Properties

Label 980.2.g.a.391.8
Level $980$
Weight $2$
Character 980.391
Analytic conductor $7.825$
Analytic rank $0$
Dimension $32$
CM no
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 391.8
Character \(\chi\) \(=\) 980.391
Dual form 980.2.g.a.391.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.34325 + 0.442358i) q^{2} +0.901278 q^{3} +(1.60864 - 1.18839i) q^{4} +1.00000i q^{5} +(-1.21064 + 0.398687i) q^{6} +(-1.63511 + 2.30790i) q^{8} -2.18770 q^{9} +O(q^{10})\) \(q+(-1.34325 + 0.442358i) q^{2} +0.901278 q^{3} +(1.60864 - 1.18839i) q^{4} +1.00000i q^{5} +(-1.21064 + 0.398687i) q^{6} +(-1.63511 + 2.30790i) q^{8} -2.18770 q^{9} +(-0.442358 - 1.34325i) q^{10} +3.74246i q^{11} +(1.44983 - 1.07107i) q^{12} +2.41990i q^{13} +0.901278i q^{15} +(1.17544 - 3.82339i) q^{16} -0.583719i q^{17} +(2.93862 - 0.967745i) q^{18} -6.15955 q^{19} +(1.18839 + 1.60864i) q^{20} +(-1.65551 - 5.02706i) q^{22} -4.31210i q^{23} +(-1.47369 + 2.08006i) q^{24} -1.00000 q^{25} +(-1.07046 - 3.25054i) q^{26} -4.67556 q^{27} -0.435463 q^{29} +(-0.398687 - 1.21064i) q^{30} -2.53865 q^{31} +(0.112397 + 5.65574i) q^{32} +3.37300i q^{33} +(0.258212 + 0.784080i) q^{34} +(-3.51922 + 2.59985i) q^{36} -11.3008 q^{37} +(8.27381 - 2.72472i) q^{38} +2.18101i q^{39} +(-2.30790 - 1.63511i) q^{40} +7.35068i q^{41} -5.80096i q^{43} +(4.44752 + 6.02027i) q^{44} -2.18770i q^{45} +(1.90749 + 5.79223i) q^{46} +11.5765 q^{47} +(1.05940 - 3.44594i) q^{48} +(1.34325 - 0.442358i) q^{50} -0.526093i q^{51} +(2.87580 + 3.89275i) q^{52} -3.11491 q^{53} +(6.28044 - 2.06827i) q^{54} -3.74246 q^{55} -5.55147 q^{57} +(0.584935 - 0.192630i) q^{58} -3.47068 q^{59} +(1.07107 + 1.44983i) q^{60} +10.3877i q^{61} +(3.41004 - 1.12299i) q^{62} +(-2.65284 - 7.54735i) q^{64} -2.41990 q^{65} +(-1.49207 - 4.53078i) q^{66} -9.84499i q^{67} +(-0.693688 - 0.938993i) q^{68} -3.88640i q^{69} +9.96771i q^{71} +(3.57712 - 5.04900i) q^{72} +9.79892i q^{73} +(15.1798 - 4.99899i) q^{74} -0.901278 q^{75} +(-9.90849 + 7.31997i) q^{76} +(-0.964785 - 2.92964i) q^{78} -0.459050i q^{79} +(3.82339 + 1.17544i) q^{80} +2.34912 q^{81} +(-3.25163 - 9.87380i) q^{82} +2.59747 q^{83} +0.583719 q^{85} +(2.56610 + 7.79213i) q^{86} -0.392473 q^{87} +(-8.63724 - 6.11933i) q^{88} +9.88016i q^{89} +(0.967745 + 2.93862i) q^{90} +(-5.12447 - 6.93662i) q^{92} -2.28803 q^{93} +(-15.5502 + 5.12097i) q^{94} -6.15955i q^{95} +(0.101301 + 5.09739i) q^{96} +4.54044i q^{97} -8.18738i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q - 4 q^{2} + 4 q^{4} - 4 q^{8} + 32 q^{9}+O(q^{10}) \) 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 \(-0.416219\pi\)
0.260177 + 0.965561i \(0.416219\pi\)
\(4\) 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 \(0.108932\pi\)
−0.942012 + 0.335580i \(0.891068\pi\)
