Properties

Label 552.2.f.c.277.7
Level $552$
Weight $2$
Character 552.277
Analytic conductor $4.408$
Analytic rank $0$
Dimension $18$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [552,2,Mod(277,552)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(552, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("552.277");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 552.f (of order \(2\), degree \(1\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(4.40774219157\)
Analytic rank: \(0\)
Dimension: \(18\)
Coefficient field: \(\mathbb{Q}[x]/(x^{18} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{18} - 4 x^{16} - 2 x^{15} + 5 x^{14} + 2 x^{13} + 6 x^{12} + 24 x^{11} - 12 x^{10} - 88 x^{9} - 24 x^{8} + 96 x^{7} + 48 x^{6} + 32 x^{5} + 160 x^{4} - 128 x^{3} - 512 x^{2} + 512 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{7} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 277.7
Root \(1.37219 - 0.342174i\) of defining polynomial
Character \(\chi\) \(=\) 552.277
Dual form 552.2.f.c.277.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.342174 - 1.37219i) q^{2} -1.00000i q^{3} +(-1.76583 + 0.939057i) q^{4} +0.957976i q^{5} +(-1.37219 + 0.342174i) q^{6} +2.14538 q^{7} +(1.89279 + 2.10175i) q^{8} -1.00000 q^{9} +O(q^{10})\) \(q+(-0.342174 - 1.37219i) q^{2} -1.00000i q^{3} +(-1.76583 + 0.939057i) q^{4} +0.957976i q^{5} +(-1.37219 + 0.342174i) q^{6} +2.14538 q^{7} +(1.89279 + 2.10175i) q^{8} -1.00000 q^{9} +(1.31453 - 0.327794i) q^{10} -5.87650i q^{11} +(0.939057 + 1.76583i) q^{12} +1.37506i q^{13} +(-0.734092 - 2.94388i) q^{14} +0.957976 q^{15} +(2.23634 - 3.31644i) q^{16} -0.163763 q^{17} +(0.342174 + 1.37219i) q^{18} -5.82746i q^{19} +(-0.899594 - 1.69163i) q^{20} -2.14538i q^{21} +(-8.06370 + 2.01078i) q^{22} -1.00000 q^{23} +(2.10175 - 1.89279i) q^{24} +4.08228 q^{25} +(1.88685 - 0.470508i) q^{26} +1.00000i q^{27} +(-3.78839 + 2.01463i) q^{28} -9.19473i q^{29} +(-0.327794 - 1.31453i) q^{30} -1.00647 q^{31} +(-5.31602 - 1.93390i) q^{32} -5.87650 q^{33} +(0.0560354 + 0.224715i) q^{34} +2.05522i q^{35} +(1.76583 - 0.939057i) q^{36} -1.82285i q^{37} +(-7.99641 + 1.99400i) q^{38} +1.37506 q^{39} +(-2.01342 + 1.81325i) q^{40} -8.24354 q^{41} +(-2.94388 + 0.734092i) q^{42} +8.14477i q^{43} +(5.51837 + 10.3769i) q^{44} -0.957976i q^{45} +(0.342174 + 1.37219i) q^{46} +8.24511 q^{47} +(-3.31644 - 2.23634i) q^{48} -2.39735 q^{49} +(-1.39685 - 5.60168i) q^{50} +0.163763i q^{51} +(-1.29126 - 2.42812i) q^{52} -2.08900i q^{53} +(1.37219 - 0.342174i) q^{54} +5.62955 q^{55} +(4.06075 + 4.50905i) q^{56} -5.82746 q^{57} +(-12.6170 + 3.14619i) q^{58} -9.20740i q^{59} +(-1.69163 + 0.899594i) q^{60} +10.7403i q^{61} +(0.344387 + 1.38107i) q^{62} -2.14538 q^{63} +(-0.834685 + 7.95634i) q^{64} -1.31727 q^{65} +(2.01078 + 8.06370i) q^{66} +6.22959i q^{67} +(0.289178 - 0.153783i) q^{68} +1.00000i q^{69} +(2.82016 - 0.703242i) q^{70} +13.1930 q^{71} +(-1.89279 - 2.10175i) q^{72} +6.18391 q^{73} +(-2.50130 + 0.623731i) q^{74} -4.08228i q^{75} +(5.47232 + 10.2903i) q^{76} -12.6073i q^{77} +(-0.470508 - 1.88685i) q^{78} +2.86636 q^{79} +(3.17707 + 2.14236i) q^{80} +1.00000 q^{81} +(2.82072 + 11.3117i) q^{82} -3.36850i q^{83} +(2.01463 + 3.78839i) q^{84} -0.156881i q^{85} +(11.1762 - 2.78693i) q^{86} -9.19473 q^{87} +(12.3509 - 11.1230i) q^{88} -8.21077 q^{89} +(-1.31453 + 0.327794i) q^{90} +2.95002i q^{91} +(1.76583 - 0.939057i) q^{92} +1.00647i q^{93} +(-2.82126 - 11.3139i) q^{94} +5.58256 q^{95} +(-1.93390 + 5.31602i) q^{96} -5.18778 q^{97} +(0.820309 + 3.28963i) q^{98} +5.87650i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 18 q - 8 q^{4} + 8 q^{7} - 6 q^{8} - 18 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 18 q - 8 q^{4} + 8 q^{7} - 6 q^{8} - 18 q^{9} + 12 q^{10} - 4 q^{12} - 14 q^{14} + 8 q^{15} + 12 q^{16} - 8 q^{17} - 16 q^{20} - 30 q^{22} - 18 q^{23} + 6 q^{24} - 22 q^{25} + 8 q^{26} - 2 q^{28} + 4 q^{30} - 44 q^{31} + 10 q^{32} - 24 q^{33} + 18 q^{34} + 8 q^{36} - 20 q^{38} - 8 q^{39} + 40 q^{40} + 28 q^{41} + 6 q^{42} - 26 q^{44} + 42 q^{49} + 60 q^{50} - 36 q^{52} + 40 q^{55} - 2 q^{56} + 12 q^{57} + 52 q^{58} + 16 q^{60} + 24 q^{62} - 8 q^{63} + 16 q^{64} - 104 q^{65} + 2 q^{66} + 54 q^{68} - 48 q^{70} - 24 q^{71} + 6 q^{72} + 12 q^{73} - 22 q^{74} - 4 q^{78} + 8 q^{79} - 32 q^{80} + 18 q^{81} - 20 q^{82} + 34 q^{84} + 12 q^{87} + 10 q^{88} + 24 q^{89} - 12 q^{90} + 8 q^{92} - 56 q^{94} - 16 q^{95} - 30 q^{96} + 12 q^{97} - 48 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/552\mathbb{Z}\right)^\times\).

\(n\) \(97\) \(185\) \(277\) \(415\)
\(\chi(n)\) \(1\) \(1\) \(-1\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.342174 1.37219i −0.241953 0.970288i
\(3\) 1.00000i 0.577350i
\(4\) −1.76583 + 0.939057i −0.882917 + 0.469529i
\(5\) 0.957976i 0.428420i 0.976788 + 0.214210i \(0.0687177\pi\)
−0.976788 + 0.214210i \(0.931282\pi\)
\(6\) −1.37219 + 0.342174i −0.560196 + 0.139692i
\(7\) 2.14538 0.810877 0.405439 0.914122i \(-0.367119\pi\)
0.405439 + 0.914122i \(0.367119\pi\)
\(8\) 1.89279 + 2.10175i 0.669203 + 0.743080i
\(9\) −1.00000 −0.333333
\(10\) 1.31453 0.327794i 0.415691 0.103658i
\(11\) 5.87650i 1.77183i −0.463845 0.885916i \(-0.653531\pi\)
0.463845 0.885916i \(-0.346469\pi\)
\(12\) 0.939057 + 1.76583i 0.271082 + 0.509753i
\(13\) 1.37506i 0.381372i 0.981651 + 0.190686i \(0.0610713\pi\)
−0.981651 + 0.190686i \(0.938929\pi\)
\(14\) −0.734092 2.94388i −0.196194 0.786784i
\(15\) 0.957976 0.247348
\(16\) 2.23634 3.31644i 0.559086 0.829110i
\(17\) −0.163763 −0.0397184 −0.0198592 0.999803i \(-0.506322\pi\)
−0.0198592 + 0.999803i \(0.506322\pi\)
\(18\) 0.342174 + 1.37219i 0.0806511 + 0.323429i
\(19\) 5.82746i 1.33691i −0.743752 0.668455i \(-0.766956\pi\)
0.743752 0.668455i \(-0.233044\pi\)
\(20\) −0.899594 1.69163i −0.201155 0.378259i
\(21\) 2.14538i 0.468160i
\(22\) −8.06370 + 2.01078i −1.71919 + 0.428701i
\(23\) −1.00000 −0.208514
\(24\) 2.10175 1.89279i 0.429017 0.386364i
\(25\) 4.08228 0.816456
\(26\) 1.88685 0.470508i 0.370041 0.0922743i
\(27\) 1.00000i 0.192450i
\(28\) −3.78839 + 2.01463i −0.715937 + 0.380730i
\(29\) 9.19473i 1.70742i −0.520750 0.853709i \(-0.674348\pi\)
0.520750 0.853709i \(-0.325652\pi\)
\(30\) −0.327794 1.31453i −0.0598467 0.239999i
\(31\) −1.00647 −0.180767 −0.0903835 0.995907i \(-0.528809\pi\)
−0.0903835 + 0.995907i \(0.528809\pi\)
\(32\) −5.31602 1.93390i −0.939748 0.341868i
\(33\) −5.87650 −1.02297
\(34\) 0.0560354 + 0.224715i 0.00960999 + 0.0385383i
\(35\) 2.05522i 0.347396i
\(36\) 1.76583 0.939057i 0.294306 0.156510i
\(37\) 1.82285i 0.299675i −0.988711 0.149837i \(-0.952125\pi\)
0.988711 0.149837i \(-0.0478750\pi\)
\(38\) −7.99641 + 1.99400i −1.29719 + 0.323470i
\(39\) 1.37506 0.220185
\(40\) −2.01342 + 1.81325i −0.318350 + 0.286700i
\(41\) −8.24354 −1.28742 −0.643712 0.765267i \(-0.722607\pi\)
