Properties

Label 980.2.g.a.391.7
Level $980$
Weight $2$
Character 980.391
Analytic conductor $7.825$
Analytic rank $0$
Dimension $32$
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [980,2,Mod(391,980)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(980, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("980.391");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 980 = 2^{2} \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 980.g (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: \(7.82533939809\)
Analytic rank: \(0\)
Dimension: \(32\)
Twist minimal: no (minimal twist has level 140)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 391.7
Character \(\chi\) \(=\) 980.391
Dual form 980.2.g.a.391.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.34325 + 0.442358i) q^{2} -0.901278 q^{3} +(1.60864 - 1.18839i) q^{4} -1.00000i q^{5} +(1.21064 - 0.398687i) q^{6} +(-1.63511 + 2.30790i) q^{8} -2.18770 q^{9} +O(q^{10})\) \(q+(-1.34325 + 0.442358i) q^{2} -0.901278 q^{3} +(1.60864 - 1.18839i) q^{4} -1.00000i q^{5} +(1.21064 - 0.398687i) q^{6} +(-1.63511 + 2.30790i) q^{8} -2.18770 q^{9} +(0.442358 + 1.34325i) q^{10} +3.74246i q^{11} +(-1.44983 + 1.07107i) q^{12} -2.41990i q^{13} +0.901278i q^{15} +(1.17544 - 3.82339i) q^{16} +0.583719i q^{17} +(2.93862 - 0.967745i) q^{18} +6.15955 q^{19} +(-1.18839 - 1.60864i) q^{20} +(-1.65551 - 5.02706i) q^{22} -4.31210i q^{23} +(1.47369 - 2.08006i) q^{24} -1.00000 q^{25} +(1.07046 + 3.25054i) q^{26} +4.67556 q^{27} -0.435463 q^{29} +(-0.398687 - 1.21064i) q^{30} +2.53865 q^{31} +(0.112397 + 5.65574i) q^{32} -3.37300i q^{33} +(-0.258212 - 0.784080i) q^{34} +(-3.51922 + 2.59985i) q^{36} -11.3008 q^{37} +(-8.27381 + 2.72472i) q^{38} +2.18101i q^{39} +(2.30790 + 1.63511i) q^{40} -7.35068i q^{41} -5.80096i q^{43} +(4.44752 + 6.02027i) q^{44} +2.18770i q^{45} +(1.90749 + 5.79223i) q^{46} -11.5765 q^{47} +(-1.05940 + 3.44594i) q^{48} +(1.34325 - 0.442358i) q^{50} -0.526093i q^{51} +(-2.87580 - 3.89275i) q^{52} -3.11491 q^{53} +(-6.28044 + 2.06827i) q^{54} +3.74246 q^{55} -5.55147 q^{57} +(0.584935 - 0.192630i) q^{58} +3.47068 q^{59} +(1.07107 + 1.44983i) q^{60} -10.3877i q^{61} +(-3.41004 + 1.12299i) q^{62} +(-2.65284 - 7.54735i) q^{64} -2.41990 q^{65} +(1.49207 + 4.53078i) q^{66} -9.84499i q^{67} +(0.693688 + 0.938993i) q^{68} +3.88640i q^{69} +9.96771i q^{71} +(3.57712 - 5.04900i) q^{72} -9.79892i q^{73} +(15.1798 - 4.99899i) q^{74} +0.901278 q^{75} +(9.90849 - 7.31997i) q^{76} +(-0.964785 - 2.92964i) q^{78} -0.459050i q^{79} +(-3.82339 - 1.17544i) q^{80} +2.34912 q^{81} +(3.25163 + 9.87380i) q^{82} -2.59747 q^{83} +0.583719 q^{85} +(2.56610 + 7.79213i) q^{86} +0.392473 q^{87} +(-8.63724 - 6.11933i) q^{88} -9.88016i q^{89} +(-0.967745 - 2.93862i) q^{90} +(-5.12447 - 6.93662i) q^{92} -2.28803 q^{93} +(15.5502 - 5.12097i) q^{94} -6.15955i q^{95} +(-0.101301 - 5.09739i) q^{96} -4.54044i q^{97} -8.18738i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q - 4 q^{2} + 4 q^{4} - 4 q^{8} + 32 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 32 q - 4 q^{2} + 4 q^{4} - 4 q^{8} + 32 q^{9} + 28 q^{16} - 8 q^{22} - 32 q^{25} - 40 q^{29} - 4 q^{32} + 60 q^{36} - 16 q^{37} + 36 q^{44} - 4 q^{46} + 4 q^{50} + 16 q^{53} + 48 q^{57} - 4 q^{58} - 28 q^{60} + 4 q^{64} - 8 q^{65} - 8 q^{72} - 76 q^{74} + 120 q^{78} + 72 q^{81} - 56 q^{86} - 8 q^{88} - 4 q^{92} + 16 q^{93}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/980\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(197\) \(491\)
\(\chi(n)\) \(-1\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.34325 + 0.442358i −0.949821 + 0.312794i
\(3\) −0.901278 −0.520353 −0.260177 0.965561i \(-0.583781\pi\)
−0.260177 + 0.965561i \(0.583781\pi\)
\(4\) 1.60864 1.18839i 0.804320 0.594197i
\(5\) 1.00000i 0.447214i
\(6\) 1.21064 0.398687i 0.494242 0.162763i
\(7\) 0 0
\(8\) −1.63511 + 2.30790i −0.578098 + 0.815967i
\(9\) −2.18770 −0.729233
\(10\) 0.442358 + 1.34325i 0.139886 + 0.424773i
\(11\) 3.74246i 1.12839i 0.825640 + 0.564197i \(0.190814\pi\)
−0.825640 + 0.564197i \(0.809186\pi\)
\(12\) −1.44983 + 1.07107i −0.418530 + 0.309192i
\(13\) 2.41990i 0.671161i −0.942012 0.335580i \(-0.891068\pi\)
0.942012 0.335580i \(-0.108932\pi\)
\(14\) 0 0
\(15\) 0.901278i 0.232709i
\(16\) 1.17544 3.82339i 0.293860 0.955848i
\(17\) 0.583719i 0.141573i 0.997492 + 0.0707863i \(0.0225508\pi\)
−0.997492 + 0.0707863i \(0.977449\pi\)
\(18\) 2.93862 0.967745i 0.692640 0.228100i
\(19\) 6.15955 1.41310 0.706549 0.707664i \(-0.250251\pi\)
0.706549 + 0.707664i \(0.250251\pi\)
\(20\) −1.18839 1.60864i −0.265733 0.359703i
\(21\) 0 0
\(22\) −1.65551 5.02706i −0.352955 1.07177i
\(23\) 4.31210i 0.899135i −0.893246 0.449568i \(-0.851578\pi\)
0.893246 0.449568i \(-0.148422\pi\)
\(24\) 1.47369 2.08006i 0.300815 0.424591i
\(25\) −1.00000 −0.200000
\(26\) 1.07046 + 3.25054i 0.209935 + 0.637482i
\(27\) 4.67556 0.899812
\(28\) 0 0
\(29\) −0.435463 −0.0808634 −0.0404317 0.999182i \(-0.512873\pi\)
