Properties

Label 520.2.q.e.321.1
Level $520$
Weight $2$
Character 520.321
Analytic conductor $4.152$
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] = [520,2,Mod(81,520)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(520, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("520.81");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 520 = 2^{3} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 520.q (of order \(3\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(4.15222090511\)
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: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 321.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 520.321
Dual form 520.2.q.e.81.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.50000 - 2.59808i) q^{3} -1.00000 q^{5} +(-1.50000 - 2.59808i) q^{7} +(-3.00000 - 5.19615i) q^{9} +O(q^{10})\) \(q+(1.50000 - 2.59808i) q^{3} -1.00000 q^{5} +(-1.50000 - 2.59808i) q^{7} +(-3.00000 - 5.19615i) q^{9} +(-2.50000 + 4.33013i) q^{11} +(-1.00000 - 3.46410i) q^{13} +(-1.50000 + 2.59808i) q^{15} +(-1.50000 - 2.59808i) q^{17} +(2.50000 + 4.33013i) q^{19} -9.00000 q^{21} +(1.50000 - 2.59808i) q^{23} +1.00000 q^{25} -9.00000 q^{27} +(2.50000 - 4.33013i) q^{29} +8.00000 q^{31} +(7.50000 + 12.9904i) q^{33} +(1.50000 + 2.59808i) q^{35} +(4.50000 - 7.79423i) q^{37} +(-10.5000 - 2.59808i) q^{39} +(-1.50000 + 2.59808i) q^{41} +(0.500000 + 0.866025i) q^{43} +(3.00000 + 5.19615i) q^{45} -12.0000 q^{47} +(-1.00000 + 1.73205i) q^{49} -9.00000 q^{51} +2.00000 q^{53} +(2.50000 - 4.33013i) q^{55} +15.0000 q^{57} +(2.50000 + 4.33013i) q^{59} +(0.500000 + 0.866025i) q^{61} +(-9.00000 + 15.5885i) q^{63} +(1.00000 + 3.46410i) q^{65} +(7.50000 - 12.9904i) q^{67} +(-4.50000 - 7.79423i) q^{69} +(0.500000 + 0.866025i) q^{71} -10.0000 q^{73} +(1.50000 - 2.59808i) q^{75} +15.0000 q^{77} -4.00000 q^{79} +(-4.50000 + 7.79423i) q^{81} +12.0000 q^{83} +(1.50000 + 2.59808i) q^{85} +(-7.50000 - 12.9904i) q^{87} +(0.500000 - 0.866025i) q^{89} +(-7.50000 + 7.79423i) q^{91} +(12.0000 - 20.7846i) q^{93} +(-2.50000 - 4.33013i) q^{95} +(-3.50000 - 6.06218i) q^{97} +30.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 3 q^{3} - 2 q^{5} - 3 q^{7} - 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 3 q^{3} - 2 q^{5} - 3 q^{7} - 6 q^{9} - 5 q^{11} - 2 q^{13} - 3 q^{15} - 3 q^{17} + 5 q^{19} - 18 q^{21} + 3 q^{23} + 2 q^{25} - 18 q^{27} + 5 q^{29} + 16 q^{31} + 15 q^{33} + 3 q^{35} + 9 q^{37} - 21 q^{39} - 3 q^{41} + q^{43} + 6 q^{45} - 24 q^{47} - 2 q^{49} - 18 q^{51} + 4 q^{53} + 5 q^{55} + 30 q^{57} + 5 q^{59} + q^{61} - 18 q^{63} + 2 q^{65} + 15 q^{67} - 9 q^{69} + q^{71} - 20 q^{73} + 3 q^{75} + 30 q^{77} - 8 q^{79} - 9 q^{81} + 24 q^{83} + 3 q^{85} - 15 q^{87} + q^{89} - 15 q^{91} + 24 q^{93} - 5 q^{95} - 7 q^{97} + 60 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/520\mathbb{Z}\right)^\times\).

\(n\) \(41\) \(261\) \(391\) \(417\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(1\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 1.50000 2.59808i 0.866025 1.50000i 1.00000i \(-0.5\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(4\) 0 0
\(5\) −1.00000 −0.447214
\(6\) 0 0
\(7\) −1.50000 2.59808i −0.566947 0.981981i −0.996866 0.0791130i \(-0.974791\pi\)
0.429919 0.902867i \(-0.358542\pi\)
\(8\) 0 0
\(9\) −3.00000 5.19615i −1.00000 1.73205i
\(10\) 0 0
\(11\) −2.50000 + 4.33013i −0.753778 + 1.30558i 0.192201 + 0.981356i \(0.438437\pi\)
−0.945979 + 0.324227i \(0.894896\pi\)
\(12\) 0 0
\(13\) −1.00000 3.46410i −0.277350 0.960769i
\(14\) 0 0
\(15\) −1.50000 + 2.59808i −0.387298 + 0.670820i
\(16\) 0 0
\(17\) −1.50000 2.59808i −0.363803 0.630126i 0.624780 0.780801i \(-0.285189\pi\)
−0.988583 + 0.150675i \(0.951855\pi\)
\(18\) 0 0
\(19\) 2.50000 + 4.33013i 0.573539 + 0.993399i 0.996199 + 0.0871106i \(0.0277634\pi\)
−0.422659 + 0.906289i \(0.638903\pi\)
\(20\) 0 0
\(21\) −9.00000 −1.96396
\(22\) 0 0
\(23\) 1.50000 2.59808i 0.312772 0.541736i −0.666190 0.745782i \(-0.732076\pi\)
0.978961 + 0.204046i \(0.0654092\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) −9.00000 −1.73205
\(28\) 0 0
\(29\) 2.50000 4.33013i 0.464238 0.804084i −0.534928 0.844897i \(-0.679661\pi\)
