Properties

Label 520.2.d.c.209.5
Level $520$
Weight $2$
Character 520.209
Analytic conductor $4.152$
Analytic rank $0$
Dimension $10$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [520,2,Mod(209,520)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(520, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("520.209");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 520 = 2^{3} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 520.d (of order \(2\), degree \(1\), 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: \(4.15222090511\)
Analytic rank: \(0\)
Dimension: \(10\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{10} - 4x^{9} + 2x^{8} + 16x^{7} - 15x^{6} - 40x^{5} - 75x^{4} + 400x^{3} + 250x^{2} - 2500x + 3125 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 209.5
Root \(1.43589 - 1.71412i\) of defining polynomial
Character \(\chi\) \(=\) 520.209
Dual form 520.2.d.c.209.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.16232i q^{3} +(-1.43589 + 1.71412i) q^{5} -4.64901i q^{7} +1.64901 q^{9} +O(q^{10})\) \(q-1.16232i q^{3} +(-1.43589 + 1.71412i) q^{5} -4.64901i q^{7} +1.64901 q^{9} -3.25486 q^{11} -1.00000i q^{13} +(1.99236 + 1.66896i) q^{15} +0.871779i q^{17} -6.93023 q^{19} -5.40364 q^{21} -6.03410i q^{23} +(-0.876443 - 4.92259i) q^{25} -5.40364i q^{27} -3.63573 q^{29} +7.78672 q^{31} +3.78319i q^{33} +(7.96899 + 6.67547i) q^{35} -8.39257i q^{37} -1.16232 q^{39} -6.44153 q^{41} -6.01882i q^{43} +(-2.36780 + 2.82662i) q^{45} +8.64901i q^{47} -14.6133 q^{49} +1.01329 q^{51} +4.53186i q^{53} +(4.67363 - 5.57924i) q^{55} +8.05513i q^{57} -3.51131 q^{59} +14.8434 q^{61} -7.66629i q^{63} +(1.71412 + 1.43589i) q^{65} +9.49618i q^{67} -7.01355 q^{69} +8.59031 q^{71} +3.31109i q^{73} +(-5.72161 + 1.01871i) q^{75} +15.1319i q^{77} +5.18113 q^{79} -1.33371 q^{81} -1.66230i q^{83} +(-1.49434 - 1.25178i) q^{85} +4.22588i q^{87} +10.6001 q^{89} -4.64901 q^{91} -9.05066i q^{93} +(9.95104 - 11.8793i) q^{95} -9.62267i q^{97} -5.36732 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q - 4 q^{5} - 30 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 10 q - 4 q^{5} - 30 q^{9} + 16 q^{11} + 4 q^{15} - 36 q^{19} + 4 q^{21} + 12 q^{25} - 4 q^{29} - 8 q^{31} + 18 q^{35} - 4 q^{39} - 24 q^{41} + 36 q^{45} - 38 q^{49} - 4 q^{51} + 32 q^{55} - 28 q^{59} + 20 q^{61} + 4 q^{65} - 72 q^{69} + 36 q^{71} + 62 q^{75} - 16 q^{79} + 18 q^{81} + 8 q^{85} + 12 q^{89} + 52 q^{95} - 68 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/520\mathbb{Z}\right)^\times\).

\(n\) \(41\) \(261\) \(391\) \(417\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(-1\)

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
\(3\) 1.16232i 0.671065i −0.942029 0.335533i \(-0.891084\pi\)
0.942029 0.335533i \(-0.108916\pi\)
\(4\) 0 0
\(5\) −1.43589 + 1.71412i −0.642149 + 0.766580i
\(6\) 0 0
\(7\) 4.64901i 1.75716i −0.477593 0.878581i \(-0.658491\pi\)
0.477593 0.878581i \(-0.341509\pi\)
\(8\) 0 0
\(9\) 1.64901 0.549672
\(10\) 0 0
\(11\) −3.25486 −0.981379 −0.490689 0.871335i \(-0.663255\pi\)
−0.490689 + 0.871335i \(0.663255\pi\)
\(12\) 0 0
\(13\) 1.00000i 0.277350i
\(14\) 0 0
\(15\) 1.99236 + 1.66896i 0.514425 + 0.430924i
\(16\) 0 0
\(17\) 0.871779i 0.211437i 0.994396 + 0.105719i \(0.0337143\pi\)
−0.994396 + 0.105719i \(0.966286\pi\)
\(18\) 0 0
\(19\) −6.93023 −1.58990 −0.794952 0.606673i \(-0.792504\pi\)
−0.794952 + 0.606673i \(0.792504\pi\)
\(20\) 0 0
\(21\) −5.40364 −1.17917
\(22\) 0 0
\(23\) 6.03410i 1.25820i −0.777326 0.629098i \(-0.783424\pi\)
0.777326 0.629098i \(-0.216576\pi\)
\(24\) 0 0
\(25\) −0.876443 4.92259i −0.175289 0.984517i
\(26\) 0 0
\(27\) 5.40364i 1.03993i
\(28\) 0 0
