Properties

Label 440.2.b.d.89.1
Level $440$
Weight $2$
Character 440.89
Analytic conductor $3.513$
Analytic rank $0$
Dimension $8$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [440,2,Mod(89,440)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(440, 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("440.89");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 440 = 2^{3} \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 440.b (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: \(3.51341768894\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: 8.0.47985531136.2
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} + 19x^{6} + 91x^{4} + 45x^{2} + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{5} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 89.1
Root \(-3.36007i\) of defining polynomial
Character \(\chi\) \(=\) 440.89
Dual form 440.2.b.d.89.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-3.36007i q^{3} +(-0.256321 - 2.22133i) q^{5} +1.08258i q^{7} -8.29009 q^{9} +O(q^{10})\) \(q-3.36007i q^{3} +(-0.256321 - 2.22133i) q^{5} +1.08258i q^{7} -8.29009 q^{9} +1.00000 q^{11} -4.00000i q^{13} +(-7.46382 + 0.861256i) q^{15} -0.107866i q^{17} +6.61228 q^{19} +3.63756 q^{21} +5.97235i q^{23} +(-4.86860 + 1.13874i) q^{25} +17.7751i q^{27} -7.80273 q^{29} +1.12492 q^{31} -3.36007i q^{33} +(2.40477 - 0.277489i) q^{35} -7.05494i q^{37} -13.4403 q^{39} +5.19045 q^{41} -5.52969i q^{43} +(2.12492 + 18.4150i) q^{45} -7.69486i q^{47} +5.82801 q^{49} -0.362439 q^{51} +4.77745i q^{53} +(-0.256321 - 2.22133i) q^{55} -22.2177i q^{57} +0.677809 q^{59} +0.197271 q^{61} -8.97472i q^{63} +(-8.88531 + 1.02528i) q^{65} -1.41737i q^{67} +20.0675 q^{69} -6.15020 q^{71} -6.16517i q^{73} +(3.82626 + 16.3588i) q^{75} +1.08258i q^{77} +9.35562 q^{79} +34.8553 q^{81} -13.7454i q^{83} +(-0.239607 + 0.0276484i) q^{85} +26.2177i q^{87} +1.29009 q^{89} +4.33034 q^{91} -3.77981i q^{93} +(-1.69486 - 14.6880i) q^{95} -6.60782i q^{97} -8.29009 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 14 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 14 q^{9} + 8 q^{11} - 12 q^{15} + 18 q^{19} - 14 q^{21} - 2 q^{25} - 6 q^{29} - 30 q^{31} + 30 q^{35} - 8 q^{39} + 20 q^{41} - 22 q^{45} - 18 q^{49} - 46 q^{51} - 12 q^{59} + 58 q^{61} - 8 q^{65} + 60 q^{69} - 2 q^{71} + 26 q^{75} + 40 q^{79} + 88 q^{81} - 26 q^{85} - 42 q^{89} + 8 q^{91} + 28 q^{95} - 14 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/440\mathbb{Z}\right)^\times\).

\(n\) \(111\) \(177\) \(221\) \(321\)
\(\chi(n)\) \(1\) \(-1\) \(1\) \(1\)

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
\(3\) 3.36007i 1.93994i −0.243227 0.969969i \(-0.578206\pi\)
0.243227 0.969969i \(-0.421794\pi\)
\(4\) 0 0
\(5\) −0.256321 2.22133i −0.114630 0.993408i
\(6\) 0 0
\(7\) 1.08258i 0.409178i 0.978848 + 0.204589i \(0.0655858\pi\)
−0.978848 + 0.204589i \(0.934414\pi\)
\(8\) 0 0
\(9\) −8.29009 −2.76336
\(10\) 0 0
\(11\) 1.00000 0.301511
\(12\) 0 0
\(13\) 4.00000i 1.10940i −0.832050 0.554700i \(-0.812833\pi\)
0.832050 0.554700i \(-0.187167\pi\)
\(14\) 0 0
\(15\) −7.46382 + 0.861256i −1.92715 + 0.222375i
\(16\) 0 0
\(17\) 0.107866i 0.0261614i −0.999914 0.0130807i \(-0.995836\pi\)
0.999914 0.0130807i \(-0.00416384\pi\)
\(18\) 0 0
\(19\) 6.61228 1.51696 0.758480 0.651696i \(-0.225942\pi\)
0.758480 + 0.651696i \(0.225942\pi\)
\(20\) 0 0
\(21\) 3.63756 0.793781
\(22\) 0 0
\(23\) 5.97235i 1.24532i 0.782492 + 0.622661i \(0.213948\pi\)
−0.782492 + 0.622661i \(0.786052\pi\)
\(24\) 0 0
\(25\) −4.86860 + 1.13874i −0.973720 + 0.227749i
\(26\) 0 0
\(27\) 17.7751i 3.42082i
\(28\) 0 0
\(29\) −7.80273 −1.44893 −0.724465 0.689311i \(-0.757913\pi\)
−0.724465 + 0.689311i \(0.757913\pi\)
