Properties

Label 520.2.d.c.209.2
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 209.2
Root \(2.19360 + 0.433733i\) of defining polynomial
Character \(\chi\) \(=\) 520.209
Dual form 520.2.d.c.209.9

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-3.05748i q^{3} +(-2.19360 - 0.433733i) q^{5} -3.34821i q^{7} -6.34821 q^{9} +O(q^{10})\) \(q-3.05748i q^{3} +(-2.19360 - 0.433733i) q^{5} -3.34821i q^{7} -6.34821 q^{9} +4.88596 q^{11} +1.00000i q^{13} +(-1.32613 + 6.70689i) q^{15} -2.38720i q^{17} -7.22901 q^{19} -10.2371 q^{21} +3.32971i q^{23} +(4.62375 + 1.90287i) q^{25} +10.2371i q^{27} -3.95061 q^{29} +2.96394 q^{31} -14.9388i q^{33} +(-1.45223 + 7.34463i) q^{35} +3.42619i q^{37} +3.05748 q^{39} +4.43135 q^{41} -3.32255i q^{43} +(13.9254 + 2.75343i) q^{45} -0.651790i q^{47} -4.21051 q^{49} -7.29882 q^{51} -7.84990i q^{53} +(-10.7178 - 2.11920i) q^{55} +22.1026i q^{57} +7.66036 q^{59} -15.0271 q^{61} +21.2551i q^{63} +(0.433733 - 2.19360i) q^{65} -10.4086i q^{67} +10.1805 q^{69} +10.6917 q^{71} -12.0656i q^{73} +(5.81800 - 14.1370i) q^{75} -16.3592i q^{77} -8.38004 q^{79} +12.2551 q^{81} -14.6470i q^{83} +(-1.03541 + 5.23655i) q^{85} +12.0789i q^{87} +8.50933 q^{89} +3.34821 q^{91} -9.06219i q^{93} +(15.8575 + 3.13546i) q^{95} -14.8114i q^{97} -31.0171 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q - 4 q^{5} - 30 q^{9}+O(q^{10}) \) 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
\(3\) 3.05748i 1.76524i −0.470088 0.882620i \(-0.655778\pi\)
0.470088 0.882620i \(-0.344222\pi\)
\(4\) 0 0
\(5\) −2.19360 0.433733i −0.981007 0.193971i
\(6\) 0 0
\(7\) 3.34821i 1.26550i −0.774354 0.632752i \(-0.781925\pi\)
0.774354 0.632752i \(-0.218075\pi\)
\(8\) 0 0
\(9\) −6.34821 −2.11607
\(10\) 0 0
\(11\) 4.88596 1.47317 0.736587 0.676343i \(-0.236436\pi\)
0.736587 + 0.676343i \(0.236436\pi\)
\(12\) 0 0
\(13\) 1.00000i 0.277350i
\(14\) 0 0
\(15\) −1.32613 + 6.70689i −0.342406 + 1.73171i
\(16\) 0 0
\(17\) 2.38720i 0.578980i −0.957181 0.289490i \(-0.906514\pi\)
0.957181 0.289490i \(-0.0934858\pi\)
\(18\) 0 0
\(19\) −7.22901 −1.65845 −0.829224 0.558917i \(-0.811217\pi\)
−0.829224 + 0.558917i \(0.811217\pi\)
\(20\) 0 0
\(21\) −10.2371 −2.23392
\(22\) 0 0
\(23\) 3.32971i 0.694293i 0.937811 + 0.347147i \(0.112849\pi\)
−0.937811 + 0.347147i \(0.887151\pi\)
\(24\) 0 0
\(25\) 4.62375 + 1.90287i 0.924750 + 0.380575i
\(26\) 0 0
\(27\) 10.2371i 1.97013i
\(28\) 0 0
\(29\) −3.95061 −0.733610 −0.366805 0.930298i \(-0.619548\pi\)
−0.366805 + 0.930298i \(0.619548\pi\)
\(30\) 0 0
\(31\) 2.96394 0.532339 0.266170 0.963926i \(-0.414242\pi\)
0.266170 + 0.963926i \(0.414242\pi\)
\(32\) 0 0
\(33\) 14.9388i 2.60050i
\(34\) 0 0
\(35\) −1.45223 + 7.34463i −0.245472 + 1.24147i
\(36\) 0 0
\(37\) 3.42619i 0.563261i 0.959523 + 0.281631i \(0.0908753\pi\)
−0.959523 + 0.281631i \(0.909125\pi\)
\(38\) 0 0
\(39\) 3.05748 0.489589
\(40\) 0 0
\(41\) 4.43135 0.692061 0.346030 0.938223i \(-0.387529\pi\)
0.346030 + 0.938223i \(0.387529\pi\)
\(42\) 0 0
\(43\) 3.32255i 0.506684i −0.967377 0.253342i \(-0.918470\pi\)
0.967377 0.253342i \(-0.0815299\pi\)
\(44\) 0 0
\(45\) 13.9254 + 2.75343i 2.07588 + 0.410457i
\(46\) 0 0
\(47\) 0.651790i 0.0950734i −0.998869 0.0475367i \(-0.984863\pi\)
0.998869 0.0475367i \(-0.0151371\pi\)
\(48\) 0 0
\(49\) −4.21051 −0.601501
\(50\) 0 0
\(51\) −7.29882 −1.02204
\(52\) 0 0
\(53\) 7.84990i 1.07827i −0.842220 0.539133i \(-0.818752\pi\)
0.842220 0.539133i \(-0.181248\pi\)
\(54\) 0 0
\(55\) −10.7178 2.11920i −1.44519 0.285753i
\(56\) 0 0
\(57\) 22.1026i 2.92756i