\(29\) −3.63573 −0.675138 −0.337569 0.941301i \(-0.609605\pi\)
−0.337569 + 0.941301i \(0.609605\pi\)
\(30\) 0 0
\(31\) 7.78672 1.39854 0.699268 0.714859i \(-0.253509\pi\)
0.699268 + 0.714859i \(0.253509\pi\)
\(32\) 0 0
\(33\) 3.78319i 0.658569i
\(34\) 0 0
\(35\) 7.96899 + 6.67547i 1.34700 + 1.12836i
\(36\) 0 0
\(37\) 8.39257i 1.37973i −0.723938 0.689865i \(-0.757670\pi\)
0.723938 0.689865i \(-0.242330\pi\)
\(38\) 0 0
\(39\) −1.16232 −0.186120
\(40\) 0 0
\(41\) −6.44153 −1.00600 −0.502999 0.864287i \(-0.667770\pi\)
−0.502999 + 0.864287i \(0.667770\pi\)
\(42\) 0 0
\(43\) 6.01882i 0.917861i −0.888472 0.458930i \(-0.848233\pi\)
0.888472 0.458930i \(-0.151767\pi\)
\(44\) 0 0
\(45\) −2.36780 + 2.82662i −0.352971 + 0.421367i
\(46\) 0 0
\(47\) 8.64901i 1.26159i 0.775950 + 0.630794i \(0.217271\pi\)
−0.775950 + 0.630794i \(0.782729\pi\)
\(48\) 0 0
\(49\) −14.6133 −2.08762
\(50\) 0 0
\(51\) 1.01329 0.141888
\(52\) 0 0
\(53\) 4.53186i 0.622499i 0.950328 + 0.311249i \(0.100747\pi\)
−0.950328 + 0.311249i \(0.899253\pi\)
\(54\) 0 0
\(55\) 4.67363 5.57924i 0.630192 0.752305i
\(56\) 0 0
\(57\) 8.05513i 1.06693i
\(58\) 0 0
\(59\) −3.51131 −0.457133 −0.228567 0.973528i \(-0.573404\pi\)
−0.228567 + 0.973528i \(0.573404\pi\)
\(60\) 0 0
\(61\) 14.8434 1.90051 0.950253 0.311478i \(-0.100824\pi\)
0.950253 + 0.311478i \(0.100824\pi\)
\(62\) 0 0
\(63\) 7.66629i 0.965862i
\(64\) 0 0
\(65\) 1.71412 + 1.43589i 0.212611 + 0.178100i
\(66\) 0 0
\(67\) 9.49618i 1.16014i 0.814565 + 0.580072i \(0.196975\pi\)
−0.814565 + 0.580072i \(0.803025\pi\)
\(68\) 0 0
\(69\) −7.01355 −0.844332
\(70\) 0 0
\(71\) 8.59031 1.01948 0.509741 0.860328i \(-0.329741\pi\)
0.509741 + 0.860328i \(0.329741\pi\)
\(72\) 0 0
\(73\) 3.31109i 0.387534i 0.981048 + 0.193767i \(0.0620706\pi\)
−0.981048 + 0.193767i \(0.937929\pi\)
\(74\) 0 0
\(75\) −5.72161 + 1.01871i −0.660675 + 0.117630i
\(76\) 0 0
\(77\) 15.1319i 1.72444i
\(78\) 0 0
\(79\) 5.18113 0.582923 0.291462 0.956583i \(-0.405858\pi\)
0.291462 + 0.956583i \(0.405858\pi\)
\(80\) 0 0
\(81\) −1.33371 −0.148189
\(82\) 0 0
\(83\) 1.66230i 0.182461i −0.995830 0.0912306i \(-0.970920\pi\)
0.995830 0.0912306i \(-0.0290800\pi\)
\(84\) 0 0
\(85\) −1.49434 1.25178i −0.162084 0.135774i
\(86\) 0 0
\(87\) 4.22588i 0.453062i
\(88\) 0 0
\(89\) 10.6001 1.12360 0.561802 0.827272i \(-0.310108\pi\)
0.561802 + 0.827272i \(0.310108\pi\)
\(90\) 0 0
\(91\) −4.64901 −0.487349
\(92\) 0 0
\(93\) 9.05066i 0.938509i
\(94\) 0 0
\(95\) 9.95104 11.8793i 1.02096 1.21879i
\(96\) 0 0
\(97\) 9.62267i 0.977034i −0.872554 0.488517i \(-0.837538\pi\)
0.872554 0.488517i \(-0.162462\pi\)
\(98\) 0 0
\(99\) −5.36732 −0.539436
\(100\) 0 0
\(101\) 19.3662 1.92701 0.963506 0.267688i \(-0.0862596\pi\)
0.963506 + 0.267688i \(0.0862596\pi\)
\(102\) 0 0
\(103\) 5.33213i 0.525390i 0.964879 + 0.262695i \(0.0846113\pi\)
−0.964879 + 0.262695i \(0.915389\pi\)
\(104\) 0 0
\(105\) 7.75903 9.26251i 0.757203 0.903928i
\(106\) 0 0
\(107\) 5.61913i 0.543222i −0.962407 0.271611i \(-0.912444\pi\)
0.962407 0.271611i \(-0.0875564\pi\)
\(108\) 0 0
\(109\) −2.68669 −0.257338 −0.128669 0.991688i \(-0.541070\pi\)
−0.128669 + 0.991688i \(0.541070\pi\)
\(110\) 0 0
\(111\) −9.75485 −0.925889
\(112\) 0 0
\(113\) 2.71695i 0.255589i −0.991801 0.127795i \(-0.959210\pi\)
0.991801 0.127795i \(-0.0407898\pi\)
\(114\) 0 0
\(115\) 10.3432 + 8.66430i 0.964508 + 0.807950i
\(116\) 0 0
\(117\) 1.64901i 0.152451i
\(118\) 0 0
\(119\) 4.05291 0.371530
\(120\) 0 0
\(121\) −0.405858 −0.0368962
\(122\) 0 0
\(123\) 7.48712i 0.675090i
\(124\) 0 0
\(125\) 9.69640 + 5.56596i 0.867272 + 0.497834i
\(126\) 0 0
\(127\) 3.61913i 0.321146i 0.987024 + 0.160573i \(0.0513342\pi\)
−0.987024 + 0.160573i \(0.948666\pi\)
\(128\) 0 0
\(129\) −6.99578 −0.615944
