Properties

Label 1815.2.c.d.364.1
Level $1815$
Weight $2$
Character 1815.364
Analytic conductor $14.493$
Analytic rank $0$
Dimension $6$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1815,2,Mod(364,1815)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1815, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([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("1815.364");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1815 = 3 \cdot 5 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1815.c (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: \(14.4928479669\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: 6.0.350464.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 4x^{2} - 4x + 2 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2 \)
Twist minimal: no (minimal twist has level 165)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 364.1
Root \(0.403032 - 0.403032i\) of defining polynomial
Character \(\chi\) \(=\) 1815.364
Dual form 1815.2.c.d.364.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.67513i q^{2} +1.00000i q^{3} -5.15633 q^{4} +(-1.48119 - 1.67513i) q^{5} +2.67513 q^{6} -2.80606i q^{7} +8.44358i q^{8} -1.00000 q^{9} +O(q^{10})\) \(q-2.67513i q^{2} +1.00000i q^{3} -5.15633 q^{4} +(-1.48119 - 1.67513i) q^{5} +2.67513 q^{6} -2.80606i q^{7} +8.44358i q^{8} -1.00000 q^{9} +(-4.48119 + 3.96239i) q^{10} -5.15633i q^{12} -5.11871i q^{13} -7.50659 q^{14} +(1.67513 - 1.48119i) q^{15} +12.2750 q^{16} -4.54420i q^{17} +2.67513i q^{18} -4.57452 q^{19} +(7.63752 + 8.63752i) q^{20} +2.80606 q^{21} -4.00000i q^{23} -8.44358 q^{24} +(-0.612127 + 4.96239i) q^{25} -13.6932 q^{26} -1.00000i q^{27} +14.4690i q^{28} -2.38787 q^{29} +(-3.96239 - 4.48119i) q^{30} -0.962389 q^{31} -15.9502i q^{32} -12.1563 q^{34} +(-4.70052 + 4.15633i) q^{35} +5.15633 q^{36} +1.61213i q^{37} +12.2374i q^{38} +5.11871 q^{39} +(14.1441 - 12.5066i) q^{40} +2.38787 q^{41} -7.50659i q^{42} +2.80606i q^{43} +(1.48119 + 1.67513i) q^{45} -10.7005 q^{46} -4.31265i q^{47} +12.2750i q^{48} -0.873992 q^{49} +(13.2750 + 1.63752i) q^{50} +4.54420 q^{51} +26.3938i q^{52} +6.57452i q^{53} -2.67513 q^{54} +23.6932 q^{56} -4.57452i q^{57} +6.38787i q^{58} +13.2750 q^{59} +(-8.63752 + 7.63752i) q^{60} -7.92478 q^{61} +2.57452i q^{62} +2.80606i q^{63} -18.1187 q^{64} +(-8.57452 + 7.58181i) q^{65} +10.7005i q^{67} +23.4314i q^{68} +4.00000 q^{69} +(11.1187 + 12.5745i) q^{70} -7.35026 q^{71} -8.44358i q^{72} +6.41819i q^{73} +4.31265 q^{74} +(-4.96239 - 0.612127i) q^{75} +23.5877 q^{76} -13.6932i q^{78} +1.35026 q^{79} +(-18.1817 - 20.5623i) q^{80} +1.00000 q^{81} -6.38787i q^{82} -0.806063i q^{83} -14.4690 q^{84} +(-7.61213 + 6.73084i) q^{85} +7.50659 q^{86} -2.38787i q^{87} +2.96239 q^{89} +(4.48119 - 3.96239i) q^{90} -14.3634 q^{91} +20.6253i q^{92} -0.962389i q^{93} -11.5369 q^{94} +(6.77575 + 7.66291i) q^{95} +15.9502 q^{96} -9.92478i q^{97} +2.33804i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - 10 q^{4} + 2 q^{5} + 6 q^{6} - 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - 10 q^{4} + 2 q^{5} + 6 q^{6} - 6 q^{9} - 16 q^{10} - 4 q^{14} + 10 q^{16} - 4 q^{19} + 14 q^{20} + 16 q^{21} - 18 q^{24} - 2 q^{25} - 16 q^{26} - 16 q^{29} - 2 q^{30} + 16 q^{31} - 52 q^{34} + 12 q^{35} + 10 q^{36} - 12 q^{39} + 12 q^{40} + 16 q^{41} - 2 q^{45} - 24 q^{46} - 22 q^{49} + 16 q^{50} + 8 q^{51} - 6 q^{54} + 76 q^{56} + 16 q^{59} - 20 q^{60} - 4 q^{61} - 66 q^{64} - 28 q^{65} + 24 q^{69} + 24 q^{70} - 24 q^{71} - 16 q^{74} - 8 q^{75} + 36 q^{76} - 12 q^{79} - 58 q^{80} + 6 q^{81} - 24 q^{84} - 44 q^{85} + 4 q^{86} - 4 q^{89} + 16 q^{90} + 16 q^{91} - 24 q^{94} + 44 q^{95} + 22 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1815\mathbb{Z}\right)^\times\).

\(n\) \(727\) \(1211\) \(1696\)
\(\chi(n)\) \(-1\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.67513i 1.89160i −0.324745 0.945802i \(-0.605279\pi\)
0.324745 0.945802i \(-0.394721\pi\)
\(3\) 1.00000i 0.577350i
\(4\) −5.15633 −2.57816
\(5\) −1.48119 1.67513i −0.662410 0.749141i
\(6\) 2.67513 1.09212
\(7\) 2.80606i 1.06059i −0.847812 0.530296i \(-0.822081\pi\)
0.847812 0.530296i \(-0.177919\pi\)
\(8\) 8.44358i 2.98526i
\(9\) −1.00000 −0.333333
\(10\) −4.48119 + 3.96239i −1.41708 + 1.25302i
\(11\) 0 0
\(12\) 5.15633i 1.48850i
\(13\) 5.11871i 1.41968i −0.704365 0.709838i \(-0.748768\pi\)
0.704365 0.709838i \(-0.251232\pi\)
\(14\) −7.50659 −2.00622
\(15\) 1.67513 1.48119i 0.432517 0.382443i
\(16\) 12.2750 3.06876
\(17\) 4.54420i 1.10213i −0.834462 0.551065i \(-0.814222\pi\)
