Properties

Label 55.2.b.a.34.2
Level $55$
Weight $2$
Character 55.34
Analytic conductor $0.439$
Analytic rank $0$
Dimension $4$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [55,2,Mod(34,55)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(55, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([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("55.34");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 55 = 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 55.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: \(0.439177211117\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{-11})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{3} - 2x^{2} - 3x + 9 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 34.2
Root \(1.68614 + 0.396143i\) of defining polynomial
Character \(\chi\) \(=\) 55.34
Dual form 55.2.b.a.34.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-0.792287i q^{2} +2.52434i q^{3} +1.37228 q^{4} +(-2.18614 + 0.469882i) q^{5} +2.00000 q^{6} -3.46410i q^{7} -2.67181i q^{8} -3.37228 q^{9} +O(q^{10})\) \(q-0.792287i q^{2} +2.52434i q^{3} +1.37228 q^{4} +(-2.18614 + 0.469882i) q^{5} +2.00000 q^{6} -3.46410i q^{7} -2.67181i q^{8} -3.37228 q^{9} +(0.372281 + 1.73205i) q^{10} -1.00000 q^{11} +3.46410i q^{12} -2.74456 q^{14} +(-1.18614 - 5.51856i) q^{15} +0.627719 q^{16} +5.04868i q^{17} +2.67181i q^{18} -4.00000 q^{19} +(-3.00000 + 0.644810i) q^{20} +8.74456 q^{21} +0.792287i q^{22} -2.52434i q^{23} +6.74456 q^{24} +(4.55842 - 2.05446i) q^{25} -0.939764i q^{27} -4.75372i q^{28} +2.74456 q^{29} +(-4.37228 + 0.939764i) q^{30} -2.37228 q^{31} -5.84096i q^{32} -2.52434i q^{33} +4.00000 q^{34} +(1.62772 + 7.57301i) q^{35} -4.62772 q^{36} +11.0371i q^{37} +3.16915i q^{38} +(1.25544 + 5.84096i) q^{40} -2.74456 q^{41} -6.92820i q^{42} +3.46410i q^{43} -1.37228 q^{44} +(7.37228 - 1.58457i) q^{45} -2.00000 q^{46} -6.63325i q^{47} +1.58457i q^{48} -5.00000 q^{49} +(-1.62772 - 3.61158i) q^{50} -12.7446 q^{51} -3.16915i q^{53} -0.744563 q^{54} +(2.18614 - 0.469882i) q^{55} -9.25544 q^{56} -10.0974i q^{57} -2.17448i q^{58} +1.62772 q^{59} +(-1.62772 - 7.57301i) q^{60} +10.7446 q^{61} +1.87953i q^{62} +11.6819i q^{63} -3.37228 q^{64} -2.00000 q^{66} +0.644810i q^{67} +6.92820i q^{68} +6.37228 q^{69} +(6.00000 - 1.28962i) q^{70} +7.11684 q^{71} +9.01011i q^{72} -6.92820i q^{73} +8.74456 q^{74} +(5.18614 + 11.5070i) q^{75} -5.48913 q^{76} +3.46410i q^{77} -12.7446 q^{79} +(-1.37228 + 0.294954i) q^{80} -7.74456 q^{81} +2.17448i q^{82} -6.63325i q^{83} +12.0000 q^{84} +(-2.37228 - 11.0371i) q^{85} +2.74456 q^{86} +6.92820i q^{87} +2.67181i q^{88} +4.37228 q^{89} +(-1.25544 - 5.84096i) q^{90} -3.46410i q^{92} -5.98844i q^{93} -5.25544 q^{94} +(8.74456 - 1.87953i) q^{95} +14.7446 q^{96} +4.10891i q^{97} +3.96143i q^{98} +3.37228 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 6 q^{4} - 3 q^{5} + 8 q^{6} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 6 q^{4} - 3 q^{5} + 8 q^{6} - 2 q^{9} - 10 q^{10} - 4 q^{11} + 12 q^{14} + q^{15} + 14 q^{16} - 16 q^{19} - 12 q^{20} + 12 q^{21} + 4 q^{24} + q^{25} - 12 q^{29} - 6 q^{30} + 2 q^{31} + 16 q^{34} + 18 q^{35} - 30 q^{36} + 28 q^{40} + 12 q^{41} + 6 q^{44} + 18 q^{45} - 8 q^{46} - 20 q^{49} - 18 q^{50} - 28 q^{51} + 20 q^{54} + 3 q^{55} - 60 q^{56} + 18 q^{59} - 18 q^{60} + 20 q^{61} - 2 q^{64} - 8 q^{66} + 14 q^{69} + 24 q^{70} - 6 q^{71} + 12 q^{74} + 15 q^{75} + 24 q^{76} - 28 q^{79} + 6 q^{80} - 8 q^{81} + 48 q^{84} + 2 q^{85} - 12 q^{86} + 6 q^{89} - 28 q^{90} - 44 q^{94} + 12 q^{95} + 36 q^{96} + 2 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/55\mathbb{Z}\right)^\times\).

\(n\) \(12\) \(46\)
\(\chi(n)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.792287i 0.560232i −0.959966 0.280116i \(-0.909627\pi\)
0.959966 0.280116i \(-0.0903729\pi\)
\(3\) 2.52434i 1.45743i 0.684819 + 0.728714i \(0.259881\pi\)
−0.684819 + 0.728714i \(0.740119\pi\)
\(4\) 1.37228 0.686141
\(5\) −2.18614 + 0.469882i −0.977672 + 0.210138i
\(6\) 2.00000 0.816497
\(7\) 3.46410i 1.30931i −0.755929 0.654654i \(-0.772814\pi\)
0.755929 0.654654i \(-0.227186\pi\)
\(8\) 2.67181i 0.944629i
\(9\) −3.37228 −1.12409
\(10\) 0.372281 + 1.73205i 0.117726 + 0.547723i
\(11\) −1.00000 −0.301511
\(12\) 3.46410i 1.00000i
\(13\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(14\) −2.74456 −0.733515
\(15\) −1.18614 5.51856i −0.306260 1.42489i
\(16\) 0.627719 0.156930
\(17\) 5.04868i 1.22448i 0.790671 + 0.612242i \(0.209732\pi\)
−0.790671 + 0.612242i \(0.790268\pi\)
\(18\) 2.67181i 0.629753i