\(30\) 0 0
\(31\) 1.12492 0.202042 0.101021 0.994884i \(-0.467789\pi\)
0.101021 + 0.994884i \(0.467789\pi\)
\(32\) 0 0
\(33\) 3.36007i 0.584914i
\(34\) 0 0
\(35\) 2.40477 0.277489i 0.406481 0.0469041i
\(36\) 0 0
\(37\) 7.05494i 1.15982i −0.814679 0.579912i \(-0.803087\pi\)
0.814679 0.579912i \(-0.196913\pi\)
\(38\) 0 0
\(39\) −13.4403 −2.15217
\(40\) 0 0
\(41\) 5.19045 0.810612 0.405306 0.914181i \(-0.367165\pi\)
0.405306 + 0.914181i \(0.367165\pi\)
\(42\) 0 0
\(43\) 5.52969i 0.843271i −0.906766 0.421635i \(-0.861456\pi\)
0.906766 0.421635i \(-0.138544\pi\)
\(44\) 0 0
\(45\) 2.12492 + 18.4150i 0.316764 + 2.74515i
\(46\) 0 0
\(47\) 7.69486i 1.12241i −0.827676 0.561206i \(-0.810338\pi\)
0.827676 0.561206i \(-0.189662\pi\)
\(48\) 0 0
\(49\) 5.82801 0.832573
\(50\) 0 0
\(51\) −0.362439 −0.0507516
\(52\) 0 0
\(53\) 4.77745i 0.656233i 0.944637 + 0.328116i \(0.106414\pi\)
−0.944637 + 0.328116i \(0.893586\pi\)
\(54\) 0 0
\(55\) −0.256321 2.22133i −0.0345623 0.299524i
\(56\) 0 0
\(57\) 22.2177i 2.94281i
\(58\) 0 0
\(59\) 0.677809 0.0882433 0.0441216 0.999026i \(-0.485951\pi\)
0.0441216 + 0.999026i \(0.485951\pi\)
\(60\) 0 0
\(61\) 0.197271 0.0252579 0.0126290 0.999920i \(-0.495980\pi\)
0.0126290 + 0.999920i \(0.495980\pi\)
\(62\) 0 0
\(63\) 8.97472i 1.13071i
\(64\) 0 0
\(65\) −8.88531 + 1.02528i −1.10209 + 0.127171i
\(66\) 0 0
\(67\) 1.41737i 0.173160i −0.996245 0.0865799i \(-0.972406\pi\)
0.996245 0.0865799i \(-0.0275938\pi\)
\(68\) 0 0
\(69\) 20.0675 2.41585
\(70\) 0 0
\(71\) −6.15020 −0.729895 −0.364947 0.931028i \(-0.618913\pi\)
−0.364947 + 0.931028i \(0.618913\pi\)
\(72\) 0 0
\(73\) 6.16517i 0.721578i −0.932647 0.360789i \(-0.882507\pi\)
0.932647 0.360789i \(-0.117493\pi\)
\(74\) 0 0
\(75\) 3.82626 + 16.3588i 0.441819 + 1.88896i
\(76\) 0 0
\(77\) 1.08258i 0.123372i
\(78\) 0 0
\(79\) 9.35562 1.05259 0.526295 0.850302i \(-0.323581\pi\)
0.526295 + 0.850302i \(0.323581\pi\)
\(80\) 0 0
\(81\) 34.8553 3.87281
\(82\) 0 0
\(83\) 13.7454i 1.50876i −0.656440 0.754378i \(-0.727938\pi\)
0.656440 0.754378i \(-0.272062\pi\)
\(84\) 0 0
\(85\) −0.239607 + 0.0276484i −0.0259890 + 0.00299889i
\(86\) 0 0
\(87\) 26.2177i 2.81084i
\(88\) 0 0
\(89\) 1.29009 0.136749 0.0683745 0.997660i \(-0.478219\pi\)
0.0683745 + 0.997660i \(0.478219\pi\)
\(90\) 0 0
\(91\) 4.33034 0.453943
\(92\) 0 0
\(93\) 3.77981i 0.391948i
\(94\) 0 0
\(95\) −1.69486 14.6880i −0.173889 1.50696i
\(96\) 0 0
\(97\) 6.60782i 0.670923i −0.942054 0.335461i \(-0.891108\pi\)
0.942054 0.335461i \(-0.108892\pi\)
\(98\) 0 0
\(99\) −8.29009 −0.833185
\(100\) 0 0
\(101\) −15.4403 −1.53637 −0.768183 0.640230i \(-0.778839\pi\)
−0.768183 + 0.640230i \(0.778839\pi\)
\(102\) 0 0
\(103\) 5.74543i 0.566114i 0.959103 + 0.283057i \(0.0913485\pi\)
−0.959103 + 0.283057i \(0.908651\pi\)
\(104\) 0 0
\(105\) −0.932382 8.08022i −0.0909911 0.788549i
\(106\) 0 0
\(107\) 4.30514i 0.416193i 0.978108 + 0.208097i \(0.0667269\pi\)
−0.978108 + 0.208097i \(0.933273\pi\)
\(108\) 0 0
\(109\) 2.33034 0.223206 0.111603 0.993753i \(-0.464402\pi\)
0.111603 + 0.993753i \(0.464402\pi\)
\(110\) 0 0
\(111\) −23.7051 −2.24999
\(112\) 0 0
\(113\) 10.9471i 1.02981i −0.857246 0.514907i \(-0.827827\pi\)
0.857246 0.514907i \(-0.172173\pi\)
\(114\) 0 0
\(115\) 13.2666 1.53084i 1.23711 0.142751i
\(116\) 0 0
\(117\) 33.1604i 3.06568i
\(118\) 0 0
\(119\) 0.116774 0.0107047
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) 0 0
\(123\) 17.4403i 1.57254i
\(124\) 0 0
\(125\) 3.77745 + 10.5229i 0.337865 + 0.941195i
\(126\) 0 0
\(127\) 12.5802i 1.11631i 0.829737 + 0.558155i \(0.188491\pi\)
−0.829737 + 0.558155i \(0.811509\pi\)
\(128\) 0 0
\(129\) −18.5802 −1.63589
\(130\) 0 0
\(131\) 15.2430 1.33179 0.665894 0.746046i \(-0.268050\pi\)
