Properties

Label 768.4.f.b.383.3
Level $768$
Weight $4$
Character 768.383
Analytic conductor $45.313$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [768,4,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, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("768.383");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 768 = 2^{8} \cdot 3 \)
Weight: \( k \) \(=\) \( 4 \)
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: \(45.3134668844\)
Analytic rank: \(0\)
Dimension: \(8\)
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: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{16}\cdot 3^{2} \)
Twist minimal: no (minimal twist has level 48)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 383.3
Root \(0.258819 + 0.965926i\) of defining polynomial
Character \(\chi\) \(=\) 768.383
Dual form 768.4.f.b.383.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.73205 + 4.89898i) q^{3} -16.9706 q^{5} -17.3205i q^{7} +(-21.0000 - 16.9706i) q^{9} +O(q^{10})\) \(q+(-1.73205 + 4.89898i) q^{3} -16.9706 q^{5} -17.3205i q^{7} +(-21.0000 - 16.9706i) q^{9} -29.3939i q^{11} +26.0000i q^{13} +(29.3939 - 83.1384i) q^{15} -67.8823i q^{17} +107.387 q^{19} +(84.8528 + 30.0000i) q^{21} -176.363 q^{23} +163.000 q^{25} +(119.512 - 73.4847i) q^{27} -16.9706 q^{29} +31.1769i q^{31} +(144.000 + 50.9117i) q^{33} +293.939i q^{35} +206.000i q^{37} +(-127.373 - 45.0333i) q^{39} -305.470i q^{41} -93.5307 q^{43} +(356.382 + 288.000i) q^{45} -117.576 q^{47} +43.0000 q^{49} +(332.554 + 117.576i) q^{51} +50.9117 q^{53} +498.831i q^{55} +(-186.000 + 526.087i) q^{57} +558.484i q^{59} -278.000i q^{61} +(-293.939 + 363.731i) q^{63} -441.235i q^{65} -890.274 q^{67} +(305.470 - 864.000i) q^{69} -58.7878 q^{71} +422.000 q^{73} +(-282.324 + 798.534i) q^{75} -509.117 q^{77} +668.572i q^{79} +(153.000 + 712.764i) q^{81} -29.3939i q^{83} +1152.00i q^{85} +(29.3939 - 83.1384i) q^{87} -373.352i q^{89} +450.333 q^{91} +(-152.735 - 54.0000i) q^{93} -1822.42 q^{95} -1070.00 q^{97} +(-498.831 + 617.271i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 168 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 168 q^{9} + 1304 q^{25} + 1152 q^{33} + 344 q^{49} - 1488 q^{57} + 3376 q^{73} + 1224 q^{81} - 8560 q^{97}+O(q^{100}) \) 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
\(3\) −1.73205 + 4.89898i −0.333333 + 0.942809i
\(4\) 0 0
\(5\) −16.9706 −1.51789 −0.758947 0.651153i \(-0.774286\pi\)
−0.758947 + 0.651153i \(0.774286\pi\)
\(6\) 0 0
\(7\) 17.3205i 0.935220i −0.883935 0.467610i \(-0.845115\pi\)
0.883935 0.467610i \(-0.154885\pi\)
\(8\) 0 0
\(9\) −21.0000 16.9706i −0.777778 0.628539i
\(10\) 0 0
\(11\) 29.3939i 0.805690i −0.915268 0.402845i \(-0.868021\pi\)
0.915268 0.402845i \(-0.131979\pi\)
\(12\) 0 0
\(13\) 26.0000i 0.554700i 0.960769 + 0.277350i \(0.0894562\pi\)
−0.960769 + 0.277350i \(0.910544\pi\)
\(14\) 0 0
\(15\) 29.3939 83.1384i 0.505964 1.43108i
\(16\) 0 0
\(17\) 67.8823i 0.968463i −0.874940 0.484231i \(-0.839099\pi\)
0.874940 0.484231i \(-0.160901\pi\)
\(18\) 0 0
\(19\) 107.387 1.29665 0.648324 0.761365i \(-0.275470\pi\)
0.648324 + 0.761365i \(0.275470\pi\)
\(20\) 0 0
\(21\) 84.8528 + 30.0000i 0.881733 + 0.311740i
\(22\) 0 0
\(23\) −176.363 −1.59888 −0.799441 0.600745i \(-0.794871\pi\)
−0.799441 + 0.600745i \(0.794871\pi\)
\(24\) 0 0
\(25\) 163.000 1.30400
\(26\) 0 0
\(27\) 119.512 73.4847i 0.851852 0.523783i
\(28\) 0 0
\(29\) −16.9706 −0.108667 −0.0543337 0.998523i \(-0.517303\pi\)
−0.0543337 + 0.998523i \(0.517303\pi\)
\(30\) 0 0
\(31\) 31.1769i 0.180630i 0.995913 + 0.0903151i \(0.0287874\pi\)
−0.995913 + 0.0903151i \(0.971213\pi\)
\(32\) 0 0
\(33\) 144.000 + 50.9117i 0.759612 + 0.268563i
\(34\) 0 0
\(35\) 293.939i 1.41956i
\(36\) 0 0
\(37\) 206.000i 0.915302i 0.889132 + 0.457651i \(0.151309\pi\)
