Properties

Label 1575.2.bc.a.1349.4
Level $1575$
Weight $2$
Character 1575.1349
Analytic conductor $12.576$
Analytic rank $0$
Dimension $8$
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1575,2,Mod(899,1575)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1575, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 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("1575.899");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1575 = 3^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1575.bc (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: \(12.5764383184\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{24})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - x^{4} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 63)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 1349.4
Root \(0.965926 + 0.258819i\) of defining polynomial
Character \(\chi\) \(=\) 1575.1349
Dual form 1575.2.bc.a.899.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.707107 - 1.22474i) q^{2} +(2.59808 - 0.500000i) q^{7} +2.82843 q^{8} +O(q^{10})\) \(q+(0.707107 - 1.22474i) q^{2} +(2.59808 - 0.500000i) q^{7} +2.82843 q^{8} +(1.22474 - 0.707107i) q^{11} +5.19615 q^{13} +(1.22474 - 3.53553i) q^{14} +(2.00000 - 3.46410i) q^{16} +(-4.24264 + 2.44949i) q^{17} +(-1.50000 - 0.866025i) q^{19} -2.00000i q^{22} +(-2.82843 + 4.89898i) q^{23} +(3.67423 - 6.36396i) q^{26} +2.82843i q^{29} +(1.50000 - 0.866025i) q^{31} +6.92820i q^{34} +(0.866025 + 0.500000i) q^{37} +(-2.12132 + 1.22474i) q^{38} +7.34847 q^{41} +1.00000i q^{43} +(4.00000 + 6.92820i) q^{46} +(-10.6066 - 6.12372i) q^{47} +(6.50000 - 2.59808i) q^{49} +(1.41421 + 2.44949i) q^{53} +(7.34847 - 1.41421i) q^{56} +(3.46410 + 2.00000i) q^{58} +(-2.44949 - 4.24264i) q^{59} +(-3.00000 - 1.73205i) q^{61} -2.44949i q^{62} +8.00000 q^{64} +(9.52628 - 5.50000i) q^{67} -7.07107i q^{71} +(-0.866025 - 1.50000i) q^{73} +(1.22474 - 0.707107i) q^{74} +(2.82843 - 2.44949i) q^{77} +(2.50000 - 4.33013i) q^{79} +(5.19615 - 9.00000i) q^{82} +7.34847i q^{83} +(1.22474 + 0.707107i) q^{86} +(3.46410 - 2.00000i) q^{88} +(2.44949 - 4.24264i) q^{89} +(13.5000 - 2.59808i) q^{91} +(-15.0000 + 8.66025i) q^{94} -10.3923 q^{97} +(1.41421 - 9.79796i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 16 q^{16} - 12 q^{19} + 12 q^{31} + 32 q^{46} + 52 q^{49} - 24 q^{61} + 64 q^{64} + 20 q^{79} + 108 q^{91} - 120 q^{94}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1575\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(451\) \(1226\)
\(\chi(n)\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.707107 1.22474i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(3\) 0 0
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) 2.59808 0.500000i 0.981981 0.188982i
\(8\) 2.82843 1.00000
\(9\) 0 0
\(10\) 0 0
\(11\) 1.22474 0.707107i 0.369274 0.213201i −0.303867 0.952714i \(-0.598278\pi\)
0.673141 + 0.739514i \(0.264945\pi\)
\(12\) 0 0
\(13\) 5.19615 1.44115 0.720577 0.693375i \(-0.243877\pi\)
0.720577 + 0.693375i \(0.243877\pi\)
\(14\) 1.22474 3.53553i 0.327327 0.944911i
\(15\) 0 0
\(16\) 2.00000 3.46410i 0.500000 0.866025i
\(17\) −4.24264 + 2.44949i −1.02899 + 0.594089i −0.916696 0.399586i \(-0.869154\pi\)
−0.112296 + 0.993675i \(0.535820\pi\)
\(18\) 0 0
\(19\) −1.50000 0.866025i −0.344124 0.198680i 0.317970 0.948101i \(-0.396999\pi\)
−0.662094 + 0.749421i \(0.730332\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 2.00000i 0.426401i
\(23\) −2.82843 + 4.89898i −0.589768 + 1.02151i 0.404495 + 0.914540i \(0.367447\pi\)
−0.994263 + 0.106967i \(0.965886\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 3.67423 6.36396i 0.720577 1.24808i
\(27\) 0 0
\(28\) 0 0
\(29\) 2.82843i 0.525226i 0.964901 + 0.262613i \(0.0845842\pi\)
−0.964901 + 0.262613i \(0.915416\pi\)
\(30\) 0 0
\(31\) 1.50000 0.866025i 0.269408 0.155543i −0.359211 0.933257i \(-0.616954\pi\)
0.628619 + 0.777714i \(0.283621\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 6.92820i 1.18818i
\(35\) 0 0
\(36\) 0 0
\(37\) 0.866025 + 0.500000i 0.142374 + 0.0821995i 0.569495 0.821995i \(-0.307139\pi\)