−0.0404317 + 0.999182i \(0.512873\pi\)
\(30\) −0.398687 1.21064i −0.0727900 0.221032i
\(31\) 2.53865 0.455955 0.227978 0.973666i \(-0.426789\pi\)
0.227978 + 0.973666i \(0.426789\pi\)
\(32\) 0.112397 + 5.65574i 0.0198692 + 0.999803i
\(33\) 3.37300i 0.587164i
\(34\) −0.258212 0.784080i −0.0442831 0.134469i
\(35\) 0 0
\(36\) −3.51922 + 2.59985i −0.586536 + 0.433308i
\(37\) −11.3008 −1.85784 −0.928918 0.370285i \(-0.879260\pi\)
−0.928918 + 0.370285i \(0.879260\pi\)
\(38\) −8.27381 + 2.72472i −1.34219 + 0.442009i
\(39\) 2.18101i 0.349241i
\(40\) 2.30790 + 1.63511i 0.364912 + 0.258533i
\(41\) 7.35068i 1.14798i −0.818861 0.573992i \(-0.805394\pi\)
0.818861 0.573992i \(-0.194606\pi\)
\(42\) 0 0
\(43\) 5.80096i 0.884637i −0.896858 0.442319i \(-0.854156\pi\)
0.896858 0.442319i \(-0.145844\pi\)
\(44\) 4.44752 + 6.02027i 0.670489 + 0.907590i
\(45\) 2.18770i 0.326123i
\(46\) 1.90749 + 5.79223i 0.281244 + 0.854018i
\(47\) −11.5765 −1.68861 −0.844305 0.535863i \(-0.819986\pi\)
−0.844305 + 0.535863i \(0.819986\pi\)
\(48\) −1.05940 + 3.44594i −0.152911 + 0.497379i
\(49\) 0 0
\(50\) 1.34325 0.442358i 0.189964 0.0625588i
\(51\) 0.526093i 0.0736677i
\(52\) −2.87580 3.89275i −0.398802 0.539828i
\(53\) −3.11491 −0.427866 −0.213933 0.976848i \(-0.568627\pi\)
−0.213933 + 0.976848i \(0.568627\pi\)
\(54\) −6.28044 + 2.06827i −0.854660 + 0.281456i
\(55\) 3.74246 0.504633
\(56\) 0 0
\(57\) −5.55147 −0.735310
\(58\) 0.584935 0.192630i 0.0768057 0.0252936i
\(59\) 3.47068 0.451844 0.225922 0.974145i \(-0.427461\pi\)
0.225922 + 0.974145i \(0.427461\pi\)
\(60\) 1.07107 + 1.44983i 0.138275 + 0.187172i
\(61\) 10.3877i 1.33000i −0.746842 0.665001i \(-0.768431\pi\)
0.746842 0.665001i \(-0.231569\pi\)
\(62\) −3.41004 + 1.12299i −0.433076 + 0.142620i
\(63\) 0 0
\(64\) −2.65284 7.54735i −0.331605 0.943418i
\(65\) −2.41990 −0.300152
\(66\) 1.49207 + 4.53078i 0.183661 + 0.557700i
\(67\) 9.84499i 1.20276i −0.798964 0.601379i \(-0.794618\pi\)
0.798964 0.601379i \(-0.205382\pi\)
\(68\) 0.693688 + 0.938993i 0.0841220 + 0.113870i
\(69\) 3.88640i 0.467868i
\(70\) 0 0
\(71\) 9.96771i 1.18295i 0.806324 + 0.591475i \(0.201454\pi\)
−0.806324 + 0.591475i \(0.798546\pi\)
\(72\) 3.57712 5.04900i 0.421568 0.595030i
\(73\) 9.79892i 1.14688i −0.819249 0.573439i \(-0.805609\pi\)
0.819249 0.573439i \(-0.194391\pi\)
\(74\) 15.1798 4.99899i 1.76461 0.581120i
\(75\) 0.901278 0.104071
\(76\) 9.90849 7.31997i 1.13658 0.839658i
\(77\) 0 0
\(78\) −0.964785 2.92964i −0.109240 0.331716i
\(79\) 0.459050i 0.0516472i −0.999667 0.0258236i \(-0.991779\pi\)
0.999667 0.0258236i \(-0.00822082\pi\)
\(80\) −3.82339 1.17544i −0.427468 0.131418i
\(81\) 2.34912 0.261013
\(82\) 3.25163 + 9.87380i 0.359083 + 1.09038i
\(83\) −2.59747 −0.285109 −0.142554 0.989787i \(-0.545532\pi\)
−0.142554 + 0.989787i \(0.545532\pi\)
\(84\) 0 0
\(85\) 0.583719 0.0633132
\(86\) 2.56610 + 7.79213i 0.276709 + 0.840247i
\(87\) 0.392473 0.0420775
\(88\) −8.63724 6.11933i −0.920733 0.652323i
\(89\) 9.88016i 1.04730i −0.851935 0.523648i \(-0.824571\pi\)
0.851935 0.523648i \(-0.175429\pi\)
\(90\) −0.967745 2.93862i −0.102009 0.309758i
\(91\) 0 0
\(92\) −5.12447 6.93662i −0.534263 0.723192i
\(93\) −2.28803 −0.237258
\(94\) 15.5502 5.12097i 1.60388 0.528187i
\(95\) 6.15955i 0.631956i
\(96\) −0.101301 5.09739i −0.0103390 0.520250i
\(97\) 4.54044i 0.461011i −0.973071 0.230506i \(-0.925962\pi\)
0.973071 0.230506i \(-0.0740380\pi\)
\(98\) 0 0
\(99\) 8.18738i 0.822862i
\(100\) −1.60864 + 1.18839i −0.160864 + 0.118839i
\(101\) 9.14442i 0.909903i −0.890516 0.454952i \(-0.849657\pi\)
0.890516 0.454952i \(-0.150343\pi\)
\(102\) 0.232721 + 0.706674i 0.0230428 + 0.0699712i
\(103\) 10.2319 1.00818 0.504092 0.863650i \(-0.331827\pi\)
0.504092 + 0.863650i \(0.331827\pi\)
\(104\) 5.58490 + 3.95681i 0.547645 + 0.387997i
\(105\) 0 0
\(106\) 4.18410 1.37790i 0.406396 0.133834i
\(107\) 6.33201i 0.612139i −0.952009 0.306069i \(-0.900986\pi\)
0.952009 0.306069i \(-0.0990139\pi\)
\(108\) 7.52129 5.55640i 0.723736 0.534665i
\(109\) −18.7605 −1.79693 −0.898467 0.439040i \(-0.855318\pi\)
−0.898467 + 0.439040i \(0.855318\pi\)
\(110\) −5.02706 + 1.65551i −0.479311 + 0.157846i
\(111\) 10.1851 0.966731
\(112\) 0 0
\(113\) 4.17847 0.393077 0.196539 0.980496i \(-0.437030\pi\)
0.196539 + 0.980496i \(0.437030\pi\)
\(114\) 7.45701 2.45573i 0.698413 0.230001i
\(115\) −4.31210 −0.402106
\(116\) −0.700502 + 0.517501i −0.0650400 + 0.0480488i
\(117\) 5.29402i 0.489432i
\(118\) −4.66198 + 1.53528i −0.429170 + 0.141334i
\(119\) 0 0
\(120\) −2.08006 1.47369i −0.189883 0.134529i
\(121\) −3.00602 −0.273275
\(122\) 4.59506 + 13.9532i 0.416017 + 1.26326i
\(123\) 6.62501i 0.597357i
\(124\) 4.08377 3.01692i 0.366734 0.270927i
\(125\) 1.00000i 0.0894427i
\(126\) 0 0
\(127\) 4.91036i 0.435724i −0.975980 0.217862i \(-0.930092\pi\)
0.975980 0.217862i \(-0.0699083\pi\)
\(128\) 6.90205 + 8.96447i 0.610061 + 0.792355i
\(129\) 5.22827i 0.460324i
\(130\) 3.25054 1.07046i 0.285091 0.0938858i
\(131\) 15.8745 1.38696 0.693479 0.720477i \(-0.256077\pi\)
