Properties

Label 441.2.i.d.68.16
Level $441$
Weight $2$
Character 441.68
Analytic conductor $3.521$
Analytic rank $0$
Dimension $48$
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] = [441,2,Mod(68,441)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(441, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([5, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("441.68");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 441.i (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: \(3.52140272914\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(24\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 68.16
Character \(\chi\) \(=\) 441.68
Dual form 441.2.i.d.227.10

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+0.664297i q^{2} +(1.15747 + 1.28852i) q^{3} +1.55871 q^{4} +(0.0141520 + 0.0245119i) q^{5} +(-0.855956 + 0.768901i) q^{6} +2.36404i q^{8} +(-0.320544 + 2.98283i) q^{9} +O(q^{10})\) \(q+0.664297i q^{2} +(1.15747 + 1.28852i) q^{3} +1.55871 q^{4} +(0.0141520 + 0.0245119i) q^{5} +(-0.855956 + 0.768901i) q^{6} +2.36404i q^{8} +(-0.320544 + 2.98283i) q^{9} +(-0.0162832 + 0.00940110i) q^{10} +(0.885324 + 0.511142i) q^{11} +(1.80415 + 2.00842i) q^{12} +(-4.87844 - 2.81657i) q^{13} +(-0.0152036 + 0.0466067i) q^{15} +1.54700 q^{16} +(2.83940 + 4.91798i) q^{17} +(-1.98148 - 0.212936i) q^{18} +(-1.81237 - 1.04637i) q^{19} +(0.0220588 + 0.0382070i) q^{20} +(-0.339550 + 0.588118i) q^{22} +(6.28849 - 3.63066i) q^{23} +(-3.04610 + 2.73630i) q^{24} +(2.49960 - 4.32943i) q^{25} +(1.87104 - 3.24073i) q^{26} +(-4.21444 + 3.03949i) q^{27} +(-3.52577 + 2.03560i) q^{29} +(-0.0309607 - 0.0100997i) q^{30} -3.31820i q^{31} +5.75574i q^{32} +(0.366118 + 1.73238i) q^{33} +(-3.26700 + 1.88620i) q^{34} +(-0.499635 + 4.64936i) q^{36} +(1.23632 - 2.14137i) q^{37} +(0.695101 - 1.20395i) q^{38} +(-2.01744 - 9.54604i) q^{39} +(-0.0579471 + 0.0334558i) q^{40} +(3.52867 - 6.11183i) q^{41} +(-1.15994 - 2.00908i) q^{43} +(1.37996 + 0.796722i) q^{44} +(-0.0776511 + 0.0343557i) q^{45} +(2.41184 + 4.17742i) q^{46} -10.8799 q^{47} +(1.79060 + 1.99333i) q^{48} +(2.87603 + 1.66048i) q^{50} +(-3.05039 + 9.35101i) q^{51} +(-7.60408 - 4.39022i) q^{52} +(-10.0454 + 5.79973i) q^{53} +(-2.01913 - 2.79964i) q^{54} +0.0289346i q^{55} +(-0.749489 - 3.54640i) q^{57} +(-1.35224 - 2.34215i) q^{58} +6.02222 q^{59} +(-0.0236979 + 0.0726464i) q^{60} +2.36968i q^{61} +2.20427 q^{62} -0.729528 q^{64} -0.159440i q^{65} +(-1.15082 + 0.243211i) q^{66} +12.7799 q^{67} +(4.42580 + 7.66571i) q^{68} +(11.9569 + 3.90045i) q^{69} -7.93415i q^{71} +(-7.05152 - 0.757778i) q^{72} +(9.43889 - 5.44955i) q^{73} +(1.42251 + 0.821285i) q^{74} +(8.47174 - 1.79040i) q^{75} +(-2.82496 - 1.63099i) q^{76} +(6.34140 - 1.34018i) q^{78} -15.6004 q^{79} +(0.0218930 + 0.0379198i) q^{80} +(-8.79450 - 1.91225i) q^{81} +(4.06007 + 2.34408i) q^{82} +(3.07406 + 5.32442i) q^{83} +(-0.0803661 + 0.139198i) q^{85} +(1.33463 - 0.770546i) q^{86} +(-6.70386 - 2.18686i) q^{87} +(-1.20836 + 2.09294i) q^{88} +(6.02582 - 10.4370i) q^{89} +(-0.0228224 - 0.0515834i) q^{90} +(9.80194 - 5.65915i) q^{92} +(4.27555 - 3.84070i) q^{93} -7.22751i q^{94} -0.0592328i q^{95} +(-7.41636 + 6.66208i) q^{96} +(6.77565 - 3.91192i) q^{97} +(-1.80843 + 2.47692i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q - 48 q^{4} - 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 48 q - 48 q^{4} - 8 q^{9} + 24 q^{11} - 40 q^{15} + 48 q^{16} - 16 q^{18} + 48 q^{23} - 24 q^{25} - 24 q^{30} - 8 q^{36} - 56 q^{39} - 96 q^{44} + 48 q^{50} - 24 q^{51} - 48 q^{53} + 80 q^{57} + 168 q^{60} - 48 q^{64} - 88 q^{72} + 168 q^{74} - 88 q^{78} + 48 q^{79} - 24 q^{81} - 24 q^{85} - 24 q^{86} - 144 q^{92} + 16 q^{93} - 72 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(344\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.664297i 0.469729i 0.972028 + 0.234864i \(0.0754646\pi\)
−0.972028 + 0.234864i \(0.924535\pi\)
\(3\) 1.15747 + 1.28852i 0.668263 + 0.743925i
\(4\) 1.55871 0.779355
\(5\) 0.0141520 + 0.0245119i 0.00632895 + 0.0109621i 0.869173 0.494509i \(-0.164652\pi\)
−0.862844 + 0.505471i \(0.831319\pi\)
\(6\) −0.855956 + 0.768901i −0.349443 + 0.313903i
\(7\) 0 0
\(8\) 2.36404i 0.835814i
\(9\) −0.320544 + 2.98283i −0.106848 + 0.994275i
\(10\) −0.0162832 + 0.00940110i −0.00514919 + 0.00297289i
\(11\) 0.885324 + 0.511142i 0.266935 + 0.154115i 0.627494 0.778621i \(-0.284081\pi\)
−0.360559 + 0.932736i \(0.617414\pi\)
\(12\) 1.80415 + 2.00842i 0.520814 + 0.579781i
\(13\) −4.87844 2.81657i −1.35304 0.781176i −0.364363 0.931257i \(-0.618713\pi\)
−0.988674 + 0.150081i \(0.952047\pi\)
\(14\) 0 0
\(15\) −0.0152036 + 0.0466067i −0.00392554 + 0.0120338i
\(16\) 1.54700 0.386749
\(17\) 2.83940 + 4.91798i 0.688656 + 1.19279i 0.972273 + 0.233849i \(0.0751321\pi\)
−0.283617 + 0.958938i \(0.591535\pi\)
\(18\) −1.98148 0.212936i −0.467040 0.0501895i
\(19\) −1.81237 1.04637i −0.415786 0.240054i 0.277487 0.960729i \(-0.410498\pi\)
−0.693273 + 0.720675i \(0.743832\pi\)
\(20\) 0.0220588 + 0.0382070i 0.00493250 + 0.00854334i
\(21\) 0 0
\(22\) −0.339550 + 0.588118i −0.0723923 + 0.125387i
\(23\) 6.28849 3.63066i 1.31124 0.757046i 0.328940 0.944351i \(-0.393309\pi\)
0.982302 + 0.187305i \(0.0599754\pi\)
\(24\) −3.04610 + 2.73630i −0.621783 + 0.558544i
\(25\) 2.49960 4.32943i 0.499920 0.865887i
\(26\) 1.87104 3.24073i 0.366941 0.635560i
\(27\) −4.21444 + 3.03949i −0.811069 + 0.584951i
\(28\) 0 0
\(29\) −3.52577 + 2.03560i −0.654718 + 0.378002i −0.790262 0.612770i \(-0.790055\pi\)
0.135543 + 0.990771i \(0.456722\pi\)
\(30\) −0.0309607 0.0100997i −0.00565262 0.00184394i
\(31\) 3.31820i 0.595966i −0.954571 0.297983i \(-0.903686\pi\)
0.954571 0.297983i \(-0.0963139\pi\)
\(32\) 5.75574i 1.01748i
\(33\) 0.366118 + 1.73238i 0.0637330 + 0.301569i
\(34\) −3.26700 + 1.88620i −0.560286 + 0.323481i
\(35\) 0 0
\(36\) −0.499635 + 4.64936i −0.0832725 + 0.774893i
\(37\) 1.23632 2.14137i 0.203250 0.352040i −0.746324 0.665583i \(-0.768183\pi\)
0.949574 + 0.313543i \(0.101516\pi\)
\(38\) 0.695101 1.20395i 0.112760 0.195306i
\(39\) −2.01744 9.54604i −0.323049 1.52859i
\(40\) −0.0579471 + 0.0334558i −0.00916224 + 0.00528982i
\(41\) 3.52867 6.11183i 0.551085 0.954508i −0.447111 0.894478i \(-0.647547\pi\)
0.998197 0.0600295i \(-0.0191195\pi\)
\(42\) 0 0
\(43\) −1.15994 2.00908i −0.176890 0.306382i 0.763924 0.645306i \(-0.223270\pi\)
−0.940814 + 0.338924i \(0.889937\pi\)
\(44\) 1.37996 + 0.796722i 0.208037 + 0.120110i
\(45\) −0.0776511 + 0.0343557i −0.0115755 + 0.00512144i
\(46\) 2.41184 + 4.17742i 0.355606 + 0.615928i
\(47\) −10.8799 −1.58700 −0.793502 0.608568i \(-0.791744\pi\)
−0.793502 + 0.608568i \(0.791744\pi\)
\(48\) 1.79060 + 1.99333i 0.258450 + 0.287712i
\(49\) 0 0
\(50\) 2.87603 + 1.66048i 0.406732 + 0.234827i
\(51\) −3.05039 + 9.35101i −0.427140 + 1.30940i
\(52\) −7.60408 4.39022i −1.05450 0.608814i
\(53\) −10.0454 + 5.79973i −1.37985 + 0.796655i −0.992141 0.125128i \(-0.960066\pi\)
−0.387706 + 0.921783i \(0.626732\pi\)
\(54\) −2.01913 2.79964i −0.274768 0.380982i
\(55\) 0.0289346i 0.00390155i
\(56\) 0 0
\(57\) −0.749489 3.54640i −0.0992723 0.469733i
\(58\) −1.35224 2.34215i −0.177558 0.307540i