−0.643712 + 0.765267i \(0.722607\pi\)
\(42\) −2.94388 + 0.734092i −0.454250 + 0.113273i
\(43\) 8.14477i 1.24207i 0.783784 + 0.621033i \(0.213287\pi\)
−0.783784 + 0.621033i \(0.786713\pi\)
\(44\) 5.51837 + 10.3769i 0.831926 + 1.56438i
\(45\) 0.957976i 0.142807i
\(46\) 0.342174 + 1.37219i 0.0504507 + 0.202319i
\(47\) 8.24511 1.20267 0.601336 0.798996i \(-0.294635\pi\)
0.601336 + 0.798996i \(0.294635\pi\)
\(48\) −3.31644 2.23634i −0.478687 0.322788i
\(49\) −2.39735 −0.342478
\(50\) −1.39685 5.60168i −0.197544 0.792198i
\(51\) 0.163763i 0.0229314i
\(52\) −1.29126 2.42812i −0.179065 0.336720i
\(53\) 2.08900i 0.286946i −0.989654 0.143473i \(-0.954173\pi\)
0.989654 0.143473i \(-0.0458270\pi\)
\(54\) 1.37219 0.342174i 0.186732 0.0465639i
\(55\) 5.62955 0.759088
\(56\) 4.06075 + 4.50905i 0.542641 + 0.602547i
\(57\) −5.82746 −0.771866
\(58\) −12.6170 + 3.14619i −1.65669 + 0.413115i
\(59\) 9.20740i 1.19870i −0.800486 0.599351i \(-0.795425\pi\)
0.800486 0.599351i \(-0.204575\pi\)
\(60\) −1.69163 + 0.899594i −0.218388 + 0.116137i
\(61\) 10.7403i 1.37516i 0.726109 + 0.687579i \(0.241327\pi\)
−0.726109 + 0.687579i \(0.758673\pi\)
\(62\) 0.344387 + 1.38107i 0.0437371 + 0.175396i
\(63\) −2.14538 −0.270292
\(64\) −0.834685 + 7.95634i −0.104336 + 0.994542i
\(65\) −1.31727 −0.163388
\(66\) 2.01078 + 8.06370i 0.247510 + 0.992573i
\(67\) 6.22959i 0.761066i 0.924767 + 0.380533i \(0.124259\pi\)
−0.924767 + 0.380533i \(0.875741\pi\)
\(68\) 0.289178 0.153783i 0.0350680 0.0186489i
\(69\) 1.00000i 0.120386i
\(70\) 2.82016 0.703242i 0.337074 0.0840536i
\(71\) 13.1930 1.56572 0.782860 0.622198i \(-0.213760\pi\)
0.782860 + 0.622198i \(0.213760\pi\)
\(72\) −1.89279 2.10175i −0.223068 0.247693i
\(73\) 6.18391 0.723771 0.361886 0.932222i \(-0.382133\pi\)
0.361886 + 0.932222i \(0.382133\pi\)
\(74\) −2.50130 + 0.623731i −0.290771 + 0.0725073i
\(75\) 4.08228i 0.471381i
\(76\) 5.47232 + 10.2903i 0.627718 + 1.18038i
\(77\) 12.6073i 1.43674i
\(78\) −0.470508 1.88685i −0.0532746 0.213643i
\(79\) 2.86636 0.322491 0.161245 0.986914i \(-0.448449\pi\)
0.161245 + 0.986914i \(0.448449\pi\)
\(80\) 3.17707 + 2.14236i 0.355207 + 0.239523i
\(81\) 1.00000 0.111111
\(82\) 2.82072 + 11.3117i 0.311497 + 1.24917i
\(83\) 3.36850i 0.369741i −0.982763 0.184871i \(-0.940813\pi\)
0.982763 0.184871i \(-0.0591866\pi\)
\(84\) 2.01463 + 3.78839i 0.219815 + 0.413347i
\(85\) 0.156881i 0.0170161i
\(86\) 11.1762 2.78693i 1.20516 0.300522i
\(87\) −9.19473 −0.985778
\(88\) 12.3509 11.1230i 1.31661 1.18571i
\(89\) −8.21077 −0.870340 −0.435170 0.900348i \(-0.643312\pi\)
−0.435170 + 0.900348i \(0.643312\pi\)
\(90\) −1.31453 + 0.327794i −0.138564 + 0.0345525i
\(91\) 2.95002i 0.309246i
\(92\) 1.76583 0.939057i 0.184101 0.0979035i
\(93\) 1.00647i 0.104366i
\(94\) −2.82126 11.3139i −0.290991 1.16694i
\(95\) 5.58256 0.572759
\(96\) −1.93390 + 5.31602i −0.197378 + 0.542564i
\(97\) −5.18778 −0.526739 −0.263370 0.964695i \(-0.584834\pi\)
−0.263370 + 0.964695i \(0.584834\pi\)
\(98\) 0.820309 + 3.28963i 0.0828637 + 0.332302i
\(99\) 5.87650i 0.590611i
\(100\) −7.20864 + 3.83350i −0.720864 + 0.383350i
\(101\) 5.89378i 0.586453i 0.956043 + 0.293226i \(0.0947290\pi\)
−0.956043 + 0.293226i \(0.905271\pi\)
\(102\) 0.224715 0.0560354i 0.0222501 0.00554833i
\(103\) 8.05266 0.793452 0.396726 0.917937i \(-0.370146\pi\)
0.396726 + 0.917937i \(0.370146\pi\)
\(104\) −2.89002 + 2.60270i −0.283390 + 0.255215i
\(105\) 2.05522 0.200569
\(106\) −2.86651 + 0.714799i −0.278420 + 0.0694274i
\(107\) 17.9336i 1.73370i −0.498567 0.866851i \(-0.666140\pi\)
0.498567 0.866851i \(-0.333860\pi\)
\(108\) −0.939057 1.76583i −0.0903608 0.169918i
\(109\) 15.2577i 1.46142i −0.682685 0.730712i \(-0.739188\pi\)
0.682685 0.730712i \(-0.260812\pi\)
\(110\) −1.92628 7.72483i −0.183664 0.736534i
\(111\) −1.82285 −0.173017
\(112\) 4.79780 7.11502i 0.453350 0.672306i
\(113\) 5.74351 0.540304 0.270152 0.962818i \(-0.412926\pi\)
0.270152 + 0.962818i \(0.412926\pi\)
\(114\) 1.99400 + 7.99641i 0.186755 + 0.748932i
\(115\) 0.957976i 0.0893317i
\(116\) 8.63438 + 16.2364i 0.801682 + 1.50751i
\(117\) 1.37506i 0.127124i
\(118\) −12.6343 + 3.15053i −1.16309 + 0.290030i
\(119\) −0.351334 −0.0322067
\(120\) 1.81325 + 2.01342i 0.165526 + 0.183800i
\(121\) −23.5333 −2.13939
\(122\) 14.7378 3.67506i 1.33430 0.332724i
\(123\) 8.24354i 0.743295i
\(124\) 1.77726 0.945131i 0.159602 0.0848752i
\(125\) 8.70061i 0.778206i
\(126\) 0.734092 + 2.94388i 0.0653981 + 0.262261i
\(127\) 5.66040 0.502279 0.251139 0.967951i \(-0.419195\pi\)
0.251139 + 0.967951i \(0.419195\pi\)
\(128\) 11.2032 1.57710i 0.990237 0.139397i
\(129\) 8.14477 0.717107
\(130\) 0.450736 + 1.80755i 0.0395321 + 0.158533i
\(131\) 12.7656i 1.11533i 0.830065 + 0.557666i \(0.188303\pi\)
−0.830065 + 0.557666i \(0.811697\pi\)
\(132\) 10.3769 5.51837i 0.903196 0.480313i
\(133\) 12.5021i 1.08407i
\(134\) 8.54821 2.13160i 0.738453 0.184142i
\(135\) −0.957976 −0.0824494
\(136\) −0.309969 0.344189i −0.0265796 0.0295139i
\(137\) 10.6909 0.913382 0.456691 0.889625i \(-0.349035\pi\)
0.456691 + 0.889625i \(0.349035\pi\)
\(138\) 1.37219 0.342174i 0.116809 0.0291277i
\(139\) 8.76418i 0.743368i 0.928359 + 0.371684i \(0.121220\pi\)
−0.928359 + 0.371684i \(0.878780\pi\)
\(140\) −1.92997 3.62918i −0.163112 0.306722i
\(141\) 8.24511i 0.694364i
\(142\) −4.51429 18.1034i −0.378831 1.51920i
\(143\) 8.08053 0.675728
\(144\) −2.23634 + 3.31644i −0.186362 + 0.276370i
\(145\) 8.80833 0.731492
\(146\) −2.11597 8.48552i −0.175119 0.702267i
\(147\) 2.39735i 0.197730i
\(148\) 1.71176 + 3.21885i 0.140706 + 0.264588i
\(149\) 20.4589i 1.67606i 0.545624 + 0.838030i \(0.316293\pi\)
−0.545624 + 0.838030i \(0.683707\pi\)
\(150\) −5.60168 + 1.39685i −0.457376 + 0.114052i
\(151\) 14.2531 1.15990 0.579952 0.814651i \(-0.303071\pi\)
0.579952 + 0.814651i \(0.303071\pi\)
\(152\) 12.2478 11.0302i 0.993432 0.894664i
\(153\) 0.163763 0.0132395
\(154\) −17.2997 + 4.31389i −1.39405 + 0.347624i
\(155\) 0.964172i 0.0774441i
\(156\) −2.42812 + 1.29126i −0.194406 + 0.103383i
\(157\) 3.79042i 0.302508i −0.988495 0.151254i \(-0.951669\pi\)
0.988495 0.151254i \(-0.0483312\pi\)
\(158\) −0.980793 3.93321i −0.0780277 0.312909i
\(159\) −2.08900 −0.165668
\(160\) 1.85263 5.09262i 0.146463 0.402607i
\(161\) −2.14538 −0.169080
\(162\) −0.342174 1.37219i −0.0268837 0.107810i
\(163\) 4.87780i 0.382059i 0.981584 + 0.191030i \(0.0611826\pi\)
−0.981584 + 0.191030i \(0.938817\pi\)
\(164\) 14.5567 7.74116i 1.13669 0.604483i
\(165\) 5.62955i 0.438260i
\(166\) −4.62224 + 1.15261i −0.358755 + 0.0894601i
\(167\) −18.4925 −1.43100 −0.715498 0.698615i \(-0.753800\pi\)
−0.715498 + 0.698615i \(0.753800\pi\)
\(168\) 4.50905 4.06075i 0.347880 0.313294i
\(169\) 11.1092 0.854555
\(170\) −0.215271 + 0.0536805i −0.0165105 + 0.00411711i
\(171\) 5.82746i 0.445637i
\(172\) −7.64841 14.3823i −0.583186 1.09664i
