Properties

Label 882.2.l.c.227.2
Level $882$
Weight $2$
Character 882.227
Analytic conductor $7.043$
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] = [882,2,Mod(227,882)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(882, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([1, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("882.227");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 882.l (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: \(7.04280545828\)
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 227.2
Character \(\chi\) \(=\) 882.227
Dual form 882.2.l.c.509.14

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000i q^{2} +(-1.63594 - 0.568941i) q^{3} -1.00000 q^{4} +(1.55389 - 2.69141i) q^{5} +(-0.568941 + 1.63594i) q^{6} +1.00000i q^{8} +(2.35261 + 1.86151i) q^{9} +O(q^{10})\) \(q-1.00000i q^{2} +(-1.63594 - 0.568941i) q^{3} -1.00000 q^{4} +(1.55389 - 2.69141i) q^{5} +(-0.568941 + 1.63594i) q^{6} +1.00000i q^{8} +(2.35261 + 1.86151i) q^{9} +(-2.69141 - 1.55389i) q^{10} +(1.07339 - 0.619720i) q^{11} +(1.63594 + 0.568941i) q^{12} +(4.97533 - 2.87251i) q^{13} +(-4.07332 + 3.51892i) q^{15} +1.00000 q^{16} +(0.783943 - 1.35783i) q^{17} +(1.86151 - 2.35261i) q^{18} +(5.82814 - 3.36488i) q^{19} +(-1.55389 + 2.69141i) q^{20} +(-0.619720 - 1.07339i) q^{22} +(-1.52367 - 0.879693i) q^{23} +(0.568941 - 1.63594i) q^{24} +(-2.32913 - 4.03417i) q^{25} +(-2.87251 - 4.97533i) q^{26} +(-2.78965 - 4.38382i) q^{27} +(-3.46914 - 2.00291i) q^{29} +(3.51892 + 4.07332i) q^{30} +9.94737i q^{31} -1.00000i q^{32} +(-2.10858 + 0.403133i) q^{33} +(-1.35783 - 0.783943i) q^{34} +(-2.35261 - 1.86151i) q^{36} +(2.63234 + 4.55934i) q^{37} +(-3.36488 - 5.82814i) q^{38} +(-9.77363 + 1.86859i) q^{39} +(2.69141 + 1.55389i) q^{40} +(-5.70540 - 9.88204i) q^{41} +(-1.38634 + 2.40121i) q^{43} +(-1.07339 + 0.619720i) q^{44} +(8.66578 - 3.43928i) q^{45} +(-0.879693 + 1.52367i) q^{46} -0.263735 q^{47} +(-1.63594 - 0.568941i) q^{48} +(-4.03417 + 2.32913i) q^{50} +(-2.05501 + 1.77531i) q^{51} +(-4.97533 + 2.87251i) q^{52} +(10.4795 + 6.05036i) q^{53} +(-4.38382 + 2.78965i) q^{54} -3.85190i q^{55} +(-11.4489 + 2.18888i) q^{57} +(-2.00291 + 3.46914i) q^{58} -10.7630 q^{59} +(4.07332 - 3.51892i) q^{60} -9.36774i q^{61} +9.94737 q^{62} -1.00000 q^{64} -17.8542i q^{65} +(0.403133 + 2.10858i) q^{66} -2.83202 q^{67} +(-0.783943 + 1.35783i) q^{68} +(1.99215 + 2.30601i) q^{69} -0.534528i q^{71} +(-1.86151 + 2.35261i) q^{72} +(-8.05423 - 4.65011i) q^{73} +(4.55934 - 2.63234i) q^{74} +(1.51512 + 7.92481i) q^{75} +(-5.82814 + 3.36488i) q^{76} +(1.86859 + 9.77363i) q^{78} -16.3298 q^{79} +(1.55389 - 2.69141i) q^{80} +(2.06958 + 8.75882i) q^{81} +(-9.88204 + 5.70540i) q^{82} +(-4.82027 + 8.34895i) q^{83} +(-2.43632 - 4.21982i) q^{85} +(2.40121 + 1.38634i) q^{86} +(4.53577 + 5.25037i) q^{87} +(0.619720 + 1.07339i) q^{88} +(3.06418 + 5.30732i) q^{89} +(-3.43928 - 8.66578i) q^{90} +(1.52367 + 0.879693i) q^{92} +(5.65946 - 16.2733i) q^{93} +0.263735i q^{94} -20.9146i q^{95} +(-0.568941 + 1.63594i) q^{96} +(1.29936 + 0.750184i) q^{97} +(3.67888 + 0.540156i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q - 48 q^{4} + 16 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 48 q - 48 q^{4} + 16 q^{9} - 48 q^{11} + 48 q^{15} + 48 q^{16} + 16 q^{18} - 48 q^{23} - 24 q^{25} - 16 q^{30} - 16 q^{36} + 32 q^{39} + 48 q^{44} - 48 q^{50} - 48 q^{51} + 96 q^{53} - 80 q^{57} - 48 q^{60} - 48 q^{64} - 16 q^{72} + 32 q^{78} - 96 q^{79} + 96 q^{81} + 48 q^{85} - 96 q^{86} + 48 q^{92} + 104 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(785\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) −1.63594 0.568941i −0.944512 0.328478i
\(4\) −1.00000 −0.500000
\(5\) 1.55389 2.69141i 0.694919 1.20364i −0.275288 0.961362i \(-0.588773\pi\)
0.970208 0.242274i \(-0.0778933\pi\)
\(6\) −0.568941 + 1.63594i −0.232269 + 0.667871i
\(7\) 0 0
\(8\) 1.00000i 0.353553i
\(9\) 2.35261 + 1.86151i 0.784204 + 0.620503i
\(10\) −2.69141 1.55389i −0.851099 0.491382i
\(11\) 1.07339 0.619720i 0.323638 0.186853i −0.329375 0.944199i \(-0.606838\pi\)
0.653013 + 0.757347i \(0.273505\pi\)
\(12\) 1.63594 + 0.568941i 0.472256 + 0.164239i
\(13\) 4.97533 2.87251i 1.37991 0.796690i 0.387759 0.921761i \(-0.373249\pi\)
0.992148 + 0.125071i \(0.0399159\pi\)
\(14\) 0 0
\(15\) −4.07332 + 3.51892i −1.05173 + 0.908582i
\(16\) 1.00000 0.250000
\(17\) 0.783943 1.35783i 0.190134 0.329322i −0.755160 0.655540i \(-0.772441\pi\)
0.945295 + 0.326218i \(0.105774\pi\)
\(18\) 1.86151 2.35261i 0.438762 0.554516i
\(19\) 5.82814 3.36488i 1.33707 0.771956i 0.350695 0.936490i \(-0.385945\pi\)
0.986371 + 0.164534i \(0.0526121\pi\)
\(20\) −1.55389 + 2.69141i −0.347460 + 0.601818i
\(21\) 0 0
\(22\) −0.619720 1.07339i −0.132125 0.228847i
\(23\) −1.52367 0.879693i −0.317708 0.183429i 0.332663 0.943046i \(-0.392053\pi\)
−0.650370 + 0.759617i \(0.725386\pi\)
\(24\) 0.568941 1.63594i 0.116135 0.333935i
\(25\) −2.32913 4.03417i −0.465826 0.806835i
\(26\) −2.87251 4.97533i −0.563345 0.975742i
\(27\) −2.78965 4.38382i −0.536869 0.843666i
\(28\) 0 0
\(29\) −3.46914 2.00291i −0.644203 0.371931i 0.142029 0.989862i \(-0.454637\pi\)
−0.786232 + 0.617932i \(0.787971\pi\)
\(30\) 3.51892 + 4.07332i 0.642465 + 0.743684i
\(31\) 9.94737i 1.78660i 0.449461 + 0.893300i \(0.351616\pi\)
−0.449461 + 0.893300i \(0.648384\pi\)
\(32\) 1.00000i 0.176777i
\(33\) −2.10858 + 0.403133i −0.367057 + 0.0701764i
\(34\) −1.35783 0.783943i −0.232866 0.134445i
\(35\) 0 0
\(36\) −2.35261 1.86151i −0.392102 0.310251i
\(37\) 2.63234 + 4.55934i 0.432753 + 0.749551i 0.997109 0.0759809i \(-0.0242088\pi\)
−0.564356 + 0.825532i \(0.690875\pi\)
\(38\) −3.36488 5.82814i −0.545855 0.945449i
\(39\) −9.77363 + 1.86859i −1.56503 + 0.299213i
\(40\) 2.69141 + 1.55389i 0.425550 + 0.245691i
\(41\) −5.70540 9.88204i −0.891034 1.54332i −0.838638 0.544690i \(-0.816647\pi\)
−0.0523962 0.998626i \(-0.516686\pi\)
\(42\) 0 0
\(43\) −1.38634 + 2.40121i −0.211415 + 0.366181i −0.952158 0.305608i \(-0.901140\pi\)
0.740743 + 0.671789i \(0.234474\pi\)
\(44\) −1.07339 + 0.619720i −0.161819 + 0.0934263i
\(45\) 8.66578 3.43928i 1.29182 0.512697i
\(46\) −0.879693 + 1.52367i −0.129704 + 0.224653i
\(47\) −0.263735 −0.0384698 −0.0192349 0.999815i \(-0.506123\pi\)
−0.0192349 + 0.999815i \(0.506123\pi\)
\(48\) −1.63594 0.568941i −0.236128 0.0821195i
\(49\) 0 0
\(50\) −4.03417 + 2.32913i −0.570518 + 0.329389i
\(51\) −2.05501 + 1.77531i −0.287759 + 0.248593i
\(52\) −4.97533 + 2.87251i −0.689953 + 0.398345i
\(53\) 10.4795 + 6.05036i 1.43947 + 0.831081i 0.997813 0.0661005i \(-0.0210558\pi\)
0.441662 + 0.897182i \(0.354389\pi\)
\(54\) −4.38382 + 2.78965i −0.596562 + 0.379623i
\(55\) 3.85190i 0.519390i
\(56\) 0 0
\(57\) −11.4489 + 2.18888i −1.51645 + 0.289924i
\(58\) −2.00291 + 3.46914i −0.262995 + 0.455520i
\(59\) −10.7630 −1.40122 −0.700609 0.713545i \(-0.747088\pi\)
−0.700609 + 0.713545i \(0.747088\pi\)
\(60\) 4.07332 3.51892i 0.525864 0.454291i
\(61\) 9.36774i 1.19942i −0.800219 0.599708i \(-0.795283\pi\)