0.999167 + 0.0408130i \(0.0129948\pi\)
\(30\) 0 0
\(31\) 8.00000 1.43684 0.718421 0.695608i \(-0.244865\pi\)
0.718421 + 0.695608i \(0.244865\pi\)
\(32\) 0 0
\(33\) 7.50000 + 12.9904i 1.30558 + 2.26134i
\(34\) 0 0
\(35\) 1.50000 + 2.59808i 0.253546 + 0.439155i
\(36\) 0 0
\(37\) 4.50000 7.79423i 0.739795 1.28136i −0.212792 0.977098i \(-0.568256\pi\)
0.952587 0.304266i \(-0.0984111\pi\)
\(38\) 0 0
\(39\) −10.5000 2.59808i −1.68135 0.416025i
\(40\) 0 0
\(41\) −1.50000 + 2.59808i −0.234261 + 0.405751i −0.959058 0.283211i \(-0.908600\pi\)
0.724797 + 0.688963i \(0.241934\pi\)
\(42\) 0 0
\(43\) 0.500000 + 0.866025i 0.0762493 + 0.132068i 0.901629 0.432511i \(-0.142372\pi\)
−0.825380 + 0.564578i \(0.809039\pi\)
\(44\) 0 0
\(45\) 3.00000 + 5.19615i 0.447214 + 0.774597i
\(46\) 0 0
\(47\) −12.0000 −1.75038 −0.875190 0.483779i \(-0.839264\pi\)
−0.875190 + 0.483779i \(0.839264\pi\)
\(48\) 0 0
\(49\) −1.00000 + 1.73205i −0.142857 + 0.247436i
\(50\) 0 0
\(51\) −9.00000 −1.26025
\(52\) 0 0
\(53\) 2.00000 0.274721 0.137361 0.990521i \(-0.456138\pi\)
0.137361 + 0.990521i \(0.456138\pi\)
\(54\) 0 0
\(55\) 2.50000 4.33013i 0.337100 0.583874i
\(56\) 0 0
\(57\) 15.0000 1.98680
\(58\) 0 0
\(59\) 2.50000 + 4.33013i 0.325472 + 0.563735i 0.981608 0.190909i \(-0.0611434\pi\)
−0.656136 + 0.754643i \(0.727810\pi\)
\(60\) 0 0
\(61\) 0.500000 + 0.866025i 0.0640184 + 0.110883i 0.896258 0.443533i \(-0.146275\pi\)
−0.832240 + 0.554416i \(0.812942\pi\)
\(62\) 0 0
\(63\) −9.00000 + 15.5885i −1.13389 + 1.96396i
\(64\) 0 0
\(65\) 1.00000 + 3.46410i 0.124035 + 0.429669i
\(66\) 0 0
\(67\) 7.50000 12.9904i 0.916271 1.58703i 0.111241 0.993793i \(-0.464517\pi\)
0.805030 0.593234i \(-0.202149\pi\)
\(68\) 0 0
\(69\) −4.50000 7.79423i −0.541736 0.938315i
\(70\) 0 0
\(71\) 0.500000 + 0.866025i 0.0593391 + 0.102778i 0.894169 0.447730i \(-0.147767\pi\)
−0.834830 + 0.550508i \(0.814434\pi\)
\(72\) 0 0
\(73\) −10.0000 −1.17041 −0.585206 0.810885i \(-0.698986\pi\)
−0.585206 + 0.810885i \(0.698986\pi\)
\(74\) 0 0
\(75\) 1.50000 2.59808i 0.173205 0.300000i
\(76\) 0 0
\(77\) 15.0000 1.70941
\(78\) 0 0
\(79\) −4.00000 −0.450035 −0.225018 0.974355i \(-0.572244\pi\)
−0.225018 + 0.974355i \(0.572244\pi\)
\(80\) 0 0
\(81\) −4.50000 + 7.79423i −0.500000 + 0.866025i
\(82\) 0 0
\(83\) 12.0000 1.31717 0.658586 0.752506i \(-0.271155\pi\)
0.658586 + 0.752506i \(0.271155\pi\)
\(84\) 0 0
\(85\) 1.50000 + 2.59808i 0.162698 + 0.281801i
\(86\) 0 0
\(87\) −7.50000 12.9904i −0.804084 1.39272i
\(88\) 0 0
\(89\) 0.500000 0.866025i 0.0529999 0.0917985i −0.838308 0.545197i \(-0.816455\pi\)
0.891308 + 0.453398i \(0.149788\pi\)
\(90\) 0 0
\(91\) −7.50000 + 7.79423i −0.786214 + 0.817057i
\(92\) 0 0
\(93\) 12.0000 20.7846i 1.24434 2.15526i
\(94\) 0 0
\(95\) −2.50000 4.33013i −0.256495 0.444262i
\(96\) 0 0
\(97\) −3.50000 6.06218i −0.355371 0.615521i 0.631810 0.775123i \(-0.282312\pi\)
−0.987181 + 0.159602i \(0.948979\pi\)
\(98\) 0 0
\(99\) 30.0000 3.01511
\(100\) 0 0
\(101\) 8.50000 14.7224i 0.845782 1.46494i −0.0391591 0.999233i \(-0.512468\pi\)
0.884941 0.465704i \(-0.154199\pi\)
\(102\) 0 0
\(103\) 8.00000 0.788263 0.394132 0.919054i \(-0.371045\pi\)
0.394132 + 0.919054i \(0.371045\pi\)
\(104\) 0 0
\(105\) 9.00000 0.878310
\(106\) 0 0
\(107\) −6.50000 + 11.2583i −0.628379 + 1.08838i 0.359498 + 0.933146i \(0.382948\pi\)
−0.987877 + 0.155238i \(0.950386\pi\)
\(108\) 0 0
\(109\) 2.00000 0.191565 0.0957826 0.995402i \(-0.469465\pi\)
0.0957826 + 0.995402i \(0.469465\pi\)
\(110\) 0 0
\(111\) −13.5000 23.3827i −1.28136 2.21939i
\(112\) 0 0
\(113\) 10.5000 + 18.1865i 0.987757 + 1.71085i 0.628979 + 0.777422i \(0.283473\pi\)
0.358778 + 0.933423i \(0.383194\pi\)
\(114\) 0 0
\(115\) −1.50000 + 2.59808i −0.139876 + 0.242272i
\(116\) 0 0
\(117\) −15.0000 + 15.5885i −1.38675 + 1.44115i
\(118\) 0 0
\(119\) −4.50000 + 7.79423i −0.412514 + 0.714496i
\(120\) 0 0
\(121\) −7.00000 12.1244i −0.636364 1.10221i
\(122\) 0 0
\(123\) 4.50000 + 7.79423i 0.405751 + 0.702782i
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) −8.50000 + 14.7224i −0.754253 + 1.30640i 0.191492 + 0.981494i \(0.438667\pi\)
−0.945745 + 0.324910i \(0.894666\pi\)
\(128\) 0 0
\(129\) 3.00000 0.264135
