Properties

Label 520.2.d.c.209.10
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 209.10
Root \(1.64680 - 1.51263i\) of defining polynomial
Character \(\chi\) \(=\) 520.209
Dual form 520.2.d.c.209.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+3.08870i q^{3} +(-1.64680 + 1.51263i) q^{5} -3.54010i q^{7} -6.54010 q^{9} +O(q^{10})\) \(q+3.08870i q^{3} +(-1.64680 + 1.51263i) q^{5} -3.54010i q^{7} -6.54010 q^{9} -3.86747 q^{11} +1.00000i q^{13} +(-4.67206 - 5.08649i) q^{15} -1.29361i q^{17} -3.69006 q^{19} +10.9343 q^{21} +8.38231i q^{23} +(0.423922 - 4.98200i) q^{25} -10.9343i q^{27} +7.53566 q^{29} -8.36045 q^{31} -11.9455i q^{33} +(5.35484 + 5.82984i) q^{35} +1.04712i q^{37} -3.08870 q^{39} -2.97032 q^{41} -4.96180i q^{43} +(10.7703 - 9.89272i) q^{45} -0.459905i q^{47} -5.53228 q^{49} +3.99557 q^{51} +12.2279i q^{53} +(6.36896 - 5.85004i) q^{55} -11.3975i q^{57} -3.28026 q^{59} +0.582376 q^{61} +23.1526i q^{63} +(-1.51263 - 1.64680i) q^{65} +8.15554i q^{67} -25.8905 q^{69} -11.8315 q^{71} +11.7131i q^{73} +(15.3879 + 1.30937i) q^{75} +13.6912i q^{77} -3.87310 q^{79} +14.1526 q^{81} -3.54453i q^{83} +(1.95674 + 2.13032i) q^{85} +23.2754i q^{87} -1.46329 q^{89} +3.54010 q^{91} -25.8229i q^{93} +(6.07680 - 5.58168i) q^{95} -2.90278i q^{97} +25.2936 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q - 4 q^{5} - 30 q^{9}+O(q^{10}) \) 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
\(3\) 3.08870i 1.78326i 0.452760 + 0.891632i \(0.350439\pi\)
−0.452760 + 0.891632i \(0.649561\pi\)
\(4\) 0 0
\(5\) −1.64680 + 1.51263i −0.736473 + 0.676467i
\(6\) 0 0
\(7\) 3.54010i 1.33803i −0.743249 0.669015i \(-0.766716\pi\)
0.743249 0.669015i \(-0.233284\pi\)
\(8\) 0 0
\(9\) −6.54010 −2.18003
\(10\) 0 0
\(11\) −3.86747 −1.16609 −0.583043 0.812441i \(-0.698138\pi\)
−0.583043 + 0.812441i \(0.698138\pi\)
\(12\) 0 0
\(13\) 1.00000i 0.277350i
\(14\) 0 0
\(15\) −4.67206 5.08649i −1.20632 1.31333i
\(16\) 0 0
\(17\) 1.29361i 0.313746i −0.987619 0.156873i \(-0.949859\pi\)
0.987619 0.156873i \(-0.0501413\pi\)
\(18\) 0 0
\(19\) −3.69006 −0.846558 −0.423279 0.905999i \(-0.639121\pi\)
−0.423279 + 0.905999i \(0.639121\pi\)
\(20\) 0 0
\(21\) 10.9343 2.38606
\(22\) 0 0
\(23\) 8.38231i 1.74783i 0.486076 + 0.873916i \(0.338428\pi\)
−0.486076 + 0.873916i \(0.661572\pi\)
\(24\) 0 0
\(25\) 0.423922 4.98200i 0.0847844 0.996399i
\(26\) 0 0
\(27\) 10.9343i 2.10431i
\(28\) 0 0
\(29\) 7.53566 1.39934 0.699669 0.714467i \(-0.253331\pi\)
0.699669 + 0.714467i \(0.253331\pi\)
\(30\) 0 0
\(31\) −8.36045 −1.50158 −0.750790 0.660541i \(-0.770327\pi\)
−0.750790 + 0.660541i \(0.770327\pi\)
\(32\) 0 0
\(33\) 11.9455i 2.07944i
\(34\) 0 0
\(35\) 5.35484 + 5.82984i 0.905134 + 0.985423i
\(36\) 0 0
\(37\) 1.04712i 0.172145i 0.996289 + 0.0860725i \(0.0274317\pi\)
−0.996289 + 0.0860725i \(0.972568\pi\)
\(38\) 0 0
\(39\) −3.08870 −0.494589
\(40\) 0 0
\(41\) −2.97032 −0.463885 −0.231943 0.972729i \(-0.574508\pi\)
−0.231943 + 0.972729i \(0.574508\pi\)
\(42\) 0 0
\(43\) 4.96180i 0.756668i −0.925669 0.378334i \(-0.876497\pi\)
0.925669 0.378334i \(-0.123503\pi\)
\(44\) 0 0
\(45\) 10.7703 9.89272i 1.60553 1.47472i
\(46\) 0 0
\(47\) 0.459905i 0.0670840i −0.999437 0.0335420i \(-0.989321\pi\)
0.999437 0.0335420i \(-0.0106788\pi\)
\(48\) 0 0
\(49\) −5.53228 −0.790325
\(50\) 0 0
\(51\) 3.99557 0.559491
\(52\) 0 0
\(53\) 12.2279i 1.67963i 0.542870 + 0.839817i \(0.317338\pi\)
−0.542870 + 0.839817i \(0.682662\pi\)
\(54\) 0 0
\(55\) 6.36896 5.85004i 0.858790 0.788819i
\(56\) 0 0
\(57\) 11.3975i 1.50964i
\(58\) 0 0