\(130\) 0 0
\(131\) 14.1452 1.23587 0.617936 0.786229i \(-0.287969\pi\)
0.617936 + 0.786229i \(0.287969\pi\)
\(132\) 0 0
\(133\) 32.2187i 2.79372i
\(134\) 0 0
\(135\) 9.26251 + 7.75903i 0.797190 + 0.667791i
\(136\) 0 0
\(137\) 1.30202i 0.111239i −0.998452 0.0556197i \(-0.982287\pi\)
0.998452 0.0556197i \(-0.0177135\pi\)
\(138\) 0 0
\(139\) −6.07752 −0.515489 −0.257744 0.966213i \(-0.582979\pi\)
−0.257744 + 0.966213i \(0.582979\pi\)
\(140\) 0 0
\(141\) 10.0529 0.846608
\(142\) 0 0
\(143\) 3.25486i 0.272185i
\(144\) 0 0
\(145\) 5.22051 6.23209i 0.433539 0.517547i
\(146\) 0 0
\(147\) 16.9854i 1.40093i
\(148\) 0 0
\(149\) −12.0863 −0.990151 −0.495075 0.868850i \(-0.664860\pi\)
−0.495075 + 0.868850i \(0.664860\pi\)
\(150\) 0 0
\(151\) −14.9526 −1.21682 −0.608412 0.793622i \(-0.708193\pi\)
−0.608412 + 0.793622i \(0.708193\pi\)
\(152\) 0 0
\(153\) 1.43758i 0.116221i
\(154\) 0 0
\(155\) −11.1809 + 13.3474i −0.898069 + 1.07209i
\(156\) 0 0
\(157\) 0.887061i 0.0707952i −0.999373 0.0353976i \(-0.988730\pi\)
0.999373 0.0353976i \(-0.0112698\pi\)
\(158\) 0 0
\(159\) 5.26746 0.417737
\(160\) 0 0
\(161\) −28.0526 −2.21086
\(162\) 0 0
\(163\) 1.42851i 0.111889i 0.998434 + 0.0559447i \(0.0178171\pi\)
−0.998434 + 0.0559447i \(0.982183\pi\)
\(164\) 0 0
\(165\) −6.48486 5.43224i −0.504845 0.422900i
\(166\) 0 0
\(167\) 14.9116i 1.15390i −0.816781 0.576948i \(-0.804243\pi\)
0.816781 0.576948i \(-0.195757\pi\)
\(168\) 0 0
\(169\) −1.00000 −0.0769231
\(170\) 0 0
\(171\) −11.4280 −0.873925
\(172\) 0 0
\(173\) 9.18113i 0.698029i 0.937117 + 0.349014i \(0.113484\pi\)
−0.937117 + 0.349014i \(0.886516\pi\)
\(174\) 0 0
\(175\) −22.8852 + 4.07460i −1.72996 + 0.308011i
\(176\) 0 0
\(177\) 4.08126i 0.306766i
\(178\) 0 0
\(179\) 10.7076 0.800325 0.400163 0.916444i \(-0.368954\pi\)
0.400163 + 0.916444i \(0.368954\pi\)
\(180\) 0 0
\(181\) 19.3753 1.44015 0.720077 0.693894i \(-0.244106\pi\)
0.720077 + 0.693894i \(0.244106\pi\)
\(182\) 0 0
\(183\) 17.2528i 1.27536i
\(184\) 0 0
\(185\) 14.3859 + 12.0508i 1.05767 + 0.885993i
\(186\) 0 0
\(187\) 2.83752i 0.207500i
\(188\) 0 0
\(189\) −25.1216 −1.82733
\(190\) 0 0
\(191\) 14.3928 1.04143 0.520714 0.853731i \(-0.325666\pi\)
0.520714 + 0.853731i \(0.325666\pi\)
\(192\) 0 0
\(193\) 3.34725i 0.240940i 0.992717 + 0.120470i \(0.0384402\pi\)
−0.992717 + 0.120470i \(0.961560\pi\)
\(194\) 0 0
\(195\) 1.66896 1.99236i 0.119517 0.142676i
\(196\) 0 0
\(197\) 18.3529i 1.30759i −0.756670 0.653796i \(-0.773175\pi\)
0.756670 0.653796i \(-0.226825\pi\)
\(198\) 0 0
\(199\) −18.4792 −1.30995 −0.654977 0.755649i \(-0.727322\pi\)
−0.654977 + 0.755649i \(0.727322\pi\)
\(200\) 0 0
\(201\) 11.0376 0.778532
\(202\) 0 0
\(203\) 16.9026i 1.18633i
\(204\) 0 0
\(205\) 9.24933 11.0416i 0.646001 0.771178i
\(206\) 0 0
\(207\) 9.95032i 0.691595i
\(208\) 0 0
\(209\) 22.5569 1.56030
\(210\) 0 0
\(211\) −17.5641 −1.20916 −0.604582 0.796543i \(-0.706660\pi\)
−0.604582 + 0.796543i \(0.706660\pi\)
\(212\) 0 0
\(213\) 9.98468i 0.684139i
\(214\) 0 0
\(215\) 10.3170 + 8.64235i 0.703613 + 0.589404i
\(216\) 0 0
\(217\) 36.2006i 2.45746i
\(218\) 0 0
\(219\) 3.84854 0.260061
\(220\) 0 0
\(221\) 0.871779 0.0586422
\(222\) 0 0
\(223\) 14.5963i 0.977442i −0.872440 0.488721i \(-0.837464\pi\)
0.872440 0.488721i \(-0.162536\pi\)
\(224\) 0 0
\(225\) −1.44527 8.11742i −0.0963512 0.541161i
\(226\) 0 0
\(227\) 2.68891i 0.178469i −0.996011 0.0892345i \(-0.971558\pi\)
0.996011 0.0892345i \(-0.0284421\pi\)
\(228\) 0 0
\(229\) 0.241160 0.0159363 0.00796814 0.999968i \(-0.497464\pi\)
0.00796814 + 0.999968i \(0.497464\pi\)
\(230\) 0 0
\(231\) 17.5881 1.15721
\(232\) 0 0
\(233\) 17.7965i 1.16589i 0.812513 + 0.582943i \(0.198099\pi\)
−0.812513 + 0.582943i \(0.801901\pi\)
