Properties

Label 690.2.h.b.689.8
Level $690$
Weight $2$
Character 690.689
Analytic conductor $5.510$
Analytic rank $0$
Dimension $24$
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] = [690,2,Mod(689,690)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(690, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("690.689");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 690.h (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: \(5.50967773947\)
Analytic rank: \(0\)
Dimension: \(24\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 689.8
Character \(\chi\) \(=\) 690.689
Dual form 690.2.h.b.689.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} +(-1.44698 + 0.951967i) q^{3} +1.00000 q^{4} +(1.42959 - 1.71938i) q^{5} +(-1.44698 + 0.951967i) q^{6} -4.73682 q^{7} +1.00000 q^{8} +(1.18752 - 2.75496i) q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +(-1.44698 + 0.951967i) q^{3} +1.00000 q^{4} +(1.42959 - 1.71938i) q^{5} +(-1.44698 + 0.951967i) q^{6} -4.73682 q^{7} +1.00000 q^{8} +(1.18752 - 2.75496i) q^{9} +(1.42959 - 1.71938i) q^{10} -0.109553 q^{11} +(-1.44698 + 0.951967i) q^{12} -2.46994i q^{13} -4.73682 q^{14} +(-0.431808 + 3.84884i) q^{15} +1.00000 q^{16} -3.72035i q^{17} +(1.18752 - 2.75496i) q^{18} -6.76462i q^{19} +(1.42959 - 1.71938i) q^{20} +(6.85409 - 4.50929i) q^{21} -0.109553 q^{22} +(4.67990 - 1.04813i) q^{23} +(-1.44698 + 0.951967i) q^{24} +(-0.912517 - 4.91603i) q^{25} -2.46994i q^{26} +(0.904315 + 5.11686i) q^{27} -4.73682 q^{28} +7.05802i q^{29} +(-0.431808 + 3.84884i) q^{30} -9.34339 q^{31} +1.00000 q^{32} +(0.158521 - 0.104291i) q^{33} -3.72035i q^{34} +(-6.77173 + 8.14437i) q^{35} +(1.18752 - 2.75496i) q^{36} -1.34148 q^{37} -6.76462i q^{38} +(2.35130 + 3.57395i) q^{39} +(1.42959 - 1.71938i) q^{40} -7.38300i q^{41} +(6.85409 - 4.50929i) q^{42} +2.31465 q^{43} -0.109553 q^{44} +(-3.03915 - 5.98027i) q^{45} +(4.67990 - 1.04813i) q^{46} +5.53476 q^{47} +(-1.44698 + 0.951967i) q^{48} +15.4374 q^{49} +(-0.912517 - 4.91603i) q^{50} +(3.54165 + 5.38329i) q^{51} -2.46994i q^{52} -3.77179i q^{53} +(0.904315 + 5.11686i) q^{54} +(-0.156616 + 0.188362i) q^{55} -4.73682 q^{56} +(6.43970 + 9.78829i) q^{57} +7.05802i q^{58} -4.18459i q^{59} +(-0.431808 + 3.84884i) q^{60} -7.57377i q^{61} -9.34339 q^{62} +(-5.62505 + 13.0497i) q^{63} +1.00000 q^{64} +(-4.24675 - 3.53101i) q^{65} +(0.158521 - 0.104291i) q^{66} -5.95975 q^{67} -3.72035i q^{68} +(-5.77394 + 5.97173i) q^{69} +(-6.77173 + 8.14437i) q^{70} -9.66771i q^{71} +(1.18752 - 2.75496i) q^{72} +9.28694i q^{73} -1.34148 q^{74} +(6.00029 + 6.24472i) q^{75} -6.76462i q^{76} +0.518931 q^{77} +(2.35130 + 3.57395i) q^{78} +12.3843i q^{79} +(1.42959 - 1.71938i) q^{80} +(-6.17961 - 6.54312i) q^{81} -7.38300i q^{82} +16.6139i q^{83} +(6.85409 - 4.50929i) q^{84} +(-6.39669 - 5.31860i) q^{85} +2.31465 q^{86} +(-6.71900 - 10.2128i) q^{87} -0.109553 q^{88} +10.2277 q^{89} +(-3.03915 - 5.98027i) q^{90} +11.6996i q^{91} +(4.67990 - 1.04813i) q^{92} +(13.5197 - 8.89460i) q^{93} +5.53476 q^{94} +(-11.6309 - 9.67067i) q^{95} +(-1.44698 + 0.951967i) q^{96} -9.94453 q^{97} +15.4374 q^{98} +(-0.130096 + 0.301813i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q + 24 q^{2} - 2 q^{3} + 24 q^{4} - 2 q^{6} + 24 q^{8} + 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 24 q + 24 q^{2} - 2 q^{3} + 24 q^{4} - 2 q^{6} + 24 q^{8} + 6 q^{9} - 2 q^{12} + 24 q^{16} + 6 q^{18} + 4 q^{23} - 2 q^{24} + 12 q^{25} - 2 q^{27} - 28 q^{31} + 24 q^{32} - 8 q^{35} + 6 q^{36} + 4 q^{46} - 16 q^{47} - 2 q^{48} - 4 q^{49} + 12 q^{50} - 2 q^{54} + 4 q^{55} - 28 q^{62} + 24 q^{64} - 8 q^{69} - 8 q^{70} + 6 q^{72} - 6 q^{75} - 8 q^{77} + 14 q^{81} - 44 q^{85} - 28 q^{87} + 4 q^{92} + 4 q^{93} - 16 q^{94} - 4 q^{95} - 2 q^{96} - 4 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).

\(n\) \(277\) \(461\) \(511\)
\(\chi(n)\) \(-1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) −1.44698 + 0.951967i −0.835416 + 0.549618i
\(4\) 1.00000 0.500000
\(5\) 1.42959 1.71938i 0.639334 0.768929i
\(6\) −1.44698 + 0.951967i −0.590728 + 0.388639i
\(7\) −4.73682 −1.79035 −0.895174 0.445717i \(-0.852949\pi\)
−0.895174 + 0.445717i \(0.852949\pi\)
\(8\) 1.00000 0.353553
\(9\) 1.18752 2.75496i 0.395839 0.918320i
\(10\) 1.42959 1.71938i 0.452078 0.543715i
\(11\) −0.109553 −0.0330314 −0.0165157 0.999864i \(-0.505257\pi\)
−0.0165157 + 0.999864i \(0.505257\pi\)
\(12\) −1.44698 + 0.951967i −0.417708 + 0.274809i
\(13\) 2.46994i 0.685037i −0.939511 0.342518i \(-0.888720\pi\)
0.939511 0.342518i \(-0.111280\pi\)
\(14\) −4.73682 −1.26597
\(15\) −0.431808 + 3.84884i −0.111492 + 0.993765i
\(16\) 1.00000 0.250000
\(17\) 3.72035i 0.902318i −0.892443 0.451159i \(-0.851011\pi\)
0.892443 0.451159i \(-0.148989\pi\)
\(18\) 1.18752 2.75496i 0.279900 0.649350i
\(19\) 6.76462i 1.55191i −0.630788 0.775955i \(-0.717268\pi\)
0.630788 0.775955i \(-0.282732\pi\)
\(20\) 1.42959 1.71938i 0.319667 0.384464i
\(21\) 6.85409 4.50929i 1.49568 0.984008i
\(22\) −0.109553 −0.0233567
\(23\) 4.67990 1.04813i 0.975826 0.218551i
\(24\) −1.44698 + 0.951967i −0.295364 + 0.194319i
\(25\) −0.912517 4.91603i −0.182503 0.983205i
\(26\) 2.46994i 0.484394i
\(27\) 0.904315 + 5.11686i 0.174035 + 0.984739i
\(28\) −4.73682 −0.895174
\(29\) 7.05802i 1.31064i 0.755351 + 0.655320i \(0.227466\pi\)
−0.755351 + 0.655320i \(0.772534\pi\)
\(30\) −0.431808 + 3.84884i −0.0788370 + 0.702698i
\(31\) −9.34339 −1.67812 −0.839061 0.544038i \(-0.816895\pi\)
−0.839061 + 0.544038i \(0.816895\pi\)
\(32\) 1.00000 0.176777
\(33\) 0.158521 0.104291i 0.0275949 0.0181547i
\(34\) 3.72035i 0.638035i
\(35\) −6.77173 + 8.14437i −1.14463 + 1.37665i
\(36\) 1.18752 2.75496i 0.197920 0.459160i
\(37\) −1.34148 −0.220538 −0.110269 0.993902i \(-0.535171\pi\)
−0.110269 + 0.993902i \(0.535171\pi\)
\(38\) 6.76462i 1.09737i
\(39\) 2.35130 + 3.57395i 0.376509 + 0.572291i
\(40\) 1.42959 1.71938i 0.226039 0.271857i
\(41\) 7.38300i 1.15303i −0.817086 0.576516i \(-0.804412\pi\)
0.817086 0.576516i \(-0.195588\pi\)
\(42\) 6.85409 4.50929i 1.05761 0.695799i
\(43\) 2.31465 0.352980 0.176490 0.984302i \(-0.443526\pi\)
0.176490 + 0.984302i \(0.443526\pi\)
\(44\) −0.109553 −0.0165157
\(45\) −3.03915 5.98027i −0.453049 0.891485i
\(46\) 4.67990 1.04813i 0.690013 0.154539i
\(47\) 5.53476 0.807327 0.403664 0.914907i \(-0.367737\pi\)
0.403664 + 0.914907i \(0.367737\pi\)
\(48\) −1.44698 + 0.951967i −0.208854 + 0.137405i
\(49\) 15.4374 2.20535
\(50\) −0.912517 4.91603i −0.129049 0.695231i
\(51\) 3.54165 + 5.38329i 0.495931 + 0.753811i
\(52\) 2.46994i 0.342518i
\(53\) 3.77179i 0.518096i −0.965864 0.259048i \(-0.916591\pi\)
0.965864 0.259048i \(-0.0834087\pi\)
\(54\) 0.904315 + 5.11686i 0.123062 + 0.696316i
