Properties

Label 520.2.d.c.209.3
Level $520$
Weight $2$
Character 520.209
Analytic conductor $4.152$
Analytic rank $0$
Dimension $10$
Inner twists $2$

Related objects

Downloads

Learn more

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 209.3
Root \(-1.11501 - 1.93823i\) of defining polynomial
Character \(\chi\) \(=\) 520.209
Dual form 520.2.d.c.209.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.57527i q^{3} +(1.11501 + 1.93823i) q^{5} +0.632021i q^{7} -3.63202 q^{9} +O(q^{10})\) \(q-2.57527i q^{3} +(1.11501 + 1.93823i) q^{5} +0.632021i q^{7} -3.63202 q^{9} +6.16324 q^{11} -1.00000i q^{13} +(4.99148 - 2.87145i) q^{15} -4.23002i q^{17} +5.31378 q^{19} +1.62762 q^{21} -2.34525i q^{23} +(-2.51351 + 4.32230i) q^{25} +1.62762i q^{27} -10.2614 q^{29} -3.56084 q^{31} -15.8720i q^{33} +(-1.22500 + 0.704709i) q^{35} +7.09206i q^{37} -2.57527 q^{39} +5.01698 q^{41} -8.32821i q^{43} +(-4.04974 - 7.03971i) q^{45} +3.36798i q^{47} +6.60055 q^{49} -10.8934 q^{51} +2.60240i q^{53} +(6.87207 + 11.9458i) q^{55} -13.6844i q^{57} -4.29680 q^{59} +1.37801 q^{61} -2.29551i q^{63} +(1.93823 - 1.11501i) q^{65} -8.36613i q^{67} -6.03966 q^{69} -0.481365 q^{71} +7.11089i q^{73} +(11.1311 + 6.47296i) q^{75} +3.89529i q^{77} +8.90348 q^{79} -6.70449 q^{81} +15.5255i q^{83} +(8.19877 - 4.71651i) q^{85} +26.4260i q^{87} +1.29290 q^{89} +0.632021 q^{91} +9.17013i q^{93} +(5.92492 + 10.2994i) q^{95} -1.88650i q^{97} -22.3850 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q - 4 q^{5} - 30 q^{9}+O(q^{10}) \) 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
\(3\) 2.57527i 1.48683i −0.668829 0.743417i \(-0.733204\pi\)
0.668829 0.743417i \(-0.266796\pi\)
\(4\) 0 0
\(5\) 1.11501 + 1.93823i 0.498648 + 0.866805i
\(6\) 0 0
\(7\) 0.632021i 0.238881i 0.992841 + 0.119441i \(0.0381101\pi\)
−0.992841 + 0.119441i \(0.961890\pi\)
\(8\) 0 0
\(9\) −3.63202 −1.21067
\(10\) 0 0
\(11\) 6.16324 1.85829 0.929143 0.369720i \(-0.120546\pi\)
0.929143 + 0.369720i \(0.120546\pi\)
\(12\) 0 0
\(13\) 1.00000i 0.277350i
\(14\) 0 0
\(15\) 4.99148 2.87145i 1.28879 0.741406i
\(16\) 0 0
\(17\) 4.23002i 1.02593i −0.858409 0.512965i \(-0.828547\pi\)
0.858409 0.512965i \(-0.171453\pi\)
\(18\) 0 0
\(19\) 5.31378 1.21906 0.609532 0.792761i \(-0.291357\pi\)
0.609532 + 0.792761i \(0.291357\pi\)
\(20\) 0 0
\(21\) 1.62762 0.355177
\(22\) 0 0
\(23\) 2.34525i 0.489019i −0.969647 0.244509i \(-0.921373\pi\)
0.969647 0.244509i \(-0.0786269\pi\)
\(24\) 0 0
\(25\) −2.51351 + 4.32230i −0.502701 + 0.864460i
\(26\) 0 0
\(27\) 1.62762i 0.313236i
\(28\) 0 0
\(29\) −10.2614 −1.90550 −0.952750 0.303757i \(-0.901759\pi\)
−0.952750 + 0.303757i \(0.901759\pi\)
\(30\) 0 0
\(31\) −3.56084 −0.639546 −0.319773 0.947494i \(-0.603607\pi\)
−0.319773 + 0.947494i \(0.603607\pi\)
\(32\) 0 0
\(33\) 15.8720i 2.76296i
\(34\) 0 0
\(35\) −1.22500 + 0.704709i −0.207063 + 0.119118i
\(36\) 0 0
\(37\) 7.09206i 1.16593i 0.812498 + 0.582964i \(0.198107\pi\)
−0.812498 + 0.582964i \(0.801893\pi\)
\(38\) 0 0
\(39\) −2.57527 −0.412373
\(40\) 0 0
\(41\) 5.01698 0.783520 0.391760 0.920067i \(-0.371866\pi\)
0.391760 + 0.920067i \(0.371866\pi\)
\(42\) 0 0
\(43\) 8.32821i 1.27004i −0.772496 0.635020i \(-0.780992\pi\)
0.772496 0.635020i \(-0.219008\pi\)
\(44\) 0 0
\(45\) −4.04974 7.03971i −0.603699 1.04942i
\(46\) 0 0
\(47\) 3.36798i 0.491270i 0.969362 + 0.245635i \(0.0789965\pi\)
−0.969362 + 0.245635i \(0.921003\pi\)
\(48\) 0 0
\(49\) 6.60055 0.942936
\(50\) 0 0
\(51\) −10.8934 −1.52539
\(52\) 0 0
\(53\) 2.60240i 0.357467i 0.983898 + 0.178733i \(0.0571999\pi\)