\(19\) −4.00000 −0.917663 −0.458831 0.888523i \(-0.651732\pi\)
−0.458831 + 0.888523i \(0.651732\pi\)
\(20\) −3.00000 + 0.644810i −0.670820 + 0.144184i
\(21\) 8.74456 1.90822
\(22\) 0.792287i 0.168916i
\(23\) 2.52434i 0.526361i −0.964747 0.263180i \(-0.915229\pi\)
0.964747 0.263180i \(-0.0847714\pi\)
\(24\) 6.74456 1.37673
\(25\) 4.55842 2.05446i 0.911684 0.410891i
\(26\) 0 0
\(27\) 0.939764i 0.180858i
\(28\) 4.75372i 0.898369i
\(29\) 2.74456 0.509652 0.254826 0.966987i \(-0.417982\pi\)
0.254826 + 0.966987i \(0.417982\pi\)
\(30\) −4.37228 + 0.939764i −0.798266 + 0.171577i
\(31\) −2.37228 −0.426074 −0.213037 0.977044i \(-0.568336\pi\)
−0.213037 + 0.977044i \(0.568336\pi\)
\(32\) 5.84096i 1.03255i
\(33\) 2.52434i 0.439431i
\(34\) 4.00000 0.685994
\(35\) 1.62772 + 7.57301i 0.275135 + 1.28007i
\(36\) −4.62772 −0.771286
\(37\) 11.0371i 1.81449i 0.420602 + 0.907245i \(0.361819\pi\)
−0.420602 + 0.907245i \(0.638181\pi\)
\(38\) 3.16915i 0.514104i
\(39\) 0 0
\(40\) 1.25544 + 5.84096i 0.198502 + 0.923537i
\(41\) −2.74456 −0.428629 −0.214314 0.976765i \(-0.568752\pi\)
−0.214314 + 0.976765i \(0.568752\pi\)
\(42\) 6.92820i 1.06904i
\(43\) 3.46410i 0.528271i 0.964486 + 0.264135i \(0.0850865\pi\)
−0.964486 + 0.264135i \(0.914913\pi\)
\(44\) −1.37228 −0.206879
\(45\) 7.37228 1.58457i 1.09899 0.236214i
\(46\) −2.00000 −0.294884
\(47\) 6.63325i 0.967559i −0.875190 0.483779i \(-0.839264\pi\)
0.875190 0.483779i \(-0.160736\pi\)
\(48\) 1.58457i 0.228714i
\(49\) −5.00000 −0.714286
\(50\) −1.62772 3.61158i −0.230194 0.510754i
\(51\) −12.7446 −1.78460
\(52\) 0 0
\(53\) 3.16915i 0.435316i −0.976025 0.217658i \(-0.930158\pi\)
0.976025 0.217658i \(-0.0698417\pi\)
\(54\) −0.744563 −0.101322
\(55\) 2.18614 0.469882i 0.294779 0.0633589i
\(56\) −9.25544 −1.23681
\(57\) 10.0974i 1.33743i
\(58\) 2.17448i 0.285523i
\(59\) 1.62772 0.211911 0.105955 0.994371i \(-0.466210\pi\)
0.105955 + 0.994371i \(0.466210\pi\)
\(60\) −1.62772 7.57301i −0.210138 0.977672i
\(61\) 10.7446 1.37570 0.687850 0.725853i \(-0.258555\pi\)
0.687850 + 0.725853i \(0.258555\pi\)
\(62\) 1.87953i 0.238700i
\(63\) 11.6819i 1.47178i
\(64\) −3.37228 −0.421535
\(65\) 0 0
\(66\) −2.00000 −0.246183
\(67\) 0.644810i 0.0787761i 0.999224 + 0.0393880i \(0.0125408\pi\)
−0.999224 + 0.0393880i \(0.987459\pi\)
\(68\) 6.92820i 0.840168i
\(69\) 6.37228 0.767133
\(70\) 6.00000 1.28962i 0.717137 0.154139i
\(71\) 7.11684 0.844614 0.422307 0.906453i \(-0.361220\pi\)
0.422307 + 0.906453i \(0.361220\pi\)
\(72\) 9.01011i 1.06185i
\(73\) 6.92820i 0.810885i −0.914121 0.405442i \(-0.867117\pi\)
0.914121 0.405442i \(-0.132883\pi\)
\(74\) 8.74456 1.01653
\(75\) 5.18614 + 11.5070i 0.598844 + 1.32871i
\(76\) −5.48913 −0.629646
\(77\) 3.46410i 0.394771i
\(78\) 0 0
\(79\) −12.7446 −1.43388 −0.716938 0.697137i \(-0.754457\pi\)
−0.716938 + 0.697137i \(0.754457\pi\)
\(80\) −1.37228 + 0.294954i −0.153426 + 0.0329768i
\(81\) −7.74456 −0.860507
\(82\) 2.17448i 0.240131i
\(83\) 6.63325i 0.728094i −0.931381 0.364047i \(-0.881395\pi\)
0.931381 0.364047i \(-0.118605\pi\)
\(84\) 12.0000 1.30931
\(85\) −2.37228 11.0371i −0.257310 1.19714i
\(86\) 2.74456 0.295954
\(87\) 6.92820i 0.742781i
\(88\) 2.67181i 0.284816i
\(89\) 4.37228 0.463461 0.231730 0.972780i \(-0.425561\pi\)
0.231730 + 0.972780i \(0.425561\pi\)
\(90\) −1.25544 5.84096i −0.132335 0.615692i
\(91\) 0 0
\(92\) 3.46410i 0.361158i
\(93\) 5.98844i 0.620972i
\(94\) −5.25544 −0.542057
\(95\) 8.74456 1.87953i 0.897173 0.192835i
\(96\) 14.7446 1.50486
\(97\) 4.10891i 0.417197i 0.978001 + 0.208598i \(0.0668902\pi\)
−0.978001 + 0.208598i \(0.933110\pi\)
\(98\) 3.96143i 0.400165i
\(99\) 3.37228 0.338927
\(100\) 6.25544 2.81929i 0.625544 0.281929i
\(101\) 6.00000 0.597022 0.298511 0.954406i \(-0.403510\pi\)
0.298511 + 0.954406i \(0.403510\pi\)
\(102\) 10.0974i 0.999787i
\(103\) 10.3923i 1.02398i −0.858990 0.511992i \(-0.828908\pi\)
0.858990 0.511992i \(-0.171092\pi\)
\(104\) 0 0
\(105\) −19.1168 + 4.10891i −1.86561 + 0.400989i
\(106\) −2.51087 −0.243878
\(107\) 6.63325i 0.641260i −0.947204 0.320630i \(-0.896105\pi\)
0.947204 0.320630i \(-0.103895\pi\)
\(108\) 1.28962i 0.124094i
\(109\) −10.0000 −0.957826 −0.478913 0.877862i \(-0.658969\pi\)
−0.478913 + 0.877862i \(0.658969\pi\)
\(110\) −0.372281 1.73205i −0.0354956 0.165145i
\(111\) −27.8614 −2.64449
\(112\) 2.17448i 0.205469i
\(113\) 16.0858i 1.51322i 0.653864 + 0.756612i \(0.273147\pi\)
−0.653864 + 0.756612i \(0.726853\pi\)
\(114\) −8.00000 −0.749269
\(115\) 1.18614 + 5.51856i 0.110608 + 0.514608i
\(116\) 3.76631 0.349693
\(117\) 0 0
\(118\) 1.28962i 0.118719i
\(119\) 17.4891 1.60323