\(58\) 0 0
\(59\) 7.66036 0.997294 0.498647 0.866805i \(-0.333830\pi\)
0.498647 + 0.866805i \(0.333830\pi\)
\(60\) 0 0
\(61\) −15.0271 −1.92402 −0.962009 0.273017i \(-0.911978\pi\)
−0.962009 + 0.273017i \(0.911978\pi\)
\(62\) 0 0
\(63\) 21.2551i 2.67790i
\(64\) 0 0
\(65\) 0.433733 2.19360i 0.0537980 0.272082i
\(66\) 0 0
\(67\) 10.4086i 1.27162i −0.771848 0.635808i \(-0.780667\pi\)
0.771848 0.635808i \(-0.219333\pi\)
\(68\) 0 0
\(69\) 10.1805 1.22559
\(70\) 0 0
\(71\) 10.6917 1.26887 0.634436 0.772975i \(-0.281232\pi\)
0.634436 + 0.772975i \(0.281232\pi\)
\(72\) 0 0
\(73\) 12.0656i 1.41217i −0.708128 0.706085i \(-0.750460\pi\)
0.708128 0.706085i \(-0.249540\pi\)
\(74\) 0 0
\(75\) 5.81800 14.1370i 0.671805 1.63241i
\(76\) 0 0
\(77\) 16.3592i 1.86431i
\(78\) 0 0
\(79\) −8.38004 −0.942828 −0.471414 0.881912i \(-0.656256\pi\)
−0.471414 + 0.881912i \(0.656256\pi\)
\(80\) 0 0
\(81\) 12.2551 1.36168
\(82\) 0 0
\(83\) 14.6470i 1.60772i −0.594818 0.803860i \(-0.702776\pi\)
0.594818 0.803860i \(-0.297224\pi\)
\(84\) 0 0
\(85\) −1.03541 + 5.23655i −0.112306 + 0.567984i
\(86\) 0 0
\(87\) 12.0789i 1.29500i
\(88\) 0 0
\(89\) 8.50933 0.901987 0.450993 0.892527i \(-0.351070\pi\)
0.450993 + 0.892527i \(0.351070\pi\)
\(90\) 0 0
\(91\) 3.34821 0.350988
\(92\) 0 0
\(93\) 9.06219i 0.939706i
\(94\) 0 0
\(95\) 15.8575 + 3.13546i 1.62695 + 0.321691i
\(96\) 0 0
\(97\) 14.8114i 1.50387i −0.659238 0.751934i \(-0.729121\pi\)
0.659238 0.751934i \(-0.270879\pi\)
\(98\) 0 0
\(99\) −31.0171 −3.11734
\(100\) 0 0
\(101\) −2.03699 −0.202688 −0.101344 0.994851i \(-0.532314\pi\)
−0.101344 + 0.994851i \(0.532314\pi\)
\(102\) 0 0
\(103\) 13.3667i 1.31706i 0.752554 + 0.658530i \(0.228822\pi\)
−0.752554 + 0.658530i \(0.771178\pi\)
\(104\) 0 0
\(105\) 22.4561 + 4.44017i 2.19149 + 0.433316i
\(106\) 0 0
\(107\) 2.83657i 0.274222i −0.990556 0.137111i \(-0.956218\pi\)
0.990556 0.137111i \(-0.0437817\pi\)
\(108\) 0 0
\(109\) −12.0442 −1.15362 −0.576810 0.816878i \(-0.695703\pi\)
−0.576810 + 0.816878i \(0.695703\pi\)
\(110\) 0 0
\(111\) 10.4755 0.994291
\(112\) 0 0
\(113\) 1.80706i 0.169994i −0.996381 0.0849968i \(-0.972912\pi\)
0.996381 0.0849968i \(-0.0270880\pi\)
\(114\) 0 0
\(115\) 1.44421 7.30405i 0.134673 0.681107i
\(116\) 0 0
\(117\) 6.34821i 0.586892i
\(118\) 0 0
\(119\) −7.99284 −0.732702
\(120\) 0 0
\(121\) 12.8726 1.17024
\(122\) 0 0
\(123\) 13.5488i 1.22165i
\(124\) 0 0
\(125\) −9.31732 6.17961i −0.833366 0.552722i
\(126\) 0 0
\(127\) 4.83657i 0.429176i 0.976705 + 0.214588i \(0.0688409\pi\)
−0.976705 + 0.214588i \(0.931159\pi\)
\(128\) 0 0
\(129\) −10.1586 −0.894419
\(130\) 0 0
\(131\) 7.06041 0.616871 0.308435 0.951245i \(-0.400195\pi\)
0.308435 + 0.951245i \(0.400195\pi\)
\(132\) 0 0
\(133\) 24.2042i 2.09877i
\(134\) 0 0
\(135\) 4.44017 22.4561i 0.382149 1.93271i
\(136\) 0 0
\(137\) 15.2057i 1.29911i 0.760313 + 0.649557i \(0.225046\pi\)
−0.760313 + 0.649557i \(0.774954\pi\)
\(138\) 0 0
\(139\) 13.3625 1.13339 0.566695 0.823928i \(-0.308222\pi\)
0.566695 + 0.823928i \(0.308222\pi\)
\(140\) 0 0
\(141\) −1.99284 −0.167827
\(142\) 0 0
\(143\) 4.88596i 0.408585i
\(144\) 0 0
\(145\) 8.66605 + 1.71351i 0.719676 + 0.142299i
\(146\) 0 0
\(147\) 12.8736i 1.06179i
\(148\) 0 0
\(149\) 3.62091 0.296637 0.148318 0.988940i \(-0.452614\pi\)
0.148318 + 0.988940i \(0.452614\pi\)
\(150\) 0 0
\(151\) 10.0684 0.819352 0.409676 0.912231i \(-0.365642\pi\)
0.409676 + 0.912231i \(0.365642\pi\)
\(152\) 0 0
\(153\) 15.1544i 1.22516i
\(154\) 0 0
\(155\) −6.50169 1.28556i −0.522228 0.103259i
\(156\) 0 0