\(59\) −3.28026 −0.427053 −0.213526 0.976937i \(-0.568495\pi\)
−0.213526 + 0.976937i \(0.568495\pi\)
\(60\) 0 0
\(61\) 0.582376 0.0745656 0.0372828 0.999305i \(-0.488130\pi\)
0.0372828 + 0.999305i \(0.488130\pi\)
\(62\) 0 0
\(63\) 23.1526i 2.91695i
\(64\) 0 0
\(65\) −1.51263 1.64680i −0.187618 0.204261i
\(66\) 0 0
\(67\) 8.15554i 0.996358i 0.867074 + 0.498179i \(0.165998\pi\)
−0.867074 + 0.498179i \(0.834002\pi\)
\(68\) 0 0
\(69\) −25.8905 −3.11685
\(70\) 0 0
\(71\) −11.8315 −1.40414 −0.702068 0.712110i \(-0.747740\pi\)
−0.702068 + 0.712110i \(0.747740\pi\)
\(72\) 0 0
\(73\) 11.7131i 1.37091i 0.728114 + 0.685456i \(0.240397\pi\)
−0.728114 + 0.685456i \(0.759603\pi\)
\(74\) 0 0
\(75\) 15.3879 + 1.30937i 1.77684 + 0.151193i
\(76\) 0 0
\(77\) 13.6912i 1.56026i
\(78\) 0 0
\(79\) −3.87310 −0.435757 −0.217879 0.975976i \(-0.569914\pi\)
−0.217879 + 0.975976i \(0.569914\pi\)
\(80\) 0 0
\(81\) 14.1526 1.57251
\(82\) 0 0
\(83\) 3.54453i 0.389062i −0.980896 0.194531i \(-0.937681\pi\)
0.980896 0.194531i \(-0.0623185\pi\)
\(84\) 0 0
\(85\) 1.95674 + 2.13032i 0.212239 + 0.231065i
\(86\) 0 0
\(87\) 23.2754i 2.49539i
\(88\) 0 0
\(89\) −1.46329 −0.155109 −0.0775544 0.996988i \(-0.524711\pi\)
−0.0775544 + 0.996988i \(0.524711\pi\)
\(90\) 0 0
\(91\) 3.54010 0.371103
\(92\) 0 0
\(93\) 25.8229i 2.67771i
\(94\) 0 0
\(95\) 6.07680 5.58168i 0.623467 0.572669i
\(96\) 0 0
\(97\) 2.90278i 0.294733i −0.989082 0.147366i \(-0.952920\pi\)
0.989082 0.147366i \(-0.0470797\pi\)
\(98\) 0 0
\(99\) 25.2936 2.54210
\(100\) 0 0
\(101\) 7.68443 0.764629 0.382315 0.924032i \(-0.375127\pi\)
0.382315 + 0.924032i \(0.375127\pi\)
\(102\) 0 0
\(103\) 8.69788i 0.857028i 0.903535 + 0.428514i \(0.140963\pi\)
−0.903535 + 0.428514i \(0.859037\pi\)
\(104\) 0 0
\(105\) −18.0067 + 16.5395i −1.75727 + 1.61409i
\(106\) 0 0
\(107\) 17.4031i 1.68242i 0.540705 + 0.841212i \(0.318157\pi\)
−0.540705 + 0.841212i \(0.681843\pi\)
\(108\) 0 0
\(109\) −5.73608 −0.549417 −0.274708 0.961528i \(-0.588581\pi\)
−0.274708 + 0.961528i \(0.588581\pi\)
\(110\) 0 0
\(111\) −3.23424 −0.306980
\(112\) 0 0
\(113\) 16.6704i 1.56822i −0.620623 0.784109i \(-0.713120\pi\)
0.620623 0.784109i \(-0.286880\pi\)
\(114\) 0 0
\(115\) −12.6793 13.8040i −1.18235 1.28723i
\(116\) 0 0
\(117\) 6.54010i 0.604632i
\(118\) 0 0
\(119\) −4.57949 −0.419801
\(120\) 0 0
\(121\) 3.95731 0.359756
\(122\) 0 0
\(123\) 9.17443i 0.827230i
\(124\) 0 0
\(125\) 6.83778 + 8.84560i 0.611590 + 0.791175i
\(126\) 0 0
\(127\) 15.4031i 1.36681i −0.730041 0.683403i \(-0.760499\pi\)
0.730041 0.683403i \(-0.239501\pi\)
\(128\) 0 0
\(129\) 15.3255 1.34934
\(130\) 0 0
\(131\) −11.6956 −1.02185 −0.510926 0.859624i \(-0.670698\pi\)
−0.510926 + 0.859624i \(0.670698\pi\)
\(132\) 0 0
\(133\) 13.0632i 1.13272i
\(134\) 0 0
\(135\) 16.5395 + 18.0067i 1.42350 + 1.54977i
\(136\) 0 0
\(137\) 5.61690i 0.479884i 0.970787 + 0.239942i \(0.0771284\pi\)
−0.970787 + 0.239942i \(0.922872\pi\)
\(138\) 0 0
\(139\) −7.32956 −0.621686 −0.310843 0.950461i \(-0.600611\pi\)
−0.310843 + 0.950461i \(0.600611\pi\)
\(140\) 0 0
\(141\) 1.42051 0.119628
\(142\) 0 0
\(143\) 3.86747i 0.323414i
\(144\) 0 0
\(145\) −12.4098 + 11.3986i −1.03057 + 0.946606i
\(146\) 0 0
\(147\) 17.0876i 1.40936i
\(148\) 0 0
\(149\) 21.8953 1.79373 0.896867 0.442300i \(-0.145837\pi\)
0.896867 + 0.442300i \(0.145837\pi\)
\(150\) 0 0
\(151\) 23.5777 1.91872 0.959361 0.282181i \(-0.0910578\pi\)
0.959361 + 0.282181i \(0.0910578\pi\)
\(152\) 0 0
\(153\) 8.46031i 0.683976i
\(154\) 0 0
\(155\) 13.7680 12.6462i 1.10587 1.01577i