0.665894 + 0.746046i \(0.268050\pi\)
\(132\) 0 0
\(133\) 7.15835i 0.620707i
\(134\) 0 0
\(135\) 39.4843 4.55612i 3.39827 0.392128i
\(136\) 0 0
\(137\) 14.6078i 1.24803i 0.781412 + 0.624015i \(0.214500\pi\)
−0.781412 + 0.624015i \(0.785500\pi\)
\(138\) 0 0
\(139\) 20.4150 1.73158 0.865789 0.500409i \(-0.166817\pi\)
0.865789 + 0.500409i \(0.166817\pi\)
\(140\) 0 0
\(141\) −25.8553 −2.17741
\(142\) 0 0
\(143\) 4.00000i 0.334497i
\(144\) 0 0
\(145\) 2.00000 + 17.3324i 0.166091 + 1.43938i
\(146\) 0 0
\(147\) 19.5825i 1.61514i
\(148\) 0 0
\(149\) 15.8874 1.30155 0.650773 0.759272i \(-0.274445\pi\)
0.650773 + 0.759272i \(0.274445\pi\)
\(150\) 0 0
\(151\) 6.58018 0.535487 0.267744 0.963490i \(-0.413722\pi\)
0.267744 + 0.963490i \(0.413722\pi\)
\(152\) 0 0
\(153\) 0.894222i 0.0722935i
\(154\) 0 0
\(155\) −0.288340 2.49882i −0.0231600 0.200710i
\(156\) 0 0
\(157\) 6.38535i 0.509607i 0.966993 + 0.254803i \(0.0820108\pi\)
−0.966993 + 0.254803i \(0.917989\pi\)
\(158\) 0 0
\(159\) 16.0526 1.27305
\(160\) 0 0
\(161\) −6.46557 −0.509559
\(162\) 0 0
\(163\) 18.3071i 1.43393i 0.697111 + 0.716963i \(0.254468\pi\)
−0.697111 + 0.716963i \(0.745532\pi\)
\(164\) 0 0
\(165\) −7.46382 + 0.861256i −0.581058 + 0.0670487i
\(166\) 0 0
\(167\) 0.197271i 0.0152653i 0.999971 + 0.00763263i \(0.00242956\pi\)
−0.999971 + 0.00763263i \(0.997570\pi\)
\(168\) 0 0
\(169\) −3.00000 −0.230769
\(170\) 0 0
\(171\) −54.8164 −4.19191
\(172\) 0 0
\(173\) 14.7201i 1.11915i −0.828779 0.559576i \(-0.810964\pi\)
0.828779 0.559576i \(-0.189036\pi\)
\(174\) 0 0
\(175\) −1.23279 5.27067i −0.0931899 0.398425i
\(176\) 0 0
\(177\) 2.27749i 0.171187i
\(178\) 0 0
\(179\) −11.8518 −0.885845 −0.442923 0.896560i \(-0.646058\pi\)
−0.442923 + 0.896560i \(0.646058\pi\)
\(180\) 0 0
\(181\) −10.7625 −0.799969 −0.399984 0.916522i \(-0.630984\pi\)
−0.399984 + 0.916522i \(0.630984\pi\)
\(182\) 0 0
\(183\) 0.662843i 0.0489988i
\(184\) 0 0
\(185\) −15.6713 + 1.80833i −1.15218 + 0.132951i
\(186\) 0 0
\(187\) 0.107866i 0.00788797i
\(188\) 0 0
\(189\) −19.2430 −1.39972
\(190\) 0 0
\(191\) 1.70309 0.123231 0.0616157 0.998100i \(-0.480375\pi\)
0.0616157 + 0.998100i \(0.480375\pi\)
\(192\) 0 0
\(193\) 10.8280i 0.779417i −0.920938 0.389709i \(-0.872576\pi\)
0.920938 0.389709i \(-0.127424\pi\)
\(194\) 0 0
\(195\) 3.44502 + 29.8553i 0.246703 + 2.13798i
\(196\) 0 0
\(197\) 6.72015i 0.478791i −0.970922 0.239395i \(-0.923051\pi\)
0.970922 0.239395i \(-0.0769492\pi\)
\(198\) 0 0
\(199\) 10.8280 0.767577 0.383789 0.923421i \(-0.374619\pi\)
0.383789 + 0.923421i \(0.374619\pi\)
\(200\) 0 0
\(201\) −4.76248 −0.335920
\(202\) 0 0
\(203\) 8.44711i 0.592871i
\(204\) 0 0
\(205\) −1.33042 11.5297i −0.0929205 0.805269i
\(206\) 0 0
\(207\) 49.5113i 3.44127i
\(208\) 0 0
\(209\) 6.61228 0.457381
\(210\) 0 0
\(211\) 0.447111 0.0307804 0.0153902 0.999882i \(-0.495101\pi\)
0.0153902 + 0.999882i \(0.495101\pi\)
\(212\) 0 0
\(213\) 20.6651i 1.41595i
\(214\) 0 0
\(215\) −12.2833 + 1.41737i −0.837712 + 0.0966641i
\(216\) 0 0
\(217\) 1.21782i 0.0826710i
\(218\) 0 0
\(219\) −20.7154 −1.39982
\(220\) 0 0
\(221\) −0.431465 −0.0290235
\(222\) 0 0
\(223\) 17.8577i 1.19584i 0.801555 + 0.597922i \(0.204007\pi\)
−0.801555 + 0.597922i \(0.795993\pi\)
\(224\) 0 0
\(225\) 40.3611 9.44029i 2.69074 0.629353i
\(226\) 0 0
\(227\) 1.31396i 0.0872107i 0.999049 + 0.0436054i \(0.0138844\pi\)
−0.999049 + 0.0436054i \(0.986116\pi\)
\(228\) 0 0
\(229\) −4.84298 −0.320033 −0.160016 0.987114i \(-0.551155\pi\)
−0.160016 + 0.987114i \(0.551155\pi\)
\(230\) 0 0
\(231\) 3.63756 0.239334
\(232\) 0 0
\(233\) 20.3829i 1.33533i 0.744462 + 0.667664i \(0.232706\pi\)
−0.744462 + 0.667664i \(0.767294\pi\)
\(234\) 0 0
\(235\) −17.0928 + 1.97235i −1.11501 + 0.128662i
