Properties

Label 700.2.t.c.299.2
Level $700$
Weight $2$
Character 700.299
Analytic conductor $5.590$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [700,2,Mod(199,700)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(700, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 3, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("700.199");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 700 = 2^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 700.t (of order \(6\), degree \(2\), not 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: \(5.58952814149\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(16\) over \(\Q(\zeta_{6})\)
Twist minimal: no (minimal twist has level 140)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 299.2
Character \(\chi\) \(=\) 700.299
Dual form 700.2.t.c.199.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.32225 - 0.501653i) q^{2} +(-1.55083 + 0.895374i) q^{3} +(1.49669 + 1.32662i) q^{4} +(2.49976 - 0.405928i) q^{6} +(2.56598 - 0.644798i) q^{7} +(-1.31349 - 2.50494i) q^{8} +(0.103389 - 0.179074i) q^{9} +O(q^{10})\) \(q+(-1.32225 - 0.501653i) q^{2} +(-1.55083 + 0.895374i) q^{3} +(1.49669 + 1.32662i) q^{4} +(2.49976 - 0.405928i) q^{6} +(2.56598 - 0.644798i) q^{7} +(-1.31349 - 2.50494i) q^{8} +(0.103389 - 0.179074i) q^{9} +(3.66757 - 2.11747i) q^{11} +(-3.50894 - 0.717273i) q^{12} -2.98261 q^{13} +(-3.71633 - 0.434646i) q^{14} +(0.480152 + 3.97108i) q^{16} +(-1.10901 - 1.92087i) q^{17} +(-0.226539 + 0.184916i) q^{18} +(2.28341 - 3.95499i) q^{19} +(-3.40207 + 3.29748i) q^{21} +(-5.91168 + 0.959979i) q^{22} +(-1.02992 + 1.78388i) q^{23} +(4.27987 + 2.70868i) q^{24} +(3.94375 + 1.49624i) q^{26} -5.00196i q^{27} +(4.69587 + 2.43902i) q^{28} -6.42784 q^{29} +(1.20072 + 2.07971i) q^{31} +(1.35722 - 5.49163i) q^{32} +(-3.79186 + 6.56769i) q^{33} +(0.502784 + 3.09621i) q^{34} +(0.392304 - 0.130861i) q^{36} +(3.74511 + 2.16224i) q^{37} +(-5.00327 + 4.08400i) q^{38} +(4.62553 - 2.67055i) q^{39} -4.88552i q^{41} +(6.15257 - 2.65344i) q^{42} +12.3733 q^{43} +(8.29829 + 1.69628i) q^{44} +(2.25671 - 1.84207i) q^{46} +(5.85833 + 3.38231i) q^{47} +(-4.30023 - 5.72856i) q^{48} +(6.16847 - 3.30908i) q^{49} +(3.43979 + 1.98597i) q^{51} +(-4.46404 - 3.95679i) q^{52} +(11.1174 - 6.41865i) q^{53} +(-2.50925 + 6.61384i) q^{54} +(-4.98557 - 5.58069i) q^{56} +8.17803i q^{57} +(8.49921 + 3.22455i) q^{58} +(-6.99014 - 12.1073i) q^{59} +(0.0195769 + 0.0113027i) q^{61} +(-0.544360 - 3.35224i) q^{62} +(0.149826 - 0.526165i) q^{63} +(-4.54948 + 6.58044i) q^{64} +(8.30848 - 6.78193i) q^{66} +(2.53010 + 4.38227i) q^{67} +(0.888418 - 4.34619i) q^{68} -3.68867i q^{69} -4.07391i q^{71} +(-0.584371 - 0.0237699i) q^{72} +(1.66682 + 2.88701i) q^{73} +(-3.86728 - 4.73777i) q^{74} +(8.66433 - 2.89016i) q^{76} +(8.04555 - 7.79822i) q^{77} +(-7.45579 + 1.21072i) q^{78} +(3.14131 + 1.81364i) q^{79} +(4.78879 + 8.29442i) q^{81} +(-2.45084 + 6.45988i) q^{82} -11.7373i q^{83} +(-9.46634 + 0.422052i) q^{84} +(-16.3606 - 6.20713i) q^{86} +(9.96851 - 5.75532i) q^{87} +(-10.1215 - 6.40577i) q^{88} +(14.4625 + 8.34991i) q^{89} +(-7.65330 + 1.92318i) q^{91} +(-3.90801 + 1.30359i) q^{92} +(-3.72424 - 2.15019i) q^{93} +(-6.04943 - 7.41111i) q^{94} +(2.81223 + 9.73181i) q^{96} -12.0198 q^{97} +(-9.81627 + 1.28099i) q^{98} -0.875689i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q + 2 q^{4} + 16 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 32 q + 2 q^{4} + 16 q^{9} - 14 q^{12} - 8 q^{13} - 2 q^{14} - 14 q^{16} + 54 q^{18} - 12 q^{21} - 36 q^{24} + 30 q^{26} + 32 q^{28} + 40 q^{29} + 60 q^{32} - 24 q^{33} + 60 q^{36} - 60 q^{37} - 46 q^{38} + 78 q^{42} + 18 q^{44} + 2 q^{46} - 28 q^{48} + 16 q^{49} - 46 q^{52} - 12 q^{53} - 12 q^{54} - 4 q^{56} + 42 q^{58} + 24 q^{61} + 8 q^{62} - 4 q^{64} + 24 q^{66} - 4 q^{68} + 90 q^{72} - 24 q^{73} - 38 q^{74} + 20 q^{77} - 36 q^{81} + 8 q^{82} + 20 q^{84} + 28 q^{86} - 78 q^{88} + 60 q^{89} + 72 q^{93} - 18 q^{94} - 60 q^{96} - 48 q^{97} - 124 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/700\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(351\) \(477\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.32225 0.501653i −0.934972 0.354722i
\(3\) −1.55083 + 0.895374i −0.895374 + 0.516944i −0.875696 0.482862i \(-0.839597\pi\)
−0.0196774 + 0.999806i \(0.506264\pi\)
\(4\) 1.49669 + 1.32662i 0.748344 + 0.663311i
\(5\) 0 0
\(6\) 2.49976 0.405928i 1.02052 0.165719i
\(7\) 2.56598 0.644798i 0.969848 0.243711i
\(8\) −1.31349 2.50494i −0.464389 0.885631i
\(9\) 0.103389 0.179074i 0.0344628 0.0596914i
\(10\) 0 0
\(11\) 3.66757 2.11747i 1.10581 0.638442i 0.168072 0.985775i \(-0.446246\pi\)
0.937742 + 0.347333i \(0.112913\pi\)
\(12\) −3.50894 0.717273i −1.01294 0.207059i
\(13\) −2.98261 −0.827227 −0.413613 0.910453i \(-0.635733\pi\)
−0.413613 + 0.910453i \(0.635733\pi\)
\(14\) −3.71633 0.434646i −0.993230 0.116164i
\(15\) 0 0
\(16\) 0.480152 + 3.97108i 0.120038 + 0.992769i
\(17\) −1.10901 1.92087i −0.268976 0.465879i 0.699622 0.714513i \(-0.253352\pi\)
−0.968598 + 0.248634i \(0.920018\pi\)
\(18\) −0.226539 + 0.184916i −0.0533957 + 0.0435850i
\(19\) 2.28341 3.95499i 0.523851 0.907336i −0.475764 0.879573i \(-0.657828\pi\)
0.999615 0.0277631i \(-0.00883842\pi\)
\(20\) 0 0
\(21\) −3.40207 + 3.29748i −0.742391 + 0.719570i
\(22\) −5.91168 + 0.959979i −1.26037 + 0.204668i
\(23\) −1.02992 + 1.78388i −0.214754 + 0.371965i −0.953196 0.302352i \(-0.902228\pi\)
0.738443 + 0.674316i \(0.235562\pi\)
\(24\) 4.27987 + 2.70868i 0.873624 + 0.552907i
\(25\) 0 0
\(26\) 3.94375 + 1.49624i 0.773434 + 0.293436i
\(27\) 5.00196i 0.962627i
\(28\) 4.69587 + 2.43902i 0.887436 + 0.460931i
\(29\) −6.42784 −1.19362 −0.596810 0.802383i \(-0.703565\pi\)
−0.596810 + 0.802383i \(0.703565\pi\)
\(30\) 0 0
\(31\) 1.20072 + 2.07971i 0.215656 + 0.373527i 0.953475 0.301471i \(-0.0974777\pi\)
−0.737819 + 0.674998i \(0.764144\pi\)
\(32\) 1.35722 5.49163i 0.239925 0.970791i
\(33\) −3.79186 + 6.56769i −0.660078 + 1.14329i
\(34\) 0.502784 + 3.09621i 0.0862267 + 0.530996i
\(35\) 0 0
\(36\) 0.392304 0.130861i 0.0653840 0.0218101i
\(37\) 3.74511 + 2.16224i 0.615692 + 0.355470i 0.775190 0.631728i \(-0.217654\pi\)
−0.159498 + 0.987198i \(0.550987\pi\)
\(38\) −5.00327 + 4.08400i −0.811638 + 0.662512i
\(39\) 4.62553 2.67055i 0.740677 0.427630i
\(40\) 0 0
\(41\) 4.88552i 0.762990i −0.924371 0.381495i \(-0.875409\pi\)
0.924371 0.381495i \(-0.124591\pi\)
\(42\) 6.15257 2.65344i 0.949362 0.409435i
\(43\) 12.3733 1.88692 0.943459 0.331490i \(-0.107551\pi\)
0.943459 + 0.331490i \(0.107551\pi\)
\(44\) 8.29829 + 1.69628i 1.25101 + 0.255724i
\(45\) 0 0
\(46\) 2.25671 1.84207i 0.332733 0.271598i
\(47\) 5.85833 + 3.38231i 0.854525 + 0.493360i 0.862175 0.506610i \(-0.169102\pi\)
−0.00764982 + 0.999971i \(0.502435\pi\)
\(48\) −4.30023 5.72856i −0.620685 0.826847i
\(49\) 6.16847 3.30908i 0.881210 0.472725i
\(50\) 0 0
\(51\) 3.43979 + 1.98597i 0.481667 + 0.278091i
\(52\) −4.46404 3.95679i −0.619050 0.548708i
\(53\) 11.1174 6.41865i 1.52710 0.881670i 0.527615 0.849484i \(-0.323086\pi\)