\(156\) 0 0
\(157\) 14.6377i 1.16822i 0.811676 + 0.584109i \(0.198556\pi\)
−0.811676 + 0.584109i \(0.801444\pi\)
\(158\) 0 0
\(159\) −37.7684 −2.99523
\(160\) 0 0
\(161\) 29.6742 2.33865
\(162\) 0 0
\(163\) 10.8697i 0.851378i −0.904870 0.425689i \(-0.860032\pi\)
0.904870 0.425689i \(-0.139968\pi\)
\(164\) 0 0
\(165\) 18.0690 + 19.6718i 1.40667 + 1.53145i
\(166\) 0 0
\(167\) 5.34700i 0.413763i 0.978366 + 0.206882i \(0.0663315\pi\)
−0.978366 + 0.206882i \(0.933669\pi\)
\(168\) 0 0
\(169\) −1.00000 −0.0769231
\(170\) 0 0
\(171\) 24.1333 1.84552
\(172\) 0 0
\(173\) 0.126903i 0.00964825i −0.999988 0.00482412i \(-0.998464\pi\)
0.999988 0.00482412i \(-0.00153557\pi\)
\(174\) 0 0
\(175\) −17.6367 1.50072i −1.33321 0.113444i
\(176\) 0 0
\(177\) 10.1317i 0.761548i
\(178\) 0 0
\(179\) −5.23533 −0.391307 −0.195653 0.980673i \(-0.562683\pi\)
−0.195653 + 0.980673i \(0.562683\pi\)
\(180\) 0 0
\(181\) −11.6455 −0.865606 −0.432803 0.901488i \(-0.642475\pi\)
−0.432803 + 0.901488i \(0.642475\pi\)
\(182\) 0 0
\(183\) 1.79879i 0.132970i
\(184\) 0 0
\(185\) −1.58390 1.72440i −0.116450 0.126780i
\(186\) 0 0
\(187\) 5.00298i 0.365854i
\(188\) 0 0
\(189\) −38.7085 −2.81563
\(190\) 0 0
\(191\) 22.9420 1.66003 0.830014 0.557743i \(-0.188333\pi\)
0.830014 + 0.557743i \(0.188333\pi\)
\(192\) 0 0
\(193\) 6.73792i 0.485006i −0.970151 0.242503i \(-0.922032\pi\)
0.970151 0.242503i \(-0.0779684\pi\)
\(194\) 0 0
\(195\) 5.08649 4.67206i 0.364251 0.334573i
\(196\) 0 0
\(197\) 3.68886i 0.262821i 0.991328 + 0.131410i \(0.0419505\pi\)
−0.991328 + 0.131410i \(0.958049\pi\)
\(198\) 0 0
\(199\) 6.95329 0.492906 0.246453 0.969155i \(-0.420735\pi\)
0.246453 + 0.969155i \(0.420735\pi\)
\(200\) 0 0
\(201\) −25.1901 −1.77677
\(202\) 0 0
\(203\) 26.6770i 1.87236i
\(204\) 0 0
\(205\) 4.89152 4.49298i 0.341639 0.313803i
\(206\) 0 0
\(207\) 54.8211i 3.81033i
\(208\) 0 0
\(209\) 14.2712 0.987159
\(210\) 0 0
\(211\) 11.2858 0.776949 0.388474 0.921459i \(-0.373002\pi\)
0.388474 + 0.921459i \(0.373002\pi\)
\(212\) 0 0
\(213\) 36.5439i 2.50395i
\(214\) 0 0
\(215\) 7.50535 + 8.17111i 0.511861 + 0.557265i
\(216\) 0 0
\(217\) 29.5968i 2.00916i
\(218\) 0 0
\(219\) −36.1782 −2.44470
\(220\) 0 0
\(221\) 1.29361 0.0870174
\(222\) 0 0
\(223\) 2.26547i 0.151707i −0.997119 0.0758535i \(-0.975832\pi\)
0.997119 0.0758535i \(-0.0241681\pi\)
\(224\) 0 0
\(225\) −2.77249 + 32.5827i −0.184833 + 2.17218i
\(226\) 0 0
\(227\) 17.7131i 1.17566i 0.808985 + 0.587829i \(0.200017\pi\)
−0.808985 + 0.587829i \(0.799983\pi\)
\(228\) 0 0
\(229\) −13.9313 −0.920608 −0.460304 0.887761i \(-0.652260\pi\)
−0.460304 + 0.887761i \(0.652260\pi\)
\(230\) 0 0
\(231\) −42.2881 −2.78235
\(232\) 0 0
\(233\) 10.0077i 0.655628i −0.944742 0.327814i \(-0.893688\pi\)
0.944742 0.327814i \(-0.106312\pi\)
\(234\) 0 0
\(235\) 0.695664 + 0.757372i 0.0453801 + 0.0494055i
\(236\) 0 0
\(237\) 11.9629i 0.777071i
\(238\) 0 0
\(239\) 8.82190 0.570641 0.285321 0.958432i \(-0.407900\pi\)
0.285321 + 0.958432i \(0.407900\pi\)
\(240\) 0 0
\(241\) 8.52784 0.549327 0.274663 0.961540i \(-0.411434\pi\)
0.274663 + 0.961540i \(0.411434\pi\)
\(242\) 0 0
\(243\) 10.9102i 0.699887i
\(244\) 0 0
\(245\) 9.11057 8.36827i 0.582053 0.534629i
\(246\) 0 0
\(247\) 3.69006i 0.234793i
\(248\) 0 0
\(249\) 10.9480 0.693801
\(250\) 0 0
\(251\) −29.1307 −1.83871 −0.919357 0.393425i \(-0.871290\pi\)
−0.919357 + 0.393425i \(0.871290\pi\)
\(252\) 0 0
\(253\) 32.4183i 2.03812i
\(254\) 0 0
\(255\) −6.57992 + 6.04380i −0.412050 + 0.378478i
\(256\) 0 0
\(257\) 4.57949i 0.285661i 0.989747 + 0.142830i \(0.0456203\pi\)
