Properties

Label 768.2.f.b.383.3
Level $768$
Weight $2$
Character 768.383
Analytic conductor $6.133$
Analytic rank $0$
Dimension $4$
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [768,2,Mod(383,768)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(768, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("768.383");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 768 = 2^{8} \cdot 3 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 768.f (of order \(2\), degree \(1\), 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: \(6.13251087523\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(i, \sqrt{5})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} + 3x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 384)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 383.3
Root \(-1.61803i\) of defining polynomial
Character \(\chi\) \(=\) 768.383
Dual form 768.2.f.b.383.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.618034 - 1.61803i) q^{3} +1.23607 q^{5} +3.23607i q^{7} +(-2.23607 - 2.00000i) q^{9} +O(q^{10})\) \(q+(0.618034 - 1.61803i) q^{3} +1.23607 q^{5} +3.23607i q^{7} +(-2.23607 - 2.00000i) q^{9} -0.763932i q^{11} -4.47214i q^{13} +(0.763932 - 2.00000i) q^{15} -6.47214i q^{17} +5.23607 q^{19} +(5.23607 + 2.00000i) q^{21} +6.47214 q^{23} -3.47214 q^{25} +(-4.61803 + 2.38197i) q^{27} +9.23607 q^{29} +0.763932i q^{31} +(-1.23607 - 0.472136i) q^{33} +4.00000i q^{35} -0.472136i q^{37} +(-7.23607 - 2.76393i) q^{39} -2.47214i q^{41} +2.76393 q^{43} +(-2.76393 - 2.47214i) q^{45} -8.00000 q^{47} -3.47214 q^{49} +(-10.4721 - 4.00000i) q^{51} +1.23607 q^{53} -0.944272i q^{55} +(3.23607 - 8.47214i) q^{57} -3.23607i q^{59} +8.47214i q^{61} +(6.47214 - 7.23607i) q^{63} -5.52786i q^{65} -3.70820 q^{67} +(4.00000 - 10.4721i) q^{69} -11.4164 q^{71} +2.00000 q^{73} +(-2.14590 + 5.61803i) q^{75} +2.47214 q^{77} +13.7082i q^{79} +(1.00000 + 8.94427i) q^{81} +7.23607i q^{83} -8.00000i q^{85} +(5.70820 - 14.9443i) q^{87} +4.00000i q^{89} +14.4721 q^{91} +(1.23607 + 0.472136i) q^{93} +6.47214 q^{95} -8.47214 q^{97} +(-1.52786 + 1.70820i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 2 q^{3} - 4 q^{5}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 2 q^{3} - 4 q^{5} + 12 q^{15} + 12 q^{19} + 12 q^{21} + 8 q^{23} + 4 q^{25} - 14 q^{27} + 28 q^{29} + 4 q^{33} - 20 q^{39} + 20 q^{43} - 20 q^{45} - 32 q^{47} + 4 q^{49} - 24 q^{51} - 4 q^{53} + 4 q^{57} + 8 q^{63} + 12 q^{67} + 16 q^{69} + 8 q^{71} + 8 q^{73} - 22 q^{75} - 8 q^{77} + 4 q^{81} - 4 q^{87} + 40 q^{91} - 4 q^{93} + 8 q^{95} - 16 q^{97} - 24 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/768\mathbb{Z}\right)^\times\).

\(n\) \(257\) \(511\) \(517\)
\(\chi(n)\) \(-1\) \(-1\) \(-1\)

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
\(3\) 0.618034 1.61803i 0.356822 0.934172i
\(4\) 0 0
\(5\) 1.23607 0.552786 0.276393 0.961045i \(-0.410861\pi\)
0.276393 + 0.961045i \(0.410861\pi\)
\(6\) 0 0
\(7\) 3.23607i 1.22312i 0.791199 + 0.611559i \(0.209457\pi\)
−0.791199 + 0.611559i \(0.790543\pi\)
\(8\) 0 0
\(9\) −2.23607 2.00000i −0.745356 0.666667i
\(10\) 0 0
\(11\) 0.763932i 0.230334i −0.993346 0.115167i \(-0.963260\pi\)
0.993346 0.115167i \(-0.0367403\pi\)
\(12\) 0 0
\(13\) 4.47214i 1.24035i −0.784465 0.620174i \(-0.787062\pi\)
0.784465 0.620174i \(-0.212938\pi\)
\(14\) 0 0
\(15\) 0.763932 2.00000i 0.197246 0.516398i
\(16\) 0 0
\(17\) 6.47214i 1.56972i −0.619671 0.784862i \(-0.712734\pi\)
0.619671 0.784862i \(-0.287266\pi\)
\(18\) 0 0
\(19\) 5.23607 1.20124 0.600618 0.799536i \(-0.294921\pi\)
0.600618 + 0.799536i \(0.294921\pi\)
\(20\) 0 0
\(21\) 5.23607 + 2.00000i 1.14260 + 0.436436i
\(22\) 0 0
\(23\) 6.47214 1.34953 0.674767 0.738031i \(-0.264244\pi\)
0.674767 + 0.738031i \(0.264244\pi\)
\(24\) 0 0
\(25\) −3.47214 −0.694427
\(26\) 0 0
\(27\) −4.61803 + 2.38197i −0.888741 + 0.458410i