0.834462 0.551065i \(-0.185778\pi\)
\(18\) 2.67513i 0.630534i
\(19\) −4.57452 −1.04947 −0.524733 0.851267i \(-0.675835\pi\)
−0.524733 + 0.851267i \(0.675835\pi\)
\(20\) 7.63752 + 8.63752i 1.70780 + 1.93141i
\(21\) 2.80606 0.612333
\(22\) 0 0
\(23\) 4.00000i 0.834058i −0.908893 0.417029i \(-0.863071\pi\)
0.908893 0.417029i \(-0.136929\pi\)
\(24\) −8.44358 −1.72354
\(25\) −0.612127 + 4.96239i −0.122425 + 0.992478i
\(26\) −13.6932 −2.68546
\(27\) 1.00000i 0.192450i
\(28\) 14.4690i 2.73438i
\(29\) −2.38787 −0.443417 −0.221708 0.975113i \(-0.571163\pi\)
−0.221708 + 0.975113i \(0.571163\pi\)
\(30\) −3.96239 4.48119i −0.723430 0.818150i
\(31\) −0.962389 −0.172850 −0.0864250 0.996258i \(-0.527544\pi\)
−0.0864250 + 0.996258i \(0.527544\pi\)
\(32\) 15.9502i 2.81962i
\(33\) 0 0
\(34\) −12.1563 −2.08479
\(35\) −4.70052 + 4.15633i −0.794533 + 0.702547i
\(36\) 5.15633 0.859388
\(37\) 1.61213i 0.265032i 0.991181 + 0.132516i \(0.0423056\pi\)
−0.991181 + 0.132516i \(0.957694\pi\)
\(38\) 12.2374i 1.98517i
\(39\) 5.11871 0.819650
\(40\) 14.1441 12.5066i 2.23638 1.97747i
\(41\) 2.38787 0.372923 0.186462 0.982462i \(-0.440298\pi\)
0.186462 + 0.982462i \(0.440298\pi\)
\(42\) 7.50659i 1.15829i
\(43\) 2.80606i 0.427921i 0.976842 + 0.213960i \(0.0686363\pi\)
−0.976842 + 0.213960i \(0.931364\pi\)
\(44\) 0 0
\(45\) 1.48119 + 1.67513i 0.220803 + 0.249714i
\(46\) −10.7005 −1.57771
\(47\) 4.31265i 0.629065i −0.949247 0.314532i \(-0.898152\pi\)
0.949247 0.314532i \(-0.101848\pi\)
\(48\) 12.2750i 1.77175i
\(49\) −0.873992 −0.124856
\(50\) 13.2750 + 1.63752i 1.87737 + 0.231580i
\(51\) 4.54420 0.636315
\(52\) 26.3938i 3.66015i
\(53\) 6.57452i 0.903079i 0.892251 + 0.451540i \(0.149125\pi\)
−0.892251 + 0.451540i \(0.850875\pi\)
\(54\) −2.67513 −0.364039
\(55\) 0 0
\(56\) 23.6932 3.16614
\(57\) 4.57452i 0.605909i
\(58\) 6.38787i 0.838769i
\(59\) 13.2750 1.72826 0.864131 0.503266i \(-0.167868\pi\)
0.864131 + 0.503266i \(0.167868\pi\)
\(60\) −8.63752 + 7.63752i −1.11510 + 0.986000i
\(61\) −7.92478 −1.01466 −0.507332 0.861751i \(-0.669368\pi\)
−0.507332 + 0.861751i \(0.669368\pi\)
\(62\) 2.57452i 0.326964i
\(63\) 2.80606i 0.353531i
\(64\) −18.1187 −2.26484
\(65\) −8.57452 + 7.58181i −1.06354 + 0.940408i
\(66\) 0 0
\(67\) 10.7005i 1.30728i 0.756807 + 0.653639i \(0.226758\pi\)
−0.756807 + 0.653639i \(0.773242\pi\)
\(68\) 23.4314i 2.84147i
\(69\) 4.00000 0.481543
\(70\) 11.1187 + 12.5745i 1.32894 + 1.50294i
\(71\) −7.35026 −0.872316 −0.436158 0.899870i \(-0.643661\pi\)
−0.436158 + 0.899870i \(0.643661\pi\)
\(72\) 8.44358i 0.995086i
\(73\) 6.41819i 0.751192i 0.926783 + 0.375596i \(0.122562\pi\)
−0.926783 + 0.375596i \(0.877438\pi\)
\(74\) 4.31265 0.501335
\(75\) −4.96239 0.612127i −0.573007 0.0706823i
\(76\) 23.5877 2.70569
\(77\) 0 0
\(78\) 13.6932i 1.55045i
\(79\) 1.35026 0.151916 0.0759582 0.997111i \(-0.475798\pi\)
0.0759582 + 0.997111i \(0.475798\pi\)
\(80\) −18.1817 20.5623i −2.03278 2.29893i
\(81\) 1.00000 0.111111
\(82\) 6.38787i 0.705423i
\(83\) 0.806063i 0.0884770i −0.999021 0.0442385i \(-0.985914\pi\)
0.999021 0.0442385i \(-0.0140861\pi\)
\(84\) −14.4690 −1.57869
\(85\) −7.61213 + 6.73084i −0.825651 + 0.730062i
\(86\) 7.50659 0.809456
\(87\) 2.38787i 0.256007i
\(88\) 0 0
\(89\) 2.96239 0.314013 0.157006 0.987598i \(-0.449816\pi\)
0.157006 + 0.987598i \(0.449816\pi\)
\(90\) 4.48119 3.96239i 0.472359 0.417672i
\(91\) −14.3634 −1.50570
\(92\) 20.6253i 2.15034i
\(93\) 0.962389i 0.0997950i
\(94\) −11.5369 −1.18994
\(95\) 6.77575 + 7.66291i 0.695177 + 0.786198i
\(96\) 15.9502 1.62791
\(97\) 9.92478i 1.00771i −0.863789 0.503854i \(-0.831915\pi\)
0.863789 0.503854i \(-0.168085\pi\)
\(98\) 2.33804i 0.236178i
\(99\) 0 0
\(100\) 3.15633 25.5877i 0.315633 2.55877i
\(101\) 13.6121 1.35446 0.677229 0.735773i \(-0.263181\pi\)
0.677229 + 0.735773i \(0.263181\pi\)
\(102\) 12.1563i 1.20366i
\(103\) 16.3127i 1.60733i −0.595080 0.803667i \(-0.702880\pi\)
0.595080 0.803667i \(-0.297120\pi\)
\(104\) 43.2203 4.23810
\(105\) −4.15633 4.70052i −0.405616 0.458724i
\(106\) 17.5877 1.70827
\(107\) 9.43136i 0.911764i 0.890040 + 0.455882i \(0.150676\pi\)
−0.890040 + 0.455882i \(0.849324\pi\)
\(108\) 5.15633i 0.496168i
\(109\) −15.4010 −1.47515 −0.737576 0.675264i \(-0.764030\pi\)
−0.737576 + 0.675264i \(0.764030\pi\)
\(110\) 0 0
\(111\) −1.61213 −0.153016
\(112\) 34.4445i 3.25470i
\(113\) 13.7381i 1.29238i 0.763179 + 0.646188i \(0.223638\pi\)
−0.763179 + 0.646188i \(0.776362\pi\)
\(114\) −12.2374 −1.14614
\(115\) −6.70052 + 5.92478i −0.624827 + 0.552488i
\(116\) 12.3127 1.14320