\(234\) 0 0
\(235\) −14.8255 12.4190i −0.967108 0.810128i
\(236\) 0 0
\(237\) 6.02213i 0.391179i
\(238\) 0 0
\(239\) −19.0473 −1.23207 −0.616035 0.787719i \(-0.711262\pi\)
−0.616035 + 0.787719i \(0.711262\pi\)
\(240\) 0 0
\(241\) 14.6266 0.942184 0.471092 0.882084i \(-0.343860\pi\)
0.471092 + 0.882084i \(0.343860\pi\)
\(242\) 0 0
\(243\) 14.6607i 0.940486i
\(244\) 0 0
\(245\) 20.9831 25.0491i 1.34056 1.60033i
\(246\) 0 0
\(247\) 6.93023i 0.440960i
\(248\) 0 0
\(249\) −1.93212 −0.122443
\(250\) 0 0
\(251\) 0.154526 0.00975361 0.00487680 0.999988i \(-0.498448\pi\)
0.00487680 + 0.999988i \(0.498448\pi\)
\(252\) 0 0
\(253\) 19.6402i 1.23477i
\(254\) 0 0
\(255\) −1.45497 + 1.73690i −0.0911135 + 0.108769i
\(256\) 0 0
\(257\) 4.05291i 0.252814i 0.991978 + 0.126407i \(0.0403445\pi\)
−0.991978 + 0.126407i \(0.959656\pi\)
\(258\) 0 0
\(259\) −39.0172 −2.42441
\(260\) 0 0
\(261\) −5.99537 −0.371104
\(262\) 0 0
\(263\) 16.7321i 1.03174i −0.856666 0.515872i \(-0.827468\pi\)
0.856666 0.515872i \(-0.172532\pi\)
\(264\) 0 0
\(265\) −7.76817 6.50725i −0.477195 0.399737i
\(266\) 0 0
\(267\) 12.3206i 0.754011i
\(268\) 0 0
\(269\) −20.0155 −1.22037 −0.610183 0.792260i \(-0.708904\pi\)
−0.610183 + 0.792260i \(0.708904\pi\)
\(270\) 0 0
\(271\) 10.0319 0.609393 0.304697 0.952449i \(-0.401445\pi\)
0.304697 + 0.952449i \(0.401445\pi\)
\(272\) 0 0
\(273\) 5.40364i 0.327043i
\(274\) 0 0
\(275\) 2.85270 + 16.0223i 0.172024 + 0.966184i
\(276\) 0 0
\(277\) 16.2227i 0.974729i −0.873199 0.487364i \(-0.837958\pi\)
0.873199 0.487364i \(-0.162042\pi\)
\(278\) 0 0
\(279\) 12.8404 0.768736
\(280\) 0 0
\(281\) −10.9057 −0.650581 −0.325290 0.945614i \(-0.605462\pi\)
−0.325290 + 0.945614i \(0.605462\pi\)
\(282\) 0 0
\(283\) 3.33213i 0.198074i 0.995084 + 0.0990372i \(0.0315763\pi\)
−0.995084 + 0.0990372i \(0.968424\pi\)
\(284\) 0 0
\(285\) −13.8075 11.5663i −0.817886 0.685127i
\(286\) 0 0
\(287\) 29.9468i 1.76770i
\(288\) 0 0
\(289\) 16.2400 0.955294
\(290\) 0 0
\(291\) −11.1846 −0.655653
\(292\) 0 0
\(293\) 14.4191i 0.842375i −0.906974 0.421188i \(-0.861613\pi\)
0.906974 0.421188i \(-0.138387\pi\)
\(294\) 0 0
\(295\) 5.04185 6.01882i 0.293548 0.350429i
\(296\) 0 0
\(297\) 17.5881i 1.02057i
\(298\) 0 0
\(299\) −6.03410 −0.348961
\(300\) 0 0
\(301\) −27.9816 −1.61283
\(302\) 0 0
\(303\) 22.5097i 1.29315i
\(304\) 0 0
\(305\) −21.3135 + 25.4435i −1.22041 + 1.45689i
\(306\) 0 0
\(307\) 16.9643i 0.968205i 0.875011 + 0.484103i \(0.160854\pi\)
−0.875011 + 0.484103i \(0.839146\pi\)
\(308\) 0 0
\(309\) 6.19763 0.352571
\(310\) 0 0
\(311\) −14.2072 −0.805618 −0.402809 0.915284i \(-0.631966\pi\)
−0.402809 + 0.915284i \(0.631966\pi\)
\(312\) 0 0
\(313\) 29.1627i 1.64837i −0.566318 0.824187i \(-0.691633\pi\)
0.566318 0.824187i \(-0.308367\pi\)
\(314\) 0 0
\(315\) 13.1410 + 11.0080i 0.740410 + 0.620228i
\(316\) 0 0
\(317\) 19.9604i 1.12109i −0.828125 0.560543i \(-0.810592\pi\)
0.828125 0.560543i \(-0.189408\pi\)
\(318\) 0 0
\(319\) 11.8338 0.662566
\(320\) 0 0
\(321\) −6.53123 −0.364537
\(322\) 0 0
\(323\) 6.04163i 0.336165i
\(324\) 0 0
\(325\) −4.92259 + 0.876443i −0.273056 + 0.0486163i
\(326\) 0 0
\(327\) 3.12279i 0.172691i
\(328\) 0 0
\(329\) 40.2094 2.21682
\(330\) 0 0
\(331\) −4.20169 −0.230946 −0.115473 0.993311i \(-0.536838\pi\)
−0.115473 + 0.993311i \(0.536838\pi\)
\(332\) 0 0
\(333\) 13.8395i 0.758399i
\(334\) 0 0
\(335\) −16.2776 13.6355i −0.889342 0.744985i
\(336\) 0 0
\(337\) 24.1964i 1.31806i 0.752116 + 0.659030i \(0.229033\pi\)
−0.752116 + 0.659030i \(0.770967\pi\)
\(338\) 0 0
\(339\) −3.15796 −0.171517
\(340\) 0 0
\(341\) −25.3447 −1.37249
\(342\) 0 0
\(343\) 35.3945i 1.91112i
\(344\) 0 0
\(345\) 10.0707 12.0221i 0.542187 0.647247i