\(130\) 0 0
\(131\) 12.0000 1.04844 0.524222 0.851581i \(-0.324356\pi\)
0.524222 + 0.851581i \(0.324356\pi\)
\(132\) 0 0
\(133\) 7.50000 12.9904i 0.650332 1.12641i
\(134\) 0 0
\(135\) 9.00000 0.774597
\(136\) 0 0
\(137\) 8.50000 + 14.7224i 0.726204 + 1.25782i 0.958477 + 0.285171i \(0.0920506\pi\)
−0.232273 + 0.972651i \(0.574616\pi\)
\(138\) 0 0
\(139\) −5.50000 9.52628i −0.466504 0.808008i 0.532764 0.846264i \(-0.321153\pi\)
−0.999268 + 0.0382553i \(0.987820\pi\)
\(140\) 0 0
\(141\) −18.0000 + 31.1769i −1.51587 + 2.62557i
\(142\) 0 0
\(143\) 17.5000 + 4.33013i 1.46342 + 0.362103i
\(144\) 0 0
\(145\) −2.50000 + 4.33013i −0.207614 + 0.359597i
\(146\) 0 0
\(147\) 3.00000 + 5.19615i 0.247436 + 0.428571i
\(148\) 0 0
\(149\) 4.50000 + 7.79423i 0.368654 + 0.638528i 0.989355 0.145519i \(-0.0464853\pi\)
−0.620701 + 0.784047i \(0.713152\pi\)
\(150\) 0 0
\(151\) 16.0000 1.30206 0.651031 0.759051i \(-0.274337\pi\)
0.651031 + 0.759051i \(0.274337\pi\)
\(152\) 0 0
\(153\) −9.00000 + 15.5885i −0.727607 + 1.26025i
\(154\) 0 0
\(155\) −8.00000 −0.642575
\(156\) 0 0
\(157\) −14.0000 −1.11732 −0.558661 0.829396i \(-0.688685\pi\)
−0.558661 + 0.829396i \(0.688685\pi\)
\(158\) 0 0
\(159\) 3.00000 5.19615i 0.237915 0.412082i
\(160\) 0 0
\(161\) −9.00000 −0.709299
\(162\) 0 0
\(163\) 8.50000 + 14.7224i 0.665771 + 1.15315i 0.979076 + 0.203497i \(0.0652307\pi\)
−0.313304 + 0.949653i \(0.601436\pi\)
\(164\) 0 0
\(165\) −7.50000 12.9904i −0.583874 1.01130i
\(166\) 0 0
\(167\) −10.5000 + 18.1865i −0.812514 + 1.40732i 0.0985846 + 0.995129i \(0.468568\pi\)
−0.911099 + 0.412188i \(0.864765\pi\)
\(168\) 0 0
\(169\) −11.0000 + 6.92820i −0.846154 + 0.532939i
\(170\) 0 0
\(171\) 15.0000 25.9808i 1.14708 1.98680i
\(172\) 0 0
\(173\) −3.50000 6.06218i −0.266100 0.460899i 0.701751 0.712422i \(-0.252402\pi\)
−0.967851 + 0.251523i \(0.919068\pi\)
\(174\) 0 0
\(175\) −1.50000 2.59808i −0.113389 0.196396i
\(176\) 0 0
\(177\) 15.0000 1.12747
\(178\) 0 0
\(179\) 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
\(181\) 10.0000 0.743294 0.371647 0.928374i \(-0.378793\pi\)
0.371647 + 0.928374i \(0.378793\pi\)
\(182\) 0 0
\(183\) 3.00000 0.221766
\(184\) 0 0
\(185\) −4.50000 + 7.79423i −0.330847 + 0.573043i
\(186\) 0 0
\(187\) 15.0000 1.09691
\(188\) 0 0
\(189\) 13.5000 + 23.3827i 0.981981 + 1.70084i
\(190\) 0 0
\(191\) −1.50000 2.59808i −0.108536 0.187990i 0.806641 0.591041i \(-0.201283\pi\)
−0.915177 + 0.403051i \(0.867950\pi\)
\(192\) 0 0
\(193\) 10.5000 18.1865i 0.755807 1.30910i −0.189166 0.981945i \(-0.560578\pi\)
0.944972 0.327150i \(-0.106088\pi\)
\(194\) 0 0
\(195\) 10.5000 + 2.59808i 0.751921 + 0.186052i
\(196\) 0 0
\(197\) −1.50000 + 2.59808i −0.106871 + 0.185105i −0.914501 0.404584i \(-0.867416\pi\)
0.807630 + 0.589689i \(0.200750\pi\)
\(198\) 0 0
\(199\) 4.50000 + 7.79423i 0.318997 + 0.552518i 0.980279 0.197619i \(-0.0633208\pi\)
−0.661282 + 0.750137i \(0.729987\pi\)
\(200\) 0 0
\(201\) −22.5000 38.9711i −1.58703 2.74881i
\(202\) 0 0
\(203\) −15.0000 −1.05279
\(204\) 0 0
\(205\) 1.50000 2.59808i 0.104765 0.181458i
\(206\) 0 0
\(207\) −18.0000 −1.25109
\(208\) 0 0
\(209\) −25.0000 −1.72929
\(210\) 0 0
\(211\) 5.50000 9.52628i 0.378636 0.655816i −0.612228 0.790681i \(-0.709727\pi\)
0.990864 + 0.134865i \(0.0430600\pi\)
\(212\) 0 0
\(213\) 3.00000 0.205557
\(214\) 0 0
\(215\) −0.500000 0.866025i −0.0340997 0.0590624i
\(216\) 0 0
\(217\) −12.0000 20.7846i −0.814613 1.41095i
\(218\) 0 0
\(219\) −15.0000 + 25.9808i −1.01361 + 1.75562i
\(220\) 0 0
\(221\) −7.50000 + 7.79423i −0.504505 + 0.524297i
\(222\) 0 0
\(223\) −6.50000 + 11.2583i −0.435272 + 0.753914i −0.997318 0.0731927i \(-0.976681\pi\)
0.562046 + 0.827106i \(0.310015\pi\)
\(224\) 0 0
\(225\) −3.00000 5.19615i −0.200000 0.346410i
\(226\) 0 0
\(227\) 2.50000 + 4.33013i 0.165931 + 0.287401i 0.936985 0.349368i \(-0.113604\pi\)
−0.771055 + 0.636769i \(0.780270\pi\)
\(228\) 0 0
\(229\) −14.0000 −0.925146 −0.462573 0.886581i \(-0.653074\pi\)
−0.462573 + 0.886581i \(0.653074\pi\)
\(230\) 0 0
\(231\) 22.5000 38.9711i 1.48039 2.56411i
\(232\) 0 0
\(233\) −18.0000 −1.17922 −0.589610 0.807688i \(-0.700718\pi\)
−0.589610 + 0.807688i \(0.700718\pi\)
\(234\) 0 0