−0.889132 + 0.457651i \(0.848691\pi\)
\(38\) 0 0
\(39\) −127.373 45.0333i −0.522976 0.184900i
\(40\) 0 0
\(41\) 305.470i 1.16357i −0.813342 0.581786i \(-0.802354\pi\)
0.813342 0.581786i \(-0.197646\pi\)
\(42\) 0 0
\(43\) −93.5307 −0.331705 −0.165852 0.986151i \(-0.553038\pi\)
−0.165852 + 0.986151i \(0.553038\pi\)
\(44\) 0 0
\(45\) 356.382 + 288.000i 1.18058 + 0.954056i
\(46\) 0 0
\(47\) −117.576 −0.364897 −0.182448 0.983215i \(-0.558402\pi\)
−0.182448 + 0.983215i \(0.558402\pi\)
\(48\) 0 0
\(49\) 43.0000 0.125364
\(50\) 0 0
\(51\) 332.554 + 117.576i 0.913075 + 0.322821i
\(52\) 0 0
\(53\) 50.9117 0.131948 0.0659741 0.997821i \(-0.478985\pi\)
0.0659741 + 0.997821i \(0.478985\pi\)
\(54\) 0 0
\(55\) 498.831i 1.22295i
\(56\) 0 0
\(57\) −186.000 + 526.087i −0.432216 + 1.22249i
\(58\) 0 0
\(59\) 558.484i 1.23235i 0.787611 + 0.616173i \(0.211318\pi\)
−0.787611 + 0.616173i \(0.788682\pi\)
\(60\) 0 0
\(61\) 278.000i 0.583512i −0.956493 0.291756i \(-0.905760\pi\)
0.956493 0.291756i \(-0.0942396\pi\)
\(62\) 0 0
\(63\) −293.939 + 363.731i −0.587822 + 0.727393i
\(64\) 0 0
\(65\) 441.235i 0.841976i
\(66\) 0 0
\(67\) −890.274 −1.62335 −0.811674 0.584111i \(-0.801443\pi\)
−0.811674 + 0.584111i \(0.801443\pi\)
\(68\) 0 0
\(69\) 305.470 864.000i 0.532961 1.50744i
\(70\) 0 0
\(71\) −58.7878 −0.0982651 −0.0491326 0.998792i \(-0.515646\pi\)
−0.0491326 + 0.998792i \(0.515646\pi\)
\(72\) 0 0
\(73\) 422.000 0.676594 0.338297 0.941039i \(-0.390149\pi\)
0.338297 + 0.941039i \(0.390149\pi\)
\(74\) 0 0
\(75\) −282.324 + 798.534i −0.434667 + 1.22942i
\(76\) 0 0
\(77\) −509.117 −0.753497
\(78\) 0 0
\(79\) 668.572i 0.952154i 0.879404 + 0.476077i \(0.157942\pi\)
−0.879404 + 0.476077i \(0.842058\pi\)
\(80\) 0 0
\(81\) 153.000 + 712.764i 0.209877 + 0.977728i
\(82\) 0 0
\(83\) 29.3939i 0.0388723i −0.999811 0.0194361i \(-0.993813\pi\)
0.999811 0.0194361i \(-0.00618710\pi\)
\(84\) 0 0
\(85\) 1152.00i 1.47002i
\(86\) 0 0
\(87\) 29.3939 83.1384i 0.0362225 0.102453i
\(88\) 0 0
\(89\) 373.352i 0.444666i −0.974971 0.222333i \(-0.928633\pi\)
0.974971 0.222333i \(-0.0713672\pi\)
\(90\) 0 0
\(91\) 450.333 0.518766
\(92\) 0 0
\(93\) −152.735 54.0000i −0.170300 0.0602101i
\(94\) 0 0
\(95\) −1822.42 −1.96817
\(96\) 0 0
\(97\) −1070.00 −1.12002 −0.560011 0.828486i \(-0.689203\pi\)
−0.560011 + 0.828486i \(0.689203\pi\)
\(98\) 0 0
\(99\) −498.831 + 617.271i −0.506408 + 0.626648i
\(100\) 0 0
\(101\) −1781.91 −1.75551 −0.877755 0.479109i \(-0.840960\pi\)
−0.877755 + 0.479109i \(0.840960\pi\)
\(102\) 0 0
\(103\) 17.3205i 0.0165693i −0.999966 0.00828466i \(-0.997363\pi\)
0.999966 0.00828466i \(-0.00263712\pi\)
\(104\) 0 0
\(105\) −1440.00 509.117i −1.33838 0.473188i
\(106\) 0 0
\(107\) 1381.51i 1.24819i 0.781350 + 0.624093i \(0.214531\pi\)
−0.781350 + 0.624093i \(0.785469\pi\)
\(108\) 0 0
\(109\) 358.000i 0.314589i −0.987552 0.157294i \(-0.949723\pi\)
0.987552 0.157294i \(-0.0502772\pi\)
\(110\) 0 0
\(111\) −1009.19 356.802i −0.862955 0.305101i
\(112\) 0 0
\(113\) 67.8823i 0.0565117i −0.999601 0.0282559i \(-0.991005\pi\)
0.999601 0.0282559i \(-0.00899532\pi\)
\(114\) 0 0
\(115\) 2992.98 2.42693
\(116\) 0 0
\(117\) 441.235 546.000i 0.348651 0.431433i
\(118\) 0 0
\(119\) −1175.76 −0.905725
\(120\) 0 0
\(121\) 467.000 0.350864
\(122\) 0 0
\(123\) 1496.49 + 529.090i 1.09703 + 0.387857i
\(124\) 0 0
\(125\) −644.881 −0.461440
\(126\) 0 0
\(127\) 31.1769i 0.0217835i 0.999941 + 0.0108917i \(0.00346702\pi\)
−0.999941 + 0.0108917i \(0.996533\pi\)
\(128\) 0 0
\(129\) 162.000 458.205i 0.110568 0.312734i
\(130\) 0 0
\(131\) 1734.24i 1.15665i 0.815806 + 0.578325i \(0.196293\pi\)
−0.815806 + 0.578325i \(0.803707\pi\)
\(132\) 0 0
\(133\) 1860.00i 1.21265i
\(134\) 0 0
\(135\) −2028.18 + 1247.08i −1.29302 + 0.795046i
\(136\) 0 0
\(137\) 2274.06i 1.41814i 0.705136 + 0.709072i \(0.250886\pi\)