−0.983898 + 0.178733i \(0.942800\pi\)
\(54\) 0 0
\(55\) 6.87207 + 11.9458i 0.926630 + 1.61077i
\(56\) 0 0
\(57\) 13.6844i 1.81255i
\(58\) 0 0
\(59\) −4.29680 −0.559396 −0.279698 0.960088i \(-0.590234\pi\)
−0.279698 + 0.960088i \(0.590234\pi\)
\(60\) 0 0
\(61\) 1.37801 0.176436 0.0882181 0.996101i \(-0.471883\pi\)
0.0882181 + 0.996101i \(0.471883\pi\)
\(62\) 0 0
\(63\) 2.29551i 0.289207i
\(64\) 0 0
\(65\) 1.93823 1.11501i 0.240408 0.138300i
\(66\) 0 0
\(67\) 8.36613i 1.02209i −0.859555 0.511043i \(-0.829259\pi\)
0.859555 0.511043i \(-0.170741\pi\)
\(68\) 0 0
\(69\) −6.03966 −0.727089
\(70\) 0 0
\(71\) −0.481365 −0.0571275 −0.0285637 0.999592i \(-0.509093\pi\)
−0.0285637 + 0.999592i \(0.509093\pi\)
\(72\) 0 0
\(73\) 7.11089i 0.832266i 0.909304 + 0.416133i \(0.136615\pi\)
−0.909304 + 0.416133i \(0.863385\pi\)
\(74\) 0 0
\(75\) 11.1311 + 6.47296i 1.28531 + 0.747433i
\(76\) 0 0
\(77\) 3.89529i 0.443910i
\(78\) 0 0
\(79\) 8.90348 1.00172 0.500860 0.865528i \(-0.333017\pi\)
0.500860 + 0.865528i \(0.333017\pi\)
\(80\) 0 0
\(81\) −6.70449 −0.744943
\(82\) 0 0
\(83\) 15.5255i 1.70414i 0.523427 + 0.852071i \(0.324653\pi\)
−0.523427 + 0.852071i \(0.675347\pi\)
\(84\) 0 0
\(85\) 8.19877 4.71651i 0.889282 0.511578i
\(86\) 0 0
\(87\) 26.4260i 2.83316i
\(88\) 0 0
\(89\) 1.29290 0.137047 0.0685234 0.997650i \(-0.478171\pi\)
0.0685234 + 0.997650i \(0.478171\pi\)
\(90\) 0 0
\(91\) 0.632021 0.0662538
\(92\) 0 0
\(93\) 9.17013i 0.950899i
\(94\) 0 0
\(95\) 5.92492 + 10.2994i 0.607884 + 1.05669i
\(96\) 0 0
\(97\) 1.88650i 0.191545i −0.995403 0.0957726i \(-0.969468\pi\)
0.995403 0.0957726i \(-0.0305322\pi\)
\(98\) 0 0
\(99\) −22.3850 −2.24978
\(100\) 0 0
\(101\) 1.42646 0.141938 0.0709691 0.997479i \(-0.477391\pi\)
0.0709691 + 0.997479i \(0.477391\pi\)
\(102\) 0 0
\(103\) 8.91879i 0.878795i −0.898293 0.439397i \(-0.855192\pi\)
0.898293 0.439397i \(-0.144808\pi\)
\(104\) 0 0
\(105\) 1.81482 + 3.15472i 0.177108 + 0.307869i
\(106\) 0 0
\(107\) 10.4247i 1.00779i 0.863765 + 0.503895i \(0.168100\pi\)
−0.863765 + 0.503895i \(0.831900\pi\)
\(108\) 0 0
\(109\) −19.2470 −1.84353 −0.921764 0.387751i \(-0.873252\pi\)
−0.921764 + 0.387751i \(0.873252\pi\)
\(110\) 0 0
\(111\) 18.2640 1.73354
\(112\) 0 0
\(113\) 20.8746i 1.96372i 0.189609 + 0.981860i \(0.439278\pi\)
−0.189609 + 0.981860i \(0.560722\pi\)
\(114\) 0 0
\(115\) 4.54565 2.61498i 0.423884 0.243848i
\(116\) 0 0
\(117\) 3.63202i 0.335780i
\(118\) 0 0
\(119\) 2.67346 0.245076
\(120\) 0 0
\(121\) 26.9855 2.45323
\(122\) 0 0
\(123\) 12.9201i 1.16496i
\(124\) 0 0
\(125\) −11.1802 0.0523533i −0.999989 0.00468262i
\(126\) 0 0
\(127\) 12.4247i 1.10251i −0.834337 0.551255i \(-0.814149\pi\)
0.834337 0.551255i \(-0.185851\pi\)
\(128\) 0 0
\(129\) −21.4474 −1.88834
\(130\) 0 0
\(131\) −8.99815 −0.786172 −0.393086 0.919502i \(-0.628593\pi\)
−0.393086 + 0.919502i \(0.628593\pi\)
\(132\) 0 0
\(133\) 3.35842i 0.291212i
\(134\) 0 0
\(135\) −3.15472 + 1.81482i −0.271515 + 0.156195i
\(136\) 0 0
\(137\) 2.55694i 0.218454i −0.994017 0.109227i \(-0.965162\pi\)
0.994017 0.109227i \(-0.0348375\pi\)
\(138\) 0 0
\(139\) −12.1776 −1.03289 −0.516443 0.856321i \(-0.672744\pi\)
−0.516443 + 0.856321i \(0.672744\pi\)
\(140\) 0 0
\(141\) 8.67346 0.730437
\(142\) 0 0
\(143\) 6.16324i 0.515396i
\(144\) 0 0
\(145\) −11.4416 19.8891i −0.950173 1.65170i
\(146\) 0 0
\(147\) 16.9982i 1.40199i
\(148\) 0 0
\(149\) −9.79839 −0.802716 −0.401358 0.915921i \(-0.631462\pi\)
−0.401358 + 0.915921i \(0.631462\pi\)
\(150\) 0 0
\(151\) −13.3256 −1.08442 −0.542211 0.840243i \(-0.682413\pi\)
−0.542211 + 0.840243i \(0.682413\pi\)