−0.989747 + 0.142830i \(0.954380\pi\)
\(258\) 0 0
\(259\) 3.70690 0.230335
\(260\) 0 0
\(261\) −49.2840 −3.05060
\(262\) 0 0
\(263\) 14.7654i 0.910474i 0.890370 + 0.455237i \(0.150446\pi\)
−0.890370 + 0.455237i \(0.849554\pi\)
\(264\) 0 0
\(265\) −18.4963 20.1370i −1.13622 1.23700i
\(266\) 0 0
\(267\) 4.51968i 0.276600i
\(268\) 0 0
\(269\) −16.0392 −0.977930 −0.488965 0.872303i \(-0.662625\pi\)
−0.488965 + 0.872303i \(0.662625\pi\)
\(270\) 0 0
\(271\) 0.405316 0.0246212 0.0123106 0.999924i \(-0.496081\pi\)
0.0123106 + 0.999924i \(0.496081\pi\)
\(272\) 0 0
\(273\) 10.9343i 0.661774i
\(274\) 0 0
\(275\) −1.63951 + 19.2677i −0.0988659 + 1.16189i
\(276\) 0 0
\(277\) 8.36607i 0.502669i −0.967900 0.251334i \(-0.919131\pi\)
0.967900 0.251334i \(-0.0808694\pi\)
\(278\) 0 0
\(279\) 54.6781 3.27349
\(280\) 0 0
\(281\) −17.7676 −1.05993 −0.529963 0.848021i \(-0.677794\pi\)
−0.529963 + 0.848021i \(0.677794\pi\)
\(282\) 0 0
\(283\) 10.6979i 0.635923i 0.948104 + 0.317961i \(0.102998\pi\)
−0.948104 + 0.317961i \(0.897002\pi\)
\(284\) 0 0
\(285\) 17.2402 + 18.7694i 1.02122 + 1.11181i
\(286\) 0 0
\(287\) 10.5152i 0.620693i
\(288\) 0 0
\(289\) 15.3266 0.901564
\(290\) 0 0
\(291\) 8.96584 0.525587
\(292\) 0 0
\(293\) 13.0383i 0.761703i 0.924636 + 0.380851i \(0.124369\pi\)
−0.924636 + 0.380851i \(0.875631\pi\)
\(294\) 0 0
\(295\) 5.40194 4.96180i 0.314513 0.288887i
\(296\) 0 0
\(297\) 42.2881i 2.45380i
\(298\) 0 0
\(299\) −8.38231 −0.484762
\(300\) 0 0
\(301\) −17.5653 −1.01244
\(302\) 0 0
\(303\) 23.7349i 1.36354i
\(304\) 0 0
\(305\) −0.959058 + 0.880917i −0.0549155 + 0.0504412i
\(306\) 0 0
\(307\) 16.0724i 0.917299i −0.888617 0.458649i \(-0.848333\pi\)
0.888617 0.458649i \(-0.151667\pi\)
\(308\) 0 0
\(309\) −26.8652 −1.52831
\(310\) 0 0
\(311\) 6.40532 0.363213 0.181606 0.983371i \(-0.441870\pi\)
0.181606 + 0.983371i \(0.441870\pi\)
\(312\) 0 0
\(313\) 9.69215i 0.547833i 0.961753 + 0.273916i \(0.0883192\pi\)
−0.961753 + 0.273916i \(0.911681\pi\)
\(314\) 0 0
\(315\) −35.0212 38.1277i −1.97322 2.14825i
\(316\) 0 0
\(317\) 12.6417i 0.710031i 0.934860 + 0.355016i \(0.115524\pi\)
−0.934860 + 0.355016i \(0.884476\pi\)
\(318\) 0 0
\(319\) −29.1439 −1.63175
\(320\) 0 0
\(321\) −53.7531 −3.00021
\(322\) 0 0
\(323\) 4.77349i 0.265604i
\(324\) 0 0
\(325\) 4.98200 + 0.423922i 0.276351 + 0.0235150i
\(326\) 0 0
\(327\) 17.7171i 0.979755i
\(328\) 0 0
\(329\) −1.62811 −0.0897604
\(330\) 0 0
\(331\) 21.3813 1.17522 0.587610 0.809144i \(-0.300069\pi\)
0.587610 + 0.809144i \(0.300069\pi\)
\(332\) 0 0
\(333\) 6.84825i 0.375282i
\(334\) 0 0
\(335\) −12.3363 13.4306i −0.674004 0.733791i
\(336\) 0 0
\(337\) 14.2046i 0.773771i −0.922128 0.386886i \(-0.873551\pi\)
0.922128 0.386886i \(-0.126449\pi\)
\(338\) 0 0
\(339\) 51.4899 2.79655
\(340\) 0 0
\(341\) 32.3338 1.75097
\(342\) 0 0
\(343\) 5.19589i 0.280551i
\(344\) 0 0
\(345\) 42.6365 39.1626i 2.29547 2.10845i
\(346\) 0 0
\(347\) 8.40945i 0.451443i −0.974192 0.225722i \(-0.927526\pi\)
0.974192 0.225722i \(-0.0724740\pi\)
\(348\) 0 0
\(349\) −12.8579 −0.688268 −0.344134 0.938921i \(-0.611827\pi\)
−0.344134 + 0.938921i \(0.611827\pi\)
\(350\) 0 0
\(351\) 10.9343 0.583630
\(352\) 0 0
\(353\) 20.4947i 1.09082i −0.838168 0.545412i \(-0.816373\pi\)
0.838168 0.545412i \(-0.183627\pi\)
\(354\) 0 0
\(355\) 19.4841 17.8966i 1.03411 0.949852i
\(356\) 0 0
\(357\) 14.1447i 0.748617i
\(358\) 0 0
\(359\) 5.48437 0.289454 0.144727 0.989472i \(-0.453770\pi\)
0.144727 + 0.989472i \(0.453770\pi\)
\(360\) 0 0
\(361\) −5.38346 −0.283340
\(362\) 0 0