0.800219 0.599708i \(-0.204717\pi\)
\(62\) 9.94737 1.26332
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 17.8542i 2.21454i
\(66\) 0.403133 + 2.10858i 0.0496222 + 0.259549i
\(67\) −2.83202 −0.345987 −0.172993 0.984923i \(-0.555344\pi\)
−0.172993 + 0.984923i \(0.555344\pi\)
\(68\) −0.783943 + 1.35783i −0.0950670 + 0.164661i
\(69\) 1.99215 + 2.30601i 0.239826 + 0.277611i
\(70\) 0 0
\(71\) 0.534528i 0.0634368i −0.999497 0.0317184i \(-0.989902\pi\)
0.999497 0.0317184i \(-0.0100980\pi\)
\(72\) −1.86151 + 2.35261i −0.219381 + 0.277258i
\(73\) −8.05423 4.65011i −0.942676 0.544254i −0.0518779 0.998653i \(-0.516521\pi\)
−0.890798 + 0.454399i \(0.849854\pi\)
\(74\) 4.55934 2.63234i 0.530012 0.306003i
\(75\) 1.51512 + 7.92481i 0.174951 + 0.915078i
\(76\) −5.82814 + 3.36488i −0.668533 + 0.385978i
\(77\) 0 0
\(78\) 1.86859 + 9.77363i 0.211576 + 1.10665i
\(79\) −16.3298 −1.83725 −0.918625 0.395130i \(-0.870700\pi\)
−0.918625 + 0.395130i \(0.870700\pi\)
\(80\) 1.55389 2.69141i 0.173730 0.300909i
\(81\) 2.06958 + 8.75882i 0.229953 + 0.973202i
\(82\) −9.88204 + 5.70540i −1.09129 + 0.630056i
\(83\) −4.82027 + 8.34895i −0.529093 + 0.916416i 0.470331 + 0.882490i \(0.344134\pi\)
−0.999424 + 0.0339263i \(0.989199\pi\)
\(84\) 0 0
\(85\) −2.43632 4.21982i −0.264256 0.457704i
\(86\) 2.40121 + 1.38634i 0.258929 + 0.149493i
\(87\) 4.53577 + 5.25037i 0.486286 + 0.562899i
\(88\) 0.619720 + 1.07339i 0.0660624 + 0.114423i
\(89\) 3.06418 + 5.30732i 0.324802 + 0.562574i 0.981472 0.191604i \(-0.0613688\pi\)
−0.656670 + 0.754178i \(0.728036\pi\)
\(90\) −3.43928 8.66578i −0.362532 0.913453i
\(91\) 0 0
\(92\) 1.52367 + 0.879693i 0.158854 + 0.0917143i
\(93\) 5.65946 16.2733i 0.586859 1.68746i
\(94\) 0.263735i 0.0272022i
\(95\) 20.9146i 2.14579i
\(96\) −0.568941 + 1.63594i −0.0580673 + 0.166968i
\(97\) 1.29936 + 0.750184i 0.131930 + 0.0761697i 0.564512 0.825425i \(-0.309064\pi\)
−0.432583 + 0.901594i \(0.642398\pi\)
\(98\) 0 0
\(99\) 3.67888 + 0.540156i 0.369741 + 0.0542878i
\(100\) 2.32913 + 4.03417i 0.232913 + 0.403417i
\(101\) −3.42652 5.93491i −0.340952 0.590546i 0.643658 0.765313i \(-0.277416\pi\)
−0.984610 + 0.174767i \(0.944083\pi\)
\(102\) 1.77531 + 2.05501i 0.175782 + 0.203476i
\(103\) 4.74363 + 2.73874i 0.467404 + 0.269856i 0.715152 0.698969i \(-0.246357\pi\)
−0.247748 + 0.968824i \(0.579691\pi\)
\(104\) 2.87251 + 4.97533i 0.281672 + 0.487871i
\(105\) 0 0
\(106\) 6.05036 10.4795i 0.587663 1.01786i
\(107\) 14.5748 8.41476i 1.40900 0.813485i 0.413706 0.910411i \(-0.364234\pi\)
0.995292 + 0.0969253i \(0.0309008\pi\)
\(108\) 2.78965 + 4.38382i 0.268434 + 0.421833i
\(109\) −0.690425 + 1.19585i −0.0661307 + 0.114542i −0.897195 0.441635i \(-0.854399\pi\)
0.831064 + 0.556176i \(0.187732\pi\)
\(110\) −3.85190 −0.367264
\(111\) −1.71235 8.95646i −0.162530 0.850109i
\(112\) 0 0
\(113\) 10.9568 6.32593i 1.03073 0.595093i 0.113537 0.993534i \(-0.463782\pi\)
0.917194 + 0.398441i \(0.130449\pi\)
\(114\) 2.18888 + 11.4489i 0.205007 + 1.07229i
\(115\) −4.73523 + 2.73389i −0.441563 + 0.254936i
\(116\) 3.46914 + 2.00291i 0.322101 + 0.185965i
\(117\) 17.0522 + 2.50372i 1.57648 + 0.231469i
\(118\) 10.7630i 0.990811i
\(119\) 0 0
\(120\) −3.51892 4.07332i −0.321232 0.371842i
\(121\) −4.73189 + 8.19588i −0.430172 + 0.745080i
\(122\) −9.36774 −0.848116
\(123\) 3.71141 + 19.4125i 0.334646 + 1.75036i
\(124\) 9.94737i 0.893300i
\(125\) 1.06204 0.0949921
\(126\) 0 0
\(127\) 10.7906 0.957513 0.478756 0.877948i \(-0.341088\pi\)
0.478756 + 0.877948i \(0.341088\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 3.63412 3.13950i 0.319966 0.276417i
\(130\) −17.8542 −1.56592
\(131\) −1.87338 + 3.24479i −0.163678 + 0.283499i −0.936185 0.351507i \(-0.885669\pi\)
0.772507 + 0.635006i \(0.219003\pi\)
\(132\) 2.10858 0.403133i 0.183529 0.0350882i
\(133\) 0 0
\(134\) 2.83202i 0.244650i
\(135\) −16.1335 + 0.696141i −1.38855 + 0.0599143i
\(136\) 1.35783 + 0.783943i 0.116433 + 0.0672225i
\(137\) −0.987927 + 0.570380i −0.0844043 + 0.0487308i −0.541608 0.840631i \(-0.682184\pi\)
0.457204 + 0.889362i \(0.348851\pi\)
\(138\) 2.30601 1.99215i 0.196300 0.169583i
\(139\) 9.69504 5.59744i 0.822323 0.474768i −0.0288941 0.999582i \(-0.509199\pi\)
0.851217 + 0.524814i \(0.175865\pi\)
\(140\) 0 0
\(141\) 0.431456 + 0.150050i 0.0363351 + 0.0126365i
\(142\) −0.534528 −0.0448566
\(143\) 3.56030 6.16662i 0.297727 0.515678i
\(144\) 2.35261 + 1.86151i 0.196051 + 0.155126i
\(145\) −10.7813 + 6.22458i −0.895338 + 0.516924i
\(146\) −4.65011 + 8.05423i −0.384846 + 0.666573i
\(147\) 0 0
\(148\) −2.63234 4.55934i −0.216377 0.374775i
\(149\) 5.73752 + 3.31256i 0.470036 + 0.271375i 0.716255 0.697839i \(-0.245855\pi\)
−0.246219 + 0.969214i \(0.579188\pi\)
\(150\) 7.92481 1.51512i 0.647058 0.123709i
\(151\) 0.0942803 + 0.163298i 0.00767242 + 0.0132890i 0.869836 0.493341i \(-0.164224\pi\)
−0.862164 + 0.506630i \(0.830891\pi\)
\(152\) 3.36488 + 5.82814i 0.272928 + 0.472724i
\(153\) 4.37192 1.73513i 0.353449 0.140277i
\(154\) 0 0
\(155\) 26.7725 + 15.4571i 2.15042 + 1.24154i
\(156\) 9.77363 1.86859i 0.782517 0.149607i
\(157\) 14.3413i 1.14456i 0.820060 + 0.572278i \(0.193940\pi\)
−0.820060 + 0.572278i \(0.806060\pi\)
\(158\) 16.3298i 1.29913i
\(159\) −13.7016 15.8603i −1.08661 1.25780i
\(160\) −2.69141 1.55389i −0.212775 0.122846i
\(161\) 0 0
\(162\) 8.75882 2.06958i 0.688158 0.162601i
\(163\) 4.92077 + 8.52302i 0.385424 + 0.667575i 0.991828 0.127582i \(-0.0407217\pi\)
−0.606404 + 0.795157i \(0.707388\pi\)
\(164\) 5.70540 + 9.88204i 0.445517 + 0.771658i
\(165\) −2.19150 + 6.30149i −0.170608 + 0.490570i
\(166\) 8.34895 + 4.82027i 0.648004 + 0.374125i
\(167\) 0.261517 + 0.452961i 0.0202368 + 0.0350512i 0.875966 0.482372i \(-0.160225\pi\)
−0.855730 + 0.517423i \(0.826891\pi\)
\(168\) 0 0
\(169\) 10.0026 17.3250i 0.769429 1.33269i
\(170\) −4.21982 + 2.43632i −0.323646 + 0.186857i
\(171\) 19.9751 + 2.93287i 1.52753 + 0.224282i
\(172\) 1.38634 2.40121i 0.105707 0.183091i
\(173\) −3.73085 −0.283651 −0.141826 0.989892i \(-0.545297\pi\)
−0.141826 + 0.989892i \(0.545297\pi\)
\(174\) 5.25037 4.53577i 0.398030 0.343856i
\(175\) 0 0
\(176\) 1.07339 0.619720i 0.0809096 0.0467132i
\(177\) 17.6076 + 6.12349i 1.32347 + 0.460270i
\(178\) 5.30732 3.06418i 0.397800 0.229670i
\(179\) −6.53507 3.77303i −0.488454 0.282009i 0.235479 0.971880i \(-0.424334\pi\)
−0.723933 + 0.689870i \(0.757668\pi\)
\(180\) −8.66578 + 3.43928i −0.645909 + 0.256349i
\(181\) 16.6098i 1.23460i 0.786729 + 0.617299i \(0.211773\pi\)
−0.786729 + 0.617299i \(0.788227\pi\)
\(182\) 0 0
\(183\) −5.32969 + 15.3251i −0.393982 + 1.13286i
\(184\) 0.879693 1.52367i 0.0648518 0.112327i
\(185\) 16.3614 1.20291
\(186\) −16.2733 5.65946i −1.19322 0.414972i
\(187\) 1.94330i 0.142108i
\(188\) 0.263735 0.0192349
\(189\) 0 0
\(190\) −20.9146 −1.51730
\(191\) 5.64208i 0.408246i −0.978945 0.204123i \(-0.934566\pi\)
0.978945 0.204123i \(-0.0654343\pi\)
\(192\) 1.63594 + 0.568941i 0.118064 + 0.0410598i
\(193\) 9.42027 0.678086 0.339043 0.940771i \(-0.389897\pi\)
0.339043 + 0.940771i \(0.389897\pi\)
\(194\) 0.750184 1.29936i 0.0538601 0.0932884i