0.693479 + 0.720477i \(0.256077\pi\)
\(132\) −4.00845 5.42594i −0.348891 0.472267i
\(133\) 0 0
\(134\) 4.35501 + 13.2243i 0.376216 + 1.14240i
\(135\) 4.67556i 0.402408i
\(136\) −1.34717 0.954444i −0.115519 0.0818429i
\(137\) −7.84221 −0.670005 −0.335002 0.942217i \(-0.608737\pi\)
−0.335002 + 0.942217i \(0.608737\pi\)
\(138\) −1.71918 5.22041i −0.146346 0.444391i
\(139\) −17.4044 −1.47623 −0.738113 0.674677i \(-0.764283\pi\)
−0.738113 + 0.674677i \(0.764283\pi\)
\(140\) 0 0
\(141\) 10.4337 0.878674
\(142\) −4.40929 13.3891i −0.370020 1.12359i
\(143\) 9.05640 0.757334
\(144\) −2.57151 + 8.36443i −0.214292 + 0.697036i
\(145\) 0.435463i 0.0361632i
\(146\) 4.33463 + 13.1624i 0.358736 + 1.08933i
\(147\) 0 0
\(148\) −18.1789 + 13.4298i −1.49429 + 1.10392i
\(149\) 1.65155 0.135300 0.0676502 0.997709i \(-0.478450\pi\)
0.0676502 + 0.997709i \(0.478450\pi\)
\(150\) −1.21064 + 0.398687i −0.0988485 + 0.0325527i
\(151\) 7.35613i 0.598633i −0.954154 0.299317i \(-0.903241\pi\)
0.954154 0.299317i \(-0.0967587\pi\)
\(152\) −10.0715 + 14.2156i −0.816909 + 1.15304i
\(153\) 1.27700i 0.103239i
\(154\) 0 0
\(155\) 2.53865i 0.203909i
\(156\) 2.59189 + 3.50845i 0.207518 + 0.280901i
\(157\) 3.08251i 0.246011i 0.992406 + 0.123005i \(0.0392532\pi\)
−0.992406 + 0.123005i \(0.960747\pi\)
\(158\) 0.203065 + 0.616619i 0.0161549 + 0.0490556i
\(159\) 2.80740 0.222641
\(160\) 5.65574 0.112397i 0.447125 0.00888579i
\(161\) 0 0
\(162\) −3.15545 + 1.03915i −0.247915 + 0.0816433i
\(163\) 4.51816i 0.353889i 0.984221 + 0.176945i \(0.0566214\pi\)
−0.984221 + 0.176945i \(0.943379\pi\)
\(164\) −8.73551 11.8246i −0.682128 0.923346i
\(165\) −3.37300 −0.262588
\(166\) 3.48905 1.14901i 0.270802 0.0891804i
\(167\) −16.9358 −1.31053 −0.655266 0.755398i \(-0.727444\pi\)
−0.655266 + 0.755398i \(0.727444\pi\)
\(168\) 0 0
\(169\) 7.14406 0.549543
\(170\) −0.784080 + 0.258212i −0.0601362 + 0.0198040i
\(171\) −13.4752 −1.03048
\(172\) −6.89382 9.33165i −0.525649 0.711531i
\(173\) 0.132697i 0.0100888i 0.999987 + 0.00504439i \(0.00160569\pi\)
−0.999987 + 0.00504439i \(0.998394\pi\)
\(174\) −0.527189 + 0.173613i −0.0399661 + 0.0131616i
\(175\) 0 0
\(176\) 14.3089 + 4.39904i 1.07857 + 0.331590i
\(177\) −3.12804 −0.235118
\(178\) 4.37057 + 13.2715i 0.327588 + 0.994743i
\(179\) 16.0991i 1.20330i −0.798760 0.601650i \(-0.794510\pi\)
0.798760 0.601650i \(-0.205490\pi\)
\(180\) 2.59985 + 3.51922i 0.193781 + 0.262307i
\(181\) 3.99317i 0.296810i −0.988927 0.148405i \(-0.952586\pi\)
0.988927 0.148405i \(-0.0474139\pi\)
\(182\) 0 0
\(183\) 9.36216i 0.692071i
\(184\) 9.95191 + 7.05076i 0.733665 + 0.519789i
\(185\) 11.3008i 0.830850i
\(186\) 3.07340 1.01213i 0.225352 0.0742128i
\(187\) −2.18455 −0.159750
\(188\) −18.6225 + 13.7575i −1.35818 + 1.00337i
\(189\) 0 0
\(190\) 2.72472 + 8.27381i 0.197672 + 0.600245i
\(191\) 20.0500i 1.45077i 0.688344 + 0.725385i \(0.258338\pi\)
−0.688344 + 0.725385i \(0.741662\pi\)
\(192\) 2.39094 + 6.80226i 0.172552 + 0.490911i
\(193\) 19.3392 1.39206 0.696032 0.718011i \(-0.254947\pi\)
0.696032 + 0.718011i \(0.254947\pi\)
\(194\) 2.00850 + 6.09894i 0.144202 + 0.437878i
\(195\) 2.18101 0.156185
\(196\) 0 0
\(197\) −1.63738 −0.116659 −0.0583293 0.998297i \(-0.518577\pi\)
−0.0583293 + 0.998297i \(0.518577\pi\)
\(198\) 3.62175 + 10.9977i 0.257386 + 0.781572i
\(199\) −0.783264 −0.0555241 −0.0277621 0.999615i \(-0.508838\pi\)
−0.0277621 + 0.999615i \(0.508838\pi\)
\(200\) 1.63511 2.30790i 0.115620 0.163193i
\(201\) 8.87308i 0.625859i
\(202\) 4.04510 + 12.2832i 0.284612 + 0.864245i
\(203\) 0 0
\(204\) −0.625205 0.846294i −0.0437731 0.0592524i
\(205\) −7.35068 −0.513394
\(206\) −13.7441 + 4.52618i −0.957594 + 0.315354i
\(207\) 9.43358i 0.655679i
\(208\) −9.25225 2.84445i −0.641528 0.197227i
\(209\) 23.0519i 1.59453i
\(210\) 0 0
\(211\) 9.22534i 0.635099i 0.948242 + 0.317549i \(0.102860\pi\)
−0.948242 + 0.317549i \(0.897140\pi\)
\(212\) −5.01077 + 3.70174i −0.344141 + 0.254237i
\(213\) 8.98368i 0.615551i
\(214\) 2.80101 + 8.50547i 0.191473 + 0.581422i
\(215\) −5.80096 −0.395622
\(216\) −7.64505 + 10.7907i −0.520180 + 0.734217i
\(217\) 0 0
\(218\) 25.2001 8.29887i 1.70677 0.562071i
\(219\) 8.83155i 0.596781i
\(220\) 6.02027 4.44752i 0.405887 0.299852i
\(221\) 1.41254 0.0950179
\(222\) −13.6812 + 4.50548i −0.918221 + 0.302388i
\(223\) 24.2380 1.62310 0.811550 0.584284i \(-0.198624\pi\)
0.811550 + 0.584284i \(0.198624\pi\)
\(224\) 0 0
\(225\) 2.18770 0.145847
\(226\) −5.61273 + 1.84838i −0.373353 + 0.122952i
\(227\) −10.6325 −0.705701 −0.352851 0.935680i \(-0.614788\pi\)
−0.352851 + 0.935680i \(0.614788\pi\)
\(228\) −8.93031 + 6.59733i −0.591424 + 0.436919i
\(229\) 29.5128i 1.95026i −0.221626 0.975132i \(-0.571136\pi\)
0.221626 0.975132i \(-0.428864\pi\)
\(230\) 5.79223 1.90749i 0.381928 0.125776i
\(231\) 0 0
\(232\) 0.712029 1.00501i 0.0467470 0.0659819i
\(233\) 28.0703 1.83894 0.919472 0.393155i \(-0.128616\pi\)
0.919472 + 0.393155i \(0.128616\pi\)
\(234\) −2.34185 7.11119i −0.153092 0.464873i