\(235\) 12.0000 0.782794
\(236\) 0 0
\(237\) −6.00000 + 10.3923i −0.389742 + 0.675053i
\(238\) 0 0
\(239\) −8.00000 −0.517477 −0.258738 0.965947i \(-0.583307\pi\)
−0.258738 + 0.965947i \(0.583307\pi\)
\(240\) 0 0
\(241\) −9.50000 16.4545i −0.611949 1.05993i −0.990912 0.134515i \(-0.957053\pi\)
0.378963 0.925412i \(-0.376281\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 1.00000 1.73205i 0.0638877 0.110657i
\(246\) 0 0
\(247\) 12.5000 12.9904i 0.795356 0.826558i
\(248\) 0 0
\(249\) 18.0000 31.1769i 1.14070 1.97576i
\(250\) 0 0
\(251\) 0.500000 + 0.866025i 0.0315597 + 0.0546630i 0.881374 0.472419i \(-0.156619\pi\)
−0.849814 + 0.527082i \(0.823286\pi\)
\(252\) 0 0
\(253\) 7.50000 + 12.9904i 0.471521 + 0.816698i
\(254\) 0 0
\(255\) 9.00000 0.563602
\(256\) 0 0
\(257\) 6.50000 11.2583i 0.405459 0.702275i −0.588916 0.808194i \(-0.700445\pi\)
0.994375 + 0.105919i \(0.0337784\pi\)
\(258\) 0 0
\(259\) −27.0000 −1.67770
\(260\) 0 0
\(261\) −30.0000 −1.85695
\(262\) 0 0
\(263\) 9.50000 16.4545i 0.585795 1.01463i −0.408981 0.912543i \(-0.634116\pi\)
0.994776 0.102084i \(-0.0325510\pi\)
\(264\) 0 0
\(265\) −2.00000 −0.122859
\(266\) 0 0
\(267\) −1.50000 2.59808i −0.0917985 0.159000i
\(268\) 0 0
\(269\) 2.50000 + 4.33013i 0.152428 + 0.264013i 0.932119 0.362151i \(-0.117958\pi\)
−0.779692 + 0.626164i \(0.784624\pi\)
\(270\) 0 0
\(271\) −6.50000 + 11.2583i −0.394847 + 0.683895i −0.993082 0.117426i \(-0.962536\pi\)
0.598235 + 0.801321i \(0.295869\pi\)
\(272\) 0 0
\(273\) 9.00000 + 31.1769i 0.544705 + 1.88691i
\(274\) 0 0
\(275\) −2.50000 + 4.33013i −0.150756 + 0.261116i
\(276\) 0 0
\(277\) 6.50000 + 11.2583i 0.390547 + 0.676448i 0.992522 0.122068i \(-0.0389525\pi\)
−0.601975 + 0.798515i \(0.705619\pi\)
\(278\) 0 0
\(279\) −24.0000 41.5692i −1.43684 2.48868i
\(280\) 0 0
\(281\) 6.00000 0.357930 0.178965 0.983855i \(-0.442725\pi\)
0.178965 + 0.983855i \(0.442725\pi\)
\(282\) 0 0
\(283\) 5.50000 9.52628i 0.326941 0.566279i −0.654962 0.755662i \(-0.727315\pi\)
0.981903 + 0.189383i \(0.0606488\pi\)
\(284\) 0 0
\(285\) −15.0000 −0.888523
\(286\) 0 0
\(287\) 9.00000 0.531253
\(288\) 0 0
\(289\) 4.00000 6.92820i 0.235294 0.407541i
\(290\) 0 0
\(291\) −21.0000 −1.23104
\(292\) 0 0
\(293\) 4.50000 + 7.79423i 0.262893 + 0.455344i 0.967009 0.254741i \(-0.0819901\pi\)
−0.704117 + 0.710084i \(0.748657\pi\)
\(294\) 0 0
\(295\) −2.50000 4.33013i −0.145556 0.252110i
\(296\) 0 0
\(297\) 22.5000 38.9711i 1.30558 2.26134i
\(298\) 0 0
\(299\) −10.5000 2.59808i −0.607231 0.150251i
\(300\) 0 0
\(301\) 1.50000 2.59808i 0.0864586 0.149751i
\(302\) 0 0
\(303\) −25.5000 44.1673i −1.46494 2.53734i
\(304\) 0 0
\(305\) −0.500000 0.866025i −0.0286299 0.0495885i
\(306\) 0 0
\(307\) −20.0000 −1.14146 −0.570730 0.821138i \(-0.693340\pi\)
−0.570730 + 0.821138i \(0.693340\pi\)
\(308\) 0 0
\(309\) 12.0000 20.7846i 0.682656 1.18240i
\(310\) 0 0
\(311\) −8.00000 −0.453638 −0.226819 0.973937i \(-0.572833\pi\)
−0.226819 + 0.973937i \(0.572833\pi\)
\(312\) 0 0
\(313\) 6.00000 0.339140 0.169570 0.985518i \(-0.445762\pi\)
0.169570 + 0.985518i \(0.445762\pi\)
\(314\) 0 0
\(315\) 9.00000 15.5885i 0.507093 0.878310i
\(316\) 0 0
\(317\) −2.00000 −0.112331 −0.0561656 0.998421i \(-0.517887\pi\)
−0.0561656 + 0.998421i \(0.517887\pi\)
\(318\) 0 0
\(319\) 12.5000 + 21.6506i 0.699866 + 1.21220i
\(320\) 0 0
\(321\) 19.5000 + 33.7750i 1.08838 + 1.88514i
\(322\) 0 0
\(323\) 7.50000 12.9904i 0.417311 0.722804i
\(324\) 0 0
\(325\) −1.00000 3.46410i −0.0554700 0.192154i
\(326\) 0 0
\(327\) 3.00000 5.19615i 0.165900 0.287348i
\(328\) 0 0
\(329\) 18.0000 + 31.1769i 0.992372 + 1.71884i
\(330\) 0 0
\(331\) 12.5000 + 21.6506i 0.687062 + 1.19003i 0.972784 + 0.231714i \(0.0744333\pi\)
−0.285722 + 0.958313i \(0.592233\pi\)
\(332\) 0 0
\(333\) −54.0000 −2.95918
\(334\) 0 0
\(335\) −7.50000 + 12.9904i −0.409769 + 0.709740i
\(336\) 0 0
\(337\) −18.0000 −0.980522 −0.490261 0.871576i \(-0.663099\pi\)
−0.490261 + 0.871576i \(0.663099\pi\)
\(338\) 0 0
\(339\) 63.0000 3.42169
\(340\) 0 0
\(341\) −20.0000 + 34.6410i −1.08306 + 1.87592i
\(342\) 0 0
\(343\) −15.0000 −0.809924
\(344\) 0 0
\(345\) 4.50000 + 7.79423i 0.242272 + 0.419627i
\(346\) 0 0