−0.427121 + 0.904194i \(0.640472\pi\)
\(38\) −2.12132 + 1.22474i −0.344124 + 0.198680i
\(39\) 0 0
\(40\) 0 0
\(41\) 7.34847 1.14764 0.573819 0.818982i \(-0.305461\pi\)
0.573819 + 0.818982i \(0.305461\pi\)
\(42\) 0 0
\(43\) 1.00000i 0.152499i 0.997089 + 0.0762493i \(0.0242945\pi\)
−0.997089 + 0.0762493i \(0.975706\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 4.00000 + 6.92820i 0.589768 + 1.02151i
\(47\) −10.6066 6.12372i −1.54713 0.893237i −0.998359 0.0572655i \(-0.981762\pi\)
−0.548773 0.835971i \(-0.684905\pi\)
\(48\) 0 0
\(49\) 6.50000 2.59808i 0.928571 0.371154i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 1.41421 + 2.44949i 0.194257 + 0.336463i 0.946657 0.322244i \(-0.104437\pi\)
−0.752400 + 0.658707i \(0.771104\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 7.34847 1.41421i 0.981981 0.188982i
\(57\) 0 0
\(58\) 3.46410 + 2.00000i 0.454859 + 0.262613i
\(59\) −2.44949 4.24264i −0.318896 0.552345i 0.661362 0.750067i \(-0.269979\pi\)
−0.980258 + 0.197722i \(0.936646\pi\)
\(60\) 0 0
\(61\) −3.00000 1.73205i −0.384111 0.221766i 0.295495 0.955344i \(-0.404516\pi\)
−0.679605 + 0.733578i \(0.737849\pi\)
\(62\) 2.44949i 0.311086i
\(63\) 0 0
\(64\) 8.00000 1.00000
\(65\) 0 0
\(66\) 0 0
\(67\) 9.52628 5.50000i 1.16382 0.671932i 0.211604 0.977356i \(-0.432131\pi\)
0.952217 + 0.305424i \(0.0987981\pi\)
\(68\) 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
\(73\) −0.866025 1.50000i −0.101361 0.175562i 0.810885 0.585206i \(-0.198986\pi\)
−0.912245 + 0.409644i \(0.865653\pi\)
\(74\) 1.22474 0.707107i 0.142374 0.0821995i
\(75\) 0 0
\(76\) 0 0
\(77\) 2.82843 2.44949i 0.322329 0.279145i
\(78\) 0 0
\(79\) 2.50000 4.33013i 0.281272 0.487177i −0.690426 0.723403i \(-0.742577\pi\)
0.971698 + 0.236225i \(0.0759104\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 5.19615 9.00000i 0.573819 0.993884i
\(83\) 7.34847i 0.806599i 0.915068 + 0.403300i \(0.132137\pi\)
−0.915068 + 0.403300i \(0.867863\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 1.22474 + 0.707107i 0.132068 + 0.0762493i
\(87\) 0 0
\(88\) 3.46410 2.00000i 0.369274 0.213201i
\(89\) 2.44949 4.24264i 0.259645 0.449719i −0.706502 0.707712i \(-0.749728\pi\)
0.966147 + 0.257993i \(0.0830610\pi\)
\(90\) 0 0
\(91\) 13.5000 2.59808i 1.41518 0.272352i
\(92\) 0 0
\(93\) 0 0
\(94\) −15.0000 + 8.66025i −1.54713 + 0.893237i
\(95\) 0 0
\(96\) 0 0
\(97\) −10.3923 −1.05518 −0.527589 0.849500i \(-0.676904\pi\)
−0.527589 + 0.849500i \(0.676904\pi\)
\(98\) 1.41421 9.79796i 0.142857 0.989743i
\(99\) 0 0
\(100\) 0 0
\(101\) −8.57321 14.8492i −0.853067 1.47755i −0.878427 0.477876i \(-0.841407\pi\)
0.0253604 0.999678i \(-0.491927\pi\)
\(102\) 0 0
\(103\) −4.33013 + 7.50000i −0.426660 + 0.738997i −0.996574 0.0827075i \(-0.973643\pi\)
0.569914 + 0.821705i \(0.306977\pi\)
\(104\) 14.6969 1.44115
\(105\) 0 0
\(106\) 4.00000 0.388514
\(107\) −1.41421 + 2.44949i −0.136717 + 0.236801i −0.926252 0.376905i \(-0.876988\pi\)
0.789535 + 0.613706i \(0.210322\pi\)
\(108\) 0 0
\(109\) −0.500000 0.866025i −0.0478913 0.0829502i 0.841086 0.540901i \(-0.181917\pi\)
−0.888977 + 0.457951i \(0.848583\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 3.46410 10.0000i 0.327327 0.944911i
\(113\) 1.41421 0.133038 0.0665190 0.997785i \(-0.478811\pi\)
0.0665190 + 0.997785i \(0.478811\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) −6.92820 −0.637793
\(119\) −9.79796 + 8.48528i −0.898177 + 0.777844i
\(120\) 0 0
\(121\) −4.50000 + 7.79423i −0.409091 + 0.708566i
\(122\) −4.24264 + 2.44949i −0.384111 + 0.221766i
\(123\) 0 0
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 11.0000i 0.976092i 0.872818 + 0.488046i \(0.162290\pi\)
−0.872818 + 0.488046i \(0.837710\pi\)
\(128\) 5.65685 9.79796i 0.500000 0.866025i
\(129\) 0 0
\(130\) 0 0
\(131\) 1.22474 2.12132i 0.107006 0.185341i −0.807550 0.589799i \(-0.799207\pi\)
0.914556 + 0.404459i \(0.132540\pi\)
\(132\) 0 0
\(133\) −4.33013 1.50000i −0.375470 0.130066i
\(134\) 15.5563i 1.34386i
\(135\) 0 0
\(136\) −12.0000 + 6.92820i −1.02899 + 0.594089i
