Properties

Label 950.2.q.f.107.7
Level $950$
Weight $2$
Character 950.107
Analytic conductor $7.586$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [950,2,Mod(107,950)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(950, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([3, 10]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("950.107");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 950.q (of order \(12\), degree \(4\), 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: \(7.58578819202\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(8\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 107.7
Character \(\chi\) \(=\) 950.107
Dual form 950.2.q.f.293.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.965926 + 0.258819i) q^{2} +(0.313773 - 1.17102i) q^{3} +(0.866025 + 0.500000i) q^{4} +(0.606164 - 1.04991i) q^{6} +(-1.88504 - 1.88504i) q^{7} +(0.707107 + 0.707107i) q^{8} +(1.32525 + 0.765131i) q^{9} +O(q^{10})\) \(q+(0.965926 + 0.258819i) q^{2} +(0.313773 - 1.17102i) q^{3} +(0.866025 + 0.500000i) q^{4} +(0.606164 - 1.04991i) q^{6} +(-1.88504 - 1.88504i) q^{7} +(0.707107 + 0.707107i) q^{8} +(1.32525 + 0.765131i) q^{9} +5.08711 q^{11} +(0.857245 - 0.857245i) q^{12} +(1.59907 - 0.428469i) q^{13} +(-1.33292 - 2.30869i) q^{14} +(0.500000 + 0.866025i) q^{16} +(-2.07389 + 7.73985i) q^{17} +(1.08206 + 1.08206i) q^{18} +(1.52448 - 4.08362i) q^{19} +(-2.79888 + 1.61594i) q^{21} +(4.91377 + 1.31664i) q^{22} +(-2.16907 - 8.09508i) q^{23} +(1.04991 - 0.606164i) q^{24} +1.65548 q^{26} +(3.88354 - 3.88354i) q^{27} +(-0.689971 - 2.57501i) q^{28} +(-0.858351 + 1.48671i) q^{29} -7.07909i q^{31} +(0.258819 + 0.965926i) q^{32} +(1.59620 - 5.95710i) q^{33} +(-4.00644 + 6.93936i) q^{34} +(0.765131 + 1.32525i) q^{36} +(0.618567 - 0.618567i) q^{37} +(2.52945 - 3.54991i) q^{38} -2.00698i q^{39} +(4.93587 - 2.84972i) q^{41} +(-3.12175 + 0.836470i) q^{42} +(4.23321 + 1.13429i) q^{43} +(4.40557 + 2.54356i) q^{44} -8.38064i q^{46} +(-9.97760 + 2.67349i) q^{47} +(1.17102 - 0.313773i) q^{48} +0.106718i q^{49} +(8.41277 + 4.85711i) q^{51} +(1.59907 + 0.428469i) q^{52} +(6.22361 - 1.66761i) q^{53} +(4.75635 - 2.74608i) q^{54} -2.66584i q^{56} +(-4.30366 - 3.06652i) q^{57} +(-1.21389 + 1.21389i) q^{58} +(7.18753 + 12.4492i) q^{59} +(-2.82198 + 4.88781i) q^{61} +(1.83220 - 6.83787i) q^{62} +(-1.05584 - 3.94044i) q^{63} +1.00000i q^{64} +(3.08362 - 5.34099i) q^{66} +(0.363940 + 1.35824i) q^{67} +(-5.66596 + 5.66596i) q^{68} -10.1601 q^{69} +(-13.2313 + 7.63907i) q^{71} +(0.396061 + 1.47812i) q^{72} +(-1.99861 - 0.535526i) q^{73} +(0.757586 - 0.437393i) q^{74} +(3.36205 - 2.77428i) q^{76} +(-9.58939 - 9.58939i) q^{77} +(0.519445 - 1.93859i) q^{78} +(2.01507 + 3.49020i) q^{79} +(-1.03375 - 1.79051i) q^{81} +(5.50524 - 1.47513i) q^{82} +(-3.12063 + 3.12063i) q^{83} -3.23187 q^{84} +(3.79539 + 2.19127i) q^{86} +(1.47163 + 1.47163i) q^{87} +(3.59713 + 3.59713i) q^{88} +(-5.26392 + 9.11738i) q^{89} +(-3.82198 - 2.20662i) q^{91} +(2.16907 - 8.09508i) q^{92} +(-8.28974 - 2.22123i) q^{93} -10.3296 q^{94} +1.21233 q^{96} +(-10.0259 - 2.68643i) q^{97} +(-0.0276208 + 0.103082i) q^{98} +(6.74168 + 3.89231i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q + 4 q^{6}+O(q^{10}) \) Copy content Toggle raw display \( 32 q + 4 q^{6} + 72 q^{11} + 16 q^{16} + 60 q^{21} + 8 q^{26} - 28 q^{36} - 84 q^{41} - 84 q^{51} - 52 q^{61} - 24 q^{71} + 16 q^{76} + 64 q^{81} - 36 q^{86} - 84 q^{91} + 8 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/950\mathbb{Z}\right)^\times\).

\(n\) \(77\) \(401\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(e\left(\frac{5}{6}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.965926 + 0.258819i 0.683013 + 0.183013i
\(3\) 0.313773 1.17102i 0.181157 0.676088i −0.814263 0.580495i \(-0.802859\pi\)
0.995421 0.0955921i \(-0.0304744\pi\)
\(4\) 0.866025 + 0.500000i 0.433013 + 0.250000i
\(5\) 0 0
\(6\) 0.606164 1.04991i 0.247465 0.428622i
\(7\) −1.88504 1.88504i −0.712476 0.712476i 0.254576 0.967053i \(-0.418064\pi\)
−0.967053 + 0.254576i \(0.918064\pi\)
\(8\) 0.707107 + 0.707107i 0.250000 + 0.250000i
\(9\) 1.32525 + 0.765131i 0.441749 + 0.255044i
\(10\) 0 0
\(11\) 5.08711 1.53382 0.766911 0.641753i \(-0.221793\pi\)
0.766911 + 0.641753i \(0.221793\pi\)
\(12\) 0.857245 0.857245i 0.247465 0.247465i
\(13\) 1.59907 0.428469i 0.443502 0.118836i −0.0301554 0.999545i \(-0.509600\pi\)
0.473657 + 0.880709i \(0.342934\pi\)
\(14\) −1.33292 2.30869i −0.356238 0.617023i
\(15\) 0 0
\(16\) 0.500000 + 0.866025i 0.125000 + 0.216506i
\(17\) −2.07389 + 7.73985i −0.502991 + 1.87719i −0.0233430 + 0.999728i \(0.507431\pi\)
−0.479648 + 0.877461i \(0.659236\pi\)
\(18\) 1.08206 + 1.08206i 0.255044 + 0.255044i
\(19\) 1.52448 4.08362i 0.349739 0.936847i
\(20\) 0 0
\(21\) −2.79888 + 1.61594i −0.610767 + 0.352626i
\(22\) 4.91377 + 1.31664i 1.04762 + 0.280709i
\(23\) −2.16907 8.09508i −0.452282 1.68794i −0.695957 0.718083i \(-0.745020\pi\)
0.243675 0.969857i \(-0.421647\pi\)
\(24\) 1.04991 0.606164i 0.214311 0.123733i
\(25\) 0 0
\(26\) 1.65548 0.324666
\(27\) 3.88354 3.88354i 0.747388 0.747388i
\(28\) −0.689971 2.57501i −0.130392 0.486630i
\(29\) −0.858351 + 1.48671i −0.159392 + 0.276075i −0.934649 0.355570i \(-0.884287\pi\)
0.775258 + 0.631645i \(0.217620\pi\)
\(30\) 0 0
\(31\) 7.07909i 1.27144i −0.771919 0.635721i \(-0.780703\pi\)
0.771919 0.635721i \(-0.219297\pi\)
\(32\) 0.258819 + 0.965926i 0.0457532 + 0.170753i
\(33\) 1.59620 5.95710i 0.277863 1.03700i
\(34\) −4.00644 + 6.93936i −0.687099 + 1.19009i
\(35\) 0 0
\(36\) 0.765131 + 1.32525i 0.127522 + 0.220874i
\(37\) 0.618567 0.618567i 0.101692 0.101692i −0.654430 0.756122i \(-0.727092\pi\)
0.756122 + 0.654430i \(0.227092\pi\)
\(38\) 2.52945 3.54991i 0.410331 0.575872i
\(39\) 2.00698i 0.321374i
\(40\) 0 0
\(41\) 4.93587 2.84972i 0.770853 0.445052i −0.0623260 0.998056i \(-0.519852\pi\)
0.833179 + 0.553004i \(0.186519\pi\)
\(42\) −3.12175 + 0.836470i −0.481697 + 0.129070i
\(43\) 4.23321 + 1.13429i 0.645559 + 0.172977i 0.566720 0.823910i \(-0.308212\pi\)
0.0788388 + 0.996887i \(0.474879\pi\)
\(44\) 4.40557 + 2.54356i 0.664164 + 0.383456i
\(45\) 0 0
\(46\) 8.38064i 1.23566i
\(47\) −9.97760 + 2.67349i −1.45538 + 0.389968i −0.897892 0.440215i \(-0.854902\pi\)
−0.557490 + 0.830184i \(0.688235\pi\)
\(48\) 1.17102 0.313773i 0.169022 0.0452893i
\(49\) 0.106718i 0.0152455i
\(50\) 0 0
\(51\) 8.41277 + 4.85711i 1.17802 + 0.680132i
\(52\) 1.59907 + 0.428469i 0.221751 + 0.0594180i
\(53\) 6.22361 1.66761i 0.854878 0.229064i 0.195340 0.980735i \(-0.437419\pi\)
0.659538 + 0.751672i \(0.270752\pi\)
\(54\) 4.75635 2.74608i 0.647257 0.373694i
\(55\) 0 0
\(56\) 2.66584i 0.356238i
\(57\) −4.30366 3.06652i −0.570033 0.406171i
\(58\) −1.21389 + 1.21389i −0.159392 + 0.159392i
\(59\) 7.18753 + 12.4492i 0.935736 + 1.62074i 0.773316 + 0.634021i \(0.218597\pi\)