\(14\) 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 \(-0.977449\pi\)
0.997492 0.0707863i \(-0.0225508\pi\)
\(18\) 2.93862 0.967745i 0.692640 0.228100i
\(19\) −6.15955 −1.41310 −0.706549 0.707664i \(-0.749749\pi\)
−0.706549 + 0.707664i \(0.749749\pi\)
\(20\) 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 \(-0.573211\pi\)
−0.227978 + 0.973666i \(0.573211\pi\)
\(32\) 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 \(0.194606\pi\)
−0.818861 + 0.573992i \(0.805394\pi\)
\(42\) 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 \(-0.180014\pi\)
0.844305 + 0.535863i \(0.180014\pi\)
\(48\) 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 \(-0.572539\pi\)
−0.225922 + 0.974145i \(0.572539\pi\)
\(60\) 1.07107 + 1.44983i 0.138275 + 0.187172i
\(61\) 10.3877i 1.33000i 0.746842 + 0.665001i \(0.231569\pi\)
−0.746842 + 0.665001i \(0.768431\pi\)
\(62\) 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 \(0.194391\pi\)
−0.819249 + 0.573439i \(0.805609\pi\)
\(74\) 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 \(-0.454468\pi\)
0.142554 + 0.989787i \(0.454468\pi\)
\(84\) 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 \(0.175429\pi\)
−0.851935 + 0.523648i \(0.824571\pi\)
\(90\) 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 \(0.0740380\pi\)
−0.973071 + 0.230506i \(0.925962\pi\)
\(98\) 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 \(0.150343\pi\)
−0.890516 + 0.454952i \(0.849657\pi\)
\(102\) 0.232721 + 0.706674i 0.0230428 + 0.0699712i
\(103\) −10.2319 −1.00818 −0.504092 0.863650i \(-0.668173\pi\)
−0.504092 + 0.863650i \(0.668173\pi\)
\(104\) −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 \(-0.743923\pi\)
−0.693479 + 0.720477i \(0.743923\pi\)
\(132\) 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 \(-0.235717\pi\)
0.738113 + 0.674677i \(0.235717\pi\)
\(140\) 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 \(-0.960747\pi\)
0.992406 0.123005i \(-0.0392532\pi\)
\(158\) 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 \(-0.272556\pi\)
0.655266 + 0.755398i \(0.272556\pi\)
\(168\) 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 \(-0.998394\pi\)
0.999987 0.00504439i \(-0.00160569\pi\)
\(174\) 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 \(0.0474139\pi\)
−0.988927 + 0.148405i \(0.952586\pi\)
\(182\) 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 \(-0.491162\pi\)
0.0277621 + 0.999615i \(0.491162\pi\)
\(200\) 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 \(-0.801376\pi\)
−0.811550 + 0.584284i \(0.801376\pi\)
\(224\) 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 \(-0.385212\pi\)
0.352851 + 0.935680i \(0.385212\pi\)
\(228\) −8.93031 + 6.59733i −0.591424 + 0.436919i
\(229\) 29.5128i 1.95026i 0.221626 + 0.975132i \(0.428864\pi\)