\(152\) 0 0
\(153\) 15.3635i 1.24207i
\(154\) 0 0
\(155\) −3.97038 6.90175i −0.318908 0.554362i
\(156\) 0 0
\(157\) 10.2130i 0.815084i 0.913186 + 0.407542i \(0.133614\pi\)
−0.913186 + 0.407542i \(0.866386\pi\)
\(158\) 0 0
\(159\) 6.70187 0.531493
\(160\) 0 0
\(161\) 1.48225 0.116817
\(162\) 0 0
\(163\) 12.8096i 1.00332i 0.865064 + 0.501662i \(0.167278\pi\)
−0.865064 + 0.501662i \(0.832722\pi\)
\(164\) 0 0
\(165\) 30.7637 17.6974i 2.39495 1.37774i
\(166\) 0 0
\(167\) 5.93149i 0.458992i 0.973310 + 0.229496i \(0.0737078\pi\)
−0.973310 + 0.229496i \(0.926292\pi\)
\(168\) 0 0
\(169\) −1.00000 −0.0769231
\(170\) 0 0
\(171\) −19.2998 −1.47589
\(172\) 0 0
\(173\) 12.9035i 0.981033i 0.871432 + 0.490517i \(0.163192\pi\)
−0.871432 + 0.490517i \(0.836808\pi\)
\(174\) 0 0
\(175\) −2.73178 1.58859i −0.206503 0.120086i
\(176\) 0 0
\(177\) 11.0654i 0.831729i
\(178\) 0 0
\(179\) −26.3617 −1.97036 −0.985182 0.171512i \(-0.945135\pi\)
−0.985182 + 0.171512i \(0.945135\pi\)
\(180\) 0 0
\(181\) 3.98041 0.295861 0.147931 0.988998i \(-0.452739\pi\)
0.147931 + 0.988998i \(0.452739\pi\)
\(182\) 0 0
\(183\) 3.54875i 0.262331i
\(184\) 0 0
\(185\) −13.7461 + 7.90772i −1.01063 + 0.581387i
\(186\) 0 0
\(187\) 26.0706i 1.90647i
\(188\) 0 0
\(189\) −1.02869 −0.0748263
\(190\) 0 0
\(191\) 9.84104 0.712073 0.356036 0.934472i \(-0.384128\pi\)
0.356036 + 0.934472i \(0.384128\pi\)
\(192\) 0 0
\(193\) 7.74415i 0.557436i 0.960373 + 0.278718i \(0.0899094\pi\)
−0.960373 + 0.278718i \(0.910091\pi\)
\(194\) 0 0
\(195\) −2.87145 4.99148i −0.205629 0.357447i
\(196\) 0 0
\(197\) 12.3199i 0.877757i −0.898546 0.438879i \(-0.855376\pi\)
0.898546 0.438879i \(-0.144624\pi\)
\(198\) 0 0
\(199\) −11.6394 −0.825098 −0.412549 0.910935i \(-0.635361\pi\)
−0.412549 + 0.910935i \(0.635361\pi\)
\(200\) 0 0
\(201\) −21.5451 −1.51967
\(202\) 0 0
\(203\) 6.48543i 0.455188i
\(204\) 0 0
\(205\) 5.59398 + 9.72408i 0.390701 + 0.679159i
\(206\) 0 0
\(207\) 8.51800i 0.592042i
\(208\) 0 0
\(209\) 32.7501 2.26537
\(210\) 0 0
\(211\) 18.6087 1.28108 0.640539 0.767926i \(-0.278711\pi\)
0.640539 + 0.767926i \(0.278711\pi\)
\(212\) 0 0
\(213\) 1.23964i 0.0849390i
\(214\) 0 0
\(215\) 16.1420 9.28604i 1.10088 0.633302i
\(216\) 0 0
\(217\) 2.25053i 0.152776i
\(218\) 0 0
\(219\) 18.3125 1.23744
\(220\) 0 0
\(221\) −4.23002 −0.284542
\(222\) 0 0
\(223\) 4.40502i 0.294982i −0.989063 0.147491i \(-0.952880\pi\)
0.989063 0.147491i \(-0.0471198\pi\)
\(224\) 0 0
\(225\) 9.12910 15.6987i 0.608607 1.04658i
\(226\) 0 0
\(227\) 1.11089i 0.0737320i 0.999320 + 0.0368660i \(0.0117375\pi\)
−0.999320 + 0.0368660i \(0.988263\pi\)
\(228\) 0 0
\(229\) 16.4430 1.08658 0.543292 0.839544i \(-0.317178\pi\)
0.543292 + 0.839544i \(0.317178\pi\)
\(230\) 0 0
\(231\) 10.0314 0.660020
\(232\) 0 0
\(233\) 6.21342i 0.407055i 0.979069 + 0.203527i \(0.0652406\pi\)
−0.979069 + 0.203527i \(0.934759\pi\)
\(234\) 0 0
\(235\) −6.52793 + 3.75533i −0.425835 + 0.244971i
\(236\) 0 0
\(237\) 22.9289i 1.48939i
\(238\) 0 0
\(239\) 13.7708 0.890759 0.445379 0.895342i \(-0.353069\pi\)
0.445379 + 0.895342i \(0.353069\pi\)
\(240\) 0 0
\(241\) −18.4940 −1.19130 −0.595652 0.803243i \(-0.703106\pi\)
−0.595652 + 0.803243i \(0.703106\pi\)
\(242\) 0 0
\(243\) 22.1487i 1.42084i
\(244\) 0 0
\(245\) 7.35968 + 12.7934i 0.470193 + 0.817341i
\(246\) 0 0
\(247\) 5.31378i 0.338108i
\(248\) 0 0
\(249\) 39.9823 2.53377
\(250\) 0 0
\(251\) −9.51110 −0.600336 −0.300168 0.953886i \(-0.597043\pi\)
−0.300168 + 0.953886i \(0.597043\pi\)
\(252\) 0 0
\(253\) 14.4543i 0.908737i
\(254\) 0 0
\(255\) −12.1463 21.1141i −0.760631 1.32221i
