Properties

Label 768.2.f.b.383.1
Level $768$
Weight $2$
Character 768.383
Analytic conductor $6.133$
Analytic rank $0$
Dimension $4$
Inner twists $2$

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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 383.1
Root \(-0.618034i\) of defining polynomial
Character \(\chi\) \(=\) 768.383
Dual form 768.2.f.b.383.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.61803 - 0.618034i) q^{3} -3.23607 q^{5} +1.23607i q^{7} +(2.23607 + 2.00000i) q^{9} +O(q^{10})\) \(q+(-1.61803 - 0.618034i) q^{3} -3.23607 q^{5} +1.23607i q^{7} +(2.23607 + 2.00000i) q^{9} +5.23607i q^{11} -4.47214i q^{13} +(5.23607 + 2.00000i) q^{15} -2.47214i q^{17} +0.763932 q^{19} +(0.763932 - 2.00000i) q^{21} -2.47214 q^{23} +5.47214 q^{25} +(-2.38197 - 4.61803i) q^{27} +4.76393 q^{29} -5.23607i q^{31} +(3.23607 - 8.47214i) q^{33} -4.00000i q^{35} -8.47214i q^{37} +(-2.76393 + 7.23607i) q^{39} -6.47214i q^{41} +7.23607 q^{43} +(-7.23607 - 6.47214i) q^{45} -8.00000 q^{47} +5.47214 q^{49} +(-1.52786 + 4.00000i) q^{51} -3.23607 q^{53} -16.9443i q^{55} +(-1.23607 - 0.472136i) q^{57} -1.23607i q^{59} +0.472136i q^{61} +(-2.47214 + 2.76393i) q^{63} +14.4721i q^{65} +9.70820 q^{67} +(4.00000 + 1.52786i) q^{69} +15.4164 q^{71} +2.00000 q^{73} +(-8.85410 - 3.38197i) q^{75} -6.47214 q^{77} -0.291796i q^{79} +(1.00000 + 8.94427i) q^{81} -2.76393i q^{83} +8.00000i q^{85} +(-7.70820 - 2.94427i) q^{87} -4.00000i q^{89} +5.52786 q^{91} +(-3.23607 + 8.47214i) q^{93} -2.47214 q^{95} +0.472136 q^{97} +(-10.4721 + 11.7082i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 2 q^{3} - 4 q^{5}+O(q^{10}) \) 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
\(3\) −1.61803 0.618034i −0.934172 0.356822i
\(4\) 0 0
\(5\) −3.23607 −1.44721 −0.723607 0.690212i \(-0.757517\pi\)
−0.723607 + 0.690212i \(0.757517\pi\)
\(6\) 0 0
\(7\) 1.23607i 0.467190i 0.972334 + 0.233595i \(0.0750489\pi\)
−0.972334 + 0.233595i \(0.924951\pi\)
\(8\) 0 0
\(9\) 2.23607 + 2.00000i 0.745356 + 0.666667i
\(10\) 0 0
\(11\) 5.23607i 1.57873i 0.613922 + 0.789367i \(0.289591\pi\)
−0.613922 + 0.789367i \(0.710409\pi\)
\(12\) 0 0
\(13\) 4.47214i 1.24035i −0.784465 0.620174i \(-0.787062\pi\)
0.784465 0.620174i \(-0.212938\pi\)
\(14\) 0 0
\(15\) 5.23607 + 2.00000i 1.35195 + 0.516398i
\(16\) 0 0
\(17\) 2.47214i 0.599581i −0.954005 0.299791i \(-0.903083\pi\)
0.954005 0.299791i \(-0.0969168\pi\)
\(18\) 0 0
\(19\) 0.763932 0.175258 0.0876290 0.996153i \(-0.472071\pi\)
0.0876290 + 0.996153i \(0.472071\pi\)
\(20\) 0 0
\(21\) 0.763932 2.00000i 0.166704 0.436436i
\(22\) 0 0
\(23\) −2.47214 −0.515476 −0.257738 0.966215i \(-0.582977\pi\)
−0.257738 + 0.966215i \(0.582977\pi\)
\(24\) 0 0
\(25\) 5.47214 1.09443
\(26\) 0 0
\(27\) −2.38197 4.61803i −0.458410 0.888741i
\(28\) 0 0
\(29\) 4.76393 0.884640 0.442320 0.896857i \(-0.354156\pi\)
0.442320 + 0.896857i \(0.354156\pi\)
\(30\) 0 0
\(31\) 5.23607i 0.940426i −0.882553 0.470213i \(-0.844177\pi\)
0.882553 0.470213i \(-0.155823\pi\)
\(32\) 0 0
\(33\) 3.23607 8.47214i 0.563327 1.47481i
\(34\) 0 0
\(35\) 4.00000i 0.676123i
\(36\) 0 0
\(37\) 8.47214i 1.39281i −0.717649 0.696405i \(-0.754782\pi\)
0.717649 0.696405i \(-0.245218\pi\)
\(38\) 0 0
\(39\) −2.76393 + 7.23607i −0.442583 + 1.15870i
\(40\) 0 0
\(41\) 6.47214i 1.01078i −0.862892 0.505389i \(-0.831349\pi\)
0.862892 0.505389i \(-0.168651\pi\)
\(42\) 0 0
\(43\) 7.23607 1.10349 0.551745 0.834013i \(-0.313962\pi\)
0.551745 + 0.834013i \(0.313962\pi\)
\(44\) 0 0
\(45\) −7.23607 6.47214i −1.07869 0.964809i
\(46\) 0 0
\(47\) −8.00000 −1.16692 −0.583460 0.812142i \(-0.698301\pi\)
−0.583460 + 0.812142i \(0.698301\pi\)
\(48\) 0 0
\(49\) 5.47214 0.781734
\(50\) 0 0