\(236\) 0 0
\(237\) 31.4356i 2.04196i
\(238\) 0 0
\(239\) 9.35562 0.605165 0.302582 0.953123i \(-0.402151\pi\)
0.302582 + 0.953123i \(0.402151\pi\)
\(240\) 0 0
\(241\) 22.3004 1.43650 0.718248 0.695788i \(-0.244944\pi\)
0.718248 + 0.695788i \(0.244944\pi\)
\(242\) 0 0
\(243\) 63.7911i 4.09220i
\(244\) 0 0
\(245\) −1.49384 12.9459i −0.0954379 0.827085i
\(246\) 0 0
\(247\) 26.4491i 1.68292i
\(248\) 0 0
\(249\) −46.1856 −2.92690
\(250\) 0 0
\(251\) −10.9276 −0.689747 −0.344874 0.938649i \(-0.612078\pi\)
−0.344874 + 0.938649i \(0.612078\pi\)
\(252\) 0 0
\(253\) 5.97235i 0.375479i
\(254\) 0 0
\(255\) 0.0929005 + 0.805096i 0.00581766 + 0.0504170i
\(256\) 0 0
\(257\) 21.4403i 1.33741i 0.743528 + 0.668704i \(0.233151\pi\)
−0.743528 + 0.668704i \(0.766849\pi\)
\(258\) 0 0
\(259\) 7.63756 0.474575
\(260\) 0 0
\(261\) 64.6853 4.00392
\(262\) 0 0
\(263\) 6.52287i 0.402218i 0.979569 + 0.201109i \(0.0644545\pi\)
−0.979569 + 0.201109i \(0.935546\pi\)
\(264\) 0 0
\(265\) 10.6123 1.22456i 0.651907 0.0752240i
\(266\) 0 0
\(267\) 4.33479i 0.265285i
\(268\) 0 0
\(269\) −5.60546 −0.341771 −0.170885 0.985291i \(-0.554663\pi\)
−0.170885 + 0.985291i \(0.554663\pi\)
\(270\) 0 0
\(271\) −28.9446 −1.75826 −0.879130 0.476582i \(-0.841876\pi\)
−0.879130 + 0.476582i \(0.841876\pi\)
\(272\) 0 0
\(273\) 14.5502i 0.880621i
\(274\) 0 0
\(275\) −4.86860 + 1.13874i −0.293588 + 0.0686689i
\(276\) 0 0
\(277\) 25.3850i 1.52524i 0.646849 + 0.762618i \(0.276086\pi\)
−0.646849 + 0.762618i \(0.723914\pi\)
\(278\) 0 0
\(279\) −9.32569 −0.558314
\(280\) 0 0
\(281\) −27.1604 −1.62025 −0.810125 0.586257i \(-0.800601\pi\)
−0.810125 + 0.586257i \(0.800601\pi\)
\(282\) 0 0
\(283\) 22.0205i 1.30898i 0.756070 + 0.654490i \(0.227117\pi\)
−0.756070 + 0.654490i \(0.772883\pi\)
\(284\) 0 0
\(285\) −49.3529 + 5.69486i −2.92341 + 0.337335i
\(286\) 0 0
\(287\) 5.61910i 0.331685i
\(288\) 0 0
\(289\) 16.9884 0.999316
\(290\) 0 0
\(291\) −22.2028 −1.30155
\(292\) 0 0
\(293\) 1.44029i 0.0841427i −0.999115 0.0420713i \(-0.986604\pi\)
0.999115 0.0420713i \(-0.0133957\pi\)
\(294\) 0 0
\(295\) −0.173736 1.50564i −0.0101153 0.0876616i
\(296\) 0 0
\(297\) 17.7751i 1.03141i
\(298\) 0 0
\(299\) 23.8894 1.38156
\(300\) 0 0
\(301\) 5.98636 0.345048
\(302\) 0 0
\(303\) 51.8805i 2.98046i
\(304\) 0 0
\(305\) −0.0505645 0.438203i −0.00289532 0.0250914i
\(306\) 0 0
\(307\) 2.80955i 0.160349i −0.996781 0.0801747i \(-0.974452\pi\)
0.996781 0.0801747i \(-0.0255478\pi\)
\(308\) 0 0
\(309\) 19.3051 1.09823
\(310\) 0 0
\(311\) −11.5529 −0.655104 −0.327552 0.944833i \(-0.606224\pi\)
−0.327552 + 0.944833i \(0.606224\pi\)
\(312\) 0 0
\(313\) 26.1580i 1.47854i −0.673411 0.739268i \(-0.735171\pi\)
0.673411 0.739268i \(-0.264829\pi\)
\(314\) 0 0
\(315\) −19.9358 + 2.30040i −1.12325 + 0.129613i
\(316\) 0 0
\(317\) 29.3805i 1.65018i 0.565005 + 0.825088i \(0.308874\pi\)
−0.565005 + 0.825088i \(0.691126\pi\)
\(318\) 0 0
\(319\) −7.80273 −0.436869
\(320\) 0 0
\(321\) 14.4656 0.807390
\(322\) 0 0
\(323\) 0.713242i 0.0396859i
\(324\) 0 0
\(325\) 4.55498 + 19.4744i 0.252665 + 1.08025i
\(326\) 0 0
\(327\) 7.83010i 0.433005i
\(328\) 0 0
\(329\) 8.33034 0.459266
\(330\) 0 0
\(331\) 12.2833 0.675149 0.337575 0.941299i \(-0.390393\pi\)
0.337575 + 0.941299i \(0.390393\pi\)
\(332\) 0 0
\(333\) 58.4860i 3.20502i
\(334\) 0 0
\(335\) −3.14845 + 0.363302i −0.172018 + 0.0198493i
\(336\) 0 0
\(337\) 21.3324i 1.16205i −0.813885 0.581026i \(-0.802652\pi\)
0.813885 0.581026i \(-0.197348\pi\)
\(338\) 0 0
\(339\) −36.7829 −1.99778
\(340\) 0 0
\(341\) 1.12492 0.0609178
\(342\) 0 0
\(343\) 13.8874i 0.749849i
\(344\) 0 0
\(345\) −5.14372 44.5766i −0.276929 2.39992i
\(346\) 0 0
\(347\) 10.4150i 0.559107i 0.960130 + 0.279553i \(0.0901864\pi\)