−0.705136 + 0.709072i \(0.749114\pi\)
\(138\) 0 0
\(139\) 1541.53 0.940651 0.470325 0.882493i \(-0.344137\pi\)
0.470325 + 0.882493i \(0.344137\pi\)
\(140\) 0 0
\(141\) 203.647 576.000i 0.121632 0.344028i
\(142\) 0 0
\(143\) 764.241 0.446916
\(144\) 0 0
\(145\) 288.000 0.164946
\(146\) 0 0
\(147\) −74.4782 + 210.656i −0.0417881 + 0.118195i
\(148\) 0 0
\(149\) 2358.91 1.29698 0.648488 0.761225i \(-0.275402\pi\)
0.648488 + 0.761225i \(0.275402\pi\)
\(150\) 0 0
\(151\) 2040.36i 1.09961i −0.835292 0.549807i \(-0.814701\pi\)
0.835292 0.549807i \(-0.185299\pi\)
\(152\) 0 0
\(153\) −1152.00 + 1425.53i −0.608717 + 0.753249i
\(154\) 0 0
\(155\) 529.090i 0.274178i
\(156\) 0 0
\(157\) 106.000i 0.0538836i 0.999637 + 0.0269418i \(0.00857687\pi\)
−0.999637 + 0.0269418i \(0.991423\pi\)
\(158\) 0 0
\(159\) −88.1816 + 249.415i −0.0439828 + 0.124402i
\(160\) 0 0
\(161\) 3054.70i 1.49531i
\(162\) 0 0
\(163\) 79.6743 0.0382857 0.0191429 0.999817i \(-0.493906\pi\)
0.0191429 + 0.999817i \(0.493906\pi\)
\(164\) 0 0
\(165\) −2443.76 864.000i −1.15301 0.407650i
\(166\) 0 0
\(167\) −3115.75 −1.44374 −0.721868 0.692030i \(-0.756716\pi\)
−0.721868 + 0.692030i \(0.756716\pi\)
\(168\) 0 0
\(169\) 1521.00 0.692308
\(170\) 0 0
\(171\) −2255.13 1822.42i −1.00850 0.814994i
\(172\) 0 0
\(173\) 2223.14 0.977009 0.488504 0.872561i \(-0.337543\pi\)
0.488504 + 0.872561i \(0.337543\pi\)
\(174\) 0 0
\(175\) 2823.24i 1.21953i
\(176\) 0 0
\(177\) −2736.00 967.322i −1.16187 0.410782i
\(178\) 0 0
\(179\) 2792.42i 1.16601i 0.812470 + 0.583003i \(0.198122\pi\)
−0.812470 + 0.583003i \(0.801878\pi\)
\(180\) 0 0
\(181\) 4510.00i 1.85208i 0.377431 + 0.926038i \(0.376808\pi\)
−0.377431 + 0.926038i \(0.623192\pi\)
\(182\) 0 0
\(183\) 1361.92 + 481.510i 0.550141 + 0.194504i
\(184\) 0 0
\(185\) 3495.94i 1.38933i
\(186\) 0 0
\(187\) −1995.32 −0.780280
\(188\) 0 0
\(189\) −1272.79 2070.00i −0.489852 0.796668i
\(190\) 0 0
\(191\) −1881.21 −0.712667 −0.356334 0.934359i \(-0.615973\pi\)
−0.356334 + 0.934359i \(0.615973\pi\)
\(192\) 0 0
\(193\) 4994.00 1.86257 0.931285 0.364292i \(-0.118689\pi\)
0.931285 + 0.364292i \(0.118689\pi\)
\(194\) 0 0
\(195\) 2161.60 + 764.241i 0.793822 + 0.280659i
\(196\) 0 0
\(197\) 2155.26 0.779472 0.389736 0.920927i \(-0.372566\pi\)
0.389736 + 0.920927i \(0.372566\pi\)
\(198\) 0 0
\(199\) 3973.32i 1.41538i 0.706521 + 0.707692i \(0.250264\pi\)
−0.706521 + 0.707692i \(0.749736\pi\)
\(200\) 0 0
\(201\) 1542.00 4361.43i 0.541116 1.53051i
\(202\) 0 0
\(203\) 293.939i 0.101628i
\(204\) 0 0
\(205\) 5184.00i 1.76618i
\(206\) 0 0
\(207\) 3703.63 + 2992.98i 1.24357 + 1.00496i
\(208\) 0 0
\(209\) 3156.52i 1.04470i
\(210\) 0 0
\(211\) −4908.63 −1.60154 −0.800768 0.598974i \(-0.795575\pi\)
−0.800768 + 0.598974i \(0.795575\pi\)
\(212\) 0 0
\(213\) 101.823 288.000i 0.0327550 0.0926452i
\(214\) 0 0
\(215\) 1587.27 0.503492
\(216\) 0 0
\(217\) 540.000 0.168929
\(218\) 0 0
\(219\) −730.925 + 2067.37i −0.225531 + 0.637899i
\(220\) 0 0
\(221\) 1764.94 0.537206
\(222\) 0 0
\(223\) 4021.82i 1.20772i 0.797091 + 0.603859i \(0.206371\pi\)
−0.797091 + 0.603859i \(0.793629\pi\)
\(224\) 0 0
\(225\) −3423.00 2766.20i −1.01422 0.819615i
\(226\) 0 0
\(227\) 2968.78i 0.868039i −0.900903 0.434020i \(-0.857095\pi\)
0.900903 0.434020i \(-0.142905\pi\)
\(228\) 0 0
\(229\) 430.000i 0.124084i 0.998074 + 0.0620419i \(0.0197612\pi\)
−0.998074 + 0.0620419i \(0.980239\pi\)
\(230\) 0 0
\(231\) 881.816 2494.15i 0.251166 0.710404i
\(232\) 0 0
\(233\) 6346.99i 1.78457i 0.451471 + 0.892286i \(0.350899\pi\)
−0.451471 + 0.892286i \(0.649101\pi\)
\(234\) 0 0
\(235\) 1995.32 0.553874
\(236\) 0 0
\(237\) −3275.32 1158.00i −0.897700 0.317385i
\(238\) 0 0
\(239\) 4115.14 1.11375 0.556875 0.830596i \(-0.312000\pi\)
0.556875 + 0.830596i \(0.312000\pi\)
\(240\) 0 0