\(346\) 0 0
\(347\) 19.9058i 1.06860i 0.845294 + 0.534301i \(0.179425\pi\)
−0.845294 + 0.534301i \(0.820575\pi\)
\(348\) 0 0
\(349\) 25.4413 1.36184 0.680920 0.732358i \(-0.261580\pi\)
0.680920 + 0.732358i \(0.261580\pi\)
\(350\) 0 0
\(351\) −5.40364 −0.288425
\(352\) 0 0
\(353\) 29.6778i 1.57959i 0.613371 + 0.789795i \(0.289813\pi\)
−0.613371 + 0.789795i \(0.710187\pi\)
\(354\) 0 0
\(355\) −12.3347 + 14.7249i −0.654660 + 0.781514i
\(356\) 0 0
\(357\) 4.71078i 0.249321i
\(358\) 0 0
\(359\) 0.556889 0.0293915 0.0146957 0.999892i \(-0.495322\pi\)
0.0146957 + 0.999892i \(0.495322\pi\)
\(360\) 0 0
\(361\) 29.0280 1.52779
\(362\) 0 0
\(363\) 0.471736i 0.0247597i
\(364\) 0 0
\(365\) −5.67562 4.75436i −0.297076 0.248855i
\(366\) 0 0
\(367\) 12.4185i 0.648240i −0.946016 0.324120i \(-0.894932\pi\)
0.946016 0.324120i \(-0.105068\pi\)
\(368\) 0 0
\(369\) −10.6222 −0.552969
\(370\) 0 0
\(371\) 21.0687 1.09383
\(372\) 0 0
\(373\) 23.2188i 1.20222i −0.799166 0.601111i \(-0.794725\pi\)
0.799166 0.601111i \(-0.205275\pi\)
\(374\) 0 0
\(375\) 6.46942 11.2703i 0.334079 0.581996i
\(376\) 0 0
\(377\) 3.63573i 0.187250i
\(378\) 0 0
\(379\) 23.5763 1.21104 0.605518 0.795832i \(-0.292966\pi\)
0.605518 + 0.795832i \(0.292966\pi\)
\(380\) 0 0
\(381\) 4.20659 0.215510
\(382\) 0 0
\(383\) 25.0874i 1.28191i −0.767580 0.640953i \(-0.778539\pi\)
0.767580 0.640953i \(-0.221461\pi\)
\(384\) 0 0
\(385\) −25.9380 21.7278i −1.32192 1.10735i
\(386\) 0 0
\(387\) 9.92512i 0.504522i
\(388\) 0 0
\(389\) −6.00000 −0.304212 −0.152106 0.988364i \(-0.548606\pi\)
−0.152106 + 0.988364i \(0.548606\pi\)
\(390\) 0 0
\(391\) 5.26040 0.266030
\(392\) 0 0
\(393\) 16.4412i 0.829350i
\(394\) 0 0
\(395\) −7.43954 + 8.88111i −0.374324 + 0.446857i
\(396\) 0 0
\(397\) 39.1073i 1.96274i 0.192135 + 0.981369i \(0.438459\pi\)
−0.192135 + 0.981369i \(0.561541\pi\)
\(398\) 0 0
\(399\) 37.4484 1.87477
\(400\) 0 0
\(401\) −15.3473 −0.766405 −0.383203 0.923664i \(-0.625179\pi\)
−0.383203 + 0.923664i \(0.625179\pi\)
\(402\) 0 0
\(403\) 7.78672i 0.387884i
\(404\) 0 0
\(405\) 1.91505 2.28614i 0.0951598 0.113599i
\(406\) 0 0
\(407\) 27.3167i 1.35404i
\(408\) 0 0
\(409\) −1.09376 −0.0540830 −0.0270415 0.999634i \(-0.508609\pi\)
−0.0270415 + 0.999634i \(0.508609\pi\)
\(410\) 0 0
\(411\) −1.51337 −0.0746489
\(412\) 0 0
\(413\) 16.3241i 0.803257i
\(414\) 0 0
\(415\) 2.84939 + 2.38688i 0.139871 + 0.117167i
\(416\) 0 0
\(417\) 7.06402i 0.345927i
\(418\) 0 0
\(419\) −21.1567 −1.03357 −0.516787 0.856114i \(-0.672872\pi\)
−0.516787 + 0.856114i \(0.672872\pi\)
\(420\) 0 0
\(421\) 8.43025 0.410865 0.205433 0.978671i \(-0.434140\pi\)
0.205433 + 0.978671i \(0.434140\pi\)
\(422\) 0 0
\(423\) 14.2624i 0.693459i
\(424\) 0 0
\(425\) 4.29141 0.764064i 0.208164 0.0370626i
\(426\) 0 0
\(427\) 69.0073i 3.33950i
\(428\) 0 0
\(429\) 3.78319 0.182654
\(430\) 0 0
\(431\) 12.3038 0.592654 0.296327 0.955087i \(-0.404238\pi\)
0.296327 + 0.955087i \(0.404238\pi\)
\(432\) 0 0
\(433\) 0.781453i 0.0375543i −0.999824 0.0187771i \(-0.994023\pi\)
0.999824 0.0187771i \(-0.00597730\pi\)
\(434\) 0 0
\(435\) −7.24368 6.06789i −0.347308 0.290933i
\(436\) 0 0
\(437\) 41.8177i 2.00041i
\(438\) 0 0
\(439\) −19.2949 −0.920894 −0.460447 0.887687i \(-0.652311\pi\)
−0.460447 + 0.887687i \(0.652311\pi\)
\(440\) 0 0
\(441\) −24.0976 −1.14751
\(442\) 0 0
\(443\) 12.0489i 0.572459i −0.958161 0.286229i \(-0.907598\pi\)
0.958161 0.286229i \(-0.0924019\pi\)
\(444\) 0 0
\(445\) −15.2205 + 18.1698i −0.721521 + 0.861332i
\(446\) 0 0
\(447\) 14.0482i 0.664456i
\(448\) 0 0
\(449\) −6.12796 −0.289196 −0.144598 0.989490i \(-0.546189\pi\)
−0.144598 + 0.989490i \(0.546189\pi\)
\(450\) 0 0
\(451\) 20.9663 0.987265
\(452\) 0 0