\(117\) 5.11871i 0.473225i
\(118\) 35.5125i 3.26919i
\(119\) −12.7513 −1.16891
\(120\) 12.5066 + 14.1441i 1.14169 + 1.29117i
\(121\) 0 0
\(122\) 21.1998i 1.91934i
\(123\) 2.38787i 0.215307i
\(124\) 4.96239 0.445636
\(125\) 9.21933 6.32487i 0.824602 0.565713i
\(126\) 7.50659 0.668740
\(127\) 12.4182i 1.10194i −0.834526 0.550968i \(-0.814259\pi\)
0.834526 0.550968i \(-0.185741\pi\)
\(128\) 16.5696i 1.46456i
\(129\) −2.80606 −0.247060
\(130\) 20.2823 + 22.9380i 1.77888 + 2.01179i
\(131\) −5.92478 −0.517650 −0.258825 0.965924i \(-0.583335\pi\)
−0.258825 + 0.965924i \(0.583335\pi\)
\(132\) 0 0
\(133\) 12.8364i 1.11306i
\(134\) 28.6253 2.47285
\(135\) −1.67513 + 1.48119i −0.144172 + 0.127481i
\(136\) 38.3693 3.29014
\(137\) 9.79877i 0.837165i 0.908179 + 0.418583i \(0.137473\pi\)
−0.908179 + 0.418583i \(0.862527\pi\)
\(138\) 10.7005i 0.910889i
\(139\) −2.12601 −0.180326 −0.0901628 0.995927i \(-0.528739\pi\)
−0.0901628 + 0.995927i \(0.528739\pi\)
\(140\) 24.2374 21.4314i 2.04844 1.81128i
\(141\) 4.31265 0.363191
\(142\) 19.6629i 1.65007i
\(143\) 0 0
\(144\) −12.2750 −1.02292
\(145\) 3.53690 + 4.00000i 0.293724 + 0.332182i
\(146\) 17.1695 1.42096
\(147\) 0.873992i 0.0720856i
\(148\) 8.31265i 0.683296i
\(149\) 8.31265 0.680999 0.340499 0.940245i \(-0.389404\pi\)
0.340499 + 0.940245i \(0.389404\pi\)
\(150\) −1.63752 + 13.2750i −0.133703 + 1.08390i
\(151\) 15.2750 1.24307 0.621533 0.783388i \(-0.286510\pi\)
0.621533 + 0.783388i \(0.286510\pi\)
\(152\) 38.6253i 3.13293i
\(153\) 4.54420i 0.367377i
\(154\) 0 0
\(155\) 1.42548 + 1.61213i 0.114498 + 0.129489i
\(156\) −26.3938 −2.11319
\(157\) 7.01317i 0.559712i 0.960042 + 0.279856i \(0.0902868\pi\)
−0.960042 + 0.279856i \(0.909713\pi\)
\(158\) 3.61213i 0.287365i
\(159\) −6.57452 −0.521393
\(160\) −26.7186 + 23.6253i −2.11229 + 1.86774i
\(161\) −11.2243 −0.884595
\(162\) 2.67513i 0.210178i
\(163\) 6.76116i 0.529575i −0.964307 0.264787i \(-0.914698\pi\)
0.964307 0.264787i \(-0.0853018\pi\)
\(164\) −12.3127 −0.961456
\(165\) 0 0
\(166\) −2.15633 −0.167363
\(167\) 11.8192i 0.914600i 0.889312 + 0.457300i \(0.151183\pi\)
−0.889312 + 0.457300i \(0.848817\pi\)
\(168\) 23.6932i 1.82797i
\(169\) −13.2012 −1.01548
\(170\) 18.0059 + 20.3634i 1.38099 + 1.56180i
\(171\) 4.57452 0.349822
\(172\) 14.4690i 1.10325i
\(173\) 6.99271i 0.531646i 0.964022 + 0.265823i \(0.0856436\pi\)
−0.964022 + 0.265823i \(0.914356\pi\)
\(174\) −6.38787 −0.484263
\(175\) 13.9248 + 1.71767i 1.05261 + 0.129843i
\(176\) 0 0
\(177\) 13.2750i 0.997813i
\(178\) 7.92478i 0.593987i
\(179\) 2.70052 0.201847 0.100923 0.994894i \(-0.467820\pi\)
0.100923 + 0.994894i \(0.467820\pi\)
\(180\) −7.63752 8.63752i −0.569267 0.643803i
\(181\) −21.1998 −1.57577 −0.787885 0.615822i \(-0.788824\pi\)
−0.787885 + 0.615822i \(0.788824\pi\)
\(182\) 38.4241i 2.84818i
\(183\) 7.92478i 0.585816i
\(184\) 33.7743 2.48988
\(185\) 2.70052 2.38787i 0.198546 0.175560i
\(186\) −2.57452 −0.188773
\(187\) 0 0
\(188\) 22.2374i 1.62183i
\(189\) −2.80606 −0.204111
\(190\) 20.4993 18.1260i 1.48717 1.31500i
\(191\) 13.1490 0.951430 0.475715 0.879599i \(-0.342189\pi\)
0.475715 + 0.879599i \(0.342189\pi\)
\(192\) 18.1187i 1.30761i
\(193\) 5.89446i 0.424293i 0.977238 + 0.212146i \(0.0680453\pi\)
−0.977238 + 0.212146i \(0.931955\pi\)
\(194\) −26.5501 −1.90618
\(195\) −7.58181 8.57452i −0.542945 0.614034i
\(196\) 4.50659 0.321899
\(197\) 20.3938i 1.45299i −0.687169 0.726497i \(-0.741147\pi\)
0.687169 0.726497i \(-0.258853\pi\)
\(198\) 0 0
\(199\) −17.4010 −1.23353 −0.616764 0.787148i \(-0.711557\pi\)
−0.616764 + 0.787148i \(0.711557\pi\)
\(200\) −41.9003 5.16854i −2.96280 0.365471i
\(201\) −10.7005 −0.754757
\(202\) 36.4142i 2.56210i
\(203\) 6.70052i 0.470285i
\(204\) −23.4314 −1.64052
\(205\) −3.53690 4.00000i −0.247028 0.279372i
\(206\) −43.6385 −3.04044
\(207\) 4.00000i 0.278019i
\(208\) 62.8324i 4.35664i
\(209\) 0 0
\(210\) −12.5745 + 11.1187i −0.867724 + 0.767264i
\(211\) −18.1260 −1.24785 −0.623923 0.781486i \(-0.714462\pi\)
−0.623923 + 0.781486i \(0.714462\pi\)
\(212\) 33.9003i 2.32828i
\(213\) 7.35026i 0.503632i
\(214\) 25.2301 1.72470
\(215\) 4.70052 4.15633i 0.320573 0.283459i
\(216\) 8.44358 0.574513
\(217\) 2.70052i 0.183323i
\(218\) 41.1998i 2.79040i
\(219\) −6.41819 −0.433701
\(220\) 0 0
\(221\) −23.2605 −1.56467
\(222\) 4.31265i 0.289446i
\(223\) 23.6385i 1.58295i −0.611202 0.791475i \(-0.709314\pi\)
0.611202 0.791475i \(-0.290686\pi\)
\(224\) −44.7572 −2.99047
\(225\) 0.612127 4.96239i 0.0408085 0.330826i
\(226\) 36.7513 2.44466