\(157\) 9.03946i 0.721428i 0.932677 + 0.360714i \(0.117467\pi\)
−0.932677 + 0.360714i \(0.882533\pi\)
\(158\) 0 0
\(159\) −24.0009 −1.90340
\(160\) 0 0
\(161\) 11.1486 0.878631
\(162\) 0 0
\(163\) 10.0143i 0.784377i 0.919885 + 0.392189i \(0.128282\pi\)
−0.919885 + 0.392189i \(0.871718\pi\)
\(164\) 0 0
\(165\) −6.47943 + 32.7696i −0.504423 + 2.55111i
\(166\) 0 0
\(167\) 20.3676i 1.57610i −0.615614 0.788048i \(-0.711092\pi\)
0.615614 0.788048i \(-0.288908\pi\)
\(168\) 0 0
\(169\) −1.00000 −0.0769231
\(170\) 0 0
\(171\) 45.8912 3.50939
\(172\) 0 0
\(173\) 4.38004i 0.333008i 0.986041 + 0.166504i \(0.0532479\pi\)
−0.986041 + 0.166504i \(0.946752\pi\)
\(174\) 0 0
\(175\) 6.37122 15.4813i 0.481619 1.17028i
\(176\) 0 0
\(177\) 23.4214i 1.76046i
\(178\) 0 0
\(179\) 20.2148 1.51093 0.755464 0.655190i \(-0.227411\pi\)
0.755464 + 0.655190i \(0.227411\pi\)
\(180\) 0 0
\(181\) −7.17716 −0.533474 −0.266737 0.963769i \(-0.585946\pi\)
−0.266737 + 0.963769i \(0.585946\pi\)
\(182\) 0 0
\(183\) 45.9450i 3.39635i
\(184\) 0 0
\(185\) 1.48605 7.51568i 0.109257 0.552563i
\(186\) 0 0
\(187\) 11.6638i 0.852938i
\(188\) 0 0
\(189\) 34.2760 2.49321
\(190\) 0 0
\(191\) 0.544458 0.0393956 0.0196978 0.999806i \(-0.493730\pi\)
0.0196978 + 0.999806i \(0.493730\pi\)
\(192\) 0 0
\(193\) 27.4357i 1.97486i 0.158045 + 0.987432i \(0.449481\pi\)
−0.158045 + 0.987432i \(0.550519\pi\)
\(194\) 0 0
\(195\) −6.70689 1.32613i −0.480291 0.0949663i
\(196\) 0 0
\(197\) 5.26183i 0.374890i 0.982275 + 0.187445i \(0.0600206\pi\)
−0.982275 + 0.187445i \(0.939979\pi\)
\(198\) 0 0
\(199\) 11.0765 0.785189 0.392595 0.919712i \(-0.371578\pi\)
0.392595 + 0.919712i \(0.371578\pi\)
\(200\) 0 0
\(201\) −31.8242 −2.24471
\(202\) 0 0
\(203\) 13.2275i 0.928386i
\(204\) 0 0
\(205\) −9.72061 1.92202i −0.678917 0.134240i
\(206\) 0 0
\(207\) 21.1377i 1.46917i
\(208\) 0 0
\(209\) −35.3207 −2.44318
\(210\) 0 0
\(211\) −21.9498 −1.51108 −0.755542 0.655100i \(-0.772627\pi\)
−0.755542 + 0.655100i \(0.772627\pi\)
\(212\) 0 0
\(213\) 32.6897i 2.23986i
\(214\) 0 0
\(215\) −1.44110 + 7.28834i −0.0982823 + 0.497061i
\(216\) 0 0
\(217\) 9.92389i 0.673677i
\(218\) 0 0
\(219\) −36.8903 −2.49282
\(220\) 0 0
\(221\) 2.38720 0.160580
\(222\) 0 0
\(223\) 26.2746i 1.75948i −0.475460 0.879738i \(-0.657718\pi\)
0.475460 0.879738i \(-0.342282\pi\)
\(224\) 0 0
\(225\) −29.3525 12.0798i −1.95684 0.805323i
\(226\) 0 0
\(227\) 6.06558i 0.402587i −0.979531 0.201293i \(-0.935486\pi\)
0.979531 0.201293i \(-0.0645144\pi\)
\(228\) 0 0
\(229\) −9.42666 −0.622931 −0.311466 0.950257i \(-0.600820\pi\)
−0.311466 + 0.950257i \(0.600820\pi\)
\(230\) 0 0
\(231\) −50.0181 −3.29095
\(232\) 0 0
\(233\) 8.78156i 0.575299i −0.957736 0.287649i \(-0.907126\pi\)
0.957736 0.287649i \(-0.0928738\pi\)
\(234\) 0 0
\(235\) −0.282703 + 1.42977i −0.0184415 + 0.0932677i
\(236\) 0 0
\(237\) 25.6218i 1.66432i
\(238\) 0 0
\(239\) 28.0066 1.81159 0.905797 0.423711i \(-0.139273\pi\)
0.905797 + 0.423711i \(0.139273\pi\)
\(240\) 0 0
\(241\) −4.08831 −0.263351 −0.131676 0.991293i \(-0.542036\pi\)
−0.131676 + 0.991293i \(0.542036\pi\)
\(242\) 0 0
\(243\) 6.75860i 0.433564i
\(244\) 0 0
\(245\) 9.23617 + 1.82624i 0.590077 + 0.116674i
\(246\) 0 0
\(247\) 7.22901i 0.459971i
\(248\) 0 0
\(249\) −44.7831 −2.83801
\(250\) 0 0
\(251\) −20.9615 −1.32308 −0.661539 0.749911i \(-0.730096\pi\)
−0.661539 + 0.749911i \(0.730096\pi\)
\(252\) 0 0
\(253\) 16.2689i 1.02281i
\(254\) 0 0
\(255\) 16.0107 + 3.16574i 1.00263 + 0.198246i
\(256\) 0 0
\(257\) 7.99284i 0.498580i 0.968429 + 0.249290i \(0.0801972\pi\)