\(59\) 6.02222 0.784027 0.392013 0.919960i \(-0.371779\pi\)
0.392013 + 0.919960i \(0.371779\pi\)
\(60\) −0.0236979 + 0.0726464i −0.00305939 + 0.00937861i
\(61\) 2.36968i 0.303406i 0.988426 + 0.151703i \(0.0484757\pi\)
−0.988426 + 0.151703i \(0.951524\pi\)
\(62\) 2.20427 0.279942
\(63\) 0 0
\(64\) −0.729528 −0.0911909
\(65\) 0.159440i 0.0197761i
\(66\) −1.15082 + 0.243211i −0.141656 + 0.0299372i
\(67\) 12.7799 1.56131 0.780656 0.624960i \(-0.214885\pi\)
0.780656 + 0.624960i \(0.214885\pi\)
\(68\) 4.42580 + 7.66571i 0.536707 + 0.929604i
\(69\) 11.9569 + 3.90045i 1.43944 + 0.469559i
\(70\) 0 0
\(71\) 7.93415i 0.941610i −0.882237 0.470805i \(-0.843964\pi\)
0.882237 0.470805i \(-0.156036\pi\)
\(72\) −7.05152 0.757778i −0.831029 0.0893050i
\(73\) 9.43889 5.44955i 1.10474 0.637821i 0.167277 0.985910i \(-0.446503\pi\)
0.937462 + 0.348089i \(0.113169\pi\)
\(74\) 1.42251 + 0.821285i 0.165363 + 0.0954725i
\(75\) 8.47174 1.79040i 0.978233 0.206738i
\(76\) −2.82496 1.63099i −0.324045 0.187087i
\(77\) 0 0
\(78\) 6.34140 1.34018i 0.718022 0.151745i
\(79\) −15.6004 −1.75518 −0.877588 0.479415i \(-0.840849\pi\)
−0.877588 + 0.479415i \(0.840849\pi\)
\(80\) 0.0218930 + 0.0379198i 0.00244772 + 0.00423957i
\(81\) −8.79450 1.91225i −0.977167 0.212473i
\(82\) 4.06007 + 2.34408i 0.448360 + 0.258861i
\(83\) 3.07406 + 5.32442i 0.337421 + 0.584431i 0.983947 0.178461i \(-0.0571119\pi\)
−0.646526 + 0.762892i \(0.723779\pi\)
\(84\) 0 0
\(85\) −0.0803661 + 0.139198i −0.00871693 + 0.0150982i
\(86\) 1.33463 0.770546i 0.143916 0.0830902i
\(87\) −6.70386 2.18686i −0.718729 0.234456i
\(88\) −1.20836 + 2.09294i −0.128812 + 0.223108i
\(89\) 6.02582 10.4370i 0.638736 1.10632i −0.346975 0.937874i \(-0.612791\pi\)
0.985711 0.168448i \(-0.0538756\pi\)
\(90\) −0.0228224 0.0515834i −0.00240569 0.00543736i
\(91\) 0 0
\(92\) 9.80194 5.65915i 1.02192 0.590007i
\(93\) 4.27555 3.84070i 0.443354 0.398262i
\(94\) 7.22751i 0.745461i
\(95\) 0.0592328i 0.00607716i
\(96\) −7.41636 + 6.66208i −0.756929 + 0.679946i
\(97\) 6.77565 3.91192i 0.687963 0.397196i −0.114885 0.993379i \(-0.536650\pi\)
0.802848 + 0.596183i \(0.203317\pi\)
\(98\) 0 0
\(99\) −1.80843 + 2.47692i −0.181754 + 0.248940i
\(100\) 3.89615 6.74833i 0.389615 0.674833i
\(101\) −0.226924 + 0.393043i −0.0225797 + 0.0391093i −0.877094 0.480318i \(-0.840521\pi\)
0.854515 + 0.519427i \(0.173855\pi\)
\(102\) −6.21185 2.02636i −0.615064 0.200640i
\(103\) −4.58316 + 2.64609i −0.451592 + 0.260727i −0.708502 0.705708i \(-0.750629\pi\)
0.256910 + 0.966435i \(0.417296\pi\)
\(104\) 6.65848 11.5328i 0.652918 1.13089i
\(105\) 0 0
\(106\) −3.85274 6.67315i −0.374212 0.648153i
\(107\) −7.85273 4.53377i −0.759152 0.438296i 0.0698394 0.997558i \(-0.477751\pi\)
−0.828991 + 0.559262i \(0.811085\pi\)
\(108\) −6.56908 + 4.73769i −0.632110 + 0.455885i
\(109\) −2.36514 4.09654i −0.226539 0.392377i 0.730241 0.683190i \(-0.239408\pi\)
−0.956780 + 0.290812i \(0.906074\pi\)
\(110\) −0.0192212 −0.00183267
\(111\) 4.19020 0.885547i 0.397716 0.0840524i
\(112\) 0 0
\(113\) −8.21108 4.74067i −0.772433 0.445965i 0.0613086 0.998119i \(-0.480473\pi\)
−0.833742 + 0.552154i \(0.813806\pi\)
\(114\) 2.35586 0.497883i 0.220647 0.0466310i
\(115\) 0.177989 + 0.102762i 0.0165976 + 0.00958261i
\(116\) −5.49565 + 3.17291i −0.510258 + 0.294598i
\(117\) 9.96510 13.6487i 0.921273 1.26182i
\(118\) 4.00054i 0.368280i
\(119\) 0 0
\(120\) −0.110180 0.0359418i −0.0100580 0.00328102i
\(121\) −4.97747 8.62123i −0.452497 0.783748i
\(122\) −1.57417 −0.142519
\(123\) 11.9595 2.52750i 1.07835 0.227897i
\(124\) 5.17211i 0.464469i
\(125\) 0.283017 0.0253138
\(126\) 0 0
\(127\) 4.37297 0.388039 0.194019 0.980998i \(-0.437848\pi\)
0.194019 + 0.980998i \(0.437848\pi\)
\(128\) 11.0269i 0.974646i
\(129\) 1.24614 3.82005i 0.109716 0.336336i
\(130\) 0.105915 0.00928940
\(131\) 1.27231 + 2.20371i 0.111162 + 0.192539i 0.916239 0.400632i \(-0.131209\pi\)
−0.805077 + 0.593171i \(0.797876\pi\)
\(132\) 0.570672 + 2.70028i 0.0496706 + 0.235029i
\(133\) 0 0
\(134\) 8.48964i 0.733393i
\(135\) −0.134146 0.0602891i −0.0115455 0.00518886i
\(136\) −11.6263 + 6.71245i −0.996948 + 0.575588i
\(137\) 9.82536 + 5.67267i 0.839437 + 0.484649i 0.857073 0.515195i \(-0.172281\pi\)
−0.0176357 + 0.999844i \(0.505614\pi\)
\(138\) −2.59106 + 7.94292i −0.220565 + 0.676146i
\(139\) 3.04891 + 1.76029i 0.258605 + 0.149306i 0.623698 0.781665i \(-0.285629\pi\)
−0.365093 + 0.930971i \(0.618963\pi\)
\(140\) 0 0
\(141\) −12.5932 14.0190i −1.06054 1.18061i
\(142\) 5.27063 0.442301
\(143\) −2.87933 4.98715i −0.240782 0.417047i
\(144\) −0.495880 + 4.61442i −0.0413233 + 0.384535i
\(145\) −0.0997930 0.0576155i −0.00828736 0.00478471i
\(146\) 3.62012 + 6.27022i 0.299603 + 0.518927i
\(147\) 0 0
\(148\) 1.92707 3.33778i 0.158404 0.274364i
\(149\) 13.7806 7.95623i 1.12895 0.651800i 0.185279 0.982686i \(-0.440681\pi\)
0.943671 + 0.330886i \(0.107348\pi\)
\(150\) 1.18936 + 5.62775i 0.0971106 + 0.459504i
\(151\) −1.73008 + 2.99659i −0.140792 + 0.243859i −0.927795 0.373090i \(-0.878298\pi\)
0.787003 + 0.616949i \(0.211632\pi\)
\(152\) 2.47366 4.28451i 0.200640 0.347520i
\(153\) −15.5796 + 6.89301i −1.25954 + 0.557267i
\(154\) 0 0
\(155\) 0.0813354 0.0469590i 0.00653302 0.00377184i
\(156\) −3.14460 14.8795i −0.251770 1.19131i
\(157\) 16.3488i 1.30478i 0.757883 + 0.652390i \(0.226234\pi\)
−0.757883 + 0.652390i \(0.773766\pi\)
\(158\) 10.3633i 0.824457i
\(159\) −19.1003 6.23070i −1.51475 0.494127i
\(160\) −0.141084 + 0.0814550i −0.0111537 + 0.00643959i
\(161\) 0 0
\(162\) 1.27030 5.84216i 0.0998044 0.459003i
\(163\) −5.17782 + 8.96824i −0.405558 + 0.702447i −0.994386 0.105811i \(-0.966256\pi\)
0.588828 + 0.808258i \(0.299589\pi\)
\(164\) 5.50017 9.52657i 0.429491 0.743900i
\(165\) −0.0372827 + 0.0334909i −0.00290246 + 0.00260726i
\(166\) −3.53699 + 2.04208i −0.274524 + 0.158497i
\(167\) −2.94297 + 5.09738i −0.227734 + 0.394447i −0.957136 0.289638i \(-0.906465\pi\)
0.729402 + 0.684085i \(0.239798\pi\)
\(168\) 0 0
\(169\) 9.36614 + 16.2226i 0.720473 + 1.24790i
\(170\) −0.0924689 0.0533870i −0.00709204 0.00409459i
\(171\) 3.70209 5.07057i 0.283106 0.387756i
\(172\) −1.80802 3.13157i −0.137860 0.238780i
\(173\) −4.86551 −0.369918 −0.184959 0.982746i \(-0.559215\pi\)
−0.184959 + 0.982746i \(0.559215\pi\)
\(174\) 1.45273 4.45335i 0.110131 0.337608i
\(175\) 0 0
\(176\) 1.36959 + 0.790735i 0.103237 + 0.0596039i
\(177\) 6.97052 + 7.75973i 0.523936 + 0.583257i
\(178\) 6.93328 + 4.00293i 0.519671 + 0.300032i
\(179\) −0.175495 + 0.101322i −0.0131171 + 0.00757319i −0.506544 0.862214i \(-0.669077\pi\)
0.493427 + 0.869787i \(0.335744\pi\)
\(180\) −0.121036 + 0.0535506i −0.00902146 + 0.00399142i
\(181\) 6.26273i 0.465505i −0.972536 0.232753i \(-0.925227\pi\)
0.972536 0.232753i \(-0.0747732\pi\)
\(182\) 0 0
\(183\) −3.05337 + 2.74282i −0.225711 + 0.202755i
\(184\) 8.58303 + 14.8662i 0.632749 + 1.09595i
\(185\) 0.0699856 0.00514544
\(186\) 2.55137 + 2.84023i 0.187075 + 0.208256i
\(187\) 5.80534i 0.424529i
\(188\) −16.9587 −1.23684
\(189\) 0 0
\(190\) 0.0393482 0.00285462
\(191\) 13.8034i 0.998776i 0.866379 + 0.499388i \(0.166442\pi\)
−0.866379 + 0.499388i \(0.833558\pi\)
\(192\) −0.844404 0.940007i −0.0609396 0.0678392i
