Properties

Label 441.2.p.a.80.2
Level $441$
Weight $2$
Character 441.80
Analytic conductor $3.521$
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] = [441,2,Mod(80,441)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(441, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("441.80");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 441.p (of order \(6\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.52140272914\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\sqrt{-2}, \sqrt{-3})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - 2x^{2} + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 63)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 80.2
Root \(1.22474 - 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 441.80
Dual form 441.2.p.a.215.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.22474 - 0.707107i) q^{2} +(1.22474 + 2.12132i) q^{5} +2.82843i q^{8} +O(q^{10})\) \(q+(1.22474 - 0.707107i) q^{2} +(1.22474 + 2.12132i) q^{5} +2.82843i q^{8} +(3.00000 + 1.73205i) q^{10} +(-1.22474 - 0.707107i) q^{11} +5.19615i q^{13} +(2.00000 + 3.46410i) q^{16} +(2.44949 - 4.24264i) q^{17} +(-1.50000 + 0.866025i) q^{19} -2.00000 q^{22} +(4.89898 - 2.82843i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(3.67423 + 6.36396i) q^{26} -2.82843i q^{29} +(-1.50000 - 0.866025i) q^{31} -6.92820i q^{34} +(0.500000 + 0.866025i) q^{37} +(-1.22474 + 2.12132i) q^{38} +(-6.00000 + 3.46410i) q^{40} +7.34847 q^{41} -1.00000 q^{43} +(4.00000 - 6.92820i) q^{46} +(-6.12372 - 10.6066i) q^{47} +1.41421i q^{50} +(2.44949 + 1.41421i) q^{53} -3.46410i q^{55} +(-2.00000 - 3.46410i) q^{58} +(2.44949 - 4.24264i) q^{59} +(3.00000 - 1.73205i) q^{61} -2.44949 q^{62} -8.00000 q^{64} +(-11.0227 + 6.36396i) q^{65} +(-5.50000 + 9.52628i) q^{67} -7.07107i q^{71} +(-1.50000 - 0.866025i) q^{73} +(1.22474 + 0.707107i) q^{74} +(-2.50000 - 4.33013i) q^{79} +(-4.89898 + 8.48528i) q^{80} +(9.00000 - 5.19615i) q^{82} -7.34847 q^{83} +12.0000 q^{85} +(-1.22474 + 0.707107i) q^{86} +(2.00000 - 3.46410i) q^{88} +(-2.44949 - 4.24264i) q^{89} +(-15.0000 - 8.66025i) q^{94} +(-3.67423 - 2.12132i) q^{95} +10.3923i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 12 q^{10} + 8 q^{16} - 6 q^{19} - 8 q^{22} - 2 q^{25} - 6 q^{31} + 2 q^{37} - 24 q^{40} - 4 q^{43} + 16 q^{46} - 8 q^{58} + 12 q^{61} - 32 q^{64} - 22 q^{67} - 6 q^{73} - 10 q^{79} + 36 q^{82} + 48 q^{85} + 8 q^{88} - 60 q^{94}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(344\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.22474 0.707107i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(3\) 0 0
\(4\) 0 0
\(5\) 1.22474 + 2.12132i 0.547723 + 0.948683i 0.998430 + 0.0560116i \(0.0178384\pi\)
−0.450708 + 0.892672i \(0.648828\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 2.82843i 1.00000i
\(9\) 0 0
\(10\) 3.00000 + 1.73205i 0.948683 + 0.547723i
\(11\) −1.22474 0.707107i −0.369274 0.213201i 0.303867 0.952714i \(-0.401722\pi\)
−0.673141 + 0.739514i \(0.735055\pi\)
\(12\) 0 0
\(13\) 5.19615i 1.44115i 0.693375 + 0.720577i \(0.256123\pi\)
−0.693375 + 0.720577i \(0.743877\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 2.00000 + 3.46410i 0.500000 + 0.866025i
\(17\) 2.44949 4.24264i 0.594089 1.02899i −0.399586 0.916696i \(-0.630846\pi\)
0.993675 0.112296i \(-0.0358205\pi\)
\(18\) 0 0
\(19\) −1.50000 + 0.866025i −0.344124 + 0.198680i −0.662094 0.749421i \(-0.730332\pi\)
0.317970 + 0.948101i \(0.396999\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) −2.00000 −0.426401
\(23\) 4.89898 2.82843i 1.02151 0.589768i 0.106967 0.994263i \(-0.465886\pi\)
0.914540 + 0.404495i \(0.132553\pi\)
\(24\) 0 0
\(25\) −0.500000 + 0.866025i −0.100000 + 0.173205i
\(26\) 3.67423 + 6.36396i 0.720577 + 1.24808i
\(27\) 0 0
\(28\) 0 0
\(29\) 2.82843i 0.525226i −0.964901 0.262613i \(-0.915416\pi\)
0.964901 0.262613i \(-0.0845842\pi\)
\(30\) 0 0
\(31\) −1.50000 0.866025i −0.269408 0.155543i 0.359211 0.933257i \(-0.383046\pi\)
−0.628619 + 0.777714i \(0.716379\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 6.92820i 1.18818i
\(35\) 0 0
\(36\) 0 0
\(37\) 0.500000 + 0.866025i 0.0821995 + 0.142374i 0.904194 0.427121i \(-0.140472\pi\)