\(227\) 1.26916i 0.0842371i 0.999113 + 0.0421185i \(0.0134107\pi\)
−0.999113 + 0.0421185i \(0.986589\pi\)
\(228\) 23.5877i 1.56213i
\(229\) −16.1768 −1.06899 −0.534496 0.845171i \(-0.679499\pi\)
−0.534496 + 0.845171i \(0.679499\pi\)
\(230\) 15.8496 + 17.9248i 1.04509 + 1.18192i
\(231\) 0 0
\(232\) 20.1622i 1.32371i
\(233\) 18.4690i 1.20994i −0.796247 0.604971i \(-0.793185\pi\)
0.796247 0.604971i \(-0.206815\pi\)
\(234\) 13.6932 0.895154
\(235\) −7.22425 + 6.38787i −0.471258 + 0.416699i
\(236\) −68.4504 −4.45574
\(237\) 1.35026i 0.0877089i
\(238\) 34.1114i 2.21111i
\(239\) 19.3258 1.25008 0.625042 0.780591i \(-0.285082\pi\)
0.625042 + 0.780591i \(0.285082\pi\)
\(240\) 20.5623 18.1817i 1.32729 1.17362i
\(241\) −28.5501 −1.83907 −0.919536 0.393006i \(-0.871435\pi\)
−0.919536 + 0.393006i \(0.871435\pi\)
\(242\) 0 0
\(243\) 1.00000i 0.0641500i
\(244\) 40.8627 2.61597
\(245\) 1.29455 + 1.46405i 0.0827059 + 0.0935348i
\(246\) 6.38787 0.407276
\(247\) 23.4156i 1.48990i
\(248\) 8.12601i 0.516002i
\(249\) 0.806063 0.0510822
\(250\) −16.9199 24.6629i −1.07011 1.55982i
\(251\) 23.1998 1.46436 0.732180 0.681112i \(-0.238503\pi\)
0.732180 + 0.681112i \(0.238503\pi\)
\(252\) 14.4690i 0.911460i
\(253\) 0 0
\(254\) −33.2203 −2.08443
\(255\) −6.73084 7.61213i −0.421502 0.476690i
\(256\) 8.08840 0.505525
\(257\) 10.8872i 0.679123i −0.940584 0.339561i \(-0.889721\pi\)
0.940584 0.339561i \(-0.110279\pi\)
\(258\) 7.50659i 0.467340i
\(259\) 4.52373 0.281091
\(260\) 44.2130 39.0943i 2.74197 2.42452i
\(261\) 2.38787 0.147806
\(262\) 15.8496i 0.979189i
\(263\) 9.11871i 0.562284i 0.959666 + 0.281142i \(0.0907132\pi\)
−0.959666 + 0.281142i \(0.909287\pi\)
\(264\) 0 0
\(265\) 11.0132 9.73813i 0.676534 0.598209i
\(266\) 34.3390 2.10546
\(267\) 2.96239i 0.181295i
\(268\) 55.1754i 3.37037i
\(269\) 11.2995 0.688941 0.344471 0.938797i \(-0.388058\pi\)
0.344471 + 0.938797i \(0.388058\pi\)
\(270\) 3.96239 + 4.48119i 0.241143 + 0.272717i
\(271\) −25.1998 −1.53078 −0.765390 0.643567i \(-0.777454\pi\)
−0.765390 + 0.643567i \(0.777454\pi\)
\(272\) 55.7802i 3.38217i
\(273\) 14.3634i 0.869315i
\(274\) 26.2130 1.58358
\(275\) 0 0
\(276\) −20.6253 −1.24150
\(277\) 2.41819i 0.145295i 0.997358 + 0.0726475i \(0.0231448\pi\)
−0.997358 + 0.0726475i \(0.976855\pi\)
\(278\) 5.68735i 0.341105i
\(279\) 0.962389 0.0576167
\(280\) −35.0943 39.6893i −2.09728 2.37189i
\(281\) −30.4894 −1.81885 −0.909424 0.415870i \(-0.863477\pi\)
−0.909424 + 0.415870i \(0.863477\pi\)
\(282\) 11.5369i 0.687013i
\(283\) 8.35756i 0.496805i 0.968657 + 0.248403i \(0.0799056\pi\)
−0.968657 + 0.248403i \(0.920094\pi\)
\(284\) 37.9003 2.24897
\(285\) −7.66291 + 6.77575i −0.453912 + 0.401361i
\(286\) 0 0
\(287\) 6.70052i 0.395519i
\(288\) 15.9502i 0.939873i
\(289\) −3.64974 −0.214690
\(290\) 10.7005 9.46168i 0.628356 0.555609i
\(291\) 9.92478 0.581801
\(292\) 33.0943i 1.93670i
\(293\) 23.0943i 1.34918i −0.738192 0.674591i \(-0.764320\pi\)
0.738192 0.674591i \(-0.235680\pi\)
\(294\) −2.33804 −0.136357
\(295\) −19.6629 22.2374i −1.14482 1.29471i
\(296\) −13.6121 −0.791189
\(297\) 0 0
\(298\) 22.2374i 1.28818i
\(299\) −20.4749 −1.18409
\(300\) 25.5877 + 3.15633i 1.47731 + 0.182231i
\(301\) 7.87399 0.453849
\(302\) 40.8627i 2.35139i
\(303\) 13.6121i 0.781996i
\(304\) −56.1524 −3.22056
\(305\) 11.7381 + 13.2750i 0.672124 + 0.760127i
\(306\) 12.1563 0.694931
\(307\) 2.65562i 0.151564i −0.997124 0.0757821i \(-0.975855\pi\)
0.997124 0.0757821i \(-0.0241453\pi\)
\(308\) 0 0
\(309\) 16.3127 0.927994
\(310\) 4.31265 3.81336i 0.244942 0.216584i
\(311\) −15.9756 −0.905891 −0.452946 0.891538i \(-0.649627\pi\)
−0.452946 + 0.891538i \(0.649627\pi\)
\(312\) 43.2203i 2.44687i
\(313\) 0.0606343i 0.00342726i 0.999999 + 0.00171363i \(0.000545465\pi\)
−0.999999 + 0.00171363i \(0.999455\pi\)
\(314\) 18.7612 1.05875
\(315\) 4.70052 4.15633i 0.264844 0.234182i
\(316\) −6.96239 −0.391665
\(317\) 3.81336i 0.214180i 0.994249 + 0.107090i \(0.0341532\pi\)
−0.994249 + 0.107090i \(0.965847\pi\)
\(318\) 17.5877i 0.986269i
\(319\) 0 0
\(320\) 26.8373 + 30.3512i 1.50025 + 1.69668i
\(321\) −9.43136 −0.526407
\(322\) 30.0263i 1.67330i
\(323\) 20.7875i 1.15665i
\(324\) −5.15633 −0.286463
\(325\) 25.4010 + 3.13330i 1.40900 + 0.173804i
\(326\) −18.0870 −1.00175
\(327\) 15.4010i 0.851680i
\(328\) 20.1622i 1.11327i
\(329\) −12.1016 −0.667181
\(330\) 0 0
\(331\) 24.2882 1.33500 0.667500 0.744609i \(-0.267364\pi\)
0.667500 + 0.744609i \(0.267364\pi\)
\(332\) 4.15633i 0.228108i
\(333\) 1.61213i 0.0883440i
\(334\) 31.6180 1.73006
\(335\) 17.9248 15.8496i 0.979335 0.865954i