\(51\) −1.52786 + 4.00000i −0.213944 + 0.560112i
\(52\) 0 0
\(53\) −3.23607 −0.444508 −0.222254 0.974989i \(-0.571341\pi\)
−0.222254 + 0.974989i \(0.571341\pi\)
\(54\) 0 0
\(55\) 16.9443i 2.28477i
\(56\) 0 0
\(57\) −1.23607 0.472136i −0.163721 0.0625359i
\(58\) 0 0
\(59\) 1.23607i 0.160922i −0.996758 0.0804612i \(-0.974361\pi\)
0.996758 0.0804612i \(-0.0256393\pi\)
\(60\) 0 0
\(61\) 0.472136i 0.0604508i 0.999543 + 0.0302254i \(0.00962251\pi\)
−0.999543 + 0.0302254i \(0.990377\pi\)
\(62\) 0 0
\(63\) −2.47214 + 2.76393i −0.311460 + 0.348223i
\(64\) 0 0
\(65\) 14.4721i 1.79505i
\(66\) 0 0
\(67\) 9.70820 1.18605 0.593023 0.805186i \(-0.297934\pi\)
0.593023 + 0.805186i \(0.297934\pi\)
\(68\) 0 0
\(69\) 4.00000 + 1.52786i 0.481543 + 0.183933i
\(70\) 0 0
\(71\) 15.4164 1.82959 0.914796 0.403917i \(-0.132352\pi\)
0.914796 + 0.403917i \(0.132352\pi\)
\(72\) 0 0
\(73\) 2.00000 0.234082 0.117041 0.993127i \(-0.462659\pi\)
0.117041 + 0.993127i \(0.462659\pi\)
\(74\) 0 0
\(75\) −8.85410 3.38197i −1.02238 0.390516i
\(76\) 0 0
\(77\) −6.47214 −0.737568
\(78\) 0 0
\(79\) 0.291796i 0.0328296i −0.999865 0.0164148i \(-0.994775\pi\)
0.999865 0.0164148i \(-0.00522523\pi\)
\(80\) 0 0
\(81\) 1.00000 + 8.94427i 0.111111 + 0.993808i
\(82\) 0 0
\(83\) 2.76393i 0.303381i −0.988428 0.151690i \(-0.951528\pi\)
0.988428 0.151690i \(-0.0484717\pi\)
\(84\) 0 0
\(85\) 8.00000i 0.867722i
\(86\) 0 0
\(87\) −7.70820 2.94427i −0.826406 0.315659i
\(88\) 0 0
\(89\) 4.00000i 0.423999i −0.977270 0.212000i \(-0.932002\pi\)
0.977270 0.212000i \(-0.0679975\pi\)
\(90\) 0 0
\(91\) 5.52786 0.579478
\(92\) 0 0
\(93\) −3.23607 + 8.47214i −0.335565 + 0.878520i
\(94\) 0 0
\(95\) −2.47214 −0.253636
\(96\) 0 0
\(97\) 0.472136 0.0479381 0.0239691 0.999713i \(-0.492370\pi\)
0.0239691 + 0.999713i \(0.492370\pi\)
\(98\) 0 0
\(99\) −10.4721 + 11.7082i −1.05249 + 1.17672i
\(100\) 0 0
\(101\) 1.70820 0.169973 0.0849863 0.996382i \(-0.472915\pi\)
0.0849863 + 0.996382i \(0.472915\pi\)
\(102\) 0 0
\(103\) 14.1803i 1.39723i 0.715498 + 0.698615i \(0.246200\pi\)
−0.715498 + 0.698615i \(0.753800\pi\)
\(104\) 0 0
\(105\) −2.47214 + 6.47214i −0.241256 + 0.631616i
\(106\) 0 0
\(107\) 14.1803i 1.37087i −0.728136 0.685433i \(-0.759613\pi\)
0.728136 0.685433i \(-0.240387\pi\)
\(108\) 0 0
\(109\) 8.47214i 0.811483i 0.913988 + 0.405742i \(0.132987\pi\)
−0.913988 + 0.405742i \(0.867013\pi\)
\(110\) 0 0
\(111\) −5.23607 + 13.7082i −0.496986 + 1.30113i
\(112\) 0 0
\(113\) 8.00000i 0.752577i −0.926503 0.376288i \(-0.877200\pi\)
0.926503 0.376288i \(-0.122800\pi\)
\(114\) 0 0
\(115\) 8.00000 0.746004
\(116\) 0 0
\(117\) 8.94427 10.0000i 0.826898 0.924500i
\(118\) 0 0
\(119\) 3.05573 0.280118
\(120\) 0 0
\(121\) −16.4164 −1.49240
\(122\) 0 0
\(123\) −4.00000 + 10.4721i −0.360668 + 0.944241i
\(124\) 0 0
\(125\) −1.52786 −0.136656
\(126\) 0 0
\(127\) 13.2361i 1.17451i −0.809402 0.587256i \(-0.800208\pi\)
0.809402 0.587256i \(-0.199792\pi\)
\(128\) 0 0
\(129\) −11.7082 4.47214i −1.03085 0.393750i
\(130\) 0 0
\(131\) 6.76393i 0.590967i 0.955348 + 0.295484i \(0.0954808\pi\)
−0.955348 + 0.295484i \(0.904519\pi\)
\(132\) 0 0
\(133\) 0.944272i 0.0818788i
\(134\) 0 0
\(135\) 7.70820 + 14.9443i 0.663417 + 1.28620i
\(136\) 0 0
\(137\) 1.52786i 0.130534i −0.997868 0.0652671i \(-0.979210\pi\)
0.997868 0.0652671i \(-0.0207899\pi\)
\(138\) 0 0
\(139\) −9.70820 −0.823439 −0.411720 0.911311i \(-0.635072\pi\)
−0.411720 + 0.911311i \(0.635072\pi\)
\(140\) 0 0
\(141\) 12.9443 + 4.94427i 1.09010 + 0.416383i
\(142\) 0 0
\(143\) 23.4164 1.95818
\(144\) 0 0
\(145\) −15.4164 −1.28026
\(146\) 0 0
\(147\) −8.85410 3.38197i −0.730274 0.278940i
\(148\) 0 0
\(149\) 9.70820 0.795327 0.397664 0.917531i \(-0.369821\pi\)