−0.968429 + 0.249290i \(0.919803\pi\)
\(258\) 0 0
\(259\) 11.4716 0.712810
\(260\) 0 0
\(261\) 25.0793 1.55237
\(262\) 0 0
\(263\) 0.123966i 0.00764406i 0.999993 + 0.00382203i \(0.00121659\pi\)
−0.999993 + 0.00382203i \(0.998783\pi\)
\(264\) 0 0
\(265\) −3.40476 + 17.2195i −0.209153 + 1.05779i
\(266\) 0 0
\(267\) 26.0171i 1.59222i
\(268\) 0 0
\(269\) 18.2669 1.11375 0.556877 0.830595i \(-0.311999\pi\)
0.556877 + 0.830595i \(0.311999\pi\)
\(270\) 0 0
\(271\) 25.4394 1.54534 0.772668 0.634810i \(-0.218922\pi\)
0.772668 + 0.634810i \(0.218922\pi\)
\(272\) 0 0
\(273\) 10.2371i 0.619577i
\(274\) 0 0
\(275\) 22.5915 + 9.29737i 1.36232 + 0.560652i
\(276\) 0 0
\(277\) 10.3021i 0.618991i −0.950901 0.309495i \(-0.899840\pi\)
0.950901 0.309495i \(-0.100160\pi\)
\(278\) 0 0
\(279\) −18.8157 −1.12647
\(280\) 0 0
\(281\) 9.00433 0.537153 0.268577 0.963258i \(-0.413447\pi\)
0.268577 + 0.963258i \(0.413447\pi\)
\(282\) 0 0
\(283\) 15.3667i 0.913456i 0.889606 + 0.456728i \(0.150979\pi\)
−0.889606 + 0.456728i \(0.849021\pi\)
\(284\) 0 0
\(285\) 9.58662 48.4842i 0.567862 2.87195i
\(286\) 0 0
\(287\) 14.8371i 0.875806i
\(288\) 0 0
\(289\) 11.3013 0.664782
\(290\) 0 0
\(291\) −45.2856 −2.65469
\(292\) 0 0
\(293\) 7.17145i 0.418961i −0.977813 0.209480i \(-0.932823\pi\)
0.977813 0.209480i \(-0.0671772\pi\)
\(294\) 0 0
\(295\) −16.8038 3.32255i −0.978352 0.193446i
\(296\) 0 0
\(297\) 50.0181i 2.90234i
\(298\) 0 0
\(299\) −3.32971 −0.192562
\(300\) 0 0
\(301\) −11.1246 −0.641211
\(302\) 0 0
\(303\) 6.22807i 0.357794i
\(304\) 0 0
\(305\) 32.9633 + 6.51774i 1.88748 + 0.373205i
\(306\) 0 0
\(307\) 14.5587i 0.830910i −0.909614 0.415455i \(-0.863622\pi\)
0.909614 0.415455i \(-0.136378\pi\)
\(308\) 0 0
\(309\) 40.8685 2.32493
\(310\) 0 0
\(311\) −25.9649 −1.47233 −0.736166 0.676801i \(-0.763366\pi\)
−0.736166 + 0.676801i \(0.763366\pi\)
\(312\) 0 0
\(313\) 1.25544i 0.0709615i −0.999370 0.0354807i \(-0.988704\pi\)
0.999370 0.0354807i \(-0.0112962\pi\)
\(314\) 0 0
\(315\) 9.21906 46.6252i 0.519435 2.62703i
\(316\) 0 0
\(317\) 11.8356i 0.664756i 0.943146 + 0.332378i \(0.107851\pi\)
−0.943146 + 0.332378i \(0.892149\pi\)
\(318\) 0 0
\(319\) −19.3025 −1.08073
\(320\) 0 0
\(321\) −8.67277 −0.484067
\(322\) 0 0
\(323\) 17.2571i 0.960209i
\(324\) 0 0
\(325\) −1.90287 + 4.62375i −0.105552 + 0.256480i
\(326\) 0 0
\(327\) 36.8248i 2.03642i
\(328\) 0 0
\(329\) −2.18233 −0.120316
\(330\) 0 0
\(331\) −5.13022 −0.281983 −0.140991 0.990011i \(-0.545029\pi\)
−0.140991 + 0.990011i \(0.545029\pi\)
\(332\) 0 0
\(333\) 21.7501i 1.19190i
\(334\) 0 0
\(335\) −4.51456 + 22.8323i −0.246657 + 1.24746i
\(336\) 0 0
\(337\) 6.90686i 0.376241i 0.982146 + 0.188120i \(0.0602395\pi\)
−0.982146 + 0.188120i \(0.939761\pi\)
\(338\) 0 0
\(339\) −5.52505 −0.300079
\(340\) 0 0
\(341\) 14.4817 0.784228
\(342\) 0 0
\(343\) 9.33980i 0.504302i
\(344\) 0 0
\(345\) −22.3320 4.41564i −1.20232 0.237730i
\(346\) 0 0
\(347\) 5.46218i 0.293225i 0.989194 + 0.146613i \(0.0468370\pi\)
−0.989194 + 0.146613i \(0.953163\pi\)
\(348\) 0 0
\(349\) 11.5920 0.620505 0.310253 0.950654i \(-0.399586\pi\)
0.310253 + 0.950654i \(0.399586\pi\)
\(350\) 0 0
\(351\) −10.2371 −0.546416
\(352\) 0 0
\(353\) 24.9140i 1.32604i 0.748603 + 0.663018i \(0.230725\pi\)
−0.748603 + 0.663018i \(0.769275\pi\)
\(354\) 0 0
\(355\) −23.4533 4.63735i −1.24477 0.246125i
\(356\) 0 0
\(357\) 24.4380i 1.29339i
\(358\) 0 0
\(359\) 6.31978 0.333545 0.166773 0.985995i \(-0.446665\pi\)
0.166773 + 0.985995i \(0.446665\pi\)
\(360\) 0 0
\(361\) 33.2585 1.75045
\(362\) 0 0
