i
\(582\) 0 0
\(583\) −18.0000 + 10.3923i −0.745484 + 0.430405i
\(584\) −12.0000 −0.496564
\(585\) 0 0
\(586\) −24.0000 −0.991431
\(587\) −9.00000 + 5.19615i −0.371470 + 0.214468i −0.674100 0.738640i \(-0.735468\pi\)
0.302631 + 0.953108i \(0.402135\pi\)
\(588\) 0 0
\(589\) 7.50000 12.9904i 0.309032 0.535259i
\(590\) −9.00000 + 5.19615i −0.370524 + 0.213922i
\(591\) 0 0
\(592\) 25.9808i 1.06780i
\(593\) 27.7128i 1.13803i −0.822328 0.569014i \(-0.807325\pi\)
0.822328 0.569014i \(-0.192675\pi\)
\(594\) 0 0
\(595\) 4.50000 7.79423i 0.184482 0.319532i
\(596\) 0 0
\(597\) 0 0
\(598\) −18.0000 5.19615i −0.736075 0.212486i
\(599\) 13.5000 + 23.3827i 0.551595 + 0.955391i 0.998160 + 0.0606393i \(0.0193139\pi\)
−0.446565 + 0.894751i \(0.647353\pi\)
\(600\) 0 0
\(601\) −11.0000 19.0526i −0.448699 0.777170i 0.549602 0.835426i \(-0.314779\pi\)
−0.998302 + 0.0582563i \(0.981446\pi\)
\(602\) 1.50000 + 2.59808i 0.0611354 + 0.105890i
\(603\) 0 0
\(604\) −10.5000 + 6.06218i −0.427239 + 0.246667i
\(605\) 1.73205i 0.0704179i
\(606\) 0 0
\(607\) −4.00000 + 6.92820i −0.162355 + 0.281207i −0.935713 0.352763i \(-0.885242\pi\)
0.773358 + 0.633970i \(0.218576\pi\)
\(608\) −9.00000 −0.364998
\(609\) 0 0
\(610\) −7.50000 + 12.9904i −0.303666 + 0.525965i
\(611\) −4.50000 18.1865i −0.182051 0.735748i
\(612\) 0 0
\(613\) −10.5000 6.06218i −0.424091 0.244849i 0.272735 0.962089i \(-0.412072\pi\)
−0.696826 + 0.717240i \(0.745405\pi\)
\(614\) 21.0000 + 36.3731i 0.847491 + 1.46790i
\(615\) 0 0
\(616\) 9.00000 5.19615i 0.362620 0.209359i
\(617\) 24.0000 + 13.8564i 0.966204 + 0.557838i 0.898077 0.439839i \(-0.144964\pi\)
0.0681269 + 0.997677i \(0.478298\pi\)
\(618\) 0 0
\(619\) −22.5000 12.9904i −0.904351 0.522127i −0.0257420 0.999669i \(-0.508195\pi\)
−0.878609 + 0.477541i \(0.841528\pi\)
\(620\) 7.50000 + 12.9904i 0.301207 + 0.521706i
\(621\) 0 0
\(622\) 40.5000 + 23.3827i 1.62390 + 0.937560i
\(623\) −13.5000 + 23.3827i −0.540866 + 0.936808i
\(624\) 0 0
\(625\) 5.50000 + 9.52628i 0.220000 + 0.381051i
\(626\) 32.9090i 1.31531i
\(627\) 0 0
\(628\) −23.0000 −0.917800
\(629\) 15.5885i 0.621552i
\(630\) 0 0
\(631\) −7.50000 + 4.33013i −0.298570 + 0.172380i −0.641800 0.766872i \(-0.721812\pi\)
0.343230 + 0.939251i \(0.388479\pi\)
\(632\) 16.5000 + 9.52628i 0.656335 + 0.378935i
\(633\) 0 0
\(634\) 15.0000 0.595726
\(635\) 8.66025i 0.343672i
\(636\) 0 0
\(637\) −10.0000 10.3923i −0.396214 0.411758i
\(638\) −36.0000 −1.42525
\(639\) 0 0
\(640\) −10.5000 + 18.1865i −0.415049 + 0.718886i
\(641\) −39.0000 −1.54041 −0.770204 0.637798i \(-0.779845\pi\)
−0.770204 + 0.637798i \(0.779845\pi\)