−0.221626 + 0.975132i \(0.571136\pi\)
\(230\) −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 \(-0.956732\pi\)
0.990776 0.135512i \(-0.0432678\pi\)
\(242\) 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 \(-0.296784\pi\)
0.595928 + 0.803038i \(0.296784\pi\)
\(252\) 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 \(-0.701759\pi\)
0.592247 0.805757i \(-0.298241\pi\)
\(258\) 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 \(-0.917920\pi\)
0.966937 0.255015i \(-0.0820805\pi\)
\(270\) 2.06827 + 6.28044i 0.125871 + 0.382216i
\(271\) 27.1113 1.64690 0.823448 0.567392i \(-0.192048\pi\)
0.823448 + 0.567392i \(0.192048\pi\)
\(272\) −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 \(-0.568703\pi\)
−0.214165 + 0.976797i \(0.568703\pi\)
\(284\) 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 \(0.0796642\pi\)
−0.968845 + 0.247668i \(0.920336\pi\)
\(294\) 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 \(-0.596170\pi\)
−0.297552 + 0.954706i \(0.596170\pi\)
\(308\) 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 \(-0.572146\pi\)
−0.224719 + 0.974424i \(0.572146\pi\)
\(312\) −5.03355 3.56618i −0.284969 0.201895i
\(313\) 14.4667i 0.817703i −0.912601 0.408852i \(-0.865929\pi\)
0.912601 0.408852i \(-0.134071\pi\)
\(314\) 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 \(-0.735339\pi\)
0.673801 0.738913i \(-0.264661\pi\)
\(350\) 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 \(0.257113\pi\)
−0.691131 + 0.722730i \(0.742887\pi\)
\(354\) 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 \(-0.429266\pi\)
0.220393 + 0.975411i \(0.429266\pi\)
\(368\) −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 \(-0.507784\pi\)
−0.0244514 + 0.999701i \(0.507784\pi\)
\(384\) 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 \(0.0497825\pi\)
−0.987795 + 0.155760i \(0.950217\pi\)
\(398\) −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 \(-0.849645\pi\)
0.890500 0.454984i \(-0.150355\pi\)
\(410\) 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 \(-0.830072\pi\)
−0.860856 + 0.508848i \(0.830072\pi\)
\(420\) 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 \(0.105948\pi\)
−0.945116 + 0.326734i \(0.894052\pi\)
\(434\) 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 \(-0.743810\pi\)
−0.693224 + 0.720722i \(0.743810\pi\)
\(440\) 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 \(0.0963089\pi\)
−0.954576 + 0.297968i \(0.903691\pi\)
\(462\) 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 \(-0.324756\pi\)
0.523152 + 0.852239i \(0.324756\pi\)
\(468\) −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 \(-0.332532\pi\)
0.502180 + 0.864763i \(0.332532\pi\)
\(480\) −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 \(-0.373923\pi\)