\(453\) 17.3797i 0.816568i
\(454\) 0 0
\(455\) 6.67547 7.96899i 0.312951 0.373592i
\(456\) 0 0
\(457\) 4.50973i 0.210956i 0.994422 + 0.105478i \(0.0336373\pi\)
−0.994422 + 0.105478i \(0.966363\pi\)
\(458\) 0 0
\(459\) 4.71078 0.219880
\(460\) 0 0
\(461\) −14.5853 −0.679305 −0.339652 0.940551i \(-0.610309\pi\)
−0.339652 + 0.940551i \(0.610309\pi\)
\(462\) 0 0
\(463\) 16.3337i 0.759092i −0.925173 0.379546i \(-0.876080\pi\)
0.925173 0.379546i \(-0.123920\pi\)
\(464\) 0 0
\(465\) 15.5139 + 12.9957i 0.719442 + 0.602663i
\(466\) 0 0
\(467\) 8.05223i 0.372613i −0.982492 0.186306i \(-0.940348\pi\)
0.982492 0.186306i \(-0.0596517\pi\)
\(468\) 0 0
\(469\) 44.1479 2.03856
\(470\) 0 0
\(471\) −1.03105 −0.0475082
\(472\) 0 0
\(473\) 19.5904i 0.900769i
\(474\) 0 0
\(475\) 6.07395 + 34.1146i 0.278692 + 1.56529i
\(476\) 0 0
\(477\) 7.47310i 0.342170i
\(478\) 0 0
\(479\) −1.42467 −0.0650950 −0.0325475 0.999470i \(-0.510362\pi\)
−0.0325475 + 0.999470i \(0.510362\pi\)
\(480\) 0 0
\(481\) −8.39257 −0.382668
\(482\) 0 0
\(483\) 32.6061i 1.48363i
\(484\) 0 0
\(485\) 16.4944 + 13.8171i 0.748974 + 0.627402i
\(486\) 0 0
\(487\) 29.2547i 1.32566i 0.748771 + 0.662829i \(0.230644\pi\)
−0.748771 + 0.662829i \(0.769356\pi\)
\(488\) 0 0
\(489\) 1.66038 0.0750851
\(490\) 0 0
\(491\) −5.01329 −0.226246 −0.113123 0.993581i \(-0.536085\pi\)
−0.113123 + 0.993581i \(0.536085\pi\)
\(492\) 0 0
\(493\) 3.16955i 0.142749i
\(494\) 0 0
\(495\) 7.70688 9.20025i 0.346398 0.413521i
\(496\) 0 0
\(497\) 39.9365i 1.79140i
\(498\) 0 0
\(499\) 22.4731 1.00603 0.503017 0.864276i \(-0.332223\pi\)
0.503017 + 0.864276i \(0.332223\pi\)
\(500\) 0 0
\(501\) −17.3321 −0.774340
\(502\) 0 0
\(503\) 11.3321i 0.505275i 0.967561 + 0.252637i \(0.0812979\pi\)
−0.967561 + 0.252637i \(0.918702\pi\)
\(504\) 0 0
\(505\) −27.8078 + 33.1961i −1.23743 + 1.47721i
\(506\) 0 0
\(507\) 1.16232i 0.0516204i
\(508\) 0 0
\(509\) 41.8078 1.85310 0.926548 0.376176i \(-0.122761\pi\)
0.926548 + 0.376176i \(0.122761\pi\)
\(510\) 0 0
\(511\) 15.3933 0.680960
\(512\) 0 0
\(513\) 37.4484i 1.65339i
\(514\) 0 0
\(515\) −9.13993 7.65635i −0.402753 0.337379i
\(516\) 0 0
\(517\) 28.1514i 1.23810i
\(518\) 0 0
\(519\) 10.6714 0.468423
\(520\) 0 0
\(521\) 31.5289 1.38131 0.690654 0.723186i \(-0.257323\pi\)
0.690654 + 0.723186i \(0.257323\pi\)
\(522\) 0 0
\(523\) 16.9061i 0.739252i −0.929181 0.369626i \(-0.879486\pi\)
0.929181 0.369626i \(-0.120514\pi\)
\(524\) 0 0
\(525\) 4.73598 + 26.5999i 0.206695 + 1.16091i
\(526\) 0 0
\(527\) 6.78830i 0.295703i
\(528\) 0 0
\(529\) −13.4103 −0.583058
\(530\) 0 0
\(531\) −5.79020 −0.251273
\(532\) 0 0
\(533\) 6.44153i 0.279014i
\(534\) 0 0
\(535\) 9.63189 + 8.06846i 0.416423 + 0.348830i
\(536\) 0 0
\(537\) 12.4457i 0.537070i
\(538\) 0 0
\(539\) 47.5644 2.04875
\(540\) 0 0
\(541\) −19.7022 −0.847062 −0.423531 0.905882i \(-0.639209\pi\)
−0.423531 + 0.905882i \(0.639209\pi\)
\(542\) 0 0
\(543\) 22.5203i 0.966437i
\(544\) 0 0
\(545\) 3.85779 4.60532i 0.165249 0.197270i
\(546\) 0 0
\(547\) 30.4572i 1.30226i −0.758968 0.651128i \(-0.774296\pi\)
0.758968 0.651128i \(-0.225704\pi\)
\(548\) 0 0
\(549\) 24.4770 1.04465
\(550\) 0 0
\(551\) 25.1964 1.07340
\(552\) 0 0
\(553\) 24.0872i 1.02429i
\(554\) 0 0
\(555\) 14.0069 16.7210i 0.594559 0.709768i
\(556\) 0 0
\(557\) 4.15826i 0.176191i 0.996112 + 0.0880956i \(0.0280781\pi\)
−0.996112 + 0.0880956i \(0.971922\pi\)
\(558\) 0 0
\(559\) −6.01882 −0.254569
\(560\) 0 0
\(561\) −3.29811 −0.139246
\(562\) 0 0
\(563\) 9.64096i 0.406318i 0.979146 + 0.203159i \(0.0651208\pi\)
−0.979146 + 0.203159i \(0.934879\pi\)
\(564\) 0 0
\(565\) 4.65719 + 3.90124i 0.195929 + 0.164126i
\(566\) 0 0
\(567\) 6.20042i 0.260393i
\(568\) 0 0