\(336\) 34.4445 1.87910
\(337\) 22.5804i 1.23003i 0.788514 + 0.615016i \(0.210851\pi\)
−0.788514 + 0.615016i \(0.789149\pi\)
\(338\) 35.3150i 1.92088i
\(339\) −13.7381 −0.746153
\(340\) 39.2506 34.7064i 2.12866 1.88222i
\(341\) 0 0
\(342\) 12.2374i 0.661724i
\(343\) 17.1900i 0.928171i
\(344\) −23.6932 −1.27745
\(345\) −5.92478 6.70052i −0.318979 0.360744i
\(346\) 18.7064 1.00566
\(347\) 20.1925i 1.08399i −0.840381 0.541996i \(-0.817669\pi\)
0.840381 0.541996i \(-0.182331\pi\)
\(348\) 12.3127i 0.660027i
\(349\) −27.2506 −1.45869 −0.729346 0.684145i \(-0.760175\pi\)
−0.729346 + 0.684145i \(0.760175\pi\)
\(350\) 4.59498 37.2506i 0.245612 1.99113i
\(351\) −5.11871 −0.273217
\(352\) 0 0
\(353\) 5.02302i 0.267349i −0.991025 0.133674i \(-0.957322\pi\)
0.991025 0.133674i \(-0.0426776\pi\)
\(354\) 35.5125 1.88747
\(355\) 10.8872 + 12.3127i 0.577831 + 0.653488i
\(356\) −15.2750 −0.809575
\(357\) 12.7513i 0.674871i
\(358\) 7.22425i 0.381814i
\(359\) −18.1768 −0.959334 −0.479667 0.877450i \(-0.659243\pi\)
−0.479667 + 0.877450i \(0.659243\pi\)
\(360\) −14.1441 + 12.5066i −0.745460 + 0.659155i
\(361\) 1.92619 0.101379
\(362\) 56.7123i 2.98073i
\(363\) 0 0
\(364\) 74.0625 3.88193
\(365\) 10.7513 9.50659i 0.562749 0.497598i
\(366\) −21.1998 −1.10813
\(367\) 8.56467i 0.447072i −0.974696 0.223536i \(-0.928240\pi\)
0.974696 0.223536i \(-0.0717600\pi\)
\(368\) 49.1002i 2.55952i
\(369\) −2.38787 −0.124308
\(370\) −6.38787 7.22425i −0.332090 0.375571i
\(371\) 18.4485 0.957799
\(372\) 4.96239i 0.257288i
\(373\) 7.81924i 0.404865i 0.979296 + 0.202432i \(0.0648846\pi\)
−0.979296 + 0.202432i \(0.935115\pi\)
\(374\) 0 0
\(375\) 6.32487 + 9.21933i 0.326615 + 0.476084i
\(376\) 36.4142 1.87792
\(377\) 12.2228i 0.629508i
\(378\) 7.50659i 0.386097i
\(379\) −1.14903 −0.0590218 −0.0295109 0.999564i \(-0.509395\pi\)
−0.0295109 + 0.999564i \(0.509395\pi\)
\(380\) −34.9380 39.5125i −1.79228 2.02695i
\(381\) 12.4182 0.636203
\(382\) 35.1754i 1.79973i
\(383\) 34.0870i 1.74176i −0.491493 0.870882i \(-0.663549\pi\)
0.491493 0.870882i \(-0.336451\pi\)
\(384\) −16.5696 −0.845563
\(385\) 0 0
\(386\) 15.7685 0.802593
\(387\) 2.80606i 0.142640i
\(388\) 51.1754i 2.59804i
\(389\) −23.7743 −1.20541 −0.602703 0.797965i \(-0.705910\pi\)
−0.602703 + 0.797965i \(0.705910\pi\)
\(390\) −22.9380 + 20.2823i −1.16151 + 1.02704i
\(391\) −18.1768 −0.919240
\(392\) 7.37962i 0.372727i
\(393\) 5.92478i 0.298865i
\(394\) −54.5560 −2.74849
\(395\) −2.00000 2.26187i −0.100631 0.113807i
\(396\) 0 0
\(397\) 4.15045i 0.208305i −0.994561 0.104152i \(-0.966787\pi\)
0.994561 0.104152i \(-0.0332130\pi\)
\(398\) 46.5501i 2.33334i
\(399\) −12.8364 −0.642623
\(400\) −7.51388 + 60.9135i −0.375694 + 3.04568i
\(401\) −33.9149 −1.69363 −0.846815 0.531887i \(-0.821483\pi\)
−0.846815 + 0.531887i \(0.821483\pi\)
\(402\) 28.6253i 1.42770i
\(403\) 4.92619i 0.245391i
\(404\) −70.1886 −3.49201
\(405\) −1.48119 1.67513i −0.0736011 0.0832379i
\(406\) 17.9248 0.889592
\(407\) 0 0
\(408\) 38.3693i 1.89956i
\(409\) 8.55008 0.422774 0.211387 0.977402i \(-0.432202\pi\)
0.211387 + 0.977402i \(0.432202\pi\)
\(410\) −10.7005 + 9.46168i −0.528461 + 0.467279i
\(411\) −9.79877 −0.483338
\(412\) 84.1133i 4.14397i
\(413\) 37.2506i 1.83298i
\(414\) 10.7005 0.525902
\(415\) −1.35026 + 1.19394i −0.0662817 + 0.0586080i
\(416\) −81.6444 −4.00294
\(417\) 2.12601i 0.104111i
\(418\) 0 0
\(419\) −13.2995 −0.649722 −0.324861 0.945762i \(-0.605318\pi\)
−0.324861 + 0.945762i \(0.605318\pi\)
\(420\) 21.4314 + 24.2374i 1.04574 + 1.18267i
\(421\) 33.3014 1.62301 0.811505 0.584345i \(-0.198649\pi\)
0.811505 + 0.584345i \(0.198649\pi\)
\(422\) 48.4894i 2.36043i
\(423\) 4.31265i 0.209688i
\(424\) −55.5125 −2.69592
\(425\) 22.5501 + 2.78163i 1.09384 + 0.134929i
\(426\) −19.6629 −0.952671
\(427\) 22.2374i 1.07614i
\(428\) 48.6312i 2.35068i
\(429\) 0 0
\(430\) −11.1187 12.5745i −0.536192 0.606397i
\(431\) −2.07522 −0.0999600 −0.0499800 0.998750i \(-0.515916\pi\)
−0.0499800 + 0.998750i \(0.515916\pi\)
\(432\) 12.2750i 0.590583i
\(433\) 37.4010i 1.79738i 0.438585 + 0.898690i \(0.355480\pi\)
−0.438585 + 0.898690i \(0.644520\pi\)
\(434\) 7.22425 0.346775
\(435\) −4.00000 + 3.53690i −0.191785 + 0.169582i
\(436\) 79.4128 3.80318
\(437\) 18.2981i 0.875315i
\(438\) 17.1695i 0.820390i
\(439\) −6.02444 −0.287531 −0.143765 0.989612i \(-0.545921\pi\)
−0.143765 + 0.989612i \(0.545921\pi\)
\(440\) 0 0
\(441\) 0.873992 0.0416187
\(442\) 62.2247i 2.95973i
\(443\) 10.1359i 0.481569i 0.970579 + 0.240785i \(0.0774047\pi\)
−0.970579 + 0.240785i \(0.922595\pi\)