0.397664 + 0.917531i \(0.369821\pi\)
\(150\) 0 0
\(151\) 19.7082i 1.60383i −0.597438 0.801915i \(-0.703814\pi\)
0.597438 0.801915i \(-0.296186\pi\)
\(152\) 0 0
\(153\) 4.94427 5.52786i 0.399721 0.446901i
\(154\) 0 0
\(155\) 16.9443i 1.36100i
\(156\) 0 0
\(157\) 4.47214i 0.356915i −0.983948 0.178458i \(-0.942889\pi\)
0.983948 0.178458i \(-0.0571108\pi\)
\(158\) 0 0
\(159\) 5.23607 + 2.00000i 0.415247 + 0.158610i
\(160\) 0 0
\(161\) 3.05573i 0.240825i
\(162\) 0 0
\(163\) −4.18034 −0.327429 −0.163715 0.986508i \(-0.552348\pi\)
−0.163715 + 0.986508i \(0.552348\pi\)
\(164\) 0 0
\(165\) −10.4721 + 27.4164i −0.815255 + 2.13436i
\(166\) 0 0
\(167\) −13.5279 −1.04682 −0.523409 0.852082i \(-0.675340\pi\)
−0.523409 + 0.852082i \(0.675340\pi\)
\(168\) 0 0
\(169\) −7.00000 −0.538462
\(170\) 0 0
\(171\) 1.70820 + 1.52786i 0.130630 + 0.116839i
\(172\) 0 0
\(173\) 22.6525 1.72224 0.861118 0.508405i \(-0.169765\pi\)
0.861118 + 0.508405i \(0.169765\pi\)
\(174\) 0 0
\(175\) 6.76393i 0.511305i
\(176\) 0 0
\(177\) −0.763932 + 2.00000i −0.0574206 + 0.150329i
\(178\) 0 0
\(179\) 6.18034i 0.461940i −0.972961 0.230970i \(-0.925810\pi\)
0.972961 0.230970i \(-0.0741900\pi\)
\(180\) 0 0
\(181\) 20.4721i 1.52168i 0.648938 + 0.760841i \(0.275213\pi\)
−0.648938 + 0.760841i \(0.724787\pi\)
\(182\) 0 0
\(183\) 0.291796 0.763932i 0.0215702 0.0564715i
\(184\) 0 0
\(185\) 27.4164i 2.01569i
\(186\) 0 0
\(187\) 12.9443 0.946579
\(188\) 0 0
\(189\) 5.70820 2.94427i 0.415211 0.214164i
\(190\) 0 0
\(191\) −12.9443 −0.936615 −0.468307 0.883566i \(-0.655136\pi\)
−0.468307 + 0.883566i \(0.655136\pi\)
\(192\) 0 0
\(193\) −11.8885 −0.855756 −0.427878 0.903836i \(-0.640739\pi\)
−0.427878 + 0.903836i \(0.640739\pi\)
\(194\) 0 0
\(195\) 8.94427 23.4164i 0.640513 1.67688i
\(196\) 0 0
\(197\) 4.76393 0.339416 0.169708 0.985494i \(-0.445718\pi\)
0.169708 + 0.985494i \(0.445718\pi\)
\(198\) 0 0
\(199\) 6.18034i 0.438113i 0.975712 + 0.219056i \(0.0702979\pi\)
−0.975712 + 0.219056i \(0.929702\pi\)
\(200\) 0 0
\(201\) −15.7082 6.00000i −1.10797 0.423207i
\(202\) 0 0
\(203\) 5.88854i 0.413295i
\(204\) 0 0
\(205\) 20.9443i 1.46281i
\(206\) 0 0
\(207\) −5.52786 4.94427i −0.384213 0.343651i
\(208\) 0 0
\(209\) 4.00000i 0.276686i
\(210\) 0 0
\(211\) −11.2361 −0.773523 −0.386761 0.922180i \(-0.626406\pi\)
−0.386761 + 0.922180i \(0.626406\pi\)
\(212\) 0 0
\(213\) −24.9443 9.52786i −1.70915 0.652838i
\(214\) 0 0
\(215\) −23.4164 −1.59699
\(216\) 0 0
\(217\) 6.47214 0.439357
\(218\) 0 0
\(219\) −3.23607 1.23607i −0.218673 0.0835257i
\(220\) 0 0
\(221\) −11.0557 −0.743689
\(222\) 0 0
\(223\) 10.1803i 0.681726i −0.940113 0.340863i \(-0.889281\pi\)
0.940113 0.340863i \(-0.110719\pi\)
\(224\) 0 0
\(225\) 12.2361 + 10.9443i 0.815738 + 0.729618i
\(226\) 0 0
\(227\) 2.18034i 0.144714i 0.997379 + 0.0723571i \(0.0230521\pi\)
−0.997379 + 0.0723571i \(0.976948\pi\)
\(228\) 0 0
\(229\) 11.5279i 0.761783i −0.924620 0.380891i \(-0.875617\pi\)
0.924620 0.380891i \(-0.124383\pi\)
\(230\) 0 0
\(231\) 10.4721 + 4.00000i 0.689016 + 0.263181i
\(232\) 0 0
\(233\) 24.9443i 1.63415i 0.576529 + 0.817077i \(0.304407\pi\)
−0.576529 + 0.817077i \(0.695593\pi\)
\(234\) 0 0
\(235\) 25.8885 1.68878
\(236\) 0 0
\(237\) −0.180340 + 0.472136i −0.0117143 + 0.0306685i
\(238\) 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
\(243\) 3.90983 15.0902i 0.250816 0.968035i
\(244\) 0 0
\(245\) −17.7082 −1.13134
\(246\) 0 0
\(247\) 3.41641i 0.217381i
\(248\) 0 0
\(249\) −1.70820 + 4.47214i −0.108253 + 0.283410i
\(250\) 0 0
\(251\) 23.7082i 1.49645i −0.663446 0.748224i \(-0.730907\pi\)
0.663446 0.748224i \(-0.269093\pi\)
\(252\) 0 0
\(253\) 12.9443i 0.813799i
\(254\) 0 0