\(137\) −5.65685 9.79796i −0.483298 0.837096i 0.516518 0.856276i \(-0.327228\pi\)
−0.999816 + 0.0191800i \(0.993894\pi\)
\(138\) 0 0
\(139\) 5.19615i 0.440732i −0.975417 0.220366i \(-0.929275\pi\)
0.975417 0.220366i \(-0.0707252\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −8.66025 5.00000i −0.726752 0.419591i
\(143\) 6.36396 3.67423i 0.532181 0.307255i
\(144\) 0 0
\(145\) 0 0
\(146\) −2.44949 −0.202721
\(147\) 0 0
\(148\) 0 0
\(149\) 4.89898 + 2.82843i 0.401340 + 0.231714i 0.687062 0.726599i \(-0.258900\pi\)
−0.285722 + 0.958313i \(0.592233\pi\)
\(150\) 0 0
\(151\) 11.0000 + 19.0526i 0.895167 + 1.55048i 0.833597 + 0.552372i \(0.186277\pi\)
0.0615699 + 0.998103i \(0.480389\pi\)
\(152\) −4.24264 2.44949i −0.344124 0.198680i
\(153\) 0 0
\(154\) −1.00000 5.19615i −0.0805823 0.418718i
\(155\) 0 0
\(156\) 0 0
\(157\) 8.66025 + 15.0000i 0.691164 + 1.19713i 0.971457 + 0.237216i \(0.0762349\pi\)
−0.280293 + 0.959914i \(0.590432\pi\)
\(158\) −3.53553 6.12372i −0.281272 0.487177i
\(159\) 0 0
\(160\) 0 0
\(161\) −4.89898 + 14.1421i −0.386094 + 1.11456i
\(162\) 0 0
\(163\) −8.66025 5.00000i −0.678323 0.391630i 0.120900 0.992665i \(-0.461422\pi\)
−0.799223 + 0.601035i \(0.794755\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 9.00000 + 5.19615i 0.698535 + 0.403300i
\(167\) 7.34847i 0.568642i 0.958729 + 0.284321i \(0.0917681\pi\)
−0.958729 + 0.284321i \(0.908232\pi\)
\(168\) 0 0
\(169\) 14.0000 1.07692
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −8.48528 4.89898i −0.645124 0.372463i 0.141462 0.989944i \(-0.454820\pi\)
−0.786586 + 0.617481i \(0.788153\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 5.65685i 0.426401i
\(177\) 0 0
\(178\) −3.46410 6.00000i −0.259645 0.449719i
\(179\) −8.57321 + 4.94975i −0.640792 + 0.369961i −0.784920 0.619598i \(-0.787296\pi\)
0.144127 + 0.989559i \(0.453962\pi\)
\(180\) 0 0
\(181\) 15.5885i 1.15868i −0.815086 0.579340i \(-0.803310\pi\)
0.815086 0.579340i \(-0.196690\pi\)
\(182\) 6.36396 18.3712i 0.471728 1.36176i
\(183\) 0 0
\(184\) −8.00000 + 13.8564i −0.589768 + 1.02151i
\(185\) 0 0
\(186\) 0 0
\(187\) −3.46410 + 6.00000i −0.253320 + 0.438763i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −1.22474 0.707107i −0.0886194 0.0511645i 0.455035 0.890473i \(-0.349627\pi\)
−0.543655 + 0.839309i \(0.682960\pi\)
\(192\) 0 0
\(193\) −9.52628 + 5.50000i −0.685717 + 0.395899i −0.802005 0.597317i \(-0.796234\pi\)
0.116289 + 0.993215i \(0.462900\pi\)
\(194\) −7.34847 + 12.7279i −0.527589 + 0.913812i
\(195\) 0 0
\(196\) 0 0
\(197\) 19.7990 1.41062 0.705310 0.708899i \(-0.250808\pi\)
0.705310 + 0.708899i \(0.250808\pi\)
\(198\) 0 0
\(199\) 12.0000 6.92820i 0.850657 0.491127i −0.0102152 0.999948i \(-0.503252\pi\)
0.860873 + 0.508821i \(0.169918\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) −24.2487 −1.70613
\(203\) 1.41421 + 7.34847i 0.0992583 + 0.515761i
\(204\) 0 0
\(205\) 0 0
\(206\) 6.12372 + 10.6066i 0.426660 + 0.738997i
\(207\) 0 0
\(208\) 10.3923 18.0000i 0.720577 1.24808i
\(209\) −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
\(215\) 0 0
\(216\) 0 0
\(217\) 3.46410 3.00000i 0.235159 0.203653i
\(218\) −1.41421 −0.0957826
\(219\) 0 0
\(220\) 0 0
\(221\) −22.0454 + 12.7279i −1.48293 + 0.856173i
\(222\) 0 0
\(223\) −20.7846 −1.39184 −0.695920 0.718119i \(-0.745003\pi\)
−0.695920 + 0.718119i \(0.745003\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 1.00000 1.73205i 0.0665190 0.115214i
\(227\) −23.3345 + 13.4722i −1.54877 + 0.894181i −0.550530 + 0.834815i \(0.685575\pi\)
−0.998236 + 0.0593658i \(0.981092\pi\)
\(228\) 0 0
\(229\) −19.5000 11.2583i −1.28860 0.743971i −0.310192 0.950674i \(-0.600393\pi\)
−0.978404 + 0.206702i \(0.933727\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 8.00000i 0.525226i
\(233\) −4.94975 + 8.57321i −0.324269 + 0.561650i −0.981364 0.192158i \(-0.938452\pi\)
0.657095 + 0.753807i \(0.271785\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 3.46410 + 18.0000i 0.224544 + 1.16677i
\(239\) 26.8701i 1.73808i −0.494742 0.869040i \(-0.664738\pi\)
