Properties

Label 80.2.n.b.47.2
Level $80$
Weight $2$
Character 80.47
Analytic conductor $0.639$
Analytic rank $0$
Dimension $4$
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [80,2,Mod(47,80)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(80, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 0, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("80.47");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 80 = 2^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 80.n (of order \(4\), 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: \(0.638803216170\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(i)\)
Coefficient field: \(\Q(\zeta_{12})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 2^{3} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 47.2
Root \(-0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 80.47
Dual form 80.2.n.b.63.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.73205 + 1.73205i) q^{3} +(-1.00000 - 2.00000i) q^{5} +(-1.73205 + 1.73205i) q^{7} +3.00000i q^{9} +O(q^{10})\) \(q+(1.73205 + 1.73205i) q^{3} +(-1.00000 - 2.00000i) q^{5} +(-1.73205 + 1.73205i) q^{7} +3.00000i q^{9} -3.46410i q^{11} +(1.00000 - 1.00000i) q^{13} +(1.73205 - 5.19615i) q^{15} +(1.00000 + 1.00000i) q^{17} -6.92820 q^{19} -6.00000 q^{21} +(1.73205 + 1.73205i) q^{23} +(-3.00000 + 4.00000i) q^{25} -4.00000i q^{29} +3.46410i q^{31} +(6.00000 - 6.00000i) q^{33} +(5.19615 + 1.73205i) q^{35} +(5.00000 + 5.00000i) q^{37} +3.46410 q^{39} +2.00000 q^{41} +(1.73205 + 1.73205i) q^{43} +(6.00000 - 3.00000i) q^{45} +(-1.73205 + 1.73205i) q^{47} +1.00000i q^{49} +3.46410i q^{51} +(-7.00000 + 7.00000i) q^{53} +(-6.92820 + 3.46410i) q^{55} +(-12.0000 - 12.0000i) q^{57} +6.92820 q^{59} +6.00000 q^{61} +(-5.19615 - 5.19615i) q^{63} +(-3.00000 - 1.00000i) q^{65} +(5.19615 - 5.19615i) q^{67} +6.00000i q^{69} -10.3923i q^{71} +(-7.00000 + 7.00000i) q^{73} +(-12.1244 + 1.73205i) q^{75} +(6.00000 + 6.00000i) q^{77} +9.00000 q^{81} +(-12.1244 - 12.1244i) q^{83} +(1.00000 - 3.00000i) q^{85} +(6.92820 - 6.92820i) q^{87} -8.00000i q^{89} +3.46410i q^{91} +(-6.00000 + 6.00000i) q^{93} +(6.92820 + 13.8564i) q^{95} +(-7.00000 - 7.00000i) q^{97} +10.3923 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 4 q^{5}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 4 q^{5} + 4 q^{13} + 4 q^{17} - 24 q^{21} - 12 q^{25} + 24 q^{33} + 20 q^{37} + 8 q^{41} + 24 q^{45} - 28 q^{53} - 48 q^{57} + 24 q^{61} - 12 q^{65} - 28 q^{73} + 24 q^{77} + 36 q^{81} + 4 q^{85} - 24 q^{93} - 28 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/80\mathbb{Z}\right)^\times\).

\(n\) \(17\) \(21\) \(31\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(1\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 1.73205 + 1.73205i 1.00000 + 1.00000i 1.00000 \(0\)
1.00000i \(0.5\pi\)
\(4\) 0 0
\(5\) −1.00000 2.00000i −0.447214 0.894427i
\(6\) 0 0
\(7\) −1.73205 + 1.73205i −0.654654 + 0.654654i −0.954110 0.299456i \(-0.903195\pi\)
0.299456 + 0.954110i \(0.403195\pi\)
\(8\) 0 0
\(9\) 3.00000i 1.00000i
\(10\) 0 0
\(11\) 3.46410i 1.04447i −0.852803 0.522233i \(-0.825099\pi\)
0.852803 0.522233i \(-0.174901\pi\)
\(12\) 0 0
\(13\) 1.00000 1.00000i 0.277350 0.277350i −0.554700 0.832050i \(-0.687167\pi\)
0.832050 + 0.554700i \(0.187167\pi\)
\(14\) 0 0
\(15\) 1.73205 5.19615i 0.447214 1.34164i
\(16\) 0 0
\(17\) 1.00000 + 1.00000i 0.242536 + 0.242536i 0.817898 0.575363i \(-0.195139\pi\)
−0.575363 + 0.817898i \(0.695139\pi\)
\(18\) 0 0
\(19\) −6.92820 −1.58944 −0.794719 0.606977i \(-0.792382\pi\)
−0.794719 + 0.606977i \(0.792382\pi\)
\(20\) 0 0
\(21\) −6.00000 −1.30931
\(22\) 0 0
\(23\) 1.73205 + 1.73205i 0.361158 + 0.361158i 0.864239 0.503081i \(-0.167800\pi\)
−0.503081 + 0.864239i \(0.667800\pi\)
\(24\) 0 0
\(25\) −3.00000 + 4.00000i −0.600000 + 0.800000i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 4.00000i 0.742781i −0.928477 0.371391i \(-0.878881\pi\)
0.928477 0.371391i \(-0.121119\pi\)
\(30\) 0 0
\(31\) 3.46410i 0.622171i 0.950382 + 0.311086i \(0.100693\pi\)
−0.950382 + 0.311086i \(0.899307\pi\)