\(347\) 8.50000 + 14.7224i 0.456304 + 0.790342i 0.998762 0.0497412i \(-0.0158397\pi\)
−0.542458 + 0.840083i \(0.682506\pi\)
\(348\) 0 0
\(349\) −3.50000 + 6.06218i −0.187351 + 0.324501i −0.944366 0.328896i \(-0.893323\pi\)
0.757015 + 0.653397i \(0.226657\pi\)
\(350\) 0 0
\(351\) 9.00000 + 31.1769i 0.480384 + 1.66410i
\(352\) 0 0
\(353\) −7.50000 + 12.9904i −0.399185 + 0.691408i −0.993626 0.112731i \(-0.964040\pi\)
0.594441 + 0.804139i \(0.297373\pi\)
\(354\) 0 0
\(355\) −0.500000 0.866025i −0.0265372 0.0459639i
\(356\) 0 0
\(357\) 13.5000 + 23.3827i 0.714496 + 1.23754i
\(358\) 0 0
\(359\) −24.0000 −1.26667 −0.633336 0.773877i \(-0.718315\pi\)
−0.633336 + 0.773877i \(0.718315\pi\)
\(360\) 0 0
\(361\) −3.00000 + 5.19615i −0.157895 + 0.273482i
\(362\) 0 0
\(363\) −42.0000 −2.20443
\(364\) 0 0
\(365\) 10.0000 0.523424
\(366\) 0 0
\(367\) 1.50000 2.59808i 0.0782994 0.135618i −0.824217 0.566274i \(-0.808384\pi\)
0.902516 + 0.430656i \(0.141718\pi\)
\(368\) 0 0
\(369\) 18.0000 0.937043
\(370\) 0 0
\(371\) −3.00000 5.19615i −0.155752 0.269771i
\(372\) 0 0
\(373\) 6.50000 + 11.2583i 0.336557 + 0.582934i 0.983783 0.179364i \(-0.0574041\pi\)
−0.647225 + 0.762299i \(0.724071\pi\)
\(374\) 0 0
\(375\) −1.50000 + 2.59808i −0.0774597 + 0.134164i
\(376\) 0 0
\(377\) −17.5000 4.33013i −0.901296 0.223013i
\(378\) 0 0
\(379\) −10.5000 + 18.1865i −0.539349 + 0.934179i 0.459590 + 0.888131i \(0.347996\pi\)
−0.998939 + 0.0460485i \(0.985337\pi\)
\(380\) 0 0
\(381\) 25.5000 + 44.1673i 1.30640 + 2.26276i
\(382\) 0 0
\(383\) −9.50000 16.4545i −0.485427 0.840785i 0.514432 0.857531i \(-0.328003\pi\)
−0.999860 + 0.0167461i \(0.994669\pi\)
\(384\) 0 0
\(385\) −15.0000 −0.764471
\(386\) 0 0
\(387\) 3.00000 5.19615i 0.152499 0.264135i
\(388\) 0 0
\(389\) 6.00000 0.304212 0.152106 0.988364i \(-0.451394\pi\)
0.152106 + 0.988364i \(0.451394\pi\)
\(390\) 0 0
\(391\) −9.00000 −0.455150
\(392\) 0 0
\(393\) 18.0000 31.1769i 0.907980 1.57267i
\(394\) 0 0
\(395\) 4.00000 0.201262
\(396\) 0 0
\(397\) −13.5000 23.3827i −0.677546 1.17354i −0.975718 0.219031i \(-0.929710\pi\)
0.298172 0.954512i \(-0.403623\pi\)
\(398\) 0 0
\(399\) −22.5000 38.9711i −1.12641 1.95100i
\(400\) 0 0
\(401\) 14.5000 25.1147i 0.724095 1.25417i −0.235250 0.971935i \(-0.575591\pi\)
0.959345 0.282235i \(-0.0910758\pi\)
\(402\) 0 0
\(403\) −8.00000 27.7128i −0.398508 1.38047i
\(404\) 0 0
\(405\) 4.50000 7.79423i 0.223607 0.387298i
\(406\) 0 0
\(407\) 22.5000 + 38.9711i 1.11528 + 1.93173i
\(408\) 0 0
\(409\) 2.50000 + 4.33013i 0.123617 + 0.214111i 0.921192 0.389109i \(-0.127217\pi\)
−0.797574 + 0.603220i \(0.793884\pi\)
\(410\) 0 0
\(411\) 51.0000 2.51564
\(412\) 0 0
\(413\) 7.50000 12.9904i 0.369051 0.639215i
\(414\) 0 0
\(415\) −12.0000 −0.589057
\(416\) 0 0
\(417\) −33.0000 −1.61602
\(418\) 0 0
\(419\) −0.500000 + 0.866025i −0.0244266 + 0.0423081i −0.877980 0.478697i \(-0.841109\pi\)
0.853554 + 0.521005i \(0.174443\pi\)
\(420\) 0 0
\(421\) 34.0000 1.65706 0.828529 0.559946i \(-0.189178\pi\)
0.828529 + 0.559946i \(0.189178\pi\)
\(422\) 0 0
\(423\) 36.0000 + 62.3538i 1.75038 + 3.03175i
\(424\) 0 0
\(425\) −1.50000 2.59808i −0.0727607 0.126025i
\(426\) 0 0
\(427\) 1.50000 2.59808i 0.0725901 0.125730i
\(428\) 0 0
\(429\) 37.5000 38.9711i 1.81052 1.88154i
\(430\) 0 0
\(431\) −16.5000 + 28.5788i −0.794777 + 1.37659i 0.128204 + 0.991748i \(0.459079\pi\)
−0.922981 + 0.384846i \(0.874254\pi\)
\(432\) 0 0
\(433\) 14.5000 + 25.1147i 0.696826 + 1.20694i 0.969561 + 0.244848i \(0.0787382\pi\)
−0.272736 + 0.962089i \(0.587929\pi\)
\(434\) 0 0
\(435\) 7.50000 + 12.9904i 0.359597 + 0.622841i
\(436\) 0 0
\(437\) 15.0000 0.717547
\(438\) 0 0
\(439\) −4.50000 + 7.79423i −0.214773 + 0.371998i −0.953202 0.302333i \(-0.902235\pi\)
0.738429 + 0.674331i \(0.235568\pi\)
\(440\) 0 0
\(441\) 12.0000 0.571429
\(442\) 0 0
\(443\) −20.0000 −0.950229 −0.475114 0.879924i \(-0.657593\pi\)
−0.475114 + 0.879924i \(0.657593\pi\)
\(444\) 0 0
\(445\) −0.500000 + 0.866025i −0.0237023 + 0.0410535i
\(446\) 0 0
\(447\) 27.0000 1.27706
\(448\) 0 0
\(449\) −9.50000 16.4545i −0.448333 0.776535i 0.549945 0.835201i \(-0.314649\pi\)
−0.998278 + 0.0586659i \(0.981315\pi\)
\(450\) 0 0
\(451\) −7.50000 12.9904i −0.353161 0.611693i
\(452\) 0 0