\(256\) 0 0
\(257\) 2.67346i 0.166766i 0.996518 + 0.0833829i \(0.0265725\pi\)
−0.996518 + 0.0833829i \(0.973428\pi\)
\(258\) 0 0
\(259\) −4.48233 −0.278518
\(260\) 0 0
\(261\) 37.2697 2.30694
\(262\) 0 0
\(263\) 11.7883i 0.726898i −0.931614 0.363449i \(-0.881599\pi\)
0.931614 0.363449i \(-0.118401\pi\)
\(264\) 0 0
\(265\) −5.04405 + 2.90170i −0.309854 + 0.178250i
\(266\) 0 0
\(267\) 3.32956i 0.203766i
\(268\) 0 0
\(269\) −7.72754 −0.471157 −0.235578 0.971855i \(-0.575698\pi\)
−0.235578 + 0.971855i \(0.575698\pi\)
\(270\) 0 0
\(271\) 26.7031 1.62210 0.811050 0.584977i \(-0.198896\pi\)
0.811050 + 0.584977i \(0.198896\pi\)
\(272\) 0 0
\(273\) 1.62762i 0.0985083i
\(274\) 0 0
\(275\) −15.4913 + 26.6394i −0.934163 + 1.60641i
\(276\) 0 0
\(277\) 0.820601i 0.0493052i 0.999696 + 0.0246526i \(0.00784796\pi\)
−0.999696 + 0.0246526i \(0.992152\pi\)
\(278\) 0 0
\(279\) 12.9331 0.774282
\(280\) 0 0
\(281\) −26.7611 −1.59643 −0.798217 0.602369i \(-0.794223\pi\)
−0.798217 + 0.602369i \(0.794223\pi\)
\(282\) 0 0
\(283\) 10.9188i 0.649055i −0.945876 0.324527i \(-0.894795\pi\)
0.945876 0.324527i \(-0.105205\pi\)
\(284\) 0 0
\(285\) 26.5236 15.2583i 1.57112 0.903822i
\(286\) 0 0
\(287\) 3.17083i 0.187168i
\(288\) 0 0
\(289\) −0.893069 −0.0525335
\(290\) 0 0
\(291\) −4.85825 −0.284796
\(292\) 0 0
\(293\) 24.8790i 1.45344i 0.686932 + 0.726722i \(0.258957\pi\)
−0.686932 + 0.726722i \(0.741043\pi\)
\(294\) 0 0
\(295\) −4.79098 8.32821i −0.278941 0.484887i
\(296\) 0 0
\(297\) 10.0314i 0.582083i
\(298\) 0 0
\(299\) −2.34525 −0.135629
\(300\) 0 0
\(301\) 5.26360 0.303389
\(302\) 0 0
\(303\) 3.67352i 0.211038i
\(304\) 0 0
\(305\) 1.53650 + 2.67091i 0.0879795 + 0.152936i
\(306\) 0 0
\(307\) 1.03147i 0.0588691i 0.999567 + 0.0294346i \(0.00937067\pi\)
−0.999567 + 0.0294346i \(0.990629\pi\)
\(308\) 0 0
\(309\) −22.9683 −1.30662
\(310\) 0 0
\(311\) −9.45185 −0.535965 −0.267983 0.963424i \(-0.586357\pi\)
−0.267983 + 0.963424i \(0.586357\pi\)
\(312\) 0 0
\(313\) 0.360120i 0.0203552i 0.999948 + 0.0101776i \(0.00323968\pi\)
−0.999948 + 0.0101776i \(0.996760\pi\)
\(314\) 0 0
\(315\) 4.44924 2.55952i 0.250686 0.144213i
\(316\) 0 0
\(317\) 29.4120i 1.65194i −0.563714 0.825970i \(-0.690628\pi\)
0.563714 0.825970i \(-0.309372\pi\)
\(318\) 0 0
\(319\) −63.2436 −3.54096
\(320\) 0 0
\(321\) 26.8463 1.49842
\(322\) 0 0
\(323\) 22.4774i 1.25068i
\(324\) 0 0
\(325\) 4.32230 + 2.51351i 0.239758 + 0.139424i
\(326\) 0 0
\(327\) 49.5662i 2.74102i
\(328\) 0 0
\(329\) −2.12863 −0.117355
\(330\) 0 0
\(331\) −5.20907 −0.286317 −0.143158 0.989700i \(-0.545726\pi\)
−0.143158 + 0.989700i \(0.545726\pi\)
\(332\) 0 0
\(333\) 25.7585i 1.41156i
\(334\) 0 0
\(335\) 16.2155 9.32832i 0.885949 0.509661i
\(336\) 0 0
\(337\) 15.2810i 0.832407i −0.909272 0.416203i \(-0.863360\pi\)
0.909272 0.416203i \(-0.136640\pi\)
\(338\) 0 0
\(339\) 53.7578 2.91972
\(340\) 0 0
\(341\) −21.9463 −1.18846
\(342\) 0 0
\(343\) 8.59583i 0.464131i
\(344\) 0 0
\(345\) −6.73428 11.7063i −0.362561 0.630244i
\(346\) 0 0
\(347\) 26.0862i 1.40038i −0.713955 0.700192i \(-0.753098\pi\)
0.713955 0.700192i \(-0.246902\pi\)
\(348\) 0 0
\(349\) 23.0288 1.23270 0.616352 0.787471i \(-0.288610\pi\)
0.616352 + 0.787471i \(0.288610\pi\)
\(350\) 0 0
\(351\) 1.62762 0.0868762
\(352\) 0 0
\(353\) 0.202076i 0.0107554i 0.999986 + 0.00537772i \(0.00171179\pi\)
−0.999986 + 0.00537772i \(0.998288\pi\)
\(354\) 0 0
\(355\) −0.536726 0.932997i −0.0284865 0.0495184i
\(356\) 0 0
\(357\) 6.88488i 0.364387i
\(358\) 0 0
\(359\) −7.60630 −0.401445 −0.200723 0.979648i \(-0.564329\pi\)