\(363\) 12.2230i 0.641540i
\(364\) 0 0
\(365\) −17.7175 19.2891i −0.927377 1.00964i
\(366\) 0 0
\(367\) 21.3267i 1.11325i −0.830765 0.556623i \(-0.812097\pi\)
0.830765 0.556623i \(-0.187903\pi\)
\(368\) 0 0
\(369\) 19.4261 1.01128
\(370\) 0 0
\(371\) 43.2880 2.24740
\(372\) 0 0
\(373\) 7.79670i 0.403698i −0.979417 0.201849i \(-0.935305\pi\)
0.979417 0.201849i \(-0.0646950\pi\)
\(374\) 0 0
\(375\) −27.3215 + 21.1199i −1.41087 + 1.09063i
\(376\) 0 0
\(377\) 7.53566i 0.388106i
\(378\) 0 0
\(379\) 30.9542 1.59001 0.795006 0.606601i \(-0.207468\pi\)
0.795006 + 0.606601i \(0.207468\pi\)
\(380\) 0 0
\(381\) 47.5757 2.43738
\(382\) 0 0
\(383\) 16.3396i 0.834914i 0.908697 + 0.417457i \(0.137079\pi\)
−0.908697 + 0.417457i \(0.862921\pi\)
\(384\) 0 0
\(385\) −20.7097 22.5467i −1.05546 1.14909i
\(386\) 0 0
\(387\) 32.4507i 1.64956i
\(388\) 0 0
\(389\) −6.00000 −0.304212 −0.152106 0.988364i \(-0.548606\pi\)
−0.152106 + 0.988364i \(0.548606\pi\)
\(390\) 0 0
\(391\) 10.8434 0.548375
\(392\) 0 0
\(393\) 36.1244i 1.82223i
\(394\) 0 0
\(395\) 6.37823 5.85855i 0.320924 0.294776i
\(396\) 0 0
\(397\) 32.8000i 1.64619i 0.567906 + 0.823093i \(0.307754\pi\)
−0.567906 + 0.823093i \(0.692246\pi\)
\(398\) 0 0
\(399\) −40.3483 −2.01994
\(400\) 0 0
\(401\) −18.7379 −0.935727 −0.467864 0.883801i \(-0.654976\pi\)
−0.467864 + 0.883801i \(0.654976\pi\)
\(402\) 0 0
\(403\) 8.36045i 0.416463i
\(404\) 0 0
\(405\) −23.3065 + 21.4075i −1.15811 + 1.06375i
\(406\) 0 0
\(407\) 4.04969i 0.200736i
\(408\) 0 0
\(409\) 37.5574 1.85710 0.928548 0.371213i \(-0.121058\pi\)
0.928548 + 0.371213i \(0.121058\pi\)
\(410\) 0 0
\(411\) −17.3489 −0.855760
\(412\) 0 0
\(413\) 11.6124i 0.571410i
\(414\) 0 0
\(415\) 5.36155 + 5.83714i 0.263188 + 0.286534i
\(416\) 0 0
\(417\) 22.6389i 1.10863i
\(418\) 0 0
\(419\) 15.0870 0.737049 0.368524 0.929618i \(-0.379863\pi\)
0.368524 + 0.929618i \(0.379863\pi\)
\(420\) 0 0
\(421\) 12.3233 0.600600 0.300300 0.953845i \(-0.402913\pi\)
0.300300 + 0.953845i \(0.402913\pi\)
\(422\) 0 0
\(423\) 3.00782i 0.146245i
\(424\) 0 0
\(425\) −6.44474 0.548388i −0.312616 0.0266007i
\(426\) 0 0
\(427\) 2.06167i 0.0997710i
\(428\) 0 0
\(429\) 11.9455 0.576733
\(430\) 0 0
\(431\) −2.14265 −0.103208 −0.0516038 0.998668i \(-0.516433\pi\)
−0.0516038 + 0.998668i \(0.516433\pi\)
\(432\) 0 0
\(433\) 14.4918i 0.696433i 0.937414 + 0.348217i \(0.113213\pi\)
−0.937414 + 0.348217i \(0.886787\pi\)
\(434\) 0 0
\(435\) −35.2070 38.3301i −1.68805 1.83779i
\(436\) 0 0
\(437\) 30.9312i 1.47964i
\(438\) 0 0
\(439\) −5.82917 −0.278211 −0.139106 0.990278i \(-0.544423\pi\)
−0.139106 + 0.990278i \(0.544423\pi\)
\(440\) 0 0
\(441\) 36.1816 1.72293
\(442\) 0 0
\(443\) 4.06340i 0.193058i −0.995330 0.0965291i \(-0.969226\pi\)
0.995330 0.0965291i \(-0.0307741\pi\)
\(444\) 0 0
\(445\) 2.40976 2.21342i 0.114233 0.104926i
\(446\) 0 0
\(447\) 67.6282i 3.19870i
\(448\) 0 0
\(449\) 29.1218 1.37434 0.687172 0.726495i \(-0.258852\pi\)
0.687172 + 0.726495i \(0.258852\pi\)
\(450\) 0 0
\(451\) 11.4876 0.540930
\(452\) 0 0
\(453\) 72.8244i 3.42159i
\(454\) 0 0
\(455\) −5.82984 + 5.35484i −0.273307 + 0.251039i
\(456\) 0 0
\(457\) 5.73494i 0.268269i −0.990963 0.134135i \(-0.957175\pi\)
0.990963 0.134135i \(-0.0428254\pi\)
\(458\) 0 0
\(459\) −14.1447 −0.660218
\(460\) 0 0
\(461\) −20.9824 −0.977249 −0.488624 0.872494i \(-0.662501\pi\)
−0.488624 + 0.872494i \(0.662501\pi\)
\(462\) 0 0
\(463\) 0.847438i 0.0393838i 0.999806 + 0.0196919i \(0.00626853\pi\)
−0.999806 + 0.0196919i \(0.993731\pi\)
\(464\) 0 0