\(444\) 8.31265 0.394501
\(445\) −4.38787 4.96239i −0.208005 0.235240i
\(446\) −63.2360 −2.99431
\(447\) 8.31265i 0.393175i
\(448\) 50.8423i 2.40207i
\(449\) 11.4861 0.542063 0.271032 0.962570i \(-0.412635\pi\)
0.271032 + 0.962570i \(0.412635\pi\)
\(450\) −13.2750 1.63752i −0.625791 0.0771934i
\(451\) 0 0
\(452\) 70.8383i 3.33195i
\(453\) 15.2750i 0.717684i
\(454\) 3.39517 0.159343
\(455\) 21.2750 + 24.0606i 0.997389 + 1.12798i
\(456\) 38.6253 1.80880
\(457\) 15.0435i 0.703705i 0.936055 + 0.351852i \(0.114448\pi\)
−0.936055 + 0.351852i \(0.885552\pi\)
\(458\) 43.2750i 2.02211i
\(459\) −4.54420 −0.212105
\(460\) 34.5501 30.5501i 1.61091 1.42440i
\(461\) 26.2374 1.22200 0.610999 0.791631i \(-0.290768\pi\)
0.610999 + 0.791631i \(0.290768\pi\)
\(462\) 0 0
\(463\) 5.46168i 0.253826i 0.991914 + 0.126913i \(0.0405069\pi\)
−0.991914 + 0.126913i \(0.959493\pi\)
\(464\) −29.3112 −1.36074
\(465\) −1.61213 + 1.42548i −0.0747606 + 0.0661053i
\(466\) −49.4069 −2.28873
\(467\) 2.70052i 0.124965i −0.998046 0.0624827i \(-0.980098\pi\)
0.998046 0.0624827i \(-0.0199018\pi\)
\(468\) 26.3938i 1.22005i
\(469\) 30.0263 1.38649
\(470\) 17.0884 + 19.3258i 0.788229 + 0.891434i
\(471\) −7.01317 −0.323150
\(472\) 112.089i 5.15931i
\(473\) 0 0
\(474\) 3.61213 0.165910
\(475\) 2.80018 22.7005i 0.128481 1.04157i
\(476\) 65.7499 3.01364
\(477\) 6.57452i 0.301026i
\(478\) 51.6991i 2.36466i
\(479\) 16.7757 0.766503 0.383252 0.923644i \(-0.374804\pi\)
0.383252 + 0.923644i \(0.374804\pi\)
\(480\) −23.6253 26.7186i −1.07834 1.21953i
\(481\) 8.25202 0.376260
\(482\) 76.3752i 3.47879i
\(483\) 11.2243i 0.510721i
\(484\) 0 0
\(485\) −16.6253 + 14.7005i −0.754916 + 0.667516i
\(486\) 2.67513 0.121346
\(487\) 34.3996i 1.55880i −0.626529 0.779398i \(-0.715525\pi\)
0.626529 0.779398i \(-0.284475\pi\)
\(488\) 66.9135i 3.02903i
\(489\) 6.76116 0.305750
\(490\) 3.91653 3.46310i 0.176931 0.156447i
\(491\) −14.9525 −0.674799 −0.337399 0.941362i \(-0.609547\pi\)
−0.337399 + 0.941362i \(0.609547\pi\)
\(492\) 12.3127i 0.555097i
\(493\) 10.8510i 0.488703i
\(494\) 62.6399 2.81830
\(495\) 0 0
\(496\) −11.8134 −0.530435
\(497\) 20.6253i 0.925171i
\(498\) 2.15633i 0.0966272i
\(499\) 2.85097 0.127627 0.0638135 0.997962i \(-0.479674\pi\)
0.0638135 + 0.997962i \(0.479674\pi\)
\(500\) −47.5379 + 32.6131i −2.12596 + 1.45850i
\(501\) −11.8192 −0.528045
\(502\) 62.0625i 2.76999i
\(503\) 1.48024i 0.0660006i 0.999455 + 0.0330003i \(0.0105062\pi\)
−0.999455 + 0.0330003i \(0.989494\pi\)
\(504\) −23.6932 −1.05538
\(505\) −20.1622 22.8021i −0.897206 1.01468i
\(506\) 0 0
\(507\) 13.2012i 0.586287i
\(508\) 64.0322i 2.84097i
\(509\) 23.2995 1.03273 0.516366 0.856368i \(-0.327285\pi\)
0.516366 + 0.856368i \(0.327285\pi\)
\(510\) −20.3634 + 18.0059i −0.901708 + 0.797314i
\(511\) 18.0098 0.796709
\(512\) 11.5017i 0.508306i
\(513\) 4.57452i 0.201970i
\(514\) −29.1246 −1.28463
\(515\) −27.3258 + 24.1622i −1.20412 + 1.06471i
\(516\) 14.4690 0.636961
\(517\) 0 0
\(518\) 12.1016i 0.531712i
\(519\) −6.99271 −0.306946
\(520\) −64.0176 72.3996i −2.80736 3.17493i
\(521\) −6.81194 −0.298437 −0.149218 0.988804i \(-0.547676\pi\)
−0.149218 + 0.988804i \(0.547676\pi\)
\(522\) 6.38787i 0.279590i
\(523\) 16.0567i 0.702109i −0.936355 0.351054i \(-0.885823\pi\)
0.936355 0.351054i \(-0.114177\pi\)
\(524\) 30.5501 1.33459
\(525\) −1.71767 + 13.9248i −0.0749651 + 0.607727i
\(526\) 24.3938 1.06362
\(527\) 4.37328i 0.190503i
\(528\) 0 0
\(529\) 7.00000 0.304348
\(530\) −26.0508 29.4617i −1.13157 1.27973i
\(531\) −13.2750 −0.576088
\(532\) 66.1886i 2.86964i
\(533\) 12.2228i 0.529430i
\(534\) 7.92478 0.342939
\(535\) 15.7988 13.9697i 0.683040 0.603962i
\(536\) −90.3508 −3.90256
\(537\) 2.70052i 0.116536i
\(538\) 30.2276i 1.30320i
\(539\) 0 0
\(540\) 8.63752 7.63752i 0.371700 0.328667i
\(541\) −6.62530 −0.284844 −0.142422 0.989806i \(-0.545489\pi\)
−0.142422 + 0.989806i \(0.545489\pi\)
\(542\) 67.4128i 2.89563i
\(543\) 21.1998i 0.909771i
\(544\) −72.4807 −3.10759
\(545\) 22.8119 + 25.7988i 0.977156 + 1.10510i
\(546\) −38.4241 −1.64440
\(547\) 5.75860i 0.246220i 0.992393 + 0.123110i \(0.0392868\pi\)
−0.992393 + 0.123110i \(0.960713\pi\)
\(548\) 50.5256i 2.15835i
\(549\) 7.92478 0.338221
\(550\) 0 0
\(551\) 10.9234 0.465351
\(552\) 33.7743i 1.43753i
\(553\) 3.78892i 0.161121i
\(554\) 6.46898 0.274840
\(555\) 2.38787 + 2.70052i 0.101360 + 0.114631i
\(556\) 10.9624 0.464909
\(557\) 19.8700i 0.841920i −0.907079 0.420960i \(-0.861693\pi\)
0.907079 0.420960i \(-0.138307\pi\)
\(558\) 2.57452i 0.108988i