0.162420 + 0.986722i \(0.448070\pi\)
\(60\) 0 0
\(61\) −2.82198 + 4.88781i −0.361318 + 0.625820i −0.988178 0.153311i \(-0.951006\pi\)
0.626860 + 0.779132i \(0.284340\pi\)
\(62\) 1.83220 6.83787i 0.232690 0.868411i
\(63\) −1.05584 3.94044i −0.133023 0.496448i
\(64\) 1.00000i 0.125000i
\(65\) 0 0
\(66\) 3.08362 5.34099i 0.379568 0.657430i
\(67\) 0.363940 + 1.35824i 0.0444624 + 0.165936i 0.984587 0.174895i \(-0.0559584\pi\)
−0.940125 + 0.340830i \(0.889292\pi\)
\(68\) −5.66596 + 5.66596i −0.687099 + 0.687099i
\(69\) −10.1601 −1.22313
\(70\) 0 0
\(71\) −13.2313 + 7.63907i −1.57026 + 0.906591i −0.574126 + 0.818767i \(0.694658\pi\)
−0.996136 + 0.0878239i \(0.972009\pi\)
\(72\) 0.396061 + 1.47812i 0.0466763 + 0.174198i
\(73\) −1.99861 0.535526i −0.233920 0.0626786i 0.139955 0.990158i \(-0.455304\pi\)
−0.373874 + 0.927479i \(0.621971\pi\)
\(74\) 0.757586 0.437393i 0.0880676 0.0508459i
\(75\) 0 0
\(76\) 3.36205 2.77428i 0.385653 0.318232i
\(77\) −9.58939 9.58939i −1.09281 1.09281i
\(78\) 0.519445 1.93859i 0.0588155 0.219503i
\(79\) 2.01507 + 3.49020i 0.226713 + 0.392678i 0.956832 0.290642i \(-0.0938688\pi\)
−0.730119 + 0.683320i \(0.760536\pi\)
\(80\) 0 0
\(81\) −1.03375 1.79051i −0.114861 0.198946i
\(82\) 5.50524 1.47513i 0.607952 0.162900i
\(83\) −3.12063 + 3.12063i −0.342534 + 0.342534i −0.857319 0.514785i \(-0.827872\pi\)
0.514785 + 0.857319i \(0.327872\pi\)
\(84\) −3.23187 −0.352626
\(85\) 0 0
\(86\) 3.79539 + 2.19127i 0.409268 + 0.236291i
\(87\) 1.47163 + 1.47163i 0.157776 + 0.157776i
\(88\) 3.59713 + 3.59713i 0.383456 + 0.383456i
\(89\) −5.26392 + 9.11738i −0.557974 + 0.966440i 0.439691 + 0.898149i \(0.355088\pi\)
−0.997665 + 0.0682908i \(0.978245\pi\)
\(90\) 0 0
\(91\) −3.82198 2.20662i −0.400652 0.231317i
\(92\) 2.16907 8.09508i 0.226141 0.843970i
\(93\) −8.28974 2.22123i −0.859606 0.230331i
\(94\) −10.3296 −1.06541
\(95\) 0 0
\(96\) 1.21233 0.123733
\(97\) −10.0259 2.68643i −1.01798 0.272766i −0.289017 0.957324i \(-0.593329\pi\)
−0.728958 + 0.684558i \(0.759995\pi\)
\(98\) −0.0276208 + 0.103082i −0.00279012 + 0.0104129i
\(99\) 6.74168 + 3.89231i 0.677564 + 0.391192i
\(100\) 0 0
\(101\) −3.30520 + 5.72477i −0.328879 + 0.569636i −0.982290 0.187368i \(-0.940004\pi\)
0.653410 + 0.757004i \(0.273338\pi\)
\(102\) 6.86900 + 6.86900i 0.680132 + 0.680132i
\(103\) 6.38060 + 6.38060i 0.628699 + 0.628699i 0.947741 0.319041i \(-0.103361\pi\)
−0.319041 + 0.947741i \(0.603361\pi\)
\(104\) 1.43369 + 0.827739i 0.140584 + 0.0811665i
\(105\) 0 0
\(106\) 6.44315 0.625814
\(107\) −6.54875 + 6.54875i −0.633092 + 0.633092i −0.948842 0.315750i \(-0.897744\pi\)
0.315750 + 0.948842i \(0.397744\pi\)
\(108\) 5.30502 1.42148i 0.510476 0.136782i
\(109\) 2.10586 + 3.64745i 0.201705 + 0.349363i 0.949078 0.315042i \(-0.102019\pi\)
−0.747373 + 0.664404i \(0.768685\pi\)
\(110\) 0 0
\(111\) −0.530263 0.918442i −0.0503303 0.0871747i
\(112\) 0.689971 2.57501i 0.0651961 0.243315i
\(113\) −6.93263 6.93263i −0.652167 0.652167i 0.301347 0.953515i \(-0.402564\pi\)
−0.953515 + 0.301347i \(0.902564\pi\)
\(114\) −3.36334 4.07590i −0.315005 0.381743i
\(115\) 0 0
\(116\) −1.48671 + 0.858351i −0.138037 + 0.0796958i
\(117\) 2.44700 + 0.655670i 0.226225 + 0.0606168i
\(118\) 3.72054 + 13.8852i 0.342503 + 1.27824i
\(119\) 18.4992 10.6805i 1.69582 0.979083i
\(120\) 0 0
\(121\) 14.8787 1.35261
\(122\) −3.99088 + 3.99088i −0.361318 + 0.361318i
\(123\) −1.78833 6.67416i −0.161249 0.601788i
\(124\) 3.53954 6.13067i 0.317860 0.550550i
\(125\) 0 0
\(126\) 4.07944i 0.363425i
\(127\) 3.06175 + 11.4266i 0.271687 + 1.01395i 0.958029 + 0.286670i \(0.0925483\pi\)
−0.686343 + 0.727278i \(0.740785\pi\)
\(128\) −0.258819 + 0.965926i −0.0228766 + 0.0853766i
\(129\) 2.65654 4.60126i 0.233895 0.405118i
\(130\) 0 0
\(131\) −2.90308 5.02829i −0.253644 0.439324i 0.710883 0.703311i \(-0.248296\pi\)
−0.964526 + 0.263987i \(0.914962\pi\)
\(132\) 4.36090 4.36090i 0.379568 0.379568i
\(133\) −10.5715 + 4.82408i −0.916662 + 0.418301i
\(134\) 1.40616i 0.121474i
\(135\) 0 0
\(136\) −6.93936 + 4.00644i −0.595045 + 0.343549i
\(137\) 16.5912 4.44559i 1.41748 0.379812i 0.532890 0.846185i \(-0.321106\pi\)
0.884588 + 0.466373i \(0.154439\pi\)
\(138\) −9.81388 2.62962i −0.835413 0.223848i
\(139\) −11.7743 6.79791i −0.998686 0.576591i −0.0908265 0.995867i \(-0.528951\pi\)
−0.907859 + 0.419275i \(0.862284\pi\)
\(140\) 0 0
\(141\) 12.5228i 1.05461i
\(142\) −14.7576 + 3.95427i −1.23843 + 0.331835i
\(143\) 8.13464 2.17967i 0.680253 0.182273i
\(144\) 1.53026i 0.127522i
\(145\) 0 0
\(146\) −1.79190 1.03456i −0.148299 0.0856205i
\(147\) 0.124969 + 0.0334854i 0.0103073 + 0.00276183i
\(148\) 0.844978 0.226411i 0.0694567 0.0186109i
\(149\) −8.23647 + 4.75533i −0.674758 + 0.389572i −0.797877 0.602820i \(-0.794044\pi\)
0.123119 + 0.992392i \(0.460710\pi\)
\(150\) 0 0
\(151\) 6.21129i 0.505468i −0.967536 0.252734i \(-0.918670\pi\)
0.967536 0.252734i \(-0.0813297\pi\)
\(152\) 3.96552 1.80959i 0.321647 0.146777i
\(153\) −8.67041 + 8.67041i −0.700961 + 0.700961i
\(154\) −6.78072 11.7446i −0.546406 0.946403i
\(155\) 0 0
\(156\) 1.00349 1.73810i 0.0803435 0.139159i
\(157\) 3.70862 13.8408i 0.295980 1.10461i −0.644456 0.764641i \(-0.722916\pi\)
0.940436 0.339971i \(-0.110417\pi\)
\(158\) 1.04308 + 3.89281i 0.0829826 + 0.309695i
\(159\) 7.81121i 0.619469i
\(160\) 0 0
\(161\) −11.1707 + 19.3483i −0.880377 + 1.52486i
\(162\) −0.535110 1.99706i −0.0420422 0.156904i
\(163\) −1.78065 + 1.78065i −0.139471 + 0.139471i −0.773395 0.633924i \(-0.781443\pi\)
0.633924 + 0.773395i \(0.281443\pi\)
\(164\) 5.69945 0.445052
\(165\) 0 0
\(166\) −3.82198 + 2.20662i −0.296643 + 0.171267i
\(167\) −3.47427 12.9661i −0.268847 1.00335i −0.959853 0.280502i \(-0.909499\pi\)
0.691006 0.722849i \(-0.257168\pi\)
\(168\) −3.12175 0.836470i −0.240848 0.0645351i
\(169\) −8.88490 + 5.12970i −0.683454 + 0.394592i
\(170\) 0 0
\(171\) 5.14482 4.24538i 0.393434 0.324652i
\(172\) 3.09893 + 3.09893i 0.236291 + 0.236291i
\(173\) −2.67657 + 9.98909i −0.203496 + 0.759457i 0.786407 + 0.617709i \(0.211939\pi\)
−0.989903 + 0.141748i \(0.954728\pi\)
\(174\) 1.04060 + 1.80237i 0.0788878 + 0.136638i
\(175\) 0 0
\(176\) 2.54356 + 4.40557i 0.191728 + 0.332082i
\(177\) 16.8334 4.51051i 1.26528 0.339031i
\(178\) −7.44431 + 7.44431i −0.557974 + 0.557974i
\(179\) 15.2968 1.14333 0.571666 0.820486i \(-0.306297\pi\)
0.571666 + 0.820486i \(0.306297\pi\)
\(180\) 0 0
\(181\) −13.3780 7.72382i −0.994382 0.574107i −0.0878009 0.996138i \(-0.527984\pi\)
−0.906581 + 0.422031i \(0.861317\pi\)
\(182\) −3.12063 3.12063i −0.231317 0.231317i
\(183\) 4.83826 + 4.83826i 0.357654 + 0.357654i
\(184\) 4.19032 7.25785i 0.308914 0.535056i
\(185\) 0 0
\(186\) −7.43238 4.29108i −0.544968 0.314638i
\(187\) −10.5501 + 39.3735i −0.771499 + 2.87927i
\(188\) −9.97760 2.67349i −0.727691 0.194984i
\(189\) −14.6412 −1.06499
\(190\) 0 0