\(193\) −21.0774 −1.51719 −0.758593 0.651565i \(-0.774113\pi\)
−0.758593 + 0.651565i \(0.774113\pi\)
\(194\) 2.59868 + 4.50104i 0.186574 + 0.323156i
\(195\) 0.205441 0.184546i 0.0147119 0.0132156i
\(196\) 0 0
\(197\) 15.1679i 1.08067i 0.841451 + 0.540334i \(0.181702\pi\)
−0.841451 + 0.540334i \(0.818298\pi\)
\(198\) −1.64541 1.20134i −0.116934 0.0853752i
\(199\) 8.38940 4.84362i 0.594709 0.343355i −0.172249 0.985054i \(-0.555103\pi\)
0.766957 + 0.641698i \(0.221770\pi\)
\(200\) 10.2349 + 5.90915i 0.723720 + 0.417840i
\(201\) 14.7923 + 16.4671i 1.04337 + 1.16150i
\(202\) −0.261097 0.150745i −0.0183707 0.0106064i
\(203\) 0 0
\(204\) −4.75467 + 14.5755i −0.332894 + 1.02049i
\(205\) 0.199750 0.0139512
\(206\) −1.75779 3.04458i −0.122471 0.212126i
\(207\) 8.81390 + 19.9213i 0.612608 + 1.38462i
\(208\) −7.54694 4.35723i −0.523286 0.302119i
\(209\) −1.06969 1.85275i −0.0739919 0.128158i
\(210\) 0 0
\(211\) −7.05942 + 12.2273i −0.485991 + 0.841761i −0.999870 0.0161017i \(-0.994874\pi\)
0.513880 + 0.857862i \(0.328208\pi\)
\(212\) −15.6579 + 9.04010i −1.07539 + 0.620877i
\(213\) 10.2233 9.18351i 0.700487 0.629243i
\(214\) 3.01177 5.21654i 0.205880 0.356595i
\(215\) 0.0328309 0.0568649i 0.00223905 0.00387815i
\(216\) −7.18549 9.96309i −0.488910 0.677903i
\(217\) 0 0
\(218\) 2.72132 1.57115i 0.184311 0.106412i
\(219\) 17.9470 + 5.85449i 1.21275 + 0.395610i
\(220\) 0.0451007i 0.00304069i
\(221\) 31.9895i 2.15185i
\(222\) 0.588266 + 2.78353i 0.0394818 + 0.186819i
\(223\) −2.58777 + 1.49405i −0.173290 + 0.100049i −0.584136 0.811656i \(-0.698567\pi\)
0.410846 + 0.911705i \(0.365233\pi\)
\(224\) 0 0
\(225\) 12.1127 + 8.84364i 0.807514 + 0.589576i
\(226\) 3.14921 5.45459i 0.209482 0.362834i
\(227\) −14.3867 + 24.9184i −0.954876 + 1.65389i −0.220224 + 0.975449i \(0.570679\pi\)
−0.734652 + 0.678444i \(0.762654\pi\)
\(228\) −1.16824 5.52781i −0.0773684 0.366088i
\(229\) 7.67401 4.43059i 0.507113 0.292782i −0.224533 0.974466i \(-0.572086\pi\)
0.731646 + 0.681685i \(0.238752\pi\)
\(230\) −0.0682645 + 0.118238i −0.00450122 + 0.00779635i
\(231\) 0 0
\(232\) −4.81224 8.33505i −0.315939 0.547223i
\(233\) −11.1789 6.45412i −0.732351 0.422823i 0.0869305 0.996214i \(-0.472294\pi\)
−0.819282 + 0.573391i \(0.805628\pi\)
\(234\) 9.06680 + 6.61978i 0.592715 + 0.432749i
\(235\) −0.153973 0.266688i −0.0100441 0.0173968i
\(236\) 9.38690 0.611035
\(237\) −18.0569 20.1013i −1.17292 1.30572i
\(238\) 0 0
\(239\) −4.85712 2.80426i −0.314181 0.181392i 0.334615 0.942355i \(-0.391394\pi\)
−0.648796 + 0.760963i \(0.724727\pi\)
\(240\) −0.0235199 + 0.0721005i −0.00151820 + 0.00465406i
\(241\) 9.51481 + 5.49338i 0.612903 + 0.353860i 0.774101 0.633063i \(-0.218202\pi\)
−0.161198 + 0.986922i \(0.551536\pi\)
\(242\) 5.72705 3.30652i 0.368149 0.212551i
\(243\) −7.71537 13.5452i −0.494941 0.868926i
\(244\) 3.69364i 0.236461i
\(245\) 0 0
\(246\) 1.67901 + 7.94466i 0.107050 + 0.506533i
\(247\) 5.89436 + 10.2093i 0.375049 + 0.649604i
\(248\) 7.84435 0.498117
\(249\) −3.30248 + 10.1238i −0.209286 + 0.641570i
\(250\) 0.188007i 0.0118906i
\(251\) −24.2241 −1.52901 −0.764505 0.644618i \(-0.777016\pi\)
−0.764505 + 0.644618i \(0.777016\pi\)
\(252\) 0 0
\(253\) 7.42314 0.466689
\(254\) 2.90495i 0.182273i
\(255\) −0.272380 + 0.0575643i −0.0170571 + 0.00360481i
\(256\) −8.78416 −0.549010
\(257\) 8.86142 + 15.3484i 0.552760 + 0.957409i 0.998074 + 0.0620341i \(0.0197588\pi\)
−0.445314 + 0.895375i \(0.646908\pi\)
\(258\) 2.53765 + 0.827804i 0.157987 + 0.0515368i
\(259\) 0 0
\(260\) 0.248521i 0.0154126i
\(261\) −4.94168 11.1692i −0.305883 0.691359i
\(262\) −1.46392 + 0.845193i −0.0904411 + 0.0522162i
\(263\) −2.51031 1.44933i −0.154793 0.0893695i 0.420603 0.907245i \(-0.361819\pi\)
−0.575396 + 0.817875i \(0.695152\pi\)
\(264\) −4.09542 + 0.865518i −0.252056 + 0.0532689i
\(265\) −0.284325 0.164155i −0.0174660 0.0100840i
\(266\) 0 0
\(267\) 20.4230 4.31614i 1.24986 0.264144i
\(268\) 19.9202 1.21682
\(269\) −10.9469 18.9606i −0.667444 1.15605i −0.978616 0.205694i \(-0.934055\pi\)
0.311172 0.950354i \(-0.399278\pi\)
\(270\) 0.0400498 0.0891130i 0.00243736 0.00542324i
\(271\) 7.77992 + 4.49174i 0.472596 + 0.272854i 0.717326 0.696738i \(-0.245366\pi\)
−0.244730 + 0.969591i \(0.578699\pi\)
\(272\) 4.39254 + 7.60811i 0.266337 + 0.461309i
\(273\) 0 0
\(274\) −3.76834 + 6.52695i −0.227654 + 0.394308i
\(275\) 4.42591 2.55530i 0.266892 0.154090i
\(276\) 18.6373 + 6.07967i 1.12183 + 0.365953i
\(277\) −7.95091 + 13.7714i −0.477724 + 0.827442i −0.999674 0.0255339i \(-0.991871\pi\)
0.521950 + 0.852976i \(0.325205\pi\)
\(278\) −1.16936 + 2.02538i −0.0701333 + 0.121474i
\(279\) 9.89761 + 1.06363i 0.592554 + 0.0636777i
\(280\) 0 0
\(281\) −4.50324 + 2.59995i −0.268641 + 0.155100i −0.628270 0.777996i \(-0.716237\pi\)
0.359629 + 0.933095i \(0.382903\pi\)
\(282\) 9.31276 8.36560i 0.554567 0.498164i
\(283\) 18.7739i 1.11599i 0.829844 + 0.557995i \(0.188429\pi\)
−0.829844 + 0.557995i \(0.811571\pi\)
\(284\) 12.3670i 0.733848i
\(285\) 0.0763224 0.0685600i 0.00452095 0.00406114i
\(286\) 3.31295 1.91273i 0.195899 0.113102i
\(287\) 0 0
\(288\) −17.1684 1.84497i −1.01166 0.108716i
\(289\) −7.62438 + 13.2058i −0.448493 + 0.776813i
\(290\) 0.0382738 0.0662922i 0.00224751 0.00389281i
\(291\) 12.8832 + 4.20261i 0.755224 + 0.246361i
\(292\) 14.7125 8.49426i 0.860983 0.497089i
\(293\) −11.4201 + 19.7802i −0.667169 + 1.15557i 0.311523 + 0.950238i \(0.399161\pi\)
−0.978692 + 0.205332i \(0.934173\pi\)
\(294\) 0 0
\(295\) 0.0852263 + 0.147616i 0.00496206 + 0.00859455i
\(296\) 5.06229 + 2.92272i 0.294240 + 0.169879i
\(297\) −5.28475 + 0.536762i −0.306652 + 0.0311461i
\(298\) 5.28530 + 9.15440i 0.306169 + 0.530300i
\(299\) −40.9041 −2.36554
\(300\) 13.2050 2.79072i 0.762390 0.161122i
\(301\) 0 0
\(302\) −1.99062 1.14929i −0.114548 0.0661341i
\(303\) −0.769099 + 0.162540i −0.0441836 + 0.00933766i
\(304\) −2.80373 1.61873i −0.160805 0.0928407i
\(305\) −0.0580853 + 0.0335356i −0.00332596 + 0.00192024i
\(306\) −4.57900 10.3495i −0.261764 0.591642i
\(307\) 18.6325i 1.06341i 0.846928 + 0.531707i \(0.178449\pi\)
−0.846928 + 0.531707i \(0.821551\pi\)
\(308\) 0 0
\(309\) −8.71438 2.84271i −0.495744 0.161716i
\(310\) 0.0311947 + 0.0540308i 0.00177174 + 0.00306875i
\(311\) −20.5495 −1.16526 −0.582628 0.812739i \(-0.697975\pi\)
−0.582628 + 0.812739i \(0.697975\pi\)
\(312\) 22.5672 4.76931i 1.27762 0.270009i
\(313\) 0.721071i 0.0407574i 0.999792 + 0.0203787i \(0.00648718\pi\)
−0.999792 + 0.0203787i \(0.993513\pi\)
\(314\) −10.8605 −0.612893
\(315\) 0 0
\(316\) −24.3164 −1.36791
\(317\) 21.9295i 1.23168i −0.787871 0.615841i \(-0.788816\pi\)
0.787871 0.615841i \(-0.211184\pi\)
\(318\) 4.13903 12.6883i 0.232105 0.711523i
\(319\) −4.16193 −0.233023
\(320\) −0.0103242 0.0178821i −0.000577143 0.000999641i
\(321\) −3.24743 15.3660i −0.181254 0.857649i
\(322\) 0 0
\(323\) 11.8843i 0.661258i
\(324\) −13.7081 2.98065i −0.761560 0.165592i
\(325\) −24.3883 + 14.0806i −1.35282 + 0.781051i
\(326\) −5.95757 3.43961i −0.329959 0.190502i
\(327\) 2.54089 7.78912i 0.140511 0.430739i
\(328\) 14.4486 + 8.34191i 0.797791 + 0.460605i
\(329\) 0 0
\(330\) −0.0222479 0.0247668i −0.00122470 0.00136337i