\(55\) −0.156616 + 0.188362i −0.0211181 + 0.0253988i
\(56\) −4.73682 −0.632984
\(57\) 6.43970 + 9.78829i 0.852959 + 1.29649i
\(58\) 7.05802i 0.926763i
\(59\) 4.18459i 0.544788i −0.962186 0.272394i \(-0.912185\pi\)
0.962186 0.272394i \(-0.0878154\pi\)
\(60\) −0.431808 + 3.84884i −0.0557462 + 0.496883i
\(61\) 7.57377i 0.969722i −0.874591 0.484861i \(-0.838870\pi\)
0.874591 0.484861i \(-0.161130\pi\)
\(62\) −9.34339 −1.18661
\(63\) −5.62505 + 13.0497i −0.708690 + 1.64411i
\(64\) 1.00000 0.125000
\(65\) −4.24675 3.53101i −0.526745 0.437967i
\(66\) 0.158521 0.104291i 0.0195126 0.0128373i
\(67\) −5.95975 −0.728099 −0.364050 0.931380i \(-0.618606\pi\)
−0.364050 + 0.931380i \(0.618606\pi\)
\(68\) 3.72035i 0.451159i
\(69\) −5.77394 + 5.97173i −0.695101 + 0.718912i
\(70\) −6.77173 + 8.14437i −0.809376 + 0.973439i
\(71\) 9.66771i 1.14735i −0.819084 0.573673i \(-0.805518\pi\)
0.819084 0.573673i \(-0.194482\pi\)
\(72\) 1.18752 2.75496i 0.139950 0.324675i
\(73\) 9.28694i 1.08695i 0.839424 + 0.543477i \(0.182892\pi\)
−0.839424 + 0.543477i \(0.817108\pi\)
\(74\) −1.34148 −0.155944
\(75\) 6.00029 + 6.24472i 0.692854 + 0.721078i
\(76\) 6.76462i 0.775955i
\(77\) 0.518931 0.0591377
\(78\) 2.35130 + 3.57395i 0.266232 + 0.404671i
\(79\) 12.3843i 1.39334i 0.717389 + 0.696672i \(0.245337\pi\)
−0.717389 + 0.696672i \(0.754663\pi\)
\(80\) 1.42959 1.71938i 0.159834 0.192232i
\(81\) −6.17961 6.54312i −0.686623 0.727014i
\(82\) 7.38300i 0.815316i
\(83\) 16.6139i 1.82362i 0.410616 + 0.911808i \(0.365314\pi\)
−0.410616 + 0.911808i \(0.634686\pi\)
\(84\) 6.85409 4.50929i 0.747842 0.492004i
\(85\) −6.39669 5.31860i −0.693819 0.576883i
\(86\) 2.31465 0.249595
\(87\) −6.71900 10.2128i −0.720352 1.09493i
\(88\) −0.109553 −0.0116784
\(89\) 10.2277 1.08413 0.542067 0.840335i \(-0.317642\pi\)
0.542067 + 0.840335i \(0.317642\pi\)
\(90\) −3.03915 5.98027i −0.320354 0.630375i
\(91\) 11.6996i 1.22645i
\(92\) 4.67990 1.04813i 0.487913 0.109275i
\(93\) 13.5197 8.89460i 1.40193 0.922327i
\(94\) 5.53476 0.570867
\(95\) −11.6309 9.67067i −1.19331 0.992190i
\(96\) −1.44698 + 0.951967i −0.147682 + 0.0971597i
\(97\) −9.94453 −1.00971 −0.504857 0.863203i \(-0.668455\pi\)
−0.504857 + 0.863203i \(0.668455\pi\)
\(98\) 15.4374 1.55941
\(99\) −0.130096 + 0.301813i −0.0130751 + 0.0303334i
\(100\) −0.912517 4.91603i −0.0912517 0.491603i
\(101\) 8.68562i 0.864251i 0.901813 + 0.432126i \(0.142236\pi\)
−0.901813 + 0.432126i \(0.857764\pi\)
\(102\) 3.54165 + 5.38329i 0.350676 + 0.533025i
\(103\) 3.27739 0.322931 0.161465 0.986878i \(-0.448378\pi\)
0.161465 + 0.986878i \(0.448378\pi\)
\(104\) 2.46994i 0.242197i
\(105\) 2.04540 18.2312i 0.199610 1.77919i
\(106\) 3.77179i 0.366349i
\(107\) 1.42323i 0.137589i 0.997631 + 0.0687945i \(0.0219153\pi\)
−0.997631 + 0.0687945i \(0.978085\pi\)
\(108\) 0.904315 + 5.11686i 0.0870177 + 0.492370i
\(109\) 18.7318i 1.79418i 0.441849 + 0.897090i \(0.354323\pi\)
−0.441849 + 0.897090i \(0.645677\pi\)
\(110\) −0.156616 + 0.188362i −0.0149327 + 0.0179597i
\(111\) 1.94110 1.27704i 0.184241 0.121212i
\(112\) −4.73682 −0.447587
\(113\) 3.47135i 0.326557i −0.986580 0.163278i \(-0.947793\pi\)
0.986580 0.163278i \(-0.0522069\pi\)
\(114\) 6.43970 + 9.78829i 0.603133 + 0.916757i
\(115\) 4.88822 9.54491i 0.455829 0.890067i
\(116\) 7.05802i 0.655320i
\(117\) −6.80457 2.93309i −0.629083 0.271164i
\(118\) 4.18459i 0.385223i
\(119\) 17.6226i 1.61546i
\(120\) −0.431808 + 3.84884i −0.0394185 + 0.351349i
\(121\) −10.9880 −0.998909
\(122\) 7.57377i 0.685697i
\(123\) 7.02838 + 10.6831i 0.633727 + 0.963261i
\(124\) −9.34339 −0.839061
\(125\) −9.75703 5.45897i −0.872696 0.488265i
\(126\) −5.62505 + 13.0497i −0.501119 + 1.16256i
\(127\) 3.36092i 0.298234i 0.988820 + 0.149117i \(0.0476431\pi\)
−0.988820 + 0.149117i \(0.952357\pi\)
\(128\) 1.00000 0.0883883
\(129\) −3.34925 + 2.20347i −0.294885 + 0.194005i
\(130\) −4.24675 3.53101i −0.372465 0.309690i
\(131\) 13.6399i 1.19173i −0.803086 0.595863i \(-0.796810\pi\)
0.803086 0.595863i \(-0.203190\pi\)
\(132\) 0.158521 0.104291i 0.0137975 0.00907733i
\(133\) 32.0428i 2.77846i
\(134\) −5.95975 −0.514844
\(135\) 10.0906 + 5.76017i 0.868461 + 0.495757i
\(136\) 3.72035i 0.319018i
\(137\) 0.102320i 0.00874176i 0.999990 + 0.00437088i \(0.00139130\pi\)
−0.999990 + 0.00437088i \(0.998609\pi\)
\(138\) −5.77394 + 5.97173i −0.491510 + 0.508348i
\(139\) 1.57186 0.133323 0.0666617 0.997776i \(-0.478765\pi\)
0.0666617 + 0.997776i \(0.478765\pi\)
\(140\) −6.77173 + 8.14437i −0.572315 + 0.688325i
\(141\) −8.00870 + 5.26891i −0.674454 + 0.443722i
\(142\) 9.66771i 0.811296i
\(143\) 0.270588i 0.0226277i
\(144\) 1.18752 2.75496i 0.0989598 0.229580i
\(145\) 12.1354 + 10.0901i 1.00779 + 0.837937i
\(146\) 9.28694i 0.768592i
\(147\) −22.3377 + 14.6959i −1.84238 + 1.21210i
\(148\) −1.34148 −0.110269
\(149\) −10.9226 −0.894817 −0.447408 0.894330i \(-0.647653\pi\)
−0.447408 + 0.894330i \(0.647653\pi\)
\(150\) 6.00029 + 6.24472i 0.489922 + 0.509879i
\(151\) 6.42872 0.523162 0.261581 0.965182i \(-0.415756\pi\)
0.261581 + 0.965182i \(0.415756\pi\)
\(152\) 6.76462i 0.548683i
\(153\) −10.2494 4.41798i −0.828617 0.357173i
\(154\) 0.518931 0.0418166
\(155\) −13.3573 + 16.0648i −1.07288 + 1.29036i
\(156\) 2.35130 + 3.57395i 0.188254 + 0.286145i
\(157\) 24.1285 1.92567 0.962834 0.270095i \(-0.0870552\pi\)
0.962834 + 0.270095i \(0.0870552\pi\)
\(158\) 12.3843i 0.985244i
\(159\) 3.59062 + 5.45772i 0.284755 + 0.432825i
\(160\) 1.42959 1.71938i 0.113019 0.135929i
\(161\) −22.1678 + 4.96481i −1.74707 + 0.391281i
\(162\) −6.17961 6.54312i −0.485516 0.514076i
\(163\) 15.4395i 1.20932i −0.796485 0.604659i \(-0.793310\pi\)
0.796485 0.604659i \(-0.206690\pi\)
\(164\) 7.38300i 0.576516i
\(165\) 0.0473058 0.421650i 0.00368275 0.0328254i
\(166\) 16.6139i 1.28949i
\(167\) 4.86290 0.376302 0.188151 0.982140i \(-0.439751\pi\)
0.188151 + 0.982140i \(0.439751\pi\)
\(168\) 6.85409 4.50929i 0.528804 0.347899i
\(169\) 6.89942 0.530725
\(170\) −6.39669 5.31860i −0.490604 0.407918i
\(171\) −18.6363 8.03310i −1.42515 0.614307i
\(172\) 2.31465 0.176490
\(173\) 17.0492 1.29623 0.648114 0.761543i \(-0.275558\pi\)
0.648114 + 0.761543i \(0.275558\pi\)
\(174\) −6.71900 10.2128i −0.509366 0.774232i
\(175\) 4.32242 + 23.2863i 0.326745 + 1.76028i
\(176\) −0.109553 −0.00825785
\(177\) 3.98360 + 6.05503i 0.299425 + 0.455124i
\(178\) 10.2277 0.766598
\(179\) 8.37101i 0.625679i −0.949806 0.312839i \(-0.898720\pi\)
0.949806 0.312839i \(-0.101280\pi\)
\(180\) −3.03915 5.98027i −0.226525 0.445743i
\(181\) 3.91727i 0.291169i 0.989346 + 0.145584i \(0.0465062\pi\)
−0.989346 + 0.145584i \(0.953494\pi\)
\(182\) 11.6996i 0.867234i
\(183\) 7.20998 + 10.9591i 0.532977 + 0.810121i
\(184\) 4.67990 1.04813i 0.345006 0.0772693i
\(185\) −1.91777 + 2.30651i −0.140997 + 0.169578i