0.494742 0.869040i \(-0.335262\pi\)
\(240\) 0 0
\(241\) −12.0000 + 6.92820i −0.772988 + 0.446285i −0.833939 0.551856i \(-0.813920\pi\)
0.0609515 + 0.998141i \(0.480586\pi\)
\(242\) 6.36396 + 11.0227i 0.409091 + 0.708566i
\(243\) 0 0
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −7.79423 4.50000i −0.495935 0.286328i
\(248\) 4.24264 2.44949i 0.269408 0.155543i
\(249\) 0 0
\(250\) 0 0
\(251\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(252\) 0 0
\(253\) 8.00000i 0.502956i
\(254\) 13.4722 + 7.77817i 0.845321 + 0.488046i
\(255\) 0 0
\(256\) 0 0
\(257\) 2.12132 + 1.22474i 0.132324 + 0.0763975i 0.564701 0.825296i \(-0.308992\pi\)
−0.432377 + 0.901693i \(0.642325\pi\)
\(258\) 0 0
\(259\) 2.50000 + 0.866025i 0.155342 + 0.0538122i
\(260\) 0 0
\(261\) 0 0
\(262\) −1.73205 3.00000i −0.107006 0.185341i
\(263\) −7.07107 12.2474i −0.436021 0.755210i 0.561358 0.827573i \(-0.310279\pi\)
−0.997378 + 0.0723633i \(0.976946\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) −4.89898 + 4.24264i −0.300376 + 0.260133i
\(267\) 0 0
\(268\) 0 0
\(269\) 8.57321 + 14.8492i 0.522718 + 0.905374i 0.999651 + 0.0264343i \(0.00841529\pi\)
−0.476932 + 0.878940i \(0.658251\pi\)
\(270\) 0 0
\(271\) −12.0000 6.92820i −0.728948 0.420858i 0.0890891 0.996024i \(-0.471604\pi\)
−0.818037 + 0.575165i \(0.804938\pi\)
\(272\) 19.5959i 1.18818i
\(273\) 0 0
\(274\) −16.0000 −0.966595
\(275\) 0 0
\(276\) 0 0
\(277\) 19.9186 11.5000i 1.19679 0.690968i 0.236953 0.971521i \(-0.423851\pi\)
0.959839 + 0.280553i \(0.0905179\pi\)
\(278\) −6.36396 3.67423i −0.381685 0.220366i
\(279\) 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
\(283\) −0.866025 1.50000i −0.0514799 0.0891657i 0.839137 0.543920i \(-0.183060\pi\)
−0.890617 + 0.454754i \(0.849727\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 10.3923i 0.614510i
\(287\) 19.0919 3.67423i 1.12696 0.216883i
\(288\) 0 0
\(289\) 3.50000 6.06218i 0.205882 0.356599i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 14.6969i 0.858604i 0.903161 + 0.429302i \(0.141240\pi\)
−0.903161 + 0.429302i \(0.858760\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 2.44949 + 1.41421i 0.142374 + 0.0821995i
\(297\) 0 0
\(298\) 6.92820 4.00000i 0.401340 0.231714i
\(299\) −14.6969 + 25.4558i −0.849946 + 1.47215i
\(300\) 0 0
\(301\) 0.500000 + 2.59808i 0.0288195 + 0.149751i
\(302\) 31.1127 1.79033
\(303\) 0 0
\(304\) −6.00000 + 3.46410i −0.344124 + 0.198680i
\(305\) 0 0
\(306\) 0 0
\(307\) −15.5885 −0.889680 −0.444840 0.895610i \(-0.646740\pi\)
−0.444840 + 0.895610i \(0.646740\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −8.57321 14.8492i −0.486142 0.842023i 0.513731 0.857951i \(-0.328263\pi\)
−0.999873 + 0.0159282i \(0.994930\pi\)
\(312\) 0 0
\(313\) 6.06218 10.5000i 0.342655 0.593495i −0.642270 0.766478i \(-0.722007\pi\)
0.984925 + 0.172983i \(0.0553406\pi\)
\(314\) 24.4949 1.38233
\(315\) 0 0
\(316\) 0 0
\(317\) 7.07107 12.2474i 0.397151 0.687885i −0.596222 0.802819i \(-0.703332\pi\)
0.993373 + 0.114934i \(0.0366657\pi\)
\(318\) 0 0
\(319\) 2.00000 + 3.46410i 0.111979 + 0.193952i
\(320\) 0 0
\(321\) 0 0
\(322\) 13.8564 + 16.0000i 0.772187 + 0.891645i
\(323\) 8.48528 0.472134
\(324\) 0 0
\(325\) 0 0
\(326\) −12.2474 + 7.07107i −0.678323 + 0.391630i
\(327\) 0 0
\(328\) 20.7846 1.14764
\(329\) −30.6186 10.6066i −1.68806 0.584761i
\(330\) 0 0
\(331\) 15.5000 26.8468i 0.851957 1.47563i −0.0274825 0.999622i \(-0.508749\pi\)
0.879440 0.476011i \(-0.157918\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 9.00000 + 5.19615i 0.492458 + 0.284321i
\(335\) 0 0
\(336\) 0 0
\(337\) 23.0000i 1.25289i 0.779466 + 0.626445i \(0.215491\pi\)
−0.779466 + 0.626445i \(0.784509\pi\)
\(338\) 9.89949 17.1464i 0.538462 0.932643i
\(339\) 0 0
\(340\) 0 0
\(341\) 1.22474 2.12132i 0.0663237 0.114876i
\(342\) 0 0
\(343\) 15.5885 10.0000i 0.841698 0.539949i
\(344\) 2.82843i 0.152499i
\(345\) 0 0
\(346\) −12.0000 + 6.92820i −0.645124 + 0.372463i
\(347\) 15.5563 + 26.9444i 0.835109 + 1.44645i 0.893942 + 0.448183i \(0.147929\pi\)
−0.0588334 + 0.998268i \(0.518738\pi\)