−0.200723 + 0.979648i \(0.564329\pi\)
\(360\) 0 0
\(361\) 9.23626 0.486119
\(362\) 0 0
\(363\) 69.4950i 3.64754i
\(364\) 0 0
\(365\) −13.7826 + 7.92871i −0.721412 + 0.415008i
\(366\) 0 0
\(367\) 33.0811i 1.72682i −0.504504 0.863409i \(-0.668325\pi\)
0.504504 0.863409i \(-0.331675\pi\)
\(368\) 0 0
\(369\) −18.2218 −0.948587
\(370\) 0 0
\(371\) −1.64477 −0.0853921
\(372\) 0 0
\(373\) 31.5599i 1.63411i −0.576560 0.817055i \(-0.695605\pi\)
0.576560 0.817055i \(-0.304395\pi\)
\(374\) 0 0
\(375\) −0.134824 + 28.7921i −0.00696227 + 1.48682i
\(376\) 0 0
\(377\) 10.2614i 0.528490i
\(378\) 0 0
\(379\) −22.2593 −1.14338 −0.571691 0.820469i \(-0.693712\pi\)
−0.571691 + 0.820469i \(0.693712\pi\)
\(380\) 0 0
\(381\) −31.9969 −1.63925
\(382\) 0 0
\(383\) 30.8956i 1.57869i 0.613950 + 0.789345i \(0.289579\pi\)
−0.613950 + 0.789345i \(0.710421\pi\)
\(384\) 0 0
\(385\) −7.54999 + 4.34329i −0.384783 + 0.221355i
\(386\) 0 0
\(387\) 30.2482i 1.53760i
\(388\) 0 0
\(389\) −6.00000 −0.304212 −0.152106 0.988364i \(-0.548606\pi\)
−0.152106 + 0.988364i \(0.548606\pi\)
\(390\) 0 0
\(391\) −9.92046 −0.501699
\(392\) 0 0
\(393\) 23.1727i 1.16891i
\(394\) 0 0
\(395\) 9.92747 + 17.2570i 0.499505 + 0.868295i
\(396\) 0 0
\(397\) 3.16860i 0.159027i 0.996834 + 0.0795137i \(0.0253367\pi\)
−0.996834 + 0.0795137i \(0.974663\pi\)
\(398\) 0 0
\(399\) 8.64884 0.432983
\(400\) 0 0
\(401\) −19.7441 −0.985976 −0.492988 0.870036i \(-0.664095\pi\)
−0.492988 + 0.870036i \(0.664095\pi\)
\(402\) 0 0
\(403\) 3.56084i 0.177378i
\(404\) 0 0
\(405\) −7.47557 12.9949i −0.371464 0.645720i
\(406\) 0 0
\(407\) 43.7101i 2.16663i
\(408\) 0 0
\(409\) 36.6273 1.81111 0.905553 0.424234i \(-0.139457\pi\)
0.905553 + 0.424234i \(0.139457\pi\)
\(410\) 0 0
\(411\) −6.58481 −0.324805
\(412\) 0 0
\(413\) 2.71567i 0.133629i
\(414\) 0 0
\(415\) −30.0920 + 17.3111i −1.47716 + 0.849766i
\(416\) 0 0
\(417\) 31.3605i 1.53573i
\(418\) 0 0
\(419\) −11.1099 −0.542754 −0.271377 0.962473i \(-0.587479\pi\)
−0.271377 + 0.962473i \(0.587479\pi\)
\(420\) 0 0
\(421\) 14.7870 0.720672 0.360336 0.932823i \(-0.382662\pi\)
0.360336 + 0.932823i \(0.382662\pi\)
\(422\) 0 0
\(423\) 12.2326i 0.594768i
\(424\) 0 0
\(425\) 18.2834 + 10.6322i 0.886876 + 0.515736i
\(426\) 0 0
\(427\) 0.870932i 0.0421473i
\(428\) 0 0
\(429\) −15.8720 −0.766308
\(430\) 0 0
\(431\) 26.8907 1.29528 0.647640 0.761946i \(-0.275756\pi\)
0.647640 + 0.761946i \(0.275756\pi\)
\(432\) 0 0
\(433\) 13.8494i 0.665559i 0.943005 + 0.332780i \(0.107987\pi\)
−0.943005 + 0.332780i \(0.892013\pi\)
\(434\) 0 0
\(435\) −51.2197 + 29.4652i −2.45580 + 1.41275i
\(436\) 0 0
\(437\) 12.4621i 0.596145i
\(438\) 0 0
\(439\) 30.5106 1.45619 0.728096 0.685475i \(-0.240406\pi\)
0.728096 + 0.685475i \(0.240406\pi\)
\(440\) 0 0
\(441\) −23.9733 −1.14159
\(442\) 0 0
\(443\) 19.5039i 0.926659i 0.886186 + 0.463329i \(0.153345\pi\)
−0.886186 + 0.463329i \(0.846655\pi\)
\(444\) 0 0
\(445\) 1.44159 + 2.50594i 0.0683381 + 0.118793i
\(446\) 0 0
\(447\) 25.2335i 1.19350i
\(448\) 0 0
\(449\) −20.2758 −0.956874 −0.478437 0.878122i \(-0.658796\pi\)
−0.478437 + 0.878122i \(0.658796\pi\)
\(450\) 0 0
\(451\) 30.9208 1.45601
\(452\) 0 0
\(453\) 34.3170i 1.61235i
\(454\) 0 0
\(455\) 0.704709 + 1.22500i 0.0330373 + 0.0574291i
\(456\) 0 0
\(457\) 14.3265i 0.670164i −0.942189 0.335082i \(-0.891236\pi\)
0.942189 0.335082i \(-0.108764\pi\)
\(458\) 0 0
\(459\) 6.88488 0.321359
\(460\) 0 0
\(461\) −33.1421 −1.54358 −0.771790 0.635878i \(-0.780638\pi\)
−0.771790 + 0.635878i \(0.780638\pi\)
\(462\) 0 0
\(463\) 21.7045i 1.00869i −0.863501 0.504347i \(-0.831733\pi\)