0.385807 + 0.922580i \(0.373923\pi\)
\(504\) 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 \(0.0982570\pi\)
−0.952734 + 0.303805i \(0.901743\pi\)
\(510\) −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 \(0.293214\pi\)
−0.604897 + 0.796304i \(0.706786\pi\)
\(522\) −1.27966 + 0.421417i −0.0560093 + 0.0184449i
\(523\) 4.26422 0.186461 0.0932306 0.995645i \(-0.470281\pi\)
0.0932306 + 0.995645i \(0.470281\pi\)
\(524\) −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 \(-0.481639\pi\)
0.0576509 + 0.998337i \(0.481639\pi\)
\(564\) 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 \(-0.746461\pi\)
0.699203 0.714924i \(-0.253539\pi\)
\(578\) −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 \(-0.810762\pi\)
−0.828423 + 0.560103i \(0.810762\pi\)
\(588\) 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 \(-0.927926\pi\)
0.974475 0.224496i \(-0.0720736\pi\)
\(594\) 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 \(-0.893431\pi\)
0.944477 0.328577i \(-0.106569\pi\)
\(602\) 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 \(-0.562784\pi\)
−0.195967 + 0.980611i \(0.562784\pi\)
\(608\) −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 \(-0.515907\pi\)
−0.0499517 + 0.998752i \(0.515907\pi\)
\(620\) −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 \(-0.341293\pi\)
0.478190 + 0.878256i \(0.341293\pi\)
\(644\) 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 \(-0.700105\pi\)
−0.588053 + 0.808823i \(0.700105\pi\)
\(648\) −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 \(0.113323\pi\)
−0.937293 + 0.348542i \(0.886677\pi\)
\(662\) 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 \(0.161309\pi\)
−0.874318 + 0.485353i \(0.838691\pi\)
\(678\) −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 \(-0.388058\pi\)
0.344471 + 0.938797i \(0.388058\pi\)
\(692\) −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 \(-0.622897\pi\)
−0.376573 + 0.926387i \(0.622897\pi\)
\(720\) −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 \(-0.564138\pi\)
−0.200136 + 0.979768i \(0.564138\pi\)
\(728\) 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 \(-0.957358\pi\)
0.991040 0.133564i \(-0.0426422\pi\)
\(734\) −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 \(-0.948032\pi\)
0.986702 0.162538i \(-0.0519681\pi\)
\(762\) 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 \(-0.996708\pi\)
0.999947 0.0103419i \(-0.00329197\pi\)
\(770\) 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 \(-0.975082\pi\)
0.996938 0.0782023i \(-0.0249180\pi\)
\(774\) −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
\(783\) 2.03603 0.0727618
\(784\) 0 0
\(785\) 3.08251 0.110019
\(786\) 19.2183 6.32895i 0.685493 0.225746i
\(787\) −21.0496 −0.750337 −0.375168 0.926957i \(-0.622415\pi\)