\(28\) 0 0
\(29\) 9.23607 1.71509 0.857547 0.514405i \(-0.171987\pi\)
0.857547 + 0.514405i \(0.171987\pi\)
\(30\) 0 0
\(31\) 0.763932i 0.137206i 0.997644 + 0.0686031i \(0.0218542\pi\)
−0.997644 + 0.0686031i \(0.978146\pi\)
\(32\) 0 0
\(33\) −1.23607 0.472136i −0.215172 0.0821883i
\(34\) 0 0
\(35\) 4.00000i 0.676123i
\(36\) 0 0
\(37\) 0.472136i 0.0776187i −0.999247 0.0388093i \(-0.987644\pi\)
0.999247 0.0388093i \(-0.0123565\pi\)
\(38\) 0 0
\(39\) −7.23607 2.76393i −1.15870 0.442583i
\(40\) 0 0
\(41\) 2.47214i 0.386083i −0.981191 0.193041i \(-0.938165\pi\)
0.981191 0.193041i \(-0.0618352\pi\)
\(42\) 0 0
\(43\) 2.76393 0.421496 0.210748 0.977540i \(-0.432410\pi\)
0.210748 + 0.977540i \(0.432410\pi\)
\(44\) 0 0
\(45\) −2.76393 2.47214i −0.412023 0.368524i
\(46\) 0 0
\(47\) −8.00000 −1.16692 −0.583460 0.812142i \(-0.698301\pi\)
−0.583460 + 0.812142i \(0.698301\pi\)
\(48\) 0 0
\(49\) −3.47214 −0.496019
\(50\) 0 0
\(51\) −10.4721 4.00000i −1.46639 0.560112i
\(52\) 0 0
\(53\) 1.23607 0.169787 0.0848935 0.996390i \(-0.472945\pi\)
0.0848935 + 0.996390i \(0.472945\pi\)
\(54\) 0 0
\(55\) 0.944272i 0.127326i
\(56\) 0 0
\(57\) 3.23607 8.47214i 0.428628 1.12216i
\(58\) 0 0
\(59\) 3.23607i 0.421300i −0.977562 0.210650i \(-0.932442\pi\)
0.977562 0.210650i \(-0.0675581\pi\)
\(60\) 0 0
\(61\) 8.47214i 1.08475i 0.840138 + 0.542373i \(0.182474\pi\)
−0.840138 + 0.542373i \(0.817526\pi\)
\(62\) 0 0
\(63\) 6.47214 7.23607i 0.815412 0.911659i
\(64\) 0 0
\(65\) 5.52786i 0.685647i
\(66\) 0 0
\(67\) −3.70820 −0.453029 −0.226515 0.974008i \(-0.572733\pi\)
−0.226515 + 0.974008i \(0.572733\pi\)
\(68\) 0 0
\(69\) 4.00000 10.4721i 0.481543 1.26070i
\(70\) 0 0
\(71\) −11.4164 −1.35488 −0.677439 0.735579i \(-0.736910\pi\)
−0.677439 + 0.735579i \(0.736910\pi\)
\(72\) 0 0
\(73\) 2.00000 0.234082 0.117041 0.993127i \(-0.462659\pi\)
0.117041 + 0.993127i \(0.462659\pi\)
\(74\) 0 0
\(75\) −2.14590 + 5.61803i −0.247787 + 0.648715i
\(76\) 0 0
\(77\) 2.47214 0.281726
\(78\) 0 0
\(79\) 13.7082i 1.54229i 0.636657 + 0.771147i \(0.280317\pi\)
−0.636657 + 0.771147i \(0.719683\pi\)
\(80\) 0 0
\(81\) 1.00000 + 8.94427i 0.111111 + 0.993808i
\(82\) 0 0
\(83\) 7.23607i 0.794262i 0.917762 + 0.397131i \(0.129994\pi\)
−0.917762 + 0.397131i \(0.870006\pi\)
\(84\) 0 0
\(85\) 8.00000i 0.867722i
\(86\) 0 0
\(87\) 5.70820 14.9443i 0.611984 1.60219i
\(88\) 0 0
\(89\) 4.00000i 0.423999i 0.977270 + 0.212000i \(0.0679975\pi\)
−0.977270 + 0.212000i \(0.932002\pi\)
\(90\) 0 0
\(91\) 14.4721 1.51709
\(92\) 0 0
\(93\) 1.23607 + 0.472136i 0.128174 + 0.0489582i
\(94\) 0 0
\(95\) 6.47214 0.664027
\(96\) 0 0
\(97\) −8.47214 −0.860215 −0.430108 0.902778i \(-0.641524\pi\)
−0.430108 + 0.902778i \(0.641524\pi\)
\(98\) 0 0
\(99\) −1.52786 + 1.70820i −0.153556 + 0.171681i
\(100\) 0 0
\(101\) −11.7082 −1.16501 −0.582505 0.812827i \(-0.697927\pi\)
−0.582505 + 0.812827i \(0.697927\pi\)
\(102\) 0 0
\(103\) 8.18034i 0.806033i 0.915193 + 0.403016i \(0.132038\pi\)
−0.915193 + 0.403016i \(0.867962\pi\)
\(104\) 0 0
\(105\) 6.47214 + 2.47214i 0.631616 + 0.241256i
\(106\) 0 0
\(107\) 8.18034i 0.790823i −0.918504 0.395412i \(-0.870602\pi\)
0.918504 0.395412i \(-0.129398\pi\)
\(108\) 0 0
\(109\) 0.472136i 0.0452224i 0.999744 + 0.0226112i \(0.00719799\pi\)
−0.999744 + 0.0226112i \(0.992802\pi\)
\(110\) 0 0
\(111\) −0.763932 0.291796i −0.0725092 0.0276961i
\(112\) 0 0
\(113\) 8.00000i 0.752577i 0.926503 + 0.376288i \(0.122800\pi\)
−0.926503 + 0.376288i \(0.877200\pi\)
\(114\) 0 0
\(115\) 8.00000 0.746004
\(116\) 0 0
\(117\) −8.94427 + 10.0000i −0.826898 + 0.924500i
\(118\) 0 0
\(119\) 20.9443 1.91996
\(120\) 0 0
\(121\) 10.4164 0.946946
\(122\) 0 0
\(123\) −4.00000 1.52786i −0.360668 0.137763i
\(124\) 0 0
\(125\) −10.4721 −0.936656
\(126\) 0 0
\(127\) 8.76393i 0.777673i 0.921307 + 0.388837i \(0.127123\pi\)
−0.921307 + 0.388837i \(0.872877\pi\)
\(128\) 0 0