\(331\) 21.6676 1.19096 0.595480 0.803370i \(-0.296962\pi\)
0.595480 + 0.803370i \(0.296962\pi\)
\(332\) 4.79156 + 8.29923i 0.262971 + 0.455479i
\(333\) 5.99105 + 4.37414i 0.328308 + 0.239701i
\(334\) −3.38617 1.95501i −0.185283 0.106973i
\(335\) 0.180861 + 0.313260i 0.00988147 + 0.0171152i
\(336\) 0 0
\(337\) 12.6455 21.9026i 0.688844 1.19311i −0.283369 0.959011i \(-0.591452\pi\)
0.972212 0.234101i \(-0.0752147\pi\)
\(338\) −10.7766 + 6.22190i −0.586172 + 0.338427i
\(339\) −3.39562 16.0673i −0.184425 0.872654i
\(340\) −0.125268 + 0.216970i −0.00679358 + 0.0117668i
\(341\) 1.69607 2.93768i 0.0918474 0.159084i
\(342\) 3.36836 + 2.45928i 0.182140 + 0.132983i
\(343\) 0 0
\(344\) 4.74955 2.74215i 0.256078 0.147847i
\(345\) 0.0736058 + 0.348285i 0.00396281 + 0.0187510i
\(346\) 3.23215i 0.173761i
\(347\) 5.68598i 0.305239i 0.988285 + 0.152620i \(0.0487709\pi\)
−0.988285 + 0.152620i \(0.951229\pi\)
\(348\) −10.4494 3.40869i −0.560145 0.182725i
\(349\) 9.68412 5.59113i 0.518379 0.299286i −0.217892 0.975973i \(-0.569918\pi\)
0.736271 + 0.676687i \(0.236585\pi\)
\(350\) 0 0
\(351\) 29.1208 2.95775i 1.55436 0.157873i
\(352\) −2.94200 + 5.09570i −0.156809 + 0.271601i
\(353\) −7.02111 + 12.1609i −0.373696 + 0.647260i −0.990131 0.140146i \(-0.955243\pi\)
0.616435 + 0.787406i \(0.288576\pi\)
\(354\) −5.15476 + 4.63049i −0.273972 + 0.246108i
\(355\) 0.194481 0.112284i 0.0103220 0.00595940i
\(356\) 9.39250 16.2683i 0.497802 0.862218i
\(357\) 0 0
\(358\) −0.0673081 0.116581i −0.00355734 0.00616150i
\(359\) −23.5052 13.5707i −1.24056 0.716235i −0.271348 0.962481i \(-0.587469\pi\)
−0.969207 + 0.246246i \(0.920803\pi\)
\(360\) −0.0812182 0.183570i −0.00428058 0.00967500i
\(361\) −7.31022 12.6617i −0.384748 0.666403i
\(362\) 4.16031 0.218661
\(363\) 5.34733 16.3923i 0.280662 0.860374i
\(364\) 0 0
\(365\) 0.267158 + 0.154244i 0.0139837 + 0.00807347i
\(366\) −1.82205 2.02834i −0.0952399 0.106023i
\(367\) 5.95891 + 3.44038i 0.311053 + 0.179586i 0.647397 0.762153i \(-0.275857\pi\)
−0.336345 + 0.941739i \(0.609191\pi\)
\(368\) 9.72828 5.61662i 0.507122 0.292787i
\(369\) 17.0994 + 12.4845i 0.890161 + 0.649918i
\(370\) 0.0464912i 0.00241696i
\(371\) 0 0
\(372\) 6.66434 5.98654i 0.345530 0.310388i
\(373\) 0.123926 + 0.214645i 0.00641662 + 0.0111139i 0.869216 0.494433i \(-0.164624\pi\)
−0.862799 + 0.505547i \(0.831291\pi\)
\(374\) −3.85647 −0.199413
\(375\) 0.327582 + 0.364671i 0.0169163 + 0.0188315i
\(376\) 25.7206i 1.32644i
\(377\) 22.9337 1.18114
\(378\) 0 0
\(379\) −8.91863 −0.458119 −0.229060 0.973412i \(-0.573565\pi\)
−0.229060 + 0.973412i \(0.573565\pi\)
\(380\) 0.0923268i 0.00473626i
\(381\) 5.06157 + 5.63465i 0.259312 + 0.288672i
\(382\) −9.16952 −0.469154
\(383\) −0.163545 0.283268i −0.00835675 0.0144743i 0.861817 0.507220i \(-0.169327\pi\)
−0.870174 + 0.492745i \(0.835993\pi\)
\(384\) −14.2083 + 12.7632i −0.725063 + 0.651320i
\(385\) 0 0
\(386\) 14.0017i 0.712665i
\(387\) 6.36455 2.81591i 0.323528 0.143141i
\(388\) 10.5613 6.09755i 0.536167 0.309556i
\(389\) 5.72348 + 3.30445i 0.290192 + 0.167542i 0.638028 0.770013i \(-0.279750\pi\)
−0.347837 + 0.937555i \(0.613084\pi\)
\(390\) 0.122594 + 0.136474i 0.00620777 + 0.00691061i
\(391\) 35.7111 + 20.6178i 1.80599 + 1.04269i
\(392\) 0 0
\(393\) −1.36686 + 4.19011i −0.0689487 + 0.211363i
\(394\) −10.0760 −0.507621
\(395\) −0.220776 0.382394i −0.0111084 0.0192404i
\(396\) −2.81882 + 3.86080i −0.141651 + 0.194013i
\(397\) 6.50435 + 3.75529i 0.326444 + 0.188472i 0.654261 0.756269i \(-0.272980\pi\)
−0.327817 + 0.944741i \(0.606313\pi\)
\(398\) 3.21760 + 5.57305i 0.161284 + 0.279352i
\(399\) 0 0
\(400\) 3.86687 6.69762i 0.193344 0.334881i
\(401\) 5.48595 3.16732i 0.273956 0.158168i −0.356728 0.934208i \(-0.616108\pi\)
0.630684 + 0.776040i \(0.282774\pi\)
\(402\) −10.9390 + 9.82647i −0.545589 + 0.490100i
\(403\) −9.34594 + 16.1876i −0.465555 + 0.806364i
\(404\) −0.353708 + 0.612640i −0.0175976 + 0.0304800i
\(405\) −0.0775865 0.242632i −0.00385530 0.0120565i
\(406\) 0 0
\(407\) 2.18909 1.26387i 0.108509 0.0626479i
\(408\) −22.1062 7.21124i −1.09442 0.357010i
\(409\) 33.4915i 1.65605i −0.560693 0.828024i \(-0.689465\pi\)
0.560693 0.828024i \(-0.310535\pi\)
\(410\) 0.132693i 0.00655326i
\(411\) 4.06319 + 19.2261i 0.200423 + 0.948351i
\(412\) −7.14382 + 4.12448i −0.351951 + 0.203199i
\(413\) 0 0
\(414\) −13.2336 + 5.85504i −0.650398 + 0.287760i
\(415\) −0.0870078 + 0.150702i −0.00427105 + 0.00739767i
\(416\) 16.2115 28.0791i 0.794832 1.37669i
\(417\) 1.26085 + 5.96605i 0.0617442 + 0.292159i
\(418\) 1.23078 0.710590i 0.0601993 0.0347561i
\(419\) −0.896459 + 1.55271i −0.0437949 + 0.0758550i −0.887092 0.461593i \(-0.847278\pi\)
0.843297 + 0.537448i \(0.180611\pi\)
\(420\) 0 0
\(421\) 1.90262 + 3.29543i 0.0927278 + 0.160609i 0.908658 0.417541i \(-0.137108\pi\)
−0.815930 + 0.578150i \(0.803775\pi\)
\(422\) −8.12254 4.68955i −0.395399 0.228284i
\(423\) 3.48750 32.4530i 0.169568 1.57792i
\(424\) −13.7108 23.7478i −0.665855 1.15330i
\(425\) 28.3894 1.37709
\(426\) 6.10057 + 6.79128i 0.295574 + 0.329039i
\(427\) 0 0
\(428\) −12.2401 7.06684i −0.591649 0.341589i
\(429\) 3.09329 9.48253i 0.149346 0.457821i
\(430\) 0.0377751 + 0.0218095i 0.00182168 + 0.00105175i
\(431\) −1.15145 + 0.664787i −0.0554632 + 0.0320217i −0.527475 0.849570i \(-0.676861\pi\)
0.472012 + 0.881592i \(0.343528\pi\)
\(432\) −6.51972 + 4.70209i −0.313680 + 0.226229i
\(433\) 37.4292i 1.79873i −0.437194 0.899367i \(-0.644028\pi\)
0.437194 0.899367i \(-0.355972\pi\)
\(434\) 0 0
\(435\) −0.0412686 0.195273i −0.00197868 0.00936262i
\(436\) −3.68656 6.38531i −0.176554 0.305801i
\(437\) −15.1961 −0.726927
\(438\) −3.88912 + 11.9221i −0.185829 + 0.569662i
\(439\) 23.7388i 1.13299i 0.824064 + 0.566496i \(0.191702\pi\)
−0.824064 + 0.566496i \(0.808298\pi\)
\(440\) −0.0684026 −0.00326097
\(441\) 0 0
\(442\) 21.2505 1.01078
\(443\) 11.2504i 0.534525i 0.963624 + 0.267262i \(0.0861191\pi\)
−0.963624 + 0.267262i \(0.913881\pi\)
\(444\) 6.53130 1.38031i 0.309962 0.0655067i
\(445\) 0.341109 0.0161701
\(446\) −0.992491 1.71904i −0.0469958 0.0813991i
\(447\) 26.2023 + 8.54744i 1.23933 + 0.404280i
\(448\) 0 0
\(449\) 14.3953i 0.679357i 0.940542 + 0.339679i \(0.110318\pi\)
−0.940542 + 0.339679i \(0.889682\pi\)
\(450\) −5.87480 + 8.04644i −0.276941 + 0.379313i
\(451\) 6.24803 3.60730i 0.294208 0.169861i
\(452\) −12.7987 7.38933i −0.602000 0.347565i
\(453\) −5.86366 + 1.23921i −0.275499 + 0.0582234i
\(454\) −16.5532 9.55701i −0.776881 0.448533i
\(455\) 0 0
\(456\) 8.38384 1.77182i 0.392609 0.0829732i
\(457\) −20.6269 −0.964888 −0.482444 0.875927i \(-0.660251\pi\)
−0.482444 + 0.875927i \(0.660251\pi\)
\(458\) 2.94323 + 5.09782i 0.137528 + 0.238206i
\(459\) −26.9147 12.0962i −1.25627 0.564602i
\(460\) 0.277433 + 0.160176i 0.0129354 + 0.00746825i
\(461\) 0.832511 + 1.44195i 0.0387739 + 0.0671584i 0.884761 0.466045i \(-0.154321\pi\)
−0.845987 + 0.533203i \(0.820988\pi\)
\(462\) 0 0
\(463\) 0.604175 1.04646i 0.0280784 0.0486332i −0.851645 0.524119i \(-0.824395\pi\)
0.879723 + 0.475486i \(0.157728\pi\)
\(464\) −5.45435 + 3.14907i −0.253212 + 0.146192i
\(465\) 0.154650 + 0.0504484i 0.00717174 + 0.00233949i