\(186\) 13.5197 8.89460i 0.991314 0.652183i
\(187\) 0.407575i 0.0298048i
\(188\) 5.53476 0.403664
\(189\) −4.28357 24.2376i −0.311584 1.76303i
\(190\) −11.6309 9.67067i −0.843797 0.701584i
\(191\) 10.0632 0.728147 0.364073 0.931370i \(-0.381386\pi\)
0.364073 + 0.931370i \(0.381386\pi\)
\(192\) −1.44698 + 0.951967i −0.104427 + 0.0687023i
\(193\) 1.36921i 0.0985576i 0.998785 + 0.0492788i \(0.0156923\pi\)
−0.998785 + 0.0492788i \(0.984308\pi\)
\(194\) −9.94453 −0.713976
\(195\) 9.50638 + 1.06654i 0.680766 + 0.0763764i
\(196\) 15.4374 1.10267
\(197\) 3.46037 0.246541 0.123271 0.992373i \(-0.460662\pi\)
0.123271 + 0.992373i \(0.460662\pi\)
\(198\) −0.130096 + 0.301813i −0.00924550 + 0.0214489i
\(199\) 2.84735i 0.201843i −0.994894 0.100922i \(-0.967821\pi\)
0.994894 0.100922i \(-0.0321791\pi\)
\(200\) −0.912517 4.91603i −0.0645247 0.347616i
\(201\) 8.62365 5.67348i 0.608265 0.400177i
\(202\) 8.68562i 0.611118i
\(203\) 33.4325i 2.34650i
\(204\) 3.54165 + 5.38329i 0.247965 + 0.376906i
\(205\) −12.6942 10.5547i −0.886599 0.737173i
\(206\) 3.27739 0.228347
\(207\) 2.66990 14.1376i 0.185571 0.982631i
\(208\) 2.46994i 0.171259i
\(209\) 0.741083i 0.0512618i
\(210\) 2.04540 18.2312i 0.141146 1.25807i
\(211\) −11.9262 −0.821033 −0.410517 0.911853i \(-0.634652\pi\)
−0.410517 + 0.911853i \(0.634652\pi\)
\(212\) 3.77179i 0.259048i
\(213\) 9.20334 + 13.9890i 0.630603 + 0.958511i
\(214\) 1.42323i 0.0972901i
\(215\) 3.30901 3.97975i 0.225672 0.271417i
\(216\) 0.904315 + 5.11686i 0.0615308 + 0.348158i
\(217\) 44.2579 3.00442
\(218\) 18.7318i 1.26868i
\(219\) −8.84086 13.4380i −0.597410 0.908058i
\(220\) −0.156616 + 0.188362i −0.0105590 + 0.0126994i
\(221\) −9.18903 −0.618121
\(222\) 1.94110 1.27704i 0.130278 0.0857095i
\(223\) 18.5236i 1.24043i −0.784432 0.620215i \(-0.787045\pi\)
0.784432 0.620215i \(-0.212955\pi\)
\(224\) −4.73682 −0.316492
\(225\) −14.6271 3.32392i −0.975139 0.221595i
\(226\) 3.47135i 0.230910i
\(227\) 15.3110i 1.01623i −0.861290 0.508115i \(-0.830343\pi\)
0.861290 0.508115i \(-0.169657\pi\)
\(228\) 6.43970 + 9.78829i 0.426479 + 0.648245i
\(229\) 5.31624i 0.351307i −0.984452 0.175654i \(-0.943796\pi\)
0.984452 0.175654i \(-0.0562038\pi\)
\(230\) 4.88822 9.54491i 0.322320 0.629373i
\(231\) −0.750884 + 0.494005i −0.0494045 + 0.0325032i
\(232\) 7.05802i 0.463381i
\(233\) 8.00870 0.524667 0.262334 0.964977i \(-0.415508\pi\)
0.262334 + 0.964977i \(0.415508\pi\)
\(234\) −6.80457 2.93309i −0.444829 0.191742i
\(235\) 7.91246 9.51634i 0.516152 0.620777i
\(236\) 4.18459i 0.272394i
\(237\) −11.7895 17.9199i −0.765808 1.16402i
\(238\) 17.6226i 1.14231i
\(239\) 1.30708i 0.0845482i −0.999106 0.0422741i \(-0.986540\pi\)
0.999106 0.0422741i \(-0.0134603\pi\)
\(240\) −0.431808 + 3.84884i −0.0278731 + 0.248441i
\(241\) 9.16266i 0.590219i 0.955463 + 0.295109i \(0.0953561\pi\)
−0.955463 + 0.295109i \(0.904644\pi\)
\(242\) −10.9880 −0.706335
\(243\) 15.1706 + 3.58500i 0.973196 + 0.229978i
\(244\) 7.57377i 0.484861i
\(245\) 22.0693 26.5427i 1.40995 1.69575i
\(246\) 7.02838 + 10.6831i 0.448113 + 0.681128i
\(247\) −16.7082 −1.06312
\(248\) −9.34339 −0.593306
\(249\) −15.8159 24.0401i −1.00229 1.52348i
\(250\) −9.75703 5.45897i −0.617089 0.345255i
\(251\) 24.8840 1.57067 0.785333 0.619073i \(-0.212492\pi\)
0.785333 + 0.619073i \(0.212492\pi\)
\(252\) −5.62505 + 13.0497i −0.354345 + 0.822056i
\(253\) −0.512695 + 0.114826i −0.0322329 + 0.00721903i
\(254\) 3.36092i 0.210883i
\(255\) 14.3190 + 1.60648i 0.896693 + 0.100602i
\(256\) 1.00000 0.0625000
\(257\) −18.7650 −1.17053 −0.585264 0.810843i \(-0.699009\pi\)
−0.585264 + 0.810843i \(0.699009\pi\)
\(258\) −3.34925 + 2.20347i −0.208515 + 0.137182i
\(259\) 6.35434 0.394839
\(260\) −4.24675 3.53101i −0.263372 0.218984i
\(261\) 19.4445 + 8.38151i 1.20359 + 0.518803i
\(262\) 13.6399i 0.842677i
\(263\) 9.31348i 0.574294i 0.957887 + 0.287147i \(0.0927068\pi\)
−0.957887 + 0.287147i \(0.907293\pi\)
\(264\) 0.158521 0.104291i 0.00975628 0.00641864i
\(265\) −6.48514 5.39214i −0.398379 0.331236i
\(266\) 32.0428i 1.96467i
\(267\) −14.7993 + 9.73643i −0.905702 + 0.595860i
\(268\) −5.95975 −0.364050
\(269\) 14.0040i 0.853841i −0.904289 0.426921i \(-0.859598\pi\)
0.904289 0.426921i \(-0.140402\pi\)
\(270\) 10.0906 + 5.76017i 0.614095 + 0.350553i
\(271\) 19.5682 1.18868 0.594340 0.804214i \(-0.297413\pi\)
0.594340 + 0.804214i \(0.297413\pi\)
\(272\) 3.72035i 0.225580i
\(273\) −11.1377 16.9292i −0.674082 1.02460i
\(274\) 0.102320i 0.00618136i
\(275\) 0.0999687 + 0.538564i 0.00602834 + 0.0324766i
\(276\) −5.77394 + 5.97173i −0.347550 + 0.359456i
\(277\) 12.1168i 0.728026i 0.931394 + 0.364013i \(0.118594\pi\)
−0.931394 + 0.364013i \(0.881406\pi\)
\(278\) 1.57186 0.0942739
\(279\) −11.0954 + 25.7407i −0.664266 + 1.54105i
\(280\) −6.77173 + 8.14437i −0.404688 + 0.486719i
\(281\) −0.997575 −0.0595103 −0.0297552 0.999557i \(-0.509473\pi\)
−0.0297552 + 0.999557i \(0.509473\pi\)
\(282\) −8.00870 + 5.26891i −0.476911 + 0.313759i
\(283\) 8.27225 0.491734 0.245867 0.969304i \(-0.420927\pi\)
0.245867 + 0.969304i \(0.420927\pi\)
\(284\) 9.66771i 0.573673i
\(285\) 26.0359 + 2.92102i 1.54223 + 0.173026i
\(286\) 0.270588i 0.0160002i
\(287\) 34.9719i 2.06433i
\(288\) 1.18752 2.75496i 0.0699751 0.162338i
\(289\) 3.15896 0.185821
\(290\) 12.1354 + 10.0901i 0.712615 + 0.592511i
\(291\) 14.3896 9.46687i 0.843531 0.554958i
\(292\) 9.28694i 0.543477i
\(293\) 5.35051i 0.312580i −0.987711 0.156290i \(-0.950047\pi\)
0.987711 0.156290i \(-0.0499535\pi\)
\(294\) −22.3377 + 14.6959i −1.30276 + 0.857083i
\(295\) −7.19490 5.98227i −0.418903 0.348301i
\(296\) −1.34148 −0.0779718
\(297\) −0.0990701 0.560565i −0.00574863 0.0325273i
\(298\) −10.9226 −0.632731
\(299\) −2.58882 11.5590i −0.149715 0.668476i
\(300\) 6.00029 + 6.24472i 0.346427 + 0.360539i
\(301\) −10.9641 −0.631958
\(302\) 6.42872 0.369931
\(303\) −8.26842 12.5679i −0.475008 0.722009i
\(304\) 6.76462i 0.387978i
\(305\) −13.0222 10.8274i −0.745648 0.619977i
\(306\) −10.2494 4.41798i −0.585921 0.252559i
\(307\) 23.6777i 1.35136i −0.737197 0.675678i \(-0.763851\pi\)
0.737197 0.675678i \(-0.236149\pi\)
\(308\) 0.518931 0.0295688
\(309\) −4.74232 + 3.11997i −0.269781 + 0.177489i
\(310\) −13.3573 + 16.0648i −0.758641 + 0.912420i
\(311\) 12.8720i 0.729906i 0.931026 + 0.364953i \(0.118915\pi\)
−0.931026 + 0.364953i \(0.881085\pi\)
\(312\) 2.35130 + 3.57395i 0.133116 + 0.202335i
\(313\) −4.59243 −0.259579 −0.129790 0.991542i \(-0.541430\pi\)
−0.129790 + 0.991542i \(0.541430\pi\)
\(314\) 24.1285 1.36165
\(315\) 14.3959 + 28.3274i 0.811116 + 1.59607i
\(316\) 12.3843i 0.696672i
\(317\) 3.67077 0.206171 0.103085 0.994673i \(-0.467129\pi\)
0.103085 + 0.994673i \(0.467129\pi\)
\(318\) 3.59062 + 5.45772i 0.201352 + 0.306054i