\(129\) 1.70820 4.47214i 0.150399 0.393750i
\(130\) 0 0
\(131\) 11.2361i 0.981700i −0.871244 0.490850i \(-0.836686\pi\)
0.871244 0.490850i \(-0.163314\pi\)
\(132\) 0 0
\(133\) 16.9443i 1.46925i
\(134\) 0 0
\(135\) −5.70820 + 2.94427i −0.491284 + 0.253403i
\(136\) 0 0
\(137\) 10.4721i 0.894695i 0.894360 + 0.447347i \(0.147631\pi\)
−0.894360 + 0.447347i \(0.852369\pi\)
\(138\) 0 0
\(139\) 3.70820 0.314526 0.157263 0.987557i \(-0.449733\pi\)
0.157263 + 0.987557i \(0.449733\pi\)
\(140\) 0 0
\(141\) −4.94427 + 12.9443i −0.416383 + 1.09010i
\(142\) 0 0
\(143\) −3.41641 −0.285694
\(144\) 0 0
\(145\) 11.4164 0.948081
\(146\) 0 0
\(147\) −2.14590 + 5.61803i −0.176991 + 0.463368i
\(148\) 0 0
\(149\) −3.70820 −0.303788 −0.151894 0.988397i \(-0.548537\pi\)
−0.151894 + 0.988397i \(0.548537\pi\)
\(150\) 0 0
\(151\) 6.29180i 0.512019i 0.966674 + 0.256010i \(0.0824079\pi\)
−0.966674 + 0.256010i \(0.917592\pi\)
\(152\) 0 0
\(153\) −12.9443 + 14.4721i −1.04648 + 1.17000i
\(154\) 0 0
\(155\) 0.944272i 0.0758457i
\(156\) 0 0
\(157\) 4.47214i 0.356915i −0.983948 0.178458i \(-0.942889\pi\)
0.983948 0.178458i \(-0.0571108\pi\)
\(158\) 0 0
\(159\) 0.763932 2.00000i 0.0605838 0.158610i
\(160\) 0 0
\(161\) 20.9443i 1.65064i
\(162\) 0 0
\(163\) 18.1803 1.42399 0.711997 0.702182i \(-0.247791\pi\)
0.711997 + 0.702182i \(0.247791\pi\)
\(164\) 0 0
\(165\) −1.52786 0.583592i −0.118944 0.0454326i
\(166\) 0 0
\(167\) −22.4721 −1.73895 −0.869473 0.493980i \(-0.835541\pi\)
−0.869473 + 0.493980i \(0.835541\pi\)
\(168\) 0 0
\(169\) −7.00000 −0.538462
\(170\) 0 0
\(171\) −11.7082 10.4721i −0.895349 0.800824i
\(172\) 0 0
\(173\) −8.65248 −0.657836 −0.328918 0.944359i \(-0.606684\pi\)
−0.328918 + 0.944359i \(0.606684\pi\)
\(174\) 0 0
\(175\) 11.2361i 0.849367i
\(176\) 0 0
\(177\) −5.23607 2.00000i −0.393567 0.150329i
\(178\) 0 0
\(179\) 16.1803i 1.20938i −0.796463 0.604688i \(-0.793298\pi\)
0.796463 0.604688i \(-0.206702\pi\)
\(180\) 0 0
\(181\) 11.5279i 0.856859i −0.903575 0.428430i \(-0.859067\pi\)
0.903575 0.428430i \(-0.140933\pi\)
\(182\) 0 0
\(183\) 13.7082 + 5.23607i 1.01334 + 0.387061i
\(184\) 0 0
\(185\) 0.583592i 0.0429065i
\(186\) 0 0
\(187\) −4.94427 −0.361561
\(188\) 0 0
\(189\) −7.70820 14.9443i −0.560689 1.08704i
\(190\) 0 0
\(191\) 4.94427 0.357755 0.178877 0.983871i \(-0.442753\pi\)
0.178877 + 0.983871i \(0.442753\pi\)
\(192\) 0 0
\(193\) 23.8885 1.71954 0.859768 0.510686i \(-0.170608\pi\)
0.859768 + 0.510686i \(0.170608\pi\)
\(194\) 0 0
\(195\) −8.94427 3.41641i −0.640513 0.244654i
\(196\) 0 0
\(197\) 9.23607 0.658043 0.329021 0.944323i \(-0.393281\pi\)
0.329021 + 0.944323i \(0.393281\pi\)
\(198\) 0 0
\(199\) 16.1803i 1.14699i 0.819208 + 0.573497i \(0.194414\pi\)
−0.819208 + 0.573497i \(0.805586\pi\)
\(200\) 0 0
\(201\) −2.29180 + 6.00000i −0.161651 + 0.423207i
\(202\) 0 0
\(203\) 29.8885i 2.09776i
\(204\) 0 0
\(205\) 3.05573i 0.213421i
\(206\) 0 0
\(207\) −14.4721 12.9443i −1.00588 0.899689i
\(208\) 0 0
\(209\) 4.00000i 0.276686i
\(210\) 0 0
\(211\) −6.76393 −0.465648 −0.232824 0.972519i \(-0.574797\pi\)
−0.232824 + 0.972519i \(0.574797\pi\)
\(212\) 0 0
\(213\) −7.05573 + 18.4721i −0.483451 + 1.26569i
\(214\) 0 0
\(215\) 3.41641 0.232997
\(216\) 0 0
\(217\) −2.47214 −0.167820
\(218\) 0 0
\(219\) 1.23607 3.23607i 0.0835257 0.218673i
\(220\) 0 0
\(221\) −28.9443 −1.94700
\(222\) 0 0
\(223\) 12.1803i 0.815656i −0.913059 0.407828i \(-0.866286\pi\)
0.913059 0.407828i \(-0.133714\pi\)
\(224\) 0 0
\(225\) 7.76393 + 6.94427i 0.517595 + 0.462951i
\(226\) 0 0
\(227\) 20.1803i 1.33942i 0.742624 + 0.669708i \(0.233581\pi\)
−0.742624 + 0.669708i \(0.766419\pi\)
\(228\) 0 0
\(229\) 20.4721i 1.35284i 0.736518 + 0.676418i \(0.236469\pi\)
−0.736518 + 0.676418i \(0.763531\pi\)
\(230\) 0 0
\(231\) 1.52786 4.00000i 0.100526 0.263181i
\(232\) 0 0
\(233\) 7.05573i 0.462236i −0.972926 0.231118i \(-0.925762\pi\)