−0.821995 + 0.569495i \(0.807139\pi\)
\(38\) −1.22474 + 2.12132i −0.198680 + 0.344124i
\(39\) 0 0
\(40\) −6.00000 + 3.46410i −0.948683 + 0.547723i
\(41\) 7.34847 1.14764 0.573819 0.818982i \(-0.305461\pi\)
0.573819 + 0.818982i \(0.305461\pi\)
\(42\) 0 0
\(43\) −1.00000 −0.152499 −0.0762493 0.997089i \(-0.524294\pi\)
−0.0762493 + 0.997089i \(0.524294\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 4.00000 6.92820i 0.589768 1.02151i
\(47\) −6.12372 10.6066i −0.893237 1.54713i −0.835971 0.548773i \(-0.815095\pi\)
−0.0572655 0.998359i \(-0.518238\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 1.41421i 0.200000i
\(51\) 0 0
\(52\) 0 0
\(53\) 2.44949 + 1.41421i 0.336463 + 0.194257i 0.658707 0.752400i \(-0.271104\pi\)
−0.322244 + 0.946657i \(0.604437\pi\)
\(54\) 0 0
\(55\) 3.46410i 0.467099i
\(56\) 0 0
\(57\) 0 0
\(58\) −2.00000 3.46410i −0.262613 0.454859i
\(59\) 2.44949 4.24264i 0.318896 0.552345i −0.661362 0.750067i \(-0.730021\pi\)
0.980258 + 0.197722i \(0.0633545\pi\)
\(60\) 0 0
\(61\) 3.00000 1.73205i 0.384111 0.221766i −0.295495 0.955344i \(-0.595484\pi\)
0.679605 + 0.733578i \(0.262151\pi\)
\(62\) −2.44949 −0.311086
\(63\) 0 0
\(64\) −8.00000 −1.00000
\(65\) −11.0227 + 6.36396i −1.36720 + 0.789352i
\(66\) 0 0
\(67\) −5.50000 + 9.52628i −0.671932 + 1.16382i 0.305424 + 0.952217i \(0.401202\pi\)
−0.977356 + 0.211604i \(0.932131\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 7.07107i 0.839181i −0.907713 0.419591i \(-0.862174\pi\)
0.907713 0.419591i \(-0.137826\pi\)
\(72\) 0 0
\(73\) −1.50000 0.866025i −0.175562 0.101361i 0.409644 0.912245i \(-0.365653\pi\)
−0.585206 + 0.810885i \(0.698986\pi\)
\(74\) 1.22474 + 0.707107i 0.142374 + 0.0821995i
\(75\) 0 0
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −2.50000 4.33013i −0.281272 0.487177i 0.690426 0.723403i \(-0.257423\pi\)
−0.971698 + 0.236225i \(0.924090\pi\)
\(80\) −4.89898 + 8.48528i −0.547723 + 0.948683i
\(81\) 0 0
\(82\) 9.00000 5.19615i 0.993884 0.573819i
\(83\) −7.34847 −0.806599 −0.403300 0.915068i \(-0.632137\pi\)
−0.403300 + 0.915068i \(0.632137\pi\)
\(84\) 0 0
\(85\) 12.0000 1.30158
\(86\) −1.22474 + 0.707107i −0.132068 + 0.0762493i
\(87\) 0 0
\(88\) 2.00000 3.46410i 0.213201 0.369274i
\(89\) −2.44949 4.24264i −0.259645 0.449719i 0.706502 0.707712i \(-0.250272\pi\)
−0.966147 + 0.257993i \(0.916939\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) −15.0000 8.66025i −1.54713 0.893237i
\(95\) −3.67423 2.12132i −0.376969 0.217643i
\(96\) 0 0
\(97\) 10.3923i 1.05518i 0.849500 + 0.527589i \(0.176904\pi\)
−0.849500 + 0.527589i \(0.823096\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −8.57321 + 14.8492i −0.853067 + 1.47755i 0.0253604 + 0.999678i \(0.491927\pi\)
−0.878427 + 0.477876i \(0.841407\pi\)
\(102\) 0 0
\(103\) 7.50000 4.33013i 0.738997 0.426660i −0.0827075 0.996574i \(-0.526357\pi\)
0.821705 + 0.569914i \(0.193023\pi\)
\(104\) −14.6969 −1.44115
\(105\) 0 0
\(106\) 4.00000 0.388514
\(107\) −2.44949 + 1.41421i −0.236801 + 0.136717i −0.613706 0.789535i \(-0.710322\pi\)
0.376905 + 0.926252i \(0.376988\pi\)
\(108\) 0 0
\(109\) 0.500000 0.866025i 0.0478913 0.0829502i −0.841086 0.540901i \(-0.818083\pi\)
0.888977 + 0.457951i \(0.151417\pi\)
\(110\) −2.44949 4.24264i −0.233550 0.404520i
\(111\) 0 0
\(112\) 0 0
\(113\) 1.41421i 0.133038i 0.997785 + 0.0665190i \(0.0211893\pi\)
−0.997785 + 0.0665190i \(0.978811\pi\)
\(114\) 0 0
\(115\) 12.0000 + 6.92820i 1.11901 + 0.646058i
\(116\) 0 0
\(117\) 0 0
\(118\) 6.92820i 0.637793i
\(119\) 0 0
\(120\) 0 0
\(121\) −4.50000 7.79423i −0.409091 0.708566i
\(122\) 2.44949 4.24264i 0.221766 0.384111i
\(123\) 0 0
\(124\) 0 0
\(125\) 9.79796 0.876356
\(126\) 0 0
\(127\) 11.0000 0.976092 0.488046 0.872818i \(-0.337710\pi\)
0.488046 + 0.872818i \(0.337710\pi\)
\(128\) −9.79796 + 5.65685i −0.866025 + 0.500000i
\(129\) 0 0
\(130\) −9.00000 + 15.5885i −0.789352 + 1.36720i
\(131\) 1.22474 + 2.12132i 0.107006 + 0.185341i 0.914556 0.404459i \(-0.132540\pi\)
−0.807550 + 0.589799i \(0.799207\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 15.5563i 1.34386i
\(135\) 0 0
\(136\) 12.0000 + 6.92820i 1.02899 + 0.594089i
\(137\) 9.79796 + 5.65685i 0.837096 + 0.483298i 0.856276 0.516518i \(-0.172772\pi\)