\(120\) −14.7446 + 3.16915i −1.34599 + 0.289302i
\(121\) 1.00000 0.0909091
\(122\) 8.51278i 0.770711i
\(123\) 6.92820i 0.624695i
\(124\) −3.25544 −0.292347
\(125\) −9.00000 + 6.63325i −0.804984 + 0.593296i
\(126\) 9.25544 0.824540
\(127\) 11.6819i 1.03660i −0.855198 0.518302i \(-0.826564\pi\)
0.855198 0.518302i \(-0.173436\pi\)
\(128\) 9.01011i 0.796389i
\(129\) −8.74456 −0.769916
\(130\) 0 0
\(131\) 8.74456 0.764016 0.382008 0.924159i \(-0.375233\pi\)
0.382008 + 0.924159i \(0.375233\pi\)
\(132\) 3.46410i 0.301511i
\(133\) 13.8564i 1.20150i
\(134\) 0.510875 0.0441329
\(135\) 0.441578 + 2.05446i 0.0380050 + 0.176819i
\(136\) 13.4891 1.15668
\(137\) 2.22938i 0.190469i 0.995455 + 0.0952346i \(0.0303601\pi\)
−0.995455 + 0.0952346i \(0.969640\pi\)
\(138\) 5.04868i 0.429772i
\(139\) −18.2337 −1.54656 −0.773281 0.634064i \(-0.781386\pi\)
−0.773281 + 0.634064i \(0.781386\pi\)
\(140\) 2.23369 + 10.3923i 0.188781 + 0.878310i
\(141\) 16.7446 1.41015
\(142\) 5.63858i 0.473179i
\(143\) 0 0
\(144\) −2.11684 −0.176404
\(145\) −6.00000 + 1.28962i −0.498273 + 0.107097i
\(146\) −5.48913 −0.454283
\(147\) 12.6217i 1.04102i
\(148\) 15.1460i 1.24500i
\(149\) −11.4891 −0.941226 −0.470613 0.882340i \(-0.655967\pi\)
−0.470613 + 0.882340i \(0.655967\pi\)
\(150\) 9.11684 4.10891i 0.744387 0.335491i
\(151\) 22.2337 1.80935 0.904676 0.426100i \(-0.140113\pi\)
0.904676 + 0.426100i \(0.140113\pi\)
\(152\) 10.6873i 0.866851i
\(153\) 17.0256i 1.37643i
\(154\) 2.74456 0.221163
\(155\) 5.18614 1.11469i 0.416561 0.0895342i
\(156\) 0 0
\(157\) 5.39853i 0.430850i −0.976520 0.215425i \(-0.930886\pi\)
0.976520 0.215425i \(-0.0691136\pi\)
\(158\) 10.0974i 0.803302i
\(159\) 8.00000 0.634441
\(160\) 2.74456 + 12.7692i 0.216977 + 1.00949i
\(161\) −8.74456 −0.689168
\(162\) 6.13592i 0.482083i
\(163\) 3.46410i 0.271329i −0.990755 0.135665i \(-0.956683\pi\)
0.990755 0.135665i \(-0.0433170\pi\)
\(164\) −3.76631 −0.294100
\(165\) 1.18614 + 5.51856i 0.0923409 + 0.429619i
\(166\) −5.25544 −0.407901
\(167\) 22.3692i 1.73098i 0.500927 + 0.865490i \(0.332993\pi\)
−0.500927 + 0.865490i \(0.667007\pi\)
\(168\) 23.3639i 1.80256i
\(169\) 13.0000 1.00000
\(170\) −8.74456 + 1.87953i −0.670677 + 0.144153i
\(171\) 13.4891 1.03154
\(172\) 4.75372i 0.362468i
\(173\) 1.87953i 0.142898i −0.997444 0.0714489i \(-0.977238\pi\)
0.997444 0.0714489i \(-0.0227623\pi\)
\(174\) 5.48913 0.416130
\(175\) −7.11684 15.7908i −0.537983 1.19368i
\(176\) −0.627719 −0.0473161
\(177\) 4.10891i 0.308845i
\(178\) 3.46410i 0.259645i
\(179\) 15.8614 1.18554 0.592769 0.805373i \(-0.298035\pi\)
0.592769 + 0.805373i \(0.298035\pi\)
\(180\) 10.1168 2.17448i 0.754065 0.162076i
\(181\) 6.88316 0.511621 0.255810 0.966727i \(-0.417658\pi\)
0.255810 + 0.966727i \(0.417658\pi\)
\(182\) 0 0
\(183\) 27.1229i 2.00498i
\(184\) −6.74456 −0.497216
\(185\) −5.18614 24.1287i −0.381293 1.77398i
\(186\) −4.74456 −0.347888
\(187\) 5.04868i 0.369196i
\(188\) 9.10268i 0.663881i
\(189\) −3.25544 −0.236798
\(190\) −1.48913 6.92820i −0.108033 0.502625i
\(191\) −13.6277 −0.986067 −0.493034 0.870010i \(-0.664112\pi\)
−0.493034 + 0.870010i \(0.664112\pi\)
\(192\) 8.51278i 0.614357i
\(193\) 23.3639i 1.68177i 0.541216 + 0.840883i \(0.317964\pi\)
−0.541216 + 0.840883i \(0.682036\pi\)
\(194\) 3.25544 0.233727
\(195\) 0 0
\(196\) −6.86141 −0.490100
\(197\) 1.87953i 0.133911i −0.997756 0.0669554i \(-0.978671\pi\)
0.997756 0.0669554i \(-0.0213285\pi\)
\(198\) 2.67181i 0.189878i
\(199\) 8.00000 0.567105 0.283552 0.958957i \(-0.408487\pi\)
0.283552 + 0.958957i \(0.408487\pi\)
\(200\) −5.48913 12.1793i −0.388140 0.861204i
\(201\) −1.62772 −0.114810
\(202\) 4.75372i 0.334471i
\(203\) 9.50744i 0.667292i
\(204\) −17.4891 −1.22448
\(205\) 6.00000 1.28962i 0.419058 0.0900710i
\(206\) −8.23369 −0.573668
\(207\) 8.51278i 0.591679i
\(208\) 0 0
\(209\) 4.00000 0.276686
\(210\) 3.25544 + 15.1460i 0.224647 + 1.04518i
\(211\) −21.4891 −1.47937 −0.739686 0.672952i \(-0.765026\pi\)
−0.739686 + 0.672952i \(0.765026\pi\)
\(212\) 4.34896i 0.298688i
\(213\) 17.9653i 1.23096i
\(214\) −5.25544 −0.359254
\(215\) −1.62772 7.57301i −0.111009 0.516475i
\(216\) −2.51087 −0.170843
\(217\) 8.21782i 0.557862i
\(218\) 7.92287i 0.536604i
\(219\) 17.4891 1.18181
\(220\) 3.00000 0.644810i 0.202260 0.0434731i
\(221\) 0 0
\(222\) 22.0742i 1.48153i
\(223\) 7.57301i 0.507126i 0.967319 + 0.253563i \(0.0816026\pi\)
−0.967319 + 0.253563i \(0.918397\pi\)
\(224\) −20.2337 −1.35192
\(225\) −15.3723 + 6.92820i −1.02482 + 0.461880i
\(226\) 12.7446 0.847756
\(227\) 9.80240i 0.650608i 0.945609 + 0.325304i \(0.105467\pi\)
−0.945609 + 0.325304i \(0.894533\pi\)