0.972926 0.231118i \(-0.0742384\pi\)
\(234\) 0 0
\(235\) −9.88854 −0.645057
\(236\) 0 0
\(237\) 22.1803 + 8.47214i 1.44077 + 0.550324i
\(238\) 0 0
\(239\) 8.00000 0.517477 0.258738 0.965947i \(-0.416693\pi\)
0.258738 + 0.965947i \(0.416693\pi\)
\(240\) 0 0
\(241\) −2.00000 −0.128831 −0.0644157 0.997923i \(-0.520518\pi\)
−0.0644157 + 0.997923i \(0.520518\pi\)
\(242\) 0 0
\(243\) 15.0902 + 3.90983i 0.968035 + 0.250816i
\(244\) 0 0
\(245\) −4.29180 −0.274193
\(246\) 0 0
\(247\) 23.4164i 1.48995i
\(248\) 0 0
\(249\) 11.7082 + 4.47214i 0.741977 + 0.283410i
\(250\) 0 0
\(251\) 10.2918i 0.649612i 0.945781 + 0.324806i \(0.105299\pi\)
−0.945781 + 0.324806i \(0.894701\pi\)
\(252\) 0 0
\(253\) 4.94427i 0.310844i
\(254\) 0 0
\(255\) −12.9443 4.94427i −0.810602 0.309622i
\(256\) 0 0
\(257\) 3.05573i 0.190611i 0.995448 + 0.0953055i \(0.0303828\pi\)
−0.995448 + 0.0953055i \(0.969617\pi\)
\(258\) 0 0
\(259\) 1.52786 0.0949369
\(260\) 0 0
\(261\) −20.6525 18.4721i −1.27836 1.14340i
\(262\) 0 0
\(263\) −1.52786 −0.0942121 −0.0471061 0.998890i \(-0.515000\pi\)
−0.0471061 + 0.998890i \(0.515000\pi\)
\(264\) 0 0
\(265\) 1.52786 0.0938559
\(266\) 0 0
\(267\) 6.47214 + 2.47214i 0.396088 + 0.151292i
\(268\) 0 0
\(269\) 6.18034 0.376822 0.188411 0.982090i \(-0.439666\pi\)
0.188411 + 0.982090i \(0.439666\pi\)
\(270\) 0 0
\(271\) 13.7082i 0.832714i 0.909201 + 0.416357i \(0.136693\pi\)
−0.909201 + 0.416357i \(0.863307\pi\)
\(272\) 0 0
\(273\) 8.94427 23.4164i 0.541332 1.41723i
\(274\) 0 0
\(275\) 2.65248i 0.159950i
\(276\) 0 0
\(277\) 16.4721i 0.989715i −0.868974 0.494857i \(-0.835220\pi\)
0.868974 0.494857i \(-0.164780\pi\)
\(278\) 0 0
\(279\) 1.52786 1.70820i 0.0914708 0.102267i
\(280\) 0 0
\(281\) 7.05573i 0.420909i 0.977604 + 0.210455i \(0.0674945\pi\)
−0.977604 + 0.210455i \(0.932506\pi\)
\(282\) 0 0
\(283\) −25.2361 −1.50013 −0.750064 0.661365i \(-0.769977\pi\)
−0.750064 + 0.661365i \(0.769977\pi\)
\(284\) 0 0
\(285\) 4.00000 10.4721i 0.236940 0.620316i
\(286\) 0 0
\(287\) 8.00000 0.472225
\(288\) 0 0
\(289\) −24.8885 −1.46403
\(290\) 0 0
\(291\) −5.23607 + 13.7082i −0.306944 + 0.803589i
\(292\) 0 0
\(293\) 25.2361 1.47431 0.737153 0.675725i \(-0.236169\pi\)
0.737153 + 0.675725i \(0.236169\pi\)
\(294\) 0 0
\(295\) 4.00000i 0.232889i
\(296\) 0 0
\(297\) 1.81966 + 3.52786i 0.105587 + 0.204707i
\(298\) 0 0
\(299\) 28.9443i 1.67389i
\(300\) 0 0
\(301\) 8.94427i 0.515539i
\(302\) 0 0
\(303\) −7.23607 + 18.9443i −0.415701 + 1.08832i
\(304\) 0 0
\(305\) 10.4721i 0.599633i
\(306\) 0 0
\(307\) −21.5967 −1.23259 −0.616296 0.787515i \(-0.711367\pi\)
−0.616296 + 0.787515i \(0.711367\pi\)
\(308\) 0 0
\(309\) 13.2361 + 5.05573i 0.752974 + 0.287610i
\(310\) 0 0
\(311\) −14.4721 −0.820640 −0.410320 0.911942i \(-0.634583\pi\)
−0.410320 + 0.911942i \(0.634583\pi\)
\(312\) 0 0
\(313\) −8.47214 −0.478873 −0.239437 0.970912i \(-0.576963\pi\)
−0.239437 + 0.970912i \(0.576963\pi\)
\(314\) 0 0
\(315\) 8.00000 8.94427i 0.450749 0.503953i
\(316\) 0 0
\(317\) 27.1246 1.52347 0.761735 0.647889i \(-0.224348\pi\)
0.761735 + 0.647889i \(0.224348\pi\)
\(318\) 0 0
\(319\) 7.05573i 0.395045i
\(320\) 0 0
\(321\) −13.2361 5.05573i −0.738765 0.282183i
\(322\) 0 0
\(323\) 33.8885i 1.88561i
\(324\) 0 0
\(325\) 15.5279i 0.861331i
\(326\) 0 0
\(327\) 0.763932 + 0.291796i 0.0422455 + 0.0161364i
\(328\) 0 0
\(329\) 25.8885i 1.42728i
\(330\) 0 0
\(331\) 34.5410 1.89855 0.949273 0.314453i \(-0.101821\pi\)
0.949273 + 0.314453i \(0.101821\pi\)
\(332\) 0 0
\(333\) −0.944272 + 1.05573i −0.0517458 + 0.0578535i
\(334\) 0 0
\(335\) −4.58359 −0.250428
\(336\) 0 0
\(337\) −22.3607 −1.21806 −0.609032 0.793146i \(-0.708442\pi\)
−0.609032 + 0.793146i \(0.708442\pi\)
\(338\) 0 0
\(339\) 12.9443 + 4.94427i 0.703036 + 0.268536i
\(340\) 0 0
\(341\) 0.583592 0.0316033
\(342\) 0 0
\(343\) 11.4164i 0.616428i
\(344\) 0 0
\(345\) 4.94427 12.9443i 0.266191 0.696896i