\(642\) 0 0
\(643\) −3.00000 1.73205i −0.118308 0.0683054i 0.439678 0.898155i \(-0.355093\pi\)
−0.557986 + 0.829850i \(0.688426\pi\)
\(644\) −4.50000 2.59808i −0.177325 0.102379i
\(645\) 0 0
\(646\) −9.00000 −0.354100
\(647\) −4.50000 + 7.79423i −0.176913 + 0.306423i −0.940822 0.338902i \(-0.889945\pi\)
0.763908 + 0.645325i \(0.223278\pi\)
\(648\) 0 0
\(649\) −12.0000 −0.471041
\(650\) 9.00000 8.66025i 0.353009 0.339683i
\(651\) 0 0
\(652\) 12.1244i 0.474826i
\(653\) 45.0000 1.76099 0.880493 0.474059i \(-0.157212\pi\)
0.880493 + 0.474059i \(0.157212\pi\)
\(654\) 0 0
\(655\) 22.5000 + 12.9904i 0.879148 + 0.507576i
\(656\) −52.5000 + 30.3109i −2.04978 + 1.18344i
\(657\) 0 0
\(658\) 15.5885i 0.607701i
\(659\) −39.0000 −1.51922 −0.759612 0.650376i \(-0.774611\pi\)
−0.759612 + 0.650376i \(0.774611\pi\)
\(660\) 0 0
\(661\) 46.7654i 1.81896i −0.415745 0.909481i \(-0.636479\pi\)
0.415745 0.909481i \(-0.363521\pi\)
\(662\) −13.5000 23.3827i −0.524692 0.908794i
\(663\) 0 0
\(664\) −4.50000 + 7.79423i −0.174634 + 0.302475i
\(665\) 4.50000 + 2.59808i 0.174503 + 0.100749i
\(666\) 0 0
\(667\) −9.00000 15.5885i −0.348481 0.603587i
\(668\) −4.50000 2.59808i −0.174110 0.100523i
\(669\) 0 0
\(670\) 31.5000 + 18.1865i 1.21695 + 0.702607i
\(671\) −15.0000 + 8.66025i −0.579069 + 0.334325i
\(672\) 0 0
\(673\) 17.0000 + 29.4449i 0.655302 + 1.13502i 0.981818 + 0.189824i \(0.0607919\pi\)
−0.326516 + 0.945192i \(0.605875\pi\)
\(674\) 43.5000 + 25.1147i 1.67556 + 0.967384i
\(675\) 0 0
\(676\) 11.0000 + 6.92820i 0.423077 + 0.266469i
\(677\) −10.5000 + 18.1865i −0.403548 + 0.698965i −0.994151 0.107997i \(-0.965556\pi\)
0.590603 + 0.806962i \(0.298890\pi\)
\(678\) 0 0
\(679\) −27.0000 −1.03616
\(680\) −4.50000 + 7.79423i −0.172567 + 0.298895i
\(681\) 0 0
\(682\) 51.9615i 1.98971i
\(683\) 19.5000 11.2583i 0.746147 0.430788i −0.0781532 0.996941i \(-0.524902\pi\)
0.824300 + 0.566153i \(0.191569\pi\)
\(684\) 0 0
\(685\) −4.50000 7.79423i −0.171936 0.297802i
\(686\) −16.5000 28.5788i −0.629973 1.09115i
\(687\) 0 0
\(688\) −2.50000 4.33013i −0.0953116 0.165085i
\(689\) 15.0000 + 15.5885i 0.571454 + 0.593873i
\(690\) 0 0
\(691\) −15.0000 + 8.66025i −0.570627 + 0.329452i −0.757400 0.652952i \(-0.773531\pi\)
0.186773 + 0.982403i \(0.440197\pi\)
\(692\) 10.5000 18.1865i 0.399150 0.691348i
\(693\) 0 0
\(694\) 20.7846i 0.788973i
\(695\) 27.7128i 1.05121i
\(696\) 0 0
\(697\) −31.5000 + 18.1865i −1.19315 + 0.688864i
\(698\) −24.0000 + 41.5692i −0.908413 + 1.57342i
\(699\) 0 0
\(700\) 3.00000 1.73205i 0.113389 0.0654654i
\(701\) 30.0000 1.13308 0.566542 0.824033i \(-0.308281\pi\)