\(255\) 4.94427 12.9443i 0.309622 0.810602i
\(256\) 0 0
\(257\) 20.9443i 1.30647i −0.757156 0.653234i \(-0.773412\pi\)
0.757156 0.653234i \(-0.226588\pi\)
\(258\) 0 0
\(259\) 10.4721 0.650707
\(260\) 0 0
\(261\) 10.6525 + 9.52786i 0.659372 + 0.589760i
\(262\) 0 0
\(263\) −10.4721 −0.645740 −0.322870 0.946443i \(-0.604648\pi\)
−0.322870 + 0.946443i \(0.604648\pi\)
\(264\) 0 0
\(265\) 10.4721 0.643298
\(266\) 0 0
\(267\) −2.47214 + 6.47214i −0.151292 + 0.396088i
\(268\) 0 0
\(269\) −16.1803 −0.986533 −0.493266 0.869878i \(-0.664197\pi\)
−0.493266 + 0.869878i \(0.664197\pi\)
\(270\) 0 0
\(271\) 0.291796i 0.0177253i −0.999961 0.00886267i \(-0.997179\pi\)
0.999961 0.00886267i \(-0.00282111\pi\)
\(272\) 0 0
\(273\) −8.94427 3.41641i −0.541332 0.206770i
\(274\) 0 0
\(275\) 28.6525i 1.72781i
\(276\) 0 0
\(277\) 7.52786i 0.452306i 0.974092 + 0.226153i \(0.0726149\pi\)
−0.974092 + 0.226153i \(0.927385\pi\)
\(278\) 0 0
\(279\) 10.4721 11.7082i 0.626950 0.700952i
\(280\) 0 0
\(281\) 24.9443i 1.48805i −0.668151 0.744025i \(-0.732914\pi\)
0.668151 0.744025i \(-0.267086\pi\)
\(282\) 0 0
\(283\) −20.7639 −1.23429 −0.617144 0.786850i \(-0.711710\pi\)
−0.617144 + 0.786850i \(0.711710\pi\)
\(284\) 0 0
\(285\) 4.00000 + 1.52786i 0.236940 + 0.0905029i
\(286\) 0 0
\(287\) 8.00000 0.472225
\(288\) 0 0
\(289\) 10.8885 0.640503
\(290\) 0 0
\(291\) −0.763932 0.291796i −0.0447825 0.0171054i
\(292\) 0 0
\(293\) 20.7639 1.21304 0.606521 0.795068i \(-0.292565\pi\)
0.606521 + 0.795068i \(0.292565\pi\)
\(294\) 0 0
\(295\) 4.00000i 0.232889i
\(296\) 0 0
\(297\) 24.1803 12.4721i 1.40309 0.723707i
\(298\) 0 0
\(299\) 11.0557i 0.639369i
\(300\) 0 0
\(301\) 8.94427i 0.515539i
\(302\) 0 0
\(303\) −2.76393 1.05573i −0.158784 0.0606500i
\(304\) 0 0
\(305\) 1.52786i 0.0874852i
\(306\) 0 0
\(307\) 27.5967 1.57503 0.787515 0.616296i \(-0.211367\pi\)
0.787515 + 0.616296i \(0.211367\pi\)
\(308\) 0 0
\(309\) 8.76393 22.9443i 0.498563 1.30525i
\(310\) 0 0
\(311\) −5.52786 −0.313456 −0.156728 0.987642i \(-0.550095\pi\)
−0.156728 + 0.987642i \(0.550095\pi\)
\(312\) 0 0
\(313\) 0.472136 0.0266867 0.0133434 0.999911i \(-0.495753\pi\)
0.0133434 + 0.999911i \(0.495753\pi\)
\(314\) 0 0
\(315\) 8.00000 8.94427i 0.450749 0.503953i
\(316\) 0 0
\(317\) −13.1246 −0.737152 −0.368576 0.929598i \(-0.620155\pi\)
−0.368576 + 0.929598i \(0.620155\pi\)
\(318\) 0 0
\(319\) 24.9443i 1.39661i
\(320\) 0 0
\(321\) −8.76393 + 22.9443i −0.489155 + 1.28062i
\(322\) 0 0
\(323\) 1.88854i 0.105081i
\(324\) 0 0
\(325\) 24.4721i 1.35747i
\(326\) 0 0
\(327\) 5.23607 13.7082i 0.289555 0.758065i
\(328\) 0 0
\(329\) 9.88854i 0.545173i
\(330\) 0 0
\(331\) −32.5410 −1.78862 −0.894308 0.447452i \(-0.852332\pi\)
−0.894308 + 0.447452i \(0.852332\pi\)
\(332\) 0 0
\(333\) 16.9443 18.9443i 0.928540 1.03814i
\(334\) 0 0
\(335\) −31.4164 −1.71646
\(336\) 0 0
\(337\) 22.3607 1.21806 0.609032 0.793146i \(-0.291558\pi\)
0.609032 + 0.793146i \(0.291558\pi\)
\(338\) 0 0
\(339\) −4.94427 + 12.9443i −0.268536 + 0.703036i
\(340\) 0 0
\(341\) 27.4164 1.48468
\(342\) 0 0
\(343\) 15.4164i 0.832408i
\(344\) 0 0
\(345\) −12.9443 4.94427i −0.696896 0.266191i
\(346\) 0 0
\(347\) 23.7082i 1.27272i −0.771391 0.636362i \(-0.780439\pi\)
0.771391 0.636362i \(-0.219561\pi\)
\(348\) 0 0
\(349\) 28.4721i 1.52408i −0.647531 0.762039i \(-0.724198\pi\)
0.647531 0.762039i \(-0.275802\pi\)
\(350\) 0 0
\(351\) −20.6525 + 10.6525i −1.10235 + 0.568587i
\(352\) 0 0
\(353\) 9.88854i 0.526314i −0.964753 0.263157i \(-0.915236\pi\)
0.964753 0.263157i \(-0.0847637\pi\)
\(354\) 0 0
\(355\) −49.8885 −2.64781
\(356\) 0 0
\(357\) −4.94427 1.88854i −0.261679 0.0999523i
\(358\) 0 0
\(359\) 31.4164 1.65809 0.829047 0.559178i \(-0.188883\pi\)