0.999482 0.0321861i \(-0.0102469\pi\)
\(54\) −2.50925 + 6.61384i −0.341465 + 0.900029i
\(55\) 0 0
\(56\) −4.98557 5.58069i −0.666225 0.745751i
\(57\) 8.17803i 1.08321i
\(58\) 8.49921 + 3.22455i 1.11600 + 0.423404i
\(59\) −6.99014 12.1073i −0.910039 1.57623i −0.814006 0.580856i \(-0.802718\pi\)
−0.0960332 0.995378i \(-0.530615\pi\)
\(60\) 0 0
\(61\) 0.0195769 + 0.0113027i 0.00250657 + 0.00144717i 0.501253 0.865301i \(-0.332873\pi\)
−0.498746 + 0.866748i \(0.666206\pi\)
\(62\) −0.544360 3.35224i −0.0691338 0.425735i
\(63\) 0.149826 0.526165i 0.0188763 0.0662905i
\(64\) −4.54948 + 6.58044i −0.568685 + 0.822556i
\(65\) 0 0
\(66\) 8.30848 6.78193i 1.02270 0.834798i
\(67\) 2.53010 + 4.38227i 0.309101 + 0.535379i 0.978166 0.207825i \(-0.0666384\pi\)
−0.669065 + 0.743204i \(0.733305\pi\)
\(68\) 0.888418 4.34619i 0.107736 0.527052i
\(69\) 3.68867i 0.444063i
\(70\) 0 0
\(71\) 4.07391i 0.483485i −0.970340 0.241742i \(-0.922281\pi\)
0.970340 0.241742i \(-0.0777189\pi\)
\(72\) −0.584371 0.0237699i −0.0688687 0.00280131i
\(73\) 1.66682 + 2.88701i 0.195086 + 0.337899i 0.946929 0.321443i \(-0.104168\pi\)
−0.751843 + 0.659343i \(0.770835\pi\)
\(74\) −3.86728 4.73777i −0.449562 0.550754i
\(75\) 0 0
\(76\) 8.66433 2.89016i 0.993867 0.331524i
\(77\) 8.04555 7.79822i 0.916876 0.888690i
\(78\) −7.45579 + 1.21072i −0.844202 + 0.137087i
\(79\) 3.14131 + 1.81364i 0.353425 + 0.204050i 0.666193 0.745780i \(-0.267923\pi\)
−0.312768 + 0.949830i \(0.601256\pi\)
\(80\) 0 0
\(81\) 4.78879 + 8.29442i 0.532087 + 0.921603i
\(82\) −2.45084 + 6.45988i −0.270650 + 0.713374i
\(83\) 11.7373i 1.28834i −0.764884 0.644168i \(-0.777204\pi\)
0.764884 0.644168i \(-0.222796\pi\)
\(84\) −9.46634 + 0.422052i −1.03286 + 0.0460496i
\(85\) 0 0
\(86\) −16.3606 6.20713i −1.76421 0.669332i
\(87\) 9.96851 5.75532i 1.06874 0.617035i
\(88\) −10.1215 6.40577i −1.07895 0.682857i
\(89\) 14.4625 + 8.34991i 1.53302 + 0.885089i 0.999220 + 0.0394771i \(0.0125692\pi\)
0.533798 + 0.845612i \(0.320764\pi\)
\(90\) 0 0
\(91\) −7.65330 + 1.92318i −0.802284 + 0.201604i
\(92\) −3.90801 + 1.30359i −0.407438 + 0.135909i
\(93\) −3.72424 2.15019i −0.386185 0.222964i
\(94\) −6.04943 7.41111i −0.623951 0.764397i
\(95\) 0 0
\(96\) 2.81223 + 9.73181i 0.287022 + 0.993249i
\(97\) −12.0198 −1.22042 −0.610211 0.792239i \(-0.708916\pi\)
−0.610211 + 0.792239i \(0.708916\pi\)
\(98\) −9.81627 + 1.28099i −0.991593 + 0.129400i
\(99\) 0.875689i 0.0880100i
\(100\) 0 0
\(101\) 6.06956 3.50426i 0.603943 0.348687i −0.166648 0.986016i \(-0.553294\pi\)
0.770591 + 0.637330i \(0.219961\pi\)
\(102\) −3.55200 4.35152i −0.351700 0.430865i
\(103\) 1.78406 + 1.03003i 0.175789 + 0.101492i 0.585313 0.810808i \(-0.300972\pi\)
−0.409524 + 0.912299i \(0.634305\pi\)
\(104\) 3.91763 + 7.47126i 0.384155 + 0.732618i
\(105\) 0 0
\(106\) −17.9200 + 2.90997i −1.74054 + 0.282641i
\(107\) −2.26529 + 3.92360i −0.218994 + 0.379309i −0.954501 0.298209i \(-0.903611\pi\)
0.735507 + 0.677517i \(0.236944\pi\)
\(108\) 6.63570 7.48637i 0.638521 0.720376i
\(109\) 5.97295 + 10.3454i 0.572105 + 0.990914i 0.996350 + 0.0853668i \(0.0272062\pi\)
−0.424245 + 0.905547i \(0.639460\pi\)
\(110\) 0 0
\(111\) −7.74405 −0.735033
\(112\) 3.79260 + 9.88009i 0.358367 + 0.933581i
\(113\) 1.40568i 0.132235i −0.997812 0.0661177i \(-0.978939\pi\)
0.997812 0.0661177i \(-0.0210613\pi\)
\(114\) 4.10254 10.8134i 0.384238 1.01277i
\(115\) 0 0
\(116\) −9.62047 8.52731i −0.893238 0.791741i
\(117\) −0.308368 + 0.534108i −0.0285086 + 0.0493783i
\(118\) 3.16906 + 19.5155i 0.291735 + 1.79655i
\(119\) −4.08428 4.21382i −0.374405 0.386280i
\(120\) 0 0
\(121\) 3.46737 6.00566i 0.315215 0.545969i
\(122\) −0.0202155 0.0247659i −0.00183023 0.00224220i
\(123\) 4.37437 + 7.57663i 0.394423 + 0.683161i
\(124\) −0.961882 + 4.70558i −0.0863796 + 0.422574i
\(125\) 0 0
\(126\) −0.462059 + 0.620561i −0.0411635 + 0.0552839i
\(127\) 14.8435 1.31715 0.658573 0.752517i \(-0.271161\pi\)
0.658573 + 0.752517i \(0.271161\pi\)
\(128\) 9.31665 6.41873i 0.823483 0.567341i
\(129\) −19.1890 + 11.0788i −1.68950 + 0.975431i
\(130\) 0 0
\(131\) −1.49660 + 2.59219i −0.130759 + 0.226480i −0.923969 0.382467i \(-0.875075\pi\)
0.793211 + 0.608947i \(0.208408\pi\)
\(132\) −14.3881 + 4.79942i −1.25232 + 0.417736i
\(133\) 3.30901 11.6207i 0.286928 1.00765i
\(134\) −1.14705 7.06369i −0.0990901 0.610210i
\(135\) 0 0
\(136\) −3.35499 + 5.30106i −0.287688 + 0.454563i
\(137\) −13.1076 + 7.56769i −1.11986 + 0.646551i −0.941365 0.337390i \(-0.890456\pi\)
−0.178495 + 0.983941i \(0.557123\pi\)
\(138\) −1.85043 + 4.87734i −0.157519 + 0.415187i
\(139\) 6.82740 0.579093 0.289546 0.957164i \(-0.406496\pi\)
0.289546 + 0.957164i \(0.406496\pi\)
\(140\) 0 0
\(141\) −12.1137 −1.02016
\(142\) −2.04369 + 5.38673i −0.171503 + 0.452044i
\(143\) −10.9389 + 6.31559i −0.914758 + 0.528136i
\(144\) 0.760760 + 0.324581i 0.0633966 + 0.0270484i
\(145\) 0 0
\(146\) −0.755670 4.65351i −0.0625397 0.385128i
\(147\) −6.60341 + 10.6549i −0.544640 + 0.878802i
\(148\) 2.73679 + 8.20454i 0.224963 + 0.674409i
\(149\) 7.41324 12.8401i 0.607316 1.05190i −0.384365 0.923181i \(-0.625580\pi\)
0.991681 0.128721i \(-0.0410871\pi\)
\(150\) 0 0
\(151\) −11.0583 + 6.38449i −0.899909 + 0.519563i −0.877171 0.480179i \(-0.840572\pi\)
−0.0227383 + 0.999741i \(0.507238\pi\)
\(152\) −12.9063 0.524976i −1.04684 0.0425812i
\(153\) −0.458638 −0.0370786
\(154\) −14.5502 + 6.27512i −1.17249 + 0.505664i
\(155\) 0 0
\(156\) 10.4658 + 2.13934i 0.837933 + 0.171285i
\(157\) −6.03430 10.4517i −0.481589 0.834137i 0.518187 0.855267i \(-0.326607\pi\)
−0.999777 + 0.0211298i \(0.993274\pi\)
\(158\) −3.24378 3.97393i −0.258061 0.316149i
\(159\) −11.4942 + 19.9085i −0.911548 + 1.57885i
\(160\) 0 0
\(161\) −1.49252 + 5.24149i −0.117627 + 0.413087i
\(162\) −2.17105 13.3696i −0.170574 1.05042i
\(163\) −1.96460 + 3.40279i −0.153879 + 0.266527i −0.932650 0.360781i \(-0.882510\pi\)
0.778771 + 0.627308i \(0.215843\pi\)
\(164\) 6.48124 7.31210i 0.506099 0.570979i
\(165\) 0 0
\(166\) −5.88806 + 15.5196i −0.457002 + 1.20456i
\(167\) 3.08397i 0.238645i 0.992856 + 0.119323i \(0.0380722\pi\)
−0.992856 + 0.119323i \(0.961928\pi\)
\(168\) 12.7286 + 4.19076i 0.982032 + 0.323324i
\(169\) −4.10404 −0.315696
\(170\) 0 0
\(171\) −0.472157 0.817801i −0.0361068 0.0625388i
\(172\) 18.5190 + 16.4147i 1.41206 + 1.25161i
\(173\) −5.81013 + 10.0634i −0.441736 + 0.765109i −0.997818 0.0660179i \(-0.978971\pi\)
0.556082 + 0.831127i \(0.312304\pi\)
\(174\) −16.0680 + 2.60924i −1.21811 + 0.197806i
\(175\) 0 0
\(176\) 10.1696 + 13.5475i 0.766565 + 1.02118i
\(177\) 21.6811 + 12.5176i 1.62965 + 0.940879i
\(178\) −14.9342 18.2958i −1.11937 1.37133i
\(179\) −5.05528 + 2.91866i −0.377849 + 0.218151i −0.676882 0.736092i \(-0.736669\pi\)
0.299033 + 0.954243i \(0.403336\pi\)
\(180\) 0 0
\(181\) 9.78262i 0.727136i −0.931568 0.363568i \(-0.881558\pi\)
0.931568 0.363568i \(-0.118442\pi\)
\(182\) 11.0843 + 1.29638i 0.821627 + 0.0960939i
\(183\) −0.0404807 −0.00299242
\(184\) 5.82131 + 0.236788i 0.429153 + 0.0174562i
\(185\) 0 0