−0.0191800 + 0.999816i \(0.506106\pi\)
\(138\) 0 0
\(139\) 5.19615i 0.440732i 0.975417 + 0.220366i \(0.0707252\pi\)
−0.975417 + 0.220366i \(0.929275\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −5.00000 8.66025i −0.419591 0.726752i
\(143\) 3.67423 6.36396i 0.307255 0.532181i
\(144\) 0 0
\(145\) 6.00000 3.46410i 0.498273 0.287678i
\(146\) −2.44949 −0.202721
\(147\) 0 0
\(148\) 0 0
\(149\) 4.89898 2.82843i 0.401340 0.231714i −0.285722 0.958313i \(-0.592233\pi\)
0.687062 + 0.726599i \(0.258900\pi\)
\(150\) 0 0
\(151\) 11.0000 19.0526i 0.895167 1.55048i 0.0615699 0.998103i \(-0.480389\pi\)
0.833597 0.552372i \(-0.186277\pi\)
\(152\) −2.44949 4.24264i −0.198680 0.344124i
\(153\) 0 0
\(154\) 0 0
\(155\) 4.24264i 0.340777i
\(156\) 0 0
\(157\) −15.0000 8.66025i −1.19713 0.691164i −0.237216 0.971457i \(-0.576235\pi\)
−0.959914 + 0.280293i \(0.909568\pi\)
\(158\) −6.12372 3.53553i −0.487177 0.281272i
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 5.00000 + 8.66025i 0.391630 + 0.678323i 0.992665 0.120900i \(-0.0385779\pi\)
−0.601035 + 0.799223i \(0.705245\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) −9.00000 + 5.19615i −0.698535 + 0.403300i
\(167\) 7.34847 0.568642 0.284321 0.958729i \(-0.408232\pi\)
0.284321 + 0.958729i \(0.408232\pi\)
\(168\) 0 0
\(169\) −14.0000 −1.07692
\(170\) 14.6969 8.48528i 1.12720 0.650791i
\(171\) 0 0
\(172\) 0 0
\(173\) 4.89898 + 8.48528i 0.372463 + 0.645124i 0.989944 0.141462i \(-0.0451802\pi\)
−0.617481 + 0.786586i \(0.711847\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 5.65685i 0.426401i
\(177\) 0 0
\(178\) −6.00000 3.46410i −0.449719 0.259645i
\(179\) −8.57321 4.94975i −0.640792 0.369961i 0.144127 0.989559i \(-0.453962\pi\)
−0.784920 + 0.619598i \(0.787296\pi\)
\(180\) 0 0
\(181\) 15.5885i 1.15868i −0.815086 0.579340i \(-0.803310\pi\)
0.815086 0.579340i \(-0.196690\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 8.00000 + 13.8564i 0.589768 + 1.02151i
\(185\) −1.22474 + 2.12132i −0.0900450 + 0.155963i
\(186\) 0 0
\(187\) −6.00000 + 3.46410i −0.438763 + 0.253320i
\(188\) 0 0
\(189\) 0 0
\(190\) −6.00000 −0.435286
\(191\) 1.22474 0.707107i 0.0886194 0.0511645i −0.455035 0.890473i \(-0.650373\pi\)
0.543655 + 0.839309i \(0.317040\pi\)
\(192\) 0 0
\(193\) −5.50000 + 9.52628i −0.395899 + 0.685717i −0.993215 0.116289i \(-0.962900\pi\)
0.597317 + 0.802005i \(0.296234\pi\)
\(194\) 7.34847 + 12.7279i 0.527589 + 0.913812i
\(195\) 0 0
\(196\) 0 0
\(197\) 19.7990i 1.41062i −0.708899 0.705310i \(-0.750808\pi\)
0.708899 0.705310i \(-0.249192\pi\)
\(198\) 0 0
\(199\) 12.0000 + 6.92820i 0.850657 + 0.491127i 0.860873 0.508821i \(-0.169918\pi\)
−0.0102152 + 0.999948i \(0.503252\pi\)
\(200\) −2.44949 1.41421i −0.173205 0.100000i
\(201\) 0 0
\(202\) 24.2487i 1.70613i
\(203\) 0 0
\(204\) 0 0
\(205\) 9.00000 + 15.5885i 0.628587 + 1.08875i
\(206\) 6.12372 10.6066i 0.426660 0.738997i
\(207\) 0 0
\(208\) −18.0000 + 10.3923i −1.24808 + 0.720577i
\(209\) 2.44949 0.169435
\(210\) 0 0
\(211\) −22.0000 −1.51454 −0.757271 0.653101i \(-0.773468\pi\)
−0.757271 + 0.653101i \(0.773468\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) −2.00000 + 3.46410i −0.136717 + 0.236801i
\(215\) −1.22474 2.12132i −0.0835269 0.144673i
\(216\) 0 0
\(217\) 0 0
\(218\) 1.41421i 0.0957826i
\(219\) 0 0
\(220\) 0 0
\(221\) 22.0454 + 12.7279i 1.48293 + 0.856173i
\(222\) 0 0
\(223\) 20.7846i 1.39184i −0.718119 0.695920i \(-0.754997\pi\)
0.718119 0.695920i \(-0.245003\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 1.00000 + 1.73205i 0.0665190 + 0.115214i
\(227\) 13.4722 23.3345i 0.894181 1.54877i 0.0593658 0.998236i \(-0.481092\pi\)
0.834815 0.550530i \(-0.185575\pi\)
\(228\) 0 0
\(229\) −19.5000 + 11.2583i −1.28860 + 0.743971i −0.978404 0.206702i \(-0.933727\pi\)
−0.310192 + 0.950674i \(0.600393\pi\)
\(230\) 19.5959 1.29212
\(231\) 0 0
\(232\) 8.00000 0.525226
\(233\) 8.57321 4.94975i 0.561650 0.324269i −0.192158 0.981364i \(-0.561548\pi\)
0.753807 + 0.657095i \(0.228215\pi\)
\(234\) 0 0
\(235\) 15.0000 25.9808i 0.978492 1.69480i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 26.8701i 1.73808i 0.494742 + 0.869040i \(0.335262\pi\)
−0.494742 + 0.869040i \(0.664738\pi\)