0.566542 + 0.824033i \(0.308281\pi\)
\(702\) 0 0
\(703\) 9.00000 0.339441
\(704\) −3.00000 + 1.73205i −0.113067 + 0.0652791i
\(705\) 0 0
\(706\) −6.00000 + 10.3923i −0.225813 + 0.391120i
\(707\) −9.00000 + 5.19615i −0.338480 + 0.195421i
\(708\) 0 0
\(709\) 12.1244i 0.455340i 0.973738 + 0.227670i \(0.0731107\pi\)
−0.973738 + 0.227670i \(0.926889\pi\)
\(710\) 25.9808i 0.975041i
\(711\) 0 0
\(712\) 13.5000 23.3827i 0.505934 0.876303i
\(713\) −22.5000 + 12.9904i −0.842632 + 0.486494i
\(714\) 0 0
\(715\) −21.0000 + 5.19615i −0.785355 + 0.194325i
\(716\) −1.50000 2.59808i −0.0560576 0.0970947i
\(717\) 0 0
\(718\) 9.00000 + 15.5885i 0.335877 + 0.581756i
\(719\) −19.5000 33.7750i −0.727227 1.25959i −0.958051 0.286599i \(-0.907475\pi\)
0.230823 0.972996i \(-0.425858\pi\)
\(720\) 0 0
\(721\) 19.5000 11.2583i 0.726218 0.419282i
\(722\) 27.7128i 1.03136i
\(723\) 0 0
\(724\) −11.0000 + 19.0526i −0.408812 + 0.708083i
\(725\) 12.0000 0.445669
\(726\) 0 0
\(727\) −0.500000 + 0.866025i −0.0185440 + 0.0321191i −0.875148 0.483854i \(-0.839236\pi\)
0.856605 + 0.515974i \(0.172570\pi\)
\(728\) −7.50000 7.79423i −0.277968 0.288873i
\(729\) 0 0
\(730\) 18.0000 + 10.3923i 0.666210 + 0.384636i
\(731\) −1.50000 2.59808i −0.0554795 0.0960933i
\(732\) 0 0
\(733\) 16.5000 9.52628i 0.609441 0.351861i −0.163305 0.986576i \(-0.552216\pi\)
0.772747 + 0.634714i \(0.218882\pi\)
\(734\) −12.0000 6.92820i −0.442928 0.255725i
\(735\) 0 0
\(736\) 13.5000 + 7.79423i 0.497617 + 0.287299i
\(737\) 21.0000 + 36.3731i 0.773545 + 1.33982i
\(738\) 0 0
\(739\) −28.5000 16.4545i −1.04839 0.605288i −0.126191 0.992006i \(-0.540275\pi\)
−0.922198 + 0.386718i \(0.873609\pi\)
\(740\) −4.50000 + 7.79423i −0.165423 + 0.286522i
\(741\) 0 0
\(742\) 9.00000 + 15.5885i 0.330400 + 0.572270i
\(743\) 12.1244i 0.444799i −0.974956 0.222400i \(-0.928611\pi\)
0.974956 0.222400i \(-0.0713890\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 24.2487i 0.887808i
\(747\) 0 0
\(748\) 9.00000 5.19615i 0.329073 0.189990i
\(749\) −22.5000 12.9904i −0.822132 0.474658i
\(750\) 0 0
\(751\) −19.0000 −0.693320 −0.346660 0.937991i \(-0.612684\pi\)
−0.346660 + 0.937991i \(0.612684\pi\)
\(752\) 25.9808i 0.947421i
\(753\) 0 0
\(754\) 9.00000 + 36.3731i 0.327761 + 1.32463i
\(755\) −21.0000 −0.764268
\(756\) 0 0
\(757\) −3.50000 + 6.06218i −0.127210 + 0.220334i −0.922595 0.385771i \(-0.873935\pi\)
0.795385 + 0.606105i \(0.207269\pi\)
\(758\) −21.0000 −0.762754
\(759\) 0 0
\(760\) −4.50000 2.59808i −0.163232 0.0942421i
\(761\) −12.0000 6.92820i −0.435000 0.251147i 0.266475 0.963842i \(-0.414141\pi\)