−0.960130 + 0.279553i \(0.909814\pi\)
\(348\) 0 0
\(349\) 13.4909 0.722149 0.361074 0.932537i \(-0.382410\pi\)
0.361074 + 0.932537i \(0.382410\pi\)
\(350\) 0 0
\(351\) 71.1003 3.79505
\(352\) 0 0
\(353\) 12.7177i 0.676895i 0.940985 + 0.338447i \(0.109902\pi\)
−0.940985 + 0.338447i \(0.890098\pi\)
\(354\) 0 0
\(355\) 1.57642 + 13.6616i 0.0836679 + 0.725083i
\(356\) 0 0
\(357\) 0.392370i 0.0207664i
\(358\) 0 0
\(359\) 19.8212 1.04612 0.523061 0.852295i \(-0.324790\pi\)
0.523061 + 0.852295i \(0.324790\pi\)
\(360\) 0 0
\(361\) 24.7222 1.30117
\(362\) 0 0
\(363\) 3.36007i 0.176358i
\(364\) 0 0
\(365\) −13.6949 + 1.58026i −0.716822 + 0.0827146i
\(366\) 0 0
\(367\) 10.3027i 0.537796i 0.963169 + 0.268898i \(0.0866594\pi\)
−0.963169 + 0.268898i \(0.913341\pi\)
\(368\) 0 0
\(369\) −43.0293 −2.24002
\(370\) 0 0
\(371\) −5.17199 −0.268516
\(372\) 0 0
\(373\) 23.3344i 1.20821i −0.796904 0.604105i \(-0.793531\pi\)
0.796904 0.604105i \(-0.206469\pi\)
\(374\) 0 0
\(375\) 35.3576 12.6925i 1.82586 0.655438i
\(376\) 0 0
\(377\) 31.2109i 1.60744i
\(378\) 0 0
\(379\) 21.2074 1.08935 0.544676 0.838647i \(-0.316653\pi\)
0.544676 + 0.838647i \(0.316653\pi\)
\(380\) 0 0
\(381\) 42.2703 2.16557
\(382\) 0 0
\(383\) 0.972434i 0.0496891i 0.999691 + 0.0248445i \(0.00790908\pi\)
−0.999691 + 0.0248445i \(0.992091\pi\)
\(384\) 0 0
\(385\) 2.40477 0.277489i 0.122559 0.0141421i
\(386\) 0 0
\(387\) 45.8417i 2.33026i
\(388\) 0 0
\(389\) −2.76248 −0.140063 −0.0700317 0.997545i \(-0.522310\pi\)
−0.0700317 + 0.997545i \(0.522310\pi\)
\(390\) 0 0
\(391\) 0.644216 0.0325794
\(392\) 0 0
\(393\) 51.2177i 2.58359i
\(394\) 0 0
\(395\) −2.39804 20.7819i −0.120658 1.04565i
\(396\) 0 0
\(397\) 11.2751i 0.565882i −0.959137 0.282941i \(-0.908690\pi\)
0.959137 0.282941i \(-0.0913101\pi\)
\(398\) 0 0
\(399\) 24.0526 1.20413
\(400\) 0 0
\(401\) −10.4471 −0.521704 −0.260852 0.965379i \(-0.584003\pi\)
−0.260852 + 0.965379i \(0.584003\pi\)
\(402\) 0 0
\(403\) 4.49968i 0.224145i
\(404\) 0 0
\(405\) −8.93413 77.4251i −0.443940 3.84728i
\(406\) 0 0
\(407\) 7.05494i 0.349700i
\(408\) 0 0
\(409\) 1.27512 0.0630507 0.0315254 0.999503i \(-0.489963\pi\)
0.0315254 + 0.999503i \(0.489963\pi\)
\(410\) 0 0
\(411\) 49.0834 2.42110
\(412\) 0 0
\(413\) 0.733786i 0.0361072i
\(414\) 0 0
\(415\) −30.5331 + 3.52324i −1.49881 + 0.172949i
\(416\) 0 0
\(417\) 68.5959i 3.35916i
\(418\) 0 0
\(419\) −18.7795 −0.917436 −0.458718 0.888582i \(-0.651691\pi\)
−0.458718 + 0.888582i \(0.651691\pi\)
\(420\) 0 0
\(421\) −1.27512 −0.0621457 −0.0310728 0.999517i \(-0.509892\pi\)
−0.0310728 + 0.999517i \(0.509892\pi\)
\(422\) 0 0
\(423\) 63.7911i 3.10163i
\(424\) 0 0
\(425\) 0.122832 + 0.525158i 0.00595824 + 0.0254739i
\(426\) 0 0
\(427\) 0.213562i 0.0103350i
\(428\) 0 0
\(429\) −13.4403 −0.648903
\(430\) 0 0
\(431\) 1.63556 0.0787820 0.0393910 0.999224i \(-0.487458\pi\)
0.0393910 + 0.999224i \(0.487458\pi\)
\(432\) 0 0
\(433\) 26.4932i 1.27318i 0.771201 + 0.636591i \(0.219656\pi\)
−0.771201 + 0.636591i \(0.780344\pi\)
\(434\) 0 0
\(435\) 58.2382 6.72015i 2.79231 0.322206i
\(436\) 0 0
\(437\) 39.4909i 1.88910i
\(438\) 0 0
\(439\) −31.9358 −1.52421 −0.762106 0.647452i \(-0.775835\pi\)
−0.762106 + 0.647452i \(0.775835\pi\)
\(440\) 0 0
\(441\) −48.3147 −2.30070
\(442\) 0 0
\(443\) 2.02765i 0.0963365i 0.998839 + 0.0481682i \(0.0153384\pi\)
−0.998839 + 0.0481682i \(0.984662\pi\)
\(444\) 0 0
\(445\) −0.330676 2.86571i −0.0156756 0.135848i
\(446\) 0 0
\(447\) 53.3828i 2.52492i
\(448\) 0 0
\(449\) 10.0675 0.475116 0.237558 0.971373i \(-0.423653\pi\)
0.237558 + 0.971373i \(0.423653\pi\)
\(450\) 0 0
\(451\) 5.19045 0.244409
\(452\) 0 0
\(453\) 22.1099i 1.03881i
\(454\) 0 0