\(173\) 14.2971i 1.08699i 0.839414 + 0.543493i \(0.182899\pi\)
−0.839414 + 0.543493i \(0.817101\pi\)
\(174\) 3.14619 + 12.6170i 0.238512 + 0.956489i
\(175\) 8.75804 0.662046
\(176\) −19.4891 13.1419i −1.46904 0.990606i
\(177\) −9.20740 −0.692071
\(178\) 2.80951 + 11.2668i 0.210582 + 0.844481i
\(179\) 24.4035i 1.82400i 0.410189 + 0.912000i \(0.365463\pi\)
−0.410189 + 0.912000i \(0.634537\pi\)
\(180\) 0.899594 + 1.69163i 0.0670518 + 0.126086i
\(181\) 20.6424i 1.53434i 0.641445 + 0.767169i \(0.278335\pi\)
−0.641445 + 0.767169i \(0.721665\pi\)
\(182\) 4.04800 1.00942i 0.300058 0.0748231i
\(183\) 10.7403 0.793948
\(184\) −1.89279 2.10175i −0.139538 0.154943i
\(185\) 1.74625 0.128387
\(186\) 1.38107 0.344387i 0.101265 0.0252517i
\(187\) 0.962354i 0.0703743i
\(188\) −14.5595 + 7.74263i −1.06186 + 0.564689i
\(189\) 2.14538i 0.156053i
\(190\) −1.91021 7.66036i −0.138581 0.555741i
\(191\) −10.0790 −0.729290 −0.364645 0.931147i \(-0.618810\pi\)
−0.364645 + 0.931147i \(0.618810\pi\)
\(192\) 7.95634 + 0.834685i 0.574199 + 0.0602382i
\(193\) 13.8031 0.993566 0.496783 0.867875i \(-0.334514\pi\)
0.496783 + 0.867875i \(0.334514\pi\)
\(194\) 1.77512 + 7.11864i 0.127446 + 0.511089i
\(195\) 1.31727i 0.0943318i
\(196\) 4.23332 2.25125i 0.302380 0.160803i
\(197\) 8.40195i 0.598614i 0.954157 + 0.299307i \(0.0967555\pi\)
−0.954157 + 0.299307i \(0.903244\pi\)
\(198\) 8.06370 2.01078i 0.573062 0.142900i
\(199\) −5.07488 −0.359749 −0.179874 0.983690i \(-0.557569\pi\)
−0.179874 + 0.983690i \(0.557569\pi\)
\(200\) 7.72691 + 8.57993i 0.546375 + 0.606692i
\(201\) 6.22959 0.439401
\(202\) 8.08741 2.01669i 0.569028 0.141894i
\(203\) 19.7262i 1.38451i
\(204\) −0.153783 0.289178i −0.0107670 0.0202465i
\(205\) 7.89711i 0.551558i
\(206\) −2.75541 11.0498i −0.191978 0.769877i
\(207\) 1.00000 0.0695048
\(208\) 4.56030 + 3.07510i 0.316200 + 0.213220i
\(209\) −34.2451 −2.36878
\(210\) −0.703242 2.82016i −0.0485283 0.194610i
\(211\) 26.2297i 1.80572i 0.429930 + 0.902862i \(0.358538\pi\)
−0.429930 + 0.902862i \(0.641462\pi\)
\(212\) 1.96169 + 3.68882i 0.134729 + 0.253349i
\(213\) 13.1930i 0.903969i
\(214\) −24.6083 + 6.13639i −1.68219 + 0.419475i
\(215\) −7.80249 −0.532126
\(216\) −2.10175 + 1.89279i −0.143006 + 0.128788i
\(217\) −2.15925 −0.146580
\(218\) −20.9366 + 5.22079i −1.41800 + 0.353596i
\(219\) 6.18391i 0.417870i
\(220\) −9.94085 + 5.28647i −0.670212 + 0.356414i
\(221\) 0.225184i 0.0151475i
\(222\) 0.623731 + 2.50130i 0.0418621 + 0.167877i
\(223\) −19.5439 −1.30876 −0.654379 0.756166i \(-0.727070\pi\)
−0.654379 + 0.756166i \(0.727070\pi\)
\(224\) −11.4049 4.14895i −0.762020 0.277213i
\(225\) −4.08228 −0.272152
\(226\) −1.96528 7.88122i −0.130728 0.524251i
\(227\) 1.06802i 0.0708873i 0.999372 + 0.0354436i \(0.0112844\pi\)
−0.999372 + 0.0354436i \(0.988716\pi\)
\(228\) 10.2903 5.47232i 0.681494 0.362413i
\(229\) 19.1138i 1.26308i −0.775344 0.631539i \(-0.782424\pi\)
0.775344 0.631539i \(-0.217576\pi\)
\(230\) −1.31453 + 0.327794i −0.0866775 + 0.0216141i
\(231\) −12.6073 −0.829501
\(232\) 19.3250 17.4037i 1.26875 1.14261i
\(233\) −6.40572 −0.419652 −0.209826 0.977739i \(-0.567290\pi\)
−0.209826 + 0.977739i \(0.567290\pi\)
\(234\) −1.88685 + 0.470508i −0.123347 + 0.0307581i
\(235\) 7.89862i 0.515249i
\(236\) 8.64628 + 16.2587i 0.562825 + 1.05835i
\(237\) 2.86636i 0.186190i
\(238\) 0.120217 + 0.482098i 0.00779252 + 0.0312498i
\(239\) −6.99571 −0.452515 −0.226257 0.974068i \(-0.572649\pi\)
−0.226257 + 0.974068i \(0.572649\pi\)
\(240\) 2.14236 3.17707i 0.138289 0.205079i
\(241\) −0.0382051 −0.00246101 −0.00123050 0.999999i \(-0.500392\pi\)
−0.00123050 + 0.999999i \(0.500392\pi\)
\(242\) 8.05247 + 32.2922i 0.517632 + 2.07582i
\(243\) 1.00000i 0.0641500i
\(244\) −10.0858 18.9656i −0.645676 1.21415i
\(245\) 2.29660i 0.146724i
\(246\) 11.3117 2.82072i 0.721210 0.179843i
\(247\) 8.01309 0.509861
\(248\) −1.90503 2.11534i −0.120970 0.134324i
\(249\) −3.36850 −0.213470
\(250\) 11.9389 2.97712i 0.755084 0.188289i
\(251\) 16.4795i 1.04017i −0.854113 0.520087i \(-0.825899\pi\)
0.854113 0.520087i \(-0.174101\pi\)
\(252\) 3.78839 2.01463i 0.238646 0.126910i
\(253\) 5.87650i 0.369453i
\(254\) −1.93684 7.76716i −0.121528 0.487355i
\(255\) −0.156881 −0.00982427
\(256\) −5.99754 14.8334i −0.374846 0.927087i
\(257\) −5.93490 −0.370209 −0.185105 0.982719i \(-0.559262\pi\)
−0.185105 + 0.982719i \(0.559262\pi\)
\(258\) −2.78693 11.1762i −0.173506 0.695800i
\(259\) 3.91071i 0.242999i
\(260\) 2.32608 1.23699i 0.144258 0.0767151i
\(261\) 9.19473i 0.569139i
\(262\) 17.5168 4.36804i 1.08219 0.269858i
\(263\) 24.4364 1.50681 0.753406 0.657556i \(-0.228410\pi\)
0.753406 + 0.657556i \(0.228410\pi\)
\(264\) −11.1230 12.3509i −0.684573 0.760147i
\(265\) 2.00121 0.122933
\(266\) −17.1553 + 4.27789i −1.05186 + 0.262294i
\(267\) 8.21077i 0.502491i
\(268\) −5.84994 11.0004i −0.357342 0.671958i
\(269\) 12.0472i 0.734533i 0.930116 + 0.367267i \(0.119706\pi\)
−0.930116 + 0.367267i \(0.880294\pi\)
\(270\) 0.327794 + 1.31453i 0.0199489 + 0.0799997i
\(271\) 7.03469 0.427327 0.213663 0.976907i \(-0.431460\pi\)
0.213663 + 0.976907i \(0.431460\pi\)
\(272\) −0.366230 + 0.543110i −0.0222060 + 0.0329309i
\(273\) 2.95002 0.178543
\(274\) −3.65813 14.6699i −0.220996 0.886243i
\(275\) 23.9895i 1.44662i
\(276\) −0.939057 1.76583i −0.0565246 0.106291i
\(277\) 11.0796i 0.665711i 0.942978 + 0.332856i \(0.108012\pi\)
−0.942978 + 0.332856i \(0.891988\pi\)
\(278\) 12.0262 2.99887i 0.721281 0.179860i
\(279\) 1.00647 0.0602556
\(280\) −4.31956 + 3.89010i −0.258143 + 0.232478i
\(281\) −4.12434 −0.246037 −0.123019 0.992404i \(-0.539258\pi\)
−0.123019 + 0.992404i \(0.539258\pi\)
\(282\) −11.3139 + 2.82126i −0.673733 + 0.168004i
\(283\) 4.43435i 0.263595i 0.991277 + 0.131797i \(0.0420748\pi\)
−0.991277 + 0.131797i \(0.957925\pi\)
\(284\) −23.2966 + 12.3890i −1.38240 + 0.735151i
\(285\) 5.58256i 0.330683i
\(286\) −2.76494 11.0881i −0.163495 0.655651i
\(287\) −17.6855 −1.04394
\(288\) 5.31602 + 1.93390i 0.313249 + 0.113956i
\(289\) −16.9732 −0.998422
\(290\) −3.01398 12.0867i −0.176987 0.709758i
\(291\) 5.18778i 0.304113i
\(292\) −10.9198 + 5.80704i −0.639030 + 0.339831i
\(293\) 13.6440i 0.797093i 0.917148 + 0.398547i \(0.130485\pi\)
−0.917148 + 0.398547i \(0.869515\pi\)
\(294\) 3.28963 0.820309i 0.191855 0.0478414i
\(295\) 8.82047 0.513548
\(296\) 3.83117 3.45027i 0.222682 0.200543i
\(297\) 5.87650 0.340989
\(298\) 28.0736 7.00050i 1.62626 0.405528i
\(299\) 1.37506i 0.0795217i
\(300\) 3.83350 + 7.20864i 0.221327 + 0.416191i
\(301\) 17.4736i 1.00716i
\(302\) −4.87705 19.5581i −0.280642 1.12544i
\(303\) 5.89378 0.338589
\(304\) −19.3264 13.0322i −1.10845 0.747448i
\(305\) −10.2890 −0.589145
\(306\) −0.0560354 0.224715i −0.00320333 0.0128461i
\(307\) 14.5188i 0.828631i −0.910133 0.414315i \(-0.864021\pi\)
0.910133 0.414315i \(-0.135979\pi\)