\(346\) 0 0
\(347\) 10.2918i 0.552493i 0.961087 + 0.276246i \(0.0890905\pi\)
−0.961087 + 0.276246i \(0.910909\pi\)
\(348\) 0 0
\(349\) 19.5279i 1.04530i 0.852547 + 0.522651i \(0.175057\pi\)
−0.852547 + 0.522651i \(0.824943\pi\)
\(350\) 0 0
\(351\) 10.6525 + 20.6525i 0.568587 + 1.10235i
\(352\) 0 0
\(353\) 25.8885i 1.37791i −0.724805 0.688954i \(-0.758070\pi\)
0.724805 0.688954i \(-0.241930\pi\)
\(354\) 0 0
\(355\) −14.1115 −0.748958
\(356\) 0 0
\(357\) 12.9443 33.8885i 0.685084 1.79357i
\(358\) 0 0
\(359\) 4.58359 0.241913 0.120956 0.992658i \(-0.461404\pi\)
0.120956 + 0.992658i \(0.461404\pi\)
\(360\) 0 0
\(361\) 8.41641 0.442969
\(362\) 0 0
\(363\) 6.43769 16.8541i 0.337891 0.884611i
\(364\) 0 0
\(365\) 2.47214 0.129398
\(366\) 0 0
\(367\) 0.763932i 0.0398769i 0.999801 + 0.0199385i \(0.00634703\pi\)
−0.999801 + 0.0199385i \(0.993653\pi\)
\(368\) 0 0
\(369\) −4.94427 + 5.52786i −0.257389 + 0.287769i
\(370\) 0 0
\(371\) 4.00000i 0.207670i
\(372\) 0 0
\(373\) 29.4164i 1.52312i −0.648092 0.761562i \(-0.724433\pi\)
0.648092 0.761562i \(-0.275567\pi\)
\(374\) 0 0
\(375\) −6.47214 + 16.9443i −0.334220 + 0.874998i
\(376\) 0 0
\(377\) 41.3050i 2.12731i
\(378\) 0 0
\(379\) 20.6525 1.06085 0.530423 0.847733i \(-0.322033\pi\)
0.530423 + 0.847733i \(0.322033\pi\)
\(380\) 0 0
\(381\) 14.1803 + 5.41641i 0.726481 + 0.277491i
\(382\) 0 0
\(383\) 11.0557 0.564921 0.282461 0.959279i \(-0.408849\pi\)
0.282461 + 0.959279i \(0.408849\pi\)
\(384\) 0 0
\(385\) 3.05573 0.155734
\(386\) 0 0
\(387\) −6.18034 5.52786i −0.314164 0.280997i
\(388\) 0 0
\(389\) −9.81966 −0.497877 −0.248938 0.968519i \(-0.580082\pi\)
−0.248938 + 0.968519i \(0.580082\pi\)
\(390\) 0 0
\(391\) 41.8885i 2.11839i
\(392\) 0 0
\(393\) −18.1803 6.94427i −0.917077 0.350292i
\(394\) 0 0
\(395\) 16.9443i 0.852559i
\(396\) 0 0
\(397\) 9.41641i 0.472596i −0.971681 0.236298i \(-0.924066\pi\)
0.971681 0.236298i \(-0.0759341\pi\)
\(398\) 0 0
\(399\) 27.4164 + 10.4721i 1.37254 + 0.524263i
\(400\) 0 0
\(401\) 16.3607i 0.817013i 0.912755 + 0.408507i \(0.133950\pi\)
−0.912755 + 0.408507i \(0.866050\pi\)
\(402\) 0 0
\(403\) 3.41641 0.170183
\(404\) 0 0
\(405\) 1.23607 + 11.0557i 0.0614207 + 0.549364i
\(406\) 0 0
\(407\) −0.360680 −0.0178782
\(408\) 0 0
\(409\) −3.88854 −0.192276 −0.0961381 0.995368i \(-0.530649\pi\)
−0.0961381 + 0.995368i \(0.530649\pi\)
\(410\) 0 0
\(411\) 16.9443 + 6.47214i 0.835799 + 0.319247i
\(412\) 0 0
\(413\) 10.4721 0.515300
\(414\) 0 0
\(415\) 8.94427i 0.439057i
\(416\) 0 0
\(417\) 2.29180 6.00000i 0.112230 0.293821i
\(418\) 0 0
\(419\) 12.1803i 0.595049i 0.954714 + 0.297524i \(0.0961609\pi\)
−0.954714 + 0.297524i \(0.903839\pi\)
\(420\) 0 0
\(421\) 5.41641i 0.263980i −0.991251 0.131990i \(-0.957863\pi\)
0.991251 0.131990i \(-0.0421366\pi\)
\(422\) 0 0
\(423\) 17.8885 + 16.0000i 0.869771 + 0.777947i
\(424\) 0 0
\(425\) 22.4721i 1.09006i
\(426\) 0 0
\(427\) −27.4164 −1.32677
\(428\) 0 0
\(429\) −2.11146 + 5.52786i −0.101942 + 0.266888i
\(430\) 0 0
\(431\) 8.00000 0.385346 0.192673 0.981263i \(-0.438284\pi\)
0.192673 + 0.981263i \(0.438284\pi\)
\(432\) 0 0
\(433\) 7.52786 0.361766 0.180883 0.983505i \(-0.442104\pi\)
0.180883 + 0.983505i \(0.442104\pi\)
\(434\) 0 0
\(435\) 7.05573 18.4721i 0.338296 0.885671i
\(436\) 0 0
\(437\) 33.8885 1.62111
\(438\) 0 0
\(439\) 0.180340i 0.00860715i 0.999991 + 0.00430358i \(0.00136988\pi\)
−0.999991 + 0.00430358i \(0.998630\pi\)
\(440\) 0 0
\(441\) 7.76393 + 6.94427i 0.369711 + 0.330680i
\(442\) 0 0
\(443\) 29.7082i 1.41148i −0.708471 0.705740i \(-0.750615\pi\)
0.708471 0.705740i \(-0.249385\pi\)
\(444\) 0 0
\(445\) 4.94427i 0.234381i
\(446\) 0 0
\(447\) −2.29180 + 6.00000i −0.108398 + 0.283790i
\(448\) 0 0
\(449\) 27.4164i 1.29386i −0.762549 0.646930i \(-0.776053\pi\)
0.762549 0.646930i \(-0.223947\pi\)
\(450\) 0 0
\(451\) −1.88854 −0.0889281
\(452\) 0 0
\(453\) 10.1803 + 3.88854i 0.478314 + 0.182700i