\(559\) 14.3634 0.607509
\(560\) −57.6991 + 51.0191i −2.43823 + 2.15595i
\(561\) 0 0
\(562\) 81.5633i 3.44054i
\(563\) 5.83383i 0.245866i 0.992415 + 0.122933i \(0.0392301\pi\)
−0.992415 + 0.122933i \(0.960770\pi\)
\(564\) −22.2374 −0.936365
\(565\) 23.0132 20.3488i 0.968171 0.856082i
\(566\) 22.3576 0.939758
\(567\) 2.80606i 0.117844i
\(568\) 62.0625i 2.60409i
\(569\) 46.7123 1.95828 0.979140 0.203185i \(-0.0651293\pi\)
0.979140 + 0.203185i \(0.0651293\pi\)
\(570\) 18.1260 + 20.4993i 0.759215 + 0.858621i
\(571\) 24.4241 1.02212 0.511058 0.859546i \(-0.329254\pi\)
0.511058 + 0.859546i \(0.329254\pi\)
\(572\) 0 0
\(573\) 13.1490i 0.549309i
\(574\) −17.9248 −0.748166
\(575\) 19.8496 + 2.44851i 0.827784 + 0.102110i
\(576\) 18.1187 0.754946
\(577\) 16.5647i 0.689596i 0.938677 + 0.344798i \(0.112053\pi\)
−0.938677 + 0.344798i \(0.887947\pi\)
\(578\) 9.76353i 0.406109i
\(579\) −5.89446 −0.244965
\(580\) −18.2374 20.6253i −0.757268 0.856419i
\(581\) −2.26187 −0.0938380
\(582\) 26.5501i 1.10054i
\(583\) 0 0
\(584\) −54.1925 −2.24250
\(585\) 8.57452 7.58181i 0.354513 0.313469i
\(586\) −61.7802 −2.55212
\(587\) 27.3258i 1.12786i 0.825823 + 0.563929i \(0.190711\pi\)
−0.825823 + 0.563929i \(0.809289\pi\)
\(588\) 4.50659i 0.185849i
\(589\) 4.40246 0.181400
\(590\) −59.4880 + 52.6009i −2.44908 + 2.16554i
\(591\) 20.3938 0.838887
\(592\) 19.7889i 0.813320i
\(593\) 12.6048i 0.517618i −0.965928 0.258809i \(-0.916670\pi\)
0.965928 0.258809i \(-0.0833301\pi\)
\(594\) 0 0
\(595\) 18.8872 + 21.3601i 0.774298 + 0.875679i
\(596\) −42.8627 −1.75573
\(597\) 17.4010i 0.712177i
\(598\) 54.7729i 2.23983i
\(599\) −10.5990 −0.433061 −0.216531 0.976276i \(-0.569474\pi\)
−0.216531 + 0.976276i \(0.569474\pi\)
\(600\) 5.16854 41.9003i 0.211005 1.71057i
\(601\) 22.4749 0.916768 0.458384 0.888754i \(-0.348428\pi\)
0.458384 + 0.888754i \(0.348428\pi\)
\(602\) 21.0640i 0.858503i
\(603\) 10.7005i 0.435759i
\(604\) −78.7631 −3.20482
\(605\) 0 0
\(606\) 36.4142 1.47923
\(607\) 33.5183i 1.36047i −0.732995 0.680234i \(-0.761878\pi\)
0.732995 0.680234i \(-0.238122\pi\)
\(608\) 72.9643i 2.95909i
\(609\) −6.70052 −0.271519
\(610\) 35.5125 31.4010i 1.43786 1.27139i
\(611\) −22.0752 −0.893068
\(612\) 23.4314i 0.947157i
\(613\) 11.5672i 0.467196i 0.972333 + 0.233598i \(0.0750499\pi\)
−0.972333 + 0.233598i \(0.924950\pi\)
\(614\) −7.10413 −0.286699
\(615\) 4.00000 3.53690i 0.161296 0.142622i
\(616\) 0 0
\(617\) 33.3357i 1.34204i −0.741438 0.671022i \(-0.765856\pi\)
0.741438 0.671022i \(-0.234144\pi\)
\(618\) 43.6385i 1.75540i
\(619\) −4.43866 −0.178405 −0.0892024 0.996014i \(-0.528432\pi\)
−0.0892024 + 0.996014i \(0.528432\pi\)
\(620\) −7.35026 8.31265i −0.295194 0.333844i
\(621\) −4.00000 −0.160514
\(622\) 42.7367i 1.71359i
\(623\) 8.31265i 0.333039i
\(624\) 62.8324 2.51531
\(625\) −24.2506 6.07522i −0.970024 0.243009i
\(626\) 0.162205 0.00648301
\(627\) 0 0
\(628\) 36.1622i 1.44303i
\(629\) 7.32582 0.292100
\(630\) −11.1187 12.5745i −0.442980 0.500981i
\(631\) −39.8496 −1.58639 −0.793193 0.608971i \(-0.791583\pi\)
−0.793193 + 0.608971i \(0.791583\pi\)
\(632\) 11.4010i 0.453509i
\(633\) 18.1260i 0.720444i
\(634\) 10.2012 0.405143
\(635\) −20.8021 + 18.3938i −0.825506 + 0.729934i
\(636\) 33.9003 1.34424
\(637\) 4.47371i 0.177255i
\(638\) 0 0
\(639\) 7.35026 0.290772
\(640\) 27.7562 24.5428i 1.09716 0.970139i
\(641\) −3.88858 −0.153590 −0.0767948 0.997047i \(-0.524469\pi\)
−0.0767948 + 0.997047i \(0.524469\pi\)
\(642\) 25.2301i 0.995754i
\(643\) 40.9380i 1.61444i −0.590254 0.807218i \(-0.700972\pi\)
0.590254 0.807218i \(-0.299028\pi\)
\(644\) 57.8759 2.28063
\(645\) 4.15633 + 4.70052i 0.163655 + 0.185083i
\(646\) 55.6093 2.18792
\(647\) 1.76257i 0.0692939i 0.999400 + 0.0346469i \(0.0110307\pi\)
−0.999400 + 0.0346469i \(0.988969\pi\)
\(648\) 8.44358i 0.331695i
\(649\) 0 0
\(650\) 8.38199 67.9511i 0.328769 2.66526i
\(651\) −2.70052 −0.105842
\(652\) 34.8627i 1.36533i
\(653\) 7.03761i 0.275403i 0.990474 + 0.137702i \(0.0439715\pi\)
−0.990474 + 0.137702i \(0.956029\pi\)
\(654\) −41.1998 −1.61104
\(655\) 8.77575 + 9.92478i 0.342897 + 0.387793i
\(656\) 29.3112 1.14441
\(657\) 6.41819i 0.250397i
\(658\) 32.3733i 1.26204i
\(659\) −12.6253 −0.491812 −0.245906 0.969294i \(-0.579085\pi\)
−0.245906 + 0.969294i \(0.579085\pi\)
\(660\) 0 0
\(661\) 13.2243 0.514364 0.257182 0.966363i \(-0.417206\pi\)
0.257182 + 0.966363i \(0.417206\pi\)
\(662\) 64.9741i 2.52529i
\(663\) 23.2605i 0.903361i
\(664\) 6.80606 0.264126
\(665\) 21.5026 19.0132i 0.833836 0.737299i
\(666\) −4.31265 −0.167112