\(32\) 0 0
\(33\) 6.00000 6.00000i 1.04447 1.04447i
\(34\) 0 0
\(35\) 5.19615 + 1.73205i 0.878310 + 0.292770i
\(36\) 0 0
\(37\) 5.00000 + 5.00000i 0.821995 + 0.821995i 0.986394 0.164399i \(-0.0525685\pi\)
−0.164399 + 0.986394i \(0.552568\pi\)
\(38\) 0 0
\(39\) 3.46410 0.554700
\(40\) 0 0
\(41\) 2.00000 0.312348 0.156174 0.987730i \(-0.450084\pi\)
0.156174 + 0.987730i \(0.450084\pi\)
\(42\) 0 0
\(43\) 1.73205 + 1.73205i 0.264135 + 0.264135i 0.826732 0.562596i \(-0.190197\pi\)
−0.562596 + 0.826732i \(0.690197\pi\)
\(44\) 0 0
\(45\) 6.00000 3.00000i 0.894427 0.447214i
\(46\) 0 0
\(47\) −1.73205 + 1.73205i −0.252646 + 0.252646i −0.822054 0.569409i \(-0.807172\pi\)
0.569409 + 0.822054i \(0.307172\pi\)
\(48\) 0 0
\(49\) 1.00000i 0.142857i
\(50\) 0 0
\(51\) 3.46410i 0.485071i
\(52\) 0 0
\(53\) −7.00000 + 7.00000i −0.961524 + 0.961524i −0.999287 0.0377628i \(-0.987977\pi\)
0.0377628 + 0.999287i \(0.487977\pi\)
\(54\) 0 0
\(55\) −6.92820 + 3.46410i −0.934199 + 0.467099i
\(56\) 0 0
\(57\) −12.0000 12.0000i −1.58944 1.58944i
\(58\) 0 0
\(59\) 6.92820 0.901975 0.450988 0.892530i \(-0.351072\pi\)
0.450988 + 0.892530i \(0.351072\pi\)
\(60\) 0 0
\(61\) 6.00000 0.768221 0.384111 0.923287i \(-0.374508\pi\)
0.384111 + 0.923287i \(0.374508\pi\)
\(62\) 0 0
\(63\) −5.19615 5.19615i −0.654654 0.654654i
\(64\) 0 0
\(65\) −3.00000 1.00000i −0.372104 0.124035i
\(66\) 0 0
\(67\) 5.19615 5.19615i 0.634811 0.634811i −0.314460 0.949271i \(-0.601823\pi\)
0.949271 + 0.314460i \(0.101823\pi\)
\(68\) 0 0
\(69\) 6.00000i 0.722315i
\(70\) 0 0
\(71\) 10.3923i 1.23334i −0.787222 0.616670i \(-0.788481\pi\)
0.787222 0.616670i \(-0.211519\pi\)
\(72\) 0 0
\(73\) −7.00000 + 7.00000i −0.819288 + 0.819288i −0.986005 0.166717i \(-0.946683\pi\)
0.166717 + 0.986005i \(0.446683\pi\)
\(74\) 0 0
\(75\) −12.1244 + 1.73205i −1.40000 + 0.200000i
\(76\) 0 0
\(77\) 6.00000 + 6.00000i 0.683763 + 0.683763i
\(78\) 0 0
\(79\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(80\) 0 0
\(81\) 9.00000 1.00000
\(82\) 0 0
\(83\) −12.1244 12.1244i −1.33082 1.33082i −0.904636 0.426185i \(-0.859857\pi\)
−0.426185 0.904636i \(-0.640143\pi\)
\(84\) 0 0
\(85\) 1.00000 3.00000i 0.108465 0.325396i
\(86\) 0 0
\(87\) 6.92820 6.92820i 0.742781 0.742781i
\(88\) 0 0
\(89\) 8.00000i 0.847998i −0.905663 0.423999i \(-0.860626\pi\)
0.905663 0.423999i \(-0.139374\pi\)
\(90\) 0 0
\(91\) 3.46410i 0.363137i
\(92\) 0 0
\(93\) −6.00000 + 6.00000i −0.622171 + 0.622171i
\(94\) 0 0
\(95\) 6.92820 + 13.8564i 0.710819 + 1.42164i
\(96\) 0 0
\(97\) −7.00000 7.00000i −0.710742 0.710742i 0.255948 0.966691i \(-0.417612\pi\)
−0.966691 + 0.255948i \(0.917612\pi\)
\(98\) 0 0
\(99\) 10.3923 1.04447
\(100\) 0 0
\(101\) −10.0000 −0.995037 −0.497519 0.867453i \(-0.665755\pi\)
−0.497519 + 0.867453i \(0.665755\pi\)
\(102\) 0 0
\(103\) 1.73205 + 1.73205i 0.170664 + 0.170664i 0.787271 0.616607i \(-0.211493\pi\)
−0.616607 + 0.787271i \(0.711493\pi\)
\(104\) 0 0
\(105\) 6.00000 + 12.0000i 0.585540 + 1.17108i
\(106\) 0 0
\(107\) −8.66025 + 8.66025i −0.837218 + 0.837218i −0.988492 0.151274i \(-0.951663\pi\)
0.151274 + 0.988492i \(0.451663\pi\)
\(108\) 0 0
\(109\) 12.0000i 1.14939i −0.818367 0.574696i \(-0.805120\pi\)
0.818367 0.574696i \(-0.194880\pi\)
\(110\) 0 0
\(111\) 17.3205i 1.64399i
\(112\) 0 0
\(113\) 9.00000 9.00000i 0.846649 0.846649i −0.143065 0.989713i \(-0.545696\pi\)
0.989713 + 0.143065i \(0.0456957\pi\)
\(114\) 0 0
\(115\) 1.73205 5.19615i 0.161515 0.484544i
\(116\) 0 0
\(117\) 3.00000 + 3.00000i 0.277350 + 0.277350i
\(118\) 0 0
\(119\) −3.46410 −0.317554
\(120\) 0 0
\(121\) −1.00000 −0.0909091
\(122\) 0 0
\(123\) 3.46410 + 3.46410i 0.312348 + 0.312348i
\(124\) 0 0
\(125\) 11.0000 + 2.00000i 0.983870 + 0.178885i
\(126\) 0 0
\(127\) 12.1244 12.1244i 1.07586 1.07586i 0.0789869 0.996876i \(-0.474831\pi\)
0.996876 0.0789869i \(-0.0251685\pi\)
\(128\) 0 0
\(129\) 6.00000i 0.528271i
\(130\) 0 0
\(131\) 10.3923i 0.907980i 0.891007 + 0.453990i \(0.150000\pi\)
−0.891007 + 0.453990i \(0.850000\pi\)
\(132\) 0 0