\(363\) 39.3579i 2.06575i
\(364\) 0 0
\(365\) −5.23324 + 26.4670i −0.273920 + 1.38535i
\(366\) 0 0
\(367\) 2.19147i 0.114394i 0.998363 + 0.0571969i \(0.0182163\pi\)
−0.998363 + 0.0571969i \(0.981784\pi\)
\(368\) 0 0
\(369\) −28.1312 −1.46445
\(370\) 0 0
\(371\) −26.2831 −1.36455
\(372\) 0 0
\(373\) 9.02514i 0.467304i −0.972320 0.233652i \(-0.924932\pi\)
0.972320 0.233652i \(-0.0750676\pi\)
\(374\) 0 0
\(375\) −18.8941 + 28.4875i −0.975686 + 1.47109i
\(376\) 0 0
\(377\) 3.95061i 0.203467i
\(378\) 0 0
\(379\) −3.22407 −0.165609 −0.0828046 0.996566i \(-0.526388\pi\)
−0.0828046 + 0.996566i \(0.526388\pi\)
\(380\) 0 0
\(381\) 14.7877 0.757599
\(382\) 0 0
\(383\) 4.00270i 0.204528i −0.994757 0.102264i \(-0.967391\pi\)
0.994757 0.102264i \(-0.0326087\pi\)
\(384\) 0 0
\(385\) −7.09554 + 35.8856i −0.361622 + 1.82890i
\(386\) 0 0
\(387\) 21.0923i 1.07218i
\(388\) 0 0
\(389\) −6.00000 −0.304212 −0.152106 0.988364i \(-0.548606\pi\)
−0.152106 + 0.988364i \(0.548606\pi\)
\(390\) 0 0
\(391\) 7.94868 0.401982
\(392\) 0 0
\(393\) 21.5871i 1.08892i
\(394\) 0 0
\(395\) 18.3824 + 3.63470i 0.924921 + 0.182882i
\(396\) 0 0
\(397\) 11.6914i 0.586774i −0.955994 0.293387i \(-0.905218\pi\)
0.955994 0.293387i \(-0.0947825\pi\)
\(398\) 0 0
\(399\) 74.0040 3.70484
\(400\) 0 0
\(401\) 15.4357 0.770821 0.385411 0.922745i \(-0.374060\pi\)
0.385411 + 0.922745i \(0.374060\pi\)
\(402\) 0 0
\(403\) 2.96394i 0.147644i
\(404\) 0 0
\(405\) −26.8829 5.31546i −1.33582 0.264127i
\(406\) 0 0
\(407\) 16.7402i 0.829782i
\(408\) 0 0
\(409\) −38.7678 −1.91694 −0.958472 0.285187i \(-0.907944\pi\)
−0.958472 + 0.285187i \(0.907944\pi\)
\(410\) 0 0
\(411\) 46.4913 2.29325
\(412\) 0 0
\(413\) 25.6485i 1.26208i
\(414\) 0 0
\(415\) −6.35290 + 32.1297i −0.311852 + 1.57719i
\(416\) 0 0
\(417\) 40.8555i 2.00070i
\(418\) 0 0
\(419\) 29.9296 1.46216 0.731078 0.682294i \(-0.239017\pi\)
0.731078 + 0.682294i \(0.239017\pi\)
\(420\) 0 0
\(421\) 20.8185 1.01463 0.507317 0.861760i \(-0.330637\pi\)
0.507317 + 0.861760i \(0.330637\pi\)
\(422\) 0 0
\(423\) 4.13770i 0.201182i
\(424\) 0 0
\(425\) 4.54253 11.0378i 0.220345 0.535412i
\(426\) 0 0
\(427\) 50.3138i 2.43485i
\(428\) 0 0
\(429\) 14.9388 0.721250
\(430\) 0 0
\(431\) −13.6019 −0.655179 −0.327590 0.944820i \(-0.606236\pi\)
−0.327590 + 0.944820i \(0.606236\pi\)
\(432\) 0 0
\(433\) 11.8941i 0.571592i −0.958291 0.285796i \(-0.907742\pi\)
0.958291 0.285796i \(-0.0922579\pi\)
\(434\) 0 0
\(435\) 5.23903 26.4963i 0.251192 1.27040i
\(436\) 0 0
\(437\) 24.0705i 1.15145i
\(438\) 0 0
\(439\) 6.91956 0.330252 0.165126 0.986272i \(-0.447197\pi\)
0.165126 + 0.986272i \(0.447197\pi\)
\(440\) 0 0
\(441\) 26.7292 1.27282
\(442\) 0 0
\(443\) 33.7454i 1.60329i 0.597798 + 0.801647i \(0.296043\pi\)
−0.597798 + 0.801647i \(0.703957\pi\)
\(444\) 0 0
\(445\) −18.6661 3.69078i −0.884856 0.174960i
\(446\) 0 0
\(447\) 11.0709i 0.523635i
\(448\) 0 0
\(449\) −1.63615 −0.0772147 −0.0386074 0.999254i \(-0.512292\pi\)
−0.0386074 + 0.999254i \(0.512292\pi\)
\(450\) 0 0
\(451\) 21.6514 1.01953
\(452\) 0 0
\(453\) 30.7839i 1.44635i
\(454\) 0 0
\(455\) −7.34463 1.45223i −0.344322 0.0680816i
\(456\) 0 0
\(457\) 11.7719i 0.550667i 0.961349 + 0.275334i \(0.0887884\pi\)
−0.961349 + 0.275334i \(0.911212\pi\)
\(458\) 0 0
\(459\) 24.4380 1.14067
\(460\) 0 0
\(461\) 11.9064 0.554536 0.277268 0.960793i \(-0.410571\pi\)
0.277268 + 0.960793i \(0.410571\pi\)
\(462\) 0 0
\(463\) 2.74486i 0.127565i 0.997964 + 0.0637823i \(0.0203163\pi\)
−0.997964 + 0.0637823i \(0.979684\pi\)
\(464\) 0 0