\(241\) 4690.00 1.25357 0.626783 0.779194i \(-0.284371\pi\)
0.626783 + 0.779194i \(0.284371\pi\)
\(242\) 0 0
\(243\) −3756.82 484.999i −0.991770 0.128036i
\(244\) 0 0
\(245\) −729.734 −0.190290
\(246\) 0 0
\(247\) 2792.07i 0.719251i
\(248\) 0 0
\(249\) 144.000 + 50.9117i 0.0366491 + 0.0129574i
\(250\) 0 0
\(251\) 1263.94i 0.317845i 0.987291 + 0.158922i \(0.0508019\pi\)
−0.987291 + 0.158922i \(0.949198\pi\)
\(252\) 0 0
\(253\) 5184.00i 1.28820i
\(254\) 0 0
\(255\) −5643.62 1995.32i −1.38595 0.490008i
\(256\) 0 0
\(257\) 271.529i 0.0659047i 0.999457 + 0.0329524i \(0.0104910\pi\)
−0.999457 + 0.0329524i \(0.989509\pi\)
\(258\) 0 0
\(259\) 3568.02 0.856009
\(260\) 0 0
\(261\) 356.382 + 288.000i 0.0845191 + 0.0683017i
\(262\) 0 0
\(263\) 5114.53 1.19915 0.599574 0.800320i \(-0.295337\pi\)
0.599574 + 0.800320i \(0.295337\pi\)
\(264\) 0 0
\(265\) −864.000 −0.200283
\(266\) 0 0
\(267\) 1829.05 + 646.665i 0.419235 + 0.148222i
\(268\) 0 0
\(269\) 3173.50 0.719299 0.359649 0.933087i \(-0.382896\pi\)
0.359649 + 0.933087i \(0.382896\pi\)
\(270\) 0 0
\(271\) 668.572i 0.149863i 0.997189 + 0.0749314i \(0.0238738\pi\)
−0.997189 + 0.0749314i \(0.976126\pi\)
\(272\) 0 0
\(273\) −780.000 + 2206.17i −0.172922 + 0.489098i
\(274\) 0 0
\(275\) 4791.20i 1.05062i
\(276\) 0 0
\(277\) 2018.00i 0.437725i −0.975756 0.218863i \(-0.929765\pi\)
0.975756 0.218863i \(-0.0702346\pi\)
\(278\) 0 0
\(279\) 529.090 654.715i 0.113533 0.140490i
\(280\) 0 0
\(281\) 4717.82i 1.00157i −0.865572 0.500785i \(-0.833045\pi\)
0.865572 0.500785i \(-0.166955\pi\)
\(282\) 0 0
\(283\) −5081.84 −1.06743 −0.533717 0.845663i \(-0.679205\pi\)
−0.533717 + 0.845663i \(0.679205\pi\)
\(284\) 0 0
\(285\) 3156.52 8928.00i 0.656057 1.85561i
\(286\) 0 0
\(287\) −5290.90 −1.08819
\(288\) 0 0
\(289\) 305.000 0.0620802
\(290\) 0 0
\(291\) 1853.29 5241.91i 0.373340 1.05597i
\(292\) 0 0
\(293\) −424.264 −0.0845931 −0.0422965 0.999105i \(-0.513467\pi\)
−0.0422965 + 0.999105i \(0.513467\pi\)
\(294\) 0 0
\(295\) 9477.78i 1.87057i
\(296\) 0 0
\(297\) −2160.00 3512.91i −0.422006 0.686328i
\(298\) 0 0
\(299\) 4585.44i 0.886900i
\(300\) 0 0
\(301\) 1620.00i 0.310217i
\(302\) 0 0
\(303\) 3086.36 8729.54i 0.585170 1.65511i
\(304\) 0 0
\(305\) 4717.82i 0.885709i
\(306\) 0 0
\(307\) −3522.99 −0.654944 −0.327472 0.944861i \(-0.606197\pi\)
−0.327472 + 0.944861i \(0.606197\pi\)
\(308\) 0 0
\(309\) 84.8528 + 30.0000i 0.0156217 + 0.00552311i
\(310\) 0 0
\(311\) 9464.83 1.72573 0.862864 0.505437i \(-0.168669\pi\)
0.862864 + 0.505437i \(0.168669\pi\)
\(312\) 0 0
\(313\) 3718.00 0.671418 0.335709 0.941966i \(-0.391024\pi\)
0.335709 + 0.941966i \(0.391024\pi\)
\(314\) 0 0
\(315\) 4988.31 6172.71i 0.892251 1.10410i
\(316\) 0 0
\(317\) −7212.49 −1.27790 −0.638949 0.769249i \(-0.720631\pi\)
−0.638949 + 0.769249i \(0.720631\pi\)
\(318\) 0 0
\(319\) 498.831i 0.0875522i
\(320\) 0 0
\(321\) −6768.00 2392.85i −1.17680 0.416062i
\(322\) 0 0
\(323\) 7289.68i 1.25575i
\(324\) 0 0
\(325\) 4238.00i 0.723329i
\(326\) 0 0
\(327\) 1753.83 + 620.074i 0.296597 + 0.104863i
\(328\) 0 0
\(329\) 2036.47i 0.341259i
\(330\) 0 0
\(331\) 1541.53 0.255982 0.127991 0.991775i \(-0.459147\pi\)
0.127991 + 0.991775i \(0.459147\pi\)
\(332\) 0 0
\(333\) 3495.94 4326.00i 0.575304 0.711902i
\(334\) 0 0
\(335\) 15108.5 2.46407
\(336\) 0 0
\(337\) 2530.00 0.408955 0.204478 0.978871i \(-0.434450\pi\)
0.204478 + 0.978871i \(0.434450\pi\)
\(338\) 0 0
\(339\) 332.554 + 117.576i 0.0532798 + 0.0188372i
\(340\) 0 0
\(341\) 916.410 0.145532
\(342\) 0 0
\(343\) 6685.72i 1.05246i
\(344\) 0 0
\(345\) −5184.00 + 14662.6i −0.808977 + 2.28813i
\(346\) 0 0
\(347\) 5555.44i 0.859458i −0.902958 0.429729i \(-0.858609\pi\)
0.902958 0.429729i \(-0.141391\pi\)
\(348\) 0 0
\(349\) 7786.00i 1.19420i 0.802168 + 0.597099i \(0.203680\pi\)
−0.802168 + 0.597099i \(0.796320\pi\)