\(191\) −14.4216 −1.04351 −0.521755 0.853095i \(-0.674723\pi\)
−0.521755 + 0.853095i \(0.674723\pi\)
\(192\) 1.17102 + 0.313773i 0.0845109 + 0.0226446i
\(193\) −1.98826 + 7.42030i −0.143118 + 0.534125i 0.856714 + 0.515793i \(0.172502\pi\)
−0.999832 + 0.0183327i \(0.994164\pi\)
\(194\) −8.98897 5.18979i −0.645371 0.372605i
\(195\) 0 0
\(196\) −0.0533592 + 0.0924208i −0.00381137 + 0.00660149i
\(197\) 15.0397 + 15.0397i 1.07153 + 1.07153i 0.997236 + 0.0742953i \(0.0236708\pi\)
0.0742953 + 0.997236i \(0.476329\pi\)
\(198\) 5.50456 + 5.50456i 0.391192 + 0.391192i
\(199\) −3.99272 2.30520i −0.283036 0.163411i 0.351761 0.936090i \(-0.385583\pi\)
−0.634797 + 0.772679i \(0.718916\pi\)
\(200\) 0 0
\(201\) 1.70472 0.120242
\(202\) −4.67426 + 4.67426i −0.328879 + 0.328879i
\(203\) 4.42052 1.18447i 0.310259 0.0831338i
\(204\) 4.85711 + 8.41277i 0.340066 + 0.589012i
\(205\) 0 0
\(206\) 4.51177 + 7.81461i 0.314350 + 0.544470i
\(207\) 3.31925 12.3876i 0.230704 0.860997i
\(208\) 1.17060 + 1.17060i 0.0811665 + 0.0811665i
\(209\) 7.75519 20.7738i 0.536437 1.43696i
\(210\) 0 0
\(211\) −1.99020 + 1.14904i −0.137011 + 0.0791032i −0.566939 0.823760i \(-0.691872\pi\)
0.429928 + 0.902863i \(0.358539\pi\)
\(212\) 6.22361 + 1.66761i 0.427439 + 0.114532i
\(213\) 4.79387 + 17.8910i 0.328471 + 1.22587i
\(214\) −8.02055 + 4.63067i −0.548274 + 0.316546i
\(215\) 0 0
\(216\) 5.49216 0.373694
\(217\) −13.3443 + 13.3443i −0.905872 + 0.905872i
\(218\) 1.09007 + 4.06820i 0.0738290 + 0.275534i
\(219\) −1.25422 + 2.17237i −0.0847524 + 0.146795i
\(220\) 0 0
\(221\) 13.2651i 0.892310i
\(222\) −0.274484 1.02439i −0.0184222 0.0687525i
\(223\) −5.34017 + 19.9298i −0.357604 + 1.33460i 0.519572 + 0.854427i \(0.326091\pi\)
−0.877176 + 0.480169i \(0.840575\pi\)
\(224\) 1.33292 2.30869i 0.0890596 0.154256i
\(225\) 0 0
\(226\) −4.90211 8.49071i −0.326084 0.564794i
\(227\) −2.31642 + 2.31642i −0.153746 + 0.153746i −0.779789 0.626043i \(-0.784674\pi\)
0.626043 + 0.779789i \(0.284674\pi\)
\(228\) −2.19381 4.80751i −0.145289 0.318385i
\(229\) 7.45517i 0.492651i 0.969187 + 0.246326i \(0.0792233\pi\)
−0.969187 + 0.246326i \(0.920777\pi\)
\(230\) 0 0
\(231\) −14.2382 + 8.22045i −0.936807 + 0.540866i
\(232\) −1.65821 + 0.444315i −0.108867 + 0.0291707i
\(233\) 10.8912 + 2.91830i 0.713509 + 0.191184i 0.597274 0.802037i \(-0.296251\pi\)
0.116236 + 0.993222i \(0.462917\pi\)
\(234\) 2.19392 + 1.26666i 0.143421 + 0.0828040i
\(235\) 0 0
\(236\) 14.3751i 0.935736i
\(237\) 4.71936 1.26455i 0.306555 0.0821412i
\(238\) 20.6332 5.52865i 1.33745 0.358369i
\(239\) 13.3826i 0.865650i −0.901478 0.432825i \(-0.857517\pi\)
0.901478 0.432825i \(-0.142483\pi\)
\(240\) 0 0
\(241\) −16.2007 9.35347i −1.04358 0.602510i −0.122734 0.992440i \(-0.539166\pi\)
−0.920845 + 0.389929i \(0.872499\pi\)
\(242\) 14.3717 + 3.85089i 0.923850 + 0.247545i
\(243\) 13.4940 3.61570i 0.865639 0.231947i
\(244\) −4.88781 + 2.82198i −0.312910 + 0.180659i
\(245\) 0 0
\(246\) 6.90959i 0.440540i
\(247\) 0.688037 7.18318i 0.0437788 0.457055i
\(248\) 5.00567 5.00567i 0.317860 0.317860i
\(249\) 2.67515 + 4.63349i 0.169531 + 0.293636i
\(250\) 0 0
\(251\) 9.16442 15.8732i 0.578453 1.00191i −0.417204 0.908813i \(-0.636990\pi\)
0.995657 0.0930973i \(-0.0296768\pi\)
\(252\) 1.05584 3.94044i 0.0665115 0.248224i
\(253\) −11.0343 41.1806i −0.693720 2.58900i
\(254\) 11.8297i 0.742262i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −0.399675 1.49161i −0.0249310 0.0930438i 0.952339 0.305041i \(-0.0986700\pi\)
−0.977270 + 0.211997i \(0.932003\pi\)
\(258\) 3.75691 3.75691i 0.233895 0.233895i
\(259\) −2.33204 −0.144906
\(260\) 0 0
\(261\) −2.27505 + 1.31350i −0.140822 + 0.0813037i
\(262\) −1.50275 5.60833i −0.0928400 0.346484i
\(263\) 1.08181 + 0.289870i 0.0667072 + 0.0178741i 0.292018 0.956413i \(-0.405673\pi\)
−0.225311 + 0.974287i \(0.572340\pi\)
\(264\) 5.34099 3.08362i 0.328715 0.189784i
\(265\) 0 0
\(266\) −11.4598 + 1.92361i −0.702646 + 0.117944i
\(267\) 9.02493 + 9.02493i 0.552317 + 0.552317i
\(268\) −0.363940 + 1.35824i −0.0222312 + 0.0829680i
\(269\) −1.94303 3.36542i −0.118468 0.205193i 0.800693 0.599076i \(-0.204465\pi\)
−0.919161 + 0.393882i \(0.871132\pi\)
\(270\) 0 0
\(271\) 1.49369 + 2.58714i 0.0907350 + 0.157158i 0.907821 0.419359i \(-0.137745\pi\)
−0.817086 + 0.576516i \(0.804412\pi\)
\(272\) −7.73985 + 2.07389i −0.469297 + 0.125748i
\(273\) −3.78323 + 3.78323i −0.228971 + 0.228971i
\(274\) 17.1764 1.03767
\(275\) 0 0
\(276\) −8.79888 5.08004i −0.529631 0.305782i
\(277\) −15.9817 15.9817i −0.960248 0.960248i 0.0389918 0.999240i \(-0.487585\pi\)
−0.999240 + 0.0389918i \(0.987585\pi\)
\(278\) −9.61370 9.61370i −0.576591 0.576591i
\(279\) 5.41643 9.38154i 0.324273 0.561658i
\(280\) 0 0
\(281\) 20.6331 + 11.9125i 1.23087 + 0.710641i 0.967210 0.253976i \(-0.0817385\pi\)
0.263655 + 0.964617i \(0.415072\pi\)
\(282\) −3.24114 + 12.0961i −0.193007 + 0.720313i
\(283\) 8.49923 + 2.27736i 0.505227 + 0.135375i 0.502425 0.864621i \(-0.332441\pi\)
0.00280196 + 0.999996i \(0.499108\pi\)
\(284\) −15.2781 −0.906591
\(285\) 0 0
\(286\) 8.42160 0.497980
\(287\) −14.6761 3.93245i −0.866304 0.232125i
\(288\) −0.396061 + 1.47812i −0.0233381 + 0.0870991i
\(289\) −40.8818 23.6031i −2.40481 1.38842i
\(290\) 0 0
\(291\) −6.29172 + 10.8976i −0.368827 + 0.638827i
\(292\) −1.46308 1.46308i −0.0856205 0.0856205i
\(293\) −13.9858 13.9858i −0.817062 0.817062i 0.168619 0.985681i \(-0.446069\pi\)
−0.985681 + 0.168619i \(0.946069\pi\)
\(294\) 0.112044 + 0.0646888i 0.00653456 + 0.00377273i
\(295\) 0 0
\(296\) 0.874785 0.0508459
\(297\) 19.7560 19.7560i 1.14636 1.14636i
\(298\) −9.18659 + 2.46154i −0.532165 + 0.142593i
\(299\) −6.93698 12.0152i −0.401176 0.694857i
\(300\) 0 0
\(301\) −5.84159 10.1179i −0.336703 0.583188i
\(302\) 1.60760 5.99964i 0.0925070 0.345241i
\(303\) 5.66673 + 5.66673i 0.325545 + 0.325545i
\(304\) 4.29876 0.721575i 0.246551 0.0413852i
\(305\) 0 0
\(306\) −10.6190 + 6.13091i −0.607050 + 0.350481i
\(307\) 11.9567 + 3.20378i 0.682404 + 0.182849i 0.583336 0.812231i \(-0.301747\pi\)
0.0990679 + 0.995081i \(0.468414\pi\)
\(308\) −3.50996 13.0993i −0.199999 0.746405i
\(309\) 9.47386 5.46974i 0.538949 0.311162i
\(310\) 0 0
\(311\) −12.9658 −0.735224 −0.367612 0.929979i \(-0.619825\pi\)
−0.367612 + 0.929979i \(0.619825\pi\)
\(312\) 1.41915 1.41915i 0.0803435 0.0803435i
\(313\) −1.08434 4.04681i −0.0612904 0.228739i 0.928486 0.371368i \(-0.121111\pi\)
−0.989776 + 0.142629i \(0.954444\pi\)
\(314\) 7.16450 12.4093i 0.404316 0.700296i
\(315\) 0 0
\(316\) 4.03013i 0.226713i
\(317\) 2.18344 + 8.14871i 0.122634 + 0.457677i 0.999744 0.0226121i \(-0.00719827\pi\)
−0.877110 + 0.480290i \(0.840532\pi\)
\(318\) 2.02169 7.54505i 0.113371 0.423105i
\(319\) −4.36653 + 7.56304i −0.244479 + 0.423449i
\(320\) 0 0
\(321\) 5.61389 + 9.72353i 0.313337 + 0.542715i
\(322\) −15.7978 + 15.7978i −0.880377 + 0.880377i