−0.375168 + 0.926957i \(0.622415\pi\)
\(788\) −2.63396 + 1.94585i −0.0938308 + 0.0693181i
\(789\) 9.64110i 0.343232i
\(790\) −0.616619 + 0.203065i −0.0219383 + 0.00722471i
\(791\) 0 0
\(792\) 18.8957 + 13.3873i 0.671428 + 0.475695i
\(793\) −25.1371 −0.892645
\(794\) −2.74570 8.33752i −0.0974414 0.295887i
\(795\) 2.80740i 0.0995682i
\(796\) 1.25999 0.930826i 0.0446591 0.0329922i
\(797\) 14.7349i 0.521938i −0.965347 0.260969i \(-0.915958\pi\)
0.965347 0.260969i \(-0.0840420\pi\)
\(798\) 0 0
\(799\) 6.75744i 0.239061i
\(800\) −0.112397 5.65574i −0.00397385 0.199961i
\(801\) 21.6148i 0.763722i
\(802\) −35.3449 + 11.6397i −1.24807 + 0.411014i
\(803\) −36.6721 −1.29413
\(804\) −10.5447 14.2736i −0.371883 0.503390i
\(805\) 0 0
\(806\) 2.71753 + 8.25198i 0.0957210 + 0.290663i
\(807\) 7.53930i 0.265396i
\(808\) −21.1044 14.9521i −0.742451 0.526014i
\(809\) −14.4762 −0.508955 −0.254477 0.967079i \(-0.581903\pi\)
−0.254477 + 0.967079i \(0.581903\pi\)
\(810\) −1.03915 3.15545i −0.0365120 0.110871i
\(811\) 18.5825 0.652521 0.326260 0.945280i \(-0.394211\pi\)
0.326260 + 0.945280i \(0.394211\pi\)
\(812\) 0 0
\(813\) 24.4348 0.856967
\(814\) 18.7085 + 56.8097i 0.655733 + 1.99118i
\(815\) −4.51816 −0.158264
\(816\) −2.01146 0.618391i −0.0704152 0.0216480i
\(817\) 35.7313i 1.25008i
\(818\) 8.14069 + 24.7198i 0.284633 + 0.864306i
\(819\) 0 0
\(820\) −11.8246 + 8.73551i −0.412933 + 0.305057i
\(821\) −16.4055 −0.572556 −0.286278 0.958147i \(-0.592418\pi\)
−0.286278 + 0.958147i \(0.592418\pi\)
\(822\) 9.49410 3.12659i 0.331145 0.109052i
\(823\) 43.8972i 1.53016i 0.643934 + 0.765081i \(0.277301\pi\)
−0.643934 + 0.765081i \(0.722699\pi\)
\(824\) 16.7303 23.6143i 0.582829 0.822645i
\(825\) 3.37300i 0.117433i
\(826\) 0 0
\(827\) 8.10796i 0.281941i −0.990014 0.140971i \(-0.954978\pi\)
0.990014 0.140971i \(-0.0450224\pi\)
\(828\) 11.2108 + 15.1752i 0.389602 + 0.527375i
\(829\) 42.2224i 1.46645i −0.679989 0.733223i \(-0.738015\pi\)
0.679989 0.733223i \(-0.261985\pi\)
\(830\) −1.14901 3.48905i −0.0398827 0.121107i
\(831\) 3.02814 0.105045
\(832\) 18.2639 6.41961i 0.633185 0.222560i
\(833\) 0 0
\(834\) −21.0705 + 6.93893i −0.729613 + 0.240275i
\(835\) 16.9358i 0.586088i
\(836\) −27.3947 37.0822i −0.947466 1.28251i
\(837\) 11.8696 0.410274
\(838\) 47.3396 15.5898i 1.63532 0.538542i
\(839\) 31.8404 1.09925 0.549627 0.835410i \(-0.314770\pi\)
0.549627 + 0.835410i \(0.314770\pi\)
\(840\) 0 0
\(841\) −28.8104 −0.993461
\(842\) 21.0446 6.93037i 0.725243 0.238836i
\(843\) −6.61491 −0.227829
\(844\) 10.9633 + 14.8403i 0.377374 + 0.510823i
\(845\) 7.14406i 0.245763i
\(846\) 34.0191 11.2031i 1.16960 0.385171i
\(847\) 0 0
\(848\) −3.66139 + 11.9095i −0.125733 + 0.408975i
\(849\) −6.49429 −0.222883
\(850\) −0.258212 0.784080i −0.00885662 0.0268937i