\(465\) −3.93057 + 19.8788i −0.182276 + 0.921858i
\(466\) 0 0
\(467\) 4.95063i 0.229088i −0.993418 0.114544i \(-0.963459\pi\)
0.993418 0.114544i \(-0.0365406\pi\)
\(468\) 0 0
\(469\) −34.8502 −1.60923
\(470\) 0 0
\(471\) 27.6380 1.27349
\(472\) 0 0
\(473\) 16.2339i 0.746434i
\(474\) 0 0
\(475\) −33.4251 13.7559i −1.53365 0.631163i
\(476\) 0 0
\(477\) 49.8328i 2.28169i
\(478\) 0 0
\(479\) 21.1952 0.968433 0.484216 0.874948i \(-0.339105\pi\)
0.484216 + 0.874948i \(0.339105\pi\)
\(480\) 0 0
\(481\) −3.42619 −0.156221
\(482\) 0 0
\(483\) 34.0866i 1.55099i
\(484\) 0 0
\(485\) −6.42419 + 32.4902i −0.291707 + 1.47531i
\(486\) 0 0
\(487\) 12.6795i 0.574565i −0.957846 0.287282i \(-0.907248\pi\)
0.957846 0.287282i \(-0.0927518\pi\)
\(488\) 0 0
\(489\) 30.6184 1.38461
\(490\) 0 0
\(491\) 3.29882 0.148874 0.0744368 0.997226i \(-0.476284\pi\)
0.0744368 + 0.997226i \(0.476284\pi\)
\(492\) 0 0
\(493\) 9.43088i 0.424746i
\(494\) 0 0
\(495\) 68.0391 + 13.4532i 3.05813 + 0.604674i
\(496\) 0 0
\(497\) 35.7981i 1.60576i
\(498\) 0 0
\(499\) −0.147647 −0.00660960 −0.00330480 0.999995i \(-0.501052\pi\)
−0.00330480 + 0.999995i \(0.501052\pi\)
\(500\) 0 0
\(501\) −62.2737 −2.78219
\(502\) 0 0
\(503\) 7.36671i 0.328465i 0.986422 + 0.164233i \(0.0525148\pi\)
−0.986422 + 0.164233i \(0.947485\pi\)
\(504\) 0 0
\(505\) 4.46835 + 0.883511i 0.198839 + 0.0393157i
\(506\) 0 0
\(507\) 3.05748i 0.135788i
\(508\) 0 0
\(509\) 9.53165 0.422483 0.211242 0.977434i \(-0.432249\pi\)
0.211242 + 0.977434i \(0.432249\pi\)
\(510\) 0 0
\(511\) −40.3981 −1.78711
\(512\) 0 0
\(513\) 74.0040i 3.26736i
\(514\) 0 0
\(515\) 5.79758 29.3212i 0.255472 1.29205i
\(516\) 0 0
\(517\) 3.18462i 0.140060i
\(518\) 0 0
\(519\) 13.3919 0.587839
\(520\) 0 0
\(521\) −8.43405 −0.369502 −0.184751 0.982785i \(-0.559148\pi\)
−0.184751 + 0.982785i \(0.559148\pi\)
\(522\) 0 0
\(523\) 29.2023i 1.27693i −0.769652 0.638463i \(-0.779570\pi\)
0.769652 0.638463i \(-0.220430\pi\)
\(524\) 0 0
\(525\) −47.3338 19.4799i −2.06582 0.850173i
\(526\) 0 0
\(527\) 7.07551i 0.308214i
\(528\) 0 0
\(529\) 11.9130 0.517957
\(530\) 0 0
\(531\) −48.6296 −2.11034
\(532\) 0 0
\(533\) 4.43135i 0.191943i
\(534\) 0 0
\(535\) −1.23032 + 6.22230i −0.0531912 + 0.269014i
\(536\) 0 0
\(537\) 61.8066i 2.66715i
\(538\) 0 0
\(539\) −20.5724 −0.886116
\(540\) 0 0
\(541\) 33.4019 1.43606 0.718029 0.696013i \(-0.245044\pi\)
0.718029 + 0.696013i \(0.245044\pi\)
\(542\) 0 0
\(543\) 21.9441i 0.941710i
\(544\) 0 0
\(545\) 26.4200 + 5.22395i 1.13171 + 0.223769i
\(546\) 0 0
\(547\) 0.0229604i 0.000981715i 1.00000 0.000490858i \(0.000156245\pi\)
−1.00000 0.000490858i \(0.999844\pi\)
\(548\) 0 0
\(549\) 95.3950 4.07136
\(550\) 0 0
\(551\) 28.5590 1.21665
\(552\) 0 0
\(553\) 28.0581i 1.19315i
\(554\) 0 0
\(555\) −22.9791 4.54358i −0.975407 0.192864i
\(556\) 0 0
\(557\) 21.8224i 0.924645i −0.886712 0.462323i \(-0.847016\pi\)
0.886712 0.462323i \(-0.152984\pi\)
\(558\) 0 0
\(559\) 3.32255 0.140529
\(560\) 0 0
\(561\) −35.6618 −1.50564
\(562\) 0 0
\(563\) 6.37049i 0.268484i 0.990949 + 0.134242i \(0.0428599\pi\)
−0.990949 + 0.134242i \(0.957140\pi\)
\(564\) 0 0
\(565\) −0.783780 + 3.96396i −0.0329739 + 0.166765i
\(566\) 0 0
\(567\) 41.0328i 1.72321i
\(568\) 0 0
\(569\) 15.9107 0.667012 0.333506 0.942748i \(-0.391768\pi\)
0.333506 + 0.942748i \(0.391768\pi\)
\(570\) 0 0
\(571\) 21.2484 0.889219 0.444609 0.895725i \(-0.353343\pi\)
0.444609 + 0.895725i \(0.353343\pi\)
\(572\) 0 0
\(573\) 1.66467i 0.0695427i
\(574\) 0 0
\(575\) −6.33602 + 15.3958i −0.264230 + 0.642048i
\(576\) 0 0