\(186\) 3.84572 + 4.71136i 0.281982 + 0.345454i
\(187\) −8.13477 4.69661i −0.594873 0.343450i
\(188\) 4.28105 + 12.8340i 0.312228 + 0.936019i
\(189\) −3.22525 12.8349i −0.234603 0.933602i
\(190\) 0 0
\(191\) 13.6837 + 7.90026i 0.990115 + 0.571643i 0.905309 0.424755i \(-0.139640\pi\)
0.0848061 + 0.996397i \(0.472973\pi\)
\(192\) 1.16352 14.2787i 0.0839701 1.03047i
\(193\) −3.65822 + 2.11208i −0.263325 + 0.152031i −0.625850 0.779943i \(-0.715248\pi\)
0.362526 + 0.931974i \(0.381915\pi\)
\(194\) 15.8931 + 6.02976i 1.14106 + 0.432911i
\(195\) 0 0
\(196\) 13.6222 + 3.23057i 0.973012 + 0.230755i
\(197\) 9.28951i 0.661850i −0.943657 0.330925i \(-0.892639\pi\)
0.943657 0.330925i \(-0.107361\pi\)
\(198\) −0.439292 + 1.15788i −0.0312191 + 0.0822869i
\(199\) 7.52975 + 13.0419i 0.533770 + 0.924517i 0.999222 + 0.0394437i \(0.0125586\pi\)
−0.465452 + 0.885073i \(0.654108\pi\)
\(200\) 0 0
\(201\) −7.84754 4.53078i −0.553523 0.319576i
\(202\) −9.78339 + 1.58869i −0.688357 + 0.111780i
\(203\) −16.4937 + 4.14466i −1.15763 + 0.290898i
\(204\) 2.51367 + 7.53567i 0.175992 + 0.527603i
\(205\) 0 0
\(206\) −1.84226 2.25693i −0.128356 0.157248i
\(207\) 0.212965 + 0.368865i 0.0148021 + 0.0256379i
\(208\) −1.43210 11.8442i −0.0992986 0.821245i
\(209\) 19.3402i 1.33779i
\(210\) 0 0
\(211\) 22.9573i 1.58045i −0.612818 0.790224i \(-0.709964\pi\)
0.612818 0.790224i \(-0.290036\pi\)
\(212\) 25.1545 + 5.14190i 1.72761 + 0.353147i
\(213\) 3.64768 + 6.31796i 0.249935 + 0.432900i
\(214\) 4.96357 4.05159i 0.339302 0.276961i
\(215\) 0 0
\(216\) −12.5296 + 6.57003i −0.852533 + 0.447034i
\(217\) 4.42202 + 4.56226i 0.300186 + 0.309707i
\(218\) −2.70790 16.6756i −0.183402 1.12942i
\(219\) −5.16991 2.98485i −0.349350 0.201697i
\(220\) 0 0
\(221\) 3.30776 + 5.72920i 0.222504 + 0.385388i
\(222\) 10.2396 + 3.88483i 0.687235 + 0.260733i
\(223\) 12.2328i 0.819169i −0.912272 0.409585i \(-0.865674\pi\)
0.912272 0.409585i \(-0.134326\pi\)
\(224\) −0.0583893 14.9665i −0.00390130 0.999992i
\(225\) 0 0
\(226\) −0.705164 + 1.85866i −0.0469068 + 0.123636i
\(227\) −13.9147 + 8.03366i −0.923552 + 0.533213i −0.884767 0.466035i \(-0.845682\pi\)
−0.0387855 + 0.999248i \(0.512349\pi\)
\(228\) −10.8492 + 12.2400i −0.718503 + 0.810612i
\(229\) −15.3282 8.84975i −1.01292 0.584808i −0.100873 0.994899i \(-0.532164\pi\)
−0.912045 + 0.410091i \(0.865497\pi\)
\(230\) 0 0
\(231\) −5.49498 + 19.2975i −0.361543 + 1.26968i
\(232\) 8.44292 + 16.1014i 0.554305 + 1.05711i
\(233\) −6.90060 3.98406i −0.452073 0.261005i 0.256632 0.966509i \(-0.417387\pi\)
−0.708705 + 0.705505i \(0.750720\pi\)
\(234\) 0.675676 0.551531i 0.0441703 0.0360547i
\(235\) 0 0
\(236\) 5.59972 27.3941i 0.364510 1.78320i
\(237\) −6.49553 −0.421930
\(238\) 3.28656 + 7.62061i 0.213036 + 0.493971i
\(239\) 11.3845i 0.736401i −0.929747 0.368200i \(-0.879974\pi\)
0.929747 0.368200i \(-0.120026\pi\)
\(240\) 0 0
\(241\) −14.1199 + 8.15213i −0.909543 + 0.525125i −0.880284 0.474447i \(-0.842648\pi\)
−0.0292587 + 0.999572i \(0.509315\pi\)
\(242\) −7.59749 + 6.20157i −0.488385 + 0.398652i
\(243\) −1.85775 1.07257i −0.119175 0.0688056i
\(244\) 0.0143061 + 0.0428878i 0.000915854 + 0.00274561i
\(245\) 0 0
\(246\) −1.98317 12.2126i −0.126442 0.778647i
\(247\) −6.81053 + 11.7962i −0.433343 + 0.750573i
\(248\) 3.63242 5.73942i 0.230659 0.364454i
\(249\) 10.5093 + 18.2026i 0.665998 + 1.15354i
\(250\) 0 0
\(251\) 3.30769 0.208779 0.104390 0.994536i \(-0.466711\pi\)
0.104390 + 0.994536i \(0.466711\pi\)
\(252\) 0.922264 0.588743i 0.0580972 0.0370873i
\(253\) 8.72333i 0.548431i
\(254\) −19.6268 7.44627i −1.23149 0.467221i
\(255\) 0 0
\(256\) −15.5389 + 3.81344i −0.971182 + 0.238340i
\(257\) −3.65064 + 6.32310i −0.227721 + 0.394424i −0.957132 0.289651i \(-0.906461\pi\)
0.729411 + 0.684075i \(0.239794\pi\)
\(258\) 30.9303 5.02268i 1.92564 0.312698i
\(259\) 11.0041 + 3.13342i 0.683760 + 0.194701i
\(260\) 0 0
\(261\) −0.664565 + 1.15106i −0.0411355 + 0.0712488i
\(262\) 3.27926 2.67674i 0.202593 0.165370i
\(263\) −0.803288 1.39134i −0.0495329 0.0857935i 0.840196 0.542283i \(-0.182440\pi\)
−0.889729 + 0.456490i \(0.849107\pi\)
\(264\) 21.4323 + 0.871780i 1.31906 + 0.0536543i
\(265\) 0 0
\(266\) −10.2049 + 13.7055i −0.625704 + 0.840341i
\(267\) −29.9052 −1.83017
\(268\) −2.02683 + 9.91538i −0.123809 + 0.605678i
\(269\) −21.0856 + 12.1738i −1.28561 + 0.742247i −0.977868 0.209223i \(-0.932907\pi\)
−0.307742 + 0.951470i \(0.599573\pi\)
\(270\) 0 0
\(271\) 1.37857 2.38775i 0.0837422 0.145046i −0.821112 0.570767i \(-0.806646\pi\)
0.904855 + 0.425721i \(0.139979\pi\)
\(272\) 7.09543 5.32629i 0.430223 0.322954i
\(273\) 10.1470 9.83510i 0.614126 0.595247i
\(274\) 21.1279 3.43089i 1.27638 0.207268i
\(275\) 0 0
\(276\) 4.89346 5.52078i 0.294552 0.332312i
\(277\) 16.6524 9.61429i 1.00055 0.577667i 0.0921377 0.995746i \(-0.470630\pi\)
0.908410 + 0.418080i \(0.137297\pi\)
\(278\) −9.02753 3.42499i −0.541435 0.205417i
\(279\) 0.496563 0.0297285
\(280\) 0 0
\(281\) 2.61717 0.156128 0.0780638 0.996948i \(-0.475126\pi\)
0.0780638 + 0.996948i \(0.475126\pi\)
\(282\) 16.0174 + 6.07689i 0.953820 + 0.361873i
\(283\) 21.4276 12.3712i 1.27374 0.735393i 0.298049 0.954551i \(-0.403664\pi\)
0.975690 + 0.219157i \(0.0703308\pi\)
\(284\) 5.40454 6.09738i 0.320701 0.361813i
\(285\) 0 0
\(286\) 17.6322 2.86324i 1.04261 0.169307i
\(287\) −3.15018 12.5361i −0.185949 0.739984i
\(288\) −0.843087 0.810815i −0.0496794 0.0477777i
\(289\) 6.04017 10.4619i 0.355304 0.615405i
\(290\) 0 0
\(291\) 18.6407 10.7622i 1.09273 0.630891i
\(292\) −1.33527 + 6.53219i −0.0781405 + 0.382268i
\(293\) −13.9941 −0.817542 −0.408771 0.912637i \(-0.634043\pi\)
−0.408771 + 0.912637i \(0.634043\pi\)
\(294\) 14.0764 10.7758i 0.820954 0.628459i
\(295\) 0 0
\(296\) 0.497117 12.2214i 0.0288943 0.710353i
\(297\) −10.5915 18.3450i −0.614581 1.06449i
\(298\) −16.2434 + 13.2589i −0.940956 + 0.768070i
\(299\) 3.07186 5.32062i 0.177650 0.307699i
\(300\) 0 0
\(301\) 31.7497 7.97831i 1.83002 0.459862i
\(302\) 17.8246 2.89448i 1.02569 0.166559i
\(303\) −6.27524 + 10.8690i −0.360503 + 0.624410i
\(304\) 16.8019 + 7.16862i 0.963658 + 0.411148i
\(305\) 0 0
\(306\) 0.606433 + 0.230077i 0.0346675 + 0.0131526i
\(307\) 26.2375i 1.49746i −0.662878 0.748728i \(-0.730665\pi\)
0.662878 0.748728i \(-0.269335\pi\)
\(308\) 22.3870 0.998111i 1.27562 0.0568727i
\(309\) −3.68904 −0.209862
\(310\) 0 0
\(311\) 3.72950 + 6.45969i 0.211481 + 0.366295i 0.952178 0.305543i \(-0.0988381\pi\)
−0.740697 + 0.671839i \(0.765505\pi\)
\(312\) −12.7652 8.07894i −0.722685 0.457380i
\(313\) −2.12920 + 3.68788i −0.120349 + 0.208451i −0.919905 0.392140i \(-0.871735\pi\)
0.799556 + 0.600591i \(0.205068\pi\)
\(314\) 2.73572 + 16.8469i 0.154385 + 0.950725i
\(315\) 0 0
\(316\) 2.29556 + 6.88178i 0.129135 + 0.387131i
\(317\) −5.23441 3.02209i −0.293994 0.169737i 0.345748 0.938327i \(-0.387625\pi\)
−0.639742 + 0.768590i \(0.720959\pi\)
\(318\) 25.1854 20.5579i 1.41232 1.15283i
\(319\) −23.5745 + 13.6108i −1.31992 + 0.762057i
\(320\) 0 0
\(321\) 8.11313i 0.452831i
\(322\) 4.60289 6.18183i 0.256509 0.344500i