\(195\) −10.1580 + 29.2084i −0.727428 + 2.09166i
\(196\) 0 0
\(197\) 19.6757i 1.40184i −0.713242 0.700918i \(-0.752774\pi\)
0.713242 0.700918i \(-0.247226\pi\)
\(198\) 0.540156 3.67888i 0.0383872 0.261446i
\(199\) 12.6517 + 7.30448i 0.896858 + 0.517801i 0.876179 0.481985i \(-0.160084\pi\)
0.0206785 + 0.999786i \(0.493417\pi\)
\(200\) 4.03417 2.32913i 0.285259 0.164694i
\(201\) 4.63303 + 1.61125i 0.326788 + 0.113649i
\(202\) −5.93491 + 3.42652i −0.417579 + 0.241089i
\(203\) 0 0
\(204\) 2.05501 1.77531i 0.143879 0.124297i
\(205\) −35.4622 −2.47679
\(206\) 2.73874 4.74363i 0.190817 0.330504i
\(207\) −1.94706 4.90591i −0.135330 0.340984i
\(208\) 4.97533 2.87251i 0.344977 0.199172i
\(209\) 4.17056 7.22363i 0.288484 0.499669i
\(210\) 0 0
\(211\) 7.90946 + 13.6996i 0.544510 + 0.943118i 0.998638 + 0.0521819i \(0.0166176\pi\)
−0.454128 + 0.890936i \(0.650049\pi\)
\(212\) −10.4795 6.05036i −0.719737 0.415541i
\(213\) −0.304115 + 0.874457i −0.0208376 + 0.0599168i
\(214\) −8.41476 14.5748i −0.575221 0.996312i
\(215\) 4.30843 + 7.46242i 0.293832 + 0.508933i
\(216\) 4.38382 2.78965i 0.298281 0.189812i
\(217\) 0 0
\(218\) 1.19585 + 0.690425i 0.0809933 + 0.0467615i
\(219\) 10.5306 + 12.1897i 0.711593 + 0.823703i
\(220\) 3.85190i 0.259695i
\(221\) 9.00752i 0.605911i
\(222\) −8.95646 + 1.71235i −0.601118 + 0.114926i
\(223\) 1.09788 + 0.633859i 0.0735192 + 0.0424463i 0.536309 0.844022i \(-0.319818\pi\)
−0.462790 + 0.886468i \(0.653152\pi\)
\(224\) 0 0
\(225\) 2.03010 13.8265i 0.135340 0.921770i
\(226\) −6.32593 10.9568i −0.420794 0.728837i
\(227\) −8.55423 14.8164i −0.567764 0.983396i −0.996787 0.0801026i \(-0.974475\pi\)
0.429022 0.903294i \(-0.358858\pi\)
\(228\) 11.4489 2.18888i 0.758223 0.144962i
\(229\) −9.54337 5.50987i −0.630644 0.364102i 0.150358 0.988632i \(-0.451957\pi\)
−0.781001 + 0.624529i \(0.785291\pi\)
\(230\) 2.73389 + 4.73523i 0.180267 + 0.312232i
\(231\) 0 0
\(232\) 2.00291 3.46914i 0.131497 0.227760i
\(233\) −19.8834 + 11.4797i −1.30261 + 0.752060i −0.980850 0.194763i \(-0.937606\pi\)
−0.321756 + 0.946823i \(0.604273\pi\)
\(234\) 2.50372 17.0522i 0.163673 1.11474i
\(235\) −0.409815 + 0.709821i −0.0267334 + 0.0463036i
\(236\) 10.7630 0.700609
\(237\) 26.7147 + 9.29071i 1.73530 + 0.603496i
\(238\) 0 0
\(239\) −9.63609 + 5.56340i −0.623307 + 0.359866i −0.778155 0.628072i \(-0.783844\pi\)
0.154849 + 0.987938i \(0.450511\pi\)
\(240\) −4.07332 + 3.51892i −0.262932 + 0.227146i
\(241\) 0.384876 0.222208i 0.0247920 0.0143137i −0.487553 0.873094i \(-0.662110\pi\)
0.512345 + 0.858780i \(0.328777\pi\)
\(242\) 8.19588 + 4.73189i 0.526851 + 0.304178i
\(243\) 1.59754 15.5064i 0.102482 0.994735i
\(244\) 9.36774i 0.599708i
\(245\) 0 0
\(246\) 19.4125 3.71141i 1.23769 0.236631i
\(247\) 19.3313 33.4827i 1.23002 2.13045i
\(248\) −9.94737 −0.631659
\(249\) 12.6357 10.9160i 0.800757 0.691770i
\(250\) 1.06204i 0.0671696i
\(251\) −18.9568 −1.19655 −0.598273 0.801292i \(-0.704146\pi\)
−0.598273 + 0.801292i \(0.704146\pi\)
\(252\) 0 0
\(253\) −2.18065 −0.137096
\(254\) 10.7906i 0.677064i
\(255\) 1.58484 + 8.28951i 0.0992467 + 0.519109i
\(256\) 1.00000 0.0625000
\(257\) 8.66124 15.0017i 0.540273 0.935781i −0.458615 0.888635i \(-0.651654\pi\)
0.998888 0.0471456i \(-0.0150125\pi\)
\(258\) −3.13950 3.63412i −0.195456 0.226250i
\(259\) 0 0
\(260\) 17.8542i 1.10727i
\(261\) −4.43311 11.1699i −0.274403 0.691399i
\(262\) 3.24479 + 1.87338i 0.200464 + 0.115738i
\(263\) 2.43723 1.40713i 0.150286 0.0867675i −0.422971 0.906143i \(-0.639013\pi\)
0.573257 + 0.819375i \(0.305680\pi\)
\(264\) −0.403133 2.10858i −0.0248111 0.129774i
\(265\) 32.5680 18.8032i 2.00064 1.15507i
\(266\) 0 0
\(267\) −1.99327 10.4258i −0.121986 0.638049i
\(268\) 2.83202 0.172993
\(269\) 12.6555 21.9200i 0.771620 1.33648i −0.165055 0.986284i \(-0.552780\pi\)
0.936675 0.350200i \(-0.113886\pi\)
\(270\) 0.696141 + 16.1335i 0.0423658 + 0.981851i
\(271\) −24.2642 + 14.0089i −1.47394 + 0.850982i −0.999569 0.0293402i \(-0.990659\pi\)
−0.474375 + 0.880323i \(0.657326\pi\)
\(272\) 0.783943 1.35783i 0.0475335 0.0823304i
\(273\) 0 0
\(274\) 0.570380 + 0.987927i 0.0344579 + 0.0596828i
\(275\) −5.00012 2.88682i −0.301518 0.174082i
\(276\) −1.99215 2.30601i −0.119913 0.138805i
\(277\) −1.85995 3.22152i −0.111753 0.193562i 0.804724 0.593649i \(-0.202313\pi\)
−0.916477 + 0.400087i \(0.868980\pi\)
\(278\) −5.59744 9.69504i −0.335712 0.581470i
\(279\) −18.5171 + 23.4023i −1.10859 + 1.40106i
\(280\) 0 0
\(281\) 6.40645 + 3.69877i 0.382177 + 0.220650i 0.678765 0.734356i \(-0.262516\pi\)
−0.296588 + 0.955005i \(0.595849\pi\)
\(282\) 0.150050 0.431456i 0.00893534 0.0256928i
\(283\) 13.5292i 0.804226i 0.915590 + 0.402113i \(0.131724\pi\)
−0.915590 + 0.402113i \(0.868276\pi\)
\(284\) 0.534528i 0.0317184i
\(285\) −11.8991 + 34.2150i −0.704844 + 2.02672i
\(286\) −6.16662 3.56030i −0.364640 0.210525i
\(287\) 0 0
\(288\) 1.86151 2.35261i 0.109690 0.138629i
\(289\) 7.27087 + 12.5935i 0.427698 + 0.740795i
\(290\) 6.22458 + 10.7813i 0.365520 + 0.633099i
\(291\) −1.69886 1.96652i −0.0995891 0.115279i
\(292\) 8.05423 + 4.65011i 0.471338 + 0.272127i
\(293\) 2.50771 + 4.34349i 0.146502 + 0.253749i 0.929932 0.367731i \(-0.119865\pi\)
−0.783430 + 0.621480i \(0.786532\pi\)
\(294\) 0 0
\(295\) −16.7244 + 28.9676i −0.973734 + 1.68656i
\(296\) −4.55934 + 2.63234i −0.265006 + 0.153001i
\(297\) −5.71111 2.97673i −0.331392 0.172727i
\(298\) 3.31256 5.73752i 0.191891 0.332366i
\(299\) −10.1077 −0.584543
\(300\) −1.51512 7.92481i −0.0874754 0.457539i
\(301\) 0 0
\(302\) 0.163298 0.0942803i 0.00939676 0.00542522i
\(303\) 2.22898 + 11.6587i 0.128052 + 0.669773i
\(304\) 5.82814 3.36488i 0.334267 0.192989i
\(305\) −25.2125 14.5564i −1.44366 0.833498i
\(306\) −1.73513 4.37192i −0.0991907 0.249926i
\(307\) 10.7290i 0.612334i −0.951978 0.306167i \(-0.900953\pi\)
0.951978 0.306167i \(-0.0990466\pi\)
\(308\) 0 0
\(309\) −6.20213 7.17926i −0.352827 0.408414i
\(310\) 15.4571 26.7725i 0.877904 1.52057i
\(311\) 1.07969 0.0612236 0.0306118 0.999531i \(-0.490254\pi\)
0.0306118 + 0.999531i \(0.490254\pi\)
\(312\) −1.86859 9.77363i −0.105788 0.553323i
\(313\) 23.8521i 1.34820i 0.738639 + 0.674101i \(0.235469\pi\)
−0.738639 + 0.674101i \(0.764531\pi\)
\(314\) 14.3413 0.809324
\(315\) 0 0
\(316\) 16.3298 0.918625
\(317\) 22.0867i 1.24051i 0.784399 + 0.620256i \(0.212971\pi\)
−0.784399 + 0.620256i \(0.787029\pi\)
\(318\) −15.8603 + 13.7016i −0.889400 + 0.768348i
\(319\) −4.96497 −0.277985
\(320\) −1.55389 + 2.69141i −0.0868649 + 0.150454i
\(321\) −28.6310 + 5.47386i −1.59803 + 0.305521i
\(322\) 0 0
\(323\) 10.5515i 0.587100i
\(324\) −2.06958 8.75882i −0.114976 0.486601i
\(325\) −23.1764 13.3809i −1.28559 0.742238i
\(326\) 8.52302 4.92077i 0.472047 0.272536i
\(327\) 1.80986 1.56353i 0.100086 0.0864635i
\(328\) 9.88204 5.70540i 0.545645 0.315028i
\(329\) 0 0
\(330\) 6.30149 + 2.19150i 0.346885 + 0.120638i
\(331\) 14.3102 0.786561 0.393281 0.919418i \(-0.371340\pi\)
0.393281 + 0.919418i \(0.371340\pi\)
\(332\) 4.82027 8.34895i 0.264547 0.458208i
\(333\) −2.29438 + 15.6265i −0.125731 + 0.856325i