\(577\) 4.79713i 0.199707i −0.995002 0.0998535i \(-0.968163\pi\)
0.995002 0.0998535i \(-0.0318374\pi\)
\(578\) 0 0
\(579\) 83.8842 3.48611
\(580\) 0 0
\(581\) −49.0413 −2.03458
\(582\) 0 0
\(583\) 38.3543i 1.58847i
\(584\) 0 0
\(585\) −2.75343 + 13.9254i −0.113840 + 0.575745i
\(586\) 0 0
\(587\) 5.78432i 0.238745i −0.992850 0.119372i \(-0.961912\pi\)
0.992850 0.119372i \(-0.0380882\pi\)
\(588\) 0 0
\(589\) −21.4263 −0.882856
\(590\) 0 0
\(591\) 16.0879 0.661770
\(592\) 0 0
\(593\) 29.0463i 1.19279i −0.802692 0.596394i \(-0.796600\pi\)
0.802692 0.596394i \(-0.203400\pi\)
\(594\) 0 0
\(595\) 17.5331 + 3.46676i 0.718786 + 0.142123i
\(596\) 0 0
\(597\) 33.8661i 1.38605i
\(598\) 0 0
\(599\) −19.8878 −0.812595 −0.406298 0.913741i \(-0.633180\pi\)
−0.406298 + 0.913741i \(0.633180\pi\)
\(600\) 0 0
\(601\) 9.92217 0.404734 0.202367 0.979310i \(-0.435137\pi\)
0.202367 + 0.979310i \(0.435137\pi\)
\(602\) 0 0
\(603\) 66.0761i 2.69083i
\(604\) 0 0
\(605\) −28.2374 5.58329i −1.14801 0.226993i
\(606\) 0 0
\(607\) 0.735927i 0.0298704i −0.999888 0.0149352i \(-0.995246\pi\)
0.999888 0.0149352i \(-0.00475419\pi\)
\(608\) 0 0
\(609\) 40.4428 1.63882
\(610\) 0 0
\(611\) 0.651790 0.0263686
\(612\) 0 0
\(613\) 31.9564i 1.29071i 0.763884 + 0.645353i \(0.223290\pi\)
−0.763884 + 0.645353i \(0.776710\pi\)
\(614\) 0 0
\(615\) −5.87656 + 29.7206i −0.236966 + 1.19845i
\(616\) 0 0
\(617\) 39.5335i 1.59156i 0.605586 + 0.795780i \(0.292939\pi\)
−0.605586 + 0.795780i \(0.707061\pi\)
\(618\) 0 0
\(619\) 15.9046 0.639261 0.319630 0.947542i \(-0.396441\pi\)
0.319630 + 0.947542i \(0.396441\pi\)
\(620\) 0 0
\(621\) −34.0866 −1.36785
\(622\) 0 0
\(623\) 28.4910i 1.14147i
\(624\) 0 0
\(625\) 17.7581 + 17.5968i 0.710326 + 0.703873i
\(626\) 0 0
\(627\) 107.992i 4.31280i
\(628\) 0 0
\(629\) 8.17898 0.326117
\(630\) 0 0
\(631\) 22.3334 0.889080 0.444540 0.895759i \(-0.353367\pi\)
0.444540 + 0.895759i \(0.353367\pi\)
\(632\) 0 0
\(633\) 67.1111i 2.66743i
\(634\) 0 0
\(635\) 2.09778 10.6095i 0.0832479 0.421025i
\(636\) 0 0
\(637\) 4.21051i 0.166826i
\(638\) 0 0
\(639\) −67.8732 −2.68502
\(640\) 0 0
\(641\) −36.3089 −1.43411 −0.717057 0.697015i \(-0.754511\pi\)
−0.717057 + 0.697015i \(0.754511\pi\)
\(642\) 0 0
\(643\) 1.08977i 0.0429762i 0.999769 + 0.0214881i \(0.00684040\pi\)
−0.999769 + 0.0214881i \(0.993160\pi\)
\(644\) 0 0
\(645\) 22.2840 + 4.40614i 0.877432 + 0.173492i
\(646\) 0 0
\(647\) 43.2812i 1.70156i −0.525522 0.850780i \(-0.676130\pi\)
0.525522 0.850780i \(-0.323870\pi\)
\(648\) 0 0
\(649\) 37.4282 1.46919
\(650\) 0 0
\(651\) −30.3421 −1.18920
\(652\) 0 0
\(653\) 12.0389i 0.471117i 0.971860 + 0.235558i \(0.0756919\pi\)
−0.971860 + 0.235558i \(0.924308\pi\)
\(654\) 0 0
\(655\) −15.4877 3.06233i −0.605155 0.119655i
\(656\) 0 0
\(657\) 76.5948i 2.98825i
\(658\) 0 0
\(659\) 24.0285 0.936018 0.468009 0.883724i \(-0.344971\pi\)
0.468009 + 0.883724i \(0.344971\pi\)
\(660\) 0 0
\(661\) 30.3138 1.17907 0.589534 0.807743i \(-0.299311\pi\)
0.589534 + 0.807743i \(0.299311\pi\)
\(662\) 0 0
\(663\) 7.29882i 0.283463i
\(664\) 0 0
\(665\) 10.4982 53.0944i 0.407102 2.05891i
\(666\) 0 0
\(667\) 13.1544i 0.509340i
\(668\) 0 0
\(669\) −80.3341 −3.10589
\(670\) 0 0
\(671\) −73.4217 −2.83441
\(672\) 0 0
\(673\) 37.1274i 1.43116i −0.698533 0.715578i \(-0.746163\pi\)
0.698533 0.715578i \(-0.253837\pi\)
\(674\) 0 0
\(675\) −19.4799 + 47.3338i −0.749782 + 1.82188i
\(676\) 0 0
\(677\) 38.2899i 1.47160i 0.677198 + 0.735801i \(0.263194\pi\)
−0.677198 + 0.735801i \(0.736806\pi\)
\(678\) 0 0
\(679\) −49.5916 −1.90315
\(680\) 0 0