\(667\) 9.55149i 0.369835i
\(668\) 60.9438i 2.35799i
\(669\) 23.6385 0.913916
\(670\) −42.3996 47.9511i −1.63804 1.85251i
\(671\) 0 0
\(672\) 44.7572i 1.72655i
\(673\) 18.2677i 0.704170i 0.935968 + 0.352085i \(0.114527\pi\)
−0.935968 + 0.352085i \(0.885473\pi\)
\(674\) 60.4055 2.32673
\(675\) 4.96239 + 0.612127i 0.191002 + 0.0235608i
\(676\) 68.0698 2.61807
\(677\) 33.0191i 1.26903i 0.772912 + 0.634513i \(0.218799\pi\)
−0.772912 + 0.634513i \(0.781201\pi\)
\(678\) 36.7513i 1.41143i
\(679\) −27.8496 −1.06877
\(680\) −56.8324 64.2736i −2.17942 2.46478i
\(681\) −1.26916 −0.0486343
\(682\) 0 0
\(683\) 30.8627i 1.18093i −0.807063 0.590465i \(-0.798944\pi\)
0.807063 0.590465i \(-0.201056\pi\)
\(684\) −23.5877 −0.901898
\(685\) 16.4142 14.5139i 0.627155 0.554547i
\(686\) −45.9854 −1.75573
\(687\) 16.1768i 0.617183i
\(688\) 34.4445i 1.31319i
\(689\) 33.6531 1.28208
\(690\) −17.9248 + 15.8496i −0.682385 + 0.603382i
\(691\) 27.6991 1.05372 0.526862 0.849951i \(-0.323369\pi\)
0.526862 + 0.849951i \(0.323369\pi\)
\(692\) 36.0567i 1.37067i
\(693\) 0 0
\(694\) −54.0176 −2.05048
\(695\) 3.14903 + 3.56134i 0.119450 + 0.135089i
\(696\) 20.1622 0.764246
\(697\) 10.8510i 0.411010i
\(698\) 72.8989i 2.75927i
\(699\) 18.4690 0.698561
\(700\) −71.8007 8.85685i −2.71381 0.334757i
\(701\) 38.9643 1.47166 0.735831 0.677166i \(-0.236792\pi\)
0.735831 + 0.677166i \(0.236792\pi\)
\(702\) 13.6932i 0.516818i
\(703\) 7.37470i 0.278142i
\(704\) 0 0
\(705\) −6.38787 7.22425i −0.240581 0.272081i
\(706\) −13.4372 −0.505717
\(707\) 38.1965i 1.43653i
\(708\) 68.4504i 2.57252i
\(709\) 4.32250 0.162335 0.0811674 0.996700i \(-0.474135\pi\)
0.0811674 + 0.996700i \(0.474135\pi\)
\(710\) 32.9380 29.1246i 1.23614 1.09303i
\(711\) −1.35026 −0.0506388
\(712\) 25.0132i 0.937408i
\(713\) 3.84955i 0.144167i
\(714\) −34.1114 −1.27659
\(715\) 0 0
\(716\) −13.9248 −0.520393
\(717\) 19.3258i 0.721736i
\(718\) 48.6253i 1.81468i
\(719\) 38.3996 1.43206 0.716032 0.698067i \(-0.245956\pi\)
0.716032 + 0.698067i \(0.245956\pi\)
\(720\) 18.1817 + 20.5623i 0.677593 + 0.766312i
\(721\) −45.7743 −1.70473
\(722\) 5.15282i 0.191768i
\(723\) 28.5501i 1.06179i
\(724\) 109.313 4.06259
\(725\) 1.46168 11.8496i 0.0542855 0.440081i
\(726\) 0 0
\(727\) 21.6728i 0.803798i −0.915684 0.401899i \(-0.868350\pi\)
0.915684 0.401899i \(-0.131650\pi\)
\(728\) 121.279i 4.49489i
\(729\) −1.00000 −0.0370370
\(730\) −25.4314 28.7612i −0.941257 1.06450i
\(731\) 12.7513 0.471624
\(732\) 40.8627i 1.51033i
\(733\) 25.0698i 0.925976i 0.886365 + 0.462988i \(0.153223\pi\)
−0.886365 + 0.462988i \(0.846777\pi\)
\(734\) −22.9116 −0.845683
\(735\) −1.46405 + 1.29455i −0.0540023 + 0.0477503i
\(736\) −63.8007 −2.35172
\(737\) 0 0
\(738\) 6.38787i 0.235141i
\(739\) −18.9018 −0.695312 −0.347656 0.937622i \(-0.613022\pi\)
−0.347656 + 0.937622i \(0.613022\pi\)
\(740\) −13.9248 + 12.3127i −0.511885 + 0.452622i
\(741\) −23.4156 −0.860195
\(742\) 49.3522i 1.81178i
\(743\) 43.6688i 1.60205i 0.598629 + 0.801026i \(0.295712\pi\)
−0.598629 + 0.801026i \(0.704288\pi\)
\(744\) 8.12601 0.297914
\(745\) −12.3127 13.9248i −0.451101 0.510164i
\(746\) 20.9175 0.765843
\(747\) 0.806063i 0.0294923i
\(748\) 0 0
\(749\) 26.4650 0.967010
\(750\) 24.6629 16.9199i 0.900562 0.617826i
\(751\) −47.0541 −1.71703 −0.858514 0.512789i \(-0.828612\pi\)
−0.858514 + 0.512789i \(0.828612\pi\)
\(752\) 52.9380i 1.93045i
\(753\) 23.1998i 0.845448i
\(754\) 32.6977 1.19078
\(755\) −22.6253 25.5877i −0.823419 0.931231i
\(756\) 14.4690 0.526232
\(757\) 26.9116i 0.978119i −0.872250 0.489059i \(-0.837340\pi\)
0.872250 0.489059i \(-0.162660\pi\)
\(758\) 3.07381i 0.111646i
\(759\) 0 0
\(760\) −64.7024 + 57.2116i −2.34700 + 2.07528i
\(761\) −16.6859 −0.604865 −0.302432 0.953171i \(-0.597799\pi\)
−0.302432 + 0.953171i \(0.597799\pi\)
\(762\) 33.2203i 1.20344i
\(763\) 43.2163i 1.56454i
\(764\) −67.8007 −2.45294
\(765\) 7.61213 6.73084i 0.275217 0.243354i
\(766\) −91.1871 −3.29473
\(767\) 67.9511i 2.45357i
\(768\) 8.08840i 0.291865i
\(769\) 23.2995 0.840201 0.420100 0.907478i \(-0.361995\pi\)
0.420100 + 0.907478i \(0.361995\pi\)
\(770\) 0 0
\(771\) 10.8872 0.392092
\(772\) 30.3938i 1.09390i
\(773\) 1.63656i 0.0588631i 0.999567 + 0.0294316i \(0.00936971\pi\)
−0.999567 + 0.0294316i \(0.990630\pi\)
\(774\) −7.50659 −0.269819
\(775\) 0.589104 4.77575i 0.0211612 0.171550i
\(776\) 83.8007 3.00827
\(777\) 4.52373i 0.162288i
\(778\) 63.5994i 2.28015i
\(779\) −10.9234 −0.391370
\(780\) 39.0943 + 44.2130i 1.39980 + 1.58308i
\(781\) 0 0
\(782\) 48.6253i 1.73884i
\(783\) 2.38787i 0.0853356i