0.829047 + 0.559178i \(0.188883\pi\)
\(360\) 0 0
\(361\) −18.4164 −0.969285
\(362\) 0 0
\(363\) 26.5623 + 10.1459i 1.39416 + 0.532522i
\(364\) 0 0
\(365\) −6.47214 −0.338767
\(366\) 0 0
\(367\) 5.23607i 0.273321i −0.990618 0.136660i \(-0.956363\pi\)
0.990618 0.136660i \(-0.0436369\pi\)
\(368\) 0 0
\(369\) 12.9443 14.4721i 0.673852 0.753389i
\(370\) 0 0
\(371\) 4.00000i 0.207670i
\(372\) 0 0
\(373\) 2.58359i 0.133773i 0.997761 + 0.0668867i \(0.0213066\pi\)
−0.997761 + 0.0668867i \(0.978693\pi\)
\(374\) 0 0
\(375\) 2.47214 + 0.944272i 0.127661 + 0.0487620i
\(376\) 0 0
\(377\) 21.3050i 1.09726i
\(378\) 0 0
\(379\) −10.6525 −0.547181 −0.273590 0.961846i \(-0.588211\pi\)
−0.273590 + 0.961846i \(0.588211\pi\)
\(380\) 0 0
\(381\) −8.18034 + 21.4164i −0.419092 + 1.09720i
\(382\) 0 0
\(383\) 28.9443 1.47898 0.739492 0.673166i \(-0.235066\pi\)
0.739492 + 0.673166i \(0.235066\pi\)
\(384\) 0 0
\(385\) 20.9443 1.06742
\(386\) 0 0
\(387\) 16.1803 + 14.4721i 0.822493 + 0.735660i
\(388\) 0 0
\(389\) −32.1803 −1.63161 −0.815804 0.578328i \(-0.803705\pi\)
−0.815804 + 0.578328i \(0.803705\pi\)
\(390\) 0 0
\(391\) 6.11146i 0.309070i
\(392\) 0 0
\(393\) 4.18034 10.9443i 0.210870 0.552065i
\(394\) 0 0
\(395\) 0.944272i 0.0475115i
\(396\) 0 0
\(397\) 17.4164i 0.874104i −0.899436 0.437052i \(-0.856022\pi\)
0.899436 0.437052i \(-0.143978\pi\)
\(398\) 0 0
\(399\) 0.583592 1.52786i 0.0292161 0.0764889i
\(400\) 0 0
\(401\) 28.3607i 1.41626i 0.706080 + 0.708132i \(0.250462\pi\)
−0.706080 + 0.708132i \(0.749538\pi\)
\(402\) 0 0
\(403\) −23.4164 −1.16645
\(404\) 0 0
\(405\) −3.23607 28.9443i −0.160802 1.43825i
\(406\) 0 0
\(407\) 44.3607 2.19888
\(408\) 0 0
\(409\) 31.8885 1.57679 0.788394 0.615171i \(-0.210913\pi\)
0.788394 + 0.615171i \(0.210913\pi\)
\(410\) 0 0
\(411\) −0.944272 + 2.47214i −0.0465775 + 0.121941i
\(412\) 0 0
\(413\) 1.52786 0.0751813
\(414\) 0 0
\(415\) 8.94427i 0.439057i
\(416\) 0 0
\(417\) 15.7082 + 6.00000i 0.769234 + 0.293821i
\(418\) 0 0
\(419\) 10.1803i 0.497342i 0.968588 + 0.248671i \(0.0799938\pi\)
−0.968588 + 0.248671i \(0.920006\pi\)
\(420\) 0 0
\(421\) 21.4164i 1.04377i −0.853015 0.521886i \(-0.825229\pi\)
0.853015 0.521886i \(-0.174771\pi\)
\(422\) 0 0
\(423\) −17.8885 16.0000i −0.869771 0.777947i
\(424\) 0 0
\(425\) 13.5279i 0.656198i
\(426\) 0 0
\(427\) −0.583592 −0.0282420
\(428\) 0 0
\(429\) −37.8885 14.4721i −1.82928 0.698721i
\(430\) 0 0
\(431\) 8.00000 0.385346 0.192673 0.981263i \(-0.438284\pi\)
0.192673 + 0.981263i \(0.438284\pi\)
\(432\) 0 0
\(433\) 16.4721 0.791600 0.395800 0.918337i \(-0.370467\pi\)
0.395800 + 0.918337i \(0.370467\pi\)
\(434\) 0 0
\(435\) 24.9443 + 9.52786i 1.19599 + 0.456826i
\(436\) 0 0
\(437\) −1.88854 −0.0903413
\(438\) 0 0
\(439\) 22.1803i 1.05861i 0.848432 + 0.529305i \(0.177547\pi\)
−0.848432 + 0.529305i \(0.822453\pi\)
\(440\) 0 0
\(441\) 12.2361 + 10.9443i 0.582670 + 0.521156i
\(442\) 0 0
\(443\) 16.2918i 0.774047i 0.922070 + 0.387023i \(0.126497\pi\)
−0.922070 + 0.387023i \(0.873503\pi\)
\(444\) 0 0
\(445\) 12.9443i 0.613617i
\(446\) 0 0
\(447\) −15.7082 6.00000i −0.742973 0.283790i
\(448\) 0 0
\(449\) 0.583592i 0.0275414i 0.999905 + 0.0137707i \(0.00438349\pi\)
−0.999905 + 0.0137707i \(0.995617\pi\)
\(450\) 0 0
\(451\) 33.8885 1.59575
\(452\) 0 0
\(453\) −12.1803 + 31.8885i −0.572282 + 1.49825i
\(454\) 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
\(459\) −11.4164 + 5.88854i −0.532872 + 0.274854i
\(460\) 0 0
\(461\) −8.18034 −0.380996 −0.190498 0.981688i \(-0.561010\pi\)
−0.190498 + 0.981688i \(0.561010\pi\)
\(462\) 0 0
\(463\) 34.7639i 1.61562i 0.589445 + 0.807808i \(0.299346\pi\)
−0.589445 + 0.807808i \(0.700654\pi\)
\(464\) 0 0
\(465\) 10.4721 27.4164i 0.485634 1.27141i