\(466\) 4.28745 7.42608i 0.198612 0.344006i
\(467\) −4.61994 + 8.00197i −0.213785 + 0.370287i −0.952896 0.303297i \(-0.901913\pi\)
0.739111 + 0.673584i \(0.235246\pi\)
\(468\) 15.5327 21.2744i 0.717999 0.983409i
\(469\) 0 0
\(470\) 0.177160 0.102283i 0.00817179 0.00471798i
\(471\) −21.0657 + 18.9232i −0.970658 + 0.871937i
\(472\) 14.2368i 0.655300i
\(473\) 2.37158i 0.109045i
\(474\) 13.3532 11.9951i 0.613334 0.550954i
\(475\) −9.06039 + 5.23102i −0.415719 + 0.240016i
\(476\) 0 0
\(477\) −14.0796 31.8229i −0.644660 1.45707i
\(478\) 1.86286 3.22657i 0.0852052 0.147580i
\(479\) 8.77241 15.1943i 0.400822 0.694243i −0.593004 0.805200i \(-0.702058\pi\)
0.993825 + 0.110956i \(0.0353914\pi\)
\(480\) −0.268256 0.0875078i −0.0122442 0.00399417i
\(481\) −12.0627 + 6.96438i −0.550010 + 0.317549i
\(482\) −3.64923 + 6.32066i −0.166218 + 0.287898i
\(483\) 0 0
\(484\) −7.75843 13.4380i −0.352656 0.610818i
\(485\) 0.191777 + 0.110723i 0.00870817 + 0.00502766i
\(486\) 8.99804 5.12530i 0.408160 0.232488i
\(487\) 21.5949 + 37.4034i 0.978558 + 1.69491i 0.667657 + 0.744469i \(0.267297\pi\)
0.310900 + 0.950442i \(0.399369\pi\)
\(488\) −5.60201 −0.253591
\(489\) −17.5489 + 3.70874i −0.793587 + 0.167715i
\(490\) 0 0
\(491\) 23.0046 + 13.2817i 1.03818 + 0.599396i 0.919319 0.393514i \(-0.128741\pi\)
0.118866 + 0.992910i \(0.462074\pi\)
\(492\) 18.6414 3.93963i 0.840419 0.177612i
\(493\) −20.0221 11.5598i −0.901751 0.520626i
\(494\) −6.78202 + 3.91560i −0.305138 + 0.176171i
\(495\) −0.0863070 0.00927482i −0.00387921 0.000416872i
\(496\) 5.13324i 0.230489i
\(497\) 0 0
\(498\) −6.72521 2.19383i −0.301364 0.0983078i
\(499\) −2.65759 4.60308i −0.118970 0.206062i 0.800390 0.599480i \(-0.204626\pi\)
−0.919360 + 0.393418i \(0.871293\pi\)
\(500\) 0.441141 0.0197284
\(501\) −9.97445 + 2.10798i −0.445625 + 0.0941776i
\(502\) 16.0920i 0.718220i
\(503\) 35.5334 1.58436 0.792178 0.610290i \(-0.208947\pi\)
0.792178 + 0.610290i \(0.208947\pi\)
\(504\) 0 0
\(505\) −0.0128457 −0.000571624
\(506\) 4.93116i 0.219217i
\(507\) −10.0621 + 30.8456i −0.446874 + 1.36990i
\(508\) 6.81620 0.302420
\(509\) −6.81654 11.8066i −0.302138 0.523318i 0.674482 0.738291i \(-0.264367\pi\)
−0.976620 + 0.214973i \(0.931034\pi\)
\(510\) −0.0382397 0.180941i −0.00169328 0.00801221i
\(511\) 0 0
\(512\) 16.2184i 0.716760i
\(513\) 10.8185 1.09882i 0.477651 0.0485141i
\(514\) −10.1959 + 5.88661i −0.449722 + 0.259647i
\(515\) −0.129721 0.0748947i −0.00571621 0.00330025i
\(516\) 1.94236 5.95435i 0.0855078 0.262125i
\(517\) −9.63227 5.56120i −0.423627 0.244581i
\(518\) 0 0
\(519\) −5.63167 6.26929i −0.247203 0.275191i
\(520\) 0.376922 0.0165291
\(521\) −5.11259 8.85526i −0.223987 0.387956i 0.732028 0.681274i \(-0.238574\pi\)
−0.956015 + 0.293318i \(0.905241\pi\)
\(522\) 7.41969 3.28274i 0.324751 0.143682i
\(523\) −4.48150 2.58740i −0.195962 0.113139i 0.398808 0.917034i \(-0.369424\pi\)
−0.594771 + 0.803895i \(0.702757\pi\)
\(524\) 1.98317 + 3.43495i 0.0866350 + 0.150056i
\(525\) 0 0
\(526\) 0.962785 1.66759i 0.0419794 0.0727105i
\(527\) 16.3189 9.42169i 0.710860 0.410415i
\(528\) 0.566383 + 2.67999i 0.0246487 + 0.116632i
\(529\) 14.8634 25.7442i 0.646236 1.11931i
\(530\) 0.109048 0.188876i 0.00473673 0.00820426i
\(531\) −1.93039 + 17.9632i −0.0837716 + 0.779538i
\(532\) 0 0
\(533\) −34.4288 + 19.8775i −1.49128 + 0.860990i
\(534\) 2.86720 + 13.5669i 0.124076 + 0.587097i
\(535\) 0.256647i 0.0110958i
\(536\) 30.2122i 1.30497i
\(537\) −0.333685 0.108851i −0.0143996 0.00469728i
\(538\) 12.5955 7.27199i 0.543029 0.313518i
\(539\) 0 0
\(540\) −0.209095 0.0939732i −0.00899803 0.00404396i
\(541\) 12.7197 22.0312i 0.546864 0.947196i −0.451623 0.892209i \(-0.649155\pi\)
0.998487 0.0549871i \(-0.0175118\pi\)
\(542\) −2.98385 + 5.16817i −0.128167 + 0.221992i
\(543\) 8.06963 7.24890i 0.346301 0.311080i
\(544\) −28.3067 + 16.3429i −1.21364 + 0.700694i
\(545\) 0.0669427 0.115948i 0.00286751 0.00496667i
\(546\) 0 0
\(547\) 14.7771 + 25.5947i 0.631824 + 1.09435i 0.987179 + 0.159620i \(0.0510267\pi\)
−0.355355 + 0.934732i \(0.615640\pi\)
\(548\) 15.3149 + 8.84205i 0.654219 + 0.377714i
\(549\) −7.06833 0.759585i −0.301669 0.0324183i
\(550\) 1.69748 + 2.94012i 0.0723807 + 0.125367i
\(551\) 8.51998 0.362963
\(552\) −9.22082 + 28.2665i −0.392464 + 1.20310i
\(553\) 0 0
\(554\) −9.14828 5.28176i −0.388673 0.224401i
\(555\) 0.0810060 + 0.0901775i 0.00343851 + 0.00382782i
\(556\) 4.75237 + 2.74378i 0.201545 + 0.116362i
\(557\) 16.9788 9.80269i 0.719413 0.415353i −0.0951237 0.995465i \(-0.530325\pi\)
0.814537 + 0.580112i \(0.196991\pi\)
\(558\) −0.706565 + 6.57495i −0.0299113 + 0.278340i
\(559\) 13.0683i 0.552728i
\(560\) 0 0
\(561\) −7.48028 + 6.71949i −0.315817 + 0.283697i
\(562\) −1.72714 2.99149i −0.0728548 0.126188i
\(563\) 14.4759 0.610087 0.305044 0.952338i \(-0.401329\pi\)
0.305044 + 0.952338i \(0.401329\pi\)
\(564\) −19.6291 21.8515i −0.826534 0.920115i
\(565\) 0.268359i 0.0112899i
\(566\) −12.4714 −0.524213
\(567\) 0 0
\(568\) 18.7566 0.787011
\(569\) 7.74769i 0.324800i 0.986725 + 0.162400i \(0.0519235\pi\)
−0.986725 + 0.162400i \(0.948076\pi\)
\(570\) 0.0455442 + 0.0507007i 0.00190764 + 0.00212362i
\(571\) 16.1371 0.675318 0.337659 0.941269i \(-0.390365\pi\)
0.337659 + 0.941269i \(0.390365\pi\)
\(572\) −4.48805 7.77353i −0.187655 0.325027i
\(573\) −17.7858 + 15.9769i −0.743014 + 0.667445i
\(574\) 0 0
\(575\) 36.3008i 1.51385i
\(576\) 0.233846 2.17605i 0.00974356 0.0906689i
\(577\) 10.5403 6.08542i 0.438797 0.253339i −0.264290 0.964443i \(-0.585138\pi\)
0.703087 + 0.711104i \(0.251804\pi\)
\(578\) −8.77258 5.06485i −0.364891 0.210670i
\(579\) −24.3964 27.1586i −1.01388 1.12867i
\(580\) −0.155548 0.0898059i −0.00645879 0.00372899i
\(581\) 0 0
\(582\) −2.79178 + 8.55824i −0.115723 + 0.354750i
\(583\) −11.8579 −0.491106
\(584\) 12.8829 + 22.3139i 0.533100 + 0.923356i
\(585\) 0.475582 + 0.0511075i 0.0196629 + 0.00211304i
\(586\) −13.1399 7.58633i −0.542805 0.313388i
\(587\) −16.8761 29.2302i −0.696550 1.20646i −0.969655 0.244476i \(-0.921384\pi\)
0.273106 0.961984i \(-0.411949\pi\)
\(588\) 0 0
\(589\) −3.47207 + 6.01380i −0.143064 + 0.247794i
\(590\) −0.0980610 + 0.0566155i −0.00403711 + 0.00233082i
\(591\) −19.5441 + 17.5563i −0.803936 + 0.722171i
\(592\) 1.91259 3.31270i 0.0786069 0.136151i
\(593\) 9.15123 15.8504i 0.375796 0.650897i −0.614650 0.788800i \(-0.710703\pi\)
0.990446 + 0.137903i \(0.0440361\pi\)
\(594\) −0.356569 3.51064i −0.0146302 0.144043i
\(595\) 0 0
\(596\) 21.4799 12.4015i 0.879853 0.507983i
\(597\) 15.9515 + 5.20354i 0.652852 + 0.212967i
\(598\) 27.1724i 1.11116i
\(599\) 39.4798i 1.61310i 0.591165 + 0.806551i \(0.298668\pi\)
−0.591165 + 0.806551i \(0.701332\pi\)
\(600\) 4.23258 + 20.0275i 0.172794 + 0.817621i
\(601\) −34.4865 + 19.9108i −1.40673 + 0.812177i −0.995072 0.0991600i \(-0.968384\pi\)
−0.411661 + 0.911337i \(0.635051\pi\)
\(602\) 0 0
\(603\) −4.09652 + 38.1202i −0.166823 + 1.55237i
\(604\) −2.69670 + 4.67082i −0.109727 + 0.190053i
\(605\) 0.140882 0.244015i 0.00572766 0.00992060i
\(606\) −0.107975 0.510910i −0.00438617 0.0207543i
\(607\) 21.6104 12.4768i 0.877140 0.506417i 0.00742570 0.999972i \(-0.497636\pi\)
0.869714 + 0.493555i \(0.164303\pi\)