\(348\) 0 0
\(349\) 10.3923i 0.556287i −0.960539 0.278144i \(-0.910281\pi\)
0.960539 0.278144i \(-0.0897191\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −14.8492 + 8.57321i −0.790345 + 0.456306i −0.840084 0.542456i \(-0.817494\pi\)
0.0497387 + 0.998762i \(0.484161\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 14.0000i 0.739923i
\(359\) −24.4949 14.1421i −1.29279 0.746393i −0.313643 0.949541i \(-0.601550\pi\)
−0.979148 + 0.203148i \(0.934883\pi\)
\(360\) 0 0
\(361\) −8.00000 13.8564i −0.421053 0.729285i
\(362\) −19.0919 11.0227i −1.00345 0.579340i
\(363\) 0 0
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 0.866025 + 1.50000i 0.0452062 + 0.0782994i 0.887743 0.460339i \(-0.152272\pi\)
−0.842537 + 0.538639i \(0.818939\pi\)
\(368\) 11.3137 + 19.5959i 0.589768 + 1.02151i
\(369\) 0 0
\(370\) 0 0
\(371\) 4.89898 + 5.65685i 0.254342 + 0.293689i
\(372\) 0 0
\(373\) 25.1147 + 14.5000i 1.30039 + 0.750782i 0.980471 0.196663i \(-0.0630104\pi\)
0.319921 + 0.947444i \(0.396344\pi\)
\(374\) 4.89898 + 8.48528i 0.253320 + 0.438763i
\(375\) 0 0
\(376\) −30.0000 17.3205i −1.54713 0.893237i
\(377\) 14.6969i 0.756931i
\(378\) 0 0
\(379\) 7.00000 0.359566 0.179783 0.983706i \(-0.442460\pi\)
0.179783 + 0.983706i \(0.442460\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) −1.73205 + 1.00000i −0.0886194 + 0.0511645i
\(383\) 16.9706 + 9.79796i 0.867155 + 0.500652i 0.866402 0.499347i \(-0.166427\pi\)
0.000753393 1.00000i \(0.499760\pi\)
\(384\) 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 −0.955978 0.293437i \(-0.905201\pi\)
−0.223865 + 0.974620i \(0.571868\pi\)
\(390\) 0 0
\(391\) 27.7128i 1.40150i
\(392\) 18.3848 7.34847i 0.928571 0.371154i
\(393\) 0 0
\(394\) 14.0000 24.2487i 0.705310 1.22163i
\(395\) 0 0
\(396\) 0 0
\(397\) −0.866025 + 1.50000i −0.0434646 + 0.0752828i −0.886939 0.461886i \(-0.847173\pi\)
0.843475 + 0.537169i \(0.180506\pi\)
\(398\) 19.5959i 0.982255i
\(399\) 0 0
\(400\) 0 0
\(401\) 17.1464 + 9.89949i 0.856252 + 0.494357i 0.862755 0.505622i \(-0.168737\pi\)
−0.00650355 + 0.999979i \(0.502070\pi\)
\(402\) 0 0
\(403\) 7.79423 4.50000i 0.388258 0.224161i
\(404\) 0 0
\(405\) 0 0
\(406\) 10.0000 + 3.46410i 0.496292 + 0.171920i
\(407\) 1.41421 0.0701000
\(408\) 0 0
\(409\) −28.5000 + 16.4545i −1.40923 + 0.813622i −0.995314 0.0966915i \(-0.969174\pi\)
−0.413920 + 0.910313i \(0.635841\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −8.48528 9.79796i −0.417533 0.482126i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) −1.73205 + 3.00000i −0.0847174 + 0.146735i
\(419\) 36.7423 1.79498 0.897491 0.441034i \(-0.145388\pi\)
0.897491 + 0.441034i \(0.145388\pi\)
\(420\) 0 0
\(421\) −1.00000 −0.0487370 −0.0243685 0.999703i \(-0.507758\pi\)
−0.0243685 + 0.999703i \(0.507758\pi\)
\(422\) −15.5563 + 26.9444i −0.757271 + 1.31163i
\(423\) 0 0
\(424\) 4.00000 + 6.92820i 0.194257 + 0.336463i
\(425\) 0 0
\(426\) 0 0
\(427\) −8.66025 3.00000i −0.419099 0.145180i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −13.4722 + 7.77817i −0.648933 + 0.374661i −0.788047 0.615615i \(-0.788908\pi\)
0.139114 + 0.990276i \(0.455574\pi\)
\(432\) 0 0
\(433\) −15.5885 −0.749133 −0.374567 0.927200i \(-0.622209\pi\)
−0.374567 + 0.927200i \(0.622209\pi\)
\(434\) −1.22474 6.36396i −0.0587896 0.305480i
\(435\) 0 0
\(436\) 0 0
\(437\) 8.48528 4.89898i 0.405906 0.234350i
\(438\) 0 0
\(439\) −24.0000 13.8564i −1.14546 0.661330i −0.197681 0.980266i \(-0.563341\pi\)
−0.947776 + 0.318936i \(0.896674\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 36.0000i 1.71235i
\(443\) −19.7990 + 34.2929i −0.940678 + 1.62930i −0.176497 + 0.984301i \(0.556477\pi\)
−0.764181 + 0.645002i \(0.776857\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) −14.6969 + 25.4558i −0.695920 + 1.20537i
\(447\) 0 0
\(448\) 20.7846 4.00000i 0.981981 0.188982i
\(449\) 7.07107i 0.333704i 0.985982 + 0.166852i \(0.0533603\pi\)
−0.985982 + 0.166852i \(0.946640\pi\)
\(450\) 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
\(457\) −4.33013 2.50000i −0.202555 0.116945i 0.395292 0.918556i \(-0.370643\pi\)