\(235\) 11.5765i 0.755169i
\(236\) 5.58307 4.12453i 0.363427 0.268484i
\(237\) 0.413732i 0.0268748i
\(238\) 0 0
\(239\) 13.6279i 0.881512i 0.897627 + 0.440756i \(0.145290\pi\)
−0.897627 + 0.440756i \(0.854710\pi\)
\(240\) 3.44594 + 1.05940i 0.222435 + 0.0683839i
\(241\) 4.20741i 0.271023i 0.990776 + 0.135512i \(0.0432678\pi\)
−0.990776 + 0.135512i \(0.956732\pi\)
\(242\) 4.03784 1.32974i 0.259562 0.0854787i
\(243\) −16.1439 −1.03563
\(244\) −12.3446 16.7100i −0.790283 1.06975i
\(245\) 0 0
\(246\) −2.93062 8.89904i −0.186850 0.567382i
\(247\) 14.9055i 0.948415i
\(248\) −4.15097 + 5.85896i −0.263587 + 0.372044i
\(249\) 2.34104 0.148357
\(250\) −0.442358 1.34325i −0.0279772 0.0849546i
\(251\) −18.8826 −1.19186 −0.595928 0.803038i \(-0.703216\pi\)
−0.595928 + 0.803038i \(0.703216\pi\)
\(252\) 0 0
\(253\) 16.1379 1.01458
\(254\) 2.17214 + 6.59584i 0.136292 + 0.413860i
\(255\) −0.526093 −0.0329452
\(256\) −13.2367 8.98835i −0.827292 0.561772i
\(257\) 25.8345i 1.61151i 0.592247 + 0.805757i \(0.298241\pi\)
−0.592247 + 0.805757i \(0.701759\pi\)
\(258\) −2.31277 7.02288i −0.143987 0.437225i
\(259\) 0 0
\(260\) −3.89275 + 2.87580i −0.241418 + 0.178349i
\(261\) 0.952661 0.0589682
\(262\) −21.3234 + 7.02219i −1.31736 + 0.433832i
\(263\) 10.6971i 0.659614i 0.944048 + 0.329807i \(0.106984\pi\)
−0.944048 + 0.329807i \(0.893016\pi\)
\(264\) 7.78456 + 5.51522i 0.479106 + 0.339438i
\(265\) 3.11491i 0.191347i
\(266\) 0 0
\(267\) 8.90478i 0.544963i
\(268\) −11.6997 15.8370i −0.714675 0.967402i
\(269\) 8.36512i 0.510030i 0.966937 + 0.255015i \(0.0820805\pi\)
−0.966937 + 0.255015i \(0.917920\pi\)
\(270\) 2.06827 + 6.28044i 0.125871 + 0.382216i
\(271\) −27.1113 −1.64690 −0.823448 0.567392i \(-0.807952\pi\)
−0.823448 + 0.567392i \(0.807952\pi\)
\(272\) 2.23179 + 0.686127i 0.135322 + 0.0416025i
\(273\) 0 0
\(274\) 10.5340 3.46906i 0.636385 0.209574i
\(275\) 3.74246i 0.225679i
\(276\) 4.61858 + 6.25182i 0.278006 + 0.376315i
\(277\) 3.35983 0.201872 0.100936 0.994893i \(-0.467816\pi\)
0.100936 + 0.994893i \(0.467816\pi\)
\(278\) 23.3785 7.69899i 1.40215 0.461755i
\(279\) −5.55380 −0.332497
\(280\) 0 0
\(281\) −7.33947 −0.437836 −0.218918 0.975743i \(-0.570253\pi\)
−0.218918 + 0.975743i \(0.570253\pi\)
\(282\) −14.0150 + 4.61542i −0.834583 + 0.274844i
\(283\) 7.20564 0.428331 0.214165 0.976797i \(-0.431297\pi\)
0.214165 + 0.976797i \(0.431297\pi\)
\(284\) 11.8456 + 16.0344i 0.702905 + 0.951469i
\(285\) 5.55147i 0.328841i
\(286\) −12.1650 + 4.00617i −0.719332 + 0.236890i
\(287\) 0 0
\(288\) −0.245892 12.3730i −0.0144893 0.729089i
\(289\) 16.6593 0.979957
\(290\) −0.192630 0.584935i −0.0113116 0.0343486i
\(291\) 4.09220i 0.239889i
\(292\) −11.6450 15.7629i −0.681471 0.922456i
\(293\) 8.47879i 0.495336i −0.968845 0.247668i \(-0.920336\pi\)
0.968845 0.247668i \(-0.0796642\pi\)
\(294\) 0 0
\(295\) 3.47068i 0.202071i
\(296\) 18.4780 26.0811i 1.07401 1.51593i
\(297\) 17.4981i 1.01534i
\(298\) −2.21845 + 0.730577i −0.128511 + 0.0423212i
\(299\) −10.4349 −0.603464
\(300\) 1.44983 1.07107i 0.0837060 0.0618384i
\(301\) 0 0
\(302\) 3.25404 + 9.88112i 0.187249 + 0.568595i
\(303\) 8.24166i 0.473471i
\(304\) 7.24018 23.5504i 0.415253 1.35071i
\(305\) −10.3877 −0.594795
\(306\) 0.564891 + 1.71533i 0.0322927 + 0.0980589i
\(307\) 10.4271 0.595104 0.297552 0.954706i \(-0.403830\pi\)
0.297552 + 0.954706i \(0.403830\pi\)
\(308\) 0 0
\(309\) −9.22183 −0.524612
\(310\) 1.12299 + 3.41004i 0.0637817 + 0.193677i
\(311\) 7.92592 0.449437 0.224719 0.974424i \(-0.427854\pi\)
0.224719 + 0.974424i \(0.427854\pi\)
\(312\) −5.03355 3.56618i −0.284969 0.201895i
\(313\) 14.4667i 0.817703i 0.912601 + 0.408852i \(0.134071\pi\)
−0.912601 + 0.408852i \(0.865929\pi\)
\(314\) −1.36357 4.14058i −0.0769507 0.233666i
\(315\) 0 0
\(316\) −0.545533 0.738447i −0.0306886 0.0415409i
\(317\) 3.53706 0.198661 0.0993305 0.995054i \(-0.468330\pi\)
0.0993305 + 0.995054i \(0.468330\pi\)
\(318\) −3.77104 + 1.24188i −0.211469 + 0.0696409i
\(319\) 1.62970i 0.0912458i
\(320\) −7.54735 + 2.65284i −0.421910 + 0.148298i
\(321\) 5.70690i 0.318528i
\(322\) 0 0
\(323\) 3.59544i 0.200056i
\(324\) 3.77888 2.79167i 0.209938 0.155093i
\(325\) 2.41990i 0.134232i
\(326\) −1.99864 6.06901i −0.110695 0.336131i
\(327\) 16.9085 0.935041
\(328\) 16.9647 + 12.0192i 0.936717 + 0.663648i
\(329\) 0 0
\(330\) 4.53078 1.49207i 0.249411 0.0821359i
\(331\) 23.5297i 1.29331i −0.762782 0.646655i \(-0.776167\pi\)
0.762782 0.646655i \(-0.223833\pi\)
\(332\) −4.17839 + 3.08681i −0.229319 + 0.169411i
\(333\) 24.7227 1.35479
\(334\) 22.7490 7.49169i 1.24477 0.409927i
\(335\) −9.84499 −0.537890
\(336\) 0 0
\(337\) 5.10057 0.277846 0.138923 0.990303i \(-0.455636\pi\)
0.138923 + 0.990303i \(0.455636\pi\)
\(338\) −9.59626 + 3.16023i −0.521968 + 0.171894i
\(339\) −3.76596 −0.204539
\(340\) 0.938993 0.693688i 0.0509240 0.0376205i
\(341\) 9.50081i 0.514497i
\(342\) 18.1006 5.96087i 0.978768 0.322327i
\(343\) 0 0
\(344\) 13.3880 + 9.48520i 0.721835 + 0.511407i