\(319\) 0.773225i 0.0432923i
\(320\) 1.42959 1.71938i 0.0799168 0.0961161i
\(321\) −1.35487 2.05939i −0.0756215 0.114944i
\(322\) −22.1678 + 4.96481i −1.23536 + 0.276678i
\(323\) −25.1668 −1.40032
\(324\) −6.17961 6.54312i −0.343311 0.363507i
\(325\) −12.1423 + 2.25386i −0.673532 + 0.125022i
\(326\) 15.4395i 0.855116i
\(327\) −17.8320 27.1046i −0.986114 1.49889i
\(328\) 7.38300i 0.407658i
\(329\) −26.2171 −1.44540
\(330\) 0.0473058 0.421650i 0.00260410 0.0232111i
\(331\) −20.9486 −1.15144 −0.575721 0.817646i \(-0.695278\pi\)
−0.575721 + 0.817646i \(0.695278\pi\)
\(332\) 16.6139i 0.911808i
\(333\) −1.59303 + 3.69572i −0.0872974 + 0.202524i
\(334\) 4.86290 0.266086
\(335\) −8.52003 + 10.2471i −0.465499 + 0.559856i
\(336\) 6.85409 4.50929i 0.373921 0.246002i
\(337\) 8.58764 0.467799 0.233899 0.972261i \(-0.424851\pi\)
0.233899 + 0.972261i \(0.424851\pi\)
\(338\) 6.89942 0.375279
\(339\) 3.30461 + 5.02298i 0.179482 + 0.272811i
\(340\) −6.39669 5.31860i −0.346909 0.288442i
\(341\) 1.02359 0.0554307
\(342\) −18.6363 8.03310i −1.00773 0.434381i
\(343\) −39.9665 −2.15799
\(344\) 2.31465 0.124797
\(345\) 2.01327 + 18.4647i 0.108391 + 0.994108i
\(346\) 17.0492 0.916572
\(347\) 29.9351 1.60700 0.803499 0.595305i \(-0.202969\pi\)
0.803499 + 0.595305i \(0.202969\pi\)
\(348\) −6.71900 10.2128i −0.360176 0.547465i
\(349\) 22.4642 1.20248 0.601240 0.799068i \(-0.294673\pi\)
0.601240 + 0.799068i \(0.294673\pi\)
\(350\) 4.32242 + 23.2863i 0.231043 + 1.24471i
\(351\) 12.6383 2.23360i 0.674583 0.119221i
\(352\) −0.109553 −0.00583918
\(353\) −13.4442 −0.715563 −0.357782 0.933805i \(-0.616467\pi\)
−0.357782 + 0.933805i \(0.616467\pi\)
\(354\) 3.98360 + 6.05503i 0.211726 + 0.321821i
\(355\) −16.6224 13.8209i −0.882228 0.733538i
\(356\) 10.2277 0.542067
\(357\) −16.7762 25.4996i −0.887889 1.34958i
\(358\) 8.37101i 0.442422i
\(359\) 32.7887 1.73052 0.865260 0.501323i \(-0.167153\pi\)
0.865260 + 0.501323i \(0.167153\pi\)
\(360\) −3.03915 5.98027i −0.160177 0.315188i
\(361\) −26.7601 −1.40843
\(362\) 3.91727i 0.205887i
\(363\) 15.8994 10.4602i 0.834504 0.549019i
\(364\) 11.6996i 0.613227i
\(365\) 15.9678 + 13.2766i 0.835790 + 0.694927i
\(366\) 7.20998 + 10.9591i 0.376872 + 0.572842i
\(367\) −0.619262 −0.0323252 −0.0161626 0.999869i \(-0.505145\pi\)
−0.0161626 + 0.999869i \(0.505145\pi\)
\(368\) 4.67990 1.04813i 0.243956 0.0546376i
\(369\) −20.3399 8.76744i −1.05885 0.456415i
\(370\) −1.91777 + 2.30651i −0.0997002 + 0.119910i
\(371\) 17.8663i 0.927571i
\(372\) 13.5197 8.89460i 0.700965 0.461163i
\(373\) 33.9726 1.75904 0.879518 0.475866i \(-0.157865\pi\)
0.879518 + 0.475866i \(0.157865\pi\)
\(374\) 0.407575i 0.0210752i
\(375\) 19.3150 1.38935i 0.997423 0.0717456i
\(376\) 5.53476 0.285433
\(377\) 17.4328 0.897837
\(378\) −4.28357 24.2376i −0.220323 1.24665i
\(379\) 6.22071i 0.319537i 0.987155 + 0.159768i \(0.0510747\pi\)
−0.987155 + 0.159768i \(0.948925\pi\)
\(380\) −11.6309 9.67067i −0.596654 0.496095i
\(381\) −3.19949 4.86320i −0.163915 0.249149i
\(382\) 10.0632 0.514877
\(383\) 0.328653i 0.0167934i −0.999965 0.00839669i \(-0.997327\pi\)
0.999965 0.00839669i \(-0.00267278\pi\)
\(384\) −1.44698 + 0.951967i −0.0738410 + 0.0485799i
\(385\) 0.741861 0.892238i 0.0378087 0.0454727i
\(386\) 1.36921i 0.0696908i
\(387\) 2.74868 6.37676i 0.139723 0.324149i
\(388\) −9.94453 −0.504857
\(389\) 28.8039 1.46042 0.730208 0.683225i \(-0.239423\pi\)
0.730208 + 0.683225i \(0.239423\pi\)
\(390\) 9.50638 + 1.06654i 0.481374 + 0.0540063i
\(391\) −3.89942 17.4109i −0.197202 0.880505i
\(392\) 15.4374 0.779707
\(393\) 12.9848 + 19.7367i 0.654994 + 0.995586i
\(394\) 3.46037 0.174331
\(395\) 21.2933 + 17.7046i 1.07138 + 0.890813i
\(396\) −0.130096 + 0.301813i −0.00653756 + 0.0151667i
\(397\) 25.5527i 1.28245i −0.767352 0.641226i \(-0.778426\pi\)
0.767352 0.641226i \(-0.221574\pi\)
\(398\) 2.84735i 0.142725i
\(399\) −30.5037 46.3653i −1.52709 2.32117i
\(400\) −0.912517 4.91603i −0.0456258 0.245801i
\(401\) −16.8426 −0.841080 −0.420540 0.907274i \(-0.638159\pi\)
−0.420540 + 0.907274i \(0.638159\pi\)
\(402\) 8.62365 5.67348i 0.430109 0.282968i
\(403\) 23.0776i 1.14958i
\(404\) 8.68562i 0.432126i
\(405\) −20.0844 + 1.27106i −0.998003 + 0.0631594i
\(406\) 33.4325i 1.65923i
\(407\) 0.146963 0.00728466
\(408\) 3.54165 + 5.38329i 0.175338 + 0.266512i
\(409\) 1.73082 0.0855838 0.0427919 0.999084i \(-0.486375\pi\)
0.0427919 + 0.999084i \(0.486375\pi\)
\(410\) −12.6942 10.5547i −0.626920 0.521260i
\(411\) −0.0974049 0.148055i −0.00480463 0.00730300i
\(412\) 3.27739 0.161465
\(413\) 19.8216i 0.975359i
\(414\) 2.66990 14.1376i 0.131218 0.694825i
\(415\) 28.5656 + 23.7512i 1.40223 + 1.16590i
\(416\) 2.46994i 0.121099i
\(417\) −2.27445 + 1.49636i −0.111381 + 0.0732770i
\(418\) 0.741083i 0.0362475i
\(419\) −0.0603174 −0.00294670 −0.00147335 0.999999i \(-0.500469\pi\)
−0.00147335 + 0.999999i \(0.500469\pi\)
\(420\) 2.04540 18.2312i 0.0998051 0.889593i
\(421\) 16.7804i 0.817829i −0.912573 0.408914i \(-0.865908\pi\)
0.912573 0.408914i \(-0.134092\pi\)
\(422\) −11.9262 −0.580558
\(423\) 6.57262 15.2480i 0.319572 0.741385i
\(424\) 3.77179i 0.183174i
\(425\) −18.2894 + 3.39489i −0.887164 + 0.164676i
\(426\) 9.20334 + 13.9890i 0.445903 + 0.677770i
\(427\) 35.8756i 1.73614i
\(428\) 1.42323i 0.0687945i
\(429\) −0.257591 0.391536i −0.0124366 0.0189035i
\(430\) 3.30901 3.97975i 0.159575 0.191921i
\(431\) 4.36493 0.210251 0.105126 0.994459i \(-0.466476\pi\)
0.105126 + 0.994459i \(0.466476\pi\)
\(432\) 0.904315 + 5.11686i 0.0435089 + 0.246185i
\(433\) −29.9206 −1.43789 −0.718947 0.695065i \(-0.755375\pi\)
−0.718947 + 0.695065i \(0.755375\pi\)
\(434\) 44.2579 2.12445
\(435\) −27.1651 3.04771i −1.30247 0.146126i
\(436\) 18.7318i 0.897090i
\(437\) −7.09021 31.6577i −0.339171 1.51439i
\(438\) −8.84086 13.4380i −0.422433 0.642094i
\(439\) −16.9861 −0.810702 −0.405351 0.914161i \(-0.632851\pi\)
−0.405351 + 0.914161i \(0.632851\pi\)
\(440\) −0.156616 + 0.188362i −0.00746637 + 0.00897983i
\(441\) 18.3322 42.5295i 0.872962 2.02521i
\(442\) −9.18903 −0.437078
\(443\) −24.5257 −1.16525 −0.582626 0.812740i \(-0.697975\pi\)
−0.582626 + 0.812740i \(0.697975\pi\)
\(444\) 1.94110 1.27704i 0.0921203 0.0606058i
\(445\) 14.6215 17.5853i 0.693124 0.833622i
\(446\) 18.5236i 0.877117i
\(447\) 15.8049 10.3980i 0.747544 0.491808i
\(448\) −4.73682 −0.223793
\(449\) 16.0667i 0.758233i 0.925349 + 0.379117i \(0.123772\pi\)
−0.925349 + 0.379117i \(0.876228\pi\)
\(450\) −14.6271 3.32392i −0.689527 0.156691i
\(451\) 0.808828i 0.0380862i
\(452\) 3.47135i 0.163278i
\(453\) −9.30225 + 6.11993i −0.437058 + 0.287540i
\(454\) 15.3110i 0.718582i
\(455\) 20.1161 + 16.7257i 0.943056 + 0.784114i
\(456\) 6.43970 + 9.78829i 0.301566 + 0.458379i