\(455\) −1.10995 9.61910i −0.0520355 0.450950i
\(456\) 0 0
\(457\) 6.04839i 0.282932i −0.989943 0.141466i \(-0.954818\pi\)
0.989943 0.141466i \(-0.0451816\pi\)
\(458\) 0 0
\(459\) 1.91733 0.0894934
\(460\) 0 0
\(461\) 31.8397 1.48292 0.741460 0.670997i \(-0.234134\pi\)
0.741460 + 0.670997i \(0.234134\pi\)
\(462\) 0 0
\(463\) 30.2474i 1.40572i −0.711330 0.702858i \(-0.751907\pi\)
0.711330 0.702858i \(-0.248093\pi\)
\(464\) 0 0
\(465\) −8.39621 + 0.968844i −0.389365 + 0.0449291i
\(466\) 0 0
\(467\) 31.3417i 1.45032i −0.688580 0.725160i \(-0.741766\pi\)
0.688580 0.725160i \(-0.258234\pi\)
\(468\) 0 0
\(469\) 1.53443 0.0708533
\(470\) 0 0
\(471\) 21.4553 0.988606
\(472\) 0 0
\(473\) 5.52969i 0.254256i
\(474\) 0 0
\(475\) −32.1925 + 7.52969i −1.47709 + 0.345486i
\(476\) 0 0
\(477\) 39.6055i 1.81341i
\(478\) 0 0
\(479\) −6.59663 −0.301408 −0.150704 0.988579i \(-0.548154\pi\)
−0.150704 + 0.988579i \(0.548154\pi\)
\(480\) 0 0
\(481\) −28.2197 −1.28671
\(482\) 0 0
\(483\) 21.7248i 0.988512i
\(484\) 0 0
\(485\) −14.6781 + 1.69372i −0.666500 + 0.0769079i
\(486\) 0 0
\(487\) 1.13343i 0.0513605i −0.999670 0.0256802i \(-0.991825\pi\)
0.999670 0.0256802i \(-0.00817517\pi\)
\(488\) 0 0
\(489\) 61.5133 2.78173
\(490\) 0 0
\(491\) 43.5569 1.96570 0.982848 0.184419i \(-0.0590404\pi\)
0.982848 + 0.184419i \(0.0590404\pi\)
\(492\) 0 0
\(493\) 0.841652i 0.0379061i
\(494\) 0 0
\(495\) 2.12492 + 18.4150i 0.0955081 + 0.827693i
\(496\) 0 0
\(497\) 6.65811i 0.298657i
\(498\) 0 0
\(499\) 34.5502 1.54668 0.773341 0.633991i \(-0.218584\pi\)
0.773341 + 0.633991i \(0.218584\pi\)
\(500\) 0 0
\(501\) 0.662843 0.0296137
\(502\) 0 0
\(503\) 5.92424i 0.264149i −0.991240 0.132074i \(-0.957836\pi\)
0.991240 0.132074i \(-0.0421638\pi\)
\(504\) 0 0
\(505\) 3.95766 + 34.2980i 0.176114 + 1.52624i
\(506\) 0 0
\(507\) 10.0802i 0.447678i
\(508\) 0 0
\(509\) 42.3679 1.87793 0.938963 0.344018i \(-0.111788\pi\)
0.938963 + 0.344018i \(0.111788\pi\)
\(510\) 0 0
\(511\) 6.67431 0.295254
\(512\) 0 0
\(513\) 117.534i 5.18924i
\(514\) 0 0
\(515\) 12.7625 1.47267i 0.562382 0.0648936i
\(516\) 0 0
\(517\) 7.69486i 0.338420i
\(518\) 0 0
\(519\) −49.4608 −2.17109
\(520\) 0 0
\(521\) 21.2116 0.929297 0.464648 0.885495i \(-0.346181\pi\)
0.464648 + 0.885495i \(0.346181\pi\)
\(522\) 0 0
\(523\) 5.19045i 0.226963i 0.993540 + 0.113481i \(0.0362002\pi\)
−0.993540 + 0.113481i \(0.963800\pi\)
\(524\) 0 0
\(525\) −17.7098 + 4.14225i −0.772920 + 0.180783i
\(526\) 0 0
\(527\) 0.121341i 0.00528570i
\(528\) 0 0
\(529\) −12.6690 −0.550825
\(530\) 0 0
\(531\) −5.61910 −0.243848
\(532\) 0 0
\(533\) 20.7618i 0.899293i
\(534\) 0 0
\(535\) 9.56312 1.10350i 0.413450 0.0477083i
\(536\) 0 0
\(537\) 39.8229i 1.71849i
\(538\) 0 0
\(539\) 5.82801 0.251030
\(540\) 0 0
\(541\) −24.0185 −1.03263 −0.516317 0.856397i \(-0.672697\pi\)
−0.516317 + 0.856397i \(0.672697\pi\)
\(542\) 0 0
\(543\) 36.1627i 1.55189i
\(544\) 0 0
\(545\) −0.597313 5.17644i −0.0255861 0.221734i
\(546\) 0 0
\(547\) 12.8601i 0.549859i −0.961464 0.274929i \(-0.911346\pi\)
0.961464 0.274929i \(-0.0886545\pi\)
\(548\) 0 0
\(549\) −1.63539 −0.0697968
\(550\) 0 0
\(551\) −51.5938 −2.19797
\(552\) 0 0
\(553\) 10.1282i 0.430697i
\(554\) 0 0
\(555\) 6.07610 + 52.6568i 0.257916 + 2.23516i
\(556\) 0 0
\(557\) 31.3344i 1.32768i −0.747874 0.663841i \(-0.768925\pi\)
0.747874 0.663841i \(-0.231075\pi\)
\(558\) 0 0
\(559\) −22.1188 −0.935525
\(560\) 0 0
\(561\) −0.362439 −0.0153022
\(562\) 0 0
\(563\) 17.6901i 0.745550i 0.927922 + 0.372775i \(0.121594\pi\)
−0.927922 + 0.372775i \(0.878406\pi\)
\(564\) 0 0
\(565\) −24.3170 + 2.80596i −1.02303 + 0.118048i
\(566\) 0 0
\(567\) 37.7338i 1.58467i
\(568\) 0 0
\(569\) −26.3004 −1.10257 −0.551285 0.834317i \(-0.685862\pi\)