\(681\) −18.5454 −0.710662
\(682\) 0 0
\(683\) 28.1455i 1.07696i 0.842640 + 0.538478i \(0.181000\pi\)
−0.842640 + 0.538478i \(0.819000\pi\)
\(684\) 0 0
\(685\) 6.59524 33.3553i 0.251991 1.27444i
\(686\) 0 0
\(687\) 28.8219i 1.09962i
\(688\) 0 0
\(689\) 7.84990 0.299057
\(690\) 0 0
\(691\) −0.112517 −0.00428035 −0.00214018 0.999998i \(-0.500681\pi\)
−0.00214018 + 0.999998i \(0.500681\pi\)
\(692\) 0 0
\(693\) 103.852i 3.94500i
\(694\) 0 0
\(695\) −29.3119 5.79575i −1.11186 0.219845i
\(696\) 0 0
\(697\) 10.5785i 0.400690i
\(698\) 0 0
\(699\) −26.8495 −1.01554
\(700\) 0 0
\(701\) 8.54632 0.322790 0.161395 0.986890i \(-0.448401\pi\)
0.161395 + 0.986890i \(0.448401\pi\)
\(702\) 0 0
\(703\) 24.7679i 0.934139i
\(704\) 0 0
\(705\) 4.37149 + 0.864360i 0.164640 + 0.0325537i
\(706\) 0 0
\(707\) 6.82028i 0.256503i
\(708\) 0 0
\(709\) −21.8661 −0.821199 −0.410600 0.911816i \(-0.634681\pi\)
−0.410600 + 0.911816i \(0.634681\pi\)
\(710\) 0 0
\(711\) 53.1982 1.99509
\(712\) 0 0
\(713\) 9.86906i 0.369599i
\(714\) 0 0
\(715\) 2.11920 10.7178i 0.0792537 0.400825i
\(716\) 0 0
\(717\) 85.6297i 3.19790i
\(718\) 0 0
\(719\) 10.8799 0.405753 0.202877 0.979204i \(-0.434971\pi\)
0.202877 + 0.979204i \(0.434971\pi\)
\(720\) 0 0
\(721\) 44.7545 1.66675
\(722\) 0 0
\(723\) 12.4999i 0.464878i
\(724\) 0 0
\(725\) −18.2666 7.51751i −0.678406 0.279193i
\(726\) 0 0
\(727\) 33.9332i 1.25851i −0.777198 0.629256i \(-0.783360\pi\)
0.777198 0.629256i \(-0.216640\pi\)
\(728\) 0 0
\(729\) 16.1011 0.596338
\(730\) 0 0
\(731\) −7.93159 −0.293360
\(732\) 0 0
\(733\) 20.8495i 0.770093i −0.922897 0.385046i \(-0.874185\pi\)
0.922897 0.385046i \(-0.125815\pi\)
\(734\) 0 0
\(735\) 5.58369 28.2394i 0.205958 1.04163i
\(736\) 0 0
\(737\) 50.8561i 1.87331i
\(738\) 0 0
\(739\) −25.6545 −0.943716 −0.471858 0.881674i \(-0.656417\pi\)
−0.471858 + 0.881674i \(0.656417\pi\)
\(740\) 0 0
\(741\) −22.1026 −0.811958
\(742\) 0 0
\(743\) 24.8902i 0.913133i 0.889689 + 0.456566i \(0.150921\pi\)
−0.889689 + 0.456566i \(0.849079\pi\)
\(744\) 0 0
\(745\) −7.94283 1.57051i −0.291003 0.0575390i
\(746\) 0 0
\(747\) 92.9824i 3.40205i
\(748\) 0 0
\(749\) −9.49744 −0.347029
\(750\) 0 0
\(751\) −3.19446 −0.116568 −0.0582838 0.998300i \(-0.518563\pi\)
−0.0582838 + 0.998300i \(0.518563\pi\)
\(752\) 0 0
\(753\) 64.0894i 2.33555i
\(754\) 0 0
\(755\) −22.0859 4.36698i −0.803790 0.158931i
\(756\) 0 0
\(757\) 29.5963i 1.07569i 0.843042 + 0.537847i \(0.180762\pi\)
−0.843042 + 0.537847i \(0.819238\pi\)
\(758\) 0 0
\(759\) 49.7418 1.80551
\(760\) 0 0
\(761\) −21.5241 −0.780249 −0.390125 0.920762i \(-0.627568\pi\)
−0.390125 + 0.920762i \(0.627568\pi\)
\(762\) 0 0
\(763\) 40.3264i 1.45991i
\(764\) 0 0
\(765\) 6.57298 33.2427i 0.237647 1.20189i
\(766\) 0 0
\(767\) 7.66036i 0.276599i
\(768\) 0 0
\(769\) 34.2659 1.23566 0.617830 0.786312i \(-0.288012\pi\)
0.617830 + 0.786312i \(0.288012\pi\)
\(770\) 0 0
\(771\) 24.4380 0.880112
\(772\) 0 0
\(773\) 18.0924i 0.650739i 0.945587 + 0.325369i \(0.105489\pi\)
−0.945587 + 0.325369i \(0.894511\pi\)
\(774\) 0 0
\(775\) 13.7045 + 5.64000i 0.492281 + 0.202595i
\(776\) 0 0
\(777\) 35.0742i 1.25828i
\(778\) 0 0
\(779\) −32.0343 −1.14775
\(780\) 0 0
\(781\) 52.2393 1.86927
\(782\) 0 0
\(783\) 40.4428i 1.44531i
\(784\) 0 0
\(785\) 3.92071 19.8290i 0.139936 0.707726i
\(786\) 0 0
\(787\) 21.2551i 0.757664i 0.925465 + 0.378832i \(0.123674\pi\)
−0.925465 + 0.378832i \(0.876326\pi\)
\(788\) 0 0
\(789\) 0.379024 0.0134936
\(790\) 0 0
\(791\) −6.05040 −0.215128
\(792\) 0 0
\(793\) 15.0271i 0.533627i
\(794\) 0 0