\(457\) −13.2071 −0.617802 −0.308901 0.951094i \(-0.599961\pi\)
−0.308901 + 0.951094i \(0.599961\pi\)
\(458\) 5.31624i 0.248412i
\(459\) 19.0365 3.36437i 0.888549 0.157035i
\(460\) 4.88822 9.54491i 0.227914 0.445034i
\(461\) 25.4941i 1.18738i −0.804695 0.593689i \(-0.797671\pi\)
0.804695 0.593689i \(-0.202329\pi\)
\(462\) −0.750884 + 0.494005i −0.0349343 + 0.0229832i
\(463\) 20.0822i 0.933298i 0.884443 + 0.466649i \(0.154539\pi\)
−0.884443 + 0.466649i \(0.845461\pi\)
\(464\) 7.05802i 0.327660i
\(465\) 4.03455 35.9612i 0.187098 1.66766i
\(466\) 8.00870 0.370996
\(467\) 14.7644i 0.683215i −0.939843 0.341607i \(-0.889029\pi\)
0.939843 0.341607i \(-0.110971\pi\)
\(468\) −6.80457 2.93309i −0.314541 0.135582i
\(469\) 28.2302 1.30355
\(470\) 7.91246 9.51634i 0.364975 0.438956i
\(471\) −34.9136 + 22.9696i −1.60873 + 1.05838i
\(472\) 4.18459i 0.192612i
\(473\) −0.253576 −0.0116594
\(474\) −11.7895 17.9199i −0.541508 0.823088i
\(475\) −33.2551 + 6.17283i −1.52585 + 0.283229i
\(476\) 17.6226i 0.807732i
\(477\) −10.3911 4.47907i −0.475778 0.205082i
\(478\) 1.30708i 0.0597846i
\(479\) −0.527998 −0.0241248 −0.0120624 0.999927i \(-0.503840\pi\)
−0.0120624 + 0.999927i \(0.503840\pi\)
\(480\) −0.431808 + 3.84884i −0.0197093 + 0.175675i
\(481\) 3.31336i 0.151076i
\(482\) 9.16266i 0.417348i
\(483\) 27.3501 28.2870i 1.24447 1.28710i
\(484\) −10.9880 −0.499454
\(485\) −14.2167 + 17.0984i −0.645545 + 0.776398i
\(486\) 15.1706 + 3.58500i 0.688153 + 0.162619i
\(487\) 15.1423i 0.686164i 0.939306 + 0.343082i \(0.111471\pi\)
−0.939306 + 0.343082i \(0.888529\pi\)
\(488\) 7.57377i 0.342849i
\(489\) 14.6979 + 22.3407i 0.664663 + 1.01028i
\(490\) 22.0693 26.5427i 0.996987 1.19908i
\(491\) 23.0745i 1.04134i 0.853759 + 0.520668i \(0.174317\pi\)
−0.853759 + 0.520668i \(0.825683\pi\)
\(492\) 7.02838 + 10.6831i 0.316864 + 0.481630i
\(493\) 26.2583 1.18262
\(494\) −16.7082 −0.751736
\(495\) 0.332947 + 0.655154i 0.0149648 + 0.0294470i
\(496\) −9.34339 −0.419530
\(497\) 45.7942i 2.05415i
\(498\) −15.8159 24.0401i −0.708728 1.07726i
\(499\) 2.99246 0.133961 0.0669805 0.997754i \(-0.478663\pi\)
0.0669805 + 0.997754i \(0.478663\pi\)
\(500\) −9.75703 5.45897i −0.436348 0.244132i
\(501\) −7.03652 + 4.62932i −0.314369 + 0.206823i
\(502\) 24.8840 1.11063
\(503\) 35.8449i 1.59825i 0.601167 + 0.799123i \(0.294703\pi\)
−0.601167 + 0.799123i \(0.705297\pi\)
\(504\) −5.62505 + 13.0497i −0.250560 + 0.581281i
\(505\) 14.9339 + 12.4169i 0.664548 + 0.552545i
\(506\) −0.512695 + 0.114826i −0.0227921 + 0.00510462i
\(507\) −9.98334 + 6.56802i −0.443376 + 0.291696i
\(508\) 3.36092i 0.149117i
\(509\) 15.8139i 0.700937i 0.936575 + 0.350468i \(0.113978\pi\)
−0.936575 + 0.350468i \(0.886022\pi\)
\(510\) 14.3190 + 1.60648i 0.634058 + 0.0711361i
\(511\) 43.9905i 1.94603i
\(512\) 1.00000 0.0441942
\(513\) 34.6136 6.11735i 1.52823 0.270087i
\(514\) −18.7650 −0.827688
\(515\) 4.68534 5.63507i 0.206461 0.248311i
\(516\) −3.34925 + 2.20347i −0.147443 + 0.0970023i
\(517\) −0.606348 −0.0266671
\(518\) 6.35434 0.279193
\(519\) −24.6699 + 16.2303i −1.08289 + 0.712431i
\(520\) −4.24675 3.53101i −0.186232 0.154845i
\(521\) −21.4453 −0.939538 −0.469769 0.882789i \(-0.655663\pi\)
−0.469769 + 0.882789i \(0.655663\pi\)
\(522\) 19.4445 + 8.38151i 0.851065 + 0.366849i
\(523\) 21.4978 0.940033 0.470017 0.882658i \(-0.344248\pi\)
0.470017 + 0.882658i \(0.344248\pi\)
\(524\) 13.6399i 0.595863i
\(525\) −28.4223 29.5801i −1.24045 1.29098i
\(526\) 9.31348i 0.406087i
\(527\) 34.7607i 1.51420i
\(528\) 0.158521 0.104291i 0.00689873 0.00453866i
\(529\) 20.8028 9.81029i 0.904471 0.426534i
\(530\) −6.48514 5.39214i −0.281696 0.234219i
\(531\) −11.5284 4.96928i −0.500289 0.215648i
\(532\) 32.0428i 1.38923i
\(533\) −18.2355 −0.789869
\(534\) −14.7993 + 9.73643i −0.640428 + 0.421336i
\(535\) 2.44707 + 2.03464i 0.105796 + 0.0879654i
\(536\) −5.95975 −0.257422
\(537\) 7.96893 + 12.1127i 0.343885 + 0.522702i
\(538\) 14.0040i 0.603757i
\(539\) −1.69121 −0.0728456
\(540\) 10.0906 + 5.76017i 0.434231 + 0.247878i
\(541\) −28.9815 −1.24601 −0.623005 0.782218i \(-0.714088\pi\)
−0.623005 + 0.782218i \(0.714088\pi\)
\(542\) 19.5682 0.840524
\(543\) −3.72911 5.66822i −0.160032 0.243247i
\(544\) 3.72035i 0.159509i
\(545\) 32.2070 + 26.7789i 1.37960 + 1.14708i
\(546\) −11.1377 16.9292i −0.476648 0.724501i
\(547\) 31.1585i 1.33224i −0.745844 0.666121i \(-0.767954\pi\)
0.745844 0.666121i \(-0.232046\pi\)
\(548\) 0.102320i 0.00437088i
\(549\) −20.8654 8.99399i −0.890515 0.383854i
\(550\) 0.0999687 + 0.538564i 0.00426268 + 0.0229644i
\(551\) 47.7448 2.03400
\(552\) −5.77394 + 5.97173i −0.245755 + 0.254174i
\(553\) 58.6622i 2.49457i
\(554\) 12.1168i 0.514792i
\(555\) 0.579261 5.16313i 0.0245883 0.219163i
\(556\) 1.57186 0.0666617
\(557\) 33.0466i 1.40023i −0.714030 0.700115i \(-0.753132\pi\)
0.714030 0.700115i \(-0.246868\pi\)
\(558\) −11.0954 + 25.7407i −0.469707 + 1.08969i
\(559\) 5.71703i 0.241805i
\(560\) −6.77173 + 8.14437i −0.286158 + 0.344163i
\(561\) −0.387998 0.589754i −0.0163813 0.0248994i
\(562\) −0.997575 −0.0420801
\(563\) 22.9282i 0.966310i −0.875535 0.483155i \(-0.839491\pi\)
0.875535 0.483155i \(-0.160509\pi\)
\(564\) −8.00870 + 5.26891i −0.337227 + 0.221861i
\(565\) −5.96855 4.96262i −0.251099 0.208779i
\(566\) 8.27225 0.347709
\(567\) 29.2717 + 30.9936i 1.22929 + 1.30161i
\(568\) 9.66771i 0.405648i
\(569\) −7.12332 −0.298625 −0.149312 0.988790i \(-0.547706\pi\)
−0.149312 + 0.988790i \(0.547706\pi\)
\(570\) 26.0359 + 2.92102i 1.09052 + 0.122348i
\(571\) 15.0075i 0.628044i −0.949416 0.314022i \(-0.898323\pi\)
0.949416 0.314022i \(-0.101677\pi\)
\(572\) 0.270588i 0.0113139i
\(573\) −14.5613 + 9.57982i −0.608305 + 0.400203i
\(574\) 34.9719i 1.45970i
\(575\) −9.42312 22.0501i −0.392971 0.919551i
\(576\) 1.18752 2.75496i 0.0494799 0.114790i
\(577\) 32.3173i 1.34539i 0.739922 + 0.672693i \(0.234862\pi\)
−0.739922 + 0.672693i \(0.765138\pi\)
\(578\) 3.15896 0.131396
\(579\) −1.30344 1.98122i −0.0541691 0.0823366i
\(580\) 12.1354 + 10.0901i 0.503895 + 0.418969i
\(581\) 78.6972i 3.26491i
\(582\) 14.3896 9.46687i 0.596467 0.392414i
\(583\) 0.413210i 0.0171134i
\(584\) 9.28694i 0.384296i
\(585\) −14.7709 + 7.50650i −0.610700 + 0.310355i
\(586\) 5.35051i 0.221028i
\(587\) −9.64803 −0.398217 −0.199108 0.979977i \(-0.563805\pi\)
−0.199108 + 0.979977i \(0.563805\pi\)
\(588\) −22.3377 + 14.6959i −0.921190 + 0.606049i
\(589\) 63.2045i 2.60429i
\(590\) −7.19490 5.98227i −0.296209 0.246286i
\(591\) −5.00710 + 3.29416i −0.205964 + 0.135504i
\(592\) −1.34148 −0.0551344
\(593\) 12.6479 0.519385 0.259693 0.965691i \(-0.416379\pi\)
0.259693 + 0.965691i \(0.416379\pi\)
\(594\) −0.0990701 0.560565i −0.00406490 0.0230003i
\(595\) 30.3000 + 25.1932i 1.24218 + 1.03282i