\(465\) 39.0605 + 42.5253i 1.81139 + 1.97206i
\(466\) 0 0
\(467\) 28.2776i 1.30853i −0.756264 0.654266i \(-0.772978\pi\)
0.756264 0.654266i \(-0.227022\pi\)
\(468\) 0 0
\(469\) 28.8714 1.33316
\(470\) 0 0
\(471\) −45.2116 −2.08324
\(472\) 0 0
\(473\) 19.1896i 0.882339i
\(474\) 0 0
\(475\) −1.56430 + 18.3839i −0.0717749 + 0.843510i
\(476\) 0 0
\(477\) 79.9717i 3.66165i
\(478\) 0 0
\(479\) 13.9191 0.635981 0.317990 0.948094i \(-0.396992\pi\)
0.317990 + 0.948094i \(0.396992\pi\)
\(480\) 0 0
\(481\) −1.04712 −0.0477445
\(482\) 0 0
\(483\) 91.6548i 4.17044i
\(484\) 0 0
\(485\) 4.39082 + 4.78031i 0.199377 + 0.217063i
\(486\) 0 0
\(487\) 23.3189i 1.05668i 0.849033 + 0.528340i \(0.177185\pi\)
−0.849033 + 0.528340i \(0.822815\pi\)
\(488\) 0 0
\(489\) 33.5732 1.51823
\(490\) 0 0
\(491\) −7.99557 −0.360835 −0.180417 0.983590i \(-0.557745\pi\)
−0.180417 + 0.983590i \(0.557745\pi\)
\(492\) 0 0
\(493\) 9.74818i 0.439036i
\(494\) 0 0
\(495\) −41.6536 + 38.2598i −1.87219 + 1.71965i
\(496\) 0 0
\(497\) 41.8845i 1.87878i
\(498\) 0 0
\(499\) −39.7191 −1.77807 −0.889035 0.457840i \(-0.848623\pi\)
−0.889035 + 0.457840i \(0.848623\pi\)
\(500\) 0 0
\(501\) −16.5153 −0.737849
\(502\) 0 0
\(503\) 2.69788i 0.120293i 0.998190 + 0.0601463i \(0.0191567\pi\)
−0.998190 + 0.0601463i \(0.980843\pi\)
\(504\) 0 0
\(505\) −12.6547 + 11.6237i −0.563129 + 0.517247i
\(506\) 0 0
\(507\) 3.08870i 0.137174i
\(508\) 0 0
\(509\) 26.6547 1.18145 0.590725 0.806873i \(-0.298842\pi\)
0.590725 + 0.806873i \(0.298842\pi\)
\(510\) 0 0
\(511\) 41.4654 1.83432
\(512\) 0 0
\(513\) 40.3483i 1.78142i
\(514\) 0 0
\(515\) −13.1566 14.3237i −0.579751 0.631177i
\(516\) 0 0
\(517\) 1.77867i 0.0782257i
\(518\) 0 0
\(519\) 0.391966 0.0172054
\(520\) 0 0
\(521\) 19.3099 0.845982 0.422991 0.906134i \(-0.360980\pi\)
0.422991 + 0.906134i \(0.360980\pi\)
\(522\) 0 0
\(523\) 2.37105i 0.103679i 0.998655 + 0.0518395i \(0.0165084\pi\)
−0.998655 + 0.0518395i \(0.983492\pi\)
\(524\) 0 0
\(525\) 4.63529 54.4747i 0.202301 2.37747i
\(526\) 0 0
\(527\) 10.8151i 0.471114i
\(528\) 0 0
\(529\) −47.2631 −2.05492
\(530\) 0 0
\(531\) 21.4532 0.930989
\(532\) 0 0
\(533\) 2.97032i 0.128659i
\(534\) 0 0
\(535\) −26.3244 28.6595i −1.13810 1.23906i
\(536\) 0 0
\(537\) 16.1704i 0.697804i
\(538\) 0 0
\(539\) 21.3959 0.921587
\(540\) 0 0
\(541\) −4.50886 −0.193851 −0.0969256 0.995292i \(-0.530901\pi\)
−0.0969256 + 0.995292i \(0.530901\pi\)
\(542\) 0 0
\(543\) 35.9696i 1.54360i
\(544\) 0 0
\(545\) 9.44619 8.67654i 0.404630 0.371662i
\(546\) 0 0
\(547\) 18.9179i 0.808870i 0.914567 + 0.404435i \(0.132532\pi\)
−0.914567 + 0.404435i \(0.867468\pi\)
\(548\) 0 0
\(549\) −3.80879 −0.162555
\(550\) 0 0
\(551\) −27.8070 −1.18462
\(552\) 0 0
\(553\) 13.7111i 0.583057i
\(554\) 0 0
\(555\) 5.32615 4.89219i 0.226083 0.207662i
\(556\) 0 0
\(557\) 20.3285i 0.861347i 0.902508 + 0.430674i \(0.141724\pi\)
−0.902508 + 0.430674i \(0.858276\pi\)
\(558\) 0 0
\(559\) 4.96180 0.209862
\(560\) 0 0
\(561\) −15.4527 −0.652415
\(562\) 0 0
\(563\) 45.6544i 1.92410i 0.272866 + 0.962052i \(0.412028\pi\)
−0.272866 + 0.962052i \(0.587972\pi\)
\(564\) 0 0
\(565\) 25.2161 + 27.4528i 1.06085 + 1.15495i
\(566\) 0 0
\(567\) 50.1014i 2.10406i
\(568\) 0 0
\(569\) −38.8564 −1.62894 −0.814472 0.580203i \(-0.802973\pi\)
−0.814472 + 0.580203i \(0.802973\pi\)
\(570\) 0 0
\(571\) −43.0103 −1.79993 −0.899963 0.435966i \(-0.856407\pi\)
−0.899963 + 0.435966i \(0.856407\pi\)
\(572\) 0 0
\(573\) 70.8612i 2.96027i
\(574\) 0 0
\(575\) 41.7606 + 3.55345i 1.74154 + 0.148189i
\(576\) 0 0