\(308\) 11.8390 + 22.2625i 0.674590 + 1.26852i
\(309\) 8.05266i 0.458100i
\(310\) −1.32303 + 0.329914i −0.0751431 + 0.0187379i
\(311\) 20.9648 1.18880 0.594401 0.804169i \(-0.297389\pi\)
0.594401 + 0.804169i \(0.297389\pi\)
\(312\) 2.60270 + 2.89002i 0.147349 + 0.163615i
\(313\) 18.5992 1.05129 0.525646 0.850704i \(-0.323824\pi\)
0.525646 + 0.850704i \(0.323824\pi\)
\(314\) −5.20119 + 1.29698i −0.293520 + 0.0731929i
\(315\) 2.05522i 0.115799i
\(316\) −5.06152 + 2.69168i −0.284733 + 0.151419i
\(317\) 10.6709i 0.599338i 0.954043 + 0.299669i \(0.0968763\pi\)
−0.954043 + 0.299669i \(0.903124\pi\)
\(318\) 0.714799 + 2.86651i 0.0400839 + 0.160746i
\(319\) −54.0329 −3.02526
\(320\) −7.62198 0.799608i −0.426082 0.0446995i
\(321\) −17.9336 −1.00095
\(322\) 0.734092 + 2.94388i 0.0409094 + 0.164056i
\(323\) 0.954322i 0.0530999i
\(324\) −1.76583 + 0.939057i −0.0981019 + 0.0521698i
\(325\) 5.61337i 0.311374i
\(326\) 6.69330 1.66906i 0.370707 0.0924404i
\(327\) −15.2577 −0.843754
\(328\) −15.6033 17.3258i −0.861548 0.956660i
\(329\) 17.6889 0.975220
\(330\) −7.72483 + 1.92628i −0.425238 + 0.106038i
\(331\) 16.1398i 0.887121i −0.896244 0.443561i \(-0.853715\pi\)
0.896244 0.443561i \(-0.146285\pi\)
\(332\) 3.16322 + 5.94822i 0.173604 + 0.326451i
\(333\) 1.82285i 0.0998916i
\(334\) 6.32766 + 25.3754i 0.346234 + 1.38848i
\(335\) −5.96780 −0.326056
\(336\) −7.11502 4.79780i −0.388156 0.261742i
\(337\) −5.26522 −0.286815 −0.143407 0.989664i \(-0.545806\pi\)
−0.143407 + 0.989664i \(0.545806\pi\)
\(338\) −3.80128 15.2440i −0.206762 0.829164i
\(339\) 5.74351i 0.311945i
\(340\) 0.147320 + 0.277026i 0.00798956 + 0.0150238i
\(341\) 5.91451i 0.320289i
\(342\) 7.99641 1.99400i 0.432396 0.107823i
\(343\) −20.1609 −1.08858
\(344\) −17.1183 + 15.4164i −0.922954 + 0.831194i
\(345\) −0.957976 −0.0515757
\(346\) 19.6184 4.89208i 1.05469 0.263000i
\(347\) 7.51081i 0.403201i −0.979468 0.201601i \(-0.935386\pi\)
0.979468 0.201601i \(-0.0646143\pi\)
\(348\) 16.2364 8.63438i 0.870361 0.462851i
\(349\) 13.4864i 0.721911i −0.932583 0.360955i \(-0.882451\pi\)
0.932583 0.360955i \(-0.117549\pi\)
\(350\) −2.99677 12.0177i −0.160184 0.642375i
\(351\) −1.37506 −0.0733952
\(352\) −11.3646 + 31.2396i −0.605733 + 1.66508i
\(353\) −29.4707 −1.56857 −0.784285 0.620401i \(-0.786970\pi\)
−0.784285 + 0.620401i \(0.786970\pi\)
\(354\) 3.15053 + 12.6343i 0.167449 + 0.671508i
\(355\) 12.6386i 0.670786i
\(356\) 14.4989 7.71039i 0.768439 0.408650i
\(357\) 0.351334i 0.0185946i
\(358\) 33.4863 8.35022i 1.76981 0.441323i
\(359\) −27.4578 −1.44917 −0.724585 0.689186i \(-0.757968\pi\)
−0.724585 + 0.689186i \(0.757968\pi\)
\(360\) 2.01342 1.81325i 0.106117 0.0955666i
\(361\) −14.9593 −0.787331
\(362\) 28.3254 7.06329i 1.48875 0.371238i
\(363\) 23.5333i 1.23518i
\(364\) −2.77024 5.20925i −0.145200 0.273039i
\(365\) 5.92403i 0.310078i
\(366\) −3.67506 14.7378i −0.192098 0.770358i
\(367\) 30.8406 1.60987 0.804933 0.593366i \(-0.202201\pi\)
0.804933 + 0.593366i \(0.202201\pi\)
\(368\) −2.23634 + 3.31644i −0.116577 + 0.172881i
\(369\) 8.24354 0.429142
\(370\) −0.597519 2.39619i −0.0310636 0.124572i
\(371\) 4.48169i 0.232678i
\(372\) −0.945131 1.77726i −0.0490027 0.0921464i
\(373\) 14.5772i 0.754779i −0.926055 0.377390i \(-0.876822\pi\)
0.926055 0.377390i \(-0.123178\pi\)
\(374\) 1.32054 0.329292i 0.0682833 0.0170273i
\(375\) 8.70061 0.449297
\(376\) 15.6063 + 17.3291i 0.804832 + 0.893682i
\(377\) 12.6433 0.651162
\(378\) 2.94388 0.734092i 0.151417 0.0377576i
\(379\) 26.4365i 1.35795i −0.734160 0.678977i \(-0.762424\pi\)
0.734160 0.678977i \(-0.237576\pi\)
\(380\) −9.85789 + 5.24235i −0.505699 + 0.268927i
\(381\) 5.66040i 0.289991i
\(382\) 3.44877 + 13.8303i 0.176454 + 0.707622i
\(383\) −27.7211 −1.41648 −0.708240 0.705972i \(-0.750510\pi\)
−0.708240 + 0.705972i \(0.750510\pi\)
\(384\) −1.57710 11.2032i −0.0804809 0.571713i
\(385\) 12.0775 0.615527
\(386\) −4.72304 18.9405i −0.240397 0.964045i
\(387\) 8.14477i 0.414022i
\(388\) 9.16076 4.87162i 0.465067 0.247319i
\(389\) 1.44716i 0.0733741i −0.999327 0.0366871i \(-0.988320\pi\)
0.999327 0.0366871i \(-0.0116805\pi\)
\(390\) 1.80755 0.450736i 0.0915290 0.0228239i
\(391\) 0.163763 0.00828185
\(392\) −4.53768 5.03862i −0.229187 0.254489i
\(393\) 12.7656 0.643938
\(394\) 11.5291 2.87493i 0.580828 0.144837i
\(395\) 2.74591i 0.138162i
\(396\) −5.51837 10.3769i −0.277309 0.521460i
\(397\) 1.57533i 0.0790636i 0.999218 + 0.0395318i \(0.0125866\pi\)
−0.999218 + 0.0395318i \(0.987413\pi\)
\(398\) 1.73649 + 6.96372i 0.0870423 + 0.349060i
\(399\) −12.5021 −0.625888
\(400\) 9.12938 13.5386i 0.456469 0.676932i
\(401\) 20.9284 1.04511 0.522557 0.852604i \(-0.324978\pi\)
0.522557 + 0.852604i \(0.324978\pi\)
\(402\) −2.13160 8.54821i −0.106315 0.426346i
\(403\) 1.38395i 0.0689395i
\(404\) −5.53459 10.4074i −0.275356 0.517789i
\(405\) 0.957976i 0.0476022i
\(406\) −27.0682 + 6.74978i −1.34337 + 0.334986i
\(407\) −10.7120 −0.530973
\(408\) −0.344189 + 0.309969i −0.0170399 + 0.0153458i
\(409\) 34.4027 1.70110 0.850552 0.525890i \(-0.176268\pi\)
0.850552 + 0.525890i \(0.176268\pi\)
\(410\) −10.8364 + 2.70218i −0.535170 + 0.133451i
\(411\) 10.6909i 0.527341i
\(412\) −14.2197 + 7.56190i −0.700552 + 0.372548i
\(413\) 19.7534i 0.972000i
\(414\) −0.342174 1.37219i −0.0168169 0.0674397i
\(415\) 3.22694 0.158404
\(416\) 2.65922 7.30983i 0.130379 0.358394i
\(417\) 8.76418 0.429184
\(418\) 11.7178 + 46.9909i 0.573134 + 2.29840i
\(419\) 11.8285i 0.577858i 0.957350 + 0.288929i \(0.0932992\pi\)
−0.957350 + 0.288929i \(0.906701\pi\)
\(420\) −3.62918 + 1.92997i −0.177086 + 0.0941729i
\(421\) 4.48030i 0.218357i −0.994022 0.109178i \(-0.965178\pi\)
0.994022 0.109178i \(-0.0348219\pi\)
\(422\) 35.9922 8.97510i 1.75207 0.436901i
\(423\) −8.24511 −0.400891
\(424\) 4.39054 3.95403i 0.213224 0.192025i
\(425\) −0.668527 −0.0324283
\(426\) −18.1034 + 4.51429i −0.877110 + 0.218718i
\(427\) 23.0421i 1.11508i
\(428\) 16.8406 + 31.6677i 0.814023 + 1.53072i
\(429\) 8.08053i 0.390132i
\(430\) 2.66981 + 10.7065i 0.128750 + 0.516315i
\(431\) 37.1607 1.78997 0.894985 0.446097i \(-0.147186\pi\)
0.894985 + 0.446097i \(0.147186\pi\)
\(432\) 3.31644 + 2.23634i 0.159562 + 0.107596i
\(433\) 29.9902 1.44124 0.720620 0.693331i \(-0.243857\pi\)
0.720620 + 0.693331i \(0.243857\pi\)
\(434\) 0.738840 + 2.96292i 0.0354655 + 0.142225i
\(435\) 8.80833i 0.422327i
\(436\) 14.3279 + 26.9426i 0.686181 + 1.29032i
\(437\) 5.82746i 0.278765i
\(438\) −8.48552 + 2.11597i −0.405454 + 0.101105i
\(439\) 0.0326011 0.00155597 0.000777984 1.00000i \(-0.499752\pi\)
0.000777984 1.00000i \(0.499752\pi\)
\(440\) 10.6556 + 11.8319i 0.507984 + 0.564063i
\(441\) 2.39735 0.114159
\(442\) −0.308996 + 0.0770519i −0.0146974 + 0.00366498i
\(443\) 5.57880i 0.265057i −0.991179 0.132528i \(-0.957690\pi\)
0.991179 0.132528i \(-0.0423096\pi\)