\(596\) −10.9226 −0.447408
\(597\) 2.71058 + 4.12007i 0.110937 + 0.168623i
\(598\) −2.58882 11.5590i −0.105865 0.472684i
\(599\) 24.2565i 0.991094i −0.868581 0.495547i \(-0.834968\pi\)
0.868581 0.495547i \(-0.165032\pi\)
\(600\) 6.00029 + 6.24472i 0.244961 + 0.254940i
\(601\) 3.91095 0.159531 0.0797655 0.996814i \(-0.474583\pi\)
0.0797655 + 0.996814i \(0.474583\pi\)
\(602\) −10.9641 −0.446862
\(603\) −7.07730 + 16.4189i −0.288210 + 0.668628i
\(604\) 6.42872 0.261581
\(605\) −15.7084 + 18.8925i −0.638637 + 0.768090i
\(606\) −8.26842 12.5679i −0.335882 0.510537i
\(607\) 31.9532i 1.29694i −0.761241 0.648469i \(-0.775410\pi\)
0.761241 0.648469i \(-0.224590\pi\)
\(608\) 6.76462i 0.274342i
\(609\) 31.8267 + 48.3763i 1.28968 + 1.96031i
\(610\) −13.0222 10.8274i −0.527252 0.438390i
\(611\) 13.6705i 0.553049i
\(612\) −10.2494 4.41798i −0.414308 0.178586i
\(613\) 6.81990 0.275453 0.137727 0.990470i \(-0.456020\pi\)
0.137727 + 0.990470i \(0.456020\pi\)
\(614\) 23.6777i 0.955553i
\(615\) 28.4160 + 3.18804i 1.14584 + 0.128554i
\(616\) 0.518931 0.0209083
\(617\) 7.46733i 0.300623i 0.988639 + 0.150312i \(0.0480277\pi\)
−0.988639 + 0.150312i \(0.951972\pi\)
\(618\) −4.74232 + 3.11997i −0.190764 + 0.125503i
\(619\) 41.5273i 1.66912i −0.550915 0.834561i \(-0.685721\pi\)
0.550915 0.834561i \(-0.314279\pi\)
\(620\) −13.3573 + 16.0648i −0.536440 + 0.645178i
\(621\) 9.59524 + 22.9985i 0.385044 + 0.922898i
\(622\) 12.8720i 0.516122i
\(623\) −48.4467 −1.94098
\(624\) 2.35130 + 3.57395i 0.0941272 + 0.143073i
\(625\) −23.3346 + 8.97191i −0.933385 + 0.358877i
\(626\) −4.59243 −0.183550
\(627\) −0.705486 1.07233i −0.0281744 0.0428249i
\(628\) 24.1285 0.962834
\(629\) 4.99077i 0.198995i
\(630\) 14.3959 + 28.3274i 0.573545 + 1.12859i
\(631\) 36.9311i 1.47020i 0.677956 + 0.735102i \(0.262866\pi\)
−0.677956 + 0.735102i \(0.737134\pi\)
\(632\) 12.3843i 0.492622i
\(633\) 17.2570 11.3533i 0.685904 0.451255i
\(634\) 3.67077 0.145785
\(635\) 5.77870 + 4.80476i 0.229321 + 0.190671i
\(636\) 3.59062 + 5.45772i 0.142377 + 0.216413i
\(637\) 38.1294i 1.51074i
\(638\) 0.773225i 0.0306123i
\(639\) −26.6342 11.4806i −1.05363 0.454164i
\(640\) 1.42959 1.71938i 0.0565097 0.0679644i
\(641\) 23.5864 0.931606 0.465803 0.884888i \(-0.345765\pi\)
0.465803 + 0.884888i \(0.345765\pi\)
\(642\) −1.35487 2.05939i −0.0534725 0.0812777i
\(643\) −25.9305 −1.02260 −0.511299 0.859403i \(-0.670836\pi\)
−0.511299 + 0.859403i \(0.670836\pi\)
\(644\) −22.1678 + 4.96481i −0.873534 + 0.195641i
\(645\) −0.999484 + 8.90870i −0.0393546 + 0.350780i
\(646\) −25.1668 −0.990174
\(647\) 5.05526 0.198743 0.0993713 0.995050i \(-0.468317\pi\)
0.0993713 + 0.995050i \(0.468317\pi\)
\(648\) −6.17961 6.54312i −0.242758 0.257038i
\(649\) 0.458433i 0.0179951i
\(650\) −12.1423 + 2.25386i −0.476259 + 0.0884036i
\(651\) −64.0404 + 42.1321i −2.50994 + 1.65129i
\(652\) 15.4395i 0.604659i
\(653\) −9.19815 −0.359952 −0.179976 0.983671i \(-0.557602\pi\)
−0.179976 + 0.983671i \(0.557602\pi\)
\(654\) −17.8320 27.1046i −0.697288 1.05987i
\(655\) −23.4522 19.4996i −0.916352 0.761911i
\(656\) 7.38300i 0.288258i
\(657\) 25.5851 + 11.0284i 0.998171 + 0.430259i
\(658\) −26.2171 −1.02205
\(659\) −40.3687 −1.57254 −0.786270 0.617883i \(-0.787991\pi\)
−0.786270 + 0.617883i \(0.787991\pi\)
\(660\) 0.0473058 0.421650i 0.00184137 0.0164127i
\(661\) 16.6400i 0.647220i 0.946191 + 0.323610i \(0.104897\pi\)
−0.946191 + 0.323610i \(0.895103\pi\)
\(662\) −20.9486 −0.814192
\(663\) 13.2964 8.74766i 0.516388 0.339731i
\(664\) 16.6139i 0.644746i
\(665\) 55.0936 + 45.8082i 2.13644 + 1.77636i
\(666\) −1.59303 + 3.69572i −0.0617286 + 0.143206i
\(667\) 7.39773 + 33.0308i 0.286441 + 1.27896i
\(668\) 4.86290 0.188151
\(669\) 17.6338 + 26.8033i 0.681764 + 1.03628i
\(670\) −8.52003 + 10.2471i −0.329157 + 0.395878i
\(671\) 0.829727i 0.0320313i
\(672\) 6.85409 4.50929i 0.264402 0.173950i
\(673\) 32.2214i 1.24204i 0.783793 + 0.621022i \(0.213282\pi\)
−0.783793 + 0.621022i \(0.786718\pi\)
\(674\) 8.58764 0.330784
\(675\) 24.3294 9.11485i 0.936439 0.350831i
\(676\) 6.89942 0.265362
\(677\) 23.6610i 0.909366i 0.890653 + 0.454683i \(0.150247\pi\)
−0.890653 + 0.454683i \(0.849753\pi\)
\(678\) 3.30461 + 5.02298i 0.126913 + 0.192906i
\(679\) 47.1054 1.80774
\(680\) −6.39669 5.31860i −0.245302 0.203959i
\(681\) 14.5756 + 22.1548i 0.558538 + 0.848974i
\(682\) 1.02359 0.0391954
\(683\) 2.38670 0.0913245 0.0456622 0.998957i \(-0.485460\pi\)
0.0456622 + 0.998957i \(0.485460\pi\)
\(684\) −18.6363 8.03310i −0.712575 0.307153i
\(685\) 0.175926 + 0.146276i 0.00672179 + 0.00558890i
\(686\) −39.9665 −1.52593
\(687\) 5.06089 + 7.69251i 0.193085 + 0.293487i
\(688\) 2.31465 0.0882451
\(689\) −9.31608 −0.354915
\(690\) 2.01327 + 18.4647i 0.0766439 + 0.702941i
\(691\) 12.4301 0.472862 0.236431 0.971648i \(-0.424022\pi\)
0.236431 + 0.971648i \(0.424022\pi\)
\(692\) 17.0492 0.648114
\(693\) 0.616239 1.42963i 0.0234090 0.0543073i
\(694\) 29.9351 1.13632
\(695\) 2.24712 2.70262i 0.0852383 0.102516i
\(696\) −6.71900 10.2128i −0.254683 0.387116i
\(697\) −27.4674 −1.04040
\(698\) 22.4642 0.850282
\(699\) −11.5884 + 7.62402i −0.438315 + 0.288367i
\(700\) 4.32242 + 23.2863i 0.163372 + 0.880140i
\(701\) 40.2008 1.51836 0.759181 0.650879i \(-0.225600\pi\)
0.759181 + 0.650879i \(0.225600\pi\)
\(702\) 12.6383 2.23360i 0.477002 0.0843017i
\(703\) 9.07459i 0.342255i
\(704\) −0.109553 −0.00412892
\(705\) −2.38995 + 21.3024i −0.0900109 + 0.802294i
\(706\) −13.4442 −0.505980
\(707\) 41.1422i 1.54731i
\(708\) 3.98360 + 6.05503i 0.149713 + 0.227562i
\(709\) 4.06296i 0.152588i 0.997085 + 0.0762938i \(0.0243087\pi\)
−0.997085 + 0.0762938i \(0.975691\pi\)
\(710\) −16.6224 13.8209i −0.623829 0.518690i
\(711\) 34.1183 + 14.7066i 1.27954 + 0.551540i
\(712\) 10.2277 0.383299
\(713\) −43.7261 + 9.79310i −1.63755 + 0.366754i
\(714\) −16.7762 25.4996i −0.627832 0.954300i
\(715\) 0.465243 + 0.386831i 0.0173991 + 0.0144667i
\(716\) 8.37101i 0.312839i
\(717\) 1.24430 + 1.89133i 0.0464693 + 0.0706329i
\(718\) 32.7887 1.22366
\(719\) 27.4547i 1.02389i 0.859019 + 0.511944i \(0.171075\pi\)
−0.859019 + 0.511944i \(0.828925\pi\)
\(720\) −3.03915 5.98027i −0.113262 0.222871i
\(721\) −15.5244 −0.578158
\(722\) −26.7601 −0.995908
\(723\) −8.72255 13.2582i −0.324395 0.493078i
\(724\) 3.91727i 0.145584i
\(725\) 34.6974 6.44056i 1.28863 0.239196i
\(726\) 15.8994 10.4602i 0.590084 0.388215i
\(727\) −39.9198 −1.48054 −0.740272 0.672308i \(-0.765303\pi\)
−0.740272 + 0.672308i \(0.765303\pi\)
\(728\) 11.6996i 0.433617i
\(729\) −25.3644 + 9.25449i −0.939423 + 0.342759i
\(730\) 15.9678 + 13.2766i 0.590993 + 0.491388i
\(731\) 8.61131i 0.318501i
\(732\) 7.20998 + 10.9591i 0.266489 + 0.405061i
\(733\) 30.5739 1.12927 0.564636 0.825340i \(-0.309016\pi\)