\(323\) −10.1294 −0.563612
\(324\) −3.83624 + 18.7671i −0.213124 + 1.04262i
\(325\) 0 0
\(326\) 4.30471 3.51379i 0.238416 0.194611i
\(327\) −18.5261 10.6960i −1.02450 0.591492i
\(328\) −12.2379 + 6.41709i −0.675728 + 0.354325i
\(329\) 17.2132 + 4.90148i 0.948997 + 0.270227i
\(330\) 0 0
\(331\) −25.1826 14.5392i −1.38416 0.799145i −0.391510 0.920174i \(-0.628047\pi\)
−0.992649 + 0.121029i \(0.961380\pi\)
\(332\) 15.5710 17.5671i 0.854567 0.964119i
\(333\) 0.774403 0.447102i 0.0424370 0.0245010i
\(334\) 1.54708 4.07778i 0.0846527 0.223126i
\(335\) 0 0
\(336\) −14.7281 11.9266i −0.803482 0.650648i
\(337\) 16.6744i 0.908311i −0.890922 0.454156i \(-0.849941\pi\)
0.890922 0.454156i \(-0.150059\pi\)
\(338\) 5.42657 + 2.05881i 0.295167 + 0.111984i
\(339\) 1.25861 + 2.17998i 0.0683583 + 0.118400i
\(340\) 0 0
\(341\) 8.80745 + 5.08498i 0.476950 + 0.275367i
\(342\) 0.214058 + 1.31820i 0.0115749 + 0.0712799i
\(343\) 13.6945 12.4684i 0.739431 0.673232i
\(344\) −16.2523 30.9945i −0.876265 1.67111i
\(345\) 0 0
\(346\) 12.7308 10.3917i 0.684412 0.558662i
\(347\) −10.8223 18.7447i −0.580970 1.00627i −0.995365 0.0961725i \(-0.969340\pi\)
0.414395 0.910097i \(-0.363993\pi\)
\(348\) 22.5549 + 4.61051i 1.20907 + 0.247149i
\(349\) 4.97653i 0.266388i 0.991090 + 0.133194i \(0.0425233\pi\)
−0.991090 + 0.133194i \(0.957477\pi\)
\(350\) 0 0
\(351\) 14.9189i 0.796311i
\(352\) −6.65065 23.0148i −0.354481 1.22669i
\(353\) 4.29603 + 7.44095i 0.228655 + 0.396042i 0.957410 0.288733i \(-0.0932340\pi\)
−0.728755 + 0.684775i \(0.759901\pi\)
\(354\) −22.3883 27.4278i −1.18993 1.45777i
\(355\) 0 0
\(356\) 10.5686 + 31.6834i 0.560137 + 1.67922i
\(357\) 10.1070 + 2.87797i 0.534918 + 0.152318i
\(358\) 8.14849 1.32321i 0.430661 0.0699337i
\(359\) 18.8228 + 10.8673i 0.993429 + 0.573557i 0.906298 0.422640i \(-0.138897\pi\)
0.0871318 + 0.996197i \(0.472230\pi\)
\(360\) 0 0
\(361\) −0.927949 1.60726i −0.0488394 0.0845924i
\(362\) −4.90748 + 12.9351i −0.257931 + 0.679852i
\(363\) 12.4184i 0.651795i
\(364\) −14.0059 7.27463i −0.734111 0.381294i
\(365\) 0 0
\(366\) 0.0535256 + 0.0203073i 0.00279783 + 0.00106148i
\(367\) −0.819305 + 0.473026i −0.0427674 + 0.0246918i −0.521231 0.853415i \(-0.674527\pi\)
0.478464 + 0.878107i \(0.341194\pi\)
\(368\) −7.57844 3.23337i −0.395054 0.168551i
\(369\) −0.874871 0.505107i −0.0455439 0.0262948i
\(370\) 0 0
\(371\) 24.3883 23.6386i 1.26618 1.22726i
\(372\) −2.72153 8.15881i −0.141105 0.423015i
\(373\) 31.9654 + 18.4552i 1.65511 + 0.955576i 0.974926 + 0.222530i \(0.0714316\pi\)
0.680180 + 0.733045i \(0.261902\pi\)
\(374\) 8.40013 + 10.2909i 0.434360 + 0.532131i
\(375\) 0 0
\(376\) 0.777621 19.1174i 0.0401028 0.985906i
\(377\) 19.1717 0.987394
\(378\) −2.17408 + 18.5889i −0.111823 + 0.956110i
\(379\) 32.1315i 1.65048i 0.564780 + 0.825241i \(0.308961\pi\)
−0.564780 + 0.825241i \(0.691039\pi\)
\(380\) 0 0
\(381\) −23.0197 + 13.2905i −1.17934 + 0.680891i
\(382\) −14.1300 17.3106i −0.722955 0.885686i
\(383\) −14.4272 8.32956i −0.737196 0.425620i 0.0838528 0.996478i \(-0.473277\pi\)
−0.821049 + 0.570858i \(0.806611\pi\)
\(384\) −8.70140 + 18.2963i −0.444041 + 0.933677i
\(385\) 0 0
\(386\) 5.89661 0.957533i 0.300130 0.0487371i
\(387\) 1.27926 2.21575i 0.0650285 0.112633i
\(388\) −17.9899 15.9457i −0.913296 0.809520i
\(389\) 9.88823 + 17.1269i 0.501353 + 0.868369i 0.999999 + 0.00156294i \(0.000497498\pi\)
−0.498646 + 0.866806i \(0.666169\pi\)
\(390\) 0 0
\(391\) 4.56880 0.231054
\(392\) −16.3913 11.1052i −0.827885 0.560898i
\(393\) 5.36007i 0.270380i
\(394\) −4.66011 + 12.2830i −0.234773 + 0.618811i
\(395\) 0 0
\(396\) 1.16171 1.31063i 0.0583780 0.0658618i
\(397\) −19.4679 + 33.7193i −0.977064 + 1.69232i −0.304117 + 0.952635i \(0.598361\pi\)
−0.672948 + 0.739690i \(0.734972\pi\)
\(398\) −3.41370 21.0220i −0.171113 1.05374i
\(399\) 5.27318 + 20.9846i 0.263989 + 1.05055i
\(400\) 0 0
\(401\) −4.46848 + 7.73964i −0.223145 + 0.386499i −0.955761 0.294143i \(-0.904966\pi\)
0.732616 + 0.680642i \(0.238299\pi\)
\(402\) 8.10352 + 9.92756i 0.404167 + 0.495142i
\(403\) −3.58128 6.20296i −0.178396 0.308992i
\(404\) 13.7331 + 2.80722i 0.683245 + 0.139664i
\(405\) 0 0
\(406\) 23.8880 + 2.79383i 1.18554 + 0.138656i
\(407\) 18.3139 0.907788
\(408\) 0.456590 11.2250i 0.0226046 0.555722i
\(409\) −21.8677 + 12.6253i −1.08129 + 0.624282i −0.931244 0.364397i \(-0.881275\pi\)
−0.150044 + 0.988679i \(0.547942\pi\)
\(410\) 0 0
\(411\) 13.5518 23.4724i 0.668462 1.15781i
\(412\) 1.30373 + 3.90840i 0.0642299 + 0.192553i
\(413\) −25.7433 26.5598i −1.26675 1.30692i
\(414\) −0.0965498 0.594567i −0.00474516 0.0292214i
\(415\) 0 0
\(416\) −4.04807 + 16.3794i −0.198473 + 0.803065i
\(417\) −10.5882 + 6.11308i −0.518504 + 0.299359i
\(418\) −9.70209 + 25.5726i −0.474545 + 1.25080i
\(419\) −1.53621 −0.0750489 −0.0375245 0.999296i \(-0.511947\pi\)
−0.0375245 + 0.999296i \(0.511947\pi\)
\(420\) 0 0
\(421\) 15.7880 0.769460 0.384730 0.923029i \(-0.374295\pi\)
0.384730 + 0.923029i \(0.374295\pi\)
\(422\) −11.5166 + 30.3553i −0.560620 + 1.47767i
\(423\) 1.21137 0.699384i 0.0588987 0.0340052i
\(424\) −30.6810 19.4177i −1.49000 0.943006i
\(425\) 0 0
\(426\) −1.65371 10.1838i −0.0801227 0.493406i
\(427\) 0.0575219 + 0.0163794i 0.00278368 + 0.000792655i
\(428\) −8.59556 + 2.86722i −0.415482 + 0.138592i
\(429\) 11.3096 19.5888i 0.546034 0.945758i
\(430\) 0 0
\(431\) −10.3752 + 5.99013i −0.499756 + 0.288534i −0.728613 0.684926i \(-0.759835\pi\)
0.228857 + 0.973460i \(0.426501\pi\)
\(432\) 19.8632 2.40170i 0.955667 0.115552i
\(433\) −24.2190 −1.16389 −0.581946 0.813228i \(-0.697708\pi\)
−0.581946 + 0.813228i \(0.697708\pi\)
\(434\) −3.55834 8.25077i −0.170806 0.396050i
\(435\) 0 0
\(436\) −4.78485 + 23.4078i −0.229153 + 1.12103i
\(437\) 4.70348 + 8.14667i 0.224998 + 0.389708i
\(438\) 5.33855 + 6.54022i 0.255086 + 0.312504i
\(439\) 12.9813 22.4843i 0.619564 1.07312i −0.370002 0.929031i \(-0.620643\pi\)
0.989565 0.144085i \(-0.0460238\pi\)
\(440\) 0 0
\(441\) 0.0451790 1.44673i 0.00215138 0.0688921i
\(442\) −1.49961 9.23478i −0.0713291 0.439254i
\(443\) −8.96825 + 15.5335i −0.426094 + 0.738017i −0.996522 0.0833309i \(-0.973444\pi\)
0.570428 + 0.821348i \(0.306777\pi\)
\(444\) −11.5904 10.2734i −0.550058 0.487555i
\(445\) 0 0
\(446\) −6.13662 + 16.1748i −0.290578 + 0.765900i
\(447\) 26.5505i 1.25579i
\(448\) −7.43079 + 19.8188i −0.351072 + 0.936348i
\(449\) 4.14444 0.195588 0.0977941 0.995207i \(-0.468821\pi\)
0.0977941 + 0.995207i \(0.468821\pi\)
\(450\) 0 0
\(451\) −10.3449 17.9180i −0.487125 0.843725i
\(452\) 1.86481 2.10387i 0.0877131 0.0989575i
\(453\) 11.4330 19.8026i 0.537170 0.930406i
\(454\) 22.4288 3.64215i 1.05264 0.170935i
\(455\) 0 0
\(456\) 20.4855 10.7418i 0.959322 0.503030i
\(457\) −5.96908 3.44625i −0.279222 0.161209i 0.353849 0.935303i \(-0.384873\pi\)
−0.633071 + 0.774094i \(0.718206\pi\)
\(458\) 15.8282 + 19.3910i 0.739605 + 0.906084i
\(459\) −9.60811 + 5.54724i −0.448468 + 0.258923i
\(460\) 0 0
\(461\) 10.4266i 0.485616i 0.970074 + 0.242808i \(0.0780684\pi\)
−0.970074 + 0.242808i \(0.921932\pi\)