\(323\) 28.4450 + 20.2682i 1.58272 + 1.12775i
\(324\) 2.06751i 0.114861i
\(325\) 0 0
\(326\) −2.18084 + 1.25911i −0.120786 + 0.0697356i
\(327\) 4.93199 1.32152i 0.272740 0.0730804i
\(328\) 5.50524 + 1.47513i 0.303976 + 0.0814502i
\(329\) 23.8477 + 13.7685i 1.31477 + 0.759082i
\(330\) 0 0
\(331\) 9.62608i 0.529097i 0.964372 + 0.264549i \(0.0852230\pi\)
−0.964372 + 0.264549i \(0.914777\pi\)
\(332\) −4.26287 + 1.14223i −0.233955 + 0.0626881i
\(333\) 1.29304 0.346469i 0.0708580 0.0189864i
\(334\) 13.4235i 0.734504i
\(335\) 0 0
\(336\) −2.79888 1.61594i −0.152692 0.0881566i
\(337\) 3.54986 + 0.951182i 0.193373 + 0.0518142i 0.354206 0.935168i \(-0.384751\pi\)
−0.160833 + 0.986982i \(0.551418\pi\)
\(338\) −9.90981 + 2.65533i −0.539023 + 0.144431i
\(339\) −10.2935 + 5.94296i −0.559067 + 0.322778i
\(340\) 0 0
\(341\) 36.0121i 1.95016i
\(342\) 6.06830 2.76915i 0.328136 0.149738i
\(343\) −12.9941 + 12.9941i −0.701614 + 0.701614i
\(344\) 2.19127 + 3.79539i 0.118145 + 0.204634i
\(345\) 0 0
\(346\) −5.17073 + 8.95597i −0.277980 + 0.481476i
\(347\) 0.111421 0.415829i 0.00598139 0.0223228i −0.962871 0.269963i \(-0.912988\pi\)
0.968852 + 0.247640i \(0.0796551\pi\)
\(348\) 0.538655 + 2.01029i 0.0288749 + 0.107763i
\(349\) 11.4552i 0.613181i 0.951841 + 0.306591i \(0.0991882\pi\)
−0.951841 + 0.306591i \(0.900812\pi\)
\(350\) 0 0
\(351\) 4.54607 7.87403i 0.242652 0.420285i
\(352\) 1.31664 + 4.91377i 0.0701772 + 0.261905i
\(353\) −21.7675 + 21.7675i −1.15857 + 1.15857i −0.173784 + 0.984784i \(0.555600\pi\)
−0.984784 + 0.173784i \(0.944400\pi\)
\(354\) 17.4273 0.926249
\(355\) 0 0
\(356\) −9.11738 + 5.26392i −0.483220 + 0.278987i
\(357\) −6.70254 25.0142i −0.354736 1.32389i
\(358\) 14.7755 + 3.95909i 0.780911 + 0.209244i
\(359\) 32.2397 18.6136i 1.70154 0.982387i 0.757344 0.653016i \(-0.226497\pi\)
0.944201 0.329371i \(-0.106837\pi\)
\(360\) 0 0
\(361\) −14.3519 12.4508i −0.755365 0.655304i
\(362\) −10.9231 10.9231i −0.574107 0.574107i
\(363\) 4.66854 17.4232i 0.245035 0.914483i
\(364\) −2.20662 3.82198i −0.115658 0.200326i
\(365\) 0 0
\(366\) 3.42116 + 5.92563i 0.178827 + 0.309738i
\(367\) −0.905122 + 0.242527i −0.0472470 + 0.0126598i −0.282365 0.959307i \(-0.591119\pi\)
0.235118 + 0.971967i \(0.424452\pi\)
\(368\) 5.92601 5.92601i 0.308914 0.308914i
\(369\) 8.72165 0.454031
\(370\) 0 0
\(371\) −14.8752 8.58821i −0.772283 0.445878i
\(372\) −6.06851 6.06851i −0.314638 0.314638i
\(373\) 18.3157 + 18.3157i 0.948349 + 0.948349i 0.998730 0.0503814i \(-0.0160437\pi\)
−0.0503814 + 0.998730i \(0.516044\pi\)
\(374\) −20.3812 + 35.3013i −1.05389 + 1.82539i
\(375\) 0 0
\(376\) −8.94567 5.16478i −0.461338 0.266353i
\(377\) −0.735553 + 2.74512i −0.0378829 + 0.141381i
\(378\) −14.1423 3.78943i −0.727404 0.194907i
\(379\) −32.8155 −1.68562 −0.842810 0.538211i \(-0.819100\pi\)
−0.842810 + 0.538211i \(0.819100\pi\)
\(380\) 0 0
\(381\) 14.3415 0.734736
\(382\) −13.9302 3.73259i −0.712731 0.190976i
\(383\) −2.80563 + 10.4707i −0.143361 + 0.535030i 0.856462 + 0.516210i \(0.172658\pi\)
−0.999823 + 0.0188199i \(0.994009\pi\)
\(384\) 1.04991 + 0.606164i 0.0535778 + 0.0309332i
\(385\) 0 0
\(386\) −3.84103 + 6.65286i −0.195503 + 0.338622i
\(387\) 4.74217 + 4.74217i 0.241058 + 0.241058i
\(388\) −7.33947 7.33947i −0.372605 0.372605i
\(389\) 18.7610 + 10.8317i 0.951220 + 0.549187i 0.893460 0.449143i \(-0.148271\pi\)
0.0577605 + 0.998330i \(0.481604\pi\)
\(390\) 0 0
\(391\) 67.1530 3.39608
\(392\) −0.0754613 + 0.0754613i −0.00381137 + 0.00381137i
\(393\) −6.79913 + 1.82182i −0.342971 + 0.0918987i
\(394\) 10.6346 + 18.4198i 0.535766 + 0.927974i
\(395\) 0 0
\(396\) 3.89231 + 6.74168i 0.195596 + 0.338782i
\(397\) 6.43427 24.0130i 0.322927 1.20518i −0.593453 0.804869i \(-0.702236\pi\)
0.916380 0.400310i \(-0.131098\pi\)
\(398\) −3.26004 3.26004i −0.163411 0.163411i
\(399\) 2.33204 + 13.8930i 0.116748 + 0.695522i
\(400\) 0 0
\(401\) 25.2666 14.5877i 1.26175 0.728473i 0.288339 0.957529i \(-0.406897\pi\)
0.973413 + 0.229056i \(0.0735638\pi\)
\(402\) 1.64664 + 0.441215i 0.0821268 + 0.0220058i
\(403\) −3.03317 11.3199i −0.151093 0.563887i
\(404\) −5.72477 + 3.30520i −0.284818 + 0.164440i
\(405\) 0 0
\(406\) 4.57646 0.227126
\(407\) 3.14672 3.14672i 0.155977 0.155977i
\(408\) 2.51423 + 9.38323i 0.124473 + 0.464539i
\(409\) −6.42063 + 11.1209i −0.317480 + 0.549891i −0.979962 0.199187i \(-0.936170\pi\)
0.662482 + 0.749078i \(0.269503\pi\)
\(410\) 0 0
\(411\) 20.8234i 1.02714i
\(412\) 2.33546 + 8.71606i 0.115060 + 0.429410i
\(413\) 9.91837 37.0158i 0.488051 1.82143i
\(414\) 6.41229 11.1064i 0.315147 0.545850i
\(415\) 0 0
\(416\) 0.827739 + 1.43369i 0.0405832 + 0.0702922i
\(417\) −11.6549 + 11.6549i −0.570745 + 0.570745i
\(418\) 12.8676 18.0588i 0.629375 0.883285i
\(419\) 17.7916i 0.869177i 0.900629 + 0.434588i \(0.143106\pi\)
−0.900629 + 0.434588i \(0.856894\pi\)
\(420\) 0 0
\(421\) 29.5157 17.0409i 1.43851 0.830522i 0.440761 0.897625i \(-0.354709\pi\)
0.997746 + 0.0671023i \(0.0213754\pi\)
\(422\) −2.21978 + 0.594787i −0.108057 + 0.0289538i
\(423\) −15.2683 4.09114i −0.742372 0.198918i
\(424\) 5.57993 + 3.22158i 0.270985 + 0.156454i
\(425\) 0 0
\(426\) 18.5221i 0.897399i
\(427\) 14.5332 3.89417i 0.703313 0.188452i
\(428\) −8.94576 + 2.39701i −0.432410 + 0.115864i
\(429\) 10.2097i 0.492931i
\(430\) 0 0
\(431\) 21.0591 + 12.1585i 1.01438 + 0.585652i 0.912471 0.409142i \(-0.134172\pi\)
0.101908 + 0.994794i \(0.467505\pi\)
\(432\) 5.30502 + 1.42148i 0.255238 + 0.0683908i
\(433\) −24.8949 + 6.67057i −1.19637 + 0.320567i −0.801402 0.598126i \(-0.795912\pi\)
−0.394971 + 0.918694i \(0.629245\pi\)
\(434\) −16.3434 + 9.43587i −0.784508 + 0.452936i
\(435\) 0 0
\(436\) 4.21171i 0.201705i
\(437\) −36.3639 3.48310i −1.73952 0.166619i
\(438\) −1.77374 + 1.77374i −0.0847524 + 0.0847524i
\(439\) 0.512599 + 0.887848i 0.0244650 + 0.0423747i 0.877999 0.478663i \(-0.158878\pi\)
−0.853534 + 0.521038i \(0.825545\pi\)
\(440\) 0 0
\(441\) −0.0816536 + 0.141428i −0.00388827 + 0.00673468i
\(442\) −3.43327 + 12.8131i −0.163304 + 0.609459i
\(443\) −2.14710 8.01308i −0.102012 0.380713i 0.895977 0.444100i \(-0.146476\pi\)
−0.997989 + 0.0633869i \(0.979810\pi\)
\(444\) 1.06053i 0.0503303i
\(445\) 0 0
\(446\) −10.3164 + 17.8685i −0.488496 + 0.846100i
\(447\) 2.98419 + 11.1372i 0.141147 + 0.526769i
\(448\) 1.88504 1.88504i 0.0890596 0.0890596i
\(449\) −19.6032 −0.925134 −0.462567 0.886584i \(-0.653072\pi\)
−0.462567 + 0.886584i \(0.653072\pi\)
\(450\) 0 0
\(451\) 25.1093 14.4969i 1.18235 0.682631i
\(452\) −2.53752 9.47015i −0.119355 0.445439i
\(453\) −7.27353 1.94894i −0.341740 0.0915691i
\(454\) −2.83702 + 1.63795i −0.133148 + 0.0768729i
\(455\) 0 0
\(456\) −0.874785 5.21150i −0.0409656 0.244051i
\(457\) 19.5026 + 19.5026i 0.912293 + 0.912293i 0.996452 0.0841597i \(-0.0268206\pi\)
−0.0841597 + 0.996452i \(0.526821\pi\)
\(458\) −1.92954 + 7.20114i −0.0901615 + 0.336487i