\(453\) 24.0000 41.5692i 1.12762 1.95309i
\(454\) 0 0
\(455\) 7.50000 7.79423i 0.351605 0.365399i
\(456\) 0 0
\(457\) 0.500000 0.866025i 0.0233890 0.0405110i −0.854094 0.520119i \(-0.825888\pi\)
0.877483 + 0.479608i \(0.159221\pi\)
\(458\) 0 0
\(459\) 13.5000 + 23.3827i 0.630126 + 1.09141i
\(460\) 0 0
\(461\) −9.50000 16.4545i −0.442459 0.766362i 0.555412 0.831575i \(-0.312560\pi\)
−0.997871 + 0.0652135i \(0.979227\pi\)
\(462\) 0 0
\(463\) 8.00000 0.371792 0.185896 0.982569i \(-0.440481\pi\)
0.185896 + 0.982569i \(0.440481\pi\)
\(464\) 0 0
\(465\) −12.0000 + 20.7846i −0.556487 + 0.963863i
\(466\) 0 0
\(467\) −16.0000 −0.740392 −0.370196 0.928954i \(-0.620709\pi\)
−0.370196 + 0.928954i \(0.620709\pi\)
\(468\) 0 0
\(469\) −45.0000 −2.07791
\(470\) 0 0
\(471\) −21.0000 + 36.3731i −0.967629 + 1.67598i
\(472\) 0 0
\(473\) −5.00000 −0.229900
\(474\) 0 0
\(475\) 2.50000 + 4.33013i 0.114708 + 0.198680i
\(476\) 0 0
\(477\) −6.00000 10.3923i −0.274721 0.475831i
\(478\) 0 0
\(479\) 7.50000 12.9904i 0.342684 0.593546i −0.642246 0.766498i \(-0.721997\pi\)
0.984930 + 0.172953i \(0.0553307\pi\)
\(480\) 0 0
\(481\) −31.5000 7.79423i −1.43628 0.355386i
\(482\) 0 0
\(483\) −13.5000 + 23.3827i −0.614271 + 1.06395i
\(484\) 0 0
\(485\) 3.50000 + 6.06218i 0.158927 + 0.275269i
\(486\) 0 0
\(487\) −15.5000 26.8468i −0.702372 1.21654i −0.967632 0.252367i \(-0.918791\pi\)
0.265260 0.964177i \(-0.414542\pi\)
\(488\) 0 0
\(489\) 51.0000 2.30630
\(490\) 0 0
\(491\) 3.50000 6.06218i 0.157953 0.273582i −0.776178 0.630514i \(-0.782844\pi\)
0.934130 + 0.356932i \(0.116177\pi\)
\(492\) 0 0
\(493\) −15.0000 −0.675566
\(494\) 0 0
\(495\) −30.0000 −1.34840
\(496\) 0 0
\(497\) 1.50000 2.59808i 0.0672842 0.116540i
\(498\) 0 0
\(499\) 20.0000 0.895323 0.447661 0.894203i \(-0.352257\pi\)
0.447661 + 0.894203i \(0.352257\pi\)
\(500\) 0 0
\(501\) 31.5000 + 54.5596i 1.40732 + 2.43754i
\(502\) 0 0
\(503\) 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
\(505\) −8.50000 + 14.7224i −0.378245 + 0.655140i
\(506\) 0 0
\(507\) 1.50000 + 38.9711i 0.0666173 + 1.73077i
\(508\) 0 0
\(509\) −7.50000 + 12.9904i −0.332432 + 0.575789i −0.982988 0.183669i \(-0.941202\pi\)
0.650556 + 0.759458i \(0.274536\pi\)
\(510\) 0 0
\(511\) 15.0000 + 25.9808i 0.663561 + 1.14932i
\(512\) 0 0
\(513\) −22.5000 38.9711i −0.993399 1.72062i
\(514\) 0 0
\(515\) −8.00000 −0.352522
\(516\) 0 0
\(517\) 30.0000 51.9615i 1.31940 2.28527i
\(518\) 0 0
\(519\) −21.0000 −0.921798
\(520\) 0 0
\(521\) 30.0000 1.31432 0.657162 0.753749i \(-0.271757\pi\)
0.657162 + 0.753749i \(0.271757\pi\)
\(522\) 0 0
\(523\) 15.5000 26.8468i 0.677768 1.17393i −0.297884 0.954602i \(-0.596281\pi\)
0.975652 0.219326i \(-0.0703858\pi\)
\(524\) 0 0
\(525\) −9.00000 −0.392792
\(526\) 0 0
\(527\) −12.0000 20.7846i −0.522728 0.905392i
\(528\) 0 0
\(529\) 7.00000 + 12.1244i 0.304348 + 0.527146i
\(530\) 0 0
\(531\) 15.0000 25.9808i 0.650945 1.12747i
\(532\) 0 0
\(533\) 10.5000 + 2.59808i 0.454805 + 0.112535i
\(534\) 0 0
\(535\) 6.50000 11.2583i 0.281020 0.486740i
\(536\) 0 0
\(537\) −4.50000 7.79423i −0.194189 0.336346i
\(538\) 0 0
\(539\) −5.00000 8.66025i −0.215365 0.373024i
\(540\) 0 0
\(541\) −2.00000 −0.0859867 −0.0429934 0.999075i \(-0.513689\pi\)
−0.0429934 + 0.999075i \(0.513689\pi\)
\(542\) 0 0
\(543\) 15.0000 25.9808i 0.643712 1.11494i
\(544\) 0 0
\(545\) −2.00000 −0.0856706
\(546\) 0 0
\(547\) 28.0000 1.19719 0.598597 0.801050i \(-0.295725\pi\)
0.598597 + 0.801050i \(0.295725\pi\)
\(548\) 0 0
\(549\) 3.00000 5.19615i 0.128037 0.221766i
\(550\) 0 0
\(551\) 25.0000 1.06504
\(552\) 0 0
\(553\) 6.00000 + 10.3923i 0.255146 + 0.441926i
\(554\) 0 0
\(555\) 13.5000 + 23.3827i 0.573043 + 0.992540i
\(556\) 0 0
\(557\) −1.50000 + 2.59808i −0.0635570 + 0.110084i −0.896053 0.443947i \(-0.853578\pi\)
0.832496 + 0.554031i \(0.186911\pi\)
\(558\) 0 0
\(559\) 2.50000 2.59808i 0.105739 0.109887i
\(560\) 0 0
\(561\) 22.5000 38.9711i 0.949951 1.64536i
\(562\) 0 0
\(563\) −1.50000 2.59808i −0.0632175 0.109496i 0.832684 0.553748i \(-0.186803\pi\)
−0.895902 + 0.444252i \(0.853470\pi\)
\(564\) 0 0
\(565\) −10.5000 18.1865i −0.441738 0.765113i
\(566\) 0 0
\(567\) 27.0000 1.13389
\(568\) 0 0