\(851\) 48.7301i 1.67045i
\(852\) 10.6761 + 14.4515i 0.365759 + 0.495100i
\(853\) 16.2023i 0.554755i 0.960761 + 0.277378i \(0.0894653\pi\)
−0.960761 + 0.277378i \(0.910535\pi\)
\(854\) 0 0
\(855\) 13.4752i 0.460843i
\(856\) 14.6137 + 10.3535i 0.499485 + 0.353876i
\(857\) 40.9525i 1.39891i 0.714677 + 0.699455i \(0.246574\pi\)
−0.714677 + 0.699455i \(0.753426\pi\)
\(858\) 10.9641 3.61067i 0.374307 0.123266i
\(859\) −12.0528 −0.411236 −0.205618 0.978632i \(-0.565920\pi\)
−0.205618 + 0.978632i \(0.565920\pi\)
\(860\) 9.33165 6.89382i 0.318206 0.235077i
\(861\) 0 0
\(862\) −0.887107 2.69376i −0.0302150 0.0917499i
\(863\) 0.570852i 0.0194320i −0.999953 0.00971602i \(-0.996907\pi\)
0.999953 0.00971602i \(-0.00309275\pi\)
\(864\) −0.525521 26.4437i −0.0178786 0.899634i
\(865\) 0.132697 0.00451184
\(866\) −6.01509 18.2652i −0.204401 0.620678i
\(867\) 15.0146 0.509924
\(868\) 0 0
\(869\) 1.71798 0.0582784
\(870\) 0.173613 + 0.527189i 0.00588605 + 0.0178734i
\(871\) 23.8239 0.807243
\(872\) 30.6755 43.2975i 1.03880 1.46624i
\(873\) 9.93310i 0.336185i
\(874\) −11.7493 35.6775i −0.397426 1.20681i
\(875\) 0 0
\(876\) 10.4954 + 14.2068i 0.354605 + 0.480003i
\(877\) 18.9439 0.639689 0.319844 0.947470i \(-0.396369\pi\)
0.319844 + 0.947470i \(0.396369\pi\)
\(878\) 39.0205 12.8502i 1.31688 0.433673i
\(879\) 7.64174i 0.257750i
\(880\) −4.39904 + 14.3089i −0.148292 + 0.482353i
\(881\) 35.7695i 1.20511i 0.798079 + 0.602553i \(0.205850\pi\)
−0.798079 + 0.602553i \(0.794150\pi\)
\(882\) 0 0
\(883\) 25.4594i 0.856776i 0.903595 + 0.428388i \(0.140918\pi\)
−0.903595 + 0.428388i \(0.859082\pi\)
\(884\) 2.27227 1.67866i 0.0764248 0.0564594i
\(885\) 3.12804i 0.105148i
\(886\) −6.47462 19.6606i −0.217519 0.660512i
\(887\) −10.6049 −0.356076 −0.178038 0.984024i \(-0.556975\pi\)
−0.178038 + 0.984024i \(0.556975\pi\)
\(888\) 16.6538 23.5063i 0.558865 0.788821i
\(889\) 0 0
\(890\) 13.2715 4.37057i 0.444863 0.146502i
\(891\) 8.79148i 0.294525i
\(892\) −38.9903 + 28.8043i −1.30549 + 0.964440i
\(893\) −71.3062 −2.38617
\(894\) −1.99944 + 0.658453i −0.0668712 + 0.0220220i
\(895\) 16.0991 0.538132
\(896\) 0 0
\(897\) 9.40472 0.314014
\(898\) 36.3617 11.9746i 1.21340 0.399597i
\(899\) 1.10549 0.0368701
\(900\) 3.51922 2.59985i 0.117307 0.0866615i
\(901\) 1.81823i 0.0605741i
\(902\) 36.9523 12.1691i 1.23038 0.405187i
\(903\) 0 0
\(904\) −6.83225 + 9.64350i −0.227237 + 0.320738i
\(905\) −3.99317 −0.132737
\(906\) 2.93280 + 8.90564i 0.0974356 + 0.295870i
\(907\) 15.3638i 0.510146i −0.966922 0.255073i \(-0.917900\pi\)
0.966922 0.255073i \(-0.0820996\pi\)
\(908\) 17.1038 12.6355i 0.567609 0.419325i
\(909\) 20.0052i 0.663531i
\(910\) 0 0
\(911\) 22.0734i 0.731324i 0.930748 + 0.365662i \(0.119157\pi\)
−0.930748 + 0.365662i \(0.880843\pi\)
\(912\) −6.52542 + 21.2254i −0.216078 + 0.702845i