\(608\) 6.02264 10.4315i 0.244250 0.423054i
\(609\) 0 0
\(610\) −0.0222776 0.0385859i −0.000901992 0.00156230i
\(611\) 53.0772 + 30.6441i 2.14727 + 1.23973i
\(612\) −24.2841 + 10.7442i −0.981628 + 0.434308i
\(613\) −14.0285 24.2980i −0.566605 0.981388i −0.996898 0.0786994i \(-0.974923\pi\)
0.430294 0.902689i \(-0.358410\pi\)
\(614\) −12.3775 −0.499516
\(615\) 0.231204 + 0.257381i 0.00932305 + 0.0103786i
\(616\) 0 0
\(617\) 29.8093 + 17.2104i 1.20008 + 0.692865i 0.960573 0.278030i \(-0.0896813\pi\)
0.239506 + 0.970895i \(0.423015\pi\)
\(618\) 1.88841 5.78893i 0.0759628 0.232865i
\(619\) 17.2889 + 9.98173i 0.694898 + 0.401200i 0.805444 0.592671i \(-0.201927\pi\)
−0.110546 + 0.993871i \(0.535260\pi\)
\(620\) 0.126778 0.0731955i 0.00509154 0.00293960i
\(621\) −15.4671 + 34.4150i −0.620672 + 1.38103i
\(622\) 13.6510i 0.547354i
\(623\) 0 0
\(624\) −3.12097 14.7677i −0.124939 0.591181i
\(625\) −12.4940 21.6402i −0.499760 0.865609i
\(626\) −0.479005 −0.0191449
\(627\) 1.14917 3.52281i 0.0458936 0.140687i
\(628\) 25.4831i 1.01689i
\(629\) 14.0417 0.559878
\(630\) 0 0
\(631\) −46.8447 −1.86486 −0.932429 0.361354i \(-0.882314\pi\)
−0.932429 + 0.361354i \(0.882314\pi\)
\(632\) 36.8798i 1.46700i
\(633\) −23.9261 + 5.05649i −0.950976 + 0.200977i
\(634\) 14.5677 0.578556
\(635\) 0.0618862 + 0.107190i 0.00245588 + 0.00425370i
\(636\) −29.7718 9.71185i −1.18053 0.385100i
\(637\) 0 0
\(638\) 2.76475i 0.109458i
\(639\) 23.6662 + 2.54324i 0.936220 + 0.100609i
\(640\) −0.270290 + 0.156052i −0.0106841 + 0.00616849i
\(641\) 3.34281 + 1.92997i 0.132033 + 0.0762293i 0.564562 0.825391i \(-0.309045\pi\)
−0.432529 + 0.901620i \(0.642379\pi\)
\(642\) 10.2076 2.15726i 0.402862 0.0851401i
\(643\) −31.0233 17.9113i −1.22344 0.706352i −0.257789 0.966201i \(-0.582994\pi\)
−0.965649 + 0.259849i \(0.916327\pi\)
\(644\) 0 0
\(645\) 0.111272 0.0235160i 0.00438133 0.000925941i
\(646\) 7.89468 0.310612
\(647\) 21.8246 + 37.8013i 0.858013 + 1.48612i 0.873821 + 0.486248i \(0.161635\pi\)
−0.0158075 + 0.999875i \(0.505032\pi\)
\(648\) 4.52064 20.7906i 0.177588 0.816730i
\(649\) 5.33162 + 3.07821i 0.209284 + 0.120830i
\(650\) −9.35369 16.2011i −0.366882 0.635458i
\(651\) 0 0
\(652\) −8.07072 + 13.9789i −0.316074 + 0.547456i
\(653\) −6.45191 + 3.72501i −0.252483 + 0.145771i −0.620901 0.783889i \(-0.713233\pi\)
0.368418 + 0.929660i \(0.379900\pi\)
\(654\) 5.17429 + 1.68790i 0.202331 + 0.0660022i
\(655\) −0.0360114 + 0.0623736i −0.00140708 + 0.00243714i
\(656\) 5.45884 9.45498i 0.213132 0.369155i
\(657\) 13.2295 + 29.9014i 0.516131 + 1.16656i
\(658\) 0 0
\(659\) −7.52607 + 4.34518i −0.293174 + 0.169264i −0.639372 0.768897i \(-0.720806\pi\)
0.346198 + 0.938161i \(0.387472\pi\)
\(660\) −0.0581130 + 0.0522025i −0.00226204 + 0.00203198i
\(661\) 28.8505i 1.12215i 0.827763 + 0.561077i \(0.189613\pi\)
−0.827763 + 0.561077i \(0.810387\pi\)
\(662\) 14.3937i 0.559428i
\(663\) 41.2189 37.0267i 1.60081 1.43800i
\(664\) −12.5871 + 7.26719i −0.488476 + 0.282022i
\(665\) 0 0
\(666\) −2.90573 + 3.97984i −0.112595 + 0.154216i
\(667\) −14.7812 + 25.6017i −0.572329 + 0.991303i
\(668\) −4.58724 + 7.94534i −0.177486 + 0.307414i
\(669\) −4.92036 1.60507i −0.190232 0.0620555i
\(670\) −0.208097 + 0.120145i −0.00803950 + 0.00464161i
\(671\) −1.21124 + 2.09793i −0.0467594 + 0.0809897i
\(672\) 0 0
\(673\) −3.60695 6.24742i −0.139038 0.240820i 0.788095 0.615554i \(-0.211068\pi\)
−0.927133 + 0.374733i \(0.877734\pi\)
\(674\) 14.5498 + 8.40036i 0.560439 + 0.323570i
\(675\) 2.62489 + 25.8436i 0.101032 + 0.994722i
\(676\) 14.5991 + 25.2864i 0.561504 + 0.972553i
\(677\) 36.3821 1.39828 0.699140 0.714985i \(-0.253567\pi\)
0.699140 + 0.714985i \(0.253567\pi\)
\(678\) 10.6734 2.25570i 0.409911 0.0866297i
\(679\) 0 0
\(680\) −0.329070 0.189989i −0.0126193 0.00728573i
\(681\) −48.7598 + 10.3048i −1.86848 + 0.394881i
\(682\) 1.95149 + 1.12669i 0.0747265 + 0.0431433i
\(683\) −20.5530 + 11.8663i −0.786438 + 0.454050i −0.838707 0.544583i \(-0.816688\pi\)
0.0522688 + 0.998633i \(0.483355\pi\)
\(684\) 5.77048 7.90355i 0.220640 0.302200i
\(685\) 0.321118i 0.0122693i
\(686\) 0 0
\(687\) 14.5913 + 4.75982i 0.556693 + 0.181599i
\(688\) −1.79443 3.10804i −0.0684119 0.118493i
\(689\) 65.3415 2.48931
\(690\) −0.231365 + 0.0488961i −0.00880790 + 0.00186144i
\(691\) 3.30391i 0.125687i 0.998023 + 0.0628433i \(0.0200168\pi\)
−0.998023 + 0.0628433i \(0.979983\pi\)
\(692\) −7.58393 −0.288298
\(693\) 0 0
\(694\) −3.77718 −0.143380
\(695\) 0.0996463i 0.00377980i
\(696\) 5.16983 15.8482i 0.195962 0.600724i
\(697\) 40.0772 1.51803
\(698\) 3.71417 + 6.43313i 0.140583 + 0.243498i
\(699\) −4.62292 21.8746i −0.174855 0.827371i
\(700\) 0 0
\(701\) 0.873603i 0.0329955i 0.999864 + 0.0164978i \(0.00525164\pi\)
−0.999864 + 0.0164978i \(0.994748\pi\)
\(702\) 1.96482 + 19.3449i 0.0741574 + 0.730125i
\(703\) −4.48135 + 2.58731i −0.169017 + 0.0975821i
\(704\) −0.645868 0.372892i −0.0243421 0.0140539i
\(705\) 0.165414 0.507079i 0.00622985 0.0190977i
\(706\) −8.07845 4.66410i −0.304037 0.175536i
\(707\) 0 0
\(708\) 10.8650 + 12.0952i 0.408332 + 0.454564i
\(709\) 16.1553 0.606727 0.303363 0.952875i \(-0.401890\pi\)
0.303363 + 0.952875i \(0.401890\pi\)
\(710\) 0.0745897 + 0.129193i 0.00279930 + 0.00484853i
\(711\) 5.00060 46.5331i 0.187537 1.74513i
\(712\) 24.6735 + 14.2453i 0.924680 + 0.533864i
\(713\) −12.0473 20.8665i −0.451174 0.781456i
\(714\) 0 0
\(715\) 0.0814965 0.141156i 0.00304779 0.00527894i
\(716\) −0.273546 + 0.157932i −0.0102229 + 0.00590220i
\(717\) −2.00862 9.50430i −0.0750133 0.354945i
\(718\) 9.01498 15.6144i 0.336436 0.582724i
\(719\) −22.5953 + 39.1361i −0.842661 + 1.45953i 0.0449767 + 0.998988i \(0.485679\pi\)
−0.887637 + 0.460543i \(0.847655\pi\)
\(720\) −0.120126 + 0.0531481i −0.00447683 + 0.00198071i
\(721\) 0 0
\(722\) 8.41110 4.85615i 0.313029 0.180727i
\(723\) 3.93477 + 18.6184i 0.146336 + 0.692425i
\(724\) 9.76178i 0.362794i
\(725\) 20.3528i 0.755883i
\(726\) 10.8894 + 3.55222i 0.404142 + 0.131835i
\(727\) 7.15775 4.13253i 0.265466 0.153267i −0.361359 0.932427i \(-0.617687\pi\)
0.626826 + 0.779160i \(0.284354\pi\)
\(728\) 0 0
\(729\) 8.52294 25.6195i 0.315664 0.948871i
\(730\) −0.102463 + 0.177472i −0.00379234 + 0.00656853i
\(731\) 6.58709 11.4092i 0.243632 0.421983i
\(732\) −4.75931 + 4.27526i −0.175909 + 0.158018i
\(733\) −10.5799 + 6.10830i −0.390777 + 0.225615i −0.682497 0.730889i \(-0.739106\pi\)
0.291720 + 0.956504i \(0.405773\pi\)
\(734\) −2.28543 + 3.95849i −0.0843569 + 0.146110i
\(735\) 0 0
\(736\) 20.8972 + 36.1949i 0.770280 + 1.33416i
\(737\) 11.3143 + 6.53234i 0.416769 + 0.240622i
\(738\) −8.29342 + 11.3591i −0.305285 + 0.418134i
\(739\) 10.3536 + 17.9330i 0.380863 + 0.659674i 0.991186 0.132478i \(-0.0422935\pi\)
−0.610323 + 0.792153i \(0.708960\pi\)
\(740\) 0.109087 0.00401013
\(741\) −6.33235 + 19.4119i −0.232625 + 0.713115i
\(742\) 0 0
\(743\) 10.2862 + 5.93873i 0.377363 + 0.217871i 0.676670 0.736286i \(-0.263422\pi\)
−0.299307 + 0.954157i \(0.596756\pi\)
\(744\) 9.07957 + 10.1076i 0.332873 + 0.370561i
\(745\) 0.390045 + 0.225192i 0.0142901 + 0.00825041i
\(746\) −0.142588 + 0.0823233i −0.00522053 + 0.00301407i
\(747\) −16.8672 + 7.46266i −0.617138 + 0.273045i