\(334\) 0.452961 0.261517i 0.0247849 0.0143096i
\(335\) −4.40064 + 7.62214i −0.240433 + 0.416442i
\(336\) 0 0
\(337\) −10.0707 17.4430i −0.548588 0.950182i −0.998372 0.0570449i \(-0.981832\pi\)
0.449783 0.893138i \(-0.351501\pi\)
\(338\) −17.3250 10.0026i −0.942354 0.544068i
\(339\) −21.5238 + 4.11506i −1.16901 + 0.223500i
\(340\) 2.43632 + 4.21982i 0.132128 + 0.228852i
\(341\) 6.16458 + 10.6774i 0.333831 + 0.578212i
\(342\) 2.93287 19.9751i 0.158592 1.08013i
\(343\) 0 0
\(344\) −2.40121 1.38634i −0.129465 0.0747464i
\(345\) 9.30198 1.77842i 0.500802 0.0957467i
\(346\) 3.73085i 0.200572i
\(347\) 13.4117i 0.719975i 0.932957 + 0.359988i \(0.117219\pi\)
−0.932957 + 0.359988i \(0.882781\pi\)
\(348\) −4.53577 5.25037i −0.243143 0.281450i
\(349\) −16.4018 9.46958i −0.877968 0.506895i −0.00798005 0.999968i \(-0.502540\pi\)
−0.869988 + 0.493073i \(0.835873\pi\)
\(350\) 0 0
\(351\) −26.4720 13.7976i −1.41297 0.736463i
\(352\) −0.619720 1.07339i −0.0330312 0.0572117i
\(353\) 12.5947 + 21.8147i 0.670349 + 1.16108i 0.977805 + 0.209516i \(0.0671889\pi\)
−0.307456 + 0.951562i \(0.599478\pi\)
\(354\) 6.12349 17.6076i 0.325460 0.935832i
\(355\) −1.43863 0.830596i −0.0763548 0.0440835i
\(356\) −3.06418 5.30732i −0.162401 0.281287i
\(357\) 0 0
\(358\) −3.77303 + 6.53507i −0.199411 + 0.345389i
\(359\) 6.33158 3.65554i 0.334168 0.192932i −0.323522 0.946221i \(-0.604867\pi\)
0.657690 + 0.753289i \(0.271534\pi\)
\(360\) 3.43928 + 8.66578i 0.181266 + 0.456727i
\(361\) 13.1448 22.7674i 0.691831 1.19829i
\(362\) 16.6098 0.872992
\(363\) 12.4041 10.7158i 0.651045 0.562435i
\(364\) 0 0
\(365\) −25.0307 + 14.4515i −1.31017 + 0.756426i
\(366\) 15.3251 + 5.32969i 0.801055 + 0.278587i
\(367\) 22.6702 13.0886i 1.18337 0.683220i 0.226580 0.973993i \(-0.427245\pi\)
0.956792 + 0.290772i \(0.0939122\pi\)
\(368\) −1.52367 0.879693i −0.0794269 0.0458572i
\(369\) 4.97291 33.8693i 0.258879 1.76316i
\(370\) 16.3614i 0.850589i
\(371\) 0 0
\(372\) −5.65946 + 16.2733i −0.293429 + 0.843732i
\(373\) −10.5412 + 18.2578i −0.545801 + 0.945355i 0.452755 + 0.891635i \(0.350441\pi\)
−0.998556 + 0.0537204i \(0.982892\pi\)
\(374\) −1.94330 −0.100486
\(375\) −1.73744 0.604240i −0.0897212 0.0312028i
\(376\) 0.263735i 0.0136011i
\(377\) −23.0134 −1.18525
\(378\) 0 0
\(379\) −5.68371 −0.291953 −0.145976 0.989288i \(-0.546632\pi\)
−0.145976 + 0.989288i \(0.546632\pi\)
\(380\) 20.9146i 1.07289i
\(381\) −17.6528 6.13922i −0.904382 0.314522i
\(382\) −5.64208 −0.288674
\(383\) 0.0608136 0.105332i 0.00310743 0.00538223i −0.864468 0.502689i \(-0.832344\pi\)
0.867575 + 0.497306i \(0.165678\pi\)
\(384\) 0.568941 1.63594i 0.0290336 0.0834838i
\(385\) 0 0
\(386\) 9.42027i 0.479479i
\(387\) −7.73139 + 3.06844i −0.393009 + 0.155977i
\(388\) −1.29936 0.750184i −0.0659649 0.0380848i
\(389\) −23.8235 + 13.7545i −1.20790 + 0.697381i −0.962300 0.271991i \(-0.912318\pi\)
−0.245599 + 0.969372i \(0.578985\pi\)
\(390\) 29.2084 + 10.1580i 1.47903 + 0.514369i
\(391\) −2.38894 + 1.37926i −0.120814 + 0.0697521i
\(392\) 0 0
\(393\) 4.91084 4.24245i 0.247719 0.214003i
\(394\) −19.6757 −0.991248
\(395\) −25.3747 + 43.9503i −1.27674 + 2.21138i
\(396\) −3.67888 0.540156i −0.184871 0.0271439i
\(397\) 10.7866 6.22766i 0.541365 0.312557i −0.204267 0.978915i \(-0.565481\pi\)
0.745632 + 0.666358i \(0.232148\pi\)
\(398\) 7.30448 12.6517i 0.366141 0.634174i
\(399\) 0 0
\(400\) −2.32913 4.03417i −0.116457 0.201709i
\(401\) 24.0294 + 13.8734i 1.19997 + 0.692802i 0.960548 0.278114i \(-0.0897092\pi\)
0.239421 + 0.970916i \(0.423042\pi\)
\(402\) 1.61125 4.63303i 0.0803620 0.231074i
\(403\) 28.5739 + 49.4914i 1.42337 + 2.46534i
\(404\) 3.42652 + 5.93491i 0.170476 + 0.295273i
\(405\) 26.7895 + 8.04013i 1.33118 + 0.399517i
\(406\) 0 0
\(407\) 5.65103 + 3.26262i 0.280111 + 0.161722i
\(408\) −1.77531 2.05501i −0.0878910 0.101738i
\(409\) 11.2300i 0.555286i −0.960684 0.277643i \(-0.910447\pi\)
0.960684 0.277643i \(-0.0895533\pi\)
\(410\) 35.4622i 1.75135i
\(411\) 1.94070 0.371037i 0.0957278 0.0183019i
\(412\) −4.74363 2.73874i −0.233702 0.134928i
\(413\) 0 0
\(414\) −4.90591 + 1.94706i −0.241112 + 0.0956926i
\(415\) 14.9803 + 25.9467i 0.735354 + 1.27367i
\(416\) −2.87251 4.97533i −0.140836 0.243935i
\(417\) −19.0451 + 3.64118i −0.932644 + 0.178309i
\(418\) −7.22363 4.17056i −0.353319 0.203989i
\(419\) 1.68086 + 2.91134i 0.0821155 + 0.142228i 0.904158 0.427197i \(-0.140499\pi\)
−0.822043 + 0.569425i \(0.807166\pi\)
\(420\) 0 0
\(421\) −3.08955 + 5.35125i −0.150575 + 0.260804i −0.931439 0.363897i \(-0.881446\pi\)
0.780864 + 0.624701i \(0.214779\pi\)
\(422\) 13.6996 7.90946i 0.666885 0.385026i
\(423\) −0.620467 0.490946i −0.0301682 0.0238706i
\(424\) −6.05036 + 10.4795i −0.293832 + 0.508931i
\(425\) −7.30362 −0.354278
\(426\) 0.874457 + 0.304115i 0.0423676 + 0.0147344i
\(427\) 0 0
\(428\) −14.5748 + 8.41476i −0.704499 + 0.406743i
\(429\) −9.33288 + 8.06263i −0.450596 + 0.389267i
\(430\) 7.46242 4.30843i 0.359870 0.207771i
\(431\) 11.5265 + 6.65482i 0.555211 + 0.320551i 0.751221 0.660050i \(-0.229465\pi\)
−0.196010 + 0.980602i \(0.562798\pi\)
\(432\) −2.78965 4.38382i −0.134217 0.210916i
\(433\) 25.7161i 1.23584i 0.786242 + 0.617919i \(0.212024\pi\)
−0.786242 + 0.617919i \(0.787976\pi\)
\(434\) 0 0
\(435\) 21.1790 4.04914i 1.01545 0.194141i
\(436\) 0.690425 1.19585i 0.0330654 0.0572709i
\(437\) −11.8402 −0.566395
\(438\) 12.1897 10.5306i 0.582446 0.503172i
\(439\) 37.0419i 1.76791i −0.467570 0.883956i \(-0.654870\pi\)
0.467570 0.883956i \(-0.345130\pi\)
\(440\) 3.85190 0.183632
\(441\) 0 0
\(442\) −9.00752 −0.428444
\(443\) 22.9752i 1.09158i 0.837921 + 0.545792i \(0.183771\pi\)
−0.837921 + 0.545792i \(0.816229\pi\)
\(444\) 1.71235 + 8.95646i 0.0812648 + 0.425055i
\(445\) 19.0456 0.902846
\(446\) 0.633859 1.09788i 0.0300141 0.0519859i
\(447\) −7.50160 8.68347i −0.354814 0.410714i
\(448\) 0 0
\(449\) 0.217897i 0.0102832i 0.999987 + 0.00514159i \(0.00163663\pi\)
−0.999987 + 0.00514159i \(0.998363\pi\)
\(450\) −13.8265 2.03010i −0.651790 0.0957000i
\(451\) −12.2482 7.07150i −0.576745 0.332984i
\(452\) −10.9568 + 6.32593i −0.515366 + 0.297546i
\(453\) −0.0613301 0.320786i −0.00288154 0.0150719i
\(454\) −14.8164 + 8.55423i −0.695366 + 0.401470i
\(455\) 0 0
\(456\) −2.18888 11.4489i −0.102504 0.536144i
\(457\) −0.930228 −0.0435143 −0.0217571 0.999763i \(-0.506926\pi\)
−0.0217571 + 0.999763i \(0.506926\pi\)
\(458\) −5.50987 + 9.54337i −0.257459 + 0.445932i
\(459\) −8.13940 + 0.351206i −0.379915 + 0.0163929i
\(460\) 4.73523 2.73389i 0.220781 0.127468i
\(461\) 15.6935 27.1820i 0.730921 1.26599i −0.225570 0.974227i \(-0.572424\pi\)
0.956490 0.291764i \(-0.0942424\pi\)
\(462\) 0 0
\(463\) 10.3239 + 17.8816i 0.479795 + 0.831028i 0.999731 0.0231762i \(-0.00737788\pi\)
−0.519937 + 0.854205i \(0.674045\pi\)
\(464\) −3.46914 2.00291i −0.161051 0.0929826i
\(465\) −35.0040 40.5188i −1.62327 1.87902i
\(466\) 11.4797 + 19.8834i 0.531787 + 0.921082i
\(467\) 5.27432 + 9.13539i 0.244066 + 0.422736i 0.961869 0.273511i \(-0.0881852\pi\)
−0.717802 + 0.696247i \(0.754852\pi\)