\(466\) 0 0
\(467\) 10.7639i 0.498095i −0.968491 0.249048i \(-0.919882\pi\)
0.968491 0.249048i \(-0.0801176\pi\)
\(468\) 0 0
\(469\) 12.0000i 0.554109i
\(470\) 0 0
\(471\) −2.76393 + 7.23607i −0.127355 + 0.333420i
\(472\) 0 0
\(473\) 37.8885i 1.74212i
\(474\) 0 0
\(475\) 4.18034 0.191807
\(476\) 0 0
\(477\) −7.23607 6.47214i −0.331317 0.296339i
\(478\) 0 0
\(479\) −6.11146 −0.279240 −0.139620 0.990205i \(-0.544588\pi\)
−0.139620 + 0.990205i \(0.544588\pi\)
\(480\) 0 0
\(481\) −37.8885 −1.72757
\(482\) 0 0
\(483\) −1.88854 + 4.94427i −0.0859317 + 0.224972i
\(484\) 0 0
\(485\) −1.52786 −0.0693767
\(486\) 0 0
\(487\) 32.6525i 1.47962i −0.672813 0.739812i \(-0.734914\pi\)
0.672813 0.739812i \(-0.265086\pi\)
\(488\) 0 0
\(489\) 6.76393 + 2.58359i 0.305876 + 0.116834i
\(490\) 0 0
\(491\) 32.0689i 1.44725i −0.690194 0.723624i \(-0.742475\pi\)
0.690194 0.723624i \(-0.257525\pi\)
\(492\) 0 0
\(493\) 11.7771i 0.530413i
\(494\) 0 0
\(495\) 33.8885 37.8885i 1.52318 1.70296i
\(496\) 0 0
\(497\) 19.0557i 0.854766i
\(498\) 0 0
\(499\) −27.2361 −1.21925 −0.609627 0.792688i \(-0.708681\pi\)
−0.609627 + 0.792688i \(0.708681\pi\)
\(500\) 0 0
\(501\) 21.8885 + 8.36068i 0.977908 + 0.373528i
\(502\) 0 0
\(503\) −21.5279 −0.959880 −0.479940 0.877301i \(-0.659342\pi\)
−0.479940 + 0.877301i \(0.659342\pi\)
\(504\) 0 0
\(505\) −5.52786 −0.245987
\(506\) 0 0
\(507\) 11.3262 + 4.32624i 0.503016 + 0.192135i
\(508\) 0 0
\(509\) 25.7082 1.13950 0.569748 0.821819i \(-0.307041\pi\)
0.569748 + 0.821819i \(0.307041\pi\)
\(510\) 0 0
\(511\) 2.47214i 0.109361i
\(512\) 0 0
\(513\) −1.81966 3.52786i −0.0803400 0.155759i
\(514\) 0 0
\(515\) 45.8885i 2.02209i
\(516\) 0 0
\(517\) 41.8885i 1.84226i
\(518\) 0 0
\(519\) −36.6525 14.0000i −1.60887 0.614532i
\(520\) 0 0
\(521\) 24.3607i 1.06726i 0.845718 + 0.533630i \(0.179173\pi\)
−0.845718 + 0.533630i \(0.820827\pi\)
\(522\) 0 0
\(523\) −11.8197 −0.516838 −0.258419 0.966033i \(-0.583201\pi\)
−0.258419 + 0.966033i \(0.583201\pi\)
\(524\) 0 0
\(525\) 4.18034 10.9443i 0.182445 0.477647i
\(526\) 0 0
\(527\) −12.9443 −0.563861
\(528\) 0 0
\(529\) −16.8885 −0.734285
\(530\) 0 0
\(531\) 2.47214 2.76393i 0.107282 0.119944i
\(532\) 0 0
\(533\) −28.9443 −1.25372
\(534\) 0 0
\(535\) 45.8885i 1.98393i
\(536\) 0 0
\(537\) −3.81966 + 10.0000i −0.164831 + 0.431532i
\(538\) 0 0
\(539\) 28.6525i 1.23415i
\(540\) 0 0
\(541\) 26.3607i 1.13333i 0.823947 + 0.566667i \(0.191767\pi\)
−0.823947 + 0.566667i \(0.808233\pi\)
\(542\) 0 0
\(543\) 12.6525 33.1246i 0.542970 1.42151i
\(544\) 0 0
\(545\) 27.4164i 1.17439i
\(546\) 0 0
\(547\) −7.23607 −0.309392 −0.154696 0.987962i \(-0.549440\pi\)
−0.154696 + 0.987962i \(0.549440\pi\)
\(548\) 0 0
\(549\) −0.944272 + 1.05573i −0.0403005 + 0.0450574i
\(550\) 0 0
\(551\) 3.63932 0.155040
\(552\) 0 0
\(553\) 0.360680 0.0153377
\(554\) 0 0
\(555\) 16.9443 44.3607i 0.719244 1.88301i
\(556\) 0 0
\(557\) 14.6525 0.620845 0.310423 0.950599i \(-0.399529\pi\)
0.310423 + 0.950599i \(0.399529\pi\)
\(558\) 0 0
\(559\) 32.3607i 1.36871i
\(560\) 0 0
\(561\) −20.9443 8.00000i −0.884268 0.337760i
\(562\) 0 0
\(563\) 30.5410i 1.28715i −0.765383 0.643575i \(-0.777450\pi\)
0.765383 0.643575i \(-0.222550\pi\)
\(564\) 0 0
\(565\) 25.8885i 1.08914i
\(566\) 0 0
\(567\) −11.0557 + 1.23607i −0.464297 + 0.0519100i
\(568\) 0 0
\(569\) 46.4721i 1.94821i −0.226089 0.974107i \(-0.572594\pi\)
0.226089 0.974107i \(-0.427406\pi\)
\(570\) 0 0
\(571\) 5.12461 0.214458 0.107229 0.994234i \(-0.465802\pi\)
0.107229 + 0.994234i \(0.465802\pi\)
\(572\) 0 0
\(573\) 20.9443 + 8.00000i 0.874960 + 0.334205i
\(574\) 0 0
\(575\) −13.5279 −0.564151
\(576\) 0 0
\(577\) 28.4721 1.18531 0.592655 0.805456i \(-0.298080\pi\)