\(459\) 22.0040 + 38.1121i 1.02706 + 1.77892i
\(460\) 0 0
\(461\) 3.84973 + 6.66792i 0.179300 + 0.310556i 0.941641 0.336619i \(-0.109284\pi\)
−0.762341 + 0.647175i \(0.775950\pi\)
\(462\) −15.8807 + 4.25522i −0.738837 + 0.197971i
\(463\) 12.6250 12.6250i 0.586735 0.586735i −0.350010 0.936746i \(-0.613822\pi\)
0.936746 + 0.350010i \(0.113822\pi\)
\(464\) −1.71670 −0.0796958
\(465\) 0 0
\(466\) 9.76483 + 5.63773i 0.452347 + 0.261163i
\(467\) −10.9349 10.9349i −0.506008 0.506008i 0.407291 0.913299i \(-0.366474\pi\)
−0.913299 + 0.407291i \(0.866474\pi\)
\(468\) 1.79133 + 1.79133i 0.0828040 + 0.0828040i
\(469\) 1.87430 3.24638i 0.0865470 0.149904i
\(470\) 0 0
\(471\) −15.0441 8.68572i −0.693196 0.400217i
\(472\) −3.72054 + 13.8852i −0.171252 + 0.639120i
\(473\) 21.5348 + 5.77024i 0.990172 + 0.265316i
\(474\) 4.88584 0.224414
\(475\) 0 0
\(476\) 21.3611 0.979083
\(477\) 9.52375 + 2.55188i 0.436063 + 0.116843i
\(478\) 3.46368 12.9266i 0.158425 0.591250i
\(479\) −2.12792 1.22856i −0.0972272 0.0561341i 0.450598 0.892727i \(-0.351211\pi\)
−0.547825 + 0.836593i \(0.684544\pi\)
\(480\) 0 0
\(481\) 0.724094 1.25417i 0.0330158 0.0571851i
\(482\) −13.2278 13.2278i −0.602510 0.602510i
\(483\) 19.1521 + 19.1521i 0.871451 + 0.871451i
\(484\) 12.8853 + 7.43936i 0.585697 + 0.338153i
\(485\) 0 0
\(486\) 13.9700 0.633692
\(487\) −7.28307 + 7.28307i −0.330027 + 0.330027i −0.852597 0.522569i \(-0.824974\pi\)
0.522569 + 0.852597i \(0.324974\pi\)
\(488\) −5.45165 + 1.46076i −0.246785 + 0.0661257i
\(489\) 1.52645 + 2.64389i 0.0690286 + 0.119561i
\(490\) 0 0
\(491\) −10.4517 18.1028i −0.471678 0.816970i 0.527797 0.849370i \(-0.323018\pi\)
−0.999475 + 0.0324007i \(0.989685\pi\)
\(492\) 1.78833 6.67416i 0.0806244 0.300894i
\(493\) −9.72676 9.72676i −0.438071 0.438071i
\(494\) 2.52374 6.76035i 0.113548 0.304162i
\(495\) 0 0
\(496\) 6.13067 3.53954i 0.275275 0.158930i
\(497\) 39.3413 + 10.5415i 1.76470 + 0.472850i
\(498\) 1.38476 + 5.16799i 0.0620525 + 0.231583i
\(499\) 24.1791 13.9598i 1.08241 0.624927i 0.150861 0.988555i \(-0.451795\pi\)
0.931544 + 0.363628i \(0.118462\pi\)
\(500\) 0 0
\(501\) −16.2737 −0.727057
\(502\) 12.9604 12.9604i 0.578453 0.578453i
\(503\) −0.198659 0.741405i −0.00885777 0.0330576i 0.961356 0.275310i \(-0.0887805\pi\)
−0.970213 + 0.242252i \(0.922114\pi\)
\(504\) 2.03972 3.53290i 0.0908564 0.157368i
\(505\) 0 0
\(506\) 42.6333i 1.89528i
\(507\) 3.21912 + 12.0139i 0.142966 + 0.533558i
\(508\) −3.06175 + 11.4266i −0.135843 + 0.506974i
\(509\) −9.55337 + 16.5469i −0.423446 + 0.733430i −0.996274 0.0862459i \(-0.972513\pi\)
0.572828 + 0.819676i \(0.305846\pi\)
\(510\) 0 0
\(511\) 2.75796 + 4.77694i 0.122005 + 0.211319i
\(512\) −0.707107 + 0.707107i −0.0312500 + 0.0312500i
\(513\) −9.93855 21.7793i −0.438798 0.961580i
\(514\) 1.54422i 0.0681128i
\(515\) 0 0
\(516\) 4.60126 2.65654i 0.202559 0.116948i
\(517\) −50.7572 + 13.6003i −2.23230 + 0.598142i
\(518\) −2.25258 0.603576i −0.0989726 0.0265196i
\(519\) 10.8576 + 6.26862i 0.476594 + 0.275162i
\(520\) 0 0
\(521\) 16.6777i 0.730665i 0.930877 + 0.365332i \(0.119045\pi\)
−0.930877 + 0.365332i \(0.880955\pi\)
\(522\) −2.53749 + 0.679919i −0.111063 + 0.0297592i
\(523\) 7.84835 2.10296i 0.343185 0.0919560i −0.0831101 0.996540i \(-0.526485\pi\)
0.426295 + 0.904584i \(0.359819\pi\)
\(524\) 5.80617i 0.253644i
\(525\) 0 0
\(526\) 0.969923 + 0.559985i 0.0422907 + 0.0244165i
\(527\) 54.7910 + 14.6812i 2.38674 + 0.639524i
\(528\) 5.95710 1.59620i 0.259250 0.0694657i
\(529\) −40.9068 + 23.6176i −1.77856 + 1.02685i
\(530\) 0 0
\(531\) 21.9976i 0.954615i
\(532\) −11.5672 1.10796i −0.501502 0.0480361i
\(533\) 6.67177 6.67177i 0.288986 0.288986i
\(534\) 6.38159 + 11.0532i 0.276158 + 0.478321i
\(535\) 0 0
\(536\) −0.703079 + 1.21777i −0.0303684 + 0.0525996i
\(537\) 4.79971 17.9128i 0.207123 0.772993i
\(538\) −1.00578 3.75364i −0.0433624 0.161831i
\(539\) 0.542888i 0.0233839i
\(540\) 0 0
\(541\) −2.51329 + 4.35315i −0.108055 + 0.187157i −0.914982 0.403494i \(-0.867796\pi\)
0.806927 + 0.590651i \(0.201129\pi\)
\(542\) 0.773189 + 2.88558i 0.0332113 + 0.123946i
\(543\) −13.2424 + 13.2424i −0.568286 + 0.568286i
\(544\) −8.01288 −0.343549
\(545\) 0 0
\(546\) −4.63349 + 2.67515i −0.198295 + 0.114486i
\(547\) −11.0124 41.0987i −0.470855 1.75725i −0.636709 0.771104i \(-0.719705\pi\)
0.165854 0.986150i \(-0.446962\pi\)
\(548\) 16.5912 + 4.44559i 0.708739 + 0.189906i
\(549\) −7.47964 + 4.31837i −0.319223 + 0.184304i
\(550\) 0 0
\(551\) 4.76261 + 5.77163i 0.202894 + 0.245880i
\(552\) −7.18426 7.18426i −0.305782 0.305782i
\(553\) 2.78067 10.3776i 0.118246 0.441301i
\(554\) −11.3008 19.5735i −0.480124 0.831599i
\(555\) 0 0
\(556\) −6.79791 11.7743i −0.288296 0.499343i
\(557\) 36.1697 9.69165i 1.53256 0.410648i 0.608707 0.793395i \(-0.291688\pi\)
0.923853 + 0.382747i \(0.125022\pi\)
\(558\) 7.65999 7.65999i 0.324273 0.324273i
\(559\) 7.25520 0.306862
\(560\) 0 0
\(561\) 42.7967 + 24.7087i 1.80688 + 1.04320i
\(562\) 16.8468 + 16.8468i 0.710641 + 0.710641i
\(563\) 2.95561 + 2.95561i 0.124564 + 0.124564i 0.766641 0.642076i \(-0.221927\pi\)
−0.642076 + 0.766641i \(0.721927\pi\)
\(564\) −6.26141 + 10.8451i −0.263653 + 0.456660i
\(565\) 0 0
\(566\) 7.62020 + 4.39952i 0.320301 + 0.184926i
\(567\) −1.42652 + 5.32384i −0.0599082 + 0.223580i
\(568\) −14.7576 3.95427i −0.619213 0.165918i
\(569\) 8.11963 0.340393 0.170196 0.985410i \(-0.445560\pi\)
0.170196 + 0.985410i \(0.445560\pi\)
\(570\) 0 0
\(571\) −30.5277 −1.27754 −0.638772 0.769396i \(-0.720557\pi\)
−0.638772 + 0.769396i \(0.720557\pi\)
\(572\) 8.13464 + 2.17967i 0.340126 + 0.0911366i
\(573\) −4.52511 + 16.8880i −0.189039 + 0.705504i
\(574\) −13.1582 7.59692i −0.549214 0.317089i
\(575\) 0 0
\(576\) −0.765131 + 1.32525i −0.0318805 + 0.0552186i
\(577\) 3.75441 + 3.75441i 0.156298 + 0.156298i 0.780924 0.624626i \(-0.214749\pi\)
−0.624626 + 0.780924i \(0.714749\pi\)
\(578\) −33.3798 33.3798i −1.38842 1.38842i
\(579\) 8.06545 + 4.65659i 0.335188 + 0.193521i
\(580\) 0 0
\(581\) 11.7650 0.488095
\(582\) −8.89783 + 8.89783i −0.368827 + 0.368827i
\(583\) 31.6602 8.48332i 1.31123 0.351343i
\(584\) −1.03456 1.79190i −0.0428102 0.0741495i
\(585\) 0 0
\(586\) −9.88949 17.1291i −0.408531 0.707596i
\(587\) −0.526737 + 1.96581i −0.0217407 + 0.0811376i −0.975944 0.218022i \(-0.930040\pi\)
0.954203 + 0.299159i \(0.0967063\pi\)
\(588\) 0.0914838 + 0.0914838i 0.00377273 + 0.00377273i
\(589\) −28.9083 10.7919i −1.19115 0.444673i
\(590\) 0 0
\(591\) 22.3308 12.8927i 0.918565 0.530334i
\(592\) 0.844978 + 0.226411i 0.0347284 + 0.00930544i
\(593\) −3.63727 13.5745i −0.149365 0.557437i −0.999522 0.0309085i \(-0.990160\pi\)
0.850157 0.526529i \(-0.176507\pi\)
\(594\) 24.1961 13.9696i 0.992778 0.573180i
\(595\) 0 0
\(596\) −9.51066 −0.389572
\(597\) −3.95224 + 3.95224i −0.161754 + 0.161754i
\(598\) −3.59085 13.4012i −0.146841 0.548017i