\(462\) 16.9464 22.7596i 0.788418 1.05887i
\(463\) −9.86521 −0.458475 −0.229238 0.973370i \(-0.573623\pi\)
−0.229238 + 0.973370i \(0.573623\pi\)
\(464\) −3.08634 25.5254i −0.143280 1.18499i
\(465\) 0 0
\(466\) 7.12570 + 8.72963i 0.330092 + 0.404392i
\(467\) −3.37330 1.94758i −0.156098 0.0901231i 0.419916 0.907563i \(-0.362059\pi\)
−0.576014 + 0.817440i \(0.695393\pi\)
\(468\) −1.17009 + 0.390307i −0.0540874 + 0.0180419i
\(469\) 9.31787 + 9.61339i 0.430259 + 0.443905i
\(470\) 0 0
\(471\) 18.7164 + 10.8059i 0.862405 + 0.497910i
\(472\) −21.1466 + 33.4127i −0.973349 + 1.53795i
\(473\) 45.3801 26.2002i 2.08658 1.20469i
\(474\) 8.58872 + 3.25851i 0.394493 + 0.149668i
\(475\) 0 0
\(476\) −0.522755 11.7251i −0.0239605 0.537417i
\(477\) 2.65446i 0.121539i
\(478\) −5.71106 + 15.0531i −0.261218 + 0.688514i
\(479\) −0.547415 0.948150i −0.0250120 0.0433221i 0.853248 0.521505i \(-0.174629\pi\)
−0.878260 + 0.478183i \(0.841296\pi\)
\(480\) 0 0
\(481\) −11.1702 6.44912i −0.509317 0.294054i
\(482\) 22.7596 3.69586i 1.03667 0.168342i
\(483\) −2.37845 9.46503i −0.108223 0.430674i
\(484\) 13.1568 4.38871i 0.598037 0.199487i
\(485\) 0 0
\(486\) 1.91835 + 2.35016i 0.0870182 + 0.106605i
\(487\) −7.00816 12.1385i −0.317570 0.550048i 0.662410 0.749141i \(-0.269534\pi\)
−0.979980 + 0.199094i \(0.936200\pi\)
\(488\) 0.00259860 0.0638851i 0.000117633 0.00289194i
\(489\) 7.03621i 0.318189i
\(490\) 0 0
\(491\) 12.7049i 0.573364i 0.958026 + 0.286682i \(0.0925523\pi\)
−0.958026 + 0.286682i \(0.907448\pi\)
\(492\) −3.50425 + 17.1430i −0.157984 + 0.772865i
\(493\) 7.12857 + 12.3470i 0.321055 + 0.556083i
\(494\) 14.9228 12.1810i 0.671409 0.548048i
\(495\) 0 0
\(496\) −7.68216 + 5.76673i −0.344939 + 0.258934i
\(497\) −2.62685 10.4536i −0.117830 0.468907i
\(498\) −4.76449 29.3404i −0.213502 1.31477i
\(499\) −6.22192 3.59223i −0.278532 0.160810i 0.354227 0.935160i \(-0.384744\pi\)
−0.632758 + 0.774349i \(0.718077\pi\)
\(500\) 0 0
\(501\) −2.76131 4.78273i −0.123366 0.213676i
\(502\) −4.37359 1.65931i −0.195203 0.0740587i
\(503\) 32.4664i 1.44760i 0.690008 + 0.723802i \(0.257607\pi\)
−0.690008 + 0.723802i \(0.742393\pi\)
\(504\) −1.51481 + 0.315808i −0.0674749 + 0.0140672i
\(505\) 0 0
\(506\) 4.37609 11.5344i 0.194541 0.512768i
\(507\) 6.36469 3.67465i 0.282666 0.163197i
\(508\) 22.2160 + 19.6917i 0.985678 + 0.873676i
\(509\) −2.74567 1.58521i −0.121699 0.0702632i 0.437915 0.899017i \(-0.355717\pi\)
−0.559614 + 0.828753i \(0.689051\pi\)
\(510\) 0 0
\(511\) 6.13855 + 6.33324i 0.271554 + 0.280166i
\(512\) 22.4593 + 2.75282i 0.992572 + 0.121659i
\(513\) −19.7827 11.4215i −0.873427 0.504273i
\(514\) 7.99906 6.52936i 0.352824 0.287998i
\(515\) 0 0
\(516\) −43.4173 8.87506i −1.91134 0.390703i
\(517\) 28.6478 1.25993
\(518\) −12.9782 9.66339i −0.570231 0.424585i
\(519\) 20.8090i 0.913412i
\(520\) 0 0
\(521\) 15.5474 8.97629i 0.681143 0.393258i −0.119142 0.992877i \(-0.538015\pi\)
0.800286 + 0.599619i \(0.204681\pi\)
\(522\) 1.45615 1.18861i 0.0637341 0.0520240i
\(523\) 11.5683 + 6.67894i 0.505845 + 0.292050i 0.731124 0.682245i \(-0.238996\pi\)
−0.225279 + 0.974294i \(0.572329\pi\)
\(524\) −5.67879 + 1.89427i −0.248079 + 0.0827518i
\(525\) 0 0
\(526\) 0.364180 + 2.24267i 0.0158790 + 0.0977849i
\(527\) 2.66323 4.61286i 0.116012 0.200939i
\(528\) −27.9015 11.9043i −1.21426 0.518067i
\(529\) 9.37851 + 16.2441i 0.407762 + 0.706264i
\(530\) 0 0
\(531\) −2.89080 −0.125450
\(532\) 20.3689 13.0028i 0.883103 0.563744i
\(533\) 14.5716i 0.631166i
\(534\) 39.5421 + 15.0020i 1.71115 + 0.649201i
\(535\) 0 0
\(536\) 7.65406 12.0938i 0.330605 0.522374i
\(537\) 5.22659 9.05272i 0.225544 0.390654i
\(538\) 33.9874 5.51911i 1.46530 0.237946i
\(539\) 15.6164 25.1978i 0.672646 1.08535i
\(540\) 0 0
\(541\) −14.3702 + 24.8899i −0.617822 + 1.07010i 0.372060 + 0.928209i \(0.378652\pi\)
−0.989882 + 0.141891i \(0.954682\pi\)
\(542\) −3.02064 + 2.46564i −0.129748 + 0.105908i
\(543\) 8.75910 + 15.1712i 0.375889 + 0.651059i
\(544\) −12.0539 + 3.48324i −0.516806 + 0.149343i
\(545\) 0 0
\(546\) −18.3507 + 7.91417i −0.785338 + 0.338695i
\(547\) −11.3007 −0.483181 −0.241591 0.970378i \(-0.577669\pi\)
−0.241591 + 0.970378i \(0.577669\pi\)
\(548\) −29.6575 6.06238i −1.26690 0.258972i
\(549\) 0.00404806 0.00233715i 0.000172767 9.97470e-5i
\(550\) 0 0
\(551\) −14.6774 + 25.4220i −0.625279 + 1.08301i
\(552\) −9.23990 + 4.84503i −0.393276 + 0.206218i
\(553\) 9.22997 + 2.62824i 0.392498 + 0.111764i
\(554\) −26.8417 + 4.35874i −1.14040 + 0.185185i
\(555\) 0 0
\(556\) 10.2185 + 9.05738i 0.433361 + 0.384118i
\(557\) 2.89442 1.67109i 0.122640 0.0708065i −0.437425 0.899255i \(-0.644109\pi\)
0.560065 + 0.828449i \(0.310776\pi\)
\(558\) −0.656580 0.249102i −0.0277953 0.0105453i
\(559\) −36.9048 −1.56091
\(560\) 0 0
\(561\) 16.8209 0.710179
\(562\) −3.46056 1.31291i −0.145975 0.0553819i
\(563\) −33.5177 + 19.3515i −1.41260 + 0.815567i −0.995633 0.0933539i \(-0.970241\pi\)
−0.416970 + 0.908920i \(0.636908\pi\)
\(564\) −18.1305 16.0703i −0.763430 0.676683i
\(565\) 0 0
\(566\) −34.5387 + 5.60863i −1.45177 + 0.235748i
\(567\) 17.6361 + 18.1955i 0.740649 + 0.764139i
\(568\) −10.2049 + 5.35105i −0.428189 + 0.224525i
\(569\) 8.27513 14.3329i 0.346911 0.600868i −0.638788 0.769383i \(-0.720564\pi\)
0.985699 + 0.168515i \(0.0538971\pi\)
\(570\) 0 0
\(571\) −13.6896 + 7.90367i −0.572890 + 0.330758i −0.758303 0.651902i \(-0.773971\pi\)
0.185413 + 0.982661i \(0.440638\pi\)
\(572\) −24.7505 5.05934i −1.03487 0.211542i
\(573\) −28.2948 −1.18203
\(574\) −2.12347 + 18.1562i −0.0886319 + 0.757825i
\(575\) 0 0
\(576\) 0.708024 + 1.49504i 0.0295010 + 0.0622932i
\(577\) 0.955219 + 1.65449i 0.0397663 + 0.0688772i 0.885224 0.465166i \(-0.154005\pi\)
−0.845457 + 0.534043i \(0.820672\pi\)
\(578\) −13.2349 + 10.8032i −0.550497 + 0.449352i
\(579\) 3.78219 6.55095i 0.157183 0.272248i
\(580\) 0 0
\(581\) −7.56820 30.1176i −0.313982 1.24949i
\(582\) −30.0465 + 4.87916i −1.24547 + 0.202248i
\(583\) 27.1826 47.0817i 1.12579 1.94992i
\(584\) 5.04245 7.96735i 0.208658 0.329691i
\(585\) 0 0
\(586\) 18.5037 + 7.02017i 0.764379 + 0.290000i
\(587\) 25.0330i 1.03322i 0.856221 + 0.516611i \(0.172806\pi\)
−0.856221 + 0.516611i \(0.827194\pi\)
\(588\) −24.0183 + 7.18686i −0.990497 + 0.296381i
\(589\) 10.9670 0.451886
\(590\) 0 0
\(591\) 8.31758 + 14.4065i 0.342140 + 0.592603i
\(592\) −6.78820 + 15.9103i −0.278993 + 0.653910i
\(593\) −11.7140 + 20.2893i −0.481037 + 0.833180i −0.999763 0.0217604i \(-0.993073\pi\)
0.518727 + 0.854940i \(0.326406\pi\)
\(594\) 4.80177 + 29.5700i 0.197019 + 1.21327i
\(595\) 0 0
\(596\) 28.1293 9.38307i 1.15222 0.384346i
\(597\) −23.3548 13.4839i −0.955848 0.551859i
\(598\) −6.73087 + 5.49418i −0.275246 + 0.224674i
\(599\) 23.5836 13.6160i 0.963600 0.556335i 0.0663207 0.997798i \(-0.478874\pi\)
0.897279 + 0.441464i \(0.145541\pi\)
\(600\) 0 0
\(601\) 10.1290i 0.413171i 0.978429 + 0.206586i \(0.0662352\pi\)
−0.978429 + 0.206586i \(0.933765\pi\)
\(602\) −45.9834 5.37802i −1.87414 0.219192i
\(603\) 1.04633 0.0426101
\(604\) −25.0206 5.11454i −1.01807 0.208108i
\(605\) 0 0