\(454\) 0 0
\(455\) 17.8885 0.838628
\(456\) 0 0
\(457\) 22.0000 1.02912 0.514558 0.857455i \(-0.327956\pi\)
0.514558 + 0.857455i \(0.327956\pi\)
\(458\) 0 0
\(459\) 15.4164 + 29.8885i 0.719576 + 1.39508i
\(460\) 0 0
\(461\) 14.1803 0.660444 0.330222 0.943903i \(-0.392876\pi\)
0.330222 + 0.943903i \(0.392876\pi\)
\(462\) 0 0
\(463\) 39.2361i 1.82345i −0.410796 0.911727i \(-0.634749\pi\)
0.410796 0.911727i \(-0.365251\pi\)
\(464\) 0 0
\(465\) 1.52786 + 0.583592i 0.0708530 + 0.0270634i
\(466\) 0 0
\(467\) 15.2361i 0.705041i 0.935804 + 0.352521i \(0.114675\pi\)
−0.935804 + 0.352521i \(0.885325\pi\)
\(468\) 0 0
\(469\) 12.0000i 0.554109i
\(470\) 0 0
\(471\) −7.23607 2.76393i −0.333420 0.127355i
\(472\) 0 0
\(473\) 2.11146i 0.0970849i
\(474\) 0 0
\(475\) −18.1803 −0.834171
\(476\) 0 0
\(477\) −2.76393 2.47214i −0.126552 0.113191i
\(478\) 0 0
\(479\) −41.8885 −1.91394 −0.956968 0.290193i \(-0.906281\pi\)
−0.956968 + 0.290193i \(0.906281\pi\)
\(480\) 0 0
\(481\) −2.11146 −0.0962741
\(482\) 0 0
\(483\) 33.8885 + 12.9443i 1.54198 + 0.588985i
\(484\) 0 0
\(485\) −10.4721 −0.475515
\(486\) 0 0
\(487\) 1.34752i 0.0610621i 0.999534 + 0.0305311i \(0.00971985\pi\)
−0.999534 + 0.0305311i \(0.990280\pi\)
\(488\) 0 0
\(489\) 11.2361 29.4164i 0.508113 1.33026i
\(490\) 0 0
\(491\) 26.0689i 1.17647i −0.808689 0.588236i \(-0.799823\pi\)
0.808689 0.588236i \(-0.200177\pi\)
\(492\) 0 0
\(493\) 59.7771i 2.69222i
\(494\) 0 0
\(495\) −1.88854 + 2.11146i −0.0848837 + 0.0949029i
\(496\) 0 0
\(497\) 36.9443i 1.65718i
\(498\) 0 0
\(499\) −22.7639 −1.01905 −0.509527 0.860455i \(-0.670180\pi\)
−0.509527 + 0.860455i \(0.670180\pi\)
\(500\) 0 0
\(501\) −13.8885 + 36.3607i −0.620494 + 1.62448i
\(502\) 0 0
\(503\) −30.4721 −1.35869 −0.679343 0.733821i \(-0.737735\pi\)
−0.679343 + 0.733821i \(0.737735\pi\)
\(504\) 0 0
\(505\) −14.4721 −0.644002
\(506\) 0 0
\(507\) −4.32624 + 11.3262i −0.192135 + 0.503016i
\(508\) 0 0
\(509\) 12.2918 0.544824 0.272412 0.962181i \(-0.412179\pi\)
0.272412 + 0.962181i \(0.412179\pi\)
\(510\) 0 0
\(511\) 6.47214i 0.286310i
\(512\) 0 0
\(513\) −24.1803 + 12.4721i −1.06759 + 0.550658i
\(514\) 0 0
\(515\) 10.1115i 0.445564i
\(516\) 0 0
\(517\) 6.11146i 0.268782i
\(518\) 0 0
\(519\) −5.34752 + 14.0000i −0.234730 + 0.614532i
\(520\) 0 0
\(521\) 20.3607i 0.892018i 0.895029 + 0.446009i \(0.147155\pi\)
−0.895029 + 0.446009i \(0.852845\pi\)
\(522\) 0 0
\(523\) −34.1803 −1.49460 −0.747301 0.664486i \(-0.768651\pi\)
−0.747301 + 0.664486i \(0.768651\pi\)
\(524\) 0 0
\(525\) −18.1803 6.94427i −0.793455 0.303073i
\(526\) 0 0
\(527\) 4.94427 0.215376
\(528\) 0 0
\(529\) 18.8885 0.821241
\(530\) 0 0
\(531\) −6.47214 + 7.23607i −0.280867 + 0.314019i
\(532\) 0 0
\(533\) −11.0557 −0.478877
\(534\) 0 0
\(535\) 10.1115i 0.437156i
\(536\) 0 0
\(537\) −26.1803 10.0000i −1.12977 0.431532i
\(538\) 0 0
\(539\) 2.65248i 0.114250i
\(540\) 0 0
\(541\) 18.3607i 0.789387i 0.918813 + 0.394694i \(0.129149\pi\)
−0.918813 + 0.394694i \(0.870851\pi\)
\(542\) 0 0
\(543\) −18.6525 7.12461i −0.800454 0.305746i
\(544\) 0 0
\(545\) 0.583592i 0.0249983i
\(546\) 0 0
\(547\) −2.76393 −0.118177 −0.0590886 0.998253i \(-0.518819\pi\)
−0.0590886 + 0.998253i \(0.518819\pi\)
\(548\) 0 0
\(549\) 16.9443 18.9443i 0.723164 0.808522i
\(550\) 0 0
\(551\) 48.3607 2.06023
\(552\) 0 0
\(553\) −44.3607 −1.88641
\(554\) 0 0
\(555\) −0.944272 0.360680i −0.0400821 0.0153100i
\(556\) 0 0
\(557\) −16.6525 −0.705588 −0.352794 0.935701i \(-0.614768\pi\)
−0.352794 + 0.935701i \(0.614768\pi\)
\(558\) 0 0
\(559\) 12.3607i 0.522801i
\(560\) 0 0
\(561\) −3.05573 + 8.00000i −0.129013 + 0.337760i
\(562\) 0 0
\(563\) 36.5410i 1.54002i −0.638032 0.770010i \(-0.720251\pi\)
0.638032 0.770010i \(-0.279749\pi\)
\(564\) 0 0
\(565\) 9.88854i 0.416014i
\(566\) 0 0
\(567\) −28.9443 + 3.23607i −1.21555 + 0.135902i
\(568\) 0 0