\(444\) 3.21885 1.71176i 0.152760 0.0812366i
\(445\) 7.86572i 0.372871i
\(446\) 6.68742 + 26.8181i 0.316658 + 1.26987i
\(447\) 20.4589 0.967674
\(448\) −1.79072 + 17.0694i −0.0846034 + 0.806452i
\(449\) −14.6776 −0.692680 −0.346340 0.938109i \(-0.612576\pi\)
−0.346340 + 0.938109i \(0.612576\pi\)
\(450\) 1.39685 + 5.60168i 0.0658481 + 0.264066i
\(451\) 48.4432i 2.28110i
\(452\) −10.1421 + 5.39349i −0.477044 + 0.253688i
\(453\) 14.2531i 0.669671i
\(454\) 1.46554 0.365450i 0.0687811 0.0171514i
\(455\) −2.82605 −0.132487
\(456\) −11.0302 12.2478i −0.516535 0.573558i
\(457\) 4.17137 0.195128 0.0975642 0.995229i \(-0.468895\pi\)
0.0975642 + 0.995229i \(0.468895\pi\)
\(458\) −26.2279 + 6.54025i −1.22555 + 0.305606i
\(459\) 0.163763i 0.00764380i
\(460\) 0.899594 + 1.69163i 0.0419438 + 0.0788725i
\(461\) 28.3795i 1.32177i 0.750489 + 0.660883i \(0.229818\pi\)
−0.750489 + 0.660883i \(0.770182\pi\)
\(462\) 4.31389 + 17.2997i 0.200701 + 0.804855i
\(463\) −21.7291 −1.00984 −0.504919 0.863167i \(-0.668478\pi\)
−0.504919 + 0.863167i \(0.668478\pi\)
\(464\) −30.4938 20.5626i −1.41564 0.954593i
\(465\) −0.964172 −0.0447124
\(466\) 2.19187 + 8.78989i 0.101536 + 0.407184i
\(467\) 2.94330i 0.136199i 0.997679 + 0.0680997i \(0.0216936\pi\)
−0.997679 + 0.0680997i \(0.978306\pi\)
\(468\) 1.29126 + 2.42812i 0.0596884 + 0.112240i
\(469\) 13.3648i 0.617131i
\(470\) 10.8384 2.70270i 0.499940 0.124666i
\(471\) −3.79042 −0.174653
\(472\) 19.3516 17.4277i 0.890731 0.802174i
\(473\) 47.8628 2.20073
\(474\) −3.93321 + 0.980793i −0.180658 + 0.0450493i
\(475\) 23.7893i 1.09153i
\(476\) 0.620397 0.329923i 0.0284359 0.0151220i
\(477\) 2.08900i 0.0956485i
\(478\) 2.39375 + 9.59947i 0.109487 + 0.439070i
\(479\) 16.7957 0.767414 0.383707 0.923455i \(-0.374647\pi\)
0.383707 + 0.923455i \(0.374647\pi\)
\(480\) −5.09262 1.85263i −0.232445 0.0845605i
\(481\) 2.50652 0.114288
\(482\) 0.0130728 + 0.0524248i 0.000595448 + 0.00238788i
\(483\) 2.14538i 0.0976181i
\(484\) 41.5559 22.0991i 1.88890 1.00450i
\(485\) 4.96977i 0.225666i
\(486\) −1.37219 + 0.342174i −0.0622440 + 0.0155213i
\(487\) −22.4359 −1.01667 −0.508334 0.861160i \(-0.669739\pi\)
−0.508334 + 0.861160i \(0.669739\pi\)
\(488\) −22.5735 + 20.3292i −1.02185 + 0.920260i
\(489\) 4.87780 0.220582
\(490\) −3.15138 + 0.785836i −0.142365 + 0.0355004i
\(491\) 22.5240i 1.01650i −0.861211 0.508248i \(-0.830293\pi\)
0.861211 0.508248i \(-0.169707\pi\)
\(492\) −7.74116 14.5567i −0.348998 0.656268i
\(493\) 1.50576i 0.0678159i
\(494\) −2.74187 10.9955i −0.123363 0.494712i
\(495\) −5.62955 −0.253029
\(496\) −2.25081 + 3.33789i −0.101064 + 0.149876i
\(497\) 28.3040 1.26961
\(498\) 1.15261 + 4.62224i 0.0516498 + 0.207128i
\(499\) 15.7359i 0.704436i −0.935918 0.352218i \(-0.885428\pi\)
0.935918 0.352218i \(-0.114572\pi\)
\(500\) −8.17037 15.3638i −0.365390 0.687091i
\(501\) 18.4925i 0.826186i
\(502\) −22.6130 + 5.63883i −1.00927 + 0.251674i
\(503\) 18.9239 0.843777 0.421889 0.906648i \(-0.361367\pi\)
0.421889 + 0.906648i \(0.361367\pi\)
\(504\) −4.06075 4.50905i −0.180880 0.200849i
\(505\) −5.64610 −0.251248
\(506\) 8.06370 2.01078i 0.358475 0.0893903i
\(507\) 11.1092i 0.493378i
\(508\) −9.99532 + 5.31544i −0.443471 + 0.235834i
\(509\) 2.68826i 0.119155i 0.998224 + 0.0595776i \(0.0189754\pi\)
−0.998224 + 0.0595776i \(0.981025\pi\)
\(510\) 0.0536805 + 0.215271i 0.00237701 + 0.00953237i
\(511\) 13.2668 0.586890
\(512\) −18.3021 + 13.3054i −0.808846 + 0.588021i
\(513\) 5.82746 0.257289
\(514\) 2.03077 + 8.14384i 0.0895733 + 0.359209i
\(515\) 7.71425i 0.339930i
\(516\) −14.3823 + 7.64841i −0.633146 + 0.336702i
\(517\) 48.4524i 2.13093i
\(518\) −5.36625 + 1.33814i −0.235779 + 0.0587945i
\(519\) 14.2971 0.627572
\(520\) −2.49332 2.76857i −0.109339 0.121410i
\(521\) 25.2684 1.10703 0.553515 0.832839i \(-0.313286\pi\)
0.553515 + 0.832839i \(0.313286\pi\)
\(522\) 12.6170 3.14619i 0.552229 0.137705i
\(523\) 29.2960i 1.28103i −0.767947 0.640513i \(-0.778722\pi\)
0.767947 0.640513i \(-0.221278\pi\)
\(524\) −11.9876 22.5419i −0.523681 0.984746i
\(525\) 8.75804i 0.382232i
\(526\) −8.36148 33.5315i −0.364578 1.46204i
\(527\) 0.164822 0.00717977
\(528\) −13.1419 + 19.4891i −0.571927 + 0.848153i
\(529\) 1.00000 0.0434783
\(530\) −0.684760 2.74604i −0.0297441 0.119281i
\(531\) 9.20740i 0.399567i
\(532\) 11.7402 + 22.0767i 0.509002 + 0.957145i
\(533\) 11.3353i 0.490988i
\(534\) 11.2668 2.80951i 0.487561 0.121579i
\(535\) 17.1799 0.742752
\(536\) −13.0930 + 11.7913i −0.565533 + 0.509307i
\(537\) 24.4035 1.05309
\(538\) 16.5312 4.12225i 0.712709 0.177723i
\(539\) 14.0880i 0.606814i
\(540\) 1.69163 0.899594i 0.0727960 0.0387124i
\(541\) 26.6842i 1.14724i 0.819120 + 0.573622i \(0.194462\pi\)
−0.819120 + 0.573622i \(0.805538\pi\)
\(542\) −2.40708 9.65296i −0.103393 0.414630i
\(543\) 20.6424 0.885851
\(544\) 0.870567 + 0.316701i 0.0373252 + 0.0135785i
\(545\) 14.6165 0.626103
\(546\) −1.00942 4.04800i −0.0431992 0.173238i
\(547\) 11.2854i 0.482528i −0.970459 0.241264i \(-0.922438\pi\)
0.970459 0.241264i \(-0.0775620\pi\)
\(548\) −18.8783 + 10.0393i −0.806440 + 0.428859i
\(549\) 10.7403i 0.458386i
\(550\) −32.9183 + 8.20859i −1.40364 + 0.350015i
\(551\) −53.5819 −2.28267
\(552\) −2.10175 + 1.89279i −0.0894563 + 0.0805625i
\(553\) 6.14943 0.261501
\(554\) 15.2034 3.79116i 0.645932 0.161071i
\(555\) 1.74625i 0.0741240i
\(556\) −8.23007 15.4761i −0.349033 0.656332i
\(557\) 35.3016i 1.49578i 0.663825 + 0.747888i \(0.268932\pi\)
−0.663825 + 0.747888i \(0.731068\pi\)
\(558\) −0.344387 1.38107i −0.0145790 0.0584653i
\(559\) −11.1995 −0.473690
\(560\) 6.81602 + 4.59618i 0.288029 + 0.194224i
\(561\) 0.962354 0.0406306
\(562\) 1.41124 + 5.65939i 0.0595295 + 0.238727i
\(563\) 13.0685i 0.550772i 0.961334 + 0.275386i \(0.0888057\pi\)
−0.961334 + 0.275386i \(0.911194\pi\)
\(564\) 7.74263 + 14.5595i 0.326024 + 0.613066i
\(565\) 5.50215i 0.231477i
\(566\) 6.08479 1.51732i 0.255763 0.0637776i
\(567\) 2.14538 0.0900975
\(568\) 24.9716 + 27.7283i 1.04778 + 1.16346i
\(569\) −8.19299 −0.343468 −0.171734 0.985143i \(-0.554937\pi\)
−0.171734 + 0.985143i \(0.554937\pi\)
\(570\) −7.66036 + 1.91021i −0.320857 + 0.0800097i
\(571\) 1.89406i 0.0792638i −0.999214 0.0396319i \(-0.987381\pi\)
0.999214 0.0396319i \(-0.0126185\pi\)
\(572\) −14.2689 + 7.58808i −0.596612 + 0.317274i
\(573\) 10.0790i 0.421056i
\(574\) 6.05152 + 24.2680i 0.252586 + 1.01293i
\(575\) −4.08228 −0.170243
\(576\) 0.834685 7.95634i 0.0347785 0.331514i
\(577\) −24.4901 −1.01954 −0.509769 0.860311i \(-0.670269\pi\)
−0.509769 + 0.860311i \(0.670269\pi\)
\(578\) 5.80777 + 23.2905i 0.241572 + 0.968757i
\(579\) 13.8031i 0.573636i
\(580\) −15.5540 + 8.27152i −0.645847 + 0.343456i
\(581\) 7.22672i 0.299815i
\(582\) 7.11864 1.77512i 0.295077 0.0735812i
\(583\) −12.2760 −0.508419
\(584\) 11.7048 + 12.9970i 0.484350 + 0.537820i
\(585\) 1.31727 0.0544625