\(228\) 13.8564i 0.917663i
\(229\) −20.3723 −1.34624 −0.673119 0.739534i \(-0.735046\pi\)
−0.673119 + 0.739534i \(0.735046\pi\)
\(230\) 4.37228 0.939764i 0.288300 0.0619662i
\(231\) −8.74456 −0.575350
\(232\) 7.33296i 0.481433i
\(233\) 17.0256i 1.11538i −0.830049 0.557691i \(-0.811688\pi\)
0.830049 0.557691i \(-0.188312\pi\)
\(234\) 0 0
\(235\) 3.11684 + 14.5012i 0.203320 + 0.945955i
\(236\) 2.23369 0.145401
\(237\) 32.1716i 2.08977i
\(238\) 13.8564i 0.898177i
\(239\) 3.25544 0.210577 0.105288 0.994442i \(-0.466423\pi\)
0.105288 + 0.994442i \(0.466423\pi\)
\(240\) −0.744563 3.46410i −0.0480613 0.223607i
\(241\) 5.25544 0.338532 0.169266 0.985570i \(-0.445860\pi\)
0.169266 + 0.985570i \(0.445860\pi\)
\(242\) 0.792287i 0.0509301i
\(243\) 22.3692i 1.43498i
\(244\) 14.7446 0.943924
\(245\) 10.9307 2.34941i 0.698337 0.150098i
\(246\) −5.48913 −0.349974
\(247\) 0 0
\(248\) 6.33830i 0.402482i
\(249\) 16.7446 1.06114
\(250\) 5.25544 + 7.13058i 0.332383 + 0.450978i
\(251\) −4.88316 −0.308222 −0.154111 0.988054i \(-0.549251\pi\)
−0.154111 + 0.988054i \(0.549251\pi\)
\(252\) 16.0309i 1.00985i
\(253\) 2.52434i 0.158704i
\(254\) −9.25544 −0.580738
\(255\) 27.8614 5.98844i 1.74475 0.375011i
\(256\) −13.8832 −0.867697
\(257\) 23.9538i 1.49419i −0.664715 0.747097i \(-0.731447\pi\)
0.664715 0.747097i \(-0.268553\pi\)
\(258\) 6.92820i 0.431331i
\(259\) 38.2337 2.37573
\(260\) 0 0
\(261\) −9.25544 −0.572897
\(262\) 6.92820i 0.428026i
\(263\) 14.1514i 0.872610i 0.899799 + 0.436305i \(0.143713\pi\)
−0.899799 + 0.436305i \(0.856287\pi\)
\(264\) −6.74456 −0.415099
\(265\) 1.48913 + 6.92820i 0.0914762 + 0.425596i
\(266\) 10.9783 0.673120
\(267\) 11.0371i 0.675460i
\(268\) 0.884861i 0.0540515i
\(269\) −11.4891 −0.700504 −0.350252 0.936655i \(-0.613904\pi\)
−0.350252 + 0.936655i \(0.613904\pi\)
\(270\) 1.62772 0.349857i 0.0990598 0.0212916i
\(271\) −9.48913 −0.576423 −0.288212 0.957567i \(-0.593061\pi\)
−0.288212 + 0.957567i \(0.593061\pi\)
\(272\) 3.16915i 0.192158i
\(273\) 0 0
\(274\) 1.76631 0.106707
\(275\) −4.55842 + 2.05446i −0.274883 + 0.123888i
\(276\) 8.74456 0.526361
\(277\) 8.21782i 0.493761i −0.969046 0.246881i \(-0.920594\pi\)
0.969046 0.246881i \(-0.0794055\pi\)
\(278\) 14.4463i 0.866432i
\(279\) 8.00000 0.478947
\(280\) 20.2337 4.34896i 1.20919 0.259900i
\(281\) −23.4891 −1.40124 −0.700622 0.713533i \(-0.747094\pi\)
−0.700622 + 0.713533i \(0.747094\pi\)
\(282\) 13.2665i 0.790009i
\(283\) 4.75372i 0.282579i −0.989968 0.141290i \(-0.954875\pi\)
0.989968 0.141290i \(-0.0451249\pi\)
\(284\) 9.76631 0.579524
\(285\) 4.74456 + 22.0742i 0.281044 + 1.30756i
\(286\) 0 0
\(287\) 9.50744i 0.561207i
\(288\) 19.6974i 1.16068i
\(289\) −8.48913 −0.499360
\(290\) 1.02175 + 4.75372i 0.0599992 + 0.279148i
\(291\) −10.3723 −0.608034
\(292\) 9.50744i 0.556381i
\(293\) 10.0974i 0.589894i −0.955514 0.294947i \(-0.904698\pi\)
0.955514 0.294947i \(-0.0953019\pi\)
\(294\) −10.0000 −0.583212
\(295\) −3.55842 + 0.764836i −0.207179 + 0.0445304i
\(296\) 29.4891 1.71402
\(297\) 0.939764i 0.0545306i
\(298\) 9.10268i 0.527304i
\(299\) 0 0
\(300\) 7.11684 + 15.7908i 0.410891 + 0.911684i
\(301\) 12.0000 0.691669
\(302\) 17.6155i 1.01366i
\(303\) 15.1460i 0.870117i
\(304\) −2.51087 −0.144009
\(305\) −23.4891 + 5.04868i −1.34498 + 0.289086i
\(306\) −13.4891 −0.771122
\(307\) 28.1176i 1.60475i 0.596817 + 0.802377i \(0.296432\pi\)
−0.596817 + 0.802377i \(0.703568\pi\)
\(308\) 4.75372i 0.270868i
\(309\) 26.2337 1.49238
\(310\) −0.883156 4.10891i −0.0501599 0.233371i
\(311\) −17.4891 −0.991717 −0.495859 0.868403i \(-0.665147\pi\)
−0.495859 + 0.868403i \(0.665147\pi\)
\(312\) 0 0
\(313\) 31.8217i 1.79867i −0.437260 0.899335i \(-0.644051\pi\)
0.437260 0.899335i \(-0.355949\pi\)
\(314\) −4.27719 −0.241376
\(315\) −5.48913 25.5383i −0.309277 1.43892i
\(316\) −17.4891 −0.983840
\(317\) 3.51900i 0.197647i 0.995105 + 0.0988235i \(0.0315079\pi\)
−0.995105 + 0.0988235i \(0.968492\pi\)
\(318\) 6.33830i 0.355434i
\(319\) −2.74456 −0.153666
\(320\) 7.37228 1.58457i 0.412123 0.0885804i
\(321\) 16.7446 0.934590
\(322\) 6.92820i 0.386094i
\(323\) 20.1947i 1.12366i
\(324\) −10.6277 −0.590429
\(325\) 0 0
\(326\) −2.74456 −0.152007
\(327\) 25.2434i 1.39596i
\(328\) 7.33296i 0.404895i
\(329\) −22.9783 −1.26683
\(330\) 4.37228 0.939764i 0.240686 0.0517323i
\(331\) 3.11684 0.171317 0.0856586 0.996325i \(-0.472701\pi\)
0.0856586 + 0.996325i \(0.472701\pi\)
\(332\) 9.10268i 0.499575i
\(333\) 37.2203i 2.03966i
\(334\) 17.7228 0.969749
\(335\) −0.302985 1.40965i −0.0165538 0.0770172i
\(336\) 5.48913 0.299456