0.592655 + 0.805456i \(0.298080\pi\)
\(578\) 0 0
\(579\) 19.2361 + 7.34752i 0.799424 + 0.305353i
\(580\) 0 0
\(581\) 3.41641 0.141736
\(582\) 0 0
\(583\) 16.9443i 0.701760i
\(584\) 0 0
\(585\) −28.9443 + 32.3607i −1.19670 + 1.33795i
\(586\) 0 0
\(587\) 21.5967i 0.891393i 0.895184 + 0.445697i \(0.147044\pi\)
−0.895184 + 0.445697i \(0.852956\pi\)
\(588\) 0 0
\(589\) 4.00000i 0.164817i
\(590\) 0 0
\(591\) −7.70820 2.94427i −0.317073 0.121111i
\(592\) 0 0
\(593\) 28.9443i 1.18860i −0.804244 0.594299i \(-0.797429\pi\)
0.804244 0.594299i \(-0.202571\pi\)
\(594\) 0 0
\(595\) −9.88854 −0.405391
\(596\) 0 0
\(597\) 3.81966 10.0000i 0.156328 0.409273i
\(598\) 0 0
\(599\) 7.41641 0.303026 0.151513 0.988455i \(-0.451585\pi\)
0.151513 + 0.988455i \(0.451585\pi\)
\(600\) 0 0
\(601\) −33.7771 −1.37780 −0.688898 0.724858i \(-0.741905\pi\)
−0.688898 + 0.724858i \(0.741905\pi\)
\(602\) 0 0
\(603\) 21.7082 + 19.4164i 0.884026 + 0.790697i
\(604\) 0 0
\(605\) 53.1246 2.15982
\(606\) 0 0
\(607\) 34.7639i 1.41102i 0.708698 + 0.705512i \(0.249283\pi\)
−0.708698 + 0.705512i \(0.750717\pi\)
\(608\) 0 0
\(609\) 3.63932 9.52786i 0.147473 0.386089i
\(610\) 0 0
\(611\) 35.7771i 1.44739i
\(612\) 0 0
\(613\) 19.3050i 0.779720i 0.920874 + 0.389860i \(0.127477\pi\)
−0.920874 + 0.389860i \(0.872523\pi\)
\(614\) 0 0
\(615\) 12.9443 33.8885i 0.521963 1.36652i
\(616\) 0 0
\(617\) 21.8885i 0.881200i −0.897704 0.440600i \(-0.854766\pi\)
0.897704 0.440600i \(-0.145234\pi\)
\(618\) 0 0
\(619\) 29.1246 1.17062 0.585308 0.810811i \(-0.300973\pi\)
0.585308 + 0.810811i \(0.300973\pi\)
\(620\) 0 0
\(621\) 5.88854 + 11.4164i 0.236299 + 0.458125i
\(622\) 0 0
\(623\) 4.94427 0.198088
\(624\) 0 0
\(625\) −22.4164 −0.896656
\(626\) 0 0
\(627\) 2.47214 6.47214i 0.0987276 0.258472i
\(628\) 0 0
\(629\) −20.9443 −0.835103
\(630\) 0 0
\(631\) 19.1246i 0.761339i 0.924711 + 0.380669i \(0.124306\pi\)
−0.924711 + 0.380669i \(0.875694\pi\)
\(632\) 0 0
\(633\) 18.1803 + 6.94427i 0.722604 + 0.276010i
\(634\) 0 0
\(635\) 42.8328i 1.69977i
\(636\) 0 0
\(637\) 24.4721i 0.969621i
\(638\) 0 0
\(639\) 34.4721 + 30.8328i 1.36370 + 1.21973i
\(640\) 0 0
\(641\) 25.3050i 0.999485i 0.866174 + 0.499743i \(0.166572\pi\)
−0.866174 + 0.499743i \(0.833428\pi\)
\(642\) 0 0
\(643\) −13.3475 −0.526375 −0.263187 0.964745i \(-0.584774\pi\)
−0.263187 + 0.964745i \(0.584774\pi\)
\(644\) 0 0
\(645\) 37.8885 + 14.4721i 1.49186 + 0.569840i
\(646\) 0 0
\(647\) −33.3050 −1.30935 −0.654676 0.755909i \(-0.727195\pi\)
−0.654676 + 0.755909i \(0.727195\pi\)
\(648\) 0 0
\(649\) 6.47214 0.254054
\(650\) 0 0
\(651\) −10.4721 4.00000i −0.410435 0.156772i
\(652\) 0 0
\(653\) −14.2918 −0.559281 −0.279641 0.960105i \(-0.590215\pi\)
−0.279641 + 0.960105i \(0.590215\pi\)
\(654\) 0 0
\(655\) 21.8885i 0.855256i
\(656\) 0 0
\(657\) 4.47214 + 4.00000i 0.174475 + 0.156055i
\(658\) 0 0
\(659\) 28.2918i 1.10209i −0.834475 0.551046i \(-0.814229\pi\)
0.834475 0.551046i \(-0.185771\pi\)
\(660\) 0 0
\(661\) 51.3050i 1.99553i 0.0668107 + 0.997766i \(0.478718\pi\)
−0.0668107 + 0.997766i \(0.521282\pi\)
\(662\) 0 0
\(663\) 17.8885 + 6.83282i 0.694733 + 0.265365i
\(664\) 0 0
\(665\) 3.05573i 0.118496i
\(666\) 0 0
\(667\) −11.7771 −0.456011
\(668\) 0 0
\(669\) −6.29180 + 16.4721i −0.243255 + 0.636850i
\(670\) 0 0
\(671\) −2.47214 −0.0954358
\(672\) 0 0
\(673\) −25.4164 −0.979731 −0.489865 0.871798i \(-0.662954\pi\)
−0.489865 + 0.871798i \(0.662954\pi\)
\(674\) 0 0
\(675\) −13.0344 25.2705i −0.501696 0.972662i
\(676\) 0 0
\(677\) −14.2918 −0.549278 −0.274639 0.961547i \(-0.588558\pi\)
−0.274639 + 0.961547i \(0.588558\pi\)
\(678\) 0 0
\(679\) 0.583592i 0.0223962i
\(680\) 0 0
\(681\) 1.34752 3.52786i 0.0516372 0.135188i