\(569\) −20.4684 −0.858078 −0.429039 0.903286i \(-0.641148\pi\)
−0.429039 + 0.903286i \(0.641148\pi\)
\(570\) 0 0
\(571\) 6.35557 0.265973 0.132986 0.991118i \(-0.457543\pi\)
0.132986 + 0.991118i \(0.457543\pi\)
\(572\) 0 0
\(573\) 16.7291i 0.698867i
\(574\) 0 0
\(575\) −29.7034 + 5.28854i −1.23872 + 0.220547i
\(576\) 0 0
\(577\) 8.19416i 0.341127i −0.985347 0.170564i \(-0.945441\pi\)
0.985347 0.170564i \(-0.0545588\pi\)
\(578\) 0 0
\(579\) 3.89057 0.161687
\(580\) 0 0
\(581\) −7.72806 −0.320614
\(582\) 0 0
\(583\) 14.7506i 0.610907i
\(584\) 0 0
\(585\) 2.82662 + 2.36780i 0.116866 + 0.0978966i
\(586\) 0 0
\(587\) 11.2208i 0.463131i 0.972819 + 0.231565i \(0.0743847\pi\)
−0.972819 + 0.231565i \(0.925615\pi\)
\(588\) 0 0
\(589\) −53.9638 −2.22354
\(590\) 0 0
\(591\) −21.3320 −0.877480
\(592\) 0 0
\(593\) 14.2346i 0.584546i 0.956335 + 0.292273i \(0.0944116\pi\)
−0.956335 + 0.292273i \(0.905588\pi\)
\(594\) 0 0
\(595\) −5.81954 + 6.94720i −0.238578 + 0.284807i
\(596\) 0 0
\(597\) 21.4787i 0.879064i
\(598\) 0 0
\(599\) 34.1018 1.39336 0.696682 0.717381i \(-0.254659\pi\)
0.696682 + 0.717381i \(0.254659\pi\)
\(600\) 0 0
\(601\) 24.5296 1.00058 0.500292 0.865857i \(-0.333226\pi\)
0.500292 + 0.865857i \(0.333226\pi\)
\(602\) 0 0
\(603\) 15.6593i 0.637698i
\(604\) 0 0
\(605\) 0.582767 0.695691i 0.0236928 0.0282838i
\(606\) 0 0
\(607\) 24.8113i 1.00706i 0.863978 + 0.503530i \(0.167966\pi\)
−0.863978 + 0.503530i \(0.832034\pi\)
\(608\) 0 0
\(609\) 19.6462 0.796103
\(610\) 0 0
\(611\) 8.64901 0.349902
\(612\) 0 0
\(613\) 18.7164i 0.755949i −0.925816 0.377975i \(-0.876621\pi\)
0.925816 0.377975i \(-0.123379\pi\)
\(614\) 0 0
\(615\) −12.8338 10.7507i −0.517511 0.433509i
\(616\) 0 0
\(617\) 38.6488i 1.55594i −0.628301 0.777970i \(-0.716249\pi\)
0.628301 0.777970i \(-0.283751\pi\)
\(618\) 0 0
\(619\) 11.9452 0.480120 0.240060 0.970758i \(-0.422833\pi\)
0.240060 + 0.970758i \(0.422833\pi\)
\(620\) 0 0
\(621\) −32.6061 −1.30844
\(622\) 0 0
\(623\) 49.2798i 1.97435i
\(624\) 0 0
\(625\) −23.4637 + 8.62873i −0.938548 + 0.345149i
\(626\) 0 0
\(627\) 26.2184i 1.04706i
\(628\) 0 0
\(629\) 7.31647 0.291727
\(630\) 0 0
\(631\) −7.80907 −0.310874 −0.155437 0.987846i \(-0.549679\pi\)
−0.155437 + 0.987846i \(0.549679\pi\)
\(632\) 0 0
\(633\) 20.4151i 0.811428i
\(634\) 0 0
\(635\) −6.20365 5.19668i −0.246184 0.206224i
\(636\) 0 0
\(637\) 14.6133i 0.579002i
\(638\) 0 0
\(639\) 14.1655 0.560380
\(640\) 0 0
\(641\) −3.12485 −0.123424 −0.0617120 0.998094i \(-0.519656\pi\)
−0.0617120 + 0.998094i \(0.519656\pi\)
\(642\) 0 0
\(643\) 10.6402i 0.419609i 0.977743 + 0.209804i \(0.0672827\pi\)
−0.977743 + 0.209804i \(0.932717\pi\)
\(644\) 0 0
\(645\) 10.0452 11.9916i 0.395528 0.472170i
\(646\) 0 0
\(647\) 19.1320i 0.752155i −0.926588 0.376078i \(-0.877273\pi\)
0.926588 0.376078i \(-0.122727\pi\)
\(648\) 0 0
\(649\) 11.4288 0.448621
\(650\) 0 0
\(651\) −42.0766 −1.64911
\(652\) 0 0
\(653\) 42.5252i 1.66414i 0.554670 + 0.832070i \(0.312845\pi\)
−0.554670 + 0.832070i \(0.687155\pi\)
\(654\) 0 0
\(655\) −20.3109 + 24.2466i −0.793614 + 0.947394i
\(656\) 0 0
\(657\) 5.46004i 0.213016i
\(658\) 0 0
\(659\) 1.14298 0.0445243 0.0222621 0.999752i \(-0.492913\pi\)
0.0222621 + 0.999752i \(0.492913\pi\)
\(660\) 0 0
\(661\) 49.0073 1.90616 0.953082 0.302711i \(-0.0978917\pi\)
0.953082 + 0.302711i \(0.0978917\pi\)
\(662\) 0 0
\(663\) 1.01329i 0.0393527i
\(664\) 0 0
\(665\) −55.2269 46.2625i −2.14161 1.79398i
\(666\) 0 0
\(667\) 21.9383i 0.849456i
\(668\) 0 0
\(669\) −16.9656 −0.655927
\(670\) 0 0
\(671\) −48.3134 −1.86512
\(672\) 0 0
\(673\) 8.44491i 0.325527i −0.986665 0.162764i \(-0.947959\pi\)
0.986665 0.162764i \(-0.0520408\pi\)
\(674\) 0 0
\(675\) −26.5999 + 4.73598i −1.02383 + 0.182288i