\(337\) 12.5668i 0.684556i 0.939599 + 0.342278i \(0.111199\pi\)
−0.939599 + 0.342278i \(0.888801\pi\)
\(338\) 10.2997i 0.560232i
\(339\) −40.6060 −2.20541
\(340\) −3.25544 15.1460i −0.176551 0.821409i
\(341\) 2.37228 0.128466
\(342\) 10.6873i 0.577901i
\(343\) 6.92820i 0.374088i
\(344\) 9.25544 0.499020
\(345\) −13.9307 + 2.99422i −0.750004 + 0.161203i
\(346\) −1.48913 −0.0800559
\(347\) 29.2974i 1.57277i 0.617739 + 0.786383i \(0.288049\pi\)
−0.617739 + 0.786383i \(0.711951\pi\)
\(348\) 9.50744i 0.509652i
\(349\) 7.48913 0.400884 0.200442 0.979706i \(-0.435762\pi\)
0.200442 + 0.979706i \(0.435762\pi\)
\(350\) −12.5109 + 5.63858i −0.668734 + 0.301395i
\(351\) 0 0
\(352\) 5.84096i 0.311324i
\(353\) 21.7244i 1.15627i 0.815941 + 0.578136i \(0.196220\pi\)
−0.815941 + 0.578136i \(0.803780\pi\)
\(354\) 3.25544 0.173025
\(355\) −15.5584 + 3.34408i −0.825755 + 0.177485i
\(356\) 6.00000 0.317999
\(357\) 44.1485i 2.33658i
\(358\) 12.5668i 0.664175i
\(359\) −6.51087 −0.343631 −0.171815 0.985129i \(-0.554963\pi\)
−0.171815 + 0.985129i \(0.554963\pi\)
\(360\) −4.23369 19.6974i −0.223135 1.03814i
\(361\) −3.00000 −0.157895
\(362\) 5.45343i 0.286626i
\(363\) 2.52434i 0.132493i
\(364\) 0 0
\(365\) 3.25544 + 15.1460i 0.170397 + 0.792779i
\(366\) 21.4891 1.12325
\(367\) 24.0087i 1.25324i 0.779324 + 0.626621i \(0.215563\pi\)
−0.779324 + 0.626621i \(0.784437\pi\)
\(368\) 1.58457i 0.0826016i
\(369\) 9.25544 0.481819
\(370\) −19.1168 + 4.10891i −0.993837 + 0.213612i
\(371\) −10.9783 −0.569962
\(372\) 8.21782i 0.426074i
\(373\) 8.21782i 0.425503i 0.977106 + 0.212751i \(0.0682424\pi\)
−0.977106 + 0.212751i \(0.931758\pi\)
\(374\) −4.00000 −0.206835
\(375\) −16.7446 22.7190i −0.864685 1.17321i
\(376\) −17.7228 −0.913984
\(377\) 0 0
\(378\) 2.57924i 0.132662i
\(379\) 6.37228 0.327322 0.163661 0.986517i \(-0.447670\pi\)
0.163661 + 0.986517i \(0.447670\pi\)
\(380\) 12.0000 2.57924i 0.615587 0.132312i
\(381\) 29.4891 1.51077
\(382\) 10.7971i 0.552426i
\(383\) 5.69349i 0.290924i 0.989364 + 0.145462i \(0.0464668\pi\)
−0.989364 + 0.145462i \(0.953533\pi\)
\(384\) 22.7446 1.16068
\(385\) −1.62772 7.57301i −0.0829562 0.385957i
\(386\) 18.5109 0.942179
\(387\) 11.6819i 0.593826i
\(388\) 5.63858i 0.286256i
\(389\) 9.86141 0.499993 0.249997 0.968247i \(-0.419571\pi\)
0.249997 + 0.968247i \(0.419571\pi\)
\(390\) 0 0
\(391\) 12.7446 0.644520
\(392\) 13.3591i 0.674735i
\(393\) 22.0742i 1.11350i
\(394\) −1.48913 −0.0750210
\(395\) 27.8614 5.98844i 1.40186 0.301311i
\(396\) 4.62772 0.232552
\(397\) 23.3639i 1.17260i −0.810095 0.586299i \(-0.800584\pi\)
0.810095 0.586299i \(-0.199416\pi\)
\(398\) 6.33830i 0.317710i
\(399\) −34.9783 −1.75110
\(400\) 2.86141 1.28962i 0.143070 0.0644810i
\(401\) 11.4891 0.573740 0.286870 0.957970i \(-0.407385\pi\)
0.286870 + 0.957970i \(0.407385\pi\)
\(402\) 1.28962i 0.0643204i
\(403\) 0 0
\(404\) 8.23369 0.409641
\(405\) 16.9307 3.63903i 0.841293 0.180825i
\(406\) −7.53262 −0.373838
\(407\) 11.0371i 0.547089i
\(408\) 34.0511i 1.68578i
\(409\) −4.51087 −0.223048 −0.111524 0.993762i \(-0.535573\pi\)
−0.111524 + 0.993762i \(0.535573\pi\)
\(410\) −1.02175 4.75372i −0.0504606 0.234770i
\(411\) −5.62772 −0.277595
\(412\) 14.2612i 0.702597i
\(413\) 5.63858i 0.277457i
\(414\) 6.74456 0.331477
\(415\) 3.11684 + 14.5012i 0.153000 + 0.711837i
\(416\) 0 0
\(417\) 46.0280i 2.25400i
\(418\) 3.16915i 0.155008i
\(419\) −22.9783 −1.12256 −0.561280 0.827626i \(-0.689691\pi\)
−0.561280 + 0.827626i \(0.689691\pi\)
\(420\) −26.2337 + 5.63858i −1.28007 + 0.275135i
\(421\) 31.4891 1.53469 0.767343 0.641237i \(-0.221578\pi\)
0.767343 + 0.641237i \(0.221578\pi\)
\(422\) 17.0256i 0.828791i
\(423\) 22.3692i 1.08763i
\(424\) −8.46738 −0.411212
\(425\) 10.3723 + 23.0140i 0.503130 + 1.11634i
\(426\) 14.2337 0.689624
\(427\) 37.2203i 1.80121i
\(428\) 9.10268i 0.439995i
\(429\) 0 0
\(430\) −6.00000 + 1.28962i −0.289346 + 0.0621910i
\(431\) 31.7228 1.52803 0.764017 0.645196i \(-0.223224\pi\)
0.764017 + 0.645196i \(0.223224\pi\)
\(432\) 0.589907i 0.0283819i
\(433\) 20.5446i 0.987308i −0.869658 0.493654i \(-0.835661\pi\)
0.869658 0.493654i \(-0.164339\pi\)
\(434\) 6.51087 0.312532
\(435\) −3.25544 15.1460i −0.156086 0.726196i
\(436\) −13.7228 −0.657204
\(437\) 10.0974i 0.483022i
\(438\) 13.8564i 0.662085i
\(439\) 1.48913 0.0710721 0.0355360 0.999368i \(-0.488686\pi\)
0.0355360 + 0.999368i \(0.488686\pi\)
\(440\) −1.25544 5.84096i −0.0598506 0.278457i
\(441\) 16.8614 0.802924
\(442\) 0 0
\(443\) 15.0911i 0.717001i −0.933530 0.358500i \(-0.883288\pi\)
0.933530 0.358500i \(-0.116712\pi\)
\(444\) −38.2337 −1.81449