\(240\) 0 0
\(241\) 12.0000 + 6.92820i 0.772988 + 0.446285i 0.833939 0.551856i \(-0.186080\pi\)
−0.0609515 + 0.998141i \(0.519414\pi\)
\(242\) −11.0227 6.36396i −0.708566 0.409091i
\(243\) 0 0
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −4.50000 7.79423i −0.286328 0.495935i
\(248\) 2.44949 4.24264i 0.155543 0.269408i
\(249\) 0 0
\(250\) 12.0000 6.92820i 0.758947 0.438178i
\(251\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(252\) 0 0
\(253\) −8.00000 −0.502956
\(254\) 13.4722 7.77817i 0.845321 0.488046i
\(255\) 0 0
\(256\) 0 0
\(257\) 1.22474 + 2.12132i 0.0763975 + 0.132324i 0.901693 0.432377i \(-0.142325\pi\)
−0.825296 + 0.564701i \(0.808992\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 3.00000 + 1.73205i 0.185341 + 0.107006i
\(263\) −12.2474 7.07107i −0.755210 0.436021i 0.0723633 0.997378i \(-0.476946\pi\)
−0.827573 + 0.561358i \(0.810279\pi\)
\(264\) 0 0
\(265\) 6.92820i 0.425596i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −8.57321 + 14.8492i −0.522718 + 0.905374i 0.476932 + 0.878940i \(0.341749\pi\)
−0.999651 + 0.0264343i \(0.991585\pi\)
\(270\) 0 0
\(271\) 12.0000 6.92820i 0.728948 0.420858i −0.0890891 0.996024i \(-0.528396\pi\)
0.818037 + 0.575165i \(0.195062\pi\)
\(272\) 19.5959 1.18818
\(273\) 0 0
\(274\) 16.0000 0.966595
\(275\) 1.22474 0.707107i 0.0738549 0.0426401i
\(276\) 0 0
\(277\) −11.5000 + 19.9186i −0.690968 + 1.19679i 0.280553 + 0.959839i \(0.409482\pi\)
−0.971521 + 0.236953i \(0.923851\pi\)
\(278\) 3.67423 + 6.36396i 0.220366 + 0.381685i
\(279\) 0 0
\(280\) 0 0
\(281\) 22.6274i 1.34984i 0.737892 + 0.674919i \(0.235822\pi\)
−0.737892 + 0.674919i \(0.764178\pi\)
\(282\) 0 0
\(283\) −1.50000 0.866025i −0.0891657 0.0514799i 0.454754 0.890617i \(-0.349727\pi\)
−0.543920 + 0.839137i \(0.683060\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 10.3923i 0.614510i
\(287\) 0 0
\(288\) 0 0
\(289\) −3.50000 6.06218i −0.205882 0.356599i
\(290\) 4.89898 8.48528i 0.287678 0.498273i
\(291\) 0 0
\(292\) 0 0
\(293\) −14.6969 −0.858604 −0.429302 0.903161i \(-0.641240\pi\)
−0.429302 + 0.903161i \(0.641240\pi\)
\(294\) 0 0
\(295\) 12.0000 0.698667
\(296\) −2.44949 + 1.41421i −0.142374 + 0.0821995i
\(297\) 0 0
\(298\) 4.00000 6.92820i 0.231714 0.401340i
\(299\) 14.6969 + 25.4558i 0.849946 + 1.47215i
\(300\) 0 0
\(301\) 0 0
\(302\) 31.1127i 1.79033i
\(303\) 0 0
\(304\) −6.00000 3.46410i −0.344124 0.198680i
\(305\) 7.34847 + 4.24264i 0.420772 + 0.242933i
\(306\) 0 0
\(307\) 15.5885i 0.889680i 0.895610 + 0.444840i \(0.146740\pi\)
−0.895610 + 0.444840i \(0.853260\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −3.00000 5.19615i −0.170389 0.295122i
\(311\) −8.57321 + 14.8492i −0.486142 + 0.842023i −0.999873 0.0159282i \(-0.994930\pi\)
0.513731 + 0.857951i \(0.328263\pi\)
\(312\) 0 0
\(313\) −10.5000 + 6.06218i −0.593495 + 0.342655i −0.766478 0.642270i \(-0.777993\pi\)
0.172983 + 0.984925i \(0.444659\pi\)
\(314\) −24.4949 −1.38233
\(315\) 0 0
\(316\) 0 0
\(317\) 12.2474 7.07107i 0.687885 0.397151i −0.114934 0.993373i \(-0.536666\pi\)
0.802819 + 0.596222i \(0.203332\pi\)
\(318\) 0 0
\(319\) −2.00000 + 3.46410i −0.111979 + 0.193952i
\(320\) −9.79796 16.9706i −0.547723 0.948683i
\(321\) 0 0
\(322\) 0 0
\(323\) 8.48528i 0.472134i
\(324\) 0 0
\(325\) −4.50000 2.59808i −0.249615 0.144115i
\(326\) 12.2474 + 7.07107i 0.678323 + 0.391630i
\(327\) 0 0
\(328\) 20.7846i 1.14764i
\(329\) 0 0
\(330\) 0 0
\(331\) 15.5000 + 26.8468i 0.851957 + 1.47563i 0.879440 + 0.476011i \(0.157918\pi\)
−0.0274825 + 0.999622i \(0.508749\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 9.00000 5.19615i 0.492458 0.284321i
\(335\) −26.9444 −1.47213
\(336\) 0 0
\(337\) 23.0000 1.25289 0.626445 0.779466i \(-0.284509\pi\)
0.626445 + 0.779466i \(0.284509\pi\)
\(338\) −17.1464 + 9.89949i −0.932643 + 0.538462i
\(339\) 0 0
\(340\) 0 0
\(341\) 1.22474 + 2.12132i 0.0663237 + 0.114876i
\(342\) 0 0
\(343\) 0 0
\(344\) 2.82843i 0.152499i
\(345\) 0 0
\(346\) 12.0000 + 6.92820i 0.645124 + 0.372463i
\(347\) −26.9444 15.5563i −1.44645 0.835109i −0.448183 0.893942i \(-0.647929\pi\)
−0.998268 + 0.0588334i \(0.981262\pi\)
\(348\) 0 0
\(349\) 10.3923i 0.556287i 0.960539 + 0.278144i \(0.0897191\pi\)