\(133\) 12.0000 12.0000i 1.04053 1.04053i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 9.00000 + 9.00000i 0.768922 + 0.768922i 0.977917 0.208995i \(-0.0670192\pi\)
−0.208995 + 0.977917i \(0.567019\pi\)
\(138\) 0 0
\(139\) 6.92820 0.587643 0.293821 0.955860i \(-0.405073\pi\)
0.293821 + 0.955860i \(0.405073\pi\)
\(140\) 0 0
\(141\) −6.00000 −0.505291
\(142\) 0 0
\(143\) −3.46410 3.46410i −0.289683 0.289683i
\(144\) 0 0
\(145\) −8.00000 + 4.00000i −0.664364 + 0.332182i
\(146\) 0 0
\(147\) −1.73205 + 1.73205i −0.142857 + 0.142857i
\(148\) 0 0
\(149\) 4.00000i 0.327693i −0.986486 0.163846i \(-0.947610\pi\)
0.986486 0.163846i \(-0.0523901\pi\)
\(150\) 0 0
\(151\) 10.3923i 0.845714i −0.906196 0.422857i \(-0.861027\pi\)
0.906196 0.422857i \(-0.138973\pi\)
\(152\) 0 0
\(153\) −3.00000 + 3.00000i −0.242536 + 0.242536i
\(154\) 0 0
\(155\) 6.92820 3.46410i 0.556487 0.278243i
\(156\) 0 0
\(157\) −11.0000 11.0000i −0.877896 0.877896i 0.115421 0.993317i \(-0.463178\pi\)
−0.993317 + 0.115421i \(0.963178\pi\)
\(158\) 0 0
\(159\) −24.2487 −1.92305
\(160\) 0 0
\(161\) −6.00000 −0.472866
\(162\) 0 0
\(163\) 1.73205 + 1.73205i 0.135665 + 0.135665i 0.771678 0.636013i \(-0.219418\pi\)
−0.636013 + 0.771678i \(0.719418\pi\)
\(164\) 0 0
\(165\) −18.0000 6.00000i −1.40130 0.467099i
\(166\) 0 0
\(167\) −15.5885 + 15.5885i −1.20627 + 1.20627i −0.234045 + 0.972226i \(0.575196\pi\)
−0.972226 + 0.234045i \(0.924804\pi\)
\(168\) 0 0
\(169\) 11.0000i 0.846154i
\(170\) 0 0
\(171\) 20.7846i 1.58944i
\(172\) 0 0
\(173\) −15.0000 + 15.0000i −1.14043 + 1.14043i −0.152057 + 0.988372i \(0.548590\pi\)
−0.988372 + 0.152057i \(0.951410\pi\)
\(174\) 0 0
\(175\) −1.73205 12.1244i −0.130931 0.916515i
\(176\) 0 0
\(177\) 12.0000 + 12.0000i 0.901975 + 0.901975i
\(178\) 0 0
\(179\) −6.92820 −0.517838 −0.258919 0.965899i \(-0.583366\pi\)
−0.258919 + 0.965899i \(0.583366\pi\)
\(180\) 0 0
\(181\) 6.00000 0.445976 0.222988 0.974821i \(-0.428419\pi\)
0.222988 + 0.974821i \(0.428419\pi\)
\(182\) 0 0
\(183\) 10.3923 + 10.3923i 0.768221 + 0.768221i
\(184\) 0 0
\(185\) 5.00000 15.0000i 0.367607 1.10282i
\(186\) 0 0
\(187\) 3.46410 3.46410i 0.253320 0.253320i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 24.2487i 1.75458i −0.479965 0.877288i \(-0.659351\pi\)
0.479965 0.877288i \(-0.340649\pi\)
\(192\) 0 0
\(193\) 1.00000 1.00000i 0.0719816 0.0719816i −0.670199 0.742181i \(-0.733791\pi\)
0.742181 + 0.670199i \(0.233791\pi\)
\(194\) 0 0
\(195\) −3.46410 6.92820i −0.248069 0.496139i
\(196\) 0 0
\(197\) −3.00000 3.00000i −0.213741 0.213741i 0.592113 0.805855i \(-0.298294\pi\)
−0.805855 + 0.592113i \(0.798294\pi\)
\(198\) 0 0
\(199\) 13.8564 0.982255 0.491127 0.871088i \(-0.336585\pi\)
0.491127 + 0.871088i \(0.336585\pi\)
\(200\) 0 0
\(201\) 18.0000 1.26962
\(202\) 0 0
\(203\) 6.92820 + 6.92820i 0.486265 + 0.486265i
\(204\) 0 0
\(205\) −2.00000 4.00000i −0.139686 0.279372i
\(206\) 0 0
\(207\) −5.19615 + 5.19615i −0.361158 + 0.361158i
\(208\) 0 0
\(209\) 24.0000i 1.66011i
\(210\) 0 0
\(211\) 10.3923i 0.715436i 0.933830 + 0.357718i \(0.116445\pi\)
−0.933830 + 0.357718i \(0.883555\pi\)
\(212\) 0 0
\(213\) 18.0000 18.0000i 1.23334 1.23334i
\(214\) 0 0
\(215\) 1.73205 5.19615i 0.118125 0.354375i
\(216\) 0 0
\(217\) −6.00000 6.00000i −0.407307 0.407307i
\(218\) 0 0
\(219\) −24.2487 −1.63858
\(220\) 0 0
\(221\) 2.00000 0.134535
\(222\) 0 0
\(223\) 15.5885 + 15.5885i 1.04388 + 1.04388i 0.998992 + 0.0448883i \(0.0142932\pi\)
0.0448883 + 0.998992i \(0.485707\pi\)
\(224\) 0 0
\(225\) −12.0000 9.00000i −0.800000 0.600000i
\(226\) 0 0
\(227\) −8.66025 + 8.66025i −0.574801 + 0.574801i −0.933466 0.358665i \(-0.883232\pi\)
0.358665 + 0.933466i \(0.383232\pi\)
\(228\) 0 0
\(229\) 20.0000i 1.32164i 0.750546 + 0.660819i \(0.229791\pi\)
−0.750546 + 0.660819i \(0.770209\pi\)
\(230\) 0 0
\(231\) 20.7846i 1.36753i
\(232\) 0 0
\(233\) 1.00000 1.00000i 0.0655122 0.0655122i −0.673592 0.739104i \(-0.735249\pi\)
0.739104 + 0.673592i \(0.235249\pi\)
\(234\) 0 0
\(235\) 5.19615 + 1.73205i 0.338960 + 0.112987i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 27.7128 1.79259 0.896296 0.443455i \(-0.146248\pi\)