\(350\) 0 0
\(351\) 1910.60 + 3107.30i 0.290542 + 0.472522i
\(352\) 0 0
\(353\) 407.294i 0.0614109i 0.999528 + 0.0307054i \(0.00977538\pi\)
−0.999528 + 0.0307054i \(0.990225\pi\)
\(354\) 0 0
\(355\) 997.661 0.149156
\(356\) 0 0
\(357\) 2036.47 5760.00i 0.301908 0.853926i
\(358\) 0 0
\(359\) −8759.38 −1.28775 −0.643875 0.765131i \(-0.722674\pi\)
−0.643875 + 0.765131i \(0.722674\pi\)
\(360\) 0 0
\(361\) 4673.00 0.681295
\(362\) 0 0
\(363\) −808.868 + 2287.82i −0.116955 + 0.330798i
\(364\) 0 0
\(365\) −7161.58 −1.02700
\(366\) 0 0
\(367\) 12578.2i 1.78903i −0.447037 0.894515i \(-0.647521\pi\)
0.447037 0.894515i \(-0.352479\pi\)
\(368\) 0 0
\(369\) −5184.00 + 6414.87i −0.731350 + 0.905000i
\(370\) 0 0
\(371\) 881.816i 0.123401i
\(372\) 0 0
\(373\) 4258.00i 0.591075i −0.955331 0.295537i \(-0.904501\pi\)
0.955331 0.295537i \(-0.0954987\pi\)
\(374\) 0 0
\(375\) 1116.97 3159.26i 0.153813 0.435049i
\(376\) 0 0
\(377\) 441.235i 0.0602778i
\(378\) 0 0
\(379\) −2726.25 −0.369493 −0.184747 0.982786i \(-0.559146\pi\)
−0.184747 + 0.982786i \(0.559146\pi\)
\(380\) 0 0
\(381\) −152.735 54.0000i −0.0205377 0.00726116i
\(382\) 0 0
\(383\) −4232.72 −0.564704 −0.282352 0.959311i \(-0.591115\pi\)
−0.282352 + 0.959311i \(0.591115\pi\)
\(384\) 0 0
\(385\) 8640.00 1.14373
\(386\) 0 0
\(387\) 1964.15 + 1587.27i 0.257993 + 0.208489i
\(388\) 0 0
\(389\) −5447.55 −0.710030 −0.355015 0.934861i \(-0.615524\pi\)
−0.355015 + 0.934861i \(0.615524\pi\)
\(390\) 0 0
\(391\) 11971.9i 1.54846i
\(392\) 0 0
\(393\) −8496.00 3003.79i −1.09050 0.385550i
\(394\) 0 0
\(395\) 11346.0i 1.44527i
\(396\) 0 0
\(397\) 13574.0i 1.71602i −0.513634 0.858009i \(-0.671701\pi\)
0.513634 0.858009i \(-0.328299\pi\)
\(398\) 0 0
\(399\) 9112.10 + 3221.61i 1.14330 + 0.404217i
\(400\) 0 0
\(401\) 11743.6i 1.46247i −0.682128 0.731233i \(-0.738945\pi\)
0.682128 0.731233i \(-0.261055\pi\)
\(402\) 0 0
\(403\) −810.600 −0.100196
\(404\) 0 0
\(405\) −2596.50 12096.0i −0.318570 1.48409i
\(406\) 0 0
\(407\) 6055.14 0.737450
\(408\) 0 0
\(409\) −2890.00 −0.349392 −0.174696 0.984622i \(-0.555894\pi\)
−0.174696 + 0.984622i \(0.555894\pi\)
\(410\) 0 0
\(411\) −11140.6 3938.78i −1.33704 0.472715i
\(412\) 0 0
\(413\) 9673.22 1.15251
\(414\) 0 0
\(415\) 498.831i 0.0590039i
\(416\) 0 0
\(417\) −2670.00 + 7551.90i −0.313550 + 0.886854i
\(418\) 0 0
\(419\) 8318.47i 0.969890i 0.874545 + 0.484945i \(0.161160\pi\)
−0.874545 + 0.484945i \(0.838840\pi\)
\(420\) 0 0
\(421\) 10414.0i 1.20558i 0.797902 + 0.602788i \(0.205943\pi\)
−0.797902 + 0.602788i \(0.794057\pi\)
\(422\) 0 0
\(423\) 2469.09 + 1995.32i 0.283809 + 0.229352i
\(424\) 0 0
\(425\) 11064.8i 1.26288i
\(426\) 0 0
\(427\) −4815.10 −0.545712
\(428\) 0 0
\(429\) −1323.70 + 3744.00i −0.148972 + 0.421357i
\(430\) 0 0
\(431\) 13050.9 1.45856 0.729279 0.684216i \(-0.239855\pi\)
0.729279 + 0.684216i \(0.239855\pi\)
\(432\) 0 0
\(433\) −9214.00 −1.02262 −0.511312 0.859395i \(-0.670841\pi\)
−0.511312 + 0.859395i \(0.670841\pi\)
\(434\) 0 0
\(435\) −498.831 + 1410.91i −0.0549818 + 0.155512i
\(436\) 0 0
\(437\) −18939.1 −2.07319
\(438\) 0 0
\(439\) 7326.57i 0.796534i 0.917270 + 0.398267i \(0.130388\pi\)
−0.917270 + 0.398267i \(0.869612\pi\)
\(440\) 0 0
\(441\) −903.000 729.734i −0.0975057 0.0787965i
\(442\) 0 0
\(443\) 2204.54i 0.236435i 0.992988 + 0.118218i \(0.0377181\pi\)
−0.992988 + 0.118218i \(0.962282\pi\)
\(444\) 0 0
\(445\) 6336.00i 0.674956i
\(446\) 0 0
\(447\) −4085.75 + 11556.2i −0.432325 + 1.22280i
\(448\) 0 0
\(449\) 2851.05i 0.299665i −0.988711 0.149832i \(-0.952127\pi\)
0.988711 0.149832i \(-0.0478734\pi\)
\(450\) 0 0
\(451\) −8978.95 −0.937477
\(452\) 0 0
\(453\) 9995.66 + 3534.00i 1.03673 + 0.366538i
\(454\) 0 0
\(455\) −7642.41 −0.787432
\(456\) 0 0
\(457\) 38.0000 0.00388964 0.00194482 0.999998i \(-0.499381\pi\)