\(569\) −7.50000 + 12.9904i −0.314416 + 0.544585i −0.979313 0.202350i \(-0.935142\pi\)
0.664897 + 0.746935i \(0.268475\pi\)
\(570\) 0 0
\(571\) 28.0000 1.17176 0.585882 0.810397i \(-0.300748\pi\)
0.585882 + 0.810397i \(0.300748\pi\)
\(572\) 0 0
\(573\) −9.00000 −0.375980
\(574\) 0 0
\(575\) 1.50000 2.59808i 0.0625543 0.108347i
\(576\) 0 0
\(577\) 14.0000 0.582828 0.291414 0.956597i \(-0.405874\pi\)
0.291414 + 0.956597i \(0.405874\pi\)
\(578\) 0 0
\(579\) −31.5000 54.5596i −1.30910 2.26742i
\(580\) 0 0
\(581\) −18.0000 31.1769i −0.746766 1.29344i
\(582\) 0 0
\(583\) −5.00000 + 8.66025i −0.207079 + 0.358671i
\(584\) 0 0
\(585\) 15.0000 15.5885i 0.620174 0.644503i
\(586\) 0 0
\(587\) 19.5000 33.7750i 0.804851 1.39404i −0.111540 0.993760i \(-0.535578\pi\)
0.916392 0.400283i \(-0.131088\pi\)
\(588\) 0 0
\(589\) 20.0000 + 34.6410i 0.824086 + 1.42736i
\(590\) 0 0
\(591\) 4.50000 + 7.79423i 0.185105 + 0.320612i
\(592\) 0 0
\(593\) −10.0000 −0.410651 −0.205325 0.978694i \(-0.565825\pi\)
−0.205325 + 0.978694i \(0.565825\pi\)
\(594\) 0 0
\(595\) 4.50000 7.79423i 0.184482 0.319532i
\(596\) 0 0
\(597\) 27.0000 1.10504
\(598\) 0 0
\(599\) −20.0000 −0.817178 −0.408589 0.912719i \(-0.633979\pi\)
−0.408589 + 0.912719i \(0.633979\pi\)
\(600\) 0 0
\(601\) −17.5000 + 30.3109i −0.713840 + 1.23641i 0.249565 + 0.968358i \(0.419712\pi\)
−0.963405 + 0.268049i \(0.913621\pi\)
\(602\) 0 0
\(603\) −90.0000 −3.66508
\(604\) 0 0
\(605\) 7.00000 + 12.1244i 0.284590 + 0.492925i
\(606\) 0 0
\(607\) 16.5000 + 28.5788i 0.669714 + 1.15998i 0.977984 + 0.208680i \(0.0669168\pi\)
−0.308270 + 0.951299i \(0.599750\pi\)
\(608\) 0 0
\(609\) −22.5000 + 38.9711i −0.911746 + 1.57919i
\(610\) 0 0
\(611\) 12.0000 + 41.5692i 0.485468 + 1.68171i
\(612\) 0 0
\(613\) 0.500000 0.866025i 0.0201948 0.0349784i −0.855751 0.517387i \(-0.826905\pi\)
0.875946 + 0.482409i \(0.160238\pi\)
\(614\) 0 0
\(615\) −4.50000 7.79423i −0.181458 0.314294i
\(616\) 0 0
\(617\) −11.5000 19.9186i −0.462973 0.801892i 0.536135 0.844132i \(-0.319884\pi\)
−0.999107 + 0.0422403i \(0.986550\pi\)
\(618\) 0 0
\(619\) 44.0000 1.76851 0.884255 0.467005i \(-0.154667\pi\)
0.884255 + 0.467005i \(0.154667\pi\)
\(620\) 0 0
\(621\) −13.5000 + 23.3827i −0.541736 + 0.938315i
\(622\) 0 0
\(623\) −3.00000 −0.120192
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) −37.5000 + 64.9519i −1.49761 + 2.59393i
\(628\) 0 0
\(629\) −27.0000 −1.07656
\(630\) 0 0
\(631\) −7.50000 12.9904i −0.298570 0.517139i 0.677239 0.735763i \(-0.263176\pi\)
−0.975809 + 0.218624i \(0.929843\pi\)
\(632\) 0 0
\(633\) −16.5000 28.5788i −0.655816 1.13591i
\(634\) 0 0
\(635\) 8.50000 14.7224i 0.337312 0.584242i
\(636\) 0 0
\(637\) 7.00000 + 1.73205i 0.277350 + 0.0686264i
\(638\) 0 0
\(639\) 3.00000 5.19615i 0.118678 0.205557i
\(640\) 0 0
\(641\) 22.5000 + 38.9711i 0.888697 + 1.53927i 0.841417 + 0.540386i \(0.181722\pi\)
0.0472793 + 0.998882i \(0.484945\pi\)
\(642\) 0 0
\(643\) −3.50000 6.06218i −0.138027 0.239069i 0.788723 0.614749i \(-0.210743\pi\)
−0.926750 + 0.375680i \(0.877409\pi\)
\(644\) 0 0
\(645\) −3.00000 −0.118125
\(646\) 0 0
\(647\) 23.5000 40.7032i 0.923880 1.60021i 0.130528 0.991445i \(-0.458333\pi\)
0.793352 0.608763i \(-0.208334\pi\)
\(648\) 0 0
\(649\) −25.0000 −0.981336
\(650\) 0 0
\(651\) −72.0000 −2.82190
\(652\) 0 0
\(653\) 0.500000 0.866025i 0.0195665 0.0338902i −0.856076 0.516849i \(-0.827105\pi\)
0.875643 + 0.482959i \(0.160438\pi\)
\(654\) 0 0
\(655\) −12.0000 −0.468879
\(656\) 0 0
\(657\) 30.0000 + 51.9615i 1.17041 + 2.02721i
\(658\) 0 0
\(659\) 8.50000 + 14.7224i 0.331113 + 0.573505i 0.982730 0.185043i \(-0.0592425\pi\)
−0.651617 + 0.758548i \(0.725909\pi\)
\(660\) 0 0
\(661\) 12.5000 21.6506i 0.486194 0.842112i −0.513680 0.857982i \(-0.671718\pi\)
0.999874 + 0.0158695i \(0.00505163\pi\)
\(662\) 0 0
\(663\) 9.00000 + 31.1769i 0.349531 + 1.21081i
\(664\) 0 0
\(665\) −7.50000 + 12.9904i −0.290838 + 0.503745i
\(666\) 0 0
\(667\) −7.50000 12.9904i −0.290401 0.502990i
\(668\) 0 0
\(669\) 19.5000 + 33.7750i 0.753914 + 1.30582i
\(670\) 0 0
\(671\) −5.00000 −0.193023
\(672\) 0 0
\(673\) −23.5000 + 40.7032i −0.905858 + 1.56899i −0.0860977 + 0.996287i \(0.527440\pi\)
−0.819761 + 0.572706i \(0.805894\pi\)