\(606\) 13.7499 11.2236i 0.558553 0.455927i
\(607\) 29.2395 + 16.8814i 1.18680 + 0.685196i 0.957577 0.288179i \(-0.0930497\pi\)
0.229218 + 0.973375i \(0.426383\pi\)
\(608\) −18.6202 17.9074i −0.755149 0.726243i
\(609\) 21.8679 21.1957i 0.886133 0.858893i
\(610\) 0 0
\(611\) −17.4731 10.0881i −0.706886 0.408121i
\(612\) −0.686437 0.608438i −0.0277476 0.0245947i
\(613\) −6.15689 + 3.55468i −0.248674 + 0.143572i −0.619157 0.785267i \(-0.712526\pi\)
0.370483 + 0.928839i \(0.379192\pi\)
\(614\) −13.1621 + 34.6926i −0.531181 + 1.40008i
\(615\) 0 0
\(616\) −30.1019 9.91074i −1.21284 0.399315i
\(617\) 3.89670i 0.156875i −0.996919 0.0784377i \(-0.975007\pi\)
0.996919 0.0784377i \(-0.0249932\pi\)
\(618\) 4.87783 + 1.85062i 0.196215 + 0.0744428i
\(619\) −9.99960 17.3198i −0.401918 0.696142i 0.592039 0.805909i \(-0.298323\pi\)
−0.993957 + 0.109767i \(0.964990\pi\)
\(620\) 0 0
\(621\) 8.92289 + 5.15163i 0.358063 + 0.206728i
\(622\) −1.69081 10.4122i −0.0677954 0.417493i
\(623\) 42.4944 + 12.1003i 1.70250 + 0.484788i
\(624\) 12.8259 + 17.0861i 0.513447 + 0.683990i
\(625\) 0 0
\(626\) 4.66536 3.80818i 0.186465 0.152205i
\(627\) 17.3167 + 29.9935i 0.691564 + 1.19782i
\(628\) 4.83400 23.6482i 0.192898 0.943665i
\(629\) 9.59182i 0.382451i
\(630\) 0 0
\(631\) 45.3146i 1.80394i 0.431794 + 0.901972i \(0.357881\pi\)
−0.431794 + 0.901972i \(0.642119\pi\)
\(632\) 0.416971 10.2510i 0.0165862 0.407763i
\(633\) 20.5554 + 35.6030i 0.817004 + 1.41509i
\(634\) 5.40516 + 6.62181i 0.214666 + 0.262986i
\(635\) 0 0
\(636\) −43.6143 + 14.5484i −1.72942 + 0.576882i
\(637\) −18.3981 + 9.86968i −0.728961 + 0.391051i
\(638\) 37.9993 6.17059i 1.50441 0.244296i
\(639\) −0.729533 0.421196i −0.0288599 0.0166623i
\(640\) 0 0
\(641\) 0.302318 + 0.523631i 0.0119409 + 0.0206822i 0.871934 0.489623i \(-0.162866\pi\)
−0.859993 + 0.510305i \(0.829532\pi\)
\(642\) −4.06998 + 10.7276i −0.160629 + 0.423384i
\(643\) 41.7919i 1.64811i −0.566508 0.824056i \(-0.691706\pi\)
0.566508 0.824056i \(-0.308294\pi\)
\(644\) −9.18730 + 5.86487i −0.362030 + 0.231108i
\(645\) 0 0
\(646\) 13.3935 + 5.08142i 0.526962 + 0.199926i
\(647\) 0.281039 0.162258i 0.0110488 0.00637901i −0.494465 0.869197i \(-0.664636\pi\)
0.505514 + 0.862818i \(0.331303\pi\)
\(648\) 14.4870 22.8903i 0.569104 0.899216i
\(649\) −51.2737 29.6029i −2.01267 1.16201i
\(650\) 0 0
\(651\) −10.9427 3.11595i −0.428880 0.122124i
\(652\) −7.45461 + 2.48663i −0.291945 + 0.0973841i
\(653\) −12.4020 7.16031i −0.485328 0.280204i 0.237306 0.971435i \(-0.423736\pi\)
−0.722634 + 0.691230i \(0.757069\pi\)
\(654\) 19.1304 + 23.4365i 0.748058 + 0.916440i
\(655\) 0 0
\(656\) 19.4008 2.34579i 0.757473 0.0915877i
\(657\) 0.689319 0.0268929
\(658\) −20.3014 15.1161i −0.791430 0.589285i
\(659\) 8.70296i 0.339019i −0.985529 0.169510i \(-0.945782\pi\)
0.985529 0.169510i \(-0.0542184\pi\)
\(660\) 0 0
\(661\) −18.4070 + 10.6273i −0.715949 + 0.413354i −0.813260 0.581900i \(-0.802309\pi\)
0.0973106 + 0.995254i \(0.468976\pi\)
\(662\) 26.0040 + 31.8573i 1.01068 + 1.23817i
\(663\) −10.2596 5.92336i −0.398448 0.230044i
\(664\) −29.4013 + 15.4169i −1.14099 + 0.598290i
\(665\) 0 0
\(666\) −1.24824 + 0.202698i −0.0483685 + 0.00785440i
\(667\) 6.62018 11.4665i 0.256335 0.443984i
\(668\) −4.09126 + 4.61575i −0.158296 + 0.178589i
\(669\) 10.9529 + 18.9710i 0.423465 + 0.733463i
\(670\) 0 0
\(671\) 0.0957329 0.00369573
\(672\) 13.4912 + 23.1583i 0.520433 + 0.893350i
\(673\) 9.06372i 0.349381i −0.984623 0.174690i \(-0.944108\pi\)
0.984623 0.174690i \(-0.0558924\pi\)
\(674\) −8.36475 + 22.0477i −0.322198 + 0.849245i
\(675\) 0 0
\(676\) −6.14248 5.44451i −0.236249 0.209404i
\(677\) −8.81053 + 15.2603i −0.338616 + 0.586500i −0.984173 0.177212i \(-0.943292\pi\)
0.645557 + 0.763713i \(0.276625\pi\)
\(678\) −0.570605 3.51386i −0.0219139 0.134949i
\(679\) −30.8425 + 7.75033i −1.18362 + 0.297430i
\(680\) 0 0
\(681\) 14.3863 24.9177i 0.551283 0.954850i
\(682\) −9.09475 11.1419i −0.348256 0.426646i
\(683\) 7.28114 + 12.6113i 0.278605 + 0.482558i 0.971038 0.238924i \(-0.0767947\pi\)
−0.692433 + 0.721482i \(0.743461\pi\)
\(684\) 0.378239 1.85037i 0.0144623 0.0707505i
\(685\) 0 0
\(686\) −24.3623 + 9.61651i −0.930158 + 0.367160i
\(687\) 31.6954 1.20925
\(688\) 5.94108 + 49.1355i 0.226502 + 1.87327i
\(689\) −33.1590 + 19.1443i −1.26326 + 0.729341i
\(690\) 0 0
\(691\) 4.64423 8.04404i 0.176675 0.306010i −0.764065 0.645139i \(-0.776799\pi\)
0.940740 + 0.339130i \(0.110133\pi\)
\(692\) −22.0463 + 7.35399i −0.838076 + 0.279557i
\(693\) −0.564643 2.24700i −0.0214490 0.0853564i
\(694\) 4.90640 + 30.2142i 0.186244 + 1.14692i
\(695\) 0 0
\(696\) −27.5103 17.4110i −1.04278 0.659961i
\(697\) −9.38445 + 5.41811i −0.355461 + 0.205226i
\(698\) 2.49649 6.58022i 0.0944936 0.249065i
\(699\) 14.2689 0.539699
\(700\) 0 0
\(701\) −29.6374 −1.11939 −0.559695 0.828699i \(-0.689082\pi\)
−0.559695 + 0.828699i \(0.689082\pi\)
\(702\) 7.48410 19.7265i 0.282469 0.744528i
\(703\) 17.1033 9.87457i 0.645062 0.372427i
\(704\) −2.75162 + 33.7676i −0.103706 + 1.27266i
\(705\) 0 0
\(706\) −1.94765 11.9939i −0.0733009 0.451397i
\(707\) 13.3148 12.9055i 0.500754 0.485361i
\(708\) 15.8437 + 47.4975i 0.595444 + 1.78507i
\(709\) −10.6014 + 18.3622i −0.398144 + 0.689606i −0.993497 0.113858i \(-0.963679\pi\)
0.595353 + 0.803465i \(0.297012\pi\)
\(710\) 0 0
\(711\) 0.649551 0.375019i 0.0243601 0.0140643i
\(712\) 1.91971 47.1952i 0.0719444 1.76872i
\(713\) −4.94660 −0.185252
\(714\) −11.9202 8.87559i −0.446102 0.332160i
\(715\) 0 0
\(716\) −11.4381 2.33811i −0.427463 0.0873791i
\(717\) 10.1934 + 17.6554i 0.380678 + 0.659354i
\(718\) −19.4368 23.8119i −0.725375 0.888651i
\(719\) −9.44163 + 16.3534i −0.352113 + 0.609878i −0.986620 0.163040i \(-0.947870\pi\)
0.634506 + 0.772918i \(0.281204\pi\)
\(720\) 0 0
\(721\) 5.24202 + 1.49267i 0.195223 + 0.0555898i
\(722\) 0.420696 + 2.59070i 0.0156567 + 0.0964159i
\(723\) 14.5984 25.2852i 0.542920 0.940366i
\(724\) 12.9778 14.6415i 0.482317 0.544148i
\(725\) 0 0
\(726\) 6.22971 16.4202i 0.231206 0.609410i
\(727\) 4.07859i 0.151267i 0.997136 + 0.0756333i \(0.0240978\pi\)
−0.997136 + 0.0756333i \(0.975902\pi\)
\(728\) 14.8700 + 16.6450i 0.551119 + 0.616905i
\(729\) −24.8913 −0.921900
\(730\) 0 0
\(731\) −13.7222 23.7676i −0.507535 0.879076i
\(732\) −0.0605870 0.0537026i −0.00223936 0.00198490i
\(733\) 0.761855 1.31957i 0.0281397 0.0487395i −0.851613 0.524172i \(-0.824375\pi\)
0.879752 + 0.475432i \(0.157708\pi\)
\(734\) 1.32062 0.214452i 0.0487450 0.00791555i
\(735\) 0 0
\(736\) 8.39856 + 8.07708i 0.309575 + 0.297725i
\(737\) 18.5587 + 10.7148i 0.683617 + 0.394686i
\(738\) 0.903409 + 1.10676i 0.0332549 + 0.0407404i
\(739\) 25.1141 14.4997i 0.923839 0.533379i 0.0389810 0.999240i \(-0.487589\pi\)
0.884858 + 0.465861i \(0.154255\pi\)
\(740\) 0 0
\(741\) 24.3919i 0.896058i
\(742\) −44.1058 + 19.0217i −1.61918 + 0.698307i
\(743\) −30.8783 −1.13282 −0.566408 0.824125i \(-0.691667\pi\)
−0.566408 + 0.824125i \(0.691667\pi\)
\(744\) −0.494346 + 12.1533i −0.0181236 + 0.445560i
\(745\) 0 0
\(746\) −33.0081 40.4380i −1.20851 1.48054i