\(468\) −17.0522 2.50372i −0.788238 0.115734i
\(469\) 0 0
\(470\) 0.709821 + 0.409815i 0.0327416 + 0.0189034i
\(471\) 8.15932 23.4615i 0.375962 1.08105i
\(472\) 10.7630i 0.495406i
\(473\) 3.43657i 0.158014i
\(474\) 9.29071 26.7147i 0.426736 1.22705i
\(475\) −27.1490 15.6745i −1.24568 0.719194i
\(476\) 0 0
\(477\) 13.3915 + 33.7419i 0.613154 + 1.54494i
\(478\) 5.56340 + 9.63609i 0.254464 + 0.440744i
\(479\) −9.23071 15.9881i −0.421762 0.730513i 0.574350 0.818610i \(-0.305255\pi\)
−0.996112 + 0.0880966i \(0.971922\pi\)
\(480\) 3.51892 + 4.07332i 0.160616 + 0.185921i
\(481\) 26.1934 + 15.1228i 1.19432 + 0.689540i
\(482\) −0.222208 0.384876i −0.0101213 0.0175306i
\(483\) 0 0
\(484\) 4.73189 8.19588i 0.215086 0.372540i
\(485\) 4.03811 2.33140i 0.183361 0.105864i
\(486\) −15.5064 1.59754i −0.703384 0.0724660i
\(487\) 19.1534 33.1747i 0.867924 1.50329i 0.00381071 0.999993i \(-0.498787\pi\)
0.864114 0.503297i \(-0.167880\pi\)
\(488\) 9.36774 0.424058
\(489\) −3.20100 16.7428i −0.144754 0.757135i
\(490\) 0 0
\(491\) 9.32798 5.38551i 0.420966 0.243045i −0.274525 0.961580i \(-0.588521\pi\)
0.695490 + 0.718535i \(0.255187\pi\)
\(492\) −3.71141 19.4125i −0.167323 0.875182i
\(493\) −5.43921 + 3.14033i −0.244970 + 0.141433i
\(494\) −33.4827 19.3313i −1.50646 0.869754i
\(495\) 7.17034 9.06203i 0.322283 0.407308i
\(496\) 9.94737i 0.446650i
\(497\) 0 0
\(498\) −10.9160 12.6357i −0.489156 0.566221i
\(499\) 6.11298 10.5880i 0.273655 0.473984i −0.696140 0.717906i \(-0.745101\pi\)
0.969795 + 0.243922i \(0.0784341\pi\)
\(500\) −1.06204 −0.0474961
\(501\) −0.170119 0.889806i −0.00760036 0.0397536i
\(502\) 18.9568i 0.846086i
\(503\) 4.13307 0.184285 0.0921423 0.995746i \(-0.470629\pi\)
0.0921423 + 0.995746i \(0.470629\pi\)
\(504\) 0 0
\(505\) −21.2977 −0.947736
\(506\) 2.18065i 0.0969419i
\(507\) −26.2205 + 22.6518i −1.16449 + 1.00600i
\(508\) −10.7906 −0.478756
\(509\) −5.57958 + 9.66411i −0.247310 + 0.428354i −0.962779 0.270291i \(-0.912880\pi\)
0.715468 + 0.698645i \(0.246213\pi\)
\(510\) 8.28951 1.58484i 0.367066 0.0701780i
\(511\) 0 0
\(512\) 1.00000i 0.0441942i
\(513\) −31.0095 16.1627i −1.36910 0.713599i
\(514\) −15.0017 8.66124i −0.661697 0.382031i
\(515\) 14.7421 8.51138i 0.649616 0.375056i
\(516\) −3.63412 + 3.13950i −0.159983 + 0.138209i
\(517\) −0.283090 + 0.163442i −0.0124503 + 0.00718818i
\(518\) 0 0
\(519\) 6.10345 + 2.12263i 0.267912 + 0.0931732i
\(520\) 17.8542 0.782958
\(521\) −2.62310 + 4.54334i −0.114920 + 0.199047i −0.917748 0.397164i \(-0.869995\pi\)
0.802828 + 0.596211i \(0.203328\pi\)
\(522\) −11.1699 + 4.43311i −0.488893 + 0.194032i
\(523\) −13.6454 + 7.87819i −0.596673 + 0.344489i −0.767732 0.640772i \(-0.778615\pi\)
0.171059 + 0.985261i \(0.445281\pi\)
\(524\) 1.87338 3.24479i 0.0818391 0.141749i
\(525\) 0 0
\(526\) −1.40713 2.43723i −0.0613539 0.106268i
\(527\) 13.5068 + 7.79817i 0.588366 + 0.339693i
\(528\) −2.10858 + 0.403133i −0.0917643 + 0.0175441i
\(529\) −9.95228 17.2379i −0.432708 0.749472i
\(530\) −18.8032 32.5680i −0.816757 1.41466i
\(531\) −25.3211 20.0353i −1.09884 0.869460i
\(532\) 0 0
\(533\) −56.7724 32.7776i −2.45909 1.41975i
\(534\) −10.4258 + 1.99327i −0.451168 + 0.0862574i
\(535\) 52.3023i 2.26123i
\(536\) 2.83202i 0.122325i
\(537\) 8.54437 + 9.89052i 0.368717 + 0.426807i
\(538\) −21.9200 12.6555i −0.945037 0.545617i
\(539\) 0 0
\(540\) 16.1335 0.696141i 0.694273 0.0299572i
\(541\) −3.03172 5.25109i −0.130344 0.225762i 0.793465 0.608615i \(-0.208275\pi\)
−0.923809 + 0.382853i \(0.874941\pi\)
\(542\) 14.0089 + 24.2642i 0.601735 + 1.04224i
\(543\) 9.45000 27.1727i 0.405538 1.16609i
\(544\) −1.35783 0.783943i −0.0582164 0.0336113i
\(545\) 2.14569 + 3.71644i 0.0919110 + 0.159195i
\(546\) 0 0
\(547\) 0.412740 0.714887i 0.0176475 0.0305663i −0.857067 0.515205i \(-0.827716\pi\)
0.874714 + 0.484639i \(0.161049\pi\)
\(548\) 0.987927 0.570380i 0.0422021 0.0243654i
\(549\) 17.4381 22.0387i 0.744241 0.940588i
\(550\) −2.88682 + 5.00012i −0.123094 + 0.213206i
\(551\) −26.9581 −1.14846
\(552\) −2.30601 + 1.99215i −0.0981501 + 0.0847914i
\(553\) 0 0
\(554\) −3.22152 + 1.85995i −0.136869 + 0.0790215i
\(555\) −26.7663 9.30867i −1.13617 0.395131i
\(556\) −9.69504 + 5.59744i −0.411161 + 0.237384i
\(557\) 19.2191 + 11.0961i 0.814339 + 0.470159i 0.848460 0.529259i \(-0.177530\pi\)
−0.0341214 + 0.999418i \(0.510863\pi\)
\(558\) 23.4023 + 18.5171i 0.990699 + 0.783892i
\(559\) 15.9291i 0.673728i
\(560\) 0 0
\(561\) −1.10562 + 3.17913i −0.0466794 + 0.134223i
\(562\) 3.69877 6.40645i 0.156023 0.270240i
\(563\) −1.96694 −0.0828968 −0.0414484 0.999141i \(-0.513197\pi\)
−0.0414484 + 0.999141i \(0.513197\pi\)
\(564\) −0.431456 0.150050i −0.0181676 0.00631824i
\(565\) 39.3191i 1.65417i
\(566\) 13.5292 0.568674
\(567\) 0 0
\(568\) 0.534528 0.0224283
\(569\) 26.0453i 1.09188i 0.837825 + 0.545938i \(0.183827\pi\)
−0.837825 + 0.545938i \(0.816173\pi\)
\(570\) 34.2150 + 11.8991i 1.43311 + 0.498400i
\(571\) −6.64910 −0.278256 −0.139128 0.990274i \(-0.544430\pi\)
−0.139128 + 0.990274i \(0.544430\pi\)
\(572\) −3.56030 + 6.16662i −0.148864 + 0.257839i
\(573\) −3.21001 + 9.23011i −0.134100 + 0.385593i
\(574\) 0 0
\(575\) 8.19568i 0.341784i
\(576\) −2.35261 1.86151i −0.0980255 0.0775628i
\(577\) 1.79600 + 1.03692i 0.0747683 + 0.0431675i 0.536918 0.843634i \(-0.319588\pi\)
−0.462150 + 0.886802i \(0.652922\pi\)
\(578\) 12.5935 7.27087i 0.523821 0.302428i
\(579\) −15.4110 5.35957i −0.640460 0.222736i
\(580\) 10.7813 6.22458i 0.447669 0.258462i
\(581\) 0 0
\(582\) −1.96652 + 1.69886i −0.0815147 + 0.0704201i
\(583\) 14.9981 0.621159
\(584\) 4.65011 8.05423i 0.192423 0.333286i
\(585\) 33.2357 42.0040i 1.37413 1.73665i
\(586\) 4.34349 2.50771i 0.179428 0.103593i
\(587\) 5.82360 10.0868i 0.240366 0.416326i −0.720453 0.693504i \(-0.756066\pi\)
0.960818 + 0.277178i \(0.0893993\pi\)
\(588\) 0 0
\(589\) 33.4717 + 57.9746i 1.37918 + 2.38880i
\(590\) 28.9676 + 16.7244i 1.19258 + 0.688534i
\(591\) −11.1943 + 32.1883i −0.460473 + 1.32405i
\(592\) 2.63234 + 4.55934i 0.108188 + 0.187388i
\(593\) 12.3939 + 21.4669i 0.508956 + 0.881538i 0.999946 + 0.0103731i \(0.00330192\pi\)
−0.490990 + 0.871165i \(0.663365\pi\)
\(594\) −2.97673 + 5.71111i −0.122137 + 0.234330i
\(595\) 0 0
\(596\) −5.73752 3.31256i −0.235018 0.135688i
\(597\) −16.5417 19.1478i −0.677006 0.783667i
\(598\) 10.1077i 0.413334i
\(599\) 42.8086i 1.74911i −0.484926 0.874555i \(-0.661153\pi\)
0.484926 0.874555i \(-0.338847\pi\)
\(600\) −7.92481 + 1.51512i −0.323529 + 0.0618544i
\(601\) 9.72891 + 5.61699i 0.396851 + 0.229122i 0.685124 0.728426i \(-0.259748\pi\)
−0.288274 + 0.957548i \(0.593081\pi\)
\(602\) 0 0
\(603\) −6.66265 5.27183i −0.271324 0.214686i
\(604\) −0.0942803 0.163298i −0.00383621 0.00664451i
\(605\) 14.7057 + 25.4710i 0.597870 + 1.03554i
\(606\) 11.6587 2.22898i 0.473601 0.0905461i
\(607\) −2.61469 1.50959i −0.106127 0.0612724i 0.445997 0.895034i \(-0.352849\pi\)
−0.552124 + 0.833762i \(0.686182\pi\)
\(608\) −3.36488 5.82814i −0.136464 0.236362i
\(609\) 0 0
\(610\) −14.5564 + 25.2125i −0.589372 + 1.02082i