\(674\) 0 0
\(675\) −9.00000 −0.346410
\(676\) 0 0
\(677\) 18.0000 0.691796 0.345898 0.938272i \(-0.387574\pi\)
0.345898 + 0.938272i \(0.387574\pi\)
\(678\) 0 0
\(679\) −10.5000 + 18.1865i −0.402953 + 0.697935i
\(680\) 0 0
\(681\) 15.0000 0.574801
\(682\) 0 0
\(683\) 6.50000 + 11.2583i 0.248716 + 0.430788i 0.963170 0.268894i \(-0.0866582\pi\)
−0.714454 + 0.699682i \(0.753325\pi\)
\(684\) 0 0
\(685\) −8.50000 14.7224i −0.324768 0.562515i
\(686\) 0 0
\(687\) −21.0000 + 36.3731i −0.801200 + 1.38772i
\(688\) 0 0
\(689\) −2.00000 6.92820i −0.0761939 0.263944i
\(690\) 0 0
\(691\) −6.50000 + 11.2583i −0.247272 + 0.428287i −0.962768 0.270330i \(-0.912867\pi\)
0.715496 + 0.698617i \(0.246201\pi\)
\(692\) 0 0
\(693\) −45.0000 77.9423i −1.70941 2.96078i
\(694\) 0 0
\(695\) 5.50000 + 9.52628i 0.208627 + 0.361352i
\(696\) 0 0
\(697\) 9.00000 0.340899
\(698\) 0 0
\(699\) −27.0000 + 46.7654i −1.02123 + 1.76883i
\(700\) 0 0
\(701\) 18.0000 0.679851 0.339925 0.940452i \(-0.389598\pi\)
0.339925 + 0.940452i \(0.389598\pi\)
\(702\) 0 0
\(703\) 45.0000 1.69721
\(704\) 0 0
\(705\) 18.0000 31.1769i 0.677919 1.17419i
\(706\) 0 0
\(707\) −51.0000 −1.91805
\(708\) 0 0
\(709\) −17.5000 30.3109i −0.657226 1.13835i −0.981331 0.192328i \(-0.938396\pi\)
0.324104 0.946021i \(-0.394937\pi\)
\(710\) 0 0
\(711\) 12.0000 + 20.7846i 0.450035 + 0.779484i
\(712\) 0 0
\(713\) 12.0000 20.7846i 0.449404 0.778390i
\(714\) 0 0
\(715\) −17.5000 4.33013i −0.654463 0.161938i
\(716\) 0 0
\(717\) −12.0000 + 20.7846i −0.448148 + 0.776215i
\(718\) 0 0
\(719\) −17.5000 30.3109i −0.652640 1.13041i −0.982480 0.186369i \(-0.940328\pi\)
0.329840 0.944037i \(-0.393005\pi\)
\(720\) 0 0
\(721\) −12.0000 20.7846i −0.446903 0.774059i
\(722\) 0 0
\(723\) −57.0000 −2.11985
\(724\) 0 0
\(725\) 2.50000 4.33013i 0.0928477 0.160817i
\(726\) 0 0
\(727\) 24.0000 0.890111 0.445055 0.895503i \(-0.353184\pi\)
0.445055 + 0.895503i \(0.353184\pi\)
\(728\) 0 0
\(729\) −27.0000 −1.00000
\(730\) 0 0
\(731\) 1.50000 2.59808i 0.0554795 0.0960933i
\(732\) 0 0
\(733\) 14.0000 0.517102 0.258551 0.965998i \(-0.416755\pi\)
0.258551 + 0.965998i \(0.416755\pi\)
\(734\) 0 0
\(735\) −3.00000 5.19615i −0.110657 0.191663i
\(736\) 0 0
\(737\) 37.5000 + 64.9519i 1.38133 + 2.39253i
\(738\) 0 0
\(739\) −16.5000 + 28.5788i −0.606962 + 1.05129i 0.384776 + 0.923010i \(0.374279\pi\)
−0.991738 + 0.128279i \(0.959055\pi\)
\(740\) 0 0
\(741\) −15.0000 51.9615i −0.551039 1.90885i
\(742\) 0 0
\(743\) 7.50000 12.9904i 0.275148 0.476571i −0.695024 0.718986i \(-0.744606\pi\)
0.970173 + 0.242415i \(0.0779397\pi\)
\(744\) 0 0
\(745\) −4.50000 7.79423i −0.164867 0.285558i
\(746\) 0 0
\(747\) −36.0000 62.3538i −1.31717 2.28141i
\(748\) 0 0
\(749\) 39.0000 1.42503
\(750\) 0 0
\(751\) 13.5000 23.3827i 0.492622 0.853246i −0.507342 0.861745i \(-0.669372\pi\)
0.999964 + 0.00849853i \(0.00270520\pi\)
\(752\) 0 0
\(753\) 3.00000 0.109326
\(754\) 0 0
\(755\) −16.0000 −0.582300
\(756\) 0 0
\(757\) −3.50000 + 6.06218i −0.127210 + 0.220334i −0.922595 0.385771i \(-0.873935\pi\)
0.795385 + 0.606105i \(0.207269\pi\)
\(758\) 0 0
\(759\) 45.0000 1.63340
\(760\) 0 0
\(761\) 2.50000 + 4.33013i 0.0906249 + 0.156967i 0.907774 0.419459i \(-0.137780\pi\)
−0.817149 + 0.576426i \(0.804447\pi\)
\(762\) 0 0
\(763\) −3.00000 5.19615i −0.108607 0.188113i
\(764\) 0 0
\(765\) 9.00000 15.5885i 0.325396 0.563602i
\(766\) 0 0
\(767\) 12.5000 12.9904i 0.451349 0.469055i
\(768\) 0 0
\(769\) 6.50000 11.2583i 0.234396 0.405986i −0.724701 0.689063i \(-0.758022\pi\)
0.959097 + 0.283078i \(0.0913554\pi\)
\(770\) 0 0
\(771\) −19.5000 33.7750i −0.702275 1.21638i
\(772\) 0 0
\(773\) 18.5000 + 32.0429i 0.665399 + 1.15250i 0.979177 + 0.203008i \(0.0650718\pi\)
−0.313778 + 0.949496i \(0.601595\pi\)
\(774\) 0 0
\(775\) 8.00000 0.287368
\(776\) 0 0
\(777\) −40.5000 + 70.1481i −1.45293 + 2.51655i
\(778\) 0 0
\(779\) −15.0000 −0.537431
\(780\) 0 0
\(781\) −5.00000 −0.178914
\(782\) 0 0
\(783\) −22.5000 + 38.9711i −0.804084 + 1.39272i
\(784\) 0 0
\(785\) 14.0000 0.499681
\(786\) 0 0
\(787\) −15.5000 26.8468i −0.552515 0.956985i −0.998092 0.0617409i \(-0.980335\pi\)
0.445577 0.895244i \(-0.352999\pi\)
\(788\) 0 0
\(789\) −28.5000 49.3634i −1.01463