\(569\) 37.5279i 1.57325i 0.617431 + 0.786625i \(0.288173\pi\)
−0.617431 + 0.786625i \(0.711827\pi\)
\(570\) 0 0
\(571\) −35.1246 −1.46992 −0.734960 0.678111i \(-0.762799\pi\)
−0.734960 + 0.678111i \(0.762799\pi\)
\(572\) 0 0
\(573\) 3.05573 8.00000i 0.127655 0.334205i
\(574\) 0 0
\(575\) −22.4721 −0.937153
\(576\) 0 0
\(577\) 19.5279 0.812956 0.406478 0.913661i \(-0.366757\pi\)
0.406478 + 0.913661i \(0.366757\pi\)
\(578\) 0 0
\(579\) 14.7639 38.6525i 0.613568 1.60634i
\(580\) 0 0
\(581\) −23.4164 −0.971476
\(582\) 0 0
\(583\) 0.944272i 0.0391077i
\(584\) 0 0
\(585\) −11.0557 + 12.3607i −0.457098 + 0.511051i
\(586\) 0 0
\(587\) 27.5967i 1.13904i 0.821978 + 0.569520i \(0.192871\pi\)
−0.821978 + 0.569520i \(0.807129\pi\)
\(588\) 0 0
\(589\) 4.00000i 0.164817i
\(590\) 0 0
\(591\) 5.70820 14.9443i 0.234804 0.614725i
\(592\) 0 0
\(593\) 11.0557i 0.454004i 0.973894 + 0.227002i \(0.0728924\pi\)
−0.973894 + 0.227002i \(0.927108\pi\)
\(594\) 0 0
\(595\) 25.8885 1.06133
\(596\) 0 0
\(597\) 26.1803 + 10.0000i 1.07149 + 0.409273i
\(598\) 0 0
\(599\) −19.4164 −0.793333 −0.396666 0.917963i \(-0.629833\pi\)
−0.396666 + 0.917963i \(0.629833\pi\)
\(600\) 0 0
\(601\) 37.7771 1.54096 0.770480 0.637464i \(-0.220017\pi\)
0.770480 + 0.637464i \(0.220017\pi\)
\(602\) 0 0
\(603\) 8.29180 + 7.41641i 0.337668 + 0.302019i
\(604\) 0 0
\(605\) 12.8754 0.523459
\(606\) 0 0
\(607\) 39.2361i 1.59254i −0.604940 0.796271i \(-0.706803\pi\)
0.604940 0.796271i \(-0.293197\pi\)
\(608\) 0 0
\(609\) 48.3607 + 18.4721i 1.95967 + 0.748529i
\(610\) 0 0
\(611\) 35.7771i 1.44739i
\(612\) 0 0
\(613\) 43.3050i 1.74907i 0.484962 + 0.874535i \(0.338833\pi\)
−0.484962 + 0.874535i \(0.661167\pi\)
\(614\) 0 0
\(615\) −4.94427 1.88854i −0.199372 0.0761534i
\(616\) 0 0
\(617\) 13.8885i 0.559132i −0.960127 0.279566i \(-0.909809\pi\)
0.960127 0.279566i \(-0.0901905\pi\)
\(618\) 0 0
\(619\) −11.1246 −0.447136 −0.223568 0.974688i \(-0.571770\pi\)
−0.223568 + 0.974688i \(0.571770\pi\)
\(620\) 0 0
\(621\) −29.8885 + 15.4164i −1.19939 + 0.618639i
\(622\) 0 0
\(623\) −12.9443 −0.518601
\(624\) 0 0
\(625\) 4.41641 0.176656
\(626\) 0 0
\(627\) −6.47214 2.47214i −0.258472 0.0987276i
\(628\) 0 0
\(629\) −3.05573 −0.121840
\(630\) 0 0
\(631\) 21.1246i 0.840958i 0.907302 + 0.420479i \(0.138138\pi\)
−0.907302 + 0.420479i \(0.861862\pi\)
\(632\) 0 0
\(633\) −4.18034 + 10.9443i −0.166154 + 0.434996i
\(634\) 0 0
\(635\) 10.8328i 0.429887i
\(636\) 0 0
\(637\) 15.5279i 0.615236i
\(638\) 0 0
\(639\) 25.5279 + 22.8328i 1.00987 + 0.903252i
\(640\) 0 0
\(641\) 37.3050i 1.47346i 0.676189 + 0.736729i \(0.263630\pi\)
−0.676189 + 0.736729i \(0.736370\pi\)
\(642\) 0 0
\(643\) −44.6525 −1.76092 −0.880461 0.474119i \(-0.842767\pi\)
−0.880461 + 0.474119i \(0.842767\pi\)
\(644\) 0 0
\(645\) 2.11146 5.52786i 0.0831385 0.217659i
\(646\) 0 0
\(647\) 29.3050 1.15210 0.576048 0.817416i \(-0.304594\pi\)
0.576048 + 0.817416i \(0.304594\pi\)
\(648\) 0 0
\(649\) −2.47214 −0.0970398
\(650\) 0 0
\(651\) −1.52786 + 4.00000i −0.0598817 + 0.156772i
\(652\) 0 0
\(653\) −27.7082 −1.08431 −0.542153 0.840280i \(-0.682391\pi\)
−0.542153 + 0.840280i \(0.682391\pi\)
\(654\) 0 0
\(655\) 13.8885i 0.542670i
\(656\) 0 0
\(657\) −4.47214 4.00000i −0.174475 0.156055i
\(658\) 0 0
\(659\) 41.7082i 1.62472i 0.583156 + 0.812360i \(0.301818\pi\)
−0.583156 + 0.812360i \(0.698182\pi\)
\(660\) 0 0
\(661\) 11.3050i 0.439712i 0.975532 + 0.219856i \(0.0705587\pi\)
−0.975532 + 0.219856i \(0.929441\pi\)
\(662\) 0 0
\(663\) −17.8885 + 46.8328i −0.694733 + 1.81884i
\(664\) 0 0
\(665\) 20.9443i 0.812184i
\(666\) 0 0
\(667\) 59.7771 2.31458
\(668\) 0 0
\(669\) −19.7082 7.52786i −0.761963 0.291044i
\(670\) 0 0
\(671\) 6.47214 0.249854
\(672\) 0 0
\(673\) 1.41641 0.0545985 0.0272993 0.999627i \(-0.491309\pi\)
0.0272993 + 0.999627i \(0.491309\pi\)
\(674\) 0 0
\(675\) 16.0344 8.27051i 0.617166 0.318332i
\(676\) 0 0