0.896296 + 0.443455i \(0.146248\pi\)
\(240\) 0 0
\(241\) −22.0000 −1.41714 −0.708572 0.705638i \(-0.750660\pi\)
−0.708572 + 0.705638i \(0.750660\pi\)
\(242\) 0 0
\(243\) 15.5885 + 15.5885i 1.00000 + 1.00000i
\(244\) 0 0
\(245\) 2.00000 1.00000i 0.127775 0.0638877i
\(246\) 0 0
\(247\) −6.92820 + 6.92820i −0.440831 + 0.440831i
\(248\) 0 0
\(249\) 42.0000i 2.66164i
\(250\) 0 0
\(251\) 3.46410i 0.218652i −0.994006 0.109326i \(-0.965131\pi\)
0.994006 0.109326i \(-0.0348693\pi\)
\(252\) 0 0
\(253\) 6.00000 6.00000i 0.377217 0.377217i
\(254\) 0 0
\(255\) 6.92820 3.46410i 0.433861 0.216930i
\(256\) 0 0
\(257\) 9.00000 + 9.00000i 0.561405 + 0.561405i 0.929706 0.368302i \(-0.120061\pi\)
−0.368302 + 0.929706i \(0.620061\pi\)
\(258\) 0 0
\(259\) −17.3205 −1.07624
\(260\) 0 0
\(261\) 12.0000 0.742781
\(262\) 0 0
\(263\) −12.1244 12.1244i −0.747620 0.747620i 0.226412 0.974032i \(-0.427300\pi\)
−0.974032 + 0.226412i \(0.927300\pi\)
\(264\) 0 0
\(265\) 21.0000 + 7.00000i 1.29002 + 0.430007i
\(266\) 0 0
\(267\) 13.8564 13.8564i 0.847998 0.847998i
\(268\) 0 0
\(269\) 4.00000i 0.243884i 0.992537 + 0.121942i \(0.0389122\pi\)
−0.992537 + 0.121942i \(0.961088\pi\)
\(270\) 0 0
\(271\) 3.46410i 0.210429i 0.994450 + 0.105215i \(0.0335529\pi\)
−0.994450 + 0.105215i \(0.966447\pi\)
\(272\) 0 0
\(273\) −6.00000 + 6.00000i −0.363137 + 0.363137i
\(274\) 0 0
\(275\) 13.8564 + 10.3923i 0.835573 + 0.626680i
\(276\) 0 0
\(277\) 13.0000 + 13.0000i 0.781094 + 0.781094i 0.980015 0.198921i \(-0.0637438\pi\)
−0.198921 + 0.980015i \(0.563744\pi\)
\(278\) 0 0
\(279\) −10.3923 −0.622171
\(280\) 0 0
\(281\) −14.0000 −0.835170 −0.417585 0.908638i \(-0.637123\pi\)
−0.417585 + 0.908638i \(0.637123\pi\)
\(282\) 0 0
\(283\) −12.1244 12.1244i −0.720718 0.720718i 0.248033 0.968751i \(-0.420216\pi\)
−0.968751 + 0.248033i \(0.920216\pi\)
\(284\) 0 0
\(285\) −12.0000 + 36.0000i −0.710819 + 2.13246i
\(286\) 0 0
\(287\) −3.46410 + 3.46410i −0.204479 + 0.204479i
\(288\) 0 0
\(289\) 15.0000i 0.882353i
\(290\) 0 0
\(291\) 24.2487i 1.42148i
\(292\) 0 0
\(293\) 9.00000 9.00000i 0.525786 0.525786i −0.393527 0.919313i \(-0.628745\pi\)
0.919313 + 0.393527i \(0.128745\pi\)
\(294\) 0 0
\(295\) −6.92820 13.8564i −0.403376 0.806751i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 3.46410 0.200334
\(300\) 0 0
\(301\) −6.00000 −0.345834
\(302\) 0 0
\(303\) −17.3205 17.3205i −0.995037 0.995037i
\(304\) 0 0
\(305\) −6.00000 12.0000i −0.343559 0.687118i
\(306\) 0 0
\(307\) 5.19615 5.19615i 0.296560 0.296560i −0.543105 0.839665i \(-0.682751\pi\)
0.839665 + 0.543105i \(0.182751\pi\)
\(308\) 0 0
\(309\) 6.00000i 0.341328i
\(310\) 0 0
\(311\) 17.3205i 0.982156i 0.871116 + 0.491078i \(0.163397\pi\)
−0.871116 + 0.491078i \(0.836603\pi\)
\(312\) 0 0
\(313\) −7.00000 + 7.00000i −0.395663 + 0.395663i −0.876700 0.481037i \(-0.840260\pi\)
0.481037 + 0.876700i \(0.340260\pi\)
\(314\) 0 0
\(315\) −5.19615 + 15.5885i −0.292770 + 0.878310i
\(316\) 0 0
\(317\) −19.0000 19.0000i −1.06715 1.06715i −0.997577 0.0695692i \(-0.977838\pi\)
−0.0695692 0.997577i \(-0.522162\pi\)
\(318\) 0 0
\(319\) −13.8564 −0.775810
\(320\) 0 0
\(321\) −30.0000 −1.67444
\(322\) 0 0
\(323\) −6.92820 6.92820i −0.385496 0.385496i
\(324\) 0 0
\(325\) 1.00000 + 7.00000i 0.0554700 + 0.388290i
\(326\) 0 0
\(327\) 20.7846 20.7846i 1.14939 1.14939i
\(328\) 0 0
\(329\) 6.00000i 0.330791i
\(330\) 0 0
\(331\) 24.2487i 1.33283i 0.745581 + 0.666415i \(0.232172\pi\)
−0.745581 + 0.666415i \(0.767828\pi\)
\(332\) 0 0
\(333\) −15.0000 + 15.0000i −0.821995 + 0.821995i
\(334\) 0 0
\(335\) −15.5885 5.19615i −0.851688 0.283896i
\(336\) 0 0
\(337\) 1.00000 + 1.00000i 0.0544735 + 0.0544735i 0.733819 0.679345i \(-0.237736\pi\)
−0.679345 + 0.733819i \(0.737736\pi\)
\(338\) 0 0
\(339\) 31.1769 1.69330
\(340\) 0 0
\(341\) 12.0000 0.649836
\(342\) 0 0
\(343\) −13.8564 13.8564i −0.748176 0.748176i
\(344\) 0 0
\(345\) 12.0000 6.00000i 0.646058 0.323029i
\(346\) 0 0
\(347\) 5.19615 5.19615i 0.278944 0.278944i −0.553743 0.832687i \(-0.686801\pi\)
0.832687 + 0.553743i \(0.186801\pi\)