\(445\) −9.55842 + 2.05446i −0.453113 + 0.0973905i
\(446\) 6.00000 0.284108
\(447\) 29.0024i 1.37177i
\(448\) 11.6819i 0.551919i
\(449\) 21.8614 1.03170 0.515852 0.856678i \(-0.327476\pi\)
0.515852 + 0.856678i \(0.327476\pi\)
\(450\) 5.48913 + 12.1793i 0.258760 + 0.574136i
\(451\) 2.74456 0.129236
\(452\) 22.0742i 1.03828i
\(453\) 56.1253i 2.63700i
\(454\) 7.76631 0.364491
\(455\) 0 0
\(456\) −26.9783 −1.26337
\(457\) 20.7846i 0.972263i 0.873886 + 0.486132i \(0.161592\pi\)
−0.873886 + 0.486132i \(0.838408\pi\)
\(458\) 16.1407i 0.754205i
\(459\) 4.74456 0.221457
\(460\) 1.62772 + 7.57301i 0.0758928 + 0.353094i
\(461\) −32.2337 −1.50127 −0.750636 0.660716i \(-0.770253\pi\)
−0.750636 + 0.660716i \(0.770253\pi\)
\(462\) 6.92820i 0.322329i
\(463\) 20.1398i 0.935976i −0.883735 0.467988i \(-0.844979\pi\)
0.883735 0.467988i \(-0.155021\pi\)
\(464\) 1.72281 0.0799796
\(465\) 2.81386 + 13.0916i 0.130490 + 0.607107i
\(466\) −13.4891 −0.624872
\(467\) 4.40387i 0.203787i 0.994795 + 0.101893i \(0.0324900\pi\)
−0.994795 + 0.101893i \(0.967510\pi\)
\(468\) 0 0
\(469\) 2.23369 0.103142
\(470\) 11.4891 2.46943i 0.529954 0.113907i
\(471\) 13.6277 0.627932
\(472\) 4.34896i 0.200177i
\(473\) 3.46410i 0.159280i
\(474\) −25.4891 −1.17075
\(475\) −18.2337 + 8.21782i −0.836619 + 0.377060i
\(476\) 24.0000 1.10004
\(477\) 10.6873i 0.489336i
\(478\) 2.57924i 0.117972i
\(479\) −17.4891 −0.799099 −0.399549 0.916712i \(-0.630833\pi\)
−0.399549 + 0.916712i \(0.630833\pi\)
\(480\) −32.2337 + 6.92820i −1.47126 + 0.316228i
\(481\) 0 0
\(482\) 4.16381i 0.189657i
\(483\) 22.0742i 1.00441i
\(484\) 1.37228 0.0623764
\(485\) −1.93070 8.98266i −0.0876687 0.407882i
\(486\) −17.7228 −0.803923
\(487\) 22.7190i 1.02950i −0.857341 0.514749i \(-0.827885\pi\)
0.857341 0.514749i \(-0.172115\pi\)
\(488\) 28.7075i 1.29953i
\(489\) 8.74456 0.395443
\(490\) −1.86141 8.66025i −0.0840898 0.391230i
\(491\) 29.4891 1.33083 0.665413 0.746476i \(-0.268256\pi\)
0.665413 + 0.746476i \(0.268256\pi\)
\(492\) 9.50744i 0.428629i
\(493\) 13.8564i 0.624061i
\(494\) 0 0
\(495\) −7.37228 + 1.58457i −0.331359 + 0.0712213i
\(496\) −1.48913 −0.0668637
\(497\) 24.6535i 1.10586i
\(498\) 13.2665i 0.594486i
\(499\) 20.0000 0.895323 0.447661 0.894203i \(-0.352257\pi\)
0.447661 + 0.894203i \(0.352257\pi\)
\(500\) −12.3505 + 9.10268i −0.552333 + 0.407084i
\(501\) −56.4674 −2.52278
\(502\) 3.86886i 0.172676i
\(503\) 0.294954i 0.0131513i 0.999978 + 0.00657567i \(0.00209311\pi\)
−0.999978 + 0.00657567i \(0.997907\pi\)
\(504\) 31.2119 1.39029
\(505\) −13.1168 + 2.81929i −0.583692 + 0.125457i
\(506\) 2.00000 0.0889108
\(507\) 32.8164i 1.45743i
\(508\) 16.0309i 0.711256i
\(509\) −28.3723 −1.25758 −0.628790 0.777575i \(-0.716449\pi\)
−0.628790 + 0.777575i \(0.716449\pi\)
\(510\) −4.74456 22.0742i −0.210093 0.977463i
\(511\) −24.0000 −1.06170
\(512\) 7.02078i 0.310277i
\(513\) 3.75906i 0.165966i
\(514\) −18.9783 −0.837095
\(515\) 4.88316 + 22.7190i 0.215178 + 1.00112i
\(516\) −12.0000 −0.528271
\(517\) 6.63325i 0.291730i
\(518\) 30.2921i 1.33096i
\(519\) 4.74456 0.208263
\(520\) 0 0
\(521\) 18.6060 0.815142 0.407571 0.913173i \(-0.366376\pi\)
0.407571 + 0.913173i \(0.366376\pi\)
\(522\) 7.33296i 0.320955i
\(523\) 9.10268i 0.398033i 0.979996 + 0.199016i \(0.0637747\pi\)
−0.979996 + 0.199016i \(0.936225\pi\)
\(524\) 12.0000 0.524222
\(525\) 39.8614 17.9653i 1.73969 0.784071i
\(526\) 11.2119 0.488864
\(527\) 11.9769i 0.521721i
\(528\) 1.58457i 0.0689597i
\(529\) 16.6277 0.722944
\(530\) 5.48913 1.17981i 0.238432 0.0512479i
\(531\) −5.48913 −0.238208
\(532\) 19.0149i 0.824400i
\(533\) 0 0
\(534\) 8.74456 0.378414
\(535\) 3.11684 + 14.5012i 0.134753 + 0.626942i
\(536\) 1.72281 0.0744142
\(537\) 40.0395i 1.72783i
\(538\) 9.10268i 0.392445i
\(539\) 5.00000 0.215365
\(540\) 0.605969 + 2.81929i 0.0260768 + 0.121323i
\(541\) −0.233688 −0.0100470 −0.00502351 0.999987i \(-0.501599\pi\)
−0.00502351 + 0.999987i \(0.501599\pi\)
\(542\) 7.51811i 0.322930i
\(543\) 17.3754i 0.745650i
\(544\) 29.4891 1.26434
\(545\) 21.8614 4.69882i 0.936440 0.201275i
\(546\) 0 0
\(547\) 9.10268i 0.389203i 0.980882 + 0.194601i \(0.0623413\pi\)
−0.980882 + 0.194601i \(0.937659\pi\)
\(548\) 3.05934i 0.130689i
\(549\) −36.2337 −1.54642
\(550\) 1.62772 + 3.61158i 0.0694062 + 0.153998i
\(551\) −10.9783 −0.467689
\(552\) 17.0256i 0.724656i
\(553\) 44.1485i 1.87738i
\(554\) −6.51087 −0.276621
\(555\) 60.9090 13.0916i 2.58544 0.555706i
\(556\) −25.0217 −1.06116
\(557\) 32.1716i 1.36315i −0.731747 0.681577i \(-0.761295\pi\)
0.731747 0.681577i \(-0.238705\pi\)
\(558\) 6.33830i 0.268321i
\(559\) 0 0