\(747\) −2.10185 1.21350i −0.0769026 0.0443997i
\(748\) −5.94459 17.8211i −0.217356 0.651605i
\(749\) −3.28275 + 11.5285i −0.119949 + 0.421243i
\(750\) 0 0
\(751\) −45.9308 26.5182i −1.67604 0.967661i −0.964146 0.265374i \(-0.914505\pi\)
−0.711893 0.702288i \(-0.752162\pi\)
\(752\) −10.6185 + 24.8879i −0.387218 + 0.907568i
\(753\) −5.12967 + 2.96162i −0.186936 + 0.107927i
\(754\) −25.3498 9.61756i −0.923186 0.350251i
\(755\) 0 0
\(756\) 12.1999 23.4885i 0.443705 0.854270i
\(757\) 10.2924i 0.374082i 0.982352 + 0.187041i \(0.0598898\pi\)
−0.982352 + 0.187041i \(0.940110\pi\)
\(758\) 16.1189 42.4858i 0.585463 1.54315i
\(759\) −7.81065 13.5284i −0.283508 0.491051i
\(760\) 0 0
\(761\) −24.8716 14.3596i −0.901595 0.520536i −0.0238779 0.999715i \(-0.507601\pi\)
−0.877717 + 0.479179i \(0.840935\pi\)
\(762\) 37.1050 6.02537i 1.34417 0.218276i
\(763\) 21.9972 + 22.6948i 0.796351 + 0.821608i
\(764\) 9.99951 + 29.9773i 0.361770 + 1.08454i
\(765\) 0 0
\(766\) 14.8978 + 18.2512i 0.538281 + 0.659443i
\(767\) 20.8489 + 36.1113i 0.752809 + 1.30390i
\(768\) 20.6838 19.8271i 0.746362 0.715450i
\(769\) 31.6976i 1.14304i −0.820586 0.571522i \(-0.806353\pi\)
0.820586 0.571522i \(-0.193647\pi\)
\(770\) 0 0
\(771\) 13.0748i 0.470876i
\(772\) −8.27714 1.69196i −0.297901 0.0608949i
\(773\) 18.9867 + 32.8859i 0.682904 + 1.18282i 0.974091 + 0.226158i \(0.0726167\pi\)
−0.291186 + 0.956666i \(0.594050\pi\)
\(774\) −2.80304 + 2.28802i −0.100753 + 0.0822413i
\(775\) 0 0
\(776\) 15.7879 + 30.1088i 0.566752 + 1.08084i
\(777\) −19.8711 + 4.99335i −0.712870 + 0.179136i
\(778\) −4.48294 27.6065i −0.160721 0.989741i
\(779\) −19.3222 11.1557i −0.692289 0.399693i
\(780\) 0 0
\(781\) −8.62640 14.9414i −0.308677 0.534644i
\(782\) −6.04110 2.29195i −0.216029 0.0819601i
\(783\) 32.1518i 1.14901i
\(784\) 16.1024 + 22.9066i 0.575086 + 0.818093i
\(785\) 0 0
\(786\) −2.68889 + 7.08734i −0.0959097 + 0.252797i
\(787\) 26.4152 15.2508i 0.941600 0.543633i 0.0511385 0.998692i \(-0.483715\pi\)
0.890462 + 0.455059i \(0.150382\pi\)
\(788\) 12.3237 13.9035i 0.439012 0.495292i
\(789\) 2.49153 + 1.43849i 0.0887009 + 0.0512115i
\(790\) 0 0
\(791\) −0.906381 3.60694i −0.0322272 0.128248i
\(792\) −2.19355 + 1.15021i −0.0779444 + 0.0408709i
\(793\) −0.0583903 0.0337117i −0.00207350 0.00119714i
\(794\) 42.6568 34.8193i 1.51383 1.23569i
\(795\) 0 0
\(796\) −6.03199 + 29.5088i −0.213798 + 1.04591i
\(797\) −46.7505 −1.65599 −0.827995 0.560736i \(-0.810518\pi\)
−0.827995 + 0.560736i \(0.810518\pi\)
\(798\) 3.55455 30.3922i 0.125830 1.07587i
\(799\) 15.0041i 0.530808i
\(800\) 0 0
\(801\) 2.99051 1.72657i 0.105664 0.0610054i
\(802\) 9.79106 7.99210i 0.345734 0.282211i
\(803\) 12.2263 + 7.05887i 0.431458 + 0.249102i
\(804\) −5.73469 17.1919i −0.202247 0.606311i
\(805\) 0 0
\(806\) 1.62361 + 9.99842i 0.0571893 + 0.352179i
\(807\) 21.8001 37.7589i 0.767401 1.32918i
\(808\) −16.7503 10.6011i −0.589273 0.372945i
\(809\) −4.64834 8.05116i −0.163427 0.283064i 0.772669 0.634810i \(-0.218921\pi\)
−0.936096 + 0.351746i \(0.885588\pi\)
\(810\) 0 0
\(811\) 21.7915 0.765204 0.382602 0.923913i \(-0.375028\pi\)
0.382602 + 0.923913i \(0.375028\pi\)
\(812\) −30.1843 15.6776i −1.05926 0.550176i
\(813\) 4.93734i 0.173160i
\(814\) −24.2156 9.18724i −0.848756 0.322013i
\(815\) 0 0
\(816\) −6.23480 + 14.6132i −0.218262 + 0.511566i
\(817\) 28.2535 48.9364i 0.988463 1.71207i
\(818\) 35.2481 5.72383i 1.23242 0.200129i
\(819\) −0.446872 + 1.56934i −0.0156150 + 0.0548373i
\(820\) 0 0
\(821\) 8.02542 13.9004i 0.280089 0.485129i −0.691317 0.722551i \(-0.742969\pi\)
0.971406 + 0.237423i \(0.0763026\pi\)
\(822\) −29.6939 + 24.2381i −1.03569 + 0.845401i
\(823\) −26.2740 45.5079i −0.915854 1.58631i −0.805646 0.592397i \(-0.798182\pi\)
−0.110208 0.993909i \(-0.535152\pi\)
\(824\) 0.236812 5.82190i 0.00824974 0.202816i
\(825\) 0 0
\(826\) 20.7153 + 48.0329i 0.720777 + 1.67128i
\(827\) 5.19538 0.180661 0.0903305 0.995912i \(-0.471208\pi\)
0.0903305 + 0.995912i \(0.471208\pi\)
\(828\) −0.170603 + 0.834600i −0.00592887 + 0.0290044i
\(829\) 48.5004 28.0017i 1.68449 0.972539i 0.725873 0.687828i \(-0.241436\pi\)
0.958614 0.284710i \(-0.0918975\pi\)
\(830\) 0 0
\(831\) −17.2168 + 29.8203i −0.597243 + 1.03446i
\(832\) 13.5693 19.6269i 0.470431 0.680440i
\(833\) −13.1972 8.17901i −0.457257 0.283386i
\(834\) 17.0668 2.77143i 0.590976 0.0959668i
\(835\) 0 0
\(836\) 25.6572 28.9463i 0.887372 1.00113i
\(837\) 10.4026 6.00596i 0.359567 0.207596i
\(838\) 2.03126 + 0.770646i 0.0701686 + 0.0266215i
\(839\) 40.5836 1.40110 0.700551 0.713603i \(-0.252938\pi\)
0.700551 + 0.713603i \(0.252938\pi\)
\(840\) 0 0
\(841\) 12.3171 0.424729
\(842\) −20.8757 7.92010i −0.719423 0.272945i
\(843\) −4.05880 + 2.34335i −0.139793 + 0.0807092i
\(844\) 30.4557 34.3600i 1.04833 1.18272i
\(845\) 0 0
\(846\) −1.95258 + 0.317073i −0.0671311 + 0.0109012i
\(847\) 5.02475 17.6461i 0.172652 0.606328i
\(848\) 30.8270 + 41.0663i 1.05860 + 1.41022i
\(849\) −22.1538 + 38.3714i −0.760315 + 1.31690i
\(850\) 0 0
\(851\) −7.71435 + 4.45388i −0.264445 + 0.152677i
\(852\) −2.92211 + 14.2951i −0.100110 + 0.489742i
\(853\) 4.27019 0.146208 0.0731042 0.997324i \(-0.476709\pi\)
0.0731042 + 0.997324i \(0.476709\pi\)
\(854\) −0.0678416 0.0505137i −0.00232149 0.00172854i
\(855\) 0 0
\(856\) 12.8038 + 0.520809i 0.437626 + 0.0178009i
\(857\) 14.3624 + 24.8764i 0.490610 + 0.849761i 0.999942 0.0108089i \(-0.00344065\pi\)
−0.509332 + 0.860570i \(0.670107\pi\)
\(858\) −24.7810 + 20.2278i −0.846008 + 0.690567i
\(859\) −2.16348 + 3.74726i −0.0738170 + 0.127855i −0.900571 0.434709i \(-0.856851\pi\)
0.826754 + 0.562563i \(0.190185\pi\)
\(860\) 0 0
\(861\) 16.1099 + 16.6209i 0.549025 + 0.566437i
\(862\) 16.7236 2.71569i 0.569608 0.0924968i
\(863\) 7.26780 12.5882i 0.247399 0.428507i −0.715405 0.698710i \(-0.753758\pi\)
0.962803 + 0.270203i \(0.0870909\pi\)
\(864\) −27.4689 6.78877i −0.934510 0.230959i
\(865\) 0 0
\(866\) 32.0236 + 12.1495i 1.08821 + 0.412858i
\(867\) 21.6329i 0.734690i
\(868\) 0.565983 + 12.6946i 0.0192107 + 0.430884i
\(869\) 15.3613 0.521097
\(870\) 0 0
\(871\) −7.54631 13.0706i −0.255697 0.442880i
\(872\) 18.0693 28.5506i 0.611905 0.966844i
\(873\) −1.24271 + 2.15243i −0.0420592 + 0.0728487i
\(874\) −2.13237 13.1314i −0.0721287 0.444178i
\(875\) 0 0
\(876\) −3.77798 11.3259i −0.127646 0.382667i
\(877\) −1.85356 1.07015i −0.0625902 0.0361365i 0.468378 0.883528i \(-0.344838\pi\)
−0.530969 + 0.847392i \(0.678172\pi\)
\(878\) −28.4438 + 23.2177i −0.959933 + 0.783560i
\(879\) 21.7025 12.5299i 0.732006 0.422624i
\(880\) 0 0
\(881\) 55.7208i 1.87728i 0.344897 + 0.938640i \(0.387914\pi\)
−0.344897 + 0.938640i \(0.612086\pi\)
\(882\) −0.785497 + 1.89028i −0.0264490 + 0.0636490i
\(883\) 17.6938 0.595444 0.297722 0.954653i \(-0.403773\pi\)
0.297722 + 0.954653i \(0.403773\pi\)
\(884\) −2.64980 + 12.9630i −0.0891225 + 0.435992i
\(885\) 0 0
\(886\) 19.6507 16.0402i 0.660177 0.538880i
\(887\) 22.9419 + 13.2455i 0.770315 + 0.444742i 0.832987 0.553293i \(-0.186629\pi\)
−0.0626720 + 0.998034i \(0.519962\pi\)