\(345\) 3.88640 0.209237
\(346\) −0.0586997 0.178246i −0.00315571 0.00958254i
\(347\) 1.66642i 0.0894580i 0.998999 + 0.0447290i \(0.0142424\pi\)
−0.998999 + 0.0447290i \(0.985758\pi\)
\(348\) 0.631347 0.466412i 0.0338438 0.0250023i
\(349\) 27.6081i 1.47783i 0.673801 + 0.738913i \(0.264661\pi\)
−0.673801 + 0.738913i \(0.735339\pi\)
\(350\) 0 0
\(351\) 11.3144i 0.603918i
\(352\) −21.1664 + 0.420643i −1.12817 + 0.0224203i
\(353\) 27.1577i 1.44546i −0.691131 0.722730i \(-0.742887\pi\)
0.691131 0.722730i \(-0.257113\pi\)
\(354\) 4.20174 1.38371i 0.223320 0.0735436i
\(355\) 9.96771 0.529031
\(356\) −11.7415 15.8936i −0.622300 0.842360i
\(357\) 0 0
\(358\) 7.12154 + 21.6251i 0.376385 + 1.14292i
\(359\) 16.7549i 0.884292i 0.896943 + 0.442146i \(0.145783\pi\)
−0.896943 + 0.442146i \(0.854217\pi\)
\(360\) −5.04900 3.57712i −0.266105 0.188531i
\(361\) 18.9400 0.996845
\(362\) 1.76641 + 5.36382i 0.0928404 + 0.281916i
\(363\) 2.70926 0.142199
\(364\) 0 0
\(365\) −9.79892 −0.512899
\(366\) −4.14142 12.5757i −0.216476 0.657344i
\(367\) −8.44425 −0.440787 −0.220393 0.975411i \(-0.570734\pi\)
−0.220393 + 0.975411i \(0.570734\pi\)
\(368\) −16.4869 5.06862i −0.859437 0.264220i
\(369\) 16.0811i 0.837147i
\(370\) −4.99899 15.1798i −0.259885 0.789158i
\(371\) 0 0
\(372\) −3.68062 + 2.71908i −0.190831 + 0.140978i
\(373\) −10.3772 −0.537312 −0.268656 0.963236i \(-0.586580\pi\)
−0.268656 + 0.963236i \(0.586580\pi\)
\(374\) 2.93439 0.966350i 0.151734 0.0499688i
\(375\) 0.901278i 0.0465418i
\(376\) 18.9289 26.7175i 0.976183 1.37785i
\(377\) 1.05378i 0.0542723i
\(378\) 0 0
\(379\) 11.7976i 0.606002i 0.952990 + 0.303001i \(0.0979886\pi\)
−0.952990 + 0.303001i \(0.902011\pi\)
\(380\) −7.31997 9.90849i −0.375507 0.508295i
\(381\) 4.42560i 0.226730i
\(382\) −8.86929 26.9322i −0.453792 1.37797i
\(383\) 0.957045 0.0489027 0.0244514 0.999701i \(-0.492216\pi\)
0.0244514 + 0.999701i \(0.492216\pi\)
\(384\) −6.22067 8.07948i −0.317447 0.412304i
\(385\) 0 0
\(386\) −25.9773 + 8.55483i −1.32221 + 0.435430i
\(387\) 12.6907i 0.645107i
\(388\) −5.39583 7.30392i −0.273932 0.370801i
\(389\) −30.1641 −1.52938 −0.764689 0.644399i \(-0.777107\pi\)
−0.764689 + 0.644399i \(0.777107\pi\)
\(390\) −2.92964 + 0.964785i −0.148348 + 0.0488538i
\(391\) 2.51705 0.127293
\(392\) 0 0
\(393\) −14.3073 −0.721708
\(394\) 2.19941 0.724308i 0.110805 0.0364901i
\(395\) −0.459050 −0.0230973
\(396\) −9.72983 13.1705i −0.488942 0.661844i
\(397\) 6.20697i 0.311519i −0.987795 0.155760i \(-0.950217\pi\)
0.987795 0.155760i \(-0.0497825\pi\)
\(398\) 1.05212 0.346483i 0.0527380 0.0173676i
\(399\) 0 0
\(400\) −1.17544 + 3.82339i −0.0587720 + 0.191170i
\(401\) 26.3130 1.31401 0.657004 0.753887i \(-0.271824\pi\)
0.657004 + 0.753887i \(0.271824\pi\)
\(402\) −3.92507 11.9188i −0.195765 0.594454i
\(403\) 6.14329i 0.306019i
\(404\) −10.8672 14.7101i −0.540662 0.731853i
\(405\) 2.34912i 0.116728i
\(406\) 0 0
\(407\) 42.2927i 2.09637i
\(408\) 1.21417 + 0.860219i 0.0601105 + 0.0425872i
\(409\) 18.4030i 0.909968i 0.890500 + 0.454984i \(0.150355\pi\)
−0.890500 + 0.454984i \(0.849645\pi\)
\(410\) 9.87380 3.25163i 0.487632 0.160587i
\(411\) 7.06801 0.348639
\(412\) 16.4595 12.1596i 0.810902 0.599060i
\(413\) 0 0
\(414\) −4.17302 12.6716i −0.205093 0.622777i
\(415\) 2.59747i 0.127505i
\(416\) 13.6863 0.271991i 0.671028 0.0133355i
\(417\) 15.6862 0.768158
\(418\) −10.1972 30.9644i −0.498760 1.51452i
\(419\) 35.2426 1.72171 0.860856 0.508848i \(-0.169928\pi\)
0.860856 + 0.508848i \(0.169928\pi\)
\(420\) 0 0
\(421\) −15.6669 −0.763558 −0.381779 0.924254i \(-0.624688\pi\)
−0.381779 + 0.924254i \(0.624688\pi\)
\(422\) −4.08090 12.3919i −0.198655 0.603230i
\(423\) 25.3259 1.23139
\(424\) 5.09322 7.18891i 0.247349 0.349124i
\(425\) 0.583719i 0.0283145i
\(426\) 3.97400 + 12.0673i 0.192541 + 0.584664i
\(427\) 0 0
\(428\) −7.52492 10.1859i −0.363731 0.492355i
\(429\) −8.16233 −0.394081
\(430\) 7.79213 2.56610i 0.375770 0.123748i
\(431\) 2.00541i 0.0965970i 0.998833 + 0.0482985i \(0.0153799\pi\)
−0.998833 + 0.0482985i \(0.984620\pi\)
\(432\) 5.49584 17.8765i 0.264419 0.860083i
\(433\) 13.5978i 0.653469i −0.945116 0.326734i \(-0.894052\pi\)
0.945116 0.326734i \(-0.105948\pi\)
\(434\) 0 0
\(435\) 0.392473i 0.0188176i
\(436\) −30.1790 + 22.2949i −1.44531 + 1.06773i
\(437\) 26.5606i 1.27057i
\(438\) −3.90671 11.8630i −0.186670 0.566835i
\(439\) 29.0493 1.38645 0.693224 0.720722i \(-0.256190\pi\)
0.693224 + 0.720722i \(0.256190\pi\)
\(440\) −6.11933 + 8.63724i −0.291728 + 0.411764i
\(441\) 0 0
\(442\) −1.89740 + 0.624849i −0.0902500 + 0.0297211i
\(443\) 14.6366i 0.695406i 0.937605 + 0.347703i \(0.113038\pi\)
−0.937605 + 0.347703i \(0.886962\pi\)
\(444\) 16.3842 12.1040i 0.777561 0.574428i
\(445\) −9.88016 −0.468365
\(446\) −32.5577 + 10.7219i −1.54165 + 0.507696i
\(447\) −1.48851 −0.0704040
\(448\) 0 0
\(449\) −27.0699 −1.27751 −0.638754 0.769411i \(-0.720550\pi\)
−0.638754 + 0.769411i \(0.720550\pi\)
\(450\) −2.93862 + 0.967745i −0.138528 + 0.0456199i