\(560\) 1.02175 + 4.75372i 0.0431768 + 0.200881i
\(561\) 12.7446 0.538076
\(562\) 18.6101i 0.785021i
\(563\) 12.2718i 0.517196i −0.965985 0.258598i \(-0.916739\pi\)
0.965985 0.258598i \(-0.0832605\pi\)
\(564\) 22.9783 0.967559
\(565\) −7.55842 35.1658i −0.317985 1.47944i
\(566\) −3.76631 −0.158310
\(567\) 26.8280i 1.12667i
\(568\) 19.0149i 0.797847i
\(569\) 38.7446 1.62426 0.812128 0.583479i \(-0.198309\pi\)
0.812128 + 0.583479i \(0.198309\pi\)
\(570\) 17.4891 3.75906i 0.732539 0.157449i
\(571\) −21.4891 −0.899292 −0.449646 0.893207i \(-0.648450\pi\)
−0.449646 + 0.893207i \(0.648450\pi\)
\(572\) 0 0
\(573\) 34.4010i 1.43712i
\(574\) 7.53262 0.314406
\(575\) −5.18614 11.5070i −0.216277 0.479875i
\(576\) 11.3723 0.473845
\(577\) 31.8217i 1.32476i −0.749170 0.662378i \(-0.769547\pi\)
0.749170 0.662378i \(-0.230453\pi\)
\(578\) 6.72582i 0.279757i
\(579\) −58.9783 −2.45105
\(580\) −8.23369 + 1.76972i −0.341885 + 0.0734837i
\(581\) −22.9783 −0.953298
\(582\) 8.21782i 0.340640i
\(583\) 3.16915i 0.131253i
\(584\) −18.5109 −0.765985
\(585\) 0 0
\(586\) −8.00000 −0.330477
\(587\) 28.0078i 1.15600i 0.816035 + 0.578002i \(0.196167\pi\)
−0.816035 + 0.578002i \(0.803833\pi\)
\(588\) 17.3205i 0.714286i
\(589\) 9.48913 0.390993
\(590\) 0.605969 + 2.81929i 0.0249474 + 0.116068i
\(591\) 4.74456 0.195165
\(592\) 6.92820i 0.284747i
\(593\) 43.5586i 1.78874i 0.447333 + 0.894368i \(0.352374\pi\)
−0.447333 + 0.894368i \(0.647626\pi\)
\(594\) 0.744563 0.0305498
\(595\) −38.2337 + 8.21782i −1.56743 + 0.336898i
\(596\) −15.7663 −0.645813
\(597\) 20.1947i 0.826514i
\(598\) 0 0
\(599\) 34.9783 1.42917 0.714586 0.699547i \(-0.246615\pi\)
0.714586 + 0.699547i \(0.246615\pi\)
\(600\) 30.7446 13.8564i 1.25514 0.565685i
\(601\) 30.4674 1.24279 0.621395 0.783497i \(-0.286566\pi\)
0.621395 + 0.783497i \(0.286566\pi\)
\(602\) 9.50744i 0.387494i
\(603\) 2.17448i 0.0885517i
\(604\) 30.5109 1.24147
\(605\) −2.18614 + 0.469882i −0.0888793 + 0.0191034i
\(606\) 12.0000 0.487467
\(607\) 3.46410i 0.140604i −0.997526 0.0703018i \(-0.977604\pi\)
0.997526 0.0703018i \(-0.0223962\pi\)
\(608\) 23.3639i 0.947529i
\(609\) 24.0000 0.972529
\(610\) 4.00000 + 18.6101i 0.161955 + 0.753502i
\(611\) 0 0
\(612\) 23.3639i 0.944428i
\(613\) 44.1485i 1.78314i −0.452883 0.891570i \(-0.649605\pi\)
0.452883 0.891570i \(-0.350395\pi\)
\(614\) 22.2772 0.899034
\(615\) 3.25544 + 15.1460i 0.131272 + 0.610747i
\(616\) 9.25544 0.372912
\(617\) 3.75906i 0.151334i 0.997133 + 0.0756669i \(0.0241086\pi\)
−0.997133 + 0.0756669i \(0.975891\pi\)
\(618\) 20.7846i 0.836080i
\(619\) 3.11684 0.125277 0.0626383 0.998036i \(-0.480049\pi\)
0.0626383 + 0.998036i \(0.480049\pi\)
\(620\) 7.11684 1.52967i 0.285819 0.0614331i
\(621\) −2.37228 −0.0951964
\(622\) 13.8564i 0.555591i
\(623\) 15.1460i 0.606813i
\(624\) 0 0
\(625\) 16.5584 18.7302i 0.662337 0.749206i
\(626\) −25.2119 −1.00767
\(627\) 10.0974i 0.403249i
\(628\) 7.40830i 0.295624i
\(629\) −55.7228 −2.22181
\(630\) −20.2337 + 4.34896i −0.806129 + 0.173267i
\(631\) −16.6060 −0.661073 −0.330537 0.943793i \(-0.607230\pi\)
−0.330537 + 0.943793i \(0.607230\pi\)
\(632\) 34.0511i 1.35448i
\(633\) 54.2458i 2.15608i
\(634\) 2.78806 0.110728
\(635\) 5.48913 + 25.5383i 0.217829 + 1.01346i
\(636\) 10.9783 0.435316
\(637\) 0 0
\(638\) 2.17448i 0.0860885i
\(639\) −24.0000 −0.949425
\(640\) 4.23369 + 19.6974i 0.167351 + 0.778607i
\(641\) −19.6277 −0.775248 −0.387624 0.921818i \(-0.626704\pi\)
−0.387624 + 0.921818i \(0.626704\pi\)
\(642\) 13.2665i 0.523587i
\(643\) 39.1547i 1.54411i 0.635556 + 0.772055i \(0.280771\pi\)
−0.635556 + 0.772055i \(0.719229\pi\)
\(644\) −12.0000 −0.472866
\(645\) 19.1168 4.10891i 0.752725 0.161788i
\(646\) −16.0000 −0.629512
\(647\) 41.0342i 1.61322i −0.591083 0.806611i \(-0.701299\pi\)
0.591083 0.806611i \(-0.298701\pi\)
\(648\) 20.6920i 0.812860i
\(649\) −1.62772 −0.0638935
\(650\) 0 0
\(651\) −20.7446 −0.813044
\(652\) 4.75372i 0.186170i
\(653\) 25.5932i 1.00154i 0.865580 + 0.500770i \(0.166950\pi\)
−0.865580 + 0.500770i \(0.833050\pi\)
\(654\) −20.0000 −0.782062
\(655\) −19.1168 + 4.10891i −0.746957 + 0.160548i
\(656\) −1.72281 −0.0672646
\(657\) 23.3639i 0.911511i
\(658\) 18.2054i 0.709719i
\(659\) −32.7446 −1.27555 −0.637774 0.770224i \(-0.720144\pi\)
−0.637774 + 0.770224i \(0.720144\pi\)
\(660\) 1.62772 + 7.57301i 0.0633589 + 0.294779i
\(661\) 35.3505 1.37498 0.687488 0.726196i \(-0.258713\pi\)
0.687488 + 0.726196i \(0.258713\pi\)
\(662\) 2.46943i 0.0959773i
\(663\) 0 0
\(664\) −17.7228 −0.687779
\(665\) −6.51087 30.2921i −0.252481 1.17468i
\(666\) −29.4891 −1.14268
\(667\) 6.92820i 0.268261i