\(577\) 13.7724i 0.573354i −0.958027 0.286677i \(-0.907449\pi\)
0.958027 0.286677i \(-0.0925507\pi\)
\(578\) 0 0
\(579\) 20.8114 0.864894
\(580\) 0 0
\(581\) −12.5480 −0.520577
\(582\) 0 0
\(583\) 47.2911i 1.95860i
\(584\) 0 0
\(585\) 9.89272 + 10.7703i 0.409014 + 0.445295i
\(586\) 0 0
\(587\) 9.48516i 0.391494i −0.980654 0.195747i \(-0.937287\pi\)
0.980654 0.195747i \(-0.0627132\pi\)
\(588\) 0 0
\(589\) 30.8505 1.27117
\(590\) 0 0
\(591\) −11.3938 −0.468679
\(592\) 0 0
\(593\) 23.1923i 0.952392i −0.879339 0.476196i \(-0.842015\pi\)
0.879339 0.476196i \(-0.157985\pi\)
\(594\) 0 0
\(595\) 7.54152 6.92706i 0.309172 0.283982i
\(596\) 0 0
\(597\) 21.4767i 0.878981i
\(598\) 0 0
\(599\) −3.85607 −0.157555 −0.0787774 0.996892i \(-0.525102\pi\)
−0.0787774 + 0.996892i \(0.525102\pi\)
\(600\) 0 0
\(601\) −37.4047 −1.52577 −0.762884 0.646535i \(-0.776218\pi\)
−0.762884 + 0.646535i \(0.776218\pi\)
\(602\) 0 0
\(603\) 53.3380i 2.17209i
\(604\) 0 0
\(605\) −6.51692 + 5.98594i −0.264950 + 0.243363i
\(606\) 0 0
\(607\) 0.384705i 0.0156147i 0.999970 + 0.00780734i \(0.00248518\pi\)
−0.999970 + 0.00780734i \(0.997515\pi\)
\(608\) 0 0
\(609\) 82.3973 3.33891
\(610\) 0 0
\(611\) 0.459905 0.0186057
\(612\) 0 0
\(613\) 32.4602i 1.31106i −0.755171 0.655528i \(-0.772446\pi\)
0.755171 0.655528i \(-0.227554\pi\)
\(614\) 0 0
\(615\) 13.8775 + 15.1085i 0.559594 + 0.609233i
\(616\) 0 0
\(617\) 14.5650i 0.586364i 0.956057 + 0.293182i \(0.0947143\pi\)
−0.956057 + 0.293182i \(0.905286\pi\)
\(618\) 0 0
\(619\) −12.7941 −0.514236 −0.257118 0.966380i \(-0.582773\pi\)
−0.257118 + 0.966380i \(0.582773\pi\)
\(620\) 0 0
\(621\) 91.6548 3.67798
\(622\) 0 0
\(623\) 5.18020i 0.207540i
\(624\) 0 0
\(625\) −24.6406 4.22396i −0.985623 0.168958i
\(626\) 0 0
\(627\) 44.0795i 1.76037i
\(628\) 0 0
\(629\) 1.35456 0.0540098
\(630\) 0 0
\(631\) 43.6282 1.73681 0.868405 0.495856i \(-0.165146\pi\)
0.868405 + 0.495856i \(0.165146\pi\)
\(632\) 0 0
\(633\) 34.8586i 1.38551i
\(634\) 0 0
\(635\) 23.2992 + 25.3659i 0.924600 + 1.00662i
\(636\) 0 0
\(637\) 5.53228i 0.219197i
\(638\) 0 0
\(639\) 77.3789 3.06106
\(640\) 0 0
\(641\) −22.9206 −0.905310 −0.452655 0.891686i \(-0.649523\pi\)
−0.452655 + 0.891686i \(0.649523\pi\)
\(642\) 0 0
\(643\) 37.6848i 1.48614i −0.669212 0.743071i \(-0.733368\pi\)
0.669212 0.743071i \(-0.266632\pi\)
\(644\) 0 0
\(645\) −25.2381 + 23.1818i −0.993751 + 0.912783i
\(646\) 0 0
\(647\) 22.9044i 0.900464i −0.892912 0.450232i \(-0.851341\pi\)
0.892912 0.450232i \(-0.148659\pi\)
\(648\) 0 0
\(649\) 12.6863 0.497980
\(650\) 0 0
\(651\) −91.4157 −3.58286
\(652\) 0 0
\(653\) 39.7742i 1.55648i −0.627964 0.778242i \(-0.716112\pi\)
0.627964 0.778242i \(-0.283888\pi\)
\(654\) 0 0
\(655\) 19.2604 17.6911i 0.752567 0.691250i
\(656\) 0 0
\(657\) 76.6046i 2.98863i
\(658\) 0 0
\(659\) −17.7393 −0.691026 −0.345513 0.938414i \(-0.612295\pi\)
−0.345513 + 0.938414i \(0.612295\pi\)
\(660\) 0 0
\(661\) −22.0617 −0.858099 −0.429050 0.903281i \(-0.641151\pi\)
−0.429050 + 0.903281i \(0.641151\pi\)
\(662\) 0 0
\(663\) 3.99557i 0.155175i
\(664\) 0 0
\(665\) −19.7597 21.5125i −0.766248 0.834217i
\(666\) 0 0
\(667\) 63.1663i 2.44581i
\(668\) 0 0
\(669\) 6.99736 0.270534
\(670\) 0 0
\(671\) −2.25232 −0.0869499
\(672\) 0 0
\(673\) 15.2439i 0.587610i −0.955865 0.293805i \(-0.905078\pi\)
0.955865 0.293805i \(-0.0949216\pi\)
\(674\) 0 0
\(675\) −54.4747 4.63529i −2.09673 0.178413i
\(676\) 0 0
\(677\) 42.7334i 1.64238i −0.570655 0.821190i \(-0.693311\pi\)
0.570655 0.821190i \(-0.306689\pi\)
\(678\) 0 0
\(679\) −10.2761 −0.394361
\(680\) 0 0