−0.960539 + 0.278144i \(0.910281\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −8.57321 + 14.8492i −0.456306 + 0.790345i −0.998762 0.0497387i \(-0.984161\pi\)
0.542456 + 0.840084i \(0.317494\pi\)
\(354\) 0 0
\(355\) 15.0000 8.66025i 0.796117 0.459639i
\(356\) 0 0
\(357\) 0 0
\(358\) −14.0000 −0.739923
\(359\) −24.4949 + 14.1421i −1.29279 + 0.746393i −0.979148 0.203148i \(-0.934883\pi\)
−0.313643 + 0.949541i \(0.601550\pi\)
\(360\) 0 0
\(361\) −8.00000 + 13.8564i −0.421053 + 0.729285i
\(362\) −11.0227 19.0919i −0.579340 1.00345i
\(363\) 0 0
\(364\) 0 0
\(365\) 4.24264i 0.222070i
\(366\) 0 0
\(367\) −1.50000 0.866025i −0.0782994 0.0452062i 0.460339 0.887743i \(-0.347728\pi\)
−0.538639 + 0.842537i \(0.681061\pi\)
\(368\) 19.5959 + 11.3137i 1.02151 + 0.589768i
\(369\) 0 0
\(370\) 3.46410i 0.180090i
\(371\) 0 0
\(372\) 0 0
\(373\) −14.5000 25.1147i −0.750782 1.30039i −0.947444 0.319921i \(-0.896344\pi\)
0.196663 0.980471i \(-0.436990\pi\)
\(374\) −4.89898 + 8.48528i −0.253320 + 0.438763i
\(375\) 0 0
\(376\) 30.0000 17.3205i 1.54713 0.893237i
\(377\) 14.6969 0.756931
\(378\) 0 0
\(379\) −7.00000 −0.359566 −0.179783 0.983706i \(-0.557540\pi\)
−0.179783 + 0.983706i \(0.557540\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 1.00000 1.73205i 0.0511645 0.0886194i
\(383\) −9.79796 16.9706i −0.500652 0.867155i −1.00000 0.000753393i \(-0.999760\pi\)
0.499347 0.866402i \(-0.333573\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 15.5563i 0.791797i
\(387\) 0 0
\(388\) 0 0
\(389\) −23.2702 13.4350i −1.17984 0.681183i −0.223865 0.974620i \(-0.571868\pi\)
−0.955978 + 0.293437i \(0.905201\pi\)
\(390\) 0 0
\(391\) 27.7128i 1.40150i
\(392\) 0 0
\(393\) 0 0
\(394\) −14.0000 24.2487i −0.705310 1.22163i
\(395\) 6.12372 10.6066i 0.308118 0.533676i
\(396\) 0 0
\(397\) −1.50000 + 0.866025i −0.0752828 + 0.0434646i −0.537169 0.843475i \(-0.680506\pi\)
0.461886 + 0.886939i \(0.347173\pi\)
\(398\) 19.5959 0.982255
\(399\) 0 0
\(400\) −4.00000 −0.200000
\(401\) −17.1464 + 9.89949i −0.856252 + 0.494357i −0.862755 0.505622i \(-0.831263\pi\)
0.00650355 + 0.999979i \(0.497930\pi\)
\(402\) 0 0
\(403\) 4.50000 7.79423i 0.224161 0.388258i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 1.41421i 0.0701000i
\(408\) 0 0
\(409\) −28.5000 16.4545i −1.40923 0.813622i −0.413920 0.910313i \(-0.635841\pi\)
−0.995314 + 0.0966915i \(0.969174\pi\)
\(410\) 22.0454 + 12.7279i 1.08875 + 0.628587i
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) −9.00000 15.5885i −0.441793 0.765207i
\(416\) 0 0
\(417\) 0 0
\(418\) 3.00000 1.73205i 0.146735 0.0847174i
\(419\) −36.7423 −1.79498 −0.897491 0.441034i \(-0.854612\pi\)
−0.897491 + 0.441034i \(0.854612\pi\)
\(420\) 0 0
\(421\) −1.00000 −0.0487370 −0.0243685 0.999703i \(-0.507758\pi\)
−0.0243685 + 0.999703i \(0.507758\pi\)
\(422\) −26.9444 + 15.5563i −1.31163 + 0.757271i
\(423\) 0 0
\(424\) −4.00000 + 6.92820i −0.194257 + 0.336463i
\(425\) 2.44949 + 4.24264i 0.118818 + 0.205798i
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) −3.00000 1.73205i −0.144673 0.0835269i
\(431\) 13.4722 + 7.77817i 0.648933 + 0.374661i 0.788047 0.615615i \(-0.211092\pi\)
−0.139114 + 0.990276i \(0.544426\pi\)
\(432\) 0 0
\(433\) 15.5885i 0.749133i −0.927200 0.374567i \(-0.877791\pi\)
0.927200 0.374567i \(-0.122209\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −4.89898 + 8.48528i −0.234350 + 0.405906i
\(438\) 0 0
\(439\) −24.0000 + 13.8564i −1.14546 + 0.661330i −0.947776 0.318936i \(-0.896674\pi\)
−0.197681 + 0.980266i \(0.563341\pi\)
\(440\) 9.79796 0.467099
\(441\) 0 0
\(442\) 36.0000 1.71235
\(443\) 34.2929 19.7990i 1.62930 0.940678i 0.645002 0.764181i \(-0.276857\pi\)
0.984301 0.176497i \(-0.0564767\pi\)
\(444\) 0 0
\(445\) 6.00000 10.3923i 0.284427 0.492642i
\(446\) −14.6969 25.4558i −0.695920 1.20537i
\(447\) 0 0
\(448\) 0 0
\(449\) 7.07107i 0.333704i −0.985982 0.166852i \(-0.946640\pi\)
0.985982 0.166852i \(-0.0533603\pi\)
\(450\) 0 0
\(451\) −9.00000 5.19615i −0.423793 0.244677i
\(452\) 0 0
\(453\) 0 0
\(454\) 38.1051i 1.78836i
\(455\) 0 0
\(456\) 0 0
\(457\) −2.50000 4.33013i −0.116945 0.202555i 0.801611 0.597847i \(-0.203977\pi\)
−0.918556 + 0.395292i \(0.870643\pi\)