−0.597847 + 0.801611i \(0.703977\pi\)
\(458\) −27.5772 + 15.9217i −1.28860 + 0.743971i
\(459\) 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
\(463\) 13.0000i 0.604161i 0.953282 + 0.302081i \(0.0976812\pi\)
−0.953282 + 0.302081i \(0.902319\pi\)
\(464\) 9.79796 + 5.65685i 0.454859 + 0.262613i
\(465\) 0 0
\(466\) 7.00000 + 12.1244i 0.324269 + 0.561650i
\(467\) −23.3345 13.4722i −1.07979 0.623419i −0.148952 0.988844i \(-0.547590\pi\)
−0.930841 + 0.365426i \(0.880923\pi\)
\(468\) 0 0
\(469\) 22.0000 19.0526i 1.01587 0.879765i
\(470\) 0 0
\(471\) 0 0
\(472\) −6.92820 12.0000i −0.318896 0.552345i
\(473\) 0.707107 + 1.22474i 0.0325128 + 0.0563138i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 0 0
\(478\) −32.9090 19.0000i −1.50522 0.869040i
\(479\) −2.44949 4.24264i −0.111920 0.193851i 0.804624 0.593784i \(-0.202367\pi\)
−0.916544 + 0.399933i \(0.869033\pi\)
\(480\) 0 0
\(481\) 4.50000 + 2.59808i 0.205182 + 0.118462i
\(482\) 19.5959i 0.892570i
\(483\) 0 0
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 14.7224 8.50000i 0.667137 0.385172i −0.127854 0.991793i \(-0.540809\pi\)
0.794991 + 0.606621i \(0.207476\pi\)
\(488\) −8.48528 4.89898i −0.384111 0.221766i
\(489\) 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
\(493\) −6.92820 12.0000i −0.312031 0.540453i
\(494\) −11.0227 + 6.36396i −0.495935 + 0.286328i
\(495\) 0 0
\(496\) 6.92820i 0.311086i
\(497\) −3.53553 18.3712i −0.158590 0.824060i
\(498\) 0 0
\(499\) −12.5000 + 21.6506i −0.559577 + 0.969216i 0.437955 + 0.898997i \(0.355703\pi\)
−0.997532 + 0.0702185i \(0.977630\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 22.0454i 0.982956i 0.870890 + 0.491478i \(0.163543\pi\)
−0.870890 + 0.491478i \(0.836457\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 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 \(-0.850622\pi\)
0.837605 + 0.546276i \(0.183955\pi\)
\(510\) 0 0
\(511\) −3.00000 3.46410i −0.132712 0.153243i
\(512\) 22.6274 1.00000
\(513\) 0 0
\(514\) 3.00000 1.73205i 0.132324 0.0763975i
\(515\) 0 0
\(516\) 0 0
\(517\) −17.3205 −0.761755
\(518\) 2.82843 2.44949i 0.124274 0.107624i
\(519\) 0 0
\(520\) 0 0
\(521\) 2.44949 + 4.24264i 0.107314 + 0.185873i 0.914681 0.404176i \(-0.132442\pi\)
−0.807367 + 0.590049i \(0.799108\pi\)
\(522\) 0 0
\(523\) 0.866025 1.50000i 0.0378686 0.0655904i −0.846470 0.532437i \(-0.821276\pi\)
0.884339 + 0.466846i \(0.154610\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) −20.0000 −0.872041
\(527\) −4.24264 + 7.34847i −0.184812 + 0.320104i
\(528\) 0 0
\(529\) −4.50000 7.79423i −0.195652 0.338880i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 38.1838 1.65392
\(534\) 0 0
\(535\) 0 0
\(536\) 26.9444 15.5563i 1.16382 0.671932i
\(537\) 0 0
\(538\) 24.2487 1.04544
\(539\) 6.12372 7.77817i 0.263767 0.335030i
\(540\) 0 0
\(541\) −8.50000 + 14.7224i −0.365444 + 0.632967i −0.988847 0.148933i \(-0.952416\pi\)
0.623404 + 0.781900i \(0.285749\pi\)
\(542\) −16.9706 + 9.79796i −0.728948 + 0.420858i
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 10.0000i 0.427569i −0.976881 0.213785i \(-0.931421\pi\)
0.976881 0.213785i \(-0.0685791\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 2.44949 4.24264i 0.104352 0.180743i
\(552\) 0 0
\(553\) 4.33013 12.5000i 0.184136 0.531554i
\(554\) 32.5269i 1.38194i
\(555\) 0 0
\(556\) 0 0
\(557\) −7.77817 13.4722i −0.329572 0.570835i 0.652855 0.757483i \(-0.273571\pi\)
−0.982427 + 0.186648i \(0.940238\pi\)
\(558\) 0 0
\(559\) 5.19615i 0.219774i
\(560\) 0 0
\(561\) 0 0
\(562\) 27.7128 + 16.0000i 1.16899 + 0.674919i
\(563\) 23.3345 13.4722i 0.983433 0.567785i 0.0801281 0.996785i \(-0.474467\pi\)
0.903305 + 0.428999i \(0.141134\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) −2.44949 −0.102960
\(567\) 0 0
\(568\) 20.0000i 0.839181i
\(569\) 1.22474 + 0.707107i 0.0513440 + 0.0296435i 0.525452 0.850823i \(-0.323896\pi\)
−0.474108 + 0.880467i \(0.657229\pi\)
\(570\) 0 0
\(571\) −5.50000 9.52628i −0.230168 0.398662i 0.727690 0.685907i \(-0.240594\pi\)