\(599\) 20.6686 35.7990i 0.844495 1.46271i −0.0415632 0.999136i \(-0.513234\pi\)
0.886059 0.463573i \(-0.153433\pi\)
\(600\) 0 0
\(601\) 41.7390i 1.70257i −0.524704 0.851285i \(-0.675824\pi\)
0.524704 0.851285i \(-0.324176\pi\)
\(602\) −3.02383 11.2851i −0.123242 0.459945i
\(603\) −0.556925 + 2.07847i −0.0226797 + 0.0846419i
\(604\) 3.10564 5.37913i 0.126367 0.218874i
\(605\) 0 0
\(606\) 4.00698 + 6.94029i 0.162772 + 0.281930i
\(607\) −16.1858 + 16.1858i −0.656963 + 0.656963i −0.954660 0.297697i \(-0.903781\pi\)
0.297697 + 0.954660i \(0.403781\pi\)
\(608\) 4.33904 + 0.415613i 0.175971 + 0.0168553i
\(609\) 5.54816i 0.224823i
\(610\) 0 0
\(611\) −14.8094 + 8.55019i −0.599122 + 0.345903i
\(612\) −11.8440 + 3.17359i −0.478765 + 0.128285i
\(613\) −19.2434 5.15626i −0.777235 0.208260i −0.151670 0.988431i \(-0.548465\pi\)
−0.625566 + 0.780172i \(0.715132\pi\)
\(614\) 10.7201 + 6.18923i 0.432627 + 0.249777i
\(615\) 0 0
\(616\) 13.5614i 0.546406i
\(617\) −14.9980 + 4.01870i −0.603796 + 0.161787i −0.547751 0.836642i \(-0.684516\pi\)
−0.0560454 + 0.998428i \(0.517849\pi\)
\(618\) 10.5667 2.83134i 0.425056 0.113893i
\(619\) 32.8578i 1.32067i −0.750973 0.660333i \(-0.770415\pi\)
0.750973 0.660333i \(-0.229585\pi\)
\(620\) 0 0
\(621\) −39.8613 23.0139i −1.59958 0.923516i
\(622\) −12.5240 3.35580i −0.502168 0.134555i
\(623\) 27.1093 7.26390i 1.08611 0.291022i
\(624\) 1.73810 1.00349i 0.0695795 0.0401718i
\(625\) 0 0
\(626\) 4.18956i 0.167449i
\(627\) −21.8932 15.5997i −0.874329 0.622994i
\(628\) 10.1321 10.1321i 0.404316 0.404316i
\(629\) 3.50477 + 6.07045i 0.139744 + 0.242045i
\(630\) 0 0
\(631\) 16.1438 27.9620i 0.642676 1.11315i −0.342157 0.939643i \(-0.611157\pi\)
0.984833 0.173505i \(-0.0555093\pi\)
\(632\) −1.04308 + 3.89281i −0.0414913 + 0.154848i
\(633\) 0.721077 + 2.69110i 0.0286602 + 0.106961i
\(634\) 8.43617i 0.335043i
\(635\) 0 0
\(636\) 3.90560 6.76470i 0.154867 0.268238i
\(637\) 0.0457255 + 0.170650i 0.00181171 + 0.00676140i
\(638\) −6.17520 + 6.17520i −0.244479 + 0.244479i
\(639\) −23.3796 −0.924882
\(640\) 0 0
\(641\) −5.07111 + 2.92781i −0.200297 + 0.115642i −0.596794 0.802394i \(-0.703559\pi\)
0.396497 + 0.918036i \(0.370226\pi\)
\(642\) 2.90596 + 10.8452i 0.114689 + 0.428026i
\(643\) −10.6783 2.86125i −0.421113 0.112837i 0.0420388 0.999116i \(-0.486615\pi\)
−0.463151 + 0.886279i \(0.653281\pi\)
\(644\) −19.3483 + 11.1707i −0.762429 + 0.440189i
\(645\) 0 0
\(646\) 22.2300 + 26.9397i 0.874627 + 1.05993i
\(647\) −24.0362 24.0362i −0.944960 0.944960i 0.0536023 0.998562i \(-0.482930\pi\)
−0.998562 + 0.0536023i \(0.982930\pi\)
\(648\) 0.535110 1.99706i 0.0210211 0.0784518i
\(649\) 36.5637 + 63.3303i 1.43525 + 2.48593i
\(650\) 0 0
\(651\) 11.4394 + 19.8135i 0.448344 + 0.776554i
\(652\) −2.43241 + 0.651763i −0.0952606 + 0.0255250i
\(653\) 2.19175 2.19175i 0.0857697 0.0857697i −0.662920 0.748690i \(-0.730683\pi\)
0.748690 + 0.662920i \(0.230683\pi\)
\(654\) 5.10598 0.199659
\(655\) 0 0
\(656\) 4.93587 + 2.84972i 0.192713 + 0.111263i
\(657\) −2.23890 2.23890i −0.0873479 0.0873479i
\(658\) 19.4716 + 19.4716i 0.759082 + 0.759082i
\(659\) 2.00998 3.48139i 0.0782978 0.135616i −0.824218 0.566273i \(-0.808385\pi\)
0.902516 + 0.430657i \(0.141718\pi\)
\(660\) 0 0
\(661\) −9.46361 5.46382i −0.368092 0.212518i 0.304533 0.952502i \(-0.401500\pi\)
−0.672624 + 0.739984i \(0.734833\pi\)
\(662\) −2.49141 + 9.29808i −0.0968315 + 0.361380i
\(663\) 15.5337 + 4.16225i 0.603280 + 0.161648i
\(664\) −4.41324 −0.171267
\(665\) 0 0
\(666\) 1.33865 0.0518717
\(667\) 13.8968 + 3.72364i 0.538087 + 0.144180i
\(668\) 3.47427 12.9661i 0.134424 0.501675i
\(669\) 21.6625 + 12.5069i 0.837521 + 0.483543i
\(670\) 0 0
\(671\) −14.3557 + 24.8649i −0.554197 + 0.959897i
\(672\) −2.28528 2.28528i −0.0881566 0.0881566i
\(673\) 7.33331 + 7.33331i 0.282679 + 0.282679i 0.834176 0.551498i \(-0.185944\pi\)
−0.551498 + 0.834176i \(0.685944\pi\)
\(674\) 3.18272 + 1.83754i 0.122594 + 0.0707795i
\(675\) 0 0
\(676\) −10.2594 −0.394592
\(677\) 20.7086 20.7086i 0.795895 0.795895i −0.186550 0.982445i \(-0.559731\pi\)
0.982445 + 0.186550i \(0.0597307\pi\)
\(678\) −11.4809 + 3.07630i −0.440922 + 0.118145i
\(679\) 13.8352 + 23.9632i 0.530944 + 0.919623i
\(680\) 0 0
\(681\) 1.98573 + 3.43939i 0.0760935 + 0.131798i
\(682\) 9.32062 34.7850i 0.356905 1.33199i
\(683\) 24.6294 + 24.6294i 0.942417 + 0.942417i 0.998430 0.0560135i \(-0.0178390\pi\)
−0.0560135 + 0.998430i \(0.517839\pi\)
\(684\) 6.57823 1.10420i 0.251525 0.0422201i
\(685\) 0 0
\(686\) −15.9144 + 9.18820i −0.607616 + 0.350807i
\(687\) 8.73014 + 2.33923i 0.333075 + 0.0892473i
\(688\) 1.13429 + 4.23321i 0.0432442 + 0.161390i
\(689\) 9.23745 5.33325i 0.351919 0.203180i
\(690\) 0 0
\(691\) −25.0871 −0.954359 −0.477179 0.878806i \(-0.658341\pi\)
−0.477179 + 0.878806i \(0.658341\pi\)
\(692\) −7.31252 + 7.31252i −0.277980 + 0.277980i
\(693\) −5.37116 20.0454i −0.204034 0.761464i
\(694\) 0.215249 0.372822i 0.00817073 0.0141521i
\(695\) 0 0
\(696\) 2.08120i 0.0788878i
\(697\) 11.8200 + 44.1128i 0.447714 + 1.67089i
\(698\) −2.96482 + 11.0648i −0.112220 + 0.418810i
\(699\) 6.83477 11.8382i 0.258515 0.447761i
\(700\) 0 0
\(701\) −5.67140 9.82316i −0.214206 0.371016i 0.738821 0.673902i \(-0.235383\pi\)
−0.953027 + 0.302887i \(0.902050\pi\)
\(702\) 6.42912 6.42912i 0.242652 0.242652i
\(703\) −1.58300 3.46898i −0.0597040 0.130835i
\(704\) 5.08711i 0.191728i
\(705\) 0 0
\(706\) −26.6597 + 15.3920i −1.00335 + 0.579284i
\(707\) 17.0218 4.56098i 0.640171 0.171533i
\(708\) 16.8334 + 4.51051i 0.632640 + 0.169515i
\(709\) −23.3759 13.4961i −0.877901 0.506856i −0.00793506 0.999969i \(-0.502526\pi\)
−0.869966 + 0.493112i \(0.835859\pi\)
\(710\) 0 0
\(711\) 6.16716i 0.231287i
\(712\) −10.1691 + 2.72481i −0.381104 + 0.102116i
\(713\) −57.3057 + 15.3550i −2.14612 + 0.575050i
\(714\) 25.8966i 0.969156i
\(715\) 0 0
\(716\) 13.2474 + 7.64838i 0.495078 + 0.285833i
\(717\) −15.6713 4.19911i −0.585255 0.156819i
\(718\) 35.9587 9.63510i 1.34197 0.359579i
\(719\) 5.21897 3.01318i 0.194635 0.112372i −0.399516 0.916726i \(-0.630822\pi\)
0.594151 + 0.804354i \(0.297488\pi\)
\(720\) 0 0
\(721\) 24.0553i 0.895867i
\(722\) −10.6404 15.7411i −0.395995 0.585822i
\(723\) −16.0364 + 16.0364i −0.596401 + 0.596401i
\(724\) −7.72382 13.3780i −0.287053 0.497191i
\(725\) 0 0
\(726\) 9.01893 15.6213i 0.334724 0.579759i
\(727\) −0.343444 + 1.28175i −0.0127376 + 0.0475375i −0.972002 0.234972i \(-0.924500\pi\)
0.959265 + 0.282509i \(0.0911668\pi\)
\(728\) −1.14223 4.26287i −0.0423339 0.157992i
\(729\) 23.1387i 0.856989i
\(730\) 0 0
\(731\) −17.5584 + 30.4120i −0.649421 + 1.12483i
\(732\) 1.77092 + 6.60918i 0.0654553 + 0.244282i
\(733\) 23.2056 23.2056i 0.857120 0.857120i −0.133878 0.990998i \(-0.542743\pi\)
0.990998 + 0.133878i \(0.0427430\pi\)
\(734\) −0.937051 −0.0345872
\(735\) 0 0