\(458\) −15.9217 + 27.5772i −0.743971 + 1.28860i
\(459\) 0 0
\(460\) 0 0
\(461\) 14.6969 0.684505 0.342252 0.939608i \(-0.388810\pi\)
0.342252 + 0.939608i \(0.388810\pi\)
\(462\) 0 0
\(463\) −13.0000 −0.604161 −0.302081 0.953282i \(-0.597681\pi\)
−0.302081 + 0.953282i \(0.597681\pi\)
\(464\) 9.79796 5.65685i 0.454859 0.262613i
\(465\) 0 0
\(466\) 7.00000 12.1244i 0.324269 0.561650i
\(467\) −13.4722 23.3345i −0.623419 1.07979i −0.988844 0.148952i \(-0.952410\pi\)
0.365426 0.930841i \(-0.380923\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 42.4264i 1.95698i
\(471\) 0 0
\(472\) 12.0000 + 6.92820i 0.552345 + 0.318896i
\(473\) 1.22474 + 0.707107i 0.0563138 + 0.0325128i
\(474\) 0 0
\(475\) 1.73205i 0.0794719i
\(476\) 0 0
\(477\) 0 0
\(478\) 19.0000 + 32.9090i 0.869040 + 1.50522i
\(479\) 2.44949 4.24264i 0.111920 0.193851i −0.804624 0.593784i \(-0.797633\pi\)
0.916544 + 0.399933i \(0.130967\pi\)
\(480\) 0 0
\(481\) −4.50000 + 2.59808i −0.205182 + 0.118462i
\(482\) 19.5959 0.892570
\(483\) 0 0
\(484\) 0 0
\(485\) −22.0454 + 12.7279i −1.00103 + 0.577945i
\(486\) 0 0
\(487\) −8.50000 + 14.7224i −0.385172 + 0.667137i −0.991793 0.127854i \(-0.959191\pi\)
0.606621 + 0.794991i \(0.292524\pi\)
\(488\) 4.89898 + 8.48528i 0.221766 + 0.384111i
\(489\) 0 0
\(490\) 0 0
\(491\) 11.3137i 0.510581i −0.966864 0.255290i \(-0.917829\pi\)
0.966864 0.255290i \(-0.0821710\pi\)
\(492\) 0 0
\(493\) −12.0000 6.92820i −0.540453 0.312031i
\(494\) −11.0227 6.36396i −0.495935 0.286328i
\(495\) 0 0
\(496\) 6.92820i 0.311086i
\(497\) 0 0
\(498\) 0 0
\(499\) 12.5000 + 21.6506i 0.559577 + 0.969216i 0.997532 + 0.0702185i \(0.0223697\pi\)
−0.437955 + 0.898997i \(0.644297\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −22.0454 −0.982956 −0.491478 0.870890i \(-0.663543\pi\)
−0.491478 + 0.870890i \(0.663543\pi\)
\(504\) 0 0
\(505\) −42.0000 −1.86898
\(506\) −9.79796 + 5.65685i −0.435572 + 0.251478i
\(507\) 0 0
\(508\) 0 0
\(509\) 1.22474 + 2.12132i 0.0542859 + 0.0940259i 0.891891 0.452250i \(-0.149378\pi\)
−0.837605 + 0.546276i \(0.816045\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 22.6274i 1.00000i
\(513\) 0 0
\(514\) 3.00000 + 1.73205i 0.132324 + 0.0763975i
\(515\) 18.3712 + 10.6066i 0.809531 + 0.467383i
\(516\) 0 0
\(517\) 17.3205i 0.761755i
\(518\) 0 0
\(519\) 0 0
\(520\) −18.0000 31.1769i −0.789352 1.36720i
\(521\) 2.44949 4.24264i 0.107314 0.185873i −0.807367 0.590049i \(-0.799108\pi\)
0.914681 + 0.404176i \(0.132442\pi\)
\(522\) 0 0
\(523\) −1.50000 + 0.866025i −0.0655904 + 0.0378686i −0.532437 0.846470i \(-0.678724\pi\)
0.466846 + 0.884339i \(0.345390\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) −20.0000 −0.872041
\(527\) −7.34847 + 4.24264i −0.320104 + 0.184812i
\(528\) 0 0
\(529\) 4.50000 7.79423i 0.195652 0.338880i
\(530\) 4.89898 + 8.48528i 0.212798 + 0.368577i
\(531\) 0 0
\(532\) 0 0
\(533\) 38.1838i 1.65392i
\(534\) 0 0
\(535\) −6.00000 3.46410i −0.259403 0.149766i
\(536\) −26.9444 15.5563i −1.16382 0.671932i
\(537\) 0 0
\(538\) 24.2487i 1.04544i
\(539\) 0 0
\(540\) 0 0
\(541\) −8.50000 14.7224i −0.365444 0.632967i 0.623404 0.781900i \(-0.285749\pi\)
−0.988847 + 0.148933i \(0.952416\pi\)
\(542\) 9.79796 16.9706i 0.420858 0.728948i
\(543\) 0 0
\(544\) 0 0
\(545\) 2.44949 0.104925
\(546\) 0 0
\(547\) −10.0000 −0.427569 −0.213785 0.976881i \(-0.568579\pi\)
−0.213785 + 0.976881i \(0.568579\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 1.00000 1.73205i 0.0426401 0.0738549i
\(551\) 2.44949 + 4.24264i 0.104352 + 0.180743i
\(552\) 0 0
\(553\) 0 0
\(554\) 32.5269i 1.38194i
\(555\) 0 0
\(556\) 0 0
\(557\) 13.4722 + 7.77817i 0.570835 + 0.329572i 0.757483 0.652855i \(-0.226429\pi\)
−0.186648 + 0.982427i \(0.559762\pi\)
\(558\) 0 0
\(559\) 5.19615i 0.219774i
\(560\) 0 0
\(561\) 0 0
\(562\) 16.0000 + 27.7128i 0.674919 + 1.16899i
\(563\) 13.4722 23.3345i 0.567785 0.983433i −0.428999 0.903305i \(-0.641134\pi\)
0.996785 0.0801281i \(-0.0255329\pi\)
\(564\) 0 0
\(565\) −3.00000 + 1.73205i −0.126211 + 0.0728679i
\(566\) −2.44949 −0.102960
\(567\) 0 0
\(568\) 20.0000 0.839181
\(569\) 1.22474 0.707107i 0.0513440 0.0296435i −0.474108 0.880467i \(-0.657229\pi\)
0.525452 + 0.850823i \(0.323896\pi\)
\(570\) 0 0