\(748\) 9.04885i 0.330859i
\(749\) 0 0
\(750\) −0.242250 + 0.217612i −0.00884571 + 0.00794606i
\(751\) −11.8554 20.5342i −0.432610 0.749303i 0.564487 0.825442i \(-0.309074\pi\)
−0.997097 + 0.0761390i \(0.975741\pi\)
\(752\) −16.8312 −0.613772
\(753\) −28.0385 31.2131i −1.02178 1.13747i
\(754\) 15.2348i 0.554817i
\(755\) −0.0979362 −0.00356426
\(756\) 0 0
\(757\) 44.2494 1.60827 0.804136 0.594446i \(-0.202628\pi\)
0.804136 + 0.594446i \(0.202628\pi\)
\(758\) 5.92462i 0.215192i
\(759\) 8.59203 + 9.56482i 0.311871 + 0.347181i
\(760\) 0.140029 0.00507937
\(761\) −24.3767 42.2217i −0.883656 1.53054i −0.847246 0.531200i \(-0.821741\pi\)
−0.0364098 0.999337i \(-0.511592\pi\)
\(762\) −3.74308 + 3.36238i −0.135597 + 0.121806i
\(763\) 0 0
\(764\) 21.5154i 0.778401i
\(765\) −0.389443 0.284337i −0.0140804 0.0102802i
\(766\) 0.188174 0.108642i 0.00679900 0.00392540i
\(767\) −29.3791 16.9620i −1.06082 0.612463i
\(768\) −10.1674 11.3185i −0.366883 0.408422i
\(769\) −23.3870 13.5025i −0.843357 0.486912i 0.0150472 0.999887i \(-0.495210\pi\)
−0.858404 + 0.512975i \(0.828543\pi\)
\(770\) 0 0
\(771\) −9.51989 + 29.1834i −0.342851 + 1.05101i
\(772\) −32.8536 −1.18243
\(773\) −13.3567 23.1345i −0.480408 0.832092i 0.519339 0.854568i \(-0.326178\pi\)
−0.999747 + 0.0224765i \(0.992845\pi\)
\(774\) 1.87060 + 4.22795i 0.0672373 + 0.151971i
\(775\) −14.3659 8.29417i −0.516039 0.297935i
\(776\) 9.24794 + 16.0179i 0.331982 + 0.575009i
\(777\) 0 0
\(778\) −2.19514 + 3.80209i −0.0786994 + 0.136311i
\(779\) −12.7905 + 7.38459i −0.458267 + 0.264580i
\(780\) 0.320223 0.287654i 0.0114658 0.0102997i
\(781\) 4.05547 7.02429i 0.145116 0.251349i
\(782\) −13.6963 + 23.7228i −0.489780 + 0.848324i
\(783\) 8.67191 19.2955i 0.309909 0.689564i
\(784\) 0 0
\(785\) −0.400742 + 0.231368i −0.0143031 + 0.00825789i
\(786\) −2.78348 0.907998i −0.0992834 0.0323872i
\(787\) 47.3534i 1.68797i −0.536369 0.843983i \(-0.680205\pi\)
0.536369 0.843983i \(-0.319795\pi\)
\(788\) 23.6424i 0.842224i
\(789\) −1.03812 4.91213i −0.0369580 0.174876i
\(790\) 0.254023 0.146660i 0.00903775 0.00521795i
\(791\) 0 0
\(792\) −5.85554 4.27520i −0.208068 0.151913i
\(793\) 6.67436 11.5603i 0.237014 0.410520i
\(794\) −2.49462 + 4.32082i −0.0885309 + 0.153340i
\(795\) −0.117580 0.556362i −0.00417014 0.0197321i
\(796\) 13.0766 7.54980i 0.463489 0.267596i
\(797\) 4.42781 7.66919i 0.156841 0.271657i −0.776887 0.629640i \(-0.783202\pi\)
0.933728 + 0.357984i \(0.116536\pi\)
\(798\) 0 0
\(799\) −30.8925 53.5074i −1.09290 1.89296i
\(800\) 24.9191 + 14.3871i 0.881023 + 0.508659i
\(801\) 29.2003 + 21.3195i 1.03174 + 0.753287i
\(802\) 2.10404 + 3.64430i 0.0742962 + 0.128685i
\(803\) 11.1420 0.393191
\(804\) 23.0569 + 25.6674i 0.813154 + 0.905220i
\(805\) 0 0
\(806\) −10.7534 6.20848i −0.378772 0.218684i
\(807\) 11.7603 36.0515i 0.413984 1.26907i
\(808\) −0.929170 0.536456i −0.0326881 0.0188725i
\(809\) −6.40871 + 3.70007i −0.225318 + 0.130087i −0.608410 0.793623i \(-0.708192\pi\)
0.383092 + 0.923710i \(0.374859\pi\)
\(810\) 0.161180 0.0515404i 0.00566328 0.00181095i
\(811\) 25.0843i 0.880829i 0.897794 + 0.440415i \(0.145169\pi\)
−0.897794 + 0.440415i \(0.854831\pi\)
\(812\) 0 0
\(813\) 3.21732 + 15.2236i 0.112836 + 0.533914i
\(814\) 0.839587 + 1.45421i 0.0294275 + 0.0509699i
\(815\) −0.293105 −0.0102670
\(816\) −4.71894 + 14.4660i −0.165196 + 0.506411i
\(817\) 4.85492i 0.169852i
\(818\) 22.2483 0.777893
\(819\) 0 0
\(820\) 0.311353 0.0108729
\(821\) 21.2212i 0.740627i 0.928907 + 0.370313i \(0.120750\pi\)
−0.928907 + 0.370313i \(0.879250\pi\)
\(822\) −12.7718 + 2.69917i −0.445468 + 0.0941442i
\(823\) 16.9538 0.590972 0.295486 0.955347i \(-0.404518\pi\)
0.295486 + 0.955347i \(0.404518\pi\)
\(824\) −6.25546 10.8348i −0.217919 0.377447i
\(825\) 8.41538 + 2.74518i 0.292986 + 0.0955749i
\(826\) 0 0
\(827\) 25.3052i 0.879949i −0.898010 0.439975i \(-0.854987\pi\)
0.898010 0.439975i \(-0.145013\pi\)
\(828\) 13.7383 + 31.0515i 0.477439 + 1.07911i
\(829\) 35.9640 20.7638i 1.24908 0.721158i 0.278156 0.960536i \(-0.410277\pi\)
0.970927 + 0.239378i \(0.0769434\pi\)
\(830\) −0.100111 0.0577990i −0.00347490 0.00200623i
\(831\) −26.9475 + 5.69504i −0.934800 + 0.197559i
\(832\) 3.55896 + 2.05477i 0.123385 + 0.0712362i
\(833\) 0 0
\(834\) −3.96323 + 0.837580i −0.137235 + 0.0290030i
\(835\) −0.166595 −0.00576527
\(836\) −1.66733 2.88791i −0.0576659 0.0998803i
\(837\) 10.0856 + 13.9843i 0.348611 + 0.483369i
\(838\) −1.03146 0.595515i −0.0356312 0.0205717i
\(839\) −6.61780 11.4624i −0.228472 0.395725i 0.728884 0.684638i \(-0.240040\pi\)
−0.957355 + 0.288913i \(0.906706\pi\)
\(840\) 0 0
\(841\) −6.21265 + 10.7606i −0.214229 + 0.371056i
\(842\) −2.18914 + 1.26390i −0.0754428 + 0.0435569i
\(843\) −8.56242 2.79314i −0.294905 0.0962009i
\(844\) −11.0036 + 19.0588i −0.378759 + 0.656030i
\(845\) −0.265099 + 0.459164i −0.00911967 + 0.0157957i
\(846\) 21.5584 + 2.31673i 0.741193 + 0.0796509i
\(847\) 0 0
\(848\) −15.5403 + 8.97217i −0.533654 + 0.308106i
\(849\) −24.1904 + 21.7301i −0.830213 + 0.745776i
\(850\) 18.8590i 0.646859i
\(851\) 17.9547i 0.615479i
\(852\) 15.9351 14.3144i 0.545928 0.490404i
\(853\) 15.3814 8.88048i 0.526651 0.304062i −0.213001 0.977052i \(-0.568324\pi\)
0.739651 + 0.672990i \(0.234990\pi\)
\(854\) 0 0
\(855\) 0.176681 + 0.0189867i 0.00604237 + 0.000649332i
\(856\) 10.7180 18.5642i 0.366334 0.634510i
\(857\) −9.17157 + 15.8856i −0.313295 + 0.542643i −0.979074 0.203507i \(-0.934766\pi\)
0.665779 + 0.746149i \(0.268100\pi\)
\(858\) 6.29921 + 2.05486i 0.215052 + 0.0701519i
\(859\) −2.69126 + 1.55380i −0.0918246 + 0.0530150i −0.545209 0.838300i \(-0.683550\pi\)
0.453385 + 0.891315i \(0.350216\pi\)
\(860\) 0.0511739 0.0886358i 0.00174502 0.00302246i
\(861\) 0 0
\(862\) −0.441616 0.764902i −0.0150415 0.0260527i
\(863\) −35.8587 20.7030i −1.22064 0.704739i −0.255589 0.966786i \(-0.582269\pi\)
−0.965055 + 0.262047i \(0.915603\pi\)
\(864\) −17.4946 24.2572i −0.595177 0.825247i
\(865\) −0.0688566 0.119263i −0.00234119 0.00405507i
\(866\) 24.8641 0.844917
\(867\) −25.8409 + 5.46115i −0.877602 + 0.185471i
\(868\) 0 0
\(869\) −13.8114 7.97399i −0.468518 0.270499i
\(870\) 0.129719 0.0274146i 0.00439789 0.000929441i
\(871\) −62.3460 35.9955i −2.11251 1.21966i
\(872\) 9.68438 5.59128i 0.327954 0.189345i
\(873\) 9.49669 + 21.4645i 0.321414 + 0.726464i
\(874\) 10.0947i 0.341459i
\(875\) 0 0
\(876\) 27.9742 + 9.12545i 0.945161 + 0.308320i
\(877\) 11.3979 + 19.7417i 0.384878 + 0.666628i 0.991752 0.128170i \(-0.0409102\pi\)
−0.606874 + 0.794798i \(0.707577\pi\)
\(878\) −15.7696 −0.532199
\(879\) −38.7054 + 8.17993i −1.30550 + 0.275902i
\(880\) 0.0447618i 0.00150892i
\(881\) 43.4050 1.46235 0.731175 0.682190i \(-0.238972\pi\)
0.731175 + 0.682190i \(0.238972\pi\)
\(882\) 0 0
\(883\) −29.9309 −1.00725 −0.503627 0.863921i \(-0.668001\pi\)
−0.503627 + 0.863921i \(0.668001\pi\)
\(884\) 49.8623i 1.67705i
\(885\) −0.0915592 + 0.280676i −0.00307773 + 0.00943483i
\(886\) −7.47363 −0.251082
\(887\) −19.4788 33.7382i −0.654033 1.13282i −0.982135 0.188176i \(-0.939742\pi\)
0.328102 0.944642i \(-0.393591\pi\)
\(888\) 2.09347 + 9.90579i 0.0702522 + 0.332417i
\(889\) 0 0