−0.701474 + 0.712695i \(0.747474\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −1.50000 + 2.59808i −0.0542681 + 0.0939951i
\(765\) 0 0
\(766\) 6.00000 0.216789
\(767\) 3.00000 + 12.1244i 0.108324 + 0.437785i
\(768\) 0 0
\(769\) 22.5167i 0.811972i 0.913879 + 0.405986i \(0.133072\pi\)
−0.913879 + 0.405986i \(0.866928\pi\)
\(770\) −18.0000 −0.648675
\(771\) 0 0
\(772\) −4.50000 2.59808i −0.161959 0.0935068i
\(773\) −25.5000 + 14.7224i −0.917171 + 0.529529i −0.882732 0.469878i \(-0.844298\pi\)
−0.0344397 + 0.999407i \(0.510965\pi\)
\(774\) 0 0
\(775\) 17.3205i 0.622171i
\(776\) 27.0000 0.969244
\(777\) 0 0
\(778\) 5.19615i 0.186291i
\(779\) −10.5000 18.1865i −0.376202 0.651600i
\(780\) 0 0
\(781\) 15.0000 25.9808i 0.536742 0.929665i
\(782\) 13.5000 + 7.79423i 0.482759 + 0.278721i
\(783\) 0 0
\(784\) 10.0000 + 17.3205i 0.357143 + 0.618590i
\(785\) −34.5000 19.9186i −1.23136 0.710925i
\(786\) 0 0
\(787\) 3.00000 + 1.73205i 0.106938 + 0.0617409i 0.552515 0.833503i \(-0.313668\pi\)
−0.445577 + 0.895244i \(0.647001\pi\)
\(788\) −7.50000 + 4.33013i −0.267176 + 0.154254i
\(789\) 0 0
\(790\) −16.5000 28.5788i −0.587044 1.01679i
\(791\) −9.00000 5.19615i −0.320003 0.184754i
\(792\) 0 0
\(793\) 12.5000 + 12.9904i 0.443888 + 0.461302i
\(794\) −22.5000 + 38.9711i −0.798495 + 1.38303i
\(795\) 0 0
\(796\) −13.0000 −0.460773
\(797\) 9.00000 15.5885i 0.318796 0.552171i −0.661441 0.749997i \(-0.730055\pi\)
0.980237 + 0.197826i \(0.0633881\pi\)
\(798\) 0 0
\(799\) 15.5885i 0.551480i
\(800\) −9.00000 + 5.19615i −0.318198 + 0.183712i
\(801\) 0 0
\(802\) −25.5000 44.1673i −0.900436 1.55960i
\(803\) 12.0000 + 20.7846i 0.423471 + 0.733473i
\(804\) 0 0
\(805\) −4.50000 7.79423i −0.158604 0.274710i
\(806\) 52.5000 12.9904i 1.84923 0.457567i
\(807\) 0 0
\(808\) 9.00000 5.19615i 0.316619 0.182800i
\(809\) 13.5000 23.3827i 0.474635 0.822091i −0.524943 0.851137i \(-0.675914\pi\)
0.999578 + 0.0290457i \(0.00924684\pi\)
\(810\) 0 0
\(811\) 51.9615i 1.82462i 0.409505 + 0.912308i \(0.365701\pi\)
−0.409505 + 0.912308i \(0.634299\pi\)
\(812\) 10.3923i 0.364698i
\(813\) 0 0
\(814\) −27.0000 + 15.5885i −0.946350 + 0.546375i
\(815\) 10.5000 18.1865i 0.367799 0.637046i
\(816\) 0 0
\(817\) 1.50000 0.866025i 0.0524784 0.0302984i
\(818\) 12.0000 0.419570
\(819\) 0 0
\(820\) 21.0000 0.733352
\(821\) 24.0000 13.8564i 0.837606 0.483592i −0.0188439 0.999822i \(-0.505999\pi\)
0.856450 + 0.516231i \(0.172665\pi\)
\(822\) 0 0
\(823\) −28.0000 + 48.4974i −0.976019 + 1.69051i −0.299487 + 0.954100i \(0.596815\pi\)
−0.676532 + 0.736413i \(0.736518\pi\)
\(824\) −19.5000 + 11.2583i −0.679315 + 0.392203i