0.863501 0.504347i \(-0.168267\pi\)
\(464\) 0 0
\(465\) −17.7739 + 10.2248i −0.824244 + 0.474163i
\(466\) 0 0
\(467\) 9.45314i 0.437439i −0.975788 0.218720i \(-0.929812\pi\)
0.975788 0.218720i \(-0.0701880\pi\)
\(468\) 0 0
\(469\) 5.28757 0.244157
\(470\) 0 0
\(471\) 26.3012 1.21189
\(472\) 0 0
\(473\) 51.3287i 2.36010i
\(474\) 0 0
\(475\) −13.3562 + 22.9678i −0.612825 + 1.05383i
\(476\) 0 0
\(477\) 9.45195i 0.432775i
\(478\) 0 0
\(479\) 23.6573 1.08093 0.540465 0.841367i \(-0.318248\pi\)
0.540465 + 0.841367i \(0.318248\pi\)
\(480\) 0 0
\(481\) 7.09206 0.323370
\(482\) 0 0
\(483\) 3.81719i 0.173688i
\(484\) 0 0
\(485\) 3.65648 2.10347i 0.166032 0.0955135i
\(486\) 0 0
\(487\) 32.9648i 1.49378i −0.664948 0.746890i \(-0.731546\pi\)
0.664948 0.746890i \(-0.268454\pi\)
\(488\) 0 0
\(489\) 32.9881 1.49177
\(490\) 0 0
\(491\) 6.89345 0.311097 0.155548 0.987828i \(-0.450286\pi\)
0.155548 + 0.987828i \(0.450286\pi\)
\(492\) 0 0
\(493\) 43.4060i 1.95491i
\(494\) 0 0
\(495\) −24.9595 43.3874i −1.12185 1.95012i
\(496\) 0 0
\(497\) 0.304232i 0.0136467i
\(498\) 0 0
\(499\) −0.469550 −0.0210200 −0.0105100 0.999945i \(-0.503345\pi\)
−0.0105100 + 0.999945i \(0.503345\pi\)
\(500\) 0 0
\(501\) 15.2752 0.682445
\(502\) 0 0
\(503\) 2.91879i 0.130142i −0.997881 0.0650712i \(-0.979273\pi\)
0.997881 0.0650712i \(-0.0207275\pi\)
\(504\) 0 0
\(505\) 1.59052 + 2.76482i 0.0707771 + 0.123033i
\(506\) 0 0
\(507\) 2.57527i 0.114372i
\(508\) 0 0
\(509\) 12.4095 0.550041 0.275020 0.961438i \(-0.411315\pi\)
0.275020 + 0.961438i \(0.411315\pi\)
\(510\) 0 0
\(511\) −4.49423 −0.198813
\(512\) 0 0
\(513\) 8.64884i 0.381856i
\(514\) 0 0
\(515\) 17.2867 9.94454i 0.761743 0.438209i
\(516\) 0 0
\(517\) 20.7577i 0.912921i
\(518\) 0 0
\(519\) 33.2300 1.45863
\(520\) 0 0
\(521\) −35.9125 −1.57336 −0.786678 0.617363i \(-0.788201\pi\)
−0.786678 + 0.617363i \(0.788201\pi\)
\(522\) 0 0
\(523\) 1.82573i 0.0798337i −0.999203 0.0399169i \(-0.987291\pi\)
0.999203 0.0399169i \(-0.0127093\pi\)
\(524\) 0 0
\(525\) −4.09104 + 7.03508i −0.178548 + 0.307036i
\(526\) 0 0
\(527\) 15.0624i 0.656130i
\(528\) 0 0
\(529\) 17.4998 0.760861
\(530\) 0 0
\(531\) 15.6061 0.677246
\(532\) 0 0
\(533\) 5.01698i 0.217309i
\(534\) 0 0
\(535\) −20.2054 + 11.6236i −0.873558 + 0.502532i
\(536\) 0 0
\(537\) 67.8885i 2.92960i
\(538\) 0 0
\(539\) 40.6808 1.75224
\(540\) 0 0
\(541\) 13.2269 0.568670 0.284335 0.958725i \(-0.408227\pi\)
0.284335 + 0.958725i \(0.408227\pi\)
\(542\) 0 0
\(543\) 10.2506i 0.439897i
\(544\) 0 0
\(545\) −21.4606 37.3052i −0.919271 1.59798i
\(546\) 0 0
\(547\) 17.9353i 0.766859i 0.923570 + 0.383430i \(0.125257\pi\)
−0.923570 + 0.383430i \(0.874743\pi\)
\(548\) 0 0
\(549\) −5.00497 −0.213607
\(550\) 0 0
\(551\) −54.5270 −2.32293
\(552\) 0 0
\(553\) 5.62718i 0.239292i
\(554\) 0 0
\(555\) 20.3645 + 35.3999i 0.864426 + 1.50264i
\(556\) 0 0
\(557\) 4.62323i 0.195892i −0.995192 0.0979462i \(-0.968773\pi\)
0.995192 0.0979462i \(-0.0312273\pi\)
\(558\) 0 0
\(559\) −8.32821 −0.352246
\(560\) 0 0
\(561\) −67.1389 −2.83461
\(562\) 0 0
\(563\) 17.6515i 0.743922i −0.928248 0.371961i \(-0.878686\pi\)
0.928248 0.371961i \(-0.121314\pi\)
\(564\) 0 0
\(565\) −40.4599 + 23.2754i −1.70216 + 0.979204i
\(566\) 0 0
\(567\) 4.23737i 0.177953i
\(568\) 0 0
\(569\) 3.87077 0.162271 0.0811356 0.996703i \(-0.474145\pi\)
0.0811356 + 0.996703i \(0.474145\pi\)
\(570\) 0 0
\(571\) 17.7003 0.740733 0.370366 0.928886i \(-0.379232\pi\)
0.370366 + 0.928886i \(0.379232\pi\)
\(572\) 0 0
\(573\) 25.3434i 1.05873i
\(574\) 0 0