\(571\) −5.50000 + 9.52628i −0.230168 + 0.398662i −0.957857 0.287244i \(-0.907261\pi\)
0.727690 + 0.685907i \(0.240594\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 5.65685i 0.235907i
\(576\) 0 0
\(577\) −1.50000 0.866025i −0.0624458 0.0360531i 0.468452 0.883489i \(-0.344812\pi\)
−0.530898 + 0.847436i \(0.678145\pi\)
\(578\) −8.57321 4.94975i −0.356599 0.205882i
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −2.00000 3.46410i −0.0828315 0.143468i
\(584\) 2.44949 4.24264i 0.101361 0.175562i
\(585\) 0 0
\(586\) −18.0000 + 10.3923i −0.743573 + 0.429302i
\(587\) 14.6969 0.606608 0.303304 0.952894i \(-0.401910\pi\)
0.303304 + 0.952894i \(0.401910\pi\)
\(588\) 0 0
\(589\) 3.00000 0.123613
\(590\) 14.6969 8.48528i 0.605063 0.349334i
\(591\) 0 0
\(592\) −2.00000 + 3.46410i −0.0821995 + 0.142374i
\(593\) 8.57321 + 14.8492i 0.352060 + 0.609785i 0.986610 0.163096i \(-0.0521481\pi\)
−0.634550 + 0.772881i \(0.718815\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 36.0000 + 20.7846i 1.47215 + 0.849946i
\(599\) −4.89898 2.82843i −0.200167 0.115566i 0.396566 0.918006i \(-0.370202\pi\)
−0.596733 + 0.802440i \(0.703535\pi\)
\(600\) 0 0
\(601\) 25.9808i 1.05978i 0.848067 + 0.529889i \(0.177766\pi\)
−0.848067 + 0.529889i \(0.822234\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 11.0227 19.0919i 0.448137 0.776195i
\(606\) 0 0
\(607\) 34.5000 19.9186i 1.40031 0.808470i 0.405887 0.913923i \(-0.366962\pi\)
0.994424 + 0.105453i \(0.0336291\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 12.0000 0.485866
\(611\) 55.1135 31.8198i 2.22965 1.28729i
\(612\) 0 0
\(613\) −4.00000 + 6.92820i −0.161558 + 0.279827i −0.935428 0.353518i \(-0.884985\pi\)
0.773869 + 0.633345i \(0.218319\pi\)
\(614\) 11.0227 + 19.0919i 0.444840 + 0.770486i
\(615\) 0 0
\(616\) 0 0
\(617\) 24.0416i 0.967880i −0.875101 0.483940i \(-0.839205\pi\)
0.875101 0.483940i \(-0.160795\pi\)
\(618\) 0 0
\(619\) 25.5000 + 14.7224i 1.02493 + 0.591744i 0.915529 0.402253i \(-0.131773\pi\)
0.109403 + 0.993997i \(0.465106\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 24.2487i 0.972285i
\(623\) 0 0
\(624\) 0 0
\(625\) 14.5000 + 25.1147i 0.580000 + 1.00459i
\(626\) −8.57321 + 14.8492i −0.342655 + 0.593495i
\(627\) 0 0
\(628\) 0 0
\(629\) 4.89898 0.195335
\(630\) 0 0
\(631\) 38.0000 1.51276 0.756378 0.654135i \(-0.226967\pi\)
0.756378 + 0.654135i \(0.226967\pi\)
\(632\) 12.2474 7.07107i 0.487177 0.281272i
\(633\) 0 0
\(634\) 10.0000 17.3205i 0.397151 0.687885i
\(635\) 13.4722 + 23.3345i 0.534628 + 0.926002i
\(636\) 0 0
\(637\) 0 0
\(638\) 5.65685i 0.223957i
\(639\) 0 0
\(640\) −24.0000 13.8564i −0.948683 0.547723i
\(641\) −12.2474 7.07107i −0.483745 0.279290i 0.238231 0.971209i \(-0.423433\pi\)
−0.721976 + 0.691918i \(0.756766\pi\)
\(642\) 0 0
\(643\) 25.9808i 1.02458i −0.858812 0.512291i \(-0.828797\pi\)
0.858812 0.512291i \(-0.171203\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 6.00000 + 10.3923i 0.236067 + 0.408880i
\(647\) −8.57321 + 14.8492i −0.337048 + 0.583784i −0.983876 0.178852i \(-0.942762\pi\)
0.646828 + 0.762636i \(0.276095\pi\)
\(648\) 0 0
\(649\) −6.00000 + 3.46410i −0.235521 + 0.135978i
\(650\) −7.34847 −0.288231
\(651\) 0 0
\(652\) 0 0
\(653\) −6.12372 + 3.53553i −0.239640 + 0.138356i −0.615011 0.788518i \(-0.710849\pi\)
0.375371 + 0.926875i \(0.377515\pi\)
\(654\) 0 0
\(655\) −3.00000 + 5.19615i −0.117220 + 0.203030i
\(656\) 14.6969 + 25.4558i 0.573819 + 0.993884i
\(657\) 0 0
\(658\) 0 0
\(659\) 22.6274i 0.881439i 0.897645 + 0.440720i \(0.145277\pi\)
−0.897645 + 0.440720i \(0.854723\pi\)
\(660\) 0 0
\(661\) 25.5000 + 14.7224i 0.991835 + 0.572636i 0.905822 0.423658i \(-0.139254\pi\)
0.0860127 + 0.996294i \(0.472587\pi\)
\(662\) 37.9671 + 21.9203i 1.47563 + 0.851957i
\(663\) 0 0
\(664\) 20.7846i 0.806599i
\(665\) 0 0
\(666\) 0 0
\(667\) −8.00000 13.8564i −0.309761 0.536522i
\(668\) 0 0
\(669\) 0 0
\(670\) −33.0000 + 19.0526i −1.27490 + 0.736065i
\(671\) −4.89898 −0.189123
\(672\) 0 0
\(673\) 35.0000 1.34915 0.674575 0.738206i \(-0.264327\pi\)
0.674575 + 0.738206i \(0.264327\pi\)
\(674\) 28.1691 16.2635i 1.08503 0.626445i
\(675\) 0 0
\(676\) 0 0
\(677\) 4.89898 + 8.48528i 0.188283 + 0.326116i 0.944678 0.327999i \(-0.106374\pi\)