\(913\) 9.72092i 0.321715i
\(914\) 10.2169 3.36462i 0.337945 0.111292i
\(915\) −9.36216 −0.309504
\(916\) 35.0729 + 47.4755i 1.15884 + 1.56864i
\(917\) 0 0
\(918\) −1.20729 3.66601i −0.0398464 0.120996i
\(919\) 52.1460i 1.72014i 0.510178 + 0.860069i \(0.329580\pi\)
−0.510178 + 0.860069i \(0.670420\pi\)
\(920\) −7.05076 + 9.95191i −0.232457 + 0.328105i
\(921\) −9.39768 −0.309664
\(922\) −5.66010 17.1873i −0.186405 0.566033i
\(923\) −24.1209 −0.793949
\(924\) 0 0
\(925\) 11.3008 0.371567
\(926\) 12.3496 + 37.5005i 0.405834 + 1.23234i
\(927\) 22.3844 0.735200
\(928\) −0.0489449 2.46286i −0.00160669 0.0808474i
\(929\) 28.7182i 0.942215i −0.882076 0.471107i \(-0.843854\pi\)
0.882076 0.471107i \(-0.156146\pi\)
\(930\) 1.01213 + 3.07340i 0.0331890 + 0.100781i
\(931\) 0 0
\(932\) 45.1549 33.3585i 1.47910 1.09270i
\(933\) −7.14345 −0.233866
\(934\) −30.3720 + 10.0021i −0.993801 + 0.327278i
\(935\) 2.18455i 0.0714423i
\(936\) 12.2181 + 8.65630i 0.399361 + 0.282940i
\(937\) 44.9045i 1.46697i −0.679707 0.733484i \(-0.737893\pi\)
0.679707 0.733484i \(-0.262107\pi\)
\(938\) 0 0
\(939\) 13.0385i 0.425495i
\(940\) 13.7575 + 18.6225i 0.448719 + 0.607398i
\(941\) 17.7508i 0.578660i 0.957229 + 0.289330i \(0.0934325\pi\)
−0.957229 + 0.289330i \(0.906567\pi\)
\(942\) 1.22896 + 3.73181i 0.0400416 + 0.121589i
\(943\) 31.6969 1.03219
\(944\) −4.07957 + 13.2698i −0.132779 + 0.431894i
\(945\) 0 0
\(946\) −29.1618 + 9.60352i −0.948130 + 0.312237i
\(947\) 37.0775i 1.20486i 0.798173 + 0.602428i \(0.205800\pi\)
−0.798173 + 0.602428i \(0.794200\pi\)
\(948\) −0.491677 0.665546i −0.0159689 0.0216159i
\(949\) −23.7125 −0.769739
\(950\) −8.27381 + 2.72472i −0.268438 + 0.0884017i
\(951\) 3.18787 0.103374
\(952\) 0 0
\(953\) −28.5420 −0.924567 −0.462283 0.886732i \(-0.652970\pi\)
−0.462283 + 0.886732i \(0.652970\pi\)
\(954\) −9.15355 + 3.01444i −0.296357 + 0.0975961i
\(955\) −20.0500 −0.648804
\(956\) 16.1953 + 21.9223i 0.523792 + 0.709018i
\(957\) 1.46882i 0.0474800i
\(958\) −29.5266 + 9.72368i −0.953962 + 0.314158i
\(959\) 0 0
\(960\) 6.80226 2.39094i 0.219542 0.0771674i
\(961\) −24.5552 −0.792105
\(962\) 12.0971 + 36.7336i 0.390025 + 1.18434i
\(963\) 13.8525i 0.446391i
\(964\) −5.00006 6.76820i −0.161041 0.217989i
\(965\) 19.3392i 0.622550i
\(966\) 0 0
\(967\) 5.33936i 0.171702i 0.996308 + 0.0858510i \(0.0273609\pi\)
−0.996308 + 0.0858510i \(0.972639\pi\)
\(968\) 4.91517 6.93760i 0.157980 0.222983i
\(969\) 3.24050i 0.104100i
\(970\) 6.09894 2.00850i 0.195825 0.0644890i
\(971\) −10.9981 −0.352946 −0.176473 0.984305i \(-0.556469\pi\)
−0.176473 + 0.984305i \(0.556469\pi\)
\(972\) 25.9697 19.1853i 0.832978 0.615368i
\(973\) 0 0
\(974\) −11.2283 34.0955i −0.359778 1.09249i
\(975\) 2.18101i 0.0698481i
\(976\) 39.7161 + 12.2101i 1.27128 + 0.390835i