\(575\) 10.1369 + 5.89480i 0.422737 + 0.245830i
\(576\) 0 0
\(577\) 10.9231i 0.454733i 0.973809 + 0.227367i \(0.0730116\pi\)
−0.973809 + 0.227367i \(0.926988\pi\)
\(578\) 0 0
\(579\) 19.9433 0.828814
\(580\) 0 0
\(581\) −9.81242 −0.407088
\(582\) 0 0
\(583\) 16.0392i 0.664275i
\(584\) 0 0
\(585\) −7.03971 + 4.04974i −0.291056 + 0.167436i
\(586\) 0 0
\(587\) 5.49151i 0.226659i 0.993557 + 0.113329i \(0.0361516\pi\)
−0.993557 + 0.113329i \(0.963848\pi\)
\(588\) 0 0
\(589\) −18.9215 −0.779648
\(590\) 0 0
\(591\) −31.7271 −1.30508
\(592\) 0 0
\(593\) 41.7606i 1.71490i −0.514565 0.857452i \(-0.672046\pi\)
0.514565 0.857452i \(-0.327954\pi\)
\(594\) 0 0
\(595\) 2.98093 + 5.18179i 0.122206 + 0.212433i
\(596\) 0 0
\(597\) 29.9747i 1.22678i
\(598\) 0 0
\(599\) 19.5259 0.797808 0.398904 0.916993i \(-0.369391\pi\)
0.398904 + 0.916993i \(0.369391\pi\)
\(600\) 0 0
\(601\) 25.7377 1.04986 0.524931 0.851145i \(-0.324091\pi\)
0.524931 + 0.851145i \(0.324091\pi\)
\(602\) 0 0
\(603\) 30.3860i 1.23741i
\(604\) 0 0
\(605\) 30.0891 + 52.3042i 1.22330 + 2.12647i
\(606\) 0 0
\(607\) 40.9221i 1.66098i 0.557035 + 0.830489i \(0.311939\pi\)
−0.557035 + 0.830489i \(0.688061\pi\)
\(608\) 0 0
\(609\) −16.7017 −0.676789
\(610\) 0 0
\(611\) 3.36798 0.136254
\(612\) 0 0
\(613\) 26.7408i 1.08005i 0.841648 + 0.540026i \(0.181586\pi\)
−0.841648 + 0.540026i \(0.818414\pi\)
\(614\) 0 0
\(615\) 25.0421 14.4060i 1.00980 0.580907i
\(616\) 0 0
\(617\) 22.4349i 0.903194i −0.892222 0.451597i \(-0.850854\pi\)
0.892222 0.451597i \(-0.149146\pi\)
\(618\) 0 0
\(619\) 2.74903 0.110493 0.0552465 0.998473i \(-0.482406\pi\)
0.0552465 + 0.998473i \(0.482406\pi\)
\(620\) 0 0
\(621\) 3.81719 0.153178
\(622\) 0 0
\(623\) 0.817138i 0.0327379i
\(624\) 0 0
\(625\) −12.3646 21.7283i −0.494583 0.869130i
\(626\) 0 0
\(627\) 84.3404i 3.36823i
\(628\) 0 0
\(629\) 29.9996 1.19616
\(630\) 0 0
\(631\) −7.07853 −0.281792 −0.140896 0.990024i \(-0.544998\pi\)
−0.140896 + 0.990024i \(0.544998\pi\)
\(632\) 0 0
\(633\) 47.9225i 1.90475i
\(634\) 0 0
\(635\) 24.0819 13.8536i 0.955662 0.549764i
\(636\) 0 0
\(637\) 6.60055i 0.261523i
\(638\) 0 0
\(639\) 1.74833 0.0691627
\(640\) 0 0
\(641\) 24.7270 0.976659 0.488330 0.872659i \(-0.337606\pi\)
0.488330 + 0.872659i \(0.337606\pi\)
\(642\) 0 0
\(643\) 13.7471i 0.542134i 0.962560 + 0.271067i \(0.0873765\pi\)
−0.962560 + 0.271067i \(0.912623\pi\)
\(644\) 0 0
\(645\) −23.9141 41.5701i −0.941615 1.63682i
\(646\) 0 0
\(647\) 26.2517i 1.03206i −0.856570 0.516030i \(-0.827409\pi\)
0.856570 0.516030i \(-0.172591\pi\)
\(648\) 0 0
\(649\) −26.4822 −1.03952
\(650\) 0 0
\(651\) −5.79571 −0.227152
\(652\) 0 0
\(653\) 11.4011i 0.446158i 0.974800 + 0.223079i \(0.0716108\pi\)
−0.974800 + 0.223079i \(0.928389\pi\)
\(654\) 0 0
\(655\) −10.0330 17.4405i −0.392023 0.681458i
\(656\) 0 0
\(657\) 25.8269i 1.00760i
\(658\) 0 0
\(659\) −21.6191 −0.842162 −0.421081 0.907023i \(-0.638349\pi\)
−0.421081 + 0.907023i \(0.638349\pi\)
\(660\) 0 0
\(661\) −20.8709 −0.811785 −0.405893 0.913921i \(-0.633039\pi\)
−0.405893 + 0.913921i \(0.633039\pi\)
\(662\) 0 0
\(663\) 10.8934i 0.423066i
\(664\) 0 0
\(665\) −6.50940 + 3.74467i −0.252424 + 0.145212i
\(666\) 0 0
\(667\) 24.0656i 0.931825i
\(668\) 0 0
\(669\) −11.3441 −0.438589
\(670\) 0 0
\(671\) 8.49301 0.327869
\(672\) 0 0
\(673\) 29.9401i 1.15411i −0.816707 0.577053i \(-0.804203\pi\)
0.816707 0.577053i \(-0.195797\pi\)
\(674\) 0 0
\(675\) −7.03508 4.09104i −0.270780 0.157464i
\(676\) 0 0
\(677\) 37.9029i 1.45673i 0.685192 + 0.728363i \(0.259718\pi\)
−0.685192 + 0.728363i \(0.740282\pi\)
\(678\) 0 0