\(451\) 27.5097 1.29538
\(452\) 6.72165 4.96567i 0.316160 0.233565i
\(453\) 6.62992i 0.311501i
\(454\) 14.2820 4.70335i 0.670290 0.220739i
\(455\) 0 0
\(456\) 9.07725 12.8122i 0.425081 0.599989i
\(457\) −7.60612 −0.355799 −0.177900 0.984049i \(-0.556930\pi\)
−0.177900 + 0.984049i \(0.556930\pi\)
\(458\) 13.0552 + 39.6431i 0.610031 + 1.85240i
\(459\) 2.72921i 0.127389i
\(460\) −6.93662 + 5.12447i −0.323421 + 0.238930i
\(461\) 12.7953i 0.595936i −0.954576 0.297968i \(-0.903691\pi\)
0.954576 0.297968i \(-0.0963089\pi\)
\(462\) 0 0
\(463\) 27.9178i 1.29745i −0.761024 0.648724i \(-0.775303\pi\)
0.761024 0.648724i \(-0.224697\pi\)
\(464\) −0.511861 + 1.66495i −0.0237625 + 0.0772931i
\(465\) 2.28803i 0.106105i
\(466\) −37.7054 + 12.4171i −1.74667 + 0.575211i
\(467\) −22.6108 −1.04630 −0.523152 0.852239i \(-0.675244\pi\)
−0.523152 + 0.852239i \(0.675244\pi\)
\(468\) 6.29138 + 8.51617i 0.290819 + 0.393660i
\(469\) 0 0
\(470\) −5.12097 15.5502i −0.236213 0.717276i
\(471\) 2.77820i 0.128012i
\(472\) −5.67493 + 8.00999i −0.261210 + 0.368689i
\(473\) 21.7099 0.998220
\(474\) −0.183018 0.555745i −0.00840628 0.0255262i
\(475\) −6.15955 −0.282620
\(476\) 0 0
\(477\) 6.81448 0.312014
\(478\) −6.02838 18.3056i −0.275732 0.837279i
\(479\) −21.9815 −1.00436 −0.502180 0.864763i \(-0.667468\pi\)
−0.502180 + 0.864763i \(0.667468\pi\)
\(480\) −5.09739 + 0.101301i −0.232663 + 0.00462375i
\(481\) 27.3468i 1.24691i
\(482\) −1.86118 5.65160i −0.0847744 0.257423i
\(483\) 0 0
\(484\) −4.83560 + 3.57234i −0.219800 + 0.162379i
\(485\) −4.54044 −0.206171
\(486\) 21.6853 7.14137i 0.983663 0.323939i
\(487\) 25.3829i 1.15021i 0.818081 + 0.575103i \(0.195038\pi\)
−0.818081 + 0.575103i \(0.804962\pi\)
\(488\) 23.9737 + 16.9849i 1.08524 + 0.768872i
\(489\) 4.07212i 0.184147i
\(490\) 0 0
\(491\) 36.4635i 1.64557i −0.568350 0.822787i \(-0.692418\pi\)
0.568350 0.822787i \(-0.307582\pi\)
\(492\) 7.87312 + 10.6573i 0.354948 + 0.480466i
\(493\) 0.254188i 0.0114480i
\(494\) 6.59357 + 20.0218i 0.296659 + 0.900825i
\(495\) −8.18738 −0.367995
\(496\) 2.98403 9.70626i 0.133987 0.435824i
\(497\) 0 0
\(498\) −3.14460 + 1.03558i −0.140913 + 0.0464053i
\(499\) 11.8789i 0.531772i −0.964004 0.265886i \(-0.914335\pi\)
0.964004 0.265886i \(-0.0856646\pi\)
\(500\) 1.18839 + 1.60864i 0.0531466 + 0.0719405i
\(501\) 15.2639 0.681940
\(502\) 25.3640 8.35284i 1.13205 0.372806i
\(503\) −17.3055 −0.771614 −0.385807 0.922580i \(-0.626077\pi\)
−0.385807 + 0.922580i \(0.626077\pi\)
\(504\) 0 0
\(505\) −9.14442 −0.406921
\(506\) −21.6772 + 7.13871i −0.963669 + 0.317355i
\(507\) −6.43879 −0.285957
\(508\) −5.83544 7.89900i −0.258906 0.350462i
\(509\) 13.7083i 0.607609i −0.952734 0.303805i \(-0.901743\pi\)
0.952734 0.303805i \(-0.0982570\pi\)
\(510\) 0.706674 0.232721i 0.0312921 0.0103051i
\(511\) 0 0
\(512\) 21.7562 + 6.21824i 0.961498 + 0.274810i
\(513\) 28.7993 1.27152
\(514\) −11.4281 34.7022i −0.504072 1.53065i
\(515\) 10.2319i 0.450873i
\(516\) 6.21325 + 8.41041i 0.273523 + 0.370248i
\(517\) 43.3247i 1.90542i
\(518\) 0 0
\(519\) 0.119597i 0.00524973i
\(520\) 3.95681 5.58490i 0.173517 0.244914i
\(521\) 36.3519i 1.59261i −0.604897 0.796304i \(-0.706786\pi\)
0.604897 0.796304i \(-0.293214\pi\)
\(522\) −1.27966 + 0.421417i −0.0560093 + 0.0184449i
\(523\) −4.26422 −0.186461 −0.0932306 0.995645i \(-0.529719\pi\)
−0.0932306 + 0.995645i \(0.529719\pi\)
\(524\) 25.5363 18.8651i 1.11556 0.824126i
\(525\) 0 0
\(526\) −4.73196 14.3689i −0.206323 0.626515i
\(527\) 1.48186i 0.0645508i
\(528\) −12.8963 3.96476i −0.561239 0.172544i
\(529\) 4.40578 0.191556
\(530\) −1.37790 4.18410i −0.0598523 0.181746i
\(531\) −7.59279 −0.329499
\(532\) 0 0
\(533\) −17.7879 −0.770482
\(534\) −3.93910 11.9613i −0.170461 0.517618i
\(535\) −6.33201 −0.273757
\(536\) 22.7213 + 16.0976i 0.981411 + 0.695312i
\(537\) 14.5097i 0.626141i
\(538\) −3.70038 11.2364i −0.159535 0.484438i
\(539\) 0 0
\(540\) −5.55640 7.52129i −0.239110 0.323665i
\(541\) −6.68266 −0.287310 −0.143655 0.989628i \(-0.545886\pi\)
−0.143655 + 0.989628i \(0.545886\pi\)
\(542\) 36.4173 11.9929i 1.56426 0.515139i
\(543\) 3.59895i 0.154446i
\(544\) −3.30136 + 0.0656085i −0.141545 + 0.00281294i
\(545\) 18.7605i 0.803614i
\(546\) 0 0
\(547\) 45.6888i 1.95351i 0.214353 + 0.976756i \(0.431236\pi\)
−0.214353 + 0.976756i \(0.568764\pi\)
\(548\) −12.6153 + 9.31963i −0.538898 + 0.398115i
\(549\) 22.7250i 0.969881i
\(550\) 1.65551 + 5.02706i 0.0705910 + 0.214355i
\(551\) −2.68225 −0.114268
\(552\) −8.96944 6.35469i −0.381765 0.270474i
\(553\) 0 0
\(554\) −4.51309 + 1.48625i −0.191743 + 0.0631445i
\(555\) 10.1851i 0.432335i
\(556\) −27.9975 + 20.6833i −1.18736 + 0.877168i
\(557\) 4.88406 0.206944 0.103472 0.994632i \(-0.467005\pi\)
0.103472 + 0.994632i \(0.467005\pi\)
\(558\) 7.46014 2.45677i 0.315813 0.104003i
\(559\) −14.0378 −0.593734
\(560\) 0 0
\(561\) 1.96888 0.0831263
\(562\) 9.85875 3.24667i 0.415866 0.136953i
\(563\) −2.73584 −0.115302 −0.0576509 0.998337i \(-0.518361\pi\)
−0.0576509 + 0.998337i \(0.518361\pi\)