\(611\) −1.31217 + 0.757581i −0.0530847 + 0.0306485i
\(612\) −4.37192 + 1.73513i −0.176724 + 0.0701384i
\(613\) −15.8207 + 27.4022i −0.638990 + 1.10676i 0.346664 + 0.937989i \(0.387314\pi\)
−0.985655 + 0.168774i \(0.946019\pi\)
\(614\) −10.7290 −0.432986
\(615\) 58.0141 + 20.1759i 2.33935 + 0.813570i
\(616\) 0 0
\(617\) 7.34373 4.23990i 0.295647 0.170692i −0.344839 0.938662i \(-0.612066\pi\)
0.640486 + 0.767970i \(0.278733\pi\)
\(618\) −7.17926 + 6.20213i −0.288792 + 0.249486i
\(619\) 33.0186 19.0633i 1.32713 0.766218i 0.342274 0.939600i \(-0.388803\pi\)
0.984855 + 0.173382i \(0.0554694\pi\)
\(620\) −26.7725 15.4571i −1.07521 0.620772i
\(621\) 0.394102 + 9.13354i 0.0158148 + 0.366516i
\(622\) 1.07969i 0.0432916i
\(623\) 0 0
\(624\) −9.77363 + 1.86859i −0.391258 + 0.0748034i
\(625\) 13.2960 23.0293i 0.531838 0.921171i
\(626\) 23.8521 0.953323
\(627\) −10.9326 + 9.44463i −0.436607 + 0.377182i
\(628\) 14.3413i 0.572278i
\(629\) 8.25440 0.329124
\(630\) 0 0
\(631\) −15.1860 −0.604547 −0.302273 0.953221i \(-0.597746\pi\)
−0.302273 + 0.953221i \(0.597746\pi\)
\(632\) 16.3298i 0.649566i
\(633\) −5.14517 26.9117i −0.204502 1.06965i
\(634\) 22.0867 0.877175
\(635\) 16.7674 29.0420i 0.665394 1.15250i
\(636\) 13.7016 + 15.8603i 0.543304 + 0.628901i
\(637\) 0 0
\(638\) 4.96497i 0.196565i
\(639\) 0.995028 1.25754i 0.0393627 0.0497474i
\(640\) 2.69141 + 1.55389i 0.106387 + 0.0614228i
\(641\) −25.0395 + 14.4566i −0.989002 + 0.571001i −0.904976 0.425463i \(-0.860111\pi\)
−0.0840262 + 0.996464i \(0.526778\pi\)
\(642\) 5.47386 + 28.6310i 0.216036 + 1.12998i
\(643\) −26.4809 + 15.2888i −1.04431 + 0.602930i −0.921050 0.389445i \(-0.872667\pi\)
−0.123256 + 0.992375i \(0.539334\pi\)
\(644\) 0 0
\(645\) −2.80267 14.6593i −0.110355 0.577210i
\(646\) −10.5515 −0.415142
\(647\) −13.6686 + 23.6747i −0.537368 + 0.930749i 0.461676 + 0.887048i \(0.347248\pi\)
−0.999045 + 0.0437008i \(0.986085\pi\)
\(648\) −8.75882 + 2.06958i −0.344079 + 0.0813006i
\(649\) −11.5528 + 6.67002i −0.453488 + 0.261821i
\(650\) −13.3809 + 23.1764i −0.524841 + 0.909052i
\(651\) 0 0
\(652\) −4.92077 8.52302i −0.192712 0.333787i
\(653\) 0.875223 + 0.505310i 0.0342501 + 0.0197743i 0.517027 0.855969i \(-0.327039\pi\)
−0.482777 + 0.875743i \(0.660372\pi\)
\(654\) −1.56353 1.80986i −0.0611389 0.0707713i
\(655\) 5.82205 + 10.0841i 0.227486 + 0.394018i
\(656\) −5.70540 9.88204i −0.222758 0.385829i
\(657\) −10.2923 25.9329i −0.401539 1.01174i
\(658\) 0 0
\(659\) −27.4827 15.8671i −1.07057 0.618096i −0.142236 0.989833i \(-0.545429\pi\)
−0.928338 + 0.371737i \(0.878762\pi\)
\(660\) 2.19150 6.30149i 0.0853041 0.245285i
\(661\) 3.85538i 0.149957i −0.997185 0.0749784i \(-0.976111\pi\)
0.997185 0.0749784i \(-0.0238888\pi\)
\(662\) 14.3102i 0.556183i
\(663\) −5.12474 + 14.7358i −0.199029 + 0.572290i
\(664\) −8.34895 4.82027i −0.324002 0.187063i
\(665\) 0 0
\(666\) 15.6265 + 2.29438i 0.605513 + 0.0889054i
\(667\) 3.52389 + 6.10355i 0.136445 + 0.236330i
\(668\) −0.261517 0.452961i −0.0101184 0.0175256i
\(669\) −1.43543 1.66158i −0.0554971 0.0642405i
\(670\) 7.62214 + 4.40064i 0.294469 + 0.170012i
\(671\) −5.80538 10.0552i −0.224114 0.388177i
\(672\) 0 0
\(673\) 19.0025 32.9132i 0.732491 1.26871i −0.223324 0.974744i \(-0.571691\pi\)
0.955815 0.293968i \(-0.0949760\pi\)
\(674\) −17.4430 + 10.0707i −0.671880 + 0.387910i
\(675\) −11.1876 + 21.4644i −0.430611 + 0.826166i
\(676\) −10.0026 + 17.3250i −0.384714 + 0.666345i
\(677\) 15.4397 0.593397 0.296698 0.954971i \(-0.404114\pi\)
0.296698 + 0.954971i \(0.404114\pi\)
\(678\) 4.11506 + 21.5238i 0.158038 + 0.826617i
\(679\) 0 0
\(680\) 4.21982 2.43632i 0.161823 0.0934285i
\(681\) 5.56459 + 29.1056i 0.213236 + 1.11533i
\(682\) 10.6774 6.16458i 0.408858 0.236054i
\(683\) 14.3519 + 8.28608i 0.549161 + 0.317058i 0.748784 0.662815i \(-0.230638\pi\)
−0.199623 + 0.979873i \(0.563972\pi\)
\(684\) −19.9751 2.93287i −0.763767 0.112141i
\(685\) 3.54522i 0.135456i
\(686\) 0 0
\(687\) 12.4776 + 14.4434i 0.476051 + 0.551051i
\(688\) −1.38634 + 2.40121i −0.0528537 + 0.0915453i
\(689\) 69.5188 2.64845
\(690\) −1.77842 9.30198i −0.0677031 0.354121i
\(691\) 9.17558i 0.349056i 0.984652 + 0.174528i \(0.0558399\pi\)
−0.984652 + 0.174528i \(0.944160\pi\)
\(692\) 3.73085 0.141826
\(693\) 0 0
\(694\) 13.4117 0.509100
\(695\) 34.7911i 1.31970i
\(696\) −5.25037 + 4.53577i −0.199015 + 0.171928i
\(697\) −17.8908 −0.677663
\(698\) −9.46958 + 16.4018i −0.358429 + 0.620817i
\(699\) 39.0594 7.46763i 1.47736 0.282452i
\(700\) 0 0
\(701\) 16.6900i 0.630371i −0.949030 0.315185i \(-0.897933\pi\)
0.949030 0.315185i \(-0.102067\pi\)
\(702\) −13.7976 + 26.4720i −0.520758 + 0.999120i
\(703\) 30.6832 + 17.7150i 1.15724 + 0.668133i
\(704\) −1.07339 + 0.619720i −0.0404548 + 0.0233566i
\(705\) 1.07428 0.928065i 0.0404597 0.0349529i
\(706\) 21.8147 12.5947i 0.821006 0.474008i
\(707\) 0 0
\(708\) −17.6076 6.12349i −0.661733 0.230135i
\(709\) 41.8842 1.57299 0.786497 0.617594i \(-0.211893\pi\)
0.786497 + 0.617594i \(0.211893\pi\)
\(710\) −0.830596 + 1.43863i −0.0311717 + 0.0539910i
\(711\) −38.4178 30.3981i −1.44078 1.14002i
\(712\) −5.30732 + 3.06418i −0.198900 + 0.114835i
\(713\) 8.75063 15.1565i 0.327714 0.567617i
\(714\) 0 0
\(715\) −11.0646 19.1645i −0.413793 0.716710i
\(716\) 6.53507 + 3.77303i 0.244227 + 0.141005i
\(717\) 18.9293 3.61903i 0.706929 0.135155i
\(718\) −3.65554 6.33158i −0.136424 0.236292i
\(719\) −22.4982 38.9680i −0.839042 1.45326i −0.890697 0.454598i \(-0.849783\pi\)
0.0516552 0.998665i \(-0.483550\pi\)
\(720\) 8.66578 3.43928i 0.322955 0.128174i
\(721\) 0 0
\(722\) −22.7674 13.1448i −0.847316 0.489198i
\(723\) −0.756058 + 0.144548i −0.0281181 + 0.00537580i
\(724\) 16.6098i 0.617299i
\(725\) 18.6601i 0.693020i
\(726\) −10.7158 12.4041i −0.397701 0.460358i
\(727\) 14.5491 + 8.39992i 0.539596 + 0.311536i 0.744915 0.667159i \(-0.232490\pi\)
−0.205319 + 0.978695i \(0.565823\pi\)
\(728\) 0 0
\(729\) −11.4357 + 24.4586i −0.423544 + 0.905875i
\(730\) 14.4515 + 25.0307i 0.534874 + 0.926429i
\(731\) 2.17362 + 3.76482i 0.0803943 + 0.139247i
\(732\) 5.32969 15.3251i 0.196991 0.566432i
\(733\) 36.7850 + 21.2378i 1.35868 + 0.784436i 0.989446 0.144899i \(-0.0462857\pi\)
0.369237 + 0.929335i \(0.379619\pi\)
\(734\) −13.0886 22.6702i −0.483110 0.836771i
\(735\) 0 0
\(736\) −0.879693 + 1.52367i −0.0324259 + 0.0561633i
\(737\) −3.03986 + 1.75506i −0.111975 + 0.0646485i
\(738\) −33.8693 4.97291i −1.24675 0.183055i
\(739\) −6.22722 + 10.7859i −0.229072 + 0.396764i −0.957533 0.288323i \(-0.906902\pi\)
0.728461 + 0.685087i \(0.240236\pi\)
\(740\) −16.3614 −0.601457
\(741\) −50.6745 + 43.7774i −1.86157 + 1.60820i
\(742\) 0 0
\(743\) 23.5057 13.5710i 0.862339 0.497872i −0.00245578 0.999997i \(-0.500782\pi\)
0.864795 + 0.502125i \(0.167448\pi\)
\(744\) 16.2733 + 5.65946i 0.596609 + 0.207486i
\(745\) 17.8309 10.2947i 0.653274 0.377168i
\(746\) 18.2578 + 10.5412i 0.668467 + 0.385940i
\(747\) −26.8819 + 10.6689i −0.983556 + 0.390354i
\(748\) 1.94330i 0.0710541i
\(749\) 0 0
\(750\) −0.604240 + 1.73744i −0.0220637 + 0.0634425i