\(677\) −27.7082 −1.06491 −0.532456 0.846457i \(-0.678731\pi\)
−0.532456 + 0.846457i \(0.678731\pi\)
\(678\) 0 0
\(679\) 27.4164i 1.05215i
\(680\) 0 0
\(681\) 32.6525 + 12.4721i 1.25125 + 0.477933i
\(682\) 0 0
\(683\) 8.76393i 0.335343i −0.985843 0.167671i \(-0.946375\pi\)
0.985843 0.167671i \(-0.0536247\pi\)
\(684\) 0 0
\(685\) 12.9443i 0.494575i
\(686\) 0 0
\(687\) 33.1246 + 12.6525i 1.26378 + 0.482722i
\(688\) 0 0
\(689\) 5.52786i 0.210595i
\(690\) 0 0
\(691\) 16.2918 0.619769 0.309885 0.950774i \(-0.399710\pi\)
0.309885 + 0.950774i \(0.399710\pi\)
\(692\) 0 0
\(693\) −5.52786 4.94427i −0.209986 0.187817i
\(694\) 0 0
\(695\) 4.58359 0.173866
\(696\) 0 0
\(697\) −16.0000 −0.606043
\(698\) 0 0
\(699\) −11.4164 4.36068i −0.431808 0.164936i
\(700\) 0 0
\(701\) −27.7082 −1.04652 −0.523262 0.852172i \(-0.675285\pi\)
−0.523262 + 0.852172i \(0.675285\pi\)
\(702\) 0 0
\(703\) 2.47214i 0.0932384i
\(704\) 0 0
\(705\) −6.11146 + 16.0000i −0.230171 + 0.602595i
\(706\) 0 0
\(707\) 37.8885i 1.42495i
\(708\) 0 0
\(709\) 16.4721i 0.618624i −0.950961 0.309312i \(-0.899901\pi\)
0.950961 0.309312i \(-0.100099\pi\)
\(710\) 0 0
\(711\) 27.4164 30.6525i 1.02820 1.14956i
\(712\) 0 0
\(713\) 4.94427i 0.185164i
\(714\) 0 0
\(715\) −4.22291 −0.157928
\(716\) 0 0
\(717\) 4.94427 12.9443i 0.184647 0.483413i
\(718\) 0 0
\(719\) 22.8328 0.851520 0.425760 0.904836i \(-0.360007\pi\)
0.425760 + 0.904836i \(0.360007\pi\)
\(720\) 0 0
\(721\) −26.4721 −0.985874
\(722\) 0 0
\(723\) −1.23607 + 3.23607i −0.0459699 + 0.120351i
\(724\) 0 0
\(725\) −32.0689 −1.19101
\(726\) 0 0
\(727\) 8.18034i 0.303392i 0.988427 + 0.151696i \(0.0484735\pi\)
−0.988427 + 0.151696i \(0.951527\pi\)
\(728\) 0 0
\(729\) 15.6525 22.0000i 0.579721 0.814815i
\(730\) 0 0
\(731\) 17.8885i 0.661632i
\(732\) 0 0
\(733\) 2.58359i 0.0954272i −0.998861 0.0477136i \(-0.984807\pi\)
0.998861 0.0477136i \(-0.0151935\pi\)
\(734\) 0 0
\(735\) −2.65248 + 6.94427i −0.0978380 + 0.256143i
\(736\) 0 0
\(737\) 2.83282i 0.104348i
\(738\) 0 0
\(739\) 27.1246 0.997795 0.498897 0.866661i \(-0.333738\pi\)
0.498897 + 0.866661i \(0.333738\pi\)
\(740\) 0 0
\(741\) −37.8885 14.4721i −1.39187 0.531647i
\(742\) 0 0
\(743\) 19.4164 0.712319 0.356159 0.934425i \(-0.384086\pi\)
0.356159 + 0.934425i \(0.384086\pi\)
\(744\) 0 0
\(745\) −4.58359 −0.167930
\(746\) 0 0
\(747\) 14.4721 16.1803i 0.529508 0.592008i
\(748\) 0 0
\(749\) 26.4721 0.967271
\(750\) 0 0
\(751\) 31.5967i 1.15298i 0.817104 + 0.576491i \(0.195578\pi\)
−0.817104 + 0.576491i \(0.804422\pi\)
\(752\) 0 0
\(753\) 16.6525 + 6.36068i 0.606850 + 0.231796i
\(754\) 0 0
\(755\) 7.77709i 0.283037i
\(756\) 0 0
\(757\) 21.4164i 0.778393i −0.921155 0.389196i \(-0.872753\pi\)
0.921155 0.389196i \(-0.127247\pi\)
\(758\) 0 0
\(759\) −8.00000 3.05573i −0.290382 0.110916i
\(760\) 0 0
\(761\) 38.2492i 1.38653i 0.720681 + 0.693267i \(0.243829\pi\)
−0.720681 + 0.693267i \(0.756171\pi\)
\(762\) 0 0
\(763\) −1.52786 −0.0553124
\(764\) 0 0
\(765\) −16.0000 + 17.8885i −0.578481 + 0.646762i
\(766\) 0 0
\(767\) −14.4721 −0.522559
\(768\) 0 0
\(769\) −21.7771 −0.785302 −0.392651 0.919688i \(-0.628442\pi\)
−0.392651 + 0.919688i \(0.628442\pi\)
\(770\) 0 0
\(771\) 4.94427 + 1.88854i 0.178064 + 0.0680142i
\(772\) 0 0
\(773\) 30.1803 1.08551 0.542756 0.839891i \(-0.317381\pi\)
0.542756 + 0.839891i \(0.317381\pi\)
\(774\) 0 0
\(775\) 2.65248i 0.0952797i
\(776\) 0 0
\(777\) 0.944272 2.47214i 0.0338756 0.0886874i
\(778\) 0 0
\(779\) 12.9443i 0.463777i
\(780\) 0 0
\(781\) 8.72136i 0.312075i
\(782\) 0 0
\(783\) −42.6525 + 22.0000i −1.52428 + 0.786216i
\(784\) 0 0
\(785\) 5.52786i 0.197298i
\(786\) 0 0
\(787\) −5.81966 −0.207448 −0.103724 0.994606i \(-0.533076\pi\)
−0.103724 + 0.994606i \(0.533076\pi\)
\(788\) 0 0
\(789\) −0.944272 + 2.47214i −0.0336170 + 0.0880104i
\(790\) 0 0
\(791\) −25.8885 −0.920491
\(792\) 0 0
\(793\) 37.8885 1.34546