0.564636 + 0.825340i \(0.309016\pi\)
\(734\) −0.619262 −0.0228574
\(735\) −6.66600 + 59.4161i −0.245879 + 2.19160i
\(736\) 4.67990 1.04813i 0.172503 0.0386346i
\(737\) 0.652906 0.0240501
\(738\) −20.3399 8.76744i −0.748721 0.322734i
\(739\) 14.6803 0.540022 0.270011 0.962857i \(-0.412973\pi\)
0.270011 + 0.962857i \(0.412973\pi\)
\(740\) −1.91777 + 2.30651i −0.0704987 + 0.0847889i
\(741\) 24.1764 15.9056i 0.888144 0.584308i
\(742\) 17.8663i 0.655892i
\(743\) 11.9149i 0.437115i 0.975824 + 0.218557i \(0.0701351\pi\)
−0.975824 + 0.218557i \(0.929865\pi\)
\(744\) 13.5197 8.89460i 0.495657 0.326092i
\(745\) −15.6149 + 18.7801i −0.572087 + 0.688050i
\(746\) 33.9726 1.24383
\(747\) 45.7707 + 19.7293i 1.67466 + 0.721859i
\(748\) 0.407575i 0.0149024i
\(749\) 6.74159i 0.246332i
\(750\) 19.3150 1.38935i 0.705285 0.0507318i
\(751\) 47.3378i 1.72738i 0.504024 + 0.863690i \(0.331852\pi\)
−0.504024 + 0.863690i \(0.668148\pi\)
\(752\) 5.53476 0.201832
\(753\) −36.0068 + 23.6888i −1.31216 + 0.863267i
\(754\) 17.4328 0.634867
\(755\) 9.19047 11.0534i 0.334475 0.402274i
\(756\) −4.28357 24.2376i −0.155792 0.881513i
\(757\) −48.7061 −1.77025 −0.885126 0.465352i \(-0.845928\pi\)
−0.885126 + 0.465352i \(0.845928\pi\)
\(758\) 6.22071i 0.225947i
\(759\) 0.632551 0.654220i 0.0229601 0.0237467i
\(760\) −11.6309 9.67067i −0.421898 0.350792i
\(761\) 44.5378i 1.61450i 0.590213 + 0.807248i \(0.299044\pi\)
−0.590213 + 0.807248i \(0.700956\pi\)
\(762\) −3.19949 4.86320i −0.115905 0.176175i
\(763\) 88.7290i 3.21220i
\(764\) 10.0632 0.364073
\(765\) −22.2487 + 11.3067i −0.804404 + 0.408795i
\(766\) 0.328653i 0.0118747i
\(767\) −10.3357 −0.373200
\(768\) −1.44698 + 0.951967i −0.0522135 + 0.0343512i
\(769\) 2.64729i 0.0954636i −0.998860 0.0477318i \(-0.984801\pi\)
0.998860 0.0477318i \(-0.0151993\pi\)
\(770\) 0.741861 0.892238i 0.0267348 0.0321540i
\(771\) 27.1526 17.8636i 0.977877 0.643343i
\(772\) 1.36921i 0.0492788i
\(773\) 42.9774i 1.54579i 0.634533 + 0.772896i \(0.281192\pi\)
−0.634533 + 0.772896i \(0.718808\pi\)
\(774\) 2.74868 6.37676i 0.0987994 0.229208i
\(775\) 8.52600 + 45.9323i 0.306263 + 1.64994i
\(776\) −9.94453 −0.356988
\(777\) −9.19461 + 6.04912i −0.329855 + 0.217011i
\(778\) 28.8039 1.03267
\(779\) −49.9432 −1.78940
\(780\) 9.50638 + 1.06654i 0.340383 + 0.0381882i
\(781\) 1.05912i 0.0378984i
\(782\) −3.89942 17.4109i −0.139443 0.622611i
\(783\) −36.1148 + 6.38267i −1.29064 + 0.228098i
\(784\) 15.4374 0.551336
\(785\) 34.4940 41.4861i 1.23115 1.48070i
\(786\) 12.9848 + 19.7367i 0.463151 + 0.703986i
\(787\) −23.4951 −0.837510 −0.418755 0.908099i \(-0.637533\pi\)
−0.418755 + 0.908099i \(0.637533\pi\)
\(788\) 3.46037 0.123271
\(789\) −8.86613 13.4764i −0.315643 0.479774i
\(790\) 21.2933 + 17.7046i 0.757582 + 0.629900i
\(791\) 16.4431i 0.584650i
\(792\) −0.130096 + 0.301813i −0.00462275 + 0.0107245i
\(793\) −18.7067 −0.664295
\(794\) 25.5527i 0.906831i
\(795\) 14.5170 + 1.62869i 0.514865 + 0.0577637i
\(796\) 2.84735i 0.100922i
\(797\) 22.3667i 0.792268i −0.918193 0.396134i \(-0.870352\pi\)
0.918193 0.396134i \(-0.129648\pi\)
\(798\) −30.5037 46.3653i −1.07982 1.64131i
\(799\) 20.5913i 0.728466i
\(800\) −0.912517 4.91603i −0.0322623 0.173808i
\(801\) 12.1456 28.1769i 0.429142 0.995581i
\(802\) −16.8426 −0.594733
\(803\) 1.01741i 0.0359036i
\(804\) 8.62365 5.67348i 0.304133 0.200088i
\(805\) −23.1546 + 45.2125i −0.816092 + 1.59353i
\(806\) 23.0776i 0.812872i
\(807\) 13.3314 + 20.2636i 0.469287 + 0.713312i
\(808\) 8.68562i 0.305559i
\(809\) 49.1755i 1.72892i 0.502702 + 0.864460i \(0.332339\pi\)
−0.502702 + 0.864460i \(0.667661\pi\)
\(810\) −20.0844 + 1.27106i −0.705695 + 0.0446604i
\(811\) −42.2987 −1.48531 −0.742654 0.669675i \(-0.766433\pi\)
−0.742654 + 0.669675i \(0.766433\pi\)
\(812\) 33.4325i 1.17325i
\(813\) −28.3148 + 18.6282i −0.993043 + 0.653321i
\(814\) 0.146963 0.00515104
\(815\) −26.5464 22.0723i −0.929879 0.773158i
\(816\) 3.54165 + 5.38329i 0.123983 + 0.188453i
\(817\) 15.6577i 0.547794i
\(818\) 1.73082 0.0605169
\(819\) 32.2320 + 13.8935i 1.12628 + 0.485478i
\(820\) −12.6942 10.5547i −0.443300 0.368586i
\(821\) 0.358202i 0.0125013i 0.999980 + 0.00625067i \(0.00198966\pi\)
−0.999980 + 0.00625067i \(0.998010\pi\)
\(822\) −0.0974049 0.148055i −0.00339739 0.00516400i
\(823\) 3.19924i 0.111519i 0.998444 + 0.0557593i \(0.0177579\pi\)
−0.998444 + 0.0557593i \(0.982242\pi\)
\(824\) 3.27739 0.114173
\(825\) −0.657348 0.684126i −0.0228859 0.0238182i
\(826\) 19.8216i 0.689683i
\(827\) 40.6080i 1.41208i 0.708173 + 0.706039i \(0.249520\pi\)
−0.708173 + 0.706039i \(0.750480\pi\)
\(828\) 2.66990 14.1376i 0.0927853 0.491315i
\(829\) −16.9961 −0.590298 −0.295149 0.955451i \(-0.595369\pi\)
−0.295149 + 0.955451i \(0.595369\pi\)
\(830\) 28.5656 + 23.7512i 0.991527 + 0.824416i
\(831\) −11.5348 17.5327i −0.400136 0.608204i
\(832\) 2.46994i 0.0856296i
\(833\) 57.4327i 1.98992i
\(834\) −2.27445 + 1.49636i −0.0787579 + 0.0518147i
\(835\) 6.95197 8.36115i 0.240583 0.289350i
\(836\) 0.741083i 0.0256309i
\(837\) −8.44936 47.8088i −0.292053 1.65251i
\(838\) −0.0603174 −0.00208363
\(839\) 19.0943 0.659209 0.329605 0.944119i \(-0.393085\pi\)
0.329605 + 0.944119i \(0.393085\pi\)
\(840\) 2.04540 18.2312i 0.0705729 0.629037i
\(841\) −20.8156 −0.717779
\(842\) 16.7804i 0.578292i
\(843\) 1.44347 0.949658i 0.0497159 0.0327080i
\(844\) −11.9262 −0.410517
\(845\) 9.86338 11.8627i 0.339310 0.408090i
\(846\) 6.57262 15.2480i 0.225971 0.524238i
\(847\) 52.0481 1.78839
\(848\) 3.77179i 0.129524i
\(849\) −11.9698 + 7.87491i −0.410803 + 0.270266i
\(850\) −18.2894 + 3.39489i −0.627320 + 0.116444i
\(851\) −6.27798 + 1.40605i −0.215206 + 0.0481986i
\(852\) 9.20334 + 13.9890i 0.315301 + 0.479256i
\(853\) 3.50621i 0.120050i −0.998197 0.0600251i \(-0.980882\pi\)
0.998197 0.0600251i \(-0.0191181\pi\)
\(854\) 35.8756i 1.22764i
\(855\) −40.4542 + 20.5587i −1.38351 + 0.703092i
\(856\) 1.42323i 0.0486451i
\(857\) 26.4700 0.904198 0.452099 0.891968i \(-0.350675\pi\)
0.452099 + 0.891968i \(0.350675\pi\)
\(858\) −0.257591 0.391536i −0.00879401 0.0133668i
\(859\) 14.5773 0.497372 0.248686 0.968584i \(-0.420001\pi\)
0.248686 + 0.968584i \(0.420001\pi\)
\(860\) 3.30901 3.97975i 0.112836 0.135708i
\(861\) −33.2921 50.6038i −1.13459 1.72457i
\(862\) 4.36493 0.148670
\(863\) −11.1724 −0.380312 −0.190156 0.981754i \(-0.560899\pi\)
−0.190156 + 0.981754i \(0.560899\pi\)
\(864\) 0.904315 + 5.11686i 0.0307654 + 0.174079i
\(865\) 24.3735 29.3140i 0.828723 0.996707i
\(866\) −29.9206 −1.01674
\(867\) −4.57097 + 3.00723i −0.155238 + 0.102131i
\(868\) 44.2579 1.50221
\(869\) 1.35674i 0.0460241i
\(870\) −27.1651 3.04771i −0.920985 0.103327i
\(871\) 14.7202i 0.498775i
\(872\) 18.7318i 0.634338i
\(873\) −11.8093 + 27.3968i −0.399684 + 0.927241i