\(825\) 0 0
\(826\) 10.3923i 0.361595i
\(827\) 24.2487i 0.843210i −0.906780 0.421605i \(-0.861467\pi\)
0.906780 0.421605i \(-0.138533\pi\)
\(828\) 0 0
\(829\) 14.5000 25.1147i 0.503606 0.872271i −0.496385 0.868102i \(-0.665340\pi\)
0.999991 0.00416865i \(-0.00132693\pi\)
\(830\) 13.5000 7.79423i 0.468592 0.270542i
\(831\) 0 0
\(832\) 2.50000 + 2.59808i 0.0866719 + 0.0900721i
\(833\) 6.00000 + 10.3923i 0.207888 + 0.360072i
\(834\) 0 0
\(835\) −4.50000 7.79423i −0.155729 0.269730i
\(836\) 3.00000 + 5.19615i 0.103757 + 0.179713i
\(837\) 0 0
\(838\) −13.5000 + 7.79423i −0.466350 + 0.269247i
\(839\) 12.1244i 0.418579i −0.977854 0.209290i \(-0.932885\pi\)
0.977854 0.209290i \(-0.0671151\pi\)
\(840\) 0 0
\(841\) −3.50000 + 6.06218i −0.120690 + 0.209041i
\(842\) −15.0000 −0.516934
\(843\) 0 0
\(844\) 6.50000 11.2583i 0.223739 0.387528i
\(845\) 10.5000 + 19.9186i 0.361211 + 0.685220i
\(846\) 0 0
\(847\) −1.50000 0.866025i −0.0515406 0.0297570i
\(848\) −15.0000 25.9808i −0.515102 0.892183i
\(849\) 0 0
\(850\) −9.00000 + 5.19615i −0.308697 + 0.178227i
\(851\) −13.5000 7.79423i −0.462774 0.267183i
\(852\) 0 0
\(853\) 4.50000 + 2.59808i 0.154077 + 0.0889564i 0.575056 0.818114i \(-0.304980\pi\)
−0.420979 + 0.907070i \(0.638313\pi\)
\(854\) 7.50000 + 12.9904i 0.256645 + 0.444522i
\(855\) 0 0
\(856\) 22.5000 + 12.9904i 0.769034 + 0.444002i
\(857\) 1.50000 2.59808i 0.0512390 0.0887486i −0.839268 0.543718i \(-0.817016\pi\)
0.890507 + 0.454969i \(0.150350\pi\)
\(858\) 0 0
\(859\) 2.50000 + 4.33013i 0.0852989 + 0.147742i 0.905519 0.424307i \(-0.139482\pi\)
−0.820220 + 0.572049i \(0.806149\pi\)
\(860\) 1.73205i 0.0590624i
\(861\) 0 0
\(862\) −39.0000 −1.32835
\(863\) 17.3205i 0.589597i 0.955559 + 0.294798i \(0.0952525\pi\)
−0.955559 + 0.294798i \(0.904747\pi\)
\(864\) 0 0
\(865\) 31.5000 18.1865i 1.07103 0.618361i
\(866\) 7.50000 + 4.33013i 0.254860 + 0.147144i
\(867\) 0 0
\(868\) 15.0000 0.509133
\(869\) 38.1051i 1.29263i
\(870\) 0 0
\(871\) 31.5000 30.3109i 1.06734 1.02705i
\(872\) 0 0
\(873\) 0 0
\(874\) −4.50000 + 7.79423i −0.152215 + 0.263644i
\(875\) 21.0000 0.709930
\(876\) 0 0
\(877\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(878\) −12.0000 6.92820i −0.404980 0.233816i
\(879\) 0 0
\(880\) 30.0000 1.01130
\(881\) −4.50000 + 7.79423i −0.151609 + 0.262594i −0.931819 0.362923i \(-0.881779\pi\)
0.780210 + 0.625517i \(0.215112\pi\)
\(882\) 0 0
\(883\) 40.0000 1.34611 0.673054 0.739594i \(-0.264982\pi\)
0.673054 + 0.739594i \(0.264982\pi\)
\(884\) −7.50000 7.79423i −0.252252 0.262148i
\(885\) 0 0
\(886\) 36.3731i 1.22198i