\(586\) 18.7223 4.66863i 0.773410 0.192859i
\(587\) 21.6080i 0.891859i −0.895068 0.445929i \(-0.852873\pi\)
0.895068 0.445929i \(-0.147127\pi\)
\(588\) −2.25125 4.23332i −0.0928398 0.174579i
\(589\) 5.86515i 0.241669i
\(590\) −3.01813 12.1034i −0.124255 0.498289i
\(591\) 8.40195 0.345610
\(592\) −6.04537 4.07652i −0.248463 0.167544i
\(593\) −33.8498 −1.39004 −0.695021 0.718989i \(-0.744605\pi\)
−0.695021 + 0.718989i \(0.744605\pi\)
\(594\) −2.01078 8.06370i −0.0825035 0.330858i
\(595\) 0.336569i 0.0137980i
\(596\) −19.2121 36.1271i −0.786958 1.47982i
\(597\) 5.07488i 0.207701i
\(598\) −1.88685 + 0.470508i −0.0771589 + 0.0192405i
\(599\) −19.2826 −0.787864 −0.393932 0.919140i \(-0.628886\pi\)
−0.393932 + 0.919140i \(0.628886\pi\)
\(600\) 8.57993 7.72691i 0.350274 0.315450i
\(601\) −19.5636 −0.798015 −0.399008 0.916948i \(-0.630645\pi\)
−0.399008 + 0.916948i \(0.630645\pi\)
\(602\) 23.9772 5.97901i 0.977238 0.243686i
\(603\) 6.22959i 0.253689i
\(604\) −25.1687 + 13.3845i −1.02410 + 0.544608i
\(605\) 22.5443i 0.916557i
\(606\) −2.01669 8.08741i −0.0819226 0.328528i
\(607\) 14.8914 0.604424 0.302212 0.953241i \(-0.402275\pi\)
0.302212 + 0.953241i \(0.402275\pi\)
\(608\) −11.2697 + 30.9789i −0.457047 + 1.25636i
\(609\) −19.7262 −0.799345
\(610\) 3.52062 + 14.1185i 0.142546 + 0.571640i
\(611\) 11.3375i 0.458666i
\(612\) −0.289178 + 0.153783i −0.0116893 + 0.00621630i
\(613\) 0.628938i 0.0254026i −0.999919 0.0127013i \(-0.995957\pi\)
0.999919 0.0127013i \(-0.00404306\pi\)
\(614\) −19.9226 + 4.96794i −0.804010 + 0.200490i
\(615\) −7.89711 −0.318442
\(616\) 26.4974 23.8630i 1.06761 0.961469i
\(617\) 3.93037 0.158231 0.0791153 0.996865i \(-0.474790\pi\)
0.0791153 + 0.996865i \(0.474790\pi\)
\(618\) −11.0498 + 2.75541i −0.444488 + 0.110839i
\(619\) 38.6550i 1.55368i −0.629700 0.776838i \(-0.716822\pi\)
0.629700 0.776838i \(-0.283178\pi\)
\(620\) 0.905412 + 1.70257i 0.0363622 + 0.0683768i
\(621\) 1.00000i 0.0401286i
\(622\) −7.17358 28.7677i −0.287635 1.15348i
\(623\) −17.6152 −0.705739
\(624\) 3.07510 4.56030i 0.123103 0.182558i
\(625\) 12.0764 0.483058
\(626\) −6.36417 25.5218i −0.254363 1.02006i
\(627\) 34.2451i 1.36762i
\(628\) 3.55942 + 6.69326i 0.142036 + 0.267090i
\(629\) 0.298515i 0.0119026i
\(630\) −2.82016 + 0.703242i −0.112358 + 0.0280179i
\(631\) 34.7355 1.38280 0.691399 0.722473i \(-0.256995\pi\)
0.691399 + 0.722473i \(0.256995\pi\)
\(632\) 5.42542 + 6.02437i 0.215812 + 0.239637i
\(633\) 26.2297 1.04254
\(634\) 14.6426 3.65130i 0.581531 0.145012i
\(635\) 5.42252i 0.215186i
\(636\) 3.68882 1.96169i 0.146271 0.0777859i
\(637\) 3.29649i 0.130612i
\(638\) 18.4886 + 74.1436i 0.731971 + 2.93537i
\(639\) −13.1930 −0.521907
\(640\) 1.51082 + 10.7324i 0.0597205 + 0.424237i
\(641\) 16.3740 0.646733 0.323367 0.946274i \(-0.395185\pi\)
0.323367 + 0.946274i \(0.395185\pi\)
\(642\) 6.13639 + 24.6083i 0.242184 + 0.971213i
\(643\) 3.58023i 0.141191i −0.997505 0.0705953i \(-0.977510\pi\)
0.997505 0.0705953i \(-0.0224899\pi\)
\(644\) 3.78839 2.01463i 0.149283 0.0793877i
\(645\) 7.80249i 0.307223i
\(646\) 1.30952 0.326544i 0.0515222 0.0128477i
\(647\) 15.1628 0.596111 0.298055 0.954549i \(-0.403662\pi\)
0.298055 + 0.954549i \(0.403662\pi\)
\(648\) 1.89279 + 2.10175i 0.0743558 + 0.0825644i
\(649\) −54.1073 −2.12390
\(650\) 7.70264 1.92075i 0.302122 0.0753380i
\(651\) 2.15925i 0.0846279i
\(652\) −4.58054 8.61340i −0.179388 0.337327i
\(653\) 29.5588i 1.15673i 0.815779 + 0.578363i \(0.196308\pi\)
−0.815779 + 0.578363i \(0.803692\pi\)
\(654\) 5.22079 + 20.9366i 0.204149 + 0.818684i
\(655\) −12.2291 −0.477831
\(656\) −18.4354 + 27.3392i −0.719781 + 1.06742i
\(657\) −6.18391 −0.241257
\(658\) −6.05267 24.2726i −0.235958 0.946244i
\(659\) 12.7243i 0.495667i −0.968803 0.247833i \(-0.920281\pi\)
0.968803 0.247833i \(-0.0797185\pi\)
\(660\) 5.28647 + 9.94085i 0.205775 + 0.386947i
\(661\) 5.82562i 0.226590i −0.993561 0.113295i \(-0.963859\pi\)
0.993561 0.113295i \(-0.0361406\pi\)
\(662\) −22.1469 + 5.52260i −0.860763 + 0.214642i
\(663\) −0.225184 −0.00874541
\(664\) 7.07974 6.37587i 0.274747 0.247432i
\(665\) 11.9767 0.464437
\(666\) 2.50130 0.623731i 0.0969236 0.0241691i
\(667\) 9.19473i 0.356021i
\(668\) 32.6548 17.3656i 1.26345 0.671894i
\(669\) 19.5439i 0.755612i
\(670\) 2.04202 + 8.18898i 0.0788902 + 0.316368i
\(671\) 63.1156 2.43655
\(672\) −4.14895 + 11.4049i −0.160049 + 0.439953i
\(673\) 7.46202 0.287640 0.143820 0.989604i \(-0.454061\pi\)
0.143820 + 0.989604i \(0.454061\pi\)
\(674\) 1.80162 + 7.22490i 0.0693957 + 0.278293i
\(675\) 4.08228i 0.157127i
\(676\) −19.6170 + 10.4322i −0.754501 + 0.401238i
\(677\) 2.58854i 0.0994857i −0.998762 0.0497428i \(-0.984160\pi\)
0.998762 0.0497428i \(-0.0158402\pi\)
\(678\) −7.88122 + 1.96528i −0.302676 + 0.0754761i
\(679\) −11.1298 −0.427121
\(680\) 0.329724 0.296943i 0.0126443 0.0113872i
\(681\) 1.06802 0.0409268
\(682\) 8.11586 2.02379i 0.310772 0.0774949i
\(683\) 48.7370i 1.86487i −0.361337 0.932435i \(-0.617680\pi\)
0.361337 0.932435i \(-0.382320\pi\)
\(684\) −5.47232 10.2903i −0.209239 0.393461i
\(685\) 10.2416i 0.391311i
\(686\) 6.89852 + 27.6646i 0.263387 + 1.05624i
\(687\) −19.1138 −0.729239
\(688\) 27.0116 + 18.2145i 1.02981 + 0.694421i
\(689\) 2.87249 0.109433
\(690\) 0.327794 + 1.31453i 0.0124789 + 0.0500433i
\(691\) 40.3418i 1.53468i 0.641243 + 0.767338i \(0.278419\pi\)
−0.641243 + 0.767338i \(0.721581\pi\)
\(692\) −13.4258 25.2463i −0.510371 0.959719i
\(693\) 12.6073i 0.478913i
\(694\) −10.3063 + 2.57000i −0.391221 + 0.0975559i
\(695\) −8.39587 −0.318474
\(696\) −17.4037 19.3250i −0.659686 0.732512i
\(697\) 1.34999 0.0511344
\(698\) −18.5060 + 4.61469i −0.700461 + 0.174669i
\(699\) 6.40572i 0.242286i
\(700\) −15.4653 + 8.22431i −0.584532 + 0.310850i
\(701\) 23.8105i 0.899309i −0.893202 0.449655i \(-0.851547\pi\)
0.893202 0.449655i \(-0.148453\pi\)
\(702\) 0.470508 + 1.88685i 0.0177582 + 0.0712144i
\(703\) −10.6226 −0.400638
\(704\) 46.7554 + 4.90503i 1.76216 + 0.184865i
\(705\) 7.89862 0.297479
\(706\) 10.0841 + 40.4396i 0.379520 + 1.52196i
\(707\) 12.6444i 0.475541i
\(708\) 16.2587 8.64628i 0.611041 0.324947i
\(709\) 39.2778i 1.47511i −0.675288 0.737554i \(-0.735981\pi\)
0.675288 0.737554i \(-0.264019\pi\)
\(710\) 17.3426 4.32458i 0.650855 0.162299i
\(711\) −2.86636 −0.107497
\(712\) −15.5413 17.2570i −0.582434 0.646733i
\(713\) 1.00647 0.0376925
\(714\) 0.482098 0.120217i 0.0180421 0.00449901i
\(715\) 7.74095i 0.289495i
\(716\) −22.9163 43.0925i −0.856421 1.61044i
\(717\) 6.99571i 0.261260i
\(718\) 9.39535 + 37.6775i 0.350631 + 1.40611i
\(719\) −6.94844 −0.259133 −0.129567 0.991571i \(-0.541359\pi\)
−0.129567 + 0.991571i \(0.541359\pi\)
\(720\) −3.17707 2.14236i −0.118402 0.0798411i
\(721\) 17.2760 0.643392
\(722\) 5.11867 + 20.5270i 0.190497 + 0.763937i
\(723\) 0.0382051i 0.00142086i
\(724\) −19.3844 36.4511i −0.720416 1.35469i