\(681\) −54.7104 −2.09651
\(682\) 0 0
\(683\) 29.3308i 1.12231i 0.827710 + 0.561156i \(0.189643\pi\)
−0.827710 + 0.561156i \(0.810357\pi\)
\(684\) 0 0
\(685\) −8.49627 9.24993i −0.324626 0.353421i
\(686\) 0 0
\(687\) 43.0297i 1.64169i
\(688\) 0 0
\(689\) −12.2279 −0.465846
\(690\) 0 0
\(691\) −7.31373 −0.278228 −0.139114 0.990276i \(-0.544425\pi\)
−0.139114 + 0.990276i \(0.544425\pi\)
\(692\) 0 0
\(693\) 89.5418i 3.40141i
\(694\) 0 0
\(695\) 12.0704 11.0869i 0.457855 0.420550i
\(696\) 0 0
\(697\) 3.84242i 0.145542i
\(698\) 0 0
\(699\) 30.9109 1.16916
\(700\) 0 0
\(701\) −11.1477 −0.421044 −0.210522 0.977589i \(-0.567516\pi\)
−0.210522 + 0.977589i \(0.567516\pi\)
\(702\) 0 0
\(703\) 3.86393i 0.145731i
\(704\) 0 0
\(705\) −2.33930 + 2.14870i −0.0881031 + 0.0809247i
\(706\) 0 0
\(707\) 27.2036i 1.02310i
\(708\) 0 0
\(709\) −36.1499 −1.35764 −0.678820 0.734305i \(-0.737508\pi\)
−0.678820 + 0.734305i \(0.737508\pi\)
\(710\) 0 0
\(711\) 25.3304 0.949965
\(712\) 0 0
\(713\) 70.0799i 2.62451i
\(714\) 0 0
\(715\) 5.85004 + 6.36896i 0.218779 + 0.238186i
\(716\) 0 0
\(717\) 27.2482i 1.01760i
\(718\) 0 0
\(719\) −49.4135 −1.84281 −0.921406 0.388601i \(-0.872959\pi\)
−0.921406 + 0.388601i \(0.872959\pi\)
\(720\) 0 0
\(721\) 30.7913 1.14673
\(722\) 0 0
\(723\) 26.3400i 0.979595i
\(724\) 0 0
\(725\) 3.19453 37.5427i 0.118642 1.39430i
\(726\) 0 0
\(727\) 8.82270i 0.327216i 0.986525 + 0.163608i \(0.0523132\pi\)
−0.986525 + 0.163608i \(0.947687\pi\)
\(728\) 0 0
\(729\) 8.75944 0.324424
\(730\) 0 0
\(731\) −6.41862 −0.237401
\(732\) 0 0
\(733\) 36.9109i 1.36334i 0.731662 + 0.681668i \(0.238745\pi\)
−0.731662 + 0.681668i \(0.761255\pi\)
\(734\) 0 0
\(735\) 25.8471 + 28.1399i 0.953385 + 1.03795i
\(736\) 0 0
\(737\) 31.5413i 1.16184i
\(738\) 0 0
\(739\) −39.9336 −1.46898 −0.734491 0.678619i \(-0.762579\pi\)
−0.734491 + 0.678619i \(0.762579\pi\)
\(740\) 0 0
\(741\) 11.3975 0.418698
\(742\) 0 0
\(743\) 32.1600i 1.17984i 0.807463 + 0.589918i \(0.200840\pi\)
−0.807463 + 0.589918i \(0.799160\pi\)
\(744\) 0 0
\(745\) −36.0573 + 33.1194i −1.32104 + 1.21340i
\(746\) 0 0
\(747\) 23.1815i 0.848168i
\(748\) 0 0
\(749\) 61.6087 2.25113
\(750\) 0 0
\(751\) 10.1167 0.369162 0.184581 0.982817i \(-0.440907\pi\)
0.184581 + 0.982817i \(0.440907\pi\)
\(752\) 0 0
\(753\) 89.9761i 3.27891i
\(754\) 0 0
\(755\) −38.8278 + 35.6642i −1.41309 + 1.29795i
\(756\) 0 0
\(757\) 51.0892i 1.85687i 0.371498 + 0.928434i \(0.378844\pi\)
−0.371498 + 0.928434i \(0.621156\pi\)
\(758\) 0 0
\(759\) 100.131 3.63451
\(760\) 0 0
\(761\) −20.3683 −0.738349 −0.369175 0.929360i \(-0.620360\pi\)
−0.369175 + 0.929360i \(0.620360\pi\)
\(762\) 0 0
\(763\) 20.3063i 0.735136i
\(764\) 0 0
\(765\) −12.7973 13.9325i −0.462687 0.503729i
\(766\) 0 0
\(767\) 3.28026i 0.118443i
\(768\) 0 0
\(769\) 10.1849 0.367276 0.183638 0.982994i \(-0.441213\pi\)
0.183638 + 0.982994i \(0.441213\pi\)
\(770\) 0 0
\(771\) −14.1447 −0.509409
\(772\) 0 0
\(773\) 14.3663i 0.516719i 0.966049 + 0.258360i \(0.0831820\pi\)
−0.966049 + 0.258360i \(0.916818\pi\)
\(774\) 0 0
\(775\) −3.54418 + 41.6517i −0.127311 + 1.49617i
\(776\) 0 0
\(777\) 11.4495i 0.410749i
\(778\) 0 0
\(779\) 10.9606 0.392706
\(780\) 0 0
\(781\) 45.7578 1.63734
\(782\) 0 0
\(783\) 82.3973i 2.94464i
\(784\) 0 0
\(785\) −22.1414 24.1054i −0.790261 0.860360i
\(786\) 0 0
\(787\) 23.1526i 0.825300i 0.910890 + 0.412650i \(0.135397\pi\)
−0.910890 + 0.412650i \(0.864603\pi\)
\(788\) 0 0
\(789\) −45.6060 −1.62362
\(790\) 0 0
\(791\) −59.0148 −2.09832
\(792\) 0 0
\(793\) 0.582376i 0.0206808i
\(794\) 0 0