\(682\) 0 0
\(683\) 13.2361i 0.506464i 0.967406 + 0.253232i \(0.0814936\pi\)
−0.967406 + 0.253232i \(0.918506\pi\)
\(684\) 0 0
\(685\) 4.94427i 0.188911i
\(686\) 0 0
\(687\) −7.12461 + 18.6525i −0.271821 + 0.711636i
\(688\) 0 0
\(689\) 14.4721i 0.551344i
\(690\) 0 0
\(691\) 29.7082 1.13015 0.565077 0.825038i \(-0.308847\pi\)
0.565077 + 0.825038i \(0.308847\pi\)
\(692\) 0 0
\(693\) −14.4721 12.9443i −0.549751 0.491712i
\(694\) 0 0
\(695\) 31.4164 1.19169
\(696\) 0 0
\(697\) −16.0000 −0.606043
\(698\) 0 0
\(699\) 15.4164 40.3607i 0.583102 1.52658i
\(700\) 0 0
\(701\) −14.2918 −0.539794 −0.269897 0.962889i \(-0.586990\pi\)
−0.269897 + 0.962889i \(0.586990\pi\)
\(702\) 0 0
\(703\) 6.47214i 0.244101i
\(704\) 0 0
\(705\) −41.8885 16.0000i −1.57761 0.602595i
\(706\) 0 0
\(707\) 2.11146i 0.0794095i
\(708\) 0 0
\(709\) 7.52786i 0.282715i 0.989959 + 0.141357i \(0.0451467\pi\)
−0.989959 + 0.141357i \(0.954853\pi\)
\(710\) 0 0
\(711\) 0.583592 0.652476i 0.0218864 0.0244698i
\(712\) 0 0
\(713\) 12.9443i 0.484767i
\(714\) 0 0
\(715\) −75.7771 −2.83390
\(716\) 0 0
\(717\) −12.9443 4.94427i −0.483413 0.184647i
\(718\) 0 0
\(719\) −30.8328 −1.14987 −0.574935 0.818199i \(-0.694973\pi\)
−0.574935 + 0.818199i \(0.694973\pi\)
\(720\) 0 0
\(721\) −17.5279 −0.652772
\(722\) 0 0
\(723\) 3.23607 + 1.23607i 0.120351 + 0.0459699i
\(724\) 0 0
\(725\) 26.0689 0.968174
\(726\) 0 0
\(727\) 14.1803i 0.525920i 0.964807 + 0.262960i \(0.0846987\pi\)
−0.964807 + 0.262960i \(0.915301\pi\)
\(728\) 0 0
\(729\) −15.6525 + 22.0000i −0.579721 + 0.814815i
\(730\) 0 0
\(731\) 17.8885i 0.661632i
\(732\) 0 0
\(733\) 29.4164i 1.08652i 0.839565 + 0.543260i \(0.182810\pi\)
−0.839565 + 0.543260i \(0.817190\pi\)
\(734\) 0 0
\(735\) 28.6525 + 10.9443i 1.05686 + 0.403686i
\(736\) 0 0
\(737\) 50.8328i 1.87245i
\(738\) 0 0
\(739\) −13.1246 −0.482797 −0.241398 0.970426i \(-0.577606\pi\)
−0.241398 + 0.970426i \(0.577606\pi\)
\(740\) 0 0
\(741\) −2.11146 + 5.52786i −0.0775663 + 0.203071i
\(742\) 0 0
\(743\) −7.41641 −0.272082 −0.136041 0.990703i \(-0.543438\pi\)
−0.136041 + 0.990703i \(0.543438\pi\)
\(744\) 0 0
\(745\) −31.4164 −1.15101
\(746\) 0 0
\(747\) 5.52786 6.18034i 0.202254 0.226127i
\(748\) 0 0
\(749\) 17.5279 0.640454
\(750\) 0 0
\(751\) 17.5967i 0.642114i 0.947060 + 0.321057i \(0.104038\pi\)
−0.947060 + 0.321057i \(0.895962\pi\)
\(752\) 0 0
\(753\) −14.6525 + 38.3607i −0.533966 + 1.39794i
\(754\) 0 0
\(755\) 63.7771i 2.32109i
\(756\) 0 0
\(757\) 5.41641i 0.196863i −0.995144 0.0984313i \(-0.968618\pi\)
0.995144 0.0984313i \(-0.0313825\pi\)
\(758\) 0 0
\(759\) −8.00000 + 20.9443i −0.290382 + 0.760229i
\(760\) 0 0
\(761\) 42.2492i 1.53153i 0.643119 + 0.765767i \(0.277640\pi\)
−0.643119 + 0.765767i \(0.722360\pi\)
\(762\) 0 0
\(763\) −10.4721 −0.379117
\(764\) 0 0
\(765\) −16.0000 + 17.8885i −0.578481 + 0.646762i
\(766\) 0 0
\(767\) −5.52786 −0.199600
\(768\) 0 0
\(769\) 49.7771 1.79501 0.897504 0.441007i \(-0.145378\pi\)
0.897504 + 0.441007i \(0.145378\pi\)
\(770\) 0 0
\(771\) −12.9443 + 33.8885i −0.466177 + 1.22047i
\(772\) 0 0
\(773\) 7.81966 0.281254 0.140627 0.990063i \(-0.455088\pi\)
0.140627 + 0.990063i \(0.455088\pi\)
\(774\) 0 0
\(775\) 28.6525i 1.02923i
\(776\) 0 0
\(777\) −16.9443 6.47214i −0.607872 0.232187i
\(778\) 0 0
\(779\) 4.94427i 0.177147i
\(780\) 0 0
\(781\) 80.7214i 2.88844i
\(782\) 0 0
\(783\) −11.3475 22.0000i −0.405527 0.786216i
\(784\) 0 0
\(785\) 14.4721i 0.516533i
\(786\) 0 0
\(787\) −28.1803 −1.00452 −0.502260 0.864716i \(-0.667498\pi\)
−0.502260 + 0.864716i \(0.667498\pi\)
\(788\) 0 0
\(789\) 16.9443 + 6.47214i 0.603232 + 0.230414i
\(790\) 0 0
\(791\) 9.88854 0.351596
\(792\) 0 0
\(793\) 2.11146 0.0749800