\(564\) 16.7840 12.3993i 0.706734 0.522105i
\(565\) 4.17847i 0.175789i
\(566\) −9.67897 + 3.18747i −0.406838 + 0.133979i
\(567\) 0 0
\(568\) −23.0045 16.2983i −0.965248 0.683861i
\(569\) 4.59348 0.192569 0.0962843 0.995354i \(-0.469304\pi\)
0.0962843 + 0.995354i \(0.469304\pi\)
\(570\) −2.45573 7.45701i −0.102859 0.312340i
\(571\) 5.61846i 0.235125i 0.993065 + 0.117563i \(0.0375081\pi\)
−0.993065 + 0.117563i \(0.962492\pi\)
\(572\) 14.5685 10.7626i 0.609139 0.450006i
\(573\) 18.0707i 0.754912i
\(574\) 0 0
\(575\) 4.31210i 0.179827i
\(576\) 5.80361 + 16.5113i 0.241817 + 0.687972i
\(577\) 34.3461i 1.42985i 0.699203 + 0.714924i \(0.253539\pi\)
−0.699203 + 0.714924i \(0.746461\pi\)
\(578\) −22.3776 + 7.36936i −0.930784 + 0.306525i
\(579\) −17.4300 −0.724365
\(580\) 0.517501 + 0.700502i 0.0214881 + 0.0290868i
\(581\) 0 0
\(582\) −1.81021 5.49684i −0.0750358 0.227851i
\(583\) 11.6574i 0.482801i
\(584\) 22.6150 + 16.0223i 0.935814 + 0.663008i
\(585\) 5.29402 0.218881
\(586\) 3.75066 + 11.3891i 0.154938 + 0.470481i
\(587\) 40.1422 1.65685 0.828423 0.560103i \(-0.189238\pi\)
0.828423 + 0.560103i \(0.189238\pi\)
\(588\) 0 0
\(589\) 15.6369 0.644309
\(590\) 1.53528 + 4.66198i 0.0632065 + 0.191931i
\(591\) 1.47574 0.0607036
\(592\) −13.2834 + 43.2073i −0.545944 + 1.77581i
\(593\) 10.9337i 0.448992i 0.974475 + 0.224496i \(0.0720736\pi\)
−0.974475 + 0.224496i \(0.927926\pi\)
\(594\) −7.74042 23.5043i −0.317593 0.964394i
\(595\) 0 0
\(596\) 2.65675 1.96269i 0.108825 0.0803951i
\(597\) 0.705939 0.0288921
\(598\) 14.0166 4.61595i 0.573183 0.188760i
\(599\) 5.21309i 0.213001i 0.994313 + 0.106500i \(0.0339646\pi\)
−0.994313 + 0.106500i \(0.966035\pi\)
\(600\) −1.47369 + 2.08006i −0.0601631 + 0.0849182i
\(601\) 16.1103i 0.657154i 0.944477 + 0.328577i \(0.106569\pi\)
−0.944477 + 0.328577i \(0.893431\pi\)
\(602\) 0 0
\(603\) 21.5379i 0.877090i
\(604\) −8.74198 11.8334i −0.355706 0.481493i
\(605\) 3.00602i 0.122212i
\(606\) −3.64576 11.0706i −0.148099 0.449713i
\(607\) 9.65621 0.391933 0.195967 0.980611i \(-0.437216\pi\)
0.195967 + 0.980611i \(0.437216\pi\)
\(608\) 0.692317 + 34.8368i 0.0280772 + 1.41282i
\(609\) 0 0
\(610\) 13.9532 4.59506i 0.564949 0.186048i
\(611\) 28.0141i 1.13333i
\(612\) −1.51758 2.05423i −0.0613445 0.0830374i
\(613\) 7.84775 0.316968 0.158484 0.987362i \(-0.449339\pi\)
0.158484 + 0.987362i \(0.449339\pi\)
\(614\) −14.0061 + 4.61249i −0.565242 + 0.186145i
\(615\) 6.62501 0.267146
\(616\) 0 0
\(617\) −28.8434 −1.16119 −0.580597 0.814191i \(-0.697181\pi\)
−0.580597 + 0.814191i \(0.697181\pi\)
\(618\) 12.3872 4.07935i 0.498287 0.164095i
\(619\) 2.48557 0.0999034 0.0499517 0.998752i \(-0.484093\pi\)
0.0499517 + 0.998752i \(0.484093\pi\)
\(620\) −3.01692 4.08377i −0.121162 0.164008i
\(621\) 20.1615i 0.809052i
\(622\) −10.6465 + 3.50609i −0.426885 + 0.140581i
\(623\) 0 0
\(624\) 8.33885 + 2.56364i 0.333821 + 0.102628i
\(625\) 1.00000 0.0400000
\(626\) −6.39943 19.4323i −0.255773 0.776672i
\(627\) 20.7762i 0.829720i
\(628\) 3.66323 + 4.95864i 0.146179 + 0.197871i
\(629\) 6.59647i 0.263019i
\(630\) 0 0
\(631\) 8.90728i 0.354593i 0.984157 + 0.177297i \(0.0567352\pi\)
−0.984157 + 0.177297i \(0.943265\pi\)
\(632\) 1.05944 + 0.750598i 0.0421424 + 0.0298572i
\(633\) 8.31460i 0.330476i
\(634\) −4.75115 + 1.56465i −0.188692 + 0.0621400i
\(635\) −4.91036 −0.194862
\(636\) 4.51609 3.33630i 0.179075 0.132293i
\(637\) 0 0
\(638\) 0.720911 + 2.18910i 0.0285412 + 0.0866672i
\(639\) 21.8063i 0.862645i
\(640\) 8.96447 6.90205i 0.354352 0.272827i
\(641\) 14.6330 0.577970 0.288985 0.957334i \(-0.406682\pi\)
0.288985 + 0.957334i \(0.406682\pi\)
\(642\) −2.52449 7.66580i −0.0996338 0.302545i
\(643\) −24.2513 −0.956380 −0.478190 0.878256i \(-0.658707\pi\)
−0.478190 + 0.878256i \(0.658707\pi\)
\(644\) 0 0
\(645\) 5.22827 0.205863
\(646\) −1.59047 4.82958i −0.0625763 0.190017i
\(647\) 29.9156 1.17611 0.588053 0.808823i \(-0.299895\pi\)
0.588053 + 0.808823i \(0.299895\pi\)
\(648\) −3.84106 + 5.42153i −0.150891 + 0.212978i
\(649\) 12.9889i 0.509858i
\(650\) −1.07046 3.25054i −0.0419870 0.127496i
\(651\) 0 0
\(652\) 5.36935 + 7.26808i 0.210280 + 0.284640i
\(653\) −15.5631 −0.609031 −0.304516 0.952507i \(-0.598495\pi\)
−0.304516 + 0.952507i \(0.598495\pi\)
\(654\) −22.7123 + 7.47959i −0.888121 + 0.292475i
\(655\) 15.8745i 0.620267i
\(656\) −28.1046 8.64029i −1.09730 0.337347i
\(657\) 21.4371i 0.836340i
\(658\) 0 0
\(659\) 30.2702i 1.17916i −0.807710 0.589580i \(-0.799293\pi\)
0.807710 0.589580i \(-0.200707\pi\)
\(660\) −5.42594 + 4.00845i −0.211204 + 0.156029i
\(661\) 17.9220i 0.697084i −0.937293 0.348542i \(-0.886677\pi\)
0.937293 0.348542i \(-0.113323\pi\)
\(662\) 10.4086 + 31.6063i 0.404540 + 1.22841i
\(663\) −1.27309 −0.0494429
\(664\) 4.24714 5.99470i 0.164821 0.232640i
\(665\) 0 0
\(666\) −33.2087 + 10.9363i −1.28681 + 0.423772i
\(667\) 1.87776i 0.0727071i
\(668\) −27.2436 + 20.1264i −1.05409 + 0.778714i
\(669\) −21.8452 −0.844585
\(670\) 13.2243 4.35501i 0.510899 0.168249i