\(676\) 0 0
\(677\) 15.7211i 0.604211i 0.953274 + 0.302106i \(0.0976895\pi\)
−0.953274 + 0.302106i \(0.902310\pi\)
\(678\) 0 0
\(679\) −44.7359 −1.71681
\(680\) 0 0
\(681\) −3.12537 −0.119764
\(682\) 0 0
\(683\) 26.1823i 1.00184i 0.865495 + 0.500918i \(0.167004\pi\)
−0.865495 + 0.500918i \(0.832996\pi\)
\(684\) 0 0
\(685\) 2.23183 + 1.86956i 0.0852739 + 0.0714323i
\(686\) 0 0
\(687\) 0.280305i 0.0106943i
\(688\) 0 0
\(689\) 4.53186 0.172650
\(690\) 0 0
\(691\) 34.2659 1.30354 0.651768 0.758418i \(-0.274028\pi\)
0.651768 + 0.758418i \(0.274028\pi\)
\(692\) 0 0
\(693\) 24.9527i 0.947877i
\(694\) 0 0
\(695\) 8.72665 10.4176i 0.331021 0.395163i
\(696\) 0 0
\(697\) 5.61559i 0.212706i
\(698\) 0 0
\(699\) 20.6852 0.782385
\(700\) 0 0
\(701\) −10.7662 −0.406633 −0.203316 0.979113i \(-0.565172\pi\)
−0.203316 + 0.979113i \(0.565172\pi\)
\(702\) 0 0
\(703\) 58.1624i 2.19364i
\(704\) 0 0
\(705\) −14.4349 + 17.2319i −0.543649 + 0.648992i
\(706\) 0 0
\(707\) 90.0339i 3.38607i
\(708\) 0 0
\(709\) 15.8972 0.597034 0.298517 0.954404i \(-0.403508\pi\)
0.298517 + 0.954404i \(0.403508\pi\)
\(710\) 0 0
\(711\) 8.54377 0.320416
\(712\) 0 0
\(713\) 46.9858i 1.75963i
\(714\) 0 0
\(715\) −5.57924 4.67363i −0.208652 0.174784i
\(716\) 0 0
\(717\) 22.1391i 0.826799i
\(718\) 0 0
\(719\) 27.1956 1.01422 0.507112 0.861880i \(-0.330713\pi\)
0.507112 + 0.861880i \(0.330713\pi\)
\(720\) 0 0
\(721\) 24.7891 0.923196
\(722\) 0 0
\(723\) 17.0008i 0.632267i
\(724\) 0 0
\(725\) 3.18651 + 17.8972i 0.118344 + 0.664685i
\(726\) 0 0
\(727\) 42.6226i 1.58078i 0.612602 + 0.790392i \(0.290123\pi\)
−0.612602 + 0.790392i \(0.709877\pi\)
\(728\) 0 0
\(729\) −21.0415 −0.779317
\(730\) 0 0
\(731\) 5.24708 0.194070
\(732\) 0 0
\(733\) 26.6852i 0.985639i −0.870131 0.492820i \(-0.835966\pi\)
0.870131 0.492820i \(-0.164034\pi\)
\(734\) 0 0
\(735\) −29.1150 24.3891i −1.07392 0.899605i
\(736\) 0 0
\(737\) 30.9088i 1.13854i
\(738\) 0 0
\(739\) 8.12634 0.298932 0.149466 0.988767i \(-0.452245\pi\)
0.149466 + 0.988767i \(0.452245\pi\)
\(740\) 0 0
\(741\) 8.05513 0.295913
\(742\) 0 0
\(743\) 17.4905i 0.641665i −0.947136 0.320833i \(-0.896037\pi\)
0.947136 0.320833i \(-0.103963\pi\)
\(744\) 0 0
\(745\) 17.3546 20.7175i 0.635825 0.759029i
\(746\) 0 0
\(747\) 2.74116i 0.100294i
\(748\) 0 0
\(749\) −26.1234 −0.954530
\(750\) 0 0
\(751\) −50.2377 −1.83320 −0.916600 0.399806i \(-0.869078\pi\)
−0.916600 + 0.399806i \(0.869078\pi\)
\(752\) 0 0
\(753\) 0.179609i 0.00654531i
\(754\) 0 0
\(755\) 21.4702 25.6306i 0.781382 0.932792i
\(756\) 0 0
\(757\) 21.4761i 0.780560i −0.920696 0.390280i \(-0.872378\pi\)
0.920696 0.390280i \(-0.127622\pi\)
\(758\) 0 0
\(759\) 22.8281 0.828609
\(760\) 0 0
\(761\) −23.0495 −0.835544 −0.417772 0.908552i \(-0.637189\pi\)
−0.417772 + 0.908552i \(0.637189\pi\)
\(762\) 0 0
\(763\) 12.4905i 0.452185i
\(764\) 0 0
\(765\) −2.46418 2.06420i −0.0890928 0.0746313i
\(766\) 0 0
\(767\) 3.51131i 0.126786i
\(768\) 0 0
\(769\) −51.1473 −1.84442 −0.922210 0.386689i \(-0.873619\pi\)
−0.922210 + 0.386689i \(0.873619\pi\)
\(770\) 0 0
\(771\) 4.71078 0.169655
\(772\) 0 0
\(773\) 21.8083i 0.784391i −0.919882 0.392196i \(-0.871716\pi\)
0.919882 0.392196i \(-0.128284\pi\)
\(774\) 0 0
\(775\) −6.82462 38.3308i −0.245148 1.37688i
\(776\) 0 0
\(777\) 45.3504i 1.62694i
\(778\) 0 0
\(779\) 44.6413 1.59944
\(780\) 0 0
\(781\) −27.9603 −1.00050
\(782\) 0 0
\(783\) 19.6462i 0.702097i
\(784\) 0 0
\(785\) 1.52053 + 1.27372i 0.0542702 + 0.0454611i
\(786\) 0 0
\(787\) 7.66629i 0.273274i −0.990621 0.136637i \(-0.956371\pi\)
0.990621 0.136637i \(-0.0436294\pi\)
\(788\) 0 0
\(789\) −19.4480 −0.692367
\(790\) 0 0
\(791\) −12.6311 −0.449112
\(792\) 0 0
\(793\) 14.8434i 0.527106i
\(794\) 0 0