\(736\) 7.25785 4.19032i 0.267528 0.154457i
\(737\) 1.85141 + 6.90954i 0.0681974 + 0.254516i
\(738\) 8.42447 + 2.25733i 0.310109 + 0.0830935i
\(739\) 1.10497 0.637953i 0.0406469 0.0234675i −0.479539 0.877521i \(-0.659196\pi\)
0.520186 + 0.854053i \(0.325863\pi\)
\(740\) 0 0
\(741\) −8.19575 3.05960i −0.301078 0.112397i
\(742\) −12.1456 12.1456i −0.445878 0.445878i
\(743\) 0.0708104 0.264268i 0.00259778 0.00969505i −0.964615 0.263663i \(-0.915069\pi\)
0.967213 + 0.253968i \(0.0817359\pi\)
\(744\) −4.29108 7.43238i −0.157319 0.272484i
\(745\) 0 0
\(746\) 12.9511 + 22.4320i 0.474174 + 0.821294i
\(747\) −6.52331 + 1.74791i −0.238675 + 0.0639528i
\(748\) −28.8234 + 28.8234i −1.05389 + 1.05389i
\(749\) 24.6893 0.902126
\(750\) 0 0
\(751\) 8.25436 + 4.76566i 0.301206 + 0.173901i 0.642984 0.765879i \(-0.277696\pi\)
−0.341779 + 0.939780i \(0.611029\pi\)
\(752\) −7.30411 7.30411i −0.266353 0.266353i
\(753\) −15.7123 15.7123i −0.572588 0.572588i
\(754\) −1.42098 + 2.46121i −0.0517490 + 0.0896320i
\(755\) 0 0
\(756\) −12.6797 7.32062i −0.461156 0.266248i
\(757\) 6.68168 24.9364i 0.242850 0.906328i −0.731602 0.681732i \(-0.761227\pi\)
0.974452 0.224596i \(-0.0721063\pi\)
\(758\) −31.6974 8.49328i −1.15130 0.308490i
\(759\) −51.6855 −1.87606
\(760\) 0 0
\(761\) 33.4904 1.21403 0.607014 0.794691i \(-0.292367\pi\)
0.607014 + 0.794691i \(0.292367\pi\)
\(762\) 13.8528 + 3.71185i 0.501834 + 0.134466i
\(763\) 2.90596 10.8452i 0.105203 0.392622i
\(764\) −12.4895 7.21080i −0.451853 0.260878i
\(765\) 0 0
\(766\) −5.42005 + 9.38781i −0.195835 + 0.339195i
\(767\) 16.8274 + 16.8274i 0.607603 + 0.607603i
\(768\) 0.857245 + 0.857245i 0.0309332 + 0.0309332i
\(769\) −40.9858 23.6631i −1.47798 0.853315i −0.478294 0.878200i \(-0.658745\pi\)
−0.999690 + 0.0248847i \(0.992078\pi\)
\(770\) 0 0
\(771\) −1.87210 −0.0674222
\(772\) −5.43204 + 5.43204i −0.195503 + 0.195503i
\(773\) 31.0899 8.33051i 1.11823 0.299628i 0.348060 0.937472i \(-0.386840\pi\)
0.770165 + 0.637845i \(0.220174\pi\)
\(774\) 3.35322 + 5.80795i 0.120529 + 0.208763i
\(775\) 0 0
\(776\) −5.18979 8.98897i −0.186302 0.322685i
\(777\) −0.731732 + 2.73086i −0.0262507 + 0.0979691i
\(778\) 15.3183 + 15.3183i 0.549187 + 0.549187i
\(779\) −4.11258 24.5005i −0.147348 0.877823i
\(780\) 0 0
\(781\) −67.3089 + 38.8608i −2.40850 + 1.39055i
\(782\) 64.8649 + 17.3805i 2.31956 + 0.621525i
\(783\) 2.44025 + 9.10713i 0.0872074 + 0.325462i
\(784\) −0.0924208 + 0.0533592i −0.00330074 + 0.00190569i
\(785\) 0 0
\(786\) −7.03898 −0.251072
\(787\) −20.9433 + 20.9433i −0.746547 + 0.746547i −0.973829 0.227282i \(-0.927016\pi\)
0.227282 + 0.973829i \(0.427016\pi\)
\(788\) 5.50490 + 20.5446i 0.196104 + 0.731870i
\(789\) 0.678886 1.17586i 0.0241690 0.0418619i
\(790\) 0 0
\(791\) 26.1365i 0.929308i
\(792\) 2.01481 + 7.51937i 0.0715931 + 0.267189i
\(793\) −2.41826 + 9.02508i −0.0858751 + 0.320490i
\(794\) 12.4300 21.5295i 0.441126 0.764053i
\(795\) 0 0
\(796\) −2.30520 3.99272i −0.0817056 0.141518i
\(797\) −21.1881 + 21.1881i −0.750521 + 0.750521i −0.974576 0.224056i \(-0.928070\pi\)
0.224056 + 0.974576i \(0.428070\pi\)
\(798\) −1.34321 + 14.0232i −0.0475490 + 0.496417i
\(799\) 82.7696i 2.92818i
\(800\) 0 0
\(801\) −13.9520 + 8.05518i −0.492969 + 0.284616i
\(802\) 28.1812 7.55113i 0.995112 0.266640i
\(803\) −10.1672 2.72428i −0.358791 0.0961377i
\(804\) 1.47633 + 0.852362i 0.0520663 + 0.0300605i
\(805\) 0 0
\(806\) 11.7193i 0.412794i
\(807\) −4.55064 + 1.21934i −0.160190 + 0.0429228i
\(808\) −6.38515 + 1.71090i −0.224629 + 0.0601891i
\(809\) 17.3630i 0.610451i −0.952280 0.305226i \(-0.901268\pi\)
0.952280 0.305226i \(-0.0987319\pi\)
\(810\) 0 0
\(811\) −7.18151 4.14625i −0.252177 0.145594i 0.368584 0.929595i \(-0.379843\pi\)
−0.620761 + 0.784000i \(0.713176\pi\)
\(812\) 4.42052 + 1.18447i 0.155130 + 0.0415669i
\(813\) 3.49827 0.937358i 0.122690 0.0328746i
\(814\) 3.85393 2.22507i 0.135080 0.0779885i
\(815\) 0 0
\(816\) 9.71423i 0.340066i
\(817\) 11.0854 15.5576i 0.387830 0.544293i
\(818\) −9.08015 + 9.08015i −0.317480 + 0.317480i
\(819\) −3.37671 5.84864i −0.117992 0.204368i
\(820\) 0 0
\(821\) 6.91289 11.9735i 0.241261 0.417877i −0.719812 0.694169i \(-0.755772\pi\)
0.961074 + 0.276292i \(0.0891055\pi\)
\(822\) 5.38951 20.1139i 0.187981 0.701553i
\(823\) −0.304420 1.13611i −0.0106114 0.0396023i 0.960417 0.278566i \(-0.0898590\pi\)
−0.971029 + 0.238963i \(0.923192\pi\)
\(824\) 9.02353i 0.314350i
\(825\) 0 0
\(826\) 19.1608 33.1875i 0.666690 1.15474i
\(827\) −8.41337 31.3991i −0.292562 1.09185i −0.943135 0.332411i \(-0.892138\pi\)
0.650573 0.759444i \(-0.274529\pi\)
\(828\) 9.06835 9.06835i 0.315147 0.315147i
\(829\) −23.1927 −0.805516 −0.402758 0.915307i \(-0.631948\pi\)
−0.402758 + 0.915307i \(0.631948\pi\)
\(830\) 0 0
\(831\) −23.7295 + 13.7002i −0.823167 + 0.475256i
\(832\) 0.428469 + 1.59907i 0.0148545 + 0.0554377i
\(833\) −0.825984 0.221322i −0.0286186 0.00766834i
\(834\) −14.2743 + 8.24129i −0.494280 + 0.285373i
\(835\) 0 0
\(836\) 17.1031 14.1131i 0.591523 0.488111i
\(837\) −27.4919 27.4919i −0.950261 0.950261i
\(838\) −4.60480 + 17.1854i −0.159070 + 0.593659i
\(839\) 25.4002 + 43.9944i 0.876912 + 1.51886i 0.854712 + 0.519103i \(0.173734\pi\)
0.0222001 + 0.999754i \(0.492933\pi\)
\(840\) 0 0
\(841\) 13.0265 + 22.5625i 0.449189 + 0.778017i
\(842\) 32.9205 8.82102i 1.13451 0.303992i
\(843\) 20.4239 20.4239i 0.703435 0.703435i
\(844\) −2.29808 −0.0791032
\(845\) 0 0
\(846\) −13.6892 7.90348i −0.470645 0.271727i
\(847\) −28.0469 28.0469i −0.963703 0.963703i
\(848\) 4.55600 + 4.55600i 0.156454 + 0.156454i
\(849\) 5.33366 9.23817i 0.183051 0.317053i
\(850\) 0 0
\(851\) −6.34906 3.66563i −0.217643 0.125656i
\(852\) −4.79387 + 17.8910i −0.164235 + 0.612935i
\(853\) 35.0879 + 9.40178i 1.20139 + 0.321911i 0.803377 0.595470i \(-0.203034\pi\)
0.398010 + 0.917381i \(0.369701\pi\)
\(854\) 15.0459 0.514861
\(855\) 0 0
\(856\) −9.26134 −0.316546
\(857\) 15.7194 + 4.21201i 0.536966 + 0.143880i 0.517103 0.855923i \(-0.327010\pi\)
0.0198628 + 0.999803i \(0.493677\pi\)
\(858\) 2.64247 9.86185i 0.0902126 0.336678i
\(859\) 26.5596 + 15.3342i 0.906201 + 0.523196i 0.879207 0.476440i \(-0.158073\pi\)
0.0269944 + 0.999636i \(0.491406\pi\)
\(860\) 0 0
\(861\) −9.20995 + 15.9521i −0.313874 + 0.543646i
\(862\) 17.1947 + 17.1947i 0.585652 + 0.585652i
\(863\) −7.66348 7.66348i −0.260868 0.260868i 0.564539 0.825407i \(-0.309054\pi\)
−0.825407 + 0.564539i \(0.809054\pi\)
\(864\) 4.75635 + 2.74608i 0.161814 + 0.0934235i
\(865\) 0 0
\(866\) −25.7731 −0.875806
\(867\) −40.4673 + 40.4673i −1.37434 + 1.37434i
\(868\) −18.2287 + 4.88436i −0.618722 + 0.165786i
\(869\) 10.2509 + 17.7550i 0.347737 + 0.602298i
\(870\) 0 0
\(871\) 1.16393 + 2.01599i 0.0394383 + 0.0683092i
\(872\) −1.09007 + 4.06820i −0.0369145 + 0.137767i
\(873\) −11.2313 11.2313i −0.380122 0.380122i
\(874\) −34.2234 12.7761i −1.15762 0.432158i
\(875\) 0 0