−0.756395 + 0.654115i \(0.773041\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 33.9411i 1.30158i
\(681\) 0 0
\(682\) 3.00000 + 1.73205i 0.114876 + 0.0663237i
\(683\) −41.6413 24.0416i −1.59336 0.919927i −0.992725 0.120405i \(-0.961581\pi\)
−0.600636 0.799522i \(-0.705086\pi\)
\(684\) 0 0
\(685\) 27.7128i 1.05885i
\(686\) 0 0
\(687\) 0 0
\(688\) −2.00000 3.46410i −0.0762493 0.132068i
\(689\) −7.34847 + 12.7279i −0.279954 + 0.484895i
\(690\) 0 0
\(691\) −37.5000 + 21.6506i −1.42657 + 0.823629i −0.996848 0.0793336i \(-0.974721\pi\)
−0.429719 + 0.902963i \(0.641387\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) −44.0000 −1.67022
\(695\) −11.0227 + 6.36396i −0.418115 + 0.241399i
\(696\) 0 0
\(697\) 18.0000 31.1769i 0.681799 1.18091i
\(698\) 7.34847 + 12.7279i 0.278144 + 0.481759i
\(699\) 0 0
\(700\) 0 0
\(701\) 5.65685i 0.213656i 0.994277 + 0.106828i \(0.0340695\pi\)
−0.994277 + 0.106828i \(0.965931\pi\)
\(702\) 0 0
\(703\) −1.50000 0.866025i −0.0565736 0.0326628i
\(704\) 9.79796 + 5.65685i 0.369274 + 0.213201i
\(705\) 0 0
\(706\) 24.2487i 0.912612i
\(707\) 0 0
\(708\) 0 0
\(709\) 20.0000 + 34.6410i 0.751116 + 1.30097i 0.947282 + 0.320400i \(0.103817\pi\)
−0.196167 + 0.980571i \(0.562849\pi\)
\(710\) 12.2474 21.2132i 0.459639 0.796117i
\(711\) 0 0
\(712\) 12.0000 6.92820i 0.449719 0.259645i
\(713\) −9.79796 −0.366936
\(714\) 0 0
\(715\) 18.0000 0.673162
\(716\) 0 0
\(717\) 0 0
\(718\) −20.0000 + 34.6410i −0.746393 + 1.29279i
\(719\) −13.4722 23.3345i −0.502428 0.870231i −0.999996 0.00280593i \(-0.999107\pi\)
0.497568 0.867425i \(-0.334226\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 22.6274i 0.842105i
\(723\) 0 0
\(724\) 0 0
\(725\) 2.44949 + 1.41421i 0.0909718 + 0.0525226i
\(726\) 0 0
\(727\) 25.9808i 0.963573i 0.876289 + 0.481787i \(0.160012\pi\)
−0.876289 + 0.481787i \(0.839988\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) −3.00000 5.19615i −0.111035 0.192318i
\(731\) −2.44949 + 4.24264i −0.0905977 + 0.156920i
\(732\) 0 0
\(733\) 34.5000 19.9186i 1.27429 0.735710i 0.298495 0.954411i \(-0.403515\pi\)
0.975792 + 0.218702i \(0.0701821\pi\)
\(734\) −2.44949 −0.0904123
\(735\) 0 0
\(736\) 0 0
\(737\) 13.4722 7.77817i 0.496255 0.286513i
\(738\) 0 0
\(739\) 0.500000 0.866025i 0.0183928 0.0318573i −0.856683 0.515844i \(-0.827478\pi\)
0.875075 + 0.483987i \(0.160812\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 24.0416i 0.882002i −0.897507 0.441001i \(-0.854624\pi\)
0.897507 0.441001i \(-0.145376\pi\)
\(744\) 0 0
\(745\) 12.0000 + 6.92820i 0.439646 + 0.253830i
\(746\) −35.5176 20.5061i −1.30039 0.750782i
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −14.5000 25.1147i −0.529113 0.916450i −0.999424 0.0339490i \(-0.989192\pi\)
0.470311 0.882501i \(-0.344142\pi\)
\(752\) 24.4949 42.4264i 0.893237 1.54713i
\(753\) 0 0
\(754\) 18.0000 10.3923i 0.655521 0.378465i
\(755\) 53.8888 1.96121
\(756\) 0 0
\(757\) 2.00000 0.0726912 0.0363456 0.999339i \(-0.488428\pi\)
0.0363456 + 0.999339i \(0.488428\pi\)
\(758\) −8.57321 + 4.94975i −0.311393 + 0.179783i
\(759\) 0 0
\(760\) 6.00000 10.3923i 0.217643 0.376969i
\(761\) 12.2474 + 21.2132i 0.443970 + 0.768978i 0.997980 0.0635319i \(-0.0202365\pi\)
−0.554010 + 0.832510i \(0.686903\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) −24.0000 13.8564i −0.867155 0.500652i
\(767\) 22.0454 + 12.7279i 0.796014 + 0.459579i
\(768\) 0 0
\(769\) 25.9808i 0.936890i −0.883493 0.468445i \(-0.844814\pi\)
0.883493 0.468445i \(-0.155186\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 13.4722 23.3345i 0.484561 0.839284i −0.515282 0.857021i \(-0.672313\pi\)
0.999843 + 0.0177365i \(0.00564599\pi\)
\(774\) 0 0
\(775\) 1.50000 0.866025i 0.0538816 0.0311086i
\(776\) −29.3939 −1.05518
\(777\) 0 0
\(778\) −38.0000 −1.36237
\(779\) −11.0227 + 6.36396i −0.394929 + 0.228013i
\(780\) 0 0
\(781\) −5.00000 + 8.66025i −0.178914 + 0.309888i
\(782\) −19.5959 33.9411i −0.700749 1.21373i
\(783\) 0 0
\(784\) 0 0
\(785\) 42.4264i 1.51426i
\(786\) 0 0
\(787\) 39.0000 + 22.5167i 1.39020 + 0.802632i 0.993337 0.115246i \(-0.0367655\pi\)
0.396863 + 0.917878i \(0.370099\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\)