\(887\) 15.0000 0.503651 0.251825 0.967773i \(-0.418969\pi\)
0.251825 + 0.967773i \(0.418969\pi\)
\(888\) 0 0
\(889\) −7.50000 4.33013i −0.251542 0.145228i
\(890\) −40.5000 + 23.3827i −1.35756 + 0.783789i
\(891\) 0 0
\(892\) 3.46410i 0.115987i
\(893\) −9.00000 −0.301174
\(894\) 0 0
\(895\) 5.19615i 0.173688i
\(896\) 10.5000 + 18.1865i 0.350780 + 0.607569i
\(897\) 0 0
\(898\) −13.5000 + 23.3827i −0.450501 + 0.780290i
\(899\) 45.0000 + 25.9808i 1.50083 + 0.866507i
\(900\) 0 0
\(901\) −9.00000 15.5885i −0.299833 0.519327i
\(902\) 63.0000 + 36.3731i 2.09767 + 1.21109i
\(903\) 0 0
\(904\) 9.00000 + 5.19615i 0.299336 + 0.172821i
\(905\) −33.0000 + 19.0526i −1.09696 + 0.633328i
\(906\) 0 0
\(907\) −2.00000 3.46410i −0.0664089 0.115024i 0.830909 0.556408i \(-0.187821\pi\)
−0.897318 + 0.441384i \(0.854488\pi\)
\(908\) −10.5000 6.06218i −0.348455 0.201180i
\(909\) 0 0
\(910\) 4.50000 + 18.1865i 0.149174 + 0.602878i
\(911\) 22.5000 38.9711i 0.745458 1.29117i −0.204522 0.978862i \(-0.565564\pi\)
0.949980 0.312310i \(-0.101103\pi\)
\(912\) 0 0
\(913\) 18.0000 0.595713
\(914\) 0 0
\(915\) 0 0
\(916\) 8.66025i 0.286143i
\(917\) 22.5000 12.9904i 0.743015 0.428980i
\(918\) 0 0
\(919\) −12.5000 21.6506i −0.412337 0.714189i 0.582808 0.812610i \(-0.301954\pi\)
−0.995145 + 0.0984214i \(0.968621\pi\)
\(920\) 4.50000 + 7.79423i 0.148361 + 0.256968i
\(921\) 0 0
\(922\) 1.50000 + 2.59808i 0.0493999 + 0.0855631i
\(923\) −30.0000 8.66025i −0.987462 0.285056i
\(924\) 0 0
\(925\) 9.00000 5.19615i 0.295918 0.170848i
\(926\) 22.5000 38.9711i 0.739396 1.28067i
\(927\) 0 0
\(928\) 31.1769i 1.02343i
\(929\) 57.1577i 1.87528i 0.347604 + 0.937641i \(0.386995\pi\)
−0.347604 + 0.937641i \(0.613005\pi\)
\(930\) 0 0
\(931\) −6.00000 + 3.46410i −0.196642 + 0.113531i
\(932\) 9.00000 15.5885i 0.294805 0.510617i
\(933\) 0 0
\(934\) 18.0000 10.3923i 0.588978 0.340047i
\(935\) 18.0000 0.588663
\(936\) 0 0
\(937\) −2.00000 −0.0653372 −0.0326686 0.999466i \(-0.510401\pi\)
−0.0326686 + 0.999466i \(0.510401\pi\)
\(938\) 31.5000 18.1865i 1.02851 0.593811i
\(939\) 0 0
\(940\) 4.50000 7.79423i 0.146774 0.254220i
\(941\) 13.5000 7.79423i 0.440087 0.254085i −0.263547 0.964646i \(-0.584893\pi\)
0.703635 + 0.710562i \(0.251559\pi\)
\(942\) 0 0
\(943\) 36.3731i 1.18447i
\(944\) 17.3205i 0.563735i
\(945\) 0 0
\(946\) −3.00000 + 5.19615i −0.0975384 + 0.168941i
\(947\) −33.0000 + 19.0526i −1.07236 + 0.619125i −0.928824 0.370521i \(-0.879179\pi\)
−0.143532 + 0.989646i \(0.545846\pi\)
\(948\) 0 0
\(949\) 18.0000 17.3205i 0.584305 0.562247i
\(950\) −3.00000 5.19615i −0.0973329 0.168585i
\(951\) 0 0