\(874\) −7.09021 31.6577i −0.239830 1.07084i
\(875\) 46.2173 + 25.8581i 1.56243 + 0.874164i
\(876\) −8.84086 13.4380i −0.298705 0.454029i
\(877\) 16.8838i 0.570124i −0.958509 0.285062i \(-0.907986\pi\)
0.958509 0.285062i \(-0.0920143\pi\)
\(878\) −16.9861 −0.573253
\(879\) 5.09351 + 7.74210i 0.171800 + 0.261135i
\(880\) −0.156616 + 0.188362i −0.00527952 + 0.00634970i
\(881\) 20.1111 0.677559 0.338780 0.940866i \(-0.389986\pi\)
0.338780 + 0.940866i \(0.389986\pi\)
\(882\) 18.3322 42.5295i 0.617277 1.43204i
\(883\) 1.20645i 0.0406003i −0.999794 0.0203002i \(-0.993538\pi\)
0.999794 0.0203002i \(-0.00646219\pi\)
\(884\) −9.18903 −0.309061
\(885\) 16.1058 + 1.80694i 0.541391 + 0.0607397i
\(886\) −24.5257 −0.823958
\(887\) −19.2753 −0.647200 −0.323600 0.946194i \(-0.604893\pi\)
−0.323600 + 0.946194i \(0.604893\pi\)
\(888\) 1.94110 1.27704i 0.0651389 0.0428548i
\(889\) 15.9201i 0.533942i
\(890\) 14.6215 17.5853i 0.490112 0.589459i
\(891\) 0.676993 + 0.716817i 0.0226801 + 0.0240143i
\(892\) 18.5236i 0.620215i
\(893\) 37.4405i 1.25290i
\(894\) 15.8049 10.3980i 0.528593 0.347761i
\(895\) −14.3929 11.9672i −0.481103 0.400018i
\(896\) −4.73682 −0.158246
\(897\) 14.7498 + 14.2613i 0.492481 + 0.476170i
\(898\) 16.0667i 0.536152i
\(899\) 65.9458i 2.19941i
\(900\) −14.6271 3.32392i −0.487569 0.110797i
\(901\) −14.0324 −0.467487
\(902\) 0.808828i 0.0269310i
\(903\) 15.8648 10.4374i 0.527947 0.347336i
\(904\) 3.47135i 0.115455i
\(905\) 6.73527 + 5.60011i 0.223888 + 0.186154i
\(906\) −9.30225 + 6.11993i −0.309047 + 0.203321i
\(907\) 16.5189 0.548502 0.274251 0.961658i \(-0.411570\pi\)
0.274251 + 0.961658i \(0.411570\pi\)
\(908\) 15.3110i 0.508115i
\(909\) 23.9285 + 10.3143i 0.793659 + 0.342104i
\(910\) 20.1161 + 16.7257i 0.666841 + 0.554452i
\(911\) 1.38119 0.0457608 0.0228804 0.999738i \(-0.492716\pi\)
0.0228804 + 0.999738i \(0.492716\pi\)
\(912\) 6.43970 + 9.78829i 0.213240 + 0.324123i
\(913\) 1.82010i 0.0602366i
\(914\) −13.2071 −0.436852
\(915\) 29.1502 + 3.27042i 0.963676 + 0.108117i
\(916\) 5.31624i 0.175654i
\(917\) 64.6098i 2.13360i
\(918\) 19.0365 3.36437i 0.628299 0.111041i
\(919\) 8.35624i 0.275647i 0.990457 + 0.137823i \(0.0440107\pi\)
−0.990457 + 0.137823i \(0.955989\pi\)
\(920\) 4.88822 9.54491i 0.161160 0.314686i
\(921\) 22.5404 + 34.2612i 0.742730 + 1.12894i
\(922\) 25.4941i 0.839603i
\(923\) −23.8786 −0.785974
\(924\) −0.750884 + 0.494005i −0.0247023 + 0.0162516i
\(925\) 1.22412 + 6.59474i 0.0402489 + 0.216834i
\(926\) 20.0822i 0.659941i
\(927\) 3.89196 9.02907i 0.127829 0.296554i
\(928\) 7.05802i 0.231691i
\(929\) 3.75617i 0.123236i −0.998100 0.0616180i \(-0.980374\pi\)
0.998100 0.0616180i \(-0.0196261\pi\)
\(930\) 4.03455 35.9612i 0.132298 1.17921i
\(931\) 104.428i 3.42250i
\(932\) 8.00870 0.262334
\(933\) −12.2538 18.6256i −0.401170 0.609775i
\(934\) 14.7644i 0.483106i
\(935\) 0.700775 + 0.582667i 0.0229178 + 0.0190552i
\(936\) −6.80457 2.93309i −0.222414 0.0958711i
\(937\) −8.00163 −0.261402 −0.130701 0.991422i \(-0.541723\pi\)
−0.130701 + 0.991422i \(0.541723\pi\)
\(938\) 28.2302 0.921750
\(939\) 6.64517 4.37184i 0.216857 0.142670i
\(940\) 7.91246 9.51634i 0.258076 0.310389i
\(941\) −43.2565 −1.41012 −0.705060 0.709148i \(-0.749080\pi\)
−0.705060 + 0.709148i \(0.749080\pi\)
\(942\) −34.9136 + 22.9696i −1.13755 + 0.748389i
\(943\) −7.73836 34.5517i −0.251996 1.12516i
\(944\) 4.18459i 0.136197i
\(945\) −47.7974 27.2849i −1.55485 0.887577i
\(946\) −0.253576 −0.00824446
\(947\) 43.5718 1.41589 0.707947 0.706266i \(-0.249622\pi\)
0.707947 + 0.706266i \(0.249622\pi\)
\(948\) −11.7895 17.9199i −0.382904 0.582011i
\(949\) 22.9381 0.744603
\(950\) −33.2551 + 6.17283i −1.07894 + 0.200273i
\(951\) −5.31153 + 3.49445i −0.172238 + 0.113315i
\(952\) 17.6226i 0.571153i
\(953\) 29.1349i 0.943773i −0.881659 0.471887i \(-0.843573\pi\)
0.881659 0.471887i \(-0.156427\pi\)
\(954\) −10.3911 4.47907i −0.336426 0.145015i
\(955\) 14.3863 17.3024i 0.465529 0.559893i
\(956\) 1.30708i 0.0422741i
\(957\) 0.736084 + 1.11884i 0.0237942 + 0.0361670i
\(958\) −0.527998 −0.0170588
\(959\) 0.484669i 0.0156508i
\(960\) −0.431808 + 3.84884i −0.0139365 + 0.124221i
\(961\) 56.2989 1.81609
\(962\) 3.31336i 0.106827i
\(963\) 3.92095 + 1.69011i 0.126351 + 0.0544631i
\(964\) 9.16266i 0.295109i
\(965\) 2.35418 + 1.95741i 0.0757838 + 0.0630113i
\(966\) 27.3501 28.2870i 0.879975 0.910119i
\(967\) 13.1496i 0.422863i 0.977393 + 0.211432i \(0.0678126\pi\)
−0.977393 + 0.211432i \(0.932187\pi\)
\(968\) −10.9880 −0.353168
\(969\) 36.4159 23.9580i 1.16985 0.769640i
\(970\) −14.2167 + 17.0984i −0.456469 + 0.548997i
\(971\) −54.4195 −1.74641 −0.873203 0.487358i \(-0.837961\pi\)
−0.873203 + 0.487358i \(0.837961\pi\)
\(972\) 15.1706 + 3.58500i 0.486598 + 0.114989i
\(973\) −7.44561 −0.238695
\(974\) 15.1423i 0.485191i
\(975\) 15.4240 14.8203i 0.493965 0.474630i
\(976\) 7.57377i 0.242431i
\(977\) 59.8495i 1.91476i −0.288837 0.957378i \(-0.593269\pi\)
0.288837 0.957378i \(-0.406731\pi\)
\(978\) 14.6979 + 22.3407i 0.469988 + 0.714378i
\(979\) −1.12047 −0.0358104
\(980\) 22.0693 26.5427i 0.704977 0.847877i
\(981\) 51.6053 + 22.2443i 1.64763 + 0.710206i
\(982\) 23.0745i 0.736336i
\(983\) 50.9264i 1.62430i −0.583448 0.812150i \(-0.698297\pi\)
0.583448 0.812150i \(-0.301703\pi\)
\(984\) 7.02838 + 10.6831i 0.224056 + 0.340564i
\(985\) 4.94693 5.94968i 0.157622 0.189573i
\(986\) 26.2583 0.836235
\(987\) 37.9357 24.9578i 1.20751 0.794417i
\(988\) −16.7082 −0.531558
\(989\) 10.8323 2.42605i 0.344447 0.0771441i
\(990\) 0.332947 + 0.655154i 0.0105817 + 0.0208222i
\(991\) 31.4399 0.998722 0.499361 0.866394i \(-0.333568\pi\)
0.499361 + 0.866394i \(0.333568\pi\)
\(992\) −9.34339 −0.296653
\(993\) 30.3123 19.9424i 0.961932 0.632854i
\(994\) 45.7942i 1.45250i
\(995\) −4.89567 4.07056i −0.155203 0.129045i
\(996\) −15.8159 24.0401i −0.501147 0.761739i
\(997\) 55.3486i 1.75291i 0.481487 + 0.876453i \(0.340097\pi\)
−0.481487 + 0.876453i \(0.659903\pi\)
\(998\) 2.99246 0.0947248
\(999\) −1.21312 6.86415i −0.0383814 0.217172i
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 690.2.h.b.689.8 yes 24
3.2 odd 2 690.2.h.a.689.19 yes 24
5.4 even 2 690.2.h.a.689.18 yes 24
15.14 odd 2 inner 690.2.h.b.689.5 yes 24
23.22 odd 2 inner 690.2.h.b.689.7 yes 24
69.68 even 2 690.2.h.a.689.20 yes 24
115.114 odd 2 690.2.h.a.689.17 24
345.344 even 2 inner 690.2.h.b.689.6 yes 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
690.2.h.a.689.17 24 115.114 odd 2
690.2.h.a.689.18 yes 24 5.4 even 2
690.2.h.a.689.19 yes 24 3.2 odd 2
690.2.h.a.689.20 yes 24 69.68 even 2
690.2.h.b.689.5 yes 24 15.14 odd 2 inner
690.2.h.b.689.6 yes 24 345.344 even 2 inner
690.2.h.b.689.7 yes 24 23.22 odd 2 inner
690.2.h.b.689.8 yes 24 1.1 even 1 trivial