\(671\) 38.8754 1.50077
\(672\) 0 0
\(673\) 21.1876 0.816723 0.408362 0.912820i \(-0.366100\pi\)
0.408362 + 0.912820i \(0.366100\pi\)
\(674\) −6.85134 + 2.25628i −0.263904 + 0.0869085i
\(675\) −4.67556 −0.179962
\(676\) 11.4922 8.48996i 0.442009 0.326537i
\(677\) 25.2570i 0.970707i −0.874318 0.485353i \(-0.838691\pi\)
0.874318 0.485353i \(-0.161309\pi\)
\(678\) 5.05863 1.66590i 0.194275 0.0639786i
\(679\) 0 0
\(680\) −0.954444 + 1.34717i −0.0366012 + 0.0516615i
\(681\) 9.58280 0.367214
\(682\) −4.20275 12.7620i −0.160932 0.488680i
\(683\) 22.0999i 0.845628i −0.906216 0.422814i \(-0.861042\pi\)
0.906216 0.422814i \(-0.138958\pi\)
\(684\) −21.6768 + 16.0139i −0.828833 + 0.612306i
\(685\) 7.84221i 0.299635i
\(686\) 0 0
\(687\) 26.5993i 1.01483i
\(688\) −22.1793 6.81868i −0.845579 0.259960i
\(689\) 7.53778i 0.287167i
\(690\) −5.22041 + 1.71918i −0.198738 + 0.0654481i
\(691\) −18.1102 −0.688943 −0.344471 0.938797i \(-0.611942\pi\)
−0.344471 + 0.938797i \(0.611942\pi\)
\(692\) 0.157697 + 0.213462i 0.00599473 + 0.00811461i
\(693\) 0 0
\(694\) −0.737153 2.23841i −0.0279819 0.0849691i
\(695\) 17.4044i 0.660188i
\(696\) −0.641736 + 0.905790i −0.0243249 + 0.0343339i
\(697\) 4.29073 0.162523
\(698\) −12.2126 37.0845i −0.462255 1.40367i
\(699\) −25.2991 −0.956901
\(700\) 0 0
\(701\) 14.4315 0.545070 0.272535 0.962146i \(-0.412138\pi\)
0.272535 + 0.962146i \(0.412138\pi\)
\(702\) 5.00501 + 15.1981i 0.188902 + 0.573614i
\(703\) −69.6077 −2.62530
\(704\) 28.2457 9.92814i 1.06455 0.374181i
\(705\) 10.4337i 0.392955i
\(706\) 12.0134 + 36.4796i 0.452131 + 1.37293i
\(707\) 0 0
\(708\) −5.03189 + 3.71735i −0.189110 + 0.139706i
\(709\) −37.0262 −1.39055 −0.695275 0.718744i \(-0.744717\pi\)
−0.695275 + 0.718744i \(0.744717\pi\)
\(710\) −13.3891 + 4.40929i −0.502485 + 0.165478i
\(711\) 1.00426i 0.0376628i
\(712\) 22.8025 + 16.1551i 0.854559 + 0.605440i
\(713\) 10.9469i 0.409965i
\(714\) 0 0
\(715\) 9.05640i 0.338690i
\(716\) −19.1320 25.8976i −0.714997 0.967838i
\(717\) 12.2825i 0.458698i
\(718\) −7.41168 22.5061i −0.276601 0.839919i
\(719\) 20.1950 0.753145 0.376573 0.926387i \(-0.377103\pi\)
0.376573 + 0.926387i \(0.377103\pi\)
\(720\) 8.36443 + 2.57151i 0.311724 + 0.0958345i
\(721\) 0 0
\(722\) −25.4412 + 8.37828i −0.946824 + 0.311807i
\(723\) 3.79204i 0.141028i
\(724\) −4.74545 6.42357i −0.176363 0.238730i
\(725\) 0.435463 0.0161727
\(726\) −3.63921 + 1.19846i −0.135064 + 0.0444791i
\(727\) 10.7925 0.400272 0.200136 0.979768i \(-0.435862\pi\)
0.200136 + 0.979768i \(0.435862\pi\)
\(728\) 0 0
\(729\) 7.50278 0.277881
\(730\) 13.1624 4.33463i 0.487162 0.160432i
\(731\) 3.38613 0.125240
\(732\) 11.1259 + 15.0603i 0.411226 + 0.556646i
\(733\) 7.23222i 0.267128i 0.991040 + 0.133564i \(0.0426422\pi\)
−0.991040 + 0.133564i \(0.957358\pi\)
\(734\) 11.3427 3.73538i 0.418668 0.137875i
\(735\) 0 0
\(736\) 24.3881 0.484669i 0.898958 0.0178651i
\(737\) 36.8445 1.35719
\(738\) −7.11359 21.6009i −0.261855 0.795140i
\(739\) 1.98524i 0.0730284i −0.999333 0.0365142i \(-0.988375\pi\)
0.999333 0.0365142i \(-0.0116254\pi\)
\(740\) 13.4298 + 18.1789i 0.493688 + 0.668269i
\(741\) 13.4340i 0.493511i
\(742\) 0 0
\(743\) 19.8225i 0.727216i 0.931552 + 0.363608i \(0.118455\pi\)
−0.931552 + 0.363608i \(0.881545\pi\)
\(744\) 3.74118 5.28055i 0.137158 0.193595i
\(745\) 1.65155i 0.0605082i
\(746\) 13.9392 4.59045i 0.510351 0.168068i
\(747\) 5.68247 0.207911
\(748\) −3.51414 + 2.59610i −0.128490 + 0.0949228i
\(749\) 0 0
\(750\) 0.398687 + 1.21064i 0.0145580 + 0.0442064i
\(751\) 24.1007i 0.879448i −0.898133 0.439724i \(-0.855076\pi\)
0.898133 0.439724i \(-0.144924\pi\)
\(752\) −13.6075 + 44.2616i −0.496215 + 1.61406i
\(753\) 17.0184 0.620186
\(754\) −0.466147 1.41549i −0.0169761 0.0515490i
\(755\) −7.35613 −0.267717
\(756\) 0 0
\(757\) 34.8711 1.26741 0.633706 0.773574i \(-0.281533\pi\)
0.633706 + 0.773574i \(0.281533\pi\)
\(758\) −5.21876 15.8471i −0.189554 0.575594i
\(759\) −14.5447 −0.527940
\(760\) 14.2156 + 10.0715i 0.515656 + 0.365333i
\(761\) 8.96763i 0.325076i 0.986702 + 0.162538i \(0.0519681\pi\)
−0.986702 + 0.162538i \(0.948032\pi\)
\(762\) −1.95770 5.94469i −0.0709200 0.215353i
\(763\) 0 0
\(764\) 23.8273 + 32.2533i 0.862043 + 1.16688i
\(765\) −1.27700 −0.0461700
\(766\) −1.28555 + 0.423356i −0.0464488 + 0.0152965i
\(767\) 8.39870i 0.303260i
\(768\) 11.9299 + 8.10100i 0.430484 + 0.292320i
\(769\) 0.573577i 0.0206837i 0.999947 + 0.0103419i \(0.00329197\pi\)
−0.999947 + 0.0103419i \(0.996708\pi\)
\(770\) 0 0
\(771\) 23.2841i 0.838556i
\(772\) 31.1098 22.9826i 1.11966 0.827160i
\(773\) 4.34850i 0.156405i 0.996938 + 0.0782023i \(0.0249180\pi\)
−0.996938 + 0.0782023i \(0.975082\pi\)
\(774\) −5.61385 17.0468i −0.201786 0.612736i
\(775\) −2.53865 −0.0911910
\(776\) 10.4789 + 7.42411i 0.376170 + 0.266510i
\(777\) 0 0
\(778\) 40.5179 13.3433i 1.45264 0.478381i
\(779\) 45.2769i 1.62221i
\(780\) 3.50845 2.59189i 0.125623 0.0928047i
\(781\) −37.3038 −1.33483
\(782\) −3.38103 + 1.11344i −0.120905 + 0.0398165i