\(348\) 0 0
\(349\) 12.0000i 0.642345i 0.947021 + 0.321173i \(0.104077\pi\)
−0.947021 + 0.321173i \(0.895923\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 1.00000 1.00000i 0.0532246 0.0532246i −0.679994 0.733218i \(-0.738017\pi\)
0.733218 + 0.679994i \(0.238017\pi\)
\(354\) 0 0
\(355\) −20.7846 + 10.3923i −1.10313 + 0.551566i
\(356\) 0 0
\(357\) −6.00000 6.00000i −0.317554 0.317554i
\(358\) 0 0
\(359\) 13.8564 0.731313 0.365657 0.930750i \(-0.380844\pi\)
0.365657 + 0.930750i \(0.380844\pi\)
\(360\) 0 0
\(361\) 29.0000 1.52632
\(362\) 0 0
\(363\) −1.73205 1.73205i −0.0909091 0.0909091i
\(364\) 0 0
\(365\) 21.0000 + 7.00000i 1.09919 + 0.366397i
\(366\) 0 0
\(367\) −15.5885 + 15.5885i −0.813711 + 0.813711i −0.985188 0.171477i \(-0.945146\pi\)
0.171477 + 0.985188i \(0.445146\pi\)
\(368\) 0 0
\(369\) 6.00000i 0.312348i
\(370\) 0 0
\(371\) 24.2487i 1.25893i
\(372\) 0 0
\(373\) 1.00000 1.00000i 0.0517780 0.0517780i −0.680744 0.732522i \(-0.738343\pi\)
0.732522 + 0.680744i \(0.238343\pi\)
\(374\) 0 0
\(375\) 15.5885 + 22.5167i 0.804984 + 1.16276i
\(376\) 0 0
\(377\) −4.00000 4.00000i −0.206010 0.206010i
\(378\) 0 0
\(379\) 6.92820 0.355878 0.177939 0.984042i \(-0.443057\pi\)
0.177939 + 0.984042i \(0.443057\pi\)
\(380\) 0 0
\(381\) 42.0000 2.15173
\(382\) 0 0
\(383\) 15.5885 + 15.5885i 0.796533 + 0.796533i 0.982547 0.186014i \(-0.0595570\pi\)
−0.186014 + 0.982547i \(0.559557\pi\)
\(384\) 0 0
\(385\) 6.00000 18.0000i 0.305788 0.917365i
\(386\) 0 0
\(387\) −5.19615 + 5.19615i −0.264135 + 0.264135i
\(388\) 0 0
\(389\) 20.0000i 1.01404i −0.861934 0.507020i \(-0.830747\pi\)
0.861934 0.507020i \(-0.169253\pi\)
\(390\) 0 0
\(391\) 3.46410i 0.175187i
\(392\) 0 0
\(393\) −18.0000 + 18.0000i −0.907980 + 0.907980i
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −11.0000 11.0000i −0.552074 0.552074i 0.374965 0.927039i \(-0.377655\pi\)
−0.927039 + 0.374965i \(0.877655\pi\)
\(398\) 0 0
\(399\) 41.5692 2.08106
\(400\) 0 0
\(401\) 2.00000 0.0998752 0.0499376 0.998752i \(-0.484098\pi\)
0.0499376 + 0.998752i \(0.484098\pi\)
\(402\) 0 0
\(403\) 3.46410 + 3.46410i 0.172559 + 0.172559i
\(404\) 0 0
\(405\) −9.00000 18.0000i −0.447214 0.894427i
\(406\) 0 0
\(407\) 17.3205 17.3205i 0.858546 0.858546i
\(408\) 0 0
\(409\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(410\) 0 0
\(411\) 31.1769i 1.53784i
\(412\) 0 0
\(413\) −12.0000 + 12.0000i −0.590481 + 0.590481i
\(414\) 0 0
\(415\) −12.1244 + 36.3731i −0.595161 + 1.78548i
\(416\) 0 0
\(417\) 12.0000 + 12.0000i 0.587643 + 0.587643i
\(418\) 0 0
\(419\) −6.92820 −0.338465 −0.169232 0.985576i \(-0.554129\pi\)
−0.169232 + 0.985576i \(0.554129\pi\)
\(420\) 0 0
\(421\) −2.00000 −0.0974740 −0.0487370 0.998812i \(-0.515520\pi\)
−0.0487370 + 0.998812i \(0.515520\pi\)
\(422\) 0 0
\(423\) −5.19615 5.19615i −0.252646 0.252646i
\(424\) 0 0
\(425\) −7.00000 + 1.00000i −0.339550 + 0.0485071i
\(426\) 0 0
\(427\) −10.3923 + 10.3923i −0.502919 + 0.502919i
\(428\) 0 0
\(429\) 12.0000i 0.579365i
\(430\) 0 0
\(431\) 3.46410i 0.166860i 0.996514 + 0.0834300i \(0.0265875\pi\)
−0.996514 + 0.0834300i \(0.973413\pi\)
\(432\) 0 0
\(433\) −7.00000 + 7.00000i −0.336399 + 0.336399i −0.855010 0.518611i \(-0.826449\pi\)
0.518611 + 0.855010i \(0.326449\pi\)
\(434\) 0 0
\(435\) −20.7846 6.92820i −0.996546 0.332182i
\(436\) 0 0
\(437\) −12.0000 12.0000i −0.574038 0.574038i
\(438\) 0 0
\(439\) −13.8564 −0.661330 −0.330665 0.943748i \(-0.607273\pi\)
−0.330665 + 0.943748i \(0.607273\pi\)
\(440\) 0 0
\(441\) −3.00000 −0.142857
\(442\) 0 0
\(443\) −12.1244 12.1244i −0.576046 0.576046i 0.357766 0.933811i \(-0.383539\pi\)
−0.933811 + 0.357766i \(0.883539\pi\)
\(444\) 0 0
\(445\) −16.0000 + 8.00000i −0.758473 + 0.379236i
\(446\) 0 0
\(447\) 6.92820 6.92820i 0.327693 0.327693i
\(448\) 0 0
\(449\) 8.00000i 0.377543i 0.982021 + 0.188772i \(0.0604506\pi\)
−0.982021 + 0.188772i \(0.939549\pi\)
\(450\) 0 0
\(451\) 6.92820i 0.326236i
\(452\) 0 0
\(453\) 18.0000 18.0000i 0.845714 0.845714i
\(454\) 0 0
\(455\) 6.92820 3.46410i 0.324799 0.162400i
\(456\) 0 0