\(751\) 7.09292 12.2853i 0.258824 0.448297i −0.707103 0.707111i \(-0.749998\pi\)
0.965927 + 0.258814i \(0.0833316\pi\)
\(752\) −0.263735 −0.00961744
\(753\) 31.0123 + 10.7853i 1.13015 + 0.393039i
\(754\) 23.0134i 0.838100i
\(755\) 0.586004 0.0213269
\(756\) 0 0
\(757\) 9.83604 0.357497 0.178748 0.983895i \(-0.442795\pi\)
0.178748 + 0.983895i \(0.442795\pi\)
\(758\) 5.68371i 0.206442i
\(759\) 3.56742 + 1.24066i 0.129489 + 0.0450332i
\(760\) 20.9146 0.758651
\(761\) −24.4276 + 42.3098i −0.885499 + 1.53373i −0.0403574 + 0.999185i \(0.512850\pi\)
−0.845141 + 0.534543i \(0.820484\pi\)
\(762\) −6.13922 + 17.6528i −0.222401 + 0.639494i
\(763\) 0 0
\(764\) 5.64208i 0.204123i
\(765\) 2.12353 14.4628i 0.0767763 0.522905i
\(766\) −0.105332 0.0608136i −0.00380581 0.00219728i
\(767\) −53.5492 + 30.9167i −1.93355 + 1.11634i
\(768\) −1.63594 0.568941i −0.0590320 0.0205299i
\(769\) 12.4959 7.21451i 0.450614 0.260162i −0.257476 0.966285i \(-0.582891\pi\)
0.708089 + 0.706123i \(0.249557\pi\)
\(770\) 0 0
\(771\) −22.7044 + 19.6142i −0.817678 + 0.706388i
\(772\) −9.42027 −0.339043
\(773\) −14.1371 + 24.4861i −0.508475 + 0.880705i 0.491477 + 0.870891i \(0.336457\pi\)
−0.999952 + 0.00981408i \(0.996876\pi\)
\(774\) 3.06844 + 7.73139i 0.110293 + 0.277899i
\(775\) 40.1294 23.1687i 1.44149 0.832245i
\(776\) −0.750184 + 1.29936i −0.0269300 + 0.0466442i
\(777\) 0 0
\(778\) 13.7545 + 23.8235i 0.493123 + 0.854113i
\(779\) −66.5037 38.3959i −2.38274 1.37568i
\(780\) 10.1580 29.2084i 0.363714 1.04583i
\(781\) −0.331258 0.573755i −0.0118533 0.0205306i
\(782\) 1.37926 + 2.38894i 0.0493222 + 0.0854285i
\(783\) 0.897302 + 20.7955i 0.0320670 + 0.743170i
\(784\) 0 0
\(785\) 38.5982 + 22.2847i 1.37763 + 0.795375i
\(786\) −4.24245 4.91084i −0.151323 0.175164i
\(787\) 24.7123i 0.880898i 0.897778 + 0.440449i \(0.145181\pi\)
−0.897778 + 0.440449i \(0.854819\pi\)
\(788\) 19.6757i 0.700918i
\(789\) −4.78774 + 0.915351i −0.170448 + 0.0325874i
\(790\) 43.9503 + 25.3747i 1.56368 + 0.902792i
\(791\) 0 0
\(792\) −0.540156 + 3.67888i −0.0191936 + 0.130723i
\(793\) −26.9089 46.6076i −0.955563 1.65508i
\(794\) −6.22766 10.7866i −0.221011 0.382803i
\(795\) −63.9773 + 12.2316i −2.26904 + 0.433810i
\(796\) −12.6517 7.30448i −0.448429 0.258901i
\(797\) 14.3076 + 24.7815i 0.506802 + 0.877807i 0.999969 + 0.00787254i \(0.00250593\pi\)
−0.493167 + 0.869935i \(0.664161\pi\)
\(798\) 0 0
\(799\) −0.206753 + 0.358107i −0.00731441 + 0.0126689i
\(800\) −4.03417 + 2.32913i −0.142630 + 0.0823472i
\(801\) −2.67078 + 18.1901i −0.0943674 + 0.642714i
\(802\) 13.8734 24.0294i 0.489885 0.848506i
\(803\) −11.5271 −0.406781
\(804\) −4.63303 1.61125i −0.163394 0.0568245i
\(805\) 0 0
\(806\) 49.4914 28.5739i 1.74326 1.00647i
\(807\) −33.1748 + 28.6596i −1.16781 + 1.00886i
\(808\) 5.93491 3.42652i 0.208790 0.120545i
\(809\) 33.7618 + 19.4924i 1.18700 + 0.685317i 0.957624 0.288020i \(-0.0929971\pi\)
0.229379 + 0.973337i \(0.426330\pi\)
\(810\) 8.04013 26.7895i 0.282502 0.941286i
\(811\) 1.94541i 0.0683126i 0.999417 + 0.0341563i \(0.0108744\pi\)
−0.999417 + 0.0341563i \(0.989126\pi\)
\(812\) 0 0
\(813\) 47.6651 9.11292i 1.67169 0.319604i
\(814\) 3.26262 5.65103i 0.114355 0.198068i
\(815\) 30.5853 1.07136
\(816\) −2.05501 + 1.77531i −0.0719397 + 0.0621483i
\(817\) 18.6594i 0.652811i
\(818\) −11.2300 −0.392647
\(819\) 0 0
\(820\) 35.4622 1.23839
\(821\) 18.7810i 0.655461i 0.944771 + 0.327730i \(0.106284\pi\)
−0.944771 + 0.327730i \(0.893716\pi\)
\(822\) −0.371037 1.94070i −0.0129414 0.0676898i
\(823\) 16.0214 0.558471 0.279235 0.960223i \(-0.409919\pi\)
0.279235 + 0.960223i \(0.409919\pi\)
\(824\) −2.73874 + 4.74363i −0.0954084 + 0.165252i
\(825\) 6.53747 + 7.56744i 0.227606 + 0.263464i
\(826\) 0 0
\(827\) 6.59187i 0.229222i 0.993410 + 0.114611i \(0.0365621\pi\)
−0.993410 + 0.114611i \(0.963438\pi\)
\(828\) 1.94706 + 4.90591i 0.0676649 + 0.170492i
\(829\) 4.17189 + 2.40864i 0.144896 + 0.0836556i 0.570695 0.821162i \(-0.306674\pi\)
−0.425800 + 0.904818i \(0.640007\pi\)
\(830\) 25.9467 14.9803i 0.900622 0.519974i
\(831\) 1.20991 + 6.32842i 0.0419713 + 0.219530i
\(832\) −4.97533 + 2.87251i −0.172488 + 0.0995862i
\(833\) 0 0
\(834\) 3.64118 + 19.0451i 0.126084 + 0.659479i
\(835\) 1.62547 0.0562518
\(836\) −4.17056 + 7.22363i −0.144242 + 0.249834i
\(837\) 43.6074 27.7497i 1.50729 0.959169i
\(838\) 2.91134 1.68086i 0.100570 0.0580644i
\(839\) −22.1980 + 38.4480i −0.766360 + 1.32737i 0.173165 + 0.984893i \(0.444601\pi\)
−0.939525 + 0.342481i \(0.888733\pi\)
\(840\) 0 0
\(841\) −6.47673 11.2180i −0.223335 0.386828i
\(842\) 5.35125 + 3.08955i 0.184416 + 0.106473i
\(843\) −8.37620 9.69586i −0.288492 0.333943i
\(844\) −7.90946 13.6996i −0.272255 0.471559i
\(845\) −31.0857 53.8421i −1.06938 1.85222i
\(846\) −0.490946 + 0.620467i −0.0168791 + 0.0213321i
\(847\) 0 0
\(848\) 10.4795 + 6.05036i 0.359869 + 0.207770i
\(849\) 7.69730 22.1329i 0.264171 0.759601i
\(850\) 7.30362i 0.250512i
\(851\) 9.26259i 0.317517i
\(852\) 0.304115 0.874457i 0.0104188 0.0299584i
\(853\) −9.69461 5.59718i −0.331937 0.191644i 0.324764 0.945795i \(-0.394715\pi\)
−0.656701 + 0.754151i \(0.728049\pi\)
\(854\) 0 0
\(855\) 38.9326 49.2039i 1.33147 1.68274i
\(856\) 8.41476 + 14.5748i 0.287610 + 0.498156i
\(857\) −0.915956 1.58648i −0.0312885 0.0541932i 0.849957 0.526852i \(-0.176628\pi\)
−0.881246 + 0.472659i \(0.843294\pi\)
\(858\) 8.06263 + 9.33288i 0.275254 + 0.318619i
\(859\) 34.4844 + 19.9096i 1.17659 + 0.679306i 0.955224 0.295884i \(-0.0956141\pi\)
0.221369 + 0.975190i \(0.428947\pi\)
\(860\) −4.30843 7.46242i −0.146916 0.254466i
\(861\) 0 0
\(862\) 6.65482 11.5265i 0.226664 0.392594i
\(863\) −30.3578 + 17.5271i −1.03339 + 0.596629i −0.917954 0.396686i \(-0.870160\pi\)
−0.115437 + 0.993315i \(0.536827\pi\)
\(864\) −4.38382 + 2.78965i −0.149140 + 0.0949058i
\(865\) −5.79732 + 10.0412i −0.197115 + 0.341413i
\(866\) 25.7161 0.873869
\(867\) −4.72976 24.7389i −0.160631 0.840179i
\(868\) 0 0
\(869\) −17.5282 + 10.1199i −0.594604 + 0.343295i
\(870\) −4.04914 21.1790i −0.137279 0.718035i
\(871\) −14.0902 + 8.13500i −0.477429 + 0.275644i
\(872\) −1.19585 0.690425i −0.0404966 0.0233807i
\(873\) 1.66041 + 4.18366i 0.0561964 + 0.141595i
\(874\) 11.8402i 0.400502i
\(875\) 0 0
\(876\) −10.5306 12.1897i −0.355796 0.411851i
\(877\) 15.6443 27.0967i 0.528270 0.914990i −0.471187 0.882033i \(-0.656174\pi\)
0.999457 0.0329569i \(-0.0104924\pi\)
\(878\) −37.0419 −1.25010
\(879\) −1.63129 8.53243i −0.0550219 0.287792i
\(880\) 3.85190i 0.129848i
\(881\) −17.8567 −0.601609 −0.300805 0.953686i \(-0.597255\pi\)
−0.300805 + 0.953686i \(0.597255\pi\)
\(882\) 0 0
\(883\) 52.2623 1.75877 0.879383 0.476115i \(-0.157955\pi\)
0.879383 + 0.476115i \(0.157955\pi\)
\(884\) 9.00752i 0.302956i
\(885\) 43.8410 37.8740i 1.47370 1.27312i
\(886\) 22.9752 0.771867
\(887\) 25.6962 44.5072i 0.862796 1.49441i −0.00642400 0.999979i \(-0.502045\pi\)
0.869220 0.494426i \(-0.164622\pi\)
\(888\) 8.95646 1.71235i 0.300559 0.0574629i
\(889\) 0 0
\(890\) 19.0456i 0.638409i
\(891\) 7.64947 + 8.11904i 0.256267 + 0.271998i