\(977\) −31.4868 −1.00735 −0.503676 0.863893i \(-0.668019\pi\)
−0.503676 + 0.863893i \(0.668019\pi\)
\(978\) −1.80133 5.46987i −0.0576002 0.174907i
\(979\) −36.9761 −1.18176
\(980\) 0 0
\(981\) 41.0424 1.31038
\(982\) 16.1299 + 48.9796i 0.514726 + 1.56300i
\(983\) −34.5524 −1.10205 −0.551025 0.834489i \(-0.685763\pi\)
−0.551025 + 0.834489i \(0.685763\pi\)
\(984\) −15.2899 10.8326i −0.487424 0.345331i
\(985\) 1.63738i 0.0521713i
\(986\) −0.112442 0.341438i −0.00358088 0.0108736i
\(987\) 0 0
\(988\) −17.7136 23.9776i −0.563545 0.762829i
\(989\) −25.0143 −0.795409
\(990\) −10.9977 + 3.62175i −0.349530 + 0.115107i
\(991\) 55.2718i 1.75577i −0.478874 0.877884i \(-0.658955\pi\)
0.478874 0.877884i \(-0.341045\pi\)
\(992\) −0.285338 14.3579i −0.00905948 0.455865i
\(993\) 21.2068i 0.672978i
\(994\) 0 0
\(995\) 0.783264i 0.0248311i
\(996\) 3.76589 2.78208i 0.119327 0.0881535i
\(997\) 15.2817i 0.483978i 0.970279 + 0.241989i \(0.0777997\pi\)
−0.970279 + 0.241989i \(0.922200\pi\)
\(998\) 5.25472 + 15.9563i 0.166335 + 0.505089i
\(999\) 52.8374 1.67170
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 980.2.g.a.391.8 32
4.3 odd 2 inner 980.2.g.a.391.5 32
7.2 even 3 980.2.o.f.31.13 32
7.3 odd 6 980.2.o.f.411.9 32
7.4 even 3 140.2.o.a.131.9 yes 32
7.5 odd 6 140.2.o.a.31.13 yes 32
7.6 odd 2 inner 980.2.g.a.391.7 32
28.3 even 6 980.2.o.f.411.13 32
28.11 odd 6 140.2.o.a.131.13 yes 32
28.19 even 6 140.2.o.a.31.9 32
28.23 odd 6 980.2.o.f.31.9 32
28.27 even 2 inner 980.2.g.a.391.6 32
35.4 even 6 700.2.p.c.551.8 32
35.12 even 12 700.2.t.c.199.6 32
35.18 odd 12 700.2.t.c.299.1 32
35.19 odd 6 700.2.p.c.451.4 32
35.32 odd 12 700.2.t.d.299.16 32
35.33 even 12 700.2.t.d.199.11 32
140.19 even 6 700.2.p.c.451.8 32
140.39 odd 6 700.2.p.c.551.4 32
140.47 odd 12 700.2.t.c.199.1 32
140.67 even 12 700.2.t.d.299.11 32
140.103 odd 12 700.2.t.d.199.16 32
140.123 even 12 700.2.t.c.299.6 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
140.2.o.a.31.9 32 28.19 even 6
140.2.o.a.31.13 yes 32 7.5 odd 6
140.2.o.a.131.9 yes 32 7.4 even 3
140.2.o.a.131.13 yes 32 28.11 odd 6
700.2.p.c.451.4 32 35.19 odd 6
700.2.p.c.451.8 32 140.19 even 6
700.2.p.c.551.4 32 140.39 odd 6
700.2.p.c.551.8 32 35.4 even 6
700.2.t.c.199.1 32 140.47 odd 12
700.2.t.c.199.6 32 35.12 even 12
700.2.t.c.299.1 32 35.18 odd 12
700.2.t.c.299.6 32 140.123 even 12
700.2.t.d.199.11 32 35.33 even 12
700.2.t.d.199.16 32 140.103 odd 12
700.2.t.d.299.11 32 140.67 even 12
700.2.t.d.299.16 32 35.32 odd 12
980.2.g.a.391.5 32 4.3 odd 2 inner
980.2.g.a.391.6 32 28.27 even 2 inner
980.2.g.a.391.7 32 7.6 odd 2 inner
980.2.g.a.391.8 32 1.1 even 1 trivial
980.2.o.f.31.9 32 28.23 odd 6
980.2.o.f.31.13 32 7.2 even 3
980.2.o.f.411.9 32 7.3 odd 6
980.2.o.f.411.13 32 28.3 even 6