\(890\) 0.226597i 0.00759556i
\(891\) −6.80855 6.18820i −0.228095 0.207313i
\(892\) −4.03358 + 2.32879i −0.135054 + 0.0779736i
\(893\) 19.7185 + 11.3845i 0.659853 + 0.380966i
\(894\) −5.67803 + 17.4061i −0.189902 + 0.582147i
\(895\) −0.00496721 0.00286782i −0.000166035 9.58606e-5i
\(896\) 0 0
\(897\) −47.3451 52.7055i −1.58081 1.75979i
\(898\) −9.56277 −0.319114
\(899\) 6.75453 + 11.6992i 0.225276 + 0.390190i
\(900\) 18.8802 + 13.7847i 0.629340 + 0.459489i
\(901\) −57.0460 32.9355i −1.90048 1.09724i
\(902\) 2.39632 + 4.15054i 0.0797886 + 0.138198i
\(903\) 0 0
\(904\) 11.2071 19.4113i 0.372743 0.645611i
\(905\) 0.153512 0.0886299i 0.00510290 0.00294616i
\(906\) −0.823206 3.89521i −0.0273492 0.129410i
\(907\) 14.0526 24.3399i 0.466610 0.808192i −0.532663 0.846328i \(-0.678809\pi\)
0.999273 + 0.0381355i \(0.0121419\pi\)
\(908\) −22.4246 + 38.8406i −0.744187 + 1.28897i
\(909\) −1.09964 0.802861i −0.0364728 0.0266292i
\(910\) 0 0
\(911\) 32.3883 18.6994i 1.07307 0.619538i 0.144052 0.989570i \(-0.453987\pi\)
0.929019 + 0.370032i \(0.120653\pi\)
\(912\) −1.15946 5.48627i −0.0383935 0.181669i
\(913\) 6.28511i 0.208007i
\(914\) 13.7024i 0.453235i
\(915\) −0.110443 0.0360275i −0.00365113 0.00119103i
\(916\) 11.9616 6.90601i 0.395221 0.228181i
\(917\) 0 0
\(918\) 8.03546 17.8793i 0.265210 0.590105i
\(919\) 12.9115 22.3634i 0.425911 0.737699i −0.570594 0.821232i \(-0.693287\pi\)
0.996505 + 0.0835328i \(0.0266203\pi\)
\(920\) −0.242933 + 0.420773i −0.00800928 + 0.0138725i
\(921\) −24.0083 + 21.5665i −0.791100 + 0.710641i
\(922\) −0.957884 + 0.553034i −0.0315462 + 0.0182132i
\(923\) −22.3471 + 38.7063i −0.735563 + 1.27403i
\(924\) 0 0
\(925\) −6.18063 10.7052i −0.203218 0.351983i
\(926\) 0.695162 + 0.401352i 0.0228444 + 0.0131892i
\(927\) −6.42372 14.5190i −0.210983 0.476865i
\(928\) −11.7164 20.2934i −0.384610 0.666164i
\(929\) 15.9419 0.523036 0.261518 0.965199i \(-0.415777\pi\)
0.261518 + 0.965199i \(0.415777\pi\)
\(930\) −0.0335127 + 0.102734i −0.00109893 + 0.00336877i
\(931\) 0 0
\(932\) −17.4246 10.0601i −0.570762 0.329529i
\(933\) −23.7854 26.4783i −0.778697 0.866862i
\(934\) −5.31568 3.06901i −0.173934 0.100421i
\(935\) −0.142300 + 0.0821570i −0.00465371 + 0.00268682i
\(936\) 32.2661 + 23.5579i 1.05465 + 0.770013i
\(937\) 15.0698i 0.492308i −0.969231 0.246154i \(-0.920833\pi\)
0.969231 0.246154i \(-0.0791668\pi\)
\(938\) 0 0
\(939\) −0.929112 + 0.834616i −0.0303204 + 0.0272367i
\(940\) −0.239999 0.415690i −0.00782789 0.0135583i
\(941\) 11.5372 0.376102 0.188051 0.982159i \(-0.439783\pi\)
0.188051 + 0.982159i \(0.439783\pi\)
\(942\) −12.5706 13.9939i −0.409574 0.455946i
\(943\) 51.2456i 1.66879i
\(944\) 9.31636 0.303222
\(945\) 0 0
\(946\) 1.57543 0.0512218
\(947\) 28.3321i 0.920671i −0.887745 0.460336i \(-0.847729\pi\)
0.887745 0.460336i \(-0.152271\pi\)
\(948\) −28.1454 31.3321i −0.914121 1.01762i
\(949\) −61.3961 −1.99300
\(950\) −3.47495 6.01879i −0.112742 0.195275i
\(951\) 28.2565 25.3826i 0.916278 0.823088i
\(952\) 0 0
\(953\) 29.8498i 0.966931i 0.875364 + 0.483465i \(0.160622\pi\)
−0.875364 + 0.483465i \(0.839378\pi\)
\(954\) 21.1398 9.35303i 0.684427 0.302816i
\(955\) −0.338347 + 0.195345i −0.0109486 + 0.00632120i
\(956\) −7.57084 4.37102i −0.244858 0.141369i
\(957\) −4.81729 5.36271i −0.155721 0.173352i
\(958\) 10.0935 + 5.82748i 0.326106 + 0.188277i
\(959\) 0 0
\(960\) 0.0110914 0.0340009i 0.000357974 0.00109737i
\(961\) 19.9896 0.644824
\(962\) −4.62642 8.01319i −0.149162 0.258356i
\(963\) 16.0406 21.9700i 0.516901 0.707975i
\(964\) 14.8308 + 8.56258i 0.477669 + 0.275782i
\(965\) −0.298287 0.516648i −0.00960219 0.0166315i
\(966\) 0 0
\(967\) 8.17864 14.1658i 0.263007 0.455542i −0.704032 0.710168i \(-0.748619\pi\)
0.967040 + 0.254626i \(0.0819523\pi\)
\(968\) 20.3809 11.7669i 0.655068 0.378203i
\(969\) 15.3131 13.7556i 0.491926 0.441895i
\(970\) −0.0735528 + 0.127397i −0.00236164 + 0.00409048i
\(971\) 10.7315 18.5875i 0.344390 0.596500i −0.640853 0.767663i \(-0.721419\pi\)
0.985243 + 0.171163i \(0.0547526\pi\)
\(972\) −12.0260 21.1131i −0.385735 0.677202i
\(973\) 0 0
\(974\) −24.8470 + 14.3454i −0.796148 + 0.459657i
\(975\) −46.3717 15.1269i −1.48508 0.484448i
\(976\) 3.66588i 0.117342i
\(977\) 21.5027i 0.687932i 0.938982 + 0.343966i \(0.111770\pi\)
−0.938982 + 0.343966i \(0.888230\pi\)
\(978\) −2.46370 11.6577i −0.0787806 0.372771i
\(979\) 10.6696 6.16010i 0.341002 0.196878i
\(980\) 0 0
\(981\) 12.9774 5.74167i 0.414336 0.183318i
\(982\) −8.82301 + 15.2819i −0.281554 + 0.487665i
\(983\) 12.7097 22.0138i 0.405376 0.702131i −0.588989 0.808141i \(-0.700474\pi\)
0.994365 + 0.106009i \(0.0338073\pi\)
\(984\) 5.97510 + 28.2727i 0.190479 + 0.901302i
\(985\) −0.371794 + 0.214656i −0.0118464 + 0.00683949i
\(986\) 7.67912 13.3006i 0.244553 0.423578i
\(987\) 0 0
\(988\) 9.18759 + 15.9134i 0.292296 + 0.506272i
\(989\) −14.5886 8.42273i −0.463890 0.267827i
\(990\) 0.00616123 0.0573334i 0.000195817 0.00182218i
\(991\) −11.8768 20.5713i −0.377280 0.653468i 0.613385 0.789784i \(-0.289807\pi\)
−0.990665 + 0.136315i \(0.956474\pi\)
\(992\) 19.0987 0.606384
\(993\) 25.0795 + 27.9191i 0.795875 + 0.885985i
\(994\) 0 0
\(995\) 0.237453 + 0.137093i 0.00752776 + 0.00434615i
\(996\) −5.14761 + 15.7801i −0.163108 + 0.500011i
\(997\) 10.5366 + 6.08329i 0.333697 + 0.192660i 0.657481 0.753471i \(-0.271622\pi\)
−0.323785 + 0.946131i \(0.604955\pi\)
\(998\) 3.05781 1.76543i 0.0967934 0.0558837i
\(999\) 1.29829 + 12.7825i 0.0410762 + 0.404420i
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 441.2.i.d.68.16 48
3.2 odd 2 1323.2.i.d.1097.9 48
7.2 even 3 441.2.o.e.293.15 yes 48
7.3 odd 6 441.2.s.d.374.9 48
7.4 even 3 441.2.s.d.374.10 48
7.5 odd 6 441.2.o.e.293.16 yes 48
7.6 odd 2 inner 441.2.i.d.68.15 48
9.2 odd 6 441.2.s.d.362.9 48
9.7 even 3 1323.2.s.d.656.16 48
21.2 odd 6 1323.2.o.e.881.9 48
21.5 even 6 1323.2.o.e.881.10 48
21.11 odd 6 1323.2.s.d.962.15 48
21.17 even 6 1323.2.s.d.962.16 48
21.20 even 2 1323.2.i.d.1097.10 48
63.2 odd 6 441.2.o.e.146.16 yes 48
63.11 odd 6 inner 441.2.i.d.227.9 48
63.16 even 3 1323.2.o.e.440.10 48
63.20 even 6 441.2.s.d.362.10 48
63.25 even 3 1323.2.i.d.521.10 48
63.34 odd 6 1323.2.s.d.656.15 48
63.38 even 6 inner 441.2.i.d.227.10 48
63.47 even 6 441.2.o.e.146.15 48
63.52 odd 6 1323.2.i.d.521.9 48
63.61 odd 6 1323.2.o.e.440.9 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
441.2.i.d.68.15 48 7.6 odd 2 inner
441.2.i.d.68.16 48 1.1 even 1 trivial
441.2.i.d.227.9 48 63.11 odd 6 inner
441.2.i.d.227.10 48 63.38 even 6 inner
441.2.o.e.146.15 48 63.47 even 6
441.2.o.e.146.16 yes 48 63.2 odd 6
441.2.o.e.293.15 yes 48 7.2 even 3
441.2.o.e.293.16 yes 48 7.5 odd 6
441.2.s.d.362.9 48 9.2 odd 6
441.2.s.d.362.10 48 63.20 even 6
441.2.s.d.374.9 48 7.3 odd 6
441.2.s.d.374.10 48 7.4 even 3
1323.2.i.d.521.9 48 63.52 odd 6
1323.2.i.d.521.10 48 63.25 even 3
1323.2.i.d.1097.9 48 3.2 odd 2
1323.2.i.d.1097.10 48 21.20 even 2
1323.2.o.e.440.9 48 63.61 odd 6
1323.2.o.e.440.10 48 63.16 even 3
1323.2.o.e.881.9 48 21.2 odd 6
1323.2.o.e.881.10 48 21.5 even 6
1323.2.s.d.656.15 48 63.34 odd 6
1323.2.s.d.656.16 48 9.7 even 3
1323.2.s.d.962.15 48 21.11 odd 6
1323.2.s.d.962.16 48 21.17 even 6