−0.957857 + 0.287244i \(0.907261\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 9.00000 25.9808i 0.375653 1.08442i
\(575\) 0 0
\(576\) 0 0
\(577\) 0.866025 + 1.50000i 0.0360531 + 0.0624458i 0.883489 0.468452i \(-0.155188\pi\)
−0.847436 + 0.530898i \(0.821855\pi\)
\(578\) −4.94975 8.57321i −0.205882 0.356599i
\(579\) 0 0
\(580\) 0 0
\(581\) 3.67423 + 19.0919i 0.152433 + 0.792065i
\(582\) 0 0
\(583\) 3.46410 + 2.00000i 0.143468 + 0.0828315i
\(584\) −2.44949 4.24264i −0.101361 0.175562i
\(585\) 0 0
\(586\) 18.0000 + 10.3923i 0.743573 + 0.429302i
\(587\) 14.6969i 0.606608i 0.952894 + 0.303304i \(0.0980897\pi\)
−0.952894 + 0.303304i \(0.901910\pi\)
\(588\) 0 0
\(589\) −3.00000 −0.123613
\(590\) 0 0
\(591\) 0 0
\(592\) 3.46410 2.00000i 0.142374 0.0821995i
\(593\) −14.8492 8.57321i −0.609785 0.352060i 0.163096 0.986610i \(-0.447852\pi\)
−0.772881 + 0.634550i \(0.781185\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 20.7846 + 36.0000i 0.849946 + 1.47215i
\(599\) −4.89898 + 2.82843i −0.200167 + 0.115566i −0.596733 0.802440i \(-0.703535\pi\)
0.396566 + 0.918006i \(0.370202\pi\)
\(600\) 0 0
\(601\) 25.9808i 1.05978i 0.848067 + 0.529889i \(0.177766\pi\)
−0.848067 + 0.529889i \(0.822234\pi\)
\(602\) 3.53553 + 1.22474i 0.144098 + 0.0499169i
\(603\) 0 0
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 19.9186 34.5000i 0.808470 1.40031i −0.105453 0.994424i \(-0.533629\pi\)
0.913923 0.405887i \(-0.133038\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −55.1135 31.8198i −2.22965 1.28729i
\(612\) 0 0
\(613\) −6.92820 + 4.00000i −0.279827 + 0.161558i −0.633345 0.773869i \(-0.718319\pi\)
0.353518 + 0.935428i \(0.384985\pi\)
\(614\) −11.0227 + 19.0919i −0.444840 + 0.770486i
\(615\) 0 0
\(616\) 8.00000 6.92820i 0.322329 0.279145i
\(617\) 24.0416 0.967880 0.483940 0.875101i \(-0.339205\pi\)
0.483940 + 0.875101i \(0.339205\pi\)
\(618\) 0 0
\(619\) 25.5000 14.7224i 1.02493 0.591744i 0.109403 0.993997i \(-0.465106\pi\)
0.915529 + 0.402253i \(0.131773\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) −24.2487 −0.972285
\(623\) 4.24264 12.2474i 0.169978 0.490684i
\(624\) 0 0
\(625\) 0 0
\(626\) −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 \(0.226967\pi\)
\(632\) 7.07107 12.2474i 0.281272 0.487177i
\(633\) 0 0
\(634\) −10.0000 17.3205i −0.397151 0.687885i
\(635\) 0 0
\(636\) 0 0
\(637\) 33.7750 13.5000i 1.33821 0.534889i
\(638\) 5.65685 0.223957
\(639\) 0 0
\(640\) 0 0
\(641\) 12.2474 7.07107i 0.483745 0.279290i −0.238231 0.971209i \(-0.576567\pi\)
0.721976 + 0.691918i \(0.243234\pi\)
\(642\) 0 0
\(643\) −25.9808 −1.02458 −0.512291 0.858812i \(-0.671203\pi\)
−0.512291 + 0.858812i \(0.671203\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 6.00000 10.3923i 0.236067 0.408880i
\(647\) 14.8492 8.57321i 0.583784 0.337048i −0.178852 0.983876i \(-0.557238\pi\)
0.762636 + 0.646828i \(0.223905\pi\)
\(648\) 0 0
\(649\) −6.00000 3.46410i −0.235521 0.135978i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 3.53553 6.12372i 0.138356 0.239640i −0.788518 0.615011i \(-0.789151\pi\)
0.926875 + 0.375371i \(0.122485\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 14.6969 25.4558i 0.573819 0.993884i
\(657\) 0 0
\(658\) −34.6410 + 30.0000i −1.35045 + 1.16952i
\(659\) 22.6274i 0.881439i −0.897645 0.440720i \(-0.854723\pi\)
0.897645 0.440720i \(-0.145277\pi\)
\(660\) 0 0
\(661\) −25.5000 + 14.7224i −0.991835 + 0.572636i −0.905822 0.423658i \(-0.860746\pi\)
−0.0860127 + 0.996294i \(0.527413\pi\)
\(662\) −21.9203 37.9671i −0.851957 1.47563i
\(663\) 0 0
\(664\) 20.7846i 0.806599i
\(665\) 0 0
\(666\) 0 0
\(667\) −13.8564 8.00000i −0.536522 0.309761i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −4.89898 −0.189123
\(672\) 0 0
\(673\) 35.0000i 1.34915i −0.738206 0.674575i \(-0.764327\pi\)
0.738206 0.674575i \(-0.235673\pi\)
\(674\) 28.1691 + 16.2635i 1.08503 + 0.626445i
\(675\) 0 0
\(676\) 0 0
\(677\) 8.48528 + 4.89898i 0.326116 + 0.188283i 0.654115 0.756395i \(-0.273041\pi\)
−0.327999 + 0.944678i \(0.606374\pi\)
\(678\) 0 0
\(679\) −27.0000 + 5.19615i −1.03616 + 0.199410i
\(680\) 0 0
\(681\) 0 0