\(679\) 1.19231 0.0457566
\(680\) 0 0
\(681\) 2.86083 0.109627
\(682\) 0 0
\(683\) 46.0169i 1.76079i 0.474242 + 0.880395i \(0.342722\pi\)
−0.474242 + 0.880395i \(0.657278\pi\)
\(684\) 0 0
\(685\) 4.95595 2.85101i 0.189357 0.108932i
\(686\) 0 0
\(687\) 42.3452i 1.61557i
\(688\) 0 0
\(689\) 2.60240 0.0991434
\(690\) 0 0
\(691\) 16.0786 0.611659 0.305829 0.952086i \(-0.401066\pi\)
0.305829 + 0.952086i \(0.401066\pi\)
\(692\) 0 0
\(693\) 14.1478i 0.537430i
\(694\) 0 0
\(695\) −13.5781 23.6030i −0.515046 0.895311i
\(696\) 0 0
\(697\) 21.2219i 0.803838i
\(698\) 0 0
\(699\) 16.0012 0.605222
\(700\) 0 0
\(701\) −2.13356 −0.0805836 −0.0402918 0.999188i \(-0.512829\pi\)
−0.0402918 + 0.999188i \(0.512829\pi\)
\(702\) 0 0
\(703\) 37.6857i 1.42134i
\(704\) 0 0
\(705\) 9.67099 + 16.8112i 0.364231 + 0.633146i
\(706\) 0 0
\(707\) 0.901553i 0.0339064i
\(708\) 0 0
\(709\) 23.4544 0.880850 0.440425 0.897789i \(-0.354828\pi\)
0.440425 + 0.897789i \(0.354828\pi\)
\(710\) 0 0
\(711\) −32.3376 −1.21276
\(712\) 0 0
\(713\) 8.35107i 0.312750i
\(714\) 0 0
\(715\) 11.9458 6.87207i 0.446748 0.257001i
\(716\) 0 0
\(717\) 35.4635i 1.32441i
\(718\) 0 0
\(719\) −25.1014 −0.936124 −0.468062 0.883696i \(-0.655048\pi\)
−0.468062 + 0.883696i \(0.655048\pi\)
\(720\) 0 0
\(721\) 5.63686 0.209928
\(722\) 0 0
\(723\) 47.6271i 1.77127i
\(724\) 0 0
\(725\) 25.7922 44.3530i 0.957896 1.64723i
\(726\) 0 0
\(727\) 19.2864i 0.715292i 0.933857 + 0.357646i \(0.116421\pi\)
−0.933857 + 0.357646i \(0.883579\pi\)
\(728\) 0 0
\(729\) 36.9256 1.36761
\(730\) 0 0
\(731\) −35.2285 −1.30297
\(732\) 0 0
\(733\) 22.0012i 0.812634i −0.913732 0.406317i \(-0.866813\pi\)
0.913732 0.406317i \(-0.133187\pi\)
\(734\) 0 0
\(735\) 32.9465 18.9532i 1.21525 0.699098i
\(736\) 0 0
\(737\) 51.5625i 1.89933i
\(738\) 0 0
\(739\) −34.5490 −1.27090 −0.635452 0.772140i \(-0.719186\pi\)
−0.635452 + 0.772140i \(0.719186\pi\)
\(740\) 0 0
\(741\) −13.6844 −0.502710
\(742\) 0 0
\(743\) 47.2596i 1.73379i −0.498494 0.866893i \(-0.666114\pi\)
0.498494 0.866893i \(-0.333886\pi\)
\(744\) 0 0
\(745\) −10.9253 18.9916i −0.400272 0.695798i
\(746\) 0 0
\(747\) 56.3888i 2.06316i
\(748\) 0 0
\(749\) −6.58860 −0.240742
\(750\) 0 0
\(751\) 0.959266 0.0350041 0.0175021 0.999847i \(-0.494429\pi\)
0.0175021 + 0.999847i \(0.494429\pi\)
\(752\) 0 0
\(753\) 24.4937i 0.892599i
\(754\) 0 0
\(755\) −14.8582 25.8281i −0.540744 0.939982i
\(756\) 0 0
\(757\) 27.3634i 0.994539i 0.867596 + 0.497270i \(0.165664\pi\)
−0.867596 + 0.497270i \(0.834336\pi\)
\(758\) 0 0
\(759\) −37.2238 −1.35114
\(760\) 0 0
\(761\) 48.4851 1.75758 0.878791 0.477206i \(-0.158351\pi\)
0.878791 + 0.477206i \(0.158351\pi\)
\(762\) 0 0
\(763\) 12.1645i 0.440384i
\(764\) 0 0
\(765\) −29.7781 + 17.1305i −1.07663 + 0.619354i
\(766\) 0 0
\(767\) 4.29680i 0.155149i
\(768\) 0 0
\(769\) 46.7801 1.68693 0.843467 0.537181i \(-0.180511\pi\)
0.843467 + 0.537181i \(0.180511\pi\)
\(770\) 0 0
\(771\) 6.88488 0.247953
\(772\) 0 0
\(773\) 45.9492i 1.65268i 0.563173 + 0.826339i \(0.309580\pi\)
−0.563173 + 0.826339i \(0.690420\pi\)
\(774\) 0 0
\(775\) 8.95020 15.3910i 0.321501 0.552862i
\(776\) 0 0
\(777\) 11.5432i 0.414110i
\(778\) 0 0
\(779\) 26.6591 0.955162
\(780\) 0 0
\(781\) −2.96676 −0.106159
\(782\) 0 0
\(783\) 16.7017i 0.596872i
\(784\) 0 0
\(785\) −19.7951 + 11.3876i −0.706519 + 0.406440i
\(786\) 0 0
\(787\) 2.29551i 0.0818262i −0.999163 0.0409131i \(-0.986973\pi\)
0.999163 0.0409131i \(-0.0130267\pi\)
\(788\) 0 0
\(789\) −30.3581 −1.08078
\(790\) 0 0
\(791\) −13.1932 −0.469096
\(792\) 0 0
\(793\) 1.37801i 0.0489346i
\(794\) 0 0