\(725\) 37.5355i 1.39403i
\(726\) 32.2922 8.05247i 1.19848 0.298855i
\(727\) −43.5001 −1.61333 −0.806665 0.591008i \(-0.798730\pi\)
−0.806665 + 0.591008i \(0.798730\pi\)
\(728\) −6.20020 + 5.58377i −0.229795 + 0.206948i
\(729\) −1.00000 −0.0370370
\(730\) 8.12892 2.02705i 0.300865 0.0750244i
\(731\) 1.33381i 0.0493328i
\(732\) −18.9656 + 10.0858i −0.700990 + 0.372781i
\(733\) 33.4363i 1.23500i −0.786571 0.617499i \(-0.788146\pi\)
0.786571 0.617499i \(-0.211854\pi\)
\(734\) −10.5528 42.3193i −0.389512 1.56203i
\(735\) −2.29660 −0.0847114
\(736\) 5.31602 + 1.93390i 0.195951 + 0.0712845i
\(737\) 36.6082 1.34848
\(738\) −2.82072 11.3117i −0.103832 0.416391i
\(739\) 32.3025i 1.18827i 0.804367 + 0.594133i \(0.202505\pi\)
−0.804367 + 0.594133i \(0.797495\pi\)
\(740\) −3.08358 + 1.63983i −0.113355 + 0.0602812i
\(741\) 8.01309i 0.294368i
\(742\) −6.14975 + 1.53352i −0.225764 + 0.0562971i
\(743\) 26.3041 0.965002 0.482501 0.875895i \(-0.339728\pi\)
0.482501 + 0.875895i \(0.339728\pi\)
\(744\) −2.11534 + 1.90503i −0.0775522 + 0.0698419i
\(745\) −19.5992 −0.718057
\(746\) −20.0028 + 4.98794i −0.732353 + 0.182621i
\(747\) 3.36850i 0.123247i
\(748\) −0.903705 1.69936i −0.0330427 0.0621347i
\(749\) 38.4743i 1.40582i
\(750\) −2.97712 11.9389i −0.108709 0.435948i
\(751\) −11.2368 −0.410037 −0.205019 0.978758i \(-0.565725\pi\)
−0.205019 + 0.978758i \(0.565725\pi\)
\(752\) 18.4389 27.3444i 0.672397 0.997148i
\(753\) −16.4795 −0.600545
\(754\) −4.32620 17.3490i −0.157551 0.631815i
\(755\) 13.6542i 0.496926i
\(756\) −2.01463 3.78839i −0.0732715 0.137782i
\(757\) 35.2690i 1.28187i 0.767594 + 0.640937i \(0.221454\pi\)
−0.767594 + 0.640937i \(0.778546\pi\)
\(758\) −36.2761 + 9.04589i −1.31761 + 0.328561i
\(759\) 5.87650 0.213304
\(760\) 10.5666 + 11.7331i 0.383292 + 0.425606i
\(761\) −47.9490 −1.73815 −0.869075 0.494681i \(-0.835285\pi\)
−0.869075 + 0.494681i \(0.835285\pi\)
\(762\) −7.76716 + 1.93684i −0.281375 + 0.0701642i
\(763\) 32.7336i 1.18504i
\(764\) 17.7978 9.46475i 0.643903 0.342423i
\(765\) 0.156881i 0.00567204i
\(766\) 9.48541 + 38.0387i 0.342722 + 1.37439i
\(767\) 12.6607 0.457152
\(768\) −14.8334 + 5.99754i −0.535254 + 0.216418i
\(769\) 36.9947 1.33406 0.667032 0.745029i \(-0.267565\pi\)
0.667032 + 0.745029i \(0.267565\pi\)
\(770\) −4.13261 16.5727i −0.148929 0.597239i
\(771\) 5.93490i 0.213740i
\(772\) −24.3739 + 12.9619i −0.877237 + 0.466508i
\(773\) 33.2787i 1.19695i 0.801141 + 0.598475i \(0.204227\pi\)
−0.801141 + 0.598475i \(0.795773\pi\)
\(774\) −11.1762 + 2.78693i −0.401721 + 0.100174i
\(775\) −4.10869 −0.147588
\(776\) −9.81939 10.9034i −0.352495 0.391409i
\(777\) −3.91071 −0.140296
\(778\) −1.98579 + 0.495181i −0.0711940 + 0.0177531i
\(779\) 48.0389i 1.72117i
\(780\) −1.23699 2.32608i −0.0442915 0.0832872i
\(781\) 77.5287i 2.77419i
\(782\) −0.0560354 0.224715i −0.00200382 0.00803578i
\(783\) 9.19473 0.328593
\(784\) −5.36129 + 7.95066i −0.191475 + 0.283952i
\(785\) 3.63113 0.129601
\(786\) −4.36804 17.5168i −0.155803 0.624805i
\(787\) 6.77438i 0.241481i −0.992684 0.120740i \(-0.961473\pi\)
0.992684 0.120740i \(-0.0385268\pi\)
\(788\) −7.88991 14.8365i −0.281067 0.528527i
\(789\) 24.4364i 0.869958i
\(790\) 3.76792 0.939576i 0.134056 0.0334286i
\(791\) 12.3220 0.438120
\(792\) −12.3509 + 11.1230i −0.438871 + 0.395238i
\(793\) −14.7686 −0.524448
\(794\) 2.16166 0.539037i 0.0767145 0.0191297i
\(795\) 2.00121i 0.0709755i
\(796\) 8.96139 4.76560i 0.317628 0.168912i
\(797\) 14.0543i 0.497830i −0.968525 0.248915i \(-0.919926\pi\)
0.968525 0.248915i \(-0.0800741\pi\)
\(798\) 4.27789 + 17.1553i 0.151436 + 0.607292i
\(799\) −1.35024 −0.0477682
\(800\) −21.7015 7.89472i −0.767263 0.279121i
\(801\) 8.21077 0.290113
\(802\) −7.16115 28.7178i −0.252869 1.01406i
\(803\) 36.3397i 1.28240i
\(804\) −11.0004 + 5.84994i −0.387955 + 0.206312i
\(805\) 2.05522i 0.0724370i
\(806\) −1.89905 + 0.473552i −0.0668912 + 0.0166801i
\(807\) 12.0472 0.424083
\(808\) −12.3872 + 11.1557i −0.435781 + 0.392456i
\(809\) −7.72143 −0.271471 −0.135735 0.990745i \(-0.543340\pi\)
−0.135735 + 0.990745i \(0.543340\pi\)
\(810\) 1.31453 0.327794i 0.0461878 0.0115175i
\(811\) 22.6984i 0.797048i −0.917158 0.398524i \(-0.869523\pi\)
0.917158 0.398524i \(-0.130477\pi\)
\(812\) 18.5240 + 34.8332i 0.650065 + 1.22240i
\(813\) 7.03469i 0.246717i
\(814\) 3.66536 + 14.6989i 0.128471 + 0.515197i
\(815\) −4.67282 −0.163682
\(816\) 0.543110 + 0.366230i 0.0190127 + 0.0128206i
\(817\) 47.4633 1.66053
\(818\) −11.7717 47.2072i −0.411588 1.65056i
\(819\) 2.95002i 0.103082i
\(820\) 7.41584 + 13.9450i 0.258972 + 0.486980i
\(821\) 1.38524i 0.0483453i −0.999708 0.0241726i \(-0.992305\pi\)
0.999708 0.0241726i \(-0.00769514\pi\)
\(822\) −14.6699 + 3.65813i −0.511673 + 0.127592i
\(823\) −15.9740 −0.556819 −0.278410 0.960462i \(-0.589807\pi\)
−0.278410 + 0.960462i \(0.589807\pi\)
\(824\) 15.2420 + 16.9246i 0.530980 + 0.589598i
\(825\) −23.9895 −0.835209
\(826\) −27.1055 + 6.75908i −0.943120 + 0.235179i
\(827\) 29.8593i 1.03831i −0.854680 0.519155i \(-0.826247\pi\)
0.854680 0.519155i \(-0.173753\pi\)
\(828\) −1.76583 + 0.939057i −0.0613670 + 0.0326345i
\(829\) 14.9900i 0.520624i 0.965525 + 0.260312i \(0.0838255\pi\)
−0.965525 + 0.260312i \(0.916175\pi\)
\(830\) −1.10418 4.42799i −0.0383265 0.153698i
\(831\) 11.0796 0.384349
\(832\) −10.9404 1.14774i −0.379291 0.0397907i
\(833\) 0.392597 0.0136027
\(834\) −2.99887 12.0262i −0.103842 0.416432i
\(835\) 17.7154i 0.613067i
\(836\) 60.4711 32.1581i 2.09144 1.11221i
\(837\) 1.00647i 0.0347886i
\(838\) 16.2309 4.04739i 0.560689 0.139815i
\(839\) −25.4186 −0.877548 −0.438774 0.898597i \(-0.644587\pi\)
−0.438774 + 0.898597i \(0.644587\pi\)
\(840\) 3.89010 + 4.31956i 0.134221 + 0.149039i
\(841\) −55.5430 −1.91528
\(842\) −6.14784 + 1.53304i −0.211869 + 0.0528321i
\(843\) 4.12434i 0.142050i
\(844\) −24.6312 46.3172i −0.847839 1.59431i
\(845\) 10.6424i 0.366108i
\(846\) 2.82126 + 11.3139i 0.0969969 + 0.388980i
\(847\) −50.4878 −1.73478
\(848\) −6.92803 4.67171i −0.237909 0.160427i
\(849\) 4.43435 0.152187
\(850\) 0.228752 + 0.917349i 0.00784614 + 0.0314648i
\(851\) 1.82285i 0.0624865i
\(852\) 12.3890 + 23.2966i 0.424439 + 0.798130i
\(853\) 28.3482i 0.970623i 0.874341 + 0.485311i \(0.161294\pi\)
−0.874341 + 0.485311i \(0.838706\pi\)
\(854\) 31.6182 7.88439i 1.08195 0.269798i
\(855\) −5.58256 −0.190920
\(856\) 37.6918 33.9445i 1.28828 1.16020i
\(857\) −40.6814 −1.38965 −0.694826 0.719178i \(-0.744518\pi\)
−0.694826 + 0.719178i \(0.744518\pi\)
\(858\) −11.0881 + 2.76494i −0.378540 + 0.0943936i
\(859\) 21.2337i 0.724483i 0.932084 + 0.362242i \(0.117988\pi\)
−0.932084 + 0.362242i \(0.882012\pi\)
\(860\) 13.7779 7.32699i 0.469823 0.249848i
\(861\) 17.6855i 0.602721i
\(862\) −12.7154 50.9917i −0.433089 1.73679i
\(863\) 41.9316 1.42737 0.713683 0.700468i \(-0.247026\pi\)