\(682\) −1.73205 3.00000i −0.0663237 0.114876i
\(683\) −24.0416 41.6413i −0.919927 1.59336i −0.799522 0.600636i \(-0.794914\pi\)
−0.120405 0.992725i \(-0.538419\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) −1.22474 26.1630i −0.0467610 0.998906i
\(687\) 0 0
\(688\) 3.46410 + 2.00000i 0.132068 + 0.0762493i
\(689\) 7.34847 + 12.7279i 0.279954 + 0.484895i
\(690\) 0 0
\(691\) 37.5000 + 21.6506i 1.42657 + 0.823629i 0.996848 0.0793336i \(-0.0252792\pi\)
0.429719 + 0.902963i \(0.358613\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 44.0000 1.67022
\(695\) 0 0
\(696\) 0 0
\(697\) −31.1769 + 18.0000i −1.18091 + 0.681799i
\(698\) −12.7279 7.34847i −0.481759 0.278144i
\(699\) 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
\(703\) −0.866025 1.50000i −0.0326628 0.0565736i
\(704\) 9.79796 5.65685i 0.369274 0.213201i
\(705\) 0 0
\(706\) 24.2487i 0.912612i
\(707\) −29.6985 34.2929i −1.11693 1.28972i
\(708\) 0 0
\(709\) −20.0000 + 34.6410i −0.751116 + 1.30097i 0.196167 + 0.980571i \(0.437151\pi\)
−0.947282 + 0.320400i \(0.896183\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 6.92820 12.0000i 0.259645 0.449719i
\(713\) 9.79796i 0.366936i
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) −34.6410 + 20.0000i −1.29279 + 0.746393i
\(719\) 13.4722 23.3345i 0.502428 0.870231i −0.497568 0.867425i \(-0.665774\pi\)
0.999996 0.00280593i \(-0.000893157\pi\)
\(720\) 0 0
\(721\) −7.50000 + 21.6506i −0.279315 + 0.806312i
\(722\) −22.6274 −0.842105
\(723\) 0 0
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) −25.9808 −0.963573 −0.481787 0.876289i \(-0.660012\pi\)
−0.481787 + 0.876289i \(0.660012\pi\)
\(728\) 38.1838 7.34847i 1.41518 0.272352i
\(729\) 0 0
\(730\) 0 0
\(731\) −2.44949 4.24264i −0.0905977 0.156920i
\(732\) 0 0
\(733\) −19.9186 + 34.5000i −0.735710 + 1.27429i 0.218702 + 0.975792i \(0.429818\pi\)
−0.954411 + 0.298495i \(0.903515\pi\)
\(734\) 2.44949 0.0904123
\(735\) 0 0
\(736\) 0 0
\(737\) 7.77817 13.4722i 0.286513 0.496255i
\(738\) 0 0
\(739\) −0.500000 0.866025i −0.0183928 0.0318573i 0.856683 0.515844i \(-0.172522\pi\)
−0.875075 + 0.483987i \(0.839188\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 10.3923 2.00000i 0.381514 0.0734223i
\(743\) −24.0416 −0.882002 −0.441001 0.897507i \(-0.645376\pi\)
−0.441001 + 0.897507i \(0.645376\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 35.5176 20.5061i 1.30039 0.750782i
\(747\) 0 0
\(748\) 0 0
\(749\) −2.44949 + 7.07107i −0.0895024 + 0.258371i
\(750\) 0 0
\(751\) −14.5000 + 25.1147i −0.529113 + 0.916450i 0.470311 + 0.882501i \(0.344142\pi\)
−0.999424 + 0.0339490i \(0.989192\pi\)
\(752\) −42.4264 + 24.4949i −1.54713 + 0.893237i
\(753\) 0 0
\(754\) 18.0000 + 10.3923i 0.655521 + 0.378465i
\(755\) 0 0
\(756\) 0 0
\(757\) 2.00000i 0.0726912i 0.999339 + 0.0363456i \(0.0115717\pi\)
−0.999339 + 0.0363456i \(0.988428\pi\)
\(758\) 4.94975 8.57321i 0.179783 0.311393i
\(759\) 0 0
\(760\) 0 0
\(761\) 12.2474 21.2132i 0.443970 0.768978i −0.554010 0.832510i \(-0.686903\pi\)
0.997980 + 0.0635319i \(0.0202365\pi\)
\(762\) 0 0
\(763\) −1.73205 2.00000i −0.0627044 0.0724049i
\(764\) 0 0
\(765\) 0 0
\(766\) 24.0000 13.8564i 0.867155 0.500652i
\(767\) −12.7279 22.0454i −0.459579 0.796014i
\(768\) 0 0
\(769\) 25.9808i 0.936890i 0.883493 + 0.468445i \(0.155186\pi\)
−0.883493 + 0.468445i \(0.844814\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 23.3345 13.4722i 0.839284 0.484561i −0.0177365 0.999843i \(-0.505646\pi\)
0.857021 + 0.515282i \(0.172313\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) −29.3939 −1.05518
\(777\) 0 0
\(778\) 38.0000i 1.36237i
\(779\) −11.0227 6.36396i −0.394929 0.228013i
\(780\) 0 0
\(781\) −5.00000 8.66025i −0.178914 0.309888i
\(782\) −33.9411 19.5959i −1.21373 0.700749i
\(783\) 0 0
\(784\) 4.00000 27.7128i 0.142857 0.989743i
\(785\) 0 0
\(786\) 0 0
\(787\) −22.5167 39.0000i −0.802632 1.39020i −0.917878 0.396863i \(-0.870099\pi\)
0.115246 0.993337i \(-0.463234\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 3.67423 0.707107i 0.130641 0.0251418i
\(792\) 0 0