\(457\) 17.0000 + 17.0000i 0.795226 + 0.795226i 0.982339 0.187112i \(-0.0599128\pi\)
−0.187112 + 0.982339i \(0.559913\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −2.00000 −0.0931493 −0.0465746 0.998915i \(-0.514831\pi\)
−0.0465746 + 0.998915i \(0.514831\pi\)
\(462\) 0 0
\(463\) 1.73205 + 1.73205i 0.0804952 + 0.0804952i 0.746208 0.665713i \(-0.231872\pi\)
−0.665713 + 0.746208i \(0.731872\pi\)
\(464\) 0 0
\(465\) 18.0000 + 6.00000i 0.834730 + 0.278243i
\(466\) 0 0
\(467\) 19.0526 19.0526i 0.881647 0.881647i −0.112055 0.993702i \(-0.535743\pi\)
0.993702 + 0.112055i \(0.0357432\pi\)
\(468\) 0 0
\(469\) 18.0000i 0.831163i
\(470\) 0 0
\(471\) 38.1051i 1.75579i
\(472\) 0 0
\(473\) 6.00000 6.00000i 0.275880 0.275880i
\(474\) 0 0
\(475\) 20.7846 27.7128i 0.953663 1.27155i
\(476\) 0 0
\(477\) −21.0000 21.0000i −0.961524 0.961524i
\(478\) 0 0
\(479\) −27.7128 −1.26623 −0.633115 0.774057i \(-0.718224\pi\)
−0.633115 + 0.774057i \(0.718224\pi\)
\(480\) 0 0
\(481\) 10.0000 0.455961
\(482\) 0 0
\(483\) −10.3923 10.3923i −0.472866 0.472866i
\(484\) 0 0
\(485\) −7.00000 + 21.0000i −0.317854 + 0.953561i
\(486\) 0 0
\(487\) −1.73205 + 1.73205i −0.0784867 + 0.0784867i −0.745260 0.666774i \(-0.767675\pi\)
0.666774 + 0.745260i \(0.267675\pi\)
\(488\) 0 0
\(489\) 6.00000i 0.271329i
\(490\) 0 0
\(491\) 24.2487i 1.09433i 0.837025 + 0.547165i \(0.184293\pi\)
−0.837025 + 0.547165i \(0.815707\pi\)
\(492\) 0 0
\(493\) 4.00000 4.00000i 0.180151 0.180151i
\(494\) 0 0
\(495\) −10.3923 20.7846i −0.467099 0.934199i
\(496\) 0 0
\(497\) 18.0000 + 18.0000i 0.807410 + 0.807410i
\(498\) 0 0
\(499\) 20.7846 0.930447 0.465223 0.885193i \(-0.345974\pi\)
0.465223 + 0.885193i \(0.345974\pi\)
\(500\) 0 0
\(501\) −54.0000 −2.41254
\(502\) 0 0
\(503\) 1.73205 + 1.73205i 0.0772283 + 0.0772283i 0.744666 0.667437i \(-0.232609\pi\)
−0.667437 + 0.744666i \(0.732609\pi\)
\(504\) 0 0
\(505\) 10.0000 + 20.0000i 0.444994 + 0.889988i
\(506\) 0 0
\(507\) −19.0526 + 19.0526i −0.846154 + 0.846154i
\(508\) 0 0
\(509\) 20.0000i 0.886484i −0.896402 0.443242i \(-0.853828\pi\)
0.896402 0.443242i \(-0.146172\pi\)
\(510\) 0 0
\(511\) 24.2487i 1.07270i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 1.73205 5.19615i 0.0763233 0.228970i
\(516\) 0 0
\(517\) 6.00000 + 6.00000i 0.263880 + 0.263880i
\(518\) 0 0
\(519\) −51.9615 −2.28086
\(520\) 0 0
\(521\) −38.0000 −1.66481 −0.832405 0.554168i \(-0.813037\pi\)
−0.832405 + 0.554168i \(0.813037\pi\)
\(522\) 0 0
\(523\) −12.1244 12.1244i −0.530161 0.530161i 0.390459 0.920620i \(-0.372316\pi\)
−0.920620 + 0.390459i \(0.872316\pi\)
\(524\) 0 0
\(525\) 18.0000 24.0000i 0.785584 1.04745i
\(526\) 0 0
\(527\) −3.46410 + 3.46410i −0.150899 + 0.150899i
\(528\) 0 0
\(529\) 17.0000i 0.739130i
\(530\) 0 0
\(531\) 20.7846i 0.901975i
\(532\) 0 0
\(533\) 2.00000 2.00000i 0.0866296 0.0866296i
\(534\) 0 0
\(535\) 25.9808 + 8.66025i 1.12325 + 0.374415i
\(536\) 0 0
\(537\) −12.0000 12.0000i −0.517838 0.517838i
\(538\) 0 0
\(539\) 3.46410 0.149209
\(540\) 0 0
\(541\) −18.0000 −0.773880 −0.386940 0.922105i \(-0.626468\pi\)
−0.386940 + 0.922105i \(0.626468\pi\)
\(542\) 0 0
\(543\) 10.3923 + 10.3923i 0.445976 + 0.445976i
\(544\) 0 0
\(545\) −24.0000 + 12.0000i −1.02805 + 0.514024i
\(546\) 0 0
\(547\) −8.66025 + 8.66025i −0.370286 + 0.370286i −0.867581 0.497296i \(-0.834326\pi\)
0.497296 + 0.867581i \(0.334326\pi\)
\(548\) 0 0
\(549\) 18.0000i 0.768221i
\(550\) 0 0
\(551\) 27.7128i 1.18061i
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 34.6410 17.3205i 1.47043 0.735215i
\(556\) 0 0
\(557\) 29.0000 + 29.0000i 1.22877 + 1.22877i 0.964430 + 0.264340i \(0.0851541\pi\)
0.264340 + 0.964430i \(0.414846\pi\)
\(558\) 0 0
\(559\) 3.46410 0.146516
\(560\) 0 0
\(561\) 12.0000 0.506640
\(562\) 0 0
\(563\) 29.4449 + 29.4449i 1.24095 + 1.24095i 0.959606 + 0.281347i \(0.0907812\pi\)
0.281347 + 0.959606i \(0.409219\pi\)
\(564\) 0 0
\(565\) −27.0000 9.00000i −1.13590 0.378633i
\(566\) 0 0
\(567\) −15.5885 + 15.5885i −0.654654 + 0.654654i
\(568\) 0 0
\(569\) 16.0000i 0.670755i 0.942084 + 0.335377i \(0.108864\pi\)