0.00194482 + 0.999998i \(0.499381\pi\)
\(458\) 0 0
\(459\) −4988.31 8112.71i −0.507264 0.824987i
\(460\) 0 0
\(461\) −15833.5 −1.59966 −0.799828 0.600230i \(-0.795076\pi\)
−0.799828 + 0.600230i \(0.795076\pi\)
\(462\) 0 0
\(463\) 11365.7i 1.14084i 0.821353 + 0.570421i \(0.193220\pi\)
−0.821353 + 0.570421i \(0.806780\pi\)
\(464\) 0 0
\(465\) 2592.00 + 916.410i 0.258497 + 0.0913925i
\(466\) 0 0
\(467\) 499.696i 0.0495143i −0.999693 0.0247571i \(-0.992119\pi\)
0.999693 0.0247571i \(-0.00788125\pi\)
\(468\) 0 0
\(469\) 15420.0i 1.51819i
\(470\) 0 0
\(471\) −519.292 183.597i −0.0508019 0.0179612i
\(472\) 0 0
\(473\) 2749.23i 0.267251i
\(474\) 0 0
\(475\) 17504.1 1.69083
\(476\) 0 0
\(477\) −1069.15 864.000i −0.102626 0.0829347i
\(478\) 0 0
\(479\) −8700.59 −0.829937 −0.414969 0.909836i \(-0.636207\pi\)
−0.414969 + 0.909836i \(0.636207\pi\)
\(480\) 0 0
\(481\) −5356.00 −0.507718
\(482\) 0 0
\(483\) −14964.9 5290.90i −1.40979 0.498435i
\(484\) 0 0
\(485\) 18158.5 1.70007
\(486\) 0 0
\(487\) 4007.97i 0.372933i −0.982461 0.186466i \(-0.940296\pi\)
0.982461 0.186466i \(-0.0597035\pi\)
\(488\) 0 0
\(489\) −138.000 + 390.323i −0.0127619 + 0.0360961i
\(490\) 0 0
\(491\) 16901.5i 1.55347i 0.629828 + 0.776734i \(0.283125\pi\)
−0.629828 + 0.776734i \(0.716875\pi\)
\(492\) 0 0
\(493\) 1152.00i 0.105240i
\(494\) 0 0
\(495\) 8465.44 10475.4i 0.768673 0.951184i
\(496\) 0 0
\(497\) 1018.23i 0.0918994i
\(498\) 0 0
\(499\) 12439.6 1.11598 0.557988 0.829849i \(-0.311573\pi\)
0.557988 + 0.829849i \(0.311573\pi\)
\(500\) 0 0
\(501\) 5396.64 15264.0i 0.481246 1.36117i
\(502\) 0 0
\(503\) 12756.9 1.13082 0.565411 0.824809i \(-0.308717\pi\)
0.565411 + 0.824809i \(0.308717\pi\)
\(504\) 0 0
\(505\) 30240.0 2.66468
\(506\) 0 0
\(507\) −2634.45 + 7451.35i −0.230769 + 0.652714i
\(508\) 0 0
\(509\) 5549.37 0.483245 0.241622 0.970370i \(-0.422320\pi\)
0.241622 + 0.970370i \(0.422320\pi\)
\(510\) 0 0
\(511\) 7309.25i 0.632764i
\(512\) 0 0
\(513\) 12834.0 7891.31i 1.10455 0.679162i
\(514\) 0 0
\(515\) 293.939i 0.0251505i
\(516\) 0 0
\(517\) 3456.00i 0.293994i
\(518\) 0 0
\(519\) −3850.60 + 10891.1i −0.325670 + 0.921133i
\(520\) 0 0
\(521\) 11506.0i 0.967541i 0.875195 + 0.483770i \(0.160733\pi\)
−0.875195 + 0.483770i \(0.839267\pi\)
\(522\) 0 0
\(523\) −17441.8 −1.45827 −0.729134 0.684371i \(-0.760077\pi\)
−0.729134 + 0.684371i \(0.760077\pi\)
\(524\) 0 0
\(525\) 13831.0 + 4890.00i 1.14978 + 0.406509i
\(526\) 0 0
\(527\) 2116.36 0.174934
\(528\) 0 0
\(529\) 18937.0 1.55642
\(530\) 0 0
\(531\) 9477.78 11728.2i 0.774578 0.958491i
\(532\) 0 0
\(533\) 7942.22 0.645433
\(534\) 0 0
\(535\) 23445.0i 1.89461i
\(536\) 0 0
\(537\) −13680.0 4836.61i −1.09932 0.388669i
\(538\) 0 0
\(539\) 1263.94i 0.101005i
\(540\) 0 0
\(541\) 6794.00i 0.539920i 0.962871 + 0.269960i \(0.0870105\pi\)
−0.962871 + 0.269960i \(0.912989\pi\)
\(542\) 0 0
\(543\) −22094.4 7811.55i −1.74615 0.617358i
\(544\) 0 0
\(545\) 6075.46i 0.477512i
\(546\) 0 0
\(547\) −3910.97 −0.305706 −0.152853 0.988249i \(-0.548846\pi\)
−0.152853 + 0.988249i \(0.548846\pi\)
\(548\) 0 0
\(549\) −4717.82 + 5838.00i −0.366760 + 0.453843i
\(550\) 0 0
\(551\) −1822.42 −0.140903
\(552\) 0 0
\(553\) 11580.0 0.890473
\(554\) 0 0
\(555\) 17126.5 + 6055.14i 1.30987 + 0.463110i
\(556\) 0 0
\(557\) 22587.8 1.71827 0.859135 0.511749i \(-0.171002\pi\)
0.859135 + 0.511749i \(0.171002\pi\)
\(558\) 0 0
\(559\) 2431.80i 0.183997i
\(560\) 0 0
\(561\) 3456.00 9775.04i 0.260093 0.735655i
\(562\) 0 0
\(563\) 8729.98i 0.653508i −0.945109 0.326754i \(-0.894045\pi\)
0.945109 0.326754i \(-0.105955\pi\)
\(564\) 0 0
\(565\) 1152.00i 0.0857788i
\(566\) 0 0
\(567\) 12345.4 2650.04i 0.914390 0.196281i
\(568\) 0 0
\(569\) 16122.0i 1.18782i −0.804531 0.593911i \(-0.797583\pi\)
0.804531 0.593911i \(-0.202417\pi\)
\(570\) 0 0