\(888\) 10.1717 + 19.3984i 0.341342 + 0.650968i
\(889\) 38.0880 9.57105i 1.27743 0.321003i
\(890\) 0 0
\(891\) 35.1264 + 20.2802i 1.17678 + 0.679414i
\(892\) 16.2283 18.3087i 0.543364 0.613020i
\(893\) 26.7540 15.4464i 0.895288 0.516895i
\(894\) 13.3191 35.1064i 0.445458 1.17413i
\(895\) 0 0
\(896\) 19.7675 22.4777i 0.660386 0.750926i
\(897\) 11.0018i 0.367341i
\(898\) −5.47998 2.07907i −0.182869 0.0693795i
\(899\) −7.71804 13.3680i −0.257411 0.445849i
\(900\) 0 0
\(901\) −24.6588 14.2368i −0.821503 0.474295i
\(902\) 4.69000 + 28.8816i 0.156160 + 0.961653i
\(903\) −42.0949 + 40.8009i −1.40083 + 1.35777i
\(904\) −3.52115 + 1.84635i −0.117112 + 0.0614087i
\(905\) 0 0
\(906\) −25.0513 + 20.4485i −0.832274 + 0.679357i
\(907\) −19.7918 34.2804i −0.657175 1.13826i −0.981344 0.192262i \(-0.938418\pi\)
0.324168 0.945999i \(-0.394916\pi\)
\(908\) −31.4836 6.43567i −1.04482 0.213575i
\(909\) 1.44920i 0.0480670i
\(910\) 0 0
\(911\) 0.579839i 0.0192109i 0.999954 + 0.00960546i \(0.00305756\pi\)
−0.999954 + 0.00960546i \(0.996942\pi\)
\(912\) −32.4756 + 3.92670i −1.07537 + 0.130026i
\(913\) −24.8534 43.0474i −0.822528 1.42466i
\(914\) 6.16380 + 7.55122i 0.203880 + 0.249772i
\(915\) 0 0
\(916\) −11.2013 33.5801i −0.370101 1.10952i
\(917\) −2.16880 + 7.61650i −0.0716201 + 0.251519i
\(918\) 15.4871 2.51490i 0.511151 0.0830042i
\(919\) 3.25111 + 1.87703i 0.107244 + 0.0619174i 0.552663 0.833405i \(-0.313612\pi\)
−0.445419 + 0.895322i \(0.646945\pi\)
\(920\) 0 0
\(921\) 23.4924 + 40.6900i 0.774101 + 1.34078i
\(922\) 5.23054 13.7866i 0.172259 0.454037i
\(923\) 12.1509i 0.399951i
\(924\) −33.8248 + 21.5926i −1.11275 + 0.710345i
\(925\) 0 0
\(926\) 13.0443 + 4.94891i 0.428661 + 0.162631i
\(927\) 0.368903 0.212986i 0.0121164 0.00699538i
\(928\) −8.72401 + 35.2993i −0.286380 + 1.15876i
\(929\) 22.4184 + 12.9433i 0.735525 + 0.424655i 0.820440 0.571733i \(-0.193729\pi\)
−0.0849153 + 0.996388i \(0.527062\pi\)
\(930\) 0 0
\(931\) 0.997813 31.9522i 0.0327020 1.04719i
\(932\) −5.04270 15.1174i −0.165179 0.495186i
\(933\) −11.5677 6.67860i −0.378709 0.218648i
\(934\) 3.48334 + 4.26741i 0.113978 + 0.139634i
\(935\) 0 0
\(936\) 1.74295 + 0.0708963i 0.0569701 + 0.00231732i
\(937\) 53.4145 1.74497 0.872487 0.488636i \(-0.162506\pi\)
0.872487 + 0.488636i \(0.162506\pi\)
\(938\) −7.49796 17.3856i −0.244817 0.567661i
\(939\) 7.62571i 0.248856i
\(940\) 0 0
\(941\) 28.8728 16.6697i 0.941225 0.543417i 0.0508811 0.998705i \(-0.483797\pi\)
0.890344 + 0.455288i \(0.150464\pi\)
\(942\) −19.3269 23.6772i −0.629705 0.771446i
\(943\) 8.71518 + 5.03171i 0.283805 + 0.163855i
\(944\) 44.7226 33.5717i 1.45560 1.09267i
\(945\) 0 0
\(946\) −73.1472 + 11.8781i −2.37822 + 0.386192i
\(947\) −19.4148 + 33.6274i −0.630896 + 1.09274i 0.356473 + 0.934306i \(0.383979\pi\)
−0.987369 + 0.158438i \(0.949354\pi\)
\(948\) −9.72179 8.61712i −0.315749 0.279871i
\(949\) −4.97146 8.61083i −0.161381 0.279519i
\(950\) 0 0
\(951\) 10.8236 0.350979
\(952\) −5.19070 + 15.7657i −0.168232 + 0.510969i
\(953\) 14.1526i 0.458447i 0.973374 + 0.229224i \(0.0736187\pi\)
−0.973374 + 0.229224i \(0.926381\pi\)
\(954\) −1.33162 + 3.50986i −0.0431127 + 0.113636i
\(955\) 0 0
\(956\) 15.1029 17.0390i 0.488462 0.551081i
\(957\) 24.3734 42.2161i 0.787882 1.36465i
\(958\) 0.248177 + 1.52830i 0.00801822 + 0.0493773i
\(959\) −28.7542 + 27.8703i −0.928522 + 0.899978i
\(960\) 0 0
\(961\) 12.6165 21.8525i 0.406985 0.704919i
\(962\) 11.5346 + 14.1309i 0.371889 + 0.455599i
\(963\) 0.468410 + 0.811310i 0.0150943 + 0.0261441i
\(964\) −31.9479 6.53057i −1.02897 0.210335i
\(965\) 0 0
\(966\) −1.60326 + 13.7083i −0.0515841 + 0.441057i
\(967\) −10.9730 −0.352869 −0.176434 0.984312i \(-0.556456\pi\)
−0.176434 + 0.984312i \(0.556456\pi\)
\(968\) −19.5982 0.797177i −0.629910 0.0256223i
\(969\) 15.7089 9.06956i 0.504644 0.291356i
\(970\) 0 0
\(971\) 6.49830 11.2554i 0.208540 0.361202i −0.742715 0.669608i \(-0.766462\pi\)
0.951255 + 0.308406i \(0.0997954\pi\)
\(972\) −1.35758 4.06984i −0.0435443 0.130540i
\(973\) 17.5190 4.40230i 0.561632 0.141131i
\(974\) 3.17723 + 19.5658i 0.101805 + 0.626928i
\(975\) 0 0
\(976\) −0.0354842 + 0.0831685i −0.00113582 + 0.00266216i
\(977\) −17.9462 + 10.3612i −0.574148 + 0.331485i −0.758805 0.651318i \(-0.774216\pi\)
0.184656 + 0.982803i \(0.440883\pi\)
\(978\) −3.52974 + 9.30363i −0.112869 + 0.297497i
\(979\) 70.7228 2.26031
\(980\) 0 0
\(981\) 2.47014 0.0788654
\(982\) 6.37345 16.7990i 0.203385 0.536079i
\(983\) 26.4043 15.2445i 0.842166 0.486225i −0.0158341 0.999875i \(-0.505040\pi\)
0.858000 + 0.513650i \(0.171707\pi\)
\(984\) 13.2333 20.9094i 0.421863 0.666567i
\(985\) 0 0
\(986\) −3.23181 19.9019i −0.102922 0.633807i
\(987\) −31.0835 + 7.81091i −0.989400 + 0.248624i
\(988\) −25.8423 + 8.62021i −0.822153 + 0.274246i
\(989\) −12.7436 + 22.0726i −0.405223 + 0.701867i
\(990\) 0 0
\(991\) 38.5713 22.2691i 1.22526 0.707403i 0.259223 0.965817i \(-0.416533\pi\)
0.966034 + 0.258415i \(0.0832000\pi\)
\(992\) 13.0506 3.77128i 0.414358 0.119738i
\(993\) 52.0719 1.65245
\(994\) −1.77071 + 15.1400i −0.0561635 + 0.480211i
\(995\) 0 0
\(996\) −8.41885 + 41.1854i −0.266761 + 1.30501i
\(997\) 15.0714 + 26.1044i 0.477315 + 0.826734i 0.999662 0.0259989i \(-0.00827663\pi\)
−0.522347 + 0.852733i \(0.674943\pi\)
\(998\) 6.42488 + 7.87107i 0.203376 + 0.249154i
\(999\) 10.8154 18.7329i 0.342185 0.592682i
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 700.2.t.c.299.2 32
4.3 odd 2 inner 700.2.t.c.299.3 32
5.2 odd 4 700.2.p.c.551.11 32
5.3 odd 4 140.2.o.a.131.6 yes 32
5.4 even 2 700.2.t.d.299.15 32
7.3 odd 6 700.2.t.d.199.14 32
20.3 even 4 140.2.o.a.131.5 yes 32
20.7 even 4 700.2.p.c.551.12 32
20.19 odd 2 700.2.t.d.299.14 32
28.3 even 6 700.2.t.d.199.15 32
35.3 even 12 140.2.o.a.31.5 32
35.13 even 4 980.2.o.f.411.6 32
35.17 even 12 700.2.p.c.451.12 32
35.18 odd 12 980.2.o.f.31.5 32
35.23 odd 12 980.2.g.a.391.30 32
35.24 odd 6 inner 700.2.t.c.199.3 32
35.33 even 12 980.2.g.a.391.29 32
140.3 odd 12 140.2.o.a.31.6 yes 32
140.23 even 12 980.2.g.a.391.31 32
140.59 even 6 inner 700.2.t.c.199.2 32
140.83 odd 4 980.2.o.f.411.5 32
140.87 odd 12 700.2.p.c.451.11 32
140.103 odd 12 980.2.g.a.391.32 32
140.123 even 12 980.2.o.f.31.6 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
140.2.o.a.31.5 32 35.3 even 12
140.2.o.a.31.6 yes 32 140.3 odd 12
140.2.o.a.131.5 yes 32 20.3 even 4
140.2.o.a.131.6 yes 32 5.3 odd 4
700.2.p.c.451.11 32 140.87 odd 12
700.2.p.c.451.12 32 35.17 even 12
700.2.p.c.551.11 32 5.2 odd 4
700.2.p.c.551.12 32 20.7 even 4
700.2.t.c.199.2 32 140.59 even 6 inner
700.2.t.c.199.3 32 35.24 odd 6 inner
700.2.t.c.299.2 32 1.1 even 1 trivial
700.2.t.c.299.3 32 4.3 odd 2 inner
700.2.t.d.199.14 32 7.3 odd 6
700.2.t.d.199.15 32 28.3 even 6
700.2.t.d.299.14 32 20.19 odd 2
700.2.t.d.299.15 32 5.4 even 2
980.2.g.a.391.29 32 35.33 even 12
980.2.g.a.391.30 32 35.23 odd 12
980.2.g.a.391.31 32 140.23 even 12
980.2.g.a.391.32 32 140.103 odd 12
980.2.o.f.31.5 32 35.18 odd 12
980.2.o.f.31.6 32 140.123 even 12
980.2.o.f.411.5 32 140.83 odd 4
980.2.o.f.411.6 32 35.13 even 4