−0.942084 + 0.335377i \(0.891136\pi\)
\(570\) 0 0
\(571\) 31.1769i 1.30471i −0.757912 0.652357i \(-0.773780\pi\)
0.757912 0.652357i \(-0.226220\pi\)
\(572\) 0 0
\(573\) 42.0000 42.0000i 1.75458 1.75458i
\(574\) 0 0
\(575\) −12.1244 + 1.73205i −0.505621 + 0.0722315i
\(576\) 0 0
\(577\) −7.00000 7.00000i −0.291414 0.291414i 0.546225 0.837639i \(-0.316064\pi\)
−0.837639 + 0.546225i \(0.816064\pi\)
\(578\) 0 0
\(579\) 3.46410 0.143963
\(580\) 0 0
\(581\) 42.0000 1.74245
\(582\) 0 0
\(583\) 24.2487 + 24.2487i 1.00428 + 1.00428i
\(584\) 0 0
\(585\) 3.00000 9.00000i 0.124035 0.372104i
\(586\) 0 0
\(587\) 5.19615 5.19615i 0.214468 0.214468i −0.591694 0.806162i \(-0.701541\pi\)
0.806162 + 0.591694i \(0.201541\pi\)
\(588\) 0 0
\(589\) 24.0000i 0.988903i
\(590\) 0 0
\(591\) 10.3923i 0.427482i
\(592\) 0 0
\(593\) 33.0000 33.0000i 1.35515 1.35515i 0.475352 0.879796i \(-0.342321\pi\)
0.879796 0.475352i \(-0.157679\pi\)
\(594\) 0 0
\(595\) 3.46410 + 6.92820i 0.142014 + 0.284029i
\(596\) 0 0
\(597\) 24.0000 + 24.0000i 0.982255 + 0.982255i
\(598\) 0 0
\(599\) −13.8564 −0.566157 −0.283079 0.959097i \(-0.591356\pi\)
−0.283079 + 0.959097i \(0.591356\pi\)
\(600\) 0 0
\(601\) 18.0000 0.734235 0.367118 0.930175i \(-0.380345\pi\)
0.367118 + 0.930175i \(0.380345\pi\)
\(602\) 0 0
\(603\) 15.5885 + 15.5885i 0.634811 + 0.634811i
\(604\) 0 0
\(605\) 1.00000 + 2.00000i 0.0406558 + 0.0813116i
\(606\) 0 0
\(607\) 25.9808 25.9808i 1.05453 1.05453i 0.0561015 0.998425i \(-0.482133\pi\)
0.998425 0.0561015i \(-0.0178671\pi\)
\(608\) 0 0
\(609\) 24.0000i 0.972529i
\(610\) 0 0
\(611\) 3.46410i 0.140143i
\(612\) 0 0
\(613\) −31.0000 + 31.0000i −1.25208 + 1.25208i −0.297291 + 0.954787i \(0.596083\pi\)
−0.954787 + 0.297291i \(0.903917\pi\)
\(614\) 0 0
\(615\) 3.46410 10.3923i 0.139686 0.419058i
\(616\) 0 0
\(617\) −7.00000 7.00000i −0.281809 0.281809i 0.552021 0.833830i \(-0.313857\pi\)
−0.833830 + 0.552021i \(0.813857\pi\)
\(618\) 0 0
\(619\) −20.7846 −0.835404 −0.417702 0.908584i \(-0.637164\pi\)
−0.417702 + 0.908584i \(0.637164\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 13.8564 + 13.8564i 0.555145 + 0.555145i
\(624\) 0 0
\(625\) −7.00000 24.0000i −0.280000 0.960000i
\(626\) 0 0
\(627\) −41.5692 + 41.5692i −1.66011 + 1.66011i
\(628\) 0 0
\(629\) 10.0000i 0.398726i
\(630\) 0 0
\(631\) 17.3205i 0.689519i 0.938691 + 0.344759i \(0.112039\pi\)
−0.938691 + 0.344759i \(0.887961\pi\)
\(632\) 0 0
\(633\) −18.0000 + 18.0000i −0.715436 + 0.715436i
\(634\) 0 0
\(635\) −36.3731 12.1244i −1.44342 0.481140i
\(636\) 0 0
\(637\) 1.00000 + 1.00000i 0.0396214 + 0.0396214i
\(638\) 0 0
\(639\) 31.1769 1.23334
\(640\) 0 0
\(641\) 26.0000 1.02694 0.513469 0.858108i \(-0.328360\pi\)
0.513469 + 0.858108i \(0.328360\pi\)
\(642\) 0 0
\(643\) 15.5885 + 15.5885i 0.614749 + 0.614749i 0.944180 0.329431i \(-0.106857\pi\)
−0.329431 + 0.944180i \(0.606857\pi\)
\(644\) 0 0
\(645\) 12.0000 6.00000i 0.472500 0.236250i
\(646\) 0 0
\(647\) −1.73205 + 1.73205i −0.0680939 + 0.0680939i −0.740334 0.672240i \(-0.765332\pi\)
0.672240 + 0.740334i \(0.265332\pi\)
\(648\) 0 0
\(649\) 24.0000i 0.942082i
\(650\) 0 0
\(651\) 20.7846i 0.814613i
\(652\) 0 0
\(653\) −23.0000 + 23.0000i −0.900060 + 0.900060i −0.995441 0.0953813i \(-0.969593\pi\)
0.0953813 + 0.995441i \(0.469593\pi\)
\(654\) 0 0
\(655\) 20.7846 10.3923i 0.812122 0.406061i
\(656\) 0 0
\(657\) −21.0000 21.0000i −0.819288 0.819288i
\(658\) 0 0
\(659\) −34.6410 −1.34942 −0.674711 0.738082i \(-0.735732\pi\)
−0.674711 + 0.738082i \(0.735732\pi\)
\(660\) 0 0
\(661\) −18.0000 −0.700119 −0.350059 0.936727i \(-0.613839\pi\)
−0.350059 + 0.936727i \(0.613839\pi\)
\(662\) 0 0
\(663\) 3.46410 + 3.46410i 0.134535 + 0.134535i
\(664\) 0 0
\(665\) −36.0000 12.0000i −1.39602 0.465340i
\(666\) 0 0
\(667\) 6.92820 6.92820i 0.268261 0.268261i
\(668\) 0 0
\(669\) 54.0000i 2.08776i
\(670\) 0 0
\(671\) 20.7846i 0.802381i
\(672\) 0 0
\(673\) 25.0000 25.0000i 0.963679 0.963679i −0.0356839 0.999363i \(-0.511361\pi\)
0.999363 + 0.0356839i \(0.0113610\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −35.0000 35.0000i −1.34516 1.34516i −0.890838 0.454321i \(-0.849882\pi\)