\(571\) 9495.10 0.695898 0.347949 0.937513i \(-0.386878\pi\)
0.347949 + 0.937513i \(0.386878\pi\)
\(572\) 0 0
\(573\) 3258.35 9216.00i 0.237556 0.671909i
\(574\) 0 0
\(575\) −28747.2 −2.08494
\(576\) 0 0
\(577\) −8974.00 −0.647474 −0.323737 0.946147i \(-0.604939\pi\)
−0.323737 + 0.946147i \(0.604939\pi\)
\(578\) 0 0
\(579\) −8649.86 + 24465.5i −0.620857 + 1.75605i
\(580\) 0 0
\(581\) −509.117 −0.0363541
\(582\) 0 0
\(583\) 1496.49i 0.106309i
\(584\) 0 0
\(585\) −7488.00 + 9265.93i −0.529215 + 0.654870i
\(586\) 0 0
\(587\) 4908.78i 0.345157i 0.984996 + 0.172578i \(0.0552098\pi\)
−0.984996 + 0.172578i \(0.944790\pi\)
\(588\) 0 0
\(589\) 3348.00i 0.234214i
\(590\) 0 0
\(591\) −3733.02 + 10558.6i −0.259824 + 0.734893i
\(592\) 0 0
\(593\) 14730.4i 1.02008i 0.860151 + 0.510040i \(0.170369\pi\)
−0.860151 + 0.510040i \(0.829631\pi\)
\(594\) 0 0
\(595\) 19953.2 1.37479
\(596\) 0 0
\(597\) −19465.2 6882.00i −1.33444 0.471795i
\(598\) 0 0
\(599\) −10052.7 −0.685714 −0.342857 0.939388i \(-0.611395\pi\)
−0.342857 + 0.939388i \(0.611395\pi\)
\(600\) 0 0
\(601\) −23690.0 −1.60788 −0.803939 0.594711i \(-0.797266\pi\)
−0.803939 + 0.594711i \(0.797266\pi\)
\(602\) 0 0
\(603\) 18695.8 + 15108.5i 1.26260 + 1.02034i
\(604\) 0 0
\(605\) −7925.25 −0.532574
\(606\) 0 0
\(607\) 22589.4i 1.51050i 0.655435 + 0.755252i \(0.272485\pi\)
−0.655435 + 0.755252i \(0.727515\pi\)
\(608\) 0 0
\(609\) −1440.00 509.117i −0.0958157 0.0338760i
\(610\) 0 0
\(611\) 3056.96i 0.202408i
\(612\) 0 0
\(613\) 9422.00i 0.620801i 0.950606 + 0.310400i \(0.100463\pi\)
−0.950606 + 0.310400i \(0.899537\pi\)
\(614\) 0 0
\(615\) −25396.3 8978.95i −1.66517 0.588726i
\(616\) 0 0
\(617\) 984.293i 0.0642239i −0.999484 0.0321119i \(-0.989777\pi\)
0.999484 0.0321119i \(-0.0102233\pi\)
\(618\) 0 0
\(619\) 12238.7 0.794691 0.397345 0.917669i \(-0.369931\pi\)
0.397345 + 0.917669i \(0.369931\pi\)
\(620\) 0 0
\(621\) −21077.4 + 12960.0i −1.36201 + 0.837467i
\(622\) 0 0
\(623\) −6466.65 −0.415860
\(624\) 0 0
\(625\) −9431.00 −0.603584
\(626\) 0 0
\(627\) 15463.7 + 5467.26i 0.984948 + 0.348232i
\(628\) 0 0
\(629\) 13983.7 0.886436
\(630\) 0 0
\(631\) 13922.2i 0.878344i 0.898403 + 0.439172i \(0.144728\pi\)
−0.898403 + 0.439172i \(0.855272\pi\)
\(632\) 0 0
\(633\) 8502.00 24047.3i 0.533845 1.50994i
\(634\) 0 0
\(635\) 529.090i 0.0330650i
\(636\) 0 0
\(637\) 1118.00i 0.0695397i
\(638\) 0 0
\(639\) 1234.54 + 997.661i 0.0764284 + 0.0617635i
\(640\) 0 0
\(641\) 16427.5i 1.01224i −0.862462 0.506121i \(-0.831079\pi\)
0.862462 0.506121i \(-0.168921\pi\)
\(642\) 0 0
\(643\) 1465.31 0.0898700 0.0449350 0.998990i \(-0.485692\pi\)
0.0449350 + 0.998990i \(0.485692\pi\)
\(644\) 0 0
\(645\) −2749.23 + 7776.00i −0.167831 + 0.474697i
\(646\) 0 0
\(647\) −12286.6 −0.746581 −0.373290 0.927715i \(-0.621770\pi\)
−0.373290 + 0.927715i \(0.621770\pi\)
\(648\) 0 0
\(649\) 16416.0 0.992888
\(650\) 0 0
\(651\) −935.307 + 2645.45i −0.0563097 + 0.159268i
\(652\) 0 0
\(653\) −8502.25 −0.509523 −0.254762 0.967004i \(-0.581997\pi\)
−0.254762 + 0.967004i \(0.581997\pi\)
\(654\) 0 0
\(655\) 29431.0i 1.75567i
\(656\) 0 0
\(657\) −8862.00 7161.58i −0.526240 0.425266i
\(658\) 0 0
\(659\) 17136.6i 1.01297i 0.862248 + 0.506486i \(0.169056\pi\)
−0.862248 + 0.506486i \(0.830944\pi\)
\(660\) 0 0
\(661\) 10018.0i 0.589493i −0.955575 0.294747i \(-0.904765\pi\)
0.955575 0.294747i \(-0.0952352\pi\)
\(662\) 0 0
\(663\) −3056.96 + 8646.40i −0.179069 + 0.506483i
\(664\) 0 0
\(665\) 31565.2i 1.84067i
\(666\) 0 0
\(667\) 2992.98 0.173746
\(668\) 0 0
\(669\) −19702.8 6966.00i −1.13865 0.402573i
\(670\) 0 0
\(671\) −8171.50 −0.470130
\(672\) 0 0
\(673\) 1682.00 0.0963393 0.0481696 0.998839i \(-0.484661\pi\)
0.0481696 + 0.998839i \(0.484661\pi\)
\(674\) 0 0
\(675\) 19480.4 11978.0i 1.11081 0.683013i
\(676\) 0 0