−0.551285 + 0.834317i \(0.685862\pi\)
\(570\) 0 0
\(571\) −35.9884 −1.50607 −0.753033 0.657983i \(-0.771410\pi\)
−0.753033 + 0.657983i \(0.771410\pi\)
\(572\) 0 0
\(573\) 5.72251i 0.239061i
\(574\) 0 0
\(575\) −6.80098 29.0770i −0.283621 1.21259i
\(576\) 0 0
\(577\) 32.6031i 1.35728i −0.734469 0.678642i \(-0.762569\pi\)
0.734469 0.678642i \(-0.237431\pi\)
\(578\) 0 0
\(579\) −36.3829 −1.51202
\(580\) 0 0
\(581\) 14.8806 0.617351
\(582\) 0 0
\(583\) 4.77745i 0.197862i
\(584\) 0 0
\(585\) 73.6600 8.49968i 3.04547 0.351419i
\(586\) 0 0
\(587\) 17.6287i 0.727612i 0.931475 + 0.363806i \(0.118523\pi\)
−0.931475 + 0.363806i \(0.881477\pi\)
\(588\) 0 0
\(589\) 7.43829 0.306489
\(590\) 0 0
\(591\) −22.5802 −0.928824
\(592\) 0 0
\(593\) 13.2246i 0.543068i −0.962429 0.271534i \(-0.912469\pi\)
0.962429 0.271534i \(-0.0875309\pi\)
\(594\) 0 0
\(595\) −0.0299317 0.259394i −0.00122708 0.0106341i
\(596\) 0 0
\(597\) 36.3829i 1.48905i
\(598\) 0 0
\(599\) −37.2771 −1.52310 −0.761551 0.648105i \(-0.775562\pi\)
−0.761551 + 0.648105i \(0.775562\pi\)
\(600\) 0 0
\(601\) 17.0594 0.695867 0.347934 0.937519i \(-0.386883\pi\)
0.347934 + 0.937519i \(0.386883\pi\)
\(602\) 0 0
\(603\) 11.7502i 0.478503i
\(604\) 0 0
\(605\) −0.256321 2.22133i −0.0104209 0.0903098i
\(606\) 0 0
\(607\) 7.92624i 0.321716i 0.986978 + 0.160858i \(0.0514262\pi\)
−0.986978 + 0.160858i \(0.948574\pi\)
\(608\) 0 0
\(609\) −28.3829 −1.15013
\(610\) 0 0
\(611\) −30.7795 −1.24520
\(612\) 0 0
\(613\) 9.93596i 0.401310i −0.979662 0.200655i \(-0.935693\pi\)
0.979662 0.200655i \(-0.0643070\pi\)
\(614\) 0 0
\(615\) −38.7406 + 4.47031i −1.56217 + 0.180260i
\(616\) 0 0
\(617\) 38.1010i 1.53389i 0.641715 + 0.766944i \(0.278223\pi\)
−0.641715 + 0.766944i \(0.721777\pi\)
\(618\) 0 0
\(619\) −5.70309 −0.229227 −0.114613 0.993410i \(-0.536563\pi\)
−0.114613 + 0.993410i \(0.536563\pi\)
\(620\) 0 0
\(621\) −106.159 −4.26002
\(622\) 0 0
\(623\) 1.39663i 0.0559548i
\(624\) 0 0
\(625\) 22.4065 11.0882i 0.896261 0.443527i
\(626\) 0 0
\(627\) 22.2177i 0.887291i
\(628\) 0 0
\(629\) −0.760990 −0.0303427
\(630\) 0 0
\(631\) 17.3242 0.689665 0.344833 0.938664i \(-0.387936\pi\)
0.344833 + 0.938664i \(0.387936\pi\)
\(632\) 0 0
\(633\) 1.50232i 0.0597120i
\(634\) 0 0
\(635\) 27.9447 3.22456i 1.10895 0.127963i
\(636\) 0 0
\(637\) 23.3120i 0.923657i
\(638\) 0 0
\(639\) 50.9857 2.01696
\(640\) 0 0
\(641\) −22.3523 −0.882863 −0.441431 0.897295i \(-0.645529\pi\)
−0.441431 + 0.897295i \(0.645529\pi\)
\(642\) 0 0
\(643\) 25.2911i 0.997385i 0.866779 + 0.498693i \(0.166186\pi\)
−0.866779 + 0.498693i \(0.833814\pi\)
\(644\) 0 0
\(645\) 4.76248 + 41.2727i 0.187523 + 1.62511i
\(646\) 0 0
\(647\) 22.4262i 0.881665i 0.897589 + 0.440832i \(0.145317\pi\)
−0.897589 + 0.440832i \(0.854683\pi\)
\(648\) 0 0
\(649\) 0.677809 0.0266063
\(650\) 0 0
\(651\) 4.09197 0.160377
\(652\) 0 0
\(653\) 11.8391i 0.463301i −0.972799 0.231650i \(-0.925587\pi\)
0.972799 0.231650i \(-0.0744125\pi\)
\(654\) 0 0
\(655\) −3.90710 33.8598i −0.152663 1.32301i
\(656\) 0 0
\(657\) 51.1098i 1.99398i
\(658\) 0 0
\(659\) 15.7522 0.613617 0.306809 0.951771i \(-0.400739\pi\)
0.306809 + 0.951771i \(0.400739\pi\)
\(660\) 0 0
\(661\) −7.15702 −0.278376 −0.139188 0.990266i \(-0.544449\pi\)
−0.139188 + 0.990266i \(0.544449\pi\)
\(662\) 0 0
\(663\) 1.44976i 0.0563038i
\(664\) 0 0
\(665\) 15.9010 1.83483i 0.616616 0.0711517i
\(666\) 0 0
\(667\) 46.6006i 1.80438i
\(668\) 0 0
\(669\) 60.0033 2.31986
\(670\) 0 0
\(671\) 0.197271 0.00761555
\(672\) 0 0
\(673\) 11.4976i 0.443200i 0.975138 + 0.221600i \(0.0711279\pi\)
−0.975138 + 0.221600i \(0.928872\pi\)
\(674\) 0 0
\(675\) −20.2413 86.5398i −0.779087 3.33092i
\(676\) 0 0
\(677\) 21.9953i 0.845347i −0.906282 0.422673i \(-0.861092\pi\)