0.713683 + 0.700468i \(0.247026\pi\)
\(864\) 1.93390 5.31602i 0.0657926 0.180855i
\(865\) −13.6962 −0.465686
\(866\) −10.2619 41.1524i −0.348712 1.39842i
\(867\) 16.9732i 0.576439i
\(868\) 3.81289 2.02766i 0.129418 0.0688234i
\(869\) 16.8442i 0.571400i
\(870\) −12.0867 + 3.01398i −0.409779 + 0.102183i
\(871\) −8.56605 −0.290249
\(872\) 32.0679 28.8797i 1.08596 0.977989i
\(873\) 5.18778 0.175580
\(874\) 7.99641 1.99400i 0.270482 0.0674481i
\(875\) 18.6661i 0.631029i
\(876\) 5.80704 + 10.9198i 0.196202 + 0.368944i
\(877\) 19.1900i 0.647999i 0.946057 + 0.324000i \(0.105028\pi\)
−0.946057 + 0.324000i \(0.894972\pi\)
\(878\) −0.0111552 0.0447351i −0.000376471 0.00150974i
\(879\) 13.6440 0.460202
\(880\) 12.5896 18.6701i 0.424395 0.629367i
\(881\) 31.0035 1.04453 0.522267 0.852782i \(-0.325086\pi\)
0.522267 + 0.852782i \(0.325086\pi\)
\(882\) −0.820309 3.28963i −0.0276212 0.110767i
\(883\) 22.0192i 0.741005i −0.928832 0.370502i \(-0.879186\pi\)
0.928832 0.370502i \(-0.120814\pi\)
\(884\) 0.211460 + 0.397637i 0.00711218 + 0.0133740i
\(885\) 8.82047i 0.296497i
\(886\) −7.65520 + 1.90892i −0.257181 + 0.0641314i
\(887\) 55.3189 1.85743 0.928714 0.370797i \(-0.120915\pi\)
0.928714 + 0.370797i \(0.120915\pi\)
\(888\) −3.45027 3.83117i −0.115784 0.128566i
\(889\) 12.1437 0.407287
\(890\) −10.7933 + 2.69144i −0.361792 + 0.0902174i
\(891\) 5.87650i 0.196870i
\(892\) 34.5114 18.3529i 1.15553 0.614500i
\(893\) 48.0480i 1.60787i
\(894\) −7.00050 28.0736i −0.234132 0.938922i
\(895\) −23.3779 −0.781438
\(896\) 24.0352 3.38347i 0.802960 0.113034i
\(897\) −1.37506 −0.0459118
\(898\) 5.02230 + 20.1406i 0.167596 + 0.672099i
\(899\) 9.25420i 0.308645i
\(900\) 7.20864 3.83350i 0.240288 0.127783i
\(901\) 0.342100i 0.0113970i
\(902\) 66.4735 16.5760i 2.21332 0.551920i
\(903\) 17.4736 0.581486
\(904\) 10.8713 + 12.0714i 0.361573 + 0.401489i
\(905\) −19.7749 −0.657341
\(906\) −19.5581 + 4.87705i −0.649773 + 0.162029i
\(907\) 51.8307i 1.72101i −0.509441 0.860506i \(-0.670148\pi\)
0.509441 0.860506i \(-0.329852\pi\)
\(908\) −1.00294 1.88596i −0.0332836 0.0625876i
\(909\) 5.89378i 0.195484i
\(910\) 0.966999 + 3.87789i 0.0320557 + 0.128551i
\(911\) −48.2153 −1.59744 −0.798722 0.601701i \(-0.794490\pi\)
−0.798722 + 0.601701i \(0.794490\pi\)
\(912\) −13.0322 + 19.3264i −0.431539 + 0.639962i
\(913\) −19.7950 −0.655120
\(914\) −1.42733 5.72393i −0.0472120 0.189331i
\(915\) 10.2890i 0.340143i
\(916\) 17.9490 + 33.7519i 0.593051 + 1.11519i
\(917\) 27.3870i 0.904398i
\(918\) −0.224715 + 0.0560354i −0.00741669 + 0.00184944i
\(919\) −6.05837 −0.199847 −0.0999236 0.994995i \(-0.531860\pi\)
−0.0999236 + 0.994995i \(0.531860\pi\)
\(920\) 2.01342 1.81325i 0.0663806 0.0597810i
\(921\) −14.5188 −0.478410
\(922\) 38.9422 9.71072i 1.28249 0.319806i
\(923\) 18.1411i 0.597123i
\(924\) 22.2625 11.8390i 0.732381 0.389475i
\(925\) 7.44139i 0.244671i
\(926\) 7.43513 + 29.8166i 0.244334 + 0.979833i
\(927\) −8.05266 −0.264484
\(928\) −17.7817 + 48.8793i −0.583712 + 1.60454i
\(929\) 23.6089 0.774583 0.387292 0.921957i \(-0.373411\pi\)
0.387292 + 0.921957i \(0.373411\pi\)
\(930\) 0.329914 + 1.32303i 0.0108183 + 0.0433839i
\(931\) 13.9704i 0.457863i
\(932\) 11.3114 6.01534i 0.370518 0.197039i
\(933\) 20.9648i 0.686355i
\(934\) 4.03877 1.00712i 0.132153 0.0329539i
\(935\) −0.921912 −0.0301497
\(936\) 2.89002 2.60270i 0.0944634 0.0850718i
\(937\) −54.4608 −1.77916 −0.889578 0.456784i \(-0.849001\pi\)
−0.889578 + 0.456784i \(0.849001\pi\)
\(938\) 18.3392 4.57309i 0.598795 0.149317i
\(939\) 18.5992i 0.606963i
\(940\) −7.41725 13.9476i −0.241924 0.454922i
\(941\) 27.6530i 0.901462i 0.892660 + 0.450731i \(0.148837\pi\)
−0.892660 + 0.450731i \(0.851163\pi\)
\(942\) 1.29698 + 5.20119i 0.0422579 + 0.169464i
\(943\) 8.24354 0.268447
\(944\) −30.5358 20.5909i −0.993855 0.670177i
\(945\) −2.05522 −0.0668564
\(946\) −16.3774 65.6770i −0.532474 2.13534i
\(947\) 24.4302i 0.793874i −0.917846 0.396937i \(-0.870073\pi\)
0.917846 0.396937i \(-0.129927\pi\)
\(948\) 2.69168 + 5.06152i 0.0874216 + 0.164391i
\(949\) 8.50323i 0.276027i
\(950\) −32.6436 + 8.14008i −1.05910 + 0.264099i
\(951\) 10.6709 0.346028
\(952\) −0.665001 0.738415i −0.0215528 0.0239322i
\(953\) −17.4510 −0.565292 −0.282646 0.959224i \(-0.591212\pi\)
−0.282646 + 0.959224i \(0.591212\pi\)
\(954\) 2.86651 0.714799i 0.0928066 0.0231425i
\(955\) 9.65543i 0.312442i
\(956\) 12.3533 6.56937i 0.399533 0.212469i
\(957\) 54.0329i 1.74663i
\(958\) −5.74704 23.0469i −0.185678 0.744613i
\(959\) 22.9359 0.740640
\(960\) −0.799608 + 7.62198i −0.0258072 + 0.245998i
\(961\) −29.9870 −0.967323
\(962\) −0.857666 3.43944i −0.0276523 0.110892i
\(963\) 17.9336i 0.577901i
\(964\) 0.0674639 0.0358768i 0.00217286 0.00115551i
\(965\) 13.2230i 0.425663i
\(966\) 2.94388 0.734092i 0.0947177 0.0236190i
\(967\) −44.2308 −1.42237 −0.711183 0.703007i \(-0.751840\pi\)
−0.711183 + 0.703007i \(0.751840\pi\)
\(968\) −44.5436 49.4610i −1.43169 1.58974i
\(969\) 0.954322 0.0306573
\(970\) −6.81949 + 1.70052i −0.218961 + 0.0546005i
\(971\) 42.6198i 1.36774i 0.729606 + 0.683868i \(0.239703\pi\)
−0.729606 + 0.683868i \(0.760297\pi\)
\(972\) 0.939057 + 1.76583i 0.0301203 + 0.0566392i
\(973\) 18.8025i 0.602780i
\(974\) 7.67698 + 30.7864i 0.245986 + 0.986461i
\(975\) 5.61337 0.179772
\(976\) 35.6197 + 24.0191i 1.14016 + 0.768831i
\(977\) 37.3495 1.19492 0.597458 0.801900i \(-0.296177\pi\)
0.597458 + 0.801900i \(0.296177\pi\)
\(978\) −1.66906 6.69330i −0.0533705 0.214028i
\(979\) 48.2506i 1.54210i
\(980\) 2.15664 + 4.05542i 0.0688913 + 0.129546i
\(981\) 15.2577i 0.487142i
\(982\) −30.9074 + 7.70713i −0.986293 + 0.245944i
\(983\) 33.7223 1.07557 0.537787 0.843081i \(-0.319260\pi\)
0.537787 + 0.843081i \(0.319260\pi\)
\(984\) −17.3258 + 15.6033i −0.552328 + 0.497415i
\(985\) −8.04887 −0.256458
\(986\) 2.06619 0.515230i 0.0658009 0.0164083i
\(987\) 17.6889i 0.563044i
\(988\) −14.1498 + 7.52475i −0.450165 + 0.239394i
\(989\) 8.14477i 0.258989i
\(990\) 1.92628 + 7.72483i 0.0612213 + 0.245511i
\(991\) 39.1447 1.24347 0.621736 0.783227i \(-0.286428\pi\)
0.621736 + 0.783227i \(0.286428\pi\)
\(992\) 5.35040 + 1.94641i 0.169875 + 0.0617985i
\(993\) −16.1398 −0.512180
\(994\) −9.68487 38.8386i −0.307186 1.23188i
\(995\) 4.86161i 0.154123i
\(996\) 5.94822 3.16322i 0.188477 0.100230i
\(997\) 18.6528i 0.590742i 0.955383 + 0.295371i \(0.0954432\pi\)
−0.955383 + 0.295371i \(0.904557\pi\)
\(998\) −21.5927 + 5.38441i −0.683506 + 0.170441i
\(999\) 1.82285 0.0576724
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 552.2.f.c.277.7 18
4.3 odd 2 2208.2.f.c.1105.15 18
8.3 odd 2 2208.2.f.c.1105.4 18
8.5 even 2 inner 552.2.f.c.277.8 yes 18
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
552.2.f.c.277.7 18 1.1 even 1 trivial
552.2.f.c.277.8 yes 18 8.5 even 2 inner
2208.2.f.c.1105.4 18 8.3 odd 2
2208.2.f.c.1105.15 18 4.3 odd 2