\(952\) 4.50000 + 7.79423i 0.145846 + 0.252612i
\(953\) 13.5000 + 23.3827i 0.437308 + 0.757439i 0.997481 0.0709362i \(-0.0225987\pi\)
−0.560173 + 0.828376i \(0.689265\pi\)
\(954\) 0 0
\(955\) −4.50000 + 2.59808i −0.145617 + 0.0840718i
\(956\) 5.19615i 0.168056i
\(957\) 0 0
\(958\) 21.0000 36.3731i 0.678479 1.17516i
\(959\) −9.00000 −0.290625
\(960\) 0 0
\(961\) 22.0000 38.1051i 0.709677 1.22920i
\(962\) 22.5000 + 23.3827i 0.725429 + 0.753888i
\(963\) 0 0
\(964\) 4.50000 + 2.59808i 0.144935 + 0.0836784i
\(965\) −4.50000 7.79423i −0.144860 0.250905i
\(966\) 0 0
\(967\) 10.5000 6.06218i 0.337657 0.194946i −0.321578 0.946883i \(-0.604213\pi\)
0.659236 + 0.751936i \(0.270880\pi\)
\(968\) 1.50000 + 0.866025i 0.0482118 + 0.0278351i
\(969\) 0 0
\(970\) −40.5000 23.3827i −1.30038 0.750773i
\(971\) −13.5000 23.3827i −0.433236 0.750386i 0.563914 0.825833i \(-0.309295\pi\)
−0.997150 + 0.0754473i \(0.975962\pi\)
\(972\) 0 0
\(973\) −24.0000 13.8564i −0.769405 0.444216i
\(974\) −7.50000 + 12.9904i −0.240316 + 0.416239i
\(975\) 0 0
\(976\) −12.5000 21.6506i −0.400115 0.693020i
\(977\) 25.9808i 0.831198i 0.909548 + 0.415599i \(0.136428\pi\)
−0.909548 + 0.415599i \(0.863572\pi\)
\(978\) 0 0
\(979\) −54.0000 −1.72585
\(980\) 6.92820i 0.221313i
\(981\) 0 0
\(982\) 4.50000 2.59808i 0.143601 0.0829079i
\(983\) 4.50000 + 2.59808i 0.143528 + 0.0828658i 0.570044 0.821614i \(-0.306926\pi\)
−0.426517 + 0.904480i \(0.640259\pi\)
\(984\) 0 0
\(985\) −15.0000 −0.477940
\(986\) 31.1769i 0.992875i
\(987\) 0 0
\(988\) 4.50000 4.33013i 0.143164 0.137760i
\(989\) −3.00000 −0.0953945
\(990\) 0 0
\(991\) 18.5000 32.0429i 0.587672 1.01788i −0.406865 0.913488i \(-0.633378\pi\)
0.994537 0.104389i \(-0.0332887\pi\)
\(992\) −45.0000 −1.42875
\(993\) 0 0
\(994\) −22.5000 12.9904i −0.713657 0.412030i
\(995\) −19.5000 11.2583i −0.618192 0.356913i
\(996\) 0 0
\(997\) 23.0000 0.728417 0.364209 0.931317i \(-0.381339\pi\)
0.364209 + 0.931317i \(0.381339\pi\)
\(998\) 22.5000 38.9711i 0.712225 1.23361i
\(999\) 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 351.2.r.a.316.1 2
3.2 odd 2 117.2.r.a.43.1 yes 2
9.4 even 3 351.2.l.a.199.1 2
9.5 odd 6 117.2.l.a.4.1 2
13.10 even 6 351.2.l.a.127.1 2
39.23 odd 6 117.2.l.a.88.1 yes 2
117.23 odd 6 117.2.r.a.49.1 yes 2
117.49 even 6 inner 351.2.r.a.10.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
117.2.l.a.4.1 2 9.5 odd 6
117.2.l.a.88.1 yes 2 39.23 odd 6
117.2.r.a.43.1 yes 2 3.2 odd 2
117.2.r.a.49.1 yes 2 117.23 odd 6
351.2.l.a.127.1 2 13.10 even 6
351.2.l.a.199.1 2 9.4 even 3
351.2.r.a.10.1 2 117.49 even 6 inner
351.2.r.a.316.1 2 1.1 even 1 trivial