\(668\) 30.6968i 1.18770i
\(669\) −19.1168 −0.739100
\(670\) −1.11684 + 0.240051i −0.0431474 + 0.00927397i
\(671\) −10.7446 −0.414789
\(672\) 51.0767i 1.97033i
\(673\) 1.28962i 0.0497112i −0.999691 0.0248556i \(-0.992087\pi\)
0.999691 0.0248556i \(-0.00791260\pi\)
\(674\) 9.95650 0.383510
\(675\) −1.93070 4.28384i −0.0743128 0.164885i
\(676\) 17.8397 0.686141
\(677\) 43.4487i 1.66987i −0.550348 0.834935i \(-0.685505\pi\)
0.550348 0.834935i \(-0.314495\pi\)
\(678\) 32.1716i 1.23554i
\(679\) 14.2337 0.546239
\(680\) −29.4891 + 6.33830i −1.13086 + 0.243063i
\(681\) −24.7446 −0.948214
\(682\) 1.87953i 0.0719708i
\(683\) 44.4434i 1.70058i 0.526314 + 0.850290i \(0.323573\pi\)
−0.526314 + 0.850290i \(0.676427\pi\)
\(684\) 18.5109 0.707781
\(685\) −1.04755 4.87375i −0.0400247 0.186216i
\(686\) −5.48913 −0.209576
\(687\) 51.4265i 1.96204i
\(688\) 2.17448i 0.0829013i
\(689\) 0 0
\(690\) 2.37228 + 11.0371i 0.0903112 + 0.420176i
\(691\) 16.1386 0.613941 0.306971 0.951719i \(-0.400685\pi\)
0.306971 + 0.951719i \(0.400685\pi\)
\(692\) 2.57924i 0.0980480i
\(693\) 11.6819i 0.443760i
\(694\) 23.2119 0.881113
\(695\) 39.8614 8.56768i 1.51203 0.324991i
\(696\) 18.5109 0.701653
\(697\) 13.8564i 0.524849i
\(698\) 5.93354i 0.224588i
\(699\) 42.9783 1.62559
\(700\) −9.76631 21.6695i −0.369132 0.819029i
\(701\) −35.4891 −1.34041 −0.670203 0.742178i \(-0.733793\pi\)
−0.670203 + 0.742178i \(0.733793\pi\)
\(702\) 0 0
\(703\) 44.1485i 1.66509i
\(704\) 3.37228 0.127098
\(705\) −36.6060 + 7.86797i −1.37866 + 0.296325i
\(706\) 17.2119 0.647780
\(707\) 20.7846i 0.781686i
\(708\) 5.63858i 0.211911i
\(709\) −41.1168 −1.54418 −0.772088 0.635516i \(-0.780787\pi\)
−0.772088 + 0.635516i \(0.780787\pi\)
\(710\) 2.64947 + 12.3267i 0.0994328 + 0.462614i
\(711\) 42.9783 1.61181
\(712\) 11.6819i 0.437799i
\(713\) 5.98844i 0.224269i
\(714\) 34.9783 1.30903
\(715\) 0 0
\(716\) 21.7663 0.813445
\(717\) 8.21782i 0.306900i
\(718\) 5.15848i 0.192513i
\(719\) −21.3505 −0.796240 −0.398120 0.917333i \(-0.630337\pi\)
−0.398120 + 0.917333i \(0.630337\pi\)
\(720\) 4.62772 0.994667i 0.172465 0.0370690i
\(721\) −36.0000 −1.34071
\(722\) 2.37686i 0.0884576i
\(723\) 13.2665i 0.493386i
\(724\) 9.44563 0.351044
\(725\) 12.5109 5.63858i 0.464642 0.209412i
\(726\) 2.00000 0.0742270
\(727\) 15.7908i 0.585650i 0.956166 + 0.292825i \(0.0945953\pi\)
−0.956166 + 0.292825i \(0.905405\pi\)
\(728\) 0 0
\(729\) 33.2337 1.23088
\(730\) 12.0000 2.57924i 0.444140 0.0954620i
\(731\) −17.4891 −0.646859
\(732\) 37.2203i 1.37570i
\(733\) 30.2921i 1.11886i 0.828877 + 0.559431i \(0.188980\pi\)
−0.828877 + 0.559431i \(0.811020\pi\)
\(734\) 19.0217 0.702106
\(735\) 5.93070 + 27.5928i 0.218757 + 1.01778i
\(736\) −14.7446 −0.543492
\(737\) 0.644810i 0.0237519i
\(738\) 7.33296i 0.269930i
\(739\) −0.744563 −0.0273892 −0.0136946 0.999906i \(-0.504359\pi\)
−0.0136946 + 0.999906i \(0.504359\pi\)
\(740\) −7.11684 33.1113i −0.261620 1.21720i
\(741\) 0 0
\(742\) 8.69793i 0.319311i
\(743\) 21.7793i 0.799004i −0.916732 0.399502i \(-0.869183\pi\)
0.916732 0.399502i \(-0.130817\pi\)
\(744\) −16.0000 −0.586588
\(745\) 25.1168 5.39853i 0.920210 0.197787i
\(746\) 6.51087 0.238380
\(747\) 22.3692i 0.818446i
\(748\) 6.92820i 0.253320i
\(749\) −22.9783 −0.839607
\(750\) −18.0000 + 13.2665i −0.657267 + 0.484424i
\(751\) 21.6277 0.789207 0.394603 0.918852i \(-0.370882\pi\)
0.394603 + 0.918852i \(0.370882\pi\)
\(752\) 4.16381i 0.151839i
\(753\) 12.3267i 0.449211i
\(754\) 0 0
\(755\) −48.6060 + 10.4472i −1.76895 + 0.380213i
\(756\) −4.46738 −0.162477
\(757\) 39.7995i 1.44654i 0.690567 + 0.723269i \(0.257361\pi\)
−0.690567 + 0.723269i \(0.742639\pi\)
\(758\) 5.04868i 0.183376i
\(759\) −6.37228 −0.231299
\(760\) −5.02175 23.3639i −0.182158 0.847496i
\(761\) 21.2554 0.770509 0.385255 0.922810i \(-0.374114\pi\)
0.385255 + 0.922810i \(0.374114\pi\)
\(762\) 23.3639i 0.846383i
\(763\) 34.6410i 1.25409i
\(764\) −18.7011 −0.676581
\(765\) 8.00000 + 37.2203i 0.289241 + 1.34570i
\(766\) 4.51087 0.162985
\(767\) 0 0
\(768\) 35.0458i 1.26461i
\(769\) 51.2119 1.84675 0.923375 0.383900i \(-0.125419\pi\)
0.923375 + 0.383900i \(0.125419\pi\)
\(770\) −6.00000 + 1.28962i −0.216225 + 0.0464747i
\(771\) 60.4674 2.17768
\(772\) 32.0618i 1.15393i
\(773\) 30.8820i 1.11075i −0.831601 0.555373i \(-0.812575\pi\)
0.831601 0.555373i \(-0.187425\pi\)
\(774\) −9.25544 −0.332680
\(775\) −10.8139 + 4.87375i −0.388445 + 0.175070i
\(776\) 10.9783 0.394096
\(777\) 96.5147i 3.46245i
\(778\) 7.81306i 0.280112i
\(779\) 10.9783 0.393337
\(780\) 0 0
\(781\) −7.11684 −0.254661
\(782\) 10.0974i 0.361081i