\(876\) −2.17237 + 1.25422i −0.0733977 + 0.0423762i
\(877\) 13.5051 + 3.61868i 0.456035 + 0.122194i 0.479522 0.877530i \(-0.340810\pi\)
−0.0234870 + 0.999724i \(0.507477\pi\)
\(878\) 0.265341 + 0.990266i 0.00895482 + 0.0334198i
\(879\) −20.7661 + 11.9893i −0.700422 + 0.404389i
\(880\) 0 0
\(881\) 24.2524 0.817085 0.408542 0.912739i \(-0.366037\pi\)
0.408542 + 0.912739i \(0.366037\pi\)
\(882\) −0.115476 + 0.115476i −0.00388827 + 0.00388827i
\(883\) 1.87920 + 7.01327i 0.0632401 + 0.236015i 0.990310 0.138873i \(-0.0443479\pi\)
−0.927070 + 0.374888i \(0.877681\pi\)
\(884\) −6.63257 + 11.4879i −0.223077 + 0.386382i
\(885\) 0 0
\(886\) 8.29575i 0.278701i
\(887\) 4.01762 + 14.9940i 0.134899 + 0.503449i 0.999998 + 0.00184854i \(0.000588408\pi\)
−0.865100 + 0.501600i \(0.832745\pi\)
\(888\) 0.274484 1.02439i 0.00921109 0.0343763i
\(889\) 15.7681 27.3111i 0.528844 0.915985i
\(890\) 0 0
\(891\) −5.25882 9.10854i −0.176177 0.305148i
\(892\) −14.5896 + 14.5896i −0.488496 + 0.488496i
\(893\) −4.29310 + 44.8204i −0.143663 + 1.49986i
\(894\) 11.5300i 0.385622i
\(895\) 0 0
\(896\) 2.30869 1.33292i 0.0771278 0.0445298i
\(897\) −16.2467 + 4.35328i −0.542460 + 0.145352i
\(898\) −18.9353 5.07369i −0.631878 0.169311i
\(899\) 10.5245 + 6.07634i 0.351013 + 0.202657i
\(900\) 0 0
\(901\) 51.6282i 1.71998i
\(902\) 28.0058 7.50413i 0.932491 0.249860i
\(903\) −13.6812 + 3.66587i −0.455282 + 0.121992i
\(904\) 9.80423i 0.326084i
\(905\) 0 0
\(906\) −6.52127 3.76506i −0.216655 0.125086i
\(907\) 32.3118 + 8.65791i 1.07289 + 0.287481i 0.751682 0.659526i \(-0.229243\pi\)
0.321213 + 0.947007i \(0.395909\pi\)
\(908\) −3.16428 + 0.847867i −0.105010 + 0.0281375i
\(909\) −8.76040 + 5.05782i −0.290564 + 0.167757i
\(910\) 0 0
\(911\) 22.3197i 0.739486i −0.929134 0.369743i \(-0.879446\pi\)
0.929134 0.369743i \(-0.120554\pi\)
\(912\) 0.503858 5.26034i 0.0166844 0.174187i
\(913\) −15.8750 + 15.8750i −0.525386 + 0.525386i
\(914\) 13.7904 + 23.8857i 0.456146 + 0.790069i
\(915\) 0 0
\(916\) −3.72758 + 6.45636i −0.123163 + 0.213324i
\(917\) −4.00609 + 14.9509i −0.132293 + 0.493723i
\(918\) 11.3901 + 42.5085i 0.375930 + 1.40299i
\(919\) 50.0242i 1.65015i 0.565027 + 0.825073i \(0.308866\pi\)
−0.565027 + 0.825073i \(0.691134\pi\)
\(920\) 0 0
\(921\) 7.50337 12.9962i 0.247245 0.428240i
\(922\) 1.99276 + 7.43710i 0.0656282 + 0.244928i
\(923\) −17.8846 + 17.8846i −0.588678 + 0.588678i
\(924\) −16.4409 −0.540866
\(925\) 0 0
\(926\) 15.4625 8.92725i 0.508128 0.293368i
\(927\) 3.57387 + 13.3379i 0.117381 + 0.438073i
\(928\) −1.65821 0.444315i −0.0544333 0.0145854i
\(929\) 11.8563 6.84526i 0.388994 0.224586i −0.292730 0.956195i \(-0.594564\pi\)
0.681724 + 0.731609i \(0.261230\pi\)
\(930\) 0 0
\(931\) 0.435798 + 0.162690i 0.0142827 + 0.00533194i
\(932\) 7.97295 + 7.97295i 0.261163 + 0.261163i
\(933\) −4.06833 + 15.1832i −0.133191 + 0.497076i
\(934\) −7.73216 13.3925i −0.253004 0.438216i
\(935\) 0 0
\(936\) 1.26666 + 2.19392i 0.0414020 + 0.0717104i
\(937\) 4.32476 1.15881i 0.141284 0.0378568i −0.187484 0.982268i \(-0.560033\pi\)
0.328768 + 0.944411i \(0.393367\pi\)
\(938\) 2.65066 2.65066i 0.0865470 0.0865470i
\(939\) −5.07912 −0.165751
\(940\) 0 0
\(941\) −29.3527 16.9468i −0.956871 0.552450i −0.0616622 0.998097i \(-0.519640\pi\)
−0.895209 + 0.445648i \(0.852973\pi\)
\(942\) −12.2835 12.2835i −0.400217 0.400217i
\(943\) −33.7750 33.7750i −1.09986 1.09986i
\(944\) −7.18753 + 12.4492i −0.233934 + 0.405186i
\(945\) 0 0
\(946\) 19.3076 + 11.1472i 0.627744 + 0.362428i
\(947\) −13.1384 + 49.0334i −0.426942 + 1.59337i 0.332703 + 0.943032i \(0.392039\pi\)
−0.759645 + 0.650338i \(0.774627\pi\)
\(948\) 4.71936 + 1.26455i 0.153278 + 0.0410706i
\(949\) −3.42537 −0.111192
\(950\) 0 0
\(951\) 10.2274 0.331646
\(952\) 20.6332 + 5.52865i 0.668726 + 0.179185i
\(953\) 2.55499 9.53536i 0.0827643 0.308881i −0.912117 0.409930i \(-0.865553\pi\)
0.994881 + 0.101049i \(0.0322199\pi\)
\(954\) 8.53876 + 4.92986i 0.276453 + 0.159610i
\(955\) 0 0
\(956\) 6.69131 11.5897i 0.216413 0.374837i
\(957\) 7.48636 + 7.48636i 0.242000 + 0.242000i
\(958\) −1.73744 1.73744i −0.0561341 0.0561341i
\(959\) −39.6550 22.8948i −1.28053 0.739313i
\(960\) 0 0
\(961\) −19.1135 −0.616563
\(962\) 1.02402 1.02402i 0.0330158 0.0330158i
\(963\) −13.6894 + 3.66806i −0.441134 + 0.118201i
\(964\) −9.35347 16.2007i −0.301255 0.521789i
\(965\) 0 0
\(966\) 13.5426 + 23.4564i 0.435726 + 0.754699i
\(967\) −5.63481 + 21.0294i −0.181203 + 0.676260i 0.814208 + 0.580573i \(0.197172\pi\)
−0.995411 + 0.0956872i \(0.969495\pi\)
\(968\) 10.5208 + 10.5208i 0.338153 + 0.338153i
\(969\) 32.6597 26.9500i 1.04918 0.865759i
\(970\) 0 0
\(971\) −15.8347 + 9.14215i −0.508159 + 0.293386i −0.732077 0.681222i \(-0.761449\pi\)
0.223918 + 0.974608i \(0.428115\pi\)
\(972\) 13.4940 + 3.61570i 0.432819 + 0.115974i
\(973\) 9.38072 + 35.0093i 0.300732 + 1.12235i
\(974\) −8.91990 + 5.14991i −0.285812 + 0.165014i
\(975\) 0 0
\(976\) −5.64396 −0.180659
\(977\) 2.79812 2.79812i 0.0895197 0.0895197i −0.660929 0.750449i \(-0.729838\pi\)
0.750449 + 0.660929i \(0.229838\pi\)
\(978\) 0.790150 + 2.94888i 0.0252662 + 0.0942948i
\(979\) −26.7781 + 46.3811i −0.855833 + 1.48235i
\(980\) 0 0
\(981\) 6.44503i 0.205774i
\(982\) −5.41019 20.1911i −0.172646 0.644324i
\(983\) −1.59078 + 5.93687i −0.0507380 + 0.189357i −0.986644 0.162894i \(-0.947917\pi\)
0.935906 + 0.352251i \(0.114584\pi\)
\(984\) 3.45480 5.98388i 0.110135 0.190759i
\(985\) 0 0
\(986\) −6.87786 11.9128i −0.219036 0.379381i
\(987\) 23.6060 23.6060i 0.751386 0.751386i
\(988\) 4.18745 5.87680i 0.133221 0.186966i
\(989\) 36.7285i 1.16790i
\(990\) 0 0
\(991\) −3.11089 + 1.79607i −0.0988205 + 0.0570541i −0.548596 0.836088i \(-0.684837\pi\)
0.449775 + 0.893142i \(0.351504\pi\)
\(992\) 6.83787 1.83220i 0.217103 0.0581725i
\(993\) 11.2723 + 3.02041i 0.357716 + 0.0958498i
\(994\) 35.2725 + 20.3646i 1.11877 + 0.645925i
\(995\) 0 0
\(996\) 5.35029i 0.169531i
\(997\) −19.0140 + 5.09479i −0.602180 + 0.161354i −0.547014 0.837124i \(-0.684236\pi\)
−0.0551662 + 0.998477i \(0.517569\pi\)
\(998\) 26.9683 7.22613i 0.853666 0.228739i
\(999\) 4.80446i 0.152006i
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 950.2.q.f.107.7 yes 32
5.2 odd 4 inner 950.2.q.f.943.2 yes 32
5.3 odd 4 inner 950.2.q.f.943.7 yes 32
5.4 even 2 inner 950.2.q.f.107.2 32
19.8 odd 6 inner 950.2.q.f.407.7 yes 32
95.8 even 12 inner 950.2.q.f.293.7 yes 32
95.27 even 12 inner 950.2.q.f.293.2 yes 32
95.84 odd 6 inner 950.2.q.f.407.2 yes 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
950.2.q.f.107.2 32 5.4 even 2 inner
950.2.q.f.107.7 yes 32 1.1 even 1 trivial
950.2.q.f.293.2 yes 32 95.27 even 12 inner
950.2.q.f.293.7 yes 32 95.8 even 12 inner
950.2.q.f.407.2 yes 32 95.84 odd 6 inner
950.2.q.f.407.7 yes 32 19.8 odd 6 inner
950.2.q.f.943.2 yes 32 5.2 odd 4 inner
950.2.q.f.943.7 yes 32 5.3 odd 4 inner