\(892\) −1.09788 0.633859i −0.0367596 0.0212232i
\(893\) −1.53709 + 0.887437i −0.0514366 + 0.0296970i
\(894\) −8.68347 + 7.50160i −0.290419 + 0.250891i
\(895\) −20.3095 + 11.7257i −0.678873 + 0.391947i
\(896\) 0 0
\(897\) 16.5356 + 5.75068i 0.552107 + 0.192010i
\(898\) 0.217897 0.00727131
\(899\) 19.9237 34.5088i 0.664491 1.15093i
\(900\) −2.03010 + 13.8265i −0.0676701 + 0.460885i
\(901\) 16.4307 9.48627i 0.547386 0.316034i
\(902\) −7.07150 + 12.2482i −0.235455 + 0.407820i
\(903\) 0 0
\(904\) 6.32593 + 10.9568i 0.210397 + 0.364419i
\(905\) 44.7038 + 25.8098i 1.48601 + 0.857946i
\(906\) −0.320786 + 0.0613301i −0.0106574 + 0.00203756i
\(907\) 15.4685 + 26.7922i 0.513624 + 0.889622i 0.999875 + 0.0158032i \(0.00503052\pi\)
−0.486252 + 0.873819i \(0.661636\pi\)
\(908\) 8.55423 + 14.8164i 0.283882 + 0.491698i
\(909\) 2.98661 20.3411i 0.0990594 0.674670i
\(910\) 0 0
\(911\) −2.92291 1.68755i −0.0968405 0.0559109i 0.450798 0.892626i \(-0.351140\pi\)
−0.547638 + 0.836715i \(0.684473\pi\)
\(912\) −11.4489 + 2.18888i −0.379111 + 0.0724810i
\(913\) 11.9489i 0.395450i
\(914\) 0.930228i 0.0307692i
\(915\) 32.9644 + 38.1579i 1.08977 + 1.26146i
\(916\) 9.54337 + 5.50987i 0.315322 + 0.182051i
\(917\) 0 0
\(918\) 0.351206 + 8.13940i 0.0115915 + 0.268640i
\(919\) 20.4737 + 35.4615i 0.675366 + 1.16977i 0.976362 + 0.216143i \(0.0693477\pi\)
−0.300996 + 0.953625i \(0.597319\pi\)
\(920\) −2.73389 4.73523i −0.0901336 0.156116i
\(921\) −6.10414 + 17.5520i −0.201138 + 0.578357i
\(922\) −27.1820 15.6935i −0.895191 0.516839i
\(923\) −1.53543 2.65945i −0.0505394 0.0875369i
\(924\) 0 0
\(925\) 12.2621 21.2386i 0.403176 0.698321i
\(926\) 17.8816 10.3239i 0.587626 0.339266i
\(927\) 6.06175 + 15.2735i 0.199094 + 0.501647i
\(928\) −2.00291 + 3.46914i −0.0657486 + 0.113880i
\(929\) −3.10096 −0.101739 −0.0508696 0.998705i \(-0.516199\pi\)
−0.0508696 + 0.998705i \(0.516199\pi\)
\(930\) −40.5188 + 35.0040i −1.32867 + 1.14783i
\(931\) 0 0
\(932\) 19.8834 11.4797i 0.651303 0.376030i
\(933\) −1.76631 0.614279i −0.0578264 0.0201106i
\(934\) 9.13539 5.27432i 0.298919 0.172581i
\(935\) −5.23022 3.01967i −0.171046 0.0987537i
\(936\) −2.50372 + 17.0522i −0.0818365 + 0.557369i
\(937\) 50.5048i 1.64992i −0.565190 0.824960i \(-0.691197\pi\)
0.565190 0.824960i \(-0.308803\pi\)
\(938\) 0 0
\(939\) 13.5704 39.0207i 0.442855 1.27339i
\(940\) 0.409815 0.709821i 0.0133667 0.0231518i
\(941\) −2.65547 −0.0865659 −0.0432830 0.999063i \(-0.513782\pi\)
−0.0432830 + 0.999063i \(0.513782\pi\)
\(942\) −23.4615 8.15932i −0.764416 0.265845i
\(943\) 20.0760i 0.653765i
\(944\) −10.7630 −0.350305
\(945\) 0 0
\(946\) 3.43657 0.111732
\(947\) 46.6605i 1.51626i −0.652103 0.758131i \(-0.726113\pi\)
0.652103 0.758131i \(-0.273887\pi\)
\(948\) −26.7147 9.29071i −0.867652 0.301748i
\(949\) −53.4299 −1.73441
\(950\) −15.6745 + 27.1490i −0.508547 + 0.880830i
\(951\) 12.5660 36.1326i 0.407481 1.17168i
\(952\) 0 0
\(953\) 38.0100i 1.23127i 0.788033 + 0.615633i \(0.211100\pi\)
−0.788033 + 0.615633i \(0.788900\pi\)
\(954\) 33.7419 13.3915i 1.09243 0.433565i
\(955\) −15.1852 8.76715i −0.491380 0.283698i
\(956\) 9.63609 5.56340i 0.311653 0.179933i
\(957\) 8.12240 + 2.82477i 0.262560 + 0.0913119i
\(958\) −15.9881 + 9.23071i −0.516551 + 0.298231i
\(959\) 0 0
\(960\) 4.07332 3.51892i 0.131466 0.113573i
\(961\) −67.9501 −2.19194
\(962\) 15.1228 26.1934i 0.487578 0.844511i
\(963\) 49.9530 + 7.33442i 1.60971 + 0.236348i
\(964\) −0.384876 + 0.222208i −0.0123960 + 0.00715684i
\(965\) 14.6380 25.3538i 0.471215 0.816168i
\(966\) 0 0
\(967\) −12.3800 21.4428i −0.398115 0.689555i 0.595379 0.803445i \(-0.297002\pi\)
−0.993493 + 0.113891i \(0.963669\pi\)
\(968\) −8.19588 4.73189i −0.263426 0.152089i
\(969\) −6.00317 + 17.2616i −0.192850 + 0.554523i
\(970\) −2.33140 4.03811i −0.0748568 0.129656i
\(971\) 28.8119 + 49.9037i 0.924619 + 1.60149i 0.792173 + 0.610296i \(0.208950\pi\)
0.132445 + 0.991190i \(0.457717\pi\)
\(972\) −1.59754 + 15.5064i −0.0512412 + 0.497367i
\(973\) 0 0
\(974\) −33.1747 19.1534i −1.06299 0.613715i
\(975\) 30.3023 + 35.0763i 0.970449 + 1.12334i
\(976\) 9.36774i 0.299854i
\(977\) 32.6571i 1.04479i 0.852703 + 0.522396i \(0.174962\pi\)
−0.852703 + 0.522396i \(0.825038\pi\)
\(978\) −16.7428 + 3.20100i −0.535376 + 0.102357i
\(979\) 6.57810 + 3.79787i 0.210237 + 0.121380i
\(980\) 0 0
\(981\) −3.85039 + 1.52814i −0.122933 + 0.0487899i
\(982\) −5.38551 9.32798i −0.171859 0.297668i
\(983\) −5.43038 9.40569i −0.173202 0.299995i 0.766335 0.642441i \(-0.222078\pi\)
−0.939538 + 0.342446i \(0.888745\pi\)
\(984\) −19.4125 + 3.71141i −0.618847 + 0.118315i
\(985\) −52.9554 30.5738i −1.68730 0.974163i
\(986\) 3.14033 + 5.43921i 0.100008 + 0.173220i
\(987\) 0 0
\(988\) −19.3313 + 33.4827i −0.615009 + 1.06523i
\(989\) 4.22465 2.43911i 0.134336 0.0775590i
\(990\) −9.06203 7.17034i −0.288010 0.227888i
\(991\) −23.6511 + 40.9649i −0.751302 + 1.30129i 0.195890 + 0.980626i \(0.437240\pi\)
−0.947192 + 0.320667i \(0.896093\pi\)
\(992\) 9.94737 0.315829
\(993\) −23.4107 8.14167i −0.742916 0.258368i
\(994\) 0 0
\(995\) 39.3187 22.7007i 1.24649 0.719660i
\(996\) −12.6357 + 10.9160i −0.400379 + 0.345885i
\(997\) −50.5561 + 29.1886i −1.60113 + 0.924411i −0.609865 + 0.792505i \(0.708776\pi\)
−0.991262 + 0.131906i \(0.957890\pi\)
\(998\) −10.5880 6.11298i −0.335157 0.193503i
\(999\) 12.6440 24.2586i 0.400039 0.767509i
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 882.2.l.c.227.2 48
3.2 odd 2 2646.2.l.c.521.19 48
7.2 even 3 882.2.t.c.803.8 48
7.3 odd 6 882.2.m.c.587.17 yes 48
7.4 even 3 882.2.m.c.587.20 yes 48
7.5 odd 6 882.2.t.c.803.5 48
7.6 odd 2 inner 882.2.l.c.227.11 48
9.4 even 3 2646.2.t.c.2285.23 48
9.5 odd 6 882.2.t.c.815.5 48
21.2 odd 6 2646.2.t.c.1979.24 48
21.5 even 6 2646.2.t.c.1979.23 48
21.11 odd 6 2646.2.m.c.1763.5 48
21.17 even 6 2646.2.m.c.1763.6 48
21.20 even 2 2646.2.l.c.521.20 48
63.4 even 3 2646.2.m.c.881.6 48
63.5 even 6 inner 882.2.l.c.509.14 48
63.13 odd 6 2646.2.t.c.2285.24 48
63.23 odd 6 inner 882.2.l.c.509.23 48
63.31 odd 6 2646.2.m.c.881.5 48
63.32 odd 6 882.2.m.c.293.17 48
63.40 odd 6 2646.2.l.c.1097.19 48
63.41 even 6 882.2.t.c.815.8 48
63.58 even 3 2646.2.l.c.1097.20 48
63.59 even 6 882.2.m.c.293.20 yes 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
882.2.l.c.227.2 48 1.1 even 1 trivial
882.2.l.c.227.11 48 7.6 odd 2 inner
882.2.l.c.509.14 48 63.5 even 6 inner
882.2.l.c.509.23 48 63.23 odd 6 inner
882.2.m.c.293.17 48 63.32 odd 6
882.2.m.c.293.20 yes 48 63.59 even 6
882.2.m.c.587.17 yes 48 7.3 odd 6
882.2.m.c.587.20 yes 48 7.4 even 3
882.2.t.c.803.5 48 7.5 odd 6
882.2.t.c.803.8 48 7.2 even 3
882.2.t.c.815.5 48 9.5 odd 6
882.2.t.c.815.8 48 63.41 even 6
2646.2.l.c.521.19 48 3.2 odd 2
2646.2.l.c.521.20 48 21.20 even 2
2646.2.l.c.1097.19 48 63.40 odd 6
2646.2.l.c.1097.20 48 63.58 even 3
2646.2.m.c.881.5 48 63.31 odd 6
2646.2.m.c.881.6 48 63.4 even 3
2646.2.m.c.1763.5 48 21.11 odd 6
2646.2.m.c.1763.6 48 21.17 even 6
2646.2.t.c.1979.23 48 21.5 even 6
2646.2.t.c.1979.24 48 21.2 odd 6
2646.2.t.c.2285.23 48 9.4 even 3
2646.2.t.c.2285.24 48 63.13 odd 6