−0.454321 0.890838i \(-0.650118\pi\)
\(678\) 0 0
\(679\) 24.2487 0.930580
\(680\) 0 0
\(681\) −30.0000 −1.14960
\(682\) 0 0
\(683\) 1.73205 + 1.73205i 0.0662751 + 0.0662751i 0.739467 0.673192i \(-0.235077\pi\)
−0.673192 + 0.739467i \(0.735077\pi\)
\(684\) 0 0
\(685\) 9.00000 27.0000i 0.343872 1.03162i
\(686\) 0 0
\(687\) −34.6410 + 34.6410i −1.32164 + 1.32164i
\(688\) 0 0
\(689\) 14.0000i 0.533358i
\(690\) 0 0
\(691\) 45.0333i 1.71315i −0.516024 0.856574i \(-0.672588\pi\)
0.516024 0.856574i \(-0.327412\pi\)
\(692\) 0 0
\(693\) −18.0000 + 18.0000i −0.683763 + 0.683763i
\(694\) 0 0
\(695\) −6.92820 13.8564i −0.262802 0.525603i
\(696\) 0 0
\(697\) 2.00000 + 2.00000i 0.0757554 + 0.0757554i
\(698\) 0 0
\(699\) 3.46410 0.131024
\(700\) 0 0
\(701\) 38.0000 1.43524 0.717620 0.696435i \(-0.245231\pi\)
0.717620 + 0.696435i \(0.245231\pi\)
\(702\) 0 0
\(703\) −34.6410 34.6410i −1.30651 1.30651i
\(704\) 0 0
\(705\) 6.00000 + 12.0000i 0.225973 + 0.451946i
\(706\) 0 0
\(707\) 17.3205 17.3205i 0.651405 0.651405i
\(708\) 0 0
\(709\) 4.00000i 0.150223i 0.997175 + 0.0751116i \(0.0239313\pi\)
−0.997175 + 0.0751116i \(0.976069\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −6.00000 + 6.00000i −0.224702 + 0.224702i
\(714\) 0 0
\(715\) −3.46410 + 10.3923i −0.129550 + 0.388650i
\(716\) 0 0
\(717\) 48.0000 + 48.0000i 1.79259 + 1.79259i
\(718\) 0 0
\(719\) −27.7128 −1.03351 −0.516757 0.856132i \(-0.672861\pi\)
−0.516757 + 0.856132i \(0.672861\pi\)
\(720\) 0 0
\(721\) −6.00000 −0.223452
\(722\) 0 0
\(723\) −38.1051 38.1051i −1.41714 1.41714i
\(724\) 0 0
\(725\) 16.0000 + 12.0000i 0.594225 + 0.445669i
\(726\) 0 0
\(727\) −1.73205 + 1.73205i −0.0642382 + 0.0642382i −0.738496 0.674258i \(-0.764464\pi\)
0.674258 + 0.738496i \(0.264464\pi\)
\(728\) 0 0
\(729\) 27.0000i 1.00000i
\(730\) 0 0
\(731\) 3.46410i 0.128124i
\(732\) 0 0
\(733\) 1.00000 1.00000i 0.0369358 0.0369358i −0.688398 0.725333i \(-0.741686\pi\)
0.725333 + 0.688398i \(0.241686\pi\)
\(734\) 0 0
\(735\) 5.19615 + 1.73205i 0.191663 + 0.0638877i
\(736\) 0 0
\(737\) −18.0000 18.0000i −0.663039 0.663039i
\(738\) 0 0
\(739\) 20.7846 0.764574 0.382287 0.924044i \(-0.375137\pi\)
0.382287 + 0.924044i \(0.375137\pi\)
\(740\) 0 0
\(741\) −24.0000 −0.881662
\(742\) 0 0
\(743\) −12.1244 12.1244i −0.444799 0.444799i 0.448822 0.893621i \(-0.351844\pi\)
−0.893621 + 0.448822i \(0.851844\pi\)
\(744\) 0 0
\(745\) −8.00000 + 4.00000i −0.293097 + 0.146549i
\(746\) 0 0
\(747\) 36.3731 36.3731i 1.33082 1.33082i
\(748\) 0 0
\(749\) 30.0000i 1.09618i
\(750\) 0 0
\(751\) 3.46410i 0.126407i 0.998001 + 0.0632034i \(0.0201317\pi\)
−0.998001 + 0.0632034i \(0.979868\pi\)
\(752\) 0 0
\(753\) 6.00000 6.00000i 0.218652 0.218652i
\(754\) 0 0
\(755\) −20.7846 + 10.3923i −0.756429 + 0.378215i
\(756\) 0 0
\(757\) 29.0000 + 29.0000i 1.05402 + 1.05402i 0.998455 + 0.0555680i \(0.0176970\pi\)
0.0555680 + 0.998455i \(0.482303\pi\)
\(758\) 0 0
\(759\) 20.7846 0.754434
\(760\) 0 0
\(761\) 10.0000 0.362500 0.181250 0.983437i \(-0.441986\pi\)
0.181250 + 0.983437i \(0.441986\pi\)
\(762\) 0 0
\(763\) 20.7846 + 20.7846i 0.752453 + 0.752453i
\(764\) 0 0
\(765\) 9.00000 + 3.00000i 0.325396 + 0.108465i
\(766\) 0 0
\(767\) 6.92820 6.92820i 0.250163 0.250163i
\(768\) 0 0
\(769\) 48.0000i 1.73092i −0.500974 0.865462i \(-0.667025\pi\)
0.500974 0.865462i \(-0.332975\pi\)
\(770\) 0 0
\(771\) 31.1769i 1.12281i
\(772\) 0 0
\(773\) 1.00000 1.00000i 0.0359675 0.0359675i −0.688894 0.724862i \(-0.741904\pi\)
0.724862 + 0.688894i \(0.241904\pi\)
\(774\) 0 0
\(775\) −13.8564 10.3923i −0.497737 0.373303i
\(776\) 0 0
\(777\) −30.0000 30.0000i −1.07624 1.07624i
\(778\) 0 0
\(779\) −13.8564 −0.496457
\(780\) 0 0
\(781\) −36.0000 −1.28818
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −11.0000 + 33.0000i −0.392607 + 1.17782i
\(786\) 0 0
\(787\) 5.19615 5.19615i 0.185223 0.185223i −0.608404 0.793627i \(-0.708190\pi\)
0.793627 + 0.608404i \(0.208190\pi\)
\(788\) 0 0
\(789\) 42.0000i 1.49524i
\(790\) 0 0
\(791\) 31.1769i 1.10852i