\(677\) −9113.19 −0.517354 −0.258677 0.965964i \(-0.583286\pi\)
−0.258677 + 0.965964i \(0.583286\pi\)
\(678\) 0 0
\(679\) 18532.9i 1.04747i
\(680\) 0 0
\(681\) 14544.0 + 5142.08i 0.818395 + 0.289346i
\(682\) 0 0
\(683\) 23250.6i 1.30257i 0.758832 + 0.651287i \(0.225771\pi\)
−0.758832 + 0.651287i \(0.774229\pi\)
\(684\) 0 0
\(685\) 38592.0i 2.15259i
\(686\) 0 0
\(687\) −2106.56 744.782i −0.116987 0.0413613i
\(688\) 0 0
\(689\) 1323.70i 0.0731917i
\(690\) 0 0
\(691\) −25222.1 −1.38856 −0.694280 0.719705i \(-0.744277\pi\)
−0.694280 + 0.719705i \(0.744277\pi\)
\(692\) 0 0
\(693\) 10691.5 + 8640.00i 0.586053 + 0.473602i
\(694\) 0 0
\(695\) −26160.6 −1.42781
\(696\) 0 0
\(697\) −20736.0 −1.12688
\(698\) 0 0
\(699\) −31093.8 10993.3i −1.68251 0.594857i
\(700\) 0 0
\(701\) 16410.5 0.884190 0.442095 0.896968i \(-0.354235\pi\)
0.442095 + 0.896968i \(0.354235\pi\)
\(702\) 0 0
\(703\) 22121.8i 1.18682i
\(704\) 0 0
\(705\) −3456.00 + 9775.04i −0.184625 + 0.522198i
\(706\) 0 0
\(707\) 30863.6i 1.64179i
\(708\) 0 0
\(709\) 27602.0i 1.46208i −0.682334 0.731040i \(-0.739035\pi\)
0.682334 0.731040i \(-0.260965\pi\)
\(710\) 0 0
\(711\) 11346.0 14040.0i 0.598466 0.740564i
\(712\) 0 0
\(713\) 5498.46i 0.288806i
\(714\) 0 0
\(715\) −12969.6 −0.678371
\(716\) 0 0
\(717\) −7127.64 + 20160.0i −0.371250 + 1.05005i
\(718\) 0 0
\(719\) 31627.8 1.64050 0.820249 0.572006i \(-0.193835\pi\)
0.820249 + 0.572006i \(0.193835\pi\)
\(720\) 0 0
\(721\) −300.000 −0.0154960
\(722\) 0 0
\(723\) −8123.32 + 22976.2i −0.417855 + 1.18187i
\(724\) 0 0
\(725\) −2766.20 −0.141702
\(726\) 0 0
\(727\) 27279.8i 1.39168i 0.718197 + 0.695840i \(0.244968\pi\)
−0.718197 + 0.695840i \(0.755032\pi\)
\(728\) 0 0
\(729\) 8883.00 17564.5i 0.451303 0.892371i
\(730\) 0 0
\(731\) 6349.08i 0.321244i
\(732\) 0 0
\(733\) 15914.0i 0.801906i 0.916099 + 0.400953i \(0.131321\pi\)
−0.916099 + 0.400953i \(0.868679\pi\)
\(734\) 0 0
\(735\) 1263.94 3574.95i 0.0634299 0.179407i
\(736\) 0 0
\(737\) 26168.6i 1.30791i
\(738\) 0 0
\(739\) −2275.91 −0.113289 −0.0566447 0.998394i \(-0.518040\pi\)
−0.0566447 + 0.998394i \(0.518040\pi\)
\(740\) 0 0
\(741\) −13678.3 4836.00i −0.678116 0.239750i
\(742\) 0 0
\(743\) 8641.80 0.426698 0.213349 0.976976i \(-0.431563\pi\)
0.213349 + 0.976976i \(0.431563\pi\)
\(744\) 0 0
\(745\) −40032.0 −1.96867
\(746\) 0 0
\(747\) −498.831 + 617.271i −0.0244327 + 0.0302340i
\(748\) 0 0
\(749\) 23928.5 1.16733
\(750\) 0 0
\(751\) 16631.2i 0.808095i 0.914738 + 0.404048i \(0.132397\pi\)
−0.914738 + 0.404048i \(0.867603\pi\)
\(752\) 0 0
\(753\) −6192.00 2189.20i −0.299667 0.105948i
\(754\) 0 0
\(755\) 34626.0i 1.66910i
\(756\) 0 0
\(757\) 11422.0i 0.548401i 0.961673 + 0.274201i \(0.0884132\pi\)
−0.961673 + 0.274201i \(0.911587\pi\)
\(758\) 0 0
\(759\) −25396.3 8978.95i −1.21453 0.429401i
\(760\) 0 0
\(761\) 12660.0i 0.603057i 0.953457 + 0.301528i \(0.0974968\pi\)
−0.953457 + 0.301528i \(0.902503\pi\)
\(762\) 0 0
\(763\) −6200.74 −0.294210
\(764\) 0 0
\(765\) 19550.1 24192.0i 0.923967 1.14335i
\(766\) 0 0
\(767\) −14520.6 −0.683582
\(768\) 0 0
\(769\) 18818.0 0.882437 0.441219 0.897400i \(-0.354546\pi\)
0.441219 + 0.897400i \(0.354546\pi\)
\(770\) 0 0
\(771\) −1330.22 470.302i −0.0621356 0.0219682i
\(772\) 0 0
\(773\) −1917.67 −0.0892289 −0.0446144 0.999004i \(-0.514206\pi\)
−0.0446144 + 0.999004i \(0.514206\pi\)
\(774\) 0 0
\(775\) 5081.84i 0.235542i
\(776\) 0 0
\(777\) −6180.00 + 17479.7i −0.285336 + 0.807053i
\(778\) 0 0
\(779\) 32803.6i 1.50874i
\(780\) 0 0
\(781\) 1728.00i 0.0791712i
\(782\) 0 0
\(783\) −2028.18 + 1247.08i −0.0925685 + 0.0569181i
\(784\) 0 0
\(785\) 1798.88i 0.0817895i
\(786\) 0 0
\(787\) −19845.8 −0.898892 −0.449446 0.893308i \(-0.648379\pi\)
−0.449446 + 0.893308i \(0.648379\pi\)
\(788\) 0 0
\(789\) −8858.63 + 25056.0i −0.399716 + 1.13057i
\(790\) 0 0