0.906282 0.422673i \(-0.138908\pi\)
\(678\) 0 0
\(679\) 7.15353 0.274527
\(680\) 0 0
\(681\) 4.41501 0.169183
\(682\) 0 0
\(683\) 0.468300i 0.0179190i −0.999960 0.00895950i \(-0.997148\pi\)
0.999960 0.00895950i \(-0.00285194\pi\)
\(684\) 0 0
\(685\) 32.4488 3.74429i 1.23980 0.143062i
\(686\) 0 0
\(687\) 16.2728i 0.620844i
\(688\) 0 0
\(689\) 19.1098 0.728025
\(690\) 0 0
\(691\) −36.9140 −1.40428 −0.702138 0.712041i \(-0.747771\pi\)
−0.702138 + 0.712041i \(0.747771\pi\)
\(692\) 0 0
\(693\) 8.97472i 0.340921i
\(694\) 0 0
\(695\) −5.23279 45.3484i −0.198491 1.72016i
\(696\) 0 0
\(697\) 0.559875i 0.0212068i
\(698\) 0 0
\(699\) 68.4880 2.59046
\(700\) 0 0
\(701\) 18.6628 0.704886 0.352443 0.935833i \(-0.385351\pi\)
0.352443 + 0.935833i \(0.385351\pi\)
\(702\) 0 0
\(703\) 46.6492i 1.75941i
\(704\) 0 0
\(705\) 6.62724 + 57.4331i 0.249596 + 2.16306i
\(706\) 0 0
\(707\) 16.7154i 0.628648i
\(708\) 0 0
\(709\) −6.66135 −0.250172 −0.125086 0.992146i \(-0.539921\pi\)
−0.125086 + 0.992146i \(0.539921\pi\)
\(710\) 0 0
\(711\) −77.5589 −2.90869
\(712\) 0 0
\(713\) 6.71842i 0.251607i
\(714\) 0 0
\(715\) −8.88531 + 1.02528i −0.332292 + 0.0383434i
\(716\) 0 0
\(717\) 31.4356i 1.17398i
\(718\) 0 0
\(719\) 3.11128 0.116031 0.0580156 0.998316i \(-0.481523\pi\)
0.0580156 + 0.998316i \(0.481523\pi\)
\(720\) 0 0
\(721\) −6.21991 −0.231641
\(722\) 0 0
\(723\) 74.9310i 2.78671i
\(724\) 0 0
\(725\) 37.9884 8.88531i 1.41085 0.329992i
\(726\) 0 0
\(727\) 33.9540i 1.25928i 0.776886 + 0.629642i \(0.216798\pi\)
−0.776886 + 0.629642i \(0.783202\pi\)
\(728\) 0 0
\(729\) −109.777 −4.06581
\(730\) 0 0
\(731\) −0.596468 −0.0220612
\(732\) 0 0
\(733\) 21.0457i 0.777342i −0.921377 0.388671i \(-0.872934\pi\)
0.921377 0.388671i \(-0.127066\pi\)
\(734\) 0 0
\(735\) −43.4993 + 5.01941i −1.60449 + 0.185144i
\(736\) 0 0
\(737\) 1.41737i 0.0522097i
\(738\) 0 0
\(739\) 17.0253 0.626285 0.313143 0.949706i \(-0.398618\pi\)
0.313143 + 0.949706i \(0.398618\pi\)
\(740\) 0 0
\(741\) −88.8710 −3.26476
\(742\) 0 0
\(743\) 23.7563i 0.871536i −0.900059 0.435768i \(-0.856477\pi\)
0.900059 0.435768i \(-0.143523\pi\)
\(744\) 0 0
\(745\) −4.07227 35.2911i −0.149196 1.29297i
\(746\) 0 0
\(747\) 113.951i 4.16924i
\(748\) 0 0
\(749\) −4.66067 −0.170297
\(750\) 0 0
\(751\) −44.8654 −1.63716 −0.818582 0.574390i \(-0.805239\pi\)
−0.818582 + 0.574390i \(0.805239\pi\)
\(752\) 0 0
\(753\) 36.7177i 1.33807i
\(754\) 0 0
\(755\) −1.68663 14.6167i −0.0613829 0.531957i
\(756\) 0 0
\(757\) 41.3761i 1.50384i 0.659255 + 0.751920i \(0.270872\pi\)
−0.659255 + 0.751920i \(0.729128\pi\)
\(758\) 0 0
\(759\) 20.0675 0.728405
\(760\) 0 0
\(761\) 16.3002 0.590883 0.295442 0.955361i \(-0.404533\pi\)
0.295442 + 0.955361i \(0.404533\pi\)
\(762\) 0 0
\(763\) 2.52279i 0.0913310i
\(764\) 0 0
\(765\) 1.98636 0.229207i 0.0718170 0.00828701i
\(766\) 0 0
\(767\) 2.71124i 0.0978971i
\(768\) 0 0
\(769\) −41.1262 −1.48305 −0.741525 0.670925i \(-0.765897\pi\)
−0.741525 + 0.670925i \(0.765897\pi\)
\(770\) 0 0
\(771\) 72.0409 2.59449
\(772\) 0 0
\(773\) 9.77280i 0.351503i −0.984435 0.175752i \(-0.943764\pi\)
0.984435 0.175752i \(-0.0562355\pi\)
\(774\) 0 0
\(775\) −5.47679 + 1.28100i −0.196732 + 0.0460147i
\(776\) 0 0
\(777\) 25.6628i 0.920646i
\(778\) 0 0
\(779\) 34.3207 1.22967
\(780\) 0 0
\(781\) −6.15020 −0.220072
\(782\) 0 0
\(783\) 138.694i 4.95652i
\(784\) 0 0
\(785\) 14.1840 1.63670i 0.506248 0.0584162i
\(786\) 0 0
\(787\) 5.25466i 0.187308i 0.995605 + 0.0936541i \(0.0298548\pi\)
−0.995605 + 0.0936541i \(0.970145\pi\)
\(788\) 0 0
\(789\) 21.9173 0.780278
\(790\) 0 0
\(791\) 11.8511 0.421377
\(792\) 0 0
\(793\) 0.789082i 0.0280211i
\(794\) 0 0
\(795\) −4.11460 35.6580i −0.145930 1.26466i
\(796\) 0